LMFDB - Embedded newform 720.2.q.i.481.2

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.2
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	720.481
Dual form			720.2.q.i.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.285997 - 1.70828i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.714003 + 1.23669i) q^{7} +(-2.83641 + 0.977122i) q^{9} +O(q^{10})$	\(q+(-0.285997 - 1.70828i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.714003 + 1.23669i) q^{7} +(-2.83641 + 0.977122i) q^{9} +(1.33641 + 2.31473i) q^{11} +(-2.33641 + 4.04678i) q^{13} +(1.62241 + 0.606458i) q^{15} +2.67282 q^{17} -4.67282 q^{19} +(1.90841 - 1.57340i) q^{21} +(-2.95882 + 5.12483i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.48040 + 4.56592i) q^{27} +(4.74482 + 8.21826i) q^{29} +(3.48040 - 6.02823i) q^{31} +(3.57199 - 2.94497i) q^{33} -1.42801 q^{35} -1.81681 q^{37} +(7.58123 + 2.83387i) q^{39} +(0.735581 - 1.27406i) q^{41} +(0.235581 + 0.408039i) q^{43} +(0.571993 - 2.94497i) q^{45} +(3.47842 + 6.02480i) q^{47} +(2.48040 - 4.29618i) q^{49} +(-0.764419 - 4.56592i) q^{51} -1.14399 q^{53} -2.67282 q^{55} +(1.33641 + 7.98247i) q^{57} +(-0.571993 + 0.990721i) q^{59} +(1.26442 + 2.19004i) q^{61} +(-3.23360 - 2.81009i) q^{63} +(-2.33641 - 4.04678i) q^{65} +(-3.29523 + 5.70751i) q^{67} +(9.60083 + 3.58880i) q^{69} +12.8745 q^{71} -1.71203 q^{73} +(-1.33641 + 1.10182i) q^{75} +(-1.90841 + 3.30545i) q^{77} +(-0.143987 - 0.249392i) q^{79} +(7.09046 - 5.54304i) q^{81} +(-2.14201 - 3.71007i) q^{83} +(-1.33641 + 2.31473i) q^{85} +(12.6821 - 10.4559i) q^{87} -3.00000 q^{89} -6.67282 q^{91} +(-11.2933 - 4.22143i) q^{93} +(2.33641 - 4.04678i) q^{95} +(-3.91764 - 6.78555i) q^{97} +(-6.05239 - 5.25970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9}+O(q^{10}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9} - 2 q^{11} - 4 q^{13} - q^{15} - 4 q^{17} - 8 q^{19} + 3 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 8 q^{31} + 20 q^{33} - 10 q^{35} + 12 q^{37} + 14 q^{39} + 13 q^{41} + 10 q^{43} + 2 q^{45} + 13 q^{47} + 2 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{55} - 2 q^{57} - 2 q^{59} - q^{61} - 33 q^{63} - 4 q^{65} + 11 q^{67} + 39 q^{69} + 20 q^{71} - 16 q^{73} + 2 q^{75} + 2 q^{79} - 19 q^{81} - 15 q^{83} + 2 q^{85} + 26 q^{87} - 18 q^{89} - 20 q^{91} - 42 q^{93} + 4 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9 - 2 * q^11 - 4 * q^13 - q^15 - 4 * q^17 - 8 * q^19 + 3 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 8 * q^31 + 20 * q^33 - 10 * q^35 + 12 * q^37 + 14 * q^39 + 13 * q^41 + 10 * q^43 + 2 * q^45 + 13 * q^47 + 2 * q^49 + 4 * q^51 - 4 * q^53 + 4 * q^55 - 2 * q^57 - 2 * q^59 - q^61 - 33 * q^63 - 4 * q^65 + 11 * q^67 + 39 * q^69 + 20 * q^71 - 16 * q^73 + 2 * q^75 + 2 * q^79 - 19 * q^81 - 15 * q^83 + 2 * q^85 + 26 * q^87 - 18 * q^89 - 20 * q^91 - 42 * q^93 + 4 * q^95 + 18 * q^97 - 22 * 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
$3$	−0.285997	−	1.70828i	−0.165120	−	0.986273i
$3$	−0.285997	−	1.70828i	−0.165120	−	0.986273i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	0.714003	+	1.23669i	0.269868	+	0.467425i	0.968828	−	0.247736i	$-0.0796866\pi$
$7$	0.714003	+	1.23669i	0.269868	+	0.467425i	−0.698960	+	0.715161i	$0.746353\pi$
$8$		0			0
$9$	−2.83641	+	0.977122i	−0.945471	+	0.325707i
$10$		0			0
$11$	1.33641	+	2.31473i	0.402943	+	0.697918i	0.994080	−	0.108653i	$-0.0346538\pi$
$11$	1.33641	+	2.31473i	0.402943	+	0.697918i	−0.591136	+	0.806572i	$0.701321\pi$
$12$		0			0
$13$	−2.33641	+	4.04678i	−0.648004	+	1.12238i	0.335595	+	0.942006i	$0.391063\pi$
$13$	−2.33641	+	4.04678i	−0.648004	+	1.12238i	−0.983599	+	0.180370i	$0.942271\pi$
$14$		0			0
$15$	1.62241	+	0.606458i	0.418904	+	0.156587i
$16$		0			0
$17$	2.67282			0.648255			0.324127	−	0.946013i	$-0.394929\pi$
$17$	2.67282			0.648255			0.324127	+	0.946013i	$0.394929\pi$
$18$		0			0
$19$	−4.67282			−1.07202			−0.536010	−	0.844212i	$-0.680069\pi$
$19$	−4.67282			−1.07202			−0.536010	+	0.844212i	$0.680069\pi$
$20$		0			0
$21$	1.90841	−	1.57340i	0.416448	−	0.343345i
$22$		0			0
$23$	−2.95882	+	5.12483i	−0.616957	+	1.06860i	0.373081	+	0.927799i	$0.378301\pi$
$23$	−2.95882	+	5.12483i	−0.616957	+	1.06860i	−0.990038	+	0.140802i	$0.955032\pi$
$24$		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
$29$	4.74482	+	8.21826i	0.881090	+	1.52609i	0.850130	+	0.526573i	$0.176523\pi$
$29$	4.74482	+	8.21826i	0.881090	+	1.52609i	0.0309603	+	0.999521i	$0.490143\pi$
$30$		0			0
$31$	3.48040	−	6.02823i	0.625098	−	1.08270i	−0.363424	−	0.931624i	$-0.618392\pi$
$31$	3.48040	−	6.02823i	0.625098	−	1.08270i	0.988522	−	0.151078i	$-0.0482743\pi$
$32$		0			0
$33$	3.57199	−	2.94497i	0.621804	−	0.512653i
$34$		0			0
$35$	−1.42801			−0.241377
$36$		0			0
$37$	−1.81681			−0.298682			−0.149341	−	0.988786i	$-0.547715\pi$
$37$	−1.81681			−0.298682			−0.149341	+	0.988786i	$0.547715\pi$
$38$		0			0
$39$	7.58123	+	2.83387i	1.21397	+	0.453782i
$40$		0			0
$41$	0.735581	−	1.27406i	0.114879	−	0.198975i	−0.802853	−	0.596177i	$-0.796685\pi$
$41$	0.735581	−	1.27406i	0.114879	−	0.198975i	0.917731	+	0.397202i	$0.130019\pi$
$42$		0			0
$43$	0.235581	+	0.408039i	0.0359258	+	0.0622254i	0.883429	−	0.468565i	$-0.155229\pi$
$43$	0.235581	+	0.408039i	0.0359258	+	0.0622254i	−0.847503	+	0.530790i	$0.821895\pi$
$44$		0			0
$45$	0.571993	−	2.94497i	0.0852677	−	0.439010i
$46$		0			0
$47$	3.47842	+	6.02480i	0.507380	+	0.878808i	0.999964	+	0.00854274i	$0.00271927\pi$
$47$	3.47842	+	6.02480i	0.507380	+	0.878808i	−0.492584	+	0.870265i	$0.663947\pi$
$48$		0			0
$49$	2.48040	−	4.29618i	0.354343	−	0.613739i
$50$		0			0
$51$	−0.764419	−	4.56592i	−0.107040	−	0.639357i
$52$		0			0
$53$	−1.14399			−0.157139			−0.0785693	−	0.996909i	$-0.525035\pi$
$53$	−1.14399			−0.157139			−0.0785693	+	0.996909i	$0.525035\pi$
$54$		0			0
$55$	−2.67282			−0.360403
$56$		0			0
$57$	1.33641	+	7.98247i	0.177012	+	1.05730i
$58$		0			0
$59$	−0.571993	+	0.990721i	−0.0744672	+	0.128981i	−0.900854	−	0.434121i	$-0.857059\pi$
$59$	−0.571993	+	0.990721i	−0.0744672	+	0.128981i	0.826387	+	0.563102i	$0.190392\pi$
$60$		0			0
$61$	1.26442	+	2.19004i	0.161892	+	0.280406i	0.935547	−	0.353201i	$-0.114907\pi$
$61$	1.26442	+	2.19004i	0.161892	+	0.280406i	−0.773655	+	0.633607i	$0.781574\pi$
$62$		0			0
$63$	−3.23360	−	2.81009i	−0.407396	−	0.354039i
$64$		0			0
$65$	−2.33641	−	4.04678i	−0.289796	−	0.501942i
$66$		0			0
$67$	−3.29523	+	5.70751i	−0.402577	+	0.697283i	−0.994036	−	0.109051i	$-0.965219\pi$
$67$	−3.29523	+	5.70751i	−0.402577	+	0.697283i	0.591459	+	0.806335i	$0.298552\pi$
$68$		0			0
$69$	9.60083	+	3.58880i	1.15580	+	0.432040i
$70$		0			0
$71$	12.8745			1.52792			0.763960	−	0.645263i	$-0.223252\pi$
$71$	12.8745			1.52792			0.763960	+	0.645263i	$0.223252\pi$
