LMFDB - Embedded newform 552.2.q.a.25.1

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			25.1
Character	$\chi$	$=$	552.25
Dual form			552.2.q.a.265.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{3} +(-2.98780 - 0.877298i) q^{5} +(0.0902354 - 0.104137i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{3} +(-2.98780 - 0.877298i) q^{5} +(0.0902354 - 0.104137i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-3.50929 + 2.25528i) q^{11} +(2.59036 + 2.98943i) q^{13} +(-0.443160 + 3.08224i) q^{15} +(-1.63427 + 3.57855i) q^{17} +(0.359084 + 0.786285i) q^{19} +(-0.115919 - 0.0744967i) q^{21} +(4.49439 - 1.67346i) q^{23} +(3.95104 + 2.53918i) q^{25} +(0.415415 + 0.909632i) q^{27} +(-3.33106 + 7.29401i) q^{29} +(-0.422513 + 2.93864i) q^{31} +(2.73175 + 3.15261i) q^{33} +(-0.360965 + 0.231978i) q^{35} +(-6.87003 + 2.01722i) q^{37} +(2.59036 - 2.98943i) q^{39} +(-10.6354 - 3.12284i) q^{41} +(-1.18601 - 8.24886i) q^{43} +3.11394 q^{45} +6.11892 q^{47} +(0.993502 + 6.90996i) q^{49} +(3.77470 + 1.10835i) q^{51} +(-2.24293 + 2.58848i) q^{53} +(12.4636 - 3.65965i) q^{55} +(0.727179 - 0.467329i) q^{57} +(-3.06008 - 3.53152i) q^{59} +(-0.797742 + 5.54842i) q^{61} +(-0.0572414 + 0.125341i) q^{63} +(-5.11685 - 11.2043i) q^{65} +(-9.60615 - 6.17350i) q^{67} +(-2.29605 - 4.21048i) q^{69} +(6.42680 + 4.13025i) q^{71} +(1.14474 + 2.50662i) q^{73} +(1.95104 - 4.27219i) q^{75} +(-0.0818033 + 0.568954i) q^{77} +(0.512579 + 0.591548i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-14.7513 + 4.33138i) q^{83} +(8.02232 - 9.25825i) q^{85} +(7.69383 + 2.25911i) q^{87} +(-2.24252 - 15.5971i) q^{89} +0.545053 q^{91} +2.96886 q^{93} +(-0.383067 - 2.66429i) q^{95} +(-0.0912762 - 0.0268011i) q^{97} +(2.73175 - 3.15261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$4$		0			0
$5$	−2.98780	−	0.877298i	−1.33619	−	0.392339i	−0.465878	−	0.884849i	$-0.654262\pi$
$5$	−2.98780	−	0.877298i	−1.33619	−	0.392339i	−0.870307	+	0.492509i	$0.836080\pi$
$6$		0			0
$7$	0.0902354	−	0.104137i	0.0341058	−	0.0393602i	−0.738440	−	0.674319i	$-0.764437\pi$
$7$	0.0902354	−	0.104137i	0.0341058	−	0.0393602i	0.772546	+	0.634959i	$0.218983\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	−3.50929	+	2.25528i	−1.05809	+	0.679994i	−0.949396	−	0.314081i	$-0.898304\pi$
$11$	−3.50929	+	2.25528i	−1.05809	+	0.679994i	−0.108695	+	0.994075i	$0.534667\pi$
$12$		0			0
$13$	2.59036	+	2.98943i	0.718436	+	0.829119i	0.991118	−	0.132985i	$-0.0424562\pi$
$13$	2.59036	+	2.98943i	0.718436	+	0.829119i	−0.272682	+	0.962104i	$0.587911\pi$
$14$		0			0
$15$	−0.443160	+	3.08224i	−0.114423	+	0.795832i
$16$		0			0
$17$	−1.63427	+	3.57855i	−0.396368	+	0.867925i	0.601257	+	0.799055i	$0.294667\pi$
$17$	−1.63427	+	3.57855i	−0.396368	+	0.867925i	−0.997626	+	0.0688699i	$0.978061\pi$
$18$		0			0
$19$	0.359084	+	0.786285i	0.0823796	+	0.180386i	0.946339	−	0.323175i	$-0.104750\pi$
$19$	0.359084	+	0.786285i	0.0823796	+	0.180386i	−0.863960	+	0.503561i	$0.832023\pi$
$20$		0			0
$21$	−0.115919	−	0.0744967i	−0.0252956	−	0.0162565i
$22$		0			0
$23$	4.49439	−	1.67346i	0.937145	−	0.348941i
$23$	4.49439	−	1.67346i	0.937145	−	0.348941i
$24$		0			0
$25$	3.95104	+	2.53918i	0.790208	+	0.507836i
$26$		0			0
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$		0			0
$29$	−3.33106	+	7.29401i	−0.618563	+	1.35446i	0.297997	+	0.954567i	$0.403682\pi$
$29$	−3.33106	+	7.29401i	−0.618563	+	1.35446i	−0.916560	+	0.399897i	$0.869046\pi$
$30$		0			0
$31$	−0.422513	+	2.93864i	−0.0758855	+	0.527796i	0.916051	+	0.401061i	$0.131359\pi$
$31$	−0.422513	+	2.93864i	−0.0758855	+	0.527796i	−0.991937	+	0.126734i	$0.959550\pi$
$32$		0			0
$33$	2.73175	+	3.15261i	0.475537	+	0.548799i
$34$		0			0
$35$	−0.360965	+	0.231978i	−0.0610142	+	0.0392114i
$36$		0			0
$37$	−6.87003	+	2.01722i	−1.12943	+	0.331629i	−0.792482	−	0.609895i	$-0.791212\pi$
$37$	−6.87003	+	2.01722i	−1.12943	+	0.331629i	−0.336944	+	0.941525i	$0.609393\pi$
$38$		0			0
$39$	2.59036	−	2.98943i	0.414789	−	0.478692i
$40$		0			0
$41$	−10.6354	−	3.12284i	−1.66097	−	0.487706i	−0.689388	−	0.724392i	$-0.742121\pi$
$41$	−10.6354	−	3.12284i	−1.66097	−	0.487706i	−0.971586	+	0.236686i	$0.923939\pi$
$42$		0			0
$43$	−1.18601	−	8.24886i	−0.180864	−	1.25794i	−0.854725	−	0.519081i	$-0.826274\pi$
$43$	−1.18601	−	8.24886i	−0.180864	−	1.25794i	0.673860	−	0.738859i	$-0.264635\pi$
$44$		0			0
$45$	3.11394			0.464198
$46$		0			0
$47$	6.11892			0.892536			0.446268	−	0.894899i	$-0.352753\pi$
$47$	6.11892			0.892536			0.446268	+	0.894899i	$0.352753\pi$
$48$		0			0
$49$	0.993502	+	6.90996i	0.141929	+	0.987137i
$50$		0			0
$51$	3.77470	+	1.10835i	0.528564	+	0.155200i
$52$		0			0
$53$	−2.24293	+	2.58848i	−0.308090	+	0.355555i	−0.888587	−	0.458707i	$-0.848313\pi$
$53$	−2.24293	+	2.58848i	−0.308090	+	0.355555i	0.580498	+	0.814262i	$0.302858\pi$
$54$		0			0
$55$	12.4636	−	3.65965i	1.68059	−	0.493467i
$56$		0			0
$57$	0.727179	−	0.467329i	0.0963172	−	0.0618993i
$58$		0			0
$59$	−3.06008	−	3.53152i	−0.398389	−	0.459765i	0.520744	−	0.853713i	$-0.325655\pi$
$59$	−3.06008	−	3.53152i	−0.398389	−	0.459765i	−0.919133	+	0.393948i	$0.871109\pi$
$60$		0			0
$61$	−0.797742	+	5.54842i	−0.102140	+	0.710402i	0.872823	+	0.488037i	$0.162287\pi$
$61$	−0.797742	+	5.54842i	−0.102140	+	0.710402i	−0.974963	+	0.222365i	$0.928622\pi$
$62$		0			0
$63$	−0.0572414	+	0.125341i	−0.00721174	+	0.0157915i
$64$		0			0
$65$	−5.11685	−	11.2043i	−0.634667	−	1.38973i
$66$		0			0
$67$	−9.60615	−	6.17350i	−1.17358	−	0.754213i	−0.199383	−	0.979922i	$-0.563894\pi$
$67$	−9.60615	−	6.17350i	−1.17358	−	0.754213i	−0.974195	+	0.225709i	$0.927530\pi$
$68$		0			0
$69$	−2.29605	−	4.21048i	−0.276412	−	0.506883i
$70$		0			0
$71$	6.42680	+	4.13025i	0.762721	+	0.490171i	0.863258	−	0.504762i	$-0.168420\pi$
$71$	6.42680	+	4.13025i	0.762721	+	0.490171i	−0.100538	+	0.994933i	$0.532056\pi$
$72$		0			0
$73$	1.14474	+	2.50662i	0.133981	+	0.293378i	0.964717	−	0.263289i	$-0.0848073\pi$
$73$	1.14474	+	2.50662i	0.133981	+	0.293378i	−0.830736	+	0.556667i	$0.812080\pi$
$74$		0			0
$75$	1.95104	−	4.27219i	0.225287	−	0.493310i
$76$		0			0
$77$	−0.0818033	+	0.568954i	−0.00932235	+	0.0648384i
$78$		0			0
$79$	0.512579	+	0.591548i	0.0576697	+	0.0665543i	0.783851	−	0.620948i	$-0.213252\pi$
$79$	0.512579	+	0.591548i	0.0576697	+	0.0665543i	−0.726182	+	0.687503i	$0.758707\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	−14.7513	+	4.33138i	−1.61917	+	0.475431i	−0.960795	−	0.277261i	$-0.910573\pi$
$83$	−14.7513	+	4.33138i	−1.61917	+	0.475431i	−0.658373	+	0.752691i	$0.728755\pi$
$84$		0			0
$85$	8.02232	−	9.25825i	0.870143	−	1.00420i
$86$		0			0
$87$	7.69383	+	2.25911i	0.824865	+	0.242202i
