LMFDB - Embedded newform 52.3.k.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,3,Mod(33,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(12))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("52.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	52.k (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.41689737467$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.44991500544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 38x^{6} + 555x^{4} - 3674x^{2} + 9409 $ x^8 - 38x^6 + 555x^4 - 3674*x^2 + 9409
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.2
Root			$3.38852 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	52.37
Dual form			52.3.k.a.45.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26125 + 2.18454i) q^{3} +(1.55727 + 1.55727i) q^{5} +(0.895221 + 3.34101i) q^{7} +(1.31852 - 2.28374i) q^{9} +O(q^{10})$	\(q+(1.26125 + 2.18454i) q^{3} +(1.55727 + 1.55727i) q^{5} +(0.895221 + 3.34101i) q^{7} +(1.31852 - 2.28374i) q^{9} +(-1.53225 - 0.410566i) q^{11} +(-1.43306 - 12.9208i) q^{13} +(-1.43782 + 5.36603i) q^{15} +(-22.9609 - 13.2565i) q^{17} +(3.34407 - 0.896040i) q^{19} +(-6.16948 + 6.16948i) q^{21} +(-15.6971 + 9.06271i) q^{23} -20.1498i q^{25} +29.3543 q^{27} +(4.04930 + 7.01360i) q^{29} +(30.2741 + 30.2741i) q^{31} +(-1.03565 - 3.86510i) q^{33} +(-3.80875 + 6.59696i) q^{35} +(38.5190 + 10.3211i) q^{37} +(26.4185 - 19.4268i) q^{39} +(-12.3480 + 46.0834i) q^{41} +(-41.4488 - 23.9305i) q^{43} +(5.60969 - 1.50311i) q^{45} +(-60.4301 + 60.4301i) q^{47} +(32.0743 - 18.5181i) q^{49} -66.8787i q^{51} -1.63636 q^{53} +(-1.74677 - 3.02550i) q^{55} +(6.17513 + 6.17513i) q^{57} +(-25.0984 - 93.6684i) q^{59} +(-20.8494 + 36.1121i) q^{61} +(8.81035 + 2.36073i) q^{63} +(17.8895 - 22.3528i) q^{65} +(6.99938 - 26.1220i) q^{67} +(-39.5958 - 22.8606i) q^{69} +(-93.5282 + 25.0608i) q^{71} +(-73.5977 + 73.5977i) q^{73} +(44.0181 - 25.4139i) q^{75} -5.48682i q^{77} +82.5905 q^{79} +(25.1564 + 43.5721i) q^{81} +(34.5538 + 34.5538i) q^{83} +(-15.1124 - 56.4003i) q^{85} +(-10.2143 + 17.6918i) q^{87} +(128.847 + 34.5244i) q^{89} +(41.8855 - 16.3548i) q^{91} +(-27.9519 + 104.318i) q^{93} +(6.60300 + 3.81224i) q^{95} +(67.6244 - 18.1199i) q^{97} +(-2.95793 + 2.95793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 8 * q + 6 * q^5 + 4 * q^7 - 6 * q^9	$ 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9} + 24 q^{11} + 18 q^{13} - 60 q^{15} - 54 q^{17} - 50 q^{19} - 54 q^{21} - 24 q^{23} + 36 q^{27} + 108 q^{29} + 176 q^{31} + 114 q^{33} - 30 q^{35} + 104 q^{37} + 120 q^{39} - 168 q^{41} - 198 q^{43} + 6 q^{45} - 96 q^{47} - 162 q^{49} - 72 q^{53} + 126 q^{55} + 318 q^{57} - 18 q^{61} + 180 q^{63} - 72 q^{65} - 326 q^{67} - 498 q^{69} - 162 q^{71} - 98 q^{73} - 240 q^{75} + 192 q^{79} + 240 q^{81} + 408 q^{83} + 318 q^{85} + 36 q^{87} + 54 q^{89} + 280 q^{91} - 66 q^{93} + 312 q^{95} + 182 q^{97}+O(q^{100}) $ 8 * q + 6 * q^5 + 4 * q^7 - 6 * q^9 + 24 * q^11 + 18 * q^13 - 60 * q^15 - 54 * q^17 - 50 * q^19 - 54 * q^21 - 24 * q^23 + 36 * q^27 + 108 * q^29 + 176 * q^31 + 114 * q^33 - 30 * q^35 + 104 * q^37 + 120 * q^39 - 168 * q^41 - 198 * q^43 + 6 * q^45 - 96 * q^47 - 162 * q^49 - 72 * q^53 + 126 * q^55 + 318 * q^57 - 18 * q^61 + 180 * q^63 - 72 * q^65 - 326 * q^67 - 498 * q^69 - 162 * q^71 - 98 * q^73 - 240 * q^75 + 192 * q^79 + 240 * q^81 + 408 * q^83 + 318 * q^85 + 36 * q^87 + 54 * q^89 + 280 * q^91 - 66 * q^93 + 312 * q^95 + 182 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$

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
$3$	1.26125	+	2.18454i	0.420415	+	0.728181i	0.995980	−	0.0895755i	$-0.0285510\pi$
$3$	1.26125	+	2.18454i	0.420415	+	0.728181i	−0.575565	+	0.817756i	$0.695218\pi$
$4$		0			0
$5$	1.55727	+	1.55727i	0.311454	+	0.311454i	0.845473	−	0.534019i	$-0.179319\pi$
$5$	1.55727	+	1.55727i	0.311454	+	0.311454i	−0.534019	+	0.845473i	$0.679319\pi$
$6$		0			0
$7$	0.895221	+	3.34101i	0.127889	+	0.477287i	0.999926	−	0.0121521i	$-0.00386822\pi$
$7$	0.895221	+	3.34101i	0.127889	+	0.477287i	−0.872037	+	0.489439i	$0.837202\pi$
$8$		0			0
$9$	1.31852	−	2.28374i	0.146502	−	0.253749i
$10$		0			0
$11$	−1.53225	−	0.410566i	−0.139296	−	0.0373242i	0.188497	−	0.982074i	$-0.439638\pi$
$11$	−1.53225	−	0.410566i	−0.139296	−	0.0373242i	−0.327793	+	0.944749i	$0.606305\pi$
$12$		0			0
$13$	−1.43306	−	12.9208i	−0.110235	−	0.993906i
$13$	−1.43306	−	12.9208i	−0.110235	−	0.993906i
$14$		0			0
$15$	−1.43782	+	5.36603i	−0.0958548	+	0.357735i
$16$		0			0
$17$	−22.9609	−	13.2565i	−1.35064	−	0.779793i	−0.362302	−	0.932061i	$-0.618009\pi$
$17$	−22.9609	−	13.2565i	−1.35064	−	0.779793i	−0.988339	+	0.152268i	$0.951342\pi$
$18$		0			0
$19$	3.34407	−	0.896040i	0.176004	−	0.0471600i	−0.169741	−	0.985489i	$-0.554293\pi$
$19$	3.34407	−	0.896040i	0.176004	−	0.0471600i	0.345744	+	0.938329i	$0.387626\pi$
$20$		0			0
$21$	−6.16948	+	6.16948i	−0.293785	+	0.293785i
$22$		0			0
$23$	−15.6971	+	9.06271i	−0.682482	+	0.394031i	−0.800789	−	0.598946i	$-0.795586\pi$
$23$	−15.6971	+	9.06271i	−0.682482	+	0.394031i	0.118308	+	0.992977i	$0.462253\pi$
$24$		0			0
$25$		−	20.1498i		−	0.805993i
$26$		0			0
$27$	29.3543			1.08720
$28$		0			0
$29$	4.04930	+	7.01360i	0.139631	+	0.241848i	0.927357	−	0.374178i	$-0.122075\pi$
$29$	4.04930	+	7.01360i	0.139631	+	0.241848i	−0.787726	+	0.616026i	$0.788742\pi$
$30$		0			0
$31$	30.2741	+	30.2741i	0.976583	+	0.976583i	0.999732	−	0.0231492i	$-0.00736928\pi$
$31$	30.2741	+	30.2741i	0.976583	+	0.976583i	−0.0231492	+	0.999732i	$0.507369\pi$
$32$		0			0
$33$	−1.03565	−	3.86510i	−0.0313833	−	0.117124i
$34$		0			0
$35$	−3.80875	+	6.59696i	−0.108822	+	0.188484i
$36$		0			0
$37$	38.5190	+	10.3211i	1.04105	+	0.278950i	0.738550	−	0.674199i	$-0.235511\pi$
$37$	38.5190	+	10.3211i	1.04105	+	0.278950i	0.302504	+	0.953148i	$0.402178\pi$
$38$		0			0
$39$	26.4185	−	19.4268i	0.677398	−	0.498124i
$40$		0			0
$41$	−12.3480	+	46.0834i	−0.301171	+	1.12399i	0.635021	+	0.772495i	$0.280992\pi$
$41$	−12.3480	+	46.0834i	−0.301171	+	1.12399i	−0.936192	+	0.351490i	$0.885675\pi$
$42$		0			0
$43$	−41.4488	−	23.9305i	−0.963926	−	0.556523i	−0.0665471	−	0.997783i	$-0.521198\pi$
$43$	−41.4488	−	23.9305i	−0.963926	−	0.556523i	−0.897379	+	0.441260i	$0.854532\pi$
$44$		0			0
$45$	5.60969	−	1.50311i	0.124660	−	0.0334025i
$46$		0			0
$47$	−60.4301	+	60.4301i	−1.28575	+	1.28575i	−0.348402	+	0.937345i	$0.613275\pi$
$47$	−60.4301	+	60.4301i	−1.28575	+	1.28575i	−0.937345	+	0.348402i	$0.886725\pi$
$48$		0			0
$49$	32.0743	−	18.5181i	0.654578	−	0.377921i
$50$		0			0
$51$		−	66.8787i		−	1.31135i
$52$		0			0
$53$	−1.63636			−0.0308747			−0.0154374	−	0.999881i	$-0.504914\pi$
$53$	−1.63636			−0.0308747			−0.0154374	+	0.999881i	$0.504914\pi$
$54$		0			0
$55$	−1.74677	−	3.02550i	−0.0317595	−	0.0550091i
$56$		0			0
$57$	6.17513	+	6.17513i	0.108336	+	0.108336i
$58$		0			0
$59$	−25.0984	−	93.6684i	−0.425396	−	1.58760i	−0.763056	−	0.646332i	$-0.776302\pi$
