LMFDB - Embedded newform 304.2.i.e.273.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [304,2,Mod(49,304)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(304, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("304.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			273.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	304.273
Dual form			304.2.i.e.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32288 - 2.29129i) q^{3} +(-1.82288 - 3.15731i) q^{5} +1.64575 q^{7} +(-2.00000 + 3.46410i) q^{9} -0.645751 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-4.82288 + 8.35347i) q^{15} +(-4.32288 + 0.559237i) q^{19} +(-2.17712 - 3.77089i) q^{21} +(1.82288 - 3.15731i) q^{23} +(-4.14575 + 7.18065i) q^{25} +2.64575 q^{27} +(1.82288 - 3.15731i) q^{29} +0.354249 q^{31} +(0.854249 + 1.47960i) q^{33} +(-3.00000 - 5.19615i) q^{35} +5.64575 q^{37} +5.29150 q^{39} +(-5.14575 - 8.91270i) q^{41} +(0.354249 + 0.613577i) q^{43} +14.5830 q^{45} +(4.82288 - 8.35347i) q^{47} -4.29150 q^{49} +(-4.29150 + 7.43310i) q^{53} +(1.17712 + 2.03884i) q^{55} +(7.00000 + 9.16515i) q^{57} +(3.96863 + 6.87386i) q^{59} +(7.46863 - 12.9360i) q^{61} +(-3.29150 + 5.70105i) q^{63} +7.29150 q^{65} +(-2.32288 + 4.02334i) q^{67} -9.64575 q^{69} +(-6.64575 - 11.5108i) q^{71} +(-6.14575 - 10.6448i) q^{73} +21.9373 q^{75} -1.06275 q^{77} +(-2.00000 - 3.46410i) q^{79} +(2.50000 + 4.33013i) q^{81} +7.93725 q^{83} -9.64575 q^{87} +(-1.64575 + 2.85052i) q^{91} +(-0.468627 - 0.811686i) q^{93} +(9.64575 + 12.6293i) q^{95} +(7.14575 + 12.3768i) q^{97} +(1.29150 - 2.23695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} - 4 q^{7} - 8 q^{9} + 8 q^{11} - 4 q^{13} - 14 q^{15} - 12 q^{19} - 14 q^{21} + 2 q^{23} - 6 q^{25} + 2 q^{29} + 12 q^{31} + 14 q^{33} - 12 q^{35} + 12 q^{37} - 10 q^{41} + 12 q^{43} + 16 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^5 - 4 * q^7 - 8 * q^9 + 8 * q^11 - 4 * q^13 - 14 * q^15 - 12 * q^19 - 14 * q^21 + 2 * q^23 - 6 * q^25 + 2 * q^29 + 12 * q^31 + 14 * q^33 - 12 * q^35 + 12 * q^37 - 10 * q^41 + 12 * q^43 + 16 * q^45 + 14 * q^47 + 4 * q^49 + 4 * q^53 + 10 * q^55 + 28 * q^57 + 14 * q^61 + 8 * q^63 + 8 * q^65 - 4 * q^67 - 28 * q^69 - 16 * q^71 - 14 * q^73 + 56 * q^75 - 36 * q^77 - 8 * q^79 + 10 * q^81 - 28 * q^87 + 4 * q^91 + 14 * q^93 + 28 * q^95 + 18 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.32288	−	2.29129i	−0.763763	−	1.32288i	−0.940898	−	0.338689i	$-0.890016\pi$
$3$	−1.32288	−	2.29129i	−0.763763	−	1.32288i	0.177136	−	0.984186i	$-0.443317\pi$
$4$		0			0
$5$	−1.82288	−	3.15731i	−0.815215	−	1.41199i	−0.909174	−	0.416417i	$-0.863286\pi$
$5$	−1.82288	−	3.15731i	−0.815215	−	1.41199i	0.0939588	−	0.995576i	$-0.470048\pi$
$6$		0			0
$7$	1.64575			0.622036			0.311018	−	0.950404i	$-0.399330\pi$
$7$	1.64575			0.622036			0.311018	+	0.950404i	$0.399330\pi$
$8$		0			0
$9$	−2.00000	+	3.46410i	−0.666667	+	1.15470i
$10$		0			0
$11$	−0.645751			−0.194701			−0.0973507	−	0.995250i	$-0.531037\pi$
$11$	−0.645751			−0.194701			−0.0973507	+	0.995250i	$0.531037\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$	−4.82288	+	8.35347i	−1.24526	+	2.15686i
$16$		0			0
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−4.32288	+	0.559237i	−0.991736	+	0.128298i
$19$	−4.32288	+	0.559237i	−0.991736	+	0.128298i
$20$		0			0
$21$	−2.17712	−	3.77089i	−0.475087	−	0.822876i
$22$		0			0
$23$	1.82288	−	3.15731i	0.380096	−	0.658345i	−0.610980	−	0.791646i	$-0.709224\pi$
$23$	1.82288	−	3.15731i	0.380096	−	0.658345i	0.991076	+	0.133301i	$0.0425577\pi$
$24$		0			0
$25$	−4.14575	+	7.18065i	−0.829150	+	1.43613i
$26$		0			0
$27$	2.64575			0.509175
$28$		0			0
$29$	1.82288	−	3.15731i	0.338500	−	0.586298i	−0.645651	−	0.763632i	$-0.723414\pi$
$29$	1.82288	−	3.15731i	0.338500	−	0.586298i	0.984151	+	0.177334i	$0.0567473\pi$
$30$		0			0
$31$	0.354249			0.0636249			0.0318125	−	0.999494i	$-0.489872\pi$
$31$	0.354249			0.0636249			0.0318125	+	0.999494i	$0.489872\pi$
$32$		0			0
$33$	0.854249	+	1.47960i	0.148706	+	0.257566i
$34$		0			0
$35$	−3.00000	−	5.19615i	−0.507093	−	0.878310i
$36$		0			0
$37$	5.64575			0.928156			0.464078	−	0.885794i	$-0.346386\pi$
$37$	5.64575			0.928156			0.464078	+	0.885794i	$0.346386\pi$
$38$		0			0
$39$	5.29150			0.847319
$40$		0			0
$41$	−5.14575	−	8.91270i	−0.803631	−	1.39193i	−0.917211	−	0.398401i	$-0.869565\pi$
$41$	−5.14575	−	8.91270i	−0.803631	−	1.39193i	0.113580	−	0.993529i	$-0.463768\pi$
$42$		0			0
$43$	0.354249	+	0.613577i	0.0540224	+	0.0935696i	0.891772	−	0.452485i	$-0.149462\pi$
$43$	0.354249	+	0.613577i	0.0540224	+	0.0935696i	−0.837750	+	0.546055i	$0.816129\pi$
$44$		0			0
$45$	14.5830			2.17391
$46$		0			0
$47$	4.82288	−	8.35347i	0.703489	−	1.21848i	−0.263745	−	0.964592i	$-0.584958\pi$
$47$	4.82288	−	8.35347i	0.703489	−	1.21848i	0.967234	−	0.253886i	$-0.0817088\pi$
$48$		0			0
$49$	−4.29150			−0.613072
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.29150	+	7.43310i	−0.589483	+	1.02101i	0.404817	+	0.914398i	$0.367335\pi$
$53$	−4.29150	+	7.43310i	−0.589483	+	1.02101i	−0.994300	+	0.106617i	$0.965998\pi$
$54$		0			0
$55$	1.17712	+	2.03884i	0.158723	+	0.274917i
$56$		0			0
$57$	7.00000	+	9.16515i	0.927173	+	1.21395i
$58$		0			0
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	0.999813	+	0.0193585i	$0.00616237\pi$
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	−0.483141	+	0.875542i	$0.660504\pi$
$60$		0			0
$61$	7.46863	−	12.9360i	0.956260	−	1.65629i	0.224801	−	0.974405i	$-0.427827\pi$
$61$	7.46863	−	12.9360i	0.956260	−	1.65629i	0.731459	−	0.681886i	$-0.238840\pi$
$62$		0			0
$63$	−3.29150	+	5.70105i	−0.414690	+	0.718265i
$64$		0			0
$65$	7.29150			0.904400
$66$		0			0
$67$	−2.32288	+	4.02334i	−0.283784	+	0.491529i	−0.972314	−	0.233680i	$-0.924923\pi$
$67$	−2.32288	+	4.02334i	−0.283784	+	0.491529i	0.688529	+	0.725209i	$0.258257\pi$
$68$		0			0
$69$	−9.64575			−1.16121
$70$		0			0
$71$	−6.64575	−	11.5108i	−0.788706	−	1.36608i	−0.926760	−	0.375654i	$-0.877418\pi$
$71$	−6.64575	−	11.5108i	−0.788706	−	1.36608i	0.138055	−	0.990425i	$-0.455915\pi$
$72$		0			0
$73$	−6.14575	−	10.6448i	−0.719306	−	1.24587i	−0.961275	−	0.275590i	$-0.911127\pi$
$73$	−6.14575	−	10.6448i	−0.719306	−	1.24587i	0.241969	−	0.970284i	$-0.422207\pi$
$74$		0			0
