LMFDB - Embedded newform 1764.2.j.h.589.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(589,1764)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1764.589"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.5
Root			$-0.674693 - 1.59524i$ of defining polynomial
Character	$\chi$	$=$	1764.589
Dual form			1764.2.j.h.1177.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04417 - 1.38192i) q^{3} +(2.07260 - 3.58985i) q^{5} +(-0.819413 - 2.88592i) q^{9} +(-0.434429 - 0.752453i) q^{11} +(-2.86231 + 4.95766i) q^{13} +(-2.79674 - 6.61258i) q^{15} -2.89227 q^{17} -4.01406 q^{19} +(2.91488 - 5.04873i) q^{23} +(-6.09133 - 10.5505i) q^{25} +(-4.84373 - 1.88104i) q^{27} +(-0.900417 - 1.55957i) q^{29} +(-1.48046 + 2.56422i) q^{31} +(-1.49345 - 0.185343i) q^{33} +5.29851 q^{37} +(3.86236 + 9.13213i) q^{39} +(5.89325 - 10.2074i) q^{41} +(-2.00703 - 3.47627i) q^{43} +(-12.0583 - 3.03980i) q^{45} +(1.17218 + 2.03028i) q^{47} +(-3.02002 + 3.99689i) q^{51} +2.18233 q^{53} -3.60159 q^{55} +(-4.19136 + 5.54711i) q^{57} +(-1.52715 + 2.64510i) q^{59} +(2.81659 + 4.87848i) q^{61} +(11.8648 + 20.5505i) q^{65} +(1.25539 - 2.17440i) q^{67} +(-3.93331 - 9.29988i) q^{69} -1.09143 q^{71} +1.44657 q^{73} +(-20.9403 - 2.59878i) q^{75} +(1.06464 + 1.84401i) q^{79} +(-7.65712 + 4.72953i) q^{81} +(-2.18784 - 3.78946i) q^{83} +(-5.99451 + 10.3828i) q^{85} +(-3.09539 - 0.384150i) q^{87} +11.6675 q^{89} +(1.99771 + 4.72336i) q^{93} +(-8.31953 + 14.4098i) q^{95} +(3.98779 + 6.90706i) q^{97} +(-1.81555 + 1.87030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} + 2 q^{5} - 5 q^{9} + 2 q^{11} - 2 q^{13} + 7 q^{15} + 4 q^{17} + 14 q^{19} + 11 q^{23} - 9 q^{25} - 9 q^{27} + q^{29} + q^{31} + q^{33} - 20 q^{37} + 22 q^{39} + 33 q^{41} + 7 q^{43}+ \cdots + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 + 2 * q^5 - 5 * q^9 + 2 * q^11 - 2 * q^13 + 7 * q^15 + 4 * q^17 + 14 * q^19 + 11 * q^23 - 9 * q^25 - 9 * q^27 + q^29 + q^31 + q^33 - 20 * q^37 + 22 * q^39 + 33 * q^41 + 7 * q^43 - 5 * q^45 + 3 * q^47 - 7 * q^51 + 30 * q^53 + 28 * q^55 - 18 * q^57 + 14 * q^59 + 10 * q^61 + 15 * q^65 + 6 * q^67 + 43 * q^69 + 2 * q^71 + 42 * q^73 - 43 * q^75 - 10 * q^79 + 7 * q^81 + 25 * q^83 + 8 * q^85 + 26 * q^87 - 12 * q^89 - 38 * q^93 - 28 * q^95 + 18 * q^97 + 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.04417	−	1.38192i	0.602853	−	0.797853i
$3$	1.04417	−	1.38192i	0.602853	−	0.797853i
$4$		0			0
$5$	2.07260	−	3.58985i	0.926894	−	1.60543i	0.138409	−	0.990375i	$-0.455801\pi$
$5$	2.07260	−	3.58985i	0.926894	−	1.60543i	0.788486	−	0.615053i	$-0.210865\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.819413	−	2.88592i	−0.273138	−	0.961975i
$10$		0			0
$11$	−0.434429	−	0.752453i	−0.130985	−	0.226873i	0.793071	−	0.609129i	$-0.208481\pi$
$11$	−0.434429	−	0.752453i	−0.130985	−	0.226873i	−0.924057	+	0.382256i	$0.875147\pi$
$12$		0			0
$13$	−2.86231	+	4.95766i	−0.793861	+	1.37501i	0.129698	+	0.991554i	$0.458599\pi$
$13$	−2.86231	+	4.95766i	−0.793861	+	1.37501i	−0.923560	+	0.383455i	$0.874734\pi$
$14$		0			0
$15$	−2.79674	−	6.61258i	−0.722115	−	1.70736i
$16$		0			0
$17$	−2.89227			−0.701478			−0.350739	−	0.936473i	$-0.614070\pi$
$17$	−2.89227			−0.701478			−0.350739	+	0.936473i	$0.614070\pi$
$18$		0			0
$19$	−4.01406			−0.920888			−0.460444	−	0.887689i	$-0.652310\pi$
$19$	−4.01406			−0.920888			−0.460444	+	0.887689i	$0.652310\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.91488	−	5.04873i	0.607795	−	1.05273i	−0.383808	−	0.923413i	$-0.625387\pi$
$23$	2.91488	−	5.04873i	0.607795	−	1.05273i	0.991603	−	0.129319i	$-0.0412792\pi$
$24$		0			0
$25$	−6.09133	−	10.5505i	−1.21827	−	2.11010i
$26$		0			0
$27$	−4.84373	−	1.88104i	−0.932176	−	0.362005i
$28$		0			0
$29$	−0.900417	−	1.55957i	−0.167203	−	0.289604i	0.770232	−	0.637763i	$-0.220140\pi$
$29$	−0.900417	−	1.55957i	−0.167203	−	0.289604i	−0.937435	+	0.348159i	$0.886807\pi$
$30$		0			0
$31$	−1.48046	+	2.56422i	−0.265898	+	0.460548i	−0.967798	−	0.251727i	$-0.919002\pi$
$31$	−1.48046	+	2.56422i	−0.265898	+	0.460548i	0.701901	+	0.712275i	$0.252335\pi$
$32$		0			0
$33$	−1.49345	−	0.185343i	−0.259976	−	0.0322641i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.29851			0.871070			0.435535	−	0.900172i	$-0.356559\pi$
$37$	5.29851			0.871070			0.435535	+	0.900172i	$0.356559\pi$
$38$		0			0
$39$	3.86236	+	9.13213i	0.618473	+	1.46231i
$40$		0			0
$41$	5.89325	−	10.2074i	0.920371	−	1.59413i	0.121528	−	0.992588i	$-0.461220\pi$
$41$	5.89325	−	10.2074i	0.920371	−	1.59413i	0.798842	−	0.601541i	$-0.205446\pi$
$42$		0			0
$43$	−2.00703	−	3.47627i	−0.306069	−	0.530127i	0.671430	−	0.741068i	$-0.265680\pi$
$43$	−2.00703	−	3.47627i	−0.306069	−	0.530127i	−0.977499	+	0.210941i	$0.932347\pi$
$44$		0			0
$45$	−12.0583	−	3.03980i	−1.79755	−	0.453146i
$46$		0			0
$47$	1.17218	+	2.03028i	0.170980	+	0.296147i	0.938763	−	0.344564i	$-0.111973\pi$
$47$	1.17218	+	2.03028i	0.170980	+	0.296147i	−0.767783	+	0.640711i	$0.778640\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.02002	+	3.99689i	−0.422888	+	0.559676i
$52$		0			0
$53$	2.18233			0.299766			0.149883	−	0.988704i	$-0.452110\pi$
$53$	2.18233			0.299766			0.149883	+	0.988704i	$0.452110\pi$
$54$		0			0
$55$	−3.60159			−0.485638
$56$		0			0
$57$	−4.19136	+	5.54711i	−0.555159	+	0.734733i
$58$		0			0
$59$	−1.52715	+	2.64510i	−0.198818	+	0.344363i	−0.948146	−	0.317837i	$-0.897044\pi$
$59$	−1.52715	+	2.64510i	−0.198818	+	0.344363i	0.749327	+	0.662200i	$0.230377\pi$
$60$		0			0
$61$	2.81659	+	4.87848i	0.360628	+	0.624625i	0.988064	−	0.154042i	$-0.0492292\pi$
$61$	2.81659	+	4.87848i	0.360628	+	0.624625i	−0.627437	+	0.778668i	$0.715896\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	11.8648	+	20.5505i	1.47165	+	2.54898i
$66$		0			0
$67$	1.25539	−	2.17440i	0.153370	−	0.265645i	−0.779094	−	0.626907i	$-0.784321\pi$
$67$	1.25539	−	2.17440i	0.153370	−	0.265645i	0.932464	+	0.361262i	$0.117654\pi$
$68$		0			0
$69$	−3.93331	−	9.29988i	−0.473514	−	1.11957i
$70$		0			0
$71$	−1.09143			−0.129529			−0.0647647	−	0.997901i	$-0.520630\pi$
$71$	−1.09143			−0.129529			−0.0647647	+	0.997901i	$0.520630\pi$
$72$		0			0
$73$	1.44657			0.169308			0.0846541	−	0.996410i	$-0.473021\pi$
$73$	1.44657			0.169308			0.0846541	+	0.996410i	$0.473021\pi$
$74$		0			0
$75$	−20.9403	−	2.59878i	−2.41798	−	0.300082i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.06464	+	1.84401i	0.119781	+	0.207468i	0.919681	−	0.392666i	$-0.128447\pi$
$79$	1.06464	+	1.84401i	0.119781	+	0.207468i	−0.799900	+	0.600134i	$0.795114\pi$
