LMFDB - Embedded newform 380.2.u.a.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(61,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 $ x^18 - 3x^17 + 3x^15 + 36x^14 + 72x^13 - 134x^12 - 741x^11 + 486x^10 + 5700x^9 + 11637x^8 + 13878x^7 + 13978x^6 + 10005x^5 + 5949x^4 + 2649x^3 + 819x^2 + 135x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			161.3
Root			$-1.48541 + 0.540646i$ of defining polynomial
Character	$\chi$	$=$	380.161
Dual form			380.2.u.a.321.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21092 - 1.01608i) q^{3} +(0.939693 + 0.342020i) q^{5} +(1.77958 - 3.08232i) q^{7} +(-0.0870410 + 0.493634i) q^{9} +O(q^{10})$	\(q+(1.21092 - 1.01608i) q^{3} +(0.939693 + 0.342020i) q^{5} +(1.77958 - 3.08232i) q^{7} +(-0.0870410 + 0.493634i) q^{9} +(1.71921 + 2.97776i) q^{11} +(-2.46113 - 2.06513i) q^{13} +(1.48541 - 0.540646i) q^{15} +(-0.843610 - 4.78435i) q^{17} +(4.05569 + 1.59731i) q^{19} +(-0.976964 - 5.54064i) q^{21} +(-6.41442 + 2.33466i) q^{23} +(0.766044 + 0.642788i) q^{25} +(2.76729 + 4.79308i) q^{27} +(0.331754 - 1.88147i) q^{29} +(1.52175 - 2.63575i) q^{31} +(5.10747 + 1.85897i) q^{33} +(2.72647 - 2.28778i) q^{35} +7.81318 q^{37} -5.07858 q^{39} +(-6.22608 + 5.22431i) q^{41} +(-10.6275 - 3.86808i) q^{43} +(-0.250624 + 0.434094i) q^{45} +(-0.899912 + 5.10365i) q^{47} +(-2.83380 - 4.90828i) q^{49} +(-5.88284 - 4.93629i) q^{51} +(6.97841 - 2.53993i) q^{53} +(0.597075 + 3.38618i) q^{55} +(6.53411 - 2.18670i) q^{57} +(1.53157 + 8.68599i) q^{59} +(-7.19444 + 2.61856i) q^{61} +(1.36664 + 1.14675i) q^{63} +(-1.60639 - 2.78235i) q^{65} +(1.15738 - 6.56383i) q^{67} +(-5.39514 + 9.34466i) q^{69} +(7.66249 + 2.78892i) q^{71} +(-5.87461 + 4.92939i) q^{73} +1.58074 q^{75} +12.2379 q^{77} +(-10.4195 + 8.74297i) q^{79} +(6.80808 + 2.47794i) q^{81} +(-8.21708 + 14.2324i) q^{83} +(0.843610 - 4.78435i) q^{85} +(-1.51000 - 2.61540i) q^{87} +(2.74230 + 2.30106i) q^{89} +(-10.7452 + 3.91092i) q^{91} +(-0.835422 - 4.73792i) q^{93} +(3.26479 + 2.88811i) q^{95} +(0.167924 + 0.952344i) q^{97} +(-1.61956 + 0.589473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 9 * q^9	$ 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^9 + 9 * q^13 - 3 * q^15 + 12 * q^17 + 18 * q^19 + 15 * q^21 - 9 * q^23 - 33 * q^29 - 18 * q^31 + 9 * q^33 + 12 * q^35 + 60 * q^37 - 84 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 15 * q^47 - 15 * q^49 - 9 * q^51 + 24 * q^53 + 3 * q^55 + 66 * q^57 + 48 * q^59 - 18 * q^61 - 54 * q^63 + 3 * q^65 - 36 * q^67 - 9 * q^69 + 18 * q^73 - 6 * q^75 + 9 * q^79 - 9 * q^81 - 30 * q^83 - 12 * q^85 - 9 * q^87 + 6 * q^89 + 30 * q^91 + 21 * q^95 + 21 * q^97 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

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
$3$	1.21092	−	1.01608i	0.699125	−	0.586636i	−0.222400	−	0.974956i	$-0.571389\pi$
$3$	1.21092	−	1.01608i	0.699125	−	0.586636i	0.921525	+	0.388320i	$0.126944\pi$
$4$		0			0
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$6$		0			0
$7$	1.77958	−	3.08232i	0.672617	−	1.16501i	−0.304542	−	0.952499i	$-0.598503\pi$
$7$	1.77958	−	3.08232i	0.672617	−	1.16501i	0.977159	−	0.212508i	$-0.0681633\pi$
$8$		0			0
$9$	−0.0870410	+	0.493634i	−0.0290137	+	0.164545i
$10$		0			0
$11$	1.71921	+	2.97776i	0.518361	+	0.897828i	0.999772	+	0.0213331i	$0.00679104\pi$
$11$	1.71921	+	2.97776i	0.518361	+	0.897828i	−0.481411	+	0.876495i	$0.659876\pi$
$12$		0			0
$13$	−2.46113	−	2.06513i	−0.682595	−	0.572765i	0.234169	−	0.972196i	$-0.424763\pi$
$13$	−2.46113	−	2.06513i	−0.682595	−	0.572765i	−0.916763	+	0.399431i	$0.869208\pi$
$14$		0			0
$15$	1.48541	−	0.540646i	0.383532	−	0.139594i
$16$		0			0
$17$	−0.843610	−	4.78435i	−0.204605	−	1.16038i	−0.898059	−	0.439874i	$-0.855023\pi$
$17$	−0.843610	−	4.78435i	−0.204605	−	1.16038i	0.693454	−	0.720501i	$-0.256088\pi$
$18$		0			0
$19$	4.05569	+	1.59731i	0.930439	+	0.366448i
$19$	4.05569	+	1.59731i	0.930439	+	0.366448i
$20$		0			0
$21$	−0.976964	−	5.54064i	−0.213191	−	1.20907i
$22$		0			0
$23$	−6.41442	+	2.33466i	−1.33750	+	0.486810i	−0.909024	−	0.416744i	$-0.863171\pi$
$23$	−6.41442	+	2.33466i	−1.33750	+	0.486810i	−0.428475	+	0.903554i	$0.640949\pi$
$24$		0			0
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$		0			0
$27$	2.76729	+	4.79308i	0.532565	+	0.922430i
$28$		0			0
$29$	0.331754	−	1.88147i	0.0616052	−	0.349380i	−0.938388	−	0.345585i	$-0.887681\pi$
$29$	0.331754	−	1.88147i	0.0616052	−	0.349380i	0.999993	−	0.00379579i	$-0.00120824\pi$
$30$		0			0
$31$	1.52175	−	2.63575i	0.273315	−	0.473396i	−0.696394	−	0.717660i	$-0.745213\pi$
$31$	1.52175	−	2.63575i	0.273315	−	0.473396i	0.969709	+	0.244265i	$0.0785465\pi$
$32$		0			0
$33$	5.10747	+	1.85897i	0.889097	+	0.323605i
$34$		0			0
$35$	2.72647	−	2.28778i	0.460858	−	0.386706i
$36$		0			0
$37$	7.81318			1.28448			0.642240	−	0.766504i	$-0.278005\pi$
$37$	7.81318			1.28448			0.642240	+	0.766504i	$0.278005\pi$
$38$		0			0
$39$	−5.07858			−0.813223
$40$		0			0
$41$	−6.22608	+	5.22431i	−0.972351	+	0.815899i	−0.982918	−	0.184045i	$-0.941081\pi$
$41$	−6.22608	+	5.22431i	−0.972351	+	0.815899i	0.0105668	+	0.999944i	$0.496636\pi$
$42$		0			0
$43$	−10.6275	−	3.86808i	−1.62067	−	0.589877i	−0.637164	−	0.770728i	$-0.719893\pi$
$43$	−10.6275	−	3.86808i	−1.62067	−	0.589877i	−0.983510	+	0.180851i	$0.942115\pi$
$44$		0			0
$45$	−0.250624	+	0.434094i	−0.0373609	+	0.0647110i
$46$		0			0
$47$	−0.899912	+	5.10365i	−0.131266	+	0.744444i	0.846122	+	0.532989i	$0.178931\pi$
$47$	−0.899912	+	5.10365i	−0.131266	+	0.744444i	−0.977388	+	0.211455i	$0.932180\pi$
$48$		0			0
$49$	−2.83380	−	4.90828i	−0.404828	−	0.701183i
$50$		0			0
$51$	−5.88284	−	4.93629i	−0.823762	−	0.691219i
$52$		0			0
$53$	6.97841	−	2.53993i	0.958558	−	0.348887i	0.185090	−	0.982722i	$-0.440742\pi$
$53$	6.97841	−	2.53993i	0.958558	−	0.348887i	0.773468	+	0.633835i	$0.218520\pi$
$54$		0			0
$55$	0.597075	+	3.38618i	0.0805096	+	0.456593i
$56$		0			0
$57$	6.53411	−	2.18670i	0.865464	−	0.289636i
$58$		0			0
$59$	1.53157	+	8.68599i	0.199394	+	1.13082i	0.906021	+	0.423233i	$0.139105\pi$
$59$	1.53157	+	8.68599i	0.199394	+	1.13082i	−0.706627	+	0.707586i	$0.749784\pi$
$60$		0			0
$61$	−7.19444	+	2.61856i	−0.921153	+	0.335272i	−0.758697	−	0.651443i	$-0.774164\pi$
$61$	−7.19444	+	2.61856i	−0.921153	+	0.335272i	−0.162456	+	0.986716i	$0.551942\pi$
$62$		0			0
$63$	1.36664	+	1.14675i	0.172181	+	0.144477i
$64$		0			0
$65$	−1.60639	−	2.78235i	−0.199248	−	0.345108i
$66$		0			0
$67$	1.15738	−	6.56383i	0.141396	−	0.801899i	−0.828794	−	0.559554i	$-0.810972\pi$
$67$	1.15738	−	6.56383i	0.141396	−	0.801899i	0.970190	−	0.242345i	$-0.0779165\pi$
$68$		0			0
$69$	−5.39514	+	9.34466i	−0.649499	+	1.12496i
$70$		0			0
$71$	7.66249	+	2.78892i	0.909370	+	0.330984i	0.754001	−	0.656873i	$-0.228121\pi$