$75$	21.9373			2.53310
$76$		0			0
$77$	−1.06275			−0.121111
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$		0			0
$83$	7.93725			0.871227			0.435613	−	0.900134i	$-0.356531\pi$
$83$	7.93725			0.871227			0.435613	+	0.900134i	$0.356531\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−9.64575			−1.03413
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−1.64575	+	2.85052i	−0.172522	+	0.298816i
$92$		0			0
$93$	−0.468627	−	0.811686i	−0.0485944	−	0.0841679i
$94$		0			0
$95$	9.64575	+	12.6293i	0.989633	+	1.29573i
$96$		0			0
$97$	7.14575	+	12.3768i	0.725541	+	1.25667i	0.958751	+	0.284248i	$0.0917438\pi$
$97$	7.14575	+	12.3768i	0.725541	+	1.25667i	−0.233210	+	0.972426i	$0.574923\pi$
$98$		0			0
$99$	1.29150	−	2.23695i	0.129801	−	0.224822i
$100$		0			0
$101$	4.17712	−	7.23499i	0.415639	−	0.719909i	−0.579856	−	0.814719i	$-0.696891\pi$
$101$	4.17712	−	7.23499i	0.415639	−	0.719909i	0.995495	+	0.0948105i	$0.0302245\pi$
$102$		0			0
$103$	2.70850			0.266876			0.133438	−	0.991057i	$-0.457398\pi$
$103$	2.70850			0.266876			0.133438	+	0.991057i	$0.457398\pi$
$104$		0			0
$105$	−7.93725	+	13.7477i	−0.774597	+	1.34164i
$106$		0			0
$107$	−4.70850			−0.455188			−0.227594	−	0.973756i	$-0.573086\pi$
$107$	−4.70850			−0.455188			−0.227594	+	0.973756i	$0.573086\pi$
$108$		0			0
$109$	3.29150	+	5.70105i	0.315269	+	0.546062i	0.979495	−	0.201470i	$-0.0645720\pi$
$109$	3.29150	+	5.70105i	0.315269	+	0.546062i	−0.664226	+	0.747532i	$0.731239\pi$
$110$		0			0
$111$	−7.46863	−	12.9360i	−0.708891	−	1.22783i
$112$		0			0
$113$	5.58301			0.525205			0.262602	−	0.964904i	$-0.415419\pi$
$113$	5.58301			0.525205			0.262602	+	0.964904i	$0.415419\pi$
$114$		0			0
$115$	−13.2915			−1.23944
$116$		0			0
$117$	−4.00000	−	6.92820i	−0.369800	−	0.640513i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.5830			−0.962091
$122$		0			0
$123$	−13.6144	+	23.5808i	−1.22757	+	2.12621i
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	−1.35425	+	2.34563i	−0.120170	+	0.208141i	−0.919835	−	0.392306i	$-0.871677\pi$
$127$	−1.35425	+	2.34563i	−0.120170	+	0.208141i	0.799665	+	0.600447i	$0.205011\pi$
$128$		0			0
$129$	0.937254	−	1.62337i	0.0825206	−	0.142930i
$130$		0			0
$131$	−6.96863	−	12.0700i	−0.608852	−	1.05456i	−0.991430	−	0.130639i	$-0.958297\pi$
$131$	−6.96863	−	12.0700i	−0.608852	−	1.05456i	0.382578	−	0.923923i	$-0.375036\pi$
$132$		0			0
$133$	−7.11438	+	0.920365i	−0.616895	+	0.0798058i
$134$		0			0
$135$	−4.82288	−	8.35347i	−0.415087	−	0.718952i
$136$		0			0
$137$	2.79150	−	4.83502i	0.238494	−	0.413084i	−0.721788	−	0.692114i	$-0.756680\pi$
$137$	2.79150	−	4.83502i	0.238494	−	0.413084i	0.960282	+	0.279030i	$0.0900129\pi$
$138$		0			0
$139$	6.67712	−	11.5651i	0.566346	−	0.980941i	−0.430577	−	0.902554i	$-0.641690\pi$
$139$	6.67712	−	11.5651i	0.566346	−	0.980941i	0.996923	−	0.0783866i	$-0.0249768\pi$
$140$		0			0
$141$	−25.5203			−2.14919
$142$		0			0
$143$	0.645751	−	1.11847i	0.0540004	−	0.0935315i
$144$		0			0
$145$	−13.2915			−1.10380
$146$		0			0
$147$	5.67712	+	9.83307i	0.468241	+	0.811018i
$148$		0			0
$149$	2.46863	+	4.27579i	0.202238	+	0.350286i	0.949249	−	0.314525i	$-0.101845\pi$
$149$	2.46863	+	4.27579i	0.202238	+	0.350286i	−0.747011	+	0.664811i	$0.768512\pi$
$150$		0			0
$151$	2.93725			0.239030			0.119515	−	0.992832i	$-0.461866\pi$
$151$	2.93725			0.239030			0.119515	+	0.992832i	$0.461866\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.645751	−	1.11847i	−0.0518680	−	0.0898380i
$156$		0			0
$157$	−5.29150	−	9.16515i	−0.422308	−	0.731459i	0.573857	−	0.818956i	$-0.305447\pi$
$157$	−5.29150	−	9.16515i	−0.422308	−	0.731459i	−0.996165	+	0.0874969i	$0.972113\pi$
$158$		0			0
$159$	22.7085			1.80090
$160$		0			0
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$		0			0
$163$	11.9373			0.934998			0.467499	−	0.883994i	$-0.345155\pi$
$163$	11.9373			0.934998			0.467499	+	0.883994i	$0.345155\pi$
$164$		0			0
$165$	3.11438	−	5.39426i	0.242454	−	0.419943i
$166$		0			0
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	6.70850	−	16.0934i	0.513012	−	1.23069i
$172$		0			0
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−6.82288	+	11.8176i	−0.515761	+	0.893324i
$176$		0			0
$177$	10.5000	−	18.1865i	0.789228	−	1.36698i
$178$		0			0
$179$	−19.9373			−1.49018			−0.745090	−	0.666964i	$-0.767594\pi$
$179$	−19.9373			−1.49018			−0.745090	+	0.666964i	$0.767594\pi$
$180$		0			0
$181$	2.11438	−	3.66221i	0.157160	−	0.272210i	−0.776683	−	0.629892i	$-0.783099\pi$
$181$	2.11438	−	3.66221i	0.157160	−	0.272210i	0.933844	+	0.357682i	$0.116433\pi$
$182$		0			0
$183$	−39.5203			−2.92142
$184$		0			0
$185$	−10.2915	−	17.8254i	−0.756646	−	1.31055i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	4.35425			0.316725
$190$		0			0
$191$	14.5830			1.05519			0.527595	−	0.849496i	$-0.323094\pi$
$191$	14.5830			1.05519			0.527595	+	0.849496i	$0.323094\pi$
$192$		0			0
$193$	3.29150	+	5.70105i	0.236928	+	0.410371i	0.959831	−	0.280578i	$-0.0905263\pi$
$193$	3.29150	+	5.70105i	0.236928	+	0.410371i	−0.722904	+	0.690949i	$0.757193\pi$
$194$		0			0
$195$	−9.64575	−	16.7069i	−0.690747	−	1.19641i
$196$		0			0
$197$	−2.35425			−0.167733			−0.0838666	−	0.996477i	$-0.526727\pi$
$197$	−2.35425			−0.167733			−0.0838666	+	0.996477i	$0.526727\pi$
$198$		0			0
$199$	5.93725	−	10.2836i	0.420881	−	0.728987i	−0.575145	−	0.818051i	$-0.695054\pi$
$199$	5.93725	−	10.2836i	0.420881	−	0.728987i	0.996026	+	0.0890645i	$0.0283877\pi$
$200$		0			0
$201$	12.2915			0.866976
$202$		0			0
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		0			0
$205$	−18.7601	+	32.4935i	−1.31026	+	2.26944i
$206$		0			0
$207$	7.29150	+	12.6293i	0.506794	+	0.877794i
$208$		0			0
$209$	2.79150	−	0.361128i	0.193092	−	0.0249797i
$210$		0			0
$211$	−1.35425	−	2.34563i	−0.0932303	−	0.161480i	0.815638	−	0.578562i	$-0.196386\pi$
$211$	−1.35425	−	2.34563i	−0.0932303	−	0.161480i	−0.908869	+	0.417082i	$0.863053\pi$
$212$		0			0
$213$	−17.5830	+	30.4547i	−1.20477	+	2.08672i
$214$		0			0
$215$	1.29150	−	2.23695i	0.0880797	−	0.152559i
$216$		0			0
$217$	0.583005			0.0395770
$218$		0			0
$219$	−16.2601	+	28.1634i	−1.09876	+	1.90310i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	14.4059	+	24.9517i	0.964689	+	1.67089i	0.710448	+	0.703750i	$0.248492\pi$
