LMFDB - Embedded newform 208.2.k.b.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(31,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("208.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.k (of order $4$, 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:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 147x^{8} + 662x^{6} + 2233x^{4} + 588x^{2} + 144 $ x^12 + 14x^10 + 147x^8 + 662x^6 + 2233x^4 + 588*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.2
Root			$1.17542 - 2.03589i$ of defining polynomial
Character	$\chi$	$=$	208.47
Dual form			208.2.k.b.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.35084i q^{3} +(2.79911 + 2.79911i) q^{5} +(2.49735 + 2.49735i) q^{7} -2.52644 q^{9} +(-1.73205 - 1.73205i) q^{11} +(-2.79911 - 2.27267i) q^{13} +(6.58024 - 6.58024i) q^{15} -1.52644i q^{17} +(0.618787 - 0.618787i) q^{19} +(5.87088 - 5.87088i) q^{21} -6.23228 q^{23} +10.6700i q^{25} -1.11326i q^{27} -2.54533 q^{29} +(-4.08289 + 4.08289i) q^{31} +(-4.07177 + 4.07177i) q^{33} +13.9807i q^{35} +(6.79911 - 6.79911i) q^{37} +(-5.34267 + 6.58024i) q^{39} +(-1.07177 - 1.07177i) q^{41} +1.11326 q^{43} +(-7.07177 - 7.07177i) q^{45} +(5.66842 + 5.66842i) q^{47} +5.47356i q^{49} -3.58841 q^{51} -5.59821 q^{53} -9.69639i q^{55} +(-1.45467 - 1.45467i) q^{57} +(-4.37592 - 4.37592i) q^{59} +5.19642 q^{61} +(-6.30942 - 6.30942i) q^{63} +(-1.47356 - 14.1964i) q^{65} +(0.201443 - 0.201443i) q^{67} +14.6511i q^{69} +(-5.66842 + 5.66842i) q^{71} +(-0.526440 + 0.526440i) q^{73} +25.0834 q^{75} -8.65109i q^{77} -6.63517i q^{79} -10.1964 q^{81} +(-5.19615 + 5.19615i) q^{83} +(4.27267 - 4.27267i) q^{85} +5.98366i q^{87} +(-4.12465 + 4.12465i) q^{89} +(-1.31471 - 12.6660i) q^{91} +(9.59821 + 9.59821i) q^{93} +3.46410 q^{95} +(4.59821 + 4.59821i) q^{97} +(4.37592 + 4.37592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} - 20 q^{9} - 4 q^{13} - 8 q^{21} + 8 q^{29} + 52 q^{37} + 36 q^{41} - 36 q^{45} - 8 q^{53} - 56 q^{57} - 56 q^{61} - 28 q^{65} + 4 q^{73} - 4 q^{81} + 32 q^{85} + 20 q^{89} + 56 q^{93} - 4 q^{97}+O(q^{100}) $ 12 * q + 4 * q^5 - 20 * q^9 - 4 * q^13 - 8 * q^21 + 8 * q^29 + 52 * q^37 + 36 * q^41 - 36 * q^45 - 8 * q^53 - 56 * q^57 - 56 * q^61 - 28 * q^65 + 4 * q^73 - 4 * q^81 + 32 * q^85 + 20 * q^89 + 56 * q^93 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$		−	2.35084i		−	1.35726i	−0.734482	−	0.678629i	$-0.762575\pi$
$3$		−	2.35084i		−	1.35726i	0.734482	−	0.678629i	$-0.237425\pi$
$4$		0			0
$5$	2.79911	+	2.79911i	1.25180	+	1.25180i	0.954913	+	0.296885i	$0.0959477\pi$
$5$	2.79911	+	2.79911i	1.25180	+	1.25180i	0.296885	+	0.954913i	$0.404052\pi$
$6$		0			0
$7$	2.49735	+	2.49735i	0.943911	+	0.943911i	0.998508	−	0.0545971i	$-0.0173875\pi$
$7$	2.49735	+	2.49735i	0.943911	+	0.943911i	−0.0545971	+	0.998508i	$0.517387\pi$
$8$		0			0
$9$	−2.52644			−0.842147
$10$		0			0
$11$	−1.73205	−	1.73205i	−0.522233	−	0.522233i	0.396012	−	0.918245i	$-0.370394\pi$
$11$	−1.73205	−	1.73205i	−0.522233	−	0.522233i	−0.918245	+	0.396012i	$0.870394\pi$
$12$		0			0
$13$	−2.79911	−	2.27267i	−0.776332	−	0.630324i
$13$	−2.79911	−	2.27267i	−0.776332	−	0.630324i
$14$		0			0
$15$	6.58024	−	6.58024i	1.69901	−	1.69901i
$16$		0			0
$17$		−	1.52644i		−	0.370216i	−0.982718	−	0.185108i	$-0.940737\pi$
$17$		−	1.52644i		−	0.370216i	0.982718	−	0.185108i	$-0.0592635\pi$
$18$		0			0
$19$	0.618787	−	0.618787i	0.141960	−	0.141960i	−0.632555	−	0.774515i	$-0.717994\pi$
$19$	0.618787	−	0.618787i	0.141960	−	0.141960i	0.774515	+	0.632555i	$0.217994\pi$
$20$		0			0
$21$	5.87088	−	5.87088i	1.28113	−	1.28113i
$22$		0			0
$23$	−6.23228			−1.29952			−0.649761	−	0.760139i	$-0.725131\pi$
$23$	−6.23228			−1.29952			−0.649761	+	0.760139i	$0.725131\pi$
$24$		0			0
$25$			10.6700i			2.13400i
$26$		0			0
$27$		−	1.11326i		−	0.214248i
$28$		0			0
$29$	−2.54533			−0.472656			−0.236328	−	0.971673i	$-0.575944\pi$
$29$	−2.54533			−0.472656			−0.236328	+	0.971673i	$0.575944\pi$
$30$		0			0
$31$	−4.08289	+	4.08289i	−0.733308	+	0.733308i	−0.971274	−	0.237965i	$-0.923520\pi$
$31$	−4.08289	+	4.08289i	−0.733308	+	0.733308i	0.237965	+	0.971274i	$0.423520\pi$
$32$		0			0
$33$	−4.07177	+	4.07177i	−0.708804	+	0.708804i
$34$		0			0
$35$			13.9807i			2.36317i
$36$		0			0
$37$	6.79911	−	6.79911i	1.11777	−	1.11777i	0.125697	−	0.992069i	$-0.459883\pi$
$37$	6.79911	−	6.79911i	1.11777	−	1.11777i	0.992069	−	0.125697i	$-0.0401168\pi$
$38$		0			0
$39$	−5.34267	+	6.58024i	−0.855512	+	1.05368i
$40$		0			0
$41$	−1.07177	−	1.07177i	−0.167383	−	0.167383i	0.618445	−	0.785828i	$-0.287763\pi$
$41$	−1.07177	−	1.07177i	−0.167383	−	0.167383i	−0.785828	+	0.618445i	$0.787763\pi$
$42$		0			0
$43$	1.11326			0.169771			0.0848855	−	0.996391i	$-0.472948\pi$
$43$	1.11326			0.169771			0.0848855	+	0.996391i	$0.472948\pi$
$44$		0			0
$45$	−7.07177	−	7.07177i	−1.05420	−	1.05420i
$46$		0			0
$47$	5.66842	+	5.66842i	0.826824	+	0.826824i	0.987076	−	0.160252i	$-0.0512306\pi$
$47$	5.66842	+	5.66842i	0.826824	+	0.826824i	−0.160252	+	0.987076i	$0.551231\pi$
$48$		0			0
$49$			5.47356i			0.781937i
$50$		0			0
$51$	−3.58841			−0.502478
$52$		0			0
$53$	−5.59821			−0.768973			−0.384487	−	0.923131i	$-0.625622\pi$
$53$	−5.59821			−0.768973			−0.384487	+	0.923131i	$0.625622\pi$
$54$		0			0
$55$		−	9.69639i		−	1.30746i
$56$		0			0
$57$	−1.45467	−	1.45467i	−0.192676	−	0.192676i
$58$		0			0
$59$	−4.37592	−	4.37592i	−0.569697	−	0.569697i	0.362347	−	0.932043i	$-0.381976\pi$
$59$	−4.37592	−	4.37592i	−0.569697	−	0.569697i	−0.932043	+	0.362347i	$0.881976\pi$
$60$		0			0
$61$	5.19642			0.665334			0.332667	−	0.943044i	$-0.392052\pi$
$61$	5.19642			0.665334			0.332667	+	0.943044i	$0.392052\pi$
$62$		0			0
$63$	−6.30942	−	6.30942i	−0.794912	−	0.794912i
$64$		0			0
$65$	−1.47356	−	14.1964i	−0.182773	−	1.76085i
$66$		0			0
$67$	0.201443	−	0.201443i	0.0246102	−	0.0246102i	−0.694695	−	0.719305i	$-0.744460\pi$
$67$	0.201443	−	0.201443i	0.0246102	−	0.0246102i	0.719305	+	0.694695i	$0.244460\pi$
$68$		0			0
$69$			14.6511i			1.76378i
$70$		0			0
$71$	−5.66842	+	5.66842i	−0.672718	+	0.672718i	−0.958342	−	0.285624i	$-0.907799\pi$
$71$	−5.66842	+	5.66842i	−0.672718	+	0.672718i	0.285624	+	0.958342i	$0.407799\pi$
