LMFDB - Embedded newform 1350.2.e.j.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(451,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1350.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.e (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:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1350.451
Dual form			1350.2.e.j.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.22474 + 3.85337i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.22474 + 3.85337i) q^{7} +1.00000 q^{8} +(0.724745 - 1.25529i) q^{11} +(1.22474 + 2.12132i) q^{13} +(-2.22474 - 3.85337i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.89898 q^{17} -0.550510 q^{19} +(0.724745 + 1.25529i) q^{22} +(-1.44949 - 2.51059i) q^{23} -2.44949 q^{26} +4.44949 q^{28} +(-3.00000 + 5.19615i) q^{29} +(-3.22474 - 5.58542i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.94949 - 3.37662i) q^{34} +8.00000 q^{37} +(0.275255 - 0.476756i) q^{38} +(-0.500000 - 0.866025i) q^{41} +(-3.72474 + 6.45145i) q^{43} -1.44949 q^{44} +2.89898 q^{46} +(0.224745 - 0.389270i) q^{47} +(-6.39898 - 11.0834i) q^{49} +(1.22474 - 2.12132i) q^{52} -8.44949 q^{53} +(-2.22474 + 3.85337i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(-5.62372 - 9.74058i) q^{59} +(0.224745 - 0.389270i) q^{61} +6.44949 q^{62} +1.00000 q^{64} +(-4.72474 - 8.18350i) q^{67} +(1.94949 + 3.37662i) q^{68} -2.44949 q^{71} -4.79796 q^{73} +(-4.00000 + 6.92820i) q^{74} +(0.275255 + 0.476756i) q^{76} +(3.22474 + 5.58542i) q^{77} +(3.67423 - 6.36396i) q^{79} +1.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-3.72474 - 6.45145i) q^{86} +(0.724745 - 1.25529i) q^{88} -12.8990 q^{89} -10.8990 q^{91} +(-1.44949 + 2.51059i) q^{92} +(0.224745 + 0.389270i) q^{94} +(-6.50000 + 11.2583i) q^{97} +12.7980 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} - 2 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{17} - 12 q^{19} - 2 q^{22} + 4 q^{23} + 8 q^{28} - 12 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{34} + 32 q^{37} + 6 q^{38} - 2 q^{41} - 10 q^{43} + 4 q^{44} - 8 q^{46} - 4 q^{47} - 6 q^{49} - 24 q^{53} - 4 q^{56} - 12 q^{58} + 2 q^{59} - 4 q^{61} + 16 q^{62} + 4 q^{64} - 14 q^{67} - 2 q^{68} + 20 q^{73} - 16 q^{74} + 6 q^{76} + 8 q^{77} + 4 q^{82} - 8 q^{83} - 10 q^{86} - 2 q^{88} - 32 q^{89} - 24 q^{91} + 4 q^{92} - 4 q^{94} - 26 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 - 2 * q^11 - 4 * q^14 - 2 * q^16 + 4 * q^17 - 12 * q^19 - 2 * q^22 + 4 * q^23 + 8 * q^28 - 12 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^34 + 32 * q^37 + 6 * q^38 - 2 * q^41 - 10 * q^43 + 4 * q^44 - 8 * q^46 - 4 * q^47 - 6 * q^49 - 24 * q^53 - 4 * q^56 - 12 * q^58 + 2 * q^59 - 4 * q^61 + 16 * q^62 + 4 * q^64 - 14 * q^67 - 2 * q^68 + 20 * q^73 - 16 * q^74 + 6 * q^76 + 8 * q^77 + 4 * q^82 - 8 * q^83 - 10 * q^86 - 2 * q^88 - 32 * q^89 - 24 * q^91 + 4 * q^92 - 4 * q^94 - 26 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.22474	+	3.85337i	−0.840875	+	1.45644i	0.0482818	+	0.998834i	$0.484625\pi$
$7$	−2.22474	+	3.85337i	−0.840875	+	1.45644i	−0.889156	+	0.457604i	$0.848708\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	0.724745	−	1.25529i	0.218519	−	0.378486i	−0.735837	−	0.677159i	$-0.763211\pi$
$11$	0.724745	−	1.25529i	0.218519	−	0.378486i	0.954355	+	0.298674i	$0.0965442\pi$
$12$		0			0
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	0.984373	−	0.176096i	$-0.0563468\pi$
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	−0.644690	+	0.764444i	$0.723014\pi$
$14$	−2.22474	−	3.85337i	−0.594588	−	1.02986i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.89898			−0.945641			−0.472821	−	0.881159i	$-0.656764\pi$
$17$	−3.89898			−0.945641			−0.472821	+	0.881159i	$0.656764\pi$
$18$		0			0
$19$	−0.550510			−0.126296			−0.0631479	−	0.998004i	$-0.520114\pi$
$19$	−0.550510			−0.126296			−0.0631479	+	0.998004i	$0.520114\pi$
$20$		0			0
$21$		0			0
$22$	0.724745	+	1.25529i	0.154516	+	0.267630i
$23$	−1.44949	−	2.51059i	−0.302240	−	0.523494i	0.674403	−	0.738363i	$-0.264401\pi$
$23$	−1.44949	−	2.51059i	−0.302240	−	0.523494i	−0.976643	+	0.214869i	$0.931068\pi$
$24$		0			0
$25$		0			0
$26$	−2.44949			−0.480384
$27$		0			0
$28$	4.44949			0.840875
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	−3.22474	−	5.58542i	−0.579181	−	1.00317i	−0.995573	−	0.0939863i	$-0.970039\pi$
$31$	−3.22474	−	5.58542i	−0.579181	−	1.00317i	0.416392	−	0.909185i	$-0.363294\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.94949	−	3.37662i	0.334335	−	0.579085i
$35$		0			0
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	0.275255	−	0.476756i	0.0446523	−	0.0773400i
$39$		0			0
$40$		0			0
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	0.824338	−	0.566099i	$-0.191548\pi$
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	−0.902424	+	0.430848i	$0.858214\pi$
$42$		0			0
$43$	−3.72474	+	6.45145i	−0.568018	+	0.983836i	0.428744	+	0.903426i	$0.358956\pi$
$43$	−3.72474	+	6.45145i	−0.568018	+	0.983836i	−0.996762	+	0.0804103i	$0.974377\pi$
$44$	−1.44949			−0.218519
$45$		0			0
$46$	2.89898			0.427431
$47$	0.224745	−	0.389270i	0.0327824	−	0.0567808i	−0.849169	−	0.528122i	$-0.822896\pi$
$47$	0.224745	−	0.389270i	0.0327824	−	0.0567808i	0.881951	+	0.471341i	$0.156230\pi$
$48$		0			0
$49$	−6.39898	−	11.0834i	−0.914140	−	1.58334i
$50$		0			0
$51$		0			0
$52$	1.22474	−	2.12132i	0.169842	−	0.294174i
$53$	−8.44949			−1.16063			−0.580313	−	0.814393i	$-0.697070\pi$
$53$	−8.44949			−1.16063			−0.580313	+	0.814393i	$0.697070\pi$
$54$		0			0
$55$		0			0
$56$	−2.22474	+	3.85337i	−0.297294	+	0.514928i
$57$		0			0
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	−5.62372	−	9.74058i	−0.732147	−	1.26812i	−0.955964	−	0.293484i	$-0.905185\pi$
$59$	−5.62372	−	9.74058i	−0.732147	−	1.26812i	0.223817	−	0.974631i	$-0.428148\pi$
$60$		0			0
$61$	0.224745	−	0.389270i	0.0287756	−	0.0498409i	−0.851279	−	0.524713i	$-0.824173\pi$
$61$	0.224745	−	0.389270i	0.0287756	−	0.0498409i	0.880055	+	0.474873i	$0.157506\pi$
$62$	6.44949			0.819086
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−4.72474	−	8.18350i	−0.577219	−	0.999773i	−0.995797	−	0.0915922i	$-0.970804\pi$
$67$	−4.72474	−	8.18350i	−0.577219	−	0.999773i	0.418577	−	0.908181i	$-0.362529\pi$
$68$	1.94949	+	3.37662i	0.236410	+	0.409475i
$69$		0			0
$70$		0			0
$71$	−2.44949			−0.290701			−0.145350	−	0.989380i	$-0.546431\pi$
$71$	−2.44949			−0.290701			−0.145350	+	0.989380i	$0.546431\pi$
$72$		0			0
$73$	−4.79796			−0.561559			−0.280779	−	0.959772i	$-0.590593\pi$
$73$	−4.79796			−0.561559			−0.280779	+	0.959772i	$0.590593\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	0.275255	+	0.476756i	0.0315739	+	0.0546876i
