LMFDB - Embedded newform 1155.2.c.f.694.15

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			694.15
Root			$1.40171i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.f.694.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.40171i q^{2} -1.00000i q^{3} +0.0352144 q^{4} +(-2.22487 - 0.223473i) q^{5} +1.40171 q^{6} -1.00000i q^{7} +2.85278i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.40171i q^{2} -1.00000i q^{3} +0.0352144 q^{4} +(-2.22487 - 0.223473i) q^{5} +1.40171 q^{6} -1.00000i q^{7} +2.85278i q^{8} -1.00000 q^{9} +(0.313244 - 3.11862i) q^{10} +1.00000 q^{11} -0.0352144i q^{12} -1.11469i q^{13} +1.40171 q^{14} +(-0.223473 + 2.22487i) q^{15} -3.92833 q^{16} -3.90149i q^{17} -1.40171i q^{18} +6.16229 q^{19} +(-0.0783475 - 0.00786945i) q^{20} -1.00000 q^{21} +1.40171i q^{22} -5.20203i q^{23} +2.85278 q^{24} +(4.90012 + 0.994397i) q^{25} +1.56247 q^{26} +1.00000i q^{27} -0.0352144i q^{28} -8.42741 q^{29} +(-3.11862 - 0.313244i) q^{30} +8.95281 q^{31} +0.199179i q^{32} -1.00000i q^{33} +5.46876 q^{34} +(-0.223473 + 2.22487i) q^{35} -0.0352144 q^{36} -0.540909i q^{37} +8.63773i q^{38} -1.11469 q^{39} +(0.637518 - 6.34707i) q^{40} +3.36720 q^{41} -1.40171i q^{42} -9.48334i q^{43} +0.0352144 q^{44} +(2.22487 + 0.223473i) q^{45} +7.29173 q^{46} -3.04186i q^{47} +3.92833i q^{48} -1.00000 q^{49} +(-1.39385 + 6.86854i) q^{50} -3.90149 q^{51} -0.0392530i q^{52} -2.86404i q^{53} -1.40171 q^{54} +(-2.22487 - 0.223473i) q^{55} +2.85278 q^{56} -6.16229i q^{57} -11.8128i q^{58} +11.5606 q^{59} +(-0.00786945 + 0.0783475i) q^{60} +10.3786 q^{61} +12.5492i q^{62} +1.00000i q^{63} -8.13585 q^{64} +(-0.249102 + 2.48004i) q^{65} +1.40171 q^{66} -5.35976i q^{67} -0.137389i q^{68} -5.20203 q^{69} +(-3.11862 - 0.313244i) q^{70} +11.2413 q^{71} -2.85278i q^{72} +0.333198i q^{73} +0.758197 q^{74} +(0.994397 - 4.90012i) q^{75} +0.217001 q^{76} -1.00000i q^{77} -1.56247i q^{78} -0.575756 q^{79} +(8.74004 + 0.877875i) q^{80} +1.00000 q^{81} +4.71984i q^{82} +0.318582i q^{83} -0.0352144 q^{84} +(-0.871878 + 8.68033i) q^{85} +13.2929 q^{86} +8.42741i q^{87} +2.85278i q^{88} -6.02585 q^{89} +(-0.313244 + 3.11862i) q^{90} -1.11469 q^{91} -0.183186i q^{92} -8.95281i q^{93} +4.26379 q^{94} +(-13.7103 - 1.37710i) q^{95} +0.199179 q^{96} -0.903942i q^{97} -1.40171i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.40171i			0.991157i	0.868563	+	0.495579i	$0.165044\pi$
$2$			1.40171i			0.991157i	−0.868563	+	0.495579i	$0.834956\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.0352144			0.0176072
$5$	−2.22487	−	0.223473i	−0.994993	−	0.0999401i
$5$	−2.22487	−	0.223473i	−0.994993	−	0.0999401i
$6$	1.40171			0.572245
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			2.85278i			1.00861i
$9$	−1.00000			−0.333333
$10$	0.313244	−	3.11862i	0.0990563	−	0.986195i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	0.0352144i		−	0.0101655i
$13$		−	1.11469i		−	0.309159i	−0.987980	−	0.154579i	$-0.950598\pi$
$13$		−	1.11469i		−	0.309159i	0.987980	−	0.154579i	$-0.0494022\pi$
$14$	1.40171			0.374622
$15$	−0.223473	+	2.22487i	−0.0577004	+	0.574460i
$16$	−3.92833			−0.982083
$17$		−	3.90149i		−	0.946251i	−0.880995	−	0.473126i	$-0.843126\pi$
$17$		−	3.90149i		−	0.946251i	0.880995	−	0.473126i	$-0.156874\pi$
$18$		−	1.40171i		−	0.330386i
$19$	6.16229			1.41373			0.706863	−	0.707351i	$-0.250110\pi$
$19$	6.16229			1.41373			0.706863	+	0.707351i	$0.250110\pi$
$20$	−0.0783475	−	0.00786945i	−0.0175190	−	0.00175966i
$21$	−1.00000			−0.218218
$22$			1.40171i			0.298845i
$23$		−	5.20203i		−	1.08470i	−0.840153	−	0.542349i	$-0.817535\pi$
$23$		−	5.20203i		−	1.08470i	0.840153	−	0.542349i	$-0.182465\pi$
$24$	2.85278			0.582321
$25$	4.90012	+	0.994397i	0.980024	+	0.198879i
$26$	1.56247			0.306425
$27$			1.00000i			0.192450i
$28$		−	0.0352144i		−	0.00665489i
$29$	−8.42741			−1.56493			−0.782465	−	0.622695i	$-0.786038\pi$
$29$	−8.42741			−1.56493			−0.782465	+	0.622695i	$0.786038\pi$
$30$	−3.11862	−	0.313244i	−0.569380	−	0.0571902i
$31$	8.95281			1.60797			0.803986	−	0.594648i	$-0.202709\pi$
$31$	8.95281			1.60797			0.803986	+	0.594648i	$0.202709\pi$
$32$			0.199179i			0.0352103i
$33$		−	1.00000i		−	0.174078i
$34$	5.46876			0.937884
$35$	−0.223473	+	2.22487i	−0.0377738	+	0.376072i
$36$	−0.0352144			−0.00586906
$37$		−	0.540909i		−	0.0889250i	−0.999011	−	0.0444625i	$-0.985842\pi$
$37$		−	0.540909i		−	0.0889250i	0.999011	−	0.0444625i	$-0.0141575\pi$
$38$			8.63773i			1.40122i
$39$	−1.11469			−0.178493
$40$	0.637518	−	6.34707i	0.100800	−	1.00356i
$41$	3.36720			0.525869			0.262934	−	0.964814i	$-0.415310\pi$
$41$	3.36720			0.525869			0.262934	+	0.964814i	$0.415310\pi$
$42$		−	1.40171i		−	0.216288i
$43$		−	9.48334i		−	1.44620i	−0.690746	−	0.723098i	$-0.742718\pi$
$43$		−	9.48334i		−	1.44620i	0.690746	−	0.723098i	$-0.257282\pi$
$44$	0.0352144			0.00530877
$45$	2.22487	+	0.223473i	0.331664	+	0.0333134i
$46$	7.29173			1.07511
$47$		−	3.04186i		−	0.443700i	−0.975081	−	0.221850i	$-0.928790\pi$
$47$		−	3.04186i		−	0.443700i	0.975081	−	0.221850i	$-0.0712096\pi$
$48$			3.92833i			0.567006i
$49$	−1.00000			−0.142857
$50$	−1.39385	+	6.86854i	−0.197121	+	0.971358i
$51$	−3.90149			−0.546318
$52$		−	0.0392530i		−	0.00544341i
$53$		−	2.86404i		−	0.393406i	−0.980463	−	0.196703i	$-0.936977\pi$
$53$		−	2.86404i		−	0.393406i	0.980463	−	0.196703i	$-0.0630234\pi$
$54$	−1.40171			−0.190748
$55$	−2.22487	−	0.223473i	−0.300002	−	0.0301331i
$56$	2.85278			0.381218
$57$		−	6.16229i		−	0.816215i
$58$		−	11.8128i		−	1.55109i
$59$	11.5606			1.50506			0.752532	−	0.658556i	$-0.228832\pi$
$59$	11.5606			1.50506			0.752532	+	0.658556i	$0.228832\pi$
$60$	−0.00786945	+	0.0783475i	−0.00101594	+	0.0101146i
$61$	10.3786			1.32884			0.664420	−	0.747360i	$-0.268679\pi$
$61$	10.3786			1.32884			0.664420	+	0.747360i	$0.268679\pi$
$62$			12.5492i			1.59375i
$63$			1.00000i			0.125988i
$64$	−8.13585			−1.01698
$65$	−0.249102	+	2.48004i	−0.0308973	+	0.307611i
$66$	1.40171			0.172538
$67$		−	5.35976i		−	0.654799i	−0.944886	−	0.327399i	$-0.893828\pi$
$67$		−	5.35976i		−	0.654799i	0.944886	−	0.327399i	$-0.106172\pi$
$68$		−	0.137389i		−	0.0166608i
$69$	−5.20203			−0.626251
$70$	−3.11862	−	0.313244i	−0.372747	−	0.0374398i
$71$	11.2413			1.33409			0.667047	−	0.745016i	$-0.267558\pi$
$71$	11.2413			1.33409			0.667047	+	0.745016i	$0.267558\pi$
$72$		−	2.85278i		−	0.336203i
$73$			0.333198i			0.0389979i	0.999810	+	0.0194989i	$0.00620710\pi$
$73$			0.333198i			0.0389979i	−0.999810	+	0.0194989i	$0.993793\pi$
$74$	0.758197			0.0881386
$75$	0.994397	−	4.90012i	0.114823	−	0.565817i
$76$	0.217001			0.0248917
$77$		−	1.00000i		−	0.113961i
$78$		−	1.56247i		−	0.176914i
$79$	−0.575756			−0.0647776			−0.0323888	−	0.999475i	$-0.510311\pi$
$79$	−0.575756			−0.0647776			−0.0323888	+	0.999475i	$0.510311\pi$
$80$	8.74004	+	0.877875i	0.977166	+	0.0981494i
$81$	1.00000			0.111111