$72$		0			0
$73$	−0.526440	+	0.526440i	−0.0616151	+	0.0616151i	−0.737243	−	0.675628i	$-0.763873\pi$
$73$	−0.526440	+	0.526440i	−0.0616151	+	0.0616151i	0.675628	+	0.737243i	$0.263873\pi$
$74$		0			0
$75$	25.0834			2.89638
$76$		0			0
$77$		−	8.65109i		−	0.985883i
$78$		0			0
$79$		−	6.63517i		−	0.746515i	−0.927728	−	0.373257i	$-0.878241\pi$
$79$		−	6.63517i		−	0.746515i	0.927728	−	0.373257i	$-0.121759\pi$
$80$		0			0
$81$	−10.1964			−1.13294
$82$		0			0
$83$	−5.19615	+	5.19615i	−0.570352	+	0.570352i	−0.932227	−	0.361875i	$-0.882137\pi$
$83$	−5.19615	+	5.19615i	−0.570352	+	0.570352i	0.361875	+	0.932227i	$0.382137\pi$
$84$		0			0
$85$	4.27267	−	4.27267i	0.463436	−	0.463436i
$86$		0			0
$87$			5.98366i			0.641516i
$88$		0			0
$89$	−4.12465	+	4.12465i	−0.437212	+	0.437212i	−0.891073	−	0.453861i	$-0.850046\pi$
$89$	−4.12465	+	4.12465i	−0.437212	+	0.437212i	0.453861	+	0.891073i	$0.350046\pi$
$90$		0			0
$91$	−1.31471	−	12.6660i	−0.137819	−	1.32776i
$92$		0			0
$93$	9.59821	+	9.59821i	0.995288	+	0.995288i
$94$		0			0
$95$	3.46410			0.355409
$96$		0			0
$97$	4.59821	+	4.59821i	0.466878	+	0.466878i	0.900901	−	0.434024i	$-0.142907\pi$
$97$	4.59821	+	4.59821i	0.466878	+	0.466878i	−0.434024	+	0.900901i	$0.642907\pi$
$98$		0			0
$99$	4.37592	+	4.37592i	0.439797	+	0.439797i
$100$		0			0
$101$			11.1964i			1.11409i	0.830484	+	0.557043i	$0.188064\pi$
$101$			11.1964i			1.11409i	−0.830484	+	0.557043i	$0.811936\pi$
$102$		0			0
$103$	17.8622			1.76001			0.880006	−	0.474963i	$-0.157539\pi$
$103$	17.8622			1.76001			0.880006	+	0.474963i	$0.157539\pi$
$104$		0			0
$105$	32.8664			3.20743
$106$		0			0
$107$			15.9287i			1.53988i	0.638115	+	0.769941i	$0.279715\pi$
$107$			15.9287i			1.53988i	−0.638115	+	0.769941i	$0.720285\pi$
$108$		0			0
$109$	−4.39732	−	4.39732i	−0.421186	−	0.421186i	0.464426	−	0.885612i	$-0.346261\pi$
$109$	−4.39732	−	4.39732i	−0.421186	−	0.421186i	−0.885612	+	0.464426i	$0.846261\pi$
$110$		0			0
$111$	−15.9836	−	15.9836i	−1.51710	−	1.51710i
$112$		0			0
$113$	−2.94712			−0.277242			−0.138621	−	0.990346i	$-0.544267\pi$
$113$	−2.94712			−0.277242			−0.138621	+	0.990346i	$0.544267\pi$
$114$		0			0
$115$	−17.4448	−	17.4448i	−1.62674	−	1.62674i
$116$		0			0
$117$	7.07177	+	5.74175i	0.653785	+	0.530825i
$118$		0			0
$119$	3.81206	−	3.81206i	0.349451	−	0.349451i
$120$		0			0
$121$		−	5.00000i		−	0.454545i
$122$		0			0
$123$	−2.51956	+	2.51956i	−0.227181	+	0.227181i
$124$		0			0
$125$	−15.8709	+	15.8709i	−1.41953	+	1.41953i
$126$		0			0
$127$	20.0887			1.78258			0.891292	−	0.453431i	$-0.149800\pi$
$127$	20.0887			1.78258			0.891292	+	0.453431i	$0.149800\pi$
$128$		0			0
$129$		−	2.61710i		−	0.230423i
$130$		0			0
$131$		−	19.2685i		−	1.68349i	−0.539873	−	0.841747i	$-0.681528\pi$
$131$		−	19.2685i		−	1.68349i	0.539873	−	0.841747i	$-0.318472\pi$
$132$		0			0
$133$	3.09066			0.267994
$134$		0			0
$135$	3.11614	−	3.11614i	0.268195	−	0.268195i
$136$		0			0
$137$	5.14354	−	5.14354i	0.439442	−	0.439442i	−0.452382	−	0.891824i	$-0.649426\pi$
$137$	5.14354	−	5.14354i	0.439442	−	0.439442i	0.891824	+	0.452382i	$0.149426\pi$
$138$		0			0
$139$		−	5.41205i		−	0.459044i	−0.973303	−	0.229522i	$-0.926284\pi$
$139$		−	5.41205i		−	0.459044i	0.973303	−	0.229522i	$-0.0737163\pi$
$140$		0			0
$141$	13.3255	−	13.3255i	1.12221	−	1.12221i
$142$		0			0
$143$	0.911820	+	8.78457i	0.0762502	+	0.734602i
$144$		0			0
$145$	−7.12465	−	7.12465i	−0.591670	−	0.591670i
$146$		0			0
$147$	12.8675			1.06129
$148$		0			0
$149$	−7.57932	−	7.57932i	−0.620922	−	0.620922i	0.324845	−	0.945767i	$-0.394688\pi$
$149$	−7.57932	−	7.57932i	−0.620922	−	0.620922i	−0.945767	+	0.324845i	$0.894688\pi$
$150$		0			0
$151$	2.49735	+	2.49735i	0.203232	+	0.203232i	0.801383	−	0.598151i	$-0.204098\pi$
$151$	2.49735	+	2.49735i	0.203232	+	0.203232i	−0.598151	+	0.801383i	$0.704098\pi$
$152$		0			0
$153$			3.85646i			0.311776i
$154$		0			0
$155$	−22.8569			−1.83591
$156$		0			0
$157$	−21.3400			−1.70311			−0.851557	−	0.524262i	$-0.824341\pi$
$157$	−21.3400			−1.70311			−0.851557	+	0.524262i	$0.824341\pi$
$158$		0			0
$159$			13.1605i			1.04369i
$160$		0			0
$161$	−15.5642	−	15.5642i	−1.22663	−	1.22663i
$162$		0			0
$163$	16.1301	+	16.1301i	1.26341	+	1.26341i	0.949430	+	0.313977i	$0.101662\pi$
$163$	16.1301	+	16.1301i	1.26341	+	1.26341i	0.313977	+	0.949430i	$0.398338\pi$
$164$		0			0
$165$	−22.7946			−1.77456
$166$		0			0
$167$	1.85636	+	1.85636i	0.143650	+	0.143650i	0.775274	−	0.631625i	$-0.217612\pi$
$167$	1.85636	+	1.85636i	0.143650	+	0.143650i	−0.631625	+	0.775274i	$0.717612\pi$
$168$		0			0
$169$	2.66998	+	12.7229i	0.205383	+	0.978682i
$170$		0			0
$171$	−1.56333	+	1.56333i	−0.119551	+	0.119551i
$172$		0			0
$173$		−	5.70397i		−	0.433665i	−0.976209	−	0.216832i	$-0.930427\pi$
$173$		−	5.70397i		−	0.433665i	0.976209	−	0.216832i	$-0.0695725\pi$
$174$		0			0
$175$	−26.6467	+	26.6467i	−2.01430	+	2.01430i
$176$		0			0
$177$	−10.2871	+	10.2871i	−0.773225	+	0.773225i
$178$		0			0
$179$	5.22887			0.390824			0.195412	−	0.980721i	$-0.437396\pi$
$179$	5.22887			0.390824			0.195412	+	0.980721i	$0.437396\pi$
$180$		0			0
$181$			6.50755i			0.483702i	0.970313	+	0.241851i	$0.0777546\pi$
$181$			6.50755i			0.483702i	−0.970313	+	0.241851i	$0.922245\pi$
$182$		0			0
$183$		−	12.2159i		−	0.903029i
$184$		0			0
$185$	38.0628			2.79843
$186$		0			0
$187$	−2.64387	+	2.64387i	−0.193339	+	0.193339i
$188$		0			0
$189$	2.78021	−	2.78021i	0.202231	−	0.202231i
$190$		0			0
$191$			4.16002i			0.301009i	0.988609	+	0.150504i	$0.0480897\pi$
$191$			4.16002i			0.301009i	−0.988609	+	0.150504i	$0.951910\pi$
$192$		0			0
$193$	7.65109	−	7.65109i	0.550738	−	0.550738i	−0.375916	−	0.926654i	$-0.622672\pi$
$193$	7.65109	−	7.65109i	0.550738	−	0.550738i	0.926654	+	0.375916i	$0.122672\pi$
$194$		0			0
$195$	−33.3735	+	3.46410i	−2.38993	+	0.248069i
$196$		0			0
$197$	11.3444	+	11.3444i	0.808258	+	0.808258i	0.984370	−	0.176112i	$-0.0563522\pi$
$197$	11.3444	+	11.3444i	0.808258	+	0.808258i	−0.176112	+	0.984370i	$0.556352\pi$
$198$		0			0
$199$	−6.23228			−0.441795			−0.220897	−	0.975297i	$-0.570899\pi$
$199$	−6.23228			−0.441795			−0.220897	+	0.975297i	$0.570899\pi$
$200$		0			0
