LMFDB - Embedded newform 1008.2.cz.i.607.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.13
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.i.367.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00453 - 1.41100i) q^{3} +(1.92313 - 1.11032i) q^{5} +(-1.98797 - 1.74585i) q^{7} +(-0.981826 - 2.83479i) q^{9} +O(q^{10})$	\(q+(1.00453 - 1.41100i) q^{3} +(1.92313 - 1.11032i) q^{5} +(-1.98797 - 1.74585i) q^{7} +(-0.981826 - 2.83479i) q^{9} +(-3.11664 - 1.79939i) q^{11} +(-0.699925 - 0.404102i) q^{13} +(0.365190 - 3.82888i) q^{15} +(1.37926 - 0.796318i) q^{17} +(-1.63568 + 2.83308i) q^{19} +(-4.46037 + 1.05125i) q^{21} +(-1.46305 + 0.844692i) q^{23} +(-0.0343794 + 0.0595469i) q^{25} +(-4.98615 - 1.46228i) q^{27} +(-2.13167 - 3.69216i) q^{29} -1.26036 q^{31} +(-5.66970 + 2.59002i) q^{33} +(-5.76157 - 1.15022i) q^{35} +(3.94387 - 6.83099i) q^{37} +(-1.27328 + 0.581658i) q^{39} +(7.57153 + 4.37143i) q^{41} +(7.47162 - 4.31374i) q^{43} +(-5.03570 - 4.36152i) q^{45} +0.665571 q^{47} +(0.904012 + 6.94138i) q^{49} +(0.261913 - 2.74607i) q^{51} +(6.27101 + 10.8617i) q^{53} -7.99160 q^{55} +(2.35437 + 5.15386i) q^{57} +4.30730 q^{59} -8.59298i q^{61} +(-2.99728 + 7.34958i) q^{63} -1.79473 q^{65} -0.102572i q^{67} +(-0.277823 + 2.91288i) q^{69} -11.8438i q^{71} +(-5.30908 + 3.06520i) q^{73} +(0.0494852 + 0.108326i) q^{75} +(3.05430 + 9.01830i) q^{77} -4.31692i q^{79} +(-7.07203 + 5.56654i) q^{81} +(-5.33369 - 9.23823i) q^{83} +(1.76834 - 3.06285i) q^{85} +(-7.35096 - 0.701117i) q^{87} +(1.69926 + 0.981066i) q^{89} +(0.685925 + 2.02530i) q^{91} +(-1.26607 + 1.77836i) q^{93} +7.26451i q^{95} +(15.3268 - 8.84892i) q^{97} +(-2.04089 + 10.6017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9}+O(q^{10}) $ 32 * q - 4 * q^9	$ 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85} - 18 q^{89} - 38 q^{93} + 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00453	−	1.41100i	0.579967	−	0.814640i
$3$	1.00453	−	1.41100i	0.579967	−	0.814640i
$4$		0			0
$5$	1.92313	−	1.11032i	0.860050	−	0.496550i	−0.00397896	−	0.999992i	$-0.501267\pi$
$5$	1.92313	−	1.11032i	0.860050	−	0.496550i	0.864029	+	0.503442i	$0.167933\pi$
$6$		0			0
$7$	−1.98797	−	1.74585i	−0.751380	−	0.659869i
$7$	−1.98797	−	1.74585i	−0.751380	−	0.659869i
$8$		0			0
$9$	−0.981826	−	2.83479i	−0.327275	−	0.944929i
$10$		0			0
$11$	−3.11664	−	1.79939i	−0.939701	−	0.542537i	−0.0498344	−	0.998757i	$-0.515869\pi$
$11$	−3.11664	−	1.79939i	−0.939701	−	0.542537i	−0.889867	+	0.456221i	$0.849203\pi$
$12$		0			0
$13$	−0.699925	−	0.404102i	−0.194124	−	0.112078i	0.399788	−	0.916608i	$-0.369084\pi$
$13$	−0.699925	−	0.404102i	−0.194124	−	0.112078i	−0.593912	+	0.804530i	$0.702417\pi$
$14$		0			0
$15$	0.365190	−	3.82888i	0.0942917	−	0.988614i
$16$		0			0
$17$	1.37926	−	0.796318i	0.334521	−	0.193136i	−0.323326	−	0.946288i	$-0.604801\pi$
$17$	1.37926	−	0.796318i	0.334521	−	0.193136i	0.657846	+	0.753152i	$0.271468\pi$
$18$		0			0
$19$	−1.63568	+	2.83308i	−0.375251	+	0.649953i	−0.990365	−	0.138485i	$-0.955777\pi$
$19$	−1.63568	+	2.83308i	−0.375251	+	0.649953i	0.615114	+	0.788438i	$0.289110\pi$
$20$		0			0
$21$	−4.46037	+	1.05125i	−0.973332	+	0.229401i
$22$		0			0
$23$	−1.46305	+	0.844692i	−0.305067	+	0.176130i	−0.644717	−	0.764422i	$-0.723025\pi$
$23$	−1.46305	+	0.844692i	−0.305067	+	0.176130i	0.339650	+	0.940552i	$0.389691\pi$
$24$		0			0
$25$	−0.0343794	+	0.0595469i	−0.00687588	+	0.0119094i
$26$		0			0
$27$	−4.98615	−	1.46228i	−0.959586	−	0.281417i
$28$		0			0
$29$	−2.13167	−	3.69216i	−0.395841	−	0.685617i	0.597367	−	0.801968i	$-0.296214\pi$
$29$	−2.13167	−	3.69216i	−0.395841	−	0.685617i	−0.993208	+	0.116351i	$0.962880\pi$
$30$		0			0
$31$	−1.26036			−0.226367			−0.113183	−	0.993574i	$-0.536105\pi$
$31$	−1.26036			−0.226367			−0.113183	+	0.993574i	$0.536105\pi$
$32$		0			0
$33$	−5.66970	+	2.59002i	−0.986968	+	0.450864i
$34$		0			0
$35$	−5.76157	−	1.15022i	−0.973883	−	0.194423i
$36$		0			0
$37$	3.94387	−	6.83099i	0.648369	−	1.12301i	−0.335144	−	0.942167i	$-0.608785\pi$
$37$	3.94387	−	6.83099i	0.648369	−	1.12301i	0.983512	−	0.180840i	$-0.0578817\pi$
$38$		0			0
$39$	−1.27328	+	0.581658i	−0.203889	+	0.0931399i
$40$		0			0
$41$	7.57153	+	4.37143i	1.18247	+	0.682702i	0.956586	−	0.291451i	$-0.0941380\pi$
$41$	7.57153	+	4.37143i	1.18247	+	0.682702i	0.225889	+	0.974153i	$0.427471\pi$
$42$		0			0
$43$	7.47162	−	4.31374i	1.13941	−	0.657839i	0.193126	−	0.981174i	$-0.438137\pi$
$43$	7.47162	−	4.31374i	1.13941	−	0.657839i	0.946285	+	0.323335i	$0.104804\pi$
$44$		0			0
$45$	−5.03570	−	4.36152i	−0.750678	−	0.650178i
$46$		0			0
$47$	0.665571			0.0970835			0.0485417	−	0.998821i	$-0.484543\pi$
$47$	0.665571			0.0970835			0.0485417	+	0.998821i	$0.484543\pi$
$48$		0			0
$49$	0.904012	+	6.94138i	0.129145	+	0.991626i
$50$		0			0
$51$	0.261913	−	2.74607i	0.0366752	−	0.384526i
$52$		0			0
$53$	6.27101	+	10.8617i	0.861390	+	1.49197i	0.870588	+	0.492014i	$0.163739\pi$
$53$	6.27101	+	10.8617i	0.861390	+	1.49197i	−0.00919746	+	0.999958i	$0.502928\pi$
$54$		0			0
$55$	−7.99160			−1.07759
$56$		0			0
$57$	2.35437	+	5.15386i	0.311844	+	0.682646i
$58$		0			0
$59$	4.30730			0.560762			0.280381	−	0.959889i	$-0.409539\pi$
$59$	4.30730			0.560762			0.280381	+	0.959889i	$0.409539\pi$
$60$		0			0
$61$		−	8.59298i		−	1.10022i	−0.835093	−	0.550109i	$-0.814586\pi$
$61$		−	8.59298i		−	1.10022i	0.835093	−	0.550109i	$-0.185414\pi$
$62$		0			0
$63$	−2.99728	+	7.34958i	−0.377621	+	0.925960i
$64$		0			0
$65$	−1.79473			−0.222609
$66$		0			0
$67$		−	0.102572i		−	0.0125312i	−0.999980	−	0.00626558i	$-0.998006\pi$
$67$		−	0.102572i		−	0.0125312i	0.999980	−	0.00626558i	$-0.00199441\pi$
$68$		0			0
$69$	−0.277823	+	2.91288i	−0.0334460	+	0.350669i
$70$		0			0
$71$		−	11.8438i		−	1.40560i	−0.711390	−	0.702798i	$-0.751934\pi$
$71$		−	11.8438i		−	1.40560i	0.711390	−	0.702798i	$-0.248066\pi$
$72$		0			0
$73$	−5.30908	+	3.06520i	−0.621381	+	0.358754i	−0.777406	−	0.628999i	$-0.783465\pi$
$73$	−5.30908	+	3.06520i	−0.621381	+	0.358754i	0.156026	+	0.987753i	$0.450132\pi$
$74$		0			0
$75$	0.0494852	+	0.108326i	0.00571406	+	0.0125084i
$76$		0			0
$77$	3.05430	+	9.01830i	0.348069	+	1.02773i
$78$		0			0
$79$		−	4.31692i		−	0.485691i	−0.970065	−	0.242846i	$-0.921919\pi$
$79$		−	4.31692i		−	0.485691i	0.970065	−	0.242846i	$-0.0780809\pi$
$80$		0			0
$81$	−7.07203	+	5.56654i	−0.785782	+	0.618504i
$82$		0			0
$83$	−5.33369	−	9.23823i	−0.585449	−	1.01403i	−0.994819	−	0.101659i	$-0.967585\pi$
$83$	−5.33369	−	9.23823i	−0.585449	−	1.01403i	0.409370	−	0.912368i	$-0.365748\pi$
$84$		0			0
$85$	1.76834	−	3.06285i	0.191803	−	0.332213i
