LMFDB - Embedded newform 1155.2.l.e.1121.11

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			1121.11
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.e.1121.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80850 q^{2} +(-1.28663 + 1.15956i) q^{3} +1.27068 q^{4} +1.00000i q^{5} +(2.32688 - 2.09707i) q^{6} -1.00000i q^{7} +1.31898 q^{8} +(0.310844 - 2.98385i) q^{9} +O(q^{10})$	\(q-1.80850 q^{2} +(-1.28663 + 1.15956i) q^{3} +1.27068 q^{4} +1.00000i q^{5} +(2.32688 - 2.09707i) q^{6} -1.00000i q^{7} +1.31898 q^{8} +(0.310844 - 2.98385i) q^{9} -1.80850i q^{10} +(-1.44078 + 2.98733i) q^{11} +(-1.63490 + 1.47343i) q^{12} +1.34941i q^{13} +1.80850i q^{14} +(-1.15956 - 1.28663i) q^{15} -4.92673 q^{16} +3.37791 q^{17} +(-0.562161 + 5.39630i) q^{18} -6.55028i q^{19} +1.27068i q^{20} +(1.15956 + 1.28663i) q^{21} +(2.60565 - 5.40260i) q^{22} +0.712889i q^{23} +(-1.69704 + 1.52943i) q^{24} -1.00000 q^{25} -2.44042i q^{26} +(3.06001 + 4.19956i) q^{27} -1.27068i q^{28} +0.481775 q^{29} +(2.09707 + 2.32688i) q^{30} -10.7144 q^{31} +6.27205 q^{32} +(-1.61024 - 5.51427i) q^{33} -6.10895 q^{34} +1.00000 q^{35} +(0.394982 - 3.79152i) q^{36} -7.74452 q^{37} +11.8462i q^{38} +(-1.56473 - 1.73620i) q^{39} +1.31898i q^{40} -4.14472 q^{41} +(-2.09707 - 2.32688i) q^{42} +8.37596i q^{43} +(-1.83076 + 3.79594i) q^{44} +(2.98385 + 0.310844i) q^{45} -1.28926i q^{46} +8.28479i q^{47} +(6.33889 - 5.71284i) q^{48} -1.00000 q^{49} +1.80850 q^{50} +(-4.34612 + 3.91688i) q^{51} +1.71467i q^{52} -12.2763i q^{53} +(-5.53404 - 7.59492i) q^{54} +(-2.98733 - 1.44078i) q^{55} -1.31898i q^{56} +(7.59543 + 8.42779i) q^{57} -0.871291 q^{58} +1.07631i q^{59} +(-1.47343 - 1.63490i) q^{60} -9.12424i q^{61} +19.3770 q^{62} +(-2.98385 - 0.310844i) q^{63} -1.48955 q^{64} -1.34941 q^{65} +(2.91213 + 9.97256i) q^{66} +13.1988 q^{67} +4.29224 q^{68} +(-0.826638 - 0.917226i) q^{69} -1.80850 q^{70} -3.34547i q^{71} +(0.409996 - 3.93564i) q^{72} -8.92255i q^{73} +14.0060 q^{74} +(1.28663 - 1.15956i) q^{75} -8.32330i q^{76} +(2.98733 + 1.44078i) q^{77} +(2.82981 + 3.13992i) q^{78} -17.6143i q^{79} -4.92673i q^{80} +(-8.80675 - 1.85502i) q^{81} +7.49574 q^{82} +0.931766 q^{83} +(1.47343 + 1.63490i) q^{84} +3.37791i q^{85} -15.1479i q^{86} +(-0.619867 + 0.558647i) q^{87} +(-1.90035 + 3.94023i) q^{88} +5.94550i q^{89} +(-5.39630 - 0.562161i) q^{90} +1.34941 q^{91} +0.905854i q^{92} +(13.7855 - 12.4240i) q^{93} -14.9831i q^{94} +6.55028 q^{95} +(-8.06982 + 7.27281i) q^{96} +12.9386 q^{97} +1.80850 q^{98} +(8.46591 + 5.22766i) 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 $

$2$	−1.80850			−1.27880			−0.639402	−	0.768873i	$-0.720818\pi$
$2$	−1.80850			−1.27880			−0.639402	+	0.768873i	$0.720818\pi$
$3$	−1.28663	+	1.15956i	−0.742837	+	0.669472i
$3$	−1.28663	+	1.15956i	−0.742837	+	0.669472i
$4$	1.27068			0.635340
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	2.32688	−	2.09707i	0.949943	−	0.856123i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.31898			0.466329
$9$	0.310844	−	2.98385i	0.103615	−	0.994618i
$10$		−	1.80850i		−	0.571899i
$11$	−1.44078	+	2.98733i	−0.434411	+	0.900715i
$11$	−1.44078	+	2.98733i	−0.434411	+	0.900715i
$12$	−1.63490	+	1.47343i	−0.471954	+	0.425342i
$13$			1.34941i			0.374260i	0.982335	+	0.187130i	$0.0599186\pi$
$13$			1.34941i			0.374260i	−0.982335	+	0.187130i	$0.940081\pi$
$14$			1.80850i			0.483342i
$15$	−1.15956	−	1.28663i	−0.299397	−	0.332207i
$16$	−4.92673			−1.23168
$17$	3.37791			0.819263			0.409631	−	0.912251i	$-0.365657\pi$
$17$	3.37791			0.819263			0.409631	+	0.912251i	$0.365657\pi$
$18$	−0.562161	+	5.39630i	−0.132503	+	1.27192i
$19$		−	6.55028i		−	1.50274i	−0.659883	−	0.751368i	$-0.729394\pi$
$19$		−	6.55028i		−	1.50274i	0.659883	−	0.751368i	$-0.270606\pi$
$20$			1.27068i			0.284132i
$21$	1.15956	+	1.28663i	0.253037	+	0.280766i
$22$	2.60565	−	5.40260i	0.555526	−	1.15184i
$23$			0.712889i			0.148648i	0.997234	+	0.0743239i	$0.0236799\pi$
$23$			0.712889i			0.148648i	−0.997234	+	0.0743239i	$0.976320\pi$
$24$	−1.69704	+	1.52943i	−0.346407	+	0.312194i
$25$	−1.00000			−0.200000
$26$		−	2.44042i		−	0.478605i
$27$	3.06001	+	4.19956i	0.588900	+	0.808206i
$28$		−	1.27068i		−	0.240136i
$29$	0.481775			0.0894634			0.0447317	−	0.998999i	$-0.485757\pi$
$29$	0.481775			0.0894634			0.0447317	+	0.998999i	$0.485757\pi$
$30$	2.09707	+	2.32688i	0.382870	+	0.424828i
$31$	−10.7144			−1.92436			−0.962180	−	0.272413i	$-0.912178\pi$
$31$	−10.7144			−1.92436			−0.962180	+	0.272413i	$0.912178\pi$
$32$	6.27205			1.10875
$33$	−1.61024	−	5.51427i	−0.280307	−	0.959910i
$34$	−6.10895			−1.04768
$35$	1.00000			0.169031
$36$	0.394982	−	3.79152i	0.0658304	−	0.631920i
$37$	−7.74452			−1.27319			−0.636595	−	0.771198i	$-0.719658\pi$
$37$	−7.74452			−1.27319			−0.636595	+	0.771198i	$0.719658\pi$
$38$			11.8462i			1.92170i
$39$	−1.56473	−	1.73620i	−0.250557	−	0.278014i
$40$			1.31898i			0.208549i
$41$	−4.14472			−0.647297			−0.323648	−	0.946177i	$-0.604909\pi$
$41$	−4.14472			−0.647297			−0.323648	+	0.946177i	$0.604909\pi$
$42$	−2.09707	−	2.32688i	−0.323584	−	0.359045i
$43$			8.37596i			1.27732i	0.769488	+	0.638661i	$0.220511\pi$
$43$			8.37596i			1.27732i	−0.769488	+	0.638661i	$0.779489\pi$
$44$	−1.83076	+	3.79594i	−0.275998	+	0.572260i
$45$	2.98385	+	0.310844i	0.444806	+	0.0463378i
$46$		−	1.28926i		−	0.190091i
$47$			8.28479i			1.20846i	0.796810	+	0.604230i	$0.206519\pi$
$47$			8.28479i			1.20846i	−0.796810	+	0.604230i	$0.793481\pi$
$48$	6.33889	−	5.71284i	0.914940	−	0.824577i
$49$	−1.00000			−0.142857
$50$	1.80850			0.255761
$51$	−4.34612	+	3.91688i	−0.608579	+	0.548474i
$52$			1.71467i			0.237782i
$53$		−	12.2763i		−	1.68627i	−0.537699	−	0.843137i	$-0.680706\pi$
$53$		−	12.2763i		−	1.68627i	0.537699	−	0.843137i	$-0.319294\pi$
$54$	−5.53404	−	7.59492i	−0.753087	−	1.03354i
$55$	−2.98733	−	1.44078i	−0.402812	−	0.194274i
$56$		−	1.31898i		−	0.176256i
$57$	7.59543	+	8.42779i	1.00604	+	1.11629i
$58$	−0.871291			−0.114406
$59$			1.07631i			0.140124i	0.997543	+	0.0700620i	$0.0223197\pi$
$59$			1.07631i			0.140124i	−0.997543	+	0.0700620i	$0.977680\pi$
$60$	−1.47343	−	1.63490i	−0.190219	−	0.211064i
$61$		−	9.12424i		−	1.16824i	−0.811668	−	0.584120i	$-0.801440\pi$
$61$		−	9.12424i		−	1.16824i	0.811668	−	0.584120i	$-0.198560\pi$
$62$	19.3770			2.46088
$63$	−2.98385	−	0.310844i	−0.375930	−	0.0391626i
$64$	−1.48955			−0.186193
$65$	−1.34941			−0.167374
$66$	2.91213	+	9.97256i	0.358458	+	1.22754i
$67$	13.1988			1.61248			0.806242	−	0.591585i	$-0.201498\pi$
$67$	13.1988			1.61248			0.806242	+	0.591585i	$0.201498\pi$
$68$	4.29224			0.520510
$69$	−0.826638	−	0.917226i	−0.0995155	−	0.110421i
$70$	−1.80850			−0.216157
$71$		−	3.34547i		−	0.397034i	−0.980097	−	0.198517i	$-0.936388\pi$
$71$		−	3.34547i		−	0.397034i	0.980097	−	0.198517i	$-0.0636125\pi$
$72$	0.409996	−	3.93564i	0.0483185	−	0.463819i
$73$		−	8.92255i		−	1.04431i	−0.852852	−	0.522153i	$-0.825129\pi$
$73$		−	8.92255i		−	1.04431i	0.852852	−	0.522153i	$-0.174871\pi$
$74$	14.0060			1.62816
$75$	1.28663	−	1.15956i	0.148567	−	0.133894i
$76$		−	8.32330i		−	0.954748i
$77$	2.98733	+	1.44078i	0.340438	+	0.164192i
$78$	2.82981	+	3.13992i	0.320413	+	0.355526i
$79$		−	17.6143i		−	1.98177i	−0.134723	−	0.990883i	$-0.543014\pi$
$79$		−	17.6143i		−	1.98177i	0.134723	−	0.990883i	$-0.456986\pi$
