LMFDB - Embedded newform 804.2.s.b.5.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0434100 - 1.73151i) q^{3} +(-1.09364 + 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(-2.99623 - 0.150329i) q^{9} +O(q^{10})$	\(q+(0.0434100 - 1.73151i) q^{3} +(-1.09364 + 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(-2.99623 - 0.150329i) q^{9} +(-3.69014 + 1.08352i) q^{11} +(-1.65469 - 2.57474i) q^{13} +(0.508549 + 1.90758i) q^{15} +(-4.10573 - 0.590315i) q^{17} +(-4.90683 - 5.66278i) q^{19} +(3.22732 - 3.54116i) q^{21} +(1.08727 - 0.496537i) q^{23} +(-3.11334 + 2.00082i) q^{25} +(-0.390363 + 5.18147i) q^{27} -7.40032i q^{29} +(0.00434668 - 0.00676357i) q^{31} +(1.71594 + 6.43654i) q^{33} +(-2.86801 - 1.30978i) q^{35} +4.76894 q^{37} +(-4.53001 + 2.75333i) q^{39} +(-0.919315 + 6.39398i) q^{41} +(-7.53507 - 1.08338i) q^{43} +(3.32507 - 0.797748i) q^{45} +(-3.24748 + 1.48308i) q^{47} +(0.0927634 + 0.645184i) q^{49} +(-1.20036 + 7.08347i) q^{51} +(0.624559 + 4.34391i) q^{53} +(3.68774 - 2.36997i) q^{55} +(-10.0182 + 8.25039i) q^{57} +(7.02119 - 10.9252i) q^{59} +(-0.929884 + 3.16689i) q^{61} +(-5.99145 - 5.74186i) q^{63} +(2.63643 + 2.28448i) q^{65} +(-4.74764 + 6.66783i) q^{67} +(-0.812560 - 1.90416i) q^{69} +(-11.4234 + 1.64244i) q^{71} +(11.3262 + 3.32568i) q^{73} +(3.32929 + 5.47763i) q^{75} +(-9.67720 - 4.41943i) q^{77} +(-0.942057 - 1.46587i) q^{79} +(8.95480 + 0.900844i) q^{81} +(2.07934 + 7.08159i) q^{83} +(4.67975 - 0.672846i) q^{85} +(-12.8137 - 0.321248i) q^{87} +(5.41699 + 2.47386i) q^{89} +(1.20487 - 8.38004i) q^{91} +(-0.0115225 - 0.00781992i) q^{93} +(7.18474 + 4.61735i) q^{95} -6.48460i q^{97} +(11.2194 - 2.69175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$	$1$

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
$3$	0.0434100	−	1.73151i	0.0250628	−	0.999686i
$3$	0.0434100	−	1.73151i	0.0250628	−	0.999686i
$4$		0			0
$5$	−1.09364	+	0.321121i	−0.489090	+	0.143610i	−0.516974	−	0.856001i	$-0.672941\pi$
$5$	−1.09364	+	0.321121i	−0.489090	+	0.143610i	0.0278834	+	0.999611i	$0.491123\pi$
$6$		0			0
$7$	2.09055	+	1.81147i	0.790153	+	0.684672i	0.953332	−	0.301925i	$-0.0976292\pi$
$7$	2.09055	+	1.81147i	0.790153	+	0.684672i	−0.163179	+	0.986597i	$0.552175\pi$
$8$		0			0
$9$	−2.99623	−	0.150329i	−0.998744	−	0.0501098i
$10$		0			0
$11$	−3.69014	+	1.08352i	−1.11262	+	0.326695i	−0.785855	−	0.618411i	$-0.787777\pi$
$11$	−3.69014	+	1.08352i	−1.11262	+	0.326695i	−0.326765	+	0.945106i	$0.605959\pi$
$12$		0			0
$13$	−1.65469	−	2.57474i	−0.458927	−	0.714105i	0.532259	−	0.846582i	$-0.321343\pi$
$13$	−1.65469	−	2.57474i	−0.458927	−	0.714105i	−0.991186	+	0.132477i	$0.957707\pi$
$14$		0			0
$15$	0.508549	+	1.90758i	0.131307	+	0.492536i
$16$		0			0
$17$	−4.10573	−	0.590315i	−0.995785	−	0.143172i	−0.374893	−	0.927068i	$-0.622321\pi$
$17$	−4.10573	−	0.590315i	−0.995785	−	0.143172i	−0.620892	+	0.783896i	$0.713230\pi$
$18$		0			0
$19$	−4.90683	−	5.66278i	−1.12570	−	1.29913i	−0.949144	−	0.314842i	$-0.898048\pi$
$19$	−4.90683	−	5.66278i	−1.12570	−	1.29913i	−0.176560	−	0.984290i	$-0.556497\pi$
$20$		0			0
$21$	3.22732	−	3.54116i	0.704260	−	0.772745i
$22$		0			0
$23$	1.08727	−	0.496537i	0.226710	−	0.103535i	−0.298822	−	0.954309i	$-0.596594\pi$
$23$	1.08727	−	0.496537i	0.226710	−	0.103535i	0.525532	+	0.850774i	$0.323866\pi$
$24$		0			0
$25$	−3.11334	+	2.00082i	−0.622668	+	0.400164i
$26$		0			0
$27$	−0.390363	+	5.18147i	−0.0751254	+	0.997174i
$28$		0			0
$29$		−	7.40032i		−	1.37420i	−0.726561	−	0.687102i	$-0.758882\pi$
$29$		−	7.40032i		−	1.37420i	0.726561	−	0.687102i	$-0.241118\pi$
$30$		0			0
$31$	0.00434668	−	0.00676357i	0.000780687	−	0.00121477i	−0.840863	−	0.541248i	$-0.817952\pi$
$31$	0.00434668	−	0.00676357i	0.000780687	−	0.00121477i	0.841644	+	0.540033i	$0.181588\pi$
$32$		0			0
$33$	1.71594	+	6.43654i	0.298707	+	1.12046i
$34$		0			0
$35$	−2.86801	−	1.30978i	−0.484782	−	0.221392i
$36$		0			0
$37$	4.76894			0.784009			0.392004	−	0.919963i	$-0.371782\pi$
$37$	4.76894			0.784009			0.392004	+	0.919963i	$0.371782\pi$
$38$		0			0
$39$	−4.53001	+	2.75333i	−0.725383	+	0.440886i
$40$		0			0
$41$	−0.919315	+	6.39398i	−0.143573	+	0.998571i	0.782883	+	0.622169i	$0.213748\pi$
$41$	−0.919315	+	6.39398i	−0.143573	+	0.998571i	−0.926456	+	0.376403i	$0.877161\pi$
$42$		0			0
$43$	−7.53507	−	1.08338i	−1.14909	−	0.165214i	−0.458657	−	0.888613i	$-0.651669\pi$
$43$	−7.53507	−	1.08338i	−1.14909	−	0.165214i	−0.690430	+	0.723400i	$0.742578\pi$
$44$		0			0
$45$	3.32507	−	0.797748i	0.495672	−	0.118921i
$46$		0			0
$47$	−3.24748	+	1.48308i	−0.473694	+	0.216329i	−0.637933	−	0.770092i	$-0.720210\pi$
$47$	−3.24748	+	1.48308i	−0.473694	+	0.216329i	0.164239	+	0.986421i	$0.447483\pi$
$48$		0			0
$49$	0.0927634	+	0.645184i	0.0132519	+	0.0921691i
$50$		0			0
$51$	−1.20036	+	7.08347i	−0.168084	+	0.991884i
$52$		0			0
$53$	0.624559	+	4.34391i	0.0857898	+	0.596681i	0.986685	+	0.162644i	$0.0520023\pi$
$53$	0.624559	+	4.34391i	0.0857898	+	0.596681i	−0.900895	+	0.434037i	$0.857089\pi$
$54$		0			0
$55$	3.68774	−	2.36997i	0.497255	−	0.319566i
$56$		0			0
$57$	−10.0182	+	8.25039i	−1.32694	+	1.09279i
$58$		0			0
$59$	7.02119	−	10.9252i	0.914081	−	1.42234i	0.00765668	−	0.999971i	$-0.497563\pi$
$59$	7.02119	−	10.9252i	0.914081	−	1.42234i	0.906425	−	0.422368i	$-0.138801\pi$
$60$		0			0
$61$	−0.929884	+	3.16689i	−0.119059	+	0.405479i	−0.997359	−	0.0726319i	$-0.976860\pi$
$61$	−0.929884	+	3.16689i	−0.119059	+	0.405479i	0.878299	+	0.478111i	$0.158678\pi$
$62$		0			0
$63$	−5.99145	−	5.74186i	−0.754852	−	0.723406i
$64$		0			0
$65$	2.63643	+	2.28448i	0.327009	+	0.283355i
$66$		0			0
$67$	−4.74764	+	6.66783i	−0.580017	+	0.814605i
$67$	−4.74764	+	6.66783i	−0.580017	+	0.814605i
$68$		0			0
$69$	−0.812560	−	1.90416i	−0.0978207	−	0.229234i
$70$		0			0
$71$	−11.4234	+	1.64244i	−1.35571	+	0.194921i	−0.781560	−	0.623830i	$-0.785576\pi$
$71$	−11.4234	+	1.64244i	−1.35571	+	0.194921i	−0.574148	+	0.818752i	$0.694667\pi$
$72$		0			0
$73$	11.3262	+	3.32568i	1.32563	+	0.389241i	0.866523	−	0.499137i	$-0.166350\pi$
$73$	11.3262	+	3.32568i	1.32563	+	0.389241i	0.459111	+	0.888379i	$0.348168\pi$
$74$		0			0
$75$	3.32929	+	5.47763i	0.384433	+	0.632502i
$76$		0			0
$77$	−9.67720	−	4.41943i	−1.10282	−	0.503640i
$78$		0			0
$79$	−0.942057	−	1.46587i	−0.105990	−	0.164923i	0.784207	−	0.620499i	$-0.213070\pi$
$79$	−0.942057	−	1.46587i	−0.105990	−	0.164923i	−0.890197	+	0.455576i	$0.849433\pi$
$80$		0			0
$81$	8.95480	+	0.900844i	0.994978	+	0.100094i
$82$		0			0
$83$	2.07934	+	7.08159i	0.228237	+	0.777305i	0.991373	+	0.131067i	$0.0418404\pi$
$83$	2.07934	+	7.08159i	0.228237	+	0.777305i	−0.763136	+	0.646238i	$0.776341\pi$
$84$		0			0
$85$	4.67975	−	0.672846i	0.507590	−	0.0729804i
