LMFDB - Embedded newform 1148.2.r.a.81.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			81.13
Character	$\chi$	$=$	1148.81
Dual form			1148.2.r.a.737.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.388672 - 0.224400i) q^{3} +(-0.254464 - 0.440744i) q^{5} +(2.49203 - 0.888703i) q^{7} +(-1.39929 - 2.42364i) q^{9} +O(q^{10})$	\(q+(-0.388672 - 0.224400i) q^{3} +(-0.254464 - 0.440744i) q^{5} +(2.49203 - 0.888703i) q^{7} +(-1.39929 - 2.42364i) q^{9} +(-0.882455 - 0.509486i) q^{11} -1.40924i q^{13} +0.228406i q^{15} +(-1.94156 - 1.12096i) q^{17} +(-4.34088 + 2.50621i) q^{19} +(-1.16801 - 0.213797i) q^{21} +(-1.64528 - 2.84971i) q^{23} +(2.37050 - 4.10582i) q^{25} +2.60240i q^{27} +6.91177i q^{29} +(1.54680 - 2.67914i) q^{31} +(0.228657 + 0.396045i) q^{33} +(-1.02582 - 0.872204i) q^{35} +(-3.57736 - 6.19617i) q^{37} +(-0.316233 + 0.547732i) q^{39} +(-2.71980 + 5.79678i) q^{41} -4.41304 q^{43} +(-0.712137 + 1.23346i) q^{45} +(2.96410 - 1.71132i) q^{47} +(5.42042 - 4.42934i) q^{49} +(0.503085 + 0.871369i) q^{51} +(-5.47783 - 3.16263i) q^{53} +0.518582i q^{55} +2.24957 q^{57} +(2.98513 - 5.17040i) q^{59} +(-5.80910 - 10.0617i) q^{61} +(-5.64097 - 4.79623i) q^{63} +(-0.621114 + 0.358600i) q^{65} +(-6.50812 - 3.75747i) q^{67} +1.47680i q^{69} -5.32199i q^{71} +(-2.33519 + 4.04466i) q^{73} +(-1.84269 + 1.06388i) q^{75} +(-2.65188 - 0.485413i) q^{77} +(10.0035 - 5.77552i) q^{79} +(-3.61389 + 6.25944i) q^{81} +9.00110 q^{83} +1.14097i q^{85} +(1.55100 - 2.68641i) q^{87} +(-5.78365 + 3.33919i) q^{89} +(-1.25240 - 3.51187i) q^{91} +(-1.20239 + 0.694202i) q^{93} +(2.20919 + 1.27548i) q^{95} -5.65532i q^{97} +2.85167i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.388672	−	0.224400i	−0.224400	−	0.129557i	0.383586	−	0.923505i	$-0.374689\pi$
$3$	−0.388672	−	0.224400i	−0.224400	−	0.129557i	−0.607986	+	0.793948i	$0.708022\pi$
$4$		0			0
$5$	−0.254464	−	0.440744i	−0.113800	−	0.197107i	0.803500	−	0.595305i	$-0.202969\pi$
$5$	−0.254464	−	0.440744i	−0.113800	−	0.197107i	−0.917299	+	0.398199i	$0.869636\pi$
$6$		0			0
$7$	2.49203	−	0.888703i	0.941898	−	0.335898i
$7$	2.49203	−	0.888703i	0.941898	−	0.335898i
$8$		0			0
$9$	−1.39929	−	2.42364i	−0.466430	−	0.807880i
$10$		0			0
$11$	−0.882455	−	0.509486i	−0.266070	−	0.153616i	0.361030	−	0.932554i	$-0.382425\pi$
$11$	−0.882455	−	0.509486i	−0.266070	−	0.153616i	−0.627100	+	0.778938i	$0.715758\pi$
$12$		0			0
$13$		−	1.40924i		−	0.390853i	−0.980718	−	0.195426i	$-0.937391\pi$
$13$		−	1.40924i		−	0.390853i	0.980718	−	0.195426i	$-0.0626091\pi$
$14$		0			0
$15$			0.228406i			0.0589742i
$16$		0			0
$17$	−1.94156	−	1.12096i	−0.470896	−	0.271872i	0.245718	−	0.969341i	$-0.420976\pi$
$17$	−1.94156	−	1.12096i	−0.470896	−	0.271872i	−0.716615	+	0.697469i	$0.754309\pi$
$18$		0			0
$19$	−4.34088	+	2.50621i	−0.995866	+	0.574964i	−0.907023	−	0.421082i	$-0.861651\pi$
$19$	−4.34088	+	2.50621i	−0.995866	+	0.574964i	−0.0888437	+	0.996046i	$0.528317\pi$
$20$		0			0
$21$	−1.16801	−	0.213797i	−0.254880	−	0.0466543i
$22$		0			0
$23$	−1.64528	−	2.84971i	−0.343065	−	0.594206i	0.641935	−	0.766759i	$-0.278132\pi$
$23$	−1.64528	−	2.84971i	−0.343065	−	0.594206i	−0.985000	+	0.172553i	$0.944798\pi$
$24$		0			0
$25$	2.37050	−	4.10582i	0.474099	−	0.821164i
$26$		0			0
$27$			2.60240i			0.500832i
$28$		0			0
$29$			6.91177i			1.28348i	0.766921	+	0.641741i	$0.221788\pi$
$29$			6.91177i			1.28348i	−0.766921	+	0.641741i	$0.778212\pi$
$30$		0			0
$31$	1.54680	−	2.67914i	0.277813	−	0.481187i	−0.693028	−	0.720911i	$-0.743724\pi$
$31$	1.54680	−	2.67914i	0.277813	−	0.481187i	0.970841	+	0.239724i	$0.0770570\pi$
$32$		0			0
$33$	0.228657	+	0.396045i	0.0398040	+	0.0689426i
$34$		0			0
$35$	−1.02582	−	0.872204i	−0.173395	−	0.147429i
$36$		0			0
$37$	−3.57736	−	6.19617i	−0.588115	−	1.01864i	−0.994479	−	0.104933i	$-0.966537\pi$
$37$	−3.57736	−	6.19617i	−0.588115	−	1.01864i	0.406365	−	0.913711i	$-0.366796\pi$
$38$		0			0
$39$	−0.316233	+	0.547732i	−0.0506378	+	0.0877072i
$40$		0			0
$41$	−2.71980	+	5.79678i	−0.424761	+	0.905305i
$41$	−2.71980	+	5.79678i	−0.424761	+	0.905305i
$42$		0			0
$43$	−4.41304			−0.672983			−0.336492	−	0.941686i	$-0.609240\pi$
$43$	−4.41304			−0.672983			−0.336492	+	0.941686i	$0.609240\pi$
$44$		0			0
$45$	−0.712137	+	1.23346i	−0.106159	+	0.183873i
$46$		0			0
$47$	2.96410	−	1.71132i	0.432358	−	0.249622i	−0.267993	−	0.963421i	$-0.586360\pi$
$47$	2.96410	−	1.71132i	0.432358	−	0.249622i	0.700351	+	0.713799i	$0.253027\pi$
$48$		0			0
$49$	5.42042	−	4.42934i	0.774345	−	0.632764i
$50$		0			0
$51$	0.503085	+	0.871369i	0.0704460	+	0.122016i
$52$		0			0
$53$	−5.47783	−	3.16263i	−0.752438	−	0.434420i	0.0741362	−	0.997248i	$-0.476380\pi$
$53$	−5.47783	−	3.16263i	−0.752438	−	0.434420i	−0.826574	+	0.562828i	$0.809713\pi$
$54$		0			0
$55$			0.518582i			0.0699256i
$56$		0			0
$57$	2.24957			0.297963
$58$		0			0
$59$	2.98513	−	5.17040i	0.388631	−	0.673129i	−0.603634	−	0.797261i	$-0.706281\pi$
$59$	2.98513	−	5.17040i	0.388631	−	0.673129i	0.992266	+	0.124132i	$0.0396147\pi$
$60$		0			0
$61$	−5.80910	−	10.0617i	−0.743780	−	1.28826i	−0.950763	−	0.309920i	$-0.899698\pi$
$61$	−5.80910	−	10.0617i	−0.743780	−	1.28826i	0.206983	−	0.978345i	$-0.433635\pi$
$62$		0			0
$63$	−5.64097	−	4.79623i	−0.710695	−	0.604268i
$64$		0			0
$65$	−0.621114	+	0.358600i	−0.0770397	+	0.0444789i
$66$		0			0
$67$	−6.50812	−	3.75747i	−0.795094	−	0.459048i	0.0466589	−	0.998911i	$-0.485143\pi$
$67$	−6.50812	−	3.75747i	−0.795094	−	0.459048i	−0.841753	+	0.539863i	$0.818476\pi$
$68$		0			0
$69$			1.47680i			0.177786i
$70$		0			0
$71$		−	5.32199i		−	0.631604i	−0.948825	−	0.315802i	$-0.897726\pi$
$71$		−	5.32199i		−	0.631604i	0.948825	−	0.315802i	$-0.102274\pi$
$72$		0			0
$73$	−2.33519	+	4.04466i	−0.273313	+	0.473392i	−0.969708	−	0.244267i	$-0.921453\pi$
$73$	−2.33519	+	4.04466i	−0.273313	+	0.473392i	0.696395	+	0.717659i	$0.254786\pi$
$74$		0			0
$75$	−1.84269	+	1.06388i	−0.212775	+	0.122846i
$76$		0			0
$77$	−2.65188	−	0.485413i	−0.302210	−	0.0553179i
$78$		0			0
$79$	10.0035	−	5.77552i	1.12548	−	0.649796i	0.182686	−	0.983171i	$-0.441521\pi$
$79$	10.0035	−	5.77552i	1.12548	−	0.649796i	0.942794	+	0.333375i	$0.108187\pi$
$80$		0			0
$81$	−3.61389	+	6.25944i	−0.401544	+	0.695494i
$82$		0			0
$83$	9.00110			0.987999			0.493999	−	0.869462i	$-0.335535\pi$
