LMFDB - Embedded newform 289.2.h.a.115.2

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			115.2
Character	$\chi$	$=$	289.115
Dual form			289.2.h.a.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79334 + 1.96720i) q^{2} +(-1.02781 + 1.84528i) q^{3} +(-0.469274 - 5.06428i) q^{4} +(0.00658298 - 0.0471919i) q^{5} +(-1.78682 - 5.33113i) q^{6} +(1.01357 - 4.30943i) q^{7} +(6.55547 + 4.95046i) q^{8} +(-0.769355 - 1.24255i) q^{9} +O(q^{10})$	\(q+(-1.79334 + 1.96720i) q^{2} +(-1.02781 + 1.84528i) q^{3} +(-0.469274 - 5.06428i) q^{4} +(0.00658298 - 0.0471919i) q^{5} +(-1.78682 - 5.33113i) q^{6} +(1.01357 - 4.30943i) q^{7} +(6.55547 + 4.95046i) q^{8} +(-0.769355 - 1.24255i) q^{9} +(0.0810305 + 0.0975813i) q^{10} +(3.46325 + 2.87584i) q^{11} +(9.82732 + 4.33919i) q^{12} +(2.03226 - 2.69115i) q^{13} +(6.65986 + 9.72219i) q^{14} +(0.0803160 + 0.0606518i) q^{15} +(-11.4960 + 2.14898i) q^{16} +(-2.54282 - 3.24562i) q^{17} +(3.82407 + 0.714842i) q^{18} +(-1.77447 - 1.94650i) q^{19} +(-0.242082 - 0.0111921i) q^{20} +(6.91034 + 6.29961i) q^{21} +(-11.8682 + 1.65554i) q^{22} +(1.71648 - 7.29802i) q^{23} +(-15.8728 + 7.00852i) q^{24} +(4.80694 + 1.36769i) q^{25} +(1.64950 + 8.82402i) q^{26} +(-3.24628 + 0.150085i) q^{27} +(-22.2998 - 3.11069i) q^{28} +(-2.04908 + 2.46761i) q^{29} +(-0.263349 + 0.0492284i) q^{30} +(7.04239 - 0.982371i) q^{31} +(7.73988 - 12.5003i) q^{32} +(-8.86630 + 3.43482i) q^{33} +(10.9450 + 0.818274i) q^{34} +(-0.196698 - 0.0762012i) q^{35} +(-5.93158 + 4.47932i) q^{36} +(1.81970 + 4.12123i) q^{37} +7.01138 q^{38} +(2.87713 + 6.51608i) q^{39} +(0.276776 - 0.276776i) q^{40} +(1.25966 + 0.701627i) q^{41} +(-24.7852 + 2.29669i) q^{42} +(-1.04922 + 5.61283i) q^{43} +(12.9389 - 18.8884i) q^{44} +(-0.0637029 + 0.0281276i) q^{45} +(11.2784 + 16.4645i) q^{46} +(0.110880 + 0.0686541i) q^{47} +(7.85030 - 23.4221i) q^{48} +(-11.2778 - 5.61566i) q^{49} +(-11.3110 + 7.00350i) q^{50} +(8.60262 - 1.35631i) q^{51} +(-14.5824 - 9.02904i) q^{52} +(0.882616 + 1.42547i) q^{53} +(5.52644 - 6.65524i) q^{54} +(0.158515 - 0.144505i) q^{55} +(27.9781 - 23.2327i) q^{56} +(5.41564 - 1.27375i) q^{57} +(-1.17959 - 8.45622i) q^{58} +(6.07856 - 3.02676i) q^{59} +(0.269467 - 0.435205i) q^{60} +(2.19653 + 6.55356i) q^{61} +(-10.6969 + 15.6155i) q^{62} +(-6.13449 + 2.05607i) q^{63} +(4.30938 + 15.1459i) q^{64} +(-0.113622 - 0.113622i) q^{65} +(9.14333 - 23.6016i) q^{66} +(9.02962 - 8.23159i) q^{67} +(-15.2435 + 14.4006i) q^{68} +(11.7026 + 10.6684i) q^{69} +(0.502650 - 0.250290i) q^{70} +(2.40263 + 0.565093i) q^{71} +(1.10772 - 11.9542i) q^{72} +(1.24365 + 0.851917i) q^{73} +(-11.3707 - 3.81106i) q^{74} +(-7.46442 + 7.46442i) q^{75} +(-9.02488 + 9.89982i) q^{76} +(15.9035 - 12.0098i) q^{77} +(-17.9782 - 6.02567i) q^{78} +(0.459445 - 9.93765i) q^{79} +(0.0257362 + 0.556666i) q^{80} +(5.01389 - 10.0693i) q^{81} +(-3.63925 + 1.21975i) q^{82} +(-5.14486 - 1.46384i) q^{83} +(28.6601 - 37.9521i) q^{84} +(-0.169906 + 0.0986345i) q^{85} +(-9.15996 - 12.1298i) q^{86} +(-2.44736 - 6.31736i) q^{87} +(8.46646 + 35.9972i) q^{88} +(1.70531 + 2.25820i) q^{89} +(0.0589085 - 0.175759i) q^{90} +(-9.53749 - 11.4856i) q^{91} +(-37.7647 - 5.26794i) q^{92} +(-5.42551 + 14.0049i) q^{93} +(-0.333903 + 0.0950036i) q^{94} +(-0.103540 + 0.0709266i) q^{95} +(15.1114 + 27.1302i) q^{96} +(-15.0258 - 3.53404i) q^{97} +(31.2720 - 12.1148i) q^{98} +(0.908916 - 6.51581i) 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 $

$2$	−1.79334	+	1.96720i	−1.26809	+	1.39102i	−0.384247	+	0.923230i	$0.625539\pi$
$2$	−1.79334	+	1.96720i	−1.26809	+	1.39102i	−0.883838	+	0.467793i	$0.845049\pi$
$3$	−1.02781	+	1.84528i	−0.593408	+	1.06537i	0.395728	+	0.918368i	$0.370492\pi$
$3$	−1.02781	+	1.84528i	−0.593408	+	1.06537i	−0.989136	+	0.147004i	$0.953037\pi$
$4$	−0.469274	−	5.06428i	−0.234637	−	2.53214i
$5$	0.00658298	−	0.0471919i	0.00294400	−	0.0211048i	−0.988882	−	0.148701i	$-0.952491\pi$
$5$	0.00658298	−	0.0471919i	0.00294400	−	0.0211048i	0.991826	+	0.127596i	$0.0407261\pi$
$6$	−1.78682	−	5.33113i	−0.729465	−	2.17643i
$7$	1.01357	−	4.30943i	0.383093	−	1.62881i	−0.341673	−	0.939819i	$-0.610994\pi$
$7$	1.01357	−	4.30943i	0.383093	−	1.62881i	0.724767	−	0.688994i	$-0.241948\pi$
$8$	6.55547	+	4.95046i	2.31771	+	1.75025i
$9$	−0.769355	−	1.24255i	−0.256452	−	0.414184i
$10$	0.0810305	+	0.0975813i	0.0256241	+	0.0308579i
$11$	3.46325	+	2.87584i	1.04421	+	0.867100i	0.991316	−	0.131500i	$-0.0419795\pi$
$11$	3.46325	+	2.87584i	1.04421	+	0.867100i	0.0528924	+	0.998600i	$0.483156\pi$
$12$	9.82732	+	4.33919i	2.83690	+	1.25262i
$13$	2.03226	−	2.69115i	0.563648	−	0.746390i	−0.423553	−	0.905871i	$-0.639217\pi$
$13$	2.03226	−	2.69115i	0.563648	−	0.746390i	0.987201	+	0.159481i	$0.0509821\pi$
$14$	6.65986	+	9.72219i	1.77992	+	2.59837i
$15$	0.0803160	+	0.0606518i	0.0207375	+	0.0156602i
$16$	−11.4960	+	2.14898i	−2.87401	+	0.537245i
$17$	−2.54282	−	3.24562i	−0.616724	−	0.787179i
$17$	−2.54282	−	3.24562i	−0.616724	−	0.787179i
$18$	3.82407	+	0.714842i	0.901341	+	0.168490i
$19$	−1.77447	−	1.94650i	−0.407090	−	0.446557i	0.500927	−	0.865490i	$-0.332993\pi$
$19$	−1.77447	−	1.94650i	−0.407090	−	0.446557i	−0.908017	+	0.418933i	$0.862404\pi$
$20$	−0.242082	−	0.0111921i	−0.0541311	−	0.00250263i
$21$	6.91034	+	6.29961i	1.50796	+	1.37469i
$22$	−11.8682	+	1.65554i	−2.53030	+	0.352962i
$23$	1.71648	−	7.29802i	0.357910	−	1.52174i	−0.428217	−	0.903676i	$-0.640858\pi$
$23$	1.71648	−	7.29802i	0.357910	−	1.52174i	0.786127	−	0.618065i	$-0.212083\pi$
$24$	−15.8728	+	7.00852i	−3.24002	+	1.43061i
$25$	4.80694	+	1.36769i	0.961389	+	0.273539i
$26$	1.64950	+	8.82402i	0.323493	+	1.73053i
$27$	−3.24628	+	0.150085i	−0.624747	+	0.0288838i
$28$	−22.2998	−	3.11069i	−4.21427	−	0.587865i
$29$	−2.04908	+	2.46761i	−0.380504	+	0.458223i	−0.924679	−	0.380748i	$-0.875666\pi$
$29$	−2.04908	+	2.46761i	−0.380504	+	0.458223i	0.544175	+	0.838972i	$0.316843\pi$
$30$	−0.263349	+	0.0492284i	−0.0480807	+	0.00898784i
$31$	7.04239	−	0.982371i	1.26485	−	0.176439i	0.526102	−	0.850421i	$-0.323653\pi$
$31$	7.04239	−	0.982371i	1.26485	−	0.176439i	0.738748	+	0.673982i	$0.235418\pi$
$32$	7.73988	−	12.5003i	1.36823	−	2.20977i
$33$	−8.86630	+	3.43482i	−1.54343	+	0.597926i
$34$	10.9450	+	0.818274i	1.87704	+	0.140333i
$35$	−0.196698	−	0.0762012i	−0.0332480	−	0.0128803i
$36$	−5.93158	+	4.47932i	−0.988597	+	0.746554i
$37$	1.81970	+	4.12123i	0.299157	+	0.677526i	0.999336	−	0.0364414i	$-0.0116022\pi$
$37$	1.81970	+	4.12123i	0.299157	+	0.677526i	−0.700179	+	0.713968i	$0.746896\pi$
$38$	7.01138			1.13740
$39$	2.87713	+	6.51608i	0.460710	+	1.04341i
$40$	0.276776	−	0.276776i	0.0437621	−	0.0437621i
$41$	1.25966	+	0.701627i	0.196726	+	0.109576i	0.581873	−	0.813279i	$-0.302320\pi$
$41$	1.25966	+	0.701627i	0.196726	+	0.109576i	−0.385147	+	0.922855i	$0.625849\pi$
$42$	−24.7852	+	2.29669i	−3.82445	+	0.354387i
$43$	−1.04922	+	5.61283i	−0.160004	+	0.855948i	0.804913	+	0.593393i	$0.202212\pi$
$43$	−1.04922	+	5.61283i	−0.160004	+	0.855948i	−0.964917	+	0.262555i	$0.915435\pi$
$44$	12.9389	−	18.8884i	1.95061	−	2.84753i
$45$	−0.0637029	+	0.0281276i	−0.00949627	+	0.00419301i
$46$	11.2784	+	16.4645i	1.66292	+	2.42756i
$47$	0.110880	+	0.0686541i	0.0161735	+	0.0100142i	0.534495	−	0.845172i	$-0.320502\pi$
$47$	0.110880	+	0.0686541i	0.0161735	+	0.0100142i	−0.518322	+	0.855186i	$0.673443\pi$
$48$	7.85030	−	23.4221i	1.13309	−	3.38069i
$49$	−11.2778	−	5.61566i	−1.61111	−	0.802237i
$50$	−11.3110	+	7.00350i	−1.59962	+	0.990444i
$51$	8.60262	−	1.35631i	1.20461	−	0.189922i
$52$	−14.5824	−	9.02904i	−2.02222	−	1.25210i
$53$	0.882616	+	1.42547i	0.121237	+	0.195804i	0.905180	−	0.425029i	$-0.139736\pi$
$53$	0.882616	+	1.42547i	0.121237	+	0.195804i	−0.783943	+	0.620832i	$0.786795\pi$
$54$	5.52644	−	6.65524i	0.752054	−	0.905664i
$55$	0.158515	−	0.144505i	0.0213742	−	0.0194851i
$56$	27.9781	−	23.2327i	3.73873	−	3.10460i
$57$	5.41564	−	1.27375i	0.717320	−	0.168712i
$58$	−1.17959	−	8.45622i	−0.154888	−	1.11036i
$59$	6.07856	−	3.02676i	0.791361	−	0.394051i	−0.00414890	−	0.999991i	$-0.501321\pi$
$59$	6.07856	−	3.02676i	0.791361	−	0.394051i	0.795510	+	0.605940i	$0.207203\pi$
$60$	0.269467	−	0.435205i	0.0347881	−	0.0561847i
$61$	2.19653	+	6.55356i	0.281237	+	0.839098i	0.990905	+	0.134561i	$0.0429626\pi$
$61$	2.19653	+	6.55356i	0.281237	+	0.839098i	−0.709668	+	0.704536i	$0.751155\pi$
$62$	−10.6969	+	15.6155i	−1.35851	+	1.98318i
$63$	−6.13449	+	2.05607i	−0.772872	+	0.259041i
$64$	4.30938	+	15.1459i	0.538673	+	1.89324i
$65$	−0.113622	−	0.113622i	−0.0140931	−	0.0140931i
$66$	9.14333	−	23.6016i	1.12547	−	2.90516i
$67$	9.02962	−	8.23159i	1.10314	−	1.00565i	0.103204	−	0.994660i	$-0.467091\pi$
$67$	9.02962	−	8.23159i	1.10314	−	1.00565i	0.999940	−	0.0109880i	$-0.00349765\pi$
$68$	−15.2435	+	14.4006i	−1.84854	+	1.74633i
$69$	11.7026	+	10.6684i	1.40883	+	1.28432i
$70$	0.502650	−	0.250290i	0.0600782	−	0.0299154i
$71$	2.40263	+	0.565093i	0.285139	+	0.0670642i	0.369051	−	0.929409i	$-0.379683\pi$
$71$	2.40263	+	0.565093i	0.285139	+	0.0670642i	−0.0839120	+	0.996473i	$0.526741\pi$
$72$	1.10772	−	11.9542i	0.130546	−	1.40881i
$73$	1.24365	+	0.851917i	0.145558	+	0.0997093i	0.635712	−	0.771926i	$-0.280707\pi$
$73$	1.24365	+	0.851917i	0.145558	+	0.0997093i	−0.490154	+	0.871636i	$0.663060\pi$
$74$	−11.3707	−	3.81106i	−1.32181	−	0.443027i
$75$	−7.46442	+	7.46442i	−0.861916	+	0.861916i
