LMFDB - Embedded newform 740.2.i.a.121.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(121,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, 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("740.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,-7] 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 204x^{10} + 727x^{8} + 1008x^{6} + 426x^{4} + 64x^{2} + 3 $ x^14 + 24x^12 + 204x^10 + 727x^8 + 1008x^6 + 426x^4 + 64x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.5
Root			$-2.93925i$ of defining polynomial
Character	$\chi$	$=$	740.121
Dual form			740.2.i.a.581.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.627876 + 1.08751i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.536763 - 0.929701i) q^{7} +(0.711543 - 1.23243i) q^{9} -0.938843 q^{11} +(-3.28901 - 5.69673i) q^{13} +(0.627876 - 1.08751i) q^{15} +(1.89707 - 3.28581i) q^{17} +(-0.743544 - 1.28786i) q^{19} +(0.674042 - 1.16747i) q^{21} +5.86243 q^{23} +(-0.500000 + 0.866025i) q^{25} +5.55430 q^{27} +0.295422 q^{29} -7.86903 q^{31} +(-0.589477 - 1.02100i) q^{33} +(-0.536763 + 0.929701i) q^{35} +(2.00979 + 5.74114i) q^{37} +(4.13018 - 7.15368i) q^{39} +(-2.16222 - 3.74508i) q^{41} +9.07388 q^{43} -1.42309 q^{45} -7.93093 q^{47} +(2.92377 - 5.06412i) q^{49} +4.76449 q^{51} +(0.658455 - 1.14048i) q^{53} +(0.469422 + 0.813062i) q^{55} +(0.933707 - 1.61723i) q^{57} +(3.12411 - 5.41112i) q^{59} +(1.38905 + 2.40591i) q^{61} -1.52772 q^{63} +(-3.28901 + 5.69673i) q^{65} +(7.37895 + 12.7807i) q^{67} +(3.68088 + 6.37548i) q^{69} +(-5.36436 - 9.29135i) q^{71} -5.92359 q^{73} -1.25575 q^{75} +(0.503937 + 0.872844i) q^{77} +(5.55057 + 9.61387i) q^{79} +(1.35278 + 2.34309i) q^{81} +(0.512248 - 0.887239i) q^{83} -3.79413 q^{85} +(0.185489 + 0.321276i) q^{87} +(5.89192 - 10.2051i) q^{89} +(-3.53083 + 6.11558i) q^{91} +(-4.94078 - 8.55767i) q^{93} +(-0.743544 + 1.28786i) q^{95} +8.64581 q^{97} +(-0.668027 + 1.15706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) $ 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.627876	+	1.08751i	0.362505	+	0.627876i	0.988372	−	0.152053i	$-0.0485884\pi$
$3$	0.627876	+	1.08751i	0.362505	+	0.627876i	−0.625868	+	0.779929i	$0.715255\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.536763	−	0.929701i	−0.202877	−	0.351394i	0.746577	−	0.665299i	$-0.231696\pi$
$7$	−0.536763	−	0.929701i	−0.202877	−	0.351394i	−0.949454	+	0.313905i	$0.898363\pi$
$8$		0			0
$9$	0.711543	−	1.23243i	0.237181	−	0.410809i
$10$		0			0
$11$	−0.938843			−0.283072			−0.141536	−	0.989933i	$-0.545204\pi$
$11$	−0.938843			−0.283072			−0.141536	+	0.989933i	$0.545204\pi$
$12$		0			0
$13$	−3.28901	−	5.69673i	−0.912206	−	1.57999i	−0.810941	−	0.585128i	$-0.801044\pi$
$13$	−3.28901	−	5.69673i	−0.912206	−	1.57999i	−0.101265	−	0.994859i	$-0.532289\pi$
$14$		0			0
$15$	0.627876	−	1.08751i	0.162117	−	0.280795i
$16$		0			0
$17$	1.89707	−	3.28581i	0.460106	−	0.796927i	−0.538860	−	0.842396i	$-0.681145\pi$
$17$	1.89707	−	3.28581i	0.460106	−	0.796927i	0.998966	+	0.0454684i	$0.0144780\pi$
$18$		0			0
$19$	−0.743544	−	1.28786i	−0.170581	−	0.295454i	0.768042	−	0.640399i	$-0.221231\pi$
$19$	−0.743544	−	1.28786i	−0.170581	−	0.295454i	−0.938623	+	0.344945i	$0.887898\pi$
$20$		0			0
$21$	0.674042	−	1.16747i	0.147088	−	0.254764i
$22$		0			0
$23$	5.86243			1.22240			0.611201	−	0.791475i	$-0.290687\pi$
$23$	5.86243			1.22240			0.611201	+	0.791475i	$0.290687\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	5.55430			1.06893
$28$		0			0
$29$	0.295422			0.0548586			0.0274293	−	0.999624i	$-0.491268\pi$
$29$	0.295422			0.0548586			0.0274293	+	0.999624i	$0.491268\pi$
$30$		0			0
$31$	−7.86903			−1.41332			−0.706660	−	0.707554i	$-0.749799\pi$
$31$	−7.86903			−1.41332			−0.706660	+	0.707554i	$0.749799\pi$
$32$		0			0
$33$	−0.589477	−	1.02100i	−0.102615	−	0.177734i
$34$		0			0
$35$	−0.536763	+	0.929701i	−0.0907295	+	0.157148i
$36$		0			0
$37$	2.00979	+	5.74114i	0.330407	+	0.943838i
$37$	2.00979	+	5.74114i	0.330407	+	0.943838i
$38$		0			0
$39$	4.13018	−	7.15368i	0.661358	−	1.14551i
$40$		0			0
$41$	−2.16222	−	3.74508i	−0.337682	−	0.584883i	0.646314	−	0.763071i	$-0.276310\pi$
$41$	−2.16222	−	3.74508i	−0.337682	−	0.584883i	−0.983996	+	0.178189i	$0.942976\pi$
$42$		0			0
$43$	9.07388			1.38375			0.691877	−	0.722016i	$-0.256784\pi$
$43$	9.07388			1.38375			0.691877	+	0.722016i	$0.256784\pi$
$44$		0			0
$45$	−1.42309			−0.212141
$46$		0			0
$47$	−7.93093			−1.15685			−0.578423	−	0.815737i	$-0.696332\pi$
$47$	−7.93093			−1.15685			−0.578423	+	0.815737i	$0.696332\pi$
$48$		0			0
$49$	2.92377	−	5.06412i	0.417682	−	0.723446i
$50$		0			0
$51$	4.76449			0.667162
$52$		0			0
$53$	0.658455	−	1.14048i	0.0904457	−	0.156657i	−0.817253	−	0.576279i	$-0.804504\pi$
$53$	0.658455	−	1.14048i	0.0904457	−	0.156657i	0.907699	+	0.419622i	$0.137838\pi$
$54$		0			0
$55$	0.469422	+	0.813062i	0.0632968	+	0.109633i
$56$		0			0
$57$	0.933707	−	1.61723i	0.123673	−	0.214207i
$58$		0			0
$59$	3.12411	−	5.41112i	0.406725	−	0.704468i	−0.587796	−	0.809010i	$-0.700004\pi$
$59$	3.12411	−	5.41112i	0.406725	−	0.704468i	0.994521	+	0.104541i	$0.0333374\pi$
$60$		0			0
$61$	1.38905	+	2.40591i	0.177850	+	0.308045i	0.941144	−	0.338006i	$-0.109753\pi$
$61$	1.38905	+	2.40591i	0.177850	+	0.308045i	−0.763294	+	0.646051i	$0.776419\pi$
$62$		0			0
$63$	−1.52772			−0.192475
$64$		0			0
$65$	−3.28901	+	5.69673i	−0.407951	+	0.706592i
$66$		0			0
$67$	7.37895	+	12.7807i	0.901483	+	1.56141i	0.825570	+	0.564299i	$0.190853\pi$
$67$	7.37895	+	12.7807i	0.901483	+	1.56141i	0.0759120	+	0.997115i	$0.475813\pi$
$68$		0			0
$69$	3.68088	+	6.37548i	0.443126	+	0.767517i
$70$		0			0
$71$	−5.36436	−	9.29135i	−0.636633	−	1.10268i	−0.986167	−	0.165756i	$-0.946993\pi$
$71$	−5.36436	−	9.29135i	−0.636633	−	1.10268i	0.349534	−	0.936924i	$-0.386340\pi$
$72$		0			0
$73$	−5.92359			−0.693304			−0.346652	−	0.937994i	$-0.612681\pi$
$73$	−5.92359			−0.693304			−0.346652	+	0.937994i	$0.612681\pi$
$74$		0			0
$75$	−1.25575			−0.145002
$76$		0			0
$77$	0.503937	+	0.872844i	0.0574289	+	0.0994698i
$78$		0			0
$79$	5.55057	+	9.61387i	0.624488	+	1.08164i	0.988640	+	0.150305i	$0.0480256\pi$
$79$	5.55057	+	9.61387i	0.624488	+	1.08164i	−0.364152	+	0.931340i	$0.618641\pi$
