LMFDB - Embedded newform 552.2.q.c.193.3

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			193.3
Character	$\chi$	$=$	552.193
Dual form			552.2.q.c.409.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(0.373689 + 2.59907i) q^{5} +(-0.503412 + 1.10232i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(0.373689 + 2.59907i) q^{5} +(-0.503412 + 1.10232i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(4.11232 + 1.20749i) q^{11} +(-0.475938 - 1.04216i) q^{13} +(-1.71953 + 1.98444i) q^{15} +(-5.64229 - 3.62608i) q^{17} +(-3.45172 + 2.21829i) q^{19} +(-1.16274 + 0.341412i) q^{21} +(1.47673 + 4.56281i) q^{23} +(-1.81803 + 0.533823i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(6.89835 + 4.43330i) q^{29} +(-4.60844 + 5.31843i) q^{31} +(1.78044 + 3.89862i) q^{33} +(-3.05312 - 0.896476i) q^{35} +(0.293299 - 2.03994i) q^{37} +(0.475938 - 1.04216i) q^{39} +(-1.36069 - 9.46381i) q^{41} +(-1.90678 - 2.20054i) q^{43} -2.62579 q^{45} +7.43941 q^{47} +(3.62234 + 4.18041i) q^{49} +(-0.954505 - 6.63873i) q^{51} +(5.01192 - 10.9746i) q^{53} +(-1.60161 + 11.1394i) q^{55} +(-3.93686 - 1.15597i) q^{57} +(3.56571 + 7.80781i) q^{59} +(-2.15072 + 2.48206i) q^{61} +(-1.01945 - 0.655164i) q^{63} +(2.53079 - 1.62644i) q^{65} +(1.61579 - 0.474440i) q^{67} +(-2.48129 + 4.10405i) q^{69} +(3.54931 - 1.04217i) q^{71} +(-0.819149 + 0.526435i) q^{73} +(-1.59399 - 1.02440i) q^{75} +(-3.40123 + 3.92522i) q^{77} +(3.11302 + 6.81655i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(1.05121 - 7.31133i) q^{83} +(7.31595 - 16.0197i) q^{85} +(1.16699 + 8.11662i) q^{87} +(4.11504 + 4.74901i) q^{89} +1.38838 q^{91} -7.03729 q^{93} +(-7.05534 - 8.14229i) q^{95} +(-2.20862 - 15.3613i) q^{97} +(-1.78044 + 3.89862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.373689	+	2.59907i	0.167119	+	1.16234i	0.884802	+	0.465967i	$0.154294\pi$
$5$	0.373689	+	2.59907i	0.167119	+	1.16234i	−0.717683	+	0.696370i	$0.754797\pi$
$6$		0			0
$7$	−0.503412	+	1.10232i	−0.190272	+	0.416637i	−0.980593	−	0.196056i	$-0.937187\pi$
$7$	−0.503412	+	1.10232i	−0.190272	+	0.416637i	0.790321	+	0.612693i	$0.209914\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	4.11232	+	1.20749i	1.23991	+	0.364071i	0.834982	−	0.550277i	$-0.185478\pi$
$11$	4.11232	+	1.20749i	1.23991	+	0.364071i	0.404930	+	0.914348i	$0.367296\pi$
$12$		0			0
$13$	−0.475938	−	1.04216i	−0.132002	−	0.289043i	0.832077	−	0.554660i	$-0.187152\pi$
$13$	−0.475938	−	1.04216i	−0.132002	−	0.289043i	−0.964079	+	0.265617i	$0.914424\pi$
$14$		0			0
$15$	−1.71953	+	1.98444i	−0.443980	+	0.512381i
$16$		0			0
$17$	−5.64229	−	3.62608i	−1.36846	−	0.879453i	−0.369691	−	0.929155i	$-0.620537\pi$
$17$	−5.64229	−	3.62608i	−1.36846	−	0.879453i	−0.998764	+	0.0497017i	$0.984173\pi$
$18$		0			0
$19$	−3.45172	+	2.21829i	−0.791879	+	0.508910i	−0.872956	−	0.487798i	$-0.837800\pi$
$19$	−3.45172	+	2.21829i	−0.791879	+	0.508910i	0.0810777	+	0.996708i	$0.474164\pi$
$20$		0			0
$21$	−1.16274	+	0.341412i	−0.253731	+	0.0745021i
$22$		0			0
$23$	1.47673	+	4.56281i	0.307920	+	0.951412i
$23$	1.47673	+	4.56281i	0.307920	+	0.951412i
$24$		0			0
$25$	−1.81803	+	0.533823i	−0.363607	+	0.106765i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	6.89835	+	4.43330i	1.28099	+	0.823243i	0.991010	−	0.133789i	$-0.0427144\pi$
$29$	6.89835	+	4.43330i	1.28099	+	0.823243i	0.289982	+	0.957032i	$0.406351\pi$
$30$		0			0
$31$	−4.60844	+	5.31843i	−0.827701	+	0.955218i	−0.999553	−	0.0299050i	$-0.990480\pi$
$31$	−4.60844	+	5.31843i	−0.827701	+	0.955218i	0.171852	+	0.985123i	$0.445025\pi$
$32$		0			0
$33$	1.78044	+	3.89862i	0.309935	+	0.678663i
$34$		0			0
$35$	−3.05312	−	0.896476i	−0.516071	−	0.151532i
$36$		0			0
$37$	0.293299	−	2.03994i	0.0482181	−	0.335364i	−0.951406	−	0.307940i	$-0.900360\pi$
$37$	0.293299	−	2.03994i	0.0482181	−	0.335364i	0.999624	−	0.0274242i	$-0.00873048\pi$
$38$		0			0
$39$	0.475938	−	1.04216i	0.0762111	−	0.166879i
$40$		0			0
$41$	−1.36069	−	9.46381i	−0.212504	−	1.47800i	−0.764755	−	0.644321i	$-0.777140\pi$
$41$	−1.36069	−	9.46381i	−0.212504	−	1.47800i	0.552251	−	0.833678i	$-0.313769\pi$
$42$		0			0
$43$	−1.90678	−	2.20054i	−0.290781	−	0.335579i	0.591498	−	0.806307i	$-0.298537\pi$
$43$	−1.90678	−	2.20054i	−0.290781	−	0.335579i	−0.882278	+	0.470728i	$0.843991\pi$
$44$		0			0
$45$	−2.62579			−0.391430
$46$		0			0
$47$	7.43941			1.08515			0.542574	−	0.840008i	$-0.317450\pi$
$47$	7.43941			1.08515			0.542574	+	0.840008i	$0.317450\pi$
$48$		0			0
$49$	3.62234	+	4.18041i	0.517478	+	0.597201i
$50$		0			0
$51$	−0.954505	−	6.63873i	−0.133657	−	0.929608i
$52$		0			0
$53$	5.01192	−	10.9746i	0.688441	−	1.50748i	−0.165005	−	0.986293i	$-0.552764\pi$
$53$	5.01192	−	10.9746i	0.688441	−	1.50748i	0.853445	−	0.521182i	$-0.174509\pi$
$54$		0			0
$55$	−1.60161	+	11.1394i	−0.215961	+	1.50204i
$56$		0			0
$57$	−3.93686	−	1.15597i	−0.521450	−	0.153112i
$58$		0			0
$59$	3.56571	+	7.80781i	0.464216	+	1.01649i	0.986506	+	0.163723i	$0.0523503\pi$
$59$	3.56571	+	7.80781i	0.464216	+	1.01649i	−0.522291	+	0.852767i	$0.674922\pi$
$60$		0			0
$61$	−2.15072	+	2.48206i	−0.275372	+	0.317796i	−0.876542	−	0.481325i	$-0.840156\pi$
$61$	−2.15072	+	2.48206i	−0.275372	+	0.317796i	0.601171	+	0.799121i	$0.294701\pi$
$62$		0			0
$63$	−1.01945	−	0.655164i	−0.128439	−	0.0825429i
$64$		0			0
$65$	2.53079	−	1.62644i	0.313906	−	0.201735i
$66$		0			0
$67$	1.61579	−	0.474440i	0.197401	−	0.0579621i	−0.181538	−	0.983384i	$-0.558107\pi$
$67$	1.61579	−	0.474440i	0.197401	−	0.0579621i	0.378938	+	0.925422i	$0.376289\pi$
$68$		0			0
$69$	−2.48129	+	4.10405i	−0.298712	+	0.494069i
$70$		0			0
$71$	3.54931	−	1.04217i	0.421226	−	0.123683i	−0.0642487	−	0.997934i	$-0.520465\pi$
$71$	3.54931	−	1.04217i	0.421226	−	0.123683i	0.485474	+	0.874251i	$0.338647\pi$
$72$		0			0
$73$	−0.819149	+	0.526435i	−0.0958741	+	0.0616145i	−0.587699	−	0.809079i	$-0.699966\pi$
$73$	−0.819149	+	0.526435i	−0.0958741	+	0.0616145i	0.491825	+	0.870694i	$0.336330\pi$
$74$		0			0
$75$	−1.59399	−	1.02440i	−0.184059	−	0.118287i
$76$		0			0
$77$	−3.40123	+	3.92522i	−0.387606	+	0.447321i
$78$		0			0
$79$	3.11302	+	6.81655i	0.350242	+	0.766922i	0.999977	+	0.00676183i	$0.00215237\pi$
$79$	3.11302	+	6.81655i	0.350242	+	0.766922i	−0.649736	+	0.760160i	$0.725120\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	1.05121	−	7.31133i	0.115385	−	0.802523i	−0.847148	−	0.531358i	$-0.821682\pi$
$83$	1.05121	−	7.31133i	0.115385	−	0.802523i	0.962533	−	0.271165i	$-0.0874089\pi$
$84$		0			0
$85$	7.31595	−	16.0197i	0.793526	−	1.73758i
$86$		0			0
$87$	1.16699	+	8.11662i	0.125115	+	0.870193i
$88$		0			0
