LMFDB - Embedded newform 572.2.n.a.521.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 22 x^{18} - 72 x^{17} + 236 x^{16} - 556 x^{15} + 1232 x^{14} - 1981 x^{13} + \cdots + 400 $ x^20 - 4x^19 + 22x^18 - 72x^17 + 236x^16 - 556x^15 + 1232x^14 - 1981x^13 + 3407x^12 - 4130x^11 + 5358x^10 - 6093x^9 + 10112x^8 - 14136x^7 + 17259x^6 - 10035x^5 + 2921x^4 + 440x^3 + 560x^2 - 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			521.4
Root			$1.06177 + 0.771421i$ of defining polynomial
Character	$\chi$	$=$	572.521
Dual form			572.2.n.a.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.405560 - 1.24819i) q^{3} +(1.75793 - 1.27721i) q^{5} +(-1.12323 - 3.45694i) q^{7} +(1.03356 + 0.750928i) q^{9} +O(q^{10})$	\(q+(0.405560 - 1.24819i) q^{3} +(1.75793 - 1.27721i) q^{5} +(-1.12323 - 3.45694i) q^{7} +(1.03356 + 0.750928i) q^{9} +(-1.01097 - 3.15879i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(-0.881249 - 2.71221i) q^{15} +(-6.38080 + 4.63592i) q^{17} +(-0.410852 + 1.26447i) q^{19} -4.77044 q^{21} +8.86400 q^{23} +(-0.0860364 + 0.264793i) q^{25} +(4.54178 - 3.29980i) q^{27} +(-0.449033 - 1.38198i) q^{29} +(-3.60412 - 2.61855i) q^{31} +(-4.35276 - 0.0191977i) q^{33} +(-6.38980 - 4.64246i) q^{35} +(-0.231785 - 0.713361i) q^{37} +(-1.06177 + 0.771421i) q^{39} +(1.95423 - 6.01451i) q^{41} +4.99652 q^{43} +2.77602 q^{45} +(-2.27493 + 7.00151i) q^{47} +(-5.02568 + 3.65137i) q^{49} +(3.19869 + 9.84456i) q^{51} +(1.93825 + 1.40822i) q^{53} +(-5.81165 - 4.26170i) q^{55} +(1.41167 + 1.02564i) q^{57} +(-0.952776 - 2.93234i) q^{59} +(8.36654 - 6.07865i) q^{61} +(1.43499 - 4.41643i) q^{63} -2.17292 q^{65} -7.64147 q^{67} +(3.59488 - 11.0639i) q^{69} +(8.43294 - 6.12689i) q^{71} +(-0.608347 - 1.87230i) q^{73} +(0.295618 + 0.214779i) q^{75} +(-9.78419 + 7.04291i) q^{77} +(12.0188 + 8.73218i) q^{79} +(-1.09243 - 3.36216i) q^{81} +(-4.40056 + 3.19720i) q^{83} +(-5.29594 + 16.2992i) q^{85} -1.90708 q^{87} +4.17375 q^{89} +(-1.12323 + 3.45694i) q^{91} +(-4.73012 + 3.43663i) q^{93} +(0.892748 + 2.74760i) q^{95} +(12.3159 + 8.94799i) q^{97} +(1.32712 - 4.02397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.405560	−	1.24819i	0.234150	−	0.720640i	−0.763083	−	0.646301i	$-0.776315\pi$
$3$	0.405560	−	1.24819i	0.234150	−	0.720640i	0.997233	−	0.0743394i	$-0.0236848\pi$
$4$		0			0
$5$	1.75793	−	1.27721i	0.786170	−	0.571186i	−0.120655	−	0.992695i	$-0.538499\pi$
$5$	1.75793	−	1.27721i	0.786170	−	0.571186i	0.906824	+	0.421509i	$0.138499\pi$
$6$		0			0
$7$	−1.12323	−	3.45694i	−0.424540	−	1.30660i	−0.903434	−	0.428728i	$-0.858962\pi$
$7$	−1.12323	−	3.45694i	−0.424540	−	1.30660i	0.478893	−	0.877873i	$-0.341038\pi$
$8$		0			0
$9$	1.03356	+	0.750928i	0.344521	+	0.250309i
$10$		0			0
$11$	−1.01097	−	3.15879i	−0.304819	−	0.952410i
$11$	−1.01097	−	3.15879i	−0.304819	−	0.952410i
$12$		0			0
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$		0			0
$15$	−0.881249	−	2.71221i	−0.227538	−	0.700289i
$16$		0			0
$17$	−6.38080	+	4.63592i	−1.54757	+	1.12438i	−0.602215	+	0.798334i	$0.705715\pi$
$17$	−6.38080	+	4.63592i	−1.54757	+	1.12438i	−0.945355	+	0.326041i	$0.894285\pi$
$18$		0			0
$19$	−0.410852	+	1.26447i	−0.0942558	+	0.290090i	−0.987059	−	0.160357i	$-0.948735\pi$
$19$	−0.410852	+	1.26447i	−0.0942558	+	0.290090i	0.892803	+	0.450447i	$0.148735\pi$
$20$		0			0
$21$	−4.77044			−1.04100
$22$		0			0
$23$	8.86400			1.84827			0.924136	−	0.382065i	$-0.124787\pi$
$23$	8.86400			1.84827			0.924136	+	0.382065i	$0.124787\pi$
$24$		0			0
$25$	−0.0860364	+	0.264793i	−0.0172073	+	0.0529586i
$26$		0			0
$27$	4.54178	−	3.29980i	0.874066	−	0.635046i
$28$		0			0
$29$	−0.449033	−	1.38198i	−0.0833833	−	0.256627i	0.900669	−	0.434505i	$-0.143077\pi$
$29$	−0.449033	−	1.38198i	−0.0833833	−	0.256627i	−0.984053	+	0.177878i	$0.943077\pi$
$30$		0			0
$31$	−3.60412	−	2.61855i	−0.647319	−	0.470305i	0.215038	−	0.976606i	$-0.431013\pi$
$31$	−3.60412	−	2.61855i	−0.647319	−	0.470305i	−0.862357	+	0.506301i	$0.831013\pi$
$32$		0			0
$33$	−4.35276	−	0.0191977i	−0.757718	−	0.00334189i
$34$		0			0
$35$	−6.38980	−	4.64246i	−1.08007	−	0.784719i
$36$		0			0
$37$	−0.231785	−	0.713361i	−0.0381052	−	0.117276i	0.930195	−	0.367067i	$-0.119638\pi$
$37$	−0.231785	−	0.713361i	−0.0381052	−	0.117276i	−0.968300	+	0.249791i	$0.919638\pi$
$38$		0			0
$39$	−1.06177	+	0.771421i	−0.170019	+	0.123526i
$40$		0			0
$41$	1.95423	−	6.01451i	0.305200	−	0.939308i	−0.674403	−	0.738364i	$-0.735599\pi$
$41$	1.95423	−	6.01451i	0.305200	−	0.939308i	0.979603	−	0.200945i	$-0.0644011\pi$
$42$		0			0
$43$	4.99652			0.761962			0.380981	−	0.924583i	$-0.375586\pi$
$43$	4.99652			0.761962			0.380981	+	0.924583i	$0.375586\pi$
$44$		0			0
$45$	2.77602			0.413825
$46$		0			0
$47$	−2.27493	+	7.00151i	−0.331832	+	1.02127i	0.636429	+	0.771335i	$0.280411\pi$
$47$	−2.27493	+	7.00151i	−0.331832	+	1.02127i	−0.968261	+	0.249940i	$0.919589\pi$
$48$		0			0
$49$	−5.02568	+	3.65137i	−0.717954	+	0.521624i
$50$		0			0
$51$	3.19869	+	9.84456i	0.447906	+	1.37851i
$52$		0			0
$53$	1.93825	+	1.40822i	0.266239	+	0.193434i	0.712893	−	0.701273i	$-0.247384\pi$
$53$	1.93825	+	1.40822i	0.266239	+	0.193434i	−0.446654	+	0.894707i	$0.647384\pi$
$54$		0			0
$55$	−5.81165	−	4.26170i	−0.783643	−	0.574648i
$56$		0			0
$57$	1.41167	+	1.02564i	0.186980	+	0.135849i
$58$		0			0
$59$	−0.952776	−	2.93234i	−0.124041	−	0.381759i	0.869684	−	0.493609i	$-0.164322\pi$
$59$	−0.952776	−	2.93234i	−0.124041	−	0.381759i	−0.993725	+	0.111850i	$0.964322\pi$
$60$		0			0
$61$	8.36654	−	6.07865i	1.07123	−	0.778291i	0.0950940	−	0.995468i	$-0.469685\pi$
$61$	8.36654	−	6.07865i	1.07123	−	0.778291i	0.976132	+	0.217177i	$0.0696848\pi$
$62$		0			0
$63$	1.43499	−	4.41643i	0.180791	−	0.556418i
$64$		0			0
$65$	−2.17292			−0.269518
$66$		0			0
$67$	−7.64147			−0.933554			−0.466777	−	0.884375i	$-0.654585\pi$
$67$	−7.64147			−0.933554			−0.466777	+	0.884375i	$0.654585\pi$
$68$		0			0
$69$	3.59488	−	11.0639i	0.432773	−	1.33194i
$70$		0			0
$71$	8.43294	−	6.12689i	1.00081	−	0.727128i	0.0385450	−	0.999257i	$-0.487728\pi$
$71$	8.43294	−	6.12689i	1.00081	−	0.727128i	0.962261	+	0.272129i	$0.0877277\pi$
$72$		0			0
$73$	−0.608347	−	1.87230i	−0.0712016	−	0.219136i	0.909123	−	0.416527i	$-0.136753\pi$
$73$	−0.608347	−	1.87230i	−0.0712016	−	0.219136i	−0.980325	+	0.197391i	$0.936753\pi$
$74$		0			0
$75$	0.295618	+	0.214779i	0.0341350	+	0.0248005i
$76$		0			0
$77$	−9.78419	+	7.04291i	−1.11501	+	0.802614i
$78$		0			0
$79$	12.0188	+	8.73218i	1.35222	+	0.982447i	0.998897	+	0.0469468i	$0.0149491\pi$
