LMFDB - Embedded newform 820.2.y.a.137.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			137.6
Character	$\chi$	$=$	820.137
Dual form			820.2.y.a.413.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70434 - 0.705960i) q^{3} +(-1.80257 - 1.32316i) q^{5} +(-0.486096 + 1.17354i) q^{7} +(0.285071 + 0.285071i) q^{9} +(-0.170771 + 0.0707355i) q^{11} +(-2.06988 - 0.857371i) q^{13} +(2.13809 + 3.52765i) q^{15} +(3.47876 - 1.44095i) q^{17} +(-6.29520 - 2.60756i) q^{19} +(1.65694 - 1.65694i) q^{21} +(5.87283 + 5.87283i) q^{23} +(1.49851 + 4.77016i) q^{25} +(1.83327 + 4.42591i) q^{27} +(-7.26833 + 3.01064i) q^{29} +2.63759i q^{31} +0.340987 q^{33} +(2.42900 - 1.47220i) q^{35} +(2.97212 + 2.97212i) q^{37} +(2.92250 + 2.92250i) q^{39} +(3.14368 - 5.57828i) q^{41} +12.6403 q^{43} +(-0.136667 - 0.891054i) q^{45} +(3.76504 - 1.55953i) q^{47} +(3.80884 + 3.80884i) q^{49} -6.94623 q^{51} +(-2.15094 + 5.19282i) q^{53} +(0.401420 + 0.0984507i) q^{55} +(8.88832 + 8.88832i) q^{57} +13.4547i q^{59} +(-4.46735 - 4.46735i) q^{61} +(-0.473114 + 0.195970i) q^{63} +(2.59666 + 4.28424i) q^{65} +(3.93820 - 1.63126i) q^{67} +(-5.86331 - 14.1553i) q^{69} +(5.36440 + 12.9508i) q^{71} -7.79462 q^{73} +(0.813575 - 9.18787i) q^{75} -0.234790i q^{77} +(-2.69653 - 6.50999i) q^{79} -10.0469i q^{81} +(-11.4612 + 11.4612i) q^{83} +(-8.17730 - 2.00553i) q^{85} +14.5131 q^{87} +(2.18703 - 0.905899i) q^{89} +(2.01232 - 2.01232i) q^{91} +(1.86204 - 4.49536i) q^{93} +(7.89732 + 13.0298i) q^{95} +(-5.01568 - 12.1089i) q^{97} +(-0.0688464 - 0.0285171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70434	−	0.705960i	−0.984001	−	0.407586i	−0.168095	−	0.985771i	$-0.553761\pi$
$3$	−1.70434	−	0.705960i	−0.984001	−	0.407586i	−0.815906	+	0.578184i	$0.803761\pi$
$4$		0			0
$5$	−1.80257	−	1.32316i	−0.806133	−	0.591734i
$5$	−1.80257	−	1.32316i	−0.806133	−	0.591734i
$6$		0			0
$7$	−0.486096	+	1.17354i	−0.183727	+	0.443556i	−0.988729	−	0.149716i	$-0.952164\pi$
$7$	−0.486096	+	1.17354i	−0.183727	+	0.443556i	0.805002	+	0.593272i	$0.202164\pi$
$8$		0			0
$9$	0.285071	+	0.285071i	0.0950237	+	0.0950237i
$10$		0			0
$11$	−0.170771	+	0.0707355i	−0.0514893	+	0.0213276i	−0.408279	−	0.912857i	$-0.633871\pi$
$11$	−0.170771	+	0.0707355i	−0.0514893	+	0.0213276i	0.356790	+	0.934185i	$0.383871\pi$
$12$		0			0
$13$	−2.06988	−	0.857371i	−0.574081	−	0.237792i	0.0767046	−	0.997054i	$-0.475560\pi$
$13$	−2.06988	−	0.857371i	−0.574081	−	0.237792i	−0.650785	+	0.759262i	$0.725560\pi$
$14$		0			0
$15$	2.13809	+	3.52765i	0.552053	+	0.910835i
$16$		0			0
$17$	3.47876	−	1.44095i	0.843722	−	0.349481i	0.0814021	−	0.996681i	$-0.474060\pi$
$17$	3.47876	−	1.44095i	0.843722	−	0.349481i	0.762320	+	0.647200i	$0.224060\pi$
$18$		0			0
$19$	−6.29520	−	2.60756i	−1.44422	−	0.598214i	−0.483401	−	0.875399i	$-0.660599\pi$
$19$	−6.29520	−	2.60756i	−1.44422	−	0.598214i	−0.960817	+	0.277185i	$0.910599\pi$
$20$		0			0
$21$	1.65694	−	1.65694i	0.361575	−	0.361575i
$22$		0			0
$23$	5.87283	+	5.87283i	1.22457	+	1.22457i	0.965990	+	0.258581i	$0.0832549\pi$
$23$	5.87283	+	5.87283i	1.22457	+	1.22457i	0.258581	+	0.965990i	$0.416745\pi$
$24$		0			0
$25$	1.49851	+	4.77016i	0.299702	+	0.954033i
$26$		0			0
$27$	1.83327	+	4.42591i	0.352813	+	0.851767i
$28$		0			0
$29$	−7.26833	+	3.01064i	−1.34970	+	0.559062i	−0.936208	−	0.351447i	$-0.885690\pi$
$29$	−7.26833	+	3.01064i	−1.34970	+	0.559062i	−0.413488	+	0.910510i	$0.635690\pi$
$30$		0			0
$31$			2.63759i			0.473726i	0.971543	+	0.236863i	$0.0761193\pi$
$31$			2.63759i			0.473726i	−0.971543	+	0.236863i	$0.923881\pi$
$32$		0			0
$33$	0.340987			0.0593583
$34$		0			0
$35$	2.42900	−	1.47220i	0.410575	−	0.248848i
$36$		0			0
$37$	2.97212	+	2.97212i	0.488614	+	0.488614i	0.907869	−	0.419254i	$-0.137708\pi$
$37$	2.97212	+	2.97212i	0.488614	+	0.488614i	−0.419254	+	0.907869i	$0.637708\pi$
$38$		0			0
$39$	2.92250	+	2.92250i	0.467975	+	0.467975i
$40$		0			0
$41$	3.14368	−	5.57828i	0.490961	−	0.871182i
$41$	3.14368	−	5.57828i	0.490961	−	0.871182i
$42$		0			0
$43$	12.6403			1.92763			0.963815	−	0.266573i	$-0.0858914\pi$
$43$	12.6403			1.92763			0.963815	+	0.266573i	$0.0858914\pi$
$44$		0			0
$45$	−0.136667	−	0.891054i	−0.0203731	−	0.132831i
$46$		0			0
$47$	3.76504	−	1.55953i	0.549188	−	0.227481i	−0.0907958	−	0.995870i	$-0.528941\pi$
$47$	3.76504	−	1.55953i	0.549188	−	0.227481i	0.639984	+	0.768388i	$0.278941\pi$
$48$		0			0
$49$	3.80884	+	3.80884i	0.544120	+	0.544120i
$50$		0			0
$51$	−6.94623			−0.972667
$52$		0			0
$53$	−2.15094	+	5.19282i	−0.295454	+	0.713288i	0.704540	+	0.709665i	$0.251154\pi$
$53$	−2.15094	+	5.19282i	−0.295454	+	0.713288i	−0.999993	+	0.00362385i	$0.998846\pi$
$54$		0			0
$55$	0.401420	+	0.0984507i	0.0541275	+	0.0132751i
$56$		0			0
$57$	8.88832	+	8.88832i	1.17729	+	1.17729i
$58$		0			0
$59$			13.4547i			1.75165i	0.482626	+	0.875826i	$0.339683\pi$
$59$			13.4547i			1.75165i	−0.482626	+	0.875826i	$0.660317\pi$
$60$		0			0
$61$	−4.46735	−	4.46735i	−0.571985	−	0.571985i	0.360697	−	0.932683i	$-0.382539\pi$
$61$	−4.46735	−	4.46735i	−0.571985	−	0.571985i	−0.932683	+	0.360697i	$0.882539\pi$
$62$		0			0
$63$	−0.473114	+	0.195970i	−0.0596068	+	0.0246899i
$64$		0			0
$65$	2.59666	+	4.28424i	0.322076	+	0.531395i
$66$		0			0
$67$	3.93820	−	1.63126i	0.481128	−	0.199290i	−0.128919	−	0.991655i	$-0.541151\pi$
$67$	3.93820	−	1.63126i	0.481128	−	0.199290i	0.610047	+	0.792365i	$0.291151\pi$
$68$		0			0
$69$	−5.86331	−	14.1553i	−0.705860	−	1.70410i
$70$		0			0
$71$	5.36440	+	12.9508i	0.636637	+	1.53698i	0.831133	+	0.556074i	$0.187693\pi$
$71$	5.36440	+	12.9508i	0.636637	+	1.53698i	−0.194496	+	0.980903i	$0.562307\pi$
$72$		0			0
$73$	−7.79462			−0.912292			−0.456146	−	0.889905i	$-0.650770\pi$
$73$	−7.79462			−0.912292			−0.456146	+	0.889905i	$0.650770\pi$
$74$		0			0
$75$	0.813575	−	9.18787i	0.0939435	−	1.06092i
$76$		0			0
$77$		−	0.234790i		−	0.0267568i
$78$		0			0
$79$	−2.69653	−	6.50999i	−0.303383	−	0.732431i	−0.999889	−	0.0148807i	$-0.995263\pi$
$79$	−2.69653	−	6.50999i	−0.303383	−	0.732431i	0.696506	−	0.717551i	$-0.254737\pi$
$80$		0			0
$81$		−	10.0469i		−	1.11632i
$82$		0			0
$83$	−11.4612	+	11.4612i	−1.25803	+	1.25803i	−0.305998	+	0.952032i	$0.598990\pi$
$83$	−11.4612	+	11.4612i	−1.25803	+	1.25803i	−0.952032	+	0.305998i	$0.901010\pi$
$84$		0			0
$85$	−8.17730	−	2.00553i	−0.886953	−	0.217530i
$86$		0			0
$87$	14.5131			1.55597
$88$		0			0
$89$	2.18703	−	0.905899i	0.231825	−	0.0960251i	−0.263747	−	0.964592i	$-0.584958\pi$