$86$		0			0
$87$	−7.35096	−	0.701117i	−0.788105	−	0.0751676i
$88$		0			0
$89$	1.69926	+	0.981066i	0.180121	+	0.103993i	0.587349	−	0.809333i	$-0.300171\pi$
$89$	1.69926	+	0.981066i	0.180121	+	0.103993i	−0.407229	+	0.913326i	$0.633505\pi$
$90$		0			0
$91$	0.685925	+	2.02530i	0.0719045	+	0.212310i
$92$		0			0
$93$	−1.26607	+	1.77836i	−0.131285	+	0.184407i
$94$		0			0
$95$			7.26451i			0.745323i
$96$		0			0
$97$	15.3268	−	8.84892i	1.55620	−	0.898471i	0.558583	−	0.829449i	$-0.311345\pi$
$97$	15.3268	−	8.84892i	1.55620	−	0.898471i	0.997615	−	0.0690225i	$-0.0219880\pi$
$98$		0			0
$99$	−2.04089	+	10.6017i	−0.205118	+	1.06551i
$100$		0			0
$101$	−0.0191062	−	0.0110310i	−0.00190114	−	0.00109762i	0.499049	−	0.866574i	$-0.333683\pi$
$101$	−0.0191062	−	0.0110310i	−0.00190114	−	0.00109762i	−0.500950	+	0.865476i	$0.667016\pi$
$102$		0			0
$103$	−9.68644	−	16.7774i	−0.954434	−	1.65313i	−0.735659	−	0.677352i	$-0.763127\pi$
$103$	−9.68644	−	16.7774i	−0.954434	−	1.65313i	−0.218775	−	0.975775i	$-0.570206\pi$
$104$		0			0
$105$	−7.41065	+	6.97412i	−0.723205	+	0.680605i
$106$		0			0
$107$	12.5854	+	7.26619i	1.21668	+	0.702449i	0.964206	−	0.265155i	$-0.0854230\pi$
$107$	12.5854	+	7.26619i	1.21668	+	0.702449i	0.252472	+	0.967604i	$0.418756\pi$
$108$		0			0
$109$	−9.78443	−	16.9471i	−0.937178	−	1.62324i	−0.770703	−	0.637195i	$-0.780095\pi$
$109$	−9.78443	−	16.9471i	−0.937178	−	1.62324i	−0.166475	−	0.986046i	$-0.553239\pi$
$110$		0			0
$111$	−5.67675	−	12.4267i	−0.538814	−	1.17949i
$112$		0			0
$113$	1.32050	−	2.28716i	0.124222	−	0.215158i	−0.797207	−	0.603706i	$-0.793690\pi$
$113$	1.32050	−	2.28716i	0.124222	−	0.215158i	0.921428	+	0.388548i	$0.127023\pi$
$114$		0			0
$115$	−1.87576	+	3.24890i	−0.174915	+	0.302962i
$116$		0			0
$117$	−0.458338	+	2.38090i	−0.0423734	+	0.220114i
$118$		0			0
$119$	−4.13218	−	0.824935i	−0.378796	−	0.0756217i
$120$		0			0
$121$	0.975611	+	1.68981i	0.0886919	+	0.153619i
$122$		0			0
$123$	13.7739	−	6.29217i	1.24195	−	0.567346i
$124$		0			0
$125$			11.2559i			1.00676i
$126$		0			0
$127$		−	3.06503i		−	0.271978i	−0.990710	−	0.135989i	$-0.956579\pi$
$127$		−	3.06503i		−	0.271978i	0.990710	−	0.135989i	$-0.0434211\pi$
$128$		0			0
$129$	1.41881	−	14.8757i	0.124919	−	1.30973i
$130$		0			0
$131$	6.56024	+	11.3627i	0.573171	+	0.992762i	0.996238	+	0.0866630i	$0.0276203\pi$
$131$	6.56024	+	11.3627i	0.573171	+	0.992762i	−0.423067	+	0.906099i	$0.639046\pi$
$132$		0			0
$133$	8.19781	−	2.77641i	0.710840	−	0.240746i
$134$		0			0
$135$	−11.2126	+	2.72406i	−0.965029	+	0.234450i
$136$		0			0
$137$	−7.53721	+	13.0548i	−0.643948	+	1.11535i	0.340596	+	0.940210i	$0.389371\pi$
$137$	−7.53721	+	13.0548i	−0.643948	+	1.11535i	−0.984544	+	0.175140i	$0.943962\pi$
$138$		0			0
$139$	−4.77397	+	8.26877i	−0.404923	+	0.701348i	−0.994313	−	0.106502i	$-0.966035\pi$
$139$	−4.77397	+	8.26877i	−0.404923	+	0.701348i	0.589389	+	0.807849i	$0.299368\pi$
$140$		0			0
$141$	0.668588	−	0.939118i	0.0563053	−	0.0790880i
$142$		0			0
$143$	1.45427	+	2.51888i	0.121612	+	0.210639i
$144$		0			0
$145$	−8.19895	−	4.73367i	−0.680886	−	0.393110i
$146$		0			0
$147$	10.7024	+	5.69729i	0.882717	+	0.469904i
$148$		0			0
$149$	5.70556	+	9.88232i	0.467418	+	0.809591i	0.999307	−	0.0372227i	$-0.0118511\pi$
$149$	5.70556	+	9.88232i	0.467418	+	0.809591i	−0.531889	+	0.846814i	$0.678518\pi$
$150$		0			0
$151$	8.27511	+	4.77764i	0.673419	+	0.388798i	0.797371	−	0.603490i	$-0.206224\pi$
$151$	8.27511	+	4.77764i	0.673419	+	0.388798i	−0.123952	+	0.992288i	$0.539557\pi$
$152$		0			0
$153$	−3.61159	−	3.12807i	−0.291980	−	0.252890i
$154$		0			0
$155$	−2.42383	+	1.39940i	−0.194687	+	0.112402i
$156$		0			0
$157$		−	16.2321i		−	1.29547i	−0.761867	−	0.647733i	$-0.775717\pi$
$157$		−	16.2321i		−	1.29547i	0.761867	−	0.647733i	$-0.224283\pi$
$158$		0			0
$159$	21.6253	+	2.06257i	1.71500	+	0.163572i
$160$		0			0
$161$	4.38320	+	0.875047i	0.345444	+	0.0689634i
$162$		0			0
$163$	15.9670	+	9.21855i	1.25063	+	0.722053i	0.971235	−	0.238123i	$-0.0765321\pi$
$163$	15.9670	+	9.21855i	1.25063	+	0.722053i	0.279397	+	0.960176i	$0.409865\pi$
$164$		0			0
$165$	−8.02782	+	11.2761i	−0.624965	+	0.877845i
$166$		0			0
$167$	0.233104	−	0.403747i	0.0180381	−	0.0312429i	−0.856865	−	0.515540i	$-0.827591\pi$
$167$	0.233104	−	0.403747i	0.0180381	−	0.0312429i	0.874904	+	0.484297i	$0.160925\pi$
$168$		0			0
$169$	−6.17340	−	10.6926i	−0.474877	−	0.822511i
$170$		0			0
$171$	9.63713	+	1.85521i	0.736970	+	0.141871i
$172$		0			0
$173$		−	2.81617i		−	0.214109i	−0.994253	−	0.107055i	$-0.965858\pi$
$173$		−	2.81617i		−	0.214109i	0.994253	−	0.107055i	$-0.0341420\pi$
$174$		0			0
$175$	0.172305	−	0.0583558i	0.0130250	−	0.00441129i
$176$		0			0
$177$	4.32682	−	6.07758i	0.325224	−	0.456819i
$178$		0			0
$179$	6.65834	−	3.84419i	0.497668	−	0.287328i	−0.230082	−	0.973171i	$-0.573900\pi$
$179$	6.65834	−	3.84419i	0.497668	−	0.287328i	0.727750	+	0.685843i	$0.240566\pi$
$180$		0			0
$181$		−	13.2163i		−	0.982357i	−0.871059	−	0.491178i	$-0.836566\pi$
$181$		−	13.2163i		−	0.982357i	0.871059	−	0.491178i	$-0.163434\pi$
$182$		0			0
$183$	−12.1247	−	8.63193i	−0.896282	−	0.638091i
$184$		0			0
$185$		−	17.5158i		−	1.28779i
$186$		0			0
$187$	−5.73155			−0.419132
$188$		0			0
$189$	7.35937	+	11.6120i	0.535316	+	0.844652i
$190$		0			0
$191$			15.2301i			1.10201i	0.834503	+	0.551004i	$0.185755\pi$
$191$			15.2301i			1.10201i	−0.834503	+	0.551004i	$0.814245\pi$
$192$		0			0
$193$	−6.72851			−0.484329			−0.242164	−	0.970235i	$-0.577857\pi$
$193$	−6.72851			−0.484329			−0.242164	+	0.970235i	$0.577857\pi$
$194$		0			0
$195$	−1.80286	+	2.53236i	−0.129106	+	0.181346i
$196$		0			0
$197$	10.0724			0.717628			0.358814	−	0.933409i	$-0.383181\pi$
$197$	10.0724			0.717628			0.358814	+	0.933409i	$0.383181\pi$
$198$		0			0
$199$	0.574431	+	0.994943i	0.0407203	+	0.0705296i	0.885667	−	0.464320i	$-0.153701\pi$
$199$	0.574431	+	0.994943i	0.0407203	+	0.0705296i	−0.844947	+	0.534850i	$0.820368\pi$
$200$		0			0
$201$	−0.144729	−	0.103037i	−0.0102084	−	0.00726767i
$202$		0			0
$203$	−2.20827	+	11.0615i	−0.154990	+	0.776362i
$204$		0			0
$205$	19.4147			1.35598
$206$		0			0
$207$	3.83098	+	3.31809i	0.266272	+	0.230623i
$208$		0			0
$209$	10.1956	−	5.88645i	0.705247	−	0.407174i
$210$		0			0
$211$	21.2256	+	12.2546i	1.46123	+	0.843642i	0.999068	−	0.0431532i	$-0.0137404\pi$
$211$	21.2256	+	12.2546i	1.46123	+	0.843642i	0.462162	+	0.886795i	$0.347074\pi$
$212$		0			0
$213$	−16.7115	−	11.8974i	−1.14505	−	0.815200i
$214$		0			0
$215$	9.57926	−	16.5918i	0.653300	−	1.13155i
$216$		0			0
$217$	2.50554	+	2.20039i	0.170087	+	0.149372i
