LMFDB - Embedded newform 552.2.q.c.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	552.193
Dual form			552.2.q.c.409.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(-0.291779 - 2.02937i) q^{5} +(-2.05584 + 4.50166i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(-0.291779 - 2.02937i) q^{5} +(-2.05584 + 4.50166i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-4.13828 - 1.21511i) q^{11} +(2.04524 + 4.47845i) q^{13} +(1.34262 - 1.54946i) q^{15} +(4.19582 + 2.69649i) q^{17} +(-5.89881 + 3.79094i) q^{19} +(-4.74842 + 1.39426i) q^{21} +(2.12848 + 4.29762i) q^{23} +(0.764275 - 0.224411i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-2.36107 - 1.51737i) q^{29} +(3.39004 - 3.91232i) q^{31} +(-1.79168 - 3.92323i) q^{33} +(9.73537 + 2.85856i) q^{35} +(0.133689 - 0.929825i) q^{37} +(-2.04524 + 4.47845i) q^{39} +(-0.307002 - 2.13525i) q^{41} +(1.77961 + 2.05378i) q^{43} +2.05023 q^{45} +6.81196 q^{47} +(-11.4545 - 13.2192i) q^{49} +(0.709806 + 4.93681i) q^{51} +(-5.84418 + 12.7970i) q^{53} +(-1.25844 + 8.75262i) q^{55} +(-6.72790 - 1.97549i) q^{57} +(-3.18599 - 6.97635i) q^{59} +(3.39969 - 3.92346i) q^{61} +(-4.16327 - 2.67557i) q^{63} +(8.49165 - 5.45725i) q^{65} +(-12.9835 + 3.81231i) q^{67} +(-1.85407 + 4.42294i) q^{69} +(4.07648 - 1.19696i) q^{71} +(-2.84177 + 1.82629i) q^{73} +(0.670093 + 0.430642i) q^{75} +(13.9776 - 16.1311i) q^{77} +(0.713653 + 1.56268i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.391072 - 2.71996i) q^{83} +(4.24791 - 9.30162i) q^{85} +(-0.399422 - 2.77804i) q^{87} +(-0.255996 - 0.295435i) q^{89} -24.3652 q^{91} +5.17674 q^{93} +(9.41434 + 10.8647i) q^{95} +(-0.166249 - 1.15629i) q^{97} +(1.79168 - 3.92323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	−0.291779	−	2.02937i	−0.130487	−	0.907560i	−0.944920	−	0.327302i	$-0.893861\pi$
$5$	−0.291779	−	2.02937i	−0.130487	−	0.907560i	0.814433	−	0.580258i	$-0.197048\pi$
$6$		0			0
$7$	−2.05584	+	4.50166i	−0.777035	+	1.70147i	−0.0665216	+	0.997785i	$0.521190\pi$
$7$	−2.05584	+	4.50166i	−0.777035	+	1.70147i	−0.710513	+	0.703684i	$0.751537\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−4.13828	−	1.21511i	−1.24774	−	0.366369i	−0.409821	−	0.912166i	$-0.634409\pi$
$11$	−4.13828	−	1.21511i	−1.24774	−	0.366369i	−0.837917	+	0.545797i	$0.816227\pi$
$12$		0			0
$13$	2.04524	+	4.47845i	0.567247	+	1.24210i	0.948250	+	0.317524i	$0.102851\pi$
$13$	2.04524	+	4.47845i	0.567247	+	1.24210i	−0.381003	+	0.924574i	$0.624421\pi$
$14$		0			0
$15$	1.34262	−	1.54946i	0.346662	−	0.400070i
$16$		0			0
$17$	4.19582	+	2.69649i	1.01764	+	0.653994i	0.939358	−	0.342937i	$-0.111422\pi$
$17$	4.19582	+	2.69649i	1.01764	+	0.653994i	0.0782768	+	0.996932i	$0.475058\pi$
$18$		0			0
$19$	−5.89881	+	3.79094i	−1.35328	+	0.869700i	−0.997884	−	0.0650155i	$-0.979290\pi$
$19$	−5.89881	+	3.79094i	−1.35328	+	0.869700i	−0.355396	+	0.934716i	$0.615654\pi$
$20$		0			0
$21$	−4.74842	+	1.39426i	−1.03619	+	0.304253i
$22$		0			0
$23$	2.12848	+	4.29762i	0.443819	+	0.896116i
$23$	2.12848	+	4.29762i	0.443819	+	0.896116i
$24$		0			0
$25$	0.764275	−	0.224411i	0.152855	−	0.0448823i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	−2.36107	−	1.51737i	−0.438439	−	0.281768i	0.302742	−	0.953072i	$-0.402098\pi$
$29$	−2.36107	−	1.51737i	−0.438439	−	0.281768i	−0.741182	+	0.671305i	$0.765734\pi$
$30$		0			0
$31$	3.39004	−	3.91232i	0.608870	−	0.702673i	−0.364684	−	0.931131i	$-0.618823\pi$
$31$	3.39004	−	3.91232i	0.608870	−	0.702673i	0.973554	+	0.228458i	$0.0733684\pi$
$32$		0			0
$33$	−1.79168	−	3.92323i	−0.311891	−	0.682946i
$34$		0			0
$35$	9.73537	+	2.85856i	1.64558	+	0.483185i
$36$		0			0
$37$	0.133689	−	0.929825i	0.0219783	−	0.152862i	−0.975877	−	0.218321i	$-0.929942\pi$
$37$	0.133689	−	0.929825i	0.0219783	−	0.152862i	0.997855	+	0.0654588i	$0.0208511\pi$
$38$		0			0
$39$	−2.04524	+	4.47845i	−0.327500	+	0.717126i
$40$		0			0
$41$	−0.307002	−	2.13525i	−0.0479457	−	0.333470i	−0.999650	−	0.0264536i	$-0.991579\pi$
$41$	−0.307002	−	2.13525i	−0.0479457	−	0.333470i	0.951704	−	0.307016i	$-0.0993305\pi$
$42$		0			0
$43$	1.77961	+	2.05378i	0.271388	+	0.313198i	0.875041	−	0.484049i	$-0.160834\pi$
$43$	1.77961	+	2.05378i	0.271388	+	0.313198i	−0.603653	+	0.797247i	$0.706289\pi$
$44$		0			0
$45$	2.05023			0.305631
$46$		0			0
$47$	6.81196			0.993627			0.496813	−	0.867857i	$-0.334503\pi$
$47$	6.81196			0.993627			0.496813	+	0.867857i	$0.334503\pi$
$48$		0			0
$49$	−11.4545	−	13.2192i	−1.63635	−	1.88845i
$50$		0			0
$51$	0.709806	+	4.93681i	0.0993928	+	0.691292i
$52$		0			0
$53$	−5.84418	+	12.7970i	−0.802760	+	1.75780i	−0.166932	+	0.985968i	$0.553386\pi$
$53$	−5.84418	+	12.7970i	−0.802760	+	1.75780i	−0.635828	+	0.771830i	$0.719341\pi$
$54$		0			0
$55$	−1.25844	+	8.75262i	−0.169688	+	1.18020i
$56$		0			0
$57$	−6.72790	−	1.97549i	−0.891132	−	0.261660i
$58$		0			0
$59$	−3.18599	−	6.97635i	−0.414781	−	0.908243i	−0.995555	−	0.0941786i	$-0.969978\pi$
$59$	−3.18599	−	6.97635i	−0.414781	−	0.908243i	0.580775	−	0.814064i	$-0.302750\pi$
$60$		0			0
$61$	3.39969	−	3.92346i	0.435286	−	0.502347i	−0.495147	−	0.868809i	$-0.664886\pi$
$61$	3.39969	−	3.92346i	0.435286	−	0.502347i	0.930433	+	0.366462i	$0.119431\pi$
$62$		0			0
$63$	−4.16327	−	2.67557i	−0.524522	−	0.337090i
$64$		0			0
$65$	8.49165	−	5.45725i	1.05326	−	0.676889i
$66$		0			0
$67$	−12.9835	+	3.81231i	−1.58619	+	0.465748i	−0.951661	−	0.307150i	$-0.900625\pi$
$67$	−12.9835	+	3.81231i	−1.58619	+	0.465748i	−0.634531	+	0.772898i	$0.718807\pi$
$68$		0			0
$69$	−1.85407	+	4.42294i	−0.223204	+	0.532460i
$70$		0			0
$71$	4.07648	−	1.19696i	0.483789	−	0.142053i	−0.0307380	−	0.999527i	$-0.509786\pi$
$71$	4.07648	−	1.19696i	0.483789	−	0.142053i	0.514527	+	0.857474i	$0.327968\pi$
$72$		0			0
$73$	−2.84177	+	1.82629i	−0.332604	+	0.213752i	−0.696274	−	0.717776i	$-0.745160\pi$
$73$	−2.84177	+	1.82629i	−0.332604	+	0.213752i	0.363670	+	0.931528i	$0.381524\pi$
$74$		0			0
$75$	0.670093	+	0.430642i	0.0773756	+	0.0497263i
$76$		0			0
$77$	13.9776	−	16.1311i	1.59290	−	1.83831i
$78$		0			0
$79$	0.713653	+	1.56268i	0.0802923	+	0.175816i	0.945520	−	0.325563i	$-0.105554\pi$
$79$	0.713653	+	1.56268i	0.0802923	+	0.175816i	−0.865228	+	0.501378i	$0.832826\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	0.391072	−	2.71996i	0.0429257	−	0.298555i	−0.957037	−	0.289965i	$-0.906356\pi$
$83$	0.391072	−	2.71996i	0.0429257	−	0.298555i	0.999963	−	0.00859031i	$-0.00273441\pi$
$84$		0			0
$85$	4.24791	−	9.30162i	0.460750	−	1.00890i
$86$		0			0
$87$	−0.399422	−	2.77804i	−0.0428225	−	0.297837i
$88$		0			0