$223$	14.4059	+	24.9517i	0.964689	+	1.67089i	0.254241	+	0.967141i	$0.418174\pi$
$224$		0			0
$225$	−16.5830	−	28.7226i	−1.10553	−	1.91484i
$226$		0			0
$227$	12.6458			0.839328			0.419664	−	0.907680i	$-0.362148\pi$
$227$	12.6458			0.839328			0.419664	+	0.907680i	$0.362148\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$		0			0
$231$	1.40588	+	2.43506i	0.0925002	+	0.160215i
$232$		0			0
$233$	6.43725	+	11.1497i	0.421719	+	0.730438i	0.996108	−	0.0881444i	$-0.0280937\pi$
$233$	6.43725	+	11.1497i	0.421719	+	0.730438i	−0.574389	+	0.818582i	$0.694760\pi$
$234$		0			0
$235$	−35.1660			−2.29398
$236$		0			0
$237$	−5.29150	+	9.16515i	−0.343720	+	0.595341i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−6.79150	+	11.7632i	−0.437479	+	0.757736i	−0.997494	−	0.0707462i	$-0.977462\pi$
$241$	−6.79150	+	11.7632i	−0.437479	+	0.757736i	0.560015	+	0.828482i	$0.310795\pi$
$242$		0			0
$243$	10.5830	−	18.3303i	0.678900	−	1.17589i
$244$		0			0
$245$	7.82288	+	13.5496i	0.499785	+	0.865653i
$246$		0			0
$247$	3.35425	−	8.04668i	0.213426	−	0.511998i
$248$		0			0
$249$	−10.5000	−	18.1865i	−0.665410	−	1.15252i
$250$		0			0
$251$	1.38562	−	2.39997i	0.0874597	−	0.151485i	−0.818977	−	0.573826i	$-0.805458\pi$
$251$	1.38562	−	2.39997i	0.0874597	−	0.151485i	0.906437	+	0.422342i	$0.138792\pi$
$252$		0			0
$253$	−1.17712	+	2.03884i	−0.0740052	+	0.128181i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.854249	+	1.47960i	−0.0532866	+	0.0922950i	−0.891438	−	0.453142i	$-0.850303\pi$
$257$	−0.854249	+	1.47960i	−0.0532866	+	0.0922950i	0.838152	+	0.545437i	$0.183636\pi$
$258$		0			0
$259$	9.29150			0.577346
$260$		0			0
$261$	7.29150	+	12.6293i	0.451333	+	0.781731i
$262$		0			0
$263$	2.46863	+	4.27579i	0.152222	+	0.263656i	0.932044	−	0.362345i	$-0.118024\pi$
$263$	2.46863	+	4.27579i	0.152222	+	0.263656i	−0.779822	+	0.626001i	$0.784690\pi$
$264$		0			0
$265$	31.2915			1.92222
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	8.82288	+	15.2817i	0.535952	+	0.928295i	0.999117	+	0.0420233i	$0.0133804\pi$
$271$	8.82288	+	15.2817i	0.535952	+	0.928295i	−0.463165	+	0.886272i	$0.653286\pi$
$272$		0			0
$273$	8.70850			0.527062
$274$		0			0
$275$	2.67712	−	4.63692i	0.161437	−	0.279617i
$276$		0			0
$277$	9.52026			0.572017			0.286008	−	0.958227i	$-0.407671\pi$
$277$	9.52026			0.572017			0.286008	+	0.958227i	$0.407671\pi$
$278$		0			0
$279$	−0.708497	+	1.22715i	−0.0424166	+	0.0734678i
$280$		0			0
$281$	13.7288	−	23.7789i	0.818989	−	1.41853i	−0.0874389	−	0.996170i	$-0.527868\pi$
$281$	13.7288	−	23.7789i	0.818989	−	1.41853i	0.906428	−	0.422361i	$-0.138798\pi$
$282$		0			0
$283$	12.6771	+	21.9574i	0.753577	+	1.30523i	0.946079	+	0.323937i	$0.105007\pi$
$283$	12.6771	+	21.9574i	0.753577	+	1.30523i	−0.192502	+	0.981297i	$0.561660\pi$
$284$		0			0
$285$	16.1771	−	38.8081i	0.958250	−	2.29879i
$286$		0			0
$287$	−8.46863	−	14.6681i	−0.499887	−	0.865830i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	18.9059	−	32.7459i	1.10828	−	1.91960i
$292$		0			0
$293$	13.0627			0.763134			0.381567	−	0.924341i	$-0.375385\pi$
$293$	13.0627			0.763134			0.381567	+	0.924341i	$0.375385\pi$
$294$		0			0
$295$	14.4686	−	25.0604i	0.842396	−	1.45907i
$296$		0			0
$297$	−1.70850			−0.0991371
$298$		0			0
$299$	3.64575	+	6.31463i	0.210839	+	0.365184i
$300$		0			0
$301$	0.583005	+	1.00979i	0.0336039	+	0.0582036i
$302$		0			0
$303$	−22.1033			−1.26980
$304$		0			0
$305$	−54.4575			−3.11823
$306$		0			0
$307$	−2.32288	−	4.02334i	−0.132574	−	0.229624i	0.792094	−	0.610399i	$-0.208991\pi$
$307$	−2.32288	−	4.02334i	−0.132574	−	0.229624i	−0.924668	+	0.380775i	$0.875657\pi$
$308$		0			0
$309$	−3.58301	−	6.20595i	−0.203830	−	0.353044i
$310$		0			0
$311$	−8.35425			−0.473726			−0.236863	−	0.971543i	$-0.576119\pi$
$311$	−8.35425			−0.473726			−0.236863	+	0.971543i	$0.576119\pi$
$312$		0			0
$313$	11.4373	−	19.8099i	0.646472	−	1.11972i	−0.337488	−	0.941330i	$-0.609577\pi$
$313$	11.4373	−	19.8099i	0.646472	−	1.11972i	0.983959	−	0.178392i	$-0.0570895\pi$
$314$		0			0
$315$	24.0000			1.35225
$316$		0			0
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	−1.17712	+	2.03884i	−0.0659063	+	0.114153i
$320$		0			0
$321$	6.22876	+	10.7885i	0.347655	+	0.602157i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−8.29150	−	14.3613i	−0.459930	−	0.796622i
$326$		0			0
$327$	8.70850	−	15.0836i	0.481581	−	0.834123i
$328$		0			0
$329$	7.93725	−	13.7477i	0.437595	−	0.757937i
$330$		0			0
$331$	27.8118			1.52867			0.764336	−	0.644818i	$-0.223067\pi$
$331$	27.8118			1.52867			0.764336	+	0.644818i	$0.223067\pi$
$332$		0			0
$333$	−11.2915	+	19.5575i	−0.618771	+	1.07174i
$334$		0			0
$335$	16.9373			0.925381
$336$		0			0
$337$	10.1458	+	17.5730i	0.552674	+	0.957260i	0.998080	+	0.0619313i	$0.0197260\pi$
$337$	10.1458	+	17.5730i	0.552674	+	0.957260i	−0.445406	+	0.895329i	$0.646941\pi$
$338$		0			0
$339$	−7.38562	−	12.7923i	−0.401132	−	0.694781i
$340$		0			0
$341$	−0.228757			−0.0123879
$342$		0			0
$343$	−18.5830			−1.00339
$344$		0			0
$345$	17.5830	+	30.4547i	0.946637	+	1.63962i
$346$		0			0
$347$	1.61438	+	2.79619i	0.0866644	+	0.150107i	0.906099	−	0.423065i	$-0.139046\pi$
$347$	1.61438	+	2.79619i	0.0866644	+	0.150107i	−0.819435	+	0.573172i	$0.805713\pi$
$348$		0			0
$349$	−21.1660			−1.13299			−0.566495	−	0.824065i	$-0.691701\pi$
$349$	−21.1660			−1.13299			−0.566495	+	0.824065i	$0.691701\pi$
$350$		0			0
$351$	−2.64575	+	4.58258i	−0.141220	+	0.244600i
$352$		0			0
$353$	−18.8745			−1.00459			−0.502294	−	0.864697i	$-0.667511\pi$
$353$	−18.8745			−1.00459			−0.502294	+	0.864697i	$0.667511\pi$
$354$		0			0
$355$	−24.2288	+	41.9654i	−1.28593	+	2.22729i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.46863	+	9.47194i	0.288623	+	0.499910i	0.973481	−	0.228766i	$-0.0734692\pi$
$359$	5.46863	+	9.47194i	0.288623	+	0.499910i	−0.684858	+	0.728676i	$0.740136\pi$
$360$		0			0
$361$	18.3745	−	4.83502i	0.967079	−	0.254475i
$362$		0			0
$363$	14.0000	+	24.2487i	0.734809	+	1.27273i
$364$		0			0
$365$	−22.4059	+	38.8081i	−1.17278	+	2.03131i
$366$		0			0
$367$	−5.11438	+	8.85836i	−0.266968	+	0.462403i	−0.968077	−	0.250651i	$-0.919355\pi$
$367$	−5.11438	+	8.85836i	−0.266968	+	0.462403i	0.701109	+	0.713054i	$0.252689\pi$
$368$		0			0
$369$	41.1660			2.14302
$370$		0			0
