LMFDB - Embedded newform 672.2.bb.a.271.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(271,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("672.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.6
Character	$\chi$	$=$	672.271
Dual form			672.2.bb.a.367.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(0.225540 - 0.390646i) q^{5} +(0.458196 + 2.60577i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{3} +(0.225540 - 0.390646i) q^{5} +(0.458196 + 2.60577i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.360048 + 0.623622i) q^{11} +3.48975 q^{13} +0.451079i q^{15} +(-3.55796 + 2.05419i) q^{17} +(-3.97736 - 2.29633i) q^{19} +(-1.69970 - 2.02757i) q^{21} +(-0.0459022 - 0.0265016i) q^{23} +(2.39826 + 4.15391i) q^{25} +1.00000i q^{27} +7.85260i q^{29} +(4.58331 + 7.93852i) q^{31} +(-0.623622 - 0.360048i) q^{33} +(1.12128 + 0.408713i) q^{35} +(7.51467 + 4.33860i) q^{37} +(-3.02222 + 1.74488i) q^{39} -3.94348i q^{41} -5.17408 q^{43} +(-0.225540 - 0.390646i) q^{45} +(-0.460124 + 0.796959i) q^{47} +(-6.58011 + 2.38791i) q^{49} +(2.05419 - 3.55796i) q^{51} +(-2.71489 + 1.56744i) q^{53} +0.324821 q^{55} +4.59266 q^{57} +(4.86409 - 2.80828i) q^{59} +(-2.54813 + 4.41348i) q^{61} +(2.48576 + 0.906077i) q^{63} +(0.787078 - 1.36326i) q^{65} +(4.93346 + 8.54500i) q^{67} +0.0530032 q^{69} -11.1608i q^{71} +(-3.33103 + 1.92317i) q^{73} +(-4.15391 - 2.39826i) q^{75} +(-1.46004 + 1.22395i) q^{77} +(8.40929 + 4.85511i) q^{79} +(-0.500000 - 0.866025i) q^{81} +9.53613i q^{83} +1.85320i q^{85} +(-3.92630 - 6.80056i) q^{87} +(-12.6107 - 7.28081i) q^{89} +(1.59899 + 9.09351i) q^{91} +(-7.93852 - 4.58331i) q^{93} +(-1.79410 + 1.03583i) q^{95} -5.14572i q^{97} +0.720096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^9	$ 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$	0.225540	−	0.390646i	0.100864	−	0.174702i	−0.811177	−	0.584801i	$-0.801173\pi$
$5$	0.225540	−	0.390646i	0.100864	−	0.174702i	0.912041	+	0.410099i	$0.134506\pi$
$6$		0			0
$7$	0.458196	+	2.60577i	0.173182	+	0.984890i
$7$	0.458196	+	2.60577i	0.173182	+	0.984890i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	0.360048	+	0.623622i	0.108559	+	0.188029i	0.915187	−	0.403030i	$-0.132043\pi$
$11$	0.360048	+	0.623622i	0.108559	+	0.188029i	−0.806628	+	0.591060i	$0.798710\pi$
$12$		0			0
$13$	3.48975			0.967884			0.483942	−	0.875100i	$-0.339205\pi$
$13$	3.48975			0.967884			0.483942	+	0.875100i	$0.339205\pi$
$14$		0			0
$15$			0.451079i			0.116468i
$16$		0			0
$17$	−3.55796	+	2.05419i	−0.862931	+	0.498214i	−0.864993	−	0.501784i	$-0.832677\pi$
$17$	−3.55796	+	2.05419i	−0.862931	+	0.498214i	0.00206160	+	0.999998i	$0.499344\pi$
$18$		0			0
$19$	−3.97736	−	2.29633i	−0.912468	−	0.526814i	−0.0312438	−	0.999512i	$-0.509947\pi$
$19$	−3.97736	−	2.29633i	−0.912468	−	0.526814i	−0.881225	+	0.472698i	$0.843280\pi$
$20$		0			0
$21$	−1.69970	−	2.02757i	−0.370904	−	0.442452i
$22$		0			0
$23$	−0.0459022	−	0.0265016i	−0.00957126	−	0.00552597i	0.495207	−	0.868775i	$-0.335092\pi$
$23$	−0.0459022	−	0.0265016i	−0.00957126	−	0.00552597i	−0.504778	+	0.863249i	$0.668426\pi$
$24$		0			0
$25$	2.39826	+	4.15391i	0.479653	+	0.830783i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$			7.85260i			1.45819i	0.684411	+	0.729096i	$0.260059\pi$
$29$			7.85260i			1.45819i	−0.684411	+	0.729096i	$0.739941\pi$
$30$		0			0
$31$	4.58331	+	7.93852i	0.823186	+	1.42580i	0.903298	+	0.429015i	$0.141139\pi$
$31$	4.58331	+	7.93852i	0.823186	+	1.42580i	−0.0801113	+	0.996786i	$0.525528\pi$
$32$		0			0
$33$	−0.623622	−	0.360048i	−0.108559	−	0.0626764i
$34$		0			0
$35$	1.12128	+	0.408713i	0.189530	+	0.0690850i
$36$		0			0
$37$	7.51467	+	4.33860i	1.23540	+	0.713261i	0.968151	−	0.250366i	$-0.0805508\pi$
$37$	7.51467	+	4.33860i	1.23540	+	0.713261i	0.267253	+	0.963626i	$0.413884\pi$
$38$		0			0
$39$	−3.02222	+	1.74488i	−0.483942	+	0.279404i
$40$		0			0
$41$		−	3.94348i		−	0.615868i	−0.951408	−	0.307934i	$-0.900362\pi$
$41$		−	3.94348i		−	0.615868i	0.951408	−	0.307934i	$-0.0996375\pi$
$42$		0			0
$43$	−5.17408			−0.789039			−0.394520	−	0.918888i	$-0.629089\pi$
$43$	−5.17408			−0.789039			−0.394520	+	0.918888i	$0.629089\pi$
$44$		0			0
$45$	−0.225540	−	0.390646i	−0.0336215	−	0.0582341i
$46$		0			0
$47$	−0.460124	+	0.796959i	−0.0671160	+	0.116248i	−0.897631	−	0.440748i	$-0.854713\pi$
$47$	−0.460124	+	0.796959i	−0.0671160	+	0.116248i	0.830515	+	0.556997i	$0.188046\pi$
$48$		0			0
$49$	−6.58011	+	2.38791i	−0.940016	+	0.341130i
$50$		0			0
$51$	2.05419	−	3.55796i	0.287644	−	0.498214i
$52$		0			0
$53$	−2.71489	+	1.56744i	−0.372919	+	0.215305i	−0.674733	−	0.738062i	$-0.735741\pi$
$53$	−2.71489	+	1.56744i	−0.372919	+	0.215305i	0.301814	+	0.953367i	$0.402408\pi$
$54$		0			0
$55$	0.324821			0.0437988
$56$		0			0
$57$	4.59266			0.608312
$58$		0			0
$59$	4.86409	−	2.80828i	0.633250	−	0.365607i	−0.148759	−	0.988873i	$-0.547528\pi$
$59$	4.86409	−	2.80828i	0.633250	−	0.365607i	0.782010	+	0.623266i	$0.214195\pi$
$60$		0			0
$61$	−2.54813	+	4.41348i	−0.326254	+	0.565089i	−0.981765	−	0.190097i	$-0.939120\pi$
$61$	−2.54813	+	4.41348i	−0.326254	+	0.565089i	0.655511	+	0.755185i	$0.272453\pi$
$62$		0			0
$63$	2.48576	+	0.906077i	0.313177	+	0.114155i
$64$		0			0
$65$	0.787078	−	1.36326i	0.0976250	−	0.169091i
$66$		0			0
$67$	4.93346	+	8.54500i	0.602718	+	1.04394i	0.992408	+	0.122992i	$0.0392490\pi$
$67$	4.93346	+	8.54500i	0.602718	+	1.04394i	−0.389690	+	0.920946i	$0.627418\pi$
$68$		0			0
$69$	0.0530032			0.00638084
$70$		0			0
$71$		−	11.1608i		−	1.32454i	−0.749266	−	0.662270i	$-0.769593\pi$
$71$		−	11.1608i		−	1.32454i	0.749266	−	0.662270i	$-0.230407\pi$
$72$		0			0
$73$	−3.33103	+	1.92317i	−0.389867	+	0.225090i	−0.682103	−	0.731256i	$-0.738934\pi$
$73$	−3.33103	+	1.92317i	−0.389867	+	0.225090i	0.292235	+	0.956346i	$0.405601\pi$
$74$		0			0
$75$	−4.15391	−	2.39826i	−0.479653	−	0.276928i
$76$		0			0
$77$	−1.46004	+	1.22395i	−0.166388	+	0.139482i
$78$		0			0
$79$	8.40929	+	4.85511i	0.946119	+	0.546242i	0.891873	−	0.452285i	$-0.149391\pi$
$79$	8.40929	+	4.85511i	0.946119	+	0.546242i	0.0542460	+	0.998528i	$0.482724\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			9.53613i			1.04673i	0.852110	+	0.523363i	$0.175323\pi$
$83$			9.53613i			1.04673i	−0.852110	+	0.523363i	$0.824677\pi$
$84$		0			0
$85$			1.85320i			0.201008i
$86$		0			0
$87$	−3.92630	−	6.80056i	−0.420944	−	0.729096i
$88$		0			0
$89$	−12.6107	−	7.28081i	−1.33673	−	0.771764i	−0.350413	−	0.936595i	$-0.613959\pi$
