LMFDB - Embedded newform 1155.2.c.f.694.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15210x^12 + 40640x^10 + 63865x^8 + 55281x^6 + 22984x^4 + 3428*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.2
Root			$-2.55795i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.f.694.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55795i q^{2} +1.00000i q^{3} -4.54312 q^{4} +(0.0738813 + 2.23485i) q^{5} +2.55795 q^{6} +1.00000i q^{7} +6.50518i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.55795i q^{2} +1.00000i q^{3} -4.54312 q^{4} +(0.0738813 + 2.23485i) q^{5} +2.55795 q^{6} +1.00000i q^{7} +6.50518i q^{8} -1.00000 q^{9} +(5.71663 - 0.188985i) q^{10} +1.00000 q^{11} -4.54312i q^{12} -3.07946i q^{13} +2.55795 q^{14} +(-2.23485 + 0.0738813i) q^{15} +7.55370 q^{16} -2.96227i q^{17} +2.55795i q^{18} -6.66619 q^{19} +(-0.335652 - 10.1532i) q^{20} -1.00000 q^{21} -2.55795i q^{22} +3.16515i q^{23} -6.50518 q^{24} +(-4.98908 + 0.330227i) q^{25} -7.87711 q^{26} -1.00000i q^{27} -4.54312i q^{28} -7.70372 q^{29} +(0.188985 + 5.71663i) q^{30} +4.22596 q^{31} -6.31165i q^{32} +1.00000i q^{33} -7.57735 q^{34} +(-2.23485 + 0.0738813i) q^{35} +4.54312 q^{36} +6.02692i q^{37} +17.0518i q^{38} +3.07946 q^{39} +(-14.5381 + 0.480611i) q^{40} -9.67658 q^{41} +2.55795i q^{42} +2.22251i q^{43} -4.54312 q^{44} +(-0.0738813 - 2.23485i) q^{45} +8.09630 q^{46} +0.862680i q^{47} +7.55370i q^{48} -1.00000 q^{49} +(0.844704 + 12.7618i) q^{50} +2.96227 q^{51} +13.9904i q^{52} -7.20541i q^{53} -2.55795 q^{54} +(0.0738813 + 2.23485i) q^{55} -6.50518 q^{56} -6.66619i q^{57} +19.7058i q^{58} -5.15730 q^{59} +(10.1532 - 0.335652i) q^{60} -8.86048 q^{61} -10.8098i q^{62} -1.00000i q^{63} -1.03749 q^{64} +(6.88212 - 0.227514i) q^{65} +2.55795 q^{66} -1.61927i q^{67} +13.4580i q^{68} -3.16515 q^{69} +(0.188985 + 5.71663i) q^{70} +1.95649 q^{71} -6.50518i q^{72} +3.60792i q^{73} +15.4166 q^{74} +(-0.330227 - 4.98908i) q^{75} +30.2853 q^{76} +1.00000i q^{77} -7.87711i q^{78} -14.0677 q^{79} +(0.558077 + 16.8814i) q^{80} +1.00000 q^{81} +24.7522i q^{82} -17.7039i q^{83} +4.54312 q^{84} +(6.62022 - 0.218856i) q^{85} +5.68508 q^{86} -7.70372i q^{87} +6.50518i q^{88} -7.48643 q^{89} +(-5.71663 + 0.188985i) q^{90} +3.07946 q^{91} -14.3797i q^{92} +4.22596i q^{93} +2.20670 q^{94} +(-0.492507 - 14.8979i) q^{95} +6.31165 q^{96} +19.2032i q^{97} +2.55795i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$		−	2.55795i		−	1.80875i	−0.426743	−	0.904373i	$-0.640339\pi$
$2$		−	2.55795i		−	1.80875i	0.426743	−	0.904373i	$-0.359661\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−4.54312			−2.27156
$5$	0.0738813	+	2.23485i	0.0330407	+	0.999454i
$5$	0.0738813	+	2.23485i	0.0330407	+	0.999454i
$6$	2.55795			1.04428
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			6.50518i			2.29993i
$9$	−1.00000			−0.333333
$10$	5.71663	−	0.188985i	1.80776	−	0.0597622i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	4.54312i		−	1.31149i
$13$		−	3.07946i		−	0.854088i	−0.904231	−	0.427044i	$-0.859555\pi$
$13$		−	3.07946i		−	0.854088i	0.904231	−	0.427044i	$-0.140445\pi$
$14$	2.55795			0.683642
$15$	−2.23485	+	0.0738813i	−0.577035	+	0.0190761i
$16$	7.55370			1.88843
$17$		−	2.96227i		−	0.718456i	−0.933250	−	0.359228i	$-0.883040\pi$
$17$		−	2.96227i		−	0.718456i	0.933250	−	0.359228i	$-0.116960\pi$
$18$			2.55795i			0.602915i
$19$	−6.66619			−1.52933			−0.764664	−	0.644429i	$-0.777095\pi$
$19$	−6.66619			−1.52933			−0.764664	+	0.644429i	$0.777095\pi$
$20$	−0.335652	−	10.1532i	−0.0750540	−	2.27032i
$21$	−1.00000			−0.218218
$22$		−	2.55795i		−	0.545357i
$23$			3.16515i			0.659980i	0.943985	+	0.329990i	$0.107045\pi$
$23$			3.16515i			0.659980i	−0.943985	+	0.329990i	$0.892955\pi$
$24$	−6.50518			−1.32786
$25$	−4.98908	+	0.330227i	−0.997817	+	0.0660453i
$26$	−7.87711			−1.54483
$27$		−	1.00000i		−	0.192450i
$28$		−	4.54312i		−	0.858569i
$29$	−7.70372			−1.43055			−0.715273	−	0.698845i	$-0.753698\pi$
$29$	−7.70372			−1.43055			−0.715273	+	0.698845i	$0.753698\pi$
$30$	0.188985	+	5.71663i	0.0345037	+	1.04371i
$31$	4.22596			0.759006			0.379503	−	0.925191i	$-0.376095\pi$
$31$	4.22596			0.759006			0.379503	+	0.925191i	$0.376095\pi$
$32$		−	6.31165i		−	1.11575i
$33$			1.00000i			0.174078i
$34$	−7.57735			−1.29950
$35$	−2.23485	+	0.0738813i	−0.377758	+	0.0124882i
$36$	4.54312			0.757187
$37$			6.02692i			0.990820i	0.868659	+	0.495410i	$0.164982\pi$
$37$			6.02692i			0.990820i	−0.868659	+	0.495410i	$0.835018\pi$
$38$			17.0518i			2.76617i
$39$	3.07946			0.493108
$40$	−14.5381	+	0.480611i	−2.29867	+	0.0759913i
$41$	−9.67658			−1.51123			−0.755614	−	0.655018i	$-0.772661\pi$
$41$	−9.67658			−1.51123			−0.755614	+	0.655018i	$0.772661\pi$
$42$			2.55795i			0.394701i
$43$			2.22251i			0.338930i	0.985536	+	0.169465i	$0.0542039\pi$
$43$			2.22251i			0.338930i	−0.985536	+	0.169465i	$0.945796\pi$
$44$	−4.54312			−0.684901
$45$	−0.0738813	−	2.23485i	−0.0110136	−	0.333151i
$46$	8.09630			1.19374
$47$			0.862680i			0.125835i	0.998019	+	0.0629174i	$0.0200405\pi$
$47$			0.862680i			0.125835i	−0.998019	+	0.0629174i	$0.979960\pi$
$48$			7.55370i			1.09028i
$49$	−1.00000			−0.142857
$50$	0.844704	+	12.7618i	0.119459	+	1.80480i
$51$	2.96227			0.414801
$52$			13.9904i			1.94011i
$53$		−	7.20541i		−	0.989740i	−0.868967	−	0.494870i	$-0.835216\pi$
$53$		−	7.20541i		−	0.989740i	0.868967	−	0.494870i	$-0.164784\pi$
$54$	−2.55795			−0.348093
$55$	0.0738813	+	2.23485i	0.00996215	+	0.301347i
$56$	−6.50518			−0.869291
$57$		−	6.66619i		−	0.882958i
$58$			19.7058i			2.58749i
$59$	−5.15730			−0.671423			−0.335712	−	0.941965i	$-0.608977\pi$
$59$	−5.15730			−0.671423			−0.335712	+	0.941965i	$0.608977\pi$
$60$	10.1532	−	0.335652i	1.31077	−	0.0433324i
$61$	−8.86048			−1.13447			−0.567234	−	0.823557i	$-0.691986\pi$
$61$	−8.86048			−1.13447			−0.567234	+	0.823557i	$0.691986\pi$
$62$		−	10.8098i		−	1.37285i
$63$		−	1.00000i		−	0.125988i
$64$	−1.03749			−0.129686
$65$	6.88212	−	0.227514i	0.853622	−	0.0282197i
$66$	2.55795			0.314862
$67$		−	1.61927i		−	0.197826i	−0.995096	−	0.0989128i	$-0.968464\pi$
$67$		−	1.61927i		−	0.197826i	0.995096	−	0.0989128i	$-0.0315365\pi$
$68$			13.4580i			1.63202i
$69$	−3.16515			−0.381039
$70$	0.188985	+	5.71663i	0.0225880	+	0.683268i
$71$	1.95649			0.232192			0.116096	−	0.993238i	$-0.462962\pi$
$71$	1.95649			0.232192			0.116096	+	0.993238i	$0.462962\pi$
$72$		−	6.50518i		−	0.766643i
$73$			3.60792i			0.422275i	0.977456	+	0.211137i	$0.0677168\pi$
$73$			3.60792i			0.422275i	−0.977456	+	0.211137i	$0.932283\pi$
$74$	15.4166			1.79214
$75$	−0.330227	−	4.98908i	−0.0381313	−	0.576090i
$76$	30.2853			3.47396
$77$			1.00000i			0.113961i
$78$		−	7.87711i		−	0.891907i
$79$	−14.0677			−1.58274			−0.791371	−	0.611336i	$-0.790632\pi$
