LMFDB - Embedded newform 448.2.j.d.111.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(111,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.111"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			111.5
Root			$1.36166 + 0.381939i$ of defining polynomial
Character	$\chi$	$=$	448.111
Dual form			448.2.j.d.335.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03649 + 1.03649i) q^{3} +(-1.68683 - 1.68683i) q^{5} +(-1.38554 - 2.25395i) q^{7} -0.851361i q^{9} +(2.00000 + 2.00000i) q^{11} +(4.80976 - 4.80976i) q^{13} -3.49678i q^{15} -1.13424i q^{17} +(-1.21746 - 1.21746i) q^{19} +(0.900103 - 3.77231i) q^{21} +1.33620 q^{23} +0.690788i q^{25} +(3.99191 - 3.99191i) q^{27} +(5.26785 + 5.26785i) q^{29} -8.31885 q^{31} +4.14598i q^{33} +(-1.46486 + 6.13919i) q^{35} +(-4.18757 + 4.18757i) q^{37} +9.97057 q^{39} -1.63570 q^{41} +(1.33620 + 1.33620i) q^{43} +(-1.43610 + 1.43610i) q^{45} +1.93345 q^{47} +(-3.16057 + 6.24586i) q^{49} +(1.17563 - 1.17563i) q^{51} +(6.34814 - 6.34814i) q^{53} -6.74732i q^{55} -2.52377i q^{57} +(3.29044 - 3.29044i) q^{59} +(-2.04875 + 2.04875i) q^{61} +(-1.91892 + 1.17959i) q^{63} -16.2265 q^{65} +(-0.107279 + 0.107279i) q^{67} +(1.38497 + 1.38497i) q^{69} -13.0475 q^{71} -6.24586 q^{73} +(-0.715998 + 0.715998i) q^{75} +(1.73682 - 7.27897i) q^{77} -4.51184i q^{79} +5.72110 q^{81} +(9.71727 + 9.71727i) q^{83} +(-1.91327 + 1.91327i) q^{85} +10.9202i q^{87} +11.6171 q^{89} +(-17.5051 - 4.17685i) q^{91} +(-8.62244 - 8.62244i) q^{93} +4.10728i q^{95} +3.23412i q^{97} +(1.70272 - 1.70272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 32 q^{11} + 16 q^{21} - 8 q^{35} - 16 q^{39} - 16 q^{49} + 32 q^{51} - 80 q^{65} + 48 q^{67} - 32 q^{71} - 16 q^{77} + 32 q^{81} + 64 q^{85} - 8 q^{91} - 64 q^{93} - 64 q^{99}+O(q^{100}) $ 16 * q - 8 * q^7 + 32 * q^11 + 16 * q^21 - 8 * q^35 - 16 * q^39 - 16 * q^49 + 32 * q^51 - 80 * q^65 + 48 * q^67 - 32 * q^71 - 16 * q^77 + 32 * q^81 + 64 * q^85 - 8 * q^91 - 64 * q^93 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.03649	+	1.03649i	0.598420	+	0.598420i	0.939892	−	0.341472i	$-0.110925\pi$
$3$	1.03649	+	1.03649i	0.598420	+	0.598420i	−0.341472	+	0.939892i	$0.610925\pi$
$4$		0			0
$5$	−1.68683	−	1.68683i	−0.754373	−	0.754373i	0.220919	−	0.975292i	$-0.429094\pi$
$5$	−1.68683	−	1.68683i	−0.754373	−	0.754373i	−0.975292	+	0.220919i	$0.929094\pi$
$6$		0			0
$7$	−1.38554	−	2.25395i	−0.523684	−	0.851913i
$7$	−1.38554	−	2.25395i	−0.523684	−	0.851913i
$8$		0			0
$9$		−	0.851361i		−	0.283787i
$10$		0			0
$11$	2.00000	+	2.00000i	0.603023	+	0.603023i	0.941113	−	0.338091i	$-0.109781\pi$
$11$	2.00000	+	2.00000i	0.603023	+	0.603023i	−0.338091	+	0.941113i	$0.609781\pi$
$12$		0			0
$13$	4.80976	−	4.80976i	1.33399	−	1.33399i	0.432219	−	0.901769i	$-0.357731\pi$
$13$	4.80976	−	4.80976i	1.33399	−	1.33399i	0.901769	−	0.432219i	$-0.142269\pi$
$14$		0			0
$15$		−	3.49678i		−	0.902864i
$16$		0			0
$17$		−	1.13424i		−	0.275093i	−0.990495	−	0.137547i	$-0.956078\pi$
$17$		−	1.13424i		−	0.275093i	0.990495	−	0.137547i	$-0.0439217\pi$
$18$		0			0
$19$	−1.21746	−	1.21746i	−0.279303	−	0.279303i	0.553528	−	0.832831i	$-0.313281\pi$
$19$	−1.21746	−	1.21746i	−0.279303	−	0.279303i	−0.832831	+	0.553528i	$0.813281\pi$
$20$		0			0
$21$	0.900103	−	3.77231i	0.196419	−	0.823184i
$22$		0			0
$23$	1.33620			0.278618			0.139309	−	0.990249i	$-0.455512\pi$
$23$	1.33620			0.278618			0.139309	+	0.990249i	$0.455512\pi$
$24$		0			0
$25$			0.690788i			0.138158i
$26$		0			0
$27$	3.99191	−	3.99191i	0.768244	−	0.768244i
$28$		0			0
$29$	5.26785	+	5.26785i	0.978215	+	0.978215i	0.999768	−	0.0215522i	$-0.00686082\pi$
$29$	5.26785	+	5.26785i	0.978215	+	0.978215i	−0.0215522	+	0.999768i	$0.506861\pi$
$30$		0			0
$31$	−8.31885			−1.49411			−0.747055	−	0.664763i	$-0.768533\pi$
$31$	−8.31885			−1.49411			−0.747055	+	0.664763i	$0.768533\pi$
$32$		0			0
$33$			4.14598i			0.721722i
$34$		0			0
$35$	−1.46486	+	6.13919i	−0.247607	+	1.03771i
$36$		0			0
$37$	−4.18757	+	4.18757i	−0.688431	+	0.688431i	−0.961885	−	0.273454i	$-0.911834\pi$
$37$	−4.18757	+	4.18757i	−0.688431	+	0.688431i	0.273454	+	0.961885i	$0.411834\pi$
$38$		0			0
$39$	9.97057			1.59657
$40$		0			0
$41$	−1.63570			−0.255453			−0.127726	−	0.991809i	$-0.540768\pi$
$41$	−1.63570			−0.255453			−0.127726	+	0.991809i	$0.540768\pi$
$42$		0			0
$43$	1.33620	+	1.33620i	0.203769	+	0.203769i	0.801613	−	0.597844i	$-0.203976\pi$
$43$	1.33620	+	1.33620i	0.203769	+	0.203769i	−0.597844	+	0.801613i	$0.703976\pi$
$44$		0			0
$45$	−1.43610	+	1.43610i	−0.214081	+	0.214081i
$46$		0			0
$47$	1.93345			0.282023			0.141012	−	0.990008i	$-0.454965\pi$
$47$	1.93345			0.282023			0.141012	+	0.990008i	$0.454965\pi$
$48$		0			0
$49$	−3.16057	+	6.24586i	−0.451510	+	0.892266i
$50$		0			0
$51$	1.17563	−	1.17563i	0.164621	−	0.164621i
$52$		0			0
$53$	6.34814	−	6.34814i	0.871984	−	0.871984i	−0.120705	−	0.992688i	$-0.538515\pi$
$53$	6.34814	−	6.34814i	0.871984	−	0.871984i	0.992688	+	0.120705i	$0.0385154\pi$
$54$		0			0
$55$		−	6.74732i		−	0.909808i
$56$		0			0
$57$		−	2.52377i		−	0.334281i
$58$		0			0
$59$	3.29044	−	3.29044i	0.428379	−	0.428379i	−0.459697	−	0.888076i	$-0.652042\pi$
$59$	3.29044	−	3.29044i	0.428379	−	0.428379i	0.888076	+	0.459697i	$0.152042\pi$
$60$		0			0
$61$	−2.04875	+	2.04875i	−0.262316	+	0.262316i	−0.825994	−	0.563678i	$-0.809386\pi$
$61$	−2.04875	+	2.04875i	−0.262316	+	0.262316i	0.563678	+	0.825994i	$0.309386\pi$
$62$		0			0
$63$	−1.91892	+	1.17959i	−0.241762	+	0.148615i
$64$		0			0
$65$	−16.2265			−2.01265
$66$		0			0
$67$	−0.107279	+	0.107279i	−0.0131062	+	0.0131062i	−0.713630	−	0.700523i	$-0.752950\pi$
$67$	−0.107279	+	0.107279i	−0.0131062	+	0.0131062i	0.700523	+	0.713630i	$0.252950\pi$
$68$		0			0
$69$	1.38497	+	1.38497i	0.166731	+	0.166731i
$70$		0			0
$71$	−13.0475			−1.54846			−0.774229	−	0.632906i	$-0.781862\pi$
$71$	−13.0475			−1.54846			−0.774229	+	0.632906i	$0.781862\pi$
$72$		0			0
$73$	−6.24586			−0.731023			−0.365511	−	0.930807i	$-0.619106\pi$
$73$	−6.24586			−0.731023			−0.365511	+	0.930807i	$0.619106\pi$
$74$		0			0
$75$	−0.715998	+	0.715998i	−0.0826763	+	0.0826763i
$76$		0			0
$77$	1.73682	−	7.27897i	0.197929	−	0.829516i
$78$		0			0
$79$		−	4.51184i		−	0.507621i	−0.967254	−	0.253811i	$-0.918316\pi$