$76$	−9.02488	+	9.89982i	−1.03522	+	1.13559i
$77$	15.9035	−	12.0098i	1.81237	−	1.36864i
$78$	−17.9782	−	6.02567i	−2.03562	−	0.682273i
$79$	0.459445	−	9.93765i	0.0516916	−	1.11807i	−0.802010	−	0.597310i	$-0.796236\pi$
$79$	0.459445	−	9.93765i	0.0516916	−	1.11807i	0.853702	−	0.520762i	$-0.174352\pi$
$80$	0.0257362	+	0.556666i	0.00287739	+	0.0622371i
$81$	5.01389	−	10.0693i	0.557099	−	1.11881i
$82$	−3.63925	+	1.21975i	−0.401888	+	0.134699i
$83$	−5.14486	−	1.46384i	−0.564722	−	0.160677i	−0.0207560	−	0.999785i	$-0.506607\pi$
$83$	−5.14486	−	1.46384i	−0.564722	−	0.160677i	−0.543966	+	0.839107i	$0.683078\pi$
$84$	28.6601	−	37.9521i	3.12708	−	4.14092i
$85$	−0.169906	+	0.0986345i	−0.0184289	+	0.0106984i
$86$	−9.15996	−	12.1298i	−0.987744	−	1.30798i
$87$	−2.44736	−	6.31736i	−0.262384	−	0.677292i
$88$	8.46646	+	35.9972i	0.902528	+	3.83731i
$89$	1.70531	+	2.25820i	0.180763	+	0.239369i	0.879373	−	0.476134i	$-0.157962\pi$
$89$	1.70531	+	2.25820i	0.180763	+	0.239369i	−0.698610	+	0.715503i	$0.746198\pi$
$90$	0.0589085	−	0.175759i	0.00620950	−	0.0185266i
$91$	−9.53749	−	11.4856i	−0.999801	−	1.20401i
$92$	−37.7647	−	5.26794i	−3.93724	−	0.549221i
$93$	−5.42551	+	14.0049i	−0.562599	+	1.45224i
$94$	−0.333903	+	0.0950036i	−0.0344395	+	0.00979887i
$95$	−0.103540	+	0.0709266i	−0.0106230	+	0.00727691i
$96$	15.1114	+	27.1302i	1.54231	+	2.76897i
$97$	−15.0258	−	3.53404i	−1.52564	−	0.358828i	−0.620592	−	0.784134i	$-0.713108\pi$
$97$	−15.0258	−	3.53404i	−1.52564	−	0.358828i	−0.905050	+	0.425306i	$0.860167\pi$
$98$	31.2720	−	12.1148i	3.15895	−	1.22378i
$99$	0.908916	−	6.51581i	0.0913495	−	0.654863i
$100$	4.67060	−	24.9855i	0.467060	−	2.49855i
$101$	−2.55794	+	5.13704i	−0.254525	+	0.511154i	−0.985165	−	0.171608i	$-0.945104\pi$
$101$	−2.55794	+	5.13704i	−0.254525	+	0.511154i	0.730641	+	0.682762i	$0.239221\pi$
$102$	−12.7593	+	19.3554i	−1.26336	+	1.91647i
$103$	−1.83437	−	3.68392i	−0.180746	−	0.362987i	0.786198	−	0.617974i	$-0.212046\pi$
$103$	−1.83437	−	3.68392i	−0.180746	−	0.362987i	−0.966944	+	0.254987i	$0.917929\pi$
$104$	26.6448	−	7.58111i	2.61274	−	0.743389i
$105$	0.342781	−	0.284642i	0.0334520	−	0.0277782i
$106$	−4.38703	−	0.820078i	−0.426106	−	0.0796530i
$107$	−6.09453	−	0.281767i	−0.589181	−	0.0272395i	−0.250461	−	0.968127i	$-0.580582\pi$
$107$	−6.09453	−	0.281767i	−0.589181	−	0.0272395i	−0.338720	+	0.940887i	$0.609994\pi$
$108$	2.28346	+	16.3696i	0.219726	+	1.57517i
$109$	9.42744	+	16.9255i	0.902985	+	1.62117i	0.777329	+	0.629095i	$0.216574\pi$
$109$	9.42744	+	16.9255i	0.902985	+	1.62117i	0.125656	+	0.992074i	$0.459896\pi$
$110$			0.570979i			0.0544407i
$111$	−9.47513	−	0.878000i	−0.899340	−	0.0833361i
$112$	−2.39114	+	51.7195i	−0.225941	+	4.88703i
$113$	16.8266	+	9.37237i	1.58292	+	0.881679i	0.997479	+	0.0709608i	$0.0226065\pi$
$113$	16.8266	+	9.37237i	1.58292	+	0.881679i	0.585437	+	0.810718i	$0.300923\pi$
$114$	−7.20639	+	12.9379i	−0.674940	+	1.21175i
$115$	−0.333107	−	0.129046i	−0.0310624	−	0.0120336i
$116$	13.4582	+	9.21910i	1.24956	+	0.855972i
$117$	−4.90742	−	0.454739i	−0.453691	−	0.0420407i
$118$	−4.94668	+	17.3858i	−0.455379	+	1.60049i
$119$	−16.5641	+	7.66845i	−1.51843	+	0.702965i
$120$	0.226255	+	0.795203i	0.0206541	+	0.0725917i
$121$	1.70236	+	9.10682i	0.154760	+	0.827893i
$122$	−16.8313	−	7.43176i	−1.52384	−	0.672840i
$123$	−2.58939	+	1.60329i	−0.233478	+	0.144563i
$124$	−8.27981	−	35.2036i	−0.743549	−	3.16137i
$125$	0.192420	−	0.435789i	0.0172105	−	0.0389782i
$126$	6.95652	−	15.7550i	0.619736	−	1.40357i
$127$	−4.34582	−	11.2179i	−0.385629	−	0.995424i	−0.981350	−	0.192232i	$-0.938427\pi$
$127$	−4.34582	−	11.2179i	−0.385629	−	0.995424i	0.595720	−	0.803192i	$-0.296867\pi$
$128$	−11.2010	−	5.57742i	−0.990035	−	0.492979i
$129$	−9.27882	−	7.70504i	−0.816955	−	0.678391i
$130$	0.427281	−	0.0197544i	0.0374750	−	0.00173257i
$131$	−1.40693	−	1.40693i	−0.122924	−	0.122924i	0.642969	−	0.765892i	$-0.277703\pi$
$131$	−1.40693	−	1.40693i	−0.122924	−	0.122924i	−0.765892	+	0.642969i	$0.777703\pi$
$132$	21.5556	+	43.2895i	1.87618	+	3.76787i
$133$	−10.1868	+	5.67403i	−0.883311	+	0.492001i
$134$			32.5252i			2.80975i
$135$	−0.0142874	+	0.154186i	−0.00122967	+	0.0132702i
$136$	−0.602040	−	33.8647i	−0.0516245	−	2.90387i
$137$	−1.54478	−	16.6709i	−0.131980	−	1.42429i	−0.761933	−	0.647655i	$-0.775750\pi$
$137$	−1.54478	−	16.6709i	−0.131980	−	1.42429i	0.629954	−	0.776633i	$-0.283074\pi$
$138$	−41.9737	+	3.88944i	−3.57304	+	0.331091i
$139$	−0.725764	−	15.6980i	−0.0615585	−	1.33149i	−0.775528	−	0.631313i	$-0.782516\pi$
$139$	−0.725764	−	15.6980i	−0.0615585	−	1.33149i	0.713969	−	0.700177i	$-0.246896\pi$
$140$	−0.293598	+	1.03189i	−0.0248136	+	0.0872108i
$141$	−0.240650	+	0.134041i	−0.0202664	+	0.0112883i
$142$	−5.42039	+	3.71305i	−0.454869	+	0.311592i
$143$	14.7775	−	3.47565i	1.23576	−	0.290648i
$144$	11.5147	+	12.6311i	0.959562	+	1.05259i
$145$	0.102962	+	0.112944i	0.00855053	+	0.00937948i
$146$	−3.90618	+	0.918724i	−0.323278	+	0.0760342i
$147$	21.9539	−	15.0388i	1.81073	−	1.24038i
$148$	20.0171	−	11.1495i	1.64540	−	0.916480i
$149$	−3.70492	+	13.0214i	−0.303519	+	1.06676i	0.648626	+	0.761108i	$0.275344\pi$
$149$	−3.70492	+	13.0214i	−0.303519	+	1.06676i	−0.952144	+	0.305649i	$0.901126\pi$
$150$	−1.29777	−	28.0703i	−0.105962	−	2.29193i
$151$	4.29736	−	0.398209i	0.349714	−	0.0324058i	0.0840226	−	0.996464i	$-0.473223\pi$
$151$	4.29736	−	0.398209i	0.349714	−	0.0324058i	0.265692	+	0.964058i	$0.414400\pi$
$152$	−1.99640	−	21.5446i	−0.161930	−	1.74750i
$153$	−2.07652	+	5.65662i	−0.167877	+	0.457310i
$154$	−4.89478	+	52.8231i	−0.394433	+	4.25661i
$155$		−	0.338810i		−	0.0272139i
$156$	31.6491	−	17.6284i	2.53395	−	1.41140i
$157$	−2.86953	−	5.76279i	−0.229013	−	0.459920i	0.750615	−	0.660740i	$-0.229757\pi$
$157$	−2.86953	−	5.76279i	−0.229013	−	0.459920i	−0.979628	+	0.200819i	$0.935640\pi$
$158$	18.7254	+	18.7254i	1.48972	+	1.48972i
$159$	−3.53756	+	0.163551i	−0.280547	+	0.0129705i
$160$	−0.538963	−	0.447549i	−0.0426087	−	0.0353818i
$161$	−29.7105	−	14.7941i	−2.34152	−	1.16594i
$162$	10.8166	+	27.9210i	0.849836	+	2.19368i
$163$	−5.15627	+	11.6778i	−0.403870	+	0.914678i	0.590333	+	0.807160i	$0.298996\pi$
$163$	−5.15627	+	11.6778i	−0.403870	+	0.914678i	−0.994203	+	0.107519i	$0.965709\pi$
$164$	2.96211	−	6.70853i	0.231302	−	0.523848i
$165$	0.103729	+	0.441029i	0.00807529	+	0.0343340i
$166$	12.1062	−	7.49582i	0.939621	−	0.581789i
$167$	9.69254	+	4.27967i	0.750031	+	0.331171i	0.743436	−	0.668807i	$-0.233195\pi$
$167$	9.69254	+	4.27967i	0.750031	+	0.331171i	0.00659507	+	0.999978i	$0.497901\pi$
$168$	14.1146	+	75.5063i	1.08896	+	5.82544i
$169$	0.445424	+	1.56550i	0.0342634	+	0.120423i
$170$	0.110666	−	0.511126i	0.00848772	−	0.0392016i
$171$	−1.05343	+	3.70241i	−0.0805575	+	0.283130i
$172$	28.9173	+	2.67958i	2.20492	+	0.204316i
$173$	−8.17018	−	5.59670i	−0.621167	−	0.425509i	0.212976	−	0.977057i	$-0.431684\pi$
$173$	−8.17018	−	5.59670i	−0.621167	−	0.425509i	−0.834143	+	0.551548i	$0.814037\pi$
$174$	16.8165	+	6.51474i	1.27485	+	0.493881i
$175$	10.7662	−	19.3290i	0.813845	−	1.46113i
$176$	−45.9937	−	25.6183i	−3.46691	−	1.93105i
$177$	−0.662404	+	14.3276i	−0.0497893	+	1.07693i
$178$	−7.50056	−	0.695029i	−0.562190	−	0.0520946i
$179$		−	13.6556i		−	1.02067i	−0.859977	−	0.510333i	$-0.829522\pi$
$179$		−	13.6556i		−	1.02067i	0.859977	−	0.510333i	$-0.170478\pi$
$180$	0.172340	+	0.309410i	0.0128455	+	0.0230620i
$181$	1.83476	+	13.1530i	0.136377	+	0.977652i	0.929560	+	0.368670i	$0.120187\pi$
$181$	1.83476	+	13.1530i	0.136377	+	0.977652i	−0.793184	+	0.608982i	$0.791578\pi$
$182$	39.6984	+	1.83537i	2.94264	+	0.136047i
$183$	−14.3508	−	2.68262i	−1.06084	−	0.198305i
$184$	47.3809	−	39.3446i	3.49296	−	2.90052i
$185$	0.206468	−	0.0587451i	0.0151798	−	0.00431903i
$186$	−17.8206	−	35.7886i	−1.30667	−	2.62415i
$187$	0.527496	−	18.5532i	0.0385743	−	1.35674i
$188$	0.295650	−	0.593745i	0.0215625	−	0.0433033i
$189$	−2.64355	+	14.1417i	−0.192290	+	1.02866i
$190$	0.0461558	−	0.330880i	0.00334849	−	0.0240046i
$191$	−4.20657	+	1.62963i	−0.304376	+	0.117916i	−0.508586	−	0.861011i	$-0.669832\pi$
$191$	−4.20657	+	1.62963i	−0.304376	+	0.117916i	0.204210	+	0.978927i	$0.434538\pi$
$192$	−32.3776	−	7.61515i	−2.33665	−	0.549576i
$193$	−0.785155	−	1.40962i	−0.0565167	−	0.101467i	0.843890	−	0.536517i	$-0.180260\pi$
$193$	−0.785155	−	1.40962i	−0.0565167	−	0.101467i	−0.900406	+	0.435050i	$0.856731\pi$
$194$	33.8987	−	23.2211i	2.43378	−	1.66718i
$195$	0.326446	−	0.0928820i	0.0233773	−	0.00665142i
$196$	−23.1469	+	59.7490i	−1.65335	+	4.26778i
$197$	−19.7324	−	2.75255i	−1.40587	−	0.196111i	−0.605611	−	0.795761i	$-0.707071\pi$
$197$	−19.7324	−	2.75255i	−1.40587	−	0.196111i	−0.800262	+	0.599650i	$0.795306\pi$
$198$	11.1879	+	13.4731i	0.795091	+	0.957491i
$199$	−3.90285	+	11.6445i	−0.276666	+	0.825459i	0.715285	+	0.698833i	$0.246297\pi$
$199$	−3.90285	+	11.6445i	−0.276666	+	0.825459i	−0.991951	+	0.126626i	$0.959585\pi$
$200$	24.7411	+	32.7625i	1.74946	+	2.31666i
$201$	5.90880	+	25.1227i	0.416775	+	1.77202i
$202$	−5.51834	−	14.2445i	−0.388269	−	1.00224i
$203$	8.55712	+	11.3315i	0.600592	+	0.795312i
$204$	−10.9057	−	42.9296i	−0.763554	−	3.00567i
$205$	0.0414034	−	0.0548270i	0.00289174	−	0.00382928i
$206$	10.5367	+	2.99794i	0.734125	+	0.208877i
$207$	−10.3887	+	3.48195i	−0.722067	+	0.242012i
$208$	−17.5797	+	35.3048i	−1.21893	+	2.44795i
