LMFDB - Embedded newform 504.2.r.c.169.1

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			169.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	504.169
Dual form			504.2.r.c.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70574 - 0.300767i) q^{3} +(-0.266044 - 0.460802i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.81908 + 1.02606i) q^{9} +O(q^{10})$	\(q+(-1.70574 - 0.300767i) q^{3} +(-0.266044 - 0.460802i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.81908 + 1.02606i) q^{9} +(1.11334 - 1.92836i) q^{11} +(-1.03209 - 1.78763i) q^{13} +(0.315207 + 0.866025i) q^{15} +0.815207 q^{17} -7.94356 q^{19} +(1.11334 - 1.32683i) q^{21} +(-3.40033 - 5.88954i) q^{23} +(2.35844 - 4.08494i) q^{25} +(-4.50000 - 2.59808i) q^{27} +(3.73783 - 6.47410i) q^{29} +(-1.14543 - 1.98394i) q^{31} +(-2.47906 + 2.95442i) q^{33} +0.532089 q^{35} -10.2909 q^{37} +(1.22281 + 3.35965i) q^{39} +(1.29813 + 2.24843i) q^{41} +(-0.145430 + 0.251892i) q^{43} +(-0.277189 - 1.57202i) q^{45} +(-0.213011 + 0.368946i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-1.39053 - 0.245188i) q^{51} +1.41147 q^{53} -1.18479 q^{55} +(13.5496 + 2.38917i) q^{57} +(-1.71554 - 2.97140i) q^{59} +(5.23783 - 9.07218i) q^{61} +(-2.29813 + 1.92836i) q^{63} +(-0.549163 + 0.951178i) q^{65} +(2.10220 + 3.64111i) q^{67} +(4.02869 + 11.0687i) q^{69} +12.0865 q^{71} -9.09152 q^{73} +(-5.25150 + 6.25849i) q^{75} +(1.11334 + 1.92836i) q^{77} +(-3.73055 + 6.46151i) q^{79} +(6.89440 + 5.78509i) q^{81} +(8.76264 - 15.1773i) q^{83} +(-0.216881 - 0.375650i) q^{85} +(-8.32295 + 9.91890i) q^{87} -2.09833 q^{89} +2.06418 q^{91} +(1.35710 + 3.72859i) q^{93} +(2.11334 + 3.66041i) q^{95} +(-5.94222 + 10.2922i) q^{97} +(5.11721 - 4.29385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70574	−	0.300767i	−0.984808	−	0.173648i
$3$	−1.70574	−	0.300767i	−0.984808	−	0.173648i
$4$		0			0
$5$	−0.266044	−	0.460802i	−0.118979	−	0.206077i	0.800385	−	0.599487i	$-0.204629\pi$
$5$	−0.266044	−	0.460802i	−0.118979	−	0.206077i	−0.919363	+	0.393410i	$0.871295\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	2.81908	+	1.02606i	0.939693	+	0.342020i
$10$		0			0
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	−0.647931	−	0.761699i	$-0.724366\pi$
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	0.983616	+	0.180276i	$0.0576989\pi$
$12$		0			0
$13$	−1.03209	−	1.78763i	−0.286250	−	0.495799i	0.686662	−	0.726977i	$-0.259075\pi$
$13$	−1.03209	−	1.78763i	−0.286250	−	0.495799i	−0.972912	+	0.231178i	$0.925742\pi$
$14$		0			0
$15$	0.315207	+	0.866025i	0.0813862	+	0.223607i
$16$		0			0
$17$	0.815207			0.197717			0.0988584	−	0.995102i	$-0.468481\pi$
$17$	0.815207			0.197717			0.0988584	+	0.995102i	$0.468481\pi$
$18$		0			0
$19$	−7.94356			−1.82238			−0.911189	−	0.411988i	$-0.864834\pi$
$19$	−7.94356			−1.82238			−0.911189	+	0.411988i	$0.864834\pi$
$20$		0			0
$21$	1.11334	−	1.32683i	0.242951	−	0.289538i
$22$		0			0
$23$	−3.40033	−	5.88954i	−0.709018	−	1.22805i	−0.965222	−	0.261432i	$-0.915805\pi$
$23$	−3.40033	−	5.88954i	−0.709018	−	1.22805i	0.256204	−	0.966623i	$-0.417528\pi$
$24$		0			0
$25$	2.35844	−	4.08494i	0.471688	−	0.816988i
$26$		0			0
$27$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$28$		0			0
$29$	3.73783	−	6.47410i	0.694097	−	1.20221i	−0.276387	−	0.961046i	$-0.589137\pi$
$29$	3.73783	−	6.47410i	0.694097	−	1.20221i	0.970484	−	0.241165i	$-0.0775294\pi$
$30$		0			0
$31$	−1.14543	−	1.98394i	−0.205725	−	0.356327i	0.744638	−	0.667468i	$-0.232622\pi$
$31$	−1.14543	−	1.98394i	−0.205725	−	0.356327i	−0.950364	+	0.311142i	$0.899289\pi$
$32$		0			0
$33$	−2.47906	+	2.95442i	−0.431548	+	0.514299i
$34$		0			0
$35$	0.532089			0.0899394
$36$		0			0
$37$	−10.2909			−1.69181			−0.845903	−	0.533336i	$-0.820938\pi$
$37$	−10.2909			−1.69181			−0.845903	+	0.533336i	$0.820938\pi$
$38$		0			0
$39$	1.22281	+	3.35965i	0.195807	+	0.537974i
$40$		0			0
$41$	1.29813	+	2.24843i	0.202734	+	0.351146i	0.949409	−	0.314044i	$-0.101684\pi$
$41$	1.29813	+	2.24843i	0.202734	+	0.351146i	−0.746674	+	0.665190i	$0.768351\pi$
$42$		0			0
$43$	−0.145430	+	0.251892i	−0.0221778	+	0.0384131i	−0.876901	−	0.480670i	$-0.840393\pi$
$43$	−0.145430	+	0.251892i	−0.0221778	+	0.0384131i	0.854723	+	0.519084i	$0.173727\pi$
$44$		0			0
$45$	−0.277189	−	1.57202i	−0.0413209	−	0.234342i
$46$		0			0
$47$	−0.213011	+	0.368946i	−0.0310709	+	0.0538163i	−0.881143	−	0.472850i	$-0.843225\pi$
$47$	−0.213011	+	0.368946i	−0.0310709	+	0.0538163i	0.850072	+	0.526667i	$0.176558\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−1.39053	−	0.245188i	−0.194713	−	0.0343332i
$52$		0			0
$53$	1.41147			0.193881			0.0969404	−	0.995290i	$-0.469094\pi$
$53$	1.41147			0.193881			0.0969404	+	0.995290i	$0.469094\pi$
$54$		0			0
$55$	−1.18479			−0.159757
$56$		0			0
$57$	13.5496	+	2.38917i	1.79469	+	0.316453i
$58$		0			0
$59$	−1.71554	−	2.97140i	−0.223344	−	0.386843i	0.732477	−	0.680791i	$-0.238364\pi$
$59$	−1.71554	−	2.97140i	−0.223344	−	0.386843i	−0.955821	+	0.293948i	$0.905031\pi$
$60$		0			0
$61$	5.23783	−	9.07218i	0.670635	−	1.16157i	−0.307089	−	0.951681i	$-0.599355\pi$
$61$	5.23783	−	9.07218i	0.670635	−	1.16157i	0.977724	−	0.209893i	$-0.0673116\pi$
$62$		0			0
$63$	−2.29813	+	1.92836i	−0.289538	+	0.242951i
$64$		0			0
$65$	−0.549163	+	0.951178i	−0.0681153	+	0.117979i
$66$		0			0
$67$	2.10220	+	3.64111i	0.256824	+	0.444833i	0.965389	−	0.260813i	$-0.0839905\pi$
$67$	2.10220	+	3.64111i	0.256824	+	0.444833i	−0.708565	+	0.705645i	$0.750657\pi$
$68$		0			0
$69$	4.02869	+	11.0687i	0.484997	+	1.33252i
$70$		0			0
$71$	12.0865			1.43440			0.717200	−	0.696868i	$-0.245423\pi$
$71$	12.0865			1.43440			0.717200	+	0.696868i	$0.245423\pi$
$72$		0			0
$73$	−9.09152			−1.06408			−0.532041	−	0.846719i	$-0.678575\pi$
$73$	−9.09152			−1.06408			−0.532041	+	0.846719i	$0.678575\pi$
$74$		0			0
$75$	−5.25150	+	6.25849i	−0.606391	+	0.722668i
$76$		0			0
$77$	1.11334	+	1.92836i	0.126877	+	0.219757i
$78$		0			0
$79$	−3.73055	+	6.46151i	−0.419720	+	0.726976i	−0.995911	−	0.0903388i	$-0.971205\pi$
$79$	−3.73055	+	6.46151i	−0.419720	+	0.726976i	0.576191	+	0.817315i	$0.304538\pi$
$80$		0			0
$81$	6.89440	+	5.78509i	0.766044	+	0.642788i
$82$		0			0
$83$	8.76264	−	15.1773i	0.961825	−	1.66593i	0.243911	−	0.969798i	$-0.421570\pi$
$83$	8.76264	−	15.1773i	0.961825	−	1.66593i	0.717914	−	0.696132i	$-0.245097\pi$
$84$		0			0
$85$	−0.216881	−	0.375650i	−0.0235241	−	0.0407449i