$72$		0			0
$73$	−1.71203			−0.200378			−0.100189	−	0.994968i	$-0.531945\pi$
$73$	−1.71203			−0.200378			−0.100189	+	0.994968i	$0.531945\pi$
$74$		0			0
$75$	−1.33641	+	1.10182i	−0.154316	+	0.127227i
$76$		0			0
$77$	−1.90841	+	3.30545i	−0.217483	+	0.376692i
$78$		0			0
$79$	−0.143987	−	0.249392i	−0.0161998	−	0.0280588i	0.857812	−	0.513964i	$-0.171823\pi$
$79$	−0.143987	−	0.249392i	−0.0161998	−	0.0280588i	−0.874012	+	0.485905i	$0.838490\pi$
$80$		0			0
$81$	7.09046	−	5.54304i	0.787829	−	0.615894i
$82$		0			0
$83$	−2.14201	−	3.71007i	−0.235116	−	0.407233i	0.724190	−	0.689600i	$-0.242214\pi$
$83$	−2.14201	−	3.71007i	−0.235116	−	0.407233i	−0.959306	+	0.282367i	$0.908880\pi$
$84$		0			0
$85$	−1.33641	+	2.31473i	−0.144954	+	0.251068i
$86$		0			0
$87$	12.6821	−	10.4559i	1.35966	−	1.12098i
$88$		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
$91$	−6.67282			−0.699502
$92$		0			0
$93$	−11.2933	−	4.22143i	−1.17106	−	0.437742i
$94$		0			0
$95$	2.33641	−	4.04678i	0.239711	−	0.415191i
$96$		0			0
$97$	−3.91764	−	6.78555i	−0.397776	−	0.688968i	0.595675	−	0.803225i	$-0.296885\pi$
$97$	−3.91764	−	6.78555i	−0.397776	−	0.688968i	−0.993451	+	0.114257i	$0.963551\pi$
$98$		0			0
$99$	−6.05239	−	5.25970i	−0.608288	−	0.528620i
$100$		0			0
$101$	2.10083	+	3.63875i	0.209040	+	0.362069i	0.951413	−	0.307919i	$-0.0996326\pi$
$101$	2.10083	+	3.63875i	0.209040	+	0.362069i	−0.742372	+	0.669988i	$0.766299\pi$
$102$		0			0
$103$	−0.908405	+	1.57340i	−0.0895078	+	0.155032i	−0.907303	−	0.420477i	$-0.861863\pi$
$103$	−0.908405	+	1.57340i	−0.0895078	+	0.155032i	0.817795	+	0.575509i	$0.195196\pi$
$104$		0			0
$105$	0.408405	+	2.43943i	0.0398563	+	0.238064i
$106$		0			0
$107$	−11.9176			−1.15212			−0.576061	−	0.817407i	$-0.695411\pi$
$107$	−11.9176			−1.15212			−0.576061	+	0.817407i	$0.695411\pi$
$108$		0			0
$109$	−16.6521			−1.59498			−0.797491	−	0.603331i	$-0.793840\pi$
$109$	−16.6521			−1.59498			−0.797491	+	0.603331i	$0.793840\pi$
$110$		0			0
$111$	0.519602	+	3.10361i	0.0493184	+	0.294582i
$112$		0			0
$113$	−10.0616	+	17.4272i	−0.946518	+	1.63942i	−0.193836	+	0.981034i	$0.562093\pi$
$113$	−10.0616	+	17.4272i	−0.946518	+	1.63942i	−0.752682	+	0.658384i	$0.771240\pi$
$114$		0			0
$115$	−2.95882	−	5.12483i	−0.275911	−	0.477893i
$116$		0			0
$117$	2.67282	−	13.7613i	0.247103	−	1.27223i
$118$		0			0
$119$	1.90841	+	3.30545i	0.174943	+	0.303011i
$120$		0			0
$121$	1.92801	−	3.33941i	0.175273	−	0.303582i
$122$		0			0
$123$	−2.38683	−	0.892198i	−0.215213	−	0.0804468i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−2.18714			−0.194078			−0.0970388	−	0.995281i	$-0.530937\pi$
$127$	−2.18714			−0.194078			−0.0970388	+	0.995281i	$0.530937\pi$
$128$		0			0
$129$	0.629668	−	0.519136i	0.0554391	−	0.0457074i
$130$		0			0
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	−3.33641	−	5.77883i	−0.289304	−	0.501089i
$134$		0			0
$135$	−5.19440	−	0.134872i	−0.447063	−	0.0116079i
$136$		0			0
$137$	5.10083	+	8.83490i	0.435793	+	0.754816i	0.997360	−	0.0726153i	$-0.0231345\pi$
$137$	5.10083	+	8.83490i	0.435793	+	0.754816i	−0.561567	+	0.827431i	$0.689801\pi$
$138$		0			0
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$		0			0
$141$	9.29721	−	7.66518i	0.782966	−	0.645524i
$142$		0			0
$143$	−12.4896			−1.04444
$144$		0			0
$145$	−9.48963			−0.788071
$146$		0			0
$147$	−8.04844	−	3.00851i	−0.663824	−	0.248138i
$148$		0			0
$149$	10.0381	−	17.3865i	0.822351	−	1.42435i	−0.0815762	−	0.996667i	$-0.525995\pi$
$149$	10.0381	−	17.3865i	0.822351	−	1.42435i	0.903927	−	0.427687i	$-0.140671\pi$
$150$		0			0
$151$	1.51960	+	2.63203i	0.123663	+	0.214191i	0.921210	−	0.389066i	$-0.127202\pi$
$151$	1.51960	+	2.63203i	0.123663	+	0.214191i	−0.797546	+	0.603258i	$0.793869\pi$
$152$		0			0
$153$	−7.58123	+	2.61168i	−0.612906	+	0.211141i
$154$		0			0
$155$	3.48040	+	6.02823i	0.279552	+	0.484199i
$156$		0			0
$157$	−0.100830	+	0.174643i	−0.00804714	+	0.0139381i	−0.870021	−	0.493015i	$-0.835895\pi$
$157$	−0.100830	+	0.174643i	−0.00804714	+	0.0139381i	0.861974	+	0.506953i	$0.169228\pi$
$158$		0			0
$159$	0.327176	+	1.95424i	0.0259468	+	0.154982i
$160$		0			0
$161$	−8.45043			−0.665987
$162$		0			0
$163$	−17.8168			−1.39552			−0.697760	−	0.716331i	$-0.745820\pi$
$163$	−17.8168			−1.39552			−0.697760	+	0.716331i	$0.745820\pi$
$164$		0			0
$165$	0.764419	+	4.56592i	0.0595099	+	0.355456i
$166$		0			0
$167$	7.05042	−	12.2117i	0.545578	−	0.944968i	−0.452993	−	0.891514i	$-0.649644\pi$
$167$	7.05042	−	12.2117i	0.545578	−	0.944968i	0.998570	−	0.0534538i	$-0.0170230\pi$
$168$		0			0
$169$	−4.41764	−	7.65158i	−0.339819	−	0.588583i
$170$		0			0
$171$	13.2541	−	4.56592i	1.01356	−	0.349165i
$172$		0			0
$173$	−2.18319	−	3.78140i	−0.165985	−	0.287494i	0.771020	−	0.636811i	$-0.219747\pi$
$173$	−2.18319	−	3.78140i	−0.165985	−	0.287494i	−0.937005	+	0.349317i	$0.886414\pi$
$174$		0			0
$175$	0.714003	−	1.23669i	0.0539736	−	0.0934850i
$176$		0			0
$177$	1.85601	+	0.693779i	0.139507	+	0.0521476i
$178$		0			0
$179$	15.1625			1.13330			0.566648	−	0.823960i	$-0.308240\pi$
$179$	15.1625			1.13330			0.566648	+	0.823960i	$0.308240\pi$
$180$		0			0
$181$	3.20166			0.237978			0.118989	−	0.992896i	$-0.462035\pi$
$181$	3.20166			0.237978			0.118989	+	0.992896i	$0.462035\pi$
$182$		0			0
$183$	3.37957	−	2.78632i	0.249825	−	0.205971i
$184$		0			0
$185$	0.908405	−	1.57340i	0.0667873	−	0.115679i
$186$		0			0
$187$	3.57199	+	6.18687i	0.261210	+	0.452429i
$188$		0			0
$189$	−3.87562	+	6.32757i	−0.281910	+	0.460263i
$190$		0			0
$191$	−1.41877	−	2.45738i	−0.102659	−	0.177810i	0.810121	−	0.586263i	$-0.199402\pi$
$191$	−1.41877	−	2.45738i	−0.102659	−	0.177810i	−0.912779	+	0.408453i	$0.866068\pi$
$192$		0			0
$193$	9.39409	−	16.2710i	0.676201	−	1.17121i	−0.299915	−	0.953966i	$-0.596958\pi$
$193$	9.39409	−	16.2710i	0.676201	−	1.17121i	0.976116	−	0.217249i	$-0.0697083\pi$
$194$		0			0
$195$	−6.24482	+	5.14860i	−0.447201	+	0.368699i
$196$		0			0
$197$	5.83528			0.415747			0.207873	−	0.978156i	$-0.433346\pi$
$197$	5.83528			0.415747			0.207873	+	0.978156i	$0.433346\pi$
$198$		0			0
$199$	−13.0761			−0.926943			−0.463472	−	0.886112i	$-0.653396\pi$
$199$	−13.0761			−0.926943			−0.463472	+	0.886112i	$0.653396\pi$
$200$		0			0
$201$	10.6924	+	3.99684i	0.754186	+	0.281915i
$202$		0			0
$203$	−6.77563	+	11.7357i	−0.475556	+	0.823687i
$204$		0			0
$205$	0.735581	+	1.27406i	0.0513752	+	0.0889845i
$206$		0			0
$207$	3.38485	−	17.4272i	0.235263	−	1.21128i
$208$		0			0
$209$	−6.24482	−	10.8163i	−0.431963	−	0.748182i
$210$		0			0
$211$	4.19243	−	7.26149i	0.288618	−	0.499902i	−0.684862	−	0.728673i	$-0.740137\pi$
$211$	4.19243	−	7.26149i	0.288618	−	0.499902i	0.973480	+	0.228771i	$0.0734708\pi$
$212$		0			0