$80$		−	4.92673i		−	0.550825i
$81$	−8.80675	−	1.85502i	−0.978528	−	0.206114i
$82$	7.49574			0.827765
$83$	0.931766			0.102275			0.0511373	−	0.998692i	$-0.483715\pi$
$83$	0.931766			0.102275			0.0511373	+	0.998692i	$0.483715\pi$
$84$	1.47343	+	1.63490i	0.160764	+	0.178382i
$85$			3.37791i			0.366385i
$86$		−	15.1479i		−	1.63344i
$87$	−0.619867	+	0.558647i	−0.0664567	+	0.0598932i
$88$	−1.90035	+	3.94023i	−0.202578	+	0.420030i
$89$			5.94550i			0.630222i	0.949055	+	0.315111i	$0.102042\pi$
$89$			5.94550i			0.630222i	−0.949055	+	0.315111i	$0.897958\pi$
$90$	−5.39630	−	0.562161i	−0.568820	−	0.0592570i
$91$	1.34941			0.141457
$92$			0.905854i			0.0944418i
$93$	13.7855	−	12.4240i	1.42949	−	1.28831i
$94$		−	14.9831i		−	1.54538i
$95$	6.55028			0.672044
$96$	−8.06982	+	7.27281i	−0.823622	+	0.742278i
$97$	12.9386			1.31372			0.656859	−	0.754013i	$-0.271885\pi$
$97$	12.9386			1.31372			0.656859	+	0.754013i	$0.271885\pi$
$98$	1.80850			0.182686
$99$	8.46591	+	5.22766i	0.850856	+	0.525399i
$100$	−1.27068			−0.127068
$101$	−4.29671			−0.427539			−0.213769	−	0.976884i	$-0.568574\pi$
$101$	−4.29671			−0.427539			−0.213769	+	0.976884i	$0.568574\pi$
$102$	7.85997	−	7.08369i	0.778253	−	0.701390i
$103$	5.99656			0.590858			0.295429	−	0.955365i	$-0.404537\pi$
$103$	5.99656			0.590858			0.295429	+	0.955365i	$0.404537\pi$
$104$			1.77985i			0.174528i
$105$	−1.28663	+	1.15956i	−0.125562	+	0.113161i
$106$			22.2016i			2.15641i
$107$	−19.4116			−1.87659			−0.938295	−	0.345837i	$-0.887595\pi$
$107$	−19.4116			−1.87659			−0.938295	+	0.345837i	$0.887595\pi$
$108$	3.88829	+	5.33629i	0.374151	+	0.513485i
$109$		−	12.3702i		−	1.18485i	−0.805626	−	0.592424i	$-0.798171\pi$
$109$		−	12.3702i		−	1.18485i	0.805626	−	0.592424i	$-0.201829\pi$
$110$	5.40260	+	2.60565i	0.515118	+	0.248439i
$111$	9.96434	−	8.98023i	0.945773	−	0.852365i
$112$			4.92673i			0.465532i
$113$		−	9.42002i		−	0.886161i	−0.896482	−	0.443080i	$-0.853886\pi$
$113$		−	9.42002i		−	0.886161i	0.896482	−	0.443080i	$-0.146114\pi$
$114$	−13.7364	−	15.2417i	−1.28653	−	1.42751i
$115$	−0.712889			−0.0664773
$116$	0.612181			0.0568396
$117$	4.02645	+	0.419457i	0.372246	+	0.0387788i
$118$		−	1.94651i		−	0.179191i
$119$		−	3.37791i		−	0.309652i
$120$	−1.52943	−	1.69704i	−0.139618	−	0.154918i
$121$	−6.84833	−	8.60816i	−0.622575	−	0.782560i
$122$			16.5012i			1.49395i
$123$	5.33273	−	4.80605i	0.480836	−	0.433347i
$124$	−13.6145			−1.22262
$125$		−	1.00000i		−	0.0894427i
$126$	5.39630	+	0.562161i	0.480741	+	0.0500813i
$127$		−	15.9298i		−	1.41355i	−0.707441	−	0.706773i	$-0.750150\pi$
$127$		−	15.9298i		−	1.41355i	0.707441	−	0.706773i	$-0.249850\pi$
$128$	−9.85025			−0.870647
$129$	−9.71242	−	10.7768i	−0.855131	−	0.948842i
$130$	2.44042			0.214039
$131$	9.25617			0.808715			0.404358	−	0.914601i	$-0.367495\pi$
$131$	9.25617			0.808715			0.404358	+	0.914601i	$0.367495\pi$
$132$	−2.04610	−	7.00686i	−0.178090	−	0.609869i
$133$	−6.55028			−0.567981
$134$	−23.8700			−2.06205
$135$	−4.19956	+	3.06001i	−0.361441	+	0.263364i
$136$	4.45539			0.382046
$137$		−	4.85552i		−	0.414835i	−0.978253	−	0.207418i	$-0.933494\pi$
$137$		−	4.85552i		−	0.414835i	0.978253	−	0.207418i	$-0.0665059\pi$
$138$	1.49498	+	1.65881i	0.127261	+	0.141207i
$139$			8.54162i			0.724490i	0.932083	+	0.362245i	$0.117990\pi$
$139$			8.54162i			0.724490i	−0.932083	+	0.362245i	$0.882010\pi$
$140$	1.27068			0.107392
$141$	−9.60670	−	10.6595i	−0.809030	−	0.897690i
$142$			6.05028i			0.507728i
$143$	−4.03115	−	1.94420i	−0.337102	−	0.162583i
$144$	−1.53144	+	14.7006i	−0.127620	+	1.22505i
$145$			0.481775i			0.0400092i
$146$			16.1365i			1.33546i
$147$	1.28663	−	1.15956i	0.106120	−	0.0956389i
$148$	−9.84079			−0.808908
$149$	6.39327			0.523757			0.261878	−	0.965101i	$-0.415658\pi$
$149$	6.39327			0.523757			0.261878	+	0.965101i	$0.415658\pi$
$150$	−2.32688	+	2.09707i	−0.189989	+	0.171225i
$151$		−	3.08127i		−	0.250750i	−0.992109	−	0.125375i	$-0.959987\pi$
$151$		−	3.08127i		−	0.250750i	0.992109	−	0.125375i	$-0.0400134\pi$
$152$		−	8.63967i		−	0.700770i
$153$	1.05000	−	10.0792i	0.0848875	−	0.814853i
$154$	−5.40260	−	2.60565i	−0.435354	−	0.209969i
$155$		−	10.7144i		−	0.860600i
$156$	−1.98826	−	2.20615i	−0.159189	−	0.176634i
$157$	19.5792			1.56259			0.781297	−	0.624160i	$-0.214559\pi$
$157$	19.5792			1.56259			0.781297	+	0.624160i	$0.214559\pi$
$158$			31.8555i			2.53429i
$159$	14.2351	+	15.7950i	1.12891	+	1.25263i
$160$			6.27205i			0.495849i
$161$	0.712889			0.0561836
$162$	15.9270	+	3.35481i	1.25135	+	0.263579i
$163$	−17.8048			−1.39458			−0.697289	−	0.716790i	$-0.745611\pi$
$163$	−17.8048			−1.39458			−0.697289	+	0.716790i	$0.745611\pi$
$164$	−5.26661			−0.411253
$165$	5.51427	−	1.61024i	0.429285	−	0.125357i
$166$	−1.68510			−0.130789
$167$	−18.4581			−1.42833			−0.714165	−	0.699977i	$-0.753194\pi$
$167$	−18.4581			−1.42833			−0.714165	+	0.699977i	$0.753194\pi$
$168$	1.52943	+	1.69704i	0.117998	+	0.130929i
$169$	11.1791			0.859929
$170$		−	6.10895i		−	0.468535i
$171$	−19.5451	−	2.03611i	−1.49465	−	0.155705i
$172$			10.6432i			0.811533i
$173$	16.0928			1.22351			0.611757	−	0.791046i	$-0.290463\pi$
$173$	16.0928			1.22351			0.611757	+	0.791046i	$0.290463\pi$
$174$	1.12103	−	1.01031i	0.0849851	−	0.0765917i
$175$			1.00000i			0.0755929i
$176$	7.09832	−	14.7178i	0.535056	−	1.10940i
$177$	−1.24805	−	1.38482i	−0.0938091	−	0.104089i
$178$		−	10.7524i		−	0.805930i
$179$		−	6.83897i		−	0.511168i	−0.966787	−	0.255584i	$-0.917732\pi$
$179$		−	6.83897i		−	0.511168i	0.966787	−	0.255584i	$-0.0822678\pi$
$180$	3.79152	+	0.394982i	0.282603	+	0.0294403i
$181$	12.6394			0.939483			0.469741	−	0.882804i	$-0.344347\pi$
$181$	12.6394			0.939483			0.469741	+	0.882804i	$0.344347\pi$
$182$	−2.44042			−0.180896
$183$	10.5801	+	11.7395i	0.782104	+	0.867812i
$184$			0.940286i			0.0693188i
$185$		−	7.74452i		−	0.569388i
$186$	−24.9311	+	22.4688i	−1.82803	+	1.64749i
$187$	−4.86681	+	10.0909i	−0.355896	+	0.737922i
$188$			10.5273i			0.767783i
$189$	4.19956	−	3.06001i	0.305473	−	0.222583i
$190$	−11.8462			−0.859413
$191$		−	2.74904i		−	0.198913i	−0.995042	−	0.0994567i	$-0.968290\pi$
$191$		−	2.74904i		−	0.198913i	0.995042	−	0.0994567i	$-0.0317105\pi$
$192$	1.91650	−	1.72722i	0.138311	−	0.124651i
$193$			10.8177i			0.778678i	0.921095	+	0.389339i	$0.127296\pi$
$193$			10.8177i			0.778678i	−0.921095	+	0.389339i	$0.872704\pi$
$194$	−23.3995			−1.67999
$195$	1.73620	−	1.56473i	0.124332	−	0.112052i
$196$	−1.27068			−0.0907628
$197$	19.8368			1.41332			0.706658	−	0.707555i	$-0.250202\pi$
$197$	19.8368			1.41332			0.706658	+	0.707555i	$0.250202\pi$
$198$	−15.3106	−	9.45423i	−1.08808	−	0.671883i
$199$	−2.67260			−0.189456			−0.0947278	−	0.995503i	$-0.530198\pi$
$199$	−2.67260			−0.189456			−0.0947278	+	0.995503i	$0.530198\pi$
$200$	−1.31898			−0.0932659
$201$	−16.9819	+	15.3047i	−1.19781	+	1.07951i
$202$	7.77061			0.546738
$203$		−	0.481775i		−	0.0338140i
$204$	−5.52253	+	4.97710i	−0.386654	+	0.348467i
$205$		−	4.14472i		−	0.289480i
$206$	−10.8448			−0.755592
$207$	2.12716	+	0.221597i	0.147848	+	0.0154021i
$208$		−	6.64820i		−	0.460970i
$209$	19.5679	+	9.43748i	1.35354	+	0.652804i
$210$	2.32688	−	2.09707i	0.160570	−	0.144711i
$211$		−	5.81643i		−	0.400420i	−0.979753	−	0.200210i	$-0.935838\pi$
$211$		−	5.81643i		−	0.400420i	0.979753	−	0.200210i	$-0.0641624\pi$