$88$		0			0
$89$	−2.24252	−	15.5971i	−0.237707	−	1.65329i	−0.663287	−	0.748365i	$-0.730839\pi$
$89$	−2.24252	−	15.5971i	−0.237707	−	1.65329i	0.425581	−	0.904920i	$-0.360070\pi$
$90$		0			0
$91$	0.545053			0.0571371
$92$		0			0
$93$	2.96886			0.307856
$94$		0			0
$95$	−0.383067	−	2.66429i	−0.0393018	−	0.273350i
$96$		0			0
$97$	−0.0912762	−	0.0268011i	−0.00926770	−	0.00272124i	0.277095	−	0.960842i	$-0.410628\pi$
$97$	−0.0912762	−	0.0268011i	−0.00926770	−	0.00272124i	−0.286363	+	0.958121i	$0.592446\pi$
$98$		0			0
$99$	2.73175	−	3.15261i	0.274551	−	0.316849i
$100$		0			0
$101$	−6.36084	+	1.86771i	−0.632927	+	0.185844i	−0.582431	−	0.812880i	$-0.697898\pi$
$101$	−6.36084	+	1.86771i	−0.632927	+	0.185844i	−0.0504959	+	0.998724i	$0.516080\pi$
$102$		0			0
$103$	−3.08863	+	1.98494i	−0.304332	+	0.195582i	−0.683889	−	0.729586i	$-0.739713\pi$
$103$	−3.08863	+	1.98494i	−0.304332	+	0.195582i	0.379557	+	0.925168i	$0.376076\pi$
$104$		0			0
$105$	0.280988	+	0.324277i	0.0274216	+	0.0316462i
$106$		0			0
$107$	0.340511	−	2.36831i	0.0329185	−	0.228953i	−0.966720	−	0.255836i	$-0.917649\pi$
$107$	0.340511	−	2.36831i	0.0329185	−	0.228953i	0.999639	+	0.0268834i	$0.00855829\pi$
$108$		0			0
$109$	−1.14470	+	2.50655i	−0.109643	+	0.240084i	−0.956498	−	0.291740i	$-0.905766\pi$
$109$	−1.14470	+	2.50655i	−0.109643	+	0.240084i	0.846855	+	0.531824i	$0.178493\pi$
$110$		0			0
$111$	2.97440	+	6.51302i	0.282317	+	0.618189i
$112$		0			0
$113$	10.0755	+	6.47512i	0.947821	+	0.609128i	0.920602	−	0.390502i	$-0.127698\pi$
$113$	10.0755	+	6.47512i	0.947821	+	0.609128i	0.0272190	+	0.999629i	$0.491335\pi$
$114$		0			0
$115$	−14.8965	+	1.05706i	−1.38910	+	0.0985716i
$116$		0			0
$117$	−3.32765	−	2.13855i	−0.307641	−	0.197709i
$118$		0			0
$119$	0.225191	+	0.493100i	0.0206432	+	0.0452024i
$120$		0			0
$121$	2.65925	−	5.82294i	0.241750	−	0.529359i
$122$		0			0
$123$	−1.57748	+	10.9716i	−0.142236	+	0.989276i
$124$		0			0
$125$	0.618669	+	0.713982i	0.0553355	+	0.0638605i
$126$		0			0
$127$	10.1949	−	6.55186i	0.904651	−	0.581384i	−0.00351518	−	0.999994i	$-0.501119\pi$
$127$	10.1949	−	6.55186i	0.904651	−	0.581384i	0.908166	+	0.418610i	$0.137483\pi$
$128$		0			0
$129$	−7.99612	+	2.34787i	−0.704019	+	0.206719i
$130$		0			0
$131$	6.73639	−	7.77421i	0.588562	−	0.679236i	−0.380861	−	0.924632i	$-0.624373\pi$
$131$	6.73639	−	7.77421i	0.588562	−	0.679236i	0.969423	+	0.245396i	$0.0789180\pi$
$132$		0			0
$133$	0.114284	+	0.0335567i	0.00990965	+	0.00290974i
$134$		0			0
$135$	−0.443160	−	3.08224i	−0.0381411	−	0.265277i
$136$		0			0
$137$	−9.77193			−0.834872			−0.417436	−	0.908706i	$-0.637071\pi$
$137$	−9.77193			−0.834872			−0.417436	+	0.908706i	$0.637071\pi$
$138$		0			0
$139$	7.37618			0.625640			0.312820	−	0.949813i	$-0.398726\pi$
$139$	7.37618			0.625640			0.312820	+	0.949813i	$0.398726\pi$
$140$		0			0
$141$	−0.870813	−	6.05664i	−0.0733357	−	0.510061i
$142$		0			0
$143$	−15.8323	−	4.64879i	−1.32397	−	0.388752i
$144$		0			0
$145$	16.3516	−	18.8707i	1.35792	−	1.56713i
$146$		0			0
$147$	6.69823	−	1.96678i	0.552461	−	0.162217i
$148$		0			0
$149$	19.6630	−	12.6366i	1.61085	−	1.03523i	0.649332	−	0.760505i	$-0.275048\pi$
$149$	19.6630	−	12.6366i	1.61085	−	1.03523i	0.961522	−	0.274728i	$-0.0885879\pi$
$150$		0			0
$151$	−10.5110	−	12.1303i	−0.855372	−	0.987152i	0.144626	−	0.989486i	$-0.453802\pi$
$151$	−10.5110	−	12.1303i	−0.855372	−	0.987152i	−0.999997	+	0.00233489i	$0.999257\pi$
$152$		0			0
$153$	0.559875	−	3.89402i	0.0452632	−	0.314813i
$154$		0			0
$155$	3.84045	−	8.40941i	0.308472	−	0.675460i
$156$		0			0
$157$	5.65174	+	12.3756i	0.451058	+	0.987679i	0.989435	+	0.144975i	$0.0463102\pi$
$157$	5.65174	+	12.3756i	0.451058	+	0.987679i	−0.538377	+	0.842704i	$0.680963\pi$
$158$		0			0
$159$	2.88133	+	1.85172i	0.228504	+	0.146851i
$160$		0			0
$161$	0.231283	−	0.619039i	0.0182277	−	0.0487871i
$162$		0			0
$163$	13.9499	+	8.96504i	1.09264	+	0.702196i	0.957443	−	0.288623i	$-0.0931974\pi$
$163$	13.9499	+	8.96504i	1.09264	+	0.702196i	0.135196	+	0.990819i	$0.456834\pi$
$164$		0			0
$165$	−5.39616	−	11.8159i	−0.420090	−	0.919869i
$166$		0			0
$167$	−0.903107	+	1.97753i	−0.0698845	+	0.153026i	−0.941351	−	0.337430i	$-0.890442\pi$
$167$	−0.903107	+	1.97753i	−0.0698845	+	0.153026i	0.871466	+	0.490456i	$0.163170\pi$
$168$		0			0
$169$	−0.376658	+	2.61971i	−0.0289737	+	0.201516i
$170$		0			0
$171$	−0.566061	−	0.653269i	−0.0432878	−	0.0499567i
$172$		0			0
$173$	−15.5564	+	9.99749i	−1.18273	+	0.760095i	−0.975886	−	0.218279i	$-0.929956\pi$
$173$	−15.5564	+	9.99749i	−1.18273	+	0.760095i	−0.206844	+	0.978374i	$0.566319\pi$
$174$		0			0
$175$	0.620947	−	0.182326i	0.0469392	−	0.0137826i
$176$		0			0
$177$	−3.06008	+	3.53152i	−0.230010	+	0.265445i
$178$		0			0
$179$	−13.5585	−	3.98114i	−1.01341	−	0.297564i	−0.267463	−	0.963568i	$-0.586185\pi$
$179$	−13.5585	−	3.98114i	−1.01341	−	0.297564i	−0.745948	+	0.666004i	$0.768003\pi$
$180$		0			0
$181$	−1.59842	−	11.1172i	−0.118809	−	0.826337i	−0.958870	−	0.283845i	$-0.908390\pi$
$181$	−1.59842	−	11.1172i	−0.118809	−	0.826337i	0.840061	−	0.542492i	$-0.182519\pi$
$182$		0			0
$183$	5.60547			0.414368
$184$		0			0
$185$	22.2960			1.63923
$186$		0			0
$187$	−2.33552	−	16.2439i	−0.170790	−	1.18787i
$188$		0			0
$189$	0.132212	+	0.0388209i	0.00961699	+	0.00282380i
$190$		0			0
$191$	−4.42042	+	5.10144i	−0.319851	+	0.369127i	−0.892792	−	0.450469i	$-0.851257\pi$
$191$	−4.42042	+	5.10144i	−0.319851	+	0.369127i	0.572941	+	0.819596i	$0.305802\pi$
$192$		0			0
$193$	3.32913	−	0.977521i	0.239636	−	0.0703635i	−0.159709	−	0.987164i	$-0.551056\pi$
$193$	3.32913	−	0.977521i	0.239636	−	0.0703635i	0.399345	+	0.916801i	$0.369237\pi$
$194$		0			0
$195$	−10.3621	+	6.65931i	−0.742045	+	0.476883i
$196$		0			0
$197$	1.50838	+	1.74076i	0.107467	+	0.124024i	0.806935	−	0.590640i	$-0.201125\pi$
$197$	1.50838	+	1.74076i	0.107467	+	0.124024i	−0.699467	+	0.714665i	$0.746579\pi$
$198$		0			0
$199$	−1.09588	+	7.62205i	−0.0776852	+	0.540312i	0.913398	+	0.407068i	$0.133449\pi$
$199$	−1.09588	+	7.62205i	−0.0776852	+	0.540312i	−0.991083	+	0.133245i	$0.957460\pi$
$200$		0			0
$201$	−4.74356	+	10.3870i	−0.334585	+	0.732639i
$202$		0			0
$203$	0.458998	+	1.00507i	0.0322154	+	0.0705418i
$204$		0			0
$205$	29.0369	+	18.6609i	2.02802	+	1.30333i
$206$		0			0
$207$	−3.84086	+	2.87189i	−0.266958	+	0.199610i
$208$		0			0
$209$	−3.03343	−	1.94947i	−0.209827	−	0.134847i
$210$		0			0
$211$	−2.61106	−	5.71742i	−0.179753	−	0.393604i	0.798211	−	0.602378i	$-0.205780\pi$
$211$	−2.61106	−	5.71742i	−0.179753	−	0.393604i	−0.977964	+	0.208774i	$0.933053\pi$
$212$		0			0
$213$	3.17358	−	6.94918i	0.217450	−	0.476150i