$209$	−0.547594	−	11.8443i	−0.0378779	−	0.819286i
$210$	−0.0547757	+	1.18478i	−0.00377988	+	0.0817576i
$211$	2.65875	+	0.891123i	0.183036	+	0.0613474i	0.407826	−	0.913060i	$-0.366287\pi$
$211$	2.65875	+	0.891123i	0.183036	+	0.0613474i	−0.224790	+	0.974407i	$0.572170\pi$
$212$	6.80480	−	5.13875i	0.467356	−	0.352931i
$213$	−3.51221	+	3.85271i	−0.240652	+	0.263983i
$214$	11.4839	−	11.4839i	0.785022	−	0.785022i
$215$	0.257973	+	0.0864637i	0.0175936	+	0.00589678i
$216$	−22.0239	−	15.0867i	−1.49853	−	1.02652i
$217$	2.90449	−	31.3444i	0.197169	−	2.12780i
$218$	−50.2025	−	11.8075i	−3.40014	−	0.799707i
$219$	−2.85026	+	1.41926i	−0.192603	+	0.0959047i
$220$	−0.806202	−	0.734951i	−0.0543542	−	0.0495504i
$221$	−13.9021	+	0.247149i	−0.935158	+	0.0166251i
$222$	18.7194	−	17.0650i	1.25636	−	1.14532i
$223$	1.60990	−	4.15563i	0.107807	−	0.278282i	−0.868129	−	0.496338i	$-0.834678\pi$
$223$	1.60990	−	4.15563i	0.107807	−	0.278282i	0.975936	+	0.218057i	$0.0699717\pi$
$224$	−46.0245	−	46.0245i	−3.07514	−	3.07514i
$225$	−1.99882	−	7.02511i	−0.133254	−	0.468341i
$226$	−48.6133	+	16.2935i	−3.23371	+	1.08383i
$227$	−1.88807	+	2.75624i	−0.125316	+	0.182938i	−0.882569	−	0.470183i	$-0.844188\pi$
$227$	−1.88807	+	2.75624i	−0.125316	+	0.182938i	0.757253	+	0.653121i	$0.226541\pi$
$228$	−8.99203	−	26.8286i	−0.595512	−	1.77677i
$229$	11.5696	−	18.6856i	0.764543	−	1.23478i	−0.202279	−	0.979328i	$-0.564835\pi$
$229$	11.5696	−	18.6856i	0.764543	−	1.23478i	0.966822	−	0.255452i	$-0.0822241\pi$
$230$	0.851237	−	0.423865i	0.0561289	−	0.0279489i
$231$	5.81553	+	41.6902i	0.382634	+	2.74301i
$232$	−25.6485	+	6.03246i	−1.68390	+	0.396050i
$233$	−12.9332	+	10.7396i	−0.847284	+	0.703575i	−0.956906	−	0.290398i	$-0.906212\pi$
$233$	−12.9332	+	10.7396i	−0.847284	+	0.703575i	0.109622	+	0.993973i	$0.465036\pi$
$234$	9.69525	−	8.83839i	0.633798	−	0.577783i
$235$	0.00396984	−	0.00478069i	0.000258964	−	0.000311858i
$236$	−18.1809	−	29.3631i	−1.18347	−	1.91138i
$237$	17.8655	+	11.0618i	1.16049	+	0.718544i
$238$	14.6198	−	46.3372i	0.947659	−	3.00359i
$239$	−23.7549	+	14.7084i	−1.53658	+	0.951408i	−0.542819	+	0.839850i	$0.682643\pi$
$239$	−23.7549	+	14.7084i	−1.53658	+	0.951408i	−0.993758	+	0.111558i	$0.964416\pi$
$240$	−1.05365	−	0.524658i	−0.0680131	−	0.0338665i
$241$	−6.96644	+	20.7850i	−0.448748	+	1.33888i	0.447085	+	0.894491i	$0.352462\pi$
$241$	−6.96644	+	20.7850i	−0.448748	+	1.33888i	−0.895833	+	0.444390i	$0.853420\pi$
$242$	−20.9679	−	12.9828i	−1.34787	−	0.834564i
$243$	7.91758	+	11.5582i	0.507913	+	0.741462i
$244$	32.1583	−	14.1993i	2.05872	−	0.909015i
$245$	−0.339255	+	0.495251i	−0.0216742	+	0.0316404i
$246$	1.48968	−	7.96911i	0.0949788	−	0.508092i
$247$	−8.84448	+	0.819562i	−0.562761	+	0.0521475i
$248$	51.0293	+	28.4232i	3.24037	+	1.80487i
$249$	7.98914	−	7.98914i	0.506291	−	0.506291i
$250$	0.512212	+	1.16005i	0.0323951	+	0.0733679i
$251$	−7.17497			−0.452880			−0.226440	−	0.974025i	$-0.572709\pi$
$251$	−7.17497			−0.452880			−0.226440	+	0.974025i	$0.572709\pi$
$252$	13.2913	+	30.1019i	0.837271	+	1.89624i
$253$	26.9325	−	20.3385i	1.69323	−	1.27867i
$254$	29.8614	+	11.5684i	1.87367	+	0.725863i
$255$	−0.00737605	−	0.414902i	−0.000461906	−	0.0259822i
$256$	1.69175	−	0.655386i	0.105734	−	0.0409616i
$257$	−7.57693	+	12.2372i	−0.472636	+	0.763333i	−0.996055	−	0.0887425i	$-0.971715\pi$
$257$	−7.57693	+	12.2372i	−0.472636	+	0.763333i	0.523419	+	0.852076i	$0.324656\pi$
$258$	31.7975	−	4.43556i	1.97963	−	0.276146i
$259$	19.6046	−	3.66473i	1.21817	−	0.227715i
$260$	−0.522093	+	0.628733i	−0.0323788	+	0.0389923i
$261$	4.64259	+	0.647614i	0.287369	+	0.0400863i
$262$	5.29081	−	0.244609i	0.326868	−	0.0151120i
$263$	1.64943	+	8.82366i	0.101708	+	0.544090i	0.995432	+	0.0954730i	$0.0304363\pi$
$263$	1.64943	+	8.82366i	0.101708	+	0.544090i	−0.893724	+	0.448617i	$0.851917\pi$
$264$	−75.1267	−	21.3754i	−4.62373	−	1.31557i
$265$	0.0730810	−	0.0322684i	0.00448933	−	0.00198223i
$266$	7.10652	−	30.2151i	0.435729	−	1.85261i
$267$	−5.91975	+	0.825770i	−0.362283	+	0.0505363i
$268$	−45.9244	−	41.8656i	−2.80528	−	2.55735i
$269$	9.09827	+	0.420638i	0.554731	+	0.0256468i	0.321733	−	0.946830i	$-0.395735\pi$
$269$	9.09827	+	0.420638i	0.554731	+	0.0256468i	0.232998	+	0.972477i	$0.425146\pi$
$270$	−0.277693	−	0.304615i	−0.0168998	−	0.0185383i
$271$	1.07687	+	0.201303i	0.0654155	+	0.0122283i	0.216356	−	0.976315i	$-0.430583\pi$
$271$	1.07687	+	0.201303i	0.0654155	+	0.0122283i	−0.150940	+	0.988543i	$0.548230\pi$
$272$	36.2071	+	31.8473i	2.19538	+	1.93103i
$273$	30.9968	−	5.79431i	1.87601	−	0.350687i
$274$	35.5653	+	26.8577i	2.14858	+	1.62253i
$275$	12.7144	+	18.5607i	0.766705	+	1.11925i
$276$	48.5358	−	64.2718i	2.92151	−	3.86871i
$277$	19.2473	+	8.49852i	1.15646	+	0.510627i	0.891227	−	0.453558i	$-0.149845\pi$
$277$	19.2473	+	8.49852i	1.15646	+	0.510627i	0.265233	+	0.964184i	$0.414551\pi$
$278$	32.1828	+	26.7242i	1.93020	+	1.60281i
$279$	−6.63874	−	7.99473i	−0.397451	−	0.478632i
$280$	−0.912216	−	1.47328i	−0.0545153	−	0.0880453i
$281$	−5.56978	−	4.20610i	−0.332265	−	0.250915i	0.423298	−	0.905990i	$-0.360872\pi$
$281$	−5.56978	−	4.20610i	−0.332265	−	0.250915i	−0.755564	+	0.655075i	$0.772637\pi$
$282$	0.167882	−	0.713790i	0.00999722	−	0.0425056i
$283$	−8.72420	−	26.0295i	−0.518600	−	1.54729i	−0.807461	−	0.589921i	$-0.799159\pi$
$283$	−8.72420	−	26.0295i	−0.518600	−	1.54729i	0.288861	−	0.957371i	$-0.406724\pi$
$284$	1.73429	−	12.4328i	0.102911	−	0.737748i
$285$	−0.0244594	−	0.263959i	−0.00144885	−	0.0156356i
$286$	−19.6639	+	35.3035i	−1.16275	+	2.08754i
$287$	4.30037	−	4.71728i	0.253843	−	0.278452i
$288$	−21.4870			−1.26613
$289$	−4.06814	+	16.5061i	−0.239303	+	0.970945i
$290$	−0.406830			−0.0238899
$291$	21.9650	−	24.0945i	1.28761	−	1.41244i
$292$	3.73073	−	6.69794i	0.218324	−	0.391968i
$293$	−0.740620	−	7.99257i	−0.0432675	−	0.466931i	−0.989611	−	0.143769i	$-0.954078\pi$
$293$	−0.740620	−	7.99257i	−0.0432675	−	0.466931i	0.946344	−	0.323162i	$-0.104746\pi$
$294$	−9.78654	+	70.1574i	−0.570763	+	4.09166i
$295$	−0.102824	−	0.306784i	−0.00598662	−	0.0178616i
$296$	−8.47299	+	36.0250i	−0.492483	+	2.09391i
$297$	−11.6743	−	8.81601i	−0.677411	−	0.511557i
$298$	−18.9716	−	30.6402i	−1.09900	−	1.77494i
$299$	−16.1517	−	19.4508i	−0.934078	−	1.12487i
$300$	41.3047	+	34.2990i	2.38473	+	1.98025i
$301$	23.1246	+	10.2105i	1.33288	+	0.588525i
$302$	−6.92328	+	9.16791i	−0.398390	+	0.527554i
$303$	−6.85018	−	10.0000i	−0.393532	−	0.574487i
$304$	24.5823	+	18.5637i	1.40989	+	1.06470i
$305$	0.323735	−	0.0605165i	0.0185370	−	0.00346516i
$306$	−7.40380	−	14.2292i	−0.423247	−	0.813429i
$307$	−3.51396	−	0.656873i	−0.200552	−	0.0374897i	0.0825148	−	0.996590i	$-0.473705\pi$
$307$	−3.51396	−	0.656873i	−0.200552	−	0.0374897i	−0.283067	+	0.959100i	$0.591352\pi$
$308$	−68.2839	−	74.9039i	−3.89084	−	4.26804i
$309$	8.68324	+	0.401451i	0.493973	+	0.0228377i
$310$	0.666509	+	0.607603i	0.0378552	+	0.0345095i
$311$	6.30386	−	0.879351i	0.357459	−	0.0498634i	0.0428415	−	0.999082i	$-0.486359\pi$
$311$	6.30386	−	0.879351i	0.357459	−	0.0498634i	0.314618	+	0.949218i	$0.398124\pi$
$312$	−13.3967	+	56.9591i	−0.758437	+	3.22468i
$313$	−24.0789	+	10.6319i	−1.36102	+	0.600949i	−0.950449	−	0.310880i	$-0.899376\pi$
$313$	−24.0789	+	10.6319i	−1.36102	+	0.600949i	−0.410570	+	0.911829i	$0.634670\pi$
$314$	16.4826	+	4.68971i	0.930168	+	0.264656i
$315$	0.0566467	+	0.303033i	0.00319168	+	0.0170740i
$316$	−50.5426	+	2.33672i	−2.84324	+	0.131451i
$317$	13.4022	+	1.86953i	0.752745	+	0.105003i	0.504164	−	0.863608i	$-0.331801\pi$
$317$	13.4022	+	1.86953i	0.752745	+	0.105003i	0.248581	+	0.968611i	$0.420036\pi$
$318$	6.02232	−	7.25240i	0.337715	−	0.406695i
$319$	−14.1929	+	2.65312i	−0.794651	+	0.148546i
$320$	0.743132	−	0.103662i	0.0415423	−	0.00579491i
$321$	6.78398	−	10.9565i	0.378645	−	0.611533i
$322$	82.3842	−	31.9158i	4.59109	−	1.77860i
$323$	−1.80545	+	10.7088i	−0.100458	+	0.595855i
$324$	−53.3464	−	20.6665i	−2.96369	−	1.14814i
$325$	13.4496	−	10.1567i	0.746051	−	0.563392i
$326$	−13.7257	−	31.0858i	−0.760197	−	1.72168i
$327$	−40.9219			−2.26299
$328$	4.78430	+	10.8354i	0.264169	+	0.598285i
$329$	0.408245	−	0.408245i	0.0225073	−	0.0225073i
$330$	−1.05362	−	0.586860i	−0.0579996	−	0.0323056i
$331$	−1.12580	+	0.104321i	−0.0618796	+	0.00573399i	−0.123164	−	0.992386i	$-0.539304\pi$
$331$	−1.12580	+	0.104321i	−0.0618796	+	0.00573399i	0.0612840	+	0.998120i	$0.480480\pi$
$332$	−4.99893	+	26.7419i	−0.274352	+	1.46765i
$333$	3.72084	−	5.43176i	0.203901	−	0.297659i
$334$	−25.8010	+	11.3923i	−1.41177	+	0.623357i
$335$	−0.329022	−	0.480313i	−0.0179764	−	0.0262423i
$336$	−92.9792	−	57.5703i	−5.07243	−	3.14072i
$337$	−5.56430	+	16.6016i	−0.303107	+	0.904348i	0.681842	+	0.731500i	$0.261179\pi$
$337$	−5.56430	+	16.6016i	−0.303107	+	0.904348i	−0.984949	+	0.172848i	$0.944703\pi$
$338$	−3.87846	−	1.93124i	−0.210960	−	0.105046i
$339$	−34.5893	+	21.4168i	−1.87863	+	1.16320i
$340$	0.579245	+	0.814166i	0.0314140	+	0.0441543i
$341$	27.2147	+	16.8506i	1.47376	+	0.912512i
$342$	−5.39424	−	8.71199i	−0.291687	−	0.471091i
$343$	−15.8338	+	19.0679i	−0.854943	+	1.02957i
$344$	−34.6642	+	31.6006i	−1.86897	+	1.70379i
$345$	0.580499	−	0.482040i	0.0312530	−	0.0259522i
$346$	25.6618	−	6.03560i	1.37959	−	0.324476i
$347$	3.00847	+	21.5670i	0.161503	+	1.15778i	0.884369	+	0.466789i	$0.154589\pi$
