LMFDB - Embedded newform 976.2.bw.c.321.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [976,2,Mod(225,976)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("976.225"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(976, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 0, 28])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 976 = 2^{4} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	976.bw (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.79339923728$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			321.3
Character	$\chi$	$=$	976.321
Dual form			976.2.bw.c.225.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.507067 + 1.56059i) q^{3} +(-0.0538027 - 0.511898i) q^{5} +(2.89428 + 3.21442i) q^{7} +(0.248718 - 0.180704i) q^{9} -4.96132 q^{11} +(-2.23295 + 3.86759i) q^{13} +(0.771583 - 0.343531i) q^{15} +(0.640078 + 0.284981i) q^{17} +(-2.48401 + 2.75877i) q^{19} +(-3.54881 + 6.14672i) q^{21} +(-0.894569 + 0.649942i) q^{23} +(4.63159 - 0.984476i) q^{25} +(4.39068 + 3.19002i) q^{27} +(-0.498463 - 0.863364i) q^{29} +(2.93238 - 0.623298i) q^{31} +(-2.51572 - 7.74259i) q^{33} +(1.48974 - 1.65452i) q^{35} +(1.26557 - 3.89501i) q^{37} +(-7.16799 - 1.52360i) q^{39} +(-3.19296 + 9.82692i) q^{41} +(-0.917366 + 0.408438i) q^{43} +(-0.105884 - 0.117596i) q^{45} +(-5.38430 - 9.32588i) q^{47} +(-1.22396 + 11.6452i) q^{49} +(-0.120177 + 1.14341i) q^{51} +(1.19709 + 0.869735i) q^{53} +(0.266932 + 2.53969i) q^{55} +(-5.56488 - 2.47764i) q^{57} +(-3.70743 - 0.788038i) q^{59} +(6.90250 + 3.65452i) q^{61} +(1.30072 + 0.276477i) q^{63} +(2.09995 + 0.934958i) q^{65} +(0.812373 + 7.72921i) q^{67} +(-1.46790 - 1.06649i) q^{69} +(-0.758939 + 7.22082i) q^{71} +(-0.452438 + 4.30466i) q^{73} +(3.88490 + 6.72884i) q^{75} +(-14.3594 - 15.9478i) q^{77} +(15.5157 - 6.90804i) q^{79} +(-2.46694 + 7.59246i) q^{81} +(-11.9798 - 2.54638i) q^{83} +(0.111443 - 0.342987i) q^{85} +(1.09460 - 1.21568i) q^{87} +(0.704279 + 2.16755i) q^{89} +(-18.8949 + 4.01623i) q^{91} +(2.45963 + 4.26020i) q^{93} +(1.54586 + 1.12313i) q^{95} +(-10.6030 + 2.25375i) q^{97} +(-1.23397 + 0.896532i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39}+ \cdots + 31 q^{99}+O(q^{100}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/976\mathbb{Z}\right)^\times$.

$n$	$245$	$367$	$673$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{15}\right)$

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
$3$	0.507067	+	1.56059i	0.292755	+	0.901009i	0.983966	+	0.178355i	$0.0570777\pi$
$3$	0.507067	+	1.56059i	0.292755	+	0.901009i	−0.691211	+	0.722653i	$0.742922\pi$
$4$		0			0
$5$	−0.0538027	−	0.511898i	−0.0240613	−	0.228928i	−0.999943	−	0.0106301i	$-0.996616\pi$
$5$	−0.0538027	−	0.511898i	−0.0240613	−	0.228928i	0.975882	−	0.218298i	$-0.0700504\pi$
$6$		0			0
$7$	2.89428	+	3.21442i	1.09393	+	1.21494i	0.975040	+	0.222031i	$0.0712685\pi$
$7$	2.89428	+	3.21442i	1.09393	+	1.21494i	0.118895	+	0.992907i	$0.462065\pi$
$8$		0			0
$9$	0.248718	−	0.180704i	0.0829061	−	0.0602348i
$10$		0			0
$11$	−4.96132			−1.49589			−0.747947	−	0.663759i	$-0.768960\pi$
$11$	−4.96132			−1.49589			−0.747947	+	0.663759i	$0.768960\pi$
$12$		0			0
$13$	−2.23295	+	3.86759i	−0.619310	+	1.07268i	0.370302	+	0.928911i	$0.379254\pi$
$13$	−2.23295	+	3.86759i	−0.619310	+	1.07268i	−0.989612	+	0.143765i	$0.954079\pi$
$14$		0			0
$15$	0.771583	−	0.343531i	0.199222	−	0.0886993i
$16$		0			0
$17$	0.640078	+	0.284981i	0.155242	+	0.0691181i	0.482887	−	0.875683i	$-0.339588\pi$
$17$	0.640078	+	0.284981i	0.155242	+	0.0691181i	−0.327645	+	0.944801i	$0.606255\pi$
$18$		0			0
$19$	−2.48401	+	2.75877i	−0.569871	+	0.632905i	−0.957335	−	0.288979i	$-0.906684\pi$
$19$	−2.48401	+	2.75877i	−0.569871	+	0.632905i	0.387465	+	0.921884i	$0.373351\pi$
$20$		0			0
$21$	−3.54881	+	6.14672i	−0.774414	+	1.34132i
$22$		0			0
$23$	−0.894569	+	0.649942i	−0.186530	+	0.135522i	−0.677132	−	0.735862i	$-0.736777\pi$
$23$	−0.894569	+	0.649942i	−0.186530	+	0.135522i	0.490601	+	0.871384i	$0.336777\pi$
$24$		0			0
$25$	4.63159	−	0.984476i	0.926319	−	0.196895i
$26$		0			0
$27$	4.39068	+	3.19002i	0.844987	+	0.613919i
$28$		0			0
$29$	−0.498463	−	0.863364i	−0.0925623	−	0.160323i	0.816026	−	0.578015i	$-0.196172\pi$
$29$	−0.498463	−	0.863364i	−0.0925623	−	0.160323i	−0.908589	+	0.417692i	$0.862839\pi$
$30$		0			0
$31$	2.93238	−	0.623298i	0.526672	−	0.111948i	0.0631006	−	0.998007i	$-0.479901\pi$
$31$	2.93238	−	0.623298i	0.526672	−	0.111948i	0.463571	+	0.886060i	$0.346568\pi$
$32$		0			0
$33$	−2.51572	−	7.74259i	−0.437931	−	1.34781i
$34$		0			0
$35$	1.48974	−	1.65452i	0.251811	−	0.279665i
$36$		0			0
$37$	1.26557	−	3.89501i	0.208058	−	0.640336i	−0.791516	−	0.611148i	$-0.790708\pi$
$37$	1.26557	−	3.89501i	0.208058	−	0.640336i	0.999574	−	0.0291879i	$-0.00929211\pi$
$38$		0			0
$39$	−7.16799	−	1.52360i	−1.14780	−	0.243972i
$40$		0			0
$41$	−3.19296	+	9.82692i	−0.498656	+	1.53471i	0.312524	+	0.949910i	$0.398826\pi$
$41$	−3.19296	+	9.82692i	−0.498656	+	1.53471i	−0.811180	+	0.584796i	$0.801174\pi$
$42$		0			0
$43$	−0.917366	+	0.408438i	−0.139897	+	0.0622861i	−0.475491	−	0.879721i	$-0.657730\pi$
$43$	−0.917366	+	0.408438i	−0.139897	+	0.0622861i	0.335594	+	0.942007i	$0.391063\pi$
$44$		0			0
$45$	−0.105884	−	0.117596i	−0.0157842	−	0.0175302i
$46$		0			0
$47$	−5.38430	−	9.32588i	−0.785381	−	1.36032i	−0.928771	−	0.370653i	$-0.879134\pi$
$47$	−5.38430	−	9.32588i	−0.785381	−	1.36032i	0.143390	−	0.989666i	$-0.454200\pi$
$48$		0			0
$49$	−1.22396	+	11.6452i	−0.174852	+	1.66360i
$50$		0			0
$51$	−0.120177	+	1.14341i	−0.0168281	+	0.160109i
$52$		0			0
$53$	1.19709	+	0.869735i	0.164433	+	0.119467i	0.666958	−	0.745095i	$-0.267596\pi$
$53$	1.19709	+	0.869735i	0.164433	+	0.119467i	−0.502526	+	0.864562i	$0.667596\pi$
$54$		0			0
$55$	0.266932	+	2.53969i	0.0359931	+	0.342451i
$56$		0			0
$57$	−5.56488	−	2.47764i	−0.737086	−	0.328172i
$58$		0			0
$59$	−3.70743	−	0.788038i	−0.482666	−	0.102594i	−0.0398487	−	0.999206i	$-0.512688\pi$
$59$	−3.70743	−	0.788038i	−0.482666	−	0.102594i	−0.442817	+	0.896612i	$0.646021\pi$
$60$		0			0
$61$	6.90250	+	3.65452i	0.883774	+	0.467913i
$61$	6.90250	+	3.65452i	0.883774	+	0.467913i
$62$		0			0
$63$	1.30072	+	0.276477i	0.163875	+	0.0348328i
$64$		0			0
$65$	2.09995	+	0.934958i	0.260467	+	0.115967i
$66$		0			0
$67$	0.812373	+	7.72921i	0.0992471	+	0.944273i	0.924930	+	0.380138i	$0.124124\pi$
$67$	0.812373	+	7.72921i	0.0992471	+	0.944273i	−0.825683	+	0.564135i	$0.809210\pi$
$68$		0			0
$69$	−1.46790	−	1.06649i	−0.176715	−	0.128391i
$70$		0			0
$71$	−0.758939	+	7.22082i	−0.0900695	+	0.856954i	0.852451	+	0.522807i	$0.175115\pi$
$71$	−0.758939	+	7.22082i	−0.0900695	+	0.856954i	−0.942521	+	0.334148i	$0.891552\pi$
$72$		0			0
$73$	−0.452438	+	4.30466i	−0.0529539	+	0.503823i	0.935612	+	0.353031i	$0.114849\pi$