$214$		0			0
$215$	−3.69315	+	25.6865i	−0.251871	+	1.75180i
$216$		0			0
$217$	0.267896	+	0.309169i	0.0181860	+	0.0209877i
$218$		0			0
$219$	2.31819	−	1.48981i	0.156649	−	0.100672i
$220$		0			0
$221$	−14.9312	+	4.38418i	−1.00438	+	0.294912i
$222$		0			0
$223$	−15.1376	+	17.4697i	−1.01369	+	1.16986i	−0.0282893	+	0.999600i	$0.509006\pi$
$223$	−15.1376	+	17.4697i	−1.01369	+	1.16986i	−0.985399	+	0.170259i	$0.945539\pi$
$224$		0			0
$225$	−4.50637	−	1.32319i	−0.300424	−	0.0882126i
$226$		0			0
$227$	0.746652	+	5.19308i	0.0495571	+	0.344677i	0.999482	+	0.0321973i	$0.0102505\pi$
$227$	0.746652	+	5.19308i	0.0495571	+	0.344677i	−0.949924	+	0.312480i	$0.898840\pi$
$228$		0			0
$229$	2.78130			0.183793			0.0918967	−	0.995769i	$-0.470707\pi$
$229$	2.78130			0.183793			0.0918967	+	0.995769i	$0.470707\pi$
$230$		0			0
$231$	0.574805			0.0378194
$232$		0			0
$233$	3.30181	+	22.9646i	0.216309	+	1.50446i	0.751502	+	0.659731i	$0.229330\pi$
$233$	3.30181	+	22.9646i	0.216309	+	1.50446i	−0.535193	+	0.844730i	$0.679761\pi$
$234$		0			0
$235$	−18.2821	−	5.36811i	−1.19259	−	0.350177i
$236$		0			0
$237$	0.512579	−	0.591548i	0.0332956	−	0.0384252i
$238$		0			0
$239$	25.5140	−	7.49158i	1.65036	−	0.484590i	0.681424	−	0.731889i	$-0.261361\pi$
$239$	25.5140	−	7.49158i	1.65036	−	0.484590i	0.968939	+	0.247299i	$0.0795429\pi$
$240$		0			0
$241$	−15.2732	+	9.81546i	−0.983831	+	0.632270i	−0.930494	−	0.366307i	$-0.880622\pi$
$241$	−15.2732	+	9.81546i	−0.983831	+	0.632270i	−0.0533367	+	0.998577i	$0.516986\pi$
$242$		0			0
$243$	−0.654861	−	0.755750i	−0.0420093	−	0.0484814i
$244$		0			0
$245$	3.09370	−	21.5172i	0.197649	−	1.37468i
$246$		0			0
$247$	−1.42039	+	3.11022i	−0.0903771	+	0.197898i
$248$		0			0
$249$	6.38662	+	13.9848i	0.404736	+	0.886248i
$250$		0			0
$251$	17.1342	+	11.0115i	1.08150	+	0.695037i	0.954903	−	0.296917i	$-0.0959585\pi$
$251$	17.1342	+	11.0115i	1.08150	+	0.695037i	0.126596	+	0.991954i	$0.459595\pi$
$252$		0			0
$253$	−11.9980	+	16.0088i	−0.754306	+	1.00646i
$254$		0			0
$255$	−10.3057	−	6.62308i	−0.645369	−	0.414753i
$256$		0			0
$257$	4.79030	+	10.4893i	0.298811	+	0.654304i	0.998170	−	0.0604658i	$-0.0192586\pi$
$257$	4.79030	+	10.4893i	0.298811	+	0.654304i	−0.699360	+	0.714770i	$0.746531\pi$
$258$		0			0
$259$	−0.409852	+	0.897451i	−0.0254670	+	0.0557649i
$260$		0			0
$261$	1.14117	−	7.93702i	0.0706368	−	0.491289i
$262$		0			0
$263$	2.72854	+	3.14890i	0.168249	+	0.194169i	0.833612	−	0.552350i	$-0.186269\pi$
$263$	2.72854	+	3.14890i	0.168249	+	0.194169i	−0.665363	+	0.746520i	$0.731723\pi$
$264$		0			0
$265$	8.97229	−	5.76614i	0.551163	−	0.354211i
$266$		0			0
$267$	−15.1192	+	4.43939i	−0.925278	+	0.271686i
$268$		0			0
$269$	13.1710	−	15.2001i	0.803050	−	0.926769i	−0.195495	−	0.980705i	$-0.562631\pi$
$269$	13.1710	−	15.2001i	0.803050	−	0.926769i	0.998544	+	0.0539358i	$0.0171766\pi$
$270$		0			0
$271$	5.18681	+	1.52298i	0.315076	+	0.0925147i	0.435447	−	0.900214i	$-0.356590\pi$
$271$	5.18681	+	1.52298i	0.315076	+	0.0925147i	−0.120371	+	0.992729i	$0.538408\pi$
$272$		0			0
$273$	−0.0775691	−	0.539505i	−0.00469470	−	0.0326523i
$274$		0			0
$275$	−19.5919			−1.18144
$276$		0			0
$277$	−21.7420			−1.30635			−0.653175	−	0.757207i	$-0.726563\pi$
$277$	−21.7420			−1.30635			−0.653175	+	0.757207i	$0.726563\pi$
$278$		0			0
$279$	−0.422513	−	2.93864i	−0.0252952	−	0.175932i
$280$		0			0
$281$	−3.06946	−	0.901274i	−0.183109	−	0.0537655i	0.188893	−	0.981998i	$-0.439510\pi$
$281$	−3.06946	−	0.901274i	−0.183109	−	0.0537655i	−0.372001	+	0.928232i	$0.621328\pi$
$282$		0			0
$283$	−17.8667	+	20.6193i	−1.06207	+	1.22569i	−0.0887925	+	0.996050i	$0.528301\pi$
$283$	−17.8667	+	20.6193i	−1.06207	+	1.22569i	−0.973275	+	0.229641i	$0.926245\pi$
$284$		0			0
$285$	−2.58265	+	0.758335i	−0.152983	+	0.0449199i
$286$		0			0
$287$	−1.28490	+	0.825753i	−0.0758450	+	0.0487426i
$288$		0			0
$289$	0.997461	+	1.15113i	0.0586742	+	0.0677136i
$290$		0			0
$291$	−0.0135384	+	0.0941614i	−0.000793633	+	0.00551984i
$292$		0			0
$293$	3.68076	−	8.05974i	0.215032	−	0.470855i	−0.771122	−	0.636688i	$-0.780304\pi$
$293$	3.68076	−	8.05974i	0.215032	−	0.470855i	0.986154	+	0.165833i	$0.0530313\pi$
$294$		0			0
$295$	6.04472	+	13.2361i	0.351937	+	0.770635i
$296$		0			0
$297$	−3.50929	−	2.25528i	−0.203630	−	0.130865i
$298$		0			0
$299$	16.6448	+	9.10079i	0.962592	+	0.526312i
$300$		0			0
$301$	−0.966034	−	0.620832i	−0.0556813	−	0.0357842i
$302$		0			0
$303$	2.75394	+	6.03029i	0.158210	+	0.346431i
$304$		0			0
$305$	7.25111	−	15.8777i	0.415197	−	0.909155i
$306$		0			0
$307$	−1.45632	+	10.1289i	−0.0831165	+	0.578088i	0.905120	+	0.425156i	$0.139781\pi$
$307$	−1.45632	+	10.1289i	−0.0831165	+	0.578088i	−0.988237	+	0.152932i	$0.951128\pi$
$308$		0			0
$309$	2.40430	+	2.77471i	0.136776	+	0.157848i
$310$		0			0
$311$	−19.8317	+	12.7451i	−1.12455	+	0.722707i	−0.964416	−	0.264388i	$-0.914830\pi$
$311$	−19.8317	+	12.7451i	−1.12455	+	0.722707i	−0.160137	+	0.987095i	$0.551194\pi$
$312$		0			0
$313$	−27.4450	+	8.05858i	−1.55128	+	0.455498i	−0.941484	−	0.337058i	$-0.890568\pi$
$313$	−27.4450	+	8.05858i	−1.55128	+	0.455498i	−0.609799	+	0.792556i	$0.708750\pi$
$314$		0			0
$315$	0.280988	−	0.324277i	0.0158319	−	0.0182709i
$316$		0			0
$317$	18.1852	+	5.33967i	1.02138	+	0.299906i	0.749203	−	0.662340i	$-0.230437\pi$
$317$	18.1852	+	5.33967i	1.02138	+	0.299906i	0.272182	+	0.962246i	$0.412255\pi$
$318$		0			0
$319$	−4.76040	−	33.1093i	−0.266531	−	1.85377i
$320$		0			0
$321$	−2.39266			−0.133545
$322$		0			0
$323$	−3.40060			−0.189214
$324$		0			0
$325$	2.64390	+	18.3887i	0.146657	+	1.02002i
$326$		0			0
$327$	2.64394	+	0.776331i	0.146210	+	0.0429312i
$328$		0			0
$329$	0.552143	−	0.637207i	0.0304406	−	0.0351304i
$330$		0			0
$331$	−32.2088	+	9.45735i	−1.77035	+	0.519823i	−0.993894	−	0.110343i	$-0.964805\pi$
$331$	−32.2088	+	9.45735i	−1.77035	+	0.519823i	−0.776460	+	0.630166i	$0.782987\pi$
$332$		0			0
$333$	6.02343	−	3.87102i	0.330082	−	0.212131i
$334$		0			0
$335$	23.2853	+	26.8726i	1.27221	+	1.46821i
$336$		0			0
$337$	4.02926	−	28.0241i	0.219488	−	1.52657i	−0.520449	−	0.853893i	$-0.674235\pi$
$337$	4.02926	−	28.0241i	0.219488	−	1.52657i	0.739937	−	0.672677i	$-0.234855\pi$
$338$		0			0
$339$	4.97532	−	10.8944i	0.270222	−	0.591704i
$340$		0			0
$341$	−5.14475	−	11.2654i	−0.278604	−	0.610057i
$342$		0			0
$343$	1.62067	+	1.04154i	0.0875078	+	0.0562378i
$344$		0			0
$345$	3.16629	+	14.5944i	0.170467	+	0.785736i
$346$		0			0
$347$	27.7895	+	17.8592i	1.49182	+	0.958732i	0.995909	+	0.0903566i	$0.0288007\pi$
$347$	27.7895	+	17.8592i	1.49182	+	0.958732i	0.495907	+	0.868376i	$0.334836\pi$
$348$		0			0