$79$		−	4.51184i		−	0.507621i	0.967254	−	0.253811i	$-0.0816840\pi$
$80$		0			0
$81$	5.72110			0.635678
$82$		0			0
$83$	9.71727	+	9.71727i	1.06661	+	1.06661i	0.997617	+	0.0689912i	$0.0219780\pi$
$83$	9.71727	+	9.71727i	1.06661	+	1.06661i	0.0689912	+	0.997617i	$0.478022\pi$
$84$		0			0
$85$	−1.91327	+	1.91327i	−0.207523	+	0.207523i
$86$		0			0
$87$			10.9202i			1.17077i
$88$		0			0
$89$	11.6171			1.23141			0.615707	−	0.787975i	$-0.288870\pi$
$89$	11.6171			1.23141			0.615707	+	0.787975i	$0.288870\pi$
$90$		0			0
$91$	−17.5051	−	4.17685i	−1.83503	−	0.437853i
$92$		0			0
$93$	−8.62244	−	8.62244i	−0.894105	−	0.894105i
$94$		0			0
$95$			4.10728i			0.421398i
$96$		0			0
$97$			3.23412i			0.328376i	0.986429	+	0.164188i	$0.0525003\pi$
$97$			3.23412i			0.328376i	−0.986429	+	0.164188i	$0.947500\pi$
$98$		0			0
$99$	1.70272	−	1.70272i	0.171130	−	0.171130i
$100$		0			0
$101$	5.94400	+	5.94400i	0.591450	+	0.591450i	0.938023	−	0.346573i	$-0.112655\pi$
$101$	5.94400	+	5.94400i	0.591450	+	0.591450i	−0.346573	+	0.938023i	$0.612655\pi$
$102$		0			0
$103$			7.44427i			0.733505i	0.930318	+	0.366753i	$0.119530\pi$
$103$			7.44427i			0.733505i	−0.930318	+	0.366753i	$0.880470\pi$
$104$		0			0
$105$	−7.88156	+	4.84492i	−0.769161	+	0.472815i
$106$		0			0
$107$	2.83298	+	2.83298i	0.273875	+	0.273875i	0.830658	−	0.556783i	$-0.187965\pi$
$107$	2.83298	+	2.83298i	0.273875	+	0.273875i	−0.556783	+	0.830658i	$0.687965\pi$
$108$		0			0
$109$	5.51516	+	5.51516i	0.528256	+	0.528256i	0.920052	−	0.391796i	$-0.128146\pi$
$109$	5.51516	+	5.51516i	0.528256	+	0.528256i	−0.391796	+	0.920052i	$0.628146\pi$
$110$		0			0
$111$	−8.68077			−0.823942
$112$		0			0
$113$	13.5173			1.27160			0.635801	−	0.771853i	$-0.280670\pi$
$113$	13.5173			1.27160			0.635801	+	0.771853i	$0.280670\pi$
$114$		0			0
$115$	−2.25395	−	2.25395i	−0.210182	−	0.210182i
$116$		0			0
$117$	−4.09484	−	4.09484i	−0.378568	−	0.378568i
$118$		0			0
$119$	−2.55652	+	1.57153i	−0.234355	+	0.144062i
$120$		0			0
$121$		−	3.00000i		−	0.272727i
$122$		0			0
$123$	−1.69539	−	1.69539i	−0.152868	−	0.152868i
$124$		0			0
$125$	−7.26891	+	7.26891i	−0.650151	+	0.650151i
$126$		0			0
$127$			2.87835i			0.255413i	0.991812	+	0.127706i	$0.0407615\pi$
$127$			2.87835i			0.255413i	−0.991812	+	0.127706i	$0.959239\pi$
$128$		0			0
$129$			2.76994i			0.243879i
$130$		0			0
$131$	−5.20937	−	5.20937i	−0.455145	−	0.455145i	0.441913	−	0.897058i	$-0.354300\pi$
$131$	−5.20937	−	5.20937i	−0.455145	−	0.455145i	−0.897058	+	0.441913i	$0.854300\pi$
$132$		0			0
$133$	−1.05725	+	4.43091i	−0.0916754	+	0.384209i
$134$		0			0
$135$	−13.4674			−1.15908
$136$		0			0
$137$			15.8805i			1.35676i	0.734709	+	0.678382i	$0.237319\pi$
$137$			15.8805i			1.35676i	−0.734709	+	0.678382i	$0.762681\pi$
$138$		0			0
$139$	−11.7757	+	11.7757i	−0.998804	+	0.998804i	−0.999999	−	0.00119539i	$-0.999619\pi$
$139$	−11.7757	+	11.7757i	−0.998804	+	0.998804i	0.00119539	+	0.999999i	$0.499619\pi$
$140$		0			0
$141$	2.00401	+	2.00401i	0.168768	+	0.168768i
$142$		0			0
$143$	19.2390			1.60885
$144$		0			0
$145$		−	17.7719i		−	1.47588i
$146$		0			0
$147$	−9.74971	+	3.19788i	−0.804143	+	0.263757i
$148$		0			0
$149$	−7.72570	+	7.72570i	−0.632914	+	0.632914i	−0.948798	−	0.315884i	$-0.897699\pi$
$149$	−7.72570	+	7.72570i	−0.632914	+	0.632914i	0.315884	+	0.948798i	$0.397699\pi$
$150$		0			0
$151$	20.5443			1.67187			0.835936	−	0.548826i	$-0.184925\pi$
$151$	20.5443			1.67187			0.835936	+	0.548826i	$0.184925\pi$
$152$		0			0
$153$	−0.965647			−0.0780679
$154$		0			0
$155$	14.0325	+	14.0325i	1.12712	+	1.12712i
$156$		0			0
$157$	−3.07180	+	3.07180i	−0.245156	+	0.245156i	−0.818979	−	0.573823i	$-0.805460\pi$
$157$	−3.07180	+	3.07180i	−0.245156	+	0.245156i	0.573823	+	0.818979i	$0.305460\pi$
$158$		0			0
$159$	13.1596			1.04363
$160$		0			0
$161$	−1.85136	−	3.01174i	−0.145908	−	0.237358i
$162$		0			0
$163$	−3.22893	+	3.22893i	−0.252909	+	0.252909i	−0.822162	−	0.569253i	$-0.807232\pi$
$163$	−3.22893	+	3.22893i	−0.252909	+	0.252909i	0.569253	+	0.822162i	$0.307232\pi$
$164$		0			0
$165$	6.99355	−	6.99355i	0.544447	−	0.544447i
$166$		0			0
$167$			6.05037i			0.468192i	0.972214	+	0.234096i	$0.0752130\pi$
$167$			6.05037i			0.468192i	−0.972214	+	0.234096i	$0.924787\pi$
$168$		0			0
$169$		−	33.2676i		−	2.55905i
$170$		0			0
$171$	−1.03649	+	1.03649i	−0.0792627	+	0.0792627i
$172$		0			0
$173$	−4.44784	+	4.44784i	−0.338163	+	0.338163i	−0.855676	−	0.517513i	$-0.826858\pi$
$173$	−4.44784	+	4.44784i	−0.338163	+	0.338163i	0.517513	+	0.855676i	$0.326858\pi$
$174$		0			0
$175$	1.55700	−	0.957113i	0.117698	−	0.0723509i
$176$		0			0
$177$	6.82105			0.512701
$178$		0			0
$179$	9.36007	−	9.36007i	0.699605	−	0.699605i	−0.264721	−	0.964325i	$-0.585280\pi$
$179$	9.36007	−	9.36007i	0.699605	−	0.699605i	0.964325	+	0.264721i	$0.0852797\pi$
$180$		0			0
$181$	0.190668	+	0.190668i	0.0141722	+	0.0141722i	0.714157	−	0.699985i	$-0.246810\pi$
$181$	0.190668	+	0.190668i	0.0141722	+	0.0141722i	−0.699985	+	0.714157i	$0.746810\pi$
$182$		0			0
$183$	−4.24704			−0.313950
$184$		0			0
$185$	14.1274			1.03867
$186$		0			0
$187$	2.26848	−	2.26848i	0.165888	−	0.165888i
$188$		0			0
$189$	−14.5285	−	3.46662i	−1.05679	−	0.252160i
$190$		0			0
$191$			3.90133i			0.282291i	0.989989	+	0.141145i	$0.0450785\pi$
$191$			3.90133i			0.282291i	−0.989989	+	0.141145i	$0.954922\pi$
$192$		0			0
$193$	9.87523			0.710834			0.355417	−	0.934708i	$-0.384339\pi$
$193$	9.87523			0.710834			0.355417	+	0.934708i	$0.384339\pi$
$194$		0			0
$195$	−16.8187	−	16.8187i	−1.20441	−	1.20441i
$196$		0			0
$197$	−14.4021	+	14.4021i	−1.02611	+	1.02611i	−0.0264589	+	0.999650i	$0.508423\pi$
$197$	−14.4021	+	14.4021i	−1.02611	+	1.02611i	−0.999650	+	0.0264589i	$0.991577\pi$
$198$		0			0
$199$		−	25.6513i		−	1.81837i	−0.416387	−	0.909187i	$-0.636704\pi$
$199$		−	25.6513i		−	1.81837i	0.416387	−	0.909187i	$-0.363296\pi$
$200$		0			0
$201$	−0.222388			−0.0156860
$202$		0			0
$203$	4.57466	−	19.1723i	0.321078	−	1.34563i
$204$		0			0
$205$	2.75914	+	2.75914i	0.192707	+	0.192707i
$206$		0			0
$207$		−	1.13759i		−	0.0790681i
$208$		0			0
$209$		−	4.86982i		−	0.336853i
$210$		0			0
$211$	15.4141	−	15.4141i	1.06115	−	1.06115i	0.0631429	−	0.998004i	$-0.479888\pi$
$211$	15.4141	−	15.4141i	1.06115	−	1.06115i	0.998004	−	0.0631429i	$-0.0201124\pi$
$212$		0			0
