LMFDB - Embedded newform 124.2.f.b.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,2,Mod(33,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	124.f (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:	$0.990144985064$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	124.33
Dual form			124.2.f.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80902 - 1.31433i) q^{3} -0.381966 q^{5} +(0.0729490 + 0.224514i) q^{7} +(0.618034 - 1.90211i) q^{9} +O(q^{10})$	\(q+(1.80902 - 1.31433i) q^{3} -0.381966 q^{5} +(0.0729490 + 0.224514i) q^{7} +(0.618034 - 1.90211i) q^{9} +(-0.381966 - 1.17557i) q^{11} +(-3.73607 + 2.71441i) q^{13} +(-0.690983 + 0.502029i) q^{15} +(0.690983 - 2.12663i) q^{17} +(5.42705 + 3.94298i) q^{19} +(0.427051 + 0.310271i) q^{21} +(-0.545085 + 1.67760i) q^{23} -4.85410 q^{25} +(0.690983 + 2.12663i) q^{27} +(-4.54508 - 3.30220i) q^{29} +(-4.19098 + 3.66547i) q^{31} +(-2.23607 - 1.62460i) q^{33} +(-0.0278640 - 0.0857567i) q^{35} +4.70820 q^{37} +(-3.19098 + 9.82084i) q^{39} +(-8.47214 - 6.15537i) q^{41} +(-0.927051 - 0.673542i) q^{43} +(-0.236068 + 0.726543i) q^{45} +(6.92705 - 5.03280i) q^{47} +(5.61803 - 4.08174i) q^{49} +(-1.54508 - 4.75528i) q^{51} +(-2.83688 + 8.73102i) q^{53} +(0.145898 + 0.449028i) q^{55} +15.0000 q^{57} +(10.2812 - 7.46969i) q^{59} +2.00000 q^{61} +0.472136 q^{63} +(1.42705 - 1.03681i) q^{65} +3.00000 q^{67} +(1.21885 + 3.75123i) q^{69} +(4.04508 - 12.4495i) q^{71} +(0.0450850 + 0.138757i) q^{73} +(-8.78115 + 6.37988i) q^{75} +(0.236068 - 0.171513i) q^{77} +(8.89919 + 6.46564i) q^{81} +(-6.35410 - 4.61653i) q^{83} +(-0.263932 + 0.812299i) q^{85} -12.5623 q^{87} +(-4.95492 - 15.2497i) q^{89} +(-0.881966 - 0.640786i) q^{91} +(-2.76393 + 12.1392i) q^{93} +(-2.07295 - 1.50609i) q^{95} +(1.45492 + 4.47777i) q^{97} -2.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{3} - 6 q^{5} + 7 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 5 * q^3 - 6 * q^5 + 7 * q^7 - 2 * q^9	$ 4 q + 5 q^{3} - 6 q^{5} + 7 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{13} - 5 q^{15} + 5 q^{17} + 15 q^{19} - 5 q^{21} + 9 q^{23} - 6 q^{25} + 5 q^{27} - 7 q^{29} - 19 q^{31} - 18 q^{35} - 8 q^{37} - 15 q^{39} - 16 q^{41} + 3 q^{43} + 8 q^{45} + 21 q^{47} + 18 q^{49} + 5 q^{51} - 27 q^{53} + 14 q^{55} + 60 q^{57} + 21 q^{59} + 8 q^{61} - 16 q^{63} - q^{65} + 12 q^{67} + 25 q^{69} + 5 q^{71} - 11 q^{73} - 15 q^{75} - 8 q^{77} + 11 q^{81} - 12 q^{83} - 10 q^{85} - 10 q^{87} - 31 q^{89} - 8 q^{91} - 20 q^{93} - 15 q^{95} + 17 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q + 5 * q^3 - 6 * q^5 + 7 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^13 - 5 * q^15 + 5 * q^17 + 15 * q^19 - 5 * q^21 + 9 * q^23 - 6 * q^25 + 5 * q^27 - 7 * q^29 - 19 * q^31 - 18 * q^35 - 8 * q^37 - 15 * q^39 - 16 * q^41 + 3 * q^43 + 8 * q^45 + 21 * q^47 + 18 * q^49 + 5 * q^51 - 27 * q^53 + 14 * q^55 + 60 * q^57 + 21 * q^59 + 8 * q^61 - 16 * q^63 - q^65 + 12 * q^67 + 25 * q^69 + 5 * q^71 - 11 * q^73 - 15 * q^75 - 8 * q^77 + 11 * q^81 - 12 * q^83 - 10 * q^85 - 10 * q^87 - 31 * q^89 - 8 * q^91 - 20 * q^93 - 15 * q^95 + 17 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	1.80902	−	1.31433i	1.04444	−	0.758827i	0.0732898	−	0.997311i	$-0.476650\pi$
$3$	1.80902	−	1.31433i	1.04444	−	0.758827i	0.971147	+	0.238483i	$0.0766502\pi$
$4$		0			0
$5$	−0.381966			−0.170820			−0.0854102	−	0.996346i	$-0.527220\pi$
$5$	−0.381966			−0.170820			−0.0854102	+	0.996346i	$0.527220\pi$
$6$		0			0
$7$	0.0729490	+	0.224514i	0.0275721	+	0.0848583i	0.963896	−	0.266280i	$-0.0857946\pi$
$7$	0.0729490	+	0.224514i	0.0275721	+	0.0848583i	−0.936324	+	0.351138i	$0.885795\pi$
$8$		0			0
$9$	0.618034	−	1.90211i	0.206011	−	0.634038i
$10$		0			0
$11$	−0.381966	−	1.17557i	−0.115167	−	0.354448i	0.876815	−	0.480828i	$-0.159664\pi$
$11$	−0.381966	−	1.17557i	−0.115167	−	0.354448i	−0.991982	+	0.126380i	$0.959664\pi$
$12$		0			0
$13$	−3.73607	+	2.71441i	−1.03620	+	0.752843i	−0.969540	−	0.244933i	$-0.921234\pi$
$13$	−3.73607	+	2.71441i	−1.03620	+	0.752843i	−0.0666589	+	0.997776i	$0.521234\pi$
$14$		0			0
$15$	−0.690983	+	0.502029i	−0.178411	+	0.129623i
$16$		0			0
$17$	0.690983	−	2.12663i	0.167588	−	0.515783i	−0.831630	−	0.555331i	$-0.812592\pi$
$17$	0.690983	−	2.12663i	0.167588	−	0.515783i	0.999218	+	0.0395478i	$0.0125917\pi$
$18$		0			0
$19$	5.42705	+	3.94298i	1.24505	+	0.904582i	0.997924	−	0.0644007i	$-0.0205136\pi$
$19$	5.42705	+	3.94298i	1.24505	+	0.904582i	0.247127	+	0.968983i	$0.420514\pi$
$20$		0			0
$21$	0.427051	+	0.310271i	0.0931902	+	0.0677066i
$22$		0			0
$23$	−0.545085	+	1.67760i	−0.113658	+	0.349804i	−0.991665	−	0.128845i	$-0.958873\pi$
$23$	−0.545085	+	1.67760i	−0.113658	+	0.349804i	0.878007	+	0.478648i	$0.158873\pi$
$24$		0			0
$25$	−4.85410			−0.970820
$26$		0			0
$27$	0.690983	+	2.12663i	0.132980	+	0.409270i
$28$		0			0
$29$	−4.54508	−	3.30220i	−0.844001	−	0.613203i	0.0794844	−	0.996836i	$-0.474673\pi$
$29$	−4.54508	−	3.30220i	−0.844001	−	0.613203i	−0.923485	+	0.383633i	$0.874673\pi$
$30$		0			0
$31$	−4.19098	+	3.66547i	−0.752723	+	0.658338i