$347$	3.00847	+	21.5670i	0.161503	+	1.15778i	−0.722866	+	0.690988i	$0.757176\pi$
$348$	−30.8443	+	15.3587i	−1.65343	+	0.823311i
$349$	8.63777	−	13.9505i	0.462369	−	0.746752i	−0.532660	−	0.846329i	$-0.678808\pi$
$349$	8.63777	−	13.9505i	0.462369	−	0.746752i	0.995030	+	0.0995767i	$0.0317489\pi$
$350$	18.7166	+	55.8427i	1.00044	+	2.98492i
$351$	−6.19338	+	9.04123i	−0.330578	+	0.482585i
$352$	62.7541	−	21.0331i	3.34481	−	1.12107i
$353$	4.71070	+	16.5564i	0.250726	+	0.881209i	0.980334	+	0.197344i	$0.0632316\pi$
$353$	4.71070	+	16.5564i	0.250726	+	0.881209i	−0.729609	+	0.683865i	$0.760298\pi$
$354$	−26.9974	−	26.9974i	−1.43489	−	1.43489i
$355$	0.0424842	−	0.109664i	0.00225483	−	0.00582039i
$356$	10.6359	−	9.69590i	0.563701	−	0.513881i
$357$	2.87441	−	38.4471i	0.152130	−	2.03484i
$358$	26.8633	+	24.4891i	1.41977	+	1.29429i
$359$	−6.41606	+	3.19482i	−0.338627	+	0.168616i	−0.607006	−	0.794697i	$-0.707630\pi$
$359$	−6.41606	+	3.19482i	−0.338627	+	0.168616i	0.268379	+	0.963313i	$0.413512\pi$
$360$	−0.556847	−	0.130969i	−0.0293484	−	0.00690269i
$361$	1.11298	−	12.0110i	0.0585779	−	0.632156i
$362$	−29.1649	−	19.9784i	−1.53287	−	1.05004i
$363$	−18.5543	−	6.21878i	−0.973849	−	0.326401i
$364$	−53.6903	+	53.6903i	−2.81414	+	2.81414i
$365$	0.0483904	−	0.0530818i	0.00253287	−	0.00277843i
$366$	31.0131	−	23.4200i	1.62108	−	1.22418i
$367$	23.6553	+	7.92845i	1.23480	+	0.413862i	0.858585	−	0.512672i	$-0.171344\pi$
$367$	23.6553	+	7.92845i	1.23480	+	0.413862i	0.376211	+	0.926534i	$0.377227\pi$
$368$	−4.04938	+	87.5868i	−0.211089	+	4.56578i
$369$	−0.0973198	−	2.10499i	−0.00506626	−	0.109582i
$370$	−0.254704	+	0.511514i	−0.0132414	+	0.0265923i
$371$	7.03758	−	2.35876i	0.365373	−	0.122461i
$372$	73.4705	+	20.9042i	3.80927	+	1.08383i
$373$	−8.17242	+	10.8220i	−0.423152	+	0.560343i	−0.958794	−	0.284101i	$-0.908305\pi$
$373$	−8.17242	+	10.8220i	−0.423152	+	0.560343i	0.535643	+	0.844445i	$0.320069\pi$
$374$	35.5518	+	34.3099i	1.83834	+	1.77412i
$375$	0.606381	+	0.802978i	0.0313134	+	0.0414656i
$376$	0.387002	+	0.998968i	0.0199581	+	0.0515178i
$377$	2.47644	+	10.5292i	0.127543	+	0.542281i
$378$	−23.0789	−	30.5614i	−1.18705	−	1.57191i
$379$	−4.39664	+	13.1178i	−0.225840	+	0.673815i	0.773365	+	0.633961i	$0.218572\pi$
$379$	−4.39664	+	13.1178i	−0.225840	+	0.673815i	−0.999205	+	0.0398548i	$0.987310\pi$
$380$	0.407780	+	0.491071i	0.0209187	+	0.0251914i
$381$	25.1668	+	3.51061i	1.28933	+	0.179854i
$382$	4.33800	−	11.1977i	0.221951	−	0.572922i
$383$	36.7934	−	10.4686i	1.88006	−	0.534922i	0.882096	−	0.471070i	$-0.156132\pi$
$383$	36.7934	−	10.4686i	1.88006	−	0.534922i	0.997959	−	0.0638514i	$-0.0203384\pi$
$384$	21.8044	−	14.9364i	1.11270	−	0.762217i
$385$	−0.462071	−	0.829576i	−0.0235493	−	0.0422791i
$386$	4.18107	+	0.983378i	0.212811	+	0.0500526i
$387$	7.78144	−	3.01455i	0.395553	−	0.153238i
$388$	−10.8461	+	77.7534i	−0.550629	+	3.94733i
$389$	3.53192	−	18.8941i	0.179076	−	0.957970i	−0.768838	−	0.639443i	$-0.779165\pi$
$389$	3.53192	−	18.8941i	0.179076	−	0.957970i	0.947914	−	0.318527i	$-0.103188\pi$
$390$	−0.402712	+	0.808756i	−0.0203921	+	0.0409529i
$391$	−28.0513	+	12.9865i	−1.41862	+	0.656755i
$392$	−46.1309	−	92.6434i	−2.32996	−	4.67920i
$393$	4.04223	−	1.15011i	0.203903	−	0.0580155i
$394$	40.8017	−	33.8813i	2.05556	−	1.70692i
$395$	−0.465952	−	0.0871014i	−0.0234446	−	0.00438255i
$396$	−33.4244	−	1.54530i	−1.67964	−	0.0776543i
$397$	4.11317	+	29.4864i	0.206434	+	1.47988i	0.761550	+	0.648106i	$0.224439\pi$
$397$	4.11317	+	29.4864i	0.206434	+	1.47988i	−0.555116	+	0.831773i	$0.687326\pi$
$398$	−15.9080	−	28.5604i	−0.797397	−	1.43160i
$399$		−	24.6294i		−	1.23301i
$400$	−58.1999	−	5.39302i	−2.91000	−	0.269651i
$401$	−0.150155	+	3.24781i	−0.00749840	+	0.162188i	0.991887	+	0.127125i	$0.0405749\pi$
$401$	−0.150155	+	3.24781i	−0.00749840	+	0.162188i	−0.999385	+	0.0350629i	$0.988837\pi$
$402$	−60.0180	−	33.4298i	−2.99342	−	1.66733i
$403$	11.6683	−	20.9485i	0.581237	−	1.04352i
$404$	27.2158	+	10.5434i	1.35403	+	0.524556i
$405$	−0.442181	−	0.302901i	−0.0219721	−	0.0150513i
$406$	−37.6371	−	3.48759i	−1.86790	−	0.173086i
$407$	−5.54994	+	19.5060i	−0.275100	+	0.966878i
$408$	63.1086	+	33.6957i	3.12434	+	1.66818i
$409$	−9.58135	−	33.6749i	−0.473767	−	1.66512i	−0.718499	−	0.695528i	$-0.755171\pi$
$409$	−9.58135	−	33.6749i	−0.473767	−	1.66512i	0.244732	−	0.969591i	$-0.421300\pi$
$410$	0.0336053	+	0.179773i	0.00165965	+	0.00887834i
$411$	32.3501	+	14.2840i	1.59571	+	0.704577i
$412$	−17.7955	+	11.0185i	−0.876724	+	0.542844i
$413$	−6.88259	−	29.2630i	−0.338670	−	1.43994i
$414$	11.7809	−	26.6811i	0.578997	−	1.31130i
$415$	−0.102950	+	0.233159i	−0.00505361	+	0.0114453i
$416$	−17.9108	−	46.2331i	−0.878149	−	2.26676i
$417$	29.7132	+	14.7954i	1.45506	+	0.724534i
$418$	24.2821	+	20.1636i	1.18768	+	0.986236i
$419$	−18.7878	+	0.868614i	−0.917846	+	0.0424346i	−0.499944	−	0.866058i	$-0.666646\pi$
$419$	−18.7878	+	0.868614i	−0.917846	+	0.0424346i	−0.417902	+	0.908492i	$0.637234\pi$
$420$	−1.60236	−	1.60236i	−0.0781873	−	0.0781873i
$421$	−0.196773	−	0.395174i	−0.00959014	−	0.0192596i	0.890316	−	0.455342i	$-0.150483\pi$
$421$	−0.196773	−	0.395174i	−0.00959014	−	0.0192596i	−0.899907	+	0.436083i	$0.856365\pi$
$422$	−6.52107	+	3.63221i	−0.317441	+	0.176813i
$423$		−	0.190594i		−	0.00926698i
$424$	−1.27079	+	13.7140i	−0.0617150	+	0.666011i
$425$	−7.78417	−	19.0793i	−0.377588	−	0.925483i
$426$	−1.28047	−	13.8184i	−0.0620389	−	0.669506i
$427$	30.4685	−	2.82332i	1.47447	−	0.136630i
$428$	1.43306	+	30.9966i	0.0692696	+	1.49828i
$429$	−8.77502	+	30.8410i	−0.423662	+	1.48902i
$430$	−0.632725	+	0.352426i	−0.0305127	+	0.0169955i
$431$	−12.5625	+	8.60554i	−0.605116	+	0.414514i	−0.828318	−	0.560258i	$-0.810702\pi$
$431$	−12.5625	+	8.60554i	−0.605116	+	0.414514i	0.223202	+	0.974772i	$0.428349\pi$
$432$	36.9968	−	8.70156i	1.78001	−	0.418654i
$433$	18.9498	+	20.7870i	0.910671	+	0.998958i	0.999996	+	0.00295565i	$0.000940814\pi$
$433$	18.9498	+	20.7870i	0.910671	+	0.998958i	−0.0893249	+	0.996003i	$0.528471\pi$
$434$	56.4521	+	61.9250i	2.70979	+	2.97249i
$435$	−0.314239	+	0.0739083i	−0.0150666	+	0.00354363i
$436$	81.2913	−	55.6858i	3.89315	−	2.66687i
$437$	−17.2514	+	9.60896i	−0.825246	+	0.459659i
$438$	2.31952	−	8.15226i	0.110831	−	0.389530i
$439$	1.30363	+	28.1972i	0.0622191	+	1.34578i	0.769410	+	0.638756i	$0.220551\pi$
$439$	1.30363	+	28.1972i	0.0622191	+	1.34578i	−0.707191	+	0.707023i	$0.750038\pi$
$440$	1.75451	−	0.162579i	0.0836429	−	0.00775066i
$441$	1.69886	+	18.3336i	0.0808981	+	0.873029i
$442$	24.4451	−	27.7915i	1.16273	−	1.32191i
$443$	−2.23200	+	24.0872i	−0.106046	+	1.14442i	0.761879	+	0.647719i	$0.224277\pi$
$443$	−2.23200	+	24.0872i	−0.106046	+	1.14442i	−0.867925	+	0.496696i	$0.834546\pi$
$444$			48.3967i			2.29681i
$445$	0.117795	−	0.0656113i	0.00558401	−	0.00311027i
$446$	5.28787	+	10.6195i	0.250388	+	0.502847i
$447$	−20.2202	−	20.2202i	−0.956382	−	0.956382i
$448$	69.6381	−	3.21956i	3.29009	−	0.152110i
$449$	6.24348	+	5.18452i	0.294648	+	0.244673i	0.774348	−	0.632760i	$-0.218078\pi$
$449$	6.24348	+	5.18452i	0.294648	+	0.244673i	−0.479700	+	0.877433i	$0.659254\pi$
$450$	17.4044	+	8.66636i	0.820451	+	0.408536i
$451$	2.34475	+	6.05250i	0.110410	+	0.285001i
$452$	39.5680	−	89.6129i	1.86112	−	4.21504i
$453$	−3.68208	+	8.33911i	−0.172999	+	0.391806i
$454$	−2.03613	−	8.65710i	−0.0955604	−	0.406298i
$455$	−0.604810	+	0.374483i	−0.0283539	+	0.0175560i
$456$	41.8077	+	18.4599i	1.95783	+	0.864465i
$457$	−5.06288	−	27.0840i	−0.236832	−	1.26694i	−0.870050	−	0.492964i	$-0.835914\pi$
$457$	−5.06288	−	27.0840i	−0.236832	−	1.26694i	0.633218	−	0.773973i	$-0.281733\pi$
$458$	16.0101	+	56.2695i	0.748101	+	2.62930i
$459$	8.74182	+	10.1546i	0.408033	+	0.473974i
$460$	−0.497208	+	1.74751i	−0.0231825	+	0.0814779i
$461$	−38.2406	−	3.54352i	−1.78104	−	0.165038i	−0.849242	−	0.528004i	$-0.822941\pi$
$461$	−38.2406	−	3.54352i	−1.78104	−	0.165038i	−0.931802	+	0.362966i	$0.881764\pi$
$462$	−92.4424	−	63.3245i	−4.30081	−	2.94612i
$463$	−36.0317	−	13.9588i	−1.67454	−	0.648719i	−0.678251	−	0.734830i	$-0.737262\pi$
$463$	−36.0317	−	13.9588i	−1.67454	−	0.648719i	−0.996286	+	0.0861108i	$0.972556\pi$
$464$	18.2534	−	32.7711i	0.847392	−	1.52136i
$465$	0.625199	+	0.348234i	0.0289929	+	0.0161489i
$466$	2.06670	−	44.7021i	0.0957381	−	2.07078i
$467$	−3.94095	−	0.365183i	−0.182365	−	0.0168986i	0.000697987	−	1.00000i	$-0.499778\pi$
$467$	−3.94095	−	0.365183i	−0.182365	−	0.0168986i	−0.183063	+	0.983101i	$0.558601\pi$
$468$			25.0659i			1.15867i
$469$	−26.3213	−	47.2558i	−1.21541	−	2.18207i
$470$	0.00228532	+	0.0163829i	0.000105414	+	0.000755687i
$471$	13.5833	+	0.627993i	0.625884	+	0.0289364i
$472$	54.8317	+	10.2498i	2.52383	+	0.471786i
$473$	−19.7753	+	16.4212i	−0.909270	+	0.755048i
$474$	−53.7999	+	15.3074i	−2.47111	+	0.703092i
$475$	−5.86755	−	11.7836i	−0.269221	−	0.540670i
$476$	46.6082	+	80.2867i	2.13628	+	3.67993i
$477$	1.09218	−	2.19339i	0.0500074	−	0.100428i
$478$	13.6662	−	73.1080i	0.625080	−	3.34388i
$479$	−0.785798	+	5.63320i	−0.0359040	+	0.257387i	−0.999966	−	0.00829133i	$-0.997361\pi$
$479$	−0.785798	+	5.63320i	−0.0359040	+	0.257387i	0.964062	+	0.265679i	$0.0855961\pi$
$480$	1.37980	−	0.534539i	0.0629792	−	0.0243983i
$481$	14.7890	+	3.47833i	0.674318	+	0.158598i
$482$	−28.3952	−	50.9791i	−1.29336	−	2.32203i
$483$	57.8361	−	39.6187i	2.63163	−	1.80271i
