LMFDB - Embedded newform 720.2.q.k.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(241,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("720.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.q (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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.1
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	720.481
Dual form			720.2.q.k.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62241 + 0.606458i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.05042 + 3.55142i) q^{7} +(2.26442 - 1.96784i) q^{9} +O(q^{10})$	\(q+(-1.62241 + 0.606458i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.05042 + 3.55142i) q^{7} +(2.26442 - 1.96784i) q^{9} +(-1.90841 - 3.30545i) q^{11} +(-2.90841 + 5.03751i) q^{13} +(-0.285997 + 1.70828i) q^{15} +3.81681 q^{17} +1.81681 q^{19} +(-5.48040 - 4.51837i) q^{21} +(1.05042 - 1.81937i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.48040 + 4.56592i) q^{27} +(3.60083 + 6.23682i) q^{29} +(-0.908405 + 1.57340i) q^{31} +(5.10083 + 4.20543i) q^{33} +4.10083 q^{35} -6.01847 q^{37} +(1.66359 - 9.93672i) q^{39} +(-5.50924 + 9.54228i) q^{41} +(2.90841 + 5.03751i) q^{43} +(-0.571993 - 2.94497i) q^{45} +(5.95882 + 10.3210i) q^{47} +(-4.90841 + 8.50161i) q^{49} +(-6.19243 + 2.31473i) q^{51} +4.20166 q^{53} -3.81681 q^{55} +(-2.94761 + 1.10182i) q^{57} +(-2.10083 + 3.63875i) q^{59} +(1.50924 + 2.61407i) q^{61} +(11.6316 + 4.00701i) q^{63} +(2.90841 + 5.03751i) q^{65} +(1.85799 - 3.21813i) q^{67} +(-0.600830 + 3.58880i) q^{69} +2.01847 q^{71} +8.00000 q^{73} +(1.33641 + 1.10182i) q^{75} +(7.82605 - 13.5551i) q^{77} +(1.00000 + 1.73205i) q^{79} +(1.25518 - 8.91204i) q^{81} +(-1.94958 - 3.37678i) q^{83} +(1.90841 - 3.30545i) q^{85} +(-9.62438 - 7.93492i) q^{87} -3.00000 q^{89} -23.8538 q^{91} +(0.519602 - 3.10361i) q^{93} +(0.908405 - 1.57340i) q^{95} +(-6.10083 - 10.5669i) q^{97} +(-10.8260 - 3.72949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9}+O(q^{10}) $ 6 * q + q^3 + 3 * q^5 + 3 * q^7 + 5 * q^9	$ 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9} - 6 q^{13} - q^{15} - 12 q^{19} - 20 q^{21} - 3 q^{23} - 3 q^{25} - 2 q^{27} + 3 q^{29} + 6 q^{31} + 12 q^{33} + 6 q^{35} + 24 q^{37} + 20 q^{39} - 3 q^{41} + 6 q^{43} - 2 q^{45} + 15 q^{47} - 18 q^{49} - 30 q^{51} - 12 q^{53} - 32 q^{57} + 6 q^{59} - 21 q^{61} + 29 q^{63} + 6 q^{65} + 9 q^{67} + 15 q^{69} - 48 q^{71} + 48 q^{73} - 2 q^{75} - 6 q^{77} + 6 q^{79} + 29 q^{81} - 21 q^{83} - 42 q^{87} - 18 q^{89} + 16 q^{93} - 6 q^{95} - 18 q^{97} - 12 q^{99}+O(q^{100}) $ 6 * q + q^3 + 3 * q^5 + 3 * q^7 + 5 * q^9 - 6 * q^13 - q^15 - 12 * q^19 - 20 * q^21 - 3 * q^23 - 3 * q^25 - 2 * q^27 + 3 * q^29 + 6 * q^31 + 12 * q^33 + 6 * q^35 + 24 * q^37 + 20 * q^39 - 3 * q^41 + 6 * q^43 - 2 * q^45 + 15 * q^47 - 18 * q^49 - 30 * q^51 - 12 * q^53 - 32 * q^57 + 6 * q^59 - 21 * q^61 + 29 * q^63 + 6 * q^65 + 9 * q^67 + 15 * q^69 - 48 * q^71 + 48 * q^73 - 2 * q^75 - 6 * q^77 + 6 * q^79 + 29 * q^81 - 21 * q^83 - 42 * q^87 - 18 * q^89 + 16 * q^93 - 6 * q^95 - 18 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.62241	+	0.606458i	−0.936698	+	0.350138i
$3$	−1.62241	+	0.606458i	−0.936698	+	0.350138i
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.05042	+	3.55142i	0.774984	+	1.34231i	0.934803	+	0.355166i	$0.115576\pi$
$7$	2.05042	+	3.55142i	0.774984	+	1.34231i	−0.159819	+	0.987146i	$0.551091\pi$
$8$		0			0
$9$	2.26442	−	1.96784i	0.754806	−	0.655948i
$10$		0			0
$11$	−1.90841	−	3.30545i	−0.575406	−	0.996632i	−0.995997	−	0.0893820i	$-0.971511\pi$
$11$	−1.90841	−	3.30545i	−0.575406	−	0.996632i	0.420592	−	0.907250i	$-0.361823\pi$
$12$		0			0
$13$	−2.90841	+	5.03751i	−0.806646	+	1.39715i	0.108527	+	0.994093i	$0.465386\pi$
$13$	−2.90841	+	5.03751i	−0.806646	+	1.39715i	−0.915174	+	0.403059i	$0.867947\pi$
$14$		0			0
$15$	−0.285997	+	1.70828i	−0.0738440	+	0.441075i
$16$		0			0
$17$	3.81681			0.925712			0.462856	−	0.886433i	$-0.346825\pi$
$17$	3.81681			0.925712			0.462856	+	0.886433i	$0.346825\pi$
$18$		0			0
$19$	1.81681			0.416805			0.208402	−	0.978043i	$-0.433174\pi$
$19$	1.81681			0.416805			0.208402	+	0.978043i	$0.433174\pi$
$20$		0			0
$21$	−5.48040	−	4.51837i	−1.19592	−	0.985989i
$22$		0			0
$23$	1.05042	−	1.81937i	0.219027	−	0.379365i	−0.735484	−	0.677542i	$-0.763045\pi$
$23$	1.05042	−	1.81937i	0.219027	−	0.379365i	0.954511	+	0.298177i	$0.0963785\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−2.48040	+	4.56592i	−0.477353	+	0.878712i
$28$		0			0
$29$	3.60083	+	6.23682i	0.668657	+	1.15815i	0.978280	+	0.207289i	$0.0664640\pi$
$29$	3.60083	+	6.23682i	0.668657	+	1.15815i	−0.309622	+	0.950860i	$0.600203\pi$
$30$		0			0
$31$	−0.908405	+	1.57340i	−0.163154	+	0.282592i	−0.935998	−	0.352004i	$-0.885500\pi$
$31$	−0.908405	+	1.57340i	−0.163154	+	0.282592i	0.772844	+	0.634596i	$0.218834\pi$
$32$		0			0
$33$	5.10083	+	4.20543i	0.887941	+	0.732072i
$34$		0			0
$35$	4.10083			0.693167
$36$		0			0
$37$	−6.01847			−0.989431			−0.494715	−	0.869055i	$-0.664728\pi$
$37$	−6.01847			−0.989431			−0.494715	+	0.869055i	$0.664728\pi$
$38$		0			0
$39$	1.66359	−	9.93672i	0.266387	−	1.59115i
$40$		0			0
$41$	−5.50924	+	9.54228i	−0.860398	+	1.49025i	0.0111471	+	0.999938i	$0.496452\pi$
$41$	−5.50924	+	9.54228i	−0.860398	+	1.49025i	−0.871545	+	0.490315i	$0.836882\pi$
$42$		0			0
$43$	2.90841	+	5.03751i	0.443528	+	0.768212i	0.997948	−	0.0640242i	$-0.0203935\pi$
$43$	2.90841	+	5.03751i	0.443528	+	0.768212i	−0.554421	+	0.832237i	$0.687060\pi$
$44$		0			0
$45$	−0.571993	−	2.94497i	−0.0852677	−	0.439010i
$46$		0			0
$47$	5.95882	+	10.3210i	0.869183	+	1.50547i	0.862833	+	0.505490i	$0.168688\pi$
$47$	5.95882	+	10.3210i	0.869183	+	1.50547i	0.00635068	+	0.999980i	$0.497979\pi$
$48$		0			0
$49$	−4.90841	+	8.50161i	−0.701201	+	1.21452i
$50$		0			0
$51$	−6.19243	+	2.31473i	−0.867113	+	0.324127i
$52$		0			0
$53$	4.20166			0.577143			0.288571	−	0.957458i	$-0.406820\pi$
$53$	4.20166			0.577143			0.288571	+	0.957458i	$0.406820\pi$
$54$		0			0
$55$	−3.81681			−0.514659
$56$		0			0
$57$	−2.94761	+	1.10182i	−0.390420	+	0.145939i
$58$		0			0
$59$	−2.10083	+	3.63875i	−0.273505	+	0.473724i	−0.969757	−	0.244073i	$-0.921516\pi$
$59$	−2.10083	+	3.63875i	−0.273505	+	0.473724i	0.696252	+	0.717797i	$0.254850\pi$
$60$		0			0
$61$	1.50924	+	2.61407i	0.193238	+	0.334698i	0.946321	−	0.323227i	$-0.104768\pi$
$61$	1.50924	+	2.61407i	0.193238	+	0.334698i	−0.753084	+	0.657925i	$0.771434\pi$
$62$		0			0
$63$	11.6316	+	4.00701i	1.46545	+	0.504836i
$64$		0			0
$65$	2.90841	+	5.03751i	0.360743	+	0.624826i
$66$		0			0
$67$	1.85799	−	3.21813i	0.226990	−	0.393158i	−0.729925	−	0.683527i	$-0.760445\pi$
$67$	1.85799	−	3.21813i	0.226990	−	0.393158i	0.956914	+	0.290370i	$0.0937783\pi$
$68$		0			0
