LMFDB - Embedded newform 1155.2.k.a.769.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

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, 1, 1]))

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

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

chi := DirichletCharacter("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.21
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.a.769.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.226652 q^{2} -1.00000 q^{3} -1.94863 q^{4} +(0.777785 + 2.09644i) q^{5} +0.226652 q^{6} +(0.735315 + 2.54152i) q^{7} +0.894963 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.226652 q^{2} -1.00000 q^{3} -1.94863 q^{4} +(0.777785 + 2.09644i) q^{5} +0.226652 q^{6} +(0.735315 + 2.54152i) q^{7} +0.894963 q^{8} +1.00000 q^{9} +(-0.176286 - 0.475161i) q^{10} +(2.49008 - 2.19077i) q^{11} +1.94863 q^{12} -3.41850i q^{13} +(-0.166660 - 0.576039i) q^{14} +(-0.777785 - 2.09644i) q^{15} +3.69441 q^{16} +1.69080i q^{17} -0.226652 q^{18} +4.66628 q^{19} +(-1.51561 - 4.08518i) q^{20} +(-0.735315 - 2.54152i) q^{21} +(-0.564382 + 0.496542i) q^{22} -3.95479i q^{23} -0.894963 q^{24} +(-3.79010 + 3.26115i) q^{25} +0.774808i q^{26} -1.00000 q^{27} +(-1.43286 - 4.95247i) q^{28} +3.67000i q^{29} +(0.176286 + 0.475161i) q^{30} +8.62861i q^{31} -2.62727 q^{32} +(-2.49008 + 2.19077i) q^{33} -0.383223i q^{34} +(-4.75622 + 3.51830i) q^{35} -1.94863 q^{36} -3.09544i q^{37} -1.05762 q^{38} +3.41850i q^{39} +(0.696089 + 1.87623i) q^{40} +12.2944 q^{41} +(0.166660 + 0.576039i) q^{42} +0.542327 q^{43} +(-4.85225 + 4.26900i) q^{44} +(0.777785 + 2.09644i) q^{45} +0.896359i q^{46} -8.26446 q^{47} -3.69441 q^{48} +(-5.91862 + 3.73763i) q^{49} +(0.859033 - 0.739146i) q^{50} -1.69080i q^{51} +6.66138i q^{52} +6.65065i q^{53} +0.226652 q^{54} +(6.52957 + 3.51636i) q^{55} +(0.658080 + 2.27457i) q^{56} -4.66628 q^{57} -0.831811i q^{58} +5.11051i q^{59} +(1.51561 + 4.08518i) q^{60} +13.4456 q^{61} -1.95569i q^{62} +(0.735315 + 2.54152i) q^{63} -6.79335 q^{64} +(7.16666 - 2.65885i) q^{65} +(0.564382 - 0.496542i) q^{66} -8.03174i q^{67} -3.29475i q^{68} +3.95479i q^{69} +(1.07800 - 0.797428i) q^{70} -3.92235 q^{71} +0.894963 q^{72} +0.227484i q^{73} +0.701586i q^{74} +(3.79010 - 3.26115i) q^{75} -9.09285 q^{76} +(7.39888 + 4.71768i) q^{77} -0.774808i q^{78} +9.93059i q^{79} +(2.87346 + 7.74511i) q^{80} +1.00000 q^{81} -2.78654 q^{82} +14.3905i q^{83} +(1.43286 + 4.95247i) q^{84} +(-3.54466 + 1.31508i) q^{85} -0.122919 q^{86} -3.67000i q^{87} +(2.22853 - 1.96066i) q^{88} +4.81796i q^{89} +(-0.176286 - 0.475161i) q^{90} +(8.68817 - 2.51367i) q^{91} +7.70641i q^{92} -8.62861i q^{93} +1.87315 q^{94} +(3.62936 + 9.78256i) q^{95} +2.62727 q^{96} -13.2975 q^{97} +(1.34147 - 0.847141i) q^{98} +(2.49008 - 2.19077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q - 48 * q^3 + 48 * q^4 + 4 * q^5 + 48 * q^9	$ 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9} - 48 q^{12} - 4 q^{15} + 40 q^{16} + 18 q^{20} + 20 q^{25} - 48 q^{27} + 48 q^{36} + 20 q^{38} - 16 q^{44} + 4 q^{45} - 8 q^{47} - 40 q^{48} + 24 q^{49} + 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} - 20 q^{75} + 32 q^{77} + 46 q^{80} + 48 q^{81} + 32 q^{82} - 16 q^{86} - 68 q^{97}+O(q^{100}) $ 48 * q - 48 * q^3 + 48 * q^4 + 4 * q^5 + 48 * q^9 - 48 * q^12 - 4 * q^15 + 40 * q^16 + 18 * q^20 + 20 * q^25 - 48 * q^27 + 48 * q^36 + 20 * q^38 - 16 * q^44 + 4 * q^45 - 8 * q^47 - 40 * q^48 + 24 * q^49 + 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 - 20 * q^75 + 32 * q^77 + 46 * q^80 + 48 * q^81 + 32 * q^82 - 16 * q^86 - 68 * q^97

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 $

$2$	−0.226652			−0.160267			−0.0801335	−	0.996784i	$-0.525535\pi$
$2$	−0.226652			−0.160267			−0.0801335	+	0.996784i	$0.525535\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.94863			−0.974315
$5$	0.777785	+	2.09644i	0.347836	+	0.937555i
$5$	0.777785	+	2.09644i	0.347836	+	0.937555i
$6$	0.226652			0.0925302
$7$	0.735315	+	2.54152i	0.277923	+	0.960603i
$7$	0.735315	+	2.54152i	0.277923	+	0.960603i
$8$	0.894963			0.316417
$9$	1.00000			0.333333
$10$	−0.176286	−	0.475161i	−0.0557466	−	0.150259i
$11$	2.49008	−	2.19077i	0.750788	−	0.660543i
$11$	2.49008	−	2.19077i	0.750788	−	0.660543i
$12$	1.94863			0.562521
$13$		−	3.41850i		−	0.948120i	−0.880492	−	0.474060i	$-0.842788\pi$
$13$		−	3.41850i		−	0.948120i	0.880492	−	0.474060i	$-0.157212\pi$
$14$	−0.166660	−	0.576039i	−0.0445419	−	0.153953i
$15$	−0.777785	−	2.09644i	−0.200823	−	0.541298i
$16$	3.69441			0.923603
$17$			1.69080i			0.410080i	0.978754	+	0.205040i	$0.0657324\pi$
$17$			1.69080i			0.410080i	−0.978754	+	0.205040i	$0.934268\pi$
$18$	−0.226652			−0.0534223
$19$	4.66628			1.07052			0.535259	−	0.844688i	$-0.320214\pi$
$19$	4.66628			1.07052			0.535259	+	0.844688i	$0.320214\pi$
$20$	−1.51561	−	4.08518i	−0.338901	−	0.913474i
$21$	−0.735315	−	2.54152i	−0.160459	−	0.554605i
$22$	−0.564382	+	0.496542i	−0.120327	+	0.105863i
$23$		−	3.95479i		−	0.824630i	−0.911041	−	0.412315i	$-0.864720\pi$
$23$		−	3.95479i		−	0.824630i	0.911041	−	0.412315i	$-0.135280\pi$
$24$	−0.894963			−0.182684
$25$	−3.79010	+	3.26115i	−0.758020	+	0.652231i
$26$			0.774808i			0.151952i
$27$	−1.00000			−0.192450
$28$	−1.43286	−	4.95247i	−0.270784	−	0.935930i
$29$			3.67000i			0.681501i	0.940154	+	0.340751i	$0.110681\pi$
$29$			3.67000i			0.681501i	−0.940154	+	0.340751i	$0.889319\pi$
$30$	0.176286	+	0.475161i	0.0321853	+	0.0867521i
$31$			8.62861i			1.54974i	0.632118	+	0.774872i	$0.282186\pi$
$31$			8.62861i			1.54974i	−0.632118	+	0.774872i	$0.717814\pi$
$32$	−2.62727			−0.464440
$33$	−2.49008	+	2.19077i	−0.433468	+	0.381365i
$34$		−	0.383223i		−	0.0657223i
$35$	−4.75622	+	3.51830i	−0.803947	+	0.594700i
$36$	−1.94863			−0.324772
$37$		−	3.09544i		−	0.508887i	−0.967088	−	0.254443i	$-0.918108\pi$
$37$		−	3.09544i		−	0.508887i	0.967088	−	0.254443i	$-0.0818923\pi$
$38$	−1.05762			−0.171569
$39$			3.41850i			0.547398i
$40$	0.696089	+	1.87623i	0.110061	+	0.296659i
$41$	12.2944			1.92006			0.960030	−	0.279896i	$-0.0903000\pi$
$41$	12.2944			1.92006			0.960030	+	0.279896i	$0.0903000\pi$
$42$	0.166660	+	0.576039i	0.0257163	+	0.0888848i
$43$	0.542327			0.0827040			0.0413520	−	0.999145i	$-0.486833\pi$
$43$	0.542327			0.0827040			0.0413520	+	0.999145i	$0.486833\pi$
$44$	−4.85225	+	4.26900i	−0.731504	+	0.643576i
$45$	0.777785	+	2.09644i	0.115945	+	0.312518i
$46$			0.896359i			0.132161i
$47$	−8.26446			−1.20550			−0.602748	−	0.797932i	$-0.705927\pi$
$47$	−8.26446			−1.20550			−0.602748	+	0.797932i	$0.705927\pi$
$48$	−3.69441			−0.533243
$49$	−5.91862	+	3.73763i	−0.845518	+	0.533948i
$50$	0.859033	−	0.739146i	0.121486	−	0.104531i
$51$		−	1.69080i		−	0.236760i
$52$			6.66138i			0.923767i
$53$			6.65065i			0.913537i	0.889586	+	0.456768i	$0.150993\pi$
$53$			6.65065i			0.913537i	−0.889586	+	0.456768i	$0.849007\pi$
$54$	0.226652			0.0308434
$55$	6.52957	+	3.51636i	0.880447	+	0.474145i
$56$	0.658080	+	2.27457i	0.0879397	+	0.303952i
$57$	−4.66628			−0.618064
$58$		−	0.831811i		−	0.109222i
$59$			5.11051i			0.665332i	0.943045	+	0.332666i	$0.107948\pi$
$59$			5.11051i			0.665332i	−0.943045	+	0.332666i	$0.892052\pi$
$60$	1.51561	+	4.08518i	0.195665	+	0.527394i
$61$	13.4456			1.72153			0.860765	−	0.509003i	$-0.169986\pi$
$61$	13.4456			1.72153			0.860765	+	0.509003i	$0.169986\pi$
$62$		−	1.95569i		−	0.248373i
$63$	0.735315	+	2.54152i	0.0926410	+	0.320201i
$64$	−6.79335			−0.849169
$65$	7.16666	−	2.65885i	0.888915	−	0.329790i
$66$	0.564382	−	0.496542i	0.0694706	−	0.0611201i
