LMFDB - Embedded newform 414.3.k.a.35.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, 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:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.4
Character	$\chi$	$=$	414.35
Dual form			414.3.k.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.764582 - 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(2.59273 + 8.83003i) q^{5} +(-0.0998440 - 0.115226i) q^{7} +(2.79964 - 0.402527i) q^{8} +O(q^{10})$	\(q+(-0.764582 - 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(2.59273 + 8.83003i) q^{5} +(-0.0998440 - 0.115226i) q^{7} +(2.79964 - 0.402527i) q^{8} +(8.52284 - 9.83588i) q^{10} +(8.08071 - 12.5738i) q^{11} +(-4.38547 + 5.06110i) q^{13} +(-0.0607470 + 0.206885i) q^{14} +(-2.61944 - 3.02300i) q^{16} +(9.94134 - 4.54006i) q^{17} +(-13.1415 + 28.7759i) q^{19} +(-18.2183 - 2.61939i) q^{20} -21.1376 q^{22} +(17.1767 + 15.2958i) q^{23} +(-50.2158 + 32.2718i) q^{25} +(9.37431 + 1.34782i) q^{26} +(0.292580 - 0.0859093i) q^{28} +(-24.4616 + 11.1712i) q^{29} +(3.48170 + 24.2158i) q^{31} +(-1.59372 + 5.42771i) q^{32} +(-13.0023 - 8.35608i) q^{34} +(0.758581 - 1.18038i) q^{35} +(-15.0241 - 4.41149i) q^{37} +(44.2829 - 6.36691i) q^{38} +(10.8130 + 23.6772i) q^{40} +(16.6070 + 56.5583i) q^{41} +(-2.22015 + 15.4415i) q^{43} +(16.1614 + 25.1477i) q^{44} +(5.06468 - 32.1302i) q^{46} -62.0293i q^{47} +(6.97012 - 48.4782i) q^{49} +(76.7882 + 35.0680i) q^{50} +(-5.56390 - 12.1832i) q^{52} +(-50.1709 + 43.4733i) q^{53} +(131.978 + 38.7524i) q^{55} +(-0.325909 - 0.282401i) q^{56} +(31.9935 + 20.5609i) q^{58} +(57.1049 + 49.4817i) q^{59} +(-9.87831 - 68.7051i) q^{61} +(26.1477 - 22.6572i) q^{62} +(7.67594 - 2.25386i) q^{64} +(-56.0600 - 25.6018i) q^{65} +(3.89305 - 2.50191i) q^{67} +21.8579i q^{68} -1.98430 q^{70} +(21.9406 + 34.1402i) q^{71} +(-47.8397 + 104.754i) q^{73} +(6.23879 + 21.2474i) q^{74} +(-41.4327 - 47.8158i) q^{76} +(-2.25564 + 0.324313i) q^{77} +(-19.3122 + 22.2874i) q^{79} +(19.9017 - 30.9676i) q^{80} +(54.5907 - 63.0010i) q^{82} +(5.94912 - 20.2608i) q^{83} +(65.8640 + 76.0111i) q^{85} +(20.0684 - 9.16492i) q^{86} +(17.5618 - 38.4549i) q^{88} +(11.6654 + 1.67723i) q^{89} +1.02103 q^{91} +(-42.0980 + 18.5406i) q^{92} +(-73.7970 + 47.4264i) q^{94} +(-288.165 - 41.4319i) q^{95} +(-0.312802 + 0.0918470i) q^{97} +(-63.0044 + 28.7731i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 - 16 * q^7	$ 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	−0.764582	−	1.18971i	−0.382291	−	0.594856i
$2$	−0.764582	−	1.18971i	−0.382291	−	0.594856i
$3$		0			0
$3$		0			0
$4$	−0.830830	+	1.81926i	−0.207708	+	0.454816i
$5$	2.59273	+	8.83003i	0.518546	+	1.76601i	0.634683	+	0.772773i	$0.281131\pi$
$5$	2.59273	+	8.83003i	0.518546	+	1.76601i	−0.116137	+	0.993233i	$0.537051\pi$
$6$		0			0
$7$	−0.0998440	−	0.115226i	−0.0142634	−	0.0164609i	0.748573	−	0.663052i	$-0.230739\pi$
$7$	−0.0998440	−	0.115226i	−0.0142634	−	0.0164609i	−0.762836	+	0.646591i	$0.776194\pi$
$8$	2.79964	−	0.402527i	0.349955	−	0.0503159i
$9$		0			0
$10$	8.52284	−	9.83588i	0.852284	−	0.983588i
$11$	8.08071	−	12.5738i	0.734610	−	1.14308i	−0.249989	−	0.968249i	$-0.580427\pi$
$11$	8.08071	−	12.5738i	0.734610	−	1.14308i	0.984599	−	0.174827i	$-0.0559365\pi$
$12$		0			0
$13$	−4.38547	+	5.06110i	−0.337344	+	0.389316i	−0.898922	−	0.438108i	$-0.855649\pi$
$13$	−4.38547	+	5.06110i	−0.337344	+	0.389316i	0.561578	+	0.827423i	$0.310194\pi$
$14$	−0.0607470	+	0.206885i	−0.00433907	+	0.0147775i
$15$		0			0
$16$	−2.61944	−	3.02300i	−0.163715	−	0.188937i
$17$	9.94134	−	4.54006i	0.584784	−	0.267062i	−0.100977	−	0.994889i	$-0.532197\pi$
$17$	9.94134	−	4.54006i	0.584784	−	0.267062i	0.685761	+	0.727827i	$0.259469\pi$
$18$		0			0
$19$	−13.1415	+	28.7759i	−0.691660	+	1.51452i	0.158140	+	0.987417i	$0.449450\pi$
$19$	−13.1415	+	28.7759i	−0.691660	+	1.51452i	−0.849799	+	0.527107i	$0.823277\pi$
$20$	−18.2183	−	2.61939i	−0.910914	−	0.130970i
$21$		0			0
$22$	−21.1376			−0.960800
$23$	17.1767	+	15.2958i	0.746811	+	0.665036i
$23$	17.1767	+	15.2958i	0.746811	+	0.665036i
$24$		0			0
$25$	−50.2158	+	32.2718i	−2.00863	+	1.29087i
$26$	9.37431	+	1.34782i	0.360550	+	0.0518393i
$27$		0			0
$28$	0.292580	−	0.0859093i	0.0104493	−	0.00306819i
$29$	−24.4616	+	11.1712i	−0.843504	+	0.385215i	−0.789817	−	0.613343i	$-0.789825\pi$
$29$	−24.4616	+	11.1712i	−0.843504	+	0.385215i	−0.0536868	+	0.998558i	$0.517097\pi$
$30$		0			0
$31$	3.48170	+	24.2158i	0.112313	+	0.781154i	0.965660	+	0.259810i	$0.0836600\pi$
$31$	3.48170	+	24.2158i	0.112313	+	0.781154i	−0.853347	+	0.521344i	$0.825431\pi$
$32$	−1.59372	+	5.42771i	−0.0498038	+	0.169616i
$33$		0			0
$34$	−13.0023	−	8.35608i	−0.382421	−	0.245767i
$35$	0.758581	−	1.18038i	0.0216738	−	0.0337250i
$36$		0			0
$37$	−15.0241	−	4.41149i	−0.406058	−	0.119229i	0.0723240	−	0.997381i	$-0.476958\pi$
$37$	−15.0241	−	4.41149i	−0.406058	−	0.119229i	−0.478382	+	0.878152i	$0.658777\pi$
$38$	44.2829	−	6.36691i	1.16534	−	0.167550i
$39$		0			0
$40$	10.8130	+	23.6772i	0.270326	+	0.591931i
$41$	16.6070	+	56.5583i	0.405049	+	1.37947i	0.869527	+	0.493885i	$0.164424\pi$
$41$	16.6070	+	56.5583i	0.405049	+	1.37947i	−0.464478	+	0.885585i	$0.653758\pi$
$42$		0			0
$43$	−2.22015	+	15.4415i	−0.0516313	+	0.359104i	0.947584	+	0.319506i	$0.103517\pi$
$43$	−2.22015	+	15.4415i	−0.0516313	+	0.359104i	−0.999216	+	0.0395981i	$0.987392\pi$
$44$	16.1614	+	25.1477i	0.367305	+	0.571538i
$45$		0			0
$46$	5.06468	−	32.1302i	0.110102	−	0.698482i
$47$		−	62.0293i		−	1.31977i	−0.751366	−	0.659886i	$-0.770605\pi$
$47$		−	62.0293i		−	1.31977i	0.751366	−	0.659886i	$-0.229395\pi$
$48$		0			0
$49$	6.97012	−	48.4782i	0.142247	−	0.989352i
$50$	76.7882	+	35.0680i	1.53576	+	0.701360i
$51$		0			0
$52$	−5.56390	−	12.1832i	−0.106998	−	0.234293i
$53$	−50.1709	+	43.4733i	−0.946620	+	0.820251i	−0.983839	−	0.179056i	$-0.942696\pi$
$53$	−50.1709	+	43.4733i	−0.946620	+	0.820251i	0.0372187	+	0.999307i	$0.488150\pi$
$54$		0			0
$55$	131.978	+	38.7524i	2.39961	+	0.704588i
$56$	−0.325909	−	0.282401i	−0.00581980	−	0.00504288i
$57$		0			0
$58$	31.9935	+	20.5609i	0.551611	+	0.354499i
$59$	57.1049	+	49.4817i	0.967880	+	0.838673i	0.986931	−	0.161146i	$-0.0515188\pi$
$59$	57.1049	+	49.4817i	0.967880	+	0.838673i	−0.0190504	+	0.999819i	$0.506064\pi$
$60$		0			0
$61$	−9.87831	−	68.7051i	−0.161939	−	1.12631i	−0.894973	−	0.446121i	$-0.852805\pi$
$61$	−9.87831	−	68.7051i	−0.161939	−	1.12631i	0.733033	−	0.680193i	$-0.238104\pi$
$62$	26.1477	−	22.6572i	0.421738	−	0.365438i
$63$		0			0
$64$	7.67594	−	2.25386i	0.119937	−	0.0352166i
$65$	−56.0600	−	25.6018i	−0.862462	−	0.393873i
$66$		0			0
$67$	3.89305	−	2.50191i	0.0581053	−	0.0373420i	−0.511266	−	0.859423i	$-0.670823\pi$
$67$	3.89305	−	2.50191i	0.0581053	−	0.0373420i	0.569371	+	0.822081i	$0.307187\pi$
$68$			21.8579i			0.321440i
$69$		0			0
$70$	−1.98430			−0.0283472
$71$	21.9406	+	34.1402i	0.309022	+	0.480848i	0.960677	−	0.277668i	$-0.0895614\pi$
$71$	21.9406	+	34.1402i	0.309022	+	0.480848i	−0.651655	+	0.758515i	$0.725925\pi$
$72$		0			0
$73$	−47.8397	+	104.754i	−0.655339	+	1.43499i	0.231464	+	0.972844i	$0.425649\pi$
$73$	−47.8397	+	104.754i	−0.655339	+	1.43499i	−0.886802	+	0.462149i	$0.847079\pi$
$74$	6.23879	+	21.2474i	0.0843079	+	0.287126i
$75$		0			0
$76$	−41.4327	−	47.8158i	−0.545167	−	0.629156i
$77$	−2.25564	+	0.324313i	−0.0292941	+	0.00421185i
$78$		0			0
$79$	−19.3122	+	22.2874i	−0.244458	+	0.282119i	−0.864697	−	0.502293i	$-0.832490\pi$
$79$	−19.3122	+	22.2874i	−0.244458	+	0.282119i	0.620240	+	0.784412i	$0.287035\pi$
