LMFDB - Embedded newform 368.2.m.e.305.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(49,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("368.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			305.3
Character	$\chi$	$=$	368.305
Dual form			368.2.m.e.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.02810 + 0.889130i) q^{3} +(-0.0517063 + 0.0332296i) q^{5} +(0.363207 - 2.52616i) q^{7} +(5.85508 + 3.76283i) q^{9} +O(q^{10})$	\(q+(3.02810 + 0.889130i) q^{3} +(-0.0517063 + 0.0332296i) q^{5} +(0.363207 - 2.52616i) q^{7} +(5.85508 + 3.76283i) q^{9} +(-1.86394 - 4.08146i) q^{11} +(0.152824 + 1.06292i) q^{13} +(-0.186117 + 0.0546490i) q^{15} +(-2.33478 + 2.69448i) q^{17} +(3.72815 + 4.30251i) q^{19} +(3.34591 - 7.32652i) q^{21} +(-2.65898 - 3.99122i) q^{23} +(-2.07551 + 4.54472i) q^{25} +(8.18401 + 9.44485i) q^{27} +(-3.31250 + 3.82283i) q^{29} +(-9.18075 + 2.69571i) q^{31} +(-2.01525 - 14.0164i) q^{33} +(0.0651632 + 0.142688i) q^{35} +(-5.38759 - 3.46239i) q^{37} +(-0.482304 + 3.35450i) q^{39} +(-0.351797 + 0.226086i) q^{41} +(-1.29593 - 0.380519i) q^{43} -0.427782 q^{45} +9.28734 q^{47} +(0.466898 + 0.137094i) q^{49} +(-9.46571 + 6.08324i) q^{51} +(0.396470 - 2.75751i) q^{53} +(0.232003 + 0.149099i) q^{55} +(7.46371 + 16.3433i) q^{57} +(-1.94473 - 13.5259i) q^{59} +(11.8135 - 3.46876i) q^{61} +(11.6321 - 13.4242i) q^{63} +(-0.0432223 - 0.0498812i) q^{65} +(2.90777 - 6.36713i) q^{67} +(-4.50294 - 14.4500i) q^{69} +(0.0848341 - 0.185761i) q^{71} +(-0.450289 - 0.519661i) q^{73} +(-10.3257 + 11.9165i) q^{75} +(-10.9874 + 3.22620i) q^{77} +(1.58382 + 11.0157i) q^{79} +(7.71050 + 16.8836i) q^{81} +(-5.83837 - 3.75209i) q^{83} +(0.0311864 - 0.216906i) q^{85} +(-13.4296 + 8.63067i) q^{87} +(-6.64101 - 1.94998i) q^{89} +2.74060 q^{91} -30.1971 q^{93} +(-0.335740 - 0.0985821i) q^{95} +(5.80879 - 3.73308i) q^{97} +(4.44433 - 30.9110i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$	$1$

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
$3$	3.02810	+	0.889130i	1.74827	+	0.513340i	0.990300	−	0.138945i	$-0.0443711\pi$
$3$	3.02810	+	0.889130i	1.74827	+	0.513340i	0.757974	+	0.652285i	$0.226189\pi$
$4$		0			0
$5$	−0.0517063	+	0.0332296i	−0.0231238	+	0.0148607i	−0.552152	−	0.833744i	$-0.686193\pi$
$5$	−0.0517063	+	0.0332296i	−0.0231238	+	0.0148607i	0.529028	+	0.848604i	$0.322557\pi$
$6$		0			0
$7$	0.363207	−	2.52616i	0.137279	−	0.954798i	−0.798446	−	0.602067i	$-0.794344\pi$
$7$	0.363207	−	2.52616i	0.137279	−	0.954798i	0.935725	−	0.352731i	$-0.114747\pi$
$8$		0			0
$9$	5.85508	+	3.76283i	1.95169	+	1.25428i
$10$		0			0
$11$	−1.86394	−	4.08146i	−0.562000	−	1.23061i	−0.950949	−	0.309348i	$-0.899889\pi$
$11$	−1.86394	−	4.08146i	−0.562000	−	1.23061i	0.388949	−	0.921259i	$-0.372838\pi$
$12$		0			0
$13$	0.152824	+	1.06292i	0.0423858	+	0.294800i	0.999978	+	0.00667186i	$0.00212373\pi$
$13$	0.152824	+	1.06292i	0.0423858	+	0.294800i	−0.957592	+	0.288128i	$0.906967\pi$
$14$		0			0
$15$	−0.186117	+	0.0546490i	−0.0480553	+	0.0141103i
$16$		0			0
$17$	−2.33478	+	2.69448i	−0.566268	+	0.653508i	−0.964595	−	0.263735i	$-0.915046\pi$
$17$	−2.33478	+	2.69448i	−0.566268	+	0.653508i	0.398327	+	0.917244i	$0.369591\pi$
$18$		0			0
$19$	3.72815	+	4.30251i	0.855296	+	0.987064i	0.999997	−	0.00241098i	$-0.000767441\pi$
$19$	3.72815	+	4.30251i	0.855296	+	0.987064i	−0.144701	+	0.989475i	$0.546222\pi$
$20$		0			0
$21$	3.34591	−	7.32652i	0.730137	−	1.59878i
$22$		0			0
$23$	−2.65898	−	3.99122i	−0.554435	−	0.832227i
$23$	−2.65898	−	3.99122i	−0.554435	−	0.832227i
$24$		0			0
$25$	−2.07551	+	4.54472i	−0.415101	+	0.908945i
$26$		0			0
$27$	8.18401	+	9.44485i	1.57501	+	1.81766i
$28$		0			0
$29$	−3.31250	+	3.82283i	−0.615116	+	0.709882i	−0.974772	−	0.223203i	$-0.928349\pi$
$29$	−3.31250	+	3.82283i	−0.615116	+	0.709882i	0.359656	+	0.933085i	$0.382894\pi$
$30$		0			0
$31$	−9.18075	+	2.69571i	−1.64891	+	0.484164i	−0.968572	−	0.248734i	$-0.919986\pi$
$31$	−9.18075	+	2.69571i	−1.64891	+	0.484164i	−0.680339	+	0.732898i	$0.738167\pi$
$32$		0			0
$33$	−2.01525	−	14.0164i	−0.350810	−	2.43994i
$34$		0			0
$35$	0.0651632	+	0.142688i	0.0110146	+	0.0241186i
$36$		0			0
$37$	−5.38759	−	3.46239i	−0.885714	−	0.569214i	0.0168077	−	0.999859i	$-0.494650\pi$
$37$	−5.38759	−	3.46239i	−0.885714	−	0.569214i	−0.902521	+	0.430645i	$0.858286\pi$
$38$		0			0
$39$	−0.482304	+	3.35450i	−0.0772304	+	0.537149i
$40$		0			0
$41$	−0.351797	+	0.226086i	−0.0549415	+	0.0353088i	−0.567823	−	0.823151i	$-0.692214\pi$
$41$	−0.351797	+	0.226086i	−0.0549415	+	0.0353088i	0.512882	+	0.858459i	$0.328578\pi$
$42$		0			0
$43$	−1.29593	−	0.380519i	−0.197627	−	0.0580286i	0.181421	−	0.983406i	$-0.441930\pi$
$43$	−1.29593	−	0.380519i	−0.197627	−	0.0580286i	−0.379048	+	0.925377i	$0.623749\pi$
$44$		0			0
$45$	−0.427782			−0.0637699
$46$		0			0
$47$	9.28734			1.35470			0.677349	−	0.735662i	$-0.263129\pi$
$47$	9.28734			1.35470			0.677349	+	0.735662i	$0.263129\pi$
$48$		0			0
$49$	0.466898	+	0.137094i	0.0666997	+	0.0195848i
$50$		0			0
$51$	−9.46571	+	6.08324i	−1.32546	+	0.851824i
$52$		0			0
$53$	0.396470	−	2.75751i	0.0544593	−	0.378773i	−0.944305	−	0.329072i	$-0.893264\pi$
$53$	0.396470	−	2.75751i	0.0544593	−	0.378773i	0.998764	−	0.0497009i	$-0.0158268\pi$
$54$		0			0
$55$	0.232003	+	0.149099i	0.0312833	+	0.0201046i
$56$		0			0
$57$	7.46371	+	16.3433i	0.988593	+	2.16472i
$58$		0			0
$59$	−1.94473	−	13.5259i	−0.253182	−	1.76092i	−0.578846	−	0.815437i	$-0.696497\pi$
$59$	−1.94473	−	13.5259i	−0.253182	−	1.76092i	0.325664	−	0.945486i	$-0.394412\pi$
$60$		0			0
$61$	11.8135	−	3.46876i	1.51257	−	0.444130i	0.582904	−	0.812541i	$-0.301916\pi$
$61$	11.8135	−	3.46876i	1.51257	−	0.444130i	0.929663	+	0.368411i	$0.120098\pi$
$62$		0			0
$63$	11.6321	−	13.4242i	1.46551	−	1.69128i
$64$		0			0
$65$	−0.0432223	−	0.0498812i	−0.00536106	−	0.00618700i
$66$		0			0
$67$	2.90777	−	6.36713i	0.355241	−	0.777869i	−0.644669	−	0.764462i	$-0.723005\pi$
$67$	2.90777	−	6.36713i	0.355241	−	0.777869i	0.999910	−	0.0134075i	$-0.00426787\pi$
$68$		0			0
$69$	−4.50294	−	14.4500i	−0.542090	−	1.73957i
$70$		0			0
$71$	0.0848341	−	0.185761i	0.0100680	−	0.0220458i	−0.904531	−	0.426407i	$-0.859779\pi$
$71$	0.0848341	−	0.185761i	0.0100680	−	0.0220458i	0.914599	+	0.404362i	$0.132506\pi$
$72$		0			0
$73$	−0.450289	−	0.519661i	−0.0527024	−	0.0608218i	0.728786	−	0.684741i	$-0.240085\pi$
$73$	−0.450289	−	0.519661i	−0.0527024	−	0.0608218i	−0.781489	+	0.623919i	$0.785539\pi$
$74$		0			0
$75$	−10.3257	+	11.9165i	−1.19231	+	1.37600i
$76$		0			0
$77$	−10.9874	+	3.22620i	−1.25213	+	0.367659i
$78$		0			0
$79$	1.58382	+	11.0157i	0.178194	+	1.23936i	0.860939	+	0.508708i	$0.169877\pi$
$79$	1.58382	+	11.0157i	0.178194	+	1.23936i	−0.682746	+	0.730656i	$0.739214\pi$
$80$		0			0