$86$		0			0
$87$	−8.32295	+	9.91890i	−0.892314	+	1.06342i
$88$		0			0
$89$	−2.09833			−0.222422			−0.111211	−	0.993797i	$-0.535473\pi$
$89$	−2.09833			−0.222422			−0.111211	+	0.993797i	$0.535473\pi$
$90$		0			0
$91$	2.06418			0.216385
$92$		0			0
$93$	1.35710	+	3.72859i	0.140724	+	0.386637i
$94$		0			0
$95$	2.11334	+	3.66041i	0.216824	+	0.375551i
$96$		0			0
$97$	−5.94222	+	10.2922i	−0.603341	+	1.04502i	0.388970	+	0.921250i	$0.372831\pi$
$97$	−5.94222	+	10.2922i	−0.603341	+	1.04502i	−0.992311	+	0.123767i	$0.960503\pi$
$98$		0			0
$99$	5.11721	−	4.29385i	0.514299	−	0.431548i
$100$		0			0
$101$	−3.68866	+	6.38895i	−0.367036	+	0.635724i	−0.989101	−	0.147241i	$-0.952961\pi$
$101$	−3.68866	+	6.38895i	−0.367036	+	0.635724i	0.622065	+	0.782966i	$0.286294\pi$
$102$		0			0
$103$	3.19594	+	5.53553i	0.314905	+	0.545431i	0.979417	−	0.201846i	$-0.0646940\pi$
$103$	3.19594	+	5.53553i	0.314905	+	0.545431i	−0.664512	+	0.747277i	$0.731361\pi$
$104$		0			0
$105$	−0.907604	−	0.160035i	−0.0885731	−	0.0156178i
$106$		0			0
$107$	−0.0196004			−0.00189484			−0.000947419	−	1.00000i	$-0.500302\pi$
$107$	−0.0196004			−0.00189484			−0.000947419		1.00000i	$0.500302\pi$
$108$		0			0
$109$	1.24897			0.119630			0.0598148	−	0.998209i	$-0.480949\pi$
$109$	1.24897			0.119630			0.0598148	+	0.998209i	$0.480949\pi$
$110$		0			0
$111$	17.5535	+	3.09516i	1.66610	+	0.293779i
$112$		0			0
$113$	6.10607	+	10.5760i	0.574410	+	0.994908i	0.996105	+	0.0881703i	$0.0281020\pi$
$113$	6.10607	+	10.5760i	0.574410	+	0.994908i	−0.421695	+	0.906738i	$0.638565\pi$
$114$		0			0
$115$	−1.80928	+	3.13376i	−0.168716	+	0.292225i
$116$		0			0
$117$	−1.07532	−	6.09845i	−0.0994136	−	0.563802i
$118$		0			0
$119$	−0.407604	+	0.705990i	−0.0373650	+	0.0647180i
$120$		0			0
$121$	3.02094	+	5.23243i	0.274631	+	0.475675i
$122$		0			0
$123$	−1.53802	−	4.22567i	−0.138678	−	0.381016i
$124$		0			0
$125$	−5.17024			−0.462441
$126$		0			0
$127$	1.41921			0.125935			0.0629675	−	0.998016i	$-0.479944\pi$
$127$	1.41921			0.125935			0.0629675	+	0.998016i	$0.479944\pi$
$128$		0			0
$129$	0.323826	−	0.385920i	0.0285113	−	0.0339784i
$130$		0			0
$131$	4.61721	+	7.99724i	0.403408	+	0.698722i	0.994135	−	0.108149i	$-0.0344923\pi$
$131$	4.61721	+	7.99724i	0.403408	+	0.698722i	−0.590727	+	0.806871i	$0.701159\pi$
$132$		0			0
$133$	3.97178	−	6.87933i	0.344397	−	0.596513i
$134$		0			0
$135$			2.76481i			0.237957i
$136$		0			0
$137$	0.975185	−	1.68907i	0.0833157	−	0.144307i	−0.821357	−	0.570415i	$-0.806782\pi$
$137$	0.975185	−	1.68907i	0.0833157	−	0.144307i	0.904672	+	0.426108i	$0.140116\pi$
$138$		0			0
$139$	5.05556	+	8.75649i	0.428807	+	0.742715i	0.996767	−	0.0803403i	$-0.0256007\pi$
$139$	5.05556	+	8.75649i	0.428807	+	0.742715i	−0.567961	+	0.823056i	$0.692267\pi$
$140$		0			0
$141$	0.474308	−	0.565258i	0.0399439	−	0.0476033i
$142$		0			0
$143$	−4.59627			−0.384359
$144$		0			0
$145$	−3.97771			−0.330331
$146$		0			0
$147$	0.592396	+	1.62760i	0.0488600	+	0.134242i
$148$		0			0
$149$	−6.81567	−	11.8051i	−0.558362	−	0.967111i	−0.997633	−	0.0687567i	$-0.978097\pi$
$149$	−6.81567	−	11.8051i	−0.558362	−	0.967111i	0.439272	−	0.898354i	$-0.355237\pi$
$150$		0			0
$151$	4.92262	−	8.52623i	0.400597	−	0.693854i	−0.593201	−	0.805054i	$-0.702136\pi$
$151$	4.92262	−	8.52623i	0.400597	−	0.693854i	0.993798	+	0.111200i	$0.0354694\pi$
$152$		0			0
$153$	2.29813	+	0.836452i	0.185793	+	0.0676231i
$154$		0			0
$155$	−0.609470	+	1.05563i	−0.0489538	+	0.0847905i
$156$		0			0
$157$	−7.58765	−	13.1422i	−0.605560	−	1.04886i	−0.991963	−	0.126531i	$-0.959616\pi$
$157$	−7.58765	−	13.1422i	−0.605560	−	1.04886i	0.386402	−	0.922330i	$-0.373718\pi$
$158$		0			0
$159$	−2.40760	−	0.424525i	−0.190935	−	0.0336671i
$160$		0			0
$161$	6.80066			0.535967
$162$		0			0
$163$	−21.5699			−1.68948			−0.844741	−	0.535176i	$-0.820245\pi$
$163$	−21.5699			−1.68948			−0.844741	+	0.535176i	$0.820245\pi$
$164$		0			0
$165$	2.02094	+	0.356347i	0.157330	+	0.0277416i
$166$		0			0
$167$	−9.97565	−	17.2783i	−0.771939	−	1.33704i	−0.936499	−	0.350671i	$-0.885954\pi$
$167$	−9.97565	−	17.2783i	−0.771939	−	1.33704i	0.164560	−	0.986367i	$-0.447380\pi$
$168$		0			0
$169$	4.36959	−	7.56834i	0.336122	−	0.582180i
$170$		0			0
$171$	−22.3935	−	8.15058i	−1.71248	−	0.623290i
$172$		0			0
$173$	−0.515015	+	0.892032i	−0.0391558	+	0.0678199i	−0.884939	−	0.465707i	$-0.845800\pi$
$173$	−0.515015	+	0.892032i	−0.0391558	+	0.0678199i	0.845783	+	0.533527i	$0.179134\pi$
$174$		0			0
$175$	2.35844	+	4.08494i	0.178281	+	0.308792i
$176$		0			0
$177$	2.03256	+	5.58440i	0.152776	+	0.419749i
$178$		0			0
$179$	26.4962			1.98042			0.990209	−	0.139593i	$-0.0445794\pi$
$179$	26.4962			1.98042			0.990209	+	0.139593i	$0.0445794\pi$
$180$		0			0
$181$	−1.35504			−0.100719			−0.0503596	−	0.998731i	$-0.516037\pi$
$181$	−1.35504			−0.100719			−0.0503596	+	0.998731i	$0.516037\pi$
$182$		0			0
$183$	−11.6630	+	13.8994i	−0.862152	+	1.02747i
$184$		0			0
$185$	2.73783	+	4.74205i	0.201289	+	0.348643i
$186$		0			0
$187$	0.907604	−	1.57202i	0.0663706	−	0.114957i
$188$		0			0
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$		0			0
$191$	3.10354	−	5.37549i	0.224564	−	0.388957i	−0.731624	−	0.681708i	$-0.761237\pi$
$191$	3.10354	−	5.37549i	0.224564	−	0.388957i	0.956189	+	0.292751i	$0.0945708\pi$
$192$		0			0
$193$	3.34864	+	5.80002i	0.241040	+	0.417494i	0.961011	−	0.276510i	$-0.0891780\pi$
$193$	3.34864	+	5.80002i	0.241040	+	0.417494i	−0.719971	+	0.694005i	$0.755845\pi$
$194$		0			0
$195$	1.22281	−	1.45729i	0.0875673	−	0.104359i
$196$		0			0
$197$	−19.0223			−1.35528			−0.677641	−	0.735393i	$-0.736998\pi$
$197$	−19.0223			−1.35528			−0.677641	+	0.735393i	$0.736998\pi$
$198$		0			0
$199$	7.99319			0.566622			0.283311	−	0.959028i	$-0.408567\pi$
$199$	7.99319			0.566622			0.283311	+	0.959028i	$0.408567\pi$
$200$		0			0
$201$	−2.49067	−	6.84305i	−0.175678	−	0.482672i
$202$		0			0
$203$	3.73783	+	6.47410i	0.262344	+	0.454393i
$204$		0			0
$205$	0.690722	−	1.19637i	0.0482421	−	0.0835578i
$206$		0			0
$207$	−3.54277	−	20.0920i	−0.246239	−	1.39649i
$208$		0			0
$209$	−8.84389	+	15.3181i	−0.611745	+	1.05957i
$210$		0			0
$211$	11.3648	+	19.6845i	0.782388	+	1.35514i	0.930547	+	0.366172i	$0.119332\pi$
$211$	11.3648	+	19.6845i	0.782388	+	1.35514i	−0.148160	+	0.988963i	$0.547335\pi$
$212$		0			0
$213$	−20.6163	−	3.63522i	−1.41261	−	0.249081i
$214$		0			0
$215$	0.154763			0.0105548
$216$		0			0
$217$	2.29086			0.155514