$71$	7.66249	+	2.78892i	0.909370	+	0.330984i	0.155369	+	0.987857i	$0.450343\pi$
$72$		0			0
$73$	−5.87461	+	4.92939i	−0.687572	+	0.576941i	−0.918208	−	0.396099i	$-0.870364\pi$
$73$	−5.87461	+	4.92939i	−0.687572	+	0.576941i	0.230636	+	0.973040i	$0.425919\pi$
$74$		0			0
$75$	1.58074			0.182529
$76$		0			0
$77$	12.2379			1.39463
$78$		0			0
$79$	−10.4195	+	8.74297i	−1.17228	+	0.983661i	−0.999999	−	0.00138681i	$-0.999559\pi$
$79$	−10.4195	+	8.74297i	−1.17228	+	0.983661i	−0.172282	+	0.985048i	$0.555114\pi$
$80$		0			0
$81$	6.80808	+	2.47794i	0.756453	+	0.275326i
$82$		0			0
$83$	−8.21708	+	14.2324i	−0.901942	+	1.56221i	−0.0769710	+	0.997033i	$0.524525\pi$
$83$	−8.21708	+	14.2324i	−0.901942	+	1.56221i	−0.824971	+	0.565175i	$0.808808\pi$
$84$		0			0
$85$	0.843610	−	4.78435i	0.0915024	−	0.518936i
$86$		0			0
$87$	−1.51000	−	2.61540i	−0.161889	−	0.280400i
$88$		0			0
$89$	2.74230	+	2.30106i	0.290683	+	0.243912i	0.776454	−	0.630174i	$-0.217017\pi$
$89$	2.74230	+	2.30106i	0.290683	+	0.243912i	−0.485771	+	0.874086i	$0.661461\pi$
$90$		0			0
$91$	−10.7452	+	3.91092i	−1.12640	+	0.409976i
$92$		0			0
$93$	−0.835422	−	4.73792i	−0.0866293	−	0.491299i
$94$		0			0
$95$	3.26479	+	2.88811i	0.334960	+	0.296313i
$96$		0			0
$97$	0.167924	+	0.952344i	0.0170501	+	0.0966959i	0.992145	−	0.125091i	$-0.0399222\pi$
$97$	0.167924	+	0.952344i	0.0170501	+	0.0966959i	−0.975095	+	0.221787i	$0.928811\pi$
$98$		0			0
$99$	−1.61956	+	0.589473i	−0.162772	+	0.0592443i
$100$		0			0
$101$	−7.82623	−	6.56699i	−0.778739	−	0.653440i	0.164192	−	0.986428i	$-0.447498\pi$
$101$	−7.82623	−	6.56699i	−0.778739	−	0.653440i	−0.942931	+	0.332989i	$0.891943\pi$
$102$		0			0
$103$	0.292743	+	0.507046i	0.0288448	+	0.0499607i	0.880087	−	0.474812i	$-0.157484\pi$
$103$	0.292743	+	0.507046i	0.0288448	+	0.0499607i	−0.851243	+	0.524772i	$0.824150\pi$
$104$		0			0
$105$	0.976964	−	5.54064i	0.0953420	−	0.540711i
$106$		0			0
$107$	0.376505	−	0.652125i	0.0363981	−	0.0630433i	−0.847253	−	0.531190i	$-0.821745\pi$
$107$	0.376505	−	0.652125i	0.0363981	−	0.0630433i	0.883651	+	0.468147i	$0.155078\pi$
$108$		0			0
$109$	−16.4360	−	5.98221i	−1.57428	−	0.572992i	−0.600331	−	0.799752i	$-0.704964\pi$
$109$	−16.4360	−	5.98221i	−1.57428	−	0.572992i	−0.973951	+	0.226760i	$0.927187\pi$
$110$		0			0
$111$	9.46114	−	7.93884i	0.898012	−	0.753521i
$112$		0			0
$113$	−1.03497			−0.0973620			−0.0486810	−	0.998814i	$-0.515502\pi$
$113$	−1.03497			−0.0973620			−0.0486810	+	0.998814i	$0.515502\pi$
$114$		0			0
$115$	−6.82608			−0.636535
$116$		0			0
$117$	1.23364	−	1.03515i	0.114050	−	0.0956993i
$118$		0			0
$119$	−16.2482	−	5.91385i	−1.48947	−	0.542122i
$120$		0			0
$121$	−0.411363	+	0.712502i	−0.0373967	+	0.0647729i
$122$		0			0
$123$	−2.23097	+	12.6524i	−0.201159	+	1.14083i
$124$		0			0
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$		0			0
$127$	1.47363	+	1.23652i	0.130764	+	0.109724i	0.705824	−	0.708387i	$-0.250577\pi$
$127$	1.47363	+	1.23652i	0.130764	+	0.109724i	−0.575060	+	0.818111i	$0.695021\pi$
$128$		0			0
$129$	−16.7993	+	6.11445i	−1.47910	+	0.538347i
$130$		0			0
$131$	2.35438	+	13.3523i	0.205703	+	1.16660i	0.896330	+	0.443388i	$0.146224\pi$
$131$	2.35438	+	13.3523i	0.205703	+	1.16660i	−0.690626	+	0.723212i	$0.742665\pi$
$132$		0			0
$133$	12.1408	−	9.65839i	1.05274	−	0.837489i
$134$		0			0
$135$	0.961069	+	5.45049i	0.0827157	+	0.469104i
$136$		0			0
$137$	3.10060	−	1.12853i	0.264902	−	0.0964165i	−0.206155	−	0.978519i	$-0.566095\pi$
$137$	3.10060	−	1.12853i	0.264902	−	0.0964165i	0.471057	+	0.882103i	$0.343873\pi$
$138$		0			0
$139$	−2.96484	−	2.48780i	−0.251475	−	0.211012i	0.508332	−	0.861161i	$-0.330262\pi$
$139$	−2.96484	−	2.48780i	−0.251475	−	0.211012i	−0.759807	+	0.650149i	$0.774707\pi$
$140$		0			0
$141$	4.09601	+	7.09450i	0.344946	+	0.597465i
$142$		0			0
$143$	1.91827	−	10.8790i	0.160414	−	0.909752i
$144$		0			0
$145$	0.955248	−	1.65454i	0.0793290	−	0.137402i
$146$		0			0
$147$	−8.41872	−	3.06416i	−0.694364	−	0.252728i
$148$		0			0
$149$	16.6257	−	13.9506i	1.36203	−	1.14288i	0.386679	−	0.922214i	$-0.373622\pi$
$149$	16.6257	−	13.9506i	1.36203	−	1.14288i	0.975350	−	0.220664i	$-0.0708224\pi$
$150$		0			0
$151$	20.6330			1.67909			0.839547	−	0.543288i	$-0.182821\pi$
$151$	20.6330			1.67909			0.839547	+	0.543288i	$0.182821\pi$
$152$		0			0
$153$	2.43515			0.196870
$154$		0			0
$155$	2.33146	−	1.95633i	0.187268	−	0.157136i
$156$		0			0
$157$	−9.27210	−	3.37477i	−0.739994	−	0.269336i	−0.0556052	−	0.998453i	$-0.517709\pi$
$157$	−9.27210	−	3.37477i	−0.739994	−	0.269336i	−0.684389	+	0.729117i	$0.739931\pi$
$158$		0			0
$159$	5.86951	−	10.1663i	0.465483	−	0.806239i
$160$		0			0
$161$	−4.21880	+	23.9260i	−0.332488	+	1.88563i
$162$		0			0
$163$	4.08509	+	7.07559i	0.319969	+	0.554203i	0.980481	−	0.196613i	$-0.0629941\pi$
$163$	4.08509	+	7.07559i	0.319969	+	0.554203i	−0.660512	+	0.750815i	$0.729661\pi$
$164$		0			0
$165$	4.16365	+	3.49372i	0.324140	+	0.271986i
$166$		0			0
$167$	10.2165	−	3.71851i	0.790579	−	0.287747i	0.0850022	−	0.996381i	$-0.472910\pi$
$167$	10.2165	−	3.71851i	0.790579	−	0.287747i	0.705577	+	0.708634i	$0.250688\pi$
$168$		0			0
$169$	−0.465041	−	2.63738i	−0.0357724	−	0.202875i
$170$		0			0
$171$	−1.14150	+	1.86299i	−0.0872924	+	0.142467i
$172$		0			0
$173$	−0.722899	−	4.09976i	−0.0549610	−	0.311699i	0.944917	−	0.327310i	$-0.106142\pi$
$173$	−0.722899	−	4.09976i	−0.0549610	−	0.311699i	−0.999878	+	0.0156103i	$0.995031\pi$
$174$		0			0
$175$	3.34451	−	1.21730i	0.252821	−	0.0920195i
$176$		0			0
$177$	10.6803	+	8.96183i	0.802780	+	0.673612i
$178$		0			0
$179$	−6.14600	−	10.6452i	−0.459374	−	0.795658i	0.539554	−	0.841951i	$-0.318593\pi$
$179$	−6.14600	−	10.6452i	−0.459374	−	0.795658i	−0.998928	+	0.0462925i	$0.985259\pi$
$180$		0			0
$181$	4.38678	−	24.8787i	0.326067	−	1.84922i	−0.176004	−	0.984389i	$-0.556317\pi$
$181$	4.38678	−	24.8787i	0.326067	−	1.84922i	0.502071	−	0.864826i	$-0.332572\pi$
$182$		0			0
$183$	−6.05122	+	10.4810i	−0.447319	+	0.774779i
$184$		0			0
$185$	7.34199	+	2.67227i	0.539794	+	0.196469i
$186$		0			0
$187$	12.7963	−	10.7374i	0.935758	−	0.785194i
$188$		0			0
$189$	19.6984			1.43285
$190$		0			0
$191$	5.98781			0.433263			0.216631	−	0.976253i	$-0.430493\pi$
$191$	5.98781			0.433263			0.216631	+	0.976253i	$0.430493\pi$
$192$		0			0
$193$	12.1442	−	10.1902i	0.874157	−	0.733505i	−0.0908123	−	0.995868i	$-0.528946\pi$
$193$	12.1442	−	10.1902i	0.874157	−	0.733505i	0.964969	+	0.262363i	$0.0845019\pi$
$194$		0			0
$195$	−4.77230	−	1.73698i	−0.341752	−	0.124387i
$196$		0			0
$197$	0.0256952	−	0.0445054i	0.00183071	−	0.00317088i	−0.865109	−	0.501585i	$-0.832751\pi$
$197$	0.0256952	−	0.0445054i	0.00183071	−	0.00317088i	0.866939	+	0.498414i	$0.166084\pi$
$198$		0			0
$199$	−0.877053	+	4.97401i	−0.0621726	+	0.352598i	0.937813	+	0.347142i	$0.112848\pi$