$80$		0			0
$81$	1.35278	+	2.34309i	0.150309	+	0.260344i
$82$		0			0
$83$	0.512248	−	0.887239i	0.0562265	−	0.0973872i	−0.836542	−	0.547903i	$-0.815426\pi$
$83$	0.512248	−	0.887239i	0.0562265	−	0.0973872i	0.892769	+	0.450515i	$0.148760\pi$
$84$		0			0
$85$	−3.79413			−0.411531
$86$		0			0
$87$	0.185489	+	0.321276i	0.0198865	+	0.0344444i
$88$		0			0
$89$	5.89192	−	10.2051i	0.624542	−	1.08174i	−0.364087	−	0.931365i	$-0.618619\pi$
$89$	5.89192	−	10.2051i	0.624542	−	1.08174i	0.988629	−	0.150374i	$-0.0480478\pi$
$90$		0			0
$91$	−3.53083	+	6.11558i	−0.370132	+	0.641087i
$92$		0			0
$93$	−4.94078	−	8.55767i	−0.512335	−	0.887389i
$94$		0			0
$95$	−0.743544	+	1.28786i	−0.0762860	+	0.132131i
$96$		0			0
$97$	8.64581			0.877849			0.438924	−	0.898524i	$-0.355360\pi$
$97$	8.64581			0.877849			0.438924	+	0.898524i	$0.355360\pi$
$98$		0			0
$99$	−0.668027	+	1.15706i	−0.0671393	+	0.116289i
$100$		0			0
$101$	−19.8755			−1.97769			−0.988845	−	0.148948i	$-0.952411\pi$
$101$	−19.8755			−1.97769			−0.988845	+	0.148948i	$0.952411\pi$
$102$		0			0
$103$	8.14076			0.802133			0.401067	−	0.916049i	$-0.368640\pi$
$103$	8.14076			0.802133			0.401067	+	0.916049i	$0.368640\pi$
$104$		0			0
$105$	−1.34808			−0.131559
$106$		0			0
$107$	1.49420	+	2.58803i	0.144450	+	0.250195i	0.929168	−	0.369659i	$-0.120525\pi$
$107$	1.49420	+	2.58803i	0.144450	+	0.250195i	−0.784718	+	0.619853i	$0.787192\pi$
$108$		0			0
$109$	1.30287	−	2.25664i	0.124792	−	0.216147i	−0.796859	−	0.604165i	$-0.793507\pi$
$109$	1.30287	−	2.25664i	0.124792	−	0.216147i	0.921652	+	0.388018i	$0.126840\pi$
$110$		0			0
$111$	−4.98167	+	5.79040i	−0.472840	+	0.549601i
$112$		0			0
$113$	−7.10075	+	12.2989i	−0.667982	+	1.15698i	0.310485	+	0.950578i	$0.399509\pi$
$113$	−7.10075	+	12.2989i	−0.667982	+	1.15698i	−0.978467	+	0.206401i	$0.933825\pi$
$114$		0			0
$115$	−2.93122	−	5.07702i	−0.273337	−	0.473434i
$116$		0			0
$117$	−9.36107			−0.865432
$118$		0			0
$119$	−4.07310			−0.373381
$120$		0			0
$121$	−10.1186			−0.919870
$122$		0			0
$123$	2.71521	−	4.70289i	0.244823	−	0.424045i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	9.06498	−	15.7010i	0.804387	−	1.39324i	−0.112317	−	0.993672i	$-0.535827\pi$
$127$	9.06498	−	15.7010i	0.804387	−	1.39324i	0.916704	−	0.399567i	$-0.130840\pi$
$128$		0			0
$129$	5.69727	+	9.86796i	0.501617	+	0.868826i
$130$		0			0
$131$	−1.54708	+	2.67962i	−0.135169	+	0.234119i	−0.925662	−	0.378352i	$-0.876491\pi$
$131$	−1.54708	+	2.67962i	−0.135169	+	0.234119i	0.790493	+	0.612471i	$0.209824\pi$
$132$		0			0
$133$	−0.798214	+	1.38255i	−0.0692139	+	0.119882i
$134$		0			0
$135$	−2.77715	−	4.81017i	−0.239019	−	0.413993i
$136$		0			0
$137$	9.58745			0.819111			0.409556	−	0.912285i	$-0.365684\pi$
$137$	9.58745			0.819111			0.409556	+	0.912285i	$0.365684\pi$
$138$		0			0
$139$	−1.84400	+	3.19390i	−0.156406	+	0.270903i	−0.933570	−	0.358395i	$-0.883324\pi$
$139$	−1.84400	+	3.19390i	−0.156406	+	0.270903i	0.777164	+	0.629298i	$0.216658\pi$
$140$		0			0
$141$	−4.97964	−	8.62500i	−0.419362	−	0.726356i
$142$		0			0
$143$	3.08786	+	5.34833i	0.258220	+	0.447250i
$144$		0			0
$145$	−0.147711	−	0.255843i	−0.0122667	−	0.0212466i
$146$		0			0
$147$	7.34306			0.605646
$148$		0			0
$149$	−20.7143			−1.69699			−0.848493	−	0.529207i	$-0.822489\pi$
$149$	−20.7143			−1.69699			−0.848493	+	0.529207i	$0.822489\pi$
$150$		0			0
$151$	1.25053	+	2.16597i	0.101766	+	0.176264i	0.912412	−	0.409272i	$-0.134217\pi$
$151$	1.25053	+	2.16597i	0.101766	+	0.176264i	−0.810646	+	0.585536i	$0.800884\pi$
$152$		0			0
$153$	−2.69969	−	4.67600i	−0.218257	−	0.378032i
$154$		0			0
$155$	3.93451	+	6.81478i	0.316028	+	0.547376i
$156$		0			0
$157$	1.65317	−	2.86337i	0.131937	−	0.228522i	−0.792486	−	0.609890i	$-0.791214\pi$
$157$	1.65317	−	2.86337i	0.131937	−	0.228522i	0.924423	+	0.381368i	$0.124547\pi$
$158$		0			0
$159$	1.65371			0.131148
$160$		0			0
$161$	−3.14674	−	5.45031i	−0.247998	−	0.429545i
$162$		0			0
$163$	−6.80662	+	11.7894i	−0.533135	+	0.923417i	0.466116	+	0.884724i	$0.345653\pi$
$163$	−6.80662	+	11.7894i	−0.533135	+	0.923417i	−0.999251	+	0.0386937i	$0.987680\pi$
$164$		0			0
$165$	−0.589477	+	1.02100i	−0.0458908	+	0.0794851i
$166$		0			0
$167$	0.765424	+	1.32575i	0.0592303	+	0.102590i	0.894120	−	0.447827i	$-0.147802\pi$
$167$	0.765424	+	1.32575i	0.0592303	+	0.102590i	−0.834890	+	0.550417i	$0.814469\pi$
$168$		0			0
$169$	−15.1351	+	26.2148i	−1.16424	+	2.01652i
$170$		0			0
$171$	−2.11625			−0.161834
$172$		0			0
$173$	−12.6499	+	21.9102i	−0.961751	+	1.66580i	−0.243649	+	0.969864i	$0.578344\pi$
$173$	−12.6499	+	21.9102i	−0.961751	+	1.66580i	−0.718102	+	0.695938i	$0.754989\pi$
$174$		0			0
$175$	1.07353			0.0811510
$176$		0			0
$177$	7.84623			0.589759
$178$		0			0
$179$	14.7550			1.10284			0.551421	−	0.834227i	$-0.314086\pi$
$179$	14.7550			1.10284			0.551421	+	0.834227i	$0.314086\pi$
$180$		0			0
$181$	10.5624	+	18.2946i	0.785095	+	1.35982i	0.928942	+	0.370224i	$0.120719\pi$
$181$	10.5624	+	18.2946i	0.785095	+	1.35982i	−0.143847	+	0.989600i	$0.545947\pi$
$182$		0			0
$183$	−1.74431	+	3.02123i	−0.128943	+	0.223335i
$184$		0			0
$185$	3.96708	−	4.61110i	0.291666	−	0.339015i
$186$		0			0
$187$	−1.78105	+	3.08487i	−0.130243	+	0.225588i
$188$		0			0
$189$	−2.98134	−	5.16384i	−0.216861	−	0.375614i
$190$		0			0
$191$	−3.76835			−0.272668			−0.136334	−	0.990663i	$-0.543532\pi$
$191$	−3.76835			−0.272668			−0.136334	+	0.990663i	$0.543532\pi$
$192$		0			0
$193$	1.48225			0.106695			0.0533474	−	0.998576i	$-0.483011\pi$
$193$	1.48225			0.106695			0.0533474	+	0.998576i	$0.483011\pi$
$194$		0			0
$195$	−8.26035			−0.591536
$196$		0			0
$197$	5.55301	−	9.61809i	0.395635	−	0.685261i	−0.597547	−	0.801834i	$-0.703858\pi$
$197$	5.55301	−	9.61809i	0.395635	−	0.685261i	0.993182	+	0.116574i	$0.0371911\pi$
$198$		0			0
$199$	−0.419105			−0.0297096			−0.0148548	−	0.999890i	$-0.504729\pi$
$199$	−0.419105			−0.0297096			−0.0148548	+	0.999890i	$0.504729\pi$
$200$		0			0
$201$	−9.26614	+	16.0494i	−0.653583	+	1.13204i
$202$		0			0
$203$	−0.158572	−	0.274655i	−0.0111296	−	0.0192770i
$204$		0			0
$205$	−2.16222	+	3.74508i	−0.151016	+	0.261567i
$206$		0			0
$207$	4.17137	−	7.22503i	0.289930	−	0.502174i