$69$	−0.600830	+	3.58880i	−0.0723315	+	0.432040i
$70$		0			0
$71$	2.01847			0.239548			0.119774	−	0.992801i	$-0.461783\pi$
$71$	2.01847			0.239548			0.119774	+	0.992801i	$0.461783\pi$
$72$		0			0
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$		0			0
$75$	1.33641	+	1.10182i	0.154316	+	0.127227i
$76$		0			0
$77$	7.82605	−	13.5551i	0.891861	−	1.54475i
$78$		0			0
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	0.916781	−	0.399390i	$-0.130778\pi$
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	−0.804272	+	0.594261i	$0.797445\pi$
$80$		0			0
$81$	1.25518	−	8.91204i	0.139465	−	0.990227i
$82$		0			0
$83$	−1.94958	−	3.37678i	−0.213995	−	0.370650i	0.738966	−	0.673742i	$-0.235314\pi$
$83$	−1.94958	−	3.37678i	−0.213995	−	0.370650i	−0.952961	+	0.303093i	$0.901981\pi$
$84$		0			0
$85$	1.90841	−	3.30545i	0.206996	−	0.358527i
$86$		0			0
$87$	−9.62438	−	7.93492i	−1.03184	−	0.850713i
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	−23.8538			−2.50055
$92$		0			0
$93$	0.519602	−	3.10361i	0.0538802	−	0.321830i
$94$		0			0
$95$	0.908405	−	1.57340i	0.0932004	−	0.161428i
$96$		0			0
$97$	−6.10083	−	10.5669i	−0.619445	−	1.07291i	−0.989587	−	0.143936i	$-0.954024\pi$
$97$	−6.10083	−	10.5669i	−0.619445	−	1.07291i	0.370142	−	0.928975i	$-0.379309\pi$
$98$		0			0
$99$	−10.8260	−	3.72949i	−1.08806	−	0.374828i
$100$		0			0
$101$	−8.10083	−	14.0310i	−0.806063	−	1.39614i	−0.915571	−	0.402156i	$-0.868261\pi$
$101$	−8.10083	−	14.0310i	−0.806063	−	1.39614i	0.109508	−	0.993986i	$-0.465072\pi$
$102$		0			0
$103$	−4.72522	+	8.18431i	−0.465589	+	0.806424i	−0.999228	−	0.0392883i	$-0.987491\pi$
$103$	−4.72522	+	8.18431i	−0.465589	+	0.806424i	0.533639	+	0.845713i	$0.320824\pi$
$104$		0			0
$105$	−6.65322	+	2.48698i	−0.649288	+	0.242704i
$106$		0			0
$107$	−4.66887			−0.451357			−0.225678	−	0.974202i	$-0.572460\pi$
$107$	−4.66887			−0.451357			−0.225678	+	0.974202i	$0.572460\pi$
$108$		0			0
$109$	8.81681			0.844497			0.422249	−	0.906480i	$-0.361241\pi$
$109$	8.81681			0.844497			0.422249	+	0.906480i	$0.361241\pi$
$110$		0			0
$111$	9.76442	−	3.64995i	0.926798	−	0.346438i
$112$		0			0
$113$	5.10083	−	8.83490i	0.479846	−	0.831117i	−0.519887	−	0.854235i	$-0.674026\pi$
$113$	5.10083	−	8.83490i	0.479846	−	0.831117i	0.999733	+	0.0231178i	$0.00735928\pi$
$114$		0			0
$115$	−1.05042	−	1.81937i	−0.0979517	−	0.169657i
$116$		0			0
$117$	3.32718	+	17.1303i	0.307598	+	1.58370i
$118$		0			0
$119$	7.82605	+	13.5551i	0.717412	+	1.24259i
$120$		0			0
$121$	−1.78402	+	3.09001i	−0.162184	+	0.280910i
$122$		0			0
$123$	3.15125	−	18.8226i	0.284138	−	1.69718i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.284020			−0.0252027			−0.0126014	−	0.999921i	$-0.504011\pi$
$127$	−0.284020			−0.0252027			−0.0126014	+	0.999921i	$0.504011\pi$
$128$		0			0
$129$	−7.77365	−	6.40907i	−0.684432	−	0.564287i
$130$		0			0
$131$	10.6336	−	18.4180i	0.929064	−	1.60919i	0.144172	−	0.989553i	$-0.453948\pi$
$131$	10.6336	−	18.4180i	0.929064	−	1.60919i	0.784892	−	0.619633i	$-0.212719\pi$
$132$		0			0
$133$	3.72522	+	6.45226i	0.323017	+	0.559482i
$134$		0			0
$135$	2.71400	+	4.43105i	0.233584	+	0.381364i
$136$		0			0
$137$	1.28402	+	2.22399i	0.109701	+	0.190008i	0.915649	−	0.401978i	$-0.131677\pi$
$137$	1.28402	+	2.22399i	0.109701	+	0.190008i	−0.805948	+	0.591986i	$0.798344\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	−15.9269	−	13.1311i	−1.34128	−	1.10584i
$142$		0			0
$143$	22.2017			1.85660
$144$		0			0
$145$	7.20166			0.598065
$146$		0			0
$147$	2.80757	−	16.7698i	0.231565	−	1.38315i
$148$		0			0
$149$	7.22522	−	12.5144i	0.591913	−	1.02522i	−0.402062	−	0.915612i	$-0.631706\pi$
$149$	7.22522	−	12.5144i	0.591913	−	1.02522i	0.993975	−	0.109610i	$-0.0349603\pi$
$150$		0			0
$151$	−4.29326	−	7.43614i	−0.349380	−	0.605144i	0.636759	−	0.771063i	$-0.280274\pi$
$151$	−4.29326	−	7.43614i	−0.349380	−	0.605144i	−0.986139	+	0.165918i	$0.946941\pi$
$152$		0			0
$153$	8.64286	−	7.51089i	0.698733	−	0.607219i
$154$		0			0
$155$	0.908405	+	1.57340i	0.0729649	+	0.126379i
$156$		0			0
$157$	−9.91764	+	17.1779i	−0.791514	+	1.37094i	0.133515	+	0.991047i	$0.457373\pi$
$157$	−9.91764	+	17.1779i	−0.791514	+	1.37094i	−0.925029	+	0.379896i	$0.875960\pi$
$158$		0			0
$159$	−6.81681	+	2.54813i	−0.540608	+	0.202080i
$160$		0			0
$161$	8.61515			0.678969
$162$		0			0
$163$	13.8168			1.08222			0.541108	−	0.840953i	$-0.318005\pi$
$163$	13.8168			1.08222			0.541108	+	0.840953i	$0.318005\pi$
$164$		0			0
$165$	6.19243	−	2.31473i	0.482080	−	0.180202i
$166$		0			0
$167$	3.04118	−	5.26748i	0.235334	−	0.407610i	−0.724036	−	0.689762i	$-0.757715\pi$
$167$	3.04118	−	5.26748i	0.235334	−	0.407610i	0.959370	+	0.282153i	$0.0910484\pi$
$168$		0			0
$169$	−10.4176	−	18.0439i	−0.801357	−	1.38799i
$170$		0			0
$171$	4.11402	−	3.57520i	0.314607	−	0.273402i
$172$		0			0
$173$	2.18319	+	3.78140i	0.165985	+	0.287494i	0.937005	−	0.349317i	$-0.113586\pi$
$173$	2.18319	+	3.78140i	0.165985	+	0.287494i	−0.771020	+	0.636811i	$0.780253\pi$
$174$		0			0
$175$	2.05042	−	3.55142i	0.154997	−	0.268462i
$176$		0			0
$177$	1.20166	−	7.17760i	0.0903224	−	0.539501i
$178$		0			0
$179$	−6.38485			−0.477226			−0.238613	−	0.971115i	$-0.576693\pi$
$179$	−6.38485			−0.477226			−0.238613	+	0.971115i	$0.576693\pi$
$180$		0			0
$181$	10.0656			0.748169			0.374084	−	0.927395i	$-0.377957\pi$
$181$	10.0656			0.748169			0.374084	+	0.927395i	$0.377957\pi$
$182$		0			0
$183$	−4.03392	−	3.32581i	−0.298196	−	0.245851i
$184$		0			0
$185$	−3.00924	+	5.21215i	−0.221243	+	0.383205i
$186$		0			0
$187$	−7.28402	−	12.6163i	−0.532660	−	0.922595i
$188$		0			0
$189$	−21.3014	+	0.553087i	−1.54945	+	0.0402311i
$190$		0			0
$191$	−7.82605	−	13.5551i	−0.566273	−	0.980813i	−0.996930	−	0.0782977i	$-0.975052\pi$
$191$	−7.82605	−	13.5551i	−0.566273	−	0.980813i	0.430657	−	0.902516i	$-0.358282\pi$
$192$		0			0
$193$	−6.72522	+	11.6484i	−0.484092	+	0.838471i	−0.999833	−	0.0182730i	$-0.994183\pi$
$193$	−6.72522	+	11.6484i	−0.484092	+	0.838471i	0.515741	+	0.856744i	$0.327517\pi$
$194$		0			0
$195$	−7.77365	−	6.40907i	−0.556683	−	0.458963i
$196$		0			0
$197$	−1.79834			−0.128126			−0.0640632	−	0.997946i	$-0.520406\pi$
$197$	−1.79834			−0.128126			−0.0640632	+	0.997946i	$0.520406\pi$
$198$		0			0
$199$	22.2201			1.57514			0.787572	−	0.616223i	$-0.211338\pi$
$199$	22.2201			1.57514			0.787572	+	0.616223i	$0.211338\pi$
$200$		0			0
$201$	−1.06276	+	6.34792i	−0.0749611	+	0.447748i
$202$		0			0
$203$	−14.7664	+	25.5761i	−1.03640	+	1.79509i
$204$		0			0
$205$	5.50924	+	9.54228i	0.384782	+	0.666461i
$206$		0			0
$207$	−1.20166	−	6.18687i	−0.0835212	−	0.430017i
$208$		0			0
$209$	−3.46721	−	6.00538i	−0.239832	−	0.415401i
$210$		0			0
$211$	−14.1101	+	24.4394i	−0.971377	+	1.68247i	−0.279970	+	0.960009i	$0.590325\pi$
$211$	−14.1101	+	24.4394i	−0.971377	+	1.68247i	−0.691407	+	0.722466i	$0.743009\pi$
