LMFDB - Embedded newform 154.2.c.a.153.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(153,154)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("154.153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			153.3
Root			$0.323042 - 0.323042i$ of defining polynomial
Character	$\chi$	$=$	154.153
Dual form			154.2.c.a.153.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +0.646084i q^{3} -1.00000 q^{4} +3.09557i q^{5} +0.646084 q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000i q^{8} +2.58258 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +0.646084i q^{3} -1.00000 q^{4} +3.09557i q^{5} +0.646084 q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000i q^{8} +2.58258 q^{9} +3.09557 q^{10} +(-1.79129 - 2.79129i) q^{11} -0.646084i q^{12} +0.646084 q^{13} +(1.00000 - 2.44949i) q^{14} -2.00000 q^{15} +1.00000 q^{16} -3.74166 q^{17} -2.58258i q^{18} -1.80341 q^{19} -3.09557i q^{20} +(-0.646084 + 1.58258i) q^{21} +(-2.79129 + 1.79129i) q^{22} +4.00000 q^{23} -0.646084 q^{24} -4.58258 q^{25} -0.646084i q^{26} +3.60681i q^{27} +(-2.44949 - 1.00000i) q^{28} +1.58258i q^{29} +2.00000i q^{30} -8.64064i q^{31} -1.00000i q^{32} +(1.80341 - 1.15732i) q^{33} +3.74166i q^{34} +(-3.09557 + 7.58258i) q^{35} -2.58258 q^{36} +3.58258 q^{37} +1.80341i q^{38} +0.417424i q^{39} -3.09557 q^{40} -9.93280 q^{41} +(1.58258 + 0.646084i) q^{42} -7.16515i q^{43} +(1.79129 + 2.79129i) q^{44} +7.99455i q^{45} -4.00000i q^{46} -9.93280i q^{47} +0.646084i q^{48} +(5.00000 + 4.89898i) q^{49} +4.58258i q^{50} -2.41742i q^{51} -0.646084 q^{52} -11.5826 q^{53} +3.60681 q^{54} +(8.64064 - 5.54506i) q^{55} +(-1.00000 + 2.44949i) q^{56} -1.16515i q^{57} +1.58258 q^{58} -0.646084i q^{59} +2.00000 q^{60} +1.93825 q^{61} -8.64064 q^{62} +(6.32599 + 2.58258i) q^{63} -1.00000 q^{64} +2.00000i q^{65} +(-1.15732 - 1.80341i) q^{66} -7.58258 q^{67} +3.74166 q^{68} +2.58434i q^{69} +(7.58258 + 3.09557i) q^{70} +2.00000 q^{71} +2.58258i q^{72} +16.1240 q^{73} -3.58258i q^{74} -2.96073i q^{75} +1.80341 q^{76} +(-1.59645 - 8.62852i) q^{77} +0.417424 q^{78} -4.00000i q^{79} +3.09557i q^{80} +5.41742 q^{81} +9.93280i q^{82} +12.8935 q^{83} +(0.646084 - 1.58258i) q^{84} -11.5826i q^{85} -7.16515 q^{86} -1.02248 q^{87} +(2.79129 - 1.79129i) q^{88} +9.79796i q^{89} +7.99455 q^{90} +(1.58258 + 0.646084i) q^{91} -4.00000 q^{92} +5.58258 q^{93} -9.93280 q^{94} -5.58258i q^{95} +0.646084 q^{96} -8.50579i q^{97} +(4.89898 - 5.00000i) q^{98} +(-4.62614 - 7.20871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 16 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 16 * q^9	$ 8 q - 8 q^{4} - 16 q^{9} + 4 q^{11} + 8 q^{14} - 16 q^{15} + 8 q^{16} - 4 q^{22} + 32 q^{23} + 16 q^{36} - 8 q^{37} - 24 q^{42} - 4 q^{44} + 40 q^{49} - 56 q^{53} - 8 q^{56} - 24 q^{58} + 16 q^{60} - 8 q^{64} - 24 q^{67} + 24 q^{70} + 16 q^{71} + 4 q^{77} + 40 q^{78} + 80 q^{81} + 16 q^{86} + 4 q^{88} - 24 q^{91} - 32 q^{92} + 8 q^{93} - 92 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 16 * q^9 + 4 * q^11 + 8 * q^14 - 16 * q^15 + 8 * q^16 - 4 * q^22 + 32 * q^23 + 16 * q^36 - 8 * q^37 - 24 * q^42 - 4 * q^44 + 40 * q^49 - 56 * q^53 - 8 * q^56 - 24 * q^58 + 16 * q^60 - 8 * q^64 - 24 * q^67 + 24 * q^70 + 16 * q^71 + 4 * q^77 + 40 * q^78 + 80 * q^81 + 16 * q^86 + 4 * q^88 - 24 * q^91 - 32 * q^92 + 8 * q^93 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			0.646084i			0.373017i	0.982453	+	0.186508i	$0.0597171\pi$
$3$			0.646084i			0.373017i	−0.982453	+	0.186508i	$0.940283\pi$
$4$	−1.00000			−0.500000
$5$			3.09557i			1.38438i	0.721714	+	0.692191i	$0.243355\pi$
$5$			3.09557i			1.38438i	−0.721714	+	0.692191i	$0.756645\pi$
$6$	0.646084			0.263763
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$8$			1.00000i			0.353553i
$9$	2.58258			0.860859
$10$	3.09557			0.978906
$11$	−1.79129	−	2.79129i	−0.540094	−	0.841605i
$11$	−1.79129	−	2.79129i	−0.540094	−	0.841605i
$12$		−	0.646084i		−	0.186508i
$13$	0.646084			0.179191			0.0895957	−	0.995978i	$-0.471443\pi$
$13$	0.646084			0.179191			0.0895957	+	0.995978i	$0.471443\pi$
$14$	1.00000	−	2.44949i	0.267261	−	0.654654i
$15$	−2.00000			−0.516398
$16$	1.00000			0.250000
$17$	−3.74166			−0.907485			−0.453743	−	0.891133i	$-0.649911\pi$
$17$	−3.74166			−0.907485			−0.453743	+	0.891133i	$0.649911\pi$
$18$		−	2.58258i		−	0.608719i
$19$	−1.80341			−0.413730			−0.206865	−	0.978370i	$-0.566326\pi$
$19$	−1.80341			−0.413730			−0.206865	+	0.978370i	$0.566326\pi$
$20$		−	3.09557i		−	0.692191i
$21$	−0.646084	+	1.58258i	−0.140987	+	0.345346i
$22$	−2.79129	+	1.79129i	−0.595105	+	0.381904i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$	−0.646084			−0.131881
$25$	−4.58258			−0.916515
$26$		−	0.646084i		−	0.126707i
$27$			3.60681i			0.694131i
$28$	−2.44949	−	1.00000i	−0.462910	−	0.188982i
$29$			1.58258i			0.293877i	0.989146	+	0.146938i	$0.0469419\pi$
$29$			1.58258i			0.293877i	−0.989146	+	0.146938i	$0.953058\pi$
$30$			2.00000i			0.365148i
$31$		−	8.64064i		−	1.55190i	−0.630792	−	0.775952i	$-0.717270\pi$
$31$		−	8.64064i		−	1.55190i	0.630792	−	0.775952i	$-0.282730\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.80341	−	1.15732i	0.313933	−	0.201464i
$34$			3.74166i			0.641689i
$35$	−3.09557	+	7.58258i	−0.523247	+	1.28169i
$36$	−2.58258			−0.430429
$37$	3.58258			0.588972			0.294486	−	0.955656i	$-0.404852\pi$
$37$	3.58258			0.588972			0.294486	+	0.955656i	$0.404852\pi$
$38$			1.80341i			0.292551i
$39$			0.417424i			0.0668414i
$40$	−3.09557			−0.489453
$41$	−9.93280			−1.55124			−0.775622	−	0.631198i	$-0.782564\pi$
$41$	−9.93280			−1.55124			−0.775622	+	0.631198i	$0.782564\pi$
$42$	1.58258	+	0.646084i	0.244197	+	0.0996929i
$43$		−	7.16515i		−	1.09268i	−0.837565	−	0.546338i	$-0.816022\pi$
$43$		−	7.16515i		−	1.09268i	0.837565	−	0.546338i	$-0.183978\pi$
$44$	1.79129	+	2.79129i	0.270047	+	0.420802i
$45$			7.99455i			1.19176i
$46$		−	4.00000i		−	0.589768i
$47$		−	9.93280i		−	1.44885i	−0.689354	−	0.724424i	$-0.742106\pi$
$47$		−	9.93280i		−	1.44885i	0.689354	−	0.724424i	$-0.257894\pi$
$48$			0.646084i			0.0932542i
$49$	5.00000	+	4.89898i	0.714286	+	0.699854i
$50$			4.58258i			0.648074i
$51$		−	2.41742i		−	0.338507i
$52$	−0.646084			−0.0895957
$53$	−11.5826			−1.59099			−0.795495	−	0.605961i	$-0.792789\pi$
$53$	−11.5826			−1.59099			−0.795495	+	0.605961i	$0.792789\pi$
$54$	3.60681			0.490825
$55$	8.64064	−	5.54506i	1.16510	−	0.747696i
$56$	−1.00000	+	2.44949i	−0.133631	+	0.327327i
$57$		−	1.16515i		−	0.154328i
$58$	1.58258			0.207802
$59$		−	0.646084i		−	0.0841129i	−0.999115	−	0.0420565i	$-0.986609\pi$
$59$		−	0.646084i		−	0.0841129i	0.999115	−	0.0420565i	$-0.0133909\pi$
$60$	2.00000			0.258199
$61$	1.93825			0.248168			0.124084	−	0.992272i	$-0.460401\pi$
$61$	1.93825			0.248168			0.124084	+	0.992272i	$0.460401\pi$
$62$	−8.64064			−1.09736
$63$	6.32599	+	2.58258i	0.797000	+	0.325374i
$64$	−1.00000			−0.125000
$65$			2.00000i			0.248069i
$66$	−1.15732	−	1.80341i	−0.142457	−	0.221984i
$67$	−7.58258			−0.926359			−0.463180	−	0.886264i	$-0.653291\pi$
$67$	−7.58258			−0.926359			−0.463180	+	0.886264i	$0.653291\pi$
