LMFDB - Embedded newform 1815.2.c.k.364.7

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			364.7
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.k.364.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27093i q^{2} -1.00000i q^{3} +0.384732 q^{4} +(1.01340 - 1.99324i) q^{5} -1.27093 q^{6} -0.483291i q^{7} -3.03083i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.27093i q^{2} -1.00000i q^{3} +0.384732 q^{4} +(1.01340 - 1.99324i) q^{5} -1.27093 q^{6} -0.483291i q^{7} -3.03083i q^{8} -1.00000 q^{9} +(-2.53328 - 1.28796i) q^{10} -0.384732i q^{12} +3.14412i q^{13} -0.614230 q^{14} +(-1.99324 - 1.01340i) q^{15} -3.08252 q^{16} +2.51013i q^{17} +1.27093i q^{18} -3.72015 q^{19} +(0.389888 - 0.766865i) q^{20} -0.483291 q^{21} -8.53218i q^{23} -3.03083 q^{24} +(-2.94604 - 4.03991i) q^{25} +3.99597 q^{26} +1.00000i q^{27} -0.185938i q^{28} -9.98293 q^{29} +(-1.28796 + 2.53328i) q^{30} -5.78984 q^{31} -2.14399i q^{32} +3.19020 q^{34} +(-0.963317 - 0.489767i) q^{35} -0.384732 q^{36} +3.20765i q^{37} +4.72805i q^{38} +3.14412 q^{39} +(-6.04119 - 3.07145i) q^{40} +7.86565 q^{41} +0.614230i q^{42} -5.97016i q^{43} +(-1.01340 + 1.99324i) q^{45} -10.8438 q^{46} -6.13097i q^{47} +3.08252i q^{48} +6.76643 q^{49} +(-5.13445 + 3.74422i) q^{50} +2.51013 q^{51} +1.20965i q^{52} -1.58220i q^{53} +1.27093 q^{54} -1.46477 q^{56} +3.72015i q^{57} +12.6876i q^{58} +0.377932 q^{59} +(-0.766865 - 0.389888i) q^{60} -3.00852 q^{61} +7.35850i q^{62} +0.483291i q^{63} -8.88991 q^{64} +(6.26701 + 3.18626i) q^{65} -5.98082i q^{67} +0.965727i q^{68} -8.53218 q^{69} +(-0.622461 + 1.22431i) q^{70} +8.34418 q^{71} +3.03083i q^{72} -0.151416i q^{73} +4.07670 q^{74} +(-4.03991 + 2.94604i) q^{75} -1.43126 q^{76} -3.99597i q^{78} +7.48541 q^{79} +(-3.12382 + 6.14421i) q^{80} +1.00000 q^{81} -9.99670i q^{82} +4.05723i q^{83} -0.185938 q^{84} +(5.00330 + 2.54377i) q^{85} -7.58767 q^{86} +9.98293i q^{87} +17.0317 q^{89} +(2.53328 + 1.28796i) q^{90} +1.51953 q^{91} -3.28260i q^{92} +5.78984i q^{93} -7.79204 q^{94} +(-3.77000 + 7.41516i) q^{95} -2.14399 q^{96} -3.60977i q^{97} -8.59967i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.27093i		−	0.898685i	−0.893360	−	0.449342i	$-0.851658\pi$
$2$		−	1.27093i		−	0.898685i	0.893360	−	0.449342i	$-0.148342\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.384732			0.192366
$5$	1.01340	−	1.99324i	0.453206	−	0.891406i
$5$	1.01340	−	1.99324i	0.453206	−	0.891406i
$6$	−1.27093			−0.518856
$7$		−	0.483291i		−	0.182667i	−0.995820	−	0.0913334i	$-0.970887\pi$
$7$		−	0.483291i		−	0.182667i	0.995820	−	0.0913334i	$-0.0291129\pi$
$8$		−	3.03083i		−	1.07156i
$9$	−1.00000			−0.333333
$10$	−2.53328	−	1.28796i	−0.801092	−	0.407290i
$11$		0			0
$11$		0			0
$12$		−	0.384732i		−	0.111063i
$13$			3.14412i			0.872023i	0.899941	+	0.436012i	$0.143609\pi$
$13$			3.14412i			0.872023i	−0.899941	+	0.436012i	$0.856391\pi$
$14$	−0.614230			−0.164160
$15$	−1.99324	−	1.01340i	−0.514653	−	0.261659i
$16$	−3.08252			−0.770629
$17$			2.51013i			0.608796i	0.952545	+	0.304398i	$0.0984552\pi$
$17$			2.51013i			0.608796i	−0.952545	+	0.304398i	$0.901545\pi$
$18$			1.27093i			0.299562i
$19$	−3.72015			−0.853460			−0.426730	−	0.904379i	$-0.640335\pi$
$19$	−3.72015			−0.853460			−0.426730	+	0.904379i	$0.640335\pi$
$20$	0.389888	−	0.766865i	0.0871815	−	0.171476i
$21$	−0.483291			−0.105463
$22$		0			0
$23$		−	8.53218i		−	1.77908i	−0.456855	−	0.889541i	$-0.651024\pi$
$23$		−	8.53218i		−	1.77908i	0.456855	−	0.889541i	$-0.348976\pi$
$24$	−3.03083			−0.618666
$25$	−2.94604	−	4.03991i	−0.589208	−	0.807981i
$26$	3.99597			0.783674
$27$			1.00000i			0.192450i
$28$		−	0.185938i		−	0.0351389i
$29$	−9.98293			−1.85378			−0.926891	−	0.375330i	$-0.877529\pi$
$29$	−9.98293			−1.85378			−0.926891	+	0.375330i	$0.877529\pi$
$30$	−1.28796	+	2.53328i	−0.235149	+	0.462511i
$31$	−5.78984			−1.03989			−0.519943	−	0.854201i	$-0.674047\pi$
$31$	−5.78984			−1.03989			−0.519943	+	0.854201i	$0.674047\pi$
$32$		−	2.14399i		−	0.379008i
$33$		0			0
$34$	3.19020			0.547115
$35$	−0.963317	−	0.489767i	−0.162830	−	0.0827858i
$36$	−0.384732			−0.0641220
$37$			3.20765i			0.527334i	0.964614	+	0.263667i	$0.0849319\pi$
$37$			3.20765i			0.527334i	−0.964614	+	0.263667i	$0.915068\pi$
$38$			4.72805i			0.766992i
$39$	3.14412			0.503463
$40$	−6.04119	−	3.07145i	−0.955195	−	0.485638i
$41$	7.86565			1.22841			0.614204	−	0.789148i	$-0.289477\pi$
$41$	7.86565			1.22841			0.614204	+	0.789148i	$0.289477\pi$
$42$			0.614230i			0.0947778i
$43$		−	5.97016i		−	0.910441i	−0.890379	−	0.455221i	$-0.849560\pi$
$43$		−	5.97016i		−	0.910441i	0.890379	−	0.455221i	$-0.150440\pi$
$44$		0			0
$45$	−1.01340	+	1.99324i	−0.151069	+	0.297135i
$46$	−10.8438			−1.59883
$47$		−	6.13097i		−	0.894294i	−0.894461	−	0.447147i	$-0.852440\pi$
$47$		−	6.13097i		−	0.894294i	0.894461	−	0.447147i	$-0.147560\pi$
$48$			3.08252i			0.444923i
$49$	6.76643			0.966633
$50$	−5.13445	+	3.74422i	−0.726120	+	0.529512i
$51$	2.51013			0.351488
$52$			1.20965i			0.167748i
$53$		−	1.58220i		−	0.217332i	−0.994078	−	0.108666i	$-0.965342\pi$
$53$		−	1.58220i		−	0.217332i	0.994078	−	0.108666i	$-0.0346579\pi$
$54$	1.27093			0.172952
$55$		0			0
$56$	−1.46477			−0.195739
$57$			3.72015i			0.492746i
$58$			12.6876i			1.66597i
$59$	0.377932			0.0492026			0.0246013	−	0.999697i	$-0.492168\pi$
$59$	0.377932			0.0492026			0.0246013	+	0.999697i	$0.492168\pi$
$60$	−0.766865	−	0.389888i	−0.0990018	−	0.0503343i
$61$	−3.00852			−0.385201			−0.192600	−	0.981277i	$-0.561692\pi$
$61$	−3.00852			−0.385201			−0.192600	+	0.981277i	$0.561692\pi$
$62$			7.35850i			0.934530i
$63$			0.483291i			0.0608890i
$64$	−8.88991			−1.11124
$65$	6.26701	+	3.18626i	0.777326	+	0.395207i
$66$		0			0
$67$		−	5.98082i		−	0.730674i	−0.930875	−	0.365337i	$-0.880954\pi$
$67$		−	5.98082i		−	0.730674i	0.930875	−	0.365337i	$-0.119046\pi$
$68$			0.965727i			0.117112i
$69$	−8.53218			−1.02715
$70$	−0.622461	+	1.22431i	−0.0743983	+	0.146333i
$71$	8.34418			0.990272			0.495136	−	0.868815i	$-0.335118\pi$
$71$	8.34418			0.990272			0.495136	+	0.868815i	$0.335118\pi$
$72$			3.03083i			0.357187i
$73$		−	0.151416i		−	0.0177219i	−0.999961	−	0.00886093i	$-0.997179\pi$
$73$		−	0.151416i		−	0.0177219i	0.999961	−	0.00886093i	$-0.00282056\pi$
$74$	4.07670			0.473907
$75$	−4.03991	+	2.94604i	−0.466488	+	0.340179i
$76$	−1.43126			−0.164177
$77$		0			0
$78$		−	3.99597i		−	0.452454i
$79$	7.48541			0.842175			0.421087	−	0.907020i	$-0.361649\pi$
$79$	7.48541			0.842175			0.421087	+	0.907020i	$0.361649\pi$
$80$	−3.12382	+	6.14421i	−0.349254	+	0.686943i
$81$	1.00000			0.111111
$82$		−	9.99670i		−	1.10395i
$83$			4.05723i			0.445339i	0.974894	+	0.222669i	$0.0714770\pi$
