LMFDB - Embedded newform 92.2.e.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(9,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("92.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
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} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + \cdots + 529 $ x^20 - 9x^19 + 51x^18 - 200x^17 + 633x^16 - 1688x^15 + 3957x^14 - 8161x^13 + 14788x^12 - 23925x^11 + 35080x^10 - 43945x^9 + 57269x^8 - 57348x^7 + 52821x^6 - 34986x^5 + 26231x^4 + 96928x^3 + 49370x^2 + 8165*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			9.2
Root			$1.20400 - 2.63640i$ of defining polynomial
Character	$\chi$	$=$	92.9
Dual form			92.2.e.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89799 + 2.19040i) q^{3} +(-0.556197 - 3.86843i) q^{5} +(-1.06324 + 2.32817i) q^{7} +(-0.768534 + 5.34527i) q^{9} +O(q^{10})$	\(q+(1.89799 + 2.19040i) q^{3} +(-0.556197 - 3.86843i) q^{5} +(-1.06324 + 2.32817i) q^{7} +(-0.768534 + 5.34527i) q^{9} +(-2.52183 - 0.740475i) q^{11} +(-0.904981 - 1.98163i) q^{13} +(7.41777 - 8.56056i) q^{15} +(-0.0617222 - 0.0396665i) q^{17} +(0.698502 - 0.448900i) q^{19} +(-7.11766 + 2.08993i) q^{21} +(1.49943 - 4.55540i) q^{23} +(-9.85797 + 2.89456i) q^{25} +(-5.85230 + 3.76105i) q^{27} +(6.31971 + 4.06143i) q^{29} +(-4.12070 + 4.75554i) q^{31} +(-3.16447 - 6.92922i) q^{33} +(9.59776 + 2.81816i) q^{35} +(0.834432 - 5.80361i) q^{37} +(2.62292 - 5.74340i) q^{39} +(0.336574 + 2.34092i) q^{41} +(5.43299 + 6.27000i) q^{43} +21.1053 q^{45} -4.84198 q^{47} +(0.294111 + 0.339422i) q^{49} +(-0.0302629 - 0.210483i) q^{51} +(0.347961 - 0.761928i) q^{53} +(-1.46185 + 10.1674i) q^{55} +(2.30902 + 0.677991i) q^{57} +(-0.679933 - 1.48885i) q^{59} +(-7.80313 + 9.00529i) q^{61} +(-11.6276 - 7.47260i) q^{63} +(-7.16247 + 4.60304i) q^{65} +(1.65680 - 0.486481i) q^{67} +(12.8241 - 5.36178i) q^{69} +(-2.30706 + 0.677414i) q^{71} +(9.00849 - 5.78941i) q^{73} +(-25.0506 - 16.0990i) q^{75} +(4.40526 - 5.08395i) q^{77} +(3.03929 + 6.65512i) q^{79} +(-3.80136 - 1.11618i) q^{81} +(0.102309 - 0.711573i) q^{83} +(-0.119117 + 0.260831i) q^{85} +(3.09861 + 21.5513i) q^{87} +(0.113687 + 0.131202i) q^{89} +5.57580 q^{91} -18.2376 q^{93} +(-2.12505 - 2.45243i) q^{95} +(-2.24709 - 15.6289i) q^{97} +(5.89614 - 12.9108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.89799	+	2.19040i	1.09581	+	1.26463i	0.961831	+	0.273644i	$0.0882291\pi$
$3$	1.89799	+	2.19040i	1.09581	+	1.26463i	0.133976	+	0.990985i	$0.457225\pi$
$4$		0			0
$5$	−0.556197	−	3.86843i	−0.248739	−	1.73002i	−0.605521	−	0.795829i	$-0.707035\pi$
$5$	−0.556197	−	3.86843i	−0.248739	−	1.73002i	0.356782	−	0.934188i	$-0.383874\pi$
$6$		0			0
$7$	−1.06324	+	2.32817i	−0.401868	+	0.879967i	0.595210	+	0.803570i	$0.297069\pi$
$7$	−1.06324	+	2.32817i	−0.401868	+	0.879967i	−0.997077	+	0.0763970i	$0.975658\pi$
$8$		0			0
$9$	−0.768534	+	5.34527i	−0.256178	+	1.78176i
$10$		0			0
$11$	−2.52183	−	0.740475i	−0.760359	−	0.223262i	−0.121506	−	0.992591i	$-0.538772\pi$
$11$	−2.52183	−	0.740475i	−0.760359	−	0.223262i	−0.638853	+	0.769329i	$0.720591\pi$
$12$		0			0
$13$	−0.904981	−	1.98163i	−0.250997	−	0.549606i	0.741631	−	0.670808i	$-0.234052\pi$
$13$	−0.904981	−	1.98163i	−0.250997	−	0.549606i	−0.992628	+	0.121202i	$0.961325\pi$
$14$		0			0
$15$	7.41777	−	8.56056i	1.91526	−	2.21033i
$16$		0			0
$17$	−0.0617222	−	0.0396665i	−0.0149698	−	0.00962053i	0.533134	−	0.846031i	$-0.321014\pi$
$17$	−0.0617222	−	0.0396665i	−0.0149698	−	0.00962053i	−0.548104	+	0.836410i	$0.684650\pi$
$18$		0			0
$19$	0.698502	−	0.448900i	0.160247	−	0.102985i	−0.458059	−	0.888922i	$-0.651455\pi$
$19$	0.698502	−	0.448900i	0.160247	−	0.102985i	0.618307	+	0.785937i	$0.287819\pi$
$20$		0			0
$21$	−7.11766	+	2.08993i	−1.55320	+	0.456061i
$22$		0			0
$23$	1.49943	−	4.55540i	0.312653	−	0.949868i
$23$	1.49943	−	4.55540i	0.312653	−	0.949868i
$24$		0			0
$25$	−9.85797	+	2.89456i	−1.97159	+	0.578912i
$26$		0			0
$27$	−5.85230	+	3.76105i	−1.12628	+	0.723814i
$28$		0			0
$29$	6.31971	+	4.06143i	1.17354	+	0.754189i	0.974188	−	0.225739i	$-0.0724796\pi$
$29$	6.31971	+	4.06143i	1.17354	+	0.754189i	0.199353	+	0.979928i	$0.436116\pi$
$30$		0			0
$31$	−4.12070	+	4.75554i	−0.740100	+	0.854121i	−0.993570	−	0.113222i	$-0.963883\pi$
$31$	−4.12070	+	4.75554i	−0.740100	+	0.854121i	0.253470	+	0.967343i	$0.418428\pi$
$32$		0			0
$33$	−3.16447	−	6.92922i	−0.550864	−	1.20622i
$34$		0			0
$35$	9.59776	+	2.81816i	1.62232	+	0.476356i
$36$		0			0
$37$	0.834432	−	5.80361i	0.137180	−	0.954107i	−0.798685	−	0.601749i	$-0.794471\pi$
$37$	0.834432	−	5.80361i	0.137180	−	0.954107i	0.935865	−	0.352358i	$-0.114620\pi$
$38$		0			0
$39$	2.62292	−	5.74340i	0.420003	−	0.919679i
$40$		0			0
$41$	0.336574	+	2.34092i	0.0525640	+	0.365590i	0.999078	+	0.0429282i	$0.0136687\pi$
$41$	0.336574	+	2.34092i	0.0525640	+	0.365590i	−0.946514	+	0.322662i	$0.895422\pi$
$42$		0			0
$43$	5.43299	+	6.27000i	0.828523	+	0.956166i	0.999577	−	0.0290952i	$-0.00926261\pi$
$43$	5.43299	+	6.27000i	0.828523	+	0.956166i	−0.171054	+	0.985262i	$0.554717\pi$
$44$		0			0
$45$	21.1053			3.14619
$46$		0			0
$47$	−4.84198			−0.706275			−0.353138	−	0.935571i	$-0.614885\pi$
$47$	−4.84198			−0.706275			−0.353138	+	0.935571i	$0.614885\pi$
$48$		0			0
$49$	0.294111	+	0.339422i	0.0420158	+	0.0484889i
$50$		0			0
$51$	−0.0302629	−	0.210483i	−0.00423766	−	0.0294735i
$52$		0			0
$53$	0.347961	−	0.761928i	0.0477961	−	0.104659i	−0.884227	−	0.467056i	$-0.845314\pi$
$53$	0.347961	−	0.761928i	0.0477961	−	0.104659i	0.932024	+	0.362398i	$0.118042\pi$
$54$		0			0
$55$	−1.46185	+	10.1674i	−0.197115	+	1.37097i
$56$		0			0
$57$	2.30902	+	0.677991i	0.305838	+	0.0898021i
$58$		0			0
$59$	−0.679933	−	1.48885i	−0.0885197	−	0.193831i	0.860195	−	0.509966i	$-0.170342\pi$
$59$	−0.679933	−	1.48885i	−0.0885197	−	0.193831i	−0.948714	+	0.316135i	$0.897615\pi$
$60$		0			0
$61$	−7.80313	+	9.00529i	−0.999088	+	1.15301i	−0.0108728	+	0.999941i	$0.503461\pi$
$61$	−7.80313	+	9.00529i	−0.999088	+	1.15301i	−0.988216	+	0.153069i	$0.951084\pi$
$62$		0			0
$63$	−11.6276	−	7.47260i	−1.46494	−	0.941458i
$64$		0			0
$65$	−7.16247	+	4.60304i	−0.888395	+	0.570937i
$66$		0			0
$67$	1.65680	−	0.486481i	0.202411	−	0.0594331i	−0.178956	−	0.983857i	$-0.557272\pi$
$67$	1.65680	−	0.486481i	0.202411	−	0.0594331i	0.381366	+	0.924424i	$0.375454\pi$
$68$		0			0
$69$	12.8241	−	5.36178i	1.54384	−	0.645482i
$70$		0			0
$71$	−2.30706	+	0.677414i	−0.273797	+	0.0803942i	−0.415749	−	0.909479i	$-0.636480\pi$
$71$	−2.30706	+	0.677414i	−0.273797	+	0.0803942i	0.141951	+	0.989874i	$0.454662\pi$
$72$		0			0
$73$	9.00849	−	5.78941i	1.05436	−	0.677599i	0.105866	−	0.994380i	$-0.466239\pi$
$73$	9.00849	−	5.78941i	1.05436	−	0.677599i	0.948498	+	0.316782i	$0.102602\pi$
$74$		0			0
$75$	−25.0506	−	16.0990i	−2.89259	−	1.85896i