$80$	19.9017	−	30.9676i	0.248771	−	0.387095i
$81$		0			0
$82$	54.5907	−	63.0010i	0.665740	−	0.768305i
$83$	5.94912	−	20.2608i	0.0716762	−	0.244107i	−0.915860	−	0.401497i	$-0.868490\pi$
$83$	5.94912	−	20.2608i	0.0716762	−	0.244107i	0.987536	+	0.157391i	$0.0503082\pi$
$84$		0			0
$85$	65.8640	+	76.0111i	0.774871	+	0.894249i
$86$	20.0684	−	9.16492i	0.233353	−	0.106569i
$87$		0			0
$88$	17.5618	−	38.4549i	0.199565	−	0.436987i
$89$	11.6654	+	1.67723i	0.131072	+	0.0188453i	0.207539	−	0.978227i	$-0.433455\pi$
$89$	11.6654	+	1.67723i	0.131072	+	0.0188453i	−0.0764666	+	0.997072i	$0.524364\pi$
$90$		0			0
$91$	1.02103			0.0112202
$92$	−42.0980	+	18.5406i	−0.457587	+	0.201529i
$93$		0			0
$94$	−73.7970	+	47.4264i	−0.785074	+	0.504536i
$95$	−288.165	−	41.4319i	−3.03331	−	0.436125i
$96$		0			0
$97$	−0.312802	+	0.0918470i	−0.00322476	+	0.000946876i	−0.283345	−	0.959018i	$-0.591444\pi$
$97$	−0.312802	+	0.0918470i	−0.00322476	+	0.000946876i	0.280120	+	0.959965i	$0.409626\pi$
$98$	−63.0044	+	28.7731i	−0.642902	+	0.293603i
$99$		0			0
$100$	−16.9900	−	118.168i	−0.169900	−	1.18168i
$101$	51.5137	−	175.440i	0.510037	−	1.73703i	−0.152796	−	0.988258i	$-0.548828\pi$
$101$	51.5137	−	175.440i	0.510037	−	1.73703i	0.662833	−	0.748767i	$-0.269354\pi$
$102$		0			0
$103$	−39.2747	−	25.2403i	−0.381307	−	0.245051i	0.335920	−	0.941890i	$-0.390953\pi$
$103$	−39.2747	−	25.2403i	−0.381307	−	0.245051i	−0.717227	+	0.696839i	$0.754589\pi$
$104$	−10.2405	+	15.9345i	−0.0984663	+	0.153217i
$105$		0			0
$106$	90.0804	+	26.4500i	0.849816	+	0.249528i
$107$	172.666	−	24.8256i	1.61370	−	0.232015i	0.724412	−	0.689368i	$-0.242111\pi$
$107$	172.666	−	24.8256i	1.61370	−	0.232015i	0.889285	+	0.457353i	$0.151202\pi$
$108$		0			0
$109$	−24.3214	−	53.2564i	−0.223132	−	0.488591i	0.764648	−	0.644449i	$-0.222913\pi$
$109$	−24.3214	−	53.2564i	−0.223132	−	0.488591i	−0.987779	+	0.155858i	$0.950186\pi$
$110$	−54.8041	−	186.646i	−0.498219	−	1.69678i
$111$		0			0
$112$	−0.0867927	+	0.603656i	−0.000774935	+	0.00538979i
$113$	54.2535	+	84.4200i	0.480119	+	0.747080i	0.993834	−	0.110881i	$-0.0353673\pi$
$113$	54.2535	+	84.4200i	0.480119	+	0.747080i	−0.513714	+	0.857961i	$0.671731\pi$
$114$		0			0
$115$	−90.5282	+	191.328i	−0.787202	+	1.66372i
$116$		−	53.7835i		−	0.463651i
$117$		0			0
$118$	15.2076	−	105.771i	0.128878	−	0.896366i
$119$	−1.51572	−	0.692204i	−0.0127371	−	0.00581684i
$120$		0			0
$121$	−42.5381	−	93.1454i	−0.351554	−	0.769797i
$122$	−74.1866	+	64.2830i	−0.608087	+	0.526910i
$123$		0			0
$124$	−46.9476	−	13.7851i	−0.378609	−	0.111170i
$125$	−241.281	−	209.071i	−1.93025	−	1.67257i
$126$		0			0
$127$	66.6362	+	42.8245i	0.524694	+	0.337200i	0.776026	−	0.630700i	$-0.217232\pi$
$127$	66.6362	+	42.8245i	0.524694	+	0.337200i	−0.251332	+	0.967901i	$0.580869\pi$
$128$	−8.55033	−	7.40890i	−0.0667995	−	0.0578821i
$129$		0			0
$130$	12.4037	+	86.2700i	0.0954134	+	0.663615i
$131$	−142.993	+	123.904i	−1.09155	+	0.945832i	−0.998757	−	0.0498538i	$-0.984124\pi$
$131$	−142.993	+	123.904i	−1.09155	+	0.945832i	−0.0927915	+	0.995686i	$0.529579\pi$
$132$		0			0
$133$	4.62784	−	1.35886i	0.0347958	−	0.0102170i
$134$	−5.95311	−	2.71870i	−0.0444262	−	0.0202888i
$135$		0			0
$136$	26.0046	−	16.7122i	0.191211	−	0.122884i
$137$			127.795i			0.932812i	0.884571	+	0.466406i	$0.154451\pi$
$137$			127.795i			0.932812i	−0.884571	+	0.466406i	$0.845549\pi$
$138$		0			0
$139$	125.823			0.905202			0.452601	−	0.891713i	$-0.350496\pi$
$139$	125.823			0.905202			0.452601	+	0.891713i	$0.350496\pi$
$140$	1.51716	+	2.36075i	0.0108369	+	0.0168625i
$141$		0			0
$142$	23.8416	−	52.2059i	0.167899	−	0.367647i
$143$	28.1997	+	96.0395i	0.197201	+	0.671605i
$144$		0			0
$145$	−162.065	−	187.033i	−1.11769	−	1.28988i
$146$	161.205	−	23.1778i	1.10414	−	0.158752i
$147$		0			0
$148$	20.5082	−	23.6677i	0.138569	−	0.159917i
$149$	88.0524	−	137.012i	0.590956	−	0.919545i	−0.409020	−	0.912526i	$-0.634129\pi$
$149$	88.0524	−	137.012i	0.590956	−	0.919545i	0.999975	−	0.00701929i	$-0.00223433\pi$
$150$		0			0
$151$	74.7595	−	86.2770i	0.495096	−	0.571371i	−0.452124	−	0.891955i	$-0.649334\pi$
$151$	74.7595	−	86.2770i	0.495096	−	0.571371i	0.947220	+	0.320584i	$0.103879\pi$
$152$	−25.2084	+	85.8520i	−0.165845	+	0.564816i
$153$		0			0
$154$	2.11046	+	2.43560i	0.0137043	+	0.0158156i
$155$	−204.799	+	93.5285i	−1.32128	+	0.603410i
$156$		0			0
$157$	63.2054	−	138.401i	0.402582	−	0.881533i	−0.594419	−	0.804155i	$-0.702618\pi$
$157$	63.2054	−	138.401i	0.402582	−	0.881533i	0.997002	−	0.0773774i	$-0.0246546\pi$
$158$	41.2814	+	5.93536i	0.261274	+	0.0375656i
$159$		0			0
$160$	−52.0589			−0.325368
$161$	0.0474929	−	3.50640i	0.000294987	−	0.0217789i
$162$		0			0
$163$	92.1374	−	59.2131i	0.565260	−	0.363271i	−0.226586	−	0.973991i	$-0.572756\pi$
$163$	92.1374	−	59.2131i	0.565260	−	0.363271i	0.791846	+	0.610721i	$0.209120\pi$
$164$	−116.692	−	16.7778i	−0.711537	−	0.102304i
$165$		0			0
$166$	−28.6532	+	8.41333i	−0.172609	+	0.0506827i
$167$	113.148	−	51.6731i	0.677535	−	0.309420i	−0.0467641	−	0.998906i	$-0.514891\pi$
$167$	113.148	−	51.6731i	0.677535	−	0.309420i	0.724299	+	0.689486i	$0.242164\pi$
$168$		0			0
$169$	17.6688	+	122.889i	0.104549	+	0.727155i
$170$	40.0730	−	136.476i	0.235723	−	0.802800i
$171$		0			0
$172$	−26.2475	−	16.8683i	−0.152602	−	0.0980713i
$173$	169.552	−	263.828i	0.980068	−	1.52502i	0.134662	−	0.990892i	$-0.457005\pi$
$173$	169.552	−	263.828i	0.980068	−	1.52502i	0.845406	−	0.534124i	$-0.179358\pi$
$174$		0			0
$175$	8.73230	+	2.56403i	0.0498989	+	0.0146516i
$176$	−59.1776	+	8.50846i	−0.336236	+	0.0483435i
$177$		0			0
$178$	−6.92373	−	15.1608i	−0.0388973	−	0.0851733i
$179$	−86.7756	−	295.531i	−0.484780	−	1.65101i	−0.731439	−	0.681906i	$-0.761151\pi$
$179$	−86.7756	−	295.531i	−0.484780	−	1.65101i	0.246660	−	0.969102i	$-0.420667\pi$
$180$		0			0
$181$	13.5377	−	94.1568i	0.0747939	−	0.520203i	−0.917639	−	0.397415i	$-0.869907\pi$
$181$	13.5377	−	94.1568i	0.0747939	−	0.520203i	0.992433	−	0.122788i	$-0.0391836\pi$
$182$	−0.780664	−	1.21474i	−0.00428936	−	0.00667438i
$183$		0			0
$184$	54.2454	+	35.9087i	0.294812	+	0.195156i
$185$		−	144.101i		−	0.778927i
$186$		0			0
$187$	23.2472	−	161.688i	0.124316	−	0.864639i
$188$	112.848	+	51.5358i	0.600253	+	0.274126i
$189$		0			0
$190$	171.034	+	374.511i	0.900177	+	1.97111i
$191$	−193.168	+	167.381i	−1.01135	+	0.876342i	−0.992347	−	0.123477i	$-0.960595\pi$
$191$	−193.168	+	167.381i	−1.01135	+	0.876342i	−0.0190053	+	0.999819i	$0.506050\pi$
$192$		0			0
$193$	312.563	+	91.7768i	1.61950	+	0.475528i	0.960884	−	0.276953i	$-0.0893245\pi$
$193$	312.563	+	91.7768i	1.61950	+	0.475528i	0.658615	+	0.752480i	$0.271143\pi$
$194$	0.348434	+	0.301920i	0.00179605	+	0.00155629i
$195$		0			0
$196$	82.4037	+	52.9577i	0.420427	+	0.270192i
$197$	−203.319	−	176.177i	−1.03208	−	0.894301i	−0.0376053	−	0.999293i	$-0.511973\pi$
$197$	−203.319	−	176.177i	−1.03208	−	0.894301i	−0.994473	+	0.104992i	$0.966518\pi$
$198$		0			0
$199$	−14.5792	−	101.401i	−0.0732623	−	0.509551i	−0.993102	−	0.117256i	$-0.962590\pi$
$199$	−14.5792	−	101.401i	−0.0732623	−	0.509551i	0.919839	−	0.392295i	$-0.128319\pi$
$200$	−127.596	+	110.562i	−0.637980	+	0.552812i
$201$		0			0
$202$	−248.109	+	72.8514i	−1.22826	+	0.360650i
$203$	3.72956	+	1.70323i	0.0183722	+	0.00839032i
$204$		0			0
$205$	−456.354	+	293.281i	−2.22612	+	1.43064i
$206$			66.0238i			0.320504i
$207$		0			0
$208$	26.7872			0.128785
$209$	255.631	+	397.769i	1.22311	+	1.90320i
$210$		0			0