$89$	−12.6107	−	7.28081i	−1.33673	−	0.771764i	−0.986322	+	0.164831i	$0.947292\pi$
$90$		0			0
$91$	1.59899	+	9.09351i	0.167620	+	0.953259i
$92$		0			0
$93$	−7.93852	−	4.58331i	−0.823186	−	0.475267i
$94$		0			0
$95$	−1.79410	+	1.03583i	−0.184071	+	0.106273i
$96$		0			0
$97$		−	5.14572i		−	0.522469i	−0.965275	−	0.261235i	$-0.915870\pi$
$97$		−	5.14572i		−	0.522469i	0.965275	−	0.261235i	$-0.0841296\pi$
$98$		0			0
$99$	0.720096			0.0723724
$100$		0			0
$101$	−7.14490	−	12.3753i	−0.710944	−	1.23139i	−0.964503	−	0.264072i	$-0.914934\pi$
$101$	−7.14490	−	12.3753i	−0.710944	−	1.23139i	0.253559	−	0.967320i	$-0.418399\pi$
$102$		0			0
$103$	7.46214	−	12.9248i	0.735267	−	1.27352i	−0.219339	−	0.975649i	$-0.570390\pi$
$103$	7.46214	−	12.9248i	0.735267	−	1.27352i	0.954606	−	0.297871i	$-0.0962764\pi$
$104$		0			0
$105$	−1.17541	+	0.206683i	−0.114708	+	0.0201702i
$106$		0			0
$107$	7.90786	−	13.6968i	0.764482	−	1.32412i	−0.176039	−	0.984383i	$-0.556328\pi$
$107$	7.90786	−	13.6968i	0.764482	−	1.32412i	0.940520	−	0.339738i	$-0.110338\pi$
$108$		0			0
$109$	0.208805	−	0.120553i	0.0199999	−	0.0115469i	−0.489967	−	0.871741i	$-0.662991\pi$
$109$	0.208805	−	0.120553i	0.0199999	−	0.0115469i	0.509967	+	0.860194i	$0.329658\pi$
$110$		0			0
$111$	−8.67719			−0.823603
$112$		0			0
$113$	13.3327			1.25423			0.627116	−	0.778926i	$-0.284235\pi$
$113$	13.3327			1.25423			0.627116	+	0.778926i	$0.284235\pi$
$114$		0			0
$115$	−0.0207055	+	0.0119543i	−0.00193080	+	0.00111475i
$116$		0			0
$117$	1.74488	−	3.02222i	0.161314	−	0.279404i
$118$		0			0
$119$	−6.98299	−	8.33001i	−0.640130	−	0.763611i
$120$		0			0
$121$	5.24073	−	9.07721i	0.476430	−	0.825201i
$122$		0			0
$123$	1.97174	+	3.41515i	0.177786	+	0.307934i
$124$		0			0
$125$	4.41901			0.395248
$126$		0			0
$127$		−	0.517396i		−	0.0459115i	−0.999736	−	0.0229557i	$-0.992692\pi$
$127$		−	0.517396i		−	0.0459115i	0.999736	−	0.0229557i	$-0.00730768\pi$
$128$		0			0
$129$	4.48088	−	2.58704i	0.394520	−	0.227776i
$130$		0			0
$131$	−11.6665	−	6.73566i	−1.01931	−	0.588497i	−0.105404	−	0.994429i	$-0.533614\pi$
$131$	−11.6665	−	6.73566i	−1.01931	−	0.588497i	−0.913903	+	0.405932i	$0.866947\pi$
$132$		0			0
$133$	4.16130	−	11.4163i	0.360831	−	0.989915i
$134$		0			0
$135$	0.390646	+	0.225540i	0.0336215	+	0.0194114i
$136$		0			0
$137$	11.2294	+	19.4498i	0.959389	+	1.66171i	0.723989	+	0.689811i	$0.242306\pi$
$137$	11.2294	+	19.4498i	0.959389	+	1.66171i	0.235399	+	0.971899i	$0.424360\pi$
$138$		0			0
$139$		−	1.05090i		−	0.0891361i	−0.999006	−	0.0445681i	$-0.985809\pi$
$139$		−	1.05090i		−	0.0891361i	0.999006	−	0.0445681i	$-0.0141912\pi$
$140$		0			0
$141$		−	0.920249i		−	0.0774989i
$142$		0			0
$143$	1.25648	+	2.17629i	0.105072	+	0.181990i
$144$		0			0
$145$	3.06759	+	1.77107i	0.254749	+	0.147080i
$146$		0			0
$147$	4.50459	−	5.35805i	0.371532	−	0.441924i
$148$		0			0
$149$	−10.9331	−	6.31222i	−0.895673	−	0.517117i	−0.0198791	−	0.999802i	$-0.506328\pi$
$149$	−10.9331	−	6.31222i	−0.895673	−	0.517117i	−0.875794	+	0.482685i	$0.839661\pi$
$150$		0			0
$151$	−2.86647	+	1.65496i	−0.233270	+	0.134679i	−0.612080	−	0.790796i	$-0.709667\pi$
$151$	−2.86647	+	1.65496i	−0.233270	+	0.134679i	0.378810	+	0.925475i	$0.376334\pi$
$152$		0			0
$153$			4.10837i			0.332142i
$154$		0			0
$155$	4.13487			0.332121
$156$		0			0
$157$	1.75915	+	3.04694i	0.140396	+	0.243172i	0.927646	−	0.373462i	$-0.121829\pi$
$157$	1.75915	+	3.04694i	0.140396	+	0.243172i	−0.787250	+	0.616634i	$0.788496\pi$
$158$		0			0
$159$	1.56744	−	2.71489i	0.124306	−	0.215305i
$160$		0			0
$161$	0.0480250	−	0.131754i	0.00378490	−	0.0103836i
$162$		0			0
$163$	9.35173	−	16.1977i	0.732484	−	1.26870i	−0.223335	−	0.974742i	$-0.571694\pi$
$163$	9.35173	−	16.1977i	0.732484	−	1.26870i	0.955819	−	0.293957i	$-0.0949724\pi$
$164$		0			0
$165$	−0.281303	+	0.162410i	−0.0218994	+	0.0126436i
$166$		0			0
$167$	−23.5845			−1.82502			−0.912510	−	0.409054i	$-0.865859\pi$
$167$	−23.5845			−1.82502			−0.912510	+	0.409054i	$0.865859\pi$
$168$		0			0
$169$	−0.821615			−0.0632012
$170$		0			0
$171$	−3.97736	+	2.29633i	−0.304156	+	0.175605i
$172$		0			0
$173$	12.4108	−	21.4961i	0.943572	−	1.63432i	0.184988	−	0.982741i	$-0.440775\pi$
$173$	12.4108	−	21.4961i	0.943572	−	1.63432i	0.758585	−	0.651575i	$-0.225891\pi$
$174$		0			0
$175$	−9.72529	+	8.15264i	−0.735163	+	0.616282i
$176$		0			0
$177$	−2.80828	+	4.86409i	−0.211083	+	0.365607i
$178$		0			0
$179$	−0.498970	−	0.864242i	−0.0372948	−	0.0645965i	0.846776	−	0.531950i	$-0.178541\pi$
$179$	−0.498970	−	0.864242i	−0.0372948	−	0.0645965i	−0.884070	+	0.467354i	$0.845207\pi$
$180$		0			0
$181$	5.81455			0.432192			0.216096	−	0.976372i	$-0.430668\pi$
$181$	5.81455			0.432192			0.216096	+	0.976372i	$0.430668\pi$
$182$		0			0
$183$		−	5.09625i		−	0.376726i
$184$		0			0
$185$	3.38971	−	1.95705i	0.249216	−	0.143885i
$186$		0			0
$187$	−2.56207	−	1.47921i	−0.187357	−	0.108171i
$188$		0			0
$189$	−2.60577	+	0.458196i	−0.189542	+	0.0333289i
$190$		0			0
$191$	11.6440	+	6.72270i	0.842534	+	0.486437i	0.858125	−	0.513441i	$-0.171630\pi$
$191$	11.6440	+	6.72270i	0.842534	+	0.486437i	−0.0155908	+	0.999878i	$0.504963\pi$
$192$		0			0
$193$	3.70703	+	6.42076i	0.266838	+	0.462176i	0.968043	−	0.250783i	$-0.0806879\pi$
$193$	3.70703	+	6.42076i	0.266838	+	0.462176i	−0.701206	+	0.712959i	$0.747355\pi$
$194$		0			0
$195$			1.57416i			0.112728i
$196$		0			0
$197$		−	6.62804i		−	0.472228i	−0.971725	−	0.236114i	$-0.924126\pi$
$197$		−	6.62804i		−	0.472228i	0.971725	−	0.236114i	$-0.0758739\pi$
$198$		0			0
$199$	−5.39583	−	9.34584i	−0.382500	−	0.662509i	0.608919	−	0.793232i	$-0.291603\pi$
$199$	−5.39583	−	9.34584i	−0.382500	−	0.662509i	−0.991419	+	0.130723i	$0.958270\pi$
$200$		0			0
$201$	−8.54500	−	4.93346i	−0.602718	−	0.347979i
$202$		0			0
$203$	−20.4621	+	3.59803i	−1.43616	+	0.252532i
$204$		0			0
$205$	−1.54050	−	0.889410i	−0.107593	−	0.0621191i
$206$		0			0
$207$	−0.0459022	+	0.0265016i	−0.00319042	+	0.00184199i
$208$		0			0
$209$		−	3.30716i		−	0.228761i
$210$		0			0
$211$	−5.17795			−0.356465			−0.178232	−	0.983988i	$-0.557038\pi$
$211$	−5.17795			−0.356465			−0.178232	+	0.983988i	$0.557038\pi$
$212$		0			0
$213$	5.58038	+	9.66551i	0.382362	+	0.662270i
$214$		0			0
$215$	−1.16696	+	2.02123i	−0.0795859	+	0.137847i
$216$		0			0
$217$	−18.5859	+	15.5805i	−1.26170	+	1.05767i
$218$		0			0
$219$	1.92317	−	3.33103i	0.129956	−	0.225090i
$220$		0			0
$221$	−12.4164	+	7.16861i	−0.835217	+	0.482213i
$222$		0			0
$223$	19.0791			1.27763			0.638815	−	0.769361i	$-0.279425\pi$