$89$	4.11504	+	4.74901i	0.436193	+	0.503394i	0.930702	−	0.365779i	$-0.119197\pi$
$89$	4.11504	+	4.74901i	0.436193	+	0.503394i	−0.494508	+	0.869173i	$0.664652\pi$
$90$		0			0
$91$	1.38838			0.145542
$92$		0			0
$93$	−7.03729			−0.729733
$94$		0			0
$95$	−7.05534	−	8.14229i	−0.723862	−	0.835382i
$96$		0			0
$97$	−2.20862	−	15.3613i	−0.224251	−	1.55970i	−0.721699	−	0.692207i	$-0.756638\pi$
$97$	−2.20862	−	15.3613i	−0.224251	−	1.55970i	0.497447	−	0.867494i	$-0.334271\pi$
$98$		0			0
$99$	−1.78044	+	3.89862i	−0.178941	+	0.391826i
$100$		0			0
$101$	1.62875	−	11.3282i	0.162066	−	1.12720i	−0.732664	−	0.680591i	$-0.761723\pi$
$101$	1.62875	−	11.3282i	0.162066	−	1.12720i	0.894730	−	0.446607i	$-0.147368\pi$
$102$		0			0
$103$	3.47468	+	1.02026i	0.342370	+	0.100529i	0.448398	−	0.893834i	$-0.351995\pi$
$103$	3.47468	+	1.02026i	0.342370	+	0.100529i	−0.106027	+	0.994363i	$0.533813\pi$
$104$		0			0
$105$	−1.32185	−	2.89446i	−0.129000	−	0.282470i
$106$		0			0
$107$	8.80656	−	10.1633i	0.851363	−	0.982525i	−0.148617	−	0.988895i	$-0.547482\pi$
$107$	8.80656	−	10.1633i	0.851363	−	0.982525i	0.999980	+	0.00636992i	$0.00202762\pi$
$108$		0			0
$109$	−8.96047	−	5.75854i	−0.858257	−	0.551569i	0.0358826	−	0.999356i	$-0.488576\pi$
$109$	−8.96047	−	5.75854i	−0.858257	−	0.551569i	−0.894140	+	0.447787i	$0.852212\pi$
$110$		0			0
$111$	1.73375	−	1.11422i	0.164561	−	0.105757i
$112$		0			0
$113$	−10.9970	+	3.22902i	−1.03451	+	0.303760i	−0.754544	−	0.656249i	$-0.772142\pi$
$113$	−10.9970	+	3.22902i	−1.03451	+	0.303760i	−0.279968	+	0.960009i	$0.590324\pi$
$114$		0			0
$115$	−11.3072	+	5.54320i	−1.05440	+	0.516906i
$116$		0			0
$117$	1.09929	−	0.322779i	0.101629	−	0.0298410i
$118$		0			0
$119$	6.83748	−	4.39418i	0.626791	−	0.402814i
$120$		0			0
$121$	6.19939	+	3.98410i	0.563581	+	0.362191i
$122$		0			0
$123$	6.26121	−	7.22582i	0.564554	−	0.651530i
$124$		0			0
$125$	3.38715	+	7.41682i	0.302956	+	0.663381i
$126$		0			0
$127$	10.2767	+	3.01752i	0.911913	+	0.267762i	0.703846	−	0.710353i	$-0.251465\pi$
$127$	10.2767	+	3.01752i	0.911913	+	0.267762i	0.208067	+	0.978115i	$0.433283\pi$
$128$		0			0
$129$	0.414382	−	2.88209i	0.0364843	−	0.253754i
$130$		0			0
$131$	6.31601	−	13.8301i	0.551832	−	1.20834i	−0.404089	−	0.914720i	$-0.632411\pi$
$131$	6.31601	−	13.8301i	0.551832	−	1.20834i	0.955921	−	0.293624i	$-0.0948614\pi$
$132$		0			0
$133$	−0.707620	−	4.92160i	−0.0613584	−	0.426757i
$134$		0			0
$135$	−1.71953	−	1.98444i	−0.147993	−	0.170794i
$136$		0			0
$137$	8.87590			0.758319			0.379160	−	0.925331i	$-0.376213\pi$
$137$	8.87590			0.758319			0.379160	+	0.925331i	$0.376213\pi$
$138$		0			0
$139$	−20.5293			−1.74128			−0.870638	−	0.491925i	$-0.836293\pi$
$139$	−20.5293			−1.74128			−0.870638	+	0.491925i	$0.836293\pi$
$140$		0			0
$141$	4.87178	+	5.62233i	0.410277	+	0.473485i
$142$		0			0
$143$	−0.698818	−	4.86039i	−0.0584381	−	0.406446i
$144$		0			0
$145$	−8.94460	+	19.5859i	−0.742809	+	1.62652i
$146$		0			0
$147$	−0.787211	+	5.47517i	−0.0649280	+	0.451584i
$148$		0			0
$149$	−2.55800	−	0.751097i	−0.209560	−	0.0615323i	0.175268	−	0.984521i	$-0.443921\pi$
$149$	−2.55800	−	0.751097i	−0.209560	−	0.0615323i	−0.384828	+	0.922989i	$0.625739\pi$
$150$		0			0
$151$	−3.28292	−	7.18859i	−0.267160	−	0.585000i	0.727741	−	0.685852i	$-0.240570\pi$
$151$	−3.28292	−	7.18859i	−0.267160	−	0.585000i	−0.994901	+	0.100852i	$0.967843\pi$
$152$		0			0
$153$	4.39215	−	5.06881i	0.355084	−	0.409789i
$154$		0			0
$155$	−15.5451	−	9.99021i	−1.24861	−	0.802433i
$156$		0			0
$157$	5.91629	−	3.80217i	0.472172	−	0.303446i	−0.282829	−	0.959170i	$-0.591273\pi$
$157$	5.91629	−	3.80217i	0.472172	−	0.303446i	0.755001	+	0.655724i	$0.227637\pi$
$158$		0			0
$159$	11.5762	−	3.39906i	0.918048	−	0.269563i
$160$		0			0
$161$	−5.77307	−	0.669146i	−0.454982	−	0.0527361i
$162$		0			0
$163$	14.4916	−	4.25512i	1.13507	−	0.333287i	0.340372	−	0.940291i	$-0.389447\pi$
$163$	14.4916	−	4.25512i	1.13507	−	0.333287i	0.794699	+	0.607004i	$0.207629\pi$
$164$		0			0
$165$	−9.46744	+	6.08436i	−0.737039	+	0.473666i
$166$		0			0
$167$	11.1993	+	7.19737i	0.866630	+	0.556950i	0.896720	−	0.442598i	$-0.145943\pi$
$167$	11.1993	+	7.19737i	0.866630	+	0.556950i	−0.0300899	+	0.999547i	$0.509579\pi$
$168$		0			0
$169$	7.65361	−	8.83274i	0.588739	−	0.679441i
$170$		0			0
$171$	−1.70448	−	3.73228i	−0.130344	−	0.285415i
$172$		0			0
$173$	10.9516	+	3.21567i	0.832633	+	0.244483i	0.670148	−	0.742228i	$-0.266231\pi$
$173$	10.9516	+	3.21567i	0.832633	+	0.244483i	0.162486	+	0.986711i	$0.448049\pi$
$174$		0			0
$175$	0.326777	−	2.27278i	0.0247020	−	0.171806i
$176$		0			0
$177$	−3.56571	+	7.80781i	−0.268015	+	0.586871i
$178$		0			0
$179$	−0.0560348	−	0.389731i	−0.00418824	−	0.0291299i	0.987620	−	0.156864i	$-0.0501385\pi$
$179$	−0.0560348	−	0.389731i	−0.00418824	−	0.0291299i	−0.991808	+	0.127735i	$0.959229\pi$
$180$		0			0
$181$	−1.52257	−	1.75714i	−0.113171	−	0.130607i	0.696337	−	0.717715i	$-0.254812\pi$
$181$	−1.52257	−	1.75714i	−0.113171	−	0.130607i	−0.809509	+	0.587108i	$0.800266\pi$
$182$		0			0
$183$	−3.28424			−0.242778
$184$		0			0
$185$	5.41154			0.397864
$186$		0			0
$187$	−18.8245	−	21.7246i	−1.37658	−	1.58866i
$188$		0			0
$189$	−0.172461	−	1.19949i	−0.0125447	−	0.0872503i
$190$		0			0
$191$	−3.53363	+	7.73758i	−0.255685	+	0.559872i	−0.993329	−	0.115319i	$-0.963211\pi$
$191$	−3.53363	+	7.73758i	−0.255685	+	0.559872i	0.737644	+	0.675190i	$0.235938\pi$
$192$		0			0
$193$	0.440868	−	3.06631i	0.0317344	−	0.220718i	−0.967783	−	0.251786i	$-0.918982\pi$
$193$	0.440868	−	3.06631i	0.0317344	−	0.220718i	0.999517	+	0.0310687i	$0.00989108\pi$
$194$		0			0
$195$	2.88649	+	0.847551i	0.206706	+	0.0606944i
$196$		0			0
$197$	11.1718	+	24.4628i	0.795955	+	1.74290i	0.658757	+	0.752355i	$0.271082\pi$
$197$	11.1718	+	24.4628i	0.795955	+	1.74290i	0.137198	+	0.990544i	$0.456190\pi$
$198$		0			0
$199$	2.14329	−	2.47349i	0.151934	−	0.175341i	−0.674680	−	0.738110i	$-0.735719\pi$
$199$	2.14329	−	2.47349i	0.151934	−	0.175341i	0.826614	+	0.562769i	$0.190264\pi$
$200$		0			0
$201$	1.41668	+	0.910444i	0.0999248	+	0.0642177i
$202$		0			0
$203$	−8.35962	+	5.37240i	−0.586730	+	0.377069i
$204$		0			0
$205$	24.0886	−	7.07305i	1.68242	−	0.494003i
$206$		0			0
$207$	−4.72653	+	0.812344i	−0.328517	+	0.0564618i
$208$		0			0
$209$	−16.8731	+	4.95440i	−1.16714	+	0.342703i
$210$		0			0
$211$	−18.2165	+	11.7070i	−1.25408	+	0.805946i	−0.987462	−	0.157857i	$-0.949542\pi$
$211$	−18.2165	+	11.7070i	−1.25408	+	0.805946i	−0.266615	+	0.963803i	$0.585905\pi$
$212$		0			0
$213$	3.11193	+	1.99991i	0.213226	+	0.137032i
$214$		0			0
$215$	5.00680	−	5.77815i	0.341461	−	0.394067i
