LMFDB - Embedded newform 416.2.k.e.255.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(31,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, 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("416.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 17x^{6} + 84x^{4} + 100x^{2} + 16 $ x^8 + 17x^6 + 84x^4 + 100*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			255.2
Root			$1.20241i$ of defining polynomial
Character	$\chi$	$=$	416.255
Dual form			416.2.k.e.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.46091i q^{3} +(1.87831 + 1.87831i) q^{5} +(0.675897 + 0.675897i) q^{7} +0.865736 q^{9} +(-0.202412 - 0.202412i) q^{11} +(0.675897 + 3.54163i) q^{13} +(2.74404 - 2.74404i) q^{15} -0.539088i q^{17} +(-1.66332 + 1.66332i) q^{19} +(0.987427 - 0.987427i) q^{21} +4.67844 q^{23} +2.05609i q^{25} -5.64750i q^{27} -4.27362 q^{29} +(5.66332 - 5.66332i) q^{31} +(-0.295706 + 0.295706i) q^{33} +2.53909i q^{35} +(4.80013 - 4.80013i) q^{37} +(5.17401 - 0.987427i) q^{39} +(2.21753 + 2.21753i) q^{41} -12.5693 q^{43} +(1.62612 + 1.62612i) q^{45} +(-1.08072 - 1.08072i) q^{47} -6.08633i q^{49} -0.787560 q^{51} +3.75662 q^{53} -0.760383i q^{55} +(2.42997 + 2.42997i) q^{57} +(3.41994 + 3.41994i) q^{59} -12.6533 q^{61} +(0.585148 + 0.585148i) q^{63} +(-5.38274 + 7.92182i) q^{65} +(-9.28568 + 9.28568i) q^{67} -6.83479i q^{69} +(-9.35434 + 9.35434i) q^{71} +(-0.865736 + 0.865736i) q^{73} +3.00377 q^{75} -0.273619i q^{77} +13.0833i q^{79} -5.65330 q^{81} +(3.12424 - 3.12424i) q^{83} +(1.01257 - 1.01257i) q^{85} +6.24338i q^{87} +(6.21753 - 6.21753i) q^{89} +(-1.93694 + 2.85062i) q^{91} +(-8.27362 - 8.27362i) q^{93} -6.24847 q^{95} +(-7.67844 - 7.67844i) q^{97} +(-0.175235 - 0.175235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{7} - 20 q^{9} + 6 q^{11} - 2 q^{13} - 20 q^{15} + 6 q^{19} - 4 q^{21} - 16 q^{23} + 4 q^{29} + 26 q^{31} + 16 q^{33} + 8 q^{39} - 24 q^{41} - 44 q^{43} + 8 q^{45} + 14 q^{47} + 44 q^{51} + 28 q^{57}+ \cdots - 66 q^{99}+O(q^{100}) $ 8 * q - 2 * q^7 - 20 * q^9 + 6 * q^11 - 2 * q^13 - 20 * q^15 + 6 * q^19 - 4 * q^21 - 16 * q^23 + 4 * q^29 + 26 * q^31 + 16 * q^33 + 8 * q^39 - 24 * q^41 - 44 * q^43 + 8 * q^45 + 14 * q^47 + 44 * q^51 + 28 * q^57 - 22 * q^59 - 24 * q^61 - 38 * q^63 - 8 * q^65 + 2 * q^67 - 14 * q^71 + 20 * q^73 + 76 * q^75 + 32 * q^81 - 6 * q^83 + 20 * q^85 + 8 * q^89 + 42 * q^91 - 28 * q^93 + 12 * q^95 - 8 * q^97 - 66 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$		−	1.46091i		−	0.843458i	−0.906722	−	0.421729i	$-0.861423\pi$
$3$		−	1.46091i		−	0.843458i	0.906722	−	0.421729i	$-0.138577\pi$
$4$		0			0
$5$	1.87831	+	1.87831i	0.840005	+	0.840005i	0.988859	−	0.148854i	$-0.0475584\pi$
$5$	1.87831	+	1.87831i	0.840005	+	0.840005i	−0.148854	+	0.988859i	$0.547558\pi$
$6$		0			0
$7$	0.675897	+	0.675897i	0.255465	+	0.255465i	0.823207	−	0.567742i	$-0.192183\pi$
$7$	0.675897	+	0.675897i	0.255465	+	0.255465i	−0.567742	+	0.823207i	$0.692183\pi$
$8$		0			0
$9$	0.865736			0.288579
$10$		0			0
$11$	−0.202412	−	0.202412i	−0.0610294	−	0.0610294i	0.675933	−	0.736963i	$-0.263741\pi$
$11$	−0.202412	−	0.202412i	−0.0610294	−	0.0610294i	−0.736963	+	0.675933i	$0.763741\pi$
$12$		0			0
$13$	0.675897	+	3.54163i	0.187460	+	0.982272i
$13$	0.675897	+	3.54163i	0.187460	+	0.982272i
$14$		0			0
$15$	2.74404	−	2.74404i	0.708509	−	0.708509i
$16$		0			0
$17$		−	0.539088i		−	0.130748i	−0.997861	−	0.0653740i	$-0.979176\pi$
$17$		−	0.539088i		−	0.130748i	0.997861	−	0.0653740i	$-0.0208240\pi$
$18$		0			0
$19$	−1.66332	+	1.66332i	−0.381593	+	0.381593i	−0.871676	−	0.490083i	$-0.836966\pi$
$19$	−1.66332	+	1.66332i	−0.381593	+	0.381593i	0.490083	+	0.871676i	$0.336966\pi$
$20$		0			0
$21$	0.987427	−	0.987427i	0.215474	−	0.215474i
$22$		0			0
$23$	4.67844			0.975523			0.487761	−	0.872977i	$-0.337814\pi$
$23$	4.67844			0.975523			0.487761	+	0.872977i	$0.337814\pi$
$24$		0			0
$25$			2.05609i			0.411218i
$26$		0			0
$27$		−	5.64750i		−	1.08686i
$28$		0			0
$29$	−4.27362			−0.793591			−0.396796	−	0.917907i	$-0.629878\pi$
$29$	−4.27362			−0.793591			−0.396796	+	0.917907i	$0.629878\pi$
$30$		0			0
$31$	5.66332	−	5.66332i	1.01716	−	1.01716i	0.0173129	−	0.999850i	$-0.494489\pi$
$31$	5.66332	−	5.66332i	1.01716	−	1.01716i	0.999850	−	0.0173129i	$-0.00551113\pi$
$32$		0			0
$33$	−0.295706	+	0.295706i	−0.0514757	+	0.0514757i
$34$		0			0
$35$			2.53909i			0.429184i
$36$		0			0
$37$	4.80013	−	4.80013i	0.789137	−	0.789137i	−0.192216	−	0.981353i	$-0.561567\pi$
$37$	4.80013	−	4.80013i	0.789137	−	0.789137i	0.981353	+	0.192216i	$0.0615673\pi$
$38$		0			0
$39$	5.17401	−	0.987427i	0.828505	−	0.158115i
$40$		0			0
$41$	2.21753	+	2.21753i	0.346320	+	0.346320i	0.858737	−	0.512417i	$-0.171250\pi$
$41$	2.21753	+	2.21753i	0.346320	+	0.346320i	−0.512417	+	0.858737i	$0.671250\pi$
$42$		0			0
$43$	−12.5693			−1.91680			−0.958402	−	0.285422i	$-0.907866\pi$
$43$	−12.5693			−1.91680			−0.958402	+	0.285422i	$0.907866\pi$
$44$		0			0
$45$	1.62612	+	1.62612i	0.242407	+	0.242407i
$46$		0			0
$47$	−1.08072	−	1.08072i	−0.157639	−	0.157639i	0.623880	−	0.781520i	$-0.285555\pi$
$47$	−1.08072	−	1.08072i	−0.157639	−	0.157639i	−0.781520	+	0.623880i	$0.785555\pi$
$48$		0			0
$49$		−	6.08633i		−	0.869475i
$50$		0			0
$51$	−0.787560			−0.110280
$52$		0			0
$53$	3.75662			0.516011			0.258006	−	0.966143i	$-0.416935\pi$
$53$	3.75662			0.516011			0.258006	+	0.966143i	$0.416935\pi$
$54$		0			0
$55$		−	0.760383i		−	0.102530i
$56$		0			0
$57$	2.42997	+	2.42997i	0.321857	+	0.321857i
$58$		0			0
$59$	3.41994	+	3.41994i	0.445238	+	0.445238i	0.893768	−	0.448530i	$-0.148052\pi$
$59$	3.41994	+	3.41994i	0.445238	+	0.445238i	−0.448530	+	0.893768i	$0.648052\pi$
$60$		0			0
$61$	−12.6533			−1.62009			−0.810044	−	0.586369i	$-0.800557\pi$
$61$	−12.6533			−1.62009			−0.810044	+	0.586369i	$0.800557\pi$
$62$		0			0
$63$	0.585148	+	0.585148i	0.0737218	+	0.0737218i
$64$		0			0
$65$	−5.38274	+	7.92182i	−0.667646	+	0.982581i
$66$		0			0
$67$	−9.28568	+	9.28568i	−1.13443	+	1.13443i	−0.144993	+	0.989433i	$0.546316\pi$
$67$	−9.28568	+	9.28568i	−1.13443	+	1.13443i	−0.989433	+	0.144993i	$0.953684\pi$
$68$		0			0
$69$		−	6.83479i		−	0.822812i
$70$		0			0
$71$	−9.35434	+	9.35434i	−1.11016	+	1.11016i	−0.117027	+	0.993129i	$0.537336\pi$