$59$	−25.0984	−	93.6684i	−0.425396	−	1.58760i	0.337660	−	0.941268i	$-0.390365\pi$
$60$		0			0
$61$	−20.8494	+	36.1121i	−0.341793	+	0.592002i	−0.984766	−	0.173887i	$-0.944367\pi$
$61$	−20.8494	+	36.1121i	−0.341793	+	0.592002i	0.642973	+	0.765889i	$0.277701\pi$
$62$		0			0
$63$	8.81035	+	2.36073i	0.139847	+	0.0374719i
$64$		0			0
$65$	17.8895	−	22.3528i	0.275223	−	0.343889i
$66$		0			0
$67$	6.99938	−	26.1220i	0.104468	−	0.389881i	−0.893816	−	0.448434i	$-0.851982\pi$
$67$	6.99938	−	26.1220i	0.104468	−	0.389881i	0.998284	+	0.0585528i	$0.0186486\pi$
$68$		0			0
$69$	−39.5958	−	22.8606i	−0.573852	−	0.331313i
$70$		0			0
$71$	−93.5282	+	25.0608i	−1.31730	+	0.352969i	−0.847965	−	0.530052i	$-0.822172\pi$
$71$	−93.5282	+	25.0608i	−1.31730	+	0.352969i	−0.469333	+	0.883021i	$0.655506\pi$
$72$		0			0
$73$	−73.5977	+	73.5977i	−1.00819	+	1.00819i	−0.00822113	+	0.999966i	$0.502617\pi$
$73$	−73.5977	+	73.5977i	−1.00819	+	1.00819i	−0.999966	+	0.00822113i	$0.997383\pi$
$74$		0			0
$75$	44.0181	−	25.4139i	0.586908	−	0.338852i
$76$		0			0
$77$		−	5.48682i		−	0.0712574i
$78$		0			0
$79$	82.5905			1.04545			0.522724	−	0.852502i	$-0.324916\pi$
$79$	82.5905			1.04545			0.522724	+	0.852502i	$0.324916\pi$
$80$		0			0
$81$	25.1564	+	43.5721i	0.310573	+	0.537927i
$82$		0			0
$83$	34.5538	+	34.5538i	0.416311	+	0.416311i	0.883930	−	0.467619i	$-0.154888\pi$
$83$	34.5538	+	34.5538i	0.416311	+	0.416311i	−0.467619	+	0.883930i	$0.654888\pi$
$84$		0			0
$85$	−15.1124	−	56.4003i	−0.177793	−	0.663533i
$86$		0			0
$87$	−10.2143	+	17.6918i	−0.117406	+	0.203353i
$88$		0			0
$89$	128.847	+	34.5244i	1.44772	+	0.387915i	0.895230	−	0.445605i	$-0.147012\pi$
$89$	128.847	+	34.5244i	1.44772	+	0.387915i	0.552489	+	0.833520i	$0.313678\pi$
$90$		0			0
$91$	41.8855	−	16.3548i	0.460280	−	0.179723i
$92$		0			0
$93$	−27.9519	+	104.318i	−0.300558	+	1.12170i
$94$		0			0
$95$	6.60300	+	3.81224i	0.0695052	+	0.0401289i
$96$		0			0
$97$	67.6244	−	18.1199i	0.697158	−	0.186803i	0.107201	−	0.994237i	$-0.465811\pi$
$97$	67.6244	−	18.1199i	0.697158	−	0.186803i	0.589957	+	0.807434i	$0.299145\pi$
$98$		0			0
$99$	−2.95793	+	2.95793i	−0.0298781	+	0.0298781i
$100$		0			0
$101$	49.6106	−	28.6427i	0.491194	−	0.283591i	−0.233876	−	0.972266i	$-0.575141\pi$
$101$	49.6106	−	28.6427i	0.491194	−	0.283591i	0.725070	+	0.688676i	$0.241808\pi$
$102$		0			0
$103$			43.2990i			0.420378i	0.977661	+	0.210189i	$0.0674080\pi$
$103$			43.2990i			0.420378i	−0.977661	+	0.210189i	$0.932592\pi$
$104$		0			0
$105$	−19.2151			−0.183001
$106$		0			0
$107$	−26.2568	−	45.4781i	−0.245390	−	0.425029i	0.716851	−	0.697226i	$-0.245583\pi$
$107$	−26.2568	−	45.4781i	−0.245390	−	0.425029i	−0.962241	+	0.272198i	$0.912249\pi$
$108$		0			0
$109$	−39.4413	−	39.4413i	−0.361847	−	0.361847i	0.502646	−	0.864493i	$-0.332360\pi$
$109$	−39.4413	−	39.4413i	−0.361847	−	0.361847i	−0.864493	+	0.502646i	$0.832360\pi$
$110$		0			0
$111$	26.0350	+	97.1639i	0.234549	+	0.875350i
$112$		0			0
$113$	−19.3343	+	33.4879i	−0.171100	+	0.296353i	−0.938805	−	0.344450i	$-0.888065\pi$
$113$	−19.3343	+	33.4879i	−0.171100	+	0.296353i	0.767705	+	0.640803i	$0.221399\pi$
$114$		0			0
$115$	−38.5577	−	10.3315i	−0.335284	−	0.0898392i
$116$		0			0
$117$	−31.3972	−	13.7635i	−0.268352	−	0.117637i
$118$		0			0
$119$	23.7350	−	88.5801i	0.199453	−	0.744370i
$120$		0			0
$121$	−102.610	−	59.2418i	−0.848015	−	0.489602i
$122$		0			0
$123$	−116.245	+	31.1478i	−0.945082	+	0.253234i
$124$		0			0
$125$	70.3105	−	70.3105i	0.562484	−	0.562484i
$126$		0			0
$127$	−146.563	+	84.6181i	−1.15404	+	0.666285i	−0.949868	−	0.312651i	$-0.898783\pi$
$127$	−146.563	+	84.6181i	−1.15404	+	0.666285i	−0.204171	+	0.978935i	$0.565450\pi$
$128$		0			0
$129$		−	120.729i		−	0.935883i
$130$		0			0
$131$	17.6975			0.135096			0.0675478	−	0.997716i	$-0.478482\pi$
$131$	17.6975			0.135096			0.0675478	+	0.997716i	$0.478482\pi$
$132$		0			0
$133$	5.98736	+	10.3704i	0.0450177	+	0.0779730i
$134$		0			0
$135$	45.7126	+	45.7126i	0.338612	+	0.338612i
$136$		0			0
$137$	−16.3478	−	61.0107i	−0.119327	−	0.445334i	0.880247	−	0.474515i	$-0.157377\pi$
$137$	−16.3478	−	61.0107i	−0.119327	−	0.445334i	−0.999574	+	0.0291815i	$0.990710\pi$
$138$		0			0
$139$	71.1875	−	123.300i	0.512140	−	0.887053i	−0.487760	−	0.872978i	$-0.662186\pi$
$139$	71.1875	−	123.300i	0.512140	−	0.887053i	0.999901	−	0.0140758i	$-0.00448062\pi$
$140$		0			0
$141$	−208.229	−	55.7949i	−1.47680	−	0.395708i
$142$		0			0
$143$	−3.10902	+	20.3863i	−0.0217414	+	0.142561i
$144$		0			0
$145$	−4.61621	+	17.2279i	−0.0318359	+	0.118813i
$146$		0			0
$147$	80.9072	+	46.7118i	0.550389	+	0.317767i
$148$		0			0
$149$	229.982	−	61.6236i	1.54351	−	0.413581i	0.616109	−	0.787661i	$-0.288708\pi$
$149$	229.982	−	61.6236i	1.54351	−	0.413581i	0.927397	+	0.374080i	$0.122041\pi$
$150$		0			0
$151$	31.6723	−	31.6723i	0.209750	−	0.209750i	−0.594411	−	0.804161i	$-0.702615\pi$
$151$	31.6723	−	31.6723i	0.209750	−	0.209750i	0.804161	+	0.594411i	$0.202615\pi$
$152$		0			0
$153$	−60.5487	+	34.9578i	−0.395743	+	0.228482i
$154$		0			0
$155$			94.2898i			0.608322i
$156$		0			0
$157$	−110.702			−0.705110			−0.352555	−	0.935791i	$-0.614687\pi$
$157$	−110.702			−0.705110			−0.352555	+	0.935791i	$0.614687\pi$
$158$		0			0
$159$	−2.06385	−	3.57470i	−0.0129802	−	0.0224824i
$160$		0			0
$161$	−44.3310	−	44.3310i	−0.275348	−	0.275348i
$162$		0			0
$163$	76.2623	+	284.615i	0.467867	+	1.74610i	0.647205	+	0.762316i	$0.275938\pi$
$163$	76.2623	+	284.615i	0.467867	+	1.74610i	−0.179338	+	0.983788i	$0.557396\pi$
$164$		0			0
$165$	4.40622	−	7.63179i	0.0267044	−	0.0462533i
$166$		0			0
$167$	33.9173	+	9.08811i	0.203097	+	0.0544198i	0.358933	−	0.933363i	$-0.383140\pi$
$167$	33.9173	+	9.08811i	0.203097	+	0.0544198i	−0.155836	+	0.987783i	$0.549807\pi$
$168$		0			0
$169$	−164.893	+	37.0324i	−0.975696	+	0.219127i
$170$		0			0
$171$	2.36289	−	8.81842i	0.0138181	−	0.0515697i
$172$		0			0
$173$	200.792	+	115.928i	1.16065	+	0.670101i	0.951460	−	0.307774i	$-0.0995839\pi$
$173$	200.792	+	115.928i	1.16065	+	0.670101i	0.209190	+	0.977875i	$0.432917\pi$
$174$		0			0
$175$	67.3207	−	18.0385i	0.384690	−	0.103077i
$176$		0			0
$177$	172.967	−	172.967i	0.977217	−	0.977217i
$178$		0			0
$179$	33.6924	−	19.4523i	0.188226	−	0.108672i	−0.402926	−	0.915233i	$-0.632007\pi$
$179$	33.6924	−	19.4523i	0.188226	−	0.108672i	0.591152	+	0.806560i	$0.298673\pi$
$180$		0			0
$181$			183.696i			1.01490i	0.861682	+	0.507449i	$0.169411\pi$
$181$			183.696i			1.01490i	−0.861682	+	0.507449i	$0.830589\pi$
$182$		0			0
$183$	−105.185			−0.574779
$184$		0			0
$185$	43.9117	+	76.0573i	0.237361	+	0.411121i
$186$		0			0
$187$	29.7393	+	29.7393i	0.159034	+	0.159034i
$188$		0			0
$189$	26.2786	+	98.0731i	0.139040	+	0.518905i
$190$		0			0
$191$	79.4850	−	137.672i	0.416152	−	0.720796i	−0.579397	−	0.815046i	$-0.696712\pi$
$191$	79.4850	−	137.672i	0.416152	−	0.720796i	0.995549	+	0.0942495i	$0.0300452\pi$
$192$		0			0
$193$	−57.3924	−	15.3782i	−0.297370	−	0.0796800i	0.107049	−	0.994254i	$-0.465860\pi$