$86$		0			0
$87$	−12.8137	−	0.321248i	−1.37377	−	0.0344414i
$88$		0			0
$89$	5.41699	+	2.47386i	0.574200	+	0.262228i	0.681281	−	0.732022i	$-0.261423\pi$
$89$	5.41699	+	2.47386i	0.574200	+	0.262228i	−0.107081	+	0.994250i	$0.534150\pi$
$90$		0			0
$91$	1.20487	−	8.38004i	0.126304	−	0.878467i
$92$		0			0
$93$	−0.0115225	−	0.00781992i	−0.00119483	−	0.000810888i
$94$		0			0
$95$	7.18474	+	4.61735i	0.737139	+	0.473731i
$96$		0			0
$97$		−	6.48460i		−	0.658412i	−0.944258	−	0.329206i	$-0.893219\pi$
$97$		−	6.48460i		−	0.658412i	0.944258	−	0.329206i	$-0.106781\pi$
$98$		0			0
$99$	11.2194	−	2.69175i	1.12759	−	0.270531i
$100$		0			0
$101$	8.92133	+	10.2958i	0.887706	+	1.02447i	0.999527	+	0.0307386i	$0.00978593\pi$
$101$	8.92133	+	10.2958i	0.887706	+	1.02447i	−0.111822	+	0.993728i	$0.535669\pi$
$102$		0			0
$103$	−11.7843	−	7.57331i	−1.16114	−	0.746221i	−0.189315	−	0.981916i	$-0.560627\pi$
$103$	−11.7843	−	7.57331i	−1.16114	−	0.746221i	−0.971827	+	0.235696i	$0.924263\pi$
$104$		0			0
$105$	−2.39238	+	4.90912i	−0.233473	+	0.479081i
$106$		0			0
$107$	5.60348	−	19.0837i	0.541709	−	1.84489i	0.00680961	−	0.999977i	$-0.497832\pi$
$107$	5.60348	−	19.0837i	0.541709	−	1.84489i	0.534900	−	0.844916i	$-0.320349\pi$
$108$		0			0
$109$	0.920825	+	1.43283i	0.0881990	+	0.137240i	0.882550	−	0.470219i	$-0.155825\pi$
$109$	0.920825	+	1.43283i	0.0881990	+	0.137240i	−0.794351	+	0.607459i	$0.792189\pi$
$110$		0			0
$111$	0.207020	−	8.25745i	0.0196494	−	0.783762i
$112$		0			0
$113$	−0.577431	−	0.169549i	−0.0543201	−	0.0159498i	0.254460	−	0.967083i	$-0.418102\pi$
$113$	−0.577431	−	0.169549i	−0.0543201	−	0.0159498i	−0.308780	+	0.951134i	$0.599921\pi$
$114$		0			0
$115$	−1.02963	+	0.892177i	−0.0960132	+	0.0831959i
$116$		0			0
$117$	4.57076	+	7.96327i	0.422567	+	0.736205i
$118$		0			0
$119$	−7.51389	−	8.67149i	−0.688797	−	0.794914i
$120$		0			0
$121$	3.18935	−	2.04967i	0.289941	−	0.186334i
$122$		0			0
$123$	11.0313	+	1.86936i	0.994659	+	0.168555i
$124$		0			0
$125$	6.49445	−	7.49499i	0.580881	−	0.670372i
$126$		0			0
$127$	13.6009	−	15.6963i	1.20689	−	1.39282i	0.309896	−	0.950770i	$-0.399706\pi$
$127$	13.6009	−	15.6963i	1.20689	−	1.39282i	0.896990	−	0.442051i	$-0.145749\pi$
$128$		0			0
$129$	−2.20298	+	13.0000i	−0.193961	+	1.14459i
$130$		0			0
$131$	5.58640	−	2.55122i	0.488086	−	0.222902i	−0.156142	−	0.987735i	$-0.549906\pi$
$131$	5.58640	−	2.55122i	0.488086	−	0.222902i	0.644229	+	0.764833i	$0.277179\pi$
$132$		0			0
$133$		−	20.7269i		−	1.79725i
$134$		0			0
$135$	−1.23696	−	5.79201i	−0.106461	−	0.498497i
$136$		0			0
$137$	0.685286	+	1.50057i	0.0585479	+	0.128202i	0.936645	−	0.350281i	$-0.113914\pi$
$137$	0.685286	+	1.50057i	0.0585479	+	0.128202i	−0.878097	+	0.478483i	$0.841187\pi$
$138$		0			0
$139$	−5.68952	−	19.3767i	−0.482579	−	1.64351i	−0.736611	−	0.676316i	$-0.763575\pi$
$139$	−5.68952	−	19.3767i	−0.482579	−	1.64351i	0.254033	−	0.967196i	$-0.418243\pi$
$140$		0			0
$141$	2.42698	+	5.68742i	0.204389	+	0.478967i
$142$		0			0
$143$	8.89583	+	7.70828i	0.743906	+	0.644599i
$144$		0			0
$145$	2.37640	+	8.09328i	0.197349	+	0.672110i
$146$		0			0
$147$	1.12117	−	0.132613i	0.0924723	−	0.0109377i
$148$		0			0
$149$	−12.1484	+	10.5266i	−0.995232	+	0.862373i	−0.990486	−	0.137616i	$-0.956056\pi$
$149$	−12.1484	+	10.5266i	−0.995232	+	0.862373i	−0.00474598	+	0.999989i	$0.501511\pi$
$150$		0			0
$151$	−1.94375	+	13.5191i	−0.158180	+	1.10017i	0.743804	+	0.668397i	$0.233019\pi$
$151$	−1.94375	+	13.5191i	−0.158180	+	1.10017i	−0.901984	+	0.431769i	$0.857890\pi$
$152$		0			0
$153$	12.2130	+	2.38593i	0.987360	+	0.192891i
$154$		0			0
$155$	−0.00258177	+	0.00879272i	−0.000207373	+	0.000706248i
$156$		0			0
$157$	−1.61205	−	3.52989i	−0.128655	−	0.281716i	0.834332	−	0.551262i	$-0.185854\pi$
$157$	−1.61205	−	3.52989i	−0.128655	−	0.281716i	−0.962987	+	0.269546i	$0.913126\pi$
$158$		0			0
$159$	7.54861	−	0.892860i	0.598644	−	0.0708084i
$160$		0			0
$161$	3.17244	+	0.931513i	0.250024	+	0.0734135i
$162$		0			0
$163$	−11.9476			−0.935806			−0.467903	−	0.883780i	$-0.654990\pi$
$163$	−11.9476			−0.935806			−0.467903	+	0.883780i	$0.654990\pi$
$164$		0			0
$165$	−3.94353	−	6.48823i	−0.307003	−	0.505108i
$166$		0			0
$167$	−8.83963	+	7.65959i	−0.684031	+	0.592717i	−0.925980	−	0.377573i	$-0.876759\pi$
$167$	−8.83963	+	7.65959i	−0.684031	+	0.592717i	0.241949	+	0.970289i	$0.422213\pi$
$168$		0			0
$169$	1.50908	−	3.30443i	0.116083	−	0.254187i
$170$		0			0
$171$	13.8507	+	17.7047i	1.05919	+	1.35391i
$172$		0			0
$173$	−5.21190	+	8.10988i	−0.396253	+	0.616582i	−0.980855	−	0.194738i	$-0.937614\pi$
$173$	−5.21190	+	8.10988i	−0.396253	+	0.616582i	0.584602	+	0.811320i	$0.301251\pi$
$174$		0			0
$175$	−10.1330	−	1.45691i	−0.765984	−	0.110132i
$176$		0			0
$177$	−18.6122	−	12.6315i	−1.39898	−	0.949442i
$178$		0			0
$179$	0.610074	−	1.33588i	0.0455990	−	0.0998480i	−0.885461	−	0.464713i	$-0.846158\pi$
$179$	0.610074	−	1.33588i	0.0455990	−	0.0998480i	0.931060	+	0.364865i	$0.118885\pi$
$180$		0			0
$181$	−3.40577	−	7.45760i	−0.253149	−	0.554319i	0.739805	−	0.672822i	$-0.234918\pi$
$181$	−3.40577	−	7.45760i	−0.253149	−	0.554319i	−0.992954	+	0.118502i	$0.962191\pi$
$182$		0			0
$183$	5.44313	+	1.74757i	0.402368	+	0.129184i
$184$		0			0
$185$	−5.21550	+	1.53141i	−0.383451	+	0.112591i
$186$		0			0
$187$	15.7903	−	2.27031i	1.15470	−	0.166021i
$188$		0			0
$189$	−10.2022	+	10.1250i	−0.742097	+	0.736484i
$190$		0			0
$191$	8.90948	−	19.5091i	0.644668	−	1.41163i	−0.251477	−	0.967863i	$-0.580916\pi$
$191$	8.90948	−	19.5091i	0.644668	−	1.41163i	0.896145	−	0.443762i	$-0.146356\pi$
$192$		0			0
$193$	−11.8842	−	7.63752i	−0.855444	−	0.549761i	0.0378242	−	0.999284i	$-0.487957\pi$
$193$	−11.8842	−	7.63752i	−0.855444	−	0.549761i	−0.893268	+	0.449524i	$0.851594\pi$
$194$		0			0
$195$	4.07005	−	4.46584i	0.291462	−	0.319805i
$196$		0			0
$197$	−0.402118	−	2.79679i	−0.0286497	−	0.199263i	0.970470	−	0.241224i	$-0.0775487\pi$
$197$	−0.402118	−	2.79679i	−0.0286497	−	0.199263i	−0.999119	+	0.0419605i	$0.986640\pi$
$198$		0			0
$199$	4.32271	−	4.98868i	0.306429	−	0.353638i	−0.581559	−	0.813504i	$-0.697557\pi$
$199$	4.32271	−	4.98868i	0.306429	−	0.353638i	0.887988	+	0.459866i	$0.152103\pi$
$200$		0			0
$201$	11.3393	+	8.51002i	0.799812	+	0.600251i
$202$		0			0
$203$	13.4055	−	15.4707i	0.940879	−	1.08583i
$204$		0			0
$205$	−1.04784	−	7.28792i	−0.0731846	−	0.509010i
$206$		0			0
$207$	−3.33234	+	1.32429i	−0.231614	+	0.0920447i
$208$		0			0
$209$	24.2427	+	15.5798i	1.67690	+	1.07768i
$210$		0			0
$211$	−4.70976	+	10.3129i	−0.324233	+	0.709972i	−0.999622	−	0.0274900i	$-0.991249\pi$
$211$	−4.70976	+	10.3129i	−0.324233	+	0.709972i	0.675389	+	0.737462i	$0.263976\pi$
$212$		0			0