$89$	−0.255996	−	0.295435i	−0.0271355	−	0.0313160i	0.742020	−	0.670378i	$-0.233868\pi$
$89$	−0.255996	−	0.295435i	−0.0271355	−	0.0313160i	−0.769155	+	0.639062i	$0.779323\pi$
$90$		0			0
$91$	−24.3652			−2.55416
$92$		0			0
$93$	5.17674			0.536803
$94$		0			0
$95$	9.41434	+	10.8647i	0.965891	+	1.11470i
$96$		0			0
$97$	−0.166249	−	1.15629i	−0.0168800	−	0.117403i	0.979639	−	0.200766i	$-0.0643431\pi$
$97$	−0.166249	−	1.15629i	−0.0168800	−	0.117403i	−0.996519	+	0.0833628i	$0.973434\pi$
$98$		0			0
$99$	1.79168	−	3.92323i	0.180070	−	0.394299i
$100$		0			0
$101$	−0.190834	+	1.32728i	−0.0189886	+	0.132069i	−0.997111	−	0.0759633i	$-0.975797\pi$
$101$	−0.190834	+	1.32728i	−0.0189886	+	0.132069i	0.978122	+	0.208032i	$0.0667059\pi$
$102$		0			0
$103$	16.6381	+	4.88539i	1.63940	+	0.481372i	0.966137	−	0.258030i	$-0.0830733\pi$
$103$	16.6381	+	4.88539i	1.63940	+	0.481372i	0.673265	+	0.739402i	$0.264891\pi$
$104$		0			0
$105$	4.21495	+	9.22946i	0.411337	+	0.900703i
$106$		0			0
$107$	12.5625	−	14.4980i	1.21447	−	1.40157i	0.324289	−	0.945958i	$-0.394875\pi$
$107$	12.5625	−	14.4980i	1.21447	−	1.40157i	0.890178	−	0.455612i	$-0.150580\pi$
$108$		0			0
$109$	12.2231	+	7.85533i	1.17076	+	0.752404i	0.973666	−	0.227980i	$-0.0732120\pi$
$109$	12.2231	+	7.85533i	1.17076	+	0.752404i	0.197098	+	0.980384i	$0.436848\pi$
$110$		0			0
$111$	0.790262	−	0.507870i	0.0750083	−	0.0482049i
$112$		0			0
$113$	−0.250785	+	0.0736372i	−0.0235919	+	0.00692721i	−0.293507	−	0.955957i	$-0.594822\pi$
$113$	−0.250785	+	0.0736372i	−0.0235919	+	0.00692721i	0.269915	+	0.962884i	$0.413004\pi$
$114$		0			0
$115$	8.10040	−	5.57342i	0.755367	−	0.519724i
$116$		0			0
$117$	−4.72393	+	1.38707i	−0.436728	+	0.128235i
$118$		0			0
$119$	−20.7646	+	13.3446i	−1.90349	+	1.22330i
$120$		0			0
$121$	6.39507	+	4.10986i	0.581370	+	0.373624i
$122$		0			0
$123$	1.41267	−	1.63031i	0.127376	−	0.147000i
$124$		0			0
$125$	−4.93690	−	10.8103i	−0.441570	−	0.966903i
$126$		0			0
$127$	13.3906	+	3.93184i	1.18822	+	0.348894i	0.815339	−	0.578983i	$-0.196550\pi$
$127$	13.3906	+	3.93184i	1.18822	+	0.348894i	0.372885	+	0.927877i	$0.378369\pi$
$128$		0			0
$129$	−0.386746	+	2.68988i	−0.0340511	+	0.236831i
$130$		0			0
$131$	5.46580	−	11.9684i	0.477549	−	1.04569i	−0.505581	−	0.862779i	$-0.668722\pi$
$131$	5.46580	−	11.9684i	0.477549	−	1.04569i	0.983130	−	0.182908i	$-0.0585509\pi$
$132$		0			0
$133$	−4.93850	−	34.3480i	−0.428222	−	2.97835i
$134$		0			0
$135$	1.34262	+	1.54946i	0.115554	+	0.133357i
$136$		0			0
$137$	0.534803			0.0456913			0.0228457	−	0.999739i	$-0.492727\pi$
$137$	0.534803			0.0456913			0.0228457	+	0.999739i	$0.492727\pi$
$138$		0			0
$139$	11.9617			1.01458			0.507290	−	0.861776i	$-0.330647\pi$
$139$	11.9617			1.01458			0.507290	+	0.861776i	$0.330647\pi$
$140$		0			0
$141$	4.46089	+	5.14814i	0.375674	+	0.433551i
$142$		0			0
$143$	−3.02197	−	21.0182i	−0.252710	−	1.75763i
$144$		0			0
$145$	−2.39038	+	5.23420i	−0.198510	+	0.434677i
$146$		0			0
$147$	2.48929	−	17.3134i	0.205313	−	1.42799i
$148$		0			0
$149$	8.04356	+	2.36180i	0.658954	+	0.193486i	0.594079	−	0.804407i	$-0.297517\pi$
$149$	8.04356	+	2.36180i	0.658954	+	0.193486i	0.0648756	+	0.997893i	$0.479335\pi$
$150$		0			0
$151$	−5.76692	−	12.6278i	−0.469306	−	1.02764i	−0.985267	−	0.171024i	$-0.945292\pi$
$151$	−5.76692	−	12.6278i	−0.469306	−	1.02764i	0.515961	−	0.856612i	$-0.327435\pi$
$152$		0			0
$153$	−3.26617	+	3.76936i	−0.264054	+	0.304735i
$154$		0			0
$155$	−8.92867	−	5.73811i	−0.717168	−	0.460896i
$156$		0			0
$157$	−2.04416	+	1.31370i	−0.163142	+	0.104845i	−0.619664	−	0.784867i	$-0.712731\pi$
$157$	−2.04416	+	1.31370i	−0.163142	+	0.104845i	0.456522	+	0.889712i	$0.349095\pi$
$158$		0			0
$159$	−13.4984	+	3.96350i	−1.07050	+	0.314326i
$160$		0			0
$161$	−23.7223	+	0.746475i	−1.86958	+	0.0588305i
$162$		0			0
$163$	−16.9423	+	4.97472i	−1.32703	+	0.389650i	−0.867024	−	0.498267i	$-0.833970\pi$
$163$	−16.9423	+	4.97472i	−1.32703	+	0.389650i	−0.460003	+	0.887917i	$0.652152\pi$
$164$		0			0
$165$	−7.43889	+	4.78069i	−0.579117	+	0.372176i
$166$		0			0
$167$	5.63413	+	3.62084i	0.435982	+	0.280189i	0.740165	−	0.672425i	$-0.234747\pi$
$167$	5.63413	+	3.62084i	0.435982	+	0.280189i	−0.304183	+	0.952614i	$0.598384\pi$
$168$		0			0
$169$	−7.36031	+	8.49425i	−0.566177	+	0.653403i
$170$		0			0
$171$	−2.91286	−	6.37828i	−0.222752	−	0.487759i
$172$		0			0
$173$	−7.59638	−	2.23050i	−0.577542	−	0.169582i	−0.0201006	−	0.999798i	$-0.506399\pi$
$173$	−7.59638	−	2.23050i	−0.577542	−	0.169582i	−0.557441	+	0.830216i	$0.688217\pi$
$174$		0			0
$175$	−0.561003	+	3.90186i	−0.0424079	+	0.294953i
$176$		0			0
$177$	3.18599	−	6.97635i	0.239474	−	0.524374i
$178$		0			0
$179$	1.94882	+	13.5544i	0.145662	+	1.01310i	0.923215	+	0.384284i	$0.125552\pi$
$179$	1.94882	+	13.5544i	0.145662	+	1.01310i	−0.777553	+	0.628817i	$0.783539\pi$
$180$		0			0
$181$	7.96908	+	9.19681i	0.592337	+	0.683593i	0.970210	−	0.242264i	$-0.0778900\pi$
$181$	7.96908	+	9.19681i	0.592337	+	0.683593i	−0.377874	+	0.925857i	$0.623345\pi$
$182$		0			0
$183$	5.19148			0.383765
$184$		0			0
$185$	−1.92596			−0.141599
$186$		0			0
$187$	−14.0869	−	16.2572i	−1.03014	−	1.18884i
$188$		0			0
$189$	−0.704300	−	4.89851i	−0.0512303	−	0.356314i
$190$		0			0
$191$	5.04329	−	11.0433i	0.364920	−	0.799062i	−0.634734	−	0.772731i	$-0.718890\pi$
$191$	5.04329	−	11.0433i	0.364920	−	0.799062i	0.999653	−	0.0263315i	$-0.00838255\pi$
$192$		0			0
$193$	−1.14158	+	7.93985i	−0.0821726	+	0.571523i	0.906588	+	0.422017i	$0.138678\pi$
$193$	−1.14158	+	7.93985i	−0.0821726	+	0.571523i	−0.988761	+	0.149507i	$0.952231\pi$
$194$		0			0
$195$	9.68517	+	2.84382i	0.693569	+	0.203650i
$196$		0			0
$197$	0.624804	+	1.36813i	0.0445154	+	0.0974752i	0.930583	−	0.366081i	$-0.119301\pi$
$197$	0.624804	+	1.36813i	0.0445154	+	0.0974752i	−0.886068	+	0.463556i	$0.846573\pi$
$198$		0			0
$199$	−17.3823	+	20.0602i	−1.23220	+	1.42203i	−0.359942	+	0.932975i	$0.617204\pi$
$199$	−17.3823	+	20.0602i	−1.23220	+	1.42203i	−0.872253	+	0.489055i	$0.837342\pi$
$200$		0			0
$201$	−11.3836	−	7.31577i	−0.802935	−	0.516015i
$202$		0			0
$203$	11.6847	−	7.50927i	0.820102	−	0.527047i
$204$		0			0
$205$	−4.24362	+	1.24604i	−0.296387	+	0.0870271i
$206$		0			0
$207$	−4.55679	+	1.49520i	−0.316719	+	0.103924i
$208$		0			0
$209$	29.0173	−	8.52025i	2.00717	−	0.589358i
$210$		0			0
$211$	15.5563	−	9.99740i	1.07094	−	0.688250i	0.118491	−	0.992955i	$-0.462194\pi$
$211$	15.5563	−	9.99740i	1.07094	−	0.688250i	0.952447	+	0.304706i	$0.0985581\pi$
$212$		0			0
$213$	3.57413	+	2.29695i	0.244895	+	0.157385i
$214$		0			0
$215$	3.64862	−	4.21073i	0.248834	−	0.287169i
$216$		0			0
