LMFDB - Embedded newform 804.2.s.b.5.16

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			5.16
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33701 + 1.10109i) q^{3} +(1.09364 - 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(0.575207 + 2.94434i) q^{9} +O(q^{10})$	\(q+(1.33701 + 1.10109i) q^{3} +(1.09364 - 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(0.575207 + 2.94434i) q^{9} +(3.69014 - 1.08352i) q^{11} +(-1.65469 - 2.57474i) q^{13} +(1.81579 + 0.774850i) q^{15} +(4.10573 + 0.590315i) q^{17} +(-4.90683 - 5.66278i) q^{19} +(0.800501 + 4.72384i) q^{21} +(-1.08727 + 0.496537i) q^{23} +(-3.11334 + 2.00082i) q^{25} +(-2.47292 + 4.56997i) q^{27} +7.40032i q^{29} +(0.00434668 - 0.00676357i) q^{31} +(6.12683 + 2.61449i) q^{33} +(2.86801 + 1.30978i) q^{35} +4.76894 q^{37} +(0.622682 - 5.26442i) q^{39} +(0.919315 - 6.39398i) q^{41} +(-7.53507 - 1.08338i) q^{43} +(1.57456 + 3.03533i) q^{45} +(3.24748 - 1.48308i) q^{47} +(0.0927634 + 0.645184i) q^{49} +(4.83942 + 5.31003i) q^{51} +(-0.624559 - 4.34391i) q^{53} +(3.68774 - 2.36997i) q^{55} +(-0.325269 - 12.9741i) q^{57} +(-7.02119 + 10.9252i) q^{59} +(-0.929884 + 3.16689i) q^{61} +(-4.13109 + 7.19726i) q^{63} +(-2.63643 - 2.28448i) q^{65} +(-4.74764 + 6.66783i) q^{67} +(-2.00042 - 0.533298i) q^{69} +(11.4234 - 1.64244i) q^{71} +(11.3262 + 3.32568i) q^{73} +(-6.36566 - 0.752938i) q^{75} +(9.67720 + 4.41943i) q^{77} +(-0.942057 - 1.46587i) q^{79} +(-8.33827 + 3.38721i) q^{81} +(-2.07934 - 7.08159i) q^{83} +(4.67975 - 0.672846i) q^{85} +(-8.14841 + 9.89432i) q^{87} +(-5.41699 - 2.47386i) q^{89} +(1.20487 - 8.38004i) q^{91} +(0.0132589 - 0.00425690i) q^{93} +(-7.18474 - 4.61735i) q^{95} -6.48460i q^{97} +(5.31286 + 10.2418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.33701	+	1.10109i	0.771925	+	0.635714i
$3$	1.33701	+	1.10109i	0.771925	+	0.635714i
$4$		0			0
$5$	1.09364	−	0.321121i	0.489090	−	0.143610i	−0.0278834	−	0.999611i	$-0.508877\pi$
$5$	1.09364	−	0.321121i	0.489090	−	0.143610i	0.516974	+	0.856001i	$0.327059\pi$
$6$		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
$9$	0.575207	+	2.94434i	0.191736	+	0.981447i
$10$		0			0
$11$	3.69014	−	1.08352i	1.11262	−	0.326695i	0.326765	−	0.945106i	$-0.394041\pi$
$11$	3.69014	−	1.08352i	1.11262	−	0.326695i	0.785855	+	0.618411i	$0.212223\pi$
$12$		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
$15$	1.81579	+	0.774850i	0.468836	+	0.200065i
$16$		0			0
$17$	4.10573	+	0.590315i	0.995785	+	0.143172i	0.620892	−	0.783896i	$-0.286770\pi$
$17$	4.10573	+	0.590315i	0.995785	+	0.143172i	0.374893	+	0.927068i	$0.377679\pi$
$18$		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
$21$	0.800501	+	4.72384i	0.174684	+	1.03083i
$22$		0			0
$23$	−1.08727	+	0.496537i	−0.226710	+	0.103535i	−0.525532	−	0.850774i	$-0.676134\pi$
$23$	−1.08727	+	0.496537i	−0.226710	+	0.103535i	0.298822	+	0.954309i	$0.403406\pi$
$24$		0			0
$25$	−3.11334	+	2.00082i	−0.622668	+	0.400164i
$26$		0			0
$27$	−2.47292	+	4.56997i	−0.475914	+	0.879492i
$28$		0			0
$29$			7.40032i			1.37420i	0.726561	+	0.687102i	$0.241118\pi$
$29$			7.40032i			1.37420i	−0.726561	+	0.687102i	$0.758882\pi$
$30$		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
$33$	6.12683	+	2.61449i	1.06654	+	0.455124i
$34$		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
$39$	0.622682	−	5.26442i	0.0997090	−	0.842982i
$40$		0			0
$41$	0.919315	−	6.39398i	0.143573	−	0.998571i	−0.782883	−	0.622169i	$-0.786252\pi$
$41$	0.919315	−	6.39398i	0.143573	−	0.998571i	0.926456	−	0.376403i	$-0.122839\pi$
$42$		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
$45$	1.57456	+	3.03533i	0.234722	+	0.452481i
$46$		0			0
$47$	3.24748	−	1.48308i	0.473694	−	0.216329i	−0.164239	−	0.986421i	$-0.552517\pi$
$47$	3.24748	−	1.48308i	0.473694	−	0.216329i	0.637933	+	0.770092i	$0.279790\pi$
$48$		0			0
$49$	0.0927634	+	0.645184i	0.0132519	+	0.0921691i
$50$		0			0
$51$	4.83942	+	5.31003i	0.677655	+	0.743553i
$52$		0			0
$53$	−0.624559	−	4.34391i	−0.0857898	−	0.596681i	−0.986685	−	0.162644i	$-0.947998\pi$
$53$	−0.624559	−	4.34391i	−0.0857898	−	0.596681i	0.900895	−	0.434037i	$-0.142911\pi$
$54$		0			0
$55$	3.68774	−	2.36997i	0.497255	−	0.319566i
$56$		0			0
$57$	−0.325269	−	12.9741i	−0.0430829	−	1.71846i
$58$		0			0
$59$	−7.02119	+	10.9252i	−0.914081	+	1.42234i	−0.00765668	+	0.999971i	$0.502437\pi$
$59$	−7.02119	+	10.9252i	−0.914081	+	1.42234i	−0.906425	+	0.422368i	$0.861199\pi$
$60$		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