$76$		0			0
$77$	4.40526	−	5.08395i	0.502026	−	0.579369i
$78$		0			0
$79$	3.03929	+	6.65512i	0.341947	+	0.748759i	0.999991	−	0.00422015i	$-0.00134332\pi$
$79$	3.03929	+	6.65512i	0.341947	+	0.748759i	−0.658044	+	0.752979i	$0.728616\pi$
$80$		0			0
$81$	−3.80136	−	1.11618i	−0.422374	−	0.124020i
$82$		0			0
$83$	0.102309	−	0.711573i	0.0112298	−	0.0781053i	−0.983436	−	0.181257i	$-0.941984\pi$
$83$	0.102309	−	0.711573i	0.0112298	−	0.0781053i	0.994666	+	0.103151i	$0.0328926\pi$
$84$		0			0
$85$	−0.119117	+	0.260831i	−0.0129201	+	0.0282911i
$86$		0			0
$87$	3.09861	+	21.5513i	0.332205	+	2.31054i
$88$		0			0
$89$	0.113687	+	0.131202i	0.0120508	+	0.0139073i	0.761743	−	0.647879i	$-0.224344\pi$
$89$	0.113687	+	0.131202i	0.0120508	+	0.0139073i	−0.749692	+	0.661787i	$0.769798\pi$
$90$		0			0
$91$	5.57580			0.584503
$92$		0			0
$93$	−18.2376			−1.89115
$94$		0			0
$95$	−2.12505	−	2.45243i	−0.218025	−	0.251614i
$96$		0			0
$97$	−2.24709	−	15.6289i	−0.228158	−	1.58687i	−0.705861	−	0.708351i	$-0.749440\pi$
$97$	−2.24709	−	15.6289i	−0.228158	−	1.58687i	0.477703	−	0.878521i	$-0.341469\pi$
$98$		0			0
$99$	5.89614	−	12.9108i	0.592585	−	1.29758i
$100$		0			0
$101$	2.46014	−	17.1106i	0.244793	−	1.70257i	−0.382639	−	0.923898i	$-0.624985\pi$
$101$	2.46014	−	17.1106i	0.244793	−	1.70257i	0.627431	−	0.778672i	$-0.284106\pi$
$102$		0			0
$103$	−0.384988	−	0.113043i	−0.0379340	−	0.0111384i	0.262710	−	0.964875i	$-0.415384\pi$
$103$	−0.384988	−	0.113043i	−0.0379340	−	0.0111384i	−0.300645	+	0.953736i	$0.597202\pi$
$104$		0			0
$105$	12.0436	+	26.3718i	1.17533	+	2.57362i
$106$		0			0
$107$	−3.42951	+	3.95787i	−0.331543	+	0.382621i	−0.896906	−	0.442221i	$-0.854191\pi$
$107$	−3.42951	+	3.95787i	−0.331543	+	0.382621i	0.565363	+	0.824842i	$0.308736\pi$
$108$		0			0
$109$	5.43936	+	3.49567i	0.520997	+	0.334824i	0.774566	−	0.632493i	$-0.217968\pi$
$109$	5.43936	+	3.49567i	0.520997	+	0.334824i	−0.253570	+	0.967317i	$0.581605\pi$
$110$		0			0
$111$	14.2960	−	9.18746i	1.35691	−	0.872035i
$112$		0			0
$113$	−18.7840	+	5.51547i	−1.76705	+	0.518852i	−0.993394	−	0.114756i	$-0.963391\pi$
$113$	−18.7840	+	5.51547i	−1.76705	+	0.518852i	−0.773654	+	0.633608i	$0.781573\pi$
$114$		0			0
$115$	−18.4563	−	3.26674i	−1.72106	−	0.304625i
$116$		0			0
$117$	11.2879	−	3.31442i	1.04356	−	0.306418i
$118$		0			0
$119$	0.157976	−	0.101525i	0.0144817	−	0.00930679i
$120$		0			0
$121$	−3.44249	−	2.21235i	−0.312954	−	0.201123i
$122$		0			0
$123$	−4.48874	+	5.18028i	−0.404736	+	0.467090i
$124$		0			0
$125$	8.56273	+	18.7498i	0.765874	+	1.67703i
$126$		0			0
$127$	−12.6978	−	3.72841i	−1.12675	−	0.330843i	−0.335319	−	0.942105i	$-0.608844\pi$
$127$	−12.6978	−	3.72841i	−1.12675	−	0.330843i	−0.791429	+	0.611262i	$0.790662\pi$
$128$		0			0
$129$	−3.42205	+	23.8008i	−0.301294	+	2.09555i
$130$		0			0
$131$	8.20198	−	17.9598i	0.716610	−	1.56916i	−0.101985	−	0.994786i	$-0.532519\pi$
$131$	8.20198	−	17.9598i	0.716610	−	1.56916i	0.818595	−	0.574371i	$-0.194753\pi$
$132$		0			0
$133$	0.302441	+	2.10353i	0.0262250	+	0.182399i
$134$		0			0
$135$	17.8044	+	20.5474i	1.53236	+	1.76844i
$136$		0			0
$137$	0.349833			0.0298882			0.0149441	−	0.999888i	$-0.495243\pi$
$137$	0.349833			0.0298882			0.0149441	+	0.999888i	$0.495243\pi$
$138$		0			0
$139$	20.1757			1.71128			0.855639	−	0.517574i	$-0.173165\pi$
$139$	20.1757			1.71128			0.855639	+	0.517574i	$0.173165\pi$
$140$		0			0
$141$	−9.19004	−	10.6059i	−0.773941	−	0.893176i
$142$		0			0
$143$	0.814855	+	5.66744i	0.0681416	+	0.473936i
$144$		0			0
$145$	12.1964	−	26.7063i	1.01285	−	2.21784i
$146$		0			0
$147$	−0.185250	+	1.28844i	−0.0152792	+	0.106269i
$148$		0			0
$149$	−4.81994	−	1.41526i	−0.394865	−	0.115943i	0.0782712	−	0.996932i	$-0.475060\pi$
$149$	−4.81994	−	1.41526i	−0.394865	−	0.115943i	−0.473136	+	0.880989i	$0.656878\pi$
$150$		0			0
$151$	−0.698041	−	1.52850i	−0.0568057	−	0.124387i	0.879100	−	0.476637i	$-0.158144\pi$
$151$	−0.698041	−	1.52850i	−0.0568057	−	0.124387i	−0.935906	+	0.352249i	$0.885417\pi$
$152$		0			0
$153$	0.259464	−	0.299437i	0.0209764	−	0.0242081i
$154$		0			0
$155$	20.6884	+	13.2956i	1.66173	+	1.06793i
$156$		0			0
$157$	10.4861	−	6.73902i	0.836883	−	0.537832i	−0.0505753	−	0.998720i	$-0.516105\pi$
$157$	10.4861	−	6.73902i	0.836883	−	0.537832i	0.887458	+	0.460888i	$0.152469\pi$
$158$		0			0
$159$	2.32936	−	0.683961i	0.184730	−	0.0542416i
$160$		0			0
$161$	9.01152	+	8.33443i	0.710207	+	0.656845i
$162$		0			0
$163$	5.94482	−	1.74556i	0.465634	−	0.136722i	−0.0404959	−	0.999180i	$-0.512894\pi$
$163$	5.94482	−	1.74556i	0.465634	−	0.136722i	0.506130	+	0.862457i	$0.331076\pi$
$164$		0			0
$165$	−25.0452	+	16.0956i	−1.94977	+	1.25304i
$166$		0			0
$167$	−6.19797	−	3.98319i	−0.479613	−	0.308229i	0.278403	−	0.960464i	$-0.410195\pi$
$167$	−6.19797	−	3.98319i	−0.479613	−	0.308229i	−0.758016	+	0.652236i	$0.773831\pi$
$168$		0			0
$169$	5.40532	−	6.23807i	0.415793	−	0.479851i
$170$		0			0
$171$	1.86267	+	4.07868i	0.142442	+	0.311904i
$172$		0			0
$173$	−8.04645	−	2.36265i	−0.611760	−	0.179629i	−0.0388472	−	0.999245i	$-0.512369\pi$
$173$	−8.04645	−	2.36265i	−0.611760	−	0.179629i	−0.572913	+	0.819616i	$0.694187\pi$
$174$		0			0
$175$	3.74236	−	26.0287i	0.282896	−	1.96758i
$176$		0			0
$177$	1.97066	−	4.31514i	0.148124	−	0.324346i
$178$		0			0
$179$	0.737222	+	5.12749i	0.0551025	+	0.383247i	0.998647	+	0.0520008i	$0.0165598\pi$
$179$	0.737222	+	5.12749i	0.0551025	+	0.383247i	−0.943545	+	0.331246i	$0.892531\pi$
$180$		0			0
$181$	−3.51001	−	4.05076i	−0.260897	−	0.301091i	0.610155	−	0.792282i	$-0.291107\pi$
$181$	−3.51001	−	4.05076i	−0.260897	−	0.301091i	−0.871052	+	0.491191i	$0.836562\pi$
$182$		0			0
$183$	−34.5355			−2.55294
$184$		0			0
$185$	−22.9150			−1.68474
$186$		0			0
$187$	0.126281	+	0.145736i	0.00923456	+	0.0106572i
$188$		0			0
$189$	−2.53396	−	17.6241i	−0.184319	−	1.28196i
$190$		0			0
$191$	−3.46725	+	7.59222i	−0.250881	+	0.549354i	−0.992610	−	0.121346i	$-0.961279\pi$
$191$	−3.46725	+	7.59222i	−0.250881	+	0.549354i	0.741729	+	0.670700i	$0.234006\pi$
$192$		0			0
$193$	−3.55295	+	24.7113i	−0.255747	+	1.77876i	0.306581	+	0.951844i	$0.400815\pi$
$193$	−3.55295	+	24.7113i	−0.255747	+	1.77876i	−0.562328	+	0.826914i	$0.690094\pi$
$194$		0			0
$195$	−23.6768	−	6.95214i	−1.69553	−	0.497853i
$196$		0			0
$197$	−0.375369	−	0.821944i	−0.0267439	−	0.0585611i	0.895789	−	0.444480i	$-0.146612\pi$
$197$	−0.375369	−	0.821944i	−0.0267439	−	0.0585611i	−0.922533	+	0.385919i	$0.873884\pi$
$198$		0			0
$199$	−11.4528	+	13.2172i	−0.811865	+	0.936942i	−0.998969	−	0.0453983i	$-0.985544\pi$
$199$	−11.4528	+	13.2172i	−0.811865	+	0.936942i	0.187104	+	0.982340i	$0.440090\pi$
$200$		0			0
$201$	4.21019	+	2.70572i	0.296964	+	0.190847i
$202$		0			0
$203$	−16.1751	+	10.3951i	−1.13527	+	0.729594i
$204$		0			0