$31$	−4.19098	+	3.66547i	−0.752723	+	0.658338i
$32$		0			0
$33$	−2.23607	−	1.62460i	−0.389249	−	0.282806i
$34$		0			0
$35$	−0.0278640	−	0.0857567i	−0.00470988	−	0.0144955i
$36$		0			0
$37$	4.70820			0.774024			0.387012	−	0.922075i	$-0.373507\pi$
$37$	4.70820			0.774024			0.387012	+	0.922075i	$0.373507\pi$
$38$		0			0
$39$	−3.19098	+	9.82084i	−0.510966	+	1.57259i
$40$		0			0
$41$	−8.47214	−	6.15537i	−1.32313	−	0.961307i	−0.999888	−	0.0149890i	$-0.995229\pi$
$41$	−8.47214	−	6.15537i	−1.32313	−	0.961307i	−0.323238	−	0.946318i	$-0.604771\pi$
$42$		0			0
$43$	−0.927051	−	0.673542i	−0.141374	−	0.102714i	0.514850	−	0.857280i	$-0.327847\pi$
$43$	−0.927051	−	0.673542i	−0.141374	−	0.102714i	−0.656224	+	0.754566i	$0.727847\pi$
$44$		0			0
$45$	−0.236068	+	0.726543i	−0.0351909	+	0.108307i
$46$		0			0
$47$	6.92705	−	5.03280i	1.01041	−	0.734109i	0.0461183	−	0.998936i	$-0.485315\pi$
$47$	6.92705	−	5.03280i	1.01041	−	0.734109i	0.964296	+	0.264827i	$0.0853149\pi$
$48$		0			0
$49$	5.61803	−	4.08174i	0.802576	−	0.583106i
$50$		0			0
$51$	−1.54508	−	4.75528i	−0.216355	−	0.665873i
$52$		0			0
$53$	−2.83688	+	8.73102i	−0.389676	+	1.19930i	0.543356	+	0.839503i	$0.317154\pi$
$53$	−2.83688	+	8.73102i	−0.389676	+	1.19930i	−0.933031	+	0.359795i	$0.882846\pi$
$54$		0			0
$55$	0.145898	+	0.449028i	0.0196729	+	0.0605469i
$56$		0			0
$57$	15.0000			1.98680
$58$		0			0
$59$	10.2812	−	7.46969i	1.33849	−	0.972471i	0.338994	−	0.940788i	$-0.389913\pi$
$59$	10.2812	−	7.46969i	1.33849	−	0.972471i	0.999498	−	0.0316830i	$-0.0100867\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$	0.472136			0.0594835
$64$		0			0
$65$	1.42705	−	1.03681i	0.177004	−	0.128601i
$66$		0			0
$67$	3.00000			0.366508			0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000			0.366508			0.183254	+	0.983066i	$0.441337\pi$
$68$		0			0
$69$	1.21885	+	3.75123i	0.146732	+	0.451594i
$70$		0			0
$71$	4.04508	−	12.4495i	0.480063	−	1.47748i	−0.358942	−	0.933360i	$-0.616862\pi$
$71$	4.04508	−	12.4495i	0.480063	−	1.47748i	0.839005	−	0.544123i	$-0.183138\pi$
$72$		0			0
$73$	0.0450850	+	0.138757i	0.00527680	+	0.0162403i	0.953660	−	0.300886i	$-0.0972822\pi$
$73$	0.0450850	+	0.138757i	0.00527680	+	0.0162403i	−0.948383	+	0.317126i	$0.897282\pi$
$74$		0			0
$75$	−8.78115	+	6.37988i	−1.01396	+	0.736685i
$76$		0			0
$77$	0.236068	−	0.171513i	0.0269024	−	0.0195458i
$78$		0			0
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$		0			0
$81$	8.89919	+	6.46564i	0.988799	+	0.718404i
$82$		0			0
$83$	−6.35410	−	4.61653i	−0.697453	−	0.506729i	0.181649	−	0.983364i	$-0.441857\pi$
$83$	−6.35410	−	4.61653i	−0.697453	−	0.506729i	−0.879102	+	0.476634i	$0.841857\pi$
$84$		0			0
$85$	−0.263932	+	0.812299i	−0.0286274	+	0.0881062i
$86$		0			0
$87$	−12.5623			−1.34682
$88$		0			0
$89$	−4.95492	−	15.2497i	−0.525220	−	1.61646i	−0.763880	−	0.645358i	$-0.776708\pi$
$89$	−4.95492	−	15.2497i	−0.525220	−	1.61646i	0.238661	−	0.971103i	$-0.423292\pi$
$90$		0			0
$91$	−0.881966	−	0.640786i	−0.0924552	−	0.0671726i
$92$		0			0
$93$	−2.76393	+	12.1392i	−0.286606	+	1.25878i
$94$		0			0
$95$	−2.07295	−	1.50609i	−0.212680	−	0.154521i
$96$		0			0
$97$	1.45492	+	4.47777i	0.147724	+	0.454648i	0.997351	−	0.0727356i	$-0.0231729\pi$
$97$	1.45492	+	4.47777i	0.147724	+	0.454648i	−0.849627	+	0.527384i	$0.823173\pi$
$98$		0			0
$99$	−2.47214			−0.248459
$100$		0			0
$101$	−2.85410	+	8.78402i	−0.283994	+	0.874043i	0.702705	+	0.711482i	$0.251976\pi$
$101$	−2.85410	+	8.78402i	−0.283994	+	0.874043i	−0.986698	+	0.162561i	$0.948024\pi$
$102$		0			0
$103$	−5.78115	−	4.20025i	−0.569634	−	0.413863i	0.265338	−	0.964155i	$-0.414516\pi$
$103$	−5.78115	−	4.20025i	−0.569634	−	0.413863i	−0.834972	+	0.550292i	$0.814516\pi$
$104$		0			0
$105$	−0.163119	−	0.118513i	−0.0159188	−	0.0115657i
$106$		0			0
$107$	−1.26393	+	3.88998i	−0.122189	+	0.376059i	−0.993378	−	0.114888i	$-0.963349\pi$
$107$	−1.26393	+	3.88998i	−0.122189	+	0.376059i	0.871190	+	0.490947i	$0.163349\pi$
$108$		0			0
$109$	−5.66312	+	4.11450i	−0.542428	+	0.394097i	−0.824986	−	0.565153i	$-0.808817\pi$
$109$	−5.66312	+	4.11450i	−0.542428	+	0.394097i	0.282558	+	0.959250i	$0.408817\pi$
$110$		0			0
$111$	8.51722	−	6.18812i	0.808419	−	0.587351i
$112$		0			0
$113$	2.44427	+	7.52270i	0.229938	+	0.707676i	0.997753	+	0.0670040i	$0.0213440\pi$
$113$	2.44427	+	7.52270i	0.229938	+	0.707676i	−0.767815	+	0.640672i	$0.778656\pi$
$114$		0			0
$115$	0.208204	−	0.640786i	0.0194151	−	0.0597536i
$116$		0			0
$117$	2.85410	+	8.78402i	0.263862	+	0.812083i
$118$		0			0
$119$	0.527864			0.0483892
$120$		0			0
$121$	7.66312	−	5.56758i	0.696647	−	0.506144i
$122$		0			0
$123$	−23.4164			−2.11139
$124$		0			0
$125$	3.76393			0.336656
$126$		0			0
$127$	7.28115	−	5.29007i	0.646098	−	0.469418i	−0.215842	−	0.976428i	$-0.569250\pi$
$127$	7.28115	−	5.29007i	0.646098	−	0.469418i	0.861940	+	0.507011i	$0.169250\pi$
$128$		0			0
$129$	−2.56231			−0.225598
$130$		0			0
$131$	4.33688	+	13.3475i	0.378915	+	1.16618i	0.940799	+	0.338965i	$0.110077\pi$
$131$	4.33688	+	13.3475i	0.378915	+	1.16618i	−0.561884	+	0.827216i	$0.689923\pi$