$77$	3.22474	+	5.58542i	0.367494	+	0.636518i
$78$		0			0
$79$	3.67423	−	6.36396i	0.413384	−	0.716002i	−0.581874	−	0.813279i	$-0.697680\pi$
$79$	3.67423	−	6.36396i	0.413384	−	0.716002i	0.995257	+	0.0972777i	$0.0310135\pi$
$80$		0			0
$81$		0			0
$82$	1.00000			0.110432
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	−0.954664	−	0.297686i	$-0.903785\pi$
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	0.735135	+	0.677920i	$0.237119\pi$
$84$		0			0
$85$		0			0
$86$	−3.72474	−	6.45145i	−0.401650	−	0.695677i
$87$		0			0
$88$	0.724745	−	1.25529i	0.0772581	−	0.133815i
$89$	−12.8990			−1.36729			−0.683645	−	0.729815i	$-0.739606\pi$
$89$	−12.8990			−1.36729			−0.683645	+	0.729815i	$0.739606\pi$
$90$		0			0
$91$	−10.8990			−1.14252
$92$	−1.44949	+	2.51059i	−0.151120	+	0.261747i
$93$		0			0
$94$	0.224745	+	0.389270i	0.0231807	+	0.0401501i
$95$		0			0
$96$		0			0
$97$	−6.50000	+	11.2583i	−0.659975	+	1.14311i	0.320647	+	0.947199i	$0.396100\pi$
$97$	−6.50000	+	11.2583i	−0.659975	+	1.14311i	−0.980622	+	0.195911i	$0.937234\pi$
$98$	12.7980			1.29279
$99$		0			0
$100$		0			0
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	−0.993481	−	0.113998i	$-0.963634\pi$
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	0.595466	+	0.803380i	$0.296967\pi$
$102$		0			0
$103$	−5.12372	−	8.87455i	−0.504856	−	0.874435i	−0.999984	−	0.00561582i	$-0.998212\pi$
$103$	−5.12372	−	8.87455i	−0.504856	−	0.874435i	0.495129	−	0.868820i	$-0.335121\pi$
$104$	1.22474	+	2.12132i	0.120096	+	0.208013i
$105$		0			0
$106$	4.22474	−	7.31747i	0.410343	−	0.710736i
$107$	−1.65153			−0.159660			−0.0798298	−	0.996809i	$-0.525438\pi$
$107$	−1.65153			−0.159660			−0.0798298	+	0.996809i	$0.525438\pi$
$108$		0			0
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$		0			0
$111$		0			0
$112$	−2.22474	−	3.85337i	−0.210219	−	0.364109i
$113$	2.44949	+	4.24264i	0.230429	+	0.399114i	0.957934	−	0.286988i	$-0.0926538\pi$
$113$	2.44949	+	4.24264i	0.230429	+	0.399114i	−0.727506	+	0.686102i	$0.759321\pi$
$114$		0			0
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$	11.2474			1.03541
$119$	8.67423	−	15.0242i	0.795166	−	1.37727i
$120$		0			0
$121$	4.44949	+	7.70674i	0.404499	+	0.700613i
$122$	0.224745	+	0.389270i	0.0203474	+	0.0352428i
$123$		0			0
$124$	−3.22474	+	5.58542i	−0.289591	+	0.501586i
$125$		0			0
$126$		0			0
$127$	−2.89898			−0.257243			−0.128621	−	0.991694i	$-0.541055\pi$
$127$	−2.89898			−0.257243			−0.128621	+	0.991694i	$0.541055\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−2.44949	−	4.24264i	−0.214013	−	0.370681i	0.738954	−	0.673756i	$-0.235320\pi$
$131$	−2.44949	−	4.24264i	−0.214013	−	0.370681i	−0.952967	+	0.303075i	$0.901987\pi$
$132$		0			0
$133$	1.22474	−	2.12132i	0.106199	−	0.183942i
$134$	9.44949			0.816312
$135$		0			0
$136$	−3.89898			−0.334335
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	5.62372	+	9.74058i	0.476998	+	0.826185i	0.999653	−	0.0263597i	$-0.00839153\pi$
$139$	5.62372	+	9.74058i	0.476998	+	0.826185i	−0.522654	+	0.852545i	$0.675058\pi$
$140$		0			0
$141$		0			0
$142$	1.22474	−	2.12132i	0.102778	−	0.178017i
$143$	3.55051			0.296909
$144$		0			0
$145$		0			0
$146$	2.39898	−	4.15515i	0.198541	−	0.343883i
$147$		0			0
$148$	−4.00000	−	6.92820i	−0.328798	−	0.569495i
$149$	8.12372	+	14.0707i	0.665521	+	1.15272i	0.979144	+	0.203169i	$0.0651241\pi$
$149$	8.12372	+	14.0707i	0.665521	+	1.15272i	−0.313622	+	0.949548i	$0.601543\pi$
$150$		0			0
$151$	3.44949	−	5.97469i	0.280715	−	0.486213i	−0.690846	−	0.723002i	$-0.742762\pi$
$151$	3.44949	−	5.97469i	0.280715	−	0.486213i	0.971561	+	0.236789i	$0.0760949\pi$
$152$	−0.550510			−0.0446523
$153$		0			0
$154$	−6.44949			−0.519715
$155$		0			0
$156$		0			0
$157$	−8.00000	−	13.8564i	−0.638470	−	1.10586i	−0.985769	−	0.168107i	$-0.946235\pi$
$157$	−8.00000	−	13.8564i	−0.638470	−	1.10586i	0.347299	−	0.937754i	$-0.387099\pi$
$158$	3.67423	+	6.36396i	0.292306	+	0.506290i
$159$		0			0
$160$		0			0
$161$	12.8990			1.01658
$162$		0			0
$163$	−0.898979			−0.0704135			−0.0352068	−	0.999380i	$-0.511209\pi$
$163$	−0.898979			−0.0704135			−0.0352068	+	0.999380i	$0.511209\pi$
$164$	−0.500000	+	0.866025i	−0.0390434	+	0.0676252i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	−12.1237	−	20.9989i	−0.938162	−	1.62494i	−0.768896	−	0.639374i	$-0.779194\pi$
$167$	−12.1237	−	20.9989i	−0.938162	−	1.62494i	−0.169266	−	0.985570i	$-0.554140\pi$
$168$		0			0
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$		0			0
$171$		0			0
$172$	7.44949			0.568018
$173$	3.89898	−	6.75323i	0.296434	−	0.513439i	−0.678884	−	0.734246i	$-0.737536\pi$
$173$	3.89898	−	6.75323i	0.296434	−	0.513439i	0.975317	+	0.220807i	$0.0708692\pi$
$174$		0			0
$175$		0			0
$176$	0.724745	+	1.25529i	0.0546297	+	0.0946214i
$177$		0			0
$178$	6.44949	−	11.1708i	0.483410	−	0.837290i
$179$	−8.89898			−0.665141			−0.332570	−	0.943078i	$-0.607916\pi$
$179$	−8.89898			−0.665141			−0.332570	+	0.943078i	$0.607916\pi$
$180$		0			0
$181$	10.4495			0.776704			0.388352	−	0.921511i	$-0.373044\pi$
$181$	10.4495			0.776704			0.388352	+	0.921511i	$0.373044\pi$
$182$	5.44949	−	9.43879i	0.403943	−	0.699650i
$183$		0			0
$184$	−1.44949	−	2.51059i	−0.106858	−	0.185083i
$185$		0			0
$186$		0			0
$187$	−2.82577	+	4.89437i	−0.206640	+	0.357912i
$188$	−0.449490			−0.0327824
$189$		0			0
$190$		0			0
$191$	−3.12372	+	5.41045i	−0.226025	+	0.391486i	−0.956626	−	0.291318i	$-0.905906\pi$
$191$	−3.12372	+	5.41045i	−0.226025	+	0.391486i	0.730602	+	0.682804i	$0.239240\pi$
$192$		0			0
$193$	7.84847	+	13.5939i	0.564945	+	0.978514i	0.997055	+	0.0766927i	$0.0244360\pi$
$193$	7.84847	+	13.5939i	0.564945	+	0.978514i	−0.432110	+	0.901821i	$0.642231\pi$
$194$	−6.50000	−	11.2583i	−0.466673	−	0.808301i
$195$		0			0
$196$	−6.39898	+	11.0834i	−0.457070	+	0.791668i
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$		0			0
$199$	20.4495			1.44963			0.724813	−	0.688946i	$-0.241926\pi$
$199$	20.4495			1.44963			0.724813	+	0.688946i	$0.241926\pi$
$200$		0			0
$201$		0			0
$202$	−4.00000	−	6.92820i	−0.281439	−	0.487467i
$203$	−13.3485	−	23.1202i	−0.936879	−	1.62272i
$204$		0			0
$205$		0			0
$206$	10.2474			0.713974
$207$		0			0
$208$	−2.44949			−0.169842
$209$	−0.398979	+	0.691053i	−0.0275980	+	0.0478011i
$210$		0			0
$211$	7.89898	+	13.6814i	0.543788	+	0.941869i	0.998682	+	0.0513231i	$0.0163438\pi$
$211$	7.89898	+	13.6814i	0.543788	+	0.941869i	−0.454894	+	0.890546i	$0.650323\pi$
$212$	4.22474	+	7.31747i	0.290157	+	0.502566i
$213$		0			0
$214$	0.825765	−	1.43027i	0.0564482	−	0.0977711i
$215$		0			0
$216$		0			0
$217$	28.6969			1.94808
$218$	4.00000	−	6.92820i	0.270914	−	0.469237i