$73$	−0.452438	+	4.30466i	−0.0529539	+	0.503823i	−0.988566	+	0.150792i	$0.951818\pi$
$74$		0			0
$75$	3.88490	+	6.72884i	0.448589	+	0.776979i
$76$		0			0
$77$	−14.3594	−	15.9478i	−1.63641	−	1.81742i
$78$		0			0
$79$	15.5157	−	6.90804i	1.74565	−	0.777215i	0.752748	−	0.658309i	$-0.228728\pi$
$79$	15.5157	−	6.90804i	1.74565	−	0.777215i	0.992906	−	0.118906i	$-0.0379387\pi$
$80$		0			0
$81$	−2.46694	+	7.59246i	−0.274104	+	0.843607i
$82$		0			0
$83$	−11.9798	−	2.54638i	−1.31495	−	0.279501i	−0.503536	−	0.863974i	$-0.667968\pi$
$83$	−11.9798	−	2.54638i	−1.31495	−	0.279501i	−0.811413	+	0.584473i	$0.801301\pi$
$84$		0			0
$85$	0.111443	−	0.342987i	0.0120877	−	0.0372022i
$86$		0			0
$87$	1.09460	−	1.21568i	0.117354	−	0.130335i
$88$		0			0
$89$	0.704279	+	2.16755i	0.0746534	+	0.229760i	0.981419	−	0.191875i	$-0.0614567\pi$
$89$	0.704279	+	2.16755i	0.0746534	+	0.229760i	−0.906766	+	0.421634i	$0.861457\pi$
$90$		0			0
$91$	−18.8949	+	4.01623i	−1.98072	+	0.421015i
$92$		0			0
$93$	2.45963	+	4.26020i	0.255052	+	0.441763i
$94$		0			0
$95$	1.54586	+	1.12313i	0.158601	+	0.115231i
$96$		0			0
$97$	−10.6030	+	2.25375i	−1.07658	+	0.228833i	−0.711885	−	0.702296i	$-0.752158\pi$
$97$	−10.6030	+	2.25375i	−1.07658	+	0.228833i	−0.364690	+	0.931129i	$0.618825\pi$
$98$		0			0
$99$	−1.23397	+	0.896532i	−0.124019	+	0.0901049i
$100$		0			0
$101$	2.07335	−	3.59115i	0.206306	−	0.357332i	−0.744242	−	0.667910i	$-0.767189\pi$
$101$	2.07335	−	3.59115i	0.206306	−	0.357332i	0.950548	+	0.310578i	$0.100522\pi$
$102$		0			0
$103$	−4.29978	+	4.77539i	−0.423670	+	0.470533i	−0.916756	−	0.399448i	$-0.869202\pi$
$103$	−4.29978	+	4.77539i	−0.423670	+	0.470533i	0.493086	+	0.869980i	$0.335869\pi$
$104$		0			0
$105$	3.33743	+	1.48592i	0.325700	+	0.145011i
$106$		0			0
$107$	11.9833	−	5.33529i	1.15847	−	0.515782i	0.264706	−	0.964329i	$-0.414725\pi$
$107$	11.9833	−	5.33529i	1.15847	−	0.515782i	0.893759	+	0.448547i	$0.148058\pi$
$108$		0			0
$109$	8.14737	−	14.1117i	0.780377	−	1.35165i	−0.151345	−	0.988481i	$-0.548361\pi$
$109$	8.14737	−	14.1117i	0.780377	−	1.35165i	0.931722	−	0.363171i	$-0.118306\pi$
$110$		0			0
$111$	6.72026			0.637859
$112$		0			0
$113$	0.447983	−	0.325479i	0.0421427	−	0.0306185i	−0.566515	−	0.824052i	$-0.691708\pi$
$113$	0.447983	−	0.325479i	0.0421427	−	0.0306185i	0.608657	+	0.793433i	$0.291708\pi$
$114$		0			0
$115$	0.380834	+	0.422959i	0.0355130	+	0.0394412i
$116$		0			0
$117$	0.143514	+	1.36545i	0.0132679	+	0.126235i
$118$		0			0
$119$	0.936515	+	2.88230i	0.0858501	+	0.264220i
$120$		0			0
$121$	13.6147			1.23770
$122$		0			0
$123$	−16.9549			−1.52877
$124$		0			0
$125$	−1.54843	−	4.76556i	−0.138495	−	0.426245i
$126$		0			0
$127$	−2.26685	−	21.5676i	−0.201150	−	1.91381i	−0.371504	−	0.928431i	$-0.621158\pi$
$127$	−2.26685	−	21.5676i	−0.201150	−	1.91381i	0.170354	−	0.985383i	$-0.445509\pi$
$128$		0			0
$129$	−1.10257	−	1.22453i	−0.0970760	−	0.107814i
$130$		0			0
$131$	11.0773	−	8.04815i	0.967831	−	0.703170i	0.0128746	−	0.999917i	$-0.495902\pi$
$131$	11.0773	−	8.04815i	0.967831	−	0.703170i	0.954956	+	0.296747i	$0.0959018\pi$
$132$		0			0
$133$	−16.0573			−1.39234
$134$		0			0
$135$	1.39673	−	2.41921i	0.120212	−	0.208213i
$136$		0			0
$137$	14.5378	−	6.47264i	1.24205	−	0.552995i	0.322722	−	0.946494i	$-0.395402\pi$
$137$	14.5378	−	6.47264i	1.24205	−	0.552995i	0.919325	+	0.393499i	$0.128735\pi$
$138$		0			0
$139$	13.7934	+	6.14123i	1.16994	+	0.520892i	0.897385	−	0.441248i	$-0.145464\pi$
$139$	13.7934	+	6.14123i	1.16994	+	0.520892i	0.272557	+	0.962140i	$0.412131\pi$
$140$		0			0
$141$	11.8237	−	13.1315i	0.995735	−	1.10588i
$142$		0			0
$143$	11.0784	−	19.1883i	0.926422	−	1.60461i
$144$		0			0
$145$	−0.415136	+	0.301614i	−0.0344751	+	0.0250477i
$146$		0			0
$147$	−18.7941	+	3.99480i	−1.55011	+	0.329486i
$148$		0			0
$149$	6.36765	+	4.62637i	0.521658	+	0.379007i	0.817228	−	0.576314i	$-0.195509\pi$
$149$	6.36765	+	4.62637i	0.521658	+	0.379007i	−0.295570	+	0.955321i	$0.595509\pi$
$150$		0			0
$151$	2.97270	+	5.14886i	0.241915	+	0.419009i	0.961260	−	0.275644i	$-0.0888913\pi$
$151$	2.97270	+	5.14886i	0.241915	+	0.419009i	−0.719345	+	0.694653i	$0.755558\pi$
$152$		0			0
$153$	0.210696	−	0.0447849i	0.0170338	−	0.00362065i
$154$		0			0
$155$	−0.476835	−	1.46755i	−0.0383003	−	0.117876i
$156$		0			0
$157$	−1.62187	+	1.80127i	−0.129439	+	0.143757i	−0.804380	−	0.594115i	$-0.797502\pi$
$157$	−1.62187	+	1.80127i	−0.129439	+	0.143757i	0.674941	+	0.737872i	$0.264169\pi$
$158$		0			0
$159$	−0.750298	+	2.30918i	−0.0595025	+	0.183130i
$160$		0			0
$161$	−4.67832	−	0.994408i	−0.368703	−	0.0783703i
$162$		0			0
$163$	−2.44624	+	7.52875i	−0.191604	+	0.589697i	0.808395	+	0.588640i	$0.200337\pi$
$163$	−2.44624	+	7.52875i	−0.191604	+	0.589697i	−0.999999	+	0.00105723i	$0.999663\pi$
$164$		0			0
$165$	−3.82807	+	1.70437i	−0.298015	+	0.132685i
$166$		0			0
$167$	−0.0937025	−	0.104067i	−0.00725091	−	0.00805296i	0.739508	−	0.673147i	$-0.235058\pi$
$167$	−0.0937025	−	0.104067i	−0.00725091	−	0.00805296i	−0.746759	+	0.665094i	$0.768391\pi$
$168$		0			0
$169$	−3.47217	−	6.01397i	−0.267090	−	0.462613i
$170$		0			0
$171$	−0.119296	+	1.13503i	−0.00912281	+	0.0867978i
$172$		0			0
$173$	0.491602	−	4.67728i	0.0373758	−	0.355607i	−0.959811	−	0.280648i	$-0.909451\pi$
$173$	0.491602	−	4.67728i	0.0373758	−	0.355607i	0.997187	−	0.0749590i	$-0.0238826\pi$
$174$		0			0
$175$	16.5696	+	12.0386i	1.25255	+	0.910029i
$176$		0			0
$177$	−0.650109	−	6.18537i	−0.0488652	−	0.464921i
$178$		0			0
$179$	9.52240	+	4.23965i	0.711738	+	0.316886i	0.730476	−	0.682938i	$-0.239298\pi$
$179$	9.52240	+	4.23965i	0.711738	+	0.316886i	−0.0187383	+	0.999824i	$0.505965\pi$
$180$		0			0
$181$	0.238702	+	0.0507376i	0.0177426	+	0.00377130i	0.216774	−	0.976222i	$-0.430446\pi$
$181$	0.238702	+	0.0507376i	0.0177426	+	0.00377130i	−0.199032	+	0.979993i	$0.563780\pi$
$182$		0			0
$183$	−2.20319	+	12.6251i	−0.162864	+	0.933273i
$184$		0			0
$185$	−2.06194	−	0.438279i	−0.151597	−	0.0322229i
$186$		0			0
$187$	−3.17563	−	1.41388i	−0.232225	−	0.103393i
$188$		0			0
$189$	2.45380	+	23.3463i	0.178487	+	1.69819i
$190$		0			0
$191$	3.60182	+	2.61688i	0.260619	+	0.189350i	0.710420	−	0.703778i	$-0.248505\pi$
$191$	3.60182	+	2.61688i	0.260619	+	0.189350i	−0.449801	+	0.893129i	$0.648505\pi$
$192$		0			0
$193$	0.869668	−	8.27434i	0.0626001	−	0.595600i	−0.917588	−	0.397532i	$-0.869867\pi$
$193$	0.869668	−	8.27434i	0.0626001	−	0.595600i	0.980188	−	0.198068i	$-0.0634666\pi$
$194$		0			0
$195$	−0.394273	+	3.75125i	−0.0282345	+	0.268633i
$196$		0			0
$197$	4.53140	+	7.84861i	0.322849	+	0.559190i	0.981075	−	0.193630i	$-0.0620261\pi$
$197$	4.53140	+	7.84861i	0.322849	+	0.559190i	−0.658226	+	0.752821i	$0.728693\pi$
$198$		0			0
$199$	8.25608	+	9.16931i	0.585258	+	0.649995i	0.960941	−	0.276753i	$-0.0892585\pi$
$199$	8.25608	+	9.16931i	0.585258	+	0.649995i	−0.375683	+	0.926748i	$0.622592\pi$
$200$		0			0