$371$	−7.06275	+	12.2330i	−0.366680	+	0.635108i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	−15.8745	−	27.4955i	−0.819756	−	1.41986i
$376$		0			0
$377$	3.64575	+	6.31463i	0.187766	+	0.325220i
$378$		0			0
$379$	−21.2915			−1.09367			−0.546836	−	0.837240i	$-0.684168\pi$
$379$	−21.2915			−1.09367			−0.546836	+	0.837240i	$0.684168\pi$
$380$		0			0
$381$	7.16601			0.367126
$382$		0			0
$383$	−15.7601	−	27.2973i	−0.805305	−	1.39483i	−0.916085	−	0.400984i	$-0.868668\pi$
$383$	−15.7601	−	27.2973i	−0.805305	−	1.39483i	0.110780	−	0.993845i	$-0.464665\pi$
$384$		0			0
$385$	1.93725	+	3.35542i	0.0987316	+	0.171008i
$386$		0			0
$387$	−2.83399			−0.144060
$388$		0			0
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	−0.977086	−	0.212847i	$-0.931726\pi$
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	0.672874	+	0.739758i	$0.265060\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−18.4373	+	31.9343i	−0.930036	+	1.61087i
$394$		0			0
$395$	−7.29150	+	12.6293i	−0.366875	+	0.635447i
$396$		0			0
$397$	−18.4686	−	31.9886i	−0.926914	−	1.60546i	−0.788454	−	0.615094i	$-0.789118\pi$
$397$	−18.4686	−	31.9886i	−0.926914	−	1.60546i	−0.138460	−	0.990368i	$-0.544215\pi$
$398$		0			0
$399$	11.5203	+	15.0836i	0.576734	+	0.755122i
$400$		0			0
$401$	−3.20850	−	5.55728i	−0.160225	−	0.277517i	0.774724	−	0.632299i	$-0.217889\pi$
$401$	−3.20850	−	5.55728i	−0.160225	−	0.277517i	−0.934949	+	0.354782i	$0.884555\pi$
$402$		0			0
$403$	−0.354249	+	0.613577i	−0.0176464	+	0.0305644i
$404$		0			0
$405$	9.11438	−	15.7866i	0.452897	−	0.784441i
$406$		0			0
$407$	−3.64575			−0.180713
$408$		0			0
$409$	−6.79150	+	11.7632i	−0.335818	+	0.581654i	−0.983642	−	0.180136i	$-0.942346\pi$
$409$	−6.79150	+	11.7632i	−0.335818	+	0.581654i	0.647823	+	0.761790i	$0.275679\pi$
$410$		0			0
$411$	−14.7712			−0.728612
$412$		0			0
$413$	6.53137	+	11.3127i	0.321388	+	0.556660i
$414$		0			0
$415$	−14.4686	−	25.0604i	−0.710237	−	1.23017i
$416$		0			0
$417$	−35.3320			−1.73022
$418$		0			0
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$		0			0
$421$	−11.4059	−	19.7556i	−0.555889	−	0.962827i	−0.997834	−	0.0657853i	$-0.979045\pi$
$421$	−11.4059	−	19.7556i	−0.555889	−	0.962827i	0.441945	−	0.897042i	$-0.354289\pi$
$422$		0			0
$423$	19.2915	+	33.4139i	0.937985	+	1.62464i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.2915	−	21.2895i	0.594828	−	1.03027i
$428$		0			0
$429$	−3.41699			−0.164974
$430$		0			0
$431$	−1.93725	+	3.35542i	−0.0933142	+	0.161625i	−0.908904	−	0.417006i	$-0.863079\pi$
$431$	−1.93725	+	3.35542i	−0.0933142	+	0.161625i	0.815590	+	0.578631i	$0.196413\pi$
$432$		0			0
$433$	6.93725	−	12.0157i	0.333383	−	0.577437i	−0.649790	−	0.760114i	$-0.725143\pi$
$433$	6.93725	−	12.0157i	0.333383	−	0.577437i	0.983173	+	0.182677i	$0.0584764\pi$
$434$		0			0
$435$	17.5830	+	30.4547i	0.843041	+	1.46019i
$436$		0			0
$437$	−6.11438	+	14.6681i	−0.292490	+	0.701670i
$438$		0			0
$439$	−18.4059	−	31.8799i	−0.878465	−	1.52155i	−0.853025	−	0.521869i	$-0.825235\pi$
$439$	−18.4059	−	31.8799i	−0.878465	−	1.52155i	−0.0254393	−	0.999676i	$-0.508098\pi$
$440$		0			0
$441$	8.58301	−	14.8662i	0.408715	−	0.707914i
$442$		0			0
$443$	2.67712	−	4.63692i	0.127194	−	0.220306i	−0.795394	−	0.606092i	$-0.792736\pi$
$443$	2.67712	−	4.63692i	0.127194	−	0.220306i	0.922588	+	0.385786i	$0.126070\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	6.53137	−	11.3127i	0.308923	−	0.535071i
$448$		0			0
$449$	−13.7085			−0.646944			−0.323472	−	0.946238i	$-0.604850\pi$
$449$	−13.7085			−0.646944			−0.323472	+	0.946238i	$0.604850\pi$
$450$		0			0
$451$	3.32288	+	5.75539i	0.156468	+	0.271011i
$452$		0			0
$453$	−3.88562	−	6.73009i	−0.182562	−	0.316207i
$454$		0			0
$455$	12.0000			0.562569
$456$		0			0
$457$	1.12549			0.0526483			0.0263242	−	0.999653i	$-0.491620\pi$
$457$	1.12549			0.0526483			0.0263242	+	0.999653i	$0.491620\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.5830	+	20.0624i	0.539474	+	0.934397i	0.998932	+	0.0461975i	$0.0147103\pi$
$461$	11.5830	+	20.0624i	0.539474	+	0.934397i	−0.459458	+	0.888200i	$0.651956\pi$
$462$		0			0
$463$	−14.4575			−0.671898			−0.335949	−	0.941880i	$-0.609057\pi$
$463$	−14.4575			−0.671898			−0.335949	+	0.941880i	$0.609057\pi$
$464$		0			0
$465$	−1.70850	+	2.95920i	−0.0792297	+	0.137230i
$466$		0			0
$467$	24.6458			1.14047			0.570235	−	0.821482i	$-0.306852\pi$
$467$	24.6458			1.14047			0.570235	+	0.821482i	$0.306852\pi$
$468$		0			0
$469$	−3.82288	+	6.62141i	−0.176524	+	0.305749i
$470$		0			0
$471$	−14.0000	+	24.2487i	−0.645086	+	1.11732i
$472$		0			0
$473$	−0.228757	−	0.396218i	−0.0105182	−	0.0182181i
$474$		0			0
$475$	13.9059	−	33.3595i	0.638046	−	1.53064i
$476$		0			0
$477$	−17.1660	−	29.7324i	−0.785978	−	1.36135i
$478$		0			0
$479$	−7.29150	+	12.6293i	−0.333157	+	0.577045i	−0.983129	−	0.182913i	$-0.941447\pi$
$479$	−7.29150	+	12.6293i	−0.333157	+	0.577045i	0.649972	+	0.759958i	$0.274781\pi$
$480$		0			0
$481$	−5.64575	+	9.77873i	−0.257424	+	0.445872i
$482$		0			0
$483$	−15.8745			−0.722315
$484$		0			0
$485$	26.0516	−	45.1228i	1.18294	−	2.04892i
$486$		0			0
$487$	22.2288			1.00728			0.503641	−	0.863913i	$-0.331994\pi$
$487$	22.2288			1.00728			0.503641	+	0.863913i	$0.331994\pi$
$488$		0			0
$489$	−15.7915	−	27.3517i	−0.714116	−	1.23689i
$490$		0			0
$491$	14.3542	+	24.8623i	0.647798	+	1.12202i	0.983648	+	0.180104i	$0.0576433\pi$
$491$	14.3542	+	24.8623i	0.647798	+	1.12202i	−0.335849	+	0.941916i	$0.609023\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−9.41699			−0.423262
$496$		0			0
$497$	−10.9373	−	18.9439i	−0.490603	−	0.849749i
$498$		0			0
$499$	−15.6144	−	27.0449i	−0.698996	−	1.21070i	−0.968815	−	0.247785i	$-0.920297\pi$
$499$	−15.6144	−	27.0449i	−0.698996	−	1.21070i	0.269819	−	0.962911i	$-0.413036\pi$
$500$		0			0
$501$	31.7490			1.41844
$502$		0			0
$503$	−12.5314	+	21.7050i	−0.558746	+	0.967777i	0.438855	+	0.898558i	$0.355384\pi$
$503$	−12.5314	+	21.7050i	−0.558746	+	0.967777i	−0.997601	+	0.0692192i	$0.977949\pi$
$504$		0			0
$505$	−30.4575			−1.35534
$506$		0			0
$507$	11.9059	−	20.6216i	0.528759	−	0.915837i
$508$		0			0
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	0.263560	+	0.964643i	$0.415103\pi$
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	−0.967185	+	0.254072i	$0.918230\pi$