$212$		0			0
$213$	−3.27478	+	1.22412i	−0.224385	+	0.0838751i
$214$		0			0
$215$	5.81681			0.396703
$216$		0			0
$217$	−7.45043			−0.505768
$218$		0			0
$219$	−12.9793	+	4.85166i	−0.877058	+	0.327845i
$220$		0			0
$221$	−11.1008	+	19.2272i	−0.746723	+	1.29336i
$222$		0			0
$223$	0.958820	+	1.66073i	0.0642074	+	0.111210i	0.896342	−	0.443363i	$-0.146215\pi$
$223$	0.958820	+	1.66073i	0.0642074	+	0.111210i	−0.832135	+	0.554573i	$0.812881\pi$
$224$		0			0
$225$	−2.83641	−	0.977122i	−0.189094	−	0.0651415i
$226$		0			0
$227$	−4.00924	−	6.94420i	−0.266102	−	0.460903i	0.701750	−	0.712424i	$-0.252403\pi$
$227$	−4.00924	−	6.94420i	−0.266102	−	0.460903i	−0.967852	+	0.251521i	$0.919069\pi$
$228$		0			0
$229$	9.41764	−	16.3118i	0.622335	−	1.07792i	−0.366715	−	0.930334i	$-0.619517\pi$
$229$	9.41764	−	16.3118i	0.622335	−	1.07792i	0.989050	−	0.147583i	$-0.0471493\pi$
$230$		0			0
$231$	−4.47645	+	26.7381i	−0.294528	+	1.75924i
$232$		0			0
$233$	−14.0185			−0.918381			−0.459190	−	0.888338i	$-0.651860\pi$
$233$	−14.0185			−0.918381			−0.459190	+	0.888338i	$0.651860\pi$
$234$		0			0
$235$	11.9176			0.777421
$236$		0			0
$237$	−2.67282	−	2.20364i	−0.173619	−	0.143142i
$238$		0			0
$239$	5.10083	−	8.83490i	0.329945	−	0.571482i	−0.652555	−	0.757741i	$-0.726303\pi$
$239$	5.10083	−	8.83490i	0.329945	−	0.571482i	0.982501	+	0.186259i	$0.0596364\pi$
$240$		0			0
$241$	−8.61007	−	14.9131i	−0.554623	−	0.960635i	−0.997933	−	0.0642669i	$-0.979529\pi$
$241$	−8.61007	−	14.9131i	−0.554623	−	0.960635i	0.443310	−	0.896369i	$-0.353804\pi$
$242$		0			0
$243$	3.36836	+	15.2202i	0.216080	+	0.976376i
$244$		0			0
$245$	4.90841	+	8.50161i	0.313587	+	0.543148i
$246$		0			0
$247$	−5.28402	+	9.15219i	−0.336214	+	0.582340i
$248$		0			0
$249$	5.21090	+	4.29618i	0.330227	+	0.272259i
$250$		0			0
$251$	0.384851			0.0242916			0.0121458	−	0.999926i	$-0.496134\pi$
$251$	0.384851			0.0242916			0.0121458	+	0.999926i	$0.496134\pi$
$252$		0			0
$253$	−8.01847			−0.504117
$254$		0			0
$255$	−1.09159	+	6.52016i	−0.0683583	+	0.408309i
$256$		0			0
$257$	−4.63362	+	8.02567i	−0.289037	+	0.500627i	−0.973580	−	0.228345i	$-0.926668\pi$
$257$	−4.63362	+	8.02567i	−0.289037	+	0.500627i	0.684543	+	0.728973i	$0.260002\pi$
$258$		0			0
$259$	−12.3404	−	21.3741i	−0.766793	−	1.32812i
$260$		0			0
$261$	20.4269	+	7.03690i	1.26439	+	0.435573i
$262$		0			0
$263$	−12.9269	−	22.3900i	−0.797105	−	1.38063i	−0.921494	−	0.388393i	$-0.873030\pi$
$263$	−12.9269	−	22.3900i	−0.797105	−	1.38063i	0.124388	−	0.992234i	$-0.460303\pi$
$264$		0			0
$265$	2.10083	−	3.63875i	0.129053	−	0.223526i
$266$		0			0
$267$	4.86723	−	1.81937i	0.297869	−	0.111344i
$268$		0			0
$269$	28.0841			1.71231			0.856157	−	0.516715i	$-0.172845\pi$
$269$	28.0841			1.71231			0.856157	+	0.516715i	$0.172845\pi$
$270$		0			0
$271$	21.4504			1.30302			0.651510	−	0.758640i	$-0.274136\pi$
$271$	21.4504			1.30302			0.651510	+	0.758640i	$0.274136\pi$
$272$		0			0
$273$	38.7005	−	14.4663i	2.34226	−	0.875540i
$274$		0			0
$275$	−1.90841	+	3.30545i	−0.115081	+	0.199326i
$276$		0			0
$277$	3.90841	+	6.76956i	0.234833	+	0.406743i	0.959224	−	0.282646i	$-0.0912122\pi$
$277$	3.90841	+	6.76956i	0.234833	+	0.406743i	−0.724391	+	0.689389i	$0.757879\pi$
$278$		0			0
$279$	1.03920	+	5.35044i	0.0622155	+	0.320323i
$280$		0			0
$281$	−2.59159	−	4.48877i	−0.154602	−	0.267778i	0.778312	−	0.627877i	$-0.216076\pi$
$281$	−2.59159	−	4.48877i	−0.154602	−	0.267778i	−0.932914	+	0.360100i	$0.882743\pi$
$282$		0			0
$283$	−9.05042	+	15.6758i	−0.537991	+	0.931828i	0.461021	+	0.887389i	$0.347483\pi$
$283$	−9.05042	+	15.6758i	−0.537991	+	0.931828i	−0.999012	+	0.0444390i	$0.985850\pi$
$284$		0			0
$285$	−0.519602	+	3.10361i	−0.0307785	+	0.183842i
$286$		0			0
$287$	−45.1849			−2.66718
$288$		0			0
$289$	−2.43196			−0.143056
$290$		0			0
$291$	16.3064	+	13.4440i	0.955901	+	0.788102i
$292$		0			0
$293$	8.29326	−	14.3643i	0.484497	−	0.839174i	−0.515344	−	0.856983i	$-0.672336\pi$
$293$	8.29326	−	14.3643i	0.484497	−	0.839174i	0.999841	+	0.0178096i	$0.00566926\pi$
$294$		0			0
$295$	2.10083	+	3.63875i	0.122315	+	0.211856i
$296$		0			0
$297$	19.8260	−	0.514780i	1.15042	−	0.0298706i
$298$		0			0
$299$	6.11007	+	10.5829i	0.353354	+	0.612027i
$300$		0			0
$301$	−11.9269	+	20.6580i	−0.687454	+	1.19070i
$302$		0			0
$303$	21.6521	+	17.8513i	1.24388	+	1.02553i
$304$		0			0
$305$	3.01847			0.172837
$306$		0			0
$307$	22.3025			1.27287			0.636435	−	0.771330i	$-0.280408\pi$
$307$	22.3025			1.27287			0.636435	+	0.771330i	$0.280408\pi$
$308$		0			0
$309$	2.70279	−	16.1439i	0.153756	−	0.918397i
$310$		0			0
$311$	−13.8260	+	23.9474i	−0.784003	+	1.35793i	0.145590	+	0.989345i	$0.453492\pi$
$311$	−13.8260	+	23.9474i	−0.784003	+	1.35793i	−0.929593	+	0.368588i	$0.879841\pi$
$312$		0			0
$313$	−5.82605	−	10.0910i	−0.329308	−	0.570377i	0.653067	−	0.757300i	$-0.273482\pi$
$313$	−5.82605	−	10.0910i	−0.329308	−	0.570377i	−0.982375	+	0.186923i	$0.940149\pi$
$314$		0			0
$315$	9.28600	−	8.06979i	0.523207	−	0.454681i
$316$		0			0
$317$	−5.80757	−	10.0590i	−0.326186	−	0.564971i	0.655566	−	0.755138i	$-0.272430\pi$
$317$	−5.80757	−	10.0590i	−0.326186	−	0.564971i	−0.981752	+	0.190168i	$0.939097\pi$
$318$		0			0
$319$	13.7437	−	23.8048i	0.769499	−	1.33281i
$320$		0			0
$321$	7.57482	−	2.83147i	0.422785	−	0.158037i
$322$		0			0
$323$	6.93442			0.385841
$324$		0			0
$325$	5.81681			0.322659
$326$		0			0
$327$	−14.3045	+	5.34702i	−0.791039	+	0.295691i
$328$		0			0
$329$	−24.4361	+	42.3246i	−1.34721	+	2.33343i
$330$		0			0
$331$	−9.71598	−	16.8286i	−0.534039	−	0.924982i	−0.999209	−	0.0397609i	$-0.987340\pi$
$331$	−9.71598	−	16.8286i	−0.534039	−	0.924982i	0.465171	−	0.885221i	$-0.345993\pi$
$332$		0			0
$333$	−13.6283	+	11.8434i	−0.746828	+	0.649015i
$334$		0			0
$335$	−1.85799	−	3.21813i	−0.101513	−	0.175825i
$336$		0			0
$337$	4.91764	−	8.51760i	0.267881	−	0.463983i	−0.700433	−	0.713718i	$-0.747010\pi$
$337$	4.91764	−	8.51760i	0.267881	−	0.463983i	0.968314	+	0.249734i	$0.0803433\pi$
$338$		0			0
$339$	−2.91764	+	17.4272i	−0.158464	+	0.946518i
$340$		0			0
$341$	6.93442			0.375520
$342$		0			0
$343$	−11.5513			−0.623709
$344$		0			0
$345$	2.80757	+	2.31473i	0.151155	+	0.124621i
$346$		0			0
$347$	11.2933	−	19.5605i	0.606254	−	1.05006i	−0.385598	−	0.922667i	$-0.626005\pi$
$347$	11.2933	−	19.5605i	0.606254	−	1.05006i	0.991852	−	0.127395i	$-0.0406617\pi$
$348$		0			0
$349$	−2.93196	−	5.07830i	−0.156944	−	0.271835i	0.776821	−	0.629721i	$-0.216831\pi$
$349$	−2.93196	−	5.07830i	−0.156944	−	0.271835i	−0.933765	+	0.357886i	$0.883498\pi$
$350$		0			0
$351$	−15.7868	−	25.7746i	−0.842639	−	1.37574i
$352$		0			0
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$		0			0
$355$	1.00924	−	1.74805i	0.0535647	−	0.0927767i
$356$		0			0