$201$	−0.473560	−	0.473560i	−0.0334024	−	0.0334024i
$202$		0			0
$203$	−6.35659	−	6.35659i	−0.446145	−	0.446145i
$204$		0			0
$205$		−	6.00000i		−	0.419058i
$206$		0			0
$207$	15.7455			1.09439
$208$		0			0
$209$	−2.14354			−0.148272
$210$		0			0
$211$			3.99130i			0.274772i	0.990518	+	0.137386i	$0.0438701\pi$
$211$			3.99130i			0.274772i	−0.990518	+	0.137386i	$0.956130\pi$
$212$		0			0
$213$	13.3255	+	13.3255i	0.913051	+	0.913051i
$214$		0			0
$215$	3.11614	+	3.11614i	0.212519	+	0.212519i
$216$		0			0
$217$	−20.3928			−1.38436
$218$		0			0
$219$	1.23757	+	1.23757i	0.0836275	+	0.0836275i
$220$		0			0
$221$	−3.46909	+	4.27267i	−0.233356	+	0.287411i
$222$		0			0
$223$	3.73493	−	3.73493i	0.250109	−	0.250109i	−0.570906	−	0.821015i	$-0.693408\pi$
$223$	3.73493	−	3.73493i	0.250109	−	0.250109i	0.821015	+	0.570906i	$0.193408\pi$
$224$		0			0
$225$		−	26.9571i		−	1.79714i
$226$		0			0
$227$	17.5364	−	17.5364i	1.16393	−	1.16393i	0.180325	−	0.983607i	$-0.442285\pi$
$227$	17.5364	−	17.5364i	1.16393	−	1.16393i	0.983607	−	0.180325i	$-0.0577151\pi$
$228$		0			0
$229$	1.30665	−	1.30665i	0.0863461	−	0.0863461i	−0.662615	−	0.748961i	$-0.730553\pi$
$229$	1.30665	−	1.30665i	0.0863461	−	0.0863461i	0.748961	+	0.662615i	$0.230553\pi$
$230$		0			0
$231$	−20.3373			−1.33810
$232$		0			0
$233$		−	21.6700i		−	1.41965i	−0.704379	−	0.709824i	$-0.748775\pi$
$233$		−	21.6700i		−	1.41965i	0.704379	−	0.709824i	$-0.251225\pi$
$234$		0			0
$235$			31.7330i			2.07003i
$236$		0			0
$237$	−15.5982			−1.01321
$238$		0			0
$239$	−4.72388	+	4.72388i	−0.305563	+	0.305563i	−0.843185	−	0.537623i	$-0.819322\pi$
$239$	−4.72388	+	4.72388i	−0.305563	+	0.305563i	0.537623	+	0.843185i	$0.319322\pi$
$240$		0			0
$241$	3.07177	−	3.07177i	0.197870	−	0.197870i	−0.601216	−	0.799086i	$-0.705317\pi$
$241$	3.07177	−	3.07177i	0.197870	−	0.197870i	0.799086	+	0.601216i	$0.205317\pi$
$242$		0			0
$243$			20.6303i			1.32344i
$244$		0			0
$245$	−15.3211	+	15.3211i	−0.978827	+	0.978827i
$246$		0			0
$247$	−3.13835	+	0.325754i	−0.199688	+	0.0207272i
$248$		0			0
$249$	12.2153	+	12.2153i	0.774114	+	0.774114i
$250$		0			0
$251$	−1.64046			−0.103545			−0.0517725	−	0.998659i	$-0.516487\pi$
$251$	−1.64046			−0.103545			−0.0517725	+	0.998659i	$0.516487\pi$
$252$		0			0
$253$	10.7946	+	10.7946i	0.678653	+	0.678653i
$254$		0			0
$255$	−10.0443	−	10.0443i	−0.629001	−	0.629001i
$256$		0			0
$257$			5.38290i			0.335776i	0.985806	+	0.167888i	$0.0536947\pi$
$257$			5.38290i			0.335776i	−0.985806	+	0.167888i	$0.946305\pi$
$258$		0			0
$259$	33.9596			2.11014
$260$		0			0
$261$	6.43063			0.398046
$262$		0			0
$263$		−	17.3205i		−	1.06803i	−0.845476	−	0.534014i	$-0.820683\pi$
$263$		−	17.3205i		−	1.06803i	0.845476	−	0.534014i	$-0.179317\pi$
$264$		0			0
$265$	−15.6700	−	15.6700i	−0.962599	−	0.962599i
$266$		0			0
$267$	9.69639	+	9.69639i	0.593409	+	0.593409i
$268$		0			0
$269$	−17.1964			−1.04848			−0.524242	−	0.851569i	$-0.675651\pi$
$269$	−17.1964			−1.04848			−0.524242	+	0.851569i	$0.675651\pi$
$270$		0			0
$271$	−13.1383	−	13.1383i	−0.798094	−	0.798094i	0.184701	−	0.982795i	$-0.440868\pi$
$271$	−13.1383	−	13.1383i	−0.798094	−	0.798094i	−0.982795	+	0.184701i	$0.940868\pi$
$272$		0			0
$273$	−29.7757	+	3.09066i	−1.80211	+	0.187055i
$274$		0			0
$275$	18.4810	−	18.4810i	1.11444	−	1.11444i
$276$		0			0
$277$			31.3400i			1.88304i	0.336963	+	0.941518i	$0.390600\pi$
$277$			31.3400i			1.88304i	−0.336963	+	0.941518i	$0.609400\pi$
$278$		0			0
$279$	10.3152	−	10.3152i	0.617553	−	0.617553i
$280$		0			0
$281$	15.2153	−	15.2153i	0.907669	−	0.907669i	−0.0884143	−	0.996084i	$-0.528180\pi$
$281$	15.2153	−	15.2153i	0.907669	−	0.907669i	0.996084	+	0.0884143i	$0.0281799\pi$
$282$		0			0
$283$	−19.3928			−1.15278			−0.576390	−	0.817175i	$-0.695539\pi$
$283$	−19.3928			−1.15278			−0.576390	+	0.817175i	$0.695539\pi$
$284$		0			0
$285$		−	8.14354i		−	0.482382i
$286$		0			0
$287$		−	5.35318i		−	0.315988i
$288$		0			0
$289$	14.6700			0.862940
$290$		0			0
$291$	10.8096	−	10.8096i	0.633673	−	0.633673i
$292$		0			0
$293$	11.7462	−	11.7462i	0.686222	−	0.686222i	−0.275173	−	0.961395i	$-0.588735\pi$
$293$	11.7462	−	11.7462i	0.686222	−	0.686222i	0.961395	+	0.275173i	$0.0887351\pi$
$294$		0			0
$295$		−	24.4973i		−	1.42629i
$296$		0			0
$297$	−1.92823	+	1.92823i	−0.111887	+	0.111887i
$298$		0			0
$299$	17.4448	+	14.1639i	1.00886	+	0.819119i
$300$		0			0
$301$	2.78021	+	2.78021i	0.160249	+	0.160249i
$302$		0			0
$303$	26.3210			1.51210
$304$		0			0
$305$	14.5453	+	14.5453i	0.832863	+	0.832863i
$306$		0			0
$307$	−16.0058	−	16.0058i	−0.913499	−	0.913499i	0.0830464	−	0.996546i	$-0.473535\pi$
$307$	−16.0058	−	16.0058i	−0.913499	−	0.913499i	−0.996546	+	0.0830464i	$0.973535\pi$
$308$		0			0
$309$		−	41.9911i		−	2.38879i
$310$		0			0
$311$	−8.56866			−0.485884			−0.242942	−	0.970041i	$-0.578113\pi$
$311$	−8.56866			−0.485884			−0.242942	+	0.970041i	$0.578113\pi$
$312$		0			0
$313$	−2.86640			−0.162019			−0.0810093	−	0.996713i	$-0.525814\pi$
$313$	−2.86640			−0.162019			−0.0810093	+	0.996713i	$0.525814\pi$
$314$		0			0
$315$		−	35.3214i		−	1.99014i
$316$		0			0
$317$	15.6171	+	15.6171i	0.877144	+	0.877144i	0.993238	−	0.116094i	$-0.0370375\pi$
$317$	15.6171	+	15.6171i	0.877144	+	0.877144i	−0.116094	+	0.993238i	$0.537037\pi$
$318$		0			0
$319$	4.40864	+	4.40864i	0.246837	+	0.246837i
$320$		0			0
$321$	37.4457			2.09002
$322$		0			0
$323$	−0.944541	−	0.944541i	−0.0525557	−	0.0525557i
$324$		0			0
$325$	24.2493	−	29.8664i	1.34511	−	1.65669i
$326$		0			0
$327$	−10.3374	+	10.3374i	−0.571658	+	0.571658i
$328$		0			0
$329$			28.3121i			1.56090i
$330$		0			0
$331$	6.43373	−	6.43373i	0.353630	−	0.353630i	−0.507829	−	0.861458i	$-0.669552\pi$
$331$	6.43373	−	6.43373i	0.353630	−	0.353630i	0.861458	+	0.507829i	$0.169552\pi$
$332$		0			0
$333$	−17.1775	+	17.1775i	−0.941323	+	0.941323i
$334$		0			0
$335$	1.12772			0.0616140
$336$		0			0
$337$			22.7606i			1.23985i	0.784661	+	0.619926i	$0.212837\pi$
$337$			22.7606i			1.23985i	−0.784661	+	0.619926i	$0.787163\pi$
$338$		0			0
$339$			6.92820i			0.376288i
$340$		0			0
$341$	14.1435			0.765916
$342$		0			0
$343$	3.81206	−	3.81206i	0.205832	−	0.205832i
$344$		0			0