$68$	3.74166			0.453743
$69$			2.58434i			0.311117i
$70$	7.58258	+	3.09557i	0.906291	+	0.369992i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$			2.58258i			0.304359i
$73$	16.1240			1.88717			0.943583	−	0.331136i	$-0.107432\pi$
$73$	16.1240			1.88717			0.943583	+	0.331136i	$0.107432\pi$
$74$		−	3.58258i		−	0.416466i
$75$		−	2.96073i		−	0.341875i
$76$	1.80341			0.206865
$77$	−1.59645	−	8.62852i	−0.181933	−	0.983311i
$78$	0.417424			0.0472640
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$			3.09557i			0.346096i
$81$	5.41742			0.601936
$82$			9.93280i			1.09689i
$83$	12.8935			1.41525			0.707625	−	0.706589i	$-0.249767\pi$
$83$	12.8935			1.41525			0.707625	+	0.706589i	$0.249767\pi$
$84$	0.646084	−	1.58258i	0.0704935	−	0.172673i
$85$		−	11.5826i		−	1.25631i
$86$	−7.16515			−0.772638
$87$	−1.02248			−0.109621
$88$	2.79129	−	1.79129i	0.297552	−	0.190952i
$89$			9.79796i			1.03858i	0.854598	+	0.519291i	$0.173804\pi$
$89$			9.79796i			1.03858i	−0.854598	+	0.519291i	$0.826196\pi$
$90$	7.99455			0.842700
$91$	1.58258	+	0.646084i	0.165899	+	0.0677280i
$92$	−4.00000			−0.417029
$93$	5.58258			0.578886
$94$	−9.93280			−1.02449
$95$		−	5.58258i		−	0.572760i
$96$	0.646084			0.0659407
$97$		−	8.50579i		−	0.863632i	−0.901962	−	0.431816i	$-0.857873\pi$
$97$		−	8.50579i		−	0.863632i	0.901962	−	0.431816i	$-0.142127\pi$
$98$	4.89898	−	5.00000i	0.494872	−	0.505076i
$99$	−4.62614	−	7.20871i	−0.464944	−	0.724503i
$100$	4.58258			0.458258
$101$	−11.7362			−1.16780			−0.583898	−	0.811827i	$-0.698473\pi$
$101$	−11.7362			−1.16780			−0.583898	+	0.811827i	$0.698473\pi$
$102$	−2.41742			−0.239361
$103$			6.05630i			0.596745i	0.954449	+	0.298373i	$0.0964438\pi$
$103$			6.05630i			0.596745i	−0.954449	+	0.298373i	$0.903556\pi$
$104$			0.646084i			0.0633537i
$105$	−4.89898	−	2.00000i	−0.478091	−	0.195180i
$106$			11.5826i			1.12500i
$107$			17.5826i			1.69977i	0.526967	+	0.849886i	$0.323329\pi$
$107$			17.5826i			1.69977i	−0.526967	+	0.849886i	$0.676671\pi$
$108$		−	3.60681i		−	0.347066i
$109$			17.1652i			1.64412i	0.569398	+	0.822062i	$0.307176\pi$
$109$			17.1652i			1.64412i	−0.569398	+	0.822062i	$0.692824\pi$
$110$	−5.54506	−	8.64064i	−0.528701	−	0.823852i
$111$			2.31464i			0.219696i
$112$	2.44949	+	1.00000i	0.231455	+	0.0944911i
$113$	10.7477			1.01106			0.505531	−	0.862809i	$-0.331297\pi$
$113$	10.7477			1.01106			0.505531	+	0.862809i	$0.331297\pi$
$114$	−1.16515			−0.109126
$115$			12.3823i			1.15465i
$116$		−	1.58258i		−	0.146938i
$117$	1.66856			0.154258
$118$	−0.646084			−0.0594768
$119$	−9.16515	−	3.74166i	−0.840168	−	0.342997i
$120$		−	2.00000i		−	0.182574i
$121$	−4.58258	+	10.0000i	−0.416598	+	0.909091i
$122$		−	1.93825i		−	0.175481i
$123$		−	6.41742i		−	0.578640i
$124$			8.64064i			0.775952i
$125$			1.29217i			0.115575i
$126$	2.58258	−	6.32599i	0.230074	−	0.563564i
$127$		−	3.58258i		−	0.317902i	−0.987286	−	0.158951i	$-0.949189\pi$
$127$		−	3.58258i		−	0.317902i	0.987286	−	0.158951i	$-0.0508112\pi$
$128$			1.00000i			0.0883883i
$129$	4.62929			0.407586
$130$	2.00000			0.175412
$131$	−16.7700			−1.46520			−0.732602	−	0.680657i	$-0.761694\pi$
$131$	−16.7700			−1.46520			−0.732602	+	0.680657i	$0.761694\pi$
$132$	−1.80341	+	1.15732i	−0.156966	+	0.100732i
$133$	−4.41742	−	1.80341i	−0.383039	−	0.156375i
$134$			7.58258i			0.655035i
$135$	−11.1652			−0.960943
$136$		−	3.74166i		−	0.320844i
$137$	−3.16515			−0.270417			−0.135209	−	0.990817i	$-0.543170\pi$
$137$	−3.16515			−0.270417			−0.135209	+	0.990817i	$0.543170\pi$
$138$	2.58434			0.219993
$139$	−15.4779			−1.31282			−0.656408	−	0.754406i	$-0.727925\pi$
$139$	−15.4779			−1.31282			−0.656408	+	0.754406i	$0.727925\pi$
$140$	3.09557	−	7.58258i	0.261624	−	0.640845i
$141$	6.41742			0.540445
$142$		−	2.00000i		−	0.167836i
$143$	−1.15732	−	1.80341i	−0.0967801	−	0.150808i
$144$	2.58258			0.215215
$145$	−4.89898			−0.406838
$146$		−	16.1240i		−	1.33443i
$147$	−3.16515	+	3.23042i	−0.261057	+	0.266440i
$148$	−3.58258			−0.294486
$149$		−	14.0000i		−	1.14692i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$		−	14.0000i		−	1.14692i	0.819232	−	0.573462i	$-0.194400\pi$
$150$	−2.96073			−0.241742
$151$			5.58258i			0.454304i	0.973859	+	0.227152i	$0.0729414\pi$
$151$			5.58258i			0.454304i	−0.973859	+	0.227152i	$0.927059\pi$
$152$		−	1.80341i		−	0.146276i
$153$	−9.66311			−0.781216
$154$	−8.62852	+	1.59645i	−0.695306	+	0.128646i
$155$	26.7477			2.14843
$156$		−	0.417424i		−	0.0334207i
$157$		−	13.1632i		−	1.05054i	−0.850936	−	0.525270i	$-0.823964\pi$
$157$		−	13.1632i		−	1.05054i	0.850936	−	0.525270i	$-0.176036\pi$
$158$	−4.00000			−0.318223
$159$		−	7.48331i		−	0.593465i
$160$	3.09557			0.244727
$161$	9.79796	+	4.00000i	0.772187	+	0.315244i
$162$		−	5.41742i		−	0.425633i
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	9.93280			0.775622
$165$	3.58258	+	5.58258i	0.278903	+	0.434603i
$166$		−	12.8935i		−	1.00073i
$167$	1.29217			0.0999909			0.0499955	−	0.998749i	$-0.484079\pi$
$167$	1.29217			0.0999909			0.0499955	+	0.998749i	$0.484079\pi$
$168$	−1.58258	−	0.646084i	−0.122098	−	0.0498464i
$169$	−12.5826			−0.967890
$170$	−11.5826			−0.888343
$171$	−4.65743			−0.356163
$172$			7.16515i			0.546338i
$173$	10.7137			0.814550			0.407275	−	0.913306i	$-0.366479\pi$
$173$	10.7137			0.814550			0.407275	+	0.913306i	$0.366479\pi$
$174$			1.02248i			0.0775137i
$175$	−11.2250	−	4.58258i	−0.848528	−	0.346410i
$176$	−1.79129	−	2.79129i	−0.135023	−	0.210401i
$177$	0.417424			0.0313755
$178$	9.79796			0.734388
$179$	11.1652			0.834523			0.417261	−	0.908787i	$-0.362990\pi$
$179$	11.1652			0.834523			0.417261	+	0.908787i	$0.362990\pi$
$180$		−	7.99455i		−	0.595879i
$181$			5.41022i			0.402138i	0.979577	+	0.201069i	$0.0644416\pi$
$181$			5.41022i			0.402138i	−0.979577	+	0.201069i	$0.935558\pi$
$182$	0.646084	−	1.58258i	0.0478909	−	0.117308i
$183$			1.25227i			0.0925707i
$184$			4.00000i			0.294884i
$185$			11.0901i			0.815362i
$186$		−	5.58258i		−	0.409334i
$187$	6.70239	+	10.4440i	0.490127	+	0.763744i
$188$			9.93280i			0.724424i
$189$	−3.60681	+	8.83485i	−0.262357	+	0.642641i
$190$	−5.58258			−0.405003
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		−	0.646084i		−	0.0466271i
$193$			16.3303i			1.17548i	0.809050	+	0.587740i	$0.199982\pi$
$193$			16.3303i			1.17548i	−0.809050	+	0.587740i	$0.800018\pi$
$194$	−8.50579			−0.610680
$195$	−1.29217			−0.0925340
$196$	−5.00000	−	4.89898i	−0.357143	−	0.349927i
$197$			8.74773i			0.623250i	0.950205	+	0.311625i	$0.100873\pi$
$197$			8.74773i			0.623250i	−0.950205	+	0.311625i	$0.899127\pi$
$198$	−7.20871	+	4.62614i	−0.512301	+	0.328765i
$199$		−	9.66311i		−	0.685000i	−0.939518	−	0.342500i	$-0.888726\pi$
$199$		−	9.66311i		−	0.685000i	0.939518	−	0.342500i	$-0.111274\pi$
$200$		−	4.58258i		−	0.324037i
$201$		−	4.89898i		−	0.345547i
$202$			11.7362i			0.825757i
$203$	−1.58258	+	3.87650i	−0.111075	+	0.272077i
$204$			2.41742i			0.169254i
$205$		−	30.7477i		−	2.14751i
$206$	6.05630			0.421963
$207$	10.3303			0.718006
$208$	0.646084			0.0447979
$209$	3.23042	+	5.03383i	0.223453	+	0.348197i
$210$	−2.00000	+	4.89898i	−0.138013	+	0.338062i
