LMFDB - Embedded newform 1815.2.c.d.364.1

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:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.1
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.d.364.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67513i q^{2} +1.00000i q^{3} -5.15633 q^{4} +(-1.48119 - 1.67513i) q^{5} +2.67513 q^{6} -2.80606i q^{7} +8.44358i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.67513i q^{2} +1.00000i q^{3} -5.15633 q^{4} +(-1.48119 - 1.67513i) q^{5} +2.67513 q^{6} -2.80606i q^{7} +8.44358i q^{8} -1.00000 q^{9} +(-4.48119 + 3.96239i) q^{10} -5.15633i q^{12} -5.11871i q^{13} -7.50659 q^{14} +(1.67513 - 1.48119i) q^{15} +12.2750 q^{16} -4.54420i q^{17} +2.67513i q^{18} -4.57452 q^{19} +(7.63752 + 8.63752i) q^{20} +2.80606 q^{21} -4.00000i q^{23} -8.44358 q^{24} +(-0.612127 + 4.96239i) q^{25} -13.6932 q^{26} -1.00000i q^{27} +14.4690i q^{28} -2.38787 q^{29} +(-3.96239 - 4.48119i) q^{30} -0.962389 q^{31} -15.9502i q^{32} -12.1563 q^{34} +(-4.70052 + 4.15633i) q^{35} +5.15633 q^{36} +1.61213i q^{37} +12.2374i q^{38} +5.11871 q^{39} +(14.1441 - 12.5066i) q^{40} +2.38787 q^{41} -7.50659i q^{42} +2.80606i q^{43} +(1.48119 + 1.67513i) q^{45} -10.7005 q^{46} -4.31265i q^{47} +12.2750i q^{48} -0.873992 q^{49} +(13.2750 + 1.63752i) q^{50} +4.54420 q^{51} +26.3938i q^{52} +6.57452i q^{53} -2.67513 q^{54} +23.6932 q^{56} -4.57452i q^{57} +6.38787i q^{58} +13.2750 q^{59} +(-8.63752 + 7.63752i) q^{60} -7.92478 q^{61} +2.57452i q^{62} +2.80606i q^{63} -18.1187 q^{64} +(-8.57452 + 7.58181i) q^{65} +10.7005i q^{67} +23.4314i q^{68} +4.00000 q^{69} +(11.1187 + 12.5745i) q^{70} -7.35026 q^{71} -8.44358i q^{72} +6.41819i q^{73} +4.31265 q^{74} +(-4.96239 - 0.612127i) q^{75} +23.5877 q^{76} -13.6932i q^{78} +1.35026 q^{79} +(-18.1817 - 20.5623i) q^{80} +1.00000 q^{81} -6.38787i q^{82} -0.806063i q^{83} -14.4690 q^{84} +(-7.61213 + 6.73084i) q^{85} +7.50659 q^{86} -2.38787i q^{87} +2.96239 q^{89} +(4.48119 - 3.96239i) q^{90} -14.3634 q^{91} +20.6253i q^{92} -0.962389i q^{93} -11.5369 q^{94} +(6.77575 + 7.66291i) q^{95} +15.9502 q^{96} -9.92478i q^{97} +2.33804i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^9	$ 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9} - 16 q^{10} - 4 q^{14} + 10 q^{16} - 4 q^{19} + 14 q^{20} + 16 q^{21} - 18 q^{24} - 2 q^{25} - 16 q^{26} - 16 q^{29} - 2 q^{30} + 16 q^{31} - 52 q^{34} + 12 q^{35} + 10 q^{36} - 12 q^{39} + 12 q^{40} + 16 q^{41} - 2 q^{45} - 24 q^{46} - 22 q^{49} + 16 q^{50} + 8 q^{51} - 6 q^{54} + 76 q^{56} + 16 q^{59} - 20 q^{60} - 4 q^{61} - 66 q^{64} - 28 q^{65} + 24 q^{69} + 24 q^{70} - 24 q^{71} - 16 q^{74} - 8 q^{75} + 36 q^{76} - 12 q^{79} - 58 q^{80} + 6 q^{81} - 24 q^{84} - 44 q^{85} + 4 q^{86} - 4 q^{89} + 16 q^{90} + 16 q^{91} - 24 q^{94} + 44 q^{95} + 22 q^{96}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^9 - 16 * q^10 - 4 * q^14 + 10 * q^16 - 4 * q^19 + 14 * q^20 + 16 * q^21 - 18 * q^24 - 2 * q^25 - 16 * q^26 - 16 * q^29 - 2 * q^30 + 16 * q^31 - 52 * q^34 + 12 * q^35 + 10 * q^36 - 12 * q^39 + 12 * q^40 + 16 * q^41 - 2 * q^45 - 24 * q^46 - 22 * q^49 + 16 * q^50 + 8 * q^51 - 6 * q^54 + 76 * q^56 + 16 * q^59 - 20 * q^60 - 4 * q^61 - 66 * q^64 - 28 * q^65 + 24 * q^69 + 24 * q^70 - 24 * q^71 - 16 * q^74 - 8 * q^75 + 36 * q^76 - 12 * q^79 - 58 * q^80 + 6 * q^81 - 24 * q^84 - 44 * q^85 + 4 * q^86 - 4 * q^89 + 16 * q^90 + 16 * q^91 - 24 * q^94 + 44 * q^95 + 22 * 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 $

$2$		−	2.67513i		−	1.89160i	−0.324745	−	0.945802i	$-0.605279\pi$
$2$		−	2.67513i		−	1.89160i	0.324745	−	0.945802i	$-0.394721\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−5.15633			−2.57816
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$6$	2.67513			1.09212
$7$		−	2.80606i		−	1.06059i	−0.847812	−	0.530296i	$-0.822081\pi$
$7$		−	2.80606i		−	1.06059i	0.847812	−	0.530296i	$-0.177919\pi$
$8$			8.44358i			2.98526i
$9$	−1.00000			−0.333333
$10$	−4.48119	+	3.96239i	−1.41708	+	1.25302i
$11$		0			0
$11$		0			0
$12$		−	5.15633i		−	1.48850i
$13$		−	5.11871i		−	1.41968i	−0.704365	−	0.709838i	$-0.748768\pi$
$13$		−	5.11871i		−	1.41968i	0.704365	−	0.709838i	$-0.251232\pi$
$14$	−7.50659			−2.00622
$15$	1.67513	−	1.48119i	0.432517	−	0.382443i
$16$	12.2750			3.06876
$17$		−	4.54420i		−	1.10213i	−0.834462	−	0.551065i	$-0.814222\pi$
$17$		−	4.54420i		−	1.10213i	0.834462	−	0.551065i	$-0.185778\pi$
$18$			2.67513i			0.630534i
$19$	−4.57452			−1.04947			−0.524733	−	0.851267i	$-0.675835\pi$
$19$	−4.57452			−1.04947			−0.524733	+	0.851267i	$0.675835\pi$
$20$	7.63752	+	8.63752i	1.70780	+	1.93141i
$21$	2.80606			0.612333
$22$		0			0
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−8.44358			−1.72354
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$	−13.6932			−2.68546
$27$		−	1.00000i		−	0.192450i
$28$			14.4690i			2.73438i
$29$	−2.38787			−0.443417			−0.221708	−	0.975113i	$-0.571163\pi$
$29$	−2.38787			−0.443417			−0.221708	+	0.975113i	$0.571163\pi$
$30$	−3.96239	−	4.48119i	−0.723430	−	0.818150i
$31$	−0.962389			−0.172850			−0.0864250	−	0.996258i	$-0.527544\pi$
$31$	−0.962389			−0.172850			−0.0864250	+	0.996258i	$0.527544\pi$
$32$		−	15.9502i		−	2.81962i
$33$		0			0
$34$	−12.1563			−2.08479
$35$	−4.70052	+	4.15633i	−0.794533	+	0.702547i
$36$	5.15633			0.859388
$37$			1.61213i			0.265032i	0.991181	+	0.132516i	$0.0423056\pi$
$37$			1.61213i			0.265032i	−0.991181	+	0.132516i	$0.957694\pi$
$38$			12.2374i			1.98517i
$39$	5.11871			0.819650
$40$	14.1441	−	12.5066i	2.23638	−	1.97747i
$41$	2.38787			0.372923			0.186462	−	0.982462i	$-0.440298\pi$
$41$	2.38787			0.372923			0.186462	+	0.982462i	$0.440298\pi$
$42$		−	7.50659i		−	1.15829i
$43$			2.80606i			0.427921i	0.976842	+	0.213960i	$0.0686363\pi$
$43$			2.80606i			0.427921i	−0.976842	+	0.213960i	$0.931364\pi$
$44$		0			0
$45$	1.48119	+	1.67513i	0.220803	+	0.249714i
$46$	−10.7005			−1.57771
$47$		−	4.31265i		−	0.629065i	−0.949247	−	0.314532i	$-0.898152\pi$
$47$		−	4.31265i		−	0.629065i	0.949247	−	0.314532i	$-0.101848\pi$
$48$			12.2750i			1.77175i
$49$	−0.873992			−0.124856
$50$	13.2750	+	1.63752i	1.87737	+	0.231580i
$51$	4.54420			0.636315
$52$			26.3938i			3.66015i
$53$			6.57452i			0.903079i	0.892251	+	0.451540i	$0.149125\pi$
$53$			6.57452i			0.903079i	−0.892251	+	0.451540i	$0.850875\pi$
$54$	−2.67513			−0.364039
$55$		0			0
$56$	23.6932			3.16614
$57$		−	4.57452i		−	0.605909i
$58$			6.38787i			0.838769i
$59$	13.2750			1.72826			0.864131	−	0.503266i	$-0.167868\pi$
$59$	13.2750			1.72826			0.864131	+	0.503266i	$0.167868\pi$
$60$	−8.63752	+	7.63752i	−1.11510	+	0.986000i
$61$	−7.92478			−1.01466			−0.507332	−	0.861751i	$-0.669368\pi$
$61$	−7.92478			−1.01466			−0.507332	+	0.861751i	$0.669368\pi$
$62$			2.57452i			0.326964i
$63$			2.80606i			0.353531i
$64$	−18.1187			−2.26484