$213$	−3.68206	−	21.9932i	−0.252291	−	1.50695i
$214$		0			0
$215$	−0.471163			−0.0321330
$216$		0			0
$217$	9.94006			0.674776
$218$		0			0
$219$	0.489634	+	2.92461i	0.0330864	+	0.197627i
$220$		0			0
$221$	−6.24482	+	10.8163i	−0.420072	+	0.727586i
$222$		0			0
$223$	4.58321	+	7.93834i	0.306914	+	0.531591i	0.977686	−	0.210073i	$-0.0673702\pi$
$223$	4.58321	+	7.93834i	0.306914	+	0.531591i	−0.670772	+	0.741664i	$0.734037\pi$
$224$		0			0
$225$	2.26442	+	1.96784i	0.150961	+	0.131190i
$226$		0			0
$227$	−1.33641	−	2.31473i	−0.0887008	−	0.153634i	0.818261	−	0.574846i	$-0.194938\pi$
$227$	−1.33641	−	2.31473i	−0.0887008	−	0.153634i	−0.906962	+	0.421212i	$0.861605\pi$
$228$		0			0
$229$	−1.27365	+	2.20603i	−0.0841654	+	0.145779i	−0.905035	−	0.425336i	$-0.860156\pi$
$229$	−1.27365	+	2.20603i	−0.0841654	+	0.145779i	0.820870	+	0.571115i	$0.193489\pi$
$230$		0			0
$231$	6.19243	+	2.31473i	0.407432	+	0.152298i
$232$		0			0
$233$	−6.22013			−0.407494			−0.203747	−	0.979024i	$-0.565312\pi$
$233$	−6.22013			−0.407494			−0.203747	+	0.979024i	$0.565312\pi$
$234$		0			0
$235$	−6.95684			−0.453814
$236$		0			0
$237$	−0.384851	+	0.317294i	−0.0249987	+	0.0206105i
$238$		0			0
$239$	4.06163	−	7.03494i	0.262725	−	0.455053i	−0.704240	−	0.709962i	$-0.748712\pi$
$239$	4.06163	−	7.03494i	0.262725	−	0.455053i	0.966965	+	0.254909i	$0.0820455\pi$
$240$		0			0
$241$	13.1821	+	22.8320i	0.849131	+	1.47074i	0.881985	+	0.471278i	$0.156207\pi$
$241$	13.1821	+	22.8320i	0.849131	+	1.47074i	−0.0328536	+	0.999460i	$0.510460\pi$
$242$		0			0
$243$	−11.4969	−	10.5272i	−0.737526	−	0.675319i
$244$		0			0
$245$	2.48040	+	4.29618i	0.158467	+	0.274473i
$246$		0			0
$247$	10.9176	−	18.9099i	0.694673	−	1.20321i
$248$		0			0
$249$	−5.72522	+	4.72021i	−0.362821	+	0.299131i
$250$		0			0
$251$	0.549569			0.0346885			0.0173443	−	0.999850i	$-0.494479\pi$
$251$	0.549569			0.0346885			0.0173443	+	0.999850i	$0.494479\pi$
$252$		0			0
$253$	−15.8168			−0.994394
$254$		0			0
$255$	4.33641	+	1.62095i	0.271557	+	0.101508i
$256$		0			0
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$		0			0
$259$	−1.29721	−	2.24683i	−0.0806046	−	0.139611i
$260$		0			0
$261$	−21.4885	−	18.6741i	−1.33010	−	1.15590i
$262$		0			0
$263$	5.94761	+	10.3016i	0.366745	+	0.635221i	0.989055	−	0.147550i	$-0.0471387\pi$
$263$	5.94761	+	10.3016i	0.366745	+	0.635221i	−0.622309	+	0.782771i	$0.713805\pi$
$264$		0			0
$265$	0.571993	−	0.990721i	0.0351373	−	0.0608595i
$266$		0			0
$267$	0.857990	+	5.12483i	0.0525081	+	0.313634i
$268$		0			0
$269$	28.5737			1.74217			0.871084	−	0.491134i	$-0.163417\pi$
$269$	28.5737			1.74217			0.871084	+	0.491134i	$0.163417\pi$
$270$		0			0
$271$	23.3641			1.41927			0.709635	−	0.704570i	$-0.248860\pi$
$271$	23.3641			1.41927			0.709635	+	0.704570i	$0.248860\pi$
$272$		0			0
$273$	1.90841	+	11.3990i	0.115502	+	0.689900i
$274$		0			0
$275$	1.33641	−	2.31473i	0.0805887	−	0.139584i
$276$		0			0
$277$	7.53807	+	13.0563i	0.452919	+	0.784479i	0.998566	−	0.0535366i	$-0.0170494\pi$
$277$	7.53807	+	13.0563i	0.452919	+	0.784479i	−0.545647	+	0.838015i	$0.683716\pi$
$278$		0			0
$279$	−3.98153	+	20.4993i	−0.238368	+	1.22726i
$280$		0			0
$281$	−3.32605	−	5.76088i	−0.198415	−	0.343665i	0.749599	−	0.661892i	$-0.230246\pi$
$281$	−3.32605	−	5.76088i	−0.198415	−	0.343665i	−0.948015	+	0.318226i	$0.896913\pi$
$282$		0			0
$283$	13.4485	−	23.2934i	0.799428	−	1.38465i	−0.120562	−	0.992706i	$-0.538470\pi$
$283$	13.4485	−	23.2934i	0.799428	−	1.38465i	0.919989	−	0.391943i	$-0.128197\pi$
$284$		0			0
$285$	−7.58123	−	2.83387i	−0.449073	−	0.167864i
$286$		0			0
$287$	2.10083			0.124008
$288$		0			0
$289$	−9.85601			−0.579765
$290$		0			0
$291$	−10.4712	+	8.63306i	−0.613830	+	0.506079i
$292$		0			0
$293$	−6.19243	+	10.7256i	−0.361765	+	0.626596i	−0.988251	−	0.152837i	$-0.951159\pi$
$293$	−6.19243	+	10.7256i	−0.361765	+	0.626596i	0.626486	+	0.779433i	$0.284493\pi$
$294$		0			0
$295$	−0.571993	−	0.990721i	−0.0333027	−	0.0576820i
$296$		0			0
$297$	−7.25405	+	11.8434i	−0.420923	+	0.687224i
$298$		0			0
$299$	−13.8260	−	23.9474i	−0.799581	−	1.38491i
$300$		0			0
$301$	−0.336412	+	0.582682i	−0.0193905	+	0.0335853i
$302$		0			0
$303$	5.61515	−	4.62947i	0.322582	−	0.265956i
$304$		0			0
$305$	−2.52884			−0.144801
$306$		0			0
$307$	2.49359			0.142317			0.0711583	−	0.997465i	$-0.477330\pi$
$307$	2.49359			0.142317			0.0711583	+	0.997465i	$0.477330\pi$
$308$		0			0
$309$	2.94761	+	1.10182i	0.167684	+	0.0626802i
$310$		0			0
$311$	−12.1101	+	20.9752i	−0.686699	+	1.18940i	0.286201	+	0.958170i	$0.407608\pi$
$311$	−12.1101	+	20.9752i	−0.686699	+	1.18940i	−0.972900	+	0.231228i	$0.925726\pi$
$312$		0			0
$313$	17.5420	+	30.3837i	0.991534	+	1.71739i	0.608219	+	0.793770i	$0.291884\pi$
$313$	17.5420	+	30.3837i	0.991534	+	1.71739i	0.383315	+	0.923618i	$0.374782\pi$
$314$		0			0
$315$	4.05042	−	1.39534i	0.228215	−	0.0786183i
$316$		0			0
$317$	5.23558	+	9.06829i	0.294060	+	0.509326i	0.974766	−	0.223231i	$-0.0716603\pi$
$317$	5.23558	+	9.06829i	0.294060	+	0.509326i	−0.680706	+	0.732557i	$0.738327\pi$
$318$		0			0
$319$	−12.6821	+	21.9660i	−0.710059	+	1.22986i
$320$		0			0
$321$	3.40841	+	20.3586i	0.190239	+	1.13631i
$322$		0			0
$323$	−12.4896			−0.694942
$324$		0			0
$325$	4.67282			0.259202
$326$		0			0
$327$	4.76244	+	28.4464i	0.263364	+	1.57309i
$328$		0			0
$329$	−4.96721	+	8.60346i	−0.273851	+	0.474324i
$330$		0			0
$331$	8.38880	+	14.5298i	0.461090	+	0.798632i	0.999016	−	0.0443606i	$-0.0141251\pi$
$331$	8.38880	+	14.5298i	0.461090	+	0.798632i	−0.537925	+	0.842993i	$0.680792\pi$
$332$		0			0
$333$	5.15322	−	1.77525i	0.282395	−	0.0972829i
$334$		0			0
$335$	−3.29523	−	5.70751i	−0.180038	−	0.311835i
$336$		0			0
$337$	13.5905	−	23.5394i	0.740320	−	1.28227i	−0.212030	−	0.977263i	$-0.568007\pi$
$337$	13.5905	−	23.5394i	0.740320	−	1.28227i	0.952350	−	0.305008i	$-0.0986592\pi$
$338$		0			0
$339$	32.6481	+	12.2039i	1.77320	+	0.662825i
$340$		0			0
$341$	18.6050			1.00752
$342$		0			0
$343$	17.0801			0.922239
$344$		0			0
$345$	−7.90841	+	6.52016i	−0.425774	+	0.351034i
$346$		0			0
$347$	−11.7829	+	20.4086i	−0.632539	+	1.09559i	0.354492	+	0.935059i	$0.384654\pi$
$347$	−11.7829	+	20.4086i	−0.632539	+	1.09559i	−0.987031	+	0.160530i	$0.948680\pi$
$348$		0			0
$349$	5.35601	+	9.27689i	0.286701	+	0.496580i	0.973020	−	0.230720i	$-0.0741081\pi$
$349$	5.35601	+	9.27689i	0.286701	+	0.496580i	−0.686319	+	0.727300i	$0.740775\pi$
$350$		0			0
$351$	−24.2725	−	0.630233i	−1.29557	−	0.0336393i
$352$		0			0
$353$	−13.6336	−	23.6141i	−0.725644	−	1.25685i	−0.958708	−	0.284392i	$-0.908208\pi$
$353$	−13.6336	−	23.6141i	−0.725644	−	1.25685i	0.233064	−	0.972461i	$-0.425125\pi$
$354$		0			0
$355$	−6.43724	+	11.1496i	−0.341653	+	0.591761i
$356$		0			0