$79$	−14.0677			−1.58274			−0.791371	+	0.611336i	$0.790632\pi$
$80$	0.558077	+	16.8814i	0.0623949	+	1.88739i
$81$	1.00000			0.111111
$82$			24.7522i			2.73343i
$83$		−	17.7039i		−	1.94325i	−0.236517	−	0.971627i	$-0.576006\pi$
$83$		−	17.7039i		−	1.94325i	0.236517	−	0.971627i	$-0.423994\pi$
$84$	4.54312			0.495695
$85$	6.62022	−	0.218856i	0.718064	−	0.0237383i
$86$	5.68508			0.613038
$87$		−	7.70372i		−	0.825926i
$88$			6.50518i			0.693455i
$89$	−7.48643			−0.793560			−0.396780	−	0.917914i	$-0.629872\pi$
$89$	−7.48643			−0.793560			−0.396780	+	0.917914i	$0.629872\pi$
$90$	−5.71663	+	0.188985i	−0.602586	+	0.0199207i
$91$	3.07946			0.322815
$92$		−	14.3797i		−	1.49918i
$93$			4.22596i			0.438212i
$94$	2.20670			0.227603
$95$	−0.492507	−	14.8979i	−0.0505301	−	1.52849i
$96$	6.31165			0.644180
$97$			19.2032i			1.94979i	0.222664	+	0.974895i	$0.428525\pi$
$97$			19.2032i			1.94979i	−0.222664	+	0.974895i	$0.571475\pi$
$98$			2.55795i			0.258392i
$99$	−1.00000			−0.100504
$100$	22.6660	−	1.50026i	2.26660	−	0.150026i
$101$	4.09704			0.407671			0.203835	−	0.979005i	$-0.434659\pi$
$101$	4.09704			0.407671			0.203835	+	0.979005i	$0.434659\pi$
$102$		−	7.57735i		−	0.750269i
$103$			16.7352i			1.64897i	0.565883	+	0.824486i	$0.308536\pi$
$103$			16.7352i			1.64897i	−0.565883	+	0.824486i	$0.691464\pi$
$104$	20.0324			1.96434
$105$	−0.0738813	−	2.23485i	−0.00721007	−	0.218099i
$106$	−18.4311			−1.79019
$107$		−	8.75612i		−	0.846486i	−0.906016	−	0.423243i	$-0.860892\pi$
$107$		−	8.75612i		−	0.846486i	0.906016	−	0.423243i	$-0.139108\pi$
$108$			4.54312i			0.437162i
$109$	3.29316			0.315428			0.157714	−	0.987485i	$-0.449588\pi$
$109$	3.29316			0.315428			0.157714	+	0.987485i	$0.449588\pi$
$110$	5.71663	−	0.188985i	0.545060	−	0.0180190i
$111$	−6.02692			−0.572050
$112$			7.55370i			0.713758i
$113$			10.0284i			0.943389i	0.881762	+	0.471695i	$0.156358\pi$
$113$			10.0284i			0.943389i	−0.881762	+	0.471695i	$0.843642\pi$
$114$	−17.0518			−1.59705
$115$	−7.07363	+	0.233845i	−0.659619	+	0.0218062i
$116$	34.9989			3.24957
$117$			3.07946i			0.284696i
$118$			13.1921i			1.21443i
$119$	2.96227			0.271551
$120$	−0.480611	−	14.5381i	−0.0438736	−	1.32714i
$121$	1.00000			0.0909091
$122$			22.6647i			2.05196i
$123$		−	9.67658i		−	0.872507i
$124$	−19.1991			−1.72413
$125$	−1.10661	−	11.1254i	−0.0989779	−	0.995090i
$126$	−2.55795			−0.227881
$127$		−	12.9029i		−	1.14495i	−0.819924	−	0.572473i	$-0.805984\pi$
$127$		−	12.9029i		−	1.14495i	0.819924	−	0.572473i	$-0.194016\pi$
$128$		−	9.96944i		−	0.881183i
$129$	−2.22251			−0.195681
$130$	−0.581971	−	17.6041i	−0.0510422	−	1.54398i
$131$	−5.40783			−0.472484			−0.236242	−	0.971694i	$-0.575916\pi$
$131$	−5.40783			−0.472484			−0.236242	+	0.971694i	$0.575916\pi$
$132$		−	4.54312i		−	0.395428i
$133$		−	6.66619i		−	0.578032i
$134$	−4.14202			−0.357816
$135$	2.23485	−	0.0738813i	0.192345	−	0.00635869i
$136$	19.2701			1.65240
$137$		−	14.6988i		−	1.25581i	−0.778291	−	0.627904i	$-0.783913\pi$
$137$		−	14.6988i		−	1.25581i	0.778291	−	0.627904i	$-0.216087\pi$
$138$			8.09630i			0.689203i
$139$	−7.99339			−0.677990			−0.338995	−	0.940788i	$-0.610087\pi$
$139$	−7.99339			−0.677990			−0.338995	+	0.940788i	$0.610087\pi$
$140$	10.1532	−	0.335652i	0.858100	−	0.0283677i
$141$	−0.862680			−0.0726508
$142$		−	5.00460i		−	0.419977i
$143$		−	3.07946i		−	0.257517i
$144$	−7.55370			−0.629475
$145$	−0.569161	−	17.2166i	−0.0472662	−	1.42976i
$146$	9.22888			0.763788
$147$		−	1.00000i		−	0.0824786i
$148$		−	27.3810i		−	2.25071i
$149$	3.30587			0.270828			0.135414	−	0.990789i	$-0.456764\pi$
$149$	3.30587			0.270828			0.135414	+	0.990789i	$0.456764\pi$
$150$	−12.7618	+	0.844704i	−1.04200	+	0.0689698i
$151$	8.49695			0.691472			0.345736	−	0.938332i	$-0.387629\pi$
$151$	8.49695			0.691472			0.345736	+	0.938332i	$0.387629\pi$
$152$		−	43.3648i		−	3.51735i
$153$			2.96227i			0.239485i
$154$	2.55795			0.206126
$155$	0.312220	+	9.44438i	0.0250781	+	0.758591i
$156$	−13.9904			−1.12012
$157$			19.8302i			1.58262i	0.611413	+	0.791311i	$0.290601\pi$
$157$			19.8302i			1.58262i	−0.611413	+	0.791311i	$0.709399\pi$
$158$			35.9846i			2.86278i
$159$	7.20541			0.571426
$160$	14.1056	−	0.466313i	1.11514	−	0.0368653i
$161$	−3.16515			−0.249449
$162$		−	2.55795i		−	0.200972i
$163$		−	5.20580i		−	0.407750i	−0.978997	−	0.203875i	$-0.934646\pi$
$163$		−	5.20580i		−	0.407750i	0.978997	−	0.203875i	$-0.0653536\pi$
$164$	43.9618			3.43284
$165$	−2.23485	+	0.0738813i	−0.173983	+	0.00575165i
$166$	−45.2857			−3.51485
$167$			14.2801i			1.10502i	0.833505	+	0.552512i	$0.186331\pi$
$167$			14.2801i			1.10502i	−0.833505	+	0.552512i	$0.813669\pi$
$168$		−	6.50518i		−	0.501886i
$169$	3.51693			0.270533
$170$	−0.559824	−	16.9342i	−0.0429366	−	1.29880i
$171$	6.66619			0.509776
$172$		−	10.0971i		−	0.769899i
$173$		−	10.2366i		−	0.778271i	−0.921180	−	0.389136i	$-0.872774\pi$
$173$		−	10.2366i		−	0.778271i	0.921180	−	0.389136i	$-0.127226\pi$
$174$	−19.7058			−1.49389
$175$	−0.330227	−	4.98908i	−0.0249628	−	0.377139i
$176$	7.55370			0.569382
$177$		−	5.15730i		−	0.387646i
$178$			19.1499i			1.43535i
$179$	18.6427			1.39342			0.696712	−	0.717351i	$-0.254646\pi$
$179$	18.6427			1.39342			0.696712	+	0.717351i	$0.254646\pi$
$180$	0.335652	+	10.1532i	0.0250180	+	0.756773i
$181$	7.95159			0.591037			0.295518	−	0.955337i	$-0.404508\pi$
$181$	7.95159			0.591037			0.295518	+	0.955337i	$0.404508\pi$
$182$		−	7.87711i		−	0.583890i
$183$		−	8.86048i		−	0.654985i
$184$	−20.5899			−1.51791
$185$	−13.4693	+	0.445277i	−0.990279	+	0.0327374i
$186$	10.8098			0.792614
$187$		−	2.96227i		−	0.216623i
$188$		−	3.91926i		−	0.285841i
$189$	1.00000			0.0727393
$190$	−38.1082	+	1.25981i	−2.76466	+	0.0913961i
$191$	−4.76297			−0.344636			−0.172318	−	0.985041i	$-0.555126\pi$
$191$	−4.76297			−0.344636			−0.172318	+	0.985041i	$0.555126\pi$
$192$		−	1.03749i		−	0.0748745i
$193$			3.19789i			0.230189i	0.993355	+	0.115095i	$0.0367172\pi$
$193$			3.19789i			0.230189i	−0.993355	+	0.115095i	$0.963283\pi$
$194$	49.1209			3.52667
$195$	0.227514	+	6.88212i	0.0162926	+	0.492839i
$196$	4.54312			0.324509
$197$			20.1314i			1.43430i	0.696917	+	0.717152i	$0.254555\pi$
$197$			20.1314i			1.43430i	−0.696917	+	0.717152i	$0.745445\pi$
$198$			2.55795i			0.181786i
$199$	1.88964			0.133953			0.0669764	−	0.997755i	$-0.478665\pi$
$199$	1.88964			0.133953			0.0669764	+	0.997755i	$0.478665\pi$
$200$	−2.14818	−	32.4549i	−0.151900	−	2.29491i
$201$	1.61927			0.114215
$202$		−	10.4800i		−	0.737373i
$203$		−	7.70372i		−	0.540695i
$204$	−13.4580			−0.942245
$205$	−0.714918	−	21.6257i	−0.0499320	−	1.51040i
$206$	42.8079			2.98257
$207$		−	3.16515i		−	0.219993i
$208$		−	23.2613i		−	1.61288i
$209$	−6.66619			−0.461110
$210$	−5.71663	+	0.188985i	−0.394485	+	0.0130412i