$201$	−11.6502	+	5.18701i	−0.821743	+	0.365864i
$202$		0			0
$203$	1.33252	−	4.10109i	0.0935249	−	0.287840i
$204$		0			0
$205$	5.20217	+	1.10576i	0.363335	+	0.0772293i
$206$		0			0
$207$	−0.105048	+	0.323305i	−0.00730135	+	0.0224713i
$208$		0			0
$209$	12.3239	−	13.6871i	0.852465	−	0.946759i
$210$		0			0
$211$	−4.98082	−	15.3294i	−0.342894	−	1.05532i	−0.962702	−	0.270565i	$-0.912789\pi$
$211$	−4.98082	−	15.3294i	−0.342894	−	1.05532i	0.619808	−	0.784754i	$-0.287211\pi$
$212$		0			0
$213$	−11.6536	+	2.47705i	−0.798491	+	0.169725i
$214$		0			0
$215$	0.258435	+	0.447623i	0.0176251	+	0.0305276i
$216$		0			0
$217$	10.4907	+	7.62193i	0.712154	+	0.517410i
$218$		0			0
$219$	−6.94724	+	1.47668i	−0.469451	+	0.0997850i
$220$		0			0
$221$	−2.53145	+	1.83921i	−0.170284	+	0.123719i
$222$		0			0
$223$	5.73806	−	9.93861i	0.384249	−	0.665539i	−0.607416	−	0.794384i	$-0.707794\pi$
$223$	5.73806	−	9.93861i	0.384249	−	0.665539i	0.991665	+	0.128845i	$0.0411271\pi$
$224$		0			0
$225$	0.974063	−	1.08181i	0.0649375	−	0.0721204i
$226$		0			0
$227$	−4.98427	−	2.21914i	−0.330817	−	0.147289i	0.234605	−	0.972091i	$-0.424620\pi$
$227$	−4.98427	−	2.21914i	−0.330817	−	0.147289i	−0.565423	+	0.824801i	$0.691287\pi$
$228$		0			0
$229$	2.63635	−	1.17378i	0.174215	−	0.0775654i	−0.317776	−	0.948166i	$-0.602936\pi$
$229$	2.63635	−	1.17378i	0.174215	−	0.0775654i	0.491991	+	0.870600i	$0.336269\pi$
$230$		0			0
$231$	17.6068	−	30.4958i	1.15844	−	2.00648i
$232$		0			0
$233$	27.1947			1.78158			0.890792	−	0.454411i	$-0.150150\pi$
$233$	27.1947			1.78158			0.890792	+	0.454411i	$0.150150\pi$
$234$		0			0
$235$	−4.48421	+	3.25797i	−0.292518	+	0.212527i
$236$		0			0
$237$	18.6481	+	20.7109i	1.21133	+	1.34531i
$238$		0			0
$239$	−2.02078	−	19.2264i	−0.130713	−	1.24366i	−0.841504	−	0.540251i	$-0.818329\pi$
$239$	−2.02078	−	19.2264i	−0.130713	−	1.24366i	0.710790	−	0.703404i	$-0.248337\pi$
$240$		0			0
$241$	−1.69567	−	5.21872i	−0.109227	−	0.336168i	0.881472	−	0.472236i	$-0.156553\pi$
$241$	−1.69567	−	5.21872i	−0.109227	−	0.336168i	−0.990699	+	0.136069i	$0.956553\pi$
$242$		0			0
$243$	3.18190			0.204119
$244$		0			0
$245$	6.02702			0.385052
$246$		0			0
$247$	−5.12312	−	15.7673i	−0.325976	−	1.00325i
$248$		0			0
$249$	−2.10069	−	19.9867i	−0.133126	−	1.26661i
$250$		0			0
$251$	8.28494	+	9.20136i	0.522941	+	0.580784i	0.945529	−	0.325537i	$-0.105545\pi$
$251$	8.28494	+	9.20136i	0.522941	+	0.580784i	−0.422589	+	0.906322i	$0.638878\pi$
$252$		0			0
$253$	4.43824	−	3.22457i	0.279030	−	0.202727i
$254$		0			0
$255$	0.591773			0.0370583
$256$		0			0
$257$	−11.7087	+	20.2801i	−0.730369	+	1.26504i	0.226357	+	0.974044i	$0.427318\pi$
$257$	−11.7087	+	20.2801i	−0.730369	+	1.26504i	−0.956726	+	0.290991i	$0.906015\pi$
$258$		0			0
$259$	16.1831	−	7.20519i	1.00557	−	0.447709i
$260$		0			0
$261$	−0.279991	−	0.124660i	−0.0173310	−	0.00771625i
$262$		0			0
$263$	17.6616	−	19.6152i	1.08906	−	1.20952i	0.112641	−	0.993636i	$-0.464069\pi$
$263$	17.6616	−	19.6152i	1.08906	−	1.20952i	0.976418	−	0.215887i	$-0.0692643\pi$
$264$		0			0
$265$	0.380809	−	0.659581i	0.0233929	−	0.0405177i
$266$		0			0
$267$	−3.02554	+	2.19819i	−0.185160	+	0.134527i
$268$		0			0
$269$	−4.64195	+	0.986677i	−0.283025	+	0.0601588i	−0.347237	−	0.937778i	$-0.612880\pi$
$269$	−4.64195	+	0.986677i	−0.283025	+	0.0601588i	0.0642120	+	0.997936i	$0.479547\pi$
$270$		0			0
$271$	−11.2328	−	8.16109i	−0.682343	−	0.495751i	0.191791	−	0.981436i	$-0.438570\pi$
$271$	−11.2328	−	8.16109i	−0.682343	−	0.495751i	−0.874134	+	0.485685i	$0.838570\pi$
$272$		0			0
$273$	−15.8487	−	27.4507i	−0.959205	−	1.66139i
$274$		0			0
$275$	−22.9788	+	4.88429i	−1.38567	+	0.294534i
$276$		0			0
$277$	−1.21913	−	3.75209i	−0.0732503	−	0.225441i	0.907728	−	0.419559i	$-0.137815\pi$
$277$	−1.21913	−	3.75209i	−0.0732503	−	0.225441i	−0.980978	+	0.194118i	$0.937815\pi$
$278$		0			0
$279$	0.616705	−	0.684921i	0.0369212	−	0.0410051i
$280$		0			0
$281$	−2.90963	+	8.95492i	−0.173574	+	0.534206i	−0.999565	−	0.0294768i	$-0.990616\pi$
$281$	−2.90963	+	8.95492i	−0.173574	+	0.534206i	0.825991	+	0.563683i	$0.190616\pi$
$282$		0			0
$283$	3.98967	+	0.848030i	0.237161	+	0.0504102i	0.324959	−	0.945728i	$-0.394650\pi$
$283$	3.98967	+	0.848030i	0.237161	+	0.0504102i	−0.0877976	+	0.996138i	$0.527983\pi$
$284$		0			0
$285$	−0.968895	+	2.98195i	−0.0573924	+	0.176636i
$286$		0			0
$287$	−40.8292	+	18.1783i	−2.41007	+	1.07303i
$288$		0			0
$289$	−11.0467	−	12.2686i	−0.649808	−	0.721685i
$290$		0			0
$291$	−8.89364	−	15.4042i	−0.521354	−	0.903012i
$292$		0			0
$293$	2.73326	−	26.0052i	0.159679	−	1.51924i	−0.562072	−	0.827089i	$-0.689995\pi$
$293$	2.73326	−	26.0052i	0.159679	−	1.51924i	0.721750	−	0.692154i	$-0.243338\pi$
$294$		0			0
$295$	−0.203926	+	1.94022i	−0.0118730	+	0.112964i
$296$		0			0
$297$	−21.7836	−	15.8267i	−1.26401	−	0.918357i
$298$		0			0
$299$	−0.516179	−	4.91112i	−0.0298514	−	0.284017i
$300$		0			0
$301$	−3.96800	−	1.76667i	−0.228712	−	0.101829i
$302$		0			0
$303$	6.65565	+	1.41470i	0.382357	+	0.0812725i
$304$		0			0
$305$	1.49937	−	3.73000i	0.0858537	−	0.213579i
$306$		0			0
$307$	−4.15488	−	0.883148i	−0.237132	−	0.0504039i	0.0878127	−	0.996137i	$-0.472012\pi$
$307$	−4.15488	−	0.883148i	−0.237132	−	0.0504039i	−0.324945	+	0.945733i	$0.605346\pi$
$308$		0			0
$309$	−9.63271	−	4.28876i	−0.547986	−	0.243979i
$310$		0			0
$311$	−0.209676	−	1.99494i	−0.0118897	−	0.113123i	0.986967	−	0.160921i	$-0.0514463\pi$
$311$	−0.209676	−	1.99494i	−0.0118897	−	0.113123i	−0.998857	+	0.0477980i	$0.984780\pi$
$312$		0			0
$313$	−23.4278	−	17.0213i	−1.32422	−	0.962099i	−0.999869	−	0.0161608i	$-0.994856\pi$
$313$	−23.4278	−	17.0213i	−1.32422	−	0.962099i	−0.324346	−	0.945938i	$-0.605144\pi$
$314$		0			0
$315$	0.0715457	−	0.680712i	0.00403114	−	0.0383538i
$316$		0			0
$317$	−1.41458	+	13.4589i	−0.0794509	+	0.755925i	0.880176	+	0.474648i	$0.157425\pi$
$317$	−1.41458	+	13.4589i	−0.0794509	+	0.755925i	−0.959627	+	0.281277i	$0.909242\pi$
$318$		0			0
$319$	2.47303	+	4.28342i	0.138463	+	0.239826i
$320$		0			0
$321$	14.4025	+	15.9956i	0.803871	+	0.892789i
$322$		0			0
$323$	−2.37616	+	1.05793i	−0.132213	+	0.0588650i
$324$		0			0
$325$	−6.53459	+	20.1114i	−0.362474	+	1.11558i
$326$		0			0
$327$	26.1538	+	5.55917i	1.44631	+	0.307423i
$328$		0			0
$329$	14.3937	−	44.2991i	0.793548	−	2.44229i
$330$		0			0
$331$	−8.12318	+	9.02171i	−0.446491	+	0.495878i	−0.923810	−	0.382852i	$-0.874942\pi$
$331$	−8.12318	+	9.02171i	−0.446491	+	0.495878i	0.477319	+	0.878730i	$0.341609\pi$
$332$		0			0
$333$	−0.389077	−	1.19745i	−0.0213213	−	0.0656201i
$334$		0			0
$335$	3.91286	−	0.831704i	0.213782	−	0.0454408i
$336$		0			0
$337$	3.23410	+	5.60163i	0.176173	+	0.305140i	0.940567	−	0.339609i	$-0.110295\pi$
$337$	3.23410	+	5.60163i	0.176173	+	0.305140i	−0.764394	+	0.644750i	$0.776962\pi$
$338$		0			0
$339$	0.735097	+	0.534079i	0.0399250	+	0.0290072i