$79$	12.0188	+	8.73218i	1.35222	+	0.982447i	0.353325	+	0.935501i	$0.385051\pi$
$80$		0			0
$81$	−1.09243	−	3.36216i	−0.121381	−	0.373574i
$82$		0			0
$83$	−4.40056	+	3.19720i	−0.483025	+	0.350938i	−0.802496	−	0.596658i	$-0.796495\pi$
$83$	−4.40056	+	3.19720i	−0.483025	+	0.350938i	0.319471	+	0.947596i	$0.396495\pi$
$84$		0			0
$85$	−5.29594	+	16.2992i	−0.574426	+	1.76790i
$86$		0			0
$87$	−1.90708			−0.204460
$88$		0			0
$89$	4.17375			0.442417			0.221208	−	0.975227i	$-0.429000\pi$
$89$	4.17375			0.442417			0.221208	+	0.975227i	$0.429000\pi$
$90$		0			0
$91$	−1.12323	+	3.45694i	−0.117746	+	0.362386i
$92$		0			0
$93$	−4.73012	+	3.43663i	−0.490490	+	0.356362i
$94$		0			0
$95$	0.892748	+	2.74760i	0.0915940	+	0.281897i
$96$		0			0
$97$	12.3159	+	8.94799i	1.25049	+	0.908531i	0.998250	−	0.0591345i	$-0.0188341\pi$
$97$	12.3159	+	8.94799i	1.25049	+	0.908531i	0.252236	+	0.967666i	$0.418834\pi$
$98$		0			0
$99$	1.32712	−	4.02397i	0.133380	−	0.404425i
$100$		0			0
$101$	−0.399211	−	0.290044i	−0.0397230	−	0.0288604i	0.567747	−	0.823203i	$-0.307815\pi$
$101$	−0.399211	−	0.290044i	−0.0397230	−	0.0288604i	−0.607470	+	0.794343i	$0.707815\pi$
$102$		0			0
$103$	0.648837	+	1.99691i	0.0639318	+	0.196762i	0.977920	−	0.208978i	$-0.0670138\pi$
$103$	0.648837	+	1.99691i	0.0639318	+	0.196762i	−0.913989	+	0.405740i	$0.867014\pi$
$104$		0			0
$105$	−8.38609	+	6.09285i	−0.818399	+	0.594602i
$106$		0			0
$107$	4.32538	−	13.3121i	0.418150	−	1.28693i	−0.491253	−	0.871017i	$-0.663461\pi$
$107$	4.32538	−	13.3121i	0.418150	−	1.28693i	0.909403	−	0.415916i	$-0.136539\pi$
$108$		0			0
$109$	2.41212			0.231039			0.115520	−	0.993305i	$-0.463147\pi$
$109$	2.41212			0.231039			0.115520	+	0.993305i	$0.463147\pi$
$110$		0			0
$111$	−0.984409			−0.0934360
$112$		0			0
$113$	−4.95218	+	15.2412i	−0.465861	+	1.43377i	0.392034	+	0.919951i	$0.371771\pi$
$113$	−4.95218	+	15.2412i	−0.465861	+	1.43377i	−0.857896	+	0.513824i	$0.828229\pi$
$114$		0			0
$115$	15.5823	−	11.3212i	1.45305	−	1.05571i
$116$		0			0
$117$	−0.394786	−	1.21503i	−0.0364980	−	0.112329i
$118$		0			0
$119$	23.1932	+	16.8508i	2.12612	+	1.54471i
$120$		0			0
$121$	−8.95587	+	6.38689i	−0.814170	+	0.580626i
$122$		0			0
$123$	−6.71466	−	4.87849i	−0.605440	−	0.439878i
$124$		0			0
$125$	3.54430	+	10.9082i	0.317011	+	0.975661i
$126$		0			0
$127$	−12.6894	+	9.21937i	−1.12600	+	0.818087i	−0.985108	−	0.171938i	$-0.944997\pi$
$127$	−12.6894	+	9.21937i	−1.12600	+	0.818087i	−0.140892	+	0.990025i	$0.544997\pi$
$128$		0			0
$129$	2.02639	−	6.23658i	0.178413	−	0.549100i
$130$		0			0
$131$	5.47045			0.477956			0.238978	−	0.971025i	$-0.423188\pi$
$131$	5.47045			0.477956			0.238978	+	0.971025i	$0.423188\pi$
$132$		0			0
$133$	4.83268			0.419047
$134$		0			0
$135$	3.76959	−	11.6016i	0.324435	−	0.998508i
$136$		0			0
$137$	10.8448	−	7.87921i	0.926534	−	0.673166i	−0.0186077	−	0.999827i	$-0.505923\pi$
$137$	10.8448	−	7.87921i	0.926534	−	0.673166i	0.945142	+	0.326661i	$0.105923\pi$
$138$		0			0
$139$	2.70631	+	8.32916i	0.229546	+	0.706470i	0.997798	+	0.0663226i	$0.0211267\pi$
$139$	2.70631	+	8.32916i	0.229546	+	0.706470i	−0.768252	+	0.640147i	$0.778873\pi$
$140$		0			0
$141$	7.81656	+	5.67906i	0.658273	+	0.478263i
$142$		0			0
$143$	−1.03880	+	3.14975i	−0.0868684	+	0.263395i
$144$		0			0
$145$	−2.55445	−	1.85591i	−0.212135	−	0.154125i
$146$		0			0
$147$	2.51937	+	7.75383i	0.207794	+	0.639525i
$148$		0			0
$149$	9.82030	−	7.13486i	0.804510	−	0.584511i	−0.107724	−	0.994181i	$-0.534356\pi$
$149$	9.82030	−	7.13486i	0.804510	−	0.584511i	0.912234	+	0.409670i	$0.134356\pi$
$150$		0			0
$151$	−6.02948	+	18.5568i	−0.490672	+	1.51013i	0.332922	+	0.942954i	$0.391965\pi$
$151$	−6.02948	+	18.5568i	−0.490672	+	1.51013i	−0.823594	+	0.567179i	$0.808035\pi$
$152$		0			0
$153$	−10.0762			−0.814612
$154$		0			0
$155$	−9.68022			−0.777534
$156$		0			0
$157$	−5.72313	+	17.6140i	−0.456755	+	1.40575i	0.412307	+	0.911045i	$0.364723\pi$
$157$	−5.72313	+	17.6140i	−0.456755	+	1.40575i	−0.869062	+	0.494703i	$0.835277\pi$
$158$		0			0
$159$	2.54380	−	1.84818i	0.201736	−	0.146570i
$160$		0			0
$161$	−9.95629	−	30.6423i	−0.784666	−	2.41495i
$162$		0			0
$163$	5.71924	+	4.15527i	0.447966	+	0.325466i	0.788792	−	0.614660i	$-0.210707\pi$
$163$	5.71924	+	4.15527i	0.447966	+	0.325466i	−0.340826	+	0.940126i	$0.610707\pi$
$164$		0			0
$165$	−7.67636	+	5.52564i	−0.597604	+	0.430171i
$166$		0			0
$167$	−5.04792	−	3.66753i	−0.390619	−	0.283802i	0.375090	−	0.926988i	$-0.377612\pi$
$167$	−5.04792	−	3.66753i	−0.390619	−	0.283802i	−0.765709	+	0.643187i	$0.777612\pi$
$168$		0			0
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$		0			0
$171$	−1.37417	+	0.998392i	−0.105085	+	0.0763489i
$172$		0			0
$173$	−7.37209	+	22.6890i	−0.560490	+	1.72501i	0.120496	+	0.992714i	$0.461551\pi$
$173$	−7.37209	+	22.6890i	−0.560490	+	1.72501i	−0.680986	+	0.732297i	$0.738449\pi$
$174$		0			0
$175$	1.01201			0.0765009
$176$		0			0
$177$	−4.04652			−0.304155
$178$		0			0
$179$	6.62428	−	20.3874i	0.495122	−	1.52383i	−0.321645	−	0.946860i	$-0.604236\pi$
$179$	6.62428	−	20.3874i	0.495122	−	1.52383i	0.816767	−	0.576968i	$-0.195764\pi$
$180$		0			0
$181$	−3.39179	+	2.46428i	−0.252110	+	0.183168i	−0.706661	−	0.707552i	$-0.749800\pi$
$181$	−3.39179	+	2.46428i	−0.252110	+	0.183168i	0.454552	+	0.890720i	$0.349800\pi$
$182$		0			0
$183$	−4.19415	−	12.9083i	−0.310040	−	0.954206i
$184$		0			0
$185$	−1.31857	−	0.958000i	−0.0969434	−	0.0704335i
$186$		0			0
$187$	21.0947	+	15.4688i	1.54260	+	1.13119i
$188$		0			0
$189$	−16.5086	−	11.9942i	−1.20083	−	0.872452i
$190$		0			0
$191$	−7.03833	−	21.6617i	−0.509276	−	1.56739i	−0.793462	−	0.608620i	$-0.791723\pi$
$191$	−7.03833	−	21.6617i	−0.509276	−	1.56739i	0.284186	−	0.958769i	$-0.408277\pi$
$192$		0			0
$193$	−8.72212	+	6.33699i	−0.627832	+	0.456147i	−0.855648	−	0.517558i	$-0.826841\pi$
$193$	−8.72212	+	6.33699i	−0.627832	+	0.456147i	0.227817	+	0.973704i	$0.426841\pi$
$194$		0			0
$195$	−0.881249	+	2.71221i	−0.0631076	+	0.194225i
$196$		0			0
$197$	17.5902			1.25325			0.626625	−	0.779321i	$-0.284436\pi$
$197$	17.5902			1.25325			0.626625	+	0.779321i	$0.284436\pi$
$198$		0			0
$199$	−23.2817			−1.65040			−0.825198	−	0.564843i	$-0.808937\pi$
$199$	−23.2817			−1.65040			−0.825198	+	0.564843i	$0.808937\pi$
$200$		0			0
$201$	−3.09907	+	9.53797i	−0.218592	+	0.672757i
$202$		0			0
$203$	−4.27306	+	3.10456i	−0.299910	+	0.217897i
$204$		0			0
$205$	−4.24639	−	13.0690i	−0.296581	−	0.912781i
$206$		0			0
$207$	9.16151	+	6.65622i	0.636769	+	0.462640i