$216$		0			0
$217$	−3.54265	−	7.75733i	−0.240491	−	0.526602i
$218$		0			0
$219$	−0.934281	−	0.274330i	−0.0631329	−	0.0185375i
$220$		0			0
$221$	−1.09357	+	7.60595i	−0.0735616	+	0.511632i
$222$		0			0
$223$	6.02619	−	13.1955i	0.403543	−	0.883637i	−0.593355	−	0.804941i	$-0.702197\pi$
$223$	6.02619	−	13.1955i	0.403543	−	0.883637i	0.996899	−	0.0786962i	$-0.0250757\pi$
$224$		0			0
$225$	−0.269656	−	1.87550i	−0.0179771	−	0.125033i
$226$		0			0
$227$	−15.7867	−	18.2188i	−1.04780	−	1.20923i	−0.977332	−	0.211713i	$-0.932096\pi$
$227$	−15.7867	−	18.2188i	−1.04780	−	1.20923i	−0.0704689	−	0.997514i	$-0.522450\pi$
$228$		0			0
$229$	−10.1824			−0.672874			−0.336437	−	0.941706i	$-0.609222\pi$
$229$	−10.1824			−0.672874			−0.336437	+	0.941706i	$0.609222\pi$
$230$		0			0
$231$	−5.19382			−0.341728
$232$		0			0
$233$	5.29763	+	6.11380i	0.347060	+	0.400528i	0.902263	−	0.431187i	$-0.141905\pi$
$233$	5.29763	+	6.11380i	0.347060	+	0.400528i	−0.555203	+	0.831715i	$0.687359\pi$
$234$		0			0
$235$	2.78003	+	19.3355i	0.181349	+	1.26131i
$236$		0			0
$237$	−3.11302	+	6.81655i	−0.202212	+	0.442783i
$238$		0			0
$239$	−0.967619	+	6.72994i	−0.0625901	+	0.435324i	0.934298	+	0.356493i	$0.116028\pi$
$239$	−0.967619	+	6.72994i	−0.0625901	+	0.435324i	−0.996888	+	0.0788304i	$0.974881\pi$
$240$		0			0
$241$	−0.567468	−	0.166624i	−0.0365538	−	0.0107332i	0.263405	−	0.964685i	$-0.415155\pi$
$241$	−0.567468	−	0.166624i	−0.0365538	−	0.0107332i	−0.299958	+	0.953952i	$0.596973\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−9.51152	+	10.9769i	−0.607669	+	0.701287i
$246$		0			0
$247$	3.95461	+	2.54148i	0.251626	+	0.161710i
$248$		0			0
$249$	6.21393	−	3.99345i	0.393792	−	0.253075i
$250$		0			0
$251$	−19.6143	+	5.75927i	−1.23804	+	0.363522i	−0.834280	−	0.551342i	$-0.814116\pi$
$251$	−19.6143	+	5.75927i	−1.23804	+	0.363522i	−0.403763	+	0.914864i	$0.632298\pi$
$252$		0			0
$253$	0.563259	+	20.5469i	0.0354118	+	1.29177i
$254$		0			0
$255$	16.8978	−	4.96164i	1.05818	−	0.310710i
$256$		0			0
$257$	−4.87608	+	3.13367i	−0.304162	+	0.195473i	−0.683814	−	0.729656i	$-0.739680\pi$
$257$	−4.87608	+	3.13367i	−0.304162	+	0.195473i	0.379652	+	0.925129i	$0.376044\pi$
$258$		0			0
$259$	2.10101	+	1.35024i	0.130551	+	0.0838997i
$260$		0			0
$261$	−5.36991	+	6.19721i	−0.332389	+	0.383598i
$262$		0			0
$263$	9.67183	+	21.1783i	0.596390	+	1.30591i	0.931503	+	0.363735i	$0.118499\pi$
$263$	9.67183	+	21.1783i	0.596390	+	1.30591i	−0.335112	+	0.942178i	$0.608774\pi$
$264$		0			0
$265$	30.3966	+	8.92524i	1.86725	+	0.548273i
$266$		0			0
$267$	−0.894284	+	6.21988i	−0.0547293	+	0.380651i
$268$		0			0
$269$	−2.85588	+	6.25350i	−0.174126	+	0.381283i	−0.976493	−	0.215548i	$-0.930846\pi$
$269$	−2.85588	+	6.25350i	−0.174126	+	0.381283i	0.802367	+	0.596831i	$0.203574\pi$
$270$		0			0
$271$	0.324922	+	2.25988i	0.0197376	+	0.137278i	0.997308	−	0.0733331i	$-0.0233636\pi$
$271$	0.324922	+	2.25988i	0.0197376	+	0.137278i	−0.977570	+	0.210611i	$0.932455\pi$
$272$		0			0
$273$	0.909199	+	1.04927i	0.0550272	+	0.0635048i
$274$		0			0
$275$	−8.12092			−0.489710
$276$		0			0
$277$	−4.88526			−0.293527			−0.146764	−	0.989172i	$-0.546886\pi$
$277$	−4.88526			−0.293527			−0.146764	+	0.989172i	$0.546886\pi$
$278$		0			0
$279$	−4.60844	−	5.31843i	−0.275900	−	0.318406i
$280$		0			0
$281$	0.766415	+	5.33054i	0.0457205	+	0.317993i	0.999828	+	0.0185297i	$0.00589854\pi$
$281$	0.766415	+	5.33054i	0.0457205	+	0.317993i	−0.954108	+	0.299463i	$0.903192\pi$
$282$		0			0
$283$	−2.80006	+	6.13128i	−0.166446	+	0.364467i	−0.974414	−	0.224760i	$-0.927840\pi$
$283$	−2.80006	+	6.13128i	−0.166446	+	0.364467i	0.807968	+	0.589227i	$0.200567\pi$
$284$		0			0
$285$	1.53327	−	10.6641i	0.0908232	−	0.631689i
$286$		0			0
$287$	11.1171	+	3.26428i	0.656223	+	0.192684i
$288$		0			0
$289$	11.6249	+	25.4550i	0.683818	+	1.49735i
$290$		0			0
$291$	10.1629	−	11.7287i	0.595762	−	0.687546i
$292$		0			0
$293$	−26.0982	−	16.7723i	−1.52467	−	0.979848i	−0.990956	−	0.134184i	$-0.957159\pi$
$293$	−26.0982	−	16.7723i	−1.52467	−	0.979848i	−0.533716	−	0.845664i	$-0.679205\pi$
$294$		0			0
$295$	−18.9605	+	12.1852i	−1.10393	+	0.709450i
$296$		0			0
$297$	−4.11232	+	1.20749i	−0.238621	+	0.0700655i
$298$		0			0
$299$	4.05235	−	3.71061i	0.234353	−	0.214590i
$300$		0			0
$301$	3.38558	−	0.994097i	0.195142	−	0.0572988i
$302$		0			0
$303$	9.62788	−	6.18746i	0.553107	−	0.355460i
$304$		0			0
$305$	−7.25475	−	4.66234i	−0.415406	−	0.266965i
$306$		0			0
$307$	10.6858	−	12.3320i	0.609869	−	0.703826i	−0.363882	−	0.931445i	$-0.618549\pi$
$307$	10.6858	−	12.3320i	0.609869	−	0.703826i	0.973750	+	0.227619i	$0.0730942\pi$
$308$		0			0
$309$	1.50437	+	3.29411i	0.0855807	+	0.187396i
$310$		0			0
$311$	−4.43444	−	1.30207i	−0.251454	−	0.0738336i	0.153576	−	0.988137i	$-0.450921\pi$
$311$	−4.43444	−	1.30207i	−0.251454	−	0.0738336i	−0.405030	+	0.914303i	$0.632739\pi$
$312$		0			0
$313$	−3.53351	+	24.5761i	−0.199726	+	1.38912i	0.605355	+	0.795956i	$0.293031\pi$
$313$	−3.53351	+	24.5761i	−0.199726	+	1.38912i	−0.805080	+	0.593166i	$0.797878\pi$
$314$		0			0
$315$	1.32185	−	2.89446i	0.0744781	−	0.163084i
$316$		0			0
$317$	0.754461	+	5.24739i	0.0423748	+	0.294723i	0.999978	+	0.00663265i	$0.00211125\pi$
$317$	0.754461	+	5.24739i	0.0423748	+	0.294723i	−0.957603	+	0.288090i	$0.906980\pi$
$318$		0			0
$319$	23.0151	+	26.5608i	1.28860	+	1.48712i
$320$		0			0
$321$	13.4480			0.750594
$322$		0			0
$323$	27.5193			1.53121
$324$		0			0
$325$	1.42160	+	1.64061i	0.0788562	+	0.0910049i
$326$		0			0
$327$	−1.51584	−	10.5429i	−0.0838263	−	0.583025i
$328$		0			0
$329$	−3.74508	+	8.20059i	−0.206473	+	0.452113i
$330$		0			0
$331$	4.96777	−	34.5516i	0.273053	−	1.89913i	−0.142893	−	0.989738i	$-0.545641\pi$
$331$	4.96777	−	34.5516i	0.273053	−	1.89913i	0.415946	−	0.909389i	$-0.363450\pi$
$332$		0			0
$333$	1.97744	+	0.580627i	0.108363	+	0.0318182i
$334$		0			0
$335$	1.83691	+	4.02226i	0.100361	+	0.219760i
$336$		0			0
$337$	−22.0813	+	25.4832i	−1.20285	+	1.38816i	−0.302408	+	0.953179i	$0.597790\pi$
$337$	−22.0813	+	25.4832i	−1.20285	+	1.38816i	−0.900440	+	0.434981i	$0.856755\pi$
$338$		0			0
$339$	−9.64184	−	6.19643i	−0.523673	−	0.336544i
$340$		0			0
$341$	−25.3733	+	16.3065i	−1.37404	+	0.883044i
$342$		0			0
$343$	−14.5709	+	4.27839i	−0.786752	+	0.231011i
$344$		0			0
$345$	−11.5939	−	4.91540i	−0.624195	−	0.264636i
$346$		0			0
$347$	−14.1987	+	4.16913i	−0.762228	+	0.223810i	−0.639669	−	0.768651i	$-0.720928\pi$
$347$	−14.1987	+	4.16913i	−0.762228	+	0.223810i	−0.122560	+	0.992461i	$0.539110\pi$
$348$		0			0
$349$	9.79737	−	6.29639i	0.524441	−	0.337038i	−0.251485	−	0.967861i	$-0.580919\pi$
