LMFDB - Embedded newform 368.2.m.e.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(49,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("368.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	368.49
Dual form			368.2.m.e.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.246469 - 0.539692i) q^{3} +(-1.62555 + 1.87599i) q^{5} +(3.01490 - 1.93756i) q^{7} +(1.73406 + 2.00121i) q^{9} +(0.0440765 - 0.306559i) q^{11} +(-0.908855 - 0.584086i) q^{13} +(0.611808 + 1.33967i) q^{15} +(5.48698 + 1.61112i) q^{17} +(1.75191 - 0.514408i) q^{19} +(-0.302605 - 2.10467i) q^{21} +(1.56872 + 4.53201i) q^{23} +(-0.165336 - 1.14994i) q^{25} +(3.21526 - 0.944085i) q^{27} +(5.76293 + 1.69215i) q^{29} +(-2.88600 - 6.31946i) q^{31} +(-0.154584 - 0.0993451i) q^{33} +(-1.26604 + 8.80552i) q^{35} +(-6.47749 - 7.47543i) q^{37} +(-0.539231 + 0.346543i) q^{39} +(4.32093 - 4.98662i) q^{41} +(-1.19479 + 2.61623i) q^{43} -6.57307 q^{45} -12.3753 q^{47} +(2.42757 - 5.31565i) q^{49} +(2.22188 - 2.56419i) q^{51} +(-6.96589 + 4.47671i) q^{53} +(0.503453 + 0.581015i) q^{55} +(0.154170 - 1.07228i) q^{57} +(-2.93452 - 1.88590i) q^{59} +(3.34920 + 7.33372i) q^{61} +(9.10548 + 2.67361i) q^{63} +(2.57313 - 0.755540i) q^{65} +(-0.211823 - 1.47326i) q^{67} +(2.83253 + 0.270376i) q^{69} +(0.758305 + 5.27413i) q^{71} +(-8.17609 + 2.40072i) q^{73} +(-0.661364 - 0.194194i) q^{75} +(-0.461089 - 1.00964i) q^{77} +(-7.14090 - 4.58918i) q^{79} +(-0.847596 + 5.89516i) q^{81} +(-2.29959 - 2.65387i) q^{83} +(-11.9418 + 7.67455i) q^{85} +(2.33362 - 2.69315i) q^{87} +(-0.450235 + 0.985878i) q^{89} -3.87180 q^{91} -4.12187 q^{93} +(-1.88280 + 4.12277i) q^{95} +(0.692559 - 0.799256i) q^{97} +(0.689921 - 0.443385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41}+ \cdots + 17 q^{99}+O(q^{100}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$	$1$

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
$3$	0.246469	−	0.539692i	0.142299	−	0.311592i	−0.825041	−	0.565072i	$-0.808848\pi$
$3$	0.246469	−	0.539692i	0.142299	−	0.311592i	0.967340	+	0.253481i	$0.0815755\pi$
$4$		0			0
$5$	−1.62555	+	1.87599i	−0.726970	+	0.838968i	−0.992127	−	0.125237i	$-0.960031\pi$
$5$	−1.62555	+	1.87599i	−0.726970	+	0.838968i	0.265157	+	0.964205i	$0.414576\pi$
$6$		0			0
$7$	3.01490	−	1.93756i	1.13952	−	0.732328i	0.171998	−	0.985097i	$-0.444978\pi$
$7$	3.01490	−	1.93756i	1.13952	−	0.732328i	0.967526	+	0.252770i	$0.0813415\pi$
$8$		0			0
$9$	1.73406	+	2.00121i	0.578020	+	0.667071i
$10$		0			0
$11$	0.0440765	−	0.306559i	0.0132896	−	0.0924310i	−0.982097	−	0.188375i	$-0.939678\pi$
$11$	0.0440765	−	0.306559i	0.0132896	−	0.0924310i	0.995387	+	0.0959441i	$0.0305870\pi$
$12$		0			0
$13$	−0.908855	−	0.584086i	−0.252071	−	0.161996i	0.408503	−	0.912757i	$-0.366051\pi$
$13$	−0.908855	−	0.584086i	−0.252071	−	0.161996i	−0.660574	+	0.750761i	$0.729687\pi$
$14$		0			0
$15$	0.611808	+	1.33967i	0.157968	+	0.345902i
$16$		0			0
$17$	5.48698	+	1.61112i	1.33079	+	0.390755i	0.868374	−	0.495909i	$-0.165165\pi$
$17$	5.48698	+	1.61112i	1.33079	+	0.390755i	0.462414	+	0.886664i	$0.346983\pi$
$18$		0			0
$19$	1.75191	−	0.514408i	0.401916	−	0.118013i	−0.0745260	−	0.997219i	$-0.523744\pi$
$19$	1.75191	−	0.514408i	0.401916	−	0.118013i	0.476442	+	0.879206i	$0.341926\pi$
$20$		0			0
$21$	−0.302605	−	2.10467i	−0.0660339	−	0.459276i
$22$		0			0
$23$	1.56872	+	4.53201i	0.327100	+	0.944990i
$23$	1.56872	+	4.53201i	0.327100	+	0.944990i
$24$		0			0
$25$	−0.165336	−	1.14994i	−0.0330673	−	0.229988i
$26$		0			0
$27$	3.21526	−	0.944085i	0.618777	−	0.181689i
$28$		0			0
$29$	5.76293	+	1.69215i	1.07015	+	0.314224i	0.768931	−	0.639331i	$-0.220789\pi$
$29$	5.76293	+	1.69215i	1.07015	+	0.314224i	0.301218	+	0.953555i	$0.402607\pi$
$30$		0			0
$31$	−2.88600	−	6.31946i	−0.518341	−	1.13501i	−0.970064	−	0.242850i	$-0.921918\pi$
$31$	−2.88600	−	6.31946i	−0.518341	−	1.13501i	0.451723	−	0.892158i	$-0.350809\pi$
$32$		0			0
$33$	−0.154584	−	0.0993451i	−0.0269096	−	0.0172938i
$34$		0			0
$35$	−1.26604	+	8.80552i	−0.214000	+	1.48840i
$36$		0			0
$37$	−6.47749	−	7.47543i	−1.06489	−	1.22895i	−0.972420	−	0.233237i	$-0.925068\pi$
$37$	−6.47749	−	7.47543i	−1.06489	−	1.22895i	−0.0924735	−	0.995715i	$-0.529477\pi$
$38$		0			0
$39$	−0.539231	+	0.346543i	−0.0863461	+	0.0554913i
$40$		0			0
$41$	4.32093	−	4.98662i	0.674816	−	0.778779i	−0.310306	−	0.950637i	$-0.600432\pi$
$41$	4.32093	−	4.98662i	0.674816	−	0.778779i	0.985122	+	0.171858i	$0.0549770\pi$
$42$		0			0
$43$	−1.19479	+	2.61623i	−0.182204	+	0.398972i	−0.978591	−	0.205816i	$-0.934015\pi$
$43$	−1.19479	+	2.61623i	−0.182204	+	0.398972i	0.796386	+	0.604788i	$0.206742\pi$
$44$		0			0
$45$	−6.57307			−0.979855
$46$		0			0
$47$	−12.3753			−1.80513			−0.902563	−	0.430557i	$-0.858317\pi$
$47$	−12.3753			−1.80513			−0.902563	+	0.430557i	$0.858317\pi$
$48$		0			0
$49$	2.42757	−	5.31565i	0.346796	−	0.759378i
$50$		0			0
$51$	2.22188	−	2.56419i	0.311126	−	0.359058i
$52$		0			0
$53$	−6.96589	+	4.47671i	−0.956839	+	0.614923i	−0.923122	−	0.384508i	$-0.874371\pi$
$53$	−6.96589	+	4.47671i	−0.956839	+	0.614923i	−0.0337176	+	0.999431i	$0.510735\pi$
$54$		0			0
$55$	0.503453	+	0.581015i	0.0678855	+	0.0783441i
$56$		0			0
$57$	0.154170	−	1.07228i	0.0204204	−	0.142027i
$58$		0			0
$59$	−2.93452	−	1.88590i	−0.382042	−	0.245523i	0.335498	−	0.942041i	$-0.391095\pi$
$59$	−2.93452	−	1.88590i	−0.382042	−	0.245523i	−0.717540	+	0.696518i	$0.754732\pi$
$60$		0			0
$61$	3.34920	+	7.33372i	0.428821	+	0.938986i	0.993517	+	0.113687i	$0.0362661\pi$
$61$	3.34920	+	7.33372i	0.428821	+	0.938986i	−0.564696	+	0.825299i	$0.691007\pi$
$62$		0			0
$63$	9.10548	+	2.67361i	1.14718	+	0.336843i
$64$		0			0
$65$	2.57313	−	0.755540i	0.319158	−	0.0937132i
$66$		0			0
$67$	−0.211823	−	1.47326i	−0.0258783	−	0.179988i	0.972783	−	0.231719i	$-0.0744351\pi$
$67$	−0.211823	−	1.47326i	−0.0258783	−	0.179988i	−0.998661	+	0.0517315i	$0.983526\pi$
$68$		0			0
$69$	2.83253	+	0.270376i	0.340997	+	0.0325494i
$70$		0			0
$71$	0.758305	+	5.27413i	0.0899943	+	0.625924i	0.984040	+	0.177948i	$0.0569459\pi$
$71$	0.758305	+	5.27413i	0.0899943	+	0.625924i	−0.894046	+	0.447976i	$0.852145\pi$
$72$		0			0
$73$	−8.17609	+	2.40072i	−0.956939	+	0.280983i	−0.722673	−	0.691190i	$-0.757087\pi$
$73$	−8.17609	+	2.40072i	−0.956939	+	0.280983i	−0.234266	+	0.972173i	$0.575269\pi$
$74$		0			0
$75$	−0.661364	−	0.194194i	−0.0763678	−	0.0224236i
$76$		0			0
$77$	−0.461089	−	1.00964i	−0.0525460	−	0.115060i
$78$		0			0
$79$	−7.14090	−	4.58918i	−0.803414	−	0.516323i	0.0733140	−	0.997309i	$-0.476642\pi$
$79$	−7.14090	−	4.58918i	−0.803414	−	0.516323i	−0.876728	+	0.480986i	$0.840279\pi$
$80$		0			0
$81$	−0.847596	+	5.89516i	−0.0941773	+	0.655018i
$82$		0			0
