LMFDB - Embedded newform 693.2.i.i.298.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (of order $3$, degree $2$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.10423593216.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.2
Root			$-0.276205 - 0.478401i$ of defining polynomial
Character	$\chi$	$=$	693.298
Dual form			693.2.i.i.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.276205 - 0.478401i) q^{2} +(0.847422 - 1.46778i) q^{4} +(0.795012 + 1.37700i) q^{5} +(0.886763 - 2.49272i) q^{7} -2.04107 q^{8} +O(q^{10})$	\(q+(-0.276205 - 0.478401i) q^{2} +(0.847422 - 1.46778i) q^{4} +(0.795012 + 1.37700i) q^{5} +(0.886763 - 2.49272i) q^{7} -2.04107 q^{8} +(0.439172 - 0.760669i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.87834 q^{13} +(-1.43745 + 0.264273i) q^{14} +(-1.13109 - 1.95911i) q^{16} +(2.41864 - 4.18921i) q^{17} +(0.572943 + 0.992366i) q^{19} +2.69484 q^{20} +0.552409 q^{22} +(-1.82594 - 3.16261i) q^{23} +(1.23591 - 2.14066i) q^{25} +(-0.795012 - 1.37700i) q^{26} +(-2.90730 - 3.41396i) q^{28} +0.325935 q^{29} +(-3.22577 + 5.58719i) q^{31} +(-2.66589 + 4.61746i) q^{32} -2.67216 q^{34} +(4.13747 - 0.760669i) q^{35} +(-0.847422 - 1.46778i) q^{37} +(0.316499 - 0.548192i) q^{38} +(-1.62267 - 2.81055i) q^{40} +4.05839 q^{41} +4.62764 q^{43} +(0.847422 + 1.46778i) q^{44} +(-1.00866 + 1.74706i) q^{46} +(0.152578 + 0.264273i) q^{47} +(-5.42730 - 4.42090i) q^{49} -1.36546 q^{50} +(2.43917 - 4.22477i) q^{52} +(2.85686 - 4.94822i) q^{53} -1.59002 q^{55} +(-1.80994 + 5.08781i) q^{56} +(-0.0900249 - 0.155928i) q^{58} +(5.93075 - 10.2724i) q^{59} +(-0.886763 - 1.53592i) q^{61} +3.56389 q^{62} -1.57904 q^{64} +(2.28832 + 3.96349i) q^{65} +(-7.63574 + 13.2255i) q^{67} +(-4.09922 - 7.10005i) q^{68} +(-1.50669 - 1.76927i) q^{70} -9.16666 q^{71} +(5.86648 - 10.1610i) q^{73} +(-0.468124 + 0.810814i) q^{74} +1.94210 q^{76} +(1.71538 + 2.01432i) q^{77} +(4.35513 + 7.54331i) q^{79} +(1.79846 - 3.11503i) q^{80} +(-1.12095 - 1.94154i) q^{82} -8.40856 q^{83} +7.69139 q^{85} +(-1.27818 - 2.21387i) q^{86} +(1.02053 - 1.76762i) q^{88} +(-2.87489 - 4.97946i) q^{89} +(2.55241 - 7.17491i) q^{91} -6.18935 q^{92} +(0.0842856 - 0.145987i) q^{94} +(-0.910993 + 1.57789i) q^{95} -3.65329 q^{97} +(-0.615916 + 3.81750i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8	$ 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8 - 10 * q^10 - 4 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^17 - 4 * q^22 + 4 * q^23 - 4 * q^25 - 4 * q^26 - 22 * q^28 - 16 * q^29 + 12 * q^31 + 26 * q^32 - 32 * q^34 + 2 * q^35 + 4 * q^37 + 8 * q^38 + 6 * q^40 - 4 * q^41 + 36 * q^43 - 4 * q^44 + 14 * q^46 + 12 * q^47 - 4 * q^49 - 4 * q^50 + 6 * q^52 - 12 * q^53 - 8 * q^55 - 48 * q^56 + 4 * q^58 + 12 * q^59 - 2 * q^61 + 52 * q^62 + 112 * q^64 - 4 * q^65 - 28 * q^67 - 48 * q^68 - 32 * q^70 - 24 * q^71 - 6 * q^73 - 16 * q^74 - 36 * q^76 - 4 * q^77 - 2 * q^79 + 16 * q^80 + 12 * q^82 + 24 * q^83 + 36 * q^85 + 36 * q^86 + 12 * q^88 + 8 * q^89 + 12 * q^91 + 32 * q^92 - 20 * q^94 + 34 * q^95 - 88 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.276205	−	0.478401i	−0.195306	−	0.338280i	0.751695	−	0.659511i	$-0.229237\pi$
$2$	−0.276205	−	0.478401i	−0.195306	−	0.338280i	−0.947001	+	0.321231i	$0.895903\pi$
$3$		0			0
$3$		0			0
$4$	0.847422	−	1.46778i	0.423711	−	0.733889i
$5$	0.795012	+	1.37700i	0.355540	+	0.615814i	0.987210	−	0.159423i	$-0.0509635\pi$
$5$	0.795012	+	1.37700i	0.355540	+	0.615814i	−0.631670	+	0.775237i	$0.717630\pi$
$6$		0			0
$7$	0.886763	−	2.49272i	0.335165	−	0.942159i
$7$	0.886763	−	2.49272i	0.335165	−	0.942159i
$8$	−2.04107			−0.721626
$9$		0			0
$10$	0.439172	−	0.760669i	0.138879	−	0.240545i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	2.87834			0.798309			0.399155	−	0.916884i	$-0.369304\pi$
$13$	2.87834			0.798309			0.399155	+	0.916884i	$0.369304\pi$
$14$	−1.43745	+	0.264273i	−0.384174	+	0.0706299i
$15$		0			0
$16$	−1.13109	−	1.95911i	−0.282773	−	0.489777i
$17$	2.41864	−	4.18921i	0.586606	−	1.01603i	−0.408067	−	0.912952i	$-0.633797\pi$
$17$	2.41864	−	4.18921i	0.586606	−	1.01603i	0.994673	−	0.103080i	$-0.0328697\pi$
$18$		0			0
$19$	0.572943	+	0.992366i	0.131442	+	0.227664i	0.924233	−	0.381830i	$-0.124706\pi$
$19$	0.572943	+	0.992366i	0.131442	+	0.227664i	−0.792791	+	0.609494i	$0.791373\pi$
$20$	2.69484			0.602585
$21$		0			0
$22$	0.552409			0.117774
$23$	−1.82594	−	3.16261i	−0.380734	−	0.659450i	0.610434	−	0.792068i	$-0.290995\pi$
$23$	−1.82594	−	3.16261i	−0.380734	−	0.659450i	−0.991167	+	0.132617i	$0.957662\pi$
$24$		0			0
$25$	1.23591	−	2.14066i	0.247182	−	0.428132i
$26$	−0.795012	−	1.37700i	−0.155915	−	0.270052i
$27$		0			0
$28$	−2.90730	−	3.41396i	−0.549427	−	0.645177i
$29$	0.325935			0.0605247			0.0302623	−	0.999542i	$-0.490366\pi$
$29$	0.325935			0.0605247			0.0302623	+	0.999542i	$0.490366\pi$
$30$		0			0
$31$	−3.22577	+	5.58719i	−0.579365	+	1.00349i	0.416188	+	0.909279i	$0.363366\pi$
$31$	−3.22577	+	5.58719i	−0.579365	+	1.00349i	−0.995552	+	0.0942105i	$0.969967\pi$
$32$	−2.66589	+	4.61746i	−0.471268	+	0.816259i
$33$		0			0
$34$	−2.67216			−0.458271
$35$	4.13747	−	0.760669i	0.699360	−	0.128577i
$36$		0			0
$37$	−0.847422	−	1.46778i	−0.139315	−	0.241301i	0.787922	−	0.615775i	$-0.211157\pi$
$37$	−0.847422	−	1.46778i	−0.139315	−	0.241301i	−0.927238	+	0.374473i	$0.877823\pi$
$38$	0.316499	−	0.548192i	0.0513429	−	0.0889285i
$39$		0			0
$40$	−1.62267	−	2.81055i	−0.256567	−	0.444387i
$41$	4.05839			0.633815			0.316907	−	0.948456i	$-0.397356\pi$
$41$	4.05839			0.633815			0.316907	+	0.948456i	$0.397356\pi$
$42$		0			0
$43$	4.62764			0.705709			0.352854	−	0.935678i	$-0.385211\pi$
$43$	4.62764			0.705709			0.352854	+	0.935678i	$0.385211\pi$
$44$	0.847422	+	1.46778i	0.127754	+	0.221276i
$45$		0			0
$46$	−1.00866	+	1.74706i	−0.148719	+	0.257590i
$47$	0.152578	+	0.264273i	0.0222558	+	0.0385482i	0.876939	−	0.480602i	$-0.159582\pi$
$47$	0.152578	+	0.264273i	0.0222558	+	0.0385482i	−0.854683	+	0.519150i	$0.826249\pi$
$48$		0			0
$49$	−5.42730	−	4.42090i	−0.775329	−	0.631558i
$50$	−1.36546			−0.193105
$51$		0			0
$52$	2.43917	−	4.22477i	0.338252	−	0.585870i
$53$	2.85686	−	4.94822i	0.392420	−	0.679691i	−0.600348	−	0.799739i	$-0.704971\pi$
$53$	2.85686	−	4.94822i	0.392420	−	0.679691i	0.992768	+	0.120048i	$0.0383048\pi$
$54$		0			0
$55$	−1.59002			−0.214399
$56$	−1.80994	+	5.08781i	−0.241864	+	0.679887i
$57$		0			0
$58$	−0.0900249	−	0.155928i	−0.0118208	−	0.0204743i
$59$	5.93075	−	10.2724i	0.772118	−	1.33735i	−0.164281	−	0.986414i	$-0.552531\pi$
$59$	5.93075	−	10.2724i	0.772118	−	1.33735i	0.936400	−	0.350935i	$-0.114136\pi$
$60$		0			0
$61$	−0.886763	−	1.53592i	−0.113538	−	0.196654i	0.803656	−	0.595094i	$-0.202885\pi$
$61$	−0.886763	−	1.53592i	−0.113538	−	0.196654i	−0.917195	+	0.398440i	$0.869552\pi$
$62$	3.56389			0.452614
$63$		0			0
$64$	−1.57904			−0.197380
$65$	2.28832	+	3.96349i	0.283831	+	0.491610i
$66$		0			0
$67$	−7.63574	+	13.2255i	−0.932854	+	1.61575i	−0.154438	+	0.988002i	$0.549357\pi$
$67$	−7.63574	+	13.2255i	−0.932854	+	1.61575i	−0.778416	+	0.627749i	$0.783977\pi$
$68$	−4.09922	−	7.10005i	−0.497103	−	0.861007i
$69$		0			0
$70$	−1.50669	−	1.76927i	−0.180084	−	0.211468i