$89$	2.18703	−	0.905899i	0.231825	−	0.0960251i	0.495572	+	0.868567i	$0.334958\pi$
$90$		0			0
$91$	2.01232	−	2.01232i	0.210948	−	0.210948i
$92$		0			0
$93$	1.86204	−	4.49536i	0.193084	−	0.466147i
$94$		0			0
$95$	7.89732	+	13.0298i	0.810248	+	1.33683i
$96$		0			0
$97$	−5.01568	−	12.1089i	−0.509265	−	1.22948i	−0.944307	−	0.329065i	$-0.893266\pi$
$97$	−5.01568	−	12.1089i	−0.509265	−	1.22948i	0.435042	−	0.900410i	$-0.356734\pi$
$98$		0			0
$99$	−0.0688464	−	0.0285171i	−0.00691932	−	0.00286608i
$100$		0			0
$101$	−5.16472	+	12.4687i	−0.513909	+	1.24069i	0.427683	+	0.903929i	$0.359330\pi$
$101$	−5.16472	+	12.4687i	−0.513909	+	1.24069i	−0.941592	+	0.336757i	$0.890670\pi$
$102$		0			0
$103$			4.00866i			0.394985i	0.980304	+	0.197492i	$0.0632798\pi$
$103$			4.00866i			0.394985i	−0.980304	+	0.197492i	$0.936720\pi$
$104$		0			0
$105$	−5.17915	+	0.794359i	−0.505434	+	0.0775215i
$106$		0			0
$107$	0.248757	−	0.248757i	0.0240483	−	0.0240483i	−0.694980	−	0.719029i	$-0.744587\pi$
$107$	0.248757	−	0.248757i	0.0240483	−	0.0240483i	0.719029	+	0.694980i	$0.244587\pi$
$108$		0			0
$109$	3.33082	−	8.04132i	0.319035	−	0.770219i	−0.680271	−	0.732961i	$-0.738138\pi$
$109$	3.33082	−	8.04132i	0.319035	−	0.770219i	0.999306	−	0.0372576i	$-0.0118622\pi$
$110$		0			0
$111$	−2.96731	−	7.16371i	−0.281644	−	0.679949i
$112$		0			0
$113$	−6.59685	−	6.59685i	−0.620580	−	0.620580i	0.325100	−	0.945680i	$-0.394602\pi$
$113$	−6.59685	−	6.59685i	−0.620580	−	0.620580i	−0.945680	+	0.325100i	$0.894602\pi$
$114$		0			0
$115$	−2.81551	−	18.3569i	−0.262548	−	1.71179i
$116$		0			0
$117$	−0.345650	−	0.834474i	−0.0319554	−	0.0771471i
$118$		0			0
$119$			4.78289i			0.438447i
$120$		0			0
$121$	−7.75402	+	7.75402i	−0.704911	+	0.704911i
$122$		0			0
$123$	−9.29595	+	7.28797i	−0.838188	+	0.657134i
$124$		0			0
$125$	3.61050	−	10.5813i	0.322933	−	0.946422i
$126$		0			0
$127$	−8.78254	+	8.78254i	−0.779324	+	0.779324i	−0.979716	−	0.200392i	$-0.935779\pi$
$127$	−8.78254	+	8.78254i	−0.779324	+	0.779324i	0.200392	+	0.979716i	$0.435779\pi$
$128$		0			0
$129$	−21.5434	−	8.92356i	−1.89679	−	0.785675i
$130$		0			0
$131$	−7.54803	+	7.54803i	−0.659475	+	0.659475i	−0.955256	−	0.295781i	$-0.904420\pi$
$131$	−7.54803	+	7.54803i	−0.659475	+	0.659475i	0.295781	+	0.955256i	$0.404420\pi$
$132$		0			0
$133$	6.12014	−	6.12014i	0.530683	−	0.530683i
$134$		0			0
$135$	2.55157	−	10.4037i	0.219605	−	0.895409i
$136$		0			0
$137$	3.46919	−	1.43698i	0.296393	−	0.122770i	−0.229532	−	0.973301i	$-0.573719\pi$
$137$	3.46919	−	1.43698i	0.296393	−	0.122770i	0.525924	+	0.850531i	$0.323719\pi$
$138$		0			0
$139$		−	9.75476i		−	0.827388i	−0.910416	−	0.413694i	$-0.864238\pi$
$139$		−	9.75476i		−	0.827388i	0.910416	−	0.413694i	$-0.135762\pi$
$140$		0			0
$141$	−7.51788			−0.633119
$142$		0			0
$143$	0.414121			0.0346305
$144$		0			0
$145$	17.0852	+	4.19025i	1.41885	+	0.347982i
$146$		0			0
$147$	−3.80267	−	9.18045i	−0.313639	−	0.757191i
$148$		0			0
$149$	−1.72511	−	0.714562i	−0.141326	−	0.0585392i	0.310899	−	0.950443i	$-0.399370\pi$
$149$	−1.72511	−	0.714562i	−0.141326	−	0.0585392i	−0.452226	+	0.891904i	$0.649370\pi$
$150$		0			0
$151$	8.05608	−	3.33694i	0.655594	−	0.271556i	−0.0299891	−	0.999550i	$-0.509547\pi$
$151$	8.05608	−	3.33694i	0.655594	−	0.271556i	0.685583	+	0.727994i	$0.259547\pi$
$152$		0			0
$153$	1.40247	+	0.580920i	0.113383	+	0.0469646i
$154$		0			0
$155$	3.48995	−	4.75445i	0.280320	−	0.381886i
$156$		0			0
$157$	10.3738	+	4.29698i	0.827922	+	0.342937i	0.756080	−	0.654479i	$-0.227112\pi$
$157$	10.3738	+	4.29698i	0.827922	+	0.342937i	0.0718425	+	0.997416i	$0.477112\pi$
$158$		0			0
$159$	7.33185	−	7.33185i	0.581453	−	0.581453i
$160$		0			0
$161$	−9.74676	+	4.03724i	−0.768152	+	0.318179i
$162$		0			0
$163$	11.7086	+	11.7086i	0.917085	+	0.917085i	0.996816	−	0.0797310i	$-0.0254061\pi$
$163$	11.7086	+	11.7086i	0.917085	+	0.917085i	−0.0797310	+	0.996816i	$0.525406\pi$
$164$		0			0
$165$	−0.614653	−	0.451180i	−0.0478507	−	0.0351243i
$166$		0			0
$167$	1.68112	−	4.05857i	0.130089	−	0.314062i	−0.845392	−	0.534146i	$-0.820633\pi$
$167$	1.68112	−	4.05857i	0.130089	−	0.314062i	0.975481	+	0.220084i	$0.0706332\pi$
$168$		0			0
$169$	−5.64308	−	5.64308i	−0.434083	−	0.434083i
$170$		0			0
$171$	−1.05124	−	2.53792i	−0.0803903	−	0.194079i
$172$		0			0
$173$			1.73349i			0.131795i	0.997826	+	0.0658975i	$0.0209910\pi$
$173$			1.73349i			0.131795i	−0.997826	+	0.0658975i	$0.979009\pi$
$174$		0			0
$175$	−6.32639	−	0.560195i	−0.478230	−	0.0423467i
$176$		0			0
$177$	9.49848	−	22.9314i	0.713950	−	1.72363i
$178$		0			0
$179$	2.20698	−	5.32812i	0.164957	−	0.398242i	−0.819688	−	0.572811i	$-0.805853\pi$
$179$	2.20698	−	5.32812i	0.164957	−	0.398242i	0.984645	+	0.174568i	$0.0558530\pi$
$180$		0			0
$181$	−1.70433	+	4.11462i	−0.126682	+	0.305837i	−0.974477	−	0.224486i	$-0.927930\pi$
$181$	−1.70433	+	4.11462i	−0.126682	+	0.305837i	0.847795	+	0.530324i	$0.177930\pi$
$182$		0			0
$183$	4.46011	+	10.7676i	0.329700	+	0.795967i
$184$		0			0
$185$	−1.42487	−	9.29005i	−0.104759	−	0.683018i
$186$		0			0
$187$	−0.492143	+	0.492143i	−0.0359891	+	0.0359891i
$188$		0			0
$189$	−6.08512			−0.442628
$190$		0			0
$191$	−17.6370	−	7.30549i	−1.27617	−	0.528607i	−0.361336	−	0.932436i	$-0.617679\pi$
$191$	−17.6370	−	7.30549i	−1.27617	−	0.528607i	−0.914835	+	0.403829i	$0.867679\pi$
$192$		0			0
$193$	−1.42088	−	0.588548i	−0.102277	−	0.0423646i	0.330958	−	0.943645i	$-0.392628\pi$
$193$	−1.42088	−	0.588548i	−0.102277	−	0.0423646i	−0.433235	+	0.901281i	$0.642628\pi$
$194$		0			0
$195$	−1.40108	−	9.13494i	−0.100334	−	0.654167i
$196$		0			0
$197$			7.63343i			0.543860i	0.962317	+	0.271930i	$0.0876619\pi$
$197$			7.63343i			0.543860i	−0.962317	+	0.271930i	$0.912338\pi$
$198$		0			0
$199$	−5.66541	+	13.6775i	−0.401610	+	0.969572i	0.585665	+	0.810553i	$0.300833\pi$
$199$	−5.66541	+	13.6775i	−0.401610	+	0.969572i	−0.987275	+	0.159020i	$0.949167\pi$
$200$		0			0
$201$	−7.86363			−0.554658
$202$		0			0
$203$		−	9.99313i		−	0.701380i
$204$		0			0
$205$	−13.0477	+	5.89565i	−0.911288	+	0.411770i
$206$		0			0
$207$			3.34835i			0.232726i
$208$		0			0
$209$	1.25948			0.0871202
$210$		0			0
$211$	4.44470	−	10.7305i	0.305986	−	0.738716i	−0.693841	−	0.720128i	$-0.744083\pi$
$211$	4.44470	−	10.7305i	0.305986	−	0.738716i	0.999827	−	0.0185876i	$-0.00591695\pi$
$212$		0			0
$213$		−	25.8596i		−	1.77187i
$214$		0			0
