LMFDB - Embedded newform 504.2.r.c.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(169,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, 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("504.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.r (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.2
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	504.337
Dual form			504.2.r.c.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.592396 - 1.62760i) q^{3} +(0.326352 - 0.565258i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})$	\(q+(0.592396 - 1.62760i) q^{3} +(0.326352 - 0.565258i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.29813 - 1.92836i) q^{9} +(-1.70574 - 2.95442i) q^{11} +(0.152704 - 0.264490i) q^{13} +(-0.726682 - 0.866025i) q^{15} -0.226682 q^{17} -2.16250 q^{19} +(-1.70574 + 0.300767i) q^{21} +(3.35117 - 5.80439i) q^{23} +(2.28699 + 3.96118i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(0.254900 + 0.441500i) q^{29} +(2.85844 - 4.95096i) q^{31} +(-5.81908 + 1.02606i) q^{33} -0.652704 q^{35} -2.28312 q^{37} +(-0.340022 - 0.405223i) q^{39} +(-0.479055 + 0.829748i) q^{41} +(3.85844 + 6.68302i) q^{43} +(-1.84002 + 0.669713i) q^{45} +(-4.14543 - 7.18009i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-0.134285 + 0.368946i) q^{51} -3.18479 q^{53} -2.22668 q^{55} +(-1.28106 + 3.51968i) q^{57} +(6.07785 - 10.5271i) q^{59} +(1.75490 + 3.03958i) q^{61} +(-0.520945 + 2.95442i) q^{63} +(-0.0996702 - 0.172634i) q^{65} +(-2.87211 + 4.97464i) q^{67} +(-7.46198 - 8.89284i) q^{69} +14.0273 q^{71} +12.4192 q^{73} +(7.80200 - 1.37570i) q^{75} +(-1.70574 + 2.95442i) q^{77} +(5.98293 + 10.3627i) q^{79} +(1.56283 + 8.86327i) q^{81} +(-2.13563 - 3.69902i) q^{83} +(-0.0739780 + 0.128134i) q^{85} +(0.869585 - 0.153331i) q^{87} -1.19934 q^{89} -0.305407 q^{91} +(-6.36484 - 7.58532i) q^{93} +(-0.705737 + 1.22237i) q^{95} +(7.48932 + 12.9719i) q^{97} +(-1.77719 + 10.0789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^5 - 3 * q^7	$ 6 q + 3 q^{5} - 3 q^{7} + 3 q^{13} + 9 q^{15} + 12 q^{17} - 18 q^{19} - 6 q^{23} + 6 q^{25} - 27 q^{27} + 3 q^{29} + 9 q^{31} - 18 q^{33} - 6 q^{35} - 30 q^{37} + 18 q^{39} - 6 q^{41} + 15 q^{43} + 9 q^{45} - 9 q^{47} - 3 q^{49} + 9 q^{51} - 12 q^{53} + 27 q^{57} - 3 q^{59} + 12 q^{61} - 15 q^{65} + 12 q^{67} - 27 q^{69} + 42 q^{71} + 6 q^{73} + 9 q^{75} + 15 q^{79} + 6 q^{83} + 15 q^{85} - 9 q^{87} - 36 q^{89} - 6 q^{91} + 9 q^{93} + 6 q^{95} - 15 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 - 3 * q^7 + 3 * q^13 + 9 * q^15 + 12 * q^17 - 18 * q^19 - 6 * q^23 + 6 * q^25 - 27 * q^27 + 3 * q^29 + 9 * q^31 - 18 * q^33 - 6 * q^35 - 30 * q^37 + 18 * q^39 - 6 * q^41 + 15 * q^43 + 9 * q^45 - 9 * q^47 - 3 * q^49 + 9 * q^51 - 12 * q^53 + 27 * q^57 - 3 * q^59 + 12 * q^61 - 15 * q^65 + 12 * q^67 - 27 * q^69 + 42 * q^71 + 6 * q^73 + 9 * q^75 + 15 * q^79 + 6 * q^83 + 15 * q^85 - 9 * q^87 - 36 * q^89 - 6 * q^91 + 9 * q^93 + 6 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.592396	−	1.62760i	0.342020	−	0.939693i
$3$	0.592396	−	1.62760i	0.342020	−	0.939693i
$4$		0			0
$5$	0.326352	−	0.565258i	0.145949	−	0.252791i	−0.783778	−	0.621042i	$-0.786710\pi$
$5$	0.326352	−	0.565258i	0.145949	−	0.252791i	0.929727	+	0.368251i	$0.120043\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	−2.29813	−	1.92836i	−0.766044	−	0.642788i
$10$		0			0
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	−0.999862	−	0.0165906i	$-0.994719\pi$
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	0.485563	−	0.874202i	$-0.338615\pi$
$12$		0			0
$13$	0.152704	−	0.264490i	0.0423524	−	0.0733565i	−0.844072	−	0.536230i	$-0.819848\pi$
$13$	0.152704	−	0.264490i	0.0423524	−	0.0733565i	0.886425	+	0.462873i	$0.153181\pi$
$14$		0			0
$15$	−0.726682	−	0.866025i	−0.187628	−	0.223607i
$16$		0			0
$17$	−0.226682			−0.0549784			−0.0274892	−	0.999622i	$-0.508751\pi$
$17$	−0.226682			−0.0549784			−0.0274892	+	0.999622i	$0.508751\pi$
$18$		0			0
$19$	−2.16250			−0.496112			−0.248056	−	0.968746i	$-0.579792\pi$
$19$	−2.16250			−0.496112			−0.248056	+	0.968746i	$0.579792\pi$
$20$		0			0
$21$	−1.70574	+	0.300767i	−0.372222	+	0.0656328i
$22$		0			0
$23$	3.35117	−	5.80439i	0.698767	−	1.21030i	−0.270128	−	0.962824i	$-0.587066\pi$
$23$	3.35117	−	5.80439i	0.698767	−	1.21030i	0.968894	−	0.247475i	$-0.0796007\pi$
$24$		0			0
$25$	2.28699	+	3.96118i	0.457398	+	0.792236i
$26$		0			0
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$		0			0
$29$	0.254900	+	0.441500i	0.0473338	+	0.0819845i	0.888722	−	0.458447i	$-0.151594\pi$
$29$	0.254900	+	0.441500i	0.0473338	+	0.0819845i	−0.841388	+	0.540432i	$0.818261\pi$
$30$		0			0
$31$	2.85844	−	4.95096i	0.513391	−	0.889219i	−0.486488	−	0.873687i	$-0.661722\pi$
$31$	2.85844	−	4.95096i	0.513391	−	0.889219i	0.999879	−	0.0155324i	$-0.00494430\pi$
$32$		0			0
$33$	−5.81908	+	1.02606i	−1.01297	+	0.178614i
$34$		0			0
$35$	−0.652704			−0.110327
$36$		0			0
$37$	−2.28312			−0.375342			−0.187671	−	0.982232i	$-0.560094\pi$
$37$	−2.28312			−0.375342			−0.187671	+	0.982232i	$0.560094\pi$
$38$		0			0
$39$	−0.340022	−	0.405223i	−0.0544472	−	0.0648876i
$40$		0			0
$41$	−0.479055	+	0.829748i	−0.0748159	+	0.129585i	−0.901006	−	0.433806i	$-0.857170\pi$
$41$	−0.479055	+	0.829748i	−0.0748159	+	0.129585i	0.826190	+	0.563391i	$0.190504\pi$
$42$		0			0
$43$	3.85844	+	6.68302i	0.588407	+	1.01915i	0.994441	+	0.105293i	$0.0335779\pi$
$43$	3.85844	+	6.68302i	0.588407	+	1.01915i	−0.406035	+	0.913858i	$0.633089\pi$
$44$		0			0
$45$	−1.84002	+	0.669713i	−0.274294	+	0.0998350i
$46$		0			0
$47$	−4.14543	−	7.18009i	−0.604673	−	1.04732i	−0.992103	−	0.125425i	$-0.959970\pi$
$47$	−4.14543	−	7.18009i	−0.604673	−	1.04732i	0.387430	−	0.921899i	$-0.373363\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−0.134285	+	0.368946i	−0.0188037	+	0.0516628i
$52$		0			0
$53$	−3.18479			−0.437465			−0.218732	−	0.975785i	$-0.570192\pi$
$53$	−3.18479			−0.437465			−0.218732	+	0.975785i	$0.570192\pi$
$54$		0			0
$55$	−2.22668			−0.300246
$56$		0			0
$57$	−1.28106	+	3.51968i	−0.169680	+	0.466193i
$58$		0			0
$59$	6.07785	−	10.5271i	0.791268	−	1.37052i	−0.133913	−	0.990993i	$-0.542754\pi$
$59$	6.07785	−	10.5271i	0.791268	−	1.37052i	0.925182	−	0.379524i	$-0.123912\pi$
$60$		0			0
$61$	1.75490	+	3.03958i	0.224692	+	0.389178i	0.956227	−	0.292626i	$-0.0945291\pi$
$61$	1.75490	+	3.03958i	0.224692	+	0.389178i	−0.731535	+	0.681804i	$0.761196\pi$
$62$		0			0
$63$	−0.520945	+	2.95442i	−0.0656328	+	0.372222i
$64$		0			0
$65$	−0.0996702	−	0.172634i	−0.0123626	−	0.0214126i
$66$		0			0
$67$	−2.87211	+	4.97464i	−0.350884	+	0.607749i	−0.986405	−	0.164335i	$-0.947452\pi$
