LMFDB - Embedded newform 1155.2.k.b.769.27

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			769.27
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.28

$q$-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} +(5.90005 - 0.435211i) 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} +(2.65607 - 6.92425i) 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} +(1.33726 - 0.0986412i) 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	$-0.474465\pi$
$2$	0.226652			0.160267			0.0801335	+	0.996784i	$0.474465\pi$
$3$	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	$-0.889319\pi$
$29$		−	3.67000i		−	0.681501i	0.940154	−	0.340751i	$-0.110681\pi$
$30$	−0.176286	−	0.475161i	−0.0321853	−	0.0867521i
$31$		−	8.62861i		−	1.54974i	−0.632118	−	0.774872i	$-0.717814\pi$
$31$		−	8.62861i		−	1.54974i	0.632118	−	0.774872i	$-0.282186\pi$
$32$	2.62727			0.464440
$33$	2.49008	+	2.19077i	0.433468	+	0.381365i
$34$			0.383223i			0.0657223i
$35$	5.90005	−	0.435211i	0.997290	−	0.0735640i
$36$	−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	$-0.513167\pi$
$43$	−0.542327			−0.0827040			−0.0413520	+	0.999145i	$0.513167\pi$
$44$	−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	$-0.294073\pi$
$47$	8.26446			1.20550			0.602748	+	0.797932i	$0.294073\pi$
$48$	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
$55$	2.65607	−	6.92425i	0.358144	−	0.933666i
$56$	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	$-0.892052\pi$
$59$		−	5.11051i		−	0.665332i	0.943045	−	0.332666i	$-0.107948\pi$
$60$	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
$70$	1.33726	−	0.0986412i	0.159833	−	0.0117899i
$71$	−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	$-0.811324\pi$
$79$		−	9.93059i		−	1.11728i	0.829411	−	0.558639i	$-0.188676\pi$
$80$	−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	$-0.917809\pi$
$89$		−	4.81796i		−	0.510703i	0.966848	−	0.255351i	$-0.0821912\pi$
$90$	−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	$-0.264111\pi$
$97$	13.2975			1.35015			0.675077	+	0.737748i	$0.264111\pi$
$98$	−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	$-0.636067\pi$
$103$	−8.41477			−0.829132			−0.414566	+	0.910019i	$0.636067\pi$
$104$			3.05943i			0.300002i
$105$	5.90005	−	0.435211i	0.575786	−	0.0424722i
$106$			1.50738i			0.146410i
$107$	−20.2692			−1.95950			−0.979748	−	0.200237i	$-0.935829\pi$
$107$	−20.2692			−1.95950			−0.979748	+	0.200237i	$0.935829\pi$
$108$	−1.94863			−0.187507
$109$			11.6322i			1.11416i	0.830459	+	0.557080i	$0.188078\pi$
$109$			11.6322i			1.11416i	−0.830459	+	0.557080i	$0.811922\pi$
$110$	0.602003	−	1.56939i	0.0573987	−	0.149636i
$111$		−	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	$-0.151113\pi$
$127$	20.0464			1.77883			0.889413	+	0.457104i	$0.151113\pi$
$128$	−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	$0.499221\pi$
$140$	−11.4970	+	0.848064i	−0.971675	+	0.0716745i
$141$	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	$-0.752945\pi$
$149$		−	17.1022i		−	1.40107i	0.713618	−	0.700535i	$-0.247055\pi$
$150$	−0.859033	+	0.739146i	−0.0701398	+	0.0603510i
$151$			10.1755i			0.828071i	0.910261	+	0.414035i	$0.135881\pi$
$151$			10.1755i			0.828071i	−0.910261	+	0.414035i	$0.864119\pi$
$152$	−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	$-0.349813\pi$
$157$	11.3901			0.909026			0.454513	+	0.890740i	$0.349813\pi$
$158$		−	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
$165$	2.65607	−	6.92425i	0.206775	−	0.539052i
$166$			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
$175$	−5.50136	−	12.0306i	−0.415864	−	0.909427i
$176$	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	$-0.884027\pi$