$82$			4.71984i			0.521219i
$83$			0.318582i			0.0349689i	0.999847	+	0.0174844i	$0.00556575\pi$
$83$			0.318582i			0.0349689i	−0.999847	+	0.0174844i	$0.994434\pi$
$84$	−0.0352144			−0.00384220
$85$	−0.871878	+	8.68033i	−0.0945684	+	0.941514i
$86$	13.2929			1.43341
$87$			8.42741i			0.903513i
$88$			2.85278i			0.304107i
$89$	−6.02585			−0.638739			−0.319369	−	0.947630i	$-0.603471\pi$
$89$	−6.02585			−0.638739			−0.319369	+	0.947630i	$0.603471\pi$
$90$	−0.313244	+	3.11862i	−0.0330188	+	0.328732i
$91$	−1.11469			−0.116851
$92$		−	0.183186i		−	0.0190985i
$93$		−	8.95281i		−	0.928363i
$94$	4.26379			0.439777
$95$	−13.7103	−	1.37710i	−1.40665	−	0.141288i
$96$	0.199179			0.0203287
$97$		−	0.903942i		−	0.0917814i	−0.998946	−	0.0458907i	$-0.985387\pi$
$97$		−	0.903942i		−	0.0917814i	0.998946	−	0.0458907i	$-0.0146126\pi$
$98$		−	1.40171i		−	0.141594i
$99$	−1.00000			−0.100504
$100$	0.172555	+	0.0350171i	0.0172555	+	0.00350171i
$101$	−0.151109			−0.0150359			−0.00751797	−	0.999972i	$-0.502393\pi$
$101$	−0.151109			−0.0150359			−0.00751797	+	0.999972i	$0.502393\pi$
$102$		−	5.46876i		−	0.541487i
$103$		−	16.1396i		−	1.59028i	−0.606426	−	0.795140i	$-0.707397\pi$
$103$		−	16.1396i		−	1.59028i	0.606426	−	0.795140i	$-0.292603\pi$
$104$	3.17995			0.311820
$105$	2.22487	+	0.223473i	0.217125	+	0.0218087i
$106$	4.01454			0.389927
$107$			7.81577i			0.755579i	0.925891	+	0.377790i	$0.123316\pi$
$107$			7.81577i			0.755579i	−0.925891	+	0.377790i	$0.876684\pi$
$108$			0.0352144i			0.00338850i
$109$	−18.2292			−1.74604			−0.873018	−	0.487687i	$-0.837841\pi$
$109$	−18.2292			−1.74604			−0.873018	+	0.487687i	$0.837841\pi$
$110$	0.313244	−	3.11862i	0.0298666	−	0.297349i
$111$	−0.540909			−0.0513409
$112$			3.92833i			0.371192i
$113$			2.28487i			0.214942i	0.994208	+	0.107471i	$0.0342753\pi$
$113$			2.28487i			0.214942i	−0.994208	+	0.107471i	$0.965725\pi$
$114$	8.63773			0.808997
$115$	−1.16251	+	11.5739i	−0.108405	+	1.07927i
$116$	−0.296766			−0.0275540
$117$			1.11469i			0.103053i
$118$			16.2046i			1.49175i
$119$	−3.90149			−0.357649
$120$	−6.34707	−	0.637518i	−0.579405	−	0.0581972i
$121$	1.00000			0.0909091
$122$			14.5477i			1.31709i
$123$		−	3.36720i		−	0.303611i
$124$	0.315268			0.0283119
$125$	−10.6799	−	3.30745i	−0.955241	−	0.295827i
$126$	−1.40171			−0.124874
$127$			5.17876i			0.459541i	0.973245	+	0.229770i	$0.0737975\pi$
$127$			5.17876i			0.459541i	−0.973245	+	0.229770i	$0.926202\pi$
$128$		−	11.0057i		−	0.972779i
$129$	−9.48334			−0.834962
$130$	−3.47629	−	0.349169i	−0.304891	−	0.0306241i
$131$	−9.72484			−0.849663			−0.424831	−	0.905272i	$-0.639667\pi$
$131$	−9.72484			−0.849663			−0.424831	+	0.905272i	$0.639667\pi$
$132$		−	0.0352144i		−	0.00306502i
$133$		−	6.16229i		−	0.534338i
$134$	7.51282			0.649009
$135$	0.223473	−	2.22487i	0.0192335	−	0.191487i
$136$	11.1301			0.954397
$137$			10.0185i			0.855939i	0.903793	+	0.427969i	$0.140771\pi$
$137$			10.0185i			0.855939i	−0.903793	+	0.427969i	$0.859229\pi$
$138$		−	7.29173i		−	0.620713i
$139$	5.15308			0.437079			0.218539	−	0.975828i	$-0.429871\pi$
$139$	5.15308			0.437079			0.218539	+	0.975828i	$0.429871\pi$
$140$	−0.00786945	+	0.0783475i	−0.000665090	+	0.00662157i
$141$	−3.04186			−0.256170
$142$			15.7570i			1.32230i
$143$		−	1.11469i		−	0.0932148i
$144$	3.92833			0.327361
$145$	18.7499	+	1.88330i	1.55710	+	0.156399i
$146$	−0.467046			−0.0386530
$147$			1.00000i			0.0824786i
$148$		−	0.0190478i		−	0.00156572i
$149$	6.59892			0.540604			0.270302	−	0.962776i	$-0.412876\pi$
$149$	6.59892			0.540604			0.270302	+	0.962776i	$0.412876\pi$
$150$	6.86854	+	1.39385i	0.560814	+	0.113808i
$151$	−4.74431			−0.386086			−0.193043	−	0.981190i	$-0.561836\pi$
$151$	−4.74431			−0.386086			−0.193043	+	0.981190i	$0.561836\pi$
$152$			17.5796i			1.42590i
$153$			3.90149i			0.315417i
$154$	1.40171			0.112953
$155$	−19.9189	−	2.00071i	−1.59992	−	0.160701i
$156$	−0.0392530			−0.00314276
$157$		−	11.3377i		−	0.904847i	−0.891803	−	0.452424i	$-0.850559\pi$
$157$		−	11.3377i		−	0.904847i	0.891803	−	0.452424i	$-0.149441\pi$
$158$		−	0.807042i		−	0.0642048i
$159$	−2.86404			−0.227133
$160$	0.0445112	−	0.443149i	0.00351892	−	0.0350340i
$161$	−5.20203			−0.409977
$162$			1.40171i			0.110129i
$163$			20.0942i			1.57390i	0.617017	+	0.786950i	$0.288341\pi$
$163$			20.0942i			1.57390i	−0.617017	+	0.786950i	$0.711659\pi$
$164$	0.118574			0.00925907
$165$	−0.223473	+	2.22487i	−0.0173973	+	0.173206i
$166$	−0.446558			−0.0346597
$167$			20.2877i			1.56991i	0.619551	+	0.784956i	$0.287315\pi$
$167$			20.2877i			1.56991i	−0.619551	+	0.784956i	$0.712685\pi$
$168$		−	2.85278i		−	0.220096i
$169$	11.7575			0.904421
$170$	−12.1673	−	1.22212i	−0.933188	−	0.0937322i
$171$	−6.16229			−0.471242
$172$		−	0.333950i		−	0.0254634i
$173$			0.813028i			0.0618134i	0.999522	+	0.0309067i	$0.00983948\pi$
$173$			0.813028i			0.0618134i	−0.999522	+	0.0309067i	$0.990161\pi$
$174$	−11.8128			−0.895523
$175$	0.994397	−	4.90012i	0.0751694	−	0.370414i
$176$	−3.92833			−0.296109
$177$		−	11.5606i		−	0.868949i
$178$		−	8.44648i		−	0.633090i
$179$	5.71923			0.427476			0.213738	−	0.976891i	$-0.431436\pi$
$179$	5.71923			0.427476			0.213738	+	0.976891i	$0.431436\pi$
$180$	0.0783475	+	0.00786945i	0.00583968	+	0.000586555i
$181$	−19.2397			−1.43008			−0.715039	−	0.699085i	$-0.753591\pi$
$181$	−19.2397			−1.43008			−0.715039	+	0.699085i	$0.753591\pi$
$182$		−	1.56247i		−	0.115818i
$183$		−	10.3786i		−	0.767206i
$184$	14.8402			1.09404
$185$	−0.120879	+	1.20345i	−0.00888717	+	0.0884798i
$186$	12.5492			0.920154
$187$		−	3.90149i		−	0.285305i
$188$		−	0.107117i		−	0.00781231i
$189$	1.00000			0.0727393
$190$	1.93030	−	19.2178i	0.140038	−	1.39421i
$191$	−12.3909			−0.896572			−0.448286	−	0.893890i	$-0.647965\pi$
$191$	−12.3909			−0.896572			−0.448286	+	0.893890i	$0.647965\pi$
$192$			8.13585i			0.587155i
$193$			16.1704i			1.16397i	0.813198	+	0.581987i	$0.197724\pi$
$193$			16.1704i			1.16397i	−0.813198	+	0.581987i	$0.802276\pi$
$194$	1.26706			0.0909698
$195$	2.48004	+	0.249102i	0.177599	+	0.0178386i
$196$	−0.0352144			−0.00251531
$197$			16.7925i			1.19641i	0.801342	+	0.598207i	$0.204120\pi$
$197$			16.7925i			1.19641i	−0.801342	+	0.598207i	$0.795880\pi$
$198$		−	1.40171i		−	0.0996151i
$199$	−24.1930			−1.71500			−0.857499	−	0.514486i	$-0.827983\pi$
$199$	−24.1930			−1.71500			−0.857499	+	0.514486i	$0.827983\pi$
$200$	−2.83679	+	13.9789i	−0.200592	+	0.988461i
$201$	−5.35976			−0.378048
$202$		−	0.211811i		−	0.0149030i
$203$			8.42741i			0.591488i
$204$	−0.137389			−0.00961913
$205$	−7.49160	−	0.752479i	−0.523236	−	0.0525554i
$206$	22.6230			1.57622
$207$			5.20203i			0.361566i
$208$			4.37886i			0.303619i
$209$	6.16229			0.426254
$210$	−0.313244	+	3.11862i	−0.0216159	+	0.215205i
$211$	−4.37957			−0.301502			−0.150751	−	0.988572i	$-0.548169\pi$
$211$	−4.37957			−0.301502			−0.150751	+	0.988572i	$0.548169\pi$