$193$	−57.3924	−	15.3782i	−0.297370	−	0.0796800i	−0.404419	+	0.914574i	$0.632526\pi$
$194$		0			0
$195$	71.3937	+	10.8879i	0.366121	+	0.0558356i
$196$		0			0
$197$	45.3531	−	169.260i	0.230219	−	0.859189i	−0.750027	−	0.661407i	$-0.769960\pi$
$197$	45.3531	−	169.260i	0.230219	−	0.859189i	0.980246	−	0.197782i	$-0.0633737\pi$
$198$		0			0
$199$	126.931	+	73.2836i	0.637844	+	0.368260i	0.783784	−	0.621034i	$-0.213287\pi$
$199$	126.931	+	73.2836i	0.637844	+	0.368260i	−0.145939	+	0.989294i	$0.546620\pi$
$200$		0			0
$201$	65.8926	−	17.6559i	0.327824	−	0.0878402i
$202$		0			0
$203$	−19.8075	+	19.8075i	−0.0975738	+	0.0975738i
$204$		0			0
$205$	−90.9935	+	52.5351i	−0.443871	+	0.256269i
$206$		0			0
$207$			47.7974i			0.230905i
$208$		0			0
$209$	−5.49185			−0.0262768
$210$		0			0
$211$	−130.454	−	225.953i	−0.618264	−	1.07087i	−0.989802	−	0.142448i	$-0.954503\pi$
$211$	−130.454	−	225.953i	−0.618264	−	1.07087i	0.371538	−	0.928418i	$-0.378831\pi$
$212$		0			0
$213$	−172.708	−	172.708i	−0.810838	−	0.810838i
$214$		0			0
$215$	−27.2808	−	101.813i	−0.126887	−	0.473550i
$216$		0			0
$217$	−74.0440	+	128.248i	−0.341216	+	0.591004i
$218$		0			0
$219$	−253.602	−	67.9525i	−1.15800	−	0.310285i
$220$		0			0
$221$	−138.380	+	315.670i	−0.626152	+	1.42837i
$222$		0			0
$223$	56.4389	−	210.633i	0.253089	−	0.944541i	−0.716054	−	0.698044i	$-0.754054\pi$
$223$	56.4389	−	210.633i	0.253089	−	0.944541i	0.969144	−	0.246497i	$-0.0792796\pi$
$224$		0			0
$225$	−46.0169	−	26.5679i	−0.204520	−	0.118079i
$226$		0			0
$227$	−346.219	+	92.7692i	−1.52520	+	0.408675i	−0.921448	−	0.388501i	$-0.872993\pi$
$227$	−346.219	+	92.7692i	−1.52520	+	0.408675i	−0.603747	+	0.797176i	$0.706326\pi$
$228$		0			0
$229$	284.994	−	284.994i	1.24451	−	1.24451i	0.286405	−	0.958109i	$-0.407540\pi$
$229$	284.994	−	284.994i	1.24451	−	1.24451i	0.958109	−	0.286405i	$-0.0924601\pi$
$230$		0			0
$231$	11.9862	−	6.92023i	0.0518883	−	0.0299577i
$232$		0			0
$233$			167.229i			0.717721i	0.933391	+	0.358860i	$0.116835\pi$
$233$			167.229i			0.717721i	−0.933391	+	0.358860i	$0.883165\pi$
$234$		0			0
$235$	−188.212			−0.800902
$236$		0			0
$237$	104.167	+	180.422i	0.439523	+	0.761276i
$238$		0			0
$239$	−281.704	−	281.704i	−1.17868	−	1.17868i	−0.980082	−	0.198595i	$-0.936362\pi$
$239$	−281.704	−	281.704i	−1.17868	−	1.17868i	−0.198595	−	0.980082i	$-0.563638\pi$
$240$		0			0
$241$	−33.6975	−	125.761i	−0.139824	−	0.521829i	−0.999931	−	0.0117165i	$-0.996270\pi$
$241$	−33.6975	−	125.761i	−0.139824	−	0.521829i	0.860108	−	0.510112i	$-0.170396\pi$
$242$		0			0
$243$	68.6377	−	118.884i	0.282460	−	0.489235i
$244$		0			0
$245$	78.7861	+	21.1107i	0.321576	+	0.0861660i
$246$		0			0
$247$	−16.3698	−	41.9239i	−0.0662744	−	0.169732i
$248$		0			0
$249$	−31.9034	+	119.065i	−0.128126	+	0.478173i
$250$		0			0
$251$	383.045	+	221.151i	1.52608	+	0.881081i	0.999521	+	0.0309396i	$0.00984994\pi$
$251$	383.045	+	221.151i	1.52608	+	0.881081i	0.526555	+	0.850141i	$0.323483\pi$
$252$		0			0
$253$	27.7728	−	7.44169i	0.109774	−	0.0294138i
$254$		0			0
$255$	104.148	−	104.148i	0.408425	−	0.408425i
$256$		0			0
$257$	295.431	−	170.567i	1.14954	−	0.663685i	0.200762	−	0.979640i	$-0.435658\pi$
$257$	295.431	−	170.567i	1.14954	−	0.663685i	0.948774	+	0.315955i	$0.102325\pi$
$258$		0			0
$259$			137.932i			0.532556i
$260$		0			0
$261$	21.3563			0.0818249
$262$		0			0
$263$	−251.804	−	436.137i	−0.957429	−	1.65832i	−0.728709	−	0.684824i	$-0.759879\pi$
$263$	−251.804	−	436.137i	−0.957429	−	1.65832i	−0.228720	−	0.973492i	$-0.573454\pi$
$264$		0			0
$265$	−2.54826	−	2.54826i	−0.00961606	−	0.00961606i
$266$		0			0
$267$	87.0876	+	325.015i	0.326171	+	1.21729i
$268$		0			0
$269$	−178.230	+	308.703i	−0.662564	+	1.14759i	0.317376	+	0.948300i	$0.397198\pi$
$269$	−178.230	+	308.703i	−0.662564	+	1.14759i	−0.979940	+	0.199294i	$0.936135\pi$
$270$		0			0
$271$	164.253	+	44.0115i	0.606100	+	0.162404i	0.548801	−	0.835953i	$-0.315084\pi$
$271$	164.253	+	44.0115i	0.606100	+	0.162404i	0.0572991	+	0.998357i	$0.481751\pi$
$272$		0			0
$273$	88.5557	+	70.8732i	0.324380	+	0.259609i
$274$		0			0
$275$	−8.27284	+	30.8746i	−0.0300830	+	0.112271i
$276$		0			0
$277$	131.478	+	75.9091i	0.474652	+	0.274040i	0.718185	−	0.695852i	$-0.244973\pi$
$277$	131.478	+	75.9091i	0.474652	+	0.274040i	−0.243533	+	0.969893i	$0.578307\pi$
$278$		0			0
$279$	109.055	−	29.2212i	0.390878	−	0.104735i
$280$		0			0
$281$	−172.706	+	172.706i	−0.614612	+	0.614612i	−0.944144	−	0.329532i	$-0.893109\pi$
$281$	−172.706	+	172.706i	−0.614612	+	0.614612i	0.329532	+	0.944144i	$0.393109\pi$
$282$		0			0
$283$	24.0794	−	13.9022i	0.0850861	−	0.0491245i	−0.456853	−	0.889542i	$-0.651024\pi$
$283$	24.0794	−	13.9022i	0.0850861	−	0.0491245i	0.541939	+	0.840418i	$0.317690\pi$
$284$		0			0
$285$			19.2327i			0.0674832i
$286$		0			0
$287$	−165.019			−0.574980
$288$		0			0
$289$	206.969	+	358.480i	0.716154	+	1.24042i
$290$		0			0
$291$	124.875	+	124.875i	0.429122	+	0.429122i
$292$		0			0
$293$	−77.4105	−	288.900i	−0.264200	−	0.986006i	−0.962738	−	0.270434i	$-0.912833\pi$
$293$	−77.4105	−	288.900i	−0.264200	−	0.986006i	0.698539	−	0.715572i	$-0.253834\pi$
$294$		0			0
$295$	106.782	−	184.952i	0.361973	−	0.626956i
$296$		0			0
$297$	−44.9783	−	12.0519i	−0.151442	−	0.0405788i
$298$		0			0
$299$	139.592	+	189.831i	0.466863	+	0.634886i
$300$		0			0
$301$	42.8461	−	159.904i	0.142346	−	0.531242i
$302$		0			0
$303$	125.142	+	72.2509i	0.413011	+	0.238452i
$304$		0			0
$305$	−88.7045	+	23.7683i	−0.290834	+	0.0779288i
$306$		0			0
$307$	1.05825	−	1.05825i	0.00344706	−	0.00344706i	−0.705381	−	0.708828i	$-0.749224\pi$
$307$	1.05825	−	1.05825i	0.00344706	−	0.00344706i	0.708828	+	0.705381i	$0.249224\pi$
$308$		0			0
$309$	−94.5884	+	54.6106i	−0.306111	+	0.176733i
$310$		0			0
$311$			207.852i			0.668336i	0.942514	+	0.334168i	$0.108455\pi$
$311$			207.852i			0.668336i	−0.942514	+	0.334168i	$0.891545\pi$
$312$		0			0
$313$	208.884			0.667362			0.333681	−	0.942686i	$-0.391709\pi$
$313$	208.884			0.667362			0.333681	+	0.942686i	$0.391709\pi$
$314$		0			0
$315$	10.0438	+	17.3964i	0.0318851	+	0.0552267i
$316$		0			0
$317$	−125.535	−	125.535i	−0.396010	−	0.396010i	0.480813	−	0.876823i	$-0.340342\pi$
$317$	−125.535	−	125.535i	−0.396010	−	0.396010i	−0.876823	+	0.480813i	$0.840342\pi$
$318$		0			0
$319$	−3.32502	−	12.4091i	−0.0104232	−	0.0389001i
$320$		0			0
$321$	66.2325	−	114.718i	0.206332	−	0.357377i
$322$		0			0
$323$	−88.6612	−	23.7567i	−0.274493	−	0.0735501i
$324$		0			0
$325$	−260.351	+	28.8759i	−0.801081	+	0.0888488i
$326$		0			0
$327$	36.4160	−	135.906i	0.111364	−	0.415616i
$328$		0			0
$329$	−255.996	−	147.799i	−0.778103	−	0.449238i
$330$		0			0
$331$	52.5979	−	14.0936i	0.158906	−	0.0425788i	−0.178489	−	0.983942i	$-0.557121\pi$
$331$	52.5979	−	14.0936i	0.158906	−	0.0425788i	0.337395	+	0.941363i	$0.390454\pi$
$332$		0			0
$333$	74.3587	−	74.3587i	0.223299	−	0.223299i
$334$		0			0
$335$	51.5790	−	29.7791i	0.153967	−	0.0888930i
$336$		0			0