$63$	−4.13109	+	7.19726i	−0.520468	+	0.906769i
$64$		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
$69$	−2.00042	−	0.533298i	−0.240822	−	0.0642016i
$70$		0			0
$71$	11.4234	−	1.64244i	1.35571	−	0.194921i	0.574148	−	0.818752i	$-0.305333\pi$
$71$	11.4234	−	1.64244i	1.35571	−	0.194921i	0.781560	+	0.623830i	$0.214424\pi$
$72$		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
$75$	−6.36566	−	0.752938i	−0.735043	−	0.0869418i
$76$		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
$81$	−8.33827	+	3.38721i	−0.926475	+	0.376357i
$82$		0			0
$83$	−2.07934	−	7.08159i	−0.228237	−	0.777305i	−0.991373	−	0.131067i	$-0.958160\pi$
$83$	−2.07934	−	7.08159i	−0.228237	−	0.777305i	0.763136	−	0.646238i	$-0.223659\pi$
$84$		0			0
$85$	4.67975	−	0.672846i	0.507590	−	0.0729804i
$86$		0			0
$87$	−8.14841	+	9.89432i	−0.873601	+	1.06078i
$88$		0			0
$89$	−5.41699	−	2.47386i	−0.574200	−	0.262228i	0.107081	−	0.994250i	$-0.465850\pi$
$89$	−5.41699	−	2.47386i	−0.574200	−	0.262228i	−0.681281	+	0.732022i	$0.738577\pi$
$90$		0			0
$91$	1.20487	−	8.38004i	0.126304	−	0.878467i
$92$		0			0
$93$	0.0132589	−	0.00425690i	0.00137488	−	0.000441420i
$94$		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
$99$	5.31286	+	10.2418i	0.533963	+	1.02934i
$100$		0			0
$101$	−8.92133	−	10.2958i	−0.887706	−	1.02447i	−0.999527	−	0.0307386i	$-0.990214\pi$
$101$	−8.92133	−	10.2958i	−0.887706	−	1.02447i	0.111822	−	0.993728i	$-0.464331\pi$
$102$		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	$0.502168\pi$
$107$	−5.60348	+	19.0837i	−0.541709	+	1.84489i	−0.534900	+	0.844916i	$0.679651\pi$
$108$		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
$111$	6.37613	+	5.25102i	0.605196	+	0.498405i
$112$		0			0
$113$	0.577431	+	0.169549i	0.0543201	+	0.0159498i	0.308780	−	0.951134i	$-0.400079\pi$
$113$	0.577431	+	0.169549i	0.0543201	+	0.0159498i	−0.254460	+	0.967083i	$0.581898\pi$
$114$		0			0
$115$	−1.02963	+	0.892177i	−0.0960132	+	0.0831959i
$116$		0			0
$117$	6.62913	−	6.35297i	0.612863	−	0.587332i
$118$		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
$123$	8.26947	−	7.53658i	0.745633	−	0.679551i
$124$		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
$129$	−8.88159	−	9.74527i	−0.781980	−	0.858023i
$130$		0			0
$131$	−5.58640	+	2.55122i	−0.488086	+	0.222902i	−0.644229	−	0.764833i	$-0.722821\pi$
$131$	−5.58640	+	2.55122i	−0.488086	+	0.222902i	0.156142	+	0.987735i	$0.450094\pi$
$132$		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	0.878097	−	0.478483i	$-0.158813\pi$
$137$	−0.685286	−	1.50057i	−0.0585479	−	0.128202i	−0.936645	+	0.350281i	$0.886086\pi$
$138$		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
$141$	5.97492	+	1.59288i	0.503179	+	0.134144i
$142$		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
$147$	−0.586379	+	0.964760i	−0.0483637	+	0.0795721i
$148$		0			0
$149$	12.1484	−	10.5266i	0.995232	−	0.862373i	0.00474598	−	0.999989i	$-0.498489\pi$
$149$	12.1484	−	10.5266i	0.995232	−	0.862373i	0.990486	+	0.137616i	$0.0439438\pi$
$150$		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
$153$	0.623559	+	12.4282i	0.0504117	+	1.00476i
$154$		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
$159$	3.94798	−	6.49555i	0.313095	−	0.515131i
$160$		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
$165$	7.54011	+	0.891853i	0.586996	+	0.0694307i
$166$		0			0
$167$	8.83963	−	7.65959i	0.684031	−	0.592717i	−0.241949	−	0.970289i	$-0.577787\pi$
$167$	8.83963	−	7.65959i	0.684031	−	0.592717i	0.925980	+	0.377573i	$0.123241\pi$
$168$		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	−0.584602	−	0.811320i	$-0.698749\pi$
$173$	5.21190	−	8.10988i	0.396253	−	0.616582i	0.980855	+	0.194738i	$0.0623856\pi$
$174$		0			0
$175$	−10.1330	−	1.45691i	−0.765984	−	0.110132i
$176$		0			0
$177$	−21.4170	+	6.87616i	−1.60980	+	0.516844i
$178$		0			0
$179$	−0.610074	+	1.33588i	−0.0455990	+	0.0998480i	−0.931060	−	0.364865i	$-0.881115\pi$
$179$	−0.610074	+	1.33588i	−0.0455990	+	0.0998480i	0.885461	+	0.464713i	$0.153842\pi$
$180$		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
$183$	−4.73030	+	3.21029i	−0.349674	+	0.237312i
$184$		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
$189$	−13.4481	+	5.07413i	−0.978208	+	0.369089i
$190$		0			0
$191$	−8.90948	+	19.5091i	−0.644668	+	1.41163i	0.251477	+	0.967863i	$0.419084\pi$
$191$	−8.90948	+	19.5091i	−0.644668	+	1.41163i	−0.896145	+	0.443762i	$0.853644\pi$
$192$		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
$195$	−1.00953	−	5.95733i	−0.0722938	−	0.426613i