$67$	−2.87211	+	4.97464i	−0.350884	+	0.607749i	0.635520	+	0.772084i	$0.280786\pi$
$68$		0			0
$69$	−7.46198	−	8.89284i	−0.898317	−	1.07057i
$70$		0			0
$71$	14.0273			1.66474			0.832370	−	0.554221i	$-0.186984\pi$
$71$	14.0273			1.66474			0.832370	+	0.554221i	$0.186984\pi$
$72$		0			0
$73$	12.4192			1.45356			0.726780	−	0.686871i	$-0.241016\pi$
$73$	12.4192			1.45356			0.726780	+	0.686871i	$0.241016\pi$
$74$		0			0
$75$	7.80200	−	1.37570i	0.900898	−	0.158853i
$76$		0			0
$77$	−1.70574	+	2.95442i	−0.194387	+	0.336688i
$78$		0			0
$79$	5.98293	+	10.3627i	0.673132	+	1.16590i	0.977011	+	0.213188i	$0.0683847\pi$
$79$	5.98293	+	10.3627i	0.673132	+	1.16590i	−0.303879	+	0.952710i	$0.598282\pi$
$80$		0			0
$81$	1.56283	+	8.86327i	0.173648	+	0.984808i
$82$		0			0
$83$	−2.13563	−	3.69902i	−0.234416	−	0.406020i	0.724687	−	0.689078i	$-0.241984\pi$
$83$	−2.13563	−	3.69902i	−0.234416	−	0.406020i	−0.959103	+	0.283058i	$0.908651\pi$
$84$		0			0
$85$	−0.0739780	+	0.128134i	−0.00802404	+	0.0138980i
$86$		0			0
$87$	0.869585	−	0.153331i	0.0932293	−	0.0164388i
$88$		0			0
$89$	−1.19934			−0.127130			−0.0635649	−	0.997978i	$-0.520247\pi$
$89$	−1.19934			−0.127130			−0.0635649	+	0.997978i	$0.520247\pi$
$90$		0			0
$91$	−0.305407			−0.0320154
$92$		0			0
$93$	−6.36484	−	7.58532i	−0.660003	−	0.786561i
$94$		0			0
$95$	−0.705737	+	1.22237i	−0.0724071	+	0.125413i
$96$		0			0
$97$	7.48932	+	12.9719i	0.760425	+	1.31710i	0.942631	+	0.333835i	$0.108343\pi$
$97$	7.48932	+	12.9719i	0.760425	+	1.31710i	−0.182206	+	0.983260i	$0.558324\pi$
$98$		0			0
$99$	−1.77719	+	10.0789i	−0.178614	+	1.01297i
$100$		0			0
$101$	−0.655230	−	1.13489i	−0.0651978	−	0.112926i	0.831584	−	0.555399i	$-0.187435\pi$
$101$	−0.655230	−	1.13489i	−0.0651978	−	0.112926i	−0.896782	+	0.442473i	$0.854101\pi$
$102$		0			0
$103$	6.39306	−	11.0731i	0.629927	−	1.09106i	−0.357639	−	0.933860i	$-0.616418\pi$
$103$	6.39306	−	11.0731i	0.629927	−	1.09106i	0.987566	−	0.157205i	$-0.0502483\pi$
$104$		0			0
$105$	−0.386659	+	1.06234i	−0.0377341	+	0.103674i
$106$		0			0
$107$	10.9709			1.06060			0.530299	−	0.847811i	$-0.322080\pi$
$107$	10.9709			1.06060			0.530299	+	0.847811i	$0.322080\pi$
$108$		0			0
$109$	−0.0787257			−0.00754055			−0.00377028	−	0.999993i	$-0.501200\pi$
$109$	−0.0787257			−0.00754055			−0.00377028	+	0.999993i	$0.501200\pi$
$110$		0			0
$111$	−1.35251	+	3.71599i	−0.128375	+	0.352706i
$112$		0			0
$113$	−2.94356	+	5.09840i	−0.276907	+	0.479617i	−0.970615	−	0.240640i	$-0.922643\pi$
$113$	−2.94356	+	5.09840i	−0.276907	+	0.479617i	0.693707	+	0.720257i	$0.255976\pi$
$114$		0			0
$115$	−2.18732	−	3.78855i	−0.203969	−	0.353284i
$116$		0			0
$117$	−0.860967	+	0.313366i	−0.0795964	+	0.0289707i
$118$		0			0
$119$	0.113341	+	0.196312i	0.0103899	+	0.0179959i
$120$		0			0
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$		0			0
$123$	1.06670	+	1.27125i	0.0961815	+	0.114625i
$124$		0			0
$125$	6.24897			0.558925
$126$		0			0
$127$	−11.3277			−1.00517			−0.502585	−	0.864528i	$-0.667618\pi$
$127$	−11.3277			−1.00517			−0.502585	+	0.864528i	$0.667618\pi$
$128$		0			0
$129$	13.1630	−	2.32099i	1.15893	−	0.204351i
$130$		0			0
$131$	−2.27719	+	3.94421i	−0.198959	+	0.344607i	−0.948191	−	0.317700i	$-0.897089\pi$
$131$	−2.27719	+	3.94421i	−0.198959	+	0.344607i	0.749232	+	0.662307i	$0.230423\pi$
$132$		0			0
$133$	1.08125	+	1.87278i	0.0937564	+	0.162391i
$134$		0			0
$135$			3.39155i			0.291898i
$136$		0			0
$137$	8.39053	+	14.5328i	0.716851	+	1.24162i	0.962241	+	0.272198i	$0.0877507\pi$
$137$	8.39053	+	14.5328i	0.716851	+	1.24162i	−0.245390	+	0.969424i	$0.578916\pi$
$138$		0			0
$139$	−11.1951	+	19.3904i	−0.949553	+	1.64467i	−0.203184	+	0.979141i	$0.565129\pi$
$139$	−11.1951	+	19.3904i	−0.949553	+	1.64467i	−0.746369	+	0.665533i	$0.768204\pi$
$140$		0			0
$141$	−14.1420	+	2.49362i	−1.19097	+	0.210001i
$142$		0			0
$143$	−1.04189			−0.0871271
$144$		0			0
$145$	0.332748			0.0276333
$146$		0			0
$147$	1.11334	+	1.32683i	0.0918268	+	0.109435i
$148$		0			0
$149$	8.60741	−	14.9085i	0.705147	−	1.22135i	−0.261492	−	0.965206i	$-0.584215\pi$
$149$	8.60741	−	14.9085i	0.705147	−	1.22135i	0.966639	−	0.256144i	$-0.0824522\pi$
$150$		0			0
$151$	2.48158	+	4.29823i	0.201948	+	0.349785i	0.949156	−	0.314806i	$-0.101939\pi$
$151$	2.48158	+	4.29823i	0.201948	+	0.349785i	−0.747208	+	0.664590i	$0.768606\pi$
$152$		0			0
$153$	0.520945	+	0.437124i	0.0421159	+	0.0353394i
$154$		0			0
$155$	−1.86571	−	3.23151i	−0.149858	−	0.259561i
$156$		0			0
$157$	9.84776	−	17.0568i	0.785937	−	1.36128i	−0.142501	−	0.989795i	$-0.545514\pi$
$157$	9.84776	−	17.0568i	0.785937	−	1.36128i	0.928438	−	0.371488i	$-0.121152\pi$
$158$		0			0
$159$	−1.88666	+	5.18355i	−0.149622	+	0.411083i
$160$		0			0
$161$	−6.70233			−0.528218
$162$		0			0
$163$	−8.39424			−0.657487			−0.328744	−	0.944419i	$-0.606625\pi$
$163$	−8.39424			−0.657487			−0.328744	+	0.944419i	$0.606625\pi$
$164$		0			0
$165$	−1.31908	+	3.62414i	−0.102690	+	0.282139i
$166$		0			0
$167$	−3.00980	+	5.21313i	−0.232905	+	0.403404i	−0.958662	−	0.284548i	$-0.908157\pi$
$167$	−3.00980	+	5.21313i	−0.232905	+	0.403404i	0.725757	+	0.687952i	$0.241490\pi$
$168$		0			0
$169$	6.45336	+	11.1776i	0.496413	+	0.859812i
$170$		0			0
$171$	4.96972	+	4.17009i	0.380044	+	0.318895i
$172$		0			0
$173$	1.40508	+	2.43367i	0.106826	+	0.185028i	0.914483	−	0.404625i	$-0.132598\pi$
$173$	1.40508	+	2.43367i	0.106826	+	0.185028i	−0.807657	+	0.589653i	$0.799265\pi$
$174$		0			0
$175$	2.28699	−	3.96118i	0.172880	−	0.299437i
$176$		0			0
$177$	−13.5334	−	16.1285i	−1.01724	−	1.21229i
$178$		0			0
$179$	−20.2226			−1.51151			−0.755753	−	0.654857i	$-0.772729\pi$
$179$	−20.2226			−1.51151			−0.755753	+	0.654857i	$0.772729\pi$
$180$		0			0
$181$	9.02229			0.670621			0.335311	−	0.942108i	$-0.391159\pi$
$181$	9.02229			0.670621			0.335311	+	0.942108i	$0.391159\pi$
$182$		0			0
$183$	5.98680	−	1.05563i	0.442557	−	0.0780347i
$184$		0			0
$185$	−0.745100	+	1.29055i	−0.0547808	+	0.0948832i
$186$		0			0
$187$	0.386659	+	0.669713i	0.0282753	+	0.0489743i
$188$		0			0
$189$	4.50000	+	2.59808i	0.327327	+	0.188982i
$190$		0			0
$191$	5.77972	+	10.0108i	0.418206	+	0.724353i	0.995759	−	0.0919996i	$-0.0293259\pi$
$191$	5.77972	+	10.0108i	0.418206	+	0.724353i	−0.577554	+	0.816353i	$0.695993\pi$
$192$		0			0
$193$	8.77244	−	15.1943i	0.631454	−	1.09371i	−0.355800	−	0.934562i	$-0.615792\pi$
$193$	8.77244	−	15.1943i	0.631454	−	1.09371i	0.987255	−	0.159149i	$-0.0508749\pi$
$194$		0			0
$195$	−0.340022	+	0.0599551i	−0.0243495	+	0.00429348i
$196$		0			0
$197$	−23.3327			−1.66239			−0.831195	−	0.555981i	$-0.812343\pi$
$197$	−23.3327			−1.66239			−0.831195	+	0.555981i	$0.812343\pi$
$198$		0			0
$199$	−12.6186			−0.894506			−0.447253	−	0.894408i	$-0.647598\pi$