$211$			16.7477i			1.15296i	0.817111	+	0.576481i	$0.195574\pi$
$211$			16.7477i			1.15296i	−0.817111	+	0.576481i	$0.804426\pi$
$212$	11.5826			0.795495
$213$			1.29217i			0.0885379i
$214$	17.5826			1.20192
$215$	22.1803			1.51268
$216$	−3.60681			−0.245412
$217$	8.64064	−	21.1652i	0.586565	−	1.43678i
$218$	17.1652			1.16257
$219$			10.4174i			0.703944i
$220$	−8.64064	+	5.54506i	−0.582552	+	0.373848i
$221$	−2.41742			−0.162614
$222$	2.31464			0.155349
$223$			16.1240i			1.07974i	0.841749	+	0.539870i	$0.181527\pi$
$223$			16.1240i			1.07974i	−0.841749	+	0.539870i	$0.818473\pi$
$224$	1.00000	−	2.44949i	0.0668153	−	0.163663i
$225$	−11.8348			−0.788990
$226$		−	10.7477i		−	0.714928i
$227$	−0.511238			−0.0339321			−0.0169660	−	0.999856i	$-0.505401\pi$
$227$	−0.511238			−0.0339321			−0.0169660	+	0.999856i	$0.505401\pi$
$228$			1.16515i			0.0771640i
$229$		−	5.67991i		−	0.375339i	−0.982232	−	0.187669i	$-0.939907\pi$
$229$		−	5.67991i		−	0.375339i	0.982232	−	0.187669i	$-0.0600934\pi$
$230$	12.3823			0.816464
$231$	5.57475	−	1.03144i	0.366791	−	0.0678639i
$232$	−1.58258			−0.103901
$233$		−	27.1652i		−	1.77965i	−0.456304	−	0.889824i	$-0.650827\pi$
$233$		−	27.1652i		−	1.77965i	0.456304	−	0.889824i	$-0.349173\pi$
$234$		−	1.66856i		−	0.109077i
$235$	30.7477			2.00576
$236$			0.646084i			0.0420565i
$237$	2.58434			0.167871
$238$	−3.74166	+	9.16515i	−0.242536	+	0.594089i
$239$		−	8.41742i		−	0.544478i	−0.962230	−	0.272239i	$-0.912236\pi$
$239$		−	8.41742i		−	0.544478i	0.962230	−	0.272239i	$-0.0877641\pi$
$240$	−2.00000			−0.129099
$241$	−3.47197			−0.223649			−0.111825	−	0.993728i	$-0.535669\pi$
$241$	−3.47197			−0.223649			−0.111825	+	0.993728i	$0.535669\pi$
$242$	10.0000	+	4.58258i	0.642824	+	0.294579i
$243$			14.3205i			0.918663i
$244$	−1.93825			−0.124084
$245$	−15.1652	+	15.4779i	−0.968866	+	0.988845i
$246$	−6.41742			−0.409160
$247$	−1.16515			−0.0741368
$248$	8.64064			0.548681
$249$			8.33030i			0.527911i
$250$	1.29217			0.0817239
$251$			24.1185i			1.52235i	0.648549	+	0.761173i	$0.275376\pi$
$251$			24.1185i			1.52235i	−0.648549	+	0.761173i	$0.724624\pi$
$252$	−6.32599	−	2.58258i	−0.398500	−	0.162687i
$253$	−7.16515	−	11.1652i	−0.450469	−	0.701947i
$254$	−3.58258			−0.224791
$255$	7.48331			0.468623
$256$	1.00000			0.0625000
$257$		−	4.89898i		−	0.305590i	−0.988258	−	0.152795i	$-0.951173\pi$
$257$		−	4.89898i		−	0.305590i	0.988258	−	0.152795i	$-0.0488274\pi$
$258$		−	4.62929i		−	0.288207i
$259$	8.77548	+	3.58258i	0.545282	+	0.222610i
$260$		−	2.00000i		−	0.124035i
$261$			4.08712i			0.252986i
$262$			16.7700i			1.03606i
$263$		−	8.33030i		−	0.513668i	−0.966455	−	0.256834i	$-0.917321\pi$
$263$		−	8.33030i		−	0.513668i	0.966455	−	0.256834i	$-0.0826794\pi$
$264$	1.15732	+	1.80341i	0.0712283	+	0.110992i
$265$		−	35.8547i		−	2.20254i
$266$	−1.80341	+	4.41742i	−0.110574	+	0.270850i
$267$	−6.33030			−0.387408
$268$	7.58258			0.463180
$269$		−	16.5003i		−	1.00604i	−0.864274	−	0.503022i	$-0.832222\pi$
$269$		−	16.5003i		−	1.00604i	0.864274	−	0.503022i	$-0.167778\pi$
$270$			11.1652i			0.679489i
$271$	−4.89898			−0.297592			−0.148796	−	0.988868i	$-0.547540\pi$
$271$	−4.89898			−0.297592			−0.148796	+	0.988868i	$0.547540\pi$
$272$	−3.74166			−0.226871
$273$	−0.417424	+	1.02248i	−0.0252637	+	0.0618831i
$274$			3.16515i			0.191214i
$275$	8.20871	+	12.7913i	0.495004	+	0.771344i
$276$		−	2.58434i		−	0.155559i
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$			15.4779i			0.928301i
$279$		−	22.3151i		−	1.33597i
$280$	−7.58258	−	3.09557i	−0.453146	−	0.184996i
$281$			11.1652i			0.666057i	0.942917	+	0.333029i	$0.108071\pi$
$281$			11.1652i			0.666057i	−0.942917	+	0.333029i	$0.891929\pi$
$282$		−	6.41742i		−	0.382152i
$283$	−18.0622			−1.07369			−0.536843	−	0.843682i	$-0.680383\pi$
$283$	−18.0622			−1.07369			−0.536843	+	0.843682i	$0.680383\pi$
$284$	−2.00000			−0.118678
$285$	3.60681			0.213649
$286$	−1.80341	+	1.15732i	−0.106638	+	0.0684339i
$287$	−24.3303	−	9.93280i	−1.43617	−	0.586315i
$288$		−	2.58258i		−	0.152180i
$289$	−3.00000			−0.176471
$290$			4.89898i			0.287678i
$291$	5.49545			0.322149
$292$	−16.1240			−0.943583
$293$	25.1410			1.46875			0.734376	−	0.678743i	$-0.237475\pi$
$293$	25.1410			1.46875			0.734376	+	0.678743i	$0.237475\pi$
$294$	3.23042	+	3.16515i	0.188402	+	0.184595i
$295$	2.00000			0.116445
$296$			3.58258i			0.208233i
$297$	10.0677	−	6.46084i	0.584184	−	0.374896i
$298$	−14.0000			−0.810998
$299$	2.58434			0.149456
$300$			2.96073i			0.170938i
$301$	7.16515	−	17.5510i	0.412992	−	1.01162i
$302$	5.58258			0.321241
$303$		−	7.58258i		−	0.435608i
$304$	−1.80341			−0.103432
$305$			6.00000i			0.343559i
$306$			9.66311i			0.552403i
$307$	−10.5789			−0.603769			−0.301885	−	0.953344i	$-0.597616\pi$
$307$	−10.5789			−0.603769			−0.301885	+	0.953344i	$0.597616\pi$
$308$	1.59645	+	8.62852i	0.0909664	+	0.491655i
$309$	−3.91288			−0.222596
$310$		−	26.7477i		−	1.51917i
$311$			5.03383i			0.285442i	0.989763	+	0.142721i	$0.0455852\pi$
$311$			5.03383i			0.285442i	−0.989763	+	0.142721i	$0.954415\pi$
$312$	−0.417424			−0.0236320
$313$		−	23.4724i		−	1.32674i	−0.748292	−	0.663370i	$-0.769126\pi$
$313$		−	23.4724i		−	1.32674i	0.748292	−	0.663370i	$-0.230874\pi$
$314$	−13.1632			−0.742844
$315$	−7.99455	+	19.5826i	−0.450442	+	1.10335i
$316$			4.00000i			0.225018i
$317$	9.16515			0.514766			0.257383	−	0.966309i	$-0.417140\pi$
$317$	9.16515			0.514766			0.257383	+	0.966309i	$0.417140\pi$
$318$	−7.48331			−0.419643
$319$	4.41742	−	2.83485i	0.247328	−	0.158721i
$320$		−	3.09557i		−	0.173048i
$321$	−11.3598			−0.634043
$322$	4.00000	−	9.79796i	0.222911	−	0.546019i
$323$	6.74773			0.375454
$324$	−5.41742			−0.300968
$325$	−2.96073			−0.164232
$326$		−	4.00000i		−	0.221540i
$327$	−11.0901			−0.613285
$328$		−	9.93280i		−	0.548447i
$329$	9.93280	−	24.3303i	0.547613	−	1.34137i
$330$	5.58258	−	3.58258i	0.307311	−	0.197214i
$331$	−23.5826			−1.29622			−0.648108	−	0.761549i	$-0.724439\pi$
$331$	−23.5826			−1.29622			−0.648108	+	0.761549i	$0.724439\pi$
$332$	−12.8935			−0.707625
$333$	9.25227			0.507021
$334$		−	1.29217i		−	0.0707043i
$335$		−	23.4724i		−	1.28244i
$336$	−0.646084	+	1.58258i	−0.0352468	+	0.0863366i
$337$			10.8348i			0.590212i	0.955465	+	0.295106i	$0.0953549\pi$
$337$			10.8348i			0.590212i	−0.955465	+	0.295106i	$0.904645\pi$
$338$			12.5826i			0.684402i
$339$			6.94393i			0.377143i
$340$			11.5826i			0.628153i
$341$	−24.1185	+	15.4779i	−1.30609	+	0.838174i
$342$			4.65743i			0.251845i
$343$	7.34847	+	17.0000i	0.396780	+	0.917914i
$344$	7.16515			0.386319
$345$	−8.00000			−0.430706
$346$		−	10.7137i		−	0.575974i
$347$		−	19.1652i		−	1.02884i	−0.857539	−	0.514420i	$-0.828007\pi$
$347$		−	19.1652i		−	1.02884i	0.857539	−	0.514420i	$-0.171993\pi$
$348$	1.02248			0.0548105
$349$	24.1185			1.29103			0.645517	−	0.763746i	$-0.276642\pi$
$349$	24.1185			1.29103			0.645517	+	0.763746i	$0.276642\pi$
$350$	−4.58258	+	11.2250i	−0.244949	+	0.600000i
$351$			2.33030i			0.124382i
$352$	−2.79129	+	1.79129i	−0.148776	+	0.0954760i
$353$			7.48331i			0.398297i	0.979969	+	0.199148i	$0.0638176\pi$