$81$	7.71050	+	16.8836i	0.856722	+	1.87596i
$82$		0			0
$83$	−5.83837	−	3.75209i	−0.640845	−	0.411846i	0.179466	−	0.983764i	$-0.442563\pi$
$83$	−5.83837	−	3.75209i	−0.640845	−	0.411846i	−0.820311	+	0.571918i	$0.806199\pi$
$84$		0			0
$85$	0.0311864	−	0.216906i	0.00338264	−	0.0235267i
$86$		0			0
$87$	−13.4296	+	8.63067i	−1.43980	+	0.925304i
$88$		0			0
$89$	−6.64101	−	1.94998i	−0.703946	−	0.206697i	−0.0898809	−	0.995953i	$-0.528649\pi$
$89$	−6.64101	−	1.94998i	−0.703946	−	0.206697i	−0.614065	+	0.789255i	$0.710467\pi$
$90$		0			0
$91$	2.74060			0.287293
$92$		0			0
$93$	−30.1971			−3.13129
$94$		0			0
$95$	−0.335740	−	0.0985821i	−0.0344462	−	0.0101143i
$96$		0			0
$97$	5.80879	−	3.73308i	0.589793	−	0.379037i	−0.211438	−	0.977391i	$-0.567815\pi$
$97$	5.80879	−	3.73308i	0.589793	−	0.379037i	0.801232	+	0.598354i	$0.204178\pi$
$98$		0			0
$99$	4.44433	−	30.9110i	0.446672	−	3.10667i
$100$		0			0
$101$	3.10208	+	1.99359i	0.308669	+	0.198370i	0.685799	−	0.727791i	$-0.259453\pi$
$101$	3.10208	+	1.99359i	0.308669	+	0.198370i	−0.377130	+	0.926160i	$0.623089\pi$
$102$		0			0
$103$	5.24589	+	11.4869i	0.516893	+	1.13184i	0.970602	+	0.240688i	$0.0773731\pi$
$103$	5.24589	+	11.4869i	0.516893	+	1.13184i	−0.453709	+	0.891150i	$0.649900\pi$
$104$		0			0
$105$	0.0704529	+	0.490011i	0.00687550	+	0.0478201i
$106$		0			0
$107$	−17.0674	+	5.01143i	−1.64996	+	0.484473i	−0.968838	−	0.247694i	$-0.920327\pi$
$107$	−17.0674	+	5.01143i	−1.64996	+	0.484473i	−0.681125	+	0.732167i	$0.738509\pi$
$108$		0			0
$109$	−0.483724	+	0.558247i	−0.0463324	+	0.0534704i	−0.778443	−	0.627716i	$-0.783990\pi$
$109$	−0.483724	+	0.558247i	−0.0463324	+	0.0534704i	0.732110	+	0.681186i	$0.238536\pi$
$110$		0			0
$111$	−13.2356	−	15.2747i	−1.25627	−	1.44981i
$112$		0			0
$113$	1.72981	−	3.78775i	0.162726	−	0.356321i	−0.810651	−	0.585530i	$-0.800887\pi$
$113$	1.72981	−	3.78775i	0.162726	−	0.356321i	0.973377	+	0.229209i	$0.0736138\pi$
$114$		0			0
$115$	0.270113	+	0.118014i	0.0251881	+	0.0110049i
$116$		0			0
$117$	−3.10477	+	6.79850i	−0.287036	+	0.628522i
$118$		0			0
$119$	5.95868	+	6.87669i	0.546232	+	0.630385i
$120$		0			0
$121$	−5.98059	+	6.90197i	−0.543690	+	0.627452i
$122$		0			0
$123$	−1.26630	+	0.371819i	−0.114178	+	0.0335258i
$124$		0			0
$125$	−0.0874385	−	0.608148i	−0.00782074	−	0.0543944i
$126$		0			0
$127$	−1.12818	−	2.47036i	−0.100109	−	0.219209i	0.852950	−	0.521993i	$-0.174811\pi$
$127$	−1.12818	−	2.47036i	−0.100109	−	0.219209i	−0.953059	+	0.302784i	$0.902084\pi$
$128$		0			0
$129$	−3.58587	−	2.30450i	−0.315718	−	0.202900i
$130$		0			0
$131$	1.35720	−	9.43954i	0.118579	−	0.824737i	−0.840543	−	0.541745i	$-0.817764\pi$
$131$	1.35720	−	9.43954i	0.118579	−	0.824737i	0.959122	−	0.282992i	$-0.0913270\pi$
$132$		0			0
$133$	12.2229	−	7.85519i	1.05986	−	0.681132i
$134$		0			0
$135$	−0.737014	−	0.216407i	−0.0634321	−	0.0186253i
$136$		0			0
$137$	7.21517			0.616433			0.308217	−	0.951316i	$-0.400268\pi$
$137$	7.21517			0.616433			0.308217	+	0.951316i	$0.400268\pi$
$138$		0			0
$139$	3.94176			0.334336			0.167168	−	0.985928i	$-0.446538\pi$
$139$	3.94176			0.334336			0.167168	+	0.985928i	$0.446538\pi$
$140$		0			0
$141$	28.1230	+	8.25766i	2.36838	+	0.695420i
$142$		0			0
$143$	4.05340	−	2.60496i	0.338962	−	0.217838i
$144$		0			0
$145$	0.0442460	−	0.307738i	0.00367443	−	0.0255562i
$146$		0			0
$147$	1.29192	+	0.830267i	0.106556	+	0.0684792i
$148$		0			0
$149$	−2.43878	−	5.34019i	−0.199793	−	0.437486i	0.783043	−	0.621968i	$-0.213667\pi$
$149$	−2.43878	−	5.34019i	−0.199793	−	0.437486i	−0.982836	+	0.184482i	$0.940939\pi$
$150$		0			0
$151$	2.34008	+	16.2756i	0.190433	+	1.32449i	0.830864	+	0.556476i	$0.187847\pi$
$151$	2.34008	+	16.2756i	0.190433	+	1.32449i	−0.640430	+	0.768016i	$0.721244\pi$
$152$		0			0
$153$	−23.8092	+	6.99102i	−1.92486	+	0.565190i
$154$		0			0
$155$	0.385125	−	0.444458i	0.0309340	−	0.0356997i
$156$		0			0
$157$	−1.44761	−	1.67063i	−0.115532	−	0.133331i	0.695037	−	0.718973i	$-0.255388\pi$
$157$	−1.44761	−	1.67063i	−0.115532	−	0.133331i	−0.810570	+	0.585642i	$0.800842\pi$
$158$		0			0
$159$	3.65233	−	7.99750i	0.289649	−	0.634243i
$160$		0			0
$161$	−11.0482	+	5.26736i	−0.870721	+	0.415126i
$162$		0			0
$163$	−1.92738	+	4.22037i	−0.150964	+	0.330565i	−0.969972	−	0.243217i	$-0.921797\pi$
$163$	−1.92738	+	4.22037i	−0.150964	+	0.330565i	0.819008	+	0.573782i	$0.194524\pi$
$164$		0			0
$165$	0.569960	+	0.657769i	0.0443713	+	0.0512072i
$166$		0			0
$167$	−9.99096	+	11.5302i	−0.773124	+	0.892233i	−0.996593	−	0.0824784i	$-0.973716\pi$
$167$	−9.99096	+	11.5302i	−0.773124	+	0.892233i	0.223469	+	0.974711i	$0.428262\pi$
$168$		0			0
$169$	11.3670	−	3.33764i	0.874383	−	0.256742i
$170$		0			0
$171$	5.63897	+	39.2199i	0.431223	+	2.99922i
$172$		0			0
$173$	5.50802	+	12.0609i	0.418767	+	0.916972i	0.995018	+	0.0996988i	$0.0317879\pi$
$173$	5.50802	+	12.0609i	0.418767	+	0.916972i	−0.576251	+	0.817273i	$0.695485\pi$
$174$		0			0
$175$	10.7269	+	6.89373i	0.810874	+	0.521117i
$176$		0			0
$177$	6.13745	−	42.6869i	0.461319	−	3.20854i
$178$		0			0
$179$	9.74995	−	6.26591i	0.728746	−	0.468336i	−0.122924	−	0.992416i	$-0.539227\pi$
$179$	9.74995	−	6.26591i	0.728746	−	0.468336i	0.851669	+	0.524080i	$0.175591\pi$
$180$		0			0
$181$	−13.0605	−	3.83491i	−0.970779	−	0.285046i	−0.242366	−	0.970185i	$-0.577923\pi$
$181$	−13.0605	−	3.83491i	−0.970779	−	0.285046i	−0.728413	+	0.685139i	$0.759742\pi$
$182$		0			0
$183$	38.8567			2.87237
$184$		0			0
$185$	0.393626			0.0289400
$186$		0			0
$187$	15.3493	+	4.50697i	1.12245	+	0.329583i
$188$		0			0
$189$	26.8317	−	17.2437i	1.95172	−	1.25429i
$190$		0			0
$191$	−0.984280	+	6.84582i	−0.0712200	+	0.495346i	0.922724	+	0.385461i	$0.125957\pi$
$191$	−0.984280	+	6.84582i	−0.0712200	+	0.495346i	−0.993944	+	0.109885i	$0.964952\pi$
$192$		0			0
$193$	18.7624	+	12.0579i	1.35055	+	0.867944i	0.997703	−	0.0677378i	$-0.0215781\pi$
$193$	18.7624	+	12.0579i	1.35055	+	0.867944i	0.352844	+	0.935682i	$0.385214\pi$
$194$		0			0
$195$	−0.0865305	−	0.189475i	−0.00619658	−	0.0135686i
$196$		0			0
$197$	0.458095	+	3.18612i	0.0326379	+	0.227002i	0.999611	−	0.0278752i	$-0.00887409\pi$
$197$	0.458095	+	3.18612i	0.0326379	+	0.227002i	−0.966973	+	0.254877i	$0.917965\pi$
$198$		0			0
$199$	13.2456	−	3.88926i	0.938957	−	0.275703i	0.223775	−	0.974641i	$-0.428162\pi$
$199$	13.2456	−	3.88926i	0.938957	−	0.275703i	0.715182	+	0.698938i	$0.246344\pi$
$200$		0			0
$201$	14.4662	−	16.6949i	1.02037	−	1.17757i
$202$		0			0
$203$	8.45395	+	9.75638i	0.593351	+	0.684763i
$204$		0			0
$205$	0.0106774	−	0.0233802i	0.000745741	−	0.00163294i
$206$		0			0
$207$	−0.550245	−	33.3742i	−0.0382447	−	2.31967i
$208$		0			0
$209$	10.6115	−	23.2359i	0.734013	−	1.60726i
$210$		0			0
