LMFDB - Embedded newform 1792.2.m.h.1345.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(449,1792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.3091920422$
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} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1345.5
Root			$-0.424637 - 3.22544i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.h.449.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.171192 + 0.171192i) q^{3} +(-0.268425 + 0.268425i) q^{5} -1.00000i q^{7} -2.94139i q^{9} +O(q^{10})$	\(q+(0.171192 + 0.171192i) q^{3} +(-0.268425 + 0.268425i) q^{5} -1.00000i q^{7} -2.94139i q^{9} +(-1.84927 + 1.84927i) q^{11} +(1.63574 + 1.63574i) q^{13} -0.0919045 q^{15} -7.37134 q^{17} +(3.84975 + 3.84975i) q^{19} +(0.171192 - 0.171192i) q^{21} +6.44892i q^{23} +4.85590i q^{25} +(1.01712 - 1.01712i) q^{27} +(3.58700 + 3.58700i) q^{29} +6.10161 q^{31} -0.633164 q^{33} +(0.268425 + 0.268425i) q^{35} +(7.41852 - 7.41852i) q^{37} +0.560052i q^{39} -0.836588i q^{41} +(3.88949 - 3.88949i) q^{43} +(0.789540 + 0.789540i) q^{45} +6.02070 q^{47} -1.00000 q^{49} +(-1.26192 - 1.26192i) q^{51} +(0.575460 - 0.575460i) q^{53} -0.992782i q^{55} +1.31810i q^{57} +(-5.33013 + 5.33013i) q^{59} +(0.929862 + 0.929862i) q^{61} -2.94139 q^{63} -0.878144 q^{65} +(6.21819 + 6.21819i) q^{67} +(-1.10401 + 1.10401i) q^{69} +11.4285i q^{71} -3.68616i q^{73} +(-0.831293 + 0.831293i) q^{75} +(1.84927 + 1.84927i) q^{77} +4.21672 q^{79} -8.47591 q^{81} +(12.0147 + 12.0147i) q^{83} +(1.97865 - 1.97865i) q^{85} +1.22813i q^{87} -9.32780i q^{89} +(1.63574 - 1.63574i) q^{91} +(1.04455 + 1.04455i) q^{93} -2.06673 q^{95} -13.9032 q^{97} +(5.43943 + 5.43943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^3 + 4 * q^5	$ 16 q + 4 q^{3} + 4 q^{5} - 8 q^{11} - 12 q^{13} - 8 q^{17} + 4 q^{19} + 4 q^{21} - 56 q^{27} - 8 q^{31} + 16 q^{33} - 4 q^{35} + 8 q^{37} - 24 q^{43} + 36 q^{45} - 40 q^{47} - 16 q^{49} + 24 q^{51} + 32 q^{53} - 4 q^{59} + 20 q^{61} + 24 q^{63} + 72 q^{65} + 32 q^{67} - 56 q^{69} - 28 q^{75} + 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} - 8 q^{93} - 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 + 4 * q^5 - 8 * q^11 - 12 * q^13 - 8 * q^17 + 4 * q^19 + 4 * q^21 - 56 * q^27 - 8 * q^31 + 16 * q^33 - 4 * q^35 + 8 * q^37 - 24 * q^43 + 36 * q^45 - 40 * q^47 - 16 * q^49 + 24 * q^51 + 32 * q^53 - 4 * q^59 + 20 * q^61 + 24 * q^63 + 72 * q^65 + 32 * q^67 - 56 * q^69 - 28 * q^75 + 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 - 8 * q^93 - 80 * q^95 - 72 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.171192	+	0.171192i	0.0988380	+	0.0988380i	0.754797	−	0.655959i	$-0.227735\pi$
$3$	0.171192	+	0.171192i	0.0988380	+	0.0988380i	−0.655959	+	0.754797i	$0.727735\pi$
$4$		0			0
$5$	−0.268425	+	0.268425i	−0.120043	+	0.120043i	−0.764576	−	0.644533i	$-0.777052\pi$
$5$	−0.268425	+	0.268425i	−0.120043	+	0.120043i	0.644533	+	0.764576i	$0.277052\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$		−	2.94139i		−	0.980462i
$10$		0			0
$11$	−1.84927	+	1.84927i	−0.557577	+	0.557577i	−0.928617	−	0.371040i	$-0.879001\pi$
$11$	−1.84927	+	1.84927i	−0.557577	+	0.557577i	0.371040	+	0.928617i	$0.379001\pi$
$12$		0			0
$13$	1.63574	+	1.63574i	0.453672	+	0.453672i	0.896571	−	0.442899i	$-0.146050\pi$
$13$	1.63574	+	1.63574i	0.453672	+	0.453672i	−0.442899	+	0.896571i	$0.646050\pi$
$14$		0			0
$15$	−0.0919045			−0.0237296
$16$		0			0
$17$	−7.37134			−1.78781			−0.893906	−	0.448255i	$-0.852046\pi$
$17$	−7.37134			−1.78781			−0.893906	+	0.448255i	$0.852046\pi$
$18$		0			0
$19$	3.84975	+	3.84975i	0.883193	+	0.883193i	0.993858	−	0.110665i	$-0.0352979\pi$
$19$	3.84975	+	3.84975i	0.883193	+	0.883193i	−0.110665	+	0.993858i	$0.535298\pi$
$20$		0			0
$21$	0.171192	−	0.171192i	0.0373573	−	0.0373573i
$22$		0			0
$23$			6.44892i			1.34469i	0.740236	+	0.672347i	$0.234714\pi$
$23$			6.44892i			1.34469i	−0.740236	+	0.672347i	$0.765286\pi$
$24$		0			0
$25$			4.85590i			0.971179i
$26$		0			0
$27$	1.01712	−	1.01712i	0.195745	−	0.195745i
$28$		0			0
$29$	3.58700	+	3.58700i	0.666089	+	0.666089i	0.956808	−	0.290720i	$-0.0938947\pi$
$29$	3.58700	+	3.58700i	0.666089	+	0.666089i	−0.290720	+	0.956808i	$0.593895\pi$
$30$		0			0
$31$	6.10161			1.09588			0.547941	−	0.836517i	$-0.315412\pi$
$31$	6.10161			1.09588			0.547941	+	0.836517i	$0.315412\pi$
$32$		0			0
$33$	−0.633164			−0.110220
$34$		0			0
$35$	0.268425	+	0.268425i	0.0453720	+	0.0453720i
$36$		0			0
$37$	7.41852	−	7.41852i	1.21960	−	1.21960i	0.251825	−	0.967773i	$-0.418969\pi$
$37$	7.41852	−	7.41852i	1.21960	−	1.21960i	0.967773	−	0.251825i	$-0.0810307\pi$
$38$		0			0
$39$			0.560052i			0.0896801i
$40$		0			0
$41$		−	0.836588i		−	0.130653i	−0.997864	−	0.0653265i	$-0.979191\pi$
$41$		−	0.836588i		−	0.130653i	0.997864	−	0.0653265i	$-0.0208089\pi$
$42$		0			0
$43$	3.88949	−	3.88949i	0.593141	−	0.593141i	−0.345337	−	0.938479i	$-0.612236\pi$
$43$	3.88949	−	3.88949i	0.593141	−	0.593141i	0.938479	+	0.345337i	$0.112236\pi$
$44$		0			0
$45$	0.789540	+	0.789540i	0.117698	+	0.117698i
$46$		0			0
$47$	6.02070			0.878209			0.439104	−	0.898436i	$-0.355296\pi$
$47$	6.02070			0.878209			0.439104	+	0.898436i	$0.355296\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−1.26192	−	1.26192i	−0.176704	−	0.176704i
$52$		0			0
$53$	0.575460	−	0.575460i	0.0790455	−	0.0790455i	−0.666479	−	0.745524i	$-0.732199\pi$
$53$	0.575460	−	0.575460i	0.0790455	−	0.0790455i	0.745524	+	0.666479i	$0.232199\pi$
$54$		0			0
$55$		−	0.992782i		−	0.133867i
$56$		0			0
$57$			1.31810i			0.174586i
$58$		0			0
$59$	−5.33013	+	5.33013i	−0.693924	+	0.693924i	−0.963093	−	0.269169i	$-0.913251\pi$
$59$	−5.33013	+	5.33013i	−0.693924	+	0.693924i	0.269169	+	0.963093i	$0.413251\pi$
$60$		0			0
$61$	0.929862	+	0.929862i	0.119057	+	0.119057i	0.764125	−	0.645068i	$-0.223171\pi$
$61$	0.929862	+	0.929862i	0.119057	+	0.119057i	−0.645068	+	0.764125i	$0.723171\pi$
$62$		0			0
$63$	−2.94139			−0.370580
$64$		0			0
$65$	−0.878144			−0.108920
$66$		0			0
$67$	6.21819	+	6.21819i	0.759672	+	0.759672i	0.976263	−	0.216590i	$-0.0694935\pi$
$67$	6.21819	+	6.21819i	0.759672	+	0.759672i	−0.216590	+	0.976263i	$0.569494\pi$
$68$		0			0
$69$	−1.10401	+	1.10401i	−0.132907	+	0.132907i
$70$		0			0