$345$	−41.0099	+	41.0099i	−2.20790	+	2.20790i
$346$		0			0
$347$			17.6280i			0.946321i	0.880976	+	0.473160i	$0.156887\pi$
$347$			17.6280i			0.946321i	−0.880976	+	0.473160i	$0.843113\pi$
$348$		0			0
$349$	7.34444	−	7.34444i	0.393139	−	0.393139i	−0.482666	−	0.875805i	$-0.660331\pi$
$349$	7.34444	−	7.34444i	0.393139	−	0.393139i	0.875805	+	0.482666i	$0.160331\pi$
$350$		0			0
$351$	−2.53008	+	3.11614i	−0.135045	+	0.166327i
$352$		0			0
$353$	−0.348910	−	0.348910i	−0.0185706	−	0.0185706i	0.697761	−	0.716331i	$-0.254180\pi$
$353$	−0.348910	−	0.348910i	−0.0185706	−	0.0185706i	−0.716331	+	0.697761i	$0.754180\pi$
$354$		0			0
$355$	−31.7330			−1.68421
$356$		0			0
$357$	−8.96154	−	8.96154i	−0.474295	−	0.474295i
$358$		0			0
$359$	21.0005	+	21.0005i	1.10836	+	1.10836i	0.993366	+	0.114999i	$0.0366865\pi$
$359$	21.0005	+	21.0005i	1.10836	+	1.10836i	0.114999	+	0.993366i	$0.463314\pi$
$360$		0			0
$361$			18.2342i			0.959695i
$362$		0			0
$363$	−11.7542			−0.616935
$364$		0			0
$365$	−2.94712			−0.154259
$366$		0			0
$367$			9.44776i			0.493169i	0.969121	+	0.246585i	$0.0793083\pi$
$367$			9.44776i			0.493169i	−0.969121	+	0.246585i	$0.920692\pi$
$368$		0			0
$369$	2.70776	+	2.70776i	0.140961	+	0.140961i
$370$		0			0
$371$	−13.9807	−	13.9807i	−0.725843	−	0.725843i
$372$		0			0
$373$	31.4457			1.62820			0.814099	−	0.580726i	$-0.197231\pi$
$373$	31.4457			1.62820			0.814099	+	0.580726i	$0.197231\pi$
$374$		0			0
$375$	37.3099	+	37.3099i	1.92667	+	1.92667i
$376$		0			0
$377$	7.12465	+	5.78469i	0.366938	+	0.297927i
$378$		0			0
$379$	−8.36722	+	8.36722i	−0.429795	+	0.429795i	−0.888559	−	0.458763i	$-0.848293\pi$
$379$	−8.36722	+	8.36722i	−0.429795	+	0.429795i	0.458763	+	0.888559i	$0.348293\pi$
$380$		0			0
$381$		−	47.2253i		−	2.41942i
$382$		0			0
$383$	2.90024	−	2.90024i	0.148195	−	0.148195i	−0.629116	−	0.777311i	$-0.716583\pi$
$383$	2.90024	−	2.90024i	0.148195	−	0.148195i	0.777311	+	0.629116i	$0.216583\pi$
$384$		0			0
$385$	24.2153	−	24.2153i	1.23413	−	1.23413i
$386$		0			0
$387$	−2.81259			−0.142972
$388$		0			0
$389$			27.4835i			1.39347i	0.717329	+	0.696735i	$0.245364\pi$
$389$			27.4835i			1.39347i	−0.717329	+	0.696735i	$0.754636\pi$
$390$		0			0
$391$			9.51321i			0.481103i
$392$		0			0
$393$	−45.2970			−2.28493
$394$		0			0
$395$	18.5725	−	18.5725i	0.934486	−	0.934486i
$396$		0			0
$397$	−11.5793	+	11.5793i	−0.581149	+	0.581149i	−0.935219	−	0.354070i	$-0.884798\pi$
$397$	−11.5793	+	11.5793i	−0.581149	+	0.581149i	0.354070	+	0.935219i	$0.384798\pi$
$398$		0			0
$399$		−	7.26565i		−	0.363737i
$400$		0			0
$401$	−11.9471	+	11.9471i	−0.596611	+	0.596611i	−0.939409	−	0.342798i	$-0.888625\pi$
$401$	−11.9471	+	11.9471i	−0.596611	+	0.596611i	0.342798	+	0.939409i	$0.388625\pi$
$402$		0			0
$403$	20.7075	−	2.14939i	1.03151	−	0.107069i
$404$		0			0
$405$	−28.5409	−	28.5409i	−1.41821	−	1.41821i
$406$		0			0
$407$	−23.5528			−1.16747
$408$		0			0
$409$	−24.4457	−	24.4457i	−1.20876	−	1.20876i	−0.971428	−	0.237335i	$-0.923726\pi$
$409$	−24.4457	−	24.4457i	−1.20876	−	1.20876i	−0.237335	−	0.971428i	$-0.576274\pi$
$410$		0			0
$411$	−12.0916	−	12.0916i	−0.596436	−	0.596436i
$412$		0			0
$413$		−	21.8565i		−	1.07549i
$414$		0			0
$415$	−29.0892			−1.42793
$416$		0			0
$417$	−12.7229			−0.623041
$418$		0			0
$419$		−	1.51615i		−	0.0740688i	−0.999314	−	0.0370344i	$-0.988209\pi$
$419$		−	1.51615i		−	0.0740688i	0.999314	−	0.0370344i	$-0.0117911\pi$
$420$		0			0
$421$	−12.1391	−	12.1391i	−0.591622	−	0.591622i	0.346447	−	0.938069i	$-0.387388\pi$
$421$	−12.1391	−	12.1391i	−0.591622	−	0.591622i	−0.938069	+	0.346447i	$0.887388\pi$
$422$		0			0
$423$	−14.3209	−	14.3209i	−0.696307	−	0.696307i
$424$		0			0
$425$	16.2871			0.790040
$426$		0			0
$427$	12.9773	+	12.9773i	0.628016	+	0.628016i
$428$		0			0
$429$	20.6511	−	2.14354i	0.997044	−	0.103491i
$430$		0			0
$431$	9.13252	−	9.13252i	0.439898	−	0.439898i	−0.452079	−	0.891978i	$-0.649318\pi$
$431$	9.13252	−	9.13252i	0.439898	−	0.439898i	0.891978	+	0.452079i	$0.149318\pi$
$432$		0			0
$433$			4.51134i			0.216801i	0.994107	+	0.108401i	$0.0345729\pi$
$433$			4.51134i			0.216801i	−0.994107	+	0.108401i	$0.965427\pi$
$434$		0			0
$435$	−16.7489	+	16.7489i	−0.803048	+	0.803048i
$436$		0			0
$437$	−3.85646	+	3.85646i	−0.184479	+	0.184479i
$438$		0			0
$439$	3.06122			0.146104			0.0730519	−	0.997328i	$-0.476726\pi$
$439$	3.06122			0.146104			0.0730519	+	0.997328i	$0.476726\pi$
$440$		0			0
$441$		−	13.8286i		−	0.658506i
$442$		0			0
$443$		−	5.41205i		−	0.257134i	−0.991701	−	0.128567i	$-0.958962\pi$
$443$		−	5.41205i		−	0.257134i	0.991701	−	0.128567i	$-0.0410378\pi$
$444$		0			0
$445$	−23.0907			−1.09460
$446$		0			0
$447$	−17.8178	+	17.8178i	−0.842751	+	0.842751i
$448$		0			0
$449$	16.7418	−	16.7418i	0.790092	−	0.790092i	−0.191417	−	0.981509i	$-0.561308\pi$
$449$	16.7418	−	16.7418i	0.790092	−	0.790092i	0.981509	+	0.191417i	$0.0613082\pi$
$450$		0			0
$451$			3.71272i			0.174825i
$452$		0			0
$453$	5.87088	−	5.87088i	0.275838	−	0.275838i
$454$		0			0
$455$	31.7735	−	39.1335i	1.48956	−	1.83461i
$456$		0			0
$457$	−13.2153	−	13.2153i	−0.618186	−	0.618186i	0.326880	−	0.945066i	$-0.394003\pi$
$457$	−13.2153	−	13.2153i	−0.618186	−	0.618186i	−0.945066	+	0.326880i	$0.894003\pi$
$458$		0			0
$459$	−1.69933			−0.0793179
$460$		0			0
$461$	13.5937	+	13.5937i	0.633123	+	0.633123i	0.948850	−	0.315727i	$-0.102248\pi$
$461$	13.5937	+	13.5937i	0.633123	+	0.633123i	−0.315727	+	0.948850i	$0.602248\pi$
$462$		0			0
$463$	11.2597	+	11.2597i	0.523283	+	0.523283i	0.918561	−	0.395278i	$-0.129352\pi$
$463$	11.2597	+	11.2597i	0.523283	+	0.523283i	−0.395278	+	0.918561i	$0.629352\pi$
$464$		0			0
$465$			53.7328i			2.49180i
$466$		0			0
$467$	−26.0724			−1.20648			−0.603242	−	0.797558i	$-0.706125\pi$
$467$	−26.0724			−1.20648			−0.603242	+	0.797558i	$0.706125\pi$
$468$		0			0
$469$	1.00615			0.0464597
$470$		0			0
$471$			50.1668i			2.31156i
$472$		0			0
$473$	−1.92823	−	1.92823i	−0.0886601	−	0.0886601i
$474$		0			0
$475$	6.60245	+	6.60245i	0.302941	+	0.302941i
$476$		0			0
$477$	14.1435			0.647588
$478$		0			0
$479$	−7.74069	−	7.74069i	−0.353681	−	0.353681i	0.507796	−	0.861477i	$-0.330460\pi$
