LMFDB - Embedded newform 820.2.u.b.221.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.1
Character	$\chi$	$=$	820.221
Dual form			820.2.u.b.141.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.40143 q^{3} +(0.809017 + 0.587785i) q^{5} +(-1.56474 - 4.81578i) q^{7} +8.56970 q^{9} +(-0.551520 + 0.400703i) q^{11} +(-1.03830 + 3.19557i) q^{13} +(-2.75181 - 1.99931i) q^{15} +(4.60122 - 3.34298i) q^{17} +(0.481775 + 1.48275i) q^{19} +(5.32235 + 16.3805i) q^{21} +(-0.583664 + 1.79633i) q^{23} +(0.309017 + 0.951057i) q^{25} -18.9449 q^{27} +(-4.99301 - 3.62763i) q^{29} +(4.82048 - 3.50229i) q^{31} +(1.87595 - 1.36296i) q^{33} +(1.56474 - 4.81578i) q^{35} +(-8.81426 - 6.40393i) q^{37} +(3.53171 - 10.8695i) q^{39} +(-3.81306 - 5.14399i) q^{41} +(-1.81560 + 5.58784i) q^{43} +(6.93303 + 5.03714i) q^{45} +(-0.116620 + 0.358921i) q^{47} +(-15.0802 + 10.9564i) q^{49} +(-15.6507 + 11.3709i) q^{51} +(-7.32537 - 5.32219i) q^{53} -0.681716 q^{55} +(-1.63872 - 5.04347i) q^{57} +(-0.172613 + 0.531249i) q^{59} +(1.48400 + 4.56729i) q^{61} +(-13.4094 - 41.2698i) q^{63} +(-2.71832 + 1.97497i) q^{65} +(-0.0569224 - 0.0413565i) q^{67} +(1.98529 - 6.11009i) q^{69} +(-7.59300 + 5.51664i) q^{71} -8.44935 q^{73} +(-1.05110 - 3.23495i) q^{75} +(2.79268 + 2.02900i) q^{77} -9.24771 q^{79} +38.7306 q^{81} +5.97459 q^{83} +5.68742 q^{85} +(16.9833 + 12.3391i) q^{87} +(1.33243 + 4.10080i) q^{89} +17.0138 q^{91} +(-16.3965 + 11.9128i) q^{93} +(-0.481775 + 1.48275i) q^{95} +(3.81249 + 2.76994i) q^{97} +(-4.72636 + 3.43390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	−3.40143			−1.96381			−0.981907	−	0.189364i	$-0.939357\pi$
$3$	−3.40143			−1.96381			−0.981907	+	0.189364i	$0.939357\pi$
$4$		0			0
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	−1.56474	−	4.81578i	−0.591417	−	1.82019i	−0.571810	−	0.820386i	$-0.693759\pi$
$7$	−1.56474	−	4.81578i	−0.591417	−	1.82019i	−0.0196067	−	0.999808i	$-0.506241\pi$
$8$		0			0
$9$	8.56970			2.85657
$10$		0			0
$11$	−0.551520	+	0.400703i	−0.166290	+	0.120816i	−0.667818	−	0.744325i	$-0.732771\pi$
$11$	−0.551520	+	0.400703i	−0.166290	+	0.120816i	0.501528	+	0.865141i	$0.332771\pi$
$12$		0			0
$13$	−1.03830	+	3.19557i	−0.287974	+	0.886292i	0.697518	+	0.716567i	$0.254288\pi$
$13$	−1.03830	+	3.19557i	−0.287974	+	0.886292i	−0.985492	+	0.169725i	$0.945712\pi$
$14$		0			0
$15$	−2.75181	−	1.99931i	−0.710515	−	0.516219i
$16$		0			0
$17$	4.60122	−	3.34298i	1.11596	−	0.810791i	0.132367	−	0.991201i	$-0.457742\pi$
$17$	4.60122	−	3.34298i	1.11596	−	0.810791i	0.983592	+	0.180409i	$0.0577422\pi$
$18$		0			0
$19$	0.481775	+	1.48275i	0.110527	+	0.340166i	0.990988	−	0.133952i	$-0.0427668\pi$
$19$	0.481775	+	1.48275i	0.110527	+	0.340166i	−0.880461	+	0.474119i	$0.842767\pi$
$20$		0			0
$21$	5.32235	+	16.3805i	1.16143	+	3.57452i
$22$		0			0
$23$	−0.583664	+	1.79633i	−0.121702	+	0.374561i	−0.993286	−	0.115686i	$-0.963093\pi$
$23$	−0.583664	+	1.79633i	−0.121702	+	0.374561i	0.871584	+	0.490247i	$0.163093\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−18.9449			−3.64595
$28$		0			0
$29$	−4.99301	−	3.62763i	−0.927178	−	0.673634i	0.0181222	−	0.999836i	$-0.494231\pi$
$29$	−4.99301	−	3.62763i	−0.927178	−	0.673634i	−0.945300	+	0.326201i	$0.894231\pi$
$30$		0			0
$31$	4.82048	−	3.50229i	0.865784	−	0.629029i	−0.0636681	−	0.997971i	$-0.520280\pi$
$31$	4.82048	−	3.50229i	0.865784	−	0.629029i	0.929452	+	0.368942i	$0.120280\pi$
$32$		0			0
$33$	1.87595	−	1.36296i	0.326562	−	0.237261i
$34$		0			0
$35$	1.56474	−	4.81578i	0.264490	−	0.814015i
$36$		0			0
$37$	−8.81426	−	6.40393i	−1.44906	−	1.05280i	−0.986051	−	0.166444i	$-0.946772\pi$
$37$	−8.81426	−	6.40393i	−1.44906	−	1.05280i	−0.463004	−	0.886356i	$-0.653228\pi$
$38$		0			0
$39$	3.53171	−	10.8695i	0.565527	−	1.74051i
$40$		0			0
$41$	−3.81306	−	5.14399i	−0.595499	−	0.803356i
$41$	−3.81306	−	5.14399i	−0.595499	−	0.803356i
$42$		0			0
$43$	−1.81560	+	5.58784i	−0.276876	+	0.852138i	0.711841	+	0.702341i	$0.247862\pi$
$43$	−1.81560	+	5.58784i	−0.276876	+	0.852138i	−0.988717	+	0.149796i	$0.952138\pi$
$44$		0			0
$45$	6.93303	+	5.03714i	1.03352	+	0.750893i
$46$		0			0
$47$	−0.116620	+	0.358921i	−0.0170108	+	0.0523540i	−0.959202	−	0.282723i	$-0.908762\pi$
$47$	−0.116620	+	0.358921i	−0.0170108	+	0.0523540i	0.942191	+	0.335077i	$0.108762\pi$
$48$		0			0
$49$	−15.0802	+	10.9564i	−2.15431	+	1.56520i
$50$		0			0
$51$	−15.6507	+	11.3709i	−2.19154	+	1.59224i
$52$		0			0
$53$	−7.32537	−	5.32219i	−1.00622	−	0.731059i	−0.0428044	−	0.999083i	$-0.513629\pi$
$53$	−7.32537	−	5.32219i	−1.00622	−	0.731059i	−0.963412	+	0.268024i	$0.913629\pi$
$54$		0			0
$55$	−0.681716			−0.0919226
$56$		0			0
$57$	−1.63872	−	5.04347i	−0.217054	−	0.668024i
$58$		0			0
$59$	−0.172613	+	0.531249i	−0.0224723	+	0.0691628i	−0.961664	−	0.274231i	$-0.911577\pi$
$59$	−0.172613	+	0.531249i	−0.0224723	+	0.0691628i	0.939191	+	0.343394i	$0.111577\pi$
$60$		0			0
$61$	1.48400	+	4.56729i	0.190007	+	0.584782i	0.999999	−	0.00165969i	$-0.000528297\pi$
$61$	1.48400	+	4.56729i	0.190007	+	0.584782i	−0.809991	+	0.586442i	$0.800528\pi$
$62$		0			0
$63$	−13.4094	−	41.2698i	−1.68942	−	5.19950i
$64$		0			0
$65$	−2.71832	+	1.97497i	−0.337166	+	0.244965i
$66$		0			0
$67$	−0.0569224	−	0.0413565i	−0.00695417	−	0.00505250i	0.584303	−	0.811536i	$-0.301368\pi$
$67$	−0.0569224	−	0.0413565i	−0.00695417	−	0.00505250i	−0.591257	+	0.806483i	$0.701368\pi$
$68$		0			0
$69$	1.98529	−	6.11009i	0.239001	−	0.735569i
$70$		0			0
$71$	−7.59300	+	5.51664i	−0.901123	+	0.654704i	−0.938754	−	0.344587i	$-0.888019\pi$
$71$	−7.59300	+	5.51664i	−0.901123	+	0.654704i	0.0376311	+	0.999292i	$0.488019\pi$
$72$		0			0
$73$	−8.44935			−0.988922			−0.494461	−	0.869200i	$-0.664635\pi$
$73$	−8.44935			−0.988922			−0.494461	+	0.869200i	$0.664635\pi$
$74$		0			0
$75$	−1.05110	−	3.23495i	−0.121370	−	0.373540i
$76$		0			0
$77$	2.79268	+	2.02900i	0.318256	+	0.231226i
$78$		0			0
$79$	−9.24771			−1.04045			−0.520225	−	0.854029i	$-0.674152\pi$
$79$	−9.24771			−1.04045			−0.520225	+	0.854029i	$0.674152\pi$
$80$		0			0
$81$	38.7306			4.30340
$82$		0			0
$83$	5.97459			0.655796			0.327898	−	0.944713i	$-0.393660\pi$
$83$	5.97459			0.655796			0.327898	+	0.944713i	$0.393660\pi$
$84$		0			0
$85$	5.68742			0.616887
$86$		0			0
$87$	16.9833	+	12.3391i	1.82081	+	1.32289i
$88$		0			0
$89$	1.33243	+	4.10080i	0.141237	+	0.434684i	0.996508	−	0.0834975i	$-0.0266091\pi$
