LMFDB - Embedded newform 740.2.i.b.121.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(121,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 13 x^{12} - 6 x^{11} + 130 x^{10} - 44 x^{9} + 466 x^{8} - 4 x^{7} + 1211 x^{6} - 162 x^{5} + \cdots + 81 $ x^14 + 13x^12 - 6x^11 + 130x^10 - 44x^9 + 466x^8 - 4x^7 + 1211x^6 - 162x^5 + 973x^4 - 577x^3 + 670x^2 - 225x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{37}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.6
Root			$-0.743604 - 1.28796i$ of defining polynomial
Character	$\chi$	$=$	740.121
Dual form			740.2.i.b.581.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.743604 + 1.28796i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.37759 + 2.38605i) q^{7} +(0.394106 - 0.682612i) q^{9} +0.532549 q^{11} +(1.80515 + 3.12662i) q^{13} +(-0.743604 + 1.28796i) q^{15} +(-0.777065 + 1.34592i) q^{17} +(-2.21268 - 3.83247i) q^{19} +(-2.04876 + 3.54855i) q^{21} -0.557928 q^{23} +(-0.500000 + 0.866025i) q^{25} +5.63386 q^{27} +6.32906 q^{29} -8.41061 q^{31} +(0.396005 + 0.685901i) q^{33} +(-1.37759 + 2.38605i) q^{35} +(-1.59156 + 5.87085i) q^{37} +(-2.68464 + 4.64993i) q^{39} +(1.28258 + 2.22149i) q^{41} -3.84565 q^{43} +0.788212 q^{45} +0.809982 q^{47} +(-0.295484 + 0.511794i) q^{49} -2.31131 q^{51} +(0.278334 - 0.482089i) q^{53} +(0.266274 + 0.461201i) q^{55} +(3.29072 - 5.69969i) q^{57} +(0.122204 - 0.211664i) q^{59} +(-2.85766 - 4.94962i) q^{61} +2.17166 q^{63} +(-1.80515 + 3.12662i) q^{65} +(-1.28609 - 2.22758i) q^{67} +(-0.414877 - 0.718588i) q^{69} +(3.87967 + 6.71979i) q^{71} +1.48847 q^{73} -1.48721 q^{75} +(0.733631 + 1.27069i) q^{77} +(-0.440351 - 0.762710i) q^{79} +(3.00704 + 5.20835i) q^{81} +(0.671903 - 1.16377i) q^{83} -1.55413 q^{85} +(4.70631 + 8.15157i) q^{87} +(5.35327 - 9.27214i) q^{89} +(-4.97350 + 8.61436i) q^{91} +(-6.25416 - 10.8325i) q^{93} +(2.21268 - 3.83247i) q^{95} +9.38181 q^{97} +(0.209881 - 0.363524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 7 q^{5} - 2 q^{7} - 5 q^{9} - 10 q^{11} - 2 q^{13} - 5 q^{17} - 8 q^{19} + 9 q^{21} + 8 q^{23} - 7 q^{25} - 18 q^{27} - 4 q^{29} + 16 q^{31} - 7 q^{33} + 2 q^{35} + 4 q^{37} + 13 q^{39} + 9 q^{41}+ \cdots + 26 q^{99}+O(q^{100}) $ 14 * q + 7 * q^5 - 2 * q^7 - 5 * q^9 - 10 * q^11 - 2 * q^13 - 5 * q^17 - 8 * q^19 + 9 * q^21 + 8 * q^23 - 7 * q^25 - 18 * q^27 - 4 * q^29 + 16 * q^31 - 7 * q^33 + 2 * q^35 + 4 * q^37 + 13 * q^39 + 9 * q^41 + 22 * q^43 - 10 * q^45 + 36 * q^47 - 7 * q^49 - 62 * q^51 + 2 * q^53 - 5 * q^55 - 38 * q^57 + 12 * q^59 - 20 * q^61 - 38 * q^63 + 2 * q^65 + 12 * q^67 + q^69 - 13 * q^71 - 12 * q^73 - q^77 - 21 * q^79 - 11 * q^81 + 7 * q^83 - 10 * q^85 + 41 * q^87 + 16 * q^89 - 6 * q^91 - 3 * q^93 + 8 * q^95 - 6 * q^97 + 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.743604	+	1.28796i	0.429320	+	0.743604i	0.996813	−	0.0797742i	$-0.0254199\pi$
$3$	0.743604	+	1.28796i	0.429320	+	0.743604i	−0.567493	+	0.823378i	$0.692087\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	1.37759	+	2.38605i	0.520678	+	0.901841i	0.999711	+	0.0240443i	$0.00765428\pi$
$7$	1.37759	+	2.38605i	0.520678	+	0.901841i	−0.479032	+	0.877797i	$0.659012\pi$
$8$		0			0
$9$	0.394106	−	0.682612i	0.131369	−	0.227537i
$10$		0			0
$11$	0.532549			0.160569			0.0802847	−	0.996772i	$-0.474417\pi$
$11$	0.532549			0.160569			0.0802847	+	0.996772i	$0.474417\pi$
$12$		0			0
$13$	1.80515	+	3.12662i	0.500659	+	0.867167i	1.00000		0.000761341i	$0.000242342\pi$
$13$	1.80515	+	3.12662i	0.500659	+	0.867167i	−0.499341	+	0.866406i	$0.666424\pi$
$14$		0			0
$15$	−0.743604	+	1.28796i	−0.191998	+	0.332550i
$16$		0			0
$17$	−0.777065	+	1.34592i	−0.188466	+	0.326432i	−0.944739	−	0.327824i	$-0.893685\pi$
$17$	−0.777065	+	1.34592i	−0.188466	+	0.326432i	0.756273	+	0.654256i	$0.227018\pi$
$18$		0			0
$19$	−2.21268	−	3.83247i	−0.507624	−	0.879230i	−0.999961	−	0.00882557i	$-0.997191\pi$
$19$	−2.21268	−	3.83247i	−0.507624	−	0.879230i	0.492337	−	0.870404i	$-0.336143\pi$
$20$		0			0
$21$	−2.04876	+	3.54855i	−0.447075	+	0.774357i
$22$		0			0
$23$	−0.557928			−0.116336			−0.0581680	−	0.998307i	$-0.518526\pi$
$23$	−0.557928			−0.116336			−0.0581680	+	0.998307i	$0.518526\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	5.63386			1.08424
$28$		0			0
$29$	6.32906			1.17528			0.587638	−	0.809124i	$-0.300058\pi$
$29$	6.32906			1.17528			0.587638	+	0.809124i	$0.300058\pi$
$30$		0			0
$31$	−8.41061			−1.51059			−0.755295	−	0.655385i	$-0.772507\pi$
$31$	−8.41061			−1.51059			−0.755295	+	0.655385i	$0.772507\pi$
$32$		0			0
$33$	0.396005	+	0.685901i	0.0689357	+	0.119400i
$34$		0			0
$35$	−1.37759	+	2.38605i	−0.232854	+	0.403316i
$36$		0			0
$37$	−1.59156	+	5.87085i	−0.261651	+	0.965163i
$37$	−1.59156	+	5.87085i	−0.261651	+	0.965163i
$38$		0			0
$39$	−2.68464	+	4.64993i	−0.429886	+	0.744584i
$40$		0			0
$41$	1.28258	+	2.22149i	0.200305	+	0.346938i	0.948627	−	0.316398i	$-0.102473\pi$
$41$	1.28258	+	2.22149i	0.200305	+	0.346938i	−0.748322	+	0.663336i	$0.769140\pi$
$42$		0			0
$43$	−3.84565			−0.586456			−0.293228	−	0.956043i	$-0.594729\pi$
$43$	−3.84565			−0.586456			−0.293228	+	0.956043i	$0.594729\pi$
$44$		0			0
$45$	0.788212			0.117500
$46$		0			0
$47$	0.809982			0.118148			0.0590740	−	0.998254i	$-0.481185\pi$
$47$	0.809982			0.118148			0.0590740	+	0.998254i	$0.481185\pi$
$48$		0			0
$49$	−0.295484	+	0.511794i	−0.0422120	+	0.0731134i
$50$		0			0
$51$	−2.31131			−0.323649
$52$		0			0
$53$	0.278334	−	0.482089i	0.0382321	−	0.0662199i	−0.846276	−	0.532744i	$-0.821161\pi$
$53$	0.278334	−	0.482089i	0.0382321	−	0.0662199i	0.884508	+	0.466524i	$0.154494\pi$
$54$		0			0
$55$	0.266274	+	0.461201i	0.0359044	+	0.0621883i
$56$		0			0
$57$	3.29072	−	5.69969i	0.435866	−	0.754942i
$58$		0			0
$59$	0.122204	−	0.211664i	0.0159096	−	0.0275563i	−0.857961	−	0.513715i	$-0.828269\pi$
$59$	0.122204	−	0.211664i	0.0159096	−	0.0275563i	0.873871	+	0.486159i	$0.161602\pi$
$60$		0			0
$61$	−2.85766	−	4.94962i	−0.365886	−	0.633733i	0.623032	−	0.782197i	$-0.285901\pi$
$61$	−2.85766	−	4.94962i	−0.365886	−	0.633733i	−0.988918	+	0.148463i	$0.952567\pi$
$62$		0			0
$63$	2.17166			0.273603
$64$		0			0
$65$	−1.80515	+	3.12662i	−0.223902	+	0.387809i
$66$		0			0
$67$	−1.28609	−	2.22758i	−0.157121	−	0.272142i	0.776708	−	0.629861i	$-0.216888\pi$
$67$	−1.28609	−	2.22758i	−0.157121	−	0.272142i	−0.933829	+	0.357718i	$0.883555\pi$
$68$		0			0
$69$	−0.414877	−	0.718588i	−0.0499454	−	0.0865079i
