LMFDB - Embedded newform 1755.2.i.f.1171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (of order $3$, degree $2$, not 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:	$14.0137455547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.1
Root			$1.79305 - 1.53983i$ of defining polynomial
Character	$\chi$	$=$	1755.1171
Dual form			1755.2.i.f.586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29305 - 2.23963i) q^{2} +(-2.34397 + 4.05987i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.13745 + 3.70217i) q^{7} +6.95128 q^{8} +O(q^{10})$	\(q+(-1.29305 - 2.23963i) q^{2} +(-2.34397 + 4.05987i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.13745 + 3.70217i) q^{7} +6.95128 q^{8} +2.58610 q^{10} +(2.19223 + 3.79706i) q^{11} +(0.500000 - 0.866025i) q^{13} +(5.52766 - 9.57419i) q^{14} +(-4.30043 - 7.44856i) q^{16} -0.619151 q^{17} -2.61288 q^{19} +(-2.34397 - 4.05987i) q^{20} +(5.66934 - 9.81959i) q^{22} +(2.71443 - 4.70154i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.58610 q^{26} -20.0404 q^{28} +(3.47887 + 6.02558i) q^{29} +(3.44304 - 5.96353i) q^{31} +(-4.17008 + 7.22278i) q^{32} +(0.800595 + 1.38667i) q^{34} -4.27489 q^{35} -4.02164 q^{37} +(3.37859 + 5.85188i) q^{38} +(-3.47564 + 6.01998i) q^{40} +(-2.03714 + 3.52842i) q^{41} +(5.01845 + 8.69221i) q^{43} -20.5541 q^{44} -14.0396 q^{46} +(-0.202993 - 0.351595i) q^{47} +(-5.63736 + 9.76419i) q^{49} +(-1.29305 + 2.23963i) q^{50} +(2.34397 + 4.05987i) q^{52} +8.71205 q^{53} -4.38446 q^{55} +(14.8580 + 25.7348i) q^{56} +(8.99672 - 15.5828i) q^{58} +(-5.36073 + 9.28505i) q^{59} +(-2.53609 - 4.39263i) q^{61} -17.8081 q^{62} +4.36679 q^{64} +(0.500000 + 0.866025i) q^{65} +(-7.27894 + 12.6075i) q^{67} +(1.45127 - 2.51367i) q^{68} +(5.52766 + 9.57419i) q^{70} -6.57523 q^{71} +16.7313 q^{73} +(5.20019 + 9.00700i) q^{74} +(6.12450 - 10.6079i) q^{76} +(-9.37156 + 16.2320i) q^{77} +(-7.27288 - 12.5970i) q^{79} +8.60086 q^{80} +10.5365 q^{82} +(-1.52057 - 2.63370i) q^{83} +(0.309576 - 0.536201i) q^{85} +(12.9782 - 22.4790i) q^{86} +(15.2388 + 26.3944i) q^{88} -7.27070 q^{89} +4.27489 q^{91} +(12.7251 + 22.0405i) q^{92} +(-0.524962 + 0.909260i) q^{94} +(1.30644 - 2.26282i) q^{95} +(4.81738 + 8.34394i) q^{97} +29.1576 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−1.29305	−	2.23963i	−0.914326	−	1.58366i	−0.807885	−	0.589340i	$-0.799388\pi$
$2$	−1.29305	−	2.23963i	−0.914326	−	1.58366i	−0.106440	−	0.994319i	$-0.533945\pi$
$3$		0			0
$3$		0			0
$4$	−2.34397	+	4.05987i	−1.17198	+	2.02993i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	2.13745	+	3.70217i	0.807879	+	1.39929i	0.914330	+	0.404969i	$0.132718\pi$
$7$	2.13745	+	3.70217i	0.807879	+	1.39929i	−0.106451	+	0.994318i	$0.533949\pi$
$8$	6.95128			2.45765
$9$		0			0
$10$	2.58610			0.817798
$11$	2.19223	+	3.79706i	0.660983	+	1.14486i	0.980358	+	0.197227i	$0.0631938\pi$
$11$	2.19223	+	3.79706i	0.660983	+	1.14486i	−0.319375	+	0.947628i	$0.603473\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	5.52766	−	9.57419i	1.47733	−	2.55881i
$15$		0			0
$16$	−4.30043	−	7.44856i	−1.07511	−	1.86214i
$17$	−0.619151			−0.150166			−0.0750831	−	0.997177i	$-0.523922\pi$
$17$	−0.619151			−0.150166			−0.0750831	+	0.997177i	$0.523922\pi$
$18$		0			0
$19$	−2.61288			−0.599435			−0.299718	−	0.954028i	$-0.596892\pi$
$19$	−2.61288			−0.599435			−0.299718	+	0.954028i	$0.596892\pi$
$20$	−2.34397	−	4.05987i	−0.524127	−	0.907814i
$21$		0			0
$22$	5.66934	−	9.81959i	1.20871	−	2.09354i
$23$	2.71443	−	4.70154i	0.565998	−	0.980338i	−0.430958	−	0.902372i	$-0.641824\pi$
$23$	2.71443	−	4.70154i	0.565998	−	0.980338i	0.996956	−	0.0779658i	$-0.0248425\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.58610			−0.507177
$27$		0			0
$28$	−20.0404			−3.78728
$29$	3.47887	+	6.02558i	0.646010	+	1.11892i	0.984067	+	0.177796i	$0.0568968\pi$
$29$	3.47887	+	6.02558i	0.646010	+	1.11892i	−0.338057	+	0.941125i	$0.609770\pi$
$30$		0			0
$31$	3.44304	−	5.96353i	0.618389	−	1.07108i	−0.371391	−	0.928477i	$-0.621119\pi$
$31$	3.44304	−	5.96353i	0.618389	−	1.07108i	0.989780	−	0.142605i	$-0.0455477\pi$
$32$	−4.17008	+	7.22278i	−0.737172	+	1.27682i
$33$		0			0
$34$	0.800595	+	1.38667i	0.137301	+	0.237812i
$35$	−4.27489			−0.722589
$36$		0			0
$37$	−4.02164			−0.661154			−0.330577	−	0.943779i	$-0.607243\pi$
$37$	−4.02164			−0.661154			−0.330577	+	0.943779i	$0.607243\pi$
$38$	3.37859	+	5.85188i	0.548079	+	0.949301i
$39$		0			0
$40$	−3.47564	+	6.01998i	−0.549547	+	0.951843i
$41$	−2.03714	+	3.52842i	−0.318147	+	0.551047i	−0.980101	−	0.198497i	$-0.936394\pi$
$41$	−2.03714	+	3.52842i	−0.318147	+	0.551047i	0.661954	+	0.749544i	$0.269727\pi$
$42$		0			0
$43$	5.01845	+	8.69221i	0.765307	+	1.32555i	0.940084	+	0.340942i	$0.110746\pi$
$43$	5.01845	+	8.69221i	0.765307	+	1.32555i	−0.174778	+	0.984608i	$0.555921\pi$
$44$	−20.5541			−3.09864
$45$		0			0
$46$	−14.0396			−2.07003
$47$	−0.202993	−	0.351595i	−0.0296096	−	0.0512854i	0.850841	−	0.525423i	$-0.176093\pi$
$47$	−0.202993	−	0.351595i	−0.0296096	−	0.0512854i	−0.880450	+	0.474138i	$0.842760\pi$
$48$		0			0
$49$	−5.63736	+	9.76419i	−0.805337	+	1.39488i
$50$	−1.29305	+	2.23963i	−0.182865	+	0.316732i
$51$		0			0
$52$	2.34397	+	4.05987i	0.325050	+	0.563003i
$53$	8.71205			1.19669			0.598346	−	0.801238i	$-0.295825\pi$
$53$	8.71205			1.19669			0.598346	+	0.801238i	$0.295825\pi$
$54$		0			0
$55$	−4.38446			−0.591201
$56$	14.8580	+	25.7348i	1.98548	+	3.43895i
$57$		0			0
$58$	8.99672	−	15.5828i	1.18133	−	2.04612i
$59$	−5.36073	+	9.28505i	−0.697907	+	1.20881i	0.271284	+	0.962499i	$0.412552\pi$
$59$	−5.36073	+	9.28505i	−0.697907	+	1.20881i	−0.969191	+	0.246311i	$0.920782\pi$
$60$		0			0
$61$	−2.53609	−	4.39263i	−0.324713	−	0.562419i	0.656742	−	0.754116i	$-0.271934\pi$
$61$	−2.53609	−	4.39263i	−0.324713	−	0.562419i	−0.981454	+	0.191697i	$0.938601\pi$
$62$	−17.8081			−2.26164
$63$		0			0
$64$	4.36679			0.545849
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	−7.27894	+	12.6075i	−0.889264	+	1.54025i	−0.0485164	+	0.998822i	$0.515449\pi$
$67$	−7.27894	+	12.6075i	−0.889264	+	1.54025i	−0.840747	+	0.541428i	$0.817884\pi$
$68$	1.45127	−	2.51367i	0.175992	−	0.304828i
$69$		0			0
$70$	5.52766	+	9.57419i	0.660682	+	1.14433i
$71$	−6.57523			−0.780336			−0.390168	−	0.920744i	$-0.627583\pi$
$71$	−6.57523			−0.780336			−0.390168	+	0.920744i	$0.627583\pi$
$72$		0			0
$73$	16.7313			1.95825			0.979125	−	0.203257i	$-0.0651527\pi$
$73$	16.7313			1.95825			0.979125	+	0.203257i	$0.0651527\pi$
$74$	5.20019	+	9.00700i	0.604510	+	1.04704i
$75$		0			0
$76$	6.12450	−	10.6079i	0.702528	−	1.21681i
$77$	−9.37156	+	16.2320i	−1.06799	+	1.84981i
$78$		0			0
$79$	−7.27288	−	12.5970i	−0.818263	−	1.41727i	−0.906961	−	0.421214i	$-0.861604\pi$
$79$	−7.27288	−	12.5970i	−0.818263	−	1.41727i	0.0886982	−	0.996059i	$-0.471729\pi$
$80$	8.60086			0.961605
$81$		0			0