$212$		−	0.100855i		−	0.00692677i
$213$		−	11.2413i		−	0.770239i
$214$	−10.9554			−0.748898
$215$	−2.11927	+	21.0992i	−0.144533	+	1.43896i
$216$	−2.85278			−0.194107
$217$		−	8.95281i		−	0.607756i
$218$		−	25.5520i		−	1.73060i
$219$	0.333198			0.0225154
$220$	−0.0783475	−	0.00786945i	−0.00528219	−	0.000530559i
$221$	−4.34894			−0.292542
$222$		−	0.758197i		−	0.0508869i
$223$			15.7451i			1.05437i	0.849750	+	0.527186i	$0.176753\pi$
$223$			15.7451i			1.05437i	−0.849750	+	0.527186i	$0.823247\pi$
$224$	0.199179			0.0133082
$225$	−4.90012	−	0.994397i	−0.326675	−	0.0662931i
$226$	−3.20272			−0.213042
$227$		−	26.6766i		−	1.77059i	−0.465032	−	0.885294i	$-0.653957\pi$
$227$		−	26.6766i		−	1.77059i	0.465032	−	0.885294i	$-0.346043\pi$
$228$		−	0.217001i		−	0.0143712i
$229$	−12.4550			−0.823052			−0.411526	−	0.911398i	$-0.635004\pi$
$229$	−12.4550			−0.823052			−0.411526	+	0.911398i	$0.635004\pi$
$230$	−16.2232	−	1.62950i	−1.06972	−	0.107446i
$231$	−1.00000			−0.0657952
$232$		−	24.0415i		−	1.57840i
$233$		−	19.4102i		−	1.27160i	−0.771853	−	0.635801i	$-0.780670\pi$
$233$		−	19.4102i		−	1.27160i	0.771853	−	0.635801i	$-0.219330\pi$
$234$	−1.56247			−0.102142
$235$	−0.679772	+	6.76774i	−0.0443434	+	0.441479i
$236$	0.407100			0.0264999
$237$			0.575756i			0.0373994i
$238$		−	5.46876i		−	0.354487i
$239$	−15.8535			−1.02548			−0.512740	−	0.858544i	$-0.671369\pi$
$239$	−15.8535			−1.02548			−0.512740	+	0.858544i	$0.671369\pi$
$240$	0.877875	−	8.74004i	0.0566666	−	0.564167i
$241$	18.1106			1.16661			0.583304	−	0.812254i	$-0.301760\pi$
$241$	18.1106			1.16661			0.583304	+	0.812254i	$0.301760\pi$
$242$			1.40171i			0.0901052i
$243$		−	1.00000i		−	0.0641500i
$244$	0.365475			0.0233971
$245$	2.22487	+	0.223473i	0.142142	+	0.0142772i
$246$	4.71984			0.300926
$247$		−	6.86902i		−	0.437065i
$248$			25.5404i			1.62182i
$249$	0.318582			0.0201893
$250$	4.63608	−	14.9701i	0.293212	−	0.946795i
$251$	−3.24386			−0.204751			−0.102375	−	0.994746i	$-0.532644\pi$
$251$	−3.24386			−0.204751			−0.102375	+	0.994746i	$0.532644\pi$
$252$			0.0352144i			0.00221830i
$253$		−	5.20203i		−	0.327049i
$254$	−7.25911			−0.455477
$255$	8.68033	+	0.871878i	0.543583	+	0.0545991i
$256$	−0.844881			−0.0528051
$257$		−	23.6248i		−	1.47367i	−0.676071	−	0.736837i	$-0.736319\pi$
$257$		−	23.6248i		−	1.47367i	0.676071	−	0.736837i	$-0.263681\pi$
$258$		−	13.2929i		−	0.827578i
$259$	−0.540909			−0.0336105
$260$	−0.00877198	+	0.0873329i	−0.000544015	+	0.00541616i
$261$	8.42741			0.521643
$262$		−	13.6314i		−	0.842150i
$263$			3.88432i			0.239517i	0.992803	+	0.119759i	$0.0382121\pi$
$263$			3.88432i			0.239517i	−0.992803	+	0.119759i	$0.961788\pi$
$264$	2.85278			0.175576
$265$	−0.640034	+	6.37212i	−0.0393170	+	0.391436i
$266$	8.63773			0.529613
$267$			6.02585i			0.368776i
$268$		−	0.188741i		−	0.0115292i
$269$	−0.573778			−0.0349839			−0.0174919	−	0.999847i	$-0.505568\pi$
$269$	−0.573778			−0.0349839			−0.0174919	+	0.999847i	$0.505568\pi$
$270$	3.11862	+	0.313244i	0.189793	+	0.0190634i
$271$	24.9842			1.51768			0.758842	−	0.651275i	$-0.225766\pi$
$271$	24.9842			1.51768			0.758842	+	0.651275i	$0.225766\pi$
$272$			15.3264i			0.929297i
$273$			1.11469i			0.0674639i
$274$	−14.0430			−0.848370
$275$	4.90012	+	0.994397i	0.295488	+	0.0599644i
$276$	−0.183186			−0.0110265
$277$			18.7064i			1.12396i	0.827151	+	0.561979i	$0.189960\pi$
$277$			18.7064i			1.12396i	−0.827151	+	0.561979i	$0.810040\pi$
$278$			7.22312i			0.433214i
$279$	−8.95281			−0.535991
$280$	−6.34707	−	0.637518i	−0.379310	−	0.0380990i
$281$	10.8364			0.646446			0.323223	−	0.946323i	$-0.395234\pi$
$281$	10.8364			0.646446			0.323223	+	0.946323i	$0.395234\pi$
$282$		−	4.26379i		−	0.253905i
$283$		−	11.1910i		−	0.665237i	−0.943061	−	0.332619i	$-0.892068\pi$
$283$		−	11.1910i		−	0.665237i	0.943061	−	0.332619i	$-0.107932\pi$
$284$	0.395854			0.0234896
$285$	−1.37710	+	13.7103i	−0.0815726	+	0.812128i
$286$	1.56247			0.0923905
$287$		−	3.36720i		−	0.198760i
$288$		−	0.199179i		−	0.0117368i
$289$	1.77835			0.104609
$290$	−2.63983	+	26.2819i	−0.155016	+	1.54333i
$291$	−0.903942			−0.0529900
$292$			0.0117334i			0.000686643i
$293$		−	3.82893i		−	0.223689i	−0.993726	−	0.111844i	$-0.964324\pi$
$293$		−	3.82893i		−	0.223689i	0.993726	−	0.111844i	$-0.0356758\pi$
$294$	−1.40171			−0.0817493
$295$	−25.7209	−	2.58348i	−1.49753	−	0.150416i
$296$	1.54309			0.0896905
$297$			1.00000i			0.0580259i
$298$			9.24975i			0.535824i
$299$	−5.79864			−0.335344
$300$	0.0350171	−	0.172555i	0.00202171	−	0.00996245i
$301$	−9.48334			−0.546611
$302$		−	6.65013i		−	0.382672i
$303$			0.151109i			0.00868101i
$304$	−24.2075			−1.38840
$305$	−23.0910	−	2.31933i	−1.32219	−	0.132804i
$306$	−5.46876			−0.312628
$307$			22.7405i			1.29787i	0.760844	+	0.648934i	$0.224785\pi$
$307$			22.7405i			1.29787i	−0.760844	+	0.648934i	$0.775215\pi$
$308$		−	0.0352144i		−	0.00200653i
$309$	−16.1396			−0.918149
$310$	2.80441	−	27.9204i	0.159280	−	1.58577i
$311$	22.6476			1.28423			0.642115	−	0.766608i	$-0.278057\pi$
$311$	22.6476			1.28423			0.642115	+	0.766608i	$0.278057\pi$
$312$		−	3.17995i		−	0.180029i
$313$		−	22.8832i		−	1.29344i	−0.762729	−	0.646719i	$-0.776141\pi$
$313$		−	22.8832i		−	1.29344i	0.762729	−	0.646719i	$-0.223859\pi$
$314$	15.8922			0.896846
$315$	0.223473	−	2.22487i	0.0125913	−	0.125357i
$316$	−0.0202749			−0.00114055
$317$		−	28.2934i		−	1.58911i	−0.607189	−	0.794557i	$-0.707703\pi$
$317$		−	28.2934i		−	1.58911i	0.607189	−	0.794557i	$-0.292297\pi$
$318$		−	4.01454i		−	0.225124i
$319$	−8.42741			−0.471844
$320$	18.1012	+	1.81814i	1.01189	+	0.101637i
$321$	7.81577			0.436234
$322$		−	7.29173i		−	0.406352i
$323$		−	24.0421i		−	1.33774i
$324$	0.0352144			0.00195635
$325$	1.10844	−	5.46210i	0.0614853	−	0.302983i
$326$	−28.1662			−1.55998
$327$			18.2292i			1.00807i
$328$			9.60588i			0.530396i
$329$	−3.04186			−0.167703
$330$	−3.11862	−	0.313244i	−0.171675	−	0.0172435i
$331$	−1.50467			−0.0827042			−0.0413521	−	0.999145i	$-0.513167\pi$
$331$	−1.50467			−0.0827042			−0.0413521	+	0.999145i	$0.513167\pi$
$332$			0.0112187i			0.000615704i
$333$			0.540909i			0.0296417i
$334$	−28.4375			−1.55603
$335$	−1.19776	+	11.9248i	−0.0654407	+	0.651521i
$336$	3.92833			0.214308
$337$		−	7.26220i		−	0.395597i	−0.980243	−	0.197799i	$-0.936621\pi$
$337$		−	7.26220i		−	0.395597i	0.980243	−	0.197799i	$-0.0633792\pi$
$338$			16.4805i			0.896423i
$339$	2.28487			0.124097
$340$	−0.0307026	+	0.305672i	−0.00166508	+	0.0165774i
$341$	8.95281			0.484822
$342$		−	8.63773i		−	0.467075i
$343$			1.00000i			0.0539949i
$344$	27.0538			1.45865
$345$	11.5739	+	1.16251i	0.623116	+	0.0625876i
$346$	−1.13963			−0.0612668
$347$			12.1412i			0.651772i	0.945409	+	0.325886i	$0.105663\pi$
$347$			12.1412i			0.651772i	−0.945409	+	0.325886i	$0.894337\pi$
$348$			0.296766i			0.0159083i
$349$	−23.1231			−1.23775			−0.618875	−	0.785490i	$-0.712411\pi$