$211$	−78.1091	+	171.035i	−0.370186	+	0.810593i	0.629257	+	0.777198i	$0.283359\pi$
$211$	−78.1091	+	171.035i	−0.370186	+	0.810593i	−0.999442	+	0.0333957i	$0.989368\pi$
$212$	−37.4060	−	127.393i	−0.176443	−	0.600910i
$213$		0			0
$214$	−161.552	−	186.441i	−0.754917	−	0.871220i
$215$	−142.105	+	20.4316i	−0.660953	+	0.0950307i
$216$		0			0
$217$	2.44266	−	2.81898i	0.0112565	−	0.0129907i
$218$	−44.7641	+	69.6543i	−0.205340	+	0.319515i
$219$		0			0
$220$	−180.152	+	207.907i	−0.818874	+	0.945031i
$221$	−20.6197	+	70.2244i	−0.0933020	+	0.317758i
$222$		0			0
$223$	−157.681	−	181.974i	−0.707092	−	0.816027i	0.282600	−	0.959238i	$-0.408803\pi$
$223$	−157.681	−	181.974i	−0.707092	−	0.816027i	−0.989692	+	0.143210i	$0.954257\pi$
$224$	0.784538	−	0.358286i	0.00350240	−	0.00159949i
$225$		0			0
$226$	58.9544	−	129.092i	0.260860	−	0.571204i
$227$	157.372	+	22.6267i	0.693269	+	0.0996771i	0.479937	−	0.877303i	$-0.340659\pi$
$227$	157.372	+	22.6267i	0.693269	+	0.0996771i	0.213332	+	0.976980i	$0.431568\pi$
$228$		0			0
$229$	−266.583			−1.16412			−0.582058	−	0.813147i	$-0.697752\pi$
$229$	−266.583			−1.16412			−0.582058	+	0.813147i	$0.697752\pi$
$230$	296.842	−	38.5837i	1.29062	−	0.167755i
$231$		0			0
$232$	−63.9869	+	41.1219i	−0.275806	+	0.177250i
$233$	104.754	+	15.0613i	0.449586	+	0.0646407i	0.363389	−	0.931637i	$-0.381619\pi$
$233$	104.754	+	15.0613i	0.449586	+	0.0646407i	0.0861969	+	0.996278i	$0.472529\pi$
$234$		0			0
$235$	547.720	−	160.825i	2.33072	−	0.684362i
$236$	−137.465	+	62.7781i	−0.582478	+	0.266009i
$237$		0			0
$238$	0.335365	+	2.33251i	0.00140909	+	0.00980047i
$239$	−14.0564	+	47.8715i	−0.0588132	+	0.200299i	−0.983659	−	0.180044i	$-0.942376\pi$
$239$	−14.0564	+	47.8715i	−0.0588132	+	0.200299i	0.924845	+	0.380343i	$0.124194\pi$
$240$		0			0
$241$	37.7438	+	24.2565i	0.156613	+	0.100649i	0.616600	−	0.787277i	$-0.288510\pi$
$241$	37.7438	+	24.2565i	0.156613	+	0.100649i	−0.459987	+	0.887926i	$0.652146\pi$
$242$	−78.2924	+	121.825i	−0.323522	+	0.503411i
$243$		0			0
$244$	133.200	+	39.1110i	0.545901	+	0.160291i
$245$	446.136	−	64.1447i	1.82096	−	0.261815i
$246$		0			0
$247$	−88.0062	−	192.707i	−0.356300	−	0.780189i
$248$	19.4950	+	66.3939i	0.0786089	+	0.267717i
$249$		0			0
$250$	−64.2556	+	446.907i	−0.257022	+	1.78763i
$251$	59.7216	+	92.9286i	0.237935	+	0.370233i	0.939601	−	0.342272i	$-0.111197\pi$
$251$	59.7216	+	92.9286i	0.237935	+	0.370233i	−0.701666	+	0.712506i	$0.747560\pi$
$252$		0			0
$253$	331.127	−	92.3752i	1.30880	−	0.365119i
$254$		−	112.021i		−	0.441026i
$255$		0			0
$256$	−2.27704	+	15.8371i	−0.00889468	+	0.0618638i
$257$	47.8745	+	21.8636i	0.186282	+	0.0850722i	0.506373	−	0.862315i	$-0.330986\pi$
$257$	47.8745	+	21.8636i	0.186282	+	0.0850722i	−0.320090	+	0.947387i	$0.603713\pi$
$258$		0			0
$259$	0.991752	+	2.17163i	0.00382916	+	0.00838469i
$260$	93.1527	−	80.7173i	0.358280	−	0.310451i
$261$		0			0
$262$	256.740	+	75.3856i	0.979923	+	0.287731i
$263$	358.335	+	310.499i	1.36249	+	1.18060i	0.964769	+	0.263098i	$0.0847444\pi$
$263$	358.335	+	310.499i	1.36249	+	1.18060i	0.397721	+	0.917506i	$0.369801\pi$
$264$		0			0
$265$	−513.950	−	330.296i	−1.93943	−	1.24640i
$266$	−5.15501	−	4.46684i	−0.0193797	−	0.0167926i
$267$		0			0
$268$	1.31718	+	9.16116i	0.00491483	+	0.0341834i
$269$	−16.4679	+	14.2695i	−0.0612190	+	0.0530466i	−0.684933	−	0.728606i	$-0.740168\pi$
$269$	−16.4679	+	14.2695i	−0.0612190	+	0.0530466i	0.623714	+	0.781653i	$0.285623\pi$
$270$		0			0
$271$	254.271	−	74.6607i	0.938269	−	0.275501i	0.223374	−	0.974733i	$-0.428293\pi$
$271$	254.271	−	74.6607i	0.938269	−	0.275501i	0.714895	+	0.699232i	$0.246475\pi$
$272$	−39.7653	−	18.1602i	−0.146196	−	0.0667655i
$273$		0			0
$274$	152.039	−	97.7098i	0.554889	−	0.356605i
$275$			892.184i			3.24431i
$276$		0			0
$277$	424.990			1.53426			0.767130	−	0.641492i	$-0.221684\pi$
$277$	424.990			1.53426			0.767130	+	0.641492i	$0.221684\pi$
$278$	−96.2021	−	149.693i	−0.346051	−	0.538465i
$279$		0			0
$280$	1.64862	−	3.60997i	0.00588793	−	0.0128928i
$281$	83.3764	+	283.954i	0.296713	+	1.01051i	0.964042	+	0.265750i	$0.0856194\pi$
$281$	83.3764	+	283.954i	0.296713	+	1.01051i	−0.667329	+	0.744763i	$0.732562\pi$
$282$		0			0
$283$	10.3319	+	11.9236i	0.0365083	+	0.0421328i	0.773710	−	0.633540i	$-0.218399\pi$
$283$	10.3319	+	11.9236i	0.0365083	+	0.0421328i	−0.737202	+	0.675673i	$0.763853\pi$
$284$	−80.3389	+	11.5510i	−0.282883	+	0.0406725i
$285$		0			0
$286$	92.6983	−	106.980i	0.324120	−	0.374054i
$287$	4.85888	−	7.56056i	0.0169299	−	0.0263434i
$288$		0			0
$289$	−111.037	+	128.143i	−0.384210	+	0.443402i
$290$	−98.6034	+	335.812i	−0.340012	+	1.15797i
$291$		0			0
$292$	−150.829	−	174.066i	−0.516539	−	0.596117i
$293$	388.384	−	177.369i	1.32554	−	0.605355i	0.378244	−	0.925706i	$-0.376528\pi$
$293$	388.384	−	177.369i	1.32554	−	0.605355i	0.947299	+	0.320350i	$0.103801\pi$
$294$		0			0
$295$	−288.867	+	632.531i	−0.979211	+	2.14417i
$296$	−43.8379	−	6.30294i	−0.148101	−	0.0212937i
$297$		0			0
$298$	−230.328			−0.772914
$299$	−152.742	+	19.8534i	−0.510841	+	0.0663994i
$300$		0			0
$301$	2.00093	−	1.28592i	0.00664760	−	0.00427216i
$302$	−159.805	−	22.9764i	−0.529154	−	0.0760809i
$303$		0			0
$304$	121.413	−	35.6501i	0.399385	−	0.117270i
$305$	581.057	−	265.360i	1.90510	−	0.870032i
$306$		0			0
$307$	27.3597	+	190.291i	0.0891196	+	0.619841i	0.984611	+	0.174761i	$0.0559154\pi$
$307$	27.3597	+	190.291i	0.0891196	+	0.619841i	−0.895491	+	0.445079i	$0.853176\pi$
$308$	1.28405	−	4.37306i	0.00416898	−	0.0141982i
$309$		0			0
$310$	267.857	+	172.142i	0.864056	+	0.555295i
$311$	190.403	−	296.272i	0.612227	−	0.952644i	−0.387302	−	0.921953i	$-0.626593\pi$
$311$	190.403	−	296.272i	0.612227	−	0.952644i	0.999529	−	0.0306908i	$-0.00977071\pi$
$312$		0			0
$313$	−402.534	−	118.195i	−1.28605	−	0.377619i	−0.433922	−	0.900950i	$-0.642871\pi$
$313$	−402.534	−	118.195i	−1.28605	−	0.377619i	−0.852129	+	0.523331i	$0.824689\pi$
$314$	−212.983	+	30.6223i	−0.678289	+	0.0975232i
$315$		0			0
$316$	−24.5016	−	53.6510i	−0.0775367	−	0.169782i
$317$	−86.0036	−	292.901i	−0.271305	−	0.923979i	−0.976600	−	0.215065i	$-0.931004\pi$
$317$	−86.0036	−	292.901i	−0.271305	−	0.923979i	0.705295	−	0.708914i	$-0.250815\pi$
$318$		0			0
$319$	−57.2019	+	397.848i	−0.179316	+	1.24717i
$320$	39.8033	+	61.9352i	0.124385	+	0.193547i
$321$		0			0
$322$	−4.20791	+	2.62442i	−0.0130681	+	0.00815038i
$323$			345.735i			1.07039i
$324$		0			0
$325$	56.8894	−	395.674i	0.175044	−	1.21746i
$326$	−140.893	−	64.3437i	−0.432187	−	0.197373i
$327$		0			0
$328$	69.2598	+	151.658i	0.211158	+	0.462372i
$329$	−7.14739	+	6.19325i	−0.0217246	+	0.0188245i
$330$		0			0
$331$	22.5046	+	6.60795i	0.0679898	+	0.0199636i	0.315551	−	0.948909i	$-0.397811\pi$
$331$	22.5046	+	6.60795i	0.0679898	+	0.0199636i	−0.247561	+	0.968872i	$0.579629\pi$
$332$	31.9171	+	27.6563i	0.0961359	+	0.0833022i
$333$		0			0
$334$	−147.987	−	95.1056i	−0.443075	−	0.284747i
$335$	32.1856	+	27.8890i	0.0960765	+	0.0832507i
$336$		0			0
$337$	−0.714559	−	4.96986i	−0.00212035	−	0.0147474i	0.988734	−	0.149685i	$-0.0478258\pi$
$337$	−0.714559	−	4.96986i	−0.00212035	−	0.0147474i	−0.990854	+	0.134937i	$0.956917\pi$
$338$	132.694	−	114.980i	0.392584	−	0.340176i
$339$		0			0
$340$	−193.006	+	56.6717i	−0.567665	+	0.166682i
$341$	332.620	+	151.902i	0.975424	+	0.445461i
$342$		0			0
$343$	−12.5667	+	8.07616i	−0.0366378	+	0.0235457i
$344$			44.1242i			0.128268i
$345$		0			0
$346$	−443.515			−1.28184
$347$	−211.173	−	328.591i	−0.608567	−	0.946949i	−0.999646	−	0.0265923i	$-0.991534\pi$