$213$	−13.5237	−	13.5237i	−0.926628	−	0.926628i
$214$		0			0
$215$		−	4.50790i		−	0.307436i
$216$		0			0
$217$	11.5261	+	18.7503i	0.782441	+	1.27285i
$218$		0			0
$219$	−6.47380	−	6.47380i	−0.437459	−	0.437459i
$220$		0			0
$221$	−5.45542	−	5.45542i	−0.366971	−	0.366971i
$222$		0			0
$223$	15.4012			1.03134			0.515670	−	0.856787i	$-0.327543\pi$
$223$	15.4012			1.03134			0.515670	+	0.856787i	$0.327543\pi$
$224$		0			0
$225$	0.588110			0.0392073
$226$		0			0
$227$	−7.60285	−	7.60285i	−0.504619	−	0.504619i	0.408251	−	0.912870i	$-0.366139\pi$
$227$	−7.60285	−	7.60285i	−0.504619	−	0.504619i	−0.912870	+	0.408251i	$0.866139\pi$
$228$		0			0
$229$	17.6096	+	17.6096i	1.16368	+	1.16368i	0.983665	+	0.180011i	$0.0576134\pi$
$229$	17.6096	+	17.6096i	1.16368	+	1.16368i	0.180011	+	0.983665i	$0.442387\pi$
$230$		0			0
$231$	9.34482	−	5.74440i	0.614844	−	0.377954i
$232$		0			0
$233$		−	6.72639i		−	0.440661i	−0.975425	−	0.220330i	$-0.929286\pi$
$233$		−	6.72639i		−	0.440661i	0.975425	−	0.220330i	$-0.0707135\pi$
$234$		0			0
$235$	−3.26141	−	3.26141i	−0.212751	−	0.212751i
$236$		0			0
$237$	4.67649	−	4.67649i	0.303771	−	0.303771i
$238$		0			0
$239$			9.53354i			0.616673i	0.951277	+	0.308337i	$0.0997723\pi$
$239$			9.53354i			0.616673i	−0.951277	+	0.308337i	$0.900228\pi$
$240$		0			0
$241$		−	21.3762i		−	1.37696i	−0.725255	−	0.688481i	$-0.758278\pi$
$241$		−	21.3762i		−	1.37696i	0.725255	−	0.688481i	$-0.241722\pi$
$242$		0			0
$243$	−6.04585	−	6.04585i	−0.387841	−	0.387841i
$244$		0			0
$245$	15.8671	−	5.20436i	1.01371	−	0.332494i
$246$		0			0
$247$	−11.7113			−0.745174
$248$		0			0
$249$			20.1438i			1.27656i
$250$		0			0
$251$	3.97286	−	3.97286i	0.250765	−	0.250765i	−0.570519	−	0.821284i	$-0.693258\pi$
$251$	3.97286	−	3.97286i	0.250765	−	0.250765i	0.821284	+	0.570519i	$0.193258\pi$
$252$		0			0
$253$	2.67241	+	2.67241i	0.168013	+	0.168013i
$254$		0			0
$255$	−3.96618			−0.248372
$256$		0			0
$257$			6.91591i			0.431403i	0.976459	+	0.215701i	$0.0692038\pi$
$257$			6.91591i			0.431403i	−0.976459	+	0.215701i	$0.930796\pi$
$258$		0			0
$259$	15.2406	+	3.63653i	0.947004	+	0.225963i
$260$		0			0
$261$	4.48484	−	4.48484i	0.277605	−	0.277605i
$262$		0			0
$263$	17.7806			1.09640			0.548199	−	0.836348i	$-0.315314\pi$
$263$	17.7806			1.09640			0.548199	+	0.836348i	$0.315314\pi$
$264$		0			0
$265$	−21.4165			−1.31560
$266$		0			0
$267$	12.0411	+	12.0411i	0.736903	+	0.736903i
$268$		0			0
$269$	9.95044	−	9.95044i	0.606689	−	0.606689i	−0.335390	−	0.942079i	$-0.608868\pi$
$269$	9.95044	−	9.95044i	0.606689	−	0.606689i	0.942079	+	0.335390i	$0.108868\pi$
$270$		0			0
$271$	−19.6010			−1.19067			−0.595337	−	0.803476i	$-0.702981\pi$
$271$	−19.6010			−1.19067			−0.595337	+	0.803476i	$0.702981\pi$
$272$		0			0
$273$	−13.8146	−	22.4732i	−0.836098	−	1.36014i
$274$		0			0
$275$	−1.38158	+	1.38158i	−0.0833122	+	0.0833122i
$276$		0			0
$277$	13.6430	−	13.6430i	0.819727	−	0.819727i	−0.166341	−	0.986068i	$-0.553195\pi$
$277$	13.6430	−	13.6430i	0.819727	−	0.819727i	0.986068	+	0.166341i	$0.0531952\pi$
$278$		0			0
$279$			7.08234i			0.424009i
$280$		0			0
$281$			7.16702i			0.427548i	0.976883	+	0.213774i	$0.0685757\pi$
$281$			7.16702i			0.427548i	−0.976883	+	0.213774i	$0.931424\pi$
$282$		0			0
$283$	−11.6238	+	11.6238i	−0.690964	+	0.690964i	−0.962444	−	0.271480i	$-0.912487\pi$
$283$	−11.6238	+	11.6238i	−0.690964	+	0.690964i	0.271480	+	0.962444i	$0.412487\pi$
$284$		0			0
$285$	−4.25717	+	4.25717i	−0.252173	+	0.252173i
$286$		0			0
$287$	2.26632	+	3.68678i	0.133777	+	0.217624i
$288$		0			0
$289$	15.7135			0.924324
$290$		0			0
$291$	−3.35215	+	3.35215i	−0.196507	+	0.196507i
$292$		0			0
$293$	−0.108531	−	0.108531i	−0.00634048	−	0.00634048i	0.703929	−	0.710270i	$-0.251427\pi$
$293$	−0.108531	−	0.108531i	−0.00634048	−	0.00634048i	−0.710270	+	0.703929i	$0.751427\pi$
$294$		0			0
$295$	−11.1008			−0.646315
$296$		0			0
$297$	15.9676			0.926537
$298$		0			0
$299$	6.42682	−	6.42682i	0.371673	−	0.371673i
$300$		0			0
$301$	1.16038	−	4.86310i	0.0668829	−	0.280304i
$302$		0			0
$303$			12.3218i			0.707871i
$304$		0			0
$305$	6.91179			0.395768
$306$		0			0
$307$	−1.23198	−	1.23198i	−0.0703130	−	0.0703130i	0.671076	−	0.741389i	$-0.265833\pi$
$307$	−1.23198	−	1.23198i	−0.0703130	−	0.0703130i	−0.741389	+	0.671076i	$0.765833\pi$
$308$		0			0
$309$	−7.71594	+	7.71594i	−0.438944	+	0.438944i
$310$		0			0
$311$			15.0393i			0.852799i	0.904535	+	0.426399i	$0.140218\pi$
$311$			15.0393i			0.852799i	−0.904535	+	0.426399i	$0.859782\pi$
$312$		0			0
$313$	−33.6455			−1.90176			−0.950879	−	0.309563i	$-0.899817\pi$
$313$	−33.6455			−1.90176			−0.950879	+	0.309563i	$0.899817\pi$
$314$		0			0
$315$	5.22667	+	1.24713i	0.294489	+	0.0702676i
$316$		0			0
$317$	4.05086	+	4.05086i	0.227519	+	0.227519i	0.811655	−	0.584136i	$-0.198567\pi$
$317$	4.05086	+	4.05086i	0.227519	+	0.227519i	−0.584136	+	0.811655i	$0.698567\pi$
$318$		0			0
$319$			21.0714i			1.17977i
$320$		0			0
$321$			5.87274i			0.327784i
$322$		0			0
$323$	−1.38089	+	1.38089i	−0.0768345	+	0.0768345i
$324$		0			0
$325$	3.32253	+	3.32253i	0.184301	+	0.184301i
$326$		0			0
$327$			11.4329i			0.632238i
$328$		0			0
$329$	−2.67887	−	4.35790i	−0.147691	−	0.240259i
$330$		0			0
$331$	−11.3981	−	11.3981i	−0.626497	−	0.626497i	0.320688	−	0.947185i	$-0.396086\pi$
$331$	−11.3981	−	11.3981i	−0.626497	−	0.626497i	−0.947185	+	0.320688i	$0.896086\pi$
$332$		0			0
$333$	3.56513	+	3.56513i	0.195368	+	0.195368i
$334$		0			0
$335$	0.361923			0.0197739
$336$		0			0
$337$	−11.0356			−0.601148			−0.300574	−	0.953759i	$-0.597178\pi$
$337$	−11.0356			−0.601148			−0.300574	+	0.953759i	$0.597178\pi$
$338$		0			0
$339$	14.0106	+	14.0106i	0.760953	+	0.760953i
$340$		0			0
$341$	−16.6377	−	16.6377i	−0.900982	−	0.900982i
$342$		0			0
$343$	18.4569	−	1.53010i	0.996581	−	0.0826178i
$344$		0			0
$345$		−	4.67241i		−	0.251554i
$346$		0			0
$347$	−13.6494	−	13.6494i	−0.732740	−	0.732740i	0.238422	−	0.971162i	$-0.423370\pi$
$347$	−13.6494	−	13.6494i	−0.732740	−	0.732740i	−0.971162	+	0.238422i	$0.923370\pi$
$348$		0			0
$349$	−5.59100	+	5.59100i	−0.299280	+	0.299280i	−0.840732	−	0.541452i	$-0.817875\pi$
$349$	−5.59100	+	5.59100i	−0.299280	+	0.299280i	0.541452	+	0.840732i	$0.317875\pi$
$350$		0			0
$351$		−	38.4003i		−	2.04966i
$352$		0			0