$218$		0			0
$219$	15.5077	+	2.73443i	1.04792	+	0.184776i
$220$		0			0
$221$	−0.841367	−	1.45729i	−0.0565964	−	0.0980279i
$222$		0			0
$223$	10.2442	−	17.7435i	0.686004	−	1.18819i	−0.287116	−	0.957896i	$-0.592697\pi$
$223$	10.2442	−	17.7435i	0.686004	−	1.18819i	0.973120	−	0.230298i	$-0.0739700\pi$
$224$		0			0
$225$	10.8400	−	9.09586i	0.722668	−	0.606391i
$226$		0			0
$227$	−5.81655	+	10.0746i	−0.386058	+	0.668672i	−0.991915	−	0.126901i	$-0.959497\pi$
$227$	−5.81655	+	10.0746i	−0.386058	+	0.668672i	0.605857	+	0.795573i	$0.292830\pi$
$228$		0			0
$229$	−1.20233	−	2.08250i	−0.0794524	−	0.137616i	0.823561	−	0.567227i	$-0.191984\pi$
$229$	−1.20233	−	2.08250i	−0.0794524	−	0.137616i	−0.903014	+	0.429612i	$0.858651\pi$
$230$		0			0
$231$	−1.31908	−	3.62414i	−0.0867890	−	0.238451i
$232$		0			0
$233$	−16.6313			−1.08956			−0.544778	−	0.838580i	$-0.683386\pi$
$233$	−16.6313			−1.08956			−0.544778	+	0.838580i	$0.683386\pi$
$234$		0			0
$235$	0.226682			0.0147871
$236$		0			0
$237$	8.30675	−	9.89960i	0.539581	−	0.643048i
$238$		0			0
$239$	−13.3229	−	23.0760i	−0.861790	−	1.49266i	−0.870200	−	0.492699i	$-0.836010\pi$
$239$	−13.3229	−	23.0760i	−0.861790	−	1.49266i	0.00840979	−	0.999965i	$-0.497323\pi$
$240$		0			0
$241$	6.27972	−	10.8768i	0.404512	−	0.700635i	−0.589753	−	0.807584i	$-0.700775\pi$
$241$	6.27972	−	10.8768i	0.404512	−	0.700635i	0.994265	+	0.106949i	$0.0341081\pi$
$242$		0			0
$243$	−10.0201	−	11.9415i	−0.642788	−	0.766044i
$244$		0			0
$245$	−0.266044	+	0.460802i	−0.0169970	+	0.0294396i
$246$		0			0
$247$	8.19846	+	14.2002i	0.521656	+	0.903534i
$248$		0			0
$249$	−19.5116	+	23.2530i	−1.23650	+	1.47360i
$250$		0			0
$251$	18.7023			1.18048			0.590240	−	0.807228i	$-0.299033\pi$
$251$	18.7023			1.18048			0.590240	+	0.807228i	$0.299033\pi$
$252$		0			0
$253$	−15.1429			−0.952026
$254$		0			0
$255$	0.256959	+	0.705990i	0.0160914	+	0.0442108i
$256$		0			0
$257$	6.57398	+	11.3865i	0.410073	+	0.710268i	0.994897	−	0.100892i	$-0.0321697\pi$
$257$	6.57398	+	11.3865i	0.410073	+	0.710268i	−0.584824	+	0.811160i	$0.698836\pi$
$258$		0			0
$259$	5.14543	−	8.91215i	0.319721	−	0.553774i
$260$		0			0
$261$	17.1800	−	14.4158i	1.06342	−	0.892314i
$262$		0			0
$263$	−11.4474	+	19.8275i	−0.705879	+	1.22262i	0.260494	+	0.965475i	$0.416114\pi$
$263$	−11.4474	+	19.8275i	−0.705879	+	1.22262i	−0.966373	+	0.257143i	$0.917219\pi$
$264$		0			0
$265$	−0.375515	−	0.650411i	−0.0230677	−	0.0399544i
$266$		0			0
$267$	3.57919	+	0.631108i	0.219043	+	0.0386232i
$268$		0			0
$269$	−26.3432			−1.60617			−0.803086	−	0.595863i	$-0.796810\pi$
$269$	−26.3432			−1.60617			−0.803086	+	0.595863i	$0.796810\pi$
$270$		0			0
$271$	10.7246			0.651474			0.325737	−	0.945460i	$-0.394388\pi$
$271$	10.7246			0.651474			0.325737	+	0.945460i	$0.394388\pi$
$272$		0			0
$273$	−3.52094	−	0.620838i	−0.213097	−	0.0375748i
$274$		0			0
$275$	−5.25150	−	9.09586i	−0.316677	−	0.548501i
$276$		0			0
$277$	2.49138	−	4.31520i	0.149693	−	0.259275i	−0.781421	−	0.624004i	$-0.785505\pi$
$277$	2.49138	−	4.31520i	0.149693	−	0.259275i	0.931114	+	0.364729i	$0.118838\pi$
$278$		0			0
$279$	−1.19341	−	6.76817i	−0.0714476	−	0.405200i
$280$		0			0
$281$	4.30928	−	7.46389i	0.257070	−	0.445258i	−0.708386	−	0.705826i	$-0.750576\pi$
$281$	4.30928	−	7.46389i	0.257070	−	0.445258i	0.965456	+	0.260567i	$0.0839096\pi$
$282$		0			0
$283$	1.18227	+	2.04775i	0.0702784	+	0.121726i	0.899023	−	0.437901i	$-0.144278\pi$
$283$	1.18227	+	2.04775i	0.0702784	+	0.121726i	−0.828745	+	0.559627i	$0.810945\pi$
$284$		0			0
$285$	−2.50387	−	6.87933i	−0.148316	−	0.407496i
$286$		0			0
$287$	−2.59627			−0.153253
$288$		0			0
$289$	−16.3354			−0.960908
$290$		0			0
$291$	13.2314	−	15.7686i	0.775640	−	0.924372i
$292$		0			0
$293$	8.73783	+	15.1344i	0.510469	+	0.884159i	0.999926	+	0.0121313i	$0.00386162\pi$
$293$	8.73783	+	15.1344i	0.510469	+	0.884159i	−0.489457	+	0.872027i	$0.662805\pi$
$294$		0			0
$295$	−0.912818	+	1.58105i	−0.0531463	+	0.0920522i
$296$		0			0
$297$	−10.0201	+	5.78509i	−0.581423	+	0.335685i
$298$		0			0
$299$	−7.01889	+	12.1571i	−0.405913	+	0.703061i
$300$		0			0
$301$	−0.145430	−	0.251892i	−0.00838243	−	0.0145188i
$302$		0			0
$303$	8.21348	−	9.78844i	0.471852	−	0.562331i
$304$		0			0
$305$	−5.57398			−0.319165
$306$		0			0
$307$	25.6928			1.46637			0.733184	−	0.680030i	$-0.238033\pi$
$307$	25.6928			1.46637			0.733184	+	0.680030i	$0.238033\pi$
$308$		0			0
$309$	−3.78652	−	10.4034i	−0.215408	−	0.591828i
$310$		0			0
$311$	3.91400	+	6.77925i	0.221943	+	0.384416i	0.955398	−	0.295322i	$-0.0954269\pi$
$311$	3.91400	+	6.77925i	0.221943	+	0.384416i	−0.733455	+	0.679738i	$0.762094\pi$
$312$		0			0
$313$	9.51620	−	16.4825i	0.537887	−	0.931648i	−0.461130	−	0.887332i	$-0.652556\pi$
$313$	9.51620	−	16.4825i	0.537887	−	0.931648i	0.999018	−	0.0443156i	$-0.0141107\pi$
$314$		0			0
$315$	1.50000	+	0.545955i	0.0845154	+	0.0307611i
$316$		0			0
$317$	15.5890	−	27.0009i	0.875565	−	1.51652i	0.0194055	−	0.999812i	$-0.493823\pi$
$317$	15.5890	−	27.0009i	0.875565	−	1.51652i	0.856160	−	0.516711i	$-0.172844\pi$
$318$		0			0
$319$	−8.32295	−	14.4158i	−0.465996	−	0.807128i
$320$		0			0
$321$	0.0334331	+	0.00589515i	0.00186605	+	0.000329035i
$322$		0			0
$323$	−6.47565			−0.360315
$324$		0			0
$325$	−9.73648			−0.540083
$326$		0			0
$327$	−2.13041	−	0.375650i	−0.117812	−	0.0207735i
$328$		0			0
$329$	−0.213011	−	0.368946i	−0.0117437	−	0.0203406i
$330$		0			0
$331$	−13.4427	+	23.2834i	−0.738877	+	1.27977i	0.214125	+	0.976806i	$0.431310\pi$
$331$	−13.4427	+	23.2834i	−0.738877	+	1.27977i	−0.953001	+	0.302966i	$0.902023\pi$
$332$		0			0
$333$	−29.0107	−	10.5590i	−1.58978	−	0.578632i
$334$		0			0
$335$	1.11856	−	1.93739i	0.0611132	−	0.105851i
$336$		0			0
$337$	3.08512	+	5.34359i	0.168057	+	0.291084i	0.937737	−	0.347347i	$-0.112917\pi$
$337$	3.08512	+	5.34359i	0.168057	+	0.291084i	−0.769679	+	0.638431i	$0.779584\pi$
$338$		0			0
$339$	−7.23442	−	19.8764i	−0.392920	−	1.07954i
$340$		0			0
$341$	−5.10101			−0.276235
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	4.02869	−	4.80120i	0.216897	−	0.258488i
$346$		0			0
$347$	7.06330	+	12.2340i	0.379178	+	0.656755i	0.990943	−	0.134284i	$-0.0428735\pi$
$347$	7.06330	+	12.2340i	0.379178	+	0.656755i	−0.611765	+	0.791040i	$0.709540\pi$
$348$		0			0
$349$	−12.3628	+	21.4130i	−0.661764	+	1.14621i	0.318387	+	0.947961i	$0.396859\pi$
$349$	−12.3628	+	21.4130i	−0.661764	+	1.14621i	−0.980152	+	0.198249i	$0.936475\pi$