$196$		0			0
$197$	0.402118	+	2.79679i	0.0286497	+	0.199263i	0.999119	−	0.0419605i	$-0.0133604\pi$
$197$	0.402118	+	2.79679i	0.0286497	+	0.199263i	−0.970470	+	0.241224i	$0.922451\pi$
$198$		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
$201$	−13.6895	+	3.68740i	−0.965585	+	0.260089i
$202$		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
$207$	−2.08738	−	2.91567i	−0.145083	−	0.202653i
$208$		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
$213$	17.0817	+	10.3822i	1.17042	+	0.711377i
$214$		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
$219$	11.4814	+	16.9177i	0.775844	+	1.14319i
$220$		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
$225$	−7.68192	−	8.01584i	−0.512128	−	0.534390i
$226$		0			0
$227$	−17.6790	−	2.54186i	−1.17340	−	0.168709i	−0.472079	−	0.881556i	$-0.656496\pi$
$227$	−17.6790	−	2.54186i	−1.17340	−	0.168709i	−0.701320	+	0.712847i	$0.747405\pi$
$228$		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	−0.790547	−	0.612402i	$-0.790203\pi$
$233$	2.89983	−	6.34973i	0.189974	−	0.415985i	0.980520	+	0.196417i	$0.0629307\pi$
$234$		0			0
$235$	3.07533	−	2.66479i	0.200612	−	0.173831i
$236$		0			0
$237$	0.354510	−	2.99718i	0.0230279	−	0.194687i
$238$		0			0
$239$	1.00374			0.0649266			0.0324633	−	0.999473i	$-0.489665\pi$
$239$	1.00374			0.0649266			0.0324633	+	0.999473i	$0.489665\pi$
$240$		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
$243$	−14.8780	−	4.65243i	−0.954424	−	0.298454i
$244$		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
$249$	5.01735	−	11.7577i	0.317961	−	0.745115i
$250$		0			0
$251$	1.74308	−	12.1234i	0.110022	−	0.765220i	−0.857872	−	0.513863i	$-0.828214\pi$
$251$	1.74308	−	12.1234i	0.110022	−	0.765220i	0.967894	−	0.251357i	$-0.0808768\pi$
$252$		0			0
$253$	−3.47415	+	3.01037i	−0.218418	+	0.189260i
$254$		0			0
$255$	6.99775	+	4.25321i	0.438216	+	0.266347i
$256$		0			0
$257$	0.555928	+	1.89332i	0.0346778	+	0.118102i	0.975013	−	0.222148i	$-0.0713067\pi$
$257$	0.555928	+	1.89332i	0.0346778	+	0.118102i	−0.940335	+	0.340249i	$0.889489\pi$
$258$		0			0
$259$	9.96970	+	8.63879i	0.619487	+	0.536788i
$260$		0			0
$261$	−21.7891	+	4.25672i	−1.34871	+	0.263484i
$262$		0			0
$263$	−3.92129	−	13.3547i	−0.241797	−	0.823486i	−0.987556	−	0.157270i	$-0.949731\pi$
$263$	−3.92129	−	13.3547i	−0.241797	−	0.823486i	0.745758	−	0.666216i	$-0.232087\pi$
$264$		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	$0.0477842\pi$
$269$			4.90578i			0.299111i	−0.988753	+	0.149555i	$0.952216\pi$
$270$		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
$273$	10.8381	−	9.87756i	0.655951	−	0.597817i
$274$		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
$279$	0.0224145	+	0.00890765i	0.00134192	+	0.000533287i
$280$		0			0
$281$	13.9279	−	8.95093i	0.830870	−	0.533968i	−0.0546844	−	0.998504i	$-0.517415\pi$
$281$	13.9279	−	8.95093i	0.830870	−	0.533968i	0.885554	+	0.464536i	$0.153779\pi$
$282$		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
$285$	−4.52198	−	14.0845i	−0.267859	−	0.834294i
$286$		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
$291$	7.14012	−	8.67000i	0.418561	−	0.508244i
$292$		0			0
$293$	6.01047	+	9.35248i	0.351135	+	0.546377i	0.971228	−	0.238151i	$-0.0765414\pi$
$293$	6.01047	+	9.35248i	0.351135	+	0.546377i	−0.620093	+	0.784529i	$0.712905\pi$
$294$		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
$303$	−0.591385	−	23.5887i	−0.0339742	−	1.35514i
$304$		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
$309$	−7.41688	−	23.1012i	−0.421932	−	1.31418i
$310$		0			0
$311$	−3.61950	+	25.1742i	−0.205243	+	1.42750i	0.583170	+	0.812350i	$0.301812\pi$
$311$	−3.61950	+	25.1742i	−0.205243	+	1.42750i	−0.788413	+	0.615146i	$0.789097\pi$
$312$		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
$315$	−2.20672	+	9.19778i	−0.124335	+	0.518236i
$316$		0			0
$317$	18.1791	−	2.61376i	1.02104	−	0.146803i	0.388595	−	0.921409i	$-0.372960\pi$
$317$	18.1791	−	2.61376i	1.02104	−	0.146803i	0.632445	+	0.774605i	$0.282051\pi$
$318$		0			0
$319$	8.01842	+	27.3082i	0.448945	+	1.52897i
$320$		0			0
$321$	−28.5048	+	19.3452i	−1.59098	+	1.07975i
$322$		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
$327$	−0.346520	+	2.92962i	−0.0191626	+	0.162009i
$328$		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
$333$	2.74313	+	14.0414i	0.150323	+	0.769462i
$334$		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
$339$	0.585344	+	0.862492i	0.0317915	+	0.0468441i
$340$		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