$83$	−2.29959	−	2.65387i	−0.252413	−	0.291300i	0.615375	−	0.788234i	$-0.289004\pi$
$83$	−2.29959	−	2.65387i	−0.252413	−	0.291300i	−0.867788	+	0.496934i	$0.834459\pi$
$84$		0			0
$85$	−11.9418	+	7.67455i	−1.29527	+	0.832422i
$86$		0			0
$87$	2.33362	−	2.69315i	0.250191	−	0.288736i
$88$		0			0
$89$	−0.450235	+	0.985878i	−0.0477248	+	0.104503i	−0.931992	−	0.362478i	$-0.881931\pi$
$89$	−0.450235	+	0.985878i	−0.0477248	+	0.104503i	0.884268	+	0.466981i	$0.154658\pi$
$90$		0			0
$91$	−3.87180			−0.405875
$92$		0			0
$93$	−4.12187			−0.427418
$94$		0			0
$95$	−1.88280	+	4.12277i	−0.193172	+	0.422987i
$96$		0			0
$97$	0.692559	−	0.799256i	0.0703187	−	0.0811521i	−0.719500	−	0.694492i	$-0.755629\pi$
$97$	0.692559	−	0.799256i	0.0703187	−	0.0811521i	0.789819	+	0.613340i	$0.210175\pi$
$98$		0			0
$99$	0.689921	−	0.443385i	0.0693397	−	0.0445619i
$100$		0			0
$101$	4.53515	+	5.23385i	0.451265	+	0.520787i	0.935106	−	0.354369i	$-0.115304\pi$
$101$	4.53515	+	5.23385i	0.451265	+	0.520787i	−0.483841	+	0.875156i	$0.660759\pi$
$102$		0			0
$103$	2.22281	−	15.4600i	0.219020	−	1.52331i	−0.522649	−	0.852548i	$-0.675056\pi$
$103$	2.22281	−	15.4600i	0.219020	−	1.52331i	0.741668	−	0.670767i	$-0.234035\pi$
$104$		0			0
$105$	4.44023	+	2.85356i	0.433322	+	0.278479i
$106$		0			0
$107$	−6.50514	−	14.2443i	−0.628876	−	1.37705i	−0.908884	−	0.417048i	$-0.863065\pi$
$107$	−6.50514	−	14.2443i	−0.628876	−	1.37705i	0.280009	−	0.959997i	$-0.409663\pi$
$108$		0			0
$109$	−14.3291	−	4.20741i	−1.37248	−	0.402997i	−0.489336	−	0.872095i	$-0.662761\pi$
$109$	−14.3291	−	4.20741i	−1.37248	−	0.402997i	−0.883146	+	0.469098i	$0.844579\pi$
$110$		0			0
$111$	−5.63093	+	1.65339i	−0.534465	+	0.156933i
$112$		0			0
$113$	−2.34780	−	16.3293i	−0.220862	−	1.53613i	−0.734789	−	0.678296i	$-0.762719\pi$
$113$	−2.34780	−	16.3293i	−0.220862	−	1.53613i	0.513927	−	0.857834i	$-0.328190\pi$
$114$		0			0
$115$	−11.0520	−	4.42413i	−1.03061	−	0.412552i
$116$		0			0
$117$	−0.407130	−	2.83165i	−0.0376392	−	0.261786i
$118$		0			0
$119$	19.6643	−	5.77397i	1.80263	−	0.529299i
$120$		0			0
$121$	10.4624	+	3.07203i	0.951126	+	0.279276i
$122$		0			0
$123$	−1.62626	−	3.56102i	−0.146635	−	0.321086i
$124$		0			0
$125$	−8.01514	−	5.15102i	−0.716896	−	0.460721i
$126$		0			0
$127$	−2.22074	+	15.4456i	−0.197059	+	1.37057i	0.615704	+	0.787978i	$0.288872\pi$
$127$	−2.22074	+	15.4456i	−0.197059	+	1.37057i	−0.812762	+	0.582595i	$0.802037\pi$
$128$		0			0
$129$	1.11748	+	1.28964i	0.0983888	+	0.113547i
$130$		0			0
$131$	−7.21902	+	4.63938i	−0.630729	+	0.405345i	−0.816579	−	0.577233i	$-0.804132\pi$
$131$	−7.21902	+	4.63938i	−0.630729	+	0.405345i	0.185851	+	0.982578i	$0.440496\pi$
$132$		0			0
$133$	4.28514	−	4.94532i	0.371569	−	0.428813i
$134$		0			0
$135$	−3.45548	+	7.56645i	−0.297401	+	0.651217i
$136$		0			0
$137$	6.38302			0.545338			0.272669	−	0.962108i	$-0.412094\pi$
$137$	6.38302			0.545338			0.272669	+	0.962108i	$0.412094\pi$
$138$		0			0
$139$	21.1827			1.79670			0.898348	−	0.439284i	$-0.144768\pi$
$139$	21.1827			1.79670			0.898348	+	0.439284i	$0.144768\pi$
$140$		0			0
$141$	−3.05014	+	6.67887i	−0.256868	+	0.562462i
$142$		0			0
$143$	−0.219116	+	0.252873i	−0.0183234	+	0.0211463i
$144$		0			0
$145$	−12.5424	+	8.06052i	−1.04159	+	0.669389i
$146$		0			0
$147$	−2.27049	−	2.62029i	−0.187267	−	0.216118i
$148$		0			0
$149$	0.782734	−	5.44403i	0.0641241	−	0.445993i	−0.932313	−	0.361652i	$-0.882213\pi$
$149$	0.782734	−	5.44403i	0.0641241	−	0.445993i	0.996437	−	0.0843401i	$-0.0268782\pi$
$150$		0			0
$151$	0.794712	+	0.510731i	0.0646728	+	0.0415627i	0.572578	−	0.819850i	$-0.305944\pi$
$151$	0.794712	+	0.510731i	0.0646728	+	0.0415627i	−0.507905	+	0.861413i	$0.669580\pi$
$152$		0			0
$153$	6.29056	+	13.7744i	0.508562	+	1.11359i
$154$		0			0
$155$	16.5466	+	4.85852i	1.32905	+	0.390245i
$156$		0			0
$157$	21.2087	−	6.22742i	1.69264	−	0.497003i	0.713576	−	0.700578i	$-0.247074\pi$
$157$	21.2087	−	6.22742i	1.69264	−	0.497003i	0.979059	+	0.203575i	$0.0652561\pi$
$158$		0			0
$159$	0.699167	+	4.86281i	0.0554475	+	0.385646i
$160$		0			0
$161$	13.5106	+	10.6241i	1.06478	+	0.837294i
$162$		0			0
$163$	2.83323	+	19.7056i	0.221916	+	1.54346i	0.730781	+	0.682612i	$0.239156\pi$
$163$	2.83323	+	19.7056i	0.221916	+	1.54346i	−0.508865	+	0.860846i	$0.669935\pi$
$164$		0			0
$165$	0.437655	−	0.128507i	0.0340714	−	0.0100043i
$166$		0			0
$167$	6.12254	+	1.79774i	0.473776	+	0.139113i	0.509899	−	0.860234i	$-0.329683\pi$
$167$	6.12254	+	1.79774i	0.473776	+	0.139113i	−0.0361230	+	0.999347i	$0.511501\pi$
$168$		0			0
$169$	−4.91553	−	10.7635i	−0.378118	−	0.827963i
$170$		0			0
$171$	4.06736	+	2.61393i	0.311039	+	0.199893i
$172$		0			0
$173$	−0.139777	+	0.972168i	−0.0106270	+	0.0739125i	−0.994445	−	0.105259i	$-0.966433\pi$
$173$	−0.139777	+	0.972168i	−0.0106270	+	0.0739125i	0.983818	+	0.179172i	$0.0573418\pi$
$174$		0			0
$175$	−2.72655	−	3.14660i	−0.206108	−	0.237861i
$176$		0			0
$177$	−1.74107	+	1.11892i	−0.130867	+	0.0841032i
$178$		0			0
$179$	−16.3587	+	18.8789i	−1.22270	+	1.41108i	−0.340477	+	0.940253i	$0.610588\pi$
$179$	−16.3587	+	18.8789i	−1.22270	+	1.41108i	−0.882228	+	0.470823i	$0.843957\pi$
$180$		0			0
$181$	6.78983	−	14.8677i	0.504684	−	1.10510i	−0.470234	−	0.882542i	$-0.655830\pi$
$181$	6.78983	−	14.8677i	0.504684	−	1.10510i	0.974918	−	0.222563i	$-0.0714423\pi$
$182$		0			0
$183$	4.78342			0.353601
$184$		0			0
$185$	24.5533			1.80520
$186$		0			0
$187$	0.735751	−	1.61107i	0.0538035	−	0.117813i
$188$		0			0
$189$	7.86446	−	9.07607i	0.572055	−	0.660187i
$190$		0			0
$191$	−8.24418	+	5.29821i	−0.596528	+	0.383365i	−0.803784	−	0.594922i	$-0.797183\pi$
$191$	−8.24418	+	5.29821i	−0.596528	+	0.383365i	0.207256	+	0.978287i	$0.433547\pi$
$192$		0			0
$193$	−13.0379	−	15.0466i	−0.938491	−	1.08308i	−0.996402	−	0.0847550i	$-0.972989\pi$
$193$	−13.0379	−	15.0466i	−0.938491	−	1.08308i	0.0579104	−	0.998322i	$-0.481556\pi$
$194$		0			0
$195$	0.226439	−	1.57492i	0.0162156	−	0.112782i
$196$		0			0
$197$	5.37943	+	3.45715i	0.383268	+	0.246312i	0.718061	−	0.695980i	$-0.245030\pi$
$197$	5.37943	+	3.45715i	0.383268	+	0.246312i	−0.334793	+	0.942292i	$0.608666\pi$
$198$		0			0
$199$	−6.56077	−	14.3661i	−0.465080	−	1.01838i	−0.986300	−	0.164961i	$-0.947250\pi$
$199$	−6.56077	−	14.3661i	−0.465080	−	1.01838i	0.521220	−	0.853423i	$-0.325477\pi$
$200$		0			0
$201$	−0.847317	−	0.248795i	−0.0597651	−	0.0175486i
$202$		0			0
$203$	20.6533	−	6.06435i	1.44958	−	0.425634i
$204$		0			0
$205$	2.33094	+	16.2120i	0.162800	+	1.13230i
$206$		0			0
$207$	−6.34927	+	10.9981i	−0.441305	+	0.764423i
$208$		0			0
$209$	−0.0804781	−	0.559737i	−0.00556679	−	0.0387178i
$210$		0			0
$211$	−7.18001	+	2.10824i	−0.494292	+	0.145137i	−0.519372	−	0.854548i	$-0.673834\pi$