$65$	−8.57452	+	7.58181i	−1.06354	+	0.940408i
$66$		0			0
$67$			10.7005i			1.30728i	0.756807	+	0.653639i	$0.226758\pi$
$67$			10.7005i			1.30728i	−0.756807	+	0.653639i	$0.773242\pi$
$68$			23.4314i			2.84147i
$69$	4.00000			0.481543
$70$	11.1187	+	12.5745i	1.32894	+	1.50294i
$71$	−7.35026			−0.872316			−0.436158	−	0.899870i	$-0.643661\pi$
$71$	−7.35026			−0.872316			−0.436158	+	0.899870i	$0.643661\pi$
$72$		−	8.44358i		−	0.995086i
$73$			6.41819i			0.751192i	0.926783	+	0.375596i	$0.122562\pi$
$73$			6.41819i			0.751192i	−0.926783	+	0.375596i	$0.877438\pi$
$74$	4.31265			0.501335
$75$	−4.96239	−	0.612127i	−0.573007	−	0.0706823i
$76$	23.5877			2.70569
$77$		0			0
$78$		−	13.6932i		−	1.55045i
$79$	1.35026			0.151916			0.0759582	−	0.997111i	$-0.475798\pi$
$79$	1.35026			0.151916			0.0759582	+	0.997111i	$0.475798\pi$
$80$	−18.1817	−	20.5623i	−2.03278	−	2.29893i
$81$	1.00000			0.111111
$82$		−	6.38787i		−	0.705423i
$83$		−	0.806063i		−	0.0884770i	−0.999021	−	0.0442385i	$-0.985914\pi$
$83$		−	0.806063i		−	0.0884770i	0.999021	−	0.0442385i	$-0.0140861\pi$
$84$	−14.4690			−1.57869
$85$	−7.61213	+	6.73084i	−0.825651	+	0.730062i
$86$	7.50659			0.809456
$87$		−	2.38787i		−	0.256007i
$88$		0			0
$89$	2.96239			0.314013			0.157006	−	0.987598i	$-0.449816\pi$
$89$	2.96239			0.314013			0.157006	+	0.987598i	$0.449816\pi$
$90$	4.48119	−	3.96239i	0.472359	−	0.417672i
$91$	−14.3634			−1.50570
$92$			20.6253i			2.15034i
$93$		−	0.962389i		−	0.0997950i
$94$	−11.5369			−1.18994
$95$	6.77575	+	7.66291i	0.695177	+	0.786198i
$96$	15.9502			1.62791
$97$		−	9.92478i		−	1.00771i	−0.863789	−	0.503854i	$-0.831915\pi$
$97$		−	9.92478i		−	1.00771i	0.863789	−	0.503854i	$-0.168085\pi$
$98$			2.33804i			0.236178i
$99$		0			0
$100$	3.15633	−	25.5877i	0.315633	−	2.55877i
$101$	13.6121			1.35446			0.677229	−	0.735773i	$-0.263181\pi$
$101$	13.6121			1.35446			0.677229	+	0.735773i	$0.263181\pi$
$102$		−	12.1563i		−	1.20366i
$103$		−	16.3127i		−	1.60733i	−0.595080	−	0.803667i	$-0.702880\pi$
$103$		−	16.3127i		−	1.60733i	0.595080	−	0.803667i	$-0.297120\pi$
$104$	43.2203			4.23810
$105$	−4.15633	−	4.70052i	−0.405616	−	0.458724i
$106$	17.5877			1.70827
$107$			9.43136i			0.911764i	0.890040	+	0.455882i	$0.150676\pi$
$107$			9.43136i			0.911764i	−0.890040	+	0.455882i	$0.849324\pi$
$108$			5.15633i			0.496168i
$109$	−15.4010			−1.47515			−0.737576	−	0.675264i	$-0.764030\pi$
$109$	−15.4010			−1.47515			−0.737576	+	0.675264i	$0.764030\pi$
$110$		0			0
$111$	−1.61213			−0.153016
$112$		−	34.4445i		−	3.25470i
$113$			13.7381i			1.29238i	0.763179	+	0.646188i	$0.223638\pi$
$113$			13.7381i			1.29238i	−0.763179	+	0.646188i	$0.776362\pi$
$114$	−12.2374			−1.14614
$115$	−6.70052	+	5.92478i	−0.624827	+	0.552488i
$116$	12.3127			1.14320
$117$			5.11871i			0.473225i
$118$		−	35.5125i		−	3.26919i
$119$	−12.7513			−1.16891
$120$	12.5066	+	14.1441i	1.14169	+	1.29117i
$121$		0			0
$122$			21.1998i			1.91934i
$123$			2.38787i			0.215307i
$124$	4.96239			0.445636
$125$	9.21933	−	6.32487i	0.824602	−	0.565713i
$126$	7.50659			0.668740
$127$		−	12.4182i		−	1.10194i	−0.834526	−	0.550968i	$-0.814259\pi$
$127$		−	12.4182i		−	1.10194i	0.834526	−	0.550968i	$-0.185741\pi$
$128$			16.5696i			1.46456i
$129$	−2.80606			−0.247060
$130$	20.2823	+	22.9380i	1.77888	+	2.01179i
$131$	−5.92478			−0.517650			−0.258825	−	0.965924i	$-0.583335\pi$
$131$	−5.92478			−0.517650			−0.258825	+	0.965924i	$0.583335\pi$
$132$		0			0
$133$			12.8364i			1.11306i
$134$	28.6253			2.47285
$135$	−1.67513	+	1.48119i	−0.144172	+	0.127481i
$136$	38.3693			3.29014
$137$			9.79877i			0.837165i	0.908179	+	0.418583i	$0.137473\pi$
$137$			9.79877i			0.837165i	−0.908179	+	0.418583i	$0.862527\pi$
$138$		−	10.7005i		−	0.910889i
$139$	−2.12601			−0.180326			−0.0901628	−	0.995927i	$-0.528739\pi$
$139$	−2.12601			−0.180326			−0.0901628	+	0.995927i	$0.528739\pi$
$140$	24.2374	−	21.4314i	2.04844	−	1.81128i
$141$	4.31265			0.363191
$142$			19.6629i			1.65007i
$143$		0			0
$144$	−12.2750			−1.02292
$145$	3.53690	+	4.00000i	0.293724	+	0.332182i
$146$	17.1695			1.42096
$147$		−	0.873992i		−	0.0720856i
$148$		−	8.31265i		−	0.683296i
$149$	8.31265			0.680999			0.340499	−	0.940245i	$-0.389404\pi$
$149$	8.31265			0.680999			0.340499	+	0.940245i	$0.389404\pi$
$150$	−1.63752	+	13.2750i	−0.133703	+	1.08390i
$151$	15.2750			1.24307			0.621533	−	0.783388i	$-0.286510\pi$
$151$	15.2750			1.24307			0.621533	+	0.783388i	$0.286510\pi$
$152$		−	38.6253i		−	3.13293i
$153$			4.54420i			0.367377i
$154$		0			0
$155$	1.42548	+	1.61213i	0.114498	+	0.129489i
$156$	−26.3938			−2.11319
$157$			7.01317i			0.559712i	0.960042	+	0.279856i	$0.0902868\pi$
$157$			7.01317i			0.559712i	−0.960042	+	0.279856i	$0.909713\pi$
$158$		−	3.61213i		−	0.287365i
$159$	−6.57452			−0.521393
$160$	−26.7186	+	23.6253i	−2.11229	+	1.86774i
$161$	−11.2243			−0.884595
$162$		−	2.67513i		−	0.210178i
$163$		−	6.76116i		−	0.529575i	−0.964307	−	0.264787i	$-0.914698\pi$
$163$		−	6.76116i		−	0.529575i	0.964307	−	0.264787i	$-0.0853018\pi$
$164$	−12.3127			−0.961456
$165$		0			0
$166$	−2.15633			−0.167363
$167$			11.8192i			0.914600i	0.889312	+	0.457300i	$0.151183\pi$
$167$			11.8192i			0.914600i	−0.889312	+	0.457300i	$0.848817\pi$
$168$			23.6932i			1.82797i
$169$	−13.2012			−1.01548
$170$	18.0059	+	20.3634i	1.38099	+	1.56180i
$171$	4.57452			0.349822
$172$		−	14.4690i		−	1.10325i
$173$			6.99271i			0.531646i	0.964022	+	0.265823i	$0.0856436\pi$
$173$			6.99271i			0.531646i	−0.964022	+	0.265823i	$0.914356\pi$
$174$	−6.38787			−0.484263
$175$	13.9248	+	1.71767i	1.05261	+	0.129843i
$176$		0			0
$177$			13.2750i			0.997813i
$178$		−	7.92478i		−	0.593987i
$179$	2.70052			0.201847			0.100923	−	0.994894i	$-0.467820\pi$
$179$	2.70052			0.201847			0.100923	+	0.994894i	$0.467820\pi$
$180$	−7.63752	−	8.63752i	−0.569267	−	0.643803i
$181$	−21.1998			−1.57577			−0.787885	−	0.615822i	$-0.788824\pi$
$181$	−21.1998			−1.57577			−0.787885	+	0.615822i	$0.788824\pi$
$182$			38.4241i			2.84818i
$183$		−	7.92478i		−	0.585816i
$184$	33.7743			2.48988
$185$	2.70052	−	2.38787i	0.198546	−	0.175560i
$186$	−2.57452			−0.188773
$187$		0			0
$188$			22.2374i			1.62183i
$189$	−2.80606			−0.204111
$190$	20.4993	−	18.1260i	1.48717	−	1.31500i
$191$	13.1490			0.951430			0.475715	−	0.879599i	$-0.342189\pi$
$191$	13.1490			0.951430			0.475715	+	0.879599i	$0.342189\pi$
$192$		−	18.1187i		−	1.30761i
$193$			5.89446i			0.424293i	0.977238	+	0.212146i	$0.0680453\pi$
$193$			5.89446i			0.424293i	−0.977238	+	0.212146i	$0.931955\pi$
$194$	−26.5501			−1.90618
$195$	−7.58181	−	8.57452i	−0.542945	−	0.614034i
$196$	4.50659			0.321899
$197$		−	20.3938i		−	1.45299i	−0.687169	−	0.726497i	$-0.741147\pi$
$197$		−	20.3938i		−	1.45299i	0.687169	−	0.726497i	$-0.258853\pi$
$198$		0			0
$199$	−17.4010			−1.23353			−0.616764	−	0.787148i	$-0.711557\pi$
$199$	−17.4010			−1.23353			−0.616764	+	0.787148i	$0.711557\pi$