$357$	5.10083	−	4.20543i	0.269965	−	0.222575i
$358$		0			0
$359$	10.6807			0.563707			0.281854	−	0.959457i	$-0.409051\pi$
$359$	10.6807			0.563707			0.281854	+	0.959457i	$0.409051\pi$
$360$		0			0
$361$	2.83528			0.149225
$362$		0			0
$363$	−6.25603	−	2.33851i	−0.328356	−	0.122740i
$364$		0			0
$365$	0.856013	−	1.48266i	0.0448058	−	0.0776059i
$366$		0			0
$367$	−4.23558	−	7.33624i	−0.221096	−	0.382949i	0.734045	−	0.679100i	$-0.237630\pi$
$367$	−4.23558	−	7.33624i	−0.221096	−	0.382949i	−0.955141	+	0.296152i	$0.904297\pi$
$368$		0			0
$369$	−0.841495	+	4.33252i	−0.0438065	+	0.225542i
$370$		0			0
$371$	−0.816810	−	1.41476i	−0.0424067	−	0.0734505i
$372$		0			0
$373$	−5.06163	+	8.76700i	−0.262081	+	0.453938i	−0.966795	−	0.255554i	$-0.917742\pi$
$373$	−5.06163	+	8.76700i	−0.262081	+	0.453938i	0.704714	+	0.709492i	$0.251075\pi$
$374$		0			0
$375$	−0.285997	−	1.70828i	−0.0147688	−	0.0882150i
$376$		0			0
$377$	−44.3434			−2.28380
$378$		0			0
$379$	−11.9216			−0.612371			−0.306186	−	0.951972i	$-0.599053\pi$
$379$	−11.9216			−0.612371			−0.306186	+	0.951972i	$0.599053\pi$
$380$		0			0
$381$	0.625515	+	3.73624i	0.0320461	+	0.191414i
$382$		0			0
$383$	4.90841	−	8.50161i	0.250808	−	0.434412i	−0.712941	−	0.701224i	$-0.752637\pi$
$383$	4.90841	−	8.50161i	0.250808	−	0.434412i	0.963748	+	0.266813i	$0.0859705\pi$
$384$		0			0
$385$	−1.90841	−	3.30545i	−0.0972613	−	0.168462i
$386$		0			0
$387$	−1.06691	−	0.927175i	−0.0542341	−	0.0471309i
$388$		0			0
$389$	−4.61007	−	7.98487i	−0.233740	−	0.404849i	0.725166	−	0.688574i	$-0.241763\pi$
$389$	−4.61007	−	7.98487i	−0.233740	−	0.404849i	−0.958906	+	0.283725i	$0.908430\pi$
$390$		0			0
$391$	−7.90841	+	13.6978i	−0.399945	+	0.692725i
$392$		0			0
$393$	9.73445	+	3.63875i	0.491038	+	0.183550i
$394$		0			0
$395$	0.287973			0.0144895
$396$		0			0
$397$	−22.9793			−1.15330			−0.576648	−	0.816993i	$-0.695640\pi$
$397$	−22.9793			−1.15330			−0.576648	+	0.816993i	$0.695640\pi$
$398$		0			0
$399$	−8.91764	+	7.35224i	−0.446440	+	0.368072i
$400$		0			0
$401$	5.53279	−	9.58307i	0.276294	−	0.478556i	−0.694167	−	0.719814i	$-0.744227\pi$
$401$	5.53279	−	9.58307i	0.276294	−	0.478556i	0.970461	+	0.241259i	$0.0775602\pi$
$402$		0			0
$403$	16.2633	+	28.1688i	0.810132	+	1.40319i
$404$		0			0
$405$	1.25518	+	8.91204i	0.0623705	+	0.442843i
$406$		0			0
$407$	−2.42801	−	4.20543i	−0.120352	−	0.208455i
$408$		0			0
$409$	8.81681	−	15.2712i	0.435963	−	0.755110i	−0.561411	−	0.827537i	$-0.689741\pi$
$409$	8.81681	−	15.2712i	0.435963	−	0.755110i	0.997374	+	0.0724270i	$0.0230744\pi$
$410$		0			0
$411$	13.6336	−	11.2404i	0.672497	−	0.554447i
$412$		0			0
$413$	−1.63362			−0.0803852
$414$		0			0
$415$	4.28402			0.210294
$416$		0			0
$417$	−12.9793	−	4.85166i	−0.635597	−	0.237587i
$418$		0			0
$419$	18.5173	−	32.0730i	0.904631	−	1.56687i	0.0832199	−	0.996531i	$-0.473480\pi$
$419$	18.5173	−	32.0730i	0.904631	−	1.56687i	0.821411	−	0.570336i	$-0.193187\pi$
$420$		0			0
$421$	−2.52884	−	4.38007i	−0.123248	−	0.213472i	0.797799	−	0.602924i	$-0.205998\pi$
$421$	−2.52884	−	4.38007i	−0.123248	−	0.213472i	−0.921047	+	0.389452i	$0.872664\pi$
$422$		0			0
$423$	−15.7532	−	13.6900i	−0.765947	−	0.665630i
$424$		0			0
$425$	−1.33641	−	2.31473i	−0.0648255	−	0.112281i
$426$		0			0
$427$	−1.80560	+	3.12739i	−0.0873790	+	0.151345i
$428$		0			0
$429$	3.57199	+	21.3357i	0.172457	+	1.03010i
$430$		0			0
$431$	5.23030			0.251935			0.125967	−	0.992034i	$-0.459797\pi$
$431$	5.23030			0.251935			0.125967	+	0.992034i	$0.459797\pi$
$432$		0			0
$433$	34.3434			1.65044			0.825219	−	0.564813i	$-0.191052\pi$
$433$	34.3434			1.65044			0.825219	+	0.564813i	$0.191052\pi$
$434$		0			0
$435$	2.71400	+	16.2109i	0.130127	+	0.777254i
$436$		0			0
$437$	13.8260	−	23.9474i	0.661389	−	1.14556i
$438$		0			0
$439$	−9.77365	−	16.9285i	−0.466471	−	0.807952i	0.532796	−	0.846244i	$-0.321141\pi$
$439$	−9.77365	−	16.9285i	−0.466471	−	0.807952i	−0.999267	+	0.0382924i	$0.987808\pi$
$440$		0			0
$441$	−2.83754	+	14.6094i	−0.135121	+	0.695685i
$442$		0			0
$443$	5.25208	+	9.09686i	0.249534	+	0.432205i	0.963396	−	0.268081i	$-0.0863893\pi$
$443$	5.25208	+	9.09686i	0.249534	+	0.432205i	−0.713863	+	0.700286i	$0.753056\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$		0			0
$447$	−32.5717	−	12.1753i	−1.54059	−	0.575873i
$448$		0			0
$449$	22.8560			1.07864			0.539321	−	0.842100i	$-0.318681\pi$
$449$	22.8560			1.07864			0.539321	+	0.842100i	$0.318681\pi$
$450$		0			0
$451$	3.93216			0.185158
$452$		0			0
$453$	4.06163	−	3.34865i	0.190832	−	0.157333i
$454$		0			0
$455$	3.33641	−	5.77883i	0.156413	−	0.270916i
$456$		0			0
$457$	7.01319	+	12.1472i	0.328063	+	0.568222i	0.982127	−	0.188217i	$-0.0602708\pi$
$457$	7.01319	+	12.1472i	0.328063	+	0.568222i	−0.654064	+	0.756439i	$0.726937\pi$
$458$		0			0
$459$	6.62967	+	12.2039i	0.309446	+	0.569629i
$460$		0			0
$461$	12.0513	+	20.8734i	0.561283	+	0.972171i	0.997385	+	0.0722736i	$0.0230255\pi$
$461$	12.0513	+	20.8734i	0.561283	+	0.972171i	−0.436102	+	0.899897i	$0.643641\pi$
$462$		0			0
$463$	−16.9700	+	29.3930i	−0.788664	+	1.36601i	0.138121	+	0.990415i	$0.455894\pi$
$463$	−16.9700	+	29.3930i	−0.788664	+	1.36601i	−0.926785	+	0.375591i	$0.877440\pi$
$464$		0			0
$465$	9.30249	−	7.66953i	0.431393	−	0.355666i
$466$		0			0
$467$	27.3720			1.26663			0.633313	−	0.773896i	$-0.281695\pi$
$467$	27.3720			1.26663			0.633313	+	0.773896i	$0.281695\pi$
$468$		0			0
$469$	−9.41123			−0.434570
$470$		0			0
$471$	0.327176	+	0.122299i	0.0150755	+	0.00563523i
$472$		0			0
$473$	−0.629668	+	1.09062i	−0.0289521	+	0.0501466i
$474$		0			0
$475$	2.33641	+	4.04678i	0.107202	+	0.185679i
$476$		0			0
$477$	3.24482	−	1.11781i	0.148570	−	0.0511812i
$478$		0			0
$479$	2.61515	+	4.52957i	0.119489	+	0.206961i	0.919565	−	0.392937i	$-0.128541\pi$
$479$	2.61515	+	4.52957i	0.119489	+	0.206961i	−0.800076	+	0.599898i	$0.795208\pi$
$480$		0			0
$481$	4.24482	−	7.35224i	0.193547	−	0.335233i
$482$		0			0
$483$	2.41679	+	14.4357i	0.109968	+	0.656846i
$484$		0			0
$485$	7.83528			0.355782
$486$		0			0
$487$	24.0185			1.08838			0.544190	−	0.838962i	$-0.316837\pi$
$487$	24.0185			1.08838			0.544190	+	0.838962i	$0.316837\pi$
$488$		0			0
$489$	5.09555	+	30.4360i	0.230429	+	1.37636i
$490$		0			0
$491$	7.38880	−	12.7978i	0.333452	−	0.577556i	−0.649734	−	0.760161i	$-0.725120\pi$
$491$	7.38880	−	12.7978i	0.333452	−	0.577556i	0.983186	+	0.182606i	$0.0584531\pi$
$492$		0			0
$493$	12.6821	+	21.9660i	0.571171	+	0.989298i
$494$		0			0
$495$	7.58123	−	2.61168i	0.340751	−	0.117386i
$496$		0			0
$497$	9.19243	+	15.9217i	0.412337	+	0.714188i
$498$		0			0
$499$	12.4280	−	21.5259i	0.556354	−	0.963633i	−0.441443	−	0.897289i	$-0.645533\pi$
$499$	12.4280	−	21.5259i	0.556354	−	0.963633i	0.997797	−	0.0663440i	$-0.0211335\pi$