$67$		−	8.03174i		−	0.981234i	−0.871375	−	0.490617i	$-0.836772\pi$
$67$		−	8.03174i		−	0.981234i	0.871375	−	0.490617i	$-0.163228\pi$
$68$		−	3.29475i		−	0.399547i
$69$			3.95479i			0.476100i
$70$	1.07800	−	0.797428i	0.128846	−	0.0953108i
$71$	−3.92235			−0.465497			−0.232748	−	0.972537i	$-0.574772\pi$
$71$	−3.92235			−0.465497			−0.232748	+	0.972537i	$0.574772\pi$
$72$	0.894963			0.105472
$73$			0.227484i			0.0266249i	0.999911	+	0.0133125i	$0.00423761\pi$
$73$			0.227484i			0.0266249i	−0.999911	+	0.0133125i	$0.995762\pi$
$74$			0.701586i			0.0815577i
$75$	3.79010	−	3.26115i	0.437643	−	0.376566i
$76$	−9.09285			−1.04302
$77$	7.39888	+	4.71768i	0.843181	+	0.537630i
$78$		−	0.774808i		−	0.0877297i
$79$			9.93059i			1.11728i	0.829411	+	0.558639i	$0.188676\pi$
$79$			9.93059i			1.11728i	−0.829411	+	0.558639i	$0.811324\pi$
$80$	2.87346	+	7.74511i	0.321262	+	0.865929i
$81$	1.00000			0.111111
$82$	−2.78654			−0.307722
$83$			14.3905i			1.57956i	0.613388	+	0.789782i	$0.289806\pi$
$83$			14.3905i			1.57956i	−0.613388	+	0.789782i	$0.710194\pi$
$84$	1.43286	+	4.95247i	0.156337	+	0.540359i
$85$	−3.54466	+	1.31508i	−0.384473	+	0.142641i
$86$	−0.122919			−0.0132547
$87$		−	3.67000i		−	0.393465i
$88$	2.22853	−	1.96066i	0.237562	−	0.209007i
$89$			4.81796i			0.510703i	0.966848	+	0.255351i	$0.0821912\pi$
$89$			4.81796i			0.510703i	−0.966848	+	0.255351i	$0.917809\pi$
$90$	−0.176286	−	0.475161i	−0.0185822	−	0.0500864i
$91$	8.68817	−	2.51367i	0.910768	−	0.263504i
$92$			7.70641i			0.803449i
$93$		−	8.62861i		−	0.894745i
$94$	1.87315			0.193201
$95$	3.62936	+	9.78256i	0.372364	+	1.00367i
$96$	2.62727			0.268145
$97$	−13.2975			−1.35015			−0.675077	−	0.737748i	$-0.735889\pi$
$97$	−13.2975			−1.35015			−0.675077	+	0.737748i	$0.735889\pi$
$98$	1.34147	−	0.847141i	0.135509	−	0.0855741i
$99$	2.49008	−	2.19077i	0.250263	−	0.220181i
$100$	7.38550	−	6.35478i	0.738550	−	0.635478i
$101$	−0.121921			−0.0121315			−0.00606577	−	0.999982i	$-0.501931\pi$
$101$	−0.121921			−0.0121315			−0.00606577	+	0.999982i	$0.501931\pi$
$102$			0.383223i			0.0379448i
$103$	8.41477			0.829132			0.414566	−	0.910019i	$-0.363933\pi$
$103$	8.41477			0.829132			0.414566	+	0.910019i	$0.363933\pi$
$104$		−	3.05943i		−	0.300002i
$105$	4.75622	−	3.51830i	0.464159	−	0.343350i
$106$		−	1.50738i		−	0.146410i
$107$	20.2692			1.95950			0.979748	−	0.200237i	$-0.0641711\pi$
$107$	20.2692			1.95950			0.979748	+	0.200237i	$0.0641711\pi$
$108$	1.94863			0.187507
$109$		−	11.6322i		−	1.11416i	−0.830459	−	0.557080i	$-0.811922\pi$
$109$		−	11.6322i		−	1.11416i	0.830459	−	0.557080i	$-0.188078\pi$
$110$	−1.47994	−	0.796988i	−0.141106	−	0.0759898i
$111$			3.09544i			0.293806i
$112$	2.71656	+	9.38942i	0.256691	+	0.887216i
$113$			16.3235i			1.53559i	0.640696	+	0.767795i	$0.278646\pi$
$113$			16.3235i			1.53559i	−0.640696	+	0.767795i	$0.721354\pi$
$114$	1.05762			0.0990552
$115$	8.29096	−	3.07597i	0.773136	−	0.286836i
$116$		−	7.15146i		−	0.663997i
$117$		−	3.41850i		−	0.316040i
$118$		−	1.15831i		−	0.106631i
$119$	−4.29721	+	1.24327i	−0.393924	+	0.113971i
$120$	−0.696089	−	1.87623i	−0.0635439	−	0.171276i
$121$	1.40103	−	10.9104i	0.127366	−	0.991856i
$122$	−3.04746			−0.275904
$123$	−12.2944			−1.10855
$124$		−	16.8140i		−	1.50994i
$125$	−9.78469	−	5.40924i	−0.875169	−	0.483817i
$126$	−0.166660	−	0.576039i	−0.0148473	−	0.0513176i
$127$	−20.0464			−1.77883			−0.889413	−	0.457104i	$-0.848887\pi$
$127$	−20.0464			−1.77883			−0.889413	+	0.457104i	$0.848887\pi$
$128$	6.79427			0.600534
$129$	−0.542327			−0.0477492
$130$	−1.62434	+	0.602634i	−0.142464	+	0.0528545i
$131$	−17.6457			−1.54171			−0.770854	−	0.637012i	$-0.780170\pi$
$131$	−17.6457			−1.54171			−0.770854	+	0.637012i	$0.780170\pi$
$132$	4.85225	−	4.26900i	0.422334	−	0.371569i
$133$	3.43119	+	11.8594i	0.297522	+	1.02834i
$134$			1.82041i			0.157259i
$135$	−0.777785	−	2.09644i	−0.0669410	−	0.180433i
$136$			1.51321i			0.129756i
$137$			14.4706i			1.23631i	0.786057	+	0.618154i	$0.212119\pi$
$137$			14.4706i			1.23631i	−0.786057	+	0.618154i	$0.787881\pi$
$138$		−	0.896359i		−	0.0763031i
$139$	0.0577275			0.00489638			0.00244819	−	0.999997i	$-0.499221\pi$
$139$	0.0577275			0.00489638			0.00244819	+	0.999997i	$0.499221\pi$
$140$	9.26810	−	6.85585i	0.783298	−	0.579425i
$141$	8.26446			0.695993
$142$	0.889006			0.0746038
$143$	−7.48915	−	8.51234i	−0.626274	−	0.711838i
$144$	3.69441			0.307868
$145$	−7.69392	+	2.85447i	−0.638945	+	0.237051i
$146$		−	0.0515595i		−	0.00426710i
$147$	5.91862	−	3.73763i	0.488160	−	0.308275i
$148$			6.03186i			0.495816i
$149$			17.1022i			1.40107i	0.713618	+	0.700535i	$0.247055\pi$
$149$			17.1022i			1.40107i	−0.713618	+	0.700535i	$0.752945\pi$
$150$	−0.859033	+	0.739146i	−0.0701398	+	0.0603510i
$151$		−	10.1755i		−	0.828071i	−0.910261	−	0.414035i	$-0.864119\pi$
$151$		−	10.1755i		−	0.828071i	0.910261	−	0.414035i	$-0.135881\pi$
$152$	4.17615			0.338730
$153$			1.69080i			0.136693i
$154$	−1.67697	−	1.06927i	−0.135134	−	0.0861643i
$155$	−18.0893	+	6.71120i	−1.45297	+	0.539057i
$156$		−	6.66138i		−	0.533337i
$157$	−11.3901			−0.909026			−0.454513	−	0.890740i	$-0.650187\pi$
$157$	−11.3901			−0.909026			−0.454513	+	0.890740i	$0.650187\pi$
$158$		−	2.25078i		−	0.179063i
$159$		−	6.65065i		−	0.527431i
$160$	−2.04345	−	5.50791i	−0.161549	−	0.435439i
$161$	10.0512	−	2.90801i	0.792142	−	0.229184i
$162$	−0.226652			−0.0178074
$163$		−	17.9578i		−	1.40657i	−0.710910	−	0.703283i	$-0.751717\pi$
$163$		−	17.9578i		−	1.40657i	0.710910	−	0.703283i	$-0.248283\pi$
$164$	−23.9572			−1.87074
$165$	−6.52957	−	3.51636i	−0.508326	−	0.273748i
$166$		−	3.26163i		−	0.253152i
$167$		−	15.5751i		−	1.20524i	−0.798029	−	0.602619i	$-0.794124\pi$
$167$		−	15.5751i		−	1.20524i	0.798029	−	0.602619i	$-0.205876\pi$
$168$	−0.658080	−	2.27457i	−0.0507720	−	0.175487i
$169$	1.31388			0.101068
$170$	0.803404	−	0.298065i	0.0616183	−	0.0228606i
$171$	4.66628			0.356839
$172$	−1.05679			−0.0805797
$173$			8.95282i			0.680670i	0.940304	+	0.340335i	$0.110540\pi$
$173$			8.95282i			0.680670i	−0.940304	+	0.340335i	$0.889460\pi$
$174$			0.831811i			0.0630594i
$175$	−11.0752	−	7.23464i	−0.837206	−	0.546887i
$176$	9.19940	−	8.09362i	0.693431	−	0.610079i
$177$		−	5.11051i		−	0.384129i
$178$		−	1.09200i		−	0.0818488i
$179$	−5.83650			−0.436241			−0.218120	−	0.975922i	$-0.569993\pi$
$179$	−5.83650			−0.436241			−0.218120	+	0.975922i	$0.569993\pi$
$180$	−1.51561	−	4.08518i	−0.112967	−	0.304491i
$181$			9.58793i			0.712665i	0.934359	+	0.356333i	$0.115973\pi$
$181$			9.58793i			0.712665i	−0.934359	+	0.356333i	$0.884027\pi$
$182$	−1.96919	+	0.569728i	−0.145966	+	0.0422310i
$183$	−13.4456			−0.993926
$184$		−	3.53939i		−	0.260927i
$185$	6.48939	−	2.40758i	0.477110	−	0.177009i
$186$			1.95569i			0.143398i
$187$	3.70417	+	4.21024i	0.270875	+	0.307883i
$188$	16.1044			1.17453
$189$	−0.735315	−	2.54152i	−0.0534863	−	0.184868i
$190$	−0.822600	−	2.21723i	−0.0596777	−	0.160855i
$191$	11.1711			0.808309			0.404155	−	0.914691i	$-0.367566\pi$
$191$	11.1711			0.808309			0.404155	+	0.914691i	$0.367566\pi$
$192$	6.79335			0.490268
$193$	−9.27916			−0.667929			−0.333964	−	0.942586i	$-0.608386\pi$
$193$	−9.27916			−0.667929			−0.333964	+	0.942586i	$0.608386\pi$
$194$	3.01389			0.216385
$195$	−7.16666	+	2.65885i	−0.513216	+	0.190404i
$196$	11.5332	−	7.28326i	0.823800	−	0.520233i
$197$	10.8563			0.773477			0.386739	−	0.922189i	$-0.373602\pi$
$197$	10.8563			0.773477			0.386739	+	0.922189i	$0.373602\pi$
$198$	−0.564382	+	0.496542i	−0.0401089	+	0.0352877i
$199$		−	12.5847i		−	0.892104i	−0.895007	−	0.446052i	$-0.852830\pi$
$199$		−	12.5847i		−	0.892104i	0.895007	−	0.446052i	$-0.147170\pi$