$83$	9.00110			0.987999			0.493999	+	0.869462i	$0.335535\pi$
$84$		0			0
$85$			1.14097i			0.123756i
$86$		0			0
$87$	1.55100	−	2.68641i	0.166284	−	0.288013i
$88$		0			0
$89$	−5.78365	+	3.33919i	−0.613066	+	0.353954i	−0.774164	−	0.632985i	$-0.781830\pi$
$89$	−5.78365	+	3.33919i	−0.613066	+	0.353954i	0.161098	+	0.986938i	$0.448496\pi$
$90$		0			0
$91$	−1.25240	−	3.51187i	−0.131287	−	0.368144i
$92$		0			0
$93$	−1.20239	+	0.694202i	−0.124682	+	0.0719854i
$94$		0			0
$95$	2.20919	+	1.27548i	0.226658	+	0.130861i
$96$		0			0
$97$		−	5.65532i		−	0.574211i	−0.957899	−	0.287105i	$-0.907307\pi$
$97$		−	5.65532i		−	0.574211i	0.957899	−	0.287105i	$-0.0926930\pi$
$98$		0			0
$99$			2.85167i			0.286604i
$100$		0			0
$101$	2.20255	+	1.27164i	0.219162	+	0.126533i	0.605562	−	0.795798i	$-0.292948\pi$
$101$	2.20255	+	1.27164i	0.219162	+	0.126533i	−0.386400	+	0.922331i	$0.626282\pi$
$102$		0			0
$103$	−3.50221	−	6.06601i	−0.345083	−	0.597701i	0.640286	−	0.768137i	$-0.278816\pi$
$103$	−3.50221	−	6.06601i	−0.345083	−	0.597701i	−0.985369	+	0.170435i	$0.945483\pi$
$104$		0			0
$105$	0.202985	+	0.569195i	0.0198093	+	0.0555477i
$106$		0			0
$107$	0.800121	+	1.38585i	0.0773507	+	0.133975i	0.902106	−	0.431514i	$-0.142021\pi$
$107$	0.800121	+	1.38585i	0.0773507	+	0.133975i	−0.824755	+	0.565490i	$0.808687\pi$
$108$		0			0
$109$	−5.70600	−	3.29436i	−0.546536	−	0.315543i	0.201188	−	0.979553i	$-0.435520\pi$
$109$	−5.70600	−	3.29436i	−0.546536	−	0.315543i	−0.747724	+	0.664010i	$0.768853\pi$
$110$		0			0
$111$			3.21103i			0.304778i
$112$		0			0
$113$	−15.6722			−1.47431			−0.737157	−	0.675721i	$-0.763832\pi$
$113$	−15.6722			−1.47431			−0.737157	+	0.675721i	$0.763832\pi$
$114$		0			0
$115$	−0.837328	+	1.45030i	−0.0780813	+	0.135241i
$116$		0			0
$117$	−3.41549	+	1.97194i	−0.315762	+	0.182305i
$118$		0			0
$119$	−5.83461	−	1.06799i	−0.534858	−	0.0979028i
$120$		0			0
$121$	−4.98085	−	8.62708i	−0.452804	−	0.784280i
$122$		0			0
$123$	2.35790	−	1.64272i	0.212605	−	0.148119i
$124$		0			0
$125$	−4.95746			−0.443408
$126$		0			0
$127$	18.8221			1.67019			0.835094	−	0.550107i	$-0.185413\pi$
$127$	18.8221			1.67019			0.835094	+	0.550107i	$0.185413\pi$
$128$		0			0
$129$	1.71522	+	0.990286i	0.151017	+	0.0871898i
$130$		0			0
$131$	5.95629	+	10.3166i	0.520403	+	0.901365i	0.999719	+	0.0237221i	$0.00755169\pi$
$131$	5.95629	+	10.3166i	0.520403	+	0.901365i	−0.479315	+	0.877643i	$0.659115\pi$
$132$		0			0
$133$	−8.59033	+	10.1033i	−0.744876	+	0.876067i
$134$		0			0
$135$	1.14699	−	0.662216i	0.0987173	−	0.0569945i
$136$		0			0
$137$	−2.80750	−	1.62091i	−0.239861	−	0.138484i	0.375252	−	0.926923i	$-0.377556\pi$
$137$	−2.80750	−	1.62091i	−0.239861	−	0.138484i	−0.615113	+	0.788439i	$0.710889\pi$
$138$		0			0
$139$	19.4279			1.64785			0.823927	−	0.566696i	$-0.191778\pi$
$139$	19.4279			1.64785			0.823927	+	0.566696i	$0.191778\pi$
$140$		0			0
$141$	−1.53608			−0.129361
$142$		0			0
$143$	−0.717988	+	1.24359i	−0.0600411	+	0.103994i
$144$		0			0
$145$	3.04632	−	1.75879i	0.252983	−	0.146060i
$146$		0			0
$147$	−3.10070	+	0.505221i	−0.255742	+	0.0416699i
$148$		0			0
$149$	9.85898	−	5.69208i	0.807679	−	0.466314i	−0.0384703	−	0.999260i	$-0.512248\pi$
$149$	9.85898	−	5.69208i	0.807679	−	0.466314i	0.846149	+	0.532946i	$0.178915\pi$
$150$		0			0
$151$	4.41832	+	2.55092i	0.359558	+	0.207591i	0.668887	−	0.743364i	$-0.266771\pi$
$151$	4.41832	+	2.55092i	0.359558	+	0.207591i	−0.309329	+	0.950955i	$0.600104\pi$
$152$		0			0
$153$			6.27418i			0.507237i
$154$		0			0
$155$	−1.57442			−0.126460
$156$		0			0
$157$	10.1646	+	5.86853i	0.811222	+	0.468359i	0.847380	−	0.530987i	$-0.178179\pi$
$157$	10.1646	+	5.86853i	0.811222	+	0.468359i	−0.0361578	+	0.999346i	$0.511512\pi$
$158$		0			0
$159$	1.41938	+	2.45845i	0.112565	+	0.194967i
$160$		0			0
$161$	−6.63263	−	5.63939i	−0.522725	−	0.444446i
$162$		0			0
$163$	1.18387	+	2.05052i	0.0927275	+	0.160609i	0.908658	−	0.417541i	$-0.137108\pi$
$163$	1.18387	+	2.05052i	0.0927275	+	0.160609i	−0.815930	+	0.578150i	$0.803775\pi$
$164$		0			0
$165$	0.116370	−	0.201558i	0.00905937	−	0.0156913i
$166$		0			0
$167$			8.23143i			0.636968i	0.947928	+	0.318484i	$0.103174\pi$
$167$			8.23143i			0.636968i	−0.947928	+	0.318484i	$0.896826\pi$
$168$		0			0
$169$	11.0140			0.847234
$170$		0			0
$171$	12.1483	+	7.01382i	0.929004	+	0.536361i
$172$		0			0
$173$	5.43350	+	9.41110i	0.413101	+	0.715512i	0.995227	−	0.0975864i	$-0.0311122\pi$
$173$	5.43350	+	9.41110i	0.413101	+	0.715512i	−0.582126	+	0.813099i	$0.697779\pi$
$174$		0			0
$175$	2.25849	−	12.3385i	0.170726	−	0.932702i
$176$		0			0
$177$	−2.32047	+	1.33973i	−0.174417	+	0.100700i
$178$		0			0
$179$	0.755818	+	0.436372i	0.0564925	+	0.0326160i	0.527980	−	0.849257i	$-0.322950\pi$
$179$	0.755818	+	0.436372i	0.0564925	+	0.0326160i	−0.471488	+	0.881873i	$0.656283\pi$
$180$		0			0
$181$			22.0726i			1.64064i	0.571904	+	0.820321i	$0.306205\pi$
$181$			22.0726i			1.64064i	−0.571904	+	0.820321i	$0.693795\pi$
$182$		0			0
$183$			5.21424i			0.385448i
$184$		0			0
$185$	−1.82062	+	3.15340i	−0.133854	+	0.231843i
$186$		0			0
$187$	1.14222	+	1.97839i	0.0835277	+	0.144674i
$188$		0			0
$189$	2.31276	+	6.48525i	0.168228	+	0.471733i
$190$		0			0
$191$	3.28746	−	1.89802i	0.237872	−	0.137336i	−0.376326	−	0.926487i	$-0.622813\pi$
$191$	3.28746	−	1.89802i	0.237872	−	0.137336i	0.614198	+	0.789152i	$0.289479\pi$
$192$		0			0
$193$	−7.77333	−	4.48793i	−0.559536	−	0.323049i	0.193423	−	0.981115i	$-0.438041\pi$
$193$	−7.77333	−	4.48793i	−0.559536	−	0.323049i	−0.752959	+	0.658067i	$0.771374\pi$
$194$		0			0
$195$	0.321879			0.0230502
$196$		0			0
$197$	−5.48477			−0.390773			−0.195387	−	0.980726i	$-0.562596\pi$
$197$	−5.48477			−0.390773			−0.195387	+	0.980726i	$0.562596\pi$
$198$		0			0
$199$	−6.95903	−	4.01780i	−0.493313	−	0.284814i	0.232635	−	0.972564i	$-0.425265\pi$
$199$	−6.95903	−	4.01780i	−0.493313	−	0.284814i	−0.725948	+	0.687750i	$0.758599\pi$
$200$		0			0
$201$	1.68635	+	2.92084i	0.118946	+	0.206020i
$202$		0			0
$203$	6.14250	+	17.2243i	0.431119	+	1.20891i
$204$		0			0
$205$	3.24699	−	0.276336i	0.226779	−	0.0193001i
$206$		0			0
$207$	−4.60445	+	7.97514i	−0.320031	+	0.554310i
$208$		0			0
$209$	5.10751			0.353294
$210$		0			0
$211$		−	13.9612i		−	0.961131i	−0.876959	−	0.480565i	$-0.840431\pi$
$211$		−	13.9612i		−	0.961131i	0.876959	−	0.480565i	$-0.159569\pi$