$357$	−20.9176	−	17.2458i	−1.10708	−	0.912742i
$358$		0			0
$359$	19.2488			1.01591			0.507956	−	0.861383i	$-0.330401\pi$
$359$	19.2488			1.01591			0.507956	+	0.861383i	$0.330401\pi$
$360$		0			0
$361$	−15.6992			−0.826274
$362$		0			0
$363$	1.02045	−	6.09520i	0.0535596	−	0.319915i
$364$		0			0
$365$	4.00000	−	6.92820i	0.209370	−	0.362639i
$366$		0			0
$367$	9.29326	+	16.0964i	0.485104	+	0.840225i	0.999854	−	0.0171158i	$-0.00544841\pi$
$367$	9.29326	+	16.0964i	0.485104	+	0.840225i	−0.514750	+	0.857341i	$0.672115\pi$
$368$		0			0
$369$	6.30249	+	32.4490i	0.328095	+	1.68923i
$370$		0			0
$371$	8.61515	+	14.9219i	0.447276	+	0.774705i
$372$		0			0
$373$	−0.100830	+	0.174643i	−0.00522080	+	0.00904269i	−0.868624	−	0.495472i	$-0.834995\pi$
$373$	−0.100830	+	0.174643i	−0.00522080	+	0.00904269i	0.863403	+	0.504515i	$0.168329\pi$
$374$		0			0
$375$	1.62241	−	0.606458i	0.0837808	−	0.0313173i
$376$		0			0
$377$	−41.8907			−2.15748
$378$		0			0
$379$	2.36638			0.121553			0.0607764	−	0.998151i	$-0.480642\pi$
$379$	2.36638			0.121553			0.0607764	+	0.998151i	$0.480642\pi$
$380$		0			0
$381$	0.460797	−	0.172246i	0.0236073	−	0.00882444i
$382$		0			0
$383$	12.9269	−	22.3900i	0.660533	−	1.14408i	−0.319943	−	0.947437i	$-0.603664\pi$
$383$	12.9269	−	22.3900i	0.660533	−	1.14408i	0.980476	−	0.196639i	$-0.0630028\pi$
$384$		0			0
$385$	−7.82605	−	13.5551i	−0.398852	−	0.690832i
$386$		0			0
$387$	16.4989	+	5.68373i	0.838685	+	0.288920i
$388$		0			0
$389$	8.89409	+	15.4050i	0.450948	+	0.781065i	0.998445	−	0.0557426i	$-0.0177526\pi$
$389$	8.89409	+	15.4050i	0.450948	+	0.781065i	−0.547497	+	0.836808i	$0.684419\pi$
$390$		0			0
$391$	4.00924	−	6.94420i	0.202756	−	0.351183i
$392$		0			0
$393$	−6.08236	+	36.3303i	−0.306814	+	1.83262i
$394$		0			0
$395$	2.00000			0.100631
$396$		0			0
$397$	13.6706			0.686106			0.343053	−	0.939316i	$-0.388539\pi$
$397$	13.6706			0.686106			0.343053	+	0.939316i	$0.388539\pi$
$398$		0			0
$399$	−9.95684	−	8.20902i	−0.498466	−	0.410965i
$400$		0			0
$401$	3.73445	−	6.46826i	0.186490	−	0.323009i	−0.757588	−	0.652733i	$-0.773622\pi$
$401$	3.73445	−	6.46826i	0.186490	−	0.323009i	0.944077	+	0.329724i	$0.106956\pi$
$402$		0			0
$403$	−5.28402	−	9.15219i	−0.263216	−	0.455903i
$404$		0			0
$405$	−7.09046	−	5.54304i	−0.352328	−	0.275436i
$406$		0			0
$407$	11.4857	+	19.8938i	0.569324	+	0.986098i
$408$		0			0
$409$	14.6521	−	25.3782i	0.724499	−	1.25487i	−0.234680	−	0.972073i	$-0.575404\pi$
$409$	14.6521	−	25.3782i	0.724499	−	1.25487i	0.959180	−	0.282797i	$-0.0912623\pi$
$410$		0			0
$411$	−3.43196	−	2.82951i	−0.169286	−	0.139570i
$412$		0			0
$413$	−17.2303			−0.847848
$414$		0			0
$415$	−3.89917			−0.191403
$416$		0			0
$417$	1.14399	−	6.83310i	0.0560213	−	0.334618i
$418$		0			0
$419$	−18.1101	+	31.3676i	−0.884735	+	1.53241i	−0.0387171	+	0.999250i	$0.512327\pi$
$419$	−18.1101	+	31.3676i	−0.884735	+	1.53241i	−0.846018	+	0.533155i	$0.821006\pi$
$420$		0			0
$421$	13.0185	+	22.5487i	0.634481	+	1.09895i	0.986625	+	0.163008i	$0.0521196\pi$
$421$	13.0185	+	22.5487i	0.634481	+	1.09895i	−0.352143	+	0.935946i	$0.614547\pi$
$422$		0			0
$423$	33.8033	+	11.6450i	1.64357	+	0.566199i
$424$		0			0
$425$	−1.90841	−	3.30545i	−0.0925712	−	0.160338i
$426$		0			0
$427$	−6.18912	+	10.7199i	−0.299512	+	0.518771i
$428$		0			0
$429$	−36.0202	+	13.4644i	−1.73907	+	0.650066i
$430$		0			0
$431$	−22.0369			−1.06148			−0.530741	−	0.847534i	$-0.678086\pi$
$431$	−22.0369			−1.06148			−0.530741	+	0.847534i	$0.678086\pi$
$432$		0			0
$433$	−0.183190			−0.00880354			−0.00440177	−	0.999990i	$-0.501401\pi$
$433$	−0.183190			−0.00880354			−0.00440177	+	0.999990i	$0.501401\pi$
$434$		0			0
$435$	−11.6840	+	4.36750i	−0.560207	+	0.209406i
$436$		0			0
$437$	1.90841	−	3.30545i	0.0912914	−	0.158121i
$438$		0			0
$439$	−11.3025	−	19.5765i	−0.539438	−	0.934335i	−0.998934	−	0.0461549i	$-0.985303\pi$
$439$	−11.3025	−	19.5765i	−0.539438	−	0.934335i	0.459496	−	0.888180i	$-0.348030\pi$
$440$		0			0
$441$	5.61515	+	28.9102i	0.267388	+	1.37667i
$442$		0			0
$443$	−14.9588	−	25.9094i	−0.710715	−	1.23099i	−0.964589	−	0.263757i	$-0.915038\pi$
$443$	−14.9588	−	25.9094i	−0.710715	−	1.23099i	0.253874	−	0.967237i	$-0.418295\pi$
$444$		0			0
$445$	−1.50000	+	2.59808i	−0.0711068	+	0.123161i
$446$		0			0
$447$	−4.13277	+	24.6853i	−0.195474	+	1.16758i
$448$		0			0
$449$	12.1647			0.574089			0.287044	−	0.957917i	$-0.407327\pi$
$449$	12.1647			0.574089			0.287044	+	0.957917i	$0.407327\pi$
$450$		0			0
$451$	42.0554			1.98031
$452$		0			0
$453$	11.4751	+	9.46077i	0.539148	+	0.444506i
$454$		0			0
$455$	−11.9269	+	20.6580i	−0.559141	+	0.968460i
$456$		0			0
$457$	17.0277	+	29.4929i	0.796523	+	1.37962i	0.921868	+	0.387504i	$0.126663\pi$
$457$	17.0277	+	29.4929i	0.796523	+	1.37962i	−0.125345	+	0.992113i	$0.540004\pi$
$458$		0			0
$459$	−9.46721	+	17.4272i	−0.441892	+	0.813434i
$460$		0			0
$461$	−19.2529	−	33.3470i	−0.896698	−	1.55313i	−0.831689	−	0.555242i	$-0.812626\pi$
$461$	−19.2529	−	33.3470i	−0.896698	−	1.55313i	−0.0650090	−	0.997885i	$-0.520708\pi$
$462$		0			0
$463$	−0.00923555	+	0.0159964i	−0.000429212	+	0.000743418i	−0.866240	−	0.499628i	$-0.833470\pi$
$463$	−0.00923555	+	0.0159964i	−0.000429212	+	0.000743418i	0.865811	+	0.500372i	$0.166803\pi$
$464$		0			0
$465$	−2.42801	−	2.00179i	−0.112596	−	0.0928310i
$466$		0			0
$467$	10.5865			0.489885			0.244943	−	0.969538i	$-0.421231\pi$
$467$	10.5865			0.489885			0.244943	+	0.969538i	$0.421231\pi$
$468$		0			0
$469$	15.2386			0.703653
$470$		0			0
$471$	5.67282	−	33.8841i	0.261390	−	1.56130i
$472$		0			0
$473$	11.1008	−	19.2272i	0.510417	−	0.884068i
$474$		0			0
$475$	−0.908405	−	1.57340i	−0.0416805	−	0.0721927i
$476$		0			0
$477$	9.51432	−	8.26821i	0.435631	−	0.378575i
$478$		0			0
$479$	−3.38485	−	5.86273i	−0.154658	−	0.267875i	0.778277	−	0.627922i	$-0.216094\pi$
$479$	−3.38485	−	5.86273i	−0.154658	−	0.267875i	−0.932934	+	0.360046i	$0.882761\pi$
$480$		0			0
$481$	17.5042	−	30.3181i	0.798121	−	1.38239i
$482$		0			0
$483$	−13.9773	+	5.22472i	−0.635989	+	0.237733i
$484$		0			0
$485$	−12.2017			−0.554049
$486$		0			0
$487$	−31.2857			−1.41769			−0.708845	−	0.705364i	$-0.750784\pi$
$487$	−31.2857			−1.41769			−0.708845	+	0.705364i	$0.750784\pi$
$488$		0			0
$489$	−22.4165	+	8.37931i	−1.01371	+	0.378925i
$490$		0			0
$491$	9.08236	−	15.7311i	0.409881	−	0.709935i	−0.584995	−	0.811037i	$-0.698904\pi$
$491$	9.08236	−	15.7311i	0.409881	−	0.709935i	0.994876	+	0.101102i	$0.0322368\pi$
$492$		0			0
$493$	13.7437	+	23.8048i	0.618985	+	1.07211i
$494$		0			0
$495$	−8.64286	+	7.51089i	−0.388467	+	0.337589i
$496$		0			0
$497$	4.13870	+	7.16845i	0.185646	+	0.321549i
$498$		0			0
$499$	−1.26555	+	2.19200i	−0.0566538	+	0.0981272i	−0.892961	−	0.450133i	$-0.851376\pi$
$499$	−1.26555	+	2.19200i	−0.0566538	+	0.0981272i	0.836308	+	0.548261i	$0.184710\pi$