$71$	−9.35434	+	9.35434i	−1.11016	+	1.11016i	−0.993129	+	0.117027i	$0.962664\pi$
$72$		0			0
$73$	−0.865736	+	0.865736i	−0.101327	+	0.101327i	−0.755953	−	0.654626i	$-0.772826\pi$
$73$	−0.865736	+	0.865736i	−0.101327	+	0.101327i	0.654626	+	0.755953i	$0.272826\pi$
$74$		0			0
$75$	3.00377			0.346845
$76$		0			0
$77$		−	0.273619i		−	0.0311818i
$78$		0			0
$79$			13.0833i			1.47198i	0.676991	+	0.735991i	$0.263284\pi$
$79$			13.0833i			1.47198i	−0.676991	+	0.735991i	$0.736716\pi$
$80$		0			0
$81$	−5.65330			−0.628144
$82$		0			0
$83$	3.12424	−	3.12424i	0.342929	−	0.342929i	−0.514538	−	0.857468i	$-0.672037\pi$
$83$	3.12424	−	3.12424i	0.342929	−	0.342929i	0.857468	+	0.514538i	$0.172037\pi$
$84$		0			0
$85$	1.01257	−	1.01257i	0.109829	−	0.109829i
$86$		0			0
$87$			6.24338i			0.669361i
$88$		0			0
$89$	6.21753	−	6.21753i	0.659057	−	0.659057i	−0.296100	−	0.955157i	$-0.595686\pi$
$89$	6.21753	−	6.21753i	0.659057	−	0.659057i	0.955157	+	0.296100i	$0.0956862\pi$
$90$		0			0
$91$	−1.93694	+	2.85062i	−0.203047	+	0.298826i
$92$		0			0
$93$	−8.27362	−	8.27362i	−0.857934	−	0.857934i
$94$		0			0
$95$	−6.24847			−0.641080
$96$		0			0
$97$	−7.67844	−	7.67844i	−0.779628	−	0.779628i	0.200140	−	0.979767i	$-0.435860\pi$
$97$	−7.67844	−	7.67844i	−0.779628	−	0.779628i	−0.979767	+	0.200140i	$0.935860\pi$
$98$		0			0
$99$	−0.175235	−	0.175235i	−0.0176118	−	0.0176118i
$100$		0			0
$101$			6.70359i			0.667032i	0.942744	+	0.333516i	$0.108235\pi$
$101$			6.70359i			0.667032i	−0.942744	+	0.333516i	$0.891765\pi$
$102$		0			0
$103$	−4.46021			−0.439477			−0.219739	−	0.975559i	$-0.570520\pi$
$103$	−4.46021			−0.439477			−0.219739	+	0.975559i	$0.570520\pi$
$104$		0			0
$105$	3.70938			0.361999
$106$		0			0
$107$		−	10.2485i		−	0.990757i	−0.868677	−	0.495379i	$-0.835029\pi$
$107$		−	10.2485i		−	0.990757i	0.868677	−	0.495379i	$-0.164971\pi$
$108$		0			0
$109$	−0.556751	−	0.556751i	−0.0533271	−	0.0533271i	0.679940	−	0.733267i	$-0.262006\pi$
$109$	−0.556751	−	0.556751i	−0.0533271	−	0.0533271i	−0.733267	+	0.679940i	$0.762006\pi$
$110$		0			0
$111$	−7.01257	−	7.01257i	−0.665604	−	0.665604i
$112$		0			0
$113$	−12.9962			−1.22258			−0.611291	−	0.791406i	$-0.709350\pi$
$113$	−12.9962			−1.22258			−0.611291	+	0.791406i	$0.709350\pi$
$114$		0			0
$115$	8.78756	+	8.78756i	0.819444	+	0.819444i
$116$		0			0
$117$	0.585148	+	3.06612i	0.0540970	+	0.283463i
$118$		0			0
$119$	0.364368	−	0.364368i	0.0334016	−	0.0334016i
$120$		0			0
$121$		−	10.9181i		−	0.992551i
$122$		0			0
$123$	3.23962	−	3.23962i	0.292106	−	0.292106i
$124$		0			0
$125$	5.52957	−	5.52957i	0.494580	−	0.494580i
$126$		0			0
$127$	−4.67844			−0.415145			−0.207572	−	0.978220i	$-0.566556\pi$
$127$	−4.67844			−0.415145			−0.207572	+	0.978220i	$0.566556\pi$
$128$		0			0
$129$			18.3627i			1.61674i
$130$		0			0
$131$		−	11.0802i		−	0.968082i	−0.875045	−	0.484041i	$-0.839169\pi$
$131$		−	11.0802i		−	0.968082i	0.875045	−	0.484041i	$-0.160831\pi$
$132$		0			0
$133$	−2.24847			−0.194967
$134$		0			0
$135$	10.6078	−	10.6078i	0.912970	−	0.912970i
$136$		0			0
$137$	15.6533	−	15.6533i	1.33735	−	1.33735i	0.438735	−	0.898617i	$-0.355427\pi$
$137$	15.6533	−	15.6533i	1.33735	−	1.33735i	0.898617	−	0.438735i	$-0.144573\pi$
$138$		0			0
$139$			15.8960i			1.34828i	0.738604	+	0.674139i	$0.235485\pi$
$139$			15.8960i			1.34828i	−0.738604	+	0.674139i	$0.764515\pi$
$140$		0			0
$141$	−1.57884	+	1.57884i	−0.132962	+	0.132962i
$142$		0			0
$143$	0.580058	−	0.853677i	0.0485069	−	0.0713881i
$144$		0			0
$145$	−8.02718	−	8.02718i	−0.666621	−	0.666621i
$146$		0			0
$147$	−8.89159			−0.733366
$148$		0			0
$149$	11.8178	+	11.8178i	0.968152	+	0.968152i	0.999508	−	0.0313566i	$-0.00998276\pi$
$149$	11.8178	+	11.8178i	0.968152	+	0.968152i	−0.0313566	+	0.999508i	$0.509983\pi$
$150$		0			0
$151$	0.894133	+	0.894133i	0.0727635	+	0.0727635i	0.742552	−	0.669788i	$-0.233615\pi$
$151$	0.894133	+	0.894133i	0.0727635	+	0.0727635i	−0.669788	+	0.742552i	$0.733615\pi$
$152$		0			0
$153$		−	0.466707i		−	0.0377311i
$154$		0			0
$155$	21.2749			1.70884
$156$		0			0
$157$	−11.3266			−0.903965			−0.451982	−	0.892027i	$-0.649283\pi$
$157$	−11.3266			−0.903965			−0.451982	+	0.892027i	$0.649283\pi$
$158$		0			0
$159$		−	5.48809i		−	0.435234i
$160$		0			0
$161$	3.16215	+	3.16215i	0.249212	+	0.249212i
$162$		0			0
$163$	−5.95903	−	5.95903i	−0.466747	−	0.466747i	0.434112	−	0.900859i	$-0.357062\pi$
$163$	−5.95903	−	5.95903i	−0.466747	−	0.466747i	−0.900859	+	0.434112i	$0.857062\pi$
$164$		0			0
$165$	−1.11085			−0.0864798
$166$		0			0
$167$	−16.0984	−	16.0984i	−1.24573	−	1.24573i	−0.957587	−	0.288143i	$-0.906962\pi$
$167$	−16.0984	−	16.0984i	−1.24573	−	1.24573i	−0.288143	−	0.957587i	$-0.593038\pi$
$168$		0			0
$169$	−12.0863	+	4.78756i	−0.929717	+	0.368274i
$170$		0			0
$171$	−1.44000	+	1.44000i	−0.110119	+	0.110119i
$172$		0			0
$173$			9.26985i			0.704774i	0.935854	+	0.352387i	$0.114630\pi$
$173$			9.26985i			0.704774i	−0.935854	+	0.352387i	$0.885370\pi$
$174$		0			0
$175$	−1.38970	+	1.38970i	−0.105052	+	0.105052i
$176$		0			0
$177$	4.99623	−	4.99623i	0.375540	−	0.375540i
$178$		0			0
$179$	22.1886			1.65846			0.829228	−	0.558911i	$-0.188781\pi$
$179$	22.1886			1.65846			0.829228	+	0.558911i	$0.188781\pi$
$180$		0			0
$181$		−	2.49185i		−	0.185218i	−0.995703	−	0.0926090i	$-0.970479\pi$
$181$		−	2.49185i		−	0.185218i	0.995703	−	0.0926090i	$-0.0295207\pi$
$182$		0			0
$183$			18.4854i			1.36648i
$184$		0			0
$185$	18.0323			1.32576
$186$		0			0
$187$	−0.109118	+	0.109118i	−0.00797947	+	0.00797947i
$188$		0			0
$189$	3.81713	−	3.81713i	0.277655	−	0.277655i
$190$		0			0
$191$			15.2396i			1.10270i	0.834274	+	0.551350i	$0.185887\pi$
$191$			15.2396i			1.10270i	−0.834274	+	0.551350i	$0.814113\pi$
$192$		0			0
$193$	−11.1917	+	11.1917i	−0.805595	+	0.805595i	−0.983964	−	0.178369i	$-0.942918\pi$
$193$	−11.1917	+	11.1917i	−0.805595	+	0.805595i	0.178369	+	0.983964i	$0.442918\pi$
$194$		0			0
$195$	11.5731	+	7.86371i	0.828766	+	0.563132i
$196$		0			0
$197$	1.23010	+	1.23010i	0.0876412	+	0.0876412i	0.749568	−	0.661927i	$-0.230261\pi$
$197$	1.23010	+	1.23010i	0.0876412	+	0.0876412i	−0.661927	+	0.749568i	$0.730261\pi$
$198$		0			0