$484$	45.3206	−	12.8948i	2.06003	−	0.586128i
$485$	−0.265693	+	0.685832i	−0.0120645	+	0.0311420i
$486$	−36.9364	−	5.15240i	−1.67547	−	0.233718i
$487$	11.6846	+	14.0713i	0.529481	+	0.637630i	0.964906	−	0.262595i	$-0.0845783\pi$
$487$	11.6846	+	14.0713i	0.529481	+	0.637630i	−0.435425	+	0.900225i	$0.643402\pi$
$488$	−18.0438	+	53.8355i	−0.816807	+	2.43702i
$489$	−16.2492	−	21.5174i	−0.734813	−	0.973049i
$490$	−0.365859	−	1.55554i	−0.0165278	−	0.0702720i
$491$	6.59849	+	17.0327i	0.297786	+	0.768674i	0.998475	+	0.0552072i	$0.0175819\pi$
$491$	6.59849	+	17.0327i	0.297786	+	0.768674i	−0.700689	+	0.713467i	$0.747124\pi$
$492$	9.33461	+	12.3610i	0.420837	+	0.557278i
$493$	13.2194	+	0.375848i	0.595370	+	0.0169273i
$494$	14.2489	−	18.8687i	0.641091	−	0.848941i
$495$	−0.301510	−	0.0857869i	−0.0135518	−	0.00385583i
$496$	−78.8484	+	26.4273i	−3.54040	+	1.18662i
$497$	4.87046	−	9.78121i	0.218470	−	0.438747i
$498$	1.38900	+	30.0436i	0.0622425	+	1.34628i
$499$	−0.651975	+	14.1020i	−0.0291864	+	0.631292i	0.933159	+	0.359463i	$0.117040\pi$
$499$	−0.651975	+	14.1020i	−0.0291864	+	0.631292i	−0.962346	+	0.271829i	$0.912372\pi$
$500$	−2.29725	−	0.769962i	−0.102736	−	0.0344337i
$501$	−17.8593	+	13.4867i	−0.797895	+	0.602542i
$502$	12.8672	−	14.1146i	0.574290	−	0.629966i
$503$	10.7503	−	10.7503i	0.479330	−	0.479330i	−0.425587	−	0.904917i	$-0.639932\pi$
$503$	10.7503	−	10.7503i	0.479330	−	0.479330i	0.904917	+	0.425587i	$0.139932\pi$
$504$	−50.3929	−	16.8900i	−2.24468	−	0.752341i
$505$	0.225588	+	0.154531i	0.0100385	+	0.00687654i
$506$	−8.28929	+	89.4557i	−0.368504	+	3.97679i
$507$	−3.34660	−	0.787113i	−0.148628	−	0.0349569i
$508$	−54.7709	+	27.2727i	−2.43007	+	1.21003i
$509$	−29.3231	−	26.7316i	−1.29973	−	1.18486i	−0.970635	−	0.240558i	$-0.922670\pi$
$509$	−29.3231	−	26.7316i	−1.29973	−	1.18486i	−0.329090	−	0.944298i	$-0.606742\pi$
$510$	0.829425	+	0.729552i	0.0367276	+	0.0323051i
$511$	4.93180	−	4.49593i	0.218170	−	0.198888i
$512$	7.29566	−	18.8323i	0.322426	−	0.832276i
$513$	6.05255	+	6.05255i	0.267226	+	0.267226i
$514$	−10.4850	−	36.8508i	−0.462472	−	1.62542i
$515$	−0.185927	+	0.0623163i	−0.00819290	+	0.00274598i
$516$	−34.6661	+	50.6063i	−1.52609	+	2.22782i
$517$	0.186567	+	0.556640i	0.00820521	+	0.0244810i
$518$	−27.9485	+	45.1383i	−1.22798	+	1.98326i
$519$	18.7249	−	9.32389i	0.821931	−	0.409273i
$520$	−0.182364	−	1.30733i	−0.00799720	−	0.0573300i
$521$	23.3166	−	5.48402i	1.02152	−	0.240259i	0.315856	−	0.948807i	$-0.397708\pi$
$521$	23.3166	−	5.48402i	1.02152	−	0.240259i	0.705663	+	0.708548i	$0.250649\pi$
$522$	−9.59976	+	7.97154i	−0.420170	+	0.348905i
$523$	12.5880	−	11.4755i	0.550436	−	0.501788i	−0.350017	−	0.936744i	$-0.613824\pi$
$523$	12.5880	−	11.4755i	0.550436	−	0.501788i	0.900452	+	0.434955i	$0.143236\pi$
$524$	−6.46483	+	7.78530i	−0.282417	+	0.340102i
$525$	24.6017	+	39.7331i	1.07371	+	1.73410i
$526$	−20.3159	−	12.5791i	−0.885817	−	0.548475i
$527$	−21.0959	−	20.3589i	−0.918953	−	0.886849i
$528$	94.5459	−	58.5403i	4.11458	−	2.54764i
$529$	−29.7260	−	14.8018i	−1.29243	−	0.643555i
$530$	−0.0675808	+	0.201634i	−0.00293552	+	0.00875840i
$531$	−8.43748	−	5.22426i	−0.366155	−	0.226714i
$532$	33.5153	+	48.9263i	1.45307	+	2.12122i
$533$	4.44814	−	1.96405i	0.192671	−	0.0850724i
$534$	8.99169	−	13.1263i	0.389109	−	0.568028i
$535$	−0.0534173	+	0.285758i	−0.00230943	+	0.0123544i
$536$	99.9435	−	9.26113i	4.31690	−	0.400020i
$537$	25.1983	+	14.0354i	1.08739	+	0.605671i
$538$	−17.1438	+	17.1438i	−0.739122	+	0.739122i
$539$	−22.9079	−	51.8815i	−0.986714	−	2.23469i
$540$	0.787545			0.0338905
$541$	−8.12171	−	18.3939i	−0.349180	−	0.790816i	−0.999514	−	0.0311684i	$-0.990077\pi$
$541$	−8.12171	−	18.3939i	−0.349180	−	0.790816i	0.650335	−	0.759648i	$-0.274629\pi$
$542$	−2.32721	+	1.75743i	−0.0999622	+	0.0754879i
$543$	−26.1567	−	10.1331i	−1.12249	−	0.434855i
$544$	−60.2525	+	6.66535i	−2.58330	+	0.285775i
$545$	0.860806	−	0.333478i	0.0368729	−	0.0142846i
$546$	−44.1893	+	71.3682i	−1.89113	+	3.05428i
$547$	−11.6279	+	1.62202i	−0.497174	+	0.0693528i	−0.382321	−	0.924030i	$-0.624875\pi$
$547$	−11.6279	+	1.62202i	−0.497174	+	0.0693528i	−0.114853	+	0.993382i	$0.536640\pi$
$548$	−83.7009	+	15.6464i	−3.57553	+	0.668382i
$549$	6.45322	−	7.77132i	0.275417	−	0.331672i
$550$	−59.3139	−	8.27393i	−2.52915	−	0.352802i
$551$	8.43920	−	0.390168i	0.359522	−	0.0166217i
$552$	23.9030	+	127.870i	1.01738	+	5.44250i
$553$	−42.3600	−	12.0524i	−1.80133	−	0.512522i
$554$	−51.2354	+	22.6226i	−2.17678	+	0.961144i
$555$	−0.103809	+	0.441369i	−0.00440645	+	0.0187351i
$556$	−79.1586	+	11.0422i	−3.35707	+	0.468292i
$557$	−5.39374	−	4.91705i	−0.228540	−	0.208342i	0.551323	−	0.834292i	$-0.314123\pi$
$557$	−5.39374	−	4.91705i	−0.228540	−	0.208342i	−0.779863	+	0.625950i	$0.784711\pi$
$558$	27.6328	+	1.27754i	1.16979	+	0.0540826i
$559$	12.9727	+	14.2303i	0.548685	+	0.601879i
$560$	2.42500	+	0.453311i	0.102475	+	0.0191559i
$561$	33.6936	+	20.0425i	1.42254	+	0.846197i
$562$	18.2628	−	3.41391i	0.770369	−	0.144007i
$563$	−3.08505	−	2.32972i	−0.130019	−	0.0981860i	0.535622	−	0.844458i	$-0.320077\pi$
$563$	−3.08505	−	2.32972i	−0.130019	−	0.0981860i	−0.665641	+	0.746272i	$0.731842\pi$
$564$	0.791752	+	1.15582i	0.0333388	+	0.0486686i
$565$	0.553069	−	0.732382i	0.0232678	−	0.0308115i
$566$	66.8508	+	29.5175i	2.80995	+	1.24071i
$567$	−38.3109	−	31.8129i	−1.60891	−	1.33602i
$568$	12.9529	+	15.5986i	0.543491	+	0.654501i
$569$	12.7497	+	20.5915i	0.534495	+	0.863239i	0.999759	−	0.0219325i	$-0.00698190\pi$
$569$	12.7497	+	20.5915i	0.534495	+	0.863239i	−0.465264	+	0.885172i	$0.654041\pi$
$570$	0.563126	+	0.425253i	0.0235868	+	0.0178119i
$571$	1.21070	−	5.14757i	0.0506661	−	0.215419i	−0.942128	−	0.335254i	$-0.891178\pi$
$571$	1.21070	−	5.14757i	0.0506661	−	0.215419i	0.992794	+	0.119835i	$0.0382366\pi$
$572$	−24.5364	−	73.2065i	−1.02592	−	3.06092i
$573$	1.31644	−	9.43724i	0.0549950	−	0.394246i
$574$	1.56781	+	16.9194i	0.0654393	+	0.706203i
$575$	18.2325	−	32.7335i	0.760346	−	1.36508i
$576$	15.5041	−	17.0072i	0.646004	−	0.708633i
$577$	4.18438			0.174198			0.0870990	−	0.996200i	$-0.472240\pi$
$577$	4.18438			0.174198			0.0870990	+	0.996200i	$0.472240\pi$
$578$	−25.1752	−	37.6039i	−1.04715	−	1.56412i
$579$	3.40814			0.141637
$580$	0.523662	−	0.574430i	0.0217439	−	0.0238519i
$581$	−11.5230	+	20.6877i	−0.478054	+	0.858272i
$582$	8.00794	+	86.4194i	0.331940	+	3.58220i
$583$	−1.04272	+	7.47503i	−0.0431852	+	0.309584i
$584$	3.93530	+	11.7413i	0.162844	+	0.485860i
$585$	−0.0537654	+	0.228597i	−0.00222293	+	0.00945131i
$586$	17.0512	+	12.8765i	0.704378	+	0.531922i
$587$	−15.4029	−	24.8765i	−0.635744	−	1.02676i	−0.995596	−	0.0937525i	$-0.970114\pi$
$587$	−15.4029	−	24.8765i	−0.635744	−	1.02676i	0.359851	−	0.933010i	$-0.382827\pi$
$588$	−86.4628	−	104.123i	−3.56566	−	4.29397i
$589$	−14.4086	−	11.9648i	−0.593698	−	0.493001i
$590$	0.787904	+	0.347894i	0.0324375	+	0.0143226i
$591$	25.3604	−	33.5826i	1.04319	−	1.38140i
$592$	−29.7758	−	43.4673i	−1.22378	−	1.78649i
$593$	−8.06844	−	6.09300i	−0.331331	−	0.250210i	0.423840	−	0.905737i	$-0.360682\pi$
$593$	−8.06844	−	6.09300i	−0.331331	−	0.250210i	−0.755171	+	0.655527i	$0.772446\pi$
$594$	38.2789	−	7.15557i	1.57060	−	0.293596i
$595$	0.252847	+	0.832173i	0.0103657	+	0.0341158i
$596$	67.6827	+	12.6521i	2.77239	+	0.518250i
$597$	−17.4760	−	19.1703i	−0.715245	−	0.784586i
$598$	67.2292	+	3.10819i	2.74921	+	0.127103i
$599$	3.59715	+	3.27924i	0.146976	+	0.133986i	0.743844	−	0.668353i	$-0.233000\pi$
$599$	3.59715	+	3.27924i	0.146976	+	0.133986i	−0.596869	+	0.802339i	$0.703589\pi$
$600$	−85.8850	+	11.9805i	−3.50624	+	0.489100i
$601$	−3.82645	+	16.2691i	−0.156084	+	0.663630i	0.837098	+	0.547054i	$0.184251\pi$
$601$	−3.82645	+	16.2691i	−0.156084	+	0.663630i	−0.993182	+	0.116576i	$0.962808\pi$
$602$	−61.5566	+	27.1799i	−2.50886	+	1.10777i
$603$	−17.1751	−	4.88675i	−0.699426	−	0.199004i
$604$	−4.03328	−	21.5761i	−0.164112	−	0.877921i
$605$	0.440974	−	0.0203875i	0.0179282	−	0.000828869i
$606$	31.9568	+	4.45779i	1.29816	+	0.181085i
$607$	−11.4521	+	13.7913i	−0.464828	+	0.559771i	−0.949030	−	0.315185i	$-0.897933\pi$
$607$	−11.4521	+	13.7913i	−0.464828	+	0.559771i	0.484202	+	0.874956i	$0.339110\pi$
$608$	−38.0660	+	7.11577i	−1.54378	+	0.288582i
$609$	−29.7048	+	4.14364i	−1.20370	+	0.167909i
$610$	−0.461519	+	0.745379i	−0.0186864	+	0.0301795i
$611$	0.410096	−	0.158872i	0.0165907	−	0.00642727i
$612$	29.6211	+	7.86157i	1.19736	+	0.317785i
$613$	8.77926	+	3.40110i	0.354591	+	0.137369i	0.531947	−	0.846777i	$-0.321460\pi$
$613$	8.77926	+	3.40110i	0.354591	+	0.137369i	−0.177356	+	0.984147i	$0.556755\pi$
$614$	7.59394	−	5.73468i	0.306466	−	0.231433i
$615$	0.0586161	+	0.132753i	0.00236363	+	0.00535311i
$616$	163.709			6.59602
$617$	−5.38086	−	12.1865i	−0.216625	−	0.490609i	0.772978	−	0.634433i	$-0.218766\pi$
$617$	−5.38086	−	12.1865i	−0.216625	−	0.490609i	−0.989603	+	0.143823i	$0.954060\pi$
$618$	−16.3618	+	16.3618i	−0.658167	+	0.658167i
$619$	−9.29977	−	5.17994i	−0.373789	−	0.208199i	0.288444	−	0.957497i	$-0.406862\pi$
$619$	−9.29977	−	5.17994i	−0.373789	−	0.208199i	−0.662234	+	0.749297i	$0.730391\pi$
$620$	−1.71583	+	0.158995i	−0.0689093	+	0.00638539i
$621$	−4.47684	+	23.9490i	−0.179650	+	0.961040i
$622$	−9.57512	+	13.9780i	−0.383928	+	0.560465i
$623$	11.4600	−	5.06010i	0.459136	−	0.202728i
$624$	−47.0785	−	68.7262i	−1.88465	−	2.75125i