$219$		0			0
$220$		0			0
$221$	−4.77526	−	8.27098i	−0.321218	−	0.556367i
$222$		0			0
$223$	−9.44949	+	16.3670i	−0.632785	+	1.09602i	0.354195	+	0.935171i	$0.384755\pi$
$223$	−9.44949	+	16.3670i	−0.632785	+	1.09602i	−0.986980	+	0.160844i	$0.948579\pi$
$224$	4.44949			0.297294
$225$		0			0
$226$	−4.89898			−0.325875
$227$	0.724745	−	1.25529i	0.0481030	−	0.0833169i	−0.840971	−	0.541080i	$-0.818016\pi$
$227$	0.724745	−	1.25529i	0.0481030	−	0.0833169i	0.889074	+	0.457763i	$0.151349\pi$
$228$		0			0
$229$	6.77526	+	11.7351i	0.447721	+	0.775476i	0.998237	−	0.0593484i	$-0.0189023\pi$
$229$	6.77526	+	11.7351i	0.447721	+	0.775476i	−0.550516	+	0.834825i	$0.685569\pi$
$230$		0			0
$231$		0			0
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	−15.6969			−1.02834			−0.514170	−	0.857688i	$-0.671900\pi$
$233$	−15.6969			−1.02834			−0.514170	+	0.857688i	$0.671900\pi$
$234$		0			0
$235$		0			0
$236$	−5.62372	+	9.74058i	−0.366073	+	0.634058i
$237$		0			0
$238$	8.67423	+	15.0242i	0.562267	+	0.973875i
$239$	14.3485	+	24.8523i	0.928125	+	1.60756i	0.786456	+	0.617646i	$0.211914\pi$
$239$	14.3485	+	24.8523i	0.928125	+	1.60756i	0.141669	+	0.989914i	$0.454753\pi$
$240$		0			0
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$	−8.89898			−0.572048
$243$		0			0
$244$	−0.449490			−0.0287756
$245$		0			0
$246$		0			0
$247$	−0.674235	−	1.16781i	−0.0429005	−	0.0743059i
$248$	−3.22474	−	5.58542i	−0.204772	−	0.354675i
$249$		0			0
$250$		0			0
$251$	−11.4495			−0.722685			−0.361343	−	0.932433i	$-0.617682\pi$
$251$	−11.4495			−0.722685			−0.361343	+	0.932433i	$0.617682\pi$
$252$		0			0
$253$	−4.20204			−0.264180
$254$	1.44949	−	2.51059i	0.0909491	−	0.157528i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.94949	+	17.2330i	0.620632	+	1.07497i	0.989368	+	0.145432i	$0.0464573\pi$
$257$	9.94949	+	17.2330i	0.620632	+	1.07497i	−0.368736	+	0.929534i	$0.620209\pi$
$258$		0			0
$259$	−17.7980	+	30.8270i	−1.10591	+	1.91549i
$260$		0			0
$261$		0			0
$262$	4.89898			0.302660
$263$	−3.77526	+	6.53893i	−0.232792	+	0.403208i	−0.958629	−	0.284659i	$-0.908120\pi$
$263$	−3.77526	+	6.53893i	−0.232792	+	0.403208i	0.725837	+	0.687867i	$0.241453\pi$
$264$		0			0
$265$		0			0
$266$	1.22474	+	2.12132i	0.0750939	+	0.130066i
$267$		0			0
$268$	−4.72474	+	8.18350i	−0.288610	+	0.499887i
$269$	28.0454			1.70996			0.854979	−	0.518662i	$-0.173570\pi$
$269$	28.0454			1.70996			0.854979	+	0.518662i	$0.173570\pi$
$270$		0			0
$271$	23.5959			1.43335			0.716675	−	0.697407i	$-0.245663\pi$
$271$	23.5959			1.43335			0.716675	+	0.697407i	$0.245663\pi$
$272$	1.94949	−	3.37662i	0.118205	−	0.204737i
$273$		0			0
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$		0			0
$276$		0			0
$277$	−4.79796	+	8.31031i	−0.288281	+	0.499318i	−0.973400	−	0.229114i	$-0.926417\pi$
$277$	−4.79796	+	8.31031i	−0.288281	+	0.499318i	0.685118	+	0.728432i	$0.259751\pi$
$278$	−11.2474			−0.674577
$279$		0			0
$280$		0			0
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	−0.629685	−	0.776851i	$-0.716816\pi$
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	0.987615	+	0.156898i	$0.0501493\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	1.22474	+	2.12132i	0.0726752	+	0.125877i
$285$		0			0
$286$	−1.77526	+	3.07483i	−0.104973	+	0.181819i
$287$	4.44949			0.262645
$288$		0			0
$289$	−1.79796			−0.105762
$290$		0			0
$291$		0			0
$292$	2.39898	+	4.15515i	0.140390	+	0.243162i
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	0.999549	+	0.0300351i	$0.00956192\pi$
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	−0.473763	+	0.880652i	$0.657105\pi$
$294$		0			0
$295$		0			0
$296$	8.00000			0.464991
$297$		0			0
$298$	−16.2474			−0.941189
$299$	3.55051	−	6.14966i	0.205331	−	0.355644i
$300$		0			0
$301$	−16.5732	−	28.7056i	−0.955264	−	1.65457i
$302$	3.44949	+	5.97469i	0.198496	+	0.343805i
$303$		0			0
$304$	0.275255	−	0.476756i	0.0157870	−	0.0273438i
$305$		0			0
$306$		0			0
$307$	−23.9444			−1.36658			−0.683289	−	0.730148i	$-0.739451\pi$
$307$	−23.9444			−1.36658			−0.683289	+	0.730148i	$0.739451\pi$
$308$	3.22474	−	5.58542i	0.183747	−	0.318259i
$309$		0			0
$310$		0			0
$311$	11.4495	+	19.8311i	0.649241	+	1.12452i	0.983304	+	0.181968i	$0.0582467\pi$
$311$	11.4495	+	19.8311i	0.649241	+	1.12452i	−0.334063	+	0.942551i	$0.608420\pi$
$312$		0			0
$313$	−3.84847	+	6.66574i	−0.217528	+	0.376770i	−0.954052	−	0.299642i	$-0.903133\pi$
$313$	−3.84847	+	6.66574i	−0.217528	+	0.376770i	0.736523	+	0.676412i	$0.236466\pi$
$314$	16.0000			0.902932
$315$		0			0
$316$	−7.34847			−0.413384
$317$	−15.4722	+	26.7986i	−0.869005	+	1.50516i	−0.00599020	+	0.999982i	$0.501907\pi$
$317$	−15.4722	+	26.7986i	−0.869005	+	1.50516i	−0.863015	+	0.505179i	$0.831427\pi$
$318$		0			0
$319$	4.34847	+	7.53177i	0.243468	+	0.421698i
$320$		0			0
$321$		0			0
$322$	−6.44949	+	11.1708i	−0.359416	+	0.622527i
$323$	2.14643			0.119430
$324$		0			0
$325$		0			0
$326$	0.449490	−	0.778539i	0.0248949	−	0.0431193i
$327$		0			0
$328$	−0.500000	−	0.866025i	−0.0276079	−	0.0478183i
$329$	1.00000	+	1.73205i	0.0551318	+	0.0954911i
$330$		0			0
$331$	−16.6969	+	28.9199i	−0.917747	+	1.58958i	−0.114917	+	0.993375i	$0.536660\pi$
$331$	−16.6969	+	28.9199i	−0.917747	+	1.58958i	−0.802829	+	0.596209i	$0.796673\pi$
$332$	4.00000			0.219529
$333$		0			0
$334$	24.2474			1.32676
$335$		0			0
$336$		0			0
$337$	10.2980	+	17.8366i	0.560966	+	0.971621i	0.997413	+	0.0718909i	$0.0229033\pi$
$337$	10.2980	+	17.8366i	0.560966	+	0.971621i	−0.436447	+	0.899730i	$0.643763\pi$
$338$	3.50000	+	6.06218i	0.190375	+	0.329739i
$339$		0			0
$340$		0			0
$341$	−9.34847			−0.506248
$342$		0			0
$343$	25.7980			1.39296
$344$	−3.72474	+	6.45145i	−0.200825	+	0.347839i
$345$		0			0
$346$	3.89898	+	6.75323i	0.209610	+	0.363056i
$347$	−7.62372	−	13.2047i	−0.409263	−	0.708864i	0.585544	−	0.810640i	$-0.300881\pi$
$347$	−7.62372	−	13.2047i	−0.409263	−	0.708864i	−0.994807	+	0.101776i	$0.967547\pi$
$348$		0			0
$349$	−5.79796	+	10.0424i	−0.310358	+	0.537555i	−0.978440	−	0.206532i	$-0.933782\pi$
$349$	−5.79796	+	10.0424i	−0.310358	+	0.537555i	0.668082	+	0.744088i	$0.267115\pi$
$350$		0			0
$351$		0			0
$352$	−1.44949			−0.0772581
$353$	−3.29796	+	5.71223i	−0.175533	+	0.304031i	−0.940345	−	0.340221i	$-0.889498\pi$
$353$	−3.29796	+	5.71223i	−0.175533	+	0.304031i	0.764813	+	0.644253i	$0.222831\pi$
$354$		0			0
$355$		0			0
$356$	6.44949	+	11.1708i	0.341822	+	0.592054i
$357$		0			0
$358$	4.44949	−	7.70674i	0.235163	−	0.407314i
$359$	−8.44949			−0.445947			−0.222974	−	0.974825i	$-0.571576\pi$
$359$	−8.44949			−0.445947			−0.222974	+	0.974825i	$0.571576\pi$
$360$		0			0
$361$	−18.6969			−0.984049