$80$		0			0
$81$	−7.65712	+	4.72953i	−0.850792	+	0.525503i
$82$		0			0
$83$	−2.18784	−	3.78946i	−0.240147	−	0.415947i	0.720609	−	0.693342i	$-0.243862\pi$
$83$	−2.18784	−	3.78946i	−0.240147	−	0.415947i	−0.960756	+	0.277395i	$0.910529\pi$
$84$		0			0
$85$	−5.99451	+	10.3828i	−0.650196	+	1.12617i
$86$		0			0
$87$	−3.09539	−	0.384150i	−0.331861	−	0.0411852i
$88$		0			0
$89$	11.6675			1.23675			0.618374	−	0.785884i	$-0.287792\pi$
$89$	11.6675			1.23675			0.618374	+	0.785884i	$0.287792\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.99771	+	4.72336i	0.207153	+	0.489790i
$94$		0			0
$95$	−8.31953	+	14.4098i	−0.853566	+	1.47842i
$96$		0			0
$97$	3.98779	+	6.90706i	0.404899	+	0.701306i	0.994310	−	0.106528i	$-0.0339733\pi$
$97$	3.98779	+	6.90706i	0.404899	+	0.701306i	−0.589411	+	0.807834i	$0.700640\pi$
$98$		0			0
$99$	−1.81555	+	1.87030i	−0.182469	+	0.187972i
$100$		0			0
$101$	−1.88185	−	3.25946i	−0.187251	−	0.324329i	0.757082	−	0.653320i	$-0.226624\pi$
$101$	−1.88185	−	3.25946i	−0.187251	−	0.324329i	−0.944333	+	0.328992i	$0.893291\pi$
$102$		0			0
$103$	5.42778	−	9.40119i	0.534815	−	0.926327i	−0.464357	−	0.885648i	$-0.653715\pi$
$103$	5.42778	−	9.40119i	0.534815	−	0.926327i	0.999172	−	0.0406786i	$-0.0129520\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.64686			0.932597			0.466298	−	0.884627i	$-0.345587\pi$
$107$	9.64686			0.932597			0.466298	+	0.884627i	$0.345587\pi$
$108$		0			0
$109$	11.7226			1.12282			0.561412	−	0.827536i	$-0.310258\pi$
$109$	11.7226			1.12282			0.561412	+	0.827536i	$0.310258\pi$
$110$		0			0
$111$	5.53255	−	7.32212i	0.525127	−	0.694985i
$112$		0			0
$113$	2.88981	−	5.00530i	0.271851	−	0.470859i	−0.697485	−	0.716599i	$-0.745698\pi$
$113$	2.88981	−	5.00530i	0.271851	−	0.470859i	0.969336	+	0.245740i	$0.0790310\pi$
$114$		0			0
$115$	−12.0828	−	20.9280i	−1.12672	−	1.95154i
$116$		0			0
$117$	16.6529	+	4.19803i	1.53956	+	0.388108i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.12254	−	8.87250i	0.465686	−	0.806591i
$122$		0			0
$123$	−7.95227	−	18.8023i	−0.717032	−	1.69534i
$124$		0			0
$125$	−29.7736			−2.66303
$126$		0			0
$127$	6.47468			0.574535			0.287268	−	0.957850i	$-0.407253\pi$
$127$	6.47468			0.574535			0.287268	+	0.957850i	$0.407253\pi$
$128$		0			0
$129$	−6.89962	−	0.856271i	−0.607478	−	0.0753904i
$130$		0			0
$131$	−8.86514	+	15.3549i	−0.774551	+	1.34156i	0.160495	+	0.987037i	$0.448691\pi$
$131$	−8.86514	+	15.3549i	−0.774551	+	1.34156i	−0.935046	+	0.354525i	$0.884643\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−16.7917	+	13.4896i	−1.44520	+	1.16100i
$136$		0			0
$137$	−1.36116	−	2.35760i	−0.116292	−	0.201423i	0.802004	−	0.597319i	$-0.203767\pi$
$137$	−1.36116	−	2.35760i	−0.116292	−	0.201423i	−0.918295	+	0.395896i	$0.870434\pi$
$138$		0			0
$139$	−8.65431	+	14.9897i	−0.734049	+	1.27141i	0.221090	+	0.975253i	$0.429038\pi$
$139$	−8.65431	+	14.9897i	−0.734049	+	1.27141i	−0.955139	+	0.296157i	$0.904295\pi$
$140$		0			0
$141$	4.02964	+	0.500095i	0.339357	+	0.0421156i
$142$		0			0
$143$	4.97388			0.415937
$144$		0			0
$145$	−7.46481			−0.619919
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.42343	−	5.92955i	0.280458	−	0.485767i	−0.691040	−	0.722817i	$-0.742847\pi$
$149$	3.42343	−	5.92955i	0.280458	−	0.485767i	0.971498	+	0.237049i	$0.0761803\pi$
$150$		0			0
$151$	−4.64083	−	8.03816i	−0.377666	−	0.654136i	0.613057	−	0.790039i	$-0.289940\pi$
$151$	−4.64083	−	8.03816i	−0.377666	−	0.654136i	−0.990722	+	0.135903i	$0.956606\pi$
$152$		0			0
$153$	2.36996	+	8.34687i	0.191600	+	0.674804i
$154$		0			0
$155$	6.13678	+	10.6292i	0.492918	+	0.853759i
$156$		0			0
$157$	6.83840	−	11.8445i	0.545764	−	0.945291i	−0.452795	−	0.891615i	$-0.649573\pi$
$157$	6.83840	−	11.8445i	0.545764	−	0.945291i	0.998558	−	0.0536759i	$-0.0170938\pi$
$158$		0			0
$159$	2.27872	−	3.01581i	0.180715	−	0.239169i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	3.30005			0.258480			0.129240	−	0.991613i	$-0.458746\pi$
$163$	3.30005			0.258480			0.129240	+	0.991613i	$0.458746\pi$
$164$		0			0
$165$	−3.76068	+	4.97711i	−0.292768	+	0.387468i
$166$		0			0
$167$	−5.96228	+	10.3270i	−0.461375	+	0.799125i	−0.999030	−	0.0440399i	$-0.985977\pi$
$167$	−5.96228	+	10.3270i	−0.461375	+	0.799125i	0.537655	+	0.843165i	$0.319310\pi$
$168$		0			0
$169$	−9.88562	−	17.1224i	−0.760432	−	1.31711i
$170$		0			0
$171$	3.28917	+	11.5843i	0.251529	+	0.885871i
$172$		0			0
$173$	−4.81694	−	8.34319i	−0.366225	−	0.634321i	0.622747	−	0.782424i	$-0.286017\pi$
$173$	−4.81694	−	8.34319i	−0.366225	−	0.634321i	−0.988972	+	0.148103i	$0.952683\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.06072	+	4.87234i	0.154893	+	0.366228i
$178$		0			0
$179$	23.0570			1.72336			0.861682	−	0.507448i	$-0.169411\pi$
$179$	23.0570			1.72336			0.861682	+	0.507448i	$0.169411\pi$
$180$		0			0
$181$	11.8325			0.879504			0.439752	−	0.898119i	$-0.355066\pi$
$181$	11.8325			0.879504			0.439752	+	0.898119i	$0.355066\pi$
$182$		0			0
$183$	9.68268	+	1.20166i	0.715764	+	0.0888292i
$184$		0			0
$185$	10.9817	−	19.0208i	0.807390	−	1.39844i
$186$		0			0
$187$	1.25649	+	2.17630i	0.0918833	+	0.159147i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.14254	+	5.44303i	0.227386	+	0.393844i	0.957033	−	0.289980i	$-0.0936487\pi$
$191$	3.14254	+	5.44303i	0.227386	+	0.393844i	−0.729647	+	0.683824i	$0.760315\pi$
$192$		0			0
$193$	−6.86559	+	11.8915i	−0.494196	+	0.855972i	−0.999978	−	0.00668919i	$-0.997871\pi$
$193$	−6.86559	+	11.8915i	−0.494196	+	0.855972i	0.505782	+	0.862661i	$0.331204\pi$
$194$		0			0
$195$	40.7881	+	5.06197i	2.92090	+	0.362495i
$196$		0			0
$197$	−0.161495			−0.0115061			−0.00575303	−	0.999983i	$-0.501831\pi$
$197$	−0.161495			−0.0115061			−0.00575303	+	0.999983i	$0.501831\pi$
$198$		0			0
$199$	−24.8279			−1.76001			−0.880003	−	0.474968i	$-0.842460\pi$
$199$	−24.8279			−1.76001			−0.880003	+	0.474968i	$0.842460\pi$
$200$		0			0
$201$	−1.69400	−	4.00529i	−0.119486	−	0.282511i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−24.4287	−	42.3117i	−1.70617	−	2.95518i
$206$		0			0
$207$	−16.9587	−	4.27514i	−1.17871	−	0.297143i
$208$		0			0
$209$	1.74382	+	3.02039i	0.120623	+	0.208925i
$210$		0			0
$211$	9.44607	−	16.3611i	0.650295	−	1.12634i	−0.332757	−	0.943013i	$-0.607979\pi$
$211$	9.44607	−	16.3611i	0.650295	−	1.12634i	0.983051	−	0.183331i	$-0.0586879\pi$
$212$		0			0
$213$	−1.13964	+	1.50828i	−0.0780871	+	0.103345i
$214$		0			0
$215$	−16.6391			−1.13477
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.51047	−	1.99905i	0.102068	−	0.135083i