$132$		0			0
$133$	−0.489357	+	1.50609i	−0.0424326	+	0.130594i
$134$		0			0
$135$	−0.263932	−	0.812299i	−0.0227157	−	0.0699116i
$136$		0			0
$137$	−8.47214	+	6.15537i	−0.723823	+	0.525888i	−0.887603	−	0.460608i	$-0.847631\pi$
$137$	−8.47214	+	6.15537i	−0.723823	+	0.525888i	0.163780	+	0.986497i	$0.447631\pi$
$138$		0			0
$139$	−11.3992	+	8.28199i	−0.966866	+	0.702470i	−0.954735	−	0.297457i	$-0.903862\pi$
$139$	−11.3992	+	8.28199i	−0.966866	+	0.702470i	−0.0121312	+	0.999926i	$0.503862\pi$
$140$		0			0
$141$	5.91641	−	18.2088i	0.498251	−	1.53346i
$142$		0			0
$143$	4.61803	+	3.35520i	0.386179	+	0.280576i
$144$		0			0
$145$	1.73607	+	1.26133i	0.144173	+	0.104748i
$146$		0			0
$147$	4.79837	−	14.7679i	0.395763	−	1.21803i
$148$		0			0
$149$	5.56231			0.455682			0.227841	−	0.973698i	$-0.426833\pi$
$149$	5.56231			0.455682			0.227841	+	0.973698i	$0.426833\pi$
$150$		0			0
$151$	1.66312	+	5.11855i	0.135343	+	0.416542i	0.995643	−	0.0932453i	$-0.0297241\pi$
$151$	1.66312	+	5.11855i	0.135343	+	0.416542i	−0.860300	+	0.509787i	$0.829724\pi$
$152$		0			0
$153$	−3.61803	−	2.62866i	−0.292501	−	0.212514i
$154$		0			0
$155$	1.60081	−	1.40008i	0.128580	−	0.112457i
$156$		0			0
$157$	−15.9443	−	11.5842i	−1.27249	−	0.924519i	−0.273193	−	0.961959i	$-0.588080\pi$
$157$	−15.9443	−	11.5842i	−1.27249	−	0.924519i	−0.999299	+	0.0374402i	$0.988080\pi$
$158$		0			0
$159$	6.34346	+	19.5232i	0.503069	+	1.54829i
$160$		0			0
$161$	−0.416408			−0.0328175
$162$		0			0
$163$	−2.45492	+	7.55545i	−0.192284	+	0.591789i	0.807714	+	0.589575i	$0.200705\pi$
$163$	−2.45492	+	7.55545i	−0.192284	+	0.591789i	−0.999998	+	0.00221381i	$0.999295\pi$
$164$		0			0
$165$	0.854102	+	0.620541i	0.0664917	+	0.0483091i
$166$		0			0
$167$	−15.0902	−	10.9637i	−1.16771	−	0.848393i	−0.176979	−	0.984215i	$-0.556633\pi$
$167$	−15.0902	−	10.9637i	−1.16771	−	0.848393i	−0.990733	+	0.135822i	$0.956633\pi$
$168$		0			0
$169$	2.57295	−	7.91872i	0.197919	−	0.609133i
$170$		0			0
$171$	10.8541	−	7.88597i	0.830034	−	0.603055i
$172$		0			0
$173$	−7.78115	+	5.65334i	−0.591590	+	0.429815i	−0.842884	−	0.538095i	$-0.819144\pi$
$173$	−7.78115	+	5.65334i	−0.591590	+	0.429815i	0.251294	+	0.967911i	$0.419144\pi$
$174$		0			0
$175$	−0.354102	−	1.08981i	−0.0267676	−	0.0823822i
$176$		0			0
$177$	8.78115	−	27.0256i	0.660032	−	2.03137i
$178$		0			0
$179$	2.28115	+	7.02067i	0.170501	+	0.524749i	0.999399	−	0.0346503i	$-0.0110317\pi$
$179$	2.28115	+	7.02067i	0.170501	+	0.524749i	−0.828898	+	0.559400i	$0.811032\pi$
$180$		0			0
$181$	16.4164			1.22022			0.610111	−	0.792316i	$-0.291125\pi$
$181$	16.4164			1.22022			0.610111	+	0.792316i	$0.291125\pi$
$182$		0			0
$183$	3.61803	−	2.62866i	0.267453	−	0.194316i
$184$		0			0
$185$	−1.79837			−0.132219
$186$		0			0
$187$	−2.76393			−0.202119
$188$		0			0
$189$	−0.427051	+	0.310271i	−0.0310634	+	0.0225689i
$190$		0			0
$191$	21.3820			1.54714			0.773572	−	0.633708i	$-0.218468\pi$
$191$	21.3820			1.54714			0.773572	+	0.633708i	$0.218468\pi$
$192$		0			0
$193$	3.51722	+	10.8249i	0.253175	+	0.779193i	0.994184	+	0.107697i	$0.0343477\pi$
$193$	3.51722	+	10.8249i	0.253175	+	0.779193i	−0.741009	+	0.671496i	$0.765652\pi$
$194$		0			0
$195$	1.21885	−	3.75123i	0.0872835	−	0.268631i
$196$		0			0
$197$	8.30902	+	25.5725i	0.591993	+	1.82197i	0.569159	+	0.822228i	$0.307269\pi$
$197$	8.30902	+	25.5725i	0.591993	+	1.82197i	0.0228342	+	0.999739i	$0.492731\pi$
$198$		0			0
$199$	17.7533	−	12.8985i	1.25850	−	0.914352i	0.259814	−	0.965659i	$-0.416339\pi$
$199$	17.7533	−	12.8985i	1.25850	−	0.914352i	0.998683	+	0.0513068i	$0.0163386\pi$
$200$		0			0
$201$	5.42705	−	3.94298i	0.382795	−	0.278117i
$202$		0			0
$203$	0.409830	−	1.26133i	0.0287644	−	0.0885278i
$204$		0			0
$205$	3.23607	+	2.35114i	0.226017	+	0.164211i
$206$		0			0
$207$	2.85410	+	2.07363i	0.198374	+	0.144127i
$208$		0			0
$209$	2.56231	−	7.88597i	0.177238	−	0.545484i
$210$		0			0
$211$	−9.88854			−0.680755			−0.340378	−	0.940289i	$-0.610555\pi$
$211$	−9.88854			−0.680755			−0.340378	+	0.940289i	$0.610555\pi$
$212$		0			0
$213$	−9.04508	−	27.8379i	−0.619759	−	1.90742i
$214$		0			0
$215$	0.354102	+	0.257270i	0.0241496	+	0.0175457i
$216$		0			0
$217$	−1.12868	−	0.673542i	−0.0766196	−	0.0457230i
$218$		0			0
$219$	0.263932	+	0.191758i	0.0178349	+	0.0129578i
$220$		0			0
$221$	3.19098	+	9.82084i	0.214649	+	0.660621i
$222$		0			0
$223$	−3.47214			−0.232511			−0.116256	−	0.993219i	$-0.537089\pi$
$223$	−3.47214			−0.232511			−0.116256	+	0.993219i	$0.537089\pi$
$224$		0			0
$225$	−3.00000	+	9.23305i	−0.200000	+	0.615537i
$226$		0			0
$227$	19.6803	+	14.2986i	1.30623	+	0.949032i	0.999996	−	0.00292450i	$-0.000930897\pi$
$227$	19.6803	+	14.2986i	1.30623	+	0.949032i	0.306234	+	0.951956i	$0.400931\pi$
$228$		0			0
$229$	−16.7082	−	12.1392i	−1.10411	−	0.802182i	−0.122383	−	0.992483i	$-0.539054\pi$
$229$	−16.7082	−	12.1392i	−1.10411	−	0.802182i	−0.981726	+	0.190301i	$0.939054\pi$
$230$		0			0
$231$	0.201626	−	0.620541i	0.0132660	−	0.0408286i
$232$		0			0
$233$	−16.2533	+	11.8087i	−1.06479	+	0.773614i	−0.974968	−	0.222344i	$-0.928629\pi$