$340$		0			0
$341$	−14.5485	+	3.09238i	−0.787845	+	0.167462i
$342$		0			0
$343$	−16.4797	+	11.9732i	−0.889820	+	0.646492i
$344$		0			0
$345$	−0.466959	+	0.808796i	−0.0251402	+	0.0435441i
$346$		0			0
$347$	22.7618	−	25.2795i	1.22192	−	1.35708i	0.307889	−	0.951422i	$-0.400378\pi$
$347$	22.7618	−	25.2795i	1.22192	−	1.35708i	0.914027	−	0.405653i	$-0.132956\pi$
$348$		0			0
$349$	25.0361	+	11.1468i	1.34015	+	0.596675i	0.946536	−	0.322599i	$-0.104557\pi$
$349$	25.0361	+	11.1468i	1.34015	+	0.596675i	0.393618	+	0.919274i	$0.371223\pi$
$350$		0			0
$351$	−22.1419	+	9.85819i	−1.18185	+	0.526191i
$352$		0			0
$353$	1.92005	−	3.32563i	0.102194	−	0.177005i	−0.810394	−	0.585885i	$-0.800747\pi$
$353$	1.92005	−	3.32563i	0.102194	−	0.177005i	0.912588	+	0.408880i	$0.134080\pi$
$354$		0			0
$355$	3.73716			0.198348
$356$		0			0
$357$	−4.02321	+	2.92304i	−0.212931	+	0.154703i
$358$		0			0
$359$	4.40364	+	4.89074i	0.232415	+	0.258123i	0.848060	−	0.529901i	$-0.177771\pi$
$359$	4.40364	+	4.89074i	0.232415	+	0.258123i	−0.615644	+	0.788024i	$0.711104\pi$
$360$		0			0
$361$	0.545523	+	5.19030i	0.0287117	+	0.273174i
$362$		0			0
$363$	6.90355	+	21.2469i	0.362342	+	1.11518i
$364$		0			0
$365$	2.22789			0.116613
$366$		0			0
$367$	0.258455			0.0134912			0.00674562	−	0.999977i	$-0.497853\pi$
$367$	0.258455			0.0134912			0.00674562	+	0.999977i	$0.497853\pi$
$368$		0			0
$369$	0.981620	+	3.02112i	0.0511011	+	0.157273i
$370$		0			0
$371$	0.669010	+	6.36520i	0.0347333	+	0.330465i
$372$		0			0
$373$	−1.12011	−	1.24401i	−0.0579972	−	0.0644125i	0.713448	−	0.700708i	$-0.247132\pi$
$373$	−1.12011	−	1.24401i	−0.0579972	−	0.0644125i	−0.771445	+	0.636296i	$0.780466\pi$
$374$		0			0
$375$	6.65195	−	4.83292i	0.343505	−	0.249571i
$376$		0			0
$377$	4.45218			0.229299
$378$		0			0
$379$	−15.9264	+	27.5854i	−0.818086	+	1.41697i	0.0890053	+	0.996031i	$0.471631\pi$
$379$	−15.9264	+	27.5854i	−0.818086	+	1.41697i	−0.907091	+	0.420935i	$0.861702\pi$
$380$		0			0
$381$	32.5088	−	14.4738i	1.66548	−	0.741517i
$382$		0			0
$383$	2.24352	+	0.998878i	0.114638	+	0.0510403i	0.463254	−	0.886225i	$-0.346682\pi$
$383$	2.24352	+	0.998878i	0.114638	+	0.0510403i	−0.348616	+	0.937266i	$0.613348\pi$
$384$		0			0
$385$	−7.39106	+	8.20860i	−0.376683	+	0.418349i
$386$		0			0
$387$	−0.154359	+	0.267358i	−0.00784652	+	0.0135906i
$388$		0			0
$389$	−14.8048	+	10.7563i	−0.750632	+	0.545366i	−0.896023	−	0.444009i	$-0.853556\pi$
$389$	−14.8048	+	10.7563i	−0.750632	+	0.545366i	0.145391	+	0.989374i	$0.453556\pi$
$390$		0			0
$391$	−0.757815	+	0.161079i	−0.0383243	+	0.00814609i
$392$		0			0
$393$	18.1768	+	13.2062i	0.916900	+	0.666167i
$394$		0			0
$395$	−4.37100	−	7.57079i	−0.219929	−	0.380928i
$396$		0			0
$397$	−8.25091	+	1.75379i	−0.414101	+	0.0880200i	−0.410251	−	0.911973i	$-0.634559\pi$
$397$	−8.25091	+	1.75379i	−0.414101	+	0.0880200i	−0.00385034	+	0.999993i	$0.501226\pi$
$398$		0			0
$399$	−8.14212	−	25.0589i	−0.407616	−	1.25451i
$400$		0			0
$401$	−8.94093	+	9.92991i	−0.446489	+	0.495876i	−0.923809	−	0.382853i	$-0.874941\pi$
$401$	−8.94093	+	9.92991i	−0.446489	+	0.495876i	0.477320	+	0.878729i	$0.341608\pi$
$402$		0			0
$403$	−4.13722	+	12.7331i	−0.206090	+	0.634279i
$404$		0			0
$405$	4.01929	+	0.854327i	0.199720	+	0.0424519i
$406$		0			0
$407$	−6.27888	+	19.3244i	−0.311232	+	0.957875i
$408$		0			0
$409$	−19.5222	+	8.69186i	−0.965312	+	0.429785i	−0.827991	−	0.560742i	$-0.810516\pi$
$409$	−19.5222	+	8.69186i	−0.965312	+	0.429785i	−0.137322	+	0.990527i	$0.543849\pi$
$410$		0			0
$411$	17.4728	+	19.4055i	0.861869	+	0.957203i
$412$		0			0
$413$	−8.19724	−	14.1980i	−0.403360	−	0.698640i
$414$		0			0
$415$	−0.658942	+	6.26942i	−0.0323462	+	0.307754i
$416$		0			0
$417$	−2.58976	+	24.6399i	−0.126821	+	1.20662i
$418$		0			0
$419$	−12.6029	−	9.15656i	−0.615693	−	0.447327i	0.235722	−	0.971821i	$-0.424255\pi$
$419$	−12.6029	−	9.15656i	−0.615693	−	0.447327i	−0.851414	+	0.524494i	$0.824255\pi$
$420$		0			0
$421$	−0.407205	−	3.87430i	−0.0198460	−	0.188822i	0.980108	−	0.198467i	$-0.0635964\pi$
$421$	−0.407205	−	3.87430i	−0.0198460	−	0.188822i	−0.999953	+	0.00964549i	$0.996930\pi$
$422$		0			0
$423$	−3.02440	−	1.34655i	−0.147051	−	0.0654715i
$424$		0			0
$425$	3.24514	+	0.689775i	0.157412	+	0.0334590i
$426$		0			0
$427$	8.23058	+	32.7647i	0.398306	+	1.58560i
$428$		0			0
$429$	35.5627	+	7.55908i	1.71698	+	0.364956i
$430$		0			0
$431$	23.0229	+	10.2505i	1.10897	+	0.493747i	0.877733	−	0.479149i	$-0.159055\pi$
$431$	23.0229	+	10.2505i	1.10897	+	0.493747i	0.231241	+	0.972896i	$0.425721\pi$
$432$		0			0
$433$	1.27319	+	12.1135i	0.0611854	+	0.582140i	0.981567	+	0.191119i	$0.0612115\pi$
$433$	1.27319	+	12.1135i	0.0611854	+	0.582140i	−0.920382	+	0.391021i	$0.872122\pi$
$434$		0			0
$435$	−0.681198	−	0.494919i	−0.0326609	−	0.0237296i
$436$		0			0
$437$	0.429074	−	4.08237i	0.0205254	−	0.195286i
$438$		0			0
$439$	0.165446	−	1.57411i	0.00789630	−	0.0751283i	−0.989864	−	0.142018i	$-0.954641\pi$
$439$	0.165446	−	1.57411i	0.00789630	−	0.0751283i	0.997760	+	0.0668897i	$0.0213076\pi$
$440$		0			0
$441$	1.79992	+	3.11755i	0.0857105	+	0.148455i
$442$		0			0
$443$	−11.4812	−	12.7511i	−0.545486	−	0.605824i	0.405865	−	0.913933i	$-0.366970\pi$
$443$	−11.4812	−	12.7511i	−0.545486	−	0.605824i	−0.951351	+	0.308109i	$0.900304\pi$
$444$		0			0
$445$	1.07167	−	0.477139i	0.0508021	−	0.0226185i
$446$		0			0
$447$	−3.99105	+	12.2832i	−0.188770	+	0.580975i
$448$		0			0
$449$	−3.14016	−	0.667462i	−0.148193	−	0.0314995i	0.133218	−	0.991087i	$-0.457469\pi$
$449$	−3.14016	−	0.667462i	−0.148193	−	0.0314995i	−0.281411	+	0.959587i	$0.590802\pi$
$450$		0			0
$451$	15.8413	−	48.7544i	0.745937	−	2.29576i
$452$		0			0
$453$	−6.52792	+	7.24999i	−0.306708	+	0.340634i
$454$		0			0
$455$	3.07249	+	9.45616i	0.144041	+	0.443312i
$456$		0			0
$457$	21.4594	−	4.56133i	1.00383	−	0.213370i	0.323460	−	0.946242i	$-0.395154\pi$
$457$	21.4594	−	4.56133i	1.00383	−	0.213370i	0.680366	+	0.732872i	$0.261821\pi$
$458$		0			0
$459$	1.90128	+	3.29312i	0.0887443	+	0.153710i
$460$		0			0
$461$	−28.1844	−	20.4772i	−1.31268	−	0.953718i	−0.999993	−	0.00386186i	$-0.998771\pi$
$461$	−28.1844	−	20.4772i	−1.31268	−	0.953718i	−0.312688	−	0.949856i	$-0.601229\pi$
$462$		0			0
$463$	5.53057	−	1.17556i	0.257028	−	0.0546329i	−0.0775956	−	0.996985i	$-0.524724\pi$
$463$	5.53057	−	1.17556i	0.257028	−	0.0546329i	0.334623	+	0.942352i	$0.391391\pi$
$464$		0			0
$465$	2.04846	−	1.48829i	0.0949949	−	0.0690178i
$466$		0			0
$467$	−11.7680	+	20.3828i	−0.544560	+	0.943206i	0.454074	+	0.890964i	$0.349970\pi$
$467$	−11.7680	+	20.3828i	−0.544560	+	0.943206i	−0.998634	+	0.0522420i	$0.983363\pi$
$468$		0			0
$469$	−22.4937	+	24.9818i	−1.03866	+	1.15355i
$470$		0			0
$471$	−3.63344	−	1.61771i	−0.167420	−	0.0745403i
$472$		0			0
$473$	4.55134	−	2.02639i	0.209271	−	0.0931734i
$474$		0			0
