LMFDB - Embedded newform 1815.2.c.k.364.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (of order $2$, degree $1$, 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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.11
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.k.364.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.298064i q^{2} +1.00000i q^{3} +1.91116 q^{4} +(-1.68093 + 1.47460i) q^{5} +0.298064 q^{6} +2.32107i q^{7} -1.16578i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.298064i q^{2} +1.00000i q^{3} +1.91116 q^{4} +(-1.68093 + 1.47460i) q^{5} +0.298064 q^{6} +2.32107i q^{7} -1.16578i q^{8} -1.00000 q^{9} +(0.439527 + 0.501026i) q^{10} +1.91116i q^{12} +4.59081i q^{13} +0.691827 q^{14} +(-1.47460 - 1.68093i) q^{15} +3.47484 q^{16} +5.14046i q^{17} +0.298064i q^{18} +5.69187 q^{19} +(-3.21253 + 2.81820i) q^{20} -2.32107 q^{21} -6.02600i q^{23} +1.16578 q^{24} +(0.651081 - 4.95743i) q^{25} +1.36836 q^{26} -1.00000i q^{27} +4.43592i q^{28} -6.09737 q^{29} +(-0.501026 + 0.439527i) q^{30} -8.43171 q^{31} -3.36728i q^{32} +1.53219 q^{34} +(-3.42266 - 3.90156i) q^{35} -1.91116 q^{36} -3.17279i q^{37} -1.69654i q^{38} -4.59081 q^{39} +(1.71906 + 1.95959i) q^{40} -0.468592 q^{41} +0.691827i q^{42} +8.08805i q^{43} +(1.68093 - 1.47460i) q^{45} -1.79614 q^{46} +9.18736i q^{47} +3.47484i q^{48} +1.61265 q^{49} +(-1.47763 - 0.194064i) q^{50} -5.14046 q^{51} +8.77376i q^{52} +4.25892i q^{53} -0.298064 q^{54} +2.70584 q^{56} +5.69187i q^{57} +1.81741i q^{58} -6.65971 q^{59} +(-2.81820 - 3.21253i) q^{60} +1.82041 q^{61} +2.51319i q^{62} -2.32107i q^{63} +5.94601 q^{64} +(-6.76963 - 7.71685i) q^{65} -8.86541i q^{67} +9.82424i q^{68} +6.02600 q^{69} +(-1.16292 + 1.02017i) q^{70} -2.44868 q^{71} +1.16578i q^{72} +9.08299i q^{73} -0.945695 q^{74} +(4.95743 + 0.651081i) q^{75} +10.8781 q^{76} +1.36836i q^{78} -12.9262 q^{79} +(-5.84098 + 5.12401i) q^{80} +1.00000 q^{81} +0.139670i q^{82} -8.34751i q^{83} -4.43592 q^{84} +(-7.58015 - 8.64078i) q^{85} +2.41076 q^{86} -6.09737i q^{87} +3.73882 q^{89} +(-0.439527 - 0.501026i) q^{90} -10.6556 q^{91} -11.5166i q^{92} -8.43171i q^{93} +2.73842 q^{94} +(-9.56766 + 8.39325i) q^{95} +3.36728 q^{96} +5.58998i q^{97} -0.480673i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9 + 6 * q^10 - 12 * q^14 + 48 * q^16 - 32 * q^19 - 2 * q^20 + 16 * q^21 - 24 * q^24 + 2 * q^25 + 32 * q^26 + 8 * q^30 - 12 * q^34 - 10 * q^35 + 24 * q^36 - 36 * q^39 - 34 * q^40 + 2 * q^45 + 56 * q^46 - 24 * q^49 - 46 * q^50 + 36 * q^51 - 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 + 40 * q^61 + 12 * q^64 - 10 * q^65 - 2 * q^70 + 64 * q^71 + 136 * q^74 + 20 * q^75 + 68 * q^76 - 64 * q^79 + 76 * q^80 + 24 * q^81 - 60 * q^84 - 72 * q^86 + 20 * q^89 - 6 * q^90 + 4 * q^94 - 64 * q^95 + 56 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	0.298064i		−	0.210763i	−0.994432	−	0.105382i	$-0.966394\pi$
$2$		−	0.298064i		−	0.210763i	0.994432	−	0.105382i	$-0.0336064\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.91116			0.955579
$5$	−1.68093	+	1.47460i	−0.751737	+	0.659463i
$5$	−1.68093	+	1.47460i	−0.751737	+	0.659463i
$6$	0.298064			0.121684
$7$			2.32107i			0.877281i	0.898663	+	0.438640i	$0.144540\pi$
$7$			2.32107i			0.877281i	−0.898663	+	0.438640i	$0.855460\pi$
$8$		−	1.16578i		−	0.412164i
$9$	−1.00000			−0.333333
$10$	0.439527	+	0.501026i	0.138991	+	0.158438i
$11$		0			0
$11$		0			0
$12$			1.91116i			0.551704i
$13$			4.59081i			1.27326i	0.771169	+	0.636631i	$0.219672\pi$
$13$			4.59081i			1.27326i	−0.771169	+	0.636631i	$0.780328\pi$
$14$	0.691827			0.184899
$15$	−1.47460	−	1.68093i	−0.380741	−	0.434015i
$16$	3.47484			0.868710
$17$			5.14046i			1.24675i	0.781925	+	0.623373i	$0.214238\pi$
$17$			5.14046i			1.24675i	−0.781925	+	0.623373i	$0.785762\pi$
$18$			0.298064i			0.0702544i
$19$	5.69187			1.30580			0.652902	−	0.757442i	$-0.273551\pi$
$19$	5.69187			1.30580			0.652902	+	0.757442i	$0.273551\pi$
$20$	−3.21253	+	2.81820i	−0.718344	+	0.630169i
$21$	−2.32107			−0.506498
$22$		0			0
$23$		−	6.02600i		−	1.25651i	−0.778008	−	0.628254i	$-0.783770\pi$
$23$		−	6.02600i		−	1.25651i	0.778008	−	0.628254i	$-0.216230\pi$
$24$	1.16578			0.237963
$25$	0.651081	−	4.95743i	0.130216	−	0.991486i
$26$	1.36836			0.268357
$27$		−	1.00000i		−	0.192450i
$28$			4.43592i			0.838311i
$29$	−6.09737			−1.13225			−0.566127	−	0.824318i	$-0.691559\pi$
$29$	−6.09737			−1.13225			−0.566127	+	0.824318i	$0.691559\pi$
$30$	−0.501026	+	0.439527i	−0.0914745	+	0.0802463i
$31$	−8.43171			−1.51438			−0.757190	−	0.653195i	$-0.773428\pi$
$31$	−8.43171			−1.51438			−0.757190	+	0.653195i	$0.773428\pi$
$32$		−	3.36728i		−	0.595256i
$33$		0			0
$34$	1.53219			0.262768
$35$	−3.42266	−	3.90156i	−0.578534	−	0.659484i
$36$	−1.91116			−0.318526
$37$		−	3.17279i		−	0.521604i	−0.965392	−	0.260802i	$-0.916013\pi$
$37$		−	3.17279i		−	0.521604i	0.965392	−	0.260802i	$-0.0839869\pi$
$38$		−	1.69654i		−	0.275215i
$39$	−4.59081			−0.735118
$40$	1.71906	+	1.95959i	0.271807	+	0.309839i
$41$	−0.468592			−0.0731817			−0.0365909	−	0.999330i	$-0.511650\pi$
$41$	−0.468592			−0.0731817			−0.0365909	+	0.999330i	$0.511650\pi$
$42$			0.691827i			0.106751i
$43$			8.08805i			1.23342i	0.787192	+	0.616708i	$0.211534\pi$
$43$			8.08805i			1.23342i	−0.787192	+	0.616708i	$0.788466\pi$
$44$		0			0
$45$	1.68093	−	1.47460i	0.250579	−	0.219821i
$46$	−1.79614			−0.264826
$47$			9.18736i			1.34011i	0.742309	+	0.670057i	$0.233730\pi$
$47$			9.18736i			1.34011i	−0.742309	+	0.670057i	$0.766270\pi$
$48$			3.47484i			0.501550i
$49$	1.61265			0.230378
$50$	−1.47763	−	0.194064i	−0.208969	−	0.0274448i
$51$	−5.14046			−0.719809
$52$			8.77376i			1.21670i
$53$			4.25892i			0.585007i	0.956264	+	0.292504i	$0.0944883\pi$
$53$			4.25892i			0.585007i	−0.956264	+	0.292504i	$0.905512\pi$
$54$	−0.298064			−0.0405614
$55$		0			0
$56$	2.70584			0.361584
$57$			5.69187i			0.753906i
$58$			1.81741i			0.238637i
$59$	−6.65971			−0.867021			−0.433510	−	0.901149i	$-0.642725\pi$
$59$	−6.65971			−0.867021			−0.433510	+	0.901149i	$0.642725\pi$
$60$	−2.81820	−	3.21253i	−0.363828	−	0.414736i
$61$	1.82041			0.233079			0.116540	−	0.993186i	$-0.462820\pi$
$61$	1.82041			0.233079			0.116540	+	0.993186i	$0.462820\pi$
$62$			2.51319i			0.319175i
$63$		−	2.32107i		−	0.292427i
$64$	5.94601			0.743252
$65$	−6.76963	−	7.71685i	−0.839669	−	0.957157i
$66$		0			0
$67$		−	8.86541i		−	1.08308i	−0.840674	−	0.541541i	$-0.817841\pi$
$67$		−	8.86541i		−	1.08308i	0.840674	−	0.541541i	$-0.182159\pi$
$68$			9.82424i			1.19136i
$69$	6.02600			0.725445
$70$	−1.16292	+	1.02017i	−0.138995	+	0.121934i
$71$	−2.44868			−0.290604			−0.145302	−	0.989387i	$-0.546415\pi$
$71$	−2.44868			−0.290604			−0.145302	+	0.989387i	$0.546415\pi$
$72$			1.16578i			0.137388i
$73$			9.08299i			1.06308i	0.847032	+	0.531542i	$0.178387\pi$