$349$	−12.2469	−	26.8171i	−0.655564	−	1.43548i	−0.886599	−	0.462539i	$-0.846939\pi$
$349$	−12.2469	−	26.8171i	−0.655564	−	1.43548i	0.231035	−	0.972945i	$-0.425789\pi$
$350$		0			0
$351$	−1.64321	+	3.59813i	−0.0877080	+	0.192054i
$352$		0			0
$353$	0.914185	−	6.35830i	0.0486572	−	0.338418i	−0.950923	−	0.309429i	$-0.899862\pi$
$353$	0.914185	−	6.35830i	0.0486572	−	0.338418i	0.999580	−	0.0289890i	$-0.00922879\pi$
$354$		0			0
$355$	−15.5785	−	17.9786i	−0.826823	−	0.954205i
$356$		0			0
$357$	0.456033	−	0.293074i	0.0241358	−	0.0155111i
$358$		0			0
$359$	30.9188	−	9.07856i	1.63183	−	0.479148i	0.667667	−	0.744460i	$-0.267293\pi$
$359$	30.9188	−	9.07856i	1.63183	−	0.479148i	0.964163	+	0.265312i	$0.0854750\pi$
$360$		0			0
$361$	11.9531	−	13.7946i	0.629108	−	0.726029i
$362$		0			0
$363$	−6.14213	−	1.80349i	−0.322378	−	0.0946587i
$364$		0			0
$365$	−1.22119	−	8.49356i	−0.0639200	−	0.444573i
$366$		0			0
$367$	−26.5692			−1.38690			−0.693449	−	0.720506i	$-0.743910\pi$
$367$	−26.5692			−1.38690			−0.693449	+	0.720506i	$0.743910\pi$
$368$		0			0
$369$	11.0844			0.577032
$370$		0			0
$371$	0.0671652	+	0.467144i	0.00348704	+	0.0242529i
$372$		0			0
$373$	28.1984	+	8.27979i	1.46006	+	0.428711i	0.912853	−	0.408288i	$-0.133874\pi$
$373$	28.1984	+	8.27979i	1.46006	+	0.428711i	0.547204	+	0.836999i	$0.315692\pi$
$374$		0			0
$375$	0.618669	−	0.713982i	0.0319479	−	0.0368699i
$376$		0			0
$377$	−30.4336	+	8.93611i	−1.56741	+	0.460233i
$378$		0			0
$379$	−3.99337	+	2.56639i	−0.205126	+	0.131826i	−0.639171	−	0.769065i	$-0.720722\pi$
$379$	−3.99337	+	2.56639i	−0.205126	+	0.131826i	0.434045	+	0.900891i	$0.357086\pi$
$380$		0			0
$381$	−7.93606	−	9.15870i	−0.406577	−	0.469214i
$382$		0			0
$383$	−1.71375	+	11.9194i	−0.0875687	+	0.609054i	0.898028	+	0.439939i	$0.145000\pi$
$383$	−1.71375	+	11.9194i	−0.0875687	+	0.609054i	−0.985596	+	0.169115i	$0.945909\pi$
$384$		0			0
$385$	0.743554	−	1.62816i	0.0378950	−	0.0829786i
$386$		0			0
$387$	3.46194	+	7.58059i	0.175980	+	0.385343i
$388$		0			0
$389$	23.0005	+	14.7815i	1.16617	+	0.749452i	0.972794	−	0.231672i	$-0.0744197\pi$
$389$	23.0005	+	14.7815i	1.16617	+	0.749452i	0.193377	+	0.981125i	$0.438056\pi$
$390$		0			0
$391$	−1.35646	+	18.8183i	−0.0685993	+	0.951681i
$392$		0			0
$393$	−8.65377	−	5.56144i	−0.436525	−	0.280538i
$394$		0			0
$395$	−1.01252	−	2.21711i	−0.0509455	−	0.111555i
$396$		0			0
$397$	−0.321775	+	0.704589i	−0.0161494	+	0.0353623i	−0.917535	−	0.397655i	$-0.869824\pi$
$397$	−0.321775	+	0.704589i	−0.0161494	+	0.0353623i	0.901385	+	0.433018i	$0.142551\pi$
$398$		0			0
$399$	0.0169509	−	0.117896i	0.000848606	−	0.00590218i
$400$		0			0
$401$	13.3517	+	15.4087i	0.666752	+	0.769472i	0.983864	−	0.178915i	$-0.0572589\pi$
$401$	13.3517	+	15.4087i	0.666752	+	0.769472i	−0.317113	+	0.948388i	$0.602713\pi$
$402$		0			0
$403$	−9.87933	+	6.34906i	−0.492124	+	0.316269i
$404$		0			0
$405$	−2.98780	+	0.877298i	−0.148465	+	0.0435933i
$406$		0			0
$407$	19.5595	−	22.5729i	0.969530	−	1.11890i
$408$		0			0
$409$	13.9887	+	4.10745i	0.691697	+	0.203101i	0.608643	−	0.793444i	$-0.291714\pi$
$409$	13.9887	+	4.10745i	0.691697	+	0.203101i	0.0830543	+	0.996545i	$0.473533\pi$
$410$		0			0
$411$	1.39069	+	9.67246i	0.0685977	+	0.477107i
$412$		0			0
$413$	−0.643890			−0.0316838
$414$		0			0
$415$	47.8739			2.35004
$416$		0			0
$417$	−1.04974	−	7.30110i	−0.0514060	−	0.357537i
$418$		0			0
$419$	−31.3066	−	9.19243i	−1.52943	−	0.449080i	−0.594551	−	0.804058i	$-0.702670\pi$
$419$	−31.3066	−	9.19243i	−1.52943	−	0.449080i	−0.934875	+	0.354978i	$0.884488\pi$
$420$		0			0
$421$	−7.28946	+	8.41249i	−0.355267	+	0.410000i	−0.905048	−	0.425309i	$-0.860166\pi$
$421$	−7.28946	+	8.41249i	−0.355267	+	0.410000i	0.549782	+	0.835308i	$0.314711\pi$
$422$		0			0
$423$	−5.87106	+	1.72390i	−0.285461	+	0.0838188i
$424$		0			0
$425$	−15.5436	+	9.98929i	−0.753977	+	0.484552i
$426$		0			0
$427$	0.505812	+	0.583738i	0.0244780	+	0.0282491i
$428$		0			0
$429$	−2.34830	+	16.3328i	−0.113377	+	0.788554i
$430$		0			0
$431$	11.5849	−	25.3674i	0.558025	−	1.22190i	−0.394907	−	0.918721i	$-0.629223\pi$
$431$	11.5849	−	25.3674i	0.558025	−	1.22190i	0.952932	−	0.303183i	$-0.0980495\pi$
$432$		0			0
$433$	−1.43216	−	3.13600i	−0.0688254	−	0.150707i	0.872093	−	0.489340i	$-0.162762\pi$
$433$	−1.43216	−	3.13600i	−0.0688254	−	0.150707i	−0.940918	+	0.338634i	$0.890035\pi$
$434$		0			0
$435$	−21.0057	−	13.4996i	−1.00715	−	0.647254i
$436$		0			0
$437$	2.92968	+	2.93295i	0.140146	+	0.140302i
$438$		0			0
$439$	23.1209	+	14.8589i	1.10350	+	0.709175i	0.959867	−	0.280456i	$-0.0904857\pi$
$439$	23.1209	+	14.8589i	1.10350	+	0.709175i	0.143631	+	0.989631i	$0.454122\pi$
$440$		0			0
$441$	−2.90002	−	6.35015i	−0.138096	−	0.302388i
$442$		0			0
$443$	6.73021	−	14.7371i	0.319762	−	0.700181i	−0.679683	−	0.733506i	$-0.737883\pi$
$443$	6.73021	−	14.7371i	0.319762	−	0.700181i	0.999445	+	0.0333254i	$0.0106098\pi$
$444$		0			0
$445$	−6.98307	+	48.5683i	−0.331029	+	2.30236i
$446$		0			0
$447$	−15.3063	−	17.6645i	−0.723965	−	0.835500i
$448$		0			0
$449$	−25.4306	+	16.3433i	−1.20015	+	0.771287i	−0.978981	−	0.203950i	$-0.934622\pi$
$449$	−25.4306	+	16.3433i	−1.20015	+	0.771287i	−0.221164	+	0.975237i	$0.570986\pi$
$450$		0			0
$451$	44.3657	−	13.0269i	2.08910	−	0.613415i
$452$		0			0
$453$	−10.5110	+	12.1303i	−0.493849	+	0.569932i
$454$		0			0
$455$	−1.62851	−	0.478174i	−0.0763458	−	0.0224171i
$456$		0			0
$457$	−3.21038	−	22.3287i	−0.150175	−	1.04449i	−0.915924	−	0.401351i	$-0.868541\pi$
$457$	−3.21038	−	22.3287i	−0.150175	−	1.04449i	0.765749	−	0.643140i	$-0.222368\pi$
$458$		0			0
$459$	−3.93406			−0.183626
$460$		0			0
$461$	20.1094			0.936586			0.468293	−	0.883573i	$-0.344869\pi$
$461$	20.1094			0.936586			0.468293	+	0.883573i	$0.344869\pi$
$462$		0			0
$463$	1.40194	+	9.75073i	0.0651538	+	0.453155i	0.996117	+	0.0880413i	$0.0280607\pi$
$463$	1.40194	+	9.75073i	0.0651538	+	0.453155i	−0.930963	+	0.365114i	$0.881030\pi$
$464$		0			0
$465$	−8.87037	−	2.60457i	−0.411353	−	0.120784i
$466$		0			0
$467$	0.539613	−	0.622746i	0.0249703	−	0.0288173i	−0.743127	−	0.669150i	$-0.766658\pi$
$467$	0.539613	−	0.622746i	0.0249703	−	0.0288173i	0.768097	+	0.640333i	$0.221204\pi$
$468$		0			0
$469$	−1.50971	+	0.443290i	−0.0697117	+	0.0204692i
$470$		0			0
$471$	11.4453	−	7.35544i	0.527371	−	0.338921i
$472$		0			0
$473$	22.7656	+	26.2729i	1.04676	+	1.20803i
$474$		0			0
$475$	−0.577762	+	4.01842i	−0.0265095	+	0.184378i
$476$		0			0
$477$	1.42281	−	3.11553i	0.0651462	−	0.142650i
$478$		0			0
$479$	2.06838	+	4.52913i	0.0945069	+	0.206941i	0.950981	−	0.309248i	$-0.100077\pi$
$479$	2.06838	+	4.52913i	0.0945069	+	0.206941i	−0.856474	+	0.516189i	$0.827350\pi$