$208$		0			0
$209$	4.40956	+	0.0194482i	0.305015	+	0.00134526i
$210$		0			0
$211$	4.30950	+	3.13104i	0.296678	+	0.215550i	0.726159	−	0.687526i	$-0.241303\pi$
$211$	4.30950	+	3.13104i	0.296678	+	0.215550i	−0.429481	+	0.903076i	$0.641303\pi$
$212$		0			0
$213$	−4.22743	−	13.0107i	−0.289659	−	0.891478i
$214$		0			0
$215$	8.78352	−	6.38160i	0.599031	−	0.435222i
$216$		0			0
$217$	−5.00391	+	15.4005i	−0.339688	+	1.04545i
$218$		0			0
$219$	−2.58370			−0.174590
$220$		0			0
$221$	7.88710			0.530544
$222$		0			0
$223$	−0.760634	+	2.34099i	−0.0509358	+	0.156764i	−0.973289	−	0.229584i	$-0.926264\pi$
$223$	−0.760634	+	2.34099i	−0.0509358	+	0.156764i	0.922353	+	0.386348i	$0.126264\pi$
$224$		0			0
$225$	−0.287765	+	0.209073i	−0.0191843	+	0.0139382i
$226$		0			0
$227$	−8.51029	−	26.1920i	−0.564847	−	1.73842i	−0.668404	−	0.743798i	$-0.733022\pi$
$227$	−8.51029	−	26.1920i	−0.564847	−	1.73842i	0.103557	−	0.994624i	$-0.466978\pi$
$228$		0			0
$229$	11.8382	+	8.60096i	0.782291	+	0.568367i	0.905666	−	0.423993i	$-0.139372\pi$
$229$	11.8382	+	8.60096i	0.782291	+	0.568367i	−0.123375	+	0.992360i	$0.539372\pi$
$230$		0			0
$231$	4.82278	+	15.0688i	0.317316	+	0.991454i
$232$		0			0
$233$	−6.80219	−	4.94208i	−0.445626	−	0.323766i	0.342240	−	0.939612i	$-0.388814\pi$
$233$	−6.80219	−	4.94208i	−0.445626	−	0.323766i	−0.787866	+	0.615846i	$0.788814\pi$
$234$		0			0
$235$	4.94323	+	15.2137i	0.322461	+	0.992433i
$236$		0			0
$237$	15.7737	−	11.4603i	1.02461	−	0.744426i
$238$		0			0
$239$	0.175715	−	0.540795i	0.0113660	−	0.0349811i	−0.945213	−	0.326455i	$-0.894146\pi$
$239$	0.175715	−	0.540795i	0.0113660	−	0.0349811i	0.956579	+	0.291474i	$0.0941457\pi$
$240$		0			0
$241$	−14.0946			−0.907916			−0.453958	−	0.891023i	$-0.649988\pi$
$241$	−14.0946			−0.907916			−0.453958	+	0.891023i	$0.649988\pi$
$242$		0			0
$243$	12.2022			0.782771
$244$		0			0
$245$	−4.17122	+	12.8377i	−0.266490	+	0.820170i
$246$		0			0
$247$	1.07562	−	0.781486i	0.0684403	−	0.0497248i
$248$		0			0
$249$	2.20600	+	6.78937i	0.139800	+	0.430259i
$250$		0			0
$251$	−8.79786	−	6.39202i	−0.555316	−	0.403460i	0.274426	−	0.961608i	$-0.411512\pi$
$251$	−8.79786	−	6.39202i	−0.555316	−	0.403460i	−0.829742	+	0.558148i	$0.811512\pi$
$252$		0			0
$253$	−8.96125	−	27.9995i	−0.563389	−	1.76031i
$254$		0			0
$255$	18.1966	+	13.2206i	1.13952	+	0.827908i
$256$		0			0
$257$	−6.41788	−	19.7522i	−0.400336	−	1.23211i	−0.924727	−	0.380631i	$-0.875707\pi$
$257$	−6.41788	−	19.7522i	−0.400336	−	1.23211i	0.524391	−	0.851478i	$-0.324293\pi$
$258$		0			0
$259$	−2.20570	+	1.60253i	−0.137055	+	0.0995766i
$260$		0			0
$261$	0.573664	−	1.76556i	0.0355089	−	0.109285i
$262$		0			0
$263$	12.5911			0.776401			0.388201	−	0.921575i	$-0.373097\pi$
$263$	12.5911			0.776401			0.388201	+	0.921575i	$0.373097\pi$
$264$		0			0
$265$	5.20590			0.319796
$266$		0			0
$267$	1.69271	−	5.20962i	0.103592	−	0.318823i
$268$		0			0
$269$	0.822700	−	0.597727i	0.0501609	−	0.0364440i	−0.562422	−	0.826850i	$-0.690130\pi$
$269$	0.822700	−	0.597727i	0.0501609	−	0.0364440i	0.612583	+	0.790406i	$0.290130\pi$
$270$		0			0
$271$	−1.85443	−	5.70735i	−0.112649	−	0.346697i	0.878801	−	0.477189i	$-0.158344\pi$
$271$	−1.85443	−	5.70735i	−0.112649	−	0.346697i	−0.991449	+	0.130492i	$0.958344\pi$
$272$		0			0
$273$	3.85937	+	2.80399i	0.233579	+	0.169705i
$274$		0			0
$275$	0.923405	+	0.00407265i	0.0556834	+	0.000245590i
$276$		0			0
$277$	6.29504	+	4.57361i	0.378232	+	0.274802i	0.760616	−	0.649202i	$-0.224897\pi$
$277$	6.29504	+	4.57361i	0.378232	+	0.274802i	−0.382384	+	0.924003i	$0.624897\pi$
$278$		0			0
$279$	−1.75875	−	5.41287i	−0.105293	−	0.324060i
$280$		0			0
$281$	1.71496	−	1.24599i	0.102306	−	0.0743296i	−0.535456	−	0.844563i	$-0.679860\pi$
$281$	1.71496	−	1.24599i	0.102306	−	0.0743296i	0.637762	+	0.770233i	$0.279860\pi$
$282$		0			0
$283$	−1.55023	+	4.77111i	−0.0921514	+	0.283613i	−0.986501	−	0.163756i	$-0.947639\pi$
$283$	−1.55023	+	4.77111i	−0.0921514	+	0.283613i	0.894349	+	0.447369i	$0.147639\pi$
$284$		0			0
$285$	3.79157			0.224593
$286$		0			0
$287$	−22.9868			−1.35687
$288$		0			0
$289$	13.9695	−	42.9937i	0.821736	−	2.52904i
$290$		0			0
$291$	16.1636	−	11.7435i	0.947525	−	0.688418i
$292$		0			0
$293$	8.52979	+	26.2520i	0.498316	+	1.53366i	0.811725	+	0.584040i	$0.198529\pi$
$293$	8.52979	+	26.2520i	0.498316	+	1.53366i	−0.313409	+	0.949618i	$0.601471\pi$
$294$		0			0
$295$	−5.42013	−	3.93796i	−0.315572	−	0.229277i
$296$		0			0
$297$	−15.0150	−	11.0105i	−0.871256	−	0.638895i
$298$		0			0
$299$	−7.17112	−	5.21013i	−0.414717	−	0.301309i
$300$		0			0
$301$	−5.61223	−	17.2727i	−0.323484	−	0.995580i
$302$		0			0
$303$	−0.523932	+	0.380659i	−0.0300991	+	0.0218683i
$304$		0			0
$305$	6.94408	−	21.3717i	0.397617	−	1.22374i
$306$		0			0
$307$	−2.45289			−0.139994			−0.0699969	−	0.997547i	$-0.522299\pi$
$307$	−2.45289			−0.139994			−0.0699969	+	0.997547i	$0.522299\pi$
$308$		0			0
$309$	2.75566			0.156764
$310$		0			0
$311$	1.47566	−	4.54162i	0.0836772	−	0.257532i	−0.900461	−	0.434938i	$-0.856770\pi$
$311$	1.47566	−	4.54162i	0.0836772	−	0.257532i	0.984138	+	0.177406i	$0.0567705\pi$
$312$		0			0
$313$	−21.6545	+	15.7329i	−1.22399	+	0.889279i	−0.996425	−	0.0844851i	$-0.973075\pi$
$313$	−21.6545	+	15.7329i	−1.22399	+	0.889279i	−0.227562	+	0.973764i	$0.573075\pi$
$314$		0			0
$315$	−3.11811	−	9.59655i	−0.175686	−	0.540704i
$316$		0			0
$317$	−7.98713	−	5.80299i	−0.448602	−	0.325928i	0.340442	−	0.940266i	$-0.389423\pi$
$317$	−7.98713	−	5.80299i	−0.448602	−	0.325928i	−0.789044	+	0.614337i	$0.789423\pi$
$318$		0			0
$319$	−3.91142	+	2.81554i	−0.218998	+	0.157640i
$320$		0			0
$321$	−14.8618	−	10.7977i	−0.829506	−	0.602671i
$322$		0			0
$323$	−3.24043	−	9.97301i	−0.180302	−	0.554913i
$324$		0			0
$325$	0.225246	−	0.163651i	0.0124944	−	0.00907772i
$326$		0			0
$327$	0.978260	−	3.01077i	0.0540979	−	0.166496i
$328$		0			0
$329$	26.7591			1.47527
$330$		0			0
$331$	−33.9019			−1.86342			−0.931710	−	0.363204i	$-0.881683\pi$
$331$	−33.9019			−1.86342			−0.931710	+	0.363204i	$0.881683\pi$
$332$		0			0
$333$	0.296118	−	0.911358i	0.0162272	−	0.0499421i
$334$		0			0
$335$	−13.4332	+	9.75976i	−0.733932	+	0.533233i
$336$		0			0
$337$	−6.09096	−	18.7460i	−0.331796	−	1.02116i	−0.968279	−	0.249872i	$-0.919612\pi$
$337$	−6.09096	−	18.7460i	−0.331796	−	1.02116i	0.636483	−	0.771291i	$-0.280388\pi$
$338$		0			0
$339$	17.0155	+	12.3625i	0.924154	+	0.671437i
$340$		0			0
$341$	−4.62777	+	14.0319i	−0.250608	+	0.759872i
$342$		0			0
$343$	−2.31699	−	1.68339i	−0.125106	−	0.0908947i