$211$	−7.18001	+	2.10824i	−0.494292	+	0.145137i	0.0250801	+	0.999685i	$0.492016\pi$
$212$		0			0
$213$	3.03331	+	0.890659i	0.207839	+	0.0610270i
$214$		0			0
$215$	−2.96583	−	6.49425i	−0.202268	−	0.442904i
$216$		0			0
$217$	−20.9453	−	13.4607i	−1.42186	−	0.913774i
$218$		0			0
$219$	−0.719507	+	5.00428i	−0.0486197	+	0.338158i
$220$		0			0
$221$	−4.04584	−	4.66914i	−0.272152	−	0.314081i
$222$		0			0
$223$	16.3662	−	10.5179i	1.09596	−	0.704331i	0.137770	−	0.990464i	$-0.456006\pi$
$223$	16.3662	−	10.5179i	1.09596	−	0.704331i	0.958190	+	0.286133i	$0.0923701\pi$
$224$		0			0
$225$	2.01457	−	2.32494i	0.134305	−	0.154996i
$226$		0			0
$227$	7.90097	−	17.3007i	0.524406	−	1.14829i	−0.443339	−	0.896354i	$-0.646206\pi$
$227$	7.90097	−	17.3007i	0.524406	−	1.14829i	0.967744	−	0.251934i	$-0.0810666\pi$
$228$		0			0
$229$	4.93124			0.325865			0.162933	−	0.986637i	$-0.447905\pi$
$229$	4.93124			0.325865			0.162933	+	0.986637i	$0.447905\pi$
$230$		0			0
$231$	−0.658542			−0.0433289
$232$		0			0
$233$	−5.24823	+	11.4920i	−0.343823	+	0.752867i	−0.999998	−	0.00174111i	$-0.999446\pi$
$233$	−5.24823	+	11.4920i	−0.343823	+	0.752867i	0.656176	+	0.754608i	$0.272173\pi$
$234$		0			0
$235$	20.1168	−	23.2160i	1.31227	−	1.51444i
$236$		0			0
$237$	−4.23676	+	2.72280i	−0.275207	+	0.176865i
$238$		0			0
$239$	−3.80518	−	4.39141i	−0.246137	−	0.284057i	0.619216	−	0.785221i	$-0.287451\pi$
$239$	−3.80518	−	4.39141i	−0.246137	−	0.284057i	−0.865352	+	0.501164i	$0.832905\pi$
$240$		0			0
$241$	−1.73209	+	12.0470i	−0.111574	+	0.776013i	0.854816	+	0.518931i	$0.173670\pi$
$241$	−1.73209	+	12.0470i	−0.111574	+	0.776013i	−0.966390	+	0.257082i	$0.917239\pi$
$242$		0			0
$243$	11.4298	+	7.34547i	0.733221	+	0.471212i
$244$		0			0
$245$	6.02595	+	13.1950i	0.384984	+	0.842996i
$246$		0			0
$247$	−1.89269	−	0.555744i	−0.120429	−	0.0353612i
$248$		0			0
$249$	−1.99905	+	0.586975i	−0.126685	+	0.0371980i
$250$		0			0
$251$	3.35422	+	23.3291i	0.211716	+	1.47252i	0.767423	+	0.641141i	$0.221539\pi$
$251$	3.35422	+	23.3291i	0.211716	+	1.47252i	−0.555707	+	0.831378i	$0.687552\pi$
$252$		0			0
$253$	1.45847	−	0.281149i	0.0916933	−	0.0176757i
$254$		0			0
$255$	1.19860	+	8.33646i	0.0750594	+	0.522049i
$256$		0			0
$257$	−19.7021	+	5.78506i	−1.22898	+	0.360862i	−0.830866	−	0.556472i	$-0.812155\pi$
$257$	−19.7021	+	5.78506i	−1.22898	+	0.360862i	−0.398118	+	0.917334i	$0.630337\pi$
$258$		0			0
$259$	−34.0130	−	9.98713i	−2.11347	−	0.620570i
$260$		0			0
$261$	6.60692	+	14.4671i	0.408958	+	0.895493i
$262$		0			0
$263$	2.93961	+	1.88917i	0.181264	+	0.116491i	0.628126	−	0.778112i	$-0.283822\pi$
$263$	2.93961	+	1.88917i	0.181264	+	0.116491i	−0.446862	+	0.894603i	$0.647459\pi$
$264$		0			0
$265$	2.92518	−	20.3451i	0.179692	−	1.24979i
$266$		0			0
$267$	0.421102	+	0.485977i	0.0257710	+	0.0297413i
$268$		0			0
$269$	0.114678	−	0.0736992i	0.00699205	−	0.00449352i	−0.537140	−	0.843493i	$-0.680495\pi$
$269$	0.114678	−	0.0736992i	0.00699205	−	0.00449352i	0.544132	+	0.839000i	$0.316859\pi$
$270$		0			0
$271$	−10.4770	+	12.0911i	−0.636432	+	0.734481i	−0.978740	−	0.205107i	$-0.934246\pi$
$271$	−10.4770	+	12.0911i	−0.636432	+	0.734481i	0.342308	+	0.939588i	$0.388791\pi$
$272$		0			0
$273$	−0.954281	+	2.08958i	−0.0577557	+	0.126467i
$274$		0			0
$275$	−0.359812			−0.0216975
$276$		0			0
$277$	25.2361			1.51629			0.758147	−	0.652084i	$-0.226105\pi$
$277$	25.2361			1.51629			0.758147	+	0.652084i	$0.226105\pi$
$278$		0			0
$279$	7.64208	−	16.7338i	0.457520	−	1.00183i
$280$		0			0
$281$	−9.10072	+	10.5028i	−0.542904	+	0.626544i	−0.959215	−	0.282678i	$-0.908777\pi$
$281$	−9.10072	+	10.5028i	−0.542904	+	0.626544i	0.416311	+	0.909222i	$0.363323\pi$
$282$		0			0
$283$	−5.32239	+	3.42049i	−0.316383	+	0.203327i	−0.689188	−	0.724583i	$-0.742033\pi$
$283$	−5.32239	+	3.42049i	−0.316383	+	0.203327i	0.372805	+	0.927910i	$0.378396\pi$
$284$		0			0
$285$	1.76097	+	2.03227i	0.104311	+	0.120381i
$286$		0			0
$287$	3.36530	−	23.4062i	0.198647	−	1.38162i
$288$		0			0
$289$	13.2099	+	8.48951i	0.777055	+	0.499383i
$290$		0			0
$291$	−0.260658	−	0.570761i	−0.0152800	−	0.0334586i
$292$		0			0
$293$	1.36988	+	0.402234i	0.0800294	+	0.0234988i	0.321502	−	0.946909i	$-0.395812\pi$
$293$	1.36988	+	0.402234i	0.0800294	+	0.0234988i	−0.241473	+	0.970408i	$0.577630\pi$
$294$		0			0
$295$	8.30814	−	2.43949i	0.483719	−	0.142033i
$296$		0			0
$297$	−0.147700	−	1.02728i	−0.00857044	−	0.0596087i
$298$		0			0
$299$	1.22134	−	5.03521i	0.0706322	−	0.291193i
$300$		0			0
$301$	1.46692	+	10.2027i	0.0845519	+	0.588072i
$302$		0			0
$303$	3.94244	−	1.15761i	0.226487	−	0.0665027i
$304$		0			0
$305$	−19.2023	−	5.63830i	−1.09952	−	0.322848i
$306$		0			0
$307$	−8.39838	−	18.3899i	−0.479321	−	1.04957i	−0.982650	−	0.185472i	$-0.940619\pi$
$307$	−8.39838	−	18.3899i	−0.479321	−	1.04957i	0.503328	−	0.864095i	$-0.332109\pi$
$308$		0			0
$309$	−7.79577	−	5.01004i	−0.443486	−	0.285011i
$310$		0			0
$311$	−1.30206	+	9.05600i	−0.0738329	+	0.513519i	0.919023	+	0.394203i	$0.128979\pi$
$311$	−1.30206	+	9.05600i	−0.0738329	+	0.513519i	−0.992856	+	0.119316i	$0.961930\pi$
$312$		0			0
$313$	−12.4699	−	14.3910i	−0.704838	−	0.813426i	0.284560	−	0.958658i	$-0.408153\pi$
$313$	−12.4699	−	14.3910i	−0.704838	−	0.813426i	−0.989398	+	0.145232i	$0.953607\pi$
$314$		0			0
$315$	−19.8171	+	12.7357i	−1.11657	+	0.717575i
$316$		0			0
$317$	−9.87888	+	11.4008i	−0.554853	+	0.640335i	−0.962007	−	0.273025i	$-0.911976\pi$
$317$	−9.87888	+	11.4008i	−0.554853	+	0.640335i	0.407154	+	0.913360i	$0.366521\pi$
$318$		0			0
$319$	0.772753	−	1.69209i	0.0432659	−	0.0947390i
$320$		0			0
$321$	−9.29084			−0.518564
$322$		0			0
$323$	10.4415			0.580980
$324$		0			0
$325$	−0.521397	+	1.14170i	−0.0289219	+	0.0633301i
$326$		0			0
$327$	−5.80240	+	6.69633i	−0.320873	+	0.370308i
$328$		0			0
$329$	−37.3103	+	23.9779i	−2.05699	+	1.32194i
$330$		0			0
$331$	−6.46311	−	7.45883i	−0.355245	−	0.409974i	0.549796	−	0.835299i	$-0.314705\pi$
$331$	−6.46311	−	7.45883i	−0.355245	−	0.409974i	−0.905041	+	0.425324i	$0.860160\pi$
$332$		0			0
$333$	3.72755	−	25.9257i	0.204269	−	1.42072i
$334$		0			0
$335$	3.10816	+	1.99749i	0.169817	+	0.109135i
$336$		0			0
$337$	−3.90314	−	8.54669i	−0.212618	−	0.465568i	0.773033	−	0.634366i	$-0.218739\pi$
$337$	−3.90314	−	8.54669i	−0.212618	−	0.465568i	−0.985651	+	0.168798i	$0.946011\pi$
$338$		0			0
$339$	−9.39145	−	2.75758i	−0.510074	−	0.149771i
$340$		0			0
$341$	−2.06449	+	0.606189i	−0.111798	+	0.0328270i
$342$		0			0
$343$	0.589730	+	4.10167i	0.0318425	+	0.221469i
$344$		0			0
$345$	−5.11166	+	4.87429i	−0.275202	+	0.262423i
$346$		0			0
$347$	−1.49296	−	10.3838i	−0.0801462	−	0.557429i	−0.989844	−	0.142158i	$-0.954596\pi$