$82$	10.5365			1.16356
$83$	−1.52057	−	2.63370i	−0.166904	−	0.289086i	0.770426	−	0.637530i	$-0.220044\pi$
$83$	−1.52057	−	2.63370i	−0.166904	−	0.289086i	−0.937330	+	0.348444i	$0.886710\pi$
$84$		0			0
$85$	0.309576	−	0.536201i	0.0335782	−	0.0581591i
$86$	12.9782	−	22.4790i	1.39948	−	2.42397i
$87$		0			0
$88$	15.2388	+	26.3944i	1.62446	+	2.81365i
$89$	−7.27070			−0.770693			−0.385347	−	0.922772i	$-0.625918\pi$
$89$	−7.27070			−0.770693			−0.385347	+	0.922772i	$0.625918\pi$
$90$		0			0
$91$	4.27489			0.448131
$92$	12.7251	+	22.0405i	1.32668	+	2.29788i
$93$		0			0
$94$	−0.524962	+	0.909260i	−0.0541457	+	0.0937830i
$95$	1.30644	−	2.26282i	0.134038	−	0.232160i
$96$		0			0
$97$	4.81738	+	8.34394i	0.489130	+	0.847199i	0.999922	−	0.0125059i	$-0.00398085\pi$
$97$	4.81738	+	8.34394i	0.489130	+	0.847199i	−0.510791	+	0.859705i	$0.670648\pi$
$98$	29.1576			2.94536
$99$		0			0
$100$	4.68793			0.468793
$101$	3.89976	+	6.75458i	0.388041	+	0.672106i	0.992186	−	0.124768i	$-0.0398187\pi$
$101$	3.89976	+	6.75458i	0.388041	+	0.672106i	−0.604145	+	0.796874i	$0.706485\pi$
$102$		0			0
$103$	−0.496621	+	0.860172i	−0.0489335	+	0.0847553i	−0.889455	−	0.457023i	$-0.848916\pi$
$103$	−0.496621	+	0.860172i	−0.0489335	+	0.0847553i	0.840521	+	0.541779i	$0.182249\pi$
$104$	3.47564	−	6.01998i	0.340814	−	0.590308i
$105$		0			0
$106$	−11.2651	−	19.5118i	−1.09417	−	1.89515i
$107$	−4.24171			−0.410062			−0.205031	−	0.978755i	$-0.565730\pi$
$107$	−4.24171			−0.410062			−0.205031	+	0.978755i	$0.565730\pi$
$108$		0			0
$109$	4.72247			0.452330			0.226165	−	0.974089i	$-0.427381\pi$
$109$	4.72247			0.452330			0.226165	+	0.974089i	$0.427381\pi$
$110$	5.66934	+	9.81959i	0.540550	+	0.936261i
$111$		0			0
$112$	18.3839	−	31.8418i	1.73711	−	3.00877i
$113$	−1.77704	+	3.07792i	−0.167170	+	0.289546i	−0.937424	−	0.348191i	$-0.886796\pi$
$113$	−1.77704	+	3.07792i	−0.167170	+	0.289546i	0.770254	+	0.637737i	$0.220129\pi$
$114$		0			0
$115$	2.71443	+	4.70154i	0.253122	+	0.438420i
$116$	−32.6174			−3.02845
$117$		0			0
$118$	27.7268			2.55246
$119$	−1.32340	−	2.29220i	−0.121316	−	0.210126i
$120$		0			0
$121$	−4.11176	+	7.12178i	−0.373797	+	0.647435i
$122$	−6.55858	+	11.3598i	−0.593786	+	1.02847i
$123$		0			0
$124$	16.1408	+	27.9566i	1.44948	+	2.51058i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−13.6413			−1.21047			−0.605234	−	0.796048i	$-0.706920\pi$
$127$	−13.6413			−1.21047			−0.605234	+	0.796048i	$0.706920\pi$
$128$	2.69366	+	4.66556i	0.238088	+	0.412381i
$129$		0			0
$130$	1.29305	−	2.23963i	0.113408	−	0.196429i
$131$	4.18118	−	7.24202i	0.365312	−	0.632738i	−0.623514	−	0.781812i	$-0.714296\pi$
$131$	4.18118	−	7.24202i	0.365312	−	0.632738i	0.988826	+	0.149073i	$0.0476291\pi$
$132$		0			0
$133$	−5.58489	−	9.67331i	−0.484271	−	0.838782i
$134$	37.6482			3.25231
$135$		0			0
$136$	−4.30389			−0.369056
$137$	−3.37544	−	5.84643i	−0.288383	−	0.499494i	0.685041	−	0.728505i	$-0.259784\pi$
$137$	−3.37544	−	5.84643i	−0.288383	−	0.499494i	−0.973424	+	0.229010i	$0.926451\pi$
$138$		0			0
$139$	−1.75288	+	3.03608i	−0.148678	+	0.257517i	−0.930739	−	0.365684i	$-0.880835\pi$
$139$	−1.75288	+	3.03608i	−0.148678	+	0.257517i	0.782061	+	0.623201i	$0.214168\pi$
$140$	10.0202	−	17.3555i	0.846862	−	1.46681i
$141$		0			0
$142$	8.50211	+	14.7261i	0.713481	+	1.23579i
$143$	4.38446			0.366647
$144$		0			0
$145$	−6.95774			−0.577809
$146$	−21.6344	−	37.4720i	−1.79048	−	3.10120i
$147$		0			0
$148$	9.42660	−	16.3273i	0.774861	−	1.34210i
$149$	6.13951	−	10.6339i	0.502968	−	0.871166i	−0.497026	−	0.867736i	$-0.665575\pi$
$149$	6.13951	−	10.6339i	0.502968	−	0.871166i	0.999994	−	0.00343063i	$-0.00109201\pi$
$150$		0			0
$151$	8.34821	+	14.4595i	0.679367	+	1.17670i	0.975172	+	0.221450i	$0.0710791\pi$
$151$	8.34821	+	14.4595i	0.679367	+	1.17670i	−0.295804	+	0.955249i	$0.595588\pi$
$152$	−18.1628			−1.47320
$153$		0			0
$154$	48.4717			3.90596
$155$	3.44304	+	5.96353i	0.276552	+	0.479002i
$156$		0			0
$157$	−3.99844	+	6.92550i	−0.319110	+	0.552715i	−0.980303	−	0.197501i	$-0.936717\pi$
$157$	−3.99844	+	6.92550i	−0.319110	+	0.552715i	0.661192	+	0.750216i	$0.270051\pi$
$158$	−18.8084	+	32.5771i	−1.49632	+	2.59170i
$159$		0			0
$160$	−4.17008	−	7.22278i	−0.329674	−	0.571011i
$161$	23.2078			1.82903
$162$		0			0
$163$	−17.3723			−1.36071			−0.680353	−	0.732885i	$-0.738173\pi$
$163$	−17.3723			−1.36071			−0.680353	+	0.732885i	$0.738173\pi$
$164$	−9.54996	−	16.5410i	−0.745727	−	1.29164i
$165$		0			0
$166$	−3.93234	+	6.81102i	−0.305209	+	0.528637i
$167$	2.13795	−	3.70303i	0.165439	−	0.286549i	−0.771372	−	0.636385i	$-0.780429\pi$
$167$	2.13795	−	3.70303i	0.165439	−	0.286549i	0.936811	+	0.349835i	$0.113762\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−1.60119			−0.122806
$171$		0			0
$172$	−47.0523			−3.58771
$173$	6.47793	+	11.2201i	0.492508	+	0.853049i	0.999963	−	0.00862929i	$-0.00274682\pi$
$173$	6.47793	+	11.2201i	0.492508	+	0.853049i	−0.507455	+	0.861679i	$0.669413\pi$
$174$		0			0
$175$	2.13745	−	3.70217i	0.161576	−	0.279857i
$176$	18.8551	−	32.6579i	1.42125	−	2.46169i
$177$		0			0
$178$	9.40140	+	16.2837i	0.704665	+	1.22051i
$179$	−18.8530			−1.40914			−0.704571	−	0.709633i	$-0.748861\pi$
$179$	−18.8530			−1.40914			−0.704571	+	0.709633i	$0.748861\pi$
$180$		0			0
$181$	−21.2593			−1.58019			−0.790097	−	0.612982i	$-0.789970\pi$
$181$	−21.2593			−1.58019			−0.790097	+	0.612982i	$0.789970\pi$
$182$	−5.52766	−	9.57419i	−0.409737	−	0.709686i
$183$		0			0
$184$	18.8688	−	32.6817i	1.39102	−	2.40933i
$185$	2.01082	−	3.48284i	0.147838	−	0.256064i
$186$		0			0
$187$	−1.35732	−	2.35095i	−0.0992573	−	0.171919i
$188$	1.90324			0.138808
$189$		0			0
$190$	−6.75717			−0.490217
$191$	−7.70849	−	13.3515i	−0.557767	−	0.966081i	−0.997682	−	0.0680415i	$-0.978325\pi$
$191$	−7.70849	−	13.3515i	−0.557767	−	0.966081i	0.439916	−	0.898039i	$-0.355008\pi$
$192$		0			0
$193$	−0.944008	+	1.63507i	−0.0679512	+	0.117695i	−0.897999	−	0.439997i	$-0.854980\pi$
$193$	−0.944008	+	1.63507i	−0.0679512	+	0.117695i	0.830048	+	0.557692i	$0.188313\pi$
$194$	12.4582	−	21.5783i	0.894449	−	1.54923i
$195$		0			0
$196$	−26.4276	−	45.7739i	−1.88768	−	3.26956i
$197$	10.8597			0.773723			0.386862	−	0.922138i	$-0.373559\pi$
$197$	10.8597			0.773723			0.386862	+	0.922138i	$0.373559\pi$
$198$		0			0
$199$	−1.20110			−0.0851436			−0.0425718	−	0.999093i	$-0.513555\pi$
$199$	−1.20110			−0.0851436			−0.0425718	+	0.999093i	$0.513555\pi$
$200$	−3.47564	−	6.01998i	−0.245765	−	0.425677i
$201$		0			0
$202$	10.0852	−	17.4681i	0.709591	−	1.22905i
$203$	−14.8718	+	25.7587i	−1.04380	+	1.80791i
$204$		0			0
$205$	−2.03714	−	3.52842i	−0.142280	−	0.246436i
$206$	2.56863			0.178965
$207$		0			0
$208$	−8.60086			−0.596362
$209$	−5.72803	−	9.92125i	−0.396216	−	0.686267i
$210$		0			0
$211$	0.117606	−	0.203699i	0.00809632	−	0.0140232i	−0.861949	−	0.506995i	$-0.830756\pi$