$212$		−	15.5992i		−	1.07136i
$213$	3.87927	+	4.30438i	0.265803	+	0.294931i
$214$	35.1059			2.39979
$215$	−8.37596			−0.571235
$216$	4.03609	+	5.53913i	0.274621	+	0.376890i
$217$			10.7144i			0.727340i
$218$			22.3715i			1.51519i
$219$	10.3462	+	11.4800i	0.699133	+	0.775749i
$220$	−3.79594	−	1.83076i	−0.255922	−	0.123430i
$221$			4.55820i			0.306617i
$222$	−18.0205	+	16.2408i	−1.20946	+	1.09001i
$223$	−6.54973			−0.438603			−0.219301	−	0.975657i	$-0.570378\pi$
$223$	−6.54973			−0.438603			−0.219301	+	0.975657i	$0.570378\pi$
$224$		−	6.27205i		−	0.419069i
$225$	−0.310844	+	2.98385i	−0.0207229	+	0.198924i
$226$			17.0361i			1.13323i
$227$	5.43050			0.360435			0.180217	−	0.983627i	$-0.442320\pi$
$227$	5.43050			0.360435			0.180217	+	0.983627i	$0.442320\pi$
$228$	9.65136	+	10.7090i	0.639177	+	0.709222i
$229$	−20.0789			−1.32685			−0.663424	−	0.748243i	$-0.730898\pi$
$229$	−20.0789			−1.32685			−0.663424	+	0.748243i	$0.730898\pi$
$230$	1.28926			0.0850114
$231$	−5.51427	+	1.61024i	−0.362812	+	0.105946i
$232$	0.635451			0.0417194
$233$	−27.7256			−1.81636			−0.908181	−	0.418578i	$-0.862529\pi$
$233$	−27.7256			−1.81636			−0.908181	+	0.418578i	$0.862529\pi$
$234$	−7.28185	−	0.758588i	−0.476029	−	0.0495905i
$235$	−8.28479			−0.540440
$236$			1.36765i			0.0890264i
$237$	20.4249	+	22.6632i	1.32674	+	1.47213i
$238$			6.10895i			0.395985i
$239$	−8.21641			−0.531475			−0.265738	−	0.964045i	$-0.585616\pi$
$239$	−8.21641			−0.531475			−0.265738	+	0.964045i	$0.585616\pi$
$240$	5.71284	+	6.33889i	0.368762	+	0.409174i
$241$		−	16.7068i		−	1.07618i	−0.842888	−	0.538089i	$-0.819146\pi$
$241$		−	16.7068i		−	1.07618i	0.842888	−	0.538089i	$-0.180854\pi$
$242$	12.3852	+	15.5679i	0.796151	+	1.00074i
$243$	13.4821	−	7.82522i	0.864874	−	0.501988i
$244$		−	11.5940i		−	0.742229i
$245$		−	1.00000i		−	0.0638877i
$246$	−9.64425	+	8.69175i	−0.614895	+	0.554166i
$247$	8.83903			0.562414
$248$	−14.1320			−0.897386
$249$	−1.19884	+	1.08044i	−0.0759734	+	0.0684700i
$250$			1.80850i			0.114380i
$251$		−	18.8961i		−	1.19271i	−0.802720	−	0.596356i	$-0.796615\pi$
$251$		−	18.8961i		−	1.19271i	0.802720	−	0.596356i	$-0.203385\pi$
$252$	−3.79152	−	0.394982i	−0.238843	−	0.0248816i
$253$	−2.12964	−	1.02711i	−0.133889	−	0.0645741i
$254$			28.8092i			1.80765i
$255$	−3.91688	−	4.34612i	−0.245285	−	0.272165i
$256$	20.7933			1.29958
$257$		−	13.4096i		−	0.836467i	−0.908339	−	0.418234i	$-0.862649\pi$
$257$		−	13.4096i		−	0.836467i	0.908339	−	0.418234i	$-0.137351\pi$
$258$	17.5649	+	19.4898i	1.09354	+	1.21338i
$259$			7.74452i			0.481221i
$260$	−1.71467			−0.106339
$261$	0.149757	−	1.43755i	0.00926970	−	0.0889818i
$262$	−16.7398			−1.03419
$263$	−31.5525			−1.94561			−0.972806	−	0.231623i	$-0.925596\pi$
$263$	−31.5525			−1.94561			−0.972806	+	0.231623i	$0.925596\pi$
$264$	−2.12387	−	7.27320i	−0.130715	−	0.447634i
$265$	12.2763			0.754125
$266$	11.8462			0.726336
$267$	−6.89416	−	7.64967i	−0.421916	−	0.468152i
$268$	16.7714			1.02448
$269$			20.2967i			1.23751i	0.785584	+	0.618755i	$0.212363\pi$
$269$			20.2967i			1.23751i	−0.785584	+	0.618755i	$0.787637\pi$
$270$	7.59492	−	5.53404i	0.462212	−	0.336791i
$271$			12.2583i			0.744640i	0.928104	+	0.372320i	$0.121438\pi$
$271$			12.2583i			0.744640i	−0.928104	+	0.372320i	$0.878562\pi$
$272$	−16.6420			−1.00907
$273$	−1.73620	+	1.56473i	−0.105080	+	0.0947015i
$274$			8.78122i			0.530493i
$275$	1.44078	−	2.98733i	0.0868821	−	0.180143i
$276$	−1.05039	−	1.16550i	−0.0632261	−	0.0701549i
$277$		−	25.8088i		−	1.55070i	−0.631533	−	0.775349i	$-0.717574\pi$
$277$		−	25.8088i		−	1.55070i	0.631533	−	0.775349i	$-0.282426\pi$
$278$		−	15.4475i		−	0.926481i
$279$	−3.33050	+	31.9701i	−0.199392	+	1.91400i
$280$	1.31898			0.0788240
$281$	−5.43734			−0.324365			−0.162182	−	0.986761i	$-0.551853\pi$
$281$	−5.43734			−0.324365			−0.162182	+	0.986761i	$0.551853\pi$
$282$	17.3737	+	19.2777i	1.03459	+	1.14797i
$283$			1.91108i			0.113602i	0.998386	+	0.0568009i	$0.0180900\pi$
$283$			1.91108i			0.113602i	−0.998386	+	0.0568009i	$0.981910\pi$
$284$		−	4.25101i		−	0.252251i
$285$	−8.42779	+	7.59543i	−0.499219	+	0.449915i
$286$	7.29034	+	3.51610i	0.431087	+	0.207911i
$287$			4.14472i			0.244655i
$288$	1.94963	−	18.7149i	0.114883	−	1.10278i
$289$	−5.58974			−0.328808
$290$		−	0.871291i		−	0.0511640i
$291$	−16.6472	+	15.0031i	−0.975879	+	0.879497i
$292$		−	11.3377i		−	0.663489i
$293$	15.5671			0.909441			0.454721	−	0.890634i	$-0.349739\pi$
$293$	15.5671			0.909441			0.454721	+	0.890634i	$0.349739\pi$
$294$	−2.32688	+	2.09707i	−0.135706	+	0.122303i
$295$	−1.07631			−0.0626654
$296$	−10.2148			−0.593726
$297$	−16.9543	+	3.09065i	−0.983788	+	0.179338i
$298$	−11.5622			−0.669782
$299$	−0.961983			−0.0556329
$300$	1.63490	−	1.47343i	0.0943908	−	0.0850684i
$301$	8.37596			0.482782
$302$			5.57248i			0.320660i
$303$	5.52829	−	4.98229i	0.317592	−	0.286225i
$304$			32.2715i			1.85089i
$305$	9.12424			0.522453
$306$	−1.89893	+	18.2282i	−0.108555	+	1.04204i
$307$			12.6856i			0.724005i	0.932177	+	0.362003i	$0.117907\pi$
$307$			12.6856i			0.724005i	−0.932177	+	0.362003i	$0.882093\pi$
$308$	3.79594	+	1.83076i	0.216294	+	0.104317i
$309$	−7.71536	+	6.95336i	−0.438911	+	0.395563i
$310$			19.3770i			1.10054i
$311$			8.96954i			0.508616i	0.967123	+	0.254308i	$0.0818477\pi$
$311$			8.96954i			0.508616i	−0.967123	+	0.254308i	$0.918152\pi$
$312$	−2.06384	−	2.29001i	−0.116842	−	0.129646i
$313$	−27.8760			−1.57565			−0.787823	−	0.615901i	$-0.788792\pi$
$313$	−27.8760			−1.57565			−0.787823	+	0.615901i	$0.788792\pi$
$314$	−35.4091			−1.99825
$315$	0.310844	−	2.98385i	0.0175141	−	0.168121i
$316$		−	22.3822i		−	1.25909i
$317$		−	6.74310i		−	0.378730i	−0.981907	−	0.189365i	$-0.939357\pi$
$317$		−	6.74310i		−	0.378730i	0.981907	−	0.189365i	$-0.0606430\pi$
$318$	−25.7441	−	28.5653i	−1.44366	−	1.60186i
$319$	−0.694130	+	1.43922i	−0.0388638	+	0.0805810i
$320$		−	1.48955i		−	0.0832682i
$321$	24.9756	−	22.5089i	1.39400	−	1.25632i
$322$	−1.28926			−0.0718477
$323$		−	22.1262i		−	1.23114i
$324$	−11.1906	−	2.35714i	−0.621698	−	0.130952i
$325$		−	1.34941i		−	0.0748520i
$326$	32.2000			1.78339
$327$	14.3440	+	15.9159i	0.793222	+	0.880149i
$328$	−5.46680			−0.301853
$329$	8.28479			0.456755
$330$	−9.97256	+	2.91213i	−0.548971	+	0.160307i
$331$	14.4244			0.792836			0.396418	−	0.918070i	$-0.370253\pi$
$331$	14.4244			0.792836			0.396418	+	0.918070i	$0.370253\pi$
$332$	1.18398			0.0649791
$333$	−2.40733	+	23.1085i	−0.131921	+	1.26634i
$334$	33.3815			1.82655
$335$			13.1988i			0.721125i
$336$	−5.71284	−	6.33889i	−0.311661	−	0.345815i
$337$			4.87912i			0.265782i	0.991131	+	0.132891i	$0.0424261\pi$
$337$			4.87912i			0.265782i	−0.991131	+	0.132891i	$0.957574\pi$
$338$	−20.2174			−1.09968
$339$	10.9231	+	12.1201i	0.593260	+	0.658273i
$340$			4.29224i			0.232779i
$341$	15.4370	−	32.0074i	0.835962	−	1.73330i
$342$	35.3473	+	3.68231i	1.91136	+	0.199117i
$343$			1.00000i			0.0539949i
$344$			11.0477i			0.595652i
$345$	0.917226	−	0.826638i	0.0493818	−	0.0445047i
$346$	−29.1039			−1.56463
$347$	29.4139			1.57902			0.789512	−	0.613736i	$-0.210334\pi$
$347$	29.4139			1.57902			0.789512	+	0.613736i	$0.210334\pi$
$348$	−0.787652	+	0.709861i	−0.0422226	+	0.0380525i
$349$		−	9.49356i		−	0.508178i	−0.967181	−	0.254089i	$-0.918224\pi$