$362$	−5.22474	+	9.04952i	−0.274606	+	0.475632i
$363$		0			0
$364$	5.44949	+	9.43879i	0.285631	+	0.494727i
$365$		0			0
$366$		0			0
$367$	5.79796	−	10.0424i	0.302651	−	0.524207i	−0.674085	−	0.738654i	$-0.735462\pi$
$367$	5.79796	−	10.0424i	0.302651	−	0.524207i	0.976736	+	0.214447i	$0.0687950\pi$
$368$	2.89898			0.151120
$369$		0			0
$370$		0			0
$371$	18.7980	−	32.5590i	0.975941	−	1.69038i
$372$		0			0
$373$	−12.7980	−	22.1667i	−0.662653	−	1.14775i	−0.979916	−	0.199411i	$-0.936097\pi$
$373$	−12.7980	−	22.1667i	−0.662653	−	1.14775i	0.317263	−	0.948338i	$-0.397236\pi$
$374$	−2.82577	−	4.89437i	−0.146117	−	0.253082i
$375$		0			0
$376$	0.224745	−	0.389270i	0.0115903	−	0.0200750i
$377$	−14.6969			−0.756931
$378$		0			0
$379$	−30.1464			−1.54852			−0.774259	−	0.632869i	$-0.781877\pi$
$379$	−30.1464			−1.54852			−0.774259	+	0.632869i	$0.781877\pi$
$380$		0			0
$381$		0			0
$382$	−3.12372	−	5.41045i	−0.159824	−	0.276823i
$383$	0.898979	+	1.55708i	0.0459357	+	0.0795630i	0.888079	−	0.459691i	$-0.152040\pi$
$383$	0.898979	+	1.55708i	0.0459357	+	0.0795630i	−0.842143	+	0.539254i	$0.818706\pi$
$384$		0			0
$385$		0			0
$386$	−15.6969			−0.798953
$387$		0			0
$388$	13.0000			0.659975
$389$	11.2247	−	19.4418i	0.569117	−	0.985740i	−0.427536	−	0.903998i	$-0.640618\pi$
$389$	11.2247	−	19.4418i	0.569117	−	0.985740i	0.996654	−	0.0817417i	$-0.0260483\pi$
$390$		0			0
$391$	5.65153	+	9.78874i	0.285810	+	0.495038i
$392$	−6.39898	−	11.0834i	−0.323197	−	0.559794i
$393$		0			0
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$		0			0
$396$		0			0
$397$	17.7980			0.893254			0.446627	−	0.894720i	$-0.352625\pi$
$397$	17.7980			0.893254			0.446627	+	0.894720i	$0.352625\pi$
$398$	−10.2247	+	17.7098i	−0.512520	+	0.887711i
$399$		0			0
$400$		0			0
$401$	14.3990	+	24.9398i	0.719051	+	1.24543i	0.961376	+	0.275237i	$0.0887565\pi$
$401$	14.3990	+	24.9398i	0.719051	+	1.24543i	−0.242326	+	0.970195i	$0.577910\pi$
$402$		0			0
$403$	7.89898	−	13.6814i	0.393476	−	0.681521i
$404$	8.00000			0.398015
$405$		0			0
$406$	26.6969			1.32495
$407$	5.79796	−	10.0424i	0.287394	−	0.497781i
$408$		0			0
$409$	−3.05051	−	5.28364i	−0.150838	−	0.261259i	0.780698	−	0.624909i	$-0.214864\pi$
$409$	−3.05051	−	5.28364i	−0.150838	−	0.261259i	−0.931536	+	0.363650i	$0.881531\pi$
$410$		0			0
$411$		0			0
$412$	−5.12372	+	8.87455i	−0.252428	+	0.437218i
$413$	50.0454			2.46257
$414$		0			0
$415$		0			0
$416$	1.22474	−	2.12132i	0.0600481	−	0.104006i
$417$		0			0
$418$	−0.398979	−	0.691053i	−0.0195147	−	0.0338005i
$419$	0.449490	+	0.778539i	0.0219590	+	0.0380341i	0.876796	−	0.480862i	$-0.159676\pi$
$419$	0.449490	+	0.778539i	0.0219590	+	0.0380341i	−0.854837	+	0.518896i	$0.826343\pi$
$420$		0			0
$421$	8.22474	−	14.2457i	0.400850	−	0.694292i	−0.592979	−	0.805218i	$-0.702048\pi$
$421$	8.22474	−	14.2457i	0.400850	−	0.694292i	0.993829	+	0.110926i	$0.0353817\pi$
$422$	−15.7980			−0.769033
$423$		0			0
$424$	−8.44949			−0.410343
$425$		0			0
$426$		0			0
$427$	1.00000	+	1.73205i	0.0483934	+	0.0838198i
$428$	0.825765	+	1.43027i	0.0399149	+	0.0691346i
$429$		0			0
$430$		0			0
$431$	−13.7526			−0.662437			−0.331219	−	0.943554i	$-0.607460\pi$
$431$	−13.7526			−0.662437			−0.331219	+	0.943554i	$0.607460\pi$
$432$		0			0
$433$	23.0000			1.10531			0.552655	−	0.833410i	$-0.313615\pi$
$433$	23.0000			1.10531			0.552655	+	0.833410i	$0.313615\pi$
$434$	−14.3485	+	24.8523i	−0.688749	+	1.19295i
$435$		0			0
$436$	4.00000	+	6.92820i	0.191565	+	0.331801i
$437$	0.797959	+	1.38211i	0.0381716	+	0.0661151i
$438$		0			0
$439$	11.0227	−	19.0919i	0.526085	−	0.911206i	−0.473453	−	0.880819i	$-0.656993\pi$
$439$	11.0227	−	19.0919i	0.526085	−	0.911206i	0.999538	−	0.0303869i	$-0.00967395\pi$
$440$		0			0
$441$		0			0
$442$	9.55051			0.454271
$443$	−1.62372	+	2.81237i	−0.0771455	+	0.133620i	−0.902017	−	0.431700i	$-0.857914\pi$
$443$	−1.62372	+	2.81237i	−0.0771455	+	0.133620i	0.824872	+	0.565320i	$0.191247\pi$
$444$		0			0
$445$		0			0
$446$	−9.44949	−	16.3670i	−0.447446	−	0.775000i
$447$		0			0
$448$	−2.22474	+	3.85337i	−0.105109	+	0.182055i
$449$	0.797959			0.0376580			0.0188290	−	0.999823i	$-0.494006\pi$
$449$	0.797959			0.0376580			0.0188290	+	0.999823i	$0.494006\pi$
$450$		0			0
$451$	−1.44949			−0.0682538
$452$	2.44949	−	4.24264i	0.115214	−	0.199557i
$453$		0			0
$454$	0.724745	+	1.25529i	0.0340140	+	0.0589139i
$455$		0			0
$456$		0			0
$457$	4.05051	−	7.01569i	0.189475	−	0.328180i	−0.755600	−	0.655033i	$-0.772655\pi$
$457$	4.05051	−	7.01569i	0.189475	−	0.328180i	0.945075	+	0.326853i	$0.105988\pi$
$458$	−13.5505			−0.633174
$459$		0			0
$460$		0			0
$461$	1.22474	−	2.12132i	0.0570421	−	0.0987997i	−0.836094	−	0.548586i	$-0.815166\pi$
$461$	1.22474	−	2.12132i	0.0570421	−	0.0987997i	0.893136	+	0.449786i	$0.148500\pi$
$462$		0			0
$463$	−12.0000	−	20.7846i	−0.557687	−	0.965943i	−0.997689	−	0.0679458i	$-0.978356\pi$
$463$	−12.0000	−	20.7846i	−0.557687	−	0.965943i	0.440002	−	0.897997i	$-0.354978\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	7.84847	−	13.5939i	0.363573	−	0.629727i
$467$	−4.34847			−0.201223			−0.100612	−	0.994926i	$-0.532080\pi$
$467$	−4.34847			−0.201223			−0.100612	+	0.994926i	$0.532080\pi$
$468$		0			0
$469$	42.0454			1.94148
$470$		0			0
$471$		0			0
$472$	−5.62372	−	9.74058i	−0.258853	−	0.448346i
$473$	5.39898	+	9.35131i	0.248245	+	0.429974i
$474$		0			0
$475$		0			0
$476$	−17.3485			−0.795166
$477$		0			0
$478$	−28.6969			−1.31257
$479$	−6.34847	+	10.9959i	−0.290069	+	0.502414i	−0.973826	−	0.227296i	$-0.927012\pi$
$479$	−6.34847	+	10.9959i	−0.290069	+	0.502414i	0.683757	+	0.729710i	$0.260345\pi$
$480$		0			0
$481$	9.79796	+	16.9706i	0.446748	+	0.773791i
$482$	−0.500000	−	0.866025i	−0.0227744	−	0.0394464i
$483$		0			0
$484$	4.44949	−	7.70674i	0.202250	−	0.350306i
$485$		0			0
$486$		0			0
$487$	−34.8990			−1.58142			−0.790712	−	0.612188i	$-0.790289\pi$
$487$	−34.8990			−1.58142			−0.790712	+	0.612188i	$0.790289\pi$
$488$	0.224745	−	0.389270i	0.0101737	−	0.0176214i
$489$		0			0
$490$		0			0
$491$	11.7247	+	20.3079i	0.529130	+	0.916481i	0.999423	+	0.0339700i	$0.0108151\pi$
$491$	11.7247	+	20.3079i	0.529130	+	0.916481i	−0.470293	+	0.882511i	$0.655852\pi$
$492$		0			0
$493$	11.6969	−	20.2597i	0.526804	−	0.912451i
$494$	1.34847			0.0606705
$495$		0			0
$496$	6.44949			0.289591
$497$	5.44949	−	9.43879i	0.244443	−	0.423388i
$498$		0			0
$499$	−1.62372	−	2.81237i	−0.0726879	−	0.125899i	0.827391	−	0.561627i	$-0.189824\pi$
$499$	−1.62372	−	2.81237i	−0.0726879	−	0.125899i	−0.900078	+	0.435728i	$0.856491\pi$
$500$		0			0
$501$		0			0
$502$	5.72474	−	9.91555i	0.255508	−	0.442553i
$503$	−9.55051			−0.425836			−0.212918	−	0.977070i	$-0.568297\pi$