$213$	2.34800	+	19.8510i	0.160882	+	1.36017i
$214$		0			0
$215$	8.58854	−	1.23485i	0.585734	−	0.0842158i
$216$		0			0
$217$	0.0213390	−	0.00626568i	0.00144858	−	0.000425342i
$218$		0			0
$219$	6.25011	−	19.4671i	0.422343	−	1.31546i
$220$		0			0
$221$	5.27378	+	11.5480i	0.354753	+	0.776801i
$222$		0			0
$223$	−2.85396	+	6.24929i	−0.191115	+	0.418484i	−0.980797	−	0.195033i	$-0.937519\pi$
$223$	−2.85396	+	6.24929i	−0.191115	+	0.418484i	0.789682	+	0.613517i	$0.210246\pi$
$224$		0			0
$225$	9.62907	−	5.52690i	0.641938	−	0.368460i
$226$		0			0
$227$	17.6790	+	2.54186i	1.17340	+	0.168709i	0.701320	−	0.712847i	$-0.252595\pi$
$227$	17.6790	+	2.54186i	1.17340	+	0.168709i	0.472079	+	0.881556i	$0.343504\pi$
$228$		0			0
$229$	9.84576	−	15.3203i	0.650626	−	1.01239i	−0.346604	−	0.938012i	$-0.612665\pi$
$229$	9.84576	−	15.3203i	0.650626	−	1.01239i	0.997230	−	0.0743824i	$-0.0236985\pi$
$230$		0			0
$231$	−8.07236	+	16.5643i	−0.531122	+	1.08985i
$232$		0			0
$233$	−2.89983	+	6.34973i	−0.189974	+	0.415985i	−0.980520	−	0.196417i	$-0.937069\pi$
$233$	−2.89983	+	6.34973i	−0.189974	+	0.415985i	0.790547	+	0.612402i	$0.209797\pi$
$234$		0			0
$235$	3.07533	−	2.66479i	0.200612	−	0.173831i
$236$		0			0
$237$	−2.57906	+	1.56755i	−0.167528	+	0.101823i
$238$		0			0
$239$	−1.00374			−0.0649266			−0.0324633	−	0.999473i	$-0.510335\pi$
$239$	−1.00374			−0.0649266			−0.0324633	+	0.999473i	$0.510335\pi$
$240$		0			0
$241$	25.1298	+	7.37876i	1.61875	+	0.475308i	0.960682	−	0.277651i	$-0.0895557\pi$
$241$	25.1298	+	7.37876i	1.61875	+	0.475308i	0.658068	+	0.752958i	$0.271374\pi$
$242$		0			0
$243$	1.94855	−	15.4662i	0.124999	−	0.992157i
$244$		0			0
$245$	−0.308632	−	0.675810i	−0.0197178	−	0.0431759i
$246$		0			0
$247$	−6.46095	+	22.0040i	−0.411100	+	1.40008i
$248$		0			0
$249$	12.3521	−	3.29298i	0.782781	−	0.208684i
$250$		0			0
$251$	−1.74308	+	12.1234i	−0.110022	+	0.765220i	0.857872	+	0.513863i	$0.171786\pi$
$251$	−1.74308	+	12.1234i	−0.110022	+	0.765220i	−0.967894	+	0.251357i	$0.919123\pi$
$252$		0			0
$253$	−3.47415	+	3.01037i	−0.218418	+	0.189260i
$254$		0			0
$255$	−0.961890	−	8.13222i	−0.0602359	−	0.509260i
$256$		0			0
$257$	−0.555928	−	1.89332i	−0.0346778	−	0.118102i	0.940335	−	0.340249i	$-0.110511\pi$
$257$	−0.555928	−	1.89332i	−0.0346778	−	0.118102i	−0.975013	+	0.222148i	$0.928693\pi$
$258$		0			0
$259$	9.96970	+	8.63879i	0.619487	+	0.536788i
$260$		0			0
$261$	−1.11249	+	22.1731i	−0.0688612	+	1.37248i
$262$		0			0
$263$	3.92129	+	13.3547i	0.241797	+	0.823486i	0.987556	+	0.157270i	$0.0502691\pi$
$263$	3.92129	+	13.3547i	0.241797	+	0.823486i	−0.745758	+	0.666216i	$0.767913\pi$
$264$		0			0
$265$	−2.07796	−	4.55011i	−0.127648	−	0.279511i
$266$		0			0
$267$	4.51865	−	9.27217i	0.276537	−	0.567448i
$268$		0			0
$269$		−	4.90578i		−	0.299111i	−0.988753	−	0.149555i	$-0.952216\pi$
$269$		−	4.90578i		−	0.299111i	0.988753	−	0.149555i	$-0.0477842\pi$
$270$		0			0
$271$	−27.8623	+	12.7243i	−1.69251	+	0.772945i	−0.693913	+	0.720059i	$0.744115\pi$
$271$	−27.8623	+	12.7243i	−1.69251	+	0.772945i	−0.998601	+	0.0528861i	$0.983158\pi$
$272$		0			0
$273$	−14.4578	−	2.45001i	−0.875025	−	0.148282i
$274$		0			0
$275$	9.32073	−	10.7567i	0.562061	−	0.648653i
$276$		0			0
$277$	7.92339	−	9.14408i	0.476071	−	0.549415i	−0.466020	−	0.884774i	$-0.654312\pi$
$277$	7.92339	−	9.14408i	0.476071	−	0.549415i	0.942090	+	0.335360i	$0.108858\pi$
$278$		0			0
$279$	−0.0140404	+	0.0196118i	−0.000840578	+	0.00117413i
$280$		0			0
$281$	−13.9279	+	8.95093i	−0.830870	+	0.533968i	−0.885554	−	0.464536i	$-0.846221\pi$
$281$	−13.9279	+	8.95093i	−0.830870	+	0.533968i	0.0546844	+	0.998504i	$0.482585\pi$
$282$		0			0
$283$	−3.29329	−	3.80066i	−0.195766	−	0.225926i	0.649377	−	0.760467i	$-0.275030\pi$
$283$	−3.29329	−	3.80066i	−0.195766	−	0.225926i	−0.845142	+	0.534541i	$0.820484\pi$
$284$		0			0
$285$	8.30687	−	12.2400i	0.492056	−	0.725035i
$286$		0			0
$287$	−13.5044	+	11.7016i	−0.797138	+	0.690724i
$288$		0			0
$289$	0.197150	+	0.0578886i	0.0115971	+	0.00340521i
$290$		0			0
$291$	−11.2281	−	0.281497i	−0.658205	−	0.0165016i
$292$		0			0
$293$	−6.01047	−	9.35248i	−0.351135	−	0.546377i	0.620093	−	0.784529i	$-0.287095\pi$
$293$	−6.01047	−	9.35248i	−0.351135	−	0.546377i	−0.971228	+	0.238151i	$0.923459\pi$
$294$		0			0
$295$	−4.17034	+	14.2029i	−0.242806	+	0.826923i
$296$		0			0
$297$	−4.17375	−	19.5433i	−0.242186	−	1.13402i
$298$		0			0
$299$	−3.07754	−	1.97781i	−0.177979	−	0.114380i
$300$		0			0
$301$	−13.7899	−	15.9144i	−0.794837	−	0.917291i
$302$		0			0
$303$	18.2145	−	15.0004i	1.04639	−	0.861751i
$304$		0			0
$305$		−	3.76204i		−	0.215414i
$306$		0			0
$307$	−13.2632	−	8.52373i	−0.756969	−	0.486475i	0.104349	−	0.994541i	$-0.466724\pi$
$307$	−13.2632	−	8.52373i	−0.756969	−	0.486475i	−0.861318	+	0.508066i	$0.830361\pi$
$308$		0			0
$309$	−13.6248	+	20.0758i	−0.775088	+	1.14208i
$310$		0			0
$311$	3.61950	−	25.1742i	0.205243	−	1.42750i	−0.583170	−	0.812350i	$-0.698188\pi$
$311$	3.61950	−	25.1742i	0.205243	−	1.42750i	0.788413	−	0.615146i	$-0.210903\pi$
$312$		0			0
$313$	20.7512	+	9.47674i	1.17293	+	0.535657i	0.904012	−	0.427507i	$-0.140608\pi$
$313$	20.7512	+	9.47674i	1.17293	+	0.535657i	0.268914	+	0.963164i	$0.413335\pi$
$314$		0			0
$315$	8.39632	+	4.35554i	0.473079	+	0.245407i
$316$		0			0
$317$	−18.1791	+	2.61376i	−1.02104	+	0.146803i	−0.632445	−	0.774605i	$-0.717949\pi$
$317$	−18.1791	+	2.61376i	−1.02104	+	0.146803i	−0.388595	+	0.921409i	$0.627040\pi$
$318$		0			0
$319$	8.01842	+	27.3082i	0.448945	+	1.52897i
$320$		0			0
$321$	−32.8003	−	10.5309i	−1.83074	−	0.587777i
$322$		0			0
$323$	16.8033	+	26.1464i	0.934960	+	1.45483i
$324$		0			0
$325$	10.3032	+	4.70532i	0.571519	+	0.261004i
$326$		0			0
$327$	2.52093	−	1.53222i	0.139408	−	0.0847317i
$328$		0			0
$329$	−9.47557	−	2.78228i	−0.522405	−	0.153392i
$330$		0			0
$331$	−8.39413	+	1.20689i	−0.461383	+	0.0663369i	−0.369087	−	0.929395i	$-0.620330\pi$
$331$	−8.39413	+	1.20689i	−0.461383	+	0.0663369i	−0.0922958	+	0.995732i	$0.529421\pi$
$332$		0			0
$333$	−14.2888	−	0.716912i	−0.783024	−	0.0392865i
$334$		0			0
$335$	3.05102	−	8.81676i	0.166695	−	0.481711i
$336$		0			0
$337$	−1.80903	−	1.56754i	−0.0985443	−	0.0853891i	0.604195	−	0.796836i	$-0.293495\pi$
$337$	−1.80903	−	1.56754i	−0.0985443	−	0.0853891i	−0.702740	+	0.711447i	$0.748040\pi$
$338$		0			0
$339$	−0.318642	+	0.992466i	−0.0173062	+	0.0539033i
$340$		0			0
$341$	−0.00871139	+	0.0296683i	−0.000471748	+	0.00160663i
$342$		0			0
$343$	9.49381	−	14.7727i	0.512618	−	0.797648i
$344$		0			0
$345$	1.50011	+	1.82154i	0.0807634	+	0.0980682i
$346$		0			0
$347$	−15.5069	+	9.96571i	−0.832456	+	0.534987i	−0.886058	−	0.463575i	$-0.846566\pi$
$347$	−15.5069	+	9.96571i	−0.832456	+	0.534987i	0.0536012	+	0.998562i	$0.482930\pi$