$71$	−9.16666			−1.08788			−0.543941	−	0.839123i	$-0.683069\pi$
$71$	−9.16666			−1.08788			−0.543941	+	0.839123i	$0.683069\pi$
$72$		0			0
$73$	5.86648	−	10.1610i	0.686619	−	1.18926i	−0.286306	−	0.958138i	$-0.592427\pi$
$73$	5.86648	−	10.1610i	0.686619	−	1.18926i	0.972925	−	0.231121i	$-0.0742393\pi$
$74$	−0.468124	+	0.810814i	−0.0544183	+	0.0942553i
$75$		0			0
$76$	1.94210			0.222774
$77$	1.71538	+	2.01432i	0.195485	+	0.229553i
$78$		0			0
$79$	4.35513	+	7.54331i	0.489991	+	0.848689i	0.999934	−	0.0115194i	$-0.00366683\pi$
$79$	4.35513	+	7.54331i	0.489991	+	0.848689i	−0.509943	+	0.860208i	$0.670333\pi$
$80$	1.79846	−	3.11503i	0.201074	−	0.348271i
$81$		0			0
$82$	−1.12095	−	1.94154i	−0.123788	−	0.214407i
$83$	−8.40856			−0.922959			−0.461480	−	0.887151i	$-0.652681\pi$
$83$	−8.40856			−0.922959			−0.461480	+	0.887151i	$0.652681\pi$
$84$		0			0
$85$	7.69139			0.834249
$86$	−1.27818	−	2.21387i	−0.137829	−	0.238727i
$87$		0			0
$88$	1.02053	−	1.76762i	0.108789	−	0.188428i
$89$	−2.87489	−	4.97946i	−0.304738	−	0.527822i	0.672465	−	0.740129i	$-0.265236\pi$
$89$	−2.87489	−	4.97946i	−0.304738	−	0.527822i	−0.977203	+	0.212307i	$0.931902\pi$
$90$		0			0
$91$	2.55241	−	7.17491i	0.267565	−	0.752135i
$92$	−6.18935			−0.645284
$93$		0			0
$94$	0.0842856	−	0.145987i	0.00869339	−	0.0150574i
$95$	−0.910993	+	1.57789i	−0.0934659	+	0.161888i
$96$		0			0
$97$	−3.65329			−0.370935			−0.185467	−	0.982650i	$-0.559380\pi$
$97$	−3.65329			−0.370935			−0.185467	+	0.982650i	$0.559380\pi$
$98$	−0.615916	+	3.81750i	−0.0622169	+	0.385626i
$99$		0			0
$100$	−2.09468	−	3.62808i	−0.209468	−	0.362808i
$101$	0.142189	−	0.246278i	0.0141483	−	0.0245056i	−0.858865	−	0.512203i	$-0.828830\pi$
$101$	0.142189	−	0.246278i	0.0141483	−	0.0245056i	0.873013	+	0.487697i	$0.162163\pi$
$102$		0			0
$103$	8.34671	+	14.4569i	0.822426	+	1.42448i	0.903871	+	0.427806i	$0.140713\pi$
$103$	8.34671	+	14.4569i	0.822426	+	1.42448i	−0.0814443	+	0.996678i	$0.525953\pi$
$104$	−5.87489			−0.576081
$105$		0			0
$106$	−3.15631			−0.306568
$107$	8.97475	+	15.5447i	0.867621	+	1.50276i	0.864421	+	0.502769i	$0.167686\pi$
$107$	8.97475	+	15.5447i	0.867621	+	1.50276i	0.00320086	+	0.999995i	$0.498981\pi$
$108$		0			0
$109$	−5.54399	+	9.60247i	−0.531018	+	0.919750i	0.468327	+	0.883555i	$0.344857\pi$
$109$	−5.54399	+	9.60247i	−0.531018	+	0.919750i	−0.999345	+	0.0361949i	$0.988476\pi$
$110$	0.439172	+	0.760669i	0.0418734	+	0.0725269i
$111$		0			0
$112$	−5.88652	+	1.08223i	−0.556224	+	0.102261i
$113$	−1.72443			−0.162221			−0.0811105	−	0.996705i	$-0.525847\pi$
$113$	−1.72443			−0.162221			−0.0811105	+	0.996705i	$0.525847\pi$
$114$		0			0
$115$	2.90328	−	5.02863i	0.270732	−	0.468922i
$116$	0.276205	−	0.478401i	0.0256450	−	0.0444184i
$117$		0			0
$118$	−6.55241			−0.603198
$119$	−8.29776	−	9.74382i	−0.760654	−	0.893215i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.489856	+	0.848456i	−0.0443495	+	0.0768156i
$123$		0			0
$124$	5.46717	+	9.46942i	0.490966	+	0.850379i
$125$	11.8804			1.06261
$126$		0			0
$127$	20.3675			1.80732			0.903661	−	0.428248i	$-0.140869\pi$
$127$	20.3675			1.80732			0.903661	+	0.428248i	$0.140869\pi$
$128$	5.76792	+	9.99033i	0.509817	+	0.883029i
$129$		0			0
$130$	1.26409	−	2.18947i	0.110868	−	0.192029i
$131$	10.0910	+	17.4782i	0.881659	+	1.52708i	0.849496	+	0.527595i	$0.176906\pi$
$131$	10.0910	+	17.4782i	0.881659	+	1.52708i	0.0321623	+	0.999483i	$0.489761\pi$
$132$		0			0
$133$	2.98175	−	0.548192i	0.258551	−	0.0475343i
$134$	8.43611			0.728769
$135$		0			0
$136$	−4.93660	+	8.55045i	−0.423310	+	0.733195i
$137$	−10.6316	+	18.4144i	−0.908317	+	1.57325i	−0.0919163	+	0.995767i	$0.529299\pi$
$137$	−10.6316	+	18.4144i	−0.908317	+	1.57325i	−0.816401	+	0.577485i	$0.804034\pi$
$138$		0			0
$139$	5.27951			0.447802			0.223901	−	0.974612i	$-0.428121\pi$
$139$	5.27951			0.447802			0.223901	+	0.974612i	$0.428121\pi$
$140$	2.38969	−	6.71749i	0.201965	−	0.567732i
$141$		0			0
$142$	2.53188	+	4.38534i	0.212470	+	0.368009i
$143$	−1.43917	+	2.49272i	−0.120350	+	0.208452i
$144$		0			0
$145$	0.259123	+	0.448814i	0.0215190	+	0.0372719i
$146$	−6.48139			−0.536404
$147$		0			0
$148$	−2.87250			−0.236118
$149$	0.682729	+	1.18252i	0.0559313	+	0.0968759i	0.892635	−	0.450779i	$-0.148854\pi$
$149$	0.682729	+	1.18252i	0.0559313	+	0.0968759i	−0.836704	+	0.547655i	$0.815521\pi$
$150$		0			0
$151$	−7.97450	+	13.8122i	−0.648956	+	1.12402i	0.334417	+	0.942425i	$0.391461\pi$
$151$	−7.97450	+	13.8122i	−0.648956	+	1.12402i	−0.983373	+	0.181599i	$0.941873\pi$
$152$	−1.16941	−	2.02549i	−0.0948520	−	0.164289i
$153$		0			0
$154$	0.489856	−	1.37700i	0.0394737	−	0.110962i
$155$	−10.2581			−0.823950
$156$		0			0
$157$	4.19830	−	7.27166i	0.335060	−	0.580342i	−0.648436	−	0.761269i	$-0.724577\pi$
$157$	4.19830	−	7.27166i	0.335060	−	0.580342i	0.983496	+	0.180927i	$0.0579099\pi$
$158$	2.40582	−	4.16700i	0.191396	−	0.331508i
$159$		0			0
$160$	−8.47767			−0.670219
$161$	−9.50268	+	1.74706i	−0.748916	+	0.137687i
$162$		0			0
$163$	8.65652	+	14.9935i	0.678031	+	1.17438i	0.975573	+	0.219675i	$0.0704999\pi$
$163$	8.65652	+	14.9935i	0.678031	+	1.17438i	−0.297542	+	0.954709i	$0.596167\pi$
$164$	3.43917	−	5.95682i	0.268554	−	0.465150i
$165$		0			0
$166$	2.32248	+	4.02266i	0.180260	+	0.312219i
$167$	−18.4945			−1.43115			−0.715574	−	0.698537i	$-0.753835\pi$
$167$	−18.4945			−1.43115			−0.715574	+	0.698537i	$0.753835\pi$
$168$		0			0
$169$	−4.71513			−0.362702
$170$	−2.12440	−	3.67957i	−0.162934	−	0.282210i
$171$		0			0
$172$	3.92156	−	6.79235i	0.299016	−	0.517912i
$173$	6.13402	+	10.6244i	0.466361	+	0.807760i	0.999262	−	0.0384172i	$-0.0122316\pi$
$173$	6.13402	+	10.6244i	0.466361	+	0.807760i	−0.532901	+	0.846177i	$0.678898\pi$
$174$		0			0
$175$	−4.24010	−	4.97904i	−0.320522	−	0.376380i
$176$	2.26218			0.170518
$177$		0			0
$178$	−1.58812	+	2.75070i	−0.119035	+	0.206174i
$179$	6.90582	−	11.9612i	0.516165	−	0.894024i	−0.483659	−	0.875257i	$-0.660692\pi$
$179$	6.90582	−	11.9612i	0.516165	−	0.894024i	0.999824	−	0.0187674i	$-0.00597419\pi$
$180$		0			0
$181$	−18.7687			−1.39506			−0.697532	−	0.716554i	$-0.745718\pi$
$181$	−18.7687			−1.39506			−0.697532	+	0.716554i	$0.745718\pi$
$182$	−4.13747	+	0.760669i	−0.306689	+	0.0563845i
$183$		0			0
$184$	3.72686	+	6.45510i	0.274747	+	0.475877i
$185$	1.34742	−	2.33380i	0.0990644	−	0.171585i
$186$		0			0
$187$	2.41864	+	4.18921i	0.176868	+	0.306345i
$188$	0.517192			0.0377201
$189$		0			0
$190$	1.00648			0.0730179
$191$	4.05839	+	7.02935i	0.293655	+	0.508626i	0.974671	−	0.223643i	$-0.0717949\pi$
$191$	4.05839	+	7.02935i	0.293655	+	0.508626i	−0.681016	+	0.732269i	$0.738462\pi$
$192$		0			0
$193$	−0.595383	+	1.03123i	−0.0428566	+	0.0742298i	−0.886658	−	0.462426i	$-0.846979\pi$
$193$	−0.595383	+	1.03123i	−0.0428566	+	0.0742298i	0.843801	+	0.536656i	$0.180313\pi$
$194$	1.00905	+	1.74773i	0.0724459	+	0.125480i
$195$		0			0
$196$	−11.0881	+	4.21970i	−0.792008	+	0.301407i
$197$	26.7523			1.90602			0.953012	−	0.302933i	$-0.0979659\pi$
$197$	26.7523			1.90602			0.953012	+	0.302933i	$0.0979659\pi$
$198$		0			0
$199$	3.01684	−	5.22531i	0.213858	−	0.370413i	−0.739061	−	0.673639i	$-0.764730\pi$
$199$	3.01684	−	5.22531i	0.213858	−	0.370413i	0.952919	+	0.303226i	$0.0980637\pi$
$200$	−2.52258	+	4.36923i	−0.178373	+	0.308951i