$344$		0			0
$345$	−7.81139	−	24.0410i	−0.420551	−	1.29432i
$346$		0			0
$347$	−18.0823	+	13.1375i	−0.970707	+	0.705260i	−0.955613	−	0.294626i	$-0.904805\pi$
$347$	−18.0823	+	13.1375i	−0.970707	+	0.705260i	−0.0150948	+	0.999886i	$0.504805\pi$
$348$		0			0
$349$	−5.97755	+	18.3970i	−0.319971	+	0.984770i	0.653688	+	0.756764i	$0.273221\pi$
$349$	−5.97755	+	18.3970i	−0.319971	+	0.984770i	−0.973660	+	0.228006i	$0.926779\pi$
$350$		0			0
$351$	−5.61395			−0.299650
$352$		0			0
$353$	−9.30869			−0.495451			−0.247726	−	0.968830i	$-0.579683\pi$
$353$	−9.30869			−0.495451			−0.247726	+	0.968830i	$0.579683\pi$
$354$		0			0
$355$	6.99918	−	21.5413i	0.371478	−	1.14329i
$356$		0			0
$357$	30.4392	−	22.1154i	1.61101	−	1.17047i
$358$		0			0
$359$	−4.56814	−	14.0593i	−0.241097	−	0.742021i	−0.996254	−	0.0864766i	$-0.972439\pi$
$359$	−4.56814	−	14.0593i	−0.241097	−	0.742021i	0.755157	−	0.655544i	$-0.227561\pi$
$360$		0			0
$361$	13.9412	+	10.1289i	0.733749	+	0.533100i
$362$		0			0
$363$	4.33988	+	13.7689i	0.227784	+	0.722677i
$364$		0			0
$365$	−3.46075	−	2.51438i	−0.181144	−	0.131609i
$366$		0			0
$367$	−5.72442	−	17.6179i	−0.298812	−	0.919649i	−0.981914	−	0.189326i	$-0.939370\pi$
$367$	−5.72442	−	17.6179i	−0.298812	−	0.919649i	0.683102	−	0.730323i	$-0.260630\pi$
$368$		0			0
$369$	6.53628	−	4.74889i	0.340265	−	0.247217i
$370$		0			0
$371$	2.69104	−	8.28217i	0.139712	−	0.429989i
$372$		0			0
$373$	21.2738			1.10152			0.550759	−	0.834664i	$-0.314338\pi$
$373$	21.2738			1.10152			0.550759	+	0.834664i	$0.314338\pi$
$374$		0			0
$375$	15.0529			0.777329
$376$		0			0
$377$	−0.449033	+	1.38198i	−0.0231264	+	0.0711756i
$378$		0			0
$379$	4.90544	−	3.56401i	0.251976	−	0.183071i	−0.454626	−	0.890682i	$-0.650227\pi$
$379$	4.90544	−	3.56401i	0.251976	−	0.183071i	0.706602	+	0.707611i	$0.250227\pi$
$380$		0			0
$381$	6.36118	+	19.5777i	0.325893	+	1.00300i
$382$		0			0
$383$	6.82109	+	4.95581i	0.348542	+	0.253230i	0.748257	−	0.663409i	$-0.230891\pi$
$383$	6.82109	+	4.95581i	0.348542	+	0.253230i	−0.399715	+	0.916639i	$0.630891\pi$
$384$		0			0
$385$	−8.20464	+	24.8774i	−0.418147	+	1.26787i
$386$		0			0
$387$	5.16422	+	3.75202i	0.262512	+	0.190726i
$388$		0			0
$389$	5.66236	+	17.4269i	0.287093	+	0.883581i	0.985764	+	0.168138i	$0.0537753\pi$
$389$	5.66236	+	17.4269i	0.287093	+	0.883581i	−0.698671	+	0.715443i	$0.746225\pi$
$390$		0			0
$391$	−56.5594	+	41.0928i	−2.86033	+	2.07815i
$392$		0			0
$393$	2.21860	−	6.82814i	0.111913	−	0.344434i
$394$		0			0
$395$	32.2811			1.62424
$396$		0			0
$397$	29.8072			1.49598			0.747991	−	0.663709i	$-0.231018\pi$
$397$	29.8072			1.49598			0.747991	+	0.663709i	$0.231018\pi$
$398$		0			0
$399$	1.95994	−	6.03208i	0.0981199	−	0.301982i
$400$		0			0
$401$	10.7346	−	7.79917i	0.536062	−	0.389472i	−0.286558	−	0.958063i	$-0.592511\pi$
$401$	10.7346	−	7.79917i	0.536062	−	0.389472i	0.822620	+	0.568591i	$0.192511\pi$
$402$		0			0
$403$	1.37665	+	4.23690i	0.0685759	+	0.211055i
$404$		0			0
$405$	−6.21461	−	4.51518i	−0.308806	−	0.224361i
$406$		0			0
$407$	−2.01903	+	1.45335i	−0.100079	+	0.0720397i
$408$		0			0
$409$	14.1013	+	10.2452i	0.697264	+	0.506592i	0.879040	−	0.476748i	$-0.158185\pi$
$409$	14.1013	+	10.2452i	0.697264	+	0.506592i	−0.181776	+	0.983340i	$0.558185\pi$
$410$		0			0
$411$	−5.43650	−	16.7318i	−0.268163	−	0.825319i
$412$		0			0
$413$	−9.06675	+	6.58738i	−0.446146	+	0.324144i
$414$		0			0
$415$	−3.65239	+	11.2409i	−0.179289	+	0.551794i
$416$		0			0
$417$	11.4939			0.562859
$418$		0			0
$419$	−3.38086			−0.165166			−0.0825829	−	0.996584i	$-0.526317\pi$
$419$	−3.38086			−0.165166			−0.0825829	+	0.996584i	$0.526317\pi$
$420$		0			0
$421$	5.93450	−	18.2645i	0.289230	−	0.890158i	−0.695869	−	0.718169i	$-0.744981\pi$
$421$	5.93450	−	18.2645i	0.289230	−	0.890158i	0.985099	−	0.171989i	$-0.0550195\pi$
$422$		0			0
$423$	−7.60891	+	5.52820i	−0.369958	+	0.268790i
$424$		0			0
$425$	−0.678578	−	2.08845i	−0.0329159	−	0.101305i
$426$		0			0
$427$	−30.4111	−	22.0949i	−1.47170	−	1.06925i
$428$		0			0
$429$	3.51017	+	2.57402i	0.169473	+	0.124275i
$430$		0			0
$431$	−0.209523	−	0.152227i	−0.0100924	−	0.00733253i	0.582728	−	0.812668i	$-0.301985\pi$
$431$	−0.209523	−	0.152227i	−0.0100924	−	0.00733253i	−0.592820	+	0.805335i	$0.701985\pi$
$432$		0			0
$433$	3.20746	+	9.87156i	0.154141	+	0.474397i	0.998073	−	0.0620535i	$-0.0197649\pi$
$433$	3.20746	+	9.87156i	0.154141	+	0.474397i	−0.843932	+	0.536450i	$0.819765\pi$
$434$		0			0
$435$	−3.35251	+	2.43574i	−0.160740	+	0.116785i
$436$		0			0
$437$	−3.64179	+	11.2083i	−0.174210	+	0.536164i
$438$		0			0
$439$	0.279690			0.0133489			0.00667445	−	0.999978i	$-0.497875\pi$
$439$	0.279690			0.0133489			0.00667445	+	0.999978i	$0.497875\pi$
$440$		0			0
$441$	−7.93628			−0.377918
$442$		0			0
$443$	−6.90542	+	21.2527i	−0.328087	+	1.00975i	0.641941	+	0.766754i	$0.278129\pi$
$443$	−6.90542	+	21.2527i	−0.328087	+	1.00975i	−0.970028	+	0.242993i	$0.921871\pi$
$444$		0			0
$445$	7.33716	−	5.33076i	0.347815	−	0.252702i
$446$		0			0
$447$	−4.92291	−	15.1512i	−0.232846	−	0.716625i
$448$		0			0
$449$	1.60584	+	1.16671i	0.0757842	+	0.0550605i	0.625032	−	0.780599i	$-0.285086\pi$
$449$	1.60584	+	1.16671i	0.0757842	+	0.0550605i	−0.549248	+	0.835659i	$0.685086\pi$
$450$		0			0
$451$	−20.9742	−	0.0925061i	−0.987637	−	0.00435594i
$452$		0			0
$453$	20.7170	+	15.0518i	0.973372	+	0.707196i
$454$		0			0
$455$	2.44068	+	7.51166i	0.114421	+	0.352152i
$456$		0			0
$457$	−29.5705	+	21.4843i	−1.38325	+	1.00499i	−0.386684	+	0.922212i	$0.626379\pi$
$457$	−29.5705	+	21.4843i	−1.38325	+	1.00499i	−0.996568	+	0.0827785i	$0.973621\pi$
$458$		0			0
$459$	−13.6826	+	42.1106i	−0.638648	+	1.96556i
$460$		0			0
$461$	−2.21407			−0.103120			−0.0515599	−	0.998670i	$-0.516419\pi$
$461$	−2.21407			−0.103120			−0.0515599	+	0.998670i	$0.516419\pi$
$462$		0			0
$463$	−28.1056			−1.30618			−0.653089	−	0.757281i	$-0.726527\pi$
$463$	−28.1056			−1.30618			−0.653089	+	0.757281i	$0.726527\pi$
$464$		0			0
$465$	−3.92591	+	12.0827i	−0.182060	+	0.560322i
$466$		0			0
$467$	3.04492	−	2.21226i	0.140902	−	0.102371i	−0.515101	−	0.857129i	$-0.672246\pi$
$467$	3.04492	−	2.21226i	0.140902	−	0.102371i	0.656003	+	0.754758i	$0.272246\pi$
$468$		0			0
$469$	8.58312	+	26.4161i	0.396331	+	1.21978i
$470$		0			0
$471$	19.6644	+	14.2870i	0.906089	+	0.658312i
$472$		0			0
$473$	−5.05134	−	15.7829i	−0.232261	−	0.725700i
$474$		0			0
$475$	−0.299475	−	0.217581i	−0.0137408	−	0.00998331i
$476$		0			0
$477$	0.945832	+	2.91097i	0.0433067	+	0.133284i