$217$	10.6426	+	23.3039i	0.722464	+	1.58198i
$218$		0			0
$219$	−3.24118	−	0.951697i	−0.219019	−	0.0643097i
$220$		0			0
$221$	−3.49463	+	24.3057i	−0.235074	+	1.63498i
$222$		0			0
$223$	−2.53027	+	5.54052i	−0.169439	+	0.371021i	−0.975234	−	0.221174i	$-0.929011\pi$
$223$	−2.53027	+	5.54052i	−0.169439	+	0.371021i	0.805795	+	0.592195i	$0.201738\pi$
$224$		0			0
$225$	0.113360	+	0.788433i	0.00755730	+	0.0525622i
$226$		0			0
$227$	5.92603	+	6.83900i	0.393324	+	0.453921i	0.917527	−	0.397673i	$-0.130182\pi$
$227$	5.92603	+	6.83900i	0.393324	+	0.453921i	−0.524203	+	0.851593i	$0.675637\pi$
$228$		0			0
$229$	15.2058			1.00483			0.502414	−	0.864627i	$-0.332445\pi$
$229$	15.2058			1.00483			0.502414	+	0.864627i	$0.332445\pi$
$230$		0			0
$231$	21.3445			1.40436
$232$		0			0
$233$	11.4190	+	13.1782i	0.748082	+	0.863333i	0.994381	−	0.105861i	$-0.0337599\pi$
$233$	11.4190	+	13.1782i	0.748082	+	0.863333i	−0.246299	+	0.969194i	$0.579214\pi$
$234$		0			0
$235$	−1.98759	−	13.8240i	−0.129656	−	0.901776i
$236$		0			0
$237$	−0.713653	+	1.56268i	−0.0463568	+	0.101507i
$238$		0			0
$239$	−1.06620	+	7.41556i	−0.0689665	+	0.479673i	0.925842	+	0.377910i	$0.123357\pi$
$239$	−1.06620	+	7.41556i	−0.0689665	+	0.479673i	−0.994809	+	0.101762i	$0.967552\pi$
$240$		0			0
$241$	18.0247	+	5.29254i	1.16108	+	0.340923i	0.804851	−	0.593477i	$-0.202245\pi$
$241$	18.0247	+	5.29254i	1.16108	+	0.340923i	0.356225	+	0.934400i	$0.384064\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−23.4843	+	27.1024i	−1.50036	+	1.73151i
$246$		0			0
$247$	−29.0420	−	18.6642i	−1.84790	−	1.18757i
$248$		0			0
$249$	2.31171	−	1.48565i	0.146499	−	0.0941489i
$250$		0			0
$251$	−13.6812	+	4.01717i	−0.863551	+	0.253562i	−0.683370	−	0.730072i	$-0.739487\pi$
$251$	−13.6812	+	4.01717i	−0.863551	+	0.253562i	−0.180181	+	0.983633i	$0.557668\pi$
$252$		0			0
$253$	−3.58617	−	20.3711i	−0.225461	−	1.28072i
$254$		0			0
$255$	9.81149	−	2.88091i	0.614419	−	0.180410i
$256$		0			0
$257$	−11.3379	+	7.28641i	−0.707238	+	0.454514i	−0.844176	−	0.536066i	$-0.819910\pi$
$257$	−11.3379	+	7.28641i	−0.707238	+	0.454514i	0.136939	+	0.990580i	$0.456274\pi$
$258$		0			0
$259$	3.91091	+	2.51339i	0.243012	+	0.156175i
$260$		0			0
$261$	1.83794	−	2.12109i	0.113765	−	0.131292i
$262$		0			0
$263$	4.86467	+	10.6521i	0.299969	+	0.656840i	0.998259	−	0.0589745i	$-0.0187831\pi$
$263$	4.86467	+	10.6521i	0.299969	+	0.656840i	−0.698291	+	0.715814i	$0.746056\pi$
$264$		0			0
$265$	27.6749	+	8.12609i	1.70006	+	0.499182i
$266$		0			0
$267$	0.0556332	−	0.386938i	0.00340470	−	0.0236802i
$268$		0			0
$269$	−8.44168	+	18.4847i	−0.514699	+	1.12703i	0.456709	+	0.889616i	$0.349028\pi$
$269$	−8.44168	+	18.4847i	−0.514699	+	1.12703i	−0.971408	+	0.237417i	$0.923699\pi$
$270$		0			0
$271$	2.18061	+	15.1665i	0.132462	+	0.921297i	0.942330	+	0.334684i	$0.108630\pi$
$271$	2.18061	+	15.1665i	0.132462	+	0.921297i	−0.809868	+	0.586612i	$0.800461\pi$
$272$		0			0
$273$	−15.9558	−	18.4140i	−0.965688	−	1.11446i
$274$		0			0
$275$	−3.43547			−0.207166
$276$		0			0
$277$	−5.65676			−0.339882			−0.169941	−	0.985454i	$-0.554358\pi$
$277$	−5.65676			−0.339882			−0.169941	+	0.985454i	$0.554358\pi$
$278$		0			0
$279$	3.39004	+	3.91232i	0.202957	+	0.234224i
$280$		0			0
$281$	−1.43260	−	9.96393i	−0.0854616	−	0.594398i	−0.986881	−	0.161451i	$-0.948383\pi$
$281$	−1.43260	−	9.96393i	−0.0854616	−	0.594398i	0.901419	−	0.432947i	$-0.142526\pi$
$282$		0			0
$283$	−3.80770	+	8.33771i	−0.226345	+	0.495625i	−0.988398	−	0.151889i	$-0.951464\pi$
$283$	−3.80770	+	8.33771i	−0.226345	+	0.495625i	0.762053	+	0.647515i	$0.224192\pi$
$284$		0			0
$285$	−2.04593	+	14.2298i	−0.121191	+	0.842899i
$286$		0			0
$287$	10.2433	+	3.00771i	0.604643	+	0.177539i
$288$		0			0
$289$	3.27178	+	7.16420i	0.192458	+	0.421423i
$290$		0			0
$291$	0.764994	−	0.882850i	0.0448447	−	0.0517536i
$292$		0			0
$293$	−11.2048	−	7.20086i	−0.654589	−	0.420678i	0.170752	−	0.985314i	$-0.445380\pi$
$293$	−11.2048	−	7.20086i	−0.654589	−	0.420678i	−0.825340	+	0.564636i	$0.809017\pi$
$294$		0			0
$295$	−13.2280	+	8.50109i	−0.770161	+	0.494953i
$296$		0			0
$297$	4.13828	−	1.21511i	0.240127	−	0.0705077i
$298$		0			0
$299$	−14.8934	+	18.3220i	−0.861309	+	1.05959i
$300$		0			0
$301$	−12.9040	+	3.78896i	−0.743775	+	0.218392i
$302$		0			0
$303$	−1.12806	+	0.724959i	−0.0648052	+	0.0416478i
$304$		0			0
$305$	−8.95409	−	5.75444i	−0.512709	−	0.329498i
$306$		0			0
$307$	2.86477	−	3.30612i	0.163501	−	0.188690i	−0.668087	−	0.744083i	$-0.732887\pi$
$307$	2.86477	−	3.30612i	0.163501	−	0.188690i	0.831588	+	0.555393i	$0.187432\pi$
$308$		0			0
$309$	7.20351	+	15.7735i	0.409794	+	0.897323i
$310$		0			0
$311$	−9.64631	−	2.83241i	−0.546992	−	0.160611i	−0.00345105	−	0.999994i	$-0.501099\pi$
$311$	−9.64631	−	2.83241i	−0.546992	−	0.160611i	−0.543541	+	0.839383i	$0.682917\pi$
$312$		0			0
$313$	3.42712	−	23.8361i	0.193712	−	1.34730i	−0.628364	−	0.777920i	$-0.716275\pi$
$313$	3.42712	−	23.8361i	0.193712	−	1.34730i	0.822076	−	0.569378i	$-0.192816\pi$
$314$		0			0
$315$	−4.21495	+	9.22946i	−0.237486	+	0.520021i
$316$		0			0
$317$	0.285717	+	1.98721i	0.0160475	+	0.111613i	0.996271	−	0.0862821i	$-0.0274986\pi$
$317$	0.285717	+	1.98721i	0.0160475	+	0.111613i	−0.980223	+	0.197895i	$0.936590\pi$
$318$		0			0
$319$	7.92699	+	9.14824i	0.443826	+	0.512203i
$320$		0			0
$321$	19.1835			1.07072
$322$		0			0
$323$	−34.9725			−1.94592
$324$		0			0
$325$	2.56814	+	2.96379i	0.142455	+	0.164402i
$326$		0			0
$327$	2.06779	+	14.3818i	0.114349	+	0.795314i
$328$		0			0
$329$	−14.0043	+	30.6652i	−0.772083	+	1.69062i
$330$		0			0
$331$	3.31235	−	23.0379i	0.182063	−	1.26628i	−0.669810	−	0.742532i	$-0.733625\pi$
$331$	3.31235	−	23.0379i	0.182063	−	1.26628i	0.851874	−	0.523747i	$-0.175466\pi$
$332$		0			0
$333$	0.901334	+	0.264656i	0.0493928	+	0.0145030i
$334$		0			0
$335$	11.5249	+	25.2360i	0.629672	+	1.37879i
$336$		0			0
$337$	−21.8226	+	25.1847i	−1.18876	+	1.37190i	−0.277152	+	0.960826i	$0.589391\pi$
$337$	−21.8226	+	25.1847i	−1.18876	+	1.37190i	−0.911603	+	0.411071i	$0.865155\pi$
$338$		0			0
$339$	−0.219881	−	0.141309i	−0.0119423	−	0.00767484i
$340$		0			0
$341$	−18.7828	+	12.0710i	−1.01715	+	0.653681i
$342$		0			0
$343$	49.8178	−	14.6278i	2.68991	−	0.789829i
$344$		0			0
$345$	9.51675	+	2.47206i	0.512364	+	0.133091i
$346$		0			0
$347$	0.167834	−	0.0492806i	0.00900981	−	0.00264552i	−0.277225	−	0.960805i	$-0.589415\pi$
$347$	0.167834	−	0.0492806i	0.00900981	−	0.00264552i	0.286234	+	0.958160i	$0.407596\pi$
$348$		0			0
$349$	−7.41633	+	4.76618i	−0.396987	+	0.255128i	−0.723869	−	0.689937i	$-0.757638\pi$