$73$			9.08299i			1.06308i	−0.847032	+	0.531542i	$0.821613\pi$
$74$	−0.945695			−0.109935
$75$	4.95743	+	0.651081i	0.572434	+	0.0751804i
$76$	10.8781			1.24780
$77$		0			0
$78$			1.36836i			0.154936i
$79$	−12.9262			−1.45431			−0.727154	−	0.686474i	$-0.759157\pi$
$79$	−12.9262			−1.45431			−0.727154	+	0.686474i	$0.759157\pi$
$80$	−5.84098	+	5.12401i	−0.653041	+	0.572882i
$81$	1.00000			0.111111
$82$			0.139670i			0.0154240i
$83$		−	8.34751i		−	0.916259i	−0.888886	−	0.458129i	$-0.848520\pi$
$83$		−	8.34751i		−	0.916259i	0.888886	−	0.458129i	$-0.151480\pi$
$84$	−4.43592			−0.483999
$85$	−7.58015	−	8.64078i	−0.822183	−	0.937225i
$86$	2.41076			0.259959
$87$		−	6.09737i		−	0.653707i
$88$		0			0
$89$	3.73882			0.396314			0.198157	−	0.980170i	$-0.436504\pi$
$89$	3.73882			0.396314			0.198157	+	0.980170i	$0.436504\pi$
$90$	−0.439527	−	0.501026i	−0.0463302	−	0.0528128i
$91$	−10.6556			−1.11701
$92$		−	11.5166i		−	1.20069i
$93$		−	8.43171i		−	0.874327i
$94$	2.73842			0.282447
$95$	−9.56766	+	8.39325i	−0.981621	+	0.861130i
$96$	3.36728			0.343671
$97$			5.58998i			0.567576i	0.958887	+	0.283788i	$0.0915912\pi$
$97$			5.58998i			0.567576i	−0.958887	+	0.283788i	$0.908409\pi$
$98$		−	0.480673i		−	0.0485553i
$99$		0			0
$100$	1.24432	−	9.47443i	0.124432	−	0.947443i
$101$	1.61415			0.160614			0.0803069	−	0.996770i	$-0.474410\pi$
$101$	1.61415			0.160614			0.0803069	+	0.996770i	$0.474410\pi$
$102$			1.53219i			0.151709i
$103$			8.51841i			0.839344i	0.907676	+	0.419672i	$0.137855\pi$
$103$			8.51841i			0.839344i	−0.907676	+	0.419672i	$0.862145\pi$
$104$	5.35186			0.524793
$105$	3.90156	−	3.42266i	0.380753	−	0.334017i
$106$	1.26943			0.123298
$107$		−	6.11405i		−	0.591067i	−0.955332	−	0.295534i	$-0.904503\pi$
$107$		−	6.11405i		−	0.591067i	0.955332	−	0.295534i	$-0.0954974\pi$
$108$		−	1.91116i		−	0.183901i
$109$	5.73259			0.549082			0.274541	−	0.961575i	$-0.411474\pi$
$109$	5.73259			0.549082			0.274541	+	0.961575i	$0.411474\pi$
$110$		0			0
$111$	3.17279			0.301148
$112$			8.06533i			0.762102i
$113$		−	8.24031i		−	0.775183i	−0.921831	−	0.387592i	$-0.873307\pi$
$113$		−	8.24031i		−	0.775183i	0.921831	−	0.387592i	$-0.126693\pi$
$114$	1.69654			0.158896
$115$	8.88597	+	10.1293i	0.828621	+	0.944563i
$116$	−11.6530			−1.08196
$117$		−	4.59081i		−	0.424420i
$118$			1.98502i			0.182736i
$119$	−11.9314			−1.09375
$120$	−1.95959	+	1.71906i	−0.178886	+	0.156928i
$121$		0			0
$122$		−	0.542598i		−	0.0491245i
$123$		−	0.468592i		−	0.0422515i
$124$	−16.1143			−1.44711
$125$	6.21582	+	9.29320i	0.555960	+	0.831209i
$126$	−0.691827			−0.0616328
$127$			12.0783i			1.07177i	0.844290	+	0.535887i	$0.180023\pi$
$127$			12.0783i			1.07177i	−0.844290	+	0.535887i	$0.819977\pi$
$128$		−	8.50685i		−	0.751906i
$129$	−8.08805			−0.712113
$130$	−2.30012	+	2.01778i	−0.201734	+	0.176971i
$131$	−3.28131			−0.286689			−0.143345	−	0.989673i	$-0.545786\pi$
$131$	−3.28131			−0.286689			−0.143345	+	0.989673i	$0.545786\pi$
$132$		0			0
$133$			13.2112i			1.14556i
$134$	−2.64246			−0.228274
$135$	1.47460	+	1.68093i	0.126914	+	0.144672i
$136$	5.99263			0.513864
$137$		−	4.01740i		−	0.343230i	−0.985164	−	0.171615i	$-0.945102\pi$
$137$		−	4.01740i		−	0.343230i	0.985164	−	0.171615i	$-0.0548984\pi$
$138$		−	1.79614i		−	0.152897i
$139$	−1.77948			−0.150934			−0.0754670	−	0.997148i	$-0.524045\pi$
$139$	−1.77948			−0.150934			−0.0754670	+	0.997148i	$0.524045\pi$
$140$	−6.54124	−	7.45650i	−0.552835	−	0.630189i
$141$	−9.18736			−0.773715
$142$			0.729862i			0.0612487i
$143$		0			0
$144$	−3.47484			−0.289570
$145$	10.2493	−	8.99122i	0.851157	−	0.746680i
$146$	2.70732			0.224059
$147$			1.61265i			0.133009i
$148$		−	6.06370i		−	0.498433i
$149$	−2.20781			−0.180871			−0.0904354	−	0.995902i	$-0.528826\pi$
$149$	−2.20781			−0.180871			−0.0904354	+	0.995902i	$0.528826\pi$
$150$	0.194064	−	1.47763i	0.0158453	−	0.120648i
$151$	12.8536			1.04601			0.523007	−	0.852329i	$-0.324810\pi$
$151$	12.8536			1.04601			0.523007	+	0.852329i	$0.324810\pi$
$152$		−	6.63544i		−	0.538205i
$153$		−	5.14046i		−	0.415582i
$154$		0			0
$155$	14.1731	−	12.4334i	1.13841	−	0.998677i
$156$	−8.77376			−0.702463
$157$			0.839648i			0.0670112i	0.999439	+	0.0335056i	$0.0106672\pi$
$157$			0.839648i			0.0670112i	−0.999439	+	0.0335056i	$0.989333\pi$
$158$			3.85283i			0.306515i
$159$	−4.25892			−0.337754
$160$	4.96540	+	5.66017i	0.392550	+	0.447476i
$161$	13.9868			1.10231
$162$		−	0.298064i		−	0.0234181i
$163$			11.0879i			0.868469i	0.900800	+	0.434234i	$0.142981\pi$
$163$			11.0879i			0.868469i	−0.900800	+	0.434234i	$0.857019\pi$
$164$	−0.895553			−0.0699309
$165$		0			0
$166$	−2.48810			−0.193114
$167$		−	4.46477i		−	0.345494i	−0.984966	−	0.172747i	$-0.944736\pi$
$167$		−	4.46477i		−	0.345494i	0.984966	−	0.172747i	$-0.0552644\pi$
$168$			2.70584i			0.208760i
$169$	−8.07553			−0.621195
$170$	−2.57551	+	2.25937i	−0.197533	+	0.173286i
$171$	−5.69187			−0.435268
$172$			15.4575i			1.17863i
$173$			18.0670i			1.37361i	0.726843	+	0.686803i	$0.240987\pi$
$173$			18.0670i			1.37361i	−0.726843	+	0.686803i	$0.759013\pi$
$174$	−1.81741			−0.137777
$175$	11.5065	+	1.51120i	0.869811	+	0.114236i
$176$		0			0
$177$		−	6.65971i		−	0.500575i
$178$		−	1.11441i		−	0.0835285i
$179$	11.9744			0.895010			0.447505	−	0.894281i	$-0.352313\pi$
$179$	11.9744			0.895010			0.447505	+	0.894281i	$0.352313\pi$
$180$	3.21253	−	2.81820i	0.239448	−	0.210056i
$181$	15.8185			1.17578			0.587890	−	0.808941i	$-0.299959\pi$
$181$	15.8185			1.17578			0.587890	+	0.808941i	$0.299959\pi$
$182$			3.17605i			0.235424i
$183$			1.82041i			0.134568i
$184$	−7.02497			−0.517888
$185$	4.67861	+	5.33325i	0.343978	+	0.392109i
$186$	−2.51319			−0.184276
$187$		0			0
$188$			17.5585i			1.28059i
$189$	2.32107			0.168833
$190$	2.50173	+	2.85178i	0.181494	+	0.206890i
$191$	9.00747			0.651757			0.325879	−	0.945412i	$-0.394340\pi$
$191$	9.00747			0.651757			0.325879	+	0.945412i	$0.394340\pi$
$192$			5.94601i			0.429117i
$193$		−	3.83930i		−	0.276359i	−0.990407	−	0.138179i	$-0.955875\pi$
$193$		−	3.83930i		−	0.276359i	0.990407	−	0.138179i	$-0.0441250\pi$
$194$	1.66617			0.119624
$195$	7.71685	−	6.76963i	0.552615	−	0.484783i
$196$	3.08203			0.220145
$197$			8.33739i			0.594015i	0.954875	+	0.297007i	$0.0959886\pi$
$197$			8.33739i			0.594015i	−0.954875	+	0.297007i	$0.904011\pi$
$198$		0			0
$199$	−2.22397			−0.157653			−0.0788266	−	0.996888i	$-0.525117\pi$
$199$	−2.22397			−0.157653			−0.0788266	+	0.996888i	$0.525117\pi$
$200$	−5.77925	−	0.759015i	−0.408655	−	0.0536705i
$201$	8.86541			0.625318
$202$		−	0.481120i		−	0.0338515i
$203$		−	14.1524i		−	0.993305i
$204$	−9.82424			−0.687834
$205$	0.787672	−	0.690988i	0.0550134	−	0.0482607i
$206$	2.53903			0.176903
$207$			6.02600i			0.418836i
$208$			15.9523i			1.10609i
$209$		0			0