$480$		0			0
$481$	−23.8262	−	15.3122i	−1.08638	−	0.698174i
$482$		0			0
$483$	−0.645653	−	0.140831i	−0.0293782	−	0.00640801i
$484$		0			0
$485$	0.249203	+	0.160153i	0.0113157	+	0.00727217i
$486$		0			0
$487$	−15.0293	−	32.9095i	−0.681041	−	1.49127i	−0.861536	−	0.507696i	$-0.830497\pi$
$487$	−15.0293	−	32.9095i	−0.681041	−	1.49127i	0.180495	−	0.983576i	$-0.442230\pi$
$488$		0			0
$489$	6.88851	−	15.0837i	0.311509	−	0.682110i
$490$		0			0
$491$	4.94016	−	34.3596i	0.222946	−	1.55063i	−0.503861	−	0.863785i	$-0.668087\pi$
$491$	4.94016	−	34.3596i	0.222946	−	1.55063i	0.726807	−	0.686842i	$-0.241003\pi$
$492$		0			0
$493$	−20.6581	−	23.8407i	−0.930395	−	1.07373i
$494$		0			0
$495$	−10.9277	+	7.02282i	−0.491164	+	0.315652i
$496$		0			0
$497$	1.01004	−	0.296574i	0.0453064	−	0.0133032i
$498$		0			0
$499$	28.0366	−	32.3559i	1.25509	−	1.44845i	0.411545	−	0.911389i	$-0.364989\pi$
$499$	28.0366	−	32.3559i	1.25509	−	1.44845i	0.843544	−	0.537061i	$-0.180465\pi$
$500$		0			0
$501$	2.08593	+	0.612483i	0.0931923	+	0.0273637i
$502$		0			0
$503$	−4.10272	−	28.5351i	−0.182931	−	1.27232i	−0.849786	−	0.527128i	$-0.823269\pi$
$503$	−4.10272	−	28.5351i	−0.182931	−	1.27232i	0.666855	−	0.745188i	$-0.267640\pi$
$504$		0			0
$505$	20.6435			0.918622
$506$		0			0
$507$	2.64665			0.117542
$508$		0			0
$509$	−3.65370	−	25.4121i	−0.161948	−	1.12637i	−0.894957	−	0.446152i	$-0.852794\pi$
$509$	−3.65370	−	25.4121i	−0.161948	−	1.12637i	0.733010	−	0.680218i	$-0.238115\pi$
$510$		0			0
$511$	0.364328	+	0.106976i	0.0161169	+	0.00473236i
$512$		0			0
$513$	−0.566061	+	0.653269i	−0.0249922	+	0.0288425i
$514$		0			0
$515$	10.9696	−	3.22097i	0.483379	−	0.141933i
$516$		0			0
$517$	−21.4731	+	13.7999i	−0.944384	+	0.606919i
$518$		0			0
$519$	12.1096	+	13.9753i	0.531554	+	0.613446i
$520$		0			0
$521$	−1.44666	+	10.0617i	−0.0633793	+	0.440813i	0.933281	+	0.359148i	$0.116933\pi$
$521$	−1.44666	+	10.0617i	−0.0633793	+	0.440813i	−0.996660	+	0.0816647i	$0.973976\pi$
$522$		0			0
$523$	8.32045	−	18.2192i	0.363828	−	0.796672i	−0.635863	−	0.771802i	$-0.719356\pi$
$523$	8.32045	−	18.2192i	0.363828	−	0.796672i	0.999691	−	0.0248696i	$-0.00791706\pi$
$524$		0			0
$525$	−0.268841	−	0.588679i	−0.0117332	−	0.0256921i
$526$		0			0
$527$	−9.82557	−	6.31451i	−0.428009	−	0.275064i
$528$		0			0
$529$	17.3990	−	15.0424i	0.756480	−	0.654017i
$530$		0			0
$531$	3.93107	+	2.52635i	0.170594	+	0.109634i
$532$		0			0
$533$	−18.2140	−	39.8832i	−0.788937	−	1.72753i
$534$		0			0
$535$	−3.09509	+	6.77730i	−0.133812	+	0.293008i
$536$		0			0
$537$	−2.01104	+	13.9871i	−0.0867827	+	0.603587i
$538$		0			0
$539$	−19.0704	−	22.0084i	−0.821420	−	0.947970i
$540$		0			0
$541$	−13.6542	+	8.77501i	−0.587039	+	0.377267i	−0.800185	−	0.599753i	$-0.795265\pi$
$541$	−13.6542	+	8.77501i	−0.587039	+	0.377267i	0.213146	+	0.977020i	$0.431629\pi$
$542$		0			0
$543$	−10.7766	+	3.16429i	−0.462468	+	0.135793i
$544$		0			0
$545$	5.61913	−	6.48482i	0.240697	−	0.277779i
$546$		0			0
$547$	20.6076	+	6.05092i	0.881115	+	0.258719i	0.690836	−	0.723011i	$-0.257243\pi$
$547$	20.6076	+	6.05092i	0.881115	+	0.258719i	0.190279	+	0.981730i	$0.439061\pi$
$548$		0			0
$549$	−0.797742	−	5.54842i	−0.0340468	−	0.236801i
$550$		0			0
$551$	−6.93131			−0.295284
$552$		0			0
$553$	0.107855			0.00458646
$554$		0			0
$555$	−3.17305	−	22.0691i	−0.134689	−	0.936779i
$556$		0			0
$557$	22.1968	+	6.51758i	0.940511	+	0.276159i	0.715831	−	0.698274i	$-0.246048\pi$
$557$	22.1968	+	6.51758i	0.940511	+	0.276159i	0.224680	+	0.974433i	$0.427866\pi$
$558$		0			0
$559$	21.5872	−	24.9130i	0.913043	−	1.05371i
$560$		0			0
$561$	−15.7462	+	4.62350i	−0.664804	+	0.195204i
$562$		0			0
$563$	−17.2031	+	11.0558i	−0.725026	+	0.465946i	−0.850382	−	0.526166i	$-0.823629\pi$
$563$	−17.2031	+	11.0558i	−0.725026	+	0.465946i	0.125356	+	0.992112i	$0.459993\pi$
$564$		0			0
$565$	−24.4229	−	28.1856i	−1.02748	−	1.18578i
$566$		0			0
$567$	0.0196100	−	0.136391i	0.000823544	−	0.00572787i
$568$		0			0
$569$	0.362538	−	0.793847i	0.0151984	−	0.0332798i	−0.901881	−	0.431985i	$-0.857813\pi$
$569$	0.362538	−	0.793847i	0.0151984	−	0.0332798i	0.917079	+	0.398706i	$0.130540\pi$
$570$		0			0
$571$	0.831461	+	1.82064i	0.0347955	+	0.0761916i	0.926232	−	0.376955i	$-0.123029\pi$
$571$	0.831461	+	1.82064i	0.0347955	+	0.0761916i	−0.891436	+	0.453146i	$0.850301\pi$
$572$		0			0
$573$	5.67861	+	3.64942i	0.237227	+	0.152457i
$574$		0			0
$575$	22.0067	+	4.80013i	0.917744	+	0.200179i
$576$		0			0
$577$	−30.6697	−	19.7102i	−1.27680	−	0.820547i	−0.286307	−	0.958138i	$-0.592428\pi$
$577$	−30.6697	−	19.7102i	−1.27680	−	0.820547i	−0.990489	+	0.137590i	$0.956064\pi$
$578$		0			0
$579$	−1.44136	−	3.15613i	−0.0599007	−	0.131164i
$580$		0			0
$581$	−0.880034	+	1.92701i	−0.0365100	+	0.0799457i
$582$		0			0
$583$	2.03333	−	14.1422i	0.0842121	−	0.585708i
$584$		0			0
$585$	8.06621	+	9.30890i	0.333497	+	0.384876i
$586$		0			0
$587$	4.27147	−	2.74511i	0.176302	−	0.113303i	−0.449513	−	0.893274i	$-0.648403\pi$
$587$	4.27147	−	2.74511i	0.176302	−	0.113303i	0.625816	+	0.779971i	$0.284766\pi$
$588$		0			0
$589$	−2.46233	+	0.723004i	−0.101458	+	0.0297909i
$590$		0			0
$591$	1.50838	−	1.74076i	0.0620464	−	0.0716053i
$592$		0			0
$593$	11.4279	+	3.35555i	0.469290	+	0.137796i	0.507823	−	0.861461i	$-0.330450\pi$
$593$	11.4279	+	3.35555i	0.469290	+	0.137796i	−0.0385334	+	0.999257i	$0.512269\pi$
$594$		0			0
$595$	−0.240231	−	1.67084i	−0.00984852	−	0.0684979i
$596$		0			0
$597$	7.70042			0.315157
$598$		0			0
$599$	−41.2785			−1.68659			−0.843297	−	0.537447i	$-0.819389\pi$
$599$	−41.2785			−1.68659			−0.843297	+	0.537447i	$0.819389\pi$
$600$		0			0
$601$	5.42685	+	37.7445i	0.221366	+	1.53963i	0.732880	+	0.680357i	$0.238175\pi$
$601$	5.42685	+	37.7445i	0.221366	+	1.53963i	−0.511515	+	0.859274i	$0.670915\pi$
$602$		0			0
$603$	10.9563	+	3.21706i	0.446175	+	0.131009i
$604$		0			0
$605$	−13.0538	+	15.0649i	−0.530711	+	0.612473i
$606$		0			0
$607$	3.58675	−	1.05317i	0.145582	−	0.0427467i	−0.208130	−	0.978101i	$-0.566738\pi$
$607$	3.58675	−	1.05317i	0.145582	−	0.0427467i	0.353712	+	0.935355i	$0.384919\pi$
$608$		0			0
$609$	0.929514	−	0.597362i	0.0376658	−	0.0242063i
$610$		0			0
$611$	15.8502	+	18.2921i	0.641230	+	0.740019i
$612$		0			0
$613$	3.69443	−	25.6953i	0.149217	−	1.03782i	−0.768290	−	0.640102i	$-0.778892\pi$
$613$	3.69443	−	25.6953i	0.149217	−	1.03782i	0.917506	−	0.397722i	$-0.130199\pi$
$614$		0			0
$615$	14.3386	−	31.3971i	0.578186	−	1.26605i
$616$		0			0
$617$	20.4741	+	44.8320i	0.824256	+	1.80487i	0.526332	+	0.850279i	$0.323567\pi$
$617$	20.4741	+	44.8320i	0.824256	+	1.80487i	0.297924	+	0.954590i	$0.403706\pi$
