LMFDB - Embedded newform 1155.2.l.e.1121.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.20
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.e.1121.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.164753 q^{2} +(1.34733 + 1.08845i) q^{3} -1.97286 q^{4} +1.00000i q^{5} +(0.221976 + 0.179324i) q^{6} -1.00000i q^{7} -0.654539 q^{8} +(0.630571 + 2.93298i) q^{9} +O(q^{10})$	\(q+0.164753 q^{2} +(1.34733 + 1.08845i) q^{3} -1.97286 q^{4} +1.00000i q^{5} +(0.221976 + 0.179324i) q^{6} -1.00000i q^{7} -0.654539 q^{8} +(0.630571 + 2.93298i) q^{9} +0.164753i q^{10} +(3.08208 + 1.22506i) q^{11} +(-2.65808 - 2.14735i) q^{12} -1.60623i q^{13} -0.164753i q^{14} +(-1.08845 + 1.34733i) q^{15} +3.83788 q^{16} -5.07000 q^{17} +(0.103888 + 0.483217i) q^{18} +5.56494i q^{19} -1.97286i q^{20} +(1.08845 - 1.34733i) q^{21} +(0.507781 + 0.201832i) q^{22} +6.91443i q^{23} +(-0.881877 - 0.712430i) q^{24} -1.00000 q^{25} -0.264630i q^{26} +(-2.34281 + 4.63802i) q^{27} +1.97286i q^{28} +9.80529 q^{29} +(-0.179324 + 0.221976i) q^{30} -5.21936 q^{31} +1.94138 q^{32} +(2.81915 + 5.00523i) q^{33} -0.835296 q^{34} +1.00000 q^{35} +(-1.24403 - 5.78635i) q^{36} -11.6040 q^{37} +0.916840i q^{38} +(1.74829 - 2.16411i) q^{39} -0.654539i q^{40} -3.68468 q^{41} +(0.179324 - 0.221976i) q^{42} +0.866776i q^{43} +(-6.08050 - 2.41687i) q^{44} +(-2.93298 + 0.630571i) q^{45} +1.13917i q^{46} -2.37172i q^{47} +(5.17087 + 4.17732i) q^{48} -1.00000 q^{49} -0.164753 q^{50} +(-6.83094 - 5.51842i) q^{51} +3.16885i q^{52} +6.59669i q^{53} +(-0.385984 + 0.764127i) q^{54} +(-1.22506 + 3.08208i) q^{55} +0.654539i q^{56} +(-6.05714 + 7.49779i) q^{57} +1.61545 q^{58} +0.691458i q^{59} +(2.14735 - 2.65808i) q^{60} +9.81153i q^{61} -0.859904 q^{62} +(2.93298 - 0.630571i) q^{63} -7.35590 q^{64} +1.60623 q^{65} +(0.464463 + 0.824626i) q^{66} +5.99357 q^{67} +10.0024 q^{68} +(-7.52599 + 9.31599i) q^{69} +0.164753 q^{70} +7.38360i q^{71} +(-0.412733 - 1.91975i) q^{72} -16.3251i q^{73} -1.91179 q^{74} +(-1.34733 - 1.08845i) q^{75} -10.9788i q^{76} +(1.22506 - 3.08208i) q^{77} +(0.288036 - 0.356543i) q^{78} +8.79401i q^{79} +3.83788i q^{80} +(-8.20476 + 3.69890i) q^{81} -0.607061 q^{82} -2.46408 q^{83} +(-2.14735 + 2.65808i) q^{84} -5.07000i q^{85} +0.142804i q^{86} +(13.2109 + 10.6725i) q^{87} +(-2.01734 - 0.801850i) q^{88} -7.69808i q^{89} +(-0.483217 + 0.103888i) q^{90} -1.60623 q^{91} -13.6412i q^{92} +(-7.03218 - 5.68099i) q^{93} -0.390748i q^{94} -5.56494 q^{95} +(2.61567 + 2.11309i) q^{96} +1.23311 q^{97} -0.164753 q^{98} +(-1.64961 + 9.81218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.164753			0.116498			0.0582489	−	0.998302i	$-0.481448\pi$
$2$	0.164753			0.116498			0.0582489	+	0.998302i	$0.481448\pi$
$3$	1.34733	+	1.08845i	0.777879	+	0.628415i
$3$	1.34733	+	1.08845i	0.777879	+	0.628415i
$4$	−1.97286			−0.986428
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.221976	+	0.179324i	0.0906211	+	0.0732089i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.654539			−0.231415
$9$	0.630571	+	2.93298i	0.210190	+	0.977661i
$10$			0.164753i			0.0520994i
$11$	3.08208	+	1.22506i	0.929283	+	0.369370i
$11$	3.08208	+	1.22506i	0.929283	+	0.369370i
$12$	−2.65808	−	2.14735i	−0.767321	−	0.619886i
$13$		−	1.60623i		−	0.445487i	−0.974877	−	0.222743i	$-0.928499\pi$
$13$		−	1.60623i		−	0.445487i	0.974877	−	0.222743i	$-0.0715012\pi$
$14$		−	0.164753i		−	0.0440320i
$15$	−1.08845	+	1.34733i	−0.281036	+	0.347878i
$16$	3.83788			0.959469
$17$	−5.07000			−1.22966			−0.614828	−	0.788662i	$-0.710774\pi$
$17$	−5.07000			−1.22966			−0.614828	+	0.788662i	$0.710774\pi$
$18$	0.103888	+	0.483217i	0.0244867	+	0.113895i
$19$			5.56494i			1.27669i	0.769752	+	0.638343i	$0.220380\pi$
$19$			5.56494i			1.27669i	−0.769752	+	0.638343i	$0.779620\pi$
$20$		−	1.97286i		−	0.441144i
$21$	1.08845	−	1.34733i	0.237518	−	0.294010i
$22$	0.507781	+	0.201832i	0.108259	+	0.0430308i
$23$			6.91443i			1.44176i	0.693060	+	0.720880i	$0.256262\pi$
$23$			6.91443i			1.44176i	−0.693060	+	0.720880i	$0.743738\pi$
$24$	−0.881877	−	0.712430i	−0.180012	−	0.145424i
$25$	−1.00000			−0.200000
$26$		−	0.264630i		−	0.0518982i
$27$	−2.34281	+	4.63802i	−0.450874	+	0.892588i
$28$			1.97286i			0.372835i
$29$	9.80529			1.82080			0.910398	−	0.413733i	$-0.135775\pi$
$29$	9.80529			1.82080			0.910398	+	0.413733i	$0.135775\pi$
$30$	−0.179324	+	0.221976i	−0.0327400	+	0.0405270i
$31$	−5.21936			−0.937425			−0.468712	−	0.883351i	$-0.655282\pi$
$31$	−5.21936			−0.937425			−0.468712	+	0.883351i	$0.655282\pi$
$32$	1.94138			0.343191
$33$	2.81915	+	5.00523i	0.490752	+	0.871300i
$34$	−0.835296			−0.143252
$35$	1.00000			0.169031
$36$	−1.24403	−	5.78635i	−0.207338	−	0.964392i
$37$	−11.6040			−1.90769			−0.953844	−	0.300303i	$-0.902912\pi$
$37$	−11.6040			−1.90769			−0.953844	+	0.300303i	$0.902912\pi$
$38$			0.916840i			0.148731i
$39$	1.74829	−	2.16411i	0.279950	−	0.346535i
$40$		−	0.654539i		−	0.103492i
$41$	−3.68468			−0.575450			−0.287725	−	0.957713i	$-0.592899\pi$
$41$	−3.68468			−0.575450			−0.287725	+	0.957713i	$0.592899\pi$
$42$	0.179324	−	0.221976i	0.0276704	−	0.0342516i
$43$			0.866776i			0.132182i	0.997814	+	0.0660910i	$0.0210528\pi$
$43$			0.866776i			0.132182i	−0.997814	+	0.0660910i	$0.978947\pi$
$44$	−6.08050	−	2.41687i	−0.916671	−	0.364357i
$45$	−2.93298	+	0.630571i	−0.437223	+	0.0939999i
$46$			1.13917i			0.167962i
$47$		−	2.37172i		−	0.345951i	−0.984926	−	0.172976i	$-0.944662\pi$
$47$		−	2.37172i		−	0.345951i	0.984926	−	0.172976i	$-0.0553382\pi$
$48$	5.17087	+	4.17732i	0.746350	+	0.602944i
$49$	−1.00000			−0.142857
$50$	−0.164753			−0.0232996
$51$	−6.83094	−	5.51842i	−0.956523	−	0.772733i
$52$			3.16885i			0.439441i
$53$			6.59669i			0.906125i	0.891479	+	0.453063i	$0.149669\pi$
$53$			6.59669i			0.906125i	−0.891479	+	0.453063i	$0.850331\pi$
$54$	−0.385984	+	0.764127i	−0.0525258	+	0.103985i
$55$	−1.22506	+	3.08208i	−0.165187	+	0.415588i
$56$			0.654539i			0.0874665i
$57$	−6.05714	+	7.49779i	−0.802288	+	0.993106i
$58$	1.61545			0.212119
$59$			0.691458i			0.0900202i	0.998987	+	0.0450101i	$0.0143320\pi$
$59$			0.691458i			0.0900202i	−0.998987	+	0.0450101i	$0.985668\pi$
$60$	2.14735	−	2.65808i	0.277221	−	0.343157i
$61$			9.81153i			1.25624i	0.778118	+	0.628119i	$0.216175\pi$
$61$			9.81153i			1.25624i	−0.778118	+	0.628119i	$0.783825\pi$
$62$	−0.859904			−0.109208
$63$	2.93298	−	0.630571i	0.369521	−	0.0794444i
$64$	−7.35590			−0.919488
$65$	1.60623			0.199228
$66$	0.464463	+	0.824626i	0.0571715	+	0.101504i
$67$	5.99357			0.732232			0.366116	−	0.930569i	$-0.380687\pi$
$67$	5.99357			0.732232			0.366116	+	0.930569i	$0.380687\pi$
$68$	10.0024			1.21297
$69$	−7.52599	+	9.31599i	−0.906022	+	1.12151i
$70$	0.164753			0.0196917
$71$			7.38360i			0.876272i	0.898909	+	0.438136i	$0.144361\pi$
$71$			7.38360i			0.876272i	−0.898909	+	0.438136i	$0.855639\pi$
$72$	−0.412733	−	1.91975i	−0.0486411	−	0.226245i
$73$		−	16.3251i		−	1.91071i	−0.295460	−	0.955355i	$-0.595473\pi$
$73$		−	16.3251i		−	1.91071i	0.295460	−	0.955355i	$-0.404527\pi$
$74$	−1.91179			−0.222241
$75$	−1.34733	−	1.08845i	−0.155576	−	0.125683i
$76$		−	10.9788i		−	1.25936i
$77$	1.22506	−	3.08208i	0.139609	−	0.351236i
$78$	0.288036	−	0.356543i	0.0326136	−	0.0403705i
$79$			8.79401i			0.989403i	0.869063	+	0.494701i	$0.164723\pi$
$79$			8.79401i			0.989403i	−0.869063	+	0.494701i	$0.835277\pi$