$347$	−1.49296	−	10.3838i	−0.0801462	−	0.557429i	0.909698	−	0.415271i	$-0.136313\pi$
$348$		0			0
$349$	29.5251	−	8.66936i	1.58044	−	0.464060i	0.630425	−	0.776251i	$-0.282881\pi$
$349$	29.5251	−	8.66936i	1.58044	−	0.464060i	0.950020	+	0.312190i	$0.101063\pi$
$350$		0			0
$351$	−3.47363	−	1.01995i	−0.185409	−	0.0544409i
$352$		0			0
$353$	−6.26251	−	13.7130i	−0.333320	−	0.729868i	0.666559	−	0.745452i	$-0.267767\pi$
$353$	−6.26251	−	13.7130i	−0.333320	−	0.729868i	−0.999879	+	0.0155840i	$0.995039\pi$
$354$		0			0
$355$	−11.1269	−	7.15081i	−0.590553	−	0.379526i
$356$		0			0
$357$	1.73049	−	12.0358i	0.0915870	−	0.637002i
$358$		0			0
$359$	0.897049	+	1.03525i	0.0473444	+	0.0546384i	0.778928	−	0.627114i	$-0.215764\pi$
$359$	0.897049	+	1.03525i	0.0473444	+	0.0546384i	−0.731583	+	0.681752i	$0.761218\pi$
$360$		0			0
$361$	−13.1792	+	8.46978i	−0.693644	+	0.445778i
$362$		0			0
$363$	4.23661	−	4.88931i	0.222364	−	0.256622i
$364$		0			0
$365$	8.78696	−	19.2408i	0.459931	−	1.00711i
$366$		0			0
$367$	−31.6797			−1.65367			−0.826834	−	0.562447i	$-0.809860\pi$
$367$	−31.6797			−1.65367			−0.826834	+	0.562447i	$0.809860\pi$
$368$		0			0
$369$	17.4720			0.909558
$370$		0			0
$371$	−12.3276	+	26.9936i	−0.640016	+	1.40144i
$372$		0			0
$373$	−13.8466	+	15.9798i	−0.716947	+	0.827401i	−0.990936	−	0.134331i	$-0.957111\pi$
$373$	−13.8466	+	15.9798i	−0.716947	+	0.827401i	0.273989	+	0.961733i	$0.411657\pi$
$374$		0			0
$375$	−4.75545	+	3.05614i	−0.245570	+	0.157818i
$376$		0			0
$377$	−4.24931	−	4.90396i	−0.218850	−	0.252567i
$378$		0			0
$379$	−3.27690	+	22.7913i	−0.168323	+	1.17071i	0.714027	+	0.700118i	$0.246869\pi$
$379$	−3.27690	+	22.7913i	−0.168323	+	1.17071i	−0.882350	+	0.470594i	$0.844040\pi$
$380$		0			0
$381$	7.78852	+	5.00538i	0.399018	+	0.256433i
$382$		0			0
$383$	4.94585	+	10.8299i	0.252721	+	0.553382i	0.992890	−	0.119039i	$-0.0379815\pi$
$383$	4.94585	+	10.8299i	0.252721	+	0.553382i	−0.740168	+	0.672422i	$0.765254\pi$
$384$		0			0
$385$	2.64361	+	0.776233i	0.134731	+	0.0395605i
$386$		0			0
$387$	−7.30749	+	2.14567i	−0.371461	+	0.109071i
$388$		0			0
$389$	−3.28950	−	22.8790i	−0.166784	−	1.16001i	−0.885477	−	0.464683i	$-0.846168\pi$
$389$	−3.28950	−	22.8790i	−0.166784	−	1.16001i	0.718693	−	0.695328i	$-0.244741\pi$
$390$		0			0
$391$	1.30590	+	27.3945i	0.0660423	+	1.38540i
$392$		0			0
$393$	0.724573	+	5.03952i	0.0365499	+	0.254210i
$394$		0			0
$395$	20.2172	−	5.93630i	1.01724	−	0.298688i
$396$		0			0
$397$	5.91139	+	1.73574i	0.296684	+	0.0871143i	0.426687	−	0.904399i	$-0.359681\pi$
$397$	5.91139	+	1.73574i	0.296684	+	0.0871143i	−0.130003	+	0.991514i	$0.541499\pi$
$398$		0			0
$399$	−1.61279	−	3.53153i	−0.0807407	−	0.176797i
$400$		0			0
$401$	8.66777	+	5.57044i	0.432848	+	0.278174i	0.738867	−	0.673851i	$-0.235361\pi$
$401$	8.66777	+	5.57044i	0.432848	+	0.278174i	−0.306020	+	0.952025i	$0.598997\pi$
$402$		0			0
$403$	−1.06815	+	7.42914i	−0.0532083	+	0.370072i
$404$		0			0
$405$	−9.68144	−	11.1730i	−0.481075	−	0.555190i
$406$		0			0
$407$	−2.57716	+	1.65624i	−0.127745	+	0.0820969i
$408$		0			0
$409$	−0.00533396	+	0.00615572i	−0.000263747	+	0.000304381i	−0.755881	−	0.654709i	$-0.772791\pi$
$409$	−0.00533396	+	0.00615572i	−0.000263747	+	0.000304381i	0.755618	+	0.655013i	$0.227337\pi$
$410$		0			0
$411$	1.57322	−	3.44487i	0.0776011	−	0.169923i
$412$		0			0
$413$	−12.5013			−0.615149
$414$		0			0
$415$	8.71675			0.427888
$416$		0			0
$417$	5.22089	−	11.4322i	0.255668	−	0.559835i
$418$		0			0
$419$	17.6065	−	20.3190i	0.860133	−	0.992647i	−0.139864	−	0.990171i	$-0.544666\pi$
$419$	17.6065	−	20.3190i	0.860133	−	0.992647i	0.999997	−	0.00247601i	$-0.000788139\pi$
$420$		0			0
$421$	−2.78101	+	1.78725i	−0.135538	+	0.0871051i	−0.606653	−	0.794967i	$-0.707488\pi$
$421$	−2.78101	+	1.78725i	−0.135538	+	0.0871051i	0.471115	+	0.882072i	$0.343852\pi$
$422$		0			0
$423$	−21.4596	−	24.7657i	−1.04340	−	1.20415i
$424$		0			0
$425$	0.945497	−	6.57608i	0.0458634	−	0.318987i
$426$		0			0
$427$	24.3070	+	15.6211i	1.17630	+	0.755960i
$428$		0			0
$429$	0.0824684	+	0.180581i	0.00398161	+	0.00871851i
$430$		0			0
$431$	11.7525	+	3.45085i	0.566098	+	0.166221i	0.552244	−	0.833683i	$-0.313772\pi$
$431$	11.7525	+	3.45085i	0.566098	+	0.166221i	0.0138544	+	0.999904i	$0.495590\pi$
$432$		0			0
$433$	2.51713	−	0.739096i	0.120966	−	0.0355187i	−0.220689	−	0.975344i	$-0.570831\pi$
$433$	2.51713	−	0.739096i	0.120966	−	0.0355187i	0.341655	+	0.939825i	$0.389013\pi$
$434$		0			0
$435$	1.25888	+	8.75571i	0.0603587	+	0.419804i
$436$		0			0
$437$	5.07956	+	7.13272i	0.242988	+	0.341204i
$438$		0			0
$439$	0.869632	+	6.04842i	0.0415053	+	0.288676i	0.999994	+	0.00354414i	$0.00112814\pi$
$439$	0.869632	+	6.04842i	0.0415053	+	0.288676i	−0.958488	+	0.285131i	$0.907963\pi$
$440$		0			0
$441$	14.8473	−	4.35956i	0.707015	−	0.207598i
$442$		0			0
$443$	−23.3023	−	6.84216i	−1.10712	−	0.325081i	−0.323445	−	0.946247i	$-0.604841\pi$
$443$	−23.3023	−	6.84216i	−1.10712	−	0.325081i	−0.783679	+	0.621166i	$0.786659\pi$
$444$		0			0
$445$	−1.11761	−	2.44724i	−0.0529800	−	0.116010i
$446$		0			0
$447$	−2.74518	−	1.76422i	−0.129843	−	0.0834449i
$448$		0			0
$449$	−5.10853	+	35.5306i	−0.241087	+	1.67679i	0.405610	+	0.914046i	$0.367059\pi$
$449$	−5.10853	+	35.5306i	−0.241087	+	1.67679i	−0.646696	+	0.762747i	$0.723850\pi$
$450$		0			0
$451$	−1.33824	−	1.54441i	−0.0630153	−	0.0727235i
$452$		0			0
$453$	0.471510	−	0.303021i	0.0221535	−	0.0142372i
$454$		0			0
$455$	6.29383	−	7.26346i	0.295059	−	0.340516i
$456$		0			0
$457$	11.3343	−	24.8186i	0.530195	−	1.16097i	−0.435238	−	0.900315i	$-0.643336\pi$
$457$	11.3343	−	24.8186i	0.530195	−	1.16097i	0.965433	−	0.260650i	$-0.0839369\pi$
$458$		0			0
$459$	19.1631			0.894457
$460$		0			0
$461$	−3.54919			−0.165302			−0.0826510	−	0.996579i	$-0.526339\pi$
$461$	−3.54919			−0.165302			−0.0826510	+	0.996579i	$0.526339\pi$
$462$		0			0
$463$	−10.1750	+	22.2802i	−0.472873	+	1.03545i	0.511489	+	0.859290i	$0.329094\pi$
$463$	−10.1750	+	22.2802i	−0.472873	+	1.03545i	−0.984362	+	0.176158i	$0.943633\pi$
$464$		0			0
$465$	6.70033	−	7.73259i	0.310720	−	0.358590i
$466$		0			0
$467$	−26.7657	+	17.2013i	−1.23857	+	0.795980i	−0.985203	−	0.171391i	$-0.945174\pi$
$467$	−26.7657	+	17.2013i	−1.23857	+	0.795980i	−0.253365	+	0.967371i	$0.581537\pi$
$468$		0			0
$469$	−3.49316	−	4.03132i	−0.161299	−	0.186149i
$470$		0			0
$471$	1.86639	−	12.9810i	0.0859987	−	0.598134i
$472$		0			0
$473$	0.749368	+	0.481589i	0.0344560	+	0.0221435i
$474$		0			0
$475$	−0.881193	−	1.92954i	−0.0404319	−	0.0885335i
$476$		0			0
$477$	−21.0381	−	6.17735i	−0.963270	−	0.282842i
$478$		0			0
$479$	−14.9643	+	4.39392i	−0.683737	+	0.200763i	−0.605111	−	0.796141i	$-0.706871\pi$
$479$	−14.9643	+	4.39392i	−0.683737	+	0.200763i	−0.0786258	+	0.996904i	$0.525053\pi$