$479$	−7.74069	−	7.74069i	−0.353681	−	0.353681i	−0.861477	+	0.507796i	$0.830460\pi$
$480$		0			0
$481$	−34.4835	+	3.57932i	−1.57231	+	0.163203i
$482$		0			0
$483$	−36.5890	+	36.5890i	−1.66486	+	1.66486i
$484$		0			0
$485$			25.7418i			1.16887i
$486$		0			0
$487$	16.9503	−	16.9503i	0.768093	−	0.768093i	−0.209677	−	0.977771i	$-0.567241\pi$
$487$	16.9503	−	16.9503i	0.768093	−	0.768093i	0.977771	+	0.209677i	$0.0672413\pi$
$488$		0			0
$489$	37.9193	−	37.9193i	1.71477	−	1.71477i
$490$		0			0
$491$	−40.1185			−1.81052			−0.905262	−	0.424855i	$-0.860325\pi$
$491$	−40.1185			−1.81052			−0.905262	+	0.424855i	$0.860325\pi$
$492$		0			0
$493$			3.88529i			0.174985i
$494$		0			0
$495$			24.4973i			1.10107i
$496$		0			0
$497$	−28.3121			−1.26997
$498$		0			0
$499$	−19.0226	+	19.0226i	−0.851569	+	0.851569i	−0.990326	−	0.138758i	$-0.955689\pi$
$499$	−19.0226	+	19.0226i	−0.851569	+	0.851569i	0.138758	+	0.990326i	$0.455689\pi$
$500$		0			0
$501$	4.36401	−	4.36401i	0.194969	−	0.194969i
$502$		0			0
$503$		−	29.7851i		−	1.32805i	−0.747710	−	0.664025i	$-0.768847\pi$
$503$		−	29.7851i		−	1.32805i	0.747710	−	0.664025i	$-0.231153\pi$
$504$		0			0
$505$	−31.3400	+	31.3400i	−1.39461	+	1.39461i
$506$		0			0
$507$	29.9094	−	6.27669i	1.32832	−	0.278758i
$508$		0			0
$509$	−23.0628	−	23.0628i	−1.02224	−	1.02224i	−0.999747	−	0.0224948i	$-0.992839\pi$
$509$	−23.0628	−	23.0628i	−1.02224	−	1.02224i	−0.0224948	−	0.999747i	$-0.507161\pi$
$510$		0			0
$511$	−2.62941			−0.116318
$512$		0			0
$513$	−0.688873	−	0.688873i	−0.0304145	−	0.0304145i
$514$		0			0
$515$	49.9981	+	49.9981i	2.20318	+	2.20318i
$516$		0			0
$517$		−	19.6360i		−	0.863590i
$518$		0			0
$519$	−13.4091			−0.588595
$520$		0			0
$521$	12.6171			0.552765			0.276383	−	0.961048i	$-0.410864\pi$
$521$	12.6171			0.552765			0.276383	+	0.961048i	$0.410864\pi$
$522$		0			0
$523$			15.9287i			0.696512i	0.937399	+	0.348256i	$0.113226\pi$
$523$			15.9287i			0.696512i	−0.937399	+	0.348256i	$0.886774\pi$
$524$		0			0
$525$	62.6421	+	62.6421i	2.73393	+	2.73393i
$526$		0			0
$527$	6.23228	+	6.23228i	0.271483	+	0.271483i
$528$		0			0
$529$	15.8414			0.688755
$530$		0			0
$531$	11.0555	+	11.0555i	0.479768	+	0.479768i
$532$		0			0
$533$	0.564223	+	5.43578i	0.0244392	+	0.235450i
$534$		0			0
$535$	−44.5860	+	44.5860i	−1.92762	+	1.92762i
$536$		0			0
$537$		−	12.2922i		−	0.530449i
$538$		0			0
$539$	9.48048	−	9.48048i	0.408353	−	0.408353i
$540$		0			0
$541$	−2.35953	+	2.35953i	−0.101444	+	0.101444i	−0.756007	−	0.654563i	$-0.772853\pi$
$541$	−2.35953	+	2.35953i	−0.101444	+	0.101444i	0.654563	+	0.756007i	$0.272853\pi$
$542$		0			0
$543$	15.2982			0.656508
$544$		0			0
$545$		−	24.6171i		−	1.05448i
$546$		0			0
$547$		−	33.6221i		−	1.43758i	−0.695228	−	0.718789i	$-0.744697\pi$
$547$		−	33.6221i		−	1.43758i	0.695228	−	0.718789i	$-0.255303\pi$
$548$		0			0
$549$	−13.1284			−0.560308
$550$		0			0
$551$	−1.57502	+	1.57502i	−0.0670980	+	0.0670980i
$552$		0			0
$553$	16.5704	−	16.5704i	0.704644	−	0.704644i
$554$		0			0
$555$		−	89.4795i		−	3.79819i
$556$		0			0
$557$	17.0484	−	17.0484i	0.722364	−	0.722364i	−0.246722	−	0.969086i	$-0.579353\pi$
$557$	17.0484	−	17.0484i	0.722364	−	0.722364i	0.969086	+	0.246722i	$0.0793535\pi$
$558$		0			0
$559$	−3.11614	−	2.53008i	−0.131799	−	0.107011i
$560$		0			0
$561$	6.21531	+	6.21531i	0.262411	+	0.262411i
$562$		0			0
$563$	21.0921			0.888926			0.444463	−	0.895797i	$-0.353395\pi$
$563$	21.0921			0.888926			0.444463	+	0.895797i	$0.353395\pi$
$564$		0			0
$565$	−8.24930	−	8.24930i	−0.347051	−	0.347051i
$566$		0			0
$567$	−25.4641	−	25.4641i	−1.06939	−	1.06939i
$568$		0			0
$569$		−	1.52644i		−	0.0639917i	−0.999488	−	0.0319958i	$-0.989814\pi$
$569$		−	1.52644i		−	0.0639917i	0.999488	−	0.0319958i	$-0.0101863\pi$
$570$		0			0
$571$	24.3730			1.01998			0.509990	−	0.860181i	$-0.329649\pi$
$571$	24.3730			1.01998			0.509990	+	0.860181i	$0.329649\pi$
$572$		0			0
$573$	9.77954			0.408546
$574$		0			0
$575$		−	66.4984i		−	2.77317i
$576$		0			0
$577$	21.0628	+	21.0628i	0.876857	+	0.876857i	0.993208	−	0.116351i	$-0.0371198\pi$
$577$	21.0628	+	21.0628i	0.876857	+	0.876857i	−0.116351	+	0.993208i	$0.537120\pi$
$578$		0			0
$579$	−17.9865	−	17.9865i	−0.747492	−	0.747492i
$580$		0			0
$581$	−25.9533			−1.07672
$582$		0			0
$583$	9.69639	+	9.69639i	0.401583	+	0.401583i
$584$		0			0
$585$	3.72286	+	35.8664i	0.153921	+	1.48289i
$586$		0			0
$587$	14.8925	−	14.8925i	0.614681	−	0.614681i	−0.329481	−	0.944162i	$-0.606874\pi$
$587$	14.8925	−	14.8925i	0.614681	−	0.614681i	0.944162	+	0.329481i	$0.106874\pi$
$588$		0			0
$589$			5.05288i			0.208200i
$590$		0			0
$591$	26.6689	−	26.6689i	1.09701	−	1.09701i
$592$		0			0
$593$	−2.59821	+	2.59821i	−0.106696	+	0.106696i	−0.758439	−	0.651744i	$-0.774038\pi$
$593$	−2.59821	+	2.59821i	−0.106696	+	0.106696i	0.651744	+	0.758439i	$0.274038\pi$
$594$		0			0
$595$	21.3407			0.874884
$596$		0			0
$597$			14.6511i			0.599629i
$598$		0			0
$599$			15.6800i			0.640669i	0.947304	+	0.320335i	$0.103795\pi$
$599$			15.6800i			0.640669i	−0.947304	+	0.320335i	$0.896205\pi$
$600$		0			0
$601$	11.0099			0.449105			0.224553	−	0.974462i	$-0.427908\pi$
$601$	11.0099			0.449105			0.224553	+	0.974462i	$0.427908\pi$
$602$		0			0
$603$	−0.508934	+	0.508934i	−0.0207254	+	0.0207254i
$604$		0			0
$605$	13.9955	−	13.9955i	0.568999	−	0.568999i
$606$		0			0
$607$			16.1773i			0.656616i	0.944571	+	0.328308i	$0.106478\pi$
$607$			16.1773i			0.656616i	−0.944571	+	0.328308i	$0.893522\pi$
$608$		0			0
$609$	−14.9433	+	14.9433i	−0.605534	+	0.605534i
$610$		0			0
$611$	−2.98408	−	28.7489i	−0.120723	−	1.16306i
$612$		0			0
$613$	−27.1775	−	27.1775i	−1.09769	−	1.09769i	−0.994680	−	0.103010i	$-0.967153\pi$
$613$	−27.1775	−	27.1775i	−1.09769	−	1.09769i	−0.103010	−	0.994680i	$-0.532847\pi$
$614$		0			0
$615$	−14.1050			−0.568770
$616$		0			0
$617$	13.5793	+	13.5793i	0.546683	+	0.546683i	0.925480	−	0.378797i	$-0.123662\pi$
$617$	13.5793	+	13.5793i	0.546683	+	0.546683i	−0.378797	+	0.925480i	$0.623662\pi$
$618$		0			0
$619$	−16.1157	−	16.1157i	−0.647743	−	0.647743i	0.304704	−	0.952447i	$-0.401442\pi$
$619$	−16.1157	−	16.1157i	−0.647743	−	0.647743i	−0.952447	+	0.304704i	$0.901442\pi$
$620$		0			0