$349$		−	9.49356i		−	0.508178i	0.967181	−	0.254089i	$-0.0817757\pi$
$350$		−	1.80850i		−	0.0966685i
$351$	−5.66695	+	4.12923i	−0.302479	+	0.220402i
$352$	−9.03662	+	18.7367i	−0.481654	+	0.998670i
$353$		−	2.78697i		−	0.148335i	−0.997246	−	0.0741677i	$-0.976370\pi$
$353$		−	2.78697i		−	0.148335i	0.997246	−	0.0741677i	$-0.0236300\pi$
$354$	2.25710	+	2.50445i	0.119964	+	0.133110i
$355$	3.34547			0.177559
$356$			7.55482i			0.400405i
$357$	3.91688	+	4.34612i	0.207304	+	0.230021i
$358$			12.3683i			0.653684i
$359$	−7.84969			−0.414291			−0.207145	−	0.978310i	$-0.566417\pi$
$359$	−7.84969			−0.414291			−0.207145	+	0.978310i	$0.566417\pi$
$360$	3.93564	+	0.409996i	0.207426	+	0.0216087i
$361$	−23.9061			−1.25822
$362$	−22.8585			−1.20141
$363$	18.7929	+	3.13449i	0.986374	+	0.164518i
$364$	1.71467			0.0898733
$365$	8.92255			0.467028
$366$	−19.1341	−	21.2310i	−1.00016	−	1.10976i
$367$	−13.2221			−0.690191			−0.345095	−	0.938568i	$-0.612153\pi$
$367$	−13.2221			−0.690191			−0.345095	+	0.938568i	$0.612153\pi$
$368$		−	3.51222i		−	0.183087i
$369$	−1.28836	+	12.3672i	−0.0670693	+	0.643813i
$370$			14.0060i			0.728136i
$371$	−12.2763			−0.637352
$372$	17.5169	−	15.7869i	0.908209	−	0.818511i
$373$		−	12.5690i		−	0.650796i	−0.945577	−	0.325398i	$-0.894502\pi$
$373$		−	12.5690i		−	0.650796i	0.945577	−	0.325398i	$-0.105498\pi$
$374$	8.80163	−	18.2495i	0.455122	−	0.943658i
$375$	1.15956	+	1.28663i	0.0598794	+	0.0664414i
$376$			10.9275i			0.563541i
$377$			0.650114i			0.0334826i
$378$	−7.59492	+	5.53404i	−0.390640	+	0.284640i
$379$	−5.11078			−0.262523			−0.131262	−	0.991348i	$-0.541903\pi$
$379$	−5.11078			−0.262523			−0.131262	+	0.991348i	$0.541903\pi$
$380$	8.32330			0.426976
$381$	18.4716	+	20.4958i	0.946329	+	1.05003i
$382$			4.97164i			0.254371i
$383$			17.7960i			0.909331i	0.890662	+	0.454666i	$0.150241\pi$
$383$			17.7960i			0.909331i	−0.890662	+	0.454666i	$0.849759\pi$
$384$	12.6736	−	11.4220i	0.646749	−	0.582874i
$385$	−1.44078	+	2.98733i	−0.0734288	+	0.152249i
$386$		−	19.5639i		−	0.995776i
$387$	24.9926	+	2.60361i	1.27045	+	0.132349i
$388$	16.4408			0.834657
$389$		−	20.4353i		−	1.03611i	−0.855347	−	0.518056i	$-0.826656\pi$
$389$		−	20.4353i		−	1.03611i	0.855347	−	0.518056i	$-0.173344\pi$
$390$	−3.13992	+	2.82981i	−0.158996	+	0.143293i
$391$			2.40807i			0.121782i
$392$	−1.31898			−0.0666185
$393$	−11.9093	+	10.7331i	−0.600744	+	0.541412i
$394$	−35.8750			−1.80735
$395$	17.6143			0.886273
$396$	10.7575	+	6.64268i	0.540582	+	0.333807i
$397$	12.9022			0.647541			0.323771	−	0.946136i	$-0.395049\pi$
$397$	12.9022			0.647541			0.323771	+	0.946136i	$0.395049\pi$
$398$	4.83340			0.242277
$399$	8.42779	−	7.59543i	0.421917	−	0.380247i
$400$	4.92673			0.246337
$401$			32.9426i			1.64507i	0.568712	+	0.822537i	$0.307442\pi$
$401$			32.9426i			1.64507i	−0.568712	+	0.822537i	$0.692558\pi$
$402$	30.7119	−	27.6787i	1.53177	−	1.38049i
$403$		−	14.4581i		−	0.720212i
$404$	−5.45974			−0.271632
$405$	1.85502	−	8.80675i	0.0921768	−	0.437611i
$406$			0.871291i			0.0432414i
$407$	11.1581	−	23.1355i	0.553087	−	1.14678i
$408$	−5.73244	+	5.16629i	−0.283798	+	0.255769i
$409$		−	15.0977i		−	0.746535i	−0.927724	−	0.373268i	$-0.878237\pi$
$409$		−	15.0977i		−	0.746535i	0.927724	−	0.373268i	$-0.121763\pi$
$410$			7.49574i			0.370188i
$411$	5.63026	+	6.24727i	0.277720	+	0.308155i
$412$	7.61970			0.375396
$413$	1.07631			0.0529619
$414$	−3.84697	−	0.400759i	−0.189068	−	0.0196962i
$415$			0.931766i			0.0457386i
$416$			8.46359i			0.414962i
$417$	−9.90451	−	10.9899i	−0.485026	−	0.538179i
$418$	−35.3885	−	17.0677i	−1.73091	−	0.834809i
$419$		−	1.01087i		−	0.0493843i	−0.999695	−	0.0246921i	$-0.992139\pi$
$419$		−	1.01087i		−	0.0493843i	0.999695	−	0.0246921i	$-0.00786055\pi$
$420$	−1.63490	+	1.47343i	−0.0797748	+	0.0718959i
$421$	−9.68547			−0.472041			−0.236020	−	0.971748i	$-0.575843\pi$
$421$	−9.68547			−0.472041			−0.236020	+	0.971748i	$0.575843\pi$
$422$			10.5190i			0.512058i
$423$	24.7206	+	2.57527i	1.20196	+	0.125214i
$424$		−	16.1921i		−	0.786359i
$425$	−3.37791			−0.163853
$426$	−7.01566	−	7.78448i	−0.339910	−	0.377160i
$427$	−9.12424			−0.441553
$428$	−24.6659			−1.19227
$429$	7.44103	−	2.17288i	0.359256	−	0.104908i
$430$	15.1479			0.730498
$431$	10.2582			0.494120			0.247060	−	0.969000i	$-0.420535\pi$
$431$	10.2582			0.494120			0.247060	+	0.969000i	$0.420535\pi$
$432$	−15.0759	−	20.6901i	−0.725338	−	0.995454i
$433$	−21.8399			−1.04956			−0.524779	−	0.851238i	$-0.675852\pi$
$433$	−21.8399			−1.04956			−0.524779	+	0.851238i	$0.675852\pi$
$434$		−	19.3770i		−	0.930125i
$435$	−0.558647	−	0.619867i	−0.0267851	−	0.0297204i
$436$		−	15.7185i		−	0.752781i
$437$	4.66962			0.223378
$438$	−18.7112	−	20.7617i	−0.894055	−	0.992031i
$439$		−	10.3704i		−	0.494951i	−0.968894	−	0.247476i	$-0.920399\pi$
$439$		−	10.3704i		−	0.494951i	0.968894	−	0.247476i	$-0.0796010\pi$
$440$	−3.94023	−	1.90035i	−0.187843	−	0.0905958i
$441$	−0.310844	+	2.98385i	−0.0148021	+	0.142088i
$442$		−	8.24351i		−	0.392104i
$443$			3.33075i			0.158249i	0.996865	+	0.0791244i	$0.0252124\pi$
$443$			3.33075i			0.158249i	−0.996865	+	0.0791244i	$0.974788\pi$
$444$	12.6615	−	11.4110i	0.600887	−	0.541541i
$445$	−5.94550			−0.281844
$446$	11.8452			0.560887
$447$	−8.22578	+	7.41337i	−0.389066	+	0.350640i
$448$			1.48955i			0.0703744i
$449$		−	10.3191i		−	0.486987i	−0.969903	−	0.243493i	$-0.921707\pi$
$449$		−	10.3191i		−	0.486987i	0.969903	−	0.243493i	$-0.0782934\pi$
$450$	0.562161	−	5.39630i	0.0265005	−	0.254384i
$451$	5.97162	−	12.3817i	0.281192	−	0.583030i
$452$		−	11.9698i		−	0.563013i
$453$	3.57291	+	3.96446i	0.167870	+	0.186266i
$454$	−9.82106			−0.460925
$455$			1.34941i			0.0632615i
$456$	10.0182	+	11.1161i	0.469146	+	0.520558i
$457$			8.34569i			0.390395i	0.980764	+	0.195197i	$0.0625347\pi$
$457$			8.34569i			0.390395i	−0.980764	+	0.195197i	$0.937465\pi$
$458$	36.3127			1.69678
$459$	10.3364	+	14.1857i	0.482464	+	0.662133i
$460$	−0.905854			−0.0422356
$461$	−7.11685			−0.331465			−0.165732	−	0.986171i	$-0.552999\pi$
$461$	−7.11685			−0.331465			−0.165732	+	0.986171i	$0.552999\pi$
$462$	9.97256	−	2.91213i	0.463965	−	0.135484i
$463$	−36.5457			−1.69842			−0.849211	−	0.528054i	$-0.822922\pi$
$463$	−36.5457			−1.69842			−0.849211	+	0.528054i	$0.822922\pi$
$464$	−2.37358			−0.110191
$465$	12.4240	+	13.7855i	0.576148	+	0.639286i
$466$	50.1417			2.32277
$467$		−	11.1574i		−	0.516303i	−0.966104	−	0.258152i	$-0.916887\pi$
$467$		−	11.1574i		−	0.516303i	0.966104	−	0.258152i	$-0.0831134\pi$
$468$	5.11633	+	0.532995i	0.236502	+	0.0246377i
$469$		−	13.1988i		−	0.609462i
$470$	14.9831			0.691117
$471$	−25.1913	+	22.7033i	−1.16075	+	1.04611i
$472$			1.41963i			0.0653440i
$473$	−25.0218	−	12.0679i	−1.15050	−	0.554882i
$474$	−36.9384	−	40.9864i	−1.69664	−	1.88257i
$475$			6.55028i			0.300547i
$476$		−	4.29224i		−	0.196734i
$477$	−36.6305	−	3.81600i	−1.67720	−	0.174722i
$478$	14.8594			0.679653
$479$	−9.15741			−0.418413			−0.209206	−	0.977871i	$-0.567088\pi$
$479$	−9.15741			−0.418413			−0.209206	+	0.977871i	$0.567088\pi$
$480$	−7.27281	−	8.06982i	−0.331957	−	0.368335i
$481$		−	10.4506i		−	0.476505i
$482$			30.2142i			1.37622i
$483$	−0.917226	+	0.826638i	−0.0417352	+	0.0376133i
$484$	−8.70202	−	10.9382i	−0.395547	−	0.497191i
$485$			12.9386i			0.587513i
$486$	−24.3823	+	14.1519i	−1.10600	+	0.641944i