$211$	−14.5678	−	16.8121i	−1.00289	−	1.15739i	−0.987517	−	0.157511i	$-0.949653\pi$
$211$	−14.5678	−	16.8121i	−1.00289	−	1.15739i	−0.0153697	−	0.999882i	$-0.504893\pi$
$212$		0			0
$213$	0.422052	−	0.487074i	0.0289185	−	0.0333738i
$214$		0			0
$215$	0.0796522	−	0.0233880i	0.00543223	−	0.00159505i
$216$		0			0
$217$	3.47528	+	24.1711i	0.235917	+	1.64084i
$218$		0			0
$219$	−0.901474	−	1.97395i	−0.0609160	−	0.133387i
$220$		0			0
$221$	−3.22082	−	2.06990i	−0.216656	−	0.139236i
$222$		0			0
$223$	1.30961	−	9.10856i	0.0876982	−	0.609954i	−0.897817	−	0.440368i	$-0.854848\pi$
$223$	1.30961	−	9.10856i	0.0876982	−	0.609954i	0.985515	−	0.169586i	$-0.0542431\pi$
$224$		0			0
$225$	−29.2533	+	18.7999i	−1.95022	+	1.25333i
$226$		0			0
$227$	11.2595	+	3.30610i	0.747322	+	0.219433i	0.633152	−	0.774028i	$-0.281761\pi$
$227$	11.2595	+	3.30610i	0.747322	+	0.219433i	0.114170	+	0.993461i	$0.463579\pi$
$228$		0			0
$229$	12.6272			0.834428			0.417214	−	0.908808i	$-0.363007\pi$
$229$	12.6272			0.834428			0.417214	+	0.908808i	$0.363007\pi$
$230$		0			0
$231$	−36.1395			−2.37780
$232$		0			0
$233$	−0.0578678	−	0.0169915i	−0.00379105	−	0.00111315i	0.279836	−	0.960048i	$-0.409720\pi$
$233$	−0.0578678	−	0.0169915i	−0.00379105	−	0.00111315i	−0.283628	+	0.958935i	$0.591538\pi$
$234$		0			0
$235$	−0.480214	+	0.308615i	−0.0313257	+	0.0201318i
$236$		0			0
$237$	−4.99843	+	34.7649i	−0.324683	+	2.25822i
$238$		0			0
$239$	−16.5319	−	10.6244i	−1.06936	−	0.687237i	−0.117286	−	0.993098i	$-0.537419\pi$
$239$	−16.5319	−	10.6244i	−1.06936	−	0.687237i	−0.952076	+	0.305861i	$0.901056\pi$
$240$		0			0
$241$	8.20254	+	17.9611i	0.528372	+	1.15697i	0.966171	+	0.257901i	$0.0830307\pi$
$241$	8.20254	+	17.9611i	0.528372	+	1.15697i	−0.437800	+	0.899073i	$0.644242\pi$
$242$		0			0
$243$	3.00074	+	20.8706i	0.192498	+	1.33885i
$244$		0			0
$245$	−0.0286972	+	0.00842625i	−0.00183339	+	0.000538333i
$246$		0			0
$247$	−4.00346	+	4.62024i	−0.254734	+	0.293979i
$248$		0			0
$249$	−14.3431	−	16.5528i	−0.908955	−	1.04899i
$250$		0			0
$251$	0.809805	−	1.77323i	0.0511145	−	0.111925i	−0.882352	−	0.470591i	$-0.844041\pi$
$251$	0.809805	−	1.77323i	0.0511145	−	0.111925i	0.933466	+	0.358666i	$0.116768\pi$
$252$		0			0
$253$	−11.3338	+	18.2919i	−0.712552	+	1.15000i
$254$		0			0
$255$	0.287293	−	0.629084i	0.0179910	−	0.0393948i
$256$		0			0
$257$	5.20343	+	6.00508i	0.324581	+	0.374587i	0.894465	−	0.447139i	$-0.147557\pi$
$257$	5.20343	+	6.00508i	0.324581	+	0.374587i	−0.569883	+	0.821726i	$0.693012\pi$
$258$		0			0
$259$	−10.7034	+	12.3523i	−0.665074	+	0.767536i
$260$		0			0
$261$	−33.7796	+	9.91858i	−2.09090	+	0.613945i
$262$		0			0
$263$	−1.61279	−	11.2172i	−0.0994491	−	0.691684i	−0.977162	−	0.212496i	$-0.931841\pi$
$263$	−1.61279	−	11.2172i	−0.0994491	−	0.691684i	0.877713	−	0.479187i	$-0.159068\pi$
$264$		0			0
$265$	0.0711310	+	0.155755i	0.00436954	+	0.00956796i
$266$		0			0
$267$	−18.3759	−	11.8095i	−1.12458	−	0.722727i
$268$		0			0
$269$	1.73792	−	12.0875i	0.105963	−	0.736986i	−0.865691	−	0.500578i	$-0.833121\pi$
$269$	1.73792	−	12.0875i	0.105963	−	0.736986i	0.971654	−	0.236408i	$-0.0759702\pi$
$270$		0			0
$271$	−1.85018	+	1.18904i	−0.112391	+	0.0722291i	−0.595629	−	0.803260i	$-0.703097\pi$
$271$	−1.85018	+	1.18904i	−0.112391	+	0.0722291i	0.483238	+	0.875489i	$0.339461\pi$
$272$		0			0
$273$	8.29881	+	2.43675i	0.502267	+	0.147479i
$274$		0			0
$275$	22.4177			1.35184
$276$		0			0
$277$	4.15114			0.249418			0.124709	−	0.992193i	$-0.460200\pi$
$277$	4.15114			0.249418			0.124709	+	0.992193i	$0.460200\pi$
$278$		0			0
$279$	−63.8975	−	18.7620i	−3.82544	−	1.12325i
$280$		0			0
$281$	−18.1187	+	11.6442i	−1.08087	+	0.694635i	−0.954759	−	0.297381i	$-0.903887\pi$
$281$	−18.1187	+	11.6442i	−1.08087	+	0.694635i	−0.126114	+	0.992016i	$0.540251\pi$
$282$		0			0
$283$	0.762039	−	5.30010i	0.0452985	−	0.315058i	−0.954556	−	0.298030i	$-0.903670\pi$
$283$	0.762039	−	5.30010i	0.0452985	−	0.315058i	0.999855	−	0.0170282i	$-0.00542050\pi$
$284$		0			0
$285$	−0.929002	−	0.597033i	−0.0550293	−	0.0353652i
$286$		0			0
$287$	0.443355	+	0.970812i	0.0261704	+	0.0573052i
$288$		0			0
$289$	0.610323	+	4.24489i	0.0359013	+	0.249699i
$290$		0			0
$291$	20.9088	−	6.13938i	1.22570	−	0.359897i
$292$		0			0
$293$	6.47453	−	7.47200i	0.378246	−	0.436519i	−0.534424	−	0.845217i	$-0.679471\pi$
$293$	6.47453	−	7.47200i	0.378246	−	0.436519i	0.912670	+	0.408697i	$0.134017\pi$
$294$		0			0
$295$	0.550016	+	0.634752i	0.0320232	+	0.0369567i
$296$		0			0
$297$	23.2943	−	51.0074i	1.35167	−	2.95975i
$298$		0			0
$299$	3.83597	−	3.43622i	0.221840	−	0.198722i
$300$		0			0
$301$	−1.43194	+	3.13551i	−0.0825356	+	0.180728i
$302$		0			0
$303$	7.62086	+	8.79494i	0.437807	+	0.505256i
$304$		0			0
$305$	−0.495568	+	0.571916i	−0.0283762	+	0.0327478i
$306$		0			0
$307$	16.9798	−	4.98572i	0.969088	−	0.284550i	0.241375	−	0.970432i	$-0.422402\pi$
$307$	16.9798	−	4.98572i	0.969088	−	0.284550i	0.727713	+	0.685882i	$0.240583\pi$
$308$		0			0
$309$	5.67173	+	39.4478i	0.322654	+	2.24410i
$310$		0			0
$311$	5.30284	+	11.6116i	0.300696	+	0.658433i	0.998314	−	0.0580366i	$-0.0184840\pi$
$311$	5.30284	+	11.6116i	0.300696	+	0.658433i	−0.697618	+	0.716470i	$0.745757\pi$
$312$		0			0
$313$	−18.8692	−	12.1265i	−1.06655	−	0.685430i	−0.115137	−	0.993350i	$-0.536731\pi$
$313$	−18.8692	−	12.1265i	−1.06655	−	0.685430i	−0.951412	+	0.307920i	$0.900367\pi$
$314$		0			0
$315$	−0.155373	+	1.08064i	−0.00875429	+	0.0608874i
$316$		0			0
$317$	24.8020	−	15.9393i	1.39302	−	0.895240i	0.393312	−	0.919405i	$-0.371329\pi$
$317$	24.8020	−	15.9393i	1.39302	−	0.895240i	0.999708	+	0.0241654i	$0.00769283\pi$
$318$		0			0
$319$	21.7770	+	6.39432i	1.21928	+	0.358013i
$320$		0			0
$321$	−56.1375			−3.13329
$322$		0			0
$323$	−20.2975			−1.12938
$324$		0			0
$325$	−5.14785	−	1.51154i	−0.285551	−	0.0838454i
$326$		0			0
$327$	−1.96112	+	1.26033i	−0.108450	+	0.0696967i
$328$		0			0
$329$	3.37322	−	23.4613i	0.185972	−	1.29346i
$330$		0			0
$331$	−6.28968	−	4.04213i	−0.345712	−	0.222176i	0.356249	−	0.934391i	$-0.384056\pi$
$331$	−6.28968	−	4.04213i	−0.345712	−	0.222176i	−0.701961	+	0.712215i	$0.747692\pi$
$332$		0			0
$333$	−18.5163	−	40.5451i	−1.01469	−	2.22186i
$334$		0			0
$335$	0.0612273	+	0.425845i	0.00334521	+	0.0232664i
$336$		0			0
$337$	−26.1881	+	7.68953i	−1.42656	+	0.418875i	−0.901718	−	0.432325i	$-0.857693\pi$
$337$	−26.1881	+	7.68953i	−1.42656	+	0.418875i	−0.524841	+	0.851200i	$0.675875\pi$
$338$		0			0
$339$	8.60582	−	9.93165i	0.467404	−	0.539413i
$340$		0			0
$341$	28.1148	+	32.4462i	1.52250	+	1.75706i
$342$		0			0
$343$	7.93727	−	17.3802i	0.428572	−	0.938442i
$344$		0			0
$345$	0.712998	+	0.597525i	0.0383865	+	0.0321697i
$346$		0			0
$347$	−5.26738	+	11.5340i	−0.282768	+	0.619175i	−0.996712	−	0.0810277i	$-0.974180\pi$