$215$	−22.7850	−	16.7251i	−1.55393	−	1.14064i
$216$		0			0
$217$	−3.09532	−	1.28212i	−0.210124	−	0.0870362i
$218$		0			0
$219$	13.2847	+	5.50270i	0.897696	+	0.371838i
$220$		0			0
$221$	−8.43602			−0.567468
$222$		0			0
$223$	−3.45494	+	3.45494i	−0.231360	+	0.231360i	−0.813260	−	0.581900i	$-0.802309\pi$
$223$	−3.45494	+	3.45494i	−0.231360	+	0.231360i	0.581900	+	0.813260i	$0.302309\pi$
$224$		0			0
$225$	−0.932654	+	1.78702i	−0.0621769	+	0.119135i
$226$		0			0
$227$	−2.96458	−	7.15712i	−0.196766	−	0.475035i	0.794443	−	0.607338i	$-0.207763\pi$
$227$	−2.96458	−	7.15712i	−0.196766	−	0.475035i	−0.991209	+	0.132304i	$0.957763\pi$
$228$		0			0
$229$	8.86532	−	21.4028i	0.585837	−	1.41434i	−0.301613	−	0.953431i	$-0.597525\pi$
$229$	8.86532	−	21.4028i	0.585837	−	1.41434i	0.887450	−	0.460905i	$-0.152475\pi$
$230$		0			0
$231$	−0.165753	+	0.400162i	−0.0109057	+	0.0263287i
$232$		0			0
$233$	−11.1579	+	26.9376i	−0.730978	+	1.76474i	−0.0916669	+	0.995790i	$0.529220\pi$
$233$	−11.1579	+	26.9376i	−0.730978	+	1.76474i	−0.639311	+	0.768948i	$0.720780\pi$
$234$		0			0
$235$	−8.85026	−	2.17058i	−0.577327	−	0.141593i
$236$		0			0
$237$			12.9989i			0.844368i
$238$		0			0
$239$	7.26969	+	17.5506i	0.470237	+	1.13525i	0.964059	+	0.265690i	$0.0855998\pi$
$239$	7.26969	+	17.5506i	0.470237	+	1.13525i	−0.493821	+	0.869564i	$0.664400\pi$
$240$		0			0
$241$	9.20318	+	9.20318i	0.592829	+	0.592829i	0.938395	−	0.345566i	$-0.112313\pi$
$241$	9.20318	+	9.20318i	0.592829	+	0.592829i	−0.345566	+	0.938395i	$0.612313\pi$
$242$		0			0
$243$	−1.59291	+	3.84563i	−0.102185	+	0.246697i
$244$		0			0
$245$	−1.82601	−	11.9054i	−0.116659	−	0.760608i
$246$		0			0
$247$	10.7946	+	10.7946i	0.686847	+	0.686847i
$248$		0			0
$249$	27.6249	−	11.4426i	1.75066	−	0.725146i
$250$		0			0
$251$	−8.50694	+	8.50694i	−0.536953	+	0.536953i	−0.922633	−	0.385680i	$-0.873967\pi$
$251$	−8.50694	+	8.50694i	−0.536953	+	0.536953i	0.385680	+	0.922633i	$0.373967\pi$
$252$		0			0
$253$	−1.41833	−	0.587490i	−0.0891693	−	0.0369351i
$254$		0			0
$255$	12.5211	+	9.19095i	0.784099	+	0.575560i
$256$		0			0
$257$	22.1202	+	9.16248i	1.37982	+	0.571540i	0.944433	−	0.328705i	$-0.106612\pi$
$257$	22.1202	+	9.16248i	1.37982	+	0.571540i	0.435386	+	0.900244i	$0.356612\pi$
$258$		0			0
$259$	−4.93264	+	2.04317i	−0.306499	+	0.126956i
$260$		0			0
$261$	−2.93024	−	1.21374i	−0.181377	−	0.0751289i
$262$		0			0
$263$	6.79987	+	16.4163i	0.419298	+	1.01227i	0.982552	+	0.185991i	$0.0595494\pi$
$263$	6.79987	+	16.4163i	0.419298	+	1.01227i	−0.563254	+	0.826284i	$0.690451\pi$
$264$		0			0
$265$	10.7481	−	6.51439i	0.660252	−	0.400176i
$266$		0			0
$267$	−4.36698			−0.267255
$268$		0			0
$269$	29.1478			1.77717			0.888586	−	0.458709i	$-0.151688\pi$
$269$	29.1478			1.77717			0.888586	+	0.458709i	$0.151688\pi$
$270$		0			0
$271$		−	6.03560i		−	0.366637i	−0.983054	−	0.183318i	$-0.941316\pi$
$271$		−	6.03560i		−	0.366637i	0.983054	−	0.183318i	$-0.0586839\pi$
$272$		0			0
$273$	−4.85029	+	2.00905i	−0.293553	+	0.121593i
$274$		0			0
$275$	−0.593322	−	0.708606i	−0.0357786	−	0.0427305i
$276$		0			0
$277$	−19.4638	+	19.4638i	−1.16947	+	1.16947i	−0.187133	+	0.982335i	$0.559919\pi$
$277$	−19.4638	+	19.4638i	−1.16947	+	1.16947i	−0.982335	+	0.187133i	$0.940081\pi$
$278$		0			0
$279$	−0.751902	+	0.751902i	−0.0450152	+	0.0450152i
$280$		0			0
$281$	−14.5996	−	6.04737i	−0.870942	−	0.360756i	−0.0979648	−	0.995190i	$-0.531233\pi$
$281$	−14.5996	−	6.04737i	−0.870942	−	0.360756i	−0.772977	+	0.634434i	$0.781233\pi$
$282$		0			0
$283$	−16.5976	+	16.5976i	−0.986623	+	0.986623i	−0.999912	−	0.0132884i	$-0.995770\pi$
$283$	−16.5976	+	16.5976i	−0.986623	+	0.986623i	0.0132884	+	0.999912i	$0.495770\pi$
$284$		0			0
$285$	−4.26117	−	27.7825i	−0.252410	−	1.64569i
$286$		0			0
$287$	5.01820	+	6.40082i	0.296215	+	0.377828i
$288$		0			0
$289$	−1.99540	+	1.99540i	−0.117377	+	0.117377i
$290$		0			0
$291$			24.1786i			1.41737i
$292$		0			0
$293$	−6.84694	−	16.5300i	−0.400003	−	0.965692i	−0.987664	−	0.156585i	$-0.949951\pi$
$293$	−6.84694	−	16.5300i	−0.400003	−	0.965692i	0.587662	−	0.809107i	$-0.300049\pi$
$294$		0			0
$295$	17.8027	−	24.2530i	1.03651	−	1.41207i
$296$		0			0
$297$	−0.626138	−	0.626138i	−0.0363322	−	0.0363322i
$298$		0			0
$299$	−7.12085	−	17.1912i	−0.411809	−	0.994195i
$300$		0			0
$301$	−6.14440	+	14.8339i	−0.354157	+	0.855012i
$302$		0			0
$303$	17.6049	−	17.6049i	1.01137	−	1.01137i
$304$		0			0
$305$	2.14170	+	13.9637i	0.122633	+	0.799560i
$306$		0			0
$307$		−	12.9449i		−	0.738806i	−0.929269	−	0.369403i	$-0.879562\pi$
$307$		−	12.9449i		−	0.738806i	0.929269	−	0.369403i	$-0.120438\pi$
$308$		0			0
$309$	2.82995	−	6.83211i	0.160990	−	0.388665i
$310$		0			0
$311$	22.4956	+	9.31797i	1.27561	+	0.528374i	0.914664	−	0.404214i	$-0.132455\pi$
$311$	22.4956	+	9.31797i	1.27561	+	0.528374i	0.360943	+	0.932588i	$0.382455\pi$
$312$		0			0
$313$	−2.04778	−	4.94378i	−0.115747	−	0.279439i	0.855380	−	0.518001i	$-0.173324\pi$
$313$	−2.04778	−	4.94378i	−0.115747	−	0.279439i	−0.971127	+	0.238563i	$0.923324\pi$
$314$		0			0
$315$	1.11212	+	0.272754i	0.0626609	+	0.0153680i
$316$		0			0
$317$	−7.31488	+	17.6597i	−0.410845	+	0.991867i	0.574067	+	0.818808i	$0.305365\pi$
$317$	−7.31488	+	17.6597i	−0.410845	+	0.991867i	−0.984912	+	0.173058i	$0.944635\pi$
$318$		0			0
$319$	1.02826	−	1.02826i	0.0575714	−	0.0575714i
$320$		0			0
$321$	−0.599579	+	0.248354i	−0.0334652	+	0.0138618i
$322$		0			0
$323$	−25.6568			−1.42758
$324$		0			0
$325$	0.988066	−	11.1584i	0.0548081	−	0.618959i
$326$		0			0
$327$	−11.3537	+	11.3537i	−0.627861	+	0.627861i
$328$		0			0
$329$			5.17651i			0.285390i
$330$		0			0
$331$	−3.08622	−	7.45079i	−0.169634	−	0.409532i	0.816085	−	0.577932i	$-0.196140\pi$
$331$	−3.08622	−	7.45079i	−0.169634	−	0.409532i	−0.985719	+	0.168400i	$0.946140\pi$
$332$		0			0
$333$			1.69453i			0.0928599i
$334$		0			0
$335$	−9.25729	−	2.27041i	−0.505780	−	0.124046i
$336$		0			0
$337$	35.7899			1.94960			0.974799	−	0.223085i	$-0.0716127\pi$
$337$	35.7899			1.94960			0.974799	+	0.223085i	$0.0716127\pi$
$338$		0			0
$339$	6.58616	+	15.9004i	0.357711	+	0.863590i
$340$		0			0
$341$	−0.186572	−	0.450424i	−0.0101034	−	0.0243918i
$342$		0			0
$343$	−14.5361	+	6.02103i	−0.784873	+	0.325105i
$344$		0			0
$345$	−8.16064	+	33.2740i	−0.439354	+	1.79141i
$346$		0			0
$347$	−12.2140	+	5.05920i	−0.655681	+	0.271592i	−0.685620	−	0.727960i	$-0.740469\pi$
$347$	−12.2140	+	5.05920i	−0.655681	+	0.271592i	0.0299386	+	0.999552i	$0.490469\pi$