$71$			11.4285i			1.35631i	0.734919	+	0.678155i	$0.237220\pi$
$71$			11.4285i			1.35631i	−0.734919	+	0.678155i	$0.762780\pi$
$72$		0			0
$73$		−	3.68616i		−	0.431433i	−0.976456	−	0.215716i	$-0.930791\pi$
$73$		−	3.68616i		−	0.431433i	0.976456	−	0.215716i	$-0.0692087\pi$
$74$		0			0
$75$	−0.831293	+	0.831293i	−0.0959895	+	0.0959895i
$76$		0			0
$77$	1.84927	+	1.84927i	0.210744	+	0.210744i
$78$		0			0
$79$	4.21672			0.474418			0.237209	−	0.971459i	$-0.423767\pi$
$79$	4.21672			0.474418			0.237209	+	0.971459i	$0.423767\pi$
$80$		0			0
$81$	−8.47591			−0.941768
$82$		0			0
$83$	12.0147	+	12.0147i	1.31878	+	1.31878i	0.914742	+	0.404038i	$0.132393\pi$
$83$	12.0147	+	12.0147i	1.31878	+	1.31878i	0.404038	+	0.914742i	$0.367607\pi$
$84$		0			0
$85$	1.97865	−	1.97865i	0.214614	−	0.214614i
$86$		0			0
$87$			1.22813i			0.131670i
$88$		0			0
$89$		−	9.32780i		−	0.988745i	−0.869250	−	0.494373i	$-0.835398\pi$
$89$		−	9.32780i		−	0.988745i	0.869250	−	0.494373i	$-0.164602\pi$
$90$		0			0
$91$	1.63574	−	1.63574i	0.171472	−	0.171472i
$92$		0			0
$93$	1.04455	+	1.04455i	0.108315	+	0.108315i
$94$		0			0
$95$	−2.06673			−0.212043
$96$		0			0
$97$	−13.9032			−1.41166			−0.705828	−	0.708384i	$-0.749425\pi$
$97$	−13.9032			−1.41166			−0.705828	+	0.708384i	$0.749425\pi$
$98$		0			0
$99$	5.43943	+	5.43943i	0.546683	+	0.546683i
$100$		0			0
$101$	0.813911	−	0.813911i	0.0809872	−	0.0809872i	−0.665453	−	0.746440i	$-0.731762\pi$
$101$	0.813911	−	0.813911i	0.0809872	−	0.0809872i	0.746440	+	0.665453i	$0.231762\pi$
$102$		0			0
$103$			8.39975i			0.827652i	0.910356	+	0.413826i	$0.135808\pi$
$103$			8.39975i			0.827652i	−0.910356	+	0.413826i	$0.864192\pi$
$104$		0			0
$105$			0.0919045i			0.00896896i
$106$		0			0
$107$	0.705176	−	0.705176i	0.0681719	−	0.0681719i	−0.672199	−	0.740371i	$-0.734650\pi$
$107$	0.705176	−	0.705176i	0.0681719	−	0.0681719i	0.740371	+	0.672199i	$0.234650\pi$
$108$		0			0
$109$	12.1263	+	12.1263i	1.16149	+	1.16149i	0.984150	+	0.177337i	$0.0567481\pi$
$109$	12.1263	+	12.1263i	1.16149	+	1.16149i	0.177337	+	0.984150i	$0.443252\pi$
$110$		0			0
$111$	2.53999			0.241085
$112$		0			0
$113$	−3.51705			−0.330856			−0.165428	−	0.986222i	$-0.552901\pi$
$113$	−3.51705			−0.330856			−0.165428	+	0.986222i	$0.552901\pi$
$114$		0			0
$115$	−1.73105	−	1.73105i	−0.161421	−	0.161421i
$116$		0			0
$117$	4.81133	−	4.81133i	0.444808	−	0.444808i
$118$		0			0
$119$			7.37134i			0.675729i
$120$		0			0
$121$			4.16036i			0.378215i
$122$		0			0
$123$	0.143218	−	0.143218i	0.0129135	−	0.0129135i
$124$		0			0
$125$	−2.64556	−	2.64556i	−0.236626	−	0.236626i
$126$		0			0
$127$	5.86352			0.520303			0.260152	−	0.965568i	$-0.416227\pi$
$127$	5.86352			0.520303			0.260152	+	0.965568i	$0.416227\pi$
$128$		0			0
$129$	1.33170			0.117250
$130$		0			0
$131$	−7.79029	−	7.79029i	−0.680641	−	0.680641i	0.279504	−	0.960145i	$-0.409830\pi$
$131$	−7.79029	−	7.79029i	−0.680641	−	0.680641i	−0.960145	+	0.279504i	$0.909830\pi$
$132$		0			0
$133$	3.84975	−	3.84975i	0.333816	−	0.333816i
$134$		0			0
$135$			0.546040i			0.0469957i
$136$		0			0
$137$		−	6.34879i		−	0.542414i	−0.962521	−	0.271207i	$-0.912577\pi$
$137$		−	6.34879i		−	0.542414i	0.962521	−	0.271207i	$-0.0874228\pi$
$138$		0			0
$139$	−14.1119	+	14.1119i	−1.19696	+	1.19696i	−0.221885	+	0.975073i	$0.571221\pi$
$139$	−14.1119	+	14.1119i	−1.19696	+	1.19696i	−0.975073	+	0.221885i	$0.928779\pi$
$140$		0			0
$141$	1.03070	+	1.03070i	0.0868004	+	0.0868004i
$142$		0			0
$143$	−6.04986			−0.505914
$144$		0			0
$145$	−1.92568			−0.159919
$146$		0			0
$147$	−0.171192	−	0.171192i	−0.0141197	−	0.0141197i
$148$		0			0
$149$	−7.08686	+	7.08686i	−0.580578	+	0.580578i	−0.935062	−	0.354484i	$-0.884657\pi$
$149$	−7.08686	+	7.08686i	−0.580578	+	0.580578i	0.354484	+	0.935062i	$0.384657\pi$
$150$		0			0
$151$		−	8.28521i		−	0.674241i	−0.941462	−	0.337120i	$-0.890547\pi$
$151$		−	8.28521i		−	0.674241i	0.941462	−	0.337120i	$-0.109453\pi$
$152$		0			0
$153$			21.6819i			1.75288i
$154$		0			0
$155$	−1.63782	+	1.63782i	−0.131553	+	0.131553i
$156$		0			0
$157$	−7.68999	−	7.68999i	−0.613728	−	0.613728i	0.330188	−	0.943915i	$-0.392888\pi$
$157$	−7.68999	−	7.68999i	−0.613728	−	0.613728i	−0.943915	+	0.330188i	$0.892888\pi$
$158$		0			0
$159$	0.197029			0.0156254
$160$		0			0
$161$	6.44892			0.508246
$162$		0			0
$163$	4.46953	+	4.46953i	0.350081	+	0.350081i	0.860140	−	0.510059i	$-0.170376\pi$
$163$	4.46953	+	4.46953i	0.350081	+	0.350081i	−0.510059	+	0.860140i	$0.670376\pi$
$164$		0			0
$165$	0.169957	−	0.169957i	0.0132311	−	0.0132311i
$166$		0			0
$167$		−	12.8905i		−	0.997493i	−0.866748	−	0.498747i	$-0.833794\pi$
$167$		−	12.8905i		−	0.997493i	0.866748	−	0.498747i	$-0.166206\pi$
$168$		0			0
$169$		−	7.64873i		−	0.588364i
$170$		0			0
$171$	11.3236	−	11.3236i	0.865938	−	0.865938i
$172$		0			0
$173$	6.21257	+	6.21257i	0.472333	+	0.472333i	0.902669	−	0.430336i	$-0.141605\pi$
$173$	6.21257	+	6.21257i	0.472333	+	0.472333i	−0.430336	+	0.902669i	$0.641605\pi$
$174$		0			0
$175$	4.85590			0.367071
$176$		0			0
$177$	−1.82496			−0.137172
$178$		0			0
$179$	−2.03654	−	2.03654i	−0.152218	−	0.152218i	0.626890	−	0.779108i	$-0.284328\pi$
$179$	−2.03654	−	2.03654i	−0.152218	−	0.152218i	−0.779108	+	0.626890i	$0.784328\pi$
$180$		0			0
$181$	−16.7116	+	16.7116i	−1.24217	+	1.24217i	−0.283064	+	0.959101i	$0.591351\pi$
$181$	−16.7116	+	16.7116i	−1.24217	+	1.24217i	−0.959101	+	0.283064i	$0.908649\pi$
$182$		0			0
$183$			0.318371i			0.0235346i
$184$		0			0
$185$			3.98263i			0.292809i
$186$		0			0
$187$	13.6316	−	13.6316i	0.996843	−	0.996843i
$188$		0			0
$189$	−1.01712	−	1.01712i	−0.0739846	−	0.0739846i
$190$		0			0
$191$	−5.11015			−0.369758			−0.184879	−	0.982761i	$-0.559189\pi$
$191$	−5.11015			−0.369758			−0.184879	+	0.982761i	$0.559189\pi$
$192$		0			0
$193$	0.676235			0.0486765			0.0243382	−	0.999704i	$-0.492252\pi$
$193$	0.676235			0.0486765			0.0243382	+	0.999704i	$0.492252\pi$
$194$		0			0
$195$	−0.150332	−	0.150332i	−0.0107655	−	0.0107655i
$196$		0			0
$197$	14.3449	−	14.3449i	1.02203	−	1.02203i	0.0222782	−	0.999752i	$-0.492908\pi$
$197$	14.3449	−	14.3449i	1.02203	−	1.02203i	0.999752	−	0.0222782i	$-0.00709197\pi$
$198$		0			0
$199$			4.94660i			0.350655i	0.984510	+	0.175328i	$0.0560984\pi$
$199$			4.94660i			0.350655i	−0.984510	+	0.175328i	$0.943902\pi$