$181$		−	9.58793i		−	0.712665i	0.934359	−	0.356333i	$-0.115973\pi$
$182$	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	$-0.391614\pi$
$193$	9.27916			0.667929			0.333964	+	0.942586i	$0.391614\pi$
$194$	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	$-0.626398\pi$
$197$	−10.8563			−0.773477			−0.386739	+	0.922189i	$0.626398\pi$
$198$	0.564382	+	0.496542i	0.0401089	+	0.0352877i
$199$			12.5847i			0.892104i	0.895007	+	0.446052i	$0.147170\pi$
$199$			12.5847i			0.892104i	−0.895007	+	0.446052i	$0.852830\pi$
$200$	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
$210$	1.33726	−	0.0986412i	0.0922794	−	0.00680689i
$211$			9.40195i			0.647257i	0.946184	+	0.323629i	$0.104903\pi$
$211$			9.40195i			0.647257i	−0.946184	+	0.323629i	$0.895097\pi$
$212$		−	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
$220$	−5.17569	+	13.4928i	−0.348945	+	0.909685i
$221$	5.78000			0.388805
$222$		−	0.701586i		−	0.0470874i
$223$	−23.7661			−1.59149			−0.795747	−	0.605629i	$-0.792922\pi$
$223$	−23.7661			−1.59149			−0.795747	+	0.605629i	$0.792922\pi$
$224$	−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	$-0.837613\pi$
$229$		−	14.7790i		−	0.976622i	0.872670	−	0.488311i	$-0.162387\pi$
$230$	−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	$-0.618433\pi$
$233$	−11.0985			−0.727088			−0.363544	+	0.931577i	$0.618433\pi$
$234$		−	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	$-0.963250\pi$
$239$		−	3.56183i		−	0.230396i	0.993343	−	0.115198i	$-0.0367502\pi$
$240$	−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
$245$	−3.23230	+	15.3151i	−0.206504	+	0.978446i
$246$	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	$0.195841\pi$
$251$			18.2881i			1.15433i	−0.816627	+	0.577166i	$0.804159\pi$
$252$	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	$-0.586779\pi$
$257$	−8.63315			−0.538521			−0.269261	+	0.963067i	$0.586779\pi$
$258$	−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	$-0.627021\pi$
$263$	−12.6022			−0.777086			−0.388543	+	0.921431i	$0.627021\pi$
$264$	−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	$-0.934333\pi$
$269$		−	6.71917i		−	0.409675i	0.978796	−	0.204837i	$-0.0656666\pi$
$270$	−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
$275$	−16.5821	−	0.182707i	−0.999939	−	0.0110177i
$276$			7.70641i			0.463871i
$277$	−11.1171			−0.667960			−0.333980	−	0.942580i	$-0.608392\pi$
$277$	−11.1171			−0.667960			−0.333980	+	0.942580i	$0.608392\pi$
$278$	0.0130840			0.000784729
$279$		−	8.62861i		−	0.516581i
$280$	−5.28033	+	0.389498i	−0.315560	+	0.0232769i
$281$		−	0.161176i		−	0.00961497i	−0.999988	−	0.00480749i	$-0.998470\pi$
$281$		−	0.161176i		−	0.00961497i	0.999988	−	0.00480749i	$-0.00153028\pi$
$282$	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	$-0.888522\pi$
$311$		−	12.1013i		−	0.686204i	0.939298	−	0.343102i	$-0.111478\pi$
$312$			3.05943i			0.173206i
$313$	1.74964			0.0988956			0.0494478	−	0.998777i	$-0.484254\pi$
$313$	1.74964			0.0988956			0.0494478	+	0.998777i	$0.484254\pi$
$314$	2.58158			0.145687
$315$	5.90005	−	0.435211i	0.332430	−	0.0245213i
$316$			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
$330$	0.602003	−	1.56939i	0.0331392	−	0.0863923i
$331$	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	$-0.760645\pi$
$337$	−26.8150			−1.46071			−0.730354	+	0.683069i	$0.760645\pi$
$338$	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	$-0.637215\pi$
$347$	−15.5673			−0.835696			−0.417848	+	0.908517i	$0.637215\pi$
$348$			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	$0.495525\pi$
$350$	−1.24689	−	2.72675i	−0.0666492	−	0.145751i
$351$		−	3.41850i		−	0.182466i
$352$	6.54213	+	5.75575i	0.348696	+	0.306783i