$83$			4.05723i			0.445339i	−0.974894	+	0.222669i	$0.928523\pi$
$84$	−0.185938			−0.0202875
$85$	5.00330	+	2.54377i	0.542684	+	0.275910i
$86$	−7.58767			−0.818200
$87$			9.98293i			1.07028i
$88$		0			0
$89$	17.0317			1.80535			0.902677	−	0.430318i	$-0.141599\pi$
$89$	17.0317			1.80535			0.902677	+	0.430318i	$0.141599\pi$
$90$	2.53328	+	1.28796i	0.267031	+	0.135763i
$91$	1.51953			0.159290
$92$		−	3.28260i		−	0.342235i
$93$			5.78984i			0.600379i
$94$	−7.79204			−0.803688
$95$	−3.77000	+	7.41516i	−0.386794	+	0.760779i
$96$	−2.14399			−0.218821
$97$		−	3.60977i		−	0.366517i	−0.983065	−	0.183259i	$-0.941335\pi$
$97$		−	3.60977i		−	0.366517i	0.983065	−	0.183259i	$-0.0586645\pi$
$98$		−	8.59967i		−	0.868698i
$99$		0			0
$100$	−1.13344	−	1.55428i	−0.113344	−	0.155428i
$101$	−7.59573			−0.755803			−0.377902	−	0.925846i	$-0.623354\pi$
$101$	−7.59573			−0.755803			−0.377902	+	0.925846i	$0.623354\pi$
$102$		−	3.19020i		−	0.315877i
$103$		−	3.80758i		−	0.375172i	−0.982248	−	0.187586i	$-0.939934\pi$
$103$		−	3.80758i		−	0.375172i	0.982248	−	0.187586i	$-0.0600663\pi$
$104$	9.52931			0.934426
$105$	−0.489767	+	0.963317i	−0.0477964	+	0.0940101i
$106$	−2.01087			−0.195313
$107$		−	0.477465i		−	0.0461583i	−0.999734	−	0.0230791i	$-0.992653\pi$
$107$		−	0.477465i		−	0.0461583i	0.999734	−	0.0230791i	$-0.00734697\pi$
$108$			0.384732i			0.0370209i
$109$	−6.92083			−0.662895			−0.331447	−	0.943474i	$-0.607537\pi$
$109$	−6.92083			−0.662895			−0.331447	+	0.943474i	$0.607537\pi$
$110$		0			0
$111$	3.20765			0.304456
$112$			1.48975i			0.140768i
$113$		−	10.8641i		−	1.02201i	−0.859578	−	0.511004i	$-0.829274\pi$
$113$		−	10.8641i		−	1.02201i	0.859578	−	0.511004i	$-0.170726\pi$
$114$	4.72805			0.442823
$115$	−17.0067	−	8.64651i	−1.58588	−	0.806291i
$116$	−3.84075			−0.356605
$117$		−	3.14412i		−	0.290674i
$118$		−	0.480326i		−	0.0442176i
$119$	1.21312			0.111207
$120$	−3.07145	+	6.04119i	−0.280383	+	0.551482i
$121$		0			0
$122$			3.82362i			0.346174i
$123$		−	7.86565i		−	0.709221i
$124$	−2.22754			−0.200039
$125$	−11.0380	+	1.77813i	−0.987272	+	0.159041i
$126$	0.614230			0.0547200
$127$		−	5.99218i		−	0.531720i	−0.964012	−	0.265860i	$-0.914344\pi$
$127$		−	5.99218i		−	0.531720i	0.964012	−	0.265860i	$-0.0856559\pi$
$128$			7.01048i			0.619644i
$129$	−5.97016			−0.525644
$130$	4.04952	−	7.96494i	0.355166	−	0.698571i
$131$	10.9819			0.959491			0.479746	−	0.877408i	$-0.340729\pi$
$131$	10.9819			0.959491			0.479746	+	0.877408i	$0.340729\pi$
$132$		0			0
$133$			1.79791i			0.155899i
$134$	−7.60122			−0.656645
$135$	1.99324	+	1.01340i	0.171551	+	0.0872196i
$136$	7.60778			0.652362
$137$			1.09210i			0.0933043i	0.998911	+	0.0466522i	$0.0148552\pi$
$137$			1.09210i			0.0933043i	−0.998911	+	0.0466522i	$0.985145\pi$
$138$			10.8438i			0.923087i
$139$	−8.42516			−0.714613			−0.357306	−	0.933987i	$-0.616305\pi$
$139$	−8.42516			−0.714613			−0.357306	+	0.933987i	$0.616305\pi$
$140$	−0.370619	−	0.188429i	−0.0313230	−	0.0159252i
$141$	−6.13097			−0.516321
$142$		−	10.6049i		−	0.889943i
$143$		0			0
$144$	3.08252			0.256876
$145$	−10.1167	+	19.8984i	−0.840146	+	1.65247i
$146$	−0.192439			−0.0159264
$147$		−	6.76643i		−	0.558086i
$148$			1.23408i			0.101441i
$149$	17.2296			1.41151			0.705754	−	0.708457i	$-0.250609\pi$
$149$	17.2296			1.41151			0.705754	+	0.708457i	$0.250609\pi$
$150$	3.74422	+	5.13445i	0.305714	+	0.419226i
$151$	13.0838			1.06475			0.532374	−	0.846509i	$-0.321300\pi$
$151$	13.0838			1.06475			0.532374	+	0.846509i	$0.321300\pi$
$152$			11.2751i			0.914535i
$153$		−	2.51013i		−	0.202932i
$154$		0			0
$155$	−5.86743	+	11.5406i	−0.471283	+	0.926961i
$156$	1.20965			0.0968492
$157$			23.5086i			1.87619i	0.346379	+	0.938095i	$0.387411\pi$
$157$			23.5086i			1.87619i	−0.346379	+	0.938095i	$0.612589\pi$
$158$		−	9.51345i		−	0.756849i
$159$	−1.58220			−0.125477
$160$	−4.27350	−	2.17273i	−0.337850	−	0.171769i
$161$	−4.12353			−0.324979
$162$		−	1.27093i		−	0.0998538i
$163$			19.9396i			1.56179i	0.624663	+	0.780895i	$0.285236\pi$
$163$			19.9396i			1.56179i	−0.624663	+	0.780895i	$0.714764\pi$
$164$	3.02617			0.236304
$165$		0			0
$166$	5.15646			0.400219
$167$			19.2762i			1.49164i	0.666149	+	0.745819i	$0.267942\pi$
$167$			19.2762i			1.49164i	−0.666149	+	0.745819i	$0.732058\pi$
$168$			1.46477i			0.113010i
$169$	3.11448			0.239575
$170$	3.23295	−	6.35885i	0.247956	−	0.487702i
$171$	3.72015			0.284487
$172$		−	2.29691i		−	0.175138i
$173$		−	3.86887i		−	0.294145i	−0.989126	−	0.147072i	$-0.953015\pi$
$173$		−	3.86887i		−	0.294145i	0.989126	−	0.147072i	$-0.0469851\pi$
$174$	12.6876			0.961846
$175$	−1.95245	+	1.42379i	−0.147591	+	0.107629i
$176$		0			0
$177$		−	0.377932i		−	0.0284071i
$178$		−	21.6461i		−	1.62244i
$179$	17.1863			1.28456			0.642282	−	0.766469i	$-0.277988\pi$
$179$	17.1863			1.28456			0.642282	+	0.766469i	$0.277988\pi$
$180$	−0.389888	+	0.766865i	−0.0290605	+	0.0571587i
$181$	−6.98972			−0.519542			−0.259771	−	0.965670i	$-0.583647\pi$
$181$	−6.98972			−0.519542			−0.259771	+	0.965670i	$0.583647\pi$
$182$		−	1.93122i		−	0.143151i
$183$			3.00852i			0.222396i
$184$	−25.8596			−1.90639
$185$	6.39362	+	3.25063i	0.470068	+	0.238991i
$186$	7.35850			0.539551
$187$		0			0
$188$		−	2.35878i		−	0.172032i
$189$	0.483291			0.0351543
$190$	9.42416	+	4.79141i	0.683701	+	0.347606i
$191$	−9.99835			−0.723455			−0.361727	−	0.932284i	$-0.617813\pi$
$191$	−9.99835			−0.723455			−0.361727	+	0.932284i	$0.617813\pi$
$192$			8.88991i			0.641574i
$193$		−	23.7968i		−	1.71293i	−0.516205	−	0.856465i	$-0.672656\pi$
$193$		−	23.7968i		−	1.71293i	0.516205	−	0.856465i	$-0.327344\pi$
$194$	−4.58778			−0.329383
$195$	3.18626	−	6.26701i	0.228173	−	0.448790i
$196$	2.60326			0.185947
$197$			24.6381i			1.75539i	0.479221	+	0.877694i	$0.340919\pi$
$197$			24.6381i			1.75539i	−0.479221	+	0.877694i	$0.659081\pi$
$198$		0			0
$199$	15.3559			1.08855			0.544277	−	0.838906i	$-0.316804\pi$
$199$	15.3559			1.08855			0.544277	+	0.838906i	$0.316804\pi$
$200$	−12.2443	+	8.92895i	−0.865801	+	0.631372i
$201$	−5.98082			−0.421855
$202$			9.65365i			0.679229i
$203$			4.82466i			0.338625i
$204$	0.965727			0.0676144
$205$	7.97105	−	15.6781i	0.556722	−	1.09501i
$206$	−4.83918			−0.337161
$207$			8.53218i			0.593027i
$208$		−	9.69182i		−	0.672007i
$209$		0			0
$210$	1.22431	+	0.622461i	0.0844854	+	0.0429539i
$211$	25.8608			1.78033			0.890165	−	0.455639i	$-0.150589\pi$
$211$	25.8608			1.78033			0.890165	+	0.455639i	$0.150589\pi$
$212$		−	0.608723i		−	0.0418073i
$213$		−	8.34418i		−	0.571734i
$214$	−0.606826			−0.0414817
$215$	−11.9000	−	6.05017i	−0.811572	−	0.412618i
$216$	3.03083			0.206222
$217$			2.79818i			0.189953i