$211$	27.6484			1.90339			0.951697	−	0.307040i	$-0.0993386\pi$
$211$	27.6484			1.90339			0.951697	+	0.307040i	$0.0993386\pi$
$212$			32.7351i			2.24825i
$213$			1.95649i			0.134056i
$214$	−22.3977			−1.53108
$215$	−4.96697	+	0.164202i	−0.338745	+	0.0111985i
$216$	6.50518			0.442621
$217$			4.22596i			0.286877i
$218$		−	8.42376i		−	0.570529i
$219$	−3.60792			−0.243801
$220$	−0.335652	−	10.1532i	−0.0226296	−	0.684527i
$221$	−9.12219			−0.613625
$222$			15.4166i			1.03469i
$223$		−	7.83653i		−	0.524773i	−0.964963	−	0.262386i	$-0.915491\pi$
$223$		−	7.83653i		−	0.524773i	0.964963	−	0.262386i	$-0.0845095\pi$
$224$	6.31165			0.421715
$225$	4.98908	−	0.330227i	0.332606	−	0.0220151i
$226$	25.6521			1.70635
$227$			0.565299i			0.0375202i	0.999824	+	0.0187601i	$0.00597188\pi$
$227$			0.565299i			0.0375202i	−0.999824	+	0.0187601i	$0.994028\pi$
$228$			30.2853i			2.00569i
$229$	21.4294			1.41609			0.708047	−	0.706165i	$-0.249576\pi$
$229$	21.4294			1.41609			0.708047	+	0.706165i	$0.249576\pi$
$230$	0.598165	+	18.0940i	0.0394419	+	1.19308i
$231$	−1.00000			−0.0657952
$232$		−	50.1141i		−	3.29015i
$233$		−	3.39708i		−	0.222550i	−0.993790	−	0.111275i	$-0.964507\pi$
$233$		−	3.39708i		−	0.222550i	0.993790	−	0.111275i	$-0.0354935\pi$
$234$	7.87711			0.514943
$235$	−1.92796	+	0.0637359i	−0.125766	+	0.00415767i
$236$	23.4302			1.52518
$237$		−	14.0677i		−	0.913797i
$238$		−	7.57735i		−	0.491167i
$239$	10.6863			0.691238			0.345619	−	0.938375i	$-0.387669\pi$
$239$	10.6863			0.691238			0.345619	+	0.938375i	$0.387669\pi$
$240$	−16.8814	+	0.558077i	−1.08969	+	0.0360237i
$241$	−19.3010			−1.24328			−0.621642	−	0.783301i	$-0.713534\pi$
$241$	−19.3010			−1.24328			−0.621642	+	0.783301i	$0.713534\pi$
$242$		−	2.55795i		−	0.164431i
$243$			1.00000i			0.0641500i
$244$	40.2542			2.57701
$245$	−0.0738813	−	2.23485i	−0.00472010	−	0.142779i
$246$	−24.7522			−1.57814
$247$			20.5283i			1.30618i
$248$			27.4907i			1.74566i
$249$	17.7039			1.12194
$250$	−28.4583	+	2.83065i	−1.79986	+	0.179026i
$251$	−19.8687			−1.25410			−0.627050	−	0.778979i	$-0.715738\pi$
$251$	−19.8687			−1.25410			−0.627050	+	0.778979i	$0.715738\pi$
$252$			4.54312i			0.286190i
$253$			3.16515i			0.198991i
$254$	−33.0050			−2.07092
$255$	0.218856	+	6.62022i	0.0137053	+	0.414575i
$256$	−27.5763			−1.72352
$257$		−	10.4415i		−	0.651322i	−0.945487	−	0.325661i	$-0.894413\pi$
$257$		−	10.4415i		−	0.651322i	0.945487	−	0.325661i	$-0.105587\pi$
$258$			5.68508i			0.353937i
$259$	−6.02692			−0.374495
$260$	−31.2663	+	1.03363i	−1.93905	+	0.0641027i
$261$	7.70372			0.476848
$262$			13.8330i			0.854603i
$263$			22.6825i			1.39866i	0.714799	+	0.699330i	$0.246518\pi$
$263$			22.6825i			1.39866i	−0.714799	+	0.699330i	$0.753482\pi$
$264$	−6.50518			−0.400366
$265$	16.1030	−	0.532345i	0.989199	−	0.0327017i
$266$	−17.0518			−1.04551
$267$		−	7.48643i		−	0.458162i
$268$			7.35655i			0.449373i
$269$	17.8438			1.08795			0.543977	−	0.839100i	$-0.316918\pi$
$269$	17.8438			1.08795			0.543977	+	0.839100i	$0.316918\pi$
$270$	−0.188985	−	5.71663i	−0.0115012	−	0.347903i
$271$	−29.9619			−1.82006			−0.910028	−	0.414548i	$-0.863940\pi$
$271$	−29.9619			−1.82006			−0.910028	+	0.414548i	$0.863940\pi$
$272$		−	22.3761i		−	1.35675i
$273$			3.07946i			0.186377i
$274$	−37.5989			−2.27144
$275$	−4.98908	+	0.330227i	−0.300853	+	0.0199134i
$276$	14.3797			0.865554
$277$			22.6094i			1.35846i	0.733923	+	0.679232i	$0.237687\pi$
$277$			22.6094i			1.35846i	−0.733923	+	0.679232i	$0.762313\pi$
$278$			20.4467i			1.22631i
$279$	−4.22596			−0.253002
$280$	−0.480611	−	14.5381i	−0.0287220	−	0.868817i
$281$	−18.7711			−1.11979			−0.559895	−	0.828563i	$-0.689159\pi$
$281$	−18.7711			−1.11979			−0.559895	+	0.828563i	$0.689159\pi$
$282$			2.20670i			0.131407i
$283$		−	13.0685i		−	0.776840i	−0.921482	−	0.388420i	$-0.873021\pi$
$283$		−	13.0685i		−	0.776840i	0.921482	−	0.388420i	$-0.126979\pi$
$284$	−8.88855			−0.527438
$285$	14.8979	−	0.492507i	0.882476	−	0.0291736i
$286$	−7.87711			−0.465783
$287$		−	9.67658i		−	0.571190i
$288$			6.31165i			0.371917i
$289$	8.22495			0.483820
$290$	−44.0394	+	1.45589i	−2.58608	+	0.0854926i
$291$	−19.2032			−1.12571
$292$		−	16.3912i		−	0.959223i
$293$		−	8.27156i		−	0.483229i	−0.970372	−	0.241615i	$-0.922323\pi$
$293$		−	8.27156i		−	0.483229i	0.970372	−	0.241615i	$-0.0776770\pi$
$294$	−2.55795			−0.149183
$295$	−0.381028	−	11.5258i	−0.0221843	−	0.671056i
$296$	−39.2062			−2.27882
$297$		−	1.00000i		−	0.0580259i
$298$		−	8.45627i		−	0.489858i
$299$	9.74695			0.563681
$300$	1.50026	+	22.6660i	0.0866175	+	1.30862i
$301$	−2.22251			−0.128103
$302$		−	21.7348i		−	1.25070i
$303$			4.09704i			0.235369i
$304$	−50.3544			−2.88802
$305$	−0.654623	−	19.8018i	−0.0374836	−	1.13385i
$306$	7.57735			0.433168
$307$			17.0792i			0.974764i	0.873189	+	0.487382i	$0.162048\pi$
$307$			17.0792i			0.974764i	−0.873189	+	0.487382i	$0.837952\pi$
$308$		−	4.54312i		−	0.258868i
$309$	−16.7352			−0.952034
$310$	24.1583	−	0.798643i	1.37210	−	0.0453599i
$311$	−18.3234			−1.03903			−0.519513	−	0.854463i	$-0.673886\pi$
$311$	−18.3234			−1.03903			−0.519513	+	0.854463i	$0.673886\pi$
$312$			20.0324i			1.13411i
$313$			34.6119i			1.95638i	0.207717	+	0.978189i	$0.433397\pi$
$313$			34.6119i			1.95638i	−0.207717	+	0.978189i	$0.566603\pi$
$314$	50.7247			2.86256
$315$	2.23485	−	0.0738813i	0.125919	−	0.00416274i
$316$	63.9114			3.59529
$317$		−	9.88458i		−	0.555173i	−0.960701	−	0.277587i	$-0.910465\pi$
$317$		−	9.88458i		−	0.555173i	0.960701	−	0.277587i	$-0.0895345\pi$
$318$		−	18.4311i		−	1.03356i
$319$	−7.70372			−0.431326
$320$	−0.0766512	−	2.31863i	−0.00428493	−	0.129616i
$321$	8.75612			0.488719
$322$			8.09630i			0.451189i
$323$			19.7471i			1.09876i
$324$	−4.54312			−0.252396
$325$	1.01692	+	15.3637i	0.0564086	+	0.852224i
$326$	−13.3162			−0.737516
$327$			3.29316i			0.182112i
$328$		−	62.9479i		−	3.47571i
$329$	−0.862680			−0.0475611
$330$	0.188985	+	5.71663i	0.0104033	+	0.314690i
$331$	−21.4874			−1.18105			−0.590527	−	0.807018i	$-0.701080\pi$
$331$	−21.4874			−1.18105			−0.590527	+	0.807018i	$0.701080\pi$
$332$			80.4309i			4.41422i
$333$		−	6.02692i		−	0.330273i
$334$	36.5277			1.99871
$335$	3.61882	−	0.119634i	0.197718	−	0.00653630i
$336$	−7.55370			−0.412088
$337$			21.0290i			1.14552i	0.819722	+	0.572762i	$0.194128\pi$
$337$			21.0290i			1.14552i	−0.819722	+	0.572762i	$0.805872\pi$
$338$		−	8.99614i		−	0.489326i
$339$	−10.0284			−0.544666
$340$	−30.0765	+	0.994291i	−1.63113	+	0.0539230i
$341$	4.22596			0.228849
$342$		−	17.0518i		−	0.922055i
$343$		−	1.00000i		−	0.0539949i
$344$	−14.4578			−0.779514
$345$	−0.233845	−	7.07363i	−0.0125898	−	0.380831i
$346$	−26.1846			−1.40769
$347$		−	0.159652i		−	0.00857057i	−0.999991	−	0.00428529i	$-0.998636\pi$