$199$	−0.877053	+	4.97401i	−0.0621726	+	0.352598i	−0.999985	+	0.00545618i	$0.998263\pi$
$200$		0			0
$201$	−5.26789	−	9.12426i	−0.371569	−	0.643576i
$202$		0			0
$203$	−5.20891	−	4.37080i	−0.365594	−	0.306770i
$204$		0			0
$205$	−7.63742	+	2.77979i	−0.533421	+	0.194149i
$206$		0			0
$207$	−0.594149	−	3.36958i	−0.0412962	−	0.234202i
$208$		0			0
$209$	2.21618	+	14.8230i	0.153296	+	1.02533i
$210$		0			0
$211$	−4.17249	−	23.6634i	−0.287246	−	1.62906i	−0.697149	−	0.716926i	$-0.745549\pi$
$211$	−4.17249	−	23.6634i	−0.287246	−	1.62906i	0.409903	−	0.912129i	$-0.365563\pi$
$212$		0			0
$213$	12.1124	−	4.40856i	0.829930	−	0.302070i
$214$		0			0
$215$	−8.66359	−	7.26962i	−0.590852	−	0.495784i
$216$		0			0
$217$	−5.41616	−	9.38106i	−0.367673	−	0.636828i
$218$		0			0
$219$	−2.10502	+	11.9382i	−0.142244	+	0.806708i
$220$		0			0
$221$	−7.80409	+	13.5171i	−0.524960	+	0.909257i
$222$		0			0
$223$	16.0031	+	5.82465i	1.07165	+	0.390047i	0.816792	−	0.576932i	$-0.195750\pi$
$223$	16.0031	+	5.82465i	1.07165	+	0.390047i	0.254854	+	0.966979i	$0.417973\pi$
$224$		0			0
$225$	−0.383979	+	0.322197i	−0.0255986	+	0.0214798i
$226$		0			0
$227$	7.89987			0.524333			0.262166	−	0.965023i	$-0.415563\pi$
$227$	7.89987			0.524333			0.262166	+	0.965023i	$0.415563\pi$
$228$		0			0
$229$	−5.63673			−0.372485			−0.186243	−	0.982504i	$-0.559631\pi$
$229$	−5.63673			−0.372485			−0.186243	+	0.982504i	$0.559631\pi$
$230$		0			0
$231$	14.8191	−	12.4347i	0.975024	−	0.818142i
$232$		0			0
$233$	0.388467	+	0.141390i	0.0254493	+	0.00926279i	0.354713	−	0.934975i	$-0.384578\pi$
$233$	0.388467	+	0.141390i	0.0254493	+	0.00926279i	−0.329264	+	0.944238i	$0.606801\pi$
$234$		0			0
$235$	−2.59119	+	4.48808i	−0.169031	+	0.292770i
$236$		0			0
$237$	−3.73356	+	21.1741i	−0.242521	+	1.37540i
$238$		0			0
$239$	−0.391298	−	0.677747i	−0.0253109	−	0.0438398i	0.853092	−	0.521760i	$-0.174724\pi$
$239$	−0.391298	−	0.677747i	−0.0253109	−	0.0438398i	−0.878403	+	0.477920i	$0.841391\pi$
$240$		0			0
$241$	−7.81257	−	6.55553i	−0.503252	−	0.422279i	0.355495	−	0.934678i	$-0.384312\pi$
$241$	−7.81257	−	6.55553i	−0.503252	−	0.422279i	−0.858747	+	0.512400i	$0.828757\pi$
$242$		0			0
$243$	−4.84058	+	1.76183i	−0.310523	+	0.113021i
$244$		0			0
$245$	−0.984167	−	5.58149i	−0.0628761	−	0.356588i
$246$		0			0
$247$	−6.68292	−	12.3067i	−0.425224	−	0.783058i
$248$		0			0
$249$	4.51107	+	25.5835i	0.285877	+	1.62129i
$250$		0			0
$251$	17.1166	−	6.22993i	1.08039	−	0.393230i	0.260337	−	0.965518i	$-0.416166\pi$
$251$	17.1166	−	6.22993i	1.08039	−	0.393230i	0.820052	+	0.572288i	$0.193944\pi$
$252$		0			0
$253$	−17.9798	−	15.0868i	−1.13038	−	0.948500i
$254$		0			0
$255$	−3.83975	−	6.65064i	−0.240454	−	0.416479i
$256$		0			0
$257$	−3.06253	+	17.3685i	−0.191036	+	1.08342i	0.726917	+	0.686726i	$0.240953\pi$
$257$	−3.06253	+	17.3685i	−0.191036	+	1.08342i	−0.917952	+	0.396691i	$0.870158\pi$
$258$		0			0
$259$	13.9042	−	24.0827i	0.863963	−	1.49643i
$260$		0			0
$261$	0.899881	+	0.327530i	0.0557013	+	0.0202736i
$262$		0			0
$263$	8.55858	−	7.18150i	0.527745	−	0.442830i	−0.339577	−	0.940578i	$-0.610284\pi$
$263$	8.55858	−	7.18150i	0.527745	−	0.442830i	0.867322	+	0.497748i	$0.165840\pi$
$264$		0			0
$265$	7.42627			0.456192
$266$		0			0
$267$	5.65877			0.346311
$268$		0			0
$269$	18.8693	−	15.8332i	1.15048	−	0.965370i	0.150753	−	0.988572i	$-0.451830\pi$
$269$	18.8693	−	15.8332i	1.15048	−	0.965370i	0.999731	+	0.0232012i	$0.00738584\pi$
$270$		0			0
$271$	−16.9412	−	6.16610i	−1.02911	−	0.374564i	−0.228366	−	0.973575i	$-0.573338\pi$
$271$	−16.9412	−	6.16610i	−1.02911	−	0.374564i	−0.800740	+	0.599012i	$0.795560\pi$
$272$		0			0
$273$	−9.03773	+	15.6538i	−0.546988	+	0.947411i
$274$		0			0
$275$	−0.597075	+	3.38618i	−0.0360050	+	0.204194i
$276$		0			0
$277$	−9.41987	−	16.3157i	−0.565985	−	0.980315i	−0.996957	−	0.0779498i	$-0.975163\pi$
$277$	−9.41987	−	16.3157i	−0.565985	−	0.980315i	0.430972	−	0.902365i	$-0.358171\pi$
$278$		0			0
$279$	1.16864	+	0.980608i	0.0699648	+	0.0587074i
$280$		0			0
$281$	−30.1565	+	10.9761i	−1.79899	+	0.654778i	−0.800528	+	0.599296i	$0.795447\pi$
$281$	−30.1565	+	10.9761i	−1.79899	+	0.654778i	−0.998460	+	0.0554820i	$0.982330\pi$
$282$		0			0
$283$	0.903537	+	5.12421i	0.0537097	+	0.304603i	0.999815	−	0.0192577i	$-0.00613028\pi$
$283$	0.903537	+	5.12421i	0.0537097	+	0.304603i	−0.946105	+	0.323860i	$0.895019\pi$
$284$		0			0
$285$	6.88795	+	0.179971i	0.408007	+	0.0106606i
$286$		0			0
$287$	5.02318	+	28.4878i	0.296509	+	1.68158i
$288$		0			0
$289$	−6.20355	+	2.25791i	−0.364915	+	0.132818i
$290$		0			0
$291$	1.17100	+	0.982588i	0.0686454	+	0.0576003i
$292$		0			0
$293$	−4.72077	−	8.17662i	−0.275790	−	0.477683i	0.694544	−	0.719450i	$-0.255606\pi$
$293$	−4.72077	−	8.17662i	−0.275790	−	0.477683i	−0.970334	+	0.241767i	$0.922273\pi$
$294$		0			0
$295$	−1.53157	+	8.68599i	−0.0891717	+	0.505718i
$296$		0			0
$297$	−9.51510	+	16.4806i	−0.552122	+	0.956303i
$298$		0			0
$299$	20.6081	+	7.50073i	1.19180	+	0.433779i
$300$		0			0
$301$	−30.8351	+	25.8737i	−1.77730	+	1.49134i
$302$		0			0
$303$	−16.1495			−0.927767
$304$		0			0
$305$	−7.65616			−0.438391
$306$		0			0
$307$	−0.260664	+	0.218723i	−0.0148769	+	0.0124832i	−0.650196	−	0.759767i	$-0.725313\pi$
$307$	−0.260664	+	0.218723i	−0.0148769	+	0.0124832i	0.635319	+	0.772250i	$0.280869\pi$
$308$		0			0
$309$	0.869688	+	0.316541i	0.0494748	+	0.0180074i
$310$		0			0
$311$	−1.14512	+	1.98340i	−0.0649337	+	0.112468i	−0.896665	−	0.442711i	$-0.854017\pi$
$311$	−1.14512	+	1.98340i	−0.0649337	+	0.112468i	0.831731	+	0.555179i	$0.187350\pi$
$312$		0			0
$313$	−4.51557	+	25.6091i	−0.255235	+	1.44751i	0.540233	+	0.841515i	$0.318336\pi$
$313$	−4.51557	+	25.6091i	−0.255235	+	1.44751i	−0.795468	+	0.605995i	$0.792775\pi$
$314$		0			0
$315$	0.892012	+	1.54501i	0.0502592	+	0.0870514i
$316$		0			0
$317$	−23.6442	−	19.8398i	−1.32799	−	1.11432i	−0.984543	−	0.175145i	$-0.943960\pi$
$317$	−23.6442	−	19.8398i	−1.32799	−	1.11432i	−0.343449	−	0.939171i	$-0.611595\pi$
$318$		0			0
$319$	6.17292	−	2.24676i	0.345617	−	0.125794i
$320$		0			0
$321$	−0.206696	−	1.17223i	−0.0115366	−	0.0654276i
$322$		0			0
$323$	4.22066	−	20.7513i	0.234844	−	1.15464i
$324$		0			0
$325$	−0.557893	−	3.16397i	−0.0309463	−	0.175505i
$326$		0			0
$327$	−25.9811	+	9.45634i	−1.43676	+	0.522937i
$328$		0			0
$329$	14.1296	+	11.8562i	0.778992	+	0.653652i
$330$		0			0
$331$	7.63635	+	13.2265i	0.419732	+	0.726996i	0.995912	−	0.0903260i	$-0.0287909\pi$
$331$	7.63635	+	13.2265i	0.419732	+	0.726996i	−0.576181	+	0.817322i	$0.695458\pi$
$332$		0			0
$333$	−0.680067	+	3.85685i	−0.0372674	+	0.211354i
$334$		0			0
$335$	3.33254	−	5.77213i	0.182076	−	0.315365i
$336$		0			0
$337$	4.75785	+	1.73172i	0.259177	+	0.0943327i	0.468341	−	0.883548i	$-0.344852\pi$
$337$	4.75785	+	1.73172i	0.259177	+	0.0943327i	−0.209164	+	0.977881i	$0.567074\pi$