$211$	0.117606	−	0.203699i	0.00809632	−	0.0140232i	0.870045	+	0.492972i	$0.164089\pi$
$212$	−20.4208	+	35.3698i	−1.40250	+	2.42921i
$213$		0			0
$214$	5.48476	+	9.49988i	0.374930	+	0.649398i
$215$	−10.0369			−0.684511
$216$		0			0
$217$	29.4373			1.99833
$218$	−6.10639	−	10.5766i	−0.413577	−	0.716337i
$219$		0			0
$220$	10.2770	−	17.8004i	0.692878	−	1.20010i
$221$	−0.309576	+	0.536201i	−0.0208243	+	0.0360688i
$222$		0			0
$223$	8.37747	+	14.5102i	0.560997	+	0.971675i	0.997410	+	0.0719287i	$0.0229154\pi$
$223$	8.37747	+	14.5102i	0.560997	+	0.971675i	−0.436413	+	0.899747i	$0.643751\pi$
$224$	−35.6533			−2.38218
$225$		0			0
$226$	9.19121			0.611390
$227$	11.4002	+	19.7457i	0.756656	+	1.31057i	0.944547	+	0.328377i	$0.106502\pi$
$227$	11.4002	+	19.7457i	0.756656	+	1.31057i	−0.187891	+	0.982190i	$0.560165\pi$
$228$		0			0
$229$	3.48739	−	6.04033i	0.230453	−	0.399156i	−0.727488	−	0.686120i	$-0.759313\pi$
$229$	3.48739	−	6.04033i	0.230453	−	0.399156i	0.957942	+	0.286964i	$0.0926459\pi$
$230$	7.01981	−	12.1587i	0.462872	−	0.801718i
$231$		0			0
$232$	24.1826	+	41.8855i	1.58766	+	2.74992i
$233$	8.63201			0.565502			0.282751	−	0.959193i	$-0.408753\pi$
$233$	8.63201			0.565502			0.282751	+	0.959193i	$0.408753\pi$
$234$		0			0
$235$	0.405987			0.0264836
$236$	−25.1307	−	43.5277i	−1.63587	−	2.83341i
$237$		0			0
$238$	−3.42246	+	5.92787i	−0.221845	+	0.384247i
$239$	−1.53550	+	2.65957i	−0.0993235	+	0.172033i	−0.911405	−	0.411511i	$-0.865001\pi$
$239$	−1.53550	+	2.65957i	−0.0993235	+	0.172033i	0.812081	+	0.583544i	$0.198335\pi$
$240$		0			0
$241$	−2.91634	−	5.05125i	−0.187858	−	0.325379i	0.756678	−	0.653788i	$-0.226821\pi$
$241$	−2.91634	−	5.05125i	−0.187858	−	0.325379i	−0.944536	+	0.328408i	$0.893488\pi$
$242$	21.2669			1.36709
$243$		0			0
$244$	23.7780			1.52223
$245$	−5.63736	−	9.76419i	−0.360157	−	0.623811i
$246$		0			0
$247$	−1.30644	+	2.26282i	−0.0831267	+	0.143980i
$248$	23.9336	−	41.4541i	1.51978	−	2.63234i
$249$		0			0
$250$	−1.29305	−	2.23963i	−0.0817798	−	0.141647i
$251$	23.7101			1.49657			0.748285	−	0.663378i	$-0.230878\pi$
$251$	23.7101			1.49657			0.748285	+	0.663378i	$0.230878\pi$
$252$		0			0
$253$	23.8027			1.49646
$254$	17.6389	+	30.5514i	1.10676	+	1.91697i
$255$		0			0
$256$	11.3329	−	19.6291i	0.708305	−	1.22682i
$257$	9.65384	−	16.7209i	0.602190	−	1.04302i	−0.390299	−	0.920688i	$-0.627628\pi$
$257$	9.65384	−	16.7209i	0.602190	−	1.04302i	0.992489	−	0.122335i	$-0.0390383\pi$
$258$		0			0
$259$	−8.59604	−	14.8888i	−0.534132	−	0.925144i
$260$	−4.68793			−0.290733
$261$		0			0
$262$	−21.6260			−1.33606
$263$	−5.85985	−	10.1496i	−0.361334	−	0.625848i	0.626847	−	0.779142i	$-0.284345\pi$
$263$	−5.85985	−	10.1496i	−0.361334	−	0.625848i	−0.988181	+	0.153294i	$0.951012\pi$
$264$		0			0
$265$	−4.35603	+	7.54486i	−0.267589	+	0.463477i
$266$	−14.4431	+	25.0162i	−0.885563	+	1.53384i
$267$		0			0
$268$	−34.1232	−	59.1031i	−2.08440	−	3.61029i
$269$	17.0088			1.03705			0.518524	−	0.855063i	$-0.326482\pi$
$269$	17.0088			1.03705			0.518524	+	0.855063i	$0.326482\pi$
$270$		0			0
$271$	−12.4840			−0.758348			−0.379174	−	0.925325i	$-0.623792\pi$
$271$	−12.4840			−0.758348			−0.379174	+	0.925325i	$0.623792\pi$
$272$	2.66262	+	4.61179i	0.161445	+	0.279631i
$273$		0			0
$274$	−8.72924	+	15.1195i	−0.527353	+	0.913401i
$275$	2.19223	−	3.79706i	0.132197	−	0.228971i
$276$		0			0
$277$	−10.1444	−	17.5705i	−0.609516	−	1.05571i	−0.991320	−	0.131469i	$-0.958031\pi$
$277$	−10.1444	−	17.5705i	−0.609516	−	1.05571i	0.381805	−	0.924243i	$-0.375303\pi$
$278$	9.06628			0.543759
$279$		0			0
$280$	−29.7160			−1.77587
$281$	−4.18725	−	7.25252i	−0.249790	−	0.432649i	0.713677	−	0.700475i	$-0.247028\pi$
$281$	−4.18725	−	7.25252i	−0.249790	−	0.432649i	−0.963467	+	0.267825i	$0.913695\pi$
$282$		0			0
$283$	1.11281	−	1.92745i	0.0661498	−	0.114575i	−0.831054	−	0.556192i	$-0.812262\pi$
$283$	1.11281	−	1.92745i	0.0661498	−	0.114575i	0.897203	+	0.441617i	$0.145595\pi$
$284$	15.4121	−	26.6946i	0.914541	−	1.58403i
$285$		0			0
$286$	−5.66934	−	9.81959i	−0.335235	−	0.580644i
$287$	−17.4171			−1.02810
$288$		0			0
$289$	−16.6167			−0.977450
$290$	8.99672	+	15.5828i	0.528305	+	0.915052i
$291$		0			0
$292$	−39.2176	+	67.9269i	−2.29504	+	3.97512i
$293$	−1.26944	+	2.19873i	−0.0741613	+	0.128451i	−0.900721	−	0.434398i	$-0.856961\pi$
$293$	−1.26944	+	2.19873i	−0.0741613	+	0.128451i	0.826560	+	0.562849i	$0.190295\pi$
$294$		0			0
$295$	−5.36073	−	9.28505i	−0.312114	−	0.540596i
$296$	−27.9555			−1.62488
$297$		0			0
$298$	−31.7548			−1.83951
$299$	−2.71443	−	4.70154i	−0.156980	−	0.271897i
$300$		0			0
$301$	−21.4533	+	37.1583i	−1.23655	+	2.14177i
$302$	21.5893	−	37.3938i	1.24233	−	2.15177i
$303$		0			0
$304$	11.2365	+	19.4622i	0.644457	+	1.11623i
$305$	5.07217			0.290432
$306$		0			0
$307$	19.2343			1.09776			0.548881	−	0.835901i	$-0.315054\pi$
$307$	19.2343			1.09776			0.548881	+	0.835901i	$0.315054\pi$
$308$	−43.9332	−	76.0946i	−2.50333	−	4.33589i
$309$		0			0
$310$	8.90407	−	15.4223i	0.505717	−	0.875928i
$311$	4.38021	−	7.58674i	0.248379	−	0.430205i	−0.714697	−	0.699434i	$-0.753436\pi$
$311$	4.38021	−	7.58674i	0.248379	−	0.430205i	0.963076	+	0.269229i	$0.0867689\pi$
$312$		0			0
$313$	6.08910	+	10.5466i	0.344176	+	0.596131i	0.985204	−	0.171387i	$-0.0548248\pi$
$313$	6.08910	+	10.5466i	0.344176	+	0.596131i	−0.641027	+	0.767518i	$0.721491\pi$
$314$	20.6808			1.16708
$315$		0			0
$316$	68.1896			3.83596
$317$	8.66227	+	15.0035i	0.486521	+	0.842680i	0.999880	−	0.0154945i	$-0.00493225\pi$
$317$	8.66227	+	15.0035i	0.486521	+	0.842680i	−0.513359	+	0.858174i	$0.671599\pi$
$318$		0			0
$319$	−15.2530	+	26.4189i	−0.854003	+	1.47918i
$320$	−2.18340	+	3.78175i	−0.122056	+	0.211407i
$321$		0			0
$322$	−30.0089	−	51.9770i	−1.67233	−	2.89656i
$323$	1.61777			0.0900149
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	22.4633	+	38.9076i	1.24413	+	2.15489i
$327$		0			0
$328$	−14.1607	+	24.5270i	−0.781894	+	1.35428i
$329$	0.867775	−	1.50303i	0.0478420	−	0.0828647i
$330$		0			0
$331$	−1.23037	−	2.13106i	−0.0676272	−	0.117134i	0.830229	−	0.557422i	$-0.188210\pi$
$331$	−1.23037	−	2.13106i	−0.0676272	−	0.117134i	−0.897856	+	0.440288i	$0.854876\pi$
$332$	14.2566			0.782434
$333$		0			0
$334$	−11.0579			−0.605062
$335$	−7.27894	−	12.6075i	−0.397691	−	0.688821i
$336$		0			0
$337$	−10.3743	+	17.9688i	−0.565123	+	0.978821i	0.431915	+	0.901914i	$0.357838\pi$
$337$	−10.3743	+	17.9688i	−0.565123	+	0.978821i	−0.997038	+	0.0769073i	$0.975495\pi$
$338$	−1.29305	+	2.23963i	−0.0703328	+	0.121820i
$339$		0			0
$340$	1.45127	+	2.51367i	0.0787062	+	0.136323i
$341$	30.1918			1.63498
$342$		0			0
$343$	−18.2739			−0.986700
$344$	34.8846	+	60.4220i	1.88085	+	3.25773i
$345$		0			0
$346$	16.7526	−	29.0164i	0.900626	−	1.55993i
$347$	−6.29383	+	10.9012i	−0.337871	+	0.585209i	−0.984032	−	0.177992i	$-0.943040\pi$