$80$			3.83788i			0.429088i
$81$	−8.20476	+	3.69890i	−0.911640	+	0.410989i
$82$	−0.607061			−0.0670386
$83$	−2.46408			−0.270468			−0.135234	−	0.990814i	$-0.543179\pi$
$83$	−2.46408			−0.270468			−0.135234	+	0.990814i	$0.543179\pi$
$84$	−2.14735	+	2.65808i	−0.234295	+	0.290020i
$85$		−	5.07000i		−	0.549919i
$86$			0.142804i			0.0153989i
$87$	13.2109	+	10.6725i	1.41636	+	1.14422i
$88$	−2.01734	−	0.801850i	−0.215049	−	0.0854775i
$89$		−	7.69808i		−	0.815994i	−0.912983	−	0.407997i	$-0.866227\pi$
$89$		−	7.69808i		−	0.815994i	0.912983	−	0.407997i	$-0.133773\pi$
$90$	−0.483217	+	0.103888i	−0.0509355	+	0.0109508i
$91$	−1.60623			−0.168378
$92$		−	13.6412i		−	1.42219i
$93$	−7.03218	−	5.68099i	−0.729203	−	0.589091i
$94$		−	0.390748i		−	0.0403026i
$95$	−5.56494			−0.570951
$96$	2.61567	+	2.11309i	0.266961	+	0.215666i
$97$	1.23311			0.125203			0.0626017	−	0.998039i	$-0.480060\pi$
$97$	1.23311			0.125203			0.0626017	+	0.998039i	$0.480060\pi$
$98$	−0.164753			−0.0166425
$99$	−1.64961	+	9.81218i	−0.165792	+	0.986161i
$100$	1.97286			0.197286
$101$	12.7212			1.26581			0.632904	−	0.774230i	$-0.281863\pi$
$101$	12.7212			1.26581			0.632904	+	0.774230i	$0.281863\pi$
$102$	−1.12542	−	0.909175i	−0.111433	−	0.0900217i
$103$	18.5748			1.83023			0.915117	−	0.403188i	$-0.132098\pi$
$103$	18.5748			1.83023			0.915117	+	0.403188i	$0.132098\pi$
$104$			1.05134i			0.103092i
$105$	1.34733	+	1.08845i	0.131485	+	0.106221i
$106$			1.08682i			0.105562i
$107$	−4.91310			−0.474967			−0.237484	−	0.971392i	$-0.576323\pi$
$107$	−4.91310			−0.474967			−0.237484	+	0.971392i	$0.576323\pi$
$108$	4.62202	−	9.15015i	0.444755	−	0.880474i
$109$		−	16.4406i		−	1.57473i	−0.616489	−	0.787363i	$-0.711446\pi$
$109$		−	16.4406i		−	1.57473i	0.616489	−	0.787363i	$-0.288554\pi$
$110$	−0.201832	+	0.507781i	−0.0192439	+	0.0484151i
$111$	−15.6344	−	12.6303i	−1.48395	−	1.19882i
$112$		−	3.83788i		−	0.362645i
$113$			18.6923i			1.75843i	0.476429	+	0.879213i	$0.341931\pi$
$113$			18.6923i			1.75843i	−0.476429	+	0.879213i	$0.658069\pi$
$114$	−0.997930	+	1.23528i	−0.0934648	+	0.115695i
$115$	−6.91443			−0.644774
$116$	−19.3444			−1.79609
$117$	4.71103	−	1.01284i	0.435535	−	0.0936370i
$118$			0.113920i			0.0104872i
$119$			5.07000i			0.464766i
$120$	0.712430	−	0.881877i	0.0650357	−	0.0805040i
$121$	7.99845	+	7.55147i	0.727132	+	0.686498i
$122$			1.61648i			0.146349i
$123$	−4.96446	−	4.01057i	−0.447630	−	0.361621i
$124$	10.2970			0.924702
$125$		−	1.00000i		−	0.0894427i
$126$	0.483217	−	0.103888i	0.0430484	−	0.00925510i
$127$			2.71890i			0.241263i	0.992697	+	0.120632i	$0.0384920\pi$
$127$			2.71890i			0.241263i	−0.992697	+	0.120632i	$0.961508\pi$
$128$	−5.09466			−0.450309
$129$	−0.943439	+	1.16783i	−0.0830651	+	0.102822i
$130$	0.264630			0.0232096
$131$	10.7410			0.938446			0.469223	−	0.883080i	$-0.344534\pi$
$131$	10.7410			0.938446			0.469223	+	0.883080i	$0.344534\pi$
$132$	−5.56179	−	9.87461i	−0.484091	−	0.859474i
$133$	5.56494			0.482542
$134$	0.987458			0.0853034
$135$	−4.63802	−	2.34281i	−0.399177	−	0.201637i
$136$	3.31851			0.284560
$137$		−	13.6590i		−	1.16697i	−0.812124	−	0.583485i	$-0.801689\pi$
$137$		−	13.6590i		−	1.16697i	0.812124	−	0.583485i	$-0.198311\pi$
$138$	−1.23993	+	1.53484i	−0.105550	+	0.130654i
$139$		−	11.3198i		−	0.960135i	−0.877232	−	0.480067i	$-0.840612\pi$
$139$		−	11.3198i		−	0.960135i	0.877232	−	0.480067i	$-0.159388\pi$
$140$	−1.97286			−0.166737
$141$	2.58149	−	3.19548i	0.217401	−	0.269108i
$142$			1.21647i			0.102084i
$143$	1.96772	−	4.95052i	0.164549	−	0.413983i
$144$	2.42005	+	11.2564i	0.201671	+	0.938035i
$145$			9.80529i			0.814285i
$146$		−	2.68961i		−	0.222594i
$147$	−1.34733	−	1.08845i	−0.111126	−	0.0897735i
$148$	22.8931			1.88180
$149$	−4.63763			−0.379929			−0.189965	−	0.981791i	$-0.560837\pi$
$149$	−4.63763			−0.379929			−0.189965	+	0.981791i	$0.560837\pi$
$150$	−0.221976	−	0.179324i	−0.0181242	−	0.0146418i
$151$		−	3.52407i		−	0.286784i	−0.989666	−	0.143392i	$-0.954199\pi$
$151$		−	3.52407i		−	0.286784i	0.989666	−	0.143392i	$-0.0458010\pi$
$152$		−	3.64247i		−	0.295444i
$153$	−3.19699	−	14.8702i	−0.258461	−	1.20219i
$154$	0.201832	−	0.507781i	0.0162641	−	0.0409182i
$155$		−	5.21936i		−	0.419229i
$156$	−3.44913	+	4.26948i	−0.276151	+	0.341832i
$157$	−3.46009			−0.276145			−0.138073	−	0.990422i	$-0.544091\pi$
$157$	−3.46009			−0.276145			−0.138073	+	0.990422i	$0.544091\pi$
$158$			1.44884i			0.115263i
$159$	−7.18014	+	8.88789i	−0.569422	+	0.704855i
$160$			1.94138i			0.153479i
$161$	6.91443			0.544934
$162$	−1.35176	+	0.609405i	−0.106204	+	0.0478793i
$163$	15.3341			1.20106			0.600530	−	0.799602i	$-0.294956\pi$
$163$	15.3341			1.20106			0.600530	+	0.799602i	$0.294956\pi$
$164$	7.26934			0.567640
$165$	−5.00523	+	2.81915i	−0.389657	+	0.219471i
$166$	−0.405964			−0.0315089
$167$	−10.8563			−0.840086			−0.420043	−	0.907504i	$-0.637985\pi$
$167$	−10.8563			−0.840086			−0.420043	+	0.907504i	$0.637985\pi$
$168$	−0.712430	+	0.881877i	−0.0549652	+	0.0680383i
$169$	10.4200			0.801541
$170$		−	0.835296i		−	0.0640643i
$171$	−16.3219	+	3.50909i	−1.24816	+	0.268347i
$172$		−	1.71002i		−	0.130388i
$173$	14.4202			1.09635			0.548175	−	0.836364i	$-0.315323\pi$
$173$	14.4202			1.09635			0.548175	+	0.836364i	$0.315323\pi$
$174$	2.17653	+	1.75833i	0.165003	+	0.133299i
$175$			1.00000i			0.0755929i
$176$	11.8286	+	4.70163i	0.891618	+	0.354399i
$177$	−0.752615	+	0.931619i	−0.0565700	+	0.0700248i
$178$		−	1.26828i		−	0.0950615i
$179$		−	1.78301i		−	0.133268i	−0.997777	−	0.0666342i	$-0.978774\pi$
$179$		−	1.78301i		−	0.133268i	0.997777	−	0.0666342i	$-0.0212261\pi$
$180$	5.78635	−	1.24403i	0.431289	−	0.0927242i
$181$	13.6953			1.01796			0.508982	−	0.860777i	$-0.330022\pi$
$181$	13.6953			1.01796			0.508982	+	0.860777i	$0.330022\pi$
$182$	−0.264630			−0.0196157
$183$	−10.6793	+	13.2193i	−0.789438	+	0.977200i
$184$		−	4.52577i		−	0.333644i
$185$		−	11.6040i		−	0.853144i
$186$	−1.15857	−	0.935959i	−0.0849505	−	0.0686279i
$187$	−15.6261	−	6.21106i	−1.14270	−	0.454197i
$188$			4.67907i			0.341256i
$189$	4.63802	+	2.34281i	0.337366	+	0.170414i
$190$	−0.916840			−0.0665145
$191$			12.0931i			0.875029i	0.899211	+	0.437515i	$0.144141\pi$
$191$			12.0931i			0.875029i	−0.899211	+	0.437515i	$0.855859\pi$
$192$	−9.91080	−	8.00650i	−0.715250	−	0.577820i
$193$			20.8719i			1.50239i	0.660079	+	0.751196i	$0.270523\pi$
$193$			20.8719i			1.50239i	−0.660079	+	0.751196i	$0.729477\pi$
$194$	0.203159			0.0145859
$195$	2.16411	+	1.74829i	0.154975	+	0.125198i
$196$	1.97286			0.140918
$197$	25.5943			1.82352			0.911758	−	0.410728i	$-0.134726\pi$
$197$	25.5943			1.82352			0.911758	+	0.410728i	$0.134726\pi$
$198$	−0.271778	+	1.61658i	−0.0193144	+	0.114886i
$199$	10.9858			0.778766			0.389383	−	0.921076i	$-0.372688\pi$
$199$	10.9858			0.778766			0.389383	+	0.921076i	$0.372688\pi$
$200$	0.654539			0.0462829
$201$	8.07529	+	6.52368i	0.569587	+	0.460145i
$202$	2.09585			0.147464
$203$		−	9.80529i		−	0.688197i
$204$	13.4765	+	10.8871i	0.943541	+	0.762246i
$205$		−	3.68468i		−	0.257349i
$206$	3.06026			0.213218
$207$	−20.2799	+	4.36004i	−1.40955	+	0.303044i
$208$		−	6.16450i		−	0.427431i
$209$	−6.81739	+	17.1516i	−0.471569	+	1.18640i
$210$	0.221976	+	0.179324i	0.0153178	+	0.0123746i
$211$		−	25.9658i		−	1.78756i	−0.448504	−	0.893781i	$-0.648043\pi$
$211$		−	25.9658i		−	1.78756i	0.448504	−	0.893781i	$-0.351957\pi$