$338$		0			0
$339$	−1.25327	+	1.05162i	−0.0680682	+	0.0571160i
$340$		0			0
$341$	10.4649			0.566704
$342$		0			0
$343$	4.74225			0.256057
$344$		0			0
$345$	−8.26584	+	6.93586i	−0.445018	+	0.373414i
$346$		0			0
$347$	−7.71229	−	2.80704i	−0.414017	−	0.150690i	0.126609	−	0.991953i	$-0.459591\pi$
$347$	−7.71229	−	2.80704i	−0.414017	−	0.150690i	−0.540627	+	0.841263i	$0.681813\pi$
$348$		0			0
$349$	8.00920	−	13.8723i	0.428723	−	0.742569i	−0.568037	−	0.823003i	$-0.692297\pi$
$349$	8.00920	−	13.8723i	0.428723	−	0.742569i	0.996760	+	0.0804334i	$0.0256304\pi$
$350$		0			0
$351$	3.08770	−	17.5112i	0.164809	−	0.934680i
$352$		0			0
$353$	−15.2156	−	26.3543i	−0.809847	−	1.40270i	−0.912970	−	0.408027i	$-0.866217\pi$
$353$	−15.2156	−	26.3543i	−0.809847	−	1.40270i	0.103123	−	0.994669i	$-0.467116\pi$
$354$		0			0
$355$	6.24652	+	5.24145i	0.331531	+	0.278187i
$356$		0			0
$357$	−25.6842	+	9.34828i	−1.35935	+	0.494763i
$358$		0			0
$359$	−0.324004	−	1.83752i	−0.0171003	−	0.0969806i	0.975063	−	0.221928i	$-0.0712349\pi$
$359$	−0.324004	−	1.83752i	−0.0171003	−	0.0969806i	−0.992163	+	0.124947i	$0.960124\pi$
$360$		0			0
$361$	13.8972	+	12.9564i	0.731432	+	0.681914i
$362$		0			0
$363$	0.225833	+	1.28076i	0.0118532	+	0.0672226i
$364$		0			0
$365$	−7.20628	+	2.62287i	−0.377194	+	0.137287i
$366$		0			0
$367$	−24.3882	−	20.4641i	−1.27305	−	1.06822i	−0.994162	−	0.107896i	$-0.965589\pi$
$367$	−24.3882	−	20.4641i	−1.27305	−	1.06822i	−0.278891	−	0.960323i	$-0.589967\pi$
$368$		0			0
$369$	−2.03697	−	3.52813i	−0.106040	−	0.183667i
$370$		0			0
$371$	4.58974	−	26.0297i	0.238287	−	1.35139i
$372$		0			0
$373$	−1.59251	+	2.75831i	−0.0824572	+	0.142820i	−0.904305	−	0.426887i	$-0.859610\pi$
$373$	−1.59251	+	2.75831i	−0.0824572	+	0.142820i	0.821848	+	0.569707i	$0.192943\pi$
$374$		0			0
$375$	1.48541	+	0.540646i	0.0767064	+	0.0279189i
$376$		0			0
$377$	−4.70198	+	3.94543i	−0.242164	+	0.203200i
$378$		0			0
$379$	37.5855			1.93064			0.965320	−	0.261070i	$-0.0840753\pi$
$379$	37.5855			1.93064			0.965320	+	0.261070i	$0.0840753\pi$
$380$		0			0
$381$	3.04086			0.155788
$382$		0			0
$383$	−11.5073	+	9.65579i	−0.587997	+	0.493388i	−0.887562	−	0.460688i	$-0.847603\pi$
$383$	−11.5073	+	9.65579i	−0.587997	+	0.493388i	0.299566	+	0.954076i	$0.403158\pi$
$384$		0			0
$385$	11.4998	+	4.18560i	0.586086	+	0.213318i
$386$		0			0
$387$	2.83444	−	4.90940i	0.144083	−	0.249559i
$388$		0			0
$389$	−3.79034	+	21.4961i	−0.192178	+	1.08990i	0.724203	+	0.689587i	$0.242208\pi$
$389$	−3.79034	+	21.4961i	−0.192178	+	1.08990i	−0.916381	+	0.400308i	$0.868903\pi$
$390$		0			0
$391$	16.5811	+	28.7193i	0.838541	+	1.45240i
$392$		0			0
$393$	16.4181	+	13.7764i	0.828181	+	0.694927i
$394$		0			0
$395$	−12.7814	+	4.65204i	−0.643100	+	0.234069i
$396$		0			0
$397$	4.20882	+	23.8694i	0.211235	+	1.19797i	0.887322	+	0.461150i	$0.152563\pi$
$397$	4.20882	+	23.8694i	0.211235	+	1.19797i	−0.676088	+	0.736821i	$0.736326\pi$
$398$		0			0
$399$	4.88785	−	24.0316i	0.244699	−	1.20309i
$400$		0			0
$401$	3.79091	+	21.4993i	0.189309	+	1.07363i	0.920293	+	0.391231i	$0.127951\pi$
$401$	3.79091	+	21.4993i	0.189309	+	1.07363i	−0.730983	+	0.682395i	$0.760938\pi$
$402$		0			0
$403$	−9.18842	+	3.34431i	−0.457708	+	0.166592i
$404$		0			0
$405$	5.54999	+	4.65700i	0.275781	+	0.231408i
$406$		0			0
$407$	13.4325	+	23.2658i	0.665824	+	1.15324i
$408$		0			0
$409$	1.53859	−	8.72579i	0.0760785	−	0.431463i	−0.922849	−	0.385162i	$-0.874146\pi$
$409$	1.53859	−	8.72579i	0.0760785	−	0.431463i	0.998928	−	0.0463008i	$-0.0147433\pi$
$410$		0			0
$411$	2.60790	−	4.51702i	0.128638	−	0.222808i
$412$		0			0
$413$	29.4985	+	10.7366i	1.45153	+	0.528313i
$414$		0			0
$415$	−12.5893	+	10.5637i	−0.617984	+	0.518550i
$416$		0			0
$417$	−6.11800			−0.299600
$418$		0			0
$419$	−13.0697			−0.638496			−0.319248	−	0.947671i	$-0.603430\pi$
$419$	−13.0697			−0.638496			−0.319248	+	0.947671i	$0.603430\pi$
$420$		0			0
$421$	11.9984	−	10.0678i	0.584764	−	0.490675i	−0.301744	−	0.953389i	$-0.597569\pi$
$421$	11.9984	−	10.0678i	0.584764	−	0.490675i	0.886508	+	0.462714i	$0.153124\pi$
$422$		0			0
$423$	−2.44101	−	0.888454i	−0.118686	−	0.0431981i
$424$		0			0
$425$	2.42908	−	4.20729i	0.117828	−	0.204083i
$426$		0			0
$427$	−4.73182	+	26.8355i	−0.228989	+	1.29866i
$428$		0			0
$429$	−8.73114	−	15.1228i	−0.421543	−	0.730135i
$430$		0			0
$431$	−11.3818	−	9.55043i	−0.548240	−	0.460028i	0.326105	−	0.945334i	$-0.394264\pi$
$431$	−11.3818	−	9.55043i	−0.548240	−	0.460028i	−0.874344	+	0.485306i	$0.838708\pi$
$432$		0			0
$433$	22.3940	−	8.15074i	1.07619	−	0.391700i	0.257699	−	0.966225i	$-0.417036\pi$
$433$	22.3940	−	8.15074i	1.07619	−	0.391700i	0.818487	+	0.574526i	$0.194813\pi$
$434$		0			0
$435$	−0.524418	−	2.97412i	−0.0251439	−	0.142598i
$436$		0			0
$437$	−29.7440	−	0.777164i	−1.42285	−	0.0371768i
$438$		0			0
$439$	3.72592	+	21.1307i	0.177828	+	1.00852i	0.934828	+	0.355100i	$0.115553\pi$
$439$	3.72592	+	21.1307i	0.177828	+	1.00852i	−0.757000	+	0.653415i	$0.773336\pi$
$440$		0			0
$441$	2.66955	−	0.971636i	0.127121	−	0.0462684i
$442$		0			0
$443$	−29.3056	−	24.5903i	−1.39235	−	1.16832i	−0.964378	−	0.264530i	$-0.914783\pi$
$443$	−29.3056	−	24.5903i	−1.39235	−	1.16832i	−0.427973	−	0.903791i	$-0.640772\pi$
$444$		0			0
$445$	1.78991	+	3.10021i	0.0848497	+	0.146964i
$446$		0			0
$447$	5.95741	−	33.7861i	0.281776	−	1.59803i
$448$		0			0
$449$	−9.36701	+	16.2241i	−0.442056	+	0.765664i	−0.997842	−	0.0656615i	$-0.979084\pi$
$449$	−9.36701	+	16.2241i	−0.442056	+	0.765664i	0.555786	+	0.831326i	$0.312418\pi$
$450$		0			0
$451$	−26.2607	−	9.55810i	−1.23657	−	0.450073i
$452$		0			0
$453$	24.9850	−	20.9649i	1.17390	−	0.985016i
$454$		0			0
$455$	−11.4348			−0.536071
$456$		0			0
$457$	−23.4274			−1.09589			−0.547943	−	0.836516i	$-0.684589\pi$
$457$	−23.4274			−1.09589			−0.547943	+	0.836516i	$0.684589\pi$
$458$		0			0
$459$	20.5973	−	17.2832i	0.961399	−	0.806709i
$460$		0			0
$461$	27.2784	+	9.92851i	1.27048	+	0.462417i	0.887273	−	0.461245i	$-0.152597\pi$
$461$	27.2784	+	9.92851i	1.27048	+	0.462417i	0.383207	+	0.923662i	$0.374819\pi$
$462$		0			0
$463$	−4.54270	+	7.86818i	−0.211117	+	0.365665i	−0.952064	−	0.305898i	$-0.901043\pi$
$463$	−4.54270	+	7.86818i	−0.211117	+	0.365665i	0.740947	+	0.671563i	$0.234377\pi$
$464$		0			0
$465$	0.835422	−	4.73792i	0.0387418	−	0.219716i
$466$		0			0
$467$	−5.74457	−	9.94989i	−0.265827	−	0.460426i	0.701953	−	0.712223i	$-0.252312\pi$
$467$	−5.74457	−	9.94989i	−0.265827	−	0.460426i	−0.967780	+	0.251797i	$0.918978\pi$
$468$		0			0
$469$	−18.1722	−	15.2483i	−0.839112	−	0.704099i
$470$		0			0
$471$	−14.6568	+	5.33465i	−0.675351	+	0.245808i
$472$		0			0
$473$	−6.75263	−	38.2961i	−0.310486	−	1.76086i
$474$		0			0
$475$	2.08011	+	3.83056i	0.0954419	+	0.175758i
$476$		0			0