$348$		0			0
$349$	17.5342	+	17.5342i	0.938582	+	0.938582i	0.998220	−	0.0596379i	$-0.0189946\pi$
$349$	17.5342	+	17.5342i	0.938582	+	0.938582i	−0.0596379	+	0.998220i	$0.518995\pi$
$350$		0			0
$351$		−	10.7329i		−	0.572879i
$352$		0			0
$353$	15.5402	+	15.5402i	0.827124	+	0.827124i	0.987118	−	0.159994i	$-0.0511475\pi$
$353$	15.5402	+	15.5402i	0.827124	+	0.827124i	−0.159994	+	0.987118i	$0.551148\pi$
$354$		0			0
$355$	7.46624	−	30.4427i	0.396267	−	1.61573i
$356$		0			0
$357$	3.37653	−	8.15167i	0.178705	−	0.431432i
$358$		0			0
$359$	−11.7961			−0.622575			−0.311288	−	0.950316i	$-0.600760\pi$
$359$	−11.7961			−0.622575			−0.311288	+	0.950316i	$0.600760\pi$
$360$		0			0
$361$	19.3951	+	19.3951i	1.02080	+	1.02080i
$362$		0			0
$363$	18.6895	−	7.74144i	0.980944	−	0.406320i
$364$		0			0
$365$	14.0503	+	10.3135i	0.735429	+	0.539834i
$366$		0			0
$367$	−17.4818			−0.912545			−0.456273	−	0.889840i	$-0.650816\pi$
$367$	−17.4818			−0.912545			−0.456273	+	0.889840i	$0.650816\pi$
$368$		0			0
$369$	2.48638	−	0.694034i	0.129436	−	0.0361300i
$370$		0			0
$371$	−5.04841	−	5.04841i	−0.262101	−	0.262101i
$372$		0			0
$373$	0.999842	+	0.999842i	0.0517699	+	0.0517699i	0.732518	−	0.680748i	$-0.238345\pi$
$373$	0.999842	+	0.999842i	0.0517699	+	0.0517699i	−0.680748	+	0.732518i	$0.738345\pi$
$374$		0			0
$375$	−13.6235	+	15.4853i	−0.703515	+	0.799656i
$376$		0			0
$377$	17.6258			0.907775
$378$		0			0
$379$		−	28.1101i		−	1.44392i	−0.691935	−	0.721959i	$-0.743242\pi$
$379$		−	28.1101i		−	1.44392i	0.691935	−	0.721959i	$-0.256758\pi$
$380$		0			0
$381$	21.1685	−	8.76830i	1.08450	−	0.449213i
$382$		0			0
$383$	1.08277	+	2.61405i	0.0553272	+	0.133572i	0.949126	−	0.314896i	$-0.101970\pi$
$383$	1.08277	+	2.61405i	0.0553272	+	0.133572i	−0.893799	+	0.448468i	$0.851970\pi$
$384$		0			0
$385$	−0.310664	+	0.423226i	−0.0158329	+	0.0215696i
$386$		0			0
$387$	3.60339	+	3.60339i	0.183170	+	0.183170i
$388$		0			0
$389$	−9.41091	+	9.41091i	−0.477152	+	0.477152i	−0.904220	−	0.427068i	$-0.859547\pi$
$389$	−9.41091	+	9.41091i	−0.477152	+	0.477152i	0.427068	+	0.904220i	$0.359547\pi$
$390$		0			0
$391$	28.8926	+	11.9677i	1.46116	+	0.605233i
$392$		0			0
$393$	18.1930	−	7.53580i	0.917716	−	0.380131i
$394$		0			0
$395$	−3.75306	+	15.3026i	−0.188837	+	0.769959i
$396$		0			0
$397$	9.09987	+	3.76929i	0.456709	+	0.189175i	0.599164	−	0.800626i	$-0.295500\pi$
$397$	9.09987	+	3.76929i	0.456709	+	0.189175i	−0.142455	+	0.989801i	$0.545500\pi$
$398$		0			0
$399$	−14.7514	+	6.11021i	−0.738492	+	0.305893i
$400$		0			0
$401$	5.38223	+	5.38223i	0.268776	+	0.268776i	0.828607	−	0.559831i	$-0.189134\pi$
$401$	5.38223	+	5.38223i	0.268776	+	0.268776i	−0.559831	+	0.828607i	$0.689134\pi$
$402$		0			0
$403$	2.26140	−	5.45950i	0.112648	−	0.271957i
$404$		0			0
$405$	−13.2937	+	18.1103i	−0.660567	+	0.899907i
$406$		0			0
$407$	−0.717786	−	0.297317i	−0.0355793	−	0.0147374i
$408$		0			0
$409$	−32.8389			−1.62378			−0.811891	−	0.583810i	$-0.801561\pi$
$409$	−32.8389			−1.62378			−0.811891	+	0.583810i	$0.801561\pi$
$410$		0			0
$411$	−6.92713			−0.341690
$412$		0			0
$413$	−15.7896	−	6.54027i	−0.776956	−	0.321826i
$414$		0			0
$415$	35.8246	−	5.49464i	1.75856	−	0.269721i
$416$		0			0
$417$	−6.88648	+	16.6254i	−0.337232	+	0.814151i
$418$		0			0
$419$	−2.74262	−	2.74262i	−0.133986	−	0.133986i	0.636933	−	0.770919i	$-0.280203\pi$
$419$	−2.74262	−	2.74262i	−0.133986	−	0.133986i	−0.770919	+	0.636933i	$0.780203\pi$
$420$		0			0
$421$	3.02621	−	1.25350i	0.147488	−	0.0610916i	−0.307718	−	0.951478i	$-0.599565\pi$
$421$	3.02621	−	1.25350i	0.147488	−	0.0610916i	0.455207	+	0.890386i	$0.349565\pi$
$422$		0			0
$423$	1.51788	+	0.628728i	0.0738020	+	0.0305698i
$424$		0			0
$425$	12.0865	+	14.4350i	0.586282	+	0.700198i
$426$		0			0
$427$	7.41417	−	3.07105i	0.358797	−	0.148618i
$428$		0			0
$429$	−0.705802	−	0.292353i	−0.0340764	−	0.0141149i
$430$		0			0
$431$	−18.6912	+	18.6912i	−0.900322	+	0.900322i	−0.995464	−	0.0951414i	$-0.969670\pi$
$431$	−18.6912	+	18.6912i	−0.900322	+	0.900322i	0.0951414	+	0.995464i	$0.469670\pi$
$432$		0			0
$433$	−12.1399	−	12.1399i	−0.583408	−	0.583408i	0.352430	−	0.935838i	$-0.385356\pi$
$433$	−12.1399	−	12.1399i	−0.583408	−	0.583408i	−0.935838	+	0.352430i	$0.885356\pi$
$434$		0			0
$435$	−26.1609	−	19.2031i	−1.25432	−	0.920719i
$436$		0			0
$437$	−21.6569	−	52.2844i	−1.03599	−	2.50110i
$438$		0			0
$439$	−21.2684	+	8.80967i	−1.01509	+	0.420462i	−0.827308	−	0.561749i	$-0.810129\pi$
$439$	−21.2684	+	8.80967i	−1.01509	+	0.420462i	−0.187778	+	0.982211i	$0.560129\pi$
$440$		0			0
$441$			2.17158i			0.103409i
$442$		0			0
$443$	16.5788			0.787683			0.393841	−	0.919178i	$-0.371146\pi$
$443$	16.5788			0.787683			0.393841	+	0.919178i	$0.371146\pi$
$444$		0			0
$445$	−5.14093	−	1.26084i	−0.243703	−	0.0597697i
$446$		0			0
$447$	2.43571	+	2.43571i	0.115205	+	0.115205i
$448$		0			0
$449$	9.03090	+	9.03090i	0.426194	+	0.426194i	0.887330	−	0.461135i	$-0.152558\pi$
$449$	9.03090	+	9.03090i	0.426194	+	0.426194i	−0.461135	+	0.887330i	$0.652558\pi$
$450$		0			0
$451$	−0.142266	+	1.17498i	−0.00669905	+	0.0553275i
$452$		0			0
$453$	−16.0860			−0.755788
$454$		0			0
$455$	−6.28995	+	0.964729i	−0.294877	+	0.0452272i
$456$		0			0
$457$	−21.8289	+	9.04182i	−1.02111	+	0.422958i	−0.829497	−	0.558512i	$-0.811373\pi$
$457$	−21.8289	+	9.04182i	−1.02111	+	0.422958i	−0.191615	+	0.981470i	$0.561373\pi$
$458$		0			0
$459$	12.7550	+	12.7550i	0.595353	+	0.595353i
$460$		0			0
$461$	13.5597			0.631540			0.315770	−	0.948836i	$-0.397737\pi$
$461$	13.5597			0.631540			0.315770	+	0.948836i	$0.397737\pi$
$462$		0			0
$463$	7.63673	−	18.4367i	0.354909	−	0.856826i	−0.641091	−	0.767465i	$-0.721518\pi$
$463$	7.63673	−	18.4367i	0.354909	−	0.856826i	0.995999	−	0.0893603i	$-0.0284823\pi$
$464$		0			0
$465$	−9.30451	+	5.63942i	−0.431486	+	0.261522i
$466$		0			0
$467$	25.9559	+	25.9559i	1.20109	+	1.20109i	0.973834	+	0.227260i	$0.0729768\pi$
$467$	25.9559	+	25.9559i	1.20109	+	1.20109i	0.227260	+	0.973834i	$0.427023\pi$
$468$		0			0
$469$			5.41458i			0.250022i
$470$		0			0
$471$	−14.6470	−	14.6470i	−0.674900	−	0.674900i
$472$		0			0
$473$	−2.15859	+	0.894119i	−0.0992522	+	0.0411116i
$474$		0			0
$475$	3.00504	−	33.9366i	0.137881	−	1.55712i
$476$		0			0
$477$	−2.09349	+	0.867153i	−0.0958544	+	0.0397042i
$478$		0			0
$479$	6.43583	+	15.5375i	0.294060	+	0.709925i	0.999999	+	0.00165118i	$0.000525589\pi$