$337$		−	434.342i		−	1.28885i	−0.764668	−	0.644425i	$-0.777097\pi$
$337$		−	434.342i		−	1.28885i	0.764668	−	0.644425i	$-0.222903\pi$
$338$		0			0
$339$	−97.5410			−0.287732
$340$		0			0
$341$	−33.9581	−	58.8171i	−0.0995837	−	0.172484i
$342$		0			0
$343$	210.426	+	210.426i	0.613488	+	0.613488i
$344$		0			0
$345$	−26.0611	−	97.2615i	−0.0755395	−	0.281917i
$346$		0			0
$347$	−154.227	+	267.130i	−0.444459	+	0.769826i	−0.998014	−	0.0629864i	$-0.979938\pi$
$347$	−154.227	+	267.130i	−0.444459	+	0.769826i	0.553555	+	0.832813i	$0.313271\pi$
$348$		0			0
$349$	−209.568	−	56.1537i	−0.600482	−	0.160899i	−0.0542427	−	0.998528i	$-0.517274\pi$
$349$	−209.568	−	56.1537i	−0.600482	−	0.160899i	−0.546239	+	0.837629i	$0.683941\pi$
$350$		0			0
$351$	−42.0665	−	379.281i	−0.119847	−	1.08057i
$352$		0			0
$353$	4.32322	−	16.1345i	0.0122471	−	0.0457068i	−0.959532	−	0.281600i	$-0.909135\pi$
$353$	4.32322	−	16.1345i	0.0122471	−	0.0457068i	0.971779	+	0.235893i	$0.0758016\pi$
$354$		0			0
$355$	−184.675	−	106.622i	−0.520212	−	0.300344i
$356$		0			0
$357$	223.442	−	59.8712i	0.625889	−	0.167707i
$358$		0			0
$359$	−424.165	+	424.165i	−1.18152	+	1.18152i	−0.202168	+	0.979351i	$0.564799\pi$
$359$	−424.165	+	424.165i	−1.18152	+	1.18152i	−0.979351	+	0.202168i	$0.935201\pi$
$360$		0			0
$361$	−302.255	+	174.507i	−0.837272	+	0.483399i
$362$		0			0
$363$		−	298.874i		−	0.823344i
$364$		0			0
$365$	−229.223			−0.628008
$366$		0			0
$367$	−86.7154	−	150.196i	−0.236282	−	0.409252i	0.723363	−	0.690468i	$-0.242596\pi$
$367$	−86.7154	−	150.196i	−0.236282	−	0.409252i	−0.959644	+	0.281216i	$0.909262\pi$
$368$		0			0
$369$	88.9614	+	88.9614i	0.241088	+	0.241088i
$370$		0			0
$371$	−1.46490	−	5.46709i	−0.00394853	−	0.0147361i
$372$		0			0
$373$	237.999	−	412.226i	0.638067	−	1.10516i	−0.347790	−	0.937572i	$-0.613068\pi$
$373$	237.999	−	412.226i	0.638067	−	1.10516i	0.985857	−	0.167591i	$-0.0535989\pi$
$374$		0			0
$375$	242.275	+	64.9174i	0.646067	+	0.173113i
$376$		0			0
$377$	84.8183	−	62.3710i	0.224982	−	0.165440i
$378$		0			0
$379$	−186.161	+	694.761i	−0.491189	+	1.83314i	0.0592158	+	0.998245i	$0.481140\pi$
$379$	−186.161	+	694.761i	−0.491189	+	1.83314i	−0.550405	+	0.834898i	$0.685527\pi$
$380$		0			0
$381$	−369.704	−	213.449i	−0.970351	−	0.560233i
$382$		0			0
$383$	−204.072	+	54.6809i	−0.532825	+	0.142770i	−0.515193	−	0.857074i	$-0.672280\pi$
$383$	−204.072	+	54.6809i	−0.532825	+	0.142770i	−0.0176326	+	0.999845i	$0.505613\pi$
$384$		0			0
$385$	8.54447	−	8.54447i	0.0221934	−	0.0221934i
$386$		0			0
$387$	−109.302	+	63.1055i	−0.282434	+	0.163063i
$388$		0			0
$389$		−	117.917i		−	0.303129i	−0.988447	−	0.151565i	$-0.951569\pi$
$389$		−	117.917i		−	0.303129i	0.988447	−	0.151565i	$-0.0484312\pi$
$390$		0			0
$391$	480.559			1.22905
$392$		0			0
$393$	22.3209	+	38.6610i	0.0567962	+	0.0983740i
$394$		0			0
$395$	128.616	+	128.616i	0.325609	+	0.325609i
$396$		0			0
$397$	95.5247	+	356.503i	0.240616	+	0.897992i	0.975536	+	0.219839i	$0.0705530\pi$
$397$	95.5247	+	356.503i	0.240616	+	0.897992i	−0.734920	+	0.678154i	$0.762780\pi$
$398$		0			0
$399$	−15.1031	+	26.1593i	−0.0378523	+	0.0655621i
$400$		0			0
$401$	352.906	+	94.5609i	0.880065	+	0.235813i	0.670435	−	0.741968i	$-0.266107\pi$
$401$	352.906	+	94.5609i	0.880065	+	0.235813i	0.209630	+	0.977781i	$0.432774\pi$
$402$		0			0
$403$	347.780	−	434.549i	0.862977	−	1.07828i
$404$		0			0
$405$	−28.6783	+	107.029i	−0.0708106	+	0.264269i
$406$		0			0
$407$	−54.7834	−	31.6292i	−0.134603	−	0.0777130i
$408$		0			0
$409$	348.547	−	93.3928i	0.852192	−	0.228344i	0.193820	−	0.981037i	$-0.437912\pi$
$409$	348.547	−	93.3928i	0.852192	−	0.228344i	0.658372	+	0.752693i	$0.271245\pi$
$410$		0			0
$411$	112.662	−	112.662i	0.274117	−	0.274117i
$412$		0			0
$413$	290.478	−	167.708i	0.703338	−	0.406072i
$414$		0			0
$415$			107.619i			0.259323i
$416$		0			0
$417$	359.140			0.861247
$418$		0			0
$419$	247.487	+	428.661i	0.590662	+	1.02306i	0.994143	+	0.108068i	$0.0344666\pi$
$419$	247.487	+	428.661i	0.590662	+	1.02306i	−0.403482	+	0.914988i	$0.632200\pi$
$420$		0			0
$421$	174.055	+	174.055i	0.413433	+	0.413433i	0.882933	−	0.469500i	$-0.155566\pi$
$421$	174.055	+	174.055i	0.413433	+	0.413433i	−0.469500	+	0.882933i	$0.655566\pi$
$422$		0			0
$423$	58.3284	+	217.685i	0.137892	+	0.514621i
$424$		0			0
$425$	−267.116	+	462.658i	−0.628507	+	1.08861i
$426$		0			0
$427$	−139.316	−	37.3295i	−0.326266	−	0.0874228i
$428$		0			0
$429$	−48.4559	+	18.9203i	−0.112951	+	0.0441033i
$430$		0			0
$431$	39.4647	−	147.284i	0.0915654	−	0.341727i	−0.904911	−	0.425601i	$-0.860063\pi$
$431$	39.4647	−	147.284i	0.0915654	−	0.341727i	0.996476	+	0.0838743i	$0.0267294\pi$
$432$		0			0
$433$	−452.369	−	261.175i	−1.04473	−	0.603176i	−0.123562	−	0.992337i	$-0.539432\pi$
$433$	−452.369	−	261.175i	−1.04473	−	0.603176i	−0.921170	+	0.389160i	$0.872765\pi$
$434$		0			0
$435$	−43.4573	+	11.6444i	−0.0999019	+	0.0267686i
$436$		0			0
$437$	−44.3715	+	44.3715i	−0.101537	+	0.101537i
$438$		0			0
$439$	−346.267	+	199.917i	−0.788763	+	0.455392i	−0.839527	−	0.543318i	$-0.817168\pi$
$439$	−346.267	+	199.917i	−0.788763	+	0.455392i	0.0507642	+	0.998711i	$0.483834\pi$
$440$		0			0
$441$		−	97.6658i		−	0.221464i
$442$		0			0
$443$	441.108			0.995729			0.497864	−	0.867255i	$-0.334118\pi$
$443$	441.108			0.995729			0.497864	+	0.867255i	$0.334118\pi$
$444$		0			0
$445$	146.886	+	254.413i	0.330080	+	0.571716i
$446$		0			0
$447$	424.684	+	424.684i	0.950075	+	0.950075i
$448$		0			0
$449$	−162.362	−	605.941i	−0.361607	−	1.34954i	−0.871963	−	0.489572i	$-0.837153\pi$
$449$	−162.362	−	605.941i	−0.361607	−	1.34954i	0.510356	−	0.859963i	$-0.329514\pi$
$450$		0			0
$451$	37.8406	−	65.5418i	0.0839037	−	0.145326i
$452$		0			0
$453$	109.136	+	29.2429i	0.240918	+	0.0645539i
$454$		0			0
$455$	90.6959	+	39.7582i	0.199332	+	0.0873807i
$456$		0			0
$457$	−90.3367	+	337.141i	−0.197673	+	0.737727i	0.793885	+	0.608068i	$0.208055\pi$
$457$	−90.3367	+	337.141i	−0.197673	+	0.737727i	−0.991559	+	0.129659i	$0.958612\pi$
$458$		0			0
$459$	−674.002	−	389.135i	−1.46841	−	0.847789i
$460$		0			0
$461$	−416.842	+	111.692i	−0.904212	+	0.242283i	−0.680824	−	0.732447i	$-0.738378\pi$
$461$	−416.842	+	111.692i	−0.904212	+	0.242283i	−0.223388	+	0.974730i	$0.571712\pi$
$462$		0			0
$463$	−315.999	+	315.999i	−0.682503	+	0.682503i	−0.960564	−	0.278060i	$-0.910308\pi$
$463$	−315.999	+	315.999i	−0.682503	+	0.682503i	0.278060	+	0.960564i	$0.410308\pi$
$464$		0			0
$465$	−205.980	+	118.923i	−0.442968	+	0.255748i
$466$		0			0
$467$		−	621.499i		−	1.33083i	−0.746472	−	0.665417i	$-0.768254\pi$
$467$		−	621.499i		−	1.33083i	0.746472	−	0.665417i	$-0.231746\pi$
$468$		0			0
$469$	93.5399			0.199445
$470$		0			0
$471$	−139.623	−	241.834i	−0.296439	−	0.513448i
$472$		0			0
$473$	53.6851	+	53.6851i	0.113499	+	0.113499i
$474$		0			0
$475$	−18.0550	−	67.3824i	−0.0380106	−	0.141858i
$476$		0			0
$477$	−2.15757	+	3.73702i	−0.00452320	+	0.00783442i
$478$		0			0