$349$	9.79737	−	6.29639i	0.524441	−	0.337038i	0.775927	+	0.630823i	$0.217283\pi$
$350$		0			0
$351$	0.963819	+	0.619409i	0.0514449	+	0.0330616i
$352$		0			0
$353$	19.8927	−	22.9574i	1.05878	−	1.22190i	0.0845334	−	0.996421i	$-0.473060\pi$
$353$	19.8927	−	22.9574i	1.05878	−	1.22190i	0.974248	−	0.225478i	$-0.0723945\pi$
$354$		0			0
$355$	4.03501	+	8.83544i	0.214156	+	0.468937i
$356$		0			0
$357$	7.79850	+	2.28985i	0.412740	+	0.121192i
$358$		0			0
$359$	−2.67998	+	18.6396i	−0.141444	+	0.983763i	0.788231	+	0.615380i	$0.210997\pi$
$359$	−2.67998	+	18.6396i	−0.141444	+	0.983763i	−0.929674	+	0.368383i	$0.879912\pi$
$360$		0			0
$361$	−0.899310	+	1.96921i	−0.0473321	+	0.103643i
$362$		0			0
$363$	1.04875	+	7.29422i	0.0550451	+	0.382847i
$364$		0			0
$365$	−1.67435	−	1.93230i	−0.0876393	−	0.101141i
$366$		0			0
$367$	−2.28233			−0.119137			−0.0595684	−	0.998224i	$-0.518972\pi$
$367$	−2.28233			−0.119137			−0.0595684	+	0.998224i	$0.518972\pi$
$368$		0			0
$369$	9.56113			0.497732
$370$		0			0
$371$	9.57442	+	11.0495i	0.497079	+	0.573660i
$372$		0			0
$373$	−5.33936	−	37.1361i	−0.276462	−	1.92283i	−0.373655	−	0.927568i	$-0.621896\pi$
$373$	−5.33936	−	37.1361i	−0.276462	−	1.92283i	0.0971936	−	0.995265i	$-0.469013\pi$
$374$		0			0
$375$	−3.38715	+	7.41682i	−0.174912	+	0.383003i
$376$		0			0
$377$	1.33702	−	9.29916i	0.0688599	−	0.478931i
$378$		0			0
$379$	33.7129	+	9.89899i	1.73171	+	0.508477i	0.987249	−	0.159184i	$-0.0508864\pi$
$379$	33.7129	+	9.89899i	1.73171	+	0.508477i	0.744465	+	0.667661i	$0.232705\pi$
$380$		0			0
$381$	4.44934	+	9.74270i	0.227947	+	0.499133i
$382$		0			0
$383$	−11.0985	+	12.8084i	−0.567109	+	0.654478i	−0.964783	−	0.263048i	$-0.915272\pi$
$383$	−11.0985	+	12.8084i	−0.567109	+	0.654478i	0.397674	+	0.917527i	$0.369818\pi$
$384$		0			0
$385$	−11.4729	−	7.37320i	−0.584714	−	0.375773i
$386$		0			0
$387$	2.44950	−	1.57420i	0.124515	−	0.0800210i
$388$		0			0
$389$	−33.2157	+	9.75300i	−1.68410	+	0.494497i	−0.977112	−	0.212727i	$-0.931765\pi$
$389$	−33.2157	+	9.75300i	−1.68410	+	0.494497i	−0.706990	+	0.707224i	$0.749947\pi$
$390$		0			0
$391$	8.21297	−	31.0994i	0.415348	−	1.57277i
$392$		0			0
$393$	14.5882	−	4.28349i	0.735878	−	0.216073i
$394$		0			0
$395$	−16.5534	+	10.6382i	−0.832890	+	0.535266i
$396$		0			0
$397$	−5.67366	−	3.64624i	−0.284753	−	0.182999i	0.390465	−	0.920618i	$-0.372314\pi$
$397$	−5.67366	−	3.64624i	−0.284753	−	0.182999i	−0.675218	+	0.737618i	$0.735950\pi$
$398$		0			0
$399$	3.25611	−	3.75775i	0.163009	−	0.188123i
$400$		0			0
$401$	−4.56230	−	9.99005i	−0.227831	−	0.498879i	0.760848	−	0.648931i	$-0.224783\pi$
$401$	−4.56230	−	9.99005i	−0.227831	−	0.498879i	−0.988678	+	0.150051i	$0.952056\pi$
$402$		0			0
$403$	7.73599	+	2.27149i	0.385357	+	0.113151i
$404$		0			0
$405$	0.373689	−	2.59907i	0.0185688	−	0.129149i
$406$		0			0
$407$	3.66934	−	8.03474i	0.181883	−	0.398267i
$408$		0			0
$409$	−2.20221	−	15.3167i	−0.108892	−	0.757363i	−0.968966	−	0.247193i	$-0.920492\pi$
$409$	−2.20221	−	15.3167i	−0.108892	−	0.757363i	0.860074	−	0.510170i	$-0.170417\pi$
$410$		0			0
$411$	5.81248	+	6.70796i	0.286708	+	0.330879i
$412$		0			0
$413$	−10.4017			−0.511835
$414$		0			0
$415$	19.3955			0.952085
$416$		0			0
$417$	−13.4439	−	15.5150i	−0.658348	−	0.759775i
$418$		0			0
$419$	0.534663	+	3.71866i	0.0261200	+	0.181669i	0.998705	−	0.0508800i	$-0.0162026\pi$
$419$	0.534663	+	3.71866i	0.0261200	+	0.181669i	−0.972585	+	0.232549i	$0.925294\pi$
$420$		0			0
$421$	5.33117	−	11.6736i	0.259825	−	0.568938i	−0.734094	−	0.679048i	$-0.762393\pi$
$421$	5.33117	−	11.6736i	0.259825	−	0.568938i	0.993919	+	0.110110i	$0.0351202\pi$
$422$		0			0
$423$	−1.05874	+	7.36368i	−0.0514776	+	0.358035i
$424$		0			0
$425$	12.1935	+	3.58035i	0.591474	+	0.173672i
$426$		0			0
$427$	−1.65333	−	3.62028i	−0.0800100	−	0.175198i
$428$		0			0
$429$	3.21561	−	3.71101i	0.155251	−	0.179169i
$430$		0			0
$431$	−32.3890	−	20.8151i	−1.56012	−	1.00263i	−0.982486	−	0.186335i	$-0.940339\pi$
$431$	−32.3890	−	20.8151i	−1.56012	−	1.00263i	−0.577635	−	0.816295i	$-0.696024\pi$
$432$		0			0
$433$	20.0199	−	12.8660i	0.962093	−	0.618300i	0.0375167	−	0.999296i	$-0.488055\pi$
$433$	20.0199	−	12.8660i	0.962093	−	0.618300i	0.924577	+	0.380996i	$0.124419\pi$
$434$		0			0
$435$	−20.6595	+	6.06619i	−0.990549	+	0.290851i
$436$		0			0
$437$	−15.2189	−	12.4737i	−0.728018	−	0.596700i
$438$		0			0
$439$	−30.7518	+	9.02955i	−1.46770	+	0.430957i	−0.915352	−	0.402654i	$-0.868088\pi$
$439$	−30.7518	+	9.02955i	−1.46770	+	0.430957i	−0.552352	+	0.833611i	$0.686270\pi$
$440$		0			0
$441$	−4.65337	+	2.99054i	−0.221589	+	0.142407i
$442$		0			0
$443$	−13.1438	−	8.44700i	−0.624481	−	0.401329i	0.189782	−	0.981826i	$-0.439222\pi$
$443$	−13.1438	−	8.44700i	−0.624481	−	0.401329i	−0.814262	+	0.580497i	$0.802858\pi$
$444$		0			0
$445$	−10.8052	+	12.4699i	−0.512218	+	0.591131i
$446$		0			0
$447$	−1.10749	−	2.42507i	−0.0523827	−	0.114702i
$448$		0			0
$449$	1.00614	+	0.295429i	0.0474826	+	0.0139421i	0.305388	−	0.952228i	$-0.401214\pi$
$449$	1.00614	+	0.295429i	0.0474826	+	0.0139421i	−0.257905	+	0.966170i	$0.583032\pi$
$450$		0			0
$451$	5.83183	−	40.5613i	0.274610	−	1.90996i
$452$		0			0
$453$	3.28292	−	7.18859i	0.154245	−	0.337750i
$454$		0			0
$455$	0.518824	+	3.60850i	0.0243229	+	0.169169i
$456$		0			0
$457$	0.539767	+	0.622925i	0.0252493	+	0.0291392i	0.768234	−	0.640169i	$-0.221136\pi$
$457$	0.539767	+	0.622925i	0.0252493	+	0.0291392i	−0.742984	+	0.669309i	$0.766590\pi$
$458$		0			0
$459$	6.70700			0.313056
$460$		0			0
$461$	21.3858			0.996035			0.498017	−	0.867167i	$-0.334062\pi$
$461$	21.3858			0.996035			0.498017	+	0.867167i	$0.334062\pi$
$462$		0			0
$463$	−13.4452	−	15.5166i	−0.624851	−	0.721117i	0.351770	−	0.936087i	$-0.385580\pi$
$463$	−13.4452	−	15.5166i	−0.624851	−	0.721117i	−0.976621	+	0.214970i	$0.931035\pi$
$464$		0			0
$465$	−2.62976	−	18.2904i	−0.121952	−	0.848196i
$466$		0			0
$467$	−1.39123	+	3.04638i	−0.0643786	+	0.140969i	−0.939086	−	0.343681i	$-0.888326\pi$
$467$	−1.39123	+	3.04638i	−0.0643786	+	0.140969i	0.874708	+	0.484651i	$0.161053\pi$
$468$		0			0
$469$	−0.290426	+	2.01996i	−0.0134106	+	0.0932730i
$470$		0			0
$471$	6.74784	+	1.98134i	0.310924	+	0.0912955i
$472$		0			0
$473$	−5.18416	−	11.3517i	−0.238368	−	0.521953i
$474$		0			0
$475$	5.09117	−	5.87552i	0.233599	−	0.269587i
$476$		0			0
$477$	10.1496	+	6.52276i	0.464719	+	0.298657i
$478$		0			0
$479$	−21.9656	+	14.1164i	−1.00363	+	0.644996i	−0.935738	−	0.352697i	$-0.885265\pi$
$479$	−21.9656	+	14.1164i	−1.00363	+	0.644996i	−0.0678952	+	0.997692i	$0.521628\pi$
$480$		0			0