$200$		0			0
$201$			2.12901i			0.150169i
$202$		0			0
$203$	3.58700	−	3.58700i	0.251758	−	0.251758i
$204$		0			0
$205$	0.224561	+	0.224561i	0.0156840	+	0.0156840i
$206$		0			0
$207$	18.9688			1.31842
$208$		0			0
$209$	−14.2385			−0.984897
$210$		0			0
$211$	−4.67810	−	4.67810i	−0.322054	−	0.322054i	0.527501	−	0.849555i	$-0.323129\pi$
$211$	−4.67810	−	4.67810i	−0.322054	−	0.322054i	−0.849555	+	0.527501i	$0.823129\pi$
$212$		0			0
$213$	−1.95647	+	1.95647i	−0.134055	+	0.134055i
$214$		0			0
$215$			2.08807i			0.142405i
$216$		0			0
$217$		−	6.10161i		−	0.414204i
$218$		0			0
$219$	0.631044	−	0.631044i	0.0426420	−	0.0426420i
$220$		0			0
$221$	−12.0576	−	12.0576i	−0.811080	−	0.811080i
$222$		0			0
$223$	4.16691			0.279037			0.139518	−	0.990219i	$-0.455445\pi$
$223$	4.16691			0.279037			0.139518	+	0.990219i	$0.455445\pi$
$224$		0			0
$225$	14.2831			0.952204
$226$		0			0
$227$	12.1022	+	12.1022i	0.803248	+	0.803248i	0.983602	−	0.180353i	$-0.0577241\pi$
$227$	12.1022	+	12.1022i	0.803248	+	0.803248i	−0.180353	+	0.983602i	$0.557724\pi$
$228$		0			0
$229$	13.5287	−	13.5287i	0.893999	−	0.893999i	−0.100898	−	0.994897i	$-0.532171\pi$
$229$	13.5287	−	13.5287i	0.893999	−	0.893999i	0.994897	+	0.100898i	$0.0321714\pi$
$230$		0			0
$231$			0.633164i			0.0416591i
$232$		0			0
$233$		−	13.3857i		−	0.876924i	−0.898750	−	0.438462i	$-0.855523\pi$
$233$		−	13.3857i		−	0.876924i	0.898750	−	0.438462i	$-0.144477\pi$
$234$		0			0
$235$	−1.61610	+	1.61610i	−0.105423	+	0.105423i
$236$		0			0
$237$	0.721871	+	0.721871i	0.0468905	+	0.0468905i
$238$		0			0
$239$	−20.6475			−1.33558			−0.667788	−	0.744352i	$-0.732759\pi$
$239$	−20.6475			−1.33558			−0.667788	+	0.744352i	$0.732759\pi$
$240$		0			0
$241$	−0.401861			−0.0258861			−0.0129431	−	0.999916i	$-0.504120\pi$
$241$	−0.401861			−0.0258861			−0.0129431	+	0.999916i	$0.504120\pi$
$242$		0			0
$243$	−4.50237	−	4.50237i	−0.288827	−	0.288827i
$244$		0			0
$245$	0.268425	−	0.268425i	0.0171490	−	0.0171490i
$246$		0			0
$247$			12.5944i			0.801360i
$248$		0			0
$249$			4.11364i			0.260691i
$250$		0			0
$251$	−9.25468	+	9.25468i	−0.584150	+	0.584150i	−0.936041	−	0.351891i	$-0.885539\pi$
$251$	−9.25468	+	9.25468i	−0.584150	+	0.584150i	0.351891	+	0.936041i	$0.385539\pi$
$252$		0			0
$253$	−11.9258	−	11.9258i	−0.749771	−	0.749771i
$254$		0			0
$255$	0.677459			0.0424241
$256$		0			0
$257$	16.3273			1.01847			0.509234	−	0.860628i	$-0.329929\pi$
$257$	16.3273			1.01847			0.509234	+	0.860628i	$0.329929\pi$
$258$		0			0
$259$	−7.41852	−	7.41852i	−0.460965	−	0.460965i
$260$		0			0
$261$	10.5507	−	10.5507i	0.653075	−	0.653075i
$262$		0			0
$263$		−	13.3352i		−	0.822284i	−0.911571	−	0.411142i	$-0.865130\pi$
$263$		−	13.3352i		−	0.822284i	0.911571	−	0.411142i	$-0.134870\pi$
$264$		0			0
$265$			0.308935i			0.0189777i
$266$		0			0
$267$	1.59685	−	1.59685i	0.0977256	−	0.0977256i
$268$		0			0
$269$	19.3277	+	19.3277i	1.17843	+	1.17843i	0.980145	+	0.198284i	$0.0635367\pi$
$269$	19.3277	+	19.3277i	1.17843	+	1.17843i	0.198284	+	0.980145i	$0.436463\pi$
$270$		0			0
$271$	−24.5968			−1.49415			−0.747074	−	0.664741i	$-0.768542\pi$
$271$	−24.5968			−1.49415			−0.747074	+	0.664741i	$0.768542\pi$
$272$		0			0
$273$	0.560052			0.0338959
$274$		0			0
$275$	−8.97989	−	8.97989i	−0.541508	−	0.541508i
$276$		0			0
$277$	−17.9974	+	17.9974i	−1.08136	+	1.08136i	−0.0849786	+	0.996383i	$0.527082\pi$
$277$	−17.9974	+	17.9974i	−1.08136	+	1.08136i	−0.996383	+	0.0849786i	$0.972918\pi$
$278$		0			0
$279$		−	17.9472i		−	1.07447i
$280$		0			0
$281$		−	13.7357i		−	0.819404i	−0.912219	−	0.409702i	$-0.865633\pi$
$281$		−	13.7357i		−	0.819404i	0.912219	−	0.409702i	$-0.134367\pi$
$282$		0			0
$283$	−10.0342	+	10.0342i	−0.596473	+	0.596473i	−0.939372	−	0.342900i	$-0.888591\pi$
$283$	−10.0342	+	10.0342i	−0.596473	+	0.596473i	0.342900	+	0.939372i	$0.388591\pi$
$284$		0			0
$285$	−0.353810	−	0.353810i	−0.0209579	−	0.0209579i
$286$		0			0
$287$	−0.836588			−0.0493822
$288$		0			0
$289$	37.3366			2.19627
$290$		0			0
$291$	−2.38012	−	2.38012i	−0.139525	−	0.139525i
$292$		0			0
$293$	−19.7376	+	19.7376i	−1.15308	+	1.15308i	−0.167151	+	0.985931i	$0.553457\pi$
$293$	−19.7376	+	19.7376i	−1.15308	+	1.15308i	−0.985931	+	0.167151i	$0.946543\pi$
$294$		0			0
$295$		−	2.86148i		−	0.166602i
$296$		0			0
$297$			3.76187i			0.218286i
$298$		0			0
$299$	−10.5487	+	10.5487i	−0.610050	+	0.610050i
$300$		0			0
$301$	−3.88949	−	3.88949i	−0.224186	−	0.224186i
$302$		0			0
$303$	0.278671			0.0160092
$304$		0			0
$305$	−0.499195			−0.0285838
$306$		0			0
$307$	−3.14804	−	3.14804i	−0.179668	−	0.179668i	0.611543	−	0.791211i	$-0.290549\pi$
$307$	−3.14804	−	3.14804i	−0.179668	−	0.179668i	−0.791211	+	0.611543i	$0.790549\pi$
$308$		0			0
$309$	−1.43797	+	1.43797i	−0.0818035	+	0.0818035i
$310$		0			0
$311$		−	32.2711i		−	1.82993i	−0.403535	−	0.914964i	$-0.632219\pi$
$311$		−	32.2711i		−	1.82993i	0.403535	−	0.914964i	$-0.367781\pi$
$312$		0			0
$313$			22.3372i			1.26257i	0.775550	+	0.631286i	$0.217473\pi$
$313$			22.3372i			1.26257i	−0.775550	+	0.631286i	$0.782527\pi$
$314$		0			0
$315$	0.789540	−	0.789540i	0.0444856	−	0.0444856i
$316$		0			0
$317$	0.148346	+	0.148346i	0.00833196	+	0.00833196i	0.711260	−	0.702929i	$-0.248125\pi$
$317$	0.148346	+	0.148346i	0.00833196	+	0.00833196i	−0.702929	+	0.711260i	$0.748125\pi$
$318$		0			0
$319$	−13.2667			−0.742792
$320$		0			0
$321$	0.241442			0.0134760
$322$		0			0
$323$	−28.3778	−	28.3778i	−1.57898	−	1.57898i
$324$		0			0
$325$	−7.94297	+	7.94297i	−0.440597	+	0.440597i
$326$		0			0
$327$			4.15186i			0.229598i
$328$		0			0
$329$		−	6.02070i		−	0.331932i
$330$		0			0
$331$	20.1427	−	20.1427i	1.10714	−	1.10714i	0.113618	−	0.993525i	$-0.463756\pi$
$331$	20.1427	−	20.1427i	1.10714	−	1.10714i	0.993525	−	0.113618i	$-0.0362440\pi$
$332$		0			0
$333$	−21.8207	−	21.8207i	−1.19577	−	1.19577i
$334$		0			0
$335$	−3.33823			−0.182387
$336$		0			0
$337$	6.83335			0.372236			0.186118	−	0.982527i	$-0.440409\pi$
$337$	6.83335			0.372236			0.186118	+	0.982527i	$0.440409\pi$
$338$		0			0
$339$	−0.602092	−	0.602092i	−0.0327012	−	0.0327012i
$340$		0			0
$341$	−11.2836	+	11.2836i	−0.611039	+	0.611039i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	0.592685i		−	0.0319091i
$346$		0			0