$350$		0			0
$351$			10.7258i			0.572500i
$352$		0			0
$353$	−9.55097	+	16.5428i	−0.508347	+	0.880483i	0.491606	+	0.870818i	$0.336410\pi$
$353$	−9.55097	+	16.5428i	−0.508347	+	0.880483i	−0.999953	+	0.00966532i	$0.996923\pi$
$354$		0			0
$355$	−3.21554	−	5.56947i	−0.170663	−	0.295597i
$356$		0			0
$357$	0.907604	−	1.08164i	0.0480355	−	0.0572465i
$358$		0			0
$359$	−19.3233			−1.01984			−0.509921	−	0.860221i	$-0.670325\pi$
$359$	−19.3233			−1.01984			−0.509921	+	0.860221i	$0.670325\pi$
$360$		0			0
$361$	44.1002			2.32106
$362$		0			0
$363$	−3.57919	−	9.83375i	−0.187859	−	0.516138i
$364$		0			0
$365$	2.41875	+	4.18939i	0.126603	+	0.219283i
$366$		0			0
$367$	17.0180	−	29.4761i	0.888333	−	1.53864i	0.0464873	−	0.998919i	$-0.485197\pi$
$367$	17.0180	−	29.4761i	0.888333	−	1.53864i	0.841845	−	0.539719i	$-0.181469\pi$
$368$		0			0
$369$	1.35251	+	7.67047i	0.0704089	+	0.399309i
$370$		0			0
$371$	−0.705737	+	1.22237i	−0.0366400	+	0.0634624i
$372$		0			0
$373$	10.5765	+	18.3190i	0.547631	+	0.948524i	0.998436	+	0.0559019i	$0.0178034\pi$
$373$	10.5765	+	18.3190i	0.547631	+	0.948524i	−0.450806	+	0.892622i	$0.648863\pi$
$374$		0			0
$375$	8.81908	+	1.55504i	0.455415	+	0.0803020i
$376$		0			0
$377$	−15.4311			−0.794741
$378$		0			0
$379$	−11.4757			−0.589465			−0.294732	−	0.955580i	$-0.595230\pi$
$379$	−11.4757			−0.589465			−0.294732	+	0.955580i	$0.595230\pi$
$380$		0			0
$381$	−2.42081	−	0.426854i	−0.124022	−	0.0218684i
$382$		0			0
$383$	2.41400	+	4.18117i	0.123350	+	0.213648i	0.921087	−	0.389358i	$-0.127303\pi$
$383$	2.41400	+	4.18117i	0.123350	+	0.213648i	−0.797737	+	0.603006i	$0.793970\pi$
$384$		0			0
$385$	0.592396	−	1.02606i	0.0301913	−	0.0522929i
$386$		0			0
$387$	−0.668434	+	0.560882i	−0.0339784	+	0.0285113i
$388$		0			0
$389$	−8.01367	+	13.8801i	−0.406309	+	0.703748i	−0.994473	−	0.104994i	$-0.966518\pi$
$389$	−8.01367	+	13.8801i	−0.406309	+	0.703748i	0.588164	+	0.808742i	$0.299851\pi$
$390$		0			0
$391$	−2.77197	−	4.80120i	−0.140185	−	0.242807i
$392$		0			0
$393$	−5.47044	−	15.0299i	−0.275947	−	0.758158i
$394$		0			0
$395$	3.96997			0.199751
$396$		0			0
$397$	35.5827			1.78584			0.892921	−	0.450213i	$-0.148652\pi$
$397$	35.5827			1.78584			0.892921	+	0.450213i	$0.148652\pi$
$398$		0			0
$399$	−8.84389	+	10.5397i	−0.442748	+	0.527647i
$400$		0			0
$401$	−14.0792	−	24.3859i	−0.703081	−	1.21777i	−0.967380	−	0.253332i	$-0.918474\pi$
$401$	−14.0792	−	24.3859i	−0.703081	−	1.21777i	0.264298	−	0.964441i	$-0.414860\pi$
$402$		0			0
$403$	−2.36437	+	4.09521i	−0.117778	+	0.203997i
$404$		0			0
$405$	0.831566	−	4.71605i	0.0413209	−	0.234342i
$406$		0			0
$407$	−11.4572	+	19.8445i	−0.567914	+	0.983656i
$408$		0			0
$409$	13.3969	+	23.2042i	0.662435	+	1.14737i	0.979974	+	0.199126i	$0.0638104\pi$
$409$	13.3969	+	23.2042i	0.662435	+	1.14737i	−0.317538	+	0.948245i	$0.602856\pi$
$410$		0			0
$411$	−2.17143	+	2.58781i	−0.107109	+	0.127647i
$412$		0			0
$413$	3.43107			0.168832
$414$		0			0
$415$	−9.32501			−0.457747
$416$		0			0
$417$	−5.98979	−	16.4568i	−0.293321	−	0.805893i
$418$		0			0
$419$	−10.0608	−	17.4258i	−0.491501	−	0.851305i	0.508451	−	0.861091i	$-0.330218\pi$
$419$	−10.0608	−	17.4258i	−0.491501	−	0.851305i	−0.999952	+	0.00978617i	$0.996885\pi$
$420$		0			0
$421$	4.52616	−	7.83954i	0.220591	−	0.382076i	−0.734396	−	0.678721i	$-0.762535\pi$
$421$	4.52616	−	7.83954i	0.220591	−	0.382076i	0.954988	+	0.296645i	$0.0958679\pi$
$422$		0			0
$423$	−0.979055	+	0.821525i	−0.0476033	+	0.0399439i
$424$		0			0
$425$	1.92262	−	3.33007i	0.0932607	−	0.161532i
$426$		0			0
$427$	5.23783	+	9.07218i	0.253476	+	0.439034i
$428$		0			0
$429$	7.84002	+	1.38241i	0.378520	+	0.0667433i
$430$		0			0
$431$	−19.1952			−0.924601			−0.462301	−	0.886723i	$-0.652976\pi$
$431$	−19.1952			−0.924601			−0.462301	+	0.886723i	$0.652976\pi$
$432$		0			0
$433$	−25.5080			−1.22584			−0.612919	−	0.790146i	$-0.710005\pi$
$433$	−25.5080			−1.22584			−0.612919	+	0.790146i	$0.710005\pi$
$434$		0			0
$435$	6.78493	+	1.19637i	0.325312	+	0.0573614i
$436$		0			0
$437$	27.0107	+	46.7840i	1.29210	+	2.23798i
$438$		0			0
$439$	9.45471	−	16.3760i	0.451249	−	0.781585i	−0.547215	−	0.836992i	$-0.684312\pi$
$439$	9.45471	−	16.3760i	0.451249	−	0.781585i	0.998464	+	0.0554064i	$0.0176455\pi$
$440$		0			0
$441$	−0.520945	−	2.95442i	−0.0248069	−	0.140687i
$442$		0			0
$443$	−10.3131	+	17.8629i	−0.489992	+	0.848692i	−0.999934	−	0.0115174i	$-0.996334\pi$
$443$	−10.3131	+	17.8629i	−0.489992	+	0.848692i	0.509941	+	0.860209i	$0.329667\pi$
$444$		0			0
$445$	0.558248	+	0.966914i	0.0264635	+	0.0458361i
$446$		0			0
$447$	8.07516	+	22.1863i	0.381942	+	1.04938i
$448$		0			0
$449$	34.3327			1.62026			0.810131	−	0.586248i	$-0.199396\pi$
$449$	34.3327			1.62026			0.810131	+	0.586248i	$0.199396\pi$
$450$		0			0
$451$	5.78106			0.272219
$452$		0			0
$453$	−10.9611	+	13.0629i	−0.514998	+	0.613750i
$454$		0			0
$455$	−0.549163	−	0.951178i	−0.0257452	−	0.0445919i
$456$		0			0
$457$	0.922152	−	1.59721i	0.0431364	−	0.0747145i	−0.843651	−	0.536892i	$-0.819598\pi$
$457$	0.922152	−	1.59721i	0.0431364	−	0.0747145i	0.886788	+	0.462177i	$0.152932\pi$
$458$		0			0
$459$	−3.66843	−	2.11797i	−0.171228	−	0.0988584i
$460$		0			0
$461$	16.5582	−	28.6797i	0.771194	−	1.33575i	−0.165714	−	0.986174i	$-0.552993\pi$
$461$	16.5582	−	28.6797i	0.771194	−	1.33575i	0.936909	−	0.349574i	$-0.113674\pi$
$462$		0			0
$463$	2.14631	+	3.71751i	0.0997473	+	0.172767i	0.911580	−	0.411123i	$-0.134863\pi$
$463$	2.14631	+	3.71751i	0.0997473	+	0.172767i	−0.811833	+	0.583890i	$0.801530\pi$
$464$		0			0
$465$	1.35710	−	1.61732i	0.0629338	−	0.0750016i
$466$		0			0
$467$	31.7347			1.46851			0.734254	−	0.678875i	$-0.237532\pi$
$467$	31.7347			1.46851			0.734254	+	0.678875i	$0.237532\pi$
$468$		0			0
$469$	−4.20439			−0.194141
$470$		0			0
$471$	8.98979	+	24.6992i	0.414228	+	1.13808i
$472$		0			0
$473$	0.323826	+	0.560882i	0.0148895	+	0.0257894i
$474$		0			0
$475$	−18.7344	+	32.4490i	−0.859594	+	1.48886i
$476$		0			0
$477$	3.97906	+	1.44826i	0.182188	+	0.0663112i
$478$		0			0
$479$	9.54845	−	16.5384i	0.436280	−	0.755659i	−0.561119	−	0.827735i	$-0.689629\pi$
$479$	9.54845	−	16.5384i	0.436280	−	0.755659i	0.997399	+	0.0720762i	$0.0229625\pi$
$480$		0			0
$481$	10.6211	+	18.3963i	0.484280	+	0.838797i
$482$		0			0
$483$	−11.6001	−	2.04542i	−0.527825	−	0.0930697i
$484$		0			0
$485$	6.32358			0.287139
$486$		0			0