$201$		0			0
$202$	−0.157093			−0.0110530
$203$	0.289027	−	0.812465i	0.0202857	−	0.0570239i
$204$		0			0
$205$	3.22647	+	5.58842i	0.225347	+	0.390312i
$206$	4.61080	−	7.98615i	0.321250	−	0.556421i
$207$		0			0
$208$	−3.25567	−	5.63899i	−0.225740	−	0.390993i
$209$	−1.14589			−0.0792626
$210$		0			0
$211$	−20.4601			−1.40853			−0.704264	−	0.709938i	$-0.748723\pi$
$211$	−20.4601			−1.40853			−0.704264	+	0.709938i	$0.748723\pi$
$212$	−4.84193	−	8.38647i	−0.332545	−	0.575985i
$213$		0			0
$214$	4.95773	−	8.58705i	0.338904	−	0.586998i
$215$	3.67903	+	6.37227i	0.250908	+	0.434585i
$216$		0			0
$217$	11.0668	+	12.9954i	0.751264	+	0.882188i
$218$	6.12511			0.414845
$219$		0			0
$220$	−1.34742	+	2.33380i	−0.0908432	+	0.157345i
$221$	6.96168	−	12.0580i	0.468293	−	0.811107i
$222$		0			0
$223$	−29.6048			−1.98248			−0.991242	−	0.132055i	$-0.957843\pi$
$223$	−29.6048			−1.98248			−0.991242	+	0.132055i	$0.957843\pi$
$224$	9.14602	+	10.7399i	0.611094	+	0.717591i
$225$		0			0
$226$	0.476296	+	0.824969i	0.0316828	+	0.0548761i
$227$	−12.0416	+	20.8566i	−0.799226	+	1.38430i	0.120894	+	0.992665i	$0.461424\pi$
$227$	−12.0416	+	20.8566i	−0.799226	+	1.38430i	−0.920121	+	0.391635i	$0.871910\pi$
$228$		0			0
$229$	2.60735	+	4.51607i	0.172299	+	0.298430i	0.939223	−	0.343307i	$-0.111547\pi$
$229$	2.60735	+	4.51607i	0.172299	+	0.298430i	−0.766924	+	0.641737i	$0.778214\pi$
$230$	−3.20760			−0.211503
$231$		0			0
$232$	−0.665256			−0.0436762
$233$	1.57294	+	2.72442i	0.103047	+	0.178482i	0.912939	−	0.408097i	$-0.133807\pi$
$233$	1.57294	+	2.72442i	0.103047	+	0.178482i	−0.809892	+	0.586579i	$0.800474\pi$
$234$		0			0
$235$	−0.242603	+	0.420201i	−0.0158257	+	0.0274109i
$236$	−10.0517	−	17.4101i	−0.654310	−	1.13330i
$237$		0			0
$238$	−2.36957	+	6.66094i	−0.153596	+	0.431765i
$239$	−2.75465			−0.178184			−0.0890919	−	0.996023i	$-0.528396\pi$
$239$	−2.75465			−0.178184			−0.0890919	+	0.996023i	$0.528396\pi$
$240$		0			0
$241$	4.51479	−	7.81985i	0.290823	−	0.503721i	−0.683181	−	0.730249i	$-0.739404\pi$
$241$	4.51479	−	7.81985i	0.290823	−	0.503721i	0.974005	+	0.226528i	$0.0727374\pi$
$242$	−0.276205	+	0.478401i	−0.0177551	+	0.0307528i
$243$		0			0
$244$	−3.00585			−0.192430
$245$	1.77282	−	10.9881i	0.113261	−	0.702003i
$246$		0			0
$247$	1.64913	+	2.85637i	0.104931	+	0.181747i
$248$	6.58400	−	11.4038i	0.418085	−	0.724144i
$249$		0			0
$250$	−3.28142	−	5.68358i	−0.207535	−	0.359461i
$251$	6.73133			0.424878			0.212439	−	0.977174i	$-0.431859\pi$
$251$	6.73133			0.424878			0.212439	+	0.977174i	$0.431859\pi$
$252$		0			0
$253$	3.65187			0.229591
$254$	−5.62560	−	9.74382i	−0.352981	−	0.611382i
$255$		0			0
$256$	1.60722	−	2.78378i	0.100451	−	0.173986i
$257$	13.8447	+	23.9797i	0.863607	+	1.49581i	0.868424	+	0.495823i	$0.165133\pi$
$257$	13.8447	+	23.9797i	0.863607	+	1.49581i	−0.00481687	+	0.999988i	$0.501533\pi$
$258$		0			0
$259$	−4.41022	+	0.810814i	−0.274038	+	0.0503816i
$260$	7.75669			0.481049
$261$		0			0
$262$	5.57439	−	9.65512i	0.344387	−	0.596495i
$263$	2.30170	−	3.98667i	0.141929	−	0.245829i	−0.786294	−	0.617853i	$-0.788003\pi$
$263$	2.30170	−	3.98667i	0.141929	−	0.245829i	0.928223	+	0.372024i	$0.121336\pi$
$264$		0			0
$265$	9.08495			0.558084
$266$	−1.08583	−	1.27506i	−0.0665765	−	0.0781789i
$267$		0			0
$268$	12.9414	+	22.4151i	0.790521	+	1.36922i
$269$	9.55515	−	16.5500i	0.582588	−	1.00907i	−0.412583	−	0.910920i	$-0.635373\pi$
$269$	9.55515	−	16.5500i	0.582588	−	1.00907i	0.995171	−	0.0981522i	$-0.0312932\pi$
$270$		0			0
$271$	−7.68643	−	13.3133i	−0.466917	−	0.808724i	0.532369	−	0.846513i	$-0.321302\pi$
$271$	−7.68643	−	13.3133i	−0.466917	−	0.808724i	−0.999286	+	0.0377885i	$0.987969\pi$
$272$	−10.9428			−0.663505
$273$		0			0
$274$	11.7460			0.709600
$275$	1.23591	+	2.14066i	0.0745282	+	0.129087i
$276$		0			0
$277$	4.69484	−	8.13171i	0.282086	−	0.488587i	−0.689812	−	0.723988i	$-0.742307\pi$
$277$	4.69484	−	8.13171i	0.282086	−	0.488587i	0.971898	+	0.235401i	$0.0756404\pi$
$278$	−1.45823	−	2.52572i	−0.0874586	−	0.151483i
$279$		0			0
$280$	−8.44485	+	1.55258i	−0.504676	+	0.0927842i
$281$	−26.9788			−1.60942			−0.804710	−	0.593668i	$-0.797679\pi$
$281$	−26.9788			−1.60942			−0.804710	+	0.593668i	$0.797679\pi$
$282$		0			0
$283$	11.7878	−	20.4171i	0.700712	−	1.21367i	−0.267505	−	0.963556i	$-0.586199\pi$
$283$	11.7878	−	20.4171i	0.700712	−	1.21367i	0.968217	−	0.250112i	$-0.0804673\pi$
$284$	−7.76803	+	13.4546i	−0.460948	+	0.798385i
$285$		0			0
$286$	1.59002			0.0940201
$287$	3.59883	−	10.1164i	0.212432	−	0.597155i
$288$		0			0
$289$	−3.19963	−	5.54192i	−0.188214	−	0.325995i
$290$	0.143142	−	0.247929i	0.00840558	−	0.0145589i
$291$		0			0
$292$	−9.94276	−	17.2214i	−0.581856	−	1.00780i
$293$	11.8500			0.692286			0.346143	−	0.938182i	$-0.387491\pi$
$293$	11.8500			0.692286			0.346143	+	0.938182i	$0.387491\pi$
$294$		0			0
$295$	18.8601			1.09808
$296$	1.72964	+	2.99583i	0.100534	+	0.174129i
$297$		0			0
$298$	0.377146	−	0.653236i	0.0218475	−	0.0378409i
$299$	−5.25567	−	9.10309i	−0.303943	−	0.526445i
$300$		0			0
$301$	4.10362	−	11.5354i	0.236529	−	0.664890i
$302$	8.81038			0.506980
$303$		0			0
$304$	1.29610	−	2.24491i	0.0743365	−	0.128755i
$305$	1.40998	−	2.44215i	0.0807349	−	0.139837i
$306$		0			0
$307$	19.5894			1.11803			0.559013	−	0.829159i	$-0.311180\pi$
$307$	19.5894			1.11803			0.559013	+	0.829159i	$0.311180\pi$
$308$	4.41022	−	0.810814i	0.251296	−	0.0462004i
$309$		0			0
$310$	2.83334	+	4.90748i	0.160923	+	0.278726i
$311$	−10.7008	+	18.5344i	−0.606788	+	1.05099i	0.384978	+	0.922926i	$0.374209\pi$
$311$	−10.7008	+	18.5344i	−0.606788	+	1.05099i	−0.991766	+	0.128062i	$0.959124\pi$
$312$		0			0
$313$	6.66392	+	11.5422i	0.376667	+	0.652407i	0.990575	−	0.136971i	$-0.0437367\pi$
$313$	6.66392	+	11.5422i	0.376667	+	0.652407i	−0.613908	+	0.789378i	$0.710403\pi$
$314$	−4.63836			−0.261758
$315$		0			0
$316$	14.7625			0.830458
$317$	−3.54776	−	6.14490i	−0.199262	−	0.345132i	0.749027	−	0.662539i	$-0.230521\pi$
$317$	−3.54776	−	6.14490i	−0.199262	−	0.345132i	−0.948289	+	0.317407i	$0.897188\pi$
$318$		0			0
$319$	−0.162968	+	0.282268i	−0.00912444	+	0.0158040i
$320$	−1.25535	−	2.17434i	−0.0701765	−	0.121549i
$321$		0			0
$322$	3.46048	+	4.06354i	0.192845	+	0.226452i
$323$	5.54297			0.308419
$324$		0			0
$325$	3.55738	−	6.16156i	0.197328	−	0.341782i
$326$	4.78194	−	8.28257i	0.264847	−	0.458729i
$327$		0			0
$328$	−8.28345			−0.457377
$329$	0.794059	−	0.145987i	0.0437779	−	0.00804852i
$330$		0			0
$331$	−10.3675	−	17.9570i	−0.569849	−	0.987007i	−0.996580	−	0.0826290i	$-0.973668\pi$
$331$	−10.3675	−	17.9570i	−0.569849	−	0.987007i	0.426731	−	0.904378i	$-0.359665\pi$
$332$	−7.12560	+	12.3419i	−0.391068	+	0.677350i
$333$		0			0
$334$	5.10827	+	8.84778i	0.279512	+	0.484129i
$335$	−24.2820			−1.32667
$336$		0			0
$337$	−5.30755			−0.289121			−0.144560	−	0.989496i	$-0.546177\pi$
$337$	−5.30755			−0.289121			−0.144560	+	0.989496i	$0.546177\pi$
$338$	1.30234	+	2.25572i	0.0708380	+	0.122695i
$339$		0			0
$340$	6.51785	−	11.2893i	0.353480	−	0.612246i
$341$	−3.22577	−	5.58719i	−0.174685	−	0.302563i
$342$		0			0
$343$	−15.8328	+	9.60845i	−0.854891	+	0.518808i
$344$	−9.44532			−0.509258
$345$		0			0
$346$	3.38849	−	5.86903i	0.182166	−	0.315521i