$479$	6.43583	+	15.5375i	0.294060	+	0.709925i	−0.705938	+	0.708273i	$0.749474\pi$
$480$		0			0
$481$	−3.60372	−	8.70015i	−0.164315	−	0.396693i
$482$		0			0
$483$	19.4619			0.885548
$484$		0			0
$485$	−6.98090	+	28.4637i	−0.316986	+	1.29247i
$486$		0			0
$487$			40.5470i			1.83736i	0.395004	+	0.918679i	$0.370743\pi$
$487$			40.5470i			1.83736i	−0.395004	+	0.918679i	$0.629257\pi$
$488$		0			0
$489$	−11.6896	−	28.2211i	−0.528621	−	1.27620i
$490$		0			0
$491$		−	10.4047i		−	0.469557i	−0.972049	−	0.234779i	$-0.924563\pi$
$491$		−	10.4047i		−	0.469557i	0.972049	−	0.234779i	$-0.0754365\pi$
$492$		0			0
$493$	−20.9466	+	20.9466i	−0.943387	+	0.943387i
$494$		0			0
$495$	0.0863678	+	0.142499i	0.00388194	+	0.00640484i
$496$		0			0
$497$	−17.8059			−0.798703
$498$		0			0
$499$	−3.91012	+	1.61963i	−0.175041	+	0.0725044i	−0.468483	−	0.883473i	$-0.655199\pi$
$499$	−3.91012	+	1.61963i	−0.175041	+	0.0725044i	0.293442	+	0.955977i	$0.405199\pi$
$500$		0			0
$501$	−5.73038	+	5.73038i	−0.256015	+	0.256015i
$502$		0			0
$503$	−2.98057	+	7.19574i	−0.132897	+	0.320842i	−0.976294	−	0.216449i	$-0.930552\pi$
$503$	−2.98057	+	7.19574i	−0.132897	+	0.320842i	0.843397	+	0.537291i	$0.180552\pi$
$504$		0			0
$505$	25.8079	−	15.6420i	1.14843	−	0.696061i
$506$		0			0
$507$	5.63393	+	13.6015i	0.250212	+	0.604065i
$508$		0			0
$509$	20.5095	+	8.49531i	0.909067	+	0.376548i	0.787699	−	0.616060i	$-0.211272\pi$
$509$	20.5095	+	8.49531i	0.909067	+	0.376548i	0.121368	+	0.992608i	$0.461272\pi$
$510$		0			0
$511$	3.78893	−	9.14729i	0.167613	−	0.404652i
$512$		0			0
$513$		−	32.6423i		−	1.44119i
$514$		0			0
$515$	5.30408	−	7.22588i	0.233726	−	0.318410i
$516$		0			0
$517$	−0.532644	+	0.532644i	−0.0234257	+	0.0234257i
$518$		0			0
$519$	1.22378	−	2.95446i	0.0537179	−	0.129686i
$520$		0			0
$521$	−7.26682	−	17.5437i	−0.318365	−	0.768602i	−0.999341	−	0.0362959i	$-0.988444\pi$
$521$	−7.26682	−	17.5437i	−0.318365	−	0.768602i	0.680976	−	0.732306i	$-0.261556\pi$
$522$		0			0
$523$	15.1191	+	15.1191i	0.661111	+	0.661111i	0.955642	−	0.294531i	$-0.0951635\pi$
$523$	15.1191	+	15.1191i	0.661111	+	0.661111i	−0.294531	+	0.955642i	$0.595163\pi$
$524$		0			0
$525$	10.3868	+	5.42094i	0.453319	+	0.236589i
$526$		0			0
$527$	3.80064	+	9.17555i	0.165558	+	0.399693i
$528$		0			0
$529$			45.9804i			1.99915i
$530$		0			0
$531$	−3.83555	+	3.83555i	−0.166449	+	0.166449i
$532$		0			0
$533$	−11.2897	+	8.85106i	−0.489011	+	0.383382i
$534$		0			0
$535$	−0.777546	+	0.119257i	−0.0336163	+	0.00515594i
$536$		0			0
$537$	−7.52288	+	7.52288i	−0.324636	+	0.324636i
$538$		0			0
$539$	−0.919859	−	0.381018i	−0.0396211	−	0.0164116i
$540$		0			0
$541$	−0.855317	+	0.855317i	−0.0367729	+	0.0367729i	−0.725254	−	0.688481i	$-0.758278\pi$
$541$	−0.855317	+	0.855317i	−0.0367729	+	0.0367729i	0.688481	+	0.725254i	$0.258278\pi$
$542$		0			0
$543$	5.80952	−	5.80952i	0.249310	−	0.249310i
$544$		0			0
$545$	−16.6440	+	10.0878i	−0.712949	+	0.432115i
$546$		0			0
$547$	10.5837	−	4.38392i	0.452528	−	0.187443i	−0.144766	−	0.989466i	$-0.546243\pi$
$547$	10.5837	−	4.38392i	0.452528	−	0.187443i	0.597293	+	0.802023i	$0.296243\pi$
$548$		0			0
$549$		−	2.54702i		−	0.108704i
$550$		0			0
$551$	53.6060			2.28369
$552$		0			0
$553$	8.95050			0.380614
$554$		0			0
$555$	−4.12994	+	16.8393i	−0.175306	+	0.714788i
$556$		0			0
$557$	−2.54906	−	6.15398i	−0.108007	−	0.260753i	0.860630	−	0.509230i	$-0.170070\pi$
$557$	−2.54906	−	6.15398i	−0.108007	−	0.260753i	−0.968638	+	0.248478i	$0.920070\pi$
$558$		0			0
$559$	−26.1639	−	10.8374i	−1.10661	−	0.458375i
$560$		0			0
$561$	1.18621	−	0.491345i	0.0500819	−	0.0207446i
$562$		0			0
$563$	3.34738	+	1.38653i	0.141075	+	0.0584353i	0.452104	−	0.891965i	$-0.350674\pi$
$563$	3.34738	+	1.38653i	0.141075	+	0.0584353i	−0.311029	+	0.950400i	$0.600674\pi$
$564$		0			0
$565$	3.16261	+	20.6200i	0.133052	+	0.867488i
$566$		0			0
$567$	11.7905	+	4.88377i	0.495153	+	0.205099i
$568$		0			0
$569$	24.5865	−	24.5865i	1.03072	−	1.03072i	0.0312088	−	0.999513i	$-0.490064\pi$
$569$	24.5865	−	24.5865i	1.03072	−	1.03072i	0.999513	−	0.0312088i	$-0.00993568\pi$
$570$		0			0
$571$	7.36973	−	3.05264i	0.308413	−	0.127749i	−0.223108	−	0.974794i	$-0.571620\pi$
$571$	7.36973	−	3.05264i	0.308413	−	0.127749i	0.531522	+	0.847045i	$0.321620\pi$
$572$		0			0
$573$	24.9021	+	24.9021i	1.04030	+	1.04030i
$574$		0			0
$575$	−19.2139	+	36.8149i	−0.801274	+	1.53529i
$576$		0			0
$577$	4.51165	−	10.8921i	0.187822	−	0.453443i	−0.801718	−	0.597703i	$-0.796080\pi$
$577$	4.51165	−	10.8921i	0.187822	−	0.453443i	0.989540	+	0.144260i	$0.0460801\pi$
$578$		0			0
$579$	2.00617	+	2.00617i	0.0833737	+	0.0833737i
$580$		0			0
$581$	−7.87892	−	19.0214i	−0.326873	−	0.789141i
$582$		0			0
$583$		−	1.03893i		−	0.0430280i
$584$		0			0
$585$	−0.481081	+	1.96155i	−0.0198903	+	0.0811000i
$586$		0			0
$587$	8.19090	−	19.7746i	0.338074	−	0.816184i	−0.659826	−	0.751418i	$-0.729370\pi$
$587$	8.19090	−	19.7746i	0.338074	−	0.816184i	0.997901	−	0.0647656i	$-0.0206300\pi$
$588$		0			0
$589$	6.87768	−	16.6042i	0.283390	−	0.684163i
$590$		0			0
$591$	5.38890	−	13.0100i	0.221670	−	0.535158i
$592$		0			0
$593$	−15.7223	−	37.9570i	−0.645638	−	1.55871i	−0.818965	−	0.573844i	$-0.805452\pi$
$593$	−15.7223	−	37.9570i	−0.645638	−	1.55871i	0.173327	−	0.984864i	$-0.444548\pi$
$594$		0			0
$595$	6.32852	−	8.62150i	0.259444	−	0.353447i
$596$		0			0
$597$	19.3115	−	19.3115i	0.790369	−	0.790369i
$598$		0			0
$599$	−13.9998			−0.572018			−0.286009	−	0.958227i	$-0.592329\pi$
$599$	−13.9998			−0.572018			−0.286009	+	0.958227i	$0.592329\pi$
$600$		0			0
$601$	−0.873103	−	0.361651i	−0.0356146	−	0.0147520i	0.364805	−	0.931084i	$-0.381136\pi$
$601$	−0.873103	−	0.361651i	−0.0356146	−	0.0147520i	−0.400420	+	0.916332i	$0.631136\pi$
$602$		0			0
$603$	1.58769	+	0.657643i	0.0646558	+	0.0267813i
$604$		0			0
$605$	24.2369	−	3.71737i	0.985371	−	0.151133i
$606$		0			0
$607$		−	22.3580i		−	0.907482i	−0.891134	−	0.453741i	$-0.850089\pi$
$607$		−	22.3580i		−	0.907482i	0.891134	−	0.453741i	$-0.149911\pi$
$608$		0			0
$609$	−7.05476	+	17.0317i	−0.285873	+	0.690159i
$610$		0			0
$611$	−9.13027			−0.369371
$612$		0			0
$613$			19.7712i			0.798552i	0.916831	+	0.399276i	$0.130739\pi$
$613$			19.7712i			0.798552i	−0.916831	+	0.399276i	$0.869261\pi$
$614$		0			0
$615$	26.3997	−	0.837068i	1.06454	−	0.0337538i
$616$		0			0
$617$		−	47.1754i		−	1.89921i	−0.313451	−	0.949604i	$-0.601485\pi$