$353$			7.48331i			0.398297i	−0.979969	+	0.199148i	$0.936182\pi$
$354$		−	0.417424i		−	0.0221859i
$355$			6.19115i			0.328592i
$356$		−	9.79796i		−	0.519291i
$357$	2.41742	−	5.92146i	0.127944	−	0.313397i
$358$		−	11.1652i		−	0.590097i
$359$		−	9.58258i		−	0.505749i	−0.967499	−	0.252875i	$-0.918624\pi$
$359$		−	9.58258i		−	0.505749i	0.967499	−	0.252875i	$-0.0813760\pi$
$360$	−7.99455			−0.421350
$361$	−15.7477			−0.828828
$362$	5.41022			0.284355
$363$	−6.46084	−	2.96073i	−0.339106	−	0.155398i
$364$	−1.58258	−	0.646084i	−0.0829495	−	0.0338640i
$365$			49.9129i			2.61256i
$366$	1.25227			0.0654574
$367$			21.0229i			1.09739i	0.836023	+	0.548694i	$0.184875\pi$
$367$			21.0229i			1.09739i	−0.836023	+	0.548694i	$0.815125\pi$
$368$	4.00000			0.208514
$369$	−25.6522			−1.33540
$370$	11.0901			0.576548
$371$	−28.3714	−	11.5826i	−1.47297	−	0.601337i
$372$	−5.58258			−0.289443
$373$			9.58258i			0.496167i	0.968739	+	0.248083i	$0.0798007\pi$
$373$			9.58258i			0.496167i	−0.968739	+	0.248083i	$0.920199\pi$
$374$	10.4440	−	6.70239i	0.540049	−	0.346572i
$375$	−0.834849			−0.0431114
$376$	9.93280			0.512245
$377$			1.02248i			0.0526602i
$378$	8.83485	+	3.60681i	0.454416	+	0.185514i
$379$	−22.3303			−1.14703			−0.573515	−	0.819195i	$-0.694421\pi$
$379$	−22.3303			−1.14703			−0.573515	+	0.819195i	$0.694421\pi$
$380$			5.58258i			0.286380i
$381$	2.31464			0.118583
$382$			18.0000i			0.920960i
$383$			19.7308i			1.00819i	0.863647	+	0.504097i	$0.168175\pi$
$383$			19.7308i			1.00819i	−0.863647	+	0.504097i	$0.831825\pi$
$384$	−0.646084			−0.0329703
$385$	26.7102	−	4.94194i	1.36128	−	0.251865i
$386$	16.3303			0.831191
$387$		−	18.5045i		−	0.940639i
$388$			8.50579i			0.431816i
$389$	10.0000			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$390$			1.29217i			0.0654315i
$391$	−14.9666			−0.756895
$392$	−4.89898	+	5.00000i	−0.247436	+	0.252538i
$393$		−	10.8348i		−	0.546546i
$394$	8.74773			0.440704
$395$	12.3823			0.623021
$396$	4.62614	+	7.20871i	0.232472	+	0.362251i
$397$		−	27.5905i		−	1.38473i	−0.721549	−	0.692363i	$-0.756570\pi$
$397$		−	27.5905i		−	1.38473i	0.721549	−	0.692363i	$-0.243430\pi$
$398$	−9.66311			−0.484368
$399$	1.16515	−	2.85403i	0.0583305	−	0.142880i
$400$	−4.58258			−0.229129
$401$	7.58258			0.378656			0.189328	−	0.981914i	$-0.439369\pi$
$401$	7.58258			0.378656			0.189328	+	0.981914i	$0.439369\pi$
$402$	−4.89898			−0.244339
$403$		−	5.58258i		−	0.278088i
$404$	11.7362			0.583898
$405$			16.7700i			0.833310i
$406$	3.87650	+	1.58258i	0.192388	+	0.0785419i
$407$	−6.41742	−	10.0000i	−0.318100	−	0.495682i
$408$	2.41742			0.119680
$409$	−5.03383			−0.248907			−0.124453	−	0.992225i	$-0.539718\pi$
$409$	−5.03383			−0.248907			−0.124453	+	0.992225i	$0.539718\pi$
$410$	−30.7477			−1.51852
$411$		−	2.04495i		−	0.100870i
$412$		−	6.05630i		−	0.298373i
$413$	0.646084	−	1.58258i	0.0317917	−	0.0778735i
$414$		−	10.3303i		−	0.507707i
$415$			39.9129i			1.95925i
$416$		−	0.646084i		−	0.0316769i
$417$		−	10.0000i		−	0.489702i
$418$	5.03383	−	3.23042i	0.246212	−	0.158005i
$419$			13.0284i			0.636478i	0.948011	+	0.318239i	$0.103091\pi$
$419$			13.0284i			0.636478i	−0.948011	+	0.318239i	$0.896909\pi$
$420$	4.89898	+	2.00000i	0.239046	+	0.0975900i
$421$	7.58258			0.369552			0.184776	−	0.982781i	$-0.440844\pi$
$421$	7.58258			0.369552			0.184776	+	0.982781i	$0.440844\pi$
$422$	16.7477			0.815267
$423$		−	25.6522i		−	1.24725i
$424$		−	11.5826i		−	0.562500i
$425$	17.1464			0.831724
$426$	1.29217			0.0626057
$427$	4.74773	+	1.93825i	0.229759	+	0.0937986i
$428$		−	17.5826i		−	0.849886i
$429$	1.16515	−	0.747727i	0.0562540	−	0.0361006i
$430$		−	22.1803i		−	1.06963i
$431$		−	27.9129i		−	1.34452i	−0.740317	−	0.672258i	$-0.765325\pi$
$431$		−	27.9129i		−	1.34452i	0.740317	−	0.672258i	$-0.234675\pi$
$432$			3.60681i			0.173533i
$433$			35.5850i			1.71011i	0.518540	+	0.855054i	$0.326476\pi$
$433$			35.5850i			1.71011i	−0.518540	+	0.855054i	$0.673524\pi$
$434$	−21.1652	−	8.64064i	−1.01596	−	0.414764i
$435$		−	3.16515i		−	0.151757i
$436$		−	17.1652i		−	0.822062i
$437$	−7.21362			−0.345074
$438$	10.4174			0.497764
$439$	17.2813			0.824790			0.412395	−	0.911005i	$-0.364692\pi$
$439$	17.2813			0.824790			0.412395	+	0.911005i	$0.364692\pi$
$440$	5.54506	+	8.64064i	0.264351	+	0.411926i
$441$	12.9129	+	12.6520i	0.614899	+	0.602475i
$442$			2.41742i			0.114985i
$443$	15.1652			0.720518			0.360259	−	0.932852i	$-0.382688\pi$
$443$	15.1652			0.720518			0.360259	+	0.932852i	$0.382688\pi$
$444$		−	2.31464i		−	0.109848i
$445$	−30.3303			−1.43779
$446$	16.1240			0.763491
$447$	9.04517			0.427822
$448$	−2.44949	−	1.00000i	−0.115728	−	0.0472456i
$449$	31.1652			1.47077			0.735387	−	0.677647i	$-0.237000\pi$
$449$	31.1652			1.47077			0.735387	+	0.677647i	$0.237000\pi$
$450$			11.8348i			0.557900i
$451$	17.7925	+	27.7253i	0.837817	+	1.30553i
$452$	−10.7477			−0.505531
$453$	−3.60681			−0.169463
$454$			0.511238i			0.0239936i
$455$	−2.00000	+	4.89898i	−0.0937614	+	0.229668i
$456$	1.16515			0.0545632
$457$			33.1652i			1.55140i	0.631102	+	0.775700i	$0.282603\pi$
$457$			33.1652i			1.55140i	−0.631102	+	0.775700i	$0.717397\pi$
$458$	−5.67991			−0.265405
$459$		−	13.4955i		−	0.629914i
$460$		−	12.3823i		−	0.577327i
$461$	30.0400			1.39910			0.699550	−	0.714583i	$-0.253384\pi$
$461$	30.0400			1.39910			0.699550	+	0.714583i	$0.253384\pi$
$462$	−1.03144	−	5.57475i	−0.0479871	−	0.259361i
$463$	5.16515			0.240045			0.120022	−	0.992771i	$-0.461703\pi$
$463$	5.16515			0.240045			0.120022	+	0.992771i	$0.461703\pi$
$464$			1.58258i			0.0734692i
$465$			17.2813i			0.801400i
$466$	−27.1652			−1.25840
$467$		−	11.7362i		−	0.543087i	−0.962426	−	0.271544i	$-0.912466\pi$
$467$		−	11.7362i		−	0.543087i	0.962426	−	0.271544i	$-0.0875341\pi$
$468$	−1.66856			−0.0771292
$469$	−18.5734	−	7.58258i	−0.857642	−	0.350131i
$470$		−	30.7477i		−	1.41829i
$471$	8.50455			0.391869
$472$	0.646084			0.0297384
$473$	−20.0000	+	12.8348i	−0.919601	+	0.590147i
$474$		−	2.58434i		−	0.118702i
$475$	8.26424			0.379190
$476$	9.16515	+	3.74166i	0.420084	+	0.171499i
$477$	−29.9129			−1.36962
$478$	−8.41742			−0.385004
$479$	30.9557			1.41440			0.707202	−	0.707012i	$-0.249957\pi$
$479$	30.9557			1.41440			0.707202	+	0.707012i	$0.249957\pi$
$480$			2.00000i			0.0912871i
$481$	2.31464			0.105539
$482$			3.47197i			0.158144i
$483$	−2.58434	+	6.33030i	−0.117591	+	0.288039i
$484$	4.58258	−	10.0000i	0.208299	−	0.454545i
$485$	26.3303			1.19560
$486$	14.3205			0.649593
$487$	21.4955			0.974052			0.487026	−	0.873387i	$-0.338082\pi$
$487$	21.4955			0.974052			0.487026	+	0.873387i	$0.338082\pi$
$488$			1.93825i			0.0877405i
$489$			2.58434i			0.116868i
$490$	15.4779	+	15.1652i	0.699219	+	0.685092i
$491$			33.4955i			1.51163i	0.654786	+	0.755814i	$0.272759\pi$
$491$			33.4955i			1.51163i	−0.654786	+	0.755814i	$0.727241\pi$
$492$			6.41742i			0.289320i
$493$		−	5.92146i		−	0.266689i
$494$			1.16515i			0.0524226i
$495$	22.3151	−	14.3205i	1.00299	−	0.643661i
$496$		−	8.64064i		−	0.387976i
$497$	4.89898	+	2.00000i	0.219749	+	0.0897123i
$498$	8.33030			0.373290
$499$	−17.9129			−0.801891			−0.400945	−	0.916102i	$-0.631318\pi$