$475$	−8.78897	+	15.2229i	−0.403266	+	0.698477i
$476$		0			0
$477$	0.454903			0.0208286
$478$		0			0
$479$	−11.2149	+	8.14810i	−0.512422	+	0.372296i	−0.813742	−	0.581227i	$-0.802573\pi$
$479$	−11.2149	+	8.14810i	−0.512422	+	0.372296i	0.301320	+	0.953523i	$0.402573\pi$
$480$		0			0
$481$	12.2384	+	13.5921i	0.558021	+	0.619745i
$482$		0			0
$483$	−0.820358	−	7.80518i	−0.0373276	−	0.355148i
$484$		0			0
$485$	1.72416	+	5.30642i	0.0782901	+	0.240952i
$486$		0			0
$487$	−5.73971			−0.260091			−0.130046	−	0.991508i	$-0.541512\pi$
$487$	−5.73971			−0.260091			−0.130046	+	0.991508i	$0.541512\pi$
$488$		0			0
$489$	−12.9897			−0.587416
$490$		0			0
$491$	4.49354	+	13.8297i	0.202791	+	0.624126i	0.999797	+	0.0201545i	$0.00641581\pi$
$491$	4.49354	+	13.8297i	0.202791	+	0.624126i	−0.797006	+	0.603971i	$0.793584\pi$
$492$		0			0
$493$	−0.0730130	−	0.694673i	−0.00328834	−	0.0312865i
$494$		0			0
$495$	0.525324	+	0.583431i	0.0236116	+	0.0262233i
$496$		0			0
$497$	−25.4074	+	18.4595i	−1.13968	+	0.828023i
$498$		0			0
$499$	23.8174			1.06621			0.533107	−	0.846048i	$-0.321024\pi$
$499$	23.8174			1.06621			0.533107	+	0.846048i	$0.321024\pi$
$500$		0			0
$501$	0.114893	−	0.199000i	0.00513304	−	0.00889068i
$502$		0			0
$503$	16.4567	−	7.32698i	0.733767	−	0.326694i	−0.00561142	−	0.999984i	$-0.501786\pi$
$503$	16.4567	−	7.32698i	0.733767	−	0.326694i	0.739378	+	0.673290i	$0.235120\pi$
$504$		0			0
$505$	−1.94985	−	0.868130i	−0.0867673	−	0.0386313i
$506$		0			0
$507$	7.62473	−	8.46813i	0.338626	−	0.376083i
$508$		0			0
$509$	18.3836	−	31.8414i	0.814841	−	1.41135i	−0.0946015	−	0.995515i	$-0.530158\pi$
$509$	18.3836	−	31.8414i	0.814841	−	1.41135i	0.909442	−	0.415830i	$-0.136509\pi$
$510$		0			0
$511$	−15.1465	+	11.0046i	−0.670041	+	0.486814i
$512$		0			0
$513$	−19.7070	+	4.18885i	−0.870086	+	0.184942i
$514$		0			0
$515$	2.67585	+	1.94412i	0.117912	+	0.0856681i
$516$		0			0
$517$	26.7132	+	46.2686i	1.17485	+	2.03489i
$518$		0			0
$519$	7.54860	−	1.60450i	0.331347	−	0.0704299i
$520$		0			0
$521$	5.39496	+	16.6040i	0.236358	+	0.727434i	0.996938	+	0.0781907i	$0.0249143\pi$
$521$	5.39496	+	16.6040i	0.236358	+	0.727434i	−0.760581	+	0.649243i	$0.775086\pi$
$522$		0			0
$523$	−15.7847	+	17.5306i	−0.690215	+	0.766561i	−0.981786	−	0.189988i	$-0.939155\pi$
$523$	−15.7847	+	17.5306i	−0.690215	+	0.766561i	0.291572	+	0.956549i	$0.405822\pi$
$524$		0			0
$525$	−10.3854	+	31.9628i	−0.453254	+	1.39497i
$526$		0			0
$527$	2.05458	+	0.436715i	0.0894990	+	0.0190236i
$528$		0			0
$529$	−6.72956	+	20.7115i	−0.292590	+	0.900498i
$530$		0			0
$531$	−1.06451	+	0.473949i	−0.0461957	+	0.0205676i
$532$		0			0
$533$	−30.8768	−	34.2921i	−1.33742	−	1.48536i
$534$		0			0
$535$	−3.37586	−	5.84715i	−0.145951	−	0.252794i
$536$		0			0
$537$	−1.78786	+	17.0104i	−0.0771520	+	0.734052i
$538$		0			0
$539$	6.07246	−	57.7756i	0.261559	−	2.48857i
$540$		0			0
$541$	11.4472	+	8.31685i	0.492152	+	0.357569i	0.806011	−	0.591900i	$-0.201622\pi$
$541$	11.4472	+	8.31685i	0.492152	+	0.357569i	−0.313859	+	0.949469i	$0.601622\pi$
$542$		0			0
$543$	0.0418571	+	0.398244i	0.00179626	+	0.0170903i
$544$		0			0
$545$	−7.66208	−	3.41138i	−0.328208	−	0.146127i
$546$		0			0
$547$	−18.5115	−	3.93474i	−0.791495	−	0.168237i	−0.205613	−	0.978633i	$-0.565919\pi$
$547$	−18.5115	−	3.93474i	−0.791495	−	0.168237i	−0.585883	+	0.810396i	$0.699252\pi$
$548$		0			0
$549$	2.37717	−	0.338366i	0.101455	−	0.0144411i
$550$		0			0
$551$	3.62001	+	0.769457i	0.154218	+	0.0327800i
$552$		0			0
$553$	67.1121	+	29.8802i	2.85390	+	1.27064i
$554$		0			0
$555$	−0.361568	−	3.44009i	−0.0153477	−	0.146024i
$556$		0			0
$557$	−9.37318	−	6.81001i	−0.397154	−	0.288549i	0.371227	−	0.928542i	$-0.378937\pi$
$557$	−9.37318	−	6.81001i	−0.397154	−	0.288549i	−0.768381	+	0.639993i	$0.778937\pi$
$558$		0			0
$559$	0.468767	−	4.46002i	0.0198267	−	0.188639i
$560$		0			0
$561$	0.596235	−	5.67280i	0.0251731	−	0.239506i
$562$		0			0
$563$	−2.08561	−	3.61239i	−0.0878981	−	0.152244i	0.818724	−	0.574187i	$-0.194682\pi$
$563$	−2.08561	−	3.61239i	−0.0878981	−	0.152244i	−0.906622	+	0.421943i	$0.861348\pi$
$564$		0			0
$565$	−0.190715	−	0.211810i	−0.00802342	−	0.00891091i
$566$		0			0
$567$	−31.5454	+	14.0449i	−1.32478	+	0.589831i
$568$		0			0
$569$	6.01904	−	18.5247i	0.252331	−	0.776596i	−0.742012	−	0.670386i	$-0.766128\pi$
$569$	6.01904	−	18.5247i	0.252331	−	0.776596i	0.994344	−	0.106210i	$-0.0338715\pi$
$570$		0			0
$571$	−30.6384	−	6.51239i	−1.28218	−	0.272535i	−0.484058	−	0.875036i	$-0.660838\pi$
$571$	−30.6384	−	6.51239i	−1.28218	−	0.272535i	−0.798118	+	0.602501i	$0.794171\pi$
$572$		0			0
$573$	−2.25751	+	6.94791i	−0.0943089	+	0.290253i
$574$		0			0
$575$	−3.50343	+	3.89095i	−0.146103	+	0.162264i
$576$		0			0
$577$	−4.41815	−	13.5977i	−0.183930	−	0.566079i	0.815998	−	0.578055i	$-0.196188\pi$
$577$	−4.41815	−	13.5977i	−0.183930	−	0.566079i	−0.999928	+	0.0119757i	$0.996188\pi$
$578$		0			0
$579$	13.3539	−	2.83845i	0.554967	−	0.117962i
$580$		0			0
$581$	−26.4876	−	45.8779i	−1.09889	−	1.90334i
$582$		0			0
$583$	−5.93913	−	4.31503i	−0.245974	−	0.178710i
$584$		0			0
$585$	0.691247	−	0.146929i	0.0285796	−	0.00607477i
$586$		0			0
$587$	−12.1960	+	8.86095i	−0.503385	+	0.365730i	−0.810308	−	0.586004i	$-0.800700\pi$
$587$	−12.1960	+	8.86095i	−0.503385	+	0.365730i	0.306924	+	0.951734i	$0.400700\pi$
$588$		0			0
$589$	−5.56453	+	9.63805i	−0.229283	+	0.397129i
$590$		0			0
$591$	−9.95076	+	11.0514i	−0.409320	+	0.454596i
$592$		0			0
$593$	−29.7587	−	13.2494i	−1.22204	−	0.544089i	−0.308654	−	0.951174i	$-0.599878\pi$
$593$	−29.7587	−	13.2494i	−1.22204	−	0.544089i	−0.913390	+	0.407085i	$0.866545\pi$
$594$		0			0
$595$	1.42505	−	0.634475i	0.0584215	−	0.0260109i
$596$		0			0
$597$	−10.1232	+	17.5338i	−0.414314	+	0.717612i
$598$		0			0
$599$	−2.63264			−0.107567			−0.0537834	−	0.998553i	$-0.517128\pi$
$599$	−2.63264			−0.107567			−0.0537834	+	0.998553i	$0.517128\pi$
$600$		0			0
$601$	−16.5304	+	12.0101i	−0.674291	+	0.489901i	−0.871459	−	0.490469i	$-0.836826\pi$
$601$	−16.5304	+	12.0101i	−0.674291	+	0.489901i	0.197168	+	0.980370i	$0.436826\pi$
$602$		0			0
$603$	1.59875	+	1.77560i	0.0651063	+	0.0723079i
$604$		0			0
$605$	−0.732505	−	6.96932i	−0.0297806	−	0.283343i
$606$		0			0
$607$	11.3737	+	35.0046i	0.461644	+	1.42079i	0.863155	+	0.504939i	$0.168485\pi$
$607$	11.3737	+	35.0046i	0.461644	+	1.42079i	−0.401511	+	0.915854i	$0.631515\pi$
$608$		0			0
$609$	7.07581			0.286726
$610$		0			0
$611$	48.0916			1.94558
$612$		0			0
$613$	−4.12475	−	12.6947i	−0.166597	−	0.512733i	0.832554	−	0.553945i	$-0.186878\pi$
$613$	−4.12475	−	12.6947i	−0.166597	−	0.512733i	−0.999150	+	0.0412121i	$0.986878\pi$
$614$		0			0
$615$	0.912216	+	8.67916i	0.0367841	+	0.349977i
$616$		0			0
$617$	27.7015	+	30.7657i	1.11522	+	1.23858i	0.968396	+	0.249417i	$0.0802388\pi$
$617$	27.7015	+	30.7657i	1.11522	+	1.23858i	0.146825	+	0.989162i	$0.453094\pi$