$487$	−1.40198			−0.0635297			−0.0317649	−	0.999495i	$-0.510113\pi$
$487$	−1.40198			−0.0635297			−0.0317649	+	0.999495i	$0.510113\pi$
$488$		0			0
$489$	36.7925	+	6.48751i	1.66381	+	0.293375i
$490$		0			0
$491$	10.4586	+	18.1148i	0.471989	+	0.817509i	0.999486	−	0.0320477i	$-0.0102029\pi$
$491$	10.4586	+	18.1148i	0.471989	+	0.817509i	−0.527497	+	0.849557i	$0.676870\pi$
$492$		0			0
$493$	3.04710	−	5.27774i	0.137235	−	0.237697i
$494$		0			0
$495$	−3.34002	−	1.21567i	−0.150123	−	0.0546402i
$496$		0			0
$497$	−6.04323	+	10.4672i	−0.271076	+	0.469518i
$498$		0			0
$499$	11.3105	+	19.5903i	0.506326	+	0.876982i	0.999973	+	0.00731977i	$0.00232998\pi$
$499$	11.3105	+	19.5903i	0.506326	+	0.876982i	−0.493647	+	0.869662i	$0.664337\pi$
$500$		0			0
$501$	11.8191	+	32.4726i	0.528037	+	1.45077i
$502$		0			0
$503$	−21.2327			−0.946718			−0.473359	−	0.880870i	$-0.656959\pi$
$503$	−21.2327			−0.946718			−0.473359	+	0.880870i	$0.656959\pi$
$504$		0			0
$505$	3.92539			0.174678
$506$		0			0
$507$	−9.72967	+	11.5954i	−0.432110	+	0.514969i
$508$		0			0
$509$	2.94697	+	5.10430i	0.130622	+	0.226244i	0.923917	−	0.382594i	$-0.124969\pi$
$509$	2.94697	+	5.10430i	0.130622	+	0.226244i	−0.793295	+	0.608838i	$0.791636\pi$
$510$		0			0
$511$	4.54576	−	7.87349i	0.201093	−	0.348303i
$512$		0			0
$513$	35.7460	+	20.6380i	1.57823	+	0.911189i
$514$		0			0
$515$	1.70052	−	2.94539i	0.0749340	−	0.129789i
$516$		0			0
$517$	0.474308	+	0.821525i	0.0208600	+	0.0361306i
$518$		0			0
$519$	1.14677	−	1.36667i	0.0503378	−	0.0599902i
$520$		0			0
$521$	42.5039			1.86213			0.931065	−	0.364852i	$-0.118881\pi$
$521$	42.5039			1.86213			0.931065	+	0.364852i	$0.118881\pi$
$522$		0			0
$523$	−23.7716			−1.03946			−0.519729	−	0.854331i	$-0.673967\pi$
$523$	−23.7716			−1.03946			−0.519729	+	0.854331i	$0.673967\pi$
$524$		0			0
$525$	−2.79426	−	7.67717i	−0.121952	−	0.335059i
$526$		0			0
$527$	−0.933763	−	1.61732i	−0.0406753	−	0.0704518i
$528$		0			0
$529$	−11.6245	+	20.1342i	−0.505412	+	0.875400i
$530$		0			0
$531$	−1.78740	−	10.1368i	−0.0775665	−	0.439902i
$532$		0			0
$533$	2.67958	−	4.64117i	0.116065	−	0.201031i
$534$		0			0
$535$	0.00521457	+	0.00903189i	0.000225445	+	0.000390483i
$536$		0			0
$537$	−45.1955	−	7.96919i	−1.95033	−	0.343896i
$538$		0			0
$539$	−2.22668			−0.0959100
$540$		0			0
$541$	22.6560			0.974058			0.487029	−	0.873386i	$-0.338081\pi$
$541$	22.6560			0.974058			0.487029	+	0.873386i	$0.338081\pi$
$542$		0			0
$543$	2.31134	+	0.407551i	0.0991890	+	0.0174897i
$544$		0			0
$545$	−0.332282	−	0.575529i	−0.0142334	−	0.0246529i
$546$		0			0
$547$	2.13176	−	3.69232i	0.0911474	−	0.157872i	−0.816847	−	0.576855i	$-0.804280\pi$
$547$	2.13176	−	3.69232i	0.0911474	−	0.157872i	0.907994	+	0.418983i	$0.137613\pi$
$548$		0			0
$549$	24.0744	−	20.2009i	1.02747	−	0.862152i
$550$		0			0
$551$	−29.6917	+	51.4275i	−1.26491	+	2.19088i
$552$		0			0
$553$	−3.73055	−	6.46151i	−0.158639	−	0.274771i
$554$		0			0
$555$	−3.24376	−	8.91215i	−0.137690	−	0.378300i
$556$		0			0
$557$	−2.90404			−0.123048			−0.0615240	−	0.998106i	$-0.519596\pi$
$557$	−2.90404			−0.123048			−0.0615240	+	0.998106i	$0.519596\pi$
$558$		0			0
$559$	0.600385			0.0253936
$560$		0			0
$561$	−2.02094	+	2.40847i	−0.0853243	+	0.101686i
$562$		0			0
$563$	−5.16978	−	8.95432i	−0.217880	−	0.377380i	0.736280	−	0.676678i	$-0.236581\pi$
$563$	−5.16978	−	8.95432i	−0.217880	−	0.377380i	−0.954160	+	0.299298i	$0.903248\pi$
$564$		0			0
$565$	3.24897	−	5.62738i	0.136685	−	0.236746i
$566$		0			0
$567$	−8.45723	+	3.07818i	−0.355170	+	0.129271i
$568$		0			0
$569$	17.3530	−	30.0562i	0.727475	−	1.26002i	−0.230473	−	0.973079i	$-0.574027\pi$
$569$	17.3530	−	30.0562i	0.727475	−	1.26002i	0.957947	−	0.286944i	$-0.0926395\pi$
$570$		0			0
$571$	−21.2135	−	36.7428i	−0.887756	−	1.53764i	−0.842521	−	0.538663i	$-0.818930\pi$
$571$	−21.2135	−	36.7428i	−0.887756	−	1.53764i	−0.0452350	−	0.998976i	$-0.514404\pi$
$572$		0			0
$573$	−6.91060	+	8.23573i	−0.288694	+	0.344052i
$574$		0			0
$575$	−32.0779			−1.33774
$576$		0			0
$577$	23.7811			0.990018			0.495009	−	0.868888i	$-0.335165\pi$
$577$	23.7811			0.990018			0.495009	+	0.868888i	$0.335165\pi$
$578$		0			0
$579$	−3.96744	−	10.9005i	−0.164881	−	0.453008i
$580$		0			0
$581$	8.76264	+	15.1773i	0.363536	+	0.629662i
$582$		0			0
$583$	1.57145	−	2.72183i	0.0650829	−	0.112727i
$584$		0			0
$585$	−2.52410	+	2.11797i	−0.104359	+	0.0875673i
$586$		0			0
$587$	−6.10560	+	10.5752i	−0.252005	+	0.436486i	−0.964078	−	0.265620i	$-0.914423\pi$
$587$	−6.10560	+	10.5752i	−0.252005	+	0.436486i	0.712073	+	0.702106i	$0.247757\pi$
$588$		0			0
$589$	9.09879	+	15.7596i	0.374909	+	0.649362i
$590$		0			0
$591$	32.4470	+	5.72129i	1.33469	+	0.235342i
$592$		0			0
$593$	−14.2139			−0.583694			−0.291847	−	0.956465i	$-0.594270\pi$
$593$	−14.2139			−0.583694			−0.291847	+	0.956465i	$0.594270\pi$
$594$		0			0
$595$	0.433763			0.0177825
$596$		0			0
$597$	−13.6343	−	2.40409i	−0.558014	−	0.0983930i
$598$		0			0
$599$	9.34730	+	16.1900i	0.381920	+	0.661505i	0.991337	−	0.131345i	$-0.0419296\pi$
$599$	9.34730	+	16.1900i	0.381920	+	0.661505i	−0.609417	+	0.792850i	$0.708596\pi$
$600$		0			0
$601$	−19.7096	+	34.1380i	−0.803972	+	1.39252i	0.113011	+	0.993594i	$0.463950\pi$
$601$	−19.7096	+	34.1380i	−0.803972	+	1.39252i	−0.916983	+	0.398926i	$0.869383\pi$
$602$		0			0
$603$	2.19026	+	12.4216i	0.0891941	+	0.505845i
$604$		0			0
$605$	1.60741	−	2.78412i	0.0653506	−	0.113190i
$606$		0			0
$607$	−15.1682	−	26.2721i	−0.615658	−	1.06635i	−0.990269	−	0.139168i	$-0.955557\pi$
$607$	−15.1682	−	26.2721i	−0.615658	−	1.06635i	0.374611	−	0.927182i	$-0.377776\pi$
$608$		0			0
$609$	−4.42855	−	12.1673i	−0.179454	−	0.493045i
$610$		0			0
$611$	0.879385			0.0355761
$612$		0			0
$613$	4.91622			0.198564			0.0992822	−	0.995059i	$-0.468345\pi$
$613$	4.91622			0.198564			0.0992822	+	0.995059i	$0.468345\pi$
$614$		0			0
$615$	−1.53802	+	1.83294i	−0.0620189	+	0.0739112i
$616$		0			0
$617$	−15.9440	−	27.6159i	−0.641882	−	1.11177i	−0.985012	−	0.172485i	$-0.944820\pi$
$617$	−15.9440	−	27.6159i	−0.641882	−	1.11177i	0.343130	−	0.939288i	$-0.388513\pi$
$618$		0			0
$619$	0.109470	−	0.189608i	0.00439999	−	0.00762100i	−0.863817	−	0.503806i	$-0.831933\pi$
$619$	0.109470	−	0.189608i	0.00439999	−	0.00762100i	0.868217	+	0.496185i	$0.165266\pi$
$620$		0			0
$621$			35.3373i			1.41804i
$622$		0			0
$623$	1.04916	−	1.81720i	0.0420338	−	0.0728047i
$624$		0			0
$625$	−10.4167	−	18.0422i	−0.416668	−	0.721689i