$353$			31.8994i			1.69783i	0.528528	+	0.848916i	$0.322744\pi$
$353$			31.8994i			1.69783i	−0.528528	+	0.848916i	$0.677256\pi$
$354$		0			0
$355$	22.0090	+	22.0090i	1.16812	+	1.16812i
$356$		0			0
$357$	−4.27870	−	1.02093i	−0.226453	−	0.0540335i
$358$		0			0
$359$	−8.42050			−0.444417			−0.222209	−	0.974999i	$-0.571327\pi$
$359$	−8.42050			−0.444417			−0.222209	+	0.974999i	$0.571327\pi$
$360$		0			0
$361$		−	16.0356i		−	0.843979i
$362$		0			0
$363$	3.10948	−	3.10948i	0.163205	−	0.163205i
$364$		0			0
$365$	10.5357	+	10.5357i	0.551464	+	0.551464i
$366$		0			0
$367$	10.0187			0.522972			0.261486	−	0.965207i	$-0.415787\pi$
$367$	10.0187			0.522972			0.261486	+	0.965207i	$0.415787\pi$
$368$		0			0
$369$			1.39257i			0.0724942i
$370$		0			0
$371$	−23.1040	−	5.51280i	−1.19950	−	0.286210i
$372$		0			0
$373$	−1.13115	+	1.13115i	−0.0585685	+	0.0585685i	−0.735784	−	0.677216i	$-0.763186\pi$
$373$	−1.13115	+	1.13115i	−0.0585685	+	0.0585685i	0.677216	+	0.735784i	$0.263186\pi$
$374$		0			0
$375$	−15.0684			−0.778126
$376$		0			0
$377$	50.6742			2.60985
$378$		0			0
$379$	12.6191	+	12.6191i	0.648200	+	0.648200i	0.952558	−	0.304357i	$-0.0984417\pi$
$379$	12.6191	+	12.6191i	0.648200	+	0.648200i	−0.304357	+	0.952558i	$0.598442\pi$
$380$		0			0
$381$	−2.98340	+	2.98340i	−0.152844	+	0.152844i
$382$		0			0
$383$	−16.6646			−0.851521			−0.425761	−	0.904836i	$-0.639993\pi$
$383$	−16.6646			−0.851521			−0.425761	+	0.904836i	$0.639993\pi$
$384$		0			0
$385$	−15.2081	+	9.34866i	−0.775077	+	0.476452i
$386$		0			0
$387$	1.13759	−	1.13759i	0.0578271	−	0.0578271i
$388$		0			0
$389$	2.85997	−	2.85997i	0.145006	−	0.145006i	−0.630877	−	0.775883i	$-0.717305\pi$
$389$	2.85997	−	2.85997i	0.145006	−	0.145006i	0.775883	+	0.630877i	$0.217305\pi$
$390$		0			0
$391$		−	1.51557i		−	0.0766459i
$392$		0			0
$393$		−	10.7990i		−	0.544735i
$394$		0			0
$395$	−7.61070	+	7.61070i	−0.382936	+	0.382936i
$396$		0			0
$397$	12.0302	−	12.0302i	0.603778	−	0.603778i	−0.337535	−	0.941313i	$-0.609593\pi$
$397$	12.0302	−	12.0302i	0.603778	−	0.603778i	0.941313	+	0.337535i	$0.109593\pi$
$398$		0			0
$399$	−5.68845	+	3.49678i	−0.284779	+	0.175058i
$400$		0			0
$401$	3.88812			0.194163			0.0970817	−	0.995276i	$-0.469049\pi$
$401$	3.88812			0.194163			0.0970817	+	0.995276i	$0.469049\pi$
$402$		0			0
$403$	−40.0117	+	40.0117i	−1.99312	+	1.99312i
$404$		0			0
$405$	−9.65052	−	9.65052i	−0.479538	−	0.479538i
$406$		0			0
$407$	−16.7503			−0.830280
$408$		0			0
$409$	−25.7267			−1.27210			−0.636052	−	0.771646i	$-0.719434\pi$
$409$	−25.7267			−1.27210			−0.636052	+	0.771646i	$0.719434\pi$
$410$		0			0
$411$	−16.4601	+	16.4601i	−0.811915	+	0.811915i
$412$		0			0
$413$	−11.9755	−	2.85746i	−0.589277	−	0.140606i
$414$		0			0
$415$		−	32.7827i		−	1.60924i
$416$		0			0
$417$	−24.4109			−1.19541
$418$		0			0
$419$	15.4348	+	15.4348i	0.754038	+	0.754038i	0.975230	−	0.221192i	$-0.0709948\pi$
$419$	15.4348	+	15.4348i	0.754038	+	0.754038i	−0.221192	+	0.975230i	$0.570995\pi$
$420$		0			0
$421$	−14.9338	+	14.9338i	−0.727830	+	0.727830i	−0.970187	−	0.242357i	$-0.922079\pi$
$421$	−14.9338	+	14.9338i	−0.727830	+	0.727830i	0.242357	+	0.970187i	$0.422079\pi$
$422$		0			0
$423$		−	1.64607i		−	0.0800345i
$424$		0			0
$425$	0.783519			0.0380063
$426$		0			0
$427$	7.45641	+	1.77916i	0.360841	+	0.0860996i
$428$		0			0
$429$	19.9411	+	19.9411i	0.962768	+	0.962768i
$430$		0			0
$431$		−	23.6114i		−	1.13732i	−0.822572	−	0.568660i	$-0.807462\pi$
$431$		−	23.6114i		−	1.13732i	0.822572	−	0.568660i	$-0.192538\pi$
$432$		0			0
$433$			1.78643i			0.0858505i	0.999078	+	0.0429253i	$0.0136677\pi$
$433$			1.78643i			0.0858505i	−0.999078	+	0.0429253i	$0.986332\pi$
$434$		0			0
$435$	18.4205	−	18.4205i	0.883196	−	0.883196i
$436$		0			0
$437$	−1.62677	−	1.62677i	−0.0778189	−	0.0778189i
$438$		0			0
$439$		−	26.6274i		−	1.27085i	−0.772161	−	0.635427i	$-0.780824\pi$
$439$		−	26.6274i		−	1.27085i	0.772161	−	0.635427i	$-0.219176\pi$
$440$		0			0
$441$	5.31748	+	2.69079i	0.253213	+	0.128133i
$442$		0			0
$443$	16.9403	+	16.9403i	0.804856	+	0.804856i	0.983850	−	0.178994i	$-0.0572843\pi$
$443$	16.9403	+	16.9403i	0.804856	+	0.804856i	−0.178994	+	0.983850i	$0.557284\pi$
$444$		0			0
$445$	−19.5961	−	19.5961i	−0.928946	−	0.928946i
$446$		0			0
$447$	−16.0153			−0.757497
$448$		0			0
$449$	−6.76315			−0.319173			−0.159586	−	0.987184i	$-0.551016\pi$
$449$	−6.76315			−0.319173			−0.159586	+	0.987184i	$0.551016\pi$
$450$		0			0
$451$	−3.27139	−	3.27139i	−0.154044	−	0.154044i
$452$		0			0
$453$	21.2941	+	21.2941i	1.00048	+	1.00048i
$454$		0			0
$455$	22.4824	+	36.5737i	1.05399	+	1.71460i
$456$		0			0
$457$			3.79073i			0.177323i	0.996062	+	0.0886615i	$0.0282590\pi$
$457$			3.79073i			0.177323i	−0.996062	+	0.0886615i	$0.971741\pi$
$458$		0			0
$459$	−4.52778	−	4.52778i	−0.211339	−	0.211339i
$460$		0			0
$461$	−3.04346	+	3.04346i	−0.141748	+	0.141748i	−0.774420	−	0.632672i	$-0.781958\pi$
$461$	−3.04346	+	3.04346i	−0.141748	+	0.141748i	0.632672	+	0.774420i	$0.281958\pi$
$462$		0			0
$463$			1.44348i			0.0670844i	0.999437	+	0.0335422i	$0.0106788\pi$
$463$			1.44348i			0.0670844i	−0.999437	+	0.0335422i	$0.989321\pi$
$464$		0			0
$465$			29.0892i			1.34898i
$466$		0			0
$467$	10.9302	+	10.9302i	0.505789	+	0.505789i	0.913231	−	0.407442i	$-0.133579\pi$
$467$	10.9302	+	10.9302i	0.505789	+	0.505789i	−0.407442	+	0.913231i	$0.633579\pi$
$468$		0			0
$469$	0.390440	+	0.0931623i	0.0180289	+	0.00430184i
$470$		0			0
$471$	−6.36780			−0.293413
$472$		0			0
$473$			5.34482i			0.245755i
$474$		0			0
$475$	0.841004	−	0.841004i	0.0385879	−	0.0385879i
$476$		0			0
$477$	−5.40456	−	5.40456i	−0.247458	−	0.247458i
$478$		0			0
$479$	−22.3261			−1.02011			−0.510054	−	0.860142i	$-0.670375\pi$
$479$	−22.3261			−1.02011			−0.510054	+	0.860142i	$0.670375\pi$
$480$		0			0
$481$			40.2824i			1.83672i
$482$		0			0
$483$	1.20272	−	5.04057i	0.0547258	−	0.229354i
$484$		0			0
$485$	5.45542	−	5.45542i	0.247718	−	0.247718i
$486$		0			0
$487$	5.13887			0.232865			0.116432	−	0.993199i	$-0.462854\pi$
$487$	5.13887			0.232865			0.116432	+	0.993199i	$0.462854\pi$
$488$		0			0
$489$	−6.69352			−0.302692
$490$		0			0
$491$	−6.24398	−	6.24398i	−0.281787	−	0.281787i	0.552034	−	0.833821i	$-0.313852\pi$
$491$	−6.24398	−	6.24398i	−0.281787	−	0.281787i	−0.833821	+	0.552034i	$0.813852\pi$