$70$		0			0
$71$	3.87967	+	6.71979i	0.460432	+	0.797492i	0.998982	−	0.0451016i	$-0.0143611\pi$
$71$	3.87967	+	6.71979i	0.460432	+	0.797492i	−0.538550	+	0.842593i	$0.681028\pi$
$72$		0			0
$73$	1.48847			0.174212			0.0871060	−	0.996199i	$-0.472238\pi$
$73$	1.48847			0.174212			0.0871060	+	0.996199i	$0.472238\pi$
$74$		0			0
$75$	−1.48721			−0.171728
$76$		0			0
$77$	0.733631	+	1.27069i	0.0836050	+	0.144808i
$78$		0			0
$79$	−0.440351	−	0.762710i	−0.0495433	−	0.0858116i	0.840190	−	0.542292i	$-0.182443\pi$
$79$	−0.440351	−	0.762710i	−0.0495433	−	0.0858116i	−0.889734	+	0.456480i	$0.849110\pi$
$80$		0			0
$81$	3.00704	+	5.20835i	0.334116	+	0.578706i
$82$		0			0
$83$	0.671903	−	1.16377i	0.0737509	−	0.127740i	−0.826791	−	0.562509i	$-0.809836\pi$
$83$	0.671903	−	1.16377i	0.0737509	−	0.127740i	0.900542	+	0.434768i	$0.143170\pi$
$84$		0			0
$85$	−1.55413			−0.168569
$86$		0			0
$87$	4.70631	+	8.15157i	0.504570	+	0.873940i
$88$		0			0
$89$	5.35327	−	9.27214i	0.567446	−	0.982845i	−0.429372	−	0.903128i	$-0.641265\pi$
$89$	5.35327	−	9.27214i	0.567446	−	0.982845i	0.996818	−	0.0797168i	$-0.0254016\pi$
$90$		0			0
$91$	−4.97350	+	8.61436i	−0.521365	+	0.903030i
$92$		0			0
$93$	−6.25416	−	10.8325i	−0.648527	−	1.12328i
$94$		0			0
$95$	2.21268	−	3.83247i	0.227016	−	0.393204i
$96$		0			0
$97$	9.38181			0.952578			0.476289	−	0.879289i	$-0.341982\pi$
$97$	9.38181			0.952578			0.476289	+	0.879289i	$0.341982\pi$
$98$		0			0
$99$	0.209881	−	0.363524i	0.0210938	−	0.0365355i
$100$		0			0
$101$	−1.01126			−0.100624			−0.0503118	−	0.998734i	$-0.516022\pi$
$101$	−1.01126			−0.100624			−0.0503118	+	0.998734i	$0.516022\pi$
$102$		0			0
$103$	−0.873194			−0.0860384			−0.0430192	−	0.999074i	$-0.513698\pi$
$103$	−0.873194			−0.0860384			−0.0430192	+	0.999074i	$0.513698\pi$
$104$		0			0
$105$	−4.09751			−0.399876
$106$		0			0
$107$	−6.67557	−	11.5624i	−0.645352	−	1.11778i	−0.984220	−	0.176949i	$-0.943377\pi$
$107$	−6.67557	−	11.5624i	−0.645352	−	1.11778i	0.338868	−	0.940834i	$-0.389956\pi$
$108$		0			0
$109$	5.75416	−	9.96649i	0.551148	−	0.954617i	−0.447044	−	0.894512i	$-0.647523\pi$
$109$	5.75416	−	9.96649i	0.551148	−	0.954617i	0.998192	−	0.0601047i	$-0.0191435\pi$
$110$		0			0
$111$	−8.74492	+	2.31573i	−0.830031	+	0.219799i
$112$		0			0
$113$	3.06426	−	5.30746i	0.288262	−	0.499284i	−0.685133	−	0.728418i	$-0.740256\pi$
$113$	3.06426	−	5.30746i	0.288262	−	0.499284i	0.973395	+	0.229134i	$0.0735894\pi$
$114$		0			0
$115$	−0.278964	−	0.483180i	−0.0260135	−	0.0450567i
$116$		0			0
$117$	2.84569			0.263084
$118$		0			0
$119$	−4.28189			−0.392520
$120$		0			0
$121$	−10.7164			−0.974217
$122$		0			0
$123$	−1.90746	+	3.30381i	−0.171990	+	0.297895i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.18816	−	7.25410i	0.371639	−	0.643697i	−0.618179	−	0.786037i	$-0.712129\pi$
$127$	4.18816	−	7.25410i	0.371639	−	0.643697i	0.989818	+	0.142340i	$0.0454627\pi$
$128$		0			0
$129$	−2.85964	−	4.95304i	−0.251777	−	0.436091i
$130$		0			0
$131$	−9.08367	+	15.7334i	−0.793644	+	1.37463i	0.130053	+	0.991507i	$0.458485\pi$
$131$	−9.08367	+	15.7334i	−0.793644	+	1.37463i	−0.923697	+	0.383124i	$0.874848\pi$
$132$		0			0
$133$	6.09631	−	10.5591i	0.528617	−	0.915592i
$134$		0			0
$135$	2.81693	+	4.87907i	0.242443	+	0.419923i
$136$		0			0
$137$	9.83174			0.839982			0.419991	−	0.907528i	$-0.362033\pi$
$137$	9.83174			0.839982			0.419991	+	0.907528i	$0.362033\pi$
$138$		0			0
$139$	4.19432	−	7.26477i	0.355757	−	0.616190i	−0.631490	−	0.775384i	$-0.717556\pi$
$139$	4.19432	−	7.26477i	0.355757	−	0.616190i	0.987247	+	0.159194i	$0.0508896\pi$
$140$		0			0
$141$	0.602306	+	1.04322i	0.0507233	+	0.0878553i
$142$		0			0
$143$	0.961331	+	1.66507i	0.0803906	+	0.139241i
$144$		0			0
$145$	3.16453	+	5.48112i	0.262800	+	0.455183i
$146$		0			0
$147$	−0.878893			−0.0724899
$148$		0			0
$149$	20.5908			1.68686			0.843432	−	0.537236i	$-0.180532\pi$
$149$	20.5908			1.68686			0.843432	+	0.537236i	$0.180532\pi$
$150$		0			0
$151$	−4.20755	−	7.28770i	−0.342406	−	0.593065i	0.642473	−	0.766308i	$-0.277908\pi$
$151$	−4.20755	−	7.28770i	−0.342406	−	0.593065i	−0.984879	+	0.173244i	$0.944575\pi$
$152$		0			0
$153$	0.612492	+	1.06087i	0.0495170	+	0.0857660i
$154$		0			0
$155$	−4.20531	−	7.28380i	−0.337778	−	0.585049i
$156$		0			0
$157$	5.44075	−	9.42365i	0.434219	−	0.752089i	−0.563013	−	0.826448i	$-0.690358\pi$
$157$	5.44075	−	9.42365i	0.434219	−	0.752089i	0.997232	+	0.0743593i	$0.0236912\pi$
$158$		0			0
$159$	0.827881			0.0656552
$160$		0			0
$161$	−0.768593	−	1.33124i	−0.0605736	−	0.104917i
$162$		0			0
$163$	10.6839	−	18.5051i	0.836831	−	1.44943i	−0.0556992	−	0.998448i	$-0.517739\pi$
$163$	10.6839	−	18.5051i	0.836831	−	1.44943i	0.892531	−	0.450987i	$-0.148928\pi$
$164$		0			0
$165$	−0.396005	+	0.685901i	−0.0308290	+	0.0533973i
$166$		0			0
$167$	4.33649	+	7.51102i	0.335568	+	0.581220i	0.983594	−	0.180398i	$-0.0577386\pi$
$167$	4.33649	+	7.51102i	0.335568	+	0.581220i	−0.648026	+	0.761618i	$0.724405\pi$
$168$		0			0
$169$	−0.0171504	+	0.0297053i	−0.00131926	+	0.00228503i
$170$		0			0
$171$	−3.48812			−0.266743
$172$		0			0
$173$	0.974870	−	1.68853i	0.0741180	−	0.128376i	−0.826584	−	0.562813i	$-0.809719\pi$
$173$	0.974870	−	1.68853i	0.0741180	−	0.128376i	0.900702	+	0.434437i	$0.143053\pi$
$174$		0			0
$175$	−2.75517			−0.208271
$176$		0			0
$177$	0.363486			0.0273213
$178$		0			0
$179$	−15.4970			−1.15830			−0.579150	−	0.815221i	$-0.696616\pi$
$179$	−15.4970			−1.15830			−0.579150	+	0.815221i	$0.696616\pi$
$180$		0			0
$181$	−6.49867	−	11.2560i	−0.483043	−	0.836654i	0.516768	−	0.856126i	$-0.327135\pi$
$181$	−6.49867	−	11.2560i	−0.483043	−	0.836654i	−0.999810	+	0.0194713i	$0.993802\pi$
$182$		0			0
$183$	4.24994	−	7.36111i	0.314165	−	0.544149i
$184$		0			0
$185$	−5.88009	+	1.55710i	−0.432313	+	0.114480i
$186$		0			0
$187$	−0.413825	+	0.716765i	−0.0302619	+	0.0524151i
$188$		0			0
$189$	7.76112	+	13.4427i	0.564539	+	0.977810i
$190$		0			0
$191$	18.6562			1.34992			0.674959	−	0.737855i	$-0.264161\pi$
$191$	18.6562			1.34992			0.674959	+	0.737855i	$0.264161\pi$
$192$		0			0
$193$	−23.7136			−1.70694			−0.853472	−	0.521139i	$-0.825507\pi$
$193$	−23.7136			−1.70694			−0.853472	+	0.521139i	$0.825507\pi$
$194$		0			0
$195$	−5.36927			−0.384502
$196$		0			0
$197$	12.5686	−	21.7695i	0.895476	−	1.55101i	0.0622610	−	0.998060i	$-0.480169\pi$
$197$	12.5686	−	21.7695i	0.895476	−	1.55101i	0.833215	−	0.552950i	$-0.186498\pi$
$198$		0			0