$499$	−17.9129			−0.801891			−0.400945	+	0.916102i	$0.631318\pi$
$500$		−	1.29217i		−	0.0577875i
$501$			0.834849i			0.0372983i
$502$	24.1185			1.07646
$503$	−17.0116			−0.758509			−0.379254	−	0.925292i	$-0.623820\pi$
$503$	−17.0116			−0.758509			−0.379254	+	0.925292i	$0.623820\pi$
$504$	−2.58258	+	6.32599i	−0.115037	+	0.281782i
$505$		−	36.3303i		−	1.61668i
$506$	−11.1652	+	7.16515i	−0.496352	+	0.318530i
$507$		−	8.12940i		−	0.361039i
$508$			3.58258i			0.158951i
$509$			0.780929i			0.0346141i	0.999850	+	0.0173070i	$0.00550928\pi$
$509$			0.780929i			0.0346141i	−0.999850	+	0.0173070i	$0.994491\pi$
$510$		−	7.48331i		−	0.331367i
$511$	39.4955	+	16.1240i	1.74718	+	0.713282i
$512$		−	1.00000i		−	0.0441942i
$513$		−	6.50455i		−	0.287183i
$514$	−4.89898			−0.216085
$515$	−18.7477			−0.826124
$516$	−4.62929			−0.203793
$517$	−27.7253	+	17.7925i	−1.21936	+	0.782514i
$518$	3.58258	−	8.77548i	0.157409	−	0.385573i
$519$			6.92197i			0.303841i
$520$	−2.00000			−0.0877058
$521$		−	28.1017i		−	1.23116i	−0.788075	−	0.615579i	$-0.788922\pi$
$521$		−	28.1017i		−	1.23116i	0.788075	−	0.615579i	$-0.211078\pi$
$522$	4.08712			0.178888
$523$	−14.4554			−0.632090			−0.316045	−	0.948744i	$-0.602355\pi$
$523$	−14.4554			−0.632090			−0.316045	+	0.948744i	$0.602355\pi$
$524$	16.7700			0.732602
$525$	2.96073	−	7.25227i	0.129217	−	0.316515i
$526$	−8.33030			−0.363218
$527$			32.3303i			1.40833i
$528$	1.80341	−	1.15732i	0.0784832	−	0.0503660i
$529$	−7.00000			−0.304348
$530$	−35.8547			−1.55743
$531$		−	1.66856i		−	0.0724094i
$532$	4.41742	+	1.80341i	0.191520	+	0.0781876i
$533$	−6.41742			−0.277970
$534$			6.33030i			0.273939i
$535$	−54.4282			−2.35313
$536$		−	7.58258i		−	0.327517i
$537$			7.21362i			0.311291i
$538$	−16.5003			−0.711380
$539$	4.71802	−	22.7319i	0.203220	−	0.979133i
$540$	11.1652			0.480472
$541$		−	36.7477i		−	1.57991i	−0.613166	−	0.789954i	$-0.710104\pi$
$541$		−	36.7477i		−	1.57991i	0.613166	−	0.789954i	$-0.289896\pi$
$542$			4.89898i			0.210429i
$543$	−3.49545			−0.150004
$544$			3.74166i			0.160422i
$545$	−53.1360			−2.27610
$546$	1.02248	+	0.417424i	0.0437580	+	0.0178641i
$547$		−	24.7477i		−	1.05814i	−0.848579	−	0.529068i	$-0.822542\pi$
$547$		−	24.7477i		−	1.05814i	0.848579	−	0.529068i	$-0.177458\pi$
$548$	3.16515			0.135209
$549$	5.00568			0.213637
$550$	12.7913	−	8.20871i	0.545422	−	0.350021i
$551$		−	2.85403i		−	0.121586i
$552$	−2.58434			−0.109997
$553$	4.00000	−	9.79796i	0.170097	−	0.416652i
$554$	2.00000			0.0849719
$555$	−7.16515			−0.304144
$556$	15.4779			0.656408
$557$		−	35.9129i		−	1.52168i	−0.648941	−	0.760839i	$-0.724788\pi$
$557$		−	35.9129i		−	1.52168i	0.648941	−	0.760839i	$-0.275212\pi$
$558$	−22.3151			−0.944673
$559$		−	4.62929i		−	0.195798i
$560$	−3.09557	+	7.58258i	−0.130812	+	0.320422i
$561$	−6.74773	+	4.33030i	−0.284889	+	0.182826i
$562$	11.1652			0.470973
$563$	23.7140			0.999425			0.499712	−	0.866191i	$-0.333439\pi$
$563$	23.7140			0.999425			0.499712	+	0.866191i	$0.333439\pi$
$564$	−6.41742			−0.270222
$565$			33.2704i			1.39970i
$566$			18.0622i			0.759211i
$567$	13.2699	+	5.41742i	0.557284	+	0.227510i
$568$			2.00000i			0.0839181i
$569$			39.4955i			1.65574i	0.560923	+	0.827868i	$0.310446\pi$
$569$			39.4955i			1.65574i	−0.560923	+	0.827868i	$0.689554\pi$
$570$		−	3.60681i		−	0.151073i
$571$		−	5.58258i		−	0.233624i	−0.993154	−	0.116812i	$-0.962733\pi$
$571$		−	5.58258i		−	0.233624i	0.993154	−	0.116812i	$-0.0372674\pi$
$572$	1.15732	+	1.80341i	0.0483901	+	0.0754042i
$573$		−	11.6295i		−	0.485830i
$574$	−9.93280	+	24.3303i	−0.414587	+	1.01553i
$575$	−18.3303			−0.764426
$576$	−2.58258			−0.107607
$577$			29.6636i			1.23491i	0.786606	+	0.617455i	$0.211836\pi$
$577$			29.6636i			1.23491i	−0.786606	+	0.617455i	$0.788164\pi$
$578$			3.00000i			0.124784i
$579$	−10.5507			−0.438474
$580$	4.89898			0.203419
$581$	31.5826	+	12.8935i	1.31027	+	0.534914i
$582$		−	5.49545i		−	0.227794i
$583$	20.7477	+	32.3303i	0.859283	+	1.33898i
$584$			16.1240i			0.667214i
$585$			5.16515i			0.213553i
$586$		−	25.1410i		−	1.03856i
$587$		−	39.0851i		−	1.61322i	−0.591087	−	0.806608i	$-0.701301\pi$
$587$		−	39.0851i		−	1.61322i	0.591087	−	0.806608i	$-0.298699\pi$
$588$	3.16515	−	3.23042i	0.130529	−	0.133220i
$589$			15.5826i			0.642069i
$590$		−	2.00000i		−	0.0823387i
$591$	−5.65176			−0.232483
$592$	3.58258			0.147243
$593$	−14.8318			−0.609068			−0.304534	−	0.952501i	$-0.598501\pi$
$593$	−14.8318			−0.609068			−0.304534	+	0.952501i	$0.598501\pi$
$594$	−6.46084	−	10.0677i	−0.265091	−	0.413081i
$595$	11.5826	−	28.3714i	0.474839	−	1.16311i
$596$			14.0000i			0.573462i
$597$	6.24318			0.255516
$598$		−	2.58434i		−	0.105681i
$599$	−21.1652			−0.864785			−0.432392	−	0.901686i	$-0.642330\pi$
$599$	−21.1652			−0.864785			−0.432392	+	0.901686i	$0.642330\pi$
$600$	2.96073			0.120871
$601$	21.0229			0.857543			0.428772	−	0.903413i	$-0.358947\pi$
$601$	21.0229			0.857543			0.428772	+	0.903413i	$0.358947\pi$
$602$	−17.5510	−	7.16515i	−0.715324	−	0.292030i
$603$	−19.5826			−0.797464
$604$		−	5.58258i		−	0.227152i
$605$	−30.9557	−	14.1857i	−1.25853	−	0.576731i
$606$	−7.58258			−0.308021
$607$	2.04495			0.0830021			0.0415010	−	0.999138i	$-0.486786\pi$
$607$	2.04495			0.0830021			0.0415010	+	0.999138i	$0.486786\pi$
$608$			1.80341i			0.0731378i
$609$	−2.50455	−	1.02248i	−0.101489	−	0.0414328i
$610$	6.00000			0.242933
$611$		−	6.41742i		−	0.259621i
$612$	9.66311			0.390608
$613$			31.9129i			1.28895i	0.764626	+	0.644475i	$0.222924\pi$
$613$			31.9129i			1.28895i	−0.764626	+	0.644475i	$0.777076\pi$
$614$			10.5789i			0.426929i
$615$	19.8656			0.801059
$616$	8.62852	−	1.59645i	0.347653	−	0.0643229i
$617$	−19.9129			−0.801662			−0.400831	−	0.916152i	$-0.631279\pi$
$617$	−19.9129			−0.801662			−0.400831	+	0.916152i	$0.631279\pi$
$618$			3.91288i			0.157399i
$619$		−	17.9274i		−	0.720561i	−0.932844	−	0.360281i	$-0.882681\pi$
$619$		−	17.9274i		−	0.720561i	0.932844	−	0.360281i	$-0.117319\pi$
$620$	−26.7477			−1.07421
$621$			14.4272i			0.578945i
$622$	5.03383			0.201838
$623$	−9.79796	+	24.0000i	−0.392547	+	0.961540i
$624$			0.417424i			0.0167103i
$625$	−26.9129			−1.07652
$626$	−23.4724			−0.938147
$627$	−3.25227	+	2.08712i	−0.129883	+	0.0833516i
$628$			13.1632i			0.525270i
$629$	−13.4048			−0.534483
$630$	19.5826	+	7.99455i	0.780188	+	0.318511i
$631$	13.1652			0.524096			0.262048	−	0.965055i	$-0.415602\pi$
$631$	13.1652			0.524096			0.262048	+	0.965055i	$0.415602\pi$
$632$	4.00000			0.159111
$633$	−10.8204			−0.430074
$634$		−	9.16515i		−	0.363995i
$635$	11.0901			0.440098
$636$			7.48331i			0.296733i
$637$	3.23042	+	3.16515i	0.127994	+	0.125408i
$638$	−2.83485	−	4.41742i	−0.112233	−	0.174888i
$639$	5.16515			0.204330
$640$	−3.09557			−0.122363
$641$	−15.9129			−0.628521			−0.314260	−	0.949337i	$-0.601757\pi$
$641$	−15.9129			−0.628521			−0.314260	+	0.949337i	$0.601757\pi$
$642$			11.3598i			0.448336i
$643$		−	9.42157i		−	0.371550i	−0.982592	−	0.185775i	$-0.940520\pi$
$643$		−	9.42157i		−	0.371550i	0.982592	−	0.185775i	$-0.0594796\pi$
$644$	−9.79796	−	4.00000i	−0.386094	−	0.157622i
$645$			14.3303i			0.564255i