$487$	25.3711			1.14967			0.574837	−	0.818268i	$-0.305066\pi$
$487$	25.3711			1.14967			0.574837	+	0.818268i	$0.305066\pi$
$488$		−	12.0347i		−	0.544784i
$489$	22.9082	−	20.6457i	1.03595	−	0.933631i
$490$			1.80850i			0.0816998i
$491$	−14.8041			−0.668099			−0.334050	−	0.942556i	$-0.608415\pi$
$491$	−14.8041			−0.668099			−0.334050	+	0.942556i	$0.608415\pi$
$492$	6.77619	−	6.10695i	0.305494	−	0.275322i
$493$	1.62739			0.0732940
$494$	−15.9854			−0.719218
$495$	−5.22766	+	8.46591i	−0.234966	+	0.380514i
$496$	52.7869			2.37020
$497$	−3.34547			−0.150065
$498$	2.16810	−	1.95397i	0.0971551	−	0.0875597i
$499$	3.20158			0.143322			0.0716611	−	0.997429i	$-0.477170\pi$
$499$	3.20158			0.143322			0.0716611	+	0.997429i	$0.477170\pi$
$500$		−	1.27068i		−	0.0568265i
$501$	23.7488	−	21.4033i	1.06102	−	0.956227i
$502$			34.1736i			1.52524i
$503$	−9.21332			−0.410802			−0.205401	−	0.978678i	$-0.565850\pi$
$503$	−9.21332			−0.410802			−0.205401	+	0.978678i	$0.565850\pi$
$504$	−3.93564	−	0.409996i	−0.175307	−	0.0182627i
$505$		−	4.29671i		−	0.191201i
$506$	3.85145	+	1.85754i	0.171218	+	0.0825776i
$507$	−14.3834	+	12.9628i	−0.638788	+	0.575699i
$508$		−	20.2417i		−	0.898081i
$509$		−	31.5132i		−	1.39680i	−0.715708	−	0.698400i	$-0.753896\pi$
$509$		−	31.5132i		−	1.39680i	0.715708	−	0.698400i	$-0.246104\pi$
$510$	7.08369	+	7.85997i	0.313671	+	0.348045i
$511$	−8.92255			−0.394710
$512$	−17.9042			−0.791261
$513$	27.5083	−	20.0439i	1.21452	−	0.884961i
$514$			24.2513i			1.06968i
$515$			5.99656i			0.264240i
$516$	−12.3414	−	13.6938i	−0.543298	−	0.602837i
$517$	−24.7494	−	11.9365i	−1.08848	−	0.524968i
$518$		−	14.0060i		−	0.615387i
$519$	−20.7055	+	18.6606i	−0.908872	+	0.819108i
$520$	−1.77985			−0.0780515
$521$		−	20.3217i		−	0.890311i	−0.895453	−	0.445155i	$-0.853148\pi$
$521$		−	20.3217i		−	0.890311i	0.895453	−	0.445155i	$-0.146852\pi$
$522$	−0.270835	+	2.59980i	−0.0118541	+	0.113790i
$523$			31.2911i			1.36827i	0.729358	+	0.684133i	$0.239819\pi$
$523$			31.2911i			1.36827i	−0.729358	+	0.684133i	$0.760181\pi$
$524$	11.7616			0.513809
$525$	−1.15956	−	1.28663i	−0.0506073	−	0.0561532i
$526$	57.0628			2.48806
$527$	−36.1922			−1.57656
$528$	7.93323	+	27.1673i	0.345250	+	1.18231i
$529$	22.4918			0.977904
$530$	−22.2016			−0.964377
$531$	3.21156	+	0.334565i	0.139370	+	0.0145189i
$532$	−8.32330			−0.360861
$533$		−	5.59295i		−	0.242257i
$534$	12.4681	+	13.8344i	0.539548	+	0.598675i
$535$		−	19.4116i		−	0.839236i
$536$	17.4089			0.751949
$537$	7.93019	+	8.79923i	0.342213	+	0.379715i
$538$		−	36.7066i		−	1.58253i
$539$	1.44078	−	2.98733i	0.0620586	−	0.128674i
$540$	−5.33629	+	3.88829i	−0.229638	+	0.167326i
$541$		−	37.7595i		−	1.62341i	−0.584069	−	0.811704i	$-0.698540\pi$
$541$		−	37.7595i		−	1.62341i	0.584069	−	0.811704i	$-0.301460\pi$
$542$		−	22.1692i		−	0.952249i
$543$	−16.2623	+	14.6562i	−0.697883	+	0.628957i
$544$	21.1864			0.908359
$545$	12.3702			0.529880
$546$	3.13992	−	2.82981i	0.134376	−	0.121105i
$547$		−	26.2473i		−	1.12225i	−0.827730	−	0.561126i	$-0.810368\pi$
$547$		−	26.2473i		−	1.12225i	0.827730	−	0.561126i	$-0.189632\pi$
$548$		−	6.16981i		−	0.263561i
$549$	−27.2254	−	2.83621i	−1.16195	−	0.121047i
$550$	−2.60565	+	5.40260i	−0.111105	+	0.230368i
$551$		−	3.15576i		−	0.134440i
$552$	−1.09032	−	1.20980i	−0.0464070	−	0.0514926i
$553$	−17.6143			−0.749037
$554$			46.6752i			1.98304i
$555$	8.98023	+	9.96434i	0.381189	+	0.422963i
$556$			10.8537i			0.460297i
$557$	−21.8124			−0.924219			−0.462109	−	0.886823i	$-0.652907\pi$
$557$	−21.8124			−0.924219			−0.462109	+	0.886823i	$0.652907\pi$
$558$	6.02321	−	57.8181i	0.254983	−	2.44763i
$559$	−11.3026			−0.478051
$560$	−4.92673			−0.208192
$561$	−5.43925	−	18.6267i	−0.229645	−	0.786419i
$562$	9.83344			0.414799
$563$	21.5343			0.907563			0.453782	−	0.891113i	$-0.350075\pi$
$563$	21.5343			0.907563			0.453782	+	0.891113i	$0.350075\pi$
$564$	−12.2070	−	13.5448i	−0.514009	−	0.570338i
$565$	9.42002			0.396303
$566$		−	3.45619i		−	0.145275i
$567$	−1.85502	+	8.80675i	−0.0779036	+	0.369849i
$568$		−	4.41260i		−	0.185148i
$569$	23.3610			0.979345			0.489673	−	0.871906i	$-0.337116\pi$
$569$	23.3610			0.979345			0.489673	+	0.871906i	$0.337116\pi$
$570$	15.2417	−	13.7364i	0.638404	−	0.575353i
$571$		−	3.62849i		−	0.151848i	−0.997114	−	0.0759238i	$-0.975809\pi$
$571$		−	3.62849i		−	0.151848i	0.997114	−	0.0759238i	$-0.0241906\pi$
$572$	−5.12230	−	2.47046i	−0.214174	−	0.103295i
$573$	3.18767	+	3.53700i	0.133167	+	0.147760i
$574$		−	7.49574i		−	0.312866i
$575$		−	0.712889i		−	0.0297295i
$576$	−0.463016	+	4.44459i	−0.0192923	+	0.185191i
$577$	−16.6449			−0.692936			−0.346468	−	0.938062i	$-0.612619\pi$
$577$	−16.6449			−0.692936			−0.346468	+	0.938062i	$0.612619\pi$
$578$	10.1091			0.420481
$579$	−12.5438	−	13.9184i	−0.521303	−	0.578431i
$580$			0.612181i			0.0254194i
$581$		−	0.931766i		−	0.0386562i
$582$	30.1066	−	27.1331i	1.24796	−	1.12470i
$583$	36.6733	+	17.6873i	1.51885	+	0.732535i
$584$		−	11.7687i		−	0.486990i
$585$	−0.419457	+	4.02645i	−0.0173424	+	0.166473i
$586$	−28.1532			−1.16300
$587$			44.5901i			1.84043i	0.391411	+	0.920216i	$0.371987\pi$
$587$			44.5901i			1.84043i	−0.391411	+	0.920216i	$0.628013\pi$
$588$	1.63490	−	1.47343i	0.0674220	−	0.0607631i
$589$			70.1822i			2.89181i
$590$	1.94651			0.0801368
$591$	−25.5227	+	23.0020i	−1.04986	+	0.946176i
$592$	38.1552			1.56817
$593$	14.6115			0.600023			0.300012	−	0.953936i	$-0.403009\pi$
$593$	14.6115			0.600023			0.300012	+	0.953936i	$0.403009\pi$
$594$	30.6619	−	5.58945i	1.25807	−	0.229338i
$595$	3.37791			0.138481
$596$	8.12379			0.332763
$597$	3.43865	−	3.09904i	0.140735	−	0.126835i
$598$	1.73975			0.0711436
$599$			12.6672i			0.517570i	0.965935	+	0.258785i	$0.0833221\pi$
$599$			12.6672i			0.517570i	−0.965935	+	0.258785i	$0.916678\pi$
$600$	1.69704	−	1.52943i	0.0692814	−	0.0624389i
$601$		−	19.5603i		−	0.797880i	−0.916977	−	0.398940i	$-0.869378\pi$
$601$		−	19.5603i		−	0.797880i	0.916977	−	0.398940i	$-0.130622\pi$
$602$	−15.1479			−0.617384
$603$	4.10275	−	39.3831i	0.167077	−	1.60381i
$604$		−	3.91530i		−	0.159311i
$605$	8.60816	−	6.84833i	0.349972	−	0.278424i
$606$	−9.99792	+	9.01049i	−0.406138	+	0.366026i
$607$			5.39318i			0.218903i	0.993992	+	0.109451i	$0.0349094\pi$
$607$			5.39318i			0.218903i	−0.993992	+	0.109451i	$0.965091\pi$
$608$		−	41.0836i		−	1.66616i
$609$	0.558647	+	0.619867i	0.0226375	+	0.0251183i
$610$	−16.5012			−0.668114
$611$	−11.1796			−0.452279
$612$	1.33421	−	12.8074i	0.0539324	−	0.517708i
$613$		−	6.52179i		−	0.263413i	−0.991289	−	0.131706i	$-0.957954\pi$
$613$		−	6.52179i		−	0.263413i	0.991289	−	0.131706i	$-0.0420456\pi$
$614$		−	22.9419i		−	0.925861i
$615$	4.80605	+	5.33273i	0.193799	+	0.215036i
$616$	3.94023	+	1.90035i	0.158756	+	0.0765674i
$617$		−	5.87247i		−	0.236417i	−0.992989	−	0.118208i	$-0.962285\pi$
$617$		−	5.87247i		−	0.236417i	0.992989	−	0.118208i	$-0.0377151\pi$
$618$	13.9532	−	12.5752i	0.561282	−	0.505847i
$619$	35.2371			1.41630			0.708149	−	0.706063i	$-0.249530\pi$
$619$	35.2371			1.41630			0.708149	+	0.706063i	$0.249530\pi$
$620$		−	13.6145i		−	0.546773i
$621$	−2.99382	+	2.18145i	−0.120138	+	0.0875386i
$622$		−	16.2214i		−	0.650420i
$623$	5.94550			0.238201
$624$	7.70899	+	8.55379i	0.308606	+	0.342426i
$625$	1.00000			0.0400000
$626$	50.4139			2.01494
