LMFDB - Embedded newform 1408.2.i.b.351.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1408,2,Mod(351,1408)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1408, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1408.351");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1408 = 2^{7} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1408.i (of order $4$, degree $2$, not 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:	$11.2429366046$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 176)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			351.15
Character	$\chi$	$=$	1408.351
Dual form			1408.2.i.b.1055.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766690 - 0.766690i) q^{3} +(0.946416 - 0.946416i) q^{5} +0.840189i q^{7} +1.82437i q^{9} +O(q^{10})$	\(q+(0.766690 - 0.766690i) q^{3} +(0.946416 - 0.946416i) q^{5} +0.840189i q^{7} +1.82437i q^{9} +(0.809991 + 3.21620i) q^{11} +(-4.53511 + 4.53511i) q^{13} -1.45122i q^{15} -0.629097i q^{17} +(2.53823 + 2.53823i) q^{19} +(0.644164 + 0.644164i) q^{21} -3.15531 q^{23} +3.20859i q^{25} +(3.69880 + 3.69880i) q^{27} +(-3.41256 + 3.41256i) q^{29} -2.10183i q^{31} +(3.08684 + 1.84481i) q^{33} +(0.795168 + 0.795168i) q^{35} +(-6.49024 + 6.49024i) q^{37} +6.95405i q^{39} -7.84882 q^{41} +(2.55674 - 2.55674i) q^{43} +(1.72662 + 1.72662i) q^{45} -3.26924i q^{47} +6.29408 q^{49} +(-0.482322 - 0.482322i) q^{51} +(7.27250 - 7.27250i) q^{53} +(3.81045 + 2.27727i) q^{55} +3.89206 q^{57} +(-6.06309 - 6.06309i) q^{59} +(3.33040 - 3.33040i) q^{61} -1.53282 q^{63} +8.58421i q^{65} +(8.95497 - 8.95497i) q^{67} +(-2.41915 + 2.41915i) q^{69} +4.32041 q^{71} -3.78870 q^{73} +(2.45999 + 2.45999i) q^{75} +(-2.70221 + 0.680545i) q^{77} +10.7763 q^{79} +0.198539 q^{81} +(9.42796 + 9.42796i) q^{83} +(-0.595388 - 0.595388i) q^{85} +5.23275i q^{87} +1.82212i q^{89} +(-3.81035 - 3.81035i) q^{91} +(-1.61145 - 1.61145i) q^{93} +4.80444 q^{95} -2.21091 q^{97} +(-5.86754 + 1.47773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5	$ 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1408\mathbb{Z}\right)^\times$.

$n$	$133$	$639$	$1025$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.766690	−	0.766690i	0.442649	−	0.442649i	−0.450253	−	0.892901i	$-0.648666\pi$
$3$	0.766690	−	0.766690i	0.442649	−	0.442649i	0.892901	+	0.450253i	$0.148666\pi$
$4$		0			0
$5$	0.946416	−	0.946416i	0.423250	−	0.423250i	−0.463071	−	0.886321i	$-0.653252\pi$
$5$	0.946416	−	0.946416i	0.423250	−	0.423250i	0.886321	+	0.463071i	$0.153252\pi$
$6$		0			0
$7$			0.840189i			0.317561i	0.987314	+	0.158781i	$0.0507563\pi$
$7$			0.840189i			0.317561i	−0.987314	+	0.158781i	$0.949244\pi$
$8$		0			0
$9$			1.82437i			0.608125i
$10$		0			0
$11$	0.809991	+	3.21620i	0.244222	+	0.969719i
$11$	0.809991	+	3.21620i	0.244222	+	0.969719i
$12$		0			0
$13$	−4.53511	+	4.53511i	−1.25781	+	1.25781i	−0.305680	+	0.952134i	$0.598884\pi$
$13$	−4.53511	+	4.53511i	−1.25781	+	1.25781i	−0.952134	+	0.305680i	$0.901116\pi$
$14$		0			0
$15$		−	1.45122i		−	0.374702i
$16$		0			0
$17$		−	0.629097i		−	0.152578i	−0.997086	−	0.0762892i	$-0.975693\pi$
$17$		−	0.629097i		−	0.152578i	0.997086	−	0.0762892i	$-0.0243072\pi$
$18$		0			0
$19$	2.53823	+	2.53823i	0.582309	+	0.582309i	0.935537	−	0.353228i	$-0.114916\pi$
$19$	2.53823	+	2.53823i	0.582309	+	0.582309i	−0.353228	+	0.935537i	$0.614916\pi$
$20$		0			0
$21$	0.644164	+	0.644164i	0.140568	+	0.140568i
$22$		0			0
$23$	−3.15531			−0.657928			−0.328964	−	0.944342i	$-0.606700\pi$
$23$	−3.15531			−0.657928			−0.328964	+	0.944342i	$0.606700\pi$
$24$		0			0
$25$			3.20859i			0.641718i
$26$		0			0
$27$	3.69880	+	3.69880i	0.711834	+	0.711834i
$28$		0			0
$29$	−3.41256	+	3.41256i	−0.633696	+	0.633696i	−0.948993	−	0.315297i	$-0.897896\pi$
$29$	−3.41256	+	3.41256i	−0.633696	+	0.633696i	0.315297	+	0.948993i	$0.397896\pi$
$30$		0			0
$31$		−	2.10183i		−	0.377500i	−0.982025	−	0.188750i	$-0.939556\pi$
$31$		−	2.10183i		−	0.377500i	0.982025	−	0.188750i	$-0.0604435\pi$
$32$		0			0
$33$	3.08684	+	1.84481i	0.537349	+	0.321141i
$34$		0			0
$35$	0.795168	+	0.795168i	0.134408	+	0.134408i
$36$		0			0
$37$	−6.49024	+	6.49024i	−1.06699	+	1.06699i	−0.0694005	+	0.997589i	$0.522109\pi$
$37$	−6.49024	+	6.49024i	−1.06699	+	1.06699i	−0.997589	+	0.0694005i	$0.977891\pi$
$38$		0			0
$39$			6.95405i			1.11354i
$40$		0			0
$41$	−7.84882			−1.22578			−0.612890	−	0.790168i	$-0.709993\pi$
$41$	−7.84882			−1.22578			−0.612890	+	0.790168i	$0.709993\pi$
$42$		0			0
$43$	2.55674	−	2.55674i	0.389898	−	0.389898i	−0.484753	−	0.874651i	$-0.661090\pi$
$43$	2.55674	−	2.55674i	0.389898	−	0.389898i	0.874651	+	0.484753i	$0.161090\pi$
$44$		0			0
$45$	1.72662	+	1.72662i	0.257389	+	0.257389i
$46$		0			0
$47$		−	3.26924i		−	0.476868i	−0.971159	−	0.238434i	$-0.923366\pi$
$47$		−	3.26924i		−	0.476868i	0.971159	−	0.238434i	$-0.0766340\pi$
$48$		0			0
$49$	6.29408			0.899155
$50$		0			0
$51$	−0.482322	−	0.482322i	−0.0675386	−	0.0675386i
$52$		0			0
$53$	7.27250	−	7.27250i	0.998954	−	0.998954i	−0.00104508	−	0.999999i	$-0.500333\pi$
$53$	7.27250	−	7.27250i	0.998954	−	0.998954i	0.999999	+	0.00104508i	$0.000332659\pi$
$54$		0			0
$55$	3.81045	+	2.27727i	0.513801	+	0.307067i
$56$		0			0
$57$	3.89206			0.515516
$58$		0			0
$59$	−6.06309	−	6.06309i	−0.789347	−	0.789347i	0.192040	−	0.981387i	$-0.438490\pi$
$59$	−6.06309	−	6.06309i	−0.789347	−	0.789347i	−0.981387	+	0.192040i	$0.938490\pi$
$60$		0			0
$61$	3.33040	−	3.33040i	0.426414	−	0.426414i	−0.460991	−	0.887405i	$-0.652506\pi$
$61$	3.33040	−	3.33040i	0.426414	−	0.426414i	0.887405	+	0.460991i	$0.152506\pi$
$62$		0			0
$63$	−1.53282			−0.193117
$64$		0			0
$65$			8.58421i			1.06474i
$66$		0			0
$67$	8.95497	−	8.95497i	1.09402	−	1.09402i	0.0989292	−	0.995094i	$-0.468458\pi$
$67$	8.95497	−	8.95497i	1.09402	−	1.09402i	0.995094	−	0.0989292i	$-0.0315417\pi$
$68$		0			0
$69$	−2.41915	+	2.41915i	−0.291231	+	0.291231i
$70$		0			0
$71$	4.32041			0.512738			0.256369	−	0.966579i	$-0.417474\pi$
$71$	4.32041			0.512738			0.256369	+	0.966579i	$0.417474\pi$
$72$		0			0
$73$	−3.78870			−0.443434			−0.221717	−	0.975111i	$-0.571166\pi$
$73$	−3.78870			−0.443434			−0.221717	+	0.975111i	$0.571166\pi$
$74$		0			0