$348$		0			0
$349$	3.09748	+	21.5434i	0.165804	+	1.15319i	0.887441	+	0.460921i	$0.152481\pi$
$349$	3.09748	+	21.5434i	0.165804	+	1.15319i	−0.721637	+	0.692272i	$0.756610\pi$
$350$		0			0
$351$	13.9869	−	7.56862i	0.746564	−	0.403983i
$352$		0			0
$353$	−0.253361	−	1.76217i	−0.0134851	−	0.0937906i	0.981967	−	0.189050i	$-0.0605409\pi$
$353$	−0.253361	−	1.76217i	−0.0134851	−	0.0937906i	−0.995452	+	0.0952597i	$0.969632\pi$
$354$		0			0
$355$	11.9657	−	5.46453i	0.635071	−	0.290027i
$356$		0			0
$357$	−15.3409	+	12.6339i	−0.811927	+	0.668658i
$358$		0			0
$359$	−27.8551	−	4.00496i	−1.47014	−	0.211374i	−0.639760	−	0.768575i	$-0.720966\pi$
$359$	−27.8551	−	4.00496i	−1.47014	−	0.211374i	−0.830378	+	0.557201i	$0.811875\pi$
$360$		0			0
$361$	−5.28616	+	36.7660i	−0.278219	+	1.93505i
$362$		0			0
$363$	−3.41057	−	5.61135i	−0.179008	−	0.294520i
$364$		0			0
$365$	−13.4547			−0.704254
$366$		0			0
$367$	15.3338	+	7.00272i	0.800419	+	0.365539i	0.773258	−	0.634092i	$-0.218626\pi$
$367$	15.3338	+	7.00272i	0.800419	+	0.365539i	0.0271614	+	0.999631i	$0.491353\pi$
$368$		0			0
$369$	3.71568	−	19.0196i	0.193431	−	0.990123i
$370$		0			0
$371$	−6.56319	+	10.2125i	−0.340744	+	0.530207i
$372$		0			0
$373$		−	3.91498i		−	0.202710i	−0.994850	−	0.101355i	$-0.967682\pi$
$373$		−	3.91498i		−	0.202710i	0.994850	−	0.101355i	$-0.0323178\pi$
$374$		0			0
$375$	−12.6957	−	11.5705i	−0.655603	−	0.597500i
$376$		0			0
$377$	−19.0539	+	12.2452i	−0.981327	+	0.630660i
$378$		0			0
$379$	−29.4711	+	13.4590i	−1.51383	+	0.691343i	−0.987308	−	0.158818i	$-0.949232\pi$
$379$	−29.4711	+	13.4590i	−1.51383	+	0.691343i	−0.526523	+	0.850161i	$0.676504\pi$
$380$		0			0
$381$	−26.5878	−	24.2315i	−1.36214	−	1.24142i
$382$		0			0
$383$	−19.4053	−	22.3949i	−0.991565	−	1.14433i	−0.989530	−	0.144329i	$-0.953898\pi$
$383$	−19.4053	−	22.3949i	−0.991565	−	1.14433i	−0.00203522	−	0.999998i	$-0.500648\pi$
$384$		0			0
$385$	12.0025	+	1.72570i	0.611706	+	0.0879500i
$386$		0			0
$387$	22.4139	+	4.37880i	1.13936	+	0.222587i
$388$		0			0
$389$	−17.7489	−	27.6178i	−0.899903	−	1.40028i	−0.916335	−	0.400412i	$-0.868867\pi$
$389$	−17.7489	−	27.6178i	−0.899903	−	1.40028i	0.0164322	−	0.999865i	$-0.494769\pi$
$390$		0			0
$391$	−4.75713	+	1.39682i	−0.240578	+	0.0706402i
$392$		0			0
$393$	−4.17496	−	9.78364i	−0.210599	−	0.493519i
$394$		0			0
$395$	1.50099	+	1.30062i	0.0755231	+	0.0654412i
$396$		0			0
$397$	24.0828	−	7.07136i	1.20868	−	0.354901i	0.385516	−	0.922701i	$-0.374024\pi$
$397$	24.0828	−	7.07136i	1.20868	−	0.354901i	0.823166	+	0.567800i	$0.192205\pi$
$398$		0			0
$399$	−35.8888	−	0.899755i	−1.79669	−	0.0450441i
$400$		0			0
$401$	20.4141			1.01943			0.509717	−	0.860342i	$-0.329750\pi$
$401$	20.4141			1.01943			0.509717	+	0.860342i	$0.329750\pi$
$402$		0			0
$403$	−0.0246068			−0.00122575
$404$		0			0
$405$	−10.0826	+	1.89038i	−0.501009	+	0.0939338i
$406$		0			0
$407$	−17.5981	+	5.16726i	−0.872304	+	0.256131i
$408$		0			0
$409$	16.8847	+	14.6307i	0.834896	+	0.723442i	0.963342	−	0.268275i	$-0.0864535\pi$
$409$	16.8847	+	14.6307i	0.834896	+	0.723442i	−0.128446	+	0.991716i	$0.540999\pi$
$410$		0			0
$411$	2.62799	−	1.12144i	0.129629	−	0.0553164i
$412$		0			0
$413$	34.4688	−	10.1210i	1.69610	−	0.498019i
$414$		0			0
$415$	−4.54810	−	7.07698i	−0.223257	−	0.347395i
$416$		0			0
$417$	−33.7979	+	9.01029i	−1.65509	+	0.441236i
$418$		0			0
$419$	−19.2259	−	2.76426i	−0.939245	−	0.135043i	−0.344346	−	0.938843i	$-0.611899\pi$
$419$	−19.2259	−	2.76426i	−0.939245	−	0.135043i	−0.594900	+	0.803800i	$0.702808\pi$
$420$		0			0
$421$	3.03310	+	3.50038i	0.147824	+	0.170598i	0.824833	−	0.565377i	$-0.191269\pi$
$421$	3.03310	+	3.50038i	0.147824	+	0.170598i	−0.677008	+	0.735975i	$0.736724\pi$
$422$		0			0
$423$	9.95316	−	3.95545i	0.483939	−	0.192320i
$424$		0			0
$425$	13.9636	−	6.37698i	0.677336	−	0.309329i
$426$		0			0
$427$	−7.68070	+	4.93609i	−0.371695	+	0.238874i
$428$		0			0
$429$	13.7331	−	15.0686i	0.663040	−	0.727517i
$430$		0			0
$431$			14.1768i			0.682872i	0.939905	+	0.341436i	$0.110913\pi$
$431$			14.1768i			0.682872i	−0.939905	+	0.341436i	$0.889087\pi$
$432$		0			0
$433$	−5.01481	+	7.80320i	−0.240996	+	0.374998i	−0.940591	−	0.339543i	$-0.889728\pi$
$433$	−5.01481	+	7.80320i	−0.240996	+	0.374998i	0.699594	+	0.714540i	$0.253364\pi$
$434$		0			0
$435$	14.1167	−	3.76342i	0.676845	−	0.180442i
$436$		0			0
$437$	−8.14681	−	3.72052i	−0.389715	−	0.177977i
$438$		0			0
$439$	−19.7692			−0.943531			−0.471766	−	0.881724i	$-0.656383\pi$
$439$	−19.7692			−0.943531			−0.471766	+	0.881724i	$0.656383\pi$
$440$		0			0
$441$	−0.180951	−	1.94706i	−0.00861669	−	0.0927174i
$442$		0			0
$443$	2.98481	−	20.7598i	0.141812	−	0.986328i	−0.787311	−	0.616557i	$-0.788527\pi$
$443$	2.98481	−	20.7598i	0.141812	−	0.986328i	0.929123	−	0.369771i	$-0.120564\pi$
$444$		0			0
$445$	−6.71864	−	0.965995i	−0.318494	−	0.0457926i
$446$		0			0
$447$	17.6995	+	21.4919i	0.837159	+	1.01653i
$448$		0			0
$449$	3.28217	−	1.49892i	0.154895	−	0.0707382i	−0.336459	−	0.941698i	$-0.609229\pi$
$449$	3.28217	−	1.49892i	0.154895	−	0.0707382i	0.491354	+	0.870960i	$0.336502\pi$
$450$		0			0
$451$	−3.53562	−	24.5908i	−0.166486	−	1.15794i
$452$		0			0
$453$	23.3240	+	3.95248i	1.09586	+	0.185704i
$454$		0			0
$455$	1.37332	+	9.55165i	0.0643822	+	0.447788i
$456$		0			0
$457$	3.95969	−	2.54474i	0.185227	−	0.119038i	−0.444741	−	0.895659i	$-0.646704\pi$
$457$	3.95969	−	2.54474i	0.185227	−	0.119038i	0.629968	+	0.776621i	$0.283068\pi$
$458$		0			0
$459$	4.66142	−	21.0433i	0.217576	−	0.982215i
$460$		0			0
$461$	19.9136	−	30.9862i	0.927469	−	1.44317i	0.0312737	−	0.999511i	$-0.490044\pi$
$461$	19.9136	−	30.9862i	0.927469	−	1.44317i	0.896196	−	0.443659i	$-0.146320\pi$
$462$		0			0
$463$	−1.45589	+	4.95832i	−0.0676611	+	0.230433i	−0.986381	−	0.164478i	$-0.947406\pi$
$463$	−1.45589	+	4.95832i	−0.0676611	+	0.230433i	0.918720	+	0.394910i	$0.129224\pi$
$464$		0			0
$465$	0.0151126	+	0.00485205i	0.000700829	+	0.000225009i
$466$		0			0
$467$	3.00536	+	2.60416i	0.139071	+	0.120506i	0.721619	−	0.692291i	$-0.243398\pi$
$467$	3.00536	+	2.60416i	0.139071	+	0.120506i	−0.582547	+	0.812797i	$0.697944\pi$
$468$		0			0
$469$	−22.0037	+	5.33920i	−1.01604	+	0.246541i
$470$		0			0
$471$	−6.18201	+	2.63804i	−0.284852	+	0.121554i
$472$		0			0
$473$	28.9793	−	4.16660i	1.33247	−	0.191581i
$474$		0			0
$475$	26.6069	+	7.81248i	1.22081	+	0.358461i
$476$		0			0
$477$	−1.21831	−	13.1092i	−0.0557824	−	0.600231i
$478$		0			0
$479$	−25.6151	−	11.6980i	−1.17038	−	0.534495i	−0.267153	−	0.963654i	$-0.586083\pi$
$479$	−25.6151	−	11.6980i	−1.17038	−	0.534495i	−0.903229	+	0.429159i	$0.858810\pi$
$480$		0			0
$481$	−7.89110	−	12.2788i	−0.359803	−	0.559864i