$627$	−36.1200	+	10.5475i	−1.44249	+	0.421228i
$628$	24.8789			0.992777
$629$	−26.1603			−1.04308
$630$	−0.562161	+	5.39630i	−0.0223970	+	0.214994i
$631$	20.5179			0.816803			0.408402	−	0.912802i	$-0.366086\pi$
$631$	20.5179			0.816803			0.408402	+	0.912802i	$0.366086\pi$
$632$		−	23.2329i		−	0.924156i
$633$	6.74450	+	7.48360i	0.268070	+	0.297447i
$634$			12.1949i			0.484322i
$635$	15.9298			0.632157
$636$	18.0882	+	20.0704i	0.717243	+	0.795843i
$637$		−	1.34941i		−	0.0534657i
$638$	1.25534	−	2.60284i	0.0496992	−	0.103047i
$639$	−9.98238	−	1.03992i	−0.394897	−	0.0411385i
$640$		−	9.85025i		−	0.389365i
$641$			28.0444i			1.10769i	0.832620	+	0.553844i	$0.186840\pi$
$641$			28.0444i			1.10769i	−0.832620	+	0.553844i	$0.813160\pi$
$642$	−45.1684	+	40.7074i	−1.78265	+	1.60659i
$643$	1.85589			0.0731890			0.0365945	−	0.999330i	$-0.488349\pi$
$643$	1.85589			0.0731890			0.0365945	+	0.999330i	$0.488349\pi$
$644$	0.905854			0.0356956
$645$	10.7768	−	9.71242i	0.424335	−	0.382426i
$646$			40.0153i			1.57438i
$647$		−	24.4143i		−	0.959826i	−0.877316	−	0.479913i	$-0.840668\pi$
$647$		−	24.4143i		−	0.959826i	0.877316	−	0.479913i	$-0.159332\pi$
$648$	−11.6159	−	2.44674i	−0.456316	−	0.0961168i
$649$	−3.21531	−	1.55073i	−0.126212	−	0.0608714i
$650$			2.44042i			0.0957211i
$651$	−12.4240	−	13.7855i	−0.486934	−	0.540295i
$652$	−22.6242			−0.886031
$653$		−	12.6529i		−	0.495147i	−0.968869	−	0.247574i	$-0.920367\pi$
$653$		−	12.6529i		−	0.495147i	0.968869	−	0.247574i	$-0.0796332\pi$
$654$	−25.9411	−	28.7839i	−1.01438	−	1.12554i
$655$			9.25617i			0.361668i
$656$	20.4199			0.797264
$657$	−26.6236	−	2.77352i	−1.03868	−	0.108205i
$658$	−14.9831			−0.584100
$659$	−35.4674			−1.38162			−0.690808	−	0.723038i	$-0.742745\pi$
$659$	−35.4674			−1.38162			−0.690808	+	0.723038i	$0.742745\pi$
$660$	7.00686	−	2.04610i	0.272742	−	0.0796444i
$661$	−18.6166			−0.724100			−0.362050	−	0.932159i	$-0.617923\pi$
$661$	−18.6166			−0.724100			−0.362050	+	0.932159i	$0.617923\pi$
$662$	−26.0865			−1.01388
$663$	−5.28550	−	5.86472i	−0.205272	−	0.227767i
$664$	1.22898			0.0476936
$665$		−	6.55028i		−	0.254009i
$666$	4.35367	−	41.7918i	0.168701	−	1.61940i
$667$			0.343452i			0.0132985i
$668$	−23.4543			−0.907475
$669$	8.42710	−	7.59481i	0.325810	−	0.293632i
$670$		−	23.8700i		−	0.922178i
$671$	27.2572	+	13.1460i	1.05225	+	0.507495i
$672$	7.27281	+	8.06982i	0.280555	+	0.311300i
$673$			34.4372i			1.32746i	0.747974	+	0.663728i	$0.231027\pi$
$673$			34.4372i			1.32746i	−0.747974	+	0.663728i	$0.768973\pi$
$674$		−	8.82389i		−	0.339884i
$675$	−3.06001	−	4.19956i	−0.117780	−	0.161641i
$676$	14.2050			0.546347
$677$	20.8411			0.800990			0.400495	−	0.916299i	$-0.368838\pi$
$677$	20.8411			0.800990			0.400495	+	0.916299i	$0.368838\pi$
$678$	−19.7544	−	21.9192i	−0.758663	−	0.841803i
$679$		−	12.9386i		−	0.496539i
$680$			4.45539i			0.170856i
$681$	−6.98705	+	6.29698i	−0.267744	+	0.241301i
$682$	−27.9179	+	57.8855i	−1.06903	+	2.21655i
$683$			9.02849i			0.345466i	0.984969	+	0.172733i	$0.0552597\pi$
$683$			9.02849i			0.345466i	−0.984969	+	0.172733i	$0.944740\pi$
$684$	−24.8355	−	2.58724i	−0.949609	−	0.0989257i
$685$	4.85552			0.185520
$686$		−	1.80850i		−	0.0690489i
$687$	25.8341	−	23.2826i	0.985633	−	0.888288i
$688$		−	41.2661i		−	1.57326i
$689$	16.5658			0.631105
$690$	−1.65881	+	1.49498i	−0.0631496	+	0.0569128i
$691$	−4.63005			−0.176135			−0.0880677	−	0.996114i	$-0.528069\pi$
$691$	−4.63005			−0.176135			−0.0880677	+	0.996114i	$0.528069\pi$
$692$	20.4488			0.777347
$693$	5.22766	−	8.46591i	0.198582	−	0.321593i
$694$	−53.1952			−2.01926
$695$	−8.54162			−0.324002
$696$	−0.817591	+	0.736843i	−0.0309907	+	0.0279300i
$697$	−14.0005			−0.530306
$698$			17.1691i			0.649861i
$699$	35.6726	−	32.1494i	1.34926	−	1.21600i
$700$			1.27068i			0.0480272i
$701$	−18.0507			−0.681766			−0.340883	−	0.940106i	$-0.610726\pi$
$701$	−18.0507			−0.681766			−0.340883	+	0.940106i	$0.610726\pi$
$702$	10.2487	−	7.46771i	0.386812	−	0.281851i
$703$			50.7287i			1.91327i
$704$	2.14610	−	4.44977i	0.0808843	−	0.167707i
$705$	10.6595	−	9.60670i	0.401459	−	0.361809i
$706$			5.04024i			0.189692i
$707$			4.29671i			0.161594i
$708$	−1.58587	−	1.75966i	−0.0596007	−	0.0661321i
$709$	−20.4768			−0.769023			−0.384512	−	0.923120i	$-0.625630\pi$
$709$	−20.4768			−0.769023			−0.384512	+	0.923120i	$0.625630\pi$
$710$	−6.05028			−0.227063
$711$	−52.5586	−	5.47530i	−1.97110	−	0.205340i
$712$			7.84199i			0.293891i
$713$		−	7.63817i		−	0.286052i
$714$	−7.08369	−	7.85997i	−0.265101	−	0.294152i
$715$	1.94420	−	4.03115i	0.0727091	−	0.150756i
$716$		−	8.69013i		−	0.324765i
$717$	10.5715	−	9.52742i	0.394800	−	0.355808i
$718$	14.1962			0.529796
$719$			0.347625i			0.0129642i	0.999979	+	0.00648211i	$0.00206334\pi$
$719$			0.347625i			0.0129642i	−0.999979	+	0.00648211i	$0.997937\pi$
$720$	−14.7006	−	1.53144i	−0.547861	−	0.0570735i
$721$		−	5.99656i		−	0.223323i
$722$	43.2342			1.60901
$723$	19.3725	+	21.4955i	0.720471	+	0.799426i
$724$	16.0607			0.596890
$725$	−0.481775			−0.0178927
$726$	−33.9871	−	5.66874i	−1.26138	−	0.210387i
$727$	−21.6203			−0.801852			−0.400926	−	0.916110i	$-0.631312\pi$
$727$	−21.6203			−0.801852			−0.400926	+	0.916110i	$0.631312\pi$
$728$	1.77985			0.0659656
$729$	−8.27264	+	25.7014i	−0.306394	+	0.951905i
$730$	−16.1365			−0.597237
$731$			28.2932i			1.04646i
$732$	13.4439	+	14.9172i	0.496901	+	0.551355i
$733$			11.3107i			0.417771i	0.977940	+	0.208886i	$0.0669836\pi$
$733$			11.3107i			0.417771i	−0.977940	+	0.208886i	$0.933016\pi$
$734$	23.9123			0.882618
$735$	1.15956	+	1.28663i	0.0427710	+	0.0474581i
$736$			4.47128i			0.164813i
$737$	−19.0165	+	39.4291i	−0.700480	+	1.45239i
$738$	2.33000	−	22.3662i	0.0857685	−	0.823310i
$739$		−	24.7765i		−	0.911418i	−0.890129	−	0.455709i	$-0.849386\pi$
$739$		−	24.7765i		−	0.911418i	0.890129	−	0.455709i	$-0.150614\pi$
$740$		−	9.84079i		−	0.361755i
$741$	−11.3726	+	10.2494i	−0.417782	+	0.376521i
$742$	22.2016			0.815048
$743$	−0.875821			−0.0321308			−0.0160654	−	0.999871i	$-0.505114\pi$
$743$	−0.875821			−0.0321308			−0.0160654	+	0.999871i	$0.505114\pi$
$744$	18.1827	−	16.3869i	0.666612	−	0.600775i
$745$			6.39327i			0.234231i
$746$			22.7310i			0.832240i
$747$	0.289633	−	2.78025i	0.0105971	−	0.101724i
$748$	−6.18415	+	12.8223i	−0.226115	+	0.468831i
$749$			19.4116i			0.709284i
$750$	−2.09707	−	2.32688i	−0.0765740	−	0.0849655i
$751$	−10.5229			−0.383986			−0.191993	−	0.981396i	$-0.561495\pi$
$751$	−10.5229			−0.383986			−0.191993	+	0.981396i	$0.561495\pi$
$752$		−	40.8169i		−	1.48844i
$753$	21.9112	+	24.3123i	0.798487	+	0.885991i
$754$		−	1.17573i		−	0.0428176i
$755$	3.08127			0.112139
$756$	5.33629	−	3.88829i	0.194079	−	0.141416i
$757$	−6.26326			−0.227642			−0.113821	−	0.993501i	$-0.536309\pi$
$757$	−6.26326			−0.227642			−0.113821	+	0.993501i	$0.536309\pi$
$758$	9.24286			0.335716
$759$	3.93106	−	1.14792i	0.142688	−	0.0416670i
$760$	8.63967			0.313394
$761$	−18.5137			−0.671122			−0.335561	−	0.942018i	$-0.608926\pi$
$761$	−18.5137			−0.671122			−0.335561	+	0.942018i	$0.608926\pi$
$762$	−33.4059	−	37.0668i	−1.21017	−	1.34279i
$763$	−12.3702			−0.447830
$764$		−	3.49314i		−	0.126378i
$765$	10.0792	+	1.05000i	0.364413	+	0.0379629i
$766$		−	32.1840i		−	1.16286i
$767$	−1.45239			−0.0524429
$768$	−26.7533	+	24.1111i	−0.965377	+	0.870033i