$347$	−6.29383	+	10.9012i	−0.337871	+	0.585209i	0.646161	+	0.763201i	$0.276373\pi$
$348$		0			0
$349$	9.98642	+	17.2970i	0.534561	+	0.925887i	0.999184	+	0.0403782i	$0.0128563\pi$
$349$	9.98642	+	17.2970i	0.534561	+	0.925887i	−0.464624	+	0.885508i	$0.653810\pi$
$350$	−11.0553			−0.590932
$351$		0			0
$352$	−36.5671			−1.94903
$353$	2.94467	+	5.10031i	0.156729	+	0.271462i	0.933687	−	0.358090i	$-0.116572\pi$
$353$	2.94467	+	5.10031i	0.156729	+	0.271462i	−0.776958	+	0.629552i	$0.783238\pi$
$354$		0			0
$355$	3.28761	−	5.69431i	0.174488	−	0.302223i
$356$	17.0423	−	29.5181i	0.903240	−	1.56446i
$357$		0			0
$358$	24.3780	+	42.2239i	1.28842	+	2.23160i
$359$	−17.8334			−0.941209			−0.470605	−	0.882344i	$-0.655964\pi$
$359$	−17.8334			−0.941209			−0.470605	+	0.882344i	$0.655964\pi$
$360$		0			0
$361$	−12.1729			−0.640677
$362$	27.4894	+	47.6131i	1.44481	+	2.50249i
$363$		0			0
$364$	−10.0202	+	17.3555i	−0.525202	+	0.909676i
$365$	−8.36565	+	14.4897i	−0.437878	+	0.758427i
$366$		0			0
$367$	14.9165	+	25.8361i	0.778633	+	1.34863i	0.932730	+	0.360576i	$0.117420\pi$
$367$	14.9165	+	25.8361i	0.778633	+	1.34863i	−0.154097	+	0.988056i	$0.549247\pi$
$368$	−46.6929			−2.43404
$369$		0			0
$370$	−10.4004			−0.540690
$371$	18.6215	+	32.2535i	0.966783	+	1.67452i
$372$		0			0
$373$	7.28970	−	12.6261i	0.377446	−	0.653756i	−0.613244	−	0.789894i	$-0.710136\pi$
$373$	7.28970	−	12.6261i	0.377446	−	0.653756i	0.990690	+	0.136138i	$0.0434690\pi$
$374$	−3.51018	+	6.07981i	−0.181507	+	0.314379i
$375$		0			0
$376$	−1.41106	−	2.44403i	−0.0727700	−	0.126041i
$377$	6.95774			0.358342
$378$		0			0
$379$	20.7048			1.06353			0.531766	−	0.846891i	$-0.321529\pi$
$379$	20.7048			1.06353			0.531766	+	0.846891i	$0.321529\pi$
$380$	6.12450	+	10.6079i	0.314180	+	0.544176i
$381$		0			0
$382$	−19.9350	+	34.5284i	−1.01996	+	1.76663i
$383$	−12.7832	+	22.1412i	−0.653193	+	1.13136i	0.329150	+	0.944277i	$0.393238\pi$
$383$	−12.7832	+	22.1412i	−0.653193	+	1.13136i	−0.982344	+	0.187086i	$0.940096\pi$
$384$		0			0
$385$	−9.37156	−	16.2320i	−0.477619	−	0.827260i
$386$	4.88260			0.248518
$387$		0			0
$388$	−45.1671			−2.29301
$389$	−8.56520	−	14.8354i	−0.434273	−	0.752183i	0.562963	−	0.826482i	$-0.309661\pi$
$389$	−8.56520	−	14.8354i	−0.434273	−	0.752183i	−0.997236	+	0.0742992i	$0.976328\pi$
$390$		0			0
$391$	−1.68064	+	2.91096i	−0.0849939	+	0.147214i
$392$	−39.1868	+	67.8736i	−1.97923	+	3.42813i
$393$		0			0
$394$	−14.0422	−	24.3218i	−0.707435	−	1.22531i
$395$	14.5458			0.731877
$396$		0			0
$397$	−15.8337			−0.794669			−0.397334	−	0.917674i	$-0.630065\pi$
$397$	−15.8337			−0.794669			−0.397334	+	0.917674i	$0.630065\pi$
$398$	1.55308	+	2.69002i	0.0778490	+	0.134838i
$399$		0			0
$400$	−4.30043	+	7.44856i	−0.215021	+	0.372428i
$401$	−17.0554	+	29.5408i	−0.851706	+	1.47520i	0.0279624	+	0.999609i	$0.491098\pi$
$401$	−17.0554	+	29.5408i	−0.851706	+	1.47520i	−0.879668	+	0.475588i	$0.842235\pi$
$402$		0			0
$403$	−3.44304	−	5.96353i	−0.171510	−	0.297065i
$404$	−36.5636			−1.81911
$405$		0			0
$406$	76.9200			3.81748
$407$	−8.81637	−	15.2704i	−0.437011	−	0.756926i
$408$		0			0
$409$	9.57264	−	16.5803i	0.473336	−	0.819843i	−0.526198	−	0.850362i	$-0.676383\pi$
$409$	9.57264	−	16.5803i	0.473336	−	0.819843i	0.999534	+	0.0305196i	$0.00971618\pi$
$410$	−5.26825	+	9.12487i	−0.260180	+	0.450645i
$411$		0			0
$412$	−2.32812	−	4.03243i	−0.114698	−	0.198664i
$413$	−45.8331			−2.25530
$414$		0			0
$415$	3.04113			0.149283
$416$	4.17008	+	7.22278i	0.204455	+	0.354126i
$417$		0			0
$418$	−14.8133	+	25.6574i	−0.724542	+	1.25494i
$419$	3.56749	−	6.17908i	0.174284	−	0.301868i	−0.765630	−	0.643282i	$-0.777572\pi$
$419$	3.56749	−	6.17908i	0.174284	−	0.301868i	0.939913	+	0.341414i	$0.110906\pi$
$420$		0			0
$421$	13.0809	+	22.6568i	0.637524	+	1.10422i	0.985974	+	0.166896i	$0.0533745\pi$
$421$	13.0809	+	22.6568i	0.637524	+	1.10422i	−0.348451	+	0.937327i	$0.613292\pi$
$422$	−0.608282			−0.0296107
$423$		0			0
$424$	60.5599			2.94105
$425$	0.309576	+	0.536201i	0.0150166	+	0.0260096i
$426$		0			0
$427$	10.8415	−	18.7780i	0.524657	−	0.908732i
$428$	9.94244	−	17.2208i	0.480586	−	0.832399i
$429$		0			0
$430$	12.9782	+	22.4790i	0.625866	+	1.08403i
$431$	12.4211			0.598302			0.299151	−	0.954206i	$-0.403297\pi$
$431$	12.4211			0.598302			0.299151	+	0.954206i	$0.403297\pi$
$432$		0			0
$433$	−6.04541			−0.290524			−0.145262	−	0.989393i	$-0.546402\pi$
$433$	−6.04541			−0.290524			−0.145262	+	0.989393i	$0.546402\pi$
$434$	−38.0640	−	65.9287i	−1.82713	−	3.16468i
$435$		0			0
$436$	−11.0693	+	19.1726i	−0.530124	+	0.918201i
$437$	−7.09248	+	12.2845i	−0.339279	+	0.587649i
$438$		0			0
$439$	14.3382	+	24.8345i	0.684326	+	1.18529i	0.973648	+	0.228055i	$0.0732366\pi$
$439$	14.3382	+	24.8345i	0.684326	+	1.18529i	−0.289323	+	0.957232i	$0.593430\pi$
$440$	−30.4776			−1.45296
$441$		0			0
$442$	1.60119			0.0761608
$443$	−4.57498	−	7.92410i	−0.217364	−	0.376485i	0.736637	−	0.676288i	$-0.236412\pi$
$443$	−4.57498	−	7.92410i	−0.217364	−	0.376485i	−0.954001	+	0.299803i	$0.903079\pi$
$444$		0			0
$445$	3.63535	−	6.29661i	0.172332	−	0.298488i
$446$	21.6650	−	37.5249i	1.02587	−	1.77686i
$447$		0			0
$448$	9.33379	+	16.1666i	0.440980	+	0.763800i
$449$	−35.4645			−1.67367			−0.836837	−	0.547452i	$-0.815598\pi$
$449$	−35.4645			−1.67367			−0.836837	+	0.547452i	$0.815598\pi$
$450$		0			0
$451$	−17.8635			−0.841160
$452$	−8.33064	−	14.4291i	−0.391840	−	0.678687i
$453$		0			0
$454$	29.4820	−	51.0644i	1.38366	−	2.39657i
$455$	−2.13745	+	3.70217i	−0.100205	+	0.173560i
$456$		0			0
$457$	−4.70631	−	8.15156i	−0.220152	−	0.381314i	0.734702	−	0.678390i	$-0.237322\pi$
$457$	−4.70631	−	8.15156i	−0.220152	−	0.381314i	−0.954854	+	0.297076i	$0.903989\pi$
$458$	−18.0375			−0.842837
$459$		0			0
$460$	−25.4502			−1.18662
$461$	−10.2513	−	17.7557i	−0.477450	−	0.826967i	0.522216	−	0.852813i	$-0.325105\pi$
$461$	−10.2513	−	17.7557i	−0.477450	−	0.826967i	−0.999666	+	0.0258461i	$0.991772\pi$
$462$		0			0
$463$	18.8916	−	32.7211i	0.877965	−	1.52068i	0.0243951	−	0.999702i	$-0.492234\pi$
$463$	18.8916	−	32.7211i	0.877965	−	1.52068i	0.853570	−	0.520978i	$-0.174433\pi$
$464$	29.9213	−	51.8251i	1.38906	−	2.40592i
$465$		0			0
$466$	−11.1616	−	19.3325i	−0.517053	−	0.895562i
$467$	12.8882			0.596394			0.298197	−	0.954504i	$-0.403615\pi$
$467$	12.8882			0.596394			0.298197	+	0.954504i	$0.403615\pi$
$468$		0			0
$469$	−62.2334			−2.87367
$470$	−0.524962	−	0.909260i	−0.0242147	−	0.0419411i
$471$		0			0
$472$	−37.2639	+	64.5429i	−1.71521	+	2.97083i
$473$	−22.0032	+	38.1107i	−1.01171	+	1.75233i
$474$		0			0
$475$	1.30644	+	2.26282i	0.0599435	+	0.103825i
$476$	12.4080			0.568722
$477$		0			0
$478$	7.94194			0.363256
$479$	10.0940	+	17.4833i	0.461207	+	0.798835i	0.999021	−	0.0442289i	$-0.0140831\pi$
$479$	10.0940	+	17.4833i	0.461207	+	0.798835i	−0.537814	+	0.843063i	$0.680750\pi$
$480$		0			0