$218$		0			0
$219$	−1.00816	+	10.5702i	−0.0681251	+	0.714267i
$220$		0			0
$221$	−1.28717			−0.0865847
$222$		0			0
$223$	11.4679	+	19.8631i	0.767950	+	1.33013i	0.938673	+	0.344809i	$0.112056\pi$
$223$	11.4679	+	19.8631i	0.767950	+	1.33013i	−0.170723	+	0.985319i	$0.554610\pi$
$224$		0			0
$225$	0.202557	+	0.0389936i	0.0135038	+	0.00259957i
$226$		0			0
$227$	−10.4321	+	18.0689i	−0.692403	+	1.19928i	0.278645	+	0.960394i	$0.410115\pi$
$227$	−10.4321	+	18.0689i	−0.692403	+	1.19928i	−0.971048	+	0.238884i	$0.923219\pi$
$228$		0			0
$229$	6.16237	−	3.55785i	0.407221	−	0.235109i	−0.282374	−	0.959304i	$-0.591122\pi$
$229$	6.16237	−	3.55785i	0.407221	−	0.235109i	0.689595	+	0.724195i	$0.257789\pi$
$230$		0			0
$231$	15.7929	+	4.74958i	1.03910	+	0.312500i
$232$		0			0
$233$	−11.2032	+	19.4045i	−0.733946	+	1.27123i	0.221238	+	0.975220i	$0.428990\pi$
$233$	−11.2032	+	19.4045i	−0.733946	+	1.27123i	−0.955184	+	0.296012i	$0.904343\pi$
$234$		0			0
$235$	1.27998	−	0.738996i	0.0834966	−	0.0482068i
$236$		0			0
$237$	−6.09116	−	4.33649i	−0.395663	−	0.281685i
$238$		0			0
$239$	−10.1076	−	5.83565i	−0.653809	−	0.377477i	0.136105	−	0.990694i	$-0.456541\pi$
$239$	−10.1076	−	5.83565i	−0.653809	−	0.377477i	−0.789914	+	0.613218i	$0.789875\pi$
$240$		0			0
$241$	−2.80520	−	1.61958i	−0.180699	−	0.104327i	0.406922	−	0.913463i	$-0.366602\pi$
$241$	−2.80520	−	1.61958i	−0.180699	−	0.104327i	−0.587621	+	0.809136i	$0.699935\pi$
$242$		0			0
$243$	0.750275	+	15.5704i	0.0481302	+	0.998841i
$244$		0			0
$245$	9.44569	+	12.3454i	0.603463	+	0.788721i
$246$		0			0
$247$	2.28971	−	1.32196i	0.145690	−	0.0841144i
$248$		0			0
$249$	−18.3930	−	1.75428i	−1.16561	−	0.111173i
$250$		0			0
$251$	26.4379			1.66875			0.834374	−	0.551198i	$-0.185829\pi$
$251$	26.4379			1.66875			0.834374	+	0.551198i	$0.185829\pi$
$252$		0			0
$253$	6.07972			0.382229
$254$		0			0
$255$	−2.54532	−	5.57185i	−0.159394	−	0.348923i
$256$		0			0
$257$	23.3944	−	13.5068i	1.45930	−	0.842530i	0.460328	−	0.887749i	$-0.347732\pi$
$257$	23.3944	−	13.5068i	1.45930	−	0.842530i	0.998977	+	0.0452193i	$0.0143987\pi$
$258$		0			0
$259$	−19.7662	+	6.69435i	−1.22821	+	0.415967i
$260$		0			0
$261$	−8.37355	+	9.66789i	−0.518310	+	0.598427i
$262$		0			0
$263$	−24.2295	−	13.9889i	−1.49406	−	0.862593i	−0.494079	−	0.869417i	$-0.664495\pi$
$263$	−24.2295	−	13.9889i	−1.49406	−	0.862593i	−0.999977	+	0.00682378i	$0.997828\pi$
$264$		0			0
$265$	24.1200	+	13.9257i	1.48168	+	0.855447i
$266$		0			0
$267$	3.09124	−	1.41213i	0.189181	−	0.0864211i
$268$		0			0
$269$	−14.5580	+	8.40506i	−0.887617	+	0.512466i	−0.873162	−	0.487430i	$-0.837934\pi$
$269$	−14.5580	+	8.40506i	−0.887617	+	0.512466i	−0.0144545	+	0.999896i	$0.504601\pi$
$270$		0			0
$271$	−0.722444	+	1.25131i	−0.0438854	+	0.0760117i	−0.887134	−	0.461512i	$-0.847307\pi$
$271$	−0.722444	+	1.25131i	−0.0438854	+	0.0760117i	0.843248	+	0.537524i	$0.180640\pi$
$272$		0			0
$273$	3.54673	+	1.06665i	0.214658	+	0.0645564i
$274$		0			0
$275$	0.214296	−	0.123724i	0.0129225	−	0.00746084i
$276$		0			0
$277$	−13.7772	+	23.8628i	−0.827790	+	1.43378i	0.0719774	+	0.997406i	$0.477069\pi$
$277$	−13.7772	+	23.8628i	−0.827790	+	1.43378i	−0.899768	+	0.436369i	$0.856264\pi$
$278$		0			0
$279$	1.23745	+	3.57284i	0.0740842	+	0.213900i
$280$		0			0
$281$	−2.64650	−	4.58388i	−0.157877	−	0.273451i	0.776226	−	0.630455i	$-0.217132\pi$
$281$	−2.64650	−	4.58388i	−0.157877	−	0.273451i	−0.934103	+	0.357004i	$0.883798\pi$
$282$		0			0
$283$	6.20606			0.368912			0.184456	−	0.982841i	$-0.440948\pi$
$283$	6.20606			0.368912			0.184456	+	0.982841i	$0.440948\pi$
$284$		0			0
$285$	10.2502	+	7.29744i	0.607170	+	0.432263i
$286$		0			0
$287$	−7.42009	−	21.9090i	−0.437994	−	1.29325i
$288$		0			0
$289$	−7.23175	+	12.5258i	−0.425397	+	0.736810i
$290$		0			0
$291$	2.91045	−	30.5151i	0.170614	−	1.78882i
$292$		0			0
$293$	8.29706	+	4.79031i	0.484719	+	0.279853i	0.722381	−	0.691495i	$-0.243048\pi$
$293$	8.29706	+	4.79031i	0.484719	+	0.279853i	−0.237662	+	0.971348i	$0.576381\pi$
$294$		0			0
$295$	8.28349	−	4.78248i	0.482284	−	0.278447i
$296$		0			0
$297$	12.9088	+	13.5294i	0.749045	+	0.785058i
$298$		0			0
$299$	1.36537			0.0789611
$300$		0			0
$301$	−22.3845	−	4.46876i	−1.29022	−	0.257575i
$302$		0			0
$303$	−0.0347575	+	0.0158778i	−0.00199676	+	0.000912156i
$304$		0			0
$305$	−9.54096	−	16.5254i	−0.546314	−	0.946243i
$306$		0			0
$307$	9.88024			0.563895			0.281948	−	0.959430i	$-0.409020\pi$
$307$	9.88024			0.563895			0.281948	+	0.959430i	$0.409020\pi$
$308$		0			0
$309$	−33.4032	−	3.18592i	−1.90024	−	0.181241i
$310$		0			0
$311$	17.3994			0.986628			0.493314	−	0.869851i	$-0.335785\pi$
$311$	17.3994			0.986628			0.493314	+	0.869851i	$0.335785\pi$
$312$		0			0
$313$		−	8.60324i		−	0.486284i	−0.969991	−	0.243142i	$-0.921822\pi$
$313$		−	8.60324i		−	0.486284i	0.969991	−	0.243142i	$-0.0781781\pi$
$314$		0			0
$315$	2.39623	+	17.4621i	0.135012	+	0.983880i
$316$		0			0
$317$	24.2011			1.35927			0.679636	−	0.733550i	$-0.262138\pi$
$317$	24.2011			1.35927			0.679636	+	0.733550i	$0.262138\pi$
$318$		0			0
$319$			15.3428i			0.859033i
$320$		0			0
$321$	22.8950	−	10.4589i	1.27788	−	0.583756i
$322$		0			0
$323$			5.21009i			0.289897i
$324$		0			0
$325$	0.0481260	−	0.0277856i	0.00266955	−	0.00154127i
$326$		0			0
$327$	−33.7411	−	3.21815i	−1.86589	−	0.177964i
$328$		0			0
$329$	−1.32313	−	1.16199i	−0.0729466	−	0.0640624i
$330$		0			0
$331$		−	24.1702i		−	1.32851i	−0.747505	−	0.664256i	$-0.768749\pi$
$331$		−	24.1702i		−	1.32851i	0.747505	−	0.664256i	$-0.231251\pi$
$332$		0			0
$333$	−23.2366	−	4.47319i	−1.27336	−	0.245130i
$334$		0			0
$335$	−0.113888	−	0.197259i	−0.00622235	−	0.0107774i
$336$		0			0
$337$	−11.4816	+	19.8867i	−0.625443	+	1.08330i	0.363013	+	0.931784i	$0.381748\pi$
$337$	−11.4816	+	19.8867i	−0.625443	+	1.08330i	−0.988455	+	0.151514i	$0.951585\pi$
$338$		0			0
$339$	−1.90070	−	4.16075i	−0.103232	−	0.225981i
$340$		0			0
$341$	3.92807	+	2.26787i	0.212717	+	0.122812i
$342$		0			0
$343$	10.3215	−	15.3775i	0.557307	−	0.830307i
$344$		0			0
$345$	2.69994	+	5.91032i	0.145360	+	0.318201i
$346$		0			0
$347$			28.7156i			1.54153i	0.637117	+	0.770767i	$0.280127\pi$
$347$			28.7156i			1.54153i	−0.637117	+	0.770767i	$0.719873\pi$
$348$		0			0
$349$	−5.95211	+	3.43645i	−0.318609	+	0.183949i	−0.650772	−	0.759273i	$-0.725555\pi$
$349$	−5.95211	+	3.43645i	−0.318609	+	0.183949i	0.332163	+	0.943222i	$0.392221\pi$
$350$		0			0
$351$	2.89902	+	3.03840i	0.154738	+	0.162178i
$352$		0			0
$353$	−25.5492	−	14.7508i	−1.35985	−	0.785107i	−0.370243	−	0.928935i	$-0.620726\pi$