$625$	21.2265	+	13.1429i	0.849059	+	0.525715i
$626$	22.2667	−	66.4347i	0.889955	−	2.65526i
$627$	22.4188	+	11.1632i	0.895321	+	0.445817i
$628$	−27.8377	+	17.2364i	−1.11085	+	0.687807i
$629$	8.74879	−	16.3856i	0.348837	−	0.653337i
$630$	−0.697714	−	0.432006i	−0.0277976	−	0.0172115i
$631$	−8.37535	−	13.5267i	−0.333417	−	0.538487i	0.639751	−	0.768582i	$-0.279038\pi$
$631$	−8.37535	−	13.5267i	−0.333417	−	0.538487i	−0.973168	+	0.230095i	$0.926096\pi$
$632$	52.2078	−	62.8715i	2.07672	−	2.50089i
$633$	−4.37707	+	3.99022i	−0.173973	+	0.158597i
$634$	−27.7126	+	23.0122i	−1.10061	+	0.913932i
$635$	−0.558000	+	0.131240i	−0.0221436	+	0.00520812i
$636$	2.48835	+	17.8384i	0.0986697	+	0.707340i
$637$	−38.0319	+	18.9376i	−1.50688	+	0.750337i
$638$	20.2336	−	32.6783i	0.801054	−	1.29375i
$639$	−1.14632	−	3.42014i	−0.0453476	−	0.135299i
$640$	−0.336944	+	0.491878i	−0.0133189	+	0.0194432i
$641$	−26.6858	+	8.94417i	−1.05402	+	0.353273i	−0.791192	−	0.611568i	$-0.790539\pi$
$641$	−26.6858	+	8.94417i	−1.05402	+	0.353273i	−0.262833	+	0.964841i	$0.584657\pi$
$642$	9.38767	+	32.9943i	0.370502	+	1.30218i
$643$	33.6844	+	33.6844i	1.32838	+	1.32838i	0.906779	+	0.421605i	$0.138533\pi$
$643$	33.6844	+	33.6844i	1.32838	+	1.32838i	0.421605	+	0.906779i	$0.361467\pi$
$644$	−60.9790	+	157.405i	−2.40291	+	6.20262i
$645$	−0.424697	+	0.387163i	−0.0167224	+	0.0152445i
$646$	−17.8287	−	22.7563i	−0.701459	−	0.895334i
$647$	11.7202	+	10.6844i	0.460770	+	0.420047i	0.870507	−	0.492157i	$-0.163791\pi$
$647$	11.7202	+	10.6844i	0.460770	+	0.420047i	−0.409737	+	0.912204i	$0.634380\pi$
$648$	82.7159	−	41.1876i	3.24939	−	1.61800i
$649$	29.7561	+	6.99856i	1.16803	+	0.274718i
$650$	−4.13953	+	44.6726i	−0.162366	+	1.75220i
$651$	54.8539	+	37.5758i	2.14989	+	1.47271i
$652$	61.5595	+	20.6327i	2.41085	+	0.808037i
$653$	12.8248	−	12.8248i	0.501874	−	0.501874i	−0.410146	−	0.912020i	$-0.634522\pi$
$653$	12.8248	−	12.8248i	0.501874	−	0.501874i	0.912020	+	0.410146i	$0.134522\pi$
$654$	73.3870	−	80.5017i	2.86966	−	3.14787i
$655$	−0.0756573	+	0.0571337i	−0.00295617	+	0.00223240i
$656$	−15.9889	−	5.35894i	−0.624261	−	0.209231i
$657$	0.101745	−	2.20072i	0.00396946	−	0.0858582i
$658$	0.0709778	+	1.53523i	0.00276700	+	0.0598493i
$659$	5.72629	−	11.4999i	0.223064	−	0.447974i	−0.755155	−	0.655546i	$-0.772439\pi$
$659$	5.72629	−	11.4999i	0.223064	−	0.447974i	0.978220	+	0.207572i	$0.0665562\pi$
$660$	2.18481	−	0.732276i	0.0850438	−	0.0285038i
$661$	−21.2764	−	6.05366i	−0.827556	−	0.235460i	−0.166733	−	0.986002i	$-0.553322\pi$
$661$	−21.2764	−	6.05366i	−0.827556	−	0.235460i	−0.660823	+	0.750542i	$0.729792\pi$
$662$	1.81373	−	2.40176i	0.0704925	−	0.0933472i
$663$	13.8327	−	25.9073i	0.537219	−	1.00616i
$664$	−26.4803	−	35.0656i	−1.02763	−	1.36081i
$665$	0.200708	+	0.518088i	0.00778314	+	0.0200906i
$666$	4.01263	+	17.0607i	0.155486	+	0.661087i
$667$	14.4915	+	19.1898i	0.561111	+	0.743031i
$668$	17.1250	−	51.0940i	0.662586	−	1.97689i
$669$	6.01362	+	7.24193i	0.232500	+	0.279989i
$670$	1.53492	+	0.214113i	0.0592992	+	0.00827189i
$671$	−11.2399	+	29.0135i	−0.433911	+	1.12005i
$672$	132.232	−	37.6234i	5.10098	−	1.45135i
$673$	−20.3603	+	13.9471i	−0.784833	+	0.537623i	−0.889528	−	0.456881i	$-0.848966\pi$
$673$	−20.3603	+	13.9471i	−0.784833	+	0.537623i	0.104695	+	0.994504i	$0.466613\pi$
$674$	−22.6801	−	40.7185i	−0.873603	−	1.56842i
$675$	−15.8099	−	3.71847i	−0.608525	−	0.143124i
$676$	7.71911	−	2.99040i	0.296889	−	0.115015i
$677$	4.59067	−	32.9094i	0.176434	−	1.26481i	−0.674000	−	0.738731i	$-0.735425\pi$
$677$	4.59067	−	32.9094i	0.176434	−	1.26481i	0.850434	−	0.526081i	$-0.176339\pi$
$678$	19.8993	−	106.452i	0.764227	−	4.08825i
$679$	−30.4595	+	61.1708i	−1.16893	+	2.34752i
$680$	−1.60210	−	0.194519i	−0.0614378	−	0.00745948i
$681$	−3.14545	−	6.31691i	−0.120534	−	0.242065i
$682$	−81.9538	+	23.3179i	−3.13817	+	0.892888i
$683$	−5.93557	+	4.92883i	−0.227118	+	0.188596i	−0.745408	−	0.666609i	$-0.767745\pi$
$683$	−5.93557	+	4.92883i	−0.227118	+	0.188596i	0.518290	+	0.855205i	$0.326569\pi$
$684$	19.2444	+	3.59739i	0.735826	+	0.137550i
$685$	−0.796898	−	0.0368428i	−0.0304479	−	0.00140769i
$686$	−9.11503	−	65.3435i	−0.348013	−	2.49483i
$687$	22.5887	+	40.5545i	0.861813	+	1.54725i
$688$		−	66.7799i		−	2.54596i
$689$	5.62987	+	0.521684i	0.214481	+	0.0198746i
$690$	−0.0927625	+	2.00642i	−0.00353141	+	0.0763832i
$691$	−31.2058	−	17.3815i	−1.18712	−	0.661224i	−0.236519	−	0.971627i	$-0.576007\pi$
$691$	−31.2058	−	17.3815i	−1.18712	−	0.661224i	−0.950605	+	0.310403i	$0.899536\pi$
$692$	−24.5092	+	44.0024i	−0.931699	+	1.67272i
$693$	−27.1582	−	10.5211i	−1.03165	−	0.399665i
$694$	−47.8219	−	32.7588i	−1.81529	−	1.24351i
$695$	−0.745597	−	0.0690898i	−0.0282821	−	0.00262072i
$696$	15.2302	−	53.5288i	0.577301	−	2.02900i
$697$	−0.925875	−	5.87250i	−0.0350700	−	0.222437i
$698$	11.9530	+	42.0103i	0.452426	+	1.59011i
$699$	−6.52463	−	34.9037i	−0.246784	−	1.32018i
$700$	−102.939	−	45.4522i	−3.89075	−	1.71793i
$701$	29.4298	−	18.2222i	1.11155	−	0.688242i	0.157388	−	0.987537i	$-0.449693\pi$
$701$	29.4298	−	18.2222i	1.11155	−	0.688242i	0.954161	+	0.299295i	$0.0967515\pi$
$702$	−6.67907	−	28.3977i	−0.252085	−	1.07180i
$703$	4.79296	−	10.8550i	0.180770	−	0.409405i
$704$	−28.6328	+	64.8471i	−1.07914	+	2.44402i
$705$	0.00474146	+	0.0122391i	0.000178574	+	0.000460952i
$706$	−41.0177	−	20.4244i	−1.54372	−	0.768683i
$707$	19.5451	+	16.2300i	0.735068	+	0.610393i
$708$	72.8697	−	3.36897i	2.73861	−	0.126614i
$709$	16.7830	+	16.7830i	0.630300	+	0.630300i	0.948143	−	0.317844i	$-0.102959\pi$
$709$	16.7830	+	16.7830i	0.630300	+	0.630300i	−0.317844	+	0.948143i	$0.602959\pi$
$710$	0.139544	+	0.280241i	0.00523698	+	0.0105173i
$711$	−12.7015	+	7.07469i	−0.476344	+	0.265322i
$712$			23.2457i			0.871168i
$713$	4.91874	−	53.0817i	0.184208	−	1.98792i
$714$	70.4786	+	74.6035i	2.63759	+	2.79197i
$715$	−0.0667419	−	0.720260i	−0.00249601	−	0.0269362i
$716$	−69.1556	+	6.40821i	−2.58447	+	0.239486i
$717$	−2.72551	−	58.9519i	−0.101786	−	2.20160i
$718$	5.22134	−	18.3511i	0.194859	−	0.684858i
$719$	16.5670	−	9.22777i	0.617846	−	0.344138i	−0.146243	−	0.989249i	$-0.546718\pi$
$719$	16.5670	−	9.22777i	0.617846	−	0.344138i	0.764089	+	0.645111i	$0.223189\pi$
$720$	0.671885	−	0.460252i	0.0250397	−	0.0171526i
$721$	−17.7349	+	4.17120i	−0.660481	+	0.155344i
$722$	21.6321	+	23.7293i	0.805062	+	0.883111i
$723$	−31.1940	−	34.2182i	−1.16012	−	1.27259i
$724$	65.7492	−	15.4641i	2.44355	−	0.574718i
$725$	−13.2247	+	9.05915i	−0.491154	+	0.336448i
$726$	45.5079	−	25.3477i	1.68896	−	0.940742i
$727$	0.892044	−	3.13521i	0.0330841	−	0.116278i	−0.943525	−	0.331302i	$-0.892512\pi$
$727$	0.892044	−	3.13521i	0.0330841	−	0.116278i	0.976609	+	0.215023i	$0.0689828\pi$
$728$	−5.66390	−	122.508i	−0.209918	−	4.54046i
$729$	4.13561	−	0.383221i	0.153171	−	0.0141934i
$730$	0.0176420	+	0.190388i	0.000652960	+	0.00704657i
$731$	20.8851	−	10.8670i	0.772463	−	0.401932i
$732$	−6.85110	+	73.9351i	−0.253224	+	2.73272i
$733$			11.2650i			0.416082i	0.978120	+	0.208041i	$0.0667087\pi$
$733$			11.2650i			0.416082i	−0.978120	+	0.208041i	$0.933291\pi$
$734$	−58.0189	+	32.3163i	−2.14152	+	1.19282i
$735$	−0.565185	−	1.13504i	−0.0208472	−	0.0418667i
$736$	−77.9423	−	77.9423i	−2.87299	−	2.87299i
$737$	54.9446	−	2.54024i	2.02391	−	0.0935710i
$738$	4.31548	+	3.58353i	0.158855	+	0.131912i
$739$	9.81844	+	4.88900i	0.361177	+	0.179845i	0.617162	−	0.786836i	$-0.288282\pi$
$739$	9.81844	+	4.88900i	0.361177	+	0.179845i	−0.255985	+	0.966681i	$0.582400\pi$
$740$	−0.394391	−	1.01804i	−0.0144981	−	0.0374239i
$741$	7.57816	−	17.1629i	0.278391	−	0.630494i
$742$	−7.98063	+	18.0744i	−0.292978	+	0.663533i
$743$	9.53950	+	40.5595i	0.349970	+	1.48798i	0.802726	+	0.596348i	$0.203382\pi$
$743$	9.53950	+	40.5595i	0.349970	+	1.48798i	−0.452756	+	0.891634i	$0.649559\pi$
$744$	−104.897	+	64.9496i	−3.84572	+	2.38117i
$745$	0.590116	+	0.260562i	0.0216202	+	0.00954624i
$746$	−6.63319	−	35.4844i	−0.242858	−	1.29918i
$747$	2.13933	+	7.51896i	0.0782739	+	0.275104i
$748$	−94.2058	+	6.03513i	−3.44451	+	0.220666i
$749$	−7.39149	+	25.9784i	−0.270079	+	0.949230i
$750$	−2.66707	−	0.247140i	−0.0973876	−	0.00902429i
$751$	27.2444	+	18.6628i	0.994161	+	0.681016i	0.948116	−	0.317923i	$-0.102985\pi$
$751$	27.2444	+	18.6628i	0.994161	+	0.681016i	0.0460447	+	0.998939i	$0.485338\pi$
$752$	−1.42222	−	0.550970i	−0.0518630	−	0.0200918i
$753$	7.37453	−	13.2398i	0.268743	−	0.482486i
$754$	−25.1542	−	14.0108i	−0.916061	−	0.510243i
$755$	0.00949723	−	0.205422i	0.000345639	−	0.00747607i
$756$	72.8582	+	6.75131i	2.64983	+	0.245543i
$757$			44.1678i			1.60531i	0.596447	+	0.802653i	$0.296579\pi$
$757$			44.1678i			1.60531i	−0.596447	+	0.802653i	$0.703421\pi$
$758$	−17.9207	−	32.1738i	−0.650908	−	1.16860i
$759$	9.84859	+	70.6022i	0.357481	+	2.56270i
$760$	−1.02987	−	0.0476139i	−0.0373574	−	0.00172714i
$761$	−22.0165	−	4.11560i	−0.798098	−	0.149190i	−0.231122	−	0.972925i	$-0.574240\pi$
$761$	−22.0165	−	4.11560i	−0.798098	−	0.149190i	−0.566976	+	0.823734i	$0.691887\pi$
$762$	−52.0387	+	43.2124i	−1.88516	+	1.56542i
$763$	82.4947	−	23.4718i	2.98651	−	0.849735i
$764$	10.2269	+	20.5385i	0.369998	+	0.743056i
$765$	0.253277	+	0.135232i	0.00915723	+	0.00488934i
$766$	−45.3893	+	91.1540i	−1.63998	+	3.29353i
$767$	4.20775	−	22.5095i	0.151933	−	0.812770i
$768$	−0.529429	+	3.79535i	−0.0191041	+	0.136953i