$353$	30.7903			1.63880			0.819402	−	0.573219i	$-0.194306\pi$
$353$	30.7903			1.63880			0.819402	+	0.573219i	$0.194306\pi$
$354$		−	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	$0.259689\pi$
$359$			27.5986i			1.45660i	−0.685259	+	0.728300i	$0.740311\pi$
$360$	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	$-0.275153\pi$
$367$	24.8693			1.29817			0.649083	+	0.760718i	$0.275153\pi$
$368$		−	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	$-0.701053\pi$
$373$	−22.8073			−1.18092			−0.590459	+	0.807067i	$0.701053\pi$
$374$	−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	$-0.231475\pi$
$383$	29.2397			1.49408			0.747039	+	0.664780i	$0.231475\pi$
$384$	−6.79427			−0.346719
$385$	15.6451	+	11.8420i	0.797346	+	0.603522i
$386$	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	$-0.770725\pi$
$397$	−29.9517			−1.50323			−0.751616	+	0.659601i	$0.770725\pi$
$398$			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	$0.0814445\pi$
$419$			10.3609i			0.506165i	−0.967445	+	0.253083i	$0.918556\pi$
$420$	−11.4970	+	0.848064i	−0.560997	+	0.0413813i
$421$	−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	$0.207316\pi$
$431$			25.1710i			1.21244i	−0.795296	+	0.606222i	$0.792684\pi$
$432$	3.69441			0.177748
$433$	−14.4242			−0.693182			−0.346591	−	0.938016i	$-0.612661\pi$
$433$	−14.4242			−0.693182			−0.346591	+	0.938016i	$0.612661\pi$
$434$	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	$0.697592\pi$
$440$	−2.37709	+	6.19695i	−0.113323	+	0.295428i
$441$	−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
$455$	−1.48777	−	20.1693i	−0.0697476	−	0.945551i
$456$	−4.17615			−0.195566
$457$	−22.6707			−1.06049			−0.530246	−	0.847844i	$-0.677901\pi$
$457$	−22.6707			−1.06049			−0.530246	+	0.847844i	$0.677901\pi$
$458$		−	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	$-0.550564\pi$
$467$	−6.83684			−0.316371			−0.158186	+	0.987409i	$0.550564\pi$
$468$			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
$490$	−0.732606	+	3.47119i	−0.0330958	+	0.156812i
$491$			1.24922i			0.0563767i	0.999603	+	0.0281883i	$0.00897382\pi$
$491$			1.24922i			0.0563767i	−0.999603	+	0.0281883i	$0.991026\pi$
$492$	−23.9572			−1.08007
$493$	6.20524			0.279470
$494$		−	3.61547i		−	0.162668i
$495$	2.65607	−	6.92425i	0.119381	−	0.311222i
$496$		−	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	$-0.853441\pi$
$509$		−	20.0492i		−	0.888663i	0.895862	−	0.444332i	$-0.146559\pi$
$510$	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	$-0.927524\pi$
$521$		−	10.3047i		−	0.451456i	0.974190	−	0.225728i	$-0.0724760\pi$
$522$		−	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
$525$	−5.50136	−	12.0306i	−0.240099	−	0.525058i
$526$	−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	$0.328121\pi$
$541$			39.9003i			1.71545i	−0.514112	+	0.857723i	$0.671879\pi$
$542$	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	$-0.168525\pi$
$547$	40.3720			1.72618			0.863091	+	0.505049i	$0.168525\pi$
$548$		−	28.1979i		−	1.20455i
$549$	13.4456			0.573843
$550$	−3.75836	−	0.0414109i	−0.160257	−	0.00176577i
$551$		−	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	$-0.351140\pi$
$557$	21.2784			0.901595			0.450797	+	0.892626i	$0.351140\pi$
$558$		−	1.95569i		−	0.0827909i
$559$			1.85394i			0.0784134i
$560$	21.7972	−	1.60785i	0.921101	−	0.0679440i
$561$	−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	$0.0345583\pi$
$569$			5.16934i			0.216710i	−0.994112	+	0.108355i	$0.965442\pi$
$570$	−0.822600	−	2.21723i	−0.0344549	−	0.0928697i
$571$		−	20.0448i		−	0.838848i	−0.907790	−	0.419424i	$-0.862232\pi$
$571$		−	20.0448i		−	0.838848i	0.907790	−	0.419424i	$-0.137768\pi$
$572$	−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	$-0.656707\pi$