$481$	−2.01082	+	3.48284i	−0.0916855	+	0.158804i
$482$	−7.54195	+	13.0630i	−0.343527	+	0.595006i
$483$		0			0
$484$	−19.2757	−	33.3865i	−0.876167	−	1.51757i
$485$	−9.63475			−0.437492
$486$		0			0
$487$	15.1480			0.686423			0.343212	−	0.939258i	$-0.388485\pi$
$487$	15.1480			0.686423			0.343212	+	0.939258i	$0.388485\pi$
$488$	−17.6290	−	30.5344i	−0.798029	−	1.38223i
$489$		0			0
$490$	−14.5788	+	25.2512i	−0.658603	+	1.14073i
$491$	−5.74374	+	9.94845i	−0.259211	+	0.448967i	−0.966031	−	0.258427i	$-0.916796\pi$
$491$	−5.74374	+	9.94845i	−0.259211	+	0.448967i	0.706820	+	0.707394i	$0.250129\pi$
$492$		0			0
$493$	−2.15395	−	3.73074i	−0.0970089	−	0.168024i
$494$	6.75717			0.304020
$495$		0			0
$496$	−59.2263			−2.65934
$497$	−14.0542	−	24.3426i	−0.630417	−	1.09191i
$498$		0			0
$499$	6.56005	−	11.3623i	0.293668	−	0.508648i	−0.681006	−	0.732278i	$-0.738457\pi$
$499$	6.56005	−	11.3623i	0.293668	−	0.508648i	0.974674	+	0.223630i	$0.0717906\pi$
$500$	−2.34397	+	4.05987i	−0.104825	+	0.181563i
$501$		0			0
$502$	−30.6584	−	53.1019i	−1.36835	−	2.37006i
$503$	−7.80396			−0.347961			−0.173981	−	0.984749i	$-0.555663\pi$
$503$	−7.80396			−0.347961			−0.173981	+	0.984749i	$0.555663\pi$
$504$		0			0
$505$	−7.79952			−0.347074
$506$	−30.7781	−	53.3092i	−1.36825	−	2.36988i
$507$		0			0
$508$	31.9747	−	55.3818i	1.41865	−	2.45717i
$509$	10.9919	−	19.0385i	0.487205	−	0.843865i	−0.512686	−	0.858576i	$-0.671350\pi$
$509$	10.9919	−	19.0385i	0.487205	−	0.843865i	0.999892	+	0.0147114i	$0.00468295\pi$
$510$		0			0
$511$	35.7623	+	61.9421i	1.58203	+	2.74016i
$512$	−47.8414			−2.11431
$513$		0			0
$514$	−49.9316			−2.20239
$515$	−0.496621	−	0.860172i	−0.0218837	−	0.0379037i
$516$		0			0
$517$	0.890017	−	1.54155i	0.0391429	−	0.0677975i
$518$	−22.2303	+	38.5039i	−0.976742	+	1.69177i
$519$		0			0
$520$	3.47564	+	6.01998i	0.152417	+	0.263994i
$521$	−12.1706			−0.533205			−0.266603	−	0.963807i	$-0.585901\pi$
$521$	−12.1706			−0.533205			−0.266603	+	0.963807i	$0.585901\pi$
$522$		0			0
$523$	32.5468			1.42317			0.711587	−	0.702598i	$-0.247977\pi$
$523$	32.5468			1.42317			0.711587	+	0.702598i	$0.247977\pi$
$524$	19.6011	+	33.9501i	0.856279	+	1.48312i
$525$		0			0
$526$	−15.1542	+	26.2478i	−0.660753	+	1.14446i
$527$	−2.13177	+	3.69233i	−0.0928612	+	0.160840i
$528$		0			0
$529$	−3.23629	−	5.60543i	−0.140708	−	0.243714i
$530$	22.5303			0.978653
$531$		0			0
$532$	52.3632			2.27023
$533$	2.03714	+	3.52842i	0.0882382	+	0.152833i
$534$		0			0
$535$	2.12086	−	3.67343i	0.0916927	−	0.158816i
$536$	−50.5979	+	87.6381i	−2.18550	+	3.78539i
$537$		0			0
$538$	−21.9933	−	38.0936i	−0.948199	−	1.64233i
$539$	−49.4336			−2.12925
$540$		0			0
$541$	−16.3865			−0.704511			−0.352256	−	0.935904i	$-0.614585\pi$
$541$	−16.3865			−0.704511			−0.352256	+	0.935904i	$0.614585\pi$
$542$	16.1424	+	27.9595i	0.693378	+	1.20097i
$543$		0			0
$544$	2.58191	−	4.47200i	0.110698	−	0.191735i
$545$	−2.36123	+	4.08978i	−0.101144	+	0.175187i
$546$		0			0
$547$	−9.53335	−	16.5122i	−0.407616	−	0.706012i	0.587006	−	0.809583i	$-0.300307\pi$
$547$	−9.53335	−	16.5122i	−0.407616	−	0.706012i	−0.994622	+	0.103570i	$0.966973\pi$
$548$	31.6477			1.35192
$549$		0			0
$550$	−11.3387			−0.483483
$551$	−9.08986	−	15.7441i	−0.387241	−	0.670721i
$552$		0			0
$553$	31.0908	−	53.8508i	1.32211	−	2.28997i
$554$	−26.2344	+	45.4393i	−1.11459	+	1.93053i
$555$		0			0
$556$	−8.21740	−	14.2330i	−0.348495	−	0.603612i
$557$	38.2913			1.62245			0.811227	−	0.584732i	$-0.198800\pi$
$557$	38.2913			1.62245			0.811227	+	0.584732i	$0.198800\pi$
$558$		0			0
$559$	10.0369			0.424516
$560$	18.3839	+	31.8418i	0.776860	+	1.34556i
$561$		0			0
$562$	−10.8287	+	18.7558i	−0.456779	+	0.791165i
$563$	5.17040	−	8.95540i	0.217906	−	0.377425i	−0.736261	−	0.676697i	$-0.763411\pi$
$563$	5.17040	−	8.95540i	0.217906	−	0.377425i	0.954168	+	0.299272i	$0.0967439\pi$
$564$		0			0
$565$	−1.77704	−	3.07792i	−0.0747605	−	0.129489i
$566$	−5.75569			−0.241930
$567$		0			0
$568$	−45.7062			−1.91779
$569$	−13.0134	−	22.5398i	−0.545548	−	0.944917i	−0.998572	−	0.0534187i	$-0.982988\pi$
$569$	−13.0134	−	22.5398i	−0.545548	−	0.944917i	0.453024	−	0.891498i	$-0.350345\pi$
$570$		0			0
$571$	16.1620	−	27.9933i	0.676357	−	1.17148i	−0.299713	−	0.954029i	$-0.596891\pi$
$571$	16.1620	−	27.9933i	0.676357	−	1.17148i	0.976070	−	0.217456i	$-0.0697757\pi$
$572$	−10.2770	+	17.8004i	−0.429705	+	0.744270i
$573$		0			0
$574$	22.5212	+	39.0078i	0.940016	+	1.62816i
$575$	−5.42887			−0.226399
$576$		0			0
$577$	12.4808			0.519581			0.259790	−	0.965665i	$-0.416347\pi$
$577$	12.4808			0.519581			0.259790	+	0.965665i	$0.416347\pi$
$578$	21.4862	+	37.2152i	0.893708	+	1.54795i
$579$		0			0
$580$	16.3087	−	28.2475i	0.677182	−	1.17291i
$581$	6.50026	−	11.2588i	0.269676	−	0.467093i
$582$		0			0
$583$	19.0988	+	33.0802i	0.790993	+	1.37004i
$584$	116.304			4.81269
$585$		0			0
$586$	6.56579			0.271230
$587$	−12.5975	−	21.8195i	−0.519955	−	0.900588i	−0.999731	−	0.0231969i	$-0.992616\pi$
$587$	−12.5975	−	21.8195i	−0.519955	−	0.900588i	0.479776	−	0.877391i	$-0.340718\pi$
$588$		0			0
$589$	−8.99625	+	15.5820i	−0.370684	+	0.642044i
$590$	−13.8634	+	24.0121i	−0.570747	+	0.988563i
$591$		0			0
$592$	17.2948	+	29.9554i	0.710811	+	1.23116i
$593$	38.4456			1.57877			0.789385	−	0.613898i	$-0.210399\pi$
$593$	38.4456			1.57877			0.789385	+	0.613898i	$0.210399\pi$
$594$		0			0
$595$	2.64681			0.108508
$596$	28.7816	+	49.8512i	1.17894	+	2.04198i
$597$		0			0
$598$	−7.01981	+	12.1587i	−0.287061	+	0.497205i
$599$	−23.6618	+	40.9834i	−0.966795	+	1.67454i	−0.262082	+	0.965045i	$0.584409\pi$
$599$	−23.6618	+	40.9834i	−0.966795	+	1.67454i	−0.704713	+	0.709493i	$0.748924\pi$
$600$		0			0
$601$	−20.0328	−	34.6979i	−0.817156	−	1.41536i	−0.907770	−	0.419469i	$-0.862216\pi$
$601$	−20.0328	−	34.6979i	−0.817156	−	1.41536i	0.0906140	−	0.995886i	$-0.471117\pi$
$602$	110.961			4.52244
$603$		0			0
$604$	−78.2717			−3.18483
$605$	−4.11176	−	7.12178i	−0.167167	−	0.289542i
$606$		0			0
$607$	−10.3060	+	17.8505i	−0.418306	+	0.724528i	−0.995769	−	0.0918893i	$-0.970709\pi$
$607$	−10.3060	+	17.8505i	−0.418306	+	0.724528i	0.577463	+	0.816417i	$0.304043\pi$
$608$	10.8959	−	18.8723i	0.441887	−	0.765371i
$609$		0			0
$610$	−6.55858	−	11.3598i	−0.265549	−	0.459945i
$611$	−0.405987			−0.0164245
$612$		0			0
$613$	−4.02465			−0.162554			−0.0812770	−	0.996692i	$-0.525900\pi$
$613$	−4.02465			−0.162554			−0.0812770	+	0.996692i	$0.525900\pi$
$614$	−24.8710	−	43.0778i	−1.00371	−	1.73848i
$615$		0			0
$616$	−65.1443	+	112.833i	−2.62474	+	4.54618i
$617$	14.9120	−	25.8283i	0.600334	−	1.03981i	−0.392436	−	0.919779i	$-0.628368\pi$
$617$	14.9120	−	25.8283i	0.600334	−	1.03981i	0.992770	−	0.120030i	$-0.0382991\pi$
$618$		0			0
$619$	23.7693	+	41.1696i	0.955368	+	1.65475i	0.733524	+	0.679664i	$0.237874\pi$
$619$	23.7693	+	41.1696i	0.955368	+	1.65475i	0.221844	+	0.975082i	$0.428792\pi$