$199$	−11.3006			−0.801077			−0.400539	−	0.916280i	$-0.631177\pi$
$199$	−11.3006			−0.801077			−0.400539	+	0.916280i	$0.631177\pi$
$200$		0			0
$201$	1.91269	−	3.31288i	0.134911	−	0.233672i
$202$		0			0
$203$	8.71882	+	15.1014i	0.611941	+	1.05991i
$204$		0			0
$205$	−1.28258	+	2.22149i	−0.0895790	+	0.155155i
$206$		0			0
$207$	−0.219883	+	0.380848i	−0.0152829	+	0.0264708i
$208$		0			0
$209$	−1.17836	−	2.04098i	−0.0815089	−	0.141177i
$210$		0			0
$211$	−14.1121			−0.971517			−0.485758	−	0.874093i	$-0.661457\pi$
$211$	−14.1121			−0.971517			−0.485758	+	0.874093i	$0.661457\pi$
$212$		0			0
$213$	−5.76988	+	9.99372i	−0.395345	+	0.684758i
$214$		0			0
$215$	−1.92282	−	3.33043i	−0.131135	−	0.227133i
$216$		0			0
$217$	−11.5863	−	20.0681i	−0.786532	−	1.36231i
$218$		0			0
$219$	1.10683	+	1.91709i	0.0747927	+	0.129545i
$220$		0			0
$221$	−5.61088			−0.377429
$222$		0			0
$223$	−1.70027			−0.113859			−0.0569293	−	0.998378i	$-0.518131\pi$
$223$	−1.70027			−0.113859			−0.0569293	+	0.998378i	$0.518131\pi$
$224$		0			0
$225$	0.394106	+	0.682612i	0.0262737	+	0.0455075i
$226$		0			0
$227$	−7.67530	−	13.2940i	−0.509428	−	0.882354i	−0.999940	−	0.0109204i	$-0.996524\pi$
$227$	−7.67530	−	13.2940i	−0.509428	−	0.882354i	0.490513	−	0.871434i	$-0.336809\pi$
$228$		0			0
$229$	−2.33166	−	4.03855i	−0.154080	−	0.266875i	0.778643	−	0.627467i	$-0.215908\pi$
$229$	−2.33166	−	4.03855i	−0.154080	−	0.266875i	−0.932724	+	0.360592i	$0.882575\pi$
$230$		0			0
$231$	−1.09106	+	1.88978i	−0.0717866	+	0.124338i
$232$		0			0
$233$	−7.58843			−0.497135			−0.248567	−	0.968615i	$-0.579960\pi$
$233$	−7.58843			−0.497135			−0.248567	+	0.968615i	$0.579960\pi$
$234$		0			0
$235$	0.404991	+	0.701465i	0.0264187	+	0.0457585i
$236$		0			0
$237$	0.654893	−	1.13431i	0.0425399	−	0.0736812i
$238$		0			0
$239$	2.29314	−	3.97183i	0.148331	−	0.256916i	−0.782280	−	0.622927i	$-0.785943\pi$
$239$	2.29314	−	3.97183i	0.148331	−	0.256916i	0.930611	+	0.366011i	$0.119277\pi$
$240$		0			0
$241$	6.46329	+	11.1948i	0.416337	+	0.721117i	0.995568	−	0.0940464i	$-0.0299802\pi$
$241$	6.46329	+	11.1948i	0.416337	+	0.721117i	−0.579230	+	0.815164i	$0.696647\pi$
$242$		0			0
$243$	3.97869	−	6.89130i	0.255233	−	0.442077i
$244$		0			0
$245$	−0.590969			−0.0377556
$246$		0			0
$247$	7.98845	−	13.8364i	0.508293	−	0.880389i
$248$		0			0
$249$	1.99852			0.126651
$250$		0			0
$251$	−26.0756			−1.64588			−0.822939	−	0.568129i	$-0.807667\pi$
$251$	−26.0756			−1.64588			−0.822939	+	0.568129i	$0.807667\pi$
$252$		0			0
$253$	−0.297124			−0.0186800
$254$		0			0
$255$	−1.15566	−	2.00166i	−0.0723700	−	0.125349i
$256$		0			0
$257$	4.54317	−	7.86901i	0.283395	−	0.490855i	−0.688823	−	0.724929i	$-0.741872\pi$
$257$	4.54317	−	7.86901i	0.283395	−	0.490855i	0.972219	+	0.234074i	$0.0752058\pi$
$258$		0			0
$259$	−16.2007	+	4.29007i	−1.00666	+	0.266572i
$260$		0			0
$261$	2.49432	−	4.32029i	0.154395	−	0.267419i
$262$		0			0
$263$	11.7821	+	20.4071i	0.726513	+	1.25836i	0.958348	+	0.285603i	$0.0921938\pi$
$263$	11.7821	+	20.4071i	0.726513	+	1.25836i	−0.231835	+	0.972755i	$0.574473\pi$
$264$		0			0
$265$	0.556668			0.0341958
$266$		0			0
$267$	15.9229			0.974463
$268$		0			0
$269$	29.3900			1.79194			0.895971	−	0.444112i	$-0.146481\pi$
$269$	29.3900			1.79194			0.895971	+	0.444112i	$0.146481\pi$
$270$		0			0
$271$	−9.48625	+	16.4307i	−0.576248	+	0.998092i	0.419656	+	0.907683i	$0.362151\pi$
$271$	−9.48625	+	16.4307i	−0.576248	+	0.998092i	−0.995905	+	0.0904085i	$0.971183\pi$
$272$		0			0
$273$	−14.7933			−0.895329
$274$		0			0
$275$	−0.266274	+	0.461201i	−0.0160569	+	0.0278114i
$276$		0			0
$277$	−13.5048	−	23.3910i	−0.811423	−	1.40543i	−0.911868	−	0.410483i	$-0.865360\pi$
$277$	−13.5048	−	23.3910i	−0.811423	−	1.40543i	0.100445	−	0.994943i	$-0.467973\pi$
$278$		0			0
$279$	−3.31467	+	5.74118i	−0.198444	+	0.343716i
$280$		0			0
$281$	−5.11518	+	8.85975i	−0.305146	+	0.528528i	−0.977294	−	0.211889i	$-0.932039\pi$
$281$	−5.11518	+	8.85975i	−0.305146	+	0.528528i	0.672148	+	0.740417i	$0.265372\pi$
$282$		0			0
$283$	10.8775	+	18.8404i	0.646601	+	1.11995i	0.983929	+	0.178559i	$0.0571435\pi$
$283$	10.8775	+	18.8404i	0.646601	+	1.11995i	−0.337328	+	0.941387i	$0.609523\pi$
$284$		0			0
$285$	6.58143			0.389850
$286$		0			0
$287$	−3.53372	+	6.12058i	−0.208589	+	0.361286i
$288$		0			0
$289$	7.29234	+	12.6307i	0.428961	+	0.742983i
$290$		0			0
$291$	6.97635	+	12.0834i	0.408961	+	0.708341i
$292$		0			0
$293$	11.7512	+	20.3536i	0.686511	+	1.18907i	0.972959	+	0.230976i	$0.0741919\pi$
$293$	11.7512	+	20.3536i	0.686511	+	1.18907i	−0.286449	+	0.958096i	$0.592475\pi$
$294$		0			0
$295$	0.244408			0.0142300
$296$		0			0
$297$	3.00030			0.174095
$298$		0			0
$299$	−1.00714	−	1.74443i	−0.0582447	−	0.100883i
$300$		0			0
$301$	−5.29771	−	9.17590i	−0.305355	−	0.528890i
$302$		0			0
$303$	−0.751974	−	1.30246i	−0.0431998	−	0.0748242i
$304$		0			0
$305$	2.85766	−	4.94962i	0.163629	−	0.283414i
$306$		0			0
$307$	−21.3250			−1.21708			−0.608541	−	0.793522i	$-0.708245\pi$
$307$	−21.3250			−1.21708			−0.608541	+	0.793522i	$0.708245\pi$
$308$		0			0
$309$	−0.649311	−	1.12464i	−0.0369380	−	0.0639785i
$310$		0			0
$311$	2.85790	−	4.95002i	0.162057	−	0.280690i	−0.773550	−	0.633736i	$-0.781521\pi$
$311$	2.85790	−	4.95002i	0.162057	−	0.280690i	0.935606	+	0.353046i	$0.114854\pi$
$312$		0			0
$313$	−6.99192	+	12.1104i	−0.395207	+	0.684518i	−0.993128	−	0.117037i	$-0.962660\pi$
$313$	−6.99192	+	12.1104i	−0.395207	+	0.684518i	0.597921	+	0.801555i	$0.295994\pi$
$314$		0			0
$315$	1.08583	+	1.88071i	0.0611796	+	0.105966i
$316$		0			0
$317$	−2.32903	+	4.03400i	−0.130811	+	0.226572i	−0.923990	−	0.382418i	$-0.875092\pi$
$317$	−2.32903	+	4.03400i	−0.130811	+	0.226572i	0.793178	+	0.608990i	$0.208425\pi$
$318$		0			0
$319$	3.37053			0.188713
$320$		0			0
$321$	9.92797	−	17.1957i	0.554125	−	0.959773i
$322$		0			0
$323$	6.87758			0.382679
$324$		0			0
$325$	−3.61030			−0.200264
$326$		0			0
$327$	17.1153			0.946476
$328$		0			0
$329$	1.11582	+	1.93266i	0.0615171	+	0.106551i
$330$		0			0
$331$	−0.944646	+	1.63617i	−0.0519224	+	0.0899323i	−0.890818	−	0.454359i	$-0.849868\pi$
$331$	−0.944646	+	1.63617i	−0.0519224	+	0.0899323i	0.838896	+	0.544292i	$0.183202\pi$
$332$		0			0
$333$	3.38027	+	3.40016i	0.185238	+	0.186327i
$334$		0			0
$335$	1.28609	−	2.22758i	0.0702669	−	0.121706i
$336$		0			0
$337$	12.6922	+	21.9835i	0.691386	+	1.19752i	0.971384	+	0.237515i	$0.0763330\pi$