$223$	19.0791			1.27763			0.638815	+	0.769361i	$0.279425\pi$
$224$		0			0
$225$	4.79653			0.319769
$226$		0			0
$227$	2.06649	−	1.19309i	0.137158	−	0.0791879i	−0.429851	−	0.902900i	$-0.641434\pi$
$227$	2.06649	−	1.19309i	0.137158	−	0.0791879i	0.567009	+	0.823712i	$0.308101\pi$
$228$		0			0
$229$	−5.11149	+	8.85335i	−0.337776	+	0.585046i	−0.984014	−	0.178090i	$-0.943008\pi$
$229$	−5.11149	+	8.85335i	−0.337776	+	0.585046i	0.646238	+	0.763136i	$0.276341\pi$
$230$		0			0
$231$	0.652463	−	1.78999i	0.0429289	−	0.117773i
$232$		0			0
$233$	8.53778	−	14.7879i	0.559328	−	0.968785i	−0.438224	−	0.898866i	$-0.644392\pi$
$233$	8.53778	−	14.7879i	0.559328	−	0.968785i	0.997553	−	0.0699194i	$-0.0222742\pi$
$234$		0			0
$235$	0.207553	+	0.359492i	0.0135392	+	0.0234506i
$236$		0			0
$237$	−9.71021			−0.630746
$238$		0			0
$239$			29.9136i			1.93495i	0.252968	+	0.967475i	$0.418593\pi$
$239$			29.9136i			1.93495i	−0.252968	+	0.967475i	$0.581407\pi$
$240$		0			0
$241$	14.5829	−	8.41946i	0.939369	−	0.542345i	0.0496064	−	0.998769i	$-0.484203\pi$
$241$	14.5829	−	8.41946i	0.939369	−	0.542345i	0.889762	+	0.456424i	$0.150870\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−0.551248	+	3.10906i	−0.0352179	+	0.198631i
$246$		0			0
$247$	−13.8800	−	8.01362i	−0.883163	−	0.509895i
$248$		0			0
$249$	−4.76807	−	8.25853i	−0.302164	−	0.523363i
$250$		0			0
$251$			23.1292i			1.45990i	0.683500	+	0.729951i	$0.260457\pi$
$251$			23.1292i			1.45990i	−0.683500	+	0.729951i	$0.739543\pi$
$252$		0			0
$253$		−	0.0381674i		−	0.00239957i
$254$		0			0
$255$	−0.926601	−	1.60492i	−0.0580260	−	0.100504i
$256$		0			0
$257$	−10.4388	−	6.02683i	−0.651153	−	0.375943i	0.137745	−	0.990468i	$-0.456015\pi$
$257$	−10.4388	−	6.02683i	−0.651153	−	0.375943i	−0.788898	+	0.614524i	$0.789348\pi$
$258$		0			0
$259$	−7.86221	+	21.5695i	−0.488534	+	1.34026i
$260$		0			0
$261$	6.80056	+	3.92630i	0.420944	+	0.243032i
$262$		0			0
$263$	20.2875	−	11.7130i	1.25098	−	0.722254i	0.279677	−	0.960094i	$-0.409773\pi$
$263$	20.2875	−	11.7130i	1.25098	−	0.722254i	0.971304	+	0.237840i	$0.0764394\pi$
$264$		0			0
$265$			1.41408i			0.0868664i
$266$		0			0
$267$	14.5616			0.891157
$268$		0			0
$269$	5.98880	+	10.3729i	0.365144	+	0.632447i	0.988799	−	0.149252i	$-0.0476865\pi$
$269$	5.98880	+	10.3729i	0.365144	+	0.632447i	−0.623655	+	0.781699i	$0.714353\pi$
$270$		0			0
$271$	−3.99591	+	6.92112i	−0.242734	+	0.420428i	−0.961492	−	0.274832i	$-0.911378\pi$
$271$	−3.99591	+	6.92112i	−0.242734	+	0.420428i	0.718758	+	0.695260i	$0.244711\pi$
$272$		0			0
$273$	−5.93152	−	7.07571i	−0.358992	−	0.428242i
$274$		0			0
$275$	−1.72698	+	2.99122i	−0.104141	+	0.180377i
$276$		0			0
$277$	−7.54343	+	4.35520i	−0.453241	+	0.261679i	−0.709198	−	0.705009i	$-0.750943\pi$
$277$	−7.54343	+	4.35520i	−0.453241	+	0.261679i	0.255957	+	0.966688i	$0.417609\pi$
$278$		0			0
$279$	9.16661			0.548791
$280$		0			0
$281$	6.82201			0.406967			0.203484	−	0.979078i	$-0.434774\pi$
$281$	6.82201			0.406967			0.203484	+	0.979078i	$0.434774\pi$
$282$		0			0
$283$	13.0126	−	7.51281i	0.773517	−	0.446590i	−0.0606110	−	0.998161i	$-0.519305\pi$
$283$	13.0126	−	7.51281i	0.773517	−	0.446590i	0.834128	+	0.551571i	$0.185972\pi$
$284$		0			0
$285$	1.03583	−	1.79410i	0.0613570	−	0.106273i
$286$		0			0
$287$	10.2758	−	1.80689i	0.606562	−	0.106657i
$288$		0			0
$289$	−0.0606311	+	0.105016i	−0.00356654	+	0.00617742i
$290$		0			0
$291$	2.57286	+	4.45633i	0.150824	+	0.261235i
$292$		0			0
$293$	−2.77974			−0.162394			−0.0811971	−	0.996698i	$-0.525874\pi$
$293$	−2.77974			−0.162394			−0.0811971	+	0.996698i	$0.525874\pi$
$294$		0			0
$295$		−	2.53352i		−	0.147507i
$296$		0			0
$297$	−0.623622	+	0.360048i	−0.0361862	+	0.0208921i
$298$		0			0
$299$	−0.160187	−	0.0924841i	−0.00926387	−	0.00534850i
$300$		0			0
$301$	−2.37074	−	13.4825i	−0.136647	−	0.777117i
$302$		0			0
$303$	12.3753	+	7.14490i	0.710944	+	0.410464i
$304$		0			0
$305$	1.14941	+	1.99083i	0.0658148	+	0.113995i
$306$		0			0
$307$		−	24.7943i		−	1.41508i	−0.706672	−	0.707542i	$-0.749804\pi$
$307$		−	24.7943i		−	1.41508i	0.706672	−	0.707542i	$-0.250196\pi$
$308$		0			0
$309$			14.9243i			0.849013i
$310$		0			0
$311$	1.29417	+	2.24157i	0.0733858	+	0.127108i	0.900383	−	0.435098i	$-0.143286\pi$
$311$	1.29417	+	2.24157i	0.0733858	+	0.127108i	−0.826997	+	0.562206i	$0.809953\pi$
$312$		0			0
$313$	−2.50486	−	1.44618i	−0.141583	−	0.0817431i	0.427535	−	0.903999i	$-0.359382\pi$
$313$	−2.50486	−	1.44618i	−0.141583	−	0.0817431i	−0.569118	+	0.822256i	$0.692715\pi$
$314$		0			0
$315$	0.914594	−	0.766698i	0.0515315	−	0.0431985i
$316$		0			0
$317$	29.4673	+	17.0130i	1.65505	+	0.955543i	0.974951	+	0.222421i	$0.0713960\pi$
$317$	29.4673	+	17.0130i	1.65505	+	0.955543i	0.680098	+	0.733121i	$0.261937\pi$
$318$		0			0
$319$	−4.89706	+	2.82732i	−0.274182	+	0.158299i
$320$		0			0
$321$			15.8157i			0.882747i
$322$		0			0
$323$	18.8684			1.04986
$324$		0			0
$325$	8.36935	+	14.4961i	0.464248	+	0.804101i
$326$		0			0
$327$	−0.120553	+	0.208805i	−0.00666662	+	0.0115469i
$328$		0			0
$329$	−2.28752	−	0.833817i	−0.126115	−	0.0459698i
$330$		0			0
$331$	−1.22267	+	2.11772i	−0.0672040	+	0.116401i	−0.897670	−	0.440669i	$-0.854741\pi$
$331$	−1.22267	+	2.11772i	−0.0672040	+	0.116401i	0.830466	+	0.557070i	$0.188074\pi$
$332$		0			0
$333$	7.51467	−	4.33860i	0.411801	−	0.237754i
$334$		0			0
$335$	4.45076			0.243171
$336$		0			0
$337$	−28.0906			−1.53019			−0.765097	−	0.643915i	$-0.777309\pi$
$337$	−28.0906			−1.53019			−0.765097	+	0.643915i	$0.777309\pi$
$338$		0			0
$339$	−11.5464	+	6.66633i	−0.627116	+	0.362065i
$340$		0			0
$341$	−3.30042	+	5.71650i	−0.178728	+	0.309566i
$342$		0			0
$343$	−9.23734	−	16.0522i	−0.498769	−	0.866735i
$344$		0			0
$345$	0.0119543	−	0.0207055i	0.000643599	−	0.00111475i
$346$		0			0
$347$	−8.51021	−	14.7401i	−0.456852	−	0.791291i	0.541941	−	0.840417i	$-0.317690\pi$
$347$	−8.51021	−	14.7401i	−0.456852	−	0.791291i	−0.998793	+	0.0491260i	$0.984356\pi$
$348$		0			0
$349$	−28.1655			−1.50766			−0.753831	−	0.657068i	$-0.771796\pi$
$349$	−28.1655			−1.50766			−0.753831	+	0.657068i	$0.771796\pi$
$350$		0			0
$351$			3.48975i			0.186269i
$352$		0			0
$353$	−17.9835	+	10.3828i	−0.957164	+	0.552619i	−0.895299	−	0.445466i	$-0.853038\pi$
$353$	−17.9835	+	10.3828i	−0.957164	+	0.552619i	−0.0618651	+	0.998085i	$0.519705\pi$
$354$		0			0
$355$	−4.35991	−	2.51719i	−0.231400	−	0.133599i
$356$		0			0
$357$	10.2124	+	3.72250i	0.540500	+	0.197016i
$358$		0			0