$347$	−5.26738	+	11.5340i	−0.282768	+	0.619175i	0.713944	+	0.700203i	$0.246907\pi$
$348$		0			0
$349$	9.27885	+	10.7084i	0.496686	+	0.573206i	0.947640	−	0.319341i	$-0.103462\pi$
$349$	9.27885	+	10.7084i	0.496686	+	0.573206i	−0.450954	+	0.892547i	$0.648916\pi$
$350$		0			0
$351$	−8.78836	+	10.1423i	−0.469088	+	0.541357i
$352$		0			0
$353$	20.3308	−	5.96965i	1.08210	−	0.317732i	0.308380	−	0.951263i	$-0.400213\pi$
$353$	20.3308	−	5.96965i	1.08210	−	0.317732i	0.773717	+	0.633531i	$0.218395\pi$
$354$		0			0
$355$	0.00178630	+	0.0124240i	9.48072e−5	+	0.000659398i
$356$		0			0
$357$	11.9292	+	26.1213i	0.631361	+	1.38249i
$358$		0			0
$359$	−3.44281	−	2.21256i	−0.181705	−	0.116774i	0.446626	−	0.894721i	$-0.352625\pi$
$359$	−3.44281	−	2.21256i	−0.181705	−	0.116774i	−0.628331	+	0.777946i	$0.716262\pi$
$360$		0			0
$361$	−1.90855	+	13.2742i	−0.100450	+	0.698644i
$362$		0			0
$363$	−24.2466	+	15.5823i	−1.27262	+	0.817861i
$364$		0			0
$365$	0.0405510	+	0.0119068i	0.00212253	+	0.000623232i
$366$		0			0
$367$	−28.9755			−1.51251			−0.756254	−	0.654278i	$-0.772972\pi$
$367$	−28.9755			−1.51251			−0.756254	+	0.654278i	$0.772972\pi$
$368$		0			0
$369$	−2.91052			−0.151516
$370$		0			0
$371$	−6.82190	−	2.00309i	−0.354175	−	0.103995i
$372$		0			0
$373$	18.1828	−	11.6854i	0.941470	−	0.605046i	0.0226590	−	0.999743i	$-0.492787\pi$
$373$	18.1828	−	11.6854i	0.941470	−	0.605046i	0.918811	+	0.394697i	$0.129150\pi$
$374$		0			0
$375$	0.275951	−	1.91928i	0.0142500	−	0.0991111i
$376$		0			0
$377$	−4.56958	−	2.93669i	−0.235345	−	0.151247i
$378$		0			0
$379$	0.200334	+	0.438670i	0.0102905	+	0.0225330i	0.914707	−	0.404117i	$-0.132421\pi$
$379$	0.200334	+	0.438670i	0.0102905	+	0.0225330i	−0.904417	+	0.426650i	$0.859694\pi$
$380$		0			0
$381$	−1.21976	−	8.48359i	−0.0624900	−	0.434627i
$382$		0			0
$383$	−0.810827	+	0.238080i	−0.0414313	+	0.0121653i	−0.302383	−	0.953187i	$-0.597782\pi$
$383$	−0.810827	+	0.238080i	−0.0414313	+	0.0121653i	0.260951	+	0.965352i	$0.415964\pi$
$384$		0			0
$385$	0.460913	−	0.531923i	0.0234903	−	0.0271093i
$386$		0			0
$387$	−6.15593	−	7.10432i	−0.312923	−	0.361133i
$388$		0			0
$389$	−16.1593	+	35.3840i	−0.819311	+	1.79404i	−0.258706	+	0.965956i	$0.583296\pi$
$389$	−16.1593	+	35.3840i	−0.819311	+	1.79404i	−0.560604	+	0.828084i	$0.689431\pi$
$390$		0			0
$391$	16.9624	+	2.15406i	0.857826	+	0.108935i
$392$		0			0
$393$	12.5027	−	27.3772i	0.630679	−	1.38099i
$394$		0			0
$395$	−0.447941	−	0.516952i	−0.0225384	−	0.0260107i
$396$		0			0
$397$	8.34220	−	9.62741i	0.418683	−	0.483186i	−0.506752	−	0.862092i	$-0.669154\pi$
$397$	8.34220	−	9.62741i	0.418683	−	0.483186i	0.925435	+	0.378906i	$0.123700\pi$
$398$		0			0
$399$	43.9965	−	12.9185i	2.20258	−	0.646736i
$400$		0			0
$401$	−2.75216	−	19.1417i	−0.137436	−	0.955892i	−0.935502	−	0.353321i	$-0.885052\pi$
$401$	−2.75216	−	19.1417i	−0.137436	−	0.955892i	0.798066	−	0.602570i	$-0.205857\pi$
$402$		0			0
$403$	−4.26835	−	9.34639i	−0.212622	−	0.465577i
$404$		0			0
$405$	−0.959719	−	0.616774i	−0.0476888	−	0.0306477i
$406$		0			0
$407$	−4.08948	+	28.4429i	−0.202708	+	1.40986i
$408$		0			0
$409$	−15.4490	+	9.92850i	−0.763906	+	0.490933i	−0.863657	−	0.504080i	$-0.831832\pi$
$409$	−15.4490	+	9.92850i	−0.763906	+	0.490933i	0.0997509	+	0.995012i	$0.468195\pi$
$410$		0			0
$411$	21.8482	+	6.41522i	1.07769	+	0.316440i
$412$		0			0
$413$	−34.8749			−1.71608
$414$		0			0
$415$	0.426562			0.0209391
$416$		0			0
$417$	11.9360	+	3.50474i	0.584510	+	0.171628i
$418$		0			0
$419$	−10.3021	+	6.62079i	−0.503293	+	0.323447i	−0.767532	−	0.641011i	$-0.778515\pi$
$419$	−10.3021	+	6.62079i	−0.503293	+	0.323447i	0.264239	+	0.964457i	$0.414879\pi$
$420$		0			0
$421$	5.24940	−	36.5103i	0.255840	−	1.77941i	−0.305872	−	0.952073i	$-0.598948\pi$
$421$	5.24940	−	36.5103i	0.255840	−	1.77941i	0.561712	−	0.827333i	$-0.310143\pi$
$422$		0			0
$423$	54.3781	+	34.9467i	2.64395	+	1.69917i
$424$		0			0
$425$	−7.39983	−	16.2034i	−0.358944	−	0.785979i
$426$		0			0
$427$	−4.47189	−	31.1027i	−0.216410	−	1.50517i
$428$		0			0
$429$	14.5902	−	4.28408i	0.704423	−	0.206837i
$430$		0			0
$431$	−19.0512	+	21.9862i	−0.917663	+	1.05904i	0.0803961	+	0.996763i	$0.474381\pi$
$431$	−19.0512	+	21.9862i	−0.917663	+	1.05904i	−0.998059	+	0.0622764i	$0.980164\pi$
$432$		0			0
$433$	1.23582	+	1.42622i	0.0593899	+	0.0685396i	0.784667	−	0.619917i	$-0.212834\pi$
$433$	1.23582	+	1.42622i	0.0593899	+	0.0685396i	−0.725277	+	0.688457i	$0.758288\pi$
$434$		0			0
$435$	0.407600	−	0.892520i	0.0195429	−	0.0427931i
$436$		0			0
$437$	7.25921	−	26.3202i	0.347255	−	1.25906i
$438$		0			0
$439$	−1.18642	+	2.59790i	−0.0566247	+	0.123991i	−0.935829	−	0.352454i	$-0.885347\pi$
$439$	−1.18642	+	2.59790i	−0.0566247	+	0.123991i	0.879205	+	0.476444i	$0.158075\pi$
$440$		0			0
$441$	2.21786	+	2.55955i	0.105613	+	0.121883i
$442$		0			0
$443$	−5.42079	+	6.25592i	−0.257549	+	0.297228i	−0.869768	−	0.493461i	$-0.835732\pi$
$443$	−5.42079	+	6.25592i	−0.257549	+	0.297228i	0.612219	+	0.790688i	$0.290277\pi$
$444$		0			0
$445$	0.408179	−	0.119852i	0.0193496	−	0.00568154i
$446$		0			0
$447$	−2.63676	−	18.3390i	−0.124714	−	0.867407i
$448$		0			0
$449$	−3.35754	−	7.35198i	−0.158452	−	0.346961i	0.813710	−	0.581271i	$-0.197444\pi$
$449$	−3.35754	−	7.35198i	−0.158452	−	0.346961i	−0.972162	+	0.234310i	$0.924717\pi$
$450$		0			0
$451$	1.57849	+	1.01444i	0.0743284	+	0.0477679i
$452$		0			0
$453$	−7.38516	+	51.3649i	−0.346985	+	2.41333i
$454$		0			0
$455$	−0.141706	+	0.0910691i	−0.00664329	+	0.00426939i
$456$		0			0
$457$	9.35005	+	2.74542i	0.437377	+	0.128425i	0.493006	−	0.870026i	$-0.335898\pi$
$457$	9.35005	+	2.74542i	0.437377	+	0.128425i	−0.0556288	+	0.998452i	$0.517716\pi$
$458$		0			0
$459$	−44.5569			−2.07974
$460$		0			0
$461$	−30.5887			−1.42466			−0.712329	−	0.701845i	$-0.752360\pi$
$461$	−30.5887			−1.42466			−0.712329	+	0.701845i	$0.752360\pi$
$462$		0			0
$463$	20.2268	+	5.93912i	0.940019	+	0.276014i	0.715625	−	0.698484i	$-0.246142\pi$
$463$	20.2268	+	5.93912i	0.940019	+	0.276014i	0.224393	+	0.974499i	$0.427960\pi$
$464$		0			0
$465$	1.56138	−	1.00344i	0.0724072	−	0.0465333i
$466$		0			0
$467$	−1.59190	+	11.0719i	−0.0736645	+	0.512348i	0.919265	+	0.393640i	$0.128784\pi$
$467$	−1.59190	+	11.0719i	−0.0736645	+	0.512348i	−0.992929	+	0.118708i	$0.962125\pi$
$468$		0			0
$469$	−15.0283	−	9.65808i	−0.693941	−	0.445969i
$470$		0			0
$471$	−2.89810	−	6.34596i	−0.133538	−	0.292406i
$472$		0			0
$473$	0.862461	+	5.99855i	0.0396560	+	0.275813i
$474$		0			0
$475$	−27.2915	+	8.01352i	−1.25222	+	0.367685i
$476$		0			0
$477$	12.6974	−	14.6536i	0.581374	−	0.670941i
$478$		0			0
$479$	19.2072	+	22.1663i	0.877599	+	1.01280i	0.999794	+	0.0202973i	$0.00646129\pi$
$479$	19.2072	+	22.1663i	0.877599	+	1.01280i	−0.122195	+	0.992506i	$0.538993\pi$