$479$	431.188	+	115.537i	0.900184	+	0.241204i	0.679095	−	0.734050i	$-0.262372\pi$
$479$	431.188	+	115.537i	0.900184	+	0.241204i	0.221089	+	0.975254i	$0.429039\pi$
$480$		0			0
$481$	78.1570	−	512.486i	0.162489	−	1.06546i
$482$		0			0
$483$	40.9306	−	152.755i	0.0847424	−	0.316263i
$484$		0			0
$485$	133.527	+	77.0919i	0.275313	+	0.158952i
$486$		0			0
$487$	−242.013	+	64.8472i	−0.496946	+	0.133156i	−0.498582	−	0.866842i	$-0.666146\pi$
$487$	−242.013	+	64.8472i	−0.496946	+	0.133156i	0.00163604	+	0.999999i	$0.499479\pi$
$488$		0			0
$489$	−525.568	+	525.568i	−1.07478	+	1.07478i
$490$		0			0
$491$	755.980	−	436.465i	1.53967	−	0.888932i	0.540818	−	0.841140i	$-0.318115\pi$
$491$	755.980	−	436.465i	1.53967	−	0.888932i	0.998857	−	0.0477917i	$-0.0152184\pi$
$492$		0			0
$493$		−	214.718i		−	0.435534i
$494$		0			0
$495$	−9.21259			−0.0186113
$496$		0			0
$497$	−167.457	−	290.044i	−0.336935	−	0.583589i
$498$		0			0
$499$	−489.889	−	489.889i	−0.981741	−	0.981741i	0.0180951	−	0.999836i	$-0.494240\pi$
$499$	−489.889	−	489.889i	−0.981741	−	0.981741i	−0.999836	+	0.0180951i	$0.994240\pi$
$500$		0			0
$501$	22.9247	+	85.5560i	0.0457578	+	0.170771i
$502$		0			0
$503$	76.6251	−	132.718i	0.152336	−	0.263854i	−0.779750	−	0.626091i	$-0.784654\pi$
$503$	76.6251	−	132.718i	0.152336	−	0.263854i	0.932086	+	0.362237i	$0.117987\pi$
$504$		0			0
$505$	121.861	+	32.6527i	0.241310	+	0.0646588i
$506$		0			0
$507$	−288.869	−	313.508i	−0.569762	−	0.618359i
$508$		0			0
$509$	−103.048	+	384.579i	−0.202451	+	0.755558i	0.787760	+	0.615982i	$0.211241\pi$
$509$	−103.048	+	384.579i	−0.202451	+	0.755558i	−0.990211	+	0.139576i	$0.955426\pi$
$510$		0			0
$511$	−311.777	−	180.004i	−0.610130	−	0.352259i
$512$		0			0
$513$	98.1629	−	26.3027i	0.191351	−	0.0512722i
$514$		0			0
$515$	−67.4282	+	67.4282i	−0.130929	+	0.130929i
$516$		0			0
$517$	117.405	−	67.7837i	0.227089	−	0.131110i
$518$		0			0
$519$			584.853i			1.12688i
$520$		0			0
$521$	−300.051			−0.575914			−0.287957	−	0.957643i	$-0.592976\pi$
$521$	−300.051			−0.575914			−0.287957	+	0.957643i	$0.592976\pi$
$522$		0			0
$523$	109.493	+	189.647i	0.209355	+	0.362613i	0.951511	−	0.307613i	$-0.0995303\pi$
$523$	109.493	+	189.647i	0.209355	+	0.362613i	−0.742157	+	0.670226i	$0.766197\pi$
$524$		0			0
$525$	124.314	+	124.314i	0.236788	+	0.236788i
$526$		0			0
$527$	−293.792	−	1096.45i	−0.557480	−	2.08055i
$528$		0			0
$529$	−100.234	+	173.611i	−0.189479	+	0.328188i
$530$		0			0
$531$	−247.007	−	66.1853i	−0.465173	−	0.124643i
$532$		0			0
$533$	613.129	+	93.5056i	1.15034	+	0.175433i
$534$		0			0
$535$	29.9327	−	111.711i	0.0559491	−	0.208805i
$536$		0			0
$537$	84.9888	+	49.0683i	0.158266	+	0.0913748i
$538$		0			0
$539$	−56.7489	+	15.2058i	−0.105286	+	0.0282112i
$540$		0			0
$541$	−272.550	+	272.550i	−0.503789	+	0.503789i	−0.912613	−	0.408824i	$-0.865939\pi$
$541$	−272.550	+	272.550i	−0.503789	+	0.503789i	0.408824	+	0.912613i	$0.365939\pi$
$542$		0			0
$543$	−401.293	+	231.686i	−0.739029	+	0.426678i
$544$		0			0
$545$		−	122.842i		−	0.225397i
$546$		0			0
$547$	−218.594			−0.399624			−0.199812	−	0.979834i	$-0.564033\pi$
$547$	−218.594			−0.399624			−0.199812	+	0.979834i	$0.564033\pi$
$548$		0			0
$549$	54.9804	+	95.2289i	0.100147	+	0.173459i
$550$		0			0
$551$	19.8256	+	19.8256i	0.0359812	+	0.0359812i
$552$		0			0
$553$	73.9367	+	275.935i	0.133701	+	0.498979i
$554$		0			0
$555$	−110.767	+	191.854i	−0.199580	+	0.345683i
$556$		0			0
$557$	648.103	+	173.659i	1.16356	+	0.311775i	0.788387	−	0.615179i	$-0.210916\pi$
$557$	648.103	+	173.659i	1.16356	+	0.311775i	0.375174	+	0.926954i	$0.377583\pi$
$558$		0			0
$559$	−249.802	+	569.845i	−0.446873	+	1.01940i
$560$		0			0
$561$	−27.4582	+	102.475i	−0.0489450	+	0.182665i
$562$		0			0
$563$	524.308	+	302.709i	0.931275	+	0.537672i	0.887215	−	0.461357i	$-0.152637\pi$
$563$	524.308	+	302.709i	0.931275	+	0.537672i	0.0440606	+	0.999029i	$0.485971\pi$
$564$		0			0
$565$	−82.2584	+	22.0411i	−0.145590	+	0.0390107i
$566$		0			0
$567$	−123.054	+	123.054i	−0.217027	+	0.217027i
$568$		0			0
$569$	799.994	−	461.877i	1.40596	−	0.811734i	0.410969	−	0.911649i	$-0.365191\pi$
$569$	799.994	−	461.877i	1.40596	−	0.811734i	0.994996	+	0.0999152i	$0.0318572\pi$
$570$		0			0
$571$		−	919.389i		−	1.61014i	−0.593181	−	0.805069i	$-0.702128\pi$
$571$		−	919.389i		−	1.61014i	0.593181	−	0.805069i	$-0.297872\pi$
$572$		0			0
$573$	401.001			0.699826
$574$		0			0
$575$	182.612	+	316.293i	0.317586	+	0.550075i
$576$		0			0
$577$	680.584	+	680.584i	1.17952	+	1.17952i	0.979866	+	0.199655i	$0.0639822\pi$
$577$	680.584	+	680.584i	1.17952	+	1.17952i	0.199655	+	0.979866i	$0.436018\pi$
$578$		0			0
$579$	−38.7915	−	144.772i	−0.0669974	−	0.250038i
$580$		0			0
$581$	−84.5112	+	146.378i	−0.145458	+	0.251941i
$582$		0			0
$583$	2.50732	+	0.671834i	0.00430072	+	0.00115237i
$584$		0			0
$585$	−27.4604	−	70.3274i	−0.0469408	−	0.120218i
$586$		0			0
$587$	78.9753	−	294.740i	0.134541	−	0.502112i	−0.865459	−	0.500980i	$-0.832973\pi$
$587$	78.9753	−	294.740i	0.134541	−	0.502112i	0.999999	−	0.00113205i	$-0.000360342\pi$
$588$		0			0
$589$	128.365	+	74.1118i	0.217938	+	0.125826i
$590$		0			0
$591$	426.957	−	114.403i	0.722432	−	0.193575i
$592$		0			0
$593$	−252.301	+	252.301i	−0.425465	+	0.425465i	−0.887080	−	0.461615i	$-0.847270\pi$
$593$	−252.301	+	252.301i	−0.425465	+	0.425465i	0.461615	+	0.887080i	$0.347270\pi$
$594$		0			0
$595$	174.905	−	100.981i	0.293958	−	0.169717i
$596$		0			0
$597$			369.715i			0.619288i
$598$		0			0
$599$	448.577			0.748876			0.374438	−	0.927252i	$-0.377836\pi$
$599$	448.577			0.748876			0.374438	+	0.927252i	$0.377836\pi$
$600$		0			0
$601$	−130.048	−	225.250i	−0.216387	−	0.374793i	0.737314	−	0.675550i	$-0.236094\pi$
$601$	−130.048	−	225.250i	−0.216387	−	0.374793i	−0.953701	+	0.300757i	$0.902761\pi$
$602$		0			0
$603$	−50.4271	−	50.4271i	−0.0836270	−	0.0836270i
$604$		0			0
$605$	−67.5357	−	252.047i	−0.111629	−	0.416606i
$606$		0			0
$607$	−279.832	+	484.683i	−0.461008	+	0.798490i	−0.999011	−	0.0444531i	$-0.985845\pi$
$607$	−279.832	+	484.683i	−0.461008	+	0.798490i	0.538003	+	0.842943i	$0.319179\pi$
$608$		0			0
$609$	−68.2524	−	18.2882i	−0.112073	−	0.0300298i
$610$		0			0
$611$	867.403	+	694.204i	1.41965	+	1.13618i
$612$		0			0
$613$	28.8500	−	107.670i	0.0470636	−	0.175644i	−0.938393	−	0.345569i	$-0.887686\pi$
$613$	28.8500	−	107.670i	0.0470636	−	0.175644i	0.985457	+	0.169925i	$0.0543526\pi$
$614$		0			0
$615$	−229.530	−	132.519i	−0.373220	−	0.215479i
$616$		0			0
$617$	−542.455	+	145.350i	−0.879182	+	0.235576i	−0.670054	−	0.742312i	$-0.733729\pi$
$617$	−542.455	+	145.350i	−0.879182	+	0.235576i	−0.209128	+	0.977888i	$0.567062\pi$
$618$		0			0
$619$	459.809	−	459.809i	0.742826	−	0.742826i	−0.230295	−	0.973121i	$-0.573969\pi$
$619$	459.809	−	459.809i	0.742826	−	0.742826i	0.973121	+	0.230295i	$0.0739691\pi$
$620$		0			0
$621$	−460.777	+	266.030i	−0.741992	+	0.428389i
$622$		0			0
$623$			461.386i			0.740587i
$624$		0			0
$625$	−284.760			−0.455617
$626$		0			0