$212$		0			0
$213$	−1.19425	+	2.06851i	−0.0818289	+	0.141732i
$214$		0			0
$215$	1.12296	+	1.94502i	0.0765852	+	0.132649i
$216$		0			0
$217$	1.47371	−	8.05113i	0.100042	−	0.546546i
$218$		0			0
$219$	1.81524	−	1.04803i	0.122663	−	0.0708193i
$220$		0			0
$221$	−1.57970	+	2.73612i	−0.106262	+	0.184051i
$222$		0			0
$223$	14.1402			0.946899			0.473449	−	0.880821i	$-0.343009\pi$
$223$	14.1402			0.946899			0.473449	+	0.880821i	$0.343009\pi$
$224$		0			0
$225$	−13.2680			−0.884536
$226$		0			0
$227$	21.5785	+	12.4583i	1.43221	+	0.826889i	0.997290	−	0.0735774i	$-0.0234416\pi$
$227$	21.5785	+	12.4583i	1.43221	+	0.826889i	0.434925	+	0.900467i	$0.356775\pi$
$228$		0			0
$229$	−10.7632	+	6.21413i	−0.711251	+	0.410641i	−0.811524	−	0.584319i	$-0.801362\pi$
$229$	−10.7632	+	6.21413i	−0.711251	+	0.410641i	0.100273	+	0.994960i	$0.468028\pi$
$230$		0			0
$231$	0.921786	+	0.783748i	0.0606490	+	0.0515668i
$232$		0			0
$233$	12.6007	−	7.27499i	0.825496	−	0.476600i	−0.0268120	−	0.999640i	$-0.508536\pi$
$233$	12.6007	−	7.27499i	0.825496	−	0.476600i	0.852308	+	0.523040i	$0.175202\pi$
$234$		0			0
$235$	−1.50851	−	0.870939i	−0.0984044	−	0.0568138i
$236$		0			0
$237$	−5.18409			−0.336743
$238$		0			0
$239$		−	21.3128i		−	1.37861i	−0.724472	−	0.689304i	$-0.757916\pi$
$239$		−	21.3128i		−	1.37861i	0.724472	−	0.689304i	$-0.242084\pi$
$240$		0			0
$241$	5.75644	−	9.97045i	0.370805	−	0.642253i	−0.618885	−	0.785482i	$-0.712415\pi$
$241$	5.75644	−	9.97045i	0.370805	−	0.642253i	0.989690	+	0.143229i	$0.0457485\pi$
$242$		0			0
$243$	9.57046	−	5.52551i	0.613945	−	0.354462i
$244$		0			0
$245$	−3.33151	−	1.26191i	−0.212842	−	0.0806204i
$246$		0			0
$247$	3.53185	+	6.11734i	0.224726	+	0.389237i
$248$		0			0
$249$	−3.49847	−	2.01984i	−0.221707	−	0.128002i
$250$		0			0
$251$	−15.8627			−1.00125			−0.500623	−	0.865665i	$-0.666896\pi$
$251$	−15.8627			−1.00125			−0.500623	+	0.865665i	$0.666896\pi$
$252$		0			0
$253$			3.35299i			0.210801i
$254$		0			0
$255$	0.256034	−	0.443463i	0.0160335	−	0.0277708i
$256$		0			0
$257$	21.5981	−	12.4697i	1.34725	−	0.777837i	0.359393	−	0.933186i	$-0.382984\pi$
$257$	21.5981	−	12.4697i	1.34725	−	0.777837i	0.987860	+	0.155349i	$0.0496504\pi$
$258$		0			0
$259$	−14.4214	−	12.2618i	−0.896105	−	0.761913i
$260$		0			0
$261$	16.7516	−	9.67156i	1.03690	−	0.598655i
$262$		0			0
$263$	−4.35497	−	2.51434i	−0.268539	−	0.155041i	0.359684	−	0.933074i	$-0.382884\pi$
$263$	−4.35497	−	2.51434i	−0.268539	−	0.155041i	−0.628224	+	0.778033i	$0.716218\pi$
$264$		0			0
$265$			3.21909i			0.197747i
$266$		0			0
$267$	2.99725			0.183429
$268$		0			0
$269$	−8.49118	+	14.7072i	−0.517716	+	0.896711i	0.482072	+	0.876132i	$0.339884\pi$
$269$	−8.49118	+	14.7072i	−0.517716	+	0.896711i	−0.999788	+	0.0205793i	$0.993449\pi$
$270$		0			0
$271$	9.95931	+	17.2500i	0.604985	+	1.04786i	0.992054	+	0.125814i	$0.0401542\pi$
$271$	9.95931	+	17.2500i	0.604985	+	1.04786i	−0.387069	+	0.922051i	$0.626512\pi$
$272$		0			0
$273$	−0.301291	+	1.64600i	−0.0182350	+	0.0996204i
$274$		0			0
$275$	−4.18371	+	2.41547i	−0.252287	+	0.145658i
$276$		0			0
$277$	−2.12358	+	3.67815i	−0.127594	+	0.220999i	−0.922744	−	0.385414i	$-0.874059\pi$
$277$	−2.12358	+	3.67815i	−0.127594	+	0.220999i	0.795150	+	0.606413i	$0.207392\pi$
$278$		0			0
$279$	−8.65768			−0.518322
$280$		0			0
$281$			33.3591i			1.99003i	0.0997034	+	0.995017i	$0.468211\pi$
$281$			33.3591i			1.99003i	−0.0997034	+	0.995017i	$0.531789\pi$
$282$		0			0
$283$	−7.86000	+	13.6139i	−0.467228	+	0.809263i	−0.999299	−	0.0374366i	$-0.988081\pi$
$283$	−7.86000	+	13.6139i	−0.467228	+	0.809263i	0.532071	+	0.846700i	$0.321414\pi$
$284$		0			0
$285$	−0.572434	−	0.991484i	−0.0339080	−	0.0587304i
$286$		0			0
$287$	−1.62620	+	16.8628i	−0.0959916	+	0.995382i
$288$		0			0
$289$	−5.98691	−	10.3696i	−0.352171	−	0.609978i
$290$		0			0
$291$	−1.26905	+	2.19806i	−0.0743931	+	0.128853i
$292$		0			0
$293$			5.27842i			0.308369i	0.988042	+	0.154184i	$0.0492749\pi$
$293$			5.27842i			0.308369i	−0.988042	+	0.154184i	$0.950725\pi$
$294$		0			0
$295$	−3.03843			−0.176904
$296$		0			0
$297$	1.32588	−	2.29650i	0.0769356	−	0.133256i
$298$		0			0
$299$	−4.01593	+	2.31860i	−0.232247	+	0.134088i
$300$		0			0
$301$	−10.9974	+	3.92188i	−0.633882	+	0.226054i
$302$		0			0
$303$	−0.570713	−	0.988504i	−0.0327866	−	0.0567881i
$304$		0			0
$305$	−2.95641	+	5.12066i	−0.169284	+	0.293208i
$306$		0			0
$307$	20.9635			1.19645			0.598226	−	0.801327i	$-0.295872\pi$
$307$	20.9635			1.19645			0.598226	+	0.801327i	$0.295872\pi$
$308$		0			0
$309$			3.14358i			0.178832i
$310$		0			0
$311$	13.3397	+	7.70167i	0.756424	+	0.436722i	0.828011	−	0.560713i	$-0.189473\pi$
$311$	13.3397	+	7.70167i	0.756424	+	0.436722i	−0.0715860	+	0.997434i	$0.522806\pi$
$312$		0			0
$313$	−22.8781	+	13.2087i	−1.29314	+	0.746597i	−0.979210	−	0.202848i	$-0.934980\pi$
$313$	−22.8781	+	13.2087i	−1.29314	+	0.746597i	−0.313934	+	0.949445i	$0.601647\pi$
$314$		0			0
$315$	−0.678489	+	3.70669i	−0.0382285	+	0.208848i
$316$		0			0
$317$	27.2409	−	15.7276i	1.53000	−	0.883348i	0.530642	−	0.847596i	$-0.321951\pi$
$317$	27.2409	−	15.7276i	1.53000	−	0.883348i	0.999361	−	0.0357517i	$-0.0113825\pi$
$318$		0			0
$319$	3.52145	−	6.09932i	0.197163	−	0.341496i
$320$		0			0
$321$		−	0.718188i		−	0.0400853i
$322$		0			0
$323$	11.2374			0.625267
$324$		0			0
$325$	−5.78609	−	3.34060i	−0.320954	−	0.185303i
$326$		0			0
$327$	1.47851	+	2.56085i	0.0817616	+	0.141615i
$328$		0			0
$329$	5.86576	−	6.89887i	0.323390	−	0.380347i
$330$		0			0
$331$	7.68246	−	4.43547i	0.422266	−	0.243796i	−0.273780	−	0.961792i	$-0.588274\pi$
$331$	7.68246	−	4.43547i	0.422266	−	0.243796i	0.696047	+	0.717997i	$0.254941\pi$
$332$		0			0
$333$	−10.0115	+	17.3405i	−0.548628	+	0.950252i
$334$		0			0
$335$			3.82456i			0.208958i
$336$		0			0
$337$	14.3050			0.779241			0.389620	−	0.920976i	$-0.372606\pi$
$337$	14.3050			0.779241			0.389620	+	0.920976i	$0.372606\pi$
$338$		0			0
$339$	6.09133	+	3.51683i	0.330836	+	0.191008i
$340$		0			0
$341$	−2.72996	+	1.57614i	−0.147836	+	0.0853530i
$342$		0			0
$343$	9.57146	−	15.8552i	0.516810	−	0.856100i
$344$		0			0
$345$	0.650891	−	0.375792i	0.0350428	−	0.0202320i
$346$		0			0
$347$	−14.3580	−	8.28958i	−0.770777	−	0.445008i	0.0623750	−	0.998053i	$-0.480133\pi$
$347$	−14.3580	−	8.28958i	−0.770777	−	0.445008i	−0.833152	+	0.553045i	$0.813466\pi$