$617$		−	47.1754i		−	1.89921i	0.313451	−	0.949604i	$-0.398515\pi$
$618$		0			0
$619$	−33.5171			−1.34716			−0.673582	−	0.739112i	$-0.735245\pi$
$619$	−33.5171			−1.34716			−0.673582	+	0.739112i	$0.735245\pi$
$620$		0			0
$621$	−15.2261	+	36.7591i	−0.611004	+	1.47509i
$622$		0			0
$623$			3.00692i			0.120470i
$624$		0			0
$625$	−20.5089	+	14.2963i	−0.820357	+	0.571852i
$626$		0			0
$627$	−2.14658	−	0.889144i	−0.0857263	−	0.0355090i
$628$		0			0
$629$	14.6220	+	6.05662i	0.583016	+	0.241493i
$630$		0			0
$631$	15.1068			0.601390			0.300695	−	0.953720i	$-0.402781\pi$
$631$	15.1068			0.601390			0.300695	+	0.953720i	$0.402781\pi$
$632$		0			0
$633$	−15.1506	+	15.1506i	−0.602181	+	0.602181i
$634$		0			0
$635$	27.4518	−	4.21046i	1.08939	−	0.167087i
$636$		0			0
$637$	−4.61824	−	11.1494i	−0.182982	−	0.441756i
$638$		0			0
$639$	−2.16266	+	5.22113i	−0.0855537	+	0.206545i
$640$		0			0
$641$	−6.39457	+	15.4379i	−0.252570	+	0.609759i	−0.998410	−	0.0563664i	$-0.982048\pi$
$641$	−6.39457	+	15.4379i	−0.252570	+	0.609759i	0.745840	+	0.666126i	$0.232048\pi$
$642$		0			0
$643$	5.29933	−	12.7937i	0.208985	−	0.504535i	−0.784279	−	0.620409i	$-0.786967\pi$
$643$	5.29933	−	12.7937i	0.208985	−	0.504535i	0.993264	+	0.115874i	$0.0369668\pi$
$644$		0			0
$645$	27.0262	+	44.5906i	1.06415	+	1.75575i
$646$		0			0
$647$			2.81591i			0.110705i	0.998467	+	0.0553525i	$0.0176283\pi$
$647$			2.81591i			0.110705i	−0.998467	+	0.0553525i	$0.982372\pi$
$648$		0			0
$649$	−0.951725	−	2.29767i	−0.0373585	−	0.0901913i
$650$		0			0
$651$	4.37035	+	4.37035i	0.171287	+	0.171287i
$652$		0			0
$653$	3.25217	−	7.85143i	0.127267	−	0.307250i	−0.847384	−	0.530981i	$-0.821824\pi$
$653$	3.25217	−	7.85143i	0.127267	−	0.307250i	0.974651	+	0.223731i	$0.0718236\pi$
$654$		0			0
$655$	23.5931	−	3.61862i	0.921858	−	0.141391i
$656$		0			0
$657$	−2.22202	−	2.22202i	−0.0866893	−	0.0866893i
$658$		0			0
$659$	−3.29175	+	1.36349i	−0.128228	+	0.0531140i	−0.445875	−	0.895095i	$-0.647107\pi$
$659$	−3.29175	+	1.36349i	−0.128228	+	0.0531140i	0.317647	+	0.948209i	$0.397107\pi$
$660$		0			0
$661$	20.1584	−	20.1584i	0.784072	−	0.784072i	−0.196444	−	0.980515i	$-0.562939\pi$
$661$	20.1584	−	20.1584i	0.784072	−	0.784072i	0.980515	+	0.196444i	$0.0629392\pi$
$662$		0			0
$663$	14.3778	+	5.95550i	0.558389	+	0.231292i
$664$		0			0
$665$	−19.1299	+	2.93407i	−0.741825	+	0.113778i
$666$		0			0
$667$	−60.3667	−	25.0047i	−2.33741	−	0.968186i
$668$		0			0
$669$	8.32743	−	3.44933i	0.321957	−	0.133359i
$670$		0			0
$671$	1.07889	+	0.446892i	0.0416502	+	0.0172521i
$672$		0			0
$673$	0.685647	+	1.65530i	0.0264298	+	0.0638071i	0.936543	−	0.350552i	$-0.114006\pi$
$673$	0.685647	+	1.65530i	0.0264298	+	0.0638071i	−0.910114	+	0.414359i	$0.864006\pi$
$674$		0			0
$675$	−18.3651	+	15.3773i	−0.706874	+	0.591872i
$676$		0			0
$677$	7.21198			0.277179			0.138589	−	0.990350i	$-0.455743\pi$
$677$	7.21198			0.277179			0.138589	+	0.990350i	$0.455743\pi$
$678$		0			0
$679$	16.6484			0.638907
$680$		0			0
$681$			14.2910i			0.547633i
$682$		0			0
$683$	−5.67183	+	2.34935i	−0.217027	+	0.0898953i	−0.488548	−	0.872537i	$-0.662473\pi$
$683$	−5.67183	+	2.34935i	−0.217027	+	0.0898953i	0.271521	+	0.962432i	$0.412473\pi$
$684$		0			0
$685$	−8.15481	−	2.00002i	−0.311579	−	0.0764167i
$686$		0			0
$687$	−30.2190	+	30.2190i	−1.15293	+	1.15293i
$688$		0			0
$689$	8.90435	−	8.90435i	0.339229	−	0.339229i
$690$		0			0
$691$	−32.5129	−	13.4673i	−1.23685	−	0.512319i	−0.334119	−	0.942531i	$-0.608439\pi$
$691$	−32.5129	−	13.4673i	−1.23685	−	0.512319i	−0.902728	+	0.430212i	$0.858439\pi$
$692$		0			0
$693$	0.0669319	−	0.0669319i	0.00254253	−	0.00254253i
$694$		0			0
$695$	−12.9071	+	17.5836i	−0.489594	+	0.666985i
$696$		0			0
$697$	2.89810	−	23.9354i	0.109773	−	0.906617i
$698$		0			0
$699$	38.0337	−	38.0337i	1.43857	−	1.43857i
$700$		0			0
$701$			17.9583i			0.678274i	0.940737	+	0.339137i	$0.110135\pi$
$701$			17.9583i			0.678274i	−0.940737	+	0.339137i	$0.889865\pi$
$702$		0			0
$703$	−10.9601	−	26.4601i	−0.413369	−	0.997962i
$704$		0			0
$705$	13.5515	+	9.94733i	0.510379	+	0.374638i
$706$		0			0
$707$	−12.1220	−	12.1220i	−0.455895	−	0.455895i
$708$		0			0
$709$	5.72227	+	13.8148i	0.214904	+	0.518825i	0.994164	−	0.107876i	$-0.0344048\pi$
$709$	5.72227	+	13.8148i	0.214904	+	0.518825i	−0.779260	+	0.626701i	$0.784405\pi$
$710$		0			0
$711$	1.08711	−	2.62451i	0.0407698	−	0.0984269i
$712$		0			0
$713$	−15.4902	+	15.4902i	−0.580111	+	0.580111i
$714$		0			0
$715$	−0.746481	−	0.547947i	−0.0279168	−	0.0204920i
$716$		0			0
$717$		−	35.0443i		−	1.30875i
$718$		0			0
$719$	−19.4680	+	46.9998i	−0.726032	+	1.75280i	−0.0706478	+	0.997501i	$0.522507\pi$
$719$	−19.4680	+	46.9998i	−0.726032	+	1.75280i	−0.655384	+	0.755296i	$0.727493\pi$
$720$		0			0
$721$	−4.70431	−	1.94859i	−0.175198	−	0.0725693i
$722$		0			0
$723$	−9.18825	−	22.1824i	−0.341715	−	0.824973i
$724$		0			0
$725$	−25.2529	−	30.1597i	−0.937871	−	1.12010i
$726$		0			0
$727$	0.682535	−	1.64778i	0.0253138	−	0.0611129i	−0.910717	−	0.413031i	$-0.864470\pi$
$727$	0.682535	−	1.64778i	0.0253138	−	0.0611129i	0.936031	+	0.351918i	$0.114470\pi$
$728$		0			0
$729$	−15.8830	+	15.8830i	−0.588260	+	0.588260i
$730$		0			0
$731$	43.9726	−	18.2140i	1.62638	−	0.673670i
$732$		0			0
$733$	18.9691			0.700640			0.350320	−	0.936630i	$-0.386073\pi$
$733$	18.9691			0.700640			0.350320	+	0.936630i	$0.386073\pi$
$734$		0			0
$735$	−5.29261	+	21.5799i	−0.195221	+	0.795988i
$736$		0			0
$737$	−0.557141	+	0.557141i	−0.0205226	+	0.0205226i
$738$		0			0
$739$		−	24.3436i		−	0.895495i	−0.894160	−	0.447748i	$-0.852226\pi$
$739$		−	24.3436i		−	0.895495i	0.894160	−	0.447748i	$-0.147774\pi$
$740$		0			0
$741$	−10.7771	−	26.0183i	−0.395908	−	0.955807i
$742$		0			0
$743$		−	27.3841i		−	1.00462i	−0.864686	−	0.502312i	$-0.832483\pi$
$743$		−	27.3841i		−	1.00462i	0.864686	−	0.502312i	$-0.167517\pi$
$744$		0			0
$745$	2.16414	+	3.57063i	0.0792881	+	0.130818i
$746$		0			0
$747$	−6.53451			−0.239085
$748$		0			0
$749$	0.171006	+	0.412846i	0.00624844	+	0.0150851i
$750$		0			0
$751$	−17.8950	−	43.2023i	−0.652997	−	1.57647i	−0.808407	−	0.588624i	$-0.799670\pi$
$751$	−17.8950	−	43.2023i	−0.652997	−	1.57647i	0.155410	−	0.987850i	$-0.450330\pi$
$752$		0			0
$753$	20.5043	−	8.49314i	0.747217	−	0.309507i
$754$		0			0
$755$	−18.9369	−	4.64440i	−0.689185	−	0.169027i
$756$		0			0
$757$	−6.16427	+	2.55332i	−0.224044	+	0.0928021i	−0.491882	−	0.870662i	$-0.663691\pi$