$233$	−16.2533	+	11.8087i	−1.06479	+	0.773614i	−0.0898201	+	0.995958i	$0.528629\pi$
$234$		0			0
$235$	−2.64590	+	1.92236i	−0.172599	+	0.125401i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.909830	+	2.80017i	−0.0588520	+	0.181128i	−0.976161	−	0.217049i	$-0.930357\pi$
$239$	−0.909830	+	2.80017i	−0.0588520	+	0.181128i	0.917309	+	0.398177i	$0.130357\pi$
$240$		0			0
$241$	−2.92705	−	9.00854i	−0.188548	−	0.580291i	0.811444	−	0.584431i	$-0.198682\pi$
$241$	−2.92705	−	9.00854i	−0.188548	−	0.580291i	−0.999991	+	0.00414002i	$0.998682\pi$
$242$		0			0
$243$	17.8885			1.14755
$244$		0			0
$245$	−2.14590	+	1.55909i	−0.137096	+	0.0996064i
$246$		0			0
$247$	−30.9787			−1.97113
$248$		0			0
$249$	−17.5623			−1.11297
$250$		0			0
$251$	0.763932	−	0.555029i	0.0482190	−	0.0350331i	−0.563415	−	0.826174i	$-0.690513\pi$
$251$	0.763932	−	0.555029i	0.0482190	−	0.0350331i	0.611634	+	0.791141i	$0.290513\pi$
$252$		0			0
$253$	2.18034			0.137077
$254$		0			0
$255$	0.590170	+	1.81636i	0.0369579	+	0.113745i
$256$		0			0
$257$	−7.85410	+	24.1724i	−0.489925	+	1.50784i	0.334793	+	0.942292i	$0.391334\pi$
$257$	−7.85410	+	24.1724i	−0.489925	+	1.50784i	−0.824718	+	0.565544i	$0.808666\pi$
$258$		0			0
$259$	0.343459	+	1.05706i	0.0213415	+	0.0656824i
$260$		0			0
$261$	−9.09017	+	6.60440i	−0.562667	+	0.408802i
$262$		0			0
$263$	−23.2533	+	16.8945i	−1.43386	+	1.04176i	−0.444577	+	0.895740i	$0.646646\pi$
$263$	−23.2533	+	16.8945i	−1.43386	+	1.04176i	−0.989282	+	0.146019i	$0.953354\pi$
$264$		0			0
$265$	1.08359	−	3.33495i	0.0665645	−	0.204865i
$266$		0			0
$267$	−29.0066	−	21.0745i	−1.77517	−	1.28974i
$268$		0			0
$269$	−10.0172	−	7.27794i	−0.610761	−	0.443744i	0.238921	−	0.971039i	$-0.423206\pi$
$269$	−10.0172	−	7.27794i	−0.610761	−	0.443744i	−0.849682	+	0.527295i	$0.823206\pi$
$270$		0			0
$271$	5.82624	−	17.9313i	0.353919	−	1.08925i	−0.602715	−	0.797957i	$-0.705914\pi$
$271$	5.82624	−	17.9313i	0.353919	−	1.08925i	0.956634	−	0.291293i	$-0.0940856\pi$
$272$		0			0
$273$	−2.43769			−0.147536
$274$		0			0
$275$	1.85410	+	5.70634i	0.111807	+	0.344105i
$276$		0			0
$277$	10.8262	+	7.86572i	0.650486	+	0.472605i	0.863437	−	0.504457i	$-0.168307\pi$
$277$	10.8262	+	7.86572i	0.650486	+	0.472605i	−0.212951	+	0.977063i	$0.568307\pi$
$278$		0			0
$279$	4.38197	+	10.2371i	0.262341	+	0.612880i
$280$		0			0
$281$	3.35410	+	2.43690i	0.200089	+	0.145373i	0.683318	−	0.730121i	$-0.260536\pi$
$281$	3.35410	+	2.43690i	0.200089	+	0.145373i	−0.483229	+	0.875494i	$0.660536\pi$
$282$		0			0
$283$	5.86475	+	18.0498i	0.348623	+	1.07295i	0.959616	+	0.281315i	$0.0907705\pi$
$283$	5.86475	+	18.0498i	0.348623	+	1.07295i	−0.610993	+	0.791636i	$0.709230\pi$
$284$		0			0
$285$	−5.72949			−0.339386
$286$		0			0
$287$	0.763932	−	2.35114i	0.0450935	−	0.138783i
$288$		0			0
$289$	9.70820	+	7.05342i	0.571071	+	0.414907i
$290$		0			0
$291$	8.51722	+	6.18812i	0.499288	+	0.362754i
$292$		0			0
$293$	8.36475	−	25.7440i	0.488674	−	1.50398i	−0.337915	−	0.941177i	$-0.609722\pi$
$293$	8.36475	−	25.7440i	0.488674	−	1.50398i	0.826589	−	0.562806i	$-0.190278\pi$
$294$		0			0
$295$	−3.92705	+	2.85317i	−0.228642	+	0.166118i
$296$		0			0
$297$	2.23607	−	1.62460i	0.129750	−	0.0942688i
$298$		0			0
$299$	−2.51722	−	7.74721i	−0.145575	−	0.448033i
$300$		0			0
$301$	0.0835921	−	0.257270i	0.00481817	−	0.0148288i
$302$		0			0
$303$	6.38197	+	19.6417i	0.366634	+	1.12838i
$304$		0			0
$305$	−0.763932			−0.0437426
$306$		0			0
$307$	20.9164	−	15.1967i	1.19376	−	0.867319i	0.200106	−	0.979774i	$-0.435871\pi$
$307$	20.9164	−	15.1967i	1.19376	−	0.867319i	0.993657	+	0.112455i	$0.0358715\pi$
$308$		0			0
$309$	−15.9787			−0.908997
$310$		0			0
$311$	18.9443			1.07423			0.537116	−	0.843509i	$-0.319514\pi$
$311$	18.9443			1.07423			0.537116	+	0.843509i	$0.319514\pi$
$312$		0			0
$313$	−11.5623	+	8.40051i	−0.653540	+	0.474825i	−0.864475	−	0.502675i	$-0.832349\pi$
$313$	−11.5623	+	8.40051i	−0.653540	+	0.474825i	0.210935	+	0.977500i	$0.432349\pi$
$314$		0			0
$315$	−0.180340			−0.0101610
$316$		0			0
$317$	1.52786	+	4.70228i	0.0858134	+	0.264106i	0.984751	−	0.173970i	$-0.0556597\pi$
$317$	1.52786	+	4.70228i	0.0858134	+	0.264106i	−0.898937	+	0.438077i	$0.855660\pi$
$318$		0			0
$319$	−2.14590	+	6.60440i	−0.120147	+	0.369775i
$320$		0			0
$321$	2.82624	+	8.69827i	0.157745	+	0.485490i
$322$		0			0
$323$	12.1353	−	8.81678i	0.675224	−	0.490579i
$324$		0			0
$325$	18.1353	−	13.1760i	1.00596	−	0.730875i
$326$		0			0
$327$	−4.83688	+	14.8864i	−0.267480	+	0.823219i
$328$		0			0
$329$	1.63525	+	1.18808i	0.0901545	+	0.0655011i
$330$		0			0
$331$	−12.5451	−	9.11454i	−0.689540	−	0.500980i	0.186969	−	0.982366i	$-0.440134\pi$
$331$	−12.5451	−	9.11454i	−0.689540	−	0.500980i	−0.876509	+	0.481386i	$0.840134\pi$
$332$		0			0
$333$	2.90983	−	8.95554i	0.159458	−	0.490760i
$334$		0			0
$335$	−1.14590			−0.0626071
$336$		0			0
$337$	−10.3541	−	31.8666i	−0.564024	−	1.73589i	−0.670834	−	0.741608i	$-0.734064\pi$
$337$	−10.3541	−	31.8666i	−0.564024	−	1.73589i	0.106810	−	0.994279i	$-0.465936\pi$
$338$		0			0
$339$	14.3090	+	10.3961i	0.777159	+	0.564639i