$205$	8.86850	−	2.60403i	0.619403	−	0.181873i
$206$		0			0
$207$	23.1975	+	11.5158i	1.61234	+	0.800406i
$208$		0			0
$209$	−2.09390	+	0.614825i	−0.144838	+	0.0425283i
$210$		0			0
$211$	−6.20095	+	3.98511i	−0.426891	+	0.274346i	−0.736395	−	0.676552i	$-0.763473\pi$
$211$	−6.20095	+	3.98511i	−0.426891	+	0.274346i	0.309504	+	0.950898i	$0.399837\pi$
$212$		0			0
$213$	−5.86259	−	3.76766i	−0.401698	−	0.258156i
$214$		0			0
$215$	21.2333	−	24.5045i	1.44810	−	1.67119i
$216$		0			0
$217$	−6.69043	−	14.6500i	−0.454176	−	0.994507i
$218$		0			0
$219$	29.7792	+	8.74395i	2.01229	+	0.590862i
$220$		0			0
$221$	−0.0227469	+	0.158208i	−0.00153012	+	0.0106422i
$222$		0			0
$223$	9.81674	−	21.4957i	0.657378	−	1.43946i	−0.227568	−	0.973762i	$-0.573077\pi$
$223$	9.81674	−	21.4957i	0.657378	−	1.43946i	0.884946	−	0.465694i	$-0.154195\pi$
$224$		0			0
$225$	−7.89603	−	54.9181i	−0.526402	−	3.66120i
$226$		0			0
$227$	−13.4208	−	15.4885i	−0.890772	−	1.02801i	−0.999424	−	0.0339256i	$-0.989199\pi$
$227$	−13.4208	−	15.4885i	−0.890772	−	1.02801i	0.108653	−	0.994080i	$-0.465346\pi$
$228$		0			0
$229$	−0.474619			−0.0313637			−0.0156819	−	0.999877i	$-0.504992\pi$
$229$	−0.474619			−0.0313637			−0.0156819	+	0.999877i	$0.504992\pi$
$230$		0			0
$231$	19.4970			1.28281
$232$		0			0
$233$	13.8623	+	15.9979i	0.908148	+	1.04806i	0.998639	+	0.0521612i	$0.0166109\pi$
$233$	13.8623	+	15.9979i	0.908148	+	1.04806i	−0.0904909	+	0.995897i	$0.528844\pi$
$234$		0			0
$235$	2.69309	+	18.7309i	0.175678	+	1.22187i
$236$		0			0
$237$	−8.80882	+	19.2886i	−0.572195	+	1.25293i
$238$		0			0
$239$	−0.953902	+	6.63454i	−0.0617028	+	0.429152i	0.935432	+	0.353507i	$0.115011\pi$
$239$	−0.953902	+	6.63454i	−0.0617028	+	0.429152i	−0.997135	+	0.0756456i	$0.975898\pi$
$240$		0			0
$241$	20.8817	+	6.13142i	1.34511	+	0.394960i	0.873490	−	0.486842i	$-0.161851\pi$
$241$	20.8817	+	6.13142i	1.34511	+	0.394960i	0.471619	+	0.881802i	$0.343670\pi$
$242$		0			0
$243$	3.89961	+	8.53894i	0.250160	+	0.547774i
$244$		0			0
$245$	1.14945	−	1.32653i	0.0734356	−	0.0847492i
$246$		0			0
$247$	−1.52169	−	0.977928i	−0.0968226	−	0.0622241i
$248$		0			0
$249$	1.75281	−	1.12646i	0.111080	−	0.0713867i
$250$		0			0
$251$	−13.8525	+	4.06745i	−0.874360	+	0.256735i	−0.687969	−	0.725740i	$-0.741497\pi$
$251$	−13.8525	+	4.06745i	−0.874360	+	0.256735i	−0.186391	+	0.982476i	$0.559679\pi$
$252$		0			0
$253$	−7.15446	+	10.3776i	−0.449797	+	0.652437i
$254$		0			0
$255$	−0.797408	+	0.234140i	−0.0499357	+	0.0146624i
$256$		0			0
$257$	−3.14682	+	2.02234i	−0.196293	+	0.126150i	−0.635095	−	0.772434i	$-0.719039\pi$
$257$	−3.14682	+	2.02234i	−0.196293	+	0.126150i	0.438802	+	0.898584i	$0.355403\pi$
$258$		0			0
$259$	12.6246	+	8.11334i	0.784455	+	0.504138i
$260$		0			0
$261$	−26.5664	+	30.6592i	−1.64442	+	1.89776i
$262$		0			0
$263$	−9.45844	−	20.7111i	−0.583232	−	1.27710i	−0.939446	−	0.342696i	$-0.888660\pi$
$263$	−9.45844	−	20.7111i	−0.583232	−	1.27710i	0.356214	−	0.934404i	$-0.384067\pi$
$264$		0			0
$265$	−3.14100	−	0.922282i	−0.192950	−	0.0566553i
$266$		0			0
$267$	−0.0716072	+	0.498039i	−0.00438229	+	0.0304795i
$268$		0			0
$269$	−8.43009	+	18.4593i	−0.513991	+	1.12548i	0.457673	+	0.889120i	$0.348683\pi$
$269$	−8.43009	+	18.4593i	−0.513991	+	1.12548i	−0.971665	+	0.236364i	$0.924044\pi$
$270$		0			0
$271$	3.05886	+	21.2749i	0.185813	+	1.29236i	0.842707	+	0.538373i	$0.180961\pi$
$271$	3.05886	+	21.2749i	0.185813	+	1.29236i	−0.656894	+	0.753983i	$0.728130\pi$
$272$		0			0
$273$	10.5828	+	12.2132i	0.640502	+	0.739179i
$274$		0			0
$275$	27.0034			1.62837
$276$		0			0
$277$	19.9683			1.19978			0.599890	−	0.800082i	$-0.295211\pi$
$277$	19.9683			1.19978			0.599890	+	0.800082i	$0.295211\pi$
$278$		0			0
$279$	−22.2528	−	25.6811i	−1.33224	−	1.53748i
$280$		0			0
$281$	−0.124306	−	0.864570i	−0.00741550	−	0.0515759i	0.985778	−	0.168054i	$-0.0537485\pi$
$281$	−0.124306	−	0.864570i	−0.00741550	−	0.0515759i	−0.993193	+	0.116479i	$0.962839\pi$
$282$		0			0
$283$	−2.07519	+	4.54403i	−0.123357	+	0.270114i	−0.961228	−	0.275753i	$-0.911073\pi$
$283$	−2.07519	+	4.54403i	−0.123357	+	0.270114i	0.837871	+	0.545868i	$0.183800\pi$
$284$		0			0
$285$	1.33849	−	9.30941i	0.0792853	−	0.551442i
$286$		0			0
$287$	−5.80793	−	1.70536i	−0.342831	−	0.100664i
$288$		0			0
$289$	−7.05982	−	15.4588i	−0.415283	−	0.909344i
$290$		0			0
$291$	29.9685	−	34.5855i	1.75679	−	2.02744i
$292$		0			0
$293$	9.23188	+	5.93297i	0.539332	+	0.346608i	0.781778	−	0.623557i	$-0.214313\pi$
$293$	9.23188	+	5.93297i	0.539332	+	0.346608i	−0.242445	+	0.970165i	$0.577950\pi$
$294$		0			0
$295$	−5.38132	+	3.45837i	−0.313313	+	0.201354i
$296$		0			0
$297$	17.5434	−	5.15122i	1.01797	−	0.298904i
$298$		0			0
$299$	−10.3841	+	1.15124i	−0.600527	+	0.0665778i
$300$		0			0
$301$	−20.3742	+	5.98242i	−1.17435	+	0.344821i
$302$		0			0
$303$	42.1484	−	27.0872i	2.42136	−	1.55612i
$304$		0			0
$305$	39.1765	+	25.1772i	2.24324	+	1.44164i
$306$		0			0
$307$	−11.1515	+	12.8695i	−0.636450	+	0.734503i	−0.978743	−	0.205091i	$-0.934251\pi$
$307$	−11.1515	+	12.8695i	−0.636450	+	0.734503i	0.342293	+	0.939593i	$0.388797\pi$
$308$		0			0
$309$	−0.483097	−	1.05783i	−0.0274824	−	0.0601781i
$310$		0			0
$311$	−17.4527	−	5.12459i	−0.989654	−	0.290589i	−0.253450	−	0.967348i	$-0.581565\pi$
$311$	−17.4527	−	5.12459i	−0.989654	−	0.290589i	−0.736204	+	0.676760i	$0.763384\pi$
$312$		0			0
$313$	2.73663	−	19.0337i	0.154684	−	1.07585i	−0.753552	−	0.657389i	$-0.771661\pi$
$313$	2.73663	−	19.0337i	0.154684	−	1.07585i	0.908235	−	0.418460i	$-0.137430\pi$
$314$		0			0
$315$	−22.4400	+	49.1368i	−1.26435	+	2.76854i
$316$		0			0
$317$	1.23482	+	8.58837i	0.0693545	+	0.482371i	0.994665	+	0.103160i	$0.0328954\pi$
$317$	1.23482	+	8.58837i	0.0693545	+	0.482371i	−0.925310	+	0.379211i	$0.876196\pi$
$318$		0			0
$319$	−12.9298	−	14.9218i	−0.723931	−	0.835461i
$320$		0			0
$321$	−15.1785			−0.847182
$322$		0			0
$323$	−0.0609194			−0.00338965
$324$		0			0
$325$	14.6572	+	16.9153i	0.813037	+	0.938294i
$326$		0			0
$327$	2.66696	+	18.5491i	0.147483	+	1.02577i
$328$		0			0
$329$	5.14819	−	11.2730i	0.283829	−	0.621499i
$330$		0			0
$331$	2.54386	−	17.6929i	0.139823	−	0.972492i	−0.792243	−	0.610205i	$-0.791087\pi$
$331$	2.54386	−	17.6929i	0.139823	−	0.972492i	0.932067	−	0.362287i	$-0.118004\pi$
$332$		0			0
$333$	30.3805	+	8.92053i	1.66484	+	0.488842i
$334$		0			0
$335$	−2.80343	−	6.13865i	−0.153168	−	0.335390i
$336$		0			0
$337$	−0.614867	+	0.709594i	−0.0334939	+	0.0386541i	−0.772249	−	0.635320i	$-0.780868\pi$
$337$	−0.614867	+	0.709594i	−0.0334939	+	0.0386541i	0.738755	+	0.673974i	$0.235414\pi$
$338$		0			0
$339$	−47.7330	−	30.6761i	−2.59250	−	1.66610i
$340$		0			0
$341$	13.9130	−	8.94137i	0.753434	−	0.484203i
$342$		0			0
$343$	−18.2935	+	5.37145i	−0.987756	+	0.290031i
$344$		0			0