$348$		0			0
$349$	1.46139			0.0782262			0.0391131	−	0.999235i	$-0.487547\pi$
$349$	1.46139			0.0782262			0.0391131	+	0.999235i	$0.487547\pi$
$350$		0			0
$351$	3.66740			0.195752
$352$		0			0
$353$	10.6436	−	18.4353i	0.566504	−	0.981214i	−0.430404	−	0.902636i	$-0.641629\pi$
$353$	10.6436	−	18.4353i	0.566504	−	0.981214i	0.996908	−	0.0785773i	$-0.0250378\pi$
$354$		0			0
$355$	−2.34564	+	1.35425i	−0.124493	+	0.0718763i
$356$		0			0
$357$	2.02809	+	1.72438i	0.107338	+	0.0912640i
$358$		0			0
$359$	4.99333	+	8.64870i	0.263538	+	0.456461i	0.967180	−	0.254094i	$-0.0817773\pi$
$359$	4.99333	+	8.64870i	0.263538	+	0.456461i	−0.703642	+	0.710555i	$0.748444\pi$
$360$		0			0
$361$	3.06216	−	5.30382i	0.161167	−	0.279149i
$362$		0			0
$363$			4.47080i			0.234656i
$364$		0			0
$365$	2.37688			0.124412
$366$		0			0
$367$	2.18805	−	3.78981i	0.114215	−	0.197826i	−0.803251	−	0.595641i	$-0.796898\pi$
$367$	2.18805	−	3.78981i	0.114215	−	0.197826i	0.917466	+	0.397815i	$0.130231\pi$
$368$		0			0
$369$	17.8551	−	1.51956i	0.929500	−	0.0791053i
$370$		0			0
$371$	−16.4615	−	3.01320i	−0.854641	−	0.156437i
$372$		0			0
$373$	1.53887	+	2.66539i	0.0796794	+	0.138009i	0.903112	−	0.429406i	$-0.141277\pi$
$373$	1.53887	+	2.66539i	0.0796794	+	0.138009i	−0.823432	+	0.567415i	$0.807944\pi$
$374$		0			0
$375$	1.92682	+	1.11245i	0.0995007	+	0.0574467i
$376$		0			0
$377$	9.74034			0.501653
$378$		0			0
$379$	−8.81629			−0.452863			−0.226431	−	0.974027i	$-0.572706\pi$
$379$	−8.81629			−0.452863			−0.226431	+	0.974027i	$0.572706\pi$
$380$		0			0
$381$	−7.31560	−	4.22367i	−0.374790	−	0.216385i
$382$		0			0
$383$	−15.2296	+	8.79284i	−0.778198	+	0.449293i	−0.835791	−	0.549047i	$-0.814991\pi$
$383$	−15.2296	+	8.79284i	−0.778198	+	0.449293i	0.0575930	+	0.998340i	$0.481657\pi$
$384$		0			0
$385$	0.460865	+	1.29232i	0.0234879	+	0.0658628i
$386$		0			0
$387$	6.17513	+	10.6956i	0.313899	+	0.543690i
$388$		0			0
$389$	−18.3315	+	31.7511i	−0.929444	+	1.60984i	−0.145190	+	0.989404i	$0.546379\pi$
$389$	−18.3315	+	31.7511i	−0.929444	+	1.60984i	−0.784254	+	0.620440i	$0.786954\pi$
$390$		0			0
$391$			7.37716i			0.373079i
$392$		0			0
$393$		−	5.34635i		−	0.269688i
$394$		0			0
$395$	−5.09105	−	2.93932i	−0.256158	−	0.147893i
$396$		0			0
$397$	5.15533	−	2.97643i	0.258739	−	0.149383i	−0.365020	−	0.931000i	$-0.618938\pi$
$397$	5.15533	−	2.97643i	0.258739	−	0.149383i	0.623759	+	0.781617i	$0.285605\pi$
$398$		0			0
$399$	5.60599	−	1.99920i	0.280651	−	0.100085i
$400$		0			0
$401$	−8.62280	−	14.9351i	−0.430602	−	0.745825i	0.566323	−	0.824183i	$-0.308365\pi$
$401$	−8.62280	−	14.9351i	−0.430602	−	0.745825i	−0.996925	+	0.0783584i	$0.975032\pi$
$402$		0			0
$403$	−3.77554	−	2.17981i	−0.188073	−	0.108584i
$404$		0			0
$405$	3.67842			0.182782
$406$		0			0
$407$			7.29046i			0.361375i
$408$		0			0
$409$	9.09806	−	15.7583i	0.449870	−	0.779197i	−0.548507	−	0.836146i	$-0.684804\pi$
$409$	9.09806	−	15.7583i	0.449870	−	0.779197i	0.998377	+	0.0569483i	$0.0181370\pi$
$410$		0			0
$411$	0.727463	+	1.26000i	0.0358831	+	0.0621513i
$412$		0			0
$413$	2.84409	−	15.5377i	0.139948	−	0.764560i
$414$		0			0
$415$	−2.29045	−	3.96718i	−0.112434	−	0.194741i
$416$		0			0
$417$	−7.55108	−	4.35962i	−0.369778	−	0.213491i
$418$		0			0
$419$	23.8021			1.16281			0.581405	−	0.813614i	$-0.302503\pi$
$419$	23.8021			1.16281			0.581405	+	0.813614i	$0.302503\pi$
$420$		0			0
$421$			14.5776i			0.710468i	0.934777	+	0.355234i	$0.115599\pi$
$421$			14.5776i			0.710468i	−0.934777	+	0.355234i	$0.884401\pi$
$422$		0			0
$423$	−8.29526	−	4.78927i	−0.403330	−	0.232862i
$424$		0			0
$425$	−9.20490	+	5.31445i	−0.446503	+	0.257789i
$426$		0			0
$427$	−23.4183	−	19.9114i	−1.13329	−	0.963580i
$428$		0			0
$429$	0.558123	−	0.322232i	0.0269464	−	0.0155575i
$430$		0			0
$431$	−7.06852	+	12.2430i	−0.340478	+	0.589726i	−0.984522	−	0.175263i	$-0.943922\pi$
$431$	−7.06852	+	12.2430i	−0.340478	+	0.589726i	0.644043	+	0.764989i	$0.277256\pi$
$432$		0			0
$433$	12.8398			0.617040			0.308520	−	0.951218i	$-0.400166\pi$
$433$	12.8398			0.617040			0.308520	+	0.951218i	$0.400166\pi$
$434$		0			0
$435$	−1.57869			−0.0756924
$436$		0			0
$437$	14.2839	+	8.24683i	0.683293	+	0.394500i
$438$		0			0
$439$	−12.4021	+	7.16037i	−0.591921	+	0.341746i	−0.765857	−	0.643011i	$-0.777685\pi$
$439$	−12.4021	+	7.16037i	−0.591921	+	0.341746i	0.173935	+	0.984757i	$0.444352\pi$
$440$		0			0
$441$	−18.3199	−	6.93920i	−0.872375	−	0.330438i
$442$		0			0
$443$	−16.0420	−	27.7856i	−0.762178	−	1.32013i	−0.941726	−	0.336382i	$-0.890797\pi$
$443$	−16.0420	−	27.7856i	−0.762178	−	1.32013i	0.179547	−	0.983749i	$-0.442537\pi$
$444$		0			0
$445$	2.94346	+	1.69941i	0.139533	+	0.0805596i
$446$		0			0
$447$	−5.10920			−0.241657
$448$		0			0
$449$	4.12348			0.194599			0.0972996	−	0.995255i	$-0.468979\pi$
$449$	4.12348			0.194599			0.0972996	+	0.995255i	$0.468979\pi$
$450$		0			0
$451$	5.35348	−	3.72970i	0.252085	−	0.175625i
$452$		0			0
$453$	−1.14485	−	1.98294i	−0.0537898	−	0.0931667i
$454$		0			0
$455$	−1.22915	+	1.44563i	−0.0576232	+	0.0677721i
$456$		0			0
$457$	19.8136	−	11.4394i	0.926842	−	0.535112i	0.0410306	−	0.999158i	$-0.486936\pi$
$457$	19.8136	−	11.4394i	0.926842	−	0.535112i	0.885811	+	0.464045i	$0.153603\pi$
$458$		0			0
$459$	2.91718	−	5.05270i	0.136162	−	0.235840i
$460$		0			0
$461$	−34.9186			−1.62632			−0.813161	−	0.582039i	$-0.802255\pi$
$461$	−34.9186			−1.62632			−0.813161	+	0.582039i	$0.802255\pi$
$462$		0			0
$463$		−	6.91285i		−	0.321267i	−0.987014	−	0.160634i	$-0.948646\pi$
$463$		−	6.91285i		−	0.321267i	0.987014	−	0.160634i	$-0.0513538\pi$
$464$		0			0
$465$	0.611931	+	0.353299i	0.0283776	+	0.0163838i
$466$		0			0
$467$	−9.44440	−	16.3582i	−0.437035	−	0.756967i	0.560424	−	0.828206i	$-0.310638\pi$
$467$	−9.44440	−	16.3582i	−0.437035	−	0.756967i	−0.997459	+	0.0712389i	$0.977305\pi$
$468$		0			0
$469$	−19.5577	−	3.57993i	−0.903091	−	0.165306i
$470$		0			0
$471$	−2.63379	−	4.56186i	−0.121359	−	0.210199i
$472$		0			0
$473$	3.89431	+	2.24838i	0.179061	+	0.103381i
$474$		0			0
$475$			23.7638i			1.09036i
$476$		0			0
$477$			17.7017i			0.810506i
$478$		0			0
$479$	−3.91013	−	2.25751i	−0.178658	−	0.103148i	0.408004	−	0.912980i	$-0.366225\pi$
$479$	−3.91013	−	2.25751i	−0.178658	−	0.103148i	−0.586662	+	0.809832i	$0.699558\pi$
$480$		0			0