$218$			8.79590i			0.595733i
$219$	−0.151416			−0.0102317
$220$		0			0
$221$	−7.89216			−0.530884
$222$		−	4.07670i		−	0.273610i
$223$			5.36807i			0.359473i	0.983715	+	0.179736i	$0.0575244\pi$
$223$			5.36807i			0.359473i	−0.983715	+	0.179736i	$0.942476\pi$
$224$	−1.03617			−0.0692323
$225$	2.94604	+	4.03991i	0.196403	+	0.269327i
$226$	−13.8075			−0.918463
$227$		−	7.72444i		−	0.512689i	−0.966585	−	0.256345i	$-0.917482\pi$
$227$		−	7.72444i		−	0.512689i	0.966585	−	0.256345i	$-0.0825182\pi$
$228$			1.43126i			0.0947875i
$229$	−8.08159			−0.534047			−0.267023	−	0.963690i	$-0.586040\pi$
$229$	−8.08159			−0.534047			−0.267023	+	0.963690i	$0.586040\pi$
$230$	−10.9891	+	21.6144i	−0.724602	+	1.42521i
$231$		0			0
$232$			30.2566i			1.98644i
$233$		−	25.4908i		−	1.66996i	−0.550280	−	0.834980i	$-0.685479\pi$
$233$		−	25.4908i		−	1.66996i	0.550280	−	0.834980i	$-0.314521\pi$
$234$	−3.99597			−0.261225
$235$	−12.2205	−	6.21313i	−0.797178	−	0.405300i
$236$	0.145403			0.00946491
$237$		−	7.48541i		−	0.486230i
$238$		−	1.54180i		−	0.0999398i
$239$	0.928865			0.0600833			0.0300417	−	0.999549i	$-0.490436\pi$
$239$	0.928865			0.0600833			0.0300417	+	0.999549i	$0.490436\pi$
$240$	6.14421	+	3.12382i	0.396607	+	0.201642i
$241$	−10.3759			−0.668369			−0.334184	−	0.942508i	$-0.608461\pi$
$241$	−10.3759			−0.668369			−0.334184	+	0.942508i	$0.608461\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	−1.15747			−0.0740996
$245$	6.85710	−	13.4871i	0.438084	−	0.861662i
$246$	−9.99670			−0.637366
$247$		−	11.6966i		−	0.744237i
$248$			17.5480i			1.11430i
$249$	4.05723			0.257116
$250$	2.25988	+	14.0286i	0.142928	+	0.887246i
$251$	23.5461			1.48621			0.743107	−	0.669172i	$-0.233351\pi$
$251$	23.5461			1.48621			0.743107	+	0.669172i	$0.233351\pi$
$252$			0.185938i			0.0117130i
$253$		0			0
$254$	−7.61566			−0.477849
$255$	2.54377	−	5.00330i	0.159297	−	0.313319i
$256$	−8.86997			−0.554373
$257$			16.0996i			1.00427i	0.864791	+	0.502133i	$0.167451\pi$
$257$			16.0996i			1.00427i	−0.864791	+	0.502133i	$0.832549\pi$
$258$			7.58767i			0.472388i
$259$	1.55023			0.0963264
$260$	2.41112	+	1.22586i	0.149531	+	0.0760243i
$261$	9.98293			0.617928
$262$		−	13.9572i		−	0.862280i
$263$		−	2.19036i		−	0.135063i	−0.997717	−	0.0675316i	$-0.978488\pi$
$263$		−	2.19036i		−	0.135063i	0.997717	−	0.0675316i	$-0.0215124\pi$
$264$		0			0
$265$	−3.15371	−	1.60340i	−0.193731	−	0.0984962i
$266$	2.28503			0.140104
$267$		−	17.0317i		−	1.04232i
$268$		−	2.30101i		−	0.140557i
$269$	10.4351			0.636237			0.318119	−	0.948051i	$-0.396949\pi$
$269$	10.4351			0.636237			0.318119	+	0.948051i	$0.396949\pi$
$270$	1.28796	−	2.53328i	0.0783829	−	0.154170i
$271$	1.72943			0.105055			0.0525277	−	0.998619i	$-0.483272\pi$
$271$	1.72943			0.105055			0.0525277	+	0.998619i	$0.483272\pi$
$272$		−	7.73751i		−	0.469156i
$273$		−	1.51953i		−	0.0919660i
$274$	1.38798			0.0838511
$275$		0			0
$276$	−3.28260			−0.197589
$277$		−	11.6390i		−	0.699321i	−0.936876	−	0.349661i	$-0.886297\pi$
$277$		−	11.6390i		−	0.699321i	0.936876	−	0.349661i	$-0.113703\pi$
$278$			10.7078i			0.642211i
$279$	5.78984			0.346629
$280$	−1.48440	+	2.91965i	−0.0887100	+	0.174483i
$281$	−12.0160			−0.716817			−0.358408	−	0.933565i	$-0.616680\pi$
$281$	−12.0160			−0.716817			−0.358408	+	0.933565i	$0.616680\pi$
$282$			7.79204i			0.464009i
$283$		−	27.5894i		−	1.64002i	−0.572347	−	0.820011i	$-0.693967\pi$
$283$		−	27.5894i		−	1.64002i	0.572347	−	0.820011i	$-0.306033\pi$
$284$	3.21028			0.190495
$285$	7.41516	+	3.77000i	0.439236	+	0.223315i
$286$		0			0
$287$		−	3.80140i		−	0.224389i
$288$			2.14399i			0.126336i
$289$	10.6993			0.629368
$290$	25.2895	+	12.8576i	1.48505	+	0.755026i
$291$	−3.60977			−0.211609
$292$		−	0.0582544i		−	0.00340908i
$293$			3.42861i			0.200301i	0.994972	+	0.100151i	$0.0319325\pi$
$293$			3.42861i			0.200301i	−0.994972	+	0.100151i	$0.968067\pi$
$294$	−8.59967			−0.501543
$295$	0.382997	−	0.753311i	0.0222989	−	0.0438595i
$296$	9.72183			0.565070
$297$		0			0
$298$		−	21.8977i		−	1.26850i
$299$	26.8262			1.55140
$300$	−1.55428	+	1.13344i	−0.0897365	+	0.0654390i
$301$	−2.88533			−0.166307
$302$		−	16.6287i		−	0.956872i
$303$			7.59573i			0.436363i
$304$	11.4674			0.657702
$305$	−3.04883	+	5.99670i	−0.174576	+	0.343370i
$306$	−3.19020			−0.182372
$307$		−	15.3337i		−	0.875140i	−0.899184	−	0.437570i	$-0.855839\pi$
$307$		−	15.3337i		−	0.875140i	0.899184	−	0.437570i	$-0.144161\pi$
$308$		0			0
$309$	−3.80758			−0.216606
$310$	14.6673	+	7.45710i	0.833045	+	0.423535i
$311$	−4.34207			−0.246216			−0.123108	−	0.992393i	$-0.539286\pi$
$311$	−4.34207			−0.246216			−0.123108	+	0.992393i	$0.539286\pi$
$312$		−	9.52931i		−	0.539491i
$313$			10.4437i			0.590311i	0.955449	+	0.295155i	$0.0953714\pi$
$313$			10.4437i			0.590311i	−0.955449	+	0.295155i	$0.904629\pi$
$314$	29.8778			1.68610
$315$	0.963317	+	0.489767i	0.0542768	+	0.0275953i
$316$	2.87988			0.162006
$317$		−	16.6411i		−	0.934658i	−0.884084	−	0.467329i	$-0.845216\pi$
$317$		−	16.6411i		−	0.934658i	0.884084	−	0.467329i	$-0.154784\pi$
$318$			2.01087i			0.112764i
$319$		0			0
$320$	−9.00903	+	17.7197i	−0.503620	+	0.990564i
$321$	−0.477465			−0.0266495
$322$			5.24072i			0.292054i
$323$		−	9.33805i		−	0.519583i
$324$	0.384732			0.0213740
$325$	12.7020	−	9.26272i	0.704579	−	0.513803i
$326$	25.3419			1.40356
$327$			6.92083i			0.382723i
$328$		−	23.8395i		−	1.31631i
$329$	−2.96304			−0.163358
$330$		0			0
$331$	−32.0054			−1.75917			−0.879587	−	0.475738i	$-0.842181\pi$
$331$	−32.0054			−1.75917			−0.879587	+	0.475738i	$0.842181\pi$
$332$			1.56095i			0.0856680i
$333$		−	3.20765i		−	0.175778i
$334$	24.4987			1.34051
$335$	−11.9212	−	6.06097i	−0.651327	−	0.331146i
$336$	1.48975			0.0812727
$337$			14.3255i			0.780359i	0.920739	+	0.390179i	$0.127587\pi$
$337$			14.3255i			0.780359i	−0.920739	+	0.390179i	$0.872413\pi$
$338$		−	3.95829i		−	0.215303i
$339$	−10.8641			−0.590057
$340$	1.92493	+	0.978668i	0.104394	+	0.0530757i
$341$		0			0
$342$		−	4.72805i		−	0.255664i
$343$		−	6.65319i		−	0.359239i
$344$	−18.0946			−0.975593
$345$	−8.64651	+	17.0067i	−0.465512	+	0.915610i
$346$	−4.91707			−0.264344
$347$		−	16.0635i		−	0.862334i	−0.902272	−	0.431167i	$-0.858102\pi$
$347$		−	16.0635i		−	0.862334i	0.902272	−	0.431167i	$-0.141898\pi$
$348$			3.84075i			0.205886i
$349$	3.97683			0.212875			0.106437	−	0.994319i	$-0.466056\pi$
$349$	3.97683			0.212875			0.106437	+	0.994319i	$0.466056\pi$
$350$	1.80955	+	2.48143i	0.0967243	+	0.132638i
$351$	−3.14412			−0.167821
$352$		0			0
$353$		−	9.37575i		−	0.499021i	−0.968372	−	0.249510i	$-0.919730\pi$
$353$		−	9.37575i		−	0.499021i	0.968372	−	0.249510i	$-0.0802696\pi$