$480$		0			0
$481$	1.52081	+	10.5775i	0.0693431	+	0.482292i
$482$		0			0
$483$	9.06366	−	4.67304i	0.412411	−	0.212631i
$484$		0			0
$485$	0.373603	+	2.59847i	0.0169645	+	0.117990i
$486$		0			0
$487$	32.1575	−	9.44229i	1.45719	−	0.427871i	0.545281	−	0.838253i	$-0.316423\pi$
$487$	32.1575	−	9.44229i	1.45719	−	0.427871i	0.911914	+	0.410382i	$0.134605\pi$
$488$		0			0
$489$	11.3332	+	3.32774i	0.512507	+	0.150486i
$490$		0			0
$491$	−6.89109	−	15.0894i	−0.310991	−	0.680974i	0.688009	−	0.725703i	$-0.258485\pi$
$491$	−6.89109	−	15.0894i	−0.310991	−	0.680974i	−0.998999	+	0.0447281i	$0.985758\pi$
$492$		0			0
$493$	28.8948	+	18.5696i	1.30136	+	0.836332i
$494$		0			0
$495$	−0.289718	+	2.01503i	−0.0130219	+	0.0905690i
$496$		0			0
$497$	12.5051	+	14.4317i	0.560932	+	0.647350i
$498$		0			0
$499$	13.9492	−	8.96462i	0.624453	−	0.401311i	−0.189799	−	0.981823i	$-0.560784\pi$
$499$	13.9492	−	8.96462i	0.624453	−	0.401311i	0.814252	+	0.580512i	$0.197147\pi$
$500$		0			0
$501$	2.47924	−	2.86120i	0.110764	−	0.127829i
$502$		0			0
$503$	11.2832	−	24.7067i	0.503092	−	1.10162i	−0.472360	−	0.881406i	$-0.656598\pi$
$503$	11.2832	−	24.7067i	0.503092	−	1.10162i	0.975452	−	0.220213i	$-0.0706751\pi$
$504$		0			0
$505$	−17.1908			−0.764980
$506$		0			0
$507$	−7.02052			−0.311792
$508$		0			0
$509$	3.95320	−	8.65630i	0.175223	−	0.383684i	−0.801561	−	0.597913i	$-0.795997\pi$
$509$	3.95320	−	8.65630i	0.175223	−	0.383684i	0.976783	+	0.214229i	$0.0687240\pi$
$510$		0			0
$511$	−19.9986	+	23.0796i	−0.884684	+	1.02098i
$512$		0			0
$513$	5.14720	−	3.30791i	0.227255	−	0.146048i
$514$		0			0
$515$	25.3894	+	29.3010i	1.11879	+	1.29115i
$516$		0			0
$517$	−0.545461	+	3.79377i	−0.0239894	+	0.166850i
$518$		0			0
$519$	0.490221	+	0.315046i	0.0215183	+	0.0138290i
$520$		0			0
$521$	−4.14423	−	9.07459i	−0.181562	−	0.397565i	0.796865	−	0.604157i	$-0.206490\pi$
$521$	−4.14423	−	9.07459i	−0.181562	−	0.397565i	−0.978427	+	0.206592i	$0.933763\pi$
$522$		0			0
$523$	−5.15459	−	1.51352i	−0.225394	−	0.0661818i	0.167085	−	0.985942i	$-0.446564\pi$
$523$	−5.15459	−	1.51352i	−0.225394	−	0.0661818i	−0.392480	+	0.919761i	$0.628383\pi$
$524$		0			0
$525$	−2.37021	+	0.695956i	−0.103444	+	0.0303740i
$526$		0			0
$527$	−5.65400	−	39.3244i	−0.246292	−	1.71300i
$528$		0			0
$529$	−18.0782	+	14.2189i	−0.786011	+	0.618213i
$530$		0			0
$531$	−1.31454	−	9.14286i	−0.0570464	−	0.396766i
$532$		0			0
$533$	−6.83971	+	2.00832i	−0.296261	+	0.0869900i
$534$		0			0
$535$	37.2966	+	10.9513i	1.61247	+	0.473464i
$536$		0			0
$537$	6.15690	+	13.4817i	0.265690	+	0.581779i
$538$		0			0
$539$	−1.52256	−	0.978490i	−0.0655813	−	0.0421465i
$540$		0			0
$541$	−4.66835	+	32.4691i	−0.200708	+	1.39596i	0.601482	+	0.798887i	$0.294577\pi$
$541$	−4.66835	+	32.4691i	−0.200708	+	1.39596i	−0.802190	+	0.597069i	$0.796332\pi$
$542$		0			0
$543$	−6.35048	−	7.32884i	−0.272525	−	0.314511i
$544$		0			0
$545$	31.1859	−	20.0419i	1.33586	−	0.858502i
$546$		0			0
$547$	27.2066	−	31.3981i	1.16327	−	1.34249i	0.234375	−	0.972146i	$-0.424696\pi$
$547$	27.2066	−	31.3981i	1.16327	−	1.34249i	0.928896	−	0.370340i	$-0.120759\pi$
$548$		0			0
$549$	−8.86862	+	19.4196i	−0.378503	+	0.828807i
$550$		0			0
$551$	10.9666			0.467193
$552$		0			0
$553$	−30.4209			−1.29363
$554$		0			0
$555$	6.05164	−	13.2513i	0.256878	−	0.562484i
$556$		0			0
$557$	21.5316	−	24.8488i	0.912323	−	1.05288i	−0.0860749	−	0.996289i	$-0.527432\pi$
$557$	21.5316	−	24.8488i	0.912323	−	1.05288i	0.998398	−	0.0565879i	$-0.0180221\pi$
$558$		0			0
$559$	2.61400	−	1.67992i	0.110560	−	0.0710528i
$560$		0			0
$561$	−0.688142	−	0.794159i	−0.0290534	−	0.0335294i
$562$		0			0
$563$	1.21760	−	8.46857i	0.0513156	−	0.356908i	−0.947944	−	0.318437i	$-0.896842\pi$
$563$	1.21760	−	8.46857i	0.0513156	−	0.356908i	0.999260	−	0.0384709i	$-0.0122487\pi$
$564$		0			0
$565$	34.4500	+	22.1397i	1.44932	+	0.931424i
$566$		0			0
$567$	8.86679	+	19.4156i	0.372370	+	0.815377i
$568$		0			0
$569$	23.1716	+	6.80379i	0.971403	+	0.285230i	0.728671	−	0.684864i	$-0.240138\pi$
$569$	23.1716	+	6.80379i	0.971403	+	0.285230i	0.242732	+	0.970093i	$0.421956\pi$
$570$		0			0
$571$	19.8105	−	5.81688i	0.829043	−	0.243429i	0.160437	−	0.987046i	$-0.448710\pi$
$571$	19.8105	−	5.81688i	0.829043	−	0.243429i	0.668606	+	0.743617i	$0.266891\pi$
$572$		0			0
$573$	0.827468	+	5.75517i	0.0345680	+	0.240426i
$574$		0			0
$575$	4.95218	−	2.55324i	0.206520	−	0.106477i
$576$		0			0
$577$	0.894365	+	6.22044i	0.0372329	+	0.258960i	0.999933	−	0.0116117i	$-0.00369621\pi$
$577$	0.894365	+	6.22044i	0.0372329	+	0.258960i	−0.962700	+	0.270572i	$0.912787\pi$
$578$		0			0
$579$	−11.3340	+	3.32796i	−0.471024	+	0.138305i
$580$		0			0
$581$	−12.0751	−	3.54556i	−0.500958	−	0.147095i
$582$		0			0
$583$	1.06534	+	2.33277i	0.0441220	+	0.0966137i
$584$		0			0
$585$	5.97396	+	3.83923i	0.246993	+	0.158733i
$586$		0			0
$587$	4.58353	−	31.8791i	0.189182	−	1.31579i	−0.644948	−	0.764226i	$-0.723121\pi$
$587$	4.58353	−	31.8791i	0.189182	−	1.31579i	0.834131	−	0.551567i	$-0.185970\pi$
$588$		0			0
$589$	−8.30679	−	9.58655i	−0.342275	−	0.395007i
$590$		0			0
$591$	3.19166	−	2.05116i	0.131287	−	0.0843733i
$592$		0			0
$593$	4.06316	−	4.68914i	0.166854	−	0.192560i	−0.666165	−	0.745805i	$-0.732065\pi$
$593$	4.06316	−	4.68914i	0.166854	−	0.192560i	0.833019	+	0.553245i	$0.186611\pi$
$594$		0			0
$595$	−21.1335	+	46.2760i	−0.866390	+	1.89713i
$596$		0			0
$597$	−9.37029			−0.383500
$598$		0			0
$599$	−2.67037			−0.109108			−0.0545542	−	0.998511i	$-0.517374\pi$
$599$	−2.67037			−0.109108			−0.0545542	+	0.998511i	$0.517374\pi$
$600$		0			0
$601$	0.344096	−	0.753465i	0.0140360	−	0.0307345i	−0.902484	−	0.430723i	$-0.858259\pi$
$601$	0.344096	−	0.753465i	0.0140360	−	0.0307345i	0.916520	+	0.399988i	$0.130986\pi$
$602$		0			0
$603$	2.58100	−	2.97863i	0.105106	−	0.121299i
$604$		0			0
$605$	−22.7703	+	14.6336i	−0.925744	+	0.594939i
$606$		0			0
$607$	11.2908	+	13.0302i	0.458278	+	0.528881i	0.937114	−	0.349023i	$-0.113487\pi$
$607$	11.2908	+	13.0302i	0.458278	+	0.528881i	−0.478836	+	0.877904i	$0.658941\pi$
$608$		0			0
$609$	1.81751	−	12.6411i	0.0736494	−	0.512243i
$610$		0			0
$611$	11.2474	+	7.22825i	0.455020	+	0.292424i
$612$		0			0
$613$	8.69746	+	19.0448i	0.351287	+	0.769212i	0.999967	+	0.00815017i	$0.00259431\pi$
$613$	8.69746	+	19.0448i	0.351287	+	0.769212i	−0.648680	+	0.761062i	$0.724678\pi$
$614$		0			0
$615$	9.32402	+	2.73778i	0.375981	+	0.110398i
$616$		0			0
$617$	13.8567	−	4.06871i	0.557852	−	0.163800i	0.00936021	−	0.999956i	$-0.497021\pi$
$617$	13.8567	−	4.06871i	0.557852	−	0.163800i	0.548491	+	0.836156i	$0.315202\pi$
$618$		0			0
$619$	0.154656	+	1.07565i	0.00621614	+	0.0432342i	0.992693	−	0.120664i	$-0.0385023\pi$