$200$	−3.39200	+	2.91861i	−0.239851	+	0.206377i
$201$			8.03174i			0.566515i
$202$	0.0276335			0.00194429
$203$	−9.32736	+	2.69860i	−0.654653	+	0.189405i
$204$			3.29475i			0.230679i
$205$	9.56238	+	25.7744i	0.667866	+	1.80016i
$206$	−1.90722			−0.132882
$207$		−	3.95479i		−	0.274877i
$208$		−	12.6293i		−	0.875687i
$209$	11.6194	−	10.2228i	0.803732	−	0.707123i
$210$	−1.07800	+	0.797428i	−0.0743894	+	0.0550277i
$211$		−	9.40195i		−	0.647257i	−0.946184	−	0.323629i	$-0.895097\pi$
$211$		−	9.40195i		−	0.647257i	0.946184	−	0.323629i	$-0.104903\pi$
$212$		−	12.9596i		−	0.890072i
$213$	3.92235			0.268755
$214$	−4.59404			−0.314042
$215$	0.421813	+	1.13695i	0.0287674	+	0.0775396i
$216$	−0.894963			−0.0608945
$217$	−21.9298	+	6.34475i	−1.48869	+	0.430710i
$218$			2.63645i			0.178563i
$219$		−	0.227484i		−	0.0153719i
$220$	−12.7237	−	6.85207i	−0.857832	−	0.461967i
$221$	5.78000			0.388805
$222$		−	0.701586i		−	0.0470874i
$223$	23.7661			1.59149			0.795747	−	0.605629i	$-0.207078\pi$
$223$	23.7661			1.59149			0.795747	+	0.605629i	$0.207078\pi$
$224$	−1.93187	−	6.67726i	−0.129079	−	0.446143i
$225$	−3.79010	+	3.26115i	−0.252673	+	0.217410i
$226$		−	3.69976i		−	0.246104i
$227$			6.02344i			0.399790i	0.979817	+	0.199895i	$0.0640601\pi$
$227$			6.02344i			0.399790i	−0.979817	+	0.199895i	$0.935940\pi$
$228$	9.09285			0.602188
$229$			14.7790i			0.976622i	0.872670	+	0.488311i	$0.162387\pi$
$229$			14.7790i			0.976622i	−0.872670	+	0.488311i	$0.837613\pi$
$230$	−1.87916	+	0.697174i	−0.123908	+	0.0459703i
$231$	−7.39888	−	4.71768i	−0.486811	−	0.310401i
$232$			3.28451i			0.215639i
$233$	11.0985			0.727088			0.363544	−	0.931577i	$-0.381567\pi$
$233$	11.0985			0.727088			0.363544	+	0.931577i	$0.381567\pi$
$234$			0.774808i			0.0506508i
$235$	−6.42797	−	17.3259i	−0.419314	−	1.13022i
$236$		−	9.95848i		−	0.648242i
$237$		−	9.93059i		−	0.645061i
$238$	0.973969	−	0.281790i	0.0631330	−	0.0182657i
$239$			3.56183i			0.230396i	0.993343	+	0.115198i	$0.0367502\pi$
$239$			3.56183i			0.230396i	−0.993343	+	0.115198i	$0.963250\pi$
$240$	−2.87346	−	7.74511i	−0.185481	−	0.499945i
$241$	−13.7682			−0.886885			−0.443443	−	0.896303i	$-0.646243\pi$
$241$	−13.7682			−0.886885			−0.443443	+	0.896303i	$0.646243\pi$
$242$	−0.317546	+	2.47286i	−0.0204126	+	0.158962i
$243$	−1.00000			−0.0641500
$244$	−26.2004			−1.67731
$245$	−12.4391	−	9.50095i	−0.794707	−	0.606994i
$246$	2.78654			0.177664
$247$		−	15.9517i		−	1.01498i
$248$			7.72229i			0.490366i
$249$		−	14.3905i		−	0.911961i
$250$	2.21772	+	1.22601i	0.140261	+	0.0775399i
$251$		−	18.2881i		−	1.15433i	−0.816627	−	0.577166i	$-0.804159\pi$
$251$		−	18.2881i		−	1.15433i	0.816627	−	0.577166i	$-0.195841\pi$
$252$	−1.43286	−	4.95247i	−0.0902615	−	0.311977i
$253$	−8.66404	−	9.84775i	−0.544703	−	0.619122i
$254$	4.54354			0.285087
$255$	3.54466	−	1.31508i	0.221975	−	0.0823535i
$256$	12.0468			0.752923
$257$	8.63315			0.538521			0.269261	−	0.963067i	$-0.413221\pi$
$257$	8.63315			0.538521			0.269261	+	0.963067i	$0.413221\pi$
$258$	0.122919			0.00765262
$259$	7.86711	−	2.27612i	0.488838	−	0.141431i
$260$	−13.9652	+	5.18112i	−0.866083	+	0.321319i
$261$			3.67000i			0.227167i
$262$	3.99942			0.247085
$263$	12.6022			0.777086			0.388543	−	0.921431i	$-0.372979\pi$
$263$	12.6022			0.777086			0.388543	+	0.921431i	$0.372979\pi$
$264$	−2.22853	+	1.96066i	−0.137157	+	0.120670i
$265$	−13.9427	+	5.17277i	−0.856491	+	0.317761i
$266$	−0.777684	−	2.68796i	−0.0476829	−	0.164809i
$267$		−	4.81796i		−	0.294854i
$268$			15.6509i			0.956030i
$269$			6.71917i			0.409675i	0.978796	+	0.204837i	$0.0656666\pi$
$269$			6.71917i			0.409675i	−0.978796	+	0.204837i	$0.934333\pi$
$270$	0.176286	+	0.475161i	0.0107284	+	0.0289174i
$271$	5.24453			0.318582			0.159291	−	0.987232i	$-0.449079\pi$
$271$	5.24453			0.318582			0.159291	+	0.987232i	$0.449079\pi$
$272$			6.24653i			0.378751i
$273$	−8.68817	+	2.51367i	−0.525832	+	0.152134i
$274$		−	3.27979i		−	0.198139i
$275$	−2.29323	+	16.4238i	−0.138287	+	0.990392i
$276$		−	7.70641i		−	0.463871i
$277$	11.1171			0.667960			0.333980	−	0.942580i	$-0.391608\pi$
$277$	11.1171			0.667960			0.333980	+	0.942580i	$0.391608\pi$
$278$	−0.0130840			−0.000784729
$279$			8.62861i			0.516581i
$280$	−4.25664	+	3.14875i	−0.254383	+	0.188174i
$281$			0.161176i			0.00961497i	0.999988	+	0.00480749i	$0.00153028\pi$
$281$			0.161176i			0.00961497i	−0.999988	+	0.00480749i	$0.998470\pi$
$282$	−1.87315			−0.111545
$283$		−	27.9678i		−	1.66252i	−0.555887	−	0.831258i	$-0.687621\pi$
$283$		−	27.9678i		−	1.66252i	0.555887	−	0.831258i	$-0.312379\pi$
$284$	7.64320			0.453540
$285$	−3.62936	−	9.78256i	−0.214985	−	0.579469i
$286$	1.69743	+	1.92934i	0.100371	+	0.114084i
$287$	9.04025	+	31.2464i	0.533629	+	1.84442i
$288$	−2.62727			−0.154813
$289$	14.1412			0.831834
$290$	1.74384	−	0.646970i	0.102402	−	0.0379914i
$291$	13.2975			0.779511
$292$		−	0.443281i		−	0.0259411i
$293$			23.6761i			1.38317i	0.722294	+	0.691586i	$0.243088\pi$
$293$			23.6761i			1.38317i	−0.722294	+	0.691586i	$0.756912\pi$
$294$	−1.34147	+	0.847141i	−0.0782359	+	0.0494062i
$295$	−10.7139	+	3.97487i	−0.623785	+	0.231426i
$296$		−	2.77030i		−	0.161021i
$297$	−2.49008	+	2.19077i	−0.144489	+	0.127122i
$298$		−	3.87625i		−	0.224545i
$299$	−13.5194			−0.781848
$300$	−7.38550	+	6.35478i	−0.426402	+	0.366893i
$301$	0.398781	+	1.37833i	0.0229854	+	0.0794458i
$302$			2.30629i			0.132712i
$303$	0.121921			0.00700415
$304$	17.2392			0.988734
$305$	10.4578	+	28.1878i	0.598810	+	1.61403i
$306$		−	0.383223i		−	0.0219074i
$307$		−	4.45510i		−	0.254266i	−0.991886	−	0.127133i	$-0.959422\pi$
$307$		−	4.45510i		−	0.254266i	0.991886	−	0.127133i	$-0.0405775\pi$
$308$	−14.4177	−	9.19301i	−0.821523	−	0.523821i
$309$	−8.41477			−0.478699
$310$	4.09998	−	1.52110i	0.232863	−	0.0863930i
$311$			12.1013i			0.686204i	0.939298	+	0.343102i	$0.111478\pi$
$311$			12.1013i			0.686204i	−0.939298	+	0.343102i	$0.888522\pi$
$312$			3.05943i			0.173206i
$313$	−1.74964			−0.0988956			−0.0494478	−	0.998777i	$-0.515746\pi$
$313$	−1.74964			−0.0988956			−0.0494478	+	0.998777i	$0.515746\pi$
$314$	2.58158			0.145687
$315$	−4.75622	+	3.51830i	−0.267982	+	0.198233i
$316$		−	19.3510i		−	1.08858i
$317$		−	9.93330i		−	0.557910i	−0.960304	−	0.278955i	$-0.910012\pi$
$317$		−	9.93330i		−	0.557910i	0.960304	−	0.278955i	$-0.0899880\pi$
$318$			1.50738i			0.0845297i
$319$	8.04013	+	9.13860i	0.450161	+	0.511663i
$320$	−5.28376	−	14.2418i	−0.295371	−	0.796143i
$321$	−20.2692			−1.13132
$322$	−2.27811	+	0.659106i	−0.126954	+	0.0367305i
$323$			7.88976i			0.438998i
$324$	−1.94863			−0.108257
$325$	11.1482	+	12.9565i	0.618393	+	0.718695i
$326$			4.07017i			0.225426i
$327$			11.6322i			0.643261i
$328$	11.0030			0.607540
$329$	−6.07698	−	21.0043i	−0.335035	−	1.15800i
$330$	1.47994	+	0.796988i	0.0814679	+	0.0438727i
$331$	6.45719			0.354919			0.177459	−	0.984128i	$-0.443212\pi$
$331$	6.45719			0.354919			0.177459	+	0.984128i	$0.443212\pi$
$332$		−	28.0418i		−	1.53899i
$333$		−	3.09544i		−	0.169629i
$334$			3.53012i			0.193160i
$335$	16.8380	−	6.24697i	0.919961	−	0.341308i
$336$	−2.71656	−	9.38942i	−0.148200	−	0.512235i
$337$	26.8150			1.46071			0.730354	−	0.683069i	$-0.239355\pi$
$337$	26.8150			1.46071			0.730354	+	0.683069i	$0.239355\pi$
$338$	−0.297794			−0.0161978
$339$		−	16.3235i		−	0.886573i
$340$	6.90723	−	2.56260i	0.374597	−	0.138977i
$341$	18.9033	+	21.4860i	1.02367	+	1.16353i
$342$	−1.05762			−0.0571895
$343$	−13.8513	−	12.2939i	−0.747901	−	0.663811i
$344$	0.485362			0.0261690
$345$	−8.29096	+	3.07597i	−0.446370	+	0.165605i