$208$		0			0
$209$	0.698071	+	1.20909i	0.0482866	+	0.0836348i
$210$		0			0
$211$	−0.952451			−0.0655695			−0.0327847	−	0.999462i	$-0.510438\pi$
$211$	−0.952451			−0.0655695			−0.0327847	+	0.999462i	$0.510438\pi$
$212$		0			0
$213$	6.73631	−	11.6676i	0.461564	−	0.799453i
$214$		0			0
$215$	−4.53694	−	7.85821i	−0.309417	−	0.535925i
$216$		0			0
$217$	4.22380	+	7.31584i	0.286731	+	0.496632i
$218$		0			0
$219$	−3.71928	−	6.44198i	−0.251326	−	0.435309i
$220$		0			0
$221$	−24.9578			−1.67885
$222$		0			0
$223$	16.3399			1.09420			0.547102	−	0.837066i	$-0.315731\pi$
$223$	16.3399			1.09420			0.547102	+	0.837066i	$0.315731\pi$
$224$		0			0
$225$	0.711543	+	1.23243i	0.0474362	+	0.0821619i
$226$		0			0
$227$	1.25722	+	2.17756i	0.0834445	+	0.144530i	0.904727	−	0.425991i	$-0.140075\pi$
$227$	1.25722	+	2.17756i	0.0834445	+	0.144530i	−0.821283	+	0.570521i	$0.806741\pi$
$228$		0			0
$229$	12.9482	+	22.4270i	0.855644	+	1.48202i	0.876046	+	0.482227i	$0.160172\pi$
$229$	12.9482	+	22.4270i	0.855644	+	1.48202i	−0.0204019	+	0.999792i	$0.506495\pi$
$230$		0			0
$231$	−0.632820	+	1.09608i	−0.0416365	+	0.0721165i
$232$		0			0
$233$	6.89328			0.451594			0.225797	−	0.974174i	$-0.427501\pi$
$233$	6.89328			0.451594			0.225797	+	0.974174i	$0.427501\pi$
$234$		0			0
$235$	3.96547	+	6.86839i	0.258679	+	0.448044i
$236$		0			0
$237$	−6.97014	+	12.0726i	−0.452759	+	0.784202i
$238$		0			0
$239$	11.6277	−	20.1398i	0.752134	−	1.30273i	−0.194653	−	0.980872i	$-0.562358\pi$
$239$	11.6277	−	20.1398i	0.752134	−	1.30273i	0.946787	−	0.321862i	$-0.104309\pi$
$240$		0			0
$241$	−7.70827	−	13.3511i	−0.496533	−	0.860021i	0.503459	−	0.864019i	$-0.332061\pi$
$241$	−7.70827	−	13.3511i	−0.496533	−	0.860021i	−0.999992	+	0.00399859i	$0.998727\pi$
$242$		0			0
$243$	6.63269	−	11.4882i	0.425487	−	0.736965i
$244$		0			0
$245$	−5.84754			−0.373586
$246$		0			0
$247$	−4.89104	+	8.47153i	−0.311209	+	0.539031i
$248$		0			0
$249$	1.28651			0.0815294
$250$		0			0
$251$	1.96634			0.124114			0.0620571	−	0.998073i	$-0.480234\pi$
$251$	1.96634			0.124114			0.0620571	+	0.998073i	$0.480234\pi$
$252$		0			0
$253$	−5.50391			−0.346028
$254$		0			0
$255$	−2.38225	−	4.12617i	−0.149182	−	0.258391i
$256$		0			0
$257$	−1.74766	+	3.02703i	−0.109016	+	0.188821i	−0.915372	−	0.402610i	$-0.868103\pi$
$257$	−1.74766	+	3.02703i	−0.109016	+	0.188821i	0.806356	+	0.591430i	$0.201437\pi$
$258$		0			0
$259$	4.25877	−	4.95014i	0.264627	−	0.307587i
$260$		0			0
$261$	0.210206	−	0.364087i	0.0130114	−	0.0225364i
$262$		0			0
$263$	11.6991	+	20.2635i	0.721400	+	1.24950i	0.960439	+	0.278492i	$0.0898346\pi$
$263$	11.6991	+	20.2635i	0.721400	+	1.24950i	−0.239038	+	0.971010i	$0.576832\pi$
$264$		0			0
$265$	−1.31691			−0.0808971
$266$		0			0
$267$	14.7976			0.905598
$268$		0			0
$269$	19.7745			1.20567			0.602837	−	0.797865i	$-0.294037\pi$
$269$	19.7745			1.20567			0.602837	+	0.797865i	$0.294037\pi$
$270$		0			0
$271$	1.28877	−	2.23221i	0.0782871	−	0.135597i	−0.824224	−	0.566264i	$-0.808388\pi$
$271$	1.28877	−	2.23221i	0.0782871	−	0.135597i	0.902511	+	0.430667i	$0.141722\pi$
$272$		0			0
$273$	−8.86771			−0.536698
$274$		0			0
$275$	0.469422	−	0.813062i	0.0283072	−	0.0490295i
$276$		0			0
$277$	−2.14668	−	3.71816i	−0.128982	−	0.223403i	0.794301	−	0.607525i	$-0.207838\pi$
$277$	−2.14668	−	3.71816i	−0.128982	−	0.223403i	−0.923282	+	0.384122i	$0.874504\pi$
$278$		0			0
$279$	−5.59915	+	9.69801i	−0.335212	+	0.580605i
$280$		0			0
$281$	2.97225	−	5.14809i	0.177310	−	0.307109i	−0.763648	−	0.645632i	$-0.776594\pi$
$281$	2.97225	−	5.14809i	0.177310	−	0.307109i	0.940958	+	0.338523i	$0.109927\pi$
$282$		0			0
$283$	10.8974	+	18.8749i	0.647785	+	1.12200i	0.983651	+	0.180086i	$0.0576377\pi$
$283$	10.8974	+	18.8749i	0.647785	+	1.12200i	−0.335866	+	0.941910i	$0.609029\pi$
$284$		0			0
$285$	−1.86741			−0.110616
$286$		0			0
$287$	−2.32120	+	4.02044i	−0.137016	+	0.237319i
$288$		0			0
$289$	1.30228	+	2.25562i	0.0766048	+	0.132683i
$290$		0			0
$291$	5.42850	+	9.40243i	0.318224	+	0.551180i
$292$		0			0
$293$	−6.92061	−	11.9868i	−0.404306	−	0.700279i	0.589934	−	0.807451i	$-0.299154\pi$
$293$	−6.92061	−	11.9868i	−0.404306	−	0.700279i	−0.994240	+	0.107172i	$0.965820\pi$
$294$		0			0
$295$	−6.24823			−0.363786
$296$		0			0
$297$	−5.21462			−0.302583
$298$		0			0
$299$	−19.2816	−	33.3967i	−1.11508	−	1.93138i
$300$		0			0
$301$	−4.87052	−	8.43599i	−0.280732	−	0.486243i
$302$		0			0
$303$	−12.4794	−	21.6149i	−0.716922	−	1.24174i
$304$		0			0
$305$	1.38905	−	2.40591i	0.0795369	−	0.137762i
$306$		0			0
$307$	20.8175			1.18812			0.594059	−	0.804421i	$-0.297525\pi$
$307$	20.8175			1.18812			0.594059	+	0.804421i	$0.297525\pi$
$308$		0			0
$309$	5.11139	+	8.85319i	0.290777	+	0.503640i
$310$		0			0
$311$	−4.94144	+	8.55882i	−0.280203	+	0.485326i	−0.971435	−	0.237307i	$-0.923735\pi$
$311$	−4.94144	+	8.55882i	−0.280203	+	0.485326i	0.691231	+	0.722633i	$0.257069\pi$
$312$		0			0
$313$	6.24087	−	10.8095i	0.352755	−	0.610990i	−0.633976	−	0.773353i	$-0.718578\pi$
$313$	6.24087	−	10.8095i	0.352755	−	0.610990i	0.986731	+	0.162363i	$0.0519116\pi$
$314$		0			0
$315$	0.763860	+	1.32304i	0.0430386	+	0.0745451i
$316$		0			0
$317$	13.6203	−	23.5911i	0.764994	−	1.32501i	−0.175256	−	0.984523i	$-0.556075\pi$
$317$	13.6203	−	23.5911i	0.764994	−	1.32501i	0.940250	−	0.340486i	$-0.110592\pi$
$318$		0			0
$319$	−0.277355			−0.0155289
$320$		0			0
$321$	−1.87635	+	3.24993i	−0.104728	+	0.181393i
$322$		0			0
$323$	−5.64221			−0.313941
$324$		0			0
$325$	6.57801			0.364882
$326$		0			0
$327$	3.27217			0.180951
$328$		0			0
$329$	4.25703	+	7.37340i	0.234698	+	0.406509i
$330$		0			0
$331$	−12.3546	+	21.3988i	−0.679071	+	1.17618i	0.296191	+	0.955129i	$0.404284\pi$
$331$	−12.3546	+	21.3988i	−0.679071	+	1.17618i	−0.975261	+	0.221056i	$0.929050\pi$
$332$		0			0
$333$	8.50560	+	1.60815i	0.466104	+	0.0881260i
$334$		0			0
$335$	7.37895	−	12.7807i	0.403155	−	0.698285i
$336$		0			0
$337$	−7.26642	−	12.5858i	−0.395827	−	0.685593i	0.597379	−	0.801959i	$-0.296209\pi$
$337$	−7.26642	−	12.5858i	−0.395827	−	0.685593i	−0.993206	+	0.116366i	$0.962875\pi$
$338$		0			0
$339$	−17.8336			−0.968587
$340$		0			0
$341$	7.38778			0.400071
$342$		0			0
$343$	−13.7922			−0.744707
$344$		0			0