$89$	1.33243	+	4.10080i	0.141237	+	0.434684i	−0.855271	+	0.518182i	$0.826609\pi$
$90$		0			0
$91$	17.0138			1.78354
$92$		0			0
$93$	−16.3965	+	11.9128i	−1.70024	+	1.23530i
$94$		0			0
$95$	−0.481775	+	1.48275i	−0.0494291	+	0.152127i
$96$		0			0
$97$	3.81249	+	2.76994i	0.387100	+	0.281244i	0.764266	−	0.644901i	$-0.223101\pi$
$97$	3.81249	+	2.76994i	0.387100	+	0.281244i	−0.377166	+	0.926146i	$0.623101\pi$
$98$		0			0
$99$	−4.72636	+	3.43390i	−0.475017	+	0.345120i
$100$		0			0
$101$	−5.50319	−	16.9371i	−0.547588	−	1.68530i	−0.714757	−	0.699373i	$-0.753463\pi$
$101$	−5.50319	−	16.9371i	−0.547588	−	1.68530i	0.167169	−	0.985928i	$-0.446537\pi$
$102$		0			0
$103$	−1.52018	−	4.67863i	−0.149788	−	0.460999i	0.847808	−	0.530304i	$-0.177922\pi$
$103$	−1.52018	−	4.67863i	−0.149788	−	0.460999i	−0.997596	+	0.0693044i	$0.977922\pi$
$104$		0			0
$105$	−5.32235	+	16.3805i	−0.519408	+	1.59857i
$106$		0			0
$107$	−1.05889	−	3.25894i	−0.102367	−	0.315053i	0.886736	−	0.462275i	$-0.152967\pi$
$107$	−1.05889	−	3.25894i	−0.102367	−	0.315053i	−0.989103	+	0.147222i	$0.952967\pi$
$108$		0			0
$109$	−2.00739			−0.192273			−0.0961365	−	0.995368i	$-0.530649\pi$
$109$	−2.00739			−0.192273			−0.0961365	+	0.995368i	$0.530649\pi$
$110$		0			0
$111$	29.9810	+	21.7825i	2.84567	+	2.06750i
$112$		0			0
$113$	−1.91438	+	1.39088i	−0.180090	+	0.130843i	−0.674178	−	0.738569i	$-0.735502\pi$
$113$	−1.91438	+	1.39088i	−0.180090	+	0.130843i	0.494088	+	0.869412i	$0.335502\pi$
$114$		0			0
$115$	−1.52805	+	1.11019i	−0.142492	+	0.103526i
$116$		0			0
$117$	−8.89795	+	27.3851i	−0.822616	+	2.53175i
$118$		0			0
$119$	−23.2988	−	16.9275i	−2.13579	−	1.55175i
$120$		0			0
$121$	−3.25558	+	10.0196i	−0.295961	+	0.910876i
$122$		0			0
$123$	12.9698	+	17.4969i	1.16945	+	1.57764i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	3.35956	+	2.44086i	0.298113	+	0.216592i	0.726779	−	0.686871i	$-0.241016\pi$
$127$	3.35956	+	2.44086i	0.298113	+	0.216592i	−0.428666	+	0.903463i	$0.641016\pi$
$128$		0			0
$129$	6.17563	−	19.0066i	0.543733	−	1.67344i
$130$		0			0
$131$	−8.21571	+	5.96906i	−0.717810	+	0.521519i	−0.885684	−	0.464289i	$-0.846310\pi$
$131$	−8.21571	+	5.96906i	−0.717810	+	0.521519i	0.167874	+	0.985808i	$0.446310\pi$
$132$		0			0
$133$	6.38675	−	4.64025i	0.553801	−	0.402360i
$134$		0			0
$135$	−15.3268	−	11.1355i	−1.31912	−	0.958394i
$136$		0			0
$137$	−0.753454			−0.0643719			−0.0321860	−	0.999482i	$-0.510247\pi$
$137$	−0.753454			−0.0643719			−0.0321860	+	0.999482i	$0.510247\pi$
$138$		0			0
$139$	−2.81141	−	8.65264i	−0.238461	−	0.733907i	−0.996643	−	0.0818649i	$-0.973912\pi$
$139$	−2.81141	−	8.65264i	−0.238461	−	0.733907i	0.758183	−	0.652042i	$-0.226088\pi$
$140$		0			0
$141$	0.396676	−	1.22084i	0.0334061	−	0.102814i
$142$		0			0
$143$	−0.707829	−	2.17847i	−0.0591916	−	0.182173i
$144$		0			0
$145$	−1.90716	−	5.86963i	−0.158381	−	0.487446i
$146$		0			0
$147$	51.2942	−	37.2674i	4.23067	−	3.07376i
$148$		0			0
$149$	−0.0774407	−	0.0562640i	−0.00634419	−	0.00460932i	0.584609	−	0.811315i	$-0.301248\pi$
$149$	−0.0774407	−	0.0562640i	−0.00634419	−	0.00460932i	−0.590953	+	0.806706i	$0.701248\pi$
$150$		0			0
$151$	−3.52304	+	10.8428i	−0.286701	+	0.882375i	0.699183	+	0.714943i	$0.253547\pi$
$151$	−3.52304	+	10.8428i	−0.286701	+	0.882375i	−0.985884	+	0.167432i	$0.946453\pi$
$152$		0			0
$153$	39.4310	−	28.6483i	3.18781	−	2.31608i
$154$		0			0
$155$	5.95844			0.478594
$156$		0			0
$157$	3.87817	+	11.9358i	0.309511	+	0.952578i	0.977955	+	0.208815i	$0.0669607\pi$
$157$	3.87817	+	11.9358i	0.309511	+	0.952578i	−0.668444	+	0.743763i	$0.733039\pi$
$158$		0			0
$159$	24.9167	+	18.1030i	1.97602	+	1.43566i
$160$		0			0
$161$	9.56403			0.753751
$162$		0			0
$163$	10.1093			0.791818			0.395909	−	0.918290i	$-0.370430\pi$
$163$	10.1093			0.791818			0.395909	+	0.918290i	$0.370430\pi$
$164$		0			0
$165$	2.31881			0.180519
$166$		0			0
$167$	−0.741092			−0.0573474			−0.0286737	−	0.999589i	$-0.509128\pi$
$167$	−0.741092			−0.0573474			−0.0286737	+	0.999589i	$0.509128\pi$
$168$		0			0
$169$	1.38362	+	1.00526i	0.106432	+	0.0773276i
$170$		0			0
$171$	4.12867	+	12.7067i	0.315727	+	0.971708i
$172$		0			0
$173$	−2.36462			−0.179779			−0.0898895	−	0.995952i	$-0.528651\pi$
$173$	−2.36462			−0.179779			−0.0898895	+	0.995952i	$0.528651\pi$
$174$		0			0
$175$	4.09655	−	2.97632i	0.309670	−	0.224988i
$176$		0			0
$177$	0.587131	−	1.80700i	0.0441315	−	0.135823i
$178$		0			0
$179$	−14.6613	−	10.6521i	−1.09584	−	0.796173i	−0.115462	−	0.993312i	$-0.536835\pi$
$179$	−14.6613	−	10.6521i	−1.09584	−	0.796173i	−0.980375	+	0.197139i	$0.936835\pi$
$180$		0			0
$181$	17.7833	−	12.9203i	1.32182	−	0.960360i	0.321915	−	0.946769i	$-0.395674\pi$
$181$	17.7833	−	12.9203i	1.32182	−	0.960360i	0.999908	−	0.0135913i	$-0.00432639\pi$
$182$		0			0
$183$	−5.04773	−	15.5353i	−0.373139	−	1.14840i
$184$		0			0
$185$	−3.36675	−	10.3618i	−0.247528	−	0.761813i
$186$		0			0
$187$	−1.19812	+	3.68744i	−0.0876153	+	0.269652i
$188$		0			0
$189$	29.6439	+	91.2345i	2.15628	+	6.63633i
$190$		0			0
$191$	−23.1249			−1.67326			−0.836629	−	0.547769i	$-0.815477\pi$
$191$	−23.1249			−1.67326			−0.836629	+	0.547769i	$0.815477\pi$
$192$		0			0
$193$	−3.52024	−	2.55760i	−0.253392	−	0.184100i	0.453837	−	0.891085i	$-0.350055\pi$
$193$	−3.52024	−	2.55760i	−0.253392	−	0.184100i	−0.707229	+	0.706985i	$0.750055\pi$
$194$		0			0
$195$	9.24615	−	6.71772i	0.662130	−	0.481066i
$196$		0			0
$197$	−12.4215	+	9.02471i	−0.884992	+	0.642984i	−0.934567	−	0.355786i	$-0.884213\pi$
$197$	−12.4215	+	9.02471i	−0.884992	+	0.642984i	0.0495756	+	0.998770i	$0.484213\pi$
$198$		0			0
$199$	5.77884	−	17.7854i	0.409651	−	1.26078i	−0.507297	−	0.861771i	$-0.669355\pi$
$199$	5.77884	−	17.7854i	0.409651	−	1.26078i	0.916949	−	0.399005i	$-0.130645\pi$
$200$		0			0
$201$	0.193617	+	0.140671i	0.0136567	+	0.00992217i
$202$		0			0
$203$	−9.65711	+	29.7215i	−0.677796	+	2.08604i
$204$		0			0
$205$	−0.0612688	−	6.40283i	−0.00427920	−	0.447193i
$206$		0			0
$207$	−5.00182	+	15.3940i	−0.347651	+	1.06996i
$208$		0			0
$209$	−0.859851	−	0.624718i	−0.0594771	−	0.0432127i
$210$		0			0
$211$	5.04434	−	15.5249i	0.347267	−	1.06878i	−0.613092	−	0.790012i	$-0.710074\pi$
$211$	5.04434	−	15.5249i	0.347267	−	1.06878i	0.960359	−	0.278766i	$-0.0899255\pi$
$212$		0			0
$213$	25.8270	−	18.7644i	1.76964	−	1.28572i
$214$		0			0