$212$		−	13.0143i		−	0.893828i
$213$	−8.03665	+	9.94811i	−0.550662	+	0.681633i
$214$	−0.809447			−0.0553326
$215$	−0.866776			−0.0591136
$216$	1.53346	−	3.03577i	0.104339	−	0.206558i
$217$			5.21936i			0.354313i
$218$		−	2.70864i		−	0.183452i
$219$	17.7690	−	21.9952i	1.20072	−	1.48630i
$220$	2.41687	−	6.08050i	0.162945	−	0.409948i
$221$			8.14356i			0.547795i
$222$	−2.57581	−	2.08088i	−0.172877	−	0.139660i
$223$	−3.15842			−0.211503			−0.105752	−	0.994393i	$-0.533725\pi$
$223$	−3.15842			−0.211503			−0.105752	+	0.994393i	$0.533725\pi$
$224$		−	1.94138i		−	0.129714i
$225$	−0.630571	−	2.93298i	−0.0420380	−	0.195532i
$226$			3.07961i			0.204853i
$227$	−15.7244			−1.04367			−0.521834	−	0.853047i	$-0.674752\pi$
$227$	−15.7244			−1.04367			−0.521834	+	0.853047i	$0.674752\pi$
$228$	11.9499	−	14.7921i	0.791399	−	0.979628i
$229$	24.6712			1.63032			0.815161	−	0.579235i	$-0.196649\pi$
$229$	24.6712			1.63032			0.815161	+	0.579235i	$0.196649\pi$
$230$	−1.13917			−0.0751148
$231$	5.00523	−	2.81915i	0.329320	−	0.185487i
$232$	−6.41795			−0.421359
$233$	−8.59952			−0.563373			−0.281687	−	0.959506i	$-0.590894\pi$
$233$	−8.59952			−0.563373			−0.281687	+	0.959506i	$0.590894\pi$
$234$	0.776155	−	0.166868i	0.0507389	−	0.0109085i
$235$	2.37172			0.154714
$236$		−	1.36415i		−	0.0887985i
$237$	−9.57180	+	11.8484i	−0.621755	+	0.769635i
$238$			0.835296i			0.0541442i
$239$	−18.6796			−1.20829			−0.604143	−	0.796876i	$-0.706484\pi$
$239$	−18.6796			−1.20829			−0.604143	+	0.796876i	$0.706484\pi$
$240$	−4.17732	+	5.17087i	−0.269645	+	0.333778i
$241$		−	16.4024i		−	1.05657i	−0.849067	−	0.528286i	$-0.822835\pi$
$241$		−	16.4024i		−	1.05657i	0.849067	−	0.528286i	$-0.177165\pi$
$242$	1.31777	+	1.24413i	0.0847093	+	0.0799755i
$243$	−15.0805	−	3.94681i	−0.967417	−	0.253188i
$244$		−	19.3567i		−	1.23919i
$245$		−	1.00000i		−	0.0638877i
$246$	−0.817908	−	0.660753i	−0.0521479	−	0.0421281i
$247$	8.93856			0.568747
$248$	3.41628			0.216934
$249$	−3.31992	−	2.68202i	−0.210391	−	0.169966i
$250$		−	0.164753i		−	0.0104199i
$251$			13.7451i			0.867583i	0.901013	+	0.433791i	$0.142825\pi$
$251$			13.7451i			0.867583i	−0.901013	+	0.433791i	$0.857175\pi$
$252$	−5.78635	+	1.24403i	−0.364506	+	0.0783662i
$253$	−8.47060	+	21.3108i	−0.532542	+	1.33980i
$254$			0.447946i			0.0281066i
$255$	5.51842	−	6.83094i	0.345577	−	0.427770i
$256$	13.8724			0.867028
$257$		−	12.0762i		−	0.753294i	−0.926357	−	0.376647i	$-0.877077\pi$
$257$		−	12.0762i		−	0.753294i	0.926357	−	0.376647i	$-0.122923\pi$
$258$	−0.155434	+	0.192403i	−0.00967691	+	0.0119785i
$259$			11.6040i			0.721038i
$260$	−3.16885			−0.196524
$261$	6.18293	+	28.7587i	0.382714	+	1.78012i
$262$	1.76961			0.109327
$263$	4.33250			0.267153			0.133577	−	0.991038i	$-0.457354\pi$
$263$	4.33250			0.267153			0.133577	+	0.991038i	$0.457354\pi$
$264$	−1.84525	−	3.27612i	−0.113567	−	0.201631i
$265$	−6.59669			−0.405232
$266$	0.916840			0.0562150
$267$	8.37894	−	10.3718i	0.512783	−	0.634745i
$268$	−11.8245			−0.722294
$269$		−	0.214988i		−	0.0131080i	−0.999979	−	0.00655402i	$-0.997914\pi$
$269$		−	0.214988i		−	0.0131080i	0.999979	−	0.00655402i	$-0.00208622\pi$
$270$	−0.764127	−	0.385984i	−0.0465033	−	0.0234902i
$271$			15.6267i			0.949256i	0.880186	+	0.474628i	$0.157417\pi$
$271$			15.6267i			0.949256i	−0.880186	+	0.474628i	$0.842583\pi$
$272$	−19.4580			−1.17982
$273$	−2.16411	−	1.74829i	−0.130978	−	0.105811i
$274$		−	2.25036i		−	0.135949i
$275$	−3.08208	−	1.22506i	−0.185857	−	0.0738740i
$276$	14.8477	−	18.3791i	0.893726	−	1.10629i
$277$		−	20.8624i		−	1.25350i	−0.779221	−	0.626749i	$-0.784385\pi$
$277$		−	20.8624i		−	1.25350i	0.779221	−	0.626749i	$-0.215615\pi$
$278$		−	1.86497i		−	0.111854i
$279$	−3.29117	−	15.3083i	−0.197037	−	0.916483i
$280$	−0.654539			−0.0391162
$281$	−24.6899			−1.47288			−0.736439	−	0.676504i	$-0.763494\pi$
$281$	−24.6899			−1.47288			−0.736439	+	0.676504i	$0.763494\pi$
$282$	0.425308	−	0.526465i	0.0253267	−	0.0313505i
$283$		−	31.8210i		−	1.89156i	−0.324807	−	0.945780i	$-0.605299\pi$
$283$		−	31.8210i		−	1.89156i	0.324807	−	0.945780i	$-0.394701\pi$
$284$		−	14.5668i		−	0.864379i
$285$	−7.49779	−	6.05714i	−0.444131	−	0.358794i
$286$	0.324188	−	0.815612i	0.0191696	−	0.0482281i
$287$			3.68468i			0.217500i
$288$	1.22418	+	5.69403i	0.0721353	+	0.335524i
$289$	8.70489			0.512052
$290$			1.61545i			0.0948624i
$291$	1.66140	+	1.34218i	0.0973931	+	0.0786797i
$292$			32.2071i			1.88478i
$293$	−19.4739			−1.13768			−0.568839	−	0.822449i	$-0.692607\pi$
$293$	−19.4739			−1.13768			−0.568839	+	0.822449i	$0.692607\pi$
$294$	−0.221976	−	0.179324i	−0.0129459	−	0.0104584i
$295$	−0.691458			−0.0402583
$296$	7.59528			0.441467
$297$	−12.9026	+	11.4247i	−0.748684	+	0.662927i
$298$	−0.764062			−0.0442609
$299$	11.1061			0.642285
$300$	2.65808	+	2.14735i	0.153464	+	0.123977i
$301$	0.866776			0.0499601
$302$		−	0.580599i		−	0.0334097i
$303$	17.1396	+	13.8464i	0.984645	+	0.795452i
$304$			21.3576i			1.22494i
$305$	−9.81153			−0.561806
$306$	−0.526713	−	2.44991i	−0.0301102	−	0.140052i
$307$		−	6.80411i		−	0.388331i	−0.980969	−	0.194166i	$-0.937800\pi$
$307$		−	6.80411i		−	0.388331i	0.980969	−	0.194166i	$-0.0621999\pi$
$308$	−2.41687	+	6.08050i	−0.137714	+	0.346469i
$309$	25.0264	+	20.2177i	1.42370	+	1.15015i
$310$		−	0.859904i		−	0.0488393i
$311$			7.49266i			0.424870i	0.977175	+	0.212435i	$0.0681393\pi$
$311$			7.49266i			0.424870i	−0.977175	+	0.212435i	$0.931861\pi$
$312$	−1.14432	+	1.41649i	−0.0647846	+	0.0801932i
$313$	−17.5683			−0.993021			−0.496510	−	0.868031i	$-0.665386\pi$
$313$	−17.5683			−0.993021			−0.496510	+	0.868031i	$0.665386\pi$
$314$	−0.570059			−0.0321703
$315$	0.630571	+	2.93298i	0.0355286	+	0.165255i
$316$		−	17.3493i		−	0.975975i
$317$		−	9.18109i		−	0.515661i	−0.966190	−	0.257831i	$-0.916992\pi$
$317$		−	9.18109i		−	0.515661i	0.966190	−	0.257831i	$-0.0830077\pi$
$318$	−1.18295	+	1.46430i	−0.0663364	+	0.0821141i
$319$	30.2207	+	12.0121i	1.69203	+	0.672547i
$320$		−	7.35590i		−	0.411208i
$321$	−6.61954	−	5.34764i	−0.369467	−	0.298476i
$322$	1.13917			0.0634836
$323$		−	28.2143i		−	1.56988i
$324$	16.1868	−	7.29741i	0.899268	−	0.405411i
$325$			1.60623i			0.0890974i
$326$	2.52634			0.139921
$327$	17.8947	−	22.1509i	0.989581	−	1.22495i
$328$	2.41176			0.133167
$329$	−2.37172			−0.130757
$330$	−0.824626	+	0.464463i	−0.0453942	+	0.0255679i
$331$	11.0884			0.609473			0.304736	−	0.952437i	$-0.401432\pi$
$331$	11.0884			0.609473			0.304736	+	0.952437i	$0.401432\pi$
$332$	4.86127			0.266797
$333$	−7.31715	−	34.0344i	−0.400977	−	1.86507i
$334$	−1.78860			−0.0978681
$335$			5.99357i			0.327464i
$336$	4.17732	−	5.17087i	0.227892	−	0.282094i
$337$			1.22947i			0.0669734i	0.999439	+	0.0334867i	$0.0106611\pi$
$337$			1.22947i			0.0669734i	−0.999439	+	0.0334867i	$0.989339\pi$
$338$	1.71673			0.0933778
$339$	−20.3456	+	25.1846i	−1.10502	+	1.36784i
$340$			10.0024i			0.542455i
$341$	−16.0865	−	6.39403i	−0.871132	−	0.346256i
$342$	−2.68907	+	0.578132i	−0.145408	+	0.0312618i
$343$			1.00000i			0.0539949i
$344$		−	0.567339i		−	0.0305888i
$345$	−9.31599	−	7.52599i	−0.501556	−	0.405186i
$346$	2.37577			0.127722
$347$	16.0468			0.861436			0.430718	−	0.902487i	$-0.358260\pi$
$347$	16.0468			0.861436			0.430718	+	0.902487i	$0.358260\pi$
$348$	−26.0632	−	21.0554i	−1.39714	−	1.12869i
$349$		−	11.2387i		−	0.601596i	−0.953688	−	0.300798i	$-0.902747\pi$