$347$	8.40156	−	14.5519i	0.451019	−	0.781188i	−0.547430	−	0.836851i	$-0.684394\pi$
$347$	8.40156	−	14.5519i	0.451019	−	0.781188i	0.998450	+	0.0556630i	$0.0177273\pi$
$348$		0			0
$349$	−0.870459			−0.0465946			−0.0232973	−	0.999729i	$-0.507416\pi$
$349$	−0.870459			−0.0465946			−0.0232973	+	0.999729i	$0.507416\pi$
$350$	−1.21084	+	3.40370i	−0.0647220	+	0.181936i
$351$		0			0
$352$	−2.66589	−	4.61746i	−0.142093	−	0.246111i
$353$	−0.469077	+	0.812465i	−0.0249665	+	0.0432432i	−0.878239	−	0.478223i	$-0.841281\pi$
$353$	−0.469077	+	0.812465i	−0.0249665	+	0.0432432i	0.853272	+	0.521466i	$0.174615\pi$
$354$		0			0
$355$	−7.28761	−	12.6225i	−0.386786	−	0.669934i
$356$	−9.74499			−0.516483
$357$		0			0
$358$	−7.62968			−0.403241
$359$	−13.5050	−	23.3913i	−0.712765	−	1.23454i	−0.963815	−	0.266571i	$-0.914109\pi$
$359$	−13.5050	−	23.3913i	−0.712765	−	1.23454i	0.251051	−	0.967974i	$-0.419224\pi$
$360$		0			0
$361$	8.84347	−	15.3173i	0.465446	−	0.806176i
$362$	5.18399	+	8.97894i	0.272465	+	0.471923i
$363$		0			0
$364$	−8.36820	−	9.82654i	−0.438613	−	0.515051i
$365$	18.6557			0.976483
$366$		0			0
$367$	14.2055	−	24.6046i	0.741520	−	1.28435i	−0.210283	−	0.977641i	$-0.567439\pi$
$367$	14.2055	−	24.6046i	0.741520	−	1.28435i	0.951803	−	0.306710i	$-0.0992281\pi$
$368$	−4.13060	+	7.15441i	−0.215322	+	0.372949i
$369$		0			0
$370$	−1.48866			−0.0773916
$371$	−9.80118	−	11.5092i	−0.508852	−	0.597530i
$372$		0			0
$373$	4.87338	+	8.44094i	0.252334	+	0.437055i	0.964168	−	0.265293i	$-0.0854685\pi$
$373$	4.87338	+	8.44094i	0.252334	+	0.437055i	−0.711834	+	0.702348i	$0.752135\pi$
$374$	1.33608	−	2.31416i	0.0690870	−	0.119662i
$375$		0			0
$376$	−0.311422	−	0.539399i	−0.0160604	−	0.0278174i
$377$	0.938154			0.0483174
$378$		0			0
$379$	−33.1034			−1.70041			−0.850204	−	0.526454i	$-0.823521\pi$
$379$	−33.1034			−1.70041			−0.850204	+	0.526454i	$0.823521\pi$
$380$	1.54399	+	2.67427i	0.0792051	+	0.137187i
$381$		0			0
$382$	2.24190	−	3.88308i	0.114705	−	0.198676i
$383$	−5.34418	−	9.25639i	−0.273075	−	0.472980i	0.696573	−	0.717486i	$-0.254707\pi$
$383$	−5.34418	−	9.25639i	−0.273075	−	0.472980i	−0.969648	+	0.244507i	$0.921374\pi$
$384$		0			0
$385$	−1.40998	+	3.96349i	−0.0718590	+	0.201998i
$386$	0.657790			0.0334806
$387$		0			0
$388$	−3.09587	+	5.36221i	−0.157169	+	0.272225i
$389$	−19.2942	+	33.4185i	−0.978253	+	1.69438i	−0.309501	+	0.950899i	$0.600162\pi$
$389$	−19.2942	+	33.4185i	−0.978253	+	1.69438i	−0.668753	+	0.743485i	$0.733171\pi$
$390$		0			0
$391$	−17.6651			−0.893363
$392$	11.0775	+	9.02336i	0.559498	+	0.455748i
$393$		0			0
$394$	−7.38912	−	12.7983i	−0.372258	−	0.644770i
$395$	−6.92477	+	11.9941i	−0.348423	+	0.603486i
$396$		0			0
$397$	−6.96957	−	12.0716i	−0.349793	−	0.605859i	0.636420	−	0.771343i	$-0.280415\pi$
$397$	−6.96957	−	12.0716i	−0.349793	−	0.605859i	−0.986212	+	0.165484i	$0.947081\pi$
$398$	−3.33306			−0.167071
$399$		0			0
$400$	−5.59171			−0.279586
$401$	−6.56854	−	11.3770i	−0.328017	−	0.568142i	0.654101	−	0.756407i	$-0.273047\pi$
$401$	−6.56854	−	11.3770i	−0.328017	−	0.568142i	−0.982118	+	0.188265i	$0.939714\pi$
$402$		0			0
$403$	−9.28487	+	16.0819i	−0.462512	+	0.801095i
$404$	−0.240987	−	0.417402i	−0.0119896	−	0.0207665i
$405$		0			0
$406$	−0.468515	+	0.0861359i	−0.0232520	+	0.00427485i
$407$	1.69484			0.0840103
$408$		0			0
$409$	12.5164	−	21.6791i	0.618898	−	1.07196i	−0.370789	−	0.928717i	$-0.620913\pi$
$409$	12.5164	−	21.6791i	0.618898	−	1.07196i	0.989687	−	0.143246i	$-0.0457540\pi$
$410$	1.78233	−	3.08709i	0.0880232	−	0.152461i
$411$		0			0
$412$	28.2928			1.39388
$413$	−20.3470	−	23.8929i	−1.00121	−	1.17569i
$414$		0			0
$415$	−6.68491	−	11.5786i	−0.328149	−	0.568371i
$416$	−7.67336	+	13.2906i	−0.376217	+	0.651627i
$417$		0			0
$418$	0.316499	+	0.548192i	0.0154805	+	0.0268130i
$419$	−5.04297			−0.246365			−0.123183	−	0.992384i	$-0.539310\pi$
$419$	−5.04297			−0.246365			−0.123183	+	0.992384i	$0.539310\pi$
$420$		0			0
$421$	9.94055			0.484473			0.242236	−	0.970217i	$-0.422119\pi$
$421$	9.94055			0.484473			0.242236	+	0.970217i	$0.422119\pi$
$422$	5.65116	+	9.78810i	0.275094	+	0.476477i
$423$		0			0
$424$	−5.83104	+	10.0997i	−0.283180	+	0.490483i
$425$	−5.97844	−	10.3550i	−0.289997	−	0.502290i
$426$		0			0
$427$	−4.61496	+	0.848456i	−0.223334	+	0.0410597i
$428$	30.4216			1.47048
$429$		0			0
$430$	2.03233	−	3.52010i	0.0980077	−	0.169754i
$431$	6.84379	−	11.8538i	0.329654	−	0.570977i	−0.652789	−	0.757539i	$-0.726401\pi$
$431$	6.84379	−	11.8538i	0.329654	−	0.570977i	0.982443	+	0.186562i	$0.0597347\pi$
$432$		0			0
$433$	−4.26360			−0.204895			−0.102448	−	0.994738i	$-0.532667\pi$
$433$	−4.26360			−0.204895			−0.102448	+	0.994738i	$0.532667\pi$
$434$	3.16032	−	8.88377i	0.151700	−	0.426435i
$435$		0			0
$436$	9.39620	+	16.2747i	0.449996	+	0.779417i
$437$	2.09231	−	3.62399i	0.100089	−	0.173359i
$438$		0			0
$439$	11.7016	+	20.2678i	0.558487	+	0.967328i	0.997623	+	0.0689072i	$0.0219513\pi$
$439$	11.7016	+	20.2678i	0.558487	+	0.967328i	−0.439136	+	0.898421i	$0.644715\pi$
$440$	3.24535			0.154716
$441$		0			0
$442$	−7.69139			−0.365842
$443$	−7.35960	−	12.7472i	−0.349665	−	0.605638i	0.636525	−	0.771256i	$-0.280371\pi$
$443$	−7.35960	−	12.7472i	−0.349665	−	0.605638i	−0.986190	+	0.165618i	$0.947038\pi$
$444$		0			0
$445$	4.57115	−	7.91747i	0.216693	−	0.375324i
$446$	8.17699	+	14.1630i	0.387192	+	0.670636i
$447$		0			0
$448$	−1.40023	+	3.93610i	−0.0661548	+	0.185963i
$449$	34.8625			1.64526			0.822631	−	0.568575i	$-0.192505\pi$
$449$	34.8625			1.64526			0.822631	+	0.568575i	$0.192505\pi$
$450$		0			0
$451$	−2.02920	+	3.51467i	−0.0955512	+	0.165499i
$452$	−1.46132	+	2.53108i	−0.0687348	+	0.119052i
$453$		0			0
$454$	13.3037			0.624376
$455$	11.9091	−	2.18947i	0.558305	−	0.102644i
$456$		0			0
$457$	5.30068	+	9.18105i	0.247955	+	0.429471i	0.962958	−	0.269650i	$-0.0869080\pi$
$457$	5.30068	+	9.18105i	0.247955	+	0.429471i	−0.715003	+	0.699121i	$0.753575\pi$
$458$	1.44033	−	2.49472i	0.0673020	−	0.116571i
$459$		0			0
$460$	−4.92061	−	8.52275i	−0.229425	−	0.397375i
$461$	6.84418			0.318765			0.159383	−	0.987217i	$-0.449050\pi$
$461$	6.84418			0.318765			0.159383	+	0.987217i	$0.449050\pi$
$462$		0			0
$463$	−11.7299			−0.545136			−0.272568	−	0.962137i	$-0.587873\pi$
$463$	−11.7299			−0.545136			−0.272568	+	0.962137i	$0.587873\pi$
$464$	−0.368663	−	0.638542i	−0.0171147	−	0.0296436i
$465$		0			0
$466$	0.868908	−	1.50499i	0.0402514	−	0.0697175i
$467$	−19.1443	−	33.1590i	−0.885894	−	1.53441i	−0.844685	−	0.535263i	$-0.820212\pi$
$467$	−19.1443	−	33.1590i	−0.885894	−	1.53441i	−0.0412088	−	0.999151i	$-0.513121\pi$
$468$		0			0
$469$	26.1964	+	30.7616i	1.20964	+	1.42044i
$470$	0.268032			0.0123634
$471$		0			0
$472$	−12.1051	+	20.9666i	−0.557181	+	0.965065i
$473$	−2.31382	+	4.00765i	−0.106390	+	0.184272i
$474$		0			0
$475$	2.83242			0.129961
$476$	−21.3335	+	3.92213i	−0.977818	+	0.179771i
$477$		0			0
$478$	0.760848	+	1.31783i	0.0348004	+	0.0602760i
$479$	6.31446	−	10.9370i	0.288515	−	0.499722i	−0.684941	−	0.728599i	$-0.740172\pi$
$479$	6.31446	−	10.9370i	0.288515	−	0.499722i	0.973455	+	0.228876i	$0.0735052\pi$
$480$		0			0
$481$	−2.43917	−	4.22477i	−0.111217	−	0.192633i
$482$	−4.98803			−0.227199
$483$		0			0