$353$	−25.5492	−	14.7508i	−1.35985	−	0.785107i	−0.989603	+	0.143828i	$0.954059\pi$
$354$		0			0
$355$	−13.1504	−	22.7771i	−0.697949	−	1.20888i
$356$		0			0
$357$	−5.31489	+	5.00182i	−0.281294	+	0.264724i
$358$		0			0
$359$	13.7726	+	7.95164i	0.726892	+	0.419672i	0.817284	−	0.576235i	$-0.195479\pi$
$359$	13.7726	+	7.95164i	0.726892	+	0.419672i	−0.0903918	+	0.995906i	$0.528812\pi$
$360$		0			0
$361$	4.14910	+	7.18646i	0.218374	+	0.378235i
$362$		0			0
$363$	3.36435	+	0.320883i	0.176582	+	0.0168420i
$364$		0			0
$365$	−6.80670	+	11.7896i	−0.356279	+	0.617093i
$366$		0			0
$367$	−6.77962	+	11.7427i	−0.353893	+	0.612961i	−0.986928	−	0.161162i	$-0.948476\pi$
$367$	−6.77962	+	11.7427i	−0.353893	+	0.612961i	0.633034	+	0.774124i	$0.281809\pi$
$368$		0			0
$369$	4.95813	−	25.7557i	0.258110	−	1.34079i
$370$		0			0
$371$	6.49637	−	32.5410i	0.337275	−	1.68944i
$372$		0			0
$373$	5.38387	+	9.32514i	0.278766	+	0.482837i	0.971078	−	0.238761i	$-0.0767412\pi$
$373$	5.38387	+	9.32514i	0.278766	+	0.482837i	−0.692312	+	0.721598i	$0.743408\pi$
$374$		0			0
$375$	15.8820	+	11.3069i	0.820144	+	0.583886i
$376$		0			0
$377$			3.44564i			0.177460i
$378$		0			0
$379$		−	3.98071i		−	0.204475i	−0.994760	−	0.102238i	$-0.967400\pi$
$379$		−	3.98071i		−	0.204475i	0.994760	−	0.102238i	$-0.0326002\pi$
$380$		0			0
$381$	−4.32475	−	3.07893i	−0.221564	−	0.157738i
$382$		0			0
$383$	13.4604	+	23.3141i	0.687795	+	1.19130i	0.972550	+	0.232695i	$0.0747545\pi$
$383$	13.4604	+	23.3141i	0.687795	+	1.19130i	−0.284755	+	0.958600i	$0.591912\pi$
$384$		0			0
$385$	15.8870	+	13.9521i	0.809677	+	0.711066i
$386$		0			0
$387$	−19.5644	−	16.9451i	−0.994513	−	0.861368i
$388$		0			0
$389$	−3.25871	+	5.64425i	−0.165223	+	0.286175i	−0.936734	−	0.350041i	$-0.886168\pi$
$389$	−3.25871	+	5.64425i	−0.165223	+	0.286175i	0.771511	+	0.636216i	$0.219501\pi$
$390$		0			0
$391$	−1.34529	+	2.33011i	−0.0680341	+	0.117838i
$392$		0			0
$393$	22.6227	+	2.15770i	1.14116	+	0.108841i
$394$		0			0
$395$	−4.79316	−	8.30200i	−0.241170	−	0.417719i
$396$		0			0
$397$	27.9515	+	16.1378i	1.40284	+	0.809933i	0.994684	−	0.102977i	$-0.0328369\pi$
$397$	27.9515	+	16.1378i	1.40284	+	0.809933i	0.408161	+	0.912910i	$0.366170\pi$
$398$		0			0
$399$	4.31746	−	14.3561i	0.216143	−	0.718703i
$400$		0			0
$401$	−7.86249	−	13.6182i	−0.392634	−	0.680062i	0.600162	−	0.799879i	$-0.295103\pi$
$401$	−7.86249	−	13.6182i	−0.392634	−	0.680062i	−0.992796	+	0.119816i	$0.961769\pi$
$402$		0			0
$403$	0.882154	+	0.509312i	0.0439432	+	0.0253706i
$404$		0			0
$405$	−7.41981	+	18.5574i	−0.368693	+	0.922124i
$406$		0			0
$407$	−24.5832	+	14.1931i	−1.21854	+	0.703527i
$408$		0			0
$409$		−	25.1778i		−	1.24496i	−0.782636	−	0.622480i	$-0.786125\pi$
$409$		−	25.1778i		−	1.24496i	0.782636	−	0.622480i	$-0.213875\pi$
$410$		0			0
$411$	10.8490	+	23.7490i	0.535140	+	1.17145i
$412$		0			0
$413$	−8.56275	−	7.51989i	−0.421346	−	0.370030i
$414$		0			0
$415$	−20.5148	−	11.8442i	−1.00703	−	0.581410i
$416$		0			0
$417$	6.87159	+	15.0423i	0.336503	+	0.736625i
$418$		0			0
$419$	−0.00635803	+	0.0110124i	−0.000310610	+	0.000537993i	−0.866181	−	0.499731i	$-0.833432\pi$
$419$	−0.00635803	+	0.0110124i	−0.000310610	+	0.000537993i	0.865870	+	0.500269i	$0.166766\pi$
$420$		0			0
$421$	−6.57972	−	11.3964i	−0.320676	−	0.555427i	0.659952	−	0.751308i	$-0.270577\pi$
$421$	−6.57972	−	11.3964i	−0.320676	−	0.555427i	−0.980628	+	0.195881i	$0.937243\pi$
$422$		0			0
$423$	−0.653475	−	1.88675i	−0.0317730	−	0.0917370i
$424$		0			0
$425$			0.109508i			0.00531191i
$426$		0			0
$427$	−15.0021	+	17.0825i	−0.726001	+	0.826682i
$428$		0			0
$429$	5.01499	+	0.478318i	0.242126	+	0.0230934i
$430$		0			0
$431$	−14.5079	+	8.37611i	−0.698819	+	0.403463i	−0.806907	−	0.590678i	$-0.798860\pi$
$431$	−14.5079	+	8.37611i	−0.698819	+	0.403463i	0.108088	+	0.994141i	$0.465527\pi$
$432$		0			0
$433$			2.31020i			0.111021i	0.998458	+	0.0555106i	$0.0176787\pi$
$433$			2.31020i			0.111021i	−0.998458	+	0.0555106i	$0.982321\pi$
$434$		0			0
$435$	−14.9153	+	6.81357i	−0.715135	+	0.326686i
$436$		0			0
$437$		−	5.52658i		−	0.264372i
$438$		0			0
$439$	−39.6036			−1.89018			−0.945088	−	0.326817i	$-0.894024\pi$
$439$	−39.6036			−1.89018			−0.945088	+	0.326817i	$0.894024\pi$
$440$		0			0
$441$	18.7898	−	9.37791i	0.894750	−	0.446567i
$442$		0			0
$443$			4.84775i			0.230323i	0.993347	+	0.115162i	$0.0367386\pi$
$443$			4.84775i			0.230323i	−0.993347	+	0.115162i	$0.963261\pi$
$444$		0			0
$445$	4.35719			0.206551
$446$		0			0
$447$	19.6754	+	1.87659i	0.930612	+	0.0887596i
$448$		0			0
$449$	9.19095			0.433748			0.216874	−	0.976200i	$-0.430414\pi$
$449$	9.19095			0.433748			0.216874	+	0.976200i	$0.430414\pi$
$450$		0			0
$451$	−15.7318	−	27.2483i	−0.740782	−	1.28307i
$452$		0			0
$453$	15.0539	−	6.87686i	0.707292	−	0.323103i
$454$		0			0
$455$	3.56786	+	3.13333i	0.167264	+	0.146893i
$456$		0			0
$457$	−32.4849			−1.51958			−0.759790	−	0.650169i	$-0.774698\pi$
$457$	−32.4849			−1.51958			−0.759790	+	0.650169i	$0.774698\pi$
$458$		0			0
$459$	−8.04166	+	1.95369i	−0.375353	+	0.0911905i
$460$		0			0
$461$	30.0753	−	17.3640i	1.40075	−	0.808721i	0.406276	−	0.913750i	$-0.366827\pi$
$461$	30.0753	−	17.3640i	1.40075	−	0.808721i	0.994469	+	0.105030i	$0.0334938\pi$
$462$		0			0
$463$	2.63552	+	1.52162i	0.122483	+	0.0707156i	0.559990	−	0.828500i	$-0.310805\pi$
$463$	2.63552	+	1.52162i	0.122483	+	0.0707156i	−0.437507	+	0.899215i	$0.644138\pi$
$464$		0			0
$465$	−0.460269	+	4.82576i	−0.0213445	+	0.223789i
$466$		0			0
$467$	17.6179	−	30.5151i	0.815258	−	1.41207i	−0.0938846	−	0.995583i	$-0.529928\pi$
$467$	17.6179	−	30.5151i	0.815258	−	1.41207i	0.909143	−	0.416485i	$-0.136738\pi$
$468$		0			0
$469$	−0.179075	+	0.203910i	−0.00826893	+	0.00941567i
$470$		0			0
$471$	−22.9035	−	16.3057i	−1.05534	−	0.751328i
$472$		0			0
$473$	−31.0484			−1.42761
$474$		0			0
$475$	−0.112467	−	0.194799i	−0.00516036	−	0.00893800i
$476$		0			0
$477$	24.6336	−	28.4413i	1.12790	−	1.30224i
$478$		0			0
$479$	5.81994	−	10.0804i	0.265920	−	0.460587i	−0.701884	−	0.712291i	$-0.747658\pi$
$479$	5.81994	−	10.0804i	0.265920	−	0.460587i	0.967804	+	0.251704i	$0.0809910\pi$
$480$		0			0
$481$	−5.52083	+	3.18745i	−0.251728	+	0.145335i
$482$		0			0
$483$	5.63775	−	5.30566i	0.256527	−	0.241416i
$484$		0			0
$485$	19.6503	−	34.0352i	0.892272	−	1.54546i
$486$		0			0
$487$	−8.98817	+	5.18932i	−0.407293	+	0.235151i	−0.689626	−	0.724166i	$-0.742225\pi$
$487$	−8.98817	+	5.18932i	−0.407293	+	0.235151i	0.282333	+	0.959316i	$0.408892\pi$
$488$		0			0
$489$	29.0467	−	13.2691i	1.31354	−	0.600047i
$490$		0			0