$337$	12.6922	+	21.9835i	0.691386	+	1.19752i	−0.279998	+	0.960001i	$0.590334\pi$
$338$		0			0
$339$	9.11439			0.495026
$340$		0			0
$341$	−4.47906			−0.242555
$342$		0			0
$343$	17.6580			0.953441
$344$		0			0
$345$	0.414877	−	0.718588i	0.0223362	−	0.0386875i
$346$		0			0
$347$	−8.96851			−0.481455			−0.240727	−	0.970593i	$-0.577386\pi$
$347$	−8.96851			−0.481455			−0.240727	+	0.970593i	$0.577386\pi$
$348$		0			0
$349$	−15.8757	+	27.4974i	−0.849805	+	1.47190i	0.0315779	+	0.999501i	$0.489947\pi$
$349$	−15.8757	+	27.4974i	−0.849805	+	1.47190i	−0.881382	+	0.472403i	$0.843387\pi$
$350$		0			0
$351$	10.1700	+	17.6149i	0.542833	+	0.940215i
$352$		0			0
$353$	3.53206	−	6.11771i	0.187993	−	0.325613i	−0.756588	−	0.653892i	$-0.773135\pi$
$353$	3.53206	−	6.11771i	0.187993	−	0.325613i	0.944581	+	0.328279i	$0.106469\pi$
$354$		0			0
$355$	−3.87967	+	6.71979i	−0.205911	+	0.356649i
$356$		0			0
$357$	−3.18403	−	5.51491i	−0.168517	−	0.291880i
$358$		0			0
$359$	6.16400			0.325323			0.162662	−	0.986682i	$-0.447992\pi$
$359$	6.16400			0.325323			0.162662	+	0.986682i	$0.447992\pi$
$360$		0			0
$361$	−0.291909	+	0.505601i	−0.0153636	+	0.0266106i
$362$		0			0
$363$	−7.96875	−	13.8023i	−0.418251	−	0.724432i
$364$		0			0
$365$	0.744234	+	1.28905i	0.0389550	+	0.0674720i
$366$		0			0
$367$	7.49348	+	12.9791i	0.391157	+	0.677503i	0.992602	−	0.121410i	$-0.0387417\pi$
$367$	7.49348	+	12.9791i	0.391157	+	0.677503i	−0.601446	+	0.798914i	$0.705408\pi$
$368$		0			0
$369$	2.02189			0.105255
$370$		0			0
$371$	1.53372			0.0796265
$372$		0			0
$373$	1.12859	+	1.95477i	0.0584361	+	0.101214i	0.893764	−	0.448538i	$-0.148055\pi$
$373$	1.12859	+	1.95477i	0.0584361	+	0.101214i	−0.835327	+	0.549753i	$0.814722\pi$
$374$		0			0
$375$	−0.743604	−	1.28796i	−0.0383995	−	0.0665100i
$376$		0			0
$377$	11.4249	+	19.7885i	0.588413	+	1.01916i
$378$		0			0
$379$	−7.10203	+	12.3011i	−0.364807	+	0.631864i	−0.988745	−	0.149610i	$-0.952198\pi$
$379$	−7.10203	+	12.3011i	−0.364807	+	0.631864i	0.623939	+	0.781473i	$0.285532\pi$
$380$		0			0
$381$	12.4573			0.638208
$382$		0			0
$383$	16.3185	+	28.2644i	0.833834	+	1.44424i	0.894976	+	0.446114i	$0.147192\pi$
$383$	16.3185	+	28.2644i	0.833834	+	1.44424i	−0.0611419	+	0.998129i	$0.519474\pi$
$384$		0			0
$385$	−0.733631	+	1.27069i	−0.0373893	+	0.0647602i
$386$		0			0
$387$	−1.51559	+	2.62508i	−0.0770419	+	0.133441i
$388$		0			0
$389$	−4.19304	−	7.26255i	−0.212595	−	0.368226i	0.739931	−	0.672683i	$-0.234858\pi$
$389$	−4.19304	−	7.26255i	−0.212595	−	0.368226i	−0.952526	+	0.304457i	$0.901525\pi$
$390$		0			0
$391$	0.433546	−	0.750923i	0.0219254	−	0.0379758i
$392$		0			0
$393$	−27.0186			−1.36291
$394$		0			0
$395$	0.440351	−	0.762710i	0.0221565	−	0.0383761i
$396$		0			0
$397$	−18.7023			−0.938642			−0.469321	−	0.883028i	$-0.655501\pi$
$397$	−18.7023			−0.938642			−0.469321	+	0.883028i	$0.655501\pi$
$398$		0			0
$399$	18.1330			0.907784
$400$		0			0
$401$	2.24569			0.112144			0.0560721	−	0.998427i	$-0.482142\pi$
$401$	2.24569			0.112144			0.0560721	+	0.998427i	$0.482142\pi$
$402$		0			0
$403$	−15.1824	−	26.2968i	−0.756291	−	1.30993i
$404$		0			0
$405$	−3.00704	+	5.20835i	−0.149421	+	0.258805i
$406$		0			0
$407$	−0.847583	+	3.12652i	−0.0420131	+	0.154976i
$408$		0			0
$409$	−7.92186	+	13.7211i	−0.391711	+	0.678463i	−0.992675	−	0.120813i	$-0.961450\pi$
$409$	−7.92186	+	13.7211i	−0.391711	+	0.678463i	0.600965	+	0.799276i	$0.294783\pi$
$410$		0			0
$411$	7.31092	+	12.6629i	0.360621	+	0.624614i
$412$		0			0
$413$	0.673387			0.0331352
$414$		0			0
$415$	1.34381			0.0659649
$416$		0			0
$417$	12.4756			0.610935
$418$		0			0
$419$	−1.93603	+	3.35330i	−0.0945813	+	0.163820i	−0.909434	−	0.415849i	$-0.863485\pi$
$419$	−1.93603	+	3.35330i	−0.0945813	+	0.163820i	0.814852	+	0.579668i	$0.196818\pi$
$420$		0			0
$421$	−3.37150			−0.164317			−0.0821583	−	0.996619i	$-0.526181\pi$
$421$	−3.37150			−0.164317			−0.0821583	+	0.996619i	$0.526181\pi$
$422$		0			0
$423$	0.319219	−	0.552903i	0.0155210	−	0.0268831i
$424$		0			0
$425$	−0.777065	−	1.34592i	−0.0376932	−	0.0652865i
$426$		0			0
$427$	7.87335	−	13.6370i	0.381018	−	0.659943i
$428$		0			0
$429$	−1.42970	+	2.47631i	−0.0690266	+	0.119557i
$430$		0			0
$431$	−6.46990	−	11.2062i	−0.311644	−	0.539783i	0.667074	−	0.744991i	$-0.267546\pi$
$431$	−6.46990	−	11.2062i	−0.311644	−	0.539783i	−0.978718	+	0.205208i	$0.934213\pi$
$432$		0			0
$433$	−19.0716			−0.916525			−0.458262	−	0.888817i	$-0.651528\pi$
$433$	−19.0716			−0.916525			−0.458262	+	0.888817i	$0.651528\pi$
$434$		0			0
$435$	−4.70631	+	8.15157i	−0.225650	+	0.390838i
$436$		0			0
$437$	1.23452	+	2.13824i	0.0590549	+	0.102286i
$438$		0			0
$439$	−3.18406	−	5.51495i	−0.151967	−	0.263214i	0.779984	−	0.625800i	$-0.215227\pi$
$439$	−3.18406	−	5.51495i	−0.151967	−	0.263214i	−0.931950	+	0.362586i	$0.881894\pi$
$440$		0			0
$441$	0.232904	+	0.403402i	0.0110907	+	0.0192096i
$442$		0			0
$443$	22.2323			1.05629			0.528144	−	0.849155i	$-0.322888\pi$
$443$	22.2323			1.05629			0.528144	+	0.849155i	$0.322888\pi$
$444$		0			0
$445$	10.7065			0.507539
$446$		0			0
$447$	15.3114	+	26.5201i	0.724204	+	1.25436i
$448$		0			0
$449$	4.93804	+	8.55294i	0.233041	+	0.403638i	0.958701	−	0.284414i	$-0.0917992\pi$
$449$	4.93804	+	8.55294i	0.233041	+	0.403638i	−0.725661	+	0.688053i	$0.758466\pi$
$450$		0			0
$451$	0.683034	+	1.18305i	0.0321628	+	0.0557077i
$452$		0			0
$453$	6.25751	−	10.8383i	0.294003	−	0.509229i
$454$		0			0
$455$	−9.94701			−0.466323
$456$		0			0
$457$	14.4178	+	24.9723i	0.674435	+	1.16816i	0.976634	+	0.214911i	$0.0689462\pi$
$457$	14.4178	+	24.9723i	0.674435	+	1.16816i	−0.302198	+	0.953245i	$0.597720\pi$
$458$		0			0
$459$	−4.37787	+	7.58270i	−0.204342	+	0.353930i
$460$		0			0
$461$	−10.2900	+	17.8229i	−0.479255	+	0.830094i	−0.999717	−	0.0237906i	$-0.992427\pi$
$461$	−10.2900	+	17.8229i	−0.479255	+	0.830094i	0.520462	+	0.853885i	$0.325760\pi$
$462$		0			0
$463$	−6.74227	−	11.6780i	−0.313340	−	0.542721i	0.665743	−	0.746181i	$-0.268115\pi$
$463$	−6.74227	−	11.6780i	−0.313340	−	0.542721i	−0.979083	+	0.203460i	$0.934781\pi$
$464$		0			0
$465$	6.25416	−	10.8325i	0.290030	−	0.502347i
$466$		0			0
$467$	−26.2189			−1.21326			−0.606632	−	0.794983i	$-0.707480\pi$
$467$	−26.2189			−1.21326			−0.606632	+	0.794983i	$0.707480\pi$
$468$		0			0
$469$	3.54341	−	6.13737i	0.163620	−	0.283397i
$470$		0			0
$471$	16.1830			0.745675
$472$		0			0
$473$	−2.04799			−0.0941669
$474$		0			0
$475$	4.42536			0.203049
$476$		0			0