$503$	−9.55051			−0.425836			−0.212918	+	0.977070i	$0.568297\pi$
$504$		0			0
$505$		0			0
$506$	2.10102	−	3.63907i	0.0934018	−	0.161777i
$507$		0			0
$508$	1.44949	+	2.51059i	0.0643107	+	0.111389i
$509$	−3.79796	−	6.57826i	−0.168342	−	0.291576i	0.769495	−	0.638652i	$-0.220508\pi$
$509$	−3.79796	−	6.57826i	−0.168342	−	0.291576i	−0.937837	+	0.347076i	$0.887174\pi$
$510$		0			0
$511$	10.6742	−	18.4883i	0.472200	−	0.817875i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−19.8990			−0.877706
$515$		0			0
$516$		0			0
$517$	−0.325765	−	0.564242i	−0.0143271	−	0.0248153i
$518$	−17.7980	−	30.8270i	−0.781997	−	1.35446i
$519$		0			0
$520$		0			0
$521$	7.69694			0.337209			0.168604	−	0.985684i	$-0.446074\pi$
$521$	7.69694			0.337209			0.168604	+	0.985684i	$0.446074\pi$
$522$		0			0
$523$	−29.7980			−1.30297			−0.651487	−	0.758660i	$-0.725854\pi$
$523$	−29.7980			−1.30297			−0.651487	+	0.758660i	$0.725854\pi$
$524$	−2.44949	+	4.24264i	−0.107006	+	0.185341i
$525$		0			0
$526$	−3.77526	−	6.53893i	−0.164609	−	0.285111i
$527$	12.5732	+	21.7774i	0.547698	+	0.948640i
$528$		0			0
$529$	7.29796	−	12.6404i	0.317303	−	0.549584i
$530$		0			0
$531$		0			0
$532$	−2.44949			−0.106199
$533$	1.22474	−	2.12132i	0.0530496	−	0.0918846i
$534$		0			0
$535$		0			0
$536$	−4.72474	−	8.18350i	−0.204078	−	0.353473i
$537$		0			0
$538$	−14.0227	+	24.2880i	−0.604562	+	1.04713i
$539$	−18.5505			−0.799027
$540$		0			0
$541$	−39.5959			−1.70236			−0.851181	−	0.524873i	$-0.824113\pi$
$541$	−39.5959			−1.70236			−0.851181	+	0.524873i	$0.824113\pi$
$542$	−11.7980	+	20.4347i	−0.506766	+	0.877744i
$543$		0			0
$544$	1.94949	+	3.37662i	0.0835837	+	0.144771i
$545$		0			0
$546$		0			0
$547$	3.62372	−	6.27647i	0.154939	−	0.268363i	−0.778098	−	0.628143i	$-0.783815\pi$
$547$	3.62372	−	6.27647i	0.154939	−	0.268363i	0.933037	+	0.359781i	$0.117148\pi$
$548$	−3.00000			−0.128154
$549$		0			0
$550$		0			0
$551$	1.65153	−	2.86054i	0.0703576	−	0.121863i
$552$		0			0
$553$	16.3485	+	28.3164i	0.695208	+	1.20413i
$554$	−4.79796	−	8.31031i	−0.203846	−	0.353071i
$555$		0			0
$556$	5.62372	−	9.74058i	0.238499	−	0.413092i
$557$	38.9444			1.65013			0.825063	−	0.565040i	$-0.191139\pi$
$557$	38.9444			1.65013			0.825063	+	0.565040i	$0.191139\pi$
$558$		0			0
$559$	−18.2474			−0.771785
$560$		0			0
$561$		0			0
$562$	6.00000	+	10.3923i	0.253095	+	0.438373i
$563$	18.0732	+	31.3037i	0.761695	+	1.31929i	0.941976	+	0.335680i	$0.108966\pi$
$563$	18.0732	+	31.3037i	0.761695	+	1.31929i	−0.180281	+	0.983615i	$0.557701\pi$
$564$		0			0
$565$		0			0
$566$	4.00000			0.168133
$567$		0			0
$568$	−2.44949			−0.102778
$569$	8.74745	−	15.1510i	0.366712	−	0.635164i	−0.622337	−	0.782749i	$-0.713817\pi$
$569$	8.74745	−	15.1510i	0.366712	−	0.635164i	0.989049	+	0.147585i	$0.0471501\pi$
$570$		0			0
$571$	−6.37628	−	11.0440i	−0.266839	−	0.462178i	0.701205	−	0.712960i	$-0.252646\pi$
$571$	−6.37628	−	11.0440i	−0.266839	−	0.462178i	−0.968044	+	0.250781i	$0.919312\pi$
$572$	−1.77526	−	3.07483i	−0.0742271	−	0.128565i
$573$		0			0
$574$	−2.22474	+	3.85337i	−0.0928591	+	0.160837i
$575$		0			0
$576$		0			0
$577$	13.6969			0.570211			0.285106	−	0.958496i	$-0.407971\pi$
$577$	13.6969			0.570211			0.285106	+	0.958496i	$0.407971\pi$
$578$	0.898979	−	1.55708i	0.0373926	−	0.0647659i
$579$		0			0
$580$		0			0
$581$	−8.89898	−	15.4135i	−0.369192	−	0.639459i
$582$		0			0
$583$	−6.12372	+	10.6066i	−0.253619	+	0.439281i
$584$	−4.79796			−0.198541
$585$		0			0
$586$	−18.0000			−0.743573
$587$	14.9722	−	25.9326i	0.617969	−	1.07035i	−0.371887	−	0.928278i	$-0.621289\pi$
$587$	14.9722	−	25.9326i	0.617969	−	1.07035i	0.989856	−	0.142075i	$-0.0453774\pi$
$588$		0			0
$589$	1.77526	+	3.07483i	0.0731481	+	0.126696i
$590$		0			0
$591$		0			0
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−41.3939			−1.69984			−0.849921	−	0.526910i	$-0.823351\pi$
$593$	−41.3939			−1.69984			−0.849921	+	0.526910i	$0.823351\pi$
$594$		0			0
$595$		0			0
$596$	8.12372	−	14.0707i	0.332761	−	0.576358i
$597$		0			0
$598$	3.55051	+	6.14966i	0.145191	+	0.251478i
$599$	7.10102	+	12.2993i	0.290140	+	0.502537i	0.973843	−	0.227224i	$-0.0729648\pi$
$599$	7.10102	+	12.2993i	0.290140	+	0.502537i	−0.683703	+	0.729761i	$0.739632\pi$
$600$		0			0
$601$	−9.60102	+	16.6295i	−0.391634	+	0.678330i	−0.992665	−	0.120896i	$-0.961423\pi$
$601$	−9.60102	+	16.6295i	−0.391634	+	0.678330i	0.601031	+	0.799225i	$0.294757\pi$
$602$	33.1464			1.35095
$603$		0			0
$604$	−6.89898			−0.280715
$605$		0			0
$606$		0			0
$607$	−5.79796	−	10.0424i	−0.235332	−	0.407607i	0.724037	−	0.689761i	$-0.242284\pi$
$607$	−5.79796	−	10.0424i	−0.235332	−	0.407607i	−0.959369	+	0.282154i	$0.908951\pi$
$608$	0.275255	+	0.476756i	0.0111631	+	0.0193350i
$609$		0			0
$610$		0			0
$611$	1.10102			0.0445425
$612$		0			0
$613$	16.9444			0.684377			0.342189	−	0.939631i	$-0.388832\pi$
$613$	16.9444			0.684377			0.342189	+	0.939631i	$0.388832\pi$
$614$	11.9722	−	20.7364i	0.483158	−	0.836855i
$615$		0			0
$616$	3.22474	+	5.58542i	0.129929	+	0.225043i
$617$	18.8485	+	32.6465i	0.758811	+	1.31430i	0.943457	+	0.331494i	$0.107553\pi$
$617$	18.8485	+	32.6465i	0.758811	+	1.31430i	−0.184647	+	0.982805i	$0.559114\pi$
$618$		0			0
$619$	16.7247	−	28.9681i	0.672224	−	1.16433i	−0.305048	−	0.952337i	$-0.598672\pi$
$619$	16.7247	−	28.9681i	0.672224	−	1.16433i	0.977272	−	0.211989i	$-0.0679943\pi$
$620$		0			0
$621$		0			0
$622$	−22.8990			−0.918165
$623$	28.6969	−	49.7046i	1.14972	−	1.99137i
$624$		0			0
$625$		0			0
$626$	−3.84847	−	6.66574i	−0.153816	−	0.266417i
$627$		0			0
$628$	−8.00000	+	13.8564i	−0.319235	+	0.552931i
$629$	−31.1918			−1.24370
$630$		0			0
$631$	3.34847			0.133300			0.0666502	−	0.997776i	$-0.478769\pi$
$631$	3.34847			0.133300			0.0666502	+	0.997776i	$0.478769\pi$
$632$	3.67423	−	6.36396i	0.146153	−	0.253145i
$633$		0			0
$634$	−15.4722	−	26.7986i	−0.614479	−	1.06431i
$635$		0			0
$636$		0			0
$637$	15.6742	−	27.1486i	0.621036	−	1.07567i
$638$	−8.69694			−0.344315
$639$		0			0
$640$		0			0
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	0.225876	+	0.974156i	$0.427476\pi$
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	−0.956582	+	0.291464i	$0.905858\pi$
$642$		0			0
$643$	4.62372	+	8.00853i	0.182342	+	0.315825i	0.942678	−	0.333705i	$-0.108299\pi$
$643$	4.62372	+	8.00853i	0.182342	+	0.315825i	−0.760336	+	0.649530i	$0.774966\pi$
$644$	−6.44949	−	11.1708i	−0.254145	−	0.440193i
$645$		0			0
$646$	−1.07321	+	1.85886i	−0.0422250	+	0.0731359i
$647$	−25.1010			−0.986823			−0.493411	−	0.869796i	$-0.664250\pi$
$647$	−25.1010			−0.986823			−0.493411	+	0.869796i	$0.664250\pi$
$648$		0			0
$649$	−16.3031			−0.639951
$650$		0			0
$651$		0			0