$480$		0			0
$481$	2.85688	−	6.25569i	0.130262	−	0.285235i
$482$		0			0
$483$	−38.1384	+	6.12680i	−1.73536	+	0.278779i
$484$		0			0
$485$	−0.176302	+	0.386048i	−0.00800547	+	0.0175295i
$486$		0			0
$487$	−26.7384	−	30.8577i	−1.21163	−	1.39830i	−0.892780	−	0.450492i	$-0.851249\pi$
$487$	−26.7384	−	30.8577i	−1.21163	−	1.39830i	−0.318851	−	0.947805i	$-0.603297\pi$
$488$		0			0
$489$	−9.58876	+	11.0660i	−0.433619	+	0.500423i
$490$		0			0
$491$	4.84177	−	1.42167i	0.218506	−	0.0641591i	−0.170647	−	0.985332i	$-0.554586\pi$
$491$	4.84177	−	1.42167i	0.218506	−	0.0641591i	0.389153	+	0.921173i	$0.372768\pi$
$492$		0			0
$493$	−2.56658	−	17.8510i	−0.115593	−	0.803967i
$494$		0			0
$495$	0.797360	+	1.74598i	0.0358387	+	0.0784758i
$496$		0			0
$497$	−0.438449	−	0.281774i	−0.0196671	−	0.0126393i
$498$		0			0
$499$	−0.776347	+	5.39961i	−0.0347540	+	0.241720i	−0.999792	−	0.0203901i	$-0.993509\pi$
$499$	−0.776347	+	5.39961i	−0.0347540	+	0.241720i	0.965038	+	0.262110i	$0.0844183\pi$
$500$		0			0
$501$	−40.5055	+	26.0313i	−1.80965	+	1.16299i
$502$		0			0
$503$	9.02265	+	2.64929i	0.402300	+	0.118126i	0.476622	−	0.879108i	$-0.341861\pi$
$503$	9.02265	+	2.64929i	0.402300	+	0.118126i	−0.0743219	+	0.997234i	$0.523679\pi$
$504$		0			0
$505$	−0.226644			−0.0100855
$506$		0			0
$507$	37.3879			1.66046
$508$		0			0
$509$	−4.17186	−	1.22497i	−0.184914	−	0.0542957i	0.187964	−	0.982176i	$-0.439811\pi$
$509$	−4.17186	−	1.22497i	−0.184914	−	0.0542957i	−0.372879	+	0.927880i	$0.621629\pi$
$510$		0			0
$511$	−1.47629	+	0.948757i	−0.0653074	+	0.0419705i
$512$		0			0
$513$	−10.1254	+	70.4236i	−0.447047	+	3.10928i
$514$		0			0
$515$	−0.652951	−	0.419626i	−0.0287725	−	0.0184909i
$516$		0			0
$517$	−17.3111	−	37.9060i	−0.761340	−	1.66710i
$518$		0			0
$519$	5.95514	+	41.4189i	0.261402	+	1.81809i
$520$		0			0
$521$	37.3204	−	10.9582i	1.63503	−	0.480090i	0.670033	−	0.742332i	$-0.266280\pi$
$521$	37.3204	−	10.9582i	1.63503	−	0.480090i	0.965002	+	0.262242i	$0.0844619\pi$
$522$		0			0
$523$	18.2387	−	21.0485i	0.797521	−	0.920388i	−0.200721	−	0.979648i	$-0.564329\pi$
$523$	18.2387	−	21.0485i	0.797521	−	0.920388i	0.998243	+	0.0592599i	$0.0188741\pi$
$524$		0			0
$525$	26.3526	+	30.4125i	1.15012	+	1.32731i
$526$		0			0
$527$	14.1715	−	31.0313i	0.617321	−	1.35174i
$528$		0			0
$529$	−8.85967	+	21.2251i	−0.385203	+	0.922832i
$530$		0			0
$531$	39.5091	−	86.5129i	1.71455	−	3.75434i
$532$		0			0
$533$	−0.294074	−	0.339379i	−0.0127378	−	0.0147002i
$534$		0			0
$535$	0.715962	−	0.826265i	0.0309538	−	0.0357225i
$536$		0			0
$537$	35.0950	−	10.3048i	1.51446	−	0.444686i
$538$		0			0
$539$	−0.310728	−	2.16116i	−0.0133840	−	0.0930878i
$540$		0			0
$541$	6.68149	+	14.6304i	0.287260	+	0.629011i	0.997162	−	0.0752894i	$-0.0239881\pi$
$541$	6.68149	+	14.6304i	0.287260	+	0.629011i	−0.709902	+	0.704300i	$0.751261\pi$
$542$		0			0
$543$	−36.1387	−	23.2250i	−1.55086	−	0.996678i
$544$		0			0
$545$	0.00646124	−	0.0449389i	0.000276769	−	0.00192497i
$546$		0			0
$547$	−27.4208	+	17.6223i	−1.17243	+	0.753475i	−0.973979	−	0.226636i	$-0.927227\pi$
$547$	−27.4208	+	17.6223i	−1.17243	+	0.753475i	−0.198450	+	0.980111i	$0.563591\pi$
$548$		0			0
$549$	82.2214	+	24.1424i	3.50913	+	1.03037i
$550$		0			0
$551$	−28.7973			−1.22681
$552$		0			0
$553$	28.4027			1.20780
$554$		0			0
$555$	1.19194	+	0.349985i	0.0505950	+	0.0148560i
$556$		0			0
$557$	9.34215	−	6.00384i	0.395840	−	0.254391i	−0.327545	−	0.944835i	$-0.606221\pi$
$557$	9.34215	−	6.00384i	0.395840	−	0.254391i	0.723385	+	0.690445i	$0.242585\pi$
$558$		0			0
$559$	0.206410	−	1.43561i	0.00873022	−	0.0607200i
$560$		0			0
$561$	42.4720	+	27.2951i	1.79317	+	1.15240i
$562$		0			0
$563$	−16.8552	−	36.9078i	−0.710363	−	1.55548i	−0.826936	−	0.562295i	$-0.809918\pi$
$563$	−16.8552	−	36.9078i	−0.710363	−	1.55548i	0.116574	−	0.993182i	$-0.462809\pi$
$564$		0			0
$565$	0.0364235	+	0.253331i	0.00153235	+	0.0106577i
$566$		0			0
$567$	45.4512	−	13.3457i	1.90877	−	0.560466i
$568$		0			0
$569$	−10.3313	+	11.9230i	−0.433111	+	0.499837i	−0.929786	−	0.368099i	$-0.880009\pi$
$569$	−10.3313	+	11.9230i	−0.433111	+	0.499837i	0.496675	+	0.867937i	$0.334554\pi$
$570$		0			0
$571$	9.06170	+	10.4578i	0.379220	+	0.437644i	0.912987	−	0.407988i	$-0.133769\pi$
$571$	9.06170	+	10.4578i	0.379220	+	0.437644i	−0.533767	+	0.845632i	$0.679224\pi$
$572$		0			0
$573$	−9.06733	+	19.8547i	−0.378793	+	0.829441i
$574$		0			0
$575$	23.6577	−	3.80052i	0.986595	−	0.158493i
$576$		0			0
$577$	1.39572	−	3.05620i	0.0581045	−	0.127231i	−0.878353	−	0.478013i	$-0.841357\pi$
$577$	1.39572	−	3.05620i	0.0581045	−	0.127231i	0.936457	+	0.350782i	$0.114084\pi$
$578$		0			0
$579$	46.0934	+	53.1946i	1.91558	+	2.21069i
$580$		0			0
$581$	−11.5989	+	13.3859i	−0.481204	+	0.555339i
$582$		0			0
$583$	−11.9937	+	3.52166i	−0.496727	+	0.145852i
$584$		0			0
$585$	−0.0653754	−	0.454696i	−0.00270294	−	0.0187994i
$586$		0			0
$587$	8.73991	+	19.1377i	0.360735	+	0.789899i	0.999785	+	0.0207339i	$0.00660028\pi$
$587$	8.73991	+	19.1377i	0.360735	+	0.789899i	−0.639050	+	0.769165i	$0.720672\pi$
$588$		0			0
$589$	−45.8255	−	29.4503i	−1.88821	−	1.21348i
$590$		0			0
$591$	−1.44572	+	10.0552i	−0.0594690	+	0.413616i
$592$		0			0
$593$	5.66372	−	3.63985i	0.232581	−	0.149471i	−0.419160	−	0.907912i	$-0.637675\pi$
$593$	5.66372	−	3.63985i	0.232581	−	0.149471i	0.651741	+	0.758442i	$0.274039\pi$
$594$		0			0
$595$	−0.536611	−	0.157563i	−0.0219989	−	0.00645947i
$596$		0			0
$597$	43.5671			1.78308
$598$		0			0
$599$	−3.17780			−0.129842			−0.0649208	−	0.997890i	$-0.520679\pi$
$599$	−3.17780			−0.129842			−0.0649208	+	0.997890i	$0.520679\pi$
$600$		0			0
$601$	−20.9804	−	6.16039i	−0.855807	−	0.251288i	−0.175739	−	0.984437i	$-0.556232\pi$
$601$	−20.9804	−	6.16039i	−0.855807	−	0.251288i	−0.680068	+	0.733149i	$0.738050\pi$
$602$		0			0
$603$	40.9837	−	26.3386i	1.66898	−	1.07259i
$604$		0			0
$605$	0.0798845	−	0.555609i	0.00324777	−	0.0225887i
$606$		0			0
$607$	−8.57225	−	5.50905i	−0.347937	−	0.223605i	0.354986	−	0.934872i	$-0.384486\pi$
$607$	−8.57225	−	5.50905i	−0.347937	−	0.223605i	−0.702923	+	0.711266i	$0.748122\pi$
$608$		0			0
$609$	16.9247	+	37.0599i	0.685824	+	1.50174i
$610$		0			0
$611$	1.41933	+	9.87166i	0.0574200	+	0.399365i
$612$		0			0
$613$	21.4619	−	6.30177i	0.866837	−	0.254526i	0.182067	−	0.983286i	$-0.441721\pi$
$613$	21.4619	−	6.30177i	0.866837	−	0.254526i	0.684769	+	0.728760i	$0.259903\pi$
$614$		0			0
$615$	0.0531202	−	0.0613040i	0.00214201	−	0.00247202i
$616$		0			0
$617$	−15.9184	−	18.3708i	−0.640852	−	0.739582i	0.338673	−	0.940904i	$-0.390022\pi$
$617$	−15.9184	−	18.3708i	−0.640852	−	0.739582i	−0.979525	+	0.201322i	$0.935476\pi$
$618$		0			0
$619$	−10.0949	+	22.1048i	−0.405748	+	0.888465i	0.590906	+	0.806740i	$0.298770\pi$