$618$		0			0
$619$	5.12264	−	3.72182i	0.205896	−	0.149592i	−0.480059	−	0.877236i	$-0.659385\pi$
$619$	5.12264	−	3.72182i	0.205896	−	0.149592i	0.685955	+	0.727644i	$0.259385\pi$
$620$		0			0
$621$	−6.00109			−0.240816
$622$		0			0
$623$	−4.92903	+	8.53734i	−0.197478	+	0.342041i
$624$		0			0
$625$	19.2723	−	8.58059i	0.770893	−	0.343224i
$626$		0			0
$627$	27.6091	+	12.2924i	1.10260	+	0.490910i
$628$		0			0
$629$	1.92007	−	2.13245i	0.0765580	−	0.0850263i
$630$		0			0
$631$	7.15694	−	12.3962i	0.284913	−	0.493484i	−0.687675	−	0.726019i	$-0.741369\pi$
$631$	7.15694	−	12.3962i	0.284913	−	0.493484i	0.972588	+	0.232534i	$0.0747018\pi$
$632$		0			0
$633$	21.3973	−	15.5461i	0.850468	−	0.617901i
$634$		0			0
$635$	−10.9184	+	2.32079i	−0.433285	+	0.0920976i
$636$		0			0
$637$	−42.3059	−	30.7370i	−1.67622	−	1.21785i
$638$		0			0
$639$	1.11607	+	1.93310i	0.0441512	+	0.0764721i
$640$		0			0
$641$	−30.3409	+	6.44916i	−1.19839	+	0.254727i	−0.763532	−	0.645770i	$-0.776536\pi$
$641$	−30.3409	+	6.44916i	−1.19839	+	0.254727i	−0.434863	+	0.900497i	$0.643203\pi$
$642$		0			0
$643$	−6.74812	−	20.7686i	−0.266120	−	0.819033i	−0.991433	−	0.130614i	$-0.958305\pi$
$643$	−6.74812	−	20.7686i	−0.266120	−	0.819033i	0.725313	−	0.688419i	$-0.241695\pi$
$644$		0			0
$645$	−0.567513	+	0.630287i	−0.0223458	+	0.0248175i
$646$		0			0
$647$	−9.48937	+	29.2053i	−0.373066	+	1.14818i	0.571709	+	0.820457i	$0.306281\pi$
$647$	−9.48937	+	29.2053i	−0.373066	+	1.14818i	−0.944774	+	0.327721i	$0.893719\pi$
$648$		0			0
$649$	18.3937	+	3.90970i	0.722016	+	0.153469i
$650$		0			0
$651$	−6.57524	+	20.2365i	−0.257704	+	0.793131i
$652$		0			0
$653$	39.3800	−	17.5331i	1.54106	−	0.686124i	0.552027	−	0.833826i	$-0.313855\pi$
$653$	39.3800	−	17.5331i	1.54106	−	0.686124i	0.989032	+	0.147703i	$0.0471879\pi$
$654$		0			0
$655$	−4.71582	−	5.23745i	−0.184262	−	0.204644i
$656$		0			0
$657$	0.665342	+	1.15241i	0.0259575	+	0.0449597i
$658$		0			0
$659$	1.04029	−	9.89774i	0.0405241	−	0.385561i	−0.955396	−	0.295326i	$-0.904572\pi$
$659$	1.04029	−	9.89774i	0.0405241	−	0.385561i	0.995921	−	0.0902348i	$-0.0287617\pi$
$660$		0			0
$661$	3.63599	−	34.5942i	0.141424	−	1.34556i	−0.661711	−	0.749759i	$-0.730169\pi$
$661$	3.63599	−	34.5942i	0.141424	−	1.34556i	0.803134	−	0.595798i	$-0.203164\pi$
$662$		0			0
$663$	−4.15387	−	3.01797i	−0.161323	−	0.117208i
$664$		0			0
$665$	0.863923	+	8.21968i	0.0335015	+	0.318746i
$666$		0			0
$667$	1.00705	+	0.448366i	0.0389930	+	0.0173608i
$668$		0			0
$669$	18.4197	+	3.91523i	0.712147	+	0.151372i
$670$		0			0
$671$	−34.2455	−	18.1312i	−1.32203	−	0.699949i
$672$		0			0
$673$	−7.10298	−	1.50979i	−0.273800	−	0.0581980i	0.0689653	−	0.997619i	$-0.478030\pi$
$673$	−7.10298	−	1.50979i	−0.273800	−	0.0581980i	−0.342765	+	0.939421i	$0.611364\pi$
$674$		0			0
$675$	23.4763	+	10.4523i	0.903605	+	0.402311i
$676$		0			0
$677$	3.47671	+	33.0787i	0.133621	+	1.27132i	0.831671	+	0.555269i	$0.187385\pi$
$677$	3.47671	+	33.0787i	0.133621	+	1.27132i	−0.698050	+	0.716049i	$0.745949\pi$
$678$		0			0
$679$	−37.9326	−	27.5597i	−1.45572	−	1.05764i
$680$		0			0
$681$	0.935812	−	8.90366i	0.0358604	−	0.341189i
$682$		0			0
$683$	2.06982	−	19.6930i	0.0791994	−	0.753532i	−0.880792	−	0.473503i	$-0.842989\pi$
$683$	2.06982	−	19.6930i	0.0791994	−	0.753532i	0.959992	−	0.280029i	$-0.0903441\pi$
$684$		0			0
$685$	−4.09550	−	7.09362i	−0.156481	−	0.271033i
$686$		0			0
$687$	3.16859	+	3.51908i	0.120889	+	0.134261i
$688$		0			0
$689$	−6.03682	+	2.68777i	−0.229985	+	0.102396i
$690$		0			0
$691$	5.45175	−	16.7788i	0.207395	−	0.638295i	−0.792212	−	0.610246i	$-0.791071\pi$
$691$	5.45175	−	16.7788i	0.207395	−	0.638295i	0.999607	−	0.0280488i	$-0.00892937\pi$
$692$		0			0
$693$	−6.45329	−	1.37169i	−0.245140	−	0.0521061i
$694$		0			0
$695$	2.40156	−	7.39124i	0.0910963	−	0.280366i
$696$		0			0
$697$	−4.84423	+	5.38006i	−0.183488	+	0.203784i
$698$		0			0
$699$	13.7895	+	42.4399i	0.521568	+	1.60522i
$700$		0			0
$701$	−32.6174	+	6.93304i	−1.23194	+	0.261857i	−0.777479	−	0.628908i	$-0.783502\pi$
$701$	−32.6174	+	6.93304i	−1.23194	+	0.261857i	−0.454463	+	0.890766i	$0.650169\pi$
$702$		0			0
$703$	7.60177	+	13.1667i	0.286706	+	0.496590i
$704$		0			0
$705$	−7.35816	−	5.34602i	−0.277124	−	0.201343i
$706$		0			0
$707$	17.5443	−	3.72916i	0.659822	−	0.140249i
$708$		0			0
$709$	−6.99498	+	5.08215i	−0.262702	+	0.190864i	−0.711337	−	0.702851i	$-0.751910\pi$
$709$	−6.99498	+	5.08215i	−0.262702	+	0.190864i	0.448635	+	0.893715i	$0.351910\pi$
$710$		0			0
$711$	2.61073	−	4.52191i	0.0979099	−	0.169585i
$712$		0			0
$713$	−2.21811	+	2.46346i	−0.0830690	+	0.0922574i
$714$		0			0
$715$	−10.4185	−	4.63862i	−0.389631	−	0.173475i
$716$		0			0
$717$	28.9800	−	12.9027i	1.08228	−	0.481861i
$718$		0			0
$719$	−8.17938	+	14.1671i	−0.305040	+	0.528344i	−0.977270	−	0.211998i	$-0.932003\pi$
$719$	−8.17938	+	14.1671i	−0.305040	+	0.528344i	0.672231	+	0.740342i	$0.265336\pi$
$720$		0			0
$721$	−27.7949			−1.03513
$722$		0			0
$723$	7.28449	−	5.29249i	0.270913	−	0.196830i
$724$		0			0
$725$	−3.15864	−	3.50802i	−0.117309	−	0.130285i
$726$		0			0
$727$	−0.813780	−	7.74260i	−0.0301814	−	0.287157i	−0.999194	−	0.0401452i	$-0.987218\pi$
$727$	−0.813780	−	7.74260i	−0.0301814	−	0.287157i	0.969012	−	0.247012i	$-0.0794487\pi$
$728$		0			0
$729$	9.01426	+	27.7430i	0.333861	+	1.02752i
$730$		0			0
$731$	−0.703583			−0.0260229
$732$		0			0
$733$	−24.3706			−0.900149			−0.450075	−	0.892991i	$-0.648603\pi$
$733$	−24.3706			−0.900149			−0.450075	+	0.892991i	$0.648603\pi$
$734$		0			0
$735$	3.05610	+	9.40572i	0.112726	+	0.346935i
$736$		0			0
$737$	−4.03044	−	38.3470i	−0.148463	−	1.41253i
$738$		0			0
$739$	8.03446	+	8.92317i	0.295552	+	0.328244i	0.872571	−	0.488486i	$-0.162451\pi$
$739$	8.03446	+	8.92317i	0.295552	+	0.328244i	−0.577019	+	0.816731i	$0.695784\pi$
$740$		0			0
$741$	22.0086	−	15.9902i	0.808507	−	0.587415i
$742$		0			0
$743$	−43.9139			−1.61104			−0.805522	−	0.592565i	$-0.798115\pi$
$743$	−43.9139			−1.61104			−0.805522	+	0.592565i	$0.798115\pi$
$744$		0			0
$745$	2.02563	−	3.50850i	0.0742135	−	0.128541i
$746$		0			0
$747$	−3.43973	+	1.53147i	−0.125853	+	0.0560334i
$748$		0			0
$749$	51.8328	+	23.0774i	1.89393	+	0.843231i
$750$		0			0
$751$	−5.97701	+	6.63815i	−0.218104	+	0.242229i	−0.842261	−	0.539070i	$-0.818776\pi$
$751$	−5.97701	+	6.63815i	−0.218104	+	0.242229i	0.624157	+	0.781299i	$0.285443\pi$
$752$		0			0
$753$	−10.1585	+	17.5951i	−0.370198	+	0.641202i
$754$		0			0
$755$	2.47575	−	1.79874i	0.0901019	−	0.0654629i
$756$		0			0
$757$	−34.6556	+	7.36627i	−1.25958	+	0.267732i	−0.788872	−	0.614558i	$-0.789334\pi$
$757$	−34.6556	+	7.36627i	−1.25958	+	0.267732i	−0.470707	+	0.882290i	$0.656001\pi$
$758$		0			0
$759$	7.28272	+	5.29121i	0.264346	+	0.192059i
$760$		0			0
$761$	1.46472	+	2.53696i	0.0530959	+	0.0919648i	0.891352	−	0.453312i	$-0.149758\pi$