$491$	27.3013	+	15.7624i	1.23209	+	0.711349i	0.967466	−	0.253002i	$-0.0814180\pi$
$491$	27.3013	+	15.7624i	1.23209	+	0.711349i	0.264627	+	0.964351i	$0.414751\pi$
$492$		0			0
$493$	−5.88027	−	3.39497i	−0.264834	−	0.152902i
$494$		0			0
$495$	7.84636	+	22.6545i	0.352668	+	1.01824i
$496$		0			0
$497$	−20.6774	+	23.5450i	−0.927510	+	1.05614i
$498$		0			0
$499$	21.4467	−	12.3823i	0.960088	−	0.554307i	0.0638881	−	0.997957i	$-0.479650\pi$
$499$	21.4467	−	12.3823i	0.960088	−	0.554307i	0.896200	+	0.443650i	$0.146317\pi$
$500$		0			0
$501$	−0.335526	−	0.734486i	−0.0149902	−	0.0328144i
$502$		0			0
$503$	−28.6523			−1.27754			−0.638770	−	0.769397i	$-0.720557\pi$
$503$	−28.6523			−1.27754			−0.638770	+	0.769397i	$0.720557\pi$
$504$		0			0
$505$	−0.0489916			−0.00218010
$506$		0			0
$507$	−21.2887	−	2.03046i	−0.945464	−	0.0901761i
$508$		0			0
$509$	−15.8405	+	9.14550i	−0.702116	+	0.405367i	−0.808135	−	0.588997i	$-0.799523\pi$
$509$	−15.8405	+	9.14550i	−0.702116	+	0.405367i	0.106019	+	0.994364i	$0.466190\pi$
$510$		0			0
$511$	15.9056	+	3.17535i	0.703624	+	0.140469i
$512$		0			0
$513$	12.2985	−	11.7343i	0.542993	−	0.518084i
$514$		0			0
$515$	−37.2566	−	21.5101i	−1.64172	−	0.947848i
$516$		0			0
$517$	−2.07434	−	1.19762i	−0.0912294	−	0.0526713i
$518$		0			0
$519$	−3.97361	−	2.82893i	−0.174422	−	0.124176i
$520$		0			0
$521$	11.7742	−	6.79786i	0.515839	−	0.297820i	−0.219392	−	0.975637i	$-0.570407\pi$
$521$	11.7742	−	6.79786i	0.515839	−	0.297820i	0.735230	+	0.677817i	$0.237074\pi$
$522$		0			0
$523$	1.78691	−	3.09502i	0.0781362	−	0.135336i	−0.824310	−	0.566139i	$-0.808436\pi$
$523$	1.78691	−	3.09502i	0.0781362	−	0.135336i	0.902446	+	0.430803i	$0.141770\pi$
$524$		0			0
$525$	0.0907462	−	0.301742i	0.00396049	−	0.0131691i
$526$		0			0
$527$	−1.73836	+	1.00364i	−0.0757243	+	0.0437194i
$528$		0			0
$529$	−10.0730	+	17.4469i	−0.437956	+	0.758562i
$530$		0			0
$531$	−4.22902	−	12.2103i	−0.183524	−	0.529880i
$532$		0			0
$533$	−3.53300	−	6.11934i	−0.153031	−	0.265058i
$534$		0			0
$535$	32.2712			1.39521
$536$		0			0
$537$	1.26438	−	13.2565i	0.0545618	−	0.572061i
$538$		0			0
$539$	9.67278	−	23.2604i	0.416636	−	1.00190i
$540$		0			0
$541$	9.20974	−	15.9517i	0.395958	−	0.685819i	−0.597265	−	0.802044i	$-0.703746\pi$
$541$	9.20974	−	15.9517i	0.395958	−	0.685819i	0.993223	+	0.116225i	$0.0370793\pi$
$542$		0			0
$543$	−18.6481	−	13.2762i	−0.800267	−	0.569735i
$544$		0			0
$545$	−37.6335	−	21.7277i	−1.61204	−	0.930712i
$546$		0			0
$547$	−17.7554	+	10.2511i	−0.759165	+	0.438304i	−0.828996	−	0.559255i	$-0.811087\pi$
$547$	−17.7554	+	10.2511i	−0.759165	+	0.438304i	0.0698311	+	0.997559i	$0.477754\pi$
$548$		0			0
$549$	−24.3593	+	8.43681i	−1.03963	+	0.360074i
$550$		0			0
$551$	13.9469			0.594158
$552$		0			0
$553$	−7.53669	+	8.58188i	−0.320493	+	0.364939i
$554$		0			0
$555$	−24.7148	−	17.5952i	−1.04908	−	0.746876i
$556$		0			0
$557$	−11.5232	−	19.9588i	−0.488253	−	0.845680i	0.511655	−	0.859191i	$-0.329032\pi$
$557$	−11.5232	−	19.9588i	−0.488253	−	0.845680i	−0.999909	+	0.0135111i	$0.995699\pi$
$558$		0			0
$559$	−6.97276			−0.294916
$560$		0			0
$561$	−5.75753	+	8.08720i	−0.243083	+	0.341442i
$562$		0			0
$563$	−36.3621			−1.53248			−0.766239	−	0.642555i	$-0.777874\pi$
$563$	−36.3621			−1.53248			−0.766239	+	0.642555i	$0.777874\pi$
$564$		0			0
$565$		−	5.86469i		−	0.246729i
$566$		0			0
$567$	23.7773	+	1.28063i	0.998553	+	0.0537815i
$568$		0			0
$569$	−20.0856			−0.842030			−0.421015	−	0.907054i	$-0.638326\pi$
$569$	−20.0856			−0.842030			−0.421015	+	0.907054i	$0.638326\pi$
$570$		0			0
$571$			20.8601i			0.872968i	0.899712	+	0.436484i	$0.143776\pi$
$571$			20.8601i			0.872968i	−0.899712	+	0.436484i	$0.856224\pi$
$572$		0			0
$573$	21.4896	+	15.2991i	0.897739	+	0.639129i
$574$		0			0
$575$		−	0.116160i		−	0.00484421i
$576$		0			0
$577$	−14.1029	+	8.14229i	−0.587110	+	0.338968i	−0.763954	−	0.645271i	$-0.776745\pi$
$577$	−14.1029	+	8.14229i	−0.587110	+	0.338968i	0.176844	+	0.984239i	$0.443411\pi$
$578$		0			0
$579$	−6.75901	+	9.49390i	−0.280895	+	0.394553i
$580$		0			0
$581$	−5.52537	+	27.6771i	−0.229231	+	1.14824i
$582$		0			0
$583$		−	45.1360i		−	1.86934i
$584$		0			0
$585$	1.76211	+	5.08767i	0.0728544	+	0.210349i
$586$		0			0
$587$	−15.2987	−	26.4982i	−0.631446	−	1.09370i	−0.987256	−	0.159138i	$-0.949129\pi$
$587$	−15.2987	−	26.4982i	−0.631446	−	1.09370i	0.355811	−	0.934558i	$-0.384205\pi$
$588$		0			0
$589$	2.06154	−	3.57069i	0.0849442	−	0.147128i
$590$		0			0
$591$	10.1181	−	14.2121i	0.416201	−	0.584608i
$592$		0			0
$593$	−34.0124	−	19.6370i	−1.39672	−	0.806397i	−0.402673	−	0.915344i	$-0.631919\pi$
$593$	−34.0124	−	19.6370i	−1.39672	−	0.806397i	−0.994048	+	0.108947i	$0.965252\pi$
$594$		0			0
$595$	−8.86267	+	3.00159i	−0.363334	+	0.123053i
$596$		0			0
$597$	1.98090	+	0.188933i	0.0810727	+	0.00773252i
$598$		0			0
$599$		−	28.2325i		−	1.15355i	−0.816904	−	0.576773i	$-0.804312\pi$
$599$		−	28.2325i		−	1.15355i	0.816904	−	0.576773i	$-0.195688\pi$
$600$		0			0
$601$	−21.8723	+	12.6280i	−0.892189	+	0.515106i	−0.874658	−	0.484741i	$-0.838914\pi$
$601$	−21.8723	+	12.6280i	−0.892189	+	0.515106i	−0.0175312	+	0.999846i	$0.505581\pi$
$602$		0			0
$603$	−0.290770	+	0.100708i	−0.0118411	+	0.00410114i
$604$		0			0
$605$	3.75245	+	2.16648i	0.152559	+	0.0880799i
$606$		0			0
$607$	−2.89703	−	5.01780i	−0.117587	−	0.203666i	0.801224	−	0.598364i	$-0.204182\pi$
$607$	−2.89703	−	5.01780i	−0.117587	−	0.203666i	−0.918811	+	0.394698i	$0.870849\pi$
$608$		0			0
$609$	13.3894	+	14.2275i	0.542566	+	0.576526i
$610$		0			0
$611$	−0.465849	−	0.268958i	−0.0188463	−	0.0108809i
$612$		0			0
$613$	8.08177	+	13.9980i	0.326420	+	0.565375i	0.981799	−	0.189925i	$-0.0608244\pi$
$613$	8.08177	+	13.9980i	0.326420	+	0.565375i	−0.655379	+	0.755300i	$0.727491\pi$
$614$		0			0
$615$	19.5027	−	27.3941i	0.786426	−	1.10464i
$616$		0			0
$617$	−7.85375	+	13.6031i	−0.316180	+	0.547640i	−0.979688	−	0.200530i	$-0.935734\pi$
$617$	−7.85375	+	13.6031i	−0.316180	+	0.547640i	0.663508	+	0.748170i	$0.269067\pi$
$618$		0			0
$619$	15.8260	−	27.4114i	0.636100	−	1.10176i	−0.350181	−	0.936682i	$-0.613880\pi$
$619$	15.8260	−	27.4114i	0.636100	−	1.10176i	0.986281	−	0.165076i	$-0.0527869\pi$
$620$		0			0
$621$	8.53016	−	2.07237i	0.342304	−	0.0831614i
$622$		0			0
$623$	−1.66527	−	4.91697i	−0.0667175	−	0.196994i
$624$		0			0
$625$	12.3257	+	21.3488i	0.493030	+	0.853952i
$626$		0			0
$627$	1.93608	−	20.2991i	0.0773198	−	0.810670i
$628$		0			0
$629$		−	12.5623i		−	0.500892i
$630$		0			0
$631$			32.6380i			1.29930i	0.760234	+	0.649650i	$0.225084\pi$
$631$			32.6380i			1.29930i	−0.760234	+	0.649650i	$0.774916\pi$