$210$	−1.02017	−	1.16292i	−0.0703985	−	0.0802488i
$211$	−5.02265			−0.345774			−0.172887	−	0.984942i	$-0.555310\pi$
$211$	−5.02265			−0.345774			−0.172887	+	0.984942i	$0.555310\pi$
$212$			8.13946i			0.559020i
$213$		−	2.44868i		−	0.167780i
$214$	−1.82238			−0.124575
$215$	−11.9267	−	13.5955i	−0.813393	−	0.927204i
$216$	−1.16578			−0.0793210
$217$		−	19.5706i		−	1.32854i
$218$		−	1.70868i		−	0.115726i
$219$	−9.08299			−0.613772
$220$		0			0
$221$	−23.5989			−1.58743
$222$		−	0.945695i		−	0.0634709i
$223$		−	28.3725i		−	1.89996i	−0.312310	−	0.949980i	$-0.601103\pi$
$223$		−	28.3725i		−	1.89996i	0.312310	−	0.949980i	$-0.398897\pi$
$224$	7.81568			0.522207
$225$	−0.651081	+	4.95743i	−0.0434054	+	0.330495i
$226$	−2.45614			−0.163380
$227$		−	6.58235i		−	0.436886i	−0.975850	−	0.218443i	$-0.929902\pi$
$227$		−	6.58235i		−	0.436886i	0.975850	−	0.218443i	$-0.0700978\pi$
$228$			10.8781i			0.720417i
$229$	16.5282			1.09221			0.546107	−	0.837715i	$-0.316109\pi$
$229$	16.5282			1.09221			0.546107	+	0.837715i	$0.316109\pi$
$230$	3.01919	−	2.64859i	0.199079	−	0.174643i
$231$		0			0
$232$			7.10817i			0.466674i
$233$			23.3654i			1.53072i	0.643602	+	0.765360i	$0.277439\pi$
$233$			23.3654i			1.53072i	−0.643602	+	0.765360i	$0.722561\pi$
$234$	−1.36836			−0.0894522
$235$	−13.5477	−	15.4434i	−0.883756	−	1.00741i
$236$	−12.7278			−0.828507
$237$		−	12.9262i		−	0.839645i
$238$			3.55631i			0.230521i
$239$	17.7858			1.15047			0.575233	−	0.817990i	$-0.304911\pi$
$239$	17.7858			1.15047			0.575233	+	0.817990i	$0.304911\pi$
$240$	−5.12401	−	5.84098i	−0.330754	−	0.377033i
$241$	6.95713			0.448148			0.224074	−	0.974572i	$-0.428064\pi$
$241$	6.95713			0.448148			0.224074	+	0.974572i	$0.428064\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	3.47909			0.222726
$245$	−2.71076	+	2.37802i	−0.173184	+	0.151926i
$246$	−0.139670			−0.00890506
$247$			26.1303i			1.66263i
$248$			9.82948i			0.624173i
$249$	8.34751			0.529002
$250$	2.76997	−	1.85271i	0.175188	−	0.117176i
$251$	−0.636701			−0.0401882			−0.0200941	−	0.999798i	$-0.506397\pi$
$251$	−0.636701			−0.0401882			−0.0200941	+	0.999798i	$0.506397\pi$
$252$		−	4.43592i		−	0.279437i
$253$		0			0
$254$	3.60010			0.225891
$255$	8.64078	−	7.58015i	0.541107	−	0.474688i
$256$	9.35644			0.584777
$257$		−	0.482055i		−	0.0300698i	−0.999887	−	0.0150349i	$-0.995214\pi$
$257$		−	0.482055i		−	0.0300698i	0.999887	−	0.0150349i	$-0.00478594\pi$
$258$			2.41076i			0.150087i
$259$	7.36426			0.457593
$260$	−12.9378	−	14.7481i	−0.802370	−	0.914639i
$261$	6.09737			0.377418
$262$			0.978041i			0.0604236i
$263$			18.2072i			1.12270i	0.827578	+	0.561351i	$0.189718\pi$
$263$			18.2072i			1.12270i	−0.827578	+	0.561351i	$0.810282\pi$
$264$		0			0
$265$	−6.28022	−	7.15896i	−0.385791	−	0.439771i
$266$	3.93779			0.241441
$267$			3.73882i			0.228812i
$268$		−	16.9432i		−	1.03497i
$269$	−26.0546			−1.58858			−0.794289	−	0.607540i	$-0.792156\pi$
$269$	−26.0546			−1.58858			−0.794289	+	0.607540i	$0.792156\pi$
$270$	0.501026	−	0.439527i	0.0304915	−	0.0267488i
$271$	−0.294394			−0.0178832			−0.00894158	−	0.999960i	$-0.502846\pi$
$271$	−0.294394			−0.0178832			−0.00894158	+	0.999960i	$0.502846\pi$
$272$			17.8623i			1.08306i
$273$		−	10.6556i		−	0.644905i
$274$	−1.19744			−0.0723402
$275$		0			0
$276$	11.5166			0.693220
$277$		−	30.2893i		−	1.81991i	−0.414712	−	0.909953i	$-0.636118\pi$
$277$		−	30.2893i		−	1.81991i	0.414712	−	0.909953i	$-0.363882\pi$
$278$			0.530401i			0.0318113i
$279$	8.43171			0.504793
$280$	−4.54835	+	3.99005i	−0.271816	+	0.238451i
$281$	29.7185			1.77286			0.886428	−	0.462866i	$-0.153179\pi$
$281$	29.7185			1.77286			0.886428	+	0.462866i	$0.153179\pi$
$282$			2.73842i			0.163071i
$283$			1.58988i			0.0945084i	0.998883	+	0.0472542i	$0.0150471\pi$
$283$			1.58988i			0.0945084i	−0.998883	+	0.0472542i	$0.984953\pi$
$284$	−4.67980			−0.277695
$285$	−8.39325	−	9.56766i	−0.497173	−	0.566739i
$286$		0			0
$287$		−	1.08763i		−	0.0642009i
$288$			3.36728i			0.198419i
$289$	−9.42438			−0.554375
$290$	−2.67996	−	3.05495i	−0.157373	−	0.179393i
$291$	−5.58998			−0.327690
$292$			17.3590i			1.01586i
$293$		−	0.421054i		−	0.0245982i	−0.999924	−	0.0122991i	$-0.996085\pi$
$293$		−	0.421054i		−	0.0245982i	0.999924	−	0.0122991i	$-0.00391503\pi$
$294$	0.480673			0.0280334
$295$	11.1945	−	9.82044i	0.651771	−	0.571768i
$296$	−3.69876			−0.214986
$297$		0			0
$298$			0.658069i			0.0381209i
$299$	27.6642			1.59986
$300$	9.47443	+	1.24432i	0.547006	+	0.0718408i
$301$	−18.7729			−1.08205
$302$		−	3.83121i		−	0.220461i
$303$			1.61415i			0.0927304i
$304$	19.7783			1.13436
$305$	−3.05999	+	2.68438i	−0.175214	+	0.153707i
$306$	−1.53219			−0.0875894
$307$		−	9.29536i		−	0.530514i	−0.964178	−	0.265257i	$-0.914543\pi$
$307$		−	9.29536i		−	0.530514i	0.964178	−	0.265257i	$-0.0854569\pi$
$308$		0			0
$309$	−8.51841			−0.484595
$310$	−3.70596	−	4.22451i	−0.210484	−	0.239936i
$311$	12.0947			0.685825			0.342912	−	0.939367i	$-0.388587\pi$
$311$	12.0947			0.685825			0.342912	+	0.939367i	$0.388587\pi$
$312$			5.35186i			0.302989i
$313$		−	6.97604i		−	0.394309i	−0.980372	−	0.197155i	$-0.936830\pi$
$313$		−	6.97604i		−	0.394309i	0.980372	−	0.197155i	$-0.0631701\pi$
$314$	0.250269			0.0141235
$315$	3.42266	+	3.90156i	0.192845	+	0.219828i
$316$	−24.7040			−1.38971
$317$		−	7.23947i		−	0.406609i	−0.979116	−	0.203304i	$-0.934832\pi$
$317$		−	7.23947i		−	0.406609i	0.979116	−	0.203304i	$-0.0651681\pi$
$318$			1.26943i			0.0711861i
$319$		0			0
$320$	−9.99486	+	8.76802i	−0.558730	+	0.490147i
$321$	6.11405			0.341253
$322$		−	4.16895i		−	0.232327i
$323$			29.2588i			1.62801i
$324$	1.91116			0.106175
$325$	22.7586	+	2.98899i	1.26242	+	0.165799i
$326$	3.30490			0.183041
$327$			5.73259i			0.317013i
$328$			0.546273i			0.0301629i
$329$	−21.3245			−1.17566
$330$		0			0
$331$	27.6629			1.52049			0.760244	−	0.649637i	$-0.225079\pi$
$331$	27.6629			1.52049			0.760244	+	0.649637i	$0.225079\pi$
$332$		−	15.9534i		−	0.875557i
$333$			3.17279i			0.173868i
$334$	−1.33079			−0.0728175
$335$	13.0730	+	14.9022i	0.714253	+	0.814193i
$336$	−8.06533			−0.440000
$337$		−	22.0178i		−	1.19939i	−0.800229	−	0.599694i	$-0.795289\pi$
$337$		−	22.0178i		−	1.19939i	0.800229	−	0.599694i	$-0.204711\pi$
$338$			2.40703i			0.130925i
$339$	8.24031			0.447552
$340$	−14.4869	−	16.5139i	−0.785661	−	0.895592i
$341$		0			0
$342$			1.69654i			0.0917385i
$343$			19.9905i			1.07939i
$344$	9.42886			0.508370
$345$	−10.1293	+	8.88597i	−0.545344	+	0.478405i
$346$	5.38512			0.289506
$347$		−	26.7672i		−	1.43694i	−0.695559	−	0.718469i	$-0.744843\pi$
$347$		−	26.7672i		−	1.43694i	0.695559	−	0.718469i	$-0.255157\pi$
$348$		−	11.6530i		−	0.624669i
$349$	−21.6412			−1.15843			−0.579215	−	0.815175i	$-0.696641\pi$
$349$	−21.6412			−1.15843			−0.579215	+	0.815175i	$0.696641\pi$
$350$	0.450436	−	3.42968i	0.0240768	−	0.183324i