$346$		−	2.02917i		−	0.109089i
$347$	15.5673			0.835696			0.417848	−	0.908517i	$-0.362785\pi$
$347$	15.5673			0.835696			0.417848	+	0.908517i	$0.362785\pi$
$348$			7.15146i			0.383359i
$349$	0.525259			0.0281165			0.0140582	−	0.999901i	$-0.495525\pi$
$349$	0.525259			0.0281165			0.0140582	+	0.999901i	$0.495525\pi$
$350$	2.51021	+	1.63974i	0.134176	+	0.0876479i
$351$			3.41850i			0.182466i
$352$	−6.54213	+	5.75575i	−0.348696	+	0.306783i
$353$	−30.7903			−1.63880			−0.819402	−	0.573219i	$-0.805694\pi$
$353$	−30.7903			−1.63880			−0.819402	+	0.573219i	$0.805694\pi$
$354$			1.15831i			0.0615632i
$355$	−3.05074	−	8.22296i	−0.161917	−	0.436429i
$356$		−	9.38842i		−	0.497585i
$357$	4.29721	−	1.24327i	0.227432	−	0.0658010i
$358$	1.32285			0.0699150
$359$		−	27.5986i		−	1.45660i	−0.685259	−	0.728300i	$-0.740311\pi$
$359$		−	27.5986i		−	1.45660i	0.685259	−	0.728300i	$-0.259689\pi$
$360$	0.696089	+	1.87623i	0.0366871	+	0.0988863i
$361$	2.77416			0.146008
$362$		−	2.17312i		−	0.114217i
$363$	−1.40103	+	10.9104i	−0.0735351	+	0.572648i
$364$	−16.9300	+	4.89821i	−0.887374	+	0.256736i
$365$	−0.476905	+	0.176933i	−0.0249623	+	0.00926110i
$366$	3.04746			0.159293
$367$	−24.8693			−1.29817			−0.649083	−	0.760718i	$-0.724847\pi$
$367$	−24.8693			−1.29817			−0.649083	+	0.760718i	$0.724847\pi$
$368$		−	14.6106i		−	0.761631i
$369$	12.2944			0.640020
$370$	−1.47083	+	0.545683i	−0.0764649	+	0.0283687i
$371$	−16.9027	+	4.89032i	−0.877547	+	0.253893i
$372$			16.8140i			0.871763i
$373$	22.8073			1.18092			0.590459	−	0.807067i	$-0.298947\pi$
$373$	22.8073			1.18092			0.590459	+	0.807067i	$0.298947\pi$
$374$	−0.839555	−	0.954258i	−0.0434124	−	0.0493435i
$375$	9.78469	+	5.40924i	0.505279	+	0.279332i
$376$	−7.39639			−0.381440
$377$	12.5459			0.646145
$378$	0.166660	+	0.576039i	0.00857209	+	0.0296283i
$379$	29.2322			1.50156			0.750779	−	0.660554i	$-0.229679\pi$
$379$	29.2322			1.50156			0.750779	+	0.660554i	$0.229679\pi$
$380$	−7.07228	−	19.0626i	−0.362800	−	0.977890i
$381$	20.0464			1.02701
$382$	−2.53194			−0.129545
$383$	−29.2397			−1.49408			−0.747039	−	0.664780i	$-0.768525\pi$
$383$	−29.2397			−1.49408			−0.747039	+	0.664780i	$0.768525\pi$
$384$	−6.79427			−0.346719
$385$	−4.13559	+	19.1806i	−0.210769	+	0.977536i
$386$	2.10314			0.107047
$387$	0.542327			0.0275680
$388$	25.9118			1.31547
$389$	−6.00191			−0.304309			−0.152154	−	0.988357i	$-0.548621\pi$
$389$	−6.00191			−0.304309			−0.152154	+	0.988357i	$0.548621\pi$
$390$	1.62434	−	0.602634i	0.0822515	−	0.0305155i
$391$	6.68676			0.338164
$392$	−5.29695	+	3.34504i	−0.267536	+	0.168950i
$393$	17.6457			0.890106
$394$	−2.46059			−0.123963
$395$	−20.8189	+	7.72386i	−1.04751	+	0.388629i
$396$	−4.85225	+	4.26900i	−0.243835	+	0.214525i
$397$	29.9517			1.50323			0.751616	−	0.659601i	$-0.229275\pi$
$397$	29.9517			1.50323			0.751616	+	0.659601i	$0.229275\pi$
$398$			2.85234i			0.142975i
$399$	−3.43119	−	11.8594i	−0.171774	−	0.593714i
$400$	−14.0022	+	12.0480i	−0.700110	+	0.602402i
$401$	9.46669			0.472744			0.236372	−	0.971663i	$-0.424042\pi$
$401$	9.46669			0.472744			0.236372	+	0.971663i	$0.424042\pi$
$402$		−	1.82041i		−	0.0907937i
$403$	29.4969			1.46934
$404$	0.237578			0.0118199
$405$	0.777785	+	2.09644i	0.0386484	+	0.104173i
$406$	2.11406	−	0.611643i	0.104919	−	0.0303553i
$407$	−6.78140	−	7.70790i	−0.336142	−	0.382066i
$408$		−	1.51321i		−	0.0749149i
$409$	−2.76313			−0.136628			−0.0683141	−	0.997664i	$-0.521762\pi$
$409$	−2.76313			−0.136628			−0.0683141	+	0.997664i	$0.521762\pi$
$410$	−2.16733	−	5.84181i	−0.107037	−	0.288507i
$411$		−	14.4706i		−	0.713783i
$412$	−16.3973			−0.807835
$413$	−12.9884	+	3.75783i	−0.639120	+	0.184911i
$414$			0.896359i			0.0440536i
$415$	−30.1688	+	11.1927i	−1.48093	+	0.549429i
$416$			8.98132i			0.440345i
$417$	−0.0577275			−0.00282693
$418$	−2.63356	+	2.31700i	−0.128812	+	0.113328i
$419$		−	10.3609i		−	0.506165i	−0.967445	−	0.253083i	$-0.918556\pi$
$419$		−	10.3609i		−	0.506165i	0.967445	−	0.253083i	$-0.0814445\pi$
$420$	−9.26810	+	6.85585i	−0.452237	+	0.334531i
$421$	−25.7074			−1.25290			−0.626451	−	0.779461i	$-0.715493\pi$
$421$	−25.7074			−1.25290			−0.626451	+	0.779461i	$0.715493\pi$
$422$			2.13097i			0.103734i
$423$	−8.26446			−0.401832
$424$			5.95209i			0.289059i
$425$	−5.51397	−	6.40832i	−0.267467	−	0.310849i
$426$	−0.889006			−0.0430725
$427$	9.88674	+	34.1722i	0.478453	+	1.65371i
$428$	−39.4971			−1.90916
$429$	7.48915	+	8.51234i	0.361579	+	0.410980i
$430$	−0.0956047	−	0.257693i	−0.00461047	−	0.0124270i
$431$		−	25.1710i		−	1.21244i	−0.795296	−	0.606222i	$-0.792684\pi$
$431$		−	25.1710i		−	1.21244i	0.795296	−	0.606222i	$-0.207316\pi$
$432$	−3.69441			−0.177748
$433$	14.4242			0.693182			0.346591	−	0.938016i	$-0.387339\pi$
$433$	14.4242			0.693182			0.346591	+	0.938016i	$0.387339\pi$
$434$	4.97042	−	1.43805i	0.238588	−	0.0690285i
$435$	7.69392	−	2.85447i	0.368895	−	0.136861i
$436$			22.6668i			1.08554i
$437$		−	18.4541i		−	0.882781i
$438$			0.0515595i			0.00246361i
$439$	−24.3738			−1.16330			−0.581648	−	0.813441i	$-0.697592\pi$
$439$	−24.3738			−1.16330			−0.581648	+	0.813441i	$0.697592\pi$
$440$	5.84372	+	3.14701i	0.278589	+	0.150028i
$441$	−5.91862	+	3.73763i	−0.281839	+	0.177983i
$442$	−1.31005			−0.0623126
$443$		−	21.4838i		−	1.02072i	−0.859960	−	0.510362i	$-0.829511\pi$
$443$		−	21.4838i		−	1.02072i	0.859960	−	0.510362i	$-0.170489\pi$
$444$		−	6.03186i		−	0.286259i
$445$	−10.1006	+	3.74734i	−0.478812	+	0.177641i
$446$	−5.38662			−0.255064
$447$		−	17.1022i		−	0.808909i
$448$	−4.99525	−	17.2654i	−0.236004	−	0.815714i
$449$	2.72757			0.128722			0.0643609	−	0.997927i	$-0.479499\pi$
$449$	2.72757			0.128722			0.0643609	+	0.997927i	$0.479499\pi$
$450$	0.859033	−	0.739146i	0.0404952	−	0.0348437i
$451$	30.6140	−	26.9342i	1.44156	−	1.26828i
$452$		−	31.8085i		−	1.49615i
$453$			10.1755i			0.478087i
$454$		−	1.36522i		−	0.0640731i
$455$	12.0273	+	16.2591i	0.563848	+	0.762239i
$456$	−4.17615			−0.195566
$457$	22.6707			1.06049			0.530246	−	0.847844i	$-0.322099\pi$
$457$	22.6707			1.06049			0.530246	+	0.847844i	$0.322099\pi$
$458$		−	3.34968i		−	0.156520i
$459$		−	1.69080i		−	0.0789199i
$460$	−16.1560	+	5.99393i	−0.753278	+	0.279468i
$461$	0.300295			0.0139861			0.00699307	−	0.999976i	$-0.497774\pi$
$461$	0.300295			0.0139861			0.00699307	+	0.999976i	$0.497774\pi$
$462$	1.67697	+	1.06927i	0.0780197	+	0.0497470i
$463$			26.2401i			1.21948i	0.792602	+	0.609740i	$0.208726\pi$
$463$			26.2401i			1.21948i	−0.792602	+	0.609740i	$0.791274\pi$
$464$			13.5585i			0.629437i
$465$	18.0893	−	6.71120i	0.838873	−	0.311225i
$466$	−2.51550			−0.116528
$467$	6.83684			0.316371			0.158186	−	0.987409i	$-0.449436\pi$
$467$	6.83684			0.316371			0.158186	+	0.987409i	$0.449436\pi$
$468$			6.66138i			0.307922i
$469$	20.4128	−	5.90586i	0.942576	−	0.272707i
$470$	1.45691	+	3.92695i	0.0672022	+	0.181137i
$471$	11.3901			0.524826
$472$			4.57372i			0.210522i
$473$	1.35044	−	1.18811i	0.0620932	−	0.0546296i
$474$			2.25078i			0.103382i
$475$	−17.6857	+	15.2175i	−0.811474	+	0.698225i
$476$	8.37366	−	2.42268i	0.383806	−	0.111043i
$477$			6.65065i			0.304512i
$478$		−	0.807295i		−	0.0369248i
$479$	−0.0294732			−0.00134666			−0.000673332	−	1.00000i	$-0.500214\pi$
$479$	−0.0294732			−0.00134666			−0.000673332		1.00000i	$0.500214\pi$
$480$	2.04345	+	5.50791i	0.0932704	+	0.251401i
$481$	−10.5817			−0.482486
$482$	3.12058			0.142138
$483$	−10.0512	+	2.90801i	−0.457343	+	0.132319i
$484$	−2.73009	+	21.2603i	−0.124095	+	0.966379i
$485$	−10.3426	−	27.8773i	−0.469632	−	1.26584i
$486$	0.226652			0.0102811