$484$	−1.69484			−0.0770384
$485$	−2.90441	−	5.03058i	−0.131882	−	0.228427i
$486$		0			0
$487$	−17.8070	+	30.8426i	−0.806911	+	1.39761i	0.108082	+	0.994142i	$0.465529\pi$
$487$	−17.8070	+	30.8426i	−0.806911	+	1.39761i	−0.914993	+	0.403470i	$0.867804\pi$
$488$	1.80994	+	3.13491i	0.0819322	+	0.141911i
$489$		0			0
$490$	−5.74636	+	2.18684i	−0.259594	+	0.0987915i
$491$	−7.59854			−0.342917			−0.171459	−	0.985191i	$-0.554848\pi$
$491$	−7.59854			−0.342917			−0.171459	+	0.985191i	$0.554848\pi$
$492$		0			0
$493$	0.788320	−	1.36541i	0.0355041	−	0.0614950i
$494$	0.910993	−	1.57789i	0.0409875	−	0.0709925i
$495$		0			0
$496$	14.5945			0.655315
$497$	−8.12866	+	22.8499i	−0.364620	+	1.02496i
$498$		0			0
$499$	−0.803040	−	1.39091i	−0.0359490	−	0.0622655i	0.847491	−	0.530810i	$-0.178112\pi$
$499$	−0.803040	−	1.39091i	−0.0359490	−	0.0622655i	−0.883440	+	0.468544i	$0.844779\pi$
$500$	10.0677	−	17.4378i	0.450241	−	0.779840i
$501$		0			0
$502$	−1.85923	−	3.22027i	−0.0829813	−	0.143728i
$503$	38.6291			1.72239			0.861194	−	0.508277i	$-0.169717\pi$
$503$	38.6291			1.72239			0.861194	+	0.508277i	$0.169717\pi$
$504$		0			0
$505$	0.452167			0.0201212
$506$	−1.00866	−	1.74706i	−0.0448406	−	0.0776662i
$507$		0			0
$508$	17.2599	−	29.8950i	0.765782	−	1.32637i
$509$	15.8991	+	27.5381i	0.704716	+	1.22060i	0.966794	+	0.255558i	$0.0822590\pi$
$509$	15.8991	+	27.5381i	0.704716	+	1.22060i	−0.262078	+	0.965047i	$0.584408\pi$
$510$		0			0
$511$	−20.1264	−	23.6339i	−0.890341	−	1.04550i
$512$	21.2960			0.941159
$513$		0			0
$514$	7.64793	−	13.2466i	0.337336	−	0.584282i
$515$	−13.2715	+	22.9869i	−0.584811	+	1.01292i
$516$		0			0
$517$	−0.305156			−0.0134208
$518$	1.60602	+	1.88590i	0.0705644	+	0.0828618i
$519$		0			0
$520$	−4.67061	−	8.08974i	−0.204820	−	0.354759i
$521$	6.03416	−	10.4515i	0.264362	−	0.457888i	−0.703035	−	0.711156i	$-0.748172\pi$
$521$	6.03416	−	10.4515i	0.264362	−	0.457888i	0.967396	+	0.253268i	$0.0815055\pi$
$522$		0			0
$523$	−0.142825	−	0.247380i	−0.00624531	−	0.0108172i	0.862886	−	0.505399i	$-0.168655\pi$
$523$	−0.142825	−	0.247380i	−0.00624531	−	0.0108172i	−0.869131	+	0.494582i	$0.835321\pi$
$524$	34.2055			1.49427
$525$		0			0
$526$	−2.54297			−0.110879
$527$	15.6039	+	27.0268i	0.679718	+	1.17731i
$528$		0			0
$529$	4.83192	−	8.36913i	0.210083	−	0.363875i
$530$	−2.50931	−	4.34625i	−0.108997	−	0.188789i
$531$		0			0
$532$	1.72218	−	4.84110i	0.0746660	−	0.209888i
$533$	11.6815			0.505980
$534$		0			0
$535$	−14.2701	+	24.7165i	−0.616949	+	1.06859i
$536$	15.5851	−	26.9941i	0.673172	−	1.16597i
$537$		0			0
$538$	−10.5567			−0.455132
$539$	6.54227	−	2.48973i	0.281795	−	0.107240i
$540$		0			0
$541$	−1.40501	−	2.43355i	−0.0604060	−	0.104626i	0.834241	−	0.551400i	$-0.185906\pi$
$541$	−1.40501	−	2.43355i	−0.0604060	−	0.104626i	−0.894647	+	0.446774i	$0.852573\pi$
$542$	−4.24605	+	7.35438i	−0.182384	+	0.315898i
$543$		0			0
$544$	12.8957	+	22.3359i	0.552897	+	0.957646i
$545$	−17.6302			−0.755193
$546$		0			0
$547$	−20.8781			−0.892681			−0.446341	−	0.894863i	$-0.647273\pi$
$547$	−20.8781			−0.892681			−0.446341	+	0.894863i	$0.647273\pi$
$548$	18.0189	+	31.2096i	0.769728	+	1.33321i
$549$		0			0
$550$	0.682729	−	1.18252i	0.0291116	−	0.0504229i
$551$	0.186742	+	0.323447i	0.00795549	+	0.0137793i
$552$		0			0
$553$	22.6653	−	4.16700i	0.963828	−	0.177199i
$554$	−5.18695			−0.220372
$555$		0			0
$556$	4.47397	−	7.74915i	0.189739	−	0.328637i
$557$	9.13771	−	15.8270i	0.387177	−	0.670611i	−0.604891	−	0.796308i	$-0.706783\pi$
$557$	9.13771	−	15.8270i	0.387177	−	0.670611i	0.992069	+	0.125697i	$0.0401168\pi$
$558$		0			0
$559$	13.3199			0.563374
$560$	−6.17009	−	7.24536i	−0.260734	−	0.306172i
$561$		0			0
$562$	7.45167	+	12.9067i	0.314330	+	0.544435i
$563$	8.14944	−	14.1152i	0.343458	−	0.594886i	−0.641615	−	0.767027i	$-0.721735\pi$
$563$	8.14944	−	14.1152i	0.343458	−	0.594886i	0.985072	+	0.172141i	$0.0550684\pi$
$564$		0			0
$565$	−1.37094	−	2.37455i	−0.0576761	−	0.0998979i
$566$	−13.0234			−0.547413
$567$		0			0
$568$	18.7098			0.785045
$569$	8.37221	+	14.5011i	0.350981	+	0.607918i	0.986422	−	0.164232i	$-0.0525147\pi$
$569$	8.37221	+	14.5011i	0.350981	+	0.607918i	−0.635440	+	0.772150i	$0.719181\pi$
$570$		0			0
$571$	−12.1461	+	21.0377i	−0.508300	+	0.880401i	0.491654	+	0.870791i	$0.336392\pi$
$571$	−12.1461	+	21.0377i	−0.508300	+	0.880401i	−0.999954	+	0.00961042i	$0.996941\pi$
$572$	2.43917	+	4.22477i	0.101987	+	0.176647i
$573$		0			0
$574$	−5.83373	+	1.07252i	−0.243495	+	0.0447663i
$575$	−9.02677			−0.376442
$576$		0			0
$577$	−11.1586	+	19.3273i	−0.464540	+	0.804607i	−0.999181	−	0.0404725i	$-0.987114\pi$
$577$	−11.1586	+	19.3273i	−0.464540	+	0.804607i	0.534641	+	0.845080i	$0.320447\pi$
$578$	−1.76751	+	3.06141i	−0.0735185	+	0.127338i
$579$		0			0
$580$	0.878345			0.0364713
$581$	−7.45640	+	20.9602i	−0.309344	+	0.869575i
$582$		0			0
$583$	2.85686	+	4.94822i	0.118319	+	0.204934i
$584$	−11.9739	+	20.7393i	−0.495482	+	0.858200i
$585$		0			0
$586$	−3.27303	−	5.66906i	−0.135208	−	0.234187i
$587$	26.6944			1.10180			0.550898	−	0.834572i	$-0.314285\pi$
$587$	26.6944			1.10180			0.550898	+	0.834572i	$0.314285\pi$
$588$		0			0
$589$	−7.39272			−0.304612
$590$	−5.20925	−	9.02268i	−0.214461	−	0.371458i
$591$		0			0
$592$	−1.91702	+	3.32038i	−0.0787892	+	0.136467i
$593$	−11.4721	−	19.8702i	−0.471101	−	0.815971i	0.528352	−	0.849025i	$-0.322810\pi$
$593$	−11.4721	−	19.8702i	−0.471101	−	0.815971i	−0.999454	+	0.0330538i	$0.989477\pi$
$594$		0			0
$595$	6.82044	−	19.1725i	0.279611	−	0.785995i
$596$	2.31424			0.0947948
$597$		0			0
$598$	−2.90328	+	5.02863i	−0.118724	+	0.205636i
$599$	−10.3521	+	17.9303i	−0.422974	+	0.732613i	−0.996229	−	0.0867645i	$-0.972347\pi$
$599$	−10.3521	+	17.9303i	−0.422974	+	0.732613i	0.573255	+	0.819377i	$0.305681\pi$
$600$		0			0
$601$	−11.2354			−0.458302			−0.229151	−	0.973391i	$-0.573595\pi$
$601$	−11.2354			−0.458302			−0.229151	+	0.973391i	$0.573595\pi$
$602$	−6.65199	+	1.22296i	−0.271115	+	0.0498441i
$603$		0			0
$604$	13.5155	+	23.4096i	0.549939	+	0.952523i
$605$	0.795012	−	1.37700i	0.0323219	−	0.0559831i
$606$		0			0
$607$	3.72700	+	6.45535i	0.151274	+	0.262015i	0.931696	−	0.363239i	$-0.118329\pi$
$607$	3.72700	+	6.45535i	0.151274	+	0.262015i	−0.780422	+	0.625253i	$0.784996\pi$
$608$	−6.10962			−0.247778
$609$		0			0
$610$	−1.55777			−0.0630721
$611$	0.439172	+	0.760669i	0.0177670	+	0.0307734i
$612$		0			0
$613$	−10.5940	+	18.3493i	−0.427886	+	0.741121i	−0.996685	−	0.0813559i	$-0.974075\pi$
$613$	−10.5940	+	18.3493i	−0.427886	+	0.741121i	0.568799	+	0.822477i	$0.307408\pi$
$614$	−5.41068	−	9.37158i	−0.218357	−	0.378206i
$615$		0			0
$616$	−3.50120	−	4.11136i	−0.141067	−	0.165651i
$617$	−39.7670			−1.60096			−0.800479	−	0.599361i	$-0.795422\pi$
$617$	−39.7670			−1.60096			−0.800479	+	0.599361i	$0.795422\pi$
$618$		0			0
$619$	−8.64771	+	14.9783i	−0.347581	+	0.602028i	−0.985819	−	0.167811i	$-0.946330\pi$
$619$	−8.64771	+	14.9783i	−0.347581	+	0.602028i	0.638238	+	0.769839i	$0.279663\pi$
$620$	−8.69294	+	15.0566i	−0.349117	+	0.604688i
$621$		0			0
$622$	11.8225			0.474038
$623$	−14.9618	+	2.75070i	−0.599430	+	0.110205i
$624$		0			0
$625$	3.26550	+	5.65601i	0.130620	+	0.226240i
$626$	3.68121	−	6.37605i	0.147131	−	0.254838i