$220$		0			0
$221$	8.27856	−	14.3389i	0.556876	−	0.964538i
$222$		0			0
$223$	−7.04717	−	12.2061i	−0.471914	−	0.817378i	0.527570	−	0.849512i	$-0.323103\pi$
$223$	−7.04717	−	12.2061i	−0.471914	−	0.817378i	−0.999484	+	0.0321333i	$0.989770\pi$
$224$		0			0
$225$	−25.4566	+	26.2243i	−1.69711	+	1.74829i
$226$		0			0
$227$	12.9891	+	22.4978i	0.862118	+	1.49323i	0.869881	+	0.493262i	$0.164196\pi$
$227$	12.9891	+	22.4978i	0.862118	+	1.49323i	−0.00776306	+	0.999970i	$0.502471\pi$
$228$		0			0
$229$	12.4579	−	21.5777i	0.823239	−	1.42589i	−0.0800190	−	0.996793i	$-0.525498\pi$
$229$	12.4579	−	21.5777i	0.823239	−	1.42589i	0.903258	−	0.429098i	$-0.141169\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.11846			0.400834			0.200417	−	0.979711i	$-0.435770\pi$
$233$	6.11846			0.400834			0.200417	+	0.979711i	$0.435770\pi$
$234$		0			0
$235$	9.71785			0.633923
$236$		0			0
$237$	3.65995	+	0.454214i	0.237739	+	0.0295044i
$238$		0			0
$239$	−7.71988	+	13.3712i	−0.499357	+	0.864912i	−1.00000		0.000742080i	$-0.999764\pi$
$239$	−7.71988	+	13.3712i	−0.499357	+	0.864912i	0.500643	+	0.865654i	$0.333097\pi$
$240$		0			0
$241$	4.92259	+	8.52617i	0.317092	+	0.549219i	0.979880	−	0.199588i	$-0.0639604\pi$
$241$	4.92259	+	8.52617i	0.317092	+	0.549219i	−0.662788	+	0.748807i	$0.730627\pi$
$242$		0			0
$243$	−1.45951	+	15.5200i	−0.0936277	+	0.995607i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	11.4895	−	19.9003i	0.731057	−	1.26623i
$248$		0			0
$249$	−7.52121	−	0.933413i	−0.476638	−	0.0591527i
$250$		0			0
$251$	−26.8843			−1.69692			−0.848461	−	0.529258i	$-0.822470\pi$
$251$	−26.8843			−1.69692			−0.848461	+	0.529258i	$0.822470\pi$
$252$		0			0
$253$	−5.06524			−0.318449
$254$		0			0
$255$	8.08891	+	19.1254i	0.506547	+	1.19768i
$256$		0			0
$257$	5.50636	−	9.53729i	0.343477	−	0.594920i	−0.641599	−	0.767040i	$-0.721729\pi$
$257$	5.50636	−	9.53729i	0.343477	−	0.594920i	0.985076	+	0.172121i	$0.0550619\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.76298	+	3.87647i	−0.232923	+	0.239947i
$262$		0			0
$263$	3.65547	+	6.33146i	0.225406	+	0.390415i	0.956441	−	0.291925i	$-0.0942958\pi$
$263$	3.65547	+	6.33146i	0.225406	+	0.390415i	−0.731035	+	0.682340i	$0.760962\pi$
$264$		0			0
$265$	4.52309	−	7.83423i	0.277851	−	0.481253i
$266$		0			0
$267$	12.1828	−	16.1235i	0.745576	−	0.986742i
$268$		0			0
$269$	−4.16095			−0.253698			−0.126849	−	0.991922i	$-0.540486\pi$
$269$	−4.16095			−0.253698			−0.126849	+	0.991922i	$0.540486\pi$
$270$		0			0
$271$	−8.36599			−0.508198			−0.254099	−	0.967178i	$-0.581779\pi$
$271$	−8.36599			−0.508198			−0.254099	+	0.967178i	$0.581779\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.29250	+	9.16689i	−0.319150	+	0.552784i
$276$		0			0
$277$	1.39928	+	2.42362i	0.0840745	+	0.145621i	0.904996	−	0.425419i	$-0.139873\pi$
$277$	1.39928	+	2.42362i	0.0840745	+	0.145621i	−0.820922	+	0.571040i	$0.806540\pi$
$278$		0			0
$279$	8.61326	+	2.17132i	0.515662	+	0.129994i
$280$		0			0
$281$	−5.44314	−	9.42779i	−0.324710	−	0.562415i	0.656743	−	0.754114i	$-0.271933\pi$
$281$	−5.44314	−	9.42779i	−0.324710	−	0.562415i	−0.981454	+	0.191699i	$0.938600\pi$
$282$		0			0
$283$	−1.01212	+	1.75304i	−0.0601642	+	0.104207i	−0.894539	−	0.446990i	$-0.852496\pi$
$283$	−1.01212	+	1.75304i	−0.0601642	+	0.104207i	0.834374	+	0.551198i	$0.185829\pi$
$284$		0			0
$285$	11.2263	+	26.5433i	0.664986	+	1.57229i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.63479			−0.507929
$290$		0			0
$291$	13.7090	+	1.70134i	0.803633	+	0.0997341i
$292$		0			0
$293$	9.65448	−	16.7220i	0.564021	−	0.976912i	−0.433120	−	0.901336i	$-0.642587\pi$
$293$	9.65448	−	16.7220i	0.564021	−	0.976912i	0.997140	−	0.0755757i	$-0.0240795\pi$
$294$		0			0
$295$	6.33035	+	10.9645i	0.368567	+	0.638377i
$296$		0			0
$297$	0.688866	+	4.46186i	0.0399721	+	0.258903i
$298$		0			0
$299$	16.6866	+	28.9020i	0.965011	+	1.67145i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.46929	−	0.802866i	−0.371651	−	0.0461234i
$304$		0			0
$305$	23.3507			1.33705
$306$		0			0
$307$	13.1378			0.749813			0.374907	−	0.927063i	$-0.377675\pi$
$307$	13.1378			0.749813			0.374907	+	0.927063i	$0.377675\pi$
$308$		0			0
$309$	−7.32417	−	17.3172i	−0.416658	−	0.985142i
$310$		0			0
$311$	−6.76606	+	11.7192i	−0.383668	+	0.664533i	−0.991583	−	0.129469i	$-0.958673\pi$
$311$	−6.76606	+	11.7192i	−0.383668	+	0.664533i	0.607915	+	0.794002i	$0.292006\pi$
$312$		0			0
$313$	−12.6000	−	21.8238i	−0.712194	−	1.23356i	−0.964032	−	0.265787i	$-0.914368\pi$
$313$	−12.6000	−	21.8238i	−0.712194	−	1.23356i	0.251838	−	0.967770i	$-0.418965\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.14888	+	10.6502i	0.345356	+	0.598173i	0.985418	−	0.170149i	$-0.0544250\pi$
$317$	6.14888	+	10.6502i	0.345356	+	0.598173i	−0.640063	+	0.768323i	$0.721092\pi$
$318$		0			0
$319$	−0.782335	+	1.35504i	−0.0438023	+	0.0758679i
$320$		0			0
$321$	10.0730	−	13.3312i	0.562218	−	0.744075i
$322$		0			0
$323$	11.6097			0.645982
$324$		0			0
$325$	69.7411			3.86854
$326$		0			0
$327$	12.2404	−	16.1997i	0.676897	−	0.895848i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	9.96285	+	17.2562i	0.547608	+	0.948484i	0.998438	+	0.0558745i	$0.0177947\pi$
$331$	9.96285	+	17.2562i	0.547608	+	0.948484i	−0.450830	+	0.892610i	$0.648872\pi$
$332$		0			0
$333$	−4.34167	−	15.2911i	−0.237922	−	0.837947i
$334$		0			0
$335$	−5.20383	−	9.01330i	−0.284316	−	0.492449i
$336$		0			0
$337$	−0.966380	+	1.67382i	−0.0526421	+	0.0911788i	−0.891146	−	0.453717i	$-0.850098\pi$
$337$	−0.966380	+	1.67382i	−0.0526421	+	0.0911788i	0.838504	+	0.544896i	$0.183431\pi$
$338$		0			0
$339$	−3.89947	−	9.21988i	−0.211790	−	0.500755i
$340$		0			0
$341$	2.57261			0.139315
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−41.5373	−	5.15495i	−2.23629	−	0.277533i
$346$		0			0
$347$	−8.48241	+	14.6920i	−0.455360	+	0.788706i	−0.998709	−	0.0508006i	$-0.983823\pi$
$347$	−8.48241	+	14.6920i	−0.455360	+	0.788706i	0.543349	+	0.839507i	$0.317156\pi$
$348$		0			0
$349$	6.25767	+	10.8386i	0.334966	+	0.580177i	0.983478	−	0.181027i	$-0.0579420\pi$
$349$	6.25767	+	10.8386i	0.334966	+	0.580177i	−0.648513	+	0.761204i	$0.724609\pi$
$350$		0			0
$351$	23.1898	−	18.6295i	1.23778	−	0.994368i
$352$		0			0
$353$	16.1929	+	28.0468i	0.861859	+	1.49278i	0.870133	+	0.492817i	$0.164033\pi$
$353$	16.1929	+	28.0468i	0.861859	+	1.49278i	−0.00827416	+	0.999966i	$0.502634\pi$
$354$		0			0
$355$	−2.26211	+	3.91808i	−0.120060	+	0.207950i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−17.9712			−0.948483			−0.474242	−	0.880395i	$-0.657278\pi$