$500$		0			0
$501$	−1.73953	+	10.3903i	−0.0777167	+	0.464206i
$502$		0			0
$503$	−18.6873			−0.833227			−0.416614	−	0.909084i	$-0.636783\pi$
$503$	−18.6873			−0.833227			−0.416614	+	0.909084i	$0.636783\pi$
$504$		0			0
$505$	−16.2017			−0.720964
$506$		0			0
$507$	27.8445	+	22.9567i	1.23662	+	1.01954i
$508$		0			0
$509$	−4.93196	+	8.54240i	−0.218605	+	0.378635i	−0.954382	−	0.298589i	$-0.903484\pi$
$509$	−4.93196	+	8.54240i	−0.218605	+	0.378635i	0.735777	+	0.677224i	$0.236817\pi$
$510$		0			0
$511$	16.4033	+	28.4114i	0.725640	+	1.25685i
$512$		0			0
$513$	−4.50641	+	8.29541i	−0.198963	+	0.366251i
$514$		0			0
$515$	4.72522	+	8.18431i	0.208218	+	0.360644i
$516$		0			0
$517$	22.7437	−	39.3932i	1.00027	−	1.73251i
$518$		0			0
$519$	−5.83528	−	4.81096i	−0.256140	−	0.211178i
$520$		0			0
$521$	9.60498			0.420802			0.210401	−	0.977615i	$-0.432523\pi$
$521$	9.60498			0.420802			0.210401	+	0.977615i	$0.432523\pi$
$522$		0			0
$523$	−4.32096			−0.188942			−0.0944712	−	0.995528i	$-0.530116\pi$
$523$	−4.32096			−0.188942			−0.0944712	+	0.995528i	$0.530116\pi$
$524$		0			0
$525$	−1.17282	+	7.00535i	−0.0511862	+	0.305738i
$526$		0			0
$527$	−3.46721	+	6.00538i	−0.151034	+	0.261599i
$528$		0			0
$529$	9.29326	+	16.0964i	0.404055	+	0.699843i
$530$		0			0
$531$	2.40332	+	12.3737i	0.104295	+	0.536975i
$532$		0			0
$533$	−32.0462	−	55.5056i	−1.38807	−	2.40421i
$534$		0			0
$535$	−2.33444	+	4.04336i	−0.100926	+	0.174810i
$536$		0			0
$537$	10.3588	−	3.87214i	0.447017	−	0.167095i
$538$		0			0
$539$	37.4689			1.61390
$540$		0			0
$541$	4.23030			0.181875			0.0909374	−	0.995857i	$-0.471014\pi$
$541$	4.23030			0.181875			0.0909374	+	0.995857i	$0.471014\pi$
$542$		0			0
$543$	−16.3305	+	6.10435i	−0.700808	+	0.261963i
$544$		0			0
$545$	4.40841	−	7.63558i	0.188835	−	0.327072i
$546$		0			0
$547$	−5.15125	−	8.92222i	−0.220251	−	0.381487i	0.734633	−	0.678465i	$-0.237354\pi$
$547$	−5.15125	−	8.92222i	−0.220251	−	0.381487i	−0.954884	+	0.296978i	$0.904021\pi$
$548$		0			0
$549$	8.56163	+	2.94942i	0.365401	+	0.125878i
$550$		0			0
$551$	6.54203	+	11.3311i	0.278700	+	0.482722i
$552$		0			0
$553$	−4.10083	+	7.10285i	−0.174385	+	0.302044i
$554$		0			0
$555$	1.72126	−	10.2812i	0.0730635	−	0.436413i
$556$		0			0
$557$	6.00000			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$558$		0			0
$559$	−33.8353			−1.43108
$560$		0			0
$561$	19.4689	+	16.0513i	0.821978	+	0.677688i
$562$		0			0
$563$	−4.75716	+	8.23964i	−0.200490	+	0.347260i	−0.948687	−	0.316218i	$-0.897587\pi$
$563$	−4.75716	+	8.23964i	−0.200490	+	0.347260i	0.748196	+	0.663478i	$0.230920\pi$
$564$		0			0
$565$	−5.10083	−	8.83490i	−0.214594	−	0.371687i
$566$		0			0
$567$	34.2241	−	13.8157i	1.43728	−	0.580205i
$568$		0			0
$569$	10.6336	+	18.4180i	0.445785	+	0.772122i	0.998107	−	0.0615094i	$-0.0195914\pi$
$569$	10.6336	+	18.4180i	0.445785	+	0.772122i	−0.552322	+	0.833631i	$0.686258\pi$
$570$		0			0
$571$	8.20166	−	14.2057i	0.343229	−	0.594490i	−0.641802	−	0.766871i	$-0.721813\pi$
$571$	8.20166	−	14.2057i	0.343229	−	0.594490i	0.985030	+	0.172381i	$0.0551460\pi$
$572$		0			0
$573$	20.9176	+	17.2458i	0.873847	+	0.720452i
$574$		0			0
$575$	−2.10083			−0.0876107
$576$		0			0
$577$	34.3328			1.42929			0.714647	−	0.699485i	$-0.246587\pi$
$577$	34.3328			1.42929			0.714647	+	0.699485i	$0.246587\pi$
$578$		0			0
$579$	3.84678	−	22.9770i	0.159867	−	0.954893i
$580$		0			0
$581$	7.99492	−	13.8476i	0.331685	−	0.574495i
$582$		0			0
$583$	−8.01847	−	13.8884i	−0.332091	−	0.575199i
$584$		0			0
$585$	16.4989	+	5.68373i	0.682144	+	0.234993i
$586$		0			0
$587$	8.84875	+	15.3265i	0.365227	+	0.632592i	0.988813	−	0.149163i	$-0.0476580\pi$
$587$	8.84875	+	15.3265i	0.365227	+	0.632592i	−0.623585	+	0.781755i	$0.714325\pi$
$588$		0			0
$589$	−1.65040	+	2.85858i	−0.0680035	+	0.117786i
$590$		0			0
$591$	2.91764	−	1.09062i	0.120016	−	0.0448620i
$592$		0			0
$593$	−45.3227			−1.86118			−0.930589	−	0.366065i	$-0.880705\pi$
$593$	−45.3227			−1.86118			−0.930589	+	0.366065i	$0.880705\pi$
$594$		0			0
$595$	15.6521			0.641673
$596$		0			0
$597$	−36.0501	+	13.4756i	−1.47543	+	0.551518i
$598$		0			0
$599$	−5.01847	+	8.69225i	−0.205049	+	0.355156i	−0.950148	−	0.311798i	$-0.899069\pi$
$599$	−5.01847	+	8.69225i	−0.205049	+	0.355156i	0.745099	+	0.666954i	$0.232402\pi$
$600$		0			0
$601$	−16.6521	−	28.8423i	−0.679253	−	1.17650i	−0.975206	−	0.221298i	$-0.928971\pi$
$601$	−16.6521	−	28.8423i	−0.679253	−	1.17650i	0.295953	−	0.955202i	$-0.404363\pi$
$602$		0			0
$603$	−2.12552	−	10.9434i	−0.0865577	−	0.445651i
$604$		0			0
$605$	1.78402	+	3.09001i	0.0725307	+	0.125627i
$606$		0			0
$607$	−1.87646	+	3.25013i	−0.0761632	+	0.131919i	−0.901592	−	0.432588i	$-0.857600\pi$
$607$	−1.87646	+	3.25013i	−0.0761632	+	0.131919i	0.825428	+	0.564507i	$0.190934\pi$
$608$		0			0
$609$	8.44628	−	50.4501i	0.342260	−	2.04434i
$610$		0			0
$611$	−69.3227			−2.80449
$612$		0			0
$613$	−3.45043			−0.139362			−0.0696808	−	0.997569i	$-0.522198\pi$
$613$	−3.45043			−0.139362			−0.0696808	+	0.997569i	$0.522198\pi$
$614$		0			0
$615$	−14.7252	−	12.1404i	−0.593778	−	0.489546i
$616$		0			0
$617$	−6.73445	+	11.6644i	−0.271119	+	0.469592i	−0.969149	−	0.246477i	$-0.920727\pi$
$617$	−6.73445	+	11.6644i	−0.271119	+	0.469592i	0.698030	+	0.716069i	$0.254060\pi$
$618$		0			0
$619$	1.27478	+	2.20799i	0.0512379	+	0.0887467i	0.890507	−	0.454970i	$-0.150350\pi$
$619$	1.27478	+	2.20799i	0.0512379	+	0.0887467i	−0.839269	+	0.543717i	$0.817017\pi$
$620$		0			0
$621$	5.70166	+	9.30888i	0.228800	+	0.373553i
$622$		0			0
$623$	−6.15125	−	10.6543i	−0.246444	−	0.426854i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	9.26724	+	7.64047i	0.370098	+	0.305131i
$628$		0			0
$629$	−22.9714			−0.915928
$630$		0			0
$631$	−30.2017			−1.20231			−0.601155	−	0.799133i	$-0.705292\pi$
$631$	−30.2017			−1.20231			−0.601155	+	0.799133i	$0.705292\pi$
$632$		0			0
$633$	8.07086	−	48.2078i	0.320788	−	1.91609i
$634$		0			0
$635$	−0.142010	+	0.245969i	−0.00563550	+	0.00976097i
$636$		0			0
$637$	−28.5513	−	49.4522i	−1.13124	−	1.95937i
$638$		0			0
$639$	4.57066	−	3.97204i	0.180813	−	0.157131i
$640$		0			0
$641$	−8.20674	−	14.2145i	−0.324147	−	0.561439i	0.657192	−	0.753723i	$-0.271744\pi$
$641$	−8.20674	−	14.2145i	−0.324147	−	0.561439i	−0.981339	+	0.192284i	$0.938411\pi$
$642$		0			0
$643$	−1.14201	+	1.97802i	−0.0450365	+	0.0780055i	−0.887665	−	0.460490i	$-0.847674\pi$
$643$	−1.14201	+	1.97802i	−0.0450365	+	0.0780055i	0.842628	+	0.538495i	$0.181007\pi$
$644$		0			0
$645$	−9.43724	+	3.52765i	−0.371591	+	0.138901i
$646$		0			0
$647$	−6.08236			−0.239122			−0.119561	−	0.992827i	$-0.538149\pi$
$647$	−6.08236			−0.239122			−0.119561	+	0.992827i	$0.538149\pi$
$648$		0			0
$649$	16.0369			0.629505
$650$		0			0
$651$	12.0876	−	4.51837i	0.473752	−	0.177089i