$757$	−6.16427	+	2.55332i	−0.224044	+	0.0928021i	0.267838	+	0.963464i	$0.413691\pi$
$758$		0			0
$759$	2.00256	+	2.00256i	0.0726884	+	0.0726884i
$760$		0			0
$761$			17.0252i			0.617164i	0.951198	+	0.308582i	$0.0998544\pi$
$761$			17.0252i			0.617164i	−0.951198	+	0.308582i	$0.900146\pi$
$762$		0			0
$763$	7.81770	+	7.81770i	0.283020	+	0.283020i
$764$		0			0
$765$	−1.75939	−	2.90283i	−0.0636110	−	0.104952i
$766$		0			0
$767$	11.5357	−	27.8496i	0.416529	−	1.00559i
$768$		0			0
$769$	−25.8774			−0.933161			−0.466581	−	0.884479i	$-0.654514\pi$
$769$	−25.8774			−0.933161			−0.466581	+	0.884479i	$0.654514\pi$
$770$		0			0
$771$	−31.2319	−	31.2319i	−1.12479	−	1.12479i
$772$		0			0
$773$	7.70394	−	3.19108i	0.277091	−	0.114775i	−0.239810	−	0.970820i	$-0.577085\pi$
$773$	7.70394	−	3.19108i	0.277091	−	0.114775i	0.516902	+	0.856045i	$0.327085\pi$
$774$		0			0
$775$	−12.5818	+	3.95247i	−0.451950	+	0.141977i
$776$		0			0
$777$	9.84929			0.353341
$778$		0			0
$779$	−34.3358	+	26.9191i	−1.23021	+	0.964476i
$780$		0			0
$781$	−1.83216	−	1.83216i	−0.0655599	−	0.0655599i
$782$		0			0
$783$	−26.6497	−	26.6497i	−0.952381	−	0.952381i
$784$		0			0
$785$	−13.0140	−	21.4718i	−0.464489	−	0.766362i
$786$		0			0
$787$	1.93147			0.0688495			0.0344248	−	0.999407i	$-0.489040\pi$
$787$	1.93147			0.0688495			0.0344248	+	0.999407i	$0.489040\pi$
$788$		0			0
$789$		−	32.7794i		−	1.16698i
$790$		0			0
$791$	10.9484	−	4.53496i	0.389279	−	0.161245i
$792$		0			0
$793$	5.41669	+	13.0770i	0.192352	+	0.464379i
$794$		0			0
$795$	−22.9173	+	3.51498i	−0.812795	+	0.124663i
$796$		0			0
$797$	14.3187	+	14.3187i	0.507194	+	0.507194i	0.913664	−	0.406470i	$-0.133240\pi$
$797$	14.3187	+	14.3187i	0.507194	+	0.507194i	−0.406470	+	0.913664i	$0.633240\pi$
$798$		0			0
$799$	10.8505	−	10.8505i	0.383862	−	0.383862i
$800$		0			0
$801$	0.881706	+	0.365215i	0.0311535	+	0.0129042i
$802$		0			0
$803$	1.33109	−	0.551357i	0.0469732	−	0.0194570i
$804$		0			0
$805$	22.9111	+	5.61909i	0.807510	+	0.198047i
$806$		0			0
$807$	−49.6777	−	20.5772i	−1.74874	−	0.724351i
$808$		0			0
$809$	−34.8928	+	14.4531i	−1.22677	+	0.508143i	−0.899555	−	0.436808i	$-0.856109\pi$
$809$	−34.8928	+	14.4531i	−1.22677	+	0.508143i	−0.327211	+	0.944951i	$0.606109\pi$
$810$		0			0
$811$	−29.3478	−	29.3478i	−1.03054	−	1.03054i	−0.999519	−	0.0310211i	$-0.990124\pi$
$811$	−29.3478	−	29.3478i	−1.03054	−	1.03054i	−0.0310211	−	0.999519i	$-0.509876\pi$
$812$		0			0
$813$	−4.26090	+	10.2867i	−0.149436	+	0.360771i
$814$		0			0
$815$	−5.61323	−	36.5978i	−0.196623	−	1.28196i
$816$		0			0
$817$	−79.5733	−	32.9603i	−2.78392	−	1.15314i
$818$		0			0
$819$	1.14731			0.0400901
$820$		0			0
$821$	26.5804			0.927661			0.463830	−	0.885924i	$-0.346475\pi$
$821$	26.5804			0.927661			0.463830	+	0.885924i	$0.346475\pi$
$822$		0			0
$823$	9.04496	+	3.74654i	0.315287	+	0.130596i	0.534715	−	0.845032i	$-0.320419\pi$
$823$	9.04496	+	3.74654i	0.315287	+	0.130596i	−0.219428	+	0.975629i	$0.570419\pi$
$824$		0			0
$825$	0.510974	+	1.62657i	0.0177898	+	0.0566298i
$826$		0			0
$827$	−2.69337	+	6.50238i	−0.0936577	+	0.226110i	−0.963765	−	0.266753i	$-0.914049\pi$
$827$	−2.69337	+	6.50238i	−0.0936577	+	0.226110i	0.870107	+	0.492862i	$0.164049\pi$
$828$		0			0
$829$	1.97169	+	1.97169i	0.0684797	+	0.0684797i	0.740517	−	0.672037i	$-0.234581\pi$
$829$	1.97169	+	1.97169i	0.0684797	+	0.0684797i	−0.672037	+	0.740517i	$0.734581\pi$
$830$		0			0
$831$	46.9136	−	19.4323i	1.62742	−	0.674098i
$832$		0			0
$833$	18.7384	+	7.76169i	0.649246	+	0.268927i
$834$		0			0
$835$	−8.40046	+	5.09148i	−0.290710	+	0.176198i
$836$		0			0
$837$	−11.6738	+	4.83543i	−0.403504	+	0.167137i
$838$		0			0
$839$	−38.4178	−	15.9132i	−1.32633	−	0.549384i	−0.396724	−	0.917938i	$-0.629853\pi$
$839$	−38.4178	−	15.9132i	−1.32633	−	0.549384i	−0.929606	+	0.368554i	$0.879853\pi$
$840$		0			0
$841$	23.2586	−	23.2586i	0.802021	−	0.802021i
$842$		0			0
$843$	20.6135	+	20.6135i	0.709968	+	0.709968i
$844$		0			0
$845$	2.70536	+	17.6387i	0.0930673	+	0.606791i
$846$		0			0
$847$	−5.33044	−	12.8688i	−0.183156	−	0.442178i
$848$		0			0
$849$	40.0051	−	16.5707i	1.37297	−	0.568704i
$850$		0			0
$851$			34.9096i			1.19669i
$852$		0			0
$853$	−9.26366			−0.317182			−0.158591	−	0.987344i	$-0.550695\pi$
$853$	−9.26366			−0.317182			−0.158591	+	0.987344i	$0.550695\pi$
$854$		0			0
$855$	−1.46313	+	5.96573i	−0.0500380	+	0.204024i
$856$		0			0
$857$	−0.295199	−	0.295199i	−0.0100838	−	0.0100838i	0.702047	−	0.712131i	$-0.252270\pi$
$857$	−0.295199	−	0.295199i	−0.0100838	−	0.0100838i	−0.712131	+	0.702047i	$0.752270\pi$
$858$		0			0
$859$	−16.3411	−	16.3411i	−0.557551	−	0.557551i	0.371058	−	0.928610i	$-0.378995\pi$
$859$	−16.3411	−	16.3411i	−0.557551	−	0.557551i	−0.928610	+	0.371058i	$0.878995\pi$
$860$		0			0
$861$	−4.03399	−	14.4518i	−0.137478	−	0.492516i
$862$		0			0
$863$	19.5247			0.664629			0.332315	−	0.943169i	$-0.392170\pi$
$863$	19.5247			0.664629			0.332315	+	0.943169i	$0.392170\pi$
$864$		0			0
$865$	2.29368	−	3.12474i	0.0779876	−	0.106244i
$866$		0			0
$867$	4.80952	−	1.99217i	0.163340	−	0.0676576i
$868$		0			0
$869$	0.920975	+	0.920975i	0.0312419	+	0.0312419i
$870$		0			0
$871$	−9.55019			−0.323596
$872$		0			0
$873$	2.02208	−	4.88173i	0.0684370	−	0.165222i
$874$		0			0
$875$	10.6625	+	9.38060i	0.360459	+	0.317122i
$876$		0			0
$877$	15.4571	+	15.4571i	0.521950	+	0.521950i	0.918160	−	0.396210i	$-0.129675\pi$
$877$	15.4571	+	15.4571i	0.521950	+	0.521950i	−0.396210	+	0.918160i	$0.629675\pi$
$878$		0			0
$879$			33.0064i			1.11328i
$880$		0			0
$881$	−29.7918	−	29.7918i	−1.00371	−	1.00371i	−0.999993	−	0.00371845i	$-0.998816\pi$
$881$	−29.7918	−	29.7918i	−1.00371	−	1.00371i	−0.00371845	−	0.999993i	$-0.501184\pi$
$882$		0			0
$883$	7.26055	−	3.00742i	0.244337	−	0.101208i	−0.257154	−	0.966370i	$-0.582785\pi$
$883$	7.26055	−	3.00742i	0.244337	−	0.101208i	0.501491	+	0.865163i	$0.332785\pi$
$884$		0			0
$885$	−47.4635	+	28.7674i	−1.59547	+	0.967005i
$886$		0			0
$887$	−39.5250	+	16.3718i	−1.32712	+	0.549711i	−0.929832	−	0.367983i	$-0.880048\pi$
$887$	−39.5250	+	16.3718i	−1.32712	+	0.549711i	−0.397287	+	0.917694i	$0.630048\pi$
$888$		0			0
$889$	−6.03749	−	14.5758i	−0.202491	−	0.488857i
$890$		0			0
$891$	0.710674	+	1.71572i	0.0238085	+	0.0574788i
$892$		0			0
$893$	−27.7683			−0.929229
$894$		0			0
$895$	−11.0282	+	6.68412i	−0.368631	+	0.223426i
$896$		0			0
$897$			34.3267i			1.14614i
$898$		0			0
$899$	−7.94085	−	19.1709i	−0.264842	−	0.639386i