$481$	−2.26554	+	0.665221i	−0.103300	+	0.0303315i
$482$		0			0
$483$	−3.27485	−	4.80120i	−0.149011	−	0.218462i
$484$		0			0
$485$	39.0996	−	11.4807i	1.77542	−	0.521311i
$486$		0			0
$487$	−29.9765	+	19.2647i	−1.35836	+	0.872967i	−0.998203	−	0.0599231i	$-0.980914\pi$
$487$	−29.9765	+	19.2647i	−1.35836	+	0.872967i	−0.360161	+	0.932890i	$0.617278\pi$
$488$		0			0
$489$	12.7058	+	8.16552i	0.574576	+	0.369258i
$490$		0			0
$491$	17.9562	−	20.7225i	0.810351	−	0.935195i	−0.188550	−	0.982064i	$-0.560379\pi$
$491$	17.9562	−	20.7225i	0.810351	−	0.935195i	0.998901	+	0.0468683i	$0.0149241\pi$
$492$		0			0
$493$	−22.8470	−	50.0279i	−1.02898	−	2.25314i
$494$		0			0
$495$	−10.7981	−	3.17061i	−0.485339	−	0.142508i
$496$		0			0
$497$	−0.637960	+	4.43711i	−0.0286164	+	0.199032i
$498$		0			0
$499$	1.99570	−	4.36997i	0.0893397	−	0.195627i	−0.859688	−	0.510820i	$-0.829342\pi$
$499$	1.99570	−	4.36997i	0.0893397	−	0.195627i	0.949028	+	0.315193i	$0.102069\pi$
$500$		0			0
$501$	1.89459	+	13.1772i	0.0846441	+	0.588712i
$502$		0			0
$503$	1.63210	+	1.88354i	0.0727716	+	0.0839829i	0.790968	−	0.611858i	$-0.209577\pi$
$503$	1.63210	+	1.88354i	0.0727716	+	0.0839829i	−0.718196	+	0.695841i	$0.755032\pi$
$504$		0			0
$505$	30.0514			1.33727
$506$		0			0
$507$	11.6874			0.519055
$508$		0			0
$509$	28.2478	+	32.5997i	1.25206	+	1.44495i	0.847804	+	0.530309i	$0.177924\pi$
$509$	28.2478	+	32.5997i	1.25206	+	1.44495i	0.404256	+	0.914646i	$0.367530\pi$
$510$		0			0
$511$	−0.167930	−	1.16798i	−0.00742877	−	0.0516682i
$512$		0			0
$513$	1.70448	−	3.73228i	0.0752544	−	0.164784i
$514$		0			0
$515$	−1.35327	+	9.41218i	−0.0596321	+	0.414750i
$516$		0			0
$517$	30.5932	+	8.98299i	1.34549	+	0.395071i
$518$		0			0
$519$	4.74152	+	10.3825i	0.208129	+	0.455740i
$520$		0			0
$521$	−11.8934	+	13.7258i	−0.521061	+	0.601337i	−0.953896	−	0.300136i	$-0.902968\pi$
$521$	−11.8934	+	13.7258i	−0.521061	+	0.601337i	0.432835	+	0.901473i	$0.357513\pi$
$522$		0			0
$523$	−11.2857	−	7.25287i	−0.493489	−	0.317146i	0.270118	−	0.962827i	$-0.412937\pi$
$523$	−11.2857	−	7.25287i	−0.493489	−	0.317146i	−0.763607	+	0.645681i	$0.776574\pi$
$524$		0			0
$525$	1.93165	−	1.24139i	0.0843040	−	0.0541789i
$526$		0			0
$527$	45.2872	−	13.2975i	1.97274	−	0.579249i
$528$		0			0
$529$	−18.6385	+	13.4761i	−0.810371	+	0.585917i
$530$		0			0
$531$	−8.23579	+	2.41825i	−0.357403	+	0.104943i
$532$		0			0
$533$	−9.21520	+	5.92225i	−0.399155	+	0.256521i
$534$		0			0
$535$	29.7060	+	19.0909i	1.28430	+	0.825372i
$536$		0			0
$537$	0.257844	−	0.297568i	0.0111268	−	0.0128410i
$538$		0			0
$539$	9.84846	+	21.5651i	0.424203	+	0.928875i
$540$		0			0
$541$	19.7979	+	5.81319i	0.851178	+	0.249929i	0.678091	−	0.734978i	$-0.262808\pi$
$541$	19.7979	+	5.81319i	0.851178	+	0.249929i	0.173087	+	0.984906i	$0.444626\pi$
$542$		0			0
$543$	0.330885	−	2.30136i	0.0141997	−	0.0987607i
$544$		0			0
$545$	11.6184	−	25.4408i	0.497678	−	1.08976i
$546$		0			0
$547$	1.82875	+	12.7193i	0.0781919	+	0.543837i	0.990835	+	0.135079i	$0.0431288\pi$
$547$	1.82875	+	12.7193i	0.0781919	+	0.543837i	−0.912643	+	0.408758i	$0.865962\pi$
$548$		0			0
$549$	−2.15072	−	2.48206i	−0.0917905	−	0.105932i
$550$		0			0
$551$	−33.6455			−1.43335
$552$		0			0
$553$	−9.08114			−0.386169
$554$		0			0
$555$	3.54381	+	4.08977i	0.150426	+	0.173601i
$556$		0			0
$557$	−5.75041	−	39.9950i	−0.243653	−	1.69464i	−0.633484	−	0.773756i	$-0.718376\pi$
$557$	−5.75041	−	39.9950i	−0.243653	−	1.69464i	0.389831	−	0.920886i	$-0.372533\pi$
$558$		0			0
$559$	−1.38580	+	3.03449i	−0.0586132	+	0.128345i
$560$		0			0
$561$	4.09095	−	28.4532i	0.172720	−	1.20129i
$562$		0			0
$563$	29.5395	+	8.67357i	1.24494	+	0.365547i	0.836869	−	0.547403i	$-0.184384\pi$
$563$	29.5395	+	8.67357i	1.24494	+	0.365547i	0.408071	+	0.912950i	$0.366202\pi$
$564$		0			0
$565$	−12.5019	−	27.3753i	−0.525958	−	1.15169i
$566$		0			0
$567$	0.793579	−	0.915839i	0.0333272	−	0.0384616i
$568$		0			0
$569$	9.11963	+	5.86083i	0.382315	+	0.245699i	0.717656	−	0.696398i	$-0.245215\pi$
$569$	9.11963	+	5.86083i	0.382315	+	0.245699i	−0.335341	+	0.942097i	$0.608852\pi$
$570$		0			0
$571$	−5.31357	+	3.41482i	−0.222366	+	0.142906i	−0.647081	−	0.762421i	$-0.724011\pi$
$571$	−5.31357	+	3.41482i	−0.222366	+	0.142906i	0.424715	+	0.905327i	$0.360374\pi$
$572$		0			0
$573$	−8.16171	+	2.39649i	−0.340960	+	0.100115i
$574$		0			0
$575$	−5.12048	−	7.50703i	−0.213539	−	0.313065i
$576$		0			0
$577$	−23.0052	+	6.75494i	−0.957720	+	0.281212i	−0.722998	−	0.690850i	$-0.757236\pi$
$577$	−23.0052	+	6.75494i	−0.957720	+	0.281212i	−0.234722	+	0.972062i	$0.575418\pi$
$578$		0			0
$579$	2.60607	−	1.67482i	0.108304	−	0.0696030i
$580$		0			0
$581$	7.53022	+	4.83938i	0.312406	+	0.200771i
$582$		0			0
$583$	33.8623	−	39.0792i	1.40243	−	1.61850i
$584$		0			0
$585$	1.24972	+	2.73650i	0.0516694	+	0.113140i
$586$		0			0
$587$	−26.4667	−	7.77133i	−1.09240	−	0.320757i	−0.314571	−	0.949234i	$-0.601861\pi$
$587$	−26.4667	−	7.77133i	−1.09240	−	0.320757i	−0.777828	+	0.628477i	$0.783679\pi$
$588$		0			0
$589$	4.10926	−	28.5806i	0.169319	−	1.17764i
$590$		0			0
$591$	−11.1718	+	24.4628i	−0.459545	+	1.00626i
$592$		0			0
$593$	−6.20747	−	43.1739i	−0.254910	−	1.77294i	−0.567817	−	0.823155i	$-0.692212\pi$
$593$	−6.20747	−	43.1739i	−0.254910	−	1.77294i	0.312907	−	0.949784i	$-0.398697\pi$
$594$		0			0
$595$	13.9759	+	16.1290i	0.572955	+	0.661225i
$596$		0			0
$597$	3.27289			0.133951
$598$		0			0
$599$	23.6433			0.966040			0.483020	−	0.875609i	$-0.339540\pi$
$599$	23.6433			0.966040			0.483020	+	0.875609i	$0.339540\pi$
$600$		0			0
$601$	−20.0985	−	23.1949i	−0.819835	−	0.946141i	0.179456	−	0.983766i	$-0.442566\pi$
$601$	−20.0985	−	23.1949i	−0.819835	−	0.946141i	−0.999292	+	0.0376254i	$0.988021\pi$
$602$		0			0
$603$	0.239659	+	1.66687i	0.00975968	+	0.0678801i
$604$		0			0
$605$	−8.03830	+	17.6014i	−0.326804	+	0.715600i
$606$		0			0
$607$	0.0768020	−	0.534170i	0.00311730	−	0.0216813i	−0.988203	−	0.153147i	$-0.951059\pi$
$607$	0.0768020	−	0.534170i	0.00311730	−	0.0216813i	0.991321	+	0.131466i	$0.0419683\pi$
$608$		0			0
$609$	−9.53457	−	2.79960i	−0.386360	−	0.113446i
$610$		0			0
$611$	−3.54070	−	7.75305i	−0.143241	−	0.313655i
$612$		0			0
$613$	−10.3616	+	11.9579i	−0.418500	+	0.482975i	−0.925380	−	0.379042i	$-0.876254\pi$
$613$	−10.3616	+	11.9579i	−0.418500	+	0.482975i	0.506879	+	0.862017i	$0.330799\pi$
$614$		0			0
$615$	21.1201	+	13.5731i	0.851646	+	0.547319i
$616$		0			0
$617$	20.3697	−	13.0908i	0.820053	−	0.527016i	−0.0620495	−	0.998073i	$-0.519764\pi$
$617$	20.3697	−	13.0908i	0.820053	−	0.527016i	0.882103	+	0.471057i	$0.156127\pi$
$618$		0			0