$652$		0			0
$653$	−5.76047	+	9.97742i	−0.225424	+	0.390447i	−0.956447	−	0.291907i	$-0.905710\pi$
$653$	−5.76047	+	9.97742i	−0.225424	+	0.390447i	0.731022	+	0.682354i	$0.239044\pi$
$654$		0			0
$655$	−10.6336	−	18.4180i	−0.415490	−	0.719650i
$656$		0			0
$657$	18.1153	−	15.7427i	0.706747	−	0.614183i
$658$		0			0
$659$	−14.5328	−	25.1715i	−0.566117	−	0.980544i	−0.996945	−	0.0781094i	$-0.975112\pi$
$659$	−14.5328	−	25.1715i	−0.566117	−	0.980544i	0.430828	−	0.902434i	$-0.358222\pi$
$660$		0			0
$661$	−20.4689	+	35.4532i	−0.796148	+	1.37897i	0.125960	+	0.992035i	$0.459799\pi$
$661$	−20.4689	+	35.4532i	−0.796148	+	1.37897i	−0.922108	+	0.386933i	$0.873534\pi$
$662$		0			0
$663$	6.34960	−	37.9266i	0.246598	−	1.47295i
$664$		0			0
$665$	7.45043			0.288915
$666$		0			0
$667$	15.1295			0.585815
$668$		0			0
$669$	−2.56276	−	2.11289i	−0.0990819	−	0.0816891i
$670$		0			0
$671$	5.76047	−	9.97742i	0.222380	−	0.385174i
$672$		0			0
$673$	−14.0092	−	24.2647i	−0.540016	−	0.935336i	−0.998902	−	0.0468406i	$-0.985085\pi$
$673$	−14.0092	−	24.2647i	−0.540016	−	0.935336i	0.458886	−	0.888495i	$-0.348249\pi$
$674$		0			0
$675$	5.19440	−	0.134872i	0.199933	−	0.00519122i
$676$		0			0
$677$	25.8260	+	44.7320i	0.992576	+	1.71919i	0.601622	+	0.798781i	$0.294521\pi$
$677$	25.8260	+	44.7320i	0.992576	+	1.71919i	0.390954	+	0.920410i	$0.372145\pi$
$678$		0			0
$679$	25.0185	−	43.3333i	0.960121	−	1.66298i
$680$		0			0
$681$	10.7160	+	8.83490i	0.410637	+	0.338554i
$682$		0			0
$683$	−13.8538			−0.530099			−0.265050	−	0.964235i	$-0.585388\pi$
$683$	−13.8538			−0.530099			−0.265050	+	0.964235i	$0.585388\pi$
$684$		0			0
$685$	2.56804			0.0981198
$686$		0			0
$687$	−5.38683	+	32.1759i	−0.205520	+	1.22759i
$688$		0			0
$689$	−12.2201	+	21.1659i	−0.465550	+	0.806356i
$690$		0			0
$691$	6.45043	+	11.1725i	0.245386	+	0.425021i	0.962240	−	0.272202i	$-0.0877520\pi$
$691$	6.45043	+	11.1725i	0.245386	+	0.425021i	−0.716854	+	0.697223i	$0.754419\pi$
$692$		0			0
$693$	−8.95289	−	46.0949i	−0.340092	−	1.75100i
$694$		0			0
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$		0			0
$697$	−21.0277	+	36.4211i	−0.796481	+	1.37955i
$698$		0			0
$699$	22.7437	−	8.50161i	0.860245	−	0.321560i
$700$		0			0
$701$	1.75123			0.0661430			0.0330715	−	0.999453i	$-0.489471\pi$
$701$	1.75123			0.0661430			0.0330715	+	0.999453i	$0.489471\pi$
$702$		0			0
$703$	−10.9344			−0.412399
$704$		0			0
$705$	−19.3353	+	7.22754i	−0.728209	+	0.272205i
$706$		0			0
$707$	33.2201	−	57.5390i	1.24937	−	2.16398i
$708$		0			0
$709$	−7.16887	−	12.4168i	−0.269233	−	0.466325i	0.699431	−	0.714700i	$-0.253437\pi$
$709$	−7.16887	−	12.4168i	−0.269233	−	0.466325i	−0.968664	+	0.248375i	$0.920103\pi$
$710$		0			0
$711$	5.67282	+	1.95424i	0.212748	+	0.0732899i
$712$		0			0
$713$	1.90841	+	3.30545i	0.0714703	+	0.123790i
$714$		0			0
$715$	11.1008	−	19.2272i	0.415148	−	0.719057i
$716$		0			0
$717$	−2.91764	+	17.4272i	−0.108961	+	0.650833i
$718$		0			0
$719$	12.6050			0.470087			0.235043	−	0.971985i	$-0.424477\pi$
$719$	12.6050			0.470087			0.235043	+	0.971985i	$0.424477\pi$
$720$		0			0
$721$	−38.7546			−1.44330
$722$		0			0
$723$	23.0132	+	18.9735i	0.855870	+	0.705630i
$724$		0			0
$725$	3.60083	−	6.23682i	0.133731	−	0.231630i
$726$		0			0
$727$	−21.8949	−	37.9231i	−0.812038	−	1.40649i	−0.911435	−	0.411443i	$-0.865025\pi$
$727$	−21.8949	−	37.9231i	−0.812038	−	1.40649i	0.0993972	−	0.995048i	$-0.468309\pi$
$728$		0			0
$729$	−14.6952	−	22.6506i	−0.544268	−	0.838911i
$730$		0			0
$731$	11.1008	+	19.2272i	0.410579	+	0.711144i
$732$		0			0
$733$	−3.56804	+	6.18003i	−0.131789	+	0.228265i	−0.924366	−	0.381507i	$-0.875405\pi$
$733$	−3.56804	+	6.18003i	−0.131789	+	0.228265i	0.792578	+	0.609771i	$0.208739\pi$
$734$		0			0
$735$	−13.1193	−	10.8163i	−0.483913	−	0.398967i
$736$		0			0
$737$	−14.1832			−0.522445
$738$		0			0
$739$	44.6419			1.64218			0.821090	−	0.570799i	$-0.193366\pi$
$739$	44.6419			1.64218			0.821090	+	0.570799i	$0.193366\pi$
$740$		0			0
$741$	3.02242	−	18.0531i	0.111032	−	0.663198i
$742$		0			0
$743$	−2.41679	+	4.18601i	−0.0886636	+	0.153570i	−0.906946	−	0.421246i	$-0.861593\pi$
$743$	−2.41679	+	4.18601i	−0.0886636	+	0.153570i	0.818283	+	0.574816i	$0.194926\pi$
$744$		0			0
$745$	−7.22522	−	12.5144i	−0.264711	−	0.458494i
$746$		0			0
$747$	−11.0597	−	3.80997i	−0.404651	−	0.139399i
$748$		0			0
$749$	−9.57312	−	16.5811i	−0.349794	−	0.605862i
$750$		0			0
$751$	14.4412	−	25.0129i	0.526967	−	0.912733i	−0.472539	−	0.881310i	$-0.656663\pi$
$751$	14.4412	−	25.0129i	0.526967	−	0.912733i	0.999506	−	0.0314236i	$-0.0100041\pi$
$752$		0			0
$753$	−0.624385	+	0.233396i	−0.0227539	+	0.00850541i
$754$		0			0
$755$	−8.58651			−0.312495
$756$		0			0
$757$	30.5865			1.11169			0.555843	−	0.831287i	$-0.312396\pi$
$757$	30.5865			1.11169			0.555843	+	0.831287i	$0.312396\pi$
$758$		0			0
$759$	13.0092	−	4.86286i	0.472205	−	0.176511i
$760$		0			0
$761$	17.6193	−	30.5175i	0.638699	−	1.10626i	−0.347019	−	0.937858i	$-0.612806\pi$
$761$	17.6193	−	30.5175i	0.638699	−	1.10626i	0.985718	−	0.168401i	$-0.0538605\pi$
$762$		0			0
$763$	18.0781	+	31.3122i	0.654472	+	1.13358i
$764$		0			0
$765$	−2.18319	−	11.2404i	−0.0789334	−	0.406397i
$766$		0			0
$767$	−12.2201	−	21.1659i	−0.441243	−	0.764256i
$768$		0			0
$769$	22.6193	−	39.1778i	0.815673	−	1.41279i	−0.0931709	−	0.995650i	$-0.529700\pi$
$769$	22.6193	−	39.1778i	0.815673	−	1.41279i	0.908844	−	0.417137i	$-0.136966\pi$
$770$		0			0
$771$	2.65040	−	15.8310i	0.0954518	−	0.570140i
$772$		0			0
$773$	27.2672			0.980734			0.490367	−	0.871516i	$-0.336863\pi$
$773$	27.2672			0.980734			0.490367	+	0.871516i	$0.336863\pi$
$774$		0			0
$775$	1.81681			0.0652618
$776$		0			0
$777$	32.9836	+	27.1937i	1.18328	+	0.975568i
$778$		0			0
$779$	−10.0092	+	17.3365i	−0.358618	+	0.621145i
$780$		0			0
$781$	−3.85206	−	6.67196i	−0.137838	−	0.238742i
$782$		0			0
$783$	−37.4083	+	0.971302i	−1.33686	+	0.0347115i
$784$		0			0
$785$	9.91764	+	17.1779i	0.353976	+	0.613104i
$786$		0			0
$787$	6.72522	−	11.6484i	0.239728	−	0.415221i	−0.720908	−	0.693031i	$-0.756275\pi$
$787$	6.72522	−	11.6484i	0.239728	−	0.415221i	0.960636	+	0.277809i	$0.0896084\pi$
$788$		0			0
$789$	34.5513	+	28.4861i	1.23006	+	1.01413i
$790$		0			0
$791$	41.8353			1.48749
$792$		0			0
$793$	−17.5579			−0.623498
$794$		0			0
$795$	−1.20166	+	7.17760i	−0.0426185	+	0.254563i
$796$		0			0
$797$	1.60591	−	2.78152i	0.0568844	−	0.0985266i	−0.836181	−	0.548454i	$-0.815217\pi$
$797$	1.60591	−	2.78152i	0.0568844	−	0.0985266i	0.893065	+	0.449927i	$0.148550\pi$
$798$		0			0
$799$	22.7437	+	39.3932i	0.804614	+	1.39363i
$800$		0			0
$801$	−6.79326	+	5.90353i	−0.240028	+	0.208591i
$802$		0			0
$803$	−15.2672	−	26.4436i	−0.538769	−	0.933176i
$804$		0			0
$805$	4.30757	−	7.46094i	0.151822	−	0.262964i
$806$		0			0