$345$	−2.35899	+	0.0591414i	−0.127004	+	0.00318407i
$346$		0			0
$347$	15.5069	−	9.96571i	0.832456	−	0.534987i	−0.0536012	−	0.998562i	$-0.517070\pi$
$347$	15.5069	−	9.96571i	0.832456	−	0.534987i	0.886058	+	0.463575i	$0.153434\pi$
$348$		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
$351$	15.8584	−	1.19475i	0.846460	−	0.0637708i
$352$		0			0
$353$	0.253361	+	1.76217i	0.0134851	+	0.0937906i	0.995452	−	0.0952597i	$-0.0303682\pi$
$353$	0.253361	+	1.76217i	0.0134851	+	0.0937906i	−0.981967	+	0.189050i	$0.939459\pi$
$354$		0			0
$355$	11.9657	−	5.46453i	0.635071	−	0.290027i
$356$		0			0
$357$	0.498087	+	19.8673i	0.0263616	+	1.05149i
$358$		0			0
$359$	27.8551	+	4.00496i	1.47014	+	0.211374i	0.830378	−	0.557201i	$-0.188125\pi$
$359$	27.8551	+	4.00496i	1.47014	+	0.211374i	0.639760	+	0.768575i	$0.279034\pi$
$360$		0			0
$361$	−5.28616	+	36.7660i	−0.278219	+	1.93505i
$362$		0			0
$363$	6.52107	+	0.771320i	0.342267	+	0.0404838i
$364$		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
$369$	19.3548	−	0.971088i	1.00757	−	0.0505528i
$370$		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
$375$	−16.9358	+	2.86994i	−0.874561	+	0.148203i
$376$		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
$381$	35.4676	−	6.01034i	1.81706	−	0.307919i
$382$		0			0
$383$	19.4053	+	22.3949i	0.991565	+	1.14433i	0.989530	+	0.144329i	$0.0461024\pi$
$383$	19.4053	+	22.3949i	0.991565	+	1.14433i	0.00203522	+	0.999998i	$0.499352\pi$
$384$		0			0
$385$	12.0025	+	1.72570i	0.611706	+	0.0879500i
$386$		0			0
$387$	−1.14439	−	22.8090i	−0.0581727	−	1.15944i
$388$		0			0
$389$	17.7489	+	27.6178i	0.899903	+	1.40028i	0.916335	+	0.400412i	$0.131133\pi$
$389$	17.7489	+	27.6178i	0.899903	+	1.40028i	−0.0164322	+	0.999865i	$0.505231\pi$
$390$		0			0
$391$	−4.75713	+	1.39682i	−0.240578	+	0.0706402i
$392$		0			0
$393$	−10.2782	−	2.74010i	−0.518467	−	0.138220i
$394$		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
$399$	22.8222	−	27.7121i	1.14254	−	1.38734i
$400$		0			0
$401$	−20.4141			−1.01943			−0.509717	−	0.860342i	$-0.670250\pi$
$401$	−20.4141			−1.01943			−0.509717	+	0.860342i	$0.670250\pi$
$402$		0			0
$403$	−0.0246068			−0.00122575
$404$		0			0
$405$	−8.03135	+	6.38199i	−0.399081	+	0.317123i
$406$		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
$411$	0.736021	−	2.76084i	0.0363052	−	0.136182i
$412$		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
$417$	13.7285	−	32.1716i	0.672289	−	1.57545i
$418$		0			0
$419$	19.2259	+	2.76426i	0.939245	+	0.135043i	0.594900	−	0.803800i	$-0.297192\pi$
$419$	19.2259	+	2.76426i	0.939245	+	0.135043i	0.344346	+	0.938843i	$0.388101\pi$
$420$		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
$423$	6.23466	+	8.70862i	0.303139	+	0.423427i
$424$		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
$429$	−3.40634	−	20.1012i	−0.164460	−	0.970493i
$430$		0			0
$431$		−	14.1768i		−	0.682872i	−0.939905	−	0.341436i	$-0.889087\pi$
$431$		−	14.1768i		−	0.682872i	0.939905	−	0.341436i	$-0.110913\pi$
$432$		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
$435$	−5.73414	+	13.4374i	−0.274931	+	0.644276i
$436$		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
$441$	−1.84628	+	0.644242i	−0.0879182	+	0.0306782i
$442$		0			0
$443$	−2.98481	+	20.7598i	−0.141812	+	0.986328i	0.787311	+	0.616557i	$0.211473\pi$
$443$	−2.98481	+	20.7598i	−0.141812	+	0.986328i	−0.929123	+	0.369771i	$0.879436\pi$
$444$		0			0
$445$	−6.71864	−	0.965995i	−0.318494	−	0.0457926i
$446$		0			0
$447$	27.8332	−	0.697797i	1.31647	−	0.0330047i
$448$		0			0
$449$	−3.28217	+	1.49892i	−0.154895	+	0.0707382i	−0.491354	−	0.870960i	$-0.663498\pi$
$449$	−3.28217	+	1.49892i	−0.154895	+	0.0707382i	0.336459	+	0.941698i	$0.390771\pi$
$450$		0			0
$451$	−3.53562	−	24.5908i	−0.166486	−	1.15794i
$452$		0			0
$453$	−17.4845	+	15.9349i	−0.821494	+	0.748688i
$454$		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
$459$	−12.8509	+	17.3033i	−0.599827	+	0.807648i
$460$		0			0
$461$	−19.9136	+	30.9862i	−0.927469	+	1.44317i	−0.0312737	+	0.999511i	$0.509956\pi$
$461$	−19.9136	+	30.9862i	−0.927469	+	1.44317i	−0.896196	+	0.443659i	$0.853680\pi$
$462$		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
$465$	0.0131334	−	0.00891321i	0.000609048	−	0.000413340i
$466$		0			0
$467$	−3.00536	−	2.60416i	−0.139071	−	0.120506i	0.582547	−	0.812797i	$-0.302056\pi$
$467$	−3.00536	−	2.60416i	−0.139071	−	0.120506i	−0.721619	+	0.692291i	$0.756602\pi$
$468$		0			0
$469$	−22.0037	+	5.33920i	−1.01604	+	0.246541i