$482$		0			0
$483$	1.75064	−	5.45267i	0.0796568	−	0.248105i
$484$		0			0
$485$	2.08234	+	7.09181i	0.0945544	+	0.322023i
$486$		0			0
$487$	−4.01264	+	0.576930i	−0.181830	+	0.0261432i	−0.232628	−	0.972566i	$-0.574733\pi$
$487$	−4.01264	+	0.576930i	−0.181830	+	0.0261432i	0.0507982	+	0.998709i	$0.483823\pi$
$488$		0			0
$489$	−0.518644	+	20.6873i	−0.0234539	+	0.935512i
$490$		0			0
$491$	−26.9926	−	12.3271i	−1.21816	−	0.556315i	−0.300538	−	0.953770i	$-0.597166\pi$
$491$	−26.9926	−	12.3271i	−1.21816	−	0.556315i	−0.917622	+	0.397455i	$0.869893\pi$
$492$		0			0
$493$	−4.36852	+	30.3837i	−0.196748	+	1.36841i
$494$		0			0
$495$	−11.4056	+	6.54660i	−0.512644	+	0.294248i
$496$		0			0
$497$	−26.8564	−	17.2596i	−1.20467	−	0.774197i
$498$		0			0
$499$		−	29.0682i		−	1.30127i	−0.759391	−	0.650635i	$-0.774503\pi$
$499$		−	29.0682i		−	1.30127i	0.759391	−	0.650635i	$-0.225497\pi$
$500$		0			0
$501$	12.8789	+	15.6384i	0.575387	+	0.698672i
$502$		0			0
$503$	−21.9061	−	25.2810i	−0.976744	−	1.12722i	−0.991860	−	0.127336i	$-0.959357\pi$
$503$	−21.9061	−	25.2810i	−0.976744	−	1.12722i	0.0151160	−	0.999886i	$-0.495188\pi$
$504$		0			0
$505$	−13.0629	−	8.39502i	−0.581292	−	0.373573i
$506$		0			0
$507$	−5.65614	−	2.75643i	−0.251198	−	0.122418i
$508$		0			0
$509$	−11.6770	+	39.7683i	−0.517575	+	1.76270i	0.120487	+	0.992715i	$0.461554\pi$
$509$	−11.6770	+	39.7683i	−0.517575	+	1.76270i	−0.638062	+	0.769985i	$0.720264\pi$
$510$		0			0
$511$	17.6537	+	27.4696i	0.780952	+	1.21518i
$512$		0			0
$513$	31.2570	−	23.2140i	1.38003	−	1.02493i
$514$		0			0
$515$	15.3197	+	4.49828i	0.675068	+	0.198218i
$516$		0			0
$517$	10.3767	−	8.99149i	0.456368	−	0.395445i
$518$		0			0
$519$	13.8161	+	9.37649i	0.606458	+	0.411582i
$520$		0			0
$521$	7.20556	+	8.31566i	0.315681	+	0.364315i	0.891309	−	0.453396i	$-0.149788\pi$
$521$	7.20556	+	8.31566i	0.315681	+	0.364315i	−0.575628	+	0.817712i	$0.695242\pi$
$522$		0			0
$523$	−14.9040	+	9.57823i	−0.651707	+	0.418827i	−0.824290	−	0.566168i	$-0.808425\pi$
$523$	−14.9040	+	9.57823i	−0.651707	+	0.418827i	0.172582	+	0.984995i	$0.444789\pi$
$524$		0			0
$525$	−2.96252	+	17.4821i	−0.129295	+	0.762983i
$526$		0			0
$527$	−0.0218389	+	0.0252035i	−0.000951319	+	0.00109788i
$528$		0			0
$529$	−14.1262	+	16.3025i	−0.614183	+	0.708805i
$530$		0			0
$531$	−22.6795	+	31.6789i	−0.984206	+	1.37475i
$532$		0			0
$533$	17.9840	−	8.21303i	0.778975	−	0.355746i
$534$		0			0
$535$			22.6701i			0.980114i
$536$		0			0
$537$	−2.28659	−	1.11434i	−0.0986738	−	0.0480872i
$538$		0			0
$539$	−1.04138	−	2.28031i	−0.0448555	−	0.0982199i
$540$		0			0
$541$	8.97688	+	30.5724i	0.385946	+	1.31441i	0.892049	+	0.451939i	$0.149268\pi$
$541$	8.97688	+	30.5724i	0.385946	+	1.31441i	−0.506103	+	0.862473i	$0.668914\pi$
$542$		0			0
$543$	−13.0607	+	5.57338i	−0.560490	+	0.239177i
$544$		0			0
$545$	−1.46716	−	1.27130i	−0.0628464	−	0.0544567i
$546$		0			0
$547$	5.92930	+	20.1934i	0.253519	+	0.863406i	0.983649	+	0.180097i	$0.0576413\pi$
$547$	5.92930	+	20.1934i	0.253519	+	0.863406i	−0.730130	+	0.683308i	$0.760541\pi$
$548$		0			0
$549$	3.26222	−	9.34895i	0.139228	−	0.399004i
$550$		0			0
$551$	−41.9064	+	36.3121i	−1.78527	+	1.54695i
$552$		0			0
$553$	0.685963	−	4.77098i	0.0291701	−	0.202883i
$554$		0			0
$555$	2.42524	+	9.09715i	0.102946	+	0.386152i
$556$		0			0
$557$	3.60071	−	12.2629i	0.152567	−	0.519595i	−0.847368	−	0.531006i	$-0.821814\pi$
$557$	3.60071	−	12.2629i	0.152567	−	0.519595i	0.999935	+	0.0114112i	$0.00363236\pi$
$558$		0			0
$559$	9.67875	+	21.1935i	0.409368	+	0.896390i
$560$		0			0
$561$	−3.24560	−	27.4396i	−0.137029	−	1.15850i
$562$		0			0
$563$	43.9639	+	12.9090i	1.85286	+	0.544048i	0.999751	+	0.0223106i	$0.00710228\pi$
$563$	43.9639	+	12.9090i	1.85286	+	0.544048i	0.853106	+	0.521737i	$0.174716\pi$
$564$		0			0
$565$	0.685947			0.0288580
$566$		0			0
$567$	17.0886	+	18.1046i	0.717654	+	0.760322i
$568$		0			0
$569$	8.34604	−	7.23188i	0.349884	−	0.303176i	−0.462132	−	0.886811i	$-0.652915\pi$
$569$	8.34604	−	7.23188i	0.349884	−	0.303176i	0.812016	+	0.583635i	$0.198370\pi$
$570$		0			0
$571$	−8.80710	+	19.2849i	−0.368566	+	0.807046i	0.630947	+	0.775826i	$0.282667\pi$
$571$	−8.80710	+	19.2849i	−0.368566	+	0.807046i	−0.999513	+	0.0312200i	$0.990061\pi$
$572$		0			0
$573$	−33.3933	−	16.2737i	−1.39502	−	0.679844i
$574$		0			0
$575$	−2.39154	+	3.72131i	−0.0997342	+	0.155190i
$576$		0			0
$577$	−19.0613	−	2.74060i	−0.793531	−	0.114093i	−0.266385	−	0.963867i	$-0.585829\pi$
$577$	−19.0613	−	2.74060i	−0.793531	−	0.114093i	−0.527147	+	0.849774i	$0.676738\pi$
$578$		0			0
$579$	−13.7403	+	20.2460i	−0.571028	+	0.841397i
$580$		0			0
$581$	−8.48112	+	18.5711i	−0.351856	+	0.770457i
$582$		0			0
$583$	−7.01144	−	15.3529i	−0.290384	−	0.635853i
$584$		0			0
$585$	−7.55594	−	7.24118i	−0.312400	−	0.299386i
$586$		0			0
$587$	14.3810	−	4.22263i	0.593566	−	0.174287i	0.0288662	−	0.999583i	$-0.490810\pi$
$587$	14.3810	−	4.22263i	0.593566	−	0.174287i	0.564699	+	0.825297i	$0.308992\pi$
$588$		0			0
$589$	−0.0596291	+	0.00857337i	−0.00245697	+	0.000353259i
$590$		0			0
$591$	−4.86012	+	0.574861i	−0.199919	+	0.0236466i
$592$		0			0
$593$	15.9821	−	34.9959i	0.656306	−	1.43711i	−0.229619	−	0.973281i	$-0.573748\pi$
$593$	15.9821	−	34.9959i	0.656306	−	1.43711i	0.885925	−	0.463829i	$-0.153525\pi$
$594$		0			0
$595$	11.0021	+	7.07061i	0.451041	+	0.289867i
$596$		0			0
$597$	−8.45028	−	7.70136i	−0.345847	−	0.315196i
$598$		0			0
$599$	4.01145	+	27.9002i	0.163903	+	1.13997i	0.891187	+	0.453636i	$0.149873\pi$
$599$	4.01145	+	27.9002i	0.163903	+	1.13997i	−0.727284	+	0.686337i	$0.759218\pi$
$600$		0			0
$601$	−2.81122	+	3.24432i	−0.114672	+	0.132338i	−0.810183	−	0.586177i	$-0.800632\pi$
$601$	−2.81122	+	3.24432i	−0.114672	+	0.132338i	0.695511	+	0.718515i	$0.255178\pi$
$602$		0			0
$603$	15.2274	−	19.2646i	0.620108	−	0.784517i
$604$		0			0
$605$	−2.82980	+	3.26577i	−0.115048	+	0.132772i
$606$		0			0
$607$	−0.831144	−	5.78073i	−0.0337351	−	0.234633i	0.965977	−	0.258628i	$-0.0832704\pi$
$607$	−0.831144	−	5.78073i	−0.0337351	−	0.234633i	−0.999712	+	0.0239954i	$0.992361\pi$
$608$		0			0
$609$	−26.2057	−	23.8832i	−1.06191	−	0.967797i
$610$		0			0
$611$	9.19210	+	5.90741i	0.371873	+	0.238988i
$612$		0			0
$613$	17.4434	−	38.1957i	0.704531	−	1.54271i	−0.129858	−	0.991533i	$-0.541452\pi$
$613$	17.4434	−	38.1957i	0.704531	−	1.54271i	0.834389	−	0.551176i	$-0.185821\pi$
$614$		0			0
$615$	−12.6646	+	1.49798i	−0.510684	+	0.0604044i
$616$		0			0
$617$	32.9759	−	4.74122i	1.32756	−	0.190874i	0.558209	−	0.829701i	$-0.311489\pi$
$617$	32.9759	−	4.74122i	1.32756	−	0.190874i	0.769351	+	0.638826i	$0.220580\pi$
$618$		0			0
$619$	−1.44894	+	0.425447i	−0.0582378	+	0.0171002i	−0.310722	−	0.950501i	$-0.600571\pi$