$345$	3.68088	−	6.37548i	0.198172	−	0.343244i
$346$		0			0
$347$	17.8268			0.956992			0.478496	−	0.878090i	$-0.341182\pi$
$347$	17.8268			0.956992			0.478496	+	0.878090i	$0.341182\pi$
$348$		0			0
$349$	14.5217	−	25.1523i	0.777329	−	1.34637i	−0.156147	−	0.987734i	$-0.549907\pi$
$349$	14.5217	−	25.1523i	0.777329	−	1.34637i	0.933476	−	0.358640i	$-0.116759\pi$
$350$		0			0
$351$	−18.2681	−	31.6413i	−0.975081	−	1.68889i
$352$		0			0
$353$	10.6076	−	18.3729i	0.564585	−	0.977890i	−0.432503	−	0.901633i	$-0.642369\pi$
$353$	10.6076	−	18.3729i	0.564585	−	0.977890i	0.997088	−	0.0762578i	$-0.0242972\pi$
$354$		0			0
$355$	−5.36436	+	9.29135i	−0.284711	+	0.493133i
$356$		0			0
$357$	−2.55740	−	4.42955i	−0.135352	−	0.234437i
$358$		0			0
$359$	−12.7165			−0.671150			−0.335575	−	0.942013i	$-0.608931\pi$
$359$	−12.7165			−0.671150			−0.335575	+	0.942013i	$0.608931\pi$
$360$		0			0
$361$	8.39428	−	14.5393i	0.441804	−	0.765228i
$362$		0			0
$363$	−6.35321	−	11.0041i	−0.333457	−	0.577565i
$364$		0			0
$365$	2.96180	+	5.12998i	0.155027	+	0.268515i
$366$		0			0
$367$	−11.7702	−	20.3865i	−0.614398	−	1.06417i	−0.990490	−	0.137586i	$-0.956066\pi$
$367$	−11.7702	−	20.3865i	−0.614398	−	1.06417i	0.376092	−	0.926582i	$-0.377268\pi$
$368$		0			0
$369$	−6.15405			−0.320367
$370$		0			0
$371$	−1.41374			−0.0733976
$372$		0			0
$373$	−10.3453	−	17.9187i	−0.535662	−	0.927794i	−0.999131	−	0.0416805i	$-0.986729\pi$
$373$	−10.3453	−	17.9187i	−0.535662	−	0.927794i	0.463469	−	0.886113i	$-0.346604\pi$
$374$		0			0
$375$	0.627876	+	1.08751i	0.0324234	+	0.0561590i
$376$		0			0
$377$	−0.971646	−	1.68294i	−0.0500423	−	0.0866758i
$378$		0			0
$379$	−14.1059	+	24.4322i	−0.724572	+	1.25500i	0.234578	+	0.972097i	$0.424629\pi$
$379$	−14.1059	+	24.4322i	−0.724572	+	1.25500i	−0.959150	+	0.282898i	$0.908704\pi$
$380$		0			0
$381$	22.7668			1.16638
$382$		0			0
$383$	−16.0593	−	27.8155i	−0.820590	−	1.42130i	−0.905243	−	0.424894i	$-0.860311\pi$
$383$	−16.0593	−	27.8155i	−0.820590	−	1.42130i	0.0846527	−	0.996411i	$-0.473022\pi$
$384$		0			0
$385$	0.503937	−	0.872844i	0.0256830	−	0.0444842i
$386$		0			0
$387$	6.45645	−	11.1829i	0.328200	−	0.568459i
$388$		0			0
$389$	16.8431	+	29.1730i	0.853977	+	1.47913i	0.877591	+	0.479410i	$0.159149\pi$
$389$	16.8431	+	29.1730i	0.853977	+	1.47913i	−0.0236139	+	0.999721i	$0.507517\pi$
$390$		0			0
$391$	11.1214	−	19.2629i	0.562435	−	0.974165i
$392$		0			0
$393$	−3.88549			−0.195997
$394$		0			0
$395$	5.55057	−	9.61387i	0.279279	−	0.483726i
$396$		0			0
$397$	10.4513			0.524537			0.262269	−	0.964995i	$-0.415529\pi$
$397$	10.4513			0.524537			0.262269	+	0.964995i	$0.415529\pi$
$398$		0			0
$399$	−2.00472			−0.100361
$400$		0			0
$401$	11.6922			0.583881			0.291940	−	0.956436i	$-0.405699\pi$
$401$	11.6922			0.583881			0.291940	+	0.956436i	$0.405699\pi$
$402$		0			0
$403$	25.8813	+	44.8277i	1.28924	+	2.23303i
$404$		0			0
$405$	1.35278	−	2.34309i	0.0672204	−	0.116429i
$406$		0			0
$407$	−1.88688	−	5.39004i	−0.0935291	−	0.267174i
$408$		0			0
$409$	7.14418	−	12.3741i	0.353257	−	0.611859i	−0.633561	−	0.773693i	$-0.718408\pi$
$409$	7.14418	−	12.3741i	0.353257	−	0.611859i	0.986818	+	0.161834i	$0.0517409\pi$
$410$		0			0
$411$	6.01973	+	10.4265i	0.296932	+	0.514300i
$412$		0			0
$413$	−6.70764			−0.330061
$414$		0			0
$415$	−1.02450			−0.0502905
$416$		0			0
$417$	−4.63122			−0.226792
$418$		0			0
$419$	4.17503	−	7.23137i	0.203964	−	0.353276i	−0.745838	−	0.666127i	$-0.767951\pi$
$419$	4.17503	−	7.23137i	0.203964	−	0.353276i	0.949802	+	0.312851i	$0.101284\pi$
$420$		0			0
$421$	−9.35174			−0.455776			−0.227888	−	0.973687i	$-0.573182\pi$
$421$	−9.35174			−0.455776			−0.227888	+	0.973687i	$0.573182\pi$
$422$		0			0
$423$	−5.64320	+	9.77431i	−0.274382	+	0.475243i
$424$		0			0
$425$	1.89707	+	3.28581i	0.0920212	+	0.159385i
$426$		0			0
$427$	1.49118	−	2.58281i	0.0721635	−	0.124991i
$428$		0			0
$429$	−3.87759	+	6.71618i	−0.187212	+	0.324260i
$430$		0			0
$431$	2.56484	+	4.44244i	0.123544	+	0.213985i	0.921163	−	0.389177i	$-0.127241\pi$
$431$	2.56484	+	4.44244i	0.123544	+	0.213985i	−0.797619	+	0.603162i	$0.793907\pi$
$432$		0			0
$433$	12.2729			0.589799			0.294900	−	0.955528i	$-0.404714\pi$
$433$	12.2729			0.589799			0.294900	+	0.955528i	$0.404714\pi$
$434$		0			0
$435$	0.185489	−	0.321276i	0.00889350	−	0.0154040i
$436$		0			0
$437$	−4.35898	−	7.54997i	−0.208518	−	0.361164i
$438$		0			0
$439$	15.1994	+	26.3261i	0.725427	+	1.25648i	0.958798	+	0.284088i	$0.0916908\pi$
$439$	15.1994	+	26.3261i	0.725427	+	1.25648i	−0.233372	+	0.972388i	$0.574976\pi$
$440$		0			0
$441$	−4.16078	−	7.20668i	−0.198132	−	0.343175i
$442$		0			0
$443$	6.70258			0.318449			0.159225	−	0.987242i	$-0.449101\pi$
$443$	6.70258			0.318449			0.159225	+	0.987242i	$0.449101\pi$
$444$		0			0
$445$	−11.7838			−0.558608
$446$		0			0
$447$	−13.0060	−	22.5271i	−0.615165	−	1.06550i
$448$		0			0
$449$	−13.7437	−	23.8049i	−0.648608	−	1.12342i	−0.983456	−	0.181149i	$-0.942018\pi$
$449$	−13.7437	−	23.8049i	−0.648608	−	1.12342i	0.334848	−	0.942272i	$-0.391315\pi$
$450$		0			0
$451$	2.02999	+	3.51604i	0.0955883	+	0.165564i
$452$		0			0
$453$	−1.57035	+	2.71993i	−0.0737815	+	0.127793i
$454$		0			0
$455$	7.06167			0.331056
$456$		0			0
$457$	9.90098	+	17.1490i	0.463148	+	0.802196i	0.999116	−	0.0420424i	$-0.0133864\pi$
$457$	9.90098	+	17.1490i	0.463148	+	0.802196i	−0.535968	+	0.844238i	$0.680053\pi$
$458$		0			0
$459$	10.5369	−	18.2504i	0.491819	−	0.851856i
$460$		0			0
$461$	2.10565	−	3.64709i	0.0980697	−	0.169862i	−0.812816	−	0.582521i	$-0.802067\pi$
$461$	2.10565	−	3.64709i	0.0980697	−	0.169862i	0.910886	+	0.412659i	$0.135400\pi$
$462$		0			0
$463$	11.4214	+	19.7824i	0.530797	+	0.919368i	0.999354	+	0.0359346i	$0.0114408\pi$
$463$	11.4214	+	19.7824i	0.530797	+	0.919368i	−0.468557	+	0.883433i	$0.655226\pi$
$464$		0			0
$465$	−4.94078	+	8.55767i	−0.229123	+	0.396853i
$466$		0			0
$467$	−2.24003			−0.103656			−0.0518282	−	0.998656i	$-0.516505\pi$
$467$	−2.24003			−0.103656			−0.0518282	+	0.998656i	$0.516505\pi$
$468$		0			0
$469$	7.92150	−	13.7204i	0.365781	−	0.633551i
$470$		0			0
$471$	4.15194			0.191311
$472$		0			0
$473$	−8.51895			−0.391702
$474$		0			0
$475$	1.48709			0.0682323
$476$		0			0