$199$	8.19168			0.580693			0.290346	−	0.956922i	$-0.406229\pi$
$199$	8.19168			0.580693			0.290346	+	0.956922i	$0.406229\pi$
$200$		0			0
$201$	13.5656	+	13.5656i	0.956841	+	0.956841i
$202$		0			0
$203$	−2.88853	−	2.88853i	−0.202735	−	0.202735i
$204$		0			0
$205$			8.33041i			0.581821i
$206$		0			0
$207$	4.05029			0.281515
$208$		0			0
$209$	0.673352			0.0465768
$210$		0			0
$211$		−	11.6173i		−	0.799765i	−0.916566	−	0.399883i	$-0.869051\pi$
$211$		−	11.6173i		−	0.799765i	0.916566	−	0.399883i	$-0.130949\pi$
$212$		0			0
$213$	13.6659	+	13.6659i	0.936370	+	0.936370i
$214$		0			0
$215$	−23.6091	−	23.6091i	−1.61013	−	1.61013i
$216$		0			0
$217$	7.65565			0.519699
$218$		0			0
$219$	1.26476	+	1.26476i	0.0854648	+	0.0854648i
$220$		0			0
$221$	1.90925	−	0.364368i	0.128430	−	0.0245100i
$222$		0			0
$223$	−12.2762	+	12.2762i	−0.822073	+	0.822073i	−0.986405	−	0.164332i	$-0.947453\pi$
$223$	−12.2762	+	12.2762i	−0.822073	+	0.822073i	0.164332	+	0.986405i	$0.447453\pi$
$224$		0			0
$225$			1.78003i			0.118669i
$226$		0			0
$227$	15.9118	−	15.9118i	1.05610	−	1.05610i	0.0577733	−	0.998330i	$-0.481600\pi$
$227$	15.9118	−	15.9118i	1.05610	−	1.05610i	0.998330	−	0.0577733i	$-0.0184000\pi$
$228$		0			0
$229$	4.37016	−	4.37016i	0.288789	−	0.288789i	−0.547813	−	0.836601i	$-0.684539\pi$
$229$	4.37016	−	4.37016i	0.288789	−	0.288789i	0.836601	+	0.547813i	$0.184539\pi$
$230$		0			0
$231$	−0.399733			−0.0263005
$232$		0			0
$233$			12.8379i			0.841036i	0.907284	+	0.420518i	$0.138152\pi$
$233$			12.8379i			0.841036i	−0.907284	+	0.420518i	$0.861848\pi$
$234$		0			0
$235$		−	4.05985i		−	0.264836i
$236$		0			0
$237$	19.1135			1.24156
$238$		0			0
$239$	14.2459	−	14.2459i	0.921492	−	0.921492i	−0.0756426	−	0.997135i	$-0.524101\pi$
$239$	14.2459	−	14.2459i	0.921492	−	0.921492i	0.997135	+	0.0756426i	$0.0241008\pi$
$240$		0			0
$241$	8.92112	−	8.92112i	0.574660	−	0.574660i	−0.358767	−	0.933427i	$-0.616803\pi$
$241$	8.92112	−	8.92112i	0.574660	−	0.574660i	0.933427	+	0.358767i	$0.116803\pi$
$242$		0			0
$243$		−	8.68353i		−	0.557049i
$244$		0			0
$245$	11.4320	−	11.4320i	0.730364	−	0.730364i
$246$		0			0
$247$	−7.01512	−	4.76665i	−0.446361	−	0.303294i
$248$		0			0
$249$	−4.56423	−	4.56423i	−0.289247	−	0.289247i
$250$		0			0
$251$	5.13865			0.324349			0.162174	−	0.986762i	$-0.448149\pi$
$251$	5.13865			0.324349			0.162174	+	0.986762i	$0.448149\pi$
$252$		0			0
$253$	−0.946971	−	0.946971i	−0.0595356	−	0.0595356i
$254$		0			0
$255$	−1.47928	−	1.47928i	−0.0926362	−	0.0926362i
$256$		0			0
$257$			17.9262i			1.11821i	0.829098	+	0.559103i	$0.188854\pi$
$257$			17.9262i			1.11821i	−0.829098	+	0.559103i	$0.811146\pi$
$258$		0			0
$259$	6.48879			0.403194
$260$		0			0
$261$	−3.69982			−0.229013
$262$		0			0
$263$			2.73524i			0.168662i	0.996438	+	0.0843310i	$0.0268753\pi$
$263$			2.73524i			0.168662i	−0.996438	+	0.0843310i	$0.973125\pi$
$264$		0			0
$265$	7.05609	+	7.05609i	0.433452	+	0.433452i
$266$		0			0
$267$	−9.08327	−	9.08327i	−0.555887	−	0.555887i
$268$		0			0
$269$	−31.9785			−1.94977			−0.974883	−	0.222719i	$-0.928507\pi$
$269$	−31.9785			−1.94977			−0.974883	+	0.222719i	$0.928507\pi$
$270$		0			0
$271$	2.43252	+	2.43252i	0.147765	+	0.147765i	0.777119	−	0.629354i	$-0.216680\pi$
$271$	2.43252	+	2.43252i	0.147765	+	0.147765i	−0.629354	+	0.777119i	$0.716680\pi$
$272$		0			0
$273$	4.16450	+	2.82970i	0.252047	+	0.171261i
$274$		0			0
$275$	0.416176	−	0.416176i	0.0250964	−	0.0250964i
$276$		0			0
$277$		−	26.4351i		−	1.58833i	−0.607703	−	0.794164i	$-0.707909\pi$
$277$		−	26.4351i		−	1.58833i	0.607703	−	0.794164i	$-0.292091\pi$
$278$		0			0
$279$	4.90294	−	4.90294i	0.293531	−	0.293531i
$280$		0			0
$281$	−5.32594	+	5.32594i	−0.317719	+	0.317719i	−0.847890	−	0.530171i	$-0.822128\pi$
$281$	−5.32594	+	5.32594i	−0.317719	+	0.317719i	0.530171	+	0.847890i	$0.322128\pi$
$282$		0			0
$283$	20.0000			1.18888			0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000			1.18888			0.594438	+	0.804141i	$0.297374\pi$
$284$		0			0
$285$			9.12847i			0.540724i
$286$		0			0
$287$			2.99765i			0.176945i
$288$		0			0
$289$	16.7094			0.982905
$290$		0			0
$291$	−11.2175	+	11.2175i	−0.657583	+	0.657583i
$292$		0			0
$293$	5.09278	−	5.09278i	0.297523	−	0.297523i	−0.542520	−	0.840043i	$-0.682530\pi$
$293$	5.09278	−	5.09278i	0.297523	−	0.297523i	0.840043	+	0.542520i	$0.182530\pi$
$294$		0			0
$295$			12.8474i			0.748005i
$296$		0			0
$297$	−1.14312	+	1.14312i	−0.0663305	+	0.0663305i
$298$		0			0
$299$	3.16215	+	16.5693i	0.182872	+	0.958229i
$300$		0			0
$301$	−8.49557	−	8.49557i	−0.489677	−	0.489677i
$302$		0			0
$303$	9.79336			0.562614
$304$		0			0
$305$	−23.7668	−	23.7668i	−1.36088	−	1.36088i
$306$		0			0
$307$	−23.8852	−	23.8852i	−1.36320	−	1.36320i	−0.869802	−	0.493400i	$-0.835754\pi$
$307$	−23.8852	−	23.8852i	−1.36320	−	1.36320i	−0.493400	−	0.869802i	$-0.664246\pi$
$308$		0			0
$309$			6.51597i			0.370681i
$310$		0			0
$311$	21.6254			1.22626			0.613132	−	0.789980i	$-0.289909\pi$
$311$	21.6254			1.22626			0.613132	+	0.789980i	$0.289909\pi$
$312$		0			0
$313$	−27.6274			−1.56160			−0.780798	−	0.624784i	$-0.785187\pi$
$313$	−27.6274			−1.56160			−0.780798	+	0.624784i	$0.785187\pi$
$314$		0			0
$315$			2.19818i			0.123853i
$316$		0			0
$317$	−2.34873	−	2.34873i	−0.131918	−	0.131918i	0.638065	−	0.769983i	$-0.279735\pi$
$317$	−2.34873	−	2.34873i	−0.131918	−	0.131918i	−0.769983	+	0.638065i	$0.779735\pi$
$318$		0			0
$319$	0.865030	+	0.865030i	0.0484324	+	0.0484324i
$320$		0			0
$321$	−14.9721			−0.835662
$322$		0			0
$323$	0.896678	+	0.896678i	0.0498925	+	0.0498925i
$324$		0			0
$325$	−7.28191	+	1.38970i	−0.403928	+	0.0770870i
$326$		0			0
$327$	−0.813365	+	0.813365i	−0.0449792	+	0.0449792i
$328$		0			0
$329$		−	1.46091i		−	0.0805427i
$330$		0			0
$331$	−1.90365	+	1.90365i	−0.104634	+	0.104634i	−0.757486	−	0.652852i	$-0.773572\pi$
$331$	−1.90365	+	1.90365i	−0.104634	+	0.104634i	0.652852	+	0.757486i	$0.273572\pi$
$332$		0			0
$333$	4.15565	−	4.15565i	0.227728	−	0.227728i
$334$		0			0
$335$	−34.8827			−1.90585
$336$		0			0
$337$		−	15.7396i		−	0.857392i	−0.903449	−	0.428696i	$-0.858973\pi$
$337$		−	15.7396i		−	0.857392i	0.903449	−	0.428696i	$-0.141027\pi$
$338$		0			0
$339$			18.9864i			1.03120i