$349$	−7.41633	+	4.76618i	−0.396987	+	0.255128i	0.326883	+	0.945065i	$0.394002\pi$
$350$		0			0
$351$	−4.14180	−	2.66177i	−0.221073	−	0.142075i
$352$		0			0
$353$	−0.805454	+	0.929543i	−0.0428700	+	0.0494746i	−0.776780	−	0.629773i	$-0.783148\pi$
$353$	−0.805454	+	0.929543i	−0.0428700	+	0.0494746i	0.733910	+	0.679247i	$0.237694\pi$
$354$		0			0
$355$	−3.61850	−	7.92342i	−0.192050	−	0.420531i
$356$		0			0
$357$	−23.6831	−	6.95399i	−1.25344	−	0.368044i
$358$		0			0
$359$	4.69700	−	32.6683i	0.247898	−	1.72417i	−0.362423	−	0.932014i	$-0.618050\pi$
$359$	4.69700	−	32.6683i	0.247898	−	1.72417i	0.610321	−	0.792154i	$-0.291041\pi$
$360$		0			0
$361$	12.5319	−	27.4410i	0.659573	−	1.44426i
$362$		0			0
$363$	1.08185	+	7.52446i	0.0567826	+	0.394932i
$364$		0			0
$365$	4.53539	+	5.23411i	0.237393	+	0.273966i
$366$		0			0
$367$	−11.8944			−0.620883			−0.310442	−	0.950592i	$-0.600477\pi$
$367$	−11.8944			−0.620883			−0.310442	+	0.950592i	$0.600477\pi$
$368$		0			0
$369$	2.15720			0.112300
$370$		0			0
$371$	−45.5929	−	52.6171i	−2.36707	−	2.73174i
$372$		0			0
$373$	−1.40700	−	9.78587i	−0.0728515	−	0.506693i	−0.993276	−	0.115772i	$-0.963066\pi$
$373$	−1.40700	−	9.78587i	−0.0728515	−	0.506693i	0.920424	−	0.390921i	$-0.127843\pi$
$374$		0			0
$375$	4.93690	−	10.8103i	0.254941	−	0.558242i
$376$		0			0
$377$	1.96650	−	13.6773i	0.101280	−	0.704416i
$378$		0			0
$379$	29.7284	+	8.72905i	1.52705	+	0.448381i	0.934145	−	0.356894i	$-0.116164\pi$
$379$	29.7284	+	8.72905i	1.52705	+	0.448381i	0.592901	+	0.805275i	$0.297982\pi$
$380$		0			0
$381$	5.79750	+	12.6948i	0.297015	+	0.650372i
$382$		0			0
$383$	4.10378	−	4.73601i	0.209693	−	0.241999i	−0.641154	−	0.767412i	$-0.721544\pi$
$383$	4.10378	−	4.73601i	0.209693	−	0.241999i	0.850847	+	0.525414i	$0.176089\pi$
$384$		0			0
$385$	−36.8142	−	23.6591i	−1.87623	−	1.20578i
$386$		0			0
$387$	−2.28614	+	1.46921i	−0.116211	+	0.0746843i
$388$		0			0
$389$	10.1188	−	2.97114i	0.513042	−	0.150643i	−0.0149563	−	0.999888i	$-0.504761\pi$
$389$	10.1188	−	2.97114i	0.513042	−	0.150643i	0.527998	+	0.849245i	$0.322943\pi$
$390$		0			0
$391$	−2.65777	+	23.7715i	−0.134409	+	1.20217i
$392$		0			0
$393$	12.6245	−	3.70688i	0.636820	−	0.186987i
$394$		0			0
$395$	2.96303	−	1.90422i	0.149086	−	0.0958117i
$396$		0			0
$397$	19.3458	+	12.4328i	0.970937	+	0.623983i	0.927004	−	0.375051i	$-0.122375\pi$
$397$	19.3458	+	12.4328i	0.970937	+	0.623983i	0.0439327	+	0.999034i	$0.486011\pi$
$398$		0			0
$399$	22.7245	−	26.2254i	1.13765	−	1.31291i
$400$		0			0
$401$	−10.1025	−	22.1215i	−0.504497	−	1.10469i	−0.974981	−	0.222286i	$-0.928648\pi$
$401$	−10.1025	−	22.1215i	−0.504497	−	1.10469i	0.470484	−	0.882408i	$-0.344079\pi$
$402$		0			0
$403$	24.4546	+	7.18051i	1.21817	+	0.357687i
$404$		0			0
$405$	−0.291779	+	2.02937i	−0.0144986	+	0.100840i
$406$		0			0
$407$	−1.68308	+	3.68543i	−0.0834271	+	0.182680i
$408$		0			0
$409$	1.03989	+	7.23263i	0.0514195	+	0.357630i	0.999245	+	0.0388419i	$0.0123669\pi$
$409$	1.03989	+	7.23263i	0.0514195	+	0.357630i	−0.947826	+	0.318788i	$0.896724\pi$
$410$		0			0
$411$	0.350222	+	0.404177i	0.0172752	+	0.0199366i
$412$		0			0
$413$	37.9551			1.86765
$414$		0			0
$415$	−5.63391			−0.276558
$416$		0			0
$417$	7.83326	+	9.04006i	0.383596	+	0.442694i
$418$		0			0
$419$	1.07955	+	7.50842i	0.0527393	+	0.366810i	0.999051	+	0.0435546i	$0.0138682\pi$
$419$	1.07955	+	7.50842i	0.0527393	+	0.366810i	−0.946312	+	0.323256i	$0.895223\pi$
$420$		0			0
$421$	−1.42385	+	3.11780i	−0.0693942	+	0.151952i	−0.941151	−	0.337987i	$-0.890254\pi$
$421$	−1.42385	+	3.11780i	−0.0693942	+	0.151952i	0.871756	+	0.489939i	$0.162981\pi$
$422$		0			0
$423$	−0.969443	+	6.74263i	−0.0471359	+	0.327838i
$424$		0			0
$425$	3.81188	+	1.11927i	0.184903	+	0.0542925i
$426$		0			0
$427$	10.6729	+	23.3703i	0.516495	+	1.13097i
$428$		0			0
$429$	13.9056	−	16.0479i	0.671367	−	0.774799i
$430$		0			0
$431$	−24.1183	−	15.4999i	−1.16174	−	0.746605i	−0.189797	−	0.981823i	$-0.560783\pi$
$431$	−24.1183	−	15.4999i	−1.16174	−	0.746605i	−0.971942	+	0.235219i	$0.924419\pi$
$432$		0			0
$433$	−19.8588	+	12.7625i	−0.954354	+	0.613326i	−0.922430	−	0.386164i	$-0.873800\pi$
$433$	−19.8588	+	12.7625i	−0.954354	+	0.613326i	−0.0319237	+	0.999490i	$0.510163\pi$
$434$		0			0
$435$	−5.52111	+	1.62115i	−0.264717	+	0.0777280i
$436$		0			0
$437$	−28.8475	−	17.2819i	−1.37996	−	0.826707i
$438$		0			0
$439$	5.55387	−	1.63076i	0.265072	−	0.0778321i	−0.146496	−	0.989211i	$-0.546800\pi$
$439$	5.55387	−	1.63076i	0.265072	−	0.0778321i	0.411568	+	0.911379i	$0.364981\pi$
$440$		0			0
$441$	14.7147	−	9.45660i	0.700702	−	0.450314i
$442$		0			0
$443$	20.2659	+	13.0241i	0.962862	+	0.618794i	0.924789	−	0.380481i	$-0.124242\pi$
$443$	20.2659	+	13.0241i	0.962862	+	0.618794i	0.0380735	+	0.999275i	$0.487878\pi$
$444$		0			0
$445$	−0.524851	+	0.605711i	−0.0248803	+	0.0287134i
$446$		0			0
$447$	3.48248	+	7.62557i	0.164716	+	0.360677i
$448$		0			0
$449$	12.2199	+	3.58809i	0.576694	+	0.169333i	0.557057	−	0.830475i	$-0.311931\pi$
$449$	12.2199	+	3.58809i	0.576694	+	0.169333i	0.0196374	+	0.999807i	$0.493749\pi$
$450$		0			0
$451$	−1.32410	+	9.20929i	−0.0623492	+	0.433648i
$452$		0			0
$453$	5.76692	−	12.6278i	0.270954	−	0.593306i
$454$		0			0
$455$	7.10923	+	49.4458i	0.333286	+	2.31805i
$456$		0			0
$457$	7.61981	+	8.79373i	0.356440	+	0.411353i	0.905444	−	0.424466i	$-0.139538\pi$
$457$	7.61981	+	8.79373i	0.356440	+	0.411353i	−0.549004	+	0.835820i	$0.684993\pi$
$458$		0			0
$459$	−4.98758			−0.232800
$460$		0			0
$461$	12.5118			0.582734			0.291367	−	0.956611i	$-0.405890\pi$
$461$	12.5118			0.582734			0.291367	+	0.956611i	$0.405890\pi$
$462$		0			0
$463$	−3.18592	−	3.67674i	−0.148062	−	0.170873i	0.676874	−	0.736099i	$-0.263334\pi$
$463$	−3.18592	−	3.67674i	−0.148062	−	0.170873i	−0.824936	+	0.565226i	$0.808789\pi$
$464$		0			0
$465$	−1.51046	−	10.5055i	−0.0700460	−	0.487181i
$466$		0			0
$467$	−8.36941	+	18.3264i	−0.387290	+	0.848047i	0.611112	+	0.791544i	$0.290722\pi$
$467$	−8.36941	+	18.3264i	−0.387290	+	0.848047i	−0.998402	+	0.0565030i	$0.982005\pi$
$468$		0			0
$469$	9.53035	−	66.2850i	0.440071	−	3.06076i
$470$		0			0
$471$	−2.33147	−	0.684582i	−0.107429	−	0.0315439i
$472$		0			0
$473$	−4.86896	−	10.6615i	−0.223875	−	0.490218i
$474$		0			0
$475$	−3.65759	+	4.22108i	−0.167822	+	0.193676i
$476$		0			0
$477$	−11.8350	−	7.60589i	−0.541887	−	0.348250i
$478$		0			0
$479$	−16.6986	+	10.7315i	−0.762979	+	0.490337i	−0.863345	−	0.504614i	$-0.831635\pi$
$479$	−16.6986	+	10.7315i	−0.762979	+	0.490337i	0.100366	+	0.994951i	$0.467999\pi$
$480$		0			0