$349$		−	11.2387i		−	0.601596i	0.953688	−	0.300798i	$-0.0972529\pi$
$350$			0.164753i			0.00880641i
$351$	7.44971	+	3.76308i	0.397636	+	0.200858i
$352$	5.98349	+	2.37831i	0.318921	+	0.126764i
$353$		−	10.8193i		−	0.575851i	−0.957653	−	0.287926i	$-0.907034\pi$
$353$		−	10.8193i		−	0.575851i	0.957653	−	0.287926i	$-0.0929656\pi$
$354$	−0.123995	+	0.153487i	−0.00659028	+	0.00815773i
$355$	−7.38360			−0.391881
$356$			15.1872i			0.804920i
$357$	−5.51842	+	6.83094i	−0.292066	+	0.361532i
$358$		−	0.293756i		−	0.0155255i
$359$	32.2803			1.70369			0.851845	−	0.523794i	$-0.175484\pi$
$359$	32.2803			1.70369			0.851845	+	0.523794i	$0.175484\pi$
$360$	1.91975	−	0.412733i	0.101180	−	0.0217529i
$361$	−11.9686			−0.629926
$362$	2.25634			0.118591
$363$	2.55714	+	18.8802i	0.134215	+	0.990952i
$364$	3.16885			0.166093
$365$	16.3251			0.854496
$366$	−1.75945	+	2.17792i	−0.0919678	+	0.113842i
$367$	23.4825			1.22578			0.612888	−	0.790170i	$-0.290008\pi$
$367$	23.4825			1.22578			0.612888	+	0.790170i	$0.290008\pi$
$368$			26.5367i			1.38332i
$369$	−2.32345	−	10.8071i	−0.120954	−	0.562595i
$370$		−	1.91179i		−	0.0993894i
$371$	6.59669			0.342483
$372$	13.8735	+	11.2078i	0.719306	+	0.581096i
$373$			10.6743i			0.552693i	0.961058	+	0.276347i	$0.0891238\pi$
$373$			10.6743i			0.552693i	−0.961058	+	0.276347i	$0.910876\pi$
$374$	−2.57445	−	1.02329i	−0.133122	−	0.0529130i
$375$	1.08845	−	1.34733i	0.0562071	−	0.0695756i
$376$			1.55239i			0.0800582i
$377$		−	15.7495i		−	0.811141i
$378$	0.764127	+	0.385984i	0.0393024	+	0.0198529i
$379$	10.2618			0.527113			0.263557	−	0.964644i	$-0.415104\pi$
$379$	10.2618			0.527113			0.263557	+	0.964644i	$0.415104\pi$
$380$	10.9788			0.563202
$381$	−2.95937	+	3.66324i	−0.151613	+	0.187674i
$382$			1.99238i			0.101939i
$383$			10.2114i			0.521778i	0.965369	+	0.260889i	$0.0840157\pi$
$383$			10.2114i			0.521778i	−0.965369	+	0.260889i	$0.915984\pi$
$384$	−6.86417	−	5.54527i	−0.350286	−	0.282981i
$385$	3.08208	+	1.22506i	0.157077	+	0.0624349i
$386$			3.43870i			0.175025i
$387$	−2.54224	+	0.546563i	−0.129229	+	0.0277834i
$388$	−2.43275			−0.123504
$389$			12.5054i			0.634050i	0.948417	+	0.317025i	$0.102684\pi$
$389$			12.5054i			0.634050i	−0.948417	+	0.317025i	$0.897316\pi$
$390$	0.356543	+	0.288036i	0.0180543	+	0.0145853i
$391$		−	35.0562i		−	1.77287i
$392$	0.654539			0.0330592
$393$	14.4716	+	11.6910i	0.729997	+	0.589733i
$394$	4.21672			0.212436
$395$	−8.79401			−0.442474
$396$	3.25445	−	19.3580i	0.163542	−	0.972777i
$397$	8.60397			0.431821			0.215911	−	0.976413i	$-0.430728\pi$
$397$	8.60397			0.431821			0.215911	+	0.976413i	$0.430728\pi$
$398$	1.80995			0.0907246
$399$	7.49779	+	6.05714i	0.375359	+	0.303236i
$400$	−3.83788			−0.191894
$401$		−	11.5750i		−	0.578027i	−0.957325	−	0.289013i	$-0.906673\pi$
$401$		−	11.5750i		−	0.578027i	0.957325	−	0.289013i	$-0.0933272\pi$
$402$	1.33043	+	1.07479i	0.0663557	+	0.0536059i
$403$			8.38347i			0.417610i
$404$	−25.0971			−1.24863
$405$	−3.69890	−	8.20476i	−0.183800	−	0.407698i
$406$		−	1.61545i		−	0.0801734i
$407$	−35.7645	−	14.2156i	−1.77278	−	0.704642i
$408$	4.47112	+	3.61202i	0.221353	+	0.178822i
$409$			3.74702i			0.185278i	0.995700	+	0.0926391i	$0.0295303\pi$
$409$			3.74702i			0.185278i	−0.995700	+	0.0926391i	$0.970470\pi$
$410$		−	0.607061i		−	0.0299806i
$411$	14.8671	−	18.4032i	0.733341	−	0.907761i
$412$	−36.6455			−1.80539
$413$	0.691458			0.0340244
$414$	−3.34117	+	0.718328i	−0.164210	+	0.0353039i
$415$		−	2.46408i		−	0.120957i
$416$		−	3.11829i		−	0.152887i
$417$	12.3210	−	15.2515i	0.603363	−	0.746868i
$418$	−1.12318	+	2.82577i	−0.0549367	+	0.138213i
$419$		−	16.3918i		−	0.800793i	−0.916342	−	0.400397i	$-0.868872\pi$
$419$		−	16.3918i		−	0.800793i	0.916342	−	0.400397i	$-0.131128\pi$
$420$	−2.65808	−	2.14735i	−0.129701	−	0.104780i
$421$	−27.4207			−1.33641			−0.668203	−	0.743979i	$-0.732936\pi$
$421$	−27.4207			−1.33641			−0.668203	+	0.743979i	$0.732936\pi$
$422$		−	4.27794i		−	0.208247i
$423$	6.95622	−	1.49554i	0.338223	−	0.0727156i
$424$		−	4.31779i		−	0.209691i
$425$	5.07000			0.245931
$426$	−1.32406	+	1.63898i	−0.0641509	+	0.0794088i
$427$	9.81153			0.474813
$428$	9.69284			0.468521
$429$	8.03954	−	4.52820i	0.388153	−	0.218623i
$430$	−0.142804			−0.00688661
$431$	3.53100			0.170082			0.0850411	−	0.996377i	$-0.472898\pi$
$431$	3.53100			0.170082			0.0850411	+	0.996377i	$0.472898\pi$
$432$	−8.99141	+	17.8002i	−0.432599	+	0.856410i
$433$	−27.3878			−1.31617			−0.658086	−	0.752943i	$-0.728634\pi$
$433$	−27.3878			−1.31617			−0.658086	+	0.752943i	$0.728634\pi$
$434$			0.859904i			0.0412767i
$435$	−10.6725	+	13.2109i	−0.511709	+	0.633415i
$436$			32.4350i			1.55336i
$437$	−38.4784			−1.84067
$438$	2.92749	−	3.62378i	0.139881	−	0.173151i
$439$		−	4.81180i		−	0.229655i	−0.993385	−	0.114827i	$-0.963369\pi$
$439$		−	4.81180i		−	0.229655i	0.993385	−	0.114827i	$-0.0366315\pi$
$440$	0.801850	−	2.01734i	0.0382267	−	0.0961730i
$441$	−0.630571	−	2.93298i	−0.0300272	−	0.139666i
$442$			1.34167i			0.0638169i
$443$		−	16.7792i		−	0.797202i	−0.917124	−	0.398601i	$-0.869496\pi$
$443$		−	16.7792i		−	0.797202i	0.917124	−	0.398601i	$-0.130504\pi$
$444$	30.8444	+	24.9179i	1.46381	+	1.18255i
$445$	7.69808			0.364924
$446$	−0.520358			−0.0246397
$447$	−6.24839	−	5.04780i	−0.295539	−	0.238753i
$448$			7.35590i			0.347534i
$449$		−	3.98387i		−	0.188010i	−0.995572	−	0.0940052i	$-0.970033\pi$
$449$		−	3.98387i		−	0.188010i	0.995572	−	0.0940052i	$-0.0299670\pi$
$450$	−0.103888	−	0.483217i	−0.00489734	−	0.0227791i
$451$	−11.3565	−	4.51395i	−0.534755	−	0.212554i
$452$		−	36.8773i		−	1.73456i
$453$	3.83575	−	4.74806i	0.180219	−	0.223083i
$454$	−2.59064			−0.121585
$455$		−	1.60623i		−	0.0753010i
$456$	3.96463	−	4.90760i	0.185661	−	0.229819i
$457$			13.0037i			0.608289i	0.952626	+	0.304145i	$0.0983706\pi$
$457$			13.0037i			0.608289i	−0.952626	+	0.304145i	$0.901629\pi$
$458$	4.06466			0.189929
$459$	11.8780	−	23.5148i	0.554419	−	1.09758i
$460$	13.6412			0.636024
$461$	30.1237			1.40300			0.701501	−	0.712669i	$-0.252514\pi$
$461$	30.1237			1.40300			0.701501	+	0.712669i	$0.252514\pi$
$462$	0.824626	−	0.464463i	0.0383651	−	0.0216088i
$463$	6.79948			0.315999			0.157999	−	0.987439i	$-0.449496\pi$
$463$	6.79948			0.315999			0.157999	+	0.987439i	$0.449496\pi$
$464$	37.6315			1.74700
$465$	5.68099	−	7.03218i	0.263450	−	0.326109i
$466$	−1.41679			−0.0656318
$467$		−	12.4158i		−	0.574536i	−0.957850	−	0.287268i	$-0.907253\pi$
$467$		−	12.4158i		−	0.574536i	0.957850	−	0.287268i	$-0.0927471\pi$
$468$	−9.29419	+	1.99819i	−0.429624	+	0.0923662i
$469$		−	5.99357i		−	0.276758i
$470$	0.390748			0.0180239
$471$	−4.66187	−	3.76612i	−0.214807	−	0.173534i
$472$		−	0.452586i		−	0.0208320i
$473$	−1.06185	+	2.67147i	−0.0488241	+	0.122834i
$474$	−1.57698	+	1.95205i	−0.0724331	+	0.0896608i
$475$		−	5.56494i		−	0.255337i
$476$		−	10.0024i		−	0.458458i
$477$	−19.3480	+	4.15968i	−0.885883	+	0.190459i
$478$	−3.07752			−0.140763
$479$	−34.4638			−1.57469			−0.787346	−	0.616512i	$-0.788545\pi$
$479$	−34.4638			−1.57469			−0.787346	+	0.616512i	$0.788545\pi$
$480$	−2.11309	+	2.61567i	−0.0964487	+	0.119388i
$481$			18.6387i			0.849850i
$482$		−	2.70234i		−	0.123088i
$483$	9.31599	+	7.52599i	0.423892	+	0.342444i
$484$	−15.7798	−	14.8980i	−0.717264	−	0.677181i
$485$			1.23311i			0.0559927i
$486$	−2.48456	−	0.650248i	−0.112702	−	0.0294959i