$481$	−8.73189	+	5.04136i	−0.398140	+	0.229866i
$482$		0			0
$483$	1.31244	+	3.68023i	0.0597180	+	0.167456i
$484$		0			0
$485$	−2.49255	+	1.43907i	−0.113181	+	0.0653449i
$486$		0			0
$487$	11.5836	−	20.0634i	0.524902	−	0.909157i	−0.474677	−	0.880160i	$-0.657435\pi$
$487$	11.5836	−	20.0634i	0.524902	−	0.909157i	0.999579	−	0.0289973i	$-0.00923143\pi$
$488$		0			0
$489$		−	1.06264i		−	0.0480541i
$490$		0			0
$491$	4.66008			0.210306			0.105153	−	0.994456i	$-0.466467\pi$
$491$	4.66008			0.210306			0.105153	+	0.994456i	$0.466467\pi$
$492$		0			0
$493$	7.74780	−	13.4196i	0.348943	−	0.604387i
$494$		0			0
$495$	1.25686	−	0.725647i	0.0564915	−	0.0326154i
$496$		0			0
$497$	−4.72967	−	13.2626i	−0.212155	−	0.594907i
$498$		0			0
$499$	33.2815	−	19.2151i	1.48988	−	0.860185i	0.489951	−	0.871750i	$-0.337015\pi$
$499$	33.2815	−	19.2151i	1.48988	−	0.860185i	0.999933	+	0.0115647i	$0.00368124\pi$
$500$		0			0
$501$	1.84713	−	3.19932i	0.0825237	−	0.142935i
$502$		0			0
$503$		−	12.8469i		−	0.572814i	−0.958108	−	0.286407i	$-0.907539\pi$
$503$		−	12.8469i		−	0.572814i	0.958108	−	0.286407i	$-0.0924609\pi$
$504$		0			0
$505$		−	1.29435i		−	0.0575978i
$506$		0			0
$507$	−4.28084	−	2.47155i	−0.190119	−	0.109765i
$508$		0			0
$509$	−15.1807	+	8.76458i	−0.672872	+	0.388483i	−0.797164	−	0.603763i	$-0.793667\pi$
$509$	−15.1807	+	8.76458i	−0.672872	+	0.388483i	0.124292	+	0.992246i	$0.460334\pi$
$510$		0			0
$511$	−2.22485	+	12.1547i	−0.0984216	+	0.537692i
$512$		0			0
$513$	−6.52215	−	11.2967i	−0.287960	−	0.498761i
$514$		0			0
$515$	−1.78237	+	3.08716i	−0.0785406	+	0.136036i
$516$		0			0
$517$	−3.48758			−0.153384
$518$		0			0
$519$		−	4.87710i		−	0.214081i
$520$		0			0
$521$	−29.2216	−	16.8711i	−1.28022	−	0.739136i	−0.303332	−	0.952885i	$-0.598099\pi$
$521$	−29.2216	−	16.8711i	−1.28022	−	0.739136i	−0.976889	+	0.213749i	$0.931432\pi$
$522$		0			0
$523$	−4.46527	−	7.73407i	−0.195253	−	0.338187i	0.751731	−	0.659470i	$-0.229219\pi$
$523$	−4.46527	−	7.73407i	−0.195253	−	0.338187i	−0.946983	+	0.321283i	$0.895886\pi$
$524$		0			0
$525$	−3.64656	+	4.28881i	−0.159149	+	0.187179i
$526$		0			0
$527$	−6.00639	+	3.46779i	−0.261643	+	0.151059i
$528$		0			0
$529$	6.08610	−	10.5414i	0.264613	−	0.458324i
$530$		0			0
$531$	−16.7083			−0.725077
$532$		0			0
$533$	8.16906	+	3.83285i	0.353841	+	0.166019i
$534$		0			0
$535$	0.407204	−	0.705297i	0.0176049	−	0.0304927i
$536$		0			0
$537$	−0.195843	−	0.339211i	−0.00845126	−	0.0146380i
$538$		0			0
$539$	−7.03996	+	1.14707i	−0.303233	+	0.0494080i
$540$		0			0
$541$	−10.6850	−	18.5070i	−0.459384	−	0.795676i	0.539544	−	0.841957i	$-0.318596\pi$
$541$	−10.6850	−	18.5070i	−0.459384	−	0.795676i	−0.998928	+	0.0462807i	$0.985263\pi$
$542$		0			0
$543$	4.95308	−	8.57898i	0.212557	−	0.368159i
$544$		0			0
$545$			3.35318i			0.143634i
$546$		0			0
$547$		−	22.6517i		−	0.968516i	−0.874925	−	0.484258i	$-0.839090\pi$
$547$		−	22.6517i		−	0.968516i	0.874925	−	0.484258i	$-0.160910\pi$
$548$		0			0
$549$	−16.2572	+	28.1584i	−0.693842	+	1.20177i
$550$		0			0
$551$	−17.3223	−	30.0031i	−0.737956	−	1.27818i
$552$		0			0
$553$	19.7963	−	23.2829i	0.841823	−	0.990089i
$554$		0			0
$555$	1.41524	−	0.817091i	0.0600738	−	0.0346836i
$556$		0			0
$557$	−7.04524	−	4.06757i	−0.298516	−	0.172349i	0.343260	−	0.939241i	$-0.388469\pi$
$557$	−7.04524	−	4.06757i	−0.298516	−	0.172349i	−0.641776	+	0.766892i	$0.721802\pi$
$558$		0			0
$559$			6.21904i			0.263037i
$560$		0			0
$561$		−	1.02526i		−	0.0432864i
$562$		0			0
$563$	21.2222	+	12.2527i	0.894410	+	0.516388i	0.875382	−	0.483431i	$-0.160610\pi$
$563$	21.2222	+	12.2527i	0.894410	+	0.516388i	0.0190275	+	0.999819i	$0.493943\pi$
$564$		0			0
$565$	3.98800	+	6.90742i	0.167776	+	0.290597i
$566$		0			0
$567$	−3.44314	+	18.8104i	−0.144598	+	0.789962i
$568$		0			0
$569$	10.7321	+	18.5886i	0.449915	+	0.779275i	0.998380	−	0.0568983i	$-0.0181211\pi$
$569$	10.7321	+	18.5886i	0.449915	+	0.779275i	−0.548465	+	0.836173i	$0.684788\pi$
$570$		0			0
$571$	−14.1907	−	8.19301i	−0.593863	−	0.342867i	0.172761	−	0.984964i	$-0.444731\pi$
$571$	−14.1907	−	8.19301i	−0.593863	−	0.342867i	−0.766623	+	0.642097i	$0.778065\pi$
$572$		0			0
$573$	−1.70366			−0.0711713
$574$		0			0
$575$	−15.6005			−0.650587
$576$		0			0
$577$	−19.1965	−	11.0831i	−0.799160	−	0.461396i	0.0440170	−	0.999031i	$-0.485984\pi$
$577$	−19.1965	−	11.0831i	−0.799160	−	0.461396i	−0.843178	+	0.537635i	$0.819318\pi$
$578$		0			0
$579$	2.01418	+	3.48866i	0.0837065	+	0.144984i
$580$		0			0
$581$	22.4310	−	7.99930i	0.930594	−	0.331867i
$582$		0			0
$583$	3.22263	+	5.58175i	0.133468	+	0.231173i
$584$		0			0
$585$	1.73824	+	1.00357i	0.0718673	+	0.0414926i
$586$		0			0
$587$			35.3490i			1.45901i	0.683976	+	0.729505i	$0.260249\pi$
$587$			35.3490i			1.45901i	−0.683976	+	0.729505i	$0.739751\pi$
$588$		0			0
$589$			15.5064i			0.638930i
$590$		0			0
$591$	2.13177	+	1.23078i	0.0876894	+	0.0506275i
$592$		0			0
$593$	−22.0054	+	12.7048i	−0.903652	+	0.521724i	−0.878383	−	0.477957i	$-0.841377\pi$
$593$	−22.0054	+	12.7048i	−0.903652	+	0.521724i	−0.0252686	+	0.999681i	$0.508044\pi$
$594$		0			0
$595$	1.01398	+	2.84334i	0.0415693	+	0.116565i
$596$		0			0
$597$	1.80319	+	3.12321i	0.0737995	+	0.127824i
$598$		0			0
$599$	0.720711	−	1.24831i	0.0294474	−	0.0510045i	−0.850926	−	0.525285i	$-0.823959\pi$
$599$	0.720711	−	1.24831i	0.0294474	−	0.0510045i	0.880374	+	0.474281i	$0.157292\pi$
$600$		0			0
$601$		−	3.24956i		−	0.132552i	−0.997801	−	0.0662761i	$-0.978888\pi$
$601$		−	3.24956i		−	0.132552i	0.997801	−	0.0662761i	$-0.0211118\pi$
$602$		0			0
$603$			21.0311i			0.856454i
$604$		0			0
$605$	−2.53489	+	4.39056i	−0.103058	+	0.178502i
$606$		0			0
$607$	2.57785	+	4.46496i	0.104632	+	0.181227i	0.913588	−	0.406642i	$-0.133300\pi$
$607$	2.57785	+	4.46496i	0.104632	+	0.181227i	−0.808956	+	0.587869i	$0.799967\pi$
$608$		0			0
$609$	1.47771	−	8.07298i	0.0598800	−	0.327134i
$610$		0			0
$611$	−2.41167	−	4.17713i	−0.0975655	−	0.168988i
$612$		0			0
$613$	20.1517	−	34.9038i	0.813920	−	1.40975i	−0.0961808	−	0.995364i	$-0.530663\pi$
$613$	20.1517	−	34.9038i	0.813920	−	1.40975i	0.910101	−	0.414387i	$-0.136004\pi$
$614$		0			0
$615$	−1.32402	−	0.621219i	−0.0533897	−	0.0250500i
$616$		0			0
$617$	20.9382			0.842941			0.421471	−	0.906842i	$-0.361514\pi$
$617$	20.9382			0.842941			0.421471	+	0.906842i	$0.361514\pi$
$618$		0			0