$215$	−4.75330	+	3.45347i	−0.324172	+	0.235525i
$216$		0			0
$217$	−24.4091	−	17.7342i	−1.65699	−	1.20388i
$218$		0			0
$219$	28.7398			1.94206
$220$		0			0
$221$	5.90527	+	18.1745i	0.397231	+	1.22255i
$222$		0			0
$223$	3.12195	−	9.60836i	0.209061	−	0.643423i	−0.790461	−	0.612512i	$-0.790159\pi$
$223$	3.12195	−	9.60836i	0.209061	−	0.643423i	0.999522	−	0.0309112i	$-0.00984092\pi$
$224$		0			0
$225$	2.64818	+	8.15027i	0.176545	+	0.543351i
$226$		0			0
$227$	4.05368	+	12.4759i	0.269052	+	0.828057i	0.990732	+	0.135830i	$0.0433702\pi$
$227$	4.05368	+	12.4759i	0.269052	+	0.828057i	−0.721680	+	0.692227i	$0.756630\pi$
$228$		0			0
$229$	15.4217	−	11.2045i	1.01909	−	0.740415i	0.0529973	−	0.998595i	$-0.483123\pi$
$229$	15.4217	−	11.2045i	1.01909	−	0.740415i	0.966097	+	0.258179i	$0.0831225\pi$
$230$		0			0
$231$	−9.49910	−	6.90150i	−0.624995	−	0.454085i
$232$		0			0
$233$	6.58614	−	20.2700i	0.431472	−	1.32793i	−0.465187	−	0.885213i	$-0.654013\pi$
$233$	6.58614	−	20.2700i	0.431472	−	1.32793i	0.896659	−	0.442722i	$-0.145987\pi$
$234$		0			0
$235$	−0.305316	+	0.221825i	−0.0199166	+	0.0144703i
$236$		0			0
$237$	31.4554			2.04325
$238$		0			0
$239$	1.94197	+	5.97678i	0.125616	+	0.386606i	0.994013	−	0.109264i	$-0.0348494\pi$
$239$	1.94197	+	5.97678i	0.125616	+	0.386606i	−0.868397	+	0.495870i	$0.834849\pi$
$240$		0			0
$241$	−17.0871	−	12.4145i	−1.10068	−	0.799689i	−0.119507	−	0.992833i	$-0.538131\pi$
$241$	−17.0871	−	12.4145i	−1.10068	−	0.799689i	−0.981170	+	0.193144i	$0.938131\pi$
$242$		0			0
$243$	−74.9045			−4.80513
$244$		0			0
$245$	−18.6402			−1.19088
$246$		0			0
$247$	−5.23847			−0.333316
$248$		0			0
$249$	−20.3221			−1.28786
$250$		0			0
$251$	−1.32577	−	0.963227i	−0.0836818	−	0.0607984i	0.545158	−	0.838333i	$-0.316470\pi$
$251$	−1.32577	−	0.963227i	−0.0836818	−	0.0607984i	−0.628840	+	0.777535i	$0.716470\pi$
$252$		0			0
$253$	−0.397893	−	1.22459i	−0.0250153	−	0.0769893i
$254$		0			0
$255$	−19.3453			−1.21145
$256$		0			0
$257$	6.49328	−	4.71764i	0.405040	−	0.294279i	−0.366551	−	0.930398i	$-0.619461\pi$
$257$	6.49328	−	4.71764i	0.405040	−	0.294279i	0.771591	+	0.636119i	$0.219461\pi$
$258$		0			0
$259$	−17.0479	+	52.4680i	−1.05930	+	3.26020i
$260$		0			0
$261$	−42.7886	−	31.0877i	−2.64854	−	1.92428i
$262$		0			0
$263$	−15.9529	+	11.5905i	−0.983700	+	0.714700i	−0.958533	−	0.284983i	$-0.908012\pi$
$263$	−15.9529	+	11.5905i	−0.983700	+	0.714700i	−0.0251677	+	0.999683i	$0.508012\pi$
$264$		0			0
$265$	−2.79804	−	8.61149i	−0.171882	−	0.528999i
$266$		0			0
$267$	−4.53217	−	13.9486i	−0.277364	−	0.853639i
$268$		0			0
$269$	0.0102026	−	0.0314003i	0.000622063	−	0.00191451i	−0.950745	−	0.309974i	$-0.899680\pi$
$269$	0.0102026	−	0.0314003i	0.000622063	−	0.00191451i	0.951367	+	0.308060i	$0.0996796\pi$
$270$		0			0
$271$	0.473384	+	1.45693i	0.0287560	+	0.0885020i	0.964405	−	0.264431i	$-0.0851843\pi$
$271$	0.473384	+	1.45693i	0.0287560	+	0.0885020i	−0.935648	+	0.352933i	$0.885184\pi$
$272$		0			0
$273$	−57.8713			−3.50253
$274$		0			0
$275$	−0.551520	−	0.400703i	−0.0332579	−	0.0241633i
$276$		0			0
$277$	−18.4898	+	13.4336i	−1.11094	+	0.807148i	−0.982812	−	0.184609i	$-0.940898\pi$
$277$	−18.4898	+	13.4336i	−1.11094	+	0.807148i	−0.128132	+	0.991757i	$0.540898\pi$
$278$		0			0
$279$	41.3101	−	30.0135i	2.47317	−	1.79686i
$280$		0			0
$281$	−4.00747	+	12.3337i	−0.239066	+	0.735768i	0.757490	+	0.652846i	$0.226425\pi$
$281$	−4.00747	+	12.3337i	−0.239066	+	0.735768i	−0.996556	+	0.0829219i	$0.973575\pi$
$282$		0			0
$283$	16.9881	+	12.3426i	1.00984	+	0.733690i	0.964175	−	0.265267i	$-0.0854600\pi$
$283$	16.9881	+	12.3426i	1.00984	+	0.733690i	0.0456628	+	0.998957i	$0.485460\pi$
$284$		0			0
$285$	1.63872	−	5.04347i	0.0970695	−	0.298749i
$286$		0			0
$287$	−18.8059	+	26.4119i	−1.11007	+	1.55904i
$288$		0			0
$289$	4.74239	−	14.5956i	0.278964	−	0.858563i
$290$		0			0
$291$	−12.9679	−	9.42173i	−0.760192	−	0.552312i
$292$		0			0
$293$	−2.31388	+	7.12140i	−0.135178	+	0.416037i	−0.995618	−	0.0935164i	$-0.970189\pi$
$293$	−2.31388	+	7.12140i	−0.135178	+	0.416037i	0.860439	+	0.509553i	$0.170189\pi$
$294$		0			0
$295$	−0.451908	+	0.328330i	−0.0263111	+	0.0191161i
$296$		0			0
$297$	10.4485	−	7.59128i	0.606283	−	0.440490i
$298$		0			0
$299$	−5.13429	−	3.73028i	−0.296924	−	0.215728i
$300$		0			0
$301$	29.7507			1.71480
$302$		0			0
$303$	18.7187	+	57.6102i	1.07536	+	3.30962i
$304$		0			0
$305$	−1.48400	+	4.56729i	−0.0849738	+	0.261522i
$306$		0			0
$307$	−4.33613	−	13.3452i	−0.247476	−	0.761652i	−0.995219	−	0.0976646i	$-0.968863\pi$
$307$	−4.33613	−	13.3452i	−0.247476	−	0.761652i	0.747744	−	0.663988i	$-0.231137\pi$
$308$		0			0
$309$	5.17078	+	15.9140i	0.294155	+	0.905317i
$310$		0			0
$311$	8.82037	−	6.40837i	0.500157	−	0.363385i	−0.308920	−	0.951088i	$-0.599967\pi$
$311$	8.82037	−	6.40837i	0.500157	−	0.363385i	0.809077	+	0.587703i	$0.199967\pi$
$312$		0			0
$313$	8.27962	+	6.01550i	0.467992	+	0.340016i	0.796658	−	0.604430i	$-0.206599\pi$
$313$	8.27962	+	6.01550i	0.467992	+	0.340016i	−0.328666	+	0.944446i	$0.606599\pi$
$314$		0			0
$315$	13.4094	−	41.2698i	0.755532	−	2.32529i
$316$		0			0
$317$	−7.39692	+	5.37418i	−0.415453	+	0.301844i	−0.775806	−	0.630972i	$-0.782656\pi$
$317$	−7.39692	+	5.37418i	−0.415453	+	0.301844i	0.360353	+	0.932816i	$0.382656\pi$
$318$		0			0
$319$	4.20734			0.235566
$320$		0			0
$321$	3.60175	+	11.0850i	0.201030	+	0.618706i
$322$		0			0
$323$	7.17356	+	5.21189i	0.399147	+	0.289998i
$324$		0			0
$325$	−3.36002			−0.186381
$326$		0			0
$327$	6.82799			0.377589
$328$		0			0
$329$	1.91096			0.105355
$330$		0			0
$331$	−8.34301			−0.458573			−0.229287	−	0.973359i	$-0.573639\pi$
$331$	−8.34301			−0.458573			−0.229287	+	0.973359i	$0.573639\pi$
$332$		0			0
$333$	−75.5355	−	54.8798i	−4.13932	−	3.00739i
$334$		0			0
$335$	−0.0217424	−	0.0669162i	−0.00118791	−	0.00365602i
$336$		0			0
$337$	14.6485			0.797954			0.398977	−	0.916961i	$-0.369365\pi$
$337$	14.6485			0.797954			0.398977	+	0.916961i	$0.369365\pi$
$338$		0			0
$339$	6.51161	−	4.73096i	0.353662	−	0.256951i
$340$		0			0
$341$	−1.25522	+	3.86316i	−0.0679738	+	0.209202i
$342$		0			0
$343$	47.6844	+	34.6448i	2.57472	+	1.87064i
$344$		0			0
$345$	5.19756	−	3.77625i	0.279827	−	0.203306i
$346$		0			0
$347$	−9.38445	−	28.8824i	−0.503784	−	1.55049i	−0.802806	−	0.596240i	$-0.796661\pi$
$347$	−9.38445	−	28.8824i	−0.503784	−	1.55049i	0.299022	−	0.954246i	$-0.403339\pi$