$492$		0			0
$493$	5.97500	−	5.97500i	0.269101	−	0.269101i
$494$		0			0
$495$	−5.74440			−0.258192
$496$		0			0
$497$	18.0779	+	29.4085i	0.810903	+	1.31915i
$498$		0			0
$499$	−7.56730	+	7.56730i	−0.338759	+	0.338759i	−0.855900	−	0.517141i	$-0.826996\pi$
$499$	−7.56730	+	7.56730i	−0.338759	+	0.338759i	0.517141	+	0.855900i	$0.326996\pi$
$500$		0			0
$501$	−6.27117	+	6.27117i	−0.280175	+	0.280175i
$502$		0			0
$503$		−	11.7969i		−	0.525999i	−0.964796	−	0.263000i	$-0.915288\pi$
$503$		−	11.7969i		−	0.525999i	0.964796	−	0.263000i	$-0.0847118\pi$
$504$		0			0
$505$		−	20.0530i		−	0.892348i
$506$		0			0
$507$	34.4816	−	34.4816i	1.53138	−	1.53138i
$508$		0			0
$509$	24.1062	−	24.1062i	1.06849	−	1.06849i	0.0710131	−	0.997475i	$-0.477377\pi$
$509$	24.1062	−	24.1062i	1.06849	−	1.06849i	0.997475	−	0.0710131i	$-0.0226232\pi$
$510$		0			0
$511$	8.65387	+	14.0779i	0.382825	+	0.622768i
$512$		0			0
$513$	−9.71995			−0.429146
$514$		0			0
$515$	12.5572	−	12.5572i	0.553337	−	0.553337i
$516$		0			0
$517$	3.86691	+	3.86691i	0.170066	+	0.170066i
$518$		0			0
$519$	−9.22031			−0.404727
$520$		0			0
$521$	−42.1032			−1.84457			−0.922287	−	0.386506i	$-0.873682\pi$
$521$	−42.1032			−1.84457			−0.922287	+	0.386506i	$0.873682\pi$
$522$		0			0
$523$	6.62683	−	6.62683i	0.289771	−	0.289771i	−0.547219	−	0.836990i	$-0.684313\pi$
$523$	6.62683	−	6.62683i	0.289771	−	0.289771i	0.836990	+	0.547219i	$0.184313\pi$
$524$		0			0
$525$	2.60586	+	0.621781i	0.113729	+	0.0271367i
$526$		0			0
$527$			9.43556i			0.411020i
$528$		0			0
$529$	−21.2146			−0.922372
$530$		0			0
$531$	−2.80135	−	2.80135i	−0.121568	−	0.121568i
$532$		0			0
$533$	−7.86731	+	7.86731i	−0.340771	+	0.340771i
$534$		0			0
$535$		−	9.55751i		−	0.413207i
$536$		0			0
$537$	19.4033			0.837315
$538$		0			0
$539$	−18.8129	+	6.17058i	−0.810328	+	0.265786i
$540$		0			0
$541$	1.70184	+	1.70184i	0.0731676	+	0.0731676i	0.742744	−	0.669576i	$-0.233524\pi$
$541$	1.70184	+	1.70184i	0.0731676	+	0.0731676i	−0.669576	+	0.742744i	$0.733524\pi$
$542$		0			0
$543$			0.395252i			0.0169619i
$544$		0			0
$545$		−	18.6063i		−	0.797005i
$546$		0			0
$547$	−8.86974	+	8.86974i	−0.379243	+	0.379243i	−0.870829	−	0.491586i	$-0.836417\pi$
$547$	−8.86974	+	8.86974i	−0.379243	+	0.379243i	0.491586	+	0.870829i	$0.336417\pi$
$548$		0			0
$549$	1.74423	+	1.74423i	0.0744418	+	0.0744418i
$550$		0			0
$551$		−	12.8267i		−	0.546438i
$552$		0			0
$553$	−10.1694	+	6.25132i	−0.432449	+	0.265833i
$554$		0			0
$555$	14.6430	+	14.6430i	0.621560	+	0.621560i
$556$		0			0
$557$	−9.83630	−	9.83630i	−0.416777	−	0.416777i	0.467314	−	0.884091i	$-0.345222\pi$
$557$	−9.83630	−	9.83630i	−0.416777	−	0.416777i	−0.884091	+	0.467314i	$0.845222\pi$
$558$		0			0
$559$	12.8536			0.543651
$560$		0			0
$561$	4.70253			0.198541
$562$		0			0
$563$	3.26139	+	3.26139i	0.137451	+	0.137451i	0.772485	−	0.635034i	$-0.219014\pi$
$563$	3.26139	+	3.26139i	0.137451	+	0.137451i	−0.635034	+	0.772485i	$0.719014\pi$
$564$		0			0
$565$	−22.8014	−	22.8014i	−0.959263	−	0.959263i
$566$		0			0
$567$	−7.92680	−	12.8951i	−0.332894	−	0.541542i
$568$		0			0
$569$			7.26970i			0.304762i	0.988322	+	0.152381i	$0.0486940\pi$
$569$			7.26970i			0.304762i	−0.988322	+	0.152381i	$0.951306\pi$
$570$		0			0
$571$	1.22962	+	1.22962i	0.0514579	+	0.0514579i	0.732367	−	0.680910i	$-0.238415\pi$
$571$	1.22962	+	1.22962i	0.0514579	+	0.0514579i	−0.680910	+	0.732367i	$0.738415\pi$
$572$		0			0
$573$	−4.04371	+	4.04371i	−0.168928	+	0.168928i
$574$		0			0
$575$			0.923034i			0.0384932i
$576$		0			0
$577$		−	20.1315i		−	0.838084i	−0.907967	−	0.419042i	$-0.862366\pi$
$577$		−	20.1315i		−	0.838084i	0.907967	−	0.419042i	$-0.137634\pi$
$578$		0			0
$579$	10.2356	+	10.2356i	0.425378	+	0.425378i
$580$		0			0
$581$	8.43859	−	35.3659i	0.350092	−	1.46722i
$582$		0			0
$583$	25.3926			1.05165
$584$		0			0
$585$			13.8146i			0.571163i
$586$		0			0
$587$	13.6801	−	13.6801i	0.564639	−	0.564639i	−0.365983	−	0.930622i	$-0.619267\pi$
$587$	13.6801	−	13.6801i	0.564639	−	0.564639i	0.930622	+	0.365983i	$0.119267\pi$
$588$		0			0
$589$	10.1278	+	10.1278i	0.417310	+	0.417310i
$590$		0			0
$591$	−29.8554			−1.22809
$592$		0			0
$593$		−	24.4282i		−	1.00315i	−0.865115	−	0.501573i	$-0.832755\pi$
$593$		−	24.4282i		−	1.00315i	0.865115	−	0.501573i	$-0.167245\pi$
$594$		0			0
$595$	6.96331	+	1.66150i	0.285468	+	0.0681150i
$596$		0			0
$597$	26.5875	−	26.5875i	1.08815	−	1.08815i
$598$		0			0
$599$	−25.1701			−1.02842			−0.514211	−	0.857664i	$-0.671915\pi$
$599$	−25.1701			−1.02842			−0.514211	+	0.857664i	$0.671915\pi$
$600$		0			0
$601$	−9.34866			−0.381340			−0.190670	−	0.981654i	$-0.561066\pi$
$601$	−9.34866			−0.381340			−0.190670	+	0.981654i	$0.561066\pi$
$602$		0			0
$603$	0.0913331	+	0.0913331i	0.00371937	+	0.00371937i
$604$		0			0
$605$	−5.06049	+	5.06049i	−0.205738	+	0.205738i
$606$		0			0
$607$	27.5600			1.11863			0.559314	−	0.828956i	$-0.311065\pi$
$607$	27.5600			1.11863			0.559314	+	0.828956i	$0.311065\pi$
$608$		0			0
$609$	24.6136	−	15.1303i	0.997392	−	0.613112i
$610$		0			0
$611$	9.29945	−	9.29945i	0.376215	−	0.376215i
$612$		0			0
$613$	−6.51272	+	6.51272i	−0.263046	+	0.263046i	−0.826291	−	0.563244i	$-0.809553\pi$
$613$	−6.51272	+	6.51272i	−0.263046	+	0.263046i	0.563244	+	0.826291i	$0.309553\pi$
$614$		0			0
$615$			5.71967i			0.230639i
$616$		0			0
$617$			18.3569i			0.739023i	0.929226	+	0.369511i	$0.120475\pi$
$617$			18.3569i			0.739023i	−0.929226	+	0.369511i	$0.879525\pi$
$618$		0			0
$619$	−12.2627	+	12.2627i	−0.492878	+	0.492878i	−0.909212	−	0.416334i	$-0.863315\pi$
$619$	−12.2627	+	12.2627i	−0.492878	+	0.492878i	0.416334	+	0.909212i	$0.363315\pi$
$620$		0			0
$621$	5.33401	−	5.33401i	0.214046	−	0.214046i
$622$		0			0
$623$	−16.0960	−	26.1844i	−0.644872	−	1.04906i
$624$		0			0
$625$	27.9768			1.11907
$626$		0			0
$627$	5.04754	−	5.04754i	0.201579	−	0.201579i
$628$		0			0
$629$	4.74970	+	4.74970i	0.189383	+	0.189383i
$630$		0			0
$631$	24.0987			0.959353			0.479676	−	0.877445i	$-0.340754\pi$
$631$	24.0987			0.959353			0.479676	+	0.877445i	$0.340754\pi$
$632$		0			0
$633$	31.9532			1.27002
$634$		0			0
$635$	4.85529	−	4.85529i	0.192676	−	0.192676i
$636$		0			0
$637$	14.8395	+	45.2427i	0.587962	+	1.79258i
$638$		0			0
$639$			11.1082i			0.439432i