$481$	4.43760	−	1.30300i	0.202337	−	0.0594115i
$482$		0			0
$483$	−16.0989	−	17.4393i	−0.732527	−	0.793514i
$484$		0			0
$485$	−2.29802	+	0.674760i	−0.104348	+	0.0306393i
$486$		0			0
$487$	7.04508	−	4.52760i	0.319243	−	0.205165i	−0.371198	−	0.928554i	$-0.621053\pi$
$487$	7.04508	−	4.52760i	0.319243	−	0.205165i	0.690441	+	0.723389i	$0.257417\pi$
$488$		0			0
$489$	−14.8545	−	9.54642i	−0.671745	−	0.431704i
$490$		0			0
$491$	−11.8899	+	13.7217i	−0.536586	+	0.619253i	−0.957705	−	0.287752i	$-0.907092\pi$
$491$	−11.8899	+	13.7217i	−0.536586	+	0.619253i	0.421119	+	0.907005i	$0.361637\pi$
$492$		0			0
$493$	−5.81505	−	12.7332i	−0.261897	−	0.573474i
$494$		0			0
$495$	−8.48444	−	2.49126i	−0.381347	−	0.111974i
$496$		0			0
$497$	−2.99227	+	20.8117i	−0.134222	+	0.933532i
$498$		0			0
$499$	9.05125	−	19.8195i	0.405190	−	0.887241i	−0.591528	−	0.806284i	$-0.701475\pi$
$499$	9.05125	−	19.8195i	0.405190	−	0.887241i	0.996718	−	0.0809569i	$-0.0257976\pi$
$500$		0			0
$501$	0.953126	+	6.62914i	0.0425825	+	0.296168i
$502$		0			0
$503$	−20.0462	−	23.1346i	−0.893817	−	1.03152i	−0.999312	−	0.0370997i	$-0.988188\pi$
$503$	−20.0462	−	23.1346i	−0.893817	−	1.03152i	0.105495	−	0.994420i	$-0.466357\pi$
$504$		0			0
$505$	2.74921			0.122338
$506$		0			0
$507$	−11.2395			−0.499164
$508$		0			0
$509$	−9.87492	−	11.3963i	−0.437698	−	0.505130i	0.493449	−	0.869775i	$-0.335736\pi$
$509$	−9.87492	−	11.3963i	−0.437698	−	0.505130i	−0.931147	+	0.364644i	$0.881191\pi$
$510$		0			0
$511$	−2.37914	−	16.5473i	−0.105247	−	0.732008i
$512$		0			0
$513$	2.91286	−	6.37828i	0.128606	−	0.281608i
$514$		0			0
$515$	5.05960	−	35.1903i	0.222952	−	1.55067i
$516$		0			0
$517$	−28.1898	−	8.27727i	−1.23979	−	0.364034i
$518$		0			0
$519$	−3.28887	−	7.20162i	−0.144365	−	0.316116i
$520$		0			0
$521$	26.6188	−	30.7197i	1.16619	−	1.34585i	0.239109	−	0.970993i	$-0.423145\pi$
$521$	26.6188	−	30.7197i	1.16619	−	1.34585i	0.927081	−	0.374862i	$-0.122310\pi$
$522$		0			0
$523$	−0.272351	−	0.175029i	−0.0119091	−	0.00765349i	0.534673	−	0.845059i	$-0.320435\pi$
$523$	−0.272351	−	0.175029i	−0.0119091	−	0.00765349i	−0.546582	+	0.837406i	$0.684071\pi$
$524$		0			0
$525$	−3.31621	+	2.13120i	−0.144731	+	0.0930132i
$526$		0			0
$527$	24.7735	−	7.27417i	1.07915	−	0.316868i
$528$		0			0
$529$	−13.9391	+	18.2948i	−0.606049	+	0.795427i
$530$		0			0
$531$	7.35875	−	2.16072i	0.319343	−	0.0937675i
$532$		0			0
$533$	8.93470	−	5.74198i	0.387005	−	0.248713i
$534$		0			0
$535$	−33.0871	−	21.2638i	−1.43048	−	0.919315i
$536$		0			0
$537$	−8.96750	+	10.3490i	−0.386976	+	0.446594i
$538$		0			0
$539$	31.3391	+	68.6230i	1.34987	+	2.95580i
$540$		0			0
$541$	35.6345	+	10.4632i	1.53205	+	0.449849i	0.935676	−	0.352861i	$-0.114791\pi$
$541$	35.6345	+	10.4632i	1.53205	+	0.449849i	0.596370	+	0.802710i	$0.296609\pi$
$542$		0			0
$543$	−1.73185	+	12.0453i	−0.0743206	+	0.516911i
$544$		0			0
$545$	12.3749	−	27.0972i	0.530082	−	1.16072i
$546$		0			0
$547$	−4.99046	−	34.7094i	−0.213377	−	1.48407i	−0.761771	−	0.647847i	$-0.775670\pi$
$547$	−4.99046	−	34.7094i	−0.213377	−	1.48407i	0.548394	−	0.836220i	$-0.315239\pi$
$548$		0			0
$549$	3.39969	+	3.92346i	0.145095	+	0.167449i
$550$		0			0
$551$	19.6797			0.838385
$552$		0			0
$553$	−8.50183			−0.361535
$554$		0			0
$555$	−1.26124	−	1.45554i	−0.0535365	−	0.0617844i
$556$		0			0
$557$	0.305004	+	2.12135i	0.0129234	+	0.0898844i	0.995262	−	0.0972258i	$-0.0309969\pi$
$557$	0.305004	+	2.12135i	0.0129234	+	0.0898844i	−0.982339	+	0.187110i	$0.940088\pi$
$558$		0			0
$559$	−5.55802	+	12.1704i	−0.235079	+	0.514751i
$560$		0			0
$561$	3.06138	−	21.2924i	0.129252	−	0.898965i
$562$		0			0
$563$	6.06476	+	1.78077i	0.255599	+	0.0750507i	0.407022	−	0.913418i	$-0.366567\pi$
$563$	6.06476	+	1.78077i	0.255599	+	0.0750507i	−0.151423	+	0.988469i	$0.548385\pi$
$564$		0			0
$565$	0.222611	+	0.487449i	0.00936530	+	0.0205071i
$566$		0			0
$567$	3.24083	−	3.74012i	0.136102	−	0.157070i
$568$		0			0
$569$	−4.62332	−	2.97123i	−0.193820	−	0.124560i	0.440132	−	0.897933i	$-0.354932\pi$
$569$	−4.62332	−	2.97123i	−0.193820	−	0.124560i	−0.633951	+	0.773373i	$0.718568\pi$
$570$		0			0
$571$	9.12969	−	5.86730i	0.382066	−	0.245539i	−0.335484	−	0.942046i	$-0.608900\pi$
$571$	9.12969	−	5.86730i	0.382066	−	0.245539i	0.717550	+	0.696507i	$0.245264\pi$
$572$		0			0
$573$	11.6486	−	3.42034i	0.486627	−	0.142887i
$574$		0			0
$575$	2.59118	+	2.80691i	0.108060	+	0.117056i
$576$		0			0
$577$	−6.08370	+	1.78634i	−0.253268	+	0.0743661i	−0.405902	−	0.913917i	$-0.633043\pi$
$577$	−6.08370	+	1.78634i	−0.253268	+	0.0743661i	0.152634	+	0.988283i	$0.451224\pi$
$578$		0			0
$579$	−6.74812	+	4.33675i	−0.280442	+	0.180229i
$580$		0			0
$581$	11.4404	+	7.35229i	0.474627	+	0.305024i
$582$		0			0
$583$	39.7345	−	45.8561i	1.64564	−	1.89917i
$584$		0			0
$585$	4.19322	+	9.18187i	0.173368	+	0.379623i
$586$		0			0
$587$	−21.7445	−	6.38477i	−0.897493	−	0.263528i	−0.199725	−	0.979852i	$-0.564005\pi$
$587$	−21.7445	−	6.38477i	−0.897493	−	0.263528i	−0.697768	+	0.716324i	$0.745823\pi$
$588$		0			0
$589$	−5.16588	+	35.9295i	−0.212856	+	1.48045i
$590$		0			0
$591$	−0.624804	+	1.36813i	−0.0257010	+	0.0562773i
$592$		0			0
$593$	−0.564481	−	3.92605i	−0.0231805	−	0.161224i	0.974943	−	0.222454i	$-0.0714067\pi$
$593$	−0.564481	−	3.92605i	−0.0231805	−	0.161224i	−0.998124	+	0.0612303i	$0.980498\pi$
$594$		0			0
$595$	33.1398	+	38.2453i	1.35860	+	1.56791i
$596$		0			0
$597$	−26.5434			−1.08635
$598$		0			0
$599$	−15.8367			−0.647071			−0.323535	−	0.946216i	$-0.604871\pi$
$599$	−15.8367			−0.647071			−0.323535	+	0.946216i	$0.604871\pi$
$600$		0			0
$601$	18.3116	+	21.1327i	0.746947	+	0.862022i	0.994269	−	0.106911i	$-0.0340960\pi$
$601$	18.3116	+	21.1327i	0.746947	+	0.862022i	−0.247322	+	0.968933i	$0.579551\pi$
$602$		0			0
$603$	−1.92576	−	13.3939i	−0.0784229	−	0.545443i
$604$		0			0
$605$	6.47447	−	14.1771i	0.263224	−	0.576381i
$606$		0			0
$607$	−4.62588	+	32.1737i	−0.187759	+	1.30589i	0.650036	+	0.759904i	$0.274754\pi$
$607$	−4.62588	+	32.1737i	−0.187759	+	1.30589i	−0.837794	+	0.545986i	$0.816155\pi$
$608$		0			0
$609$	13.3269	+	3.91314i	0.540035	+	0.158569i
$610$		0			0
$611$	13.9321	+	30.5070i	0.563632	+	1.23418i
$612$		0			0
$613$	−9.54539	+	11.0160i	−0.385535	+	0.444931i	−0.915032	−	0.403381i	$-0.867835\pi$
$613$	−9.54539	+	11.0160i	−0.385535	+	0.444931i	0.529497	+	0.848312i	$0.322381\pi$
$614$		0			0
$615$	−3.72067	−	2.39113i	−0.150032	−	0.0964197i
$616$		0			0
$617$	17.2184	−	11.0656i	0.693188	−	0.445485i	−0.146030	−	0.989280i	$-0.546650\pi$
$617$	17.2184	−	11.0656i	0.693188	−	0.445485i	0.839218	+	0.543795i	$0.183013\pi$