$199$	−12.6186			−0.894506			−0.447253	+	0.894408i	$0.647598\pi$
$200$		0			0
$201$	6.39528	+	7.62159i	0.451088	+	0.537586i
$202$		0			0
$203$	0.254900	−	0.441500i	0.0178905	−	0.0309872i
$204$		0			0
$205$	0.312681	+	0.541580i	0.0218386	+	0.0378256i
$206$		0			0
$207$	−18.8944	+	6.87700i	−1.31325	+	0.477984i
$208$		0			0
$209$	3.68866	+	6.38895i	0.255150	+	0.441933i
$210$		0			0
$211$	−4.50774	+	7.80764i	−0.310326	+	0.537500i	−0.978433	−	0.206565i	$-0.933771\pi$
$211$	−4.50774	+	7.80764i	−0.310326	+	0.537500i	0.668107	+	0.744065i	$0.267105\pi$
$212$		0			0
$213$	8.30974	−	22.8308i	0.569374	−	1.56434i
$214$		0			0
$215$	5.03684			0.343509
$216$		0			0
$217$	−5.71688			−0.388087
$218$		0			0
$219$	7.35710	−	20.2135i	0.497147	−	1.36590i
$220$		0			0
$221$	−0.0346151	+	0.0599551i	−0.00232846	+	0.00403302i
$222$		0			0
$223$	−9.03983	−	15.6574i	−0.605352	−	1.04850i	−0.991996	−	0.126271i	$-0.959699\pi$
$223$	−9.03983	−	15.6574i	−0.605352	−	1.04850i	0.386644	−	0.922229i	$-0.373634\pi$
$224$		0			0
$225$	2.38279	−	13.5135i	0.158853	−	0.900898i
$226$		0			0
$227$	−12.4251	−	21.5210i	−0.824686	−	1.42840i	−0.902159	−	0.431403i	$-0.858019\pi$
$227$	−12.4251	−	21.5210i	−0.824686	−	1.42840i	0.0774734	−	0.996994i	$-0.475315\pi$
$228$		0			0
$229$	11.4017	−	19.7483i	0.753444	−	1.30500i	−0.192700	−	0.981258i	$-0.561725\pi$
$229$	11.4017	−	19.7483i	0.753444	−	1.30500i	0.946144	−	0.323745i	$-0.104942\pi$
$230$		0			0
$231$	3.79813	+	4.52644i	0.249899	+	0.297818i
$232$		0			0
$233$	14.2148			0.931244			0.465622	−	0.884984i	$-0.345831\pi$
$233$	14.2148			0.931244			0.465622	+	0.884984i	$0.345831\pi$
$234$		0			0
$235$	−5.41147			−0.353006
$236$		0			0
$237$	20.4106	−	3.59894i	1.32581	−	0.233776i
$238$		0			0
$239$	−4.13041	+	7.15409i	−0.267174	+	0.462760i	−0.968131	−	0.250444i	$-0.919423\pi$
$239$	−4.13041	+	7.15409i	−0.267174	+	0.462760i	0.700957	+	0.713204i	$0.252757\pi$
$240$		0			0
$241$	−3.88326	−	6.72600i	−0.250142	−	0.433259i	0.713422	−	0.700734i	$-0.247144\pi$
$241$	−3.88326	−	6.72600i	−0.250142	−	0.433259i	−0.963565	+	0.267475i	$0.913811\pi$
$242$		0			0
$243$	15.3516	+	2.70691i	0.984808	+	0.173648i
$244$		0			0
$245$	0.326352	+	0.565258i	0.0208499	+	0.0361130i
$246$		0			0
$247$	−0.330222	+	0.571962i	−0.0210115	+	0.0363930i
$248$		0			0
$249$	−7.28564	+	1.28466i	−0.461709	+	0.0814118i
$250$		0			0
$251$	6.09833			0.384923			0.192461	−	0.981305i	$-0.438353\pi$
$251$	6.09833			0.384923			0.192461	+	0.981305i	$0.438353\pi$
$252$		0			0
$253$	−22.8648			−1.43750
$254$		0			0
$255$	0.164725	+	0.196312i	0.0103155	+	0.0122935i
$256$		0			0
$257$	−1.29086	+	2.23583i	−0.0805216	+	0.139467i	−0.903474	−	0.428643i	$-0.858992\pi$
$257$	−1.29086	+	2.23583i	−0.0805216	+	0.139467i	0.822953	+	0.568110i	$0.192325\pi$
$258$		0			0
$259$	1.14156	+	1.97724i	0.0709330	+	0.122860i
$260$		0			0
$261$	0.265578	−	1.50617i	0.0164388	−	0.0932293i
$262$		0			0
$263$	−1.59105	−	2.75578i	−0.0981085	−	0.169929i	0.812793	−	0.582552i	$-0.197946\pi$
$263$	−1.59105	−	2.75578i	−0.0981085	−	0.169929i	−0.910902	+	0.412623i	$0.864613\pi$
$264$		0			0
$265$	−1.03936	+	1.80023i	−0.0638476	+	0.110587i
$266$		0			0
$267$	−0.710485	+	1.95204i	−0.0434810	+	0.119463i
$268$		0			0
$269$	−18.8057			−1.14660			−0.573302	−	0.819344i	$-0.694338\pi$
$269$	−18.8057			−1.14660			−0.573302	+	0.819344i	$0.694338\pi$
$270$		0			0
$271$	2.43107			0.147677			0.0738386	−	0.997270i	$-0.476475\pi$
$271$	2.43107			0.147677			0.0738386	+	0.997270i	$0.476475\pi$
$272$		0			0
$273$	−0.180922	+	0.497079i	−0.0109499	+	0.0300846i
$274$		0			0
$275$	7.80200	−	13.5135i	0.470479	−	0.814893i
$276$		0			0
$277$	−11.3897	−	19.7275i	−0.684338	−	1.18531i	−0.973644	−	0.228071i	$-0.926758\pi$
$277$	−11.3897	−	19.7275i	−0.684338	−	1.18531i	0.289307	−	0.957237i	$-0.406575\pi$
$278$		0			0
$279$	−16.1163	+	5.86587i	−0.964860	+	0.351180i
$280$		0			0
$281$	4.68732	+	8.11867i	0.279622	+	0.484319i	0.971291	−	0.237895i	$-0.0764575\pi$
$281$	4.68732	+	8.11867i	0.279622	+	0.484319i	−0.691669	+	0.722215i	$0.743124\pi$
$282$		0			0
$283$	13.9500	−	24.1620i	0.829239	−	1.43628i	−0.0693970	−	0.997589i	$-0.522108\pi$
$283$	13.9500	−	24.1620i	0.829239	−	1.43628i	0.898636	−	0.438695i	$-0.144559\pi$
$284$		0			0
$285$	1.57145	+	1.87278i	0.0930848	+	0.110934i
$286$		0			0
$287$	0.958111			0.0565555
$288$		0			0
$289$	−16.9486			−0.996977
$290$		0			0
$291$	25.5496	−	4.50509i	1.49775	−	0.264093i
$292$		0			0
$293$	5.25490	−	9.10175i	0.306995	−	0.531730i	−0.670709	−	0.741721i	$-0.734010\pi$
$293$	5.25490	−	9.10175i	0.306995	−	0.531730i	0.977703	+	0.209991i	$0.0673433\pi$
$294$		0			0
$295$	−3.96703	−	6.87110i	−0.230970	−	0.400051i
$296$		0			0
$297$	15.3516	+	8.86327i	0.890792	+	0.514299i
$298$		0			0
$299$	−1.02347	−	1.77270i	−0.0591888	−	0.102518i
$300$		0			0
$301$	3.85844	−	6.68302i	0.222397	−	0.385203i
$302$		0			0
$303$	−2.23530	+	0.394144i	−0.128415	+	0.0226430i
$304$		0			0
$305$	2.29086			0.131174
$306$		0			0
$307$	−22.8239			−1.30263			−0.651314	−	0.758808i	$-0.725782\pi$
$307$	−22.8239			−1.30263			−0.651314	+	0.758808i	$0.725782\pi$
$308$		0			0
$309$	−14.2353	−	16.9650i	−0.809818	−	0.965103i
$310$		0			0
$311$	−12.4081	+	21.4914i	−0.703597	+	1.21867i	0.263598	+	0.964633i	$0.415091\pi$
$311$	−12.4081	+	21.4914i	−0.703597	+	1.21867i	−0.967195	+	0.254033i	$0.918243\pi$
$312$		0			0
$313$	−11.7802	−	20.4039i	−0.665855	−	1.15330i	−0.979053	−	0.203607i	$-0.934733\pi$
$313$	−11.7802	−	20.4039i	−0.665855	−	1.15330i	0.313197	−	0.949688i	$-0.398600\pi$
$314$		0			0
$315$	1.50000	+	1.25865i	0.0845154	+	0.0709169i
$316$		0			0
$317$	5.80406	+	10.0529i	0.325989	+	0.564629i	0.981712	−	0.190372i	$-0.0609695\pi$
$317$	5.80406	+	10.0529i	0.325989	+	0.564629i	−0.655723	+	0.755001i	$0.727636\pi$
$318$		0			0
$319$	0.869585	−	1.50617i	0.0486874	−	0.0843291i
$320$		0			0
$321$	6.49912	−	17.8562i	0.362746	−	0.996635i
$322$		0			0
$323$	0.490200			0.0272754
$324$		0			0
$325$	1.39693			0.0774875
$326$		0			0
$327$	−0.0466368	+	0.128134i	−0.00257902	+	0.00708580i
$328$		0			0
$329$	−4.14543	+	7.18009i	−0.228545	+	0.395851i
$330$		0			0
$331$	14.3701	+	24.8897i	0.789849	+	1.36806i	0.926059	+	0.377379i	$0.123175\pi$
$331$	14.3701	+	24.8897i	0.789849	+	1.36806i	−0.136209	+	0.990680i	$0.543492\pi$
$332$		0			0
$333$	5.24691	+	4.40268i	0.287529	+	0.241265i
$334$		0			0
$335$	1.87464	+	3.24697i	0.102422	+	0.177401i
$336$		0			0
$337$	−2.62449	+	4.54574i	−0.142965	+	0.247622i	−0.928612	−	0.371053i	$-0.878997\pi$
$337$	−2.62449	+	4.54574i	−0.142965	+	0.247622i	0.785647	+	0.618675i	$0.212330\pi$
$338$		0			0
$339$	6.55438	+	7.81120i	0.355985	+	0.424246i
$340$		0			0
$341$	−19.5030			−1.05615