$769$		−	3.80905i		−	0.137358i	−0.997639	−	0.0686789i	$-0.978122\pi$
$769$		−	3.80905i		−	0.137358i	0.997639	−	0.0686789i	$-0.0218784\pi$
$770$	2.60565	−	5.40260i	0.0939010	−	0.194696i
$771$	15.5492	+	17.2532i	0.559992	+	0.621359i
$772$			13.7459i			0.494725i
$773$		−	9.88973i		−	0.355709i	−0.984057	−	0.177854i	$-0.943084\pi$
$773$		−	9.88973i		−	0.355709i	0.984057	−	0.177854i	$-0.0569156\pi$
$774$	−45.1992	−	4.70864i	−1.62465	−	0.169248i
$775$	10.7144			0.384872
$776$	17.0658			0.612625
$777$	−8.98023	−	9.96434i	−0.322164	−	0.357469i
$778$			36.9573i			1.32498i
$779$			27.1491i			0.972716i
$780$	2.20615	−	1.98826i	0.0789929	−	0.0711913i
$781$	9.99402	+	4.82007i	0.357614	+	0.172476i
$782$		−	4.35501i		−	0.155735i
$783$	1.47424	+	2.02324i	0.0526850	+	0.0723048i
$784$	4.92673			0.175955
$785$			19.5792i			0.698813i
$786$	21.5380	−	19.4108i	0.768233	−	0.692360i
$787$		−	0.716991i		−	0.0255580i	−0.999918	−	0.0127790i	$-0.995932\pi$
$787$		−	0.716991i		−	0.0255580i	0.999918	−	0.0127790i	$-0.00406779\pi$
$788$	25.2063			0.897936
$789$	40.5965	−	36.5870i	1.44527	−	1.30253i
$790$	−31.8555			−1.13337
$791$	−9.42002			−0.334937
$792$	11.1663	+	6.89517i	0.396779	+	0.245009i
$793$	12.3124			0.437225
$794$	−23.3336			−0.828078
$795$	−15.7950	+	14.2351i	−0.560192	+	0.504865i
$796$	−3.39602			−0.120369
$797$			21.1338i			0.748598i	0.927308	+	0.374299i	$0.122117\pi$
$797$			21.1338i			0.748598i	−0.927308	+	0.374299i	$0.877883\pi$
$798$	−15.2417	+	13.7364i	−0.539550	+	0.486262i
$799$			27.9852i			0.990047i
$800$	−6.27205			−0.221750
$801$	17.7405	+	1.84812i	0.626830	+	0.0653001i
$802$		−	59.5767i		−	2.10373i
$803$	26.6546	+	12.8554i	0.940622	+	0.453657i
$804$	−21.5786	+	19.4474i	−0.761018	+	0.685857i
$805$			0.712889i			0.0251260i
$806$			26.1476i			0.921009i
$807$	−23.5352	−	26.1143i	−0.828478	−	0.919268i
$808$	−5.66727			−0.199374
$809$	−34.1717			−1.20141			−0.600706	−	0.799470i	$-0.705114\pi$
$809$	−34.1717			−1.20141			−0.600706	+	0.799470i	$0.705114\pi$
$810$	−3.35481	+	15.9270i	−0.117876	+	0.559619i
$811$		−	14.1555i		−	0.497066i	−0.968623	−	0.248533i	$-0.920052\pi$
$811$		−	14.1555i		−	0.497066i	0.968623	−	0.248533i	$-0.0799484\pi$
$812$		−	0.612181i		−	0.0214834i
$813$	−14.2143	−	15.7719i	−0.498516	−	0.553146i
$814$	−20.1795	+	41.8405i	−0.707290	+	1.46651i
$815$		−	17.8048i		−	0.623675i
$816$	21.4122	−	19.2974i	0.749577	−	0.675546i
$817$	54.8648			1.91948
$818$			27.3043i			0.954672i
$819$	0.419457	−	4.02645i	0.0146570	−	0.140696i
$820$		−	5.26661i		−	0.183918i
$821$	15.1317			0.528102			0.264051	−	0.964509i	$-0.414941\pi$
$821$	15.1317			0.528102			0.264051	+	0.964509i	$0.414941\pi$
$822$	−10.1823	−	11.2982i	−0.355150	−	0.394070i
$823$	4.08410			0.142363			0.0711815	−	0.997463i	$-0.477323\pi$
$823$	4.08410			0.142363			0.0711815	+	0.997463i	$0.477323\pi$
$824$	7.90933			0.275534
$825$	1.61024	+	5.51427i	0.0560614	+	0.191982i
$826$	−1.94651			−0.0677279
$827$	−17.9866			−0.625457			−0.312728	−	0.949843i	$-0.601243\pi$
$827$	−17.9866			−0.625457			−0.312728	+	0.949843i	$0.601243\pi$
$828$	2.70293	+	0.281579i	0.0939334	+	0.00978554i
$829$	44.2697			1.53755			0.768776	−	0.639518i	$-0.220866\pi$
$829$	44.2697			1.53755			0.768776	+	0.639518i	$0.220866\pi$
$830$		−	1.68510i		−	0.0584907i
$831$	29.9268	+	33.2064i	1.03815	+	1.15192i
$832$		−	2.01002i		−	0.0696847i
$833$	−3.37791			−0.117038
$834$	17.9123	+	19.8753i	0.620253	+	0.688225i
$835$		−	18.4581i		−	0.638769i
$836$	24.8645	+	11.9920i	0.859956	+	0.414752i
$837$	−32.7862	−	44.9957i	−1.13326	−	1.55528i
$838$			1.82816i			0.0631528i
$839$			50.2576i			1.73509i	0.497362	+	0.867543i	$0.334302\pi$
$839$			50.2576i			1.73509i	−0.497362	+	0.867543i	$0.665698\pi$
$840$	−1.69704	+	1.52943i	−0.0585534	+	0.0527705i
$841$	−28.7679			−0.991996
$842$	17.5162			0.603648
$843$	6.99586	−	6.30492i	0.240950	−	0.217153i
$844$		−	7.39081i		−	0.254402i
$845$			11.1791i			0.384572i
$846$	−44.7072	−	4.65739i	−1.53707	−	0.160124i
$847$	−8.60816	+	6.84833i	−0.295780	+	0.235311i
$848$			60.4818i			2.07696i
$849$	−2.21601	−	2.45886i	−0.0760533	−	0.0843877i
$850$	6.10895			0.209535
$851$		−	5.52098i		−	0.189257i
$852$	4.92930	+	5.46949i	0.168875	+	0.187382i
$853$			36.9562i			1.26536i	0.774415	+	0.632678i	$0.218044\pi$
$853$			36.9562i			1.26536i	−0.774415	+	0.632678i	$0.781956\pi$
$854$	16.5012			0.564660
$855$	2.03611	−	19.5451i	0.0696335	−	0.668427i
$856$	−25.6035			−0.875108
$857$	37.9677			1.29695			0.648476	−	0.761235i	$-0.275407\pi$
$857$	37.9677			1.29695			0.648476	+	0.761235i	$0.275407\pi$
$858$	−13.4571	+	3.92966i	−0.459418	+	0.134157i
$859$	−2.10790			−0.0719207			−0.0359604	−	0.999353i	$-0.511449\pi$
$859$	−2.10790			−0.0719207			−0.0359604	+	0.999353i	$0.511449\pi$
$860$	−10.6432			−0.362928
$861$	−4.80605	−	5.33273i	−0.163790	−	0.181739i
$862$	−18.5520			−0.631883
$863$		−	20.1493i		−	0.685890i	−0.939355	−	0.342945i	$-0.888575\pi$
$863$		−	20.1493i		−	0.685890i	0.939355	−	0.342945i	$-0.111425\pi$
$864$	19.1926	+	26.3399i	0.652944	+	0.896100i
$865$			16.0928i			0.547172i
$866$	39.4975			1.34218
$867$	7.19194	−	6.48164i	0.244251	−	0.220128i
$868$			13.6145i			0.462108i
$869$	52.6199	+	25.3783i	1.78501	+	0.860900i
$870$	1.01031	+	1.12103i	0.0342528	+	0.0380065i
$871$			17.8106i			0.603489i
$872$		−	16.3160i		−	0.552529i
$873$	4.02189	−	38.6069i	0.136120	−	1.30665i
$874$	−8.44502			−0.285657
$875$	−1.00000			−0.0338062
$876$	13.1467	+	14.5874i	0.444187	+	0.492864i
$877$			3.77883i			0.127602i	0.997963	+	0.0638011i	$0.0203223\pi$
$877$			3.77883i			0.127602i	−0.997963	+	0.0638011i	$0.979678\pi$
$878$			18.7549i			0.632946i
$879$	−20.0292	+	18.0510i	−0.675567	+	0.608845i
$880$	14.7178	+	7.09832i	0.496137	+	0.239284i
$881$		−	49.3135i		−	1.66141i	−0.556711	−	0.830707i	$-0.687937\pi$
$881$		−	49.3135i		−	1.66141i	0.556711	−	0.830707i	$-0.312063\pi$
$882$	0.562161	−	5.39630i	0.0189290	−	0.181703i
$883$	27.7348			0.933350			0.466675	−	0.884429i	$-0.345452\pi$
$883$	27.7348			0.933350			0.466675	+	0.884429i	$0.345452\pi$
$884$			5.79200i			0.194806i
$885$	1.38482	−	1.24805i	0.0465502	−	0.0419527i
$886$		−	6.02367i		−	0.202369i
$887$	−38.1323			−1.28036			−0.640179	−	0.768225i	$-0.721140\pi$
$887$	−38.1323			−1.28036			−0.640179	+	0.768225i	$0.721140\pi$
$888$	13.1428	−	11.8447i	0.441042	−	0.397483i
$889$	−15.9298			−0.534270
$890$	10.7524			0.360423
$891$	18.2301	−	23.6360i	0.610733	−	0.791837i
$892$	−8.32261			−0.278662
$893$	54.2676			1.81600
$894$	14.8763	−	13.4071i	0.497539	−	0.448400i
$895$	6.83897			0.228601
$896$			9.85025i			0.329074i
$897$	1.23772	−	1.11548i	0.0413262	−	0.0372447i
$898$			18.6620i			0.622760i
$899$	−5.16192			−0.172160
$900$	−0.394982	+	3.79152i	−0.0131661	+	0.126384i
$901$		−	41.4681i		−	1.38150i
$902$	−10.7997	+	22.3923i	−0.359590	+	0.745581i
$903$	−10.7768	+	9.71242i	−0.358629	+	0.323209i
$904$		−	12.4248i		−	0.413243i
$905$			12.6394i			0.420149i
$906$	−6.46162	−	7.16973i	−0.214673	−	0.238198i
$907$	−55.7426			−1.85090			−0.925451	−	0.378868i	$-0.876313\pi$
$907$	−55.7426			−1.85090			−0.925451	+	0.378868i	$0.876313\pi$
$908$	6.90042			0.228998
$909$	−1.33561	+	12.8208i	−0.0442992	+	0.425238i
$910$		−	2.44042i		−	0.0808991i
$911$			2.76244i			0.0915236i	0.998952	+	0.0457618i	$0.0145715\pi$
$911$			2.76244i			0.0915236i	−0.998952	+	0.0457618i	$0.985428\pi$