$348$		0			0
$349$	0.0661982	+	0.203737i	0.00354351	+	0.0109058i	0.952813	−	0.303559i	$-0.0981750\pi$
$349$	0.0661982	+	0.203737i	0.00354351	+	0.0109058i	−0.949269	+	0.314465i	$0.898175\pi$
$350$		0			0
$351$	19.6706	−	60.5398i	1.04994	−	3.23138i
$352$		0			0
$353$	−2.70957	−	8.33921i	−0.144216	−	0.443851i	0.852693	−	0.522412i	$-0.174968\pi$
$353$	−2.70957	−	8.33921i	−0.144216	−	0.443851i	−0.996909	+	0.0785606i	$0.974968\pi$
$354$		0			0
$355$	−9.38546			−0.498129
$356$		0			0
$357$	79.2490	+	57.5778i	4.19430	+	3.04734i
$358$		0			0
$359$	20.4942	−	14.8899i	1.08164	−	0.785861i	0.103676	−	0.994611i	$-0.466940\pi$
$359$	20.4942	−	14.8899i	1.08164	−	0.785861i	0.977969	+	0.208750i	$0.0669396\pi$
$360$		0			0
$361$	13.4049	−	9.73921i	0.705520	−	0.512590i
$362$		0			0
$363$	11.0736	−	34.0810i	0.581213	−	1.78879i
$364$		0			0
$365$	−6.83567	−	4.96641i	−0.357795	−	0.259954i
$366$		0			0
$367$	−8.66710	+	26.6746i	−0.452419	+	1.39240i	0.421720	+	0.906726i	$0.361427\pi$
$367$	−8.66710	+	26.6746i	−0.452419	+	1.39240i	−0.874139	+	0.485676i	$0.838573\pi$
$368$		0			0
$369$	−32.6767	−	44.0824i	−1.70108	−	2.29484i
$370$		0			0
$371$	−14.1682	+	43.6052i	−0.735576	+	2.26387i
$372$		0			0
$373$	−1.08119	−	0.785531i	−0.0559820	−	0.0406733i	0.559442	−	0.828869i	$-0.311015\pi$
$373$	−1.08119	−	0.785531i	−0.0559820	−	0.0406733i	−0.615424	+	0.788196i	$0.711015\pi$
$374$		0			0
$375$	1.05110	−	3.23495i	0.0542785	−	0.167052i
$376$		0			0
$377$	16.7766	−	12.1889i	0.864040	−	0.627762i
$378$		0			0
$379$	26.1290	−	18.9838i	1.34216	−	0.975133i	0.342794	−	0.939411i	$-0.388627\pi$
$379$	26.1290	−	18.9838i	1.34216	−	0.975133i	0.999362	−	0.0357224i	$-0.0113732\pi$
$380$		0			0
$381$	−11.4273	−	8.30242i	−0.585438	−	0.425346i
$382$		0			0
$383$	−20.7122			−1.05834			−0.529172	−	0.848515i	$-0.677497\pi$
$383$	−20.7122			−1.05834			−0.529172	+	0.848515i	$0.677497\pi$
$384$		0			0
$385$	1.06671	+	3.28299i	0.0543646	+	0.167317i
$386$		0			0
$387$	−15.5591	+	47.8861i	−0.790915	+	2.43419i
$388$		0			0
$389$	−6.70017	−	20.6210i	−0.339712	−	1.04553i	−0.964354	−	0.264616i	$-0.914755\pi$
$389$	−6.70017	−	20.6210i	−0.339712	−	1.04553i	0.624642	−	0.780912i	$-0.285245\pi$
$390$		0			0
$391$	3.31954	+	10.2165i	0.167876	+	0.516670i
$392$		0			0
$393$	27.9451	−	20.3033i	1.40964	−	1.02417i
$394$		0			0
$395$	−7.48156	−	5.43567i	−0.376438	−	0.273498i
$396$		0			0
$397$	−3.39867	+	10.4600i	−0.170574	+	0.524973i	−0.999404	−	0.0345279i	$-0.989007\pi$
$397$	−3.39867	+	10.4600i	−0.170574	+	0.524973i	0.828830	+	0.559501i	$0.189007\pi$
$398$		0			0
$399$	−21.7241	+	15.7834i	−1.08756	+	0.790161i
$400$		0			0
$401$	−36.6833			−1.83187			−0.915937	−	0.401321i	$-0.868551\pi$
$401$	−36.6833			−1.83187			−0.915937	+	0.401321i	$0.868551\pi$
$402$		0			0
$403$	6.18668	+	19.0406i	0.308180	+	0.948482i
$404$		0			0
$405$	31.3337	+	22.7653i	1.55698	+	1.13122i
$406$		0			0
$407$	7.42731			0.368158
$408$		0			0
$409$	8.15985			0.403479			0.201739	−	0.979439i	$-0.435341\pi$
$409$	8.15985			0.403479			0.201739	+	0.979439i	$0.435341\pi$
$410$		0			0
$411$	2.56282			0.126414
$412$		0			0
$413$	2.82847			0.139180
$414$		0			0
$415$	4.83354	+	3.51178i	0.237269	+	0.172386i
$416$		0			0
$417$	9.56281	+	29.4313i	0.468293	+	1.44126i
$418$		0			0
$419$	−0.432828			−0.0211450			−0.0105725	−	0.999944i	$-0.503365\pi$
$419$	−0.432828			−0.0211450			−0.0105725	+	0.999944i	$0.503365\pi$
$420$		0			0
$421$	19.1610	−	13.9213i	0.933848	−	0.678481i	−0.0130837	−	0.999914i	$-0.504165\pi$
$421$	19.1610	−	13.9213i	0.933848	−	0.678481i	0.946932	+	0.321434i	$0.104165\pi$
$422$		0			0
$423$	−0.999402	+	3.07584i	−0.0485926	+	0.149553i
$424$		0			0
$425$	4.60122	+	3.34298i	0.223192	+	0.162158i
$426$		0			0
$427$	19.6730	−	14.2933i	0.952043	−	0.691700i
$428$		0			0
$429$	2.40763	+	7.40991i	0.116241	+	0.357754i
$430$		0			0
$431$	−9.63577	−	29.6558i	−0.464139	−	1.42847i	−0.860063	−	0.510189i	$-0.829576\pi$
$431$	−9.63577	−	29.6558i	−0.464139	−	1.42847i	0.395924	−	0.918283i	$-0.370424\pi$
$432$		0			0
$433$	1.65512	−	5.09393i	0.0795400	−	0.244799i	−0.903377	−	0.428847i	$-0.858920\pi$
$433$	1.65512	−	5.09393i	0.0795400	−	0.244799i	0.982917	+	0.184048i	$0.0589201\pi$
$434$		0			0
$435$	6.48706	+	19.9651i	0.311031	+	0.957254i
$436$		0			0
$437$	−2.94471			−0.140865
$438$		0			0
$439$	−16.5339	−	12.0126i	−0.789118	−	0.573328i	0.118584	−	0.992944i	$-0.462165\pi$
$439$	−16.5339	−	12.0126i	−0.789118	−	0.573328i	−0.907702	+	0.419616i	$0.862165\pi$
$440$		0			0
$441$	−129.233	+	93.8931i	−6.15394	+	4.47110i
$442$		0			0
$443$	23.1533	−	16.8219i	1.10005	−	0.799231i	0.118980	−	0.992897i	$-0.462038\pi$
$443$	23.1533	−	16.8219i	1.10005	−	0.799231i	0.981068	+	0.193665i	$0.0620376\pi$
$444$		0			0
$445$	−1.33243	+	4.10080i	−0.0631633	+	0.194397i
$446$		0			0
$447$	0.263409	+	0.191378i	0.0124588	+	0.00905185i
$448$		0			0
$449$	−2.58642	+	7.96018i	−0.122061	+	0.375664i	−0.993354	−	0.115098i	$-0.963282\pi$
$449$	−2.58642	+	7.96018i	−0.122061	+	0.375664i	0.871293	+	0.490762i	$0.163282\pi$
$450$		0			0
$451$	4.16419	+	1.30911i	0.196084	+	0.0616435i
$452$		0			0
$453$	11.9834	−	36.8810i	0.563028	−	1.73282i
$454$		0			0
$455$	13.7645	+	10.0005i	0.645289	+	0.468830i
$456$		0			0
$457$	−4.64563	+	14.2978i	−0.217313	+	0.668822i	0.781668	+	0.623695i	$0.214369\pi$
$457$	−4.64563	+	14.2978i	−0.217313	+	0.668822i	−0.998981	+	0.0451270i	$0.985631\pi$
$458$		0			0
$459$	−87.1696	+	63.3324i	−4.06873	+	2.95610i
$460$		0			0
$461$	23.2716	−	16.9078i	1.08387	−	0.787475i	0.105513	−	0.994418i	$-0.466351\pi$
$461$	23.2716	−	16.9078i	1.08387	−	0.787475i	0.978353	+	0.206943i	$0.0663515\pi$
$462$		0			0
$463$	9.84017	+	7.14930i	0.457312	+	0.332256i	0.792476	−	0.609903i	$-0.208792\pi$
$463$	9.84017	+	7.14930i	0.457312	+	0.332256i	−0.335164	+	0.942160i	$0.608792\pi$
$464$		0			0
$465$	−20.2672			−0.939869
$466$		0			0
$467$	−3.42605	−	10.5443i	−0.158539	−	0.487931i	0.839964	−	0.542643i	$-0.182576\pi$
$467$	−3.42605	−	10.5443i	−0.158539	−	0.487931i	−0.998502	+	0.0547112i	$0.982576\pi$
$468$		0			0
$469$	−0.110095	+	0.338838i	−0.00508372	+	0.0156461i
$470$		0			0
$471$	−13.1913	−	40.5986i	−0.607823	−	1.87069i
$472$		0			0
$473$	−1.23772	−	3.80932i	−0.0569106	−	0.175153i
$474$		0			0
$475$	−1.26130	+	0.916391i	−0.0578726	+	0.0420469i
$476$		0			0
$477$	−62.7762	−	45.6096i	−2.87432	−	2.08832i
$478$		0			0