$347$		−	0.159652i		−	0.00857057i	0.999991	−	0.00428529i	$-0.00136405\pi$
$348$			34.9989i			1.87614i
$349$	−17.7616			−0.950757			−0.475378	−	0.879781i	$-0.657689\pi$
$349$	−17.7616			−0.950757			−0.475378	+	0.879781i	$0.657689\pi$
$350$	−12.7618	+	0.844704i	−0.682149	+	0.0451513i
$351$	−3.07946			−0.164369
$352$		−	6.31165i		−	0.336412i
$353$		−	14.2258i		−	0.757165i	−0.925567	−	0.378583i	$-0.876412\pi$
$353$		−	14.2258i		−	0.757165i	0.925567	−	0.378583i	$-0.123588\pi$
$354$	−13.1921			−0.701153
$355$	0.144548	+	4.37245i	0.00767179	+	0.232065i
$356$	34.0118			1.80262
$357$			2.96227i			0.156780i
$358$		−	47.6872i		−	2.52035i
$359$	0.900108			0.0475059			0.0237530	−	0.999718i	$-0.492438\pi$
$359$	0.900108			0.0475059			0.0237530	+	0.999718i	$0.492438\pi$
$360$	14.5381	−	0.480611i	0.766224	−	0.0253304i
$361$	25.4381			1.33885
$362$		−	20.3398i		−	1.06904i
$363$			1.00000i			0.0524864i
$364$	−13.9904			−0.733294
$365$	−8.06315	+	0.266558i	−0.422044	+	0.0139523i
$366$	−22.6647			−1.18470
$367$		−	35.6920i		−	1.86311i	−0.363601	−	0.931555i	$-0.618453\pi$
$367$		−	35.6920i		−	1.86311i	0.363601	−	0.931555i	$-0.381547\pi$
$368$			23.9086i			1.24632i
$369$	9.67658			0.503742
$370$	1.13900	+	34.4537i	0.0592136	+	1.79116i
$371$	7.20541			0.374086
$372$		−	19.1991i		−	0.995425i
$373$			1.66173i			0.0860411i	0.999074	+	0.0430205i	$0.0136981\pi$
$373$			1.66173i			0.0860411i	−0.999074	+	0.0430205i	$0.986302\pi$
$374$	−7.57735			−0.391815
$375$	11.1254	−	1.10661i	0.574515	−	0.0571449i
$376$	−5.61189			−0.289411
$377$			23.7233i			1.22181i
$378$		−	2.55795i		−	0.131567i
$379$	32.2753			1.65787			0.828936	−	0.559344i	$-0.188947\pi$
$379$	32.2753			1.65787			0.828936	+	0.559344i	$0.188947\pi$
$380$	2.23752	+	67.6830i	0.114782	+	3.47207i
$381$	12.9029			0.661035
$382$			12.1834i			0.623359i
$383$		−	16.3423i		−	0.835053i	−0.908665	−	0.417527i	$-0.862897\pi$
$383$		−	16.3423i		−	0.835053i	0.908665	−	0.417527i	$-0.137103\pi$
$384$	9.96944			0.508751
$385$	−2.23485	+	0.0738813i	−0.113898	+	0.00376534i
$386$	8.18006			0.416354
$387$		−	2.22251i		−	0.112977i
$388$		−	87.2425i		−	4.42907i
$389$	2.60756			0.132208			0.0661042	−	0.997813i	$-0.478943\pi$
$389$	2.60756			0.132208			0.0661042	+	0.997813i	$0.478943\pi$
$390$	17.6041	−	0.581971i	0.891420	−	0.0294692i
$391$	9.37604			0.474167
$392$		−	6.50518i		−	0.328561i
$393$		−	5.40783i		−	0.272789i
$394$	51.4952			2.59429
$395$	−1.03934	−	31.4392i	−0.0522949	−	1.58188i
$396$	4.54312			0.228300
$397$			14.3757i			0.721498i	0.932663	+	0.360749i	$0.117479\pi$
$397$			14.3757i			0.721498i	−0.932663	+	0.360749i	$0.882521\pi$
$398$		−	4.83360i		−	0.242287i
$399$	6.66619			0.333727
$400$	−37.6860	+	2.49443i	−1.88430	+	0.124722i
$401$	8.03544			0.401270			0.200635	−	0.979666i	$-0.435699\pi$
$401$	8.03544			0.401270			0.200635	+	0.979666i	$0.435699\pi$
$402$		−	4.14202i		−	0.206585i
$403$		−	13.0137i		−	0.648258i
$404$	−18.6134			−0.926049
$405$	0.0738813	+	2.23485i	0.00367119	+	0.111050i
$406$	−19.7058			−0.977980
$407$			6.02692i			0.298744i
$408$			19.2701i			0.954013i
$409$	−19.6990			−0.974050			−0.487025	−	0.873388i	$-0.661918\pi$
$409$	−19.6990			−0.974050			−0.487025	+	0.873388i	$0.661918\pi$
$410$	−55.3174	+	1.82873i	−2.73193	+	0.0903143i
$411$	14.6988			0.725041
$412$		−	76.0302i		−	3.74574i
$413$		−	5.15730i		−	0.253774i
$414$	−8.09630			−0.397912
$415$	39.5655	−	1.30799i	1.94219	−	0.0642065i
$416$	−19.4365			−0.952951
$417$		−	7.99339i		−	0.391438i
$418$			17.0518i			0.834031i
$419$	−13.4454			−0.656850			−0.328425	−	0.944530i	$-0.606518\pi$
$419$	−13.4454			−0.656850			−0.328425	+	0.944530i	$0.606518\pi$
$420$	0.335652	+	10.1532i	0.0163781	+	0.495424i
$421$	9.79324			0.477293			0.238647	−	0.971106i	$-0.423296\pi$
$421$	9.79324			0.477293			0.238647	+	0.971106i	$0.423296\pi$
$422$		−	70.7232i		−	3.44275i
$423$		−	0.862680i		−	0.0419450i
$424$	46.8725			2.27633
$425$	0.978221	+	14.7790i	0.0474507	+	0.716888i
$426$	5.00460			0.242474
$427$		−	8.86048i		−	0.428789i
$428$			39.7801i			1.92284i
$429$	3.07946			0.148678
$430$	0.420021	+	12.7053i	0.0202552	+	0.612703i
$431$	28.8964			1.39189			0.695946	−	0.718094i	$-0.254985\pi$
$431$	28.8964			1.39189			0.695946	+	0.718094i	$0.254985\pi$
$432$		−	7.55370i		−	0.363428i
$433$		−	2.26781i		−	0.108984i	−0.998514	−	0.0544921i	$-0.982646\pi$
$433$		−	2.26781i		−	0.108984i	0.998514	−	0.0544921i	$-0.0173540\pi$
$434$	10.8098			0.518888
$435$	17.2166	−	0.569161i	0.825475	−	0.0272892i
$436$	−14.9612			−0.716514
$437$		−	21.0995i		−	1.00933i
$438$			9.22888i			0.440973i
$439$	18.5771			0.886639			0.443319	−	0.896364i	$-0.353801\pi$
$439$	18.5771			0.886639			0.443319	+	0.896364i	$0.353801\pi$
$440$	−14.5381	+	0.480611i	−0.693076	+	0.0229122i
$441$	1.00000			0.0476190
$442$			23.3341i			1.10989i
$443$			20.0984i			0.954906i	0.878657	+	0.477453i	$0.158440\pi$
$443$			20.0984i			0.954906i	−0.878657	+	0.477453i	$0.841560\pi$
$444$	27.3810			1.29945
$445$	−0.553107	−	16.7310i	−0.0262198	−	0.793127i
$446$	−20.0455			−0.949180
$447$			3.30587i			0.156362i
$448$		−	1.03749i		−	0.0490169i
$449$	−20.3555			−0.960635			−0.480317	−	0.877095i	$-0.659479\pi$
$449$	−20.3555			−0.960635			−0.480317	+	0.877095i	$0.659479\pi$
$450$	−0.844704	−	12.7618i	−0.0398197	−	0.601599i
$451$	−9.67658			−0.455652
$452$		−	45.5601i		−	2.14297i
$453$			8.49695i			0.399222i
$454$	1.44601			0.0678645
$455$	0.227514	+	6.88212i	0.0106660	+	0.322639i
$456$	43.3648			2.03074
$457$			4.42398i			0.206945i	0.994632	+	0.103472i	$0.0329954\pi$
$457$			4.42398i			0.206945i	−0.994632	+	0.103472i	$0.967005\pi$
$458$		−	54.8154i		−	2.56135i
$459$	−2.96227			−0.138267
$460$	32.1363	−	1.06239i	1.49836	−	0.0495341i
$461$	27.2822			1.27066			0.635329	−	0.772242i	$-0.280865\pi$
$461$	27.2822			1.27066			0.635329	+	0.772242i	$0.280865\pi$
$462$			2.55795i			0.119007i
$463$		−	41.3504i		−	1.92172i	−0.277039	−	0.960859i	$-0.589353\pi$
$463$		−	41.3504i		−	1.92172i	0.277039	−	0.960859i	$-0.410647\pi$
$464$	−58.1916			−2.70148
$465$	−9.44438	+	0.312220i	−0.437973	+	0.0144788i
$466$	−8.68958			−0.402537
$467$		−	12.7729i		−	0.591059i	−0.955334	−	0.295529i	$-0.904504\pi$
$467$		−	12.7729i		−	0.591059i	0.955334	−	0.295529i	$-0.0954961\pi$
$468$		−	13.9904i		−	0.646704i
$469$	1.61927			0.0747710
$470$	0.163033	+	4.93163i	0.00752017	+	0.227479i
$471$	−19.8302			−0.913728
$472$		−	33.5492i		−	1.54423i
$473$			2.22251i			0.102191i
$474$	−35.9846			−1.65283
$475$	33.2582	−	2.20135i	1.52599	−	0.101005i
$476$	−13.4580			−0.616844
$477$			7.20541i			0.329913i
$478$		−	27.3350i		−	1.25027i
$479$	−20.6673			−0.944312			−0.472156	−	0.881515i	$-0.656524\pi$
$479$	−20.6673			−0.944312			−0.472156	+	0.881515i	$0.656524\pi$
$480$	0.466313	+	14.1056i	0.0212842	+	0.643828i
$481$	18.5597			0.846248