$900$		0			0
$901$			21.1639i			0.705073i
$902$		0			0
$903$	20.9443	−	20.9443i	0.696982	−	0.696982i
$904$		0			0
$905$	8.51647	−	5.16179i	0.283097	−	0.171584i
$906$		0			0
$907$	19.0737			0.633333			0.316666	−	0.948537i	$-0.397436\pi$
$907$	19.0737			0.633333			0.316666	+	0.948537i	$0.397436\pi$
$908$		0			0
$909$	−5.02679	+	2.08216i	−0.166728	+	0.0690610i
$910$		0			0
$911$	−5.94016	+	5.94016i	−0.196806	+	0.196806i	−0.798629	−	0.601823i	$-0.794441\pi$
$911$	−5.94016	+	5.94016i	−0.196806	+	0.196806i	0.601823	+	0.798629i	$0.294441\pi$
$912$		0			0
$913$	1.14652	−	2.76795i	0.0379444	−	0.0916058i
$914$		0			0
$915$	6.20764	−	25.3108i	0.205218	−	0.836751i
$916$		0			0
$917$	−5.18884	−	12.5270i	−0.171351	−	0.413677i
$918$		0			0
$919$	4.83312	+	2.00194i	0.159430	+	0.0660380i	0.460971	−	0.887415i	$-0.347501\pi$
$919$	4.83312	+	2.00194i	0.159430	+	0.0660380i	−0.301541	+	0.953453i	$0.597501\pi$
$920$		0			0
$921$	−9.13861	+	22.0625i	−0.301127	+	0.726986i
$922$		0			0
$923$		−	31.4058i		−	1.03374i
$924$		0			0
$925$	−9.72376	+	18.6313i	−0.319715	+	0.612593i
$926$		0			0
$927$	−1.14275	+	1.14275i	−0.0375329	+	0.0375329i
$928$		0			0
$929$	17.4115	−	42.0350i	0.571252	−	1.37912i	−0.329238	−	0.944247i	$-0.606792\pi$
$929$	17.4115	−	42.0350i	0.571252	−	1.37912i	0.900490	−	0.434877i	$-0.143208\pi$
$930$		0			0
$931$	−14.0456	−	33.9092i	−0.460328	−	1.11133i
$932$		0			0
$933$	−31.7620	−	31.7620i	−1.03984	−	1.03984i
$934$		0			0
$935$	1.53830	−	0.235939i	0.0503079	−	0.00771604i
$936$		0			0
$937$	−15.0171	−	36.2545i	−0.490588	−	1.18438i	−0.954422	−	0.298461i	$-0.903527\pi$
$937$	−15.0171	−	36.2545i	−0.490588	−	1.18438i	0.463834	−	0.885922i	$-0.346473\pi$
$938$		0			0
$939$			9.87152i			0.322145i
$940$		0			0
$941$	−11.4531	+	11.4531i	−0.373360	+	0.373360i	−0.868700	−	0.495339i	$-0.835044\pi$
$941$	−11.4531	+	11.4531i	−0.373360	+	0.373360i	0.495339	+	0.868700i	$0.335044\pi$
$942$		0			0
$943$	51.2227	−	14.2980i	1.66804	−	0.465607i
$944$		0			0
$945$	10.9689	+	8.05157i	0.356817	+	0.261918i
$946$		0			0
$947$	−6.43203	+	6.43203i	−0.209013	+	0.209013i	−0.803848	−	0.594835i	$-0.797217\pi$
$947$	−6.43203	+	6.43203i	−0.209013	+	0.209013i	0.594835	+	0.803848i	$0.297217\pi$
$948$		0			0
$949$	16.1339	+	6.68289i	0.523729	+	0.216936i
$950$		0			0
$951$	24.9341	−	24.9341i	0.808543	−	0.808543i
$952$		0			0
$953$	12.1178	−	12.1178i	0.392535	−	0.392535i	−0.483055	−	0.875590i	$-0.660473\pi$
$953$	12.1178	−	12.1178i	0.392535	−	0.392535i	0.875590	+	0.483055i	$0.160473\pi$
$954$		0			0
$955$	22.1256	+	36.5052i	0.715969	+	1.18128i
$956$		0			0
$957$	−2.47841	+	1.02659i	−0.0801156	+	0.0331850i
$958$		0			0
$959$			4.76974i			0.154023i
$960$		0			0
$961$	24.0431			0.775584
$962$		0			0
$963$	0.141827			0.00457031
$964$		0			0
$965$	1.78250	+	2.94095i	0.0573806	+	0.0946725i
$966$		0			0
$967$	−1.96806	−	4.75133i	−0.0632887	−	0.152792i	0.889071	−	0.457769i	$-0.151351\pi$
$967$	−1.96806	−	4.75133i	−0.0632887	−	0.152792i	−0.952360	+	0.304977i	$0.901351\pi$
$968$		0			0
$969$	43.7279	+	18.1127i	1.40474	+	0.581863i
$970$		0			0
$971$	−7.92783	+	3.28382i	−0.254416	+	0.105383i	−0.506247	−	0.862389i	$-0.668967\pi$
$971$	−7.92783	+	3.28382i	−0.254416	+	0.105383i	0.251830	+	0.967771i	$0.418967\pi$
$972$		0			0
$973$	11.4476	+	4.74175i	0.366993	+	0.152013i
$974$		0			0
$975$	−9.56141	+	18.3202i	−0.306210	+	0.586717i
$976$		0			0
$977$	40.2670	+	16.6791i	1.28826	+	0.533613i	0.918465	−	0.395502i	$-0.129429\pi$
$977$	40.2670	+	16.6791i	1.28826	+	0.533613i	0.369791	+	0.929115i	$0.379429\pi$
$978$		0			0
$979$	−0.309402	+	0.309402i	−0.00988853	+	0.00988853i
$980$		0			0
$981$	3.24187	−	1.34283i	0.103505	−	0.0428731i
$982$		0			0
$983$	−12.1599	−	12.1599i	−0.387839	−	0.387839i	0.486077	−	0.873916i	$-0.338427\pi$
$983$	−12.1599	−	12.1599i	−0.387839	−	0.387839i	−0.873916	+	0.486077i	$0.838427\pi$
$984$		0			0
$985$	10.1002	−	13.7598i	0.321820	−	0.438423i
$986$		0			0
$987$	3.65441	−	8.82252i	0.116321	−	0.280824i
$988$		0			0
$989$	74.2344	+	74.2344i	2.36052	+	2.36052i
$990$		0			0
$991$	14.8836	+	35.9322i	0.472793	+	1.14142i	0.962924	+	0.269774i	$0.0869492\pi$
$991$	14.8836	+	35.9322i	0.472793	+	1.14142i	−0.490130	+	0.871649i	$0.663051\pi$
$992$		0			0
$993$			14.8774i			0.472121i
$994$		0			0
$995$	28.3098	−	17.1584i	0.897480	−	0.543959i
$996$		0			0
$997$	−14.7351	+	35.5737i	−0.466665	+	1.12663i	0.498945	+	0.866634i	$0.333721\pi$
$997$	−14.7351	+	35.5737i	−0.466665	+	1.12663i	−0.965610	+	0.259995i	$0.916279\pi$
$998$		0			0
$999$	−7.70564	+	18.6031i	−0.243796	+	0.588575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.y.a.137.6	yes	84
5.3	odd	4		820.2.x.a.793.16	yes	84
41.3	odd	8		820.2.x.a.577.16	✓	84
205.3	even	8	inner	820.2.y.a.413.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.16	✓	84	41.3	odd	8
820.2.x.a.793.16	yes	84	5.3	odd	4
820.2.y.a.137.6	yes	84	1.1	even	1	trivial
820.2.y.a.413.6	yes	84	205.3	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70434 - 0.705960i) q^{3} +(-1.80257 - 1.32316i) q^{5} +(-0.486096 + 1.17354i) q^{7} +(0.285071 + 0.285071i) q^{9} +(-0.170771 + 0.0707355i) q^{11} +(-2.06988 - 0.857371i) q^{13} +(2.13809 + 3.52765i) q^{15} +(3.47876 - 1.44095i) q^{17} +(-6.29520 - 2.60756i) q^{19} +(1.65694 - 1.65694i) q^{21} +(5.87283 + 5.87283i) q^{23} +(1.49851 + 4.77016i) q^{25} +(1.83327 + 4.42591i) q^{27} +(-7.26833 + 3.01064i) q^{29} +2.63759i q^{31} +0.340987 q^{33} +(2.42900 - 1.47220i) q^{35} +(2.97212 + 2.97212i) q^{37} +(2.92250 + 2.92250i) q^{39} +(3.14368 - 5.57828i) q^{41} +12.6403 q^{43} +(-0.136667 - 0.891054i) q^{45} +(3.76504 - 1.55953i) q^{47} +(3.80884 + 3.80884i) q^{49} -6.94623 q^{51} +(-2.15094 + 5.19282i) q^{53} +(0.401420 + 0.0984507i) q^{55} +(8.88832 + 8.88832i) q^{57} +13.4547i q^{59} +(-4.46735 - 4.46735i) q^{61} +(-0.473114 + 0.195970i) q^{63} +(2.59666 + 4.28424i) q^{65} +(3.93820 - 1.63126i) q^{67} +(-5.86331 - 14.1553i) q^{69} +(5.36440 + 12.9508i) q^{71} -7.79462 q^{73} +(0.813575 - 9.18787i) q^{75} -0.234790i q^{77} +(-2.69653 - 6.50999i) q^{79} -10.0469i q^{81} +(-11.4612 + 11.4612i) q^{83} +(-8.17730 - 2.00553i) q^{85} +14.5131 q^{87} +(2.18703 - 0.905899i) q^{89} +(2.01232 - 2.01232i) q^{91} +(1.86204 - 4.49536i) q^{93} +(7.89732 + 13.0298i) q^{95} +(-5.01568 - 12.1089i) q^{97} +(-0.0688464 - 0.0285171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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