$619$	23.0343	−	39.8967i	0.925828	−	1.60358i	0.135605	−	0.990763i	$-0.456702\pi$
$619$	23.0343	−	39.8967i	0.925828	−	1.60358i	0.790223	−	0.612819i	$-0.209964\pi$
$620$		0			0
$621$	7.41608	−	4.28167i	0.297597	−	0.171818i
$622$		0			0
$623$	−11.4455	+	13.4613i	−0.458553	+	0.539316i
$624$		0			0
$625$	−10.5910	−	18.3441i	−0.423640	−	0.733765i
$626$		0			0
$627$	−1.98514	−	1.14612i	−0.0792790	−	0.0457717i
$628$		0			0
$629$			16.0403i			0.639568i
$630$		0			0
$631$	0.500050			0.0199067			0.00995334	−	0.999950i	$-0.496832\pi$
$631$	0.500050			0.0199067			0.00995334	+	0.999950i	$0.496832\pi$
$632$		0			0
$633$	−3.13290	+	5.42633i	−0.124521	+	0.215677i
$634$		0			0
$635$	−4.78953	−	8.29571i	−0.190067	−	0.329205i
$636$		0			0
$637$	−6.24201	−	7.63867i	−0.247317	−	0.302655i
$638$		0			0
$639$	−12.8986	+	7.44701i	−0.510261	+	0.294599i
$640$		0			0
$641$	−40.8721	−	23.5975i	−1.61435	−	0.932045i	−0.988346	−	0.152225i	$-0.951356\pi$
$641$	−40.8721	−	23.5975i	−1.61435	−	0.932045i	−0.626004	−	0.779820i	$-0.715311\pi$
$642$		0			0
$643$		−	1.80147i		−	0.0710429i	−0.999369	−	0.0355214i	$-0.988691\pi$
$643$		−	1.80147i		−	0.0710429i	0.999369	−	0.0355214i	$-0.0113092\pi$
$644$		0			0
$645$		−	1.00797i		−	0.0396887i
$646$		0			0
$647$	12.7793	−	22.1344i	0.502405	−	0.870191i	−0.497591	−	0.867412i	$-0.665782\pi$
$647$	12.7793	−	22.1344i	0.502405	−	0.870191i	0.999996	−	0.00277937i	$-0.000884702\pi$
$648$		0			0
$649$	−5.26849	+	3.04177i	−0.206806	+	0.119400i
$650$		0			0
$651$	−2.37946	+	2.79854i	−0.0932584	+	0.109684i
$652$		0			0
$653$	21.9191	−	12.6550i	0.857762	−	0.495229i	−0.00550011	−	0.999985i	$-0.501751\pi$
$653$	21.9191	−	12.6550i	0.857762	−	0.495229i	0.863262	+	0.504756i	$0.168417\pi$
$654$		0			0
$655$	3.03132	−	5.25040i	0.118443	−	0.205150i
$656$		0			0
$657$	13.0704			0.509925
$658$		0			0
$659$			26.4332i			1.02969i	0.857282	+	0.514846i	$0.172151\pi$
$659$			26.4332i			1.02969i	−0.857282	+	0.514846i	$0.827849\pi$
$660$		0			0
$661$	8.13897	−	14.0971i	0.316569	−	0.548314i	−0.663200	−	0.748442i	$-0.730802\pi$
$661$	8.13897	−	14.0971i	0.316569	−	0.548314i	0.979770	+	0.200128i	$0.0641356\pi$
$662$		0			0
$663$	1.22797	−	0.708968i	0.0476903	−	0.0275340i
$664$		0			0
$665$	6.63889	+	1.21521i	0.257445	+	0.0471239i
$666$		0			0
$667$	19.6965	−	11.3718i	0.762652	−	0.440318i
$668$		0			0
$669$	−5.49590	−	3.17306i	−0.212484	−	0.122678i
$670$		0			0
$671$			11.8386i			0.457025i
$672$		0			0
$673$		−	7.89988i		−	0.304518i	−0.988341	−	0.152259i	$-0.951345\pi$
$673$		−	7.89988i		−	0.304518i	0.988341	−	0.152259i	$-0.0486548\pi$
$674$		0			0
$675$	10.6850	+	6.16897i	0.411265	+	0.237444i
$676$		0			0
$677$	13.4754	+	23.3401i	0.517902	+	0.897033i	0.999784	+	0.0207966i	$0.00662023\pi$
$677$	13.4754	+	23.3401i	0.517902	+	0.897033i	−0.481882	+	0.876236i	$0.660046\pi$
$678$		0			0
$679$	−5.02590	−	14.0932i	−0.192876	−	0.540848i
$680$		0			0
$681$	−5.59129	−	9.68441i	−0.214259	−	0.371107i
$682$		0			0
$683$	−10.1822	−	5.87868i	−0.389610	−	0.224941i	0.292381	−	0.956302i	$-0.405552\pi$
$683$	−10.1822	−	5.87868i	−0.389610	−	0.224941i	−0.681991	+	0.731361i	$0.738886\pi$
$684$		0			0
$685$			1.64985i			0.0630375i
$686$		0			0
$687$	5.57779			0.212806
$688$		0			0
$689$	−4.45690	+	7.71958i	−0.169794	+	0.294093i
$690$		0			0
$691$	−1.34549	+	0.776817i	−0.0511847	+	0.0295515i	−0.525374	−	0.850871i	$-0.676075\pi$
$691$	−1.34549	+	0.776817i	−0.0511847	+	0.0295515i	0.474189	+	0.880423i	$0.342741\pi$
$692$		0			0
$693$	2.53429	+	7.10645i	0.0962696	+	0.269952i
$694$		0			0
$695$	−4.94370	−	8.56274i	−0.187525	−	0.324803i
$696$		0			0
$697$	11.7786	−	8.20600i	0.446146	−	0.310824i
$698$		0			0
$699$	−6.53002			−0.246988
$700$		0			0
$701$	−8.73706			−0.329994			−0.164997	−	0.986294i	$-0.552761\pi$
$701$	−8.73706			−0.329994			−0.164997	+	0.986294i	$0.552761\pi$
$702$		0			0
$703$	31.0578	+	17.9312i	1.17137	+	0.676289i
$704$		0			0
$705$	0.390877	+	0.677018i	0.0147213	+	0.0254980i
$706$		0			0
$707$	6.61894	+	1.21156i	0.248931	+	0.0455654i
$708$		0			0
$709$	−37.0719	+	21.4034i	−1.39226	+	0.803823i	−0.993565	−	0.113259i	$-0.963871\pi$
$709$	−37.0719	+	21.4034i	−1.39226	+	0.803823i	−0.398698	+	0.917082i	$0.630538\pi$
$710$		0			0
$711$	−27.9956	−	16.1632i	−1.04992	−	0.606169i
$712$		0			0
$713$	−10.1797			−0.381232
$714$		0			0
$715$	0.730807			0.0273306
$716$		0			0
$717$	−4.78258	+	8.28366i	−0.178609	+	0.309359i
$718$		0			0
$719$	43.0834	−	24.8742i	1.60674	−	0.927651i	0.616646	−	0.787240i	$-0.288491\pi$
$719$	43.0834	−	24.8742i	1.60674	−	0.927651i	0.990093	−	0.140411i	$-0.0448424\pi$
$720$		0			0
$721$	−14.1185	−	12.0042i	−0.525800	−	0.447061i
$722$		0			0
$723$	−4.47473	+	2.58349i	−0.166417	+	0.0960809i
$724$		0			0
$725$	28.3785	+	16.3843i	1.05395	+	0.608498i
$726$		0			0
$727$		−	14.3225i		−	0.531191i	−0.964084	−	0.265596i	$-0.914431\pi$
$727$		−	14.3225i		−	0.531191i	0.964084	−	0.265596i	$-0.0855686\pi$
$728$		0			0
$729$	16.7237			0.619395
$730$		0			0
$731$	8.56817	+	4.94684i	0.316905	+	0.182965i
$732$		0			0
$733$	4.41157	+	7.64107i	0.162945	+	0.282229i	0.935924	−	0.352203i	$-0.114567\pi$
$733$	4.41157	+	7.64107i	0.162945	+	0.282229i	−0.772978	+	0.634432i	$0.781234\pi$
$734$		0			0
$735$	1.01169	+	1.23806i	0.0373167	+	0.0456664i
$736$		0			0
$737$	3.82875	+	6.63159i	0.141034	+	0.244278i
$738$		0			0
$739$	−21.1964	+	36.7133i	−0.779723	+	1.35052i	0.152378	+	0.988322i	$0.451307\pi$
$739$	−21.1964	+	36.7133i	−0.779723	+	1.35052i	−0.932101	+	0.362198i	$0.882027\pi$
$740$		0			0
$741$		−	3.17018i		−	0.116460i
$742$		0			0
$743$	−28.2183			−1.03523			−0.517614	−	0.855614i	$-0.673180\pi$
$743$	−28.2183			−1.03523			−0.517614	+	0.855614i	$0.673180\pi$
$744$		0			0
$745$	−5.01750	−	2.89686i	−0.183827	−	0.106133i
$746$		0			0
$747$	−12.5951	−	21.8154i	−0.460832	−	0.798185i
$748$		0			0
$749$	3.22553	+	2.74251i	0.117858	+	0.100209i
$750$		0			0
$751$	−40.7986	+	23.5551i	−1.48876	+	0.859536i	−0.999918	−	0.0128356i	$-0.995914\pi$
$751$	−40.7986	+	23.5551i	−1.48876	+	0.859536i	−0.488843	+	0.872372i	$0.662581\pi$
$752$		0			0
$753$	6.16539	+	3.55959i	0.224679	+	0.129719i
$754$		0			0
$755$		−	2.59647i		−	0.0944951i
$756$		0			0
$757$		−	36.3981i		−	1.32291i	−0.749984	−	0.661456i	$-0.769939\pi$
$757$		−	36.3981i		−	1.32291i	0.749984	−	0.661456i	$-0.230061\pi$
$758$		0			0