$359$	−17.9712			−0.948483			−0.474242	+	0.880395i	$0.657278\pi$
$360$		0			0
$361$	−2.88735			−0.151966
$362$		0			0
$363$	−6.91229	−	16.3434i	−0.362801	−	0.857804i
$364$		0			0
$365$	2.99816	−	5.19297i	0.156931	−	0.271812i
$366$		0			0
$367$	4.08420	+	7.07404i	0.213194	+	0.369262i	0.952712	−	0.303874i	$-0.0982802\pi$
$367$	4.08420	+	7.07404i	0.213194	+	0.369262i	−0.739519	+	0.673136i	$0.764947\pi$
$368$		0			0
$369$	−34.2868	−	8.64339i	−1.78490	−	0.449957i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.58080	−	4.47008i	0.133629	−	0.231452i	−0.791444	−	0.611242i	$-0.790670\pi$
$373$	2.58080	−	4.47008i	0.133629	−	0.231452i	0.925073	+	0.379790i	$0.124004\pi$
$374$		0			0
$375$	−31.0887	+	41.1447i	−1.60541	+	2.12470i
$376$		0			0
$377$	10.3091			0.530945
$378$		0			0
$379$	21.0017			1.07878			0.539392	−	0.842055i	$-0.318654\pi$
$379$	21.0017			1.07878			0.539392	+	0.842055i	$0.318654\pi$
$380$		0			0
$381$	6.76068	−	8.94750i	0.346360	−	0.458394i
$382$		0			0
$383$	14.7794	−	25.5988i	0.755194	−	1.30804i	−0.190083	−	0.981768i	$-0.560876\pi$
$383$	14.7794	−	25.5988i	0.755194	−	1.30804i	0.945278	−	0.326267i	$-0.105791\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.38768	+	8.64064i	−0.426370	+	0.439228i
$388$		0			0
$389$	8.26895	+	14.3222i	0.419252	+	0.726166i	0.995864	−	0.0908518i	$-0.0289589\pi$
$389$	8.26895	+	14.3222i	0.419252	+	0.726166i	−0.576612	+	0.817018i	$0.695626\pi$
$390$		0			0
$391$	−8.43063	+	14.6023i	−0.426355	+	0.738469i
$392$		0			0
$393$	11.9625	+	28.2840i	0.603429	+	1.42674i
$394$		0			0
$395$	8.82629			0.444099
$396$		0			0
$397$	30.8788			1.54976			0.774881	−	0.632107i	$-0.217810\pi$
$397$	30.8788			1.54976			0.774881	+	0.632107i	$0.217810\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.31614	+	9.20782i	−0.265475	+	0.459817i	−0.967688	−	0.252150i	$-0.918862\pi$
$401$	−5.31614	+	9.20782i	−0.265475	+	0.459817i	0.702213	+	0.711967i	$0.252196\pi$
$402$		0			0
$403$	−8.47504	−	14.6792i	−0.422172	−	0.731223i
$404$		0			0
$405$	1.10814	+	37.2903i	0.0550638	+	1.85297i
$406$		0			0
$407$	−2.30183	−	3.98688i	−0.114097	−	0.197622i
$408$		0			0
$409$	−7.39782	+	12.8134i	−0.365799	+	0.633582i	−0.988904	−	0.148556i	$-0.952538\pi$
$409$	−7.39782	+	12.8134i	−0.365799	+	0.633582i	0.623105	+	0.782138i	$0.285871\pi$
$410$		0			0
$411$	−4.67930	−	0.580720i	−0.230813	−	0.0286448i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−18.1381			−0.890364
$416$		0			0
$417$	11.6780	+	27.6114i	0.571875	+	1.35214i
$418$		0			0
$419$	1.56134	−	2.70432i	0.0762765	−	0.132115i	−0.825364	−	0.564601i	$-0.809030\pi$
$419$	1.56134	−	2.70432i	0.0762765	−	0.132115i	0.901641	+	0.432486i	$0.142363\pi$
$420$		0			0
$421$	−0.644580	−	1.11645i	−0.0314149	−	0.0544122i	0.849891	−	0.526959i	$-0.176668\pi$
$421$	−0.644580	−	1.11645i	−0.0314149	−	0.0544122i	−0.881305	+	0.472547i	$0.843335\pi$
$422$		0			0
$423$	4.89873	−	5.04647i	0.238184	−	0.245368i
$424$		0			0
$425$	17.6178	+	30.5149i	0.854587	+	1.48019i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	5.19358	−	6.87351i	0.250749	−	0.331856i
$430$		0			0
$431$	23.1833			1.11670			0.558350	−	0.829606i	$-0.311435\pi$
$431$	23.1833			1.11670			0.558350	+	0.829606i	$0.311435\pi$
$432$		0			0
$433$	−35.6437			−1.71293			−0.856464	−	0.516207i	$-0.827343\pi$
$433$	−35.6437			−1.71293			−0.856464	+	0.516207i	$0.827343\pi$
$434$		0			0
$435$	−7.79454	+	10.3158i	−0.373720	+	0.494604i
$436$		0			0
$437$	−11.7005	+	20.2659i	−0.559711	+	0.969448i
$438$		0			0
$439$	8.00620	+	13.8671i	0.382115	+	0.661843i	0.991364	−	0.131136i	$-0.0418625\pi$
$439$	8.00620	+	13.8671i	0.382115	+	0.661843i	−0.609249	+	0.792979i	$0.708529\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.17778	−	12.4323i	−0.341027	−	0.590676i	0.643597	−	0.765365i	$-0.277441\pi$
$443$	−7.17778	−	12.4323i	−0.341027	−	0.590676i	−0.984624	+	0.174689i	$0.944108\pi$
$444$		0			0
$445$	24.1819	−	41.8844i	1.14633	−	1.98551i
$446$		0			0
$447$	−4.61953	−	10.9224i	−0.218496	−	0.516610i
$448$		0			0
$449$	5.72475			0.270168			0.135084	−	0.990834i	$-0.456870\pi$
$449$	5.72475			0.270168			0.135084	+	0.990834i	$0.456870\pi$
$450$		0			0
$451$	−10.2408			−0.482220
$452$		0			0
$453$	−15.9539	−	1.97995i	−0.749581	−	0.0930260i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.33175	−	12.6990i	−0.342965	−	0.594033i	0.642017	−	0.766690i	$-0.278098\pi$
$457$	−7.33175	−	12.6990i	−0.342965	−	0.594033i	−0.984982	+	0.172658i	$0.944765\pi$
$458$		0			0
$459$	14.0094	+	5.44046i	0.653901	+	0.253939i
$460$		0			0
$461$	12.9720	+	22.4681i	0.604164	+	1.04644i	0.992183	+	0.124792i	$0.0398263\pi$
$461$	12.9720	+	22.4681i	0.604164	+	1.04644i	−0.388018	+	0.921652i	$0.626840\pi$
$462$		0			0
$463$	−6.46277	+	11.1939i	−0.300351	+	0.520223i	−0.976215	−	0.216803i	$-0.930437\pi$
$463$	−6.46277	+	11.1939i	−0.300351	+	0.520223i	0.675865	+	0.737026i	$0.263770\pi$
$464$		0			0
$465$	21.0966	+	2.61817i	0.978331	+	0.121415i
$466$		0			0
$467$	−32.6208			−1.50951			−0.754755	−	0.656007i	$-0.772244\pi$
$467$	−32.6208			−1.50951			−0.754755	+	0.656007i	$0.772244\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−9.22765	−	21.8178i	−0.425188	−	1.00531i
$472$		0			0
$473$	−1.74382	+	3.02039i	−0.0801811	+	0.138878i
$474$		0			0
$475$	24.4509	+	42.3503i	1.12189	+	1.94316i
$476$		0			0
$477$	−1.78823	−	6.29804i	−0.0818774	−	0.288367i
$478$		0			0
$479$	−12.6739	−	21.9518i	−0.579084	−	1.00300i	−0.995585	−	0.0938679i	$-0.970077\pi$
$479$	−12.6739	−	21.9518i	−0.579084	−	1.00300i	0.416500	−	0.909136i	$-0.363256\pi$
$480$		0			0
$481$	−15.1660	+	26.2682i	−0.691509	+	1.19773i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	33.0604			1.50119
$486$		0			0
$487$	−35.4766			−1.60760			−0.803799	−	0.594901i	$-0.797191\pi$
$487$	−35.4766			−1.60760			−0.803799	+	0.594901i	$0.797191\pi$
$488$		0			0
$489$	3.44582	−	4.56041i	0.155825	−	0.206229i
$490$		0			0
$491$	13.2554	−	22.9590i	0.598208	−	1.03613i	−0.394877	−	0.918734i	$-0.629213\pi$
$491$	13.2554	−	22.9590i	0.598208	−	1.03613i	0.993085	−	0.117393i	$-0.0374538\pi$
$492$		0			0
$493$	2.60425	+	4.51069i	0.117289	+	0.203151i
$494$		0			0
$495$	2.95119	+	10.3939i	0.132646	+	0.467172i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.00130	−	5.19841i	0.134357	−	0.232713i	−0.790995	−	0.611823i	$-0.790437\pi$
$499$	3.00130	−	5.19841i	0.134357	−	0.232713i	0.925352	+	0.379110i	$0.123770\pi$
$500$		0			0
$501$	8.04542	+	19.0225i	0.359443	+	0.849864i