$345$	−27.8744	−	46.6269i	−1.50071	−	2.51031i
$346$		0			0
$347$	−18.3849	+	5.39830i	−0.986954	+	0.289796i	−0.735092	−	0.677967i	$-0.762861\pi$
$347$	−18.3849	+	5.39830i	−0.986954	+	0.289796i	−0.251862	+	0.967763i	$0.581043\pi$
$348$		0			0
$349$	−1.03481	+	0.665031i	−0.0553921	+	0.0355983i	−0.568044	−	0.822998i	$-0.692300\pi$
$349$	−1.03481	+	0.665031i	−0.0553921	+	0.0355983i	0.512652	+	0.858597i	$0.328663\pi$
$350$		0			0
$351$	12.7492	+	8.19343i	0.680504	+	0.437333i
$352$		0			0
$353$	12.3937	−	14.3031i	0.659648	−	0.761275i	−0.323071	−	0.946375i	$-0.604715\pi$
$353$	12.3937	−	14.3031i	0.659648	−	0.761275i	0.982720	+	0.185100i	$0.0592608\pi$
$354$		0			0
$355$	3.90371	+	8.54793i	0.207187	+	0.453677i
$356$		0			0
$357$	0.522218	+	0.153337i	0.0276387	+	0.00811546i
$358$		0			0
$359$	−5.12294	+	35.6308i	−0.270378	+	1.88052i	0.174091	+	0.984730i	$0.444301\pi$
$359$	−5.12294	+	35.6308i	−0.270378	+	1.88052i	−0.444470	+	0.895794i	$0.646608\pi$
$360$		0			0
$361$	−7.60649	+	16.6559i	−0.400342	+	0.876626i
$362$		0			0
$363$	−1.68788	−	11.7395i	−0.0885907	−	0.616162i
$364$		0			0
$365$	−27.4064	−	31.6287i	−1.43452	−	1.65552i
$366$		0			0
$367$	12.9025			0.673505			0.336752	−	0.941593i	$-0.390671\pi$
$367$	12.9025			0.673505			0.336752	+	0.941593i	$0.390671\pi$
$368$		0			0
$369$	−12.7715			−0.664859
$370$		0			0
$371$	1.40394	+	1.62023i	0.0728887	+	0.0841180i
$372$		0			0
$373$	−0.122148	−	0.849557i	−0.00632457	−	0.0439884i	0.986415	−	0.164274i	$-0.0525281\pi$
$373$	−0.122148	−	0.849557i	−0.00632457	−	0.0439884i	−0.992739	+	0.120286i	$0.961619\pi$
$374$		0			0
$375$	−24.8175	+	54.3428i	−1.28157	+	2.80625i
$376$		0			0
$377$	2.32904	−	16.1989i	0.119952	−	0.834284i
$378$		0			0
$379$	−15.0700	−	4.42495i	−0.774093	−	0.227294i	−0.129253	−	0.991612i	$-0.541258\pi$
$379$	−15.0700	−	4.42495i	−0.774093	−	0.227294i	−0.644840	+	0.764317i	$0.723076\pi$
$380$		0			0
$381$	−15.9336	−	34.8898i	−0.816305	−	1.78746i
$382$		0			0
$383$	4.62070	−	5.33257i	0.236107	−	0.272482i	−0.625315	−	0.780373i	$-0.715029\pi$
$383$	4.62070	−	5.33257i	0.236107	−	0.272482i	0.861421	+	0.507891i	$0.169575\pi$
$384$		0			0
$385$	−22.1171	−	14.2138i	−1.12719	−	0.724402i
$386$		0			0
$387$	−37.6903	+	24.2221i	−1.91591	+	1.23128i
$388$		0			0
$389$	26.2319	−	7.70237i	1.33001	−	0.390526i	0.461914	−	0.886925i	$-0.347163\pi$
$389$	26.2319	−	7.70237i	1.33001	−	0.390526i	0.868095	+	0.496399i	$0.165345\pi$
$390$		0			0
$391$	−0.273245	+	0.221693i	−0.0138186	+	0.0112115i
$392$		0			0
$393$	54.9065	−	16.1220i	2.76967	−	0.813248i
$394$		0			0
$395$	24.0544	−	15.4588i	1.21031	−	0.777819i
$396$		0			0
$397$	−13.8050	−	8.87191i	−0.692851	−	0.445268i	0.146247	−	0.989248i	$-0.453281\pi$
$397$	−13.8050	−	8.87191i	−0.692851	−	0.445268i	−0.839098	+	0.543980i	$0.816917\pi$
$398$		0			0
$399$	−4.03353	+	4.65494i	−0.201929	+	0.233039i
$400$		0			0
$401$	3.62624	+	7.94035i	0.181086	+	0.396522i	0.978306	−	0.207167i	$-0.0664242\pi$
$401$	3.62624	+	7.94035i	0.181086	+	0.396522i	−0.797220	+	0.603689i	$0.793697\pi$
$402$		0			0
$403$	13.1529	+	3.86204i	0.655192	+	0.192382i
$404$		0			0
$405$	−2.20357	+	15.3261i	−0.109496	+	0.761562i
$406$		0			0
$407$	−6.40172	+	14.0178i	−0.317321	+	0.694837i
$408$		0			0
$409$	4.04703	+	28.1477i	0.200113	+	1.39181i	0.803946	+	0.594702i	$0.202730\pi$
$409$	4.04703	+	28.1477i	0.200113	+	1.39181i	−0.603833	+	0.797111i	$0.706361\pi$
$410$		0			0
$411$	0.663980	+	0.766274i	0.0327517	+	0.0377975i
$412$		0			0
$413$	4.18922			0.206138
$414$		0			0
$415$	−2.80958			−0.137917
$416$		0			0
$417$	38.2933	+	44.1928i	1.87523	+	2.16413i
$418$		0			0
$419$	−2.67918	−	18.6341i	−0.130886	−	0.910335i	−0.944402	−	0.328792i	$-0.893358\pi$
$419$	−2.67918	−	18.6341i	−0.130886	−	0.910335i	0.813516	−	0.581543i	$-0.197551\pi$
$420$		0			0
$421$	−16.3262	+	35.7494i	−0.795690	+	1.74232i	−0.136098	+	0.990695i	$0.543456\pi$
$421$	−16.3262	+	35.7494i	−0.795690	+	1.74232i	−0.659593	+	0.751623i	$0.729271\pi$
$422$		0			0
$423$	3.72122	−	25.8817i	0.180932	−	1.25841i
$424$		0			0
$425$	0.723273	+	0.212372i	0.0350839	+	0.0103016i
$426$		0			0
$427$	−12.6693	−	27.7419i	−0.613109	−	1.34252i
$428$		0			0
$429$	−10.8674	+	12.5416i	−0.524682	+	0.605516i
$430$		0			0
$431$	0.135965	+	0.0873793i	0.00654919	+	0.00420891i	0.543911	−	0.839143i	$-0.316943\pi$
$431$	0.135965	+	0.0873793i	0.00654919	+	0.00420891i	−0.537362	+	0.843352i	$0.680579\pi$
$432$		0			0
$433$	6.95029	−	4.46668i	0.334010	−	0.214655i	−0.362876	−	0.931838i	$-0.618205\pi$
$433$	6.95029	−	4.46668i	0.334010	−	0.214655i	0.696885	+	0.717183i	$0.254569\pi$
$434$		0			0
$435$	81.6463	−	23.9735i	3.91464	−	1.14944i
$436$		0			0
$437$	−0.997568	−	3.85506i	−0.0477201	−	0.184412i
$438$		0			0
$439$	12.3975	−	3.64023i	0.591700	−	0.173739i	0.0278445	−	0.999612i	$-0.491136\pi$
$439$	12.3975	−	3.64023i	0.591700	−	0.173739i	0.563855	+	0.825873i	$0.309318\pi$
$440$		0			0
$441$	−2.04034	+	1.31124i	−0.0971589	+	0.0624402i
$442$		0			0
$443$	8.55386	+	5.49723i	0.406406	+	0.261181i	0.727835	−	0.685752i	$-0.240527\pi$
$443$	8.55386	+	5.49723i	0.406406	+	0.261181i	−0.321429	+	0.946934i	$0.604163\pi$
$444$		0			0
$445$	0.444312	−	0.512764i	0.0210624	−	0.0243073i
$446$		0			0
$447$	−6.04822	−	13.2438i	−0.286071	−	0.626409i
$448$		0			0
$449$	23.5133	+	6.90412i	1.10966	+	0.325825i	0.784683	−	0.619897i	$-0.212826\pi$
$449$	23.5133	+	6.90412i	1.10966	+	0.325825i	0.324976	+	0.945722i	$0.394644\pi$
$450$		0			0
$451$	0.884613	−	6.15262i	0.0416548	−	0.289715i
$452$		0			0
$453$	2.02314	−	4.43006i	0.0950555	−	0.208143i
$454$		0			0
$455$	−3.10124	−	21.5696i	−0.145388	−	1.01120i
$456$		0			0
$457$	−3.89797	−	4.49849i	−0.182339	−	0.210431i	0.657220	−	0.753699i	$-0.271732\pi$
$457$	−3.89797	−	4.49849i	−0.182339	−	0.210431i	−0.839559	+	0.543268i	$0.817187\pi$
$458$		0			0
$459$	0.510405			0.0238237
$460$		0			0
$461$	−15.0911			−0.702863			−0.351432	−	0.936214i	$-0.614305\pi$
$461$	−15.0911			−0.702863			−0.351432	+	0.936214i	$0.614305\pi$
$462$		0			0
$463$	9.31200	+	10.7466i	0.432765	+	0.499438i	0.929683	−	0.368360i	$-0.120081\pi$
$463$	9.31200	+	10.7466i	0.432765	+	0.499438i	−0.496918	+	0.867797i	$0.665535\pi$
$464$		0			0
$465$	10.1437	+	70.5510i	0.470403	+	3.27173i
$466$		0			0
$467$	14.1645	−	31.0159i	0.655454	−	1.43524i	−0.231244	−	0.972896i	$-0.574280\pi$
$467$	14.1645	−	31.0159i	0.655454	−	1.43524i	0.886698	−	0.462348i	$-0.152993\pi$
$468$		0			0
$469$	−0.628969	+	4.37457i	−0.0290431	+	0.201999i
$470$		0			0
$471$	34.6637	+	10.1782i	1.59722	+	0.468986i
$472$		0			0
$473$	−9.05827	−	19.8348i	−0.416500	−	0.912007i
$474$		0			0
$475$	−5.58645	+	6.44710i	−0.256324	+	0.295813i
$476$		0			0
$477$	3.80529	+	2.44551i	0.174232	+	0.111972i
$478$		0			0
$479$	−22.1518	+	14.2361i	−1.01214	+	0.650464i	−0.937947	−	0.346780i	$-0.887275\pi$