$487$		−	28.2238i		−	1.27894i	−0.768814	−	0.639472i	$-0.779153\pi$
$487$		−	28.2238i		−	1.27894i	0.768814	−	0.639472i	$-0.220847\pi$
$488$	12.0333			0.544722
$489$			17.9578i			0.812081i
$490$	2.81935	+	2.15341i	0.127365	+	0.0972810i
$491$		−	1.24922i		−	0.0563767i	−0.999603	−	0.0281883i	$-0.991026\pi$
$491$		−	1.24922i		−	0.0563767i	0.999603	−	0.0281883i	$-0.00897382\pi$
$492$	23.9572			1.08007
$493$	−6.20524			−0.279470
$494$			3.61547i			0.162668i
$495$	6.52957	+	3.51636i	0.293482	+	0.158048i
$496$			31.8777i			1.43135i
$497$	−2.88416	−	9.96871i	−0.129372	−	0.447158i
$498$			3.26163i			0.146157i
$499$	−7.85460			−0.351620			−0.175810	−	0.984424i	$-0.556254\pi$
$499$	−7.85460			−0.351620			−0.175810	+	0.984424i	$0.556254\pi$
$500$	19.0667	+	10.5406i	0.852690	+	0.471390i
$501$			15.5751i			0.695845i
$502$			4.14502i			0.185001i
$503$			11.0553i			0.492930i	0.969152	+	0.246465i	$0.0792691\pi$
$503$			11.0553i			0.492930i	−0.969152	+	0.246465i	$0.920731\pi$
$504$	0.658080	+	2.27457i	0.0293132	+	0.101317i
$505$	−0.0948279	−	0.255599i	−0.00421979	−	0.0113740i
$506$	1.96372	+	2.23201i	0.0872979	+	0.0992249i
$507$	−1.31388			−0.0583516
$508$	39.0629			1.73314
$509$			20.0492i			0.888663i	0.895862	+	0.444332i	$0.146559\pi$
$509$			20.0492i			0.888663i	−0.895862	+	0.444332i	$0.853441\pi$
$510$	−0.803404	+	0.298065i	−0.0355753	+	0.0131985i
$511$	−0.578153	+	0.167272i	−0.0255760	+	0.00739968i
$512$	−16.3190			−0.721203
$513$	−4.66628			−0.206021
$514$	−1.95672			−0.0863071
$515$	6.54488	+	17.6410i	0.288402	+	0.777357i
$516$	1.05679			0.0465227
$517$	−20.5792	+	18.1056i	−0.905072	+	0.796281i
$518$	−1.78309	+	0.515887i	−0.0783446	+	0.0226668i
$519$		−	8.95282i		−	0.392985i
$520$	6.41390	−	2.37958i	0.281268	−	0.104351i
$521$			10.3047i			0.451456i	0.974190	+	0.225728i	$0.0724760\pi$
$521$			10.3047i			0.451456i	−0.974190	+	0.225728i	$0.927524\pi$
$522$		−	0.831811i		−	0.0364074i
$523$		−	16.8212i		−	0.735538i	−0.929917	−	0.367769i	$-0.880122\pi$
$523$		−	16.8212i		−	0.735538i	0.929917	−	0.367769i	$-0.119878\pi$
$524$	34.3848			1.50211
$525$	11.0752	+	7.23464i	0.483361	+	0.315745i
$526$	−2.85631			−0.124541
$527$	−14.5893			−0.635519
$528$	−9.19940	+	8.09362i	−0.400352	+	0.352230i
$529$	7.35967			0.319986
$530$	3.16013	−	1.17242i	0.137267	−	0.0509266i
$531$			5.11051i			0.221777i
$532$	−6.68611	−	23.1096i	−0.289880	−	1.00193i
$533$		−	42.0283i		−	1.82045i
$534$			1.09200i			0.0472554i
$535$	15.7651	+	42.4931i	0.681583	+	1.83714i
$536$		−	7.18811i		−	0.310479i
$537$	5.83650			0.251864
$538$		−	1.52291i		−	0.0656573i
$539$	−6.54956	+	22.2734i	−0.282110	+	0.959382i
$540$	1.51561	+	4.08518i	0.0652216	+	0.175798i
$541$		−	39.9003i		−	1.71545i	−0.514112	−	0.857723i	$-0.671879\pi$
$541$		−	39.9003i		−	1.71545i	0.514112	−	0.857723i	$-0.328121\pi$
$542$	−1.18868			−0.0510582
$543$		−	9.58793i		−	0.411457i
$544$		−	4.44220i		−	0.190458i
$545$	24.3861	−	9.04732i	1.04459	−	0.387545i
$546$	1.96919	−	0.569728i	0.0842735	−	0.0243821i
$547$	−40.3720			−1.72618			−0.863091	−	0.505049i	$-0.831475\pi$
$547$	−40.3720			−1.72618			−0.863091	+	0.505049i	$0.831475\pi$
$548$		−	28.1979i		−	1.20455i
$549$	13.4456			0.573843
$550$	0.519763	−	3.72248i	0.0221628	−	0.158727i
$551$			17.1252i			0.729559i
$552$			3.53939i			0.150646i
$553$	−25.2388	+	7.30211i	−1.07326	+	0.310517i
$554$	−2.51970			−0.107052
$555$	−6.48939	+	2.40758i	−0.275459	+	0.102196i
$556$	−0.112490			−0.00477062
$557$	−21.2784			−0.901595			−0.450797	−	0.892626i	$-0.648860\pi$
$557$	−21.2784			−0.901595			−0.450797	+	0.892626i	$0.648860\pi$
$558$		−	1.95569i		−	0.0827909i
$559$		−	1.85394i		−	0.0784134i
$560$	−17.5714	+	12.9980i	−0.742528	+	0.549267i
$561$	−3.70417	−	4.21024i	−0.156390	−	0.177757i
$562$		−	0.0365309i		−	0.00154096i
$563$			4.42754i			0.186599i	0.995638	+	0.0932993i	$0.0297414\pi$
$563$			4.42754i			0.186599i	−0.995638	+	0.0932993i	$0.970259\pi$
$564$	−16.1044			−0.678116
$565$	−34.2213	+	12.6962i	−1.43970	+	0.534133i
$566$			6.33896i			0.266446i
$567$	0.735315	+	2.54152i	0.0308803	+	0.106734i
$568$	−3.51036			−0.147291
$569$		−	5.16934i		−	0.216710i	−0.994112	−	0.108355i	$-0.965442\pi$
$569$		−	5.16934i		−	0.216710i	0.994112	−	0.108355i	$-0.0345583\pi$
$570$	0.822600	+	2.21723i	0.0344549	+	0.0928697i
$571$			20.0448i			0.838848i	0.907790	+	0.419424i	$0.137768\pi$
$571$			20.0448i			0.838848i	−0.907790	+	0.419424i	$0.862232\pi$
$572$	14.5936	+	16.5874i	0.610188	+	0.693554i
$573$	−11.1711			−0.466678
$574$	−2.04899	−	7.08205i	−0.0855231	−	0.295599i
$575$	12.8972	+	14.9890i	0.537849	+	0.625086i
$576$	−6.79335			−0.283056
$577$	22.7074			0.945323			0.472661	−	0.881244i	$-0.343293\pi$
$577$	22.7074			0.945323			0.472661	+	0.881244i	$0.343293\pi$
$578$	−3.20512			−0.133316
$579$	9.27916			0.385629
$580$	14.9926	−	5.56230i	0.622534	−	0.230962i
$581$	−36.5737	+	10.5816i	−1.51733	+	0.438997i
$582$	−3.01389			−0.124930
$583$	14.5701	+	16.5607i	0.603430	+	0.685873i
$584$			0.203589i			0.00842459i
$585$	7.16666	−	2.65885i	0.296305	−	0.109930i
$586$		−	5.36622i		−	0.221677i
$587$	4.29985			0.177474			0.0887370	−	0.996055i	$-0.471717\pi$
$587$	4.29985			0.177474			0.0887370	+	0.996055i	$0.471717\pi$
$588$	−11.5332	+	7.28326i	−0.475621	+	0.300357i
$589$			40.2635i			1.65903i
$590$	2.42831	−	0.900912i	0.0999721	−	0.0370900i
$591$	−10.8563			−0.446567
$592$		−	11.4358i		−	0.470010i
$593$		−	4.86529i		−	0.199794i	−0.994998	−	0.0998968i	$-0.968149\pi$
$593$		−	4.86529i		−	0.199794i	0.994998	−	0.0998968i	$-0.0318513\pi$
$594$	0.564382	−	0.496542i	0.0231569	−	0.0203734i
$595$	−5.94875	−	8.04183i	−0.243875	−	0.329683i
$596$		−	33.3259i		−	1.36508i
$597$			12.5847i			0.515057i
$598$	3.06420			0.125304
$599$	−26.3759			−1.07769			−0.538845	−	0.842405i	$-0.681139\pi$
$599$	−26.3759			−1.07769			−0.538845	+	0.842405i	$0.681139\pi$
$600$	3.39200	−	2.91861i	0.138478	−	0.119152i
$601$	15.9659			0.651263			0.325632	−	0.945497i	$-0.394423\pi$
$601$	15.9659			0.651263			0.325632	+	0.945497i	$0.394423\pi$
$602$	−0.0903844	−	0.312401i	−0.00368379	−	0.0127325i
$603$		−	8.03174i		−	0.327078i
$604$			19.8283i			0.806801i
$605$	23.9627	−	5.54878i	0.974222	−	0.225590i
$606$	−0.0276335			−0.00112253
$607$		−	7.23379i		−	0.293611i	−0.989165	−	0.146805i	$-0.953101\pi$
$607$		−	7.23379i		−	0.293611i	0.989165	−	0.146805i	$-0.0468991\pi$
$608$	−12.2596			−0.497192
$609$	9.32736	−	2.69860i	0.377964	−	0.109353i
$610$	−2.37027	−	6.38882i	−0.0959694	−	0.258676i
$611$			28.2520i			1.14295i
$612$		−	3.29475i		−	0.133182i
$613$	−47.3389			−1.91200			−0.956000	−	0.293366i	$-0.905225\pi$
$613$	−47.3389			−1.91200			−0.956000	+	0.293366i	$0.905225\pi$
$614$			1.00976i			0.0407504i
$615$	−9.56238	−	25.7744i	−0.385593	−	1.03932i
$616$	6.62173	+	4.22215i	0.266797	+	0.170115i
$617$			13.5352i			0.544905i	0.962169	+	0.272453i	$0.0878348\pi$
$617$			13.5352i			0.544905i	−0.962169	+	0.272453i	$0.912165\pi$
$618$	1.90722			0.0767197
$619$			38.5778i			1.55057i	0.631611	+	0.775286i	$0.282394\pi$
$619$			38.5778i			1.55057i	−0.631611	+	0.775286i	$0.717606\pi$
$620$	35.2494	−	13.0776i	1.41565	−	0.525211i
$621$			3.95479i			0.158700i
$622$		−	2.74279i		−	0.109976i
$623$	−12.2449	+	3.54272i	−0.490583	+	0.141936i
$624$			12.6293i			0.505578i
$625$	3.72975	−	24.7202i	0.149190	−	0.988809i
$626$	0.396559			0.0158497
$627$	−11.6194	+	10.2228i	−0.464035	+	0.408258i
$628$	22.1950			0.885677
$629$	5.23378			0.208684
$630$	1.07800	−	0.797428i	0.0429487	−	0.0317703i
$631$	24.9093			0.991623			0.495811	−	0.868430i	$-0.334871\pi$
$631$	24.9093			0.991623			0.495811	+	0.868430i	$0.334871\pi$
$632$			8.88751i			0.353526i