$618$		0			0
$619$	3.83347	−	1.12561i	0.154080	−	0.0452421i	−0.203783	−	0.979016i	$-0.565324\pi$
$619$	3.83347	−	1.12561i	0.154080	−	0.0452421i	0.357863	+	0.933774i	$0.383505\pi$
$620$		0			0
$621$	−4.11406	−	2.46465i	−0.165092	−	0.0989029i
$622$		0			0
$623$	1.85624	−	0.545040i	0.0743685	−	0.0218366i
$624$		0			0
$625$	−17.1471	+	11.0198i	−0.685885	+	0.440791i
$626$		0			0
$627$	25.4415	+	16.3502i	1.01603	+	0.652966i
$628$		0			0
$629$	3.06819	−	3.54088i	0.122337	−	0.141184i
$630$		0			0
$631$	−2.91780	−	6.38910i	−0.116156	−	0.254346i	0.842620	−	0.538508i	$-0.181012\pi$
$631$	−2.91780	−	6.38910i	−0.116156	−	0.254346i	−0.958776	+	0.284162i	$0.908285\pi$
$632$		0			0
$633$	17.7427	+	5.20973i	0.705210	+	0.207068i
$634$		0			0
$635$	4.07204	−	28.3217i	0.161594	−	1.12391i
$636$		0			0
$637$	35.7742	−	78.3346i	1.41743	−	3.10373i
$638$		0			0
$639$	0.604635	+	4.20533i	0.0239190	+	0.166360i
$640$		0			0
$641$	−16.0323	−	18.5023i	−0.633238	−	0.730795i	0.344926	−	0.938630i	$-0.387904\pi$
$641$	−16.0323	−	18.5023i	−0.633238	−	0.730795i	−0.978164	+	0.207835i	$0.933358\pi$
$642$		0			0
$643$	−7.79871			−0.307551			−0.153776	−	0.988106i	$-0.549143\pi$
$643$	−7.79871			−0.307551			−0.153776	+	0.988106i	$0.549143\pi$
$644$		0			0
$645$	5.57159			0.219381
$646$		0			0
$647$	6.55813	+	7.56848i	0.257827	+	0.297548i	0.869875	−	0.493273i	$-0.164200\pi$
$647$	6.55813	+	7.56848i	0.257827	+	0.297548i	−0.612048	+	0.790821i	$0.709654\pi$
$648$		0			0
$649$	4.70750	+	32.7414i	0.184786	+	1.28521i
$650$		0			0
$651$	−10.6426	+	23.3039i	−0.417115	+	0.913354i
$652$		0			0
$653$	3.99526	−	27.7876i	0.156346	−	1.08741i	−0.748948	−	0.662629i	$-0.769441\pi$
$653$	3.99526	−	27.7876i	0.156346	−	1.08741i	0.905294	−	0.424785i	$-0.139650\pi$
$654$		0			0
$655$	−25.8831	−	7.59997i	−1.01134	−	0.296955i
$656$		0			0
$657$	−1.40328	−	3.07275i	−0.0547471	−	0.119879i
$658$		0			0
$659$	22.1741	−	25.5903i	0.863780	−	0.996855i	−0.136201	−	0.990681i	$-0.543489\pi$
$659$	22.1741	−	25.5903i	0.863780	−	0.996855i	0.999981	−	0.00617407i	$-0.00196528\pi$
$660$		0			0
$661$	−6.52367	−	4.19251i	−0.253742	−	0.163070i	0.407586	−	0.913167i	$-0.366370\pi$
$661$	−6.52367	−	4.19251i	−0.253742	−	0.163070i	−0.661328	+	0.750097i	$0.730007\pi$
$662$		0			0
$663$	−20.6575	+	13.2758i	−0.802272	+	0.515589i
$664$		0			0
$665$	−68.2637	+	20.0440i	−2.64715	+	0.777275i
$666$		0			0
$667$	1.49558	−	13.3767i	0.0579091	−	0.517947i
$668$		0			0
$669$	−5.84422	+	1.71602i	−0.225951	+	0.0663451i
$670$		0			0
$671$	−18.8363	+	12.1054i	−0.727167	+	0.467322i
$672$		0			0
$673$	17.0028	+	10.9270i	0.655411	+	0.421207i	0.825640	−	0.564198i	$-0.190814\pi$
$673$	17.0028	+	10.9270i	0.655411	+	0.421207i	−0.170229	+	0.985404i	$0.554451\pi$
$674$		0			0
$675$	−0.521623	+	0.601985i	−0.0200773	+	0.0231704i
$676$		0			0
$677$	−17.0207	−	37.2701i	−0.654157	−	1.43240i	−0.887868	−	0.460098i	$-0.847814\pi$
$677$	−17.0207	−	37.2701i	−0.654157	−	1.43240i	0.233711	−	0.972306i	$-0.424913\pi$
$678$		0			0
$679$	5.54700	+	1.62875i	0.212874	+	0.0625055i
$680$		0			0
$681$	−1.28785	+	8.95719i	−0.0493505	+	0.343240i
$682$		0			0
$683$	6.54563	−	14.3329i	0.250462	−	0.548434i	−0.742084	−	0.670307i	$-0.766163\pi$
$683$	6.54563	−	14.3329i	0.250462	−	0.548434i	0.992546	+	0.121872i	$0.0388898\pi$
$684$		0			0
$685$	−0.156044	−	1.08531i	−0.00596214	−	0.0414676i
$686$		0			0
$687$	9.95769	+	11.4918i	0.379909	+	0.438439i
$688$		0			0
$689$	−69.2633			−2.63872
$690$		0			0
$691$	−14.5672			−0.554164			−0.277082	−	0.960846i	$-0.589367\pi$
$691$	−14.5672			−0.554164			−0.277082	+	0.960846i	$0.589367\pi$
$692$		0			0
$693$	13.9776	+	16.1311i	0.530967	+	0.612769i
$694$		0			0
$695$	−3.49017	−	24.2747i	−0.132390	−	0.920792i
$696$		0			0
$697$	4.46954	−	9.78693i	0.169296	−	0.370707i
$698$		0			0
$699$	−2.48158	+	17.2598i	−0.0938620	+	0.652825i
$700$		0			0
$701$	42.6672	+	12.5282i	1.61152	+	0.473185i	0.958721	−	0.284347i	$-0.0917769\pi$
$701$	42.6672	+	12.5282i	1.61152	+	0.473185i	0.652798	+	0.757532i	$0.273595\pi$
$702$		0			0
$703$	2.73630	+	5.99166i	0.103202	+	0.225980i
$704$		0			0
$705$	9.14586	−	10.5549i	0.344453	−	0.397520i
$706$		0			0
$707$	−5.58263	−	3.58774i	−0.209956	−	0.134931i
$708$		0			0
$709$	−6.13210	+	3.94086i	−0.230296	+	0.148002i	−0.650700	−	0.759335i	$-0.725525\pi$
$709$	−6.13210	+	3.94086i	−0.230296	+	0.148002i	0.420404	+	0.907337i	$0.361888\pi$
$710$		0			0
$711$	−1.64834	+	0.483996i	−0.0618176	+	0.0181513i
$712$		0			0
$713$	24.0293	+	6.24184i	0.899905	+	0.233759i
$714$		0			0
$715$	−41.7720	+	12.2654i	−1.56218	+	0.458698i
$716$		0			0
$717$	−6.30252	+	4.05038i	−0.235372	+	0.151264i
$718$		0			0
$719$	3.93618	+	2.52963i	0.146795	+	0.0943392i	0.611977	−	0.790876i	$-0.290375\pi$
$719$	3.93618	+	2.52963i	0.146795	+	0.0943392i	−0.465182	+	0.885215i	$0.654011\pi$
$720$		0			0
$721$	−56.1977	+	64.8556i	−2.09291	+	2.41535i
$722$		0			0
$723$	7.80386	+	17.0881i	0.290229	+	0.635512i
$724$		0			0
$725$	−2.14502	−	0.629835i	−0.0796640	−	0.0233915i
$726$		0			0
$727$	3.09022	−	21.4929i	0.114610	−	0.797128i	−0.848727	−	0.528832i	$-0.822630\pi$
$727$	3.09022	−	21.4929i	0.114610	−	0.797128i	0.963336	−	0.268296i	$-0.0864607\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	1.92893	+	13.4160i	0.0713439	+	0.496208i
$732$		0			0
$733$	−26.5785	−	30.6732i	−0.981699	−	1.13294i	−0.991118	−	0.132985i	$-0.957544\pi$
$733$	−26.5785	−	30.6732i	−0.981699	−	1.13294i	0.00941946	−	0.999956i	$-0.497002\pi$
$734$		0			0
$735$	−35.8616			−1.32277
$736$		0			0
$737$	58.3619			2.14979
$738$		0			0
$739$	5.80721	+	6.70187i	0.213622	+	0.246532i	0.852440	−	0.522825i	$-0.175122\pi$
$739$	5.80721	+	6.70187i	0.213622	+	0.246532i	−0.638818	+	0.769358i	$0.720576\pi$
$740$		0			0
$741$	−4.91303	−	34.1709i	−0.180485	−	1.25530i
$742$		0			0
$743$	−21.1915	+	46.4030i	−0.777442	+	1.70236i	−0.0679062	+	0.997692i	$0.521632\pi$
$743$	−21.1915	+	46.4030i	−0.777442	+	1.70236i	−0.709536	+	0.704669i	$0.751095\pi$
$744$		0			0
$745$	2.44602	−	17.0125i	0.0896153	−	0.623288i
$746$		0			0
$747$	2.63662	+	0.774182i	0.0964690	+	0.0283259i
$748$		0			0
$749$	39.4383	+	86.3579i	1.44104	+	3.15545i
$750$		0			0
$751$	26.4050	−	30.4730i	0.963532	−	1.11197i	−0.0301281	−	0.999546i	$-0.509592\pi$
$751$	26.4050	−	30.4730i	0.963532	−	1.11197i	0.993660	−	0.112429i	$-0.0358630\pi$
$752$		0			0
$753$	−11.9953	−	7.70889i	−0.437132	−	0.280928i
$754$		0			0
$755$	−23.9438	+	15.3877i	−0.871403	+	0.560016i
$756$		0			0
$757$	14.6483	−	4.30114i	0.532403	−	0.156328i	−0.00447110	−	0.999990i	$-0.501423\pi$
$757$	14.6483	−	4.30114i	0.532403	−	0.156328i	0.536874	+	0.843662i	$0.319605\pi$