$478$		0			0
$479$	9.54551	−	6.93522i	0.436146	−	0.316878i	−0.347956	−	0.937511i	$-0.613124\pi$
$479$	9.54551	−	6.93522i	0.436146	−	0.316878i	0.784102	+	0.620633i	$0.213124\pi$
$480$		0			0
$481$	−0.231785	+	0.713361i	−0.0105685	+	0.0325265i
$482$		0			0
$483$	−42.2852			−1.92404
$484$		0			0
$485$	33.0789			1.50203
$486$		0			0
$487$	0.0864347	−	0.266019i	0.00391673	−	0.0120545i	−0.949079	−	0.315038i	$-0.897983\pi$
$487$	0.0864347	−	0.266019i	0.00391673	−	0.0120545i	0.952996	+	0.302984i	$0.0979827\pi$
$488$		0			0
$489$	7.50604	−	5.45346i	0.339435	−	0.246614i
$490$		0			0
$491$	5.89325	+	18.1376i	0.265959	+	0.818536i	0.991471	+	0.130327i	$0.0416028\pi$
$491$	5.89325	+	18.1376i	0.265959	+	0.818536i	−0.725512	+	0.688209i	$0.758397\pi$
$492$		0			0
$493$	9.27194	+	6.73646i	0.417587	+	0.303395i
$494$		0			0
$495$	−2.80648	−	8.76887i	−0.126142	−	0.394131i
$496$		0			0
$497$	−30.6524	−	22.2703i	−1.37495	−	0.998959i
$498$		0			0
$499$	−1.03832	−	3.19562i	−0.0464816	−	0.143056i	0.925122	−	0.379670i	$-0.123962\pi$
$499$	−1.03832	−	3.19562i	−0.0464816	−	0.143056i	−0.971604	+	0.236614i	$0.923962\pi$
$500$		0			0
$501$	−6.62498	+	4.81333i	−0.295982	+	0.215044i
$502$		0			0
$503$	−4.23483	+	13.0335i	−0.188822	+	0.581134i	−0.999993	−	0.00367441i	$-0.998830\pi$
$503$	−4.23483	+	13.0335i	−0.188822	+	0.581134i	0.811171	+	0.584809i	$0.198830\pi$
$504$		0			0
$505$	−1.07223			−0.0477137
$506$		0			0
$507$	1.31242			0.0582866
$508$		0			0
$509$	−8.36832	+	25.7550i	−0.370919	+	1.14157i	0.575272	+	0.817963i	$0.304896\pi$
$509$	−8.36832	+	25.7550i	−0.370919	+	1.14157i	−0.946191	+	0.323609i	$0.895104\pi$
$510$		0			0
$511$	−5.78912	+	4.20604i	−0.256095	+	0.186064i
$512$		0			0
$513$	2.30650	+	7.09868i	0.101834	+	0.313414i
$514$		0			0
$515$	3.69109	+	2.68173i	0.162649	+	0.118171i
$516$		0			0
$517$	24.4162	+	0.107687i	1.07382	+	0.00473606i
$518$		0			0
$519$	25.3302	+	18.4035i	1.11187	+	0.807823i
$520$		0			0
$521$	−9.26475	−	28.5140i	−0.405896	−	1.24922i	−0.920145	−	0.391579i	$-0.871929\pi$
$521$	−9.26475	−	28.5140i	−0.405896	−	1.24922i	0.514248	−	0.857641i	$-0.328071\pi$
$522$		0			0
$523$	−22.6277	+	16.4400i	−0.989439	+	0.718870i	−0.959798	−	0.280691i	$-0.909436\pi$
$523$	−22.6277	+	16.4400i	−0.989439	+	0.718870i	−0.0296412	+	0.999561i	$0.509436\pi$
$524$		0			0
$525$	0.410432	−	1.26318i	0.0179127	−	0.0551296i
$526$		0			0
$527$	35.1365			1.53057
$528$		0			0
$529$	55.5704			2.41611
$530$		0			0
$531$	1.21722	−	3.74623i	0.0528230	−	0.162573i
$532$		0			0
$533$	−5.11624	+	3.71717i	−0.221609	+	0.161008i
$534$		0			0
$535$	−9.39869	−	28.9262i	−0.406341	−	1.25059i
$536$		0			0
$537$	−22.7608	−	16.5367i	−0.982199	−	0.713609i
$538$		0			0
$539$	16.6147	+	12.1836i	0.715647	+	0.524786i
$540$		0			0
$541$	16.5376	+	12.0153i	0.711008	+	0.516578i	0.883499	−	0.468434i	$-0.155181\pi$
$541$	16.5376	+	12.0153i	0.711008	+	0.516578i	−0.172491	+	0.985011i	$0.555181\pi$
$542$		0			0
$543$	1.70030	+	5.23299i	0.0729670	+	0.224569i
$544$		0			0
$545$	4.24034	−	3.08079i	0.181636	−	0.131966i
$546$		0			0
$547$	12.7521	−	39.2469i	0.545239	−	1.67807i	−0.175180	−	0.984536i	$-0.556051\pi$
$547$	12.7521	−	39.2469i	0.545239	−	1.67807i	0.720420	−	0.693538i	$-0.243949\pi$
$548$		0			0
$549$	13.2120			0.563874
$550$		0			0
$551$	1.93196			0.0823043
$552$		0			0
$553$	16.6868	−	51.3566i	0.709593	−	2.18390i
$554$		0			0
$555$	−1.73052	+	1.25730i	−0.0734565	+	0.0533693i
$556$		0			0
$557$	−6.43189	−	19.7953i	−0.272528	−	0.838755i	−0.989863	−	0.142026i	$-0.954638\pi$
$557$	−6.43189	−	19.7953i	−0.272528	−	0.838755i	0.717335	−	0.696729i	$-0.245362\pi$
$558$		0			0
$559$	−4.04227	−	2.93688i	−0.170970	−	0.124217i
$560$		0			0
$561$	27.8631	−	20.0566i	1.17638	−	0.846788i
$562$		0			0
$563$	7.26191	+	5.27609i	0.306053	+	0.222361i	0.730201	−	0.683232i	$-0.239426\pi$
$563$	7.26191	+	5.27609i	0.306053	+	0.222361i	−0.424148	+	0.905593i	$0.639426\pi$
$564$		0			0
$565$	10.7607	+	33.1180i	0.452705	+	1.39328i
$566$		0			0
$567$	−10.3958	+	7.55296i	−0.436580	+	0.317194i
$568$		0			0
$569$	−3.64744	+	11.2257i	−0.152909	+	0.470605i	−0.997943	−	0.0641075i	$-0.979580\pi$
$569$	−3.64744	+	11.2257i	−0.152909	+	0.470605i	0.845034	+	0.534712i	$0.179580\pi$
$570$		0			0
$571$	1.34461			0.0562700			0.0281350	−	0.999604i	$-0.491043\pi$
$571$	1.34461			0.0562700			0.0281350	+	0.999604i	$0.491043\pi$
$572$		0			0
$573$	−29.8923			−1.24877
$574$		0			0
$575$	−0.762627	+	2.34712i	−0.0318037	+	0.0978818i
$576$		0			0
$577$	−16.7900	+	12.1987i	−0.698978	+	0.507837i	−0.879599	−	0.475716i	$-0.842189\pi$
$577$	−16.7900	+	12.1987i	−0.698978	+	0.507837i	0.180622	+	0.983553i	$0.442189\pi$
$578$		0			0
$579$	4.37240	+	13.4568i	0.181711	+	0.559248i
$580$		0			0
$581$	15.9954	+	11.6213i	0.663599	+	0.482133i
$582$		0			0
$583$	2.48875	−	7.54619i	0.103074	−	0.312531i
$584$		0			0
$585$	−2.24585	−	1.63171i	−0.0928545	−	0.0674627i
$586$		0			0
$587$	11.3450	+	34.9163i	0.468258	+	1.44115i	0.854838	+	0.518895i	$0.173656\pi$
$587$	11.3450	+	34.9163i	0.468258	+	1.44115i	−0.386580	+	0.922256i	$0.626344\pi$
$588$		0			0
$589$	4.79184	−	3.48147i	0.197444	−	0.143452i
$590$		0			0
$591$	7.13388	−	21.9558i	0.293448	−	0.903141i
$592$		0			0
$593$	−23.8123			−0.977854			−0.488927	−	0.872325i	$-0.662612\pi$
$593$	−23.8123			−0.977854			−0.488927	+	0.872325i	$0.662612\pi$
$594$		0			0
$595$	62.2940			2.55381
$596$		0			0
$597$	−9.44213	+	29.0599i	−0.386441	+	1.18934i
$598$		0			0
$599$	−11.3433	+	8.24141i	−0.463476	+	0.336735i	−0.794893	−	0.606749i	$-0.792473\pi$
$599$	−11.3433	+	8.24141i	−0.463476	+	0.336735i	0.331417	+	0.943484i	$0.392473\pi$
$600$		0			0
$601$	−1.12503	−	3.46247i	−0.0458908	−	0.141237i	0.925486	−	0.378783i	$-0.123657\pi$
$601$	−1.12503	−	3.46247i	−0.0458908	−	0.141237i	−0.971376	+	0.237545i	$0.923657\pi$
$602$		0			0
$603$	−7.89795	−	5.73819i	−0.321629	−	0.233677i
$604$		0			0
$605$	−7.58639	+	22.6662i	−0.308431	+	0.921513i
$606$		0			0
$607$	25.3918	+	18.4483i	1.03062	+	0.748792i	0.968433	−	0.249273i	$-0.0801916\pi$
$607$	25.3918	+	18.4483i	1.03062	+	0.748792i	0.0621899	+	0.998064i	$0.480192\pi$
$608$		0			0
$609$	2.14208	+	6.59265i	0.0868016	+	0.267148i
$610$		0			0
$611$	5.95584	−	4.32717i	0.240947	−	0.175059i
$612$		0			0
$613$	8.17338	−	25.1551i	0.330120	−	1.01600i	−0.638956	−	0.769243i	$-0.720634\pi$
$613$	8.17338	−	25.1551i	0.330120	−	1.01600i	0.969076	−	0.246761i	$-0.0793664\pi$
$614$		0			0
$615$	−18.0347			−0.727231
$616$		0			0
$617$	−24.6495			−0.992351			−0.496176	−	0.868222i	$-0.665263\pi$