$482$			49.3709i			2.24878i
$483$		−	3.16515i		−	0.144019i
$484$	−4.54312			−0.206505
$485$	−42.9162	+	1.41876i	−1.94873	+	0.0644225i
$486$	2.55795			0.116031
$487$		−	39.8937i		−	1.80776i	−0.427791	−	0.903878i	$-0.640708\pi$
$487$		−	39.8937i		−	1.80776i	0.427791	−	0.903878i	$-0.359292\pi$
$488$		−	57.6390i		−	2.60920i
$489$	5.20580			0.235415
$490$	−5.71663	+	0.188985i	−0.258251	+	0.00853746i
$491$	40.1453			1.81173			0.905867	−	0.423563i	$-0.139221\pi$
$491$	40.1453			1.81173			0.905867	+	0.423563i	$0.139221\pi$
$492$			43.9618i			1.98195i
$493$			22.8205i			1.02778i
$494$	52.5103			2.36255
$495$	−0.0738813	−	2.23485i	−0.00332072	−	0.100449i
$496$	31.9217			1.43333
$497$			1.95649i			0.0877604i
$498$		−	45.2857i		−	2.02930i
$499$	−8.07505			−0.361489			−0.180744	−	0.983530i	$-0.557851\pi$
$499$	−8.07505			−0.361489			−0.180744	+	0.983530i	$0.557851\pi$
$500$	5.02744	+	50.5442i	0.224834	+	2.26041i
$501$	−14.2801			−0.637986
$502$			50.8231i			2.26835i
$503$		−	34.2537i		−	1.52730i	−0.645632	−	0.763649i	$-0.723406\pi$
$503$		−	34.2537i		−	1.52730i	0.645632	−	0.763649i	$-0.276594\pi$
$504$	6.50518			0.289764
$505$	0.302695	+	9.15626i	0.0134697	+	0.407448i
$506$	8.09630			0.359925
$507$			3.51693i			0.156192i
$508$			58.6194i			2.60081i
$509$	−12.7326			−0.564362			−0.282181	−	0.959361i	$-0.591058\pi$
$509$	−12.7326			−0.564362			−0.282181	+	0.959361i	$0.591058\pi$
$510$	16.9342	−	0.559824i	0.749860	−	0.0247894i
$511$	−3.60792			−0.159605
$512$			50.6001i			2.23623i
$513$			6.66619i			0.294319i
$514$	−26.7088			−1.17807
$515$	−37.4007	+	1.23642i	−1.64807	+	0.0544832i
$516$	10.0971			0.444502
$517$			0.862680i			0.0379406i
$518$			15.4166i			0.677366i
$519$	10.2366			0.449335
$520$	1.48002	+	44.7694i	0.0649033	+	1.96327i
$521$	−5.48906			−0.240480			−0.120240	−	0.992745i	$-0.538366\pi$
$521$	−5.48906			−0.240480			−0.120240	+	0.992745i	$0.538366\pi$
$522$		−	19.7058i		−	0.862497i
$523$			31.9323i			1.39630i	0.715950	+	0.698152i	$0.245994\pi$
$523$			31.9323i			1.39630i	−0.715950	+	0.698152i	$0.754006\pi$
$524$	24.5684			1.07328
$525$	4.98908	−	0.330227i	0.217741	−	0.0144123i
$526$	58.0207			2.52982
$527$		−	12.5185i		−	0.545312i
$528$			7.55370i			0.328733i
$529$	12.9818			0.564427
$530$	−1.36171	−	41.1907i	−0.0591491	−	1.78921i
$531$	5.15730			0.223808
$532$			30.2853i			1.31303i
$533$			29.7986i			1.29072i
$534$	−19.1499			−0.828699
$535$	19.5686	−	0.646913i	0.846024	−	0.0279685i
$536$	10.5337			0.454985
$537$			18.6427i			0.804494i
$538$		−	45.6435i		−	1.96783i
$539$	−1.00000			−0.0430730
$540$	−10.1532	+	0.335652i	−0.436923	+	0.0144441i
$541$	8.12235			0.349207			0.174604	−	0.984639i	$-0.444136\pi$
$541$	8.12235			0.349207			0.174604	+	0.984639i	$0.444136\pi$
$542$			76.6411i			3.29202i
$543$			7.95159i			0.341235i
$544$	−18.6968			−0.801619
$545$	0.243303	+	7.35972i	0.0104220	+	0.315256i
$546$	7.87711			0.337109
$547$			44.5491i			1.90478i	0.304880	+	0.952391i	$0.401384\pi$
$547$			44.5491i			1.90478i	−0.304880	+	0.952391i	$0.598616\pi$
$548$			66.7786i			2.85264i
$549$	8.86048			0.378156
$550$	0.844704	+	12.7618i	0.0360183	+	0.544167i
$551$	51.3545			2.18777
$552$		−	20.5899i		−	0.876363i
$553$		−	14.0677i		−	0.598220i
$554$	57.8336			2.45712
$555$	−0.445277	−	13.4693i	−0.0189009	−	0.571738i
$556$	36.3149			1.54010
$557$			30.5951i			1.29636i	0.761489	+	0.648178i	$0.224469\pi$
$557$			30.5951i			1.29636i	−0.761489	+	0.648178i	$0.775531\pi$
$558$			10.8098i			0.457616i
$559$	6.84413			0.289476
$560$	−16.8814	+	0.558077i	−0.713368	+	0.0235831i
$561$	2.96227			0.125067
$562$			48.0156i			2.02542i
$563$		−	24.8327i		−	1.04658i	−0.852156	−	0.523288i	$-0.824705\pi$
$563$		−	24.8327i		−	1.04658i	0.852156	−	0.523288i	$-0.175295\pi$
$564$	3.91926			0.165031
$565$	−22.4119	+	0.740909i	−0.942874	+	0.0311703i
$566$	−33.4285			−1.40511
$567$			1.00000i			0.0419961i
$568$			12.7273i			0.534025i
$569$	−33.0065			−1.38371			−0.691853	−	0.722039i	$-0.743205\pi$
$569$	−33.0065			−1.38371			−0.691853	+	0.722039i	$0.743205\pi$
$570$	−1.25981	−	38.1082i	−0.0527676	−	1.59617i
$571$	31.4689			1.31693			0.658466	−	0.752611i	$-0.271206\pi$
$571$	31.4689			1.31693			0.658466	+	0.752611i	$0.271206\pi$
$572$			13.9904i			0.584966i
$573$		−	4.76297i		−	0.198976i
$574$	−24.7522			−1.03314
$575$	−1.04522	−	15.7912i	−0.0435886	−	0.658539i
$576$	1.03749			0.0432288
$577$			19.5748i			0.814909i	0.913226	+	0.407454i	$0.133583\pi$
$577$			19.5748i			0.814909i	−0.913226	+	0.407454i	$0.866417\pi$
$578$		−	21.0390i		−	0.875108i
$579$	−3.19789			−0.132900
$580$	2.58577	+	78.2173i	0.107368	+	3.24780i
$581$	17.7039			0.734481
$582$			49.1209i			2.03613i
$583$		−	7.20541i		−	0.298418i
$584$	−23.4702			−0.971202
$585$	−6.88212	+	0.227514i	−0.284541	+	0.00940656i
$586$	−21.1582			−0.874039
$587$			4.74149i			0.195702i	0.995201	+	0.0978511i	$0.0311969\pi$
$587$			4.74149i			0.195702i	−0.995201	+	0.0978511i	$0.968803\pi$
$588$			4.54312i			0.187355i
$589$	−28.1711			−1.16077
$590$	−29.4824	+	0.974651i	−1.21377	+	0.0401257i
$591$	−20.1314			−0.828096
$592$			45.5256i			1.87109i
$593$			25.1232i			1.03169i	0.856683	+	0.515844i	$0.172522\pi$
$593$			25.1232i			1.03169i	−0.856683	+	0.515844i	$0.827478\pi$
$594$	−2.55795			−0.104954
$595$	0.218856	+	6.62022i	0.00897224	+	0.271403i
$596$	−15.0190			−0.615201
$597$			1.88964i			0.0773377i
$598$		−	24.9322i		−	1.01956i
$599$	−20.7782			−0.848975			−0.424488	−	0.905434i	$-0.639546\pi$
$599$	−20.7782			−0.848975			−0.424488	+	0.905434i	$0.639546\pi$
$600$	32.4549	−	2.14818i	1.32497	−	0.0876993i
$601$	−23.9211			−0.975764			−0.487882	−	0.872910i	$-0.662230\pi$
$601$	−23.9211			−0.975764			−0.487882	+	0.872910i	$0.662230\pi$
$602$			5.68508i			0.231706i
$603$			1.61927i			0.0659418i
$604$	−38.6027			−1.57072
$605$	0.0738813	+	2.23485i	0.00300370	+	0.0908595i
$606$	10.4800			0.425722
$607$			7.25002i			0.294269i	0.989116	+	0.147135i	$0.0470050\pi$
$607$			7.25002i			0.294269i	−0.989116	+	0.147135i	$0.952995\pi$
$608$			42.0746i			1.70635i
$609$	7.70372			0.312171
$610$	−50.6521	+	1.67450i	−2.05084	+	0.0677983i
$611$	2.65659			0.107474
$612$		−	13.4580i		−	0.544006i
$613$		−	41.0082i		−	1.65631i	−0.560501	−	0.828154i	$-0.689392\pi$
$613$		−	41.0082i		−	1.65631i	0.560501	−	0.828154i	$-0.310608\pi$
$614$	43.6879			1.76310
$615$	21.6257	−	0.714918i	0.872031	−	0.0288283i
$616$	−6.50518			−0.262101
$617$			10.9673i			0.441525i	0.975328	+	0.220763i	$0.0708546\pi$
$617$			10.9673i			0.441525i	−0.975328	+	0.220763i	$0.929145\pi$
$618$			42.8079i			1.72199i
$619$	16.9429			0.680993			0.340496	−	0.940246i	$-0.389405\pi$
$619$	16.9429			0.680993			0.340496	+	0.940246i	$0.389405\pi$
$620$	−1.41845	−	42.9070i	−0.0569664	−	1.72319i
$621$	3.16515			0.127013
$622$			46.8704i			1.87933i