$75$	2.45999	+	2.45999i	0.284056	+	0.284056i
$76$		0			0
$77$	−2.70221	+	0.680545i	−0.307946	+	0.0775554i
$78$		0			0
$79$	10.7763			1.21242			0.606212	−	0.795303i	$-0.292688\pi$
$79$	10.7763			1.21242			0.606212	+	0.795303i	$0.292688\pi$
$80$		0			0
$81$	0.198539			0.0220598
$82$		0			0
$83$	9.42796	+	9.42796i	1.03485	+	1.03485i	0.999370	+	0.0354828i	$0.0112969\pi$
$83$	9.42796	+	9.42796i	1.03485	+	1.03485i	0.0354828	+	0.999370i	$0.488703\pi$
$84$		0			0
$85$	−0.595388	−	0.595388i	−0.0645788	−	0.0645788i
$86$		0			0
$87$			5.23275i			0.561009i
$88$		0			0
$89$			1.82212i			0.193144i	0.995326	+	0.0965720i	$0.0307878\pi$
$89$			1.82212i			0.193144i	−0.995326	+	0.0965720i	$0.969212\pi$
$90$		0			0
$91$	−3.81035	−	3.81035i	−0.399433	−	0.399433i
$92$		0			0
$93$	−1.61145	−	1.61145i	−0.167100	−	0.167100i
$94$		0			0
$95$	4.80444			0.492925
$96$		0			0
$97$	−2.21091			−0.224483			−0.112242	−	0.993681i	$-0.535803\pi$
$97$	−2.21091			−0.224483			−0.112242	+	0.993681i	$0.535803\pi$
$98$		0			0
$99$	−5.86754	+	1.47773i	−0.589710	+	0.148517i
$100$		0			0
$101$	0.529580	+	0.529580i	0.0526951	+	0.0526951i	0.732963	−	0.680268i	$-0.238137\pi$
$101$	0.529580	+	0.529580i	0.0526951	+	0.0526951i	−0.680268	+	0.732963i	$0.738137\pi$
$102$		0			0
$103$	2.05080			0.202071			0.101035	−	0.994883i	$-0.467784\pi$
$103$	2.05080			0.202071			0.101035	+	0.994883i	$0.467784\pi$
$104$		0			0
$105$	1.21929			0.118991
$106$		0			0
$107$	11.7771	−	11.7771i	1.13854	−	1.13854i	0.149826	−	0.988712i	$-0.452129\pi$
$107$	11.7771	−	11.7771i	1.13854	−	1.13854i	0.988712	−	0.149826i	$-0.0478713\pi$
$108$		0			0
$109$	−2.69368	+	2.69368i	−0.258008	+	0.258008i	−0.824243	−	0.566236i	$-0.808399\pi$
$109$	−2.69368	+	2.69368i	−0.258008	+	0.258008i	0.566236	+	0.824243i	$0.308399\pi$
$110$		0			0
$111$			9.95200i			0.944602i
$112$		0			0
$113$	−8.07111			−0.759266			−0.379633	−	0.925137i	$-0.623950\pi$
$113$	−8.07111			−0.759266			−0.379633	+	0.925137i	$0.623950\pi$
$114$		0			0
$115$	−2.98624	+	2.98624i	−0.278468	+	0.278468i
$116$		0			0
$117$	−8.27374	−	8.27374i	−0.764908	−	0.764908i
$118$		0			0
$119$	0.528560			0.0484530
$120$		0			0
$121$	−9.68783	+	5.21018i	−0.880712	+	0.473653i
$122$		0			0
$123$	−6.01761	+	6.01761i	−0.542590	+	0.542590i
$124$		0			0
$125$	7.76875	+	7.76875i	0.694858	+	0.694858i
$126$		0			0
$127$	11.9019			1.05612			0.528060	−	0.849207i	$-0.322920\pi$
$127$	11.9019			1.05612			0.528060	+	0.849207i	$0.322920\pi$
$128$		0			0
$129$		−	3.92045i		−	0.345176i
$130$		0			0
$131$	3.30469	+	3.30469i	0.288732	+	0.288732i	0.836579	−	0.547847i	$-0.184552\pi$
$131$	3.30469	+	3.30469i	0.288732	+	0.288732i	−0.547847	+	0.836579i	$0.684552\pi$
$132$		0			0
$133$	−2.13259	+	2.13259i	−0.184919	+	0.184919i
$134$		0			0
$135$	7.00121			0.602568
$136$		0			0
$137$			3.71278i			0.317205i	0.987343	+	0.158602i	$0.0506988\pi$
$137$			3.71278i			0.317205i	−0.987343	+	0.158602i	$0.949301\pi$
$138$		0			0
$139$	−13.9583	+	13.9583i	−1.18393	+	1.18393i	−0.205214	+	0.978717i	$0.565789\pi$
$139$	−13.9583	+	13.9583i	−1.18393	+	1.18393i	−0.978717	+	0.205214i	$0.934211\pi$
$140$		0			0
$141$	−2.50649	−	2.50649i	−0.211085	−	0.211085i
$142$		0			0
$143$	−18.2592	−	10.9124i	−1.52691	−	0.912542i
$144$		0			0
$145$			6.45940i			0.536424i
$146$		0			0
$147$	4.82561	−	4.82561i	0.398009	−	0.398009i
$148$		0			0
$149$	−3.38437	−	3.38437i	−0.277258	−	0.277258i	0.554755	−	0.832013i	$-0.312812\pi$
$149$	−3.38437	−	3.38437i	−0.277258	−	0.277258i	−0.832013	+	0.554755i	$0.812812\pi$
$150$		0			0
$151$			2.30545i			0.187615i	0.995590	+	0.0938074i	$0.0299038\pi$
$151$			2.30545i			0.187615i	−0.995590	+	0.0938074i	$0.970096\pi$
$152$		0			0
$153$	1.14771			0.0927867
$154$		0			0
$155$	−1.98921	−	1.98921i	−0.159777	−	0.159777i
$156$		0			0
$157$	11.2579	+	11.2579i	0.898475	+	0.898475i	0.995301	−	0.0968267i	$-0.0308693\pi$
$157$	11.2579	+	11.2579i	0.898475	+	0.898475i	−0.0968267	+	0.995301i	$0.530869\pi$
$158$		0			0
$159$		−	11.1515i		−	0.884371i
$160$		0			0
$161$		−	2.65106i		−	0.208933i
$162$		0			0
$163$	−4.35923	+	4.35923i	−0.341442	+	0.341442i	−0.856909	−	0.515468i	$-0.827618\pi$
$163$	−4.35923	+	4.35923i	−0.341442	+	0.341442i	0.515468	+	0.856909i	$0.327618\pi$
$164$		0			0
$165$	4.66739	−	1.17547i	0.363356	−	0.0915104i
$166$		0			0
$167$		−	16.6370i		−	1.28741i	−0.765273	−	0.643706i	$-0.777396\pi$
$167$		−	16.6370i		−	1.28741i	0.765273	−	0.643706i	$-0.222604\pi$
$168$		0			0
$169$		−	28.1345i		−	2.16419i
$170$		0			0
$171$	−4.63067	+	4.63067i	−0.354116	+	0.354116i
$172$		0			0
$173$	13.2572	−	13.2572i	1.00793	−	1.00793i	0.00795778	−	0.999968i	$-0.497467\pi$
$173$	13.2572	−	13.2572i	1.00793	−	1.00793i	0.999968	−	0.00795778i	$-0.00253307\pi$
$174$		0			0
$175$	−2.69582			−0.203785
$176$		0			0
$177$	−9.29702			−0.698807
$178$		0			0
$179$	2.10800	−	2.10800i	0.157559	−	0.157559i	−0.623925	−	0.781484i	$-0.714463\pi$
$179$	2.10800	−	2.10800i	0.157559	−	0.157559i	0.781484	+	0.623925i	$0.214463\pi$
$180$		0			0
$181$	−0.637458	+	0.637458i	−0.0473819	+	0.0473819i	−0.730401	−	0.683019i	$-0.760667\pi$
$181$	−0.637458	+	0.637458i	−0.0473819	+	0.0473819i	0.683019	+	0.730401i	$0.260667\pi$
$182$		0			0
$183$		−	5.10677i		−	0.377503i
$184$		0			0
$185$			12.2849i			0.903207i
$186$		0			0
$187$	2.02330	−	0.509563i	0.147958	−	0.0372629i
$188$		0			0
$189$	−3.10769	+	3.10769i	−0.226051	+	0.226051i
$190$		0			0
$191$			21.0757i			1.52499i	0.646996	+	0.762494i	$0.276025\pi$
$191$			21.0757i			1.52499i	−0.646996	+	0.762494i	$0.723975\pi$
$192$		0			0
$193$		−	23.1180i		−	1.66407i	−0.554726	−	0.832033i	$-0.687177\pi$
$193$		−	23.1180i		−	1.66407i	0.554726	−	0.832033i	$-0.312823\pi$
$194$		0			0
$195$	6.58143	+	6.58143i	0.471306	+	0.471306i
$196$		0			0
$197$	19.0349	+	19.0349i	1.35618	+	1.35618i	0.878576	+	0.477602i	$0.158494\pi$
$197$	19.0349	+	19.0349i	1.35618	+	1.35618i	0.477602	+	0.878576i	$0.341506\pi$
$198$		0			0
$199$	1.25568			0.0890130			0.0445065	−	0.999009i	$-0.485828\pi$
$199$	1.25568			0.0890130			0.0445065	+	0.999009i	$0.485828\pi$
$200$		0			0
$201$		−	13.7314i		−	0.968536i
$202$		0			0
$203$	−2.86719	−	2.86719i	−0.201238	−	0.201238i
$204$		0			0
$205$	−7.42825	+	7.42825i	−0.518812	+	0.518812i