$477$	−0.219386	−	0.379988i	−0.0100450	−	0.0173985i
$478$		0			0
$479$	6.78843	−	11.7579i	0.310171	−	0.537233i	−0.668228	−	0.743957i	$-0.732947\pi$
$479$	6.78843	−	11.7579i	0.310171	−	0.537233i	0.978399	+	0.206724i	$0.0662802\pi$
$480$		0			0
$481$	−21.2289	+	5.62159i	−0.967955	+	0.256323i
$482$		0			0
$483$	1.14306	−	1.97983i	0.0520109	−	0.0900856i
$484$		0			0
$485$	4.69090	+	8.12488i	0.213003	+	0.368932i
$486$		0			0
$487$	−12.7123			−0.576050			−0.288025	−	0.957623i	$-0.592999\pi$
$487$	−12.7123			−0.576050			−0.288025	+	0.957623i	$0.592999\pi$
$488$		0			0
$489$	31.7785			1.43707
$490$		0			0
$491$	28.2438			1.27463			0.637313	−	0.770605i	$-0.280046\pi$
$491$	28.2438			1.27463			0.637313	+	0.770605i	$0.280046\pi$
$492$		0			0
$493$	−4.91809	+	8.51838i	−0.221499	+	0.383648i
$494$		0			0
$495$	0.419761			0.0188669
$496$		0			0
$497$	−10.6892	+	18.5142i	−0.479474	+	0.830474i
$498$		0			0
$499$	−19.1879	−	33.2345i	−0.858970	−	1.48778i	−0.872913	−	0.487877i	$-0.837772\pi$
$499$	−19.1879	−	33.2345i	−0.858970	−	1.48778i	0.0139426	−	0.999903i	$-0.495562\pi$
$500$		0			0
$501$	−6.44926	+	11.1704i	−0.288132	+	0.499059i
$502$		0			0
$503$	−0.925795	+	1.60352i	−0.0412792	+	0.0714976i	−0.885927	−	0.463825i	$-0.846477\pi$
$503$	−0.925795	+	1.60352i	−0.0412792	+	0.0714976i	0.844648	+	0.535323i	$0.179810\pi$
$504$		0			0
$505$	−0.505628	−	0.875773i	−0.0225001	−	0.0389714i
$506$		0			0
$507$	−0.0510124			−0.00226554
$508$		0			0
$509$	−1.04809	+	1.81534i	−0.0464557	+	0.0804636i	−0.888318	−	0.459228i	$-0.848126\pi$
$509$	−1.04809	+	1.81534i	−0.0464557	+	0.0804636i	0.841863	+	0.539692i	$0.181459\pi$
$510$		0			0
$511$	2.05049	+	3.55156i	0.0907084	+	0.157112i
$512$		0			0
$513$	−12.4659	−	21.5916i	−0.550384	−	0.953294i
$514$		0			0
$515$	−0.436597	−	0.756208i	−0.0192388	−	0.0333225i
$516$		0			0
$517$	0.431355			0.0189710
$518$		0			0
$519$	2.89967			0.127281
$520$		0			0
$521$	−0.0876407	−	0.151798i	−0.00383961	−	0.00665039i	0.864099	−	0.503322i	$-0.167889\pi$
$521$	−0.0876407	−	0.151798i	−0.00383961	−	0.00665039i	−0.867939	+	0.496671i	$0.834556\pi$
$522$		0			0
$523$	−10.6646	−	18.4716i	−0.466329	−	0.807705i	0.532932	−	0.846158i	$-0.321090\pi$
$523$	−10.6646	−	18.4716i	−0.466329	−	0.807705i	−0.999260	+	0.0384533i	$0.987757\pi$
$524$		0			0
$525$	−2.04876	−	3.54855i	−0.0894151	−	0.154871i
$526$		0			0
$527$	6.53559	−	11.3200i	0.284695	−	0.493106i
$528$		0			0
$529$	−22.6887			−0.986466
$530$		0			0
$531$	−0.0963228	−	0.166836i	−0.00418005	−	0.00724007i
$532$		0			0
$533$	−4.63049	+	8.02025i	−0.200569	+	0.347396i
$534$		0			0
$535$	6.67557	−	11.5624i	0.288610	−	0.499888i
$536$		0			0
$537$	−11.5236	−	19.9595i	−0.497282	−	0.861317i
$538$		0			0
$539$	−0.157360	+	0.272555i	−0.00677796	+	0.0117398i
$540$		0			0
$541$	19.0690			0.819840			0.409920	−	0.912122i	$-0.365557\pi$
$541$	19.0690			0.819840			0.409920	+	0.912122i	$0.365557\pi$
$542$		0			0
$543$	9.66488	−	16.7401i	0.414760	−	0.718385i
$544$		0			0
$545$	11.5083			0.492962
$546$		0			0
$547$	−17.9793			−0.768738			−0.384369	−	0.923180i	$-0.625581\pi$
$547$	−17.9793			−0.768738			−0.384369	+	0.923180i	$0.625581\pi$
$548$		0			0
$549$	−4.50489			−0.192264
$550$		0			0
$551$	−14.0042	−	24.2560i	−0.596598	−	1.03334i
$552$		0			0
$553$	1.21324	−	2.10140i	0.0515923	−	0.0893605i
$554$		0			0
$555$	−6.37794	−	6.41546i	−0.270728	−	0.272321i
$556$		0			0
$557$	−16.9417	+	29.3439i	−0.717843	+	1.24334i	0.244009	+	0.969773i	$0.421537\pi$
$557$	−16.9417	+	29.3439i	−0.717843	+	1.24334i	−0.961853	+	0.273568i	$0.911796\pi$
$558$		0			0
$559$	−6.94198	−	12.0239i	−0.293614	−	0.508555i
$560$		0			0
$561$	−1.23089			−0.0519681
$562$		0			0
$563$	8.29519			0.349601			0.174800	−	0.984604i	$-0.444072\pi$
$563$	8.29519			0.349601			0.174800	+	0.984604i	$0.444072\pi$
$564$		0			0
$565$	6.12852			0.257829
$566$		0			0
$567$	−8.28492	+	14.3499i	−0.347934	+	0.602639i
$568$		0			0
$569$	−29.9439			−1.25531			−0.627657	−	0.778490i	$-0.715986\pi$
$569$	−29.9439			−1.25531			−0.627657	+	0.778490i	$0.715986\pi$
$570$		0			0
$571$	14.2517	−	24.6846i	0.596413	−	1.03302i	−0.396933	−	0.917848i	$-0.629925\pi$
$571$	14.2517	−	24.6846i	0.596413	−	1.03302i	0.993346	−	0.115170i	$-0.0367414\pi$
$572$		0			0
$573$	13.8729	+	24.0285i	0.579547	+	1.00380i
$574$		0			0
$575$	0.278964	−	0.483180i	0.0116336	−	0.0201500i
$576$		0			0
$577$	−15.7109	+	27.2120i	−0.654052	+	1.13285i	0.328079	+	0.944650i	$0.393599\pi$
$577$	−15.7109	+	27.2120i	−0.654052	+	1.13285i	−0.982131	+	0.188200i	$0.939735\pi$
$578$		0			0
$579$	−17.6335	−	30.5422i	−0.732825	−	1.26929i
$580$		0			0
$581$	3.70242			0.153602
$582$		0			0
$583$	0.148226	−	0.256736i	0.00613891	−	0.0106329i
$584$		0			0
$585$	1.42284	+	2.46444i	0.0588273	+	0.101892i
$586$		0			0
$587$	−0.353254	−	0.611854i	−0.0145803	−	0.0252539i	0.858643	−	0.512574i	$-0.171308\pi$
$587$	−0.353254	−	0.611854i	−0.0145803	−	0.0252539i	−0.873224	+	0.487320i	$0.837975\pi$
$588$		0			0
$589$	18.6100	+	32.2335i	0.766812	+	1.32816i
$590$		0			0
$591$	37.3842			1.53778
$592$		0			0
$593$	−1.81282			−0.0744437			−0.0372219	−	0.999307i	$-0.511851\pi$
$593$	−1.81282			−0.0744437			−0.0372219	+	0.999307i	$0.511851\pi$
$594$		0			0
$595$	−2.14095	−	3.70823i	−0.0877702	−	0.152023i
$596$		0			0
$597$	−8.40316	−	14.5547i	−0.343918	−	0.595684i
$598$		0			0
$599$	−20.1816	−	34.9556i	−0.824599	−	1.42825i	−0.902225	−	0.431265i	$-0.858067\pi$
$599$	−20.1816	−	34.9556i	−0.824599	−	1.42825i	0.0776257	−	0.996983i	$-0.475266\pi$
$600$		0			0
$601$	−2.08464	+	3.61071i	−0.0850344	+	0.147284i	−0.905406	−	0.424547i	$-0.860433\pi$
$601$	−2.08464	+	3.61071i	−0.0850344	+	0.147284i	0.820371	+	0.571831i	$0.193767\pi$
$602$		0			0
$603$	−2.02743			−0.0825634
$604$		0			0
$605$	−5.35820	−	9.28067i	−0.217842	−	0.377313i
$606$		0			0
$607$	−4.99052	+	8.64384i	−0.202559	+	0.350843i	−0.949352	−	0.314214i	$-0.898259\pi$
$607$	−4.99052	+	8.64384i	−0.202559	+	0.350843i	0.746793	+	0.665056i	$0.231592\pi$
$608$		0			0
$609$	−12.9667	+	22.4590i	−0.525437	+	0.910084i
$610$		0			0
$611$	1.46214	+	2.53250i	0.0591519	+	0.102454i
$612$		0			0
$613$	−0.103824	+	0.179829i	−0.00419343	+	0.00726323i	−0.868115	−	0.496364i	$-0.834668\pi$
$613$	−0.103824	+	0.179829i	−0.00419343	+	0.00726323i	0.863921	+	0.503627i	$0.168001\pi$
$614$		0			0
$615$	−3.81492			−0.153832
$616$		0			0
$617$	10.0538	−	17.4137i	0.404752	−	0.701051i	−0.589541	−	0.807739i	$-0.700691\pi$