$479$	9.87878	−	30.4038i	0.451373	−	1.38918i	−0.423968	−	0.905677i	$-0.639363\pi$
$479$	9.87878	−	30.4038i	0.451373	−	1.38918i	0.875341	−	0.483506i	$-0.160637\pi$
$480$		0			0
$481$	29.6161	−	21.5174i	1.35038	−	0.981107i
$482$		0			0
$483$	−32.5313			−1.48023
$484$		0			0
$485$	1.45624	+	4.48185i	0.0661245	+	0.203510i
$486$		0			0
$487$	−21.4975	−	15.6188i	−0.974145	−	0.707758i	−0.0177524	−	0.999842i	$-0.505651\pi$
$487$	−21.4975	−	15.6188i	−0.974145	−	0.707758i	−0.956392	+	0.292085i	$0.905651\pi$
$488$		0			0
$489$	−34.3859			−1.55498
$490$		0			0
$491$	13.2757			0.599123			0.299561	−	0.954077i	$-0.403160\pi$
$491$	13.2757			0.599123			0.299561	+	0.954077i	$0.403160\pi$
$492$		0			0
$493$	−35.1010			−1.58087
$494$		0			0
$495$	−5.84210			−0.262583
$496$		0			0
$497$	38.4480	+	27.9341i	1.72463	+	1.25302i
$498$		0			0
$499$	5.55295	+	17.0902i	0.248584	+	0.765064i	0.995026	+	0.0996134i	$0.0317606\pi$
$499$	5.55295	+	17.0902i	0.248584	+	0.765064i	−0.746442	+	0.665451i	$0.768239\pi$
$500$		0			0
$501$	2.52077			0.112620
$502$		0			0
$503$	1.62935	−	1.18379i	0.0726489	−	0.0527825i	−0.550868	−	0.834592i	$-0.685703\pi$
$503$	1.62935	−	1.18379i	0.0726489	−	0.0527825i	0.623517	+	0.781810i	$0.285703\pi$
$504$		0			0
$505$	5.50319	−	16.9371i	0.244889	−	0.753690i
$506$		0			0
$507$	−4.70628	−	3.41931i	−0.209013	−	0.151857i
$508$		0			0
$509$	−12.5096	+	9.08873i	−0.554477	+	0.402851i	−0.829433	−	0.558606i	$-0.811337\pi$
$509$	−12.5096	+	9.08873i	−0.554477	+	0.402851i	0.274956	+	0.961457i	$0.411337\pi$
$510$		0			0
$511$	13.2211	+	40.6902i	0.584865	+	1.80003i
$512$		0			0
$513$	−9.12718	−	28.0906i	−0.402975	−	1.24023i
$514$		0			0
$515$	1.52018	−	4.67863i	0.0669871	−	0.206165i
$516$		0			0
$517$	−0.0795021	−	0.244682i	−0.00349650	−	0.0107611i
$518$		0			0
$519$	8.04309			0.353052
$520$		0			0
$521$	25.0467	+	18.1975i	1.09732	+	0.797246i	0.980620	−	0.195921i	$-0.0627697\pi$
$521$	25.0467	+	18.1975i	1.09732	+	0.797246i	0.116696	+	0.993168i	$0.462770\pi$
$522$		0			0
$523$	13.6981	−	9.95222i	0.598974	−	0.435180i	−0.246540	−	0.969133i	$-0.579294\pi$
$523$	13.6981	−	9.95222i	0.598974	−	0.435180i	0.845515	+	0.533952i	$0.179294\pi$
$524$		0			0
$525$	−13.9341	+	10.1237i	−0.608134	+	0.441835i
$526$		0			0
$527$	10.4720	−	32.2295i	0.456168	−	1.40394i
$528$		0			0
$529$	15.7212	+	11.4222i	0.683532	+	0.496615i
$530$		0			0
$531$	−1.47924	+	4.55264i	−0.0641937	+	0.197568i
$532$		0			0
$533$	20.3971	−	6.84387i	0.883496	−	0.296441i
$534$		0			0
$535$	1.05889	−	3.25894i	0.0457799	−	0.140896i
$536$		0			0
$537$	49.8693	+	36.2322i	2.15202	+	1.56353i
$538$		0			0
$539$	3.92677	−	12.0854i	0.169138	−	0.520553i
$540$		0			0
$541$	−4.15808	+	3.02102i	−0.178770	+	0.129884i	−0.673571	−	0.739122i	$-0.735241\pi$
$541$	−4.15808	+	3.02102i	−0.178770	+	0.129884i	0.494802	+	0.869006i	$0.335241\pi$
$542$		0			0
$543$	−60.4886	+	43.9475i	−2.59581	+	1.88597i
$544$		0			0
$545$	−1.62401	−	1.17991i	−0.0695651	−	0.0505420i
$546$		0			0
$547$	−8.74119			−0.373746			−0.186873	−	0.982384i	$-0.559835\pi$
$547$	−8.74119			−0.373746			−0.186873	+	0.982384i	$0.559835\pi$
$548$		0			0
$549$	12.7175	+	39.1403i	0.542768	+	1.67047i
$550$		0			0
$551$	2.97337	−	9.15109i	0.126670	−	0.389850i
$552$		0			0
$553$	14.4703	+	44.5350i	0.615339	+	1.89382i
$554$		0			0
$555$	11.4517	+	35.2448i	0.486099	+	1.49606i
$556$		0			0
$557$	−3.27824	+	2.38178i	−0.138903	+	0.100919i	−0.655067	−	0.755571i	$-0.727360\pi$
$557$	−3.27824	+	2.38178i	−0.138903	+	0.100919i	0.516164	+	0.856490i	$0.327360\pi$
$558$		0			0
$559$	−15.9712	−	11.6038i	−0.675510	−	0.490786i
$560$		0			0
$561$	4.07532	−	12.5425i	0.172060	−	0.529547i
$562$		0			0
$563$	3.73920	−	2.71669i	0.157589	−	0.114495i	−0.506196	−	0.862418i	$-0.668949\pi$
$563$	3.73920	−	2.71669i	0.157589	−	0.114495i	0.663785	+	0.747923i	$0.268949\pi$
$564$		0			0
$565$	−2.36630			−0.0995510
$566$		0			0
$567$	−60.6034	−	186.518i	−2.54510	−	7.83302i
$568$		0			0
$569$	−24.0610	−	17.4813i	−1.00869	−	0.732855i	−0.0447546	−	0.998998i	$-0.514251\pi$
$569$	−24.0610	−	17.4813i	−1.00869	−	0.732855i	−0.963933	+	0.266143i	$0.914251\pi$
$570$		0			0
$571$	32.6153			1.36491			0.682453	−	0.730929i	$-0.260913\pi$
$571$	32.6153			1.36491			0.682453	+	0.730929i	$0.260913\pi$
$572$		0			0
$573$	78.6576			3.28597
$574$		0			0
$575$	−1.88878			−0.0787674
$576$		0			0
$577$	−1.38673			−0.0577303			−0.0288651	−	0.999583i	$-0.509189\pi$
$577$	−1.38673			−0.0577303			−0.0288651	+	0.999583i	$0.509189\pi$
$578$		0			0
$579$	11.9738	+	8.69949i	0.497615	+	0.361539i
$580$		0			0
$581$	−9.34869	−	28.7723i	−0.387849	−	1.19368i
$582$		0			0
$583$	6.17270			0.255647
$584$		0			0
$585$	−23.2951	+	16.9249i	−0.963135	+	0.699759i
$586$		0			0
$587$	4.20701	−	12.9478i	0.173642	−	0.534415i	−0.825927	−	0.563777i	$-0.809348\pi$
$587$	4.20701	−	12.9478i	0.173642	−	0.534415i	0.999569	+	0.0293625i	$0.00934771\pi$
$588$		0			0
$589$	7.51541	+	5.46026i	0.309667	+	0.224986i
$590$		0			0
$591$	42.2506	−	30.6969i	1.73796	−	1.26270i
$592$		0			0
$593$	11.3623	+	34.9697i	0.466595	+	1.43603i	0.856965	+	0.515374i	$0.172347\pi$
$593$	11.3623	+	34.9697i	0.466595	+	1.43603i	−0.390370	+	0.920658i	$0.627653\pi$
$594$		0			0
$595$	−8.89934	−	27.3893i	−0.364837	−	1.12285i
$596$		0			0
$597$	−19.6563	+	60.4959i	−0.804479	+	2.47593i
$598$		0			0
$599$	−12.9488	−	39.8522i	−0.529072	−	1.62832i	−0.756121	−	0.654432i	$-0.772908\pi$
$599$	−12.9488	−	39.8522i	−0.529072	−	1.62832i	0.227049	−	0.973883i	$-0.427092\pi$
$600$		0			0
$601$	−34.6974			−1.41534			−0.707669	−	0.706544i	$-0.750253\pi$
$601$	−34.6974			−1.41534			−0.707669	+	0.706544i	$0.750253\pi$
$602$		0			0
$603$	−0.487807	−	0.354413i	−0.0198650	−	0.0144328i
$604$		0			0
$605$	−8.52321	+	6.19247i	−0.346518	+	0.251760i
$606$		0			0
$607$	−22.0494	+	16.0198i	−0.894956	+	0.650224i	−0.937165	−	0.348885i	$-0.886560\pi$
$607$	−22.0494	+	16.0198i	−0.894956	+	0.650224i	0.0422095	+	0.999109i	$0.486560\pi$
$608$		0			0
$609$	32.8479	−	101.096i	1.33107	−	4.09660i
$610$		0			0
$611$	−1.02587	−	0.745338i	−0.0415023	−	0.0301532i
$612$		0			0
$613$	−1.90989	+	5.87803i	−0.0771396	+	0.237411i	−0.982189	−	0.187895i	$-0.939834\pi$
$613$	−1.90989	+	5.87803i	−0.0771396	+	0.237411i	0.905050	+	0.425306i	$0.139834\pi$
$614$		0			0
$615$	0.208401	+	21.7788i	0.00840355	+	0.878204i
$616$		0			0
$617$	−1.03527	+	3.18625i	−0.0416786	+	0.128274i	−0.969731	−	0.244177i	$-0.921482\pi$