$619$	18.2308	−	5.35306i	0.732759	−	0.215158i	0.105995	−	0.994367i	$-0.466197\pi$
$619$	18.2308	−	5.35306i	0.732759	−	0.215158i	0.626764	+	0.779209i	$0.284379\pi$
$620$		0			0
$621$	−3.70915	−	3.04010i	−0.148843	−	0.121995i
$622$		0			0
$623$	−7.30648	+	2.14538i	−0.292728	+	0.0859527i
$624$		0			0
$625$	−25.9810	+	16.6970i	−1.03924	+	0.667880i
$626$		0			0
$627$	−14.7938	−	9.50742i	−0.590809	−	0.379690i
$628$		0			0
$629$	−9.05186	+	10.4464i	−0.360921	+	0.416525i
$630$		0			0
$631$	−10.5966	−	23.2034i	−0.421845	−	0.923712i	−0.994580	−	0.103972i	$-0.966845\pi$
$631$	−10.5966	−	23.2034i	−0.421845	−	0.923712i	0.572735	−	0.819741i	$-0.305882\pi$
$632$		0			0
$633$	−20.7769	−	6.10064i	−0.825807	−	0.242479i
$634$		0			0
$635$	−4.00243	+	27.8375i	−0.158832	+	1.10470i
$636$		0			0
$637$	2.63264	−	5.76468i	0.104309	−	0.228405i
$638$		0			0
$639$	0.526444	+	3.66150i	0.0208258	+	0.144847i
$640$		0			0
$641$	32.8114	+	37.8664i	1.29597	+	1.49563i	0.757201	+	0.653182i	$0.226567\pi$
$641$	32.8114	+	37.8664i	1.29597	+	1.49563i	0.538773	+	0.842451i	$0.318888\pi$
$642$		0			0
$643$	−12.3969			−0.488886			−0.244443	−	0.969664i	$-0.578605\pi$
$643$	−12.3969			−0.488886			−0.244443	+	0.969664i	$0.578605\pi$
$644$		0			0
$645$	7.64559			0.301045
$646$		0			0
$647$	−10.3564	−	11.9519i	−0.407153	−	0.469879i	0.514728	−	0.857354i	$-0.327893\pi$
$647$	−10.3564	−	11.9519i	−0.407153	−	0.469879i	−0.921880	+	0.387475i	$0.873347\pi$
$648$		0			0
$649$	5.23551	+	36.4138i	0.205512	+	1.42937i
$650$		0			0
$651$	3.54265	−	7.75733i	0.138848	−	0.304034i
$652$		0			0
$653$	5.23403	−	36.4035i	0.204824	−	1.42458i	−0.584895	−	0.811109i	$-0.698864\pi$
$653$	5.23403	−	36.4035i	0.204824	−	1.42458i	0.789718	−	0.613470i	$-0.210227\pi$
$654$		0			0
$655$	38.3056	+	11.2475i	1.49672	+	0.439478i
$656$		0			0
$657$	−0.404500	−	0.885730i	−0.0157810	−	0.0345556i
$658$		0			0
$659$	9.15265	−	10.5627i	0.356537	−	0.411465i	−0.548940	−	0.835862i	$-0.684968\pi$
$659$	9.15265	−	10.5627i	0.356537	−	0.411465i	0.905476	+	0.424397i	$0.139514\pi$
$660$		0			0
$661$	17.2578	+	11.0909i	0.671251	+	0.431387i	0.831376	−	0.555710i	$-0.187553\pi$
$661$	17.2578	+	11.0909i	0.671251	+	0.431387i	−0.160125	+	0.987097i	$0.551190\pi$
$662$		0			0
$663$	−6.46433	+	4.15437i	−0.251054	+	0.161343i
$664$		0			0
$665$	12.5271	−	3.67830i	0.485782	−	0.142638i
$666$		0			0
$667$	−10.0413	+	38.0227i	−0.388801	+	1.47224i
$668$		0			0
$669$	13.9188	−	4.08693i	0.538133	−	0.158010i
$670$		0			0
$671$	−11.8415	+	7.61008i	−0.457137	+	0.293784i
$672$		0			0
$673$	−34.7894	−	22.3578i	−1.34103	−	0.861830i	−0.344013	−	0.938965i	$-0.611786\pi$
$673$	−34.7894	−	22.3578i	−1.34103	−	0.861830i	−0.997021	+	0.0771350i	$0.975423\pi$
$674$		0			0
$675$	1.24082	−	1.43198i	0.0477592	−	0.0551170i
$676$		0			0
$677$	−16.3451	−	35.7908i	−0.628194	−	1.37555i	−0.909407	−	0.415908i	$-0.863464\pi$
$677$	−16.3451	−	35.7908i	−0.628194	−	1.37555i	0.281212	−	0.959646i	$-0.409263\pi$
$678$		0			0
$679$	18.0449	+	5.29845i	0.692498	+	0.203336i
$680$		0			0
$681$	3.43078	−	23.8616i	0.131468	−	0.914379i
$682$		0			0
$683$	−11.3086	+	24.7624i	−0.432713	+	0.947509i	0.560166	+	0.828380i	$0.310737\pi$
$683$	−11.3086	+	24.7624i	−0.432713	+	0.947509i	−0.992879	+	0.119128i	$0.961990\pi$
$684$		0			0
$685$	3.31683	+	23.0690i	0.126729	+	0.881423i
$686$		0			0
$687$	−6.66808	−	7.69537i	−0.254403	−	0.293597i
$688$		0			0
$689$	−13.8226			−0.526601
$690$		0			0
$691$	−21.2604			−0.808782			−0.404391	−	0.914586i	$-0.632517\pi$
$691$	−21.2604			−0.808782			−0.404391	+	0.914586i	$0.632517\pi$
$692$		0			0
$693$	−3.40123	−	3.92522i	−0.129202	−	0.149107i
$694$		0			0
$695$	−7.67159	−	53.3571i	−0.291000	−	2.02395i
$696$		0			0
$697$	−26.6391	+	58.3315i	−1.00903	+	2.20946i
$698$		0			0
$699$	−1.15129	+	8.00737i	−0.0435456	+	0.302867i
$700$		0			0
$701$	−1.04834	−	0.307821i	−0.0395954	−	0.0116262i	0.261875	−	0.965102i	$-0.415659\pi$
$701$	−1.04834	−	0.307821i	−0.0395954	−	0.0116262i	−0.301470	+	0.953476i	$0.597477\pi$
$702$		0			0
$703$	3.51278	+	7.69192i	0.132487	+	0.290106i
$704$		0			0
$705$	−12.7923	+	14.7631i	−0.481785	+	0.556009i
$706$		0			0
$707$	11.6673	+	7.49814i	0.438795	+	0.281997i
$708$		0			0
$709$	−27.2946	+	17.5412i	−1.02507	+	0.658772i	−0.941251	−	0.337709i	$-0.890348\pi$
$709$	−27.2946	+	17.5412i	−1.02507	+	0.658772i	−0.0838190	+	0.996481i	$0.526712\pi$
$710$		0			0
$711$	−7.19020	+	2.11123i	−0.269654	+	0.0791774i
$712$		0			0
$713$	−31.0724	−	13.1736i	−1.16367	−	0.493354i
$714$		0			0
$715$	12.3713	−	3.63255i	0.462661	−	0.135850i
$716$		0			0
$717$	−5.71980	+	3.67589i	−0.213610	+	0.137279i
$718$		0			0
$719$	−24.5597	−	15.7836i	−0.915923	−	0.588628i	−0.00445113	−	0.999990i	$-0.501417\pi$
$719$	−24.5597	−	15.7836i	−0.915923	−	0.588628i	−0.911472	+	0.411362i	$0.865053\pi$
$720$		0			0
$721$	−2.87384	+	3.31659i	−0.107027	+	0.123516i
$722$		0			0
$723$	−0.245687	−	0.537979i	−0.00913719	−	0.0200076i
$724$		0			0
$725$	−14.9080	−	4.37739i	−0.553670	−	0.162572i
$726$		0			0
$727$	2.99416	−	20.8249i	0.111047	−	0.772352i	−0.855857	−	0.517213i	$-0.826970\pi$
$727$	2.99416	−	20.8249i	0.111047	−	0.772352i	0.966904	−	0.255139i	$-0.0821213\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	2.77926	+	19.3302i	0.102795	+	0.714952i
$732$		0			0
$733$	1.35944	+	1.56888i	0.0502122	+	0.0579480i	0.780300	−	0.625405i	$-0.215066\pi$
$733$	1.35944	+	1.56888i	0.0502122	+	0.0579480i	−0.730088	+	0.683353i	$0.760521\pi$
$734$		0			0
$735$	−14.5245			−0.535744
$736$		0			0
$737$	7.21755			0.265862
$738$		0			0
$739$	0.125367	+	0.144681i	0.00461170	+	0.00532219i	0.758051	−	0.652196i	$-0.226152\pi$
$739$	0.125367	+	0.144681i	0.00461170	+	0.00532219i	−0.753439	+	0.657518i	$0.771606\pi$
$740$		0			0
$741$	0.669002	+	4.65301i	0.0245764	+	0.170933i
$742$		0			0
$743$	−10.1534	+	22.2329i	−0.372492	+	0.815645i	0.626841	+	0.779147i	$0.284347\pi$
$743$	−10.1534	+	22.2329i	−0.372492	+	0.815645i	−0.999334	+	0.0364978i	$0.988380\pi$
$744$		0			0
$745$	0.996253	−	6.92909i	0.0364999	−	0.253862i
$746$		0			0
$747$	7.08731	+	2.08102i	0.259311	+	0.0761406i
$748$		0			0
$749$	6.76988	+	14.8240i	0.247366	+	0.541656i
$750$		0			0
$751$	−28.9762	+	33.4403i	−1.05736	+	1.22025i	−0.0826936	+	0.996575i	$0.526352\pi$
$751$	−28.9762	+	33.4403i	−1.05736	+	1.22025i	−0.974663	+	0.223679i	$0.928193\pi$
$752$		0			0
$753$	−17.1972	−	11.0520i	−0.626700	−	0.402756i
$754$		0			0
$755$	17.4568	−	11.2188i	0.635319	−	0.408295i
$756$		0			0
$757$	7.73869	−	2.27228i	0.281267	−	0.0825875i	−0.138056	−	0.990424i	$-0.544085\pi$
$757$	7.73869	−	2.27228i	0.281267	−	0.0825875i	0.419324	+	0.907837i	$0.362267\pi$