$761$	1.46472	+	2.53696i	0.0530959	+	0.0919648i	−0.838256	+	0.545277i	$0.816424\pi$
$762$		0			0
$763$	68.9416	−	14.6540i	2.49585	−	0.530510i
$764$		0			0
$765$	−0.0342613	−	0.105446i	−0.00123872	−	0.00381239i
$766$		0			0
$767$	11.3263	−	12.5792i	0.408970	−	0.454207i
$768$		0			0
$769$	9.09346	−	27.9868i	0.327918	−	1.00923i	−0.642187	−	0.766548i	$-0.721973\pi$
$769$	9.09346	−	27.9868i	0.327918	−	1.00923i	0.970106	−	0.242682i	$-0.0780271\pi$
$770$		0			0
$771$	−37.5860	−	7.98915i	−1.35363	−	0.287722i
$772$		0			0
$773$	6.02152	−	18.5323i	0.216579	−	0.666562i	−0.782459	−	0.622702i	$-0.786035\pi$
$773$	6.02152	−	18.5323i	0.216579	−	0.666562i	0.999038	−	0.0438592i	$-0.0139653\pi$
$774$		0			0
$775$	12.9680	−	5.77372i	0.465824	−	0.207398i
$776$		0			0
$777$	19.4503	+	21.6017i	0.697776	+	0.774958i
$778$		0			0
$779$	−19.1789	−	33.2188i	−0.687154	−	1.19019i
$780$		0			0
$781$	3.76534	−	35.8248i	0.134734	−	1.28191i
$782$		0			0
$783$	0.565551	−	5.38086i	0.0202112	−	0.192296i
$784$		0			0
$785$	1.00933	+	0.733318i	0.0360244	+	0.0261733i
$786$		0			0
$787$	3.03574	+	28.8832i	0.108213	+	1.02957i	0.905028	+	0.425351i	$0.139849\pi$
$787$	3.03574	+	28.8832i	0.108213	+	1.02957i	−0.796816	+	0.604222i	$0.793484\pi$
$788$		0			0
$789$	39.5669	+	17.6163i	1.40862	+	0.627157i
$790$		0			0
$791$	2.34281	+	0.497980i	0.0833009	+	0.0177061i
$792$		0			0
$793$	−29.5471	+	18.5357i	−1.04925	+	0.658220i
$794$		0			0
$795$	1.22243	+	0.259836i	0.0433552	+	0.00921544i
$796$		0			0
$797$	31.5615	+	14.0521i	1.11797	+	0.497750i	0.880690	−	0.473692i	$-0.157079\pi$
$797$	31.5615	+	14.0521i	1.11797	+	0.497750i	0.237275	+	0.971443i	$0.423746\pi$
$798$		0			0
$799$	−0.788672	−	7.50371i	−0.0279012	−	0.265462i
$800$		0			0
$801$	0.566853	+	0.411842i	0.0200288	+	0.0145517i
$802$		0			0
$803$	2.24469	−	21.3568i	0.0792134	−	0.753665i
$804$		0			0
$805$	−0.257329	+	2.44832i	−0.00906967	+	0.0862921i
$806$		0			0
$807$	−3.89358	−	6.74388i	−0.137061	−	0.237396i
$808$		0			0
$809$	−16.7210	−	18.5705i	−0.587879	−	0.652905i	0.373663	−	0.927565i	$-0.378102\pi$
$809$	−16.7210	−	18.5705i	−0.587879	−	0.652905i	−0.961542	+	0.274659i	$0.911435\pi$
$810$		0			0
$811$	21.9702	−	9.78178i	0.771479	−	0.343485i	0.0170403	−	0.999855i	$-0.494576\pi$
$811$	21.9702	−	9.78178i	0.771479	−	0.343485i	0.754439	+	0.656370i	$0.227909\pi$
$812$		0			0
$813$	7.04037	−	21.6680i	0.246916	−	0.759931i
$814$		0			0
$815$	3.98557	+	0.847159i	0.139608	+	0.0296747i
$816$		0			0
$817$	1.15196	−	3.54536i	0.0403019	−	0.124037i
$818$		0			0
$819$	−3.97375	+	4.41329i	−0.138854	+	0.154213i
$820$		0			0
$821$	1.97646	+	6.08291i	0.0689789	+	0.212295i	0.979604	−	0.200939i	$-0.0643992\pi$
$821$	1.97646	+	6.08291i	0.0689789	+	0.212295i	−0.910625	+	0.413234i	$0.864399\pi$
$822$		0			0
$823$	7.22696	−	1.53614i	0.251916	−	0.0535464i	−0.0802227	−	0.996777i	$-0.525563\pi$
$823$	7.22696	−	1.53614i	0.251916	−	0.0535464i	0.332139	+	0.943231i	$0.392230\pi$
$824$		0			0
$825$	−19.2742	−	33.3839i	−0.671041	−	1.16228i
$826$		0			0
$827$	−35.4011	−	25.7204i	−1.23102	−	0.894386i	−0.234051	−	0.972224i	$-0.575198\pi$
$827$	−35.4011	−	25.7204i	−1.23102	−	0.894386i	−0.996966	+	0.0778378i	$0.975198\pi$
$828$		0			0
$829$	7.31093	−	1.55399i	0.253919	−	0.0539722i	−0.0791933	−	0.996859i	$-0.525234\pi$
$829$	7.31093	−	1.55399i	0.253919	−	0.0539722i	0.333113	+	0.942887i	$0.391901\pi$
$830$		0			0
$831$	5.23730	−	3.80512i	0.181680	−	0.131998i
$832$		0			0
$833$	−4.10210	+	7.10504i	−0.142129	+	0.246175i
$834$		0			0
$835$	−0.0482303	+	0.0535652i	−0.00166908	+	0.00185370i
$836$		0			0
$837$	14.8635	+	6.61766i	0.513758	+	0.228740i
$838$		0			0
$839$	−28.3378	+	12.6168i	−0.978328	+	0.435580i	−0.832679	−	0.553756i	$-0.813194\pi$
$839$	−28.3378	+	12.6168i	−0.978328	+	0.435580i	−0.145650	+	0.989336i	$0.546527\pi$
$840$		0			0
$841$	14.0031	−	24.2540i	0.482864	−	0.836346i
$842$		0			0
$843$	−15.4504			−0.532139
$844$		0			0
$845$	−2.89173	+	2.10096i	−0.0994784	+	0.0722753i
$846$		0			0
$847$	39.4046	+	43.7633i	1.35396	+	1.50372i
$848$		0			0
$849$	0.699601	+	6.65626i	0.0240102	+	0.228442i
$850$		0			0
$851$	1.39940	+	4.30690i	0.0479707	+	0.147639i
$852$		0			0
$853$	7.90273			0.270584			0.135292	−	0.990806i	$-0.456803\pi$
$853$	7.90273			0.270584			0.135292	+	0.990806i	$0.456803\pi$
$854$		0			0
$855$	0.587437			0.0200899
$856$		0			0
$857$	−10.3373	−	31.8151i	−0.353117	−	1.08678i	−0.957093	−	0.289780i	$-0.906418\pi$
$857$	−10.3373	−	31.8151i	−0.353117	−	1.08678i	0.603977	−	0.797002i	$-0.293582\pi$
$858$		0			0
$859$	−2.38756	−	22.7162i	−0.0814627	−	0.775065i	−0.956642	−	0.291267i	$-0.905923\pi$
$859$	−2.38756	−	22.7162i	−0.0814627	−	0.775065i	0.875179	−	0.483799i	$-0.160743\pi$
$860$		0			0
$861$	−49.0721	−	54.5001i	−1.67237	−	1.85736i
$862$		0			0
$863$	−8.95201	+	6.50402i	−0.304730	+	0.221399i	−0.729632	−	0.683840i	$-0.760309\pi$
$863$	−8.95201	+	6.50402i	−0.304730	+	0.221399i	0.424902	+	0.905239i	$0.360309\pi$
$864$		0			0
$865$	−2.42074			−0.0823076
$866$		0			0
$867$	13.5449	−	23.4605i	0.460009	−	0.796760i
$868$		0			0
$869$	−76.9783	+	34.2730i	−2.61131	+	1.16263i
$870$		0			0
$871$	−31.7074	−	14.1170i	−1.07436	−	0.478338i
$872$		0			0
$873$	−2.22991	+	2.47656i	−0.0754710	+	0.0838190i
$874$		0			0
$875$	10.8370	−	18.7702i	0.366356	−	0.634547i
$876$		0			0
$877$	−17.5366	+	12.7411i	−0.592169	+	0.430236i	−0.843091	−	0.537771i	$-0.819266\pi$
$877$	−17.5366	+	12.7411i	−0.592169	+	0.430236i	0.250921	+	0.968007i	$0.419266\pi$
$878$		0			0
$879$	41.9695	−	8.92090i	1.41560	−	0.300894i
$880$		0			0
$881$	11.8677	+	8.62238i	0.399833	+	0.290495i	0.769473	−	0.638680i	$-0.220519\pi$
$881$	11.8677	+	8.62238i	0.399833	+	0.290495i	−0.369640	+	0.929175i	$0.620519\pi$
$882$		0			0
$883$	23.6655	+	40.9898i	0.796406	+	1.37942i	0.921942	+	0.387327i	$0.126602\pi$
$883$	23.6655	+	40.9898i	0.796406	+	1.37942i	−0.125536	+	0.992089i	$0.540065\pi$
$884$		0			0
$885$	−3.13130	+	0.665579i	−0.105258	+	0.0223732i
$886$		0			0
$887$	13.6831	+	42.1124i	0.459435	+	1.41399i	0.865849	+	0.500306i	$0.166779\pi$
$887$	13.6831	+	42.1124i	0.459435	+	1.41399i	−0.406414	+	0.913689i	$0.633221\pi$
$888$		0			0
$889$	62.7665	−	69.7092i	2.10512	−	2.33797i
$890$		0			0
$891$	12.2393	−	37.6686i	0.410031	−	1.26195i
$892$		0			0
$893$	39.1026	+	8.31152i	1.30852	+	0.278134i
$894$		0			0
$895$	1.65794	−	5.10260i	0.0554187	−	0.170561i
$896$		0			0
$897$	7.40251	−	3.29581i	0.247163	−	0.110044i
$898$		0			0
$899$	−1.99982	−	2.22102i	−0.0666977	−	0.0740753i
$900$		0			0
$901$	0.518371	+	0.897845i	0.0172695	+	0.0299116i
$902$		0			0
$903$	0.745006	−	7.08826i	0.0247922	−	0.235882i
$904$		0			0
$905$	0.0131297	−	0.124921i	0.000436446	−	0.00415251i
$906$		0			0
$907$	−12.0637	−	8.76476i	−0.400567	−	0.291029i	0.369205	−	0.929348i	$-0.379630\pi$