$359$	0.559584	+	0.323076i	0.0295337	+	0.0170513i	0.514694	−	0.857374i	$-0.327905\pi$
$359$	0.559584	+	0.323076i	0.0295337	+	0.0170513i	−0.485160	+	0.874425i	$0.661239\pi$
$360$		0			0
$361$	1.04625	+	1.81215i	0.0550656	+	0.0953764i
$362$		0			0
$363$			10.4815i			0.550134i
$364$		0			0
$365$			1.73500i			0.0908143i
$366$		0			0
$367$	3.69198	+	6.39470i	0.192720	+	0.333801i	0.946151	−	0.323726i	$-0.104936\pi$
$367$	3.69198	+	6.39470i	0.192720	+	0.333801i	−0.753431	+	0.657527i	$0.771602\pi$
$368$		0			0
$369$	−3.41515	−	1.97174i	−0.177786	−	0.102645i
$370$		0			0
$371$	−5.32836	−	6.35620i	−0.276634	−	0.329997i
$372$		0			0
$373$	9.22518	+	5.32616i	0.477662	+	0.275778i	0.719442	−	0.694553i	$-0.244398\pi$
$373$	9.22518	+	5.32616i	0.477662	+	0.275778i	−0.241780	+	0.970331i	$0.577731\pi$
$374$		0			0
$375$	−3.82697	+	2.20950i	−0.197624	+	0.114098i
$376$		0			0
$377$			27.4037i			1.41136i
$378$		0			0
$379$	−1.95468			−0.100405			−0.0502026	−	0.998739i	$-0.515987\pi$
$379$	−1.95468			−0.100405			−0.0502026	+	0.998739i	$0.515987\pi$
$380$		0			0
$381$	0.258698	+	0.448078i	0.0132535	+	0.0229557i
$382$		0			0
$383$	−2.21292	+	3.83290i	−0.113075	+	0.195852i	−0.917009	−	0.398867i	$-0.869403\pi$
$383$	−2.21292	+	3.83290i	−0.113075	+	0.195852i	0.803934	+	0.594719i	$0.202737\pi$
$384$		0			0
$385$	0.148832	+	0.846409i	0.00758516	+	0.0431370i
$386$		0			0
$387$	−2.58704	+	4.48088i	−0.131507	+	0.227776i
$388$		0			0
$389$	−9.07706	+	5.24065i	−0.460225	+	0.265711i	−0.712139	−	0.702038i	$-0.752273\pi$
$389$	−9.07706	+	5.24065i	−0.460225	+	0.265711i	0.251914	+	0.967750i	$0.418940\pi$
$390$		0			0
$391$	0.217757			0.0110125
$392$		0			0
$393$	13.4713			0.679538
$394$		0			0
$395$	3.79326	−	2.19004i	0.190859	−	0.110193i
$396$		0			0
$397$	6.09656	−	10.5596i	0.305978	−	0.529969i	−0.671501	−	0.741004i	$-0.734350\pi$
$397$	6.09656	−	10.5596i	0.305978	−	0.529969i	0.977478	+	0.211035i	$0.0676834\pi$
$398$		0			0
$399$	2.10434	+	11.9674i	0.105349	+	0.599121i
$400$		0			0
$401$	−2.50405	+	4.33714i	−0.125046	+	0.216586i	−0.921751	−	0.387782i	$-0.873241\pi$
$401$	−2.50405	+	4.33714i	−0.125046	+	0.216586i	0.796705	+	0.604369i	$0.206575\pi$
$402$		0			0
$403$	15.9946	+	27.7035i	0.796749	+	1.38001i
$404$		0			0
$405$	−0.451079			−0.0224143
$406$		0			0
$407$			6.24842i			0.309722i
$408$		0			0
$409$	26.3361	−	15.2051i	1.30223	−	0.751845i	0.321447	−	0.946928i	$-0.395831\pi$
$409$	26.3361	−	15.2051i	1.30223	−	0.751845i	0.980787	+	0.195082i	$0.0624974\pi$
$410$		0			0
$411$	−19.4498	−	11.2294i	−0.959389	−	0.553903i
$412$		0			0
$413$	9.54646	+	11.3880i	0.469750	+	0.560365i
$414$		0			0
$415$	3.72525	+	2.15078i	0.182865	+	0.105577i
$416$		0			0
$417$	0.525450	+	0.910105i	0.0257314	+	0.0445681i
$418$		0			0
$419$			1.70610i			0.0833485i	0.999131	+	0.0416743i	$0.0132692\pi$
$419$			1.70610i			0.0833485i	−0.999131	+	0.0416743i	$0.986731\pi$
$420$		0			0
$421$		−	13.0483i		−	0.635937i	−0.948101	−	0.317969i	$-0.896999\pi$
$421$		−	13.0483i		−	0.635937i	0.948101	−	0.317969i	$-0.103001\pi$
$422$		0			0
$423$	0.460124	+	0.796959i	0.0223720	+	0.0387495i
$424$		0			0
$425$	−17.0658	−	9.85296i	−0.827815	−	0.477939i
$426$		0			0
$427$	−12.6681	−	4.61760i	−0.613051	−	0.223461i
$428$		0			0
$429$	−2.17629	−	1.25648i	−0.105072	−	0.0606634i
$430$		0			0
$431$	1.95335	−	1.12777i	0.0940894	−	0.0543226i	−0.452217	−	0.891908i	$-0.649367\pi$
$431$	1.95335	−	1.12777i	0.0940894	−	0.0543226i	0.546306	+	0.837585i	$0.316033\pi$
$432$		0			0
$433$		−	7.41221i		−	0.356208i	−0.984012	−	0.178104i	$-0.943004\pi$
$433$		−	7.41221i		−	0.356208i	0.984012	−	0.178104i	$-0.0569963\pi$
$434$		0			0
$435$	−3.54215			−0.169833
$436$		0			0
$437$	0.121713	+	0.210813i	0.00582231	+	0.0100845i
$438$		0			0
$439$	−5.12867	+	8.88312i	−0.244778	+	0.423968i	−0.962069	−	0.272806i	$-0.912048\pi$
$439$	−5.12867	+	8.88312i	−0.244778	+	0.423968i	0.717291	+	0.696774i	$0.245382\pi$
$440$		0			0
$441$	−1.22206	+	6.89250i	−0.0581936	+	0.328214i
$442$		0			0
$443$	−10.6349	+	18.4201i	−0.505277	+	0.875166i	0.494704	+	0.869061i	$0.335276\pi$
$443$	−10.6349	+	18.4201i	−0.505277	+	0.875166i	−0.999981	+	0.00610446i	$0.998057\pi$
$444$		0			0
$445$	−5.68844	+	3.28422i	−0.269658	+	0.155687i
$446$		0			0
$447$	12.6244			0.597115
$448$		0			0
$449$	−15.4114			−0.727307			−0.363654	−	0.931534i	$-0.618471\pi$
$449$	−15.4114			−0.727307			−0.363654	+	0.931534i	$0.618471\pi$
$450$		0			0
$451$	2.45924	−	1.41984i	0.115801	−	0.0668577i
$452$		0			0
$453$	1.65496	−	2.86647i	0.0777567	−	0.134679i
$454$		0			0
$455$	3.91298	+	1.42631i	0.183443	+	0.0668663i
$456$		0			0
$457$	18.0425	−	31.2505i	0.843991	−	1.46184i	−0.0425032	−	0.999096i	$-0.513533\pi$
$457$	18.0425	−	31.2505i	0.843991	−	1.46184i	0.886494	−	0.462739i	$-0.153133\pi$
$458$		0			0
$459$	−2.05419	−	3.55796i	−0.0958812	−	0.166071i
$460$		0			0
$461$	30.9944			1.44355			0.721776	−	0.692127i	$-0.243326\pi$
$461$	30.9944			1.44355			0.721776	+	0.692127i	$0.243326\pi$
$462$		0			0
$463$		−	4.76599i		−	0.221494i	−0.993849	−	0.110747i	$-0.964676\pi$
$463$		−	4.76599i		−	0.221494i	0.993849	−	0.110747i	$-0.0353244\pi$
$464$		0			0
$465$	−3.58090	+	2.06743i	−0.166060	+	0.0958750i
$466$		0			0
$467$	−0.964225	−	0.556695i	−0.0446190	−	0.0257608i	0.477525	−	0.878618i	$-0.341534\pi$
$467$	−0.964225	−	0.556695i	−0.0446190	−	0.0257608i	−0.522144	+	0.852858i	$0.674867\pi$
$468$		0			0
$469$	−20.0059	+	16.7708i	−0.923784	+	0.774402i
$470$		0			0
$471$	−3.04694	−	1.75915i	−0.140396	−	0.0810574i
$472$		0			0
$473$	−1.86292	−	3.22667i	−0.0856570	−	0.148362i
$474$		0			0
$475$		−	22.0288i		−	1.01075i
$476$		0			0
$477$			3.13489i			0.143537i
$478$		0			0
$479$	13.3498	+	23.1224i	0.609966	+	1.05649i	0.991245	+	0.132032i	$0.0421501\pi$
$479$	13.3498	+	23.1224i	0.609966	+	1.05649i	−0.381280	+	0.924460i	$0.624517\pi$
$480$		0			0
$481$	26.2243	+	15.1406i	1.19573	+	0.690354i
$482$		0			0
$483$	0.0242859	+	0.138114i	0.00110505	+	0.00628442i
$484$		0			0
$485$	−2.01016	−	1.16056i	−0.0912765	−	0.0526985i
$486$		0			0
$487$	−19.3435	+	11.1680i	−0.876536	+	0.506068i	−0.869515	−	0.493907i	$-0.835568\pi$
$487$	−19.3435	+	11.1680i	−0.876536	+	0.506068i	−0.00702114	+	0.999975i	$0.502235\pi$
$488$		0			0
$489$			18.7035i			0.845799i
$490$		0			0
$491$	17.8395			0.805084			0.402542	−	0.915402i	$-0.368127\pi$
$491$	17.8395			0.805084			0.402542	+	0.915402i	$0.368127\pi$
$492$		0			0
$493$	−16.1307	−	27.9392i	−0.726491	−	1.25832i
$494$		0			0
$495$	0.162410	−	0.281303i	0.00729980	−	0.0126436i
$496$		0			0