$200$	−41.9003	−	5.16854i	−2.96280	−	0.365471i
$201$	−10.7005			−0.754757
$202$		−	36.4142i		−	2.56210i
$203$			6.70052i			0.470285i
$204$	−23.4314			−1.64052
$205$	−3.53690	−	4.00000i	−0.247028	−	0.279372i
$206$	−43.6385			−3.04044
$207$			4.00000i			0.278019i
$208$		−	62.8324i		−	4.35664i
$209$		0			0
$210$	−12.5745	+	11.1187i	−0.867724	+	0.767264i
$211$	−18.1260			−1.24785			−0.623923	−	0.781486i	$-0.714462\pi$
$211$	−18.1260			−1.24785			−0.623923	+	0.781486i	$0.714462\pi$
$212$		−	33.9003i		−	2.32828i
$213$		−	7.35026i		−	0.503632i
$214$	25.2301			1.72470
$215$	4.70052	−	4.15633i	0.320573	−	0.283459i
$216$	8.44358			0.574513
$217$			2.70052i			0.183323i
$218$			41.1998i			2.79040i
$219$	−6.41819			−0.433701
$220$		0			0
$221$	−23.2605			−1.56467
$222$			4.31265i			0.289446i
$223$		−	23.6385i		−	1.58295i	−0.611202	−	0.791475i	$-0.709314\pi$
$223$		−	23.6385i		−	1.58295i	0.611202	−	0.791475i	$-0.290686\pi$
$224$	−44.7572			−2.99047
$225$	0.612127	−	4.96239i	0.0408085	−	0.330826i
$226$	36.7513			2.44466
$227$			1.26916i			0.0842371i	0.999113	+	0.0421185i	$0.0134107\pi$
$227$			1.26916i			0.0842371i	−0.999113	+	0.0421185i	$0.986589\pi$
$228$			23.5877i			1.56213i
$229$	−16.1768			−1.06899			−0.534496	−	0.845171i	$-0.679499\pi$
$229$	−16.1768			−1.06899			−0.534496	+	0.845171i	$0.679499\pi$
$230$	15.8496	+	17.9248i	1.04509	+	1.18192i
$231$		0			0
$232$		−	20.1622i		−	1.32371i
$233$		−	18.4690i		−	1.20994i	−0.796247	−	0.604971i	$-0.793185\pi$
$233$		−	18.4690i		−	1.20994i	0.796247	−	0.604971i	$-0.206815\pi$
$234$	13.6932			0.895154
$235$	−7.22425	+	6.38787i	−0.471258	+	0.416699i
$236$	−68.4504			−4.45574
$237$			1.35026i			0.0877089i
$238$			34.1114i			2.21111i
$239$	19.3258			1.25008			0.625042	−	0.780591i	$-0.285082\pi$
$239$	19.3258			1.25008			0.625042	+	0.780591i	$0.285082\pi$
$240$	20.5623	−	18.1817i	1.32729	−	1.17362i
$241$	−28.5501			−1.83907			−0.919536	−	0.393006i	$-0.871435\pi$
$241$	−28.5501			−1.83907			−0.919536	+	0.393006i	$0.871435\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	40.8627			2.61597
$245$	1.29455	+	1.46405i	0.0827059	+	0.0935348i
$246$	6.38787			0.407276
$247$			23.4156i			1.48990i
$248$		−	8.12601i		−	0.516002i
$249$	0.806063			0.0510822
$250$	−16.9199	−	24.6629i	−1.07011	−	1.55982i
$251$	23.1998			1.46436			0.732180	−	0.681112i	$-0.238503\pi$
$251$	23.1998			1.46436			0.732180	+	0.681112i	$0.238503\pi$
$252$		−	14.4690i		−	0.911460i
$253$		0			0
$254$	−33.2203			−2.08443
$255$	−6.73084	−	7.61213i	−0.421502	−	0.476690i
$256$	8.08840			0.505525
$257$		−	10.8872i		−	0.679123i	−0.940584	−	0.339561i	$-0.889721\pi$
$257$		−	10.8872i		−	0.679123i	0.940584	−	0.339561i	$-0.110279\pi$
$258$			7.50659i			0.467340i
$259$	4.52373			0.281091
$260$	44.2130	−	39.0943i	2.74197	−	2.42452i
$261$	2.38787			0.147806
$262$			15.8496i			0.979189i
$263$			9.11871i			0.562284i	0.959666	+	0.281142i	$0.0907132\pi$
$263$			9.11871i			0.562284i	−0.959666	+	0.281142i	$0.909287\pi$
$264$		0			0
$265$	11.0132	−	9.73813i	0.676534	−	0.598209i
$266$	34.3390			2.10546
$267$			2.96239i			0.181295i
$268$		−	55.1754i		−	3.37037i
$269$	11.2995			0.688941			0.344471	−	0.938797i	$-0.388058\pi$
$269$	11.2995			0.688941			0.344471	+	0.938797i	$0.388058\pi$
$270$	3.96239	+	4.48119i	0.241143	+	0.272717i
$271$	−25.1998			−1.53078			−0.765390	−	0.643567i	$-0.777454\pi$
$271$	−25.1998			−1.53078			−0.765390	+	0.643567i	$0.777454\pi$
$272$		−	55.7802i		−	3.38217i
$273$		−	14.3634i		−	0.869315i
$274$	26.2130			1.58358
$275$		0			0
$276$	−20.6253			−1.24150
$277$			2.41819i			0.145295i	0.997358	+	0.0726475i	$0.0231448\pi$
$277$			2.41819i			0.145295i	−0.997358	+	0.0726475i	$0.976855\pi$
$278$			5.68735i			0.341105i
$279$	0.962389			0.0576167
$280$	−35.0943	−	39.6893i	−2.09728	−	2.37189i
$281$	−30.4894			−1.81885			−0.909424	−	0.415870i	$-0.863477\pi$
$281$	−30.4894			−1.81885			−0.909424	+	0.415870i	$0.863477\pi$
$282$		−	11.5369i		−	0.687013i
$283$			8.35756i			0.496805i	0.968657	+	0.248403i	$0.0799056\pi$
$283$			8.35756i			0.496805i	−0.968657	+	0.248403i	$0.920094\pi$
$284$	37.9003			2.24897
$285$	−7.66291	+	6.77575i	−0.453912	+	0.401361i
$286$		0			0
$287$		−	6.70052i		−	0.395519i
$288$			15.9502i			0.939873i
$289$	−3.64974			−0.214690
$290$	10.7005	−	9.46168i	0.628356	−	0.555609i
$291$	9.92478			0.581801
$292$		−	33.0943i		−	1.93670i
$293$		−	23.0943i		−	1.34918i	−0.738192	−	0.674591i	$-0.764320\pi$
$293$		−	23.0943i		−	1.34918i	0.738192	−	0.674591i	$-0.235680\pi$
$294$	−2.33804			−0.136357
$295$	−19.6629	−	22.2374i	−1.14482	−	1.29471i
$296$	−13.6121			−0.791189
$297$		0			0
$298$		−	22.2374i		−	1.28818i
$299$	−20.4749			−1.18409
$300$	25.5877	+	3.15633i	1.47731	+	0.182231i
$301$	7.87399			0.453849
$302$		−	40.8627i		−	2.35139i
$303$			13.6121i			0.781996i
$304$	−56.1524			−3.22056
$305$	11.7381	+	13.2750i	0.672124	+	0.760127i
$306$	12.1563			0.694931
$307$		−	2.65562i		−	0.151564i	−0.997124	−	0.0757821i	$-0.975855\pi$
$307$		−	2.65562i		−	0.151564i	0.997124	−	0.0757821i	$-0.0241453\pi$
$308$		0			0
$309$	16.3127			0.927994
$310$	4.31265	−	3.81336i	0.244942	−	0.216584i
$311$	−15.9756			−0.905891			−0.452946	−	0.891538i	$-0.649627\pi$
$311$	−15.9756			−0.905891			−0.452946	+	0.891538i	$0.649627\pi$
$312$			43.2203i			2.44687i
$313$			0.0606343i			0.00342726i	0.999999	+	0.00171363i	$0.000545465\pi$
$313$			0.0606343i			0.00342726i	−0.999999	+	0.00171363i	$0.999455\pi$
$314$	18.7612			1.05875
$315$	4.70052	−	4.15633i	0.264844	−	0.234182i
$316$	−6.96239			−0.391665
$317$			3.81336i			0.214180i	0.994249	+	0.107090i	$0.0341532\pi$
$317$			3.81336i			0.214180i	−0.994249	+	0.107090i	$0.965847\pi$
$318$			17.5877i			0.986269i
$319$		0			0
$320$	26.8373	+	30.3512i	1.50025	+	1.69668i
$321$	−9.43136			−0.526407
$322$			30.0263i			1.67330i
$323$			20.7875i			1.15665i
$324$	−5.15633			−0.286463
$325$	25.4010	+	3.13330i	1.40900	+	0.173804i
$326$	−18.0870			−1.00175
$327$		−	15.4010i		−	0.851680i
$328$			20.1622i			1.11327i
$329$	−12.1016			−0.667181
$330$		0			0
$331$	24.2882			1.33500			0.667500	−	0.744609i	$-0.267364\pi$
$331$	24.2882			1.33500			0.667500	+	0.744609i	$0.267364\pi$
$332$			4.15633i			0.228108i
$333$		−	1.61213i		−	0.0883440i
$334$	31.6180			1.73006
$335$	17.9248	−	15.8496i	0.979335	−	0.865954i
$336$	34.4445			1.87910
$337$			22.5804i			1.23003i	0.788514	+	0.615016i	$0.210851\pi$
$337$			22.5804i			1.23003i	−0.788514	+	0.615016i	$0.789149\pi$
$338$			35.3150i			1.92088i
$339$	−13.7381			−0.746153
$340$	39.2506	−	34.7064i	2.12866	−	1.88222i
$341$		0			0
$342$		−	12.2374i		−	0.661724i
$343$		−	17.1900i		−	0.928171i
$344$	−23.6932			−1.27745
$345$	−5.92478	−	6.70052i	−0.318979	−	0.360744i
$346$	18.7064			1.00566
$347$		−	20.1925i		−	1.08399i	−0.840381	−	0.541996i	$-0.817669\pi$
$347$		−	20.1925i		−	1.08399i	0.840381	−	0.541996i	$-0.182331\pi$