$477$	0.646389	+	3.66586i	0.0295961	+	0.167848i
$478$		0			0
$479$	−21.3314	+	7.76399i	−0.974656	+	0.354746i	−0.779760	−	0.626078i	$-0.784659\pi$
$479$	−21.3314	+	7.76399i	−0.974656	+	0.354746i	−0.194896	+	0.980824i	$0.562437\pi$
$480$		0			0
$481$	−19.2293	−	16.1353i	−0.876779	−	0.735705i
$482$		0			0
$483$	19.2022	+	33.2591i	0.873728	+	1.51334i
$484$		0			0
$485$	−0.167924	+	0.952344i	−0.00762504	+	0.0432437i
$486$		0			0
$487$	−10.0120	+	17.3412i	−0.453685	+	0.785806i	−0.998612	−	0.0526778i	$-0.983224\pi$
$487$	−10.0120	+	17.3412i	−0.453685	+	0.785806i	0.544926	+	0.838484i	$0.316558\pi$
$488$		0			0
$489$	12.1361	+	4.41718i	0.548813	+	0.199752i
$490$		0			0
$491$	−3.83634	+	3.21907i	−0.173132	+	0.145275i	−0.725236	−	0.688500i	$-0.758269\pi$
$491$	−3.83634	+	3.21907i	−0.173132	+	0.145275i	0.552104	+	0.833775i	$0.313825\pi$
$492$		0			0
$493$	−9.28149			−0.418017
$494$		0			0
$495$	−1.72350			−0.0774657
$496$		0			0
$497$	22.2323	−	18.6551i	0.997257	−	0.836798i
$498$		0			0
$499$	23.3303	+	8.49153i	1.04441	+	0.380133i	0.806549	−	0.591167i	$-0.201332\pi$
$499$	23.3303	+	8.49153i	1.04441	+	0.380133i	0.237858	+	0.971300i	$0.423555\pi$
$500$		0			0
$501$	8.59309	−	14.8837i	0.383911	−	0.664953i
$502$		0			0
$503$	0.109422	−	0.620563i	0.00487888	−	0.0276695i	−0.982271	−	0.187466i	$-0.939973\pi$
$503$	0.109422	−	0.620563i	0.00487888	−	0.0276695i	0.987150	+	0.159796i	$0.0510837\pi$
$504$		0			0
$505$	−5.10821	−	8.84768i	−0.227312	−	0.393716i
$506$		0			0
$507$	−3.24292	−	2.72113i	−0.144023	−	0.120850i
$508$		0			0
$509$	2.83497	−	1.03185i	0.125658	−	0.0457357i	−0.278426	−	0.960458i	$-0.589813\pi$
$509$	2.83497	−	1.03185i	0.125658	−	0.0457357i	0.404084	+	0.914722i	$0.367590\pi$
$510$		0			0
$511$	4.73961	+	26.8797i	0.209668	+	1.18909i
$512$		0			0
$513$	3.56722	+	23.8595i	0.157497	+	1.05342i
$514$		0			0
$515$	0.101669	+	0.576591i	0.00448005	+	0.0254076i
$516$		0			0
$517$	−16.7446	+	6.09453i	−0.736426	+	0.268037i
$518$		0			0
$519$	−5.04107	−	4.22996i	−0.221279	−	0.185675i
$520$		0			0
$521$	7.60555	+	13.1732i	0.333205	+	0.577129i	0.983138	−	0.182863i	$-0.0585364\pi$
$521$	7.60555	+	13.1732i	0.333205	+	0.577129i	−0.649933	+	0.759991i	$0.725203\pi$
$522$		0			0
$523$	−2.48329	+	14.0834i	−0.108587	+	0.615825i	0.881141	+	0.472855i	$0.156776\pi$
$523$	−2.48329	+	14.0834i	−0.108587	+	0.615825i	−0.989727	+	0.142970i	$0.954335\pi$
$524$		0			0
$525$	2.81306	−	4.87236i	0.122772	−	0.212647i
$526$		0			0
$527$	−13.8941	−	5.05705i	−0.605238	−	0.220289i
$528$		0			0
$529$	18.0751	−	15.1668i	0.785874	−	0.659427i
$530$		0			0
$531$	−4.42101			−0.191855
$532$		0			0
$533$	26.1121			1.13104
$534$		0			0
$535$	0.576839	−	0.484025i	0.0249389	−	0.0209262i
$536$		0			0
$537$	−18.2587	−	6.64562i	−0.787921	−	0.286780i
$538$		0			0
$539$	9.74378	−	16.8767i	0.419694	−	0.726932i
$540$		0			0
$541$	7.94419	−	45.0537i	0.341547	−	1.93701i	−0.00767520	−	0.999971i	$-0.502443\pi$
$541$	7.94419	−	45.0537i	0.341547	−	1.93701i	0.349222	−	0.937040i	$-0.386446\pi$
$542$		0			0
$543$	−19.9667	−	34.5834i	−0.856854	−	1.48412i
$544$		0			0
$545$	−13.3987	−	11.2429i	−0.573939	−	0.481592i
$546$		0			0
$547$	31.6845	−	11.5322i	1.35473	−	0.493081i	0.440309	−	0.897846i	$-0.354869\pi$
$547$	31.6845	−	11.5322i	1.35473	−	0.493081i	0.914421	+	0.404765i	$0.132647\pi$
$548$		0			0
$549$	−0.666400	−	3.77934i	−0.0284412	−	0.161298i
$550$		0			0
$551$	4.35078	−	7.10074i	0.185349	−	0.302502i
$552$		0			0
$553$	8.40637	+	47.6749i	0.357475	+	2.02734i
$554$		0			0
$555$	11.6058	−	4.22417i	0.492639	−	0.179306i
$556$		0			0
$557$	21.8724	+	18.3531i	0.926762	+	0.777646i	0.975233	−	0.221179i	$-0.0709905\pi$
$557$	21.8724	+	18.3531i	0.926762	+	0.777646i	−0.0484714	+	0.998825i	$0.515435\pi$
$558$		0			0
$559$	18.1675	+	31.4670i	0.768403	+	1.33091i
$560$		0			0
$561$	4.58524	−	26.0042i	0.193589	−	1.09790i
$562$		0			0
$563$	14.6828	−	25.4313i	0.618806	−	1.07180i	−0.370898	−	0.928673i	$-0.620950\pi$
$563$	14.6828	−	25.4313i	0.618806	−	1.07180i	0.989704	−	0.143129i	$-0.0457164\pi$
$564$		0			0
$565$	−0.972556	−	0.353981i	−0.0409157	−	0.0148921i
$566$		0			0
$567$	19.7533	−	16.5750i	0.829560	−	0.696084i
$568$		0			0
$569$	−18.9129			−0.792868			−0.396434	−	0.918063i	$-0.629752\pi$
$569$	−18.9129			−0.792868			−0.396434	+	0.918063i	$0.629752\pi$
$570$		0			0
$571$	−4.56984			−0.191242			−0.0956210	−	0.995418i	$-0.530484\pi$
$571$	−4.56984			−0.191242			−0.0956210	+	0.995418i	$0.530484\pi$
$572$		0			0
$573$	7.25076	−	6.08411i	0.302905	−	0.254167i
$574$		0			0
$575$	−6.41442	−	2.33466i	−0.267500	−	0.0973619i
$576$		0			0
$577$	5.67068	−	9.82191i	0.236074	−	0.408892i	−0.723511	−	0.690313i	$-0.757473\pi$
$577$	5.67068	−	9.82191i	0.236074	−	0.408892i	0.959584	+	0.281422i	$0.0908060\pi$
$578$		0			0
$579$	4.35157	−	24.6790i	0.180845	−	1.02562i
$580$		0			0
$581$	29.2459	+	50.6553i	1.21332	+	2.10154i
$582$		0			0
$583$	19.5606	+	16.4133i	0.810119	+	0.679771i
$584$		0			0
$585$	1.51328	−	0.550790i	0.0625665	−	0.0227723i
$586$		0			0
$587$	−0.221815	−	1.25798i	−0.00915530	−	0.0519223i	0.979888	−	0.199549i	$-0.0639477\pi$
$587$	−0.221815	−	1.25798i	−0.00915530	−	0.0519223i	−0.989043	+	0.147627i	$0.952837\pi$
$588$		0			0
$589$	10.3819	−	8.25909i	0.427778	−	0.340310i
$590$		0			0
$591$	−0.0141063	−	0.0800009i	−0.000580256	−	0.00329080i
$592$		0			0
$593$	37.0067	−	13.4693i	1.51968	−	0.553120i	0.558615	−	0.829427i	$-0.311333\pi$
$593$	37.0067	−	13.4693i	1.51968	−	0.553120i	0.961069	+	0.276308i	$0.0891109\pi$
$594$		0			0
$595$	−13.2456	−	11.1144i	−0.543018	−	0.455646i
$596$		0			0
$597$	3.99197	+	6.91429i	0.163380	+	0.282983i
$598$		0			0
$599$	−1.75174	+	9.93461i	−0.0715741	+	0.405917i	0.927880	+	0.372879i	$0.121629\pi$
$599$	−1.75174	+	9.93461i	−0.0715741	+	0.405917i	−0.999454	+	0.0330380i	$0.989482\pi$
$600$		0			0
$601$	−7.99956	+	13.8556i	−0.326309	+	0.565184i	−0.981776	−	0.190040i	$-0.939138\pi$
$601$	−7.99956	+	13.8556i	−0.326309	+	0.565184i	0.655467	+	0.755223i	$0.272472\pi$
$602$		0			0
$603$	3.13939	+	1.14264i	0.127846	+	0.0465320i
$604$		0			0
$605$	−0.630245	+	0.528838i	−0.0256231	+	0.0215003i
$606$		0			0
$607$	34.5238			1.40128			0.700639	−	0.713516i	$-0.252898\pi$
$607$	34.5238			1.40128			0.700639	+	0.713516i	$0.252898\pi$
$608$		0			0
$609$	−10.7487			−0.435558
$610$		0			0
$611$	12.7545	−	10.7023i	0.515993	−	0.432969i
$612$		0			0
$613$	14.6354	+	5.32686i	0.591119	+	0.215150i	0.620222	−	0.784427i	$-0.287043\pi$
$613$	14.6354	+	5.32686i	0.591119	+	0.215150i	−0.0291024	+	0.999576i	$0.509265\pi$
$614$		0			0
$615$	−6.42381	+	11.1264i	−0.259033	+	0.448658i
$616$		0			0
$617$	3.11076	−	17.6420i	0.125234	−	0.710240i	−0.855934	−	0.517085i	$-0.827017\pi$
$617$	3.11076	−	17.6420i	0.125234	−	0.710240i	0.981168	−	0.193155i	$-0.0618719\pi$
$618$		0			0