$340$		0			0
$341$	−2.29265			−0.124154
$342$		0			0
$343$	8.84501	−	8.84501i	0.477586	−	0.477586i
$344$		0			0
$345$	12.8379	−	12.8379i	0.691167	−	0.691167i
$346$		0			0
$347$			18.2264i			0.978444i	0.872159	+	0.489222i	$0.162719\pi$
$347$			18.2264i			0.978444i	−0.872159	+	0.489222i	$0.837281\pi$
$348$		0			0
$349$	−14.8001	+	14.8001i	−0.792233	+	0.792233i	−0.981857	−	0.189624i	$-0.939273\pi$
$349$	−14.8001	+	14.8001i	−0.792233	+	0.792233i	0.189624	+	0.981857i	$0.439273\pi$
$350$		0			0
$351$	20.0014	−	3.81713i	1.06759	−	0.203743i
$352$		0			0
$353$	3.78450	+	3.78450i	0.201429	+	0.201429i	0.800612	−	0.599183i	$-0.204508\pi$
$353$	3.78450	+	3.78450i	0.201429	+	0.201429i	−0.599183	+	0.800612i	$0.704508\pi$
$354$		0			0
$355$	−35.1407			−1.86507
$356$		0			0
$357$	−0.532310	−	0.532310i	−0.0281728	−	0.0281728i
$358$		0			0
$359$	16.9900	+	16.9900i	0.896696	+	0.896696i	0.995142	−	0.0984460i	$-0.0313872\pi$
$359$	16.9900	+	16.9900i	0.896696	+	0.896696i	−0.0984460	+	0.995142i	$0.531387\pi$
$360$		0			0
$361$			13.4667i			0.708774i
$362$		0			0
$363$	−15.9503			−0.837175
$364$		0			0
$365$	−3.25224			−0.170230
$366$		0			0
$367$			7.19544i			0.375599i	0.982207	+	0.187800i	$0.0601355\pi$
$367$			7.19544i			0.375599i	−0.982207	+	0.187800i	$0.939864\pi$
$368$		0			0
$369$	1.91979	+	1.91979i	0.0999405	+	0.0999405i
$370$		0			0
$371$	2.53909	+	2.53909i	0.131823	+	0.131823i
$372$		0			0
$373$	−1.43271			−0.0741827			−0.0370913	−	0.999312i	$-0.511809\pi$
$373$	−1.43271			−0.0741827			−0.0370913	+	0.999312i	$0.511809\pi$
$374$		0			0
$375$	−8.07822	−	8.07822i	−0.417158	−	0.417158i
$376$		0			0
$377$	−2.88853	−	15.1356i	−0.148767	−	0.779522i
$378$		0			0
$379$	−11.9893	+	11.9893i	−0.615847	+	0.615847i	−0.944464	−	0.328616i	$-0.893418\pi$
$379$	−11.9893	+	11.9893i	−0.615847	+	0.615847i	0.328616	+	0.944464i	$0.393418\pi$
$380$		0			0
$381$			6.83479i			0.350157i
$382$		0			0
$383$	5.03655	−	5.03655i	0.257356	−	0.257356i	−0.566622	−	0.823978i	$-0.691750\pi$
$383$	5.03655	−	5.03655i	0.257356	−	0.257356i	0.823978	+	0.566622i	$0.191750\pi$
$384$		0			0
$385$	0.513941	−	0.513941i	0.0261929	−	0.0261929i
$386$		0			0
$387$	−10.8817			−0.553148
$388$		0			0
$389$			3.16418i			0.160430i	0.996778	+	0.0802151i	$0.0255607\pi$
$389$			3.16418i			0.160430i	−0.996778	+	0.0802151i	$0.974439\pi$
$390$		0			0
$391$		−	2.52209i		−	0.127548i
$392$		0			0
$393$	−16.1872			−0.816537
$394$		0			0
$395$	−24.5744	+	24.5744i	−1.23647	+	1.23647i
$396$		0			0
$397$	10.7094	−	10.7094i	0.537489	−	0.537489i	−0.385302	−	0.922791i	$-0.625903\pi$
$397$	10.7094	−	10.7094i	0.537489	−	0.537489i	0.922791	+	0.385302i	$0.125903\pi$
$398$		0			0
$399$			3.28482i			0.164447i
$400$		0			0
$401$	12.8120	−	12.8120i	0.639801	−	0.639801i	−0.310705	−	0.950506i	$-0.600565\pi$
$401$	12.8120	−	12.8120i	0.639801	−	0.639801i	0.950506	+	0.310705i	$0.100565\pi$
$402$		0			0
$403$	23.8852	+	16.2296i	1.18981	+	0.808453i
$404$		0			0
$405$	−10.6186	−	10.6186i	−0.527644	−	0.527644i
$406$		0			0
$407$	−1.94321			−0.0963211
$408$		0			0
$409$	−7.54724	−	7.54724i	−0.373187	−	0.373187i	0.495450	−	0.868637i	$-0.335003\pi$
$409$	−7.54724	−	7.54724i	−0.373187	−	0.373187i	−0.868637	+	0.495450i	$0.835003\pi$
$410$		0			0
$411$	−22.8681	−	22.8681i	−1.12800	−	1.12800i
$412$		0			0
$413$			4.62306i			0.227486i
$414$		0			0
$415$	11.7366			0.576125
$416$		0			0
$417$	23.2226			1.13722
$418$		0			0
$419$			18.0082i			0.879756i	0.898058	+	0.439878i	$0.144978\pi$
$419$			18.0082i			0.879756i	−0.898058	+	0.439878i	$0.855022\pi$
$420$		0			0
$421$	16.9616	+	16.9616i	0.826657	+	0.826657i	0.987053	−	0.160396i	$-0.0512772\pi$
$421$	16.9616	+	16.9616i	0.826657	+	0.826657i	−0.160396	+	0.987053i	$0.551277\pi$
$422$		0			0
$423$	−0.935618	−	0.935618i	−0.0454913	−	0.0454913i
$424$		0			0
$425$	1.10841			0.0537659
$426$		0			0
$427$	−8.55233	−	8.55233i	−0.413876	−	0.413876i
$428$		0			0
$429$	−1.24715	−	0.847414i	−0.0602128	−	0.0409135i
$430$		0			0
$431$	−12.9546	+	12.9546i	−0.624001	+	0.624001i	−0.946552	−	0.322551i	$-0.895460\pi$
$431$	−12.9546	+	12.9546i	−0.624001	+	0.624001i	0.322551	+	0.946552i	$0.395460\pi$
$432$		0			0
$433$		−	11.1621i		−	0.536419i	−0.963361	−	0.268209i	$-0.913568\pi$
$433$		−	11.1621i		−	0.536419i	0.963361	−	0.268209i	$-0.0864319\pi$
$434$		0			0
$435$	−11.7270	+	11.7270i	−0.562267	+	0.562267i
$436$		0			0
$437$	−7.78176	+	7.78176i	−0.372252	+	0.372252i
$438$		0			0
$439$	−3.77564			−0.180202			−0.0901008	−	0.995933i	$-0.528719\pi$
$439$	−3.77564			−0.180202			−0.0901008	+	0.995933i	$0.528719\pi$
$440$		0			0
$441$		−	5.26915i		−	0.250912i
$442$		0			0
$443$		−	34.0183i		−	1.61626i	−0.589004	−	0.808130i	$-0.700480\pi$
$443$		−	34.0183i		−	1.61626i	0.589004	−	0.808130i	$-0.299520\pi$
$444$		0			0
$445$	23.3569			1.10722
$446$		0			0
$447$	17.2648	−	17.2648i	0.816595	−	0.816595i
$448$		0			0
$449$	−26.3620	+	26.3620i	−1.24410	+	1.24410i	−0.285813	+	0.958285i	$0.592264\pi$
$449$	−26.3620	+	26.3620i	−1.24410	+	1.24410i	−0.958285	+	0.285813i	$0.907736\pi$
$450$		0			0
$451$		−	0.897708i		−	0.0422714i
$452$		0			0
$453$	1.30625	−	1.30625i	0.0613729	−	0.0613729i
$454$		0			0
$455$	−8.99252	+	1.71616i	−0.421576	+	0.0804549i
$456$		0			0
$457$	−6.03094	−	6.03094i	−0.282116	−	0.282116i	0.551837	−	0.833952i	$-0.313927\pi$
$457$	−6.03094	−	6.03094i	−0.282116	−	0.282116i	−0.833952	+	0.551837i	$0.813927\pi$
$458$		0			0
$459$	−3.04450			−0.142105
$460$		0			0
$461$	−14.5618	−	14.5618i	−0.678213	−	0.678213i	0.281383	−	0.959596i	$-0.409207\pi$
$461$	−14.5618	−	14.5618i	−0.678213	−	0.678213i	−0.959596	+	0.281383i	$0.909207\pi$
$462$		0			0
$463$	26.9383	+	26.9383i	1.25193	+	1.25193i	0.954855	+	0.297073i	$0.0960103\pi$
$463$	26.9383	+	26.9383i	1.25193	+	1.25193i	0.297073	+	0.954855i	$0.403990\pi$
$464$		0			0
$465$		−	31.0808i		−	1.44134i
$466$		0			0
$467$	−16.9143			−0.782700			−0.391350	−	0.920242i	$-0.627992\pi$
$467$	−16.9143			−0.782700			−0.391350	+	0.920242i	$0.627992\pi$
$468$		0			0
$469$	−12.5523			−0.579613
$470$		0			0
$471$			16.5472i			0.762456i
$472$		0			0
$473$	2.54418	+	2.54418i	0.116981	+	0.116981i
$474$		0			0
$475$	−3.41994	−	3.41994i	−0.156918	−	0.156918i
$476$		0			0
$477$	3.25224			0.148910