$627$	−6.92657	−	11.9972i	−0.0110472	−	0.0191342i
$628$		0			0
$629$	−747.609	−	747.609i	−1.18857	−	1.18857i
$630$		0			0
$631$	68.6928	+	256.365i	0.108863	+	0.406284i	0.998755	−	0.0498887i	$-0.0158867\pi$
$631$	68.6928	+	256.365i	0.108863	+	0.406284i	−0.889891	+	0.456172i	$0.849220\pi$
$632$		0			0
$633$	329.069	−	569.964i	0.519856	−	0.900416i
$634$		0			0
$635$	−360.011	−	96.4648i	−0.566947	−	0.151913i
$636$		0			0
$637$	−285.233	−	387.887i	−0.447775	−	0.608929i
$638$		0			0
$639$	−66.0862	+	246.637i	−0.103421	+	0.385973i
$640$		0			0
$641$	660.155	+	381.140i	1.02988	+	0.594603i	0.916951	−	0.399000i	$-0.130643\pi$
$641$	660.155	+	381.140i	1.02988	+	0.594603i	0.112931	+	0.993603i	$0.463976\pi$
$642$		0			0
$643$	−236.348	+	63.3294i	−0.367571	+	0.0984905i	−0.437877	−	0.899035i	$-0.644269\pi$
$643$	−236.348	+	63.3294i	−0.367571	+	0.0984905i	0.0703052	+	0.997526i	$0.477603\pi$
$644$		0			0
$645$	188.008	−	188.008i	0.291485	−	0.291485i
$646$		0			0
$647$	70.6667	−	40.7994i	0.109222	−	0.0630594i	−0.444394	−	0.895832i	$-0.646581\pi$
$647$	70.6667	−	40.7994i	0.109222	−	0.0630594i	0.553616	+	0.832772i	$0.313248\pi$
$648$		0			0
$649$			153.828i			0.237024i
$650$		0			0
$651$	−373.551			−0.573810
$652$		0			0
$653$	−517.864	−	896.967i	−0.793054	−	1.37361i	−0.924068	−	0.382229i	$-0.875157\pi$
$653$	−517.864	−	896.967i	−0.793054	−	1.37361i	0.131014	−	0.991381i	$-0.458177\pi$
$654$		0			0
$655$	27.5598	+	27.5598i	0.0420761	+	0.0420761i
$656$		0			0
$657$	71.0380	+	265.118i	0.108125	+	0.403528i
$658$		0			0
$659$	60.5910	−	104.947i	0.0919438	−	0.159251i	−0.816385	−	0.577508i	$-0.804025\pi$
$659$	60.5910	−	104.947i	0.0919438	−	0.159251i	0.908329	+	0.418256i	$0.137359\pi$
$660$		0			0
$661$	−526.473	−	141.068i	−0.796480	−	0.213416i	−0.162442	−	0.986718i	$-0.551937\pi$
$661$	−526.473	−	141.068i	−0.796480	−	0.213416i	−0.634038	+	0.773302i	$0.718604\pi$
$662$		0			0
$663$	−864.125	+	95.8411i	−1.30336	+	0.144557i
$664$		0			0
$665$	−6.82560	+	25.4735i	−0.0102641	+	0.0383060i
$666$		0			0
$667$	−127.125	−	73.3954i	−0.190591	−	0.110038i
$668$		0			0
$669$	531.319	−	142.367i	0.794199	−	0.212805i
$670$		0			0
$671$	46.7729	−	46.7729i	0.0697063	−	0.0697063i
$672$		0			0
$673$	−280.546	+	161.973i	−0.416859	+	0.240674i	−0.693733	−	0.720233i	$-0.744035\pi$
$673$	−280.546	+	161.973i	−0.416859	+	0.240674i	0.276873	+	0.960906i	$0.410702\pi$
$674$		0			0
$675$		−	591.484i		−	0.876273i
$676$		0			0
$677$	−1192.86			−1.76197			−0.880987	−	0.473140i	$-0.843121\pi$
$677$	−1192.86			−1.76197			−0.880987	+	0.473140i	$0.843121\pi$
$678$		0			0
$679$	121.077	+	209.712i	0.178317	+	0.308855i
$680$		0			0
$681$	−639.326	−	639.326i	−0.938805	−	0.938805i
$682$		0			0
$683$	−7.76015	−	28.9613i	−0.0113619	−	0.0424031i	0.960012	−	0.279958i	$-0.0903206\pi$
$683$	−7.76015	−	28.9613i	−0.0113619	−	0.0424031i	−0.971374	+	0.237555i	$0.923654\pi$
$684$		0			0
$685$	69.5523	−	120.468i	0.101536	−	0.175866i
$686$		0			0
$687$	982.027	+	263.133i	1.42944	+	0.383018i
$688$		0			0
$689$	2.34500	+	21.1430i	0.00340348	+	0.0306865i
$690$		0			0
$691$	−53.4482	+	199.471i	−0.0773490	+	0.288670i	−0.993756	−	0.111578i	$-0.964410\pi$
$691$	−53.4482	+	199.471i	−0.0773490	+	0.288670i	0.916407	+	0.400248i	$0.131076\pi$
$692$		0			0
$693$	−12.5305	−	7.23447i	−0.0180815	−	0.0104393i
$694$		0			0
$695$	302.870	−	81.1539i	0.435785	−	0.116768i
$696$		0			0
$697$	894.425	−	894.425i	1.28325	−	1.28325i
$698$		0			0
$699$	−365.319	+	210.917i	−0.522630	+	0.301741i
$700$		0			0
$701$			481.743i			0.687223i	0.939112	+	0.343611i	$0.111650\pi$
$701$			481.743i			0.687223i	−0.939112	+	0.343611i	$0.888350\pi$
$702$		0			0
$703$	138.058			0.196384
$704$		0			0
$705$	−237.382	−	411.157i	−0.336712	−	0.583202i
$706$		0			0
$707$	140.108	+	140.108i	0.198172	+	0.198172i
$708$		0			0
$709$	158.092	+	590.009i	0.222980	+	0.832171i	0.983204	+	0.182510i	$0.0584223\pi$
$709$	158.092	+	590.009i	0.222980	+	0.832171i	−0.760224	+	0.649661i	$0.774911\pi$
$710$		0			0
$711$	108.897	−	188.615i	0.153160	−	0.265281i
$712$		0			0
$713$	−749.580	−	200.849i	−1.05130	−	0.281696i
$714$		0			0
$715$	−36.5885	+	26.9054i	−0.0511728	+	0.0376299i
$716$		0			0
$717$	260.096	−	970.691i	0.362756	−	1.35382i
$718$		0			0
$719$	−128.796	−	74.3604i	−0.179132	−	0.103422i	0.407753	−	0.913092i	$-0.366313\pi$
$719$	−128.796	−	74.3604i	−0.179132	−	0.103422i	−0.586885	+	0.809670i	$0.699646\pi$
$720$		0			0
$721$	−144.662	+	38.7621i	−0.200641	+	0.0537616i
$722$		0			0
$723$	232.229	−	232.229i	0.321202	−	0.321202i
$724$		0			0
$725$	141.323	−	81.5927i	0.194928	−	0.112542i
$726$		0			0
$727$			717.121i			0.986411i	0.869913	+	0.493206i	$0.164175\pi$
$727$			717.121i			0.986411i	−0.869913	+	0.493206i	$0.835825\pi$
$728$		0			0
$729$	799.091			1.09615
$730$		0			0
$731$	634.468	+	1098.93i	0.867946	+	1.50333i
$732$		0			0
$733$	223.882	+	223.882i	0.305433	+	0.305433i	0.843135	−	0.537702i	$-0.180708\pi$
$733$	223.882	+	223.882i	0.305433	+	0.305433i	−0.537702	+	0.843135i	$0.680708\pi$
$734$		0			0
$735$	53.2515	+	198.737i	0.0724511	+	0.270391i
$736$		0			0
$737$	−21.4497	+	37.1519i	−0.0291040	+	0.0504096i
$738$		0			0
$739$	−1051.66	−	281.791i	−1.42308	−	0.381314i	−0.536507	−	0.843896i	$-0.680256\pi$
$739$	−1051.66	−	281.791i	−1.42308	−	0.381314i	−0.886576	+	0.462582i	$0.846923\pi$
$740$		0			0
$741$	70.9381	−	88.6368i	0.0957330	−	0.119618i
$742$		0			0
$743$	79.6381	−	297.213i	0.107184	−	0.400018i	−0.891399	−	0.453219i	$-0.850276\pi$
$743$	79.6381	−	297.213i	0.107184	−	0.400018i	0.998584	+	0.0532008i	$0.0169423\pi$
$744$		0			0
$745$	454.109	+	262.180i	0.609543	+	0.351920i
$746$		0			0
$747$	124.472	−	33.3520i	0.166629	−	0.0446480i
$748$		0			0
$749$	128.437	−	128.437i	0.171478	−	0.171478i
$750$		0			0
$751$	−404.467	+	233.519i	−0.538571	+	0.310944i	−0.744500	−	0.667623i	$-0.767312\pi$
$751$	−404.467	+	233.519i	−0.538571	+	0.310944i	0.205929	+	0.978567i	$0.433979\pi$
$752$		0			0
$753$			1115.70i			1.48168i
$754$		0			0
$755$	98.6447			0.130655
$756$		0			0
$757$	−36.8428	−	63.8135i	−0.0486694	−	0.0842979i	0.840664	−	0.541556i	$-0.182165\pi$
$757$	−36.8428	−	63.8135i	−0.0486694	−	0.0842979i	−0.889334	+	0.457259i	$0.848831\pi$
$758$		0			0
$759$	51.2850	+	51.2850i	0.0675691	+	0.0675691i
$760$		0			0
$761$	232.765	+	868.692i	0.305868	+	1.14151i	0.932196	+	0.361954i	$0.117890\pi$
$761$	232.765	+	868.692i	0.305868	+	1.14151i	−0.626328	+	0.779560i	$0.715443\pi$
$762$		0			0
$763$	96.4651	−	167.082i	0.126429	−	0.218981i
$764$		0			0
$765$	−148.729	−	39.8519i	−0.194418	−	0.0520940i
$766$		0			0
$767$	−1174.30	+	458.523i	−1.53103	+	0.597813i
$768$		0			0
$769$	152.037	−	567.410i	0.197708	−	0.737855i	−0.793842	−	0.608124i	$-0.791922\pi$
$769$	152.037	−	567.410i	0.197708	−	0.737855i	0.991549	−	0.129730i	$-0.0414111\pi$
$770$		0			0
$771$	745.222	+	430.254i	0.966565	+	0.558047i
$772$		0			0
$773$	−756.535	+	202.713i	−0.978700	+	0.262242i	−0.712497	−	0.701675i	$-0.752436\pi$