$640$		0			0
$641$	−33.0833			−1.30671			−0.653357	−	0.757050i	$-0.726640\pi$
$641$	−33.0833			−1.30671			−0.653357	+	0.757050i	$0.726640\pi$
$642$		0			0
$643$	−4.99031	−	4.99031i	−0.196798	−	0.196798i	0.601828	−	0.798626i	$-0.294439\pi$
$643$	−4.99031	−	4.99031i	−0.196798	−	0.196798i	−0.798626	+	0.601828i	$0.794439\pi$
$644$		0			0
$645$	4.67241	−	4.67241i	0.183976	−	0.183976i
$646$		0			0
$647$			16.2489i			0.638809i	0.947618	+	0.319405i	$0.103483\pi$
$647$			16.2489i			0.638809i	−0.947618	+	0.319405i	$0.896517\pi$
$648$		0			0
$649$	13.1618			0.516645
$650$		0			0
$651$	−7.48782	+	31.3812i	−0.293471	+	1.22993i
$652$		0			0
$653$	−1.10728	−	1.10728i	−0.0433312	−	0.0433312i	0.685109	−	0.728440i	$-0.259754\pi$
$653$	−1.10728	−	1.10728i	−0.0433312	−	0.0433312i	−0.728440	+	0.685109i	$0.759754\pi$
$654$		0			0
$655$			17.5746i			0.686698i
$656$		0			0
$657$			5.31748i			0.207455i
$658$		0			0
$659$	−23.8965	+	23.8965i	−0.930874	+	0.930874i	−0.997761	−	0.0668864i	$-0.978693\pi$
$659$	−23.8965	+	23.8965i	−0.930874	+	0.930874i	0.0668864	+	0.997761i	$0.478693\pi$
$660$		0			0
$661$	17.0306	+	17.0306i	0.662414	+	0.662414i	0.955949	−	0.293534i	$-0.0948314\pi$
$661$	17.0306	+	17.0306i	0.662414	+	0.662414i	−0.293534	+	0.955949i	$0.594831\pi$
$662$		0			0
$663$		−	11.3090i		−	0.439206i
$664$		0			0
$665$	9.25760	−	5.69079i	0.358994	−	0.220679i
$666$		0			0
$667$	7.03893	+	7.03893i	0.272548	+	0.272548i
$668$		0			0
$669$	15.9632	+	15.9632i	0.617175	+	0.617175i
$670$		0			0
$671$	−8.19501			−0.316365
$672$		0			0
$673$	2.21456			0.0853649			0.0426825	−	0.999089i	$-0.486410\pi$
$673$	2.21456			0.0853649			0.0426825	+	0.999089i	$0.486410\pi$
$674$		0			0
$675$	2.75757	+	2.75757i	0.106139	+	0.106139i
$676$		0			0
$677$	−10.3945	−	10.3945i	−0.399493	−	0.399493i	0.478561	−	0.878054i	$-0.341158\pi$
$677$	−10.3945	−	10.3945i	−0.399493	−	0.399493i	−0.878054	+	0.478561i	$0.841158\pi$
$678$		0			0
$679$	7.28955	−	4.48100i	0.279747	−	0.171965i
$680$		0			0
$681$		−	15.7606i		−	0.603948i
$682$		0			0
$683$	−17.8265	−	17.8265i	−0.682113	−	0.682113i	0.278363	−	0.960476i	$-0.410208\pi$
$683$	−17.8265	−	17.8265i	−0.682113	−	0.682113i	−0.960476	+	0.278363i	$0.910208\pi$
$684$		0			0
$685$	26.7877	−	26.7877i	1.02351	−	1.02351i
$686$		0			0
$687$			36.5045i			1.39273i
$688$		0			0
$689$		−	61.0660i		−	2.32643i
$690$		0			0
$691$	−28.7899	−	28.7899i	−1.09522	−	1.09522i	−0.994962	−	0.100257i	$-0.968034\pi$
$691$	−28.7899	−	28.7899i	−1.09522	−	1.09522i	−0.100257	−	0.994962i	$-0.531966\pi$
$692$		0			0
$693$	−6.19703	−	1.47866i	−0.235406	−	0.0561698i
$694$		0			0
$695$	39.7273			1.50694
$696$		0			0
$697$			1.85527i			0.0702734i
$698$		0			0
$699$	6.97187	−	6.97187i	0.263700	−	0.263700i
$700$		0			0
$701$	−8.26141	−	8.26141i	−0.312029	−	0.312029i	0.533666	−	0.845695i	$-0.320814\pi$
$701$	−8.26141	−	8.26141i	−0.312029	−	0.312029i	−0.845695	+	0.533666i	$0.820814\pi$
$702$		0			0
$703$	10.1963			0.384562
$704$		0			0
$705$		−	6.76085i		−	0.254628i
$706$		0			0
$707$	5.16184	−	21.6331i	0.194131	−	0.813597i
$708$		0			0
$709$	−26.9918	+	26.9918i	−1.01370	+	1.01370i	−0.0137939	+	0.999905i	$0.504391\pi$
$709$	−26.9918	+	26.9918i	−1.01370	+	1.01370i	−0.999905	+	0.0137939i	$0.995609\pi$
$710$		0			0
$711$	−3.84120			−0.144056
$712$		0			0
$713$	−11.1157			−0.416286
$714$		0			0
$715$	−32.4530	−	32.4530i	−1.21367	−	1.21367i
$716$		0			0
$717$	−9.88145	+	9.88145i	−0.369030	+	0.369030i
$718$		0			0
$719$	6.92495			0.258257			0.129129	−	0.991628i	$-0.458782\pi$
$719$	6.92495			0.258257			0.129129	+	0.991628i	$0.458782\pi$
$720$		0			0
$721$	16.7790	−	10.3143i	0.624882	−	0.384125i
$722$		0			0
$723$	22.1563	−	22.1563i	0.824001	−	0.824001i
$724$		0			0
$725$	−3.63897	+	3.63897i	−0.135148	+	0.135148i
$726$		0			0
$727$			39.9958i			1.48336i	0.670752	+	0.741681i	$0.265971\pi$
$727$			39.9958i			1.48336i	−0.670752	+	0.741681i	$0.734029\pi$
$728$		0			0
$729$		−	29.6963i		−	1.09986i
$730$		0			0
$731$	1.51557	−	1.51557i	0.0560556	−	0.0560556i
$732$		0			0
$733$	10.2496	−	10.2496i	0.378579	−	0.378579i	−0.492010	−	0.870589i	$-0.663738\pi$
$733$	10.2496	−	10.2496i	0.378579	−	0.378579i	0.870589	+	0.492010i	$0.163738\pi$
$734$		0			0
$735$	21.8404	+	11.0518i	0.805595	+	0.407652i
$736$		0			0
$737$	−0.429116			−0.0158067
$738$		0			0
$739$	0.573743	−	0.573743i	0.0211055	−	0.0211055i	−0.696475	−	0.717581i	$-0.745249\pi$
$739$	0.573743	−	0.573743i	0.0211055	−	0.0211055i	0.717581	+	0.696475i	$0.245249\pi$
$740$		0			0
$741$	−12.1387	−	12.1387i	−0.445927	−	0.445927i
$742$		0			0
$743$	−25.9627			−0.952477			−0.476239	−	0.879316i	$-0.658000\pi$
$743$	−25.9627			−0.952477			−0.476239	+	0.879316i	$0.658000\pi$
$744$		0			0
$745$	26.0639			0.954907
$746$		0			0
$747$	8.27290	−	8.27290i	0.302690	−	0.302690i
$748$		0			0
$749$	2.46019	−	10.3106i	0.0898935	−	0.376741i
$750$		0			0
$751$		−	13.9799i		−	0.510133i	−0.966924	−	0.255067i	$-0.917903\pi$
$751$		−	13.9799i		−	0.510133i	0.966924	−	0.255067i	$-0.0820974\pi$
$752$		0			0
$753$	8.23569			0.300125
$754$		0			0
$755$	−34.6548	−	34.6548i	−1.26122	−	1.26122i
$756$		0			0
$757$	31.6014	−	31.6014i	1.14857	−	1.14857i	0.161737	−	0.986834i	$-0.448290\pi$
$757$	31.6014	−	31.6014i	1.14857	−	1.14857i	0.986834	−	0.161737i	$-0.0517096\pi$
$758$		0			0
$759$			5.53987i			0.201085i
$760$		0			0
$761$	−35.0216			−1.26953			−0.634765	−	0.772705i	$-0.718903\pi$
$761$	−35.0216			−1.26953			−0.634765	+	0.772705i	$0.718903\pi$
$762$		0			0
$763$	4.78943	−	20.0723i	0.173389	−	0.726667i
$764$		0			0
$765$	1.62888	+	1.62888i	0.0588923	+	0.0588923i
$766$		0			0
$767$		−	31.6525i		−	1.14290i
$768$		0			0
$769$		−	10.9708i		−	0.395618i	−0.980241	−	0.197809i	$-0.936617\pi$
$769$		−	10.9708i		−	0.395618i	0.980241	−	0.197809i	$-0.0633826\pi$
$770$		0			0
$771$	−7.16830	+	7.16830i	−0.258160	+	0.258160i
$772$		0			0
$773$	7.67303	+	7.67303i	0.275980	+	0.275980i	0.831502	−	0.555522i	$-0.187482\pi$
$773$	7.67303	+	7.67303i	0.275980	+	0.275980i	−0.555522	+	0.831502i	$0.687482\pi$
$774$		0			0
$775$		−	5.74656i		−	0.206423i
$776$		0			0
$777$	12.0275	+	19.5660i	0.431485	+	0.701927i
$778$		0			0
$779$	1.99139	+	1.99139i	0.0713488	+	0.0713488i
$780$		0			0
$781$	−26.0951	−	26.0951i	−0.933755	−	0.933755i
$782$		0			0
$783$	42.0576			1.50302
$784$		0			0