$620$	−32.2815			−1.29646
$621$		0			0
$622$	−22.6554			−0.908397
$623$	−15.5407	−	26.9174i	−0.622627	−	1.07842i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	15.7471	−	27.2747i	0.629379	−	1.09012i
$627$		0			0
$628$	−18.7444	−	32.4663i	−0.747984	−	1.29555i
$629$	2.49000			0.0992830
$630$		0			0
$631$	32.2213			1.28271			0.641354	−	0.767245i	$-0.278373\pi$
$631$	32.2213			1.28271			0.641354	+	0.767245i	$0.278373\pi$
$632$	−50.5558	−	87.5652i	−2.01100	−	3.48316i
$633$		0			0
$634$	22.4015	−	38.8006i	0.889678	−	1.54097i
$635$	6.82064	−	11.8137i	0.270669	−	0.468812i
$636$		0			0
$637$	5.63736	+	9.76419i	0.223360	+	0.386871i
$638$	78.8916			3.12335
$639$		0			0
$640$	−5.38732			−0.212953
$641$	1.75107	+	3.03295i	0.0691632	+	0.119794i	0.898533	−	0.438906i	$-0.144634\pi$
$641$	1.75107	+	3.03295i	0.0691632	+	0.119794i	−0.829370	+	0.558700i	$0.811300\pi$
$642$		0			0
$643$	−0.0115697	+	0.0200394i	−0.000456266	+	0.000790276i	−0.866253	−	0.499605i	$-0.833479\pi$
$643$	−0.0115697	+	0.0200394i	−0.000456266	+	0.000790276i	0.865797	+	0.500395i	$0.166812\pi$
$644$	−54.3984	+	94.2207i	−2.14360	+	3.71282i
$645$		0			0
$646$	−2.09186	−	3.62320i	−0.0823030	−	0.142553i
$647$	20.8611			0.820136			0.410068	−	0.912055i	$-0.365505\pi$
$647$	20.8611			0.820136			0.410068	+	0.912055i	$0.365505\pi$
$648$		0			0
$649$	−47.0078			−1.84522
$650$	1.29305	+	2.23963i	0.0507177	+	0.0878456i
$651$		0			0
$652$	40.7202	−	70.5294i	1.59472	−	2.76214i
$653$	5.47824	−	9.48859i	0.214380	−	0.371317i	−0.738700	−	0.674034i	$-0.764560\pi$
$653$	5.47824	−	9.48859i	0.214380	−	0.371317i	0.953081	+	0.302716i	$0.0978935\pi$
$654$		0			0
$655$	4.18118	+	7.24202i	0.163372	+	0.282969i
$656$	35.0422			1.36817
$657$		0			0
$658$	−4.48831			−0.174973
$659$	−17.0546	−	29.5395i	−0.664354	−	1.15070i	−0.979460	−	0.201639i	$-0.935373\pi$
$659$	−17.0546	−	29.5395i	−0.664354	−	1.15070i	0.315106	−	0.949057i	$-0.397960\pi$
$660$		0			0
$661$	12.0901	−	20.9406i	0.470249	−	0.814495i	−0.529172	−	0.848514i	$-0.677497\pi$
$661$	12.0901	−	20.9406i	0.470249	−	0.814495i	0.999421	+	0.0340194i	$0.0108308\pi$
$662$	−3.18186	+	5.51115i	−0.123667	+	0.214197i
$663$		0			0
$664$	−10.5699	−	18.3076i	−0.410191	−	0.710471i
$665$	11.1698			0.433145
$666$		0			0
$667$	37.7726			1.46256
$668$	10.0226	+	17.3596i	0.387784	+	0.671662i
$669$		0			0
$670$	−18.8241	+	32.6043i	−0.727238	+	1.25961i
$671$	11.1194	−	19.2593i	0.429259	−	0.743498i
$672$		0			0
$673$	−9.66073	−	16.7329i	−0.372394	−	0.645005i	0.617539	−	0.786540i	$-0.288130\pi$
$673$	−9.66073	−	16.7329i	−0.372394	−	0.645005i	−0.989933	+	0.141535i	$0.954796\pi$
$674$	53.6579			2.06683
$675$		0			0
$676$	4.68793			0.180305
$677$	−19.1367	−	33.1457i	−0.735483	−	1.27389i	−0.954511	−	0.298175i	$-0.903622\pi$
$677$	−19.1367	−	33.1457i	−0.735483	−	1.27389i	0.219028	−	0.975718i	$-0.429711\pi$
$678$		0			0
$679$	−20.5938	+	35.6695i	−0.790316	+	1.36887i
$680$	2.15195	−	3.72728i	0.0825234	−	0.142935i
$681$		0			0
$682$	−39.0396	−	67.6185i	−1.49490	−	2.58925i
$683$	−0.692198			−0.0264862			−0.0132431	−	0.999912i	$-0.504216\pi$
$683$	−0.692198			−0.0264862			−0.0132431	+	0.999912i	$0.504216\pi$
$684$		0			0
$685$	6.75088			0.257938
$686$	23.6292	+	40.9269i	0.902165	+	1.56260i
$687$		0			0
$688$	43.1630	−	74.7605i	1.64557	−	2.85022i
$689$	4.35603	−	7.54486i	0.165951	−	0.287436i
$690$		0			0
$691$	16.4956	+	28.5711i	0.627520	+	1.08690i	0.988048	+	0.154148i	$0.0492634\pi$
$691$	16.4956	+	28.5711i	0.627520	+	1.08690i	−0.360527	+	0.932749i	$0.617403\pi$
$692$	−60.7363			−2.30885
$693$		0			0
$694$	32.5530			1.23569
$695$	−1.75288	−	3.03608i	−0.0664907	−	0.115165i
$696$		0			0
$697$	1.26130	−	2.18463i	0.0477750	−	0.0827487i
$698$	25.8259	−	44.7318i	0.977526	−	1.69312i
$699$		0			0
$700$	10.0202	+	17.3555i	0.378728	+	0.655977i
$701$	18.7776			0.709219			0.354610	−	0.935014i	$-0.384614\pi$
$701$	18.7776			0.709219			0.354610	+	0.935014i	$0.384614\pi$
$702$		0			0
$703$	10.5081			0.396319
$704$	9.57303	+	16.5810i	0.360797	+	0.624919i
$705$		0			0
$706$	7.61522	−	13.1899i	0.286603	−	0.496410i
$707$	−16.6711	+	28.8751i	−0.626980	+	1.08596i
$708$		0			0
$709$	−4.04721	−	7.00997i	−0.151996	−	0.263265i	0.779965	−	0.625823i	$-0.215237\pi$
$709$	−4.04721	−	7.00997i	−0.151996	−	0.263265i	−0.931961	+	0.362558i	$0.881903\pi$
$710$	−17.0042			−0.638157
$711$		0			0
$712$	−50.5407			−1.89409
$713$	−18.6918	−	32.3752i	−0.700014	−	1.21246i
$714$		0			0
$715$	−2.19223	+	3.79706i	−0.0819848	+	0.142002i
$716$	44.1909	−	76.5409i	1.65149	−	2.86047i
$717$		0			0
$718$	23.0595	+	39.9402i	0.860572	+	1.49055i
$719$	−31.8467			−1.18768			−0.593840	−	0.804583i	$-0.702389\pi$
$719$	−31.8467			−1.18768			−0.593840	+	0.804583i	$0.702389\pi$
$720$		0			0
$721$	−4.24600			−0.158129
$722$	15.7402	+	27.2627i	0.585788	+	1.01461i
$723$		0			0
$724$	49.8312	−	86.3101i	1.85196	−	3.20769i
$725$	3.47887	−	6.02558i	0.129202	−	0.223784i
$726$		0			0
$727$	10.1546	+	17.5883i	0.376613	+	0.652313i	0.990567	−	0.137029i	$-0.0437552\pi$
$727$	10.1546	+	17.5883i	0.376613	+	0.652313i	−0.613954	+	0.789342i	$0.710422\pi$
$728$	29.7160			1.10135
$729$		0			0
$730$	43.2689			1.60145
$731$	−3.10718	−	5.38180i	−0.114923	−	0.199053i
$732$		0			0
$733$	7.15966	−	12.4009i	0.264448	−	0.458037i	−0.702971	−	0.711219i	$-0.748144\pi$
$733$	7.15966	−	12.4009i	0.264448	−	0.458037i	0.967419	+	0.253181i	$0.0814769\pi$
$734$	38.5755	−	66.8147i	1.42385	−	2.46618i
$735$		0			0
$736$	22.6388	+	39.2115i	0.834477	+	1.44536i
$737$	−63.8285			−2.35115
$738$		0			0
$739$	−32.7316			−1.20405			−0.602025	−	0.798477i	$-0.705639\pi$
$739$	−32.7316			−1.20405			−0.602025	+	0.798477i	$0.705639\pi$
$740$	9.42660	+	16.3273i	0.346529	+	0.600205i
$741$		0			0
$742$	48.1573	−	83.4108i	1.76791	−	3.06211i
$743$	19.4753	−	33.7323i	0.714481	−	1.23752i	−0.248678	−	0.968586i	$-0.579996\pi$
$743$	19.4753	−	33.7323i	0.714481	−	1.23752i	0.963159	−	0.268931i	$-0.0866705\pi$
$744$		0			0
$745$	6.13951	+	10.6339i	0.224934	+	0.389597i
$746$	−37.7038			−1.38044
$747$		0			0
$748$	12.7261			0.465312
$749$	−9.06644	−	15.7035i	−0.331280	−	0.573795i
$750$		0			0
$751$	11.5075	−	19.9316i	0.419916	−	0.727316i	−0.576015	−	0.817439i	$-0.695393\pi$
$751$	11.5075	−	19.9316i	0.419916	−	0.727316i	0.995931	+	0.0901237i	$0.0287263\pi$
$752$	−1.74592	+	3.02401i	−0.0636670	+	0.110274i
$753$		0			0
$754$	−8.99672	−	15.5828i	−0.327641	−	0.567491i
$755$	−16.6964			−0.607645
$756$		0			0
$757$	41.6474			1.51370			0.756850	−	0.653588i	$-0.226737\pi$
$757$	41.6474			1.51370			0.756850	+	0.653588i	$0.226737\pi$
$758$	−26.7723	−	46.3710i	−0.972415	−	1.68427i
$759$		0			0
$760$	9.08142	−	15.7295i	0.329418	−	0.570568i
$761$	3.44431	−	5.96571i	0.124856	−	0.216257i	−0.796821	−	0.604216i	$-0.793486\pi$
$761$	3.44431	−	5.96571i	0.124856	−	0.216257i	0.921677	+	0.387959i	$0.126820\pi$