$773$	−756.535	+	202.713i	−0.978700	+	0.262242i	−0.266203	+	0.963917i	$0.585769\pi$
$774$		0			0
$775$	610.017	−	610.017i	0.787119	−	0.787119i
$776$		0			0
$777$	−301.318	+	173.966i	−0.387797	+	0.223895i
$778$		0			0
$779$			165.170i			0.212029i
$780$		0			0
$781$	153.598			0.196668
$782$		0			0
$783$	118.865	+	205.880i	0.151807	+	0.262937i
$784$		0			0
$785$	−172.393	−	172.393i	−0.219609	−	0.219609i
$786$		0			0
$787$	308.435	+	1151.09i	0.391912	+	1.46264i	0.826977	+	0.562236i	$0.190059\pi$
$787$	308.435	+	1151.09i	0.391912	+	1.46264i	−0.435065	+	0.900399i	$0.643275\pi$
$788$		0			0
$789$	635.173	−	1100.15i	0.805036	−	1.39436i
$790$		0			0
$791$	−129.192	−	34.6168i	−0.163327	−	0.0437634i
$792$		0			0
$793$	496.475	+	217.639i	0.626072	+	0.274450i
$794$		0			0
$795$	2.35279	−	8.78075i	0.00295949	−	0.0110450i
$796$		0			0
$797$	692.353	+	399.730i	0.868698	+	0.501543i	0.866915	−	0.498455i	$-0.166099\pi$
$797$	692.353	+	399.730i	0.868698	+	0.501543i	0.00178286	+	0.999998i	$0.499432\pi$
$798$		0			0
$799$	2188.62	−	586.439i	2.73920	−	0.733966i
$800$		0			0
$801$	248.732	−	248.732i	0.310526	−	0.310526i
$802$		0			0
$803$	142.987	−	82.5536i	0.178066	−	0.102807i
$804$		0			0
$805$		−	138.071i		−	0.171516i
$806$		0			0
$807$	−899.166			−1.11421
$808$		0			0
$809$	−122.645	−	212.428i	−0.151601	−	0.262580i	0.780215	−	0.625511i	$-0.215110\pi$
$809$	−122.645	−	212.428i	−0.151601	−	0.262580i	−0.931816	+	0.362931i	$0.881776\pi$
$810$		0			0
$811$	−725.145	−	725.145i	−0.894136	−	0.894136i	0.100773	−	0.994909i	$-0.467868\pi$
$811$	−725.145	−	725.145i	−0.894136	−	0.894136i	−0.994909	+	0.100773i	$0.967868\pi$
$812$		0			0
$813$	111.019	+	414.327i	0.136554	+	0.509628i
$814$		0			0
$815$	−324.461	+	561.984i	−0.398112	+	0.689550i
$816$		0			0
$817$	−160.050	−	42.8854i	−0.195900	−	0.0524913i
$818$		0			0
$819$	17.8767	−	117.220i	0.0218274	−	0.143125i
$820$		0			0
$821$	−181.675	+	678.021i	−0.221285	+	0.825848i	0.762574	+	0.646901i	$0.223935\pi$
$821$	−181.675	+	678.021i	−0.221285	+	0.825848i	−0.983859	+	0.178946i	$0.942731\pi$
$822$		0			0
$823$	−120.391	−	69.5080i	−0.146284	−	0.0844569i	0.425072	−	0.905160i	$-0.360249\pi$
$823$	−120.391	−	69.5080i	−0.146284	−	0.0844569i	−0.571355	+	0.820703i	$0.693582\pi$
$824$		0			0
$825$	−77.8810	+	20.8682i	−0.0944013	+	0.0252947i
$826$		0			0
$827$	733.444	−	733.444i	0.886873	−	0.886873i	−0.107348	−	0.994221i	$-0.534236\pi$
$827$	733.444	−	733.444i	0.886873	−	0.886873i	0.994221	+	0.107348i	$0.0342359\pi$
$828$		0			0
$829$	−46.0698	+	26.5984i	−0.0555727	+	0.0320849i	−0.527529	−	0.849537i	$-0.676881\pi$
$829$	−46.0698	+	26.5984i	−0.0555727	+	0.0320849i	0.471956	+	0.881622i	$0.343548\pi$
$830$		0			0
$831$			382.960i			0.460843i
$832$		0			0
$833$	−981.941			−1.17880
$834$		0			0
$835$	38.6657	+	66.9710i	0.0463063	+	0.0802048i
$836$		0			0
$837$	888.675	+	888.675i	1.06174	+	1.06174i
$838$		0			0
$839$	−346.978	−	1294.94i	−0.413561	−	1.54343i	−0.787701	−	0.616058i	$-0.788729\pi$
$839$	−346.978	−	1294.94i	−0.413561	−	1.54343i	0.374140	−	0.927372i	$-0.377938\pi$
$840$		0			0
$841$	387.706	−	671.527i	0.461006	−	0.798486i
$842$		0			0
$843$	−595.109	−	159.459i	−0.705942	−	0.189156i
$844$		0			0
$845$	−314.452	−	199.113i	−0.372133	−	0.235637i
$846$		0			0
$847$	106.069	−	395.855i	0.125229	−	0.467361i
$848$		0			0
$849$	60.7400	+	35.0683i	0.0715430	+	0.0413054i
$850$		0			0
$851$	−698.173	+	187.075i	−0.820415	+	0.219830i
$852$		0			0
$853$	−437.131	+	437.131i	−0.512463	+	0.512463i	−0.915281	−	0.402817i	$-0.868031\pi$
$853$	−437.131	+	437.131i	−0.512463	+	0.512463i	0.402817	+	0.915281i	$0.368031\pi$
$854$		0			0
$855$	17.4123	−	10.0530i	0.0203653	−	0.0117579i
$856$		0			0
$857$		−	481.600i		−	0.561960i	−0.959714	−	0.280980i	$-0.909341\pi$
$857$		−	481.600i		−	0.561960i	0.959714	−	0.280980i	$-0.0906595\pi$
$858$		0			0
$859$	−761.679			−0.886704			−0.443352	−	0.896348i	$-0.646211\pi$
$859$	−761.679			−0.886704			−0.443352	+	0.896348i	$0.646211\pi$
$860$		0			0
$861$	−208.130	−	360.492i	−0.241730	−	0.418689i
$862$		0			0
$863$	−1114.08	−	1114.08i	−1.29093	−	1.29093i	−0.934210	−	0.356725i	$-0.883893\pi$
$863$	−1114.08	−	1114.08i	−1.29093	−	1.29093i	−0.356725	−	0.934210i	$-0.616107\pi$
$864$		0			0
$865$	132.158	+	493.219i	0.152783	+	0.570195i
$866$		0			0
$867$	−522.077	+	904.263i	−0.602165	+	1.04298i
$868$		0			0
$869$	−126.550	−	33.9089i	−0.145627	−	0.0390206i
$870$		0			0
$871$	−347.547	−	53.0030i	−0.399021	−	0.0608530i
$872$		0			0
$873$	47.7828	−	178.328i	0.0547340	−	0.204270i
$874$		0			0
$875$	297.851	+	171.965i	0.340402	+	0.196531i
$876$		0			0
$877$	−610.234	+	163.512i	−0.695820	+	0.186444i	−0.589357	−	0.807872i	$-0.700619\pi$
$877$	−610.234	+	163.512i	−0.695820	+	0.186444i	−0.106462	+	0.994317i	$0.533952\pi$
$878$		0			0
$879$	533.480	−	533.480i	0.606917	−	0.606917i
$880$		0			0
$881$	−511.565	+	295.352i	−0.580664	+	0.335247i	−0.761397	−	0.648285i	$-0.775486\pi$
$881$	−511.565	+	295.352i	−0.580664	+	0.335247i	0.180733	+	0.983532i	$0.442153\pi$
$882$		0			0
$883$			29.0735i			0.0329259i	0.999864	+	0.0164629i	$0.00524055\pi$
$883$			29.0735i			0.0329259i	−0.999864	+	0.0164629i	$0.994759\pi$
$884$		0			0
$885$	538.714			0.608717
$886$		0			0
$887$	−580.225	−	1004.98i	−0.654143	−	1.13301i	−0.982108	−	0.188319i	$-0.939696\pi$
$887$	−580.225	−	1004.98i	−0.654143	−	1.13301i	0.327965	−	0.944690i	$-0.393637\pi$
$888$		0			0
$889$	−413.916	−	413.916i	−0.465597	−	0.465597i
$890$		0			0
$891$	−20.6567	−	77.0919i	−0.0231837	−	0.0865229i
$892$		0			0
$893$	−147.935	+	256.230i	−0.165660	+	0.286932i
$894$		0			0
$895$	82.7607	+	22.1757i	0.0924700	+	0.0247773i
$896$		0			0
$897$	−238.634	+	544.368i	−0.266035	+	0.606877i
$898$		0			0
$899$	−89.7413	+	334.919i	−0.0998235	+	0.372546i
$900$		0			0
$901$	37.5723	+	21.6924i	0.0417007	+	0.0240759i
$902$		0			0
$903$	403.357	−	108.079i	0.446685	−	0.119689i
$904$		0			0
$905$	−286.065	+	286.065i	−0.316094	+	0.316094i
$906$		0			0
$907$	633.097	−	365.519i	0.698012	−	0.402997i	−0.108595	−	0.994086i	$-0.534635\pi$
$907$	633.097	−	365.519i	0.698012	−	0.402997i	0.806607	+	0.591089i	$0.201302\pi$
$908$		0			0
$909$		−	151.063i		−	0.166186i
$910$		0			0
$911$	162.202			0.178049			0.0890244	−	0.996029i	$-0.471625\pi$
$911$	162.202			0.178049			0.0890244	+	0.996029i	$0.471625\pi$
$912$		0			0
$913$	−38.7586	−	67.1318i	−0.0424519	−	0.0735288i
$914$		0			0
$915$	−163.801	−	163.801i	−0.179017	−	0.179017i
$916$		0			0
$917$	15.8432	+	59.1276i	0.0172772	+	0.0644793i
$918$		0			0
$919$	742.511	−	1286.07i	0.807955	−	1.39942i	−0.106323	−	0.994332i	$-0.533908\pi$
$919$	742.511	−	1286.07i	0.807955	−	1.39942i	0.914278	−	0.405088i	$-0.132759\pi$
$920$		0			0
$921$	3.64650	+	0.977076i	0.00395928	+	0.00106089i
$922$		0			0
$923$	457.836	+	1172.54i	0.496031	+	1.27036i
$924$		0			0
$925$	207.969	−	776.151i	0.224831	−	0.839082i
$926$		0			0
$927$	98.8835	+	57.0904i	0.106670	+	0.0615862i
$928$		0			0
$929$	−203.739	+	54.5916i	−0.219310	+	0.0587639i	−0.366801	−	0.930300i	$-0.619547\pi$