$477$	−0.937037	−	1.62300i	−0.0429040	−	0.0743119i
$478$		0			0
$479$	8.93388	−	15.4739i	0.408200	−	0.707022i	−0.586489	−	0.809958i	$-0.699490\pi$
$479$	8.93388	−	15.4739i	0.408200	−	0.707022i	0.994688	+	0.102935i	$0.0328234\pi$
$480$		0			0
$481$	26.0955	−	30.3319i	1.18985	−	1.38301i
$482$		0			0
$483$	3.95152	−	6.84424i	0.179801	−	0.311424i
$484$		0			0
$485$	−4.32290	−	7.48749i	−0.196293	−	0.339989i
$486$		0			0
$487$	9.30202			0.421515			0.210757	−	0.977538i	$-0.432407\pi$
$487$	9.30202			0.421515			0.210757	+	0.977538i	$0.432407\pi$
$488$		0			0
$489$	−17.0948			−0.773056
$490$		0			0
$491$	−15.2392			−0.687736			−0.343868	−	0.939018i	$-0.611737\pi$
$491$	−15.2392			−0.687736			−0.343868	+	0.939018i	$0.611737\pi$
$492$		0			0
$493$	0.560436	−	0.970703i	0.0252408	−	0.0437183i
$494$		0			0
$495$	1.33605			0.0600512
$496$		0			0
$497$	−5.75878	+	9.97451i	−0.258317	+	0.447418i
$498$		0			0
$499$	16.5979	+	28.7484i	0.743024	+	1.28695i	0.951112	+	0.308845i	$0.0999424\pi$
$499$	16.5979	+	28.7484i	0.743024	+	1.28695i	−0.208089	+	0.978110i	$0.566724\pi$
$500$		0			0
$501$	−0.961183	+	1.66482i	−0.0429425	+	0.0743785i
$502$		0			0
$503$	5.05641	−	8.75796i	0.225454	−	0.390498i	−0.731001	−	0.682376i	$-0.760947\pi$
$503$	5.05641	−	8.75796i	0.225454	−	0.390498i	0.956456	+	0.291878i	$0.0942800\pi$
$504$		0			0
$505$	9.93777	+	17.2127i	0.442225	+	0.765956i
$506$		0			0
$507$	−38.0119			−1.68817
$508$		0			0
$509$	−10.3775	+	17.9744i	−0.459977	+	0.796703i	−0.998959	−	0.0456140i	$-0.985476\pi$
$509$	−10.3775	+	17.9744i	−0.459977	+	0.796703i	0.538982	+	0.842317i	$0.318809\pi$
$510$		0			0
$511$	3.17957	+	5.50717i	0.140656	+	0.243623i
$512$		0			0
$513$	−4.12987	−	7.15314i	−0.182338	−	0.315819i
$514$		0			0
$515$	−4.07038	−	7.05011i	−0.179362	−	0.310665i
$516$		0			0
$517$	7.44590			0.327470
$518$		0			0
$519$	−31.7702			−1.39456
$520$		0			0
$521$	10.4358	+	18.0753i	0.457201	+	0.791895i	0.998812	−	0.0487341i	$-0.0155187\pi$
$521$	10.4358	+	18.0753i	0.457201	+	0.791895i	−0.541611	+	0.840629i	$0.682185\pi$
$522$		0			0
$523$	4.50153	+	7.79687i	0.196838	+	0.340933i	0.947501	−	0.319751i	$-0.103599\pi$
$523$	4.50153	+	7.79687i	0.196838	+	0.340933i	−0.750664	+	0.660685i	$0.770266\pi$
$524$		0			0
$525$	0.674042	+	1.16747i	0.0294176	+	0.0509528i
$526$		0			0
$527$	−14.9281	+	25.8562i	−0.650277	+	1.12631i
$528$		0			0
$529$	11.3681			0.494267
$530$		0			0
$531$	−4.44588	−	7.70049i	−0.192935	−	0.334173i
$532$		0			0
$533$	−14.2231	+	24.6352i	−0.616071	+	1.06707i
$534$		0			0
$535$	1.49420	−	2.58803i	0.0646000	−	0.111891i
$536$		0			0
$537$	9.26433	+	16.0463i	0.399785	+	0.692448i
$538$		0			0
$539$	−2.74496	+	4.75441i	−0.118234	+	0.204787i
$540$		0			0
$541$	18.2759			0.785743			0.392872	−	0.919593i	$-0.371482\pi$
$541$	18.2759			0.785743			0.392872	+	0.919593i	$0.371482\pi$
$542$		0			0
$543$	−13.2637	+	22.9734i	−0.569201	+	0.985885i
$544$		0			0
$545$	−2.60574			−0.111618
$546$		0			0
$547$	−35.1508			−1.50294			−0.751470	−	0.659767i	$-0.770655\pi$
$547$	−35.1508			−1.50294			−0.751470	+	0.659767i	$0.770655\pi$
$548$		0			0
$549$	3.95348			0.168730
$550$		0			0
$551$	−0.219660	−	0.380461i	−0.00935781	−	0.0162082i
$552$		0			0
$553$	5.95868	−	10.3207i	0.253389	−	0.438883i
$554$		0			0
$555$	7.50547	+	1.41905i	0.318590	+	0.0602355i
$556$		0			0
$557$	3.58771	−	6.21410i	0.152016	−	0.263300i	−0.779952	−	0.625839i	$-0.784757\pi$
$557$	3.58771	−	6.21410i	0.152016	−	0.263300i	0.931969	+	0.362539i	$0.118090\pi$
$558$		0			0
$559$	−29.8440	−	51.6914i	−1.26227	−	2.18631i
$560$		0			0
$561$	−4.47311			−0.188855
$562$		0			0
$563$	21.0982			0.889183			0.444591	−	0.895734i	$-0.353349\pi$
$563$	21.0982			0.889183			0.444591	+	0.895734i	$0.353349\pi$
$564$		0			0
$565$	14.2015			0.597462
$566$		0			0
$567$	1.45225	−	2.51537i	0.0609888	−	0.105636i
$568$		0			0
$569$	34.0899			1.42912			0.714562	−	0.699572i	$-0.246626\pi$
$569$	34.0899			1.42912			0.714562	+	0.699572i	$0.246626\pi$
$570$		0			0
$571$	3.01284	−	5.21839i	0.126083	−	0.218383i	−0.796073	−	0.605201i	$-0.793093\pi$
$571$	3.01284	−	5.21839i	0.126083	−	0.218383i	0.922156	+	0.386818i	$0.126426\pi$
$572$		0			0
$573$	−2.36605	−	4.09813i	−0.0988433	−	0.171202i
$574$		0			0
$575$	−2.93122	+	5.07702i	−0.122240	+	0.211726i
$576$		0			0
$577$	−5.14717	+	8.91516i	−0.214279	+	0.371143i	−0.953049	−	0.302815i	$-0.902074\pi$
$577$	−5.14717	+	8.91516i	−0.214279	+	0.371143i	0.738770	+	0.673958i	$0.235407\pi$
$578$		0			0
$579$	0.930670	+	1.61197i	0.0386773	+	0.0669911i
$580$		0			0
$581$	−1.09982			−0.0456283
$582$		0			0
$583$	−0.618186	+	1.07073i	−0.0256026	+	0.0443451i
$584$		0			0
$585$	4.68054	+	8.10693i	0.193516	+	0.335180i
$586$		0			0
$587$	12.8641	+	22.2813i	0.530959	+	0.919648i	0.999347	+	0.0361251i	$0.0115015\pi$
$587$	12.8641	+	22.2813i	0.530959	+	0.919648i	−0.468388	+	0.883523i	$0.655165\pi$
$588$		0			0
$589$	5.85097	+	10.1342i	0.241085	+	0.417571i
$590$		0			0
$591$	13.9464			0.573678
$592$		0			0
$593$	−7.06862			−0.290273			−0.145137	−	0.989412i	$-0.546362\pi$
$593$	−7.06862			−0.290273			−0.145137	+	0.989412i	$0.546362\pi$
$594$		0			0
$595$	2.03655	+	3.52741i	0.0834904	+	0.144610i
$596$		0			0
$597$	−0.263146	−	0.455783i	−0.0107699	−	0.0186539i
$598$		0			0
$599$	−15.9277	−	27.5877i	−0.650790	−	1.12720i	−0.982932	−	0.183972i	$-0.941104\pi$
$599$	−15.9277	−	27.5877i	−0.650790	−	1.12720i	0.332141	−	0.943230i	$-0.392229\pi$
$600$		0			0
$601$	−0.331591	+	0.574333i	−0.0135259	+	0.0234275i	−0.872709	−	0.488241i	$-0.837639\pi$
$601$	−0.331591	+	0.574333i	−0.0135259	+	0.0234275i	0.859183	+	0.511668i	$0.170972\pi$
$602$		0			0
$603$	21.0018			0.855258
$604$		0			0
$605$	5.05929	+	8.76294i	0.205689	+	0.356264i
$606$		0			0
$607$	−22.7156	+	39.3446i	−0.921998	+	1.59695i	−0.125677	+	0.992071i	$0.540110\pi$
$607$	−22.7156	+	39.3446i	−0.921998	+	1.59695i	−0.796320	+	0.604875i	$0.793223\pi$
$608$		0			0
$609$	0.199127	−	0.344898i	0.00806903	−	0.0139760i
$610$		0			0
$611$	26.0849	+	45.1803i	1.05528	+	1.82780i
$612$		0			0
$613$	14.9001	−	25.8077i	0.601809	−	1.04236i	−0.390738	−	0.920502i	$-0.627780\pi$
$613$	14.9001	−	25.8077i	0.601809	−	1.04236i	0.992547	−	0.121862i	$-0.0388866\pi$
$614$		0			0