$354$	−0.480326			−0.0255291
$355$	8.45600	−	16.6320i	0.448798	−	0.882734i
$356$	6.55263			0.347289
$357$		−	1.21312i		−	0.0642053i
$358$		−	21.8426i		−	1.15442i
$359$	21.7374			1.14725			0.573627	−	0.819117i	$-0.305536\pi$
$359$	21.7374			1.14725			0.573627	+	0.819117i	$0.305536\pi$
$360$	6.04119	+	3.07145i	0.318398	+	0.161879i
$361$	−5.16050			−0.271605
$362$			8.88346i			0.466904i
$363$		0			0
$364$	0.584611			0.0306419
$365$	−0.301808	−	0.153445i	−0.0157974	−	0.00803166i
$366$	3.82362			0.199864
$367$			31.3823i			1.63814i	0.573690	+	0.819072i	$0.305511\pi$
$367$			31.3823i			1.63814i	−0.573690	+	0.819072i	$0.694489\pi$
$368$			26.3006i			1.37101i
$369$	−7.86565			−0.409469
$370$	4.13133	−	8.12585i	0.214778	−	0.422443i
$371$	−0.764663			−0.0396993
$372$			2.22754i			0.115493i
$373$		−	23.2675i		−	1.20475i	−0.798214	−	0.602374i	$-0.794222\pi$
$373$		−	23.2675i		−	1.20475i	0.798214	−	0.602374i	$-0.205778\pi$
$374$		0			0
$375$	1.77813	+	11.0380i	0.0918223	+	0.570002i
$376$	−18.5819			−0.958290
$377$		−	31.3876i		−	1.61654i
$378$		−	0.614230i		−	0.0315926i
$379$	−13.2493			−0.680573			−0.340286	−	0.940322i	$-0.610524\pi$
$379$	−13.2493			−0.680573			−0.340286	+	0.940322i	$0.610524\pi$
$380$	−1.45044	+	2.85285i	−0.0744060	+	0.146348i
$381$	−5.99218			−0.306989
$382$			12.7072i			0.650158i
$383$		−	20.6481i		−	1.05507i	−0.849534	−	0.527534i	$-0.823117\pi$
$383$		−	20.6481i		−	1.05507i	0.849534	−	0.527534i	$-0.176883\pi$
$384$	7.01048			0.357752
$385$		0			0
$386$	−30.2441			−1.53938
$387$			5.97016i			0.303480i
$388$		−	1.38880i		−	0.0705054i
$389$	−22.8485			−1.15847			−0.579233	−	0.815162i	$-0.696648\pi$
$389$	−22.8485			−1.15847			−0.579233	+	0.815162i	$0.696648\pi$
$390$	−7.96494	−	4.04952i	−0.403320	−	0.205055i
$391$	21.4169			1.08310
$392$		−	20.5079i		−	1.03581i
$393$		−	10.9819i		−	0.553963i
$394$	31.3133			1.57754
$395$	7.58572	−	14.9203i	0.381679	−	0.750719i
$396$		0			0
$397$			7.71249i			0.387079i	0.981093	+	0.193539i	$0.0619967\pi$
$397$			7.71249i			0.387079i	−0.981093	+	0.193539i	$0.938003\pi$
$398$		−	19.5164i		−	0.978267i
$399$	1.79791			0.0900083
$400$	9.08122	+	12.4531i	0.454061	+	0.622654i
$401$	−8.19088			−0.409033			−0.204516	−	0.978863i	$-0.565562\pi$
$401$	−8.19088			−0.409033			−0.204516	+	0.978863i	$0.565562\pi$
$402$			7.60122i			0.379114i
$403$		−	18.2040i		−	0.906805i
$404$	−2.92232			−0.145391
$405$	1.01340	−	1.99324i	0.0503563	−	0.0990451i
$406$	6.13181			0.304317
$407$		0			0
$408$		−	7.60778i		−	0.376641i
$409$	−3.42306			−0.169260			−0.0846298	−	0.996412i	$-0.526971\pi$
$409$	−3.42306			−0.169260			−0.0846298	+	0.996412i	$0.526971\pi$
$410$	−19.9259	−	10.1307i	−0.984068	−	0.500318i
$411$	1.09210			0.0538693
$412$		−	1.46490i		−	0.0721704i
$413$		−	0.182651i		−	0.00898769i
$414$	10.8438			0.532944
$415$	8.08704	+	4.11160i	0.396977	+	0.201830i
$416$	6.74099			0.330504
$417$			8.42516i			0.412582i
$418$		0			0
$419$	18.3593			0.896910			0.448455	−	0.893805i	$-0.351974\pi$
$419$	18.3593			0.896910			0.448455	+	0.893805i	$0.351974\pi$
$420$	−0.188429	+	0.370619i	−0.00919440	+	0.0180843i
$421$	35.5774			1.73394			0.866968	−	0.498363i	$-0.166065\pi$
$421$	35.5774			1.73394			0.866968	+	0.498363i	$0.166065\pi$
$422$		−	32.8673i		−	1.59995i
$423$			6.13097i			0.298098i
$424$	−4.79538			−0.232884
$425$	10.1407	−	7.39494i	0.491896	−	0.358707i
$426$	−10.6049			−0.513809
$427$			1.45399i			0.0703634i
$428$		−	0.183696i		−	0.00887929i
$429$		0			0
$430$	−7.68935	+	15.1241i	−0.370813	+	0.729348i
$431$	10.7944			0.519947			0.259973	−	0.965616i	$-0.416286\pi$
$431$	10.7944			0.519947			0.259973	+	0.965616i	$0.416286\pi$
$432$		−	3.08252i		−	0.148308i
$433$		−	11.1184i		−	0.534316i	−0.963653	−	0.267158i	$-0.913915\pi$
$433$		−	11.1184i		−	0.534316i	0.963653	−	0.267158i	$-0.0860845\pi$
$434$	3.55630			0.170708
$435$	19.8984	+	10.1167i	0.954055	+	0.485059i
$436$	−2.66266			−0.127518
$437$			31.7410i			1.51838i
$438$			0.192439i			0.00919509i
$439$	−12.5701			−0.599937			−0.299969	−	0.953949i	$-0.596976\pi$
$439$	−12.5701			−0.599937			−0.299969	+	0.953949i	$0.596976\pi$
$440$		0			0
$441$	−6.76643			−0.322211
$442$			10.0304i			0.477097i
$443$			20.5582i			0.976751i	0.872633	+	0.488376i	$0.162410\pi$
$443$			20.5582i			0.976751i	−0.872633	+	0.488376i	$0.837590\pi$
$444$	1.23408			0.0585670
$445$	17.2599	−	33.9483i	0.818198	−	1.60930i
$446$	6.82245			0.323052
$447$		−	17.2296i		−	0.814934i
$448$			4.29641i			0.202986i
$449$	−14.3890			−0.679057			−0.339528	−	0.940596i	$-0.610267\pi$
$449$	−14.3890			−0.679057			−0.339528	+	0.940596i	$0.610267\pi$
$450$	5.13445	−	3.74422i	0.242040	−	0.176504i
$451$		0			0
$452$		−	4.17977i		−	0.196600i
$453$		−	13.0838i		−	0.614732i
$454$	−9.81724			−0.460746
$455$	1.53989	−	3.02879i	0.0721911	−	0.141992i
$456$	11.2751			0.528007
$457$			11.2947i			0.528344i	0.964476	+	0.264172i	$0.0850986\pi$
$457$			11.2947i			0.528344i	−0.964476	+	0.264172i	$0.914901\pi$
$458$			10.2712i			0.479939i
$459$	−2.51013			−0.117163
$460$	−6.54303	−	3.32659i	−0.305070	−	0.155103i
$461$	−35.8299			−1.66876			−0.834382	−	0.551186i	$-0.814175\pi$
$461$	−35.8299			−1.66876			−0.834382	+	0.551186i	$0.814175\pi$
$462$		0			0
$463$		−	30.6184i		−	1.42296i	−0.702708	−	0.711479i	$-0.748026\pi$
$463$		−	30.6184i		−	1.42296i	0.702708	−	0.711479i	$-0.251974\pi$
$464$	30.7725			1.42858
$465$	11.5406	+	5.86743i	0.535181	+	0.272096i
$466$	−32.3971			−1.50077
$467$			40.0654i			1.85400i	0.375055	+	0.927002i	$0.377624\pi$
$467$			40.0654i			1.85400i	−0.375055	+	0.927002i	$0.622376\pi$
$468$		−	1.20965i		−	0.0559159i
$469$	−2.89048			−0.133470
$470$	−7.89646	+	15.5314i	−0.364236	+	0.716412i
$471$	23.5086			1.08322
$472$		−	1.14545i		−	0.0527236i
$473$		0			0
$474$	−9.51345			−0.436967
$475$	10.9597	+	15.0291i	0.502866	+	0.689580i
$476$	0.466727			0.0213924
$477$			1.58220i			0.0724439i
$478$		−	1.18052i		−	0.0539959i
$479$	19.7191			0.900989			0.450495	−	0.892779i	$-0.351248\pi$
$479$	19.7191			0.900989			0.450495	+	0.892779i	$0.351248\pi$
$480$	−2.17273	+	4.27350i	−0.0991709	+	0.195058i
$481$	−10.0852			−0.459847
$482$			13.1870i			0.600653i
$483$			4.12353i			0.187627i
$484$		0			0
$485$	−7.19516	−	3.65815i	−0.326715	−	0.166108i
$486$	−1.27093			−0.0576506
$487$			18.1367i			0.821851i	0.911669	+	0.410926i	$0.134794\pi$
$487$			18.1367i			0.821851i	−0.911669	+	0.410926i	$0.865206\pi$
$488$			9.11830i			0.412766i
$489$	19.9396			0.901699
$490$	−17.1412	−	8.71491i	−0.774362	−	0.393699i
$491$	10.8170			0.488165			0.244083	−	0.969754i	$-0.421513\pi$
$491$	10.8170			0.488165			0.244083	+	0.969754i	$0.421513\pi$
$492$		−	3.02617i		−	0.136430i
$493$		−	25.0584i		−	1.12857i