$347$	−19.8489	+	19.8489i	−1.06554	+	1.06554i	−0.0678488	+	0.997696i	$0.521614\pi$
$347$	−19.8489	+	19.8489i	−1.06554	+	1.06554i	−0.997696	+	0.0678488i	$0.978386\pi$
$348$		0			0
$349$	−16.6099	−	16.6099i	−0.889105	−	0.889105i	0.105332	−	0.994437i	$-0.466409\pi$
$349$	−16.6099	−	16.6099i	−0.889105	−	0.889105i	−0.994437	+	0.105332i	$0.966409\pi$
$350$		0			0
$351$	3.32748			0.177608
$352$		0			0
$353$	5.41293			0.288101			0.144051	−	0.989570i	$-0.453987\pi$
$353$	5.41293			0.288101			0.144051	+	0.989570i	$0.453987\pi$
$354$		0			0
$355$	−3.06768	−	3.06768i	−0.162816	−	0.162816i
$356$		0			0
$357$	−1.26192	+	1.26192i	−0.0667878	+	0.0667878i
$358$		0			0
$359$			29.1561i			1.53880i	0.638768	+	0.769399i	$0.279444\pi$
$359$			29.1561i			1.53880i	−0.638768	+	0.769399i	$0.720556\pi$
$360$		0			0
$361$			10.6412i			0.560061i
$362$		0			0
$363$	−0.712223	+	0.712223i	−0.0373820	+	0.0373820i
$364$		0			0
$365$	0.989457	+	0.989457i	0.0517906	+	0.0517906i
$366$		0			0
$367$	−6.14461			−0.320746			−0.160373	−	0.987056i	$-0.551270\pi$
$367$	−6.14461			−0.320746			−0.160373	+	0.987056i	$0.551270\pi$
$368$		0			0
$369$	−2.46073			−0.128100
$370$		0			0
$371$	−0.575460	−	0.575460i	−0.0298764	−	0.0298764i
$372$		0			0
$373$	20.9348	−	20.9348i	1.08396	−	1.08396i	0.0878283	−	0.996136i	$-0.472007\pi$
$373$	20.9348	−	20.9348i	1.08396	−	1.08396i	0.996136	−	0.0878283i	$-0.0279927\pi$
$374$		0			0
$375$		−	0.905802i		−	0.0467754i
$376$		0			0
$377$			11.7348i			0.604371i
$378$		0			0
$379$	23.6398	−	23.6398i	1.21429	−	1.21429i	0.244693	−	0.969601i	$-0.421313\pi$
$379$	23.6398	−	23.6398i	1.21429	−	1.21429i	0.969601	−	0.244693i	$-0.0786872\pi$
$380$		0			0
$381$	1.00379	+	1.00379i	0.0514257	+	0.0514257i
$382$		0			0
$383$	6.99982			0.357674			0.178837	−	0.983879i	$-0.442767\pi$
$383$	6.99982			0.357674			0.178837	+	0.983879i	$0.442767\pi$
$384$		0			0
$385$	−0.992782			−0.0505968
$386$		0			0
$387$	−11.4405	−	11.4405i	−0.581552	−	0.581552i
$388$		0			0
$389$	−15.4838	+	15.4838i	−0.785060	+	0.785060i	−0.980680	−	0.195620i	$-0.937328\pi$
$389$	−15.4838	+	15.4838i	−0.785060	+	0.785060i	0.195620	+	0.980680i	$0.437328\pi$
$390$		0			0
$391$		−	47.5372i		−	2.40406i
$392$		0			0
$393$		−	2.66728i		−	0.134546i
$394$		0			0
$395$	−1.13187	+	1.13187i	−0.0569506	+	0.0569506i
$396$		0			0
$397$	−5.65923	−	5.65923i	−0.284029	−	0.284029i	0.550685	−	0.834713i	$-0.314367\pi$
$397$	−5.65923	−	5.65923i	−0.284029	−	0.284029i	−0.834713	+	0.550685i	$0.814367\pi$
$398$		0			0
$399$	1.31810			0.0659874
$400$		0			0
$401$	26.7191			1.33429			0.667144	−	0.744929i	$-0.267517\pi$
$401$	26.7191			1.33429			0.667144	+	0.744929i	$0.267517\pi$
$402$		0			0
$403$	9.98063	+	9.98063i	0.497171	+	0.497171i
$404$		0			0
$405$	2.27514	−	2.27514i	0.113053	−	0.113053i
$406$		0			0
$407$			27.4378i			1.36004i
$408$		0			0
$409$			20.7456i			1.02581i	0.858447	+	0.512903i	$0.171430\pi$
$409$			20.7456i			1.02581i	−0.858447	+	0.512903i	$0.828570\pi$
$410$		0			0
$411$	1.08687	−	1.08687i	0.0536111	−	0.0536111i
$412$		0			0
$413$	5.33013	+	5.33013i	0.262279	+	0.262279i
$414$		0			0
$415$	−6.45006			−0.316621
$416$		0			0
$417$	−4.83171			−0.236610
$418$		0			0
$419$	6.11779	+	6.11779i	0.298874	+	0.298874i	0.840573	−	0.541699i	$-0.182219\pi$
$419$	6.11779	+	6.11779i	0.298874	+	0.298874i	−0.541699	+	0.840573i	$0.682219\pi$
$420$		0			0
$421$	9.03252	−	9.03252i	0.440218	−	0.440218i	−0.451867	−	0.892085i	$-0.649242\pi$
$421$	9.03252	−	9.03252i	0.440218	−	0.440218i	0.892085	+	0.451867i	$0.149242\pi$
$422$		0			0
$423$		−	17.7092i		−	0.861050i
$424$		0			0
$425$		−	35.7945i		−	1.73629i
$426$		0			0
$427$	0.929862	−	0.929862i	0.0449992	−	0.0449992i
$428$		0			0
$429$	−1.03569	−	1.03569i	−0.0500036	−	0.0500036i
$430$		0			0
$431$	−2.81338			−0.135516			−0.0677579	−	0.997702i	$-0.521585\pi$
$431$	−2.81338			−0.135516			−0.0677579	+	0.997702i	$0.521585\pi$
$432$		0			0
$433$	−20.6954			−0.994558			−0.497279	−	0.867591i	$-0.665667\pi$
$433$	−20.6954			−0.994558			−0.497279	+	0.867591i	$0.665667\pi$
$434$		0			0
$435$	−0.329661	−	0.329661i	−0.0158060	−	0.0158060i
$436$		0			0
$437$	−24.8267	+	24.8267i	−1.18762	+	1.18762i
$438$		0			0
$439$		−	15.6336i		−	0.746151i	−0.927801	−	0.373075i	$-0.878303\pi$
$439$		−	15.6336i		−	0.746151i	0.927801	−	0.373075i	$-0.121697\pi$
$440$		0			0
$441$			2.94139i			0.140066i
$442$		0			0
$443$	18.6608	−	18.6608i	0.886603	−	0.886603i	−0.107592	−	0.994195i	$-0.534314\pi$
$443$	18.6608	−	18.6608i	0.886603	−	0.886603i	0.994195	+	0.107592i	$0.0343141\pi$
$444$		0			0
$445$	2.50381	+	2.50381i	0.118692	+	0.118692i
$446$		0			0
$447$	−2.42643			−0.114766
$448$		0			0
$449$	26.8536			1.26730			0.633650	−	0.773620i	$-0.281556\pi$
$449$	26.8536			1.26730			0.633650	+	0.773620i	$0.281556\pi$
$450$		0			0
$451$	1.54708	+	1.54708i	0.0728492	+	0.0728492i
$452$		0			0
$453$	1.41837	−	1.41837i	0.0666406	−	0.0666406i
$454$		0			0
$455$			0.878144i			0.0411680i
$456$		0			0
$457$			0.385896i			0.0180514i	0.999959	+	0.00902572i	$0.00287302\pi$
$457$			0.385896i			0.0180514i	−0.999959	+	0.00902572i	$0.997127\pi$
$458$		0			0
$459$	−7.49754	+	7.49754i	−0.349955	+	0.349955i
$460$		0			0
$461$	2.13650	+	2.13650i	0.0995065	+	0.0995065i	0.755108	−	0.655601i	$-0.227585\pi$
$461$	2.13650	+	2.13650i	0.0995065	+	0.0995065i	−0.655601	+	0.755108i	$0.727585\pi$
$462$		0			0
$463$	32.5560			1.51301			0.756503	−	0.653991i	$-0.226906\pi$
$463$	32.5560			1.51301			0.756503	+	0.653991i	$0.226906\pi$
$464$		0			0
$465$	−0.560766			−0.0260049
$466$		0			0
$467$	−8.00295	−	8.00295i	−0.370332	−	0.370332i	0.497266	−	0.867598i	$-0.334337\pi$
$467$	−8.00295	−	8.00295i	−0.370332	−	0.370332i	−0.867598	+	0.497266i	$0.834337\pi$
$468$		0			0
$469$	6.21819	−	6.21819i	0.287129	−	0.287129i
$470$		0			0
$471$		−	2.63294i		−	0.121319i
$472$		0			0
$473$			14.3855i			0.661444i
$474$		0			0
$475$	−18.6940	+	18.6940i	−0.857739	+	0.857739i
$476$		0			0
$477$	−1.69265	−	1.69265i	−0.0775012	−	0.0775012i
$478$		0			0
$479$	−20.2388			−0.924735			−0.462368	−	0.886688i	$-0.653000\pi$
$479$	−20.2388			−0.924735			−0.462368	+	0.886688i	$0.653000\pi$
$480$		0			0
$481$	24.2695			1.10659
$482$		0			0
$483$	1.10401	+	1.10401i	0.0502341	+	0.0502341i
$484$		0			0
$485$	3.73196	−	3.73196i	0.169459	−	0.169459i