$510$		0			0
$511$	−10.1144	−	17.5186i	−0.447434	−	0.774978i
$512$		0			0
$513$	−11.4373	+	1.47960i	−0.504967	+	0.0653260i
$514$		0			0
$515$	−4.93725	−	8.55157i	−0.217561	−	0.376827i
$516$		0			0
$517$	−3.11438	+	5.39426i	−0.136970	+	0.237239i
$518$		0			0
$519$	7.93725	−	13.7477i	0.348407	−	0.603458i
$520$		0			0
$521$	−22.2915			−0.976608			−0.488304	−	0.872673i	$-0.662384\pi$
$521$	−22.2915			−0.976608			−0.488304	+	0.872673i	$0.662384\pi$
$522$		0			0
$523$	14.9373	−	25.8721i	0.653161	−	1.13131i	−0.329191	−	0.944263i	$-0.606776\pi$
$523$	14.9373	−	25.8721i	0.653161	−	1.13131i	0.982352	−	0.187044i	$-0.0598906\pi$
$524$		0			0
$525$	36.1033			1.57568
$526$		0			0
$527$		0			0
$528$		0			0
$529$	4.85425	+	8.40781i	0.211054	+	0.365557i
$530$		0			0
$531$	−31.7490			−1.37779
$532$		0			0
$533$	20.5830			0.891549
$534$		0			0
$535$	8.58301	+	14.8662i	0.371076	+	0.642722i
$536$		0			0
$537$	26.3745	+	45.6820i	1.13814	+	1.97132i
$538$		0			0
$539$	2.77124			0.119366
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$		0			0
$543$	−11.1882			−0.480133
$544$		0			0
$545$	12.0000	−	20.7846i	0.514024	−	0.890315i
$546$		0			0
$547$	0.354249	−	0.613577i	0.0151466	−	0.0262346i	−0.858353	−	0.513060i	$-0.828512\pi$
$547$	0.354249	−	0.613577i	0.0151466	−	0.0262346i	0.873499	+	0.486825i	$0.161845\pi$
$548$		0			0
$549$	29.8745	+	51.7442i	1.27501	+	2.20839i
$550$		0			0
$551$	−6.11438	+	14.6681i	−0.260481	+	0.624882i
$552$		0			0
$553$	−3.29150	−	5.70105i	−0.139969	−	0.242433i
$554$		0			0
$555$	−27.2288	+	47.1616i	−1.15580	+	2.00190i
$556$		0			0
$557$	13.2915	−	23.0216i	0.563179	−	0.975455i	−0.434037	−	0.900895i	$-0.642911\pi$
$557$	13.2915	−	23.0216i	0.563179	−	0.975455i	0.997217	−	0.0745599i	$-0.0237552\pi$
$558$		0			0
$559$	−1.41699			−0.0599325
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−25.9373			−1.09312			−0.546562	−	0.837418i	$-0.684064\pi$
$563$	−25.9373			−1.09312			−0.546562	+	0.837418i	$0.684064\pi$
$564$		0			0
$565$	−10.1771	−	17.6273i	−0.428155	−	0.741586i
$566$		0			0
$567$	4.11438	+	7.12631i	0.172788	+	0.299277i
$568$		0			0
$569$	−14.5830			−0.611351			−0.305676	−	0.952136i	$-0.598882\pi$
$569$	−14.5830			−0.611351			−0.305676	+	0.952136i	$0.598882\pi$
$570$		0			0
$571$	39.8118			1.66607			0.833035	−	0.553220i	$-0.186601\pi$
$571$	39.8118			1.66607			0.833035	+	0.553220i	$0.186601\pi$
$572$		0			0
$573$	−19.2915	−	33.4139i	−0.805914	−	1.39588i
$574$		0			0
$575$	15.1144	+	26.1789i	0.630313	+	1.09173i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$	8.70850	−	15.0836i	0.361913	−	0.626851i
$580$		0			0
$581$	13.0627			0.541934
$582$		0			0
$583$	2.77124	−	4.79993i	0.114773	−	0.198793i
$584$		0			0
$585$	−14.5830	+	25.2585i	−0.602933	+	1.04431i
$586$		0			0
$587$	−22.9373	−	39.7285i	−0.946722	−	1.63977i	−0.752267	−	0.658859i	$-0.771039\pi$
$587$	−22.9373	−	39.7285i	−0.946722	−	1.63977i	−0.194455	−	0.980911i	$-0.562294\pi$
$588$		0			0
$589$	−1.53137	+	0.198109i	−0.0630991	+	0.00816294i
$590$		0			0
$591$	3.11438	+	5.39426i	0.128108	+	0.221890i
$592$		0			0
$593$	−20.1458	+	34.8935i	−0.827287	+	1.43290i	0.0728721	+	0.997341i	$0.476784\pi$
$593$	−20.1458	+	34.8935i	−0.827287	+	1.43290i	−0.900159	+	0.435562i	$0.856550\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−31.4170			−1.28581
$598$		0			0
$599$	−0.531373	+	0.920365i	−0.0217113	+	0.0376051i	−0.876677	−	0.481080i	$-0.840245\pi$
$599$	−0.531373	+	0.920365i	−0.0217113	+	0.0376051i	0.854966	+	0.518685i	$0.173578\pi$
$600$		0			0
$601$	31.5830			1.28830			0.644149	−	0.764900i	$-0.277212\pi$
$601$	31.5830			1.28830			0.644149	+	0.764900i	$0.277212\pi$
$602$		0			0
$603$	−9.29150	−	16.0934i	−0.378379	−	0.655372i
$604$		0			0
$605$	19.2915	+	33.4139i	0.784311	+	1.35847i
$606$		0			0
$607$	8.93725			0.362752			0.181376	−	0.983414i	$-0.441945\pi$
$607$	8.93725			0.362752			0.181376	+	0.983414i	$0.441945\pi$
$608$		0			0
$609$	−15.8745			−0.643268
$610$		0			0
$611$	9.64575	+	16.7069i	0.390225	+	0.675890i
$612$		0			0
$613$	−14.2915	−	24.7536i	−0.577228	−	0.999789i	−0.995796	−	0.0916030i	$-0.970801\pi$
$613$	−14.2915	−	24.7536i	−0.577228	−	0.999789i	0.418567	−	0.908186i	$-0.362532\pi$
$614$		0			0
$615$	99.2693			4.00292
$616$		0			0
$617$	−0.437254	+	0.757346i	−0.0176032	+	0.0304896i	−0.874693	−	0.484678i	$-0.838937\pi$
$617$	−0.437254	+	0.757346i	−0.0176032	+	0.0304896i	0.857090	+	0.515167i	$0.172270\pi$
$618$		0			0
$619$	−44.4575			−1.78690			−0.893449	−	0.449164i	$-0.851722\pi$
$619$	−44.4575			−1.78690			−0.893449	+	0.449164i	$0.851722\pi$
$620$		0			0
$621$	4.82288	−	8.35347i	0.193535	−	0.335213i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1.14575	−	1.98450i	−0.0458301	−	0.0793800i
$626$		0			0
$627$	−4.52026	−	5.91841i	−0.180522	−	0.236358i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	11.4059	−	19.7556i	0.454061	−	0.786457i	−0.544573	−	0.838714i	$-0.683308\pi$
$631$	11.4059	−	19.7556i	0.454061	−	0.786457i	0.998634	+	0.0522570i	$0.0166415\pi$
$632$		0			0
$633$	−3.58301	+	6.20595i	−0.142412	+	0.246664i
$634$		0			0
$635$	9.87451			0.391858
$636$		0			0
$637$	4.29150	−	7.43310i	0.170036	−	0.294510i
$638$		0			0
$639$	53.1660			2.10321
$640$		0			0
$641$	9.43725	+	16.3458i	0.372749	+	0.645620i	0.989987	−	0.141156i	$-0.0450819\pi$
$641$	9.43725	+	16.3458i	0.372749	+	0.645620i	−0.617238	+	0.786776i	$0.711749\pi$
$642$		0			0
$643$	15.2601	+	26.4313i	0.601801	+	1.04235i	0.992548	+	0.121852i	$0.0388832\pi$
$643$	15.2601	+	26.4313i	0.601801	+	1.04235i	−0.390748	+	0.920498i	$0.627783\pi$
$644$		0			0
$645$	−6.83399			−0.269088
$646$		0			0
$647$	−30.4575			−1.19741			−0.598704	−	0.800970i	$-0.704317\pi$
$647$	−30.4575			−1.19741			−0.598704	+	0.800970i	$0.704317\pi$
$648$		0			0
$649$	−2.56275	−	4.43881i	−0.100597	−	0.174238i
$650$		0			0
$651$	−0.771243	−	1.33583i	−0.0302274	−	0.0523554i
$652$		0			0
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$		0			0
$655$	−25.4059	+	44.0043i	−0.992690	+	1.71939i
$656$		0			0
$657$	49.1660			1.91815
$658$		0			0
$659$	1.29150	−	2.23695i	0.0503098	−	0.0871391i	−0.839774	−	0.542936i	$-0.817312\pi$
$659$	1.29150	−	2.23695i	0.0503098	−	0.0871391i	0.890084	+	0.455797i	$0.150646\pi$
$660$		0			0