$494$	−14.8656			−0.668835
$495$		0			0
$496$	17.8473			0.801367
$497$		−	4.03267i		−	0.180890i
$498$		−	5.15646i		−	0.231067i
$499$	5.67211			0.253919			0.126959	−	0.991908i	$-0.459478\pi$
$499$	5.67211			0.253919			0.126959	+	0.991908i	$0.459478\pi$
$500$	−4.24669	+	0.684104i	−0.189918	+	0.0305941i
$501$	19.2762			0.861197
$502$		−	29.9254i		−	1.33564i
$503$		−	31.2925i		−	1.39526i	−0.716457	−	0.697631i	$-0.754237\pi$
$503$		−	31.2925i		−	1.39526i	0.716457	−	0.697631i	$-0.245763\pi$
$504$	1.46477			0.0652462
$505$	−7.69751	+	15.1401i	−0.342535	+	0.673727i
$506$		0			0
$507$		−	3.11448i		−	0.138319i
$508$		−	2.30538i		−	0.102285i
$509$	28.9798			1.28451			0.642254	−	0.766492i	$-0.277999\pi$
$509$	28.9798			1.28451			0.642254	+	0.766492i	$0.277999\pi$
$510$	−6.35885	−	3.23295i	−0.281575	−	0.143158i
$511$	−0.0731778			−0.00323720
$512$			25.2941i			1.11785i
$513$		−	3.72015i		−	0.164249i
$514$	20.4615			0.902518
$515$	−7.58944	−	3.85860i	−0.334430	−	0.170030i
$516$	−2.29691			−0.101116
$517$		0			0
$518$		−	1.97023i		−	0.0865670i
$519$	−3.86887			−0.169825
$520$	9.65701	−	18.9942i	0.423488	−	0.832953i
$521$	21.4302			0.938874			0.469437	−	0.882966i	$-0.344457\pi$
$521$	21.4302			0.938874			0.469437	+	0.882966i	$0.344457\pi$
$522$		−	12.6876i		−	0.555322i
$523$			34.4628i			1.50695i	0.657475	+	0.753477i	$0.271625\pi$
$523$			34.4628i			1.50695i	−0.657475	+	0.753477i	$0.728375\pi$
$524$	4.22508			0.184574
$525$	1.42379	+	1.95245i	0.0621395	+	0.0852120i
$526$	−2.78380			−0.121379
$527$		−	14.5333i		−	0.633079i
$528$		0			0
$529$	−49.7980			−2.16513
$530$	−2.03781	+	4.00815i	−0.0885170	+	0.174103i
$531$	−0.377932			−0.0164009
$532$			0.691715i			0.0299897i
$533$			24.7306i			1.07120i
$534$	−21.6461			−0.936719
$535$	−0.951704	−	0.483863i	−0.0411458	−	0.0209192i
$536$	−18.1269			−0.782962
$537$		−	17.1863i		−	0.741643i
$538$		−	13.2623i		−	0.571777i
$539$		0			0
$540$	0.766865	+	0.389888i	0.0330006	+	0.0167781i
$541$	16.2343			0.697968			0.348984	−	0.937129i	$-0.386527\pi$
$541$	16.2343			0.697968			0.348984	+	0.937129i	$0.386527\pi$
$542$		−	2.19799i		−	0.0944116i
$543$			6.98972i			0.299958i
$544$	5.38170			0.230739
$545$	−7.01357	+	13.7949i	−0.300428	+	0.590908i
$546$	−1.93122			−0.0826484
$547$			0.131936i			0.00564119i	0.999996	+	0.00282059i	$0.000897824\pi$
$547$			0.131936i			0.00564119i	−0.999996	+	0.00282059i	$0.999102\pi$
$548$			0.420166i			0.0179486i
$549$	3.00852			0.128400
$550$		0			0
$551$	37.1380			1.58213
$552$			25.8596i			1.10066i
$553$		−	3.61763i		−	0.153837i
$554$	−14.7924			−0.628469
$555$	3.25063	−	6.39362i	0.137982	−	0.271394i
$556$	−3.24143			−0.137467
$557$		−	5.65287i		−	0.239520i	−0.992803	−	0.119760i	$-0.961788\pi$
$557$		−	5.65287i		−	0.239520i	0.992803	−	0.119760i	$-0.0382125\pi$
$558$		−	7.35850i		−	0.311510i
$559$	18.7709			0.793926
$560$	2.96944	+	1.50972i	0.125482	+	0.0637972i
$561$		0			0
$562$			15.2716i			0.644192i
$563$		−	35.4044i		−	1.49212i	−0.665880	−	0.746059i	$-0.731944\pi$
$563$		−	35.4044i		−	1.49212i	0.665880	−	0.746059i	$-0.268056\pi$
$564$	−2.35878			−0.0993226
$565$	−21.6548	−	11.0097i	−0.911024	−	0.463181i
$566$	−35.0643			−1.47386
$567$		−	0.483291i		−	0.0202963i
$568$		−	25.2898i		−	1.06114i
$569$	12.0702			0.506008			0.253004	−	0.967465i	$-0.418581\pi$
$569$	12.0702			0.506008			0.253004	+	0.967465i	$0.418581\pi$
$570$	4.79141	−	9.42416i	0.200690	−	0.394735i
$571$	2.74339			0.114807			0.0574037	−	0.998351i	$-0.481718\pi$
$571$	2.74339			0.114807			0.0574037	+	0.998351i	$0.481718\pi$
$572$		0			0
$573$			9.99835i			0.417687i
$574$	−4.83132			−0.201655
$575$	−34.4692	+	25.1361i	−1.43747	+	1.04825i
$576$	8.88991			0.370413
$577$		−	21.9217i		−	0.912610i	−0.889823	−	0.456305i	$-0.849173\pi$
$577$		−	21.9217i		−	0.912610i	0.889823	−	0.456305i	$-0.150827\pi$
$578$		−	13.5980i		−	0.565603i
$579$	−23.7968			−0.988961
$580$	−3.89222	+	7.65555i	−0.161616	+	0.317880i
$581$	1.96082			0.0813486
$582$			4.58778i			0.190170i
$583$		0			0
$584$	−0.458915			−0.0189900
$585$	−6.26701	−	3.18626i	−0.259109	−	0.131736i
$586$	4.35753			0.180008
$587$		−	15.4600i		−	0.638104i	−0.947737	−	0.319052i	$-0.896636\pi$
$587$		−	15.4600i		−	0.638104i	0.947737	−	0.319052i	$-0.103364\pi$
$588$		−	2.60326i		−	0.107357i
$589$	21.5391			0.887502
$590$	−0.957408	−	0.486763i	−0.0394158	−	0.0200397i
$591$	24.6381			1.01347
$592$		−	9.88762i		−	0.406379i
$593$		−	44.6178i		−	1.83223i	−0.400910	−	0.916117i	$-0.631306\pi$
$593$		−	44.6178i		−	1.83223i	0.400910	−	0.916117i	$-0.368694\pi$
$594$		0			0
$595$	1.22938	−	2.41805i	0.0503996	−	0.0991304i
$596$	6.62880			0.271526
$597$		−	15.3559i		−	0.628477i
$598$		−	34.0943i		−	1.39422i
$599$	−39.3156			−1.60639			−0.803195	−	0.595716i	$-0.796868\pi$
$599$	−39.3156			−1.60639			−0.803195	+	0.595716i	$0.796868\pi$
$600$	8.92895	+	12.2443i	0.364523	+	0.499871i
$601$	11.3809			0.464237			0.232118	−	0.972688i	$-0.425434\pi$
$601$	11.3809			0.464237			0.232118	+	0.972688i	$0.425434\pi$
$602$			3.66705i			0.149458i
$603$			5.98082i			0.243558i
$604$	5.03377			0.204821
$605$		0			0
$606$	9.65365			0.392153
$607$		−	28.9982i		−	1.17700i	−0.808497	−	0.588500i	$-0.799719\pi$
$607$		−	28.9982i		−	1.17700i	0.808497	−	0.588500i	$-0.200281\pi$
$608$			7.97598i			0.323469i
$609$	4.82466			0.195505
$610$	7.62140	+	3.87486i	0.308582	+	0.156888i
$611$	19.2765			0.779845
$612$		−	0.965727i		−	0.0390372i
$613$			13.6341i			0.550675i	0.961348	+	0.275337i	$0.0887896\pi$
$613$			13.6341i			0.550675i	−0.961348	+	0.275337i	$0.911210\pi$
$614$	−19.4881			−0.786475
$615$	−15.6781	−	7.97105i	−0.632204	−	0.321424i
$616$		0			0
$617$			16.8378i			0.677863i	0.940811	+	0.338932i	$0.110066\pi$
$617$			16.8378i			0.677863i	−0.940811	+	0.338932i	$0.889934\pi$
$618$			4.83918i			0.194660i
$619$	−22.3270			−0.897396			−0.448698	−	0.893683i	$-0.648112\pi$
$619$	−22.3270			−0.897396			−0.448698	+	0.893683i	$0.648112\pi$
$620$	−2.25739	+	4.44003i	−0.0906589	+	0.178316i
$621$	8.53218			0.342384
$622$			5.51847i			0.221271i
$623$		−	8.23126i		−	0.329778i
$624$	−9.69182			−0.387983
$625$	−7.64170	+	23.8035i	−0.305668	+	0.952138i
$626$	13.2732			0.530503
$627$		0			0
$628$			9.04451i			0.360915i
$629$	−8.05160			−0.321038
$630$	0.622461	−	1.22431i	0.0247994	−	0.0487777i
$631$	12.6184			0.502329			0.251165	−	0.967944i	$-0.419186\pi$
$631$	12.6184			0.502329			0.251165	+	0.967944i	$0.419186\pi$
$632$		−	22.6870i		−	0.902442i
$633$		−	25.8608i		−	1.02787i
$634$	−21.1497			−0.839963
$635$	−11.9439	−	6.07248i	−0.473978	−	0.240979i
$636$	−0.608723			−0.0241374
$637$			21.2745i			0.842926i
$638$		0			0
$639$	−8.34418			−0.330091
$640$	13.9736	+	7.10442i	0.552354	+	0.280827i