$347$	−211.173	−	328.591i	−0.608567	−	0.946949i	0.391079	−	0.920357i	$-0.372102\pi$
$348$		0			0
$349$	−99.2748	+	217.381i	−0.284455	+	0.622869i	−0.996885	−	0.0788741i	$-0.974867\pi$
$349$	−99.2748	+	217.381i	−0.284455	+	0.622869i	0.712430	+	0.701744i	$0.247595\pi$
$350$	−3.62609	−	12.3493i	−0.0103603	−	0.0352838i
$351$		0			0
$352$	55.3687	+	63.8989i	0.157298	+	0.181531i
$353$	392.481	−	56.4302i	1.11184	−	0.159859i	0.438173	−	0.898891i	$-0.355626\pi$
$353$	392.481	−	56.4302i	1.11184	−	0.159859i	0.673670	+	0.739032i	$0.264717\pi$
$354$		0			0
$355$	−244.573	+	282.252i	−0.688938	+	0.795077i
$356$	−12.7433	+	19.8289i	−0.0357958	+	0.0556993i
$357$		0			0
$358$	−285.249	+	329.195i	−0.796786	+	0.919540i
$359$	−26.6389	+	90.7239i	−0.0742031	+	0.252713i	−0.988238	−	0.152923i	$-0.951131\pi$
$359$	−26.6389	+	90.7239i	−0.0742031	+	0.252713i	0.914035	+	0.405635i	$0.132950\pi$
$360$		0			0
$361$	−418.950	−	483.494i	−1.16053	−	1.33932i
$362$	−122.370	+	55.8846i	−0.338039	+	0.154377i
$363$		0			0
$364$	−0.848306	+	1.85753i	−0.00233051	+	0.00510311i
$365$	−1049.02	−	150.826i	−2.87403	−	0.413223i
$366$		0			0
$367$	397.312			1.08259			0.541297	−	0.840832i	$-0.317934\pi$
$367$	397.312			1.08259			0.541297	+	0.840832i	$0.317934\pi$
$368$	1.24599	−	91.9916i	0.00338585	−	0.249977i
$369$		0			0
$370$	−171.439	+	110.177i	−0.463349	+	0.297777i
$371$	10.0185	+	1.44045i	0.0270041	+	0.00388260i
$372$		0			0
$373$	32.2492	−	9.46921i	0.0864589	−	0.0253866i	−0.238217	−	0.971212i	$-0.576563\pi$
$373$	32.2492	−	9.46921i	0.0864589	−	0.0253866i	0.324676	+	0.945825i	$0.394745\pi$
$374$	−210.136	+	95.9659i	−0.561861	+	0.256593i
$375$		0			0
$376$	−24.9685	−	173.659i	−0.0664055	−	0.461860i
$377$	50.7369	−	172.794i	0.134581	−	0.458339i
$378$		0			0
$379$	−121.705	−	78.2152i	−0.321122	−	0.206372i	0.370142	−	0.928975i	$-0.379309\pi$
$379$	−121.705	−	78.2152i	−0.321122	−	0.206372i	−0.691263	+	0.722603i	$0.742946\pi$
$380$	314.792	−	489.825i	0.828399	−	1.28901i
$381$		0			0
$382$	346.829	+	101.838i	0.907928	+	0.266592i
$383$	552.200	−	79.3944i	1.44178	−	0.207296i	0.623365	−	0.781931i	$-0.285765\pi$
$383$	552.200	−	79.3944i	1.44178	−	0.207296i	0.818410	+	0.574635i	$0.194856\pi$
$384$		0			0
$385$	−8.71197	−	19.0765i	−0.0226285	−	0.0495495i
$386$	−129.792	−	442.031i	−0.336249	−	1.14516i
$387$		0			0
$388$	0.0927915	−	0.645379i	0.000239153	−	0.00166335i
$389$	−272.825	−	424.523i	−0.701348	−	1.09132i	−0.990958	−	0.134174i	$-0.957162\pi$
$389$	−272.825	−	424.523i	−0.701348	−	1.09132i	0.289609	−	0.957145i	$-0.406475\pi$
$390$		0			0
$391$	240.203	+	74.0780i	0.614330	+	0.189458i
$392$		−	138.527i		−	0.353386i
$393$		0			0
$394$	−54.1460	+	376.594i	−0.137426	+	0.955821i
$395$	−246.870	−	112.742i	−0.624987	−	0.285422i
$396$		0			0
$397$	−154.695	−	338.734i	−0.389659	−	0.853235i	−0.998215	−	0.0597235i	$-0.980978\pi$
$397$	−154.695	−	338.734i	−0.389659	−	0.853235i	0.608556	−	0.793511i	$-0.291749\pi$
$398$	−109.491	+	94.8741i	−0.275102	+	0.238377i
$399$		0			0
$400$	229.095	+	67.2684i	0.572737	+	0.168171i
$401$	−453.643	−	393.084i	−1.13128	−	0.980260i	−0.131341	−	0.991337i	$-0.541928\pi$
$401$	−453.643	−	393.084i	−1.13128	−	0.980260i	−0.999939	+	0.0110775i	$0.996474\pi$
$402$		0			0
$403$	−137.827	−	88.5763i	−0.342004	−	0.219792i
$404$	276.372	+	239.477i	0.684088	+	0.592766i
$405$		0			0
$406$	−0.825197	−	5.73937i	−0.00203250	−	0.0141364i
$407$	−176.875	+	153.263i	−0.434582	+	0.376568i
$408$		0			0
$409$	−600.060	+	176.193i	−1.46714	+	0.430791i	−0.915168	−	0.403072i	$-0.867942\pi$
$409$	−600.060	+	176.193i	−1.46714	+	0.430791i	−0.551971	+	0.833863i	$0.686124\pi$
$410$	697.839	+	318.693i	1.70205	+	0.777299i
$411$		0			0
$412$	78.5493	−	50.4806i	0.190654	−	0.122526i
$413$		−	11.5204i		−	0.0278945i
$414$		0			0
$415$	194.328			0.468261
$416$	−20.4810	−	31.8691i	−0.0492332	−	0.0766083i
$417$		0			0
$418$	277.780	−	608.254i	0.664546	−	1.45515i
$419$	−201.328	−	685.659i	−0.480495	−	1.63642i	−0.741408	−	0.671055i	$-0.765842\pi$
$419$	−201.328	−	685.659i	−0.480495	−	1.63642i	0.260912	−	0.965362i	$-0.415977\pi$
$420$		0			0
$421$	215.342	+	248.518i	0.511502	+	0.590305i	0.951483	−	0.307702i	$-0.0995601\pi$
$421$	215.342	+	248.518i	0.511502	+	0.590305i	−0.439980	+	0.898007i	$0.645015\pi$
$422$	263.203	−	37.8429i	0.623705	−	0.0896752i
$423$		0			0
$424$	−122.961	+	141.905i	−0.290003	+	0.334681i
$425$	−352.697	+	548.807i	−0.829875	+	1.29131i
$426$		0			0
$427$	−6.93034	+	7.99803i	−0.0162303	+	0.0187308i
$428$	−98.2915	+	334.750i	−0.229653	+	0.782126i
$429$		0			0
$430$	132.958	+	153.442i	0.309206	+	0.356842i
$431$	−448.955	+	205.031i	−1.04166	+	0.475709i	−0.861409	−	0.507912i	$-0.830418\pi$
$431$	−448.955	+	205.031i	−1.04166	+	0.475709i	−0.180249	+	0.983621i	$0.557690\pi$
$432$		0			0
$433$	203.060	−	444.638i	0.468960	−	1.02688i	−0.516393	−	0.856352i	$-0.672726\pi$
$433$	203.060	−	444.638i	0.468960	−	1.02688i	0.985353	−	0.170527i	$-0.0545470\pi$
$434$	−5.22139	−	0.750723i	−0.0120309	−	0.00172978i
$435$		0			0
$436$	117.094			0.268565
$437$	−665.880	+	293.264i	−1.52375	+	0.671084i
$438$		0			0
$439$	381.897	−	245.430i	0.869925	−	0.559067i	−0.0278049	−	0.999613i	$-0.508852\pi$
$439$	381.897	−	245.430i	0.869925	−	0.559067i	0.897730	+	0.440547i	$0.145215\pi$
$440$	385.091	+	55.3677i	0.875206	+	0.125836i
$441$		0			0
$442$	99.3123	−	29.1607i	0.224689	−	0.0659745i
$443$	303.982	−	138.824i	0.686191	−	0.313373i	−0.0416371	−	0.999133i	$-0.513257\pi$
$443$	303.982	−	138.824i	0.686191	−	0.313373i	0.727828	+	0.685760i	$0.240530\pi$
$444$		0			0
$445$	15.4352	+	107.354i	0.0346859	+	0.241246i
$446$	−95.9365	+	326.730i	−0.215104	+	0.732578i
$447$		0			0
$448$	−1.02610	−	0.659435i	−0.00229040	−	0.00147195i
$449$	−345.477	+	537.573i	−0.769437	+	1.19727i	0.206336	+	0.978481i	$0.433846\pi$
$449$	−345.477	+	537.573i	−0.769437	+	1.19727i	−0.975773	+	0.218786i	$0.929790\pi$
$450$		0			0
$451$	845.350	+	248.217i	1.87439	+	0.550371i
$452$	−198.658	+	28.5627i	−0.439508	+	0.0631918i
$453$		0			0
$454$	−93.4046	−	204.527i	−0.205737	−	0.450501i
$455$	2.64727	+	9.01576i	0.00581817	+	0.0198149i
$456$		0			0
$457$	−35.5436	+	247.211i	−0.0777760	+	0.540944i	0.913263	+	0.407370i	$0.133554\pi$
$457$	−35.5436	+	247.211i	−0.0777760	+	0.540944i	−0.991039	+	0.133573i	$0.957355\pi$
$458$	203.824	+	317.157i	0.445031	+	0.692481i
$459$		0			0
$460$	−272.863	−	323.656i	−0.593181	−	0.703600i
$461$		−	147.663i		−	0.320310i	−0.987092	−	0.160155i	$-0.948801\pi$
$461$		−	147.663i		−	0.320310i	0.987092	−	0.160155i	$-0.0511994\pi$
$462$		0			0
$463$	14.0234	−	97.5348i	0.0302881	−	0.210658i	−0.969057	−	0.246836i	$-0.920609\pi$
$463$	14.0234	−	97.5348i	0.0302881	−	0.210658i	0.999345	+	0.0361776i	$0.0115182\pi$
$464$	97.8464	+	44.6850i	0.210876	+	0.0963038i
$465$		0			0
$466$	−62.1741	−	136.142i	−0.133421	−	0.292151i
$467$	371.213	−	321.658i	0.794890	−	0.688776i	−0.159547	−	0.987190i	$-0.551003\pi$
$467$	371.213	−	321.658i	0.794890	−	0.688776i	0.954436	+	0.298415i	$0.0964578\pi$
$468$		0			0
$469$	−0.676984	−	0.198780i	−0.00144346	−	0.000423839i
$470$	−610.112	−	528.665i	−1.29811	−	1.12482i
$471$		0			0
$472$	179.791	+	115.545i	0.380913	+	0.244798i
$473$	176.218	+	152.694i	0.372554	+	0.322820i
$474$		0			0
$475$	−268.737	−	1869.11i	−0.565763	−	3.93497i
$476$	2.51860	−	2.18238i	0.00529118	−	0.00458484i
$477$		0			0
$478$	67.7006	−	19.8787i	0.141633	−	0.0415872i
$479$	342.243	+	156.297i	0.714495	+	0.326299i	0.739284	−	0.673394i	$-0.235164\pi$
$479$	342.243	+	156.297i	0.714495	+	0.326299i	−0.0247889	+	0.999693i	$0.507891\pi$