$617$	−24.6495			−0.992351			−0.496176	+	0.868222i	$0.665263\pi$
$618$		0			0
$619$	−4.40467	+	13.5562i	−0.177039	+	0.544869i	−0.999721	−	0.0236326i	$-0.992477\pi$
$619$	−4.40467	+	13.5562i	−0.177039	+	0.544869i	0.822682	+	0.568502i	$0.192477\pi$
$620$		0			0
$621$	40.2583	−	29.2494i	1.61551	−	1.17374i
$622$		0			0
$623$	−4.68808	−	14.4284i	−0.187824	−	0.578062i
$624$		0			0
$625$	19.0365	+	13.8308i	0.761459	+	0.553233i
$626$		0			0
$627$	1.81261	−	5.49605i	0.0723888	−	0.219491i
$628$		0			0
$629$	4.78606	+	3.47727i	0.190833	+	0.138648i
$630$		0			0
$631$	14.0047	+	43.1020i	0.557517	+	1.71586i	0.689201	+	0.724571i	$0.257962\pi$
$631$	14.0047	+	43.1020i	0.557517	+	1.71586i	−0.131683	+	0.991292i	$0.542038\pi$
$632$		0			0
$633$	5.65588	−	4.10924i	0.224801	−	0.163327i
$634$		0			0
$635$	−10.5319	+	32.4140i	−0.417947	+	1.28631i
$636$		0			0
$637$	6.21208			0.246132
$638$		0			0
$639$	13.3168			0.526806
$640$		0			0
$641$	−9.42486	+	29.0067i	−0.372260	+	1.14570i	0.573049	+	0.819521i	$0.305760\pi$
$641$	−9.42486	+	29.0067i	−0.372260	+	1.14570i	−0.945309	+	0.326176i	$0.894240\pi$
$642$		0			0
$643$	−36.9596	+	26.8527i	−1.45754	+	1.05897i	−0.473548	+	0.880768i	$0.657027\pi$
$643$	−36.9596	+	26.8527i	−1.45754	+	1.05897i	−0.983994	+	0.178199i	$0.942973\pi$
$644$		0			0
$645$	−4.40318	−	13.5516i	−0.173375	−	0.533593i
$646$		0			0
$647$	−22.8113	−	16.5734i	−0.896804	−	0.651567i	0.0408388	−	0.999166i	$-0.486997\pi$
$647$	−22.8113	−	16.5734i	−0.896804	−	0.651567i	−0.937643	+	0.347599i	$0.886997\pi$
$648$		0			0
$649$	−8.29942	+	5.97413i	−0.325781	+	0.234505i
$650$		0			0
$651$	17.1932	+	12.4916i	0.673856	+	0.489585i
$652$		0			0
$653$	−11.9561	−	36.7971i	−0.467879	−	1.43998i	−0.855326	−	0.518090i	$-0.826643\pi$
$653$	−11.9561	−	36.7971i	−0.467879	−	1.43998i	0.387447	−	0.921892i	$-0.373357\pi$
$654$		0			0
$655$	9.61667	−	6.98692i	0.375754	−	0.273002i
$656$		0			0
$657$	0.777197	−	2.39196i	0.0303213	−	0.0933194i
$658$		0			0
$659$	−1.98294			−0.0772445			−0.0386222	−	0.999254i	$-0.512297\pi$
$659$	−1.98294			−0.0772445			−0.0386222	+	0.999254i	$0.512297\pi$
$660$		0			0
$661$	−11.6953			−0.454894			−0.227447	−	0.973790i	$-0.573038\pi$
$661$	−11.6953			−0.454894			−0.227447	+	0.973790i	$0.573038\pi$
$662$		0			0
$663$	3.19869	−	9.84456i	0.124227	−	0.382331i
$664$		0			0
$665$	8.49551	−	6.17235i	0.329442	−	0.239354i
$666$		0			0
$667$	−3.98022	−	12.2499i	−0.154115	−	0.474317i
$668$		0			0
$669$	2.61351	+	1.89882i	0.101044	+	0.0734128i
$670$		0			0
$671$	−27.6595	−	20.2828i	−1.06778	−	0.783008i
$672$		0			0
$673$	−26.9965	−	19.6141i	−1.04064	−	0.756070i	−0.0702300	−	0.997531i	$-0.522373\pi$
$673$	−26.9965	−	19.6141i	−1.04064	−	0.756070i	−0.970410	+	0.241461i	$0.922373\pi$
$674$		0			0
$675$	0.483004	+	1.48653i	0.0185908	+	0.0572167i
$676$		0			0
$677$	7.82052	−	5.68194i	0.300567	−	0.218375i	−0.427271	−	0.904123i	$-0.640525\pi$
$677$	7.82052	−	5.68194i	0.300567	−	0.218375i	0.727838	+	0.685749i	$0.240525\pi$
$678$		0			0
$679$	17.0992	−	52.6258i	0.656206	−	2.01959i
$680$		0			0
$681$	−36.1439			−1.38504
$682$		0			0
$683$	−31.2488			−1.19570			−0.597851	−	0.801607i	$-0.703979\pi$
$683$	−31.2488			−1.19570			−0.597851	+	0.801607i	$0.703979\pi$
$684$		0			0
$685$	9.00099	−	27.7022i	0.343910	−	1.05845i
$686$		0			0
$687$	15.5367	−	11.2881i	0.592762	−	0.430667i
$688$		0			0
$689$	−0.740345	−	2.27855i	−0.0282049	−	0.0868058i
$690$		0			0
$691$	−9.41793	−	6.84253i	−0.358275	−	0.260302i	0.394057	−	0.919086i	$-0.371071\pi$
$691$	−9.41793	−	6.84253i	−0.358275	−	0.260302i	−0.752332	+	0.658784i	$0.771071\pi$
$692$		0			0
$693$	−15.4013	−	0.0679269i	−0.585047	−	0.00258033i
$694$		0			0
$695$	15.3956	+	11.1855i	0.583988	+	0.424292i
$696$		0			0
$697$	15.4132	+	47.4370i	0.583817	+	1.79680i
$698$		0			0
$699$	−8.92732	+	6.48608i	−0.337662	+	0.245326i
$700$		0			0
$701$	−9.70921	+	29.8819i	−0.366712	+	1.12862i	0.582191	+	0.813052i	$0.302196\pi$
$701$	−9.70921	+	29.8819i	−0.366712	+	1.12862i	−0.948902	+	0.315570i	$0.897804\pi$
$702$		0			0
$703$	0.997254			0.0376121
$704$		0			0
$705$	20.9943			0.790691
$706$		0			0
$707$	−0.554259	+	1.70583i	−0.0208451	+	0.0641545i
$708$		0			0
$709$	−17.0376	+	12.3785i	−0.639860	+	0.464885i	−0.859802	−	0.510628i	$-0.829413\pi$
$709$	−17.0376	+	12.3785i	−0.639860	+	0.464885i	0.219942	+	0.975513i	$0.429413\pi$
$710$		0			0
$711$	5.86497	+	18.0505i	0.219954	+	0.676948i
$712$		0			0
$713$	−31.9469	−	23.2108i	−1.19642	−	0.869251i
$714$		0			0
$715$	2.19676	+	6.86379i	0.0821542	+	0.256691i
$716$		0			0
$717$	−0.603749	−	0.438649i	−0.0225474	−	0.0163817i
$718$		0			0
$719$	−5.31631	−	16.3619i	−0.198265	−	0.610197i	−0.999923	−	0.0124138i	$-0.996048\pi$
$719$	−5.31631	−	16.3619i	−0.198265	−	0.610197i	0.801658	−	0.597783i	$-0.203952\pi$
$720$		0			0
$721$	6.17442	−	4.48598i	0.229947	−	0.167067i
$722$		0			0
$723$	−5.71622	+	17.5927i	−0.212589	+	0.654281i
$724$		0			0
$725$	0.404572			0.0150254
$726$		0			0
$727$	19.2808			0.715084			0.357542	−	0.933897i	$-0.383615\pi$
$727$	19.2808			0.715084			0.357542	+	0.933897i	$0.383615\pi$
$728$		0			0
$729$	8.22602	−	25.3171i	0.304667	−	0.937670i
$730$		0			0
$731$	−31.8818	+	23.1635i	−1.17919	+	0.856731i
$732$		0			0
$733$	5.33720	+	16.4262i	0.197134	+	0.606716i	0.999945	+	0.0104826i	$0.00333678\pi$
$733$	5.33720	+	16.4262i	0.197134	+	0.606716i	−0.802811	+	0.596234i	$0.796663\pi$
$734$		0			0
$735$	14.3321	+	10.4129i	0.528649	+	0.384086i
$736$		0			0
$737$	7.72531	+	24.1378i	0.284565	+	0.889127i
$738$		0			0
$739$	28.6741	+	20.8329i	1.05479	+	0.766352i	0.973118	−	0.230307i	$-0.0739731\pi$
$739$	28.6741	+	20.8329i	1.05479	+	0.766352i	0.0816749	+	0.996659i	$0.473973\pi$
$740$		0			0
$741$	−0.539210	−	1.65952i	−0.0198084	−	0.0609639i
$742$		0			0
$743$	−15.5625	+	11.3068i	−0.570931	+	0.414806i	−0.835443	−	0.549577i	$-0.814789\pi$
$743$	−15.5625	+	11.3068i	−0.570931	+	0.414806i	0.264512	+	0.964382i	$0.414789\pi$
$744$		0			0
$745$	8.15066	−	25.0852i	0.298617	−	0.919049i
$746$		0			0
$747$	−6.94913			−0.254255
$748$		0			0
$749$	−50.8777			−1.85903
$750$		0			0
$751$	0.0289895	−	0.0892204i	0.00105784	−	0.00325570i	−0.950526	−	0.310644i	$-0.899455\pi$
$751$	0.0289895	−	0.0892204i	0.00105784	−	0.00325570i	0.951584	+	0.307389i	$0.0994552\pi$
$752$		0			0
$753$	−11.5465	+	8.38901i	−0.420777	+	0.305712i
$754$		0			0
$755$	13.1016	+	40.3225i	0.476815	+	1.46749i
$756$		0			0
$757$	26.8775	+	19.5277i	0.976881	+	0.709746i	0.957009	−	0.290057i	$-0.0936743\pi$