$619$	0.154656	+	1.07565i	0.00621614	+	0.0432342i	−0.986477	+	0.163898i	$0.947593\pi$
$620$		0			0
$621$	9.32244	+	13.0906i	0.374097	+	0.525307i
$622$		0			0
$623$	0.552781	+	3.84468i	0.0221467	+	0.154034i
$624$		0			0
$625$	28.2658	−	8.29960i	1.13063	−	0.331984i
$626$		0			0
$627$	−0.321921	−	0.0945247i	−0.0128563	−	0.00377495i
$628$		0			0
$629$	−23.4981	−	51.4536i	−0.936929	−	2.05159i
$630$		0			0
$631$	8.55998	+	5.50117i	0.340768	+	0.218998i	0.699820	−	0.714319i	$-0.253264\pi$
$631$	8.55998	+	5.50117i	0.340768	+	0.218998i	−0.359052	+	0.933317i	$0.616900\pi$
$632$		0			0
$633$	−0.631850	+	4.39461i	−0.0251138	+	0.174670i
$634$		0			0
$635$	−25.3658	−	29.2737i	−1.00661	−	1.16169i
$636$		0			0
$637$	−5.31111	+	3.41324i	−0.210434	+	0.135238i
$638$		0			0
$639$	−9.23971	+	10.6632i	−0.365517	+	0.421829i
$640$		0			0
$641$	−12.0680	+	26.4251i	−0.476656	+	1.04373i	0.506714	+	0.862114i	$0.330860\pi$
$641$	−12.0680	+	26.4251i	−0.476656	+	1.04373i	−0.983370	+	0.181616i	$0.941867\pi$
$642$		0			0
$643$	−38.2701			−1.50922			−0.754612	−	0.656171i	$-0.772175\pi$
$643$	−38.2701			−1.50922			−0.754612	+	0.656171i	$0.772175\pi$
$644$		0			0
$645$	−4.23588			−0.166788
$646$		0			0
$647$	−2.07947	+	4.55340i	−0.0817524	+	0.179013i	−0.946094	−	0.323893i	$-0.895008\pi$
$647$	−2.07947	+	4.55340i	−0.0817524	+	0.179013i	0.864341	+	0.502905i	$0.167736\pi$
$648$		0			0
$649$	−0.707483	+	0.816478i	−0.0277711	+	0.0320496i
$650$		0			0
$651$	−12.4270	+	7.98636i	−0.487053	+	0.313010i
$652$		0			0
$653$	0.714220	+	0.824254i	0.0279496	+	0.0322555i	0.769552	−	0.638584i	$-0.220479\pi$
$653$	0.714220	+	0.824254i	0.0279496	+	0.0322555i	−0.741603	+	0.670839i	$0.765934\pi$
$654$		0			0
$655$	3.03148	−	21.0844i	0.118450	−	0.823835i
$656$		0			0
$657$	−18.9822	−	12.1991i	−0.740566	−	0.475933i
$658$		0			0
$659$	10.2656	+	22.4786i	0.399893	+	0.875643i	0.997281	+	0.0736906i	$0.0234777\pi$
$659$	10.2656	+	22.4786i	0.399893	+	0.875643i	−0.597389	+	0.801952i	$0.703795\pi$
$660$		0			0
$661$	32.2253	+	9.46220i	1.25342	+	0.368037i	0.840041	−	0.542523i	$-0.182531\pi$
$661$	32.2253	+	9.46220i	1.25342	+	0.368037i	0.413378	+	0.910560i	$0.364349\pi$
$662$		0			0
$663$	−3.51708	+	1.03271i	−0.136592	+	0.0401070i
$664$		0			0
$665$	2.31163	+	16.0778i	0.0896413	+	0.623469i
$666$		0			0
$667$	1.37158	+	28.7722i	0.0531077	+	1.11406i
$668$		0			0
$669$	−1.64267	−	11.4250i	−0.0635094	−	0.441718i
$670$		0			0
$671$	2.39584	−	0.703481i	0.0924902	−	0.0271576i
$672$		0			0
$673$	8.83233	+	2.59341i	0.340461	+	0.0999685i	0.447494	−	0.894287i	$-0.352317\pi$
$673$	8.83233	+	2.59341i	0.340461	+	0.0999685i	−0.107032	+	0.994256i	$0.534135\pi$
$674$		0			0
$675$	−1.61724	−	3.54126i	−0.0622476	−	0.136303i
$676$		0			0
$677$	−10.1132	−	6.49937i	−0.388682	−	0.249791i	0.331676	−	0.943394i	$-0.392386\pi$
$677$	−10.1132	−	6.49937i	−0.388682	−	0.249791i	−0.720358	+	0.693603i	$0.756022\pi$
$678$		0			0
$679$	0.539391	−	3.75155i	0.0206999	−	0.143971i
$680$		0			0
$681$	−7.38971	−	8.52818i	−0.283174	−	0.326801i
$682$		0			0
$683$	−27.8475	+	17.8965i	−1.06555	+	0.684790i	−0.951176	−	0.308648i	$-0.900124\pi$
$683$	−27.8475	+	17.8965i	−1.06555	+	0.684790i	−0.114377	+	0.993437i	$0.536487\pi$
$684$		0			0
$685$	−10.3759	+	11.9745i	−0.396445	+	0.457521i
$686$		0			0
$687$	1.21540	−	2.66135i	0.0463704	−	0.101537i
$688$		0			0
$689$	8.94577			0.340807
$690$		0			0
$691$	28.0797			1.06820			0.534102	−	0.845420i	$-0.320650\pi$
$691$	28.0797			1.06820			0.534102	+	0.845420i	$0.320650\pi$
$692$		0			0
$693$	1.22096	−	2.67352i	0.0463803	−	0.101559i
$694$		0			0
$695$	−34.4337	+	39.7386i	−1.30614	+	1.50737i
$696$		0			0
$697$	31.7429	−	20.3999i	1.20235	−	0.772703i
$698$		0			0
$699$	4.90863	+	5.66486i	0.185661	+	0.214265i
$700$		0			0
$701$	0.547001	−	3.80448i	0.0206600	−	0.143693i	−0.976881	−	0.213786i	$-0.931420\pi$
$701$	0.547001	−	3.80448i	0.0206600	−	0.143693i	0.997540	+	0.0700929i	$0.0223296\pi$
$702$		0			0
$703$	−15.1934	−	9.76421i	−0.573030	−	0.368264i
$704$		0			0
$705$	−7.57133	−	16.5789i	−0.285153	−	0.624397i
$706$		0			0
$707$	23.8139	+	6.99239i	0.895614	+	0.262976i
$708$		0			0
$709$	4.44545	−	1.30530i	0.166952	−	0.0490216i	−0.197188	−	0.980366i	$-0.563181\pi$
$709$	4.44545	−	1.30530i	0.166952	−	0.0490216i	0.364140	+	0.931344i	$0.381363\pi$
$710$		0			0
$711$	−3.19884	−	22.2484i	−0.119966	−	0.834380i
$712$		0			0
$713$	24.1125	−	22.9928i	0.903021	−	0.861088i
$714$		0			0
$715$	−0.118203	−	0.822118i	−0.00442053	−	0.0307455i
$716$		0			0
$717$	−3.30787	+	0.971278i	−0.123535	+	0.0362731i
$718$		0			0
$719$	29.6534	+	8.70702i	1.10588	+	0.324717i	0.783188	−	0.621785i	$-0.213592\pi$
$719$	29.6534	+	8.70702i	1.10588	+	0.324717i	0.322697	+	0.946502i	$0.395411\pi$
$720$		0			0
$721$	−23.2530	−	50.9170i	−0.865987	−	1.89625i
$722$		0			0
$723$	6.07475	+	3.90400i	0.225922	+	0.145191i
$724$		0			0
$725$	0.993048	−	6.90680i	0.0368809	−	0.256512i
$726$		0			0
$727$	−13.4040	−	15.4691i	−0.497127	−	0.573715i	0.450629	−	0.892711i	$-0.351200\pi$
$727$	−13.4040	−	15.4691i	−0.497127	−	0.573715i	−0.947756	+	0.318996i	$0.896654\pi$
$728$		0			0
$729$	−8.24958	+	5.30168i	−0.305540	+	0.196359i
$730$		0			0
$731$	−10.7709	+	12.4303i	−0.398376	+	0.459750i
$732$		0			0
$733$	−11.1621	+	24.4416i	−0.412281	+	0.902769i	0.583595	+	0.812045i	$0.301646\pi$
$733$	−11.1621	+	24.4416i	−0.412281	+	0.902769i	−0.995876	+	0.0907246i	$0.971082\pi$
$734$		0			0
$735$	8.60644			0.317453
$736$		0			0
$737$	−0.460978			−0.0169804
$738$		0			0
$739$	13.6315	−	29.8488i	0.501443	−	1.09801i	−0.474555	−	0.880226i	$-0.657391\pi$
$739$	13.6315	−	29.8488i	0.501443	−	1.09801i	0.975998	−	0.217781i	$-0.0698818\pi$
$740$		0			0
$741$	−0.766421	+	0.884497i	−0.0281552	+	0.0324928i
$742$		0			0
$743$	−15.5877	+	10.0176i	−0.571856	+	0.367510i	−0.794383	−	0.607417i	$-0.792206\pi$
$743$	−15.5877	+	10.0176i	−0.571856	+	0.367510i	0.222527	+	0.974927i	$0.428569\pi$
$744$		0			0
$745$	8.94058	+	10.3180i	0.327557	+	0.378021i
$746$		0			0
$747$	1.32333	−	9.20395i	0.0484180	−	0.336755i
$748$		0			0
$749$	−47.2114	−	30.3409i	−1.72507	−	1.10863i
$750$		0			0
$751$	8.47684	+	18.5617i	0.309324	+	0.677325i	0.998900	−	0.0468879i	$-0.0149304\pi$
$751$	8.47684	+	18.5617i	0.309324	+	0.677325i	−0.689576	+	0.724213i	$0.742203\pi$
$752$		0			0
$753$	13.4172	+	3.93966i	0.488952	+	0.143569i
$754$		0			0
$755$	−2.24997	+	0.660652i	−0.0818849	+	0.0240436i
$756$		0			0
$757$	−0.787269	−	5.47557i	−0.0286138	−	0.199013i	0.970500	−	0.241100i	$-0.0775083\pi$
$757$	−0.787269	−	5.47557i	−0.0286138	−	0.199013i	−0.999114	+	0.0420873i	$0.986599\pi$
$758$		0			0
$759$	0.207734	−	0.856421i	0.00754028	−	0.0310861i
$760$		0			0