$479$	−22.1518	+	14.2361i	−1.01214	+	0.650464i	−0.0741950	+	0.997244i	$0.523639\pi$
$480$		0			0
$481$	−12.2558	+	3.59861i	−0.558814	+	0.164083i
$482$		0			0
$483$	−1.15193	+	35.5575i	−0.0524148	+	1.61792i
$484$		0			0
$485$	−59.2095	+	17.3855i	−2.68856	+	0.789433i
$486$		0			0
$487$	2.41757	−	1.55368i	0.109550	−	0.0704038i	−0.484718	−	0.874670i	$-0.661078\pi$
$487$	2.41757	−	1.55368i	0.109550	−	0.0704038i	0.594269	+	0.804266i	$0.297442\pi$
$488$		0			0
$489$	15.1067	+	9.70848i	0.683148	+	0.439033i
$490$		0			0
$491$	9.84783	−	11.3650i	0.444426	−	0.512895i	−0.488696	−	0.872454i	$-0.662527\pi$
$491$	9.84783	−	11.3650i	0.444426	−	0.512895i	0.933122	+	0.359559i	$0.117073\pi$
$492$		0			0
$493$	−0.228964	−	0.501361i	−0.0103120	−	0.0225802i
$494$		0			0
$495$	−53.2238	−	15.6279i	−2.39223	−	0.702423i
$496$		0			0
$497$	0.875824	−	6.09149i	0.0392861	−	0.273241i
$498$		0			0
$499$	−3.68189	+	8.06222i	−0.164824	+	0.360914i	−0.973964	−	0.226701i	$-0.927206\pi$
$499$	−3.68189	+	8.06222i	−0.164824	+	0.360914i	0.809140	+	0.587616i	$0.199933\pi$
$500$		0			0
$501$	−3.03891	−	21.1361i	−0.135769	−	0.944292i
$502$		0			0
$503$	26.2743	+	30.3221i	1.17151	+	1.35200i	0.923666	+	0.383198i	$0.125177\pi$
$503$	26.2743	+	30.3221i	1.17151	+	1.35200i	0.247847	+	0.968799i	$0.420277\pi$
$504$		0			0
$505$	−67.5596			−3.00636
$506$		0			0
$507$	23.9231			1.06246
$508$		0			0
$509$	−24.3794	−	28.1354i	−1.08060	−	1.24708i	−0.967332	−	0.253514i	$-0.918414\pi$
$509$	−24.3794	−	28.1354i	−1.08060	−	1.24708i	−0.113268	−	0.993564i	$-0.536132\pi$
$510$		0			0
$511$	3.90054	+	27.1289i	0.172550	+	1.20011i
$512$		0			0
$513$	−2.39951	+	5.25420i	−0.105941	+	0.231979i
$514$		0			0
$515$	−0.223169	+	1.55218i	−0.00983402	+	0.0683971i
$516$		0			0
$517$	12.2106	+	3.58536i	0.537023	+	0.157684i
$518$		0			0
$519$	−10.0970	−	22.1093i	−0.443207	−	0.970488i
$520$		0			0
$521$	−8.95907	+	10.3393i	−0.392504	+	0.452974i	−0.917266	−	0.398275i	$-0.869609\pi$
$521$	−8.95907	+	10.3393i	−0.392504	+	0.452974i	0.524762	+	0.851249i	$0.324154\pi$
$522$		0			0
$523$	24.5231	+	15.7600i	1.07232	+	0.689139i	0.952771	−	0.303689i	$-0.0982185\pi$
$523$	24.5231	+	15.7600i	1.07232	+	0.689139i	0.119550	+	0.992828i	$0.461855\pi$
$524$		0			0
$525$	64.1162	−	41.2050i	2.79826	−	1.79833i
$526$		0			0
$527$	0.442975	−	0.130069i	0.0192963	−	0.00566590i
$528$		0			0
$529$	−18.5034	−	13.6610i	−0.804497	−	0.593957i
$530$		0			0
$531$	8.48083	−	2.49020i	0.368037	−	0.108065i
$532$		0			0
$533$	4.33425	−	2.78545i	0.187737	−	0.120651i
$534$		0			0
$535$	17.2182	+	11.0655i	0.744409	+	0.478403i
$536$		0			0
$537$	−9.83202	+	11.3468i	−0.424283	+	0.489648i
$538$		0			0
$539$	−0.490363	−	1.07374i	−0.0211214	−	0.0462495i
$540$		0			0
$541$	34.6475	+	10.1734i	1.48961	+	0.437390i	0.922418	−	0.386194i	$-0.126210\pi$
$541$	34.6475	+	10.1734i	1.48961	+	0.437390i	0.567195	+	0.823584i	$0.308029\pi$
$542$		0			0
$543$	2.21083	−	15.3766i	0.0948757	−	0.659875i
$544$		0			0
$545$	10.4974	−	22.9861i	0.449659	−	0.984616i
$546$		0			0
$547$	−3.87812	−	26.9729i	−0.165816	−	1.15328i	−0.887417	−	0.460968i	$-0.847502\pi$
$547$	−3.87812	−	26.9729i	−0.165816	−	1.15328i	0.721600	−	0.692310i	$-0.243407\pi$
$548$		0			0
$549$	−42.1387	−	48.6307i	−1.79844	−	2.07551i
$550$		0			0
$551$	6.23751			0.265727
$552$		0			0
$553$	−18.7258			−0.796301
$554$		0			0
$555$	−43.4925	−	50.1930i	−1.84615	−	2.13057i
$556$		0			0
$557$	−3.55370	−	24.7165i	−0.150575	−	1.04727i	−0.915258	−	0.402867i	$-0.868014\pi$
$557$	−3.55370	−	24.7165i	−0.150575	−	1.04727i	0.764683	−	0.644406i	$-0.222895\pi$
$558$		0			0
$559$	7.50809	−	16.4404i	0.317558	−	0.695356i
$560$		0			0
$561$	−0.0795397	+	0.553211i	−0.00335817	+	0.0233566i
$562$		0			0
$563$	27.2789	+	8.00980i	1.14967	+	0.337573i	0.800409	−	0.599454i	$-0.204615\pi$
$563$	27.2789	+	8.00980i	1.14967	+	0.337573i	0.349258	+	0.937027i	$0.386434\pi$
$564$		0			0
$565$	31.7838	+	69.5969i	1.33716	+	2.92796i
$566$		0			0
$567$	6.64043	−	7.66347i	0.278872	−	0.321835i
$568$		0			0
$569$	21.9565	+	14.1106i	0.920466	+	0.591547i	0.912793	−	0.408423i	$-0.133921\pi$
$569$	21.9565	+	14.1106i	0.920466	+	0.591547i	0.00767305	+	0.999971i	$0.497558\pi$
$570$		0			0
$571$	−12.7962	+	8.22362i	−0.535504	+	0.344148i	−0.780278	−	0.625432i	$-0.784923\pi$
$571$	−12.7962	+	8.22362i	−0.535504	+	0.344148i	0.244774	+	0.969580i	$0.421286\pi$
$572$		0			0
$573$	−23.2108	+	6.81531i	−0.969646	+	0.284714i
$574$		0			0
$575$	−1.59543	+	49.2472i	−0.0665339	+	2.05375i
$576$		0			0
$577$	30.3716	−	8.91790i	1.26439	−	0.371257i	0.420260	−	0.907404i	$-0.361939\pi$
$577$	30.3716	−	8.91790i	1.26439	−	0.371257i	0.844125	+	0.536147i	$0.180121\pi$
$578$		0			0
$579$	−60.8711	+	39.1195i	−2.52972	+	1.62575i
$580$		0			0
$581$	1.54789	+	0.994767i	0.0642172	+	0.0412699i
$582$		0			0
$583$	−1.44169	+	1.66379i	−0.0597085	+	0.0689073i
$584$		0			0
$585$	−19.0999	−	41.8229i	−0.789683	−	1.72916i
$586$		0			0
$587$	−20.7470	−	6.09186i	−0.856320	−	0.251438i	−0.176033	−	0.984384i	$-0.556327\pi$
$587$	−20.7470	−	6.09186i	−0.856320	−	0.251438i	−0.680287	+	0.732946i	$0.738145\pi$
$588$		0			0
$589$	−0.743556	+	5.17154i	−0.0306377	+	0.213090i
$590$		0			0
$591$	1.08794	−	2.38225i	0.0447518	−	0.0979928i
$592$		0			0
$593$	−3.09219	−	21.5066i	−0.126981	−	0.883172i	−0.949351	−	0.314218i	$-0.898258\pi$
$593$	−3.09219	−	21.5066i	−0.126981	−	0.883172i	0.822370	−	0.568953i	$-0.192652\pi$
$594$		0			0
$595$	−0.480609	−	0.554653i	−0.0197031	−	0.0227385i
$596$		0			0
$597$	−50.6882			−2.07453
$598$		0			0
$599$	19.7674			0.807675			0.403837	−	0.914831i	$-0.367676\pi$
$599$	19.7674			0.807675			0.403837	+	0.914831i	$0.367676\pi$
$600$		0			0
$601$	−11.1214	−	12.8348i	−0.453653	−	0.523543i	0.482140	−	0.876094i	$-0.339860\pi$
$601$	−11.1214	−	12.8348i	−0.453653	−	0.523543i	−0.935793	+	0.352551i	$0.885314\pi$
$602$		0			0
$603$	1.32706	+	9.22993i	0.0540422	+	0.375872i
$604$		0			0
$605$	−6.64364	+	14.5476i	−0.270103	+	0.591442i
$606$		0			0
$607$	4.58811	−	31.9110i	0.186225	−	1.29523i	−0.655448	−	0.755240i	$-0.727520\pi$
$607$	4.58811	−	31.9110i	0.186225	−	1.29523i	0.841674	−	0.539986i	$-0.181571\pi$
$608$		0			0
$609$	−53.4697	−	15.7001i	−2.16670	−	0.636201i
$610$		0			0
$611$	4.38190	+	9.59502i	0.177273	+	0.388173i
$612$		0			0
$613$	7.58022	−	8.74804i	0.306162	−	0.353330i	−0.581730	−	0.813382i	$-0.697624\pi$
$613$	7.58022	−	8.74804i	0.306162	−	0.353330i	0.887892	+	0.460052i	$0.152169\pi$
$614$		0			0
$615$	22.5362	+	14.4831i	0.908748	+	0.584017i
$616$		0			0
$617$	−30.1164	+	19.3546i	−1.21244	+	0.779189i	−0.981066	−	0.193676i	$-0.937959\pi$
$617$	−30.1164	+	19.3546i	−1.21244	+	0.779189i	−0.231376	+	0.972864i	$0.574323\pi$
$618$		0			0
$619$	−0.445596	+	0.130839i	−0.0179100	+	0.00525885i	−0.290675	−	0.956822i	$-0.593880\pi$