$912$	−37.4207	−	41.5215i	−1.23912	−	1.37491i
$913$	−1.34247	+	2.78350i	−0.0444292	+	0.0921203i
$914$		−	15.0932i		−	0.499238i
$915$	−11.7395	+	10.5801i	−0.388097	+	0.349767i
$916$	−25.5138			−0.842999
$917$		−	9.25617i		−	0.305666i
$918$	−18.6935	−	25.6549i	−0.616977	−	0.846738i
$919$			17.3325i			0.571745i	0.958268	+	0.285873i	$0.0922835\pi$
$919$			17.3325i			0.571745i	−0.958268	+	0.285873i	$0.907717\pi$
$920$	−0.940286			−0.0310003
$921$	−14.7097	−	16.3217i	−0.484701	−	0.537818i
$922$	12.8708			0.423878
$923$	4.51442			0.148594
$924$	−7.00686	+	2.04610i	−0.230509	+	0.0673118i
$925$	7.74452			0.254638
$926$	66.0929			2.17195
$927$	1.86399	−	17.8928i	0.0612215	−	0.587678i
$928$	3.02172			0.0991927
$929$		−	22.5188i		−	0.738817i	−0.929267	−	0.369409i	$-0.879560\pi$
$929$		−	22.5188i		−	0.738817i	0.929267	−	0.369409i	$-0.120440\pi$
$930$	−22.4688	−	24.9311i	−0.736780	−	0.817521i
$931$			6.55028i			0.214677i
$932$	−35.2303			−1.15401
$933$	−10.4007	−	11.5405i	−0.340504	−	0.377819i
$934$			20.1782i			0.660251i
$935$	−10.0909	−	4.86681i	−0.330009	−	0.159162i
$936$	5.31080	+	0.553254i	0.173589	+	0.0180837i
$937$			55.0337i			1.79787i	0.438079	+	0.898936i	$0.355659\pi$
$937$			55.0337i			1.79787i	−0.438079	+	0.898936i	$0.644341\pi$
$938$			23.8700i			0.779382i
$939$	35.8662	−	32.3239i	1.17045	−	1.05485i
$940$	−10.5273			−0.343363
$941$	33.0738			1.07817			0.539087	−	0.842250i	$-0.318769\pi$
$941$	33.0738			1.07817			0.539087	+	0.842250i	$0.318769\pi$
$942$	45.5585	−	41.0589i	1.48438	−	1.33777i
$943$		−	2.95473i		−	0.0962192i
$944$		−	5.30271i		−	0.172588i
$945$	3.06001	+	4.19956i	0.0995422	+	0.136612i
$946$	45.2519	+	21.8248i	1.47127	+	0.709585i
$947$			33.1179i			1.07619i	0.842885	+	0.538094i	$0.180855\pi$
$947$			33.1179i			1.07619i	−0.842885	+	0.538094i	$0.819145\pi$
$948$	25.9534	+	28.7976i	0.842929	+	0.935302i
$949$	12.0402			0.390842
$950$		−	11.8462i		−	0.384341i
$951$	7.81902	+	8.67589i	0.253549	+	0.281335i
$952$		−	4.45539i		−	0.144400i
$953$	21.1589			0.685404			0.342702	−	0.939444i	$-0.388658\pi$
$953$	21.1589			0.685404			0.342702	+	0.939444i	$0.388658\pi$
$954$	66.2464	+	6.90124i	2.14481	+	0.223436i
$955$	2.74904			0.0889568
$956$	−10.4404			−0.337667
$957$	−0.775774	−	2.65663i	−0.0250772	−	0.0858768i
$958$	16.5612			0.535068
$959$	−4.85552			−0.156793
$960$	1.72722	+	1.91650i	0.0557457	+	0.0618547i
$961$	83.7981			2.70316
$962$			18.8999i			0.609356i
$963$	−6.03397	+	57.9213i	−0.194442	+	1.86649i
$964$		−	21.2290i		−	0.683739i
$965$	−10.8177			−0.348235
$966$	1.65881	−	1.49498i	0.0533712	−	0.0481001i
$967$		−	56.9616i		−	1.83176i	−0.401451	−	0.915881i	$-0.631494\pi$
$967$		−	56.9616i		−	1.83176i	0.401451	−	0.915881i	$-0.368506\pi$
$968$	−9.03279	−	11.3540i	−0.290325	−	0.364931i
$969$	25.6567	+	28.4683i	0.824211	+	0.914534i
$970$		−	23.3995i		−	0.751313i
$971$			55.4385i			1.77911i	0.456831	+	0.889553i	$0.348984\pi$
$971$			55.4385i			1.77911i	−0.456831	+	0.889553i	$0.651016\pi$
$972$	17.1314	−	9.94334i	0.549489	−	0.318933i
$973$	8.54162			0.273832
$974$	−45.8836			−1.47021
$975$	1.56473	+	1.73620i	0.0501113	+	0.0556029i
$976$			44.9527i			1.43890i
$977$		−	6.80568i		−	0.217733i	−0.994056	−	0.108867i	$-0.965278\pi$
$977$		−	6.80568i		−	0.217733i	0.994056	−	0.108867i	$-0.0347221\pi$
$978$	−41.4295	+	37.3378i	−1.32477	+	1.19393i
$979$	−17.7612	−	8.56614i	−0.567650	−	0.273775i
$980$		−	1.27068i		−	0.0405904i
$981$	−36.9108	−	3.84519i	−1.17847	−	0.122767i
$982$	26.7732			0.854368
$983$			2.20627i			0.0703691i	0.999381	+	0.0351845i	$0.0112019\pi$
$983$			2.20627i			0.0703691i	−0.999381	+	0.0351845i	$0.988798\pi$
$984$	7.03376	−	6.33908i	0.224228	−	0.202082i
$985$			19.8368i			0.632054i
$986$	−2.94314			−0.0937287
$987$	−10.6595	+	9.60670i	−0.339295	+	0.305785i
$988$	11.2316			0.357324
$989$	−5.97113			−0.189871
$990$	9.45423	−	15.3106i	0.300475	−	0.486603i
$991$	13.9961			0.444600			0.222300	−	0.974978i	$-0.428644\pi$
$991$	13.9961			0.444600			0.222300	+	0.974978i	$0.428644\pi$
$992$	−67.2012			−2.13364
$993$	−18.5589	+	16.7259i	−0.588948	+	0.530782i
$994$	6.05028			0.191903
$995$		−	2.67260i		−	0.0847271i
$996$	−1.52334	+	1.37289i	−0.0482689	+	0.0435017i
$997$			12.5561i			0.397655i	0.980035	+	0.198827i	$0.0637133\pi$
$997$			12.5561i			0.397655i	−0.980035	+	0.198827i	$0.936287\pi$
$998$	−5.79006			−0.183281
$999$	−23.6983	−	32.5236i	−0.749782	−	1.02900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.e.1121.11	✓	40
3.2	odd	2		1155.2.l.f.1121.30	yes	40
11.10	odd	2		1155.2.l.f.1121.29	yes	40
33.32	even	2	inner	1155.2.l.e.1121.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.11	✓	40	1.1	even	1	trivial
1155.2.l.e.1121.12	yes	40	33.32	even	2	inner
1155.2.l.f.1121.29	yes	40	11.10	odd	2
1155.2.l.f.1121.30	yes	40	3.2	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)

\(f(q)\)	\(=\)	\(q-1.80850 q^{2} +(-1.28663 + 1.15956i) q^{3} +1.27068 q^{4} +1.00000i q^{5} +(2.32688 - 2.09707i) q^{6} -1.00000i q^{7} +1.31898 q^{8} +(0.310844 - 2.98385i) q^{9} +O(q^{10})\)	\(q-1.80850 q^{2} +(-1.28663 + 1.15956i) q^{3} +1.27068 q^{4} +1.00000i q^{5} +(2.32688 - 2.09707i) q^{6} -1.00000i q^{7} +1.31898 q^{8} +(0.310844 - 2.98385i) q^{9} -1.80850i q^{10} +(-1.44078 + 2.98733i) q^{11} +(-1.63490 + 1.47343i) q^{12} +1.34941i q^{13} +1.80850i q^{14} +(-1.15956 - 1.28663i) q^{15} -4.92673 q^{16} +3.37791 q^{17} +(-0.562161 + 5.39630i) q^{18} -6.55028i q^{19} +1.27068i q^{20} +(1.15956 + 1.28663i) q^{21} +(2.60565 - 5.40260i) q^{22} +0.712889i q^{23} +(-1.69704 + 1.52943i) q^{24} -1.00000 q^{25} -2.44042i q^{26} +(3.06001 + 4.19956i) q^{27} -1.27068i q^{28} +0.481775 q^{29} +(2.09707 + 2.32688i) q^{30} -10.7144 q^{31} +6.27205 q^{32} +(-1.61024 - 5.51427i) q^{33} -6.10895 q^{34} +1.00000 q^{35} +(0.394982 - 3.79152i) q^{36} -7.74452 q^{37} +11.8462i q^{38} +(-1.56473 - 1.73620i) q^{39} +1.31898i q^{40} -4.14472 q^{41} +(-2.09707 - 2.32688i) q^{42} +8.37596i q^{43} +(-1.83076 + 3.79594i) q^{44} +(2.98385 + 0.310844i) q^{45} -1.28926i q^{46} +8.28479i q^{47} +(6.33889 - 5.71284i) q^{48} -1.00000 q^{49} +1.80850 q^{50} +(-4.34612 + 3.91688i) q^{51} +1.71467i q^{52} -12.2763i q^{53} +(-5.53404 - 7.59492i) q^{54} +(-2.98733 - 1.44078i) q^{55} -1.31898i q^{56} +(7.59543 + 8.42779i) q^{57} -0.871291 q^{58} +1.07631i q^{59} +(-1.47343 - 1.63490i) q^{60} -9.12424i q^{61} +19.3770 q^{62} +(-2.98385 - 0.310844i) q^{63} -1.48955 q^{64} -1.34941 q^{65} +(2.91213 + 9.97256i) q^{66} +13.1988 q^{67} +4.29224 q^{68} +(-0.826638 - 0.917226i) q^{69} -1.80850 q^{70} -3.34547i q^{71} +(0.409996 - 3.93564i) q^{72} -8.92255i q^{73} +14.0060 q^{74} +(1.28663 - 1.15956i) q^{75} -8.32330i q^{76} +(2.98733 + 1.44078i) q^{77} +(2.82981 + 3.13992i) q^{78} -17.6143i q^{79} -4.92673i q^{80} +(-8.80675 - 1.85502i) q^{81} +7.49574 q^{82} +0.931766 q^{83} +(1.47343 + 1.63490i) q^{84} +3.37791i q^{85} -15.1479i q^{86} +(-0.619867 + 0.558647i) q^{87} +(-1.90035 + 3.94023i) q^{88} +5.94550i q^{89} +(-5.39630 - 0.562161i) q^{90} +1.34941 q^{91} +0.905854i q^{92} +(13.7855 - 12.4240i) q^{93} -14.9831i q^{94} +6.55028 q^{95} +(-8.06982 + 7.27281i) q^{96} +12.9386 q^{97} +1.80850 q^{98} +(8.46591 + 5.22766i) 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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