$626$		0			0
$627$	19.6925	−	23.4686i	0.786444	−	0.937247i
$628$		0			0
$629$	−8.38919			−0.334499
$630$		0			0
$631$	−22.1685			−0.882514			−0.441257	−	0.897381i	$-0.645467\pi$
$631$	−22.1685			−0.882514			−0.441257	+	0.897381i	$0.645467\pi$
$632$		0			0
$633$	−13.4650	−	36.9947i	−0.535185	−	1.47041i
$634$		0			0
$635$	−0.377574	−	0.653978i	−0.0149836	−	0.0259523i
$636$		0			0
$637$	−1.03209	+	1.78763i	−0.0408929	+	0.0708285i
$638$		0			0
$639$	34.0727	+	12.4014i	1.34789	+	0.490594i
$640$		0			0
$641$	15.4996	−	26.8461i	0.612197	−	1.06036i	−0.378672	−	0.925531i	$-0.623619\pi$
$641$	15.4996	−	26.8461i	0.612197	−	1.06036i	0.990869	−	0.134825i	$-0.0430474\pi$
$642$		0			0
$643$	−21.6591	−	37.5147i	−0.854152	−	1.47943i	−0.877430	−	0.479705i	$-0.840744\pi$
$643$	−21.6591	−	37.5147i	−0.854152	−	1.47943i	0.0232784	−	0.999729i	$-0.492590\pi$
$644$		0			0
$645$	−0.263985	−	0.0465477i	−0.0103944	−	0.00183281i
$646$		0			0
$647$	24.8658			0.977574			0.488787	−	0.872403i	$-0.337439\pi$
$647$	24.8658			0.977574			0.488787	+	0.872403i	$0.337439\pi$
$648$		0			0
$649$	−7.63991			−0.299893
$650$		0			0
$651$	−3.90760	−	0.689016i	−0.153151	−	0.0270047i
$652$		0			0
$653$	−10.8883	−	18.8591i	−0.426092	−	0.738014i	0.570429	−	0.821347i	$-0.306777\pi$
$653$	−10.8883	−	18.8591i	−0.426092	−	0.738014i	−0.996522	+	0.0833330i	$0.973443\pi$
$654$		0			0
$655$	2.45677	−	4.25524i	0.0959938	−	0.166266i
$656$		0			0
$657$	−25.6297	−	9.32845i	−0.999910	−	0.363937i
$658$		0			0
$659$	20.6177	−	35.7109i	0.803151	−	1.39110i	−0.114382	−	0.993437i	$-0.536489\pi$
$659$	20.6177	−	35.7109i	0.803151	−	1.39110i	0.917532	−	0.397661i	$-0.130178\pi$
$660$		0			0
$661$	−11.6959	−	20.2580i	−0.454919	−	0.787943i	0.543764	−	0.839238i	$-0.316999\pi$
$661$	−11.6959	−	20.2580i	−0.454919	−	0.787943i	−0.998684	+	0.0512948i	$0.983665\pi$
$662$		0			0
$663$	0.996845	+	2.73881i	0.0387142	+	0.106367i
$664$		0			0
$665$	−4.22668			−0.163904
$666$		0			0
$667$	−50.8394			−1.96851
$668$		0			0
$669$	−22.8106	+	27.1846i	−0.881910	+	1.05102i
$670$		0			0
$671$	−11.6630	−	20.2009i	−0.450244	−	0.779845i
$672$		0			0
$673$	2.22621	−	3.85592i	0.0858143	−	0.148635i	−0.819924	−	0.572473i	$-0.805984\pi$
$673$	2.22621	−	3.85592i	0.0858143	−	0.148635i	0.905738	+	0.423838i	$0.139317\pi$
$674$		0			0
$675$	−21.2260	+	12.2548i	−0.816988	+	0.471688i
$676$		0			0
$677$	21.6172	−	37.4421i	0.830817	−	1.43902i	−0.0665744	−	0.997781i	$-0.521207\pi$
$677$	21.6172	−	37.4421i	0.830817	−	1.43902i	0.897391	−	0.441236i	$-0.145460\pi$
$678$		0			0
$679$	−5.94222	−	10.2922i	−0.228041	−	0.394979i
$680$		0			0
$681$	12.9516	−	15.4351i	0.496307	−	0.591475i
$682$		0			0
$683$	1.79797			0.0687975			0.0343987	−	0.999408i	$-0.489048\pi$
$683$	1.79797			0.0687975			0.0343987	+	0.999408i	$0.489048\pi$
$684$		0			0
$685$	−1.03777			−0.0396512
$686$		0			0
$687$	1.42452	+	3.91382i	0.0543487	+	0.149322i
$688$		0			0
$689$	−1.45677	−	2.52319i	−0.0554984	−	0.0961260i
$690$		0			0
$691$	2.78833	−	4.82953i	0.106073	−	0.183724i	−0.808103	−	0.589041i	$-0.799506\pi$
$691$	2.78833	−	4.82953i	0.106073	−	0.183724i	0.914176	+	0.405317i	$0.132839\pi$
$692$		0			0
$693$	1.15998	+	6.57856i	0.0440639	+	0.249899i
$694$		0			0
$695$	2.69001	−	4.65923i	0.102038	−	0.176735i
$696$		0			0
$697$	1.05825	+	1.83294i	0.0400840	+	0.0694275i
$698$		0			0
$699$	28.3687	+	5.00217i	1.07300	+	0.189199i
$700$		0			0
$701$	−11.3737			−0.429579			−0.214789	−	0.976660i	$-0.568907\pi$
$701$	−11.3737			−0.429579			−0.214789	+	0.976660i	$0.568907\pi$
$702$		0			0
$703$	81.7461			3.08311
$704$		0			0
$705$	−0.386659	−	0.0681784i	−0.0145624	−	0.00256775i
$706$		0			0
$707$	−3.68866	−	6.38895i	−0.138726	−	0.240281i
$708$		0			0
$709$	−23.2053	+	40.1928i	−0.871494	+	1.50947i	−0.0110435	+	0.999939i	$0.503515\pi$
$709$	−23.2053	+	40.1928i	−0.871494	+	1.50947i	−0.860451	+	0.509533i	$0.829818\pi$
$710$		0			0
$711$	−17.1466	+	14.3877i	−0.643048	+	0.539581i
$712$		0			0
$713$	−7.78968	+	13.4921i	−0.291726	+	0.505284i
$714$		0			0
$715$	1.22281	+	2.11797i	0.0457305	+	0.0792076i
$716$		0			0
$717$	15.7849	+	43.3687i	0.589499	+	1.61964i
$718$		0			0
$719$	29.6878			1.10717			0.553584	−	0.832793i	$-0.313260\pi$
$719$	29.6878			1.10717			0.553584	+	0.832793i	$0.313260\pi$
$720$		0			0
$721$	−6.39187			−0.238046
$722$		0			0
$723$	−13.9829	+	16.6642i	−0.520031	+	0.619748i
$724$		0			0
$725$	−17.6309	−	30.5376i	−0.654795	−	1.13414i
$726$		0			0
$727$	−14.7904	+	25.6177i	−0.548545	+	0.950108i	0.449829	+	0.893115i	$0.351485\pi$
$727$	−14.7904	+	25.6177i	−0.548545	+	0.950108i	−0.998375	+	0.0569937i	$0.981848\pi$
$728$		0			0
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$		0			0
$731$	−0.118555	+	0.205344i	−0.00438493	+	0.00759492i
$732$		0			0
$733$	2.31790	+	4.01471i	0.0856134	+	0.148287i	0.905652	−	0.424021i	$-0.139382\pi$
$733$	2.31790	+	4.01471i	0.0856134	+	0.148287i	−0.820039	+	0.572308i	$0.806048\pi$
$734$		0			0
$735$	0.592396	−	0.705990i	0.0218509	−	0.0260408i
$736$		0			0
$737$	9.36184			0.344848
$738$		0			0
$739$	−31.3492			−1.15320			−0.576599	−	0.817027i	$-0.695620\pi$
$739$	−31.3492			−1.15320			−0.576599	+	0.817027i	$0.695620\pi$
$740$		0			0
$741$	−9.71348	−	26.6876i	−0.356834	−	0.980392i
$742$		0			0
$743$	−19.9183	−	34.4996i	−0.730733	−	1.26567i	−0.956570	−	0.291502i	$-0.905845\pi$
$743$	−19.9183	−	34.4996i	−0.730733	−	1.26567i	0.225837	−	0.974165i	$-0.427488\pi$
$744$		0			0
$745$	−3.62654	+	6.28136i	−0.132866	+	0.230131i
$746$		0			0
$747$	40.2754	−	33.7951i	1.47360	−	1.23650i
$748$		0			0
$749$	0.00980018	−	0.0169744i	0.000358091	−	0.000620231i
$750$		0			0
$751$	−4.20115	−	7.27661i	−0.153302	−	0.265527i	0.779137	−	0.626853i	$-0.215657\pi$
$751$	−4.20115	−	7.27661i	−0.153302	−	0.265527i	−0.932440	+	0.361326i	$0.882324\pi$
$752$		0			0
$753$	−31.9013	−	5.62505i	−1.16255	−	0.204988i
$754$		0			0
$755$	−5.23854			−0.190650
$756$		0			0
$757$	−34.9299			−1.26955			−0.634775	−	0.772697i	$-0.718907\pi$
$757$	−34.9299			−1.26955			−0.634775	+	0.772697i	$0.718907\pi$
$758$		0			0
$759$	25.8298	+	4.55449i	0.937563	+	0.165318i
$760$		0			0
$761$	−6.01279	−	10.4145i	−0.217964	−	0.377524i	0.736222	−	0.676740i	$-0.236608\pi$
$761$	−6.01279	−	10.4145i	−0.217964	−	0.377524i	−0.954185	+	0.299216i	$0.903275\pi$
$762$		0			0
$763$	−0.624485	+	1.08164i	−0.0226079	+	0.0391580i
$764$		0			0
$765$	−0.225966	−	1.28152i	−0.00816983	−	0.0463334i
$766$		0			0