$652$	0.449490	+	0.778539i	0.0176034	+	0.0304899i
$653$	−17.0000	−	29.4449i	−0.665261	−	1.15227i	−0.979214	−	0.202828i	$-0.934987\pi$
$653$	−17.0000	−	29.4449i	−0.665261	−	1.15227i	0.313953	−	0.949439i	$-0.398347\pi$
$654$		0			0
$655$		0			0
$656$	1.00000			0.0390434
$657$		0			0
$658$	−2.00000			−0.0779681
$659$	−8.10102	+	14.0314i	−0.315571	+	0.546585i	−0.979559	−	0.201159i	$-0.935529\pi$
$659$	−8.10102	+	14.0314i	−0.315571	+	0.546585i	0.663988	+	0.747743i	$0.268863\pi$
$660$		0			0
$661$	6.89898	+	11.9494i	0.268339	+	0.464777i	0.968433	−	0.249274i	$-0.0801919\pi$
$661$	6.89898	+	11.9494i	0.268339	+	0.464777i	−0.700094	+	0.714051i	$0.746859\pi$
$662$	−16.6969	−	28.9199i	−0.648945	−	1.12401i
$663$		0			0
$664$	−2.00000	+	3.46410i	−0.0776151	+	0.134433i
$665$		0			0
$666$		0			0
$667$	17.3939			0.673494
$668$	−12.1237	+	20.9989i	−0.469081	+	0.812472i
$669$		0			0
$670$		0			0
$671$	−0.325765	−	0.564242i	−0.0125760	−	0.0217823i
$672$		0			0
$673$	9.55051	−	16.5420i	0.368145	−	0.637646i	−0.621130	−	0.783707i	$-0.713326\pi$
$673$	9.55051	−	16.5420i	0.368145	−	0.637646i	0.989276	+	0.146061i	$0.0466596\pi$
$674$	−20.5959			−0.793325
$675$		0			0
$676$	−7.00000			−0.269231
$677$	0.202041	−	0.349945i	0.00776507	−	0.0134495i	−0.862117	−	0.506710i	$-0.830862\pi$
$677$	0.202041	−	0.349945i	0.00776507	−	0.0134495i	0.869882	+	0.493260i	$0.164195\pi$
$678$		0			0
$679$	−28.9217	−	50.0938i	−1.10991	−	1.92242i
$680$		0			0
$681$		0			0
$682$	4.67423	−	8.09601i	0.178986	−	0.310012i
$683$	40.5505			1.55162			0.775811	−	0.630965i	$-0.217341\pi$
$683$	40.5505			1.55162			0.775811	+	0.630965i	$0.217341\pi$
$684$		0			0
$685$		0			0
$686$	−12.8990	+	22.3417i	−0.492485	+	0.853010i
$687$		0			0
$688$	−3.72474	−	6.45145i	−0.142005	−	0.245959i
$689$	−10.3485	−	17.9241i	−0.394245	−	0.682853i
$690$		0			0
$691$	10.7980	−	18.7026i	0.410774	−	0.711481i	−0.584201	−	0.811609i	$-0.698592\pi$
$691$	10.7980	−	18.7026i	0.410774	−	0.711481i	0.994975	+	0.100128i	$0.0319253\pi$
$692$	−7.79796			−0.296434
$693$		0			0
$694$	15.2474			0.578785
$695$		0			0
$696$		0			0
$697$	1.94949	+	3.37662i	0.0738422	+	0.127898i
$698$	−5.79796	−	10.0424i	−0.219456	−	0.380109i
$699$		0			0
$700$		0			0
$701$	−19.3939			−0.732497			−0.366248	−	0.930517i	$-0.619358\pi$
$701$	−19.3939			−0.732497			−0.366248	+	0.930517i	$0.619358\pi$
$702$		0			0
$703$	−4.40408			−0.166103
$704$	0.724745	−	1.25529i	0.0273149	−	0.0473107i
$705$		0			0
$706$	−3.29796	−	5.71223i	−0.124120	−	0.214983i
$707$	−17.7980	−	30.8270i	−0.669361	−	1.15937i
$708$		0			0
$709$	−11.3258	+	19.6168i	−0.425348	+	0.736724i	−0.996453	−	0.0841527i	$-0.973182\pi$
$709$	−11.3258	+	19.6168i	−0.425348	+	0.736724i	0.571105	+	0.820877i	$0.306515\pi$
$710$		0			0
$711$		0			0
$712$	−12.8990			−0.483410
$713$	−9.34847	+	16.1920i	−0.350103	+	0.606396i
$714$		0			0
$715$		0			0
$716$	4.44949	+	7.70674i	0.166285	+	0.288014i
$717$		0			0
$718$	4.22474	−	7.31747i	0.157666	−	0.273086i
$719$	−22.2020			−0.827996			−0.413998	−	0.910278i	$-0.635868\pi$
$719$	−22.2020			−0.827996			−0.413998	+	0.910278i	$0.635868\pi$
$720$		0			0
$721$	45.5959			1.69808
$722$	9.34847	−	16.1920i	0.347914	−	0.602605i
$723$		0			0
$724$	−5.22474	−	9.04952i	−0.194176	−	0.336323i
$725$		0			0
$726$		0			0
$727$	5.32577	−	9.22450i	0.197522	−	0.342118i	−0.750203	−	0.661208i	$-0.770044\pi$
$727$	5.32577	−	9.22450i	0.197522	−	0.342118i	0.947724	+	0.319090i	$0.103377\pi$
$728$	−10.8990			−0.403943
$729$		0			0
$730$		0			0
$731$	14.5227	−	25.1541i	0.537142	−	0.930357i
$732$		0			0
$733$	6.57321	+	11.3851i	0.242787	+	0.420520i	0.961507	−	0.274780i	$-0.0886050\pi$
$733$	6.57321	+	11.3851i	0.242787	+	0.420520i	−0.718720	+	0.695300i	$0.755272\pi$
$734$	5.79796	+	10.0424i	0.214007	+	0.370670i
$735$		0			0
$736$	−1.44949	+	2.51059i	−0.0534289	+	0.0925416i
$737$	−13.6969			−0.504533
$738$		0			0
$739$	7.24745			0.266602			0.133301	−	0.991076i	$-0.457442\pi$
$739$	7.24745			0.266602			0.133301	+	0.991076i	$0.457442\pi$
$740$		0			0
$741$		0			0
$742$	18.7980	+	32.5590i	0.690095	+	1.19528i
$743$	−6.55051	−	11.3458i	−0.240315	−	0.416238i	0.720489	−	0.693466i	$-0.243917\pi$
$743$	−6.55051	−	11.3458i	−0.240315	−	0.416238i	−0.960804	+	0.277229i	$0.910584\pi$
$744$		0			0
$745$		0			0
$746$	25.5959			0.937133
$747$		0			0
$748$	5.65153			0.206640
$749$	3.67423	−	6.36396i	0.134254	−	0.232534i
$750$		0			0
$751$	−22.4949	−	38.9623i	−0.820850	−	1.42175i	−0.905050	−	0.425306i	$-0.860167\pi$
$751$	−22.4949	−	38.9623i	−0.820850	−	1.42175i	0.0841993	−	0.996449i	$-0.473167\pi$
$752$	0.224745	+	0.389270i	0.00819560	+	0.0141952i
$753$		0			0
$754$	7.34847	−	12.7279i	0.267615	−	0.463524i
$755$		0			0
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	15.0732	−	26.1076i	0.547484	−	0.948270i
$759$		0			0
$760$		0			0
$761$	−24.2474	−	41.9978i	−0.878969	−	1.52242i	−0.852473	−	0.522771i	$-0.824898\pi$
$761$	−24.2474	−	41.9978i	−0.878969	−	1.52242i	−0.0264959	−	0.999649i	$-0.508435\pi$
$762$		0			0
$763$	17.7980	−	30.8270i	0.644329	−	1.11601i
$764$	6.24745			0.226025
$765$		0			0
$766$	−1.79796			−0.0649629
$767$	13.7753	−	23.8594i	0.497396	−	0.861515i
$768$		0			0
$769$	12.2474	+	21.2132i	0.441654	+	0.764968i	0.997812	−	0.0661088i	$-0.0210584\pi$
$769$	12.2474	+	21.2132i	0.441654	+	0.764968i	−0.556158	+	0.831076i	$0.687725\pi$
$770$		0			0
$771$		0			0
$772$	7.84847	−	13.5939i	0.282473	−	0.489257i
$773$	23.3939			0.841419			0.420710	−	0.907195i	$-0.361781\pi$
$773$	23.3939			0.841419			0.420710	+	0.907195i	$0.361781\pi$
$774$		0			0
$775$		0			0
$776$	−6.50000	+	11.2583i	−0.233336	+	0.404151i
$777$		0			0
$778$	11.2247	+	19.4418i	0.402427	+	0.697023i
$779$	0.275255	+	0.476756i	0.00986204	+	0.0170816i
$780$		0			0
$781$	−1.77526	+	3.07483i	−0.0635236	+	0.110026i
$782$	−11.3031			−0.404197
$783$		0			0
$784$	12.7980			0.457070
$785$		0			0
$786$		0			0
$787$	−3.69694	−	6.40329i	−0.131782	−	0.228252i	0.792582	−	0.609766i	$-0.208736\pi$
$787$	−3.69694	−	6.40329i	−0.131782	−	0.228252i	−0.924363	+	0.381513i	$0.875403\pi$
$788$	−4.00000	−	6.92820i	−0.142494	−	0.246807i
$789$		0			0
$790$		0			0
$791$	−21.7980			−0.775046
$792$		0			0
$793$	1.10102			0.0390984
$794$	−8.89898	+	15.4135i	−0.315813	+	0.547004i
$795$		0			0
$796$	−10.2247	−	17.7098i	−0.362406	−	0.627706i
$797$	−17.7980	−	30.8270i	−0.630436	−	1.09195i	−0.987463	−	0.157853i	$-0.949543\pi$
$797$	−17.7980	−	30.8270i	−0.630436	−	1.09195i	0.357027	−	0.934094i	$-0.383791\pi$
$798$		0			0
$799$	−0.876276	+	1.51775i	−0.0310004	+	0.0536943i
$800$		0			0
$801$		0			0
$802$	−28.7980			−1.01689
$803$	−3.47730	+	6.02285i	−0.122711	+	0.212542i
$804$		0			0
$805$		0			0