$632$		0			0
$633$	38.6130	−	17.6391i	1.53473	−	0.701092i
$634$		0			0
$635$	−3.40317	−	5.89446i	−0.135051	−	0.233915i
$636$		0			0
$637$	2.17228	−	5.22376i	0.0860690	−	0.206973i
$638$		0			0
$639$	−33.5745	+	11.6285i	−1.32819	+	0.460017i
$640$		0			0
$641$	−2.44122	+	4.22832i	−0.0964224	+	0.167008i	−0.910201	−	0.414166i	$-0.864073\pi$
$641$	−2.44122	+	4.22832i	−0.0964224	+	0.167008i	0.813779	+	0.581174i	$0.197407\pi$
$642$		0			0
$643$	−2.68987	+	4.65900i	−0.106078	+	0.183733i	−0.914178	−	0.405312i	$-0.867163\pi$
$643$	−2.68987	+	4.65900i	−0.106078	+	0.183733i	0.808100	+	0.589045i	$0.200496\pi$
$644$		0			0
$645$	−13.7883	−	30.1833i	−0.542912	−	1.18847i
$646$		0			0
$647$	4.87406	+	8.44213i	0.191619	+	0.331894i	0.945787	−	0.324788i	$-0.105293\pi$
$647$	4.87406	+	8.44213i	0.191619	+	0.331894i	−0.754168	+	0.656682i	$0.771959\pi$
$648$		0			0
$649$	−13.4243	−	7.75051i	−0.526949	−	0.304234i
$650$		0			0
$651$	5.62165	−	1.32495i	0.220330	−	0.0519288i
$652$		0			0
$653$	2.14098	+	3.70828i	0.0837830	+	0.145116i	0.904872	−	0.425684i	$-0.139966\pi$
$653$	2.14098	+	3.70828i	0.0837830	+	0.145116i	−0.821089	+	0.570800i	$0.806633\pi$
$654$		0			0
$655$	25.2324	+	14.5679i	0.985912	+	0.569216i
$656$		0			0
$657$	13.9018	+	12.0406i	0.542360	+	0.469749i
$658$		0			0
$659$	−41.7153	+	24.0843i	−1.62500	+	0.938192i	−0.639440	+	0.768841i	$0.720834\pi$
$659$	−41.7153	+	24.0843i	−1.62500	+	0.938192i	−0.985556	+	0.169351i	$0.945833\pi$
$660$		0			0
$661$		−	32.6950i		−	1.27169i	−0.771818	−	0.635843i	$-0.780652\pi$
$661$		−	32.6950i		−	1.27169i	0.771818	−	0.635843i	$-0.219348\pi$
$662$		0			0
$663$	−1.29301	+	1.81620i	−0.0502163	+	0.0705354i
$664$		0			0
$665$	12.6827	−	14.4416i	0.491816	−	0.560021i
$666$		0			0
$667$	6.23747	+	3.60121i	0.241516	+	0.139439i
$668$		0			0
$669$	39.5466	+	3.77186i	1.52896	+	0.145829i
$670$		0			0
$671$	−15.4621	+	26.7812i	−0.596909	+	1.03388i
$672$		0			0
$673$	11.0215	+	19.0899i	0.424850	+	0.735861i	0.996406	−	0.0847015i	$-0.0269937\pi$
$673$	11.0215	+	19.0899i	0.424850	+	0.735861i	−0.571557	+	0.820562i	$0.693660\pi$
$674$		0			0
$675$	0.258495	−	0.246638i	0.00994949	−	0.00949308i
$676$		0			0
$677$			30.3524i			1.16654i	0.812280	+	0.583268i	$0.198226\pi$
$677$			30.3524i			1.16654i	−0.812280	+	0.583268i	$0.801774\pi$
$678$		0			0
$679$	−45.9180	−	9.16691i	−1.76217	−	0.351794i
$680$		0			0
$681$	15.0158	+	32.8705i	0.575408	+	1.25960i
$682$		0			0
$683$	−11.4814	+	6.62877i	−0.439323	+	0.253643i	−0.703310	−	0.710883i	$-0.748296\pi$
$683$	−11.4814	+	6.62877i	−0.439323	+	0.253643i	0.263988	+	0.964526i	$0.414962\pi$
$684$		0			0
$685$			33.4749i			1.27901i
$686$		0			0
$687$	1.17019	−	12.2691i	0.0446457	−	0.468094i
$688$		0			0
$689$		−	10.1365i		−	0.386170i
$690$		0			0
$691$	2.56722			0.0976615			0.0488308	−	0.998807i	$-0.484451\pi$
$691$	2.56722			0.0976615			0.0488308	+	0.998807i	$0.484451\pi$
$692$		0			0
$693$	22.5662	−	17.5127i	0.857218	−	0.665252i
$694$		0			0
$695$			21.2026i			0.804259i
$696$		0			0
$697$	13.9242			0.527416
$698$		0			0
$699$	16.1257	+	35.3002i	0.609931	+	1.33517i
$700$		0			0
$701$	−1.80587			−0.0682068			−0.0341034	−	0.999418i	$-0.510858\pi$
$701$	−1.80587			−0.0682068			−0.0341034	+	0.999418i	$0.510858\pi$
$702$		0			0
$703$	12.9018	+	22.3466i	0.486601	+	0.842818i
$704$		0			0
$705$	0.243060	−	2.54839i	0.00915416	−	0.0959781i
$706$		0			0
$707$	0.0187240	+	0.0552857i	0.000704189	+	0.00207923i
$708$		0			0
$709$	−10.5890			−0.397679			−0.198839	−	0.980032i	$-0.563717\pi$
$709$	−10.5890			−0.397679			−0.198839	+	0.980032i	$0.563717\pi$
$710$		0			0
$711$	−12.2375	+	4.23846i	−0.458944	+	0.158955i
$712$		0			0
$713$	1.84396	−	1.06461i	0.0690569	−	0.0398700i
$714$		0			0
$715$	5.59352	+	3.22942i	0.209186	+	0.120773i
$716$		0			0
$717$	−18.3875	+	8.39975i	−0.686695	+	0.313694i
$718$		0			0
$719$	20.9089	−	36.2153i	0.779770	−	1.35060i	−0.152303	−	0.988334i	$-0.548669\pi$
$719$	20.9089	−	36.2153i	0.779770	−	1.35060i	0.932074	−	0.362268i	$-0.117998\pi$
$720$		0			0
$721$	−10.0345	+	50.2640i	−0.373706	+	1.87193i
$722$		0			0
$723$	−5.10314	+	2.33120i	−0.189788	+	0.0866984i
$724$		0			0
$725$	0.293142			0.0108870
$726$		0			0
$727$	−4.25325	−	7.36684i	−0.157744	−	0.273221i	0.776311	−	0.630351i	$-0.217089\pi$
$727$	−4.25325	−	7.36684i	−0.157744	−	0.273221i	−0.934055	+	0.357129i	$0.883755\pi$
$728$		0			0
$729$	22.7235	+	14.5823i	0.841609	+	0.540087i
$730$		0			0
$731$	6.87022	−	11.8996i	0.254104	−	0.440122i
$732$		0			0
$733$	−17.9537	+	10.3656i	−0.663136	+	0.382861i	−0.793471	−	0.608609i	$-0.791728\pi$
$733$	−17.9537	+	10.3656i	−0.663136	+	0.382861i	0.130335	+	0.991470i	$0.458395\pi$
$734$		0			0
$735$	26.9079	−	0.926435i	0.992512	−	0.0341721i
$736$		0			0
$737$	−0.184567	+	0.319680i	−0.00679862	+	0.0117755i
$738$		0			0
$739$	−7.68337	+	4.43600i	−0.282637	+	0.163181i	−0.634617	−	0.772827i	$-0.718842\pi$
$739$	−7.68337	+	4.43600i	−0.282637	+	0.163181i	0.351979	+	0.936008i	$0.385509\pi$
$740$		0			0
$741$	0.434800	−	4.55872i	0.0159728	−	0.167469i
$742$		0			0
$743$	25.8027	+	14.8972i	0.946610	+	0.546526i	0.892026	−	0.451983i	$-0.149283\pi$
$743$	25.8027	+	14.8972i	0.946610	+	0.546526i	0.0545840	+	0.998509i	$0.482617\pi$
$744$		0			0
$745$	21.9451	+	12.6700i	0.804005	+	0.464193i
$746$		0			0
$747$	−20.9516	+	24.1902i	−0.766581	+	0.885074i
$748$		0			0
$749$	−12.3337	−	36.4172i	−0.450663	−	1.33066i
$750$		0			0
$751$	41.1459	−	23.7556i	1.50143	−	0.866854i	0.501436	−	0.865195i	$-0.332805\pi$
$751$	41.1459	−	23.7556i	1.50143	−	0.866854i	0.999999	−	0.00165870i	$-0.000527982\pi$
$752$		0			0
$753$	26.5578	−	37.3039i	0.967820	−	1.35943i
$754$		0			0
$755$	21.2188			0.772232
$756$		0			0
$757$	17.9685			0.653077			0.326539	−	0.945184i	$-0.394118\pi$
$757$	17.9685			0.653077			0.326539	+	0.945184i	$0.394118\pi$
$758$		0			0
$759$	6.10728	−	8.57847i	0.221680	−	0.311379i
$760$		0			0
$761$	−10.3549	+	5.97839i	−0.375364	+	0.216717i	−0.675799	−	0.737086i	$-0.736201\pi$
$761$	−10.3549	+	5.97839i	−0.375364	+	0.216717i	0.300435	+	0.953802i	$0.402868\pi$
$762$		0			0
$763$	−10.1360	+	50.7724i	−0.366949	+	1.83809i
$764$		0			0
$765$	−10.4187	−	2.00567i	−0.376690	−	0.0725152i
$766$		0			0
$767$	−3.01478	−	1.74059i	−0.108858	−	0.0628489i
$768$		0			0
$769$	−9.46783	−	5.46625i	−0.341419	−	0.197118i	0.319481	−	0.947593i	$-0.396492\pi$
$769$	−9.46783	−	5.46625i	−0.341419	−	0.197118i	−0.660899	+	0.750475i	$0.729825\pi$
$770$		0			0
$771$	4.44245	−	46.5775i	0.159991	−	1.67745i
$772$		0			0
$773$	−3.69273	+	2.13200i	−0.132818	+	0.0766826i	−0.564937	−	0.825134i	$-0.691099\pi$