$619$	−16.3044	−	28.2401i	−0.655330	−	1.13507i	−0.981811	−	0.189862i	$-0.939196\pi$
$619$	−16.3044	−	28.2401i	−0.655330	−	1.13507i	0.326480	−	0.945204i	$-0.394137\pi$
$620$		0			0
$621$	−28.9408	−	24.2842i	−1.16135	−	0.974490i
$622$		0			0
$623$	11.9727	−	4.35772i	0.479677	−	0.174588i
$624$		0			0
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$		0			0
$627$	17.7450	+	15.6976i	0.708666	+	0.626902i
$628$		0			0
$629$	−6.59128	−	37.3810i	−0.262812	−	1.49048i
$630$		0			0
$631$	11.8466	−	4.31180i	0.471604	−	0.171650i	−0.0952746	−	0.995451i	$-0.530373\pi$
$631$	11.8466	−	4.31180i	0.471604	−	0.171650i	0.566879	+	0.823801i	$0.308151\pi$
$632$		0			0
$633$	−29.0965	−	24.4149i	−1.15648	−	0.970404i
$634$		0			0
$635$	0.961845	+	1.66597i	0.0381697	+	0.0661118i
$636$		0			0
$637$	−3.16191	+	17.9321i	−0.125279	+	0.710495i
$638$		0			0
$639$	−2.04365	+	3.53971i	−0.0808457	+	0.140029i
$640$		0			0
$641$	21.4326	+	7.80083i	0.846537	+	0.308114i	0.728627	−	0.684910i	$-0.240159\pi$
$641$	21.4326	+	7.80083i	0.846537	+	0.308114i	0.117909	+	0.993024i	$0.462381\pi$
$642$		0			0
$643$	−24.8012	+	20.8106i	−0.978062	+	0.820692i	−0.983796	−	0.179292i	$-0.942619\pi$
$643$	−24.8012	+	20.8106i	−0.978062	+	0.820692i	0.00573352	+	0.999984i	$0.498175\pi$
$644$		0			0
$645$	−17.8775			−0.703924
$646$		0			0
$647$	−4.51050			−0.177326			−0.0886630	−	0.996062i	$-0.528259\pi$
$647$	−4.51050			−0.177326			−0.0886630	+	0.996062i	$0.528259\pi$
$648$		0			0
$649$	−23.2317	+	19.4937i	−0.911923	+	0.765194i
$650$		0			0
$651$	−16.0905	−	5.85645i	−0.630635	−	0.229532i
$652$		0			0
$653$	5.78138	−	10.0136i	0.226243	−	0.391864i	−0.730449	−	0.682968i	$-0.760689\pi$
$653$	5.78138	−	10.0136i	0.226243	−	0.391864i	0.956692	+	0.291103i	$0.0940223\pi$
$654$		0			0
$655$	−2.35438	+	13.3523i	−0.0919932	+	0.521719i
$656$		0			0
$657$	−1.92198	−	3.32897i	−0.0749836	−	0.129875i
$658$		0			0
$659$	13.4591	+	11.2935i	0.524291	+	0.439932i	0.866125	−	0.499828i	$-0.166603\pi$
$659$	13.4591	+	11.2935i	0.524291	+	0.439932i	−0.341834	+	0.939760i	$0.611048\pi$
$660$		0			0
$661$	−3.55033	+	1.29221i	−0.138092	+	0.0502613i	−0.410142	−	0.912022i	$-0.634521\pi$
$661$	−3.55033	+	1.29221i	−0.138092	+	0.0502613i	0.272050	+	0.962283i	$0.412298\pi$
$662$		0			0
$663$	4.28434	+	24.2977i	0.166390	+	0.943644i
$664$		0			0
$665$	14.7120	−	4.92351i	0.570507	−	0.190926i
$666$		0			0
$667$	2.26458	+	12.8431i	0.0876849	+	0.497286i
$668$		0			0
$669$	25.2968	−	9.20728i	0.978030	−	0.355974i
$670$		0			0
$671$	−20.1662	−	16.9214i	−0.778507	−	0.653245i
$672$		0			0
$673$	−18.3166	−	31.7253i	−0.706053	−	1.22292i	−0.966310	−	0.257380i	$-0.917141\pi$
$673$	−18.3166	−	31.7253i	−0.706053	−	1.22292i	0.260257	−	0.965539i	$-0.416193\pi$
$674$		0			0
$675$	−0.961069	+	5.45049i	−0.0369916	+	0.209790i
$676$		0			0
$677$	−16.8483	+	29.1822i	−0.647534	+	1.12156i	0.336176	+	0.941799i	$0.390866\pi$
$677$	−16.8483	+	29.1822i	−0.647534	+	1.12156i	−0.983710	+	0.179763i	$0.942467\pi$
$678$		0			0
$679$	3.23426	+	1.17718i	0.124120	+	0.0451759i
$680$		0			0
$681$	9.56611	−	8.02692i	0.366574	−	0.307592i
$682$		0			0
$683$	14.9190			0.570861			0.285430	−	0.958399i	$-0.407864\pi$
$683$	14.9190			0.570861			0.285430	+	0.958399i	$0.407864\pi$
$684$		0			0
$685$	3.29959			0.126071
$686$		0			0
$687$	−6.82563	+	5.72738i	−0.260414	+	0.218513i
$688$		0			0
$689$	−22.4201	−	8.16024i	−0.854137	−	0.310880i
$690$		0			0
$691$	21.8621	−	37.8663i	0.831675	−	1.44050i	−0.0650338	−	0.997883i	$-0.520716\pi$
$691$	21.8621	−	37.8663i	0.831675	−	1.44050i	0.896709	−	0.442621i	$-0.145951\pi$
$692$		0			0
$693$	−1.06520	+	6.04103i	−0.0404635	+	0.229480i
$694$		0			0
$695$	−1.93516	−	3.35180i	−0.0734050	−	0.127141i
$696$		0			0
$697$	30.2473	+	25.3805i	1.14570	+	0.961355i
$698$		0			0
$699$	0.614067	−	0.223502i	0.0232261	−	0.00845362i
$700$		0			0
$701$	3.52875	+	20.0125i	0.133279	+	0.755862i	0.976043	+	0.217579i	$0.0698159\pi$
$701$	3.52875	+	20.0125i	0.133279	+	0.755862i	−0.842764	+	0.538283i	$0.819073\pi$
$702$		0			0
$703$	31.6878	+	12.4801i	1.19513	+	0.470695i
$704$		0			0
$705$	1.42253	+	8.06757i	0.0535756	+	0.303842i
$706$		0			0
$707$	−34.1689	+	12.4365i	−1.28506	+	0.467722i
$708$		0			0
$709$	−1.81966	−	1.52687i	−0.0683387	−	0.0573429i	0.607979	−	0.793953i	$-0.291981\pi$
$709$	−1.81966	−	1.52687i	−0.0683387	−	0.0573429i	−0.676317	+	0.736611i	$0.736425\pi$
$710$		0			0
$711$	−3.40890	−	5.90440i	−0.127844	−	0.221432i
$712$		0			0
$713$	−3.60758	+	20.4596i	−0.135105	+	0.766218i
$714$		0			0
$715$	5.52344	−	9.56687i	0.206565	−	0.357781i
$716$		0			0
$717$	−1.16248	−	0.423107i	−0.0434135	−	0.0158012i
$718$		0			0
$719$	−25.0761	+	21.0413i	−0.935179	+	0.784708i	−0.976740	−	0.214428i	$-0.931211\pi$
$719$	−25.0761	+	21.0413i	−0.935179	+	0.784708i	0.0415609	+	0.999136i	$0.486767\pi$
$720$		0			0
$721$	2.08384			0.0776061
$722$		0			0
$723$	−16.1214			−0.599560
$724$		0			0
$725$	1.46352	−	1.22804i	0.0543539	−	0.0456084i
$726$		0			0
$727$	−3.43792	−	1.25130i	−0.127506	−	0.0464082i	0.277479	−	0.960732i	$-0.410501\pi$
$727$	−3.43792	−	1.25130i	−0.127506	−	0.0464082i	−0.404985	+	0.914323i	$0.632723\pi$
$728$		0			0
$729$	−14.9389	+	25.8749i	−0.553293	+	0.958331i
$730$		0			0
$731$	−9.54082	+	54.1087i	−0.352880	+	2.00128i
$732$		0			0
$733$	−13.5536	−	23.4755i	−0.500614	−	0.867088i	−1.00000		0.000708563i	$-0.999774\pi$
$733$	−13.5536	−	23.4755i	−0.500614	−	0.867088i	0.499386	−	0.866379i	$-0.333559\pi$
$734$		0			0
$735$	−6.86300	−	5.75874i	−0.253146	−	0.212414i
$736$		0			0
$737$	21.5353	−	7.83820i	0.793262	−	0.288724i
$738$		0			0
$739$	1.34091	+	7.60465i	0.0493260	+	0.279742i	0.999487	−	0.0320170i	$-0.0101931\pi$
$739$	1.34091	+	7.60465i	0.0493260	+	0.279742i	−0.950161	+	0.311759i	$0.899082\pi$
$740$		0			0
$741$	−20.5971	−	8.11206i	−0.756654	−	0.298004i
$742$		0			0
$743$	−1.88374	−	10.6832i	−0.0691077	−	0.391929i	−0.999667	−	0.0257890i	$-0.991790\pi$
$743$	−1.88374	−	10.6832i	−0.0691077	−	0.391929i	0.930560	−	0.366140i	$-0.119321\pi$
$744$		0			0
$745$	20.3944	−	7.42296i	0.747194	−	0.271956i
$746$		0			0
$747$	−6.31037	−	5.29503i	−0.230884	−	0.193735i
$748$		0			0
$749$	−1.34004	−	2.32102i	−0.0489639	−	0.0848080i
$750$		0			0
$751$	2.92223	−	16.5728i	0.106634	−	0.604750i	−0.883921	−	0.467636i	$-0.845106\pi$
$751$	2.92223	−	16.5728i	0.106634	−	0.604750i	0.990555	−	0.137115i	$-0.0437829\pi$
$752$		0			0
$753$	14.3967	−	24.9358i	0.524645	−	0.908711i
$754$		0			0
$755$	19.3887	+	7.05692i	0.705628	+	0.256827i
$756$		0			0
$757$	2.07783	−	1.74350i	0.0755199	−	0.0633687i	−0.604246	−	0.796798i	$-0.706526\pi$
$757$	2.07783	−	1.74350i	0.0755199	−	0.0633687i	0.679766	+	0.733429i	$0.262081\pi$
$758$		0			0
$759$	−37.1015			−1.34670
$760$		0			0
$761$	−15.0957			−0.547219			−0.273609	−	0.961841i	$-0.588218\pi$
$761$	−15.0957			−0.547219			−0.273609	+	0.961841i	$0.588218\pi$