$621$			6.93817i			0.278419i
$622$		0			0
$623$	−20.6014			−0.825379
$624$		0			0
$625$	−35.4986			−1.41994
$626$		0			0
$627$			5.03912i			0.201243i
$628$		0			0
$629$	−10.3784	−	10.3784i	−0.413815	−	0.413815i
$630$		0			0
$631$	1.21537	+	1.21537i	0.0483831	+	0.0483831i	0.730884	−	0.682501i	$-0.239108\pi$
$631$	1.21537	+	1.21537i	0.0483831	+	0.0483831i	−0.682501	+	0.730884i	$0.739108\pi$
$632$		0			0
$633$	9.38290			0.372937
$634$		0			0
$635$	56.2304	+	56.2304i	2.23143	+	2.23143i
$636$		0			0
$637$	12.4396	−	15.3211i	0.492874	−	0.607043i
$638$		0			0
$639$	14.3209	−	14.3209i	0.566527	−	0.566527i
$640$		0			0
$641$		−	39.4835i		−	1.55950i	−0.626088	−	0.779752i	$-0.715345\pi$
$641$		−	39.4835i		−	1.55950i	0.626088	−	0.779752i	$-0.284655\pi$
$642$		0			0
$643$	−15.5440	+	15.5440i	−0.612997	+	0.612997i	−0.943726	−	0.330729i	$-0.892706\pi$
$643$	−15.5440	+	15.5440i	−0.612997	+	0.612997i	0.330729	+	0.943726i	$0.392706\pi$
$644$		0			0
$645$	7.32555	−	7.32555i	0.288443	−	0.288443i
$646$		0			0
$647$	−13.8564			−0.544752			−0.272376	−	0.962191i	$-0.587809\pi$
$647$	−13.8564			−0.544752			−0.272376	+	0.962191i	$0.587809\pi$
$648$		0			0
$649$			15.1586i			0.595029i
$650$		0			0
$651$			47.9403i			1.87893i
$652$		0			0
$653$	20.0378			0.784139			0.392070	−	0.919936i	$-0.371759\pi$
$653$	20.0378			0.784139			0.392070	+	0.919936i	$0.371759\pi$
$654$		0			0
$655$	53.9344	−	53.9344i	2.10739	−	2.10739i
$656$		0			0
$657$	1.33002	−	1.33002i	0.0518890	−	0.0518890i
$658$		0			0
$659$		−	22.8569i		−	0.890377i	−0.895437	−	0.445189i	$-0.853137\pi$
$659$		−	22.8569i		−	0.890377i	0.895437	−	0.445189i	$-0.146863\pi$
$660$		0			0
$661$	−25.3589	+	25.3589i	−0.986345	+	0.986345i	−0.999908	−	0.0135629i	$-0.995683\pi$
$661$	−25.3589	+	25.3589i	−0.986345	+	0.986345i	0.0135629	+	0.999908i	$0.495683\pi$
$662$		0			0
$663$	10.0443	+	8.15526i	0.390090	+	0.316724i
$664$		0			0
$665$	8.65109	+	8.65109i	0.335475	+	0.335475i
$666$		0			0
$667$	15.8632			0.614227
$668$		0			0
$669$	−8.78021	−	8.78021i	−0.339463	−	0.339463i
$670$		0			0
$671$	−9.00047	−	9.00047i	−0.347459	−	0.347459i
$672$		0			0
$673$			7.63220i			0.294200i	0.989122	+	0.147100i	$0.0469939\pi$
$673$			7.63220i			0.294200i	−0.989122	+	0.147100i	$0.953006\pi$
$674$		0			0
$675$	11.8785			0.457204
$676$		0			0
$677$	−42.8324			−1.64618			−0.823092	−	0.567908i	$-0.807753\pi$
$677$	−42.8324			−1.64618			−0.823092	+	0.567908i	$0.807753\pi$
$678$		0			0
$679$			22.9667i			0.881382i
$680$		0			0
$681$	−41.2253	−	41.2253i	−1.57976	−	1.57976i
$682$		0			0
$683$	−7.01979	−	7.01979i	−0.268605	−	0.268605i	0.559933	−	0.828538i	$-0.310827\pi$
$683$	−7.01979	−	7.01979i	−0.268605	−	0.268605i	−0.828538	+	0.559933i	$0.810827\pi$
$684$		0			0
$685$	28.7946			1.10019
$686$		0			0
$687$	−3.07173	−	3.07173i	−0.117194	−	0.117194i
$688$		0			0
$689$	15.6700	+	12.7229i	0.596979	+	0.484702i
$690$		0			0
$691$	22.5966	−	22.5966i	0.859614	−	0.859614i	−0.131679	−	0.991292i	$-0.542037\pi$
$691$	22.5966	−	22.5966i	0.859614	−	0.859614i	0.991292	+	0.131679i	$0.0420367\pi$
$692$		0			0
$693$			21.8565i			0.830258i
$694$		0			0
$695$	15.1489	−	15.1489i	0.574631	−	0.574631i
$696$		0			0
$697$	−1.63599	+	1.63599i	−0.0619677	+	0.0619677i
$698$		0			0
$699$	−50.9426			−1.92683
$700$		0			0
$701$			25.8475i			0.976247i	0.872775	+	0.488124i	$0.162318\pi$
$701$			25.8475i			0.976247i	−0.872775	+	0.488124i	$0.837682\pi$
$702$		0			0
$703$		−	8.41440i		−	0.317355i
$704$		0			0
$705$	74.5992			2.80957
$706$		0			0
$707$	−27.9614	+	27.9614i	−1.05160	+	1.05160i
$708$		0			0
$709$	−10.7757	+	10.7757i	−0.404691	+	0.404691i	−0.879883	−	0.475191i	$-0.842379\pi$
$709$	−10.7757	+	10.7757i	−0.404691	+	0.404691i	0.475191	+	0.879883i	$0.342379\pi$
$710$		0			0
$711$			16.7634i			0.628675i
$712$		0			0
$713$	25.4457	−	25.4457i	0.952950	−	0.952950i
$714$		0			0
$715$	−22.0366	+	27.1412i	−0.824124	+	1.01502i
$716$		0			0
$717$	11.1051	+	11.1051i	0.414727	+	0.414727i
$718$		0			0
$719$	−30.6642			−1.14358			−0.571790	−	0.820400i	$-0.693751\pi$
$719$	−30.6642			−1.14358			−0.571790	+	0.820400i	$0.693751\pi$
$720$		0			0
$721$	44.6082	+	44.6082i	1.66129	+	1.66129i
$722$		0			0
$723$	−7.22124	−	7.22124i	−0.268561	−	0.268561i
$724$		0			0
$725$		−	27.1586i		−	1.00865i
$726$		0			0
$727$	−13.4091			−0.497316			−0.248658	−	0.968591i	$-0.579990\pi$
$727$	−13.4091			−0.497316			−0.248658	+	0.968591i	$0.579990\pi$
$728$		0			0
$729$	17.9093			0.663309
$730$		0			0
$731$		−	1.69933i		−	0.0628520i
$732$		0			0
$733$	11.6027	+	11.6027i	0.428555	+	0.428555i	0.888136	−	0.459581i	$-0.152000\pi$
$733$	11.6027	+	11.6027i	0.428555	+	0.428555i	−0.459581	+	0.888136i	$0.652000\pi$
$734$		0			0
$735$	36.0174	+	36.0174i	1.32852	+	1.32852i
$736$		0			0
$737$	−0.697820			−0.0257045
$738$		0			0
$739$	1.02167	+	1.02167i	0.0375829	+	0.0375829i	0.725648	−	0.688066i	$-0.241540\pi$
$739$	1.02167	+	1.02167i	0.0375829	+	0.0375829i	−0.688066	+	0.725648i	$0.741540\pi$
$740$		0			0
$741$	0.765795	+	7.37775i	0.0281322	+	0.271028i
$742$		0			0
$743$	−27.6462	+	27.6462i	−1.01424	+	1.01424i	−0.0143435	+	0.999897i	$0.504566\pi$
$743$	−27.6462	+	27.6462i	−1.01424	+	1.01424i	−0.999897	+	0.0143435i	$0.995434\pi$
$744$		0			0
$745$		−	42.4306i		−	1.55454i
$746$		0			0
$747$	13.1278	−	13.1278i	0.480320	−	0.480320i
$748$		0			0
$749$	−39.7795	+	39.7795i	−1.45351	+	1.45351i
$750$		0			0
$751$	−47.1345			−1.71996			−0.859981	−	0.510326i	$-0.829525\pi$
$751$	−47.1345			−1.71996			−0.859981	+	0.510326i	$0.829525\pi$
$752$		0			0
$753$			3.85646i			0.140537i
$754$		0			0
$755$			13.9807i			0.508810i
$756$		0			0
$757$	0.507548			0.0184472			0.00922358	−	0.999957i	$-0.497064\pi$
$757$	0.507548			0.0184472			0.00922358	+	0.999957i	$0.497064\pi$
$758$		0			0
$759$	25.3764	−	25.3764i	0.921106	−	0.921106i
$760$		0			0
$761$	−35.8664	+	35.8664i	−1.30016	+	1.30016i	−0.371872	+	0.928284i	$0.621284\pi$
$761$	−35.8664	+	35.8664i	−1.30016	+	1.30016i	−0.928284	+	0.371872i	$0.878716\pi$
$762$		0			0
$763$		−	21.9633i		−	0.795125i
$764$		0			0
$765$	−10.7946	+	10.7946i	−0.390281	+	0.390281i
$766$		0			0
$767$	2.30366	+	22.1937i	0.0831803	+	0.801367i
$768$		0			0