$577$	−22.7074			−0.945323			−0.472661	+	0.881244i	$0.656707\pi$
$578$	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	$-0.528283\pi$
$587$	−4.29985			−0.177474			−0.0887370	+	0.996055i	$0.528283\pi$
$588$	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
$595$	0.735856	+	9.97582i	0.0301671	+	0.408969i
$596$			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
$605$	21.7833	−	11.4231i	0.885617	−	0.464416i
$606$	−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	$-0.0947753\pi$
$613$	47.3389			1.91200			0.956000	+	0.293366i	$0.0947753\pi$
$614$		−	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	$-0.717606\pi$
$619$		−	38.5778i		−	1.55057i	0.631611	−	0.775286i	$-0.282394\pi$
$620$	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
$630$	1.33726	−	0.0986412i	0.0532776	−	0.00392996i
$631$	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	$-0.580457\pi$
$643$	−12.6828			−0.500162			−0.250081	+	0.968225i	$0.580457\pi$
$644$	−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	$-0.386457\pi$
$647$	17.7641			0.698379			0.349190	+	0.937052i	$0.386457\pi$
$648$	−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	$0.128692\pi$
$659$			20.1965i			0.786745i	−0.919379	+	0.393372i	$0.871308\pi$
$660$	−5.17569	+	13.4928i	−0.201464	+	0.525207i
$661$			19.9142i			0.774572i	0.921960	+	0.387286i	$0.126587\pi$
$661$			19.9142i			0.774572i	−0.921960	+	0.387286i	$0.873413\pi$
$662$	1.46353			0.0568818
$663$	5.78000			0.224477
$664$		−	12.8790i		−	0.499801i
$665$	27.5313	−	2.03081i	1.06762	−	0.0787516i
$666$		−	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	$-0.567614\pi$
$673$	−10.9385			−0.421647			−0.210823	+	0.977524i	$0.567614\pi$
$674$	−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	$-0.873526\pi$
$691$		−	20.3438i		−	0.773914i	0.922098	−	0.386957i	$-0.126474\pi$
$692$		−	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
$700$	10.7201	+	23.4432i	0.405182	+	0.886068i
$701$			1.03498i			0.0390908i	0.999809	+	0.0195454i	$0.00622188\pi$
$701$			1.03498i			0.0390908i	−0.999809	+	0.0195454i	$0.993778\pi$
$702$		−	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
$715$	−23.6705	−	9.07976i	−0.885228	−	0.339564i
$716$	11.3732			0.425036
$717$		−	3.56183i		−	0.133019i
$718$			6.25527i			0.233445i
$719$			21.8889i			0.816317i	0.912911	+	0.408159i	$0.133829\pi$
$719$			21.8889i			0.816317i	−0.912911	+	0.408159i	$0.866171\pi$
$720$	−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	$-0.335009\pi$
$727$	26.7167			0.990867			0.495433	+	0.868646i	$0.335009\pi$
$728$	−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
$735$	−3.23230	+	15.3151i	−0.119225	+	0.564906i
$736$		−	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	$-0.864943\pi$
$739$		−	22.3825i		−	0.823355i	0.911330	−	0.411678i	$-0.135057\pi$
$740$	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	$-0.704172\pi$
$743$	−32.6191			−1.19668			−0.598339	+	0.801243i	$0.704172\pi$
$744$			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	$0.533671\pi$
$770$	3.54598	+	2.68400i	0.127788	+	0.0967246i
$771$	−8.63315			−0.310915
$772$	−18.0816			−0.650772
$773$	−31.1077			−1.11887			−0.559434	−	0.828875i	$-0.688981\pi$
$773$	−31.1077			−1.11887			−0.559434	+	0.828875i	$0.688981\pi$
$774$	−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	$-0.439772\pi$
$797$	10.6197			0.376170			0.188085	+	0.982153i	$0.439772\pi$
$798$	−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
$805$	−1.72116	−	23.3334i	−0.0606631	−	0.822395i
$806$	−6.68552			−0.235487
$807$		−	6.71917i		−	0.236526i
$808$	0.109114			0.00383863
$809$			9.04700i			0.318076i	0.987273	+	0.159038i	$0.0508392\pi$