$500$		0			0
$501$	−22.8773	−	8.55155i	−1.02208	−	0.382055i
$502$		0			0
$503$	−38.9154			−1.73515			−0.867576	−	0.497305i	$-0.834323\pi$
$503$	−38.9154			−1.73515			−0.867576	+	0.497305i	$0.834323\pi$
$504$		0			0
$505$	−4.20166			−0.186971
$506$		0			0
$507$	−11.8076	+	9.73487i	−0.524393	+	0.432341i
$508$		0			0
$509$	−1.01037	+	1.75001i	−0.0447837	+	0.0775676i	−0.887548	−	0.460715i	$-0.847593\pi$
$509$	−1.01037	+	1.75001i	−0.0447837	+	0.0775676i	0.842765	+	0.538282i	$0.180927\pi$
$510$		0			0
$511$	−1.22239	−	2.11725i	−0.0540755	−	0.0936615i
$512$		0			0
$513$	−11.5905	−	21.3357i	−0.511732	−	0.941996i
$514$		0			0
$515$	−0.908405	−	1.57340i	−0.0400291	−	0.0693325i
$516$		0			0
$517$	−9.29721	+	16.1032i	−0.408891	+	0.708220i
$518$		0			0
$519$	−5.83528	+	4.81096i	−0.256140	+	0.211178i
$520$		0			0
$521$	−23.0290			−1.00892			−0.504460	−	0.863435i	$-0.668308\pi$
$521$	−23.0290			−1.00892			−0.504460	+	0.863435i	$0.668308\pi$
$522$		0			0
$523$	41.1170			1.79792			0.898961	−	0.438028i	$-0.144323\pi$
$523$	41.1170			1.79792			0.898961	+	0.438028i	$0.144323\pi$
$524$		0			0
$525$	−2.31681	−	0.866025i	−0.101114	−	0.0377964i
$526$		0			0
$527$	9.30249	−	16.1124i	0.405223	−	0.701867i
$528$		0			0
$529$	−6.00924	−	10.4083i	−0.261271	−	0.452535i
$530$		0			0
$531$	0.654353	−	3.36900i	0.0283965	−	0.146202i
$532$		0			0
$533$	3.43724	+	5.95348i	0.148883	+	0.257874i
$534$		0			0
$535$	5.95882	−	10.3210i	0.257622	−	0.446215i
$536$		0			0
$537$	−4.33641	−	25.9017i	−0.187130	−	1.11774i
$538$		0			0
$539$	13.2593			0.571120
$540$		0			0
$541$	5.20957			0.223977			0.111988	−	0.993710i	$-0.464278\pi$
$541$	5.20957			0.223977			0.111988	+	0.993710i	$0.464278\pi$
$542$		0			0
$543$	−0.915664	−	5.46932i	−0.0392949	−	0.234711i
$544$		0			0
$545$	8.32605	−	14.4211i	0.356649	−	0.617734i
$546$		0			0
$547$	20.0204	+	34.6764i	0.856013	+	1.48266i	0.875702	+	0.482851i	$0.160399\pi$
$547$	20.0204	+	34.6764i	0.856013	+	1.48266i	−0.0196900	+	0.999806i	$0.506268\pi$
$548$		0			0
$549$	−5.72635	−	4.97636i	−0.244394	−	0.212386i
$550$		0			0
$551$	−22.1717	−	38.4025i	−0.944546	−	1.63600i
$552$		0			0
$553$	0.205614	−	0.356133i	0.00874359	−	0.0151443i
$554$		0			0
$555$	−2.94761	−	1.10182i	−0.125119	−	0.0467696i
$556$		0			0
$557$	−14.4033			−0.610288			−0.305144	−	0.952306i	$-0.598705\pi$
$557$	−14.4033			−0.610288			−0.305144	+	0.952306i	$0.598705\pi$
$558$		0			0
$559$	−2.20166			−0.0931203
$560$		0			0
$561$	9.54731	−	7.87137i	0.403088	−	0.332330i
$562$		0			0
$563$	14.6840	−	25.4335i	0.618858	−	1.07189i	−0.370836	−	0.928698i	$-0.620929\pi$
$563$	14.6840	−	25.4335i	0.618858	−	1.07189i	0.989694	−	0.143196i	$-0.0457378\pi$
$564$		0			0
$565$	−10.0616	−	17.4272i	−0.423296	−	0.733170i
$566$		0			0
$567$	11.9176	+	4.81096i	0.500494	+	0.202041i
$568$		0			0
$569$	−23.4033	−	40.5357i	−0.981118	−	1.69935i	−0.658056	−	0.752969i	$-0.728621\pi$
$569$	−23.4033	−	40.5357i	−0.981118	−	1.69935i	−0.323062	−	0.946378i	$-0.604712\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$		0			0
$573$	−3.79213	+	3.12646i	−0.158418	+	0.130610i
$574$		0			0
$575$	5.91764			0.246783
$576$		0			0
$577$	28.2386			1.17559			0.587794	−	0.809010i	$-0.299996\pi$
$577$	28.2386			1.17559			0.587794	+	0.809010i	$0.299996\pi$
$578$		0			0
$579$	−30.4821	−	11.3942i	−1.26679	−	0.473528i
$580$		0			0
$581$	3.05880	−	5.29801i	0.126901	−	0.219798i
$582$		0			0
$583$	−1.52884	−	2.64802i	−0.0633180	−	0.109670i
$584$		0			0
$585$	10.5812	+	9.19539i	0.437480	+	0.380182i
$586$		0			0
$587$	9.04118	+	15.6598i	0.373169	+	0.646348i	0.990051	−	0.140707i	$-0.0449377\pi$
$587$	9.04118	+	15.6598i	0.373169	+	0.646348i	−0.616882	+	0.787056i	$0.711604\pi$
$588$		0			0
$589$	−16.2633	+	28.1688i	−0.670117	+	1.16068i
$590$		0			0
$591$	−1.66887	−	9.96827i	−0.0686482	−	0.410040i
$592$		0			0
$593$	−7.73840			−0.317778			−0.158889	−	0.987296i	$-0.550791\pi$
$593$	−7.73840			−0.317778			−0.158889	+	0.987296i	$0.550791\pi$
$594$		0			0
$595$	−3.81681			−0.156474
$596$		0			0
$597$	3.73973	+	22.3377i	0.153057	+	0.914220i
$598$		0			0
$599$	−13.9608	+	24.1808i	−0.570423	+	0.988001i	0.426100	+	0.904676i	$0.359887\pi$
$599$	−13.9608	+	24.1808i	−0.570423	+	0.988001i	−0.996522	+	0.0833249i	$0.973446\pi$
$600$		0			0
$601$	−19.2201	−	33.2902i	−0.784006	−	1.35794i	−0.929591	−	0.368592i	$-0.879840\pi$
$601$	−19.2201	−	33.2902i	−0.784006	−	1.35794i	0.145586	−	0.989346i	$-0.453493\pi$
$602$		0			0
$603$	3.76970	−	19.4087i	0.153514	−	0.790383i
$604$		0			0
$605$	1.92801	+	3.33941i	0.0783846	+	0.135766i
$606$		0			0
$607$	−0.319917	+	0.554113i	−0.0129850	+	0.0224907i	−0.872445	−	0.488712i	$-0.837467\pi$
$607$	−0.319917	+	0.554113i	−0.0129850	+	0.0224907i	0.859460	+	0.511203i	$0.170800\pi$
$608$		0			0
$609$	21.9857	+	8.21826i	0.890905	+	0.333021i
$610$		0			0
$611$	−32.5081			−1.31514
$612$		0			0
$613$	42.7467			1.72652			0.863262	−	0.504757i	$-0.168418\pi$
$613$	42.7467			1.72652			0.863262	+	0.504757i	$0.168418\pi$
$614$		0			0
$615$	1.96608	−	1.62095i	0.0792800	−	0.0653632i
$616$		0			0
$617$	−10.5513	+	18.2753i	−0.424778	+	0.735737i	−0.996400	−	0.0847805i	$-0.972981\pi$
$617$	−10.5513	+	18.2753i	−0.424778	+	0.735737i	0.571622	+	0.820517i	$0.306314\pi$
$618$		0			0
$619$	−6.82605	−	11.8231i	−0.274362	−	0.475209i	0.695612	−	0.718418i	$-0.255133\pi$
$619$	−6.82605	−	11.8231i	−0.274362	−	0.475209i	−0.969974	+	0.243209i	$0.921800\pi$
$620$		0			0
$621$	−30.7386	−	0.798123i	−1.23350	−	0.0320276i
$622$		0			0
$623$	−2.14201	−	3.71007i	−0.0858178	−	0.148641i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−16.6913	+	13.7613i	−0.666586	+	0.549574i
$628$		0			0
$629$	−4.85601			−0.193622
$630$		0			0
$631$	−33.2593			−1.32403			−0.662017	−	0.749489i	$-0.730299\pi$
$631$	−33.2593			−1.32403			−0.662017	+	0.749489i	$0.730299\pi$
$632$		0			0
$633$	−13.6037	−	5.08506i	−0.540697	−	0.202113i
$634$		0			0
$635$	1.09357	−	1.89412i	0.0433971	−	0.0751659i
$636$		0			0
$637$	11.5905	+	20.0753i	0.459231	+	0.795411i
$638$		0			0
$639$	−36.5173	+	12.5799i	−1.44460	+	0.497655i
$640$		0			0
$641$	−13.1429	−	22.7641i	−0.519112	−	0.899128i	−0.999753	−	0.0222106i	$-0.992930\pi$
$641$	−13.1429	−	22.7641i	−0.519112	−	0.899128i	0.480642	−	0.876917i	$-0.340404\pi$
$642$		0			0
$643$	10.2913	−	17.8250i	0.405848	−	0.702950i	−0.588571	−	0.808445i	$-0.700309\pi$
$643$	10.2913	−	17.8250i	0.405848	−	0.702950i	0.994420	+	0.105495i	$0.0336427\pi$
$644$		0			0
$645$	0.134751	+	0.804876i	0.00530581	+	0.0316920i
$646$		0			0
$647$	−23.2527			−0.914159			−0.457079	−	0.889426i	$-0.651104\pi$
$647$	−23.2527			−0.914159			−0.457079	+	0.889426i	$0.651104\pi$
$648$		0			0
$649$	−3.05767			−0.120024
$650$		0			0
$651$	−2.84283	−	16.9804i	−0.111419	−	0.665513i