$486$		0			0
$487$		−	36.6988i		−	1.66298i	−0.555537	−	0.831492i	$-0.687487\pi$
$487$		−	36.6988i		−	1.66298i	0.555537	−	0.831492i	$-0.312513\pi$
$488$		0			0
$489$			1.53030i			0.0692026i
$490$		0			0
$491$	−13.6015	+	13.6015i	−0.613829	+	0.613829i	−0.943942	−	0.330113i	$-0.892913\pi$
$491$	−13.6015	+	13.6015i	−0.613829	+	0.613829i	0.330113	+	0.943942i	$0.392913\pi$
$492$		0			0
$493$	−26.4410	−	26.4410i	−1.19084	−	1.19084i
$494$		0			0
$495$	−2.92015			−0.131251
$496$		0			0
$497$	11.4285			0.512637
$498$		0			0
$499$	−24.1970	−	24.1970i	−1.08321	−	1.08321i	−0.996209	−	0.0869972i	$-0.972273\pi$
$499$	−24.1970	−	24.1970i	−1.08321	−	1.08321i	−0.0869972	−	0.996209i	$-0.527727\pi$
$500$		0			0
$501$	2.20675	−	2.20675i	0.0985903	−	0.0985903i
$502$		0			0
$503$		−	13.4123i		−	0.598026i	−0.954249	−	0.299013i	$-0.903343\pi$
$503$		−	13.4123i		−	0.598026i	0.954249	−	0.299013i	$-0.0966574\pi$
$504$		0			0
$505$			0.436947i			0.0194439i
$506$		0			0
$507$	1.30940	−	1.30940i	0.0581527	−	0.0581527i
$508$		0			0
$509$	−18.9792	−	18.9792i	−0.841240	−	0.841240i	0.147781	−	0.989020i	$-0.452787\pi$
$509$	−18.9792	−	18.9792i	−0.841240	−	0.841240i	−0.989020	+	0.147781i	$0.952787\pi$
$510$		0			0
$511$	−3.68616			−0.163066
$512$		0			0
$513$	7.83132			0.345761
$514$		0			0
$515$	−2.25470	−	2.25470i	−0.0993540	−	0.0993540i
$516$		0			0
$517$	−11.1339	+	11.1339i	−0.489669	+	0.489669i
$518$		0			0
$519$			2.12709i			0.0933689i
$520$		0			0
$521$		−	0.00960703i		−	0.000420892i	−1.00000		0.000210446i	$-0.999933\pi$
$521$		−	0.00960703i		−	0.000420892i	1.00000		0.000210446i	$-6.69870e-5\pi$
$522$		0			0
$523$	23.5829	−	23.5829i	1.03121	−	1.03121i	0.0317098	−	0.999497i	$-0.489905\pi$
$523$	23.5829	−	23.5829i	1.03121	−	1.03121i	0.999497	−	0.0317098i	$-0.0100952\pi$
$524$		0			0
$525$	0.831293	+	0.831293i	0.0362806	+	0.0362806i
$526$		0			0
$527$	−44.9770			−1.95923
$528$		0			0
$529$	−18.5886			−0.808201
$530$		0			0
$531$	15.6780	+	15.6780i	0.680366	+	0.680366i
$532$		0			0
$533$	1.36844	−	1.36844i	0.0592736	−	0.0592736i
$534$		0			0
$535$			0.378573i			0.0163671i
$536$		0			0
$537$		−	0.697281i		−	0.0300899i
$538$		0			0
$539$	1.84927	−	1.84927i	0.0796539	−	0.0796539i
$540$		0			0
$541$	−11.6478	−	11.6478i	−0.500776	−	0.500776i	0.410903	−	0.911679i	$-0.365214\pi$
$541$	−11.6478	−	11.6478i	−0.500776	−	0.500776i	−0.911679	+	0.410903i	$0.865214\pi$
$542$		0			0
$543$	−5.72181			−0.245546
$544$		0			0
$545$	−6.50998			−0.278857
$546$		0			0
$547$	−14.0041	−	14.0041i	−0.598773	−	0.598773i	0.341213	−	0.939986i	$-0.389162\pi$
$547$	−14.0041	−	14.0041i	−0.598773	−	0.598773i	−0.939986	+	0.341213i	$0.889162\pi$
$548$		0			0
$549$	2.73508	−	2.73508i	0.116730	−	0.116730i
$550$		0			0
$551$			27.6181i			1.17657i
$552$		0			0
$553$		−	4.21672i		−	0.179313i
$554$		0			0
$555$	−0.681796	+	0.681796i	−0.0289406	+	0.0289406i
$556$		0			0
$557$	24.3807	+	24.3807i	1.03305	+	1.03305i	0.999435	+	0.0336103i	$0.0107005\pi$
$557$	24.3807	+	24.3807i	1.03305	+	1.03305i	0.0336103	+	0.999435i	$0.489299\pi$
$558$		0			0
$559$	12.7244			0.538183
$560$		0			0
$561$	4.66727			0.197052
$562$		0			0
$563$	−26.2789	−	26.2789i	−1.10752	−	1.10752i	−0.993475	−	0.114046i	$-0.963619\pi$
$563$	−26.2789	−	26.2789i	−1.10752	−	1.10752i	−0.114046	−	0.993475i	$-0.536381\pi$
$564$		0			0
$565$	0.944062	−	0.944062i	0.0397170	−	0.0397170i
$566$		0			0
$567$			8.47591i			0.355955i
$568$		0			0
$569$		−	36.8053i		−	1.54296i	−0.636255	−	0.771479i	$-0.719517\pi$
$569$		−	36.8053i		−	1.54296i	0.636255	−	0.771479i	$-0.280483\pi$
$570$		0			0
$571$	23.0536	−	23.0536i	0.964762	−	0.964762i	−0.0346376	−	0.999400i	$-0.511028\pi$
$571$	23.0536	−	23.0536i	0.964762	−	0.964762i	0.999400	+	0.0346376i	$0.0110277\pi$
$572$		0			0
$573$	−0.874820	−	0.874820i	−0.0365461	−	0.0365461i
$574$		0			0
$575$	−31.3153			−1.30594
$576$		0			0
$577$	−3.51057			−0.146147			−0.0730735	−	0.997327i	$-0.523281\pi$
$577$	−3.51057			−0.146147			−0.0730735	+	0.997327i	$0.523281\pi$
$578$		0			0
$579$	0.115766	+	0.115766i	0.00481109	+	0.00481109i
$580$		0			0
$581$	12.0147	−	12.0147i	0.498452	−	0.498452i
$582$		0			0
$583$			2.12837i			0.0881480i
$584$		0			0
$585$			2.58296i			0.106792i
$586$		0			0
$587$	−28.0315	+	28.0315i	−1.15699	+	1.15699i	−0.171865	+	0.985120i	$0.554979\pi$
$587$	−28.0315	+	28.0315i	−1.15699	+	1.15699i	−0.985120	+	0.171865i	$0.945021\pi$
$588$		0			0
$589$	23.4897	+	23.4897i	0.967876	+	0.967876i
$590$		0			0
$591$	4.91147			0.202031
$592$		0			0
$593$	6.27767			0.257793			0.128896	−	0.991658i	$-0.458857\pi$
$593$	6.27767			0.257793			0.128896	+	0.991658i	$0.458857\pi$
$594$		0			0
$595$	−1.97865	−	1.97865i	−0.0811167	−	0.0811167i
$596$		0			0
$597$	−0.846821	+	0.846821i	−0.0346581	+	0.0346581i
$598$		0			0
$599$			10.3600i			0.423300i	0.977346	+	0.211650i	$0.0678836\pi$
$599$			10.3600i			0.423300i	−0.977346	+	0.211650i	$0.932116\pi$
$600$		0			0
$601$			23.9656i			0.977576i	0.872403	+	0.488788i	$0.162561\pi$
$601$			23.9656i			0.977576i	−0.872403	+	0.488788i	$0.837439\pi$
$602$		0			0
$603$	18.2901	−	18.2901i	0.744830	−	0.744830i
$604$		0			0
$605$	−1.11674	−	1.11674i	−0.0454021	−	0.0454021i
$606$		0			0
$607$	14.4285			0.585633			0.292817	−	0.956169i	$-0.405407\pi$
$607$	14.4285			0.585633			0.292817	+	0.956169i	$0.405407\pi$
$608$		0			0
$609$	1.22813			0.0497665
$610$		0			0
$611$	9.84828	+	9.84828i	0.398419	+	0.398419i
$612$		0			0
$613$	3.13825	−	3.13825i	0.126753	−	0.126753i	−0.640885	−	0.767637i	$-0.721432\pi$
$613$	3.13825	−	3.13825i	0.126753	−	0.126753i	0.767637	+	0.640885i	$0.221432\pi$
$614$		0			0
$615$			0.0768862i			0.00310035i
$616$		0			0
$617$		−	15.7644i		−	0.634651i	−0.948317	−	0.317325i	$-0.897215\pi$
$617$		−	15.7644i		−	0.634651i	0.948317	−	0.317325i	$-0.102785\pi$
$618$		0			0
$619$	−6.16647	+	6.16647i	−0.247851	+	0.247851i	−0.820088	−	0.572237i	$-0.806076\pi$
$619$	−6.16647	+	6.16647i	−0.247851	+	0.247851i	0.572237	+	0.820088i	$0.306076\pi$
$620$		0			0
$621$	6.55934	+	6.55934i	0.263217	+	0.263217i
$622$		0			0
$623$	−9.32780			−0.373711
$624$		0			0
$625$	−22.8592			−0.914369
$626$		0			0
$627$	−2.43752	−	2.43752i	−0.0973453	−	0.0973453i
$628$		0			0
$629$	−54.6844	+	54.6844i	−2.18041	+	2.18041i
$630$		0			0