$661$	5.11438	−	8.85836i	0.198926	−	0.344550i	−0.749254	−	0.662282i	$-0.769588\pi$
$661$	5.11438	−	8.85836i	0.198926	−	0.344550i	0.948181	+	0.317732i	$0.102921\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	15.8745	+	20.7846i	0.615587	+	0.805993i
$666$		0			0
$667$	−6.64575	−	11.5108i	−0.257325	−	0.445699i
$668$		0			0
$669$	38.1144	−	66.0160i	1.47359	−	2.55233i
$670$		0			0
$671$	−4.82288	+	8.35347i	−0.186185	+	0.322482i
$672$		0			0
$673$	17.8745			0.689012			0.344506	−	0.938784i	$-0.388046\pi$
$673$	17.8745			0.689012			0.344506	+	0.938784i	$0.388046\pi$
$674$		0			0
$675$	−10.9686	+	18.9982i	−0.422183	+	0.731242i
$676$		0			0
$677$	−32.5830			−1.25227			−0.626133	−	0.779716i	$-0.715363\pi$
$677$	−32.5830			−1.25227			−0.626133	+	0.779716i	$0.715363\pi$
$678$		0			0
$679$	11.7601	+	20.3691i	0.451312	+	0.781696i
$680$		0			0
$681$	−16.7288	−	28.9751i	−0.641047	−	1.11033i
$682$		0			0
$683$	26.5830			1.01717			0.508585	−	0.861012i	$-0.330169\pi$
$683$	26.5830			1.01717			0.508585	+	0.861012i	$0.330169\pi$
$684$		0			0
$685$	−20.3542			−0.777696
$686$		0			0
$687$	−26.4575	−	45.8258i	−1.00942	−	1.74836i
$688$		0			0
$689$	−8.58301	−	14.8662i	−0.326986	−	0.566357i
$690$		0			0
$691$	18.5830			0.706931			0.353465	−	0.935448i	$-0.385003\pi$
$691$	18.5830			0.706931			0.353465	+	0.935448i	$0.385003\pi$
$692$		0			0
$693$	2.12549	−	3.68146i	0.0807408	−	0.139847i
$694$		0			0
$695$	−48.6863			−1.84678
$696$		0			0
$697$		0			0
$698$		0			0
$699$	17.0314	−	29.4992i	0.644186	−	1.11576i
$700$		0			0
$701$	−7.82288	−	13.5496i	−0.295466	−	0.511762i	0.679627	−	0.733558i	$-0.262142\pi$
$701$	−7.82288	−	13.5496i	−0.295466	−	0.511762i	−0.975093	+	0.221796i	$0.928808\pi$
$702$		0			0
$703$	−24.4059	+	3.15731i	−0.920485	+	0.119080i
$704$		0			0
$705$	46.5203	+	80.5755i	1.75205	+	3.03465i
$706$		0			0
$707$	6.87451	−	11.9070i	0.258542	−	0.447809i
$708$		0			0
$709$	0.822876	−	1.42526i	0.0309037	−	0.0535269i	−0.850160	−	0.526525i	$-0.823495\pi$
$709$	0.822876	−	1.42526i	0.0309037	−	0.0535269i	0.881064	+	0.472998i	$0.156828\pi$
$710$		0			0
$711$	16.0000			0.600047
$712$		0			0
$713$	0.645751	−	1.11847i	0.0241836	−	0.0418872i
$714$		0			0
$715$	−4.70850			−0.176088
$716$		0			0
$717$	−15.8745	−	27.4955i	−0.592844	−	1.02684i
$718$		0			0
$719$	6.64575	+	11.5108i	0.247845	+	0.429280i	0.962928	−	0.269760i	$-0.0869444\pi$
$719$	6.64575	+	11.5108i	0.247845	+	0.429280i	−0.715083	+	0.699040i	$0.753611\pi$
$720$		0			0
$721$	4.45751			0.166006
$722$		0			0
$723$	35.9373			1.33652
$724$		0			0
$725$	15.1144	+	26.1789i	0.561334	+	0.972259i
$726$		0			0
$727$	11.2915	+	19.5575i	0.418779	+	0.725346i	0.995817	−	0.0913712i	$-0.0291250\pi$
$727$	11.2915	+	19.5575i	0.418779	+	0.725346i	−0.577038	+	0.816717i	$0.695792\pi$
$728$		0			0
$729$	−41.0000			−1.51852
$730$		0			0
$731$		0			0
$732$		0			0
$733$	42.1033			1.55512			0.777560	−	0.628809i	$-0.216457\pi$
$733$	42.1033			1.55512			0.777560	+	0.628809i	$0.216457\pi$
$734$		0			0
$735$	20.6974	−	35.8489i	0.763434	−	1.32231i
$736$		0			0
$737$	1.50000	−	2.59808i	0.0552532	−	0.0957014i
$738$		0			0
$739$	6.90588	+	11.9613i	0.254037	+	0.440005i	0.964633	−	0.263595i	$-0.0849082\pi$
$739$	6.90588	+	11.9613i	0.254037	+	0.440005i	−0.710597	+	0.703600i	$0.751575\pi$
$740$		0			0
$741$	−22.8745	+	2.95920i	−0.840316	+	0.108709i
$742$		0			0
$743$	−5.23987	−	9.07572i	−0.192232	−	0.332956i	0.753757	−	0.657153i	$-0.228239\pi$
$743$	−5.23987	−	9.07572i	−0.192232	−	0.332956i	−0.945990	+	0.324197i	$0.894906\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		0			0
$747$	−15.8745	+	27.4955i	−0.580818	+	1.00601i
$748$		0			0
$749$	−7.74902			−0.283143
$750$		0			0
$751$	11.9373	−	20.6759i	0.435597	−	0.754475i	−0.561748	−	0.827309i	$-0.689871\pi$
$751$	11.9373	−	20.6759i	0.435597	−	0.754475i	0.997344	+	0.0728333i	$0.0232041\pi$
$752$		0			0
$753$	−7.33202			−0.267194
$754$		0			0
$755$	−5.35425	−	9.27383i	−0.194861	−	0.337509i
$756$		0			0
$757$	−8.29150	−	14.3613i	−0.301360	−	0.521970i	0.675084	−	0.737740i	$-0.264107\pi$
$757$	−8.29150	−	14.3613i	−0.301360	−	0.521970i	−0.976444	+	0.215770i	$0.930774\pi$
$758$		0			0
$759$	6.22876			0.226090
$760$		0			0
$761$	11.1255			0.403299			0.201649	−	0.979458i	$-0.435370\pi$
$761$	11.1255			0.403299			0.201649	+	0.979458i	$0.435370\pi$
$762$		0			0
$763$	5.41699	+	9.38251i	0.196108	+	0.339670i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−15.8745			−0.573195
$768$		0			0
$769$	−12.3542	+	21.3982i	−0.445506	+	0.771638i	−0.998087	−	0.0618204i	$-0.980309\pi$
$769$	−12.3542	+	21.3982i	−0.445506	+	0.771638i	0.552582	+	0.833459i	$0.313643\pi$
$770$		0			0
$771$	4.52026			0.162793
$772$		0			0
$773$	−5.46863	+	9.47194i	−0.196693	+	0.340682i	−0.947454	−	0.319892i	$-0.896354\pi$
$773$	−5.46863	+	9.47194i	−0.196693	+	0.340682i	0.750761	+	0.660574i	$0.229687\pi$
$774$		0			0
$775$	−1.46863	+	2.54374i	−0.0527546	+	0.0913737i
$776$		0			0
$777$	−12.2915	−	21.2895i	−0.440955	−	0.763757i
$778$		0			0
$779$	27.2288	+	35.6508i	0.975571	+	1.27732i
$780$		0			0
$781$	4.29150	+	7.43310i	0.153562	+	0.265977i
$782$		0			0
$783$	4.82288	−	8.35347i	0.172356	−	0.298529i
$784$		0			0
$785$	−19.2915	+	33.4139i	−0.688543	+	1.19259i
$786$		0			0
$787$	5.47974			0.195332			0.0976658	−	0.995219i	$-0.468862\pi$
$787$	5.47974			0.195332			0.0976658	+	0.995219i	$0.468862\pi$
$788$		0			0
$789$	6.53137	−	11.3127i	0.232523	−	0.402742i
$790$		0			0
$791$	9.18824			0.326696
$792$		0			0
$793$	14.9373	+	25.8721i	0.530437	+	0.918745i
$794$		0			0
$795$	−41.3948	−	71.6978i	−1.46812	−	2.54286i
$796$		0			0
$797$	2.81176			0.0995977			0.0497989	−	0.998759i	$-0.484142\pi$
$797$	2.81176			0.0995977			0.0497989	+	0.998759i	$0.484142\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.96863	+	6.87386i	0.140050	+	0.242573i
$804$		0			0
$805$	−21.8745			−0.770975
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$		0			0
$811$	−10.3542	+	17.9341i	−0.363587	+	0.629751i	−0.988548	−	0.150905i	$-0.951781\pi$
$811$	−10.3542	+	17.9341i	−0.363587	+	0.629751i	0.624961	+	0.780656i	$0.285115\pi$
$812$		0			0
$813$	23.3431	−	40.4315i	0.818679	−	1.41799i
$814$		0			0
$815$	−21.7601	−	37.6897i	−0.762224	−	1.32021i
$816$		0			0
$817$	−1.87451	−	2.45431i	−0.0655807	−	0.0858653i