$652$		0			0
$653$	−9.37957	+	16.2459i	−0.367051	+	0.635751i	−0.989103	−	0.147225i	$-0.952966\pi$
$653$	−9.37957	+	16.2459i	−0.367051	+	0.635751i	0.622052	+	0.782976i	$0.286299\pi$
$654$		0			0
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$		0			0
$657$	4.85601	−	1.67286i	0.189451	−	0.0652645i
$658$		0			0
$659$	−0.140034	−	0.242545i	−0.00545494	−	0.00944823i	0.863285	−	0.504717i	$-0.168403\pi$
$659$	−0.140034	−	0.242545i	−0.00545494	−	0.00944823i	−0.868740	+	0.495268i	$0.835070\pi$
$660$		0			0
$661$	19.8930	−	34.4556i	0.773746	−	1.34017i	−0.161750	−	0.986832i	$-0.551714\pi$
$661$	19.8930	−	34.4556i	0.773746	−	1.34017i	0.935496	−	0.353336i	$-0.114953\pi$
$662$		0			0
$663$	20.2633	+	7.57443i	0.786961	+	0.294167i
$664$		0			0
$665$	6.67282			0.258761
$666$		0			0
$667$	−56.1562			−2.17438
$668$		0			0
$669$	12.2501	−	10.0997i	0.473616	−	0.390478i
$670$		0			0
$671$	−3.37957	+	5.85358i	−0.130467	+	0.225975i
$672$		0			0
$673$	−16.7644	−	29.0368i	−0.646221	−	1.11929i	−0.984018	−	0.178068i	$-0.943015\pi$
$673$	−16.7644	−	29.0368i	−0.646221	−	1.11929i	0.337797	−	0.941219i	$-0.390318\pi$
$674$		0			0
$675$	2.71400	−	4.43105i	0.104462	−	0.170551i
$676$		0			0
$677$	−13.7437	−	23.8048i	−0.528213	−	0.914891i	−0.999459	−	0.0328897i	$-0.989529\pi$
$677$	−13.7437	−	23.8048i	−0.528213	−	0.914891i	0.471246	−	0.882002i	$-0.343804\pi$
$678$		0			0
$679$	5.59442	−	9.68981i	0.214694	−	0.371861i
$680$		0			0
$681$	−3.57199	+	2.94497i	−0.136879	+	0.112851i
$682$		0			0
$683$	34.5865			1.32342			0.661708	−	0.749762i	$-0.269832\pi$
$683$	34.5865			1.32342			0.661708	+	0.749762i	$0.269832\pi$
$684$		0			0
$685$	−10.2017			−0.389785
$686$		0			0
$687$	4.13277	+	1.54483i	0.157675	+	0.0589391i
$688$		0			0
$689$	2.67282	−	4.62947i	0.101826	−	0.176369i
$690$		0			0
$691$	20.3641	+	35.2717i	0.774688	+	1.34180i	0.934970	+	0.354727i	$0.115426\pi$
$691$	20.3641	+	35.2717i	0.774688	+	1.34180i	−0.160282	+	0.987071i	$0.551240\pi$
$692$		0			0
$693$	2.18319	−	11.2404i	0.0829325	−	0.426987i
$694$		0			0
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$		0			0
$697$	1.96608	−	3.40535i	0.0744706	−	0.128987i
$698$		0			0
$699$	1.77894	+	10.6257i	0.0672856	+	0.401901i
$700$		0			0
$701$	−19.4712			−0.735416			−0.367708	−	0.929941i	$-0.619857\pi$
$701$	−19.4712			−0.735416			−0.367708	+	0.929941i	$0.619857\pi$
$702$		0			0
$703$	8.48963			0.320193
$704$		0			0
$705$	1.98963	+	11.8842i	0.0749339	+	0.447585i
$706$		0			0
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	−7.54316	−	13.0651i	−0.283289	−	0.490671i	0.688904	−	0.724853i	$-0.258092\pi$
$709$	−7.54316	−	13.0651i	−0.283289	−	0.490671i	−0.972193	+	0.234182i	$0.924759\pi$
$710$		0			0
$711$	0.652092	+	0.566686i	0.0244553	+	0.0212524i
$712$		0			0
$713$	20.5957	+	35.6729i	0.771317	+	1.33596i
$714$		0			0
$715$	6.24482	−	10.8163i	0.233543	−	0.404508i
$716$		0			0
$717$	−13.1792	−	4.92641i	−0.492188	−	0.183980i
$718$		0			0
$719$	3.43196			0.127990			0.0639952	−	0.997950i	$-0.479616\pi$
$719$	3.43196			0.127990			0.0639952	+	0.997950i	$0.479616\pi$
$720$		0			0
$721$	−2.59442			−0.0966211
$722$		0			0
$723$	35.2333	−	29.0485i	1.31034	−	1.08032i
$724$		0			0
$725$	4.74482	−	8.21826i	0.176218	−	0.305219i
$726$		0			0
$727$	−17.8857	−	30.9789i	−0.663344	−	1.14895i	−0.979732	−	0.200315i	$-0.935803\pi$
$727$	−17.8857	−	30.9789i	−0.663344	−	1.14895i	0.316388	−	0.948630i	$-0.397530\pi$
$728$		0			0
$729$	−14.6952	+	22.6506i	−0.544268	+	0.838911i
$730$		0			0
$731$	0.629668	+	1.09062i	0.0232891	+	0.0403379i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$		0			0
$735$	6.62967	−	5.46590i	0.244539	−	0.201613i
$736$		0			0
$737$	−17.6151			−0.648862
$738$		0			0
$739$	−6.08631			−0.223889			−0.111944	−	0.993714i	$-0.535708\pi$
$739$	−6.08631			−0.223889			−0.111944	+	0.993714i	$0.535708\pi$
$740$		0			0
$741$	−35.4257	−	13.2422i	−1.30140	−	0.486463i
$742$		0			0
$743$	−12.7509	+	22.0853i	−0.467787	+	0.810231i	−0.999322	−	0.0368054i	$-0.988282\pi$
$743$	−12.7509	+	22.0853i	−0.467787	+	0.810231i	0.531536	+	0.847036i	$0.321615\pi$
$744$		0			0
$745$	10.0381	+	17.3865i	0.367767	+	0.636990i
$746$		0			0
$747$	9.70081	+	8.43028i	0.354934	+	0.308448i
$748$		0			0
$749$	−8.50924	−	14.7384i	−0.310921	−	0.538530i
$750$		0			0
$751$	−9.19638	+	15.9286i	−0.335581	+	0.581243i	−0.983596	−	0.180384i	$-0.942266\pi$
$751$	−9.19638	+	15.9286i	−0.335581	+	0.581243i	0.648016	+	0.761627i	$0.275599\pi$
$752$		0			0
$753$	−0.157175	−	0.938816i	−0.00572777	−	0.0342124i
$754$		0			0
$755$	−3.03920			−0.110608
$756$		0			0
$757$	−41.8986			−1.52283			−0.761415	−	0.648264i	$-0.775495\pi$
$757$	−41.8986			−1.52283			−0.761415	+	0.648264i	$0.775495\pi$
$758$		0			0
$759$	4.52355	+	27.0195i	0.164195	+	0.980745i
$760$		0			0
$761$	3.98568	−	6.90340i	0.144481	−	0.250248i	−0.784698	−	0.619878i	$-0.787182\pi$
$761$	3.98568	−	6.90340i	0.144481	−	0.250248i	0.929179	+	0.369630i	$0.120515\pi$
$762$		0			0
$763$	−11.8896	−	20.5935i	−0.430434	−	0.745534i
$764$		0			0
$765$	1.52884	−	7.87137i	0.0552752	−	0.284590i
$766$		0			0
$767$	−2.67282	−	4.62947i	−0.0965101	−	0.167160i
$768$		0			0
$769$	−3.01432	+	5.22095i	−0.108699	+	0.188272i	−0.915244	−	0.402901i	$-0.868002\pi$
$769$	−3.01432	+	5.22095i	−0.108699	+	0.188272i	0.806544	+	0.591174i	$0.201335\pi$
$770$		0			0
$771$	−29.2034	−	10.9162i	−1.05173	−	0.393139i
$772$		0			0
$773$	44.4033			1.59708			0.798538	−	0.601944i	$-0.205607\pi$
$773$	44.4033			1.59708			0.798538	+	0.601944i	$0.205607\pi$
$774$		0			0
$775$	−6.96080			−0.250039
$776$		0			0
$777$	−3.46721	+	2.85858i	−0.124385	+	0.102551i
$778$		0			0
$779$	−3.43724	+	5.95348i	−0.123152	+	0.213305i
$780$		0			0
$781$	17.2056	+	29.8010i	0.615665	+	1.06636i
$782$		0			0
$783$	−25.7549	+	42.0490i	−0.920405	+	1.50271i
$784$		0			0
$785$	−0.100830	−	0.174643i	−0.00359879	−	0.00623329i
$786$		0			0
$787$	8.41877	−	14.5817i	0.300097	−	0.519783i	−0.676061	−	0.736846i	$-0.736314\pi$
$787$	8.41877	−	14.5817i	0.300097	−	0.519783i	0.976158	+	0.217063i	$0.0696477\pi$
$788$		0			0
$789$	15.8969	−	13.1064i	0.565945	−	0.466599i
$790$		0			0
$791$	−28.7361			−1.02174
$792$		0			0
$793$	−11.8168			−0.419627
$794$		0			0
$795$	−1.85601	−	0.693779i	−0.0658260	−	0.0246058i
$796$		0			0
$797$	16.6860	−	28.9010i	0.591049	−	1.02373i	−0.403043	−	0.915181i	$-0.632047\pi$
$797$	16.6860	−	28.9010i	0.591049	−	1.02373i	0.994091	−	0.108545i	$-0.0346193\pi$
$798$		0			0
$799$	9.29721	+	16.1032i	0.328912	+	0.569692i
$800$		0			0
$801$	8.50924	−	2.93137i	0.300659	−	0.103575i
$802$		0			0
$803$	−2.28797	−	3.96289i	−0.0807408	−	0.139847i
$804$		0			0
$805$	4.22522	−	7.31829i	0.148919	−	0.257936i
$806$		0			0
$807$	−8.17198	−	48.8117i	−0.287667	−	1.71825i