$633$			9.40195i			0.373694i
$634$			2.25140i			0.0894145i
$635$	−15.5917	−	42.0259i	−0.618740	−	1.66775i
$636$			12.9596i			0.513883i
$637$	12.7771	+	20.2328i	0.506246	+	0.801652i
$638$	−1.82231	−	2.07128i	−0.0721459	−	0.0820027i
$639$	−3.92235			−0.155166
$640$	5.28448	+	14.2438i	0.208887	+	0.563034i
$641$	35.1951			1.39012			0.695061	−	0.718951i	$-0.255377\pi$
$641$	35.1951			1.39012			0.695061	+	0.718951i	$0.255377\pi$
$642$	4.59404			0.181312
$643$	12.6828			0.500162			0.250081	−	0.968225i	$-0.419543\pi$
$643$	12.6828			0.500162			0.250081	+	0.968225i	$0.419543\pi$
$644$	−19.5860	+	5.66664i	−0.771796	+	0.223297i
$645$	−0.421813	−	1.13695i	−0.0166089	−	0.0447675i
$646$		−	1.78823i		−	0.0703568i
$647$	−17.7641			−0.698379			−0.349190	−	0.937052i	$-0.613543\pi$
$647$	−17.7641			−0.698379			−0.349190	+	0.937052i	$0.613543\pi$
$648$	0.894963			0.0351575
$649$	11.1960	+	12.7256i	0.439480	+	0.499523i
$650$	−2.52677	−	2.93660i	−0.0991080	−	0.115183i
$651$	21.9298	−	6.34475i	0.859495	−	0.248670i
$652$			34.9931i			1.37044i
$653$			26.5776i			1.04006i	0.854147	+	0.520032i	$0.174080\pi$
$653$			26.5776i			1.04006i	−0.854147	+	0.520032i	$0.825920\pi$
$654$		−	2.63645i		−	0.103093i
$655$	−13.7245	−	36.9930i	−0.536261	−	1.44544i
$656$	45.4205			1.77337
$657$			0.227484i			0.00887498i
$658$	1.37736	+	4.76065i	0.0536950	+	0.185590i
$659$		−	20.1965i		−	0.786745i	−0.919379	−	0.393372i	$-0.871308\pi$
$659$		−	20.1965i		−	0.786745i	0.919379	−	0.393372i	$-0.128692\pi$
$660$	12.7237	+	6.85207i	0.495269	+	0.266717i
$661$		−	19.9142i		−	0.774572i	−0.921960	−	0.387286i	$-0.873413\pi$
$661$		−	19.9142i		−	0.774572i	0.921960	−	0.387286i	$-0.126587\pi$
$662$	−1.46353			−0.0568818
$663$	−5.78000			−0.224477
$664$			12.8790i			0.499801i
$665$	−22.1938	+	16.4173i	−0.860640	+	0.636637i
$666$			0.701586i			0.0271859i
$667$	14.5141			0.561986
$668$			30.3501i			1.17428i
$669$	−23.7661			−0.918850
$670$	−3.81637	+	1.41589i	−0.147439	+	0.0547004i
$671$	33.4806	−	29.4562i	1.29250	−	1.13714i
$672$	1.93187	+	6.67726i	0.0745236	+	0.257581i
$673$	10.9385			0.421647			0.210823	−	0.977524i	$-0.432386\pi$
$673$	10.9385			0.421647			0.210823	+	0.977524i	$0.432386\pi$
$674$	−6.07767			−0.234103
$675$	3.79010	−	3.26115i	0.145881	−	0.125522i
$676$	−2.56027			−0.0984719
$677$			37.5557i			1.44338i	0.692215	+	0.721691i	$0.256635\pi$
$677$			37.5557i			1.44338i	−0.692215	+	0.721691i	$0.743365\pi$
$678$			3.69976i			0.142088i
$679$	−9.77783	−	33.7957i	−0.375239	−	1.29696i
$680$	−3.17234	+	1.17695i	−0.121654	+	0.0451339i
$681$		−	6.02344i		−	0.230819i
$682$	−4.28447	−	4.86983i	−0.164061	−	0.186475i
$683$		−	3.81142i		−	0.145840i	−0.997338	−	0.0729200i	$-0.976768\pi$
$683$		−	3.81142i		−	0.145840i	0.997338	−	0.0729200i	$-0.0232318\pi$
$684$	−9.09285			−0.347674
$685$	−30.3367	+	11.2550i	−1.15911	+	0.430032i
$686$	3.13942	+	2.78644i	0.119864	+	0.106387i
$687$		−	14.7790i		−	0.563853i
$688$	2.00358			0.0763857
$689$	22.7352			0.866143
$690$	1.87916	−	0.697174i	0.0715384	−	0.0265410i
$691$			20.3438i			0.773914i	0.922098	+	0.386957i	$0.126474\pi$
$691$			20.3438i			0.773914i	−0.922098	+	0.386957i	$0.873526\pi$
$692$		−	17.4457i		−	0.663187i
$693$	7.39888	+	4.71768i	0.281060	+	0.179210i
$694$	−3.52835			−0.133934
$695$	0.0448996	+	0.121022i	0.00170314	+	0.00459063i
$696$		−	3.28451i		−	0.124499i
$697$			20.7874i			0.787378i
$698$	−0.119051			−0.00450614
$699$	−11.0985			−0.419784
$700$	21.5815	+	14.0976i	0.815702	+	0.532840i
$701$		−	1.03498i		−	0.0390908i	−0.999809	−	0.0195454i	$-0.993778\pi$
$701$		−	1.03498i		−	0.0390908i	0.999809	−	0.0195454i	$-0.00622188\pi$
$702$		−	0.774808i		−	0.0292432i
$703$		−	14.4442i		−	0.544772i
$704$	−16.9160	+	14.8827i	−0.637546	+	0.560912i
$705$	6.42797	+	17.3259i	0.242091	+	0.652532i
$706$	6.97868			0.262646
$707$	−0.0896500	−	0.309863i	−0.00337164	−	0.0116536i
$708$			9.95848i			0.374263i
$709$	−4.43499			−0.166560			−0.0832798	−	0.996526i	$-0.526540\pi$
$709$	−4.43499			−0.166560			−0.0832798	+	0.996526i	$0.526540\pi$
$710$	0.691456	+	1.86375i	0.0259499	+	0.0699452i
$711$			9.93059i			0.372426i
$712$			4.31190i			0.161595i
$713$	34.1243			1.27797
$714$	−0.973969	+	0.281790i	−0.0364499	+	0.0105457i
$715$	12.0206	−	22.3213i	0.449547	−	0.834769i
$716$	11.3732			0.425036
$717$		−	3.56183i		−	0.133019i
$718$			6.25527i			0.233445i
$719$		−	21.8889i		−	0.816317i	−0.912911	−	0.408159i	$-0.866171\pi$
$719$		−	21.8889i		−	0.816317i	0.912911	−	0.408159i	$-0.133829\pi$
$720$	2.87346	+	7.74511i	0.107087	+	0.288643i
$721$	6.18751	+	21.3863i	0.230435	+	0.796467i
$722$	−0.628767			−0.0234003
$723$	13.7682			0.512043
$724$		−	18.6833i		−	0.694360i
$725$	−11.9684	−	13.9097i	−0.444496	−	0.516592i
$726$	0.317546	−	2.47286i	0.0117852	−	0.0917766i
$727$	−26.7167			−0.990867			−0.495433	−	0.868646i	$-0.664991\pi$
$727$	−26.7167			−0.990867			−0.495433	+	0.868646i	$0.664991\pi$
$728$	7.77559	−	2.24964i	0.288183	−	0.0833774i
$729$	1.00000			0.0370370
$730$	0.108091	−	0.0401022i	0.00400064	−	0.00148425i
$731$			0.916968i			0.0339153i
$732$	26.2004			0.968396
$733$			10.5953i			0.391346i	0.980669	+	0.195673i	$0.0626891\pi$
$733$			10.5953i			0.391346i	−0.980669	+	0.195673i	$0.937311\pi$
$734$	5.63666			0.208053
$735$	12.4391	+	9.50095i	0.458824	+	0.350448i
$736$			10.3903i			0.382991i
$737$	−17.5957	−	19.9997i	−0.648147	−	0.736699i
$738$	−2.78654			−0.102574
$739$			22.3825i			0.823355i	0.911330	+	0.411678i	$0.135057\pi$
$739$			22.3825i			0.823355i	−0.911330	+	0.411678i	$0.864943\pi$
$740$	−12.6454	+	4.69149i	−0.464855	+	0.172463i
$741$			15.9517i			0.585999i
$742$	3.83103	−	1.10840i	0.140642	−	0.0406906i
$743$	32.6191			1.19668			0.598339	−	0.801243i	$-0.295828\pi$
$743$	32.6191			1.19668			0.598339	+	0.801243i	$0.295828\pi$
$744$		−	7.72229i		−	0.283113i
$745$	−35.8538	+	13.3019i	−1.31358	+	0.487343i
$746$	−5.16932			−0.189262
$747$			14.3905i			0.526521i
$748$	−7.21804	−	8.20420i	−0.263918	−	0.299975i
$749$	14.9042	+	51.5145i	0.544589	+	1.88230i
$750$	−2.21772	−	1.22601i	−0.0809795	−	0.0447677i
$751$	−21.0464			−0.767995			−0.383998	−	0.923334i	$-0.625453\pi$
$751$	−21.0464			−0.767995			−0.383998	+	0.923334i	$0.625453\pi$
$752$	−30.5323			−1.11340
$753$			18.2881i			0.666454i
$754$	−2.84354			−0.103556
$755$	21.3323	−	7.91435i	0.776362	−	0.288033i
$756$	1.43286	+	4.95247i	0.0521125	+	0.180120i
$757$		−	9.11495i		−	0.331289i	−0.986186	−	0.165644i	$-0.947030\pi$
$757$		−	9.11495i		−	0.331289i	0.986186	−	0.165644i	$-0.0529704\pi$
$758$	−6.62553			−0.240650
$759$	8.66404	+	9.84775i	0.314485	+	0.357451i
$760$	3.24814	+	8.75503i	0.117823	+	0.317578i
$761$	−2.31644			−0.0839708			−0.0419854	−	0.999118i	$-0.513368\pi$
$761$	−2.31644			−0.0839708			−0.0419854	+	0.999118i	$0.513368\pi$
$762$	−4.54354			−0.164595
$763$	29.5634	−	8.55331i	1.07027	−	0.309651i
$764$	−21.7682			−0.787547
$765$	−3.54466	+	1.31508i	−0.128158	+	0.0475468i
$766$	6.62722			0.239451
$767$	17.4703			0.630814
$768$	−12.0468			−0.434700
$769$	−5.85584			−0.211167			−0.105583	−	0.994410i	$-0.533671\pi$
$769$	−5.85584			−0.211167			−0.105583	+	0.994410i	$0.533671\pi$
$770$	0.937339	−	4.34732i	0.0337793	−	0.156667i
$771$	−8.63315			−0.310915
$772$	18.0816			0.650772
$773$	31.1077			1.11887			0.559434	−	0.828875i	$-0.311019\pi$
$773$	31.1077			1.11887			0.559434	+	0.828875i	$0.311019\pi$
$774$	−0.122919			−0.00441824
$775$	−28.1392	−	32.7033i	−1.01079	−	1.17474i
$776$	−11.9007			−0.427212
$777$	−7.86711	+	2.27612i	−0.282231	+	0.0816554i
$778$	1.36034			0.0487707
$779$	57.3690			2.05546
$780$	13.9652	−	5.18112i	0.500033	−	0.185514i