$470$		0			0
$471$	1.73140	−	6.49452i	0.0797785	−	0.299252i
$472$		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
$477$	12.4307	−	4.33756i	0.569162	−	0.198603i
$478$		0			0
$479$	25.6151	+	11.6980i	1.17038	+	0.534495i	0.903229	−	0.429159i	$-0.141190\pi$
$479$	25.6151	+	11.6980i	1.17038	+	0.534495i	0.267153	+	0.963654i	$0.413917\pi$
$480$		0			0
$481$	−7.89110	−	12.2788i	−0.359803	−	0.559864i
$482$		0			0
$483$	−3.21592	−	4.73859i	−0.146329	−	0.215613i
$484$		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
$489$	−15.9740	−	13.1553i	−0.722372	−	0.594905i
$490$		0			0
$491$	26.9926	+	12.3271i	1.21816	+	0.556315i	0.917622	−	0.397455i	$-0.130107\pi$
$491$	26.9926	+	12.3271i	1.21816	+	0.556315i	0.300538	+	0.953770i	$0.402834\pi$
$492$		0			0
$493$	−4.36852	+	30.3837i	−0.196748	+	1.36841i
$494$		0			0
$495$	9.09921	+	9.49474i	0.408979	+	0.426757i
$496$		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
$501$	20.2526	−	0.507746i	0.904819	−	0.0226844i
$502$		0			0
$503$	21.9061	+	25.2810i	0.976744	+	1.12722i	0.991860	+	0.127336i	$0.0406428\pi$
$503$	21.9061	+	25.2810i	0.976744	+	1.12722i	−0.0151160	+	0.999886i	$0.504812\pi$
$504$		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	$-0.538446\pi$
$509$	11.6770	−	39.7683i	0.517575	−	1.76270i	0.638062	−	0.769985i	$-0.279736\pi$
$510$		0			0
$511$	17.6537	+	27.4696i	0.780952	+	1.21518i
$512$		0			0
$513$	38.0130	−	8.42048i	1.67831	−	0.371773i
$514$		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
$519$	15.8981	−	5.10424i	0.697848	−	0.224051i
$520$		0			0
$521$	−7.20556	−	8.31566i	−0.315681	−	0.364315i	0.575628	−	0.817712i	$-0.304758\pi$
$521$	−7.20556	−	8.31566i	−0.315681	−	0.364315i	−0.891309	+	0.453396i	$0.850212\pi$
$522$		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
$525$	−11.9438	−	13.1053i	−0.521270	−	0.571960i
$526$		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
$531$	−36.2061	−	14.3885i	−1.57121	−	0.624409i
$532$		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
$543$	3.65792	−	13.7210i	0.156976	−	0.588823i
$544$		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
$549$	−9.85928	−	0.916273i	−0.420784	−	0.0391056i
$550$		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
$555$	8.65940	+	3.69521i	0.367571	+	0.156853i
$556$		0			0
$557$	−3.60071	+	12.2629i	−0.152567	+	0.519595i	−0.999935	−	0.0114112i	$-0.996368\pi$
$557$	−3.60071	+	12.2629i	−0.152567	+	0.519595i	0.847368	+	0.531006i	$0.178186\pi$
$558$		0			0
$559$	9.67875	+	21.1935i	0.409368	+	0.896390i
$560$		0			0
$561$	23.6117	+	14.3511i	0.996887	+	0.605906i
$562$		0			0
$563$	−43.9639	−	12.9090i	−1.85286	−	0.544048i	−0.999751	−	0.0223106i	$-0.992898\pi$
$563$	−43.9639	−	12.9090i	−1.85286	−	0.544048i	−0.853106	−	0.521737i	$-0.825284\pi$
$564$		0			0
$565$	0.685947			0.0288580
$566$		0			0
$567$	−23.5674	−	8.02340i	−0.989738	−	0.336951i
$568$		0			0
$569$	−8.34604	+	7.23188i	−0.349884	+	0.303176i	−0.812016	−	0.583635i	$-0.801630\pi$
$569$	−8.34604	+	7.23188i	−0.349884	+	0.303176i	0.462132	+	0.886811i	$0.347085\pi$
$570$		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
$579$	−7.47976	−	23.2970i	−0.310848	−	0.968192i
$580$		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
$585$	5.20980	−	9.07661i	0.215399	−	0.375272i
$586$		0			0
$587$	−14.3810	+	4.22263i	−0.593566	+	0.174287i	−0.564699	−	0.825297i	$-0.691008\pi$
$587$	−14.3810	+	4.22263i	−0.593566	+	0.174287i	−0.0288662	+	0.999583i	$0.509190\pi$
$588$		0			0
$589$	−0.0596291	+	0.00857337i	−0.00245697	+	0.000353259i
$590$		0			0
$591$	−2.54188	+	4.18211i	−0.104559	+	0.172029i
$592$		0			0
$593$	−15.9821	+	34.9959i	−0.656306	+	1.43711i	0.229619	+	0.973281i	$0.426252\pi$
$593$	−15.9821	+	34.9959i	−0.656306	+	1.43711i	−0.885925	+	0.463829i	$0.846475\pi$
$594$		0			0
$595$	11.0021	+	7.07061i	0.451041	+	0.289867i
$596$		0			0
$597$	11.2725	−	1.91023i	0.461353	−	0.0781807i
$598$		0			0
$599$	−4.01145	−	27.9002i	−0.163903	−	1.13997i	−0.891187	−	0.453636i	$-0.850127\pi$
$599$	−4.01145	−	27.9002i	−0.163903	−	1.13997i	0.727284	−	0.686337i	$-0.240782\pi$
$600$		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
$603$	−22.3632	−	10.1433i	−0.910701	−	0.413067i
$604$		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
$609$	−34.9579	+	5.92396i	−1.41657	+	0.240051i
$610$		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
$615$	6.62366	−	10.8978i	0.267092	−	0.439442i
$616$		0			0
$617$	−32.9759	+	4.74122i	−1.32756	+	0.190874i	−0.769351	−	0.638826i	$-0.779420\pi$