$502$		0			0
$503$	22.9460			1.02311			0.511556	−	0.859250i	$-0.329069\pi$
$503$	22.9460			1.02311			0.511556	+	0.859250i	$0.329069\pi$
$504$		0			0
$505$	−15.6013			−0.694248
$506$		0			0
$507$	−33.9841	−	4.21756i	−1.50929	−	0.187309i
$508$		0			0
$509$	14.9348	−	25.8679i	0.661975	−	1.14657i	−0.318121	−	0.948050i	$-0.603052\pi$
$509$	14.9348	−	25.8679i	0.661975	−	1.14657i	0.980096	−	0.198524i	$-0.0636147\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	19.4430	+	7.55058i	0.858429	+	0.333366i
$514$		0			0
$515$	−22.4992	−	38.9698i	−0.991434	−	1.71721i
$516$		0			0
$517$	1.01846	−	1.76402i	0.0447918	−	0.0775817i
$518$		0			0
$519$	−16.5593	−	2.05508i	−0.726875	−	0.0902081i
$520$		0			0
$521$	31.1960			1.36672			0.683362	−	0.730080i	$-0.260517\pi$
$521$	31.1960			1.36672			0.683362	+	0.730080i	$0.260517\pi$
$522$		0			0
$523$	−6.15822			−0.269280			−0.134640	−	0.990895i	$-0.542988\pi$
$523$	−6.15822			−0.269280			−0.134640	+	0.990895i	$0.542988\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.28187	−	7.41642i	0.186521	−	0.323064i
$528$		0			0
$529$	−5.49310	−	9.51433i	−0.238830	−	0.413666i
$530$		0			0
$531$	8.88494	+	2.23981i	0.385574	+	0.0971995i
$532$		0			0
$533$	33.7366	+	58.4335i	1.46129	+	2.53103i
$534$		0			0
$535$	19.9941	−	34.6307i	0.864419	−	1.49722i
$536$		0			0
$537$	24.0755	−	31.8630i	1.03893	−	1.37499i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	27.0274			1.16200			0.580999	−	0.813904i	$-0.302662\pi$
$541$	27.0274			1.16200			0.580999	+	0.813904i	$0.302662\pi$
$542$		0			0
$543$	12.3552	−	16.3516i	0.530211	−	0.701714i
$544$		0			0
$545$	24.2963	−	42.0824i	1.04074	−	1.80261i
$546$		0			0
$547$	14.9426	+	25.8814i	0.638900	+	1.10661i	0.985675	+	0.168658i	$0.0539434\pi$
$547$	14.9426	+	25.8814i	0.638900	+	1.10661i	−0.346775	+	0.937948i	$0.612723\pi$
$548$		0			0
$549$	11.7710	−	12.1260i	0.502373	−	0.517523i
$550$		0			0
$551$	3.61432	+	6.26019i	0.153975	+	0.266693i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−14.8185	−	35.0368i	−0.629012	−	1.48723i
$556$		0			0
$557$	−21.3299			−0.903778			−0.451889	−	0.892074i	$-0.649250\pi$
$557$	−21.3299			−0.903778			−0.451889	+	0.892074i	$0.649250\pi$
$558$		0			0
$559$	22.9789			0.971905
$560$		0			0
$561$	4.31946	+	0.536062i	0.182368	+	0.0226326i
$562$		0			0
$563$	15.7317	−	27.2482i	0.663014	−	1.14837i	−0.316805	−	0.948491i	$-0.602610\pi$
$563$	15.7317	−	27.2482i	0.663014	−	1.14837i	0.979820	−	0.199884i	$-0.0640564\pi$
$564$		0			0
$565$	−11.9788	−	20.7480i	−0.503954	−	0.872873i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.6696	−	25.4084i	−0.614980	−	1.06518i	−0.990388	−	0.138317i	$-0.955831\pi$
$569$	−14.6696	−	25.4084i	−0.614980	−	1.06518i	0.375408	−	0.926860i	$-0.377503\pi$
$570$		0			0
$571$	13.7473	−	23.8111i	0.575308	−	0.996463i	−0.420700	−	0.907200i	$-0.638215\pi$
$571$	13.7473	−	23.8111i	0.575308	−	0.996463i	0.996008	−	0.0892631i	$-0.0284512\pi$
$572$		0			0
$573$	10.8032	+	1.34072i	0.451310	+	0.0560094i
$574$		0			0
$575$	−71.0221			−2.96183
$576$		0			0
$577$	−40.4586			−1.68431			−0.842156	−	0.539234i	$-0.818714\pi$
$577$	−40.4586			−1.68431			−0.842156	+	0.539234i	$0.818714\pi$
$578$		0			0
$579$	9.26433	+	21.9045i	0.385013	+	0.910320i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.948067	−	1.64210i	−0.0392649	−	0.0680089i
$584$		0			0
$585$	49.5850	−	51.0804i	2.05009	−	2.11191i
$586$		0			0
$587$	13.6559	+	23.6528i	0.563641	+	0.976255i	0.997175	+	0.0751177i	$0.0239333\pi$
$587$	13.6559	+	23.6528i	0.563641	+	0.976255i	−0.433533	+	0.901137i	$0.642733\pi$
$588$		0			0
$589$	5.94263	−	10.2929i	0.244862	−	0.424113i
$590$		0			0
$591$	−0.168629	+	0.223174i	−0.00693646	+	0.00918014i
$592$		0			0
$593$	28.5797			1.17363			0.586813	−	0.809722i	$-0.300382\pi$
$593$	28.5797			1.17363			0.586813	+	0.809722i	$0.300382\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−25.9246	+	34.3103i	−1.06102	+	1.40423i
$598$		0			0
$599$	−19.9919	+	34.6270i	−0.816848	+	1.41482i	0.0911461	+	0.995838i	$0.470947\pi$
$599$	−19.9919	+	34.6270i	−0.816848	+	1.41482i	−0.907994	+	0.418984i	$0.862386\pi$
$600$		0			0
$601$	12.6948	+	21.9880i	0.517831	+	0.896910i	0.999785	+	0.0207133i	$0.00659372\pi$
$601$	12.6948	+	21.9880i	0.517831	+	0.896910i	−0.481954	+	0.876196i	$0.660073\pi$
$602$		0			0
$603$	−7.30383	−	1.84123i	−0.297435	−	0.0749806i
$604$		0			0
$605$	−21.2340	−	36.7783i	−0.863283	−	1.49525i
$606$		0			0
$607$	−18.6469	+	32.2975i	−0.756856	+	1.31091i	0.187590	+	0.982247i	$0.439932\pi$
$607$	−18.6469	+	32.2975i	−0.756856	+	1.31091i	−0.944446	+	0.328666i	$0.893401\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13.4206			−0.542939
$612$		0			0
$613$	23.4638			0.947696			0.473848	−	0.880607i	$-0.342865\pi$
$613$	23.4638			0.947696			0.473848	+	0.880607i	$0.342865\pi$
$614$		0			0
$615$	−83.9792	−	10.4222i	−3.38637	−	0.420262i
$616$		0			0
$617$	6.56888	−	11.3776i	0.264453	−	0.458047i	−0.702967	−	0.711223i	$-0.748142\pi$
$617$	6.56888	−	11.3776i	0.264453	−	0.458047i	0.967420	+	0.253176i	$0.0814752\pi$
$618$		0			0
$619$	10.7776	+	18.6674i	0.433190	+	0.750308i	0.997146	−	0.0754975i	$-0.0240545\pi$
$619$	10.7776	+	18.6674i	0.433190	+	0.750308i	−0.563956	+	0.825805i	$0.690721\pi$
$620$		0			0
$621$	−23.6157	+	18.9717i	−0.947667	+	0.761307i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−31.2520	+	54.1300i	−1.25008	+	2.16520i
$626$		0			0
$627$	5.99479	+	0.743978i	0.239409	+	0.0297116i
$628$		0			0
$629$	−15.3247			−0.611036
$630$		0			0
$631$	−6.15223			−0.244916			−0.122458	−	0.992474i	$-0.539078\pi$
$631$	−6.15223			−0.244916			−0.122458	+	0.992474i	$0.539078\pi$
$632$		0			0
$633$	−12.7464	−	30.1375i	−0.506624	−	1.19786i
$634$		0			0
$635$	13.4194	−	23.2431i	0.532533	−	0.922375i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.894336	+	3.14980i	0.0353794	+	0.124604i
$640$		0			0
$641$	2.23682	+	3.87429i	0.0883491	+	0.153025i	0.906813	−	0.421532i	$-0.138508\pi$
$641$	2.23682	+	3.87429i	0.0883491	+	0.153025i	−0.818464	+	0.574557i	$0.805174\pi$
$642$		0			0
$643$	−8.98009	+	15.5540i	−0.354140	+	0.613389i	−0.986970	−	0.160902i	$-0.948560\pi$
$643$	−8.98009	+	15.5540i	−0.354140	+	0.613389i	0.632830	+	0.774291i	$0.281893\pi$
$644$		0			0
$645$	−17.3740	+	22.9939i	−0.684101	+	0.905383i
$646$		0			0
$647$	12.0598			0.474121			0.237061	−	0.971495i	$-0.423816\pi$
$647$	12.0598			0.474121			0.237061	+	0.971495i	$0.423816\pi$
$648$		0			0
$649$	2.65376			0.104169
$650$		0			0
$651$		0			0
$652$		0			0