$619$	−10.0949	+	22.1048i	−0.405748	+	0.888465i	−0.996655	+	0.0817251i	$0.973957\pi$
$620$		0			0
$621$	15.9354	−	57.7778i	0.639464	−	2.31854i
$622$		0			0
$623$	−7.33801	+	16.0680i	−0.293991	+	0.643751i
$624$		0			0
$625$	−16.3344	−	18.8509i	−0.653377	−	0.754037i
$626$		0			0
$627$	52.7925	−	60.9257i	2.10833	−	2.43314i
$628$		0			0
$629$	21.9082	−	6.43283i	0.873537	−	0.256494i
$630$		0			0
$631$	2.87783	+	20.0158i	0.114565	+	0.796814i	0.963383	+	0.268130i	$0.0864056\pi$
$631$	2.87783	+	20.0158i	0.114565	+	0.796814i	−0.848818	+	0.528685i	$0.822685\pi$
$632$		0			0
$633$	−29.1645	−	63.8614i	−1.15919	−	2.53826i
$634$		0			0
$635$	0.140423	+	0.0902443i	0.00557251	+	0.00358124i
$636$		0			0
$637$	−0.0743657	+	0.517225i	−0.00294647	+	0.0204932i
$638$		0			0
$639$	1.19570	−	0.768428i	0.0473010	−	0.0303985i
$640$		0			0
$641$	2.40673	+	0.706679i	0.0950601	+	0.0279122i	0.328917	−	0.944359i	$-0.393316\pi$
$641$	2.40673	+	0.706679i	0.0950601	+	0.0279122i	−0.233857	+	0.972271i	$0.575135\pi$
$642$		0			0
$643$	−33.7473			−1.33086			−0.665432	−	0.746458i	$-0.731753\pi$
$643$	−33.7473			−1.33086			−0.665432	+	0.746458i	$0.731753\pi$
$644$		0			0
$645$	0.261990			0.0103158
$646$		0			0
$647$	42.5650	+	12.4982i	1.67340	+	0.491356i	0.974599	−	0.223957i	$-0.0718976\pi$
$647$	42.5650	+	12.4982i	1.67340	+	0.491356i	0.698804	+	0.715313i	$0.253716\pi$
$648$		0			0
$649$	−51.5806	+	33.1488i	−2.02472	+	1.30121i
$650$		0			0
$651$	−10.9678	+	76.2825i	−0.429861	+	2.98975i
$652$		0			0
$653$	16.9729	+	10.9078i	0.664203	+	0.426857i	0.828831	−	0.559499i	$-0.189006\pi$
$653$	16.9729	+	10.9078i	0.664203	+	0.426857i	−0.164629	+	0.986356i	$0.552643\pi$
$654$		0			0
$655$	0.243497	+	0.533183i	0.00951420	+	0.0208332i
$656$		0			0
$657$	−0.681080	−	4.73702i	−0.0265715	−	0.184809i
$658$		0			0
$659$	8.79171	−	2.58148i	0.342476	−	0.100560i	−0.105971	−	0.994369i	$-0.533795\pi$
$659$	8.79171	−	2.58148i	0.342476	−	0.100560i	0.448448	+	0.893809i	$0.351977\pi$
$660$		0			0
$661$	−28.4587	+	32.8431i	−1.10691	+	1.27745i	−0.149490	+	0.988763i	$0.547763\pi$
$661$	−28.4587	+	32.8431i	−1.10691	+	1.27745i	−0.957424	+	0.288684i	$0.906782\pi$
$662$		0			0
$663$	−7.91256	−	9.13158i	−0.307298	−	0.354641i
$664$		0			0
$665$	−0.370977	+	0.812326i	−0.0143859	+	0.0315007i
$666$		0			0
$667$	24.0656	+	3.05610i	0.931825	+	0.118333i
$668$		0			0
$669$	12.0643	−	26.4172i	0.466434	−	1.02135i
$670$		0			0
$671$	−36.1774	−	41.7509i	−1.39661	−	1.61178i
$672$		0			0
$673$	18.1635	−	20.9618i	0.700152	−	0.808019i	−0.288621	−	0.957443i	$-0.593197\pi$
$673$	18.1635	−	20.9618i	0.700152	−	0.808019i	0.988773	+	0.149425i	$0.0477422\pi$
$674$		0			0
$675$	−59.9102	+	17.5912i	−2.30594	+	0.677086i
$676$		0			0
$677$	1.55160	+	10.7916i	0.0596329	+	0.414756i	0.997670	+	0.0682216i	$0.0217325\pi$
$677$	1.55160	+	10.7916i	0.0596329	+	0.414756i	−0.938037	+	0.346534i	$0.887358\pi$
$678$		0			0
$679$	−7.32056	−	16.0298i	−0.280937	−	0.615167i
$680$		0			0
$681$	31.1555	+	20.0224i	1.19388	+	0.767260i
$682$		0			0
$683$	−1.38924	+	9.66239i	−0.0531579	+	0.369721i	0.945827	+	0.324671i	$0.105254\pi$
$683$	−1.38924	+	9.66239i	−0.0531579	+	0.369721i	−0.998985	+	0.0450497i	$0.985655\pi$
$684$		0			0
$685$	−0.373070	+	0.239757i	−0.0142543	+	0.00916066i
$686$		0			0
$687$	38.2364	+	11.2272i	1.45881	+	0.428345i
$688$		0			0
$689$	2.99159			0.113970
$690$		0			0
$691$	−5.10327			−0.194138			−0.0970688	−	0.995278i	$-0.530947\pi$
$691$	−5.10327			−0.194138			−0.0970688	+	0.995278i	$0.530947\pi$
$692$		0			0
$693$	−76.4718	−	22.4541i	−2.90492	−	0.852962i
$694$		0			0
$695$	−0.203814	+	0.130983i	−0.00773110	+	0.00496848i
$696$		0			0
$697$	0.212185	−	1.47578i	0.00803706	−	0.0558990i
$698$		0			0
$699$	−0.160122	−	0.102904i	−0.00605636	−	0.00389219i
$700$		0			0
$701$	8.02189	+	17.5655i	0.302983	+	0.663440i	0.998482	−	0.0550876i	$-0.0175438\pi$
$701$	8.02189	+	17.5655i	0.302983	+	0.663440i	−0.695499	+	0.718527i	$0.744817\pi$
$702$		0			0
$703$	−5.18874	−	36.0885i	−0.195697	−	1.36110i
$704$		0			0
$705$	−1.72854	+	0.507544i	−0.0651004	+	0.0191152i
$706$		0			0
$707$	6.16282	−	7.11227i	0.231777	−	0.267484i
$708$		0			0
$709$	−29.8476	−	34.4459i	−1.12095	−	1.29364i	−0.951344	−	0.308132i	$-0.900296\pi$
$709$	−29.8476	−	34.4459i	−1.12095	−	1.29364i	−0.169606	−	0.985512i	$-0.554249\pi$
$710$		0			0
$711$	−32.1768	+	70.4574i	−1.20673	+	2.64236i
$712$		0			0
$713$	35.1706	+	29.4745i	1.31715	+	1.10383i
$714$		0			0
$715$	−0.123024	+	0.269386i	−0.00460085	+	0.0100745i
$716$		0			0
$717$	−40.6139	−	46.8709i	−1.51675	−	1.75043i
$718$		0			0
$719$	10.3857	−	11.9858i	0.387322	−	0.446994i	−0.528285	−	0.849067i	$-0.677165\pi$
$719$	10.3857	−	11.9858i	0.387322	−	0.446994i	0.915607	+	0.402073i	$0.131710\pi$
$720$		0			0
$721$	30.9231	−	9.07983i	1.15163	−	0.338151i
$722$		0			0
$723$	8.86839	+	61.6810i	0.329819	+	2.29394i
$724$		0			0
$725$	−10.4986	−	22.9887i	−0.389908	−	0.853779i
$726$		0			0
$727$	−34.7662	−	22.3429i	−1.28941	−	0.828653i	−0.297391	−	0.954756i	$-0.596117\pi$
$727$	−34.7662	−	22.3429i	−1.28941	−	0.828653i	−0.992017	+	0.126103i	$0.959753\pi$
$728$		0			0
$729$	−1.54566	+	10.7503i	−0.0572465	+	0.398158i
$730$		0			0
$731$	4.05101	−	2.60343i	0.149832	−	0.0962913i
$732$		0			0
$733$	11.9753	+	3.51627i	0.442318	+	0.129876i	0.495306	−	0.868719i	$-0.335056\pi$
$733$	11.9753	+	3.51627i	0.442318	+	0.129876i	−0.0529872	+	0.998595i	$0.516874\pi$
$734$		0			0
$735$	−0.0943899			−0.00348162
$736$		0			0
$737$	−31.4071			−1.15690
$738$		0			0
$739$	10.9514	+	3.21563i	0.402855	+	0.118289i	0.476882	−	0.878967i	$-0.341767\pi$
$739$	10.9514	+	3.21563i	0.402855	+	0.118289i	−0.0740267	+	0.997256i	$0.523585\pi$
$740$		0			0
$741$	−16.2309	+	10.4309i	−0.596256	+	0.383190i
$742$		0			0
$743$	5.24501	−	36.4798i	0.192421	−	1.33832i	−0.633155	−	0.774025i	$-0.718241\pi$
$743$	5.24501	−	36.4798i	0.192421	−	1.33832i	0.825576	−	0.564291i	$-0.190850\pi$
$744$		0			0
$745$	0.303553	+	0.195082i	0.0111213	+	0.00714725i
$746$		0			0
$747$	−20.0656	−	43.9376i	−0.734163	−	1.60759i
$748$		0			0
$749$	6.46068	+	44.9350i	0.236068	+	1.64189i
$750$		0			0
$751$	−49.7931	+	14.6206i	−1.81698	+	0.533512i	−0.999121	−	0.0419129i	$-0.986655\pi$
$751$	−49.7931	+	14.6206i	−1.81698	+	0.533512i	−0.817854	+	0.575425i	$0.804837\pi$
$752$		0			0
$753$	4.02880	−	4.64948i	0.146818	−	0.169437i
$754$		0			0
$755$	−0.661831	−	0.763793i	−0.0240865	−	0.0277973i
$756$		0			0
$757$	7.29758	−	15.9795i	0.265235	−	0.580783i	−0.729417	−	0.684070i	$-0.760208\pi$
$757$	7.29758	−	15.9795i	0.265235	−	0.580783i	0.994652	+	0.103286i	$0.0329357\pi$
$758$		0			0
$759$	−50.5839	+	45.3125i	−1.83608	+	1.64474i
$760$		0			0
$761$	−14.3653	+	31.4556i	−0.520741	+	1.14026i	0.448417	+	0.893825i	$0.351988\pi$