$348$			12.3127i			0.660027i
$349$	−27.2506			−1.45869			−0.729346	−	0.684145i	$-0.760175\pi$
$349$	−27.2506			−1.45869			−0.729346	+	0.684145i	$0.760175\pi$
$350$	4.59498	−	37.2506i	0.245612	−	1.99113i
$351$	−5.11871			−0.273217
$352$		0			0
$353$		−	5.02302i		−	0.267349i	−0.991025	−	0.133674i	$-0.957322\pi$
$353$		−	5.02302i		−	0.267349i	0.991025	−	0.133674i	$-0.0426776\pi$
$354$	35.5125			1.88747
$355$	10.8872	+	12.3127i	0.577831	+	0.653488i
$356$	−15.2750			−0.809575
$357$		−	12.7513i		−	0.674871i
$358$		−	7.22425i		−	0.381814i
$359$	−18.1768			−0.959334			−0.479667	−	0.877450i	$-0.659243\pi$
$359$	−18.1768			−0.959334			−0.479667	+	0.877450i	$0.659243\pi$
$360$	−14.1441	+	12.5066i	−0.745460	+	0.659155i
$361$	1.92619			0.101379
$362$			56.7123i			2.98073i
$363$		0			0
$364$	74.0625			3.88193
$365$	10.7513	−	9.50659i	0.562749	−	0.497598i
$366$	−21.1998			−1.10813
$367$		−	8.56467i		−	0.447072i	−0.974696	−	0.223536i	$-0.928240\pi$
$367$		−	8.56467i		−	0.447072i	0.974696	−	0.223536i	$-0.0717600\pi$
$368$		−	49.1002i		−	2.55952i
$369$	−2.38787			−0.124308
$370$	−6.38787	−	7.22425i	−0.332090	−	0.375571i
$371$	18.4485			0.957799
$372$			4.96239i			0.257288i
$373$			7.81924i			0.404865i	0.979296	+	0.202432i	$0.0648846\pi$
$373$			7.81924i			0.404865i	−0.979296	+	0.202432i	$0.935115\pi$
$374$		0			0
$375$	6.32487	+	9.21933i	0.326615	+	0.476084i
$376$	36.4142			1.87792
$377$			12.2228i			0.629508i
$378$			7.50659i			0.386097i
$379$	−1.14903			−0.0590218			−0.0295109	−	0.999564i	$-0.509395\pi$
$379$	−1.14903			−0.0590218			−0.0295109	+	0.999564i	$0.509395\pi$
$380$	−34.9380	−	39.5125i	−1.79228	−	2.02695i
$381$	12.4182			0.636203
$382$		−	35.1754i		−	1.79973i
$383$		−	34.0870i		−	1.74176i	−0.491493	−	0.870882i	$-0.663549\pi$
$383$		−	34.0870i		−	1.74176i	0.491493	−	0.870882i	$-0.336451\pi$
$384$	−16.5696			−0.845563
$385$		0			0
$386$	15.7685			0.802593
$387$		−	2.80606i		−	0.142640i
$388$			51.1754i			2.59804i
$389$	−23.7743			−1.20541			−0.602703	−	0.797965i	$-0.705910\pi$
$389$	−23.7743			−1.20541			−0.602703	+	0.797965i	$0.705910\pi$
$390$	−22.9380	+	20.2823i	−1.16151	+	1.02704i
$391$	−18.1768			−0.919240
$392$		−	7.37962i		−	0.372727i
$393$		−	5.92478i		−	0.298865i
$394$	−54.5560			−2.74849
$395$	−2.00000	−	2.26187i	−0.100631	−	0.113807i
$396$		0			0
$397$		−	4.15045i		−	0.208305i	−0.994561	−	0.104152i	$-0.966787\pi$
$397$		−	4.15045i		−	0.208305i	0.994561	−	0.104152i	$-0.0332130\pi$
$398$			46.5501i			2.33334i
$399$	−12.8364			−0.642623
$400$	−7.51388	+	60.9135i	−0.375694	+	3.04568i
$401$	−33.9149			−1.69363			−0.846815	−	0.531887i	$-0.821483\pi$
$401$	−33.9149			−1.69363			−0.846815	+	0.531887i	$0.821483\pi$
$402$			28.6253i			1.42770i
$403$			4.92619i			0.245391i
$404$	−70.1886			−3.49201
$405$	−1.48119	−	1.67513i	−0.0736011	−	0.0832379i
$406$	17.9248			0.889592
$407$		0			0
$408$			38.3693i			1.89956i
$409$	8.55008			0.422774			0.211387	−	0.977402i	$-0.432202\pi$
$409$	8.55008			0.422774			0.211387	+	0.977402i	$0.432202\pi$
$410$	−10.7005	+	9.46168i	−0.528461	+	0.467279i
$411$	−9.79877			−0.483338
$412$			84.1133i			4.14397i
$413$		−	37.2506i		−	1.83298i
$414$	10.7005			0.525902
$415$	−1.35026	+	1.19394i	−0.0662817	+	0.0586080i
$416$	−81.6444			−4.00294
$417$		−	2.12601i		−	0.104111i
$418$		0			0
$419$	−13.2995			−0.649722			−0.324861	−	0.945762i	$-0.605318\pi$
$419$	−13.2995			−0.649722			−0.324861	+	0.945762i	$0.605318\pi$
$420$	21.4314	+	24.2374i	1.04574	+	1.18267i
$421$	33.3014			1.62301			0.811505	−	0.584345i	$-0.198649\pi$
$421$	33.3014			1.62301			0.811505	+	0.584345i	$0.198649\pi$
$422$			48.4894i			2.36043i
$423$			4.31265i			0.209688i
$424$	−55.5125			−2.69592
$425$	22.5501	+	2.78163i	1.09384	+	0.134929i
$426$	−19.6629			−0.952671
$427$			22.2374i			1.07614i
$428$		−	48.6312i		−	2.35068i
$429$		0			0
$430$	−11.1187	−	12.5745i	−0.536192	−	0.606397i
$431$	−2.07522			−0.0999600			−0.0499800	−	0.998750i	$-0.515916\pi$
$431$	−2.07522			−0.0999600			−0.0499800	+	0.998750i	$0.515916\pi$
$432$		−	12.2750i		−	0.590583i
$433$			37.4010i			1.79738i	0.438585	+	0.898690i	$0.355480\pi$
$433$			37.4010i			1.79738i	−0.438585	+	0.898690i	$0.644520\pi$
$434$	7.22425			0.346775
$435$	−4.00000	+	3.53690i	−0.191785	+	0.169582i
$436$	79.4128			3.80318
$437$			18.2981i			0.875315i
$438$			17.1695i			0.820390i
$439$	−6.02444			−0.287531			−0.143765	−	0.989612i	$-0.545921\pi$
$439$	−6.02444			−0.287531			−0.143765	+	0.989612i	$0.545921\pi$
$440$		0			0
$441$	0.873992			0.0416187
$442$			62.2247i			2.95973i
$443$			10.1359i			0.481569i	0.970579	+	0.240785i	$0.0774047\pi$
$443$			10.1359i			0.481569i	−0.970579	+	0.240785i	$0.922595\pi$
$444$	8.31265			0.394501
$445$	−4.38787	−	4.96239i	−0.208005	−	0.235240i
$446$	−63.2360			−2.99431
$447$			8.31265i			0.393175i
$448$			50.8423i			2.40207i
$449$	11.4861			0.542063			0.271032	−	0.962570i	$-0.412635\pi$
$449$	11.4861			0.542063			0.271032	+	0.962570i	$0.412635\pi$
$450$	−13.2750	−	1.63752i	−0.625791	−	0.0771934i
$451$		0			0
$452$		−	70.8383i		−	3.33195i
$453$			15.2750i			0.717684i
$454$	3.39517			0.159343
$455$	21.2750	+	24.0606i	0.997389	+	1.12798i
$456$	38.6253			1.80880
$457$			15.0435i			0.703705i	0.936055	+	0.351852i	$0.114448\pi$
$457$			15.0435i			0.703705i	−0.936055	+	0.351852i	$0.885552\pi$
$458$			43.2750i			2.02211i
$459$	−4.54420			−0.212105
$460$	34.5501	−	30.5501i	1.61091	−	1.42440i
$461$	26.2374			1.22200			0.610999	−	0.791631i	$-0.290768\pi$
$461$	26.2374			1.22200			0.610999	+	0.791631i	$0.290768\pi$
$462$		0			0
$463$			5.46168i			0.253826i	0.991914	+	0.126913i	$0.0405069\pi$
$463$			5.46168i			0.253826i	−0.991914	+	0.126913i	$0.959493\pi$
$464$	−29.3112			−1.36074
$465$	−1.61213	+	1.42548i	−0.0747606	+	0.0661053i
$466$	−49.4069			−2.28873
$467$		−	2.70052i		−	0.124965i	−0.998046	−	0.0624827i	$-0.980098\pi$
$467$		−	2.70052i		−	0.124965i	0.998046	−	0.0624827i	$-0.0199018\pi$
$468$		−	26.3938i		−	1.22005i
$469$	30.0263			1.38649
$470$	17.0884	+	19.3258i	0.788229	+	0.891434i
$471$	−7.01317			−0.323150
$472$			112.089i			5.15931i
$473$		0			0
$474$	3.61213			0.165910
$475$	2.80018	−	22.7005i	0.128481	−	1.04157i
$476$	65.7499			3.01364
$477$		−	6.57452i		−	0.301026i
$478$		−	51.6991i		−	2.36466i
$479$	16.7757			0.766503			0.383252	−	0.923644i	$-0.374804\pi$
$479$	16.7757			0.766503			0.383252	+	0.923644i	$0.374804\pi$
$480$	−23.6253	−	26.7186i	−1.07834	−	1.21953i
$481$	8.25202			0.376260
$482$			76.3752i			3.47879i
$483$		−	11.2243i		−	0.510721i
$484$		0			0
$485$	−16.6253	+	14.7005i	−0.754916	+	0.667516i
$486$	2.67513			0.121346
$487$		−	34.3996i		−	1.55880i	−0.626529	−	0.779398i	$-0.715525\pi$
$487$		−	34.3996i		−	1.55880i	0.626529	−	0.779398i	$-0.284475\pi$
$488$		−	66.9135i		−	3.02903i
$489$	6.76116			0.305750
$490$	3.91653	−	3.46310i	0.176931	−	0.156447i