$758$		0			0
$759$	13.0470	−	16.0505i	0.473576	−	0.582595i
$760$		0			0
$761$	19.7067	−	5.78642i	0.714369	−	0.209758i	0.0957009	−	0.995410i	$-0.469491\pi$
$761$	19.7067	−	5.78642i	0.714369	−	0.209758i	0.618668	+	0.785653i	$0.287673\pi$
$762$		0			0
$763$	−60.4909	+	38.8751i	−2.18992	+	1.40737i
$764$		0			0
$765$	8.60241	+	5.52843i	0.311021	+	0.199881i
$766$		0			0
$767$	24.7271	−	28.5366i	0.892844	−	1.03040i
$768$		0			0
$769$	−13.3921	−	29.3245i	−0.482930	−	1.05747i	−0.981647	−	0.190705i	$-0.938923\pi$
$769$	−13.3921	−	29.3245i	−0.482930	−	1.05747i	0.498717	−	0.866765i	$-0.333805\pi$
$770$		0			0
$771$	−12.9314	−	3.79701i	−0.465714	−	0.136746i
$772$		0			0
$773$	7.78247	−	54.1283i	0.279916	−	1.94686i	−0.0394364	−	0.999222i	$-0.512556\pi$
$773$	7.78247	−	54.1283i	0.279916	−	1.94686i	0.319352	−	0.947636i	$-0.396535\pi$
$774$		0			0
$775$	1.71296	−	3.75085i	0.0615313	−	0.134735i
$776$		0			0
$777$	0.661609	+	4.60159i	0.0237351	+	0.165081i
$778$		0			0
$779$	9.90553	+	11.4316i	0.354902	+	0.409579i
$780$		0			0
$781$	−18.3240			−0.655686
$782$		0			0
$783$	2.80661			0.100300
$784$		0			0
$785$	3.26243	+	3.76504i	0.116441	+	0.134380i
$786$		0			0
$787$	7.06777	+	49.1574i	0.251939	+	1.75227i	0.586546	+	0.809916i	$0.300487\pi$
$787$	7.06777	+	49.1574i	0.251939	+	1.75227i	−0.334607	+	0.942358i	$0.608604\pi$
$788$		0			0
$789$	−4.86467	+	10.6521i	−0.173187	+	0.379226i
$790$		0			0
$791$	0.184085	−	1.28034i	0.00654530	−	0.0455236i
$792$		0			0
$793$	24.5242	+	7.20095i	0.870879	+	0.255713i
$794$		0			0
$795$	11.9819	+	26.2368i	0.424956	+	0.930523i
$796$		0			0
$797$	−7.06625	+	8.15489i	−0.250299	+	0.288861i	−0.866970	−	0.498360i	$-0.833936\pi$
$797$	−7.06625	+	8.15489i	−0.250299	+	0.288861i	0.616671	+	0.787221i	$0.288481\pi$
$798$		0			0
$799$	28.5817	+	18.3684i	1.01115	+	0.649826i
$800$		0			0
$801$	0.328860	−	0.211345i	0.0116197	−	0.00746752i
$802$		0			0
$803$	13.9792	−	4.10466i	0.493314	−	0.144850i
$804$		0			0
$805$	8.43653	+	47.9234i	0.297348	+	1.68908i
$806$		0			0
$807$	−19.4979	+	5.72511i	−0.686360	+	0.201533i
$808$		0			0
$809$	−11.3297	+	7.28114i	−0.398330	+	0.255991i	−0.724436	−	0.689342i	$-0.757900\pi$
$809$	−11.3297	+	7.28114i	−0.398330	+	0.255991i	0.326106	+	0.945333i	$0.394263\pi$
$810$		0			0
$811$	2.47556	+	1.59094i	0.0869285	+	0.0558656i	0.583383	−	0.812197i	$-0.301729\pi$
$811$	2.47556	+	1.59094i	0.0869285	+	0.0558656i	−0.496454	+	0.868063i	$0.665365\pi$
$812$		0			0
$813$	−10.0341	+	11.5799i	−0.351910	+	0.406125i
$814$		0			0
$815$	15.0389	+	32.9307i	0.526791	+	1.15351i
$816$		0			0
$817$	−18.2833	−	5.36847i	−0.639653	−	0.187819i
$818$		0			0
$819$	3.46752	−	24.1171i	0.121165	−	0.842721i
$820$		0			0
$821$	−21.9755	+	48.1197i	−0.766951	+	1.67939i	−0.0336992	+	0.999432i	$0.510729\pi$
$821$	−21.9755	+	48.1197i	−0.766951	+	1.67939i	−0.733252	+	0.679957i	$0.761998\pi$
$822$		0			0
$823$	−0.993982	−	6.91329i	−0.0346480	−	0.240982i	0.965136	−	0.261748i	$-0.0842988\pi$
$823$	−0.993982	−	6.91329i	−0.0346480	−	0.240982i	−0.999784	+	0.0207653i	$0.993390\pi$
$824$		0			0
$825$	−2.24975	−	2.59635i	−0.0783263	−	0.0903934i
$826$		0			0
$827$	7.62895			0.265284			0.132642	−	0.991164i	$-0.457654\pi$
$827$	7.62895			0.265284			0.132642	+	0.991164i	$0.457654\pi$
$828$		0			0
$829$	−14.5446			−0.505153			−0.252577	−	0.967577i	$-0.581278\pi$
$829$	−14.5446			−0.505153			−0.252577	+	0.967577i	$0.581278\pi$
$830$		0			0
$831$	−3.70439	−	4.27509i	−0.128504	−	0.148301i
$832$		0			0
$833$	−12.4155	−	86.3520i	−0.430173	−	2.99192i
$834$		0			0
$835$	5.70408	−	12.4902i	0.197398	−	0.432241i
$836$		0			0
$837$	−0.736727	+	5.12405i	−0.0254650	+	0.177113i
$838$		0			0
$839$	−18.3500	−	5.38806i	−0.633513	−	0.186016i	−0.0508193	−	0.998708i	$-0.516183\pi$
$839$	−18.3500	−	5.38806i	−0.633513	−	0.186016i	−0.582694	+	0.812692i	$0.698001\pi$
$840$		0			0
$841$	−8.77479	−	19.2141i	−0.302579	−	0.662556i
$842$		0			0
$843$	6.59208	−	7.60767i	0.227043	−	0.262022i
$844$		0			0
$845$	19.3855	+	12.4583i	0.666882	+	0.428579i
$846$		0			0
$847$	−31.6485	+	20.3392i	−1.08745	+	0.698864i
$848$		0			0
$849$	−8.79474	+	2.58237i	−0.301835	+	0.0886266i
$850$		0			0
$851$	4.28059	−	1.40457i	0.146737	−	0.0481481i
$852$		0			0
$853$	23.2485	−	6.82637i	0.796013	−	0.233730i	0.141656	−	0.989916i	$-0.454757\pi$
$853$	23.2485	−	6.82637i	0.796013	−	0.233730i	0.654357	+	0.756186i	$0.272939\pi$
$854$		0			0
$855$	−12.0939	+	7.77231i	−0.413604	+	0.265807i
$856$		0			0
$857$	32.2400	+	20.7194i	1.10130	+	0.707760i	0.959380	−	0.282118i	$-0.0910371\pi$
$857$	32.2400	+	20.7194i	1.10130	+	0.707760i	0.141917	+	0.989879i	$0.454673\pi$
$858$		0			0
$859$	20.3337	−	23.4663i	0.693776	−	0.800661i	−0.294121	−	0.955768i	$-0.595027\pi$
$859$	20.3337	−	23.4663i	0.693776	−	0.800661i	0.987898	+	0.155107i	$0.0495724\pi$
$860$		0			0
$861$	4.43487	+	9.71101i	0.151140	+	0.330950i
$862$		0			0
$863$	−4.06386	−	1.19326i	−0.138335	−	0.0406189i	0.211832	−	0.977306i	$-0.432057\pi$
$863$	−4.06386	−	1.19326i	−0.138335	−	0.0406189i	−0.350167	+	0.936687i	$0.613875\pi$
$864$		0			0
$865$	−2.31003	+	16.0666i	−0.0785435	+	0.546282i
$866$		0			0
$867$	−3.27178	+	7.16420i	−0.111115	+	0.243309i
$868$		0			0
$869$	−1.05447	−	7.33398i	−0.0357704	−	0.248788i
$870$		0			0
$871$	−43.6277	−	50.3490i	−1.47827	−	1.70601i
$872$		0			0
$873$	1.16818			0.0395368
$874$		0			0
$875$	58.8139			1.98827
$876$		0			0
$877$	27.0964	+	31.2709i	0.914979	+	1.05594i	0.998233	+	0.0594140i	$0.0189232\pi$
$877$	27.0964	+	31.2709i	0.914979	+	1.05594i	−0.0832541	+	0.996528i	$0.526531\pi$
$878$		0			0
$879$	−1.89551	−	13.1835i	−0.0639339	−	0.444670i
$880$		0			0
$881$	19.1620	−	41.9589i	0.645584	−	1.41363i	−0.249782	−	0.968302i	$-0.580359\pi$
$881$	19.1620	−	41.9589i	0.645584	−	1.41363i	0.895366	−	0.445330i	$-0.146914\pi$
$882$		0			0
$883$	−6.39960	+	44.5102i	−0.215364	+	1.49789i	0.539489	+	0.841993i	$0.318617\pi$
$883$	−6.39960	+	44.5102i	−0.215364	+	1.49789i	−0.754853	+	0.655894i	$0.772292\pi$
$884$		0			0
$885$	−15.0872	−	4.42999i	−0.507149	−	0.148913i
$886$		0			0
$887$	−0.459647	−	1.00649i	−0.0154334	−	0.0337945i	0.901758	−	0.432241i	$-0.142277\pi$
$887$	−0.459647	−	1.00649i	−0.0154334	−	0.0337945i	−0.917192	+	0.398446i	$0.869550\pi$
$888$		0			0
$889$	−45.2288	+	52.1968i	−1.51692	+	1.75062i
$890$		0			0
$891$	3.62831	+	2.33178i	0.121553	+	0.0781174i
$892$		0			0
$893$	−40.1825	+	25.8237i	−1.34466	+	0.864157i
$894$		0			0
$895$	26.9381	−	7.90975i	0.900443	−	0.264394i
$896$		0			0
$897$	−23.5999	+	0.742626i	−0.787979	+	0.0247955i
$898$		0			0