$758$		0			0
$759$	−15.1595	+	13.8810i	−0.550253	+	0.503850i
$760$		0			0
$761$	47.4811	−	13.9417i	1.72119	−	0.505386i	0.736017	−	0.676963i	$-0.236704\pi$
$761$	47.4811	−	13.9417i	1.72119	−	0.505386i	0.985171	+	0.171576i	$0.0548859\pi$
$762$		0			0
$763$	10.8586	−	6.97837i	0.393106	−	0.252634i
$764$		0			0
$765$	14.8155	+	9.52133i	0.535654	+	0.344244i
$766$		0			0
$767$	6.43993	−	7.43207i	0.232532	−	0.268357i
$768$		0			0
$769$	3.30471	+	7.23629i	0.119171	+	0.260947i	0.959811	−	0.280646i	$-0.0905486\pi$
$769$	3.30471	+	7.23629i	0.119171	+	0.260947i	−0.840641	+	0.541593i	$0.817821\pi$
$770$		0			0
$771$	−5.56143	−	1.63298i	−0.200290	−	0.0588104i
$772$		0			0
$773$	−1.05414	+	7.33170i	−0.0379147	+	0.263703i	−0.999958	−	0.00919513i	$-0.997073\pi$
$773$	−1.05414	+	7.33170i	−0.0379147	+	0.263703i	0.962043	+	0.272898i	$0.0879821\pi$
$774$		0			0
$775$	5.53921	−	12.1292i	0.198974	−	0.435693i
$776$		0			0
$777$	0.355428	+	2.47206i	0.0127509	+	0.0886846i
$778$		0			0
$779$	25.6902	+	29.6480i	0.920445	+	1.06225i
$780$		0			0
$781$	15.8543			0.567312
$782$		0			0
$783$	−8.20008			−0.293047
$784$		0			0
$785$	12.0929	+	13.9560i	0.431616	+	0.498111i
$786$		0			0
$787$	1.49333	+	10.3863i	0.0532313	+	0.370232i	0.998973	+	0.0453121i	$0.0144282\pi$
$787$	1.49333	+	10.3863i	0.0532313	+	0.370232i	−0.945742	+	0.324920i	$0.894663\pi$
$788$		0			0
$789$	−9.67183	+	21.1783i	−0.344326	+	0.753969i
$790$		0			0
$791$	1.97663	−	13.7477i	0.0702807	−	0.488813i
$792$		0			0
$793$	3.61032	+	1.06009i	0.128206	+	0.0376447i
$794$		0			0
$795$	13.1603	+	28.8170i	0.466747	+	1.02203i
$796$		0			0
$797$	21.8325	−	25.1961i	0.773349	−	0.892492i	−0.223262	−	0.974759i	$-0.571670\pi$
$797$	21.8325	−	25.1961i	0.773349	−	0.892492i	0.996610	+	0.0822667i	$0.0262159\pi$
$798$		0			0
$799$	−41.9753	−	26.9759i	−1.48498	−	0.954337i
$800$		0			0
$801$	−5.28630	+	3.39730i	−0.186782	+	0.120038i
$802$		0			0
$803$	−4.00427	+	1.17576i	−0.141308	+	0.0414916i
$804$		0			0
$805$	−0.418181	−	15.2547i	−0.0147389	−	0.537656i
$806$		0			0
$807$	−6.59629	+	1.93684i	−0.232200	+	0.0681802i
$808$		0			0
$809$	−20.9847	+	13.4861i	−0.737784	+	0.474145i	−0.854782	−	0.518987i	$-0.826309\pi$
$809$	−20.9847	+	13.4861i	−0.737784	+	0.474145i	0.116998	+	0.993132i	$0.462673\pi$
$810$		0			0
$811$	41.1391	+	26.4385i	1.44459	+	0.928381i	0.999458	+	0.0329152i	$0.0104791\pi$
$811$	41.1391	+	26.4385i	1.44459	+	0.928381i	0.445131	+	0.895466i	$0.353157\pi$
$812$		0			0
$813$	−1.49513	+	1.72547i	−0.0524364	+	0.0605149i
$814$		0			0
$815$	16.4747	+	36.0746i	0.577084	+	1.26364i
$816$		0			0
$817$	11.4631	+	3.36586i	0.401042	+	0.117757i
$818$		0			0
$819$	−0.197588	+	1.37425i	−0.00690427	+	0.0480203i
$820$		0			0
$821$	8.15729	−	17.8620i	0.284691	−	0.623387i	−0.712217	−	0.701959i	$-0.752309\pi$
$821$	8.15729	−	17.8620i	0.284691	−	0.623387i	0.996908	+	0.0785723i	$0.0250362\pi$
$822$		0			0
$823$	−4.53114	−	31.5148i	−0.157946	−	1.09854i	−0.902411	−	0.430876i	$-0.858205\pi$
$823$	−4.53114	−	31.5148i	−0.157946	−	1.09854i	0.744466	−	0.667661i	$-0.232704\pi$
$824$		0			0
$825$	−5.31807	−	6.13738i	−0.185152	−	0.213676i
$826$		0			0
$827$	23.1097			0.803604			0.401802	−	0.915726i	$-0.368384\pi$
$827$	23.1097			0.803604			0.401802	+	0.915726i	$0.368384\pi$
$828$		0			0
$829$	38.8962			1.35092			0.675461	−	0.737396i	$-0.263945\pi$
$829$	38.8962			1.35092			0.675461	+	0.737396i	$0.263945\pi$
$830$		0			0
$831$	−3.19917	−	3.69204i	−0.110978	−	0.128075i
$832$		0			0
$833$	−5.27982	−	36.7220i	−0.182935	−	1.27234i
$834$		0			0
$835$	−14.5214	+	31.7974i	−0.502533	+	1.10039i
$836$		0			0
$837$	1.00151	−	6.96566i	0.0346173	−	0.240768i
$838$		0			0
$839$	2.41358	+	0.708690i	0.0833260	+	0.0244667i	0.323130	−	0.946355i	$-0.395265\pi$
$839$	2.41358	+	0.708690i	0.0833260	+	0.0244667i	−0.239804	+	0.970821i	$0.577083\pi$
$840$		0			0
$841$	15.8860	+	34.7856i	0.547795	+	1.19950i
$842$		0			0
$843$	−3.52665	+	4.06998i	−0.121464	+	0.140177i
$844$		0			0
$845$	25.8169	+	16.5915i	0.888129	+	0.570766i
$846$		0			0
$847$	−7.51259	+	4.82805i	−0.258136	+	0.165894i
$848$		0			0
$849$	−6.46736	+	1.89899i	−0.221959	+	0.0651731i
$850$		0			0
$851$	9.74099	−	1.67417i	0.333917	−	0.0573900i
$852$		0			0
$853$	−35.3943	+	10.3927i	−1.21188	+	0.355840i	−0.824383	−	0.566032i	$-0.808478\pi$
$853$	−35.3943	+	10.3927i	−1.21188	+	0.355840i	−0.387495	+	0.921872i	$0.626660\pi$
$854$		0			0
$855$	9.06350	−	5.82476i	0.309965	−	0.199202i
$856$		0			0
$857$	31.4424	+	20.2068i	1.07405	+	0.690252i	0.953176	−	0.302416i	$-0.0977930\pi$
$857$	31.4424	+	20.2068i	1.07405	+	0.690252i	0.120877	+	0.992668i	$0.461429\pi$
$858$		0			0
$859$	10.9767	−	12.6678i	0.374520	−	0.432219i	−0.536932	−	0.843626i	$-0.680417\pi$
$859$	10.9767	−	12.6678i	0.374520	−	0.432219i	0.911452	+	0.411406i	$0.134962\pi$
$860$		0			0
$861$	4.81318	+	10.5394i	0.164033	+	0.359182i
$862$		0			0
$863$	23.6514	+	6.94469i	0.805104	+	0.236400i	0.658290	−	0.752764i	$-0.271280\pi$
$863$	23.6514	+	6.94469i	0.805104	+	0.236400i	0.146814	+	0.989164i	$0.453098\pi$
$864$		0			0
$865$	−4.26526	+	29.6655i	−0.145023	+	1.00866i
$866$		0			0
$867$	−11.6249	+	25.4550i	−0.394802	+	0.864497i
$868$		0			0
$869$	4.57083	+	31.7908i	0.155055	+	1.07843i
$870$		0			0
$871$	−1.26346	−	1.45811i	−0.0428107	−	0.0494062i
$872$		0			0
$873$	15.5192			0.525247
$874$		0			0
$875$	−9.88082			−0.334033
$876$		0			0
$877$	9.99980	+	11.5404i	0.337669	+	0.389691i	0.899035	−	0.437877i	$-0.144269\pi$
$877$	9.99980	+	11.5404i	0.337669	+	0.389691i	−0.561366	+	0.827568i	$0.689724\pi$
$878$		0			0
$879$	−4.41503	−	30.7072i	−0.148915	−	1.03573i
$880$		0			0
$881$	3.64579	−	7.98316i	0.122830	−	0.268960i	−0.838221	−	0.545330i	$-0.816404\pi$
$881$	3.64579	−	7.98316i	0.122830	−	0.268960i	0.961051	+	0.276370i	$0.0891316\pi$
$882$		0			0
$883$	−7.18802	+	49.9938i	−0.241896	+	1.68242i	0.400692	+	0.916213i	$0.368770\pi$
$883$	−7.18802	+	49.9938i	−0.241896	+	1.68242i	−0.642588	+	0.766212i	$0.722139\pi$
$884$		0			0
$885$	−21.6255	−	6.34981i	−0.726932	−	0.213447i
$886$		0			0
$887$	14.0363	+	30.7351i	0.471292	+	1.03198i	0.984767	+	0.173880i	$0.0556306\pi$
$887$	14.0363	+	30.7351i	0.471292	+	1.03198i	−0.513475	+	0.858104i	$0.671642\pi$
$888$		0			0
$889$	−8.49970	+	9.80917i	−0.285071	+	0.328989i
$890$		0			0
$891$	−3.60556	−	2.31715i	−0.120791	−	0.0776275i
$892$		0			0
$893$	−25.6787	+	16.5027i	−0.859306	+	0.552243i
$894$		0			0
$895$	0.991996	−	0.291276i	0.0331588	−	0.00973630i
$896$		0			0
$897$	5.45801	+	0.632628i	0.182238	+	0.0211228i
$898$		0			0
$899$	−55.3688	+	16.2578i	−1.84665	+	0.542227i
$900$		0			0