$761$	−2.21650	−	15.4161i	−0.0803480	−	0.558832i	−0.989739	−	0.142889i	$-0.954361\pi$
$761$	−2.21650	−	15.4161i	−0.0803480	−	0.558832i	0.909391	−	0.415943i	$-0.136548\pi$
$762$		0			0
$763$	−51.3530	+	15.0786i	−1.85910	+	0.545882i
$764$		0			0
$765$	−36.0663	−	10.5900i	−1.30398	−	0.382883i
$766$		0			0
$767$	1.56552	+	3.42802i	0.0565278	+	0.123779i
$768$		0			0
$769$	−8.21687	−	5.28066i	−0.296308	−	0.190425i	0.384037	−	0.923318i	$-0.374534\pi$
$769$	−8.21687	−	5.28066i	−0.296308	−	0.190425i	−0.680345	+	0.732892i	$0.738170\pi$
$770$		0			0
$771$	−1.73381	+	12.0589i	−0.0624417	+	0.434292i
$772$		0			0
$773$	10.5413	+	12.1653i	0.379143	+	0.437555i	0.912962	−	0.408044i	$-0.133789\pi$
$773$	10.5413	+	12.1653i	0.379143	+	0.437555i	−0.533819	+	0.845599i	$0.679244\pi$
$774$		0			0
$775$	−6.78984	+	4.36356i	−0.243898	+	0.156744i
$776$		0			0
$777$	−13.7731	+	15.8951i	−0.494109	+	0.570232i
$778$		0			0
$779$	5.00473	−	10.9588i	0.179313	−	0.392641i
$780$		0			0
$781$	1.65025			0.0590508
$782$		0			0
$783$	20.1268			0.719274
$784$		0			0
$785$	−22.7932	+	49.9103i	−0.813526	+	1.78137i
$786$		0			0
$787$	7.40072	−	8.54089i	0.263807	−	0.304450i	−0.608356	−	0.793664i	$-0.708171\pi$
$787$	7.40072	−	8.54089i	0.263807	−	0.304450i	0.872164	+	0.489214i	$0.162716\pi$
$788$		0			0
$789$	1.74409	−	1.12086i	0.0620914	−	0.0399037i
$790$		0			0
$791$	−38.7173	−	44.6821i	−1.37663	−	1.58871i
$792$		0			0
$793$	1.23958	−	8.62150i	0.0440189	−	0.306158i
$794$		0			0
$795$	−10.2591	−	6.59313i	−0.363853	−	0.233834i
$796$		0			0
$797$	−20.5222	−	44.9373i	−0.726934	−	1.59176i	−0.803925	−	0.594731i	$-0.797259\pi$
$797$	−20.5222	−	44.9373i	−0.726934	−	1.59176i	0.0769914	−	0.997032i	$-0.475469\pi$
$798$		0			0
$799$	−67.9032	−	19.9382i	−2.40224	−	0.705362i
$800$		0			0
$801$	−2.75369	+	0.808556i	−0.0972968	+	0.0285689i
$802$		0			0
$803$	0.375588	+	2.61227i	0.0132542	+	0.0921850i
$804$		0			0
$805$	−41.8928	+	8.07566i	−1.47653	+	0.284630i
$806$		0			0
$807$	−0.0115102	−	0.0800555i	−0.000405180	−	0.00281809i
$808$		0			0
$809$	52.8987	−	15.5325i	1.85982	−	0.546092i	0.860491	−	0.509466i	$-0.170157\pi$
$809$	52.8987	−	15.5325i	1.85982	−	0.546092i	0.999329	−	0.0366265i	$-0.0116612\pi$
$810$		0			0
$811$	48.0130	+	14.0979i	1.68596	+	0.495044i	0.977541	−	0.210745i	$-0.0675890\pi$
$811$	48.0130	+	14.0979i	1.68596	+	0.495044i	0.708422	+	0.705789i	$0.249407\pi$
$812$		0			0
$813$	3.94321	+	8.63443i	0.138294	+	0.302823i
$814$		0			0
$815$	−41.5730	−	26.7173i	−1.45624	−	0.935868i
$816$		0			0
$817$	−0.747363	+	5.19802i	−0.0261469	+	0.181856i
$818$		0			0
$819$	−6.71395	−	7.74831i	−0.234604	−	0.270748i
$820$		0			0
$821$	−16.0803	+	10.3342i	−0.561207	+	0.360666i	−0.790283	−	0.612743i	$-0.790066\pi$
$821$	−16.0803	+	10.3342i	−0.561207	+	0.360666i	0.229075	+	0.973409i	$0.426430\pi$
$822$		0			0
$823$	−0.523534	+	0.604191i	−0.0182493	+	0.0210608i	−0.764801	−	0.644267i	$-0.777163\pi$
$823$	−0.523534	+	0.604191i	−0.0182493	+	0.0210608i	0.746552	+	0.665328i	$0.231708\pi$
$824$		0			0
$825$	−0.0886826	+	0.194188i	−0.00308753	+	0.00676075i
$826$		0			0
$827$	−26.1707			−0.910046			−0.455023	−	0.890480i	$-0.650369\pi$
$827$	−26.1707			−0.910046			−0.455023	+	0.890480i	$0.650369\pi$
$828$		0			0
$829$	−23.0541			−0.800703			−0.400352	−	0.916362i	$-0.631112\pi$
$829$	−23.0541			−0.800703			−0.400352	+	0.916362i	$0.631112\pi$
$830$		0			0
$831$	6.21993	−	13.6198i	0.215767	−	0.472464i
$832$		0			0
$833$	21.8842	−	25.2557i	0.758243	−	0.875059i
$834$		0			0
$835$	−13.3251	+	8.56350i	−0.461133	+	0.296352i
$836$		0			0
$837$	−15.2453	−	17.5941i	−0.526956	−	0.608140i
$838$		0			0
$839$	−7.65382	+	53.2335i	−0.264239	+	1.83782i	0.235776	+	0.971807i	$0.424237\pi$
$839$	−7.65382	+	53.2335i	−0.264239	+	1.83782i	−0.500015	+	0.866017i	$0.666672\pi$
$840$		0			0
$841$	5.95162	+	3.82488i	0.205228	+	0.131892i
$842$		0			0
$843$	3.42523	+	7.50021i	0.117971	+	0.258321i
$844$		0			0
$845$	28.1827	+	8.27519i	0.969515	+	0.284675i
$846$		0			0
$847$	37.4953	−	11.0096i	1.28835	−	0.378294i
$848$		0			0
$849$	0.534209	+	3.71550i	0.0183340	+	0.127516i
$850$		0			0
$851$	23.7173	−	41.0829i	0.813020	−	1.40830i
$852$		0			0
$853$	4.10661	+	28.5621i	0.140608	+	0.977947i	0.930915	+	0.365236i	$0.119012\pi$
$853$	4.10661	+	28.5621i	0.140608	+	0.977947i	−0.790307	+	0.612711i	$0.790079\pi$
$854$		0			0
$855$	−11.5154	+	3.38124i	−0.393820	+	0.115636i
$856$		0			0
$857$	4.68505	+	1.37565i	0.160038	+	0.0469914i	0.360770	−	0.932655i	$-0.382514\pi$
$857$	4.68505	+	1.37565i	0.160038	+	0.0469914i	−0.200732	+	0.979646i	$0.564332\pi$
$858$		0			0
$859$	9.88345	+	21.6417i	0.337219	+	0.738406i	0.999945	−	0.0104552i	$-0.00332804\pi$
$859$	9.88345	+	21.6417i	0.337219	+	0.738406i	−0.662726	+	0.748862i	$0.730601\pi$
$860$		0			0
$861$	−11.8027	−	7.58513i	−0.402235	−	0.258501i
$862$		0			0
$863$	−4.32312	+	30.0680i	−0.147161	+	1.02353i	0.773677	+	0.633580i	$0.218415\pi$
$863$	−4.32312	+	30.0680i	−0.147161	+	1.02353i	−0.920838	+	0.389946i	$0.872494\pi$
$864$		0			0
$865$	−1.59656	−	1.84253i	−0.0542847	−	0.0626479i
$866$		0			0
$867$	7.83757	−	5.03690i	0.266178	−	0.171062i
$868$		0			0
$869$	−1.72160	+	1.98683i	−0.0584013	+	0.0673987i
$870$		0			0
$871$	−0.667995	+	1.46271i	−0.0226341	+	0.0495619i
$872$		0			0
$873$	2.80042			0.0947799
$874$		0			0
$875$	−34.1452			−1.15432
$876$		0			0
$877$	−5.34897	+	11.7126i	−0.180622	+	0.395506i	−0.978187	−	0.207726i	$-0.933394\pi$
$877$	−5.34897	+	11.7126i	−0.180622	+	0.395506i	0.797565	+	0.603233i	$0.206121\pi$
$878$		0			0
$879$	0.554717	−	0.640177i	0.0187101	−	0.0215926i
$880$		0			0
$881$	19.9494	−	12.8207i	0.672114	−	0.431941i	−0.159573	−	0.987186i	$-0.551012\pi$
$881$	19.9494	−	12.8207i	0.672114	−	0.431941i	0.831687	+	0.555245i	$0.187375\pi$
$882$		0			0
$883$	11.6711	+	13.4692i	0.392765	+	0.453275i	0.917349	−	0.398084i	$-0.130325\pi$
$883$	11.6711	+	13.4692i	0.392765	+	0.453275i	−0.524584	+	0.851359i	$0.675779\pi$
$884$		0			0
$885$	0.731127	−	5.08510i	0.0245766	−	0.170934i
$886$		0			0
$887$	−27.8497	−	17.8979i	−0.935101	−	0.600953i	−0.0180991	−	0.999836i	$-0.505761\pi$
$887$	−27.8497	−	17.8979i	−0.935101	−	0.600953i	−0.917002	+	0.398883i	$0.869398\pi$
$888$		0			0
$889$	23.2314	+	50.8696i	0.779156	+	1.70611i
$890$		0			0
$891$	1.76985	+	0.519676i	0.0592923	+	0.0174098i
$892$		0			0
$893$	−21.6805	+	6.36596i	−0.725509	+	0.213029i
$894$		0			0
$895$	−8.82474	−	61.3774i	−0.294978	−	2.05162i
$896$		0			0
$897$	−2.41644	−	1.90017i	−0.0806825	−	0.0634450i
$898$		0			0
$899$	−5.93835	−	41.3021i	−0.198055	−	1.37750i
$900$		0			0
$901$	−45.4343	+	13.3407i	−1.51363	+	0.444443i
$902$		0			0
$903$	5.86785	+	1.72296i	0.195270	+	0.0573364i
$904$		0			0
$905$	16.8543	+	36.9059i	0.560257	+	1.22679i
$906$		0			0