$487$	−9.36777			−0.424494			−0.212247	−	0.977216i	$-0.568078\pi$
$487$	−9.36777			−0.424494			−0.212247	+	0.977216i	$0.568078\pi$
$488$		−	6.42203i		−	0.290712i
$489$	20.6600	+	16.6904i	0.934280	+	0.754764i
$490$		−	0.164753i		−	0.00744277i
$491$	27.5969			1.24543			0.622716	−	0.782448i	$-0.286029\pi$
$491$	27.5969			1.24543			0.622716	+	0.782448i	$0.286029\pi$
$492$	9.79416	+	7.91228i	0.441555	+	0.356713i
$493$	−49.7128			−2.23895
$494$	1.47265			0.0662577
$495$	−9.81218	−	1.64961i	−0.441024	−	0.0741445i
$496$	−20.0313			−0.899430
$497$	7.38360			0.331200
$498$	−0.546965	−	0.441870i	−0.0245101	−	0.0198007i
$499$	−6.02643			−0.269780			−0.134890	−	0.990861i	$-0.543068\pi$
$499$	−6.02643			−0.269780			−0.134890	+	0.990861i	$0.543068\pi$
$500$			1.97286i			0.0882288i
$501$	−14.6270	−	11.8165i	−0.653485	−	0.527922i
$502$			2.26454i			0.101071i
$503$	−18.4490			−0.822600			−0.411300	−	0.911500i	$-0.634925\pi$
$503$	−18.4490			−0.822600			−0.411300	+	0.911500i	$0.634925\pi$
$504$	−1.91975	+	0.412733i	−0.0855125	+	0.0183846i
$505$			12.7212i			0.566087i
$506$	−1.39556	+	3.51102i	−0.0620400	+	0.156084i
$507$	14.0392	+	11.3416i	0.623502	+	0.503700i
$508$		−	5.36400i		−	0.237989i
$509$			27.5883i			1.22283i	0.791310	+	0.611415i	$0.209399\pi$
$509$			27.5883i			1.22283i	−0.791310	+	0.611415i	$0.790601\pi$
$510$	0.909175	−	1.12542i	0.0402589	−	0.0498342i
$511$	−16.3251			−0.722181
$512$	12.4749			0.551316
$513$	−25.8103	−	13.0376i	−1.13955	−	0.575624i
$514$		−	1.98959i		−	0.0877571i
$515$			18.5748i			0.818506i
$516$	1.86127	−	2.30396i	0.0819378	−	0.101426i
$517$	2.90551	−	7.30984i	0.127784	−	0.321487i
$518$			1.91179i			0.0839994i
$519$	19.4287	+	15.6956i	0.852827	+	0.688962i
$520$	−1.05134			−0.0461042
$521$			37.5157i			1.64359i	0.569783	+	0.821796i	$0.307027\pi$
$521$			37.5157i			1.64359i	−0.569783	+	0.821796i	$0.692973\pi$
$522$	1.01865	+	4.73808i	0.0445853	+	0.207380i
$523$		−	18.8296i		−	0.823360i	−0.911328	−	0.411680i	$-0.864942\pi$
$523$		−	18.8296i		−	0.823360i	0.911328	−	0.411680i	$-0.135058\pi$
$524$	−21.1905			−0.925710
$525$	−1.08845	+	1.34733i	−0.0475037	+	0.0588021i
$526$	0.713791			0.0311227
$527$	26.4621			1.15271
$528$	10.8196	+	19.2095i	0.470861	+	0.835985i
$529$	−24.8094			−1.07867
$530$	−1.08682			−0.0472086
$531$	−2.02803	+	0.436013i	−0.0880092	+	0.0189214i
$532$	−10.9788			−0.475993
$533$			5.91842i			0.256355i
$534$	1.38045	−	1.70878i	0.0597381	−	0.0739463i
$535$		−	4.91310i		−	0.212412i
$536$	−3.92303			−0.169449
$537$	1.94071	−	2.40229i	0.0837478	−	0.103667i
$538$		−	0.0354198i		−	0.00152706i
$539$	−3.08208	−	1.22506i	−0.132755	−	0.0527671i
$540$	9.15015	+	4.62202i	0.393760	+	0.198900i
$541$			23.6022i			1.01474i	0.861729	+	0.507368i	$0.169382\pi$
$541$			23.6022i			1.01474i	−0.861729	+	0.507368i	$0.830618\pi$
$542$			2.57455i			0.110586i
$543$	18.4520	+	14.9066i	0.791853	+	0.639704i
$544$	−9.84279			−0.422006
$545$	16.4406			0.704239
$546$	−0.356543	−	0.288036i	−0.0152586	−	0.0123268i
$547$			15.4618i			0.661097i	0.943789	+	0.330549i	$0.107234\pi$
$547$			15.4618i			0.661097i	−0.943789	+	0.330549i	$0.892766\pi$
$548$			26.9473i			1.15113i
$549$	−28.7770	+	6.18686i	−1.22817	+	0.264049i
$550$	−0.507781	−	0.201832i	−0.0216519	−	0.00860615i
$551$			54.5659i			2.32458i
$552$	4.92605	−	6.09768i	0.209667	−	0.259534i
$553$	8.79401			0.373959
$554$		−	3.43713i		−	0.146030i
$555$	12.6303	−	15.6344i	0.536128	−	0.663642i
$556$			22.3324i			0.947104i
$557$	−16.5453			−0.701047			−0.350523	−	0.936554i	$-0.613996\pi$
$557$	−16.5453			−0.701047			−0.350523	+	0.936554i	$0.613996\pi$
$558$	−0.542230	−	2.52208i	−0.0229544	−	0.106768i
$559$	1.39224			0.0588854
$560$	3.83788			0.162180
$561$	−14.2931	−	25.3765i	−0.603455	−	1.07140i
$562$	−4.06773			−0.171587
$563$	−3.09282			−0.130347			−0.0651733	−	0.997874i	$-0.520760\pi$
$563$	−3.09282			−0.130347			−0.0651733	+	0.997874i	$0.520760\pi$
$564$	−5.09292	+	6.30423i	−0.214450	+	0.265456i
$565$	−18.6923			−0.786392
$566$		−	5.24259i		−	0.220363i
$567$	3.69890	+	8.20476i	0.155339	+	0.344568i
$568$		−	4.83285i		−	0.202782i
$569$	22.6859			0.951041			0.475520	−	0.879705i	$-0.342260\pi$
$569$	22.6859			0.951041			0.475520	+	0.879705i	$0.342260\pi$
$570$	−1.23528	−	0.997930i	−0.0517402	−	0.0417987i
$571$			23.2432i			0.972700i	0.873764	+	0.486350i	$0.161672\pi$
$571$			23.2432i			0.972700i	−0.873764	+	0.486350i	$0.838328\pi$
$572$	−3.88204	+	9.76666i	−0.162316	+	0.408365i
$573$	−13.1627	+	16.2934i	−0.549881	+	0.680666i
$574$			0.607061i			0.0253382i
$575$		−	6.91443i		−	0.288352i
$576$	−4.63842	−	21.5747i	−0.193267	−	0.898947i
$577$	−5.47573			−0.227958			−0.113979	−	0.993483i	$-0.536360\pi$
$577$	−5.47573			−0.227958			−0.113979	+	0.993483i	$0.536360\pi$
$578$	1.43415			0.0596529
$579$	−22.7179	+	28.1212i	−0.944126	+	1.16868i
$580$		−	19.3444i		−	0.803234i
$581$			2.46408i			0.102227i
$582$	0.273721	+	0.221127i	0.0113461	+	0.00916601i
$583$	−8.08135	+	20.3315i	−0.334695	+	0.842046i
$584$			10.6854i			0.442166i
$585$	1.01284	+	4.71103i	0.0418757	+	0.194777i
$586$	−3.20838			−0.132537
$587$			30.9728i			1.27839i	0.769047	+	0.639193i	$0.220731\pi$
$587$			30.9728i			1.27839i	−0.769047	+	0.639193i	$0.779269\pi$
$588$	2.65808	+	2.14735i	0.109617	+	0.0885551i
$589$		−	29.0454i		−	1.19680i
$590$	−0.113920			−0.00469000
$591$	34.4838	+	27.8580i	1.41847	+	1.14592i
$592$	−44.5348			−1.83037
$593$	13.8999			0.570802			0.285401	−	0.958408i	$-0.407873\pi$
$593$	13.8999			0.570802			0.285401	+	0.958408i	$0.407873\pi$
$594$	−2.12574	+	1.88225i	−0.0872200	+	0.0772295i
$595$	−5.07000			−0.207850
$596$	9.14937			0.374773
$597$	14.8015	+	11.9575i	0.605786	+	0.489388i
$598$	1.82977			0.0748248
$599$			18.6167i			0.760656i	0.924852	+	0.380328i	$0.124189\pi$
$599$			18.6167i			0.760656i	−0.924852	+	0.380328i	$0.875811\pi$
$600$	0.881877	+	0.712430i	0.0360025	+	0.0290849i
$601$		−	1.69010i		−	0.0689406i	−0.999406	−	0.0344703i	$-0.989026\pi$
$601$		−	1.69010i		−	0.0689406i	0.999406	−	0.0344703i	$-0.0109744\pi$
$602$	0.142804			0.00582024
$603$	3.77937	+	17.5790i	0.153908	+	0.715874i
$604$			6.95248i			0.282892i
$605$	−7.55147	+	7.99845i	−0.307011	+	0.325183i
$606$	2.82380	+	2.28122i	0.114709	+	0.0926684i
$607$		−	14.2928i		−	0.580125i	−0.957008	−	0.290063i	$-0.906324\pi$
$607$		−	14.2928i		−	0.580125i	0.957008	−	0.290063i	$-0.0936762\pi$
$608$			10.8037i			0.438146i
$609$	10.6725	−	13.2109i	0.432473	−	0.535333i
$610$	−1.61648			−0.0654492
$611$	−3.80952			−0.154117
$612$	6.30721	+	29.3368i	0.254954	+	1.18587i
$613$			7.59801i			0.306881i	0.988158	+	0.153440i	$0.0490353\pi$
$613$			7.59801i			0.306881i	−0.988158	+	0.153440i	$0.950965\pi$
$614$		−	1.12100i		−	0.0452397i
$615$	4.01057	−	4.96446i	0.161722	−	0.200186i
$616$	−0.801850	+	2.01734i	−0.0323075	+	0.0812811i
$617$			21.1183i			0.850192i	0.905148	+	0.425096i	$0.139760\pi$
$617$			21.1183i			0.850192i	−0.905148	+	0.425096i	$0.860240\pi$
$618$	4.12316	+	3.33092i	0.165858	+	0.133989i
$619$	14.4276			0.579893			0.289947	−	0.957043i	$-0.406362\pi$
$619$	14.4276			0.579893			0.289947	+	0.957043i	$0.406362\pi$
$620$			10.2970i			0.413539i
$621$	−32.0693	−	16.1992i	−1.28690	−	0.650051i
$622$			1.23444i			0.0494964i
$623$	−7.69808			−0.308417
$624$	6.70972	−	8.30558i	0.268604	−	0.332489i
$625$	1.00000			0.0400000
$626$	−2.89443			−0.115685
$627$	−27.8538	+	15.6884i	−1.11238	+	0.626535i