$497$	29.0824	−	5.11382i	1.30453	−	0.229386i
$498$		0			0
$499$	3.10223	−	5.37322i	0.138875	−	0.240538i	−0.788196	−	0.615424i	$-0.788985\pi$
$499$	3.10223	−	5.37322i	0.138875	−	0.240538i	0.927071	+	0.374886i	$0.122318\pi$
$500$		0			0
$501$	20.4247	−	11.7922i	0.912510	−	0.526838i
$502$		0			0
$503$	5.86342			0.261437			0.130718	−	0.991420i	$-0.458272\pi$
$503$	5.86342			0.261437			0.130718	+	0.991420i	$0.458272\pi$
$504$		0			0
$505$	−6.44583			−0.286836
$506$		0			0
$507$	0.711540	−	0.410808i	0.0316006	−	0.0182446i
$508$		0			0
$509$	−17.5030	+	30.3161i	−0.775808	+	1.34374i	0.158530	+	0.987354i	$0.449324\pi$
$509$	−17.5030	+	30.3161i	−0.775808	+	1.34374i	−0.934339	+	0.356386i	$0.884009\pi$
$510$		0			0
$511$	−6.53761	−	7.79872i	−0.289207	−	0.344995i
$512$		0			0
$513$	2.29633	−	3.97736i	0.101385	−	0.175605i
$514$		0			0
$515$	−3.36602	−	5.83011i	−0.148324	−	0.256905i
$516$		0			0
$517$	−0.662668			−0.0291441
$518$		0			0
$519$			24.8215i			1.08954i
$520$		0			0
$521$	−6.98875	+	4.03495i	−0.306182	+	0.176775i	−0.645217	−	0.763999i	$-0.723233\pi$
$521$	−6.98875	+	4.03495i	−0.306182	+	0.176775i	0.339034	+	0.940774i	$0.389900\pi$
$522$		0			0
$523$	26.9826	+	15.5784i	1.17987	+	0.681196i	0.955984	−	0.293420i	$-0.0947936\pi$
$523$	26.9826	+	15.5784i	1.17987	+	0.681196i	0.223882	+	0.974616i	$0.428127\pi$
$524$		0			0
$525$	4.34602	−	11.9230i	0.189676	−	0.520364i
$526$		0			0
$527$	−32.6144	−	18.8299i	−1.42071	−	0.820245i
$528$		0			0
$529$	−11.4986	−	19.9162i	−0.499939	−	0.865920i
$530$		0			0
$531$		−	5.61657i		−	0.243738i
$532$		0			0
$533$		−	13.7618i		−	0.596088i
$534$		0			0
$535$	−3.56707	−	6.17835i	−0.154218	−	0.267113i
$536$		0			0
$537$	0.864242	+	0.498970i	0.0372948	+	0.0215322i
$538$		0			0
$539$	−3.85831	−	3.24374i	−0.166189	−	0.139718i
$540$		0			0
$541$	−21.2493	−	12.2683i	−0.913581	−	0.527456i	−0.0319992	−	0.999488i	$-0.510187\pi$
$541$	−21.2493	−	12.2683i	−0.913581	−	0.527456i	−0.881581	+	0.472032i	$0.843521\pi$
$542$		0			0
$543$	−5.03555	+	2.90727i	−0.216096	+	0.124763i
$544$		0			0
$545$		−	0.108758i		−	0.00465869i
$546$		0			0
$547$	−30.8257			−1.31801			−0.659005	−	0.752138i	$-0.729023\pi$
$547$	−30.8257			−1.31801			−0.659005	+	0.752138i	$0.729023\pi$
$548$		0			0
$549$	2.54813	+	4.41348i	0.108751	+	0.188363i
$550$		0			0
$551$	18.0322	−	31.2326i	0.768196	−	1.33055i
$552$		0			0
$553$	−8.79820	+	24.1373i	−0.374138	+	1.02642i
$554$		0			0
$555$	−1.95705	+	3.38971i	−0.0830722	+	0.143885i
$556$		0			0
$557$	33.2404	−	19.1914i	1.40844	−	0.813164i	0.413203	−	0.910639i	$-0.364410\pi$
$557$	33.2404	−	19.1914i	1.40844	−	0.813164i	0.995238	+	0.0974752i	$0.0310767\pi$
$558$		0			0
$559$	−18.0563			−0.763698
$560$		0			0
$561$	2.95843			0.124905
$562$		0			0
$563$	0.879959	−	0.508045i	0.0370859	−	0.0214115i	−0.481342	−	0.876533i	$-0.659851\pi$
$563$	0.879959	−	0.508045i	0.0370859	−	0.0214115i	0.518428	+	0.855121i	$0.326517\pi$
$564$		0			0
$565$	3.00704	−	5.20835i	0.126507	−	0.219117i
$566$		0			0
$567$	2.02757	−	1.69970i	0.0851499	−	0.0713805i
$568$		0			0
$569$	1.66552	−	2.88476i	0.0698220	−	0.120935i	−0.829001	−	0.559247i	$-0.811090\pi$
$569$	1.66552	−	2.88476i	0.0698220	−	0.120935i	0.898823	+	0.438312i	$0.144424\pi$
$570$		0			0
$571$	−3.34133	−	5.78735i	−0.139830	−	0.242193i	0.787602	−	0.616184i	$-0.211322\pi$
$571$	−3.34133	−	5.78735i	−0.139830	−	0.242193i	−0.927432	+	0.373991i	$0.877989\pi$
$572$		0			0
$573$	−13.4454			−0.561689
$574$		0			0
$575$		−	0.254232i		−	0.0106022i
$576$		0			0
$577$	−0.561113	+	0.323959i	−0.0233595	+	0.0134866i	−0.511634	−	0.859203i	$-0.670960\pi$
$577$	−0.561113	+	0.323959i	−0.0233595	+	0.0134866i	0.488275	+	0.872690i	$0.337626\pi$
$578$		0			0
$579$	−6.42076	−	3.70703i	−0.266838	−	0.154059i
$580$		0			0
$581$	−24.8490	+	4.36942i	−1.03091	+	0.181274i
$582$		0			0
$583$	−1.95498	−	1.12871i	−0.0809672	−	0.0467464i
$584$		0			0
$585$	−0.787078	−	1.36326i	−0.0325417	−	0.0563638i
$586$		0			0
$587$			4.35212i			0.179631i	0.995958	+	0.0898157i	$0.0286278\pi$
$587$			4.35212i			0.179631i	−0.995958	+	0.0898157i	$0.971372\pi$
$588$		0			0
$589$		−	42.0991i		−	1.73466i
$590$		0			0
$591$	3.31402	+	5.74005i	0.136321	+	0.236114i
$592$		0			0
$593$	21.7338	+	12.5480i	0.892502	+	0.515286i	0.874760	−	0.484556i	$-0.161019\pi$
$593$	21.7338	+	12.5480i	0.892502	+	0.515286i	0.0177420	+	0.999843i	$0.494352\pi$
$594$		0			0
$595$	−4.82902	+	0.849130i	−0.197971	+	0.0348109i
$596$		0			0
$597$	9.34584	+	5.39583i	0.382500	+	0.220836i
$598$		0			0
$599$	−20.4978	+	11.8344i	−0.837519	+	0.483542i	−0.856420	−	0.516279i	$-0.827317\pi$
$599$	−20.4978	+	11.8344i	−0.837519	+	0.483542i	0.0189009	+	0.999821i	$0.493983\pi$
$600$		0			0
$601$		−	14.8295i		−	0.604907i	−0.953164	−	0.302453i	$-0.902194\pi$
$601$		−	14.8295i		−	0.604907i	0.953164	−	0.302453i	$-0.0978057\pi$
$602$		0			0
$603$	9.86692			0.401812
$604$		0			0
$605$	−2.36398	−	4.09454i	−0.0961096	−	0.166467i
$606$		0			0
$607$	−0.527187	+	0.913114i	−0.0213979	+	0.0370622i	−0.876526	−	0.481354i	$-0.840145\pi$
$607$	−0.527187	+	0.913114i	−0.0213979	+	0.0370622i	0.855128	+	0.518417i	$0.173478\pi$
$608$		0			0
$609$	15.9217	−	13.3470i	0.645179	−	0.540850i
$610$		0			0
$611$	−1.60572	+	2.78119i	−0.0649605	+	0.112515i
$612$		0			0
$613$	32.6152	−	18.8304i	1.31731	−	0.760552i	0.334019	−	0.942566i	$-0.391595\pi$
$613$	32.6152	−	18.8304i	1.31731	−	0.760552i	0.983296	+	0.182015i	$0.0582618\pi$
$614$		0			0
$615$	1.77882			0.0717290
$616$		0			0
$617$	3.75729			0.151263			0.0756314	−	0.997136i	$-0.475903\pi$
$617$	3.75729			0.151263			0.0756314	+	0.997136i	$0.475903\pi$
$618$		0			0
$619$	−4.60049	+	2.65609i	−0.184909	+	0.106757i	−0.589597	−	0.807697i	$-0.700713\pi$
$619$	−4.60049	+	2.65609i	−0.184909	+	0.106757i	0.404688	+	0.914455i	$0.367380\pi$
$620$		0			0
$621$	0.0265016	−	0.0459022i	0.00106347	−	0.00184199i
$622$		0			0
$623$	13.1940	−	36.1968i	0.528605	−	1.45019i
$624$		0			0
$625$	−10.9947	+	19.0433i	−0.439786	+	0.761732i
$626$		0			0
$627$	1.65358	+	2.86408i	0.0660375	+	0.114380i
$628$		0			0
$629$	−35.6492			−1.42142
$630$		0			0
$631$		−	37.4896i		−	1.49244i	−0.665702	−	0.746218i	$-0.731868\pi$
$631$		−	37.4896i		−	1.49244i	0.665702	−	0.746218i	$-0.268132\pi$
$632$		0			0
$633$	4.48424	−	2.58898i	0.178232	−	0.102903i
$634$		0			0
$635$	−0.202119	−	0.116693i	−0.00802083	−	0.00463083i
$636$		0			0
$637$	−22.9630	+	8.33322i	−0.909826	+	0.330174i
$638$		0			0
$639$	−9.66551	−	5.58038i	−0.382362	−	0.220757i
$640$		0			0