$627$		0			0
$628$	−7.11545	−	12.3243i	−0.283938	−	0.491794i
$629$	−8.19843			−0.326893
$630$		0			0
$631$	−22.8639			−0.910198			−0.455099	−	0.890441i	$-0.650396\pi$
$631$	−22.8639			−0.910198			−0.455099	+	0.890441i	$0.650396\pi$
$632$	−8.88912	−	15.3964i	−0.353590	−	0.612436i
$633$		0			0
$634$	−1.95982	+	3.39450i	−0.0778342	+	0.134813i
$635$	16.1924	+	28.0461i	0.642576	+	1.11297i
$636$		0			0
$637$	−15.6216	−	12.7249i	−0.618952	−	0.504178i
$638$	0.180050			0.00712824
$639$		0			0
$640$	−9.17114	+	15.8849i	−0.362521	+	0.627905i
$641$	−3.36284	+	5.82462i	−0.132824	+	0.230058i	−0.924764	−	0.380541i	$-0.875738\pi$
$641$	−3.36284	+	5.82462i	−0.132824	+	0.230058i	0.791940	+	0.610599i	$0.209071\pi$
$642$		0			0
$643$	8.16118			0.321845			0.160923	−	0.986967i	$-0.448553\pi$
$643$	8.16118			0.321845			0.160923	+	0.986967i	$0.448553\pi$
$644$	−5.48849	+	15.4283i	−0.216277	+	0.607961i
$645$		0			0
$646$	−1.53099	−	2.65176i	−0.0602361	−	0.104332i
$647$	−9.83192	+	17.0294i	−0.386533	+	0.669494i	−0.991981	−	0.126391i	$-0.959661\pi$
$647$	−9.83192	+	17.0294i	−0.386533	+	0.669494i	0.605448	+	0.795885i	$0.292994\pi$
$648$		0			0
$649$	5.93075	+	10.2724i	0.232802	+	0.403226i
$650$	−3.93026			−0.154157
$651$		0			0
$652$	29.3429			1.14916
$653$	−11.1517	−	19.3154i	−0.436401	−	0.755869i	0.561008	−	0.827811i	$-0.310414\pi$
$653$	−11.1517	−	19.3154i	−0.436401	−	0.755869i	−0.997409	+	0.0719417i	$0.977080\pi$
$654$		0			0
$655$	−16.0450	+	27.7908i	−0.626930	+	1.08588i
$656$	−4.59042	−	7.95083i	−0.179226	−	0.310428i
$657$		0			0
$658$	−0.289163	−	0.339556i	−0.0112728	−	0.0132373i
$659$	−19.0497			−0.742072			−0.371036	−	0.928619i	$-0.620997\pi$
$659$	−19.0497			−0.742072			−0.371036	+	0.928619i	$0.620997\pi$
$660$		0			0
$661$	−12.1612	+	21.0638i	−0.473015	+	0.819286i	−0.999523	−	0.0308845i	$-0.990168\pi$
$661$	−12.1612	+	21.0638i	−0.473015	+	0.819286i	0.526508	+	0.850170i	$0.323501\pi$
$662$	−5.72710	+	9.91963i	−0.222590	+	0.385537i
$663$		0			0
$664$	17.1624			0.666032
$665$	3.12539	+	3.67006i	0.121198	+	0.142319i
$666$		0			0
$667$	−0.595137	−	1.03081i	−0.0230438	−	0.0399130i
$668$	−15.6726	+	27.1458i	−0.606393	+	1.05030i
$669$		0			0
$670$	6.70681	+	11.6165i	0.259107	+	0.448786i
$671$	1.77353			0.0684662
$672$		0			0
$673$	42.6054			1.64232			0.821159	−	0.570699i	$-0.193328\pi$
$673$	42.6054			1.64232			0.821159	+	0.570699i	$0.193328\pi$
$674$	1.46597	+	2.53914i	0.0564671	+	0.0978039i
$675$		0			0
$676$	−3.99571	+	6.92076i	−0.153681	+	0.266183i
$677$	−6.98302	−	12.0949i	−0.268379	−	0.464846i	0.700064	−	0.714080i	$-0.253155\pi$
$677$	−6.98302	−	12.0949i	−0.268379	−	0.464846i	−0.968443	+	0.249233i	$0.919821\pi$
$678$		0			0
$679$	−3.23960	+	9.10662i	−0.124324	+	0.349480i
$680$	−15.6986			−0.602016
$681$		0			0
$682$	−1.78194	+	3.08642i	−0.0682342	+	0.118185i
$683$	−2.64173	+	4.57561i	−0.101083	+	0.175081i	−0.912131	−	0.409899i	$-0.865564\pi$
$683$	−2.64173	+	4.57561i	−0.101083	+	0.175081i	0.811048	+	0.584979i	$0.198897\pi$
$684$		0			0
$685$	−33.8090			−1.29177
$686$	8.96978	+	4.92052i	0.342468	+	0.187866i
$687$		0			0
$688$	−5.23428	−	9.06605i	−0.199555	−	0.345640i
$689$	8.22302	−	14.2427i	0.313272	−	0.542603i
$690$		0			0
$691$	−14.0658	−	24.3627i	−0.535088	−	0.926799i	−0.999159	−	0.0410014i	$-0.986945\pi$
$691$	−14.0658	−	24.3627i	−0.535088	−	0.926799i	0.464071	−	0.885798i	$-0.346388\pi$
$692$	20.7924			0.790408
$693$		0			0
$694$	−9.28220			−0.352347
$695$	4.19728	+	7.26990i	0.159212	+	0.275763i
$696$		0			0
$697$	9.81579	−	17.0014i	0.371800	−	0.643976i
$698$	0.240425	+	0.416428i	0.00910022	+	0.0157620i
$699$		0			0
$700$	−10.9013	+	2.00419i	−0.412030	+	0.0757512i
$701$	−29.9421			−1.13090			−0.565449	−	0.824783i	$-0.691297\pi$
$701$	−29.9421			−1.13090			−0.565449	+	0.824783i	$0.691297\pi$
$702$		0			0
$703$	0.971049	−	1.68191i	0.0366238	−	0.0634343i
$704$	0.789519	−	1.36749i	0.0297561	−	0.0515391i
$705$		0			0
$706$	0.518245			0.0195044
$707$	−0.487814	−	0.572826i	−0.0183461	−	0.0215433i
$708$		0			0
$709$	8.35341	+	14.4685i	0.313719	+	0.543377i	0.979164	−	0.203070i	$-0.0650917\pi$
$709$	8.35341	+	14.4685i	0.313719	+	0.543377i	−0.665446	+	0.746446i	$0.731758\pi$
$710$	−4.02575	+	6.97280i	−0.151084	+	0.261684i
$711$		0			0
$712$	5.86785	+	10.1634i	0.219907	+	0.380890i
$713$	23.5602			0.882335
$714$		0			0
$715$	−4.57664			−0.171157
$716$	−11.7043	−	20.2724i	−0.437409	−	0.757615i
$717$		0			0
$718$	−7.46027	+	12.9216i	−0.278415	+	0.482228i
$719$	11.6748	+	20.2213i	0.435395	+	0.754127i	0.997328	−	0.0730563i	$-0.0232753\pi$
$719$	11.6748	+	20.2213i	0.435395	+	0.754127i	−0.561933	+	0.827183i	$0.689942\pi$
$720$		0			0
$721$	43.4386	−	7.98615i	1.61774	−	0.297420i
$722$	−9.77044			−0.363618
$723$		0			0
$724$	−15.9050	+	27.5482i	−0.591104	+	1.02382i
$725$	0.402827	−	0.697717i	0.0149606	−	0.0259125i
$726$		0			0
$727$	14.4262			0.535037			0.267519	−	0.963553i	$-0.413796\pi$
$727$	14.4262			0.535037			0.267519	+	0.963553i	$0.413796\pi$
$728$	−5.20964	+	14.6445i	−0.193082	+	0.542760i
$729$		0			0
$730$	−5.15279	−	8.92489i	−0.190713	−	0.330325i
$731$	11.1926	−	19.3861i	0.413973	−	0.717022i
$732$		0			0
$733$	−13.4733	−	23.3365i	−0.497649	−	0.861953i	0.502347	−	0.864666i	$-0.332470\pi$
$733$	−13.4733	−	23.3365i	−0.497649	−	0.861953i	−0.999996	+	0.00271253i	$0.999137\pi$
$734$	−15.6945			−0.579294
$735$		0			0
$736$	19.4710			0.717710
$737$	−7.63574	−	13.2255i	−0.281266	−	0.487167i
$738$		0			0
$739$	22.2858	−	38.6001i	0.819795	−	1.41993i	−0.0860388	−	0.996292i	$-0.527421\pi$
$739$	22.2858	−	38.6001i	0.819795	−	1.41993i	0.905833	−	0.423634i	$-0.139246\pi$
$740$	−2.28367	−	3.95543i	−0.0839494	−	0.145405i
$741$		0			0
$742$	−2.79890	+	7.86780i	−0.102751	+	0.288836i
$743$	−44.7041			−1.64004			−0.820018	−	0.572338i	$-0.806037\pi$
$743$	−44.7041			−1.64004			−0.820018	+	0.572338i	$0.806037\pi$
$744$		0			0
$745$	−1.08556	+	1.88024i	−0.0397717	+	0.0688866i
$746$	2.69210	−	4.66285i	0.0985648	−	0.170719i
$747$		0			0
$748$	8.19843			0.299764
$749$	46.7071	−	8.58705i	1.70664	−	0.313764i
$750$		0			0
$751$	−22.2962	−	38.6182i	−0.813600	−	1.40920i	−0.910329	−	0.413886i	$-0.864171\pi$
$751$	−22.2962	−	38.6182i	−0.813600	−	1.40920i	0.0967287	−	0.995311i	$-0.469162\pi$
$752$	0.345160	−	0.597834i	0.0125867	−	0.0218008i
$753$		0			0
$754$	−0.259123	−	0.448814i	−0.00943669	−	0.0163448i
$755$	−25.3593			−0.922920
$756$		0			0
$757$	5.85842			0.212928			0.106464	−	0.994317i	$-0.466047\pi$
$757$	5.85842			0.212928			0.106464	+	0.994317i	$0.466047\pi$
$758$	9.14332	+	15.8367i	0.332100	+	0.575214i
$759$		0			0
$760$	1.85940	−	3.22057i	0.0674475	−	0.116822i
$761$	−19.2017	−	33.2583i	−0.696061	−	1.20561i	−0.969822	−	0.243816i	$-0.921601\pi$
$761$	−19.2017	−	33.2583i	−0.696061	−	1.20561i	0.273760	−	0.961798i	$-0.411733\pi$
$762$		0			0
$763$	19.0201	+	22.3347i	0.688573	+	0.808572i
$764$	13.7567			0.497700
$765$		0			0
$766$	−2.95218	+	5.11332i	−0.106666	+	0.184752i
$767$	17.0708	−	29.5674i	0.616389	−	1.06762i
$768$		0			0
$769$	−1.44505			−0.0521099			−0.0260549	−	0.999661i	$-0.508294\pi$
$769$	−1.44505			−0.0521099			−0.0260549	+	0.999661i	$0.508294\pi$
$770$	2.28558	−	0.420201i	0.0823664	−	0.0151430i
$771$		0			0