$615$	−5.43043			−0.218976
$616$		0			0
$617$	−22.1736	+	38.4058i	−0.892676	+	1.54616i	−0.0560202	+	0.998430i	$0.517841\pi$
$617$	−22.1736	+	38.4058i	−0.892676	+	1.54616i	−0.836655	+	0.547730i	$0.815492\pi$
$618$		0			0
$619$	−6.61625			−0.265930			−0.132965	−	0.991121i	$-0.542450\pi$
$619$	−6.61625			−0.265930			−0.132965	+	0.991121i	$0.542450\pi$
$620$		0			0
$621$	32.5617			1.30666
$622$		0			0
$623$	−12.6503			−0.506822
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−0.876605	+	1.51832i	−0.0350082	+	0.0606360i
$628$		0			0
$629$	22.6770	+	4.28753i	0.904193	+	0.170955i
$630$		0			0
$631$	−2.80142	+	4.85220i	−0.111523	+	0.193163i	−0.916384	−	0.400299i	$-0.868906\pi$
$631$	−2.80142	+	4.85220i	−0.111523	+	0.193163i	0.804862	+	0.593462i	$0.202239\pi$
$632$		0			0
$633$	−0.598022	−	1.03580i	−0.0237692	−	0.0411695i
$634$		0			0
$635$	−18.1300			−0.719466
$636$		0			0
$637$	−38.4652			−1.52405
$638$		0			0
$639$	−15.2679			−0.603988
$640$		0			0
$641$	11.0443	−	19.1294i	0.436225	−	0.755564i	−0.561169	−	0.827701i	$-0.689648\pi$
$641$	11.0443	−	19.1294i	0.436225	−	0.755564i	0.997395	+	0.0721365i	$0.0229817\pi$
$642$		0			0
$643$	−20.3875			−0.804005			−0.402002	−	0.915639i	$-0.631686\pi$
$643$	−20.3875			−0.804005			−0.402002	+	0.915639i	$0.631686\pi$
$644$		0			0
$645$	5.69727	−	9.86796i	0.224330	−	0.388551i
$646$		0			0
$647$	−9.63209	−	16.6833i	−0.378677	−	0.655887i	0.612193	−	0.790708i	$-0.290287\pi$
$647$	−9.63209	−	16.6833i	−0.378677	−	0.655887i	−0.990870	+	0.134821i	$0.956954\pi$
$648$		0			0
$649$	−2.93305	+	5.08020i	−0.115132	+	0.199415i
$650$		0			0
$651$	−5.30405	+	9.18689i	−0.207882	+	0.360063i
$652$		0			0
$653$	−8.92031	−	15.4504i	−0.349079	−	0.604622i	0.637007	−	0.770858i	$-0.280172\pi$
$653$	−8.92031	−	15.4504i	−0.349079	−	0.604622i	−0.986086	+	0.166236i	$0.946839\pi$
$654$		0			0
$655$	3.09416			0.120899
$656$		0			0
$657$	−4.21489	+	7.30040i	−0.164438	+	0.284816i
$658$		0			0
$659$	−19.9204	−	34.5032i	−0.775989	−	1.34405i	−0.934237	−	0.356653i	$-0.883918\pi$
$659$	−19.9204	−	34.5032i	−0.775989	−	1.34405i	0.158248	−	0.987399i	$-0.449415\pi$
$660$		0			0
$661$	12.8727	+	22.2962i	0.500692	+	0.867223i	1.00000		0.000798872i	$0.000254289\pi$
$661$	12.8727	+	22.2962i	0.500692	+	0.867223i	−0.499308	+	0.866425i	$0.666412\pi$
$662$		0			0
$663$	−15.6704	−	27.1420i	−0.608589	−	1.05411i
$664$		0			0
$665$	1.59643			0.0619068
$666$		0			0
$667$	1.73189			0.0670592
$668$		0			0
$669$	10.2595	+	17.7699i	0.396654	+	0.687024i
$670$		0			0
$671$	−1.30410	−	2.25877i	−0.0503443	−	0.0871989i
$672$		0			0
$673$	−0.830725	−	1.43886i	−0.0320221	−	0.0554639i	0.849570	−	0.527476i	$-0.176861\pi$
$673$	−0.830725	−	1.43886i	−0.0320221	−	0.0554639i	−0.881592	+	0.472012i	$0.843528\pi$
$674$		0			0
$675$	−2.77715	+	4.81017i	−0.106893	+	0.185143i
$676$		0			0
$677$	−19.8980			−0.764744			−0.382372	−	0.924008i	$-0.624893\pi$
$677$	−19.8980			−0.764744			−0.382372	+	0.924008i	$0.624893\pi$
$678$		0			0
$679$	−4.64075	−	8.03802i	−0.178096	−	0.308471i
$680$		0			0
$681$	−1.57875	+	2.73448i	−0.0604980	+	0.104786i
$682$		0			0
$683$	−20.0401	+	34.7104i	−0.766812	+	1.32816i	0.172472	+	0.985014i	$0.444825\pi$
$683$	−20.0401	+	34.7104i	−0.766812	+	1.32816i	−0.939283	+	0.343142i	$0.888509\pi$
$684$		0			0
$685$	−4.79373	−	8.30298i	−0.183159	−	0.317240i
$686$		0			0
$687$	−16.2598	+	28.1628i	−0.620350	+	1.07448i
$688$		0			0
$689$	−8.66264			−0.330020
$690$		0			0
$691$	−20.6168	+	35.7094i	−0.784301	+	1.35845i	0.145115	+	0.989415i	$0.453645\pi$
$691$	−20.6168	+	35.7094i	−0.784301	+	1.35845i	−0.929416	+	0.369034i	$0.879688\pi$
$692$		0			0
$693$	1.43429			0.0544842
$694$		0			0
$695$	3.68800			0.139894
$696$		0			0
$697$	−16.4075			−0.621478
$698$		0			0
$699$	4.32813	+	7.49654i	0.163705	+	0.283545i
$700$		0			0
$701$	21.3746	−	37.0219i	0.807309	−	1.39830i	−0.107413	−	0.994214i	$-0.534257\pi$
$701$	21.3746	−	37.0219i	0.807309	−	1.39830i	0.914721	−	0.404085i	$-0.132410\pi$
$702$		0			0
$703$	5.89940	−	6.85711i	0.222500	−	0.258621i
$704$		0			0
$705$	−4.97964	+	8.62500i	−0.187544	+	0.324836i
$706$		0			0
$707$	10.6685	+	18.4783i	0.401229	+	0.694948i
$708$		0			0
$709$	−36.3462			−1.36501			−0.682505	−	0.730881i	$-0.739110\pi$
$709$	−36.3462			−1.36501			−0.682505	+	0.730881i	$0.739110\pi$
$710$		0			0
$711$	15.7979			0.592466
$712$		0			0
$713$	−46.1317			−1.72764
$714$		0			0
$715$	3.08786	−	5.34833i	0.115479	−	0.200016i
$716$		0			0
$717$	29.2030			1.09061
$718$		0			0
$719$	2.41550	−	4.18377i	0.0900829	−	0.156028i	−0.817463	−	0.575981i	$-0.804620\pi$
$719$	2.41550	−	4.18377i	0.0900829	−	0.156028i	0.907546	+	0.419953i	$0.137953\pi$
$720$		0			0
$721$	−4.36966	−	7.56847i	−0.162735	−	0.281865i
$722$		0			0
$723$	9.67968	−	16.7657i	0.359991	−	0.623523i
$724$		0			0
$725$	−0.147711	+	0.255843i	−0.00548586	+	0.00950178i
$726$		0			0
$727$	7.56411	+	13.1014i	0.280537	+	0.485905i	0.971517	−	0.236969i	$-0.0761540\pi$
$727$	7.56411	+	13.1014i	0.280537	+	0.485905i	−0.690980	+	0.722874i	$0.742821\pi$
$728$		0			0
$729$	24.7747			0.917583
$730$		0			0
$731$	17.2137	−	29.8151i	0.636673	−	1.10275i
$732$		0			0
$733$	11.3727	+	19.6981i	0.420060	+	0.727565i	0.995945	−	0.0899657i	$-0.0286757\pi$
$733$	11.3727	+	19.6981i	0.420060	+	0.727565i	−0.575885	+	0.817531i	$0.695342\pi$
$734$		0			0
$735$	−3.67153	−	6.35928i	−0.135427	−	0.234566i
$736$		0			0
$737$	−6.92768	−	11.9991i	−0.255184	−	0.441992i
$738$		0			0
$739$	−39.9181			−1.46841			−0.734205	−	0.678928i	$-0.762445\pi$
$739$	−39.9181			−1.46841			−0.734205	+	0.678928i	$0.762445\pi$
$740$		0			0
$741$	−12.2839			−0.451259
$742$		0			0
$743$	11.3262	+	19.6176i	0.415518	+	0.719698i	0.995483	−	0.0949433i	$-0.0302670\pi$
$743$	11.3262	+	19.6176i	0.415518	+	0.719698i	−0.579965	+	0.814642i	$0.696934\pi$
$744$		0			0
$745$	10.3572	+	17.9391i	0.379457	+	0.657240i
$746$		0			0
$747$	−0.728973	−	1.26262i	−0.0266717	−	0.0461968i
$748$		0			0
$749$	1.60407	−	2.77832i	0.0586113	−	0.101518i
$750$		0			0
$751$	4.18617			0.152755			0.0763777	−	0.997079i	$-0.475665\pi$
$751$	4.18617			0.152755			0.0763777	+	0.997079i	$0.475665\pi$
$752$		0			0
$753$	1.23462	+	2.13842i	0.0449920	+	0.0779284i
$754$		0			0