$206$		0			0
$207$		−	5.75647i		−	0.400102i
$208$		0			0
$209$	−6.10749	+	10.2194i	−0.422464	+	0.706889i
$210$		0			0
$211$	−11.3830	−	11.3830i	−0.783635	−	0.783635i	0.196807	−	0.980442i	$-0.436943\pi$
$211$	−11.3830	−	11.3830i	−0.783635	−	0.783635i	−0.980442	+	0.196807i	$0.936943\pi$
$212$		0			0
$213$	3.31241	−	3.31241i	0.226963	−	0.226963i
$214$		0			0
$215$		−	4.83947i		−	0.330049i
$216$		0			0
$217$	1.76593			0.119879
$218$		0			0
$219$	−2.90476	+	2.90476i	−0.196286	+	0.196286i
$220$		0			0
$221$	2.85303	+	2.85303i	0.191915	+	0.191915i
$222$		0			0
$223$			27.8442i			1.86458i	0.361706	+	0.932292i	$0.382194\pi$
$223$			27.8442i			1.86458i	−0.361706	+	0.932292i	$0.617806\pi$
$224$		0			0
$225$	−5.85367			−0.390245
$226$		0			0
$227$	−13.1127	−	13.1127i	−0.870322	−	0.870322i	0.122186	−	0.992507i	$-0.461010\pi$
$227$	−13.1127	−	13.1127i	−0.870322	−	0.870322i	−0.992507	+	0.122186i	$0.961010\pi$
$228$		0			0
$229$	−5.22931	+	5.22931i	−0.345562	+	0.345562i	−0.858454	−	0.512891i	$-0.828574\pi$
$229$	−5.22931	+	5.22931i	−0.345562	+	0.345562i	0.512891	+	0.858454i	$0.328574\pi$
$230$		0			0
$231$	−1.54999	+	2.59352i	−0.101982	+	0.170641i
$232$		0			0
$233$	8.63643			0.565791			0.282896	−	0.959151i	$-0.408705\pi$
$233$	8.63643			0.565791			0.282896	+	0.959151i	$0.408705\pi$
$234$		0			0
$235$	−3.09406	−	3.09406i	−0.201834	−	0.201834i
$236$		0			0
$237$	8.26205	−	8.26205i	0.536678	−	0.536678i
$238$		0			0
$239$	13.4632			0.870859			0.435430	−	0.900223i	$-0.356596\pi$
$239$	13.4632			0.870859			0.435430	+	0.900223i	$0.356596\pi$
$240$		0			0
$241$			14.7911i			0.952776i	0.879235	+	0.476388i	$0.158054\pi$
$241$			14.7911i			0.952776i	−0.879235	+	0.476388i	$0.841946\pi$
$242$		0			0
$243$	−10.9442	+	10.9442i	−0.702069	+	0.702069i
$244$		0			0
$245$	5.95682	−	5.95682i	0.380567	−	0.380567i
$246$		0			0
$247$	−23.0223			−1.46487
$248$		0			0
$249$	14.4566			0.916152
$250$		0			0
$251$	0.341430	+	0.341430i	0.0215509	+	0.0215509i	0.717800	−	0.696249i	$-0.245149\pi$
$251$	0.341430	+	0.341430i	0.0215509	+	0.0215509i	−0.696249	+	0.717800i	$0.745149\pi$
$252$		0			0
$253$	−2.55578	−	10.1481i	−0.160680	−	0.638006i
$254$		0			0
$255$	−0.912955			−0.0571715
$256$		0			0
$257$	10.5030			0.655161			0.327581	−	0.944823i	$-0.393767\pi$
$257$	10.5030			0.655161			0.327581	+	0.944823i	$0.393767\pi$
$258$		0			0
$259$	−5.45303	−	5.45303i	−0.338835	−	0.338835i
$260$		0			0
$261$	−6.22578	−	6.22578i	−0.385366	−	0.385366i
$262$		0			0
$263$		−	24.3519i		−	1.50160i	−0.660529	−	0.750800i	$-0.729668\pi$
$263$		−	24.3519i		−	1.50160i	0.660529	−	0.750800i	$-0.270332\pi$
$264$		0			0
$265$		−	13.7656i		−	0.845615i
$266$		0			0
$267$	1.39700	+	1.39700i	0.0854949	+	0.0854949i
$268$		0			0
$269$	−16.0648	−	16.0648i	−0.979489	−	0.979489i	0.0203048	−	0.999794i	$-0.493536\pi$
$269$	−16.0648	−	16.0648i	−0.979489	−	0.979489i	−0.999794	+	0.0203048i	$0.993536\pi$
$270$		0			0
$271$	−27.2466			−1.65512			−0.827558	−	0.561380i	$-0.810271\pi$
$271$	−27.2466			−1.65512			−0.827558	+	0.561380i	$0.810271\pi$
$272$		0			0
$273$	−5.84272			−0.353617
$274$		0			0
$275$	−10.3195	+	2.59893i	−0.622287	+	0.156721i
$276$		0			0
$277$	−2.12679	−	2.12679i	−0.127786	−	0.127786i	0.640321	−	0.768107i	$-0.278801\pi$
$277$	−2.12679	−	2.12679i	−0.127786	−	0.127786i	−0.768107	+	0.640321i	$0.778801\pi$
$278$		0			0
$279$	3.83452			0.229567
$280$		0			0
$281$	19.4784			1.16199			0.580993	−	0.813908i	$-0.302664\pi$
$281$	19.4784			1.16199			0.580993	+	0.813908i	$0.302664\pi$
$282$		0			0
$283$	7.56610	−	7.56610i	0.449758	−	0.449758i	−0.445516	−	0.895274i	$-0.646980\pi$
$283$	7.56610	−	7.56610i	0.449758	−	0.449758i	0.895274	+	0.445516i	$0.146980\pi$
$284$		0			0
$285$	3.68351	−	3.68351i	0.218192	−	0.218192i
$286$		0			0
$287$		−	6.59449i		−	0.389261i
$288$		0			0
$289$	16.6042			0.976720
$290$		0			0
$291$	−1.69508	+	1.69508i	−0.0993672	+	0.0993672i
$292$		0			0
$293$	7.92368	+	7.92368i	0.462906	+	0.462906i	0.899607	−	0.436701i	$-0.143853\pi$
$293$	7.92368	+	7.92368i	0.462906	+	0.462906i	−0.436701	+	0.899607i	$0.643853\pi$
$294$		0			0
$295$	−11.4764			−0.668183
$296$		0			0
$297$	−8.90006	+	14.8921i	−0.516434	+	0.864124i
$298$		0			0
$299$	14.3097	−	14.3097i	0.827552	−	0.827552i
$300$		0			0
$301$	2.14814	+	2.14814i	0.123817	+	0.123817i
$302$		0			0
$303$	0.812046			0.0466508
$304$		0			0
$305$		−	6.30389i		−	0.360960i
$306$		0			0
$307$	−20.7843	−	20.7843i	−1.18623	−	1.18623i	−0.978103	−	0.208122i	$-0.933265\pi$
$307$	−20.7843	−	20.7843i	−1.18623	−	1.18623i	−0.208122	−	0.978103i	$-0.566735\pi$
$308$		0			0
$309$	1.57232	−	1.57232i	0.0894464	−	0.0894464i
$310$		0			0
$311$	−3.41874			−0.193859			−0.0969295	−	0.995291i	$-0.530902\pi$
$311$	−3.41874			−0.193859			−0.0969295	+	0.995291i	$0.530902\pi$
$312$		0			0
$313$			25.7758i			1.45694i	0.685080	+	0.728468i	$0.259767\pi$
$313$			25.7758i			1.45694i	−0.685080	+	0.728468i	$0.740233\pi$
$314$		0			0
$315$	−1.45068	+	1.45068i	−0.0817368	+	0.0817368i
$316$		0			0
$317$	−10.6560	−	10.6560i	−0.598503	−	0.598503i	0.341411	−	0.939914i	$-0.389095\pi$
$317$	−10.6560	−	10.6560i	−0.598503	−	0.598503i	−0.939914	+	0.341411i	$0.889095\pi$
$318$		0			0
$319$	−13.7396	−	8.21131i	−0.769270	−	0.459745i
$320$		0			0
$321$		−	18.0588i		−	1.00794i
$322$		0			0
$323$	1.59679	−	1.59679i	0.0888478	−	0.0888478i
$324$		0			0
$325$	−14.5513	−	14.5513i	−0.807163	−	0.807163i
$326$		0			0
$327$			4.13043i			0.228413i
$328$		0			0
$329$	2.74678			0.151435
$330$		0			0
$331$	6.44720	+	6.44720i	0.354370	+	0.354370i	0.861733	−	0.507363i	$-0.169379\pi$
$331$	6.44720	+	6.44720i	0.354370	+	0.354370i	−0.507363	+	0.861733i	$0.669379\pi$
$332$		0			0
$333$	−11.8406	−	11.8406i	−0.648862	−	0.648862i
$334$		0			0
$335$		−	16.9503i		−	0.926092i
$336$		0			0
$337$		−	8.71808i		−	0.474904i	−0.971399	−	0.237452i	$-0.923688\pi$
$337$		−	8.71808i		−	0.474904i	0.971399	−	0.237452i	$-0.0763123\pi$
$338$		0			0
$339$	−6.18803	+	6.18803i	−0.336088	+	0.336088i
$340$		0			0
$341$	6.75990	−	1.70246i	0.366069	−	0.0921936i
$342$		0			0
$343$			11.1695i			0.603098i
$344$		0			0
$345$			4.57904i			0.246527i
$346$		0			0
$347$	11.9394	−	11.9394i	0.640943	−	0.640943i	−0.309844	−	0.950787i	$-0.600277\pi$