$641$	−24.2601			−0.958215			−0.479107	−	0.877756i	$-0.659040\pi$
$641$	−24.2601			−0.958215			−0.479107	+	0.877756i	$0.659040\pi$
$642$			0.606826i			0.0239495i
$643$			18.6281i			0.734619i	0.930099	+	0.367310i	$0.119721\pi$
$643$			18.6281i			0.734619i	−0.930099	+	0.367310i	$0.880279\pi$
$644$	−1.58645			−0.0625150
$645$	−6.05017	+	11.9000i	−0.238225	+	0.468562i
$646$	−11.8680			−0.466941
$647$		−	3.27904i		−	0.128912i	−0.997921	−	0.0644562i	$-0.979469\pi$
$647$		−	3.27904i		−	0.128912i	0.997921	−	0.0644562i	$-0.0205313\pi$
$648$		−	3.03083i		−	0.119062i
$649$		0			0
$650$	−11.7723	−	16.1433i	−0.461747	−	0.633194i
$651$	2.79818			0.109669
$652$			7.67140i			0.300435i
$653$			12.3110i			0.481768i	0.970554	+	0.240884i	$0.0774373\pi$
$653$			12.3110i			0.481768i	−0.970554	+	0.240884i	$0.922563\pi$
$654$	8.79590			0.343947
$655$	11.1290	−	21.8896i	0.434848	−	0.855296i
$656$	−24.2460			−0.946647
$657$			0.151416i			0.00590728i
$658$			3.76583i			0.146807i
$659$	28.5993			1.11407			0.557035	−	0.830489i	$-0.311939\pi$
$659$	28.5993			1.11407			0.557035	+	0.830489i	$0.311939\pi$
$660$		0			0
$661$	37.2512			1.44890			0.724452	−	0.689325i	$-0.242093\pi$
$661$	37.2512			1.44890			0.724452	+	0.689325i	$0.242093\pi$
$662$			40.6766i			1.58094i
$663$			7.89216i			0.306506i
$664$	12.2968			0.477207
$665$	3.58368	+	1.82201i	0.138969	+	0.0706544i
$666$	−4.07670			−0.157969
$667$			85.1761i			3.29803i
$668$			7.41618i			0.286940i
$669$	5.36807			0.207542
$670$	−7.70308	+	15.1511i	−0.297596	+	0.585337i
$671$		0			0
$672$			1.03617i			0.0399713i
$673$			23.8497i			0.919338i	0.888090	+	0.459669i	$0.152032\pi$
$673$			23.8497i			0.919338i	−0.888090	+	0.459669i	$0.847968\pi$
$674$	18.2067			0.701296
$675$	4.03991	−	2.94604i	0.155496	−	0.113393i
$676$	1.19824			0.0460862
$677$			4.87310i			0.187288i	0.995606	+	0.0936442i	$0.0298516\pi$
$677$			4.87310i			0.187288i	−0.995606	+	0.0936442i	$0.970148\pi$
$678$			13.8075i			0.530275i
$679$	−1.74457			−0.0669505
$680$	7.70973	−	15.1642i	0.295654	−	0.581519i
$681$	−7.72444			−0.296001
$682$		0			0
$683$		−	23.6494i		−	0.904919i	−0.891785	−	0.452459i	$-0.850547\pi$
$683$		−	23.6494i		−	0.904919i	0.891785	−	0.452459i	$-0.149453\pi$
$684$	1.43126			0.0547256
$685$	2.17682	+	1.10673i	0.0831720	+	0.0422861i
$686$	−8.45576			−0.322842
$687$			8.08159i			0.308332i
$688$			18.4031i			0.701613i
$689$	4.97463			0.189518
$690$	21.6144	+	10.9891i	0.822845	+	0.418349i
$691$	13.9286			0.529871			0.264935	−	0.964266i	$-0.414649\pi$
$691$	13.9286			0.529871			0.264935	+	0.964266i	$0.414649\pi$
$692$		−	1.48848i		−	0.0565835i
$693$		0			0
$694$	−20.4156			−0.774966
$695$	−8.53806	+	16.7934i	−0.323867	+	0.637010i
$696$	30.2566			1.14687
$697$			19.7438i			0.747849i
$698$		−	5.05428i		−	0.191307i
$699$	−25.4908			−0.964152
$700$	−0.751171	+	0.547779i	−0.0283916	+	0.0207041i
$701$	−41.2795			−1.55911			−0.779553	−	0.626336i	$-0.784554\pi$
$701$	−41.2795			−1.55911			−0.779553	+	0.626336i	$0.784554\pi$
$702$			3.99597i			0.150818i
$703$		−	11.9329i		−	0.450058i
$704$		0			0
$705$	−6.21313	+	12.2205i	−0.234000	+	0.460251i
$706$	−11.9159			−0.448462
$707$			3.67095i			0.138060i
$708$		−	0.145403i		−	0.00546457i
$709$	−22.2446			−0.835414			−0.417707	−	0.908582i	$-0.637166\pi$
$709$	−22.2446			−0.835414			−0.417707	+	0.908582i	$0.637166\pi$
$710$	−21.1381	−	10.7470i	−0.793300	−	0.403328i
$711$	−7.48541			−0.280725
$712$		−	51.6202i		−	1.93455i
$713$			49.4000i			1.85004i
$714$	−1.54180			−0.0577003
$715$		0			0
$716$	6.61212			0.247106
$717$		−	0.928865i		−	0.0346891i
$718$		−	27.6267i		−	1.03102i
$719$	−34.7352			−1.29540			−0.647702	−	0.761894i	$-0.724270\pi$
$719$	−34.7352			−1.29540			−0.647702	+	0.761894i	$0.724270\pi$
$720$	3.12382	−	6.14421i	0.116418	−	0.228981i
$721$	−1.84017			−0.0685315
$722$			6.55864i			0.244087i
$723$			10.3759i			0.385883i
$724$	−2.68917			−0.0999422
$725$	29.4101	+	40.3301i	1.09226	+	1.49782i
$726$		0			0
$727$			7.34209i			0.272303i	0.990688	+	0.136152i	$0.0434734\pi$
$727$			7.34209i			0.272303i	−0.990688	+	0.136152i	$0.956527\pi$
$728$		−	4.60543i		−	0.170689i
$729$	−1.00000			−0.0370370
$730$	−0.195018	+	0.383578i	−0.00721793	+	0.0141968i
$731$	14.9859			0.554273
$732$			1.15747i			0.0427814i
$733$			32.2227i			1.19017i	0.803662	+	0.595086i	$0.202882\pi$
$733$			32.2227i			1.19017i	−0.803662	+	0.595086i	$0.797118\pi$
$734$	39.8848			1.47218
$735$	−13.4871	−	6.85710i	−0.497481	−	0.252928i
$736$	−18.2929			−0.674287
$737$		0			0
$738$			9.99670i			0.367984i
$739$	−41.9994			−1.54497			−0.772486	−	0.635031i	$-0.780987\pi$
$739$	−41.9994			−1.54497			−0.772486	+	0.635031i	$0.780987\pi$
$740$	2.45983	+	1.25062i	0.0904251	+	0.0459737i
$741$	−11.6966			−0.429686
$742$			0.971834i			0.0356772i
$743$		−	6.94585i		−	0.254819i	−0.991850	−	0.127409i	$-0.959334\pi$
$743$		−	6.94585i		−	0.254819i	0.991850	−	0.127409i	$-0.0406662\pi$
$744$	17.5480			0.643343
$745$	17.4605	−	34.3429i	0.639704	−	1.25823i
$746$	−29.5715			−1.08269
$747$		−	4.05723i		−	0.148446i
$748$		0			0
$749$	−0.230755			−0.00843159
$750$	14.0286	−	2.25988i	0.512252	−	0.0825193i
$751$	1.61163			0.0588092			0.0294046	−	0.999568i	$-0.490639\pi$
$751$	1.61163			0.0588092			0.0294046	+	0.999568i	$0.490639\pi$
$752$			18.8988i			0.689169i
$753$		−	23.5461i		−	0.858066i
$754$	−39.8915			−1.45276
$755$	13.2592	−	26.0793i	0.482550	−	0.949122i
$756$	0.185938			0.00676248
$757$			9.23387i			0.335611i	0.985820	+	0.167805i	$0.0536680\pi$
$757$			9.23387i			0.335611i	−0.985820	+	0.167805i	$0.946332\pi$
$758$			16.8390i			0.611620i
$759$		0			0
$760$	22.4741	+	11.4262i	0.815222	+	0.414473i
$761$	−27.0382			−0.980133			−0.490067	−	0.871685i	$-0.663028\pi$
$761$	−27.0382			−0.980133			−0.490067	+	0.871685i	$0.663028\pi$
$762$			7.61566i			0.275886i
$763$			3.34477i			0.121089i
$764$	−3.84668			−0.139168
$765$	−5.00330	−	2.54377i	−0.180895	−	0.0919700i
$766$	−26.2423			−0.948173
$767$			1.18827i			0.0429058i
$768$			8.86997i			0.320068i
$769$	12.6433			0.455927			0.227964	−	0.973670i	$-0.426793\pi$
$769$	12.6433			0.455927			0.227964	+	0.973670i	$0.426793\pi$
$770$		0			0
$771$	16.0996			0.579813
$772$		−	9.15539i		−	0.329510i
$773$			11.6466i			0.418899i	0.977819	+	0.209449i	$0.0671671\pi$
$773$			11.6466i			0.418899i	−0.977819	+	0.209449i	$0.932833\pi$
$774$	7.58767			0.272733
$775$	17.0571	+	23.3904i	0.612710	+	0.840209i
$776$	−10.9406			−0.392745
$777$		−	1.55023i		−	0.0556141i
$778$			29.0389i			1.04110i
$779$	−29.2614			−1.04840
$780$	1.22586	−	2.41112i	0.0438927	−	0.0863319i
$781$		0			0
$782$		−	27.2194i		−	0.973363i
$783$		−	9.98293i		−	0.356761i
$784$	−20.8576			−0.744916