$351$	4.59081			0.245039
$352$		0			0
$353$			31.5144i			1.67734i	0.544636	+	0.838672i	$0.316668\pi$
$353$			31.5144i			1.67734i	−0.544636	+	0.838672i	$0.683332\pi$
$354$	−1.98502			−0.105503
$355$	4.11606	−	3.61083i	0.218458	−	0.191643i
$356$	7.14548			0.378710
$357$		−	11.9314i		−	0.631475i
$358$		−	3.56915i		−	0.188635i
$359$	−4.46095			−0.235440			−0.117720	−	0.993047i	$-0.537559\pi$
$359$	−4.46095			−0.235440			−0.117720	+	0.993047i	$0.537559\pi$
$360$	−1.71906	−	1.95959i	−0.0906024	−	0.103280i
$361$	13.3973			0.705124
$362$		−	4.71493i		−	0.247811i
$363$		0			0
$364$	−20.3645			−1.06739
$365$	−13.3938	−	15.2679i	−0.701065	−	0.799159i
$366$	0.542598			0.0283621
$367$			1.03300i			0.0539222i	0.999636	+	0.0269611i	$0.00858303\pi$
$367$			1.03300i			0.0539222i	−0.999636	+	0.0269611i	$0.991417\pi$
$368$		−	20.9394i		−	1.09154i
$369$	0.468592			0.0243939
$370$	1.58965	−	1.39453i	0.0826421	−	0.0724980i
$371$	−9.88523			−0.513215
$372$		−	16.1143i		−	0.835489i
$373$			32.6921i			1.69273i	0.532600	+	0.846367i	$0.321215\pi$
$373$			32.6921i			1.69273i	−0.532600	+	0.846367i	$0.678785\pi$
$374$		0			0
$375$	−9.29320	+	6.21582i	−0.479899	+	0.320984i
$376$	10.7104			0.552347
$377$		−	27.9919i		−	1.44166i
$378$		−	0.691827i		−	0.0355837i
$379$	4.28279			0.219992			0.109996	−	0.993932i	$-0.464916\pi$
$379$	4.28279			0.219992			0.109996	+	0.993932i	$0.464916\pi$
$380$	−18.2853	+	16.0408i	−0.938016	+	0.822877i
$381$	−12.0783			−0.618789
$382$		−	2.68480i		−	0.137366i
$383$		−	26.9383i		−	1.37648i	−0.725482	−	0.688241i	$-0.758383\pi$
$383$		−	26.9383i		−	1.37648i	0.725482	−	0.688241i	$-0.241617\pi$
$384$	8.50685			0.434113
$385$		0			0
$386$	−1.14436			−0.0582462
$387$		−	8.08805i		−	0.411139i
$388$			10.6833i			0.542364i
$389$	−36.7033			−1.86093			−0.930465	−	0.366382i	$-0.880597\pi$
$389$	−36.7033			−1.86093			−0.930465	+	0.366382i	$0.880597\pi$
$390$	−2.01778	−	2.30012i	−0.102174	−	0.116471i
$391$	30.9765			1.56655
$392$		−	1.87999i		−	0.0949537i
$393$		−	3.28131i		−	0.165520i
$394$	2.48508			0.125196
$395$	21.7281	−	19.0610i	1.09326	−	0.959063i
$396$		0			0
$397$			7.52289i			0.377563i	0.982019	+	0.188782i	$0.0604538\pi$
$397$			7.52289i			0.377563i	−0.982019	+	0.188782i	$0.939546\pi$
$398$			0.662887i			0.0332275i
$399$	−13.2112			−0.661387
$400$	2.26240	−	17.2263i	0.113120	−	0.861313i
$401$	15.3995			0.769013			0.384506	−	0.923122i	$-0.374372\pi$
$401$	15.3995			0.769013			0.384506	+	0.923122i	$0.374372\pi$
$402$		−	2.64246i		−	0.131794i
$403$		−	38.7084i		−	1.92820i
$404$	3.08489			0.153479
$405$	−1.68093	+	1.47460i	−0.0835263	+	0.0732737i
$406$	−4.21833			−0.209352
$407$		0			0
$408$			5.99263i			0.296679i
$409$	16.2884			0.805411			0.402706	−	0.915330i	$-0.368070\pi$
$409$	16.2884			0.805411			0.402706	+	0.915330i	$0.368070\pi$
$410$	−0.205959	−	0.234777i	−0.0101716	−	0.0115948i
$411$	4.01740			0.198164
$412$			16.2800i			0.802059i
$413$		−	15.4576i		−	0.760620i
$414$	1.79614			0.0882752
$415$	12.3093	+	14.0316i	0.604239	+	0.688785i
$416$	15.4585			0.757917
$417$		−	1.77948i		−	0.0871417i
$418$		0			0
$419$	11.3868			0.556281			0.278140	−	0.960540i	$-0.410282\pi$
$419$	11.3868			0.556281			0.278140	+	0.960540i	$0.410282\pi$
$420$	7.45650	−	6.54124i	0.363840	−	0.319180i
$421$	−11.0773			−0.539876			−0.269938	−	0.962878i	$-0.587003\pi$
$421$	−11.0773			−0.539876			−0.269938	+	0.962878i	$0.587003\pi$
$422$			1.49707i			0.0728764i
$423$		−	9.18736i		−	0.446705i
$424$	4.96494			0.241119
$425$	25.4835	+	3.34686i	1.23613	+	0.162347i
$426$	−0.729862			−0.0353620
$427$			4.22529i			0.204476i
$428$		−	11.6849i		−	0.564811i
$429$		0			0
$430$	−4.05233	+	3.55492i	−0.195421	+	0.171433i
$431$	30.4478			1.46662			0.733311	−	0.679894i	$-0.237974\pi$
$431$	30.4478			1.46662			0.733311	+	0.679894i	$0.237974\pi$
$432$		−	3.47484i		−	0.167183i
$433$			15.1047i			0.725885i	0.931812	+	0.362943i	$0.118228\pi$
$433$			15.1047i			0.725885i	−0.931812	+	0.362943i	$0.881772\pi$
$434$	−5.83328			−0.280006
$435$	8.99122	+	10.2493i	0.431096	+	0.491416i
$436$	10.9559			0.524691
$437$		−	34.2992i		−	1.64075i
$438$			2.70732i			0.129361i
$439$	23.6799			1.13018			0.565090	−	0.825030i	$-0.308842\pi$
$439$	23.6799			1.13018			0.565090	+	0.825030i	$0.308842\pi$
$440$		0			0
$441$	−1.61265			−0.0767928
$442$			7.03399i			0.334573i
$443$			30.7817i			1.46248i	0.682119	+	0.731242i	$0.261059\pi$
$443$			30.7817i			1.46248i	−0.682119	+	0.731242i	$0.738941\pi$
$444$	6.06370			0.287771
$445$	−6.28471	+	5.51329i	−0.297924	+	0.261355i
$446$	−8.45681			−0.400442
$447$		−	2.20781i		−	0.104426i
$448$			13.8011i			0.652040i
$449$	4.60851			0.217489			0.108744	−	0.994070i	$-0.465317\pi$
$449$	4.60851			0.217489			0.108744	+	0.994070i	$0.465317\pi$
$450$	1.47763	+	0.194064i	0.0696562	+	0.00914827i
$451$		0			0
$452$		−	15.7485i		−	0.740749i
$453$			12.8536i			0.603916i
$454$	−1.96196			−0.0920795
$455$	17.9113	−	15.7128i	0.839696	−	0.736626i
$456$	6.63544			0.310733
$457$		−	29.2281i		−	1.36723i	−0.729842	−	0.683616i	$-0.760406\pi$
$457$		−	29.2281i		−	1.36723i	0.729842	−	0.683616i	$-0.239594\pi$
$458$		−	4.92647i		−	0.230199i
$459$	5.14046			0.239936
$460$	16.9825	+	19.3587i	0.791813	+	0.902605i
$461$	−5.76367			−0.268441			−0.134220	−	0.990951i	$-0.542853\pi$
$461$	−5.76367			−0.268441			−0.134220	+	0.990951i	$0.542853\pi$
$462$		0			0
$463$			21.9028i			1.01791i	0.860794	+	0.508954i	$0.169968\pi$
$463$			21.9028i			1.01791i	−0.860794	+	0.508954i	$0.830032\pi$
$464$	−21.1874			−0.983600
$465$	12.4334	+	14.1731i	0.576587	+	0.657264i
$466$	6.96440			0.322620
$467$			14.6356i			0.677253i	0.940921	+	0.338627i	$0.109962\pi$
$467$			14.6356i			0.677253i	−0.940921	+	0.338627i	$0.890038\pi$
$468$		−	8.77376i		−	0.405567i
$469$	20.5772			0.950167
$470$	−4.60311	+	4.03809i	−0.212326	+	0.186263i
$471$	−0.839648			−0.0386889
$472$			7.76373i			0.357355i
$473$		0			0
$474$	−3.85283			−0.176966
$475$	3.70587	−	28.2170i	0.170037	−	1.29469i
$476$	−22.8027			−1.04516
$477$		−	4.25892i		−	0.195002i
$478$		−	5.30130i		−	0.242476i
$479$	28.8633			1.31880			0.659398	−	0.751794i	$-0.270811\pi$
$479$	28.8633			1.31880			0.659398	+	0.751794i	$0.270811\pi$
$480$	−5.66017	+	4.96540i	−0.258350	+	0.226639i
$481$	14.5657			0.664138
$482$		−	2.07367i		−	0.0944531i
$483$			13.9868i			0.636419i
$484$		0			0
$485$	−8.24301	−	9.39639i	−0.374296	−	0.426668i
$486$	0.298064			0.0135205
$487$		−	22.1587i		−	1.00411i	−0.864836	−	0.502054i	$-0.832578\pi$
$487$		−	22.1587i		−	1.00411i	0.864836	−	0.502054i	$-0.167422\pi$
$488$		−	2.12219i		−	0.0960669i
$489$	−11.0879			−0.501411
$490$	0.708803	+	0.807980i	0.0320204	+	0.0365008i
$491$	16.1229			0.727616			0.363808	−	0.931474i	$-0.381476\pi$
$491$	16.1229			0.727616			0.363808	+	0.931474i	$0.381476\pi$
$492$		−	0.895553i		−	0.0403746i