$619$	−1.44894	+	0.425447i	−0.0582378	+	0.0171002i	0.252484	+	0.967601i	$0.418753\pi$
$620$		0			0
$621$	2.14836	+	5.82746i	0.0862109	+	0.233848i
$622$		0			0
$623$	6.84317	+	14.9844i	0.274166	+	0.600339i
$624$		0			0
$625$	2.99113	−	6.54967i	0.119645	−	0.261987i
$626$		0			0
$627$	28.0289	−	41.3000i	1.11937	−	1.64936i
$628$		0			0
$629$	−19.5800	−	2.81517i	−0.780704	−	0.112248i
$630$		0			0
$631$	12.0269	−	18.7142i	0.478784	−	0.745002i	−0.514896	−	0.857253i	$-0.672170\pi$
$631$	12.0269	−	18.7142i	0.478784	−	0.745002i	0.993680	+	0.112250i	$0.0358059\pi$
$632$		0			0
$633$	17.6525	+	8.60267i	0.701623	+	0.341925i
$634$		0			0
$635$	−9.83408	+	21.5336i	−0.390254	+	0.854536i
$636$		0			0
$637$	1.50769	−	1.30642i	0.0597368	−	0.0517622i
$638$		0			0
$639$	34.4740	−	3.20385i	1.36377	−	0.126742i
$640$		0			0
$641$	−18.4942			−0.730477			−0.365239	−	0.930914i	$-0.619013\pi$
$641$	−18.4942			−0.730477			−0.365239	+	0.930914i	$0.619013\pi$
$642$		0			0
$643$	−15.6061	−	4.58236i	−0.615444	−	0.180711i	−0.0408714	−	0.999164i	$-0.513013\pi$
$643$	−15.6061	−	4.58236i	−0.615444	−	0.180711i	−0.574572	+	0.818454i	$0.694832\pi$
$644$		0			0
$645$	−1.76531	−	14.9247i	−0.0695092	−	0.587660i
$646$		0			0
$647$	17.4739	+	38.2625i	0.686969	+	1.50425i	0.855087	+	0.518485i	$0.173504\pi$
$647$	17.4739	+	38.2625i	0.686969	+	1.50425i	−0.168117	+	0.985767i	$0.553769\pi$
$648$		0			0
$649$	−14.0715	+	47.9231i	−0.552355	+	1.88115i
$650$		0			0
$651$	−0.00992275	−	0.0372205i	−0.000388903	−	0.00145879i
$652$		0			0
$653$	6.03492	−	41.9738i	0.236165	−	1.64256i	−0.434406	−	0.900717i	$-0.643042\pi$
$653$	6.03492	−	41.9738i	0.236165	−	1.64256i	0.670571	−	0.741845i	$-0.266049\pi$
$654$		0			0
$655$	−5.29026	+	4.58403i	−0.206707	+	0.179113i
$656$		0			0
$657$	−33.4360	−	11.6672i	−1.30446	−	0.455180i
$658$		0			0
$659$	10.1402	+	34.5344i	0.395006	+	1.34527i	0.881748	+	0.471721i	$0.156367\pi$
$659$	10.1402	+	34.5344i	0.395006	+	1.34527i	−0.486741	+	0.873546i	$0.661815\pi$
$660$		0			0
$661$	26.8605	+	23.2748i	1.04475	+	0.905283i	0.995618	−	0.0935088i	$-0.0298083\pi$
$661$	26.8605	+	23.2748i	1.04475	+	0.905283i	0.0491342	+	0.998792i	$0.484354\pi$
$662$		0			0
$663$	20.2243	−	8.63030i	0.785448	−	0.335173i
$664$		0			0
$665$	6.65585	+	22.6678i	0.258103	+	0.879018i
$666$		0			0
$667$	−3.67453	−	8.04611i	−0.142279	−	0.311547i
$668$		0			0
$669$	10.6968	+	5.21293i	0.413562	+	0.201543i
$670$		0			0
$671$		−	12.6938i		−	0.490040i
$672$		0			0
$673$	5.30639	−	2.42335i	0.204546	−	0.0934131i	−0.310508	−	0.950571i	$-0.600499\pi$
$673$	5.30639	−	2.42335i	0.204546	−	0.0934131i	0.515054	+	0.857158i	$0.327772\pi$
$674$		0			0
$675$	−9.15186	−	16.9127i	−0.352255	−	0.650971i
$676$		0			0
$677$	−5.62699	+	6.49390i	−0.216263	+	0.249581i	−0.853507	−	0.521081i	$-0.825529\pi$
$677$	−5.62699	+	6.49390i	−0.216263	+	0.249581i	0.637244	+	0.770662i	$0.280074\pi$
$678$		0			0
$679$	11.7467	−	13.5564i	0.450796	−	0.520246i
$680$		0			0
$681$	5.16870	−	30.5010i	0.198065	−	1.16880i
$682$		0			0
$683$	1.45684	−	0.936255i	0.0557445	−	0.0358248i	−0.512472	−	0.858704i	$-0.671270\pi$
$683$	1.45684	−	0.936255i	0.0557445	−	0.0358248i	0.568216	+	0.822879i	$0.307634\pi$
$684$		0			0
$685$	−1.23132	−	1.42102i	−0.0470463	−	0.0542943i
$686$		0			0
$687$	−26.0998	−	17.7131i	−0.995770	−	0.675795i
$688$		0			0
$689$	10.1510	−	8.79588i	0.386722	−	0.335096i
$690$		0			0
$691$	18.8649	+	5.53922i	0.717653	+	0.210722i	0.620116	−	0.784510i	$-0.287085\pi$
$691$	18.8649	+	5.53922i	0.717653	+	0.210722i	0.0975370	+	0.995232i	$0.468904\pi$
$692$		0			0
$693$	28.3307	+	14.6964i	1.07620	+	0.558270i
$694$		0			0
$695$	12.4446	+	19.3641i	0.472049	+	0.734523i
$696$		0			0
$697$	7.54892	−	25.7092i	0.285936	−	0.973807i
$698$		0			0
$699$	10.8687	+	5.29671i	0.411093	+	0.200340i
$700$		0			0
$701$	−18.3391	−	11.7859i	−0.692660	−	0.445145i	0.146371	−	0.989230i	$-0.453241\pi$
$701$	−18.3391	−	11.7859i	−0.692660	−	0.445145i	−0.839031	+	0.544084i	$0.816877\pi$
$702$		0			0
$703$	−23.4004	−	27.0055i	−0.882562	−	1.01853i
$704$		0			0
$705$	−4.48059	−	5.44063i	−0.168749	−	0.204906i
$706$		0			0
$707$			37.6845i			1.41727i
$708$		0			0
$709$	24.2498	+	15.5844i	0.910720	+	0.585284i	0.909951	−	0.414715i	$-0.136119\pi$
$709$	24.2498	+	15.5844i	0.910720	+	0.585284i	0.000768915		1.00000i	$0.499755\pi$
$710$		0			0
$711$	2.60226	+	4.53370i	0.0975923	+	0.170027i
$712$		0			0
$713$	0.00136763	−	0.00951208i	5.12182e−5	−	0.000356230i
$714$		0			0
$715$	−12.2041	−	5.57343i	−0.456408	−	0.208435i
$716$		0			0
$717$	−0.0435724	+	1.73798i	−0.00162724	+	0.0649062i
$718$		0			0
$719$	41.3844	−	5.95018i	1.54338	−	0.221904i	0.682565	−	0.730825i	$-0.260865\pi$
$719$	41.3844	−	5.95018i	1.54338	−	0.221904i	0.860813	+	0.508921i	$0.169956\pi$
$720$		0			0
$721$	−10.9168	−	37.1793i	−0.406564	−	1.38463i
$722$		0			0
$723$	13.8673	−	43.1920i	0.515729	−	1.60633i
$724$		0			0
$725$	14.8067	+	23.0397i	0.549908	+	0.855673i
$726$		0			0
$727$	19.1137	+	8.72894i	0.708888	+	0.323738i	0.737025	−	0.675866i	$-0.236230\pi$
$727$	19.1137	+	8.72894i	0.708888	+	0.323738i	−0.0281366	+	0.999604i	$0.508957\pi$
$728$		0			0
$729$	−26.6952	−	4.04531i	−0.988712	−	0.149826i
$730$		0			0
$731$	30.2974	+	8.89612i	1.12059	+	0.329035i
$732$		0			0
$733$	−24.6359	+	3.54211i	−0.909948	+	0.130831i	−0.581364	−	0.813644i	$-0.697481\pi$
$733$	−24.6359	+	3.54211i	−0.909948	+	0.130831i	−0.328584	+	0.944475i	$0.606571\pi$
$734$		0			0
$735$	−1.18357	+	0.505062i	−0.0436565	+	0.0186295i
$736$		0			0
$737$	10.2947	−	29.7494i	0.379211	−	1.09583i
$738$		0			0
$739$	0.277242	+	0.240232i	0.0101985	+	0.00883706i	0.659945	−	0.751314i	$-0.270580\pi$
$739$	0.277242	+	0.240232i	0.0101985	+	0.00883706i	−0.649747	+	0.760151i	$0.725125\pi$
$740$		0			0
$741$	37.8195	+	12.1424i	1.38934	+	0.446061i
$742$		0			0
$743$	0.132950	−	0.452788i	0.00487748	−	0.0166112i	−0.957018	−	0.290028i	$-0.906336\pi$
$743$	0.132950	−	0.452788i	0.00487748	−	0.0166112i	0.961896	+	0.273416i	$0.0881537\pi$
$744$		0			0
$745$	9.90559	−	15.4134i	0.362913	−	0.564703i
$746$		0			0
$747$	−5.16562	−	21.5307i	−0.189000	−	0.787765i
$748$		0			0
$749$	46.2839	−	29.7449i	1.69118	−	1.08685i
$750$		0			0
$751$	3.81484	+	26.5328i	0.139205	+	0.968195i	0.932966	+	0.359965i	$0.117211\pi$
$751$	3.81484	+	26.5328i	0.139205	+	0.968195i	−0.793761	+	0.608230i	$0.791880\pi$
$752$		0			0
$753$	20.9160	+	3.54442i	0.762222	+	0.129166i
$754$		0			0
$755$	−2.21550	−	15.4092i	−0.0806304	−	0.560797i
$756$		0			0
$757$	−29.0755	+	13.2783i	−1.05677	+	0.482609i	−0.866528	−	0.499129i	$-0.833654\pi$
$757$	−29.0755	+	13.2783i	−1.05677	+	0.482609i	−0.190239	+	0.981738i	$0.560926\pi$
$758$		0			0
$759$	5.06167	+	6.14620i	0.183727	+	0.223093i