$767$	−3.54117	+	6.13349i	−0.127864	+	0.221468i
$768$		0			0
$769$	−26.1695	−	45.3270i	−0.943697	−	1.63453i	−0.758339	−	0.651861i	$-0.773989\pi$
$769$	−26.1695	−	45.3270i	−0.943697	−	1.63453i	−0.185359	−	0.982671i	$-0.559345\pi$
$770$		0			0
$771$	−7.78880	−	21.3996i	−0.280507	−	0.770686i
$772$		0			0
$773$	38.2181			1.37461			0.687305	−	0.726369i	$-0.258794\pi$
$773$	38.2181			1.37461			0.687305	+	0.726369i	$0.258794\pi$
$774$		0			0
$775$	−10.8057			−0.388153
$776$		0			0
$777$	−11.4572	+	13.6542i	−0.411026	+	0.489842i
$778$		0			0
$779$	−10.3118	−	17.8606i	−0.369459	−	0.639921i
$780$		0			0
$781$	13.4564	−	23.3071i	0.481506	−	0.833993i
$782$		0			0
$783$	−33.6404	+	19.4223i	−1.20221	+	0.694097i
$784$		0			0
$785$	−4.03730	+	6.99281i	−0.144098	+	0.249584i
$786$		0			0
$787$	−19.4809	−	33.7419i	−0.694418	−	1.20277i	−0.970377	−	0.241598i	$-0.922329\pi$
$787$	−19.4809	−	33.7419i	−0.694418	−	1.20277i	0.275959	−	0.961170i	$-0.411005\pi$
$788$		0			0
$789$	25.4898	−	30.3775i	0.907461	−	1.08147i
$790$		0			0
$791$	−12.2121			−0.434213
$792$		0			0
$793$	−21.6236			−0.767877
$794$		0			0
$795$	0.444907	+	1.22237i	0.0157792	+	0.0433531i
$796$		0			0
$797$	12.4863	+	21.6270i	0.442288	+	0.766066i	0.997859	−	0.0654034i	$-0.0208334\pi$
$797$	12.4863	+	21.6270i	0.442288	+	0.766066i	−0.555570	+	0.831469i	$0.687500\pi$
$798$		0			0
$799$	−0.173648	+	0.300767i	−0.00614323	+	0.0106404i
$800$		0			0
$801$	−5.91534	−	2.15301i	−0.209008	−	0.0760728i
$802$		0			0
$803$	−10.1220	+	17.5317i	−0.357196	+	0.618682i
$804$		0			0
$805$	−1.80928	−	3.13376i	−0.0637687	−	0.110451i
$806$		0			0
$807$	44.9345	+	7.92317i	1.58177	+	0.278909i
$808$		0			0
$809$	−6.21450			−0.218490			−0.109245	−	0.994015i	$-0.534843\pi$
$809$	−6.21450			−0.218490			−0.109245	+	0.994015i	$0.534843\pi$
$810$		0			0
$811$	29.5689			1.03831			0.519153	−	0.854682i	$-0.326248\pi$
$811$	29.5689			1.03831			0.519153	+	0.854682i	$0.326248\pi$
$812$		0			0
$813$	−18.2934	−	3.22562i	−0.641577	−	0.113127i
$814$		0			0
$815$	5.73854	+	9.93944i	0.201012	+	0.348164i
$816$		0			0
$817$	1.15523	−	2.00092i	0.0404164	−	0.0700032i
$818$		0			0
$819$	5.81908	+	2.11797i	0.203335	+	0.0740079i
$820$		0			0
$821$	9.10788	−	15.7753i	0.317867	−	0.550562i	−0.662176	−	0.749349i	$-0.730367\pi$
$821$	9.10788	−	15.7753i	0.317867	−	0.550562i	0.980043	+	0.198787i	$0.0637001\pi$
$822$		0			0
$823$	−12.7939	−	22.1596i	−0.445966	−	0.772435i	0.552153	−	0.833743i	$-0.313806\pi$
$823$	−12.7939	−	22.1596i	−0.445966	−	0.772435i	−0.998119	+	0.0613074i	$0.980473\pi$
$824$		0			0
$825$	6.22193	+	17.0946i	0.216620	+	0.595158i
$826$		0			0
$827$	32.3432			1.12468			0.562341	−	0.826905i	$-0.309901\pi$
$827$	32.3432			1.12468			0.562341	+	0.826905i	$0.309901\pi$
$828$		0			0
$829$	13.7314			0.476912			0.238456	−	0.971153i	$-0.423359\pi$
$829$	13.7314			0.476912			0.238456	+	0.971153i	$0.423359\pi$
$830$		0			0
$831$	−5.54751	+	6.61127i	−0.192441	+	0.229342i
$832$		0			0
$833$	−0.407604	−	0.705990i	−0.0141226	−	0.0244611i
$834$		0			0
$835$	−5.30793	+	9.19361i	−0.183689	+	0.318158i
$836$		0			0
$837$			11.9037i			0.411450i
$838$		0			0
$839$	18.5077	−	32.0563i	0.638958	−	1.10671i	−0.346704	−	0.937975i	$-0.612699\pi$
$839$	18.5077	−	32.0563i	0.638958	−	1.10671i	0.985662	−	0.168733i	$-0.0539676\pi$
$840$		0			0
$841$	−13.4427	−	23.2834i	−0.463541	−	0.802876i
$842$		0			0
$843$	−9.59539	+	11.4353i	−0.330483	+	0.393854i
$844$		0			0
$845$	−4.65002			−0.159965
$846$		0			0
$847$	−6.04189			−0.207602
$848$		0			0
$849$	−1.40074	−	3.84850i	−0.0480733	−	0.132080i
$850$		0			0
$851$	34.9923	+	60.6085i	1.19952	+	2.07763i
$852$		0			0
$853$	−11.4893	+	19.9001i	−0.393387	+	0.681366i	−0.992894	−	0.119003i	$-0.962030\pi$
$853$	−11.4893	+	19.9001i	−0.393387	+	0.681366i	0.599507	+	0.800370i	$0.295363\pi$
$854$		0			0
$855$	2.20187	+	12.4874i	0.0753023	+	0.427060i
$856$		0			0
$857$	2.22328	−	3.85083i	0.0759457	−	0.131542i	−0.825551	−	0.564327i	$-0.809136\pi$
$857$	2.22328	−	3.85083i	0.0759457	−	0.131542i	0.901497	+	0.432785i	$0.142469\pi$
$858$		0			0
$859$	11.5196	+	19.9525i	0.393044	+	0.680772i	0.992849	−	0.119374i	$-0.0380888\pi$
$859$	11.5196	+	19.9525i	0.393044	+	0.680772i	−0.599806	+	0.800146i	$0.704755\pi$
$860$		0			0
$861$	4.42855	+	0.780873i	0.150925	+	0.0266121i
$862$		0			0
$863$	21.2395			0.723000			0.361500	−	0.932372i	$-0.382265\pi$
$863$	21.2395			0.723000			0.361500	+	0.932372i	$0.382265\pi$
$864$		0			0
$865$	0.548067			0.0186348
$866$		0			0
$867$	27.8640	+	4.91317i	0.946310	+	0.166860i
$868$		0			0
$869$	8.30675	+	14.3877i	0.281787	+	0.488070i
$870$		0			0
$871$	4.33931	−	7.51590i	0.147032	−	0.254667i
$872$		0			0
$873$	−27.3120	+	22.9175i	−0.924372	+	0.775640i
$874$		0			0
$875$	2.58512	−	4.47756i	0.0873931	−	0.151369i
$876$		0			0
$877$	23.2237	+	40.2247i	0.784210	+	1.35829i	0.929470	+	0.368898i	$0.120265\pi$
$877$	23.2237	+	40.2247i	0.784210	+	1.35829i	−0.145260	+	0.989394i	$0.546402\pi$
$878$		0			0
$879$	−10.3525	−	28.4433i	−0.349182	−	0.959368i
$880$		0			0
$881$	18.3301			0.617555			0.308778	−	0.951134i	$-0.400080\pi$
$881$	18.3301			0.617555			0.308778	+	0.951134i	$0.400080\pi$
$882$		0			0
$883$	14.4894			0.487606			0.243803	−	0.969825i	$-0.421605\pi$
$883$	14.4894			0.487606			0.243803	+	0.969825i	$0.421605\pi$
$884$		0			0
$885$	2.03256	−	2.42231i	0.0683236	−	0.0814249i
$886$		0			0
$887$	−7.49360	−	12.9793i	−0.251611	−	0.435802i	0.712359	−	0.701815i	$-0.247627\pi$
$887$	−7.49360	−	12.9793i	−0.251611	−	0.435802i	−0.963969	+	0.266013i	$0.914294\pi$
$888$		0			0
$889$	−0.709607	+	1.22908i	−0.0237995	+	0.0412219i
$890$		0			0
$891$	18.8316	−	6.85413i	0.630881	−	0.229622i
$892$		0			0
$893$	1.69207	−	2.93075i	0.0566228	−	0.0980736i
$894$		0			0
$895$	−7.04916	−	12.2095i	−0.235628	−	0.408119i
$896$		0			0
$897$	15.6288	−	18.6257i	0.521831	−	0.621894i
$898$		0			0
$899$	−17.1257			−0.571173
$900$		0			0
$901$	1.15064			0.0383335
$902$		0			0
$903$	0.172304	+	0.473401i	0.00573392	+	0.0157538i
$904$		0			0
$905$	0.360500	+	0.624404i	0.0119834	+	0.0207559i
$906$		0			0
$907$	−13.0790	+	22.6535i	−0.434282	+	0.752199i	−0.997237	−	0.0742892i	$-0.976331\pi$
$907$	−13.0790	+	22.6535i	−0.434282	+	0.752199i	0.562955	+	0.826488i	$0.309665\pi$
$908$		0			0
$909$	−16.9541	+	14.2262i	−0.562331	+	0.471852i
$910$		0			0
$911$	−13.0432	+	22.5915i	−0.432142	+	0.748491i	−0.997058	−	0.0766573i	$-0.975575\pi$