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−7.46198	+	1.31575i	−0.401740	+	0.0708375i
$346$		0			0
$347$	−17.3380	+	30.0302i	−0.930751	+	1.61211i	−0.148709	+	0.988881i	$0.547512\pi$
$347$	−17.3380	+	30.0302i	−0.930751	+	1.61211i	−0.782041	+	0.623226i	$0.785822\pi$
$348$		0			0
$349$	6.16519	+	10.6784i	0.330015	+	0.571603i	0.982514	−	0.186186i	$-0.0596128\pi$
$349$	6.16519	+	10.6784i	0.330015	+	0.571603i	−0.652499	+	0.757789i	$0.726279\pi$
$350$		0			0
$351$			1.58694i			0.0847047i
$352$		0			0
$353$	−2.37077	−	4.10629i	−0.126183	−	0.218556i	0.796012	−	0.605281i	$-0.206939\pi$
$353$	−2.37077	−	4.10629i	−0.126183	−	0.218556i	−0.922195	+	0.386726i	$0.873606\pi$
$354$		0			0
$355$	4.57785	−	7.92907i	0.242967	−	0.420831i
$356$		0			0
$357$	0.386659	−	0.0681784i	0.0204642	−	0.00360839i
$358$		0			0
$359$	31.2772			1.65075			0.825375	−	0.564585i	$-0.190964\pi$
$359$	31.2772			1.65075			0.825375	+	0.564585i	$0.190964\pi$
$360$		0			0
$361$	−14.3236			−0.753872
$362$		0			0
$363$	0.710485	+	0.846723i	0.0372908	+	0.0444414i
$364$		0			0
$365$	4.05303	−	7.02006i	0.212145	−	0.367447i
$366$		0			0
$367$	−11.0091	−	19.0683i	−0.574670	−	0.995357i	−0.996077	−	0.0884857i	$-0.971797\pi$
$367$	−11.0091	−	19.0683i	−0.574670	−	0.995357i	0.421408	−	0.906871i	$-0.361536\pi$
$368$		0			0
$369$	2.70099	−	0.983080i	0.140608	−	0.0511771i
$370$		0			0
$371$	1.59240	+	2.75811i	0.0826731	+	0.143194i
$372$		0			0
$373$	−9.01414	+	15.6129i	−0.466734	+	0.808408i	−0.999278	−	0.0379950i	$-0.987903\pi$
$373$	−9.01414	+	15.6129i	−0.466734	+	0.808408i	0.532544	+	0.846403i	$0.321236\pi$
$374$		0			0
$375$	3.70187	−	10.1708i	0.191164	−	0.525218i
$376$		0			0
$377$	0.155697			0.00801879
$378$		0			0
$379$	−4.50980			−0.231653			−0.115826	−	0.993269i	$-0.536952\pi$
$379$	−4.50980			−0.231653			−0.115826	+	0.993269i	$0.536952\pi$
$380$		0			0
$381$	−6.71048	+	18.4369i	−0.343789	+	0.944551i
$382$		0			0
$383$	−13.9081	+	24.0895i	−0.710669	+	1.23092i	0.253937	+	0.967221i	$0.418274\pi$
$383$	−13.9081	+	24.0895i	−0.710669	+	1.23092i	−0.964606	+	0.263694i	$0.915059\pi$
$384$		0			0
$385$	1.11334	+	1.92836i	0.0567411	+	0.0982785i
$386$		0			0
$387$	4.02007	−	22.7989i	0.204351	−	1.15893i
$388$		0			0
$389$	1.55690	+	2.69664i	0.0789382	+	0.136725i	0.902792	−	0.430077i	$-0.141514\pi$
$389$	1.55690	+	2.69664i	0.0789382	+	0.136725i	−0.823854	+	0.566802i	$0.808180\pi$
$390$		0			0
$391$	−0.759648	+	1.31575i	−0.0384170	+	0.0665403i
$392$		0			0
$393$	5.07057	+	6.04288i	0.255777	+	0.304823i
$394$		0			0
$395$	7.81016			0.392972
$396$		0			0
$397$	−9.19522			−0.461495			−0.230747	−	0.973014i	$-0.574117\pi$
$397$	−9.19522			−0.461495			−0.230747	+	0.973014i	$0.574117\pi$
$398$		0			0
$399$	3.68866	−	0.650411i	0.184664	−	0.0325613i
$400$		0			0
$401$	−9.78952	+	16.9559i	−0.488865	+	0.846739i	−0.999918	−	0.0128101i	$-0.995922\pi$
$401$	−9.78952	+	16.9559i	−0.488865	+	0.846739i	0.511053	+	0.859549i	$0.329256\pi$
$402$		0			0
$403$	−0.872989	−	1.51206i	−0.0434867	−	0.0753211i
$404$		0			0
$405$	5.52007	+	2.00914i	0.274294	+	0.0998350i
$406$		0			0
$407$	3.89440	+	6.74530i	0.193038	+	0.334352i
$408$		0			0
$409$	−3.66044	+	6.34008i	−0.180997	+	0.313497i	−0.942220	−	0.334994i	$-0.891266\pi$
$409$	−3.66044	+	6.34008i	−0.180997	+	0.313497i	0.761223	+	0.648490i	$0.224599\pi$
$410$		0			0
$411$	28.6241	−	5.04720i	1.41192	−	0.248960i
$412$		0			0
$413$	−12.1557			−0.598143
$414$		0			0
$415$	−2.78787			−0.136851
$416$		0			0
$417$	24.9278	+	29.7078i	1.22072	+	1.45480i
$418$		0			0
$419$	2.61468	−	4.52877i	0.127736	−	0.221245i	−0.795063	−	0.606526i	$-0.792562\pi$
$419$	2.61468	−	4.52877i	0.127736	−	0.221245i	0.922799	+	0.385282i	$0.125896\pi$
$420$		0			0
$421$	4.76130	+	8.24681i	0.232051	+	0.401925i	0.958412	−	0.285389i	$-0.0921229\pi$
$421$	4.76130	+	8.24681i	0.232051	+	0.401925i	−0.726360	+	0.687314i	$0.758790\pi$
$422$		0			0
$423$	−4.31908	+	24.4947i	−0.210001	+	1.19097i
$424$		0			0
$425$	−0.518418	−	0.897927i	−0.0251470	−	0.0435559i
$426$		0			0
$427$	1.75490	−	3.03958i	0.0849256	−	0.147095i
$428$		0			0
$429$	−0.617211	+	1.69577i	−0.0297992	+	0.0818727i
$430$		0			0
$431$	−27.3874			−1.31921			−0.659603	−	0.751614i	$-0.729276\pi$
$431$	−27.3874			−1.31921			−0.659603	+	0.751614i	$0.729276\pi$
$432$		0			0
$433$	24.0506			1.15580			0.577898	−	0.816109i	$-0.303873\pi$
$433$	24.0506			1.15580			0.577898	+	0.816109i	$0.303873\pi$
$434$		0			0
$435$	0.197119	−	0.541580i	0.00945113	−	0.0259668i
$436$		0			0
$437$	−7.24691	+	12.5520i	−0.346667	+	0.600444i
$438$		0			0
$439$	5.82888	+	10.0959i	0.278197	+	0.481852i	0.970937	−	0.239336i	$-0.0769298\pi$
$439$	5.82888	+	10.0959i	0.278197	+	0.481852i	−0.692740	+	0.721188i	$0.743596\pi$
$440$		0			0
$441$	2.81908	−	1.02606i	0.134242	−	0.0488600i
$442$		0			0
$443$	−6.61587	−	11.4590i	−0.314329	−	0.544434i	0.664965	−	0.746874i	$-0.268446\pi$
$443$	−6.61587	−	11.4590i	−0.314329	−	0.544434i	−0.979295	+	0.202440i	$0.935113\pi$
$444$		0			0
$445$	−0.391407	+	0.677937i	−0.0185545	+	0.0321373i
$446$		0			0
$447$	−19.1660	−	22.8411i	−0.906519	−	1.08035i
$448$		0			0
$449$	19.6450			0.927103			0.463552	−	0.886070i	$-0.346575\pi$
$449$	19.6450			0.927103			0.463552	+	0.886070i	$0.346575\pi$
$450$		0			0
$451$	3.26857			0.153911
$452$		0			0
$453$	8.46585	−	1.49276i	0.397760	−	0.0701359i
$454$		0			0
$455$	−0.0996702	+	0.172634i	−0.00467261	+	0.00809320i
$456$		0			0
$457$	12.8623	+	22.2782i	0.601674	+	1.04213i	0.992568	+	0.121694i	$0.0388325\pi$
$457$	12.8623	+	22.2782i	0.601674	+	1.04213i	−0.390894	+	0.920436i	$0.627834\pi$
$458$		0			0
$459$	1.02007	−	0.588936i	0.0476127	−	0.0274892i
$460$		0			0
$461$	15.6086	+	27.0349i	0.726965	+	1.25914i	0.958160	+	0.286232i	$0.0924029\pi$
$461$	15.6086	+	27.0349i	0.726965	+	1.25914i	−0.231196	+	0.972907i	$0.574264\pi$
$462$		0			0
$463$	20.1741	−	34.9426i	0.937571	−	1.62392i	0.167586	−	0.985857i	$-0.446403\pi$
$463$	20.1741	−	34.9426i	0.937571	−	1.62392i	0.769985	−	0.638063i	$-0.220264\pi$
$464$		0			0
$465$	−6.36484	+	1.12229i	−0.295162	+	0.0520451i
$466$		0			0
$467$	−23.4620			−1.08569			−0.542847	−	0.839832i	$-0.682654\pi$
$467$	−23.4620			−1.08569			−0.542847	+	0.839832i	$0.682654\pi$
$468$		0			0
$469$	5.74422			0.265244
$470$		0			0
$471$	−21.9278	−	26.1326i	−1.01038	−	1.20413i
$472$		0			0
$473$	13.1630	−	22.7989i	0.605234	−	1.04830i
$474$		0			0
$475$	−4.94562	−	8.56607i	−0.226921	−	0.393038i
$476$		0			0
$477$	7.31908	+	6.14144i	0.335118	+	0.281197i
$478$		0			0
$479$	14.0940	+	24.4116i	0.643973	+	1.11539i	0.984538	+	0.175173i	$0.0560486\pi$
$479$	14.0940	+	24.4116i	0.643973	+	1.11539i	−0.340564	+	0.940221i	$0.610618\pi$
$480$		0			0
$481$	−0.348641	+	0.603863i	−0.0158966	+	0.0275338i