$478$		0			0
$479$	−9.80334	−	9.80334i	−0.447926	−	0.447926i	0.446739	−	0.894665i	$-0.352585\pi$
$479$	−9.80334	−	9.80334i	−0.447926	−	0.447926i	−0.894665	+	0.446739i	$0.852585\pi$
$480$		0			0
$481$	20.2447	+	13.7559i	0.923079	+	0.627216i
$482$		0			0
$483$	4.61962	−	4.61962i	0.210200	−	0.210200i
$484$		0			0
$485$		−	28.8450i		−	1.30978i
$486$		0			0
$487$	4.09838	−	4.09838i	0.185716	−	0.185716i	−0.608125	−	0.793841i	$-0.708078\pi$
$487$	4.09838	−	4.09838i	0.185716	−	0.185716i	0.793841	+	0.608125i	$0.208078\pi$
$488$		0			0
$489$	−8.70562	+	8.70562i	−0.393682	+	0.393682i
$490$		0			0
$491$	31.5455			1.42363			0.711814	−	0.702368i	$-0.247874\pi$
$491$	31.5455			1.42363			0.711814	+	0.702368i	$0.247874\pi$
$492$		0			0
$493$			2.30386i			0.103760i
$494$		0			0
$495$		−	0.658291i		−	0.0295880i
$496$		0			0
$497$	−12.6451			−0.567212
$498$		0			0
$499$	1.84991	−	1.84991i	0.0828134	−	0.0828134i	−0.664487	−	0.747300i	$-0.731350\pi$
$499$	1.84991	−	1.84991i	0.0828134	−	0.0828134i	0.747300	+	0.664487i	$0.231350\pi$
$500$		0			0
$501$	−23.5183	+	23.5183i	−1.05072	+	1.05072i
$502$		0			0
$503$			38.0948i			1.69856i	0.527941	+	0.849281i	$0.322964\pi$
$503$			38.0948i			1.69856i	−0.527941	+	0.849281i	$0.677036\pi$
$504$		0			0
$505$	−12.5914	+	12.5914i	−0.560310	+	0.560310i
$506$		0			0
$507$	6.99420	+	17.6571i	0.310624	+	0.784178i
$508$		0			0
$509$	15.0082	+	15.0082i	0.665225	+	0.665225i	0.956607	−	0.291382i	$-0.0941151\pi$
$509$	15.0082	+	15.0082i	0.665225	+	0.665225i	−0.291382	+	0.956607i	$0.594115\pi$
$510$		0			0
$511$	−1.17030			−0.0517709
$512$		0			0
$513$	9.39362	+	9.39362i	0.414739	+	0.414739i
$514$		0			0
$515$	−8.37765	−	8.37765i	−0.369163	−	0.369163i
$516$		0			0
$517$			0.437501i			0.0192413i
$518$		0			0
$519$	13.5424			0.594447
$520$		0			0
$521$	−6.49491			−0.284547			−0.142274	−	0.989827i	$-0.545441\pi$
$521$	−6.49491			−0.284547			−0.142274	+	0.989827i	$0.545441\pi$
$522$		0			0
$523$		−	12.4048i		−	0.542425i	−0.962519	−	0.271213i	$-0.912575\pi$
$523$		−	12.4048i		−	0.542425i	0.962519	−	0.271213i	$-0.0874246\pi$
$524$		0			0
$525$	2.03024	+	2.03024i	0.0886068	+	0.0886068i
$526$		0			0
$527$	−3.05303	−	3.05303i	−0.132992	−	0.132992i
$528$		0			0
$529$	−1.11218			−0.0483556
$530$		0			0
$531$	2.96077	+	2.96077i	0.128486	+	0.128486i
$532$		0			0
$533$	−6.35485	+	9.35250i	−0.275259	+	0.405102i
$534$		0			0
$535$	19.2498	−	19.2498i	0.832241	−	0.832241i
$536$		0			0
$537$		−	32.4156i		−	1.39884i
$538$		0			0
$539$	−1.23194	+	1.23194i	−0.0530636	+	0.0530636i
$540$		0			0
$541$	11.4976	−	11.4976i	0.494321	−	0.494321i	−0.415344	−	0.909664i	$-0.636339\pi$
$541$	11.4976	−	11.4976i	0.494321	−	0.494321i	0.909664	+	0.415344i	$0.136339\pi$
$542$		0			0
$543$	−3.64038			−0.156224
$544$		0			0
$545$		−	2.09150i		−	0.0895901i
$546$		0			0
$547$		−	7.02991i		−	0.300577i	−0.988642	−	0.150289i	$-0.951980\pi$
$547$		−	7.02991i		−	0.300577i	0.988642	−	0.150289i	$-0.0480203\pi$
$548$		0			0
$549$	−10.9544			−0.467523
$550$		0			0
$551$	7.10841	−	7.10841i	0.302829	−	0.302829i
$552$		0			0
$553$	−8.84294	+	8.84294i	−0.376040	+	0.376040i
$554$		0			0
$555$		−	26.3436i		−	1.11822i
$556$		0			0
$557$	4.03466	−	4.03466i	0.170954	−	0.170954i	−0.616444	−	0.787398i	$-0.711427\pi$
$557$	4.03466	−	4.03466i	0.170954	−	0.170954i	0.787398	+	0.616444i	$0.211427\pi$
$558$		0			0
$559$	−8.49557	−	44.5159i	−0.359324	−	1.88282i
$560$		0			0
$561$	0.159411	+	0.159411i	0.00673035	+	0.00673035i
$562$		0			0
$563$	5.97038			0.251622			0.125811	−	0.992054i	$-0.459847\pi$
$563$	5.97038			0.251622			0.125811	+	0.992054i	$0.459847\pi$
$564$		0			0
$565$	−24.4109	−	24.4109i	−1.02698	−	1.02698i
$566$		0			0
$567$	−3.82105	−	3.82105i	−0.160469	−	0.160469i
$568$		0			0
$569$			23.5958i			0.989187i	0.869124	+	0.494594i	$0.164683\pi$
$569$			23.5958i			0.989187i	−0.869124	+	0.494594i	$0.835317\pi$
$570$		0			0
$571$	−4.83173			−0.202202			−0.101101	−	0.994876i	$-0.532236\pi$
$571$	−4.83173			−0.202202			−0.101101	+	0.994876i	$0.532236\pi$
$572$		0			0
$573$	22.2637			0.930081
$574$		0			0
$575$			9.61929i			0.401152i
$576$		0			0
$577$	27.2189	+	27.2189i	1.13314	+	1.13314i	0.989653	+	0.143483i	$0.0458302\pi$
$577$	27.2189	+	27.2189i	1.13314	+	1.13314i	0.143483	+	0.989653i	$0.454170\pi$
$578$		0			0
$579$	16.3501	+	16.3501i	0.679485	+	0.679485i
$580$		0			0
$581$	4.22333			0.175213
$582$		0			0
$583$	−0.760383	−	0.760383i	−0.0314919	−	0.0314919i
$584$		0			0
$585$	−4.66003	+	6.85820i	−0.192668	+	0.283552i
$586$		0			0
$587$	22.2880	−	22.2880i	0.919926	−	0.919926i	−0.0770980	−	0.997024i	$-0.524565\pi$
$587$	22.2880	−	22.2880i	0.919926	−	0.919926i	0.997024	+	0.0770980i	$0.0245654\pi$
$588$		0			0
$589$			18.8399i			0.776284i
$590$		0			0
$591$	1.79707	−	1.79707i	0.0739217	−	0.0739217i
$592$		0			0
$593$	19.3341	−	19.3341i	0.793956	−	0.793956i	−0.188179	−	0.982135i	$-0.560258\pi$
$593$	19.3341	−	19.3341i	0.793956	−	0.793956i	0.982135	+	0.188179i	$0.0602584\pi$
$594$		0			0
$595$	1.36879			0.0561150
$596$		0			0
$597$		−	11.9673i		−	0.489790i
$598$		0			0
$599$		−	30.0404i		−	1.22742i	−0.789532	−	0.613709i	$-0.789677\pi$
$599$		−	30.0404i		−	1.22742i	0.789532	−	0.613709i	$-0.210323\pi$
$600$		0			0
$601$	25.2427			1.02967			0.514835	−	0.857289i	$-0.327853\pi$
$601$	25.2427			1.02967			0.514835	+	0.857289i	$0.327853\pi$
$602$		0			0
$603$	−8.03894	+	8.03894i	−0.327371	+	0.327371i
$604$		0			0
$605$	20.5075	−	20.5075i	0.833748	−	0.833748i
$606$		0			0
$607$		−	32.1968i		−	1.30683i	−0.757001	−	0.653413i	$-0.773336\pi$
$607$		−	32.1968i		−	1.30683i	0.757001	−	0.653413i	$-0.226664\pi$
$608$		0			0
$609$	−4.21988	+	4.21988i	−0.170998	+	0.170998i
$610$		0			0
$611$	3.09706	−	4.55797i	0.125294	−	0.184396i
$612$		0			0
$613$	23.6061	+	23.6061i	0.953440	+	0.953440i	0.998963	−	0.0455234i	$-0.0144956\pi$
$613$	23.6061	+	23.6061i	0.953440	+	0.953440i	−0.0455234	+	0.998963i	$0.514496\pi$
$614$		0			0
$615$	12.1700			0.490742
$616$		0			0
$617$	28.2226	+	28.2226i	1.13620	+	1.13620i	0.989125	+	0.147074i	$0.0469857\pi$
$617$	28.2226	+	28.2226i	1.13620	+	1.13620i	0.147074	+	0.989125i	$0.453014\pi$
$618$		0			0
$619$	12.0542	+	12.0542i	0.484500	+	0.484500i	0.906565	−	0.422066i	$-0.138695\pi$