$653$	24.1366	−	41.8059i	0.944540	−	1.63599i	0.187870	−	0.982194i	$-0.439842\pi$
$653$	24.1366	−	41.8059i	0.944540	−	1.63599i	0.756670	−	0.653797i	$-0.226825\pi$
$654$		0			0
$655$	36.7478	+	63.6490i	1.43585	+	2.48697i
$656$		0			0
$657$	−1.18534	−	4.17469i	−0.0462445	−	0.162870i
$658$		0			0
$659$	14.5795	+	25.2525i	0.567937	+	0.983696i	0.996770	+	0.0803122i	$0.0255917\pi$
$659$	14.5795	+	25.2525i	0.567937	+	0.983696i	−0.428832	+	0.903384i	$0.641075\pi$
$660$		0			0
$661$	−7.27428	+	12.5994i	−0.282937	+	0.490061i	−0.972107	−	0.234539i	$-0.924642\pi$
$661$	−7.27428	+	12.5994i	−0.282937	+	0.490061i	0.689170	+	0.724600i	$0.257975\pi$
$662$		0			0
$663$	−11.1710	−	26.4126i	−0.433845	−	1.02578i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.4984			−0.406501
$668$		0			0
$669$	−24.2263	−	3.00658i	−0.936642	−	0.116241i
$670$		0			0
$671$	2.44722	−	4.23871i	0.0944738	−	0.163633i
$672$		0			0
$673$	11.6825	+	20.2348i	0.450329	+	0.779993i	0.998406	−	0.0564349i	$-0.0179733\pi$
$673$	11.6825	+	20.2348i	0.450329	+	0.779993i	−0.548077	+	0.836428i	$0.684640\pi$
$674$		0			0
$675$	9.65891	+	62.5617i	0.371771	+	2.40800i
$676$		0			0
$677$	−8.85875	−	15.3438i	−0.340469	−	0.589710i	0.644051	−	0.764983i	$-0.277253\pi$
$677$	−8.85875	−	15.3438i	−0.340469	−	0.589710i	−0.984520	+	0.175273i	$0.943919\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	44.6531	+	5.54163i	1.71111	+	0.212356i
$682$		0			0
$683$	−43.5537			−1.66654			−0.833269	−	0.552868i	$-0.813533\pi$
$683$	−43.5537			−1.66654			−0.833269	+	0.552868i	$0.813533\pi$
$684$		0			0
$685$	−11.2846			−0.431161
$686$		0			0
$687$	−16.8105	−	39.7466i	−0.641360	−	1.51643i
$688$		0			0
$689$	−6.24650	+	10.8193i	−0.237973	+	0.412181i
$690$		0			0
$691$	11.7672	+	20.3814i	0.447645	+	0.775345i	0.998232	−	0.0594333i	$-0.0189294\pi$
$691$	11.7672	+	20.3814i	0.447645	+	0.775345i	−0.550587	+	0.834778i	$0.685596\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	35.8738	+	62.1353i	1.36077	+	2.35693i
$696$		0			0
$697$	−17.0449	+	29.5225i	−0.645620	+	1.11825i
$698$		0			0
$699$	6.38872	−	8.45523i	0.241644	−	0.319806i
$700$		0			0
$701$	45.1804			1.70644			0.853219	−	0.521552i	$-0.174647\pi$
$701$	45.1804			1.70644			0.853219	+	0.521552i	$0.174647\pi$
$702$		0			0
$703$	−21.2685			−0.802157
$704$		0			0
$705$	10.1471	−	13.4293i	0.382162	−	0.505777i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	13.5064	+	23.3937i	0.507242	+	0.878568i	0.999965	+	0.00838223i	$0.00266818\pi$
$709$	13.5064	+	23.3937i	0.507242	+	0.878568i	−0.492723	+	0.870186i	$0.663998\pi$
$710$		0			0
$711$	4.44930	−	4.58348i	0.166862	−	0.171894i
$712$		0			0
$713$	8.63071	+	14.9488i	0.323223	+	0.559838i
$714$		0			0
$715$	10.3089	−	17.8555i	0.385529	−	0.667757i
$716$		0			0
$717$	10.4171	+	24.6301i	0.389034	+	0.919828i
$718$		0			0
$719$	−22.4192			−0.836096			−0.418048	−	0.908425i	$-0.637286\pi$
$719$	−22.4192			−0.836096			−0.418048	+	0.908425i	$0.637286\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	16.9225	+	2.10015i	0.629355	+	0.0781056i
$724$		0			0
$725$	−10.9695	+	18.9997i	−0.407396	+	0.705631i
$726$		0			0
$727$	−21.9820	−	38.0740i	−0.815268	−	1.41208i	−0.909136	−	0.416500i	$-0.863256\pi$
$727$	−21.9820	−	38.0740i	−0.815268	−	1.41208i	0.0938680	−	0.995585i	$-0.470077\pi$
$728$		0			0
$729$	19.9234	+	18.2224i	0.737904	+	0.674905i
$730$		0			0
$731$	5.80486	+	10.0543i	0.214701	+	0.371872i
$732$		0			0
$733$	0.433386	−	0.750646i	0.0160075	−	0.0277257i	−0.857911	−	0.513799i	$-0.828238\pi$
$733$	0.433386	−	0.750646i	0.0160075	−	0.0277257i	0.873918	+	0.486073i	$0.161571\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.18151			−0.0803569
$738$		0			0
$739$	−26.0883			−0.959675			−0.479838	−	0.877357i	$-0.659304\pi$
$739$	−26.0883			−0.959675			−0.479838	+	0.877357i	$0.659304\pi$
$740$		0			0
$741$	−15.5037	−	36.6569i	−0.569544	−	1.34662i
$742$		0			0
$743$	22.5842	−	39.1170i	0.828533	−	1.43506i	−0.0706551	−	0.997501i	$-0.522509\pi$
$743$	22.5842	−	39.1170i	0.828533	−	1.43506i	0.899189	−	0.437561i	$-0.144158\pi$
$744$		0			0
$745$	−14.1908	−	24.5791i	−0.519910	−	0.900510i
$746$		0			0
$747$	−9.14334	+	9.41908i	−0.334537	+	0.344626i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	10.2994	−	17.8391i	0.375831	−	0.650958i	−0.614620	−	0.788823i	$-0.710691\pi$
$751$	10.2994	−	17.8391i	0.375831	−	0.650958i	0.990451	+	0.137865i	$0.0440241\pi$
$752$		0			0
$753$	−28.0718	+	37.1520i	−1.02299	+	1.35389i
$754$		0			0
$755$	−38.4743			−1.40022
$756$		0			0
$757$	−39.0856			−1.42059			−0.710294	−	0.703905i	$-0.751438\pi$
$757$	−39.0856			−1.42059			−0.710294	+	0.703905i	$0.751438\pi$
$758$		0			0
$759$	−5.28898	+	6.99977i	−0.191978	+	0.254075i
$760$		0			0
$761$	−14.4436	+	25.0171i	−0.523581	+	0.906868i	0.476043	+	0.879422i	$0.342071\pi$
$761$	−14.4436	+	25.0171i	−0.523581	+	0.906868i	−0.999623	+	0.0274459i	$0.991263\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	34.8760	+	8.79191i	1.26094	+	0.317872i
$766$		0			0
$767$	−8.74236	−	15.1422i	−0.315668	−	0.546753i
$768$		0			0
$769$	11.1407	−	19.2962i	0.401742	−	0.695838i	−0.592194	−	0.805796i	$-0.701738\pi$
$769$	11.1407	−	19.2962i	0.401742	−	0.695838i	0.993936	+	0.109957i	$0.0350714\pi$
$770$		0			0
$771$	−7.43021	−	17.5679i	−0.267592	−	0.632693i
$772$		0			0
$773$	−42.7187			−1.53648			−0.768242	−	0.640159i	$-0.778868\pi$
$773$	−42.7187			−1.53648			−0.768242	+	0.640159i	$0.778868\pi$
$774$		0			0
$775$	36.0718			1.29574
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−23.6558	+	40.9731i	−0.847558	+	1.46801i
$780$		0			0
$781$	0.474151	+	0.821254i	0.0169665	+	0.0293868i
$782$		0			0
$783$	1.42777	+	9.24784i	0.0510245	+	0.330491i
$784$		0			0
$785$	−28.3465	−	49.0976i	−1.01173	−	1.75237i
$786$		0			0
$787$	−0.143384	+	0.248349i	−0.00511110	+	0.00885268i	−0.868570	−	0.495567i	$-0.834960\pi$
$787$	−0.143384	+	0.248349i	−0.00511110	+	0.00885268i	0.863459	+	0.504420i	$0.168294\pi$
$788$		0			0
$789$	12.5665	+	1.55956i	0.447380	+	0.0555217i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−32.2478			−1.14515
$794$		0			0
$795$	−6.10340	−	14.4308i	−0.216465	−	0.511809i
$796$		0			0
$797$	0.457746	−	0.792840i	0.0162142	−	0.0280838i	−0.857804	−	0.513976i	$-0.828172\pi$
$797$	0.457746	−	0.792840i	0.0162142	−	0.0280838i	0.874019	+	0.485892i	$0.161505\pi$
$798$		0			0
$799$	−3.39026	−	5.87211i	−0.119939	−	0.207740i
$800$		0			0
$801$	−9.56046	−	33.6714i	−0.337802	−	1.18972i
$802$		0			0