$340$		0			0
$341$	5.90983	+	3.52671i	0.320035	+	0.190982i
$342$		0			0
$343$	2.66312	+	1.93487i	0.143795	+	0.104473i
$344$		0			0
$345$	−0.465558	−	1.43284i	−0.0250648	−	0.0771415i
$346$		0			0
$347$	9.47214			0.508491			0.254245	−	0.967140i	$-0.418173\pi$
$347$	9.47214			0.508491			0.254245	+	0.967140i	$0.418173\pi$
$348$		0			0
$349$	7.63525	−	23.4989i	0.408706	−	1.25787i	−0.509055	−	0.860734i	$-0.670005\pi$
$349$	7.63525	−	23.4989i	0.408706	−	1.25787i	0.917761	−	0.397133i	$-0.129995\pi$
$350$		0			0
$351$	−8.35410	−	6.06961i	−0.445909	−	0.323972i
$352$		0			0
$353$	−7.59017	−	5.51458i	−0.403984	−	0.293512i	0.367178	−	0.930151i	$-0.380324\pi$
$353$	−7.59017	−	5.51458i	−0.403984	−	0.293512i	−0.771162	+	0.636639i	$0.780324\pi$
$354$		0			0
$355$	−1.54508	+	4.75528i	−0.0820046	+	0.252384i
$356$		0			0
$357$	0.954915	−	0.693786i	0.0505395	−	0.0367191i
$358$		0			0
$359$	−6.97214	+	5.06555i	−0.367975	+	0.267350i	−0.756371	−	0.654143i	$-0.773029\pi$
$359$	−6.97214	+	5.06555i	−0.367975	+	0.267350i	0.388396	+	0.921493i	$0.373029\pi$
$360$		0			0
$361$	8.03444	+	24.7275i	0.422865	+	1.30145i
$362$		0			0
$363$	6.54508	−	20.1437i	0.343528	−	1.05727i
$364$		0			0
$365$	−0.0172209	−	0.0530006i	−0.000901385	−	0.00277418i
$366$		0			0
$367$	−17.3820			−0.907331			−0.453666	−	0.891172i	$-0.649884\pi$
$367$	−17.3820			−0.907331			−0.453666	+	0.891172i	$0.649884\pi$
$368$		0			0
$369$	−16.9443	+	12.3107i	−0.882084	+	0.640871i
$370$		0			0
$371$	−2.16718			−0.112515
$372$		0			0
$373$	−18.7082			−0.968674			−0.484337	−	0.874881i	$-0.660939\pi$
$373$	−18.7082			−0.968674			−0.484337	+	0.874881i	$0.660939\pi$
$374$		0			0
$375$	6.80902	−	4.94704i	0.351616	−	0.255464i
$376$		0			0
$377$	25.9443			1.33620
$378$		0			0
$379$	3.92705	+	12.0862i	0.201719	+	0.620827i	0.999832	+	0.0183198i	$0.00583170\pi$
$379$	3.92705	+	12.0862i	0.201719	+	0.620827i	−0.798113	+	0.602508i	$0.794168\pi$
$380$		0			0
$381$	6.21885	−	19.1396i	0.318601	−	0.980554i
$382$		0			0
$383$	−2.89919	−	8.92278i	−0.148142	−	0.455933i	0.849260	−	0.527975i	$-0.177048\pi$
$383$	−2.89919	−	8.92278i	−0.148142	−	0.455933i	−0.997402	+	0.0720420i	$0.977048\pi$
$384$		0			0
$385$	−0.0901699	+	0.0655123i	−0.00459549	+	0.00333882i
$386$		0			0
$387$	−1.85410	+	1.34708i	−0.0942493	+	0.0684761i
$388$		0			0
$389$	8.39919	−	25.8500i	0.425856	−	1.31065i	−0.476317	−	0.879274i	$-0.658028\pi$
$389$	8.39919	−	25.8500i	0.425856	−	1.31065i	0.902173	−	0.431375i	$-0.141972\pi$
$390$		0			0
$391$	3.19098	+	2.31838i	0.161375	+	0.117246i
$392$		0			0
$393$	25.3885	+	18.4459i	1.28068	+	0.930470i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	28.1803			1.41433			0.707165	−	0.707048i	$-0.249974\pi$
$397$	28.1803			1.41433			0.707165	+	0.707048i	$0.249974\pi$
$398$		0			0
$399$	1.09424	+	3.36771i	0.0547803	+	0.168596i
$400$		0			0
$401$	−17.7533	−	12.8985i	−0.886557	−	0.644121i	0.0484211	−	0.998827i	$-0.484581\pi$
$401$	−17.7533	−	12.8985i	−0.886557	−	0.644121i	−0.934978	+	0.354706i	$0.884581\pi$
$402$		0			0
$403$	5.70820	−	25.0705i	0.284346	−	1.24885i
$404$		0			0
$405$	−3.39919	−	2.46965i	−0.168907	−	0.122718i
$406$		0			0
$407$	−1.79837	−	5.53483i	−0.0891421	−	0.274351i
$408$		0			0
$409$	4.76393			0.235561			0.117781	−	0.993040i	$-0.462422\pi$
$409$	4.76393			0.235561			0.117781	+	0.993040i	$0.462422\pi$
$410$		0			0
$411$	−7.23607	+	22.2703i	−0.356929	+	1.09851i
$412$		0			0
$413$	2.42705	+	1.76336i	0.119427	+	0.0867691i
$414$		0			0
$415$	2.42705	+	1.76336i	0.119139	+	0.0865597i
$416$		0			0
$417$	−9.73607	+	29.9645i	−0.476777	+	1.46737i
$418$		0			0
$419$	4.85410	−	3.52671i	0.237138	−	0.172291i	−0.462869	−	0.886427i	$-0.653180\pi$
$419$	4.85410	−	3.52671i	0.237138	−	0.172291i	0.700007	+	0.714136i	$0.253180\pi$
$420$		0			0
$421$	−1.38197	+	1.00406i	−0.0673529	+	0.0489347i	−0.620952	−	0.783848i	$-0.713254\pi$
$421$	−1.38197	+	1.00406i	−0.0673529	+	0.0489347i	0.553599	+	0.832783i	$0.313254\pi$
$422$		0			0
$423$	−5.29180	−	16.2865i	−0.257296	−	0.791875i
$424$		0			0
$425$	−3.35410	+	10.3229i	−0.162698	+	0.500732i
$426$		0			0
$427$	0.145898	+	0.449028i	0.00706050	+	0.0217300i
$428$		0			0
$429$	12.7639			0.616248
$430$		0			0
$431$	−0.145898	+	0.106001i	−0.00702766	+	0.00510589i	−0.591294	−	0.806456i	$-0.701383\pi$
$431$	−0.145898	+	0.106001i	−0.00702766	+	0.00510589i	0.584266	+	0.811562i	$0.301383\pi$
$432$		0			0
$433$	19.4164			0.933093			0.466547	−	0.884497i	$-0.345498\pi$
$433$	19.4164			0.933093			0.466547	+	0.884497i	$0.345498\pi$
$434$		0			0
$435$	4.79837			0.230064
$436$		0			0
$437$	−9.57295	+	6.95515i	−0.457936	+	0.332710i
$438$		0			0
$439$	−12.7082			−0.606529			−0.303265	−	0.952906i	$-0.598077\pi$
$439$	−12.7082			−0.606529			−0.303265	+	0.952906i	$0.598077\pi$
$440$		0			0
$441$	−4.29180	−	13.2088i	−0.204371	−	0.628990i
$442$		0			0
$443$	−1.14590	+	3.52671i	−0.0544433	+	0.167559i	−0.974581	−	0.224036i	$-0.928077\pi$
$443$	−1.14590	+	3.52671i	−0.0544433	+	0.167559i	0.920138	+	0.391595i	$0.128077\pi$
$444$		0			0
$445$	1.89261	+	5.82485i	0.0897183	+	0.276124i