$493$		−	31.3433i		−	1.41163i
$494$	7.78850			0.350421
$495$		0			0
$496$	−29.2988			−1.31556
$497$		−	5.68354i		−	0.254942i
$498$		−	2.48810i		−	0.111494i
$499$	30.8626			1.38160			0.690799	−	0.723047i	$-0.257259\pi$
$499$	30.8626			1.38160			0.690799	+	0.723047i	$0.257259\pi$
$500$	11.8794	+	17.7608i	0.531264	+	0.794286i
$501$	4.46477			0.199471
$502$			0.189778i			0.00847020i
$503$			8.43173i			0.375952i	0.982174	+	0.187976i	$0.0601927\pi$
$503$			8.43173i			0.375952i	−0.982174	+	0.187976i	$0.939807\pi$
$504$	−2.70584			−0.120528
$505$	−2.71328	+	2.38023i	−0.120739	+	0.105919i
$506$		0			0
$507$		−	8.07553i		−	0.358647i
$508$			23.0835i			1.02416i
$509$	29.4916			1.30719			0.653596	−	0.756843i	$-0.273259\pi$
$509$	29.4916			1.30719			0.653596	+	0.756843i	$0.273259\pi$
$510$	−2.25937	−	2.57551i	−0.100047	−	0.114045i
$511$	−21.0822			−0.932623
$512$		−	19.8025i		−	0.875156i
$513$		−	5.69187i		−	0.251302i
$514$	−0.143683			−0.00633761
$515$	−12.5613	−	14.3189i	−0.553516	−	0.630966i
$516$	−15.4575			−0.680480
$517$		0			0
$518$		−	2.19502i		−	0.0964437i
$519$	−18.0670			−0.793052
$520$	−8.99612	+	7.89187i	−0.394506	+	0.346082i
$521$	−9.61116			−0.421072			−0.210536	−	0.977586i	$-0.567521\pi$
$521$	−9.61116			−0.421072			−0.210536	+	0.977586i	$0.567521\pi$
$522$		−	1.81741i		−	0.0795458i
$523$			4.14721i			0.181345i	0.995881	+	0.0906725i	$0.0289016\pi$
$523$			4.14721i			0.181345i	−0.995881	+	0.0906725i	$0.971098\pi$
$524$	−6.27110			−0.273954
$525$	−1.51120	+	11.5065i	−0.0659543	+	0.502186i
$526$	5.42690			0.236624
$527$		−	43.3429i		−	1.88805i
$528$		0			0
$529$	−13.3127			−0.578813
$530$	−2.13383	+	1.87191i	−0.0926876	+	0.0813105i
$531$	6.65971			0.289007
$532$			25.2487i			1.09467i
$533$		−	2.15122i		−	0.0931795i
$534$	1.11441			0.0482252
$535$	9.01580	+	10.2773i	0.389787	+	0.444327i
$536$	−10.3351			−0.446408
$537$			11.9744i			0.516734i
$538$			7.76595i			0.334814i
$539$		0			0
$540$	2.81820	+	3.21253i	0.121276	+	0.138245i
$541$	−31.2524			−1.34364			−0.671822	−	0.740713i	$-0.734488\pi$
$541$	−31.2524			−1.34364			−0.671822	+	0.740713i	$0.734488\pi$
$542$			0.0877483i			0.00376911i
$543$			15.8185i			0.678836i
$544$	17.3094			0.742133
$545$	−9.63610	+	8.45330i	−0.412765	+	0.362100i
$546$	−3.17605			−0.135922
$547$		−	9.02639i		−	0.385940i	−0.981205	−	0.192970i	$-0.938188\pi$
$547$		−	9.02639i		−	0.385940i	0.981205	−	0.192970i	$-0.0618121\pi$
$548$		−	7.67788i		−	0.327983i
$549$	−1.82041			−0.0776931
$550$		0			0
$551$	−34.7054			−1.47850
$552$		−	7.02497i		−	0.299003i
$553$		−	30.0025i		−	1.27584i
$554$	−9.02815			−0.383569
$555$	−5.33325	+	4.67861i	−0.226384	+	0.198596i
$556$	−3.40088			−0.144229
$557$		−	7.20535i		−	0.305301i	−0.988280	−	0.152650i	$-0.951219\pi$
$557$		−	7.20535i		−	0.305301i	0.988280	−	0.152650i	$-0.0487808\pi$
$558$		−	2.51319i		−	0.106392i
$559$	−37.1307			−1.57046
$560$	−11.8932	−	13.5573i	−0.502579	−	0.572900i
$561$		0			0
$562$		−	8.85802i		−	0.373653i
$563$		−	26.4111i		−	1.11310i	−0.830815	−	0.556548i	$-0.812125\pi$
$563$		−	26.4111i		−	1.11310i	0.830815	−	0.556548i	$-0.187875\pi$
$564$	−17.5585			−0.739346
$565$	12.1512	+	13.8514i	0.511205	+	0.582734i
$566$	0.473885			0.0199189
$567$			2.32107i			0.0974756i
$568$			2.85461i			0.119777i
$569$	43.3048			1.81543			0.907715	−	0.419587i	$-0.137825\pi$
$569$	43.3048			1.81543			0.907715	+	0.419587i	$0.137825\pi$
$570$	−2.85178	+	2.50173i	−0.119448	+	0.104786i
$571$	1.82495			0.0763718			0.0381859	−	0.999271i	$-0.487842\pi$
$571$	1.82495			0.0763718			0.0381859	+	0.999271i	$0.487842\pi$
$572$		0			0
$573$			9.00747i			0.376292i
$574$	−0.324184			−0.0135312
$575$	−29.8735	−	3.92342i	−1.24581	−	0.163618i
$576$	−5.94601			−0.247751
$577$		−	26.0123i		−	1.08291i	−0.840731	−	0.541454i	$-0.817874\pi$
$577$		−	26.0123i		−	1.08291i	0.840731	−	0.541454i	$-0.182126\pi$
$578$			2.80907i			0.116842i
$579$	3.83930			0.159556
$580$	19.5880	−	17.1836i	0.813347	−	0.713511i
$581$	19.3751			0.803816
$582$			1.66617i			0.0690651i
$583$		0			0
$584$	10.5887			0.438165
$585$	6.76963	+	7.71685i	0.279890	+	0.319052i
$586$	−0.125501			−0.00518440
$587$		−	4.00349i		−	0.165242i	−0.996581	−	0.0826209i	$-0.973671\pi$
$587$		−	4.00349i		−	0.165242i	0.996581	−	0.0826209i	$-0.0263291\pi$
$588$			3.08203i			0.127101i
$589$	−47.9921			−1.97748
$590$	−2.92712	−	3.33669i	−0.120508	−	0.137369i
$591$	−8.33739			−0.342954
$592$		−	11.0249i		−	0.453122i
$593$			32.2116i			1.32277i	0.750045	+	0.661386i	$0.230032\pi$
$593$			32.2116i			1.32277i	−0.750045	+	0.661386i	$0.769968\pi$
$594$		0			0
$595$	20.0558	−	17.5940i	0.822209	−	0.721285i
$596$	−4.21947			−0.172836
$597$		−	2.22397i		−	0.0910212i
$598$		−	8.24572i		−	0.337192i
$599$	13.5168			0.552281			0.276140	−	0.961117i	$-0.410945\pi$
$599$	13.5168			0.552281			0.276140	+	0.961117i	$0.410945\pi$
$600$	0.759015	−	5.77925i	0.0309867	−	0.235937i
$601$	−27.4926			−1.12145			−0.560724	−	0.828003i	$-0.689477\pi$
$601$	−27.4926			−1.12145			−0.560724	+	0.828003i	$0.689477\pi$
$602$			5.59553i			0.228057i
$603$			8.86541i			0.361027i
$604$	24.5653			0.999548
$605$		0			0
$606$	0.481120			0.0195442
$607$		−	37.6114i		−	1.52660i	−0.646044	−	0.763300i	$-0.723578\pi$
$607$		−	37.6114i		−	1.52660i	0.646044	−	0.763300i	$-0.276422\pi$
$608$		−	19.1661i		−	0.777288i
$609$	14.1524			0.573485
$610$	0.800118	+	0.912072i	0.0323958	+	0.0369287i
$611$	−42.1774			−1.70632
$612$		−	9.82424i		−	0.397121i
$613$			29.0831i			1.17466i	0.809349	+	0.587328i	$0.199820\pi$
$613$			29.0831i			1.17466i	−0.809349	+	0.587328i	$0.800180\pi$
$614$	−2.77062			−0.111813
$615$	0.690988	+	0.787672i	0.0278633	+	0.0317620i
$616$		0			0
$617$		−	9.61911i		−	0.387251i	−0.981076	−	0.193625i	$-0.937975\pi$
$617$		−	9.61911i		−	0.387251i	0.981076	−	0.193625i	$-0.0620246\pi$
$618$			2.53903i			0.102135i
$619$	23.4074			0.940824			0.470412	−	0.882447i	$-0.344105\pi$
$619$	23.4074			0.940824			0.470412	+	0.882447i	$0.344105\pi$
$620$	27.0871	−	23.7623i	1.08784	−	0.954315i
$621$	−6.02600			−0.241815
$622$		−	3.60498i		−	0.144547i
$623$			8.67806i			0.347679i
$624$	−15.9523			−0.638604
$625$	−24.1522	−	6.45538i	−0.966087	−	0.258215i
$626$	−2.07931			−0.0831059
$627$		0			0
$628$			1.60470i			0.0640345i
$629$	16.3096			0.650307
$630$	1.16292	−	1.02017i	0.0463317	−	0.0406446i
$631$	−22.6565			−0.901942			−0.450971	−	0.892539i	$-0.648922\pi$
$631$	−22.6565			−0.901942			−0.450971	+	0.892539i	$0.648922\pi$
$632$			15.0690i			0.599414i
$633$		−	5.02265i		−	0.199633i
$634$	−2.15783			−0.0856982
$635$	−17.8107	−	20.3028i	−0.706796	−	0.805692i
$636$	−8.13946			−0.322751
$637$			7.40336i			0.293332i
$638$		0			0
$639$	2.44868			0.0968681
$640$	12.5442	+	14.2995i	0.495855	+	0.565236i
$641$	22.9966			0.908313			0.454156	−	0.890922i	$-0.349941\pi$