$617$	10.0538	−	17.4137i	0.404752	−	0.701051i	0.994293	+	0.106688i	$0.0340246\pi$
$618$		0			0
$619$	9.42980			0.379016			0.189508	−	0.981879i	$-0.439311\pi$
$619$	9.42980			0.379016			0.189508	+	0.981879i	$0.439311\pi$
$620$		0			0
$621$	−3.14329			−0.126136
$622$		0			0
$623$	29.4984			1.18183
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	1.75247	−	3.03536i	0.0699868	−	0.121221i
$628$		0			0
$629$	−6.66493	−	6.70414i	−0.265748	−	0.267312i
$630$		0			0
$631$	22.5649	−	39.0836i	0.898295	−	1.55589i	0.0686221	−	0.997643i	$-0.478140\pi$
$631$	22.5649	−	39.0836i	0.898295	−	1.55589i	0.829673	−	0.558250i	$-0.188527\pi$
$632$		0			0
$633$	−10.4938	−	18.1758i	−0.417092	−	0.722424i
$634$		0			0
$635$	8.37631			0.332404
$636$		0			0
$637$	−2.13358			−0.0845354
$638$		0			0
$639$	6.11601			0.241945
$640$		0			0
$641$	−10.7043	+	18.5404i	−0.422794	+	0.732300i	−0.996212	−	0.0869627i	$-0.972284\pi$
$641$	−10.7043	+	18.5404i	−0.422794	+	0.732300i	0.573418	+	0.819263i	$0.305617\pi$
$642$		0			0
$643$	−19.9523			−0.786843			−0.393422	−	0.919358i	$-0.628709\pi$
$643$	−19.9523			−0.786843			−0.393422	+	0.919358i	$0.628709\pi$
$644$		0			0
$645$	2.85964	−	4.95304i	0.112598	−	0.195026i
$646$		0			0
$647$	8.62787	+	14.9439i	0.339197	+	0.587506i	0.984282	−	0.176605i	$-0.0565115\pi$
$647$	8.62787	+	14.9439i	0.339197	+	0.587506i	−0.645085	+	0.764111i	$0.723178\pi$
$648$		0			0
$649$	0.0650796	−	0.112721i	0.00255460	−	0.00442470i
$650$		0			0
$651$	17.2313	−	29.8455i	0.675348	−	1.16974i
$652$		0			0
$653$	−22.5889	−	39.1251i	−0.883972	−	1.53108i	−0.846888	−	0.531772i	$-0.821526\pi$
$653$	−22.5889	−	39.1251i	−0.883972	−	1.53108i	−0.0370839	−	0.999312i	$-0.511807\pi$
$654$		0			0
$655$	−18.1673			−0.709857
$656$		0			0
$657$	0.586614	−	1.01605i	0.0228860	−	0.0396397i
$658$		0			0
$659$	−15.1337	−	26.2123i	−0.589524	−	1.02109i	−0.994295	−	0.106668i	$-0.965982\pi$
$659$	−15.1337	−	26.2123i	−0.589524	−	1.02109i	0.404770	−	0.914418i	$-0.367351\pi$
$660$		0			0
$661$	−24.0536	−	41.6620i	−0.935575	−	1.62046i	−0.773606	−	0.633667i	$-0.781549\pi$
$661$	−24.0536	−	41.6620i	−0.935575	−	1.62046i	−0.161969	−	0.986796i	$-0.551784\pi$
$662$		0			0
$663$	−4.17227	−	7.22659i	−0.162038	−	0.280657i
$664$		0			0
$665$	12.1926			0.472810
$666$		0			0
$667$	−3.53116			−0.136727
$668$		0			0
$669$	−1.26433	−	2.18988i	−0.0488818	−	0.0846657i
$670$		0			0
$671$	−1.52184	−	2.63591i	−0.0587501	−	0.101758i
$672$		0			0
$673$	2.28202	+	3.95257i	0.0879653	+	0.152360i	0.906651	−	0.421882i	$-0.138630\pi$
$673$	2.28202	+	3.95257i	0.0879653	+	0.152360i	−0.818686	+	0.574242i	$0.805297\pi$
$674$		0			0
$675$	−2.81693	+	4.87907i	−0.108424	+	0.187795i
$676$		0			0
$677$	−7.78474			−0.299192			−0.149596	−	0.988747i	$-0.547797\pi$
$677$	−7.78474			−0.299192			−0.149596	+	0.988747i	$0.547797\pi$
$678$		0			0
$679$	12.9242	+	22.3854i	0.495987	+	0.859074i
$680$		0			0
$681$	11.4148	−	19.7710i	0.437415	−	0.757625i
$682$		0			0
$683$	−22.2606	+	38.5565i	−0.851779	+	1.47533i	0.0278216	+	0.999613i	$0.491143\pi$
$683$	−22.2606	+	38.5565i	−0.851779	+	1.47533i	−0.879601	+	0.475712i	$0.842190\pi$
$684$		0			0
$685$	4.91587	+	8.51453i	0.187826	+	0.325324i
$686$		0			0
$687$	3.46766	−	6.00617i	0.132300	−	0.229150i
$688$		0			0
$689$	2.00974			0.0765650
$690$		0			0
$691$	12.9870	−	22.4941i	0.494049	−	0.855717i	−0.505928	−	0.862576i	$-0.668850\pi$
$691$	12.9870	−	22.4941i	0.494049	−	0.855717i	0.999976	+	0.00685862i	$0.00218318\pi$
$692$		0			0
$693$	1.15651			0.0439323
$694$		0			0
$695$	8.38864			0.318199
$696$		0			0
$697$	−3.98658			−0.151002
$698$		0			0
$699$	−5.64279	−	9.77359i	−0.213430	−	0.369671i
$700$		0			0
$701$	−12.0701	+	20.9060i	−0.455881	+	0.789608i	−0.998738	−	0.0502162i	$-0.984009\pi$
$701$	−12.0701	+	20.9060i	−0.455881	+	0.789608i	0.542858	+	0.839825i	$0.317342\pi$
$702$		0			0
$703$	26.0215	−	6.89071i	0.981420	−	0.259888i
$704$		0			0
$705$	−0.602306	+	1.04322i	−0.0226841	+	0.0392901i
$706$		0			0
$707$	−1.39309	−	2.41290i	−0.0523926	−	0.0907466i
$708$		0			0
$709$	−3.16910			−0.119018			−0.0595089	−	0.998228i	$-0.518953\pi$
$709$	−3.16910			−0.119018			−0.0595089	+	0.998228i	$0.518953\pi$
$710$		0			0
$711$	−0.694180			−0.0260338
$712$		0			0
$713$	4.69251			0.175736
$714$		0			0
$715$	−0.961331	+	1.66507i	−0.0359518	+	0.0622703i
$716$		0			0
$717$	6.82074			0.254725
$718$		0			0
$719$	−7.37079	+	12.7666i	−0.274884	+	0.476113i	−0.970106	−	0.242682i	$-0.921973\pi$
$719$	−7.37079	+	12.7666i	−0.274884	+	0.476113i	0.695222	+	0.718795i	$0.255306\pi$
$720$		0			0
$721$	−1.20290	−	2.08348i	−0.0447983	−	0.0775930i
$722$		0			0
$723$	−9.61226	+	16.6489i	−0.357484	+	0.619180i
$724$		0			0
$725$	−3.16453	+	5.48112i	−0.117528	+	0.203564i
$726$		0			0
$727$	−3.38535	−	5.86359i	−0.125556	−	0.217469i	0.796394	−	0.604778i	$-0.206738\pi$
$727$	−3.38535	−	5.86359i	−0.125556	−	0.217469i	−0.921950	+	0.387309i	$0.873405\pi$
$728$		0			0
$729$	29.8765			1.10654
$730$		0			0
$731$	2.98832	−	5.17592i	0.110527	−	0.191438i
$732$		0			0
$733$	9.04625	+	15.6686i	0.334131	+	0.578732i	0.983317	−	0.181897i	$-0.0582239\pi$
$733$	9.04625	+	15.6686i	0.334131	+	0.578732i	−0.649187	+	0.760629i	$0.724891\pi$
$734$		0			0
$735$	−0.439447	−	0.761144i	−0.0162092	−	0.0280752i
$736$		0			0
$737$	−0.684908	−	1.18630i	−0.0252289	−	0.0436978i
$738$		0			0
$739$	−12.1902			−0.448424			−0.224212	−	0.974540i	$-0.571981\pi$
$739$	−12.1902			−0.448424			−0.224212	+	0.974540i	$0.571981\pi$
$740$		0			0
$741$	23.7610			0.872881
$742$		0			0
$743$	12.8437	+	22.2459i	0.471189	+	0.816124i	0.999457	−	0.0329541i	$-0.0104915\pi$
$743$	12.8437	+	22.2459i	0.471189	+	0.816124i	−0.528268	+	0.849078i	$0.677158\pi$
$744$		0			0
$745$	10.2954	+	17.8322i	0.377194	+	0.653320i
$746$		0			0
$747$	−0.529602	−	0.917298i	−0.0193771	−	0.0335622i
$748$		0			0
$749$	18.3923	−	31.8565i	0.672042	−	1.16401i
$750$		0			0
$751$	−11.1484			−0.406811			−0.203406	−	0.979095i	$-0.565201\pi$
$751$	−11.1484			−0.406811			−0.203406	+	0.979095i	$0.565201\pi$
$752$		0			0
$753$	−19.3899	−	33.5844i	−0.706609	−	1.22388i
$754$		0			0
$755$	4.20755	−	7.28770i	0.153129	−	0.265227i
$756$		0			0
$757$	−10.6550	+	18.4550i	−0.387262	+	0.670758i	−0.992080	−	0.125606i	$-0.959913\pi$
$757$	−10.6550	+	18.4550i	−0.387262	+	0.670758i	0.604818	+	0.796364i	$0.293246\pi$
$758$		0			0
$759$	−0.220942	−	0.382683i	−0.00801970	−	0.0138905i
$760$		0			0
$761$	26.4013	−	45.7284i	0.957047	−	1.65765i	0.227435	−	0.973793i	$-0.426966\pi$