$641$	−11.0865	−	19.2023i	−0.437889	−	0.758445i	0.559638	−	0.828737i	$-0.310940\pi$
$641$	−11.0865	−	19.2023i	−0.437889	−	0.758445i	−0.997526	+	0.0702920i	$0.977607\pi$
$642$		0			0
$643$		−	29.4039i		−	1.15958i	−0.814767	−	0.579788i	$-0.803135\pi$
$643$		−	29.4039i		−	1.15958i	0.814767	−	0.579788i	$-0.196865\pi$
$644$		0			0
$645$		−	2.33392i		−	0.0918979i
$646$		0			0
$647$	−10.3938	−	18.0026i	−0.408623	−	0.707755i	0.586113	−	0.810229i	$-0.300657\pi$
$647$	−10.3938	−	18.0026i	−0.408623	−	0.707755i	−0.994736	+	0.102474i	$0.967324\pi$
$648$		0			0
$649$	3.50261	+	2.02223i	0.137490	+	0.0793796i
$650$		0			0
$651$	8.30566	−	22.7860i	0.325525	−	0.893055i
$652$		0			0
$653$	3.36065	+	1.94027i	0.131512	+	0.0759287i	0.564313	−	0.825561i	$-0.309141\pi$
$653$	3.36065	+	1.94027i	0.131512	+	0.0759287i	−0.432800	+	0.901490i	$0.642475\pi$
$654$		0			0
$655$	−5.26252	+	3.03832i	−0.205624	+	0.118717i
$656$		0			0
$657$			3.84634i			0.150060i
$658$		0			0
$659$	25.0314			0.975087			0.487543	−	0.873099i	$-0.337893\pi$
$659$	25.0314			0.975087			0.487543	+	0.873099i	$0.337893\pi$
$660$		0			0
$661$	2.76963	+	4.79715i	0.107726	+	0.186587i	0.914849	−	0.403797i	$-0.132310\pi$
$661$	2.76963	+	4.79715i	0.107726	+	0.186587i	−0.807122	+	0.590384i	$0.798976\pi$
$662$		0			0
$663$	7.16861	−	12.4164i	0.278406	−	0.482213i
$664$		0			0
$665$	−3.52118	−	4.20041i	−0.136545	−	0.162885i
$666$		0			0
$667$	0.208107	−	0.360451i	0.00805793	−	0.0139567i
$668$		0			0
$669$	−16.5230	+	9.53954i	−0.638815	+	0.368820i
$670$		0			0
$671$	−3.66979			−0.141671
$672$		0			0
$673$	−6.26781			−0.241606			−0.120803	−	0.992676i	$-0.538547\pi$
$673$	−6.26781			−0.241606			−0.120803	+	0.992676i	$0.538547\pi$
$674$		0			0
$675$	−4.15391	+	2.39826i	−0.159884	+	0.0923092i
$676$		0			0
$677$	22.2551	−	38.5470i	0.855333	−	1.48148i	−0.0210020	−	0.999779i	$-0.506686\pi$
$677$	22.2551	−	38.5470i	0.855333	−	1.48148i	0.876335	−	0.481701i	$-0.159981\pi$
$678$		0			0
$679$	13.4086	−	2.35775i	0.514575	−	0.0904822i
$680$		0			0
$681$	−1.19309	+	2.06649i	−0.0457192	+	0.0791879i
$682$		0			0
$683$	8.00201	+	13.8599i	0.306189	+	0.530334i	0.977525	−	0.210818i	$-0.0676129\pi$
$683$	8.00201	+	13.8599i	0.306189	+	0.530334i	−0.671337	+	0.741153i	$0.734280\pi$
$684$		0			0
$685$	10.1307			0.387073
$686$		0			0
$687$		−	10.2230i		−	0.390031i
$688$		0			0
$689$	−9.47431	+	5.46999i	−0.360942	+	0.208390i
$690$		0			0
$691$	32.1161	+	18.5422i	1.22175	+	0.705380i	0.965292	−	0.261175i	$-0.0841099\pi$
$691$	32.1161	+	18.5422i	1.22175	+	0.705380i	0.256462	+	0.966554i	$0.417443\pi$
$692$		0			0
$693$	0.329945	+	1.87641i	0.0125336	+	0.0712789i
$694$		0			0
$695$	−0.410530	−	0.237019i	−0.0155723	−	0.00899066i
$696$		0			0
$697$	8.10064	+	14.0307i	0.306834	+	0.531451i
$698$		0			0
$699$			17.0756i			0.645857i
$700$		0			0
$701$			21.0727i			0.795906i	0.917406	+	0.397953i	$0.130279\pi$
$701$			21.0727i			0.795906i	−0.917406	+	0.397953i	$0.869721\pi$
$702$		0			0
$703$	−19.9257	−	34.5123i	−0.751511	−	1.30166i
$704$		0			0
$705$	−0.359492	−	0.207553i	−0.0135392	−	0.00781688i
$706$		0			0
$707$	28.9736	−	24.2883i	1.08966	−	0.913457i
$708$		0			0
$709$	−16.4705	−	9.50925i	−0.618563	−	0.357127i	0.157746	−	0.987480i	$-0.449577\pi$
$709$	−16.4705	−	9.50925i	−0.618563	−	0.357127i	−0.776309	+	0.630352i	$0.782910\pi$
$710$		0			0
$711$	8.40929	−	4.85511i	0.315373	−	0.182081i
$712$		0			0
$713$		−	0.485860i		−	0.0181956i
$714$		0			0
$715$	1.13354			0.0423921
$716$		0			0
$717$	−14.9568	−	25.9059i	−0.558572	−	0.967475i
$718$		0			0
$719$	−1.02572	+	1.77660i	−0.0382529	+	0.0662559i	−0.884518	−	0.466506i	$-0.845513\pi$
$719$	−1.02572	+	1.77660i	−0.0382529	+	0.0662559i	0.846265	+	0.532762i	$0.178846\pi$
$720$		0			0
$721$	37.0983	+	13.5226i	1.38161	+	0.503606i
$722$		0			0
$723$	−8.41946	+	14.5829i	−0.313123	+	0.542345i
$724$		0			0
$725$	−32.6191	+	18.8326i	−1.21144	+	0.699426i
$726$		0			0
$727$	29.6614			1.10008			0.550039	−	0.835139i	$-0.314613\pi$
$727$	29.6614			1.10008			0.550039	+	0.835139i	$0.314613\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	18.4091	−	10.6285i	0.680886	−	0.393110i
$732$		0			0
$733$	−13.8269	+	23.9490i	−0.510710	+	0.884575i	0.489213	+	0.872164i	$0.337284\pi$
$733$	−13.8269	+	23.9490i	−0.510710	+	0.884575i	−0.999923	+	0.0124107i	$0.996049\pi$
$734$		0			0
$735$	−1.07714	−	2.96815i	−0.0397308	−	0.109482i
$736$		0			0
$737$	−3.55257	+	6.15323i	−0.130860	+	0.226657i
$738$		0			0
$739$	−1.43287	−	2.48180i	−0.0527090	−	0.0912946i	0.838467	−	0.544952i	$-0.183452\pi$
$739$	−1.43287	−	2.48180i	−0.0527090	−	0.0912946i	−0.891176	+	0.453658i	$0.850119\pi$
$740$		0			0
$741$	16.0272			0.588775
$742$		0			0
$743$		−	3.95558i		−	0.145116i	−0.997364	−	0.0725581i	$-0.976884\pi$
$743$		−	3.95558i		−	0.145116i	0.997364	−	0.0725581i	$-0.0231163\pi$
$744$		0			0
$745$	−4.93169	+	2.84731i	−0.180683	+	0.104317i
$746$		0			0
$747$	8.25853	+	4.76807i	0.302164	+	0.174454i
$748$		0			0
$749$	39.3141	+	14.3303i	1.43651	+	0.523616i
$750$		0			0
$751$	−0.443784	−	0.256219i	−0.0161939	−	0.00934956i	0.491881	−	0.870662i	$-0.336309\pi$
$751$	−0.443784	−	0.256219i	−0.0161939	−	0.00934956i	−0.508075	+	0.861313i	$0.669643\pi$
$752$		0			0
$753$	−11.5646	−	20.0305i	−0.421437	−	0.729951i
$754$		0			0
$755$			1.49303i			0.0543371i
$756$		0			0
$757$			18.0691i			0.656732i	0.944551	+	0.328366i	$0.106498\pi$
$757$			18.0691i			0.656732i	−0.944551	+	0.328366i	$0.893502\pi$
$758$		0			0
$759$	0.0190837	+	0.0330540i	0.000692695	+	0.00119978i
$760$		0			0
$761$	−34.4739	−	19.9035i	−1.24968	−	0.721501i	−0.278632	−	0.960398i	$-0.589881\pi$
$761$	−34.4739	−	19.9035i	−1.24968	−	0.721501i	−0.971045	+	0.238897i	$0.923214\pi$
$762$		0			0
$763$	0.409808	+	0.488860i	0.0148361	+	0.0176979i
$764$		0			0
$765$	1.60492	+	0.926601i	0.0580260	+	0.0335013i
$766$		0			0
$767$	16.9745	−	9.80022i	0.612913	−	0.353865i
$768$		0			0
$769$		−	45.5560i		−	1.64279i	−0.570358	−	0.821396i	$-0.693195\pi$
$769$		−	45.5560i		−	1.64279i	0.570358	−	0.821396i	$-0.306805\pi$
$770$		0			0
$771$	12.0537			0.434102
$772$		0			0
$773$	−20.8182	−	36.0581i	−0.748777	−	1.29692i	−0.948409	−	0.317049i	$-0.897308\pi$
$773$	−20.8182	−	36.0581i	−0.748777	−	1.29692i	0.199632	−	0.979871i	$-0.436025\pi$
$774$		0			0
$775$	−21.9840	+	38.0773i	−0.789687	+	1.36778i
$776$		0			0
$777$	−3.97586	−	22.6108i	−0.142633	−	0.811158i
$778$		0			0
$779$	−9.05552	+	15.6846i	−0.324448	+	0.561960i
$780$		0			0
$781$	6.96010	−	4.01841i	0.249052	−	0.143790i
$782$		0			0
$783$	−7.85260			−0.280629