$446$		0			0
$447$	10.0623	−	7.31069i	0.475931	−	0.345784i
$448$		0			0
$449$	−6.61803	+	4.80828i	−0.312324	+	0.226917i	−0.732893	−	0.680344i	$-0.761831\pi$
$449$	−6.61803	+	4.80828i	−0.312324	+	0.226917i	0.420569	+	0.907261i	$0.361831\pi$
$450$		0			0
$451$	−4.00000	+	12.3107i	−0.188353	+	0.579690i
$452$		0			0
$453$	9.73607	+	7.07367i	0.457440	+	0.332350i
$454$		0			0
$455$	0.336881	+	0.244758i	0.0157932	+	0.0114745i
$456$		0			0
$457$	−7.15248	+	22.0131i	−0.334579	+	1.02973i	0.632350	+	0.774682i	$0.282090\pi$
$457$	−7.15248	+	22.0131i	−0.334579	+	1.02973i	−0.966929	+	0.255045i	$0.917910\pi$
$458$		0			0
$459$	5.00000			0.233380
$460$		0			0
$461$	6.84346	+	21.0620i	0.318732	+	0.980955i	0.974191	+	0.225725i	$0.0724750\pi$
$461$	6.84346	+	21.0620i	0.318732	+	0.980955i	−0.655459	+	0.755230i	$0.727525\pi$
$462$		0			0
$463$	2.61803	+	1.90211i	0.121670	+	0.0883987i	0.646956	−	0.762527i	$-0.276042\pi$
$463$	2.61803	+	1.90211i	0.121670	+	0.0883987i	−0.525286	+	0.850926i	$0.676042\pi$
$464$		0			0
$465$	1.05573	−	4.63677i	0.0489582	−	0.215025i
$466$		0			0
$467$	−26.3713	−	19.1599i	−1.22032	−	0.886614i	−0.224193	−	0.974545i	$-0.571975\pi$
$467$	−26.3713	−	19.1599i	−1.22032	−	0.886614i	−0.996127	+	0.0879310i	$0.971975\pi$
$468$		0			0
$469$	0.218847	+	0.673542i	0.0101054	+	0.0311013i
$470$		0			0
$471$	−44.0689			−2.03059
$472$		0			0
$473$	−0.437694	+	1.34708i	−0.0201252	+	0.0619390i
$474$		0			0
$475$	−26.3435	−	19.1396i	−1.20872	−	0.878187i
$476$		0			0
$477$	14.8541	+	10.7921i	0.680123	+	0.494138i
$478$		0			0
$479$	4.65248	−	14.3188i	0.212577	−	0.654245i	−0.786740	−	0.617285i	$-0.788233\pi$
$479$	4.65248	−	14.3188i	0.212577	−	0.654245i	0.999317	−	0.0369600i	$-0.0117674\pi$
$480$		0			0
$481$	−17.5902	+	12.7800i	−0.802043	+	0.582718i
$482$		0			0
$483$	−0.753289	+	0.547296i	−0.0342758	+	0.0249028i
$484$		0			0
$485$	−0.555728	−	1.71036i	−0.0252343	−	0.0776632i
$486$		0			0
$487$	−4.71885	+	14.5231i	−0.213831	+	0.658105i	0.785403	+	0.618985i	$0.212456\pi$
$487$	−4.71885	+	14.5231i	−0.213831	+	0.658105i	−0.999234	+	0.0391207i	$0.987544\pi$
$488$		0			0
$489$	5.48936	+	16.8945i	0.248237	+	0.763996i
$490$		0			0
$491$	−36.0689			−1.62777			−0.813883	−	0.581029i	$-0.802650\pi$
$491$	−36.0689			−1.62777			−0.813883	+	0.581029i	$0.802650\pi$
$492$		0			0
$493$	−10.1631	+	7.38394i	−0.457724	+	0.332556i
$494$		0			0
$495$	0.944272			0.0424419
$496$		0			0
$497$	3.09017			0.138613
$498$		0			0
$499$	15.0172	−	10.9106i	0.672263	−	0.488428i	−0.198519	−	0.980097i	$-0.563613\pi$
$499$	15.0172	−	10.9106i	0.672263	−	0.488428i	0.870782	+	0.491669i	$0.163613\pi$
$500$		0			0
$501$	−41.7082			−1.86339
$502$		0			0
$503$	−7.22542	−	22.2376i	−0.322166	−	0.991524i	−0.972704	−	0.232051i	$-0.925457\pi$
$503$	−7.22542	−	22.2376i	−0.322166	−	0.991524i	0.650538	−	0.759474i	$-0.274543\pi$
$504$		0			0
$505$	1.09017	−	3.35520i	0.0485119	−	0.149304i
$506$		0			0
$507$	−5.75329	−	17.7068i	−0.255513	−	0.786387i
$508$		0			0
$509$	−1.40983	+	1.02430i	−0.0624896	+	0.0454014i	−0.618592	−	0.785713i	$-0.712296\pi$
$509$	−1.40983	+	1.02430i	−0.0624896	+	0.0454014i	0.556102	+	0.831114i	$0.312296\pi$
$510$		0			0
$511$	−0.0278640	+	0.0202444i	−0.00123263	+	0.000895560i
$512$		0			0
$513$	−4.63525	+	14.2658i	−0.204652	+	0.629853i
$514$		0			0
$515$	2.20820	+	1.60435i	0.0973051	+	0.0706963i
$516$		0			0
$517$	−8.56231	−	6.22088i	−0.376570	−	0.273594i
$518$		0			0
$519$	−6.64590	+	20.4540i	−0.291723	+	0.897830i
$520$		0			0
$521$	−27.6525			−1.21148			−0.605738	−	0.795664i	$-0.707122\pi$
$521$	−27.6525			−1.21148			−0.605738	+	0.795664i	$0.707122\pi$
$522$		0			0
$523$	11.7254	+	36.0871i	0.512717	+	1.57798i	0.787398	+	0.616445i	$0.211428\pi$
$523$	11.7254	+	36.0871i	0.512717	+	1.57798i	−0.274681	+	0.961535i	$0.588572\pi$
$524$		0			0
$525$	−2.07295	−	1.50609i	−0.0904709	−	0.0657310i
$526$		0			0
$527$	4.89919	+	11.4454i	0.213412	+	0.498571i
$528$		0			0
$529$	16.0902	+	11.6902i	0.699573	+	0.508269i
$530$		0			0
$531$	−7.85410	−	24.1724i	−0.340839	−	1.04899i
$532$		0			0
$533$	48.3607			2.09473
$534$		0			0
$535$	0.482779	−	1.48584i	0.0208724	−	0.0642385i
$536$		0			0
$537$	13.3541	+	9.70232i	0.576272	+	0.418686i
$538$		0			0
$539$	−6.94427	−	5.04531i	−0.299111	−	0.217317i
$540$		0			0
$541$	−3.96556	+	12.2047i	−0.170493	+	0.524722i	−0.999399	−	0.0346650i	$-0.988964\pi$
$541$	−3.96556	+	12.2047i	−0.170493	+	0.524722i	0.828906	+	0.559387i	$0.188964\pi$
$542$		0			0
$543$	29.6976	−	21.5765i	1.27444	−	0.925938i
$544$		0			0
$545$	2.16312	−	1.57160i	0.0926578	−	0.0673199i
$546$		0			0
$547$	1.58359	+	4.87380i	0.0677095	+	0.208388i	0.979186	−	0.202963i	$-0.0650570\pi$
$547$	1.58359	+	4.87380i	0.0677095	+	0.208388i	−0.911477	+	0.411351i	$0.865057\pi$
$548$		0			0
$549$	1.23607	−	3.80423i	0.0527541	−	0.162360i
$550$		0			0
$551$	−11.6459	−	35.8424i	−0.496132	−	1.52694i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−3.25329	+	2.36365i	−0.138094	+	0.100331i
$556$		0			0
$557$	30.0000			1.27114			0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000			1.27114			0.635570	+	0.772043i	$0.280765\pi$