$491$	−14.9525			−0.674799			−0.337399	−	0.941362i	$-0.609547\pi$
$491$	−14.9525			−0.674799			−0.337399	+	0.941362i	$0.609547\pi$
$492$		−	12.3127i		−	0.555097i
$493$			10.8510i			0.488703i
$494$	62.6399			2.81830
$495$		0			0
$496$	−11.8134			−0.530435
$497$			20.6253i			0.925171i
$498$		−	2.15633i		−	0.0966272i
$499$	2.85097			0.127627			0.0638135	−	0.997962i	$-0.479674\pi$
$499$	2.85097			0.127627			0.0638135	+	0.997962i	$0.479674\pi$
$500$	−47.5379	+	32.6131i	−2.12596	+	1.45850i
$501$	−11.8192			−0.528045
$502$		−	62.0625i		−	2.76999i
$503$			1.48024i			0.0660006i	0.999455	+	0.0330003i	$0.0105062\pi$
$503$			1.48024i			0.0660006i	−0.999455	+	0.0330003i	$0.989494\pi$
$504$	−23.6932			−1.05538
$505$	−20.1622	−	22.8021i	−0.897206	−	1.01468i
$506$		0			0
$507$		−	13.2012i		−	0.586287i
$508$			64.0322i			2.84097i
$509$	23.2995			1.03273			0.516366	−	0.856368i	$-0.327285\pi$
$509$	23.2995			1.03273			0.516366	+	0.856368i	$0.327285\pi$
$510$	−20.3634	+	18.0059i	−0.901708	+	0.797314i
$511$	18.0098			0.796709
$512$			11.5017i			0.508306i
$513$			4.57452i			0.201970i
$514$	−29.1246			−1.28463
$515$	−27.3258	+	24.1622i	−1.20412	+	1.06471i
$516$	14.4690			0.636961
$517$		0			0
$518$		−	12.1016i		−	0.531712i
$519$	−6.99271			−0.306946
$520$	−64.0176	−	72.3996i	−2.80736	−	3.17493i
$521$	−6.81194			−0.298437			−0.149218	−	0.988804i	$-0.547676\pi$
$521$	−6.81194			−0.298437			−0.149218	+	0.988804i	$0.547676\pi$
$522$		−	6.38787i		−	0.279590i
$523$		−	16.0567i		−	0.702109i	−0.936355	−	0.351054i	$-0.885823\pi$
$523$		−	16.0567i		−	0.702109i	0.936355	−	0.351054i	$-0.114177\pi$
$524$	30.5501			1.33459
$525$	−1.71767	+	13.9248i	−0.0749651	+	0.607727i
$526$	24.3938			1.06362
$527$			4.37328i			0.190503i
$528$		0			0
$529$	7.00000			0.304348
$530$	−26.0508	−	29.4617i	−1.13157	−	1.27973i
$531$	−13.2750			−0.576088
$532$		−	66.1886i		−	2.86964i
$533$		−	12.2228i		−	0.529430i
$534$	7.92478			0.342939
$535$	15.7988	−	13.9697i	0.683040	−	0.603962i
$536$	−90.3508			−3.90256
$537$			2.70052i			0.116536i
$538$		−	30.2276i		−	1.30320i
$539$		0			0
$540$	8.63752	−	7.63752i	0.371700	−	0.328667i
$541$	−6.62530			−0.284844			−0.142422	−	0.989806i	$-0.545489\pi$
$541$	−6.62530			−0.284844			−0.142422	+	0.989806i	$0.545489\pi$
$542$			67.4128i			2.89563i
$543$		−	21.1998i		−	0.909771i
$544$	−72.4807			−3.10759
$545$	22.8119	+	25.7988i	0.977156	+	1.10510i
$546$	−38.4241			−1.64440
$547$			5.75860i			0.246220i	0.992393	+	0.123110i	$0.0392868\pi$
$547$			5.75860i			0.246220i	−0.992393	+	0.123110i	$0.960713\pi$
$548$		−	50.5256i		−	2.15835i
$549$	7.92478			0.338221
$550$		0			0
$551$	10.9234			0.465351
$552$			33.7743i			1.43753i
$553$		−	3.78892i		−	0.161121i
$554$	6.46898			0.274840
$555$	2.38787	+	2.70052i	0.101360	+	0.114631i
$556$	10.9624			0.464909
$557$		−	19.8700i		−	0.841920i	−0.907079	−	0.420960i	$-0.861693\pi$
$557$		−	19.8700i		−	0.841920i	0.907079	−	0.420960i	$-0.138307\pi$
$558$		−	2.57452i		−	0.108988i
$559$	14.3634			0.607509
$560$	−57.6991	+	51.0191i	−2.43823	+	2.15595i
$561$		0			0
$562$			81.5633i			3.44054i
$563$			5.83383i			0.245866i	0.992415	+	0.122933i	$0.0392301\pi$
$563$			5.83383i			0.245866i	−0.992415	+	0.122933i	$0.960770\pi$
$564$	−22.2374			−0.936365
$565$	23.0132	−	20.3488i	0.968171	−	0.856082i
$566$	22.3576			0.939758
$567$		−	2.80606i		−	0.117844i
$568$		−	62.0625i		−	2.60409i
$569$	46.7123			1.95828			0.979140	−	0.203185i	$-0.0651293\pi$
$569$	46.7123			1.95828			0.979140	+	0.203185i	$0.0651293\pi$
$570$	18.1260	+	20.4993i	0.759215	+	0.858621i
$571$	24.4241			1.02212			0.511058	−	0.859546i	$-0.329254\pi$
$571$	24.4241			1.02212			0.511058	+	0.859546i	$0.329254\pi$
$572$		0			0
$573$			13.1490i			0.549309i
$574$	−17.9248			−0.748166
$575$	19.8496	+	2.44851i	0.827784	+	0.102110i
$576$	18.1187			0.754946
$577$			16.5647i			0.689596i	0.938677	+	0.344798i	$0.112053\pi$
$577$			16.5647i			0.689596i	−0.938677	+	0.344798i	$0.887947\pi$
$578$			9.76353i			0.406109i
$579$	−5.89446			−0.244965
$580$	−18.2374	−	20.6253i	−0.757268	−	0.856419i
$581$	−2.26187			−0.0938380
$582$		−	26.5501i		−	1.10054i
$583$		0			0
$584$	−54.1925			−2.24250
$585$	8.57452	−	7.58181i	0.354513	−	0.313469i
$586$	−61.7802			−2.55212
$587$			27.3258i			1.12786i	0.825823	+	0.563929i	$0.190711\pi$
$587$			27.3258i			1.12786i	−0.825823	+	0.563929i	$0.809289\pi$
$588$			4.50659i			0.185849i
$589$	4.40246			0.181400
$590$	−59.4880	+	52.6009i	−2.44908	+	2.16554i
$591$	20.3938			0.838887
$592$			19.7889i			0.813320i
$593$		−	12.6048i		−	0.517618i	−0.965928	−	0.258809i	$-0.916670\pi$
$593$		−	12.6048i		−	0.517618i	0.965928	−	0.258809i	$-0.0833301\pi$
$594$		0			0
$595$	18.8872	+	21.3601i	0.774298	+	0.875679i
$596$	−42.8627			−1.75573
$597$		−	17.4010i		−	0.712177i
$598$			54.7729i			2.23983i
$599$	−10.5990			−0.433061			−0.216531	−	0.976276i	$-0.569474\pi$
$599$	−10.5990			−0.433061			−0.216531	+	0.976276i	$0.569474\pi$
$600$	5.16854	−	41.9003i	0.211005	−	1.71057i
$601$	22.4749			0.916768			0.458384	−	0.888754i	$-0.348428\pi$
$601$	22.4749			0.916768			0.458384	+	0.888754i	$0.348428\pi$
$602$		−	21.0640i		−	0.858503i
$603$		−	10.7005i		−	0.435759i
$604$	−78.7631			−3.20482
$605$		0			0
$606$	36.4142			1.47923
$607$		−	33.5183i		−	1.36047i	−0.732995	−	0.680234i	$-0.761878\pi$
$607$		−	33.5183i		−	1.36047i	0.732995	−	0.680234i	$-0.238122\pi$
$608$			72.9643i			2.95909i
$609$	−6.70052			−0.271519
$610$	35.5125	−	31.4010i	1.43786	−	1.27139i
$611$	−22.0752			−0.893068
$612$		−	23.4314i		−	0.947157i
$613$			11.5672i			0.467196i	0.972333	+	0.233598i	$0.0750499\pi$
$613$			11.5672i			0.467196i	−0.972333	+	0.233598i	$0.924950\pi$
$614$	−7.10413			−0.286699
$615$	4.00000	−	3.53690i	0.161296	−	0.142622i
$616$		0			0
$617$		−	33.3357i		−	1.34204i	−0.741438	−	0.671022i	$-0.765856\pi$
$617$		−	33.3357i		−	1.34204i	0.741438	−	0.671022i	$-0.234144\pi$
$618$		−	43.6385i		−	1.75540i
$619$	−4.43866			−0.178405			−0.0892024	−	0.996014i	$-0.528432\pi$
$619$	−4.43866			−0.178405			−0.0892024	+	0.996014i	$0.528432\pi$
$620$	−7.35026	−	8.31265i	−0.295194	−	0.333844i
$621$	−4.00000			−0.160514
$622$			42.7367i			1.71359i
$623$		−	8.31265i		−	0.333039i
$624$	62.8324			2.51531
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	0.162205			0.00648301
$627$		0			0
$628$		−	36.1622i		−	1.44303i
$629$	7.32582			0.292100
$630$	−11.1187	−	12.5745i	−0.442980	−	0.500981i
$631$	−39.8496			−1.58639			−0.793193	−	0.608971i	$-0.791583\pi$
$631$	−39.8496			−1.58639			−0.793193	+	0.608971i	$0.791583\pi$
$632$			11.4010i			0.453509i
$633$		−	18.1260i		−	0.720444i
$634$	10.2012			0.405143
$635$	−20.8021	+	18.3938i	−0.825506	+	0.729934i
$636$	33.9003			1.34424
$637$			4.47371i			0.177255i
$638$		0			0
$639$	7.35026			0.290772
$640$	27.7562	−	24.5428i	1.09716	−	0.970139i
$641$	−3.88858			−0.153590			−0.0767948	−	0.997047i	$-0.524469\pi$