$646$		−	6.74773i		−	0.265486i
$647$		−	30.0681i		−	1.18210i	−0.806635	−	0.591050i	$-0.798714\pi$
$647$		−	30.0681i		−	1.18210i	0.806635	−	0.591050i	$-0.201286\pi$
$648$			5.41742i			0.212817i
$649$	−1.80341	+	1.15732i	−0.0707899	+	0.0454289i
$650$			2.96073i			0.116129i
$651$	13.6745	+	5.58258i	0.535944	+	0.218798i
$652$	−4.00000			−0.156652
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$			11.0901i			0.433658i
$655$		−	51.9129i		−	2.02840i
$656$	−9.93280			−0.387811
$657$	41.6413			1.62458
$658$	−24.3303	−	9.93280i	−0.948494	−	0.387221i
$659$		−	6.33030i		−	0.246594i	−0.992370	−	0.123297i	$-0.960653\pi$
$659$		−	6.33030i		−	0.246594i	0.992370	−	0.123297i	$-0.0393467\pi$
$660$	−3.58258	−	5.58258i	−0.139452	−	0.217301i
$661$			8.26424i			0.321442i	0.987000	+	0.160721i	$0.0513819\pi$
$661$			8.26424i			0.321442i	−0.987000	+	0.160721i	$0.948618\pi$
$662$			23.5826i			0.916563i
$663$		−	1.56186i		−	0.0606576i
$664$			12.8935i			0.500366i
$665$	5.58258	−	13.6745i	0.216483	−	0.530273i
$666$		−	9.25227i		−	0.358518i
$667$			6.33030i			0.245110i
$668$	−1.29217			−0.0499955
$669$	−10.4174			−0.402761
$670$	−23.4724			−0.906819
$671$	−3.47197	−	5.41022i	−0.134034	−	0.208859i
$672$	1.58258	+	0.646084i	0.0610492	+	0.0249232i
$673$		−	18.3303i		−	0.706581i	−0.935514	−	0.353291i	$-0.885063\pi$
$673$		−	18.3303i		−	0.706581i	0.935514	−	0.353291i	$-0.114937\pi$
$674$	10.8348			0.417343
$675$		−	16.5285i		−	0.636182i
$676$	12.5826			0.483945
$677$	5.27537			0.202749			0.101375	−	0.994848i	$-0.467676\pi$
$677$	5.27537			0.202749			0.101375	+	0.994848i	$0.467676\pi$
$678$	6.94393			0.266680
$679$	8.50579	−	20.8348i	0.326422	−	0.799568i
$680$	11.5826			0.444172
$681$		−	0.330303i		−	0.0126572i
$682$	15.4779	+	24.1185i	0.592678	+	0.923545i
$683$	−9.49545			−0.363333			−0.181667	−	0.983360i	$-0.558149\pi$
$683$	−9.49545			−0.363333			−0.181667	+	0.983360i	$0.558149\pi$
$684$	4.65743			0.178081
$685$		−	9.79796i		−	0.374361i
$686$	17.0000	−	7.34847i	0.649063	−	0.280566i
$687$	3.66970			0.140008
$688$		−	7.16515i		−	0.273169i
$689$	−7.48331			−0.285092
$690$			8.00000i			0.304555i
$691$		−	3.98320i		−	0.151528i	−0.997126	−	0.0757641i	$-0.975860\pi$
$691$		−	3.98320i		−	0.151528i	0.997126	−	0.0757641i	$-0.0241396\pi$
$692$	−10.7137			−0.407275
$693$	−4.12296	−	22.2838i	−0.156618	−	0.846492i
$694$	−19.1652			−0.727499
$695$		−	47.9129i		−	1.81744i
$696$		−	1.02248i		−	0.0387569i
$697$	37.1652			1.40773
$698$		−	24.1185i		−	0.912899i
$699$	17.5510			0.663838
$700$	11.2250	+	4.58258i	0.424264	+	0.173205i
$701$			12.3303i			0.465709i	0.972512	+	0.232855i	$0.0748066\pi$
$701$			12.3303i			0.465709i	−0.972512	+	0.232855i	$0.925193\pi$
$702$	2.33030			0.0879516
$703$	−6.46084			−0.243675
$704$	1.79129	+	2.79129i	0.0675117	+	0.105201i
$705$			19.8656i			0.748182i
$706$	7.48331			0.281638
$707$	−28.7477	−	11.7362i	−1.08117	−	0.441386i
$708$	−0.417424			−0.0156878
$709$	52.3303			1.96531			0.982653	−	0.185454i	$-0.0593757\pi$
$709$	52.3303			1.96531			0.982653	+	0.185454i	$0.0593757\pi$
$710$	6.19115			0.232350
$711$		−	10.3303i		−	0.387417i
$712$	−9.79796			−0.367194
$713$		−	34.5625i		−	1.29438i
$714$	−5.92146	−	2.41742i	−0.221605	−	0.0904698i
$715$	5.58258	−	3.58258i	0.208776	−	0.133981i
$716$	−11.1652			−0.417261
$717$	5.43836			0.203099
$718$	−9.58258			−0.357619
$719$		−	23.3376i		−	0.870345i	−0.900347	−	0.435172i	$-0.856687\pi$
$719$		−	23.3376i		−	0.870345i	0.900347	−	0.435172i	$-0.143313\pi$
$720$			7.99455i			0.297939i
$721$	−6.05630	+	14.8348i	−0.225548	+	0.552479i
$722$			15.7477i			0.586070i
$723$		−	2.24318i		−	0.0834248i
$724$		−	5.41022i		−	0.201069i
$725$		−	7.25227i		−	0.269343i
$726$	−2.96073	+	6.46084i	−0.109883	+	0.239784i
$727$			37.5514i			1.39271i	0.717700	+	0.696353i	$0.245195\pi$
$727$			37.5514i			1.39271i	−0.717700	+	0.696353i	$0.754805\pi$
$728$	−0.646084	+	1.58258i	−0.0239455	+	0.0586542i
$729$	7.00000			0.259259
$730$	49.9129			1.84736
$731$			26.8095i			0.991587i
$732$		−	1.25227i		−	0.0462853i
$733$	10.7137			0.395721			0.197860	−	0.980230i	$-0.436601\pi$
$733$	10.7137			0.395721			0.197860	+	0.980230i	$0.436601\pi$
$734$	21.0229			0.775971
$735$	−10.0000	−	9.79796i	−0.368856	−	0.361403i
$736$		−	4.00000i		−	0.147442i
$737$	13.5826	+	21.1652i	0.500321	+	0.779628i
$738$			25.6522i			0.944271i
$739$			1.58258i			0.0582160i	0.999576	+	0.0291080i	$0.00926667\pi$
$739$			1.58258i			0.0582160i	−0.999576	+	0.0291080i	$0.990733\pi$
$740$		−	11.0901i		−	0.407681i
$741$		−	0.752785i		−	0.0276543i
$742$	−11.5826	+	28.3714i	−0.425210	+	1.04155i
$743$			1.91288i			0.0701767i	0.999384	+	0.0350884i	$0.0111713\pi$
$743$			1.91288i			0.0701767i	−0.999384	+	0.0350884i	$0.988829\pi$
$744$			5.58258i			0.204667i
$745$	43.3380			1.58778
$746$	9.58258			0.350843
$747$	33.2985			1.21833
$748$	−6.70239	−	10.4440i	−0.245063	−	0.381872i
$749$	−17.5826	+	43.0683i	−0.642453	+	1.57368i
$750$			0.834849i			0.0304844i
$751$	−41.4955			−1.51419			−0.757095	−	0.653304i	$-0.773382\pi$
$751$	−41.4955			−1.51419			−0.757095	+	0.653304i	$0.773382\pi$
$752$		−	9.93280i		−	0.362212i
$753$	−15.5826			−0.567861
$754$	1.02248			0.0372364
$755$	−17.2813			−0.628930
$756$	3.60681	−	8.83485i	0.131178	−	0.321320i
$757$	−30.8348			−1.12071			−0.560356	−	0.828252i	$-0.689336\pi$
$757$	−30.8348			−1.12071			−0.560356	+	0.828252i	$0.689336\pi$
$758$			22.3303i			0.811073i
$759$	7.21362	−	4.62929i	0.261838	−	0.168033i
$760$	5.58258			0.202501
$761$	28.2366			1.02357			0.511787	−	0.859112i	$-0.328984\pi$
$761$	28.2366			1.02357			0.511787	+	0.859112i	$0.328984\pi$
$762$		−	2.31464i		−	0.0838507i
$763$	−17.1652	+	42.0459i	−0.621420	+	1.52216i
$764$	18.0000			0.651217
$765$		−	29.9129i		−	1.08150i
$766$	19.7308			0.712901
$767$		−	0.417424i		−	0.0150723i
$768$			0.646084i			0.0233135i
$769$	−15.1015			−0.544573			−0.272287	−	0.962216i	$-0.587780\pi$
$769$	−15.1015			−0.544573			−0.272287	+	0.962216i	$0.587780\pi$
$770$	−4.94194	−	26.7102i	−0.178095	−	0.962569i
$771$	3.16515			0.113990
$772$		−	16.3303i		−	0.587740i
$773$			10.0395i			0.361096i	0.983566	+	0.180548i	$0.0577871\pi$
$773$			10.0395i			0.361096i	−0.983566	+	0.180548i	$0.942213\pi$
$774$	−18.5045			−0.665132
$775$			39.5964i			1.42234i
$776$	8.50579			0.305340
$777$	−2.31464	+	5.66970i	−0.0830374	+	0.203399i
$778$		−	10.0000i		−	0.358517i
$779$	17.9129			0.641795
$780$	1.29217			0.0462670
$781$	−3.58258	−	5.58258i	−0.128195	−	0.199760i
$782$			14.9666i			0.535206i
$783$	−5.70805			−0.203989
$784$	5.00000	+	4.89898i	0.178571	+	0.174964i
$785$	40.7477			1.45435
$786$	−10.8348			−0.386466
$787$	23.2309			0.828091			0.414046	−	0.910256i	$-0.364115\pi$
$787$	23.2309			0.828091			0.414046	+	0.910256i	$0.364115\pi$
$788$		−	8.74773i		−	0.311625i
$789$	5.38207			0.191607
$790$		−	12.3823i		−	0.440542i
$791$	26.3264	+	10.7477i	0.936061	+	0.382145i
$792$	7.20871	−	4.62614i	0.256150	−	0.164383i
$793$	1.25227			0.0444695
$794$	−27.5905			−0.979149
$795$	23.1652			0.821583
$796$			9.66311i			0.342500i
$797$			25.0061i			0.885763i	0.896580	+	0.442881i	$0.146044\pi$