$619$	−0.445596	+	0.130839i	−0.0179100	+	0.00525885i	0.272765	+	0.962081i	$0.412062\pi$
$620$		0			0
$621$	8.35798	+	32.2990i	0.335394	+	1.29612i
$622$		0			0
$623$	−0.426337	+	0.125184i	−0.0170808	+	0.00501538i
$624$		0			0
$625$	24.5539	−	15.7798i	0.982157	−	0.631194i
$626$		0			0
$627$	−5.32092	−	3.41955i	−0.212497	−	0.136564i
$628$		0			0
$629$	−0.281712	+	0.325113i	−0.0112326	+	0.0129631i
$630$		0			0
$631$	8.24762	+	18.0598i	0.328332	+	0.718948i	0.999755	−	0.0221268i	$-0.00704376\pi$
$631$	8.24762	+	18.0598i	0.328332	+	0.718948i	−0.671423	+	0.741075i	$0.734316\pi$
$632$		0			0
$633$	−20.4984	−	6.01886i	−0.814737	−	0.239228i
$634$		0			0
$635$	−7.36064	+	51.1944i	−0.292098	+	2.03159i
$636$		0			0
$637$	0.406445	−	0.889990i	0.0161039	−	0.0352627i
$638$		0			0
$639$	−1.84791	−	12.8525i	−0.0731020	−	0.508436i
$640$		0			0
$641$	3.89069	+	4.49010i	0.153673	+	0.177348i	0.827366	−	0.561663i	$-0.189838\pi$
$641$	3.89069	+	4.49010i	0.153673	+	0.177348i	−0.673693	+	0.739011i	$0.735293\pi$
$642$		0			0
$643$	−29.5972			−1.16720			−0.583599	−	0.812042i	$-0.698356\pi$
$643$	−29.5972			−1.16720			−0.583599	+	0.812042i	$0.698356\pi$
$644$		0			0
$645$	93.9754			3.70028
$646$		0			0
$647$	22.4741	+	25.9364i	0.883546	+	1.01967i	0.999651	+	0.0264296i	$0.00841379\pi$
$647$	22.4741	+	25.9364i	0.883546	+	1.01967i	−0.116105	+	0.993237i	$0.537041\pi$
$648$		0			0
$649$	0.612219	+	4.25808i	0.0240317	+	0.167144i
$650$		0			0
$651$	19.3910	−	42.4603i	0.759993	−	1.66415i
$652$		0			0
$653$	−1.12775	+	7.84365i	−0.0441321	+	0.306946i	0.955785	+	0.294067i	$0.0950087\pi$
$653$	−1.12775	+	7.84365i	−0.0441321	+	0.306946i	−0.999917	+	0.0128791i	$0.995900\pi$
$654$		0			0
$655$	−74.0383	−	21.7396i	−2.89292	−	0.849437i
$656$		0			0
$657$	24.0226	+	52.6022i	0.937211	+	2.05221i
$658$		0			0
$659$	−9.89111	+	11.4149i	−0.385303	+	0.444663i	−0.914958	−	0.403550i	$-0.867776\pi$
$659$	−9.89111	+	11.4149i	−0.385303	+	0.444663i	0.529655	+	0.848213i	$0.322322\pi$
$660$		0			0
$661$	10.7706	+	6.92184i	0.418927	+	0.269228i	0.733078	−	0.680145i	$-0.238083\pi$
$661$	10.7706	+	6.92184i	0.418927	+	0.269228i	−0.314150	+	0.949373i	$0.601720\pi$
$662$		0			0
$663$	−0.389713	+	0.250453i	−0.0151352	+	0.00972680i
$664$		0			0
$665$	7.96913	−	2.33995i	0.309030	−	0.0907393i
$666$		0			0
$667$	27.9774	−	22.6990i	1.08329	−	0.878909i
$668$		0			0
$669$	65.7162	−	19.2960i	2.54074	−	0.746028i
$670$		0			0
$671$	26.3463	−	16.9318i	1.01709	−	0.653643i
$672$		0			0
$673$	−25.1715	−	16.1767i	−0.970290	−	0.623567i	−0.0434622	−	0.999055i	$-0.513839\pi$
$673$	−25.1715	−	16.1767i	−0.970290	−	0.623567i	−0.926827	+	0.375488i	$0.877475\pi$
$674$		0			0
$675$	46.8052	−	54.0161i	1.80153	−	2.07908i
$676$		0			0
$677$	15.0683	+	32.9950i	0.579122	+	1.26810i	0.941796	+	0.336185i	$0.109137\pi$
$677$	15.0683	+	32.9950i	0.579122	+	1.26810i	−0.362674	+	0.931916i	$0.618136\pi$
$678$		0			0
$679$	38.7760	+	11.3856i	1.48808	+	0.436941i
$680$		0			0
$681$	8.45330	−	58.7940i	0.323931	−	2.25299i
$682$		0			0
$683$	−11.4084	+	24.9809i	−0.436530	+	0.955868i	0.555692	+	0.831388i	$0.312453\pi$
$683$	−11.4084	+	24.9809i	−0.436530	+	0.955868i	−0.992222	+	0.124480i	$0.960274\pi$
$684$		0			0
$685$	−0.194576	−	1.35330i	−0.00743436	−	0.0517071i
$686$		0			0
$687$	−0.900824	−	1.03961i	−0.0343686	−	0.0396635i
$688$		0			0
$689$	−1.82476			−0.0695178
$690$		0			0
$691$	−5.23333			−0.199085			−0.0995426	−	0.995033i	$-0.531738\pi$
$691$	−5.23333			−0.199085			−0.0995426	+	0.995033i	$0.531738\pi$
$692$		0			0
$693$	23.7895	+	27.4545i	0.903687	+	1.04291i
$694$		0			0
$695$	−11.2216	−	78.0482i	−0.425661	−	2.96054i
$696$		0			0
$697$	0.0720820	−	0.157838i	0.00273030	−	0.00597852i
$698$		0			0
$699$	−8.73135	+	60.7279i	−0.330250	+	2.29694i
$700$		0			0
$701$	12.9682	+	3.80780i	0.489801	+	0.143819i	0.517301	−	0.855803i	$-0.326937\pi$
$701$	12.9682	+	3.80780i	0.489801	+	0.143819i	−0.0275006	+	0.999622i	$0.508755\pi$
$702$		0			0
$703$	−2.02239	−	4.42841i	−0.0762758	−	0.167021i
$704$		0			0
$705$	−35.9167	+	41.4500i	−1.35270	+	1.56110i
$706$		0			0
$707$	37.2208	+	23.9203i	1.39983	+	0.899617i
$708$		0			0
$709$	22.8063	−	14.6567i	0.856509	−	0.550445i	−0.0370893	−	0.999312i	$-0.511809\pi$
$709$	22.8063	−	14.6567i	0.856509	−	0.550445i	0.893599	+	0.448867i	$0.148172\pi$
$710$		0			0
$711$	−37.9092	+	11.1311i	−1.42171	+	0.417450i
$712$		0			0
$713$	15.4847	+	25.9021i	0.579908	+	0.970040i
$714$		0			0
$715$	21.4709	−	6.30443i	0.802967	−	0.235772i
$716$		0			0
$717$	−16.3428	+	10.5029i	−0.610333	+	0.392237i
$718$		0			0
$719$	−5.04126	−	3.23982i	−0.188007	−	0.120825i	0.443251	−	0.896397i	$-0.353825\pi$
$719$	−5.04126	−	3.23982i	−0.188007	−	0.120825i	−0.631259	+	0.775572i	$0.717461\pi$
$720$		0			0
$721$	0.672519	−	0.776129i	0.0250459	−	0.0289045i
$722$		0			0
$723$	26.2031	+	57.3767i	0.974503	+	2.13386i
$724$		0			0
$725$	−74.0556	−	21.7447i	−2.75035	−	0.807577i
$726$		0			0
$727$	0.877427	−	6.10264i	0.0325420	−	0.226334i	−0.967060	−	0.254549i	$-0.918073\pi$
$727$	0.877427	−	6.10264i	0.0325420	−	0.226334i	0.999602	+	0.0282145i	$0.00898215\pi$
$728$		0			0
$729$	−16.2397	+	35.5600i	−0.601471	+	1.31704i
$730$		0			0
$731$	−0.0866273	−	0.602506i	−0.00320403	−	0.0222845i
$732$		0			0
$733$	−7.38923	−	8.52763i	−0.272928	−	0.314975i	0.602695	−	0.797972i	$-0.294094\pi$
$733$	−7.38923	−	8.52763i	−0.272928	−	0.314975i	−0.875622	+	0.482997i	$0.839548\pi$
$734$		0			0
$735$	5.08729			0.187647
$736$		0			0
$737$	−4.53839			−0.167174
$738$		0			0
$739$	−22.8441	−	26.3635i	−0.840332	−	0.969795i	0.159516	−	0.987195i	$-0.449007\pi$
$739$	−22.8441	−	26.3635i	−0.840332	−	0.969795i	−0.999849	+	0.0174000i	$0.994461\pi$
$740$		0			0
$741$	−0.746095	−	5.18921i	−0.0274085	−	0.190630i
$742$		0			0
$743$	−11.5913	+	25.3813i	−0.425242	+	0.931151i	0.568833	+	0.822453i	$0.307395\pi$
$743$	−11.5913	+	25.3813i	−0.425242	+	0.931151i	−0.994075	+	0.108697i	$0.965332\pi$
$744$		0			0
$745$	−2.79401	+	19.4328i	−0.102365	+	0.711962i
$746$		0			0
$747$	3.72492	+	1.09374i	0.136288	+	0.0400177i
$748$		0			0
$749$	−5.56821	−	12.1927i	−0.203458	−	0.445511i
$750$		0			0
$751$	11.0905	−	12.7991i	0.404697	−	0.467046i	−0.516417	−	0.856337i	$-0.672735\pi$
$751$	11.0905	−	12.7991i	0.404697	−	0.467046i	0.921115	+	0.389291i	$0.127280\pi$
$752$		0			0
$753$	−35.2012	−	22.6225i	−1.28280	−	0.824408i
$754$		0			0
$755$	−5.52464	+	3.55047i	−0.201062	+	0.129215i
$756$		0			0
$757$	21.1844	−	6.22030i	0.769960	−	0.226081i	0.126920	−	0.991913i	$-0.459491\pi$
$757$	21.1844	−	6.22030i	0.769960	−	0.226081i	0.643040	+	0.765832i	$0.277673\pi$
$758$		0			0
$759$	−36.3103	+	4.02557i	−1.31798	+	0.146119i
$760$		0			0
$761$	31.7376	−	9.31900i	1.15049	−	0.337813i	0.349758	−	0.936840i	$-0.386264\pi$
$761$	31.7376	−	9.31900i	1.15049	−	0.337813i	0.800729	+	0.599027i	$0.204446\pi$
$762$		0			0