$619$	12.0542	+	12.0542i	0.484500	+	0.484500i	−0.422066	+	0.906565i	$0.638695\pi$
$620$		0			0
$621$		−	26.4215i		−	1.06026i
$622$		0			0
$623$	8.40482			0.336732
$624$		0			0
$625$	31.0529			1.24212
$626$		0			0
$627$		−	0.983709i		−	0.0392855i
$628$		0			0
$629$	−2.58769	−	2.58769i	−0.103178	−	0.103178i
$630$		0			0
$631$	24.6493	+	24.6493i	0.981275	+	0.981275i	0.999828	−	0.0185531i	$-0.00590599\pi$
$631$	24.6493	+	24.6493i	0.981275	+	0.981275i	−0.0185531	+	0.999828i	$0.505906\pi$
$632$		0			0
$633$	−16.9718			−0.674569
$634$		0			0
$635$	−8.78756	−	8.78756i	−0.348724	−	0.348724i
$636$		0			0
$637$	21.5555	−	4.11373i	0.854061	−	0.162992i
$638$		0			0
$639$	−8.09838	+	8.09838i	−0.320367	+	0.320367i
$640$		0			0
$641$			17.2825i			0.682617i	0.939951	+	0.341308i	$0.110870\pi$
$641$			17.2825i			0.682617i	−0.939951	+	0.341308i	$0.889130\pi$
$642$		0			0
$643$	7.04739	−	7.04739i	0.277922	−	0.277922i	−0.554357	−	0.832279i	$-0.687036\pi$
$643$	7.04739	−	7.04739i	0.277922	−	0.277922i	0.832279	+	0.554357i	$0.187036\pi$
$644$		0			0
$645$	−34.4908	+	34.4908i	−1.35807	+	1.35807i
$646$		0			0
$647$	−32.8198			−1.29028			−0.645140	−	0.764064i	$-0.723201\pi$
$647$	−32.8198			−1.29028			−0.645140	+	0.764064i	$0.723201\pi$
$648$		0			0
$649$		−	1.38447i		−	0.0543453i
$650$		0			0
$651$		−	11.1842i		−	0.438345i
$652$		0			0
$653$	−6.57747			−0.257396			−0.128698	−	0.991684i	$-0.541080\pi$
$653$	−6.57747			−0.257396			−0.128698	+	0.991684i	$0.541080\pi$
$654$		0			0
$655$	20.8120	−	20.8120i	0.813194	−	0.813194i
$656$		0			0
$657$	−0.749498	+	0.749498i	−0.0292407	+	0.0292407i
$658$		0			0
$659$		−	10.6849i		−	0.416226i	−0.978105	−	0.208113i	$-0.933268\pi$
$659$		−	10.6849i		−	0.416226i	0.978105	−	0.208113i	$-0.0667322\pi$
$660$		0			0
$661$	−10.7345	+	10.7345i	−0.417525	+	0.417525i	−0.884350	−	0.466825i	$-0.845398\pi$
$661$	−10.7345	+	10.7345i	−0.417525	+	0.417525i	0.466825	+	0.884350i	$0.345398\pi$
$662$		0			0
$663$	−0.532310	−	2.78925i	−0.0206732	−	0.108325i
$664$		0			0
$665$	−4.22333	−	4.22333i	−0.163774	−	0.163774i
$666$		0			0
$667$	−19.9939			−0.774166
$668$		0			0
$669$	17.9344	+	17.9344i	0.693384	+	0.693384i
$670$		0			0
$671$	2.56117	+	2.56117i	0.0988730	+	0.0988730i
$672$		0			0
$673$			24.0625i			0.927541i	0.885955	+	0.463771i	$0.153504\pi$
$673$			24.0625i			0.927541i	−0.885955	+	0.463771i	$0.846496\pi$
$674$		0			0
$675$	11.6118			0.446937
$676$		0			0
$677$	30.2522			1.16268			0.581342	−	0.813659i	$-0.302528\pi$
$677$	30.2522			1.16268			0.581342	+	0.813659i	$0.302528\pi$
$678$		0			0
$679$		−	10.3797i		−	0.398335i
$680$		0			0
$681$	−23.2457	−	23.2457i	−0.890779	−	0.890779i
$682$		0			0
$683$	19.3108	+	19.3108i	0.738908	+	0.738908i	0.972367	−	0.233459i	$-0.0750043\pi$
$683$	19.3108	+	19.3108i	0.738908	+	0.738908i	−0.233459	+	0.972367i	$0.575004\pi$
$684$		0			0
$685$	58.8034			2.24676
$686$		0			0
$687$	−6.38442	−	6.38442i	−0.243581	−	0.243581i
$688$		0			0
$689$	2.53909	+	13.3046i	0.0967315	+	0.506863i
$690$		0			0
$691$	−4.72247	+	4.72247i	−0.179651	+	0.179651i	−0.791204	−	0.611553i	$-0.790545\pi$
$691$	−4.72247	+	4.72247i	−0.179651	+	0.179651i	0.611553	+	0.791204i	$0.290545\pi$
$692$		0			0
$693$		−	0.236882i		−	0.00899839i
$694$		0			0
$695$	−29.8575	+	29.8575i	−1.13256	+	1.13256i
$696$		0			0
$697$	1.19544	−	1.19544i	0.0452806	−	0.0452806i
$698$		0			0
$699$	18.7550			0.709378
$700$		0			0
$701$			15.1969i			0.573977i	0.957934	+	0.286989i	$0.0926542\pi$
$701$			15.1969i			0.573977i	−0.957934	+	0.286989i	$0.907346\pi$
$702$		0			0
$703$			15.9684i			0.602258i
$704$		0			0
$705$	−5.93109			−0.223378
$706$		0			0
$707$	−4.53094	+	4.53094i	−0.170403	+	0.170403i
$708$		0			0
$709$	−20.0183	+	20.0183i	−0.751804	+	0.751804i	−0.974816	−	0.223012i	$-0.928411\pi$
$709$	−20.0183	+	20.0183i	−0.751804	+	0.751804i	0.223012	+	0.974816i	$0.428411\pi$
$710$		0			0
$711$			11.3266i			0.424782i
$712$		0			0
$713$	26.4955	−	26.4955i	0.992266	−	0.992266i
$714$		0			0
$715$	2.69300	−	0.513941i	0.100712	−	0.0192203i
$716$		0			0
$717$	−20.8120	−	20.8120i	−0.777240	−	0.777240i
$718$		0			0
$719$	−4.14138			−0.154448			−0.0772238	−	0.997014i	$-0.524606\pi$
$719$	−4.14138			−0.154448			−0.0772238	+	0.997014i	$0.524606\pi$
$720$		0			0
$721$	−3.01464	−	3.01464i	−0.112271	−	0.112271i
$722$		0			0
$723$	−13.0330	−	13.0330i	−0.484701	−	0.484701i
$724$		0			0
$725$		−	8.78694i		−	0.326339i
$726$		0			0
$727$	−31.6988			−1.17564			−0.587822	−	0.808991i	$-0.700014\pi$
$727$	−31.6988			−1.17564			−0.587822	+	0.808991i	$0.700014\pi$
$728$		0			0
$729$	−29.6458			−1.09799
$730$		0			0
$731$			6.77597i			0.250618i
$732$		0			0
$733$	−14.4205	−	14.4205i	−0.532632	−	0.532632i	0.388723	−	0.921355i	$-0.372916\pi$
$733$	−14.4205	−	14.4205i	−0.532632	−	0.532632i	−0.921355	+	0.388723i	$0.872916\pi$
$734$		0			0
$735$	−16.7011	−	16.7011i	−0.616031	−	0.616031i
$736$		0			0
$737$	3.75906			0.138467
$738$		0			0
$739$	36.8639	+	36.8639i	1.35606	+	1.35606i	0.878718	+	0.477340i	$0.158399\pi$
$739$	36.8639	+	36.8639i	1.35606	+	1.35606i	0.477340	+	0.878718i	$0.341601\pi$
$740$		0			0
$741$	−6.96365	+	10.2485i	−0.255816	+	0.376487i
$742$		0			0
$743$	7.05557	−	7.05557i	0.258844	−	0.258844i	−0.565740	−	0.824584i	$-0.691409\pi$
$743$	7.05557	−	7.05557i	0.258844	−	0.258844i	0.824584	+	0.565740i	$0.191409\pi$
$744$		0			0
$745$			44.3949i			1.62650i
$746$		0			0
$747$	2.70476	−	2.70476i	0.0989621	−	0.0989621i
$748$		0			0
$749$	6.92691	−	6.92691i	0.253104	−	0.253104i
$750$		0			0
$751$	−24.7757			−0.904076			−0.452038	−	0.891999i	$-0.649303\pi$
$751$	−24.7757			−0.904076			−0.452038	+	0.891999i	$0.649303\pi$
$752$		0			0
$753$		−	7.50712i		−	0.273574i
$754$		0			0
$755$			3.35891i			0.122243i
$756$		0			0
$757$	−26.6444			−0.968409			−0.484204	−	0.874955i	$-0.660891\pi$
$757$	−26.6444			−0.968409			−0.484204	+	0.874955i	$0.660891\pi$
$758$		0			0
$759$	−1.38344	+	1.38344i	−0.0502158	+	0.0502158i
$760$		0			0
$761$	−2.49115	+	2.49115i	−0.0903041	+	0.0903041i	−0.750816	−	0.660512i	$-0.770339\pi$
$761$	−2.49115	+	2.49115i	−0.0903041	+	0.0903041i	0.660512	+	0.750816i	$0.270339\pi$
$762$		0			0
$763$		−	0.752613i		−	0.0272464i
$764$		0			0
$765$	0.876621	−	0.876621i	0.0316943	−	0.0316943i