$907$	45.4402	+	29.2027i	1.50882	+	0.969658i	0.993643	+	0.112573i	$0.0359093\pi$
$907$	45.4402	+	29.2027i	1.50882	+	0.969658i	0.515175	+	0.857085i	$0.327727\pi$
$908$		0			0
$909$	−2.60981	+	18.1516i	−0.0865619	+	0.602051i
$910$		0			0
$911$	27.0192	+	31.1818i	0.895186	+	1.03310i	0.999257	+	0.0385300i	$0.0122675\pi$
$911$	27.0192	+	31.1818i	0.895186	+	1.03310i	−0.104071	+	0.994570i	$0.533187\pi$
$912$		0			0
$913$	−0.914926	+	0.587987i	−0.0302796	+	0.0194595i
$914$		0			0
$915$	−7.77572	+	8.97366i	−0.257057	+	0.296660i
$916$		0			0
$917$	−12.7755	+	27.9745i	−0.421885	+	0.923800i
$918$		0			0
$919$	41.8698			1.38116			0.690579	−	0.723257i	$-0.257356\pi$
$919$	41.8698			1.38116			0.690579	+	0.723257i	$0.257356\pi$
$920$		0			0
$921$	−11.9948			−0.395243
$922$		0			0
$923$	2.39135	−	5.23633i	0.0787124	−	0.172356i
$924$		0			0
$925$	−7.52533	+	8.68469i	−0.247431	+	0.285551i
$926$		0			0
$927$	34.7932	−	22.3602i	1.14276	−	0.734405i
$928$		0			0
$929$	2.16403	+	2.49742i	0.0709994	+	0.0819377i	0.790138	−	0.612929i	$-0.210009\pi$
$929$	2.16403	+	2.49742i	0.0709994	+	0.0819377i	−0.719139	+	0.694867i	$0.755463\pi$
$930$		0			0
$931$	1.51849	−	10.5613i	0.0497664	−	0.346133i
$932$		0			0
$933$	4.56654	+	2.93474i	0.149502	+	0.0960790i
$934$		0			0
$935$	1.82635	+	3.99914i	0.0597280	+	0.130786i
$936$		0			0
$937$	−11.0872	−	3.25548i	−0.362202	−	0.106352i	0.0955678	−	0.995423i	$-0.469533\pi$
$937$	−11.0872	−	3.25548i	−0.362202	−	0.106352i	−0.457770	+	0.889071i	$0.651352\pi$
$938$		0			0
$939$	−10.8401	+	3.18295i	−0.353755	+	0.103872i
$940$		0			0
$941$	1.57545	+	10.9575i	0.0513582	+	0.357204i	0.999254	+	0.0386232i	$0.0122972\pi$
$941$	1.57545	+	10.9575i	0.0513582	+	0.357204i	−0.947896	+	0.318581i	$0.896794\pi$
$942$		0			0
$943$	29.3777	+	11.7599i	0.956670	+	0.382955i
$944$		0			0
$945$	4.24251	+	29.5073i	0.138009	+	0.959872i
$946$		0			0
$947$	−46.9658	+	13.7904i	−1.52618	+	0.448128i	−0.933880	−	0.357587i	$-0.883600\pi$
$947$	−46.9658	+	13.7904i	−1.52618	+	0.448128i	−0.592304	+	0.805715i	$0.701782\pi$
$948$		0			0
$949$	8.83311	+	2.59363i	0.286735	+	0.0841929i
$950$		0			0
$951$	3.71810	+	8.14151i	0.120568	+	0.264007i
$952$		0			0
$953$	5.14369	+	3.30565i	0.166620	+	0.107080i	0.621293	−	0.783578i	$-0.286607\pi$
$953$	5.14369	+	3.30565i	0.166620	+	0.107080i	−0.454673	+	0.890658i	$0.650244\pi$
$954$		0			0
$955$	3.46197	−	24.0785i	0.112027	−	0.779163i
$956$		0			0
$957$	−0.722750	−	0.834098i	−0.0233632	−	0.0269626i
$958$		0			0
$959$	19.2442	−	12.3675i	0.621426	−	0.399366i
$960$		0			0
$961$	−11.3059	+	13.0477i	−0.364705	+	0.420892i
$962$		0			0
$963$	17.2255	−	37.7186i	0.555084	−	1.21547i
$964$		0			0
$965$	49.4211			1.59092
$966$		0			0
$967$	8.52591			0.274175			0.137087	−	0.990559i	$-0.456226\pi$
$967$	8.52591			0.274175			0.137087	+	0.990559i	$0.456226\pi$
$968$		0			0
$969$	2.57350	−	5.63519i	0.0826729	−	0.181028i
$970$		0			0
$971$	17.0305	−	19.6542i	0.546533	−	0.630733i	−0.413539	−	0.910487i	$-0.635707\pi$
$971$	17.0305	−	19.6542i	0.546533	−	0.630733i	0.960072	+	0.279754i	$0.0902528\pi$
$972$		0			0
$973$	63.8638	−	41.0428i	2.04738	−	1.31577i
$974$		0			0
$975$	0.487658	+	0.562788i	0.0156176	+	0.0180236i
$976$		0			0
$977$	1.18343	−	8.23091i	0.0378612	−	0.263330i	−0.962095	−	0.272715i	$-0.912078\pi$
$977$	1.18343	−	8.23091i	0.0378612	−	0.263330i	0.999956	+	0.00938509i	$0.00298741\pi$
$978$		0			0
$979$	0.282385	+	0.181478i	0.00902506	+	0.00580005i
$980$		0			0
$981$	−16.4277	−	35.9716i	−0.524495	−	1.14848i
$982$		0			0
$983$	−14.6122	−	4.29054i	−0.466058	−	0.136847i	0.0402686	−	0.999189i	$-0.487179\pi$
$983$	−14.6122	−	4.29054i	−0.466058	−	0.136847i	−0.506326	+	0.862342i	$0.668997\pi$
$984$		0			0
$985$	−15.2301	+	4.47197i	−0.485272	+	0.142489i
$986$		0			0
$987$	3.74484	+	26.0459i	0.119199	+	0.829051i
$988$		0			0
$989$	−13.7311	−	1.31068i	−0.436623	−	0.0416774i
$990$		0			0
$991$	3.52650	+	24.5274i	0.112023	+	0.779138i	0.965947	+	0.258740i	$0.0833072\pi$
$991$	3.52650	+	24.5274i	0.112023	+	0.779138i	−0.853924	+	0.520398i	$0.825784\pi$
$992$		0			0
$993$	−5.61843	+	1.64972i	−0.178296	+	0.0523523i
$994$		0			0
$995$	37.6155	+	11.0449i	1.19249	+	0.350147i
$996$		0			0
$997$	−18.9090	−	41.4049i	−0.598854	−	1.31131i	−0.929942	−	0.367707i	$-0.880143\pi$
$997$	−18.9090	−	41.4049i	−0.598854	−	1.31131i	0.331088	−	0.943600i	$-0.392584\pi$
$998$		0			0
$999$	−27.8843	−	17.9201i	−0.882219	−	0.566968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.49.2		30
4.3	odd	2		184.2.i.b.49.2	✓	30
23.8	even	11	inner	368.2.m.e.353.2		30
23.10	odd	22		8464.2.a.ch.1.9		15
23.13	even	11		8464.2.a.cg.1.9		15
92.31	odd	22		184.2.i.b.169.2	yes	30
92.59	odd	22		4232.2.a.bb.1.7		15
92.79	even	22		4232.2.a.ba.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.49.2	✓	30	4.3	odd	2
184.2.i.b.169.2	yes	30	92.31	odd	22
368.2.m.e.49.2		30	1.1	even	1	trivial
368.2.m.e.353.2		30	23.8	even	11	inner
4232.2.a.ba.1.7		15	92.79	even	22
4232.2.a.bb.1.7		15	92.59	odd	22
8464.2.a.cg.1.9		15	23.13	even	11
8464.2.a.ch.1.9		15	23.10	odd	22

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.246469 - 0.539692i) q^{3} +(-1.62555 + 1.87599i) q^{5} +(3.01490 - 1.93756i) q^{7} +(1.73406 + 2.00121i) q^{9} +(0.0440765 - 0.306559i) q^{11} +(-0.908855 - 0.584086i) q^{13} +(0.611808 + 1.33967i) q^{15} +(5.48698 + 1.61112i) q^{17} +(1.75191 - 0.514408i) q^{19} +(-0.302605 - 2.10467i) q^{21} +(1.56872 + 4.53201i) q^{23} +(-0.165336 - 1.14994i) q^{25} +(3.21526 - 0.944085i) q^{27} +(5.76293 + 1.69215i) q^{29} +(-2.88600 - 6.31946i) q^{31} +(-0.154584 - 0.0993451i) q^{33} +(-1.26604 + 8.80552i) q^{35} +(-6.47749 - 7.47543i) q^{37} +(-0.539231 + 0.346543i) q^{39} +(4.32093 - 4.98662i) q^{41} +(-1.19479 + 2.61623i) q^{43} -6.57307 q^{45} -12.3753 q^{47} +(2.42757 - 5.31565i) q^{49} +(2.22188 - 2.56419i) q^{51} +(-6.96589 + 4.47671i) q^{53} +(0.503453 + 0.581015i) q^{55} +(0.154170 - 1.07228i) q^{57} +(-2.93452 - 1.88590i) q^{59} +(3.34920 + 7.33372i) q^{61} +(9.10548 + 2.67361i) q^{63} +(2.57313 - 0.755540i) q^{65} +(-0.211823 - 1.47326i) q^{67} +(2.83253 + 0.270376i) q^{69} +(0.758305 + 5.27413i) q^{71} +(-8.17609 + 2.40072i) q^{73} +(-0.661364 - 0.194194i) q^{75} +(-0.461089 - 1.00964i) q^{77} +(-7.14090 - 4.58918i) q^{79} +(-0.847596 + 5.89516i) q^{81} +(-2.29959 - 2.65387i) q^{83} +(-11.9418 + 7.67455i) q^{85} +(2.33362 - 2.69315i) q^{87} +(-0.450235 + 0.985878i) q^{89} -3.87180 q^{91} -4.12187 q^{93} +(-1.88280 + 4.12277i) q^{95} +(0.692559 - 0.799256i) q^{97} +(0.689921 - 0.443385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41}+ \cdots + 17 q^{99}+O(q^{100}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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