$763$	−13.9219	+	8.94705i	−0.504006	+	0.323905i
$764$		0			0
$765$	−1.30267	−	0.837172i	−0.0470980	−	0.0302680i
$766$		0			0
$767$	−2.33502	+	2.69475i	−0.0843126	+	0.0973019i
$768$		0			0
$769$	−1.06302	−	2.32768i	−0.0383333	−	0.0839382i	0.889497	−	0.456942i	$-0.151055\pi$
$769$	−1.06302	−	2.32768i	−0.0383333	−	0.0839382i	−0.927830	+	0.373003i	$0.878328\pi$
$770$		0			0
$771$	−10.4024	−	3.05441i	−0.374633	−	0.110002i
$772$		0			0
$773$	3.58860	−	24.9593i	0.129073	−	0.897723i	−0.817659	−	0.575702i	$-0.804729\pi$
$773$	3.58860	−	24.9593i	0.129073	−	0.897723i	0.946733	−	0.322021i	$-0.104362\pi$
$774$		0			0
$775$	26.8565	−	58.8076i	0.964715	−	2.11243i
$776$		0			0
$777$	6.18994	+	43.0520i	0.222063	+	1.54448i
$778$		0			0
$779$	1.28594	+	1.48405i	0.0460735	+	0.0531716i
$780$		0			0
$781$	6.31961			0.226133
$782$		0			0
$783$	−52.2601			−1.86762
$784$		0			0
$785$	−31.9018	−	36.8166i	−1.13862	−	1.31404i
$786$		0			0
$787$	3.57991	+	24.8988i	0.127610	+	0.887548i	0.948571	+	0.316564i	$0.102529\pi$
$787$	3.57991	+	24.8988i	0.127610	+	0.887548i	−0.820961	+	0.570984i	$0.806562\pi$
$788$		0			0
$789$	27.4135	−	60.0273i	0.975948	−	2.13703i
$790$		0			0
$791$	7.13092	−	49.5967i	0.253546	−	1.76345i
$792$		0			0
$793$	24.9069	+	7.31331i	0.884468	+	0.259703i
$794$		0			0
$795$	−3.94144	−	8.63055i	−0.139788	−	0.306094i
$796$		0			0
$797$	−7.49367	+	8.64816i	−0.265439	+	0.306333i	−0.872785	−	0.488104i	$-0.837689\pi$
$797$	−7.49367	+	8.64816i	−0.265439	+	0.306333i	0.607346	+	0.794437i	$0.292234\pi$
$798$		0			0
$799$	0.298858	+	0.192064i	0.0105728	+	0.00679474i
$800$		0			0
$801$	−0.788680	+	0.506854i	−0.0278666	+	0.0179088i
$802$		0			0
$803$	−27.0047	+	7.92931i	−0.952977	+	0.279819i
$804$		0			0
$805$	27.2290	−	39.4961i	0.959697	−	1.39205i
$806$		0			0
$807$	−56.4335	+	16.5704i	−1.98655	+	0.583305i
$808$		0			0
$809$	−12.5725	+	8.07983i	−0.442024	+	0.284072i	−0.742662	−	0.669667i	$-0.766437\pi$
$809$	−12.5725	+	8.07983i	−0.442024	+	0.284072i	0.300638	+	0.953738i	$0.402801\pi$
$810$		0			0
$811$	−18.0831	−	11.6213i	−0.634985	−	0.408080i	0.183167	−	0.983082i	$-0.441365\pi$
$811$	−18.0831	−	11.6213i	−0.634985	−	0.408080i	−0.818152	+	0.575002i	$0.805001\pi$
$812$		0			0
$813$	−40.7948	+	47.0797i	−1.43074	+	1.65116i
$814$		0			0
$815$	−10.0591	−	22.0263i	−0.352353	−	0.771546i
$816$		0			0
$817$	6.60956	+	1.94074i	0.231239	+	0.0678980i
$818$		0			0
$819$	−4.28519	+	29.8041i	−0.149737	+	1.04144i
$820$		0			0
$821$	7.06693	−	15.4744i	0.246638	−	0.540061i	−0.745309	−	0.666719i	$-0.767698\pi$
$821$	7.06693	−	15.4744i	0.246638	−	0.540061i	0.991946	+	0.126658i	$0.0404252\pi$
$822$		0			0
$823$	−0.931527	−	6.47891i	−0.0324710	−	0.225841i	0.967124	−	0.254306i	$-0.0818471\pi$
$823$	−0.931527	−	6.47891i	−0.0324710	−	0.225841i	−0.999595	+	0.0284653i	$0.990938\pi$
$824$		0			0
$825$	51.2523	+	59.1483i	1.78438	+	2.05928i
$826$		0			0
$827$	−15.3528			−0.533870			−0.266935	−	0.963714i	$-0.586011\pi$
$827$	−15.3528			−0.533870			−0.266935	+	0.963714i	$0.586011\pi$
$828$		0			0
$829$	1.41193			0.0490385			0.0245192	−	0.999699i	$-0.492194\pi$
$829$	1.41193			0.0490385			0.0245192	+	0.999699i	$0.492194\pi$
$830$		0			0
$831$	37.8998	+	43.7387i	1.31473	+	1.51728i
$832$		0			0
$833$	−0.00468951	−	0.0326162i	−0.000162482	−	0.00113009i
$834$		0			0
$835$	−11.9614	+	26.1919i	−0.413942	+	0.906407i
$836$		0			0
$837$	6.22977	−	43.3290i	0.215332	−	1.49767i
$838$		0			0
$839$	32.1273	+	9.43344i	1.10916	+	0.325678i	0.784485	−	0.620148i	$-0.212927\pi$
$839$	32.1273	+	9.43344i	1.10916	+	0.325678i	0.324674	+	0.945826i	$0.394745\pi$
$840$		0			0
$841$	11.3965	+	24.9548i	0.392982	+	0.860511i
$842$		0			0
$843$	1.65782	−	1.91323i	0.0570984	−	0.0658951i
$844$		0			0
$845$	−27.1380	−	17.4405i	−0.933575	−	0.599972i
$846$		0			0
$847$	8.81094	−	5.66245i	0.302748	−	0.194564i
$848$		0			0
$849$	−13.8919	+	4.07904i	−0.476770	+	0.139992i
$850$		0			0
$851$	−25.1866	−	12.5033i	−0.863385	−	0.428607i
$852$		0			0
$853$	−25.1324	+	7.37953i	−0.860516	+	0.252670i	−0.682077	−	0.731281i	$-0.738923\pi$
$853$	−25.1324	+	7.37953i	−0.860516	+	0.252670i	−0.178439	+	0.983951i	$0.557105\pi$
$854$		0			0
$855$	14.7421	−	9.47417i	0.504169	−	0.324010i
$856$		0			0
$857$	14.2324	+	9.14659i	0.486169	+	0.312442i	0.760663	−	0.649147i	$-0.224874\pi$
$857$	14.2324	+	9.14659i	0.486169	+	0.312442i	−0.274494	+	0.961589i	$0.588510\pi$
$858$		0			0
$859$	18.3017	−	21.1212i	0.624445	−	0.720648i	−0.352100	−	0.935962i	$-0.614532\pi$
$859$	18.3017	−	21.1212i	0.624445	−	0.720648i	0.976545	+	0.215315i	$0.0690777\pi$
$860$		0			0
$861$	−7.28799	−	15.9585i	−0.248374	−	0.543863i
$862$		0			0
$863$	3.31633	+	0.973761i	0.112889	+	0.0331472i	0.337689	−	0.941258i	$-0.390355\pi$
$863$	3.31633	+	0.973761i	0.112889	+	0.0331472i	−0.224800	+	0.974405i	$0.572173\pi$
$864$		0			0
$865$	−4.66435	+	32.4413i	−0.158593	+	1.10304i
$866$		0			0
$867$	20.4616	−	44.8046i	0.694912	−	1.52164i
$868$		0			0
$869$	−2.73661	−	19.0336i	−0.0928332	−	0.645669i
$870$		0			0
$871$	−2.46340	−	2.84292i	−0.0834692	−	0.0963285i
$872$		0			0
$873$	85.2675			2.88587
$874$		0			0
$875$	−52.7570			−1.78351
$876$		0			0
$877$	−22.4326	−	25.8886i	−0.757495	−	0.874195i	0.237778	−	0.971320i	$-0.423581\pi$
$877$	−22.4326	−	25.8886i	−0.757495	−	0.874195i	−0.995272	+	0.0971243i	$0.969036\pi$
$878$		0			0
$879$	4.52647	+	31.4823i	0.152674	+	1.06187i
$880$		0			0
$881$	11.8003	−	25.8390i	0.397562	−	0.870540i	−0.599949	−	0.800038i	$-0.704813\pi$
$881$	11.8003	−	25.8390i	0.397562	−	0.870540i	0.997512	−	0.0705018i	$-0.0224601\pi$
$882$		0			0
$883$	7.98390	−	55.5292i	0.268680	−	1.86871i	−0.192355	−	0.981325i	$-0.561612\pi$
$883$	7.98390	−	55.5292i	0.268680	−	1.86871i	0.461034	−	0.887382i	$-0.347478\pi$
$884$		0			0
$885$	−17.7889	−	5.22330i	−0.597968	−	0.175579i
$886$		0			0
$887$	−4.44587	−	9.73510i	−0.149278	−	0.326873i	0.820190	−	0.572091i	$-0.193868\pi$
$887$	−4.44587	−	9.73510i	−0.149278	−	0.326873i	−0.969468	+	0.245218i	$0.921140\pi$
$888$		0			0
$889$	22.1812	−	25.5985i	0.743935	−	0.858546i
$890$		0			0
$891$	8.75987	+	5.62963i	0.293467	+	0.188600i
$892$		0			0
$893$	−3.38213	+	2.17357i	−0.113179	+	0.0727356i
$894$		0			0
$895$	19.4253	−	5.70379i	0.649317	−	0.190657i
$896$		0			0
$897$	−22.2306	−	20.5603i	−0.742258	−	0.686488i
$898$		0			0
$899$	−45.3560	+	13.3177i	−1.51271	+	0.444171i
$900$		0			0
$901$	−0.0516999	+	0.0332255i	−0.00172237	+	0.00110690i
$902$		0			0
$903$	−51.7741	−	33.2732i	−1.72293	−	1.10726i
$904$		0			0
$905$	−13.7179	+	15.8313i	−0.455997	+	0.526249i
$906$		0			0
$907$	−14.1493	−	30.9827i	−0.469820	−	1.02876i	−0.985138	−	0.171764i	$-0.945053\pi$
$907$	−14.1493	−	30.9827i	−0.469820	−	1.02876i	0.515318	−	0.856999i	$-0.327674\pi$
$908$		0			0
$909$	89.5702	+	26.3002i	2.97086	+	0.872322i
$910$		0			0