$482$		0			0
$483$	−3.97044	+	10.9087i	−0.180661	+	0.496362i
$484$		0			0
$485$	9.77662			0.443933
$486$		0			0
$487$	39.1070			1.77211			0.886054	−	0.463583i	$-0.153436\pi$
$487$	39.1070			1.77211			0.886054	+	0.463583i	$0.153436\pi$
$488$		0			0
$489$	−4.97272	+	13.6624i	−0.224874	+	0.617836i
$490$		0			0
$491$	2.75743	−	4.77600i	0.124441	−	0.215538i	−0.797073	−	0.603882i	$-0.793620\pi$
$491$	2.75743	−	4.77600i	0.124441	−	0.215538i	0.921514	+	0.388345i	$0.126953\pi$
$492$		0			0
$493$	−0.0577812	−	0.100080i	−0.00260233	−	0.00450737i
$494$		0			0
$495$	5.11721	+	4.29385i	0.230002	+	0.192994i
$496$		0			0
$497$	−7.01367	−	12.1480i	−0.314606	−	0.544914i
$498$		0			0
$499$	−7.68779	+	13.3156i	−0.344153	+	0.596090i	−0.985199	−	0.171412i	$-0.945167\pi$
$499$	−7.68779	+	13.3156i	−0.344153	+	0.596090i	0.641047	+	0.767502i	$0.278500\pi$
$500$		0			0
$501$	6.70187	+	7.98697i	0.299417	+	0.356832i
$502$		0			0
$503$	36.6195			1.63278			0.816391	−	0.577499i	$-0.195971\pi$
$503$	36.6195			1.63278			0.816391	+	0.577499i	$0.195971\pi$
$504$		0			0
$505$	−0.855342			−0.0380622
$506$		0			0
$507$	22.0155	−	3.88192i	0.977742	−	0.172402i
$508$		0			0
$509$	7.47178	−	12.9415i	0.331181	−	0.573622i	−0.651563	−	0.758595i	$-0.725886\pi$
$509$	7.47178	−	12.9415i	0.331181	−	0.573622i	0.982744	+	0.184973i	$0.0592196\pi$
$510$		0			0
$511$	−6.20961	−	10.7554i	−0.274697	−	0.475789i
$512$		0			0
$513$	9.73127	−	5.61835i	0.429646	−	0.248056i
$514$		0			0
$515$	−4.17277	−	7.22745i	−0.183874	−	0.318480i
$516$		0			0
$517$	−14.1420	+	24.4947i	−0.621966	+	1.07728i
$518$		0			0
$519$	4.79339	−	0.845203i	0.210406	−	0.0371003i
$520$		0			0
$521$	−12.3655			−0.541741			−0.270870	−	0.962616i	$-0.587312\pi$
$521$	−12.3655			−0.541741			−0.270870	+	0.962616i	$0.587312\pi$
$522$		0			0
$523$	14.6536			0.640759			0.320379	−	0.947289i	$-0.396190\pi$
$523$	14.6536			0.640759			0.320379	+	0.947289i	$0.396190\pi$
$524$		0			0
$525$	−5.09240	−	6.06888i	−0.222250	−	0.264868i
$526$		0			0
$527$	−0.647956	+	1.12229i	−0.0282254	+	0.0488878i
$528$		0			0
$529$	−10.9606	−	18.9844i	−0.476549	−	0.825408i
$530$		0			0
$531$	−34.2679	+	12.4725i	−1.48710	+	0.541260i
$532$		0			0
$533$	0.146307	+	0.253411i	0.00633726	+	0.0109765i
$534$		0			0
$535$	3.58037	−	6.20139i	0.154793	−	0.268109i
$536$		0			0
$537$	−11.9798	+	32.9141i	−0.516965	+	1.42035i
$538$		0			0
$539$	3.41147			0.146943
$540$		0			0
$541$	−42.6323			−1.83290			−0.916452	−	0.400144i	$-0.868960\pi$
$541$	−42.6323			−1.83290			−0.916452	+	0.400144i	$0.868960\pi$
$542$		0			0
$543$	5.34477	−	14.6846i	0.229366	−	0.630178i
$544$		0			0
$545$	−0.0256923	+	0.0445003i	−0.00110054	+	0.00190618i
$546$		0			0
$547$	7.69846	+	13.3341i	0.329163	+	0.570126i	0.982346	−	0.187074i	$-0.0599003\pi$
$547$	7.69846	+	13.3341i	0.329163	+	0.570126i	−0.653183	+	0.757200i	$0.726567\pi$
$548$		0			0
$549$	1.82841	−	10.3694i	0.0780347	−	0.442557i
$550$		0			0
$551$	−0.551222	−	0.954745i	−0.0234829	−	0.0406735i
$552$		0			0
$553$	5.98293	−	10.3627i	0.254420	−	0.440668i
$554$		0			0
$555$	1.65910	+	1.97724i	0.0704249	+	0.0839291i
$556$		0			0
$557$	34.9495			1.48086			0.740430	−	0.672134i	$-0.234622\pi$
$557$	34.9495			1.48086			0.740430	+	0.672134i	$0.234622\pi$
$558$		0			0
$559$	2.35679			0.0996817
$560$		0			0
$561$	1.31908	−	0.232589i	0.0556915	−	0.00981992i
$562$		0			0
$563$	−8.13176	+	14.0846i	−0.342713	+	0.593596i	−0.984935	−	0.172922i	$-0.944679\pi$
$563$	−8.13176	+	14.0846i	−0.342713	+	0.593596i	0.642223	+	0.766518i	$0.278012\pi$
$564$		0			0
$565$	1.92127	+	3.32774i	0.0808286	+	0.139999i
$566$		0			0
$567$	6.89440	−	5.78509i	0.289538	−	0.242951i
$568$		0			0
$569$	4.32026	+	7.48291i	0.181115	+	0.313700i	0.942260	−	0.334881i	$-0.108696\pi$
$569$	4.32026	+	7.48291i	0.181115	+	0.313700i	−0.761146	+	0.648581i	$0.775363\pi$
$570$		0			0
$571$	−10.7647	+	18.6450i	−0.450489	+	0.780269i	−0.998416	−	0.0562564i	$-0.982084\pi$
$571$	−10.7647	+	18.6450i	−0.450489	+	0.780269i	0.547928	+	0.836526i	$0.315417\pi$
$572$		0			0
$573$	19.7173	−	3.47670i	0.823704	−	0.145241i
$574$		0			0
$575$	30.6563			1.27846
$576$		0			0
$577$	21.2686			0.885422			0.442711	−	0.896664i	$-0.354017\pi$
$577$	21.2686			0.885422			0.442711	+	0.896664i	$0.354017\pi$
$578$		0			0
$579$	−19.5334	−	23.2790i	−0.811782	−	0.967444i
$580$		0			0
$581$	−2.13563	+	3.69902i	−0.0886008	+	0.153461i
$582$		0			0
$583$	5.43242	+	9.40923i	0.224988	+	0.389690i
$584$		0			0
$585$	−0.103845	+	0.588936i	−0.00429348	+	0.0243495i
$586$		0			0
$587$	−11.4372	−	19.8098i	−0.472062	−	0.817636i	0.527427	−	0.849601i	$-0.323157\pi$
$587$	−11.4372	−	19.8098i	−0.472062	−	0.817636i	−0.999489	+	0.0319646i	$0.989824\pi$
$588$		0			0
$589$	−6.18139	+	10.7065i	−0.254700	+	0.441153i
$590$		0			0
$591$	−13.8222	+	37.9763i	−0.568571	+	1.56214i
$592$		0			0
$593$	−40.1780			−1.64991			−0.824956	−	0.565197i	$-0.808800\pi$
$593$	−40.1780			−1.64991			−0.824956	+	0.565197i	$0.808800\pi$
$594$		0			0
$595$	0.147956			0.00606560
$596$		0			0
$597$	−7.47519	+	20.5379i	−0.305939	+	0.840560i
$598$		0			0
$599$	7.12061	−	12.3333i	0.290940	−	0.503924i	−0.683092	−	0.730332i	$-0.739365\pi$
$599$	7.12061	−	12.3333i	0.290940	−	0.503924i	0.974032	+	0.226409i	$0.0726985\pi$
$600$		0			0
$601$	−13.3362	−	23.0989i	−0.543993	−	0.942223i	−0.998670	−	0.0515669i	$-0.983578\pi$
$601$	−13.3362	−	23.0989i	−0.543993	−	0.942223i	0.454677	−	0.890657i	$-0.349755\pi$
$602$		0			0
$603$	16.1934	−	5.89392i	0.659447	−	0.240019i
$604$		0			0
$605$	0.208263	+	0.360723i	0.00846711	+	0.0146655i
$606$		0			0
$607$	−1.09358	+	1.89413i	−0.0443870	+	0.0768805i	−0.887365	−	0.461067i	$-0.847467\pi$
$607$	−1.09358	+	1.89413i	−0.0443870	+	0.0768805i	0.842978	+	0.537947i	$0.180800\pi$
$608$		0			0
$609$	−0.567581	−	0.676417i	−0.0229996	−	0.0274098i
$610$		0			0
$611$	−2.53209			−0.102437
$612$		0			0
$613$	18.2763			0.738173			0.369087	−	0.929395i	$-0.379671\pi$
$613$	18.2763			0.738173			0.369087	+	0.929395i	$0.379671\pi$
$614$		0			0
$615$	1.06670	−	0.188089i	0.0430137	−	0.00758447i
$616$		0			0
$617$	4.21823	−	7.30618i	0.169819	−	0.294136i	−0.768537	−	0.639805i	$-0.779015\pi$
$617$	4.21823	−	7.30618i	0.169819	−	0.294136i	0.938356	+	0.345670i	$0.112348\pi$
$618$		0			0
$619$	1.36571	+	2.36549i	0.0548927	+	0.0950770i	0.892166	−	0.451708i	$-0.149185\pi$
$619$	1.36571	+	2.36549i	0.0548927	+	0.0950770i	−0.837273	+	0.546785i	$0.815852\pi$
$620$		0			0
$621$			34.8263i			1.39753i
$622$		0			0
$623$	0.599670	+	1.03866i	0.0240253	+	0.0416130i
$624$		0			0
$625$	−9.39558	+	16.2736i	−0.375823	+	0.650945i
$626$		0			0
$627$	12.5838	−	2.21886i	0.502548	−	0.0886127i
$628$		0			0
$629$	0.517541			0.0206357
$630$		0			0