$641$	22.9966			0.908313			0.454156	+	0.890922i	$0.349941\pi$
$642$		−	1.82238i		−	0.0719235i
$643$		−	11.6129i		−	0.457970i	−0.973430	−	0.228985i	$-0.926459\pi$
$643$		−	11.6129i		−	0.457970i	0.973430	−	0.228985i	$-0.0735406\pi$
$644$	26.7309			1.05334
$645$	13.5955	−	11.9267i	0.535322	−	0.469613i
$646$	8.72101			0.343124
$647$			36.1713i			1.42204i	0.703172	+	0.711020i	$0.251766\pi$
$647$			36.1713i			1.42204i	−0.703172	+	0.711020i	$0.748234\pi$
$648$		−	1.16578i		−	0.0457960i
$649$		0			0
$650$	0.890911	−	6.78353i	0.0349444	−	0.266072i
$651$	19.5706			0.767030
$652$			21.1907i			0.829890i
$653$		−	8.65293i		−	0.338615i	−0.985563	−	0.169308i	$-0.945847\pi$
$653$		−	8.65293i		−	0.338615i	0.985563	−	0.169308i	$-0.0541531\pi$
$654$	1.70868			0.0668146
$655$	5.51567	−	4.83863i	0.215515	−	0.189061i
$656$	−1.62828			−0.0635737
$657$		−	9.08299i		−	0.354361i
$658$			6.35607i			0.247785i
$659$	−17.4599			−0.680143			−0.340071	−	0.940400i	$-0.610451\pi$
$659$	−17.4599			−0.680143			−0.340071	+	0.940400i	$0.610451\pi$
$660$		0			0
$661$	16.2393			0.631636			0.315818	−	0.948820i	$-0.397721\pi$
$661$	16.2393			0.631636			0.315818	+	0.948820i	$0.397721\pi$
$662$		−	8.24531i		−	0.320463i
$663$		−	23.5989i		−	0.916505i
$664$	−9.73133			−0.377649
$665$	−19.4813	−	22.2072i	−0.755453	−	0.861157i
$666$	0.945695			0.0366449
$667$			36.7428i			1.42269i
$668$		−	8.53288i		−	0.330147i
$669$	28.3725			1.09694
$670$	4.44180	−	3.89659i	0.171602	−	0.150538i
$671$		0			0
$672$			7.81568i			0.301496i
$673$			26.4394i			1.01916i	0.860422	+	0.509582i	$0.170200\pi$
$673$			26.4394i			1.01916i	−0.860422	+	0.509582i	$0.829800\pi$
$674$	−6.56273			−0.252787
$675$	−4.95743	−	0.651081i	−0.190811	−	0.0250601i
$676$	−15.4336			−0.593600
$677$			31.3550i			1.20507i	0.798093	+	0.602534i	$0.205842\pi$
$677$			31.3550i			1.20507i	−0.798093	+	0.602534i	$0.794158\pi$
$678$		−	2.45614i		−	0.0943276i
$679$	−12.9747			−0.497924
$680$	−10.0732	+	8.83676i	−0.386290	+	0.338874i
$681$	6.58235			0.252236
$682$		0			0
$683$			3.85934i			0.147674i	0.997270	+	0.0738368i	$0.0235244\pi$
$683$			3.85934i			0.147674i	−0.997270	+	0.0738368i	$0.976476\pi$
$684$	−10.8781			−0.415933
$685$	5.92408	+	6.75298i	0.226347	+	0.258018i
$686$	5.95846			0.227495
$687$			16.5282i			0.630590i
$688$			28.1047i			1.07148i
$689$	−19.5519			−0.744867
$690$	2.64859	+	3.01919i	0.100830	+	0.114938i
$691$	−22.0718			−0.839651			−0.419825	−	0.907605i	$-0.637909\pi$
$691$	−22.0718			−0.839651			−0.419825	+	0.907605i	$0.637909\pi$
$692$			34.5288i			1.31259i
$693$		0			0
$694$	−7.97835			−0.302854
$695$	2.99120	−	2.62404i	0.113463	−	0.0995354i
$696$	−7.10817			−0.269435
$697$		−	2.40878i		−	0.0912390i
$698$			6.45048i			0.244154i
$699$	−23.3654			−0.883762
$700$	21.9908	+	2.88815i	0.831173	+	0.109162i
$701$	−34.4034			−1.29940			−0.649699	−	0.760192i	$-0.725105\pi$
$701$	−34.4034			−1.29940			−0.649699	+	0.760192i	$0.725105\pi$
$702$		−	1.36836i		−	0.0516453i
$703$		−	18.0591i		−	0.681112i
$704$		0			0
$705$	15.4434	−	13.5477i	0.581630	−	0.510237i
$706$	9.39333			0.353523
$707$			3.74655i			0.140903i
$708$		−	12.7278i		−	0.478338i
$709$	25.1938			0.946172			0.473086	−	0.881016i	$-0.343140\pi$
$709$	25.1938			0.946172			0.473086	+	0.881016i	$0.343140\pi$
$710$	−1.07626	−	1.22685i	−0.0403913	−	0.0460429i
$711$	12.9262			0.484769
$712$		−	4.35863i		−	0.163347i
$713$			50.8095i			1.90283i
$714$	−3.55631			−0.133092
$715$		0			0
$716$	22.8850			0.855253
$717$			17.7858i			0.664222i
$718$			1.32965i			0.0496221i
$719$	17.4770			0.651784			0.325892	−	0.945407i	$-0.394335\pi$
$719$	17.4770			0.651784			0.325892	+	0.945407i	$0.394335\pi$
$720$	5.84098	−	5.12401i	0.217680	−	0.190961i
$721$	−19.7718			−0.736340
$722$		−	3.99327i		−	0.148614i
$723$			6.95713i			0.258738i
$724$	30.2316			1.12355
$725$	−3.96989	+	30.2273i	−0.147438	+	1.12261i
$726$		0			0
$727$			3.60045i			0.133533i	0.997769	+	0.0667666i	$0.0212683\pi$
$727$			3.60045i			0.133533i	−0.997769	+	0.0667666i	$0.978732\pi$
$728$			12.4220i			0.460391i
$729$	−1.00000			−0.0370370
$730$	−4.55082	+	3.99222i	−0.168433	+	0.147759i
$731$	−41.5763			−1.53776
$732$			3.47909i			0.128591i
$733$			21.8840i			0.808305i	0.914692	+	0.404153i	$0.132434\pi$
$733$			21.8840i			0.808305i	−0.914692	+	0.404153i	$0.867566\pi$
$734$	0.307901			0.0113648
$735$	−2.37802	−	2.71076i	−0.0877146	−	0.0999878i
$736$	−20.2912			−0.747944
$737$		0			0
$738$		−	0.139670i		−	0.00514134i
$739$	−5.74815			−0.211449			−0.105724	−	0.994395i	$-0.533716\pi$
$739$	−5.74815			−0.211449			−0.105724	+	0.994395i	$0.533716\pi$
$740$	8.94157	+	10.1927i	0.328698	+	0.374691i
$741$	−26.1303			−0.959920
$742$			2.94643i			0.108167i
$743$			18.0014i			0.660406i	0.943910	+	0.330203i	$0.107117\pi$
$743$			18.0014i			0.660406i	−0.943910	+	0.330203i	$0.892883\pi$
$744$	−9.82948			−0.360366
$745$	3.71118	−	3.25565i	0.135967	−	0.119278i
$746$	9.74435			0.356766
$747$			8.34751i			0.305420i
$748$		0			0
$749$	14.1911			0.518532
$750$	1.85271	+	2.76997i	0.0676516	+	0.101145i
$751$	−19.0167			−0.693928			−0.346964	−	0.937878i	$-0.612787\pi$
$751$	−19.0167			−0.693928			−0.346964	+	0.937878i	$0.612787\pi$
$752$			31.9246i			1.16417i
$753$		−	0.636701i		−	0.0232027i
$754$	−8.34338			−0.303848
$755$	−21.6061	+	18.9540i	−0.786326	+	0.689807i
$756$	4.43592			0.161333
$757$			2.39560i			0.0870694i	0.999052	+	0.0435347i	$0.0138619\pi$
$757$			2.39560i			0.0870694i	−0.999052	+	0.0435347i	$0.986138\pi$
$758$		−	1.27655i		−	0.0463663i
$759$		0			0
$760$	9.78466	+	11.1537i	0.354927	+	0.404589i
$761$	−45.4089			−1.64607			−0.823035	−	0.567991i	$-0.807721\pi$
$761$	−45.4089			−1.64607			−0.823035	+	0.567991i	$0.807721\pi$
$762$			3.60010i			0.130418i
$763$			13.3057i			0.481699i
$764$	17.2147			0.622806
$765$	7.58015	+	8.64078i	0.274061	+	0.312408i
$766$	−8.02934			−0.290112
$767$		−	30.5735i		−	1.10394i
$768$			9.35644i			0.337621i
$769$	−49.1931			−1.77395			−0.886975	−	0.461818i	$-0.847197\pi$
$769$	−49.1931			−1.77395			−0.886975	+	0.461818i	$0.847197\pi$
$770$		0			0
$771$	0.482055			0.0173608
$772$		−	7.33750i		−	0.264082i
$773$		−	21.2288i		−	0.763549i	−0.924256	−	0.381774i	$-0.875313\pi$
$773$		−	21.2288i		−	0.763549i	0.924256	−	0.381774i	$-0.124687\pi$
$774$	−2.41076			−0.0866529
$775$	−5.48973	+	41.7996i	−0.197197	+	1.50149i
$776$	6.51666			0.233935
$777$			7.36426i			0.264191i
$778$			10.9399i			0.392216i
$779$	−2.66716			−0.0955610
$780$	14.7481	−	12.9378i	0.528067	−	0.463249i
$781$		0			0
$782$		−	9.23297i		−	0.330170i
$783$			6.09737i			0.217902i
$784$	5.60370			0.200132
$785$	−1.23815	−	1.41139i	−0.0441914	−	0.0503748i
$786$	−0.978041			−0.0348856
$787$		−	8.25347i		−	0.294204i	−0.989121	−	0.147102i	$-0.953005\pi$
$787$		−	8.25347i		−	0.294204i	0.989121	−	0.147102i	$-0.0469946\pi$
$788$			15.9341i			0.567628i