$631$			30.5796i			1.21736i	0.793417	+	0.608678i	$0.208300\pi$
$631$			30.5796i			1.21736i	−0.793417	+	0.608678i	$0.791700\pi$
$632$		0			0
$633$		−	1.60171i		−	0.0636623i
$634$		0			0
$635$	−1.57391	+	1.57391i	−0.0624588	+	0.0624588i
$636$		0			0
$637$	−1.63574	−	1.63574i	−0.0648103	−	0.0648103i
$638$		0			0
$639$	33.6155			1.32981
$640$		0			0
$641$	−18.6228			−0.735556			−0.367778	−	0.929914i	$-0.619881\pi$
$641$	−18.6228			−0.735556			−0.367778	+	0.929914i	$0.619881\pi$
$642$		0			0
$643$	27.8340	+	27.8340i	1.09766	+	1.09766i	0.994683	+	0.102981i	$0.0328381\pi$
$643$	27.8340	+	27.8340i	1.09766	+	1.09766i	0.102981	+	0.994683i	$0.467162\pi$
$644$		0			0
$645$	−0.357461	+	0.357461i	−0.0140750	+	0.0140750i
$646$		0			0
$647$			29.2607i			1.15036i	0.818029	+	0.575178i	$0.195067\pi$
$647$			29.2607i			1.15036i	−0.818029	+	0.575178i	$0.804933\pi$
$648$		0			0
$649$		−	19.7138i		−	0.773833i
$650$		0			0
$651$	1.04455	−	1.04455i	0.0409392	−	0.0409392i
$652$		0			0
$653$	17.3825	+	17.3825i	0.680229	+	0.680229i	0.960052	−	0.279822i	$-0.0902756\pi$
$653$	17.3825	+	17.3825i	0.680229	+	0.680229i	−0.279822	+	0.960052i	$0.590276\pi$
$654$		0			0
$655$	4.18221			0.163413
$656$		0			0
$657$	−10.8424			−0.423004
$658$		0			0
$659$	27.7030	+	27.7030i	1.07916	+	1.07916i	0.996585	+	0.0825717i	$0.0263134\pi$
$659$	27.7030	+	27.7030i	1.07916	+	1.07916i	0.0825717	+	0.996585i	$0.473687\pi$
$660$		0			0
$661$	18.7539	−	18.7539i	0.729443	−	0.729443i	−0.241066	−	0.970509i	$-0.577497\pi$
$661$	18.7539	−	18.7539i	0.729443	−	0.729443i	0.970509	+	0.241066i	$0.0774970\pi$
$662$		0			0
$663$		−	4.12833i		−	0.160331i
$664$		0			0
$665$			2.06673i			0.0801445i
$666$		0			0
$667$	−23.1323	+	23.1323i	−0.895685	+	0.895685i
$668$		0			0
$669$	0.713343	+	0.713343i	0.0275794	+	0.0275794i
$670$		0			0
$671$	−3.43914			−0.132767
$672$		0			0
$673$	8.89179			0.342753			0.171377	−	0.985206i	$-0.445179\pi$
$673$	8.89179			0.342753			0.171377	+	0.985206i	$0.445179\pi$
$674$		0			0
$675$	4.93903	+	4.93903i	0.190103	+	0.190103i
$676$		0			0
$677$	23.0023	−	23.0023i	0.884049	−	0.884049i	−0.109895	−	0.993943i	$-0.535051\pi$
$677$	23.0023	−	23.0023i	0.884049	−	0.884049i	0.993943	+	0.109895i	$0.0350514\pi$
$678$		0			0
$679$			13.9032i			0.533556i
$680$		0			0
$681$			4.14360i			0.158783i
$682$		0			0
$683$	−8.13050	+	8.13050i	−0.311105	+	0.311105i	−0.845337	−	0.534233i	$-0.820601\pi$
$683$	−8.13050	+	8.13050i	−0.311105	+	0.311105i	0.534233	+	0.845337i	$0.320601\pi$
$684$		0			0
$685$	1.70417	+	1.70417i	0.0651131	+	0.0651131i
$686$		0			0
$687$	4.63201			0.176722
$688$		0			0
$689$	1.88260			0.0717215
$690$		0			0
$691$	1.09420	+	1.09420i	0.0416253	+	0.0416253i	0.727613	−	0.685988i	$-0.240630\pi$
$691$	1.09420	+	1.09420i	0.0416253	+	0.0416253i	−0.685988	+	0.727613i	$0.740630\pi$
$692$		0			0
$693$	5.43943	−	5.43943i	0.206627	−	0.206627i
$694$		0			0
$695$		−	7.57597i		−	0.287373i
$696$		0			0
$697$			6.16677i			0.233583i
$698$		0			0
$699$	2.29152	−	2.29152i	0.0866734	−	0.0866734i
$700$		0			0
$701$	−11.5656	−	11.5656i	−0.436825	−	0.436825i	0.454117	−	0.890942i	$-0.349955\pi$
$701$	−11.5656	−	11.5656i	−0.436825	−	0.436825i	−0.890942	+	0.454117i	$0.849955\pi$
$702$		0			0
$703$	57.1189			2.15428
$704$		0			0
$705$	−0.553329			−0.0208396
$706$		0			0
$707$	−0.813911	−	0.813911i	−0.0306103	−	0.0306103i
$708$		0			0
$709$	2.69651	−	2.69651i	0.101270	−	0.101270i	−0.654657	−	0.755926i	$-0.727187\pi$
$709$	2.69651	−	2.69651i	0.101270	−	0.101270i	0.755926	+	0.654657i	$0.227187\pi$
$710$		0			0
$711$		−	12.4030i		−	0.465149i
$712$		0			0
$713$			39.3488i			1.47363i
$714$		0			0
$715$	1.62393	−	1.62393i	0.0607315	−	0.0607315i
$716$		0			0
$717$	−3.53470	−	3.53470i	−0.132006	−	0.132006i
$718$		0			0
$719$	6.08527			0.226942			0.113471	−	0.993541i	$-0.463803\pi$
$719$	6.08527			0.226942			0.113471	+	0.993541i	$0.463803\pi$
$720$		0			0
$721$	8.39975			0.312823
$722$		0			0
$723$	−0.0687956	−	0.0687956i	−0.00255854	−	0.00255854i
$724$		0			0
$725$	−17.4181	+	17.4181i	−0.646891	+	0.646891i
$726$		0			0
$727$		−	41.6162i		−	1.54346i	−0.635951	−	0.771729i	$-0.719392\pi$
$727$		−	41.6162i		−	1.54346i	0.635951	−	0.771729i	$-0.280608\pi$
$728$		0			0
$729$			23.8862i			0.884674i
$730$		0			0
$731$	−28.6707	+	28.6707i	−1.06042	+	1.06042i
$732$		0			0
$733$	23.5929	+	23.5929i	0.871422	+	0.871422i	0.992627	−	0.121206i	$-0.0386760\pi$
$733$	23.5929	+	23.5929i	0.871422	+	0.871422i	−0.121206	+	0.992627i	$0.538676\pi$
$734$		0			0
$735$	0.0919045			0.00338995
$736$		0			0
$737$	−22.9983			−0.847152
$738$		0			0
$739$	−7.53135	−	7.53135i	−0.277045	−	0.277045i	0.554883	−	0.831928i	$-0.312763\pi$
$739$	−7.53135	−	7.53135i	−0.277045	−	0.277045i	−0.831928	+	0.554883i	$0.812763\pi$
$740$		0			0
$741$	−2.15606	+	2.15606i	−0.0792048	+	0.0792048i
$742$		0			0
$743$		−	14.4179i		−	0.528943i	−0.964393	−	0.264472i	$-0.914802\pi$
$743$		−	14.4179i		−	0.528943i	0.964393	−	0.264472i	$-0.0851975\pi$
$744$		0			0
$745$		−	3.80457i		−	0.139389i
$746$		0			0
$747$	35.3397	−	35.3397i	1.29301	−	1.29301i
$748$		0			0
$749$	−0.705176	−	0.705176i	−0.0257666	−	0.0257666i
$750$		0			0
$751$	17.6760			0.645008			0.322504	−	0.946568i	$-0.395475\pi$
$751$	17.6760			0.645008			0.322504	+	0.946568i	$0.395475\pi$
$752$		0			0
$753$	−3.16866			−0.115472
$754$		0			0
$755$	2.22395	+	2.22395i	0.0809379	+	0.0809379i
$756$		0			0
$757$	21.3351	−	21.3351i	0.775437	−	0.775437i	−0.203614	−	0.979051i	$-0.565269\pi$
$757$	21.3351	−	21.3351i	0.775437	−	0.775437i	0.979051	+	0.203614i	$0.0652687\pi$
$758$		0			0
$759$		−	4.08323i		−	0.148212i
$760$		0			0
$761$		−	22.2510i		−	0.806597i	−0.915068	−	0.403299i	$-0.867864\pi$
$761$		−	22.2510i		−	0.806597i	0.915068	−	0.403299i	$-0.132136\pi$
$762$		0			0
$763$	12.1263	−	12.1263i	0.439001	−	0.439001i
$764$		0			0
$765$	−5.81997	−	5.81997i	−0.210421	−	0.210421i
$766$		0			0
$767$	−17.4374			−0.629628
$768$		0			0
$769$	−30.5537			−1.10179			−0.550897	−	0.834573i	$-0.685714\pi$
$769$	−30.5537			−1.10179			−0.550897	+	0.834573i	$0.685714\pi$
$770$		0			0
$771$	2.79511	+	2.79511i	0.100663	+	0.100663i
$772$		0			0
$773$	19.1590	−	19.1590i	0.689100	−	0.689100i	−0.272933	−	0.962033i	$-0.587994\pi$
$773$	19.1590	−	19.1590i	0.689100	−	0.689100i	0.962033	+	0.272933i	$0.0879938\pi$