$761$	26.4013	−	45.7284i	0.957047	−	1.65765i	0.729612	−	0.683861i	$-0.239700\pi$
$762$		0			0
$763$	31.7074			1.14788
$764$		0			0
$765$	−0.612492	+	1.06087i	−0.0221447	+	0.0383557i
$766$		0			0
$767$	0.882388			0.0318612
$768$		0			0
$769$	36.8968			1.33053			0.665266	−	0.746606i	$-0.268318\pi$
$769$	36.8968			1.33053			0.665266	+	0.746606i	$0.268318\pi$
$770$		0			0
$771$	13.5133			0.486669
$772$		0			0
$773$	−3.41338	−	5.91215i	−0.122771	−	0.212645i	0.798089	−	0.602540i	$-0.205845\pi$
$773$	−3.41338	−	5.91215i	−0.122771	−	0.212645i	−0.920859	+	0.389895i	$0.872511\pi$
$774$		0			0
$775$	4.20531	−	7.28380i	0.151059	−	0.261642i
$776$		0			0
$777$	−17.5723	−	17.6757i	−0.630403	−	0.634112i
$778$		0			0
$779$	5.67586	−	9.83088i	0.203359	−	0.352228i
$780$		0			0
$781$	2.06611	+	3.57861i	0.0739313	+	0.128053i
$782$		0			0
$783$	35.6570			1.27428
$784$		0			0
$785$	10.8815			0.388377
$786$		0			0
$787$	23.6229			0.842066			0.421033	−	0.907045i	$-0.361668\pi$
$787$	23.6229			0.842066			0.421033	+	0.907045i	$0.361668\pi$
$788$		0			0
$789$	−17.5224	+	30.3497i	−0.623813	+	1.08048i
$790$		0			0
$791$	16.8851			0.600366
$792$		0			0
$793$	10.3170	−	17.8696i	0.366369	−	0.634569i
$794$		0			0
$795$	0.413940	+	0.716966i	0.0146810	+	0.0254282i
$796$		0			0
$797$	−23.0434	+	39.9124i	−0.816240	+	1.41377i	0.0921936	+	0.995741i	$0.470612\pi$
$797$	−23.0434	+	39.9124i	−0.816240	+	1.41377i	−0.908434	+	0.418029i	$0.862721\pi$
$798$		0			0
$799$	−0.629408	+	1.09017i	−0.0222669	+	0.0385673i
$800$		0			0
$801$	−4.21951	−	7.30841i	−0.149089	−	0.258230i
$802$		0			0
$803$	0.792681			0.0279731
$804$		0			0
$805$	0.768593	−	1.33124i	0.0270893	−	0.0469201i
$806$		0			0
$807$	21.8545	+	37.8532i	0.769317	+	1.33250i
$808$		0			0
$809$	−19.9827	−	34.6111i	−0.702555	−	1.21686i	−0.967567	−	0.252616i	$-0.918709\pi$
$809$	−19.9827	−	34.6111i	−0.702555	−	1.21686i	0.265012	−	0.964245i	$-0.414624\pi$
$810$		0			0
$811$	9.47937	+	16.4187i	0.332866	+	0.576540i	0.983072	−	0.183217i	$-0.0586511\pi$
$811$	9.47937	+	16.4187i	0.332866	+	0.576540i	−0.650207	+	0.759757i	$0.725318\pi$
$812$		0			0
$813$	−28.2160			−0.989580
$814$		0			0
$815$	21.3679			0.748485
$816$		0			0
$817$	8.50919	+	14.7383i	0.297699	+	0.515629i
$818$		0			0
$819$	3.92018	+	6.78995i	0.136982	+	0.237260i
$820$		0			0
$821$	−22.9765	−	39.7964i	−0.801885	−	1.38890i	−0.918374	−	0.395713i	$-0.870498\pi$
$821$	−22.9765	−	39.7964i	−0.801885	−	1.38890i	0.116490	−	0.993192i	$-0.462836\pi$
$822$		0			0
$823$	−3.31567	+	5.74290i	−0.115577	+	0.200185i	−0.918010	−	0.396557i	$-0.870205\pi$
$823$	−3.31567	+	5.74290i	−0.115577	+	0.200185i	0.802433	+	0.596742i	$0.203538\pi$
$824$		0			0
$825$	−0.792011			−0.0275743
$826$		0			0
$827$	9.02881	+	15.6384i	0.313963	+	0.543799i	0.979216	−	0.202818i	$-0.0650100\pi$
$827$	9.02881	+	15.6384i	0.313963	+	0.543799i	−0.665254	+	0.746617i	$0.731677\pi$
$828$		0			0
$829$	6.16996	−	10.6867i	0.214292	−	0.371164i	−0.738762	−	0.673967i	$-0.764589\pi$
$829$	6.16996	−	10.6867i	0.214292	−	0.371164i	0.953053	+	0.302803i	$0.0979224\pi$
$830$		0			0
$831$	20.0844	−	34.7872i	0.696720	−	1.20676i
$832$		0			0
$833$	−0.459221	−	0.795394i	−0.0159111	−	0.0275588i
$834$		0			0
$835$	−4.33649	+	7.51102i	−0.150070	+	0.259930i
$836$		0			0
$837$	−47.3842			−1.63784
$838$		0			0
$839$	8.63379	−	14.9542i	0.298072	−	0.516275i	−0.677623	−	0.735409i	$-0.736990\pi$
$839$	8.63379	−	14.9542i	0.298072	−	0.516275i	0.975695	+	0.219134i	$0.0703232\pi$
$840$		0			0
$841$	11.0570			0.381275
$842$		0			0
$843$	−15.2147			−0.524021
$844$		0			0
$845$	−0.0343008			−0.00117998
$846$		0			0
$847$	−14.7627	−	25.5698i	−0.507254	−	0.878590i
$848$		0			0
$849$	−16.1771	+	28.0196i	−0.555198	+	0.961630i
$850$		0			0
$851$	0.887975	−	3.27551i	0.0304394	−	0.112283i
$852$		0			0
$853$	−9.46567	+	16.3950i	−0.324098	+	0.561355i	−0.981329	−	0.192334i	$-0.938394\pi$
$853$	−9.46567	+	16.3950i	−0.324098	+	0.561355i	0.657231	+	0.753689i	$0.271728\pi$
$854$		0			0
$855$	−1.74406	−	3.02080i	−0.0596457	−	0.103309i
$856$		0			0
$857$	27.3289			0.933538			0.466769	−	0.884379i	$-0.345418\pi$
$857$	27.3289			0.933538			0.466769	+	0.884379i	$0.345418\pi$
$858$		0			0
$859$	−28.4402			−0.970366			−0.485183	−	0.874413i	$-0.661247\pi$
$859$	−28.4402			−0.970366			−0.485183	+	0.874413i	$0.661247\pi$
$860$		0			0
$861$	−10.5107			−0.358205
$862$		0			0
$863$	−25.5767	+	44.3001i	−0.870640	+	1.50799i	−0.00930361	+	0.999957i	$0.502961\pi$
$863$	−25.5767	+	44.3001i	−0.870640	+	1.50799i	−0.861336	+	0.508036i	$0.830372\pi$
$864$		0			0
$865$	1.94974			0.0662932
$866$		0			0
$867$	−10.8452	+	18.7845i	−0.368323	+	0.637955i
$868$		0			0
$869$	−0.234508	−	0.406180i	−0.00795514	−	0.0137787i
$870$		0			0
$871$	4.64319	−	8.04225i	0.157329	−	0.272501i
$872$		0			0
$873$	3.69743	−	6.40413i	0.125139	−	0.216747i
$874$		0			0
$875$	−1.37759	−	2.38605i	−0.0465709	−	0.0806632i
$876$		0			0
$877$	−38.5983			−1.30337			−0.651687	−	0.758488i	$-0.725938\pi$
$877$	−38.5983			−1.30337			−0.651687	+	0.758488i	$0.725938\pi$
$878$		0			0
$879$	−17.4764	+	30.2701i	−0.589466	+	1.02098i
$880$		0			0
$881$	18.7027	+	32.3940i	0.630109	+	1.09138i	0.987529	+	0.157437i	$0.0503230\pi$
$881$	18.7027	+	32.3940i	0.630109	+	1.09138i	−0.357420	+	0.933944i	$0.616344\pi$
$882$		0			0
$883$	−24.7260	−	42.8268i	−0.832098	−	1.44124i	−0.896372	−	0.443303i	$-0.853807\pi$
$883$	−24.7260	−	42.8268i	−0.832098	−	1.44124i	0.0642743	−	0.997932i	$-0.479527\pi$
$884$		0			0
$885$	0.181743	+	0.314788i	0.00610922	+	0.0105815i
$886$		0			0
$887$	−13.4328			−0.451029			−0.225515	−	0.974240i	$-0.572406\pi$
$887$	−13.4328			−0.451029			−0.225515	+	0.974240i	$0.572406\pi$
$888$		0			0
$889$	23.0782			0.774017
$890$		0			0
$891$	1.60140	+	2.77370i	0.0536488	+	0.0929224i
$892$		0			0
$893$	−1.79223	−	3.10424i	−0.0599747	−	0.103879i
$894$		0			0
$895$	−7.74850	−	13.4208i	−0.259004	−	0.448608i
$896$		0			0
$897$	1.49783	−	2.59432i	0.0500112	−	0.0866219i
$898$		0			0
$899$	−53.2312			−1.77536
$900$		0			0
$901$	0.432567	+	0.749228i	0.0144109	+	0.0249604i
$902$		0			0
$903$	7.87879	−	13.6465i	0.262190	−	0.454126i
$904$		0			0
$905$	6.49867	−	11.2560i	0.216023	−	0.374163i
$906$		0			0
$907$	−21.6660	−	37.5266i	−0.719408	−	1.24605i	−0.961235	−	0.275731i	$-0.911080\pi$
$907$	−21.6660	−	37.5266i	−0.719408	−	1.24605i	0.241827	−	0.970319i	$-0.422253\pi$
$908$		0			0
$909$	−0.398542	+	0.690295i	−0.0132188	+	0.0228956i