$807$	−45.5638	+	17.0318i	−1.60392	+	0.599547i
$808$		0			0
$809$	43.4689			1.52829			0.764143	−	0.645047i	$-0.223162\pi$
$809$	43.4689			1.52829			0.764143	+	0.645047i	$0.223162\pi$
$810$		0			0
$811$	18.4033			0.646228			0.323114	−	0.946360i	$-0.395270\pi$
$811$	18.4033			0.646228			0.323114	+	0.946360i	$0.395270\pi$
$812$		0			0
$813$	−34.8014	+	13.0088i	−1.22054	+	0.456238i
$814$		0			0
$815$	6.90841	−	11.9657i	0.241991	−	0.419140i
$816$		0			0
$817$	5.28402	+	9.15219i	0.184864	+	0.320195i
$818$		0			0
$819$	−54.0149	+	46.9405i	−1.88743	+	1.64023i
$820$		0			0
$821$	7.69243	+	13.3237i	0.268467	+	0.464999i	0.968466	−	0.249145i	$-0.0801495\pi$
$821$	7.69243	+	13.3237i	0.268467	+	0.464999i	−0.699999	+	0.714144i	$0.746816\pi$
$822$		0			0
$823$	−9.97729	+	17.2812i	−0.347787	+	0.602384i	−0.985856	−	0.167595i	$-0.946400\pi$
$823$	−9.97729	+	17.2812i	−0.347787	+	0.602384i	0.638069	+	0.769979i	$0.279733\pi$
$824$		0			0
$825$	1.09159	−	6.52016i	0.0380045	−	0.227003i
$826$		0			0
$827$	37.0571			1.28860			0.644301	−	0.764772i	$-0.277148\pi$
$827$	37.0571			1.28860			0.644301	+	0.764772i	$0.277148\pi$
$828$		0			0
$829$	14.9815			0.520330			0.260165	−	0.965564i	$-0.416223\pi$
$829$	14.9815			0.520330			0.260165	+	0.965564i	$0.416223\pi$
$830$		0			0
$831$	−10.4465	−	8.61270i	−0.362384	−	0.298771i
$832$		0			0
$833$	−18.7345	+	32.4490i	−0.649110	+	1.12429i
$834$		0			0
$835$	−3.04118	−	5.26748i	−0.105244	−	0.182289i
$836$		0			0
$837$	−4.93083	−	8.05037i	−0.170434	−	0.278262i
$838$		0			0
$839$	−3.27478	−	5.67209i	−0.113058	−	0.195822i	0.803944	−	0.594705i	$-0.202731\pi$
$839$	−3.27478	−	5.67209i	−0.113058	−	0.195822i	−0.917002	+	0.398883i	$0.869398\pi$
$840$		0			0
$841$	−11.4320	+	19.8007i	−0.394206	+	0.682784i
$842$		0			0
$843$	6.92688	+	5.71093i	0.238574	+	0.196695i
$844$		0			0
$845$	−20.8353			−0.716755
$846$		0			0
$847$	−14.6319			−0.502759
$848$		0			0
$849$	5.17678	−	30.9212i	0.177667	−	1.06121i
$850$		0			0
$851$	−6.32189	+	10.9498i	−0.216712	+	0.375356i
$852$		0			0
$853$	1.42272	+	2.46423i	0.0487131	+	0.0843736i	0.889354	−	0.457220i	$-0.151155\pi$
$853$	1.42272	+	2.46423i	0.0487131	+	0.0843736i	−0.840641	+	0.541593i	$0.817821\pi$
$854$		0			0
$855$	−1.03920	−	5.35044i	−0.0355400	−	0.182981i
$856$		0			0
$857$	−9.11007	−	15.7791i	−0.311194	−	0.539004i	0.667427	−	0.744675i	$-0.267396\pi$
$857$	−9.11007	−	15.7791i	−0.311194	−	0.539004i	−0.978621	+	0.205671i	$0.934062\pi$
$858$		0			0
$859$	−23.0277	+	39.8852i	−0.785695	+	1.36086i	0.142888	+	0.989739i	$0.454361\pi$
$859$	−23.0277	+	39.8852i	−0.785695	+	1.36086i	−0.928583	+	0.371125i	$0.878972\pi$
$860$		0			0
$861$	73.3083	−	27.4027i	2.49834	−	0.933882i
$862$		0			0
$863$	−36.4521			−1.24084			−0.620422	−	0.784268i	$-0.713039\pi$
$863$	−36.4521			−1.24084			−0.620422	+	0.784268i	$0.713039\pi$
$864$		0			0
$865$	4.36638			0.148461
$866$		0			0
$867$	3.94563	−	1.47488i	0.134001	−	0.0500896i
$868$		0			0
$869$	3.81681	−	6.61091i	0.129476	−	0.224260i
$870$		0			0
$871$	10.8076	+	18.7193i	0.366201	+	0.634278i
$872$		0			0
$873$	−34.6089	−	11.9225i	−1.17133	−	0.403516i
$874$		0			0
$875$	−2.05042	−	3.55142i	−0.0693167	−	0.120060i
$876$		0			0
$877$	−26.3588	+	45.6548i	−0.890075	+	1.54165i	−0.0502901	+	0.998735i	$0.516015\pi$
$877$	−26.3588	+	45.6548i	−0.890075	+	1.54165i	−0.839785	+	0.542920i	$0.817319\pi$
$878$		0			0
$879$	−4.74369	+	28.3343i	−0.160001	+	0.955693i
$880$		0			0
$881$	17.8824			0.602473			0.301237	−	0.953549i	$-0.402601\pi$
$881$	17.8824			0.602473			0.301237	+	0.953549i	$0.402601\pi$
$882$		0			0
$883$	−29.3496			−0.987693			−0.493846	−	0.869549i	$-0.664409\pi$
$883$	−29.3496			−0.987693			−0.493846	+	0.869549i	$0.664409\pi$
$884$		0			0
$885$	−5.61515	−	4.62947i	−0.188751	−	0.155618i
$886$		0			0
$887$	8.34036	−	14.4459i	0.280042	−	0.485047i	−0.691353	−	0.722517i	$-0.742985\pi$
$887$	8.34036	−	14.4459i	0.280042	−	0.485047i	0.971395	+	0.237470i	$0.0763183\pi$
$888$		0			0
$889$	−0.582359	−	1.00868i	−0.0195317	−	0.0338299i
$890$		0			0
$891$	−31.8538	+	12.8588i	−1.06714	+	0.430787i
$892$		0			0
$893$	10.8260	+	18.7513i	0.362280	+	0.627487i
$894$		0			0
$895$	−3.19243	+	5.52944i	−0.106711	+	0.184829i
$896$		0			0
$897$	−16.3311	−	13.4644i	−0.545281	−	0.449562i
$898$		0			0
$899$	−13.0841			−0.436378
$900$		0			0
$901$	16.0369			0.534268
$902$		0			0
$903$	6.82209	−	40.7488i	0.227025	−	1.35603i
$904$		0			0
$905$	5.03279	−	8.71705i	0.167296	−	0.289764i
$906$		0			0
$907$	1.12354	+	1.94603i	0.0373065	+	0.0646168i	0.884076	−	0.467344i	$-0.154789\pi$
$907$	1.12354	+	1.94603i	0.0373065	+	0.0646168i	−0.846769	+	0.531960i	$0.821456\pi$
$908$		0			0
$909$	−45.9546	−	15.8310i	−1.52422	−	0.525081i
$910$		0			0
$911$	−5.14794	−	8.91649i	−0.170559	−	0.295417i	0.768057	−	0.640382i	$-0.221224\pi$
$911$	−5.14794	−	8.91649i	−0.170559	−	0.295417i	−0.938615	+	0.344965i	$0.887891\pi$
$912$		0			0
$913$	−7.44120	+	12.8885i	−0.246268	+	0.426548i
$914$		0			0
$915$	−4.89719	+	1.83057i	−0.161896	+	0.0605169i
$916$		0			0
$917$	87.2133			2.88004
$918$		0			0
$919$	14.0369			0.463036			0.231518	−	0.972831i	$-0.425631\pi$
$919$	14.0369			0.463036			0.231518	+	0.972831i	$0.425631\pi$
$920$		0			0
$921$	−36.1838	+	13.5255i	−1.19230	+	0.445681i
$922$		0			0
$923$	−5.87053	+	10.1681i	−0.193231	+	0.334686i
$924$		0			0
$925$	3.00924	+	5.21215i	0.0989431	+	0.171374i
$926$		0			0
$927$	5.40558	+	27.8312i	0.177543	+	0.914096i
$928$		0			0
$929$	−27.2201	−	47.1467i	−0.893064	−	1.54683i	−0.836183	−	0.548450i	$-0.815218\pi$
$929$	−27.2201	−	47.1467i	−0.893064	−	1.54683i	−0.0568805	−	0.998381i	$-0.518115\pi$
$930$		0			0
$931$	−8.91764	+	15.4458i	−0.292264	+	0.506216i
$932$		0			0
$933$	7.90841	−	47.2374i	0.258910	−	1.54648i
$934$		0			0
$935$	−14.5680			−0.476426
$936$		0			0
$937$	−33.0656			−1.08021			−0.540103	−	0.841599i	$-0.681615\pi$
$937$	−33.0656			−1.08021			−0.540103	+	0.841599i	$0.681615\pi$
$938$		0			0
$939$	15.5720	+	12.8385i	0.508173	+	0.418968i
$940$		0			0
$941$	6.60083	−	11.4330i	0.215181	−	0.372704i	−0.738148	−	0.674639i	$-0.764299\pi$
$941$	6.60083	−	11.4330i	0.215181	−	0.372704i	0.953329	+	0.301935i	$0.0976325\pi$
$942$		0			0
$943$	11.5740	+	20.0467i	0.376900	+	0.652810i
$944$		0			0
$945$	−10.1717	+	18.7241i	−0.330885	+	0.609094i
$946$		0			0
$947$	−0.343671	−	0.595256i	−0.0111678	−	0.0193432i	0.860387	−	0.509640i	$-0.170222\pi$
$947$	−0.343671	−	0.595256i	−0.0111678	−	0.0193432i	−0.871555	+	0.490297i	$0.836888\pi$
$948$		0			0
$949$	−23.2672	+	40.3000i	−0.755287	+	1.30819i
$950$		0			0
$951$	15.5226	+	12.7978i	0.503356	+	0.414997i
$952$		0			0
$953$	−32.7882			−1.06211			−0.531057	−	0.847336i	$-0.678205\pi$
$953$	−32.7882			−1.06211			−0.531057	+	0.847336i	$0.678205\pi$
$954$		0			0
$955$	−15.6521			−0.506490
$956$		0			0