$761$	−14.3653	+	31.4556i	−0.520741	+	1.14026i	−0.969158	+	0.246440i	$0.920739\pi$
$762$		0			0
$763$	1.23453	+	1.42472i	0.0446929	+	0.0515784i
$764$		0			0
$765$	0.998778	−	1.15265i	0.0361109	−	0.0416742i
$766$		0			0
$767$	14.0797	−	4.13417i	0.508388	−	0.149276i
$768$		0			0
$769$	2.13152	+	14.8251i	0.0768646	+	0.534605i	0.991478	+	0.130275i	$0.0415861\pi$
$769$	2.13152	+	14.8251i	0.0768646	+	0.534605i	−0.914613	+	0.404330i	$0.867505\pi$
$770$		0			0
$771$	10.4172	+	22.8105i	0.375167	+	0.821501i
$772$		0			0
$773$	−14.2952	−	9.18696i	−0.514162	−	0.330432i	0.257697	−	0.966226i	$-0.417036\pi$
$773$	−14.2952	−	9.18696i	−0.514162	−	0.330432i	−0.771859	+	0.635794i	$0.780673\pi$
$774$		0			0
$775$	6.80343	−	47.3189i	0.244387	−	1.69975i
$776$		0			0
$777$	−43.3936	+	27.8874i	−1.55674	+	1.00046i
$778$		0			0
$779$	−2.28429	−	0.670729i	−0.0818433	−	0.0240314i
$780$		0			0
$781$	−0.916302			−0.0327879
$782$		0			0
$783$	−63.2156			−2.25914
$784$		0			0
$785$	0.130365	+	0.0382787i	0.00465294	+	0.00136623i
$786$		0			0
$787$	2.25029	−	1.44617i	0.0802141	−	0.0515505i	−0.499919	−	0.866072i	$-0.666637\pi$
$787$	2.25029	−	1.44617i	0.0802141	−	0.0515505i	0.580133	+	0.814522i	$0.303001\pi$
$788$		0			0
$789$	5.08987	−	35.4009i	0.181204	−	1.26030i
$790$		0			0
$791$	−8.94017	−	5.74550i	−0.317876	−	0.204286i
$792$		0			0
$793$	5.49240	+	12.0267i	0.195041	+	0.427080i
$794$		0			0
$795$	0.0769051	+	0.534887i	0.00272754	+	0.0189705i
$796$		0			0
$797$	−22.3818	+	6.57189i	−0.792804	+	0.232788i	−0.652967	−	0.757386i	$-0.726476\pi$
$797$	−22.3818	+	6.57189i	−0.792804	+	0.232788i	−0.139837	+	0.990175i	$0.544658\pi$
$798$		0			0
$799$	−21.6839	+	25.0246i	−0.767123	+	0.885307i
$800$		0			0
$801$	−31.5462	−	36.4063i	−1.11463	−	1.28635i
$802$		0			0
$803$	−1.28167	+	2.80646i	−0.0452290	+	0.0990377i
$804$		0			0
$805$	0.396230	−	0.639484i	0.0139653	−	0.0225388i
$806$		0			0
$807$	16.0099	−	35.0568i	0.563576	−	1.23406i
$808$		0			0
$809$	5.13980	+	5.93164i	0.180706	+	0.208545i	0.838874	−	0.544325i	$-0.183214\pi$
$809$	5.13980	+	5.93164i	0.180706	+	0.208545i	−0.658169	+	0.752870i	$0.728669\pi$
$810$		0			0
$811$	2.17749	−	2.51296i	0.0764621	−	0.0882420i	−0.716230	−	0.697865i	$-0.754134\pi$
$811$	2.17749	−	2.51296i	0.0764621	−	0.0882420i	0.792692	+	0.609623i	$0.208679\pi$
$812$		0			0
$813$	−6.65975	+	1.95548i	−0.233568	+	0.0685817i
$814$		0			0
$815$	−0.0405837	−	0.282266i	−0.00142159	−	0.00988735i
$816$		0			0
$817$	−3.19423	−	6.99438i	−0.111752	−	0.244702i
$818$		0			0
$819$	16.0464	+	10.3124i	0.560707	+	0.360345i
$820$		0			0
$821$	−0.211143	+	1.46853i	−0.00736892	+	0.0512520i	−0.993174	−	0.116641i	$-0.962787\pi$
$821$	−0.211143	+	1.46853i	−0.00736892	+	0.0512520i	0.985805	+	0.167893i	$0.0536964\pi$
$822$		0			0
$823$	26.7973	−	17.2216i	0.934095	−	0.600306i	0.0173803	−	0.999849i	$-0.494467\pi$
$823$	26.7973	−	17.2216i	0.934095	−	0.600306i	0.916715	+	0.399543i	$0.130831\pi$
$824$		0			0
$825$	67.8832	+	19.9323i	2.36339	+	0.693953i
$826$		0			0
$827$	9.87348			0.343335			0.171667	−	0.985155i	$-0.445085\pi$
$827$	9.87348			0.343335			0.171667	+	0.985155i	$0.445085\pi$
$828$		0			0
$829$	−46.1733			−1.60366			−0.801832	−	0.597549i	$-0.796141\pi$
$829$	−46.1733			−1.60366			−0.801832	+	0.597549i	$0.796141\pi$
$830$		0			0
$831$	12.5701	+	3.69090i	0.436050	+	0.128036i
$832$		0			0
$833$	−1.45950	+	0.937966i	−0.0505688	+	0.0324986i
$834$		0			0
$835$	0.133452	−	0.928180i	0.00461830	−	0.0321210i
$836$		0			0
$837$	−100.596	−	64.6491i	−3.47710	−	2.23460i
$838$		0			0
$839$	−13.2903	−	29.1016i	−0.458831	−	1.00470i	−0.987752	−	0.156029i	$-0.950131\pi$
$839$	−13.2903	−	29.1016i	−0.458831	−	1.00470i	0.528922	−	0.848671i	$-0.322597\pi$
$840$		0			0
$841$	0.485765	+	3.37857i	0.0167505	+	0.116502i
$842$		0			0
$843$	−65.2186	+	19.1499i	−2.24625	+	0.659557i
$844$		0			0
$845$	−0.476836	+	0.550298i	−0.0164036	+	0.0189308i
$846$		0			0
$847$	15.2633	+	17.6148i	0.524453	+	0.605251i
$848$		0			0
$849$	7.02001	−	15.3717i	0.240926	−	0.527555i
$850$		0			0
$851$	0.506312	+	30.7095i	0.0173561	+	1.05271i
$852$		0			0
$853$	18.3724	−	40.2300i	0.629060	−	1.37745i	−0.279683	−	0.960093i	$-0.590229\pi$
$853$	18.3724	−	40.2300i	0.629060	−	1.37745i	0.908743	−	0.417357i	$-0.137044\pi$
$854$		0			0
$855$	−1.59483	−	1.84054i	−0.0545422	−	0.0629450i
$856$		0			0
$857$	−31.9374	+	36.8578i	−1.09096	+	1.25904i	−0.127315	+	0.991862i	$0.540636\pi$
$857$	−31.9374	+	36.8578i	−1.09096	+	1.25904i	−0.963648	+	0.267175i	$0.913910\pi$
$858$		0			0
$859$	−17.7082	+	5.19960i	−0.604197	+	0.177408i	−0.569502	−	0.821990i	$-0.692864\pi$
$859$	−17.7082	+	5.19960i	−0.604197	+	0.177408i	−0.0346944	+	0.999398i	$0.511046\pi$
$860$		0			0
$861$	0.479345	+	3.33392i	0.0163360	+	0.113620i
$862$		0			0
$863$	6.33616	+	13.8743i	0.215685	+	0.472285i	0.986289	−	0.165030i	$-0.0527722\pi$
$863$	6.33616	+	13.8743i	0.215685	+	0.472285i	−0.770603	+	0.637315i	$0.780045\pi$
$864$		0			0
$865$	−0.685578	−	0.440594i	−0.0233104	−	0.0149807i
$866$		0			0
$867$	−1.92614	+	13.3966i	−0.0654151	+	0.454972i
$868$		0			0
$869$	42.0080	−	26.9969i	1.42503	−	0.915808i
$870$		0			0
$871$	7.21210	+	2.11766i	0.244373	+	0.0717543i
$872$		0			0
$873$	48.0579			1.62651
$874$		0			0
$875$	−1.56804			−0.0530093
$876$		0			0
$877$	28.8209	+	8.46259i	0.973214	+	0.285761i	0.729420	−	0.684066i	$-0.239790\pi$
$877$	28.8209	+	8.46259i	0.973214	+	0.285761i	0.243793	+	0.969827i	$0.421608\pi$
$878$		0			0
$879$	26.2491	−	16.8693i	0.885360	−	0.568987i
$880$		0			0
$881$	1.64841	−	11.4649i	0.0555363	−	0.386264i	−0.943029	−	0.332711i	$-0.892037\pi$
$881$	1.64841	−	11.4649i	0.0555363	−	0.386264i	0.998565	−	0.0535523i	$-0.0170544\pi$
$882$		0			0
$883$	27.7971	+	17.8641i	0.935447	+	0.601175i	0.917100	−	0.398657i	$-0.130523\pi$
$883$	27.7971	+	17.8641i	0.935447	+	0.601175i	0.0183464	+	0.999832i	$0.494160\pi$
$884$		0			0
$885$	1.10113	+	2.41113i	0.0370139	+	0.0810492i
$886$		0			0
$887$	−5.56370	−	38.6964i	−0.186811	−	1.29930i	−0.840200	−	0.542276i	$-0.817563\pi$
$887$	−5.56370	−	38.6964i	−0.186811	−	1.29930i	0.653390	−	0.757022i	$-0.273346\pi$
$888$		0			0
$889$	−6.65028	+	1.95270i	−0.223043	+	0.0654914i
$890$		0			0
$891$	54.5380	−	62.9402i	1.82709	−	2.10858i
$892$		0			0
$893$	34.6246	+	39.9589i	1.15867	+	1.33717i
$894$		0			0
$895$	−0.295920	+	0.647975i	−0.00989152	+	0.0216594i
$896$		0			0
$897$	14.6710	−	6.99455i	0.489849	−	0.233541i
$898$		0			0
$899$	20.1060	−	44.0260i	0.670572	−	1.46835i
$900$		0			0
$901$	6.50439	+	7.50647i	0.216693	+	0.250077i
$902$		0			0
$903$	−7.12393	+	8.22146i	−0.237070	+	0.273593i
$904$		0			0
$905$	0.802743	−	0.235706i	0.0266841	−	0.00783515i
$906$		0			0
$907$	−5.00834	−	34.8337i	−0.166299	−	1.15664i	−0.886452	−	0.462820i	$-0.846837\pi$