$789$	−18.2072			−0.648192
$790$	−5.68140	−	6.47636i	−0.202135	−	0.230418i
$791$	19.1263			0.680053
$792$		0			0
$793$			8.35714i			0.296771i
$794$	2.24231			0.0795764
$795$	7.15896	−	6.28022i	0.253902	−	0.222736i
$796$	−4.25036			−0.150650
$797$			6.29828i			0.223096i	0.993759	+	0.111548i	$0.0355809\pi$
$797$			6.29828i			0.223096i	−0.993759	+	0.111548i	$0.964419\pi$
$798$			3.93779i			0.139396i
$799$	−47.2273			−1.67078
$800$	−16.6930	−	2.19237i	−0.590188	−	0.0775121i
$801$	−3.73882			−0.132105
$802$		−	4.59003i		−	0.162080i
$803$		0			0
$804$	16.9432			0.597540
$805$	−23.5108	+	20.6249i	−0.828647	+	0.726933i
$806$	−11.5376			−0.406394
$807$		−	26.0546i		−	0.917166i
$808$		−	1.88174i		−	0.0661992i
$809$	54.5843			1.91908			0.959540	−	0.281571i	$-0.0908556\pi$
$809$	54.5843			1.91908			0.959540	+	0.281571i	$0.0908556\pi$
$810$	0.439527	+	0.501026i	0.0154434	+	0.0176043i
$811$	11.0167			0.386850			0.193425	−	0.981115i	$-0.438040\pi$
$811$	11.0167			0.386850			0.193425	+	0.981115i	$0.438040\pi$
$812$		−	27.0475i		−	0.949181i
$813$		−	0.294394i		−	0.0103248i
$814$		0			0
$815$	−16.3502	−	18.6380i	−0.572723	−	0.652860i
$816$	−17.8623			−0.625305
$817$			46.0361i			1.61060i
$818$		−	4.85500i		−	0.169751i
$819$	10.6556			0.372336
$820$	1.50537	−	1.32059i	0.0525696	−	0.0461169i
$821$	−41.7127			−1.45578			−0.727892	−	0.685692i	$-0.759500\pi$
$821$	−41.7127			−1.45578			−0.727892	+	0.685692i	$0.759500\pi$
$822$		−	1.19744i		−	0.0417656i
$823$		−	3.00669i		−	0.104806i	−0.998626	−	0.0524032i	$-0.983312\pi$
$823$		−	3.00669i		−	0.104806i	0.998626	−	0.0524032i	$-0.0166881\pi$
$824$	9.93056			0.345947
$825$		0			0
$826$	−4.60737			−0.160311
$827$			44.8126i			1.55829i	0.626846	+	0.779143i	$0.284345\pi$
$827$			44.8126i			1.55829i	−0.626846	+	0.779143i	$0.715655\pi$
$828$			11.5166i			0.400231i
$829$	38.6918			1.34382			0.671911	−	0.740631i	$-0.265474\pi$
$829$	38.6918			1.34382			0.671911	+	0.740631i	$0.265474\pi$
$830$	4.18233	−	3.66896i	0.145171	−	0.127351i
$831$	30.2893			1.05072
$832$			27.2970i			0.946354i
$833$			8.28977i			0.287223i
$834$	−0.530401			−0.0183663
$835$	6.58378	+	7.50499i	0.227841	+	0.259721i
$836$		0			0
$837$			8.43171i			0.291442i
$838$		−	3.39399i		−	0.117244i
$839$	21.2861			0.734879			0.367440	−	0.930047i	$-0.380234\pi$
$839$	21.2861			0.734879			0.367440	+	0.930047i	$0.380234\pi$
$840$	−3.99005	−	4.54835i	−0.137670	−	0.156933i
$841$	8.17796			0.281999
$842$			3.30176i			0.113786i
$843$			29.7185i			1.02356i
$844$	−9.59908			−0.330414
$845$	13.5744	−	11.9082i	0.466975	−	0.409655i
$846$	−2.73842			−0.0941490
$847$		0			0
$848$			14.7990i			0.508201i
$849$	−1.58988			−0.0545644
$850$	0.997580	−	7.59572i	0.0342167	−	0.260531i
$851$	−19.1192			−0.655399
$852$		−	4.67980i		−	0.160327i
$853$		−	23.9145i		−	0.818815i	−0.912352	−	0.409408i	$-0.865735\pi$
$853$		−	23.9145i		−	0.818815i	0.912352	−	0.409408i	$-0.134265\pi$
$854$	1.25941			0.0430960
$855$	9.56766	−	8.39325i	0.327207	−	0.287043i
$856$	−7.12761			−0.243617
$857$		−	23.7057i		−	0.809773i	−0.914367	−	0.404886i	$-0.867311\pi$
$857$		−	23.7057i		−	0.809773i	0.914367	−	0.404886i	$-0.132689\pi$
$858$		0			0
$859$	29.2131			0.996739			0.498369	−	0.866965i	$-0.333932\pi$
$859$	29.2131			0.996739			0.498369	+	0.866965i	$0.333932\pi$
$860$	−22.7938	−	25.9831i	−0.777261	−	0.886017i
$861$	1.08763			0.0370664
$862$		−	9.07541i		−	0.309110i
$863$		−	37.2828i		−	1.26912i	−0.772874	−	0.634560i	$-0.781181\pi$
$863$		−	37.2828i		−	1.26912i	0.772874	−	0.634560i	$-0.218819\pi$
$864$	−3.36728			−0.114557
$865$	−26.6417	−	30.3694i	−0.905843	−	1.03259i
$866$	4.50217			0.152990
$867$		−	9.42438i		−	0.320069i
$868$		−	37.4024i		−	1.26952i
$869$		0			0
$870$	3.05495	−	2.67996i	0.103572	−	0.0908592i
$871$	40.6994			1.37905
$872$		−	6.68291i		−	0.226312i
$873$		−	5.58998i		−	0.189192i
$874$	−10.2234			−0.345810
$875$	−21.5701	+	14.4273i	−0.729204	+	0.487733i
$876$	−17.3590			−0.586507
$877$			26.7080i			0.901865i	0.892558	+	0.450932i	$0.148908\pi$
$877$			26.7080i			0.901865i	−0.892558	+	0.450932i	$0.851092\pi$
$878$		−	7.05813i		−	0.238200i
$879$	0.421054			0.0142018
$880$		0			0
$881$	51.3146			1.72883			0.864417	−	0.502775i	$-0.167688\pi$
$881$	51.3146			1.72883			0.864417	+	0.502775i	$0.167688\pi$
$882$			0.480673i			0.0161851i
$883$			54.9200i			1.84820i	0.382145	+	0.924102i	$0.375185\pi$
$883$			54.9200i			1.84820i	−0.382145	+	0.924102i	$0.624815\pi$
$884$	−45.1012			−1.51692
$885$	9.82044	+	11.1945i	0.330111	+	0.376300i
$886$	9.17493			0.308238
$887$			5.07251i			0.170318i	0.996367	+	0.0851592i	$0.0271399\pi$
$887$			5.07251i			0.170318i	−0.996367	+	0.0851592i	$0.972860\pi$
$888$		−	3.69876i		−	0.124122i
$889$	−28.0345			−0.940247
$890$	1.64331	+	1.87325i	0.0550840	+	0.0627914i
$891$		0			0
$892$		−	54.2242i		−	1.81556i
$893$			52.2932i			1.74993i
$894$	−0.658069			−0.0220091
$895$	−20.1282	+	17.6575i	−0.672812	+	0.590226i
$896$	19.7450			0.659633
$897$			27.6642i			0.923682i
$898$		−	1.37363i		−	0.0458387i
$899$	51.4113			1.71466
$900$	−1.24432	+	9.47443i	−0.0414773	+	0.315814i
$901$	−21.8928			−0.729355
$902$		0			0
$903$		−	18.7729i		−	0.624723i
$904$	−9.60636			−0.319503
$905$	−26.5898	+	23.3260i	−0.883876	+	0.775383i
$906$	3.83121			0.127283
$907$		−	23.8325i		−	0.791346i	−0.918392	−	0.395673i	$-0.870511\pi$
$907$		−	23.8325i		−	0.791346i	0.918392	−	0.395673i	$-0.129489\pi$
$908$		−	12.5799i		−	0.417479i
$909$	−1.61415			−0.0535379
$910$	−4.68341	−	5.33872i	−0.155254	−	0.176977i
$911$	15.9409			0.528147			0.264074	−	0.964503i	$-0.414934\pi$
$911$	15.9409			0.528147			0.264074	+	0.964503i	$0.414934\pi$
$912$			19.7783i			0.654926i
$913$		0			0
$914$	−8.71185			−0.288162
$915$	−2.68438	−	3.05999i	−0.0887429	−	0.101160i
$916$	31.5880			1.04370
$917$		−	7.61614i		−	0.251507i
$918$		−	1.53219i		−	0.0505698i
$919$	−34.9656			−1.15341			−0.576705	−	0.816952i	$-0.695662\pi$
$919$	−34.9656			−1.15341			−0.576705	+	0.816952i	$0.695662\pi$
$920$	11.8085	−	10.3591i	0.389315	−	0.341528i
$921$	9.29536			0.306293
$922$			1.71794i			0.0565775i
$923$		−	11.2414i		−	0.370015i
$924$		0			0
$925$	−15.7289	−	2.06574i	−0.517162	−	0.0679213i
$926$	6.52843			0.214538
$927$		−	8.51841i		−	0.279781i
$928$			20.5315i			0.673981i
$929$	34.3129			1.12577			0.562885	−	0.826535i	$-0.309692\pi$
$929$	34.3129			1.12577			0.562885	+	0.826535i	$0.309692\pi$
$930$	4.22451	−	3.70596i	0.138527	−	0.121523i
$931$	9.17898			0.300829
$932$			44.6550i			1.46272i
$933$			12.0947i			0.395961i
$934$	4.36234			0.142740
$935$		0			0
$936$	−5.35186			−0.174931
$937$			28.9980i			0.947322i	0.880707	+	0.473661i	$0.157068\pi$
$937$			28.9980i			0.947322i	−0.880707	+	0.473661i	$0.842932\pi$
$938$		−	6.13333i		−	0.200260i
$939$	6.97604			0.227655
$940$	−25.8918	−	29.5147i	−0.844499	−	0.962663i