$762$		0			0
$763$	10.0940	+	17.4834i	0.365428	+	0.632940i
$764$	72.2738			2.61477
$765$		0			0
$766$	66.1176			2.38893
$767$	5.36073	+	9.28505i	0.193565	+	0.335264i
$768$		0			0
$769$	4.78387	−	8.28591i	0.172511	−	0.298797i	−0.766786	−	0.641903i	$-0.778145\pi$
$769$	4.78387	−	8.28591i	0.172511	−	0.298797i	0.939297	+	0.343105i	$0.111479\pi$
$770$	−24.2358	+	41.9777i	−0.873399	+	1.51277i
$771$		0			0
$772$	−4.42545	−	7.66510i	−0.159275	−	0.275873i
$773$	10.5131			0.378131			0.189066	−	0.981964i	$-0.439454\pi$
$773$	10.5131			0.378131			0.189066	+	0.981964i	$0.439454\pi$
$774$		0			0
$775$	−6.88609			−0.247356
$776$	33.4869	+	58.0010i	1.20211	+	2.08212i
$777$		0			0
$778$	−22.1505	+	38.3658i	−0.794134	+	1.37548i
$779$	5.32279	−	9.21934i	0.190709	−	0.330317i
$780$		0			0
$781$	−14.4144	−	24.9665i	−0.515789	−	0.893372i
$782$	8.69264			0.310848
$783$		0			0
$784$	96.9722			3.46329
$785$	−3.99844	−	6.92550i	−0.142710	−	0.247182i
$786$		0			0
$787$	18.0600	−	31.2808i	0.643769	−	1.11504i	−0.340816	−	0.940130i	$-0.610703\pi$
$787$	18.0600	−	31.2808i	0.643769	−	1.11504i	0.984584	−	0.174910i	$-0.0559634\pi$
$788$	−25.4548	+	44.0891i	−0.906791	+	1.57061i
$789$		0			0
$790$	−18.8084	−	32.5771i	−0.669174	−	1.15904i
$791$	−15.1933			−0.540211
$792$		0			0
$793$	−5.07217			−0.180118
$794$	20.4738	+	35.4616i	0.726586	+	1.25848i
$795$		0			0
$796$	2.81533	−	4.87630i	0.0997869	−	0.172836i
$797$	−7.37462	+	12.7732i	−0.261223	+	0.452451i	−0.966567	−	0.256414i	$-0.917459\pi$
$797$	−7.37462	+	12.7732i	−0.261223	+	0.452451i	0.705344	+	0.708865i	$0.250792\pi$
$798$		0			0
$799$	0.125684	+	0.217690i	0.00444636	+	0.00770133i
$800$	8.34015			0.294869
$801$		0			0
$802$	88.2140			3.11495
$803$	36.6789	+	63.5297i	1.29437	+	2.24192i
$804$		0			0
$805$	−11.6039	+	20.0986i	−0.408984	+	0.708381i
$806$	−8.90407	+	15.4223i	−0.313633	+	0.543227i
$807$		0			0
$808$	27.1083	+	46.9530i	0.953667	+	1.65180i
$809$	−1.81657			−0.0638672			−0.0319336	−	0.999490i	$-0.510167\pi$
$809$	−1.81657			−0.0638672			−0.0319336	+	0.999490i	$0.510167\pi$
$810$		0			0
$811$	−33.3279			−1.17030			−0.585151	−	0.810924i	$-0.698965\pi$
$811$	−33.3279			−1.17030			−0.585151	+	0.810924i	$0.698965\pi$
$812$	−69.7180	−	120.755i	−2.44662	−	4.23767i
$813$		0			0
$814$	−22.8001	+	39.4909i	−0.799142	+	1.38415i
$815$	8.68616	−	15.0449i	0.304263	−	0.526999i
$816$		0			0
$817$	−13.1126	−	22.7117i	−0.458752	−	0.794581i
$818$	−49.5117			−1.73113
$819$		0			0
$820$	19.0999			0.666998
$821$	17.7439	+	30.7333i	0.619266	+	1.07260i	0.989620	+	0.143709i	$0.0459030\pi$
$821$	17.7439	+	30.7333i	0.619266	+	1.07260i	−0.370354	+	0.928891i	$0.620764\pi$
$822$		0			0
$823$	8.28999	−	14.3587i	0.288971	−	0.500512i	−0.684594	−	0.728925i	$-0.740020\pi$
$823$	8.28999	−	14.3587i	0.288971	−	0.500512i	0.973564	+	0.228413i	$0.0733536\pi$
$824$	−3.45215	+	5.97929i	−0.120261	+	0.208299i
$825$		0			0
$826$	59.2645	+	102.649i	2.06208	+	3.57162i
$827$	−8.93071			−0.310551			−0.155276	−	0.987871i	$-0.549627\pi$
$827$	−8.93071			−0.310551			−0.155276	+	0.987871i	$0.549627\pi$
$828$		0			0
$829$	12.9059			0.448240			0.224120	−	0.974562i	$-0.428049\pi$
$829$	12.9059			0.448240			0.224120	+	0.974562i	$0.428049\pi$
$830$	−3.93234	−	6.81102i	−0.136494	−	0.236414i
$831$		0			0
$832$	2.18340	−	3.78175i	0.0756957	−	0.131109i
$833$	3.49038	−	6.04551i	0.120934	−	0.209464i
$834$		0			0
$835$	2.13795	+	3.70303i	0.0739867	+	0.128149i
$836$	53.7053			1.85744
$837$		0			0
$838$	−18.4518			−0.637408
$839$	17.4959	+	30.3039i	0.604027	+	1.04621i	0.992204	+	0.124621i	$0.0397714\pi$
$839$	17.4959	+	30.3039i	0.604027	+	1.04621i	−0.388178	+	0.921585i	$0.626895\pi$
$840$		0			0
$841$	−9.70506	+	16.8097i	−0.334657	+	0.579644i
$842$	33.8286	−	58.5928i	1.16581	−	2.01924i
$843$		0			0
$844$	0.551328	+	0.954929i	0.0189775	+	0.0328700i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−35.1547			−1.20793
$848$	−37.4656	−	64.8922i	−1.28657	−	2.22841i
$849$		0			0
$850$	0.800595	−	1.38667i	0.0274602	−	0.0475624i
$851$	−10.9165	+	18.9079i	−0.374212	+	0.648154i
$852$		0			0
$853$	10.5784	+	18.3223i	0.362198	+	0.627345i	0.988322	−	0.152378i	$-0.0486933\pi$
$853$	10.5784	+	18.3223i	0.362198	+	0.627345i	−0.626125	+	0.779723i	$0.715360\pi$
$854$	−56.0745			−1.91883
$855$		0			0
$856$	−29.4853			−1.00779
$857$	−5.81524	−	10.0723i	−0.198645	−	0.344063i	0.749444	−	0.662067i	$-0.230321\pi$
$857$	−5.81524	−	10.0723i	−0.198645	−	0.344063i	−0.948089	+	0.318004i	$0.896987\pi$
$858$		0			0
$859$	−0.890335	+	1.54211i	−0.0303778	+	0.0526160i	−0.880815	−	0.473461i	$-0.843004\pi$
$859$	−0.890335	+	1.54211i	−0.0303778	+	0.0526160i	0.850437	+	0.526077i	$0.176338\pi$
$860$	23.5262	−	40.7485i	0.802236	−	1.38951i
$861$		0			0
$862$	−16.0611	−	27.8186i	−0.547043	−	0.947506i
$863$	7.65256			0.260496			0.130248	−	0.991481i	$-0.458423\pi$
$863$	7.65256			0.260496			0.130248	+	0.991481i	$0.458423\pi$
$864$		0			0
$865$	−12.9559			−0.440513
$866$	7.81703	+	13.5395i	0.265633	+	0.460091i
$867$		0			0
$868$	−69.0000	+	119.512i	−2.34201	+	4.05649i
$869$	31.8877	−	55.2311i	1.08172	−	1.87359i
$870$		0			0
$871$	7.27894	+	12.6075i	0.246637	+	0.427188i
$872$	32.8272			1.11167
$873$		0			0
$874$	36.6838			1.24085
$875$	2.13745	+	3.70217i	0.0722589	+	0.125156i
$876$		0			0
$877$	−3.39612	+	5.88225i	−0.114679	+	0.198629i	−0.917651	−	0.397387i	$-0.869917\pi$
$877$	−3.39612	+	5.88225i	−0.114679	+	0.198629i	0.802973	+	0.596016i	$0.203251\pi$
$878$	37.0801	−	64.2246i	1.25139	−	2.16748i
$879$		0			0
$880$	18.8551	+	32.6579i	0.635604	+	1.10090i
$881$	−8.06104			−0.271583			−0.135792	−	0.990737i	$-0.543358\pi$
$881$	−8.06104			−0.271583			−0.135792	+	0.990737i	$0.543358\pi$
$882$		0			0
$883$	15.7753			0.530882			0.265441	−	0.964127i	$-0.414482\pi$
$883$	15.7753			0.530882			0.265441	+	0.964127i	$0.414482\pi$
$884$	−1.45127	−	2.51367i	−0.0488115	−	0.0845440i
$885$		0			0
$886$	−11.8314	+	20.4925i	−0.397483	+	0.688460i
$887$	−8.88157	+	15.3833i	−0.298214	+	0.516522i	−0.975727	−	0.218989i	$-0.929724\pi$
$887$	−8.88157	+	15.3833i	−0.298214	+	0.516522i	0.677513	+	0.735510i	$0.263058\pi$
$888$		0			0
$889$	−29.1575	−	50.5023i	−0.977911	−	1.69379i
$890$	−18.8028			−0.630271
$891$		0			0
$892$	−78.5461			−2.62992
$893$	0.530397	+	0.918674i	0.0177490	+	0.0307422i
$894$		0			0
$895$	9.42652	−	16.3272i	0.315094	−	0.545758i
$896$	−11.5151	+	19.9448i	−0.384693	+	0.666308i
$897$		0			0
$898$	45.8575	+	79.4274i	1.53028	+	2.65053i
$899$	47.9116			1.59794
$900$		0			0
$901$	−5.39408			−0.179703
$902$	23.0984	+	40.0077i	0.769094	+	1.33211i
$903$		0			0
$904$	−12.3527	+	21.3955i	−0.410844	+	0.711603i
$905$	10.6297	−	18.4111i	0.353342	−	0.612006i
$906$		0			0
$907$	−24.3180	−	42.1199i	−0.807464	−	1.39857i	−0.914615	−	0.404327i	$-0.867506\pi$
$907$	−24.3180	−	42.1199i	−0.807464	−	1.39857i	0.107150	−	0.994243i	$-0.465827\pi$