$641$	−3.88858			−0.153590			−0.0767948	+	0.997047i	$0.524469\pi$
$642$			25.2301i			0.995754i
$643$		−	40.9380i		−	1.61444i	−0.590254	−	0.807218i	$-0.700972\pi$
$643$		−	40.9380i		−	1.61444i	0.590254	−	0.807218i	$-0.299028\pi$
$644$	57.8759			2.28063
$645$	4.15633	+	4.70052i	0.163655	+	0.185083i
$646$	55.6093			2.18792
$647$			1.76257i			0.0692939i	0.999400	+	0.0346469i	$0.0110307\pi$
$647$			1.76257i			0.0692939i	−0.999400	+	0.0346469i	$0.988969\pi$
$648$			8.44358i			0.331695i
$649$		0			0
$650$	8.38199	−	67.9511i	0.328769	−	2.66526i
$651$	−2.70052			−0.105842
$652$			34.8627i			1.36533i
$653$			7.03761i			0.275403i	0.990474	+	0.137702i	$0.0439715\pi$
$653$			7.03761i			0.275403i	−0.990474	+	0.137702i	$0.956029\pi$
$654$	−41.1998			−1.61104
$655$	8.77575	+	9.92478i	0.342897	+	0.387793i
$656$	29.3112			1.14441
$657$		−	6.41819i		−	0.250397i
$658$			32.3733i			1.26204i
$659$	−12.6253			−0.491812			−0.245906	−	0.969294i	$-0.579085\pi$
$659$	−12.6253			−0.491812			−0.245906	+	0.969294i	$0.579085\pi$
$660$		0			0
$661$	13.2243			0.514364			0.257182	−	0.966363i	$-0.417206\pi$
$661$	13.2243			0.514364			0.257182	+	0.966363i	$0.417206\pi$
$662$		−	64.9741i		−	2.52529i
$663$		−	23.2605i		−	0.903361i
$664$	6.80606			0.264126
$665$	21.5026	−	19.0132i	0.833836	−	0.737299i
$666$	−4.31265			−0.167112
$667$			9.55149i			0.369835i
$668$		−	60.9438i		−	2.35799i
$669$	23.6385			0.913916
$670$	−42.3996	−	47.9511i	−1.63804	−	1.85251i
$671$		0			0
$672$		−	44.7572i		−	1.72655i
$673$			18.2677i			0.704170i	0.935968	+	0.352085i	$0.114527\pi$
$673$			18.2677i			0.704170i	−0.935968	+	0.352085i	$0.885473\pi$
$674$	60.4055			2.32673
$675$	4.96239	+	0.612127i	0.191002	+	0.0235608i
$676$	68.0698			2.61807
$677$			33.0191i			1.26903i	0.772912	+	0.634513i	$0.218799\pi$
$677$			33.0191i			1.26903i	−0.772912	+	0.634513i	$0.781201\pi$
$678$			36.7513i			1.41143i
$679$	−27.8496			−1.06877
$680$	−56.8324	−	64.2736i	−2.17942	−	2.46478i
$681$	−1.26916			−0.0486343
$682$		0			0
$683$		−	30.8627i		−	1.18093i	−0.807063	−	0.590465i	$-0.798944\pi$
$683$		−	30.8627i		−	1.18093i	0.807063	−	0.590465i	$-0.201056\pi$
$684$	−23.5877			−0.901898
$685$	16.4142	−	14.5139i	0.627155	−	0.554547i
$686$	−45.9854			−1.75573
$687$		−	16.1768i		−	0.617183i
$688$			34.4445i			1.31319i
$689$	33.6531			1.28208
$690$	−17.9248	+	15.8496i	−0.682385	+	0.603382i
$691$	27.6991			1.05372			0.526862	−	0.849951i	$-0.323369\pi$
$691$	27.6991			1.05372			0.526862	+	0.849951i	$0.323369\pi$
$692$		−	36.0567i		−	1.37067i
$693$		0			0
$694$	−54.0176			−2.05048
$695$	3.14903	+	3.56134i	0.119450	+	0.135089i
$696$	20.1622			0.764246
$697$		−	10.8510i		−	0.411010i
$698$			72.8989i			2.75927i
$699$	18.4690			0.698561
$700$	−71.8007	−	8.85685i	−2.71381	−	0.334757i
$701$	38.9643			1.47166			0.735831	−	0.677166i	$-0.236792\pi$
$701$	38.9643			1.47166			0.735831	+	0.677166i	$0.236792\pi$
$702$			13.6932i			0.516818i
$703$		−	7.37470i		−	0.278142i
$704$		0			0
$705$	−6.38787	−	7.22425i	−0.240581	−	0.272081i
$706$	−13.4372			−0.505717
$707$		−	38.1965i		−	1.43653i
$708$		−	68.4504i		−	2.57252i
$709$	4.32250			0.162335			0.0811674	−	0.996700i	$-0.474135\pi$
$709$	4.32250			0.162335			0.0811674	+	0.996700i	$0.474135\pi$
$710$	32.9380	−	29.1246i	1.23614	−	1.09303i
$711$	−1.35026			−0.0506388
$712$			25.0132i			0.937408i
$713$			3.84955i			0.144167i
$714$	−34.1114			−1.27659
$715$		0			0
$716$	−13.9248			−0.520393
$717$			19.3258i			0.721736i
$718$			48.6253i			1.81468i
$719$	38.3996			1.43206			0.716032	−	0.698067i	$-0.245956\pi$
$719$	38.3996			1.43206			0.716032	+	0.698067i	$0.245956\pi$
$720$	18.1817	+	20.5623i	0.677593	+	0.766312i
$721$	−45.7743			−1.70473
$722$		−	5.15282i		−	0.191768i
$723$		−	28.5501i		−	1.06179i
$724$	109.313			4.06259
$725$	1.46168	−	11.8496i	0.0542855	−	0.440081i
$726$		0			0
$727$		−	21.6728i		−	0.803798i	−0.915684	−	0.401899i	$-0.868350\pi$
$727$		−	21.6728i		−	0.803798i	0.915684	−	0.401899i	$-0.131650\pi$
$728$		−	121.279i		−	4.49489i
$729$	−1.00000			−0.0370370
$730$	−25.4314	−	28.7612i	−0.941257	−	1.06450i
$731$	12.7513			0.471624
$732$			40.8627i			1.51033i
$733$			25.0698i			0.925976i	0.886365	+	0.462988i	$0.153223\pi$
$733$			25.0698i			0.925976i	−0.886365	+	0.462988i	$0.846777\pi$
$734$	−22.9116			−0.845683
$735$	−1.46405	+	1.29455i	−0.0540023	+	0.0477503i
$736$	−63.8007			−2.35172
$737$		0			0
$738$			6.38787i			0.235141i
$739$	−18.9018			−0.695312			−0.347656	−	0.937622i	$-0.613022\pi$
$739$	−18.9018			−0.695312			−0.347656	+	0.937622i	$0.613022\pi$
$740$	−13.9248	+	12.3127i	−0.511885	+	0.452622i
$741$	−23.4156			−0.860195
$742$		−	49.3522i		−	1.81178i
$743$			43.6688i			1.60205i	0.598629	+	0.801026i	$0.295712\pi$
$743$			43.6688i			1.60205i	−0.598629	+	0.801026i	$0.704288\pi$
$744$	8.12601			0.297914
$745$	−12.3127	−	13.9248i	−0.451101	−	0.510164i
$746$	20.9175			0.765843
$747$			0.806063i			0.0294923i
$748$		0			0
$749$	26.4650			0.967010
$750$	24.6629	−	16.9199i	0.900562	−	0.617826i
$751$	−47.0541			−1.71703			−0.858514	−	0.512789i	$-0.828612\pi$
$751$	−47.0541			−1.71703			−0.858514	+	0.512789i	$0.828612\pi$
$752$		−	52.9380i		−	1.93045i
$753$			23.1998i			0.845448i
$754$	32.6977			1.19078
$755$	−22.6253	−	25.5877i	−0.823419	−	0.931231i
$756$	14.4690			0.526232
$757$		−	26.9116i		−	0.978119i	−0.872250	−	0.489059i	$-0.837340\pi$
$757$		−	26.9116i		−	0.978119i	0.872250	−	0.489059i	$-0.162660\pi$
$758$			3.07381i			0.111646i
$759$		0			0
$760$	−64.7024	+	57.2116i	−2.34700	+	2.07528i
$761$	−16.6859			−0.604865			−0.302432	−	0.953171i	$-0.597799\pi$
$761$	−16.6859			−0.604865			−0.302432	+	0.953171i	$0.597799\pi$
$762$		−	33.2203i		−	1.20344i
$763$			43.2163i			1.56454i
$764$	−67.8007			−2.45294
$765$	7.61213	−	6.73084i	0.275217	−	0.243354i
$766$	−91.1871			−3.29473
$767$		−	67.9511i		−	2.45357i
$768$			8.08840i			0.291865i
$769$	23.2995			0.840201			0.420100	−	0.907478i	$-0.361995\pi$
$769$	23.2995			0.840201			0.420100	+	0.907478i	$0.361995\pi$
$770$		0			0
$771$	10.8872			0.392092
$772$		−	30.3938i		−	1.09390i
$773$			1.63656i			0.0588631i	0.999567	+	0.0294316i	$0.00936971\pi$
$773$			1.63656i			0.0588631i	−0.999567	+	0.0294316i	$0.990630\pi$
$774$	−7.50659			−0.269819
$775$	0.589104	−	4.77575i	0.0211612	−	0.171550i
$776$	83.8007			3.00827
$777$			4.52373i			0.162288i
$778$			63.5994i			2.28015i
$779$	−10.9234			−0.391370
$780$	39.0943	+	44.2130i	1.39980	+	1.58308i
$781$		0			0
$782$			48.6253i			1.73884i
$783$			2.38787i			0.0853356i
$784$	−10.7283			−0.383153
$785$	11.7480	−	10.3879i	0.419304	−	0.370759i
$786$	−15.8496			−0.565335
$787$			2.09095i			0.0745344i	0.999305	+	0.0372672i	$0.0118653\pi$
$787$			2.09095i			0.0745344i	−0.999305	+	0.0372672i	$0.988135\pi$
$788$			105.157i			3.74606i
$789$	−9.11871			−0.324635
$790$	−6.05079	+	5.35026i	−0.215277	+	0.190354i
$791$	38.5501			1.37068