$781$	−9.76697	+	8.59297i	−0.349490	+	0.307481i
$782$	−1.51557			−0.0541965
$783$		−	3.67000i		−	0.131155i
$784$	−21.8658	+	13.8084i	−0.780923	+	0.493156i
$785$	−8.85901	−	23.8786i	−0.316192	−	0.852262i
$786$	−3.99942			−0.142654
$787$		−	21.5355i		−	0.767658i	−0.923404	−	0.383829i	$-0.874605\pi$
$787$		−	21.5355i		−	0.767658i	0.923404	−	0.383829i	$-0.125395\pi$
$788$	−21.1548			−0.753610
$789$	−12.6022			−0.448651
$790$	4.71863	−	1.75063i	0.167881	−	0.0622845i
$791$	−41.4866	+	12.0029i	−1.47509	+	0.426776i
$792$	2.22853	−	1.96066i	0.0791875	−	0.0696691i
$793$		−	45.9637i		−	1.63222i
$794$	−6.78860			−0.240918
$795$	13.9427	−	5.17277i	0.494496	−	0.183459i
$796$			24.5229i			0.869190i
$797$	−10.6197			−0.376170			−0.188085	−	0.982153i	$-0.560228\pi$
$797$	−10.6197			−0.376170			−0.188085	+	0.982153i	$0.560228\pi$
$798$	0.777684	+	2.68796i	0.0275297	+	0.0951527i
$799$		−	13.9736i		−	0.494350i
$800$	9.95763	−	8.56794i	0.352055	−	0.302922i
$801$			4.81796i			0.170234i
$802$	−2.14564			−0.0757652
$803$	0.498365	+	0.566453i	0.0175869	+	0.0199897i
$804$		−	15.6509i		−	0.551964i
$805$	13.9141	+	18.8098i	0.490408	+	0.662959i
$806$	−6.68552			−0.235487
$807$		−	6.71917i		−	0.236526i
$808$	−0.109114			−0.00383863
$809$		−	9.04700i		−	0.318076i	−0.987273	−	0.159038i	$-0.949161\pi$
$809$		−	9.04700i		−	0.318076i	0.987273	−	0.159038i	$-0.0508392\pi$
$810$	−0.176286	−	0.475161i	−0.00619406	−	0.0166955i
$811$	−47.7917			−1.67819			−0.839096	−	0.543983i	$-0.816915\pi$
$811$	−47.7917			−1.67819			−0.839096	+	0.543983i	$0.816915\pi$
$812$	18.1756	−	5.25858i	0.637837	−	0.184540i
$813$	−5.24453			−0.183934
$814$	1.53702	+	1.74701i	0.0538724	+	0.0612326i
$815$	37.6475	−	13.9673i	1.31873	−	0.489254i
$816$		−	6.24653i		−	0.218672i
$817$	2.53065			0.0885361
$818$	0.626269			0.0218970
$819$	8.68817	−	2.51367i	0.303589	−	0.0878348i
$820$	−18.6335	−	50.2248i	−0.650711	−	1.75393i
$821$			40.6149i			1.41747i	0.705476	+	0.708734i	$0.250733\pi$
$821$			40.6149i			1.41747i	−0.705476	+	0.708734i	$0.749267\pi$
$822$			3.27979i			0.114396i
$823$			15.6137i			0.544258i	0.962261	+	0.272129i	$0.0877278\pi$
$823$			15.6137i			0.544258i	−0.962261	+	0.272129i	$0.912272\pi$
$824$	7.53091			0.262352
$825$	2.29323	−	16.4238i	0.0798399	−	0.571803i
$826$	2.94385	−	0.851719i	0.102430	−	0.0296351i
$827$	11.5633			0.402094			0.201047	−	0.979582i	$-0.435566\pi$
$827$	11.5633			0.402094			0.201047	+	0.979582i	$0.435566\pi$
$828$			7.70641i			0.267816i
$829$		−	30.0885i		−	1.04502i	−0.852635	−	0.522508i	$-0.824997\pi$
$829$		−	30.0885i		−	1.04502i	0.852635	−	0.522508i	$-0.175003\pi$
$830$	6.83781	−	2.53685i	0.237344	−	0.0880553i
$831$	−11.1171			−0.385647
$832$			23.2230i			0.805114i
$833$	−6.31960	−	10.0072i	−0.218961	−	0.346730i
$834$	0.0130840			0.000453063
$835$	32.6523	−	12.1141i	1.12998	−	0.419225i
$836$	−22.6419	+	19.9204i	−0.783088	+	0.688960i
$837$		−	8.62861i		−	0.298248i
$838$			2.34833i			0.0811216i
$839$		−	45.1298i		−	1.55805i	−0.626990	−	0.779027i	$-0.715714\pi$
$839$		−	45.1298i		−	1.55805i	0.626990	−	0.779027i	$-0.284286\pi$
$840$	4.25664	−	3.14875i	0.146868	−	0.108642i
$841$	15.5311			0.535556
$842$	5.82662			0.200799
$843$		−	0.161176i		−	0.00555121i
$844$			18.3209i			0.630632i
$845$	1.02192	+	2.75447i	0.0351550	+	0.0947568i
$846$	1.87315			0.0644003
$847$	28.7592	−	4.46185i	0.988178	−	0.153311i
$848$			24.5702i			0.843746i
$849$			27.9678i			0.959854i
$850$	1.24975	+	1.45246i	0.0428661	+	0.0498188i
$851$	−12.2418			−0.419643
$852$	−7.64320			−0.261852
$853$		−	4.05956i		−	0.138997i	−0.997582	−	0.0694983i	$-0.977860\pi$
$853$		−	4.05956i		−	0.138997i	0.997582	−	0.0694983i	$-0.0221398\pi$
$854$	−2.24085	−	7.74518i	−0.0766802	−	0.265035i
$855$	3.62936	+	9.78256i	0.124121	+	0.334557i
$856$	18.1402			0.620018
$857$		−	41.3300i		−	1.41180i	−0.708309	−	0.705902i	$-0.750542\pi$
$857$		−	41.3300i		−	1.41180i	0.708309	−	0.705902i	$-0.249458\pi$
$858$	−1.69743	−	1.92934i	−0.0579492	−	0.0658665i
$859$		−	15.1143i		−	0.515692i	−0.966186	−	0.257846i	$-0.916987\pi$
$859$		−	15.1143i		−	0.515692i	0.966186	−	0.257846i	$-0.0830127\pi$
$860$	−0.821958	−	2.21550i	−0.0280285	−	0.0755480i
$861$	−9.04025	−	31.2464i	−0.308091	−	1.06487i
$862$			5.70505i			0.194315i
$863$			23.2727i			0.792210i	0.918205	+	0.396105i	$0.129638\pi$
$863$			23.2727i			0.792210i	−0.918205	+	0.396105i	$0.870362\pi$
$864$	2.62727			0.0893816
$865$	−18.7690	+	6.96336i	−0.638166	+	0.236761i
$866$	−3.26926			−0.111094
$867$	−14.1412			−0.480260
$868$	42.7330	−	12.3636i	1.45045	−	0.419647i
$869$	21.7557	+	24.7280i	0.738010	+	0.838840i
$870$	−1.74384	+	0.646970i	−0.0591217	+	0.0219343i
$871$	−27.4565			−0.930327
$872$		−	10.4104i		−	0.352540i
$873$	−13.2975			−0.450051
$874$			4.18266i			0.141481i
$875$	6.55285	−	28.8455i	0.221527	−	0.975154i
$876$			0.443281i			0.0149771i
$877$	−30.5761			−1.03248			−0.516241	−	0.856443i	$-0.672669\pi$
$877$	−30.5761			−1.03248			−0.516241	+	0.856443i	$0.672669\pi$
$878$	5.52435			0.186438
$879$		−	23.6761i		−	0.798575i
$880$	24.1229	+	12.9909i	0.813183	+	0.437922i
$881$		−	49.0932i		−	1.65399i	−0.562208	−	0.826996i	$-0.690048\pi$
$881$		−	49.0932i		−	1.65399i	0.562208	−	0.826996i	$-0.309952\pi$
$882$	1.34147	−	0.847141i	0.0451695	−	0.0285247i
$883$		−	3.94284i		−	0.132687i	−0.997797	−	0.0663436i	$-0.978867\pi$
$883$		−	3.94284i		−	0.132687i	0.997797	−	0.0663436i	$-0.0211333\pi$
$884$	−11.2631			−0.378819
$885$	10.7139	−	3.97487i	0.360143	−	0.133614i
$886$			4.86933i			0.163588i
$887$			17.0638i			0.572947i	0.958088	+	0.286474i	$0.0924831\pi$
$887$			17.0638i			0.572947i	−0.958088	+	0.286474i	$0.907517\pi$
$888$			2.77030i			0.0929653i
$889$	−14.7404	−	50.9482i	−0.494377	−	1.70875i
$890$	2.28931	−	0.849340i	0.0767378	−	0.0284699i
$891$	2.49008	−	2.19077i	0.0834209	−	0.0733936i
$892$	−46.3113			−1.55062
$893$	−38.5643			−1.29050
$894$			3.87625i			0.129641i
$895$	−4.53954	−	12.2359i	−0.151740	−	0.409000i
$896$	4.99593	+	17.2677i	0.166902	+	0.576875i
$897$	13.5194			0.451400
$898$	−0.618208			−0.0206299
$899$	−31.6670			−1.05615
$900$	7.38550	−	6.35478i	0.246183	−	0.211826i
$901$	−11.2449			−0.374623
$902$	−6.93873	+	6.10468i	−0.231034	+	0.203264i
$903$	−0.398781	−	1.37833i	−0.0132706	−	0.0458680i
$904$			14.6090i			0.485887i
$905$	−20.1005	+	7.45734i	−0.668163	+	0.247890i
$906$		−	2.30629i		−	0.0766215i
$907$			57.7700i			1.91822i	0.283028	+	0.959112i	$0.408661\pi$
$907$			57.7700i			1.91822i	−0.283028	+	0.959112i	$0.591339\pi$
$908$		−	11.7375i		−	0.389521i
$909$	−0.121921			−0.00404385
$910$	−2.72600	−	3.68515i	−0.0903661	−	0.122162i
$911$	−25.1399			−0.832920			−0.416460	−	0.909154i	$-0.636729\pi$
$911$	−25.1399			−0.832920			−0.416460	+	0.909154i	$0.636729\pi$
$912$	−17.2392			−0.570846
$913$	31.5263	+	35.8336i	1.04337	+	1.18592i
$914$	−5.13836			−0.169962
$915$	−10.4578	−	28.1878i	−0.345723	−	0.931861i
$916$		−	28.7987i		−	0.951537i
$917$	−12.9751	−	44.8467i	−0.428476	−	1.48097i
$918$			0.383223i			0.0126483i
$919$		−	30.1376i		−	0.994146i	−0.867709	−	0.497073i	$-0.834408\pi$
$919$		−	30.1376i		−	0.994146i	0.867709	−	0.497073i	$-0.165592\pi$
$920$	7.42011	−	2.75288i	0.244634	−	0.0907598i
$921$			4.45510i			0.146801i
$922$	−0.0680624			−0.00224152
$923$			13.4085i			0.441347i
$924$	14.4177	+	9.19301i	0.474307	+	0.302428i
$925$	10.0947	+	11.7320i	0.331912	+	0.385747i
$926$		−	5.94735i		−	0.195442i
$927$	8.41477			0.276377
$928$		−	9.64208i		−	0.316517i
$929$		−	36.9600i		−	1.21262i	−0.795229	−	0.606310i	$-0.792649\pi$
$929$		−	36.9600i		−	1.21262i	0.795229	−	0.606310i	$-0.207351\pi$