$908$	−106.887			−3.54715
$909$		0			0
$910$	11.0553			0.366480
$911$	9.32994	+	16.1599i	0.309115	+	0.535402i	0.978169	−	0.207811i	$-0.0666340\pi$
$911$	9.32994	+	16.1599i	0.309115	+	0.535402i	−0.669054	+	0.743214i	$0.733301\pi$
$912$		0			0
$913$	6.66687	−	11.5474i	0.220641	−	0.382162i
$914$	−12.1710	+	21.0808i	−0.402581	+	0.697290i
$915$		0			0
$916$	16.3486	+	28.3167i	0.540174	+	0.935609i
$917$	35.7482			1.18051
$918$		0			0
$919$	−13.8812			−0.457898			−0.228949	−	0.973438i	$-0.573529\pi$
$919$	−13.8812			−0.457898			−0.228949	+	0.973438i	$0.573529\pi$
$920$	18.8688	+	32.6817i	0.622085	+	1.07748i
$921$		0			0
$922$	−26.5109	+	45.9182i	−0.873089	+	1.51223i
$923$	−3.28761	+	5.69431i	−0.108213	+	0.187431i
$924$		0			0
$925$	2.01082	+	3.48284i	0.0661154	+	0.114515i
$926$	−97.7111			−3.21099
$927$		0			0
$928$	−58.0286			−1.90488
$929$	8.83587	+	15.3042i	0.289895	+	0.502114i	0.973785	−	0.227472i	$-0.0730461\pi$
$929$	8.83587	+	15.3042i	0.289895	+	0.502114i	−0.683889	+	0.729586i	$0.739713\pi$
$930$		0			0
$931$	14.7297	−	25.5126i	0.482747	−	0.836143i
$932$	−20.2331	+	35.0448i	−0.662758	+	1.14793i
$933$		0			0
$934$	−16.6651	−	28.8648i	−0.545299	−	0.944485i
$935$	2.71465			0.0887784
$936$		0			0
$937$	33.4041			1.09126			0.545632	−	0.838025i	$-0.316290\pi$
$937$	33.4041			1.09126			0.545632	+	0.838025i	$0.316290\pi$
$938$	80.4710	+	139.380i	2.62747	+	4.55091i
$939$		0			0
$940$	−0.951619	+	1.64825i	−0.0310384	+	0.0537601i
$941$	−28.9473	+	50.1383i	−0.943656	+	1.63446i	−0.185236	+	0.982694i	$0.559305\pi$
$941$	−28.9473	+	50.1383i	−0.943656	+	1.63446i	−0.758420	+	0.651766i	$0.774028\pi$
$942$		0			0
$943$	11.0593	+	19.1553i	0.360142	+	0.623784i
$944$	92.2136			3.00130
$945$		0			0
$946$	113.805			3.70013
$947$	−27.3142	−	47.3096i	−0.887593	−	1.53736i	−0.842712	−	0.538364i	$-0.819043\pi$
$947$	−27.3142	−	47.3096i	−0.887593	−	1.53736i	−0.0448808	−	0.998992i	$-0.514291\pi$
$948$		0			0
$949$	8.36565	−	14.4897i	0.271561	−	0.470357i
$950$	3.37859	−	5.85188i	0.109616	−	0.189860i
$951$		0			0
$952$	−9.19934	−	15.9337i	−0.298152	−	0.516415i
$953$	−19.7207			−0.638815			−0.319407	−	0.947618i	$-0.603484\pi$
$953$	−19.7207			−0.638815			−0.319407	+	0.947618i	$0.603484\pi$
$954$		0			0
$955$	15.4170			0.498882
$956$	−7.19834	−	12.4679i	−0.232811	−	0.403240i
$957$		0			0
$958$	26.1042	−	45.2138i	0.843388	−	1.46079i
$959$	14.4296	−	24.9929i	0.465958	−	0.807062i
$960$		0			0
$961$	−8.20911	−	14.2186i	−0.264810	−	0.458665i
$962$	10.4004			0.335322
$963$		0			0
$964$	27.3432			0.880665
$965$	−0.944008	−	1.63507i	−0.0303887	−	0.0526347i
$966$		0			0
$967$	17.6087	−	30.4992i	0.566259	−	0.980790i	−0.430672	−	0.902508i	$-0.641723\pi$
$967$	17.6087	−	30.4992i	0.566259	−	0.980790i	0.996931	−	0.0782812i	$-0.0249432\pi$
$968$	−28.5820	+	49.5055i	−0.918661	+	1.59117i
$969$		0			0
$970$	12.4582	+	21.5783i	0.400010	+	0.692837i
$971$	13.9711			0.448354			0.224177	−	0.974548i	$-0.428031\pi$
$971$	13.9711			0.448354			0.224177	+	0.974548i	$0.428031\pi$
$972$		0			0
$973$	−14.9868			−0.480454
$974$	−19.5872	−	33.9260i	−0.627614	−	1.08706i
$975$		0			0
$976$	−21.8125	+	37.7804i	−0.698201	+	1.20932i
$977$	18.2453	−	31.6017i	0.583718	−	1.01103i	−0.411316	−	0.911493i	$-0.634931\pi$
$977$	18.2453	−	31.6017i	0.583718	−	1.01103i	0.995034	−	0.0995362i	$-0.0317359\pi$
$978$		0			0
$979$	−15.9391	−	27.6073i	−0.509415	−	0.882333i
$980$	52.8551			1.68839
$981$		0			0
$982$	29.7078			0.948015
$983$	−8.75026	−	15.1559i	−0.279090	−	0.483398i	0.692069	−	0.721832i	$-0.256699\pi$
$983$	−8.75026	−	15.1559i	−0.279090	−	0.483398i	−0.971159	+	0.238433i	$0.923366\pi$
$984$		0			0
$985$	−5.42986	+	9.40480i	−0.173010	+	0.299662i
$986$	−5.57033	+	9.64809i	−0.177395	+	0.307258i
$987$		0			0
$988$	−6.12450	−	10.6079i	−0.194846	−	0.337484i
$989$	54.4890			1.73265
$990$		0			0
$991$	18.8114			0.597565			0.298783	−	0.954321i	$-0.403419\pi$
$991$	18.8114			0.597565			0.298783	+	0.954321i	$0.403419\pi$
$992$	28.7155	+	49.7367i	0.911719	+	1.57914i
$993$		0			0
$994$	−36.3456	+	62.9525i	−1.15281	+	1.99673i
$995$	0.600549	−	1.04018i	0.0190387	−	0.0329760i
$996$		0			0
$997$	−1.76712	−	3.06074i	−0.0559651	−	0.0969345i	0.836686	−	0.547684i	$-0.184490\pi$
$997$	−1.76712	−	3.06074i	−0.0559651	−	0.0969345i	−0.892651	+	0.450749i	$0.851157\pi$
$998$	−33.9299			−1.07403
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.f.1171.1		16
3.2	odd	2		585.2.i.e.391.8	yes	16
9.2	odd	6		585.2.i.e.196.8	✓	16
9.4	even	3		5265.2.a.ba.1.8		8
9.5	odd	6		5265.2.a.bf.1.1		8
9.7	even	3	inner	1755.2.i.f.586.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.8	✓	16	9.2	odd	6
585.2.i.e.391.8	yes	16	3.2	odd	2
1755.2.i.f.586.1		16	9.7	even	3	inner
1755.2.i.f.1171.1		16	1.1	even	1	trivial
5265.2.a.ba.1.8		8	9.4	even	3
5265.2.a.bf.1.1		8	9.5	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:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29305 - 2.23963i) q^{2} +(-2.34397 + 4.05987i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.13745 + 3.70217i) q^{7} +6.95128 q^{8} +O(q^{10})\)	\(q+(-1.29305 - 2.23963i) q^{2} +(-2.34397 + 4.05987i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.13745 + 3.70217i) q^{7} +6.95128 q^{8} +2.58610 q^{10} +(2.19223 + 3.79706i) q^{11} +(0.500000 - 0.866025i) q^{13} +(5.52766 - 9.57419i) q^{14} +(-4.30043 - 7.44856i) q^{16} -0.619151 q^{17} -2.61288 q^{19} +(-2.34397 - 4.05987i) q^{20} +(5.66934 - 9.81959i) q^{22} +(2.71443 - 4.70154i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.58610 q^{26} -20.0404 q^{28} +(3.47887 + 6.02558i) q^{29} +(3.44304 - 5.96353i) q^{31} +(-4.17008 + 7.22278i) q^{32} +(0.800595 + 1.38667i) q^{34} -4.27489 q^{35} -4.02164 q^{37} +(3.37859 + 5.85188i) q^{38} +(-3.47564 + 6.01998i) q^{40} +(-2.03714 + 3.52842i) q^{41} +(5.01845 + 8.69221i) q^{43} -20.5541 q^{44} -14.0396 q^{46} +(-0.202993 - 0.351595i) q^{47} +(-5.63736 + 9.76419i) q^{49} +(-1.29305 + 2.23963i) q^{50} +(2.34397 + 4.05987i) q^{52} +8.71205 q^{53} -4.38446 q^{55} +(14.8580 + 25.7348i) q^{56} +(8.99672 - 15.5828i) q^{58} +(-5.36073 + 9.28505i) q^{59} +(-2.53609 - 4.39263i) q^{61} -17.8081 q^{62} +4.36679 q^{64} +(0.500000 + 0.866025i) q^{65} +(-7.27894 + 12.6075i) q^{67} +(1.45127 - 2.51367i) q^{68} +(5.52766 + 9.57419i) q^{70} -6.57523 q^{71} +16.7313 q^{73} +(5.20019 + 9.00700i) q^{74} +(6.12450 - 10.6079i) q^{76} +(-9.37156 + 16.2320i) q^{77} +(-7.27288 - 12.5970i) q^{79} +8.60086 q^{80} +10.5365 q^{82} +(-1.52057 - 2.63370i) q^{83} +(0.309576 - 0.536201i) q^{85} +(12.9782 - 22.4790i) q^{86} +(15.2388 + 26.3944i) q^{88} -7.27070 q^{89} +4.27489 q^{91} +(12.7251 + 22.0405i) q^{92} +(-0.524962 + 0.909260i) q^{94} +(1.30644 - 2.26282i) q^{95} +(4.81738 + 8.34394i) q^{97} +29.1576 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

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