$759$	0.752409	−	1.30321i	0.0273107	−	0.0473035i
$760$		0			0
$761$	−5.17831	−	8.96910i	−0.187714	−	0.325129i	0.756774	−	0.653677i	$-0.226774\pi$
$761$	−5.17831	−	8.96910i	−0.187714	−	0.325129i	−0.944488	+	0.328547i	$0.893441\pi$
$762$		0			0
$763$	−17.1472	−	3.13871i	−0.620771	−	0.113629i
$764$		0			0
$765$	2.76531	−	1.59655i	0.0999799	−	0.0577234i
$766$		0			0
$767$	−7.28634	−	4.20677i	−0.263094	−	0.151898i
$768$		0			0
$769$	7.67648			0.276821			0.138410	−	0.990375i	$-0.455801\pi$
$769$	7.67648			0.276821			0.138410	+	0.990375i	$0.455801\pi$
$770$		0			0
$771$	−11.1928			−0.403097
$772$		0			0
$773$	−22.5087	−	12.9954i	−0.809581	−	0.467412i	0.0372293	−	0.999307i	$-0.488147\pi$
$773$	−22.5087	−	12.9954i	−0.809581	−	0.467412i	−0.846810	+	0.531895i	$0.821480\pi$
$774$		0			0
$775$	−7.33336	−	12.7018i	−0.263422	−	0.456261i
$776$		0			0
$777$	2.85365	+	8.00199i	0.102374	+	0.287070i
$778$		0			0
$779$	−2.72163	−	31.9795i	−0.0975123	−	1.14579i
$780$		0			0
$781$	−2.71148	+	4.69642i	−0.0970244	+	0.168051i
$782$		0			0
$783$	−17.9872			−0.642809
$784$		0			0
$785$		−	5.97331i		−	0.213196i
$786$		0			0
$787$	−0.0807940	+	0.139939i	−0.00288000	+	0.00498830i	−0.867462	−	0.497504i	$-0.834250\pi$
$787$	−0.0807940	+	0.139939i	−0.00288000	+	0.00498830i	0.864582	+	0.502492i	$0.167583\pi$
$788$		0			0
$789$	1.12844	+	1.95451i	0.0401734	+	0.0695823i
$790$		0			0
$791$	−39.0555	+	13.9279i	−1.38865	+	0.495219i
$792$		0			0
$793$	−14.1793	+	8.18642i	−0.503522	+	0.290708i
$794$		0			0
$795$	0.722364	−	1.25117i	0.0256196	−	0.0443744i
$796$		0			0
$797$	21.6388			0.766484			0.383242	−	0.923648i	$-0.374807\pi$
$797$	21.6388			0.766484			0.383242	+	0.923648i	$0.374807\pi$
$798$		0			0
$799$	−7.67328			−0.271461
$800$		0			0
$801$	16.1860	+	9.34500i	0.571905	+	0.330189i
$802$		0			0
$803$	4.12140	−	2.37949i	0.145441	−	0.0839703i
$804$		0			0
$805$	−0.797765	+	4.35831i	−0.0281175	+	0.153610i
$806$		0			0
$807$	6.60056	−	3.81083i	0.232351	−	0.134148i
$808$		0			0
$809$	7.23554	+	4.17744i	0.254388	+	0.146871i	0.621772	−	0.783198i	$-0.286413\pi$
$809$	7.23554	+	4.17744i	0.254388	+	0.146871i	−0.367384	+	0.930069i	$0.619746\pi$
$810$		0			0
$811$	−8.19209			−0.287663			−0.143832	−	0.989602i	$-0.545942\pi$
$811$	−8.19209			−0.287663			−0.143832	+	0.989602i	$0.545942\pi$
$812$		0			0
$813$		−	8.93946i		−	0.313521i
$814$		0			0
$815$	0.602502	−	1.04356i	0.0211047	−	0.0365544i
$816$		0			0
$817$	19.1565	−	11.0600i	0.670201	−	0.386941i
$818$		0			0
$819$	−6.75904	+	7.94948i	−0.236180	+	0.277777i
$820$		0			0
$821$	−2.45863	−	4.25846i	−0.0858066	−	0.148621i	0.819928	−	0.572467i	$-0.194013\pi$
$821$	−2.45863	−	4.25846i	−0.0858066	−	0.148621i	−0.905735	+	0.423845i	$0.860680\pi$
$822$		0			0
$823$	29.1445	+	16.8266i	1.01591	+	0.586538i	0.912918	−	0.408144i	$-0.133824\pi$
$823$	29.1445	+	16.8266i	1.01591	+	0.586538i	0.102996	+	0.994682i	$0.467157\pi$
$824$		0			0
$825$	2.16812			0.0754843
$826$		0			0
$827$		−	20.7296i		−	0.720838i	−0.932790	−	0.360419i	$-0.882634\pi$
$827$		−	20.7296i		−	0.720838i	0.932790	−	0.360419i	$-0.117366\pi$
$828$		0			0
$829$	−4.63083	+	8.02084i	−0.160835	+	0.278575i	−0.935169	−	0.354203i	$-0.884752\pi$
$829$	−4.63083	+	8.02084i	−0.160835	+	0.278575i	0.774333	+	0.632778i	$0.218086\pi$
$830$		0			0
$831$	1.65075	−	0.953062i	0.0572640	−	0.0330614i
$832$		0			0
$833$	−15.4891	+	2.52376i	−0.536667	+	0.0874432i
$834$		0			0
$835$	3.62796	−	2.09460i	0.125551	−	0.0724867i
$836$		0			0
$837$	6.97218	+	4.02539i	0.240994	+	0.139138i
$838$		0			0
$839$		−	5.17113i		−	0.178527i	−0.996008	−	0.0892637i	$-0.971549\pi$
$839$		−	5.17113i		−	0.178527i	0.996008	−	0.0892637i	$-0.0284514\pi$
$840$		0			0
$841$	−18.7725			−0.647327
$842$		0			0
$843$	7.48576	−	12.9657i	0.257823	−	0.446563i
$844$		0			0
$845$	−2.80267	−	4.85437i	−0.0964149	−	0.166996i
$846$		0			0
$847$	−20.0793	−	17.0724i	−0.689934	−	0.586616i
$848$		0			0
$849$	6.10992	−	3.52756i	0.209692	−	0.121066i
$850$		0			0
$851$	−11.7715	+	20.3889i	−0.403523	+	0.698922i
$852$		0			0
$853$	32.5617			1.11489			0.557446	−	0.830213i	$-0.311781\pi$
$853$	32.5617			1.11489			0.557446	+	0.830213i	$0.311781\pi$
$854$		0			0
$855$		−	7.13905i		−	0.244150i
$856$		0			0
$857$	12.2700	−	21.2523i	0.419137	−	0.725966i	−0.576716	−	0.816945i	$-0.695666\pi$
$857$	12.2700	−	21.2523i	0.419137	−	0.725966i	0.995853	+	0.0909783i	$0.0289994\pi$
$858$		0			0
$859$	9.46526	+	16.3943i	0.322950	+	0.559366i	0.981095	−	0.193525i	$-0.0619920\pi$
$859$	9.46526	+	16.3943i	0.322950	+	0.559366i	−0.658145	+	0.752891i	$0.728659\pi$
$860$		0			0
$861$	4.41607	−	6.18919i	0.150499	−	0.210927i
$862$		0			0
$863$	28.3697	+	49.1378i	0.965716	+	1.67267i	0.707680	+	0.706534i	$0.249742\pi$
$863$	28.3697	+	49.1378i	0.965716	+	1.67267i	0.258036	+	0.966135i	$0.416925\pi$
$864$		0			0
$865$	2.76526	−	4.78956i	0.0940215	−	0.162850i
$866$		0			0
$867$			5.37384i			0.182505i
$868$		0			0
$869$	−11.7702			−0.399276
$870$		0			0
$871$	−5.29517	+	9.17151i	−0.179420	+	0.310765i
$872$		0			0
$873$	−13.7065	+	7.91343i	−0.463893	+	0.267829i
$874$		0			0
$875$	−12.3541	+	4.40571i	−0.417646	+	0.148940i
$876$		0			0
$877$	6.71470	+	11.6302i	0.226739	+	0.392724i	0.956840	−	0.290616i	$-0.0938601\pi$
$877$	6.71470	+	11.6302i	0.226739	+	0.392724i	−0.730100	+	0.683340i	$0.760527\pi$
$878$		0			0
$879$	1.18448	−	2.05157i	0.0399514	−	0.0691978i
$880$		0			0
$881$	33.6227			1.13278			0.566388	−	0.824139i	$-0.308340\pi$
$881$	33.6227			1.13278			0.566388	+	0.824139i	$0.308340\pi$
$882$		0			0
$883$		−	27.4822i		−	0.924848i	−0.886659	−	0.462424i	$-0.846980\pi$
$883$		−	27.4822i		−	0.924848i	0.886659	−	0.462424i	$-0.153020\pi$
$884$		0			0
$885$	1.18095	+	0.681823i	0.0396973	+	0.0229192i
$886$		0			0
$887$	−33.4489	+	19.3117i	−1.12310	+	0.648425i	−0.942192	−	0.335074i	$-0.891239\pi$
$887$	−33.4489	+	19.3117i	−1.12310	+	0.648425i	−0.180913	+	0.983499i	$0.557905\pi$
$888$		0			0
$889$	46.9051	−	16.7272i	1.57315	−	0.561013i
$890$		0			0
$891$	6.37819	−	3.68245i	0.213678	−	0.123367i
$892$		0			0
$893$	−8.57787	+	14.8573i	−0.287047	+	0.497181i
$894$		0			0
$895$		−	0.444163i		−	0.0148467i
$896$		0			0
$897$	2.08117			0.0694882
$898$		0			0
$899$	18.5176	+	10.6911i	0.617595	+	0.356569i
$900$		0			0
$901$	7.09034	+	12.2808i	0.236214	+	0.409134i
$902$		0			0