$773$	−3.69273	+	2.13200i	−0.132818	+	0.0766826i	0.432119	+	0.901817i	$0.357766\pi$
$774$		0			0
$775$	0.0433303	−	0.0750503i	0.00155647	−	0.00269588i
$776$		0			0
$777$	−10.4101	+	34.6147i	−0.373458	+	1.24180i
$778$		0			0
$779$	−24.7692	+	14.3005i	−0.887449	+	0.512369i
$780$		0			0
$781$	−21.3115	+	36.9127i	−0.762587	+	1.32084i
$782$		0			0
$783$	5.22985	+	21.5268i	0.186899	+	0.769304i
$784$		0			0
$785$	−18.0229	−	31.2165i	−0.643264	−	1.11417i
$786$		0			0
$787$	−34.6093			−1.23369			−0.616843	−	0.787086i	$-0.711589\pi$
$787$	−34.6093			−1.23369			−0.616843	+	0.787086i	$0.711589\pi$
$788$		0			0
$789$	−44.0777	+	20.1354i	−1.56921	+	0.716841i
$790$		0			0
$791$	−6.61815	+	2.24142i	−0.235314	+	0.0796956i
$792$		0			0
$793$	−3.47244	+	6.01444i	−0.123310	+	0.213579i
$794$		0			0
$795$	43.8784	−	20.0444i	1.55621	−	0.710902i
$796$		0			0
$797$	−3.38779	−	1.95594i	−0.120002	−	0.0692830i	0.438798	−	0.898586i	$-0.355404\pi$
$797$	−3.38779	−	1.95594i	−0.120002	−	0.0692830i	−0.558799	+	0.829303i	$0.688738\pi$
$798$		0			0
$799$	0.917998	−	0.530006i	0.0324764	−	0.0187503i
$800$		0			0
$801$	1.11274	−	5.78027i	0.0393167	−	0.204236i
$802$		0			0
$803$	22.0620			0.778549
$804$		0			0
$805$	9.40104	−	3.18392i	0.331343	−	0.112218i
$806$		0			0
$807$	−2.76447	+	28.9845i	−0.0973139	+	1.02030i
$808$		0			0
$809$	2.04738	+	3.54616i	0.0719820	+	0.124677i	0.899770	−	0.436365i	$-0.143734\pi$
$809$	2.04738	+	3.54616i	0.0719820	+	0.124677i	−0.827788	+	0.561041i	$0.810401\pi$
$810$		0			0
$811$	12.6809			0.445287			0.222644	−	0.974900i	$-0.428531\pi$
$811$	12.6809			0.445287			0.222644	+	0.974900i	$0.428531\pi$
$812$		0			0
$813$	1.03988	+	2.27635i	0.0364700	+	0.0798351i
$814$		0			0
$815$	40.9422			1.43414
$816$		0			0
$817$			28.2236i			0.987418i
$818$		0			0
$819$	5.06785	−	3.93295i	0.177085	−	0.137428i
$820$		0			0
$821$	22.3551			0.780200			0.390100	−	0.920773i	$-0.372440\pi$
$821$	22.3551			0.780200			0.390100	+	0.920773i	$0.372440\pi$
$822$		0			0
$823$			33.0014i			1.15036i	0.818028	+	0.575178i	$0.195067\pi$
$823$			33.0014i			1.15036i	−0.818028	+	0.575178i	$0.804933\pi$
$824$		0			0
$825$	0.0406935	−	0.426656i	0.00141676	−	0.0148543i
$826$		0			0
$827$			31.7081i			1.10260i	0.834307	+	0.551300i	$0.185868\pi$
$827$			31.7081i			1.10260i	−0.834307	+	0.551300i	$0.814132\pi$
$828$		0			0
$829$	−18.0971	+	10.4484i	−0.628539	+	0.362887i	−0.780186	−	0.625547i	$-0.784876\pi$
$829$	−18.0971	+	10.4484i	−0.628539	+	0.362887i	0.151647	+	0.988435i	$0.451542\pi$
$830$		0			0
$831$	19.8307	+	43.4105i	0.687918	+	1.50589i
$832$		0			0
$833$	6.77442	+	8.85411i	0.234720	+	0.306777i
$834$		0			0
$835$		−	1.03528i		−	0.0358273i
$836$		0			0
$837$	6.28433	+	1.84300i	0.217218	+	0.0637033i
$838$		0			0
$839$	10.8863	+	18.8556i	0.375837	+	0.650968i	0.990452	−	0.137859i	$-0.0440220\pi$
$839$	10.8863	+	18.8556i	0.375837	+	0.650968i	−0.614615	+	0.788827i	$0.710689\pi$
$840$		0			0
$841$	5.41198	−	9.37382i	0.186620	−	0.323235i
$842$		0			0
$843$	−9.12634	−	0.870448i	−0.314328	−	0.0299798i
$844$		0			0
$845$	−23.7445	−	13.7089i	−0.816836	−	0.471601i
$846$		0			0
$847$	1.01067	−	5.06255i	0.0347271	−	0.173951i
$848$		0			0
$849$	6.23419	−	8.75673i	0.213957	−	0.300530i
$850$		0			0
$851$			13.3254i			0.456790i
$852$		0			0
$853$	8.78957	−	5.07466i	0.300949	−	0.173753i	−0.341920	−	0.939729i	$-0.611077\pi$
$853$	8.78957	−	5.07466i	0.300949	−	0.173753i	0.642869	+	0.765976i	$0.277744\pi$
$854$		0			0
$855$	20.5933	−	7.13249i	0.704277	−	0.243926i
$856$		0			0
$857$	28.0834	+	16.2140i	0.959311	+	0.553858i	0.895961	−	0.444133i	$-0.146488\pi$
$857$	28.0834	+	16.2140i	0.959311	+	0.553858i	0.0633498	+	0.997991i	$0.479822\pi$
$858$		0			0
$859$	−12.9435	−	22.4188i	−0.441627	−	0.764920i	0.556183	−	0.831060i	$-0.312265\pi$
$859$	−12.9435	−	22.4188i	−0.441627	−	0.764920i	−0.997810	+	0.0661393i	$0.978932\pi$
$860$		0			0
$861$	−38.3673	−	11.5386i	−1.30755	−	0.393235i
$862$		0			0
$863$	36.1895	+	20.8940i	1.23191	+	0.711242i	0.967427	−	0.253150i	$-0.0814665\pi$
$863$	36.1895	+	20.8940i	1.23191	+	0.711242i	0.264479	+	0.964391i	$0.414800\pi$
$864$		0			0
$865$	−3.12685	−	5.41586i	−0.106316	−	0.184145i
$866$		0			0
$867$	10.4093	+	22.7865i	0.353518	+	0.773871i
$868$		0			0
$869$	−7.76782	+	13.4543i	−0.263505	+	0.456405i
$870$		0			0
$871$	−0.0414495	+	0.0717927i	−0.00140446	+	0.00243260i
$872$		0			0
$873$	−40.1330	−	34.7600i	−1.35830	−	1.17645i
$874$		0			0
$875$	19.6511	−	22.3763i	0.664328	−	0.756457i
$876$		0			0
$877$	−18.7911	−	32.5472i	−0.634531	−	1.09904i	−0.986614	−	0.163072i	$-0.947860\pi$
$877$	−18.7911	−	32.5472i	−0.634531	−	1.09904i	0.352083	−	0.935969i	$-0.385474\pi$
$878$		0			0
$879$	15.0938	−	6.89510i	0.509101	−	0.232566i
$880$		0			0
$881$		−	6.16038i		−	0.207548i	−0.994601	−	0.103774i	$-0.966908\pi$
$881$		−	6.16038i		−	0.207548i	0.994601	−	0.103774i	$-0.0330919\pi$
$882$		0			0
$883$		−	44.8041i		−	1.50778i	−0.657001	−	0.753890i	$-0.728175\pi$
$883$		−	44.8041i		−	1.50778i	0.657001	−	0.753890i	$-0.271825\pi$
$884$		0			0
$885$	1.57298	−	16.4921i	0.0528752	−	0.554377i
$886$		0			0
$887$	−10.3758	−	17.9713i	−0.348384	−	0.603418i	0.637579	−	0.770385i	$-0.279936\pi$
$887$	−10.3758	−	17.9713i	−0.348384	−	0.603418i	−0.985963	+	0.166967i	$0.946603\pi$
$888$		0			0
$889$	−5.35109	+	6.09318i	−0.179470	+	0.204359i
$890$		0			0
$891$	32.0573	−	4.62352i	1.07396	−	0.154894i
$892$		0			0
$893$	−1.08866	+	1.88562i	−0.0364306	+	0.0630997i
$894$		0			0
$895$	8.53657	−	14.7858i	0.285346	−	0.494234i
$896$		0			0
$897$	1.37155	−	1.92653i	0.0457949	−	0.0643249i
$898$		0			0
$899$	2.68666	+	4.65343i	0.0896051	+	0.155201i
$900$		0			0
$901$	17.2988	+	9.98745i	0.576305	+	0.332730i
$902$		0			0
$903$	−28.7913	+	27.0954i	−0.958116	+	0.901678i
$904$		0			0
$905$	−14.6743	−	25.4166i	−0.487789	−	0.844876i
$906$		0			0
$907$	34.7077	+	20.0385i	1.15245	+	0.665368i	0.949483	−	0.313818i	$-0.101608\pi$
$907$	34.7077	+	20.0385i	1.15245	+	0.665368i	0.202967	+	0.979185i	$0.434941\pi$
$908$		0			0
$909$	−0.0125115	+	0.0649925i	−0.000414979	+	0.00215566i
$910$		0			0
$911$	5.63956	−	3.25600i	0.186847	−	0.107876i	−0.403659	−	0.914910i	$-0.632262\pi$
$911$	5.63956	−	3.25600i	0.186847	−	0.107876i	0.590506	+	0.807033i	$0.298928\pi$
$912$		0			0
$913$			38.3896i			1.27051i
$914$		0			0
$915$	−32.9015	−	3.13807i	−1.08769	−	0.103741i
$916$		0			0
$917$	6.79600	−	34.0418i	0.224424	−	1.12416i
$918$		0			0
$919$	17.4971	+	10.1020i	0.577176	+	0.333233i	0.760010	−	0.649911i	$-0.225194\pi$
$919$	17.4971	+	10.1020i	0.577176	+	0.333233i	−0.182834	+	0.983144i	$0.558527\pi$