$623$		−	7.48643i		−	0.299937i
$624$	23.2613			0.931198
$625$	24.7819	−	3.29506i	0.991276	−	0.131802i
$626$	88.5355			3.53859
$627$		−	6.66619i		−	0.266222i
$628$		−	90.0910i		−	3.59502i
$629$	17.8534			0.711861
$630$	−0.188985	−	5.71663i	−0.00752933	−	0.227756i
$631$	−39.8127			−1.58492			−0.792458	−	0.609926i	$-0.791199\pi$
$631$	−39.8127			−1.58492			−0.792458	+	0.609926i	$0.791199\pi$
$632$		−	91.5131i		−	3.64019i
$633$			27.6484i			1.09892i
$634$	−25.2843			−1.00417
$635$	28.8360	−	0.953282i	1.14432	−	0.0378298i
$636$	−32.7351			−1.29803
$637$			3.07946i			0.122013i
$638$			19.7058i			0.780158i
$639$	−1.95649			−0.0773974
$640$	22.2802	−	0.736555i	0.880701	−	0.0291149i
$641$	−20.1615			−0.796330			−0.398165	−	0.917314i	$-0.630353\pi$
$641$	−20.1615			−0.796330			−0.398165	+	0.917314i	$0.630353\pi$
$642$		−	22.3977i		−	0.883968i
$643$		−	21.0223i		−	0.829039i	−0.910040	−	0.414520i	$-0.863950\pi$
$643$		−	21.0223i		−	0.829039i	0.910040	−	0.414520i	$-0.136050\pi$
$644$	14.3797			0.566638
$645$	−0.164202	−	4.96697i	−0.00646545	−	0.195574i
$646$	50.5120			1.98737
$647$			38.1861i			1.50125i	0.660729	+	0.750625i	$0.270247\pi$
$647$			38.1861i			1.50125i	−0.660729	+	0.750625i	$0.729753\pi$
$648$			6.50518i			0.255548i
$649$	−5.15730			−0.202442
$650$	39.2996	−	2.60123i	1.54146	−	0.102029i
$651$	−4.22596			−0.165629
$652$			23.6506i			0.926229i
$653$		−	21.6028i		−	0.845384i	−0.906273	−	0.422692i	$-0.861085\pi$
$653$		−	21.6028i		−	0.845384i	0.906273	−	0.422692i	$-0.138915\pi$
$654$	8.42376			0.329395
$655$	−0.399537	−	12.0857i	−0.0156112	−	0.472226i
$656$	−73.0940			−2.85384
$657$		−	3.60792i		−	0.140758i
$658$			2.20670i			0.0860259i
$659$	−25.6429			−0.998906			−0.499453	−	0.866341i	$-0.666466\pi$
$659$	−25.6429			−0.998906			−0.499453	+	0.866341i	$0.666466\pi$
$660$	10.1532	−	0.335652i	0.395212	−	0.0130652i
$661$	22.2432			0.865161			0.432581	−	0.901595i	$-0.357603\pi$
$661$	22.2432			0.865161			0.432581	+	0.901595i	$0.357603\pi$
$662$			54.9637i			2.13623i
$663$		−	9.12219i		−	0.354277i
$664$	115.167			4.46935
$665$	14.8979	−	0.492507i	0.577716	−	0.0190986i
$666$	−15.4166			−0.597380
$667$		−	24.3834i		−	0.944131i
$668$		−	64.8760i		−	2.51013i
$669$	7.83653			0.302978
$670$	−0.306018	−	9.25678i	−0.0118225	−	0.357621i
$671$	−8.86048			−0.342055
$672$			6.31165i			0.243477i
$673$			42.3540i			1.63263i	0.577610	+	0.816313i	$0.303986\pi$
$673$			42.3540i			1.63263i	−0.577610	+	0.816313i	$0.696014\pi$
$674$	53.7913			2.07196
$675$	0.330227	+	4.98908i	0.0127104	+	0.192030i
$676$	−15.9778			−0.614532
$677$		−	1.77847i		−	0.0683521i	−0.999416	−	0.0341761i	$-0.989119\pi$
$677$		−	1.77847i		−	0.0683521i	0.999416	−	0.0341761i	$-0.0108807\pi$
$678$			25.6521i			0.985162i
$679$	−19.2032			−0.736951
$680$	1.42370	+	43.0658i	0.0545964	+	1.65150i
$681$	−0.565299			−0.0216623
$682$		−	10.8098i		−	0.413929i
$683$			11.5284i			0.441120i	0.975373	+	0.220560i	$0.0707885\pi$
$683$			11.5284i			0.441120i	−0.975373	+	0.220560i	$0.929211\pi$
$684$	−30.2853			−1.15799
$685$	32.8497	−	1.08597i	1.25512	−	0.0414928i
$686$	−2.55795			−0.0976631
$687$			21.4294i			0.817583i
$688$			16.7882i			0.640044i
$689$	−22.1888			−0.845325
$690$	−18.0940	+	0.598165i	−0.688827	+	0.0227718i
$691$	28.2219			1.07361			0.536806	−	0.843706i	$-0.319631\pi$
$691$	28.2219			1.07361			0.536806	+	0.843706i	$0.319631\pi$
$692$			46.5059i			1.76789i
$693$		−	1.00000i		−	0.0379869i
$694$	−0.408382			−0.0155020
$695$	−0.590562	−	17.8640i	−0.0224013	−	0.677620i
$696$	50.1141			1.89957
$697$			28.6646i			1.08575i
$698$			45.4333i			1.71968i
$699$	3.39708			0.128489
$700$	1.50026	+	22.6660i	0.0567045	+	0.856694i
$701$	34.1072			1.28821			0.644105	−	0.764937i	$-0.277230\pi$
$701$	34.1072			1.28821			0.644105	+	0.764937i	$0.277230\pi$
$702$			7.87711i			0.297302i
$703$		−	40.1766i		−	1.51529i
$704$	−1.03749			−0.0391019
$705$	−0.0637359	−	1.92796i	−0.00240043	−	0.0726111i
$706$	−36.3890			−1.36952
$707$			4.09704i			0.154085i
$708$			23.4302i			0.880562i
$709$	−15.1292			−0.568189			−0.284095	−	0.958796i	$-0.591693\pi$
$709$	−15.1292			−0.568189			−0.284095	+	0.958796i	$0.591693\pi$
$710$	11.1845	−	0.369746i	0.419747	−	0.0138763i
$711$	14.0677			0.527581
$712$		−	48.7006i		−	1.82513i
$713$			13.3758i			0.500928i
$714$	7.57735			0.283575
$715$	6.88212	−	0.227514i	0.257377	−	0.00850856i
$716$	−84.6962			−3.16525
$717$			10.6863i			0.399086i
$718$		−	2.30243i		−	0.0859261i
$719$	−30.9777			−1.15527			−0.577637	−	0.816294i	$-0.696025\pi$
$719$	−30.9777			−1.15527			−0.577637	+	0.816294i	$0.696025\pi$
$720$	−0.558077	−	16.8814i	−0.0207983	−	0.629131i
$721$	−16.7352			−0.623253
$722$		−	65.0694i		−	2.42163i
$723$		−	19.3010i		−	0.717811i
$724$	−36.1250			−1.34258
$725$	38.4345	−	2.54398i	1.42742	−	0.0944809i
$726$	2.55795			0.0949345
$727$		−	15.5033i		−	0.574985i	−0.957783	−	0.287493i	$-0.907178\pi$
$727$		−	15.5033i		−	0.574985i	0.957783	−	0.287493i	$-0.0928217\pi$
$728$			20.0324i			0.742452i
$729$	−1.00000			−0.0370370
$730$	0.681842	+	20.6251i	0.0252361	+	0.763371i
$731$	6.58368			0.243506
$732$			40.2542i			1.48784i
$733$			5.55773i			0.205279i	0.994719	+	0.102640i	$0.0327289\pi$
$733$			5.55773i			0.205279i	−0.994719	+	0.102640i	$0.967271\pi$
$734$	−91.2986			−3.36989
$735$	2.23485	−	0.0738813i	0.0824336	−	0.00272515i
$736$	19.9773			0.736374
$737$		−	1.61927i		−	0.0596466i
$738$		−	24.7522i		−	0.911142i
$739$	−8.16115			−0.300213			−0.150106	−	0.988670i	$-0.547962\pi$
$739$	−8.16115			−0.300213			−0.150106	+	0.988670i	$0.547962\pi$
$740$	61.1924	−	2.02295i	2.24948	−	0.0743650i
$741$	−20.5283			−0.754124
$742$		−	18.4311i		−	0.676627i
$743$		−	4.40856i		−	0.161734i	−0.996725	−	0.0808671i	$-0.974231\pi$
$743$		−	4.40856i		−	0.161734i	0.996725	−	0.0808671i	$-0.0257689\pi$
$744$	−27.4907			−1.00786
$745$	0.244242	+	7.38812i	0.00894834	+	0.270680i
$746$	4.25063			0.155626
$747$			17.7039i			0.647752i
$748$			13.4580i			0.492072i
$749$	8.75612			0.319942
$750$	−2.83065	−	28.4583i	−0.103361	−	1.03915i
$751$	1.50667			0.0549790			0.0274895	−	0.999622i	$-0.491249\pi$
$751$	1.50667			0.0549790			0.0274895	+	0.999622i	$0.491249\pi$
$752$			6.51643i			0.237630i
$753$		−	19.8687i		−	0.724055i
$754$	60.6831			2.20995
$755$	0.627766	+	18.9894i	0.0228467	+	0.691095i
$756$	−4.54312			−0.165232
$757$			51.1873i			1.86043i	0.367010	+	0.930217i	$0.380382\pi$
$757$			51.1873i			1.86043i	−0.367010	+	0.930217i	$0.619618\pi$
$758$		−	82.5587i		−	2.99867i
$759$	−3.16515			−0.114888
$760$	96.9136	−	3.20384i	3.51543	−	0.116216i
$761$	−18.7621			−0.680124			−0.340062	−	0.940403i	$-0.610448\pi$
$761$	−18.7621			−0.680124			−0.340062	+	0.940403i	$0.610448\pi$
$762$		−	33.0050i		−	1.19564i
$763$			3.29316i			0.119221i
$764$	21.6387			0.782862