$755$	1.25053	−	2.16597i	0.0455113	−	0.0788278i
$756$		0			0
$757$	16.5754	−	28.7095i	0.602445	−	1.04346i	−0.390005	−	0.920813i	$-0.627527\pi$
$757$	16.5754	−	28.7095i	0.602445	−	1.04346i	0.992450	−	0.122652i	$-0.0391399\pi$
$758$		0			0
$759$	−3.45577	−	5.98557i	−0.125437	−	0.217263i
$760$		0			0
$761$	−20.5025	+	35.5113i	−0.743214	+	1.28728i	0.207811	+	0.978169i	$0.433366\pi$
$761$	−20.5025	+	35.5113i	−0.743214	+	1.28728i	−0.951025	+	0.309115i	$0.899967\pi$
$762$		0			0
$763$	−2.79733			−0.101270
$764$		0			0
$765$	−2.69969	+	4.67600i	−0.0976074	+	0.169061i
$766$		0			0
$767$	−41.1009			−1.48407
$768$		0			0
$769$	32.8356			1.18408			0.592041	−	0.805908i	$-0.298322\pi$
$769$	32.8356			1.18408			0.592041	+	0.805908i	$0.298322\pi$
$770$		0			0
$771$	−4.38925			−0.158075
$772$		0			0
$773$	24.0216	+	41.6067i	0.863998	+	1.49649i	0.868039	+	0.496496i	$0.165380\pi$
$773$	24.0216	+	41.6067i	0.863998	+	1.49649i	−0.00404113	+	0.999992i	$0.501286\pi$
$774$		0			0
$775$	3.93451	−	6.81478i	0.141332	−	0.244794i
$776$		0			0
$777$	8.05732	+	1.52339i	0.289055	+	0.0546514i
$778$		0			0
$779$	−3.21541	+	5.56926i	−0.115204	+	0.199539i
$780$		0			0
$781$	5.03629	+	8.72312i	0.180213	+	0.312138i
$782$		0			0
$783$	1.64086			0.0586397
$784$		0			0
$785$	−3.30634			−0.118008
$786$		0			0
$787$	−23.5707			−0.840204			−0.420102	−	0.907477i	$-0.638006\pi$
$787$	−23.5707			−0.840204			−0.420102	+	0.907477i	$0.638006\pi$
$788$		0			0
$789$	−14.6912	+	25.4460i	−0.523022	+	0.905900i
$790$		0			0
$791$	15.2457			0.542074
$792$		0			0
$793$	9.13720	−	15.8261i	0.324471	−	0.562001i
$794$		0			0
$795$	−0.826856	−	1.43216i	−0.0293256	−	0.0507934i
$796$		0			0
$797$	4.19633	−	7.26825i	0.148642	−	0.257455i	−0.782084	−	0.623173i	$-0.785843\pi$
$797$	4.19633	−	7.26825i	0.148642	−	0.257455i	0.930726	+	0.365718i	$0.119177\pi$
$798$		0			0
$799$	−15.0455	+	26.0596i	−0.532272	+	0.921921i
$800$		0			0
$801$	−8.38471	−	14.5227i	−0.296259	−	0.513136i
$802$		0			0
$803$	5.56132			0.196255
$804$		0			0
$805$	−3.14674	+	5.45031i	−0.110908	+	0.192098i
$806$		0			0
$807$	12.4159	+	21.5051i	0.437062	+	0.757014i
$808$		0			0
$809$	17.3871	+	30.1154i	0.611298	+	1.05880i	0.991022	+	0.133700i	$0.0426858\pi$
$809$	17.3871	+	30.1154i	0.611298	+	1.05880i	−0.379723	+	0.925100i	$0.623981\pi$
$810$		0			0
$811$	6.80389	+	11.7847i	0.238917	+	0.413816i	0.960404	−	0.278612i	$-0.0898743\pi$
$811$	6.80389	+	11.7847i	0.238917	+	0.413816i	−0.721487	+	0.692428i	$0.756541\pi$
$812$		0			0
$813$	3.23675			0.113518
$814$		0			0
$815$	13.6132			0.476851
$816$		0			0
$817$	−6.74683	−	11.6858i	−0.236042	−	0.408836i
$818$		0			0
$819$	5.02468	+	8.70300i	0.175577	+	0.304107i
$820$		0			0
$821$	11.4772	+	19.8790i	0.400555	+	0.693782i	0.993793	−	0.111245i	$-0.0354839\pi$
$821$	11.4772	+	19.8790i	0.400555	+	0.693782i	−0.593238	+	0.805027i	$0.702151\pi$
$822$		0			0
$823$	−13.1438	+	22.7658i	−0.458165	+	0.793566i	−0.998864	−	0.0476507i	$-0.984827\pi$
$823$	−13.1438	+	22.7658i	−0.458165	+	0.793566i	0.540699	+	0.841216i	$0.318160\pi$
$824$		0			0
$825$	1.17895			0.0410459
$826$		0			0
$827$	−24.0775	−	41.7035i	−0.837258	−	1.45017i	−0.892179	−	0.451683i	$-0.850824\pi$
$827$	−24.0775	−	41.7035i	−0.837258	−	1.45017i	0.0549206	−	0.998491i	$-0.482509\pi$
$828$		0			0
$829$	−8.74108	+	15.1400i	−0.303590	+	0.525834i	−0.976946	−	0.213485i	$-0.931519\pi$
$829$	−8.74108	+	15.1400i	−0.303590	+	0.525834i	0.673356	+	0.739318i	$0.264852\pi$
$830$		0			0
$831$	2.69570	−	4.66909i	0.0935129	−	0.161969i
$832$		0			0
$833$	−11.0932	−	19.2139i	−0.384356	−	0.665723i
$834$		0			0
$835$	0.765424	−	1.32575i	0.0264886	−	0.0458796i
$836$		0			0
$837$	−43.7069			−1.51073
$838$		0			0
$839$	10.0365	−	17.3838i	0.346500	−	0.600155i	−0.639125	−	0.769103i	$-0.720704\pi$
$839$	10.0365	−	17.3838i	0.346500	−	0.600155i	0.985625	+	0.168948i	$0.0540368\pi$
$840$		0			0
$841$	−28.9127			−0.996991
$842$		0			0
$843$	7.46482			0.257102
$844$		0			0
$845$	30.2702			1.04133
$846$		0			0
$847$	5.43128	+	9.40725i	0.186621	+	0.323237i
$848$		0			0
$849$	−13.6845	+	23.7022i	−0.469650	+	0.813457i
$850$		0			0
$851$	11.7823	+	33.6571i	0.403891	+	1.15375i
$852$		0			0
$853$	17.0823	−	29.5873i	0.584885	−	1.01305i	−0.410004	−	0.912084i	$-0.634473\pi$
$853$	17.0823	−	29.5873i	0.584885	−	1.01305i	0.994890	−	0.100968i	$-0.0321938\pi$
$854$		0			0
$855$	1.05813	+	1.83273i	0.0361872	+	0.0626780i
$856$		0			0
$857$	−5.41674			−0.185032			−0.0925162	−	0.995711i	$-0.529491\pi$
$857$	−5.41674			−0.185032			−0.0925162	+	0.995711i	$0.529491\pi$
$858$		0			0
$859$	16.8997			0.576610			0.288305	−	0.957539i	$-0.406908\pi$
$859$	16.8997			0.576610			0.288305	+	0.957539i	$0.406908\pi$
$860$		0			0
$861$	−5.82971			−0.198676
$862$		0			0
$863$	7.69366	−	13.3258i	0.261895	−	0.453616i	−0.704850	−	0.709356i	$-0.748986\pi$
$863$	7.69366	−	13.3258i	0.261895	−	0.453616i	0.966746	+	0.255740i	$0.0823192\pi$
$864$		0			0
$865$	25.2997			0.860216
$866$		0			0
$867$	−1.63534	+	2.83250i	−0.0555392	+	0.0961967i
$868$		0			0
$869$	−5.21111	−	9.02592i	−0.176775	−	0.306183i
$870$		0			0
$871$	48.5388	−	84.0717i	1.64468	−	2.84866i
$872$		0			0
$873$	6.15186	−	10.6553i	0.208209	−	0.360629i
$874$		0			0
$875$	−0.536763	−	0.929701i	−0.0181459	−	0.0314296i
$876$		0			0
$877$	−16.1624			−0.545767			−0.272883	−	0.962047i	$-0.587977\pi$
$877$	−16.1624			−0.545767			−0.272883	+	0.962047i	$0.587977\pi$
$878$		0			0
$879$	8.69057	−	15.0525i	0.293126	−	0.507709i
$880$		0			0
$881$	0.222005	+	0.384523i	0.00747952	+	0.0129549i	0.869741	−	0.493509i	$-0.164286\pi$
$881$	0.222005	+	0.384523i	0.00747952	+	0.0129549i	−0.862261	+	0.506463i	$0.830953\pi$
$882$		0			0
$883$	−7.78735	−	13.4881i	−0.262065	−	0.453910i	0.704725	−	0.709480i	$-0.251070\pi$
$883$	−7.78735	−	13.4881i	−0.262065	−	0.453910i	−0.966791	+	0.255570i	$0.917737\pi$
$884$		0			0
$885$	−3.92311	−	6.79503i	−0.131874	−	0.228413i
$886$		0			0
$887$	−14.7660			−0.495793			−0.247896	−	0.968787i	$-0.579739\pi$
$887$	−14.7660			−0.495793			−0.247896	+	0.968787i	$0.579739\pi$
$888$		0			0
$889$	−19.4630			−0.652768
$890$		0			0
$891$	−1.27005	−	2.19980i	−0.0425484	−	0.0736960i
$892$		0			0
$893$	5.89700	+	10.2139i	0.197335	+	0.341795i
$894$		0			0