$899$	−13.9405	+	4.09331i	−0.464943	+	0.136520i
$900$		0			0
$901$	−59.0280	+	37.9350i	−1.96651	+	1.26380i
$902$		0			0
$903$	−11.3138	−	7.27096i	−0.376501	−	0.241963i
$904$		0			0
$905$	16.3385	−	18.8556i	0.543109	−	0.626781i
$906$		0			0
$907$	−18.8790	−	41.3391i	−0.626865	−	1.37264i	−0.910419	−	0.413687i	$-0.864241\pi$
$907$	−18.8790	−	41.3391i	−0.626865	−	1.37264i	0.283554	−	0.958956i	$-0.408487\pi$
$908$		0			0
$909$	−1.28661	−	0.377782i	−0.0426741	−	0.0125302i
$910$		0			0
$911$	1.30080	−	9.04723i	0.0430973	−	0.299748i	−0.956860	−	0.290548i	$-0.906162\pi$
$911$	1.30080	−	9.04723i	0.0430973	−	0.299748i	0.999958	−	0.00920004i	$-0.00292850\pi$
$912$		0			0
$913$	−4.92341	+	10.7808i	−0.162941	+	0.356791i
$914$		0			0
$915$	−1.51476	−	10.5354i	−0.0500765	−	0.348290i
$916$		0			0
$917$	42.6410	+	49.2104i	1.40813	+	1.62507i
$918$		0			0
$919$	28.6574			0.945320			0.472660	−	0.881245i	$-0.343294\pi$
$919$	28.6574			0.945320			0.472660	+	0.881245i	$0.343294\pi$
$920$		0			0
$921$	4.37463			0.144149
$922$		0			0
$923$	13.6979	+	15.8082i	0.450872	+	0.520334i
$924$		0			0
$925$	−0.106488	−	0.740643i	−0.00350132	−	0.0243522i
$926$		0			0
$927$	−7.20351	+	15.7735i	−0.236594	+	0.518069i
$928$		0			0
$929$	−8.57874	+	59.6665i	−0.281459	+	1.95759i	0.00659235	+	0.999978i	$0.497902\pi$
$929$	−8.57874	+	59.6665i	−0.281459	+	1.95759i	−0.288052	+	0.957615i	$0.593008\pi$
$930$		0			0
$931$	117.681	+	34.5542i	3.85683	+	1.13247i
$932$		0			0
$933$	−4.17639	−	9.14503i	−0.136729	−	0.299395i
$934$		0			0
$935$	−28.8815	+	33.3310i	−0.944526	+	1.09004i
$936$		0			0
$937$	−6.07379	−	3.90339i	−0.198422	−	0.127518i	0.437657	−	0.899142i	$-0.355808\pi$
$937$	−6.07379	−	3.90339i	−0.198422	−	0.127518i	−0.636079	+	0.771624i	$0.719445\pi$
$938$		0			0
$939$	20.2584	−	13.0193i	0.661109	−	0.424869i
$940$		0			0
$941$	−4.61950	+	1.35641i	−0.150591	+	0.0442176i	−0.356159	−	0.934425i	$-0.615914\pi$
$941$	−4.61950	+	1.35641i	−0.150591	+	0.0442176i	0.205568	+	0.978643i	$0.434096\pi$
$942$		0			0
$943$	8.52304	−	5.86421i	0.277548	−	0.190965i
$944$		0			0
$945$	−9.73537	+	2.85856i	−0.316692	+	0.0929891i
$946$		0			0
$947$	36.1350	−	23.2225i	1.17423	−	0.754631i	0.199912	−	0.979814i	$-0.435934\pi$
$947$	36.1350	−	23.2225i	1.17423	−	0.754631i	0.974317	+	0.225183i	$0.0722979\pi$
$948$		0			0
$949$	−13.9911	−	8.99151i	−0.454169	−	0.291877i
$950$		0			0
$951$	−1.31473	+	1.51728i	−0.0426329	+	0.0492010i
$952$		0			0
$953$	−15.4991	−	33.9383i	−0.502065	−	1.09937i	−0.975793	−	0.218698i	$-0.929819\pi$
$953$	−15.4991	−	33.9383i	−0.502065	−	1.09937i	0.473727	−	0.880672i	$-0.342908\pi$
$954$		0			0
$955$	−23.8823	−	7.01249i	−0.772814	−	0.226919i
$956$		0			0
$957$	−1.72270	+	11.9816i	−0.0556870	+	0.387311i
$958$		0			0
$959$	−1.09947	+	2.40750i	−0.0355038	+	0.0777424i
$960$		0			0
$961$	0.597914	+	4.15858i	0.0192876	+	0.134148i
$962$		0			0
$963$	12.5625	+	14.4980i	0.404822	+	0.467190i
$964$		0			0
$965$	16.4460			0.529414
$966$		0			0
$967$	0.332955			0.0107071			0.00535355	−	0.999986i	$-0.498296\pi$
$967$	0.332955			0.0107071			0.00535355	+	0.999986i	$0.498296\pi$
$968$		0			0
$969$	−22.9021	−	26.4305i	−0.735723	−	0.849070i
$970$		0			0
$971$	−3.06613	−	21.3254i	−0.0983967	−	0.684364i	−0.977992	−	0.208642i	$-0.933096\pi$
$971$	−3.06613	−	21.3254i	−0.0983967	−	0.684364i	0.879596	−	0.475722i	$-0.157813\pi$
$972$		0			0
$973$	−24.5914	+	53.8476i	−0.788363	+	1.72628i
$974$		0			0
$975$	−0.558110	+	3.88174i	−0.0178738	+	0.124315i
$976$		0			0
$977$	−40.8846	−	12.0048i	−1.30802	−	0.384068i	−0.447862	−	0.894103i	$-0.647814\pi$
$977$	−40.8846	−	12.0048i	−1.30802	−	0.384068i	−0.860154	+	0.510035i	$0.829633\pi$
$978$		0			0
$979$	0.700397	+	1.53365i	0.0223848	+	0.0490158i
$980$		0			0
$981$	−9.51491	+	10.9808i	−0.303788	+	0.350590i
$982$		0			0
$983$	−41.3946	−	26.6027i	−1.32028	−	0.848494i	−0.325019	−	0.945707i	$-0.605371\pi$
$983$	−41.3946	−	26.6027i	−1.32028	−	0.848494i	−0.995264	+	0.0972130i	$0.969007\pi$
$984$		0			0
$985$	2.59413	−	1.66715i	0.0826559	−	0.0531197i
$986$		0			0
$987$	−32.3461	+	9.49766i	−1.02959	+	0.302314i
$988$		0			0
$989$	−5.03850	+	12.0195i	−0.160215	+	0.382199i
$990$		0			0
$991$	−2.79013	+	0.819256i	−0.0886314	+	0.0260245i	−0.325748	−	0.945457i	$-0.605616\pi$
$991$	−2.79013	+	0.819256i	−0.0886314	+	0.0260245i	0.237116	+	0.971481i	$0.423798\pi$
$992$		0			0
$993$	19.5800	−	12.5833i	0.621354	−	0.399320i
$994$		0			0
$995$	45.7812	+	29.4218i	1.45136	+	0.932734i
$996$		0			0
$997$	11.8077	−	13.6268i	0.373952	−	0.431564i	−0.537313	−	0.843383i	$-0.680561\pi$
$997$	11.8077	−	13.6268i	0.373952	−	0.431564i	0.911266	+	0.411819i	$0.135106\pi$
$998$		0			0
$999$	0.390235	+	0.854496i	0.0123465	+	0.0270350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.193.2	✓	30
23.18	even	11	inner	552.2.q.c.409.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.193.2	✓	30	1.1	even	1	trivial
552.2.q.c.409.2	yes	30	23.18	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.291779 - 2.02937i) q^{5} +(-2.05584 + 4.50166i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.291779 - 2.02937i) q^{5} +(-2.05584 + 4.50166i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-4.13828 - 1.21511i) q^{11} +(2.04524 + 4.47845i) q^{13} +(1.34262 - 1.54946i) q^{15} +(4.19582 + 2.69649i) q^{17} +(-5.89881 + 3.79094i) q^{19} +(-4.74842 + 1.39426i) q^{21} +(2.12848 + 4.29762i) q^{23} +(0.764275 - 0.224411i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-2.36107 - 1.51737i) q^{29} +(3.39004 - 3.91232i) q^{31} +(-1.79168 - 3.92323i) q^{33} +(9.73537 + 2.85856i) q^{35} +(0.133689 - 0.929825i) q^{37} +(-2.04524 + 4.47845i) q^{39} +(-0.307002 - 2.13525i) q^{41} +(1.77961 + 2.05378i) q^{43} +2.05023 q^{45} +6.81196 q^{47} +(-11.4545 - 13.2192i) q^{49} +(0.709806 + 4.93681i) q^{51} +(-5.84418 + 12.7970i) q^{53} +(-1.25844 + 8.75262i) q^{55} +(-6.72790 - 1.97549i) q^{57} +(-3.18599 - 6.97635i) q^{59} +(3.39969 - 3.92346i) q^{61} +(-4.16327 - 2.67557i) q^{63} +(8.49165 - 5.45725i) q^{65} +(-12.9835 + 3.81231i) q^{67} +(-1.85407 + 4.42294i) q^{69} +(4.07648 - 1.19696i) q^{71} +(-2.84177 + 1.82629i) q^{73} +(0.670093 + 0.430642i) q^{75} +(13.9776 - 16.1311i) q^{77} +(0.713653 + 1.56268i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.391072 - 2.71996i) q^{83} +(4.24791 - 9.30162i) q^{85} +(-0.399422 - 2.77804i) q^{87} +(-0.255996 - 0.295435i) q^{89} -24.3652 q^{91} +5.17674 q^{93} +(9.41434 + 10.8647i) q^{95} +(-0.166249 - 1.15629i) q^{97} +(1.79168 - 3.92323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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