$929$	−203.739	+	54.5916i	−0.219310	+	0.0587639i	0.147491	+	0.989063i	$0.452880\pi$
$930$		0			0
$931$	90.6657	−	90.6657i	0.0973853	−	0.0973853i
$932$		0			0
$933$	−454.062	+	262.153i	−0.486669	+	0.280979i
$934$		0			0
$935$			92.6242i			0.0990633i
$936$		0			0
$937$	38.5557			0.0411480			0.0205740	−	0.999788i	$-0.493451\pi$
$937$	38.5557			0.0411480			0.0205740	+	0.999788i	$0.493451\pi$
$938$		0			0
$939$	263.455	+	456.317i	0.280569	+	0.485960i
$940$		0			0
$941$	672.181	+	672.181i	0.714326	+	0.714326i	0.967437	−	0.253111i	$-0.0814538\pi$
$941$	672.181	+	672.181i	0.714326	+	0.714326i	−0.253111	+	0.967437i	$0.581454\pi$
$942$		0			0
$943$	−223.813	−	835.281i	−0.237341	−	0.885770i
$944$		0			0
$945$	−111.803	+	193.649i	−0.118310	+	0.204920i
$946$		0			0
$947$	8.80835	+	2.36019i	0.00930133	+	0.00249228i	0.263467	−	0.964668i	$-0.415134\pi$
$947$	8.80835	+	2.36019i	0.00930133	+	0.00249228i	−0.254165	+	0.967161i	$0.581801\pi$
$948$		0			0
$949$	1056.41	+	845.469i	1.11318	+	0.890905i
$950$		0			0
$951$	115.906	−	432.568i	0.121878	−	0.454856i
$952$		0			0
$953$	918.201	+	530.123i	0.963485	+	0.556268i	0.897244	−	0.441536i	$-0.145566\pi$
$953$	918.201	+	530.123i	0.963485	+	0.556268i	0.0662408	+	0.997804i	$0.478899\pi$
$954$		0			0
$955$	338.172	−	90.6130i	0.354107	−	0.0948827i
$956$		0			0
$957$	22.9146	−	22.9146i	0.0239442	−	0.0239442i
$958$		0			0
$959$	189.202	−	109.236i	0.197291	−	0.113906i
$960$		0			0
$961$			872.038i			0.907428i
$962$		0			0
$963$	−138.480			−0.143801
$964$		0			0
$965$	−65.4274	−	113.324i	−0.0678004	−	0.117434i
$966$		0			0
$967$	399.225	+	399.225i	0.412849	+	0.412849i	0.882730	−	0.469881i	$-0.155703\pi$
$967$	399.225	+	399.225i	0.412849	+	0.412849i	−0.469881	+	0.882730i	$0.655703\pi$
$968$		0			0
$969$	−59.9261	−	223.647i	−0.0618432	−	0.230802i
$970$		0			0
$971$	−656.238	+	1136.64i	−0.675838	+	1.17059i	0.300386	+	0.953818i	$0.402885\pi$
$971$	−656.238	+	1136.64i	−0.675838	+	1.17059i	−0.976223	+	0.216767i	$0.930449\pi$
$972$		0			0
$973$	475.676	+	127.457i	0.488876	+	0.130994i
$974$		0			0
$975$	−391.447	−	532.329i	−0.401485	−	0.545978i
$976$		0			0
$977$	255.165	−	952.290i	0.261172	−	0.974709i	−0.703379	−	0.710815i	$-0.748326\pi$
$977$	255.165	−	952.290i	0.261172	−	0.974709i	0.964552	−	0.263894i	$-0.0850069\pi$
$978$		0			0
$979$	−183.252	−	105.800i	−0.187183	−	0.108070i
$980$		0			0
$981$	−142.078	+	38.0696i	−0.144829	+	0.0388069i
$982$		0			0
$983$	−583.284	+	583.284i	−0.593371	+	0.593371i	−0.938541	−	0.345169i	$-0.887822\pi$
$983$	−583.284	+	583.284i	−0.593371	+	0.593371i	0.345169	+	0.938541i	$0.387822\pi$
$984$		0			0
$985$	334.211	−	192.957i	0.339301	−	0.195895i
$986$		0			0
$987$		−	745.645i		−	0.755466i
$988$		0			0
$989$	867.501			0.877149
$990$		0			0
$991$	18.6872	+	32.3673i	0.0188570	+	0.0326612i	0.875300	−	0.483580i	$-0.160664\pi$
$991$	18.6872	+	32.3673i	0.0188570	+	0.0326612i	−0.856443	+	0.516242i	$0.827331\pi$
$992$		0			0
$993$	97.1269	+	97.1269i	0.0978116	+	0.0978116i
$994$		0			0
$995$	83.5435	+	311.788i	0.0839633	+	0.313355i
$996$		0			0
$997$	−694.432	+	1202.79i	−0.696521	+	1.20641i	0.273144	+	0.961973i	$0.411936\pi$
$997$	−694.432	+	1202.79i	−0.696521	+	1.20641i	−0.969665	+	0.244437i	$0.921397\pi$
$998$		0			0
$999$	1130.70	+	302.970i	1.13183	+	0.303273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.3.k.a.37.2	✓	8
3.2	odd	2		468.3.cd.b.37.1		8
4.3	odd	2		208.3.bd.e.193.1		8
13.2	odd	12		676.3.g.d.577.2		8
13.3	even	3		676.3.g.d.437.2		8
13.6	odd	12	inner	52.3.k.a.45.2	yes	8
13.10	even	6		676.3.g.c.437.2		8
13.11	odd	12		676.3.g.c.577.2		8
39.32	even	12		468.3.cd.b.253.1		8
52.19	even	12		208.3.bd.e.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.3.k.a.37.2	✓	8	1.1	even	1	trivial
52.3.k.a.45.2	yes	8	13.6	odd	12	inner
208.3.bd.e.97.1		8	52.19	even	12
208.3.bd.e.193.1		8	4.3	odd	2
468.3.cd.b.37.1		8	3.2	odd	2
468.3.cd.b.253.1		8	39.32	even	12
676.3.g.c.437.2		8	13.10	even	6
676.3.g.c.577.2		8	13.11	odd	12
676.3.g.d.437.2		8	13.3	even	3
676.3.g.d.577.2		8	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	52.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26125 + 2.18454i) q^{3} +(1.55727 + 1.55727i) q^{5} +(0.895221 + 3.34101i) q^{7} +(1.31852 - 2.28374i) q^{9} +O(q^{10})\)	\(q+(1.26125 + 2.18454i) q^{3} +(1.55727 + 1.55727i) q^{5} +(0.895221 + 3.34101i) q^{7} +(1.31852 - 2.28374i) q^{9} +(-1.53225 - 0.410566i) q^{11} +(-1.43306 - 12.9208i) q^{13} +(-1.43782 + 5.36603i) q^{15} +(-22.9609 - 13.2565i) q^{17} +(3.34407 - 0.896040i) q^{19} +(-6.16948 + 6.16948i) q^{21} +(-15.6971 + 9.06271i) q^{23} -20.1498i q^{25} +29.3543 q^{27} +(4.04930 + 7.01360i) q^{29} +(30.2741 + 30.2741i) q^{31} +(-1.03565 - 3.86510i) q^{33} +(-3.80875 + 6.59696i) q^{35} +(38.5190 + 10.3211i) q^{37} +(26.4185 - 19.4268i) q^{39} +(-12.3480 + 46.0834i) q^{41} +(-41.4488 - 23.9305i) q^{43} +(5.60969 - 1.50311i) q^{45} +(-60.4301 + 60.4301i) q^{47} +(32.0743 - 18.5181i) q^{49} -66.8787i q^{51} -1.63636 q^{53} +(-1.74677 - 3.02550i) q^{55} +(6.17513 + 6.17513i) q^{57} +(-25.0984 - 93.6684i) q^{59} +(-20.8494 + 36.1121i) q^{61} +(8.81035 + 2.36073i) q^{63} +(17.8895 - 22.3528i) q^{65} +(6.99938 - 26.1220i) q^{67} +(-39.5958 - 22.8606i) q^{69} +(-93.5282 + 25.0608i) q^{71} +(-73.5977 + 73.5977i) q^{73} +(44.0181 - 25.4139i) q^{75} -5.48682i q^{77} +82.5905 q^{79} +(25.1564 + 43.5721i) q^{81} +(34.5538 + 34.5538i) q^{83} +(-15.1124 - 56.4003i) q^{85} +(-10.2143 + 17.6918i) q^{87} +(128.847 + 34.5244i) q^{89} +(41.8855 - 16.3548i) q^{91} +(-27.9519 + 104.318i) q^{93} +(6.60300 + 3.81224i) q^{95} +(67.6244 - 18.1199i) q^{97} +(-2.95793 + 2.95793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 8 * q + 6 * q^5 + 4 * q^7 - 6 * q^9	\( 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9} + 24 q^{11} + 18 q^{13} - 60 q^{15} - 54 q^{17} - 50 q^{19} - 54 q^{21} - 24 q^{23} + 36 q^{27} + 108 q^{29} + 176 q^{31} + 114 q^{33} - 30 q^{35} + 104 q^{37} + 120 q^{39} - 168 q^{41} - 198 q^{43} + 6 q^{45} - 96 q^{47} - 162 q^{49} - 72 q^{53} + 126 q^{55} + 318 q^{57} - 18 q^{61} + 180 q^{63} - 72 q^{65} - 326 q^{67} - 498 q^{69} - 162 q^{71} - 98 q^{73} - 240 q^{75} + 192 q^{79} + 240 q^{81} + 408 q^{83} + 318 q^{85} + 36 q^{87} + 54 q^{89} + 280 q^{91} - 66 q^{93} + 312 q^{95} + 182 q^{97}+O(q^{100}) \) 8 * q + 6 * q^5 + 4 * q^7 - 6 * q^9 + 24 * q^11 + 18 * q^13 - 60 * q^15 - 54 * q^17 - 50 * q^19 - 54 * q^21 - 24 * q^23 + 36 * q^27 + 108 * q^29 + 176 * q^31 + 114 * q^33 - 30 * q^35 + 104 * q^37 + 120 * q^39 - 168 * q^41 - 198 * q^43 + 6 * q^45 - 96 * q^47 - 162 * q^49 - 72 * q^53 + 126 * q^55 + 318 * q^57 - 18 * q^61 + 180 * q^63 - 72 * q^65 - 326 * q^67 - 498 * q^69 - 162 * q^71 - 98 * q^73 - 240 * q^75 + 192 * q^79 + 240 * q^81 + 408 * q^83 + 318 * q^85 + 36 * q^87 + 54 * q^89 + 280 * q^91 - 66 * q^93 + 312 * q^95 + 182 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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