$480$		0			0
$481$	88.2150	−	56.6923i	0.183399	−	0.117863i
$482$		−	63.4503i		−	0.131640i
$483$		0			0
$484$	204.798			0.423136
$485$	−1.62202	−	2.52392i	−0.00334438	−	0.00520396i
$486$		0			0
$487$	74.3894	−	162.890i	0.152750	−	0.334477i	−0.817751	−	0.575572i	$-0.804779\pi$
$487$	74.3894	−	162.890i	0.152750	−	0.334477i	0.970501	+	0.241095i	$0.0775067\pi$
$488$	−55.3114	−	188.373i	−0.113343	−	0.386011i
$489$		0			0
$490$	−417.421	−	481.730i	−0.851880	−	0.983122i
$491$	−371.500	+	53.4137i	−0.756620	+	0.108786i	−0.509820	−	0.860281i	$-0.670288\pi$
$491$	−371.500	+	53.4137i	−0.756620	+	0.108786i	−0.246800	+	0.969066i	$0.579379\pi$
$492$		0			0
$493$	−192.463	+	222.114i	−0.390391	+	0.450536i
$494$	−161.978	+	252.042i	−0.327890	+	0.510207i
$495$		0			0
$496$	64.0841	−	73.9570i	0.129202	−	0.149107i
$497$	1.74321	−	5.93682i	0.00350746	−	0.0119453i
$498$		0			0
$499$	245.052	+	282.805i	0.491086	+	0.566744i	0.946156	−	0.323712i	$-0.104931\pi$
$499$	245.052	+	282.805i	0.491086	+	0.566744i	−0.455069	+	0.890456i	$0.650386\pi$
$500$	580.820	−	265.252i	1.16164	−	0.530503i
$501$		0			0
$502$	64.8962	−	142.103i	0.129275	−	0.283074i
$503$	97.9387	+	14.0815i	0.194709	+	0.0279950i	0.238979	−	0.971025i	$-0.423187\pi$
$503$	97.9387	+	14.0815i	0.194709	+	0.0279950i	−0.0442702	+	0.999020i	$0.514096\pi$
$504$		0			0
$505$	1682.70			3.33207
$506$	−363.073	−	323.317i	−0.717536	−	0.638967i
$507$		0			0
$508$	−133.272	+	85.6489i	−0.262347	+	0.168600i
$509$	286.919	+	41.2527i	0.563691	+	0.0810466i	0.418269	−	0.908323i	$-0.362637\pi$
$509$	286.919	+	41.2527i	0.563691	+	0.0810466i	0.145422	+	0.989370i	$0.453546\pi$
$510$		0			0
$511$	16.8470	−	4.94671i	0.0329686	−	0.00968046i
$512$	20.5826	−	9.39977i	0.0402004	−	0.0183589i
$513$		0			0
$514$	−10.5926	−	73.6734i	−0.0206082	−	0.143333i
$515$	121.044	−	412.238i	0.235037	−	0.800462i
$516$		0			0
$517$	−779.945	−	501.240i	−1.50860	−	0.969517i
$518$	1.82534	−	2.84029i	0.00352383	−	0.00548319i
$519$		0			0
$520$	−167.253	−	49.1100i	−0.321641	−	0.0944423i
$521$	−697.258	+	100.251i	−1.33831	+	0.192419i	−0.774021	−	0.633160i	$-0.781758\pi$
$521$	−697.258	+	100.251i	−1.33831	+	0.192419i	−0.564286	+	0.825579i	$0.690848\pi$
$522$		0			0
$523$	378.169	+	828.074i	0.723076	+	1.58332i	0.809543	+	0.587061i	$0.199715\pi$
$523$	378.169	+	828.074i	0.723076	+	1.58332i	−0.0864671	+	0.996255i	$0.527558\pi$
$524$	−106.611	−	363.085i	−0.203457	−	0.692910i
$525$		0			0
$526$	95.4281	−	663.717i	0.181422	−	1.26182i
$527$	144.554	+	224.930i	0.274295	+	0.426812i
$528$		0			0
$529$	61.0752	+	525.462i	0.115454	+	0.993313i
$530$			863.991i			1.63017i
$531$		0			0
$532$	−1.37283	+	9.54825i	−0.00258051	+	0.0179478i
$533$	−359.077	−	163.985i	−0.673690	−	0.307664i
$534$		0			0
$535$	666.886	+	1460.28i	1.24652	+	2.72949i
$536$	9.89205	−	8.57151i	0.0184553	−	0.0159916i
$537$		0			0
$538$	29.5677	+	8.68186i	0.0549585	+	0.0161373i
$539$	−553.234	−	479.380i	−1.02641	−	0.889387i
$540$		0			0
$541$	−834.076	−	536.028i	−1.54173	−	0.990810i	−0.987352	−	0.158545i	$-0.949320\pi$
$541$	−834.076	−	536.028i	−1.54173	−	0.990810i	−0.554379	−	0.832265i	$-0.687044\pi$
$542$	−283.235	−	245.425i	−0.522575	−	0.452814i
$543$		0			0
$544$	8.79841	+	61.1943i	0.0161735	+	0.112489i
$545$	407.197	−	352.838i	0.747150	−	0.647409i
$546$		0			0
$547$	−394.073	+	115.710i	−0.720426	+	0.211536i	−0.621338	−	0.783542i	$-0.713411\pi$
$547$	−394.073	+	115.710i	−0.720426	+	0.211536i	−0.0990880	+	0.995079i	$0.531593\pi$
$548$	−232.493	−	106.176i	−0.424258	−	0.193752i
$549$		0			0
$550$	1061.44	−	682.147i	1.92989	−	1.24027i
$551$		−	850.713i		−	1.54394i
$552$		0			0
$553$	4.49630			0.00813074
$554$	−324.939	−	505.616i	−0.586533	−	0.912664i
$555$		0			0
$556$	−104.538	+	228.906i	−0.188017	+	0.411701i
$557$	111.907	+	381.119i	0.200910	+	0.684236i	0.996882	+	0.0789031i	$0.0251418\pi$
$557$	111.907	+	381.119i	0.200910	+	0.684236i	−0.795973	+	0.605333i	$0.793040\pi$
$558$		0			0
$559$	−68.4145	−	78.9545i	−0.122387	−	0.141242i
$560$	−5.55533	+	0.798737i	−0.00992024	+	0.00142632i
$561$		0			0
$562$	274.076	−	316.300i	0.487679	−	0.562811i
$563$	124.606	−	193.890i	0.221324	−	0.344387i	−0.712780	−	0.701388i	$-0.752564\pi$
$563$	124.606	−	193.890i	0.221324	−	0.344387i	0.934104	+	0.357000i	$0.116201\pi$
$564$		0			0
$565$	−604.767	+	697.938i	−1.07038	+	1.23529i
$566$	6.28610	−	21.4085i	0.0111062	−	0.0378242i
$567$		0			0
$568$	75.1680	+	86.7485i	0.132338	+	0.152726i
$569$	131.718	−	60.1534i	0.231490	−	0.105718i	−0.296293	−	0.955097i	$-0.595751\pi$
$569$	131.718	−	60.1534i	0.231490	−	0.105718i	0.527783	+	0.849379i	$0.323023\pi$
$570$		0			0
$571$	−208.842	+	457.301i	−0.365748	+	0.800877i	0.633875	+	0.773435i	$0.281463\pi$
$571$	−208.842	+	457.301i	−0.365748	+	0.800877i	−0.999623	+	0.0274415i	$0.991264\pi$
$572$	−198.150	−	28.4897i	−0.346417	−	0.0498072i
$573$		0			0
$574$	−12.7099			−0.0221427
$575$	−1356.16	−	213.772i	−2.35855	−	0.371777i
$576$		0			0
$577$	−256.844	+	165.064i	−0.445137	+	0.286072i	−0.743945	−	0.668241i	$-0.767048\pi$
$577$	−256.844	+	165.064i	−0.445137	+	0.286072i	0.298807	+	0.954313i	$0.403411\pi$
$578$	237.350	+	34.1258i	0.410640	+	0.0590412i
$579$		0			0
$580$	474.910	−	139.446i	0.818811	−	0.240425i
$581$	−2.92856	+	1.33743i	−0.00504055	+	0.00230194i
$582$		0			0
$583$	141.210	+	982.135i	0.242212	+	1.68462i
$584$	−91.7675	+	312.531i	−0.157136	+	0.535156i
$585$		0			0
$586$	−507.970	−	326.452i	−0.866842	−	0.557086i
$587$	−589.360	+	917.062i	−1.00402	+	1.56229i	−0.189724	+	0.981837i	$0.560759\pi$
$587$	−589.360	+	917.062i	−1.00402	+	1.56229i	−0.814296	+	0.580449i	$0.802877\pi$
$588$		0			0
$589$	−742.586	−	218.043i	−1.26076	−	0.370192i
$590$	973.392	−	139.953i	1.64982	−	0.237208i
$591$		0			0
$592$	26.0190	+	56.9736i	0.0439510	+	0.0962392i
$593$	76.2988	+	259.850i	0.128666	+	0.438195i	0.998476	−	0.0551915i	$-0.0175769\pi$
$593$	76.2988	+	259.850i	0.128666	+	0.438195i	−0.869810	+	0.493387i	$0.835759\pi$
$594$		0			0
$595$	2.18234	−	15.1785i	0.00366780	−	0.0255101i
$596$	176.105	+	274.024i	0.295478	+	0.459772i
$597$		0			0
$598$	140.403	+	166.539i	0.234788	+	0.278493i
$599$			32.4437i			0.0541631i	0.999633	+	0.0270816i	$0.00862138\pi$
$599$			32.4437i			0.0541631i	−0.999633	+	0.0270816i	$0.991379\pi$
$600$		0			0
$601$	143.129	−	995.485i	0.238152	−	1.65638i	−0.423000	−	0.906129i	$-0.639023\pi$
$601$	143.129	−	995.485i	0.238152	−	1.65638i	0.661152	−	0.750252i	$-0.270068\pi$
$602$	−3.05975	−	1.39734i	−0.00508264	−	0.00232116i
$603$		0			0
$604$	94.8483	+	207.689i	0.157034	+	0.343855i
$605$	712.187	−	617.114i	1.17717	−	1.02002i
$606$		0			0
$607$	298.096	+	87.5288i	0.491097	+	0.144199i	0.517899	−	0.855442i	$-0.326714\pi$
$607$	298.096	+	87.5288i	0.491097	+	0.144199i	−0.0268023	+	0.999641i	$0.508532\pi$
$608$	−135.244	−	117.189i	−0.222440	−	0.192745i
$609$		0			0
$610$	−759.967	−	488.401i	−1.24585	−	0.800657i
$611$	313.937	+	272.028i	0.513808	+	0.445217i
$612$		0			0
$613$	103.440	+	719.439i	0.168743	+	1.17364i	0.881486	+	0.472211i	$0.156544\pi$
$613$	103.440	+	719.439i	0.168743	+	1.17364i	−0.712742	+	0.701426i	$0.752547\pi$
$614$	205.473	−	178.043i	0.334646	−	0.289973i
$615$		0			0
$616$	−6.18444	+	1.81592i	−0.0100397	+	0.00294791i
$617$	395.801	+	180.756i	0.641493	+	0.292960i	0.709479	−	0.704726i	$-0.248930\pi$
$617$	395.801	+	180.756i	0.641493	+	0.292960i	−0.0679864	+	0.997686i	$0.521657\pi$
$618$		0			0
$619$	114.587	−	73.6408i	0.185117	−	0.118967i	−0.444800	−	0.895630i	$-0.646725\pi$