$349$	−23.1231			−1.23775			−0.618875	+	0.785490i	$0.712411\pi$
$350$	6.86854	+	1.39385i	0.367139	+	0.0745047i
$351$	1.11469			0.0594976
$352$			0.199179i			0.0106163i
$353$		−	0.0323931i		−	0.00172411i	−1.00000		0.000862055i	$-0.999726\pi$
$353$		−	0.0323931i		−	0.00172411i	1.00000		0.000862055i	$-0.000274401\pi$
$354$	16.2046			0.861265
$355$	−25.0104	−	2.51212i	−1.32741	−	0.133329i
$356$	−0.212196			−0.0112464
$357$			3.90149i			0.206489i
$358$			8.01670i			0.423696i
$359$	−5.14259			−0.271415			−0.135708	−	0.990749i	$-0.543331\pi$
$359$	−5.14259			−0.271415			−0.135708	+	0.990749i	$0.543331\pi$
$360$	−0.637518	+	6.34707i	−0.0336001	+	0.334520i
$361$	18.9738			0.998620
$362$		−	26.9685i		−	1.41743i
$363$		−	1.00000i		−	0.0524864i
$364$	−0.0392530			−0.00205742
$365$	0.0744607	−	0.741323i	0.00389745	−	0.0388026i
$366$	14.5477			0.760422
$367$		−	25.9376i		−	1.35393i	−0.736014	−	0.676966i	$-0.763294\pi$
$367$		−	25.9376i		−	1.35393i	0.736014	−	0.676966i	$-0.236706\pi$
$368$			20.4353i			1.06526i
$369$	−3.36720			−0.175290
$370$	−1.68689	−	0.169436i	−0.0876974	−	0.00880858i
$371$	−2.86404			−0.148693
$372$		−	0.315268i		−	0.0163459i
$373$			26.4045i			1.36717i	0.729870	+	0.683586i	$0.239581\pi$
$373$			26.4045i			1.36717i	−0.729870	+	0.683586i	$0.760419\pi$
$374$	5.46876			0.282783
$375$	−3.30745	+	10.6799i	−0.170796	+	0.551509i
$376$	8.67774			0.447520
$377$			9.39392i			0.483811i
$378$			1.40171i			0.0720961i
$379$	−7.96861			−0.409320			−0.204660	−	0.978833i	$-0.565609\pi$
$379$	−7.96861			−0.409320			−0.204660	+	0.978833i	$0.565609\pi$
$380$	−0.482800	−	0.0484938i	−0.0247671	−	0.00248768i
$381$	5.17876			0.265316
$382$		−	17.3684i		−	0.888644i
$383$		−	0.0488882i		−	0.00249807i	−0.999999	−	0.00124904i	$-0.999602\pi$
$383$		−	0.0488882i		−	0.00249807i	0.999999	−	0.00124904i	$-0.000397581\pi$
$384$	−11.0057			−0.561634
$385$	−0.223473	+	2.22487i	−0.0113892	+	0.113390i
$386$	−22.6662			−1.15368
$387$			9.48334i			0.482065i
$388$		−	0.0318317i		−	0.00161601i
$389$	−12.8737			−0.652721			−0.326360	−	0.945245i	$-0.605822\pi$
$389$	−12.8737			−0.652721			−0.326360	+	0.945245i	$0.605822\pi$
$390$	−0.349169	+	3.47629i	−0.0176808	+	0.176029i
$391$	−20.2957			−1.02640
$392$		−	2.85278i		−	0.144087i
$393$			9.72484i			0.490553i
$394$	−23.5381			−1.18583
$395$	1.28098	+	0.128666i	0.0644533	+	0.00647388i
$396$	−0.0352144			−0.00176959
$397$		−	18.7983i		−	0.943460i	−0.881743	−	0.471730i	$-0.843630\pi$
$397$		−	18.7983i		−	0.943460i	0.881743	−	0.471730i	$-0.156370\pi$
$398$		−	33.9115i		−	1.69983i
$399$	−6.16229			−0.308500
$400$	−19.2493	−	3.90632i	−0.962465	−	0.195316i
$401$	−26.0692			−1.30183			−0.650917	−	0.759149i	$-0.725615\pi$
$401$	−26.0692			−1.30183			−0.650917	+	0.759149i	$0.725615\pi$
$402$		−	7.51282i		−	0.374705i
$403$		−	9.97958i		−	0.497118i
$404$	−0.00532122			−0.000264741
$405$	−2.22487	−	0.223473i	−0.110555	−	0.0111045i
$406$	−11.8128			−0.586258
$407$		−	0.540909i		−	0.0268119i
$408$		−	11.1301i		−	0.551022i
$409$	−5.77357			−0.285484			−0.142742	−	0.989760i	$-0.545592\pi$
$409$	−5.77357			−0.285484			−0.142742	+	0.989760i	$0.545592\pi$
$410$	1.05476	−	10.5010i	0.0520907	−	0.518609i
$411$	10.0185			0.494176
$412$		−	0.568345i		−	0.0280004i
$413$		−	11.5606i		−	0.568861i
$414$	−7.29173			−0.358369
$415$	0.0711943	−	0.708804i	0.00349479	−	0.0347938i
$416$	0.222023			0.0108856
$417$		−	5.15308i		−	0.252348i
$418$			8.63773i			0.422485i
$419$	20.7104			1.01177			0.505884	−	0.862602i	$-0.331166\pi$
$419$	20.7104			1.01177			0.505884	+	0.862602i	$0.331166\pi$
$420$	0.0783475	+	0.00786945i	0.00382297	+	0.000383990i
$421$	22.0655			1.07540			0.537702	−	0.843135i	$-0.319292\pi$
$421$	22.0655			1.07540			0.537702	+	0.843135i	$0.319292\pi$
$422$		−	6.13887i		−	0.298836i
$423$			3.04186i			0.147900i
$424$	8.17046			0.396793
$425$	3.87963	−	19.1178i	0.188190	−	0.927349i
$426$	15.7570			0.763428
$427$		−	10.3786i		−	0.502254i
$428$			0.275228i			0.0133036i
$429$	−1.11469			−0.0538176
$430$	−29.5750	−	2.97060i	−1.42623	−	0.143255i
$431$	5.07517			0.244463			0.122231	−	0.992502i	$-0.460995\pi$
$431$	5.07517			0.244463			0.122231	+	0.992502i	$0.460995\pi$
$432$		−	3.92833i		−	0.189002i
$433$			36.8250i			1.76970i	0.465879	+	0.884849i	$0.345738\pi$
$433$			36.8250i			1.76970i	−0.465879	+	0.884849i	$0.654262\pi$
$434$	12.5492			0.602382
$435$	1.88330	−	18.7499i	0.0902971	−	0.898989i
$436$	−0.641928			−0.0307428
$437$		−	32.0564i		−	1.53347i
$438$			0.467046i			0.0223163i
$439$	22.4927			1.07352			0.536758	−	0.843736i	$-0.319649\pi$
$439$	22.4927			1.07352			0.536758	+	0.843736i	$0.319649\pi$
$440$	0.637518	−	6.34707i	0.0303925	−	0.302584i
$441$	1.00000			0.0476190
$442$		−	6.09595i		−	0.289955i
$443$			10.6128i			0.504229i	0.967697	+	0.252114i	$0.0811259\pi$
$443$			10.6128i			0.504229i	−0.967697	+	0.252114i	$0.918874\pi$
$444$	−0.0190478			−0.000903968
$445$	13.4067	+	1.34661i	0.635541	+	0.0638356i
$446$	−22.0701			−1.04505
$447$		−	6.59892i		−	0.312118i
$448$			8.13585i			0.384383i
$449$	21.7038			1.02427			0.512133	−	0.858906i	$-0.328856\pi$
$449$	21.7038			1.02427			0.512133	+	0.858906i	$0.328856\pi$
$450$	1.39385	−	6.86854i	0.0657069	−	0.323786i
$451$	3.36720			0.158555
$452$			0.0804602i			0.00378453i
$453$			4.74431i			0.222907i
$454$	37.3928			1.75493
$455$	2.48004	+	0.249102i	0.116266	+	0.0116781i
$456$	17.5796			0.823241
$457$			18.8122i			0.879999i	0.897998	+	0.439999i	$0.145021\pi$
$457$			18.8122i			0.879999i	−0.897998	+	0.439999i	$0.854979\pi$
$458$		−	17.4583i		−	0.815774i
$459$	3.90149			0.182106
$460$	−0.0409371	+	0.407566i	−0.00190870	+	0.0190029i
$461$	11.8650			0.552610			0.276305	−	0.961070i	$-0.410890\pi$
$461$	11.8650			0.552610			0.276305	+	0.961070i	$0.410890\pi$
$462$		−	1.40171i		−	0.0652134i
$463$			21.3418i			0.991839i	0.868368	+	0.495920i	$0.165169\pi$
$463$			21.3418i			0.991839i	−0.868368	+	0.495920i	$0.834831\pi$
$464$	33.1056			1.53689
$465$	−2.00071	+	19.9189i	−0.0927807	+	0.923715i
$466$	27.2074			1.26036
$467$			36.9132i			1.70814i	0.520158	+	0.854070i	$0.325873\pi$
$467$			36.9132i			1.70814i	−0.520158	+	0.854070i	$0.674127\pi$
$468$			0.0392530i			0.00181447i
$469$	−5.35976			−0.247491
$470$	−9.48640	−	0.952842i	−0.437575	−	0.0439513i
$471$	−11.3377			−0.522414
$472$			32.9798i			1.51802i
$473$		−	9.48334i		−	0.436044i
$474$	−0.807042			−0.0370687
$475$	30.1959	+	6.12776i	1.38548	+	0.281161i
$476$	−0.137389			−0.00629720
$477$			2.86404i			0.131135i
$478$		−	22.2220i		−	1.01641i
$479$	−21.3170			−0.973998			−0.486999	−	0.873402i	$-0.661908\pi$
$479$	−21.3170			−0.973998			−0.486999	+	0.873402i	$0.661908\pi$
$480$	−0.443149	−	0.0445112i	−0.0202269	−	0.00203165i
$481$	−0.602945			−0.0274919
$482$			25.3858i			1.15629i
$483$			5.20203i			0.236701i
$484$	0.0352144			0.00160065
$485$	−0.202006	+	2.01116i	−0.00917264	+	0.0913219i