$765$	−6.62022	+	0.218856i	−0.239355	+	0.00791277i
$766$	−41.8029			−1.51040
$767$			15.8817i			0.573455i
$768$		−	27.5763i		−	0.995076i
$769$	−9.49671			−0.342460			−0.171230	−	0.985231i	$-0.554774\pi$
$769$	−9.49671			−0.342460			−0.171230	+	0.985231i	$0.554774\pi$
$770$	0.188985	+	5.71663i	0.00681054	+	0.206013i
$771$	10.4415			0.376041
$772$		−	14.5284i		−	0.522889i
$773$		−	15.5003i		−	0.557508i	−0.960362	−	0.278754i	$-0.910079\pi$
$773$		−	15.5003i		−	0.557508i	0.960362	−	0.278754i	$-0.0899215\pi$
$774$	−5.68508			−0.204346
$775$	−21.0837	+	1.39553i	−0.757348	+	0.0501288i
$776$	−124.920			−4.48438
$777$		−	6.02692i		−	0.216215i
$778$		−	6.67001i		−	0.239132i
$779$	64.5059			2.31116
$780$	−1.03363	−	31.2663i	−0.0370097	−	1.11951i
$781$	1.95649			0.0700086
$782$		−	23.9835i		−	0.857647i
$783$			7.70372i			0.275309i
$784$	−7.55370			−0.269775
$785$	−44.3175	+	1.46508i	−1.58176	+	0.0522910i
$786$	−13.8330			−0.493405
$787$		−	17.3241i		−	0.617538i	−0.951137	−	0.308769i	$-0.900083\pi$
$787$		−	17.3241i		−	0.617538i	0.951137	−	0.308769i	$-0.0999171\pi$
$788$		−	91.4594i		−	3.25811i
$789$	−22.6825			−0.807517
$790$	−80.4200	+	2.65859i	−2.86121	+	0.0945882i
$791$	−10.0284			−0.356568
$792$		−	6.50518i		−	0.231152i
$793$			27.2855i			0.968936i
$794$	36.7725			1.30501
$795$	0.532345	+	16.1030i	0.0188803	+	0.571114i
$796$	−8.58485			−0.304282
$797$			12.5065i			0.443005i	0.975160	+	0.221502i	$0.0710960\pi$
$797$			12.5065i			0.443005i	−0.975160	+	0.221502i	$0.928904\pi$
$798$		−	17.0518i		−	0.603627i
$799$	2.55549			0.0904069
$800$	2.08427	+	31.4893i	0.0736902	+	1.11332i
$801$	7.48643			0.264520
$802$		−	20.5543i		−	0.725796i
$803$			3.60792i			0.127321i
$804$	−7.35655			−0.259445
$805$	−0.233845	−	7.07363i	−0.00824197	−	0.249313i
$806$	−33.2884			−1.17253
$807$			17.8438i			0.628131i
$808$			26.6520i			0.937614i
$809$	−4.48140			−0.157557			−0.0787787	−	0.996892i	$-0.525102\pi$
$809$	−4.48140			−0.157557			−0.0787787	+	0.996892i	$0.525102\pi$
$810$	5.71663	−	0.188985i	0.200862	−	0.00664025i
$811$	−19.3253			−0.678602			−0.339301	−	0.940678i	$-0.610191\pi$
$811$	−19.3253			−0.678602			−0.339301	+	0.940678i	$0.610191\pi$
$812$			34.9989i			1.22822i
$813$		−	29.9619i		−	1.05081i
$814$	15.4166			0.540351
$815$	11.6342	−	0.384611i	0.407527	−	0.0134724i
$816$	22.3761			0.783321
$817$		−	14.8157i		−	0.518335i
$818$			50.3890i			1.76181i
$819$	−3.07946			−0.107605
$820$	3.24796	+	98.2480i	0.113424	+	3.43097i
$821$	23.3796			0.815955			0.407978	−	0.912992i	$-0.366234\pi$
$821$	23.3796			0.815955			0.407978	+	0.912992i	$0.366234\pi$
$822$		−	37.5989i		−	1.31141i
$823$			36.8593i			1.28484i	0.766355	+	0.642418i	$0.222069\pi$
$823$			36.8593i			1.28484i	−0.766355	+	0.642418i	$0.777931\pi$
$824$	−108.866			−3.79252
$825$	−0.330227	−	4.98908i	−0.0114970	−	0.173698i
$826$	−13.1921			−0.459013
$827$		−	55.9740i		−	1.94641i	−0.229946	−	0.973203i	$-0.573855\pi$
$827$		−	55.9740i		−	1.94641i	0.229946	−	0.973203i	$-0.426145\pi$
$828$			14.3797i			0.499728i
$829$	−21.2785			−0.739033			−0.369516	−	0.929224i	$-0.620477\pi$
$829$	−21.2785			−0.739033			−0.369516	+	0.929224i	$0.620477\pi$
$830$	−3.34577	−	101.207i	−0.116133	−	3.51293i
$831$	−22.6094			−0.784310
$832$			3.19491i			0.110764i
$833$			2.96227i			0.102637i
$834$	−20.4467			−0.708012
$835$	−31.9137	+	1.05503i	−1.10442	+	0.0365108i
$836$	30.2853			1.04744
$837$		−	4.22596i		−	0.146071i
$838$			34.3926i			1.18807i
$839$	40.8427			1.41005			0.705023	−	0.709184i	$-0.250936\pi$
$839$	40.8427			1.41005			0.705023	+	0.709184i	$0.250936\pi$
$840$	14.5381	−	0.480611i	0.501612	−	0.0165827i
$841$	30.3473			1.04646
$842$		−	25.0506i		−	0.863302i
$843$		−	18.7711i		−	0.646511i
$844$	−125.610			−4.32367
$845$	0.259835	+	7.85980i	0.00893861	+	0.270385i
$846$	−2.20670			−0.0758677
$847$			1.00000i			0.0343604i
$848$		−	54.4275i		−	1.86905i
$849$	13.0685			0.448509
$850$	37.8040	−	2.50224i	1.29667	−	0.0858262i
$851$	−19.0761			−0.653921
$852$		−	8.88855i		−	0.304517i
$853$			35.1000i			1.20180i	0.799323	+	0.600901i	$0.205191\pi$
$853$			35.1000i			1.20180i	−0.799323	+	0.600901i	$0.794809\pi$
$854$	−22.6647			−0.775569
$855$	0.492507	+	14.8979i	0.0168434	+	0.509498i
$856$	56.9601			1.94686
$857$		−	38.8811i		−	1.32815i	−0.747665	−	0.664076i	$-0.768825\pi$
$857$		−	38.8811i		−	1.32815i	0.747665	−	0.664076i	$-0.231175\pi$
$858$		−	7.87711i		−	0.268920i
$859$	−37.5667			−1.28176			−0.640880	−	0.767641i	$-0.721431\pi$
$859$	−37.5667			−1.28176			−0.640880	+	0.767641i	$0.721431\pi$
$860$	22.5656	−	0.745989i	0.769479	−	0.0254380i
$861$	9.67658			0.329777
$862$		−	73.9157i		−	2.51758i
$863$		−	4.56282i		−	0.155320i	−0.996980	−	0.0776600i	$-0.975255\pi$
$863$		−	4.56282i		−	0.155320i	0.996980	−	0.0776600i	$-0.0247449\pi$
$864$	−6.31165			−0.214727
$865$	22.8771	−	0.756290i	0.777846	−	0.0257146i
$866$	−5.80096			−0.197125
$867$			8.22495i			0.279334i
$868$		−	19.1991i		−	0.651659i
$869$	−14.0677			−0.477215
$870$	−1.45589	−	44.0394i	−0.0493592	−	1.49307i
$871$	−4.98648			−0.168960
$872$			21.4226i			0.725462i
$873$		−	19.2032i		−	0.649930i
$874$	−53.9715			−1.82561
$875$	11.1254	−	1.10661i	0.376109	−	0.0374101i
$876$	16.3912			0.553808
$877$			0.416652i			0.0140693i	0.999975	+	0.00703467i	$0.00223922\pi$
$877$			0.416652i			0.0140693i	−0.999975	+	0.00703467i	$0.997761\pi$
$878$		−	47.5194i		−	1.60370i
$879$	8.27156			0.278993
$880$	0.558077	+	16.8814i	0.0188128	+	0.569071i
$881$	7.48094			0.252039			0.126020	−	0.992028i	$-0.459780\pi$
$881$	7.48094			0.252039			0.126020	+	0.992028i	$0.459780\pi$
$882$		−	2.55795i		−	0.0861307i
$883$			4.12874i			0.138943i	0.997584	+	0.0694716i	$0.0221313\pi$
$883$			4.12874i			0.138943i	−0.997584	+	0.0694716i	$0.977869\pi$
$884$	41.4432			1.39389
$885$	11.5258	−	0.381028i	0.387435	−	0.0128081i
$886$	51.4109			1.72718
$887$			39.7750i			1.33551i	0.744379	+	0.667757i	$0.232746\pi$
$887$			39.7750i			1.33551i	−0.744379	+	0.667757i	$0.767254\pi$
$888$		−	39.2062i		−	1.31567i
$889$	12.9029			0.432749
$890$	−42.7972	+	1.41482i	−1.43456	+	0.0474249i
$891$	1.00000			0.0335013
$892$			35.6023i			1.19205i
$893$		−	5.75079i		−	0.192443i
$894$	8.45627			0.282820
$895$	1.37735	+	41.6637i	0.0460397	+	1.39266i
$896$	9.96944			0.333056
$897$			9.74695i			0.325441i
$898$			52.0684i			1.73754i
$899$	−32.5557			−1.08579
$900$	−22.6660	+	1.50026i	−0.755534	+	0.0500087i
$901$	−21.3444			−0.711085
$902$			24.7522i			0.824159i
$903$		−	2.22251i		−	0.0739605i
$904$	−65.2363			−2.16973
$905$	0.587474	+	17.7706i	0.0195283	+	0.590714i
$906$	21.7348			0.722091
$907$		−	2.62545i		−	0.0871765i	−0.999050	−	0.0435882i	$-0.986121\pi$
$907$		−	2.62545i		−	0.0871765i	0.999050	−	0.0435882i	$-0.0138790\pi$
$908$		−	2.56822i		−	0.0852294i
$909$	−4.09704			−0.135890