$901$	−68.0734	+	43.7481i	−2.26785	+	1.45746i
$902$		0			0
$903$	2.96837	+	1.90766i	0.0987813	+	0.0634829i
$904$		0			0
$905$	3.99794	−	4.61387i	0.132896	−	0.153370i
$906$		0			0
$907$	−16.5138	−	36.1602i	−0.548332	−	1.20068i	−0.957557	−	0.288245i	$-0.906928\pi$
$907$	−16.5138	−	36.1602i	−0.548332	−	1.20068i	0.409225	−	0.912433i	$-0.365799\pi$
$908$		0			0
$909$	10.9811	+	3.22434i	0.364220	+	0.106945i
$910$		0			0
$911$	6.81639	−	47.4090i	0.225837	−	1.57073i	−0.489532	−	0.871985i	$-0.662832\pi$
$911$	6.81639	−	47.4090i	0.225837	−	1.57073i	0.715369	−	0.698747i	$-0.246258\pi$
$912$		0			0
$913$	13.1513	−	28.7972i	0.435243	−	0.953049i
$914$		0			0
$915$	−1.22729	−	8.53596i	−0.0405728	−	0.282190i
$916$		0			0
$917$	12.0656	+	13.9245i	0.398443	+	0.459827i
$918$		0			0
$919$	−23.3867			−0.771456			−0.385728	−	0.922613i	$-0.626050\pi$
$919$	−23.3867			−0.771456			−0.385728	+	0.922613i	$0.626050\pi$
$920$		0			0
$921$	16.3176			0.537683
$922$		0			0
$923$	−2.77536	−	3.20294i	−0.0913522	−	0.105426i
$924$		0			0
$925$	0.555739	+	3.86525i	0.0182726	+	0.127089i
$926$		0			0
$927$	−1.50437	+	3.29411i	−0.0494100	+	0.108193i
$928$		0			0
$929$	−2.56898	+	17.8676i	−0.0842854	+	0.586218i	0.903285	+	0.429041i	$0.141148\pi$
$929$	−2.56898	+	17.8676i	−0.0842854	+	0.586218i	−0.987570	+	0.157177i	$0.949761\pi$
$930$		0			0
$931$	−21.7766	−	6.39420i	−0.713701	−	0.209561i
$932$		0			0
$933$	−1.91990	−	4.20400i	−0.0628548	−	0.137633i
$934$		0			0
$935$	49.4291	−	57.0443i	1.61651	−	1.86555i
$936$		0			0
$937$	19.0886	+	12.2675i	0.623597	+	0.400762i	0.813934	−	0.580957i	$-0.197322\pi$
$937$	19.0886	+	12.2675i	0.623597	+	0.400762i	−0.190337	+	0.981719i	$0.560958\pi$
$938$		0			0
$939$	−20.8873	+	13.4235i	−0.681632	+	0.438058i
$940$		0			0
$941$	−22.6845	+	6.66076i	−0.739493	+	0.217135i	−0.629720	−	0.776822i	$-0.716830\pi$
$941$	−22.6845	+	6.66076i	−0.739493	+	0.217135i	−0.109773	+	0.993957i	$0.535012\pi$
$942$		0			0
$943$	41.1722	−	20.1841i	1.34075	−	0.657284i
$944$		0			0
$945$	3.05312	−	0.896476i	0.0993179	−	0.0291624i
$946$		0			0
$947$	15.0127	−	9.64806i	0.487846	−	0.313520i	−0.273492	−	0.961874i	$-0.588179\pi$
$947$	15.0127	−	9.64806i	0.487846	−	0.313520i	0.761339	+	0.648354i	$0.224542\pi$
$948$		0			0
$949$	0.938494	+	0.603133i	0.0304648	+	0.0195785i
$950$		0			0
$951$	−3.47165	+	4.00650i	−0.112576	+	0.129920i
$952$		0			0
$953$	10.4079	+	22.7902i	0.337146	+	0.738247i	0.999944	−	0.0105511i	$-0.00335859\pi$
$953$	10.4079	+	22.7902i	0.337146	+	0.738247i	−0.662798	+	0.748798i	$0.730631\pi$
$954$		0			0
$955$	−21.4310	−	6.29270i	−0.693489	−	0.203627i
$956$		0			0
$957$	−5.00166	+	34.7873i	−0.161681	+	1.12451i
$958$		0			0
$959$	−4.46823	+	9.78406i	−0.144287	+	0.315944i
$960$		0			0
$961$	−2.63616	−	18.3349i	−0.0850374	−	0.591448i
$962$		0			0
$963$	8.80656	+	10.1633i	0.283788	+	0.327508i
$964$		0			0
$965$	8.13428			0.261852
$966$		0			0
$967$	−14.6566			−0.471324			−0.235662	−	0.971835i	$-0.575726\pi$
$967$	−14.6566			−0.471324			−0.235662	+	0.971835i	$0.575726\pi$
$968$		0			0
$969$	18.0213	+	20.7977i	0.578927	+	0.668117i
$970$		0			0
$971$	−0.574178	−	3.99349i	−0.0184262	−	0.128157i	0.978532	−	0.206095i	$-0.0660756\pi$
$971$	−0.574178	−	3.99349i	−0.0184262	−	0.128157i	−0.996958	+	0.0779377i	$0.975166\pi$
$972$		0			0
$973$	10.3347	−	22.6299i	0.331315	−	0.725480i
$974$		0			0
$975$	−0.308943	+	2.14875i	−0.00989410	+	0.0688150i
$976$		0			0
$977$	−47.5597	−	13.9648i	−1.52157	−	0.446774i	−0.589113	−	0.808051i	$-0.700523\pi$
$977$	−47.5597	−	13.9648i	−1.52157	−	0.446774i	−0.932458	+	0.361277i	$0.882341\pi$
$978$		0			0
$979$	11.1880	+	24.4983i	0.357570	+	0.782970i
$980$		0			0
$981$	6.97514	−	8.04974i	0.222699	−	0.257008i
$982$		0			0
$983$	−12.8007	−	8.22648i	−0.408277	−	0.262384i	0.320343	−	0.947302i	$-0.396202\pi$
$983$	−12.8007	−	8.22648i	−0.408277	−	0.262384i	−0.728621	+	0.684918i	$0.759838\pi$
$984$		0			0
$985$	−59.4055	+	38.1776i	−1.89282	+	1.21644i
$986$		0			0
$987$	−8.65010	+	2.53990i	−0.275336	+	0.0808459i
$988$		0			0
$989$	7.22484	−	11.9499i	0.229737	−	0.379984i
$990$		0			0
$991$	1.04288	−	0.306218i	0.0331283	−	0.00972735i	−0.265126	−	0.964214i	$-0.585414\pi$
$991$	1.04288	−	0.306218i	0.0331283	−	0.00972735i	0.298255	+	0.954486i	$0.403596\pi$
$992$		0			0
$993$	29.3655	−	18.8721i	0.931887	−	0.598888i
$994$		0			0
$995$	7.22968	+	4.64623i	0.229196	+	0.147296i
$996$		0			0
$997$	−35.4928	+	40.9609i	−1.12407	+	1.29724i	−0.174159	+	0.984718i	$0.555721\pi$
$997$	−35.4928	+	40.9609i	−1.12407	+	1.29724i	−0.949909	+	0.312526i	$0.898825\pi$
$998$		0			0
$999$	0.856136	+	1.87468i	0.0270869	+	0.0593121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.193.3	✓	30
23.18	even	11	inner	552.2.q.c.409.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.193.3	✓	30	1.1	even	1	trivial
552.2.q.c.409.3	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)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(0.373689 + 2.59907i) q^{5} +(-0.503412 + 1.10232i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(0.373689 + 2.59907i) q^{5} +(-0.503412 + 1.10232i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(4.11232 + 1.20749i) q^{11} +(-0.475938 - 1.04216i) q^{13} +(-1.71953 + 1.98444i) q^{15} +(-5.64229 - 3.62608i) q^{17} +(-3.45172 + 2.21829i) q^{19} +(-1.16274 + 0.341412i) q^{21} +(1.47673 + 4.56281i) q^{23} +(-1.81803 + 0.533823i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(6.89835 + 4.43330i) q^{29} +(-4.60844 + 5.31843i) q^{31} +(1.78044 + 3.89862i) q^{33} +(-3.05312 - 0.896476i) q^{35} +(0.293299 - 2.03994i) q^{37} +(0.475938 - 1.04216i) q^{39} +(-1.36069 - 9.46381i) q^{41} +(-1.90678 - 2.20054i) q^{43} -2.62579 q^{45} +7.43941 q^{47} +(3.62234 + 4.18041i) q^{49} +(-0.954505 - 6.63873i) q^{51} +(5.01192 - 10.9746i) q^{53} +(-1.60161 + 11.1394i) q^{55} +(-3.93686 - 1.15597i) q^{57} +(3.56571 + 7.80781i) q^{59} +(-2.15072 + 2.48206i) q^{61} +(-1.01945 - 0.655164i) q^{63} +(2.53079 - 1.62644i) q^{65} +(1.61579 - 0.474440i) q^{67} +(-2.48129 + 4.10405i) q^{69} +(3.54931 - 1.04217i) q^{71} +(-0.819149 + 0.526435i) q^{73} +(-1.59399 - 1.02440i) q^{75} +(-3.40123 + 3.92522i) q^{77} +(3.11302 + 6.81655i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(1.05121 - 7.31133i) q^{83} +(7.31595 - 16.0197i) q^{85} +(1.16699 + 8.11662i) q^{87} +(4.11504 + 4.74901i) q^{89} +1.38838 q^{91} -7.03729 q^{93} +(-7.05534 - 8.14229i) q^{95} +(-2.20862 - 15.3613i) q^{97} +(-1.78044 + 3.89862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 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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