$907$	−12.0637	−	8.76476i	−0.400567	−	0.291029i	−0.769772	+	0.638319i	$0.779630\pi$
$908$		0			0
$909$	−0.133256	−	1.26785i	−0.00441983	−	0.0420518i
$910$		0			0
$911$	−21.0439	−	9.36935i	−0.697216	−	0.310420i	0.0273502	−	0.999626i	$-0.491293\pi$
$911$	−21.0439	−	9.36935i	−0.697216	−	0.310420i	−0.724566	+	0.689205i	$0.757960\pi$
$912$		0			0
$913$	59.4354	+	12.6334i	1.96702	+	0.418104i
$914$		0			0
$915$	6.58129	+	0.448545i	0.217571	+	0.0148284i
$916$		0			0
$917$	57.9310	+	12.3136i	1.91305	+	0.406632i
$918$		0			0
$919$	4.31186	+	1.91976i	0.142235	+	0.0633271i	0.476620	−	0.879110i	$-0.341862\pi$
$919$	4.31186	+	1.91976i	0.142235	+	0.0633271i	−0.334385	+	0.942437i	$0.608529\pi$
$920$		0			0
$921$	−0.728572	−	6.93190i	−0.0240073	−	0.228414i
$922$		0			0
$923$	−26.2325	−	19.0590i	−0.863454	−	0.627336i
$924$		0			0
$925$	2.02704	−	19.2860i	0.0666488	−	0.634121i
$926$		0			0
$927$	−0.206500	+	1.96471i	−0.00678234	+	0.0645297i
$928$		0			0
$929$	−4.78577	−	8.28919i	−0.157016	−	0.271960i	0.776775	−	0.629778i	$-0.216854\pi$
$929$	−4.78577	−	8.28919i	−0.157016	−	0.271960i	−0.933791	+	0.357818i	$0.883521\pi$
$930$		0			0
$931$	−29.0862	−	32.3034i	−0.953260	−	1.05870i
$932$		0			0
$933$	3.00696	−	1.33879i	0.0984436	−	0.0438299i
$934$		0			0
$935$	−0.552906	+	1.70167i	−0.0180819	+	0.0556505i
$936$		0			0
$937$	−40.8409	−	8.68101i	−1.33421	−	0.283596i	−0.515053	−	0.857158i	$-0.672228\pi$
$937$	−40.8409	−	8.68101i	−1.33421	−	0.283596i	−0.819162	+	0.573562i	$0.805561\pi$
$938$		0			0
$939$	14.6838	−	45.1921i	0.479188	−	1.47479i
$940$		0			0
$941$	−24.0462	+	26.7060i	−0.783884	+	0.870592i	−0.994256	−	0.107030i	$-0.965866\pi$
$941$	−24.0462	+	26.7060i	−0.783884	+	0.870592i	0.210371	+	0.977622i	$0.432533\pi$
$942$		0			0
$943$	−3.53061	−	10.8661i	−0.114972	−	0.353849i
$944$		0			0
$945$	11.8189	−	2.51219i	0.384469	−	0.0817214i
$946$		0			0
$947$	8.18167	+	14.1711i	0.265868	+	0.460498i	0.967791	−	0.251756i	$-0.0810080\pi$
$947$	8.18167	+	14.1711i	0.265868	+	0.460498i	−0.701922	+	0.712254i	$0.747675\pi$
$948$		0			0
$949$	−15.6384	−	11.3620i	−0.507644	−	0.368825i
$950$		0			0
$951$	−21.7211	+	4.61696i	−0.704355	+	0.149715i
$952$		0			0
$953$	−15.0010	+	10.8989i	−0.485931	+	0.353050i	−0.803617	−	0.595146i	$-0.797094\pi$
$953$	−15.0010	+	10.8989i	−0.485931	+	0.353050i	0.317686	+	0.948196i	$0.397094\pi$
$954$		0			0
$955$	1.14579	−	1.98456i	0.0370768	−	0.0642188i
$956$		0			0
$957$	−5.43068	+	6.03138i	−0.175549	+	0.194967i
$958$		0			0
$959$	62.8822	+	27.9970i	2.03057	+	0.904069i
$960$		0			0
$961$	−20.1095	+	8.95334i	−0.648694	+	0.288817i
$962$		0			0
$963$	2.01635	−	3.49241i	0.0649758	−	0.112541i
$964$		0			0
$965$	−4.28241			−0.137856
$966$		0			0
$967$	29.8086	−	21.6572i	0.958581	−	0.696450i	0.00575990	−	0.999983i	$-0.498167\pi$
$967$	29.8086	−	21.6572i	0.958581	−	0.696450i	0.952821	+	0.303534i	$0.0981666\pi$
$968$		0			0
$969$	−2.85587	−	3.17177i	−0.0917439	−	0.101892i
$970$		0			0
$971$	−1.51113	−	14.3774i	−0.0484944	−	0.461394i	−0.991642	−	0.129019i	$-0.958817\pi$
$971$	−1.51113	−	14.3774i	−0.0484944	−	0.461394i	0.943148	−	0.332374i	$-0.107850\pi$
$972$		0			0
$973$	20.1815	+	62.1123i	0.646990	+	1.99123i
$974$		0			0
$975$	−34.6992			−1.11126
$976$		0			0
$977$	−11.9469			−0.382214			−0.191107	−	0.981569i	$-0.561208\pi$
$977$	−11.9469			−0.382214			−0.191107	+	0.981569i	$0.561208\pi$
$978$		0			0
$979$	−3.49415	−	10.7539i	−0.111674	−	0.343696i
$980$		0			0
$981$	−0.523639	−	4.98210i	−0.0167185	−	0.159066i
$982$		0			0
$983$	−18.4945	−	20.5402i	−0.589882	−	0.655131i	0.372116	−	0.928186i	$-0.378632\pi$
$983$	−18.4945	−	20.5402i	−0.589882	−	0.655131i	−0.961998	+	0.273056i	$0.911966\pi$
$984$		0			0
$985$	3.77389	−	2.74189i	0.120246	−	0.0873639i
$986$		0			0
$987$	76.4314			2.43284
$988$		0			0
$989$	0.555186	−	0.961610i	0.0176539	−	0.0305774i
$990$		0			0
$991$	8.10721	−	3.60956i	0.257534	−	0.114662i	−0.273909	−	0.961756i	$-0.588317\pi$
$991$	8.10721	−	3.60956i	0.257534	−	0.114662i	0.531443	+	0.847094i	$0.321650\pi$
$992$		0			0
$993$	−18.1982	−	8.10237i	−0.577503	−	0.257121i
$994$		0			0
$995$	4.24955	−	4.71961i	0.134720	−	0.149622i
$996$		0			0
$997$	13.4608	−	23.3148i	0.426307	−	0.738386i	−0.570234	−	0.821482i	$-0.693148\pi$
$997$	13.4608	−	23.3148i	0.426307	−	0.738386i	0.996542	+	0.0830961i	$0.0264808\pi$
$998$		0			0
$999$	17.9819	−	13.0646i	0.568921	−	0.413345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	976.2.bw.c.321.3		32
4.3	odd	2		61.2.i.a.16.2	✓	32
12.11	even	2		549.2.bl.b.199.3		32
61.42	even	15	inner	976.2.bw.c.225.3		32
244.15	odd	30		3721.2.a.j.1.12		16
244.103	odd	30		61.2.i.a.42.2	yes	32
244.107	odd	30		3721.2.a.l.1.5		16
732.347	even	30		549.2.bl.b.469.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.16.2	✓	32	4.3	odd	2
61.2.i.a.42.2	yes	32	244.103	odd	30
549.2.bl.b.199.3		32	12.11	even	2
549.2.bl.b.469.3		32	732.347	even	30
976.2.bw.c.225.3		32	61.42	even	15	inner
976.2.bw.c.321.3		32	1.1	even	1	trivial
3721.2.a.j.1.12		16	244.15	odd	30
3721.2.a.l.1.5		16	244.107	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 976 = 2^{4} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	976.bw (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.507067 + 1.56059i) q^{3} +(-0.0538027 - 0.511898i) q^{5} +(2.89428 + 3.21442i) q^{7} +(0.248718 - 0.180704i) q^{9} -4.96132 q^{11} +(-2.23295 + 3.86759i) q^{13} +(0.771583 - 0.343531i) q^{15} +(0.640078 + 0.284981i) q^{17} +(-2.48401 + 2.75877i) q^{19} +(-3.54881 + 6.14672i) q^{21} +(-0.894569 + 0.649942i) q^{23} +(4.63159 - 0.984476i) q^{25} +(4.39068 + 3.19002i) q^{27} +(-0.498463 - 0.863364i) q^{29} +(2.93238 - 0.623298i) q^{31} +(-2.51572 - 7.74259i) q^{33} +(1.48974 - 1.65452i) q^{35} +(1.26557 - 3.89501i) q^{37} +(-7.16799 - 1.52360i) q^{39} +(-3.19296 + 9.82692i) q^{41} +(-0.917366 + 0.408438i) q^{43} +(-0.105884 - 0.117596i) q^{45} +(-5.38430 - 9.32588i) q^{47} +(-1.22396 + 11.6452i) q^{49} +(-0.120177 + 1.14341i) q^{51} +(1.19709 + 0.869735i) q^{53} +(0.266932 + 2.53969i) q^{55} +(-5.56488 - 2.47764i) q^{57} +(-3.70743 - 0.788038i) q^{59} +(6.90250 + 3.65452i) q^{61} +(1.30072 + 0.276477i) q^{63} +(2.09995 + 0.934958i) q^{65} +(0.812373 + 7.72921i) q^{67} +(-1.46790 - 1.06649i) q^{69} +(-0.758939 + 7.22082i) q^{71} +(-0.452438 + 4.30466i) q^{73} +(3.88490 + 6.72884i) q^{75} +(-14.3594 - 15.9478i) q^{77} +(15.5157 - 6.90804i) q^{79} +(-2.46694 + 7.59246i) q^{81} +(-11.9798 - 2.54638i) q^{83} +(0.111443 - 0.342987i) q^{85} +(1.09460 - 1.21568i) q^{87} +(0.704279 + 2.16755i) q^{89} +(-18.8949 + 4.01623i) q^{91} +(2.45963 + 4.26020i) q^{93} +(1.54586 + 1.12313i) q^{95} +(-10.6030 + 2.25375i) q^{97} +(-1.23397 + 0.896532i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39}+ \cdots + 31 q^{99}+O(q^{100}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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