$760$		0			0
$761$	−39.4929	−	5.67822i	−1.43162	−	0.205835i	−0.617515	−	0.786559i	$-0.711860\pi$
$761$	−39.4929	−	5.67822i	−1.43162	−	0.205835i	−0.814100	+	0.580724i	$0.802769\pi$
$762$		0			0
$763$	−0.670503	+	4.66345i	−0.0242738	+	0.168828i
$764$		0			0
$765$	−14.1228	+	1.31250i	−0.510609	+	0.0474535i
$766$		0			0
$767$	−39.7474			−1.43520
$768$		0			0
$769$	11.1492	+	5.09166i	0.402050	+	0.183610i	0.606169	−	0.795336i	$-0.292706\pi$
$769$	11.1492	+	5.09166i	0.402050	+	0.183610i	−0.204119	+	0.978946i	$0.565433\pi$
$770$		0			0
$771$	−3.30242	+	0.880404i	−0.118934	+	0.0317070i
$772$		0			0
$773$	−6.11766	+	9.51926i	−0.220037	+	0.342384i	−0.933669	−	0.358136i	$-0.883412\pi$
$773$	−6.11766	+	9.51926i	−0.220037	+	0.342384i	0.713632	+	0.700520i	$0.247049\pi$
$774$		0			0
$775$			0.0297542i			0.00106880i
$776$		0			0
$777$	15.3909	−	16.8876i	0.552146	−	0.605839i
$778$		0			0
$779$	40.7186	−	26.1683i	1.45890	−	0.937576i
$780$		0			0
$781$	40.3744	−	18.4383i	1.44471	−	0.659776i
$782$		0			0
$783$	38.3445	+	2.88881i	1.37032	+	0.103238i
$784$		0			0
$785$	2.89652	+	3.34276i	0.103381	+	0.119308i
$786$		0			0
$787$	−13.0402	−	1.87489i	−0.464831	−	0.0668327i	−0.0940797	−	0.995565i	$-0.529991\pi$
$787$	−13.0402	−	1.87489i	−0.464831	−	0.0668327i	−0.370752	+	0.928732i	$0.620900\pi$
$788$		0			0
$789$	23.2940	−	6.21002i	0.829287	−	0.221083i
$790$		0			0
$791$	−0.900015	−	1.40045i	−0.0320008	−	0.0497943i
$792$		0			0
$793$	9.69260	−	2.84600i	0.344194	−	0.101065i
$794$		0			0
$795$	−7.96874	+	3.40049i	−0.282622	+	0.120603i
$796$		0			0
$797$	4.18471	+	3.62607i	0.148230	+	0.128442i	0.725819	−	0.687886i	$-0.241461\pi$
$797$	4.18471	+	3.62607i	0.148230	+	0.128442i	−0.577589	+	0.816328i	$0.696006\pi$
$798$		0			0
$799$	14.2088	−	4.17207i	0.502670	−	0.147597i
$800$		0			0
$801$	−15.8587	−	8.22658i	−0.560339	−	0.290672i
$802$		0			0
$803$	−45.3989			−1.60209
$804$		0			0
$805$	−3.76864			−0.132827
$806$		0			0
$807$	−8.49439	−	0.212960i	−0.299017	−	0.00749655i
$808$		0			0
$809$	−37.9927	+	11.1557i	−1.33575	+	0.392212i	−0.870152	−	0.492784i	$-0.835979\pi$
$809$	−37.9927	+	11.1557i	−1.33575	+	0.392212i	−0.465599	+	0.884996i	$0.654161\pi$
$810$		0			0
$811$	13.3438	+	11.5624i	0.468563	+	0.406012i	0.856882	−	0.515513i	$-0.172399\pi$
$811$	13.3438	+	11.5624i	0.468563	+	0.406012i	−0.388319	+	0.921525i	$0.626944\pi$
$812$		0			0
$813$	20.8227	+	48.7961i	0.730283	+	1.71135i
$814$		0			0
$815$	13.0663	−	3.83662i	0.457693	−	0.134391i
$816$		0			0
$817$	30.8384	+	47.9854i	1.07890	+	1.67880i
$818$		0			0
$819$	−4.86983	+	24.9274i	−0.170166	+	0.871034i
$820$		0			0
$821$	−10.1889	−	1.46494i	−0.355594	−	0.0511267i	−0.0377968	−	0.999285i	$-0.512034\pi$
$821$	−10.1889	−	1.46494i	−0.355594	−	0.0511267i	−0.317797	+	0.948159i	$0.602943\pi$
$822$		0			0
$823$	−23.3946	−	26.9988i	−0.815485	−	0.941119i	0.183638	−	0.982994i	$-0.441212\pi$
$823$	−23.3946	−	26.9988i	−0.815485	−	0.941119i	−0.999123	+	0.0418746i	$0.986667\pi$
$824$		0			0
$825$	−18.2207	−	16.6059i	−0.634363	−	0.578142i
$826$		0			0
$827$	10.5666	−	4.82559i	0.367436	−	0.167802i	−0.223136	−	0.974787i	$-0.571629\pi$
$827$	10.5666	−	4.82559i	0.367436	−	0.167802i	0.590572	+	0.806985i	$0.298902\pi$
$828$		0			0
$829$	−32.0341	+	20.5871i	−1.11259	+	0.715019i	−0.961856	−	0.273555i	$-0.911800\pi$
$829$	−32.0341	+	20.5871i	−1.11259	+	0.715019i	−0.150735	+	0.988574i	$0.548164\pi$
$830$		0			0
$831$	−15.4891	−	14.1164i	−0.537311	−	0.489691i
$832$		0			0
$833$		−	2.70371i		−	0.0936780i
$834$		0			0
$835$	7.20771	−	11.2154i	0.249433	−	0.388126i
$836$		0			0
$837$	0.0333484	+	0.0251624i	0.00115269	+	0.000869741i
$838$		0			0
$839$	−7.74515	−	3.53709i	−0.267392	−	0.122114i	0.277207	−	0.960810i	$-0.410591\pi$
$839$	−7.74515	−	3.53709i	−0.267392	−	0.122114i	−0.544600	+	0.838696i	$0.683318\pi$
$840$		0			0
$841$	−25.7647			−0.888439
$842$		0			0
$843$	14.8940	+	24.5048i	0.512976	+	0.843991i
$844$		0			0
$845$	−0.589269	+	4.09846i	−0.0202715	+	0.140991i
$846$		0			0
$847$	10.3804	+	1.49248i	0.356675	+	0.0512821i
$848$		0			0
$849$	−6.72383	+	5.53737i	−0.230761	+	0.190042i
$850$		0			0
$851$	5.18510	−	2.36796i	0.177743	−	0.0811725i
$852$		0			0
$853$	−6.12054	−	42.5693i	−0.209563	−	1.45754i	−0.774586	−	0.632469i	$-0.782042\pi$
$853$	−6.12054	−	42.5693i	−0.209563	−	1.45754i	0.565023	−	0.825075i	$-0.308867\pi$
$854$		0			0
$855$	−20.8330	−	14.9147i	−0.712474	−	0.510073i
$856$		0			0
$857$	−2.13169	−	14.8262i	−0.0728170	−	0.506453i	−0.993290	−	0.115648i	$-0.963106\pi$
$857$	−2.13169	−	14.8262i	−0.0728170	−	0.506453i	0.920473	−	0.390806i	$-0.127804\pi$
$858$		0			0
$859$	44.5048	−	28.6015i	1.51848	−	0.975871i	0.526409	−	0.850232i	$-0.323538\pi$
$859$	44.5048	−	28.6015i	1.51848	−	0.975871i	0.992076	−	0.125639i	$-0.0400981\pi$
$860$		0			0
$861$	19.6752	+	23.8909i	0.670529	+	0.814199i
$862$		0			0
$863$	16.5755	−	25.7920i	0.564237	−	0.877970i	−0.435516	−	0.900181i	$-0.643434\pi$
$863$	16.5755	−	25.7920i	0.564237	−	0.877970i	0.999753	+	0.0222106i	$0.00707043\pi$
$864$		0			0
$865$	3.09568	−	10.5429i	0.105256	−	0.358470i
$866$		0			0
$867$	0.108793	−	0.338854i	0.00369480	−	0.0115081i
$868$		0			0
$869$	5.06463	+	4.38853i	0.171806	+	0.148871i
$870$		0			0
$871$	25.0238	+	1.19079i	0.847899	+	0.0403485i
$872$		0			0
$873$	−0.974827	+	19.4294i	−0.0329929	+	0.657584i
$874$		0			0
$875$	27.1539	−	3.90414i	0.917970	−	0.131984i
$876$		0			0
$877$	−43.8980	−	12.8896i	−1.48233	−	0.435252i	−0.562246	−	0.826970i	$-0.690063\pi$
$877$	−43.8980	−	12.8896i	−1.48233	−	0.435252i	−0.920085	+	0.391718i	$0.871881\pi$
$878$		0			0
$879$	−16.4548	+	10.0012i	−0.555006	+	0.337331i
$880$		0			0
$881$	−16.0356	−	7.32320i	−0.540252	−	0.246725i	0.126549	−	0.991960i	$-0.459610\pi$
$881$	−16.0356	−	7.32320i	−0.540252	−	0.246725i	−0.666801	+	0.745235i	$0.732337\pi$
$882$		0			0
$883$	−17.7506	−	27.6205i	−0.597356	−	0.929504i	−0.999901	−	0.0141035i	$-0.995511\pi$
$883$	−17.7506	−	27.6205i	−0.597356	−	0.929504i	0.402545	−	0.915400i	$-0.368126\pi$
$884$		0			0
$885$	24.4113	+	7.83752i	0.820578	+	0.263455i
$886$		0			0
$887$	−6.79268	−	23.1337i	−0.228076	−	0.776755i	−0.991415	−	0.130756i	$-0.958259\pi$
$887$	−6.79268	−	23.1337i	−0.228076	−	0.776755i	0.763339	−	0.645998i	$-0.223559\pi$
$888$		0			0
$889$	56.8668	−	8.17621i	1.90725	−	0.274221i
$890$		0			0
$891$	−34.0206	+	6.37850i	−1.13973	+	0.213688i
$892$		0			0
$893$	24.3332	+	11.1126i	0.814279	+	0.371869i
$894$		0			0
$895$	−0.238222	+	1.65687i	−0.00796290	+	0.0553832i
$896$		0			0
$897$	−3.55819	+	5.24292i	−0.118805	+	0.175056i
$898$		0			0
$899$	−0.0500526	−	0.0321668i	−0.00166935	−	0.00107282i
$900$		0			0
$901$		−	18.2036i		−	0.606449i
$902$		0			0