$617$	−32.9759	+	4.74122i	−1.32756	+	0.190874i	−0.558209	+	0.829701i	$0.688511\pi$
$618$		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
$621$	0.419556	−	6.19667i	0.0168362	−	0.248664i
$622$		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
$627$	−15.2580	−	47.5238i	−0.609346	−	1.89792i
$628$		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
$639$	11.4067	+	32.6896i	0.451243	+	1.29318i
$640$		0			0
$641$	18.4942			0.730477			0.365239	−	0.930914i	$-0.380987\pi$
$641$	18.4942			0.730477			0.365239	+	0.930914i	$0.380987\pi$
$642$		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
$645$	−12.8427	−	7.80574i	−0.505679	−	0.307351i
$646$		0			0
$647$	−17.4739	−	38.2625i	−0.686969	−	1.50425i	−0.855087	−	0.518485i	$-0.826496\pi$
$647$	−17.4739	−	38.2625i	−0.686969	−	1.50425i	0.168117	−	0.985767i	$-0.446231\pi$
$648$		0			0
$649$	−14.0715	+	47.9231i	−0.552355	+	1.88115i
$650$		0			0
$651$	0.0354295	+	0.0151188i	0.00138859	+	0.000592552i
$652$		0			0
$653$	−6.03492	+	41.9738i	−0.236165	+	1.64256i	0.434406	+	0.900717i	$0.356958\pi$
$653$	−6.03492	+	41.9738i	−0.236165	+	1.64256i	−0.670571	+	0.741845i	$0.733951\pi$
$654$		0			0
$655$	−5.29026	+	4.58403i	−0.206707	+	0.179113i
$656$		0			0
$657$	−3.27700	+	35.2612i	−0.127848	+	1.37567i
$658$		0			0
$659$	−10.1402	−	34.5344i	−0.395006	−	1.34527i	−0.881748	−	0.471721i	$-0.843633\pi$
$659$	−10.1402	−	34.5344i	−0.395006	−	1.34527i	0.486741	−	0.873546i	$-0.338185\pi$
$660$		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
$663$	5.66423	−	21.2467i	0.219980	−	0.825154i
$664$		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
$675$	−1.44467	−	19.1758i	−0.0556053	−	0.738075i
$676$		0			0
$677$	5.62699	−	6.49390i	0.216263	−	0.249581i	−0.637244	−	0.770662i	$-0.719926\pi$
$677$	5.62699	−	6.49390i	0.216263	−	0.249581i	0.853507	+	0.521081i	$0.174471\pi$
$678$		0			0
$679$	11.7467	−	13.5564i	0.450796	−	0.520246i
$680$		0			0
$681$	−20.8383	−	22.8647i	−0.798525	−	0.876176i
$682$		0			0
$683$	−1.45684	+	0.936255i	−0.0557445	+	0.0358248i	−0.568216	−	0.822879i	$-0.692366\pi$
$683$	−1.45684	+	0.936255i	−0.0557445	+	0.0358248i	0.512472	+	0.858704i	$0.328730\pi$
$684$		0			0
$685$	−1.23132	−	1.42102i	−0.0470463	−	0.0542943i
$686$		0			0
$687$	30.0329	−	9.64239i	1.14583	−	0.367880i
$688$		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
$693$	−7.44590	+	31.0350i	−0.282846	+	1.17892i
$694$		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	0.839031	−	0.544084i	$-0.183123\pi$
$701$	18.3391	+	11.7859i	0.692660	+	0.445145i	−0.146371	+	0.989230i	$0.546759\pi$
$702$		0			0
$703$	−23.4004	−	27.0055i	−0.882562	−	1.01853i
$704$		0			0
$705$	7.04592	−	0.176646i	0.265365	−	0.00665287i
$706$		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
$711$	3.77414	−	3.61692i	0.141541	−	0.135645i
$712$		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
$717$	1.34201	+	1.10521i	0.0501184	+	0.0412747i
$718$		0			0
$719$	−41.3844	+	5.95018i	−1.54338	+	0.221904i	−0.860813	−	0.508921i	$-0.830044\pi$
$719$	−41.3844	+	5.95018i	−1.54338	+	0.221904i	−0.682565	+	0.730825i	$0.739135\pi$
$720$		0			0
$721$	−10.9168	−	37.1793i	−0.406564	−	1.38463i
$722$		0			0
$723$	25.4741	+	37.5356i	0.947394	+	1.39596i
$724$		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
$729$	−14.7693	−	22.6024i	−0.547013	−	0.837124i
$730$		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
$735$	−0.331482	+	1.24340i	−0.0122269	+	0.0458634i
$736$		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
$741$	−32.8667	+	22.3055i	−1.20739	+	0.819413i
$742$		0			0
$743$	−0.132950	+	0.452788i	−0.00487748	+	0.0166112i	−0.961896	−	0.273416i	$-0.911846\pi$
$743$	−0.132950	+	0.452788i	−0.00487748	+	0.0166112i	0.957018	+	0.290028i	$0.0936645\pi$
$744$		0			0
$745$	9.90559	−	15.4134i	0.362913	−	0.564703i
$746$		0			0
$747$	19.6545	−	10.1957i	0.719122	−	0.373040i
$748$		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
$753$	15.6794	−	14.2898i	0.571389	−	0.520750i
$754$		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
$759$	−7.95968	+	0.199554i	−0.288918	+	0.00724336i
$760$		0			0
$761$	39.4929	+	5.67822i	1.43162	+	0.205835i	0.814100	−	0.580724i	$-0.197231\pi$
$761$	39.4929	+	5.67822i	1.43162	+	0.205835i	0.617515	+	0.786559i	$0.288140\pi$
$762$		0			0
$763$	−0.670503	+	4.66345i	−0.0242738	+	0.168828i
$764$		0			0
$765$	4.67291	+	13.3917i	0.168950	+	0.484179i
$766$		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
$771$	−1.34143	+	3.14351i	−0.0483103	+	0.113211i
$772$		0			0