$792$		0			0
$793$			40.5647i			1.44049i
$794$	−11.1030			−0.394030
$795$	9.73813	+	11.0132i	0.345376	+	0.390597i
$796$	89.7255			3.18023
$797$		−	26.8872i		−	0.952392i	−0.879339	−	0.476196i	$-0.842015\pi$
$797$		−	26.8872i		−	0.952392i	0.879339	−	0.476196i	$-0.157985\pi$
$798$			34.3390i			1.21559i
$799$	−19.5975			−0.693311
$800$	79.1509	+	9.76353i	2.79841	+	0.345193i
$801$	−2.96239			−0.104671
$802$			90.7269i			3.20368i
$803$		0			0
$804$	55.1754			1.94589
$805$	16.6253	+	18.8021i	0.585965	+	0.662687i
$806$	13.1782			0.464183
$807$			11.2995i			0.397760i
$808$			114.935i			4.04340i
$809$	−45.4128			−1.59663			−0.798315	−	0.602241i	$-0.794275\pi$
$809$	−45.4128			−1.59663			−0.798315	+	0.602241i	$0.794275\pi$
$810$	−4.48119	+	3.96239i	−0.157453	+	0.139224i
$811$	−34.3488			−1.20615			−0.603076	−	0.797684i	$-0.706058\pi$
$811$	−34.3488			−1.20615			−0.603076	+	0.797684i	$0.706058\pi$
$812$		−	34.5501i		−	1.21247i
$813$		−	25.1998i		−	0.883796i
$814$		0			0
$815$	−11.3258	+	10.0146i	−0.396726	+	0.350796i
$816$	55.7802			1.95270
$817$		−	12.8364i		−	0.449088i
$818$		−	22.8726i		−	0.799721i
$819$	14.3634			0.501899
$820$	18.2374	+	20.6253i	0.636879	+	0.720267i
$821$	−18.7612			−0.654769			−0.327384	−	0.944891i	$-0.606167\pi$
$821$	−18.7612			−0.654769			−0.327384	+	0.944891i	$0.606167\pi$
$822$			26.2130i			0.914283i
$823$			33.0592i			1.15237i	0.817319	+	0.576186i	$0.195460\pi$
$823$			33.0592i			1.15237i	−0.817319	+	0.576186i	$0.804540\pi$
$824$	137.737			4.79830
$825$		0			0
$826$	−99.6502			−3.46728
$827$			10.8813i			0.378379i	0.981941	+	0.189190i	$0.0605861\pi$
$827$			10.8813i			0.378379i	−0.981941	+	0.189190i	$0.939414\pi$
$828$		−	20.6253i		−	0.716779i
$829$	−42.7221			−1.48380			−0.741900	−	0.670510i	$-0.766075\pi$
$829$	−42.7221			−1.48380			−0.741900	+	0.670510i	$0.766075\pi$
$830$	3.19394	+	3.61213i	0.110863	+	0.125379i
$831$	−2.41819			−0.0838861
$832$			92.7445i			3.21534i
$833$			3.97159i			0.137608i
$834$	−5.68735			−0.196937
$835$	19.7988	−	17.5066i	0.685165	−	0.605840i
$836$		0			0
$837$			0.962389i			0.0332650i
$838$			35.5778i			1.22902i
$839$	21.1735			0.730989			0.365495	−	0.930813i	$-0.380900\pi$
$839$	21.1735			0.730989			0.365495	+	0.930813i	$0.380900\pi$
$840$	39.6893	−	35.0943i	1.36941	−	1.21087i
$841$	−23.2981			−0.803381
$842$		−	89.0856i		−	3.07009i
$843$		−	30.4894i		−	1.05011i
$844$	93.4636			3.21715
$845$	19.5536	+	22.1138i	0.672664	+	0.760737i
$846$	11.5369			0.396647
$847$		0			0
$848$			80.7024i			2.77133i
$849$	−8.35756			−0.286831
$850$	7.44121	−	60.3244i	0.255232	−	2.06911i
$851$	6.44851			0.221052
$852$			37.9003i			1.29844i
$853$			54.4709i			1.86505i	0.361109	+	0.932524i	$0.382398\pi$
$853$			54.4709i			1.86505i	−0.361109	+	0.932524i	$0.617602\pi$
$854$	59.4880			2.03564
$855$	−6.77575	−	7.66291i	−0.231726	−	0.262066i
$856$	−79.6345			−2.72185
$857$		−	38.5705i		−	1.31754i	−0.752342	−	0.658772i	$-0.771076\pi$
$857$		−	38.5705i		−	1.31754i	0.752342	−	0.658772i	$-0.228924\pi$
$858$		0			0
$859$	18.5139			0.631685			0.315843	−	0.948812i	$-0.397713\pi$
$859$	18.5139			0.631685			0.315843	+	0.948812i	$0.397713\pi$
$860$	−24.2374	+	21.4314i	−0.826489	+	0.730803i
$861$	6.70052			0.228353
$862$			5.55149i			0.189085i
$863$		−	22.5383i		−	0.767213i	−0.923497	−	0.383607i	$-0.874682\pi$
$863$		−	22.5383i		−	0.767213i	0.923497	−	0.383607i	$-0.125318\pi$
$864$	−15.9502			−0.542636
$865$	11.7137	−	10.3576i	0.398278	−	0.352167i
$866$	100.053			3.39993
$867$		−	3.64974i		−	0.123952i
$868$		−	13.9248i		−	0.472638i
$869$		0			0
$870$	9.46168	+	10.7005i	0.320781	+	0.362782i
$871$	54.7729			1.85591
$872$		−	130.040i		−	4.40371i
$873$			9.92478i			0.335903i
$874$	48.9497			1.65575
$875$	−17.7480	−	25.8700i	−0.599991	−	0.874566i
$876$	33.0943			1.11815
$877$		−	18.9419i		−	0.639623i	−0.947481	−	0.319812i	$-0.896380\pi$
$877$		−	18.9419i		−	0.639623i	0.947481	−	0.319812i	$-0.103620\pi$
$878$			16.1162i			0.543894i
$879$	23.0943			0.778951
$880$		0			0
$881$	−20.0263			−0.674705			−0.337352	−	0.941378i	$-0.609531\pi$
$881$	−20.0263			−0.674705			−0.337352	+	0.941378i	$0.609531\pi$
$882$		−	2.33804i		−	0.0787260i
$883$		−	22.2981i		−	0.750390i	−0.926946	−	0.375195i	$-0.877576\pi$
$883$		−	22.2981i		−	0.750390i	0.926946	−	0.375195i	$-0.122424\pi$
$884$	119.938			4.03397
$885$	22.2374	−	19.6629i	0.747503	−	0.660962i
$886$	27.1147			0.910938
$887$		−	3.10413i		−	0.104226i	−0.998641	−	0.0521132i	$-0.983404\pi$
$887$		−	3.10413i		−	0.104226i	0.998641	−	0.0521132i	$-0.0165957\pi$
$888$		−	13.6121i		−	0.456793i
$889$	−34.8462			−1.16871
$890$	−13.2750	+	11.7381i	−0.444980	+	0.393463i
$891$		0			0
$892$			121.888i			4.08110i
$893$			19.7283i			0.660182i
$894$	22.2374			0.743731
$895$	−4.00000	−	4.52373i	−0.133705	−	0.151212i
$896$	46.4953			1.55330
$897$		−	20.4749i		−	0.683636i
$898$		−	30.7269i		−	1.02537i
$899$	2.29806			0.0766447
$900$	−3.15633	+	25.5877i	−0.105211	+	0.852923i
$901$	29.8759			0.995311
$902$		0			0
$903$			7.87399i			0.262030i
$904$	−115.999			−3.85807
$905$	31.4010	+	35.5125i	1.04381	+	1.18047i
$906$	40.8627			1.35757
$907$			10.8627i			0.360691i	0.983603	+	0.180345i	$0.0577216\pi$
$907$			10.8627i			0.360691i	−0.983603	+	0.180345i	$0.942278\pi$
$908$		−	6.54420i		−	0.217177i
$909$	−13.6121			−0.451486
$910$	64.3653	−	56.9135i	2.13369	−	1.88666i
$911$	−5.82321			−0.192931			−0.0964657	−	0.995336i	$-0.530754\pi$
$911$	−5.82321			−0.192931			−0.0964657	+	0.995336i	$0.530754\pi$
$912$		−	56.1524i		−	1.85939i
$913$		0			0
$914$	40.2433			1.33113
$915$	−13.2750	+	11.7381i	−0.438859	+	0.388051i
$916$	83.4128			2.75604
$917$			16.6253i			0.549016i
$918$			12.1563i			0.401219i
$919$	−31.2750			−1.03167			−0.515834	−	0.856688i	$-0.672518\pi$
$919$	−31.2750			−1.03167			−0.515834	+	0.856688i	$0.672518\pi$
$920$	−50.0263	−	56.5764i	−1.64932	−	1.86527i
$921$	2.65562			0.0875056
$922$		−	70.1886i		−	2.31154i
$923$			37.6239i			1.23841i
$924$		0			0
$925$	−8.00000	−	0.986826i	−0.263038	−	0.0324466i
$926$	14.6107			0.480138
$927$			16.3127i			0.535778i
$928$			38.0870i			1.25027i
$929$	21.2243			0.696345			0.348173	−	0.937430i	$-0.386802\pi$
$929$	21.2243			0.696345			0.348173	+	0.937430i	$0.386802\pi$
$930$	3.81336	+	4.31265i	0.125045	+	0.141417i
$931$	3.99809			0.131032
$932$			95.2320i			3.11943i
$933$		−	15.9756i		−	0.523016i
$934$	−7.22425			−0.236385
$935$		0			0
$936$	−43.2203			−1.41270
$937$		−	16.4328i		−	0.536835i	−0.963303	−	0.268418i	$-0.913499\pi$
$937$		−	16.4328i		−	0.536835i	0.963303	−	0.268418i	$-0.0865007\pi$
$938$		−	80.3244i		−	2.62268i
$939$	−0.0606343			−0.00197873
$940$	37.2506	−	32.9380i	1.21498	−	1.07432i
$941$	−5.86414			−0.191166			−0.0955828	−	0.995421i	$-0.530471\pi$
$941$	−5.86414			−0.191166			−0.0955828	+	0.995421i	$0.530471\pi$
$942$			18.7612i			0.611272i
$943$		−	9.55149i		−	0.311039i