$774$		0			0
$775$			29.6288i			1.06430i
$776$		0			0
$777$		−	2.53999i		−	0.0911217i
$778$		0			0
$779$	3.22065	−	3.22065i	0.115392	−	0.115392i
$780$		0			0
$781$	−21.1344	−	21.1344i	−0.756247	−	0.756247i
$782$		0			0
$783$	7.29682			0.260767
$784$		0			0
$785$	4.12836			0.147348
$786$		0			0
$787$	13.8172	+	13.8172i	0.492528	+	0.492528i	0.909102	−	0.416574i	$-0.136769\pi$
$787$	13.8172	+	13.8172i	0.492528	+	0.492528i	−0.416574	+	0.909102i	$0.636769\pi$
$788$		0			0
$789$	2.28289	−	2.28289i	0.0812729	−	0.0812729i
$790$		0			0
$791$			3.51705i			0.125052i
$792$		0			0
$793$			3.04202i			0.108025i
$794$		0			0
$795$	−0.0528874	+	0.0528874i	−0.00187572	+	0.00187572i
$796$		0			0
$797$	8.78511	+	8.78511i	0.311185	+	0.311185i	0.845368	−	0.534184i	$-0.179381\pi$
$797$	8.78511	+	8.78511i	0.311185	+	0.311185i	−0.534184	+	0.845368i	$0.679381\pi$
$798$		0			0
$799$	−44.3806			−1.57007
$800$		0			0
$801$	−27.4367			−0.969427
$802$		0			0
$803$	6.81673	+	6.81673i	0.240557	+	0.240557i
$804$		0			0
$805$	−1.73105	+	1.73105i	−0.0610115	+	0.0610115i
$806$		0			0
$807$			6.61750i			0.232947i
$808$		0			0
$809$		−	2.11808i		−	0.0744676i	−0.999307	−	0.0372338i	$-0.988145\pi$
$809$		−	2.11808i		−	0.0744676i	0.999307	−	0.0372338i	$-0.0118546\pi$
$810$		0			0
$811$	0.203189	−	0.203189i	0.00713494	−	0.00713494i	−0.703530	−	0.710665i	$-0.748394\pi$
$811$	0.203189	−	0.203189i	0.00713494	−	0.00713494i	0.710665	+	0.703530i	$0.248394\pi$
$812$		0			0
$813$	−4.21078	−	4.21078i	−0.147679	−	0.147679i
$814$		0			0
$815$	−2.39946			−0.0840496
$816$		0			0
$817$	29.9471			1.04772
$818$		0			0
$819$	−4.81133	−	4.81133i	−0.168122	−	0.168122i
$820$		0			0
$821$	20.7943	−	20.7943i	0.725726	−	0.725726i	−0.244039	−	0.969765i	$-0.578473\pi$
$821$	20.7943	−	20.7943i	0.725726	−	0.725726i	0.969765	+	0.244039i	$0.0784726\pi$
$822$		0			0
$823$			10.1430i			0.353563i	0.984250	+	0.176782i	$0.0565686\pi$
$823$			10.1430i			0.353563i	−0.984250	+	0.176782i	$0.943431\pi$
$824$		0			0
$825$		−	3.07458i		−	0.107043i
$826$		0			0
$827$	19.6137	−	19.6137i	0.682035	−	0.682035i	−0.278424	−	0.960458i	$-0.589812\pi$
$827$	19.6137	−	19.6137i	0.682035	−	0.682035i	0.960458	+	0.278424i	$0.0898120\pi$
$828$		0			0
$829$	9.25634	+	9.25634i	0.321486	+	0.321486i	0.849337	−	0.527851i	$-0.177002\pi$
$829$	9.25634	+	9.25634i	0.321486	+	0.321486i	−0.527851	+	0.849337i	$0.677002\pi$
$830$		0			0
$831$	−6.16205			−0.213759
$832$		0			0
$833$	7.37134			0.255402
$834$		0			0
$835$	3.46011	+	3.46011i	0.119742	+	0.119742i
$836$		0			0
$837$	6.20608	−	6.20608i	0.214513	−	0.214513i
$838$		0			0
$839$		−	9.57102i		−	0.330428i	−0.986258	−	0.165214i	$-0.947168\pi$
$839$		−	9.57102i		−	0.330428i	0.986258	−	0.165214i	$-0.0528315\pi$
$840$		0			0
$841$		−	3.26691i		−	0.112652i
$842$		0			0
$843$	2.35145	−	2.35145i	0.0809882	−	0.0809882i
$844$		0			0
$845$	2.05311	+	2.05311i	0.0706290	+	0.0706290i
$846$		0			0
$847$	4.16036			0.142952
$848$		0			0
$849$	−3.43557			−0.117908
$850$		0			0
$851$	47.8415	+	47.8415i	1.63999	+	1.63999i
$852$		0			0
$853$	14.2865	−	14.2865i	0.489162	−	0.489162i	−0.418880	−	0.908042i	$-0.637577\pi$
$853$	14.2865	−	14.2865i	0.489162	−	0.489162i	0.908042	+	0.418880i	$0.137577\pi$
$854$		0			0
$855$			6.07907i			0.207900i
$856$		0			0
$857$		−	37.1981i		−	1.27066i	−0.772239	−	0.635332i	$-0.780863\pi$
$857$		−	37.1981i		−	1.27066i	0.772239	−	0.635332i	$-0.219137\pi$
$858$		0			0
$859$	−36.1537	+	36.1537i	−1.23355	+	1.23355i	−0.270959	+	0.962591i	$0.587341\pi$
$859$	−36.1537	+	36.1537i	−1.23355	+	1.23355i	−0.962591	+	0.270959i	$0.912659\pi$
$860$		0			0
$861$	−0.143218	−	0.143218i	−0.00488084	−	0.00488084i
$862$		0			0
$863$	27.6826			0.942325			0.471163	−	0.882046i	$-0.343835\pi$
$863$	27.6826			0.942325			0.471163	+	0.882046i	$0.343835\pi$
$864$		0			0
$865$	−3.33521			−0.113401
$866$		0			0
$867$	6.39175	+	6.39175i	0.217075	+	0.217075i
$868$		0			0
$869$	−7.79787	+	7.79787i	−0.264525	+	0.264525i
$870$		0			0
$871$			20.3426i			0.689284i
$872$		0			0
$873$			40.8947i			1.38407i
$874$		0			0
$875$	−2.64556	+	2.64556i	−0.0894364	+	0.0894364i
$876$		0			0
$877$	2.17870	+	2.17870i	0.0735694	+	0.0735694i	0.742934	−	0.669365i	$-0.233434\pi$
$877$	2.17870	+	2.17870i	0.0735694	+	0.0735694i	−0.669365	+	0.742934i	$0.733434\pi$
$878$		0			0
$879$	−6.75785			−0.227937
$880$		0			0
$881$	−39.9678			−1.34655			−0.673276	−	0.739392i	$-0.735113\pi$
$881$	−39.9678			−1.34655			−0.673276	+	0.739392i	$0.735113\pi$
$882$		0			0
$883$	−5.53035	−	5.53035i	−0.186111	−	0.186111i	0.607901	−	0.794013i	$-0.292012\pi$
$883$	−5.53035	−	5.53035i	−0.186111	−	0.186111i	−0.794013	+	0.607901i	$0.792012\pi$
$884$		0			0
$885$	0.489863	−	0.489863i	0.0164666	−	0.0164666i
$886$		0			0
$887$			47.8800i			1.60765i	0.594865	+	0.803826i	$0.297206\pi$
$887$			47.8800i			1.60765i	−0.594865	+	0.803826i	$0.702794\pi$
$888$		0			0
$889$		−	5.86352i		−	0.196656i
$890$		0			0
$891$	15.6743	−	15.6743i	0.525109	−	0.525109i
$892$		0			0
$893$	23.1782	+	23.1782i	0.775628	+	0.775628i
$894$		0			0
$895$	1.09332			0.0365455
$896$		0			0
$897$	−3.61173			−0.120592
$898$		0			0
$899$	21.8865	+	21.8865i	0.729954	+	0.729954i
$900$		0			0
$901$	−4.24191	+	4.24191i	−0.141319	+	0.141319i
$902$		0			0
$903$		−	1.33170i		−	0.0443163i
$904$		0			0
$905$		−	8.97162i		−	0.298227i
$906$		0			0
$907$	−28.4221	+	28.4221i	−0.943740	+	0.943740i	−0.998500	−	0.0547595i	$-0.982561\pi$
$907$	−28.4221	+	28.4221i	−0.943740	+	0.943740i	0.0547595	+	0.998500i	$0.482561\pi$
$908$		0			0
$909$	−2.39403	−	2.39403i	−0.0794048	−	0.0794048i
$910$		0			0
$911$	50.4192			1.67046			0.835231	−	0.549899i	$-0.185334\pi$
$911$	50.4192			1.67046			0.835231	+	0.549899i	$0.185334\pi$
$912$		0			0
$913$	−44.4368			−1.47064
$914$		0			0
$915$	−0.0854585	−	0.0854585i	−0.00282517	−	0.00282517i
$916$		0			0
$917$	−7.79029	+	7.79029i	−0.257258	+	0.257258i
$918$		0			0
$919$			41.1782i			1.35834i	0.733980	+	0.679171i	$0.237661\pi$
$919$			41.1782i			1.35834i	−0.733980	+	0.679171i	$0.762339\pi$
$920$		0			0
$921$		−	1.07784i		−	0.0355161i
$922$		0			0
$923$	−18.6940	+	18.6940i	−0.615319	+	0.615319i
$924$		0			0
$925$	36.0236	+	36.0236i	1.18445	+	1.18445i
$926$		0			0
$927$	24.7069			0.811482
$928$		0			0