$769$	4.77574	+	4.77574i	0.172218	+	0.172218i	0.787953	−	0.615735i	$-0.211141\pi$
$769$	4.77574	+	4.77574i	0.172218	+	0.172218i	−0.615735	+	0.787953i	$0.711141\pi$
$770$		0			0
$771$	12.6543			0.455734
$772$		0			0
$773$	29.0484	+	29.0484i	1.04480	+	1.04480i	0.998948	+	0.0458502i	$0.0145997\pi$
$773$	29.0484	+	29.0484i	1.04480	+	1.04480i	0.0458502	+	0.998948i	$0.485400\pi$
$774$		0			0
$775$	−43.5644	−	43.5644i	−1.56488	−	1.56488i
$776$		0			0
$777$		−	79.8334i		−	2.86401i
$778$		0			0
$779$	−1.32640			−0.0475231
$780$		0			0
$781$	19.6360			0.702631
$782$		0			0
$783$			2.83362i			0.101265i
$784$		0			0
$785$	−59.7328	−	59.7328i	−2.13196	−	2.13196i
$786$		0			0
$787$	−8.38168	−	8.38168i	−0.298775	−	0.298775i	0.541759	−	0.840534i	$-0.317758\pi$
$787$	−8.38168	−	8.38168i	−0.298775	−	0.298775i	−0.840534	+	0.541759i	$0.817758\pi$
$788$		0			0
$789$	−40.7177			−1.44959
$790$		0			0
$791$	−7.36001	−	7.36001i	−0.261692	−	0.261692i
$792$		0			0
$793$	−14.5453	−	11.8097i	−0.516520	−	0.419376i
$794$		0			0
$795$	−36.8376	+	36.8376i	−1.30649	+	1.30649i
$796$		0			0
$797$			6.53638i			0.231531i	0.993277	+	0.115765i	$0.0369321\pi$
$797$			6.53638i			0.231531i	−0.993277	+	0.115765i	$0.963068\pi$
$798$		0			0
$799$	8.65251	−	8.65251i	0.306104	−	0.306104i
$800$		0			0
$801$	10.4207	−	10.4207i	0.368197	−	0.368197i
$802$		0			0
$803$	1.82364			0.0643549
$804$		0			0
$805$		−	87.1318i		−	3.07099i
$806$		0			0
$807$			40.4260i			1.42306i
$808$		0			0
$809$	−16.6851			−0.586616			−0.293308	−	0.956018i	$-0.594756\pi$
$809$	−16.6851			−0.586616			−0.293308	+	0.956018i	$0.594756\pi$
$810$		0			0
$811$	27.8843	−	27.8843i	0.979150	−	0.979150i	−0.0206367	−	0.999787i	$-0.506569\pi$
$811$	27.8843	−	27.8843i	0.979150	−	0.979150i	0.999787	+	0.0206367i	$0.00656934\pi$
$812$		0			0
$813$	−30.8860	+	30.8860i	−1.08322	+	1.08322i
$814$		0			0
$815$			90.2998i			3.16306i
$816$		0			0
$817$	0.688873	−	0.688873i	0.0241006	−	0.0241006i
$818$		0			0
$819$	3.32153	+	31.9999i	0.116064	+	1.11817i
$820$		0			0
$821$	29.0484	+	29.0484i	1.01380	+	1.01380i	0.999903	+	0.0138929i	$0.00442238\pi$
$821$	29.0484	+	29.0484i	1.01380	+	1.01380i	0.0138929	+	0.999903i	$0.495578\pi$
$822$		0			0
$823$	37.1162			1.29379			0.646894	−	0.762580i	$-0.276068\pi$
$823$	37.1162			1.29379			0.646894	+	0.762580i	$0.276068\pi$
$824$		0			0
$825$	−43.4457	−	43.4457i	−1.51259	−	1.51259i
$826$		0			0
$827$	−3.92862	−	3.92862i	−0.136612	−	0.136612i	0.635494	−	0.772106i	$-0.280796\pi$
$827$	−3.92862	−	3.92862i	−0.136612	−	0.136612i	−0.772106	+	0.635494i	$0.780796\pi$
$828$		0			0
$829$		−	34.1346i		−	1.18554i	−0.805371	−	0.592772i	$-0.798034\pi$
$829$		−	34.1346i		−	1.18554i	0.805371	−	0.592772i	$-0.201966\pi$
$830$		0			0
$831$	73.6752			2.55576
$832$		0			0
$833$	8.35506			0.289486
$834$		0			0
$835$			10.3923i			0.359641i
$836$		0			0
$837$	4.54533	+	4.54533i	0.157110	+	0.157110i
$838$		0			0
$839$	40.6419	+	40.6419i	1.40311	+	1.40311i	0.789974	+	0.613140i	$0.210094\pi$
$839$	40.6419	+	40.6419i	1.40311	+	1.40311i	0.613140	+	0.789974i	$0.289906\pi$
$840$		0			0
$841$	−22.5213			−0.776596
$842$		0			0
$843$	−35.7687	−	35.7687i	−1.23194	−	1.23194i
$844$		0			0
$845$	−28.1391	+	43.0862i	−0.968013	+	1.48221i
$846$		0			0
$847$	12.4868	−	12.4868i	0.429051	−	0.429051i
$848$		0			0
$849$			45.5893i			1.56462i
$850$		0			0
$851$	−42.3740	+	42.3740i	−1.45256	+	1.45256i
$852$		0			0
$853$	−24.1391	+	24.1391i	−0.826506	+	0.826506i	−0.987032	−	0.160526i	$-0.948681\pi$
$853$	−24.1391	+	24.1391i	−0.826506	+	0.826506i	0.160526	+	0.987032i	$0.448681\pi$
$854$		0			0
$855$	−8.75184			−0.299307
$856$		0			0
$857$		−	41.0907i		−	1.40363i	−0.712359	−	0.701815i	$-0.752373\pi$
$857$		−	41.0907i		−	1.40363i	0.712359	−	0.701815i	$-0.247627\pi$
$858$		0			0
$859$		−	24.0290i		−	0.819859i	−0.912117	−	0.409930i	$-0.865553\pi$
$859$		−	24.0290i		−	0.819859i	0.912117	−	0.409930i	$-0.134447\pi$
$860$		0			0
$861$	−12.5845			−0.428878
$862$		0			0
$863$	−32.9339	+	32.9339i	−1.12108	+	1.12108i	−0.129506	+	0.991579i	$0.541339\pi$
$863$	−32.9339	+	32.9339i	−1.12108	+	1.12108i	−0.991579	+	0.129506i	$0.958661\pi$
$864$		0			0
$865$	15.9660	−	15.9660i	0.542861	−	0.542861i
$866$		0			0
$867$		−	34.4868i		−	1.17123i
$868$		0			0
$869$	−11.4925	+	11.4925i	−0.389855	+	0.389855i
$870$		0			0
$871$	−1.02167	+	0.106048i	−0.0346181	+	0.00359329i
$872$		0			0
$873$	−11.6171	−	11.6171i	−0.393179	−	0.393179i
$874$		0			0
$875$	−79.2704			−2.67983
$876$		0			0
$877$	−8.25377	−	8.25377i	−0.278710	−	0.278710i	0.553884	−	0.832594i	$-0.313145\pi$
$877$	−8.25377	−	8.25377i	−0.278710	−	0.278710i	−0.832594	+	0.553884i	$0.813145\pi$
$878$		0			0
$879$	−27.6135	−	27.6135i	−0.931379	−	0.931379i
$880$		0			0
$881$		−	12.9344i		−	0.435770i	−0.975974	−	0.217885i	$-0.930084\pi$
$881$		−	12.9344i		−	0.435770i	0.975974	−	0.217885i	$-0.0699158\pi$
$882$		0			0
$883$	5.22887			0.175966			0.0879828	−	0.996122i	$-0.471958\pi$
$883$	5.22887			0.175966			0.0879828	+	0.996122i	$0.471958\pi$
$884$		0			0
$885$	−57.5893			−1.93584
$886$		0			0
$887$		−	40.3606i		−	1.35517i	−0.735442	−	0.677587i	$-0.763026\pi$
$887$		−	40.3606i		−	1.35517i	0.735442	−	0.677587i	$-0.236974\pi$
$888$		0			0
$889$	50.1686	+	50.1686i	1.68260	+	1.68260i
$890$		0			0
$891$	17.6607	+	17.6607i	0.591656	+	0.591656i
$892$		0			0
$893$	7.01510			0.234751
$894$		0			0
$895$	14.6362	+	14.6362i	0.489233	+	0.489233i
$896$		0			0
$897$	33.2970	−	41.0099i	1.11176	−	1.36928i
$898$		0			0
$899$	10.3923	−	10.3923i	0.346603	−	0.346603i
$900$		0			0
$901$			8.54533i			0.284686i
$902$		0			0
$903$	6.53583	−	6.53583i	0.217499	−	0.217499i
$904$		0			0
$905$	−18.2153	+	18.2153i	−0.605497	+	0.605497i
$906$		0			0
$907$	−10.5166			−0.349198			−0.174599	−	0.984640i	$-0.555863\pi$
$907$	−10.5166			−0.349198			−0.174599	+	0.984640i	$0.555863\pi$
$908$		0			0
$909$		−	28.2871i		−	0.938223i
$910$		0			0
$911$			30.9782i			1.02635i	0.858283	+	0.513177i	$0.171532\pi$
$911$			30.9782i			1.02635i	−0.858283	+	0.513177i	$0.828468\pi$
$912$		0			0
$913$	18.0000			0.595713
$914$		0			0
$915$	34.1937	−	34.1937i	1.13041	−	1.13041i
$916$		0			0
$917$	48.1202	−	48.1202i	1.58907	−	1.58907i