$772$	1.00908	+	1.74778i	0.0363176	+	0.0629039i
$773$	−1.05839	+	1.83319i	−0.0380678	+	0.0659354i	−0.884432	−	0.466670i	$-0.845454\pi$
$773$	−1.05839	+	1.83319i	−0.0380678	+	0.0659354i	0.846364	+	0.532605i	$0.178787\pi$
$774$		0			0
$775$	7.97352	+	13.8105i	0.286417	+	0.496089i
$776$	7.45660			0.267676
$777$		0			0
$778$	21.3166			0.764236
$779$	2.32523	+	4.02741i	0.0833099	+	0.144297i
$780$		0			0
$781$	4.58333	−	7.93856i	0.164005	−	0.284064i
$782$	4.87919	+	8.45100i	0.174479	+	0.302207i
$783$		0			0
$784$	−2.52225	+	15.6331i	−0.0900803	+	0.558326i
$785$	13.3508			0.476510
$786$		0			0
$787$	7.64321	−	13.2384i	0.272451	−	0.471899i	−0.697038	−	0.717034i	$-0.745499\pi$
$787$	7.64321	−	13.2384i	0.272451	−	0.471899i	0.969489	+	0.245135i	$0.0788324\pi$
$788$	22.6705	−	39.2665i	0.807603	−	1.39881i
$789$		0			0
$790$	7.65062			0.272197
$791$	−1.52916	+	4.29853i	−0.0543708	+	0.152838i
$792$		0			0
$793$	−2.55241	−	4.42090i	−0.0906387	−	0.156991i
$794$	−3.85006	+	6.66849i	−0.136633	+	0.236656i
$795$		0			0
$796$	−5.11307	−	8.85609i	−0.181228	−	0.313896i
$797$	−15.1839			−0.537840			−0.268920	−	0.963163i	$-0.586667\pi$
$797$	−15.1839			−0.537840			−0.268920	+	0.963163i	$0.586667\pi$
$798$		0			0
$799$	1.47613			0.0522216
$800$	6.58961	+	11.4135i	0.232978	+	0.403529i
$801$		0			0
$802$	−3.62852	+	6.28479i	−0.128128	+	0.221923i
$803$	5.86648	+	10.1610i	0.207023	+	0.358575i
$804$		0			0
$805$	−9.96045	−	11.6963i	−0.351060	−	0.412240i
$806$	10.2581			0.361326
$807$		0			0
$808$	−0.290216	+	0.502669i	−0.0102098	+	0.0176838i
$809$	−5.94467	+	10.2965i	−0.209003	+	0.362004i	−0.951401	−	0.307955i	$-0.900355\pi$
$809$	−5.94467	+	10.2965i	−0.209003	+	0.362004i	0.742398	+	0.669960i	$0.233689\pi$
$810$		0			0
$811$	−3.83804			−0.134772			−0.0673859	−	0.997727i	$-0.521466\pi$
$811$	−3.83804			−0.134772			−0.0673859	+	0.997727i	$0.521466\pi$
$812$	−0.947591	−	1.11273i	−0.0332539	−	0.0390491i
$813$		0			0
$814$	−0.468124	−	0.810814i	−0.0164077	−	0.0284190i
$815$	−13.7641	+	23.8401i	−0.482135	+	0.835082i
$816$		0			0
$817$	2.65137	+	4.59231i	0.0927598	+	0.160665i
$818$	−13.8284			−0.483499
$819$		0			0
$820$	10.9367			0.381928
$821$	15.8873	+	27.5175i	0.554469	+	0.960368i	0.997945	+	0.0640821i	$0.0204119\pi$
$821$	15.8873	+	27.5175i	0.554469	+	0.960368i	−0.443476	+	0.896286i	$0.646255\pi$
$822$		0			0
$823$	−6.19160	+	10.7242i	−0.215826	+	0.373821i	−0.953528	−	0.301305i	$-0.902578\pi$
$823$	−6.19160	+	10.7242i	−0.215826	+	0.373821i	0.737702	+	0.675126i	$0.235911\pi$
$824$	−17.0362	−	29.5076i	−0.593484	−	1.02794i
$825$		0			0
$826$	−5.81043	+	16.3333i	−0.202171	+	0.568309i
$827$	28.7072			0.998248			0.499124	−	0.866530i	$-0.333655\pi$
$827$	28.7072			0.998248			0.499124	+	0.866530i	$0.333655\pi$
$828$		0			0
$829$	−1.35827	+	2.35260i	−0.0471748	+	0.0817091i	−0.888649	−	0.458589i	$-0.848355\pi$
$829$	−1.35827	+	2.35260i	−0.0471748	+	0.0817091i	0.841474	+	0.540298i	$0.181688\pi$
$830$	−3.69281	+	6.39613i	−0.128179	+	0.222013i
$831$		0			0
$832$	−4.54502			−0.157570
$833$	−31.6468	+	12.0435i	−1.09650	+	0.417283i
$834$		0			0
$835$	−14.7034	−	25.4670i	−0.508831	−	0.881321i
$836$	−0.971049	+	1.68191i	−0.0335844	+	0.0581699i
$837$		0			0
$838$	1.39289	+	2.41256i	0.0481167	+	0.0833406i
$839$	48.9487			1.68990			0.844948	−	0.534848i	$-0.179631\pi$
$839$	48.9487			1.68990			0.844948	+	0.534848i	$0.179631\pi$
$840$		0			0
$841$	−28.8938			−0.996337
$842$	−2.74563	−	4.75557i	−0.0946206	−	0.163888i
$843$		0			0
$844$	−17.3383	+	30.0308i	−0.596809	+	1.03370i
$845$	−3.74859	−	6.49274i	−0.128955	−	0.223357i
$846$		0			0
$847$	−2.60214	+	0.478401i	−0.0894106	+	0.0164380i
$848$	−12.9255			−0.443863
$849$		0			0
$850$	−3.30255	+	5.72018i	−0.113276	+	0.196201i
$851$	−3.09468	+	5.36013i	−0.106084	+	0.183743i
$852$		0			0
$853$	−21.5962			−0.739441			−0.369721	−	0.929143i	$-0.620547\pi$
$853$	−21.5962			−0.739441			−0.369721	+	0.929143i	$0.620547\pi$
$854$	1.68058	+	1.97345i	0.0575081	+	0.0675302i
$855$		0			0
$856$	−18.3181	−	31.7278i	−0.626098	−	1.08443i
$857$	−4.72073	+	8.17655i	−0.161257	+	0.279306i	−0.935320	−	0.353803i	$-0.884888\pi$
$857$	−4.72073	+	8.17655i	−0.161257	+	0.279306i	0.774063	+	0.633109i	$0.218222\pi$
$858$		0			0
$859$	1.75465	+	3.03915i	0.0598680	+	0.103694i	0.894406	−	0.447256i	$-0.147599\pi$
$859$	1.75465	+	3.03915i	0.0598680	+	0.103694i	−0.834538	+	0.550950i	$0.814265\pi$
$860$	12.4708			0.425250
$861$		0			0
$862$	−7.56115			−0.257534
$863$	19.4393	+	33.6698i	0.661721	+	1.14613i	0.980163	+	0.198192i	$0.0635068\pi$
$863$	19.4393	+	33.6698i	0.661721	+	1.14613i	−0.318443	+	0.947942i	$0.603160\pi$
$864$		0			0
$865$	−9.75324	+	16.8931i	−0.331620	+	0.574383i
$866$	1.17763	+	2.03971i	0.0400174	+	0.0693121i
$867$		0			0
$868$	28.4527	−	5.23100i	0.965747	−	0.177552i
$869$	−8.71027			−0.295476
$870$		0			0
$871$	−21.9783	+	38.0675i	−0.744706	+	1.28987i
$872$	11.3157	−	19.5993i	0.383196	−	0.663716i
$873$		0			0
$874$	−2.31163			−0.0781919
$875$	10.5351	−	29.6145i	0.356151	−	1.00115i
$876$		0			0
$877$	−2.19728	−	3.80580i	−0.0741968	−	0.128513i	0.826540	−	0.562878i	$-0.190306\pi$
$877$	−2.19728	−	3.80580i	−0.0741968	−	0.128513i	−0.900737	+	0.434366i	$0.856973\pi$
$878$	6.46408	−	11.1961i	0.218152	−	0.377850i
$879$		0			0
$880$	1.79846	+	3.11503i	0.0606262	+	0.105008i
$881$	29.9918			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$881$	29.9918			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$882$		0			0
$883$	16.8653			0.567563			0.283782	−	0.958889i	$-0.408411\pi$
$883$	16.8653			0.567563			0.283782	+	0.958889i	$0.408411\pi$
$884$	−11.7990	−	20.4364i	−0.396842	−	0.687350i
$885$		0			0
$886$	−4.06551	+	7.04168i	−0.136584	+	0.236570i
$887$	5.01391	+	8.68434i	0.168350	+	0.291592i	0.937840	−	0.347068i	$-0.112823\pi$
$887$	5.01391	+	8.68434i	0.168350	+	0.291592i	−0.769490	+	0.638659i	$0.779489\pi$
$888$		0			0
$889$	18.0611	−	50.7705i	0.605751	−	1.70279i
$890$	−5.05030			−0.169286
$891$		0			0
$892$	−25.0878	+	43.4533i	−0.840001	+	1.45492i
$893$	−0.174837	+	0.302827i	−0.00585070	+	0.0101337i
$894$		0			0
$895$	21.9608			0.734070
$896$	30.0179	−	5.51876i	1.00283	−	0.184369i
$897$		0			0
$898$	−9.62919	−	16.6782i	−0.321330	−	0.556560i
$899$	−1.05139	+	1.82106i	−0.0350659	+	0.0607359i
$900$		0			0
$901$	−13.8194	−	23.9359i	−0.460392	−	0.797422i
$902$	2.24190			0.0746470
$903$		0			0
$904$	3.51968			0.117063
$905$	−14.9213	−	25.8445i	−0.496001	−	0.859100i
$906$		0			0
$907$	25.2758	−	43.7790i	0.839271	−	1.45366i	−0.0512348	−	0.998687i	$-0.516316\pi$
$907$	25.2758	−	43.7790i	0.839271	−	1.45366i	0.890505	−	0.454973i	$-0.150351\pi$
$908$	20.4086	+	35.3487i	0.677282	+	1.17309i
$909$		0			0
$910$	−4.33678	−	5.09256i	−0.143763	−	0.168817i
$911$	−21.7956			−0.722120			−0.361060	−	0.932543i	$-0.617585\pi$
$911$	−21.7956			−0.722120			−0.361060	+	0.932543i	$0.617585\pi$
$912$		0			0
$913$	4.20428	−	7.28203i	0.139141	−	0.241000i
$914$	2.92815	−	5.07170i	0.0968545	−	0.167757i
$915$		0			0
$916$	8.83811			0.292019
$917$	52.5166	−	9.65512i	1.73425	−	0.318840i
$918$		0			0
$919$	−11.2489	−	19.4837i	−0.371067	−	0.642708i	0.618663	−	0.785657i	$-0.287675\pi$
$919$	−11.2489	−	19.4837i	−0.371067	−	0.642708i	−0.989730	+	0.142949i	$0.954341\pi$