$486$	1.40171			0.0635828
$487$		−	40.6900i		−	1.84384i	−0.387379	−	0.921921i	$-0.626619\pi$
$487$		−	40.6900i		−	1.84384i	0.387379	−	0.921921i	$-0.373381\pi$
$488$			29.6077i			1.34028i
$489$	20.0942			0.908692
$490$	−0.313244	+	3.11862i	−0.0141509	+	0.140885i
$491$	37.0297			1.67113			0.835563	−	0.549395i	$-0.185142\pi$
$491$	37.0297			1.67113			0.835563	+	0.549395i	$0.185142\pi$
$492$		−	0.118574i		−	0.00534573i
$493$			32.8795i			1.48082i
$494$	9.62836			0.433200
$495$	2.22487	+	0.223473i	0.100001	+	0.0100444i
$496$	−35.1696			−1.57916
$497$		−	11.2413i		−	0.504240i
$498$			0.446558i			0.0200108i
$499$	−10.9316			−0.489366			−0.244683	−	0.969603i	$-0.578684\pi$
$499$	−10.9316			−0.489366			−0.244683	+	0.969603i	$0.578684\pi$
$500$	−0.376087	−	0.116470i	−0.0168191	−	0.00520869i
$501$	20.2877			0.906389
$502$		−	4.54695i		−	0.202940i
$503$			35.6225i			1.58833i	0.607703	+	0.794164i	$0.292091\pi$
$503$			35.6225i			1.58833i	−0.607703	+	0.794164i	$0.707909\pi$
$504$	−2.85278			−0.127073
$505$	0.336199	+	0.0337688i	0.0149607	+	0.00150269i
$506$	7.29173			0.324157
$507$		−	11.7575i		−	0.522168i
$508$			0.182367i			0.00809122i
$509$	39.3126			1.74250			0.871251	−	0.490838i	$-0.163309\pi$
$509$	39.3126			1.74250			0.871251	+	0.490838i	$0.163309\pi$
$510$	−1.22212	+	12.1673i	−0.0541163	+	0.538776i
$511$	0.333198			0.0147398
$512$		−	23.1957i		−	1.02512i
$513$			6.16229i			0.272072i
$514$	33.1151			1.46064
$515$	−3.60676	+	35.9085i	−0.158933	+	1.58232i
$516$	−0.333950			−0.0147013
$517$		−	3.04186i		−	0.133781i
$518$		−	0.758197i		−	0.0333133i
$519$	0.813028			0.0356880
$520$	−7.07499	−	0.710633i	−0.310259	−	0.0311633i
$521$	15.7075			0.688157			0.344078	−	0.938941i	$-0.388191\pi$
$521$	15.7075			0.688157			0.344078	+	0.938941i	$0.388191\pi$
$522$			11.8128i			0.517031i
$523$			23.6574i			1.03447i	0.855845	+	0.517233i	$0.173038\pi$
$523$			23.6574i			1.03447i	−0.855845	+	0.517233i	$0.826962\pi$
$524$	−0.342454			−0.0149602
$525$	−4.90012	−	0.994397i	−0.213859	−	0.0433991i
$526$	−5.44468			−0.237399
$527$		−	34.9293i		−	1.52155i
$528$			3.92833i			0.170959i
$529$	−4.06112			−0.176571
$530$	−8.93185	−	0.897141i	−0.387975	−	0.0389693i
$531$	−11.5606			−0.501688
$532$		−	0.217001i		−	0.00940819i
$533$		−	3.75338i		−	0.162577i
$534$	−8.44648			−0.365515
$535$	1.74661	−	17.3891i	0.0755126	−	0.751796i
$536$	15.2902			0.660436
$537$		−	5.71923i		−	0.246803i
$538$		−	0.804269i		−	0.0346745i
$539$	−1.00000			−0.0430730
$540$	0.00786945	−	0.0783475i	0.000338647	−	0.00337154i
$541$	41.0294			1.76399			0.881995	−	0.471258i	$-0.156200\pi$
$541$	41.0294			1.76399			0.881995	+	0.471258i	$0.156200\pi$
$542$			35.0206i			1.50426i
$543$			19.2397i			0.825655i
$544$	0.777097			0.0333177
$545$	40.5576	+	4.07372i	1.73730	+	0.174499i
$546$	−1.56247			−0.0668674
$547$			20.3175i			0.868716i	0.900740	+	0.434358i	$0.143025\pi$
$547$			20.3175i			0.868716i	−0.900740	+	0.434358i	$0.856975\pi$
$548$			0.352795i			0.0150707i
$549$	−10.3786			−0.442946
$550$	−1.39385	+	6.86854i	−0.0594342	+	0.292875i
$551$	−51.9321			−2.21238
$552$		−	14.8402i		−	0.631642i
$553$			0.575756i			0.0244836i
$554$	−26.2209			−1.11402
$555$	1.20345	+	0.120879i	0.0510838	+	0.00513101i
$556$	0.181463			0.00769573
$557$			45.1321i			1.91231i	0.292867	+	0.956153i	$0.405391\pi$
$557$			45.1321i			1.91231i	−0.292867	+	0.956153i	$0.594609\pi$
$558$		−	12.5492i		−	0.531251i
$559$	−10.5710			−0.447104
$560$	0.877875	−	8.74004i	0.0370970	−	0.369334i
$561$	−3.90149			−0.164721
$562$			15.1895i			0.640730i
$563$			21.8187i			0.919549i	0.888036	+	0.459774i	$0.152070\pi$
$563$			21.8187i			0.919549i	−0.888036	+	0.459774i	$0.847930\pi$
$564$	−0.107117			−0.00451044
$565$	0.510606	−	5.08354i	0.0214813	−	0.213866i
$566$	15.6865			0.659355
$567$		−	1.00000i		−	0.0419961i
$568$			32.0688i			1.34558i
$569$	−13.9550			−0.585022			−0.292511	−	0.956262i	$-0.594491\pi$
$569$	−13.9550			−0.585022			−0.292511	+	0.956262i	$0.594491\pi$
$570$	−19.2178	−	1.93030i	−0.804947	−	0.0808512i
$571$	−38.6960			−1.61938			−0.809688	−	0.586860i	$-0.800364\pi$
$571$	−38.6960			−1.61938			−0.809688	+	0.586860i	$0.800364\pi$
$572$		−	0.0392530i		−	0.00164125i
$573$			12.3909i			0.517636i
$574$	4.71984			0.197002
$575$	5.17288	−	25.4906i	0.215724	−	1.06303i
$576$	8.13585			0.338994
$577$			12.9243i			0.538045i	0.963134	+	0.269023i	$0.0867006\pi$
$577$			12.9243i			0.538045i	−0.963134	+	0.269023i	$0.913299\pi$
$578$			2.49272i			0.103684i
$579$	16.1704			0.672021
$580$	0.660266	+	0.0663191i	0.0274161	+	0.00275375i
$581$	0.318582			0.0132170
$582$		−	1.26706i		−	0.0525214i
$583$		−	2.86404i		−	0.118616i
$584$	−0.950540			−0.0393336
$585$	0.249102	−	2.48004i	0.0102991	−	0.102537i
$586$	5.36705			0.221711
$587$		−	19.1803i		−	0.791655i	−0.918325	−	0.395827i	$-0.870458\pi$
$587$		−	19.1803i		−	0.791655i	0.918325	−	0.395827i	$-0.129542\pi$
$588$			0.0352144i			0.00145222i
$589$	55.1698			2.27323
$590$	3.62129	−	36.0532i	0.149086	−	1.48429i
$591$	16.7925			0.690749
$592$			2.12487i			0.0873317i
$593$			11.2804i			0.463230i	0.972807	+	0.231615i	$0.0744010\pi$
$593$			11.2804i			0.463230i	−0.972807	+	0.231615i	$0.925599\pi$
$594$	−1.40171			−0.0575128
$595$	8.68033	+	0.871878i	0.355859	+	0.0357435i
$596$	0.232377			0.00951852
$597$			24.1930i			0.990154i
$598$		−	8.12799i		−	0.332378i
$599$	−13.1199			−0.536063			−0.268032	−	0.963410i	$-0.586373\pi$
$599$	−13.1199			−0.536063			−0.268032	+	0.963410i	$0.586373\pi$
$600$	13.9789	+	2.83679i	0.570688	+	0.115812i
$601$	38.8284			1.58384			0.791922	−	0.610623i	$-0.209081\pi$
$601$	38.8284			1.58384			0.791922	+	0.610623i	$0.209081\pi$
$602$		−	13.2929i		−	0.541777i
$603$			5.35976i			0.218266i
$604$	−0.167068			−0.00679789
$605$	−2.22487	−	0.223473i	−0.0904540	−	0.00908546i
$606$	−0.211811			−0.00860425
$607$		−	17.7809i		−	0.721703i	−0.932623	−	0.360852i	$-0.882486\pi$
$607$		−	17.7809i		−	0.721703i	0.932623	−	0.360852i	$-0.117514\pi$
$608$			1.22740i			0.0497776i
$609$	8.42741			0.341496
$610$	3.25102	−	32.3668i	0.131630	−	1.31049i
$611$	−3.39072			−0.137174
$612$			0.137389i			0.00555361i
$613$			31.1286i			1.25727i	0.777700	+	0.628636i	$0.216387\pi$
$613$			31.1286i			1.25727i	−0.777700	+	0.628636i	$0.783613\pi$
$614$	−31.8755			−1.28639
$615$	−0.752479	+	7.49160i	−0.0303429	+	0.302091i
$616$	2.85278			0.114942
$617$		−	6.29870i		−	0.253576i	−0.991930	−	0.126788i	$-0.959533\pi$
$617$		−	6.29870i		−	0.253576i	0.991930	−	0.126788i	$-0.0404668\pi$
$618$		−	22.6230i		−	0.910030i
$619$	−34.5333			−1.38801			−0.694004	−	0.719971i	$-0.744155\pi$
$619$	−34.5333			−1.38801			−0.694004	+	0.719971i	$0.744155\pi$
$620$	−0.701431	−	0.0704537i	−0.0281701	−	0.00282949i
$621$	5.20203			0.208750
$622$			31.7454i			1.27287i
$623$			6.02585i			0.241421i
$624$	4.37886			0.175295
$625$	23.0223	+	9.74533i	0.920894	+	0.389813i
$626$	32.0756			1.28200