$785$	10.3632			0.369878
$786$		0			0
$787$	18.2461	+	18.2461i	0.650404	+	0.650404i	0.953090	−	0.302686i	$-0.0978833\pi$
$787$	18.2461	+	18.2461i	0.650404	+	0.650404i	−0.302686	+	0.953090i	$0.597883\pi$
$788$		0			0
$789$	18.4295	+	18.4295i	0.656106	+	0.656106i
$790$		0			0
$791$	−18.7288	−	30.4674i	−0.665918	−	1.08329i
$792$		0			0
$793$			19.7080i			0.699852i
$794$		0			0
$795$	−22.1980	−	22.1980i	−0.787283	−	0.787283i
$796$		0			0
$797$	−22.4616	+	22.4616i	−0.795630	+	0.795630i	−0.982403	−	0.186773i	$-0.940197\pi$
$797$	−22.4616	+	22.4616i	−0.795630	+	0.795630i	0.186773	+	0.982403i	$0.440197\pi$
$798$		0			0
$799$		−	2.19300i		−	0.0775827i
$800$		0			0
$801$		−	9.89038i		−	0.349459i
$802$		0			0
$803$	−12.4917	−	12.4917i	−0.440823	−	0.440823i
$804$		0			0
$805$	−1.95736	+	8.20322i	−0.0689877	+	0.289125i
$806$		0			0
$807$	20.6271			0.726110
$808$		0			0
$809$		−	24.7622i		−	0.870592i	−0.900287	−	0.435296i	$-0.856644\pi$
$809$		−	24.7622i		−	0.870592i	0.900287	−	0.435296i	$-0.143356\pi$
$810$		0			0
$811$	5.40486	−	5.40486i	0.189790	−	0.189790i	−0.605815	−	0.795605i	$-0.707153\pi$
$811$	5.40486	−	5.40486i	0.189790	−	0.189790i	0.795605	+	0.605815i	$0.207153\pi$
$812$		0			0
$813$	−20.3163	−	20.3163i	−0.712523	−	0.712523i
$814$		0			0
$815$	10.8933			0.381575
$816$		0			0
$817$		−	3.25354i		−	0.113827i
$818$		0			0
$819$	−3.55601	+	14.9031i	−0.124257	+	0.520757i
$820$		0			0
$821$	−0.191577	+	0.191577i	−0.00668610	+	0.00668610i	−0.710442	−	0.703756i	$-0.751505\pi$
$821$	−0.191577	+	0.191577i	−0.00668610	+	0.00668610i	0.703756	+	0.710442i	$0.251505\pi$
$822$		0			0
$823$	−43.4293			−1.51385			−0.756925	−	0.653501i	$-0.773299\pi$
$823$	−43.4293			−1.51385			−0.756925	+	0.653501i	$0.773299\pi$
$824$		0			0
$825$	−2.86399			−0.0997114
$826$		0			0
$827$	38.0398	+	38.0398i	1.32277	+	1.32277i	0.911522	+	0.411252i	$0.134909\pi$
$827$	38.0398	+	38.0398i	1.32277	+	1.32277i	0.411252	+	0.911522i	$0.365091\pi$
$828$		0			0
$829$	−2.08602	+	2.08602i	−0.0724505	+	0.0724505i	−0.742403	−	0.669953i	$-0.766314\pi$
$829$	−2.08602	+	2.08602i	−0.0724505	+	0.0724505i	0.669953	+	0.742403i	$0.266314\pi$
$830$		0			0
$831$	28.2817			0.981083
$832$		0			0
$833$	7.08430	+	3.58484i	0.245456	+	0.124207i
$834$		0			0
$835$	10.2059	−	10.2059i	0.353191	−	0.353191i
$836$		0			0
$837$	−33.2081	+	33.2081i	−1.14784	+	1.14784i
$838$		0			0
$839$		−	37.7564i		−	1.30350i	−0.758436	−	0.651748i	$-0.774036\pi$
$839$		−	37.7564i		−	1.30350i	0.758436	−	0.651748i	$-0.225964\pi$
$840$		0			0
$841$			26.5005i			0.913811i
$842$		0			0
$843$	−7.42857	+	7.42857i	−0.255854	+	0.255854i
$844$		0			0
$845$	−56.1167	+	56.1167i	−1.93047	+	1.93047i
$846$		0			0
$847$	−6.76185	+	4.15661i	−0.232340	+	0.142823i
$848$		0			0
$849$	−24.0960			−0.826974
$850$		0			0
$851$	−5.59544	+	5.59544i	−0.191809	+	0.191809i
$852$		0			0
$853$	37.7120	+	37.7120i	1.29124	+	1.29124i	0.934023	+	0.357212i	$0.116273\pi$
$853$	37.7120	+	37.7120i	1.29124	+	1.29124i	0.357212	+	0.934023i	$0.383727\pi$
$854$		0			0
$855$	3.49678			0.119587
$856$		0			0
$857$	−15.3930			−0.525814			−0.262907	−	0.964821i	$-0.584681\pi$
$857$	−15.3930			−0.525814			−0.262907	+	0.964821i	$0.584681\pi$
$858$		0			0
$859$	−34.6738	+	34.6738i	−1.18306	+	1.18306i	−0.204106	+	0.978949i	$0.565429\pi$
$859$	−34.6738	+	34.6738i	−1.18306	+	1.18306i	−0.978949	+	0.204106i	$0.934571\pi$
$860$		0			0
$861$	−1.47230	+	6.17035i	−0.0501757	+	0.210285i
$862$		0			0
$863$			45.6641i			1.55443i	0.629238	+	0.777213i	$0.283367\pi$
$863$			45.6641i			1.55443i	−0.629238	+	0.777213i	$0.716633\pi$
$864$		0			0
$865$	15.0055			0.510202
$866$		0			0
$867$	16.2869	+	16.2869i	0.553134	+	0.553134i
$868$		0			0
$869$	9.02367	−	9.02367i	0.306107	−	0.306107i
$870$		0			0
$871$			1.03197i			0.0349670i
$872$		0			0
$873$	2.75341			0.0931887
$874$		0			0
$875$	26.4551	+	6.31240i	0.894345	+	0.213398i
$876$		0			0
$877$	−37.0077	−	37.0077i	−1.24966	−	1.24966i	−0.955870	−	0.293790i	$-0.905083\pi$
$877$	−37.0077	−	37.0077i	−1.24966	−	1.24966i	−0.293790	−	0.955870i	$-0.594917\pi$
$878$		0			0
$879$		−	0.224984i		−	0.00758854i
$880$		0			0
$881$			17.8630i			0.601820i	0.953653	+	0.300910i	$0.0972903\pi$
$881$			17.8630i			0.601820i	−0.953653	+	0.300910i	$0.902710\pi$
$882$		0			0
$883$	24.7949	−	24.7949i	0.834416	−	0.834416i	−0.153701	−	0.988117i	$-0.549119\pi$
$883$	24.7949	−	24.7949i	0.834416	−	0.834416i	0.988117	+	0.153701i	$0.0491193\pi$
$884$		0			0
$885$	−11.5059	−	11.5059i	−0.386768	−	0.386768i
$886$		0			0
$887$			50.7922i			1.70543i	0.522373	+	0.852717i	$0.325047\pi$
$887$			50.7922i			1.70543i	−0.522373	+	0.852717i	$0.674953\pi$
$888$		0			0
$889$	6.48766	−	3.98807i	0.217589	−	0.133755i
$890$		0			0
$891$	11.4422	+	11.4422i	0.383328	+	0.383328i
$892$		0			0
$893$	−2.35389	−	2.35389i	−0.0787700	−	0.0787700i
$894$		0			0
$895$	−31.5777			−1.05553
$896$		0			0
$897$	13.3227			0.444833
$898$		0			0
$899$	−43.8225	−	43.8225i	−1.46156	−	1.46156i
$900$		0			0
$901$	−7.20031	−	7.20031i	−0.239877	−	0.239877i
$902$		0			0
$903$	6.24329	−	3.83785i	0.207764	−	0.127716i
$904$		0			0
$905$		−	0.643249i		−	0.0213823i
$906$		0			0
$907$	34.2341	+	34.2341i	1.13673	+	1.13673i	0.989033	+	0.147693i	$0.0471847\pi$
$907$	34.2341	+	34.2341i	1.13673	+	1.13673i	0.147693	+	0.989033i	$0.452815\pi$
$908$		0			0
$909$	5.06049	−	5.06049i	0.167846	−	0.167846i
$910$		0			0
$911$			7.50342i			0.248599i	0.992245	+	0.124300i	$0.0396684\pi$
$911$			7.50342i			0.248599i	−0.992245	+	0.124300i	$0.960332\pi$
$912$		0			0
$913$			38.8691i			1.28638i
$914$		0			0
$915$	7.16403	+	7.16403i	0.236836	+	0.236836i
$916$		0			0
$917$	−4.52388	+	18.9594i	−0.149392	+	0.626095i
$918$		0			0
$919$	29.0806			0.959281			0.479640	−	0.877465i	$-0.340767\pi$
$919$	29.0806			0.959281			0.479640	+	0.877465i	$0.340767\pi$
$920$		0			0
$921$		−	2.55389i		−	0.0841535i
$922$		0			0
$923$	−62.7555	+	62.7555i	−2.06562	+	2.06562i
$924$		0			0
$925$	−2.89272	−	2.89272i	−0.0951121	−	0.0951121i
$926$		0			0
$927$	6.33776			0.208159
$928$		0			0
$929$			25.2998i			0.830059i	0.909808	+	0.415029i	$0.136229\pi$
$929$			25.2998i			0.830059i	−0.909808	+	0.415029i	$0.863771\pi$
$930$		0			0
$931$	11.4519	−	3.75620i	0.375321	−	0.123104i
$932$		0			0
$933$	−15.5881	+	15.5881i	−0.510332	+	0.510332i