$806$	7.89898	+	13.6814i	0.278230	+	0.481908i
$807$		0			0
$808$	−4.00000	+	6.92820i	−0.140720	+	0.243733i
$809$	−47.0908			−1.65562			−0.827812	−	0.561005i	$-0.810415\pi$
$809$	−47.0908			−1.65562			−0.827812	+	0.561005i	$0.810415\pi$
$810$		0			0
$811$	−17.2474			−0.605640			−0.302820	−	0.953048i	$-0.597928\pi$
$811$	−17.2474			−0.605640			−0.302820	+	0.953048i	$0.597928\pi$
$812$	−13.3485	+	23.1202i	−0.468439	+	0.811361i
$813$		0			0
$814$	5.79796	+	10.0424i	0.203218	+	0.351985i
$815$		0			0
$816$		0			0
$817$	2.05051	−	3.55159i	0.0717383	−	0.124254i
$818$	6.10102			0.213317
$819$		0			0
$820$		0			0
$821$	−21.0227	+	36.4124i	−0.733697	+	1.27080i	0.221595	+	0.975139i	$0.428874\pi$
$821$	−21.0227	+	36.4124i	−0.733697	+	1.27080i	−0.955292	+	0.295662i	$0.904460\pi$
$822$		0			0
$823$	−3.79796	−	6.57826i	−0.132389	−	0.229304i	0.792208	−	0.610251i	$-0.208931\pi$
$823$	−3.79796	−	6.57826i	−0.132389	−	0.229304i	−0.924597	+	0.380947i	$0.875598\pi$
$824$	−5.12372	−	8.87455i	−0.178493	−	0.309160i
$825$		0			0
$826$	−25.0227	+	43.3406i	−0.870651	+	1.50801i
$827$	13.7980			0.479802			0.239901	−	0.970797i	$-0.422885\pi$
$827$	13.7980			0.479802			0.239901	+	0.970797i	$0.422885\pi$
$828$		0			0
$829$	−21.5505			−0.748480			−0.374240	−	0.927332i	$-0.622096\pi$
$829$	−21.5505			−0.748480			−0.374240	+	0.927332i	$0.622096\pi$
$830$		0			0
$831$		0			0
$832$	1.22474	+	2.12132i	0.0424604	+	0.0735436i
$833$	24.9495	+	43.2138i	0.864449	+	1.49727i
$834$		0			0
$835$		0			0
$836$	0.797959			0.0275980
$837$		0			0
$838$	−0.898979			−0.0310547
$839$	7.87628	−	13.6421i	0.271919	−	0.470978i	−0.697434	−	0.716649i	$-0.745675\pi$
$839$	7.87628	−	13.6421i	0.271919	−	0.470978i	0.969353	+	0.245671i	$0.0790083\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	8.22474	+	14.2457i	0.283443	+	0.490938i
$843$		0			0
$844$	7.89898	−	13.6814i	0.271894	−	0.470934i
$845$		0			0
$846$		0			0
$847$	−39.5959			−1.36053
$848$	4.22474	−	7.31747i	0.145078	−	0.251283i
$849$		0			0
$850$		0			0
$851$	−11.5959	−	20.0847i	−0.397503	−	0.688495i
$852$		0			0
$853$	12.5732	−	21.7774i	0.430499	−	0.745646i	−0.566418	−	0.824118i	$-0.691671\pi$
$853$	12.5732	−	21.7774i	0.430499	−	0.745646i	0.996916	+	0.0784728i	$0.0250044\pi$
$854$	−2.00000			−0.0684386
$855$		0			0
$856$	−1.65153			−0.0564482
$857$	−26.6969	+	46.2405i	−0.911950	+	1.57954i	−0.100644	+	0.994923i	$0.532090\pi$
$857$	−26.6969	+	46.2405i	−0.911950	+	1.57954i	−0.811306	+	0.584621i	$0.801243\pi$
$858$		0			0
$859$	−17.8712	−	30.9538i	−0.609757	−	1.05613i	−0.991280	−	0.131770i	$-0.957934\pi$
$859$	−17.8712	−	30.9538i	−0.609757	−	1.05613i	0.381524	−	0.924359i	$-0.375399\pi$
$860$		0			0
$861$		0			0
$862$	6.87628	−	11.9101i	0.234207	−	0.405658i
$863$	−21.5505			−0.733588			−0.366794	−	0.930302i	$-0.619545\pi$
$863$	−21.5505			−0.733588			−0.366794	+	0.930302i	$0.619545\pi$
$864$		0			0
$865$		0			0
$866$	−11.5000	+	19.9186i	−0.390786	+	0.676861i
$867$		0			0
$868$	−14.3485	−	24.8523i	−0.487019	−	0.843541i
$869$	−5.32577	−	9.22450i	−0.180664	−	0.312920i
$870$		0			0
$871$	11.5732	−	20.0454i	0.392143	−	0.679212i
$872$	−8.00000			−0.270914
$873$		0			0
$874$	−1.59592			−0.0539827
$875$		0			0
$876$		0			0
$877$	27.5732	+	47.7582i	0.931081	+	1.61268i	0.781477	+	0.623934i	$0.214467\pi$
$877$	27.5732	+	47.7582i	0.931081	+	1.61268i	0.149604	+	0.988746i	$0.452200\pi$
$878$	11.0227	+	19.0919i	0.371998	+	0.644320i
$879$		0			0
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	−11.4495			−0.385306			−0.192653	−	0.981267i	$-0.561709\pi$
$883$	−11.4495			−0.385306			−0.192653	+	0.981267i	$0.561709\pi$
$884$	−4.77526	+	8.27098i	−0.160609	+	0.278183i
$885$		0			0
$886$	−1.62372	−	2.81237i	−0.0545501	−	0.0944835i
$887$	2.32577	+	4.02834i	0.0780916	+	0.135259i	0.902427	−	0.430844i	$-0.141784\pi$
$887$	2.32577	+	4.02834i	0.0780916	+	0.135259i	−0.824335	+	0.566102i	$0.808451\pi$
$888$		0			0
$889$	6.44949	−	11.1708i	0.216309	−	0.374658i
$890$		0			0
$891$		0			0
$892$	18.8990			0.632785
$893$	−0.123724	+	0.214297i	−0.00414028	+	0.00717117i
$894$		0			0
$895$		0			0
$896$	−2.22474	−	3.85337i	−0.0743235	−	0.128732i
$897$		0			0
$898$	−0.398979	+	0.691053i	−0.0133141	+	0.0230607i
$899$	38.6969			1.29062
$900$		0			0
$901$	32.9444			1.09754
$902$	0.724745	−	1.25529i	0.0241314	−	0.0417967i
$903$		0			0
$904$	2.44949	+	4.24264i	0.0814688	+	0.141108i
$905$		0			0
$906$		0			0
$907$	−16.8712	+	29.2217i	−0.560198	+	0.970292i	0.437281	+	0.899325i	$0.355942\pi$
$907$	−16.8712	+	29.2217i	−0.560198	+	0.970292i	−0.997479	+	0.0709665i	$0.977392\pi$
$908$	−1.44949			−0.0481030
$909$		0			0
$910$		0			0
$911$	−0.123724	+	0.214297i	−0.00409917	+	0.00709997i	−0.868068	−	0.496446i	$-0.834638\pi$
$911$	−0.123724	+	0.214297i	−0.00409917	+	0.00709997i	0.863969	+	0.503546i	$0.167971\pi$
$912$		0			0
$913$	2.89898	+	5.02118i	0.0959422	+	0.166177i
$914$	4.05051	+	7.01569i	0.133979	+	0.232058i
$915$		0			0
$916$	6.77526	−	11.7351i	0.223861	−	0.387738i
$917$	21.7980			0.719832
$918$		0			0
$919$	10.8990			0.359524			0.179762	−	0.983710i	$-0.442467\pi$
$919$	10.8990			0.359524			0.179762	+	0.983710i	$0.442467\pi$
$920$		0			0
$921$		0			0
$922$	1.22474	+	2.12132i	0.0403348	+	0.0698620i
$923$	−3.00000	−	5.19615i	−0.0987462	−	0.171033i
$924$		0			0
$925$		0			0
$926$	24.0000			0.788689
$927$		0			0
$928$	6.00000			0.196960
$929$	−27.7980	+	48.1475i	−0.912021	+	1.57967i	−0.100817	+	0.994905i	$0.532146\pi$
$929$	−27.7980	+	48.1475i	−0.912021	+	1.57967i	−0.811205	+	0.584762i	$0.801188\pi$
$930$		0			0
$931$	3.52270	+	6.10150i	0.115452	+	0.199969i
$932$	7.84847	+	13.5939i	0.257085	+	0.445285i
$933$		0			0
$934$	2.17423	−	3.76588i	0.0711431	−	0.123224i
$935$		0			0
$936$		0			0
$937$	−39.5959			−1.29354			−0.646771	−	0.762684i	$-0.723881\pi$
$937$	−39.5959			−1.29354			−0.646771	+	0.762684i	$0.723881\pi$
$938$	−21.0227	+	36.4124i	−0.686416	+	1.18891i
$939$		0			0
$940$		0			0
$941$	−24.8990	−	43.1263i	−0.811684	−	1.40588i	−0.911685	−	0.410890i	$-0.865218\pi$
$941$	−24.8990	−	43.1263i	−0.811684	−	1.40588i	0.100001	−	0.994987i	$-0.468115\pi$
$942$		0			0
$943$	−1.44949	+	2.51059i	−0.0472019	+	0.0817561i
$944$	11.2474			0.366073
$945$		0			0
$946$	−10.7980			−0.351072
$947$	−10.6237	+	18.4008i	−0.345225	+	0.597947i	−0.985395	−	0.170287i	$-0.945531\pi$
$947$	−10.6237	+	18.4008i	−0.345225	+	0.597947i	0.640170	+	0.768233i	$0.278864\pi$
$948$		0			0
$949$	−5.87628	−	10.1780i	−0.190752	−	0.330392i
$950$		0			0
$951$		0			0
$952$	8.67423	−	15.0242i	0.281134	−	0.486938i
$953$	50.7980			1.64551			0.822754	−	0.568398i	$-0.192437\pi$
$953$	50.7980			1.64551			0.822754	+	0.568398i	$0.192437\pi$
$954$		0			0