$784$		0			0
$785$	1.58703			0.0566436
$786$		0			0
$787$	−14.5316	+	8.38984i	−0.517997	+	0.299065i	−0.736115	−	0.676857i	$-0.763342\pi$
$787$	−14.5316	+	8.38984i	−0.517997	+	0.299065i	0.218118	+	0.975922i	$0.430008\pi$
$788$		0			0
$789$	−11.7130	+	20.2875i	−0.416994	+	0.722254i
$790$		0			0
$791$	6.10897	+	34.7419i	0.217210	+	1.23528i
$792$		0			0
$793$	−8.89233	+	15.4020i	−0.315776	+	0.546940i
$794$		0			0
$795$	−0.707041	−	1.22463i	−0.0250762	−	0.0434332i
$796$		0			0
$797$	−22.4555			−0.795415			−0.397707	−	0.917512i	$-0.630194\pi$
$797$	−22.4555			−0.795415			−0.397707	+	0.917512i	$0.630194\pi$
$798$		0			0
$799$		−	3.78073i		−	0.133752i
$800$		0			0
$801$	−12.6107	+	7.28081i	−0.445578	+	0.257255i
$802$		0			0
$803$	−2.39866	−	1.38487i	−0.0846469	−	0.0488709i
$804$		0			0
$805$	−0.0406375	−	0.0484764i	−0.00143228	−	0.00170857i
$806$		0			0
$807$	−10.3729	−	5.98880i	−0.365144	−	0.210816i
$808$		0			0
$809$	7.04864	+	12.2086i	0.247817	+	0.429232i	0.962920	−	0.269788i	$-0.0869535\pi$
$809$	7.04864	+	12.2086i	0.247817	+	0.429232i	−0.715103	+	0.699019i	$0.753620\pi$
$810$		0			0
$811$		−	14.2766i		−	0.501320i	−0.968075	−	0.250660i	$-0.919352\pi$
$811$		−	14.2766i		−	0.501320i	0.968075	−	0.250660i	$-0.0806477\pi$
$812$		0			0
$813$		−	7.99182i		−	0.280285i
$814$		0			0
$815$	−4.21837	−	7.30643i	−0.147763	−	0.255933i
$816$		0			0
$817$	20.5791	+	11.8814i	0.719973	+	0.415677i
$818$		0			0
$819$	8.67471	+	3.16199i	0.303119	+	0.110489i
$820$		0			0
$821$	−11.2178	−	6.47658i	−0.391503	−	0.226034i	0.291308	−	0.956629i	$-0.405909\pi$
$821$	−11.2178	−	6.47658i	−0.391503	−	0.226034i	−0.682811	+	0.730595i	$0.739243\pi$
$822$		0			0
$823$	8.69701	−	5.02122i	0.303159	−	0.175029i	−0.340702	−	0.940171i	$-0.610665\pi$
$823$	8.69701	−	5.02122i	0.303159	−	0.175029i	0.643861	+	0.765143i	$0.277332\pi$
$824$		0			0
$825$		−	3.45396i		−	0.120252i
$826$		0			0
$827$	−45.1481			−1.56995			−0.784976	−	0.619526i	$-0.787325\pi$
$827$	−45.1481			−1.56995			−0.784976	+	0.619526i	$0.787325\pi$
$828$		0			0
$829$	21.1728	+	36.6724i	0.735362	+	1.27368i	0.954564	+	0.298005i	$0.0963212\pi$
$829$	21.1728	+	36.6724i	0.735362	+	1.27368i	−0.219202	+	0.975679i	$0.570345\pi$
$830$		0			0
$831$	4.35520	−	7.54343i	0.151080	−	0.261679i
$832$		0			0
$833$	18.5065	−	22.0129i	0.641214	−	0.762701i
$834$		0			0
$835$	−5.31923	+	9.21318i	−0.184080	+	0.318835i
$836$		0			0
$837$	−7.93852	+	4.58331i	−0.274395	+	0.158422i
$838$		0			0
$839$	7.15440			0.246997			0.123499	−	0.992345i	$-0.460589\pi$
$839$	7.15440			0.246997			0.123499	+	0.992345i	$0.460589\pi$
$840$		0			0
$841$	−32.6634			−1.12632
$842$		0			0
$843$	−5.90804	+	3.41101i	−0.203484	+	0.117481i
$844$		0			0
$845$	−0.185307	+	0.320961i	−0.00637475	+	0.0110414i
$846$		0			0
$847$	26.0544	+	9.49701i	0.895241	+	0.326321i
$848$		0			0
$849$	−7.51281	+	13.0126i	−0.257839	+	0.446590i
$850$		0			0
$851$	−0.229960	−	0.398302i	−0.00788292	−	0.0136536i
$852$		0			0
$853$	43.0151			1.47281			0.736405	−	0.676541i	$-0.236522\pi$
$853$	43.0151			1.47281			0.736405	+	0.676541i	$0.236522\pi$
$854$		0			0
$855$			2.07165i			0.0708490i
$856$		0			0
$857$	−2.28337	+	1.31831i	−0.0779985	+	0.0450325i	−0.538492	−	0.842631i	$-0.681006\pi$
$857$	−2.28337	+	1.31831i	−0.0779985	+	0.0450325i	0.460493	+	0.887663i	$0.347672\pi$
$858$		0			0
$859$	13.8594	+	8.00171i	0.472875	+	0.273015i	0.717443	−	0.696618i	$-0.245313\pi$
$859$	13.8594	+	8.00171i	0.472875	+	0.273015i	−0.244567	+	0.969632i	$0.578646\pi$
$860$		0			0
$861$	−7.99567	+	6.70271i	−0.272492	+	0.228428i
$862$		0			0
$863$	−1.14047	−	0.658448i	−0.0388219	−	0.0224138i	0.480463	−	0.877015i	$-0.340468\pi$
$863$	−1.14047	−	0.658448i	−0.0388219	−	0.0224138i	−0.519285	+	0.854601i	$0.673802\pi$
$864$		0			0
$865$	−5.59823	−	9.69643i	−0.190346	−	0.329688i
$866$		0			0
$867$		−	0.121262i		−	0.00411828i
$868$		0			0
$869$			6.99229i			0.237197i
$870$		0			0
$871$	17.2166	+	29.8200i	0.583361	+	1.01041i
$872$		0			0
$873$	−4.45633	−	2.57286i	−0.150824	−	0.0870782i
$874$		0			0
$875$	2.02477	+	11.5149i	0.0684498	+	0.389276i
$876$		0			0
$877$	20.8705	+	12.0496i	0.704748	+	0.406886i	0.809113	−	0.587653i	$-0.199948\pi$
$877$	20.8705	+	12.0496i	0.704748	+	0.406886i	−0.104366	+	0.994539i	$0.533281\pi$
$878$		0			0
$879$	2.40733	−	1.38987i	0.0811971	−	0.0468792i
$880$		0			0
$881$			1.71827i			0.0578899i	0.999581	+	0.0289449i	$0.00921474\pi$
$881$			1.71827i			0.0578899i	−0.999581	+	0.0289449i	$0.990785\pi$
$882$		0			0
$883$	−31.5753			−1.06259			−0.531297	−	0.847185i	$-0.678295\pi$
$883$	−31.5753			−1.06259			−0.531297	+	0.847185i	$0.678295\pi$
$884$		0			0
$885$	1.26676	+	2.19409i	0.0425816	+	0.0737535i
$886$		0			0
$887$	−25.0131	+	43.3240i	−0.839859	+	1.45468i	0.0501528	+	0.998742i	$0.484029\pi$
$887$	−25.0131	+	43.3240i	−0.839859	+	1.45468i	−0.890012	+	0.455937i	$0.849304\pi$
$888$		0			0
$889$	1.34822	−	0.237069i	0.0452177	−	0.00795103i
$890$		0			0
$891$	0.360048	−	0.623622i	0.0120621	−	0.0208921i
$892$		0			0
$893$	3.66016	−	2.11319i	0.122483	−	0.0707153i
$894$		0			0
$895$	−0.450150			−0.0150469
$896$		0			0
$897$	0.184968			0.00617591
$898$		0			0
$899$	−62.3381	+	35.9909i	−2.07909	+	1.20036i
$900$		0			0
$901$	6.43964	−	11.1538i	0.214536	−	0.371587i
$902$		0			0
$903$	8.79436	+	10.4908i	0.292658	+	0.349112i
$904$		0			0
$905$	1.31141	−	2.27143i	0.0435928	−	0.0755049i
$906$		0			0
$907$	−3.95622	−	6.85238i	−0.131364	−	0.227530i	0.792838	−	0.609432i	$-0.208602\pi$
$907$	−3.95622	−	6.85238i	−0.131364	−	0.227530i	−0.924203	+	0.381902i	$0.875269\pi$
$908$		0			0
$909$	−14.2898			−0.473963
$910$		0			0
$911$		−	28.5805i		−	0.946914i	−0.880817	−	0.473457i	$-0.843006\pi$
$911$		−	28.5805i		−	0.946914i	0.880817	−	0.473457i	$-0.156994\pi$
$912$		0			0
$913$	−5.94694	+	3.43347i	−0.196815	+	0.113631i
$914$		0			0
$915$	−1.99083	−	1.14941i	−0.0658148	−	0.0379982i
$916$		0			0
$917$	12.2061	−	33.4865i	0.403080	−	1.10582i
$918$		0			0
$919$	41.7821	+	24.1229i	1.37827	+	0.795742i	0.991951	−	0.126625i	$-0.0404146\pi$
$919$	41.7821	+	24.1229i	1.37827	+	0.795742i	0.386314	+	0.922367i	$0.373748\pi$
$920$		0			0
$921$	12.3971	+	21.4725i	0.408499	+	0.707542i
$922$		0			0
$923$		−	38.9483i		−	1.28200i
$924$		0			0
$925$			41.6204i			1.36847i
$926$		0			0
$927$	−7.46214	−	12.9248i	−0.245089	−	0.424506i
$928$		0			0
$929$	44.9765	+	25.9672i	1.47563	+	0.851956i	0.999622	−	0.0274853i	$-0.00874994\pi$
$929$	44.9765	+	25.9672i	1.47563	+	0.851956i	0.476008	+	0.879441i	$0.342083\pi$