$631$	33.3141			1.32621			0.663106	−	0.748525i	$-0.269238\pi$
$631$	33.3141			1.32621			0.663106	+	0.748525i	$0.269238\pi$
$632$		0			0
$633$	10.0373	+	11.9620i	0.398947	+	0.475447i
$634$		0			0
$635$	−3.69681	+	6.40307i	−0.146704	+	0.254098i
$636$		0			0
$637$	0.152704	+	0.264490i	0.00605034	+	0.0104795i
$638$		0			0
$639$	−32.2367	−	27.0498i	−1.27526	−	1.07007i
$640$		0			0
$641$	−20.9133	−	36.2229i	−0.826025	−	1.43072i	−0.901133	−	0.433542i	$-0.857264\pi$
$641$	−20.9133	−	36.2229i	−0.826025	−	1.43072i	0.0751082	−	0.997175i	$-0.476070\pi$
$642$		0			0
$643$	−8.08466	+	14.0030i	−0.318828	+	0.552226i	−0.980244	−	0.197793i	$-0.936622\pi$
$643$	−8.08466	+	14.0030i	−0.318828	+	0.552226i	0.661416	+	0.750019i	$0.269956\pi$
$644$		0			0
$645$	2.98380	−	8.19793i	0.117487	−	0.322793i
$646$		0			0
$647$	−19.7692			−0.777207			−0.388604	−	0.921405i	$-0.627042\pi$
$647$	−19.7692			−0.777207			−0.388604	+	0.921405i	$0.627042\pi$
$648$		0			0
$649$	−41.4688			−1.62779
$650$		0			0
$651$	−3.38666	+	9.30477i	−0.132734	+	0.364683i
$652$		0			0
$653$	20.0501	−	34.7278i	0.784621	−	1.35900i	−0.144604	−	0.989490i	$-0.546191\pi$
$653$	20.0501	−	34.7278i	0.784621	−	1.35900i	0.929225	−	0.369514i	$-0.120476\pi$
$654$		0			0
$655$	1.48633	+	2.57440i	0.0580757	+	0.100590i
$656$		0			0
$657$	−28.5410	−	23.9488i	−1.11349	−	0.934330i
$658$		0			0
$659$	−0.657918	−	1.13955i	−0.0256289	−	0.0443905i	0.852927	−	0.522031i	$-0.174825\pi$
$659$	−0.657918	−	1.13955i	−0.0256289	−	0.0443905i	−0.878555	+	0.477641i	$0.841492\pi$
$660$		0			0
$661$	−14.8931	+	25.7955i	−0.579273	+	1.00333i	0.416290	+	0.909232i	$0.363330\pi$
$661$	−14.8931	+	25.7955i	−0.579273	+	1.00333i	−0.995563	+	0.0940980i	$0.970003\pi$
$662$		0			0
$663$	0.0770768	+	0.0918566i	0.00299342	+	0.00356741i
$664$		0			0
$665$	1.41147			0.0547346
$666$		0			0
$667$	3.41685			0.132301
$668$		0			0
$669$	−30.8391	+	5.43777i	−1.19231	+	0.210236i
$670$		0			0
$671$	5.98680	−	10.3694i	0.231118	−	0.400308i
$672$		0			0
$673$	10.9693	+	18.9993i	0.422834	+	0.732369i	0.996215	−	0.0869189i	$-0.0277021\pi$
$673$	10.9693	+	18.9993i	0.422834	+	0.732369i	−0.573382	+	0.819288i	$0.694369\pi$
$674$		0			0
$675$	−20.5829	−	11.8835i	−0.792236	−	0.457398i
$676$		0			0
$677$	14.7228	+	25.5007i	0.565844	+	0.980070i	0.996971	+	0.0777786i	$0.0247827\pi$
$677$	14.7228	+	25.5007i	0.565844	+	0.980070i	−0.431127	+	0.902291i	$0.641884\pi$
$678$		0			0
$679$	7.48932	−	12.9719i	0.287414	−	0.497815i
$680$		0			0
$681$	−42.3881	+	7.47416i	−1.62431	+	0.286410i
$682$		0			0
$683$	−27.0060			−1.03336			−0.516678	−	0.856180i	$-0.672831\pi$
$683$	−27.0060			−1.03336			−0.516678	+	0.856180i	$0.672831\pi$
$684$		0			0
$685$	10.9531			0.418495
$686$		0			0
$687$	−25.3879	−	30.2561i	−0.968609	−	1.15434i
$688$		0			0
$689$	−0.486329	+	0.842347i	−0.0185277	+	0.0320909i
$690$		0			0
$691$	6.50640	+	11.2694i	0.247515	+	0.428709i	0.962836	−	0.270088i	$-0.0870527\pi$
$691$	6.50640	+	11.2694i	0.247515	+	0.428709i	−0.715321	+	0.698796i	$0.753719\pi$
$692$		0			0
$693$	9.61721	−	3.50038i	0.365328	−	0.132968i
$694$		0			0
$695$	7.30706	+	12.6562i	0.277172	+	0.480077i
$696$		0			0
$697$	0.108593	−	0.188089i	0.00411326	−	0.00712437i
$698$		0			0
$699$	8.42081	−	23.1360i	0.318504	−	0.875083i
$700$		0			0
$701$	−18.7683			−0.708868			−0.354434	−	0.935081i	$-0.615326\pi$
$701$	−18.7683			−0.708868			−0.354434	+	0.935081i	$0.615326\pi$
$702$		0			0
$703$	4.93725			0.186212
$704$		0			0
$705$	−3.20574	+	8.80769i	−0.120735	+	0.331717i
$706$		0			0
$707$	−0.655230	+	1.13489i	−0.0246425	+	0.0426820i
$708$		0			0
$709$	15.5057	+	26.8566i	0.582328	+	1.00862i	0.995203	+	0.0978340i	$0.0311914\pi$
$709$	15.5057	+	26.8566i	0.582328	+	1.00862i	−0.412875	+	0.910788i	$0.635475\pi$
$710$		0			0
$711$	6.23355	−	35.3522i	0.233776	−	1.32581i
$712$		0			0
$713$	−19.1582	−	33.1830i	−0.717481	−	1.24271i
$714$		0			0
$715$	−0.340022	+	0.588936i	−0.0127161	+	0.0220250i
$716$		0			0
$717$	9.19712	+	10.9607i	0.343473	+	0.409335i
$718$		0			0
$719$	4.62267			0.172397			0.0861983	−	0.996278i	$-0.472528\pi$
$719$	4.62267			0.172397			0.0861983	+	0.996278i	$0.472528\pi$
$720$		0			0
$721$	−12.7861			−0.476180
$722$		0			0
$723$	−13.2476	+	2.33591i	−0.492685	+	0.0868736i
$724$		0			0
$725$	−1.16591	+	2.01941i	−0.0433007	+	0.0749990i
$726$		0			0
$727$	−21.1638	−	36.6569i	−0.784924	−	1.35953i	−0.929045	−	0.369968i	$-0.879369\pi$
$727$	−21.1638	−	36.6569i	−0.784924	−	1.35953i	0.144121	−	0.989560i	$-0.453965\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$		0			0
$731$	−0.874638	−	1.51492i	−0.0323496	−	0.0560312i
$732$		0			0
$733$	16.5770	−	28.7122i	0.612284	−	1.06051i	−0.378570	−	0.925573i	$-0.623584\pi$
$733$	16.5770	−	28.7122i	0.612284	−	1.06051i	0.990854	−	0.134935i	$-0.0430826\pi$
$734$		0			0
$735$	1.11334	−	0.196312i	0.0410662	−	0.00724108i
$736$		0			0
$737$	19.5963			0.721838
$738$		0			0
$739$	28.4023			1.04480			0.522398	−	0.852702i	$-0.325038\pi$
$739$	28.4023			1.04480			0.522398	+	0.852702i	$0.325038\pi$
$740$		0			0
$741$	0.735300	+	0.876296i	0.0270119	+	0.0321915i
$742$		0			0
$743$	14.8603	−	25.7387i	0.545170	−	0.944262i	−0.453426	−	0.891294i	$-0.649799\pi$
$743$	14.8603	−	25.7387i	0.545170	−	0.944262i	0.998596	−	0.0529680i	$-0.0168681\pi$
$744$		0			0
$745$	−5.61809	−	9.73081i	−0.205831	−	0.356509i
$746$		0			0
$747$	−2.22509	+	12.6191i	−0.0814118	+	0.461709i
$748$		0			0
$749$	−5.48545	−	9.50108i	−0.200434	−	0.347162i
$750$		0			0
$751$	−10.9734	+	19.0065i	−0.400426	+	0.693558i	−0.993777	−	0.111385i	$-0.964471\pi$
$751$	−10.9734	+	19.0065i	−0.400426	+	0.693558i	0.593351	+	0.804944i	$0.297805\pi$
$752$		0			0
$753$	3.61263	−	9.92561i	0.131651	−	0.361709i
$754$		0			0
$755$	3.23947			0.117897
$756$		0			0
$757$	12.0746			0.438859			0.219430	−	0.975628i	$-0.429580\pi$
$757$	12.0746			0.438859			0.219430	+	0.975628i	$0.429580\pi$
$758$		0			0
$759$	−13.5450	+	37.2147i	−0.491654	+	1.35081i
$760$		0			0
$761$	25.5895	−	44.3222i	0.927617	−	1.60668i	0.140320	−	0.990106i	$-0.455187\pi$
$761$	25.5895	−	44.3222i	0.927617	−	1.60668i	0.787297	−	0.616574i	$-0.211480\pi$
$762$		0			0
$763$	0.0393628	+	0.0681784i	0.00142503	+	0.00246823i
$764$		0			0
$765$	0.417099	−	0.151812i	0.0150803	−	0.00548876i
$766$		0			0
$767$	−1.85622	−	3.21507i	−0.0670242	−	0.116089i
$768$		0			0
$769$	−19.7454	+	34.2000i	−0.712038	+	1.23329i	0.252054	+	0.967713i	$0.418894\pi$
$769$	−19.7454	+	34.2000i	−0.712038	+	1.23329i	−0.964091	+	0.265572i	$0.914439\pi$
$770$		0			0
$771$	2.87433	+	3.42550i	0.103517	+	0.123366i
$772$		0			0
$773$	−32.0951			−1.15438			−0.577191	−	0.816609i	$-0.695851\pi$
$773$	−32.0951			−1.15438			−0.577191	+	0.816609i	$0.695851\pi$
$774$		0			0