$617$	−1.03527	+	3.18625i	−0.0416786	+	0.128274i	0.928052	+	0.372450i	$0.121482\pi$
$618$		0			0
$619$	11.6659	+	8.47574i	0.468891	+	0.340669i	0.797009	−	0.603968i	$-0.206414\pi$
$619$	11.6659	+	8.47574i	0.468891	+	0.340669i	−0.328118	+	0.944637i	$0.606414\pi$
$620$		0			0
$621$	11.0575	−	34.0314i	0.443721	−	1.36563i
$622$		0			0
$623$	17.6637	−	12.8334i	0.707679	−	0.514159i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	2.92472	+	2.12493i	0.116802	+	0.0848616i
$628$		0			0
$629$	−61.9645			−2.47069
$630$		0			0
$631$	2.58315	+	7.95013i	0.102834	+	0.316490i	0.989216	−	0.146465i	$-0.0467894\pi$
$631$	2.58315	+	7.95013i	0.102834	+	0.316490i	−0.886382	+	0.462954i	$0.846789\pi$
$632$		0			0
$633$	−17.1580	+	52.8068i	−0.681968	+	2.09888i
$634$		0			0
$635$	1.28324	+	3.94940i	0.0509237	+	0.156727i
$636$		0			0
$637$	−19.3541	−	59.5659i	−0.766839	−	2.36009i
$638$		0			0
$639$	−65.0697	+	47.2759i	−2.57412	+	1.87021i
$640$		0			0
$641$	38.6042	+	28.0476i	1.52477	+	1.10781i	0.959057	+	0.283213i	$0.0914003\pi$
$641$	38.6042	+	28.0476i	1.52477	+	1.10781i	0.565716	+	0.824600i	$0.308600\pi$
$642$		0			0
$643$	−7.53906	+	23.2028i	−0.297312	+	0.915031i	0.685124	+	0.728427i	$0.259748\pi$
$643$	−7.53906	+	23.2028i	−0.297312	+	0.915031i	−0.982435	+	0.186604i	$0.940252\pi$
$644$		0			0
$645$	16.1680	−	11.7467i	0.636614	−	0.462527i
$646$		0			0
$647$	35.2640			1.38637			0.693186	−	0.720758i	$-0.256206\pi$
$647$	35.2640			1.38637			0.693186	+	0.720758i	$0.256206\pi$
$648$		0			0
$649$	−0.117673	−	0.362161i	−0.00461908	−	0.0142161i
$650$		0			0
$651$	83.0256	+	60.3216i	3.25403	+	2.36419i
$652$		0			0
$653$	5.53063			0.216430			0.108215	−	0.994128i	$-0.465486\pi$
$653$	5.53063			0.216430			0.108215	+	0.994128i	$0.465486\pi$
$654$		0			0
$655$	−10.1552			−0.396795
$656$		0			0
$657$	−72.4084			−2.82492
$658$		0			0
$659$	8.41450			0.327783			0.163891	−	0.986478i	$-0.447595\pi$
$659$	8.41450			0.327783			0.163891	+	0.986478i	$0.447595\pi$
$660$		0			0
$661$	8.34586	+	6.06362i	0.324616	+	0.235848i	0.738143	−	0.674645i	$-0.235703\pi$
$661$	8.34586	+	6.06362i	0.324616	+	0.235848i	−0.413526	+	0.910492i	$0.635703\pi$
$662$		0			0
$663$	−20.0863	−	61.8194i	−0.780088	−	2.40086i
$664$		0			0
$665$	7.89446			0.306134
$666$		0			0
$667$	9.43067	−	6.85179i	0.365157	−	0.265302i
$668$		0			0
$669$	−10.6191	+	32.6821i	−0.410557	+	1.26356i
$670$		0			0
$671$	−2.64858	−	1.92431i	−0.102247	−	0.0742871i
$672$		0			0
$673$	10.7058	−	7.77820i	0.412677	−	0.299828i	−0.362007	−	0.932175i	$-0.617909\pi$
$673$	10.7058	−	7.77820i	0.412677	−	0.299828i	0.774685	+	0.632348i	$0.217909\pi$
$674$		0			0
$675$	−5.85430	−	18.0177i	−0.225332	−	0.693501i
$676$		0			0
$677$	−6.98615	−	21.5011i	−0.268499	−	0.826356i	−0.990867	−	0.134846i	$-0.956946\pi$
$677$	−6.98615	−	21.5011i	−0.268499	−	0.826356i	0.722367	−	0.691510i	$-0.243054\pi$
$678$		0			0
$679$	7.37384	−	22.6943i	0.282982	−	0.870929i
$680$		0			0
$681$	−13.7883	−	42.4360i	−0.528368	−	1.62615i
$682$		0			0
$683$	−0.199085			−0.00761776			−0.00380888	−	0.999993i	$-0.501212\pi$
$683$	−0.199085			−0.00761776			−0.00380888	+	0.999993i	$0.501212\pi$
$684$		0			0
$685$	−0.609557	−	0.442869i	−0.0232900	−	0.0169212i
$686$		0			0
$687$	−52.4557	+	38.1113i	−2.00131	+	1.45404i
$688$		0			0
$689$	24.6134	−	17.8827i	0.937696	−	0.681276i
$690$		0			0
$691$	−11.0111	+	33.8886i	−0.418881	+	1.28918i	0.489851	+	0.871806i	$0.337051\pi$
$691$	−11.0111	+	33.8886i	−0.418881	+	1.28918i	−0.908733	+	0.417379i	$0.862949\pi$
$692$		0			0
$693$	23.9324	+	17.3879i	0.909118	+	0.660513i
$694$		0			0
$695$	2.81141	−	8.65264i	0.106643	−	0.328213i
$696$		0			0
$697$	−34.7409	−	10.9216i	−1.31591	−	0.413686i
$698$		0			0
$699$	−22.4023	+	68.9470i	−0.847331	+	2.60782i
$700$		0			0
$701$	8.22393	+	5.97504i	0.310614	+	0.225674i	0.732160	−	0.681133i	$-0.238512\pi$
$701$	8.22393	+	5.97504i	0.310614	+	0.225674i	−0.421546	+	0.906807i	$0.638512\pi$
$702$		0			0
$703$	5.24895	−	16.1546i	0.197968	−	0.609282i
$704$		0			0
$705$	1.03851	−	0.754522i	0.0391126	−	0.0284170i
$706$		0			0
$707$	−72.9541	+	53.0043i	−2.74372	+	1.99343i
$708$		0			0
$709$	15.4671	+	11.2375i	0.580877	+	0.422032i	0.839040	−	0.544069i	$-0.183117\pi$
$709$	15.4671	+	11.2375i	0.580877	+	0.422032i	−0.258163	+	0.966101i	$0.583117\pi$
$710$		0			0
$711$	−79.2501			−2.97211
$712$		0			0
$713$	3.47773	+	10.7034i	0.130242	+	0.400844i
$714$		0			0
$715$	0.707829	−	2.17847i	0.0264713	−	0.0814703i
$716$		0			0
$717$	−6.60548	−	20.3296i	−0.246686	−	0.759222i
$718$		0			0
$719$	7.53990	+	23.2054i	0.281191	+	0.865417i	0.987515	+	0.157528i	$0.0503524\pi$
$719$	7.53990	+	23.2054i	0.281191	+	0.865417i	−0.706324	+	0.707889i	$0.749648\pi$
$720$		0			0
$721$	−20.1526	+	14.6417i	−0.750521	+	0.545285i
$722$		0			0
$723$	58.1205	+	42.2270i	2.16153	+	1.57044i
$724$		0			0
$725$	1.90716	−	5.86963i	0.0708301	−	0.217993i
$726$		0			0
$727$	18.3162	−	13.3075i	0.679310	−	0.493548i	−0.193819	−	0.981037i	$-0.562087\pi$
$727$	18.3162	−	13.3075i	0.679310	−	0.493548i	0.873129	+	0.487490i	$0.162087\pi$
$728$		0			0
$729$	138.590			5.13298
$730$		0			0
$731$	10.3261	+	31.7804i	0.381923	+	1.17544i
$732$		0			0
$733$	−15.1355	−	10.9966i	−0.559042	−	0.406168i	0.272066	−	0.962279i	$-0.412293\pi$
$733$	−15.1355	−	10.9966i	−0.559042	−	0.406168i	−0.831108	+	0.556111i	$0.812293\pi$
$734$		0			0
$735$	63.4031			2.33866
$736$		0			0
$737$	0.0479655			0.00176683
$738$		0			0
$739$	−46.1534			−1.69778			−0.848890	−	0.528569i	$-0.822729\pi$
$739$	−46.1534			−1.69778			−0.848890	+	0.528569i	$0.822729\pi$
$740$		0			0
$741$	17.8183			0.654570
$742$		0			0
$743$	11.6899	+	8.49322i	0.428861	+	0.311586i	0.781193	−	0.624289i	$-0.214611\pi$
$743$	11.6899	+	8.49322i	0.428861	+	0.311586i	−0.352332	+	0.935875i	$0.614611\pi$
$744$		0			0
$745$	−0.0295797	−	0.0910370i	−0.00108372	−	0.00333534i
$746$		0			0
$747$	51.2004			1.87333
$748$		0			0
$749$	−14.0374	+	10.1988i	−0.512917	+	0.372656i
$750$		0			0
$751$	−14.4227	+	44.3885i	−0.526292	+	1.61976i	0.235456	+	0.971885i	$0.424342\pi$
$751$	−14.4227	+	44.3885i	−0.526292	+	1.61976i	−0.761748	+	0.647874i	$0.775658\pi$
$752$		0			0
$753$	4.50950	+	3.27635i	0.164335	+	0.119397i
$754$		0			0
$755$	−9.22344	+	6.70122i	−0.335675	+	0.243883i
$756$		0			0
$757$	−0.0868966	−	0.267440i	−0.00315831	−	0.00972028i	0.949465	−	0.313873i	$-0.101627\pi$