$628$	6.82626			0.272397
$629$	58.8323			2.34580
$630$	0.103888	+	0.483217i	0.00413901	+	0.0192518i
$631$	−11.0743			−0.440862			−0.220431	−	0.975403i	$-0.570746\pi$
$631$	−11.0743			−0.440862			−0.220431	+	0.975403i	$0.570746\pi$
$632$		−	5.75602i		−	0.228962i
$633$	28.2624	−	34.9844i	1.12333	−	1.39051i
$634$		−	1.51261i		−	0.0600734i
$635$	−2.71890			−0.107896
$636$	14.1654	−	17.5345i	0.561694	−	0.695289i
$637$			1.60623i			0.0636410i
$638$	4.97894	+	1.97902i	0.197118	+	0.0783503i
$639$	−21.6560	+	4.65588i	−0.856697	+	0.184184i
$640$		−	5.09466i		−	0.201384i
$641$			38.5904i			1.52423i	0.647443	+	0.762114i	$0.275838\pi$
$641$			38.5904i			1.52423i	−0.647443	+	0.762114i	$0.724162\pi$
$642$	−1.09059	−	0.881039i	−0.0430421	−	0.0347718i
$643$	24.1224			0.951296			0.475648	−	0.879636i	$-0.342214\pi$
$643$	24.1224			0.951296			0.475648	+	0.879636i	$0.342214\pi$
$644$	−13.6412			−0.537538
$645$	−1.16783	−	0.943439i	−0.0459832	−	0.0371479i
$646$		−	4.64838i		−	0.182888i
$647$		−	34.1195i		−	1.34138i	−0.741739	−	0.670688i	$-0.765999\pi$
$647$		−	34.1195i		−	1.34138i	0.741739	−	0.670688i	$-0.234001\pi$
$648$	5.37034	−	2.42108i	0.210967	−	0.0951089i
$649$	−0.847078	+	2.13113i	−0.0332507	+	0.0836542i
$650$			0.264630i			0.0103796i
$651$	−5.68099	+	7.03218i	−0.222656	+	0.275613i
$652$	−30.2520			−1.18476
$653$			20.2950i			0.794204i	0.917774	+	0.397102i	$0.129984\pi$
$653$			20.2950i			0.794204i	−0.917774	+	0.397102i	$0.870016\pi$
$654$	2.94821	−	3.64942i	0.115284	−	0.142704i
$655$			10.7410i			0.419686i
$656$	−14.1413			−0.552126
$657$	47.8813	−	10.2941i	1.86803	−	0.401613i
$658$	−0.390748			−0.0152329
$659$	6.06278			0.236173			0.118086	−	0.993003i	$-0.462324\pi$
$659$	6.06278			0.236173			0.118086	+	0.993003i	$0.462324\pi$
$660$	9.87461	−	5.56179i	0.384369	−	0.216492i
$661$	−23.7150			−0.922408			−0.461204	−	0.887294i	$-0.652582\pi$
$661$	−23.7150			−0.922408			−0.461204	+	0.887294i	$0.652582\pi$
$662$	1.82684			0.0710022
$663$	−8.86383	+	10.9720i	−0.344243	+	0.426118i
$664$	1.61284			0.0625902
$665$			5.56494i			0.215799i
$666$	−1.20552	−	5.60725i	−0.0467130	−	0.217277i
$667$			67.7980i			2.62515i
$668$	21.4179			0.828684
$669$	−4.25542	−	3.43777i	−0.164524	−	0.132912i
$670$			0.987458i			0.0381488i
$671$	−12.0197	+	30.2399i	−0.464016	+	1.16740i
$672$	2.11309	−	2.61567i	0.0815141	−	0.100902i
$673$			17.5839i			0.677809i	0.940821	+	0.338905i	$0.110056\pi$
$673$			17.5839i			0.677809i	−0.940821	+	0.338905i	$0.889944\pi$
$674$			0.202558i			0.00780225i
$675$	2.34281	−	4.63802i	0.0901747	−	0.178518i
$676$	−20.5572			−0.790663
$677$	−23.0946			−0.887597			−0.443799	−	0.896127i	$-0.646369\pi$
$677$	−23.0946			−0.887597			−0.443799	+	0.896127i	$0.646369\pi$
$678$	−3.35199	+	4.14924i	−0.128732	+	0.159351i
$679$		−	1.23311i		−	0.0473225i
$680$			3.31851i			0.127259i
$681$	−21.1859	−	17.1152i	−0.811847	−	0.655856i
$682$	−2.65029	−	1.05343i	−0.101485	−	0.0403381i
$683$		−	35.8172i		−	1.37051i	−0.728304	−	0.685254i	$-0.759691\pi$
$683$		−	35.8172i		−	1.37051i	0.728304	−	0.685254i	$-0.240309\pi$
$684$	32.2007	−	6.92293i	1.23123	−	0.264705i
$685$	13.6590			0.521885
$686$			0.164753i			0.00629029i
$687$	33.2402	+	26.8533i	1.26819	+	1.02452i
$688$			3.32658i			0.126825i
$689$	10.5958			0.403667
$690$	−1.53484	−	1.23993i	−0.0584302	−	0.0472032i
$691$	33.6316			1.27941			0.639704	−	0.768622i	$-0.279057\pi$
$691$	33.6316			1.27941			0.639704	+	0.768622i	$0.279057\pi$
$692$	−28.4491			−1.08147
$693$	9.81218	+	1.64961i	0.372734	+	0.0626636i
$694$	2.64375			0.100355
$695$	11.3198			0.429385
$696$	−8.64706	−	6.98559i	−0.327766	−	0.264788i
$697$	18.6813			0.707605
$698$		−	1.85161i		−	0.0700846i
$699$	−11.5864	−	9.36011i	−0.438236	−	0.354032i
$700$		−	1.97286i		−	0.0745670i
$701$	16.4916			0.622880			0.311440	−	0.950266i	$-0.399189\pi$
$701$	16.4916			0.622880			0.311440	+	0.950266i	$0.399189\pi$
$702$	1.22736	+	0.619978i	0.0463237	+	0.0233996i
$703$		−	64.5757i		−	2.43552i
$704$	−22.6715	−	9.01143i	−0.854464	−	0.339631i
$705$	3.19548	+	2.58149i	0.120349	+	0.0972247i
$706$		−	1.78250i		−	0.0670854i
$707$		−	12.7212i		−	0.478430i
$708$	1.48480	−	1.83795i	0.0558022	−	0.0690744i
$709$	−48.0858			−1.80590			−0.902949	−	0.429747i	$-0.858603\pi$
$709$	−48.0858			−1.80590			−0.902949	+	0.429747i	$0.858603\pi$
$710$	−1.21647			−0.0456532
$711$	−25.7927	+	5.54524i	−0.967300	+	0.207963i
$712$			5.03869i			0.188833i
$713$		−	36.0889i		−	1.35154i
$714$	−0.909175	+	1.12542i	−0.0340250	+	0.0421176i
$715$	4.95052	+	1.96772i	0.185139	+	0.0735887i
$716$			3.51762i			0.131460i
$717$	−25.1676	−	20.3318i	−0.939900	−	0.759304i
$718$	5.31827			0.198476
$719$			8.59999i			0.320726i	0.987058	+	0.160363i	$0.0512664\pi$
$719$			8.59999i			0.320726i	−0.987058	+	0.160363i	$0.948734\pi$
$720$	−11.2564	+	2.42005i	−0.419502	+	0.0901900i
$721$		−	18.5748i		−	0.691763i
$722$	−1.97186			−0.0733849
$723$	17.8531	−	22.0994i	0.663965	−	0.821885i
$724$	−27.0189			−1.00415
$725$	−9.80529			−0.364159
$726$	0.421296	+	3.11056i	0.0156358	+	0.115444i
$727$	−37.1758			−1.37877			−0.689386	−	0.724394i	$-0.742120\pi$
$727$	−37.1758			−1.37877			−0.689386	+	0.724394i	$0.742120\pi$
$728$	1.05134			0.0389652
$729$	−16.0225	−	21.7320i	−0.593426	−	0.804889i
$730$	2.68961			0.0995469
$731$		−	4.39455i		−	0.162538i
$732$	21.0688	−	26.0798i	0.778724	−	0.963938i
$733$			25.0018i			0.923463i	0.887020	+	0.461731i	$0.152772\pi$
$733$			25.0018i			0.923463i	−0.887020	+	0.461731i	$0.847228\pi$
$734$	3.86880			0.142800
$735$	1.08845	−	1.34733i	0.0401479	−	0.0496968i
$736$			13.4235i			0.494798i
$737$	18.4727	+	7.34249i	0.680450	+	0.270464i
$738$	−0.382795	−	1.78050i	−0.0140909	−	0.0655410i
$739$			41.8835i			1.54071i	0.637616	+	0.770354i	$0.279921\pi$
$739$			41.8835i			1.54071i	−0.637616	+	0.770354i	$0.720079\pi$
$740$			22.8931i			0.841565i
$741$	12.0431	+	9.72913i	0.442416	+	0.357409i
$742$	1.08682			0.0398985
$743$	12.4238			0.455784			0.227892	−	0.973686i	$-0.426817\pi$
$743$	12.4238			0.455784			0.227892	+	0.973686i	$0.426817\pi$
$744$	4.60283	+	3.71843i	0.168748	+	0.136324i
$745$		−	4.63763i		−	0.169909i
$746$			1.75862i			0.0643875i
$747$	−1.55378	−	7.22710i	−0.0568497	−	0.264426i
$748$	30.8281	+	12.2535i	1.12719	+	0.448033i
$749$			4.91310i			0.179521i
$750$	0.179324	−	0.221976i	0.00654800	−	0.00810540i
$751$	34.7566			1.26829			0.634143	−	0.773216i	$-0.281353\pi$
$751$	34.7566			1.26829			0.634143	+	0.773216i	$0.281353\pi$
$752$		−	9.10238i		−	0.331930i
$753$	−14.9608	+	18.5191i	−0.545202	+	0.674874i
$754$		−	2.59478i		−	0.0944962i
$755$	3.52407			0.128254
$756$	−9.15015	−	4.62202i	−0.332788	−	0.168101i
$757$	−0.874310			−0.0317774			−0.0158887	−	0.999874i	$-0.505058\pi$
$757$	−0.874310			−0.0317774			−0.0158887	+	0.999874i	$0.505058\pi$
$758$	1.69066			0.0614075
$759$	−34.6084	+	19.4928i	−1.25620	+	0.707546i
$760$	3.64247			0.132126
$761$	−30.5626			−1.10789			−0.553946	−	0.832552i	$-0.686879\pi$
$761$	−30.5626			−1.10789			−0.553946	+	0.832552i	$0.686879\pi$
$762$	−0.487565	+	0.603529i	−0.0176626	+	0.0218636i
$763$	−16.4406			−0.595191
$764$		−	23.8580i		−	0.863153i
$765$	14.8702	−	3.19699i	0.537634	−	0.115587i
$766$			1.68236i			0.0607860i
$767$	1.11064			0.0401028
$768$	18.6907	+	15.0994i	0.674443	+	0.544853i
$769$			5.78713i			0.208689i	0.994541	+	0.104345i	$0.0332745\pi$