$773$	6.11766	−	9.51926i	0.220037	−	0.342384i	−0.713632	−	0.700520i	$-0.752951\pi$
$773$	6.11766	−	9.51926i	0.220037	−	0.342384i	0.933669	+	0.358136i	$0.116588\pi$
$774$		0			0
$775$			0.0297542i			0.00106880i
$776$		0			0
$777$	3.81754	+	22.5277i	0.136953	+	0.808176i
$778$		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
$783$	−33.8193	−	18.3004i	−1.20860	−	0.654003i
$784$		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
$789$	9.46189	−	22.1731i	0.336852	−	0.789383i
$790$		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
$795$	2.23181	−	8.37157i	0.0791540	−	0.296909i
$796$		0			0
$797$	−4.18471	−	3.62607i	−0.148230	−	0.128442i	0.577589	−	0.816328i	$-0.303994\pi$
$797$	−4.18471	−	3.62607i	−0.148230	−	0.128442i	−0.725819	+	0.687886i	$0.758539\pi$
$798$		0			0
$799$	14.2088	−	4.17207i	0.502670	−	0.147597i
$800$		0			0
$801$	4.16798	−	17.3725i	0.147268	−	0.613825i
$802$		0			0
$803$	45.3989			1.60209
$804$		0			0
$805$	−3.76864			−0.132827
$806$		0			0
$807$	−5.40170	+	6.55909i	−0.190149	+	0.230891i
$808$		0			0
$809$	37.9927	−	11.1557i	1.33575	−	0.392212i	0.465599	−	0.884996i	$-0.345839\pi$
$809$	37.9927	−	11.1557i	1.33575	−	0.392212i	0.870152	+	0.492784i	$0.164021\pi$
$810$		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
$813$	−51.2628	−	13.6663i	−1.79787	−	0.479299i
$814$		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
$819$	25.3667	−	1.27272i	0.886385	−	0.0444725i
$820$		0			0
$821$	10.1889	+	1.46494i	0.355594	+	0.0511267i	0.317797	−	0.948159i	$-0.397057\pi$
$821$	10.1889	+	1.46494i	0.355594	+	0.0511267i	0.0377968	+	0.999285i	$0.487966\pi$
$822$		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
$825$	−24.3060	+	4.11889i	−0.846227	+	0.143401i
$826$		0			0
$827$	−10.5666	+	4.82559i	−0.367436	+	0.167802i	−0.590572	−	0.806985i	$-0.701098\pi$
$827$	−10.5666	+	4.82559i	−0.367436	+	0.167802i	0.223136	+	0.974787i	$0.428371\pi$
$828$		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
$831$	20.6621	−	3.50140i	0.716761	−	0.121462i
$832$		0			0
$833$			2.70371i			0.0936780i
$834$		0			0
$835$	7.20771	−	11.2154i	0.249433	−	0.388126i
$836$		0			0
$837$	0.0201603	+	0.0365900i	0.000696844	+	0.00126474i
$838$		0			0
$839$	7.74515	+	3.53709i	0.267392	+	0.122114i	0.544600	−	0.838696i	$-0.316682\pi$
$839$	7.74515	+	3.53709i	0.267392	+	0.122114i	−0.277207	+	0.960810i	$0.589409\pi$
$840$		0			0
$841$	−25.7647			−0.888439
$842$		0			0
$843$	28.4776	+	3.36836i	0.980820	+	0.116013i
$844$		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
$849$	−0.218309	−	8.70774i	−0.00749234	−	0.298849i
$850$		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
$855$	9.46234	−	23.8103i	0.323605	−	0.814294i
$856$		0			0
$857$	2.13169	+	14.8262i	0.0728170	+	0.506453i	0.993290	+	0.115648i	$0.0368944\pi$
$857$	2.13169	+	14.8262i	0.0728170	+	0.506453i	−0.920473	+	0.390806i	$0.872196\pi$
$858$		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
$861$	30.9400	−	0.775687i	1.05443	−	0.0264353i
$862$		0			0
$863$	−16.5755	+	25.7920i	−0.564237	+	0.877970i	−0.999753	−	0.0222106i	$-0.992930\pi$
$863$	−16.5755	+	25.7920i	−0.564237	+	0.877970i	0.435516	+	0.900181i	$0.356566\pi$
$864$		0			0
$865$	3.09568	−	10.5429i	0.105256	−	0.358470i
$866$		0			0
$867$	0.199852	+	0.294478i	0.00678734	+	0.0100010i
$868$		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
$873$	19.0929	−	3.72999i	0.646196	−	0.126241i
$874$		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
$879$	−2.26183	+	19.1224i	−0.0762895	+	0.644984i
$880$		0			0
$881$	16.0356	+	7.32320i	0.540252	+	0.246725i	0.666801	−	0.745235i	$-0.267663\pi$
$881$	16.0356	+	7.32320i	0.540252	+	0.246725i	−0.126549	+	0.991960i	$0.540390\pi$
$882$		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
$885$	−21.2144	+	14.3975i	−0.713115	+	0.483967i
$886$		0			0
$887$	6.79268	+	23.1337i	0.228076	+	0.776755i	0.991415	+	0.130756i	$0.0417406\pi$
$887$	6.79268	+	23.1337i	0.228076	+	0.776755i	−0.763339	+	0.645998i	$0.776441\pi$
$888$		0			0
$889$	56.8668	−	8.17621i	1.90725	−	0.274221i
$890$		0			0
$891$	−27.0993	+	21.5340i	−0.907861	+	0.721417i
$892$		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
$897$	1.93696	+	6.03301i	0.0646732	+	0.201436i
$898$		0			0
$899$	0.0500526	+	0.0321668i	0.00166935	+	0.00107282i
$900$		0			0
$901$		−	18.2036i		−	0.606449i
$902$		0			0
$903$	−0.914119	−	36.4617i	−0.0304200	−	1.21337i
$904$		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	$0.279325\pi$
$911$	−9.48918	+	32.3172i	−0.314391	+	1.07072i	−0.953448	+	0.301557i	$0.902494\pi$