$775$	26.1489			0.939296
$776$		0			0
$777$	3.89440	−	0.686688i	0.139711	−	0.0246348i
$778$		0			0
$779$	1.03596	−	1.79433i	0.0371171	−	0.0642887i
$780$		0			0
$781$	−23.9270	−	41.4427i	−0.856174	−	1.48294i
$782$		0			0
$783$	−2.29410	−	1.32450i	−0.0819845	−	0.0473338i
$784$		0			0
$785$	−6.42767	−	11.1331i	−0.229413	−	0.397356i
$786$		0			0
$787$	−16.0902	+	27.8690i	−0.573553	+	0.993423i	0.422644	+	0.906296i	$0.361102\pi$
$787$	−16.0902	+	27.8690i	−0.573553	+	0.993423i	−0.996197	+	0.0871270i	$0.972231\pi$
$788$		0			0
$789$	−5.42783	+	0.957073i	−0.193236	+	0.0340727i
$790$		0			0
$791$	5.88713			0.209322
$792$		0			0
$793$	1.07192			0.0380649
$794$		0			0
$795$	2.31433	+	2.75811i	0.0820808	+	0.0978201i
$796$		0			0
$797$	22.0569	−	38.2037i	0.781296	−	1.35324i	−0.149892	−	0.988702i	$-0.547892\pi$
$797$	22.0569	−	38.2037i	0.781296	−	1.35324i	0.931187	−	0.364541i	$-0.118774\pi$
$798$		0			0
$799$	0.939693	+	1.62760i	0.0332439	+	0.0575802i
$800$		0			0
$801$	2.75624	+	2.31276i	0.0973871	+	0.0817175i
$802$		0			0
$803$	−21.1839	−	36.6916i	−0.747564	−	1.29482i
$804$		0			0
$805$	−2.18732	+	3.78855i	−0.0770929	+	0.133529i
$806$		0			0
$807$	−11.1404	+	30.6081i	−0.392162	+	1.07746i
$808$		0			0
$809$	50.6373			1.78031			0.890157	−	0.455654i	$-0.150595\pi$
$809$	50.6373			1.78031			0.890157	+	0.455654i	$0.150595\pi$
$810$		0			0
$811$	45.1557			1.58563			0.792815	−	0.609462i	$-0.208614\pi$
$811$	45.1557			1.58563			0.792815	+	0.609462i	$0.208614\pi$
$812$		0			0
$813$	1.44016	−	3.95681i	0.0505086	−	0.138771i
$814$		0			0
$815$	−2.73947	+	4.74491i	−0.0959596	+	0.166207i
$816$		0			0
$817$	−8.34389	−	14.4520i	−0.291916	−	0.505613i
$818$		0			0
$819$	0.701867	+	0.588936i	0.0245252	+	0.0205791i
$820$		0			0
$821$	−6.67247	−	11.5571i	−0.232871	−	0.403344i	0.725781	−	0.687926i	$-0.241479\pi$
$821$	−6.67247	−	11.5571i	−0.232871	−	0.403344i	−0.958652	+	0.284582i	$0.908145\pi$
$822$		0			0
$823$	21.3209	−	36.9289i	0.743199	−	1.28726i	−0.207832	−	0.978165i	$-0.566641\pi$
$823$	21.3209	−	36.9289i	0.743199	−	1.28726i	0.951031	−	0.309095i	$-0.100026\pi$
$824$		0			0
$825$	−17.3726	−	20.7038i	−0.604836	−	0.720815i
$826$		0			0
$827$	24.8057			0.862579			0.431290	−	0.902214i	$-0.358059\pi$
$827$	24.8057			0.862579			0.431290	+	0.902214i	$0.358059\pi$
$828$		0			0
$829$	26.0496			0.904741			0.452371	−	0.891830i	$-0.350578\pi$
$829$	26.0496			0.904741			0.452371	+	0.891830i	$0.350578\pi$
$830$		0			0
$831$	−38.8555	+	6.85127i	−1.34788	+	0.237668i
$832$		0			0
$833$	0.113341	−	0.196312i	0.00392703	−	0.00680181i
$834$		0			0
$835$	1.96451	+	3.40263i	0.0679846	+	0.117753i
$836$		0			0
$837$			29.7058i			1.02678i
$838$		0			0
$839$	10.3571	+	17.9390i	0.357567	+	0.619324i	0.987554	−	0.157282i	$-0.0502732\pi$
$839$	10.3571	+	17.9390i	0.357567	+	0.619324i	−0.629987	+	0.776606i	$0.716940\pi$
$840$		0			0
$841$	14.3701	−	24.8897i	0.495519	−	0.858264i
$842$		0			0
$843$	15.9907	−	2.81959i	0.550748	−	0.0971117i
$844$		0			0
$845$	8.42427			0.289804
$846$		0			0
$847$	0.638156			0.0219273
$848$		0			0
$849$	−31.0621	−	37.0184i	−1.06605	−	1.27047i
$850$		0			0
$851$	−7.65111	+	13.2521i	−0.262277	+	0.454277i
$852$		0			0
$853$	5.04710	+	8.74184i	0.172810	+	0.299315i	0.939401	−	0.342820i	$-0.111382\pi$
$853$	5.04710	+	8.74184i	0.172810	+	0.299315i	−0.766592	+	0.642135i	$0.778049\pi$
$854$		0			0
$855$	3.97906	−	1.44826i	0.136081	−	0.0495294i
$856$		0			0
$857$	−13.7208	−	23.7650i	−0.468692	−	0.811798i	0.530668	−	0.847580i	$-0.321941\pi$
$857$	−13.7208	−	23.7650i	−0.468692	−	0.811798i	−0.999360	+	0.0357817i	$0.988608\pi$
$858$		0			0
$859$	0.529096	−	0.916421i	0.0180525	−	0.0312679i	−0.856858	−	0.515552i	$-0.827587\pi$
$859$	0.529096	−	0.916421i	0.0180525	−	0.0312679i	0.874911	+	0.484285i	$0.160920\pi$
$860$		0			0
$861$	0.567581	−	1.55942i	0.0193431	−	0.0531448i
$862$		0			0
$863$	−16.0009			−0.544678			−0.272339	−	0.962201i	$-0.587797\pi$
$863$	−16.0009			−0.544678			−0.272339	+	0.962201i	$0.587797\pi$
$864$		0			0
$865$	1.83420			0.0623646
$866$		0			0
$867$	−10.0403	+	27.5855i	−0.340986	+	0.936852i
$868$		0			0
$869$	20.4106	−	35.3522i	0.692382	−	1.19924i
$870$		0			0
$871$	0.877164	+	1.51929i	0.0297216	+	0.0514793i
$872$		0			0
$873$	7.80304	−	44.2533i	0.264093	−	1.49775i
$874$		0			0
$875$	−3.12449	−	5.41177i	−0.105627	−	0.182951i
$876$		0			0
$877$	−7.10148	+	12.3001i	−0.239800	+	0.415346i	−0.960657	−	0.277738i	$-0.910415\pi$
$877$	−7.10148	+	12.3001i	−0.239800	+	0.415346i	0.720857	+	0.693084i	$0.243749\pi$
$878$		0			0
$879$	−11.7010	−	13.9447i	−0.394665	−	0.470343i
$880$		0			0
$881$	−11.6587			−0.392791			−0.196396	−	0.980525i	$-0.562924\pi$
$881$	−11.6587			−0.392791			−0.196396	+	0.980525i	$0.562924\pi$
$882$		0			0
$883$	−52.8411			−1.77825			−0.889123	−	0.457669i	$-0.848684\pi$
$883$	−52.8411			−1.77825			−0.889123	+	0.457669i	$0.848684\pi$
$884$		0			0
$885$	−13.5334	+	2.38631i	−0.454921	+	0.0802149i
$886$		0			0
$887$	−23.2947	+	40.3477i	−0.782160	+	1.35474i	0.148520	+	0.988909i	$0.452549\pi$
$887$	−23.2947	+	40.3477i	−0.782160	+	1.35474i	−0.930681	+	0.365832i	$0.880784\pi$
$888$		0			0
$889$	5.66385	+	9.81007i	0.189959	+	0.329019i
$890$		0			0
$891$	23.5201	−	19.7357i	0.787952	−	0.661170i
$892$		0			0
$893$	8.96451	+	15.5270i	0.299986	+	0.519591i
$894$		0			0
$895$	−6.59967	+	11.4310i	−0.220603	+	0.382095i
$896$		0			0
$897$	−3.49154	+	0.615653i	−0.116579	+	0.0205561i
$898$		0			0
$899$	2.91447			0.0972029
$900$		0			0
$901$	0.721934			0.0240511
$902$		0			0
$903$	−8.59152	−	10.2390i	−0.285908	−	0.340732i
$904$		0			0
$905$	2.94444	−	5.09992i	0.0978765	−	0.169527i
$906$		0			0
$907$	18.2374	+	31.5881i	0.605563	+	1.04887i	0.991962	+	0.126535i	$0.0403855\pi$
$907$	18.2374	+	31.5881i	0.605563	+	1.04887i	−0.386399	+	0.922332i	$0.626281\pi$
$908$		0			0
$909$	−0.682677	+	3.87165i	−0.0226430	+	0.128415i
$910$		0			0
$911$	−14.0137	−	24.2724i	−0.464294	−	0.804180i	0.534876	−	0.844931i	$-0.320358\pi$
$911$	−14.0137	−	24.2724i	−0.464294	−	0.804180i	−0.999169	+	0.0407506i	$0.987025\pi$
$912$		0			0
$913$	−7.28564	+	12.6191i	−0.241120	+	0.417631i
$914$		0			0
$915$	1.35710	−	3.72859i	0.0448642	−	0.123263i
$916$		0			0
$917$	4.55438			0.150399
$918$		0			0
$919$	−8.71688			−0.287543			−0.143772	−	0.989611i	$-0.545923\pi$
$919$	−8.71688			−0.287543			−0.143772	+	0.989611i	$0.545923\pi$
$920$		0			0
$921$	−13.5208	+	37.1480i	−0.445525	+	1.22407i
$922$		0			0
$923$	2.14203	−	3.71010i	0.0705056	−	0.122119i
$924$		0			0
$925$	−5.22147	−	9.04385i	−0.171681	−	0.297360i
$926$		0			0
$927$	−36.0450	+	13.1193i	−1.18387	+	0.430895i
$928$		0			0
$929$	6.23261	+	10.7952i	0.204485	+	0.354179i	0.949969	−	0.312345i	$-0.101115\pi$