$757$	−0.0868966	−	0.267440i	−0.00315831	−	0.00972028i	−0.952623	+	0.304153i	$0.901627\pi$
$758$		0			0
$759$	1.35340	+	4.16535i	0.0491255	+	0.151193i
$760$		0			0
$761$	5.68699	−	17.5028i	0.206153	−	0.634474i	−0.793511	−	0.608556i	$-0.791749\pi$
$761$	5.68699	−	17.5028i	0.206153	−	0.634474i	0.999664	−	0.0259183i	$-0.00825097\pi$
$762$		0			0
$763$	3.14105	+	9.66715i	0.113714	+	0.349974i
$764$		0			0
$765$	48.7394			1.76218
$766$		0			0
$767$	−1.51842	−	1.10320i	−0.0548270	−	0.0398341i
$768$		0			0
$769$	10.7268	−	7.79350i	0.386820	−	0.281041i	−0.377331	−	0.926078i	$-0.623158\pi$
$769$	10.7268	−	7.79350i	0.386820	−	0.281041i	0.764151	+	0.645037i	$0.223158\pi$
$770$		0			0
$771$	−22.0864	+	16.0467i	−0.795423	+	0.577908i
$772$		0			0
$773$	13.8106	−	42.5046i	0.496732	−	1.52878i	−0.317509	−	0.948255i	$-0.602846\pi$
$773$	13.8106	−	42.5046i	0.496732	−	1.52878i	0.814241	−	0.580527i	$-0.197154\pi$
$774$		0			0
$775$	4.82048	+	3.50229i	0.173157	+	0.125806i
$776$		0			0
$777$	57.9871	−	178.466i	2.08028	−	6.40244i
$778$		0			0
$779$	5.79022	−	8.13206i	0.207456	−	0.291361i
$780$		0			0
$781$	1.97716	−	6.08507i	0.0707483	−	0.217741i
$782$		0			0
$783$	94.5921	+	68.7252i	3.38044	+	2.45604i
$784$		0			0
$785$	−3.87817	+	11.9358i	−0.138418	+	0.426006i
$786$		0			0
$787$	40.6586	−	29.5402i	1.44932	−	1.05300i	0.463336	−	0.886183i	$-0.346652\pi$
$787$	40.6586	−	29.5402i	1.44932	−	1.05300i	0.985989	−	0.166813i	$-0.0533475\pi$
$788$		0			0
$789$	54.2627	−	39.4242i	1.93180	−	1.40354i
$790$		0			0
$791$	9.69366	+	7.04286i	0.344667	+	0.250415i
$792$		0			0
$793$	−16.1360			−0.573005
$794$		0			0
$795$	9.51733	+	29.2913i	0.337545	+	1.03886i
$796$		0			0
$797$	−0.699249	+	2.15207i	−0.0247687	+	0.0762301i	−0.962677	−	0.270654i	$-0.912760\pi$
$797$	−0.699249	+	2.15207i	−0.0247687	+	0.0762301i	0.937908	+	0.346884i	$0.112760\pi$
$798$		0			0
$799$	0.663269	+	2.04133i	0.0234648	+	0.0722171i
$800$		0			0
$801$	11.4185	+	35.1426i	0.403454	+	1.24170i
$802$		0			0
$803$	4.65999	−	3.38568i	0.164447	−	0.119478i
$804$		0			0
$805$	7.73746	+	5.62160i	0.272710	+	0.198135i
$806$		0			0
$807$	−0.0347033	+	0.106806i	−0.00122162	+	0.00375975i
$808$		0			0
$809$	−21.8016	+	15.8398i	−0.766504	+	0.556897i	−0.900898	−	0.434030i	$-0.857091\pi$
$809$	−21.8016	+	15.8398i	−0.766504	+	0.556897i	0.134395	+	0.990928i	$0.457091\pi$
$810$		0			0
$811$	−2.08130			−0.0730844			−0.0365422	−	0.999332i	$-0.511634\pi$
$811$	−2.08130			−0.0730844			−0.0365422	+	0.999332i	$0.511634\pi$
$812$		0			0
$813$	−1.61018	−	4.95563i	−0.0564715	−	0.173801i
$814$		0			0
$815$	8.17856	+	5.94207i	0.286482	+	0.208142i
$816$		0			0
$817$	−9.16009			−0.320471
$818$		0			0
$819$	145.804			5.09479
$820$		0			0
$821$	−48.4974			−1.69257			−0.846286	−	0.532729i	$-0.821167\pi$
$821$	−48.4974			−1.69257			−0.846286	+	0.532729i	$0.821167\pi$
$822$		0			0
$823$	31.9055			1.11215			0.556077	−	0.831131i	$-0.312306\pi$
$823$	31.9055			1.11215			0.556077	+	0.831131i	$0.312306\pi$
$824$		0			0
$825$	1.87595	+	1.36296i	0.0653123	+	0.0474522i
$826$		0			0
$827$	0.894838	+	2.75403i	0.0311166	+	0.0957670i	0.965409	−	0.260742i	$-0.0839671\pi$
$827$	0.894838	+	2.75403i	0.0311166	+	0.0957670i	−0.934292	+	0.356509i	$0.883967\pi$
$828$		0			0
$829$	41.4154			1.43842			0.719208	−	0.694795i	$-0.244505\pi$
$829$	41.4154			1.43842			0.719208	+	0.694795i	$0.244505\pi$
$830$		0			0
$831$	62.8916	−	45.6934i	2.18169	−	1.58509i
$832$		0			0
$833$	−32.7602	+	100.826i	−1.13507	+	3.49340i
$834$		0			0
$835$	−0.599556	−	0.435603i	−0.0207485	−	0.0150747i
$836$		0			0
$837$	−91.3236	+	66.3505i	−3.15661	+	2.29341i
$838$		0			0
$839$	8.20847	+	25.2631i	0.283388	+	0.872179i	0.986877	+	0.161473i	$0.0516244\pi$
$839$	8.20847	+	25.2631i	0.283388	+	0.872179i	−0.703489	+	0.710706i	$0.748376\pi$
$840$		0			0
$841$	2.80891	+	8.64494i	0.0968591	+	0.298102i
$842$		0			0
$843$	13.6311	−	41.9522i	0.469480	−	1.44491i
$844$		0			0
$845$	0.528496	+	1.62654i	0.0181808	+	0.0559547i
$846$		0			0
$847$	53.3465			1.83301
$848$		0			0
$849$	−57.7838	−	41.9824i	−1.98313	−	1.44083i
$850$		0			0
$851$	16.6482	−	12.0956i	0.570692	−	0.414632i
$852$		0			0
$853$	−18.6821	+	13.5734i	−0.639665	+	0.464744i	−0.859735	−	0.510740i	$-0.829371\pi$
$853$	−18.6821	+	13.5734i	−0.639665	+	0.464744i	0.220070	+	0.975484i	$0.429371\pi$
$854$		0			0
$855$	−4.12867	+	12.7067i	−0.141197	+	0.434561i
$856$		0			0
$857$	−14.8075	−	10.7583i	−0.505815	−	0.367496i	0.305419	−	0.952218i	$-0.401203\pi$
$857$	−14.8075	−	10.7583i	−0.505815	−	0.367496i	−0.811234	+	0.584722i	$0.801203\pi$
$858$		0			0
$859$	−11.4063	+	35.1050i	−0.389178	+	1.19777i	0.544226	+	0.838939i	$0.316823\pi$
$859$	−11.4063	+	35.1050i	−0.389178	+	1.19777i	−0.933404	+	0.358827i	$0.883177\pi$
$860$		0			0
$861$	63.9667	−	89.8380i	2.17998	−	3.06167i
$862$		0			0
$863$	1.65703	−	5.09982i	0.0564061	−	0.173600i	−0.918884	−	0.394527i	$-0.870908\pi$
$863$	1.65703	−	5.09982i	0.0564061	−	0.173600i	0.975290	+	0.220927i	$0.0709084\pi$
$864$		0			0
$865$	−1.91302	−	1.38989i	−0.0650446	−	0.0472577i
$866$		0			0
$867$	−16.1309	+	49.6457i	−0.547833	+	1.68606i
$868$		0			0
$869$	5.10030	−	3.70558i	0.173016	−	0.125703i
$870$		0			0
$871$	0.191260	−	0.138959i	0.00648061	−	0.00470844i
$872$		0			0
$873$	32.6719	+	23.7375i	1.10578	+	0.803393i
$874$		0			0
$875$	5.06361			0.171181
$876$		0			0
$877$	6.01552	+	18.5139i	0.203130	+	0.625169i	0.999785	+	0.0207353i	$0.00660071\pi$
$877$	6.01552	+	18.5139i	0.203130	+	0.625169i	−0.796655	+	0.604434i	$0.793399\pi$
$878$		0			0
$879$	7.87050	−	24.2229i	0.265465	−	0.817018i
$880$		0			0
$881$	4.77125	+	14.6844i	0.160747	+	0.494730i	0.998698	−	0.0510167i	$-0.0162462\pi$
$881$	4.77125	+	14.6844i	0.160747	+	0.494730i	−0.837950	+	0.545746i	$0.816246\pi$
$882$		0			0
$883$	−0.835994	−	2.57292i	−0.0281334	−	0.0865858i	0.936004	−	0.351990i	$-0.114495\pi$
$883$	−0.835994	−	2.57292i	−0.0281334	−	0.0865858i	−0.964137	+	0.265404i	$0.914495\pi$
$884$		0			0
$885$	1.53713	−	1.11679i	0.0516701	−	0.0375405i
$886$		0			0
$887$	19.9485	+	14.4935i	0.669806	+	0.486643i	0.869960	−	0.493122i	$-0.164144\pi$
$887$	19.9485	+	14.4935i	0.669806	+	0.486643i	−0.200154	+	0.979764i	$0.564144\pi$
$888$		0			0
$889$	6.49782	−	19.9982i	0.217930	−	0.670719i
$890$		0			0
$891$	−21.3607	+	15.5195i	−0.715610	+	0.519921i
$892$		0			0
$893$	−0.588375			−0.0196892