$757$	26.8775	+	19.5277i	0.976881	+	0.709746i	0.0198716	+	0.999803i	$0.493674\pi$
$758$		0			0
$759$	−38.5829	−	0.170168i	−1.40047	−	0.00617672i
$760$		0			0
$761$	−28.4898	−	20.6990i	−1.03275	−	0.750340i	−0.0638958	−	0.997957i	$-0.520353\pi$
$761$	−28.4898	−	20.6990i	−1.03275	−	0.750340i	−0.968858	+	0.247617i	$0.920353\pi$
$762$		0			0
$763$	−2.70936	−	8.33856i	−0.0980855	−	0.301876i
$764$		0			0
$765$	−17.7132	+	12.8694i	−0.640424	+	0.465295i
$766$		0			0
$767$	−0.952776	+	2.93234i	−0.0344028	+	0.105881i
$768$		0			0
$769$	−28.1020			−1.01339			−0.506693	−	0.862127i	$-0.669132\pi$
$769$	−28.1020			−1.01339			−0.506693	+	0.862127i	$0.669132\pi$
$770$		0			0
$771$	−27.2572			−0.981645
$772$		0			0
$773$	8.74779	−	26.9229i	0.314636	−	0.968350i	−0.661268	−	0.750150i	$-0.729981\pi$
$773$	8.74779	−	26.9229i	0.314636	−	0.968350i	0.975904	−	0.218200i	$-0.0700187\pi$
$774$		0			0
$775$	1.00346	−	0.729055i	0.0360453	−	0.0261884i
$776$		0			0
$777$	1.10572	+	3.40304i	0.0396673	+	0.122084i
$778$		0			0
$779$	6.80227	+	4.94214i	0.243717	+	0.177071i
$780$		0			0
$781$	−27.8790	−	20.4438i	−0.997589	−	0.731535i
$782$		0			0
$783$	−6.59966	−	4.79493i	−0.235853	−	0.171357i
$784$		0			0
$785$	12.4359	+	38.2738i	0.443856	+	1.36605i
$786$		0			0
$787$	25.9420	−	18.8480i	0.924734	−	0.671858i	−0.0199642	−	0.999801i	$-0.506355\pi$
$787$	25.9420	−	18.8480i	0.924734	−	0.671858i	0.944698	+	0.327942i	$0.106355\pi$
$788$		0			0
$789$	5.10645	−	15.7160i	0.181794	−	0.559506i
$790$		0			0
$791$	58.2504			2.07115
$792$		0			0
$793$	−10.3416			−0.367242
$794$		0			0
$795$	2.11130	−	6.49793i	0.0748802	−	0.230458i
$796$		0			0
$797$	37.3563	−	27.1410i	1.32323	−	0.961382i	0.323343	−	0.946282i	$-0.395193\pi$
$797$	37.3563	−	27.1410i	1.32323	−	0.961382i	0.999886	−	0.0150998i	$-0.00480661\pi$
$798$		0			0
$799$	−17.9426	−	55.2216i	−0.634763	−	1.95360i
$800$		0			0
$801$	4.31384	+	3.13419i	0.152422	+	0.110741i
$802$		0			0
$803$	−5.29917	+	3.81448i	−0.187004	+	0.134610i
$804$		0			0
$805$	−56.6391	−	41.1507i	−1.99627	−	1.45037i
$806$		0			0
$807$	−0.412419	−	1.26930i	−0.0145178	−	0.0446813i
$808$		0			0
$809$	29.0545	−	21.1094i	1.02150	−	0.742165i	0.0549126	−	0.998491i	$-0.482512\pi$
$809$	29.0545	−	21.1094i	1.02150	−	0.742165i	0.966590	+	0.256326i	$0.0825120\pi$
$810$		0			0
$811$	4.58667	−	14.1163i	0.161060	−	0.495691i	−0.837665	−	0.546185i	$-0.816080\pi$
$811$	4.58667	−	14.1163i	0.161060	−	0.495691i	0.998724	+	0.0504939i	$0.0160795\pi$
$812$		0			0
$813$	−7.87592			−0.276220
$814$		0			0
$815$	15.3612			0.538078
$816$		0			0
$817$	−2.05283	+	6.31795i	−0.0718194	+	0.221037i
$818$		0			0
$819$	−3.75684	+	2.72950i	−0.131275	+	0.0953766i
$820$		0			0
$821$	−15.8022	−	48.6341i	−0.551500	−	1.69734i	−0.705013	−	0.709195i	$-0.749059\pi$
$821$	−15.8022	−	48.6341i	−0.551500	−	1.69734i	0.153513	−	0.988147i	$-0.450941\pi$
$822$		0			0
$823$	3.58165	+	2.60222i	0.124849	+	0.0907078i	0.648457	−	0.761251i	$-0.275415\pi$
$823$	3.58165	+	2.60222i	0.124849	+	0.0907078i	−0.523609	+	0.851959i	$0.675415\pi$
$824$		0			0
$825$	0.379579	−	1.15093i	0.0132153	−	0.0400702i
$826$		0			0
$827$	−1.11095	−	0.807149i	−0.0386313	−	0.0280673i	0.568302	−	0.822820i	$-0.307601\pi$
$827$	−1.11095	−	0.807149i	−0.0386313	−	0.0280673i	−0.606933	+	0.794753i	$0.707601\pi$
$828$		0			0
$829$	−7.84097	−	24.1320i	−0.272328	−	0.838140i	−0.989914	−	0.141670i	$-0.954753\pi$
$829$	−7.84097	−	24.1320i	−0.272328	−	0.838140i	0.717586	−	0.696470i	$-0.245247\pi$
$830$		0			0
$831$	8.26173	−	6.00250i	0.286596	−	0.208224i
$832$		0			0
$833$	15.1404	−	46.5973i	0.524583	−	1.61450i
$834$		0			0
$835$	−13.5581			−0.469197
$836$		0			0
$837$	−25.0098			−0.864465
$838$		0			0
$839$	11.1414	−	34.2898i	0.384644	−	1.18381i	−0.552093	−	0.833782i	$-0.686171\pi$
$839$	11.1414	−	34.2898i	0.384644	−	1.18381i	0.936738	−	0.350032i	$-0.113829\pi$
$840$		0			0
$841$	21.7533	−	15.8047i	0.750112	−	0.544988i
$842$		0			0
$843$	−0.859709	−	2.64591i	−0.0296100	−	0.0911301i
$844$		0			0
$845$	1.75793	+	1.27721i	0.0604746	+	0.0439374i
$846$		0			0
$847$	32.1386	+	23.7860i	1.10429	+	0.817296i
$848$		0			0
$849$	5.32652	+	3.86994i	0.182806	+	0.132816i
$850$		0			0
$851$	−2.05454	−	6.32323i	−0.0704288	−	0.216758i
$852$		0			0
$853$	46.7430	−	33.9608i	1.60045	−	1.16279i	0.713802	−	0.700347i	$-0.246972\pi$
$853$	46.7430	−	33.9608i	1.60045	−	1.16279i	0.886647	−	0.462447i	$-0.153028\pi$
$854$		0			0
$855$	−1.14053	+	3.51020i	−0.0390055	+	0.120046i
$856$		0			0
$857$	−49.2368			−1.68190			−0.840949	−	0.541114i	$-0.818003\pi$
$857$	−49.2368			−1.68190			−0.840949	+	0.541114i	$0.818003\pi$
$858$		0			0
$859$	−5.96840			−0.203639			−0.101820	−	0.994803i	$-0.532466\pi$
$859$	−5.96840			−0.203639			−0.101820	+	0.994803i	$0.532466\pi$
$860$		0			0
$861$	−9.32254	+	28.6918i	−0.317711	+	0.977815i
$862$		0			0
$863$	37.4198	−	27.1870i	1.27378	−	0.925458i	0.274437	−	0.961605i	$-0.411509\pi$
$863$	37.4198	−	27.1870i	1.27378	−	0.925458i	0.999346	+	0.0361474i	$0.0115086\pi$
$864$		0			0
$865$	16.0190	+	49.3013i	0.544661	+	1.67629i
$866$		0			0
$867$	−47.9987	−	34.8731i	−1.63012	−	1.18435i
$868$		0			0
$869$	15.4324	−	46.7929i	0.523509	−	1.58734i
$870$		0			0
$871$	6.18208	+	4.49154i	0.209472	+	0.152190i
$872$		0			0
$873$	6.00992	+	18.4966i	0.203405	+	0.626017i
$874$		0			0
$875$	33.7280	−	24.5048i	1.14022	−	0.828415i
$876$		0			0
$877$	−17.5080	+	53.8842i	−0.591204	+	1.81954i	−0.0184243	+	0.999830i	$0.505865\pi$
$877$	−17.5080	+	53.8842i	−0.591204	+	1.81954i	−0.572780	+	0.819709i	$0.694135\pi$
$878$		0			0
$879$	36.2267			1.22190
$880$		0			0
$881$	14.0138			0.472138			0.236069	−	0.971736i	$-0.424141\pi$
$881$	14.0138			0.472138			0.236069	+	0.971736i	$0.424141\pi$
$882$		0			0
$883$	12.3912	−	38.1361i	0.416996	−	1.28338i	−0.493458	−	0.869770i	$-0.664267\pi$
$883$	12.3912	−	38.1361i	0.416996	−	1.28338i	0.910453	−	0.413611i	$-0.135733\pi$
$884$		0			0
$885$	−7.11349	+	5.16825i	−0.239117	+	0.173729i
$886$		0			0
$887$	10.2020	+	31.3986i	0.342550	+	1.05426i	0.962882	+	0.269922i	$0.0869979\pi$
$887$	10.2020	+	31.3986i	0.342550	+	1.05426i	−0.620332	+	0.784339i	$0.713002\pi$
$888$		0			0
$889$	46.1239	+	33.5110i	1.54694	+	1.12392i
$890$		0			0
$891$	−9.51594	+	6.84982i	−0.318796	+	0.229478i
$892$		0			0
$893$	−7.91855	−	5.75316i	−0.264984	−	0.192522i
$894$		0			0
$895$	−14.3940	−	44.3003i	−0.481139	−	1.48079i
$896$		0			0
$897$	−9.41152	+	6.83787i	−0.314242	+	0.228310i
$898$		0			0
$899$	−2.00041	+	6.15664i	−0.0667175	+	0.205335i
$900$		0			0