$627$		−	6.16229i		−	0.246098i
$628$		−	0.399250i		−	0.0159318i
$629$	−2.11035			−0.0841454
$630$	3.11862	+	0.313244i	0.124249	+	0.0124799i
$631$	23.4219			0.932410			0.466205	−	0.884677i	$-0.345621\pi$
$631$	23.4219			0.932410			0.466205	+	0.884677i	$0.345621\pi$
$632$		−	1.64250i		−	0.0653353i
$633$			4.37957i			0.174072i
$634$	39.6591			1.57506
$635$	1.15731	−	11.5221i	0.0459265	−	0.457240i
$636$	−0.100855			−0.00399917
$637$			1.11469i			0.0441655i
$638$		−	11.8128i		−	0.467672i
$639$	−11.2413			−0.444698
$640$	−2.45948	+	24.4864i	−0.0972196	+	0.967908i
$641$	25.0686			0.990149			0.495075	−	0.868850i	$-0.335141\pi$
$641$	25.0686			0.990149			0.495075	+	0.868850i	$0.335141\pi$
$642$			10.9554i			0.432376i
$643$		−	5.79812i		−	0.228656i	−0.993443	−	0.114328i	$-0.963529\pi$
$643$		−	5.79812i		−	0.228656i	0.993443	−	0.114328i	$-0.0364714\pi$
$644$	−0.183186			−0.00721855
$645$	21.0992	+	2.11927i	0.830781	+	0.0834461i
$646$	33.7000			1.32591
$647$		−	3.48606i		−	0.137051i	−0.997649	−	0.0685255i	$-0.978171\pi$
$647$		−	3.48606i		−	0.137051i	0.997649	−	0.0685255i	$-0.0218295\pi$
$648$			2.85278i			0.112068i
$649$	11.5606			0.453794
$650$	7.65627	+	1.55371i	0.300304	+	0.0609416i
$651$	−8.95281			−0.350888
$652$			0.707605i			0.0277120i
$653$		−	46.4741i		−	1.81867i	−0.416063	−	0.909336i	$-0.636591\pi$
$653$		−	46.4741i		−	1.81867i	0.416063	−	0.909336i	$-0.363409\pi$
$654$	−25.5520			−0.999161
$655$	21.6365	+	2.17324i	0.845409	+	0.0849154i
$656$	−13.2275			−0.516447
$657$		−	0.333198i		−	0.0129993i
$658$		−	4.26379i		−	0.166220i
$659$	11.3280			0.441276			0.220638	−	0.975356i	$-0.429186\pi$
$659$	11.3280			0.441276			0.220638	+	0.975356i	$0.429186\pi$
$660$	−0.00786945	+	0.0783475i	−0.000306318	+	0.00304967i
$661$	−15.9280			−0.619529			−0.309765	−	0.950813i	$-0.600250\pi$
$661$	−15.9280			−0.619529			−0.309765	+	0.950813i	$0.600250\pi$
$662$		−	2.10911i		−	0.0819729i
$663$			4.34894i			0.168899i
$664$	−0.908842			−0.0352699
$665$	−1.37710	+	13.7103i	−0.0534018	+	0.531663i
$666$	−0.758197			−0.0293795
$667$			43.8396i			1.69748i
$668$			0.714420i			0.0276417i
$669$	15.7451			0.608742
$670$	−16.7151	−	1.67891i	−0.645759	−	0.0648620i
$671$	10.3786			0.400660
$672$		−	0.199179i		−	0.00768351i
$673$			16.8069i			0.647859i	0.946081	+	0.323929i	$0.105004\pi$
$673$			16.8069i			0.647859i	−0.946081	+	0.323929i	$0.894996\pi$
$674$	10.1795			0.392099
$675$	−0.994397	+	4.90012i	−0.0382744	+	0.188606i
$676$	0.414032			0.0159243
$677$		−	49.1818i		−	1.89021i	−0.326768	−	0.945105i	$-0.605959\pi$
$677$		−	49.1818i		−	1.89021i	0.326768	−	0.945105i	$-0.394041\pi$
$678$			3.20272i			0.123000i
$679$	−0.903942			−0.0346901
$680$	−24.7630	−	2.48727i	−0.949619	−	0.0953825i
$681$	−26.6766			−1.02225
$682$			12.5492i			0.480535i
$683$		−	4.52863i		−	0.173283i	−0.996240	−	0.0866416i	$-0.972386\pi$
$683$		−	4.52863i		−	0.173283i	0.996240	−	0.0866416i	$-0.0276135\pi$
$684$	−0.217001			−0.00829724
$685$	2.23886	−	22.2899i	0.0855426	−	0.851653i
$686$	−1.40171			−0.0535175
$687$			12.4550i			0.475190i
$688$			37.2537i			1.42028i
$689$	−3.19250			−0.121625
$690$	−1.62950	+	16.2232i	−0.0620341	+	0.617606i
$691$	−27.8017			−1.05763			−0.528813	−	0.848738i	$-0.677363\pi$
$691$	−27.8017			−1.05763			−0.528813	+	0.848738i	$0.677363\pi$
$692$			0.0286303i			0.00108836i
$693$			1.00000i			0.0379869i
$694$	−17.0184			−0.646008
$695$	−11.4650	−	1.15157i	−0.434891	−	0.0436817i
$696$	−24.0415			−0.911291
$697$		−	13.1371i		−	0.497604i
$698$		−	32.4118i		−	1.22680i
$699$	−19.4102			−0.734160
$700$	0.0350171	−	0.172555i	0.00132352	−	0.00652195i
$701$	14.7884			0.558551			0.279275	−	0.960211i	$-0.409906\pi$
$701$	14.7884			0.558551			0.279275	+	0.960211i	$0.409906\pi$
$702$			1.56247i			0.0589715i
$703$		−	3.33324i		−	0.125715i
$704$	−8.13585			−0.306632
$705$	6.76774	+	0.679772i	0.254888	+	0.0256017i
$706$	0.0454056			0.00170886
$707$			0.151109i			0.00568305i
$708$		−	0.407100i		−	0.0152997i
$709$	−17.0969			−0.642088			−0.321044	−	0.947064i	$-0.604034\pi$
$709$	−17.0969			−0.642088			−0.321044	+	0.947064i	$0.604034\pi$
$710$	3.52126	−	35.0573i	0.132150	−	1.31568i
$711$	0.575756			0.0215925
$712$		−	17.1904i		−	0.644237i
$713$		−	46.5728i		−	1.74417i
$714$	−5.46876			−0.204663
$715$	−0.249102	+	2.48004i	−0.00931589	+	0.0927481i
$716$	0.201399			0.00752664
$717$			15.8535i			0.592061i
$718$		−	7.20840i		−	0.269015i
$719$	−43.0029			−1.60374			−0.801869	−	0.597500i	$-0.796161\pi$
$719$	−43.0029			−1.60374			−0.801869	+	0.597500i	$0.796161\pi$
$720$	−8.74004	−	0.877875i	−0.325722	−	0.0327165i
$721$	−16.1396			−0.601069
$722$			26.5957i			0.989789i
$723$		−	18.1106i		−	0.673542i
$724$	−0.677515			−0.0251796
$725$	−41.2953	−	8.38019i	−1.53367	−	0.311232i
$726$	1.40171			0.0520223
$727$			5.38547i			0.199736i	0.995001	+	0.0998680i	$0.0318420\pi$
$727$			5.38547i			0.199736i	−0.995001	+	0.0998680i	$0.968158\pi$
$728$		−	3.17995i		−	0.117857i
$729$	−1.00000			−0.0370370
$730$	1.03912	+	0.104372i	0.0384595	+	0.00386299i
$731$	−36.9992			−1.36846
$732$		−	0.365475i		−	0.0135083i
$733$			5.19822i			0.192001i	0.995381	+	0.0960004i	$0.0306050\pi$
$733$			5.19822i			0.192001i	−0.995381	+	0.0960004i	$0.969395\pi$
$734$	36.3570			1.34196
$735$	0.223473	−	2.22487i	0.00824292	−	0.0820657i
$736$	1.03614			0.0381925
$737$		−	5.35976i		−	0.197429i
$738$		−	4.71984i		−	0.173740i
$739$	42.4649			1.56210			0.781048	−	0.624471i	$-0.214686\pi$
$739$	42.4649			1.56210			0.781048	+	0.624471i	$0.214686\pi$
$740$	−0.00425666	+	0.0423789i	−0.000156478	+	0.00155788i
$741$	−6.86902			−0.252340
$742$		−	4.01454i		−	0.147379i
$743$		−	35.8904i		−	1.31669i	−0.752716	−	0.658346i	$-0.771257\pi$
$743$		−	35.8904i		−	1.31669i	0.752716	−	0.658346i	$-0.228743\pi$
$744$	25.5404			0.936355
$745$	−14.6818	−	1.47468i	−0.537898	−	0.0540280i
$746$	−37.0114			−1.35508
$747$		−	0.318582i		−	0.0116563i
$748$		−	0.137389i		−	0.00502343i
$749$	7.81577			0.285582
$750$	−14.9701	−	4.63608i	−0.546632	−	0.169286i
$751$	−10.6179			−0.387453			−0.193726	−	0.981056i	$-0.562057\pi$
$751$	−10.6179			−0.387453			−0.193726	+	0.981056i	$0.562057\pi$
$752$			11.9494i			0.435750i
$753$			3.24386i			0.118213i
$754$	−13.1675			−0.479533
$755$	10.5555	+	1.06022i	0.384153	+	0.0385855i
$756$	0.0352144			0.00128073
$757$			52.2844i			1.90031i	0.311779	+	0.950154i	$0.399075\pi$
$757$			52.2844i			1.90031i	−0.311779	+	0.950154i	$0.600925\pi$
$758$		−	11.1697i		−	0.405701i
$759$	−5.20203			−0.188822
$760$	3.92857	−	39.1124i	0.142504	−	1.41876i
$761$	−3.51538			−0.127433			−0.0637163	−	0.997968i	$-0.520295\pi$
$761$	−3.51538			−0.127433			−0.0637163	+	0.997968i	$0.520295\pi$
$762$			7.25911i			0.262970i
$763$			18.2292i			0.659940i
$764$	−0.436337			−0.0157861
$765$	0.871878	−	8.68033i	0.0315228	−	0.313838i
$766$	0.0685270			0.00247598
$767$		−	12.8865i		−	0.465303i
$768$			0.844881i			0.0304870i