$619$	114.587	−	73.6408i	0.185117	−	0.118967i	0.629917	+	0.776662i	$0.283089\pi$
$620$		−	450.289i		−	0.726273i
$621$		0			0
$622$	−498.057			−0.800735
$623$	−0.971459	−	1.51162i	−0.00155932	−	0.00242636i
$624$		0			0
$625$	600.609	−	1315.15i	0.960974	−	2.10424i
$626$	167.153	+	569.269i	0.267017	+	0.909376i
$627$		0			0
$628$	199.274	+	229.975i	0.317316	+	0.366202i
$629$	−169.389	+	24.3544i	−0.269298	+	0.0387192i
$630$		0			0
$631$	−196.104	+	226.316i	−0.310783	+	0.358663i	−0.889556	−	0.456826i	$-0.848986\pi$
$631$	−196.104	+	226.316i	−0.310783	+	0.358663i	0.578773	+	0.815489i	$0.303532\pi$
$632$	−45.0958	+	70.1704i	−0.0713541	+	0.111029i
$633$		0			0
$634$	−282.712	+	326.267i	−0.445917	+	0.514616i
$635$	−205.372	+	699.432i	−0.323420	+	1.10147i
$636$		0			0
$637$	214.786	+	247.876i	0.337184	+	0.389131i
$638$	517.060	−	236.133i	0.810438	−	0.370115i
$639$		0			0
$640$	43.2521	−	94.7090i	0.0675815	−	0.147983i
$641$	70.2983	+	10.1074i	0.109670	+	0.0157681i	0.196931	−	0.980417i	$-0.436902\pi$
$641$	70.2983	+	10.1074i	0.109670	+	0.0157681i	−0.0872614	+	0.996185i	$0.527812\pi$
$642$		0			0
$643$	288.967			0.449404			0.224702	−	0.974428i	$-0.427859\pi$
$643$	288.967			0.449404			0.224702	+	0.974428i	$0.427859\pi$
$644$	6.33960	+	2.99962i	0.00984410	+	0.00465780i
$645$		0			0
$646$	411.325	−	264.342i	0.636725	−	0.409199i
$647$	1027.24	+	147.695i	1.58770	+	0.228277i	0.878857	−	0.477085i	$-0.158307\pi$
$647$	1027.24	+	147.695i	1.58770	+	0.228277i	0.708847	+	0.705363i	$0.249216\pi$
$648$		0			0
$649$	1083.62	−	318.180i	1.66968	−	0.490263i
$650$	−514.235	+	234.843i	−0.791131	+	0.361298i
$651$		0			0
$652$	31.1738	+	216.818i	0.0478125	+	0.332543i
$653$	−265.224	+	903.269i	−0.406162	+	1.38326i	0.461956	+	0.886903i	$0.347148\pi$
$653$	−265.224	+	903.269i	−0.406162	+	1.38326i	−0.868118	+	0.496358i	$0.834670\pi$
$654$		0			0
$655$	−1464.82	−	941.381i	−2.23636	−	1.43722i
$656$	127.474	−	198.354i	0.194321	−	0.302369i
$657$		0			0
$658$	12.8329	+	3.76809i	0.0195030	+	0.00572659i
$659$	878.053	−	126.245i	1.33240	−	0.191571i	0.560946	−	0.827852i	$-0.310438\pi$
$659$	878.053	−	126.245i	1.33240	−	0.191571i	0.771457	+	0.636282i	$0.219528\pi$
$660$		0			0
$661$	280.025	+	613.170i	0.423639	+	0.927640i	0.994316	+	0.106465i	$0.0339533\pi$
$661$	280.025	+	613.170i	0.423639	+	0.927640i	−0.570678	+	0.821174i	$0.693319\pi$
$662$	−9.34506	−	31.8263i	−0.0141164	−	0.0480761i
$663$		0			0
$664$	8.49984	−	59.1177i	0.0128010	−	0.0890327i
$665$	23.9975	+	37.3408i	0.0360865	+	0.0561516i
$666$		0			0
$667$	−591.042	−	182.276i	−0.886120	−	0.273277i
$668$			248.778i			0.372422i
$669$		0			0
$670$	8.57135	−	59.6150i	0.0127931	−	0.0889777i
$671$	−943.710	−	430.978i	−1.40642	−	0.642292i
$672$		0			0
$673$	230.333	+	504.358i	0.342248	+	0.749418i	0.999993	−	0.00382294i	$-0.00121688\pi$
$673$	230.333	+	504.358i	0.342248	+	0.749418i	−0.657745	+	0.753241i	$0.728490\pi$
$674$	−5.36637	+	4.64999i	−0.00796197	+	0.00689909i
$675$		0			0
$676$	−238.248	−	69.9558i	−0.352437	−	0.103485i
$677$	−420.777	−	364.606i	−0.621532	−	0.538561i	0.286168	−	0.958179i	$-0.407618\pi$
$677$	−420.777	−	364.606i	−0.621532	−	0.538561i	−0.907701	+	0.419618i	$0.862164\pi$
$678$		0			0
$679$	0.0418146	+	0.0268726i	6.15826e−5	+	3.95767e-5i
$680$	214.992	+	186.292i	0.316165	+	0.273958i
$681$		0			0
$682$	−73.5948	−	511.863i	−0.107910	−	0.750533i
$683$	591.462	−	512.505i	0.865977	−	0.750373i	−0.103740	−	0.994604i	$-0.533081\pi$
$683$	591.462	−	512.505i	0.865977	−	0.750373i	0.969717	+	0.244231i	$0.0785356\pi$
$684$		0			0
$685$	−1128.44	+	331.339i	−1.64735	+	0.483706i
$686$	19.2166	+	8.77593i	0.0280126	+	0.0127929i
$687$		0			0
$688$	52.4951	−	33.7365i	0.0763010	−	0.0490357i
$689$		−	444.571i		−	0.645241i
$690$		0			0
$691$	203.431			0.294401			0.147201	−	0.989107i	$-0.452974\pi$
$691$	203.431			0.294401			0.147201	+	0.989107i	$0.452974\pi$
$692$	339.104	+	527.655i	0.490034	+	0.762508i
$693$		0			0
$694$	−229.470	+	502.470i	−0.330649	+	0.724020i
$695$	326.226	+	1111.02i	0.469389	+	1.59859i
$696$		0			0
$697$	421.874	+	486.868i	0.605270	+	0.698519i
$698$	334.525	−	48.0974i	0.479262	−	0.0689075i
$699$		0			0
$700$	−11.9197	+	13.7561i	−0.0170282	+	0.0196515i
$701$	−334.742	+	520.869i	−0.477521	+	0.743037i	−0.993533	−	0.113545i	$-0.963780\pi$
$701$	−334.742	+	520.869i	−0.477521	+	0.743037i	0.516012	+	0.856581i	$0.327416\pi$
$702$		0			0
$703$	324.385	−	374.360i	0.461430	−	0.532518i
$704$	33.6874	−	114.729i	0.0478514	−	0.162967i
$705$		0			0
$706$	−367.219	−	423.793i	−0.520140	−	0.600274i
$707$	−25.3585	+	11.5809i	−0.0358678	+	0.0163803i
$708$		0			0
$709$	−393.551	+	861.757i	−0.555079	+	1.21545i	0.399290	+	0.916825i	$0.369257\pi$
$709$	−393.551	+	861.757i	−0.555079	+	1.21545i	−0.954369	+	0.298629i	$0.903471\pi$
$710$	522.795	+	75.1666i	0.736331	+	0.105868i
$711$		0			0
$712$	33.3340			0.0468174
$713$	−310.596	+	469.201i	−0.435619	+	0.658067i
$714$		0			0
$715$	−774.917	+	498.009i	−1.08380	+	0.696516i
$716$	609.744	+	87.6679i	0.851598	+	0.122441i
$717$		0			0
$718$	128.303	−	37.6731i	0.178695	−	0.0524695i
$719$	−743.391	+	339.495i	−1.03392	+	0.472177i	−0.858769	−	0.512364i	$-0.828770\pi$
$719$	−743.391	+	339.495i	−1.03392	+	0.472177i	−0.175155	+	0.984541i	$0.556043\pi$
$720$		0			0
$721$	1.01300	+	7.04556i	0.00140499	+	0.00977192i
$722$	−254.898	+	868.101i	−0.353044	+	1.20236i
$723$		0			0
$724$	160.049	+	102.857i	0.221061	+	0.142068i
$725$	867.845	−	1350.39i	1.19703	−	1.86261i
$726$		0			0
$727$	−1043.89	−	306.515i	−1.43589	−	0.421616i	−0.531042	−	0.847345i	$-0.678200\pi$
$727$	−1043.89	−	306.515i	−1.43589	−	0.421616i	−0.904851	+	0.425729i	$0.860018\pi$
$728$	2.85853	−	0.410994i	0.00392655	−	0.000564552i
$729$		0			0
$730$	622.622	+	1363.35i	0.852906	+	1.86760i
$731$	48.0339	+	163.588i	0.0657098	+	0.223787i
$732$		0			0
$733$	−165.668	+	1152.24i	−0.226013	+	1.57196i	0.488646	+	0.872482i	$0.337491\pi$
$733$	−165.668	+	1152.24i	−0.226013	+	1.57196i	−0.714659	+	0.699473i	$0.753418\pi$
$734$	−303.777	−	472.687i	−0.413865	−	0.643987i
$735$		0			0
$736$	−110.396	+	68.8527i	−0.149995	+	0.0935498i
$737$		−	69.1678i		−	0.0938505i
$738$		0			0
$739$	−0.565295	+	3.93171i	−0.000764946	+	0.00532032i	−0.990200	−	0.139654i	$-0.955401\pi$
$739$	−0.565295	+	3.93171i	−0.000764946	+	0.00532032i	0.989435	+	0.144974i	$0.0463100\pi$
$740$	262.159	+	119.724i	0.354268	+	0.161789i
$741$		0			0
$742$	−5.94626	−	13.0205i	−0.00801383	−	0.0175478i
$743$	208.622	−	180.772i	0.280784	−	0.243301i	−0.503070	−	0.864245i	$-0.667796\pi$
$743$	208.622	−	180.772i	0.280784	−	0.243301i	0.783854	+	0.620945i	$0.213251\pi$
$744$		0			0
$745$	1438.12	+	422.269i	1.93036	+	0.566805i
$746$	−35.9228	−	31.1273i	−0.0481538	−	0.0417255i
$747$		0			0
$748$	274.838	+	176.628i	0.367430	+	0.236133i
$749$	−20.1002	−	17.4169i	−0.0268360	−	0.0232535i
$750$		0			0
$751$	−202.585	−	1409.01i	−0.269754	−	1.87618i	−0.450681	−	0.892685i	$-0.648819\pi$
$751$	−202.585	−	1409.01i	−0.269754	−	1.87618i	0.180927	−	0.983497i	$-0.442090\pi$
$752$	−187.514	+	162.482i	−0.249354	+	0.216067i
$753$		0			0
$754$	−244.368	+	71.7528i	−0.324095	+	0.0951628i
$755$	955.660	+	436.435i	1.26577	+	0.578060i
$756$		0			0
$757$	−244.961	+	157.427i	−0.323595	+	0.207962i	−0.692345	−	0.721567i	$-0.743422\pi$
$757$	−244.961	+	157.427i	−0.323595	+	0.207962i	0.368750	+	0.929529i	$0.379786\pi$
$758$			204.596i			0.269916i
$759$		0			0
$760$	−823.435			−1.08347
$761$	−618.578	−	962.527i	−0.812849	−	1.26482i	−0.961191	−	0.275882i	$-0.911030\pi$