$347$	11.9394	−	11.9394i	0.640943	−	0.640943i	0.950787	+	0.309844i	$0.100277\pi$
$348$		0			0
$349$	19.8686	−	19.8686i	1.06354	−	1.06354i	0.0657029	−	0.997839i	$-0.479071\pi$
$349$	19.8686	−	19.8686i	1.06354	−	1.06354i	0.997839	−	0.0657029i	$-0.0209289\pi$
$350$		0			0
$351$	−33.5489			−1.79071
$352$		0			0
$353$	21.7504			1.15766			0.578828	−	0.815449i	$-0.303510\pi$
$353$	21.7504			1.15766			0.578828	+	0.815449i	$0.303510\pi$
$354$		0			0
$355$	4.08891	−	4.08891i	0.217017	−	0.217017i
$356$		0			0
$357$	0.405242	−	0.405242i	0.0214477	−	0.0214477i
$358$		0			0
$359$			17.5690i			0.927256i	0.886030	+	0.463628i	$0.153453\pi$
$359$			17.5690i			0.927256i	−0.886030	+	0.463628i	$0.846547\pi$
$360$		0			0
$361$		−	6.11482i		−	0.321832i
$362$		0			0
$363$	−3.43297	+	11.4221i	−0.180184	+	0.599507i
$364$		0			0
$365$	−3.58569	+	3.58569i	−0.187684	+	0.187684i
$366$		0			0
$367$			24.9069i			1.30013i	0.759880	+	0.650064i	$0.225258\pi$
$367$			24.9069i			1.30013i	−0.759880	+	0.650064i	$0.774742\pi$
$368$		0			0
$369$		−	14.3192i		−	0.745427i
$370$		0			0
$371$	6.11027	+	6.11027i	0.317229	+	0.317229i
$372$		0			0
$373$	6.60905	+	6.60905i	0.342204	+	0.342204i	0.857195	−	0.514992i	$-0.172205\pi$
$373$	6.60905	+	6.60905i	0.342204	+	0.342204i	−0.514992	+	0.857195i	$0.672205\pi$
$374$		0			0
$375$	11.9124			0.615156
$376$		0			0
$377$		−	30.9527i		−	1.59414i
$378$		0			0
$379$	17.5192	+	17.5192i	0.899899	+	0.899899i	0.995427	−	0.0955275i	$-0.0304538\pi$
$379$	17.5192	+	17.5192i	0.899899	+	0.899899i	−0.0955275	+	0.995427i	$0.530454\pi$
$380$		0			0
$381$	9.12504	−	9.12504i	0.467490	−	0.467490i
$382$		0			0
$383$		−	19.0900i		−	0.975454i	−0.872996	−	0.487727i	$-0.837826\pi$
$383$		−	19.0900i		−	0.975454i	0.872996	−	0.487727i	$-0.162174\pi$
$384$		0			0
$385$	−1.91334	+	3.20150i	−0.0975127	+	0.163163i
$386$		0			0
$387$	4.66444	+	4.66444i	0.237107	+	0.237107i
$388$		0			0
$389$	−2.32843	+	2.32843i	−0.118056	+	0.118056i	−0.763667	−	0.645611i	$-0.776603\pi$
$389$	−2.32843	+	2.32843i	−0.118056	+	0.118056i	0.645611	+	0.763667i	$0.276603\pi$
$390$		0			0
$391$			1.98500i			0.100386i
$392$		0			0
$393$	5.06734			0.255614
$394$		0			0
$395$	10.1988	−	10.1988i	0.513159	−	0.513159i
$396$		0			0
$397$	−14.7966	−	14.7966i	−0.742620	−	0.742620i	0.230462	−	0.973081i	$-0.425976\pi$
$397$	−14.7966	−	14.7966i	−0.742620	−	0.742620i	−0.973081	+	0.230462i	$0.925976\pi$
$398$		0			0
$399$			3.27007i			0.163708i
$400$		0			0
$401$	−10.9026			−0.544451			−0.272225	−	0.962233i	$-0.587760\pi$
$401$	−10.9026			−0.544451			−0.272225	+	0.962233i	$0.587760\pi$
$402$		0			0
$403$	9.53204	+	9.53204i	0.474825	+	0.474825i
$404$		0			0
$405$	0.187900	−	0.187900i	0.00933684	−	0.00933684i
$406$		0			0
$407$	−26.1309	−	15.6169i	−1.29526	−	0.774099i
$408$		0			0
$409$	13.9046			0.687540			0.343770	−	0.939054i	$-0.388296\pi$
$409$	13.9046			0.687540			0.343770	+	0.939054i	$0.388296\pi$
$410$		0			0
$411$	2.84655	+	2.84655i	0.140410	+	0.140410i
$412$		0			0
$413$	5.09414	−	5.09414i	0.250666	−	0.250666i
$414$		0			0
$415$	17.8456			0.876004
$416$		0			0
$417$			21.4034i			1.04813i
$418$		0			0
$419$	−9.19279	+	9.19279i	−0.449097	+	0.449097i	−0.895054	−	0.445957i	$-0.852863\pi$
$419$	−9.19279	+	9.19279i	−0.449097	+	0.449097i	0.445957	+	0.895054i	$0.352863\pi$
$420$		0			0
$421$	−25.7986	+	25.7986i	−1.25735	+	1.25735i	−0.304990	+	0.952356i	$0.598653\pi$
$421$	−25.7986	+	25.7986i	−1.25735	+	1.25735i	−0.952356	+	0.304990i	$0.901347\pi$
$422$		0			0
$423$	5.96432			0.289995
$424$		0			0
$425$	2.01851			0.0979124
$426$		0			0
$427$	2.79816	+	2.79816i	0.135413	+	0.135413i
$428$		0			0
$429$	−22.3656	+	5.63272i	−1.07982	+	0.271950i
$430$		0			0
$431$	21.7073			1.04560			0.522802	−	0.852454i	$-0.324887\pi$
$431$	21.7073			1.04560			0.522802	+	0.852454i	$0.324887\pi$
$432$		0			0
$433$	−35.9899			−1.72957			−0.864783	−	0.502146i	$-0.832544\pi$
$433$	−35.9899			−1.72957			−0.864783	+	0.502146i	$0.832544\pi$
$434$		0			0
$435$	4.95236	+	4.95236i	0.237447	+	0.237447i
$436$		0			0
$437$	−8.00890	−	8.00890i	−0.383118	−	0.383118i
$438$		0			0
$439$			7.21745i			0.344470i	0.985056	+	0.172235i	$0.0550988\pi$
$439$			7.21745i			0.344470i	−0.985056	+	0.172235i	$0.944901\pi$
$440$		0			0
$441$			11.4828i			0.546798i
$442$		0			0
$443$	−14.6412	−	14.6412i	−0.695622	−	0.695622i	0.267841	−	0.963463i	$-0.413690\pi$
$443$	−14.6412	−	14.6412i	−0.695622	−	0.695622i	−0.963463	+	0.267841i	$0.913690\pi$
$444$		0			0
$445$	1.72448	+	1.72448i	0.0817482	+	0.0817482i
$446$		0			0
$447$	−5.18952			−0.245456
$448$		0			0
$449$	24.5581			1.15897			0.579483	−	0.814984i	$-0.303254\pi$
$449$	24.5581			1.15897			0.579483	+	0.814984i	$0.303254\pi$
$450$		0			0
$451$	−6.35748	−	25.2433i	−0.299362	−	1.18866i
$452$		0			0
$453$	1.76756	+	1.76756i	0.0830474	+	0.0830474i
$454$		0			0
$455$	−7.21236			−0.338121
$456$		0			0
$457$	−27.9969			−1.30964			−0.654820	−	0.755785i	$-0.727256\pi$
$457$	−27.9969			−1.30964			−0.654820	+	0.755785i	$0.727256\pi$
$458$		0			0
$459$	2.32690	−	2.32690i	0.108610	−	0.108610i
$460$		0			0
$461$	−19.8282	+	19.8282i	−0.923491	+	0.923491i	−0.997274	−	0.0737832i	$-0.976493\pi$
$461$	−19.8282	+	19.8282i	−0.923491	+	0.923491i	0.0737832	+	0.997274i	$0.476493\pi$
$462$		0			0
$463$		−	16.2467i		−	0.755046i	−0.926000	−	0.377523i	$-0.876776\pi$
$463$		−	16.2467i		−	0.755046i	0.926000	−	0.377523i	$-0.123224\pi$
$464$		0			0
$465$	−3.05021			−0.141450
$466$		0			0
$467$	−10.4656	+	10.4656i	−0.484291	+	0.484291i	−0.906499	−	0.422208i	$-0.861255\pi$
$467$	−10.4656	+	10.4656i	−0.484291	+	0.484291i	0.422208	+	0.906499i	$0.361255\pi$
$468$		0			0
$469$	7.52386	+	7.52386i	0.347420	+	0.347420i
$470$		0			0
$471$	17.2626			0.795417
$472$		0			0
$473$	10.2939	+	6.15203i	0.473314	+	0.282871i
$474$		0			0
$475$	−8.14413	+	8.14413i	−0.373678	+	0.373678i
$476$		0			0
$477$	13.2678	+	13.2678i	0.607489	+	0.607489i
$478$		0			0
$479$	21.3972			0.977662			0.488831	−	0.872378i	$-0.337423\pi$
$479$	21.3972			0.977662			0.488831	+	0.872378i	$0.337423\pi$
$480$		0			0
$481$		−	58.8680i		−	2.68415i
$482$		0			0
$483$	−2.03254	−	2.03254i	−0.0924838	−	0.0924838i
$484$		0			0
$485$	−2.09244	+	2.09244i	−0.0950127	+	0.0950127i