$895$	−7.37751	−	12.7782i	−0.246603	−	0.427129i
$896$		0			0
$897$	24.2129	−	41.9380i	0.808445	−	1.40027i
$898$		0			0
$899$	−2.32469			−0.0775326
$900$		0			0
$901$	−2.49826	−	4.32712i	−0.0832292	−	0.144157i
$902$		0			0
$903$	6.11617	−	10.5935i	0.203533	−	0.352530i
$904$		0			0
$905$	10.5624	−	18.2946i	0.351105	−	0.608132i
$906$		0			0
$907$	−6.42096	−	11.1214i	−0.213204	−	0.369281i	0.739511	−	0.673144i	$-0.235057\pi$
$907$	−6.42096	−	11.1214i	−0.213204	−	0.369281i	−0.952716	+	0.303863i	$0.901723\pi$
$908$		0			0
$909$	−14.1423	+	24.4952i	−0.469070	+	0.812454i
$910$		0			0
$911$	11.8751			0.393440			0.196720	−	0.980460i	$-0.436971\pi$
$911$	11.8751			0.393440			0.196720	+	0.980460i	$0.436971\pi$
$912$		0			0
$913$	−0.480920	+	0.832979i	−0.0159161	+	0.0275676i
$914$		0			0
$915$	3.48861			0.115330
$916$		0			0
$917$	3.32166			0.109691
$918$		0			0
$919$	−46.6548			−1.53900			−0.769500	−	0.638647i	$-0.779495\pi$
$919$	−46.6548			−1.53900			−0.769500	+	0.638647i	$0.779495\pi$
$920$		0			0
$921$	13.0708	+	22.6393i	0.430698	+	0.745991i
$922$		0			0
$923$	−35.2868	+	61.1186i	−1.16148	+	2.01174i
$924$		0			0
$925$	−5.97687	−	1.13004i	−0.196518	−	0.0371556i
$926$		0			0
$927$	5.79250	−	10.0329i	0.190251	−	0.329524i
$928$		0			0
$929$	−23.2125	−	40.2052i	−0.761576	−	1.31909i	−0.942038	−	0.335506i	$-0.891093\pi$
$929$	−23.2125	−	40.2052i	−0.761576	−	1.31909i	0.180462	−	0.983582i	$-0.442241\pi$
$930$		0			0
$931$	−8.69581			−0.284994
$932$		0			0
$933$	−12.4104			−0.406300
$934$		0			0
$935$	3.56210			0.116493
$936$		0			0
$937$	−5.78786	+	10.0249i	−0.189081	+	0.327498i	−0.944944	−	0.327232i	$-0.893884\pi$
$937$	−5.78786	+	10.0249i	−0.189081	+	0.327498i	0.755863	+	0.654730i	$0.227218\pi$
$938$		0			0
$939$	15.6740			0.511501
$940$		0			0
$941$	−6.51131	+	11.2779i	−0.212263	+	0.367650i	−0.952422	−	0.304781i	$-0.901417\pi$
$941$	−6.51131	+	11.2779i	−0.212263	+	0.367650i	0.740160	+	0.672431i	$0.234750\pi$
$942$		0			0
$943$	−12.6759	−	21.9553i	−0.412783	−	0.714962i
$944$		0			0
$945$	−2.98134	+	5.16384i	−0.0969831	+	0.167980i
$946$		0			0
$947$	−6.25087	+	10.8268i	−0.203126	+	0.351824i	−0.949534	−	0.313664i	$-0.898443\pi$
$947$	−6.25087	+	10.8268i	−0.203126	+	0.351824i	0.746408	+	0.665489i	$0.231777\pi$
$948$		0			0
$949$	19.4827	+	33.7451i	0.632436	+	1.09541i
$950$		0			0
$951$	34.2075			1.10926
$952$		0			0
$953$	9.52838	−	16.5036i	0.308655	−	0.534605i	−0.669414	−	0.742890i	$-0.733455\pi$
$953$	9.52838	−	16.5036i	0.308655	−	0.534605i	0.978068	+	0.208284i	$0.0667880\pi$
$954$		0			0
$955$	1.88417	+	3.26348i	0.0609704	+	0.105604i
$956$		0			0
$957$	−0.174145	−	0.301628i	−0.00562930	−	0.00975024i
$958$		0			0
$959$	−5.14619	−	8.91346i	−0.166179	−	0.287831i
$960$		0			0
$961$	30.9216			0.997471
$962$		0			0
$963$	4.25276			0.137043
$964$		0			0
$965$	−0.741125	−	1.28367i	−0.0238577	−	0.0413227i
$966$		0			0
$967$	10.8089	+	18.7216i	0.347592	+	0.602047i	0.985821	−	0.167799i	$-0.0536661\pi$
$967$	10.8089	+	18.7216i	0.347592	+	0.602047i	−0.638229	+	0.769846i	$0.720333\pi$
$968$		0			0
$969$	−3.54261	−	6.13598i	−0.113805	−	0.197116i
$970$		0			0
$971$	9.63053	−	16.6806i	0.309058	−	0.535305i	−0.669098	−	0.743174i	$-0.733319\pi$
$971$	9.63053	−	16.6806i	0.309058	−	0.535305i	0.978157	+	0.207869i	$0.0666528\pi$
$972$		0			0
$973$	3.95917			0.126925
$974$		0			0
$975$	4.13018	+	7.15368i	0.132272	+	0.229101i
$976$		0			0
$977$	8.56958	−	14.8430i	0.274165	−	0.474868i	−0.695759	−	0.718275i	$-0.744932\pi$
$977$	8.56958	−	14.8430i	0.274165	−	0.474868i	0.969924	+	0.243407i	$0.0782652\pi$
$978$		0			0
$979$	−5.53159	+	9.58100i	−0.176790	+	0.306210i
$980$		0			0
$981$	−1.85410	−	3.21139i	−0.0591968	−	0.102532i
$982$		0			0
$983$	−22.1911	+	38.4361i	−0.707786	+	1.22592i	0.257890	+	0.966174i	$0.416973\pi$
$983$	−22.1911	+	38.4361i	−0.707786	+	1.22592i	−0.965677	+	0.259748i	$0.916361\pi$
$984$		0			0
$985$	−11.1060			−0.353867
$986$		0			0
$987$	−5.34578	+	9.25916i	−0.170158	+	0.294722i
$988$		0			0
$989$	53.1950			1.69150
$990$		0			0
$991$	37.3377			1.18607			0.593036	−	0.805176i	$-0.297929\pi$
$991$	37.3377			1.18607			0.593036	+	0.805176i	$0.297929\pi$
$992$		0			0
$993$	−31.0287			−0.984665
$994$		0			0
$995$	0.209553	+	0.362956i	0.00664326	+	0.0115065i
$996$		0			0
$997$	−7.44038	+	12.8871i	−0.235639	+	0.408139i	−0.959458	−	0.281851i	$-0.909052\pi$
$997$	−7.44038	+	12.8871i	−0.235639	+	0.408139i	0.723819	+	0.689990i	$0.242385\pi$
$998$		0			0
$999$	11.1630	+	31.8880i	0.353181	+	1.00889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.i.a.121.5	✓	14
37.26	even	3	inner	740.2.i.a.581.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.i.a.121.5	✓	14	1.1	even	1	trivial
740.2.i.a.581.5	yes	14	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.627876 + 1.08751i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.536763 - 0.929701i) q^{7} +(0.711543 - 1.23243i) q^{9} -0.938843 q^{11} +(-3.28901 - 5.69673i) q^{13} +(0.627876 - 1.08751i) q^{15} +(1.89707 - 3.28581i) q^{17} +(-0.743544 - 1.28786i) q^{19} +(0.674042 - 1.16747i) q^{21} +5.86243 q^{23} +(-0.500000 + 0.866025i) q^{25} +5.55430 q^{27} +0.295422 q^{29} -7.86903 q^{31} +(-0.589477 - 1.02100i) q^{33} +(-0.536763 + 0.929701i) q^{35} +(2.00979 + 5.74114i) q^{37} +(4.13018 - 7.15368i) q^{39} +(-2.16222 - 3.74508i) q^{41} +9.07388 q^{43} -1.42309 q^{45} -7.93093 q^{47} +(2.92377 - 5.06412i) q^{49} +4.76449 q^{51} +(0.658455 - 1.14048i) q^{53} +(0.469422 + 0.813062i) q^{55} +(0.933707 - 1.61723i) q^{57} +(3.12411 - 5.41112i) q^{59} +(1.38905 + 2.40591i) q^{61} -1.52772 q^{63} +(-3.28901 + 5.69673i) q^{65} +(7.37895 + 12.7807i) q^{67} +(3.68088 + 6.37548i) q^{69} +(-5.36436 - 9.29135i) q^{71} -5.92359 q^{73} -1.25575 q^{75} +(0.503937 + 0.872844i) q^{77} +(5.55057 + 9.61387i) q^{79} +(1.35278 + 2.34309i) q^{81} +(0.512248 - 0.887239i) q^{83} -3.79413 q^{85} +(0.185489 + 0.321276i) q^{87} +(5.89192 - 10.2051i) q^{89} +(-3.53083 + 6.11558i) q^{91} +(-4.94078 - 8.55767i) q^{93} +(-0.743544 + 1.28786i) q^{95} +8.64581 q^{97} +(-0.668027 + 1.15706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) \) 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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