$761$	−618.578	−	962.527i	−0.812849	−	1.26482i	0.148342	−	0.988936i	$-0.452606\pi$
$762$		0			0
$763$	−3.70818	+	8.11979i	−0.00486000	+	0.0106419i
$764$	−144.021	−	490.490i	−0.188509	−	0.642002i
$765$		0			0
$766$	−516.658	−	596.255i	−0.674489	−	0.778401i
$767$	−500.864	+	72.0134i	−0.653017	+	0.0938897i
$768$		0			0
$769$	−183.314	+	211.556i	−0.238380	+	0.275105i	−0.862316	−	0.506370i	$-0.830987\pi$
$769$	−183.314	+	211.556i	−0.238380	+	0.275105i	0.623936	+	0.781475i	$0.285532\pi$
$770$	−16.0346	+	24.9503i	−0.0208241	+	0.0324030i
$771$		0			0
$772$	−426.653	+	492.384i	−0.552660	+	0.637803i
$773$	82.7132	−	281.695i	0.107003	−	0.364418i	−0.888532	−	0.458815i	$-0.848274\pi$
$773$	82.7132	−	281.695i	0.107003	−	0.364418i	0.995535	+	0.0943968i	$0.0300922\pi$
$774$		0			0
$775$	−956.322	−	1103.65i	−1.23396	−	1.42407i
$776$	−0.838762	+	0.383050i	−0.00108088	+	0.000493621i
$777$		0			0
$778$	−296.464	+	649.165i	−0.381059	+	0.834403i
$779$	−1845.76	−	265.380i	−2.36940	−	0.340668i
$780$		0			0
$781$	606.568			0.776656
$782$	−95.5232	−	342.411i	−0.122152	−	0.437866i
$783$		0			0
$784$	−164.807	+	105.915i	−0.210214	+	0.135096i
$785$	1385.96	+	199.270i	1.76555	+	0.253848i
$786$		0			0
$787$	−818.669	+	240.383i	−1.04024	+	0.305442i	−0.756868	−	0.653568i	$-0.773271\pi$
$787$	−818.669	+	240.383i	−1.04024	+	0.305442i	−0.283372	+	0.959010i	$0.591453\pi$
$788$	489.437	−	223.518i	0.621113	−	0.283653i
$789$		0			0
$790$	54.6220	+	379.904i	0.0691418	+	0.480892i
$791$	4.31051	−	14.6803i	0.00544944	−	0.0185591i
$792$		0			0
$793$	391.045	+	251.309i	0.493121	+	0.316910i
$794$	−284.719	+	443.032i	−0.358589	+	0.557975i
$795$		0			0
$796$	196.587	+	57.7232i	0.246969	+	0.0725166i
$797$	326.144	−	46.8924i	0.409215	−	0.0588362i	0.0653662	−	0.997861i	$-0.479178\pi$
$797$	326.144	−	46.8924i	0.409215	−	0.0588362i	0.343848	+	0.939025i	$0.388269\pi$
$798$		0			0
$799$	−281.616	−	616.654i	−0.352461	−	0.771782i
$800$	−95.1318	−	323.989i	−0.118915	−	0.404987i
$801$		0			0
$802$	−120.810	+	840.250i	−0.150636	+	1.04769i
$803$	930.585	+	1448.02i	1.15889	+	1.80326i
$804$		0			0
$805$	31.0847	−	8.67178i	0.0386146	−	0.0107724i
$806$			231.699i			0.287467i
$807$		0			0
$808$	73.6005	−	511.903i	0.0910897	−	0.633543i
$809$	778.032	+	355.315i	0.961720	+	0.439203i	0.833486	−	0.552541i	$-0.186342\pi$
$809$	778.032	+	355.315i	0.961720	+	0.439203i	0.128234	+	0.991744i	$0.459069\pi$
$810$		0			0
$811$	494.493	+	1082.79i	0.609732	+	1.33513i	0.922757	+	0.385382i	$0.125930\pi$
$811$	494.493	+	1082.79i	0.609732	+	1.33513i	−0.313025	+	0.949745i	$0.601342\pi$
$812$	−6.19727	+	5.36996i	−0.00763210	+	0.00661325i
$813$		0			0
$814$	317.574	+	93.2483i	0.390141	+	0.114556i
$815$	761.741	+	660.052i	0.934651	+	0.809880i
$816$		0			0
$817$	−415.167	−	266.811i	−0.508160	−	0.326575i
$818$	668.414	+	579.184i	0.817132	+	0.708049i
$819$		0			0
$820$	−154.403	−	1073.89i	−0.188296	−	1.30963i
$821$	−124.344	+	107.744i	−0.151454	+	0.131236i	−0.727292	−	0.686328i	$-0.759221\pi$
$821$	−124.344	+	107.744i	−0.151454	+	0.131236i	0.575838	+	0.817564i	$0.304676\pi$
$822$		0			0
$823$	−1202.14	+	352.981i	−1.46068	+	0.428895i	−0.913058	−	0.407830i	$-0.866286\pi$
$823$	−1202.14	+	352.981i	−1.46068	+	0.428895i	−0.547624	+	0.836725i	$0.684468\pi$
$824$	−120.115	−	54.8546i	−0.145770	−	0.0665711i
$825$		0			0
$826$	−13.7060	+	8.80831i	−0.0165932	+	0.0106638i
$827$			130.844i			0.158215i	0.996866	+	0.0791073i	$0.0252070\pi$
$827$			130.844i			0.158215i	−0.996866	+	0.0791073i	$0.974793\pi$
$828$		0			0
$829$	−1119.71			−1.35068			−0.675340	−	0.737506i	$-0.736003\pi$
$829$	−1119.71			−1.35068			−0.675340	+	0.737506i	$0.736003\pi$
$830$	−148.580	−	231.195i	−0.179012	−	0.278548i
$831$		0			0
$832$	−22.2556	+	48.7330i	−0.0267495	+	0.0585733i
$833$	−150.802	−	513.583i	−0.181034	−	0.616546i
$834$		0			0
$835$	749.638	+	865.128i	0.897770	+	1.03608i
$836$	−936.033	+	134.581i	−1.11966	+	0.160982i
$837$		0			0
$838$	−661.805	+	763.764i	−0.789744	+	0.911413i
$839$	339.515	−	528.296i	0.404666	−	0.629673i	−0.577786	−	0.816189i	$-0.696083\pi$
$839$	339.515	−	528.296i	0.404666	−	0.629673i	0.982452	+	0.186515i	$0.0597194\pi$
$840$		0			0
$841$	−77.1642	+	89.0522i	−0.0917529	+	0.105888i
$842$	131.019	−	446.208i	0.155604	−	0.529938i
$843$		0			0
$844$	−246.263	−	284.202i	−0.291780	−	0.336733i
$845$	−1039.30	+	474.635i	−1.22995	+	0.561698i
$846$		0			0
$847$	−6.48561	+	14.2015i	−0.00765716	+	0.0167668i
$848$	262.839	+	37.7906i	0.309952	+	0.0445644i
$849$		0			0
$850$	922.588			1.08540
$851$	−190.587	−	305.581i	−0.223957	−	0.359085i
$852$		0			0
$853$	628.988	−	404.226i	0.737383	−	0.473887i	−0.117261	−	0.993101i	$-0.537412\pi$
$853$	628.988	−	404.226i	0.737383	−	0.473887i	0.854644	+	0.519214i	$0.173775\pi$
$854$	14.8142	+	2.12996i	0.0173468	+	0.00249409i
$855$		0			0
$856$	473.408	−	139.005i	0.553047	−	0.162389i
$857$	22.1342	−	10.1083i	0.0258275	−	0.0117950i	−0.402459	−	0.915438i	$-0.631845\pi$
$857$	22.1342	−	10.1083i	0.0258275	−	0.0117950i	0.428287	+	0.903643i	$0.359117\pi$
$858$		0			0
$859$	−141.798	−	986.224i	−0.165073	−	1.14811i	−0.888892	−	0.458117i	$-0.848524\pi$
$859$	−141.798	−	986.224i	−0.165073	−	1.14811i	0.723819	−	0.689990i	$-0.242385\pi$
$860$	80.8945	−	275.501i	0.0940634	−	0.320351i
$861$		0			0
$862$	587.190	+	377.364i	0.681195	+	0.437777i
$863$	581.771	−	905.254i	0.674127	−	1.04896i	−0.320681	−	0.947187i	$-0.603912\pi$
$863$	581.771	−	905.254i	0.674127	−	1.04896i	0.994807	−	0.101775i	$-0.0324520\pi$
$864$		0			0
$865$	2769.21	+	813.113i	3.20140	+	0.940015i
$866$	−684.247	+	98.3799i	−0.790124	+	0.113603i
$867$		0			0
$868$	3.09904	+	6.78594i	0.00357032	+	0.00781790i
$869$	124.182	+	422.926i	0.142903	+	0.486681i
$870$		0			0
$871$	−4.41043	+	30.6752i	−0.00506364	+	0.0352184i
$872$	−89.5282	−	139.309i	−0.102670	−	0.159758i
$873$		0			0
$874$	858.019	+	567.981i	0.981715	+	0.649864i
$875$			48.6764i			0.0556302i
$876$		0			0
$877$	79.3001	−	551.544i	0.0904220	−	0.628899i	−0.893335	−	0.449392i	$-0.851641\pi$
$877$	79.3001	−	551.544i	0.0904220	−	0.628899i	0.983757	−	0.179507i	$-0.0574502\pi$
$878$	−583.983	−	266.696i	−0.665129	−	0.303754i
$879$		0			0
$880$	−228.562	−	500.480i	−0.259729	−	0.568727i
$881$	83.1921	−	72.0863i	0.0944291	−	0.0818233i	−0.606367	−	0.795185i	$-0.707374\pi$
$881$	83.1921	−	72.0863i	0.0944291	−	0.0818233i	0.700796	+	0.713362i	$0.252828\pi$
$882$		0			0
$883$	−1564.73	−	459.446i	−1.77206	−	0.520324i	−0.777914	−	0.628371i	$-0.783722\pi$
$883$	−1564.73	−	459.446i	−1.77206	−	0.520324i	−0.994146	+	0.108047i	$0.965540\pi$
$884$	−110.625	−	95.8573i	−0.125142	−	0.108436i
$885$		0			0
$886$	−397.580	−	255.509i	−0.448736	−	0.288385i
$887$	−917.445	−	794.971i	−1.03432	−	0.896247i	−0.0396392	−	0.999214i	$-0.512621\pi$
$887$	−917.445	−	794.971i	−1.03432	−	0.896247i	−0.994685	+	0.102967i	$0.967166\pi$
$888$		0			0
$889$	−1.71872	−	11.9540i	−0.00193332	−	0.0134466i
$890$	115.919	−	100.445i	0.130246	−	0.112859i
$891$		0			0
$892$	462.065	−	135.675i	0.518011	−	0.152102i
$893$	1784.95	+	815.160i	1.99882	+	0.912833i
$894$		0			0
$895$	2384.56	−	1532.46i	2.66431	−	1.71225i
$896$			1.72496i			0.00192517i
$897$		0			0
$898$	903.702			1.00635
$899$	−355.688	−	553.462i	−0.395649	−	0.615642i
$900$		0			0
$901$	−301.394	+	659.961i	−0.334511	+	0.732476i
$902$	−351.032	−	1195.51i	−0.389171	−	1.32539i
$903$		0			0
$904$	185.871	+	214.507i	0.205610	+	0.237287i
$905$	866.507	−	124.585i	0.957466	−	0.137663i
$906$		0			0
$907$	864.279	−	997.431i	0.952898	−	1.09970i	−0.0420300	−	0.999116i	$-0.513383\pi$