$486$		0			0
$487$	−17.4266			−0.789674			−0.394837	−	0.918751i	$-0.629199\pi$
$487$	−17.4266			−0.789674			−0.394837	+	0.918751i	$0.629199\pi$
$488$		0			0
$489$			6.68436i			0.302277i
$490$		0			0
$491$	−12.7015	+	12.7015i	−0.573212	+	0.573212i	−0.933025	−	0.359813i	$-0.882841\pi$
$491$	−12.7015	+	12.7015i	−0.573212	+	0.573212i	0.359813	+	0.933025i	$0.382841\pi$
$492$		0			0
$493$	2.14683	+	2.14683i	0.0966884	+	0.0966884i
$494$		0			0
$495$	−4.15459	+	6.95168i	−0.186735	+	0.312455i
$496$		0			0
$497$			3.62996i			0.162826i
$498$		0			0
$499$	23.1643	−	23.1643i	1.03698	−	1.03698i	0.0376874	−	0.999290i	$-0.488001\pi$
$499$	23.1643	−	23.1643i	1.03698	−	1.03698i	0.999290	−	0.0376874i	$-0.0119991\pi$
$500$		0			0
$501$	−12.7554	−	12.7554i	−0.569871	−	0.569871i
$502$		0			0
$503$			3.34989i			0.149364i	0.997207	+	0.0746822i	$0.0237942\pi$
$503$			3.34989i			0.149364i	−0.997207	+	0.0746822i	$0.976206\pi$
$504$		0			0
$505$	1.00241			0.0446065
$506$		0			0
$507$	−21.5705	−	21.5705i	−0.957977	−	0.957977i
$508$		0			0
$509$	18.1729	+	18.1729i	0.805499	+	0.805499i	0.983949	−	0.178450i	$-0.0571084\pi$
$509$	18.1729	+	18.1729i	0.805499	+	0.805499i	−0.178450	+	0.983949i	$0.557108\pi$
$510$		0			0
$511$		−	3.18323i		−	0.140818i
$512$		0			0
$513$			18.7768i			0.829015i
$514$		0			0
$515$	1.94091	−	1.94091i	0.0855265	−	0.0855265i
$516$		0			0
$517$	10.5145	−	2.64806i	0.462428	−	0.116461i
$518$		0			0
$519$		−	20.3283i		−	0.892314i
$520$		0			0
$521$		−	3.68129i		−	0.161280i	−0.996743	−	0.0806402i	$-0.974304\pi$
$521$		−	3.68129i		−	0.161280i	0.996743	−	0.0806402i	$-0.0256965\pi$
$522$		0			0
$523$	13.1131	−	13.1131i	0.573394	−	0.573394i	−0.359681	−	0.933075i	$-0.617114\pi$
$523$	13.1131	−	13.1131i	0.573394	−	0.573394i	0.933075	+	0.359681i	$0.117114\pi$
$524$		0			0
$525$	−2.06686	+	2.06686i	−0.0902051	+	0.0902051i
$526$		0			0
$527$	−1.32225			−0.0575983
$528$		0			0
$529$	−13.0440			−0.567130
$530$		0			0
$531$	11.0613	−	11.0613i	0.480021	−	0.480021i
$532$		0			0
$533$	35.5953	−	35.5953i	1.54180	−	1.54180i
$534$		0			0
$535$		−	22.2921i		−	0.963773i
$536$		0			0
$537$		−	3.23236i		−	0.139487i
$538$		0			0
$539$	5.09815	+	20.2430i	0.219593	+	0.871928i
$540$		0			0
$541$	19.3889	−	19.3889i	0.833596	−	0.833596i	−0.154411	−	0.988007i	$-0.549348\pi$
$541$	19.3889	−	19.3889i	0.833596	−	0.833596i	0.988007	+	0.154411i	$0.0493480\pi$
$542$		0			0
$543$			0.977465i			0.0419471i
$544$		0			0
$545$			5.09868i			0.218404i
$546$		0			0
$547$	25.3108	+	25.3108i	1.08221	+	1.08221i	0.996303	+	0.0859070i	$0.0273788\pi$
$547$	25.3108	+	25.3108i	1.08221	+	1.08221i	0.0859070	+	0.996303i	$0.472621\pi$
$548$		0			0
$549$	6.07589	+	6.07589i	0.259313	+	0.259313i
$550$		0			0
$551$	−17.3237			−0.738014
$552$		0			0
$553$			9.05409i			0.385019i
$554$		0			0
$555$	9.41874	+	9.41874i	0.399803	+	0.399803i
$556$		0			0
$557$	−10.2857	+	10.2857i	−0.435819	+	0.435819i	−0.890602	−	0.454783i	$-0.849717\pi$
$557$	−10.2857	+	10.2857i	−0.435819	+	0.435819i	0.454783	+	0.890602i	$0.349717\pi$
$558$		0			0
$559$			23.1902i			0.980840i
$560$		0			0
$561$	1.16057	−	1.94192i	0.0489991	−	0.0819879i
$562$		0			0
$563$	14.5498	+	14.5498i	0.613201	+	0.613201i	0.943779	−	0.330578i	$-0.107244\pi$
$563$	14.5498	+	14.5498i	0.613201	+	0.613201i	−0.330578	+	0.943779i	$0.607244\pi$
$564$		0			0
$565$	−7.63863	+	7.63863i	−0.321359	+	0.321359i
$566$		0			0
$567$			0.166810i			0.00700536i
$568$		0			0
$569$	29.5115			1.23719			0.618593	−	0.785712i	$-0.287703\pi$
$569$	29.5115			1.23719			0.618593	+	0.785712i	$0.287703\pi$
$570$		0			0
$571$	−30.5942	+	30.5942i	−1.28033	+	1.28033i	−0.339845	+	0.940482i	$0.610374\pi$
$571$	−30.5942	+	30.5942i	−1.28033	+	1.28033i	−0.940482	+	0.339845i	$0.889626\pi$
$572$		0			0
$573$	16.1586	+	16.1586i	0.675033	+	0.675033i
$574$		0			0
$575$		−	10.1241i		−	0.422205i
$576$		0			0
$577$	22.4261			0.933612			0.466806	−	0.884360i	$-0.345405\pi$
$577$	22.4261			0.933612			0.466806	+	0.884360i	$0.345405\pi$
$578$		0			0
$579$	−17.7243	−	17.7243i	−0.736597	−	0.736597i
$580$		0			0
$581$	−7.92127	+	7.92127i	−0.328629	+	0.328629i
$582$		0			0
$583$	29.2804	+	17.4991i	1.21267	+	0.724739i
$584$		0			0
$585$	−15.6608			−0.647495
$586$		0			0
$587$	−29.5430	−	29.5430i	−1.21937	−	1.21937i	−0.967853	−	0.251517i	$-0.919071\pi$
$587$	−29.5430	−	29.5430i	−1.21937	−	1.21937i	−0.251517	−	0.967853i	$-0.580929\pi$
$588$		0			0
$589$	5.33492	−	5.33492i	0.219822	−	0.219822i
$590$		0			0
$591$	29.1877			1.20062
$592$		0			0
$593$			26.9413i			1.10635i	0.833066	+	0.553173i	$0.186583\pi$
$593$			26.9413i			1.10635i	−0.833066	+	0.553173i	$0.813417\pi$
$594$		0			0
$595$	0.500238	−	0.500238i	0.0205078	−	0.0205078i
$596$		0			0
$597$	0.962719	−	0.962719i	0.0394015	−	0.0394015i
$598$		0			0
$599$	27.7531			1.13396			0.566979	−	0.823732i	$-0.308112\pi$
$599$	27.7531			1.13396			0.566979	+	0.823732i	$0.308112\pi$
$600$		0			0
$601$	−40.9346			−1.66976			−0.834879	−	0.550433i	$-0.814462\pi$
$601$	−40.9346			−1.66976			−0.834879	+	0.550433i	$0.814462\pi$
$602$		0			0
$603$	16.3372	+	16.3372i	0.665303	+	0.665303i
$604$		0			0
$605$	−4.23772	+	14.0997i	−0.172288	+	0.573235i
$606$		0			0
$607$	−10.1132			−0.410482			−0.205241	−	0.978711i	$-0.565798\pi$
$607$	−10.1132			−0.410482			−0.205241	+	0.978711i	$0.565798\pi$
$608$		0			0
$609$	−4.39650			−0.178155
$610$		0			0
$611$	14.8264	+	14.8264i	0.599811	+	0.599811i
$612$		0			0
$613$	−7.33677	−	7.33677i	−0.296329	−	0.296329i	0.543245	−	0.839574i	$-0.317196\pi$
$613$	−7.33677	−	7.33677i	−0.296329	−	0.296329i	−0.839574	+	0.543245i	$0.817196\pi$
$614$		0			0
$615$			11.3903i			0.459302i
$616$		0			0
$617$		−	20.3517i		−	0.819327i	−0.912237	−	0.409663i	$-0.865646\pi$
$617$		−	20.3517i		−	0.819327i	0.912237	−	0.409663i	$-0.134354\pi$
$618$		0			0
$619$	−7.15744	−	7.15744i	−0.287682	−	0.287682i	0.548481	−	0.836163i	$-0.315206\pi$
$619$	−7.15744	−	7.15744i	−0.287682	−	0.287682i	−0.836163	+	0.548481i	$0.815206\pi$
$620$		0			0
$621$	−11.6709	−	11.6709i	−0.468336	−	0.468336i
$622$		0			0
$623$	−1.53092			−0.0613351
$624$		0			0
$625$	−1.33802			−0.0535209
$626$		0			0
$627$	3.15254	+	12.5176i	0.125900	+	0.499906i
$628$		0			0