$918$		0			0
$919$		−	20.0443i		−	0.661200i	−0.943771	−	0.330600i	$-0.892749\pi$
$919$		−	20.0443i		−	0.661200i	0.943771	−	0.330600i	$-0.107251\pi$
$920$		0			0
$921$	−37.6270	+	37.6270i	−1.23985	+	1.23985i
$922$		0			0
$923$	28.7489	−	2.98408i	0.946283	−	0.0982223i
$924$		0			0
$925$	72.5463	+	72.5463i	2.38531	+	2.38531i
$926$		0			0
$927$	−45.1277			−1.48219
$928$		0			0
$929$	33.7229	+	33.7229i	1.10641	+	1.10641i	0.993619	+	0.112793i	$0.0359796\pi$
$929$	33.7229	+	33.7229i	1.10641	+	1.10641i	0.112793	+	0.993619i	$0.464020\pi$
$930$		0			0
$931$	3.38697	+	3.38697i	0.111003	+	0.111003i
$932$		0			0
$933$			20.1435i			0.659470i
$934$		0			0
$935$	−14.8009			−0.484043
$936$		0			0
$937$	49.5515			1.61878			0.809388	−	0.587274i	$-0.199799\pi$
$937$	49.5515			1.61878			0.809388	+	0.587274i	$0.199799\pi$
$938$		0			0
$939$			6.73845i			0.219901i
$940$		0			0
$941$	−32.8279	−	32.8279i	−1.07016	−	1.07016i	−0.997345	−	0.0728149i	$-0.976802\pi$
$941$	−32.8279	−	32.8279i	−1.07016	−	1.07016i	−0.0728149	−	0.997345i	$-0.523198\pi$
$942$		0			0
$943$	6.67958	+	6.67958i	0.217517	+	0.217517i
$944$		0			0
$945$	15.5642			0.506304
$946$		0			0
$947$	−1.73205	−	1.73205i	−0.0562841	−	0.0562841i	0.678405	−	0.734689i	$-0.262672\pi$
$947$	−1.73205	−	1.73205i	−0.0562841	−	0.0562841i	−0.734689	+	0.678405i	$0.762672\pi$
$948$		0			0
$949$	2.66998	−	0.277139i	0.0866713	−	0.00899631i
$950$		0			0
$951$	36.7133	−	36.7133i	1.19051	−	1.19051i
$952$		0			0
$953$		−	34.1006i		−	1.10463i	−0.833636	−	0.552314i	$-0.813745\pi$
$953$		−	34.1006i		−	1.10463i	0.833636	−	0.552314i	$-0.186255\pi$
$954$		0			0
$955$	−11.6443	+	11.6443i	−0.376802	+	0.376802i
$956$		0			0
$957$	10.3640	−	10.3640i	0.335021	−	0.335021i
$958$		0			0
$959$	25.6905			0.829589
$960$		0			0
$961$		−	2.33996i		−	0.0754827i
$962$		0			0
$963$		−	40.2428i		−	1.29681i
$964$		0			0
$965$	42.8324			1.37882
$966$		0			0
$967$	9.96721	−	9.96721i	0.320524	−	0.320524i	−0.528444	−	0.848968i	$-0.677224\pi$
$967$	9.96721	−	9.96721i	0.320524	−	0.320524i	0.848968	+	0.528444i	$0.177224\pi$
$968$		0			0
$969$	−2.22046	+	2.22046i	−0.0713316	+	0.0713316i
$970$		0			0
$971$			27.5885i			0.885357i	0.896680	+	0.442679i	$0.145972\pi$
$971$			27.5885i			0.885357i	−0.896680	+	0.442679i	$0.854028\pi$
$972$		0			0
$973$	13.5158	−	13.5158i	0.433297	−	0.433297i
$974$		0			0
$975$	−70.2111	−	57.0062i	−2.24855	−	1.82566i
$976$		0			0
$977$	2.89424	+	2.89424i	0.0925950	+	0.0925950i	0.751887	−	0.659292i	$-0.229144\pi$
$977$	2.89424	+	2.89424i	0.0925950	+	0.0925950i	−0.659292	+	0.751887i	$0.729144\pi$
$978$		0			0
$979$	14.2882			0.456653
$980$		0			0
$981$	11.1096	+	11.1096i	0.354701	+	0.354701i
$982$		0			0
$983$	12.3480	+	12.3480i	0.393840	+	0.393840i	0.876054	−	0.482214i	$-0.160167\pi$
$983$	12.3480	+	12.3480i	0.393840	+	0.393840i	−0.482214	+	0.876054i	$0.660167\pi$
$984$		0			0
$985$			63.5085i			2.02355i
$986$		0			0
$987$	66.5572			2.11854
$988$		0			0
$989$	−6.93817			−0.220621
$990$		0			0
$991$			47.2888i			1.50218i	0.660201	+	0.751089i	$0.270471\pi$
$991$			47.2888i			1.50218i	−0.660201	+	0.751089i	$0.729529\pi$
$992$		0			0
$993$	−15.1247	−	15.1247i	−0.479966	−	0.479966i
$994$		0			0
$995$	−17.4448	−	17.4448i	−0.553038	−	0.553038i
$996$		0			0
$997$	−17.4547			−0.552795			−0.276397	−	0.961043i	$-0.589141\pi$
$997$	−17.4547			−0.552795			−0.276397	+	0.961043i	$0.589141\pi$
$998$		0			0
$999$	−7.56920	−	7.56920i	−0.239479	−	0.239479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.k.b.47.2	yes	12
3.2	odd	2		1872.2.bf.o.1711.2		12
4.3	odd	2	inner	208.2.k.b.47.5	yes	12
8.3	odd	2		832.2.k.j.255.2		12
8.5	even	2		832.2.k.j.255.5		12
12.11	even	2		1872.2.bf.o.1711.1		12
13.5	odd	4	inner	208.2.k.b.31.2	✓	12
39.5	even	4		1872.2.bf.o.1279.1		12
52.31	even	4	inner	208.2.k.b.31.5	yes	12
104.5	odd	4		832.2.k.j.447.5		12
104.83	even	4		832.2.k.j.447.2		12
156.83	odd	4		1872.2.bf.o.1279.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.k.b.31.2	✓	12	13.5	odd	4	inner
208.2.k.b.31.5	yes	12	52.31	even	4	inner
208.2.k.b.47.2	yes	12	1.1	even	1	trivial
208.2.k.b.47.5	yes	12	4.3	odd	2	inner
832.2.k.j.255.2		12	8.3	odd	2
832.2.k.j.255.5		12	8.5	even	2
832.2.k.j.447.2		12	104.83	even	4
832.2.k.j.447.5		12	104.5	odd	4
1872.2.bf.o.1279.1		12	39.5	even	4
1872.2.bf.o.1279.2		12	156.83	odd	4
1872.2.bf.o.1711.1		12	12.11	even	2
1872.2.bf.o.1711.2		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.35084i q^{3} +(2.79911 + 2.79911i) q^{5} +(2.49735 + 2.49735i) q^{7} -2.52644 q^{9} +(-1.73205 - 1.73205i) q^{11} +(-2.79911 - 2.27267i) q^{13} +(6.58024 - 6.58024i) q^{15} -1.52644i q^{17} +(0.618787 - 0.618787i) q^{19} +(5.87088 - 5.87088i) q^{21} -6.23228 q^{23} +10.6700i q^{25} -1.11326i q^{27} -2.54533 q^{29} +(-4.08289 + 4.08289i) q^{31} +(-4.07177 + 4.07177i) q^{33} +13.9807i q^{35} +(6.79911 - 6.79911i) q^{37} +(-5.34267 + 6.58024i) q^{39} +(-1.07177 - 1.07177i) q^{41} +1.11326 q^{43} +(-7.07177 - 7.07177i) q^{45} +(5.66842 + 5.66842i) q^{47} +5.47356i q^{49} -3.58841 q^{51} -5.59821 q^{53} -9.69639i q^{55} +(-1.45467 - 1.45467i) q^{57} +(-4.37592 - 4.37592i) q^{59} +5.19642 q^{61} +(-6.30942 - 6.30942i) q^{63} +(-1.47356 - 14.1964i) q^{65} +(0.201443 - 0.201443i) q^{67} +14.6511i q^{69} +(-5.66842 + 5.66842i) q^{71} +(-0.526440 + 0.526440i) q^{73} +25.0834 q^{75} -8.65109i q^{77} -6.63517i q^{79} -10.1964 q^{81} +(-5.19615 + 5.19615i) q^{83} +(4.27267 - 4.27267i) q^{85} +5.98366i q^{87} +(-4.12465 + 4.12465i) q^{89} +(-1.31471 - 12.6660i) q^{91} +(9.59821 + 9.59821i) q^{93} +3.46410 q^{95} +(4.59821 + 4.59821i) q^{97} +(4.37592 + 4.37592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 20 q^{9} - 4 q^{13} - 8 q^{21} + 8 q^{29} + 52 q^{37} + 36 q^{41} - 36 q^{45} - 8 q^{53} - 56 q^{57} - 56 q^{61} - 28 q^{65} + 4 q^{73} - 4 q^{81} + 32 q^{85} + 20 q^{89} + 56 q^{93} - 4 q^{97}+O(q^{100}) \) 12 * q + 4 * q^5 - 20 * q^9 - 4 * q^13 - 8 * q^21 + 8 * q^29 + 52 * q^37 + 36 * q^41 - 36 * q^45 - 8 * q^53 - 56 * q^57 - 56 * q^61 - 28 * q^65 + 4 * q^73 - 4 * q^81 + 32 * q^85 + 20 * q^89 + 56 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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