$766$		0			0
$767$	−9.80065	+	14.4237i	−0.353881	+	0.520810i
$768$		0			0
$769$	21.8178	+	21.8178i	0.786770	+	0.786770i	0.980963	−	0.194193i	$-0.0622089\pi$
$769$	21.8178	+	21.8178i	0.786770	+	0.786770i	−0.194193	+	0.980963i	$0.562209\pi$
$770$		0			0
$771$	26.1886			0.943160
$772$		0			0
$773$	−17.0537	−	17.0537i	−0.613379	−	0.613379i	0.330446	−	0.943825i	$-0.392801\pi$
$773$	−17.0537	−	17.0537i	−0.613379	−	0.613379i	−0.943825	+	0.330446i	$0.892801\pi$
$774$		0			0
$775$	11.6443	+	11.6443i	0.418276	+	0.418276i
$776$		0			0
$777$		−	9.47956i		−	0.340077i
$778$		0			0
$779$	−7.37694			−0.264306
$780$		0			0
$781$	3.78685			0.135504
$782$		0			0
$783$			24.1353i			0.862524i
$784$		0			0
$785$	−21.2749	−	21.2749i	−0.759335	−	0.759335i
$786$		0			0
$787$	9.83739	+	9.83739i	0.350665	+	0.350665i	0.860357	−	0.509692i	$-0.170241\pi$
$787$	9.83739	+	9.83739i	0.350665	+	0.350665i	−0.509692	+	0.860357i	$0.670241\pi$
$788$		0			0
$789$	3.99594			0.142259
$790$		0			0
$791$	−8.78412	−	8.78412i	−0.312327	−	0.312327i
$792$		0			0
$793$	−8.55233	−	44.8133i	−0.303702	−	1.59137i
$794$		0			0
$795$	10.3083	−	10.3083i	0.365599	−	0.365599i
$796$		0			0
$797$			24.3531i			0.862632i	0.902201	+	0.431316i	$0.141951\pi$
$797$			24.3531i			0.862632i	−0.902201	+	0.431316i	$0.858049\pi$
$798$		0			0
$799$	−0.582603	+	0.582603i	−0.0206110	+	0.0206110i
$800$		0			0
$801$	5.38274	−	5.38274i	0.190190	−	0.190190i
$802$		0			0
$803$	0.350470			0.0123678
$804$		0			0
$805$			11.8790i			0.418679i
$806$		0			0
$807$			46.7178i			1.64455i
$808$		0			0
$809$	−35.0904			−1.23371			−0.616856	−	0.787076i	$-0.711594\pi$
$809$	−35.0904			−1.23371			−0.616856	+	0.787076i	$0.711594\pi$
$810$		0			0
$811$	13.0137	−	13.0137i	0.456973	−	0.456973i	−0.440687	−	0.897661i	$-0.645265\pi$
$811$	13.0137	−	13.0137i	0.456973	−	0.456973i	0.897661	+	0.440687i	$0.145265\pi$
$812$		0			0
$813$	3.55369	−	3.55369i	0.124633	−	0.124633i
$814$		0			0
$815$		−	22.3858i		−	0.784140i
$816$		0			0
$817$	20.9069	−	20.9069i	0.731438	−	0.731438i
$818$		0			0
$819$	−1.67688	+	2.46788i	−0.0585949	+	0.0862347i
$820$		0			0
$821$	13.7838	+	13.7838i	0.481059	+	0.481059i	0.905470	−	0.424410i	$-0.139519\pi$
$821$	13.7838	+	13.7838i	0.481059	+	0.481059i	−0.424410	+	0.905470i	$0.639519\pi$
$822$		0			0
$823$	7.28888			0.254074			0.127037	−	0.991898i	$-0.459453\pi$
$823$	7.28888			0.254074			0.127037	+	0.991898i	$0.459453\pi$
$824$		0			0
$825$	−0.607997	−	0.607997i	−0.0211677	−	0.0211677i
$826$		0			0
$827$	14.2044	+	14.2044i	0.493937	+	0.493937i	0.909544	−	0.415607i	$-0.136431\pi$
$827$	14.2044	+	14.2044i	0.493937	+	0.493937i	−0.415607	+	0.909544i	$0.636431\pi$
$828$		0			0
$829$			5.36432i			0.186311i	0.995652	+	0.0931553i	$0.0296953\pi$
$829$			5.36432i			0.186311i	−0.995652	+	0.0931553i	$0.970305\pi$
$830$		0			0
$831$	−38.6193			−1.33969
$832$		0			0
$833$	−3.28106			−0.113682
$834$		0			0
$835$		−	60.4755i		−	2.09284i
$836$		0			0
$837$	−31.9836	−	31.9836i	−1.10552	−	1.10552i
$838$		0			0
$839$	−21.9923	−	21.9923i	−0.759259	−	0.759259i	0.216928	−	0.976188i	$-0.430396\pi$
$839$	−21.9923	−	21.9923i	−0.759259	−	0.759259i	−0.976188	+	0.216928i	$0.930396\pi$
$840$		0			0
$841$	−10.7362			−0.370213
$842$		0			0
$843$	7.78073	+	7.78073i	0.267983	+	0.267983i
$844$		0			0
$845$	−31.6944	−	13.7093i	−1.09032	−	0.471616i
$846$		0			0
$847$	7.37949	−	7.37949i	0.253562	−	0.253562i
$848$		0			0
$849$		−	29.2182i		−	1.00277i
$850$		0			0
$851$	22.4571	−	22.4571i	0.769821	−	0.769821i
$852$		0			0
$853$	−6.25290	+	6.25290i	−0.214095	+	0.214095i	−0.806004	−	0.591909i	$-0.798374\pi$
$853$	−6.25290	+	6.25290i	−0.214095	+	0.214095i	0.591909	+	0.806004i	$0.298374\pi$
$854$		0			0
$855$	−5.40952			−0.185002
$856$		0			0
$857$		−	29.0442i		−	0.992130i	−0.868285	−	0.496065i	$-0.834778\pi$
$857$		−	29.0442i		−	0.992130i	0.868285	−	0.496065i	$-0.165222\pi$
$858$		0			0
$859$		−	2.78553i		−	0.0950411i	−0.998870	−	0.0475205i	$-0.984868\pi$
$859$		−	2.78553i		−	0.0950411i	0.998870	−	0.0475205i	$-0.0151320\pi$
$860$		0			0
$861$	4.37930			0.149246
$862$		0			0
$863$	−32.4678	+	32.4678i	−1.10522	+	1.10522i	−0.111448	+	0.993770i	$0.535549\pi$
$863$	−32.4678	+	32.4678i	−1.10522	+	1.10522i	−0.993770	+	0.111448i	$0.964451\pi$
$864$		0			0
$865$	−17.4116	+	17.4116i	−0.592014	+	0.592014i
$866$		0			0
$867$		−	24.4109i		−	0.829039i
$868$		0			0
$869$	2.64821	−	2.64821i	0.0898342	−	0.0898342i
$870$		0			0
$871$	−39.1626	−	26.6103i	−1.32697	−	0.901655i
$872$		0			0
$873$	−6.64750	−	6.64750i	−0.224984	−	0.224984i
$874$		0			0
$875$	7.47485			0.252696
$876$		0			0
$877$	12.3637	+	12.3637i	0.417491	+	0.417491i	0.884338	−	0.466847i	$-0.154610\pi$
$877$	12.3637	+	12.3637i	0.417491	+	0.417491i	−0.466847	+	0.884338i	$0.654610\pi$
$878$		0			0
$879$	−7.44010	−	7.44010i	−0.250948	−	0.250948i
$880$		0			0
$881$		−	45.2212i		−	1.52354i	−0.647847	−	0.761771i	$-0.724330\pi$
$881$		−	45.2212i		−	1.52354i	0.647847	−	0.761771i	$-0.275670\pi$
$882$		0			0
$883$	2.77597			0.0934188			0.0467094	−	0.998909i	$-0.485127\pi$
$883$	2.77597			0.0934188			0.0467094	+	0.998909i	$0.485127\pi$
$884$		0			0
$885$	18.7689			0.630911
$886$		0			0
$887$		−	13.9962i		−	0.469948i	−0.972002	−	0.234974i	$-0.924500\pi$
$887$		−	13.9962i		−	0.469948i	0.972002	−	0.234974i	$-0.0755005\pi$
$888$		0			0
$889$	−3.16215	−	3.16215i	−0.106055	−	0.106055i
$890$		0			0
$891$	1.14429	+	1.14429i	0.0383353	+	0.0383353i
$892$		0			0
$893$	3.59518			0.120308
$894$		0			0
$895$	41.6771	+	41.6771i	1.39311	+	1.39311i
$896$		0			0
$897$	24.2063	−	4.61962i	0.808226	−	0.154245i
$898$		0			0
$899$	−24.2029	+	24.2029i	−0.807212	+	0.807212i
$900$		0			0
$901$		−	2.02515i		−	0.0674674i
$902$		0			0
$903$	−12.4113	+	12.4113i	−0.413022	+	0.413022i
$904$		0			0
$905$	4.68047	−	4.68047i	0.155584	−	0.155584i
$906$		0			0
$907$	27.0587			0.898471			0.449235	−	0.893413i	$-0.351696\pi$
$907$	27.0587			0.898471			0.449235	+	0.893413i	$0.351696\pi$
$908$		0			0
$909$			5.80354i			0.192491i
$910$		0			0
$911$			48.1804i			1.59629i	0.602467	+	0.798144i	$0.294185\pi$
$911$			48.1804i			1.59629i	−0.602467	+	0.798144i	$0.705815\pi$
$912$		0			0
$913$	−1.26476			−0.0418576
$914$		0			0