$629$	4.08299	+	4.08299i	0.162800	+	0.162800i
$630$		0			0
$631$	8.51970			0.339164			0.169582	−	0.985516i	$-0.445758\pi$
$631$	8.51970			0.339164			0.169582	+	0.985516i	$0.445758\pi$
$632$		0			0
$633$	−17.4544			−0.693750
$634$		0			0
$635$	11.2641	−	11.2641i	0.447003	−	0.447003i
$636$		0			0
$637$	−28.5444	+	28.5444i	−1.13097	+	1.13097i
$638$		0			0
$639$			7.88204i			0.311809i
$640$		0			0
$641$	−26.0558			−1.02914			−0.514572	−	0.857447i	$-0.672049\pi$
$641$	−26.0558			−1.02914			−0.514572	+	0.857447i	$0.672049\pi$
$642$		0			0
$643$	−9.65029	+	9.65029i	−0.380570	+	0.380570i	−0.871308	−	0.490737i	$-0.836727\pi$
$643$	−9.65029	+	9.65029i	−0.380570	+	0.380570i	0.490737	+	0.871308i	$0.336727\pi$
$644$		0			0
$645$	−3.71037	−	3.71037i	−0.146096	−	0.146096i
$646$		0			0
$647$	9.11572			0.358376			0.179188	−	0.983815i	$-0.442653\pi$
$647$	9.11572			0.358376			0.179188	+	0.983815i	$0.442653\pi$
$648$		0			0
$649$	14.5890	−	24.4111i	0.572670	−	0.958221i
$650$		0			0
$651$	1.35392	−	1.35392i	0.0530644	−	0.0530644i
$652$		0			0
$653$	6.75326	+	6.75326i	0.264276	+	0.264276i	0.826788	−	0.562513i	$-0.190165\pi$
$653$	6.75326	+	6.75326i	0.264276	+	0.264276i	−0.562513	+	0.826788i	$0.690165\pi$
$654$		0			0
$655$	6.25523			0.244412
$656$		0			0
$657$		−	6.91201i		−	0.269663i
$658$		0			0
$659$	−19.6083	−	19.6083i	−0.763830	−	0.763830i	0.213183	−	0.977012i	$-0.431617\pi$
$659$	−19.6083	−	19.6083i	−0.763830	−	0.763830i	−0.977012	+	0.213183i	$0.931617\pi$
$660$		0			0
$661$	−5.18363	+	5.18363i	−0.201620	+	0.201620i	−0.800694	−	0.599074i	$-0.795536\pi$
$661$	−5.18363	+	5.18363i	−0.201620	+	0.201620i	0.599074	+	0.800694i	$0.295536\pi$
$662$		0			0
$663$	4.37477			0.169902
$664$		0			0
$665$			4.03663i			0.156534i
$666$		0			0
$667$	10.7677	−	10.7677i	0.416927	−	0.416927i
$668$		0			0
$669$	21.3478	+	21.3478i	0.825356	+	0.825356i
$670$		0			0
$671$	13.4088	+	8.01362i	0.517642	+	0.309363i
$672$		0			0
$673$			13.5902i			0.523863i	0.965087	+	0.261931i	$0.0843594\pi$
$673$			13.5902i			0.523863i	−0.965087	+	0.261931i	$0.915641\pi$
$674$		0			0
$675$	−11.8679	+	11.8679i	−0.456797	+	0.456797i
$676$		0			0
$677$	23.9899	+	23.9899i	0.922006	+	0.922006i	0.997171	−	0.0751656i	$-0.0239485\pi$
$677$	23.9899	+	23.9899i	0.922006	+	0.922006i	−0.0751656	+	0.997171i	$0.523949\pi$
$678$		0			0
$679$		−	1.85758i		−	0.0712873i
$680$		0			0
$681$	−20.1068			−0.770493
$682$		0			0
$683$	16.2981	+	16.2981i	0.623628	+	0.623628i	0.946457	−	0.322829i	$-0.104634\pi$
$683$	16.2981	+	16.2981i	0.623628	+	0.623628i	−0.322829	+	0.946457i	$0.604634\pi$
$684$		0			0
$685$	3.51384	+	3.51384i	0.134257	+	0.134257i
$686$		0			0
$687$			8.01852i			0.305925i
$688$		0			0
$689$			65.9632i			2.51300i
$690$		0			0
$691$	7.34845	−	7.34845i	0.279548	−	0.279548i	−0.553380	−	0.832929i	$-0.686662\pi$
$691$	7.34845	−	7.34845i	0.279548	−	0.279548i	0.832929	+	0.553380i	$0.186662\pi$
$692$		0			0
$693$	−1.24157	−	4.92984i	−0.0471633	−	0.187269i
$694$		0			0
$695$			26.4208i			1.00220i
$696$		0			0
$697$			4.93767i			0.187028i
$698$		0			0
$699$	6.62146	−	6.62146i	0.250447	−	0.250447i
$700$		0			0
$701$	9.67833	−	9.67833i	0.365545	−	0.365545i	−0.500304	−	0.865850i	$-0.666779\pi$
$701$	9.67833	−	9.67833i	0.365545	−	0.365545i	0.865850	+	0.500304i	$0.166779\pi$
$702$		0			0
$703$	−32.9474			−1.24263
$704$		0			0
$705$	−4.74437			−0.178683
$706$		0			0
$707$	−0.444947	+	0.444947i	−0.0167339	+	0.0167339i
$708$		0			0
$709$	−0.104842	+	0.104842i	−0.00393742	+	0.00393742i	−0.709073	−	0.705135i	$-0.750886\pi$
$709$	−0.104842	+	0.104842i	−0.00393742	+	0.00393742i	0.705135	+	0.709073i	$0.250886\pi$
$710$		0			0
$711$			19.6599i			0.737305i
$712$		0			0
$713$			6.63193i			0.248368i
$714$		0			0
$715$	−27.6085	+	6.95314i	−1.03250	+	0.260033i
$716$		0			0
$717$	10.3221	−	10.3221i	0.385485	−	0.385485i
$718$		0			0
$719$		−	27.1702i		−	1.01328i	−0.862158	−	0.506639i	$-0.830888\pi$
$719$		−	27.1702i		−	1.01328i	0.862158	−	0.506639i	$-0.169112\pi$
$720$		0			0
$721$			1.72305i			0.0641699i
$722$		0			0
$723$	11.3402	+	11.3402i	0.421745	+	0.421745i
$724$		0			0
$725$	−10.9495	−	10.9495i	−0.406655	−	0.406655i
$726$		0			0
$727$	34.5808			1.28253			0.641265	−	0.767319i	$-0.278410\pi$
$727$	34.5808			1.28253			0.641265	+	0.767319i	$0.278410\pi$
$728$		0			0
$729$			17.3772i			0.643600i
$730$		0			0
$731$	−1.60843	−	1.60843i	−0.0594901	−	0.0594901i
$732$		0			0
$733$	−12.3402	+	12.3402i	−0.455796	+	0.455796i	−0.897273	−	0.441477i	$-0.854455\pi$
$733$	−12.3402	+	12.3402i	−0.455796	+	0.455796i	0.441477	+	0.897273i	$0.354455\pi$
$734$		0			0
$735$		−	9.13407i		−	0.336915i
$736$		0			0
$737$	36.0544	+	21.5475i	1.32808	+	0.793712i
$738$		0			0
$739$	28.7963	+	28.7963i	1.05929	+	1.05929i	0.998128	+	0.0611610i	$0.0194803\pi$
$739$	28.7963	+	28.7963i	1.05929	+	1.05929i	0.0611610	+	0.998128i	$0.480520\pi$
$740$		0			0
$741$	−17.6510	+	17.6510i	−0.648424	+	0.648424i
$742$		0			0
$743$		−	4.49062i		−	0.164745i	−0.996602	−	0.0823725i	$-0.973750\pi$
$743$		−	4.49062i		−	0.164745i	0.996602	−	0.0823725i	$-0.0262497\pi$
$744$		0			0
$745$	−6.40604			−0.234699
$746$		0			0
$747$	−17.2001	+	17.2001i	−0.629320	+	0.629320i
$748$		0			0
$749$	9.89501	+	9.89501i	0.361556	+	0.361556i
$750$		0			0
$751$			6.40382i			0.233679i	0.993151	+	0.116839i	$0.0372762\pi$
$751$			6.40382i			0.233679i	−0.993151	+	0.116839i	$0.962724\pi$
$752$		0			0
$753$	0.523542			0.0190789
$754$		0			0
$755$	2.18192	+	2.18192i	0.0794080	+	0.0794080i
$756$		0			0
$757$	7.32934	−	7.32934i	0.266390	−	0.266390i	−0.561254	−	0.827644i	$-0.689681\pi$
$757$	7.32934	−	7.32934i	0.266390	−	0.266390i	0.827644	+	0.561254i	$0.189681\pi$
$758$		0			0
$759$	−9.73994	−	5.82096i	−0.353537	−	0.211288i
$760$		0			0
$761$	−37.0682			−1.34372			−0.671860	−	0.740678i	$-0.734504\pi$
$761$	−37.0682			−1.34372			−0.671860	+	0.740678i	$0.734504\pi$
$762$		0			0
$763$	−2.26320	−	2.26320i	−0.0819333	−	0.0819333i
$764$		0			0
$765$	1.08621	−	1.08621i	0.0392720	−	0.0392720i
$766$		0			0
$767$	54.9936			1.98570
$768$		0			0
$769$			15.8806i			0.572667i	0.958130	+	0.286334i	$0.0924366\pi$
$769$			15.8806i			0.572667i	−0.958130	+	0.286334i	$0.907563\pi$
$770$		0			0
$771$	8.05257	−	8.05257i	0.290006	−	0.290006i