$558$		0			0
$559$	5.29180			0.223819
$560$		0			0
$561$	−5.00000	+	3.63271i	−0.211100	+	0.153373i
$562$		0			0
$563$	−4.61803			−0.194627			−0.0973135	−	0.995254i	$-0.531025\pi$
$563$	−4.61803			−0.194627			−0.0973135	+	0.995254i	$0.531025\pi$
$564$		0			0
$565$	−0.933629	−	2.87341i	−0.0392781	−	0.120885i
$566$		0			0
$567$	−0.802439	+	2.46965i	−0.0336993	+	0.103716i
$568$		0			0
$569$	−4.14590	−	12.7598i	−0.173805	−	0.534917i	0.825772	−	0.564004i	$-0.190740\pi$
$569$	−4.14590	−	12.7598i	−0.173805	−	0.534917i	−0.999577	+	0.0290873i	$0.990740\pi$
$570$		0			0
$571$	−24.8435	+	18.0498i	−1.03967	+	0.755362i	−0.970220	−	0.242224i	$-0.922123\pi$
$571$	−24.8435	+	18.0498i	−1.03967	+	0.755362i	−0.0694460	+	0.997586i	$0.522123\pi$
$572$		0			0
$573$	38.6803	−	28.1029i	1.61589	−	1.17402i
$574$		0			0
$575$	2.64590	−	8.14324i	0.110342	−	0.339596i
$576$		0			0
$577$	17.3992	+	12.6412i	0.724338	+	0.526262i	0.887767	−	0.460293i	$-0.152256\pi$
$577$	17.3992	+	12.6412i	0.724338	+	0.526262i	−0.163429	+	0.986555i	$0.552256\pi$
$578$		0			0
$579$	20.5902	+	14.9596i	0.855698	+	0.621701i
$580$		0			0
$581$	0.572949	−	1.76336i	0.0237699	−	0.0731563i
$582$		0			0
$583$	11.3475			0.469966
$584$		0			0
$585$	−1.09017	−	3.35520i	−0.0450730	−	0.138720i
$586$		0			0
$587$	−0.0450850	−	0.0327561i	−0.00186086	−	0.00135199i	0.586854	−	0.809692i	$-0.300366\pi$
$587$	−0.0450850	−	0.0327561i	−0.00186086	−	0.00135199i	−0.588715	+	0.808340i	$0.700366\pi$
$588$		0			0
$589$	−37.1976	+	3.36771i	−1.53270	+	0.138764i
$590$		0			0
$591$	48.6418	+	35.3404i	2.00086	+	1.45371i
$592$		0			0
$593$	−13.8885	−	42.7445i	−0.570334	−	1.75531i	−0.651544	−	0.758611i	$-0.725878\pi$
$593$	−13.8885	−	42.7445i	−0.570334	−	1.75531i	0.0812097	−	0.996697i	$-0.474122\pi$
$594$		0			0
$595$	−0.201626			−0.00826587
$596$		0			0
$597$	15.1631	−	46.6673i	0.620585	−	1.90996i
$598$		0			0
$599$	17.3541	+	12.6085i	0.709069	+	0.515169i	0.882873	−	0.469611i	$-0.155606\pi$
$599$	17.3541	+	12.6085i	0.709069	+	0.515169i	−0.173804	+	0.984780i	$0.555606\pi$
$600$		0			0
$601$	24.2705	+	17.6336i	0.990015	+	0.719288i	0.959924	−	0.280259i	$-0.0904205\pi$
$601$	24.2705	+	17.6336i	0.990015	+	0.719288i	0.0300904	+	0.999547i	$0.490420\pi$
$602$		0			0
$603$	1.85410	−	5.70634i	0.0755049	−	0.232380i
$604$		0			0
$605$	−2.92705	+	2.12663i	−0.119002	+	0.0864597i
$606$		0			0
$607$	20.0902	−	14.5964i	0.815435	−	0.592448i	−0.0999664	−	0.994991i	$-0.531874\pi$
$607$	20.0902	−	14.5964i	0.815435	−	0.592448i	0.915401	+	0.402543i	$0.131874\pi$
$608$		0			0
$609$	−0.916408	−	2.82041i	−0.0371347	−	0.114289i
$610$		0			0
$611$	−12.2188	+	37.6057i	−0.494322	+	1.52137i
$612$		0			0
$613$	−9.85410	−	30.3278i	−0.398003	−	1.22493i	−0.926598	−	0.376054i	$-0.877281\pi$
$613$	−9.85410	−	30.3278i	−0.398003	−	1.22493i	0.528594	−	0.848875i	$-0.322719\pi$
$614$		0			0
$615$	8.94427			0.360668
$616$		0			0
$617$	1.71885	−	1.24882i	0.0691982	−	0.0502754i	−0.552648	−	0.833415i	$-0.686383\pi$
$617$	1.71885	−	1.24882i	0.0691982	−	0.0502754i	0.621847	+	0.783139i	$0.286383\pi$
$618$		0			0
$619$	38.8328			1.56082			0.780411	−	0.625266i	$-0.215010\pi$
$619$	38.8328			1.56082			0.780411	+	0.625266i	$0.215010\pi$
$620$		0			0
$621$	−3.94427			−0.158278
$622$		0			0
$623$	3.06231	−	2.22490i	0.122689	−	0.0891386i
$624$		0			0
$625$	22.8328			0.913313
$626$		0			0
$627$	−5.72949	−	17.6336i	−0.228814	−	0.704216i
$628$		0			0
$629$	3.25329	−	10.0126i	0.129717	−	0.399228i
$630$		0			0
$631$	−7.68034	−	23.6377i	−0.305750	−	0.941000i	−0.979396	−	0.201947i	$-0.935273\pi$
$631$	−7.68034	−	23.6377i	−0.305750	−	0.941000i	0.673647	−	0.739053i	$-0.264727\pi$
$632$		0			0
$633$	−17.8885	+	12.9968i	−0.711006	+	0.516576i
$634$		0			0
$635$	−2.78115	+	2.02063i	−0.110367	+	0.0801861i
$636$		0			0
$637$	−9.90983	+	30.4993i	−0.392642	+	1.20843i
$638$		0			0
$639$	−21.1803	−	15.3884i	−0.837881	−	0.608756i
$640$		0			0
$641$	−36.0517	−	26.1931i	−1.42396	−	1.03456i	−0.991103	−	0.133099i	$-0.957507\pi$
$641$	−36.0517	−	26.1931i	−1.42396	−	1.03456i	−0.432852	−	0.901465i	$-0.642493\pi$
$642$		0			0
$643$	−8.38854	+	25.8173i	−0.330812	+	1.01813i	0.637937	+	0.770089i	$0.279788\pi$
$643$	−8.38854	+	25.8173i	−0.330812	+	1.01813i	−0.968748	+	0.248045i	$0.920212\pi$
$644$		0			0
$645$	0.978714			0.0385368
$646$		0			0
$647$	4.29180	+	13.2088i	0.168728	+	0.519291i	0.999292	−	0.0376325i	$-0.0119816\pi$
$647$	4.29180	+	13.2088i	0.168728	+	0.519291i	−0.830564	+	0.556924i	$0.811982\pi$
$648$		0			0
$649$	−12.7082	−	9.23305i	−0.498841	−	0.362429i
$650$		0			0
$651$	−2.92705	+	0.265003i	−0.114720	+	0.0103863i
$652$		0			0
$653$	7.89919	+	5.73910i	0.309119	+	0.224588i	0.731518	−	0.681822i	$-0.238812\pi$
$653$	7.89919	+	5.73910i	0.309119	+	0.224588i	−0.422399	+	0.906410i	$0.638812\pi$
$654$		0			0
$655$	−1.65654	−	5.09831i	−0.0647264	−	0.199207i
$656$		0			0
$657$	0.291796			0.0113840
$658$		0			0
$659$	−2.91641	+	8.97578i	−0.113607	+	0.349647i	−0.991654	−	0.128928i	$-0.958846\pi$
$659$	−2.91641	+	8.97578i	−0.113607	+	0.349647i	0.878047	+	0.478575i	$0.158846\pi$