$618$		0			0
$619$	2.99516	+	1.92487i	0.120386	+	0.0773671i	0.599448	−	0.800414i	$-0.295387\pi$
$619$	2.99516	+	1.92487i	0.120386	+	0.0773671i	−0.479062	+	0.877781i	$0.659023\pi$
$620$		0			0
$621$	3.38927	+	3.39306i	0.136007	+	0.136159i
$622$		0			0
$623$	−1.82659	−	1.17388i	−0.0731808	−	0.0470304i
$624$		0			0
$625$	−10.9773	−	24.0369i	−0.439092	−	0.961477i
$626$		0			0
$627$	−1.49792	+	3.27999i	−0.0598212	+	0.130990i
$628$		0			0
$629$	4.00874	−	27.8814i	0.159839	−	1.11170i
$630$		0			0
$631$	11.3526	+	13.1016i	0.451940	+	0.521566i	0.935300	−	0.353855i	$-0.115129\pi$
$631$	11.3526	+	13.1016i	0.451940	+	0.521566i	−0.483361	+	0.875421i	$0.660584\pi$
$632$		0			0
$633$	−5.28764	+	3.39816i	−0.210165	+	0.135065i
$634$		0			0
$635$	−36.2083	+	10.6317i	−1.43688	+	0.421906i
$636$		0			0
$637$	−18.0833	+	20.8693i	−0.716487	+	0.826870i
$638$		0			0
$639$	−7.33010	−	2.15231i	−0.289974	−	0.0851441i
$640$		0			0
$641$	−0.210964	−	1.46728i	−0.00833256	−	0.0579542i	0.985231	−	0.171231i	$-0.0547744\pi$
$641$	−0.210964	−	1.46728i	−0.00833256	−	0.0579542i	−0.993563	+	0.113277i	$0.963865\pi$
$642$		0			0
$643$	−13.2628			−0.523033			−0.261516	−	0.965199i	$-0.584223\pi$
$643$	−13.2628			−0.523033			−0.261516	+	0.965199i	$0.584223\pi$
$644$		0			0
$645$	25.9506			1.02180
$646$		0			0
$647$	1.38085	+	9.60399i	0.0542867	+	0.377572i	0.998795	+	0.0490836i	$0.0156301\pi$
$647$	1.38085	+	9.60399i	0.0542867	+	0.377572i	−0.944508	+	0.328488i	$0.893461\pi$
$648$		0			0
$649$	18.7033	+	5.49178i	0.734169	+	0.215571i
$650$		0			0
$651$	0.267896	−	0.309169i	0.0104997	−	0.0121173i
$652$		0			0
$653$	11.0646	−	3.24887i	0.432992	−	0.127138i	−0.0579712	−	0.998318i	$-0.518463\pi$
$653$	11.0646	−	3.24887i	0.432992	−	0.127138i	0.490963	+	0.871180i	$0.336645\pi$
$654$		0			0
$655$	−26.9473	+	17.3180i	−1.05292	+	0.676670i
$656$		0			0
$657$	−1.80456	−	2.08258i	−0.0704027	−	0.0812490i
$658$		0			0
$659$	0.404453	−	2.81303i	0.0157552	−	0.109580i	−0.980426	−	0.196887i	$-0.936917\pi$
$659$	0.404453	−	2.81303i	0.0157552	−	0.109580i	0.996181	+	0.0873066i	$0.0278260\pi$
$660$		0			0
$661$	−13.4891	+	29.5370i	−0.524665	+	1.14886i	0.442978	+	0.896533i	$0.353922\pi$
$661$	−13.4891	+	29.5370i	−0.524665	+	1.14886i	−0.967643	+	0.252324i	$0.918805\pi$
$662$		0			0
$663$	6.46449	+	14.1552i	0.251060	+	0.549744i
$664$		0			0
$665$	−0.312018	−	0.200522i	−0.0120995	−	0.00777589i
$666$		0			0
$667$	−2.76482	+	38.3565i	−0.107054	+	1.48517i
$668$		0			0
$669$	19.4462	+	12.4973i	0.751834	+	0.483174i
$670$		0			0
$671$	−9.71375	−	21.2701i	−0.374995	−	0.821124i
$672$		0			0
$673$	5.65223	−	12.3767i	0.217877	−	0.477085i	−0.768858	−	0.639419i	$-0.779175\pi$
$673$	5.65223	−	12.3767i	0.217877	−	0.477085i	0.986736	+	0.162334i	$0.0519022\pi$
$674$		0			0
$675$	−0.668397	+	4.64881i	−0.0257266	+	0.178933i
$676$		0			0
$677$	−2.39938	−	2.76903i	−0.0922155	−	0.106422i	0.707766	−	0.706447i	$-0.249703\pi$
$677$	−2.39938	−	2.76903i	−0.0922155	−	0.106422i	−0.799982	+	0.600024i	$0.795158\pi$
$678$		0			0
$679$	−0.0110273	+	0.00708684i	−0.000423191	+	0.000271968i
$680$		0			0
$681$	5.03396	−	1.47810i	0.192902	−	0.0566411i
$682$		0			0
$683$	5.51062	−	6.35960i	0.210858	−	0.243343i	−0.640462	−	0.767990i	$-0.721257\pi$
$683$	5.51062	−	6.35960i	0.210858	−	0.243343i	0.851320	+	0.524647i	$0.175803\pi$
$684$		0			0
$685$	29.1966	+	8.57289i	1.11554	+	0.327553i
$686$		0			0
$687$	−0.395820	−	2.75299i	−0.0151015	−	0.105033i
$688$		0			0
$689$	−13.5481			−0.516140
$690$		0			0
$691$	17.8933			0.680692			0.340346	−	0.940300i	$-0.389456\pi$
$691$	17.8933			0.680692			0.340346	+	0.940300i	$0.389456\pi$
$692$		0			0
$693$	−0.0818033	−	0.568954i	−0.00310745	−	0.0216128i
$694$		0			0
$695$	−22.0386	−	6.47111i	−0.835971	−	0.245463i
$696$		0			0
$697$	28.5564	−	32.9558i	1.08165	−	1.24829i
$698$		0			0
$699$	22.2610	−	6.53641i	0.841987	−	0.247230i
$700$		0			0
$701$	−22.9485	+	14.7481i	−0.866754	+	0.557029i	−0.896758	−	0.442521i	$-0.854084\pi$
$701$	−22.9485	+	14.7481i	−0.866754	+	0.557029i	0.0300041	+	0.999550i	$0.490448\pi$
$702$		0			0
$703$	−4.05303	−	4.67745i	−0.152863	−	0.176413i
$704$		0			0
$705$	−2.71166	+	18.8600i	−0.102127	+	0.710308i
$706$		0			0
$707$	−0.379475	+	0.830933i	−0.0142716	+	0.0312505i
$708$		0			0
$709$	−10.4790	−	22.9459i	−0.393548	−	0.861750i	−0.997884	−	0.0650201i	$-0.979289\pi$
$709$	−10.4790	−	22.9459i	−0.393548	−	0.861750i	0.604336	−	0.796729i	$-0.293438\pi$
$710$		0			0
$711$	−0.658474	−	0.423176i	−0.0246947	−	0.0158703i
$712$		0			0
$713$	3.01877	+	13.9145i	0.113054	+	0.521100i
$714$		0			0
$715$	43.2255	+	27.7793i	1.61654	+	1.03889i
$716$		0			0
$717$	−11.0464	−	24.1881i	−0.412534	−	0.903322i
$718$		0			0
$719$	4.87571	−	10.6763i	0.181833	−	0.398159i	−0.796663	−	0.604424i	$-0.793403\pi$
$719$	4.87571	−	10.6763i	0.181833	−	0.398159i	0.978496	+	0.206264i	$0.0661307\pi$
$720$		0			0
$721$	−0.0719975	+	0.500754i	−0.00268133	+	0.0186490i
$722$		0			0
$723$	11.8892	+	13.7208i	0.442162	+	0.510283i
$724$		0			0
$725$	−31.6820	+	20.3608i	−1.17664	+	0.756180i
$726$		0			0
$727$	0.0736708	−	0.0216317i	0.00273230	−	0.000802276i	−0.280366	−	0.959893i	$-0.590456\pi$
$727$	0.0736708	−	0.0216317i	0.00273230	−	0.000802276i	0.283098	+	0.959091i	$0.408638\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	31.4572	+	9.23667i	1.16349	+	0.341631i
$732$		0			0
$733$	6.07412	+	42.2464i	0.224353	+	1.56041i	0.721297	+	0.692626i	$0.243546\pi$
$733$	6.07412	+	42.2464i	0.224353	+	1.56041i	−0.496944	+	0.867782i	$0.665545\pi$
$734$		0			0
$735$	−21.7384			−0.801835
$736$		0			0
$737$	47.6338			1.75461
$738$		0			0
$739$	3.00874	+	20.9263i	0.110678	+	0.769785i	0.967263	+	0.253777i	$0.0816731\pi$
$739$	3.00874	+	20.9263i	0.110678	+	0.769785i	−0.856584	+	0.516007i	$0.827418\pi$
$740$		0			0
$741$	3.28070	+	0.963301i	0.120520	+	0.0353877i
$742$		0			0
$743$	−19.7350	+	22.7754i	−0.724007	+	0.835549i	−0.991783	−	0.127933i	$-0.959166\pi$
$743$	−19.7350	+	22.7754i	−0.724007	+	0.835549i	0.267776	+	0.963481i	$0.413711\pi$
$744$		0			0
$745$	−69.8352	+	20.5055i	−2.55856	+	0.751262i
$746$		0			0
$747$	12.9335	−	8.31186i	0.473212	−	0.304115i
$748$		0			0
$749$	−0.215903	−	0.249165i	−0.00788891	−	0.00910429i
$750$		0			0
$751$	−3.39336	+	23.6014i	−0.123826	+	0.861226i	0.829333	+	0.558755i	$0.188721\pi$
$751$	−3.39336	+	23.6014i	−0.123826	+	0.861226i	−0.953159	+	0.302471i	$0.902188\pi$
$752$		0			0
$753$	8.46093	−	18.5269i	0.308334	−	0.675156i
$754$		0			0
$755$	20.7628	+	45.4643i	0.755637	+	1.65461i
$756$		0			0
$757$	40.2476	+	25.8656i	1.46282	+	0.940100i	0.998518	+	0.0544254i	$0.0173327\pi$