$930$	−4.09998	+	1.52110i	−0.134444	+	0.0498790i
$931$	−27.6179	+	17.4408i	−0.905142	+	0.571600i
$932$	−21.6269			−0.708412
$933$		−	12.1013i		−	0.396180i
$934$	−1.54958			−0.0507039
$935$	−5.94547	+	11.0402i	−0.194438	+	0.361054i
$936$		−	3.05943i		−	0.100001i
$937$		−	32.2067i		−	1.05215i	−0.850439	−	0.526074i	$-0.823664\pi$
$937$		−	32.2067i		−	1.05215i	0.850439	−	0.526074i	$-0.176336\pi$
$938$	−4.62660	+	1.33857i	−0.151064	+	0.0437060i
$939$	1.74964			0.0570974
$940$	12.5257	+	33.7618i	0.408544	+	1.10119i
$941$	1.21062			0.0394650			0.0197325	−	0.999805i	$-0.493719\pi$
$941$	1.21062			0.0394650			0.0197325	+	0.999805i	$0.493719\pi$
$942$	−2.58158			−0.0841123
$943$		−	48.6217i		−	1.58334i
$944$			18.8803i			0.614502i
$945$	4.75622	−	3.51830i	0.154720	−	0.114450i
$946$	−0.306079	+	0.269288i	−0.00995149	+	0.00875531i
$947$		−	27.6254i		−	0.897706i	−0.893606	−	0.448853i	$-0.851833\pi$
$947$		−	27.6254i		−	0.897706i	0.893606	−	0.448853i	$-0.148167\pi$
$948$			19.3510i			0.628492i
$949$	0.777652			0.0252436
$950$	4.00849	−	3.44906i	0.130053	−	0.111902i
$951$			9.93330i			0.322109i
$952$	−3.84584	+	1.11268i	−0.124644	+	0.0360623i
$953$	−23.1986			−0.751477			−0.375739	−	0.926726i	$-0.622611\pi$
$953$	−23.1986			−0.751477			−0.375739	+	0.926726i	$0.622611\pi$
$954$		−	1.50738i		−	0.0488032i
$955$	8.68867	+	23.4194i	0.281159	+	0.757835i
$956$		−	6.94069i		−	0.224478i
$957$	−8.04013	−	9.13860i	−0.259900	−	0.295409i
$958$	0.00668015			0.000215826
$959$	−36.7773	+	10.6405i	−1.18760	+	0.343599i
$960$	5.28376	+	14.2418i	0.170533	+	0.459653i
$961$	−43.4529			−1.40171
$962$	2.39837			0.0773265
$963$	20.2692			0.653165
$964$	26.8290			0.864105
$965$	−7.21719	−	19.4532i	−0.232329	−	0.626220i
$966$	2.27811	−	0.659106i	0.0732970	−	0.0212064i
$967$	25.4442			0.818231			0.409115	−	0.912483i	$-0.365837\pi$
$967$	25.4442			0.818231			0.409115	+	0.912483i	$0.365837\pi$
$968$	1.25387	−	9.76442i	0.0403010	−	0.313840i
$969$		−	7.88976i		−	0.253456i
$970$	2.34416	+	6.31844i	0.0752664	+	0.202873i
$971$		−	40.4827i		−	1.29915i	−0.760297	−	0.649576i	$-0.774946\pi$
$971$		−	40.4827i		−	1.29915i	0.760297	−	0.649576i	$-0.225054\pi$
$972$	1.94863			0.0625023
$973$	0.0424479	+	0.146716i	0.00136082	+	0.00470348i
$974$			6.39698i			0.204973i
$975$	−11.1482	−	12.9565i	−0.357029	−	0.414939i
$976$	49.6735			1.59001
$977$		−	3.11648i		−	0.0997050i	−0.998757	−	0.0498525i	$-0.984125\pi$
$977$		−	3.11648i		−	0.0997050i	0.998757	−	0.0498525i	$-0.0158751\pi$
$978$		−	4.07017i		−	0.130150i
$979$	10.5551	+	11.9971i	0.337341	+	0.383430i
$980$	24.2392	+	18.5138i	0.774294	+	0.591403i
$981$		−	11.6322i		−	0.371387i
$982$			0.283139i			0.00903532i
$983$	3.84387			0.122600			0.0613002	−	0.998119i	$-0.480475\pi$
$983$	3.84387			0.122600			0.0613002	+	0.998119i	$0.480475\pi$
$984$	−11.0030			−0.350764
$985$	8.44384	+	22.7595i	0.269043	+	0.725178i
$986$	1.40643			0.0447898
$987$	6.07698	+	21.0043i	0.193432	+	0.668573i
$988$			31.0839i			0.988909i
$989$		−	2.14479i		−	0.0682002i
$990$	−1.47994	−	0.796988i	−0.0470355	−	0.0253299i
$991$	−11.9706			−0.380258			−0.190129	−	0.981759i	$-0.560891\pi$
$991$	−11.9706			−0.380258			−0.190129	+	0.981759i	$0.560891\pi$
$992$		−	22.6697i		−	0.719764i
$993$	−6.45719			−0.204913
$994$	0.653700	+	2.25943i	0.0207341	+	0.0716646i
$995$	26.3830	−	9.78817i	0.836397	−	0.310306i
$996$			28.0418i			0.888537i
$997$		−	52.9913i		−	1.67825i	−0.543939	−	0.839125i	$-0.683068\pi$
$997$		−	52.9913i		−	1.67825i	0.543939	−	0.839125i	$-0.316932\pi$
$998$	1.78026			0.0563531
$999$			3.09544i			0.0979353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.a.769.21	✓	48
5.4	even	2		1155.2.k.b.769.28	yes	48
7.6	odd	2		1155.2.k.b.769.22	yes	48
11.10	odd	2	inner	1155.2.k.a.769.28	yes	48
35.34	odd	2	inner	1155.2.k.a.769.27	yes	48
55.54	odd	2		1155.2.k.b.769.21	yes	48
77.76	even	2		1155.2.k.b.769.27	yes	48
385.384	even	2	inner	1155.2.k.a.769.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.21	✓	48	1.1	even	1	trivial
1155.2.k.a.769.22	yes	48	385.384	even	2	inner
1155.2.k.a.769.27	yes	48	35.34	odd	2	inner
1155.2.k.a.769.28	yes	48	11.10	odd	2	inner
1155.2.k.b.769.21	yes	48	55.54	odd	2
1155.2.k.b.769.22	yes	48	7.6	odd	2
1155.2.k.b.769.27	yes	48	77.76	even	2
1155.2.k.b.769.28	yes	48	5.4	even	2

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.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.226652 q^{2} -1.00000 q^{3} -1.94863 q^{4} +(0.777785 + 2.09644i) q^{5} +0.226652 q^{6} +(0.735315 + 2.54152i) q^{7} +0.894963 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.226652 q^{2} -1.00000 q^{3} -1.94863 q^{4} +(0.777785 + 2.09644i) q^{5} +0.226652 q^{6} +(0.735315 + 2.54152i) q^{7} +0.894963 q^{8} +1.00000 q^{9} +(-0.176286 - 0.475161i) q^{10} +(2.49008 - 2.19077i) q^{11} +1.94863 q^{12} -3.41850i q^{13} +(-0.166660 - 0.576039i) q^{14} +(-0.777785 - 2.09644i) q^{15} +3.69441 q^{16} +1.69080i q^{17} -0.226652 q^{18} +4.66628 q^{19} +(-1.51561 - 4.08518i) q^{20} +(-0.735315 - 2.54152i) q^{21} +(-0.564382 + 0.496542i) q^{22} -3.95479i q^{23} -0.894963 q^{24} +(-3.79010 + 3.26115i) q^{25} +0.774808i q^{26} -1.00000 q^{27} +(-1.43286 - 4.95247i) q^{28} +3.67000i q^{29} +(0.176286 + 0.475161i) q^{30} +8.62861i q^{31} -2.62727 q^{32} +(-2.49008 + 2.19077i) q^{33} -0.383223i q^{34} +(-4.75622 + 3.51830i) q^{35} -1.94863 q^{36} -3.09544i q^{37} -1.05762 q^{38} +3.41850i q^{39} +(0.696089 + 1.87623i) q^{40} +12.2944 q^{41} +(0.166660 + 0.576039i) q^{42} +0.542327 q^{43} +(-4.85225 + 4.26900i) q^{44} +(0.777785 + 2.09644i) q^{45} +0.896359i q^{46} -8.26446 q^{47} -3.69441 q^{48} +(-5.91862 + 3.73763i) q^{49} +(0.859033 - 0.739146i) q^{50} -1.69080i q^{51} +6.66138i q^{52} +6.65065i q^{53} +0.226652 q^{54} +(6.52957 + 3.51636i) q^{55} +(0.658080 + 2.27457i) q^{56} -4.66628 q^{57} -0.831811i q^{58} +5.11051i q^{59} +(1.51561 + 4.08518i) q^{60} +13.4456 q^{61} -1.95569i q^{62} +(0.735315 + 2.54152i) q^{63} -6.79335 q^{64} +(7.16666 - 2.65885i) q^{65} +(0.564382 - 0.496542i) q^{66} -8.03174i q^{67} -3.29475i q^{68} +3.95479i q^{69} +(1.07800 - 0.797428i) q^{70} -3.92235 q^{71} +0.894963 q^{72} +0.227484i q^{73} +0.701586i q^{74} +(3.79010 - 3.26115i) q^{75} -9.09285 q^{76} +(7.39888 + 4.71768i) q^{77} -0.774808i q^{78} +9.93059i q^{79} +(2.87346 + 7.74511i) q^{80} +1.00000 q^{81} -2.78654 q^{82} +14.3905i q^{83} +(1.43286 + 4.95247i) q^{84} +(-3.54466 + 1.31508i) q^{85} -0.122919 q^{86} -3.67000i q^{87} +(2.22853 - 1.96066i) q^{88} +4.81796i q^{89} +(-0.176286 - 0.475161i) q^{90} +(8.68817 - 2.51367i) q^{91} +7.70641i q^{92} -8.62861i q^{93} +1.87315 q^{94} +(3.62936 + 9.78256i) q^{95} +2.62727 q^{96} -13.2975 q^{97} +(1.34147 - 0.847141i) q^{98} +(2.49008 - 2.19077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q - 48 * q^3 + 48 * q^4 + 4 * q^5 + 48 * q^9	\( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9} - 48 q^{12} - 4 q^{15} + 40 q^{16} + 18 q^{20} + 20 q^{25} - 48 q^{27} + 48 q^{36} + 20 q^{38} - 16 q^{44} + 4 q^{45} - 8 q^{47} - 40 q^{48} + 24 q^{49} + 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} - 20 q^{75} + 32 q^{77} + 46 q^{80} + 48 q^{81} + 32 q^{82} - 16 q^{86} - 68 q^{97}+O(q^{100}) \) 48 * q - 48 * q^3 + 48 * q^4 + 4 * q^5 + 48 * q^9 - 48 * q^12 - 4 * q^15 + 40 * q^16 + 18 * q^20 + 20 * q^25 - 48 * q^27 + 48 * q^36 + 20 * q^38 - 16 * q^44 + 4 * q^45 - 8 * q^47 - 40 * q^48 + 24 * q^49 + 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 - 20 * q^75 + 32 * q^77 + 46 * q^80 + 48 * q^81 + 32 * q^82 - 16 * q^86 - 68 * q^97

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