$912$		0			0
$913$	−15.3461	−	23.8791i	−0.507883	−	0.790281i
$914$		0			0
$915$	−4.14234	+	5.02990i	−0.136942	+	0.166283i
$916$		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
$921$	−8.34766	−	26.0003i	−0.275065	−	0.856738i
$922$		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
$927$	15.5200	−	39.0532i	0.509743	−	1.28268i
$928$		0			0
$929$	33.5330	−	38.6991i	1.10018	−	1.26968i	0.140045	−	0.990145i	$-0.455275\pi$
$929$	33.5330	−	38.6991i	1.10018	−	1.26968i	0.960136	−	0.279532i	$-0.0901793\pi$
$930$		0			0
$931$	3.19836	−	3.69111i	0.104822	−	0.120971i
$932$		0			0
$933$	−32.5583	+	29.6728i	−1.06591	+	0.971444i
$934$		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	0.999088	−	0.0427017i	$-0.0135965\pi$
$941$	9.58778	+	20.9943i	0.312553	+	0.684395i	−0.686535	+	0.727097i	$0.740869\pi$
$942$		0			0
$943$	2.17531	+	7.40842i	0.0708378	+	0.241251i
$944$		0			0
$945$	−13.0780	+	9.86775i	−0.425427	+	0.320998i
$946$		0			0
$947$	−16.8597	−	14.6090i	−0.547867	−	0.474729i	0.336395	−	0.941721i	$-0.390792\pi$
$947$	−16.8597	−	14.6090i	−0.547867	−	0.474729i	−0.884262	+	0.466992i	$0.845338\pi$
$948$		0			0
$949$	−10.1786	−	34.6651i	−0.330411	−	1.12528i
$950$		0			0
$951$	27.1837	+	16.5222i	0.881491	+	0.535768i
$952$		0			0
$953$	15.0549	−	13.0451i	0.487675	−	0.422573i	−0.376002	−	0.926619i	$-0.622701\pi$
$953$	15.0549	−	13.0451i	0.487675	−	0.422573i	0.863677	+	0.504046i	$0.168156\pi$
$954$		0			0
$955$	−3.47899	+	24.1969i	−0.112577	+	0.782993i
$956$		0			0
$957$	−19.3481	+	45.3405i	−0.625434	+	1.46565i
$958$		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
$963$	−59.4121	−	5.52147i	−1.91453	−	0.177927i
$964$		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
$969$	6.32332	−	53.4600i	0.203134	−	1.71738i
$970$		0			0
$971$	2.23324	−	1.93512i	0.0716682	−	0.0621008i	−0.618290	−	0.785950i	$-0.712174\pi$
$971$	2.23324	−	1.93512i	0.0716682	−	0.0621008i	0.689958	+	0.723849i	$0.257629\pi$
$972$		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	−0.969900	−	0.243503i	$-0.921703\pi$
$977$	−10.7990	+	16.8036i	−0.345491	+	0.537594i	0.624410	+	0.781097i	$0.285340\pi$
$978$		0			0
$979$	−22.6700	−	3.25945i	−0.724535	−	0.104172i
$980$		0			0
$981$	−3.68908	+	3.53540i	−0.117783	+	0.112877i
$982$		0			0
$983$	−3.89923	+	8.53812i	−0.124366	+	0.272324i	−0.961566	−	0.274573i	$-0.911464\pi$
$983$	−3.89923	+	8.53812i	−0.124366	+	0.272324i	0.837200	+	0.546896i	$0.184191\pi$
$984$		0			0
$985$	1.33788	+	2.92955i	0.0426285	+	0.0933433i
$986$		0			0
$987$	9.60542	+	14.1534i	0.305744	+	0.450507i
$988$		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
$993$	−12.5520	−	7.62905i	−0.398324	−	0.242100i
$994$		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
$999$	−11.7932	+	21.7939i	−0.373120	+	0.689529i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.33701 + 1.10109i) q^{3} +(1.09364 - 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(0.575207 + 2.94434i) q^{9} +O(q^{10})\)	\(q+(1.33701 + 1.10109i) q^{3} +(1.09364 - 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(0.575207 + 2.94434i) q^{9} +(3.69014 - 1.08352i) q^{11} +(-1.65469 - 2.57474i) q^{13} +(1.81579 + 0.774850i) q^{15} +(4.10573 + 0.590315i) q^{17} +(-4.90683 - 5.66278i) q^{19} +(0.800501 + 4.72384i) q^{21} +(-1.08727 + 0.496537i) q^{23} +(-3.11334 + 2.00082i) q^{25} +(-2.47292 + 4.56997i) q^{27} +7.40032i q^{29} +(0.00434668 - 0.00676357i) q^{31} +(6.12683 + 2.61449i) q^{33} +(2.86801 + 1.30978i) q^{35} +4.76894 q^{37} +(0.622682 - 5.26442i) q^{39} +(0.919315 - 6.39398i) q^{41} +(-7.53507 - 1.08338i) q^{43} +(1.57456 + 3.03533i) q^{45} +(3.24748 - 1.48308i) q^{47} +(0.0927634 + 0.645184i) q^{49} +(4.83942 + 5.31003i) q^{51} +(-0.624559 - 4.34391i) q^{53} +(3.68774 - 2.36997i) q^{55} +(-0.325269 - 12.9741i) q^{57} +(-7.02119 + 10.9252i) q^{59} +(-0.929884 + 3.16689i) q^{61} +(-4.13109 + 7.19726i) q^{63} +(-2.63643 - 2.28448i) q^{65} +(-4.74764 + 6.66783i) q^{67} +(-2.00042 - 0.533298i) q^{69} +(11.4234 - 1.64244i) q^{71} +(11.3262 + 3.32568i) q^{73} +(-6.36566 - 0.752938i) q^{75} +(9.67720 + 4.41943i) q^{77} +(-0.942057 - 1.46587i) q^{79} +(-8.33827 + 3.38721i) q^{81} +(-2.07934 - 7.08159i) q^{83} +(4.67975 - 0.672846i) q^{85} +(-8.14841 + 9.89432i) q^{87} +(-5.41699 - 2.47386i) q^{89} +(1.20487 - 8.38004i) q^{91} +(0.0132589 - 0.00425690i) q^{93} +(-7.18474 - 4.61735i) q^{95} -6.48460i q^{97} +(5.31286 + 10.2418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more