$944$	162.952			5.30362
$945$	4.15633	+	4.70052i	0.135205	+	0.152908i
$946$		0			0
$947$		−	38.7415i		−	1.25893i	−0.777030	−	0.629464i	$-0.783274\pi$
$947$		−	38.7415i		−	1.25893i	0.777030	−	0.629464i	$-0.216726\pi$
$948$		−	6.96239i		−	0.226128i
$949$	32.8529			1.06645
$950$	−60.7269	−	7.49086i	−1.97024	−	0.243036i
$951$	−3.81336			−0.123657
$952$		−	107.667i		−	3.48950i
$953$		−	6.09569i		−	0.197459i	−0.995114	−	0.0987294i	$-0.968522\pi$
$953$		−	6.09569i		−	0.197459i	0.995114	−	0.0987294i	$-0.0314778\pi$
$954$	−17.5877			−0.569422
$955$	−19.4763	−	22.0263i	−0.630237	−	0.712756i
$956$	−99.6502			−3.22292
$957$		0			0
$958$		−	44.8773i		−	1.44992i
$959$	27.4960			0.887891
$960$	−30.3512	+	26.8373i	−0.979581	+	0.866171i
$961$	−30.0738			−0.970123
$962$		−	22.0752i		−	0.711734i
$963$		−	9.43136i		−	0.303921i
$964$	147.213			4.74143
$965$	9.87399	−	8.73084i	0.317855	−	0.281056i
$966$	−30.0263			−0.966082
$967$		−	37.9697i		−	1.22102i	−0.792008	−	0.610511i	$-0.790964\pi$
$967$		−	37.9697i		−	1.22102i	0.792008	−	0.610511i	$-0.209036\pi$
$968$		0			0
$969$	−20.7875			−0.667791
$970$	39.3258	+	44.4749i	1.26268	+	1.42800i
$971$	−60.8773			−1.95365			−0.976823	−	0.214049i	$-0.931335\pi$
$971$	−60.8773			−1.95365			−0.976823	+	0.214049i	$0.931335\pi$
$972$		−	5.15633i		−	0.165389i
$973$			5.96571i			0.191252i
$974$	−92.0235			−2.94862
$975$	−3.13330	+	25.4010i	−0.100346	+	0.813485i
$976$	−97.2769			−3.11376
$977$			21.3963i			0.684529i	0.939604	+	0.342264i	$0.111194\pi$
$977$			21.3963i			0.684529i	−0.939604	+	0.342264i	$0.888806\pi$
$978$		−	18.0870i		−	0.578358i
$979$		0			0
$980$	−6.67513	−	7.54912i	−0.213229	−	0.241148i
$981$	15.4010			0.491718
$982$			40.0000i			1.27645i
$983$		−	18.8919i		−	0.602558i	−0.953536	−	0.301279i	$-0.902586\pi$
$983$		−	18.8919i		−	0.602558i	0.953536	−	0.301279i	$-0.0974136\pi$
$984$	−20.1622			−0.642748
$985$	−34.1622	+	30.2071i	−1.08850	+	0.962479i
$986$	29.0278			0.924432
$987$		−	12.1016i		−	0.385197i
$988$		−	120.739i		−	3.84121i
$989$	11.2243			0.356911
$990$		0			0
$991$	−1.33567			−0.0424291			−0.0212145	−	0.999775i	$-0.506753\pi$
$991$	−1.33567			−0.0424291			−0.0212145	+	0.999775i	$0.506753\pi$
$992$			15.3503i			0.487371i
$993$			24.2882i			0.770763i
$994$	55.1754			1.75006
$995$	25.7743	+	29.1490i	0.817101	+	0.924086i
$996$	−4.15633			−0.131698
$997$			48.9076i			1.54892i	0.632623	+	0.774460i	$0.281978\pi$
$997$			48.9076i			1.54892i	−0.632623	+	0.774460i	$0.718022\pi$
$998$		−	7.62672i		−	0.241419i
$999$	1.61213			0.0510054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.d.364.1		6
5.2	odd	4		9075.2.a.ck.1.3		3
5.3	odd	4		9075.2.a.cc.1.1		3
5.4	even	2	inner	1815.2.c.d.364.6		6
11.10	odd	2		165.2.c.a.34.6	yes	6
33.32	even	2		495.2.c.d.199.1		6
44.43	even	2		2640.2.d.i.529.1		6
55.32	even	4		825.2.a.h.1.1		3
55.43	even	4		825.2.a.n.1.3		3
55.54	odd	2		165.2.c.a.34.1	✓	6
165.32	odd	4		2475.2.a.be.1.3		3
165.98	odd	4		2475.2.a.y.1.1		3
165.164	even	2		495.2.c.d.199.6		6
220.219	even	2		2640.2.d.i.529.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.c.a.34.1	✓	6	55.54	odd	2
165.2.c.a.34.6	yes	6	11.10	odd	2
495.2.c.d.199.1		6	33.32	even	2
495.2.c.d.199.6		6	165.164	even	2
825.2.a.h.1.1		3	55.32	even	4
825.2.a.n.1.3		3	55.43	even	4
1815.2.c.d.364.1		6	1.1	even	1	trivial
1815.2.c.d.364.6		6	5.4	even	2	inner
2475.2.a.y.1.1		3	165.98	odd	4
2475.2.a.be.1.3		3	165.32	odd	4
2640.2.d.i.529.1		6	44.43	even	2
2640.2.d.i.529.4		6	220.219	even	2
9075.2.a.cc.1.1		3	5.3	odd	4
9075.2.a.ck.1.3		3	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)

\(f(q)\)	\(=\)	\(q-2.67513i q^{2} +1.00000i q^{3} -5.15633 q^{4} +(-1.48119 - 1.67513i) q^{5} +2.67513 q^{6} -2.80606i q^{7} +8.44358i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.67513i q^{2} +1.00000i q^{3} -5.15633 q^{4} +(-1.48119 - 1.67513i) q^{5} +2.67513 q^{6} -2.80606i q^{7} +8.44358i q^{8} -1.00000 q^{9} +(-4.48119 + 3.96239i) q^{10} -5.15633i q^{12} -5.11871i q^{13} -7.50659 q^{14} +(1.67513 - 1.48119i) q^{15} +12.2750 q^{16} -4.54420i q^{17} +2.67513i q^{18} -4.57452 q^{19} +(7.63752 + 8.63752i) q^{20} +2.80606 q^{21} -4.00000i q^{23} -8.44358 q^{24} +(-0.612127 + 4.96239i) q^{25} -13.6932 q^{26} -1.00000i q^{27} +14.4690i q^{28} -2.38787 q^{29} +(-3.96239 - 4.48119i) q^{30} -0.962389 q^{31} -15.9502i q^{32} -12.1563 q^{34} +(-4.70052 + 4.15633i) q^{35} +5.15633 q^{36} +1.61213i q^{37} +12.2374i q^{38} +5.11871 q^{39} +(14.1441 - 12.5066i) q^{40} +2.38787 q^{41} -7.50659i q^{42} +2.80606i q^{43} +(1.48119 + 1.67513i) q^{45} -10.7005 q^{46} -4.31265i q^{47} +12.2750i q^{48} -0.873992 q^{49} +(13.2750 + 1.63752i) q^{50} +4.54420 q^{51} +26.3938i q^{52} +6.57452i q^{53} -2.67513 q^{54} +23.6932 q^{56} -4.57452i q^{57} +6.38787i q^{58} +13.2750 q^{59} +(-8.63752 + 7.63752i) q^{60} -7.92478 q^{61} +2.57452i q^{62} +2.80606i q^{63} -18.1187 q^{64} +(-8.57452 + 7.58181i) q^{65} +10.7005i q^{67} +23.4314i q^{68} +4.00000 q^{69} +(11.1187 + 12.5745i) q^{70} -7.35026 q^{71} -8.44358i q^{72} +6.41819i q^{73} +4.31265 q^{74} +(-4.96239 - 0.612127i) q^{75} +23.5877 q^{76} -13.6932i q^{78} +1.35026 q^{79} +(-18.1817 - 20.5623i) q^{80} +1.00000 q^{81} -6.38787i q^{82} -0.806063i q^{83} -14.4690 q^{84} +(-7.61213 + 6.73084i) q^{85} +7.50659 q^{86} -2.38787i q^{87} +2.96239 q^{89} +(4.48119 - 3.96239i) q^{90} -14.3634 q^{91} +20.6253i q^{92} -0.962389i q^{93} -11.5369 q^{94} +(6.77575 + 7.66291i) q^{95} +15.9502 q^{96} -9.92478i q^{97} +2.33804i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^9	\( 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9} - 16 q^{10} - 4 q^{14} + 10 q^{16} - 4 q^{19} + 14 q^{20} + 16 q^{21} - 18 q^{24} - 2 q^{25} - 16 q^{26} - 16 q^{29} - 2 q^{30} + 16 q^{31} - 52 q^{34} + 12 q^{35} + 10 q^{36} - 12 q^{39} + 12 q^{40} + 16 q^{41} - 2 q^{45} - 24 q^{46} - 22 q^{49} + 16 q^{50} + 8 q^{51} - 6 q^{54} + 76 q^{56} + 16 q^{59} - 20 q^{60} - 4 q^{61} - 66 q^{64} - 28 q^{65} + 24 q^{69} + 24 q^{70} - 24 q^{71} - 16 q^{74} - 8 q^{75} + 36 q^{76} - 12 q^{79} - 58 q^{80} + 6 q^{81} - 24 q^{84} - 44 q^{85} + 4 q^{86} - 4 q^{89} + 16 q^{90} + 16 q^{91} - 24 q^{94} + 44 q^{95} + 22 q^{96}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^9 - 16 * q^10 - 4 * q^14 + 10 * q^16 - 4 * q^19 + 14 * q^20 + 16 * q^21 - 18 * q^24 - 2 * q^25 - 16 * q^26 - 16 * q^29 - 2 * q^30 + 16 * q^31 - 52 * q^34 + 12 * q^35 + 10 * q^36 - 12 * q^39 + 12 * q^40 + 16 * q^41 - 2 * q^45 - 24 * q^46 - 22 * q^49 + 16 * q^50 + 8 * q^51 - 6 * q^54 + 76 * q^56 + 16 * q^59 - 20 * q^60 - 4 * q^61 - 66 * q^64 - 28 * q^65 + 24 * q^69 + 24 * q^70 - 24 * q^71 - 16 * q^74 - 8 * q^75 + 36 * q^76 - 12 * q^79 - 58 * q^80 + 6 * q^81 - 24 * q^84 - 44 * q^85 + 4 * q^86 - 4 * q^89 + 16 * q^90 + 16 * q^91 - 24 * q^94 + 44 * q^95 + 22 * q^96

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