$769$	4.16354	−	1.61296i	0.150141	−	0.0581649i	−0.284999	−	0.958528i	$-0.591993\pi$
$769$	4.16354	−	1.61296i	0.150141	−	0.0581649i	0.435140	+	0.900363i	$0.356699\pi$
$770$	2.46060	+	0.578727i	0.0886738	+	0.0208559i
$771$	−14.7933	−	26.5591i	−0.532768	−	0.956501i
$772$	−6.77026	+	4.63774i	−0.243667	+	0.166916i
$773$	−38.7532	+	11.0262i	−1.39386	+	0.396587i	−0.885532	−	0.464579i	$-0.846206\pi$
$773$	−38.7532	+	11.0262i	−1.39386	+	0.396587i	−0.508325	+	0.861165i	$0.669735\pi$
$774$	−8.02457	+	20.7138i	−0.288437	+	0.744542i
$775$	35.1959	+	4.90962i	1.26428	+	0.176359i
$776$	−81.0062	−	97.5521i	−2.90795	−	3.50192i
$777$	−13.3874	+	39.9425i	−0.480270	+	1.43293i
$778$	30.8346	+	40.8317i	1.10548	+	1.46389i
$779$	−0.869512	−	3.69694i	−0.0311535	−	0.132457i
$780$	−0.623573	−	1.60963i	−0.0223275	−	0.0576339i
$781$	6.69578	+	8.86664i	0.239594	+	0.317273i
$782$	24.7585	−	78.4719i	0.885363	−	2.80615i
$783$	6.28152	−	8.31808i	0.224483	−	0.297264i
$784$	141.717	+	40.3221i	5.06133	+	1.44007i
$785$	−0.290847	+	0.0974820i	−0.0103808	+	0.00347928i
$786$	−4.98660	+	10.0144i	−0.177866	+	0.357203i
$787$	0.307833	+	6.65833i	0.0109731	+	0.237344i	0.997345	+	0.0728155i	$0.0231984\pi$
$787$	0.307833	+	6.65833i	0.0109731	+	0.237344i	−0.986372	+	0.164528i	$0.947390\pi$
$788$	−4.67977	+	101.222i	−0.166710	+	3.60588i
$789$	−17.9774	−	6.02542i	−0.640013	−	0.214511i
$790$	1.00696	−	0.760419i	0.0358259	−	0.0270545i
$791$	57.4446	−	63.0137i	2.04249	−	2.24051i
$792$	38.2146	−	38.2146i	1.35790	−	1.35790i
$793$	22.1005	+	7.40735i	0.784813	+	0.263043i
$794$	−65.3820	−	44.7877i	−2.32032	−	1.58946i
$795$	−0.0155694	+	0.168021i	−0.000552190	+	0.00595908i
$796$	60.8026	+	14.3006i	2.15509	+	0.506873i
$797$	−11.7822	+	5.86684i	−0.417347	+	0.207814i	−0.642132	−	0.766594i	$-0.721950\pi$
$797$	−11.7822	+	5.86684i	−0.417347	+	0.207814i	0.224785	+	0.974408i	$0.427832\pi$
$798$	48.4510	+	44.1690i	1.71515	+	1.56356i
$799$	−0.0591229	−	0.534450i	−0.00209162	−	0.0189075i
$800$	54.3018	−	49.5026i	1.91986	−	1.75018i
$801$	1.49394	−	3.85630i	0.0527857	−	0.136256i
$802$	−6.11982	−	6.11982i	−0.216098	−	0.216098i
$803$	1.85707	+	6.52693i	0.0655346	+	0.230330i
$804$	124.455	−	41.7132i	4.38920	−	1.47111i
$805$	−0.893745	+	1.30471i	−0.0315004	+	0.0459849i
$806$	20.2849	+	60.5218i	0.714503	+	2.13179i
$807$	−10.1275	+	16.3565i	−0.356505	+	0.575776i
$808$	−42.1992	+	21.0127i	−1.48456	+	0.739225i
$809$	−3.53267	−	25.3249i	−0.124202	−	0.890376i	−0.946816	−	0.321776i	$-0.895720\pi$
$809$	−3.53267	−	25.3249i	−0.124202	−	0.890376i	0.822614	−	0.568601i	$-0.192515\pi$
$810$	1.38885	−	0.326654i	0.0487992	−	0.0114775i
$811$	−6.77461	+	5.62557i	−0.237889	+	0.197540i	−0.750110	−	0.661313i	$-0.769999\pi$
$811$	−6.77461	+	5.62557i	−0.237889	+	0.197540i	0.512221	+	0.858854i	$0.328823\pi$
$812$	53.3700	−	48.6531i	1.87292	−	1.70739i
$813$	−1.47829	+	1.78023i	−0.0518457	+	0.0624354i
$814$	−28.4194	−	45.8989i	−0.996098	−	1.60875i
$815$	0.517155	+	0.320209i	0.0181151	+	0.0112164i
$816$	−95.9813	+	34.0791i	−3.36002	+	1.19301i
$817$	12.7871	−	7.91746i	0.447365	−	0.276997i
$818$	83.4281	+	41.5423i	2.91700	+	1.45249i
$819$	−6.93368	+	20.6873i	−0.242282	+	0.722872i
$820$	−0.297089	−	0.183949i	−0.0103748	−	0.00642379i
$821$	8.78808	+	12.8290i	0.306706	+	0.447736i	0.947396	−	0.320064i	$-0.103704\pi$
$821$	8.78808	+	12.8290i	0.306706	+	0.447736i	−0.640690	+	0.767800i	$0.721352\pi$
$822$	−86.1144	+	38.0232i	−3.00358	+	1.32621i
$823$	−2.49142	+	3.63703i	−0.0868456	+	0.126779i	−0.865981	−	0.500076i	$-0.833305\pi$
$823$	−2.49142	+	3.63703i	−0.0868456	+	0.126779i	0.779136	+	0.626855i	$0.215658\pi$
$824$	6.21191	−	33.2308i	0.216402	−	1.15765i
$825$	−47.3176	+	4.38462i	−1.64739	+	0.152653i
$826$	69.9091	+	38.9391i	2.43245	+	1.35487i
$827$	−27.7009	+	27.7009i	−0.963255	+	0.963255i	−0.999348	−	0.0360939i	$-0.988508\pi$
$827$	−27.7009	+	27.7009i	−0.963255	+	0.963255i	0.0360939	+	0.999348i	$0.488508\pi$
$828$	22.5087	+	50.9774i	0.782232	+	1.77159i
$829$	−17.4996			−0.607787			−0.303894	−	0.952706i	$-0.598287\pi$
$829$	−17.4996			−0.607787			−0.303894	+	0.952706i	$0.598287\pi$
$830$	−0.274047	−	0.620658i	−0.00951231	−	0.0215433i
$831$	−35.4648	+	26.7818i	−1.23026	+	0.929049i
$832$	49.5177	+	19.1832i	1.71672	+	0.665059i
$833$	10.4510	+	50.8830i	0.362105	+	1.76299i
$834$	−82.3915	+	31.9187i	−2.85299	+	1.10525i
$835$	0.265772	−	0.429236i	0.00919740	−	0.0148543i
$836$	−59.7257	+	8.33138i	−2.06566	+	0.288147i
$837$	−22.7141	+	4.24600i	−0.785114	+	0.146763i
$838$	31.9843	−	38.5172i	1.10488	−	1.33056i
$839$	−2.71519	−	0.378753i	−0.0937388	−	0.0130760i	0.0911322	−	0.995839i	$-0.470951\pi$
$839$	−2.71519	−	0.378753i	−0.0937388	−	0.0130760i	−0.184871	+	0.982763i	$0.559187\pi$
$840$	3.65620	−	0.169036i	0.126151	−	0.00583231i
$841$	3.43836	+	18.3936i	0.118564	+	0.634262i
$842$	1.13027	+	0.321589i	0.0389516	+	0.0110827i
$843$	13.4861	−	5.95470i	0.464487	−	0.205091i
$844$	3.26521	−	13.8828i	0.112393	−	0.477866i
$845$	0.0768112	−	0.0107147i	0.00264238	−	0.000368597i
$846$	0.374937	+	0.341800i	0.0128906	+	0.0117513i
$847$	40.9707	+	1.89419i	1.40777	+	0.0650851i
$848$	−13.2099	−	14.4906i	−0.453629	−	0.497608i
$849$	56.9985	+	10.6549i	1.95618	+	0.365674i
$850$	51.4926	+	18.9027i	1.76618	+	0.648358i
$851$	33.2003	−	6.20621i	1.13809	−	0.212746i
$852$	21.1594	+	15.9788i	0.724907	+	0.547425i
$853$	−0.799232	−	1.16673i	−0.0273652	−	0.0399482i	0.811073	−	0.584945i	$-0.198884\pi$
$853$	−0.799232	−	1.16673i	−0.0273652	−	0.0399482i	−0.838438	+	0.544997i	$0.816531\pi$
$854$	−49.0864	+	65.0009i	−1.67970	+	2.22429i
$855$	0.167789	+	0.0740860i	0.00573826	+	0.00253369i
$856$	−38.5577	−	32.0179i	−1.31787	−	1.09435i
$857$	9.60141	+	11.5625i	0.327978	+	0.394969i	0.907544	−	0.419956i	$-0.137955\pi$
$857$	9.60141	+	11.5625i	0.327978	+	0.394969i	−0.579567	+	0.814925i	$0.696778\pi$
$858$	−44.9339	−	72.5708i	−1.53402	−	2.47752i
$859$	13.6294	+	10.2924i	0.465029	+	0.351174i	0.809002	−	0.587806i	$-0.200008\pi$
$859$	13.6294	+	10.2924i	0.465029	+	0.351174i	−0.343973	+	0.938980i	$0.611773\pi$
$860$	0.316816	−	1.34702i	0.0108033	−	0.0459330i
$861$	4.28472	+	12.7839i	0.146023	+	0.435673i
$862$	5.60009	−	40.1458i	0.190740	−	1.36737i
$863$	4.31381	+	46.5534i	0.146844	+	1.58470i	0.676473	+	0.736468i	$0.263508\pi$
$863$	4.31381	+	46.5534i	0.146844	+	1.58470i	−0.529629	+	0.848230i	$0.677669\pi$
$864$	−23.2497	+	41.7412i	−0.790971	+	1.42006i
$865$	−0.317903	+	0.348723i	−0.0108090	+	0.0118569i
$866$	−74.8758			−2.54438
$867$	−26.2770	−	24.4720i	−0.892413	−	0.831113i
$868$	−160.100			−5.43414
$869$	30.1703	−	33.0952i	1.02346	−	1.12268i
$870$	0.418145	−	0.750714i	0.0141764	−	0.0254516i
$871$	−3.80188	−	41.0288i	−0.128822	−	1.39021i
$872$	−21.9877	+	157.625i	−0.744598	+	5.33785i
$873$	7.16897	+	21.3893i	0.242633	+	0.723918i
$874$	12.0349	−	51.1691i	0.407086	−	1.73082i
$875$	−1.68297	−	1.27092i	−0.0568949	−	0.0429650i
$876$	8.52508	+	13.7685i	0.288036	+	0.465194i
$877$	0.529002	+	0.637053i	0.0178631	+	0.0215117i	0.778190	−	0.628028i	$-0.216138\pi$
$877$	0.529002	+	0.637053i	0.0178631	+	0.0215117i	−0.760327	+	0.649540i	$0.774961\pi$
$878$	−57.8075	−	48.0027i	−1.95091	−	1.62001i
$879$	15.5097	+	6.84821i	0.523130	+	0.230985i
$880$	−1.51175	+	2.00188i	−0.0509612	+	0.0674835i
$881$	−1.51961	−	2.21836i	−0.0511971	−	0.0747385i	0.798552	−	0.601926i	$-0.205600\pi$
$881$	−1.51961	−	2.21836i	−0.0511971	−	0.0747385i	−0.849749	+	0.527187i	$0.823247\pi$
$882$	−39.1126	−	29.5365i	−1.31699	−	0.994545i
$883$	26.7194	−	4.99473i	0.899181	−	0.168086i	0.286187	−	0.958174i	$-0.407612\pi$
$883$	26.7194	−	4.99473i	0.899181	−	0.168086i	0.612994	+	0.790088i	$0.289965\pi$
$884$	7.77554	+	70.2882i	0.261520	+	2.36405i
$885$	0.671785	+	0.125578i	0.0225818	+	0.00422127i
$886$	−43.3816	−	47.5873i	−1.45743	−	1.59873i
$887$	−27.1293	−	1.25426i	−0.910911	−	0.0421140i	−0.414352	−	0.910117i	$-0.635992\pi$
$887$	−27.1293	−	1.25426i	−0.910911	−	0.0421140i	−0.496559	+	0.868003i	$0.665404\pi$
$888$	−57.7674	−	52.6620i	−1.93855	−	1.76722i
$889$	−52.7474	+	7.35795i	−1.76909	+	0.246778i
$890$	−0.0821757	+	0.349390i	−0.00275454	+	0.0117116i
$891$	46.3220	−	20.4532i	1.55184	−	0.685206i
$892$	−21.8007	−	6.20285i	−0.729943	−	0.207687i
$893$	−0.0631181	−	0.337652i	−0.00211217	−	0.0112991i
$894$	76.0390	−	3.51549i	2.54312	−	0.117576i
$895$	−0.644432	−	0.0898944i	−0.0215410	−	0.00300484i
$896$	−35.3885	+	42.6167i	−1.18225	+	1.42372i
$897$	52.4930	−	9.81264i	1.75269	−	0.327635i
$898$	−21.3957	+	2.98458i	−0.713985	+	0.0995966i
$899$	−12.0063	+	19.3908i	−0.400432	+	0.646720i
$900$	−34.6391	+	13.4193i	−1.15464	+	0.447309i
$901$	2.38222	−	6.48936i	0.0793632	−	0.216192i
$902$	−16.1114	−	6.24161i	−0.536453	−	0.207823i
$903$	−42.6091	+	32.1769i	−1.41794	+	1.07078i
$904$	63.9089	+	144.740i	2.12558	+	4.81398i
$905$	0.632791			0.0210347
$906$	−9.80150	−	22.1983i	−0.325633	−	0.737489i
$907$	−7.66336	+	7.66336i	−0.254458	+	0.254458i	−0.822795	−	0.568338i	$-0.807587\pi$
$907$	−7.66336	+	7.66336i	−0.254458	+	0.254458i	0.568338	+	0.822795i	$0.307587\pi$
$908$	14.8444	+	8.26827i	0.492628	+	0.274392i
$909$	8.35099	−	0.773834i	0.276985	−	0.0256664i
$910$	0.347949	−	1.86136i	0.0115344	−	0.0617035i
$911$	0.880911	−	1.28597i	0.0291859	−	0.0426061i	−0.810129	−	0.586251i	$-0.800603\pi$
$911$	0.880911	−	1.28597i	0.0291859	−	0.0426061i	0.839315	+	0.543645i	$0.182956\pi$