$934$		0			0
$935$	−7.65307			−0.250282
$936$		0			0
$937$	17.3615			0.567177			0.283588	−	0.958946i	$-0.408475\pi$
$937$	17.3615			0.567177			0.283588	+	0.958946i	$0.408475\pi$
$938$		0			0
$939$	−34.8734	−	34.8734i	−1.13805	−	1.13805i
$940$		0			0
$941$	−10.8511	+	10.8511i	−0.353735	+	0.353735i	−0.861497	−	0.507762i	$-0.830473\pi$
$941$	−10.8511	+	10.8511i	−0.353735	+	0.353735i	0.507762	+	0.861497i	$0.330473\pi$
$942$		0			0
$943$	−2.18562			−0.0711737
$944$		0			0
$945$	18.6595	+	30.3547i	0.606994	+	0.987439i
$946$		0			0
$947$	26.4451	−	26.4451i	0.859349	−	0.859349i	−0.131912	−	0.991261i	$-0.542112\pi$
$947$	26.4451	−	26.4451i	0.859349	−	0.859349i	0.991261	+	0.131912i	$0.0421117\pi$
$948$		0			0
$949$	−30.0411	+	30.0411i	−0.975175	+	0.975175i
$950$		0			0
$951$			8.39738i			0.272304i
$952$		0			0
$953$			37.5483i			1.21631i	0.793819	+	0.608154i	$0.208090\pi$
$953$			37.5483i			1.21631i	−0.793819	+	0.608154i	$0.791910\pi$
$954$		0			0
$955$	6.58089	−	6.58089i	0.212952	−	0.212952i
$956$		0			0
$957$	−21.8404	+	21.8404i	−0.705999	+	0.705999i
$958$		0			0
$959$	35.7939	−	22.0031i	1.15584	−	0.710516i
$960$		0			0
$961$	38.2032			1.23236
$962$		0			0
$963$	2.41189	−	2.41189i	0.0777221	−	0.0777221i
$964$		0			0
$965$	−16.6578	−	16.6578i	−0.536234	−	0.536234i
$966$		0			0
$967$	−37.9785			−1.22131			−0.610653	−	0.791898i	$-0.709093\pi$
$967$	−37.9785			−1.22131			−0.610653	+	0.791898i	$0.709093\pi$
$968$		0			0
$969$	−2.86256			−0.0919586
$970$		0			0
$971$	−6.43134	+	6.43134i	−0.206392	+	0.206392i	−0.802732	−	0.596340i	$-0.796621\pi$
$971$	−6.43134	+	6.43134i	−0.206392	+	0.206392i	0.596340	+	0.802732i	$0.296621\pi$
$972$		0			0
$973$	42.8576	+	10.2262i	1.37395	+	0.327836i
$974$		0			0
$975$			6.88756i			0.220578i
$976$		0			0
$977$	−3.72659			−0.119224			−0.0596121	−	0.998222i	$-0.518986\pi$
$977$	−3.72659			−0.119224			−0.0596121	+	0.998222i	$0.518986\pi$
$978$		0			0
$979$	23.2343	+	23.2343i	0.742571	+	0.742571i
$980$		0			0
$981$	4.69539	−	4.69539i	0.149912	−	0.149912i
$982$		0			0
$983$		−	17.5847i		−	0.560863i	−0.959874	−	0.280432i	$-0.909522\pi$
$983$		−	17.5847i		−	0.560863i	0.959874	−	0.280432i	$-0.0904776\pi$
$984$		0			0
$985$	48.5879			1.54814
$986$		0			0
$987$	1.74031	−	7.29357i	0.0553946	−	0.232157i
$988$		0			0
$989$	1.78544	+	1.78544i	0.0567738	+	0.0567738i
$990$		0			0
$991$			44.7264i			1.42078i	0.703808	+	0.710390i	$0.251482\pi$
$991$			44.7264i			1.42078i	−0.703808	+	0.710390i	$0.748518\pi$
$992$		0			0
$993$		−	23.6281i		−	0.749816i
$994$		0			0
$995$	−43.2694	+	43.2694i	−1.37173	+	1.37173i
$996$		0			0
$997$	0.273521	+	0.273521i	0.00866251	+	0.00866251i	0.711425	−	0.702762i	$-0.248050\pi$
$997$	0.273521	+	0.273521i	0.00866251	+	0.00866251i	−0.702762	+	0.711425i	$0.748050\pi$
$998$		0			0
$999$			33.4328i			1.05777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.j.d.111.5		16
4.3	odd	2		112.2.j.d.83.5	yes	16
7.6	odd	2	inner	448.2.j.d.111.4		16
8.3	odd	2		896.2.j.h.223.5		16
8.5	even	2		896.2.j.g.223.4		16
16.3	odd	4		896.2.j.g.671.5		16
16.5	even	4		112.2.j.d.27.6	yes	16
16.11	odd	4	inner	448.2.j.d.335.4		16
16.13	even	4		896.2.j.h.671.4		16
28.3	even	6		784.2.w.e.19.8		32
28.11	odd	6		784.2.w.e.19.7		32
28.19	even	6		784.2.w.e.227.1		32
28.23	odd	6		784.2.w.e.227.2		32
28.27	even	2		112.2.j.d.83.6	yes	16
56.13	odd	2		896.2.j.g.223.5		16
56.27	even	2		896.2.j.h.223.4		16
112.5	odd	12		784.2.w.e.619.7		32
112.13	odd	4		896.2.j.h.671.5		16
112.27	even	4	inner	448.2.j.d.335.5		16
112.37	even	12		784.2.w.e.619.8		32
112.53	even	12		784.2.w.e.411.1		32
112.69	odd	4		112.2.j.d.27.5	✓	16
112.83	even	4		896.2.j.g.671.4		16
112.101	odd	12		784.2.w.e.411.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.j.d.27.5	✓	16	112.69	odd	4
112.2.j.d.27.6	yes	16	16.5	even	4
112.2.j.d.83.5	yes	16	4.3	odd	2
112.2.j.d.83.6	yes	16	28.27	even	2
448.2.j.d.111.4		16	7.6	odd	2	inner
448.2.j.d.111.5		16	1.1	even	1	trivial
448.2.j.d.335.4		16	16.11	odd	4	inner
448.2.j.d.335.5		16	112.27	even	4	inner
784.2.w.e.19.7		32	28.11	odd	6
784.2.w.e.19.8		32	28.3	even	6
784.2.w.e.227.1		32	28.19	even	6
784.2.w.e.227.2		32	28.23	odd	6
784.2.w.e.411.1		32	112.53	even	12
784.2.w.e.411.2		32	112.101	odd	12
784.2.w.e.619.7		32	112.5	odd	12
784.2.w.e.619.8		32	112.37	even	12
896.2.j.g.223.4		16	8.5	even	2
896.2.j.g.223.5		16	56.13	odd	2
896.2.j.g.671.4		16	112.83	even	4
896.2.j.g.671.5		16	16.3	odd	4
896.2.j.h.223.4		16	56.27	even	2
896.2.j.h.223.5		16	8.3	odd	2
896.2.j.h.671.4		16	16.13	even	4
896.2.j.h.671.5		16	112.13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03649 + 1.03649i) q^{3} +(-1.68683 - 1.68683i) q^{5} +(-1.38554 - 2.25395i) q^{7} -0.851361i q^{9} +(2.00000 + 2.00000i) q^{11} +(4.80976 - 4.80976i) q^{13} -3.49678i q^{15} -1.13424i q^{17} +(-1.21746 - 1.21746i) q^{19} +(0.900103 - 3.77231i) q^{21} +1.33620 q^{23} +0.690788i q^{25} +(3.99191 - 3.99191i) q^{27} +(5.26785 + 5.26785i) q^{29} -8.31885 q^{31} +4.14598i q^{33} +(-1.46486 + 6.13919i) q^{35} +(-4.18757 + 4.18757i) q^{37} +9.97057 q^{39} -1.63570 q^{41} +(1.33620 + 1.33620i) q^{43} +(-1.43610 + 1.43610i) q^{45} +1.93345 q^{47} +(-3.16057 + 6.24586i) q^{49} +(1.17563 - 1.17563i) q^{51} +(6.34814 - 6.34814i) q^{53} -6.74732i q^{55} -2.52377i q^{57} +(3.29044 - 3.29044i) q^{59} +(-2.04875 + 2.04875i) q^{61} +(-1.91892 + 1.17959i) q^{63} -16.2265 q^{65} +(-0.107279 + 0.107279i) q^{67} +(1.38497 + 1.38497i) q^{69} -13.0475 q^{71} -6.24586 q^{73} +(-0.715998 + 0.715998i) q^{75} +(1.73682 - 7.27897i) q^{77} -4.51184i q^{79} +5.72110 q^{81} +(9.71727 + 9.71727i) q^{83} +(-1.91327 + 1.91327i) q^{85} +10.9202i q^{87} +11.6171 q^{89} +(-17.5051 - 4.17685i) q^{91} +(-8.62244 - 8.62244i) q^{93} +4.10728i q^{95} +3.23412i q^{97} +(1.70272 - 1.70272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 32 q^{11} + 16 q^{21} - 8 q^{35} - 16 q^{39} - 16 q^{49} + 32 q^{51} - 80 q^{65} + 48 q^{67} - 32 q^{71} - 16 q^{77} + 32 q^{81} + 64 q^{85} - 8 q^{91} - 64 q^{93} - 64 q^{99}+O(q^{100}) \) 16 * q - 8 * q^7 + 32 * q^11 + 16 * q^21 - 8 * q^35 - 16 * q^39 - 16 * q^49 + 32 * q^51 - 80 * q^65 + 48 * q^67 - 32 * q^71 - 16 * q^77 + 32 * q^81 + 64 * q^85 - 8 * q^91 - 64 * q^93 - 64 * q^99

Introduction

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