$920$		0			0
$921$	9.92503	−	13.9410i	0.327041	−	0.459371i
$922$		0			0
$923$	−4.78608	+	8.28974i	−0.157536	+	0.272860i
$924$		0			0
$925$	0.271176	+	0.469691i	0.00891621	+	0.0154433i
$926$		0			0
$927$	−38.0500	+	43.9315i	−1.24973	+	1.44290i
$928$		0			0
$929$		−	25.7336i		−	0.844292i	−0.906528	−	0.422146i	$-0.861277\pi$
$929$		−	25.7336i		−	0.844292i	0.906528	−	0.422146i	$-0.138723\pi$
$930$		0			0
$931$	−21.1442	−	8.79274i	−0.692972	−	0.288170i
$932$		0			0
$933$	17.4782	−	24.5505i	0.572212	−	0.803746i
$934$		0			0
$935$	−11.0225	+	6.36385i	−0.360475	+	0.208120i
$936$		0			0
$937$			12.2284i			0.399484i	0.979849	+	0.199742i	$0.0640104\pi$
$937$			12.2284i			0.399484i	−0.979849	+	0.199742i	$0.935990\pi$
$938$		0			0
$939$	−12.1391	−	8.64224i	−0.396146	−	0.282029i
$940$		0			0
$941$		−	18.7959i		−	0.612729i	−0.951914	−	0.306365i	$-0.900887\pi$
$941$		−	18.7959i		−	0.612729i	0.951914	−	0.306365i	$-0.0991126\pi$
$942$		0			0
$943$	−14.7700			−0.480978
$944$		0			0
$945$	27.0461	+	14.1602i	0.879810	+	0.460632i
$946$		0			0
$947$			45.2472i			1.47034i	0.677884	+	0.735169i	$0.262897\pi$
$947$			45.2472i			1.47034i	−0.677884	+	0.735169i	$0.737103\pi$
$948$		0			0
$949$	4.95461			0.160833
$950$		0			0
$951$	24.3108	−	34.1477i	0.788333	−	1.10732i
$952$		0			0
$953$	38.2084			1.23769			0.618845	−	0.785513i	$-0.287601\pi$
$953$	38.2084			1.23769			0.618845	+	0.785513i	$0.287601\pi$
$954$		0			0
$955$	16.9102	+	29.2894i	0.547202	+	0.947782i
$956$		0			0
$957$	21.6487	+	15.4124i	0.699802	+	0.498211i
$958$		0			0
$959$	37.7755	−	12.7937i	1.21983	−	0.413131i
$960$		0			0
$961$	−29.4115			−0.948758
$962$		0			0
$963$	8.24142	−	42.8111i	0.265576	−	1.37957i
$964$		0			0
$965$	−12.9398	+	7.47080i	−0.416547	+	0.240493i
$966$		0			0
$967$	−28.2869	−	16.3315i	−0.909646	−	0.525184i	−0.0293285	−	0.999570i	$-0.509337\pi$
$967$	−28.2869	−	16.3315i	−0.909646	−	0.525184i	−0.880317	+	0.474386i	$0.842670\pi$
$968$		0			0
$969$	7.35142	+	5.23370i	0.236162	+	0.168131i
$970$		0			0
$971$	16.0352	−	27.7737i	0.514593	−	0.891302i	−0.485263	−	0.874368i	$-0.661276\pi$
$971$	16.0352	−	27.7737i	0.514593	−	0.891302i	0.999857	−	0.0169337i	$-0.00539043\pi$
$972$		0			0
$973$	23.9265	−	8.10337i	0.767049	−	0.259782i
$974$		0			0
$975$	0.00913882	−	0.0958172i	0.000292676	−	0.00306861i
$976$		0			0
$977$	30.1717			0.965277			0.482638	−	0.875820i	$-0.339679\pi$
$977$	30.1717			0.965277			0.482638	+	0.875820i	$0.339679\pi$
$978$		0			0
$979$	−3.53064	−	6.11525i	−0.112840	−	0.195444i
$980$		0			0
$981$	−38.4349	+	44.3759i	−1.22713	+	1.41681i
$982$		0			0
$983$	−21.8352	+	37.8197i	−0.696435	+	1.20626i	0.273260	+	0.961940i	$0.411898\pi$
$983$	−21.8352	+	37.8197i	−0.696435	+	1.20626i	−0.969695	+	0.244320i	$0.921435\pi$
$984$		0			0
$985$	19.3705	−	11.1836i	0.617196	−	0.356338i
$986$		0			0
$987$	−2.96869	+	0.699680i	−0.0944944	+	0.0222711i
$988$		0			0
$989$	−7.28756	+	12.6224i	−0.231731	+	0.401370i
$990$		0			0
$991$	16.5693	−	9.56628i	0.526341	−	0.303883i	−0.213184	−	0.977012i	$-0.568383\pi$
$991$	16.5693	−	9.56628i	0.526341	−	0.303883i	0.739525	+	0.673129i	$0.235050\pi$
$992$		0			0
$993$	−34.1040	−	24.2797i	−1.08226	−	0.770494i
$994$		0			0
$995$	2.20941	+	1.27560i	0.0700430	+	0.0404393i
$996$		0			0
$997$	0.522245	+	0.301519i	0.0165397	+	0.00954919i	0.508247	−	0.861211i	$-0.330294\pi$
$997$	0.522245	+	0.301519i	0.0165397	+	0.00954919i	−0.491707	+	0.870761i	$0.663627\pi$
$998$		0			0
$999$	−29.6536	+	28.2933i	−0.938198	+	0.895160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.i.607.13	yes	32
3.2	odd	2		3024.2.cz.i.1279.6		32
4.3	odd	2	inner	1008.2.cz.i.607.4	yes	32
7.3	odd	6		1008.2.bf.i.31.15	yes	32
9.2	odd	6		3024.2.bf.i.2287.6		32
9.7	even	3		1008.2.bf.i.943.2	yes	32
12.11	even	2		3024.2.cz.i.1279.5		32
21.17	even	6		3024.2.bf.i.1711.12		32
28.3	even	6		1008.2.bf.i.31.2	✓	32
36.7	odd	6		1008.2.bf.i.943.15	yes	32
36.11	even	6		3024.2.bf.i.2287.5		32
63.38	even	6		3024.2.cz.i.2719.5		32
63.52	odd	6	inner	1008.2.cz.i.367.4	yes	32
84.59	odd	6		3024.2.bf.i.1711.11		32
252.115	even	6	inner	1008.2.cz.i.367.13	yes	32
252.227	odd	6		3024.2.cz.i.2719.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.2	✓	32	28.3	even	6
1008.2.bf.i.31.15	yes	32	7.3	odd	6
1008.2.bf.i.943.2	yes	32	9.7	even	3
1008.2.bf.i.943.15	yes	32	36.7	odd	6
1008.2.cz.i.367.4	yes	32	63.52	odd	6	inner
1008.2.cz.i.367.13	yes	32	252.115	even	6	inner
1008.2.cz.i.607.4	yes	32	4.3	odd	2	inner
1008.2.cz.i.607.13	yes	32	1.1	even	1	trivial
3024.2.bf.i.1711.11		32	84.59	odd	6
3024.2.bf.i.1711.12		32	21.17	even	6
3024.2.bf.i.2287.5		32	36.11	even	6
3024.2.bf.i.2287.6		32	9.2	odd	6
3024.2.cz.i.1279.5		32	12.11	even	2
3024.2.cz.i.1279.6		32	3.2	odd	2
3024.2.cz.i.2719.5		32	63.38	even	6
3024.2.cz.i.2719.6		32	252.227	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00453 - 1.41100i) q^{3} +(1.92313 - 1.11032i) q^{5} +(-1.98797 - 1.74585i) q^{7} +(-0.981826 - 2.83479i) q^{9} +O(q^{10})\)	\(q+(1.00453 - 1.41100i) q^{3} +(1.92313 - 1.11032i) q^{5} +(-1.98797 - 1.74585i) q^{7} +(-0.981826 - 2.83479i) q^{9} +(-3.11664 - 1.79939i) q^{11} +(-0.699925 - 0.404102i) q^{13} +(0.365190 - 3.82888i) q^{15} +(1.37926 - 0.796318i) q^{17} +(-1.63568 + 2.83308i) q^{19} +(-4.46037 + 1.05125i) q^{21} +(-1.46305 + 0.844692i) q^{23} +(-0.0343794 + 0.0595469i) q^{25} +(-4.98615 - 1.46228i) q^{27} +(-2.13167 - 3.69216i) q^{29} -1.26036 q^{31} +(-5.66970 + 2.59002i) q^{33} +(-5.76157 - 1.15022i) q^{35} +(3.94387 - 6.83099i) q^{37} +(-1.27328 + 0.581658i) q^{39} +(7.57153 + 4.37143i) q^{41} +(7.47162 - 4.31374i) q^{43} +(-5.03570 - 4.36152i) q^{45} +0.665571 q^{47} +(0.904012 + 6.94138i) q^{49} +(0.261913 - 2.74607i) q^{51} +(6.27101 + 10.8617i) q^{53} -7.99160 q^{55} +(2.35437 + 5.15386i) q^{57} +4.30730 q^{59} -8.59298i q^{61} +(-2.99728 + 7.34958i) q^{63} -1.79473 q^{65} -0.102572i q^{67} +(-0.277823 + 2.91288i) q^{69} -11.8438i q^{71} +(-5.30908 + 3.06520i) q^{73} +(0.0494852 + 0.108326i) q^{75} +(3.05430 + 9.01830i) q^{77} -4.31692i q^{79} +(-7.07203 + 5.56654i) q^{81} +(-5.33369 - 9.23823i) q^{83} +(1.76834 - 3.06285i) q^{85} +(-7.35096 - 0.701117i) q^{87} +(1.69926 + 0.981066i) q^{89} +(0.685925 + 2.02530i) q^{91} +(-1.26607 + 1.77836i) q^{93} +7.26451i q^{95} +(15.3268 - 8.84892i) q^{97} +(-2.04089 + 10.6017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9}+O(q^{10}) \) 32 * q - 4 * q^9	\( 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85} - 18 q^{89} - 38 q^{93} + 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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