$808$		0			0
$809$	29.1809			1.02595			0.512973	−	0.858404i	$-0.328544\pi$
$809$	29.1809			1.02595			0.512973	+	0.858404i	$0.328544\pi$
$810$		0			0
$811$	15.5552			0.546217			0.273109	−	0.961983i	$-0.411948\pi$
$811$	15.5552			0.546217			0.273109	+	0.961983i	$0.411948\pi$
$812$		0			0
$813$	−6.68206	−	39.9124i	−0.234350	−	1.39979i
$814$		0			0
$815$	8.90841	−	15.4298i	0.312048	−	0.540483i
$816$		0			0
$817$	−1.10083	−	1.90669i	−0.0385132	−	0.0667068i
$818$		0			0
$819$	18.9269	−	6.52016i	0.661359	−	0.227833i
$820$		0			0
$821$	11.8588	+	20.5401i	0.413876	+	0.716855i	0.995310	−	0.0967393i	$-0.0308413\pi$
$821$	11.8588	+	20.5401i	0.413876	+	0.716855i	−0.581434	+	0.813594i	$0.697508\pi$
$822$		0			0
$823$	9.68404	−	16.7732i	0.337564	−	0.584678i	−0.646410	−	0.762990i	$-0.723730\pi$
$823$	9.68404	−	16.7732i	0.337564	−	0.584678i	0.983974	+	0.178312i	$0.0570636\pi$
$824$		0			0
$825$	−4.33641	−	1.62095i	−0.150974	−	0.0564344i
$826$		0			0
$827$	−52.2241			−1.81601			−0.908005	−	0.418960i	$-0.862395\pi$
$827$	−52.2241			−1.81601			−0.908005	+	0.418960i	$0.862395\pi$
$828$		0			0
$829$	−26.6442			−0.925391			−0.462695	−	0.886517i	$-0.653118\pi$
$829$	−26.6442			−0.925391			−0.462695	+	0.886517i	$0.653118\pi$
$830$		0			0
$831$	20.1479	−	16.6112i	0.698924	−	0.576235i
$832$		0			0
$833$	6.62967	−	11.4829i	0.229704	−	0.397860i
$834$		0			0
$835$	7.05042	+	12.2117i	0.243990	+	0.422603i
$836$		0			0
$837$	36.1572	+	0.938816i	1.24977	+	0.0324502i
$838$		0			0
$839$	−12.5196	−	21.6846i	−0.432225	−	0.748635i	0.564840	−	0.825201i	$-0.308938\pi$
$839$	−12.5196	−	21.6846i	−0.432225	−	0.748635i	−0.997065	+	0.0765655i	$0.975605\pi$
$840$		0			0
$841$	−30.5266	+	52.8736i	−1.05264	+	1.82323i
$842$		0			0
$843$	−8.88993	+	7.32940i	−0.306186	+	0.252438i
$844$		0			0
$845$	8.83528			0.303943
$846$		0			0
$847$	5.50641			0.189203
$848$		0			0
$849$	−43.6378	−	16.3118i	−1.49764	−	0.559821i
$850$		0			0
$851$	5.37562	−	9.31084i	0.184274	−	0.319171i
$852$		0			0
$853$	5.43724	+	9.41758i	0.186168	+	0.322452i	0.943969	−	0.330033i	$-0.107060\pi$
$853$	5.43724	+	9.41758i	0.186168	+	0.322452i	−0.757802	+	0.652485i	$0.773727\pi$
$854$		0			0
$855$	−2.67282	+	13.7613i	−0.0914086	+	0.470627i
$856$		0			0
$857$	9.29721	+	16.1032i	0.317587	+	0.550076i	0.979984	−	0.199077i	$-0.0637942\pi$
$857$	9.29721	+	16.1032i	0.317587	+	0.550076i	−0.662397	+	0.749153i	$0.730461\pi$
$858$		0			0
$859$	−2.33246	+	4.03994i	−0.0795825	+	0.137841i	−0.903070	−	0.429494i	$-0.858692\pi$
$859$	−2.33246	+	4.03994i	−0.0795825	+	0.137841i	0.823487	+	0.567335i	$0.192025\pi$
$860$		0			0
$861$	−0.600830	−	3.58880i	−0.0204762	−	0.122306i
$862$		0			0
$863$	28.0594			0.955152			0.477576	−	0.878590i	$-0.341516\pi$
$863$	28.0594			0.955152			0.477576	+	0.878590i	$0.341516\pi$
$864$		0			0
$865$	4.36638			0.148461
$866$		0			0
$867$	2.81879	+	16.8368i	0.0957310	+	0.571807i
$868$		0			0
$869$	0.384851	−	0.666581i	0.0130552	−	0.0226122i
$870$		0			0
$871$	−15.3980	−	26.6702i	−0.521743	−	0.903685i
$872$		0			0
$873$	17.7424	+	15.4186i	0.600488	+	0.521841i
$874$		0			0
$875$	0.714003	+	1.23669i	0.0241377	+	0.0418078i
$876$		0			0
$877$	−17.3342	+	30.0236i	−0.585333	+	1.01383i	0.409501	+	0.912310i	$0.365703\pi$
$877$	−17.3342	+	30.0236i	−0.585333	+	1.01383i	−0.994834	+	0.101516i	$0.967631\pi$
$878$		0			0
$879$	20.0933	+	7.51089i	0.677730	+	0.253336i
$880$		0			0
$881$	−5.29854			−0.178512			−0.0892561	−	0.996009i	$-0.528449\pi$
$881$	−5.29854			−0.178512			−0.0892561	+	0.996009i	$0.528449\pi$
$882$		0			0
$883$	10.3025			0.346706			0.173353	−	0.984860i	$-0.444540\pi$
$883$	10.3025			0.346706			0.173353	+	0.984860i	$0.444540\pi$
$884$		0			0
$885$	−1.52884	+	1.26047i	−0.0513913	+	0.0423701i
$886$		0			0
$887$	20.7252	−	35.8971i	0.695885	−	1.20531i	−0.273997	−	0.961731i	$-0.588346\pi$
$887$	20.7252	−	35.8971i	0.695885	−	1.20531i	0.969882	−	0.243577i	$-0.0783208\pi$
$888$		0			0
$889$	−1.56163	−	2.70482i	−0.0523753	−	0.0907167i
$890$		0			0
$891$	22.3064	+	9.00475i	0.747294	+	0.301670i
$892$		0			0
$893$	−16.2541	−	28.1528i	−0.543921	−	0.942099i
$894$		0			0
$895$	−7.58123	+	13.1311i	−0.253413	+	0.438923i
$896$		0			0
$897$	−36.9546	+	30.4676i	−1.23388	+	1.01728i
$898$		0			0
$899$	66.0554			2.20307
$900$		0			0
$901$	−3.05767			−0.101866
$902$		0			0
$903$	1.09159	+	0.408039i	0.0363260	+	0.0135787i
$904$		0			0
$905$	−1.60083	+	2.77272i	−0.0532134	+	0.0921683i
$906$		0			0
$907$	−8.39606	−	14.5424i	−0.278787	−	0.482873i	0.692297	−	0.721613i	$-0.256599\pi$
$907$	−8.39606	−	14.5424i	−0.278787	−	0.482873i	−0.971083	+	0.238740i	$0.923266\pi$
$908$		0			0
$909$	−9.51432	−	8.26821i	−0.315570	−	0.274239i
$910$		0			0
$911$	18.6768	+	32.3491i	0.618789	+	1.07177i	0.989707	+	0.143109i	$0.0457098\pi$
$911$	18.6768	+	32.3491i	0.618789	+	1.07177i	−0.370918	+	0.928666i	$0.620957\pi$
$912$		0			0
$913$	5.72522	−	9.91636i	0.189477	−	0.328184i
$914$		0			0
$915$	0.723239	+	4.31995i	0.0239095	+	0.142813i
$916$		0			0
$917$	−8.56804			−0.282942
$918$		0			0
$919$	−37.1316			−1.22486			−0.612429	−	0.790526i	$-0.709807\pi$
$919$	−37.1316			−1.22486			−0.612429	+	0.790526i	$0.709807\pi$
$920$		0			0
$921$	−0.713157	−	4.25973i	−0.0234993	−	0.140363i
$922$		0			0
$923$	−30.0801	+	52.1003i	−0.990098	+	1.71490i
$924$		0			0
$925$	0.908405	+	1.57340i	0.0298682	+	0.0517332i
$926$		0			0
$927$	1.03920	−	5.35044i	0.0341319	−	0.175732i
$928$		0			0
$929$	23.9977	+	41.5653i	0.787340	+	1.36371i	0.927591	+	0.373597i	$0.121876\pi$
$929$	23.9977	+	41.5653i	0.787340	+	1.36371i	−0.140251	+	0.990116i	$0.544791\pi$
$930$		0			0
$931$	−11.5905	+	20.0753i	−0.379862	+	0.657941i
$932$		0			0
$933$	39.2949	+	14.6885i	1.28646	+	0.480879i
$934$		0			0
$935$	−7.14399			−0.233633
$936$		0			0
$937$	22.0079			0.718967			0.359483	−	0.933151i	$-0.382953\pi$
$937$	22.0079			0.718967			0.359483	+	0.933151i	$0.382953\pi$
$938$		0			0
$939$	46.8867	−	38.6562i	1.53009	−	1.26150i
$940$		0			0
$941$	−20.2921	+	35.1470i	−0.661504	+	1.14576i	0.318716	+	0.947850i	$0.396748\pi$
$941$	−20.2921	+	35.1470i	−0.661504	+	1.14576i	−0.980220	+	0.197909i	$0.936585\pi$
$942$		0			0
$943$	4.35291	+	7.53946i	0.141750	+	0.245518i
$944$		0			0
$945$	−3.54203	−	6.52016i	−0.115222	−	0.212101i
$946$		0			0
$947$	15.1160	+	26.1817i	0.491204	+	0.850790i	0.999949	−	0.0101273i	$-0.00322368\pi$
$947$	15.1160	+	26.1817i	0.491204	+	0.850790i	−0.508745	+	0.860917i	$0.669890\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$	13.9938	−	11.5373i	0.453780	−	0.374123i
$952$		0			0
$953$	2.50811			0.0812455			0.0406227	−	0.999175i	$-0.487066\pi$
$953$	2.50811			0.0812455			0.0406227	+	0.999175i	$0.487066\pi$
$954$		0			0
$955$	2.83754			0.0918207
$956$		0			0
$957$	41.1510	+	15.3823i	1.33022	+	0.497238i