$762$		0			0
$763$	−47.6882	+	40.0151i	−1.72643	+	1.44865i
$764$		0			0
$765$	2.28829	+	0.832869i	0.0827332	+	0.0301124i
$766$		0			0
$767$	14.1683	−	24.5402i	0.511588	−	0.886097i
$768$		0			0
$769$	−5.01576	+	28.4458i	−0.180873	+	1.02578i	0.750271	+	0.661130i	$0.229923\pi$
$769$	−5.01576	+	28.4458i	−0.180873	+	1.02578i	−0.931144	+	0.364652i	$0.881188\pi$
$770$		0			0
$771$	13.9393	+	24.1436i	0.502013	+	0.869512i
$772$		0			0
$773$	−30.6310	−	25.7025i	−1.10172	−	0.924454i	−0.104182	−	0.994558i	$-0.533222\pi$
$773$	−30.6310	−	25.7025i	−1.10172	−	0.924454i	−0.997540	+	0.0701039i	$0.977667\pi$
$774$		0			0
$775$	2.85996	−	1.04094i	0.102733	−	0.0373917i
$776$		0			0
$777$	−7.63320	−	43.2900i	−0.273840	−	1.55302i
$778$		0			0
$779$	−33.5959	+	11.2432i	−1.20370	+	0.402828i
$780$		0			0
$781$	4.86870	+	27.6118i	0.174216	+	0.988027i
$782$		0			0
$783$	9.93611	−	3.61645i	0.355088	−	0.129241i
$784$		0			0
$785$	−7.55869	−	6.34249i	−0.269781	−	0.226373i
$786$		0			0
$787$	−3.36252	−	5.82405i	−0.119861	−	0.207605i	0.799852	−	0.600198i	$-0.204912\pi$
$787$	−3.36252	−	5.82405i	−0.119861	−	0.207605i	−0.919712	+	0.392593i	$0.871578\pi$
$788$		0			0
$789$	3.06676	−	17.3924i	0.109179	−	0.619188i
$790$		0			0
$791$	−1.84181	+	3.19012i	−0.0654874	+	0.113427i
$792$		0			0
$793$	23.1141	+	8.41285i	0.820807	+	0.298749i
$794$		0			0
$795$	8.99261	−	7.54570i	0.318935	−	0.267618i
$796$		0			0
$797$	−18.5313			−0.656414			−0.328207	−	0.944606i	$-0.606444\pi$
$797$	−18.5313			−0.656414			−0.328207	+	0.944606i	$0.606444\pi$
$798$		0			0
$799$	25.1768			0.890692
$800$		0			0
$801$	−1.37457	+	1.15340i	−0.0485681	+	0.0407535i
$802$		0			0
$803$	−24.7782	−	9.01853i	−0.874404	−	0.318257i
$804$		0			0
$805$	−12.1475	+	21.0402i	−0.428145	+	0.741568i
$806$		0			0
$807$	6.76136	−	38.3456i	0.238011	−	1.34983i
$808$		0			0
$809$	10.3771	+	17.9737i	0.364840	+	0.631922i	0.988751	−	0.149574i	$-0.0477902\pi$
$809$	10.3771	+	17.9737i	0.364840	+	0.631922i	−0.623910	+	0.781496i	$0.714457\pi$
$810$		0			0
$811$	30.8349	+	25.8736i	1.08276	+	0.908544i	0.996147	−	0.0876980i	$-0.0279511\pi$
$811$	30.8349	+	25.8736i	1.08276	+	0.908544i	0.0866134	+	0.996242i	$0.472396\pi$
$812$		0			0
$813$	−26.7797	+	9.74703i	−0.939206	+	0.341843i
$814$		0			0
$815$	1.41874	+	8.04606i	0.0496962	+	0.281841i
$816$		0			0
$817$	−36.9232	−	32.6631i	−1.29178	−	1.14274i
$818$		0			0
$819$	−0.995294	−	5.64459i	−0.0347784	−	0.197238i
$820$		0			0
$821$	−41.6575	+	15.1621i	−1.45386	+	0.529161i	−0.943666	−	0.330899i	$-0.892648\pi$
$821$	−41.6575	+	15.1621i	−1.45386	+	0.529161i	−0.510192	+	0.860060i	$0.670426\pi$
$822$		0			0
$823$	31.1924	+	26.1735i	1.08730	+	0.912352i	0.996506	−	0.0835173i	$-0.0266154\pi$
$823$	31.1924	+	26.1735i	1.08730	+	0.912352i	0.0907930	+	0.995870i	$0.471060\pi$
$824$		0			0
$825$	2.71763	+	4.70707i	0.0946157	+	0.163879i
$826$		0			0
$827$	−5.84730	+	33.1617i	−0.203331	+	1.15315i	0.696715	+	0.717348i	$0.254644\pi$
$827$	−5.84730	+	33.1617i	−0.203331	+	1.15315i	−0.900045	+	0.435797i	$0.856467\pi$
$828$		0			0
$829$	−14.0011	+	24.2506i	−0.486277	+	0.842257i	−0.999876	−	0.0157736i	$-0.994979\pi$
$829$	−14.0011	+	24.2506i	−0.486277	+	0.842257i	0.513598	+	0.858031i	$0.328312\pi$
$830$		0			0
$831$	−27.9848	−	10.1856i	−0.970782	−	0.353336i
$832$		0			0
$833$	−21.0923	+	17.6985i	−0.730805	+	0.613218i
$834$		0			0
$835$	10.8722			0.376248
$836$		0			0
$837$	16.8445			0.582232
$838$		0			0
$839$	18.2668	−	15.3277i	0.630641	−	0.529170i	−0.270487	−	0.962724i	$-0.587185\pi$
$839$	18.2668	−	15.3277i	0.630641	−	0.529170i	0.901128	+	0.433553i	$0.142740\pi$
$840$		0			0
$841$	23.8212	+	8.67021i	0.821421	+	0.298973i
$842$		0			0
$843$	−25.3645	+	43.9327i	−0.873601	+	1.51312i
$844$		0			0
$845$	0.465041	−	2.63738i	0.0159979	−	0.0907285i
$846$		0			0
$847$	1.46411	+	2.53591i	0.0503073	+	0.0871348i
$848$		0			0
$849$	6.30073	+	5.28694i	0.216241	+	0.181447i
$850$		0			0
$851$	−50.1170	+	18.2411i	−1.71799	+	0.625297i
$852$		0			0
$853$	1.96728	+	11.1570i	0.0673585	+	0.382009i	0.999787	+	0.0206536i	$0.00657471\pi$
$853$	1.96728	+	11.1570i	0.0673585	+	0.382009i	−0.932428	+	0.361355i	$0.882314\pi$
$854$		0			0
$855$	−1.70984	+	1.36023i	−0.0584752	+	0.0465188i
$856$		0			0
$857$	−8.33674	−	47.2800i	−0.284777	−	1.61505i	−0.706079	−	0.708133i	$-0.749538\pi$
$857$	−8.33674	−	47.2800i	−0.284777	−	1.61505i	0.421302	−	0.906921i	$-0.361573\pi$
$858$		0			0
$859$	−41.8070	+	15.2165i	−1.42643	+	0.519180i	−0.935907	−	0.352246i	$-0.885418\pi$
$859$	−41.8070	+	15.2165i	−1.42643	+	0.519180i	−0.490527	+	0.871426i	$0.663196\pi$
$860$		0			0
$861$	35.0287	+	29.3925i	1.19377	+	1.00170i
$862$		0			0
$863$	−22.8285	−	39.5401i	−0.777091	−	1.34596i	−0.933612	−	0.358287i	$-0.883361\pi$
$863$	−22.8285	−	39.5401i	−0.777091	−	1.34596i	0.156520	−	0.987675i	$-0.449972\pi$
$864$		0			0
$865$	0.722899	−	4.09976i	0.0245793	−	0.139396i
$866$		0			0
$867$	−5.21778	+	9.03747i	−0.177205	+	0.306929i
$868$		0			0
$869$	−43.9477	−	15.9957i	−1.49082	−	0.542615i
$870$		0			0
$871$	−16.4036	+	13.7643i	−0.555816	+	0.466385i
$872$		0			0
$873$	−0.484726			−0.0164055
$874$		0			0
$875$	3.55916			0.120321
$876$		0			0
$877$	34.8463	−	29.2395i	1.17667	−	0.987347i	0.176679	−	0.984268i	$-0.443464\pi$
$877$	34.8463	−	29.2395i	1.17667	−	0.987347i	0.999995	−	0.00307888i	$-0.000980039\pi$
$878$		0			0
$879$	−14.0246	−	5.10454i	−0.473038	−	0.172172i
$880$		0			0
$881$	22.4777	−	38.9325i	0.757292	−	1.31167i	−0.186934	−	0.982372i	$-0.559855\pi$
$881$	22.4777	−	38.9325i	0.757292	−	1.31167i	0.944227	−	0.329296i	$-0.106812\pi$
$882$		0			0
$883$	2.32995	−	13.2138i	0.0784090	−	0.444679i	−0.920176	−	0.391504i	$-0.871955\pi$
$883$	2.32995	−	13.2138i	0.0784090	−	0.444679i	0.998585	−	0.0531750i	$-0.0169341\pi$
$884$		0			0
$885$	6.97107	+	12.0742i	0.234330	+	0.405871i
$886$		0			0
$887$	28.4412	+	23.8650i	0.954963	+	0.801309i	0.980126	−	0.198374i	$-0.0635662\pi$
$887$	28.4412	+	23.8650i	0.954963	+	0.801309i	−0.0251635	+	0.999683i	$0.508011\pi$
$888$		0			0
$889$	6.43381	−	2.34171i	0.215783	−	0.0785386i
$890$		0			0
$891$	4.32581	+	24.5329i	0.144920	+	0.821883i
$892$		0			0
$893$	−11.8019	+	19.2614i	−0.394935	+	0.644558i
$894$		0			0
$895$	−2.13448	−	12.1053i	−0.0713479	−	0.404634i
$896$		0			0
$897$	32.5761	−	11.8567i	1.08768	−	0.395885i
$898$		0			0
$899$	−4.45425	−	3.73756i	−0.148557	−	0.124655i
$900$		0			0
$901$	−18.0390	−	31.2444i	−0.600966	−	1.04090i
$902$		0			0
$903$	−11.0490	+	62.6620i	−0.367688	+	2.08526i
$904$		0			0
$905$	12.6312	−	21.8779i	0.419876	−	0.727247i
$906$		0			0
$907$	−24.3424	−	8.85991i	−0.808276	−	0.294188i	−0.0953645	−	0.995442i	$-0.530402\pi$
$907$	−24.3424	−	8.85991i	−0.808276	−	0.294188i	−0.712912	+	0.701254i	$0.752624\pi$
$908$		0			0
$909$	3.92289	−	3.29170i	0.130114	−	0.109179i