$803$	−0.628433	−	1.08848i	−0.0221769	−	0.0384115i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4.34474	+	5.75011i	−0.152942	+	0.202413i
$808$		0			0
$809$	28.7442			1.01059			0.505297	−	0.862946i	$-0.331383\pi$
$809$	28.7442			1.01059			0.505297	+	0.862946i	$0.331383\pi$
$810$		0			0
$811$	−14.3005			−0.502157			−0.251079	−	0.967967i	$-0.580785\pi$
$811$	−14.3005			−0.502157			−0.251079	+	0.967967i	$0.580785\pi$
$812$		0			0
$813$	−8.73553	+	11.5611i	−0.306368	+	0.405467i
$814$		0			0
$815$	6.83969	−	11.8467i	0.239584	−	0.414971i
$816$		0			0
$817$	8.05632	+	13.9540i	0.281855	+	0.488187i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.8125	−	30.8521i	−0.621660	−	1.07675i	−0.989177	−	0.146730i	$-0.953125\pi$
$821$	−17.8125	−	30.8521i	−0.621660	−	1.07675i	0.367516	−	0.930017i	$-0.380208\pi$
$822$		0			0
$823$	11.2157	−	19.4261i	0.390953	−	0.677151i	−0.601622	−	0.798781i	$-0.705479\pi$
$823$	11.2157	−	19.4261i	0.390953	−	0.677151i	0.992576	+	0.121630i	$0.0388121\pi$
$824$		0			0
$825$	7.14164	+	16.8856i	0.248640	+	0.587882i
$826$		0			0
$827$	−26.6728			−0.927505			−0.463753	−	0.885965i	$-0.653497\pi$
$827$	−26.6728			−0.927505			−0.463753	+	0.885965i	$0.653497\pi$
$828$		0			0
$829$	−32.0155			−1.11195			−0.555973	−	0.831200i	$-0.687654\pi$
$829$	−32.0155			−1.11195			−0.555973	+	0.831200i	$0.687654\pi$
$830$		0			0
$831$	4.81034	+	0.596983i	0.166869	+	0.0207091i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	24.7148	+	42.8074i	0.855292	+	1.48141i
$836$		0			0
$837$	11.9943	−	9.63561i	0.414584	−	0.333056i
$838$		0			0
$839$	−9.10375	−	15.7682i	−0.314296	−	0.544377i	0.664991	−	0.746851i	$-0.268435\pi$
$839$	−9.10375	−	15.7682i	−0.314296	−	0.544377i	−0.979288	+	0.202474i	$0.935102\pi$
$840$		0			0
$841$	12.8785	−	22.3062i	0.444086	−	0.769180i
$842$		0			0
$843$	−18.7120	−	2.32224i	−0.644477	−	0.0799822i
$844$		0			0
$845$	−81.9557			−2.81936
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.36574	+	3.22914i	0.0468721	+	0.110824i
$850$		0			0
$851$	15.4445	−	26.7507i	0.529432	−	0.917003i
$852$		0			0
$853$	−20.9242	−	36.2419i	−0.716432	−	1.24090i	−0.962404	−	0.271621i	$-0.912440\pi$
$853$	−20.9242	−	36.2419i	−0.716432	−	1.24090i	0.245972	−	0.969277i	$-0.420893\pi$
$854$		0			0
$855$	48.4029	+	12.2019i	1.65534	+	0.417297i
$856$		0			0
$857$	7.85704	+	13.6088i	0.268391	+	0.464867i	0.968447	−	0.249221i	$-0.0801746\pi$
$857$	7.85704	+	13.6088i	0.268391	+	0.464867i	−0.700055	+	0.714089i	$0.746841\pi$
$858$		0			0
$859$	12.1023	−	20.9618i	0.412924	−	0.715206i	−0.582284	−	0.812986i	$-0.697841\pi$
$859$	12.1023	−	20.9618i	0.412924	−	0.715206i	0.995208	+	0.0977797i	$0.0311741\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−52.1085			−1.77379			−0.886896	−	0.461969i	$-0.847143\pi$
$863$	−52.1085			−1.77379			−0.886896	+	0.461969i	$0.847143\pi$
$864$		0			0
$865$	−39.9344			−1.35781
$866$		0			0
$867$	−9.01619	+	11.9326i	−0.306206	+	0.405252i
$868$		0			0
$869$	0.925022	−	1.60219i	0.0313792	−	0.0543504i
$870$		0			0
$871$	7.18662	+	12.4476i	0.243509	+	0.421770i
$872$		0			0
$873$	16.6656	−	17.1682i	0.564045	−	0.581056i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.98841	−	12.1043i	0.235982	−	0.408733i	−0.723576	−	0.690245i	$-0.757503\pi$
$877$	6.98841	−	12.1043i	0.235982	−	0.408733i	0.959558	+	0.281512i	$0.0908360\pi$
$878$		0			0
$879$	−13.0276	−	30.8024i	−0.439411	−	1.03894i
$880$		0			0
$881$	−28.1210			−0.947421			−0.473710	−	0.880681i	$-0.657086\pi$
$881$	−28.1210			−0.947421			−0.473710	+	0.880681i	$0.657086\pi$
$882$		0			0
$883$	−35.1633			−1.18334			−0.591670	−	0.806180i	$-0.701531\pi$
$883$	−35.1633			−1.18334			−0.591670	+	0.806180i	$0.701531\pi$
$884$		0			0
$885$	21.7620	+	2.70075i	0.731522	+	0.0907849i
$886$		0			0
$887$	−13.4610	+	23.3151i	−0.451975	+	0.782844i	−0.998509	−	0.0545932i	$-0.982614\pi$
$887$	−13.4610	+	23.3151i	−0.451975	+	0.782844i	0.546533	+	0.837437i	$0.315947\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	6.88523	+	3.70698i	0.230664	+	0.124189i
$892$		0			0
$893$	−4.70520	−	8.14965i	−0.157454	−	0.272718i
$894$		0			0
$895$	47.7880	−	82.7713i	1.59738	−	2.76674i
$896$		0			0
$897$	57.3640	+	7.11911i	1.91533	+	0.237700i
$898$		0			0
$899$	5.33211			0.177836
$900$		0			0
$901$	−6.31188			−0.210279
$902$		0			0
$903$		0			0
$904$		0			0
$905$	24.5241	−	42.4769i	0.815207	−	1.41198i
$906$		0			0
$907$	22.3571	+	38.7236i	0.742355	+	1.28580i	0.951420	+	0.307895i	$0.0996246\pi$
$907$	22.3571	+	38.7236i	0.742355	+	1.28580i	−0.209065	+	0.977902i	$0.567042\pi$
$908$		0			0
$909$	−7.86455	+	8.10173i	−0.260851	+	0.268717i
$910$		0			0
$911$	−13.7822	−	23.8715i	−0.456626	−	0.790899i	0.542154	−	0.840279i	$-0.317609\pi$
$911$	−13.7822	−	23.8715i	−0.456626	−	0.790899i	−0.998780	+	0.0493800i	$0.984275\pi$
$912$		0			0
$913$	−1.90093	+	3.29250i	−0.0629115	+	0.108966i
$914$		0			0
$915$	24.3821	−	32.2688i	0.806047	−	1.06677i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	42.7673			1.41076			0.705381	−	0.708828i	$-0.250776\pi$
$919$	42.7673			1.41076			0.705381	+	0.708828i	$0.250776\pi$
$920$		0			0
$921$	13.7181	−	18.1554i	0.452027	−	0.598240i
$922$		0			0
$923$	3.12402	−	5.41096i	0.102828	−	0.178104i
$924$		0			0
$925$	−32.2750	−	55.9019i	−1.06119	−	1.83804i
$926$		0			0
$927$	−31.5787	−	7.96070i	−1.03718	−	0.261464i
$928$		0			0
$929$	23.9748	+	41.5256i	0.786589	+	1.36241i	0.928045	+	0.372468i	$0.121488\pi$
$929$	23.9748	+	41.5256i	0.786589	+	1.36241i	−0.141456	+	0.989945i	$0.545178\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	9.13003	+	21.5870i	0.298904	+	0.706726i
$934$		0			0
$935$	10.4168			0.340665
$936$		0			0
$937$	−33.9136			−1.10791			−0.553955	−	0.832547i	$-0.686882\pi$
$937$	−33.9136			−1.10791			−0.553955	+	0.832547i	$0.686882\pi$
$938$		0			0
$939$	−43.3154	−	5.37562i	−1.41354	−	0.175427i
$940$		0			0
$941$	−4.27395	+	7.40270i	−0.139327	+	0.241321i	−0.927242	−	0.374463i	$-0.877827\pi$
$941$	−4.27395	+	7.40270i	−0.139327	+	0.241321i	0.787915	+	0.615784i	$0.211161\pi$
$942$		0			0
$943$	−34.3563	−	59.5068i	−1.11879	−	1.93781i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.411563	−	0.712848i	−0.0133740	−	0.0231645i	0.859261	−	0.511538i	$-0.170924\pi$
$947$	−0.411563	−	0.712848i	−0.0133740	−	0.0231645i	−0.872635	+	0.488373i	$0.837591\pi$
$948$		0			0
$949$	−4.14053	+	7.17161i	−0.134407	+	0.232800i
$950$		0			0
$951$	21.1382	+	2.62334i	0.685453	+	0.0850675i
$952$		0			0
$953$	−44.6726			−1.44709			−0.723544	−	0.690278i	$-0.757488\pi$
$953$	−44.6726			−1.44709			−0.723544	+	0.690278i	$0.757488\pi$