$958$		0			0
$959$	−7.28402	+	12.6163i	−0.235213	+	0.407401i
$960$		0			0
$961$	−8.72635	−	15.1145i	−0.281495	−	0.487564i
$962$		0			0
$963$	33.8033	−	11.6450i	1.08930	−	0.375255i
$964$		0			0
$965$	9.39409	+	16.2710i	0.302406	+	0.523783i
$966$		0			0
$967$	−10.8765	+	18.8386i	−0.349763	+	0.605808i	−0.986207	−	0.165515i	$-0.947071\pi$
$967$	−10.8765	+	18.8386i	−0.349763	+	0.605808i	0.636444	+	0.771323i	$0.280405\pi$
$968$		0			0
$969$	3.57199	+	21.3357i	0.114749	+	0.685403i
$970$		0			0
$971$	−22.7512			−0.730122			−0.365061	−	0.930984i	$-0.618952\pi$
$971$	−22.7512			−0.730122			−0.365061	+	0.930984i	$0.618952\pi$
$972$		0			0
$973$	11.4241			0.366238
$974$		0			0
$975$	−1.33641	−	7.98247i	−0.0427994	−	0.255644i
$976$		0			0
$977$	−19.6389	+	34.0156i	−0.628304	+	1.08825i	0.359588	+	0.933111i	$0.382917\pi$
$977$	−19.6389	+	34.0156i	−0.628304	+	1.08825i	−0.987892	+	0.155143i	$0.950416\pi$
$978$		0			0
$979$	−4.00924	−	6.94420i	−0.128136	−	0.221938i
$980$		0			0
$981$	47.2322	−	16.2711i	1.50801	−	0.519497i
$982$		0			0
$983$	16.8949	+	29.2629i	0.538865	+	0.933341i	0.998966	+	0.0454743i	$0.0144799\pi$
$983$	16.8949	+	29.2629i	0.538865	+	0.933341i	−0.460101	+	0.887867i	$0.652187\pi$
$984$		0			0
$985$	−2.91764	+	5.05350i	−0.0929638	+	0.161018i
$986$		0			0
$987$	16.1177	+	6.02480i	0.513032	+	0.191772i
$988$		0			0
$989$	−2.78817			−0.0886587
$990$		0			0
$991$	23.7983			0.755979			0.377990	−	0.925810i	$-0.376616\pi$
$991$	23.7983			0.755979			0.377990	+	0.925810i	$0.376616\pi$
$992$		0			0
$993$	22.4218	−	18.4859i	0.711534	−	0.586631i
$994$		0			0
$995$	6.53807	−	11.3243i	0.207271	−	0.359004i
$996$		0			0
$997$	−25.8392	−	44.7549i	−0.818337	−	1.41740i	−0.906907	−	0.421331i	$-0.861563\pi$
$997$	−25.8392	−	44.7549i	−0.818337	−	1.41740i	0.0885702	−	0.996070i	$-0.471770\pi$
$998$		0			0
$999$	−4.50641	−	8.29541i	−0.142577	−	0.262455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.i.481.2		6
3.2	odd	2		2160.2.q.k.1441.2		6
4.3	odd	2		45.2.e.b.31.2	yes	6
9.2	odd	6		2160.2.q.k.721.2		6
9.4	even	3		6480.2.a.bv.1.2		3
9.5	odd	6		6480.2.a.bs.1.2		3
9.7	even	3	inner	720.2.q.i.241.2		6
12.11	even	2		135.2.e.b.91.2		6
20.3	even	4		225.2.k.b.49.3		12
20.7	even	4		225.2.k.b.49.4		12
20.19	odd	2		225.2.e.b.76.2		6
36.7	odd	6		45.2.e.b.16.2	✓	6
36.11	even	6		135.2.e.b.46.2		6
36.23	even	6		405.2.a.i.1.2		3
36.31	odd	6		405.2.a.j.1.2		3
60.23	odd	4		675.2.k.b.199.4		12
60.47	odd	4		675.2.k.b.199.3		12
60.59	even	2		675.2.e.b.226.2		6
180.7	even	12		225.2.k.b.124.3		12
180.23	odd	12		2025.2.b.m.649.4		6
180.43	even	12		225.2.k.b.124.4		12
180.47	odd	12		675.2.k.b.424.4		12
180.59	even	6		2025.2.a.o.1.2		3
180.67	even	12		2025.2.b.l.649.4		6
180.79	odd	6		225.2.e.b.151.2		6
180.83	odd	12		675.2.k.b.424.3		12
180.103	even	12		2025.2.b.l.649.3		6
180.119	even	6		675.2.e.b.451.2		6
180.139	odd	6		2025.2.a.n.1.2		3
180.167	odd	12		2025.2.b.m.649.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.2	✓	6	36.7	odd	6
45.2.e.b.31.2	yes	6	4.3	odd	2
135.2.e.b.46.2		6	36.11	even	6
135.2.e.b.91.2		6	12.11	even	2
225.2.e.b.76.2		6	20.19	odd	2
225.2.e.b.151.2		6	180.79	odd	6
225.2.k.b.49.3		12	20.3	even	4
225.2.k.b.49.4		12	20.7	even	4
225.2.k.b.124.3		12	180.7	even	12
225.2.k.b.124.4		12	180.43	even	12
405.2.a.i.1.2		3	36.23	even	6
405.2.a.j.1.2		3	36.31	odd	6
675.2.e.b.226.2		6	60.59	even	2
675.2.e.b.451.2		6	180.119	even	6
675.2.k.b.199.3		12	60.47	odd	4
675.2.k.b.199.4		12	60.23	odd	4
675.2.k.b.424.3		12	180.83	odd	12
675.2.k.b.424.4		12	180.47	odd	12
720.2.q.i.241.2		6	9.7	even	3	inner
720.2.q.i.481.2		6	1.1	even	1	trivial
2025.2.a.n.1.2		3	180.139	odd	6
2025.2.a.o.1.2		3	180.59	even	6
2025.2.b.l.649.3		6	180.103	even	12
2025.2.b.l.649.4		6	180.67	even	12
2025.2.b.m.649.3		6	180.167	odd	12
2025.2.b.m.649.4		6	180.23	odd	12
2160.2.q.k.721.2		6	9.2	odd	6
2160.2.q.k.1441.2		6	3.2	odd	2
6480.2.a.bs.1.2		3	9.5	odd	6
6480.2.a.bv.1.2		3	9.4	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.285997 - 1.70828i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.714003 + 1.23669i) q^{7} +(-2.83641 + 0.977122i) q^{9} +O(q^{10})\)	\(q+(-0.285997 - 1.70828i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.714003 + 1.23669i) q^{7} +(-2.83641 + 0.977122i) q^{9} +(1.33641 + 2.31473i) q^{11} +(-2.33641 + 4.04678i) q^{13} +(1.62241 + 0.606458i) q^{15} +2.67282 q^{17} -4.67282 q^{19} +(1.90841 - 1.57340i) q^{21} +(-2.95882 + 5.12483i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.48040 + 4.56592i) q^{27} +(4.74482 + 8.21826i) q^{29} +(3.48040 - 6.02823i) q^{31} +(3.57199 - 2.94497i) q^{33} -1.42801 q^{35} -1.81681 q^{37} +(7.58123 + 2.83387i) q^{39} +(0.735581 - 1.27406i) q^{41} +(0.235581 + 0.408039i) q^{43} +(0.571993 - 2.94497i) q^{45} +(3.47842 + 6.02480i) q^{47} +(2.48040 - 4.29618i) q^{49} +(-0.764419 - 4.56592i) q^{51} -1.14399 q^{53} -2.67282 q^{55} +(1.33641 + 7.98247i) q^{57} +(-0.571993 + 0.990721i) q^{59} +(1.26442 + 2.19004i) q^{61} +(-3.23360 - 2.81009i) q^{63} +(-2.33641 - 4.04678i) q^{65} +(-3.29523 + 5.70751i) q^{67} +(9.60083 + 3.58880i) q^{69} +12.8745 q^{71} -1.71203 q^{73} +(-1.33641 + 1.10182i) q^{75} +(-1.90841 + 3.30545i) q^{77} +(-0.143987 - 0.249392i) q^{79} +(7.09046 - 5.54304i) q^{81} +(-2.14201 - 3.71007i) q^{83} +(-1.33641 + 2.31473i) q^{85} +(12.6821 - 10.4559i) q^{87} -3.00000 q^{89} -6.67282 q^{91} +(-11.2933 - 4.22143i) q^{93} +(2.33641 - 4.04678i) q^{95} +(-3.91764 - 6.78555i) q^{97} +(-6.05239 - 5.25970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9}+O(q^{10}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9} - 2 q^{11} - 4 q^{13} - q^{15} - 4 q^{17} - 8 q^{19} + 3 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 8 q^{31} + 20 q^{33} - 10 q^{35} + 12 q^{37} + 14 q^{39} + 13 q^{41} + 10 q^{43} + 2 q^{45} + 13 q^{47} + 2 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{55} - 2 q^{57} - 2 q^{59} - q^{61} - 33 q^{63} - 4 q^{65} + 11 q^{67} + 39 q^{69} + 20 q^{71} - 16 q^{73} + 2 q^{75} + 2 q^{79} - 19 q^{81} - 15 q^{83} + 2 q^{85} + 26 q^{87} - 18 q^{89} - 20 q^{91} - 42 q^{93} + 4 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9 - 2 * q^11 - 4 * q^13 - q^15 - 4 * q^17 - 8 * q^19 + 3 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 8 * q^31 + 20 * q^33 - 10 * q^35 + 12 * q^37 + 14 * q^39 + 13 * q^41 + 10 * q^43 + 2 * q^45 + 13 * q^47 + 2 * q^49 + 4 * q^51 - 4 * q^53 + 4 * q^55 - 2 * q^57 - 2 * q^59 - q^61 - 33 * q^63 - 4 * q^65 + 11 * q^67 + 39 * q^69 + 20 * q^71 - 16 * q^73 + 2 * q^75 + 2 * q^79 - 19 * q^81 - 15 * q^83 + 2 * q^85 + 26 * q^87 - 18 * q^89 - 20 * q^91 - 42 * q^93 + 4 * q^95 + 18 * q^97 - 22 * q^99

Introduction

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