$769$	−0.982025			−0.0354127			−0.0177064	−	0.999843i	$-0.505636\pi$
$769$	−0.982025			−0.0354127			−0.0177064	+	0.999843i	$0.505636\pi$
$770$	−3.11862	−	0.313244i	−0.112387	−	0.0112885i
$771$	−23.6248			−0.850826
$772$			0.569432i			0.0204943i
$773$			20.2467i			0.728224i	0.931355	+	0.364112i	$0.118628\pi$
$773$			20.2467i			0.728224i	−0.931355	+	0.364112i	$0.881372\pi$
$774$	−13.2929			−0.477802
$775$	43.8699	+	8.90265i	1.57585	+	0.319793i
$776$	2.57874			0.0925715
$777$			0.540909i			0.0194050i
$778$		−	18.0451i		−	0.646949i
$779$	20.7497			0.743434
$780$	0.0873329	+	0.00877198i	0.00312702	+	0.000314087i
$781$	11.2413			0.402244
$782$		−	28.4486i		−	1.01732i
$783$		−	8.42741i		−	0.301171i
$784$	3.92833			0.140298
$785$	−2.53367	+	25.2250i	−0.0904305	+	0.900317i
$786$	−13.6314			−0.486215
$787$		−	51.1899i		−	1.82472i	−0.409385	−	0.912362i	$-0.634257\pi$
$787$		−	51.1899i		−	1.82472i	0.409385	−	0.912362i	$-0.365743\pi$
$788$			0.591336i			0.0210655i
$789$	3.88432			0.138285
$790$	−0.180352	+	1.79557i	−0.00641663	+	0.0638834i
$791$	2.28487			0.0812405
$792$		−	2.85278i		−	0.101369i
$793$		−	11.5689i		−	0.410822i
$794$	26.3497			0.935118
$795$	6.37212	+	0.640034i	0.225996	+	0.0226997i
$796$	−0.851942			−0.0301963
$797$			28.9089i			1.02400i	0.858984	+	0.512002i	$0.171096\pi$
$797$			28.9089i			1.02400i	−0.858984	+	0.512002i	$0.828904\pi$
$798$		−	8.63773i		−	0.305772i
$799$	−11.8678			−0.419852
$800$	−0.198063	+	0.976002i	−0.00700260	+	0.0345069i
$801$	6.02585			0.212913
$802$		−	36.5414i		−	1.29032i
$803$			0.333198i			0.0117583i
$804$	−0.188741			−0.00665637
$805$	11.5739	+	1.16251i	0.407925	+	0.0409732i
$806$	13.9885			0.492723
$807$			0.573778i			0.0201979i
$808$		−	0.431081i		−	0.0151654i
$809$	−4.09282			−0.143896			−0.0719480	−	0.997408i	$-0.522922\pi$
$809$	−4.09282			−0.143896			−0.0719480	+	0.997408i	$0.522922\pi$
$810$	0.313244	−	3.11862i	0.0110063	−	0.109577i
$811$	−34.4693			−1.21038			−0.605190	−	0.796081i	$-0.706903\pi$
$811$	−34.4693			−1.21038			−0.605190	+	0.796081i	$0.706903\pi$
$812$			0.296766i			0.0104144i
$813$		−	24.9842i		−	0.876235i
$814$	0.758197			0.0265748
$815$	4.49051	−	44.7071i	0.157296	−	1.56602i
$816$	15.3264			0.536530
$817$		−	58.4391i		−	2.04452i
$818$		−	8.09285i		−	0.282960i
$819$	1.11469			0.0389503
$820$	−0.263812	−	0.0264981i	−0.00921272	−	0.000925352i
$821$	−23.4118			−0.817076			−0.408538	−	0.912741i	$-0.633961\pi$
$821$	−23.4118			−0.817076			−0.408538	+	0.912741i	$0.633961\pi$
$822$			14.0430i			0.489807i
$823$			7.79607i			0.271754i	0.990726	+	0.135877i	$0.0433852\pi$
$823$			7.79607i			0.271754i	−0.990726	+	0.135877i	$0.956615\pi$
$824$	46.0426			1.60397
$825$	0.994397	−	4.90012i	0.0346205	−	0.170600i
$826$	16.2046			0.563830
$827$		−	8.05371i		−	0.280055i	−0.990148	−	0.140027i	$-0.955281\pi$
$827$		−	8.05371i		−	0.280055i	0.990148	−	0.140027i	$-0.0447191\pi$
$828$			0.183186i			0.00636616i
$829$	21.7570			0.755653			0.377827	−	0.925876i	$-0.376672\pi$
$829$	21.7570			0.755653			0.377827	+	0.925876i	$0.376672\pi$
$830$	0.993536	+	0.0997937i	0.0344861	+	0.00346389i
$831$	18.7064			0.648918
$832$			9.06893i			0.314409i
$833$			3.90149i			0.135179i
$834$	7.22312			0.250116
$835$	4.53376	−	45.1376i	0.156897	−	1.56205i
$836$	0.217001			0.00750514
$837$			8.95281i			0.309454i
$838$			29.0299i			1.00282i
$839$	24.1712			0.834481			0.417241	−	0.908796i	$-0.362997\pi$
$839$	24.1712			0.834481			0.417241	+	0.908796i	$0.362997\pi$
$840$	−0.637518	+	6.34707i	−0.0219965	+	0.218995i
$841$	42.0212			1.44901
$842$			30.9293i			1.06590i
$843$		−	10.8364i		−	0.373226i
$844$	−0.154224			−0.00530860
$845$	−26.1589	−	2.62748i	−0.899893	−	0.0903879i
$846$	−4.26379			−0.146592
$847$		−	1.00000i		−	0.0343604i
$848$			11.2509i			0.386357i
$849$	−11.1910			−0.384075
$850$	26.7976	+	5.43812i	0.919149	+	0.186526i
$851$	−2.81383			−0.0964568
$852$		−	0.395854i		−	0.0135617i
$853$			30.5632i			1.04646i	0.852191	+	0.523231i	$0.175274\pi$
$853$			30.5632i			1.04646i	−0.852191	+	0.523231i	$0.824726\pi$
$854$	14.5477			0.497813
$855$	13.7103	+	1.37710i	0.468883	+	0.0470959i
$856$	−22.2966			−0.762084
$857$			0.795673i			0.0271797i	0.999908	+	0.0135898i	$0.00432591\pi$
$857$			0.795673i			0.0271797i	−0.999908	+	0.0135898i	$0.995674\pi$
$858$		−	1.56247i		−	0.0533417i
$859$	−4.10327			−0.140002			−0.0700008	−	0.997547i	$-0.522300\pi$
$859$	−4.10327			−0.140002			−0.0700008	+	0.997547i	$0.522300\pi$
$860$	−0.0746287	+	0.742996i	−0.00254482	+	0.0253360i
$861$	−3.36720			−0.114754
$862$			7.11391i			0.242301i
$863$		−	45.3489i		−	1.54369i	−0.635808	−	0.771847i	$-0.719333\pi$
$863$		−	45.3489i		−	1.54369i	0.635808	−	0.771847i	$-0.280667\pi$
$864$	−0.199179			−0.00677622
$865$	0.181690	−	1.80888i	0.00617764	−	0.0615039i
$866$	−51.6179			−1.75405
$867$		−	1.77835i		−	0.0603958i
$868$		−	0.315268i		−	0.0107009i
$869$	−0.575756			−0.0195312
$870$	26.2819	+	2.63983i	0.891040	+	0.0894987i
$871$	−5.97445			−0.202437
$872$		−	52.0037i		−	1.76107i
$873$			0.903942i			0.0305938i
$874$	44.9337			1.51991
$875$	−3.30745	+	10.6799i	−0.111812	+	0.361047i
$876$	0.0117334			0.000396434
$877$		−	21.8578i		−	0.738084i	−0.929413	−	0.369042i	$-0.879686\pi$
$877$		−	21.8578i		−	0.738084i	0.929413	−	0.369042i	$-0.120314\pi$
$878$			31.5282i			1.06402i
$879$	−3.82893			−0.129147
$880$	8.74004	+	0.877875i	0.294627	+	0.0295932i
$881$	17.3075			0.583105			0.291553	−	0.956555i	$-0.405828\pi$
$881$	17.3075			0.583105			0.291553	+	0.956555i	$0.405828\pi$
$882$			1.40171i			0.0471980i
$883$			42.4935i			1.43002i	0.699115	+	0.715009i	$0.253578\pi$
$883$			42.4935i			1.43002i	−0.699115	+	0.715009i	$0.746422\pi$
$884$	−0.153145			−0.00515084
$885$	−2.58348	+	25.7209i	−0.0868428	+	0.864598i
$886$	−14.8760			−0.499770
$887$			20.4211i			0.685673i	0.939395	+	0.342837i	$0.111388\pi$
$887$			20.4211i			0.685673i	−0.939395	+	0.342837i	$0.888612\pi$
$888$		−	1.54309i		−	0.0517828i
$889$	5.17876			0.173690
$890$	−1.88756	+	18.7923i	−0.0632711	+	0.629921i
$891$	1.00000			0.0335013
$892$			0.554455i			0.0185645i
$893$		−	18.7448i		−	0.627270i
$894$	9.24975			0.309358
$895$	−12.7246	−	1.27809i	−0.425336	−	0.0427220i
$896$	−11.0057			−0.367676
$897$			5.79864i			0.193611i
$898$			30.4224i			1.01521i
$899$	−75.4490			−2.51636
$900$	−0.172555	−	0.0350171i	−0.00575182	−	0.00116724i
$901$	−11.1740			−0.372261
$902$			4.71984i			0.157153i
$903$			9.48334i			0.315586i
$904$	−6.51821			−0.216793
$905$	42.8059	+	4.29955i	1.42292	+	0.142922i
$906$	−6.65013			−0.220936
$907$		−	31.1605i		−	1.03467i	−0.855784	−	0.517334i	$-0.826925\pi$
$907$		−	31.1605i		−	1.03467i	0.855784	−	0.517334i	$-0.173075\pi$
$908$		−	0.939400i		−	0.0311751i
$909$	0.151109			0.00501198
$910$	−0.349169	+	3.47629i	−0.0115748	+	0.115238i
$911$	35.4090			1.17315			0.586576	−	0.809894i	$-0.300476\pi$
$911$	35.4090			1.17315			0.586576	+	0.809894i	$0.300476\pi$