$769$			5.78713i			0.208689i	−0.994541	+	0.104345i	$0.966726\pi$
$770$	0.507781	+	0.201832i	0.0182992	+	0.00727353i
$771$	13.1443	−	16.2706i	0.473381	−	0.585971i
$772$		−	41.1773i		−	1.48200i
$773$			15.0332i			0.540707i	0.962761	+	0.270353i	$0.0871405\pi$
$773$			15.0332i			0.540707i	−0.962761	+	0.270353i	$0.912859\pi$
$774$	−0.418841	+	0.0900478i	−0.0150549	+	0.00323670i
$775$	5.21936			0.187485
$776$	−0.807120			−0.0289739
$777$	−12.6303	+	15.6344i	−0.453111	+	0.560880i
$778$			2.06030i			0.0738654i
$779$		−	20.5050i		−	0.734668i
$780$	−4.26948	−	3.44913i	−0.152872	−	0.123499i
$781$	−9.04536	+	22.7569i	−0.323668	+	0.814304i
$782$		−	5.77560i		−	0.206535i
$783$	−22.9719	+	45.4772i	−0.820949	+	1.62522i
$784$	−3.83788			−0.137067
$785$		−	3.46009i		−	0.123496i
$786$	2.38424	+	1.92613i	0.0850430	+	0.0687026i
$787$		−	30.7588i		−	1.09643i	−0.836337	−	0.548216i	$-0.815307\pi$
$787$		−	30.7588i		−	1.09643i	0.836337	−	0.548216i	$-0.184693\pi$
$788$	−50.4938			−1.79877
$789$	5.83728	+	4.71569i	0.207813	+	0.167883i
$790$	−1.44884			−0.0515473
$791$	18.6923			0.664622
$792$	1.07974	−	6.42245i	0.0383667	−	0.228212i
$793$	15.7595			0.559637
$794$	1.41753			0.0503062
$795$	−8.88789	−	7.18014i	−0.315221	−	0.254653i
$796$	−21.6735			−0.768197
$797$			2.12237i			0.0751784i	0.999293	+	0.0375892i	$0.0119678\pi$
$797$			2.12237i			0.0751784i	−0.999293	+	0.0375892i	$0.988032\pi$
$798$	1.23528	+	0.997930i	0.0437285	+	0.0353264i
$799$			12.0246i			0.425401i
$800$	−1.94138			−0.0686381
$801$	22.5783	−	4.85418i	0.797765	−	0.171514i
$802$		−	1.90701i		−	0.0673388i
$803$	19.9993	−	50.3153i	0.705759	−	1.77559i
$804$	−15.9314	−	12.8703i	−0.561857	−	0.453900i
$805$			6.91443i			0.243702i
$806$			1.38120i			0.0486507i
$807$	0.234003	−	0.289658i	0.00823728	−	0.0101965i
$808$	−8.32653			−0.292926
$809$	−23.0040			−0.808779			−0.404389	−	0.914587i	$-0.632516\pi$
$809$	−23.0040			−0.808779			−0.404389	+	0.914587i	$0.632516\pi$
$810$	−0.609405	−	1.35176i	−0.0214123	−	0.0474959i
$811$		−	19.3524i		−	0.679553i	−0.940506	−	0.339777i	$-0.889648\pi$
$811$		−	19.3524i		−	0.679553i	0.940506	−	0.339777i	$-0.110352\pi$
$812$			19.3444i			0.678857i
$813$	−17.0089	+	21.0543i	−0.596527	+	0.738406i
$814$	−5.89230	−	2.34206i	−0.206525	−	0.0820893i
$815$			15.3341i			0.537131i
$816$	−26.2163	−	21.1790i	−0.917754	−	0.741414i
$817$	−4.82356			−0.168755
$818$			0.617332i			0.0215845i
$819$	−1.01284	−	4.71103i	−0.0353915	−	0.164617i
$820$			7.26934i			0.253856i
$821$	−13.7736			−0.480702			−0.240351	−	0.970686i	$-0.577262\pi$
$821$	−13.7736			−0.480702			−0.240351	+	0.970686i	$0.577262\pi$
$822$	2.44940	−	3.03197i	0.0854326	−	0.105752i
$823$	28.5635			0.995661			0.497830	−	0.867274i	$-0.334130\pi$
$823$	28.5635			0.995661			0.497830	+	0.867274i	$0.334130\pi$
$824$	−12.1580			−0.423543
$825$	−2.81915	−	5.00523i	−0.0981503	−	0.174260i
$826$	0.113920			0.00396377
$827$	−23.9846			−0.834028			−0.417014	−	0.908900i	$-0.636923\pi$
$827$	−23.9846			−0.834028			−0.417014	+	0.908900i	$0.636923\pi$
$828$	40.0093	−	8.60173i	1.39042	−	0.298931i
$829$	−1.30749			−0.0454109			−0.0227055	−	0.999742i	$-0.507228\pi$
$829$	−1.30749			−0.0454109			−0.0227055	+	0.999742i	$0.507228\pi$
$830$		−	0.405964i		−	0.0140912i
$831$	22.7076	−	28.1084i	0.787716	−	0.975069i
$832$			11.8152i			0.409620i
$833$	5.07000			0.175665
$834$	2.02992	−	2.51272i	0.0702904	−	0.0870085i
$835$		−	10.8563i		−	0.375698i
$836$	13.4497	−	33.8377i	0.465169	−	1.17030i
$837$	12.2280	−	24.2075i	0.422660	−	0.836734i
$838$		−	2.70060i		−	0.0932906i
$839$		−	43.7966i		−	1.51203i	−0.654557	−	0.756013i	$-0.727145\pi$
$839$		−	43.7966i		−	1.51203i	0.654557	−	0.756013i	$-0.272855\pi$
$840$	−0.881877	−	0.712430i	−0.0304276	−	0.0245812i
$841$	67.1437			2.31530
$842$	−4.51764			−0.155688
$843$	−33.2654	−	26.8737i	−1.14572	−	0.925578i
$844$			51.2269i			1.76330i
$845$			10.4200i			0.358460i
$846$	1.14606	−	0.246394i	0.0394022	−	0.00847121i
$847$	7.55147	−	7.99845i	0.259472	−	0.274830i
$848$			25.3173i			0.869399i
$849$	34.6354	−	42.8732i	1.18868	−	1.47140i
$850$	0.835296			0.0286504
$851$		−	80.2352i		−	2.75043i
$852$	15.8552	−	19.6262i	0.543189	−	0.672382i
$853$			27.7796i			0.951156i	0.879674	+	0.475578i	$0.157761\pi$
$853$			27.7796i			0.951156i	−0.879674	+	0.475578i	$0.842239\pi$
$854$	1.61648			0.0553147
$855$	−3.50909	−	16.3219i	−0.120008	−	0.558196i
$856$	3.21582			0.109914
$857$	32.0376			1.09438			0.547191	−	0.837008i	$-0.315697\pi$
$857$	32.0376			1.09438			0.547191	+	0.837008i	$0.315697\pi$
$858$	1.32454	−	0.746033i	0.0452189	−	0.0254691i
$859$	5.70663			0.194708			0.0973538	−	0.995250i	$-0.468962\pi$
$859$	5.70663			0.194708			0.0973538	+	0.995250i	$0.468962\pi$
$860$	1.71002			0.0583113
$861$	−4.01057	+	4.96446i	−0.136680	+	0.169188i
$862$	0.581742			0.0198142
$863$		−	12.8569i		−	0.437653i	−0.975764	−	0.218827i	$-0.929777\pi$
$863$		−	12.8569i		−	0.437653i	0.975764	−	0.218827i	$-0.0702229\pi$
$864$	−4.54828	+	9.00416i	−0.154736	+	0.306328i
$865$			14.4202i			0.490303i
$866$	−4.51221			−0.153331
$867$	11.7283	+	9.47480i	0.398314	+	0.321781i
$868$		−	10.2970i		−	0.349505i
$869$	−10.7732	+	27.1038i	−0.365456	+	0.919435i
$870$	−1.75833	+	2.17653i	−0.0596129	+	0.0737914i
$871$		−	9.62703i		−	0.326200i
$872$			10.7610i			0.364415i
$873$	0.777564	+	3.61669i	0.0263165	+	0.122407i
$874$	−6.33943			−0.214434
$875$	−1.00000			−0.0338062
$876$	−35.0557	+	43.3935i	−1.18442	+	1.46613i
$877$		−	19.8209i		−	0.669304i	−0.942342	−	0.334652i	$-0.891381\pi$
$877$		−	19.8209i		−	0.669304i	0.942342	−	0.334652i	$-0.108619\pi$
$878$		−	0.792757i		−	0.0267542i
$879$	−26.2377	−	21.1963i	−0.884976	−	0.714934i
$880$	−4.70163	+	11.8286i	−0.158492	+	0.398744i
$881$		−	33.5334i		−	1.12977i	−0.825170	−	0.564885i	$-0.808921\pi$
$881$		−	33.5334i		−	1.12977i	0.825170	−	0.564885i	$-0.191079\pi$
$882$	−0.103888	−	0.483217i	−0.00349810	−	0.0162708i
$883$	−12.4174			−0.417880			−0.208940	−	0.977928i	$-0.567001\pi$
$883$	−12.4174			−0.417880			−0.208940	+	0.977928i	$0.567001\pi$
$884$		−	16.0661i		−	0.540361i
$885$	−0.931619	−	0.752615i	−0.0313160	−	0.0252989i
$886$		−	2.76441i		−	0.0928723i
$887$	49.9984			1.67878			0.839390	−	0.543529i	$-0.182912\pi$
$887$	49.9984			1.67878			0.839390	+	0.543529i	$0.182912\pi$
$888$	10.2333	+	8.26705i	0.343407	+	0.277424i
$889$	2.71890			0.0911889
$890$	1.26828			0.0425128
$891$	−29.8191	+	1.34899i	−0.998978	+	0.0451928i
$892$	6.23110			0.208633
$893$	13.1985			0.441671
$894$	−1.02944	−	0.831640i	−0.0344296	−	0.0278142i
$895$	1.78301			0.0595994
$896$			5.09466i			0.170201i
$897$	14.9636	+	12.0884i	0.499620	+	0.403621i
$898$		−	0.656353i		−	0.0219028i
$899$	−51.1773			−1.70686
$900$	1.24403	+	5.78635i	0.0414675	+	0.192878i
$901$		−	33.4452i		−	1.11422i
$902$	−1.87101	−	0.743686i	−0.0622978	−	0.0247620i
$903$	1.16783	+	0.943439i	0.0388629	+	0.0313957i
$904$		−	12.2349i		−	0.406925i
$905$			13.6953i			0.455248i
$906$	0.631951	−	0.782256i	0.0209952	−	0.0259887i
$907$	46.5466			1.54555			0.772777	−	0.634677i	$-0.218867\pi$
$907$	46.5466			1.54555			0.772777	+	0.634677i	$0.218867\pi$
$908$	31.0221			1.02950
$909$	8.02162	+	37.3111i	0.266060	+	1.23753i
$910$		−	0.264630i		−	0.00877240i
$911$			1.80728i			0.0598778i	0.999552	+	0.0299389i	$0.00953127\pi$
$911$			1.80728i			0.0598778i	−0.999552	+	0.0299389i	$0.990469\pi$
$912$	−23.2466	+	28.7756i	−0.769770	+	0.952855i