$903$	−28.1545	+	23.1865i	−0.936924	+	0.771598i
$904$		0			0
$905$	6.11948	+	7.06226i	0.203418	+	0.234757i
$906$		0			0
$907$	19.7357	+	12.6834i	0.655313	+	0.421144i	0.825604	−	0.564250i	$-0.190835\pi$
$907$	19.7357	+	12.6834i	0.655313	+	0.421144i	−0.170291	+	0.985394i	$0.554471\pi$
$908$		0			0
$909$	−25.1826	−	32.1896i	−0.835254	−	1.06766i
$910$		0			0
$911$	9.48918	−	32.3172i	0.314391	−	1.07072i	−0.639058	−	0.769159i	$-0.720675\pi$
$911$	9.48918	−	32.3172i	0.314391	−	1.07072i	0.953448	−	0.301557i	$-0.0975064\pi$
$912$		0			0
$913$	−15.3461	−	23.8791i	−0.507883	−	0.790281i
$914$		0			0
$915$	−6.51400	−	0.163310i	−0.215346	−	0.00539887i
$916$		0			0
$917$	16.3001	+	4.78614i	0.538277	+	0.158052i
$918$		0			0
$919$	−16.1516	+	13.9955i	−0.532793	+	0.461668i	−0.879225	−	0.476408i	$-0.841939\pi$
$919$	−16.1516	+	13.9955i	−0.532793	+	0.461668i	0.346432	+	0.938075i	$0.387393\pi$
$920$		0			0
$921$	−15.3346	+	22.5953i	−0.505294	+	0.744539i
$922$		0			0
$923$	23.1310	+	26.6946i	0.761366	+	0.878663i
$924$		0			0
$925$	−14.8473	+	9.54180i	−0.488177	+	0.313732i
$926$		0			0
$927$	34.1700	+	24.4629i	1.12229	+	0.803468i
$928$		0			0
$929$	−33.5330	+	38.6991i	−1.10018	+	1.26968i	−0.140045	+	0.990145i	$0.544725\pi$
$929$	−33.5330	+	38.6991i	−1.10018	+	1.26968i	−0.960136	+	0.279532i	$0.909821\pi$
$930$		0			0
$931$	3.19836	−	3.69111i	0.104822	−	0.120971i
$932$		0			0
$933$	−43.4321	−	7.36000i	−1.42190	−	0.240956i
$934$		0			0
$935$	−16.5399	+	7.55352i	−0.540912	+	0.247026i
$936$		0			0
$937$			19.4369i			0.634977i	0.948262	+	0.317489i	$0.102840\pi$
$937$			19.4369i			0.634977i	−0.948262	+	0.317489i	$0.897160\pi$
$938$		0			0
$939$	17.3099	−	35.5194i	0.564886	−	1.15913i
$940$		0			0
$941$	−9.58778	−	20.9943i	−0.312553	−	0.684395i	0.686535	−	0.727097i	$-0.259131\pi$
$941$	−9.58778	−	20.9943i	−0.312553	−	0.684395i	−0.999088	+	0.0427017i	$0.986404\pi$
$942$		0			0
$943$	2.17531	+	7.40842i	0.0708378	+	0.241251i
$944$		0			0
$945$	7.90612	−	14.3492i	0.257186	−	0.466780i
$946$		0			0
$947$	16.8597	+	14.6090i	0.547867	+	0.474729i	0.884262	−	0.466992i	$-0.154662\pi$
$947$	16.8597	+	14.6090i	0.547867	+	0.474729i	−0.336395	+	0.941721i	$0.609208\pi$
$948$		0			0
$949$	−10.1786	−	34.6651i	−0.330411	−	1.12528i
$950$		0			0
$951$	3.73659	+	31.5907i	0.121167	+	1.02440i
$952$		0			0
$953$	−15.0549	+	13.0451i	−0.487675	+	0.422573i	−0.863677	−	0.504046i	$-0.831844\pi$
$953$	−15.0549	+	13.0451i	−0.487675	+	0.422573i	0.376002	+	0.926619i	$0.377299\pi$
$954$		0			0
$955$	−3.47899	+	24.1969i	−0.112577	+	0.782993i
$956$		0			0
$957$	47.6325	−	12.6985i	1.53974	−	0.410484i
$958$		0			0
$959$	−1.28561	+	4.37838i	−0.0415145	+	0.141385i
$960$		0			0
$961$	12.8778	+	28.1985i	0.415414	+	0.909630i
$962$		0			0
$963$	−19.6582	+	56.3369i	−0.633476	+	1.81543i
$964$		0			0
$965$	15.4496	+	4.53641i	0.497340	+	0.146032i
$966$		0			0
$967$	−23.1586			−0.744729			−0.372365	−	0.928087i	$-0.621453\pi$
$967$	−23.1586			−0.744729			−0.372365	+	0.928087i	$0.621453\pi$
$968$		0			0
$969$	46.0021	−	27.9600i	1.47780	−	0.898204i
$970$		0			0
$971$	−2.23324	+	1.93512i	−0.0716682	+	0.0621008i	−0.689958	−	0.723849i	$-0.742371\pi$
$971$	−2.23324	+	1.93512i	−0.0716682	+	0.0621008i	0.618290	+	0.785950i	$0.287826\pi$
$972$		0			0
$973$	23.2061	−	50.8144i	0.743955	−	1.62903i
$974$		0			0
$975$	8.59455	−	17.6358i	0.275246	−	0.564798i
$976$		0			0
$977$	10.7990	−	16.8036i	0.345491	−	0.537594i	−0.624410	−	0.781097i	$-0.714660\pi$
$977$	10.7990	−	16.8036i	0.345491	−	0.537594i	0.969900	+	0.243503i	$0.0782967\pi$
$978$		0			0
$979$	−22.6700	−	3.25945i	−0.724535	−	0.104172i
$980$		0			0
$981$	−2.54361	−	4.43152i	−0.0812111	−	0.141488i
$982$		0			0
$983$	3.89923	−	8.53812i	0.124366	−	0.272324i	−0.837200	−	0.546896i	$-0.815809\pi$
$983$	3.89923	−	8.53812i	0.124366	−	0.272324i	0.961566	+	0.274573i	$0.0885364\pi$
$984$		0			0
$985$	1.33788	+	2.92955i	0.0426285	+	0.0933433i
$986$		0			0
$987$	−5.22887	+	16.2862i	−0.166437	+	0.518396i
$988$		0			0
$989$	−8.73055	+	2.56352i	−0.277615	+	0.0815152i
$990$		0			0
$991$	23.5512	−	3.38616i	0.748130	−	0.107565i	0.242304	−	0.970200i	$-0.422097\pi$
$991$	23.5512	−	3.38616i	0.748130	−	0.107565i	0.505826	+	0.862636i	$0.331188\pi$
$992$		0			0
$993$	1.72535	+	14.5869i	0.0547525	+	0.462901i
$994$		0			0
$995$	−3.12552	+	6.84393i	−0.0990855	+	0.216967i
$996$		0			0
$997$	24.8484	+	15.9691i	0.786958	+	0.505747i	0.871336	−	0.490687i	$-0.163254\pi$
$997$	24.8484	+	15.9691i	0.786958	+	0.505747i	−0.0843784	+	0.996434i	$0.526890\pi$
$998$		0			0
$999$	−1.86162	+	24.7101i	−0.0588989	+	0.781793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.5.11	✓	200
3.2	odd	2	inner	804.2.s.b.5.16	yes	200
67.27	odd	22	inner	804.2.s.b.161.16	yes	200
201.161	even	22	inner	804.2.s.b.161.11	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.11	✓	200	1.1	even	1	trivial
804.2.s.b.5.16	yes	200	3.2	odd	2	inner
804.2.s.b.161.11	yes	200	201.161	even	22	inner
804.2.s.b.161.16	yes	200	67.27	odd	22	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0434100 - 1.73151i) q^{3} +(-1.09364 + 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(-2.99623 - 0.150329i) q^{9} +O(q^{10})\)	\(q+(0.0434100 - 1.73151i) q^{3} +(-1.09364 + 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(-2.99623 - 0.150329i) q^{9} +(-3.69014 + 1.08352i) q^{11} +(-1.65469 - 2.57474i) q^{13} +(0.508549 + 1.90758i) q^{15} +(-4.10573 - 0.590315i) q^{17} +(-4.90683 - 5.66278i) q^{19} +(3.22732 - 3.54116i) q^{21} +(1.08727 - 0.496537i) q^{23} +(-3.11334 + 2.00082i) q^{25} +(-0.390363 + 5.18147i) q^{27} -7.40032i q^{29} +(0.00434668 - 0.00676357i) q^{31} +(1.71594 + 6.43654i) q^{33} +(-2.86801 - 1.30978i) q^{35} +4.76894 q^{37} +(-4.53001 + 2.75333i) q^{39} +(-0.919315 + 6.39398i) q^{41} +(-7.53507 - 1.08338i) q^{43} +(3.32507 - 0.797748i) q^{45} +(-3.24748 + 1.48308i) q^{47} +(0.0927634 + 0.645184i) q^{49} +(-1.20036 + 7.08347i) q^{51} +(0.624559 + 4.34391i) q^{53} +(3.68774 - 2.36997i) q^{55} +(-10.0182 + 8.25039i) q^{57} +(7.02119 - 10.9252i) q^{59} +(-0.929884 + 3.16689i) q^{61} +(-5.99145 - 5.74186i) q^{63} +(2.63643 + 2.28448i) q^{65} +(-4.74764 + 6.66783i) q^{67} +(-0.812560 - 1.90416i) q^{69} +(-11.4234 + 1.64244i) q^{71} +(11.3262 + 3.32568i) q^{73} +(3.32929 + 5.47763i) q^{75} +(-9.67720 - 4.41943i) q^{77} +(-0.942057 - 1.46587i) q^{79} +(8.95480 + 0.900844i) q^{81} +(2.07934 + 7.08159i) q^{83} +(4.67975 - 0.672846i) q^{85} +(-12.8137 - 0.321248i) q^{87} +(5.41699 + 2.47386i) q^{89} +(1.20487 - 8.38004i) q^{91} +(-0.0115225 - 0.00781992i) q^{93} +(7.18474 + 4.61735i) q^{95} -6.48460i q^{97} +(11.2194 - 2.69175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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