$772$		0			0
$773$	10.3517	−	10.3517i	0.372324	−	0.372324i	−0.495999	−	0.868323i	$-0.665198\pi$
$773$	10.3517	−	10.3517i	0.372324	−	0.372324i	0.868323	+	0.495999i	$0.165198\pi$
$774$		0			0
$775$	6.74391			0.242249
$776$		0			0
$777$	−8.36156			−0.299969
$778$		0			0
$779$	−19.9221	−	19.9221i	−0.713783	−	0.713783i
$780$		0			0
$781$	3.49949	+	13.8953i	0.125222	+	0.497212i
$782$		0			0
$783$	−25.2447			−0.902173
$784$		0			0
$785$	21.3092			0.760559
$786$		0			0
$787$	6.67706	+	6.67706i	0.238011	+	0.238011i	0.816026	−	0.578015i	$-0.196172\pi$
$787$	6.67706	+	6.67706i	0.238011	+	0.238011i	−0.578015	+	0.816026i	$0.696172\pi$
$788$		0			0
$789$	−18.6703	−	18.6703i	−0.664681	−	0.664681i
$790$		0			0
$791$		−	6.78125i		−	0.241114i
$792$		0			0
$793$			30.2075i			1.07270i
$794$		0			0
$795$	−10.5540	−	10.5540i	−0.374310	−	0.374310i
$796$		0			0
$797$	28.4112	+	28.4112i	1.00638	+	1.00638i	0.999980	+	0.00639585i	$0.00203588\pi$
$797$	28.4112	+	28.4112i	1.00638	+	1.00638i	0.00639585	+	0.999980i	$0.497964\pi$
$798$		0			0
$799$	−2.05667			−0.0727597
$800$		0			0
$801$	−3.32422			−0.117456
$802$		0			0
$803$	−3.06882	−	12.1852i	−0.108296	−	0.430007i
$804$		0			0
$805$	−2.50901	−	2.50901i	−0.0884308	−	0.0884308i
$806$		0			0
$807$	−24.6335			−0.867139
$808$		0			0
$809$	6.00757			0.211215			0.105607	−	0.994408i	$-0.466321\pi$
$809$	6.00757			0.211215			0.105607	+	0.994408i	$0.466321\pi$
$810$		0			0
$811$	−12.7013	+	12.7013i	−0.446001	+	0.446001i	−0.894023	−	0.448021i	$-0.852129\pi$
$811$	−12.7013	+	12.7013i	−0.446001	+	0.446001i	0.448021	+	0.894023i	$0.352129\pi$
$812$		0			0
$813$	−20.8897	+	20.8897i	−0.732635	+	0.732635i
$814$		0			0
$815$			8.25130i			0.289030i
$816$		0			0
$817$	12.9791			0.454083
$818$		0			0
$819$	6.95151	−	6.95151i	0.242905	−	0.242905i
$820$		0			0
$821$	11.1573	+	11.1573i	0.389394	+	0.389394i	0.874471	−	0.485078i	$-0.161209\pi$
$821$	11.1573	+	11.1573i	0.389394	+	0.389394i	−0.485078	+	0.874471i	$0.661209\pi$
$822$		0			0
$823$	−5.80324			−0.202288			−0.101144	−	0.994872i	$-0.532250\pi$
$823$	−5.80324			−0.202288			−0.101144	+	0.994872i	$0.532250\pi$
$824$		0			0
$825$	−5.91925	+	9.90440i	−0.206082	+	0.344827i
$826$		0			0
$827$	29.5370	−	29.5370i	1.02710	−	1.02710i	0.0274799	−	0.999622i	$-0.491252\pi$
$827$	29.5370	−	29.5370i	1.02710	−	1.02710i	0.999622	−	0.0274799i	$-0.00874821\pi$
$828$		0			0
$829$	−1.50871	−	1.50871i	−0.0523997	−	0.0523997i	0.680421	−	0.732821i	$-0.261797\pi$
$829$	−1.50871	−	1.50871i	−0.0523997	−	0.0523997i	−0.732821	+	0.680421i	$0.761797\pi$
$830$		0			0
$831$	−3.26117			−0.113129
$832$		0			0
$833$		−	3.95959i		−	0.137192i
$834$		0			0
$835$	−15.7456	−	15.7456i	−0.544898	−	0.544898i
$836$		0			0
$837$	7.77424	−	7.77424i	0.268717	−	0.268717i
$838$		0			0
$839$	33.3867			1.15264			0.576318	−	0.817225i	$-0.304489\pi$
$839$	33.3867			1.15264			0.576318	+	0.817225i	$0.304489\pi$
$840$		0			0
$841$			5.70888i			0.196858i
$842$		0			0
$843$	14.9339	−	14.9339i	0.514352	−	0.514352i
$844$		0			0
$845$	−26.6270	−	26.6270i	−0.915996	−	0.915996i
$846$		0			0
$847$	−4.37753	−	8.13960i	−0.150414	−	0.279680i
$848$		0			0
$849$		−	11.6017i		−	0.398169i
$850$		0			0
$851$	20.4788	−	20.4788i	0.702003	−	0.702003i
$852$		0			0
$853$	−24.3307	−	24.3307i	−0.833066	−	0.833066i	0.154869	−	0.987935i	$-0.450504\pi$
$853$	−24.3307	−	24.3307i	−0.833066	−	0.833066i	−0.987935	+	0.154869i	$0.950504\pi$
$854$		0			0
$855$			8.76509i			0.299760i
$856$		0			0
$857$	6.63546			0.226663			0.113332	−	0.993557i	$-0.463848\pi$
$857$	6.63546			0.226663			0.113332	+	0.993557i	$0.463848\pi$
$858$		0			0
$859$	3.76924	+	3.76924i	0.128605	+	0.128605i	0.768479	−	0.639874i	$-0.221014\pi$
$859$	3.76924	+	3.76924i	0.128605	+	0.128605i	−0.639874	+	0.768479i	$0.721014\pi$
$860$		0			0
$861$	−5.05593	−	5.05593i	−0.172306	−	0.172306i
$862$		0			0
$863$		−	23.1966i		−	0.789622i	−0.918762	−	0.394811i	$-0.870810\pi$
$863$		−	23.1966i		−	0.789622i	0.918762	−	0.394811i	$-0.129190\pi$
$864$		0			0
$865$		−	25.0937i		−	0.853210i
$866$		0			0
$867$	12.7303	−	12.7303i	0.432344	−	0.432344i
$868$		0			0
$869$	8.72868	+	34.6586i	0.296100	+	1.17571i
$870$		0			0
$871$			81.2236i			2.75216i
$872$		0			0
$873$		−	4.03352i		−	0.136514i
$874$		0			0
$875$	−6.52721	+	6.52721i	−0.220660	+	0.220660i
$876$		0			0
$877$	−5.84216	+	5.84216i	−0.197276	+	0.197276i	−0.798831	−	0.601555i	$-0.794548\pi$
$877$	−5.84216	+	5.84216i	−0.197276	+	0.197276i	0.601555	+	0.798831i	$0.294548\pi$
$878$		0			0
$879$	12.1500			0.409809
$880$		0			0
$881$	−2.35424			−0.0793163			−0.0396581	−	0.999213i	$-0.512627\pi$
$881$	−2.35424			−0.0793163			−0.0396581	+	0.999213i	$0.512627\pi$
$882$		0			0
$883$	−20.0519	+	20.0519i	−0.674801	+	0.674801i	−0.958819	−	0.284018i	$-0.908332\pi$
$883$	−20.0519	+	20.0519i	−0.674801	+	0.674801i	0.284018	+	0.958819i	$0.408332\pi$
$884$		0			0
$885$	−8.79885	+	8.79885i	−0.295770	+	0.295770i
$886$		0			0
$887$			4.40837i			0.148019i	0.997258	+	0.0740094i	$0.0235795\pi$
$887$			4.40837i			0.148019i	−0.997258	+	0.0740094i	$0.976421\pi$
$888$		0			0
$889$			9.99982i			0.335383i
$890$		0			0
$891$	0.160815	+	0.638539i	0.00538749	+	0.0213919i
$892$		0			0
$893$	8.29807	−	8.29807i	0.277684	−	0.277684i
$894$		0			0
$895$		−	3.99009i		−	0.133374i
$896$		0			0
$897$		−	21.9422i		−	0.732629i
$898$		0			0
$899$	7.17262	+	7.17262i	0.239220	+	0.239220i
$900$		0			0
$901$	−4.57511	−	4.57511i	−0.152419	−	0.152419i
$902$		0			0
$903$	3.29391			0.109615
$904$		0			0
$905$			1.20660i			0.0401088i
$906$		0			0
$907$	−7.62742	−	7.62742i	−0.253264	−	0.253264i	0.569043	−	0.822308i	$-0.307314\pi$
$907$	−7.62742	−	7.62742i	−0.253264	−	0.253264i	−0.822308	+	0.569043i	$0.807314\pi$
$908$		0			0
$909$	−0.966151	+	0.966151i	−0.0320452	+	0.0320452i
$910$		0			0
$911$			32.2762i			1.06936i	0.845055	+	0.534679i	$0.179568\pi$
$911$			32.2762i			1.06936i	−0.845055	+	0.534679i	$0.820432\pi$
$912$		0			0
$913$	−22.6856	+	37.9587i	−0.750784	+	1.25625i
$914$		0			0
$915$	−4.83313	−	4.83313i	−0.159778	−	0.159778i
$916$		0			0
$917$	−2.77656	+	2.77656i	−0.0916902	+	0.0916902i
$918$		0			0
$919$			1.26821i			0.0418343i	0.999781	+	0.0209171i	$0.00665861\pi$