$957$	−7.86130	+	46.9560i	−0.254120	+	1.51787i
$958$		0			0
$959$	−5.26555	+	9.12020i	−0.170033	+	0.294507i
$960$		0			0
$961$	13.8496	+	23.9882i	0.446761	+	0.773813i
$962$		0			0
$963$	−10.5723	+	9.18761i	−0.340687	+	0.296067i
$964$		0			0
$965$	6.72522	+	11.6484i	0.216492	+	0.374976i
$966$		0			0
$967$	−2.88570	+	4.99817i	−0.0927977	+	0.160730i	−0.908687	−	0.417477i	$-0.862914\pi$
$967$	−2.88570	+	4.99817i	−0.0927977	+	0.160730i	0.815890	+	0.578208i	$0.196248\pi$
$968$		0			0
$969$	−11.2505	+	4.20543i	−0.361417	+	0.135098i
$970$		0			0
$971$	41.1210			1.31964			0.659818	−	0.751426i	$-0.270633\pi$
$971$	41.1210			1.31964			0.659818	+	0.751426i	$0.270633\pi$
$972$		0			0
$973$	−16.4033			−0.525866
$974$		0			0
$975$	−9.43724	+	3.52765i	−0.302234	+	0.112975i
$976$		0			0
$977$	6.57728	−	11.3922i	0.210426	−	0.364468i	−0.741422	−	0.671039i	$-0.765848\pi$
$977$	6.57728	−	11.3922i	0.210426	−	0.364468i	0.951848	+	0.306571i	$0.0991817\pi$
$978$		0			0
$979$	5.72522	+	9.91636i	0.182979	+	0.316928i
$980$		0			0
$981$	19.9649	−	17.3501i	0.637432	−	0.553946i
$982$		0			0
$983$	9.06889	+	15.7078i	0.289253	+	0.501000i	0.973632	−	0.228126i	$-0.0732599\pi$
$983$	9.06889	+	15.7078i	0.289253	+	0.501000i	−0.684379	+	0.729126i	$0.739927\pi$
$984$		0			0
$985$	−0.899170	+	1.55741i	−0.0286499	+	0.0496231i
$986$		0			0
$987$	13.9773	−	83.4872i	0.444902	−	2.65743i
$988$		0			0
$989$	12.2201			0.388578
$990$		0			0
$991$	−11.4320			−0.363148			−0.181574	−	0.983377i	$-0.558119\pi$
$991$	−11.4320			−0.363148			−0.181574	+	0.983377i	$0.558119\pi$
$992$		0			0
$993$	25.9691	+	21.4105i	0.824105	+	0.679441i
$994$		0			0
$995$	11.1101	−	19.2432i	0.352213	−	0.610050i
$996$		0			0
$997$	4.26555	+	7.38815i	0.135091	+	0.233985i	0.925632	−	0.378424i	$-0.123534\pi$
$997$	4.26555	+	7.38815i	0.135091	+	0.233985i	−0.790541	+	0.612409i	$0.790201\pi$
$998$		0			0
$999$	14.9282	−	27.4799i	0.472308	−	0.869424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.k.481.1		6
3.2	odd	2		2160.2.q.i.1441.3		6
4.3	odd	2		180.2.i.b.121.3	yes	6
9.2	odd	6		2160.2.q.i.721.3		6
9.4	even	3		6480.2.a.bt.1.1		3
9.5	odd	6		6480.2.a.bw.1.1		3
9.7	even	3	inner	720.2.q.k.241.1		6
12.11	even	2		540.2.i.b.361.1		6
20.3	even	4		900.2.s.c.49.5		12
20.7	even	4		900.2.s.c.49.2		12
20.19	odd	2		900.2.i.c.301.1		6
36.7	odd	6		180.2.i.b.61.3	✓	6
36.11	even	6		540.2.i.b.181.1		6
36.23	even	6		1620.2.a.j.1.3		3
36.31	odd	6		1620.2.a.i.1.3		3
60.23	odd	4		2700.2.s.c.1549.1		12
60.47	odd	4		2700.2.s.c.1549.6		12
60.59	even	2		2700.2.i.c.901.3		6
180.7	even	12		900.2.s.c.349.5		12
180.23	odd	12		8100.2.d.o.649.1		6
180.43	even	12		900.2.s.c.349.2		12
180.47	odd	12		2700.2.s.c.2449.1		12
180.59	even	6		8100.2.a.u.1.1		3
180.67	even	12		8100.2.d.p.649.6		6
180.79	odd	6		900.2.i.c.601.1		6
180.83	odd	12		2700.2.s.c.2449.6		12
180.103	even	12		8100.2.d.p.649.1		6
180.119	even	6		2700.2.i.c.1801.3		6
180.139	odd	6		8100.2.a.v.1.1		3
180.167	odd	12		8100.2.d.o.649.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.i.b.61.3	✓	6	36.7	odd	6
180.2.i.b.121.3	yes	6	4.3	odd	2
540.2.i.b.181.1		6	36.11	even	6
540.2.i.b.361.1		6	12.11	even	2
720.2.q.k.241.1		6	9.7	even	3	inner
720.2.q.k.481.1		6	1.1	even	1	trivial
900.2.i.c.301.1		6	20.19	odd	2
900.2.i.c.601.1		6	180.79	odd	6
900.2.s.c.49.2		12	20.7	even	4
900.2.s.c.49.5		12	20.3	even	4
900.2.s.c.349.2		12	180.43	even	12
900.2.s.c.349.5		12	180.7	even	12
1620.2.a.i.1.3		3	36.31	odd	6
1620.2.a.j.1.3		3	36.23	even	6
2160.2.q.i.721.3		6	9.2	odd	6
2160.2.q.i.1441.3		6	3.2	odd	2
2700.2.i.c.901.3		6	60.59	even	2
2700.2.i.c.1801.3		6	180.119	even	6
2700.2.s.c.1549.1		12	60.23	odd	4
2700.2.s.c.1549.6		12	60.47	odd	4
2700.2.s.c.2449.1		12	180.47	odd	12
2700.2.s.c.2449.6		12	180.83	odd	12
6480.2.a.bt.1.1		3	9.4	even	3
6480.2.a.bw.1.1		3	9.5	odd	6
8100.2.a.u.1.1		3	180.59	even	6
8100.2.a.v.1.1		3	180.139	odd	6
8100.2.d.o.649.1		6	180.23	odd	12
8100.2.d.o.649.6		6	180.167	odd	12
8100.2.d.p.649.1		6	180.103	even	12
8100.2.d.p.649.6		6	180.67	even	12

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62241 + 0.606458i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.05042 + 3.55142i) q^{7} +(2.26442 - 1.96784i) q^{9} +O(q^{10})\)	\(q+(-1.62241 + 0.606458i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.05042 + 3.55142i) q^{7} +(2.26442 - 1.96784i) q^{9} +(-1.90841 - 3.30545i) q^{11} +(-2.90841 + 5.03751i) q^{13} +(-0.285997 + 1.70828i) q^{15} +3.81681 q^{17} +1.81681 q^{19} +(-5.48040 - 4.51837i) q^{21} +(1.05042 - 1.81937i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.48040 + 4.56592i) q^{27} +(3.60083 + 6.23682i) q^{29} +(-0.908405 + 1.57340i) q^{31} +(5.10083 + 4.20543i) q^{33} +4.10083 q^{35} -6.01847 q^{37} +(1.66359 - 9.93672i) q^{39} +(-5.50924 + 9.54228i) q^{41} +(2.90841 + 5.03751i) q^{43} +(-0.571993 - 2.94497i) q^{45} +(5.95882 + 10.3210i) q^{47} +(-4.90841 + 8.50161i) q^{49} +(-6.19243 + 2.31473i) q^{51} +4.20166 q^{53} -3.81681 q^{55} +(-2.94761 + 1.10182i) q^{57} +(-2.10083 + 3.63875i) q^{59} +(1.50924 + 2.61407i) q^{61} +(11.6316 + 4.00701i) q^{63} +(2.90841 + 5.03751i) q^{65} +(1.85799 - 3.21813i) q^{67} +(-0.600830 + 3.58880i) q^{69} +2.01847 q^{71} +8.00000 q^{73} +(1.33641 + 1.10182i) q^{75} +(7.82605 - 13.5551i) q^{77} +(1.00000 + 1.73205i) q^{79} +(1.25518 - 8.91204i) q^{81} +(-1.94958 - 3.37678i) q^{83} +(1.90841 - 3.30545i) q^{85} +(-9.62438 - 7.93492i) q^{87} -3.00000 q^{89} -23.8538 q^{91} +(0.519602 - 3.10361i) q^{93} +(0.908405 - 1.57340i) q^{95} +(-6.10083 - 10.5669i) q^{97} +(-10.8260 - 3.72949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9}+O(q^{10}) \) 6 * q + q^3 + 3 * q^5 + 3 * q^7 + 5 * q^9	\( 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9} - 6 q^{13} - q^{15} - 12 q^{19} - 20 q^{21} - 3 q^{23} - 3 q^{25} - 2 q^{27} + 3 q^{29} + 6 q^{31} + 12 q^{33} + 6 q^{35} + 24 q^{37} + 20 q^{39} - 3 q^{41} + 6 q^{43} - 2 q^{45} + 15 q^{47} - 18 q^{49} - 30 q^{51} - 12 q^{53} - 32 q^{57} + 6 q^{59} - 21 q^{61} + 29 q^{63} + 6 q^{65} + 9 q^{67} + 15 q^{69} - 48 q^{71} + 48 q^{73} - 2 q^{75} - 6 q^{77} + 6 q^{79} + 29 q^{81} - 21 q^{83} - 42 q^{87} - 18 q^{89} + 16 q^{93} - 6 q^{95} - 18 q^{97} - 12 q^{99}+O(q^{100}) \) 6 * q + q^3 + 3 * q^5 + 3 * q^7 + 5 * q^9 - 6 * q^13 - q^15 - 12 * q^19 - 20 * q^21 - 3 * q^23 - 3 * q^25 - 2 * q^27 + 3 * q^29 + 6 * q^31 + 12 * q^33 + 6 * q^35 + 24 * q^37 + 20 * q^39 - 3 * q^41 + 6 * q^43 - 2 * q^45 + 15 * q^47 - 18 * q^49 - 30 * q^51 - 12 * q^53 - 32 * q^57 + 6 * q^59 - 21 * q^61 + 29 * q^63 + 6 * q^65 + 9 * q^67 + 15 * q^69 - 48 * q^71 + 48 * q^73 - 2 * q^75 - 6 * q^77 + 6 * q^79 + 29 * q^81 - 21 * q^83 - 42 * q^87 - 18 * q^89 + 16 * q^93 - 6 * q^95 - 18 * q^97 - 12 * q^99

Introduction

L-functions

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