$929$	6.23261	+	10.7952i	0.204485	+	0.354179i	−0.745483	+	0.666524i	$0.767781\pi$
$930$		0			0
$931$	1.08125	−	1.87278i	0.0354366	−	0.0613780i
$932$		0			0
$933$	27.6288	+	32.9267i	0.904527	+	1.07797i
$934$		0			0
$935$	0.504748			0.0165070
$936$		0			0
$937$	48.9659			1.59964			0.799822	−	0.600237i	$-0.204927\pi$
$937$	48.9659			1.59964			0.799822	+	0.600237i	$0.204927\pi$
$938$		0			0
$939$	−40.1878	+	7.08619i	−1.31148	+	0.231249i
$940$		0			0
$941$	−16.7087	+	28.9404i	−0.544689	+	0.943429i	0.453937	+	0.891034i	$0.350019\pi$
$941$	−16.7087	+	28.9404i	−0.544689	+	0.943429i	−0.998626	+	0.0523955i	$0.983314\pi$
$942$		0			0
$943$	3.21079	+	5.56125i	0.104558	+	0.181099i
$944$		0			0
$945$	2.93717	−	1.69577i	0.0955460	−	0.0551635i
$946$		0			0
$947$	11.7745	+	20.3940i	0.382620	+	0.662717i	0.991436	−	0.130594i	$-0.0416886\pi$
$947$	11.7745	+	20.3940i	0.382620	+	0.662717i	−0.608816	+	0.793311i	$0.708355\pi$
$948$		0			0
$949$	1.89646	−	3.28476i	0.0615617	−	0.106628i
$950$		0			0
$951$	19.8004	−	3.49135i	0.642072	−	0.113215i
$952$		0			0
$953$	−10.6500			−0.344988			−0.172494	−	0.985011i	$-0.555183\pi$
$953$	−10.6500			−0.344988			−0.172494	+	0.985011i	$0.555183\pi$
$954$		0			0
$955$	7.54488			0.244147
$956$		0			0
$957$	−1.93629	−	2.30758i	−0.0625913	−	0.0745934i
$958$		0			0
$959$	8.39053	−	14.5328i	0.270944	−	0.469289i
$960$		0			0
$961$	−0.841367	−	1.45729i	−0.0271409	−	0.0470093i
$962$		0			0
$963$	−25.2126	−	21.1559i	−0.812465	−	0.681739i
$964$		0			0
$965$	−5.72580	−	9.91738i	−0.184320	−	0.319252i
$966$		0			0
$967$	−2.35457	+	4.07824i	−0.0757179	+	0.131147i	−0.901398	−	0.432991i	$-0.857458\pi$
$967$	−2.35457	+	4.07824i	−0.0757179	+	0.131147i	0.825680	+	0.564138i	$0.190792\pi$
$968$		0			0
$969$	0.290393	−	0.797847i	0.00932875	−	0.0256305i
$970$		0			0
$971$	−13.4483			−0.431577			−0.215788	−	0.976440i	$-0.569232\pi$
$971$	−13.4483			−0.431577			−0.215788	+	0.976440i	$0.569232\pi$
$972$		0			0
$973$	22.3901			0.717794
$974$		0			0
$975$	0.827534	−	2.27363i	0.0265023	−	0.0728145i
$976$		0			0
$977$	−0.159511	+	0.276281i	−0.00510320	+	0.00883900i	−0.868566	−	0.495574i	$-0.834958\pi$
$977$	−0.159511	+	0.276281i	−0.00510320	+	0.00883900i	0.863463	+	0.504413i	$0.168291\pi$
$978$		0			0
$979$	2.04576	+	3.54336i	0.0653828	+	0.113246i
$980$		0			0
$981$	0.180922	+	0.151812i	0.00577640	+	0.00484697i
$982$		0			0
$983$	10.5778	+	18.3214i	0.337381	+	0.584361i	0.983939	−	0.178504i	$-0.0571256\pi$
$983$	10.5778	+	18.3214i	0.337381	+	0.584361i	−0.646558	+	0.762865i	$0.723792\pi$
$984$		0			0
$985$	−7.61468	+	13.1890i	−0.242624	+	0.420237i
$986$		0			0
$987$	9.23055	+	11.0005i	0.293812	+	0.350151i
$988$		0			0
$989$	51.7211			1.64464
$990$		0			0
$991$	12.3610			0.392661			0.196330	−	0.980538i	$-0.437097\pi$
$991$	12.3610			0.392661			0.196330	+	0.980538i	$0.437097\pi$
$992$		0			0
$993$	49.0231	−	8.64409i	1.55570	−	0.274312i
$994$		0			0
$995$	−4.11809	+	7.13274i	−0.130552	+	0.226123i
$996$		0			0
$997$	14.8580	+	25.7349i	0.470559	+	0.815031i	0.999433	−	0.0336687i	$-0.0107191\pi$
$997$	14.8580	+	25.7349i	0.470559	+	0.815031i	−0.528875	+	0.848700i	$0.677386\pi$
$998$		0			0
$999$	10.2740	−	5.93172i	0.325056	−	0.187671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.r.c.337.2	yes	6
3.2	odd	2		1512.2.r.c.1009.2		6
4.3	odd	2		1008.2.r.i.337.2		6
9.2	odd	6		1512.2.r.c.505.2		6
9.4	even	3		4536.2.a.s.1.2		3
9.5	odd	6		4536.2.a.v.1.2		3
9.7	even	3	inner	504.2.r.c.169.2	✓	6
12.11	even	2		3024.2.r.h.1009.2		6
36.7	odd	6		1008.2.r.i.673.2		6
36.11	even	6		3024.2.r.h.2017.2		6
36.23	even	6		9072.2.a.cc.1.2		3
36.31	odd	6		9072.2.a.br.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.c.169.2	✓	6	9.7	even	3	inner
504.2.r.c.337.2	yes	6	1.1	even	1	trivial
1008.2.r.i.337.2		6	4.3	odd	2
1008.2.r.i.673.2		6	36.7	odd	6
1512.2.r.c.505.2		6	9.2	odd	6
1512.2.r.c.1009.2		6	3.2	odd	2
3024.2.r.h.1009.2		6	12.11	even	2
3024.2.r.h.2017.2		6	36.11	even	6
4536.2.a.s.1.2		3	9.4	even	3
4536.2.a.v.1.2		3	9.5	odd	6
9072.2.a.br.1.2		3	36.31	odd	6
9072.2.a.cc.1.2		3	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.592396 - 1.62760i) q^{3} +(0.326352 - 0.565258i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\)	\(q+(0.592396 - 1.62760i) q^{3} +(0.326352 - 0.565258i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.29813 - 1.92836i) q^{9} +(-1.70574 - 2.95442i) q^{11} +(0.152704 - 0.264490i) q^{13} +(-0.726682 - 0.866025i) q^{15} -0.226682 q^{17} -2.16250 q^{19} +(-1.70574 + 0.300767i) q^{21} +(3.35117 - 5.80439i) q^{23} +(2.28699 + 3.96118i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(0.254900 + 0.441500i) q^{29} +(2.85844 - 4.95096i) q^{31} +(-5.81908 + 1.02606i) q^{33} -0.652704 q^{35} -2.28312 q^{37} +(-0.340022 - 0.405223i) q^{39} +(-0.479055 + 0.829748i) q^{41} +(3.85844 + 6.68302i) q^{43} +(-1.84002 + 0.669713i) q^{45} +(-4.14543 - 7.18009i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-0.134285 + 0.368946i) q^{51} -3.18479 q^{53} -2.22668 q^{55} +(-1.28106 + 3.51968i) q^{57} +(6.07785 - 10.5271i) q^{59} +(1.75490 + 3.03958i) q^{61} +(-0.520945 + 2.95442i) q^{63} +(-0.0996702 - 0.172634i) q^{65} +(-2.87211 + 4.97464i) q^{67} +(-7.46198 - 8.89284i) q^{69} +14.0273 q^{71} +12.4192 q^{73} +(7.80200 - 1.37570i) q^{75} +(-1.70574 + 2.95442i) q^{77} +(5.98293 + 10.3627i) q^{79} +(1.56283 + 8.86327i) q^{81} +(-2.13563 - 3.69902i) q^{83} +(-0.0739780 + 0.128134i) q^{85} +(0.869585 - 0.153331i) q^{87} -1.19934 q^{89} -0.305407 q^{91} +(-6.36484 - 7.58532i) q^{93} +(-0.705737 + 1.22237i) q^{95} +(7.48932 + 12.9719i) q^{97} +(-1.77719 + 10.0789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^5 - 3 * q^7	\( 6 q + 3 q^{5} - 3 q^{7} + 3 q^{13} + 9 q^{15} + 12 q^{17} - 18 q^{19} - 6 q^{23} + 6 q^{25} - 27 q^{27} + 3 q^{29} + 9 q^{31} - 18 q^{33} - 6 q^{35} - 30 q^{37} + 18 q^{39} - 6 q^{41} + 15 q^{43} + 9 q^{45} - 9 q^{47} - 3 q^{49} + 9 q^{51} - 12 q^{53} + 27 q^{57} - 3 q^{59} + 12 q^{61} - 15 q^{65} + 12 q^{67} - 27 q^{69} + 42 q^{71} + 6 q^{73} + 9 q^{75} + 15 q^{79} + 6 q^{83} + 15 q^{85} - 9 q^{87} - 36 q^{89} - 6 q^{91} + 9 q^{93} + 6 q^{95} - 15 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 - 3 * q^7 + 3 * q^13 + 9 * q^15 + 12 * q^17 - 18 * q^19 - 6 * q^23 + 6 * q^25 - 27 * q^27 + 3 * q^29 + 9 * q^31 - 18 * q^33 - 6 * q^35 - 30 * q^37 + 18 * q^39 - 6 * q^41 + 15 * q^43 + 9 * q^45 - 9 * q^47 - 3 * q^49 + 9 * q^51 - 12 * q^53 + 27 * q^57 - 3 * q^59 + 12 * q^61 - 15 * q^65 + 12 * q^67 - 27 * q^69 + 42 * q^71 + 6 * q^73 + 9 * q^75 + 15 * q^79 + 6 * q^83 + 15 * q^85 - 9 * q^87 - 36 * q^89 - 6 * q^91 + 9 * q^93 + 6 * q^95 - 15 * q^97

Introduction

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