$919$			1.26821i			0.0418343i	−0.999781	+	0.0209171i	$0.993341\pi$
$920$		0			0
$921$	−31.8703			−1.05016
$922$		0			0
$923$	−19.5935	+	19.5935i	−0.644930	+	0.644930i
$924$		0			0
$925$	−20.8245	−	20.8245i	−0.684707	−	0.684707i
$926$		0			0
$927$			3.74142i			0.122884i
$928$		0			0
$929$	−20.1181			−0.660054			−0.330027	−	0.943971i	$-0.607058\pi$
$929$	−20.1181			−0.660054			−0.330027	+	0.943971i	$0.607058\pi$
$930$		0			0
$931$	15.9758	+	15.9758i	0.523586	+	0.523586i
$932$		0			0
$933$	−2.62111	+	2.62111i	−0.0858114	+	0.0858114i
$934$		0			0
$935$	1.43262	−	2.39714i	0.0468518	−	0.0783949i
$936$		0			0
$937$	−1.55606			−0.0508341			−0.0254171	−	0.999677i	$-0.508091\pi$
$937$	−1.55606			−0.0508341			−0.0254171	+	0.999677i	$0.508091\pi$
$938$		0			0
$939$	19.7621	+	19.7621i	0.644911	+	0.644911i
$940$		0			0
$941$	1.81547	−	1.81547i	0.0591826	−	0.0591826i	−0.676896	−	0.736079i	$-0.736675\pi$
$941$	1.81547	−	1.81547i	0.0591826	−	0.0591826i	0.736079	+	0.676896i	$0.236675\pi$
$942$		0			0
$943$	24.7655			0.806476
$944$		0			0
$945$			5.88233i			0.191352i
$946$		0			0
$947$	26.2157	−	26.2157i	0.851896	−	0.851896i	−0.138470	−	0.990367i	$-0.544219\pi$
$947$	26.2157	−	26.2157i	0.851896	−	0.851896i	0.990367	+	0.138470i	$0.0442186\pi$
$948$		0			0
$949$	17.1822	−	17.1822i	0.557758	−	0.557758i
$950$		0			0
$951$	−16.3398			−0.529853
$952$		0			0
$953$	33.7864			1.09445			0.547224	−	0.836986i	$-0.315684\pi$
$953$	33.7864			1.09445			0.547224	+	0.836986i	$0.315684\pi$
$954$		0			0
$955$	19.9464	+	19.9464i	0.645451	+	0.645451i
$956$		0			0
$957$	−16.8295	+	4.23848i	−0.544022	+	0.137011i
$958$		0			0
$959$	−3.11944			−0.100732
$960$		0			0
$961$	26.5823			0.857494
$962$		0			0
$963$	21.4859	+	21.4859i	0.692373	+	0.692373i
$964$		0			0
$965$	−21.8792	−	21.8792i	−0.704317	−	0.704317i
$966$		0			0
$967$		−	36.3655i		−	1.16944i	−0.811236	−	0.584718i	$-0.801205\pi$
$967$		−	36.3655i		−	1.16944i	0.811236	−	0.584718i	$-0.198795\pi$
$968$		0			0
$969$		−	2.44848i		−	0.0786567i
$970$		0			0
$971$	36.3175	+	36.3175i	1.16548	+	1.16548i	0.983257	+	0.182227i	$0.0583305\pi$
$971$	36.3175	+	36.3175i	1.16548	+	1.16548i	0.182227	+	0.983257i	$0.441670\pi$
$972$		0			0
$973$	−11.7276	−	11.7276i	−0.375971	−	0.375971i
$974$		0			0
$975$	−22.3127			−0.714579
$976$		0			0
$977$	−7.92551			−0.253560			−0.126780	−	0.991931i	$-0.540464\pi$
$977$	−7.92551			−0.253560			−0.126780	+	0.991931i	$0.540464\pi$
$978$		0			0
$979$	−5.86028	+	1.47590i	−0.187295	+	0.0471699i
$980$		0			0
$981$	−4.91428	−	4.91428i	−0.156901	−	0.156901i
$982$		0			0
$983$	35.1777			1.12200			0.560998	−	0.827817i	$-0.310418\pi$
$983$	35.1777			1.12200			0.560998	+	0.827817i	$0.310418\pi$
$984$		0			0
$985$	36.0298			1.14801
$986$		0			0
$987$	2.10593	−	2.10593i	0.0670324	−	0.0670324i
$988$		0			0
$989$	−8.06730	+	8.06730i	−0.256525	+	0.256525i
$990$		0			0
$991$			13.7696i			0.437406i	0.975792	+	0.218703i	$0.0701825\pi$
$991$			13.7696i			0.437406i	−0.975792	+	0.218703i	$0.929817\pi$
$992$		0			0
$993$	9.88600			0.313723
$994$		0			0
$995$	1.18840	−	1.18840i	0.0376748	−	0.0376748i
$996$		0			0
$997$	20.7536	+	20.7536i	0.657272	+	0.657272i	0.954734	−	0.297462i	$-0.0961401\pi$
$997$	20.7536	+	20.7536i	0.657272	+	0.657272i	−0.297462	+	0.954734i	$0.596140\pi$
$998$		0			0
$999$	−48.0122			−1.51904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1408.2.i.b.351.15		44
4.3	odd	2		1408.2.i.a.351.7		44
8.3	odd	2		704.2.i.a.175.15		44
8.5	even	2		176.2.i.a.131.20	yes	44
11.10	odd	2	inner	1408.2.i.b.351.16		44
16.3	odd	4		176.2.i.a.43.3	✓	44
16.5	even	4		1408.2.i.a.1055.8		44
16.11	odd	4	inner	1408.2.i.b.1055.16		44
16.13	even	4		704.2.i.a.527.15		44
44.43	even	2		1408.2.i.a.351.8		44
88.21	odd	2		176.2.i.a.131.3	yes	44
88.43	even	2		704.2.i.a.175.16		44
176.21	odd	4		1408.2.i.a.1055.7		44
176.43	even	4	inner	1408.2.i.b.1055.15		44
176.109	odd	4		704.2.i.a.527.16		44
176.131	even	4		176.2.i.a.43.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.i.a.43.3	✓	44	16.3	odd	4
176.2.i.a.43.20	yes	44	176.131	even	4
176.2.i.a.131.3	yes	44	88.21	odd	2
176.2.i.a.131.20	yes	44	8.5	even	2
704.2.i.a.175.15		44	8.3	odd	2
704.2.i.a.175.16		44	88.43	even	2
704.2.i.a.527.15		44	16.13	even	4
704.2.i.a.527.16		44	176.109	odd	4
1408.2.i.a.351.7		44	4.3	odd	2
1408.2.i.a.351.8		44	44.43	even	2
1408.2.i.a.1055.7		44	176.21	odd	4
1408.2.i.a.1055.8		44	16.5	even	4
1408.2.i.b.351.15		44	1.1	even	1	trivial
1408.2.i.b.351.16		44	11.10	odd	2	inner
1408.2.i.b.1055.15		44	176.43	even	4	inner
1408.2.i.b.1055.16		44	16.11	odd	4	inner

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:	\( N \)	\(=\)	\( 1408 = 2^{7} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1408.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766690 - 0.766690i) q^{3} +(0.946416 - 0.946416i) q^{5} +0.840189i q^{7} +1.82437i q^{9} +O(q^{10})\)	\(q+(0.766690 - 0.766690i) q^{3} +(0.946416 - 0.946416i) q^{5} +0.840189i q^{7} +1.82437i q^{9} +(0.809991 + 3.21620i) q^{11} +(-4.53511 + 4.53511i) q^{13} -1.45122i q^{15} -0.629097i q^{17} +(2.53823 + 2.53823i) q^{19} +(0.644164 + 0.644164i) q^{21} -3.15531 q^{23} +3.20859i q^{25} +(3.69880 + 3.69880i) q^{27} +(-3.41256 + 3.41256i) q^{29} -2.10183i q^{31} +(3.08684 + 1.84481i) q^{33} +(0.795168 + 0.795168i) q^{35} +(-6.49024 + 6.49024i) q^{37} +6.95405i q^{39} -7.84882 q^{41} +(2.55674 - 2.55674i) q^{43} +(1.72662 + 1.72662i) q^{45} -3.26924i q^{47} +6.29408 q^{49} +(-0.482322 - 0.482322i) q^{51} +(7.27250 - 7.27250i) q^{53} +(3.81045 + 2.27727i) q^{55} +3.89206 q^{57} +(-6.06309 - 6.06309i) q^{59} +(3.33040 - 3.33040i) q^{61} -1.53282 q^{63} +8.58421i q^{65} +(8.95497 - 8.95497i) q^{67} +(-2.41915 + 2.41915i) q^{69} +4.32041 q^{71} -3.78870 q^{73} +(2.45999 + 2.45999i) q^{75} +(-2.70221 + 0.680545i) q^{77} +10.7763 q^{79} +0.198539 q^{81} +(9.42796 + 9.42796i) q^{83} +(-0.595388 - 0.595388i) q^{85} +5.23275i q^{87} +1.82212i q^{89} +(-3.81035 - 3.81035i) q^{91} +(-1.61145 - 1.61145i) q^{93} +4.80444 q^{95} -2.21091 q^{97} +(-5.86754 + 1.47773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5	\( 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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