$929$	−57.2128			−1.87709			−0.938546	−	0.345155i	$-0.887826\pi$
$929$	−57.2128			−1.87709			−0.938546	+	0.345155i	$0.887826\pi$
$930$		0			0
$931$	−3.84975	−	3.84975i	−0.126170	−	0.126170i
$932$		0			0
$933$	5.52458	−	5.52458i	0.180866	−	0.180866i
$934$		0			0
$935$			7.31813i			0.239328i
$936$		0			0
$937$			22.3565i			0.730353i	0.930938	+	0.365177i	$0.118991\pi$
$937$			22.3565i			0.730353i	−0.930938	+	0.365177i	$0.881009\pi$
$938$		0			0
$939$	−3.82396	+	3.82396i	−0.124790	+	0.124790i
$940$		0			0
$941$	15.0080	+	15.0080i	0.489246	+	0.489246i	0.908068	−	0.418822i	$-0.137557\pi$
$941$	15.0080	+	15.0080i	0.489246	+	0.489246i	−0.418822	+	0.908068i	$0.637557\pi$
$942$		0			0
$943$	5.39509			0.175688
$944$		0			0
$945$	0.546040			0.0177627
$946$		0			0
$947$	−7.21317	−	7.21317i	−0.234396	−	0.234396i	0.580129	−	0.814525i	$-0.303002\pi$
$947$	−7.21317	−	7.21317i	−0.234396	−	0.234396i	−0.814525	+	0.580129i	$0.803002\pi$
$948$		0			0
$949$	6.02960	−	6.02960i	0.195729	−	0.195729i
$950$		0			0
$951$			0.0507915i			0.00164703i
$952$		0			0
$953$		−	49.0686i		−	1.58949i	−0.606944	−	0.794744i	$-0.707605\pi$
$953$		−	49.0686i		−	1.58949i	0.606944	−	0.794744i	$-0.292395\pi$
$954$		0			0
$955$	1.37169	−	1.37169i	0.0443869	−	0.0443869i
$956$		0			0
$957$	−2.27116	−	2.27116i	−0.0734161	−	0.0734161i
$958$		0			0
$959$	−6.34879			−0.205013
$960$		0			0
$961$	6.22968			0.200957
$962$		0			0
$963$	−2.07420	−	2.07420i	−0.0668400	−	0.0668400i
$964$		0			0
$965$	−0.181518	+	0.181518i	−0.00584327	+	0.00584327i
$966$		0			0
$967$		−	3.07877i		−	0.0990064i	−0.998774	−	0.0495032i	$-0.984236\pi$
$967$		−	3.07877i		−	0.0990064i	0.998774	−	0.0495032i	$-0.0157638\pi$
$968$		0			0
$969$		−	9.71614i		−	0.312127i
$970$		0			0
$971$	−16.0104	+	16.0104i	−0.513797	+	0.513797i	−0.915688	−	0.401890i	$-0.868353\pi$
$971$	−16.0104	+	16.0104i	−0.513797	+	0.513797i	0.401890	+	0.915688i	$0.368353\pi$
$972$		0			0
$973$	14.1119	+	14.1119i	0.452408	+	0.452408i
$974$		0			0
$975$	−2.71955			−0.0870954
$976$		0			0
$977$	10.9770			0.351185			0.175592	−	0.984463i	$-0.443816\pi$
$977$	10.9770			0.351185			0.175592	+	0.984463i	$0.443816\pi$
$978$		0			0
$979$	17.2497	+	17.2497i	0.551302	+	0.551302i
$980$		0			0
$981$	35.6681	−	35.6681i	1.13879	−	1.13879i
$982$		0			0
$983$		−	15.7349i		−	0.501864i	−0.968005	−	0.250932i	$-0.919263\pi$
$983$		−	15.7349i		−	0.501864i	0.968005	−	0.250932i	$-0.0807371\pi$
$984$		0			0
$985$			7.70103i			0.245375i
$986$		0			0
$987$	1.03070	−	1.03070i	0.0328075	−	0.0328075i
$988$		0			0
$989$	25.0830	+	25.0830i	0.797593	+	0.797593i
$990$		0			0
$991$	46.7969			1.48655			0.743276	−	0.668984i	$-0.233271\pi$
$991$	46.7969			1.48655			0.743276	+	0.668984i	$0.233271\pi$
$992$		0			0
$993$	6.89656			0.218856
$994$		0			0
$995$	−1.32779	−	1.32779i	−0.0420937	−	0.0420937i
$996$		0			0
$997$	−29.1536	+	29.1536i	−0.923305	+	0.923305i	−0.997261	−	0.0739568i	$-0.976437\pi$
$997$	−29.1536	+	29.1536i	−0.923305	+	0.923305i	0.0739568	+	0.997261i	$0.476437\pi$
$998$		0			0
$999$		−	15.0911i		−	0.477460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.h.1345.5	yes	16
4.3	odd	2		1792.2.m.f.1345.4	yes	16
8.3	odd	2		1792.2.m.g.1345.5	yes	16
8.5	even	2		1792.2.m.e.1345.4	yes	16
16.3	odd	4		1792.2.m.g.449.5	yes	16
16.5	even	4	inner	1792.2.m.h.449.5	yes	16
16.11	odd	4		1792.2.m.f.449.4	yes	16
16.13	even	4		1792.2.m.e.449.4	✓	16
32.5	even	8		7168.2.a.bf.1.4		8
32.11	odd	8		7168.2.a.ba.1.4		8
32.21	even	8		7168.2.a.bb.1.5		8
32.27	odd	8		7168.2.a.be.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.e.449.4	✓	16	16.13	even	4
1792.2.m.e.1345.4	yes	16	8.5	even	2
1792.2.m.f.449.4	yes	16	16.11	odd	4
1792.2.m.f.1345.4	yes	16	4.3	odd	2
1792.2.m.g.449.5	yes	16	16.3	odd	4
1792.2.m.g.1345.5	yes	16	8.3	odd	2
1792.2.m.h.449.5	yes	16	16.5	even	4	inner
1792.2.m.h.1345.5	yes	16	1.1	even	1	trivial
7168.2.a.ba.1.4		8	32.11	odd	8
7168.2.a.bb.1.5		8	32.21	even	8
7168.2.a.be.1.5		8	32.27	odd	8
7168.2.a.bf.1.4		8	32.5	even	8

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:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.171192 + 0.171192i) q^{3} +(-0.268425 + 0.268425i) q^{5} -1.00000i q^{7} -2.94139i q^{9} +O(q^{10})\)	\(q+(0.171192 + 0.171192i) q^{3} +(-0.268425 + 0.268425i) q^{5} -1.00000i q^{7} -2.94139i q^{9} +(-1.84927 + 1.84927i) q^{11} +(1.63574 + 1.63574i) q^{13} -0.0919045 q^{15} -7.37134 q^{17} +(3.84975 + 3.84975i) q^{19} +(0.171192 - 0.171192i) q^{21} +6.44892i q^{23} +4.85590i q^{25} +(1.01712 - 1.01712i) q^{27} +(3.58700 + 3.58700i) q^{29} +6.10161 q^{31} -0.633164 q^{33} +(0.268425 + 0.268425i) q^{35} +(7.41852 - 7.41852i) q^{37} +0.560052i q^{39} -0.836588i q^{41} +(3.88949 - 3.88949i) q^{43} +(0.789540 + 0.789540i) q^{45} +6.02070 q^{47} -1.00000 q^{49} +(-1.26192 - 1.26192i) q^{51} +(0.575460 - 0.575460i) q^{53} -0.992782i q^{55} +1.31810i q^{57} +(-5.33013 + 5.33013i) q^{59} +(0.929862 + 0.929862i) q^{61} -2.94139 q^{63} -0.878144 q^{65} +(6.21819 + 6.21819i) q^{67} +(-1.10401 + 1.10401i) q^{69} +11.4285i q^{71} -3.68616i q^{73} +(-0.831293 + 0.831293i) q^{75} +(1.84927 + 1.84927i) q^{77} +4.21672 q^{79} -8.47591 q^{81} +(12.0147 + 12.0147i) q^{83} +(1.97865 - 1.97865i) q^{85} +1.22813i q^{87} -9.32780i q^{89} +(1.63574 - 1.63574i) q^{91} +(1.04455 + 1.04455i) q^{93} -2.06673 q^{95} -13.9032 q^{97} +(5.43943 + 5.43943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^3 + 4 * q^5	\( 16 q + 4 q^{3} + 4 q^{5} - 8 q^{11} - 12 q^{13} - 8 q^{17} + 4 q^{19} + 4 q^{21} - 56 q^{27} - 8 q^{31} + 16 q^{33} - 4 q^{35} + 8 q^{37} - 24 q^{43} + 36 q^{45} - 40 q^{47} - 16 q^{49} + 24 q^{51} + 32 q^{53} - 4 q^{59} + 20 q^{61} + 24 q^{63} + 72 q^{65} + 32 q^{67} - 56 q^{69} - 28 q^{75} + 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} - 8 q^{93} - 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 + 4 * q^5 - 8 * q^11 - 12 * q^13 - 8 * q^17 + 4 * q^19 + 4 * q^21 - 56 * q^27 - 8 * q^31 + 16 * q^33 - 4 * q^35 + 8 * q^37 - 24 * q^43 + 36 * q^45 - 40 * q^47 - 16 * q^49 + 24 * q^51 + 32 * q^53 - 4 * q^59 + 20 * q^61 + 24 * q^63 + 72 * q^65 + 32 * q^67 - 56 * q^69 - 28 * q^75 + 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 - 8 * q^93 - 80 * q^95 - 72 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more