$920$	−5.92579	+	10.2638i	−0.195368	+	0.338387i
$921$		0			0
$922$	−1.89040	−	3.27426i	−0.0622568	−	0.107832i
$923$	−26.3848			−0.868467
$924$		0			0
$925$	−4.18935			−0.137745
$926$	3.23986	+	5.61160i	0.106468	+	0.184409i
$927$		0			0
$928$	−0.868908	+	1.50499i	−0.0285233	+	0.0494038i
$929$	−2.83989	−	4.91884i	−0.0931738	−	0.161382i	0.815671	−	0.578516i	$-0.196368\pi$
$929$	−2.83989	−	4.91884i	−0.0931738	−	0.161382i	−0.908845	+	0.417134i	$0.863035\pi$
$930$		0			0
$931$	1.27762	−	7.91880i	0.0418723	−	0.259528i
$932$	5.33178			0.174648
$933$		0			0
$934$	−10.5755	+	18.3173i	−0.346041	+	0.599361i
$935$	−3.84570	+	6.66094i	−0.125768	+	0.217836i
$936$		0			0
$937$	40.6016			1.32640			0.663198	−	0.748444i	$-0.269199\pi$
$937$	40.6016			1.32640			0.663198	+	0.748444i	$0.269199\pi$
$938$	7.48083	−	21.0289i	0.244258	−	0.686617i
$939$		0			0
$940$	0.411174	+	0.712175i	0.0134110	+	0.0232286i
$941$	8.82365	−	15.2830i	0.287643	−	0.498212i	−0.685604	−	0.727975i	$-0.740462\pi$
$941$	8.82365	−	15.2830i	0.287643	−	0.498212i	0.973247	+	0.229763i	$0.0737951\pi$
$942$		0			0
$943$	−7.41037	−	12.8351i	−0.241315	−	0.417969i
$944$	−26.8329			−0.873337
$945$		0			0
$946$	2.55635			0.0831142
$947$	14.1472	+	24.5037i	0.459723	+	0.796263i	0.998946	−	0.0458995i	$-0.0146154\pi$
$947$	14.1472	+	24.5037i	0.459723	+	0.796263i	−0.539223	+	0.842163i	$0.681282\pi$
$948$		0			0
$949$	16.8857	−	29.2470i	0.548134	−	0.949396i
$950$	−0.782329	−	1.35503i	−0.0253821	−	0.0439631i
$951$		0			0
$952$	16.9363	+	19.8878i	0.548908	+	0.644567i
$953$	−43.3325			−1.40368			−0.701839	−	0.712335i	$-0.747638\pi$
$953$	−43.3325			−1.40368			−0.701839	+	0.712335i	$0.747638\pi$
$954$		0			0
$955$	−6.45295	+	11.1768i	−0.208813	+	0.361674i
$956$	−2.33435	+	4.04322i	−0.0754984	+	0.130767i
$957$		0			0
$958$	−6.97633			−0.225395
$959$	36.4743	+	42.8308i	1.17782	+	1.38308i
$960$		0			0
$961$	−5.31114	−	9.19917i	−0.171327	−	0.296747i
$962$	−1.34742	+	2.33380i	−0.0434426	+	0.0752448i
$963$		0			0
$964$	−7.65187	−	13.2534i	−0.246450	−	0.426864i
$965$	−1.89335			−0.0609490
$966$		0			0
$967$	−2.82833			−0.0909529			−0.0454764	−	0.998965i	$-0.514481\pi$
$967$	−2.82833			−0.0909529			−0.0454764	+	0.998965i	$0.514481\pi$
$968$	1.02053	+	1.76762i	0.0328012	+	0.0568133i
$969$		0			0
$970$	−1.60442	+	2.77894i	−0.0515149	+	0.0892264i
$971$	−14.4665	−	25.0566i	−0.464251	−	0.804106i	0.534916	−	0.844905i	$-0.320343\pi$
$971$	−14.4665	−	25.0566i	−0.464251	−	0.804106i	−0.999167	+	0.0407988i	$0.987010\pi$
$972$		0			0
$973$	4.68167	−	13.1603i	0.150088	−	0.421901i
$974$	19.6735			0.630379
$975$		0			0
$976$	−2.00602	+	3.47453i	−0.0642111	+	0.111217i
$977$	28.4958	−	49.3562i	0.911663	−	1.57905i	0.0999471	−	0.994993i	$-0.468133\pi$
$977$	28.4958	−	49.3562i	0.911663	−	1.57905i	0.811715	−	0.584053i	$-0.198534\pi$
$978$		0			0
$979$	5.74979			0.183764
$980$	−14.6257	−	11.9136i	−0.467202	−	0.380567i
$981$		0			0
$982$	2.09875	+	3.63515i	0.0669739	+	0.116002i
$983$	15.5618	−	26.9539i	0.496346	−	0.859696i	−0.503645	−	0.863911i	$-0.668008\pi$
$983$	15.5618	−	26.9539i	0.496346	−	0.859696i	0.999991	+	0.00421438i	$0.00134148\pi$
$984$		0			0
$985$	21.2684	+	36.8380i	0.677668	+	1.17376i
$986$	−0.870951			−0.0277367
$987$		0			0
$988$	5.59002			0.177842
$989$	−8.44977	−	14.6354i	−0.268687	−	0.465380i
$990$		0			0
$991$	−4.28438	+	7.42076i	−0.136098	+	0.235728i	−0.926016	−	0.377484i	$-0.876789\pi$
$991$	−4.28438	+	7.42076i	−0.136098	+	0.235728i	0.789919	+	0.613212i	$0.210123\pi$
$992$	−17.1991	−	29.7897i	−0.546072	−	0.945824i
$993$		0			0
$994$	13.1766	−	2.42250i	0.417936	−	0.0768371i
$995$	9.59369			0.304140
$996$		0			0
$997$	−7.29290	+	12.6317i	−0.230968	+	0.400049i	−0.958093	−	0.286456i	$-0.907523\pi$
$997$	−7.29290	+	12.6317i	−0.230968	+	0.400049i	0.727125	+	0.686505i	$0.240856\pi$
$998$	−0.443607	+	0.768349i	−0.0140421	+	0.0243217i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.i.i.298.2		8
3.2	odd	2		231.2.i.e.67.3	✓	8
7.2	even	3	inner	693.2.i.i.100.2		8
7.3	odd	6		4851.2.a.bu.1.3		4
7.4	even	3		4851.2.a.bt.1.3		4
21.2	odd	6		231.2.i.e.100.3	yes	8
21.11	odd	6		1617.2.a.z.1.2		4
21.17	even	6		1617.2.a.x.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.e.67.3	✓	8	3.2	odd	2
231.2.i.e.100.3	yes	8	21.2	odd	6
693.2.i.i.100.2		8	7.2	even	3	inner
693.2.i.i.298.2		8	1.1	even	1	trivial
1617.2.a.x.1.2		4	21.17	even	6
1617.2.a.z.1.2		4	21.11	odd	6
4851.2.a.bt.1.3		4	7.4	even	3
4851.2.a.bu.1.3		4	7.3	odd	6

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.276205 - 0.478401i) q^{2} +(0.847422 - 1.46778i) q^{4} +(0.795012 + 1.37700i) q^{5} +(0.886763 - 2.49272i) q^{7} -2.04107 q^{8} +O(q^{10})\)	\(q+(-0.276205 - 0.478401i) q^{2} +(0.847422 - 1.46778i) q^{4} +(0.795012 + 1.37700i) q^{5} +(0.886763 - 2.49272i) q^{7} -2.04107 q^{8} +(0.439172 - 0.760669i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.87834 q^{13} +(-1.43745 + 0.264273i) q^{14} +(-1.13109 - 1.95911i) q^{16} +(2.41864 - 4.18921i) q^{17} +(0.572943 + 0.992366i) q^{19} +2.69484 q^{20} +0.552409 q^{22} +(-1.82594 - 3.16261i) q^{23} +(1.23591 - 2.14066i) q^{25} +(-0.795012 - 1.37700i) q^{26} +(-2.90730 - 3.41396i) q^{28} +0.325935 q^{29} +(-3.22577 + 5.58719i) q^{31} +(-2.66589 + 4.61746i) q^{32} -2.67216 q^{34} +(4.13747 - 0.760669i) q^{35} +(-0.847422 - 1.46778i) q^{37} +(0.316499 - 0.548192i) q^{38} +(-1.62267 - 2.81055i) q^{40} +4.05839 q^{41} +4.62764 q^{43} +(0.847422 + 1.46778i) q^{44} +(-1.00866 + 1.74706i) q^{46} +(0.152578 + 0.264273i) q^{47} +(-5.42730 - 4.42090i) q^{49} -1.36546 q^{50} +(2.43917 - 4.22477i) q^{52} +(2.85686 - 4.94822i) q^{53} -1.59002 q^{55} +(-1.80994 + 5.08781i) q^{56} +(-0.0900249 - 0.155928i) q^{58} +(5.93075 - 10.2724i) q^{59} +(-0.886763 - 1.53592i) q^{61} +3.56389 q^{62} -1.57904 q^{64} +(2.28832 + 3.96349i) q^{65} +(-7.63574 + 13.2255i) q^{67} +(-4.09922 - 7.10005i) q^{68} +(-1.50669 - 1.76927i) q^{70} -9.16666 q^{71} +(5.86648 - 10.1610i) q^{73} +(-0.468124 + 0.810814i) q^{74} +1.94210 q^{76} +(1.71538 + 2.01432i) q^{77} +(4.35513 + 7.54331i) q^{79} +(1.79846 - 3.11503i) q^{80} +(-1.12095 - 1.94154i) q^{82} -8.40856 q^{83} +7.69139 q^{85} +(-1.27818 - 2.21387i) q^{86} +(1.02053 - 1.76762i) q^{88} +(-2.87489 - 4.97946i) q^{89} +(2.55241 - 7.17491i) q^{91} -6.18935 q^{92} +(0.0842856 - 0.145987i) q^{94} +(-0.910993 + 1.57789i) q^{95} -3.65329 q^{97} +(-0.615916 + 3.81750i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8	\( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8 - 10 * q^10 - 4 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^17 - 4 * q^22 + 4 * q^23 - 4 * q^25 - 4 * q^26 - 22 * q^28 - 16 * q^29 + 12 * q^31 + 26 * q^32 - 32 * q^34 + 2 * q^35 + 4 * q^37 + 8 * q^38 + 6 * q^40 - 4 * q^41 + 36 * q^43 - 4 * q^44 + 14 * q^46 + 12 * q^47 - 4 * q^49 - 4 * q^50 + 6 * q^52 - 12 * q^53 - 8 * q^55 - 48 * q^56 + 4 * q^58 + 12 * q^59 - 2 * q^61 + 52 * q^62 + 112 * q^64 - 4 * q^65 - 28 * q^67 - 48 * q^68 - 32 * q^70 - 24 * q^71 - 6 * q^73 - 16 * q^74 - 36 * q^76 - 4 * q^77 - 2 * q^79 + 16 * q^80 + 12 * q^82 + 24 * q^83 + 36 * q^85 + 36 * q^86 + 12 * q^88 + 8 * q^89 + 12 * q^91 + 32 * q^92 - 20 * q^94 + 34 * q^95 - 88 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more