$785$	46.8583	+	23.8236i	1.67245	+	0.850301i
$786$	−13.9572			−0.497838
$787$		−	8.87396i		−	0.316323i	−0.987413	−	0.158161i	$-0.949443\pi$
$787$		−	8.87396i		−	0.316323i	0.987413	−	0.158161i	$-0.0505566\pi$
$788$			9.47905i			0.337677i
$789$	−2.19036			−0.0779788
$790$	−18.9626	−	9.64093i	−0.674660	−	0.343009i
$791$	−5.25052			−0.186687
$792$		0			0
$793$		−	9.45915i		−	0.335904i
$794$	9.80204			0.347862
$795$	−1.60340	+	3.15371i	−0.0568668	+	0.111851i
$796$	5.90792			0.209401
$797$		−	6.92439i		−	0.245274i	−0.992452	−	0.122637i	$-0.960865\pi$
$797$		−	6.92439i		−	0.245274i	0.992452	−	0.122637i	$-0.0391352\pi$
$798$		−	2.28503i		−	0.0808891i
$799$	15.3895			0.544442
$800$	−8.66154	+	6.31629i	−0.306232	+	0.223315i
$801$	−17.0317			−0.601785
$802$			10.4100i			0.367591i
$803$		0			0
$804$	−2.30101			−0.0811505
$805$	−4.17878	+	8.21919i	−0.147283	+	0.289688i
$806$	−23.1360			−0.814932
$807$		−	10.4351i		−	0.367332i
$808$			23.0214i			0.809889i
$809$	−30.9272			−1.08734			−0.543671	−	0.839299i	$-0.682966\pi$
$809$	−30.9272			−1.08734			−0.543671	+	0.839299i	$0.682966\pi$
$810$	−2.53328	−	1.28796i	−0.0890103	−	0.0452544i
$811$	2.65803			0.0933359			0.0466680	−	0.998910i	$-0.485140\pi$
$811$	2.65803			0.0933359			0.0466680	+	0.998910i	$0.485140\pi$
$812$			1.85620i			0.0651399i
$813$		−	1.72943i		−	0.0606537i
$814$		0			0
$815$	39.7445	+	20.2068i	1.39219	+	0.707813i
$816$	−7.73751			−0.270867
$817$			22.2099i			0.777026i
$818$			4.35048i			0.152111i
$819$	−1.51953			−0.0530966
$820$	3.06672	−	6.03189i	0.107094	−	0.210643i
$821$	8.57136			0.299142			0.149571	−	0.988751i	$-0.452211\pi$
$821$	8.57136			0.299142			0.149571	+	0.988751i	$0.452211\pi$
$822$		−	1.38798i		−	0.0484115i
$823$			44.0892i			1.53685i	0.639939	+	0.768426i	$0.278960\pi$
$823$			44.0892i			1.53685i	−0.639939	+	0.768426i	$0.721040\pi$
$824$	−11.5401			−0.402020
$825$		0			0
$826$	−0.232137			−0.00807710
$827$		−	33.9542i		−	1.18070i	−0.807147	−	0.590351i	$-0.798989\pi$
$827$		−	33.9542i		−	1.18070i	0.807147	−	0.590351i	$-0.201011\pi$
$828$			3.28260i			0.114078i
$829$	−18.2588			−0.634155			−0.317078	−	0.948400i	$-0.602702\pi$
$829$	−18.2588			−0.634155			−0.317078	+	0.948400i	$0.602702\pi$
$830$	5.22556	−	10.2781i	0.181382	−	0.356757i
$831$	−11.6390			−0.403753
$832$		−	27.9510i		−	0.969026i
$833$			16.9846i			0.588482i
$834$	10.7078			0.370781
$835$	38.4222	+	19.5345i	1.32965	+	0.676020i
$836$		0			0
$837$		−	5.78984i		−	0.200126i
$838$		−	23.3334i		−	0.806039i
$839$	26.7364			0.923043			0.461522	−	0.887129i	$-0.347304\pi$
$839$	26.7364			0.923043			0.461522	+	0.887129i	$0.347304\pi$
$840$	2.91965	+	1.48440i	0.100738	+	0.0512168i
$841$	70.6588			2.43651
$842$		−	45.2165i		−	1.55826i
$843$			12.0160i			0.413854i
$844$	9.94947			0.342475
$845$	3.15622	−	6.20792i	0.108577	−	0.213559i
$846$	7.79204			0.267896
$847$		0			0
$848$			4.87716i			0.167482i
$849$	−27.5894			−0.946867
$850$	−9.39846	−	12.8881i	−0.322365	−	0.442059i
$851$	27.3682			0.938170
$852$		−	3.21028i		−	0.109982i
$853$			43.7018i			1.49632i	0.663517	+	0.748161i	$0.269063\pi$
$853$			43.7018i			1.49632i	−0.663517	+	0.748161i	$0.730937\pi$
$854$	1.84792			0.0632345
$855$	3.77000	−	7.41516i	0.128931	−	0.253593i
$856$	−1.44712			−0.0494614
$857$			26.0587i			0.890148i	0.895494	+	0.445074i	$0.146823\pi$
$857$			26.0587i			0.890148i	−0.895494	+	0.445074i	$0.853177\pi$
$858$		0			0
$859$	44.2849			1.51098			0.755491	−	0.655159i	$-0.227398\pi$
$859$	44.2849			1.51098			0.755491	+	0.655159i	$0.227398\pi$
$860$	−4.57831	−	2.32769i	−0.156119	−	0.0793737i
$861$	−3.80140			−0.129551
$862$		−	13.7189i		−	0.467268i
$863$		−	22.2415i		−	0.757110i	−0.925579	−	0.378555i	$-0.876421\pi$
$863$		−	22.2415i		−	0.757110i	0.925579	−	0.378555i	$-0.123579\pi$
$864$	2.14399			0.0729402
$865$	−7.71161	−	3.92072i	−0.262202	−	0.133308i
$866$	−14.1307			−0.480181
$867$		−	10.6993i		−	0.363366i
$868$			1.07655i			0.0365405i
$869$		0			0
$870$	12.8576	−	25.2895i	0.435915	−	0.857395i
$871$	18.8045			0.637165
$872$			20.9759i			0.710332i
$873$			3.60977i			0.122172i
$874$	40.3406			1.36454
$875$	0.859355	+	5.33458i	0.0290515	+	0.180342i
$876$	−0.0582544			−0.00196823
$877$			50.2144i			1.69562i	0.530301	+	0.847809i	$0.322079\pi$
$877$			50.2144i			1.69562i	−0.530301	+	0.847809i	$0.677921\pi$
$878$			15.9757i			0.539154i
$879$	3.42861			0.115644
$880$		0			0
$881$	−31.5451			−1.06278			−0.531391	−	0.847126i	$-0.678331\pi$
$881$	−31.5451			−1.06278			−0.531391	+	0.847126i	$0.678331\pi$
$882$			8.59967i			0.289566i
$883$		−	17.0452i		−	0.573616i	−0.957988	−	0.286808i	$-0.907406\pi$
$883$		−	17.0452i		−	0.573616i	0.957988	−	0.286808i	$-0.0925942\pi$
$884$	−3.03637			−0.102124
$885$	−0.753311	−	0.382997i	−0.0253223	−	0.0128743i
$886$	26.1281			0.877791
$887$		−	14.6249i		−	0.491058i	−0.969389	−	0.245529i	$-0.921038\pi$
$887$		−	14.6249i		−	0.491058i	0.969389	−	0.245529i	$-0.0789616\pi$
$888$		−	9.72183i		−	0.326243i
$889$	−2.89597			−0.0971277
$890$	−43.1460	−	21.9362i	−1.44626	−	0.735302i
$891$		0			0
$892$			2.06527i			0.0691503i
$893$			22.8081i			0.763244i
$894$	−21.8977			−0.732369
$895$	17.4166	−	34.2565i	0.582172	−	1.14507i
$896$	3.38810			0.113188
$897$		−	26.8262i		−	0.895702i
$898$			18.2874i			0.610258i
$899$	57.7996			1.92772
$900$	1.13344	+	1.55428i	0.0377812	+	0.0518094i
$901$	3.97152			0.132311
$902$		0			0
$903$			2.88533i			0.0960177i
$904$	−32.9273			−1.09514
$905$	−7.08339	+	13.9322i	−0.235460	+	0.463123i
$906$	−16.6287			−0.552451
$907$			8.12060i			0.269640i	0.990870	+	0.134820i	$0.0430457\pi$
$907$			8.12060i			0.269640i	−0.990870	+	0.134820i	$0.956954\pi$
$908$		−	2.97184i		−	0.0986240i
$909$	7.59573			0.251934
$910$	−3.84938	−	1.95709i	−0.127606	−	0.0648771i
$911$	7.27282			0.240959			0.120480	−	0.992716i	$-0.461557\pi$
$911$	7.27282			0.240959			0.120480	+	0.992716i	$0.461557\pi$
$912$		−	11.4674i		−	0.379724i
$913$		0			0
$914$	14.3548			0.474814
$915$	5.99670	+	3.04883i	0.198245	+	0.100791i
$916$	−3.10925			−0.102732
$917$		−	5.30744i		−	0.175267i
$918$			3.19020i			0.105292i
$919$	−49.2766			−1.62549			−0.812743	−	0.582623i	$-0.802027\pi$
$919$	−49.2766			−1.62549			−0.812743	+	0.582623i	$0.802027\pi$
$920$	−26.2061	+	51.5445i	−0.863990	+	1.69937i
$921$	−15.3337			−0.505263
$922$			45.5374i			1.49969i
$923$			26.2352i			0.863541i
$924$		0			0
$925$	12.9586	−	9.44985i	0.426076	−	0.310709i
$926$	−38.9139			−1.27879
$927$			3.80758i			0.125057i
$928$			21.4033i			0.702599i
$929$	−17.4708			−0.573200			−0.286600	−	0.958050i	$-0.592525\pi$
$929$	−17.4708			−0.573200			−0.286600	+	0.958050i	$0.592525\pi$
$930$	7.45710	−	14.6673i	0.244528	−	0.480959i