$911$	−7.04618	+	49.0073i	−0.233450	+	1.62368i	0.449543	+	0.893259i	$0.351587\pi$
$911$	−7.04618	+	49.0073i	−0.233450	+	1.62368i	−0.682994	+	0.730424i	$0.739322\pi$
$912$		0			0
$913$	−0.784906	+	1.71871i	−0.0259766	+	0.0568808i
$914$		0			0
$915$	19.2085	+	133.598i	0.635015	+	4.41662i
$916$		0			0
$917$	33.0929	+	38.1913i	1.09282	+	1.26119i
$918$		0			0
$919$	30.9821			1.02201			0.511003	−	0.859579i	$-0.329274\pi$
$919$	30.9821			1.02201			0.511003	+	0.859579i	$0.329274\pi$
$920$		0			0
$921$	−49.3549			−1.62630
$922$		0			0
$923$	3.43023	+	3.95869i	0.112907	+	0.130302i
$924$		0			0
$925$	8.57308	+	59.6271i	0.281881	+	1.96053i
$926$		0			0
$927$	0.900121	−	1.97099i	0.0295639	−	0.0647358i
$928$		0			0
$929$	−8.00121	+	55.6496i	−0.262511	+	1.82580i	0.251310	+	0.967907i	$0.419139\pi$
$929$	−8.00121	+	55.6496i	−0.262511	+	1.82580i	−0.513821	+	0.857898i	$0.671770\pi$
$930$		0			0
$931$	0.357804	+	0.105061i	0.0117265	+	0.00344322i
$932$		0			0
$933$	−21.9003	−	47.9549i	−0.716983	−	1.56997i
$934$		0			0
$935$	0.493532	−	0.569566i	0.0161402	−	0.0186268i
$936$		0			0
$937$	−13.3766	−	8.59663i	−0.436995	−	0.280840i	0.303589	−	0.952803i	$-0.401815\pi$
$937$	−13.3766	−	8.59663i	−0.436995	−	0.280840i	−0.740584	+	0.671963i	$0.765451\pi$
$938$		0			0
$939$	46.8856	−	30.1315i	1.53005	−	0.983305i
$940$		0			0
$941$	10.0512	−	2.95131i	0.327661	−	0.0962100i	−0.113765	−	0.993508i	$-0.536291\pi$
$941$	10.0512	−	2.95131i	0.327661	−	0.0962100i	0.441426	+	0.897298i	$0.354473\pi$
$942$		0			0
$943$	11.1685	+	1.97682i	0.363697	+	0.0643740i
$944$		0			0
$945$	−66.7682	+	19.6049i	−2.17197	+	0.637748i
$946$		0			0
$947$	−4.73499	+	3.04300i	−0.153867	+	0.0988841i	−0.615309	−	0.788286i	$-0.710969\pi$
$947$	−4.73499	+	3.04300i	−0.153867	+	0.0988841i	0.461442	+	0.887170i	$0.347332\pi$
$948$		0			0
$949$	−19.6250	−	12.6122i	−0.637054	−	0.409410i
$950$		0			0
$951$	−16.4683	+	19.0054i	−0.534021	+	0.616293i
$952$		0			0
$953$	−0.935350	−	2.04813i	−0.0302990	−	0.0663454i	0.893877	−	0.448311i	$-0.147974\pi$
$953$	−0.935350	−	2.04813i	−0.0302990	−	0.0663454i	−0.924176	+	0.381966i	$0.875247\pi$
$954$		0			0
$955$	31.2985	+	9.19006i	1.01279	+	0.297383i
$956$		0			0
$957$	8.14403	−	56.6430i	0.263259	−	1.83101i
$958$		0			0
$959$	−0.371957	+	0.814472i	−0.0120111	+	0.0263007i
$960$		0			0
$961$	−1.22325	−	8.50789i	−0.0394597	−	0.274448i
$962$		0			0
$963$	−18.5202	−	21.3734i	−0.596804	−	0.688749i
$964$		0			0
$965$	97.5702			3.14090
$966$		0			0
$967$	−41.8242			−1.34498			−0.672488	−	0.740108i	$-0.734774\pi$
$967$	−41.8242			−1.34498			−0.672488	+	0.740108i	$0.734774\pi$
$968$		0			0
$969$	−0.115625	−	0.133438i	−0.00371440	−	0.00428665i
$970$		0			0
$971$	−4.99174	−	34.7183i	−0.160193	−	1.11416i	−0.898269	−	0.439447i	$-0.855175\pi$
$971$	−4.99174	−	34.7183i	−0.160193	−	1.11416i	0.738076	−	0.674717i	$-0.235734\pi$
$972$		0			0
$973$	−21.4516	+	46.9725i	−0.687707	+	1.50587i
$974$		0			0
$975$	−9.23206	+	64.2104i	−0.295663	+	2.05638i
$976$		0			0
$977$	51.0350	+	14.9852i	1.63275	+	0.479420i	0.964405	−	0.264429i	$-0.0851835\pi$
$977$	51.0350	+	14.9852i	1.63275	+	0.479420i	0.668348	+	0.743849i	$0.267002\pi$
$978$		0			0
$979$	−0.189547	−	0.415049i	−0.00605794	−	0.0132650i
$980$		0			0
$981$	−22.8656	+	26.3883i	−0.730043	+	0.842514i
$982$		0			0
$983$	−15.0309	−	9.65975i	−0.479410	−	0.308098i	0.278524	−	0.960429i	$-0.410155\pi$
$983$	−15.0309	−	9.65975i	−0.479410	−	0.308098i	−0.757934	+	0.652331i	$0.773791\pi$
$984$		0			0
$985$	−2.97086	+	1.90925i	−0.0946594	+	0.0608339i
$986$		0			0
$987$	34.4636	−	10.1194i	1.09699	−	0.322105i
$988$		0			0
$989$	36.7088	−	15.3480i	1.16727	−	0.488039i
$990$		0			0
$991$	26.9955	−	7.92659i	0.857539	−	0.251796i	0.176732	−	0.984259i	$-0.443447\pi$
$991$	26.9955	−	7.92659i	0.857539	−	0.251796i	0.680807	+	0.732463i	$0.261629\pi$
$992$		0			0
$993$	43.5829	−	28.0090i	1.38306	−	0.888839i
$994$		0			0
$995$	57.4998	+	36.9529i	1.82287	+	1.17149i
$996$		0			0
$997$	4.54670	−	5.24717i	0.143995	−	0.166180i	−0.679170	−	0.733981i	$-0.737660\pi$
$997$	4.54670	−	5.24717i	0.143995	−	0.166180i	0.823166	+	0.567801i	$0.192206\pi$
$998$		0			0
$999$	16.9443	+	37.1028i	0.536093	+	1.17388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.9.2	✓	20
3.2	odd	2		828.2.q.a.469.2		20
4.3	odd	2		368.2.m.d.193.1		20
23.8	even	11		2116.2.a.j.1.1		10
23.15	odd	22		2116.2.a.i.1.1		10
23.18	even	11	inner	92.2.e.a.41.2	yes	20
69.41	odd	22		828.2.q.a.685.2		20
92.15	even	22		8464.2.a.cd.1.10		10
92.31	odd	22		8464.2.a.ce.1.10		10
92.87	odd	22		368.2.m.d.225.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.9.2	✓	20	1.1	even	1	trivial
92.2.e.a.41.2	yes	20	23.18	even	11	inner
368.2.m.d.193.1		20	4.3	odd	2
368.2.m.d.225.1		20	92.87	odd	22
828.2.q.a.469.2		20	3.2	odd	2
828.2.q.a.685.2		20	69.41	odd	22
2116.2.a.i.1.1		10	23.15	odd	22
2116.2.a.j.1.1		10	23.8	even	11
8464.2.a.cd.1.10		10	92.15	even	22
8464.2.a.ce.1.10		10	92.31	odd	22

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.89799 + 2.19040i) q^{3} +(-0.556197 - 3.86843i) q^{5} +(-1.06324 + 2.32817i) q^{7} +(-0.768534 + 5.34527i) q^{9} +O(q^{10})\)	\(q+(1.89799 + 2.19040i) q^{3} +(-0.556197 - 3.86843i) q^{5} +(-1.06324 + 2.32817i) q^{7} +(-0.768534 + 5.34527i) q^{9} +(-2.52183 - 0.740475i) q^{11} +(-0.904981 - 1.98163i) q^{13} +(7.41777 - 8.56056i) q^{15} +(-0.0617222 - 0.0396665i) q^{17} +(0.698502 - 0.448900i) q^{19} +(-7.11766 + 2.08993i) q^{21} +(1.49943 - 4.55540i) q^{23} +(-9.85797 + 2.89456i) q^{25} +(-5.85230 + 3.76105i) q^{27} +(6.31971 + 4.06143i) q^{29} +(-4.12070 + 4.75554i) q^{31} +(-3.16447 - 6.92922i) q^{33} +(9.59776 + 2.81816i) q^{35} +(0.834432 - 5.80361i) q^{37} +(2.62292 - 5.74340i) q^{39} +(0.336574 + 2.34092i) q^{41} +(5.43299 + 6.27000i) q^{43} +21.1053 q^{45} -4.84198 q^{47} +(0.294111 + 0.339422i) q^{49} +(-0.0302629 - 0.210483i) q^{51} +(0.347961 - 0.761928i) q^{53} +(-1.46185 + 10.1674i) q^{55} +(2.30902 + 0.677991i) q^{57} +(-0.679933 - 1.48885i) q^{59} +(-7.80313 + 9.00529i) q^{61} +(-11.6276 - 7.47260i) q^{63} +(-7.16247 + 4.60304i) q^{65} +(1.65680 - 0.486481i) q^{67} +(12.8241 - 5.36178i) q^{69} +(-2.30706 + 0.677414i) q^{71} +(9.00849 - 5.78941i) q^{73} +(-25.0506 - 16.0990i) q^{75} +(4.40526 - 5.08395i) q^{77} +(3.03929 + 6.65512i) q^{79} +(-3.80136 - 1.11618i) q^{81} +(0.102309 - 0.711573i) q^{83} +(-0.119117 + 0.260831i) q^{85} +(3.09861 + 21.5513i) q^{87} +(0.113687 + 0.131202i) q^{89} +5.57580 q^{91} -18.2376 q^{93} +(-2.12505 - 2.45243i) q^{95} +(-2.24709 - 15.6289i) q^{97} +(5.89614 - 12.9108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Introduction

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Varieties

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Groups

Database

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