$901$	−18.8960			−0.629516
$902$		0			0
$903$	−23.8356			−0.793198
$904$		0			0
$905$	−2.81512	+	8.66406i	−0.0935778	+	0.288003i
$906$		0			0
$907$	−22.9251	+	16.6560i	−0.761215	+	0.553055i	−0.899283	−	0.437368i	$-0.855911\pi$
$907$	−22.9251	+	16.6560i	−0.761215	+	0.553055i	0.138068	+	0.990423i	$0.455911\pi$
$908$		0			0
$909$	−0.194808	−	0.599557i	−0.00646137	−	0.0198861i
$910$		0			0
$911$	11.1630	+	8.11042i	0.369848	+	0.268710i	0.757148	−	0.653244i	$-0.226592\pi$
$911$	11.1630	+	8.11042i	0.369848	+	0.268710i	−0.387300	+	0.921954i	$0.626592\pi$
$912$		0			0
$913$	14.5481	+	10.6682i	0.481472	+	0.353065i
$914$		0			0
$915$	−23.8596	−	17.3350i	−0.788773	−	0.573077i
$916$		0			0
$917$	−6.14457	−	18.9110i	−0.202911	−	0.624497i
$918$		0			0
$919$	−8.63953	+	6.27699i	−0.284992	+	0.207059i	−0.721092	−	0.692840i	$-0.756359\pi$
$919$	−8.63953	+	6.27699i	−0.284992	+	0.207059i	0.436100	+	0.899898i	$0.356359\pi$
$920$		0			0
$921$	−0.994794	+	3.06166i	−0.0327796	+	0.100885i
$922$		0			0
$923$	−10.4237			−0.343100
$924$		0			0
$925$	0.208835			0.00686645
$926$		0			0
$927$	−0.828924	+	2.55117i	−0.0272254	+	0.0837913i
$928$		0			0
$929$	0.813444	−	0.591002i	0.0266882	−	0.0193901i	−0.574361	−	0.818602i	$-0.694749\pi$
$929$	0.813444	−	0.591002i	0.0266882	−	0.0193901i	0.601049	+	0.799212i	$0.294749\pi$
$930$		0			0
$931$	−2.55224	−	7.85500i	−0.0836464	−	0.257437i
$932$		0			0
$933$	−5.07032	−	3.68380i	−0.165995	−	0.120602i
$934$		0			0
$935$	56.8399	+	0.250690i	1.85886	+	0.00819845i
$936$		0			0
$937$	−28.0666	−	20.3916i	−0.916895	−	0.666163i	0.0258539	−	0.999666i	$-0.491770\pi$
$937$	−28.0666	−	20.3916i	−0.916895	−	0.666163i	−0.942749	+	0.333502i	$0.891770\pi$
$938$		0			0
$939$	10.8554	+	33.4095i	0.354253	+	1.09028i
$940$		0			0
$941$	37.9590	−	27.5788i	1.23743	−	0.899043i	0.240003	−	0.970772i	$-0.422852\pi$
$941$	37.9590	−	27.5788i	1.23743	−	0.899043i	0.997424	+	0.0717291i	$0.0228517\pi$
$942$		0			0
$943$	17.3223	−	53.3126i	0.564092	−	1.73610i
$944$		0			0
$945$	−44.3402			−1.44239
$946$		0			0
$947$	30.7378			0.998846			0.499423	−	0.866358i	$-0.333545\pi$
$947$	30.7378			0.998846			0.499423	+	0.866358i	$0.333545\pi$
$948$		0			0
$949$	−0.608347	+	1.87230i	−0.0197478	+	0.0607774i
$950$		0			0
$951$	−10.4825	+	7.61596i	−0.339917	+	0.246964i
$952$		0			0
$953$	8.23923	+	25.3577i	0.266895	+	0.821418i	0.991251	+	0.131992i	$0.0421372\pi$
$953$	8.23923	+	25.3577i	0.266895	+	0.821418i	−0.724356	+	0.689426i	$0.757863\pi$
$954$		0			0
$955$	−40.0395	−	29.0904i	−1.29565	−	0.941343i
$956$		0			0
$957$	1.92800	+	6.02405i	0.0623234	+	0.194730i
$958$		0			0
$959$	−39.4192	−	28.6397i	−1.27291	−	0.924824i
$960$		0			0
$961$	−3.44663	−	10.6076i	−0.111182	−	0.342182i
$962$		0			0
$963$	14.4670	−	10.5109i	0.466193	−	0.338709i
$964$		0			0
$965$	−7.23920	+	22.2800i	−0.233038	+	0.717217i
$966$		0			0
$967$	−49.0754			−1.57816			−0.789080	−	0.614291i	$-0.789442\pi$
$967$	−49.0754			−1.57816			−0.789080	+	0.614291i	$0.789442\pi$
$968$		0			0
$969$	−13.7623			−0.442110
$970$		0			0
$971$	7.33208	−	22.5658i	0.235298	−	0.724171i	−0.761784	−	0.647831i	$-0.775676\pi$
$971$	7.33208	−	22.5658i	0.235298	−	0.724171i	0.997082	−	0.0763406i	$-0.0243236\pi$
$972$		0			0
$973$	25.7536	−	18.7111i	0.825623	−	0.599850i
$974$		0			0
$975$	−0.112916	−	0.347519i	−0.00361620	−	0.0111295i
$976$		0			0
$977$	40.7532	+	29.6090i	1.30381	+	0.947274i	0.999985	−	0.00545318i	$-0.00173581\pi$
$977$	40.7532	+	29.6090i	1.30381	+	0.947274i	0.303826	+	0.952728i	$0.401736\pi$
$978$		0			0
$979$	−4.21955	−	13.1840i	−0.134857	−	0.421362i
$980$		0			0
$981$	2.49308	+	1.81133i	0.0795980	+	0.0578313i
$982$		0			0
$983$	3.33765	+	10.2722i	0.106454	+	0.327633i	0.990069	−	0.140582i	$-0.0448973\pi$
$983$	3.33765	+	10.2722i	0.106454	+	0.327633i	−0.883615	+	0.468215i	$0.844897\pi$
$984$		0			0
$985$	30.9223	−	22.4664i	0.985267	−	0.715838i
$986$		0			0
$987$	10.8524	−	33.4003i	0.345436	−	1.06314i
$988$		0			0
$989$	44.2891			1.40831
$990$		0			0
$991$	−44.8142			−1.42357			−0.711785	−	0.702397i	$-0.752113\pi$
$991$	−44.8142			−1.42357			−0.711785	+	0.702397i	$0.752113\pi$
$992$		0			0
$993$	−13.7493	+	42.3159i	−0.436320	+	1.34285i
$994$		0			0
$995$	−40.9276	+	29.7356i	−1.29749	+	0.942683i
$996$		0			0
$997$	0.323251	+	0.994864i	0.0102375	+	0.0315076i	0.956045	−	0.293221i	$-0.0947271\pi$
$997$	0.323251	+	0.994864i	0.0102375	+	0.0315076i	−0.945807	+	0.324728i	$0.894727\pi$
$998$		0			0
$999$	−3.40666	−	2.47508i	−0.107782	−	0.0783082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.a.521.4	yes	20
11.3	even	5	inner	572.2.n.a.157.4	✓	20
11.5	even	5		6292.2.a.w.1.7		10
11.6	odd	10		6292.2.a.x.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.a.157.4	✓	20	11.3	even	5	inner
572.2.n.a.521.4	yes	20	1.1	even	1	trivial
6292.2.a.w.1.7		10	11.5	even	5
6292.2.a.x.1.7		10	11.6	odd	10

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.405560 - 1.24819i) q^{3} +(1.75793 - 1.27721i) q^{5} +(-1.12323 - 3.45694i) q^{7} +(1.03356 + 0.750928i) q^{9} +O(q^{10})\)	\(q+(0.405560 - 1.24819i) q^{3} +(1.75793 - 1.27721i) q^{5} +(-1.12323 - 3.45694i) q^{7} +(1.03356 + 0.750928i) q^{9} +(-1.01097 - 3.15879i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(-0.881249 - 2.71221i) q^{15} +(-6.38080 + 4.63592i) q^{17} +(-0.410852 + 1.26447i) q^{19} -4.77044 q^{21} +8.86400 q^{23} +(-0.0860364 + 0.264793i) q^{25} +(4.54178 - 3.29980i) q^{27} +(-0.449033 - 1.38198i) q^{29} +(-3.60412 - 2.61855i) q^{31} +(-4.35276 - 0.0191977i) q^{33} +(-6.38980 - 4.64246i) q^{35} +(-0.231785 - 0.713361i) q^{37} +(-1.06177 + 0.771421i) q^{39} +(1.95423 - 6.01451i) q^{41} +4.99652 q^{43} +2.77602 q^{45} +(-2.27493 + 7.00151i) q^{47} +(-5.02568 + 3.65137i) q^{49} +(3.19869 + 9.84456i) q^{51} +(1.93825 + 1.40822i) q^{53} +(-5.81165 - 4.26170i) q^{55} +(1.41167 + 1.02564i) q^{57} +(-0.952776 - 2.93234i) q^{59} +(8.36654 - 6.07865i) q^{61} +(1.43499 - 4.41643i) q^{63} -2.17292 q^{65} -7.64147 q^{67} +(3.59488 - 11.0639i) q^{69} +(8.43294 - 6.12689i) q^{71} +(-0.608347 - 1.87230i) q^{73} +(0.295618 + 0.214779i) q^{75} +(-9.78419 + 7.04291i) q^{77} +(12.0188 + 8.73218i) q^{79} +(-1.09243 - 3.36216i) q^{81} +(-4.40056 + 3.19720i) q^{83} +(-5.29594 + 16.2992i) q^{85} -1.90708 q^{87} +4.17375 q^{89} +(-1.12323 + 3.45694i) q^{91} +(-4.73012 + 3.43663i) q^{93} +(0.892748 + 2.74760i) q^{95} +(12.3159 + 8.94799i) q^{97} +(1.32712 - 4.02397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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