$931$	−25.1721			−0.824983
$932$		−	9.80714i		−	0.321244i
$933$			4.34207i			0.142153i
$934$	50.9204			1.66617
$935$		0			0
$936$	−9.52931			−0.311475
$937$			30.2884i			0.989478i	0.869042	+	0.494739i	$0.164736\pi$
$937$			30.2884i			0.989478i	−0.869042	+	0.494739i	$0.835264\pi$
$938$			3.67360i			0.119947i
$939$	10.4437			0.340816
$940$	−4.70162	−	2.39039i	−0.153350	−	0.0779659i
$941$	−44.5717			−1.45300			−0.726498	−	0.687168i	$-0.758853\pi$
$941$	−44.5717			−1.45300			−0.726498	+	0.687168i	$0.758853\pi$
$942$		−	29.8778i		−	0.973472i
$943$		−	67.1111i		−	2.18544i
$944$	−1.16498			−0.0379170
$945$	0.489767	−	0.963317i	0.0159321	−	0.0313367i
$946$		0			0
$947$			6.29059i			0.204417i	0.994763	+	0.102208i	$0.0325908\pi$
$947$			6.29059i			0.204417i	−0.994763	+	0.102208i	$0.967409\pi$
$948$		−	2.87988i		−	0.0935341i
$949$	0.476069			0.0154539
$950$	19.1009	−	13.9290i	0.619715	−	0.451918i
$951$	−16.6411			−0.539625
$952$		−	3.67677i		−	0.119165i
$953$			11.3115i			0.366417i	0.983074	+	0.183208i	$0.0586483\pi$
$953$			11.3115i			0.366417i	−0.983074	+	0.183208i	$0.941352\pi$
$954$	2.01087			0.0651042
$955$	−10.1323	+	19.9291i	−0.327874	+	0.644892i
$956$	0.357364			0.0115580
$957$		0			0
$958$		−	25.0617i		−	0.809705i
$959$	0.527802			0.0170436
$960$	17.7197	+	9.00903i	0.571902	+	0.290765i
$961$	2.52230			0.0813645
$962$			12.8176i			0.413258i
$963$			0.477465i			0.0153861i
$964$	−3.99193			−0.128571
$965$	−47.4328	−	24.1157i	−1.52692	−	0.776311i
$966$	5.24072			0.168617
$967$			22.1756i			0.713120i	0.934272	+	0.356560i	$0.116050\pi$
$967$			22.1756i			0.713120i	−0.934272	+	0.356560i	$0.883950\pi$
$968$		0			0
$969$	−9.33805			−0.299981
$970$	−4.64926	+	9.14456i	−0.149279	+	0.293614i
$971$	5.37795			0.172587			0.0862933	−	0.996270i	$-0.472498\pi$
$971$	5.37795			0.172587			0.0862933	+	0.996270i	$0.472498\pi$
$972$		−	0.384732i		−	0.0123403i
$973$			4.07180i			0.130536i
$974$	23.0505			0.738585
$975$	−9.26272	−	12.7020i	−0.296644	−	0.406789i
$976$	9.27380			0.296847
$977$		−	3.34749i		−	0.107096i	−0.998565	−	0.0535479i	$-0.982947\pi$
$977$		−	3.34749i		−	0.107096i	0.998565	−	0.0535479i	$-0.0170530\pi$
$978$		−	25.3419i		−	0.810343i
$979$		0			0
$980$	2.63815	−	5.18894i	0.0842725	−	0.165754i
$981$	6.92083			0.220965
$982$		−	13.7477i		−	0.438707i
$983$		−	21.5101i		−	0.686067i	−0.939323	−	0.343034i	$-0.888546\pi$
$983$		−	21.5101i		−	0.686067i	0.939323	−	0.343034i	$-0.111454\pi$
$984$	−23.8395			−0.759974
$985$	49.1096	+	24.9682i	1.56476	+	0.795553i
$986$	−31.8476			−1.01423
$987$			2.96304i			0.0943147i
$988$		−	4.50006i		−	0.143166i
$989$	−50.9385			−1.61975
$990$		0			0
$991$	−3.42838			−0.108906			−0.0544530	−	0.998516i	$-0.517341\pi$
$991$	−3.42838			−0.108906			−0.0544530	+	0.998516i	$0.517341\pi$
$992$			12.4134i			0.394126i
$993$			32.0054i			1.01566i
$994$	−5.12525			−0.162563
$995$	15.5617	−	30.6081i	0.493340	−	0.970343i
$996$	1.56095			0.0494605
$997$			51.3511i			1.62631i	0.582049	+	0.813154i	$0.302251\pi$
$997$			51.3511i			1.62631i	−0.582049	+	0.813154i	$0.697749\pi$
$998$		−	7.20887i		−	0.228193i
$999$	−3.20765			−0.101485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.k.364.7		24
5.2	odd	4		9075.2.a.dx.1.10		12
5.3	odd	4		9075.2.a.ea.1.3		12
5.4	even	2	inner	1815.2.c.k.364.18		24
11.7	odd	10		165.2.s.a.49.4	✓	48
11.8	odd	10		165.2.s.a.64.9	yes	48
11.10	odd	2		1815.2.c.j.364.18		24
33.8	even	10		495.2.ba.c.64.4		48
33.29	even	10		495.2.ba.c.379.9		48
55.7	even	20		825.2.n.o.676.2		24
55.8	even	20		825.2.n.p.526.5		24
55.18	even	20		825.2.n.p.676.5		24
55.19	odd	10		165.2.s.a.64.4	yes	48
55.29	odd	10		165.2.s.a.49.9	yes	48
55.32	even	4		9075.2.a.dz.1.3		12
55.43	even	4		9075.2.a.dy.1.10		12
55.52	even	20		825.2.n.o.526.2		24
55.54	odd	2		1815.2.c.j.364.7		24
165.29	even	10		495.2.ba.c.379.4		48
165.74	even	10		495.2.ba.c.64.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.4	✓	48	11.7	odd	10
165.2.s.a.49.9	yes	48	55.29	odd	10
165.2.s.a.64.4	yes	48	55.19	odd	10
165.2.s.a.64.9	yes	48	11.8	odd	10
495.2.ba.c.64.4		48	33.8	even	10
495.2.ba.c.64.9		48	165.74	even	10
495.2.ba.c.379.4		48	165.29	even	10
495.2.ba.c.379.9		48	33.29	even	10
825.2.n.o.526.2		24	55.52	even	20
825.2.n.o.676.2		24	55.7	even	20
825.2.n.p.526.5		24	55.8	even	20
825.2.n.p.676.5		24	55.18	even	20
1815.2.c.j.364.7		24	55.54	odd	2
1815.2.c.j.364.18		24	11.10	odd	2
1815.2.c.k.364.7		24	1.1	even	1	trivial
1815.2.c.k.364.18		24	5.4	even	2	inner
9075.2.a.dx.1.10		12	5.2	odd	4
9075.2.a.dy.1.10		12	55.43	even	4
9075.2.a.dz.1.3		12	55.32	even	4
9075.2.a.ea.1.3		12	5.3	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)

\(f(q)\)	\(=\)	\(q-1.27093i q^{2} -1.00000i q^{3} +0.384732 q^{4} +(1.01340 - 1.99324i) q^{5} -1.27093 q^{6} -0.483291i q^{7} -3.03083i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.27093i q^{2} -1.00000i q^{3} +0.384732 q^{4} +(1.01340 - 1.99324i) q^{5} -1.27093 q^{6} -0.483291i q^{7} -3.03083i q^{8} -1.00000 q^{9} +(-2.53328 - 1.28796i) q^{10} -0.384732i q^{12} +3.14412i q^{13} -0.614230 q^{14} +(-1.99324 - 1.01340i) q^{15} -3.08252 q^{16} +2.51013i q^{17} +1.27093i q^{18} -3.72015 q^{19} +(0.389888 - 0.766865i) q^{20} -0.483291 q^{21} -8.53218i q^{23} -3.03083 q^{24} +(-2.94604 - 4.03991i) q^{25} +3.99597 q^{26} +1.00000i q^{27} -0.185938i q^{28} -9.98293 q^{29} +(-1.28796 + 2.53328i) q^{30} -5.78984 q^{31} -2.14399i q^{32} +3.19020 q^{34} +(-0.963317 - 0.489767i) q^{35} -0.384732 q^{36} +3.20765i q^{37} +4.72805i q^{38} +3.14412 q^{39} +(-6.04119 - 3.07145i) q^{40} +7.86565 q^{41} +0.614230i q^{42} -5.97016i q^{43} +(-1.01340 + 1.99324i) q^{45} -10.8438 q^{46} -6.13097i q^{47} +3.08252i q^{48} +6.76643 q^{49} +(-5.13445 + 3.74422i) q^{50} +2.51013 q^{51} +1.20965i q^{52} -1.58220i q^{53} +1.27093 q^{54} -1.46477 q^{56} +3.72015i q^{57} +12.6876i q^{58} +0.377932 q^{59} +(-0.766865 - 0.389888i) q^{60} -3.00852 q^{61} +7.35850i q^{62} +0.483291i q^{63} -8.88991 q^{64} +(6.26701 + 3.18626i) q^{65} -5.98082i q^{67} +0.965727i q^{68} -8.53218 q^{69} +(-0.622461 + 1.22431i) q^{70} +8.34418 q^{71} +3.03083i q^{72} -0.151416i q^{73} +4.07670 q^{74} +(-4.03991 + 2.94604i) q^{75} -1.43126 q^{76} -3.99597i q^{78} +7.48541 q^{79} +(-3.12382 + 6.14421i) q^{80} +1.00000 q^{81} -9.99670i q^{82} +4.05723i q^{83} -0.185938 q^{84} +(5.00330 + 2.54377i) q^{85} -7.58767 q^{86} +9.98293i q^{87} +17.0317 q^{89} +(2.53328 + 1.28796i) q^{90} +1.51953 q^{91} -3.28260i q^{92} +5.78984i q^{93} -7.79204 q^{94} +(-3.77000 + 7.41516i) q^{95} -2.14399 q^{96} -3.60977i q^{97} -8.59967i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

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