$907$	864.279	−	997.431i	0.952898	−	1.09970i	0.994928	−	0.100587i	$-0.0320720\pi$
$908$	−171.913	+	267.502i	−0.189332	+	0.294606i
$909$		0			0
$910$	8.70211	−	10.0428i	0.00956276	−	0.0110360i
$911$	−377.431	+	1285.41i	−0.414304	+	1.41099i	0.443158	+	0.896444i	$0.353858\pi$
$911$	−377.431	+	1285.41i	−0.414304	+	1.41099i	−0.857462	+	0.514547i	$0.827960\pi$
$912$		0			0
$913$	−206.683	−	238.525i	−0.226378	−	0.261254i
$914$	321.286	−	146.727i	0.351517	−	0.160532i
$915$		0			0
$916$	221.485	−	484.984i	0.241796	−	0.529459i
$917$	28.5539	+	4.10544i	0.0311384	+	0.00447703i
$918$		0			0
$919$	−146.053			−0.158926			−0.0794631	−	0.996838i	$-0.525321\pi$
$919$	−146.053			−0.158926			−0.0794631	+	0.996838i	$0.525321\pi$
$920$	−176.431	+	572.090i	−0.191773	+	0.621837i
$921$		0			0
$922$	−175.676	+	112.900i	−0.190538	+	0.122452i
$923$	−269.007	−	38.6773i	−0.291448	−	0.0419039i
$924$		0			0
$925$	896.817	−	263.329i	0.969532	−	0.284680i
$926$	−126.760	+	57.8895i	−0.136890	+	0.0625157i
$927$		0			0
$928$	−21.6493	−	150.574i	−0.0233290	−	0.162257i
$929$	−43.9646	+	149.730i	−0.0473247	+	0.161173i	−0.979765	−	0.200151i	$-0.935857\pi$
$929$	−43.9646	+	149.730i	−0.0473247	+	0.161173i	0.932440	+	0.361324i	$0.117675\pi$
$930$		0			0
$931$	1303.41	+	837.650i	1.40001	+	0.899732i
$932$	−114.433	+	178.061i	−0.122782	+	0.191053i
$933$		0			0
$934$	−666.504	−	195.703i	−0.713602	−	0.209532i
$935$	1487.98	−	213.939i	1.59142	−	0.228812i
$936$		0			0
$937$	−409.998	−	897.771i	−0.437565	−	0.958134i	−0.992039	−	0.125933i	$-0.959808\pi$
$937$	−409.998	−	897.771i	−0.437565	−	0.958134i	0.554474	−	0.832201i	$-0.312920\pi$
$938$	0.281118	+	0.957400i	0.000299699	+	0.00102068i
$939$		0			0
$940$	−162.479	+	1130.07i	−0.172850	+	1.20220i
$941$	124.527	+	193.768i	0.132335	+	0.205917i	0.901097	−	0.433618i	$-0.142763\pi$
$941$	124.527	+	193.768i	0.132335	+	0.205917i	−0.768762	+	0.639535i	$0.779127\pi$
$942$		0			0
$943$	−579.853	+	1225.50i	−0.614902	+	1.29958i
$944$		−	302.243i		−	0.320172i
$945$		0			0
$946$	46.9286	−	326.396i	0.0496074	−	0.345027i
$947$	144.820	+	66.1370i	0.152925	+	0.0698384i	0.490407	−	0.871493i	$-0.336848\pi$
$947$	144.820	+	66.1370i	0.152925	+	0.0698384i	−0.337482	+	0.941332i	$0.609575\pi$
$948$		0			0
$949$	−320.373	−	701.519i	−0.337590	−	0.739220i
$950$	−2018.23	+	1748.81i	−2.12445	+	1.84085i
$951$		0			0
$952$	−4.52209	−	1.32780i	−0.00475009	−	0.00139475i
$953$	266.955	+	231.318i	0.280120	+	0.242726i	0.783577	−	0.621295i	$-0.213393\pi$
$953$	266.955	+	231.318i	0.280120	+	0.242726i	−0.503456	+	0.864021i	$0.667939\pi$
$954$		0			0
$955$	−1978.82	−	1271.71i	−2.07206	−	1.33163i
$956$	−75.4125	−	65.3453i	−0.0788834	−	0.0683529i
$957$		0			0
$958$	−75.7241	−	526.673i	−0.0790440	−	0.549763i
$959$	14.7253	−	12.7596i	0.0153549	−	0.0133051i
$960$		0			0
$961$	347.792	−	102.121i	0.361906	−	0.106265i
$962$	−134.895	−	61.6045i	−0.140224	−	0.0640380i
$963$		0			0
$964$	−75.4875	+	48.5129i	−0.0783066	+	0.0503246i
$965$			2997.90i			3.10663i
$966$		0			0
$967$	1827.19			1.88954			0.944772	−	0.327729i	$-0.106283\pi$
$967$	1827.19			1.88954			0.944772	+	0.327729i	$0.106283\pi$
$968$	−156.585	−	243.651i	−0.161761	−	0.251705i
$969$		0			0
$970$	−1.76257	+	3.85948i	−0.00181708	+	0.00397885i
$971$	295.655	+	1006.91i	0.304485	+	1.03698i	0.959580	+	0.281435i	$0.0908104\pi$
$971$	295.655	+	1006.91i	0.304485	+	1.03698i	−0.655095	+	0.755547i	$0.727371\pi$
$972$		0			0
$973$	−12.5627	−	14.4981i	−0.0129113	−	0.0149004i
$974$	−250.669	+	36.0408i	−0.257361	+	0.0370029i
$975$		0			0
$976$	−181.820	+	209.831i	−0.186291	+	0.214991i
$977$	−494.701	+	769.770i	−0.506347	+	0.787891i	−0.996487	−	0.0837528i	$-0.973309\pi$
$977$	−494.701	+	769.770i	−0.506347	+	0.787891i	0.490140	+	0.871644i	$0.336946\pi$
$978$		0			0
$979$	115.354	−	133.126i	0.117828	−	0.135981i
$980$	−253.967	+	864.932i	−0.259150	+	0.882584i
$981$		0			0
$982$	347.589	+	401.139i	0.353961	+	0.408492i
$983$	1098.99	−	501.894i	1.11800	−	0.510574i	0.231283	−	0.972886i	$-0.425708\pi$
$983$	1098.99	−	501.894i	1.11800	−	0.510574i	0.886717	+	0.462313i	$0.152980\pi$
$984$		0			0
$985$	1028.50	−	2252.10i	1.04416	−	2.28639i
$986$	411.406	+	59.1512i	0.417247	+	0.0599911i
$987$		0			0
$988$	423.703			0.428849
$989$	−274.325	+	231.274i	−0.277376	+	0.233846i
$990$		0			0
$991$	−893.674	+	574.329i	−0.901790	+	0.579545i	−0.907321	−	0.420440i	$-0.861876\pi$
$991$	−893.674	+	574.329i	−0.901790	+	0.579545i	0.00553072	+	0.999985i	$0.498240\pi$
$992$	−136.985	−	19.6955i	−0.138090	−	0.0198543i
$993$		0			0
$994$	−8.39593	+	2.46527i	−0.00844661	+	0.00248015i
$995$	857.570	−	391.639i	0.861880	−	0.393607i
$996$		0			0
$997$	−169.551	−	1179.25i	−0.170061	−	1.18280i	−0.878752	−	0.477280i	$-0.841623\pi$
$997$	−169.551	−	1179.25i	−0.170061	−	1.18280i	0.708691	−	0.705519i	$-0.249286\pi$
$998$	149.094	−	507.769i	0.149393	−	0.508786i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.a.35.4	✓	80
3.2	odd	2	inner	414.3.k.a.35.5	yes	80
23.2	even	11	inner	414.3.k.a.71.5	yes	80
69.2	odd	22	inner	414.3.k.a.71.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.a.35.4	✓	80	1.1	even	1	trivial
414.3.k.a.35.5	yes	80	3.2	odd	2	inner
414.3.k.a.71.4	yes	80	69.2	odd	22	inner
414.3.k.a.71.5	yes	80	23.2	even	11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.764582 - 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(2.59273 + 8.83003i) q^{5} +(-0.0998440 - 0.115226i) q^{7} +(2.79964 - 0.402527i) q^{8} +O(q^{10})\)	\(q+(-0.764582 - 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(2.59273 + 8.83003i) q^{5} +(-0.0998440 - 0.115226i) q^{7} +(2.79964 - 0.402527i) q^{8} +(8.52284 - 9.83588i) q^{10} +(8.08071 - 12.5738i) q^{11} +(-4.38547 + 5.06110i) q^{13} +(-0.0607470 + 0.206885i) q^{14} +(-2.61944 - 3.02300i) q^{16} +(9.94134 - 4.54006i) q^{17} +(-13.1415 + 28.7759i) q^{19} +(-18.2183 - 2.61939i) q^{20} -21.1376 q^{22} +(17.1767 + 15.2958i) q^{23} +(-50.2158 + 32.2718i) q^{25} +(9.37431 + 1.34782i) q^{26} +(0.292580 - 0.0859093i) q^{28} +(-24.4616 + 11.1712i) q^{29} +(3.48170 + 24.2158i) q^{31} +(-1.59372 + 5.42771i) q^{32} +(-13.0023 - 8.35608i) q^{34} +(0.758581 - 1.18038i) q^{35} +(-15.0241 - 4.41149i) q^{37} +(44.2829 - 6.36691i) q^{38} +(10.8130 + 23.6772i) q^{40} +(16.6070 + 56.5583i) q^{41} +(-2.22015 + 15.4415i) q^{43} +(16.1614 + 25.1477i) q^{44} +(5.06468 - 32.1302i) q^{46} -62.0293i q^{47} +(6.97012 - 48.4782i) q^{49} +(76.7882 + 35.0680i) q^{50} +(-5.56390 - 12.1832i) q^{52} +(-50.1709 + 43.4733i) q^{53} +(131.978 + 38.7524i) q^{55} +(-0.325909 - 0.282401i) q^{56} +(31.9935 + 20.5609i) q^{58} +(57.1049 + 49.4817i) q^{59} +(-9.87831 - 68.7051i) q^{61} +(26.1477 - 22.6572i) q^{62} +(7.67594 - 2.25386i) q^{64} +(-56.0600 - 25.6018i) q^{65} +(3.89305 - 2.50191i) q^{67} +21.8579i q^{68} -1.98430 q^{70} +(21.9406 + 34.1402i) q^{71} +(-47.8397 + 104.754i) q^{73} +(6.23879 + 21.2474i) q^{74} +(-41.4327 - 47.8158i) q^{76} +(-2.25564 + 0.324313i) q^{77} +(-19.3122 + 22.2874i) q^{79} +(19.9017 - 30.9676i) q^{80} +(54.5907 - 63.0010i) q^{82} +(5.94912 - 20.2608i) q^{83} +(65.8640 + 76.0111i) q^{85} +(20.0684 - 9.16492i) q^{86} +(17.5618 - 38.4549i) q^{88} +(11.6654 + 1.67723i) q^{89} +1.02103 q^{91} +(-42.0980 + 18.5406i) q^{92} +(-73.7970 + 47.4264i) q^{94} +(-288.165 - 41.4319i) q^{95} +(-0.312802 + 0.0918470i) q^{97} +(-63.0044 + 28.7731i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 - 16 * q^7	\( 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

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