$809$			9.04700i			0.318076i	−0.987273	+	0.159038i	$0.949161\pi$
$810$	−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	$-0.749267\pi$
$821$		−	40.6149i		−	1.41747i	0.705476	−	0.708734i	$-0.250733\pi$
$822$			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
$825$	−16.5821	−	0.182707i	−0.577315	−	0.00636104i
$826$	2.94385	+	0.851719i	0.102430	+	0.0296351i
$827$	−11.5633			−0.402094			−0.201047	−	0.979582i	$-0.564434\pi$
$827$	−11.5633			−0.402094			−0.201047	+	0.979582i	$0.564434\pi$
$828$			7.70641i			0.267816i
$829$			30.0885i			1.04502i	0.852635	+	0.522508i	$0.175003\pi$
$829$			30.0885i			1.04502i	−0.852635	+	0.522508i	$0.824997\pi$
$830$	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	$0.284286\pi$
$839$			45.1298i			1.55805i	−0.626990	+	0.779027i	$0.715714\pi$
$840$	−5.28033	+	0.389498i	−0.182189	+	0.0134389i
$841$	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	$0.0830127\pi$
$859$			15.1143i			0.515692i	−0.966186	+	0.257846i	$0.916987\pi$
$860$	−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
$875$	−20.9425	+	20.8905i	−0.707986	+	0.706227i
$876$		−	0.443281i		−	0.0149771i
$877$	30.5761			1.03248			0.516241	−	0.856443i	$-0.327331\pi$
$877$	30.5761			1.03248			0.516241	+	0.856443i	$0.327331\pi$
$878$	−5.52435			−0.186438
$879$			23.6761i			0.798575i
$880$	9.81262	−	25.5811i	0.330783	−	0.862337i
$881$			49.0932i			1.65399i	0.562208	+	0.826996i	$0.309952\pi$
$881$			49.0932i			1.65399i	−0.562208	+	0.826996i	$0.690048\pi$
$882$	−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
$910$	−0.337205	−	4.57141i	−0.0111782	−	0.151541i
$911$	−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	$0.165592\pi$
$919$			30.1376i			0.994146i	−0.867709	+	0.497073i	$0.834408\pi$
$920$	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	$0.207351\pi$
$929$			36.9600i			1.21262i	−0.795229	+	0.606310i	$0.792649\pi$
$930$	−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
$935$	11.7076	+	4.49089i	0.382878	+	0.146868i
$936$			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
$945$	5.90005	−	0.435211i	0.191929	−	0.0141574i
$946$	−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	$-0.377389\pi$
$953$	23.1986			0.751477			0.375739	+	0.926726i	$0.377389\pi$
$954$			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	$-0.634163\pi$
$967$	−25.4442			−0.818231			−0.409115	+	0.912483i	$0.634163\pi$
$968$	−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	$0.225054\pi$
$971$			40.4827i			1.29915i	−0.760297	+	0.649576i	$0.774946\pi$
$972$	−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
$980$	6.29855	−	29.8434i	0.201200	−	0.953314i
$981$			11.6322i			0.371387i
$982$			0.283139i			0.00903532i
$983$	−3.84387			−0.122600			−0.0613002	−	0.998119i	$-0.519525\pi$
$983$	−3.84387			−0.122600			−0.0613002	+	0.998119i	$0.519525\pi$
$984$	−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
$990$	0.602003	−	1.56939i	0.0191329	−	0.0498786i
$991$	−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.b.769.27	yes	48
5.4	even	2		1155.2.k.a.769.22	yes	48
7.6	odd	2		1155.2.k.a.769.28	yes	48
11.10	odd	2	inner	1155.2.k.b.769.22	yes	48
35.34	odd	2	inner	1155.2.k.b.769.21	yes	48
55.54	odd	2		1155.2.k.a.769.27	yes	48
77.76	even	2		1155.2.k.a.769.21	✓	48
385.384	even	2	inner	1155.2.k.b.769.28	yes	48

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

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} +(5.90005 - 0.435211i) 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} +(2.65607 - 6.92425i) 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} +(1.33726 - 0.0986412i) 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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