$910$	17.6041	−	0.581971i	0.583571	−	0.0192922i
$911$	10.4571			0.346460			0.173230	−	0.984881i	$-0.444580\pi$
$911$	10.4571			0.346460			0.173230	+	0.984881i	$0.444580\pi$
$912$		−	50.3544i		−	1.66740i
$913$		−	17.7039i		−	0.585913i
$914$	11.3163			0.374311
$915$	19.8018	−	0.654623i	0.654628	−	0.0216412i
$916$	−97.3563			−3.21674
$917$		−	5.40783i		−	0.178582i
$918$			7.57735i			0.250090i
$919$	−9.40827			−0.310350			−0.155175	−	0.987887i	$-0.549594\pi$
$919$	−9.40827			−0.310350			−0.155175	+	0.987887i	$0.549594\pi$
$920$	−1.52121	−	46.0152i	−0.0501527	−	1.51708i
$921$	−17.0792			−0.562780
$922$		−	69.7865i		−	2.29830i
$923$		−	6.02492i		−	0.198313i
$924$	4.54312			0.149458
$925$	−1.99025	−	30.0688i	−0.0654391	−	0.988657i
$926$	−105.772			−3.47590
$927$		−	16.7352i		−	0.549657i
$928$			48.6232i			1.59613i
$929$	−57.5332			−1.88760			−0.943802	−	0.330512i	$-0.892779\pi$
$929$	−57.5332			−1.88760			−0.943802	+	0.330512i	$0.892779\pi$
$930$	0.798643	+	24.1583i	0.0261885	+	0.792181i
$931$	6.66619			0.218476
$932$			15.4334i			0.505536i
$933$		−	18.3234i		−	0.599881i
$934$	−32.6724			−1.06908
$935$	6.62022	−	0.218856i	0.216504	−	0.00715737i
$936$	−20.0324			−0.654781
$937$		−	33.1150i		−	1.08182i	−0.841081	−	0.540910i	$-0.818080\pi$
$937$		−	33.1150i		−	1.08182i	0.841081	−	0.540910i	$-0.181920\pi$
$938$		−	4.14202i		−	0.135242i
$939$	−34.6119			−1.12952
$940$	8.75895	−	0.289560i	0.285685	−	0.00944441i
$941$	−11.5478			−0.376447			−0.188223	−	0.982126i	$-0.560273\pi$
$941$	−11.5478			−0.376447			−0.188223	+	0.982126i	$0.560273\pi$
$942$			50.7247i			1.65270i
$943$		−	30.6278i		−	0.997379i
$944$	−38.9567			−1.26793
$945$	0.0738813	+	2.23485i	0.00240336	+	0.0726996i
$946$	5.68508			0.184838
$947$		−	30.1940i		−	0.981172i	−0.871393	−	0.490586i	$-0.836783\pi$
$947$		−	30.1940i		−	0.981172i	0.871393	−	0.490586i	$-0.163217\pi$
$948$			63.9114i			2.07574i
$949$	11.1104			0.360660
$950$	−5.63096	−	85.0728i	−0.182692	−	2.76013i
$951$	9.88458			0.320529
$952$			19.2701i			0.624548i
$953$			48.7356i			1.57870i	0.613943	+	0.789351i	$0.289583\pi$
$953$			48.7356i			1.57870i	−0.613943	+	0.789351i	$0.710417\pi$
$954$	18.4311			0.596729
$955$	−0.351894	−	10.6445i	−0.0113870	−	0.344448i
$956$	−48.5490			−1.57019
$957$		−	7.70372i		−	0.249026i
$958$			52.8659i			1.70802i
$959$	14.6988			0.474650
$960$	2.31863	−	0.0766512i	0.0748336	−	0.00247391i
$961$	−13.1412			−0.423911
$962$		−	47.4747i		−	1.53065i
$963$			8.75612i			0.282162i
$964$	87.6866			2.82420
$965$	−7.14680	+	0.236265i	−0.230064	+	0.00760562i
$966$	−8.09630			−0.260494
$967$		−	10.6933i		−	0.343873i	−0.985108	−	0.171937i	$-0.944998\pi$
$967$		−	10.6933i		−	0.343873i	0.985108	−	0.171937i	$-0.0550024\pi$
$968$			6.50518i			0.209084i
$969$	−19.7471			−0.634367
$970$	3.62911	+	109.778i	0.116524	+	3.52475i
$971$	38.8784			1.24767			0.623834	−	0.781557i	$-0.285574\pi$
$971$	38.8784			1.24767			0.623834	+	0.781557i	$0.285574\pi$
$972$		−	4.54312i		−	0.145721i
$973$		−	7.99339i		−	0.256256i
$974$	−102.046			−3.26977
$975$	−15.3637	+	1.01692i	−0.492031	+	0.0325675i
$976$	−66.9294			−2.14236
$977$			21.1716i			0.677339i	0.940905	+	0.338670i	$0.109977\pi$
$977$			21.1716i			0.677339i	−0.940905	+	0.338670i	$0.890023\pi$
$978$		−	13.3162i		−	0.425805i
$979$	−7.48643			−0.239267
$980$	0.335652	+	10.1532i	0.0107220	+	0.324331i
$981$	−3.29316			−0.105143
$982$		−	102.690i		−	3.27697i
$983$		−	11.0354i		−	0.351974i	−0.984392	−	0.175987i	$-0.943688\pi$
$983$		−	11.0354i		−	0.351974i	0.984392	−	0.175987i	$-0.0563117\pi$
$984$	62.9479			2.00670
$985$	−44.9906	+	1.48733i	−1.43352	+	0.0473904i
$986$	58.3738			1.85900
$987$		−	0.862680i		−	0.0274594i
$988$		−	93.2623i		−	2.96707i
$989$	−7.03458			−0.223687
$990$	−5.71663	+	0.188985i	−0.181687	+	0.00600633i
$991$	−52.2219			−1.65888			−0.829442	−	0.558593i	$-0.811342\pi$
$991$	−52.2219			−1.65888			−0.829442	+	0.558593i	$0.811342\pi$
$992$		−	26.6728i		−	0.846862i
$993$		−	21.4874i		−	0.681882i
$994$	5.00460			0.158736
$995$	0.139609	+	4.22305i	0.00442590	+	0.133880i
$996$	−80.4309			−2.54855
$997$			20.0476i			0.634914i	0.948273	+	0.317457i	$0.102829\pi$
$997$			20.0476i			0.634914i	−0.948273	+	0.317457i	$0.897171\pi$
$998$			20.6556i			0.653841i
$999$	6.02692			0.190683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.f.694.2	✓	20
5.2	odd	4		5775.2.a.co.1.9		10
5.3	odd	4		5775.2.a.cn.1.2		10
5.4	even	2	inner	1155.2.c.f.694.19	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.f.694.2	✓	20	1.1	even	1	trivial
1155.2.c.f.694.19	yes	20	5.4	even	2	inner
5775.2.a.cn.1.2		10	5.3	odd	4
5775.2.a.co.1.9		10	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.55795i q^{2} +1.00000i q^{3} -4.54312 q^{4} +(0.0738813 + 2.23485i) q^{5} +2.55795 q^{6} +1.00000i q^{7} +6.50518i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.55795i q^{2} +1.00000i q^{3} -4.54312 q^{4} +(0.0738813 + 2.23485i) q^{5} +2.55795 q^{6} +1.00000i q^{7} +6.50518i q^{8} -1.00000 q^{9} +(5.71663 - 0.188985i) q^{10} +1.00000 q^{11} -4.54312i q^{12} -3.07946i q^{13} +2.55795 q^{14} +(-2.23485 + 0.0738813i) q^{15} +7.55370 q^{16} -2.96227i q^{17} +2.55795i q^{18} -6.66619 q^{19} +(-0.335652 - 10.1532i) q^{20} -1.00000 q^{21} -2.55795i q^{22} +3.16515i q^{23} -6.50518 q^{24} +(-4.98908 + 0.330227i) q^{25} -7.87711 q^{26} -1.00000i q^{27} -4.54312i q^{28} -7.70372 q^{29} +(0.188985 + 5.71663i) q^{30} +4.22596 q^{31} -6.31165i q^{32} +1.00000i q^{33} -7.57735 q^{34} +(-2.23485 + 0.0738813i) q^{35} +4.54312 q^{36} +6.02692i q^{37} +17.0518i q^{38} +3.07946 q^{39} +(-14.5381 + 0.480611i) q^{40} -9.67658 q^{41} +2.55795i q^{42} +2.22251i q^{43} -4.54312 q^{44} +(-0.0738813 - 2.23485i) q^{45} +8.09630 q^{46} +0.862680i q^{47} +7.55370i q^{48} -1.00000 q^{49} +(0.844704 + 12.7618i) q^{50} +2.96227 q^{51} +13.9904i q^{52} -7.20541i q^{53} -2.55795 q^{54} +(0.0738813 + 2.23485i) q^{55} -6.50518 q^{56} -6.66619i q^{57} +19.7058i q^{58} -5.15730 q^{59} +(10.1532 - 0.335652i) q^{60} -8.86048 q^{61} -10.8098i q^{62} -1.00000i q^{63} -1.03749 q^{64} +(6.88212 - 0.227514i) q^{65} +2.55795 q^{66} -1.61927i q^{67} +13.4580i q^{68} -3.16515 q^{69} +(0.188985 + 5.71663i) q^{70} +1.95649 q^{71} -6.50518i q^{72} +3.60792i q^{73} +15.4166 q^{74} +(-0.330227 - 4.98908i) q^{75} +30.2853 q^{76} +1.00000i q^{77} -7.87711i q^{78} -14.0677 q^{79} +(0.558077 + 16.8814i) q^{80} +1.00000 q^{81} +24.7522i q^{82} -17.7039i q^{83} +4.54312 q^{84} +(6.62022 - 0.218856i) q^{85} +5.68508 q^{86} -7.70372i q^{87} +6.50518i q^{88} -7.48643 q^{89} +(-5.71663 + 0.188985i) q^{90} +3.07946 q^{91} -14.3797i q^{92} +4.22596i q^{93} +2.20670 q^{94} +(-0.492507 - 14.8979i) q^{95} +6.31165 q^{96} +19.2032i q^{97} +2.55795i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more