$907$	−5.00834	−	34.8337i	−0.166299	−	1.15664i	0.720153	−	0.693815i	$-0.244072\pi$
$908$		0			0
$909$	10.6614	+	23.3452i	0.353617	+	0.774312i
$910$		0			0
$911$	10.2157	+	6.56526i	0.338463	+	0.217517i	0.698820	−	0.715298i	$-0.253709\pi$
$911$	10.2157	+	6.56526i	0.338463	+	0.217517i	−0.360357	+	0.932814i	$0.617345\pi$
$912$		0			0
$913$	−4.43165	+	30.8228i	−0.146666	+	1.02009i
$914$		0			0
$915$	−2.00914	+	1.29119i	−0.0664201	+	0.0426856i
$916$		0			0
$917$	−23.3528	−	6.85701i	−0.771178	−	0.226438i
$918$		0			0
$919$	26.6760			0.879958			0.439979	−	0.898008i	$-0.354986\pi$
$919$	26.6760			0.879958			0.439979	+	0.898008i	$0.354986\pi$
$920$		0			0
$921$	55.8494			1.84030
$922$		0			0
$923$	0.210413	+	0.0617828i	0.00692582	+	0.00203361i
$924$		0			0
$925$	26.9176	−	17.2989i	0.885044	−	0.568784i
$926$		0			0
$927$	−12.5081	+	86.9961i	−0.410821	+	2.85733i
$928$		0			0
$929$	12.2048	+	7.84358i	0.400428	+	0.257340i	0.725320	−	0.688412i	$-0.241692\pi$
$929$	12.2048	+	7.84358i	0.400428	+	0.257340i	−0.324892	+	0.945751i	$0.605328\pi$
$930$		0			0
$931$	1.15082	+	2.51994i	0.0377166	+	0.0825878i
$932$		0			0
$933$	5.73330	+	39.8760i	0.187700	+	1.30548i
$934$		0			0
$935$	−0.943423	+	0.277014i	−0.0308532	+	0.00905933i
$936$		0			0
$937$	−32.5499	+	37.5646i	−1.06336	+	1.22718i	−0.0904710	+	0.995899i	$0.528837\pi$
$937$	−32.5499	+	37.5646i	−1.06336	+	1.22718i	−0.972887	+	0.231281i	$0.925708\pi$
$938$		0			0
$939$	−46.3558	−	53.4974i	−1.51276	−	1.74582i
$940$		0			0
$941$	−23.0411	+	50.4529i	−0.751118	+	1.64472i	0.0132291	+	0.999912i	$0.495789\pi$
$941$	−23.0411	+	50.4529i	−0.751118	+	1.64472i	−0.764347	+	0.644806i	$0.776938\pi$
$942$		0			0
$943$	1.83778	+	0.802942i	0.0598464	+	0.0261474i
$944$		0			0
$945$	−0.814366	+	1.78321i	−0.0264913	+	0.0580079i
$946$		0			0
$947$	31.5812	+	36.4466i	1.02625	+	1.18436i	0.982681	+	0.185306i	$0.0593275\pi$
$947$	31.5812	+	36.4466i	1.02625	+	1.18436i	0.0435693	+	0.999050i	$0.486127\pi$
$948$		0			0
$949$	0.483541	−	0.558036i	0.0156964	−	0.0181146i
$950$		0			0
$951$	89.2751	−	26.2135i	2.89494	−	0.850032i
$952$		0			0
$953$	7.89899	+	54.9387i	0.255874	+	1.77964i	0.561489	+	0.827484i	$0.310229\pi$
$953$	7.89899	+	54.9387i	0.255874	+	1.77964i	−0.305615	+	0.952155i	$0.598862\pi$
$954$		0			0
$955$	−0.176591	−	0.386680i	−0.00571434	−	0.0125127i
$956$		0			0
$957$	60.2577	+	38.7253i	1.94785	+	1.25181i
$958$		0			0
$959$	2.62060	−	18.2266i	0.0846235	−	0.588569i
$960$		0			0
$961$	50.9404	−	32.7374i	1.64324	−	1.05605i
$962$		0			0
$963$	−118.788	−	34.8792i	−3.82788	−	1.12397i
$964$		0			0
$965$	−1.37081			−0.0441280
$966$		0			0
$967$	−12.7805			−0.410995			−0.205497	−	0.978658i	$-0.565881\pi$
$967$	−12.7805			−0.410995			−0.205497	+	0.978658i	$0.565881\pi$
$968$		0			0
$969$	−61.4628	−	18.0471i	−1.97447	−	0.579757i
$970$		0			0
$971$	18.5359	−	11.9123i	0.594845	−	0.382284i	−0.208302	−	0.978065i	$-0.566794\pi$
$971$	18.5359	−	11.9123i	0.594845	−	0.382284i	0.803147	+	0.595781i	$0.203157\pi$
$972$		0			0
$973$	1.43167	−	9.95750i	0.0458973	−	0.319223i
$974$		0			0
$975$	−14.2442	−	9.15421i	−0.456180	−	0.293169i
$976$		0			0
$977$	−16.3877	−	35.8841i	−0.524289	−	1.14803i	−0.967790	−	0.251760i	$-0.918991\pi$
$977$	−16.3877	−	35.8841i	−0.524289	−	1.14803i	0.443500	−	0.896274i	$-0.353736\pi$
$978$		0			0
$979$	4.41970	+	30.7397i	0.141254	+	0.982445i
$980$		0			0
$981$	−4.93283	+	1.44841i	−0.157493	+	0.0462442i
$982$		0			0
$983$	−11.5923	+	13.3782i	−0.369736	+	0.426699i	−0.909878	−	0.414875i	$-0.863825\pi$
$983$	−11.5923	+	13.3782i	−0.369736	+	0.426699i	0.540142	+	0.841574i	$0.318371\pi$
$984$		0			0
$985$	−0.129560	−	0.149520i	−0.00412813	−	0.00476412i
$986$		0			0
$987$	31.0746	−	68.0439i	0.989116	−	2.16586i
$988$		0			0
$989$	1.92711	+	6.18412i	0.0612785	+	0.196644i
$990$		0			0
$991$	−4.29944	+	9.41447i	−0.136576	+	0.299060i	−0.965546	−	0.260234i	$-0.916200\pi$
$991$	−4.29944	+	9.41447i	−0.136576	+	0.299060i	0.828969	+	0.559294i	$0.188928\pi$
$992$		0			0
$993$	−15.4518	−	17.8323i	−0.490348	−	0.565892i
$994$		0			0
$995$	−0.555643	+	0.641247i	−0.0176151	+	0.0203289i
$996$		0			0
$997$	35.9080	−	10.5436i	1.13722	−	0.333918i	0.341678	−	0.939817i	$-0.389005\pi$
$997$	35.9080	−	10.5436i	1.13722	−	0.333918i	0.795541	+	0.605899i	$0.207187\pi$
$998$		0			0
$999$	−11.3903	−	79.2212i	−0.360373	−	2.50645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.305.3		30
4.3	odd	2		184.2.i.b.121.1	yes	30
23.2	even	11		8464.2.a.cg.1.1		15
23.4	even	11	inner	368.2.m.e.257.3		30
23.21	odd	22		8464.2.a.ch.1.1		15
92.27	odd	22		184.2.i.b.73.1	✓	30
92.67	even	22		4232.2.a.ba.1.15		15
92.71	odd	22		4232.2.a.bb.1.15		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.73.1	✓	30	92.27	odd	22
184.2.i.b.121.1	yes	30	4.3	odd	2
368.2.m.e.257.3		30	23.4	even	11	inner
368.2.m.e.305.3		30	1.1	even	1	trivial
4232.2.a.ba.1.15		15	92.67	even	22
4232.2.a.bb.1.15		15	92.71	odd	22
8464.2.a.cg.1.1		15	23.2	even	11
8464.2.a.ch.1.1		15	23.21	odd	22

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.02810 + 0.889130i) q^{3} +(-0.0517063 + 0.0332296i) q^{5} +(0.363207 - 2.52616i) q^{7} +(5.85508 + 3.76283i) q^{9} +O(q^{10})\)	\(q+(3.02810 + 0.889130i) q^{3} +(-0.0517063 + 0.0332296i) q^{5} +(0.363207 - 2.52616i) q^{7} +(5.85508 + 3.76283i) q^{9} +(-1.86394 - 4.08146i) q^{11} +(0.152824 + 1.06292i) q^{13} +(-0.186117 + 0.0546490i) q^{15} +(-2.33478 + 2.69448i) q^{17} +(3.72815 + 4.30251i) q^{19} +(3.34591 - 7.32652i) q^{21} +(-2.65898 - 3.99122i) q^{23} +(-2.07551 + 4.54472i) q^{25} +(8.18401 + 9.44485i) q^{27} +(-3.31250 + 3.82283i) q^{29} +(-9.18075 + 2.69571i) q^{31} +(-2.01525 - 14.0164i) q^{33} +(0.0651632 + 0.142688i) q^{35} +(-5.38759 - 3.46239i) q^{37} +(-0.482304 + 3.35450i) q^{39} +(-0.351797 + 0.226086i) q^{41} +(-1.29593 - 0.380519i) q^{43} -0.427782 q^{45} +9.28734 q^{47} +(0.466898 + 0.137094i) q^{49} +(-9.46571 + 6.08324i) q^{51} +(0.396470 - 2.75751i) q^{53} +(0.232003 + 0.149099i) q^{55} +(7.46371 + 16.3433i) q^{57} +(-1.94473 - 13.5259i) q^{59} +(11.8135 - 3.46876i) q^{61} +(11.6321 - 13.4242i) q^{63} +(-0.0432223 - 0.0498812i) q^{65} +(2.90777 - 6.36713i) q^{67} +(-4.50294 - 14.4500i) q^{69} +(0.0848341 - 0.185761i) q^{71} +(-0.450289 - 0.519661i) q^{73} +(-10.3257 + 11.9165i) q^{75} +(-10.9874 + 3.22620i) q^{77} +(1.58382 + 11.0157i) q^{79} +(7.71050 + 16.8836i) q^{81} +(-5.83837 - 3.75209i) q^{83} +(0.0311864 - 0.216906i) q^{85} +(-13.4296 + 8.63067i) q^{87} +(-6.64101 - 1.94998i) q^{89} +2.74060 q^{91} -30.1971 q^{93} +(-0.335740 - 0.0985821i) q^{95} +(5.80879 - 3.73308i) q^{97} +(4.44433 - 30.9110i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

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