$894$		0			0
$895$	−5.60012	−	17.2354i	−0.187191	−	0.576116i
$896$		0			0
$897$	17.4639	+	12.6883i	0.583103	+	0.423649i
$898$		0			0
$899$	−36.7737			−1.22647
$900$		0			0
$901$	−51.4976			−1.71563
$902$		0			0
$903$	−101.195			−3.36756
$904$		0			0
$905$	21.9814			0.730685
$906$		0			0
$907$	11.3418	+	8.24032i	0.376599	+	0.273615i	0.759942	−	0.649991i	$-0.225227\pi$
$907$	11.3418	+	8.24032i	0.376599	+	0.273615i	−0.383343	+	0.923606i	$0.625227\pi$
$908$		0			0
$909$	−47.1606	−	145.146i	−1.56422	−	4.81417i
$910$		0			0
$911$	−5.89227			−0.195220			−0.0976098	−	0.995225i	$-0.531120\pi$
$911$	−5.89227			−0.195220			−0.0976098	+	0.995225i	$0.531120\pi$
$912$		0			0
$913$	−3.29510	+	2.39403i	−0.109052	+	0.0792310i
$914$		0			0
$915$	5.04773	−	15.5353i	0.166873	−	0.513581i
$916$		0			0
$917$	41.6011	+	30.2250i	1.37379	+	0.998117i
$918$		0			0
$919$	0.825909	−	0.600058i	0.0272442	−	0.0197941i	−0.574080	−	0.818799i	$-0.694640\pi$
$919$	0.825909	−	0.600058i	0.0272442	−	0.0197941i	0.601324	+	0.799005i	$0.294640\pi$
$920$		0			0
$921$	14.7490	+	45.3928i	0.485996	+	1.49574i
$922$		0			0
$923$	−9.74496	−	29.9919i	−0.320759	−	0.987196i
$924$		0			0
$925$	3.36675	−	10.3618i	0.110698	−	0.340693i
$926$		0			0
$927$	−13.0275	−	40.0944i	−0.427878	−	1.31687i
$928$		0			0
$929$	−40.4358			−1.32666			−0.663328	−	0.748329i	$-0.730857\pi$
$929$	−40.4358			−1.32666			−0.663328	+	0.748329i	$0.730857\pi$
$930$		0			0
$931$	−23.5109	−	17.0817i	−0.770538	−	0.559829i
$932$		0			0
$933$	−30.0018	+	21.7976i	−0.982216	+	0.713621i
$934$		0			0
$935$	−3.13672	+	2.27896i	−0.102582	+	0.0745300i
$936$		0			0
$937$	−7.26941	+	22.3730i	−0.237481	+	0.730893i	0.759301	+	0.650739i	$0.225541\pi$
$937$	−7.26941	+	22.3730i	−0.237481	+	0.730893i	−0.996783	+	0.0801532i	$0.974459\pi$
$938$		0			0
$939$	−28.1625	−	20.4613i	−0.919049	−	0.667728i
$940$		0			0
$941$	3.78720	−	11.6558i	0.123459	−	0.379968i	−0.870158	−	0.492773i	$-0.835983\pi$
$941$	3.78720	−	11.6558i	0.123459	−	0.379968i	0.993617	+	0.112805i	$0.0359835\pi$
$942$		0			0
$943$	11.4659	−	3.84716i	0.373380	−	0.125281i
$944$		0			0
$945$	−29.6439	+	91.2345i	−0.964316	+	2.96786i
$946$		0			0
$947$	18.4368	+	13.3951i	0.599116	+	0.435283i	0.845565	−	0.533873i	$-0.179264\pi$
$947$	18.4368	+	13.3951i	0.599116	+	0.435283i	−0.246449	+	0.969156i	$0.579264\pi$
$948$		0			0
$949$	8.77300	−	27.0005i	0.284784	−	0.876474i
$950$		0			0
$951$	25.1601	−	18.2799i	0.815872	−	0.592766i
$952$		0			0
$953$	34.9081	−	25.3622i	1.13078	−	0.821563i	0.144975	−	0.989435i	$-0.453690\pi$
$953$	34.9081	−	25.3622i	1.13078	−	0.821563i	0.985809	+	0.167873i	$0.0536897\pi$
$954$		0			0
$955$	−18.7084	−	13.5925i	−0.605391	−	0.439842i
$956$		0			0
$957$	−14.3110			−0.462608
$958$		0			0
$959$	1.17896	+	3.62847i	0.0380706	+	0.117169i
$960$		0			0
$961$	1.39152	−	4.28267i	0.0448878	−	0.138151i
$962$		0			0
$963$	−9.07439	−	27.9281i	−0.292418	−	0.899971i
$964$		0			0
$965$	−1.34461	−	4.13829i	−0.0432846	−	0.133216i
$966$		0			0
$967$	28.7208	−	20.8669i	0.923598	−	0.671034i	−0.0208186	−	0.999783i	$-0.506627\pi$
$967$	28.7208	−	20.8669i	0.923598	−	0.671034i	0.944417	+	0.328750i	$0.106627\pi$
$968$		0			0
$969$	−24.4003	−	17.7279i	−0.783851	−	0.569501i
$970$		0			0
$971$	12.0668	−	37.1379i	0.387243	−	1.19181i	−0.547597	−	0.836742i	$-0.684457\pi$
$971$	12.0668	−	37.1379i	0.387243	−	1.19181i	0.934840	−	0.355069i	$-0.115543\pi$
$972$		0			0
$973$	−37.2701	+	27.0783i	−1.19482	+	0.868090i
$974$		0			0
$975$	11.4289			0.366017
$976$		0			0
$977$	9.58655	+	29.5044i	0.306701	+	0.943928i	0.979037	+	0.203682i	$0.0652909\pi$
$977$	9.58655	+	29.5044i	0.306701	+	0.943928i	−0.672336	+	0.740246i	$0.734709\pi$
$978$		0			0
$979$	−2.37807	−	1.72777i	−0.0760033	−	0.0552196i
$980$		0			0
$981$	−17.2027			−0.549241
$982$		0			0
$983$	−11.5781			−0.369284			−0.184642	−	0.982806i	$-0.559112\pi$
$983$	−11.5781			−0.369284			−0.184642	+	0.982806i	$0.559112\pi$
$984$		0			0
$985$	−15.3538			−0.489211
$986$		0			0
$987$	−6.50001			−0.206897
$988$		0			0
$989$	−8.97792	−	6.52284i	−0.285481	−	0.207414i
$990$		0			0
$991$	16.6977	+	51.3904i	0.530421	+	1.63247i	0.753339	+	0.657632i	$0.228442\pi$
$991$	16.6977	+	51.3904i	0.530421	+	1.63247i	−0.222918	+	0.974837i	$0.571558\pi$
$992$		0			0
$993$	28.3781			0.900553
$994$		0			0
$995$	15.1292	−	10.9920i	0.479628	−	0.348470i
$996$		0			0
$997$	13.8108	−	42.5054i	0.437393	−	1.34616i	−0.453220	−	0.891398i	$-0.649725\pi$
$997$	13.8108	−	42.5054i	0.437393	−	1.34616i	0.890614	−	0.454760i	$-0.150275\pi$
$998$		0			0
$999$	166.985	+	121.322i	5.28318	+	3.83846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.b.221.1	yes	32
41.18	even	5	inner	820.2.u.b.141.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.b.141.1	✓	32	41.18	even	5	inner
820.2.u.b.221.1	yes	32	1.1	even	1	trivial

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.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-3.40143 q^{3} +(0.809017 + 0.587785i) q^{5} +(-1.56474 - 4.81578i) q^{7} +8.56970 q^{9} +(-0.551520 + 0.400703i) q^{11} +(-1.03830 + 3.19557i) q^{13} +(-2.75181 - 1.99931i) q^{15} +(4.60122 - 3.34298i) q^{17} +(0.481775 + 1.48275i) q^{19} +(5.32235 + 16.3805i) q^{21} +(-0.583664 + 1.79633i) q^{23} +(0.309017 + 0.951057i) q^{25} -18.9449 q^{27} +(-4.99301 - 3.62763i) q^{29} +(4.82048 - 3.50229i) q^{31} +(1.87595 - 1.36296i) q^{33} +(1.56474 - 4.81578i) q^{35} +(-8.81426 - 6.40393i) q^{37} +(3.53171 - 10.8695i) q^{39} +(-3.81306 - 5.14399i) q^{41} +(-1.81560 + 5.58784i) q^{43} +(6.93303 + 5.03714i) q^{45} +(-0.116620 + 0.358921i) q^{47} +(-15.0802 + 10.9564i) q^{49} +(-15.6507 + 11.3709i) q^{51} +(-7.32537 - 5.32219i) q^{53} -0.681716 q^{55} +(-1.63872 - 5.04347i) q^{57} +(-0.172613 + 0.531249i) q^{59} +(1.48400 + 4.56729i) q^{61} +(-13.4094 - 41.2698i) q^{63} +(-2.71832 + 1.97497i) q^{65} +(-0.0569224 - 0.0413565i) q^{67} +(1.98529 - 6.11009i) q^{69} +(-7.59300 + 5.51664i) q^{71} -8.44935 q^{73} +(-1.05110 - 3.23495i) q^{75} +(2.79268 + 2.02900i) q^{77} -9.24771 q^{79} +38.7306 q^{81} +5.97459 q^{83} +5.68742 q^{85} +(16.9833 + 12.3391i) q^{87} +(1.33243 + 4.10080i) q^{89} +17.0138 q^{91} +(-16.3965 + 11.9128i) q^{93} +(-0.481775 + 1.48275i) q^{95} +(3.81249 + 2.76994i) q^{97} +(-4.72636 + 3.43390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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