$911$	−13.0432	+	22.5915i	−0.432142	+	0.748491i	0.564916	+	0.825148i	$0.308909\pi$
$912$		0			0
$913$	−19.5116	−	33.7951i	−0.645740	−	1.11845i
$914$		0			0
$915$	9.50774	+	1.67647i	0.314316	+	0.0554224i
$916$		0			0
$917$	−9.23442			−0.304947
$918$		0			0
$919$	−0.709141			−0.0233924			−0.0116962	−	0.999932i	$-0.503723\pi$
$919$	−0.709141			−0.0233924			−0.0116962	+	0.999932i	$0.503723\pi$
$920$		0			0
$921$	−43.8252	−	7.72757i	−1.44409	−	0.254632i
$922$		0			0
$923$	−12.4743	−	21.6061i	−0.410597	−	0.711175i
$924$		0			0
$925$	−24.2704	+	42.0375i	−0.798005	+	1.38219i
$926$		0			0
$927$	3.32981	+	18.8843i	0.109365	+	0.620242i
$928$		0			0
$929$	20.0929	−	34.8019i	0.659225	−	1.14181i	−0.321591	−	0.946879i	$-0.604218\pi$
$929$	20.0929	−	34.8019i	0.659225	−	1.14181i	0.980816	−	0.194933i	$-0.0624490\pi$
$930$		0			0
$931$	3.97178	+	6.87933i	0.130170	+	0.225461i
$932$		0			0
$933$	−4.63728	−	12.7408i	−0.151818	−	0.417116i
$934$		0			0
$935$	−0.965852			−0.0315867
$936$		0			0
$937$	29.5389			0.964994			0.482497	−	0.875898i	$-0.339730\pi$
$937$	29.5389			0.964994			0.482497	+	0.875898i	$0.339730\pi$
$938$		0			0
$939$	−21.1895	+	25.2527i	−0.691495	+	0.824091i
$940$		0			0
$941$	0.512326	+	0.887375i	0.0167014	+	0.0289276i	0.874255	−	0.485466i	$-0.161350\pi$
$941$	0.512326	+	0.887375i	0.0167014	+	0.0289276i	−0.857554	+	0.514394i	$0.828017\pi$
$942$		0			0
$943$	8.82816	−	15.2908i	0.287485	−	0.497938i
$944$		0			0
$945$	−2.39440	−	1.38241i	−0.0778898	−	0.0449697i
$946$		0			0
$947$	29.1891	−	50.5571i	0.948519	−	1.64288i	0.199973	−	0.979801i	$-0.435915\pi$
$947$	29.1891	−	50.5571i	0.948519	−	1.64288i	0.748547	−	0.663082i	$-0.230752\pi$
$948$		0			0
$949$	9.38326	+	16.2523i	0.304593	+	0.527571i
$950$		0			0
$951$	−34.7117	+	41.3678i	−1.12560	+	1.34144i
$952$		0			0
$953$	−33.7743			−1.09406			−0.547028	−	0.837115i	$-0.684241\pi$
$953$	−33.7743			−1.09406			−0.547028	+	0.837115i	$0.684241\pi$
$954$		0			0
$955$	−3.30272			−0.106873
$956$		0			0
$957$	9.86097	+	27.0928i	0.318760	+	0.875785i
$958$		0			0
$959$	0.975185	+	1.68907i	0.0314904	+	0.0545429i
$960$		0			0
$961$	12.8760	−	22.3019i	0.415354	−	0.719415i
$962$		0			0
$963$	−0.0552549	−	0.0201112i	−0.00178057	−	0.000648073i
$964$		0			0
$965$	1.78177	−	3.08612i	0.0573573	−	0.0993458i
$966$		0			0
$967$	−6.28699	−	10.8894i	−0.202176	−	0.350179i	0.747053	−	0.664764i	$-0.231468\pi$
$967$	−6.28699	−	10.8894i	−0.202176	−	0.350179i	−0.949229	+	0.314585i	$0.898135\pi$
$968$		0			0
$969$	11.0458	+	1.94767i	0.354841	+	0.0625680i
$970$		0			0
$971$	−2.92808			−0.0939666			−0.0469833	−	0.998896i	$-0.514961\pi$
$971$	−2.92808			−0.0939666			−0.0469833	+	0.998896i	$0.514961\pi$
$972$		0			0
$973$	−10.1111			−0.324148
$974$		0			0
$975$	16.6079	+	2.92842i	0.531878	+	0.0937844i
$976$		0			0
$977$	−20.3425	−	35.2343i	−0.650816	−	1.12725i	−0.982925	−	0.184005i	$-0.941094\pi$
$977$	−20.3425	−	35.2343i	−0.650816	−	1.12725i	0.332109	−	0.943241i	$-0.392240\pi$
$978$		0			0
$979$	−2.33615	+	4.04633i	−0.0746637	+	0.129321i
$980$		0			0
$981$	3.52094	+	1.28152i	0.112415	+	0.0409158i
$982$		0			0
$983$	2.78446	−	4.82283i	0.0888106	−	0.153824i	−0.818198	−	0.574936i	$-0.805027\pi$
$983$	2.78446	−	4.82283i	0.0888106	−	0.153824i	0.907009	+	0.421112i	$0.138360\pi$
$984$		0			0
$985$	5.06077	+	8.76552i	0.161250	+	0.279293i
$986$		0			0
$987$	0.252374	+	0.693392i	0.00803315	+	0.0220709i
$988$		0			0
$989$	1.97804			0.0628979
$990$		0			0
$991$	−31.1307			−0.988900			−0.494450	−	0.869206i	$-0.664630\pi$
$991$	−31.1307			−0.988900			−0.494450	+	0.869206i	$0.664630\pi$
$992$		0			0
$993$	29.9326	−	35.6723i	0.949882	−	1.13202i
$994$		0			0
$995$	−2.12654	−	3.68328i	−0.0674160	−	0.116768i
$996$		0			0
$997$	−14.2317	+	24.6501i	−0.450724	+	0.780676i	−0.998431	−	0.0559938i	$-0.982167\pi$
$997$	−14.2317	+	24.6501i	−0.450724	+	0.780676i	0.547708	+	0.836670i	$0.315501\pi$
$998$		0			0
$999$	46.3089	+	26.7364i	1.46515	+	0.845903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.r.c.169.1	✓	6
3.2	odd	2		1512.2.r.c.505.3		6
4.3	odd	2		1008.2.r.i.673.3		6
9.2	odd	6		4536.2.a.v.1.1		3
9.4	even	3	inner	504.2.r.c.337.1	yes	6
9.5	odd	6		1512.2.r.c.1009.3		6
9.7	even	3		4536.2.a.s.1.3		3
12.11	even	2		3024.2.r.h.2017.3		6
36.7	odd	6		9072.2.a.br.1.3		3
36.11	even	6		9072.2.a.cc.1.1		3
36.23	even	6		3024.2.r.h.1009.3		6
36.31	odd	6		1008.2.r.i.337.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.c.169.1	✓	6	1.1	even	1	trivial
504.2.r.c.337.1	yes	6	9.4	even	3	inner
1008.2.r.i.337.3		6	36.31	odd	6
1008.2.r.i.673.3		6	4.3	odd	2
1512.2.r.c.505.3		6	3.2	odd	2
1512.2.r.c.1009.3		6	9.5	odd	6
3024.2.r.h.1009.3		6	36.23	even	6
3024.2.r.h.2017.3		6	12.11	even	2
4536.2.a.s.1.3		3	9.7	even	3
4536.2.a.v.1.1		3	9.2	odd	6
9072.2.a.br.1.3		3	36.7	odd	6
9072.2.a.cc.1.1		3	36.11	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)

\(f(q)\)	\(=\)	\(q+(-1.70574 - 0.300767i) q^{3} +(-0.266044 - 0.460802i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.81908 + 1.02606i) q^{9} +O(q^{10})\)	\(q+(-1.70574 - 0.300767i) q^{3} +(-0.266044 - 0.460802i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.81908 + 1.02606i) q^{9} +(1.11334 - 1.92836i) q^{11} +(-1.03209 - 1.78763i) q^{13} +(0.315207 + 0.866025i) q^{15} +0.815207 q^{17} -7.94356 q^{19} +(1.11334 - 1.32683i) q^{21} +(-3.40033 - 5.88954i) q^{23} +(2.35844 - 4.08494i) q^{25} +(-4.50000 - 2.59808i) q^{27} +(3.73783 - 6.47410i) q^{29} +(-1.14543 - 1.98394i) q^{31} +(-2.47906 + 2.95442i) q^{33} +0.532089 q^{35} -10.2909 q^{37} +(1.22281 + 3.35965i) q^{39} +(1.29813 + 2.24843i) q^{41} +(-0.145430 + 0.251892i) q^{43} +(-0.277189 - 1.57202i) q^{45} +(-0.213011 + 0.368946i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-1.39053 - 0.245188i) q^{51} +1.41147 q^{53} -1.18479 q^{55} +(13.5496 + 2.38917i) q^{57} +(-1.71554 - 2.97140i) q^{59} +(5.23783 - 9.07218i) q^{61} +(-2.29813 + 1.92836i) q^{63} +(-0.549163 + 0.951178i) q^{65} +(2.10220 + 3.64111i) q^{67} +(4.02869 + 11.0687i) q^{69} +12.0865 q^{71} -9.09152 q^{73} +(-5.25150 + 6.25849i) q^{75} +(1.11334 + 1.92836i) q^{77} +(-3.73055 + 6.46151i) q^{79} +(6.89440 + 5.78509i) q^{81} +(8.76264 - 15.1773i) q^{83} +(-0.216881 - 0.375650i) q^{85} +(-8.32295 + 9.91890i) q^{87} -2.09833 q^{89} +2.06418 q^{91} +(1.35710 + 3.72859i) q^{93} +(2.11334 + 3.66041i) q^{95} +(-5.94222 + 10.2922i) q^{97} +(5.11721 - 4.29385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more