$941$	−16.7926			−0.547424			−0.273712	−	0.961812i	$-0.588251\pi$
$941$	−16.7926			−0.547424			−0.273712	+	0.961812i	$0.588251\pi$
$942$			0.250269i			0.00815421i
$943$			2.82373i			0.0919534i
$944$	−23.1414			−0.753189
$945$	−3.90156	+	3.42266i	−0.126918	+	0.111339i
$946$		0			0
$947$			17.4385i			0.566677i	0.959020	+	0.283338i	$0.0914419\pi$
$947$			17.4385i			0.566677i	−0.959020	+	0.283338i	$0.908558\pi$
$948$		−	24.7040i		−	0.802347i
$949$	−41.6983			−1.35358
$950$	−8.41048	−	1.10459i	−0.272872	−	0.0358375i
$951$	7.23947			0.234756
$952$			13.9093i			0.450803i
$953$			1.47790i			0.0478739i	0.999713	+	0.0239369i	$0.00762009\pi$
$953$			1.47790i			0.0478739i	−0.999713	+	0.0239369i	$0.992380\pi$
$954$	−1.26943			−0.0410993
$955$	−15.1410	+	13.2825i	−0.489950	+	0.429810i
$956$	33.9914			1.09936
$957$		0			0
$958$		−	8.60310i		−	0.277954i
$959$	9.32465			0.301109
$960$	−8.76802	−	9.99486i	−0.282987	−	0.322583i
$961$	40.0937			1.29334
$962$		−	4.34151i		−	0.139976i
$963$			6.11405i			0.197022i
$964$	13.2962			0.428241
$965$	5.66144	+	6.45360i	0.182248	+	0.207749i
$966$	4.16895			0.134134
$967$		−	26.6515i		−	0.857054i	−0.903529	−	0.428527i	$-0.859033\pi$
$967$		−	26.6515i		−	0.857054i	0.903529	−	0.428527i	$-0.140967\pi$
$968$		0			0
$969$	−29.2588			−0.939929
$970$	−2.80073	+	2.45695i	−0.0899259	+	0.0788878i
$971$	−38.7025			−1.24202			−0.621011	−	0.783802i	$-0.713278\pi$
$971$	−38.7025			−1.24202			−0.621011	+	0.783802i	$0.713278\pi$
$972$			1.91116i			0.0613004i
$973$		−	4.13030i		−	0.132411i
$974$	−6.60473			−0.211629
$975$	−2.98899	+	22.7586i	−0.0957243	+	0.728859i
$976$	6.32562			0.202478
$977$			49.7415i			1.59137i	0.605709	+	0.795686i	$0.292890\pi$
$977$			49.7415i			1.59137i	−0.605709	+	0.795686i	$0.707110\pi$
$978$			3.30490i			0.105679i
$979$		0			0
$980$	−5.18068	+	4.54477i	−0.165491	+	0.145177i
$981$	−5.73259			−0.183027
$982$		−	4.80566i		−	0.153355i
$983$		−	24.5431i		−	0.782802i	−0.920220	−	0.391401i	$-0.871991\pi$
$983$		−	24.5431i		−	0.782802i	0.920220	−	0.391401i	$-0.128009\pi$
$984$	−0.546273			−0.0174145
$985$	−12.2944	−	14.0146i	−0.391731	−	0.446543i
$986$	−9.34233			−0.297520
$987$		−	21.3245i		−	0.678766i
$988$			49.9391i			1.58877i
$989$	48.7386			1.54980
$990$		0			0
$991$	32.4673			1.03136			0.515679	−	0.856782i	$-0.327540\pi$
$991$	32.4673			1.03136			0.515679	+	0.856782i	$0.327540\pi$
$992$			28.3919i			0.901444i
$993$			27.6629i			0.877855i
$994$	−1.69406			−0.0537323
$995$	3.73835	−	3.27948i	0.118514	−	0.103967i
$996$	15.9534			0.505503
$997$		−	39.6946i		−	1.25714i	−0.777752	−	0.628571i	$-0.783640\pi$
$997$		−	39.6946i		−	1.25714i	0.777752	−	0.628571i	$-0.216360\pi$
$998$		−	9.19902i		−	0.291190i
$999$	−3.17279			−0.100383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.k.364.11		24
5.2	odd	4		9075.2.a.ea.1.6		12
5.3	odd	4		9075.2.a.dx.1.7		12
5.4	even	2	inner	1815.2.c.k.364.14		24
11.7	odd	10		165.2.s.a.49.6	✓	48
11.8	odd	10		165.2.s.a.64.7	yes	48
11.10	odd	2		1815.2.c.j.364.14		24
33.8	even	10		495.2.ba.c.64.6		48
33.29	even	10		495.2.ba.c.379.7		48
55.7	even	20		825.2.n.p.676.4		24
55.8	even	20		825.2.n.o.526.3		24
55.18	even	20		825.2.n.o.676.3		24
55.19	odd	10		165.2.s.a.64.6	yes	48
55.29	odd	10		165.2.s.a.49.7	yes	48
55.32	even	4		9075.2.a.dy.1.7		12
55.43	even	4		9075.2.a.dz.1.6		12
55.52	even	20		825.2.n.p.526.4		24
55.54	odd	2		1815.2.c.j.364.11		24
165.29	even	10		495.2.ba.c.379.6		48
165.74	even	10		495.2.ba.c.64.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.6	✓	48	11.7	odd	10
165.2.s.a.49.7	yes	48	55.29	odd	10
165.2.s.a.64.6	yes	48	55.19	odd	10
165.2.s.a.64.7	yes	48	11.8	odd	10
495.2.ba.c.64.6		48	33.8	even	10
495.2.ba.c.64.7		48	165.74	even	10
495.2.ba.c.379.6		48	165.29	even	10
495.2.ba.c.379.7		48	33.29	even	10
825.2.n.o.526.3		24	55.8	even	20
825.2.n.o.676.3		24	55.18	even	20
825.2.n.p.526.4		24	55.52	even	20
825.2.n.p.676.4		24	55.7	even	20
1815.2.c.j.364.11		24	55.54	odd	2
1815.2.c.j.364.14		24	11.10	odd	2
1815.2.c.k.364.11		24	1.1	even	1	trivial
1815.2.c.k.364.14		24	5.4	even	2	inner
9075.2.a.dx.1.7		12	5.3	odd	4
9075.2.a.dy.1.7		12	55.32	even	4
9075.2.a.dz.1.6		12	55.43	even	4
9075.2.a.ea.1.6		12	5.2	odd	4

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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.298064i q^{2} +1.00000i q^{3} +1.91116 q^{4} +(-1.68093 + 1.47460i) q^{5} +0.298064 q^{6} +2.32107i q^{7} -1.16578i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.298064i q^{2} +1.00000i q^{3} +1.91116 q^{4} +(-1.68093 + 1.47460i) q^{5} +0.298064 q^{6} +2.32107i q^{7} -1.16578i q^{8} -1.00000 q^{9} +(0.439527 + 0.501026i) q^{10} +1.91116i q^{12} +4.59081i q^{13} +0.691827 q^{14} +(-1.47460 - 1.68093i) q^{15} +3.47484 q^{16} +5.14046i q^{17} +0.298064i q^{18} +5.69187 q^{19} +(-3.21253 + 2.81820i) q^{20} -2.32107 q^{21} -6.02600i q^{23} +1.16578 q^{24} +(0.651081 - 4.95743i) q^{25} +1.36836 q^{26} -1.00000i q^{27} +4.43592i q^{28} -6.09737 q^{29} +(-0.501026 + 0.439527i) q^{30} -8.43171 q^{31} -3.36728i q^{32} +1.53219 q^{34} +(-3.42266 - 3.90156i) q^{35} -1.91116 q^{36} -3.17279i q^{37} -1.69654i q^{38} -4.59081 q^{39} +(1.71906 + 1.95959i) q^{40} -0.468592 q^{41} +0.691827i q^{42} +8.08805i q^{43} +(1.68093 - 1.47460i) q^{45} -1.79614 q^{46} +9.18736i q^{47} +3.47484i q^{48} +1.61265 q^{49} +(-1.47763 - 0.194064i) q^{50} -5.14046 q^{51} +8.77376i q^{52} +4.25892i q^{53} -0.298064 q^{54} +2.70584 q^{56} +5.69187i q^{57} +1.81741i q^{58} -6.65971 q^{59} +(-2.81820 - 3.21253i) q^{60} +1.82041 q^{61} +2.51319i q^{62} -2.32107i q^{63} +5.94601 q^{64} +(-6.76963 - 7.71685i) q^{65} -8.86541i q^{67} +9.82424i q^{68} +6.02600 q^{69} +(-1.16292 + 1.02017i) q^{70} -2.44868 q^{71} +1.16578i q^{72} +9.08299i q^{73} -0.945695 q^{74} +(4.95743 + 0.651081i) q^{75} +10.8781 q^{76} +1.36836i q^{78} -12.9262 q^{79} +(-5.84098 + 5.12401i) q^{80} +1.00000 q^{81} +0.139670i q^{82} -8.34751i q^{83} -4.43592 q^{84} +(-7.58015 - 8.64078i) q^{85} +2.41076 q^{86} -6.09737i q^{87} +3.73882 q^{89} +(-0.439527 - 0.501026i) q^{90} -10.6556 q^{91} -11.5166i q^{92} -8.43171i q^{93} +2.73842 q^{94} +(-9.56766 + 8.39325i) q^{95} +3.36728 q^{96} +5.58998i q^{97} -0.480673i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9 + 6 * q^10 - 12 * q^14 + 48 * q^16 - 32 * q^19 - 2 * q^20 + 16 * q^21 - 24 * q^24 + 2 * q^25 + 32 * q^26 + 8 * q^30 - 12 * q^34 - 10 * q^35 + 24 * q^36 - 36 * q^39 - 34 * q^40 + 2 * q^45 + 56 * q^46 - 24 * q^49 - 46 * q^50 + 36 * q^51 - 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 + 40 * q^61 + 12 * q^64 - 10 * q^65 - 2 * q^70 + 64 * q^71 + 136 * q^74 + 20 * q^75 + 68 * q^76 - 64 * q^79 + 76 * q^80 + 24 * q^81 - 60 * q^84 - 72 * q^86 + 20 * q^89 - 6 * q^90 + 4 * q^94 - 64 * q^95 + 56 * q^96

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