$955$		0			0
$956$	14.3485	−	24.8523i	0.464063	−	0.803780i
$957$		0			0
$958$	−6.34847	−	10.9959i	−0.205110	−	0.355260i
$959$	6.67423	+	11.5601i	0.215522	+	0.373296i
$960$		0			0
$961$	−5.29796	+	9.17633i	−0.170902	+	0.296011i
$962$	−19.5959			−0.631798
$963$		0			0
$964$	1.00000			0.0322078
$965$		0			0
$966$		0			0
$967$	14.3485	+	24.8523i	0.461416	+	0.799195i	0.999032	−	0.0439944i	$-0.0140084\pi$
$967$	14.3485	+	24.8523i	0.461416	+	0.799195i	−0.537616	+	0.843190i	$0.680675\pi$
$968$	4.44949	+	7.70674i	0.143012	+	0.247704i
$969$		0			0
$970$		0			0
$971$	23.3939			0.750745			0.375373	−	0.926874i	$-0.377515\pi$
$971$	23.3939			0.750745			0.375373	+	0.926874i	$0.377515\pi$
$972$		0			0
$973$	−50.0454			−1.60438
$974$	17.4495	−	30.2234i	0.559118	−	0.968420i
$975$		0			0
$976$	0.224745	+	0.389270i	0.00719391	+	0.0124602i
$977$	18.9495	+	32.8215i	0.606248	+	1.05005i	0.991853	+	0.127388i	$0.0406594\pi$
$977$	18.9495	+	32.8215i	0.606248	+	1.05005i	−0.385605	+	0.922664i	$0.626007\pi$
$978$		0			0
$979$	−9.34847	+	16.1920i	−0.298778	+	0.517499i
$980$		0			0
$981$		0			0
$982$	−23.4495			−0.748303
$983$	−18.6969	+	32.3840i	−0.596340	+	1.03289i	0.397017	+	0.917811i	$0.370046\pi$
$983$	−18.6969	+	32.3840i	−0.596340	+	1.03289i	−0.993356	+	0.115079i	$0.963288\pi$
$984$		0			0
$985$		0			0
$986$	11.6969	+	20.2597i	0.372506	+	0.645200i
$987$		0			0
$988$	−0.674235	+	1.16781i	−0.0214503	+	0.0371529i
$989$	21.5959			0.686710
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	−3.22474	+	5.58542i	−0.102386	+	0.177337i
$993$		0			0
$994$	5.44949	+	9.43879i	0.172847	+	0.299380i
$995$		0			0
$996$		0			0
$997$	16.4722	−	28.5307i	0.521680	−	0.903576i	−0.478002	−	0.878359i	$-0.658639\pi$
$997$	16.4722	−	28.5307i	0.521680	−	0.903576i	0.999682	−	0.0252170i	$-0.00802769\pi$
$998$	3.24745			0.102796
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.e.j.451.1		4
3.2	odd	2		450.2.e.n.151.2		4
5.2	odd	4		270.2.i.b.19.2		8
5.3	odd	4		270.2.i.b.19.3		8
5.4	even	2		1350.2.e.m.451.2		4
9.2	odd	6		4050.2.a.bq.1.2		2
9.4	even	3	inner	1350.2.e.j.901.1		4
9.5	odd	6		450.2.e.n.301.2		4
9.7	even	3		4050.2.a.bz.1.2		2
15.2	even	4		90.2.i.b.79.4	yes	8
15.8	even	4		90.2.i.b.79.1	yes	8
15.14	odd	2		450.2.e.k.151.1		4
20.3	even	4		2160.2.by.d.289.1		8
20.7	even	4		2160.2.by.d.289.4		8
45.2	even	12		810.2.c.f.649.1		4
45.4	even	6		1350.2.e.m.901.2		4
45.7	odd	12		810.2.c.e.649.4		4
45.13	odd	12		270.2.i.b.199.2		8
45.14	odd	6		450.2.e.k.301.1		4
45.22	odd	12		270.2.i.b.199.3		8
45.23	even	12		90.2.i.b.49.4	yes	8
45.29	odd	6		4050.2.a.bs.1.1		2
45.32	even	12		90.2.i.b.49.1	✓	8
45.34	even	6		4050.2.a.bm.1.1		2
45.38	even	12		810.2.c.f.649.3		4
45.43	odd	12		810.2.c.e.649.2		4
60.23	odd	4		720.2.by.c.529.4		8
60.47	odd	4		720.2.by.c.529.1		8
180.23	odd	12		720.2.by.c.49.1		8
180.67	even	12		2160.2.by.d.1009.1		8
180.103	even	12		2160.2.by.d.1009.4		8
180.167	odd	12		720.2.by.c.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.b.49.1	✓	8	45.32	even	12
90.2.i.b.49.4	yes	8	45.23	even	12
90.2.i.b.79.1	yes	8	15.8	even	4
90.2.i.b.79.4	yes	8	15.2	even	4
270.2.i.b.19.2		8	5.2	odd	4
270.2.i.b.19.3		8	5.3	odd	4
270.2.i.b.199.2		8	45.13	odd	12
270.2.i.b.199.3		8	45.22	odd	12
450.2.e.k.151.1		4	15.14	odd	2
450.2.e.k.301.1		4	45.14	odd	6
450.2.e.n.151.2		4	3.2	odd	2
450.2.e.n.301.2		4	9.5	odd	6
720.2.by.c.49.1		8	180.23	odd	12
720.2.by.c.49.4		8	180.167	odd	12
720.2.by.c.529.1		8	60.47	odd	4
720.2.by.c.529.4		8	60.23	odd	4
810.2.c.e.649.2		4	45.43	odd	12
810.2.c.e.649.4		4	45.7	odd	12
810.2.c.f.649.1		4	45.2	even	12
810.2.c.f.649.3		4	45.38	even	12
1350.2.e.j.451.1		4	1.1	even	1	trivial
1350.2.e.j.901.1		4	9.4	even	3	inner
1350.2.e.m.451.2		4	5.4	even	2
1350.2.e.m.901.2		4	45.4	even	6
2160.2.by.d.289.1		8	20.3	even	4
2160.2.by.d.289.4		8	20.7	even	4
2160.2.by.d.1009.1		8	180.67	even	12
2160.2.by.d.1009.4		8	180.103	even	12
4050.2.a.bm.1.1		2	45.34	even	6
4050.2.a.bq.1.2		2	9.2	odd	6
4050.2.a.bs.1.1		2	45.29	odd	6
4050.2.a.bz.1.2		2	9.7	even	3

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.22474 + 3.85337i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.22474 + 3.85337i) q^{7} +1.00000 q^{8} +(0.724745 - 1.25529i) q^{11} +(1.22474 + 2.12132i) q^{13} +(-2.22474 - 3.85337i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.89898 q^{17} -0.550510 q^{19} +(0.724745 + 1.25529i) q^{22} +(-1.44949 - 2.51059i) q^{23} -2.44949 q^{26} +4.44949 q^{28} +(-3.00000 + 5.19615i) q^{29} +(-3.22474 - 5.58542i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.94949 - 3.37662i) q^{34} +8.00000 q^{37} +(0.275255 - 0.476756i) q^{38} +(-0.500000 - 0.866025i) q^{41} +(-3.72474 + 6.45145i) q^{43} -1.44949 q^{44} +2.89898 q^{46} +(0.224745 - 0.389270i) q^{47} +(-6.39898 - 11.0834i) q^{49} +(1.22474 - 2.12132i) q^{52} -8.44949 q^{53} +(-2.22474 + 3.85337i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(-5.62372 - 9.74058i) q^{59} +(0.224745 - 0.389270i) q^{61} +6.44949 q^{62} +1.00000 q^{64} +(-4.72474 - 8.18350i) q^{67} +(1.94949 + 3.37662i) q^{68} -2.44949 q^{71} -4.79796 q^{73} +(-4.00000 + 6.92820i) q^{74} +(0.275255 + 0.476756i) q^{76} +(3.22474 + 5.58542i) q^{77} +(3.67423 - 6.36396i) q^{79} +1.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-3.72474 - 6.45145i) q^{86} +(0.724745 - 1.25529i) q^{88} -12.8990 q^{89} -10.8990 q^{91} +(-1.44949 + 2.51059i) q^{92} +(0.224745 + 0.389270i) q^{94} +(-6.50000 + 11.2583i) q^{97} +12.7980 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} - 2 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{17} - 12 q^{19} - 2 q^{22} + 4 q^{23} + 8 q^{28} - 12 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{34} + 32 q^{37} + 6 q^{38} - 2 q^{41} - 10 q^{43} + 4 q^{44} - 8 q^{46} - 4 q^{47} - 6 q^{49} - 24 q^{53} - 4 q^{56} - 12 q^{58} + 2 q^{59} - 4 q^{61} + 16 q^{62} + 4 q^{64} - 14 q^{67} - 2 q^{68} + 20 q^{73} - 16 q^{74} + 6 q^{76} + 8 q^{77} + 4 q^{82} - 8 q^{83} - 10 q^{86} - 2 q^{88} - 32 q^{89} - 24 q^{91} + 4 q^{92} - 4 q^{94} - 26 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 - 2 * q^11 - 4 * q^14 - 2 * q^16 + 4 * q^17 - 12 * q^19 - 2 * q^22 + 4 * q^23 + 8 * q^28 - 12 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^34 + 32 * q^37 + 6 * q^38 - 2 * q^41 - 10 * q^43 + 4 * q^44 - 8 * q^46 - 4 * q^47 - 6 * q^49 - 24 * q^53 - 4 * q^56 - 12 * q^58 + 2 * q^59 - 4 * q^61 + 16 * q^62 + 4 * q^64 - 14 * q^67 - 2 * q^68 + 20 * q^73 - 16 * q^74 + 6 * q^76 + 8 * q^77 + 4 * q^82 - 8 * q^83 - 10 * q^86 - 2 * q^88 - 32 * q^89 - 24 * q^91 + 4 * q^92 - 4 * q^94 - 26 * q^97 + 12 * q^98

Introduction

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