$910$		0			0
$911$	56.2861			1.86484			0.932421	−	0.361373i	$-0.117692\pi$
$911$	56.2861			1.86484			0.932421	+	0.361373i	$0.117692\pi$
$912$		0			0
$913$	−56.5075			−1.87013
$914$		0			0
$915$	−9.27100	+	7.77929i	−0.306490	+	0.257175i
$916$		0			0
$917$	45.3460	+	16.5046i	1.49746	+	0.545030i
$918$		0			0
$919$	−9.91979	+	17.1816i	−0.327224	+	0.566768i	−0.981960	−	0.189090i	$-0.939446\pi$
$919$	−9.91979	+	17.1816i	−0.327224	+	0.566768i	0.654736	+	0.755857i	$0.272780\pi$
$920$		0			0
$921$	−0.0934027	+	0.529713i	−0.00307772	+	0.0174546i
$922$		0			0
$923$	−13.0989	−	22.6880i	−0.431155	−	0.746783i
$924$		0			0
$925$	5.98525	+	5.02222i	0.196794	+	0.165129i
$926$		0			0
$927$	−0.275775	+	0.100374i	−0.00905765	+	0.00329672i
$928$		0			0
$929$	3.63369	+	20.6077i	0.119218	+	0.676116i	0.984575	+	0.174962i	$0.0559801\pi$
$929$	3.63369	+	20.6077i	0.119218	+	0.676116i	−0.865358	+	0.501155i	$0.832909\pi$
$930$		0			0
$931$	−3.65296	−	24.4329i	−0.119721	−	0.800756i
$932$		0			0
$933$	0.628655	+	3.56528i	0.0205812	+	0.116722i
$934$		0			0
$935$	15.6970	−	5.71323i	0.513346	−	0.186843i
$936$		0			0
$937$	29.3249	+	24.6065i	0.958004	+	0.803860i	0.980627	−	0.195884i	$-0.0627575\pi$
$937$	29.3249	+	24.6065i	0.958004	+	0.803860i	−0.0226236	+	0.999744i	$0.507202\pi$
$938$		0			0
$939$	20.5529	+	35.5987i	0.670720	+	1.16172i
$940$		0			0
$941$	3.75904	−	21.3185i	0.122541	−	0.694965i	−0.860197	−	0.509962i	$-0.829659\pi$
$941$	3.75904	−	21.3185i	0.122541	−	0.694965i	0.982738	−	0.185003i	$-0.0592294\pi$
$942$		0			0
$943$	27.7397	−	48.0466i	0.903330	−	1.56461i
$944$		0			0
$945$	18.5105	+	6.73726i	0.602145	+	0.219163i
$946$		0			0
$947$	−20.1282	+	16.8896i	−0.654078	+	0.548837i	−0.908305	−	0.418308i	$-0.862623\pi$
$947$	−20.1282	+	16.8896i	−0.654078	+	0.548837i	0.254227	+	0.967145i	$0.418179\pi$
$948$		0			0
$949$	24.6380			0.799784
$950$		0			0
$951$	−48.7902			−1.58213
$952$		0			0
$953$	2.06839	−	1.73559i	0.0670018	−	0.0562212i	−0.608672	−	0.793422i	$-0.708297\pi$
$953$	2.06839	−	1.73559i	0.0670018	−	0.0562212i	0.675674	+	0.737201i	$0.263853\pi$
$954$		0			0
$955$	5.62670	+	2.04795i	0.182076	+	0.0662701i
$956$		0			0
$957$	5.19202	−	8.99284i	0.167834	−	0.290697i
$958$		0			0
$959$	2.03928	−	11.5653i	0.0658518	−	0.373464i
$960$		0			0
$961$	10.8685	+	18.8248i	0.350598	+	0.607253i
$962$		0			0
$963$	0.289140	+	0.242617i	0.00931740	+	0.00781822i
$964$		0			0
$965$	14.8970	−	5.42208i	0.479553	−	0.174543i
$966$		0			0
$967$	5.85748	+	33.2194i	0.188364	+	1.06826i	0.921557	+	0.388243i	$0.126918\pi$
$967$	5.85748	+	33.2194i	0.188364	+	1.06826i	−0.733193	+	0.680020i	$0.761971\pi$
$968$		0			0
$969$	−15.9742	−	29.4168i	−0.513165	−	0.945002i
$970$		0			0
$971$	−6.17012	−	34.9925i	−0.198009	−	1.12296i	−0.908069	−	0.418821i	$-0.862443\pi$
$971$	−6.17012	−	34.9925i	−0.198009	−	1.12296i	0.710060	−	0.704141i	$-0.248668\pi$
$972$		0			0
$973$	−12.9444	+	4.71136i	−0.414977	+	0.151039i
$974$		0			0
$975$	−3.89042	−	3.26445i	−0.124593	−	0.104546i
$976$		0			0
$977$	−7.64400	−	13.2398i	−0.244553	−	0.423578i	0.717453	−	0.696607i	$-0.245308\pi$
$977$	−7.64400	−	13.2398i	−0.244553	−	0.423578i	−0.962006	+	0.273029i	$0.911975\pi$
$978$		0			0
$979$	−2.13742	+	12.1219i	−0.0683122	+	0.387418i
$980$		0			0
$981$	4.38362	−	7.59266i	0.139958	−	0.242415i
$982$		0			0
$983$	−14.1763	−	5.15975i	−0.452154	−	0.164570i	0.105897	−	0.994377i	$-0.466228\pi$
$983$	−14.1763	−	5.15975i	−0.452154	−	0.164570i	−0.558051	+	0.829807i	$0.688451\pi$
$984$		0			0
$985$	0.0393673	−	0.0330331i	0.00125435	−	0.00105252i
$986$		0			0
$987$	29.1567			0.928068
$988$		0			0
$989$	77.1997			2.45481
$990$		0			0
$991$	−16.3932	+	13.7555i	−0.520747	+	0.436958i	−0.864892	−	0.501958i	$-0.832613\pi$
$991$	−16.3932	+	13.7555i	−0.520747	+	0.436958i	0.344145	+	0.938916i	$0.388169\pi$
$992$		0			0
$993$	22.6863	+	8.25712i	0.719927	+	0.262032i
$994$		0			0
$995$	−2.52537	+	4.37407i	−0.0800597	+	0.138667i
$996$		0			0
$997$	−8.18188	+	46.4018i	−0.259123	+	1.46956i	0.526141	+	0.850397i	$0.323638\pi$
$997$	−8.18188	+	46.4018i	−0.259123	+	1.46956i	−0.785264	+	0.619161i	$0.787473\pi$
$998$		0			0
$999$	21.6213	+	37.4493i	0.684069	+	1.18484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.161.3	✓	18
19.6	even	9		7220.2.a.v.1.8		9
19.13	odd	18		7220.2.a.x.1.2		9
19.17	even	9	inner	380.2.u.a.321.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.161.3	✓	18	1.1	even	1	trivial
380.2.u.a.321.3	yes	18	19.17	even	9	inner
7220.2.a.v.1.8		9	19.6	even	9
7220.2.a.x.1.2		9	19.13	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21092 - 1.01608i) q^{3} +(0.939693 + 0.342020i) q^{5} +(1.77958 - 3.08232i) q^{7} +(-0.0870410 + 0.493634i) q^{9} +O(q^{10})\)	\(q+(1.21092 - 1.01608i) q^{3} +(0.939693 + 0.342020i) q^{5} +(1.77958 - 3.08232i) q^{7} +(-0.0870410 + 0.493634i) q^{9} +(1.71921 + 2.97776i) q^{11} +(-2.46113 - 2.06513i) q^{13} +(1.48541 - 0.540646i) q^{15} +(-0.843610 - 4.78435i) q^{17} +(4.05569 + 1.59731i) q^{19} +(-0.976964 - 5.54064i) q^{21} +(-6.41442 + 2.33466i) q^{23} +(0.766044 + 0.642788i) q^{25} +(2.76729 + 4.79308i) q^{27} +(0.331754 - 1.88147i) q^{29} +(1.52175 - 2.63575i) q^{31} +(5.10747 + 1.85897i) q^{33} +(2.72647 - 2.28778i) q^{35} +7.81318 q^{37} -5.07858 q^{39} +(-6.22608 + 5.22431i) q^{41} +(-10.6275 - 3.86808i) q^{43} +(-0.250624 + 0.434094i) q^{45} +(-0.899912 + 5.10365i) q^{47} +(-2.83380 - 4.90828i) q^{49} +(-5.88284 - 4.93629i) q^{51} +(6.97841 - 2.53993i) q^{53} +(0.597075 + 3.38618i) q^{55} +(6.53411 - 2.18670i) q^{57} +(1.53157 + 8.68599i) q^{59} +(-7.19444 + 2.61856i) q^{61} +(1.36664 + 1.14675i) q^{63} +(-1.60639 - 2.78235i) q^{65} +(1.15738 - 6.56383i) q^{67} +(-5.39514 + 9.34466i) q^{69} +(7.66249 + 2.78892i) q^{71} +(-5.87461 + 4.92939i) q^{73} +1.58074 q^{75} +12.2379 q^{77} +(-10.4195 + 8.74297i) q^{79} +(6.80808 + 2.47794i) q^{81} +(-8.21708 + 14.2324i) q^{83} +(0.843610 - 4.78435i) q^{85} +(-1.51000 - 2.61540i) q^{87} +(2.74230 + 2.30106i) q^{89} +(-10.7452 + 3.91092i) q^{91} +(-0.835422 - 4.73792i) q^{93} +(3.26479 + 2.88811i) q^{95} +(0.167924 + 0.952344i) q^{97} +(-1.61956 + 0.589473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 9 * q^9	\( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^9 + 9 * q^13 - 3 * q^15 + 12 * q^17 + 18 * q^19 + 15 * q^21 - 9 * q^23 - 33 * q^29 - 18 * q^31 + 9 * q^33 + 12 * q^35 + 60 * q^37 - 84 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 15 * q^47 - 15 * q^49 - 9 * q^51 + 24 * q^53 + 3 * q^55 + 66 * q^57 + 48 * q^59 - 18 * q^61 - 54 * q^63 + 3 * q^65 - 36 * q^67 - 9 * q^69 + 18 * q^73 - 6 * q^75 + 9 * q^79 - 9 * q^81 - 30 * q^83 - 12 * q^85 - 9 * q^87 + 6 * q^89 + 30 * q^91 + 21 * q^95 + 21 * q^97 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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