$903$	5.15446	+	0.943495i	0.171530	+	0.0313976i
$904$		0			0
$905$	9.72835	−	5.61667i	0.323381	−	0.186704i
$906$		0			0
$907$	−4.55421	+	7.88812i	−0.151220	+	0.261921i	−0.931676	−	0.363290i	$-0.881653\pi$
$907$	−4.55421	+	7.88812i	−0.151220	+	0.261921i	0.780456	+	0.625210i	$0.214987\pi$
$908$		0			0
$909$		−	7.11760i		−	0.236076i
$910$		0			0
$911$	−26.1646			−0.866873			−0.433436	−	0.901184i	$-0.642699\pi$
$911$	−26.1646			−0.866873			−0.433436	+	0.901184i	$0.642699\pi$
$912$		0			0
$913$	−7.94306	−	4.58593i	−0.262877	−	0.151772i
$914$		0			0
$915$	2.29815	−	1.32684i	0.0759744	−	0.0438638i
$916$		0			0
$917$	24.0116	+	20.4159i	0.792934	+	0.674192i
$918$		0			0
$919$	−28.5002	+	16.4546i	−0.940135	+	0.542787i	−0.890003	−	0.455956i	$-0.849298\pi$
$919$	−28.5002	+	16.4546i	−0.940135	+	0.542787i	−0.0501322	+	0.998743i	$0.515964\pi$
$920$		0			0
$921$	−8.14793	−	4.70421i	−0.268483	−	0.155009i
$922$		0			0
$923$	−7.49997			−0.246864
$924$		0			0
$925$	−33.9205			−1.11530
$926$		0			0
$927$	−9.80122	+	16.9762i	−0.321914	+	0.557572i
$928$		0			0
$929$	−0.0245189	+	0.0141560i	−0.000804440	+	0.000464443i	−0.500402	−	0.865793i	$-0.666815\pi$
$929$	−0.0245189	+	0.0141560i	−0.000804440	+	0.000464443i	0.499598	+	0.866258i	$0.333481\pi$
$930$		0			0
$931$	−12.4285	+	32.8120i	−0.407328	+	1.07537i
$932$		0			0
$933$	−3.45651	−	5.98684i	−0.113161	−	0.196000i
$934$		0			0
$935$	0.581309	−	1.00686i	0.0190108	−	0.0329277i
$936$		0			0
$937$		−	14.9052i		−	0.486930i	−0.969910	−	0.243465i	$-0.921716\pi$
$937$		−	14.9052i		−	0.486930i	0.969910	−	0.243465i	$-0.0782841\pi$
$938$		0			0
$939$	11.8561			0.386908
$940$		0			0
$941$	−8.29872	+	14.3738i	−0.270531	+	0.468573i	−0.968998	−	0.247069i	$-0.920532\pi$
$941$	−8.29872	+	14.3738i	−0.270531	+	0.468573i	0.698467	+	0.715642i	$0.253866\pi$
$942$		0			0
$943$	20.9940	−	1.78670i	0.683658	−	0.0581829i
$944$		0			0
$945$	2.26982	−	2.66959i	0.0738373	−	0.0868419i
$946$		0			0
$947$	9.72994	+	16.8528i	0.316181	+	0.547641i	0.979688	−	0.200529i	$-0.0642661\pi$
$947$	9.72994	+	16.8528i	0.316181	+	0.547641i	−0.663507	+	0.748170i	$0.730933\pi$
$948$		0			0
$949$	5.69990	+	3.29084i	0.185027	+	0.106825i
$950$		0			0
$951$	−14.1170			−0.457776
$952$		0			0
$953$	56.2843			1.82323			0.911614	−	0.411048i	$-0.134837\pi$
$953$	56.2843			1.82323			0.911614	+	0.411048i	$0.134837\pi$
$954$		0			0
$955$	−1.67308	−	0.965952i	−0.0541396	−	0.0312575i
$956$		0			0
$957$	−2.73737	+	1.58042i	−0.0884866	+	0.0510878i
$958$		0			0
$959$	−8.43687	−	1.54432i	−0.272441	−	0.0498688i
$960$		0			0
$961$	10.7148	+	18.5586i	0.345639	+	0.598665i
$962$		0			0
$963$	2.23920	−	3.87841i	0.0721573	−	0.124980i
$964$		0			0
$965$			4.56806i			0.147051i
$966$		0			0
$967$		−	32.4016i		−	1.04197i	−0.853567	−	0.520983i	$-0.825565\pi$
$967$		−	32.4016i		−	1.04197i	0.853567	−	0.520983i	$-0.174435\pi$
$968$		0			0
$969$	−4.36766	−	2.52167i	−0.140310	−	0.0810078i
$970$		0			0
$971$	41.5237	−	23.9737i	1.33256	−	0.769353i	0.346868	−	0.937914i	$-0.387245\pi$
$971$	41.5237	−	23.9737i	1.33256	−	0.769353i	0.985691	+	0.168561i	$0.0539120\pi$
$972$		0			0
$973$	48.4149	−	17.2656i	1.55211	−	0.553511i
$974$		0			0
$975$	1.49926	+	2.59679i	0.0480147	+	0.0831639i
$976$		0			0
$977$	29.3447	+	16.9422i	0.938820	+	0.542028i	0.889590	−	0.456760i	$-0.150990\pi$
$977$	29.3447	+	16.9422i	0.938820	+	0.542028i	0.0492296	+	0.998787i	$0.484323\pi$
$978$		0			0
$979$	6.80508			0.217491
$980$		0			0
$981$			18.4391i			0.588714i
$982$		0			0
$983$	−13.6865	+	23.7058i	−0.436533	+	0.756098i	−0.997419	−	0.0717953i	$-0.977127\pi$
$983$	−13.6865	+	23.7058i	−0.436533	+	0.756098i	0.560886	+	0.827893i	$0.310460\pi$
$984$		0			0
$985$	1.39567	+	2.41738i	0.0444699	+	0.0770241i
$986$		0			0
$987$	−3.82796	+	1.36512i	−0.121845	+	0.0434522i
$988$		0			0
$989$	7.26070	+	12.5759i	0.230877	+	0.399890i
$990$		0			0
$991$	48.6136	+	28.0671i	1.54426	+	0.891580i	0.998563	+	0.0535994i	$0.0170694\pi$
$991$	48.6136	+	28.0671i	1.54426	+	0.891580i	0.545700	+	0.837981i	$0.316264\pi$
$992$		0			0
$993$	−3.98127			−0.126342
$994$		0			0
$995$			4.08954i			0.129647i
$996$		0			0
$997$	−31.0921	−	17.9510i	−0.984697	−	0.568515i	−0.0810123	−	0.996713i	$-0.525815\pi$
$997$	−31.0921	−	17.9510i	−0.984697	−	0.568515i	−0.903685	+	0.428198i	$0.859149\pi$
$998$		0			0
$999$	16.1249	−	9.30972i	0.510169	−	0.294546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.81.13	✓	56
7.2	even	3	inner	1148.2.r.a.737.16	yes	56
41.40	even	2	inner	1148.2.r.a.81.16	yes	56
287.163	even	6	inner	1148.2.r.a.737.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.13	✓	56	1.1	even	1	trivial
1148.2.r.a.81.16	yes	56	41.40	even	2	inner
1148.2.r.a.737.13	yes	56	287.163	even	6	inner
1148.2.r.a.737.16	yes	56	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.388672 - 0.224400i) q^{3} +(-0.254464 - 0.440744i) q^{5} +(2.49203 - 0.888703i) q^{7} +(-1.39929 - 2.42364i) q^{9} +O(q^{10})\)	\(q+(-0.388672 - 0.224400i) q^{3} +(-0.254464 - 0.440744i) q^{5} +(2.49203 - 0.888703i) q^{7} +(-1.39929 - 2.42364i) q^{9} +(-0.882455 - 0.509486i) q^{11} -1.40924i q^{13} +0.228406i q^{15} +(-1.94156 - 1.12096i) q^{17} +(-4.34088 + 2.50621i) q^{19} +(-1.16801 - 0.213797i) q^{21} +(-1.64528 - 2.84971i) q^{23} +(2.37050 - 4.10582i) q^{25} +2.60240i q^{27} +6.91177i q^{29} +(1.54680 - 2.67914i) q^{31} +(0.228657 + 0.396045i) q^{33} +(-1.02582 - 0.872204i) q^{35} +(-3.57736 - 6.19617i) q^{37} +(-0.316233 + 0.547732i) q^{39} +(-2.71980 + 5.79678i) q^{41} -4.41304 q^{43} +(-0.712137 + 1.23346i) q^{45} +(2.96410 - 1.71132i) q^{47} +(5.42042 - 4.42934i) q^{49} +(0.503085 + 0.871369i) q^{51} +(-5.47783 - 3.16263i) q^{53} +0.518582i q^{55} +2.24957 q^{57} +(2.98513 - 5.17040i) q^{59} +(-5.80910 - 10.0617i) q^{61} +(-5.64097 - 4.79623i) q^{63} +(-0.621114 + 0.358600i) q^{65} +(-6.50812 - 3.75747i) q^{67} +1.47680i q^{69} -5.32199i q^{71} +(-2.33519 + 4.04466i) q^{73} +(-1.84269 + 1.06388i) q^{75} +(-2.65188 - 0.485413i) q^{77} +(10.0035 - 5.77552i) q^{79} +(-3.61389 + 6.25944i) q^{81} +9.00110 q^{83} +1.14097i q^{85} +(1.55100 - 2.68641i) q^{87} +(-5.78365 + 3.33919i) q^{89} +(-1.25240 - 3.51187i) q^{91} +(-1.20239 + 0.694202i) q^{93} +(2.20919 + 1.27548i) q^{95} -5.65532i q^{97} +2.85167i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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