$757$	40.2476	+	25.8656i	1.46282	+	0.940100i	0.464306	+	0.885675i	$0.346304\pi$
$758$		0			0
$759$	17.5533	+	9.59756i	0.637146	+	0.348370i
$760$		0			0
$761$	−27.1542	−	17.4509i	−0.984337	−	0.632595i	−0.0537075	−	0.998557i	$-0.517104\pi$
$761$	−27.1542	−	17.4509i	−0.984337	−	0.632595i	−0.930630	+	0.365961i	$0.880740\pi$
$762$		0			0
$763$	0.157732	+	0.345385i	0.00571029	+	0.0125038i
$764$		0			0
$765$	−5.08901	+	11.1434i	−0.183994	+	0.402890i
$766$		0			0
$767$	2.63054	−	18.2958i	0.0949833	−	0.660623i
$768$		0			0
$769$	−33.4299	−	38.5801i	−1.20551	−	1.39124i	−0.898177	−	0.439634i	$-0.855108\pi$
$769$	−33.4299	−	38.5801i	−1.20551	−	1.39124i	−0.307336	−	0.951601i	$-0.599437\pi$
$770$		0			0
$771$	9.70080	−	6.23432i	0.349366	−	0.224524i
$772$		0			0
$773$	−31.5700	+	9.26980i	−1.13550	+	0.333411i	−0.794865	−	0.606786i	$-0.792459\pi$
$773$	−31.5700	+	9.26980i	−1.13550	+	0.333411i	−0.340630	+	0.940197i	$0.610640\pi$
$774$		0			0
$775$	−9.13110	+	10.5379i	−0.327999	+	0.378531i
$776$		0			0
$777$	0.946644	+	0.277960i	0.0339607	+	0.00997175i
$778$		0			0
$779$	−1.36357	−	9.48384i	−0.0488550	−	0.339794i
$780$		0			0
$781$	−31.8684			−1.14034
$782$		0			0
$783$	−8.01864			−0.286563
$784$		0			0
$785$	−6.02921	−	41.9340i	−0.215192	−	1.49669i
$786$		0			0
$787$	44.8253	+	13.1619i	1.59785	+	0.469171i	0.954947	−	0.296777i	$-0.0959117\pi$
$787$	44.8253	+	13.1619i	1.59785	+	0.469171i	0.642903	+	0.765948i	$0.277730\pi$
$788$		0			0
$789$	2.72854	−	3.14890i	0.0971384	−	0.112104i
$790$		0			0
$791$	1.58347	−	0.464947i	0.0563016	−	0.0165316i
$792$		0			0
$793$	−18.6530	+	11.9876i	−0.662389	+	0.425692i
$794$		0			0
$795$	−6.98434	−	8.06035i	−0.247709	−	0.285871i
$796$		0			0
$797$	−1.77323	+	12.3331i	−0.0628111	+	0.436861i	0.934014	+	0.357237i	$0.116281\pi$
$797$	−1.77323	+	12.3331i	−0.0628111	+	0.436861i	−0.996825	+	0.0796242i	$0.974628\pi$
$798$		0			0
$799$	−9.99995	+	21.8968i	−0.353773	+	0.774655i
$800$		0			0
$801$	6.54588	+	14.3335i	0.231287	+	0.506449i
$802$		0			0
$803$	−9.67035	−	6.21476i	−0.341259	−	0.219314i
$804$		0			0
$805$	−1.23411	+	1.64666i	−0.0434966	+	0.0580372i
$806$		0			0
$807$	−16.9199	−	10.8737i	−0.595607	−	0.382773i
$808$		0			0
$809$	16.7266	+	36.6262i	0.588077	+	1.28771i	0.936597	+	0.350408i	$0.113957\pi$
$809$	16.7266	+	36.6262i	0.588077	+	1.28771i	−0.348520	+	0.937301i	$0.613316\pi$
$810$		0			0
$811$	−3.46926	+	7.59662i	−0.121822	+	0.266754i	−0.960712	−	0.277548i	$-0.910478\pi$
$811$	−3.46926	+	7.59662i	−0.121822	+	0.266754i	0.838889	+	0.544302i	$0.183205\pi$
$812$		0			0
$813$	0.769323	−	5.35076i	0.0269813	−	0.187659i
$814$		0			0
$815$	−33.8144	−	39.0240i	−1.18447	−	1.36695i
$816$		0			0
$817$	6.06008	−	3.89458i	0.212015	−	0.136254i
$818$		0			0
$819$	−0.522975	+	0.153559i	−0.0182742	+	0.00536579i
$820$		0			0
$821$	5.80530	−	6.69967i	0.202606	−	0.233820i	−0.645349	−	0.763888i	$-0.723288\pi$
$821$	5.80530	−	6.69967i	0.202606	−	0.233820i	0.847955	+	0.530068i	$0.177833\pi$
$822$		0			0
$823$	−27.5635	−	8.09337i	−0.960803	−	0.282117i	−0.236525	−	0.971625i	$-0.576008\pi$
$823$	−27.5635	−	8.09337i	−0.960803	−	0.282117i	−0.724278	+	0.689508i	$0.757827\pi$
$824$		0			0
$825$	2.78822	+	19.3925i	0.0970734	+	0.675160i
$826$		0			0
$827$	13.5547			0.471343			0.235671	−	0.971833i	$-0.424271\pi$
$827$	13.5547			0.471343			0.235671	+	0.971833i	$0.424271\pi$
$828$		0			0
$829$	13.7568			0.477795			0.238897	−	0.971045i	$-0.423214\pi$
$829$	13.7568			0.477795			0.238897	+	0.971045i	$0.423214\pi$
$830$		0			0
$831$	3.09421	+	21.5207i	0.107337	+	0.746544i
$832$		0			0
$833$	−26.3513	−	7.73743i	−0.913017	−	0.268086i
$834$		0			0
$835$	4.43318	−	5.11617i	0.153417	−	0.177052i
$836$		0			0
$837$	−2.84860	+	0.836425i	−0.0984620	+	0.0289111i
$838$		0			0
$839$	26.3332	−	16.9233i	0.909124	−	0.584259i	−0.000358690	−	1.00000i	$-0.500114\pi$
$839$	26.3332	−	16.9233i	0.909124	−	0.584259i	0.909483	+	0.415741i	$0.136478\pi$
$840$		0			0
$841$	−23.1157	−	26.6769i	−0.797093	−	0.919894i
$842$		0			0
$843$	−0.455271	+	3.16648i	−0.0156804	+	0.109059i
$844$		0			0
$845$	3.42364	−	7.49674i	0.117777	−	0.257896i
$846$		0			0
$847$	−0.366427	−	0.802363i	−0.0125906	−	0.0275695i
$848$		0			0
$849$	22.9522	+	14.7505i	0.787716	+	0.506234i
$850$		0			0
$851$	−27.5008	+	20.5629i	−0.942716	+	0.704888i
$852$		0			0
$853$	21.0014	+	13.4968i	0.719073	+	0.462120i	0.848314	−	0.529493i	$-0.177618\pi$
$853$	21.0014	+	13.4968i	0.719073	+	0.462120i	−0.129241	+	0.991613i	$0.541254\pi$
$854$		0			0
$855$	1.11817	+	2.44844i	0.0382405	+	0.0837350i
$856$		0			0
$857$	1.65205	−	3.61748i	0.0564329	−	0.123571i	−0.879315	−	0.476241i	$-0.841999\pi$
$857$	1.65205	−	3.61748i	0.0564329	−	0.123571i	0.935748	+	0.352670i	$0.114726\pi$
$858$		0			0
$859$	1.93958	−	13.4900i	0.0661775	−	0.460274i	−0.929607	−	0.368552i	$-0.879854\pi$
$859$	1.93958	−	13.4900i	0.0661775	−	0.460274i	0.995785	−	0.0917224i	$-0.0292373\pi$
$860$		0			0
$861$	1.00021	+	1.15430i	0.0340870	+	0.0393385i
$862$		0			0
$863$	−38.6918	+	24.8657i	−1.31709	+	0.846440i	−0.994962	−	0.100258i	$-0.968033\pi$
$863$	−38.6918	+	24.8657i	−1.31709	+	0.846440i	−0.322124	+	0.946697i	$0.604397\pi$
$864$		0			0
$865$	55.2502	−	16.2229i	1.87856	−	0.551596i
$866$		0			0
$867$	0.997461	−	1.15113i	0.0338755	−	0.0390945i
$868$		0			0
$869$	−3.13290	−	0.919902i	−0.106276	−	0.0312055i
$870$		0			0
$871$	−6.42811	−	44.7085i	−0.217808	−	1.51489i
$872$		0			0
$873$	0.0951296			0.00321965
$874$		0			0
$875$	0.130178			0.00440082
$876$		0			0
$877$	4.27931	+	29.7632i	0.144502	+	1.00503i	0.925025	+	0.379906i	$0.124044\pi$
$877$	4.27931	+	29.7632i	0.144502	+	1.00503i	−0.780523	+	0.625127i	$0.785047\pi$
$878$		0			0
$879$	−8.50153	−	2.49627i	−0.286749	−	0.0841972i
$880$		0			0
$881$	−5.74913	+	6.63485i	−0.193693	+	0.223534i	−0.844286	−	0.535893i	$-0.819975\pi$
$881$	−5.74913	+	6.63485i	−0.193693	+	0.223534i	0.650593	+	0.759427i	$0.274520\pi$
$882$		0			0
$883$	8.45176	−	2.48166i	0.284424	−	0.0835145i	−0.136409	−	0.990653i	$-0.543556\pi$
$883$	8.45176	−	2.48166i	0.284424	−	0.0835145i	0.420833	+	0.907138i	$0.361738\pi$
$884$		0			0
$885$	12.2411	−	7.86688i	0.411480	−	0.264442i
$886$		0			0
$887$	−34.3946	−	39.6935i	−1.15486	−	1.33278i	−0.933917	−	0.357490i	$-0.883633\pi$
$887$	−34.3946	−	39.6935i	−1.15486	−	1.33278i	−0.220941	−	0.975287i	$-0.570913\pi$
$888$		0			0
$889$	0.237648	−	1.65288i	0.00797046	−	0.0554358i
$890$		0			0
$891$	−1.73290	+	3.79453i	−0.0580545	+	0.127122i
$892$		0			0
$893$	2.19721	+	4.81121i	0.0735267	+	0.161001i
$894$		0			0
$895$	37.0175	+	23.7897i	1.23736	+	0.795202i
$896$		0			0
$897$	6.63936	−	17.7705i	0.221682	−	0.593341i
$898$		0			0
$899$	−20.0271	−	12.8706i	−0.667940	−	0.429259i