$818$		0			0
$819$	−6.58301	−	11.4021i	−0.230029	−	0.398422i
$820$		0			0
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$		0			0
$823$	−0.0627461	+	0.108679i	−0.00218719	+	0.00378832i	−0.867117	−	0.498105i	$-0.834030\pi$
$823$	−0.0627461	+	0.108679i	−0.00218719	+	0.00378832i	0.864930	+	0.501893i	$0.167363\pi$
$824$		0			0
$825$	−14.1660			−0.493197
$826$		0			0
$827$	−23.6771	+	41.0100i	−0.823334	+	1.42606i	0.0798514	+	0.996807i	$0.474555\pi$
$827$	−23.6771	+	41.0100i	−0.823334	+	1.42606i	−0.903186	+	0.429250i	$0.858778\pi$
$828$		0			0
$829$	25.1660			0.874052			0.437026	−	0.899449i	$-0.356032\pi$
$829$	25.1660			0.874052			0.437026	+	0.899449i	$0.356032\pi$
$830$		0			0
$831$	−12.5941	−	21.8137i	−0.436885	−	0.756707i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	43.7490			1.51400
$836$		0			0
$837$	0.937254			0.0323962
$838$		0			0
$839$	−2.23987	−	3.87957i	−0.0773289	−	0.133938i	0.824768	−	0.565472i	$-0.191306\pi$
$839$	−2.23987	−	3.87957i	−0.0773289	−	0.133938i	−0.902097	+	0.431534i	$0.857972\pi$
$840$		0			0
$841$	7.85425	+	13.6040i	0.270836	+	0.469102i
$842$		0			0
$843$	−72.6458			−2.50205
$844$		0			0
$845$	16.4059	−	28.4158i	0.564379	−	0.977534i
$846$		0			0
$847$	−17.4170			−0.598455
$848$		0			0
$849$	33.5405	−	58.0939i	1.15111	−	1.99378i
$850$		0			0
$851$	10.2915	−	17.8254i	0.352788	−	0.611047i
$852$		0			0
$853$	6.29150	+	10.8972i	0.215417	+	0.373113i	0.953401	−	0.301705i	$-0.0975556\pi$
$853$	6.29150	+	10.8972i	0.215417	+	0.373113i	−0.737985	+	0.674818i	$0.764222\pi$
$854$		0			0
$855$	−63.0405	+	8.15536i	−2.15594	+	0.278907i
$856$		0			0
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	0.629066	−	0.777352i	$-0.283437\pi$
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	−0.987739	+	0.156112i	$0.950104\pi$
$858$		0			0
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	−0.956523	−	0.291656i	$-0.905794\pi$
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	0.730843	+	0.682545i	$0.239127\pi$
$860$		0			0
$861$	−22.4059	+	38.8081i	−0.763590	+	1.32258i
$862$		0			0
$863$	46.9373			1.59776			0.798881	−	0.601489i	$-0.205425\pi$
$863$	46.9373			1.59776			0.798881	+	0.601489i	$0.205425\pi$
$864$		0			0
$865$	10.9373	−	18.9439i	0.371878	−	0.644111i
$866$		0			0
$867$	−44.9778			−1.52753
$868$		0			0
$869$	1.29150	+	2.23695i	0.0438112	+	0.0758833i
$870$		0			0
$871$	−4.64575	−	8.04668i	−0.157415	−	0.272651i
$872$		0			0
$873$	−57.1660			−1.93478
$874$		0			0
$875$	19.7490			0.667639
$876$		0			0
$877$	18.1771	+	31.4837i	0.613798	+	1.06313i	0.990594	+	0.136833i	$0.0436924\pi$
$877$	18.1771	+	31.4837i	0.613798	+	1.06313i	−0.376796	+	0.926296i	$0.622974\pi$
$878$		0			0
$879$	−17.2804	−	29.9305i	−0.582853	−	1.00953i
$880$		0			0
$881$	−5.12549			−0.172682			−0.0863411	−	0.996266i	$-0.527517\pi$
$881$	−5.12549			−0.172682			−0.0863411	+	0.996266i	$0.527517\pi$
$882$		0			0
$883$	20.1974	−	34.9829i	0.679696	−	1.17727i	−0.295376	−	0.955381i	$-0.595445\pi$
$883$	20.1974	−	34.9829i	0.679696	−	1.17727i	0.975072	−	0.221887i	$-0.0712217\pi$
$884$		0			0
$885$	−76.5608			−2.57356
$886$		0			0
$887$	−19.2915	+	33.4139i	−0.647745	+	1.12193i	0.335915	+	0.941892i	$0.390955\pi$
$887$	−19.2915	+	33.4139i	−0.647745	+	1.12193i	−0.983660	+	0.180035i	$0.942379\pi$
$888$		0			0
$889$	−2.22876	+	3.86032i	−0.0747501	+	0.129471i
$890$		0			0
$891$	−1.61438	−	2.79619i	−0.0540837	−	0.0936757i
$892$		0			0
$893$	−16.1771	+	38.8081i	−0.541347	+	1.29866i
$894$		0			0
$895$	36.3431	+	62.9482i	1.21482	+	2.10412i
$896$		0			0
$897$	9.64575	−	16.7069i	0.322062	−	0.557828i
$898$		0			0
$899$	0.645751	−	1.11847i	0.0215370	−	0.0373032i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	1.54249	−	2.67167i	0.0513307	−	0.0889075i
$904$		0			0
$905$	−15.4170			−0.512478
$906$		0			0
$907$	12.0314	+	20.8389i	0.399495	+	0.691946i	0.993664	−	0.112395i	$-0.0358521\pi$
$907$	12.0314	+	20.8389i	0.399495	+	0.691946i	−0.594168	+	0.804341i	$0.702519\pi$
$908$		0			0
$909$	16.7085	+	28.9400i	0.554186	+	0.959878i
$910$		0			0
$911$	−1.06275			−0.0352103			−0.0176052	−	0.999845i	$-0.505604\pi$
$911$	−1.06275			−0.0352103			−0.0176052	+	0.999845i	$0.505604\pi$
$912$		0			0
$913$	−5.12549			−0.169629
$914$		0			0
$915$	72.0405	+	124.778i	2.38159	+	4.12503i
$916$		0			0
$917$	−11.4686	−	19.8642i	−0.378727	−	0.655975i
$918$		0			0
$919$	−11.8745			−0.391704			−0.195852	−	0.980633i	$-0.562747\pi$
$919$	−11.8745			−0.391704			−0.195852	+	0.980633i	$0.562747\pi$
$920$		0			0
$921$	−6.14575	+	10.6448i	−0.202509	+	0.350757i
$922$		0			0
$923$	26.5830			0.874990
$924$		0			0
$925$	−23.4059	+	40.5402i	−0.769581	+	1.33295i
$926$		0			0
$927$	−5.41699	+	9.38251i	−0.177917	+	0.308162i
$928$		0			0
$929$	−5.79150	−	10.0312i	−0.190013	−	0.329112i	0.755241	−	0.655447i	$-0.227520\pi$
$929$	−5.79150	−	10.0312i	−0.190013	−	0.329112i	−0.945254	+	0.326335i	$0.894186\pi$
$930$		0			0
$931$	18.5516	−	2.39997i	0.608005	−	0.0786557i
$932$		0			0
$933$	11.0516	+	19.1420i	0.361814	+	0.626681i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−19.4373	+	33.6663i	−0.634987	+	1.09983i	0.351530	+	0.936176i	$0.385661\pi$
$937$	−19.4373	+	33.6663i	−0.634987	+	1.09983i	−0.986518	+	0.163654i	$0.947672\pi$
$938$		0			0
$939$	−60.5203			−1.97500
$940$		0			0
$941$	−29.5830	+	51.2393i	−0.964378	+	1.67035i	−0.253103	+	0.967439i	$0.581451\pi$
$941$	−29.5830	+	51.2393i	−0.964378	+	1.67035i	−0.711276	+	0.702913i	$0.751882\pi$
$942$		0			0
$943$	−37.5203			−1.22183
$944$		0			0
$945$	−7.93725	−	13.7477i	−0.258199	−	0.447214i
$946$		0			0
$947$	27.8745	+	48.2801i	0.905800	+	1.56889i	0.819840	+	0.572593i	$0.194062\pi$
$947$	27.8745	+	48.2801i	0.905800	+	1.56889i	0.0859598	+	0.996299i	$0.472604\pi$
$948$		0			0
$949$	24.5830			0.797998
$950$		0			0
$951$	−15.8745			−0.514766
$952$		0			0
$953$	−19.7288	−	34.1712i	−0.639077	−	1.10691i	−0.985636	−	0.168886i	$-0.945983\pi$
$953$	−19.7288	−	34.1712i	−0.639077	−	1.10691i	0.346559	−	0.938028i	$-0.387350\pi$
$954$		0			0
$955$	−26.5830	−	46.0431i	−0.860206	−	1.48992i
$956$		0			0
$957$	6.22876			0.201347
$958$		0			0
$959$	4.59412	−	7.95725i	0.148352	−	0.256953i
$960$		0			0
$961$	−30.8745			−0.995952
$962$		0			0
$963$	9.41699	−	16.3107i	0.303458	−	0.525605i