$797$			25.0061i			0.885763i	−0.896580	+	0.442881i	$0.853956\pi$
$798$	−2.85403	−	1.16515i	−0.101031	−	0.0412459i
$799$			37.1652i			1.31481i
$800$			4.58258i			0.162019i
$801$			25.3040i			0.894072i
$802$		−	7.58258i		−	0.267750i
$803$	−28.8826	−	45.0066i	−1.01925	−	1.58825i
$804$			4.89898i			0.172774i
$805$	−12.3823	+	30.3303i	−0.436419	+	1.06900i
$806$	−5.58258			−0.196638
$807$	10.6606			0.375271
$808$		−	11.7362i		−	0.412878i
$809$			14.8348i			0.521566i	0.965398	+	0.260783i	$0.0839806\pi$
$809$			14.8348i			0.521566i	−0.965398	+	0.260783i	$0.916019\pi$
$810$	16.7700			0.589239
$811$	3.36526			0.118170			0.0590852	−	0.998253i	$-0.481182\pi$
$811$	3.36526			0.118170			0.0590852	+	0.998253i	$0.481182\pi$
$812$	1.58258	−	3.87650i	0.0555375	−	0.136039i
$813$		−	3.16515i		−	0.111007i
$814$	−10.0000	+	6.41742i	−0.350500	+	0.224931i
$815$			12.3823i			0.433733i
$816$		−	2.41742i		−	0.0846268i
$817$			12.9217i			0.452072i
$818$			5.03383i			0.176004i
$819$	4.08712	+	1.66856i	0.142816	+	0.0583042i
$820$			30.7477i			1.07376i
$821$		−	43.4955i		−	1.51800i	−0.651090	−	0.759001i	$-0.725688\pi$
$821$		−	43.4955i		−	1.51800i	0.651090	−	0.759001i	$-0.274312\pi$
$822$	−2.04495			−0.0713259
$823$	−3.66970			−0.127918			−0.0639588	−	0.997953i	$-0.520373\pi$
$823$	−3.66970			−0.127918			−0.0639588	+	0.997953i	$0.520373\pi$
$824$	−6.05630			−0.210981
$825$	−8.26424	+	5.30352i	−0.287724	+	0.184645i
$826$	−1.58258	−	0.646084i	−0.0550649	−	0.0224801i
$827$			3.16515i			0.110063i	0.998485	+	0.0550315i	$0.0175259\pi$
$827$			3.16515i			0.110063i	−0.998485	+	0.0550315i	$0.982474\pi$
$828$	−10.3303			−0.359003
$829$			7.99455i			0.277662i	0.990316	+	0.138831i	$0.0443345\pi$
$829$			7.99455i			0.277662i	−0.990316	+	0.138831i	$0.955665\pi$
$830$	39.9129			1.38540
$831$	−1.29217			−0.0448248
$832$	−0.646084			−0.0223989
$833$	−18.7083	−	18.3303i	−0.648204	−	0.635107i
$834$	−10.0000			−0.346272
$835$			4.00000i			0.138426i
$836$	−3.23042	−	5.03383i	−0.111726	−	0.174098i
$837$	31.1652			1.07723
$838$	13.0284			0.450058
$839$		−	9.66311i		−	0.333608i	−0.985990	−	0.166804i	$-0.946655\pi$
$839$		−	9.66311i		−	0.333608i	0.985990	−	0.166804i	$-0.0533447\pi$
$840$	2.00000	−	4.89898i	0.0690066	−	0.169031i
$841$	26.4955			0.913636
$842$		−	7.58258i		−	0.261313i
$843$	−7.21362			−0.248450
$844$		−	16.7477i		−	0.576481i
$845$		−	38.9503i		−	1.33993i
$846$	−25.6522			−0.881941
$847$	−21.2250	+	19.9123i	−0.729299	+	0.684195i
$848$	−11.5826			−0.397747
$849$		−	11.6697i		−	0.400503i
$850$		−	17.1464i		−	0.588118i
$851$	14.3303			0.491236
$852$		−	1.29217i		−	0.0442689i
$853$	11.4665			0.392606			0.196303	−	0.980543i	$-0.437106\pi$
$853$	11.4665			0.392606			0.196303	+	0.980543i	$0.437106\pi$
$854$	1.93825	−	4.74773i	0.0663256	−	0.162464i
$855$		−	14.4174i		−	0.493066i
$856$	−17.5826			−0.600960
$857$	−31.0906			−1.06203			−0.531017	−	0.847361i	$-0.678190\pi$
$857$	−31.0906			−1.06203			−0.531017	+	0.847361i	$0.678190\pi$
$858$	−0.747727	−	1.16515i	−0.0255270	−	0.0397776i
$859$		−	24.3882i		−	0.832115i	−0.909338	−	0.416057i	$-0.863412\pi$
$859$		−	24.3882i		−	0.832115i	0.909338	−	0.416057i	$-0.136588\pi$
$860$	−22.1803			−0.756340
$861$	6.41742	−	15.7194i	0.218705	−	0.535716i
$862$	−27.9129			−0.950716
$863$	−14.8348			−0.504984			−0.252492	−	0.967599i	$-0.581250\pi$
$863$	−14.8348			−0.504984			−0.252492	+	0.967599i	$0.581250\pi$
$864$	3.60681			0.122706
$865$			33.1652i			1.12765i
$866$	35.5850			1.20923
$867$		−	1.93825i		−	0.0658265i
$868$	−8.64064	+	21.1652i	−0.293282	+	0.718392i
$869$	−11.1652	+	7.16515i	−0.378752	+	0.243061i
$870$	−3.16515			−0.107309
$871$	−4.89898			−0.165996
$872$	−17.1652			−0.581285
$873$		−	21.9668i		−	0.743465i
$874$			7.21362i			0.244004i
$875$	−1.29217	+	3.16515i	−0.0436832	+	0.107002i
$876$		−	10.4174i		−	0.351972i
$877$		−	6.83485i		−	0.230796i	−0.993319	−	0.115398i	$-0.963186\pi$
$877$		−	6.83485i		−	0.230796i	0.993319	−	0.115398i	$-0.0368144\pi$
$878$		−	17.2813i		−	0.583215i
$879$			16.2432i			0.547869i
$880$	8.64064	−	5.54506i	0.291276	−	0.186924i
$881$			7.21362i			0.243033i	0.992589	+	0.121517i	$0.0387758\pi$
$881$			7.21362i			0.243033i	−0.992589	+	0.121517i	$0.961224\pi$
$882$	12.6520	−	12.9129i	0.426015	−	0.434799i
$883$	12.8348			0.431927			0.215964	−	0.976401i	$-0.430711\pi$
$883$	12.8348			0.431927			0.215964	+	0.976401i	$0.430711\pi$
$884$	2.41742			0.0813068
$885$			1.29217i			0.0434357i
$886$		−	15.1652i		−	0.509483i
$887$	−53.4057			−1.79319			−0.896594	−	0.442854i	$-0.853966\pi$
$887$	−53.4057			−1.79319			−0.896594	+	0.442854i	$0.853966\pi$
$888$	−2.31464			−0.0776744
$889$	3.58258	−	8.77548i	0.120156	−	0.294320i
$890$			30.3303i			1.01667i
$891$	−9.70417	−	15.1216i	−0.325102	−	0.506592i
$892$		−	16.1240i		−	0.539870i
$893$			17.9129i			0.599432i
$894$		−	9.04517i		−	0.302516i
$895$			34.5625i			1.15530i
$896$	−1.00000	+	2.44949i	−0.0334077	+	0.0818317i
$897$			1.66970i			0.0557496i
$898$		−	31.1652i		−	1.03999i
$899$	13.6745			0.456069
$900$	11.8348			0.394495
$901$	43.3380			1.44380
$902$	27.7253	−	17.7925i	0.923152	−	0.592426i
$903$	11.3394	+	4.62929i	0.377351	+	0.154053i
$904$			10.7477i			0.357464i
$905$	−16.7477			−0.556713
$906$			3.60681i			0.119828i
$907$	5.91288			0.196334			0.0981670	−	0.995170i	$-0.468702\pi$
$907$	5.91288			0.196334			0.0981670	+	0.995170i	$0.468702\pi$
$908$	0.511238			0.0169660
$909$	−30.3097			−1.00531
$910$	4.89898	+	2.00000i	0.162400	+	0.0662994i
$911$	3.16515			0.104866			0.0524331	−	0.998624i	$-0.483302\pi$
$911$	3.16515			0.104866			0.0524331	+	0.998624i	$0.483302\pi$
$912$		−	1.16515i		−	0.0385820i
$913$	−23.0960	−	35.9896i	−0.764367	−	1.19108i
$914$	33.1652			1.09701
$915$	−3.87650			−0.128153
$916$			5.67991i			0.187669i
$917$	−41.0780	−	16.7700i	−1.35652	−	0.553795i
$918$	−13.4955			−0.445416
$919$			19.4955i			0.643096i	0.946893	+	0.321548i	$0.104203\pi$
$919$			19.4955i			0.643096i	−0.946893	+	0.321548i	$0.895797\pi$
$920$	−12.3823			−0.408232
$921$		−	6.83485i		−	0.225216i
$922$		−	30.0400i		−	0.989313i
$923$	1.29217			0.0425322
$924$	−5.57475	+	1.03144i	−0.183396	+	0.0339320i
$925$	−16.4174			−0.539802
$926$		−	5.16515i		−	0.169737i
$927$			15.6409i			0.513713i
$928$	1.58258			0.0519506
$929$			43.6077i			1.43072i	0.698755	+	0.715361i	$0.253738\pi$
$929$			43.6077i			1.43072i	−0.698755	+	0.715361i	$0.746262\pi$
$930$	17.2813			0.566675
$931$	−9.01703	−	8.83485i	−0.295521	−	0.289550i
$932$			27.1652i			0.889824i
$933$	−3.25227			−0.106475
$934$	−11.7362			−0.384021
$935$	−32.3303	+	20.7477i	−1.05731	+	0.678523i
$936$			1.66856i			0.0545386i
$937$	30.0681			0.982282			0.491141	−	0.871080i	$-0.336580\pi$
$937$	30.0681			0.982282			0.491141	+	0.871080i	$0.336580\pi$
$938$	−7.58258	+	18.5734i	−0.247580	+	0.606444i
$939$	15.1652			0.494896
$940$	−30.7477			−1.00288
$941$	−5.27537			−0.171972			−0.0859861	−	0.996296i	$-0.527404\pi$
$941$	−5.27537			−0.171972			−0.0859861	+	0.996296i	$0.527404\pi$
$942$		−	8.50455i		−	0.277093i
$943$	−39.7312			−1.29383
$944$		−	0.646084i		−	0.0210282i
$945$	−27.3489	−	11.1652i	−0.889661	−	0.363202i
$946$	12.8348	+	20.0000i	0.417297	+	0.650256i