$912$	−59.5211	+	26.2811i	−1.97094	+	0.870256i
$913$	−13.6082	−	19.8655i	−0.450364	−	0.657451i
$914$	62.3593	+	38.6112i	2.06266	+	1.27715i
$915$	−0.221069	+	0.659580i	−0.00730831	+	0.0218050i
$916$	−100.058	−	49.8232i	−3.30602	−	1.64620i
$917$	−7.48908	+	4.63704i	−0.247311	+	0.153129i
$918$	−35.6532	−	1.01368i	−1.17673	−	0.0334563i
$919$	−23.3015	−	14.4277i	−0.768644	−	0.475924i	0.0852572	−	0.996359i	$-0.472829\pi$
$919$	−23.3015	−	14.4277i	−0.768644	−	0.475924i	−0.853902	+	0.520435i	$0.825770\pi$
$920$	−1.54484	−	2.49500i	−0.0509317	−	0.0822576i
$921$	4.82381	−	5.80909i	0.158950	−	0.191416i
$922$	75.5494	−	68.8724i	2.48809	−	2.26819i
$923$	6.40351	−	5.31741i	0.210774	−	0.175025i
$924$	208.402	−	49.0156i	6.85591	−	1.61249i
$925$	3.11062	+	22.2993i	0.102277	+	0.733197i
$926$	92.0770	−	45.8489i	3.02584	−	1.50669i
$927$	−3.16617	+	5.11354i	−0.103991	+	0.167951i
$928$	14.9863	+	44.7131i	0.491950	+	1.46778i
$929$	18.4983	−	27.0041i	0.606908	−	0.885977i	−0.392522	−	0.919743i	$-0.628397\pi$
$929$	18.4983	−	27.0041i	0.606908	−	0.885977i	0.999430	+	0.0337660i	$0.0107501\pi$
$930$	−1.80624	+	0.605392i	−0.0592290	+	0.0198516i
$931$	9.08114	+	31.9169i	0.297622	+	1.04603i
$932$	60.4576	+	60.4576i	1.98035	+	1.98035i
$933$	−4.85654	+	12.5362i	−0.158996	+	0.410416i
$934$	7.78586	−	7.09775i	0.254761	−	0.232246i
$935$	−0.872085	−	0.147029i	−0.0285202	−	0.00480835i
$936$	−29.9193	−	27.2750i	−0.977942	−	0.891511i
$937$	9.12622	−	4.54432i	0.298141	−	0.148456i	−0.290444	−	0.956892i	$-0.593803\pi$
$937$	9.12622	−	4.54432i	0.298141	−	0.148456i	0.588585	+	0.808436i	$0.299685\pi$
$938$	140.165	+	32.9665i	4.57655	+	1.07639i
$939$	5.12984	−	55.3598i	0.167406	−	1.80660i
$940$	−0.0260737	−	0.0178609i	−0.000850430	−	0.000582558i
$941$	−35.6485	−	11.9482i	−1.16211	−	0.389500i	−0.329929	−	0.944006i	$-0.607025\pi$
$941$	−35.6485	−	11.9482i	−1.16211	−	0.389500i	−0.832180	+	0.554506i	$0.812907\pi$
$942$	−25.5949	+	25.5949i	−0.833926	+	0.833926i
$943$	7.28267	−	7.98871i	0.237156	−	0.260148i
$944$	−63.3748	+	47.8585i	−2.06268	+	1.55766i
$945$	0.649973	+	0.217849i	0.0211436	+	0.00708663i
$946$	3.16006	−	68.3510i	0.102742	−	2.22228i
$947$	1.80419	+	39.0240i	0.0586282	+	1.26811i	0.801222	+	0.598367i	$0.204183\pi$
$947$	1.80419	+	39.0240i	0.0586282	+	1.26811i	−0.742594	+	0.669742i	$0.766405\pi$
$948$	47.6364	−	95.6668i	1.54716	−	3.10711i
$949$	4.82005	−	1.61552i	0.156465	−	0.0524419i
$950$	33.7033	+	9.58942i	1.09348	+	0.311122i
$951$	−17.2248	+	22.8093i	−0.558553	+	0.739643i
$952$	−146.548	−	31.7298i	−4.74965	−	1.02837i
$953$	30.3504	+	40.1905i	0.983147	+	1.30190i	0.953198	+	0.302346i	$0.0977699\pi$
$953$	30.3504	+	40.1905i	0.983147	+	1.30190i	0.0299492	+	0.999551i	$0.490465\pi$
$954$	2.35619	+	6.08204i	0.0762846	+	0.196913i
$955$	0.0492136	+	0.209244i	0.00159252	+	0.00677096i
$956$	85.6350	+	113.399i	2.76963	+	3.66759i
$957$	9.69193	−	28.9168i	0.313296	−	0.934747i
$958$	−9.67245	−	11.6481i	−0.312503	−	0.376333i
$959$	−73.4077	−	10.2399i	−2.37046	−	0.330665i
$960$	−0.572515	+	1.47783i	−0.0184778	+	0.0476968i
$961$	18.8136	−	5.35292i	0.606889	−	0.172675i
$962$	−33.3643	+	22.8550i	−1.07571	+	0.736876i
$963$	4.33875	+	7.78955i	0.139814	+	0.251015i
$964$	108.530	+	25.5261i	3.49553	+	0.822140i
$965$	−0.0716914	+	0.0277734i	−0.00230783	+	0.000894057i
$966$	−25.7820	+	184.825i	−0.829523	+	5.94666i
$967$	−9.51938	+	50.9242i	−0.306122	+	1.63761i	0.390808	+	0.920472i	$0.372196\pi$
$967$	−9.51938	+	50.9242i	−0.306122	+	1.63761i	−0.696931	+	0.717139i	$0.745451\pi$
$968$	−33.9232	+	68.1269i	−1.09033	+	2.18968i
$969$	−17.9051	−	14.3382i	−0.575195	−	0.460610i
$970$	−0.872693	−	1.75260i	−0.0280205	−	0.0562727i
$971$	36.8897	−	10.4960i	1.18385	−	0.336833i	0.376222	−	0.926530i	$-0.377223\pi$
$971$	36.8897	−	10.4960i	1.18385	−	0.336833i	0.807625	+	0.589696i	$0.200753\pi$
$972$	54.8186	−	45.5208i	1.75831	−	1.46008i
$973$	−68.3853	−	12.7834i	−2.19233	−	0.409818i
$974$	−48.6356	−	2.24856i	−1.55839	−	0.0720485i
$975$	4.91821	+	35.2575i	0.157509	+	1.12914i
$976$	−39.3349	−	70.6196i	−1.25908	−	2.26048i
$977$		−	6.48881i		−	0.207595i	−0.994598	−	0.103798i	$-0.966901\pi$
$977$		−	6.48881i		−	0.207595i	0.994598	−	0.103798i	$-0.0330995\pi$
$978$	71.4694	+	6.62262i	2.28534	+	0.211768i
$979$	−0.588309	+	12.7249i	−0.0188024	+	0.406690i
$980$	2.66729	+	1.48567i	0.0852034	+	0.0474580i
$981$	13.7777	−	24.7358i	0.439889	−	0.789753i
$982$	−45.3401	−	17.5649i	−1.44686	−	0.560517i
$983$	−30.9042	−	21.1699i	−0.985692	−	0.675215i	−0.0396346	−	0.999214i	$-0.512619\pi$
$983$	−30.9042	−	21.1699i	−0.985692	−	0.675215i	−0.946057	+	0.324000i	$0.894972\pi$
$984$	−24.9117	−	2.30841i	−0.794156	−	0.0735894i
$985$	−0.259796	+	0.913087i	−0.00827778	+	0.0290934i
$986$	−24.4462	+	25.3311i	−0.778526	+	0.806708i
$987$	0.333726	+	1.17293i	0.0106226	+	0.0373346i
$988$	8.30098	+	44.4063i	0.264089	+	1.41275i
$989$	39.1615	+	17.2915i	1.24526	+	0.549838i
$990$	0.709470	−	0.439286i	0.0225485	−	0.0139614i
$991$	−9.75633	−	41.4814i	−0.309920	−	1.31770i	−0.871548	−	0.490310i	$-0.836884\pi$
$991$	−9.75633	−	41.4814i	−0.309920	−	1.31770i	0.561628	−	0.827390i	$-0.310175\pi$
$992$	42.2273	−	95.6356i	1.34072	−	3.03643i
$993$	0.964612	−	2.18464i	0.0306110	−	0.0693274i
$994$	10.5072	+	27.1222i	0.333269	+	0.860265i
$995$	0.523835	+	0.260839i	0.0166067	+	0.00826914i
$996$	−44.2083	−	36.7101i	−1.40079	−	1.16320i
$997$	21.1503	−	0.977836i	0.669836	−	0.0309684i	0.291408	−	0.956599i	$-0.405876\pi$
$997$	21.1503	−	0.977836i	0.669836	−	0.0309684i	0.378428	+	0.925631i	$0.376465\pi$
$998$	−26.5723	−	26.5723i	−0.841131	−	0.841131i
$999$	−6.52579	−	13.1056i	−0.206467	−	0.414641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.h.a.115.2	✓	768
289.191	even	68	inner	289.2.h.a.191.2	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.h.a.115.2	✓	768	1.1	even	1	trivial
289.2.h.a.191.2	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)

\(f(q)\)	\(=\)	\(q+(-1.79334 + 1.96720i) q^{2} +(-1.02781 + 1.84528i) q^{3} +(-0.469274 - 5.06428i) q^{4} +(0.00658298 - 0.0471919i) q^{5} +(-1.78682 - 5.33113i) q^{6} +(1.01357 - 4.30943i) q^{7} +(6.55547 + 4.95046i) q^{8} +(-0.769355 - 1.24255i) q^{9} +O(q^{10})\)	\(q+(-1.79334 + 1.96720i) q^{2} +(-1.02781 + 1.84528i) q^{3} +(-0.469274 - 5.06428i) q^{4} +(0.00658298 - 0.0471919i) q^{5} +(-1.78682 - 5.33113i) q^{6} +(1.01357 - 4.30943i) q^{7} +(6.55547 + 4.95046i) q^{8} +(-0.769355 - 1.24255i) q^{9} +(0.0810305 + 0.0975813i) q^{10} +(3.46325 + 2.87584i) q^{11} +(9.82732 + 4.33919i) q^{12} +(2.03226 - 2.69115i) q^{13} +(6.65986 + 9.72219i) q^{14} +(0.0803160 + 0.0606518i) q^{15} +(-11.4960 + 2.14898i) q^{16} +(-2.54282 - 3.24562i) q^{17} +(3.82407 + 0.714842i) q^{18} +(-1.77447 - 1.94650i) q^{19} +(-0.242082 - 0.0111921i) q^{20} +(6.91034 + 6.29961i) q^{21} +(-11.8682 + 1.65554i) q^{22} +(1.71648 - 7.29802i) q^{23} +(-15.8728 + 7.00852i) q^{24} +(4.80694 + 1.36769i) q^{25} +(1.64950 + 8.82402i) q^{26} +(-3.24628 + 0.150085i) q^{27} +(-22.2998 - 3.11069i) q^{28} +(-2.04908 + 2.46761i) q^{29} +(-0.263349 + 0.0492284i) q^{30} +(7.04239 - 0.982371i) q^{31} +(7.73988 - 12.5003i) q^{32} +(-8.86630 + 3.43482i) q^{33} +(10.9450 + 0.818274i) q^{34} +(-0.196698 - 0.0762012i) q^{35} +(-5.93158 + 4.47932i) q^{36} +(1.81970 + 4.12123i) q^{37} +7.01138 q^{38} +(2.87713 + 6.51608i) q^{39} +(0.276776 - 0.276776i) q^{40} +(1.25966 + 0.701627i) q^{41} +(-24.7852 + 2.29669i) q^{42} +(-1.04922 + 5.61283i) q^{43} +(12.9389 - 18.8884i) q^{44} +(-0.0637029 + 0.0281276i) q^{45} +(11.2784 + 16.4645i) q^{46} +(0.110880 + 0.0686541i) q^{47} +(7.85030 - 23.4221i) q^{48} +(-11.2778 - 5.61566i) q^{49} +(-11.3110 + 7.00350i) q^{50} +(8.60262 - 1.35631i) q^{51} +(-14.5824 - 9.02904i) q^{52} +(0.882616 + 1.42547i) q^{53} +(5.52644 - 6.65524i) q^{54} +(0.158515 - 0.144505i) q^{55} +(27.9781 - 23.2327i) q^{56} +(5.41564 - 1.27375i) q^{57} +(-1.17959 - 8.45622i) q^{58} +(6.07856 - 3.02676i) q^{59} +(0.269467 - 0.435205i) q^{60} +(2.19653 + 6.55356i) q^{61} +(-10.6969 + 15.6155i) q^{62} +(-6.13449 + 2.05607i) q^{63} +(4.30938 + 15.1459i) q^{64} +(-0.113622 - 0.113622i) q^{65} +(9.14333 - 23.6016i) q^{66} +(9.02962 - 8.23159i) q^{67} +(-15.2435 + 14.4006i) q^{68} +(11.7026 + 10.6684i) q^{69} +(0.502650 - 0.250290i) q^{70} +(2.40263 + 0.565093i) q^{71} +(1.10772 - 11.9542i) q^{72} +(1.24365 + 0.851917i) q^{73} +(-11.3707 - 3.81106i) q^{74} +(-7.46442 + 7.46442i) q^{75} +(-9.02488 + 9.89982i) q^{76} +(15.9035 - 12.0098i) q^{77} +(-17.9782 - 6.02567i) q^{78} +(0.459445 - 9.93765i) q^{79} +(0.0257362 + 0.556666i) q^{80} +(5.01389 - 10.0693i) q^{81} +(-3.63925 + 1.21975i) q^{82} +(-5.14486 - 1.46384i) q^{83} +(28.6601 - 37.9521i) q^{84} +(-0.169906 + 0.0986345i) q^{85} +(-9.15996 - 12.1298i) q^{86} +(-2.44736 - 6.31736i) q^{87} +(8.46646 + 35.9972i) q^{88} +(1.70531 + 2.25820i) q^{89} +(0.0589085 - 0.175759i) q^{90} +(-9.53749 - 11.4856i) q^{91} +(-37.7647 - 5.26794i) q^{92} +(-5.42551 + 14.0049i) q^{93} +(-0.333903 + 0.0950036i) q^{94} +(-0.103540 + 0.0709266i) q^{95} +(15.1114 + 27.1302i) q^{96} +(-15.0258 - 3.53404i) q^{97} +(31.2720 - 12.1148i) q^{98} +(0.908916 - 6.51581i) 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

Modular forms

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Database

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