$900$		0			0
$901$	−5.59744	−	12.2567i	−0.186478	−	0.408329i
$902$		0			0
$903$	−0.477032	+	1.04455i	−0.0158746	+	0.0347606i
$904$		0			0
$905$	−4.97737	+	34.6184i	−0.165453	+	1.15075i
$906$		0			0
$907$	2.80019	+	3.23159i	0.0929789	+	0.107303i	0.800332	−	0.599557i	$-0.204656\pi$
$907$	2.80019	+	3.23159i	0.0929789	+	0.107303i	−0.707353	+	0.706860i	$0.750111\pi$
$908$		0			0
$909$	5.57698	−	3.58411i	0.184977	−	0.118877i
$910$		0			0
$911$	−32.1423	+	9.43782i	−1.06492	+	0.312689i	−0.766831	−	0.641849i	$-0.778168\pi$
$911$	−32.1423	+	9.43782i	−1.06492	+	0.312689i	−0.298090	+	0.954538i	$0.596350\pi$
$912$		0			0
$913$	41.9982	−	48.4685i	1.38994	−	1.60407i
$914$		0			0
$915$	−16.7480	−	4.91767i	−0.553673	−	0.162573i
$916$		0			0
$917$	−0.201724	−	1.40302i	−0.00666150	−	0.0463318i
$918$		0			0
$919$	10.2838			0.339232			0.169616	−	0.985510i	$-0.445747\pi$
$919$	10.2838			0.339232			0.169616	+	0.985510i	$0.445747\pi$
$920$		0			0
$921$	10.2331			0.337192
$922$		0			0
$923$	4.30060	+	29.9113i	0.141556	+	0.984543i
$924$		0			0
$925$	−32.2659	−	9.47411i	−1.06090	−	0.311507i
$926$		0			0
$927$	2.40430	−	2.77471i	0.0789675	−	0.0911334i
$928$		0			0
$929$	−54.8448	+	16.1039i	−1.79940	+	0.528351i	−0.997600	−	0.0692425i	$-0.977942\pi$
$929$	−54.8448	+	16.1039i	−1.79940	+	0.528351i	−0.801799	+	0.597594i	$0.796124\pi$
$930$		0			0
$931$	−5.07644	+	3.26243i	−0.166374	+	0.106922i
$932$		0			0
$933$	15.4377	+	17.8160i	0.505407	+	0.583271i
$934$		0			0
$935$	−7.27267	+	50.5825i	−0.237842	+	1.65423i
$936$		0			0
$937$	−5.49142	+	12.0245i	−0.179397	+	0.392824i	−0.977872	−	0.209203i	$-0.932913\pi$
$937$	−5.49142	+	12.0245i	−0.179397	+	0.392824i	0.798475	+	0.602028i	$0.205640\pi$
$938$		0			0
$939$	11.8824	+	26.0188i	0.387767	+	0.849091i
$940$		0			0
$941$	25.9049	+	16.6481i	0.844477	+	0.542712i	0.889848	−	0.456258i	$-0.150811\pi$
$941$	25.9049	+	16.6481i	0.844477	+	0.542712i	−0.0453709	+	0.998970i	$0.514447\pi$
$942$		0			0
$943$	−53.0257	+	3.76274i	−1.72675	+	0.122532i
$944$		0			0
$945$	−0.360965	−	0.231978i	−0.0117422	−	0.00754625i
$946$		0			0
$947$	12.3035	+	26.9409i	0.399810	+	0.875462i	0.997289	+	0.0735780i	$0.0234418\pi$
$947$	12.3035	+	26.9409i	0.399810	+	0.875462i	−0.597479	+	0.801884i	$0.703831\pi$
$948$		0			0
$949$	−4.52810	+	9.91515i	−0.146988	+	0.321859i
$950$		0			0
$951$	2.69729	−	18.7601i	0.0874656	−	0.608336i
$952$		0			0
$953$	15.5098	+	17.8992i	0.502411	+	0.579813i	0.949139	−	0.314857i	$-0.101956\pi$
$953$	15.5098	+	17.8992i	0.502411	+	0.579813i	−0.446728	+	0.894670i	$0.647411\pi$
$954$		0			0
$955$	17.6828	−	11.3641i	0.572203	−	0.367733i
$956$		0			0
$957$	−32.0948	+	9.42389i	−1.03748	+	0.304631i
$958$		0			0
$959$	−0.881774	+	1.01762i	−0.0284740	+	0.0328607i
$960$		0			0
$961$	21.2872	+	6.25048i	0.686683	+	0.201628i
$962$		0			0
$963$	0.340511	+	2.36831i	0.0109728	+	0.0763176i
$964$		0			0
$965$	−10.8044			−0.347805
$966$		0			0
$967$	−28.4930			−0.916275			−0.458137	−	0.888881i	$-0.651483\pi$
$967$	−28.4930			−0.916275			−0.458137	+	0.888881i	$0.651483\pi$
$968$		0			0
$969$	0.483956	+	3.36598i	0.0155469	+	0.108131i
$970$		0			0
$971$	−17.2200	−	5.05624i	−0.552615	−	0.162262i	−0.00650961	−	0.999979i	$-0.502072\pi$
$971$	−17.2200	−	5.05624i	−0.552615	−	0.162262i	−0.546106	+	0.837716i	$0.683890\pi$
$972$		0			0
$973$	0.665593	−	0.768135i	0.0213379	−	0.0246253i
$974$		0			0
$975$	17.8253	−	5.23398i	0.570867	−	0.167622i
$976$		0			0
$977$	−20.8903	+	13.4254i	−0.668341	+	0.429517i	−0.830327	−	0.557276i	$-0.811846\pi$
$977$	−20.8903	+	13.4254i	−0.668341	+	0.429517i	0.161986	+	0.986793i	$0.448210\pi$
$978$		0			0
$979$	43.0455	+	49.6771i	1.37574	+	1.58769i
$980$		0			0
$981$	0.392157	−	2.72751i	0.0125206	−	0.0870828i
$982$		0			0
$983$	−10.7258	+	23.4861i	−0.342099	+	0.749091i	−0.999992	−	0.00401972i	$-0.998720\pi$
$983$	−10.7258	+	23.4861i	−0.342099	+	0.749091i	0.657893	+	0.753111i	$0.271448\pi$
$984$		0			0
$985$	−2.97957	−	6.52435i	−0.0949370	−	0.207883i
$986$		0			0
$987$	−0.709300	−	0.455839i	−0.0225773	−	0.0145095i
$988$		0			0
$989$	−19.1346	−	35.0889i	−0.608443	−	1.11576i
$990$		0			0
$991$	9.23262	+	5.93345i	0.293284	+	0.188482i	0.679006	−	0.734133i	$-0.262411\pi$
$991$	9.23262	+	5.93345i	0.293284	+	0.188482i	−0.385722	+	0.922615i	$0.626048\pi$
$992$		0			0
$993$	13.9449	+	30.5350i	0.442527	+	0.968999i
$994$		0			0
$995$	9.96109	−	21.8117i	0.315788	−	0.691479i
$996$		0			0
$997$	−6.98976	+	48.6149i	−0.221368	+	1.53965i	0.511503	+	0.859281i	$0.329089\pi$
$997$	−6.98976	+	48.6149i	−0.221368	+	1.53965i	−0.732871	+	0.680367i	$0.761820\pi$
$998$		0			0
$999$	−4.68885	−	5.41122i	−0.148348	−	0.171203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.25.1	✓	30
23.12	even	11	inner	552.2.q.a.265.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.25.1	✓	30	1.1	even	1	trivial
552.2.q.a.265.1	yes	30	23.12	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)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{3} +(-2.98780 - 0.877298i) q^{5} +(0.0902354 - 0.104137i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{3} +(-2.98780 - 0.877298i) q^{5} +(0.0902354 - 0.104137i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-3.50929 + 2.25528i) q^{11} +(2.59036 + 2.98943i) q^{13} +(-0.443160 + 3.08224i) q^{15} +(-1.63427 + 3.57855i) q^{17} +(0.359084 + 0.786285i) q^{19} +(-0.115919 - 0.0744967i) q^{21} +(4.49439 - 1.67346i) q^{23} +(3.95104 + 2.53918i) q^{25} +(0.415415 + 0.909632i) q^{27} +(-3.33106 + 7.29401i) q^{29} +(-0.422513 + 2.93864i) q^{31} +(2.73175 + 3.15261i) q^{33} +(-0.360965 + 0.231978i) q^{35} +(-6.87003 + 2.01722i) q^{37} +(2.59036 - 2.98943i) q^{39} +(-10.6354 - 3.12284i) q^{41} +(-1.18601 - 8.24886i) q^{43} +3.11394 q^{45} +6.11892 q^{47} +(0.993502 + 6.90996i) q^{49} +(3.77470 + 1.10835i) q^{51} +(-2.24293 + 2.58848i) q^{53} +(12.4636 - 3.65965i) q^{55} +(0.727179 - 0.467329i) q^{57} +(-3.06008 - 3.53152i) q^{59} +(-0.797742 + 5.54842i) q^{61} +(-0.0572414 + 0.125341i) q^{63} +(-5.11685 - 11.2043i) q^{65} +(-9.60615 - 6.17350i) q^{67} +(-2.29605 - 4.21048i) q^{69} +(6.42680 + 4.13025i) q^{71} +(1.14474 + 2.50662i) q^{73} +(1.95104 - 4.27219i) q^{75} +(-0.0818033 + 0.568954i) q^{77} +(0.512579 + 0.591548i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-14.7513 + 4.33138i) q^{83} +(8.02232 - 9.25825i) q^{85} +(7.69383 + 2.25911i) q^{87} +(-2.24252 - 15.5971i) q^{89} +0.545053 q^{91} +2.96886 q^{93} +(-0.383067 - 2.66429i) q^{95} +(-0.0912762 - 0.0268011i) q^{97} +(2.73175 - 3.15261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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