$964$		0			0
$965$	12.0000	−	20.7846i	0.386294	−	0.669080i
$966$		0			0
$967$	−1.35425	−	2.34563i	−0.0435497	−	0.0754303i	0.843429	−	0.537241i	$-0.180533\pi$
$967$	−1.35425	−	2.34563i	−0.0435497	−	0.0754303i	−0.886979	+	0.461810i	$0.847200\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.19738	+	12.4662i	0.230975	+	0.400060i	0.958095	−	0.286450i	$-0.0924751\pi$
$971$	7.19738	+	12.4662i	0.230975	+	0.400060i	−0.727120	+	0.686510i	$0.759142\pi$
$972$		0			0
$973$	10.9889	−	19.0333i	0.352288	−	0.610180i
$974$		0			0
$975$	−21.9373	+	37.9964i	−0.702554	+	1.21686i
$976$		0			0
$977$	45.4575			1.45431			0.727157	−	0.686471i	$-0.240841\pi$
$977$	45.4575			1.45431			0.727157	+	0.686471i	$0.240841\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−26.3320			−0.840717
$982$		0			0
$983$	−15.8745	−	27.4955i	−0.506318	−	0.876969i	−0.999973	−	0.00731102i	$-0.997673\pi$
$983$	−15.8745	−	27.4955i	−0.506318	−	0.876969i	0.493655	−	0.869658i	$-0.335661\pi$
$984$		0			0
$985$	4.29150	+	7.43310i	0.136739	+	0.236838i
$986$		0			0
$987$	−42.0000			−1.33687
$988$		0			0
$989$	2.58301			0.0821348
$990$		0			0
$991$	−22.5830	−	39.1149i	−0.717373	−	1.24253i	−0.962037	−	0.272918i	$-0.912011\pi$
$991$	−22.5830	−	39.1149i	−0.717373	−	1.24253i	0.244664	−	0.969608i	$-0.421322\pi$
$992$		0			0
$993$	−36.7915	−	63.7248i	−1.16754	−	2.02224i
$994$		0			0
$995$	−43.2915			−1.37243
$996$		0			0
$997$	5.11438	−	8.85836i	0.161974	−	0.280547i	−0.773603	−	0.633671i	$-0.781547\pi$
$997$	5.11438	−	8.85836i	0.161974	−	0.280547i	0.935577	+	0.353124i	$0.114881\pi$
$998$		0			0
$999$	14.9373			0.472594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.i.e.273.1		4
3.2	odd	2		2736.2.s.v.577.2		4
4.3	odd	2		38.2.c.b.7.2	✓	4
8.3	odd	2		1216.2.i.l.577.1		4
8.5	even	2		1216.2.i.k.577.2		4
12.11	even	2		342.2.g.f.235.2		4
19.7	even	3		5776.2.a.ba.1.2		2
19.11	even	3	inner	304.2.i.e.49.1		4
19.12	odd	6		5776.2.a.z.1.1		2
20.3	even	4		950.2.j.g.349.1		8
20.7	even	4		950.2.j.g.349.4		8
20.19	odd	2		950.2.e.k.501.1		4
57.11	odd	6		2736.2.s.v.1873.2		4
76.3	even	18		722.2.e.o.595.1		12
76.7	odd	6		722.2.a.j.1.1		2
76.11	odd	6		38.2.c.b.11.2	yes	4
76.15	even	18		722.2.e.o.245.2		12
76.23	odd	18		722.2.e.n.245.1		12
76.27	even	6		722.2.c.j.429.1		4
76.31	even	6		722.2.a.g.1.2		2
76.35	odd	18		722.2.e.n.595.2		12
76.43	odd	18		722.2.e.n.99.1		12
76.47	odd	18		722.2.e.n.415.2		12
76.51	even	18		722.2.e.o.423.2		12
76.55	odd	18		722.2.e.n.389.1		12
76.59	even	18		722.2.e.o.389.2		12
76.63	odd	18		722.2.e.n.423.1		12
76.67	even	18		722.2.e.o.415.1		12
76.71	even	18		722.2.e.o.99.2		12
76.75	even	2		722.2.c.j.653.1		4
152.11	odd	6		1216.2.i.l.961.1		4
152.125	even	6		1216.2.i.k.961.2		4
228.11	even	6		342.2.g.f.163.2		4
228.83	even	6		6498.2.a.ba.1.1		2
228.107	odd	6		6498.2.a.bg.1.1		2
380.87	even	12		950.2.j.g.49.1		8
380.163	even	12		950.2.j.g.49.4		8
380.239	odd	6		950.2.e.k.201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.2	✓	4	4.3	odd	2
38.2.c.b.11.2	yes	4	76.11	odd	6
304.2.i.e.49.1		4	19.11	even	3	inner
304.2.i.e.273.1		4	1.1	even	1	trivial
342.2.g.f.163.2		4	228.11	even	6
342.2.g.f.235.2		4	12.11	even	2
722.2.a.g.1.2		2	76.31	even	6
722.2.a.j.1.1		2	76.7	odd	6
722.2.c.j.429.1		4	76.27	even	6
722.2.c.j.653.1		4	76.75	even	2
722.2.e.n.99.1		12	76.43	odd	18
722.2.e.n.245.1		12	76.23	odd	18
722.2.e.n.389.1		12	76.55	odd	18
722.2.e.n.415.2		12	76.47	odd	18
722.2.e.n.423.1		12	76.63	odd	18
722.2.e.n.595.2		12	76.35	odd	18
722.2.e.o.99.2		12	76.71	even	18
722.2.e.o.245.2		12	76.15	even	18
722.2.e.o.389.2		12	76.59	even	18
722.2.e.o.415.1		12	76.67	even	18
722.2.e.o.423.2		12	76.51	even	18
722.2.e.o.595.1		12	76.3	even	18
950.2.e.k.201.1		4	380.239	odd	6
950.2.e.k.501.1		4	20.19	odd	2
950.2.j.g.49.1		8	380.87	even	12
950.2.j.g.49.4		8	380.163	even	12
950.2.j.g.349.1		8	20.3	even	4
950.2.j.g.349.4		8	20.7	even	4
1216.2.i.k.577.2		4	8.5	even	2
1216.2.i.k.961.2		4	152.125	even	6
1216.2.i.l.577.1		4	8.3	odd	2
1216.2.i.l.961.1		4	152.11	odd	6
2736.2.s.v.577.2		4	3.2	odd	2
2736.2.s.v.1873.2		4	57.11	odd	6
5776.2.a.z.1.1		2	19.12	odd	6
5776.2.a.ba.1.2		2	19.7	even	3
6498.2.a.ba.1.1		2	228.83	even	6
6498.2.a.bg.1.1		2	228.107	odd	6

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32288 - 2.29129i) q^{3} +(-1.82288 - 3.15731i) q^{5} +1.64575 q^{7} +(-2.00000 + 3.46410i) q^{9} -0.645751 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-4.82288 + 8.35347i) q^{15} +(-4.32288 + 0.559237i) q^{19} +(-2.17712 - 3.77089i) q^{21} +(1.82288 - 3.15731i) q^{23} +(-4.14575 + 7.18065i) q^{25} +2.64575 q^{27} +(1.82288 - 3.15731i) q^{29} +0.354249 q^{31} +(0.854249 + 1.47960i) q^{33} +(-3.00000 - 5.19615i) q^{35} +5.64575 q^{37} +5.29150 q^{39} +(-5.14575 - 8.91270i) q^{41} +(0.354249 + 0.613577i) q^{43} +14.5830 q^{45} +(4.82288 - 8.35347i) q^{47} -4.29150 q^{49} +(-4.29150 + 7.43310i) q^{53} +(1.17712 + 2.03884i) q^{55} +(7.00000 + 9.16515i) q^{57} +(3.96863 + 6.87386i) q^{59} +(7.46863 - 12.9360i) q^{61} +(-3.29150 + 5.70105i) q^{63} +7.29150 q^{65} +(-2.32288 + 4.02334i) q^{67} -9.64575 q^{69} +(-6.64575 - 11.5108i) q^{71} +(-6.14575 - 10.6448i) q^{73} +21.9373 q^{75} -1.06275 q^{77} +(-2.00000 - 3.46410i) q^{79} +(2.50000 + 4.33013i) q^{81} +7.93725 q^{83} -9.64575 q^{87} +(-1.64575 + 2.85052i) q^{91} +(-0.468627 - 0.811686i) q^{93} +(9.64575 + 12.6293i) q^{95} +(7.14575 + 12.3768i) q^{97} +(1.29150 - 2.23695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} - 4 q^{7} - 8 q^{9} + 8 q^{11} - 4 q^{13} - 14 q^{15} - 12 q^{19} - 14 q^{21} + 2 q^{23} - 6 q^{25} + 2 q^{29} + 12 q^{31} + 14 q^{33} - 12 q^{35} + 12 q^{37} - 10 q^{41} + 12 q^{43} + 16 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^5 - 4 * q^7 - 8 * q^9 + 8 * q^11 - 4 * q^13 - 14 * q^15 - 12 * q^19 - 14 * q^21 + 2 * q^23 - 6 * q^25 + 2 * q^29 + 12 * q^31 + 14 * q^33 - 12 * q^35 + 12 * q^37 - 10 * q^41 + 12 * q^43 + 16 * q^45 + 14 * q^47 + 4 * q^49 + 4 * q^53 + 10 * q^55 + 28 * q^57 + 14 * q^61 + 8 * q^63 + 8 * q^65 - 4 * q^67 - 28 * q^69 - 16 * q^71 - 14 * q^73 + 56 * q^75 - 36 * q^77 - 8 * q^79 + 10 * q^81 - 28 * q^87 + 4 * q^91 + 14 * q^93 + 28 * q^95 + 18 * q^97 - 16 * q^99

Introduction

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