$913$	−7.59449	−	3.01865i	−0.251341	−	0.0999026i
$914$			2.14240i			0.0708643i
$915$	−13.2193	−	10.6793i	−0.437017	−	0.353047i
$916$	−48.6728			−1.60820
$917$		−	10.7410i		−	0.354699i
$918$	1.95694	−	3.87412i	0.0645886	−	0.127865i
$919$		−	37.1521i		−	1.22553i	−0.790264	−	0.612767i	$-0.790056\pi$
$919$		−	37.1521i		−	1.22553i	0.790264	−	0.612767i	$-0.209944\pi$
$920$	4.52577			0.149210
$921$	7.40591	−	9.16735i	0.244033	−	0.302074i
$922$	4.96297			0.163447
$923$	11.8597			0.390368
$924$	−9.87461	+	5.56179i	−0.324851	+	0.182969i
$925$	11.6040			0.381538
$926$	1.12023			0.0368132
$927$	11.7128	+	54.4797i	0.384697	+	1.78935i
$928$	19.0358			0.624880
$929$		−	19.4255i		−	0.637331i	−0.947867	−	0.318666i	$-0.896765\pi$
$929$		−	19.4255i		−	0.637331i	0.947867	−	0.318666i	$-0.103235\pi$
$930$	0.935959	−	1.15857i	0.0306913	−	0.0379910i
$931$		−	5.56494i		−	0.182384i
$932$	16.9656			0.555727
$933$	−8.15535	+	10.0950i	−0.266994	+	0.330497i
$934$		−	2.04554i		−	0.0669322i
$935$	6.21106	−	15.6261i	0.203123	−	0.511030i
$936$	−3.08355	+	0.662943i	−0.100789	+	0.0216690i
$937$		−	41.2993i		−	1.34919i	−0.738189	−	0.674594i	$-0.764319\pi$
$937$		−	41.2993i		−	1.34919i	0.738189	−	0.674594i	$-0.235681\pi$
$938$		−	0.987458i		−	0.0322416i
$939$	−23.6703	−	19.1222i	−0.772450	−	0.624029i
$940$	−4.67907			−0.152614
$941$	22.5567			0.735327			0.367663	−	0.929959i	$-0.380158\pi$
$941$	22.5567			0.735327			0.367663	+	0.929959i	$0.380158\pi$
$942$	−0.768055	−	0.620479i	−0.0250246	−	0.0202163i
$943$		−	25.4775i		−	0.829660i
$944$			2.65373i			0.0863716i
$945$	−2.34281	+	4.63802i	−0.0762116	+	0.150875i
$946$	−0.174943	+	0.440133i	−0.00568790	+	0.0143099i
$947$		−	2.52485i		−	0.0820465i	−0.999158	−	0.0410232i	$-0.986938\pi$
$947$		−	2.52485i		−	0.0820465i	0.999158	−	0.0410232i	$-0.0130618\pi$
$948$	18.8838	−	23.3752i	0.613317	−	0.759190i
$949$	−26.2218			−0.851196
$950$		−	0.916840i		−	0.0297462i
$951$	9.99312	−	12.3699i	0.324049	−	0.401122i
$952$		−	3.31851i		−	0.107554i
$953$	−42.3299			−1.37120			−0.685600	−	0.727979i	$-0.740460\pi$
$953$	−42.3299			−1.37120			−0.685600	+	0.727979i	$0.740460\pi$
$954$	−3.18763	+	0.685319i	−0.103203	+	0.0221880i
$955$	−12.0931			−0.391325
$956$	36.8523			1.19189
$957$	27.6426	+	49.0778i	0.893559	+	1.58646i
$958$	−5.67801			−0.183448
$959$	−13.6590			−0.441073
$960$	8.00650	−	9.91080i	0.258409	−	0.319870i
$961$	−3.75828			−0.121235
$962$			3.07077i			0.0990056i
$963$	−3.09806	−	14.4100i	−0.0998335	−	0.464357i
$964$			32.3596i			1.04223i
$965$	−20.8719			−0.671890
$966$	1.53484	+	1.23993i	0.0493825	+	0.0398940i
$967$		−	49.7060i		−	1.59844i	−0.601040	−	0.799219i	$-0.705247\pi$
$967$		−	49.7060i		−	1.59844i	0.601040	−	0.799219i	$-0.294753\pi$
$968$	−5.23530	−	4.94274i	−0.168269	−	0.158866i
$969$	30.7097	−	38.0138i	0.986537	−	1.22118i
$970$			0.203159i			0.00652303i
$971$		−	9.68747i		−	0.310886i	−0.987845	−	0.155443i	$-0.950320\pi$
$971$		−	9.68747i		−	0.310886i	0.987845	−	0.155443i	$-0.0496804\pi$
$972$	29.7517	+	7.78650i	0.954288	+	0.249752i
$973$	−11.3198			−0.362897
$974$	−1.54337			−0.0494526
$975$	−1.74829	+	2.16411i	−0.0559901	+	0.0693069i
$976$			37.6554i			1.20532i
$977$			6.91978i			0.221384i	0.993855	+	0.110692i	$0.0353066\pi$
$977$			6.91978i			0.221384i	−0.993855	+	0.110692i	$0.964693\pi$
$978$	3.40380	+	2.74978i	0.108842	+	0.0879284i
$979$	9.43061	−	23.7261i	0.301404	−	0.758289i
$980$			1.97286i			0.0630206i
$981$	48.2201	−	10.3670i	1.53955	−	0.330992i
$982$	4.54667			0.145090
$983$			17.5943i			0.561171i	0.959829	+	0.280586i	$0.0905286\pi$
$983$			17.5943i			0.561171i	−0.959829	+	0.280586i	$0.909471\pi$
$984$	3.24943	+	2.62508i	0.103588	+	0.0836844i
$985$			25.5943i			0.815501i
$986$	−8.19032			−0.260833
$987$	−3.19548	−	2.58149i	−0.101713	−	0.0821698i
$988$	−17.6345			−0.561028
$989$	−5.99326			−0.190575
$990$	−1.61658	−	0.271778i	−0.0513784	−	0.00863767i
$991$	44.4537			1.41212			0.706059	−	0.708153i	$-0.250471\pi$
$991$	44.4537			1.41212			0.706059	+	0.708153i	$0.250471\pi$
$992$	−10.1328			−0.321715
$993$	14.9397	+	12.0691i	0.474096	+	0.383002i
$994$	1.21647			0.0385840
$995$			10.9858i			0.348275i
$996$	6.54972	+	5.29123i	0.207536	+	0.167659i
$997$			24.8859i			0.788143i	0.919080	+	0.394071i	$0.128934\pi$
$997$			24.8859i			0.788143i	−0.919080	+	0.394071i	$0.871066\pi$
$998$	−0.992871			−0.0314288
$999$	27.1860	−	53.8197i	0.860126	−	1.70278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.e.1121.20	yes	40
3.2	odd	2		1155.2.l.f.1121.21	yes	40
11.10	odd	2		1155.2.l.f.1121.22	yes	40
33.32	even	2	inner	1155.2.l.e.1121.19	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.19	✓	40	33.32	even	2	inner
1155.2.l.e.1121.20	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.21	yes	40	3.2	odd	2
1155.2.l.f.1121.22	yes	40	11.10	odd	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.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.164753 q^{2} +(1.34733 + 1.08845i) q^{3} -1.97286 q^{4} +1.00000i q^{5} +(0.221976 + 0.179324i) q^{6} -1.00000i q^{7} -0.654539 q^{8} +(0.630571 + 2.93298i) q^{9} +O(q^{10})\)	\(q+0.164753 q^{2} +(1.34733 + 1.08845i) q^{3} -1.97286 q^{4} +1.00000i q^{5} +(0.221976 + 0.179324i) q^{6} -1.00000i q^{7} -0.654539 q^{8} +(0.630571 + 2.93298i) q^{9} +0.164753i q^{10} +(3.08208 + 1.22506i) q^{11} +(-2.65808 - 2.14735i) q^{12} -1.60623i q^{13} -0.164753i q^{14} +(-1.08845 + 1.34733i) q^{15} +3.83788 q^{16} -5.07000 q^{17} +(0.103888 + 0.483217i) q^{18} +5.56494i q^{19} -1.97286i q^{20} +(1.08845 - 1.34733i) q^{21} +(0.507781 + 0.201832i) q^{22} +6.91443i q^{23} +(-0.881877 - 0.712430i) q^{24} -1.00000 q^{25} -0.264630i q^{26} +(-2.34281 + 4.63802i) q^{27} +1.97286i q^{28} +9.80529 q^{29} +(-0.179324 + 0.221976i) q^{30} -5.21936 q^{31} +1.94138 q^{32} +(2.81915 + 5.00523i) q^{33} -0.835296 q^{34} +1.00000 q^{35} +(-1.24403 - 5.78635i) q^{36} -11.6040 q^{37} +0.916840i q^{38} +(1.74829 - 2.16411i) q^{39} -0.654539i q^{40} -3.68468 q^{41} +(0.179324 - 0.221976i) q^{42} +0.866776i q^{43} +(-6.08050 - 2.41687i) q^{44} +(-2.93298 + 0.630571i) q^{45} +1.13917i q^{46} -2.37172i q^{47} +(5.17087 + 4.17732i) q^{48} -1.00000 q^{49} -0.164753 q^{50} +(-6.83094 - 5.51842i) q^{51} +3.16885i q^{52} +6.59669i q^{53} +(-0.385984 + 0.764127i) q^{54} +(-1.22506 + 3.08208i) q^{55} +0.654539i q^{56} +(-6.05714 + 7.49779i) q^{57} +1.61545 q^{58} +0.691458i q^{59} +(2.14735 - 2.65808i) q^{60} +9.81153i q^{61} -0.859904 q^{62} +(2.93298 - 0.630571i) q^{63} -7.35590 q^{64} +1.60623 q^{65} +(0.464463 + 0.824626i) q^{66} +5.99357 q^{67} +10.0024 q^{68} +(-7.52599 + 9.31599i) q^{69} +0.164753 q^{70} +7.38360i q^{71} +(-0.412733 - 1.91975i) q^{72} -16.3251i q^{73} -1.91179 q^{74} +(-1.34733 - 1.08845i) q^{75} -10.9788i q^{76} +(1.22506 - 3.08208i) q^{77} +(0.288036 - 0.356543i) q^{78} +8.79401i q^{79} +3.83788i q^{80} +(-8.20476 + 3.69890i) q^{81} -0.607061 q^{82} -2.46408 q^{83} +(-2.14735 + 2.65808i) q^{84} -5.07000i q^{85} +0.142804i q^{86} +(13.2109 + 10.6725i) q^{87} +(-2.01734 - 0.801850i) q^{88} -7.69808i q^{89} +(-0.483217 + 0.103888i) q^{90} -1.60623 q^{91} -13.6412i q^{92} +(-7.03218 - 5.68099i) q^{93} -0.390748i q^{94} -5.56494 q^{95} +(2.61567 + 2.11309i) q^{96} +1.23311 q^{97} -0.164753 q^{98} +(-1.64961 + 9.81218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

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