$954$		0			0
$955$	26.0529			0.843051
$956$		0			0
$957$	1.05567	+	2.49602i	0.0341250	+	0.0806849i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	11.1165	+	19.2544i	0.358597	+	0.621108i
$962$		0			0
$963$	−7.90476	−	27.8401i	−0.254727	−	0.897135i
$964$		0			0
$965$	28.4592	+	49.2928i	0.916135	+	1.58679i
$966$		0			0
$967$	−18.2289	+	31.5735i	−0.586203	+	1.01533i	0.408521	+	0.912749i	$0.366045\pi$
$967$	−18.2289	+	31.5735i	−0.586203	+	1.01533i	−0.994724	+	0.102585i	$0.967289\pi$
$968$		0			0
$969$	12.1225	−	16.0437i	0.389432	−	0.515399i
$970$		0			0
$971$	17.2735			0.554332			0.277166	−	0.960822i	$-0.410605\pi$
$971$	17.2735			0.554332			0.277166	+	0.960822i	$0.410605\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	72.8216	−	96.3767i	2.33216	−	3.08652i
$976$		0			0
$977$	−4.51775	+	7.82497i	−0.144536	+	0.250343i	−0.929200	−	0.369578i	$-0.879502\pi$
$977$	−4.51775	+	7.82497i	−0.144536	+	0.250343i	0.784664	+	0.619921i	$0.212835\pi$
$978$		0			0
$979$	−5.06868	−	8.77921i	−0.161996	−	0.280585i
$980$		0			0
$981$	−9.60567	−	33.8306i	−0.306686	−	1.08013i
$982$		0			0
$983$	−11.4286	−	19.7950i	−0.364517	−	0.631362i	0.624182	−	0.781279i	$-0.285432\pi$
$983$	−11.4286	−	19.7950i	−0.364517	−	0.631362i	−0.988698	+	0.149918i	$0.952099\pi$
$984$		0			0
$985$	−0.334715	+	0.579743i	−0.0106649	+	0.0184722i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−23.4010			−0.744109
$990$		0			0
$991$	8.75768			0.278197			0.139098	−	0.990279i	$-0.455580\pi$
$991$	8.75768			0.278197			0.139098	+	0.990279i	$0.455580\pi$
$992$		0			0
$993$	34.2496	+	4.25051i	1.08688	+	0.134886i
$994$		0			0
$995$	−51.4584	+	89.1285i	−1.63134	+	2.82556i
$996$		0			0
$997$	3.46535	+	6.00216i	0.109749	+	0.190090i	0.915668	−	0.401934i	$-0.131662\pi$
$997$	3.46535	+	6.00216i	0.109749	+	0.190090i	−0.805920	+	0.592025i	$0.798329\pi$
$998$		0			0
$999$	−25.6645	−	9.96668i	−0.811990	−	0.315332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.j.h.589.5		14
3.2	odd	2		5292.2.j.g.1765.1		14
7.2	even	3		1764.2.l.i.949.5		14
7.3	odd	6		252.2.i.b.121.7	yes	14
7.4	even	3		1764.2.i.i.373.1		14
7.5	odd	6		252.2.l.b.193.3	yes	14
7.6	odd	2		1764.2.j.g.589.3		14
9.2	odd	6		5292.2.j.g.3529.1		14
9.7	even	3	inner	1764.2.j.h.1177.5		14
21.2	odd	6		5292.2.l.i.361.7		14
21.5	even	6		756.2.l.b.361.1		14
21.11	odd	6		5292.2.i.i.1549.1		14
21.17	even	6		756.2.i.b.37.7		14
21.20	even	2		5292.2.j.h.1765.7		14
28.3	even	6		1008.2.q.j.625.1		14
28.19	even	6		1008.2.t.j.193.5		14
63.2	odd	6		5292.2.i.i.2125.1		14
63.5	even	6		2268.2.k.f.1621.7		14
63.11	odd	6		5292.2.l.i.3313.7		14
63.16	even	3		1764.2.i.i.1537.1		14
63.20	even	6		5292.2.j.h.3529.7		14
63.25	even	3		1764.2.l.i.961.5		14
63.31	odd	6		2268.2.k.e.1297.1		14
63.34	odd	6		1764.2.j.g.1177.3		14
63.38	even	6		756.2.l.b.289.1		14
63.40	odd	6		2268.2.k.e.1621.1		14
63.47	even	6		756.2.i.b.613.7		14
63.52	odd	6		252.2.l.b.205.3	yes	14
63.59	even	6		2268.2.k.f.1297.7		14
63.61	odd	6		252.2.i.b.25.7	✓	14
84.47	odd	6		3024.2.t.j.1873.1		14
84.59	odd	6		3024.2.q.j.2305.7		14
252.47	odd	6		3024.2.q.j.2881.7		14
252.115	even	6		1008.2.t.j.961.5		14
252.187	even	6		1008.2.q.j.529.1		14
252.227	odd	6		3024.2.t.j.289.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.7	✓	14	63.61	odd	6
252.2.i.b.121.7	yes	14	7.3	odd	6
252.2.l.b.193.3	yes	14	7.5	odd	6
252.2.l.b.205.3	yes	14	63.52	odd	6
756.2.i.b.37.7		14	21.17	even	6
756.2.i.b.613.7		14	63.47	even	6
756.2.l.b.289.1		14	63.38	even	6
756.2.l.b.361.1		14	21.5	even	6
1008.2.q.j.529.1		14	252.187	even	6
1008.2.q.j.625.1		14	28.3	even	6
1008.2.t.j.193.5		14	28.19	even	6
1008.2.t.j.961.5		14	252.115	even	6
1764.2.i.i.373.1		14	7.4	even	3
1764.2.i.i.1537.1		14	63.16	even	3
1764.2.j.g.589.3		14	7.6	odd	2
1764.2.j.g.1177.3		14	63.34	odd	6
1764.2.j.h.589.5		14	1.1	even	1	trivial
1764.2.j.h.1177.5		14	9.7	even	3	inner
1764.2.l.i.949.5		14	7.2	even	3
1764.2.l.i.961.5		14	63.25	even	3
2268.2.k.e.1297.1		14	63.31	odd	6
2268.2.k.e.1621.1		14	63.40	odd	6
2268.2.k.f.1297.7		14	63.59	even	6
2268.2.k.f.1621.7		14	63.5	even	6
3024.2.q.j.2305.7		14	84.59	odd	6
3024.2.q.j.2881.7		14	252.47	odd	6
3024.2.t.j.289.1		14	252.227	odd	6
3024.2.t.j.1873.1		14	84.47	odd	6
5292.2.i.i.1549.1		14	21.11	odd	6
5292.2.i.i.2125.1		14	63.2	odd	6
5292.2.j.g.1765.1		14	3.2	odd	2
5292.2.j.g.3529.1		14	9.2	odd	6
5292.2.j.h.1765.7		14	21.20	even	2
5292.2.j.h.3529.7		14	63.20	even	6
5292.2.l.i.361.7		14	21.2	odd	6
5292.2.l.i.3313.7		14	63.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04417 - 1.38192i) q^{3} +(2.07260 - 3.58985i) q^{5} +(-0.819413 - 2.88592i) q^{9} +(-0.434429 - 0.752453i) q^{11} +(-2.86231 + 4.95766i) q^{13} +(-2.79674 - 6.61258i) q^{15} -2.89227 q^{17} -4.01406 q^{19} +(2.91488 - 5.04873i) q^{23} +(-6.09133 - 10.5505i) q^{25} +(-4.84373 - 1.88104i) q^{27} +(-0.900417 - 1.55957i) q^{29} +(-1.48046 + 2.56422i) q^{31} +(-1.49345 - 0.185343i) q^{33} +5.29851 q^{37} +(3.86236 + 9.13213i) q^{39} +(5.89325 - 10.2074i) q^{41} +(-2.00703 - 3.47627i) q^{43} +(-12.0583 - 3.03980i) q^{45} +(1.17218 + 2.03028i) q^{47} +(-3.02002 + 3.99689i) q^{51} +2.18233 q^{53} -3.60159 q^{55} +(-4.19136 + 5.54711i) q^{57} +(-1.52715 + 2.64510i) q^{59} +(2.81659 + 4.87848i) q^{61} +(11.8648 + 20.5505i) q^{65} +(1.25539 - 2.17440i) q^{67} +(-3.93331 - 9.29988i) q^{69} -1.09143 q^{71} +1.44657 q^{73} +(-20.9403 - 2.59878i) q^{75} +(1.06464 + 1.84401i) q^{79} +(-7.65712 + 4.72953i) q^{81} +(-2.18784 - 3.78946i) q^{83} +(-5.99451 + 10.3828i) q^{85} +(-3.09539 - 0.384150i) q^{87} +11.6675 q^{89} +(1.99771 + 4.72336i) q^{93} +(-8.31953 + 14.4098i) q^{95} +(3.98779 + 6.90706i) q^{97} +(-1.81555 + 1.87030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} + 2 q^{5} - 5 q^{9} + 2 q^{11} - 2 q^{13} + 7 q^{15} + 4 q^{17} + 14 q^{19} + 11 q^{23} - 9 q^{25} - 9 q^{27} + q^{29} + q^{31} + q^{33} - 20 q^{37} + 22 q^{39} + 33 q^{41} + 7 q^{43}+ \cdots + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 + 2 * q^5 - 5 * q^9 + 2 * q^11 - 2 * q^13 + 7 * q^15 + 4 * q^17 + 14 * q^19 + 11 * q^23 - 9 * q^25 - 9 * q^27 + q^29 + q^31 + q^33 - 20 * q^37 + 22 * q^39 + 33 * q^41 + 7 * q^43 - 5 * q^45 + 3 * q^47 - 7 * q^51 + 30 * q^53 + 28 * q^55 - 18 * q^57 + 14 * q^59 + 10 * q^61 + 15 * q^65 + 6 * q^67 + 43 * q^69 + 2 * q^71 + 42 * q^73 - 43 * q^75 - 10 * q^79 + 7 * q^81 + 25 * q^83 + 8 * q^85 + 26 * q^87 - 12 * q^89 - 38 * q^93 - 28 * q^95 + 18 * q^97 + 7 * q^99

Introduction

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