$930$		0			0
$931$	31.6549	+	5.61252i	1.03745	+	0.183943i
$932$		0			0
$933$	−2.24157	−	1.29417i	−0.0733858	−	0.0423693i
$934$		0			0
$935$	−1.15570	+	0.667242i	−0.0377953	+	0.0218212i
$936$		0			0
$937$		−	10.7775i		−	0.352087i	−0.984382	−	0.176044i	$-0.943670\pi$
$937$		−	10.7775i		−	0.352087i	0.984382	−	0.176044i	$-0.0563300\pi$
$938$		0			0
$939$	2.89237			0.0943888
$940$		0			0
$941$	8.56040	+	14.8270i	0.279061	+	0.483348i	0.971152	−	0.238463i	$-0.0766435\pi$
$941$	8.56040	+	14.8270i	0.279061	+	0.483348i	−0.692091	+	0.721811i	$0.743310\pi$
$942$		0			0
$943$	−0.104509	+	0.181014i	−0.00340327	+	0.00589463i
$944$		0			0
$945$	−0.408713	+	1.12128i	−0.0132954	+	0.0364751i
$946$		0			0
$947$	−2.91463	+	5.04828i	−0.0947126	+	0.164047i	−0.909489	−	0.415729i	$-0.863527\pi$
$947$	−2.91463	+	5.04828i	−0.0947126	+	0.164047i	0.814776	+	0.579776i	$0.196860\pi$
$948$		0			0
$949$	−11.6245	+	6.71139i	−0.377346	+	0.217861i
$950$		0			0
$951$	−34.0259			−1.10337
$952$		0			0
$953$	45.9790			1.48941			0.744703	−	0.667396i	$-0.232591\pi$
$953$	45.9790			1.48941			0.744703	+	0.667396i	$0.232591\pi$
$954$		0			0
$955$	5.25239	−	3.03247i	0.169963	−	0.0981284i
$956$		0			0
$957$	2.82732	−	4.89706i	0.0913942	−	0.158299i
$958$		0			0
$959$	−45.5366	+	38.1730i	−1.47045	+	1.23267i
$960$		0			0
$961$	−26.5134	+	45.9226i	−0.855271	+	1.48137i
$962$		0			0
$963$	−7.90786	−	13.6968i	−0.254827	−	0.441374i
$964$		0			0
$965$	3.34433			0.107658
$966$		0			0
$967$			51.2560i			1.64828i	0.566384	+	0.824141i	$0.308342\pi$
$967$			51.2560i			1.64828i	−0.566384	+	0.824141i	$0.691658\pi$
$968$		0			0
$969$	−16.3405	+	9.43418i	−0.524932	+	0.303069i
$970$		0			0
$971$	11.0630	+	6.38720i	0.355027	+	0.204975i	0.666897	−	0.745150i	$-0.267622\pi$
$971$	11.0630	+	6.38720i	0.355027	+	0.204975i	−0.311870	+	0.950125i	$0.600955\pi$
$972$		0			0
$973$	2.73841	−	0.481518i	0.0877892	−	0.0154368i
$974$		0			0
$975$	−14.4961	−	8.36935i	−0.464248	−	0.268034i
$976$		0			0
$977$	−15.9469	−	27.6208i	−0.510186	−	0.883668i	−0.999930	−	0.0118021i	$-0.996243\pi$
$977$	−15.9469	−	27.6208i	−0.510186	−	0.883668i	0.489744	−	0.871866i	$-0.337090\pi$
$978$		0			0
$979$		−	10.4858i		−	0.335127i
$980$		0			0
$981$		−	0.241107i		−	0.00769795i
$982$		0			0
$983$	25.6278	+	44.3886i	0.817399	+	1.41578i	0.907593	+	0.419852i	$0.137918\pi$
$983$	25.6278	+	44.3886i	0.817399	+	1.41578i	−0.0901941	+	0.995924i	$0.528749\pi$
$984$		0			0
$985$	−2.58922	−	1.49489i	−0.0824993	−	0.0476310i
$986$		0			0
$987$	2.39796	−	0.421655i	0.0763279	−	0.0134214i
$988$		0			0
$989$	0.237501	+	0.137121i	0.00755210	+	0.00436021i
$990$		0			0
$991$	20.0234	−	11.5605i	0.636064	−	0.367232i	−0.147033	−	0.989132i	$-0.546972\pi$
$991$	20.0234	−	11.5605i	0.636064	−	0.367232i	0.783097	+	0.621900i	$0.213639\pi$
$992$		0			0
$993$		−	2.44534i		−	0.0776004i
$994$		0			0
$995$	−4.86789			−0.154322
$996$		0			0
$997$	21.7369	+	37.6494i	0.688413	+	1.19237i	0.972351	+	0.233524i	$0.0750258\pi$
$997$	21.7369	+	37.6494i	0.688413	+	1.19237i	−0.283938	+	0.958843i	$0.591641\pi$
$998$		0			0
$999$	−4.33860	+	7.51467i	−0.137267	+	0.237754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bb.a.271.6		32
3.2	odd	2		2016.2.bs.c.271.6		32
4.3	odd	2		168.2.t.a.19.10	✓	32
7.2	even	3		4704.2.p.a.3919.11		32
7.3	odd	6	inner	672.2.bb.a.367.3		32
7.5	odd	6		4704.2.p.a.3919.8		32
8.3	odd	2	inner	672.2.bb.a.271.3		32
8.5	even	2		168.2.t.a.19.13	yes	32
12.11	even	2		504.2.bk.c.19.7		32
21.17	even	6		2016.2.bs.c.1711.11		32
24.5	odd	2		504.2.bk.c.19.4		32
24.11	even	2		2016.2.bs.c.271.11		32
28.3	even	6		168.2.t.a.115.13	yes	32
28.19	even	6		1176.2.p.a.979.3		32
28.23	odd	6		1176.2.p.a.979.4		32
56.3	even	6	inner	672.2.bb.a.367.6		32
56.5	odd	6		1176.2.p.a.979.2		32
56.19	even	6		4704.2.p.a.3919.12		32
56.37	even	6		1176.2.p.a.979.1		32
56.45	odd	6		168.2.t.a.115.10	yes	32
56.51	odd	6		4704.2.p.a.3919.7		32
84.59	odd	6		504.2.bk.c.451.4		32
168.59	odd	6		2016.2.bs.c.1711.6		32
168.101	even	6		504.2.bk.c.451.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.10	✓	32	4.3	odd	2
168.2.t.a.19.13	yes	32	8.5	even	2
168.2.t.a.115.10	yes	32	56.45	odd	6
168.2.t.a.115.13	yes	32	28.3	even	6
504.2.bk.c.19.4		32	24.5	odd	2
504.2.bk.c.19.7		32	12.11	even	2
504.2.bk.c.451.4		32	84.59	odd	6
504.2.bk.c.451.7		32	168.101	even	6
672.2.bb.a.271.3		32	8.3	odd	2	inner
672.2.bb.a.271.6		32	1.1	even	1	trivial
672.2.bb.a.367.3		32	7.3	odd	6	inner
672.2.bb.a.367.6		32	56.3	even	6	inner
1176.2.p.a.979.1		32	56.37	even	6
1176.2.p.a.979.2		32	56.5	odd	6
1176.2.p.a.979.3		32	28.19	even	6
1176.2.p.a.979.4		32	28.23	odd	6
2016.2.bs.c.271.6		32	3.2	odd	2
2016.2.bs.c.271.11		32	24.11	even	2
2016.2.bs.c.1711.6		32	168.59	odd	6
2016.2.bs.c.1711.11		32	21.17	even	6
4704.2.p.a.3919.7		32	56.51	odd	6
4704.2.p.a.3919.8		32	7.5	odd	6
4704.2.p.a.3919.11		32	7.2	even	3
4704.2.p.a.3919.12		32	56.19	even	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(0.225540 - 0.390646i) q^{5} +(0.458196 + 2.60577i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(0.225540 - 0.390646i) q^{5} +(0.458196 + 2.60577i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.360048 + 0.623622i) q^{11} +3.48975 q^{13} +0.451079i q^{15} +(-3.55796 + 2.05419i) q^{17} +(-3.97736 - 2.29633i) q^{19} +(-1.69970 - 2.02757i) q^{21} +(-0.0459022 - 0.0265016i) q^{23} +(2.39826 + 4.15391i) q^{25} +1.00000i q^{27} +7.85260i q^{29} +(4.58331 + 7.93852i) q^{31} +(-0.623622 - 0.360048i) q^{33} +(1.12128 + 0.408713i) q^{35} +(7.51467 + 4.33860i) q^{37} +(-3.02222 + 1.74488i) q^{39} -3.94348i q^{41} -5.17408 q^{43} +(-0.225540 - 0.390646i) q^{45} +(-0.460124 + 0.796959i) q^{47} +(-6.58011 + 2.38791i) q^{49} +(2.05419 - 3.55796i) q^{51} +(-2.71489 + 1.56744i) q^{53} +0.324821 q^{55} +4.59266 q^{57} +(4.86409 - 2.80828i) q^{59} +(-2.54813 + 4.41348i) q^{61} +(2.48576 + 0.906077i) q^{63} +(0.787078 - 1.36326i) q^{65} +(4.93346 + 8.54500i) q^{67} +0.0530032 q^{69} -11.1608i q^{71} +(-3.33103 + 1.92317i) q^{73} +(-4.15391 - 2.39826i) q^{75} +(-1.46004 + 1.22395i) q^{77} +(8.40929 + 4.85511i) q^{79} +(-0.500000 - 0.866025i) q^{81} +9.53613i q^{83} +1.85320i q^{85} +(-3.92630 - 6.80056i) q^{87} +(-12.6107 - 7.28081i) q^{89} +(1.59899 + 9.09351i) q^{91} +(-7.93852 - 4.58331i) q^{93} +(-1.79410 + 1.03583i) q^{95} -5.14572i q^{97} +0.720096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^9	\( 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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