$912$			24.2075i			0.801591i
$913$			0.318582i			0.0105435i
$914$	−26.3692			−0.872217
$915$	−2.31933	+	23.0910i	−0.0766746	+	0.763365i
$916$	−0.438597			−0.0144916
$917$			9.72484i			0.321142i
$918$			5.46876i			0.180496i
$919$	−3.15738			−0.104153			−0.0520763	−	0.998643i	$-0.516584\pi$
$919$	−3.15738			−0.104153			−0.0520763	+	0.998643i	$0.516584\pi$
$920$	−33.0176	−	3.31639i	−1.08856	−	0.109338i
$921$	22.7405			0.749325
$922$			16.6313i			0.547723i
$923$		−	12.5305i		−	0.412446i
$924$	−0.0352144			−0.00115847
$925$	0.537879	−	2.65052i	0.0176853	−	0.0871486i
$926$	−29.9150			−0.983069
$927$			16.1396i			0.530093i
$928$		−	1.67856i		−	0.0551016i
$929$	23.3245			0.765253			0.382627	−	0.923903i	$-0.375020\pi$
$929$	23.3245			0.765253			0.382627	+	0.923903i	$0.375020\pi$
$930$	−27.9204	−	2.80441i	−0.915547	−	0.0919603i
$931$	−6.16229			−0.201961
$932$		−	0.683517i		−	0.0223893i
$933$		−	22.6476i		−	0.741451i
$934$	−51.7416			−1.69304
$935$	−0.871878	+	8.68033i	−0.0285135	+	0.283877i
$936$	−3.17995			−0.103940
$937$			20.7414i			0.677594i	0.940860	+	0.338797i	$0.110020\pi$
$937$			20.7414i			0.677594i	−0.940860	+	0.338797i	$0.889980\pi$
$938$		−	7.51282i		−	0.245302i
$939$	−22.8832			−0.746766
$940$	−0.0239377	+	0.238322i	−0.000780763	+	0.00777320i
$941$	19.2141			0.626361			0.313180	−	0.949694i	$-0.398606\pi$
$941$	19.2141			0.626361			0.313180	+	0.949694i	$0.398606\pi$
$942$		−	15.8922i		−	0.517794i
$943$		−	17.5163i		−	0.570409i
$944$	−45.4139			−1.47810
$945$	−2.22487	−	0.223473i	−0.0723751	−	0.00726957i
$946$	13.2929			0.432189
$947$			30.5000i			0.991115i	0.868575	+	0.495558i	$0.165036\pi$
$947$			30.5000i			0.991115i	−0.868575	+	0.495558i	$0.834964\pi$
$948$			0.0202749i			0.000658498i
$949$	0.371412			0.0120565
$950$	−8.58933	+	42.3259i	−0.278675	+	1.37323i
$951$	−28.2934			−0.917476
$952$		−	11.1301i		−	0.360728i
$953$		−	12.0030i		−	0.388814i	−0.980921	−	0.194407i	$-0.937722\pi$
$953$		−	12.0030i		−	0.388814i	0.980921	−	0.194407i	$-0.0622783\pi$
$954$	−4.01454			−0.129976
$955$	27.5681	+	2.76902i	0.892083	+	0.0896035i
$956$	−0.558272			−0.0180558
$957$			8.42741i			0.272419i
$958$		−	29.8802i		−	0.965385i
$959$	10.0185			0.323514
$960$	1.81814	−	18.1012i	0.0586803	−	0.584215i
$961$	49.1528			1.58558
$962$		−	0.845152i		−	0.0272488i
$963$		−	7.81577i		−	0.251860i
$964$	0.637755			0.0205407
$965$	3.61365	−	35.9772i	0.116328	−	1.15815i
$966$	−7.29173			−0.234608
$967$		−	61.6054i		−	1.98110i	−0.137163	−	0.990549i	$-0.543798\pi$
$967$		−	61.6054i		−	1.98110i	0.137163	−	0.990549i	$-0.456202\pi$
$968$			2.85278i			0.0916917i
$969$	−24.0421			−0.772344
$970$	−2.81905	−	0.283154i	−0.0905143	−	0.00909153i
$971$	14.7208			0.472414			0.236207	−	0.971703i	$-0.424096\pi$
$971$	14.7208			0.472414			0.236207	+	0.971703i	$0.424096\pi$
$972$		−	0.0352144i		−	0.00112950i
$973$		−	5.15308i		−	0.165200i
$974$	57.0356			1.82754
$975$	−5.46210	−	1.10844i	−0.174927	−	0.0354985i
$976$	−40.7705			−1.30503
$977$		−	54.5153i		−	1.74410i	−0.489418	−	0.872049i	$-0.662791\pi$
$977$		−	54.5153i		−	1.74410i	0.489418	−	0.872049i	$-0.337209\pi$
$978$			28.1662i			0.900656i
$979$	−6.02585			−0.192587
$980$	0.0783475	+	0.00786945i	0.00250272	+	0.000251381i
$981$	18.2292			0.582012
$982$			51.9048i			1.65635i
$983$			5.98139i			0.190777i	0.995440	+	0.0953884i	$0.0304093\pi$
$983$			5.98139i			0.190777i	−0.995440	+	0.0953884i	$0.969591\pi$
$984$	9.60588			0.306224
$985$	3.75266	−	37.3611i	0.119570	−	1.19042i
$986$	−46.0874			−1.46772
$987$			3.04186i			0.0968233i
$988$		−	0.241888i		−	0.00769549i
$989$	−49.3326			−1.56869
$990$	−0.313244	+	3.11862i	−0.00995554	+	0.0991163i
$991$	−16.8699			−0.535891			−0.267945	−	0.963434i	$-0.586345\pi$
$991$	−16.8699			−0.535891			−0.267945	+	0.963434i	$0.586345\pi$
$992$			1.78321i			0.0566171i
$993$			1.50467i			0.0477493i
$994$	15.7570			0.499781
$995$	53.8264	+	5.40648i	1.70641	+	0.171397i
$996$	0.0112187			0.000355477
$997$		−	14.6712i		−	0.464642i	−0.972639	−	0.232321i	$-0.925368\pi$
$997$		−	14.6712i		−	0.464642i	0.972639	−	0.232321i	$-0.0746320\pi$
$998$		−	15.3229i		−	0.485039i
$999$	0.540909			0.0171136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.f.694.15	yes	20
5.2	odd	4		5775.2.a.cn.1.4		10
5.3	odd	4		5775.2.a.co.1.7		10
5.4	even	2	inner	1155.2.c.f.694.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.f.694.6	✓	20	5.4	even	2	inner
1155.2.c.f.694.15	yes	20	1.1	even	1	trivial
5775.2.a.cn.1.4		10	5.2	odd	4
5775.2.a.co.1.7		10	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.40171i q^{2} -1.00000i q^{3} +0.0352144 q^{4} +(-2.22487 - 0.223473i) q^{5} +1.40171 q^{6} -1.00000i q^{7} +2.85278i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.40171i q^{2} -1.00000i q^{3} +0.0352144 q^{4} +(-2.22487 - 0.223473i) q^{5} +1.40171 q^{6} -1.00000i q^{7} +2.85278i q^{8} -1.00000 q^{9} +(0.313244 - 3.11862i) q^{10} +1.00000 q^{11} -0.0352144i q^{12} -1.11469i q^{13} +1.40171 q^{14} +(-0.223473 + 2.22487i) q^{15} -3.92833 q^{16} -3.90149i q^{17} -1.40171i q^{18} +6.16229 q^{19} +(-0.0783475 - 0.00786945i) q^{20} -1.00000 q^{21} +1.40171i q^{22} -5.20203i q^{23} +2.85278 q^{24} +(4.90012 + 0.994397i) q^{25} +1.56247 q^{26} +1.00000i q^{27} -0.0352144i q^{28} -8.42741 q^{29} +(-3.11862 - 0.313244i) q^{30} +8.95281 q^{31} +0.199179i q^{32} -1.00000i q^{33} +5.46876 q^{34} +(-0.223473 + 2.22487i) q^{35} -0.0352144 q^{36} -0.540909i q^{37} +8.63773i q^{38} -1.11469 q^{39} +(0.637518 - 6.34707i) q^{40} +3.36720 q^{41} -1.40171i q^{42} -9.48334i q^{43} +0.0352144 q^{44} +(2.22487 + 0.223473i) q^{45} +7.29173 q^{46} -3.04186i q^{47} +3.92833i q^{48} -1.00000 q^{49} +(-1.39385 + 6.86854i) q^{50} -3.90149 q^{51} -0.0392530i q^{52} -2.86404i q^{53} -1.40171 q^{54} +(-2.22487 - 0.223473i) q^{55} +2.85278 q^{56} -6.16229i q^{57} -11.8128i q^{58} +11.5606 q^{59} +(-0.00786945 + 0.0783475i) q^{60} +10.3786 q^{61} +12.5492i q^{62} +1.00000i q^{63} -8.13585 q^{64} +(-0.249102 + 2.48004i) q^{65} +1.40171 q^{66} -5.35976i q^{67} -0.137389i q^{68} -5.20203 q^{69} +(-3.11862 - 0.313244i) q^{70} +11.2413 q^{71} -2.85278i q^{72} +0.333198i q^{73} +0.758197 q^{74} +(0.994397 - 4.90012i) q^{75} +0.217001 q^{76} -1.00000i q^{77} -1.56247i q^{78} -0.575756 q^{79} +(8.74004 + 0.877875i) q^{80} +1.00000 q^{81} +4.71984i q^{82} +0.318582i q^{83} -0.0352144 q^{84} +(-0.871878 + 8.68033i) q^{85} +13.2929 q^{86} +8.42741i q^{87} +2.85278i q^{88} -6.02585 q^{89} +(-0.313244 + 3.11862i) q^{90} -1.11469 q^{91} -0.183186i q^{92} -8.95281i q^{93} +4.26379 q^{94} +(-13.7103 - 1.37710i) q^{95} +0.199179 q^{96} -0.903942i q^{97} -1.40171i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 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

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Modular forms

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