$915$	−34.7212	+	34.7212i	−1.14785	+	1.14785i
$916$		0			0
$917$	7.48908	−	7.48908i	0.247311	−	0.247311i
$918$		0			0
$919$		−	35.5359i		−	1.17222i	−0.810231	−	0.586111i	$-0.800658\pi$
$919$		−	35.5359i		−	1.17222i	0.810231	−	0.586111i	$-0.199342\pi$
$920$		0			0
$921$	−34.8942	+	34.8942i	−1.14980	+	1.14980i
$922$		0			0
$923$	−39.4522	−	26.8071i	−1.29859	−	0.882365i
$924$		0			0
$925$	9.86950	+	9.86950i	0.324507	+	0.324507i
$926$		0			0
$927$	−3.86136			−0.126824
$928$		0			0
$929$	8.19238	+	8.19238i	0.268783	+	0.268783i	0.828610	−	0.559826i	$-0.189132\pi$
$929$	8.19238	+	8.19238i	0.268783	+	0.268783i	−0.559826	+	0.828610i	$0.689132\pi$
$930$		0			0
$931$	10.1235	+	10.1235i	0.331785	+	0.331785i
$932$		0			0
$933$		−	31.5928i		−	1.03430i
$934$		0			0
$935$	−0.409913			−0.0134056
$936$		0			0
$937$	−35.9483			−1.17438			−0.587190	−	0.809449i	$-0.699766\pi$
$937$	−35.9483			−1.17438			−0.587190	+	0.809449i	$0.699766\pi$
$938$		0			0
$939$			40.3613i			1.31714i
$940$		0			0
$941$	−22.6387	−	22.6387i	−0.738000	−	0.738000i	0.234190	−	0.972191i	$-0.424756\pi$
$941$	−22.6387	−	22.6387i	−0.738000	−	0.738000i	−0.972191	+	0.234190i	$0.924756\pi$
$942$		0			0
$943$	10.3746	+	10.3746i	0.337843	+	0.337843i
$944$		0			0
$945$	14.3395			0.466464
$946$		0			0
$947$	6.18848	+	6.18848i	0.201098	+	0.201098i	0.800471	−	0.599372i	$-0.204583\pi$
$947$	6.18848	+	6.18848i	0.201098	+	0.201098i	−0.599372	+	0.800471i	$0.704583\pi$
$948$		0			0
$949$	−3.65127	−	2.48097i	−0.118525	−	0.0805357i
$950$		0			0
$951$	−3.43129	+	3.43129i	−0.111267	+	0.111267i
$952$		0			0
$953$			46.3124i			1.50021i	0.661321	+	0.750103i	$0.269996\pi$
$953$			46.3124i			1.50021i	−0.661321	+	0.750103i	$0.730004\pi$
$954$		0			0
$955$	−28.6247	+	28.6247i	−0.926274	+	0.926274i
$956$		0			0
$957$	1.26373	−	1.26373i	0.0408507	−	0.0408507i
$958$		0			0
$959$	21.1600			0.683293
$960$		0			0
$961$		−	33.1465i		−	1.06924i
$962$		0			0
$963$		−	8.87247i		−	0.285911i
$964$		0			0
$965$	−42.0429			−1.35341
$966$		0			0
$967$	−5.85872	+	5.85872i	−0.188404	+	0.188404i	−0.795006	−	0.606602i	$-0.792532\pi$
$967$	−5.85872	+	5.85872i	−0.188404	+	0.188404i	0.606602	+	0.795006i	$0.292532\pi$
$968$		0			0
$969$	1.30997	−	1.30997i	0.0420822	−	0.0420822i
$970$		0			0
$971$			8.81309i			0.282825i	0.989951	+	0.141413i	$0.0451645\pi$
$971$			8.81309i			0.282825i	−0.989951	+	0.141413i	$0.954836\pi$
$972$		0			0
$973$	−10.7440	+	10.7440i	−0.344438	+	0.344438i
$974$		0			0
$975$	2.03024	+	10.6382i	0.0650196	+	0.340696i
$976$		0			0
$977$	−6.68730	−	6.68730i	−0.213946	−	0.213946i	0.591996	−	0.805941i	$-0.298340\pi$
$977$	−6.68730	−	6.68730i	−0.213946	−	0.213946i	−0.805941	+	0.591996i	$0.798340\pi$
$978$		0			0
$979$	−2.51700			−0.0804437
$980$		0			0
$981$	−0.481999	−	0.481999i	−0.0153891	−	0.0153891i
$982$		0			0
$983$	15.4162	+	15.4162i	0.491701	+	0.491701i	0.908842	−	0.417141i	$-0.136968\pi$
$983$	15.4162	+	15.4162i	0.491701	+	0.491701i	−0.417141	+	0.908842i	$0.636968\pi$
$984$		0			0
$985$			4.62103i			0.147238i
$986$		0			0
$987$	−2.13426			−0.0679344
$988$		0			0
$989$	−58.8049			−1.86989
$990$		0			0
$991$		−	25.3885i		−	0.806493i	−0.915091	−	0.403247i	$-0.867882\pi$
$991$		−	25.3885i		−	0.806493i	0.915091	−	0.403247i	$-0.132118\pi$
$992$		0			0
$993$	2.78106	+	2.78106i	0.0882543	+	0.0882543i
$994$		0			0
$995$	15.3865	+	15.3865i	0.487785	+	0.487785i
$996$		0			0
$997$	15.6017			0.494110			0.247055	−	0.969001i	$-0.420537\pi$
$997$	15.6017			0.494110			0.247055	+	0.969001i	$0.420537\pi$
$998$		0			0
$999$	−27.1088	−	27.1088i	−0.857683	−	0.857683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.k.e.255.2	yes	8
4.3	odd	2		416.2.k.f.255.3	yes	8
8.3	odd	2		832.2.k.i.255.2		8
8.5	even	2		832.2.k.g.255.3		8
13.5	odd	4		416.2.k.f.31.2	yes	8
52.31	even	4	inner	416.2.k.e.31.3	✓	8
104.5	odd	4		832.2.k.i.447.3		8
104.83	even	4		832.2.k.g.447.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.k.e.31.3	✓	8	52.31	even	4	inner
416.2.k.e.255.2	yes	8	1.1	even	1	trivial
416.2.k.f.31.2	yes	8	13.5	odd	4
416.2.k.f.255.3	yes	8	4.3	odd	2
832.2.k.g.255.3		8	8.5	even	2
832.2.k.g.447.2		8	104.83	even	4
832.2.k.i.255.2		8	8.3	odd	2
832.2.k.i.447.3		8	104.5	odd	4

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.46091i q^{3} +(1.87831 + 1.87831i) q^{5} +(0.675897 + 0.675897i) q^{7} +0.865736 q^{9} +(-0.202412 - 0.202412i) q^{11} +(0.675897 + 3.54163i) q^{13} +(2.74404 - 2.74404i) q^{15} -0.539088i q^{17} +(-1.66332 + 1.66332i) q^{19} +(0.987427 - 0.987427i) q^{21} +4.67844 q^{23} +2.05609i q^{25} -5.64750i q^{27} -4.27362 q^{29} +(5.66332 - 5.66332i) q^{31} +(-0.295706 + 0.295706i) q^{33} +2.53909i q^{35} +(4.80013 - 4.80013i) q^{37} +(5.17401 - 0.987427i) q^{39} +(2.21753 + 2.21753i) q^{41} -12.5693 q^{43} +(1.62612 + 1.62612i) q^{45} +(-1.08072 - 1.08072i) q^{47} -6.08633i q^{49} -0.787560 q^{51} +3.75662 q^{53} -0.760383i q^{55} +(2.42997 + 2.42997i) q^{57} +(3.41994 + 3.41994i) q^{59} -12.6533 q^{61} +(0.585148 + 0.585148i) q^{63} +(-5.38274 + 7.92182i) q^{65} +(-9.28568 + 9.28568i) q^{67} -6.83479i q^{69} +(-9.35434 + 9.35434i) q^{71} +(-0.865736 + 0.865736i) q^{73} +3.00377 q^{75} -0.273619i q^{77} +13.0833i q^{79} -5.65330 q^{81} +(3.12424 - 3.12424i) q^{83} +(1.01257 - 1.01257i) q^{85} +6.24338i q^{87} +(6.21753 - 6.21753i) q^{89} +(-1.93694 + 2.85062i) q^{91} +(-8.27362 - 8.27362i) q^{93} -6.24847 q^{95} +(-7.67844 - 7.67844i) q^{97} +(-0.175235 - 0.175235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{7} - 20 q^{9} + 6 q^{11} - 2 q^{13} - 20 q^{15} + 6 q^{19} - 4 q^{21} - 16 q^{23} + 4 q^{29} + 26 q^{31} + 16 q^{33} + 8 q^{39} - 24 q^{41} - 44 q^{43} + 8 q^{45} + 14 q^{47} + 44 q^{51} + 28 q^{57}+ \cdots - 66 q^{99}+O(q^{100}) \) 8 * q - 2 * q^7 - 20 * q^9 + 6 * q^11 - 2 * q^13 - 20 * q^15 + 6 * q^19 - 4 * q^21 - 16 * q^23 + 4 * q^29 + 26 * q^31 + 16 * q^33 + 8 * q^39 - 24 * q^41 - 44 * q^43 + 8 * q^45 + 14 * q^47 + 44 * q^51 + 28 * q^57 - 22 * q^59 - 24 * q^61 - 38 * q^63 - 8 * q^65 + 2 * q^67 - 14 * q^71 + 20 * q^73 + 76 * q^75 + 32 * q^81 - 6 * q^83 + 20 * q^85 + 8 * q^89 + 42 * q^91 - 28 * q^93 + 12 * q^95 - 8 * q^97 - 66 * q^99

Introduction

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