$947$	3.58258			0.116418			0.0582090	−	0.998304i	$-0.481461\pi$
$947$	3.58258			0.116418			0.0582090	+	0.998304i	$0.481461\pi$
$948$	−2.58434			−0.0839353
$949$	10.4174			0.338164
$950$		−	8.26424i		−	0.268127i
$951$			5.92146i			0.192016i
$952$	3.74166	−	9.16515i	0.121268	−	0.297044i
$953$		−	18.3303i		−	0.593777i	−0.954912	−	0.296888i	$-0.904051\pi$
$953$		−	18.3303i		−	0.593777i	0.954912	−	0.296888i	$-0.0959489\pi$
$954$			29.9129i			0.968465i
$955$		−	55.7203i		−	1.80307i
$956$			8.41742i			0.272239i
$957$	1.83155	+	2.85403i	0.0592056	+	0.0922576i
$958$		−	30.9557i		−	1.00013i
$959$	−7.75301	−	3.16515i	−0.250358	−	0.102208i
$960$	2.00000			0.0645497
$961$	−43.6606			−1.40841
$962$		−	2.31464i		−	0.0746271i
$963$			45.4083i			1.46326i
$964$	3.47197			0.111825
$965$	−50.5517			−1.62732
$966$	6.33030	+	2.58434i	0.203674	+	0.0831496i
$967$		−	22.4174i		−	0.720896i	−0.932779	−	0.360448i	$-0.882624\pi$
$967$		−	22.4174i		−	0.720896i	0.932779	−	0.360448i	$-0.117376\pi$
$968$	−10.0000	−	4.58258i	−0.321412	−	0.147290i
$969$			4.35960i			0.140050i
$970$		−	26.3303i		−	0.845415i
$971$			14.0509i			0.450913i	0.974253	+	0.225457i	$0.0723874\pi$
$971$			14.0509i			0.450913i	−0.974253	+	0.225457i	$0.927613\pi$
$972$		−	14.3205i		−	0.459332i
$973$	−37.9129	−	15.4779i	−1.21543	−	0.496198i
$974$		−	21.4955i		−	0.688759i
$975$		−	1.91288i		−	0.0612611i
$976$	1.93825			0.0620419
$977$	9.16515			0.293219			0.146610	−	0.989194i	$-0.453164\pi$
$977$	9.16515			0.293219			0.146610	+	0.989194i	$0.453164\pi$
$978$	2.58434			0.0826379
$979$	27.3489	−	17.5510i	0.874075	−	0.560931i
$980$	15.1652	−	15.4779i	0.484433	−	0.494422i
$981$			44.3303i			1.41536i
$982$	33.4955			1.06888
$983$			50.6865i			1.61665i	0.588738	+	0.808324i	$0.299625\pi$
$983$			50.6865i			1.61665i	−0.588738	+	0.808324i	$0.700375\pi$
$984$	6.41742			0.204580
$985$	−27.0792			−0.862816
$986$	−5.92146			−0.188578
$987$	15.7194	+	6.41742i	0.500354	+	0.204269i
$988$	1.16515			0.0370684
$989$		−	28.6606i		−	0.911354i
$990$	−14.3205	−	22.3151i	−0.455137	−	0.709220i
$991$	46.6606			1.48222			0.741111	−	0.671382i	$-0.234299\pi$
$991$	46.6606			1.48222			0.741111	+	0.671382i	$0.234299\pi$
$992$	−8.64064			−0.274340
$993$		−	15.2363i		−	0.483510i
$994$	2.00000	−	4.89898i	0.0634361	−	0.155386i
$995$	29.9129			0.948302
$996$		−	8.33030i		−	0.263956i
$997$	22.5566			0.714376			0.357188	−	0.934032i	$-0.383736\pi$
$997$	22.5566			0.714376			0.357188	+	0.934032i	$0.383736\pi$
$998$			17.9129i			0.567022i
$999$			12.9217i			0.408824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.c.a.153.3	yes	8
3.2	odd	2		1386.2.e.b.307.5		8
4.3	odd	2		1232.2.e.e.769.3		8
7.2	even	3		1078.2.i.b.1011.2		16
7.3	odd	6		1078.2.i.b.901.6		16
7.4	even	3		1078.2.i.b.901.7		16
7.5	odd	6		1078.2.i.b.1011.3		16
7.6	odd	2	inner	154.2.c.a.153.2	✓	8
11.10	odd	2	inner	154.2.c.a.153.7	yes	8
21.20	even	2		1386.2.e.b.307.8		8
28.27	even	2		1232.2.e.e.769.6		8
33.32	even	2		1386.2.e.b.307.1		8
44.43	even	2		1232.2.e.e.769.4		8
77.10	even	6		1078.2.i.b.901.2		16
77.32	odd	6		1078.2.i.b.901.3		16
77.54	even	6		1078.2.i.b.1011.7		16
77.65	odd	6		1078.2.i.b.1011.6		16
77.76	even	2	inner	154.2.c.a.153.6	yes	8
231.230	odd	2		1386.2.e.b.307.4		8
308.307	odd	2		1232.2.e.e.769.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.c.a.153.2	✓	8	7.6	odd	2	inner
154.2.c.a.153.3	yes	8	1.1	even	1	trivial
154.2.c.a.153.6	yes	8	77.76	even	2	inner
154.2.c.a.153.7	yes	8	11.10	odd	2	inner
1078.2.i.b.901.2		16	77.10	even	6
1078.2.i.b.901.3		16	77.32	odd	6
1078.2.i.b.901.6		16	7.3	odd	6
1078.2.i.b.901.7		16	7.4	even	3
1078.2.i.b.1011.2		16	7.2	even	3
1078.2.i.b.1011.3		16	7.5	odd	6
1078.2.i.b.1011.6		16	77.65	odd	6
1078.2.i.b.1011.7		16	77.54	even	6
1232.2.e.e.769.3		8	4.3	odd	2
1232.2.e.e.769.4		8	44.43	even	2
1232.2.e.e.769.5		8	308.307	odd	2
1232.2.e.e.769.6		8	28.27	even	2
1386.2.e.b.307.1		8	33.32	even	2
1386.2.e.b.307.4		8	231.230	odd	2
1386.2.e.b.307.5		8	3.2	odd	2
1386.2.e.b.307.8		8	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +0.646084i q^{3} -1.00000 q^{4} +3.09557i q^{5} +0.646084 q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000i q^{8} +2.58258 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +0.646084i q^{3} -1.00000 q^{4} +3.09557i q^{5} +0.646084 q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000i q^{8} +2.58258 q^{9} +3.09557 q^{10} +(-1.79129 - 2.79129i) q^{11} -0.646084i q^{12} +0.646084 q^{13} +(1.00000 - 2.44949i) q^{14} -2.00000 q^{15} +1.00000 q^{16} -3.74166 q^{17} -2.58258i q^{18} -1.80341 q^{19} -3.09557i q^{20} +(-0.646084 + 1.58258i) q^{21} +(-2.79129 + 1.79129i) q^{22} +4.00000 q^{23} -0.646084 q^{24} -4.58258 q^{25} -0.646084i q^{26} +3.60681i q^{27} +(-2.44949 - 1.00000i) q^{28} +1.58258i q^{29} +2.00000i q^{30} -8.64064i q^{31} -1.00000i q^{32} +(1.80341 - 1.15732i) q^{33} +3.74166i q^{34} +(-3.09557 + 7.58258i) q^{35} -2.58258 q^{36} +3.58258 q^{37} +1.80341i q^{38} +0.417424i q^{39} -3.09557 q^{40} -9.93280 q^{41} +(1.58258 + 0.646084i) q^{42} -7.16515i q^{43} +(1.79129 + 2.79129i) q^{44} +7.99455i q^{45} -4.00000i q^{46} -9.93280i q^{47} +0.646084i q^{48} +(5.00000 + 4.89898i) q^{49} +4.58258i q^{50} -2.41742i q^{51} -0.646084 q^{52} -11.5826 q^{53} +3.60681 q^{54} +(8.64064 - 5.54506i) q^{55} +(-1.00000 + 2.44949i) q^{56} -1.16515i q^{57} +1.58258 q^{58} -0.646084i q^{59} +2.00000 q^{60} +1.93825 q^{61} -8.64064 q^{62} +(6.32599 + 2.58258i) q^{63} -1.00000 q^{64} +2.00000i q^{65} +(-1.15732 - 1.80341i) q^{66} -7.58258 q^{67} +3.74166 q^{68} +2.58434i q^{69} +(7.58258 + 3.09557i) q^{70} +2.00000 q^{71} +2.58258i q^{72} +16.1240 q^{73} -3.58258i q^{74} -2.96073i q^{75} +1.80341 q^{76} +(-1.59645 - 8.62852i) q^{77} +0.417424 q^{78} -4.00000i q^{79} +3.09557i q^{80} +5.41742 q^{81} +9.93280i q^{82} +12.8935 q^{83} +(0.646084 - 1.58258i) q^{84} -11.5826i q^{85} -7.16515 q^{86} -1.02248 q^{87} +(2.79129 - 1.79129i) q^{88} +9.79796i q^{89} +7.99455 q^{90} +(1.58258 + 0.646084i) q^{91} -4.00000 q^{92} +5.58258 q^{93} -9.93280 q^{94} -5.58258i q^{95} +0.646084 q^{96} -8.50579i q^{97} +(4.89898 - 5.00000i) q^{98} +(-4.62614 - 7.20871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 16 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 16 * q^9	\( 8 q - 8 q^{4} - 16 q^{9} + 4 q^{11} + 8 q^{14} - 16 q^{15} + 8 q^{16} - 4 q^{22} + 32 q^{23} + 16 q^{36} - 8 q^{37} - 24 q^{42} - 4 q^{44} + 40 q^{49} - 56 q^{53} - 8 q^{56} - 24 q^{58} + 16 q^{60} - 8 q^{64} - 24 q^{67} + 24 q^{70} + 16 q^{71} + 4 q^{77} + 40 q^{78} + 80 q^{81} + 16 q^{86} + 4 q^{88} - 24 q^{91} - 32 q^{92} + 8 q^{93} - 92 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 16 * q^9 + 4 * q^11 + 8 * q^14 - 16 * q^15 + 8 * q^16 - 4 * q^22 + 32 * q^23 + 16 * q^36 - 8 * q^37 - 24 * q^42 - 4 * q^44 + 40 * q^49 - 56 * q^53 - 8 * q^56 - 24 * q^58 + 16 * q^60 - 8 * q^64 - 24 * q^67 + 24 * q^70 + 16 * q^71 + 4 * q^77 + 40 * q^78 + 80 * q^81 + 16 * q^86 + 4 * q^88 - 24 * q^91 - 32 * q^92 + 8 * q^93 - 92 * q^99

Introduction

L-functions

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