$910$		0			0
$911$	54.7024			1.81237			0.906186	−	0.422879i	$-0.138981\pi$
$911$	54.7024			1.81237			0.906186	+	0.422879i	$0.138981\pi$
$912$		0			0
$913$	0.357821	−	0.619764i	0.0118421	−	0.0205112i
$914$		0			0
$915$	8.49988			0.280997
$916$		0			0
$917$	−50.0541			−1.65293
$918$		0			0
$919$	−3.06950			−0.101253			−0.0506267	−	0.998718i	$-0.516122\pi$
$919$	−3.06950			−0.101253			−0.0506267	+	0.998718i	$0.516122\pi$
$920$		0			0
$921$	−15.8574	−	27.4658i	−0.522518	−	0.905028i
$922$		0			0
$923$	−14.0068	+	24.2605i	−0.461039	+	0.798543i
$924$		0			0
$925$	−4.28853	−	4.31376i	−0.141006	−	0.141836i
$926$		0			0
$927$	−0.344131	+	0.596053i	−0.0113027	+	0.0195769i
$928$		0			0
$929$	−26.6828	−	46.2159i	−0.875433	−	1.51629i	−0.856301	−	0.516478i	$-0.827243\pi$
$929$	−26.6828	−	46.2159i	−0.875433	−	1.51629i	−0.0191327	−	0.999817i	$-0.506091\pi$
$930$		0			0
$931$	2.61525			0.0857113
$932$		0			0
$933$	8.50058			0.278296
$934$		0			0
$935$	−0.827649			−0.0270670
$936$		0			0
$937$	−8.36237	+	14.4840i	−0.273187	+	0.473173i	−0.969676	−	0.244394i	$-0.921411\pi$
$937$	−8.36237	+	14.4840i	−0.273187	+	0.473173i	0.696489	+	0.717567i	$0.254744\pi$
$938$		0			0
$939$	−20.7969			−0.678680
$940$		0			0
$941$	−9.98159	+	17.2886i	−0.325390	+	0.563593i	−0.981591	−	0.190994i	$-0.938829\pi$
$941$	−9.98159	+	17.2886i	−0.325390	+	0.563593i	0.656201	+	0.754586i	$0.272162\pi$
$942$		0			0
$943$	−0.715585	−	1.23943i	−0.0233027	−	0.0403614i
$944$		0			0
$945$	−7.76112	+	13.4427i	−0.252469	+	0.437290i
$946$		0			0
$947$	12.3504	−	21.3916i	0.401335	−	0.695133i	−0.592552	−	0.805532i	$-0.701880\pi$
$947$	12.3504	−	21.3916i	0.401335	−	0.695133i	0.993887	+	0.110399i	$0.0352130\pi$
$948$		0			0
$949$	2.68691	+	4.65387i	0.0872208	+	0.151071i
$950$		0			0
$951$	−6.92751			−0.224640
$952$		0			0
$953$	0.913614	−	1.58243i	0.0295949	−	0.0512598i	−0.850849	−	0.525411i	$-0.823912\pi$
$953$	0.913614	−	1.58243i	0.0295949	−	0.0512598i	0.880443	+	0.474151i	$0.157245\pi$
$954$		0			0
$955$	9.32812	+	16.1568i	0.301851	+	0.522821i
$956$		0			0
$957$	2.50634	+	4.34111i	0.0810185	+	0.140328i
$958$		0			0
$959$	13.5441	+	23.4590i	0.437361	+	0.757531i
$960$		0			0
$961$	39.7384			1.28188
$962$		0			0
$963$	−10.5235			−0.339116
$964$		0			0
$965$	−11.8568	−	20.5366i	−0.381684	−	0.661097i
$966$		0			0
$967$	27.5895	+	47.7865i	0.887220	+	1.53671i	0.843148	+	0.537682i	$0.180700\pi$
$967$	27.5895	+	47.7865i	0.887220	+	1.53671i	0.0440723	+	0.999028i	$0.485967\pi$
$968$		0			0
$969$	5.11420	+	8.85805i	0.164292	+	0.284562i
$970$		0			0
$971$	−8.98288	+	15.5588i	−0.288274	+	0.499306i	−0.973398	−	0.229121i	$-0.926415\pi$
$971$	−8.98288	+	15.5588i	−0.288274	+	0.499306i	0.685124	+	0.728427i	$0.259748\pi$
$972$		0			0
$973$	23.1121			0.740941
$974$		0			0
$975$	−2.68464	−	4.64993i	−0.0859772	−	0.148917i
$976$		0			0
$977$	4.65436	−	8.06159i	0.148906	−	0.257913i	−0.781917	−	0.623382i	$-0.785758\pi$
$977$	4.65436	−	8.06159i	0.148906	−	0.257913i	0.930823	+	0.365469i	$0.119091\pi$
$978$		0			0
$979$	2.85088	−	4.93786i	0.0911144	−	0.157815i
$980$		0			0
$981$	−4.53550	−	7.85571i	−0.144807	−	0.250814i
$982$		0			0
$983$	−11.7749	+	20.3947i	−0.375560	+	0.650489i	−0.990411	−	0.138155i	$-0.955883\pi$
$983$	−11.7749	+	20.3947i	−0.375560	+	0.650489i	0.614851	+	0.788643i	$0.289216\pi$
$984$		0			0
$985$	25.1372			0.800938
$986$		0			0
$987$	−1.65946	+	2.87426i	−0.0528211	+	0.0914888i
$988$		0			0
$989$	2.14559			0.0682259
$990$		0			0
$991$	−25.6234			−0.813954			−0.406977	−	0.913438i	$-0.633417\pi$
$991$	−25.6234			−0.813954			−0.406977	+	0.913438i	$0.633417\pi$
$992$		0			0
$993$	−2.80977			−0.0891654
$994$		0			0
$995$	−5.65029	−	9.78659i	−0.179126	−	0.310256i
$996$		0			0
$997$	12.4780	−	21.6125i	0.395181	−	0.684473i	−0.597943	−	0.801538i	$-0.704015\pi$
$997$	12.4780	−	21.6125i	0.395181	−	0.684473i	0.993124	+	0.117065i	$0.0373486\pi$
$998$		0			0
$999$	−8.96663	+	33.0756i	−0.283691	+	1.04646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.i.b.121.6	✓	14
37.26	even	3	inner	740.2.i.b.581.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.i.b.121.6	✓	14	1.1	even	1	trivial
740.2.i.b.581.6	yes	14	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.743604 + 1.28796i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.37759 + 2.38605i) q^{7} +(0.394106 - 0.682612i) q^{9} +0.532549 q^{11} +(1.80515 + 3.12662i) q^{13} +(-0.743604 + 1.28796i) q^{15} +(-0.777065 + 1.34592i) q^{17} +(-2.21268 - 3.83247i) q^{19} +(-2.04876 + 3.54855i) q^{21} -0.557928 q^{23} +(-0.500000 + 0.866025i) q^{25} +5.63386 q^{27} +6.32906 q^{29} -8.41061 q^{31} +(0.396005 + 0.685901i) q^{33} +(-1.37759 + 2.38605i) q^{35} +(-1.59156 + 5.87085i) q^{37} +(-2.68464 + 4.64993i) q^{39} +(1.28258 + 2.22149i) q^{41} -3.84565 q^{43} +0.788212 q^{45} +0.809982 q^{47} +(-0.295484 + 0.511794i) q^{49} -2.31131 q^{51} +(0.278334 - 0.482089i) q^{53} +(0.266274 + 0.461201i) q^{55} +(3.29072 - 5.69969i) q^{57} +(0.122204 - 0.211664i) q^{59} +(-2.85766 - 4.94962i) q^{61} +2.17166 q^{63} +(-1.80515 + 3.12662i) q^{65} +(-1.28609 - 2.22758i) q^{67} +(-0.414877 - 0.718588i) q^{69} +(3.87967 + 6.71979i) q^{71} +1.48847 q^{73} -1.48721 q^{75} +(0.733631 + 1.27069i) q^{77} +(-0.440351 - 0.762710i) q^{79} +(3.00704 + 5.20835i) q^{81} +(0.671903 - 1.16377i) q^{83} -1.55413 q^{85} +(4.70631 + 8.15157i) q^{87} +(5.35327 - 9.27214i) q^{89} +(-4.97350 + 8.61436i) q^{91} +(-6.25416 - 10.8325i) q^{93} +(2.21268 - 3.83247i) q^{95} +9.38181 q^{97} +(0.209881 - 0.363524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 7 q^{5} - 2 q^{7} - 5 q^{9} - 10 q^{11} - 2 q^{13} - 5 q^{17} - 8 q^{19} + 9 q^{21} + 8 q^{23} - 7 q^{25} - 18 q^{27} - 4 q^{29} + 16 q^{31} - 7 q^{33} + 2 q^{35} + 4 q^{37} + 13 q^{39} + 9 q^{41}+ \cdots + 26 q^{99}+O(q^{100}) \) 14 * q + 7 * q^5 - 2 * q^7 - 5 * q^9 - 10 * q^11 - 2 * q^13 - 5 * q^17 - 8 * q^19 + 9 * q^21 + 8 * q^23 - 7 * q^25 - 18 * q^27 - 4 * q^29 + 16 * q^31 - 7 * q^33 + 2 * q^35 + 4 * q^37 + 13 * q^39 + 9 * q^41 + 22 * q^43 - 10 * q^45 + 36 * q^47 - 7 * q^49 - 62 * q^51 + 2 * q^53 - 5 * q^55 - 38 * q^57 + 12 * q^59 - 20 * q^61 - 38 * q^63 + 2 * q^65 + 12 * q^67 + q^69 - 13 * q^71 - 12 * q^73 - q^77 - 21 * q^79 - 11 * q^81 + 7 * q^83 - 10 * q^85 + 41 * q^87 + 16 * q^89 - 6 * q^91 - 3 * q^93 + 8 * q^95 - 6 * q^97 + 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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