$660$		0			0
$661$	−31.9615	−	23.2214i	−1.24316	−	0.903207i	−0.245353	−	0.969434i	$-0.578904\pi$
$661$	−31.9615	−	23.2214i	−1.24316	−	0.903207i	−0.997805	+	0.0662266i	$0.978904\pi$
$662$		0			0
$663$	18.6803	+	13.5721i	0.725484	+	0.527095i
$664$		0			0
$665$	0.186918	−	0.575274i	0.00724836	−	0.0223082i
$666$		0			0
$667$	8.01722	−	5.82485i	0.310428	−	0.225539i
$668$		0			0
$669$	−6.28115	+	4.56352i	−0.242843	+	0.176436i
$670$		0			0
$671$	−0.763932	−	2.35114i	−0.0294913	−	0.0907648i
$672$		0			0
$673$	−1.72542	+	5.31031i	−0.0665102	+	0.204697i	−0.978788	−	0.204874i	$-0.934322\pi$
$673$	−1.72542	+	5.31031i	−0.0665102	+	0.204697i	0.912278	+	0.409571i	$0.134322\pi$
$674$		0			0
$675$	−3.35410	−	10.3229i	−0.129099	−	0.397327i
$676$		0			0
$677$	−30.0689			−1.15564			−0.577821	−	0.816164i	$-0.696097\pi$
$677$	−30.0689			−1.15564			−0.577821	+	0.816164i	$0.696097\pi$
$678$		0			0
$679$	−0.899187	+	0.653298i	−0.0345076	+	0.0250713i
$680$		0			0
$681$	54.3951			2.08443
$682$		0			0
$683$	36.5967			1.40034			0.700168	−	0.713978i	$-0.253109\pi$
$683$	36.5967			1.40034			0.700168	+	0.713978i	$0.253109\pi$
$684$		0			0
$685$	3.23607	−	2.35114i	0.123644	−	0.0898325i
$686$		0			0
$687$	−46.1803			−1.76189
$688$		0			0
$689$	−13.1008	−	40.3202i	−0.499101	−	1.53608i
$690$		0			0
$691$	0.0385072	−	0.118513i	0.00146488	−	0.00450844i	−0.950321	−	0.311270i	$-0.899246\pi$
$691$	0.0385072	−	0.118513i	0.00146488	−	0.00450844i	0.951786	+	0.306762i	$0.0992455\pi$
$692$		0			0
$693$	−0.180340	−	0.555029i	−0.00685055	−	0.0210838i
$694$		0			0
$695$	4.35410	−	3.16344i	0.165161	−	0.119996i
$696$		0			0
$697$	−18.9443	+	13.7638i	−0.717565	+	0.521342i
$698$		0			0
$699$	−13.8820	+	42.7243i	−0.525064	+	1.61598i
$700$		0			0
$701$	−2.63525	−	1.91462i	−0.0995322	−	0.0723144i	0.536906	−	0.843642i	$-0.319593\pi$
$701$	−2.63525	−	1.91462i	−0.0995322	−	0.0723144i	−0.636438	+	0.771328i	$0.719593\pi$
$702$		0			0
$703$	25.5517	+	18.5644i	0.963699	+	0.700168i
$704$		0			0
$705$	−2.25987	+	6.95515i	−0.0851115	+	0.261946i
$706$		0			0
$707$	−2.18034			−0.0820001
$708$		0			0
$709$	10.7705	+	33.1482i	0.404495	+	1.24491i	0.921316	+	0.388814i	$0.127115\pi$
$709$	10.7705	+	33.1482i	0.404495	+	1.24491i	−0.516821	+	0.856093i	$0.672885\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.86475	−	9.02878i	−0.144736	−	0.338131i
$714$		0			0
$715$	−1.76393	−	1.28157i	−0.0659673	−	0.0479281i
$716$		0			0
$717$	2.03444	+	6.26137i	0.0759776	+	0.233835i
$718$		0			0
$719$	9.79837			0.365418			0.182709	−	0.983167i	$-0.441513\pi$
$719$	9.79837			0.365418			0.182709	+	0.983167i	$0.441513\pi$
$720$		0			0
$721$	0.521286	−	1.60435i	0.0194137	−	0.0597493i
$722$		0			0
$723$	−17.1353	−	12.4495i	−0.637267	−	0.463002i
$724$		0			0
$725$	22.0623	+	16.0292i	0.819373	+	0.595310i
$726$		0			0
$727$	3.12868	−	9.62908i	0.116036	−	0.357123i	−0.876126	−	0.482083i	$-0.839880\pi$
$727$	3.12868	−	9.62908i	0.116036	−	0.357123i	0.992162	+	0.124960i	$0.0398804\pi$
$728$		0			0
$729$	5.66312	−	4.11450i	0.209745	−	0.152389i
$730$		0			0
$731$	−2.07295	+	1.50609i	−0.0766708	+	0.0557046i
$732$		0			0
$733$	−10.9615	−	33.7360i	−0.404872	−	1.24607i	−0.921002	−	0.389558i	$-0.872628\pi$
$733$	−10.9615	−	33.7360i	−0.404872	−	1.24607i	0.516130	−	0.856510i	$-0.327372\pi$
$734$		0			0
$735$	−1.83282	+	5.64083i	−0.0676044	+	0.208065i
$736$		0			0
$737$	−1.14590	−	3.52671i	−0.0422097	−	0.129908i
$738$		0			0
$739$	4.29180			0.157876			0.0789381	−	0.996880i	$-0.474847\pi$
$739$	4.29180			0.157876			0.0789381	+	0.996880i	$0.474847\pi$
$740$		0			0
$741$	−56.0410	+	40.7162i	−2.05872	+	1.49575i
$742$		0			0
$743$	20.0344			0.734992			0.367496	−	0.930025i	$-0.380215\pi$
$743$	20.0344			0.734992			0.367496	+	0.930025i	$0.380215\pi$
$744$		0			0
$745$	−2.12461			−0.0778398
$746$		0			0
$747$	−12.7082	+	9.23305i	−0.464969	+	0.337820i
$748$		0			0
$749$	−0.965558			−0.0352807
$750$		0			0
$751$	13.9615	+	42.9691i	0.509462	+	1.56796i	0.793137	+	0.609043i	$0.208446\pi$
$751$	13.9615	+	42.9691i	0.509462	+	1.56796i	−0.283675	+	0.958920i	$0.591554\pi$
$752$		0			0
$753$	0.652476	−	2.00811i	0.0237775	−	0.0731797i
$754$		0			0
$755$	−0.635255	−	1.95511i	−0.0231193	−	0.0711539i
$756$		0			0
$757$	27.2705	−	19.8132i	0.991164	−	0.720122i	0.0309880	−	0.999520i	$-0.490135\pi$
$757$	27.2705	−	19.8132i	0.991164	−	0.720122i	0.960176	+	0.279397i	$0.0901346\pi$
$758$		0			0
$759$	3.94427	−	2.86568i	0.143168	−	0.104018i
$760$		0			0
$761$	14.6418	−	45.0629i	0.530766	−	1.63353i	−0.221858	−	0.975079i	$-0.571212\pi$
$761$	14.6418	−	45.0629i	0.530766	−	1.63353i	0.752624	−	0.658451i	$-0.228788\pi$
$762$		0			0
$763$	−1.33688	−	0.971301i	−0.0483983	−	0.0351635i
$764$		0			0
$765$	1.38197	+	1.00406i	0.0499651	+	0.0363018i
$766$		0			0
$767$	−18.1353	+	55.8146i	−0.654826	+	2.01535i
$768$		0			0
$769$	−20.2016			−0.728489			−0.364245	−	0.931303i	$-0.618673\pi$
$769$	−20.2016			−0.728489			−0.364245	+	0.931303i	$0.618673\pi$
$770$		0			0
$771$	17.5623	+	54.0512i	0.632491	+	1.94661i
$772$		0			0
$773$	−0.545085	−	0.396027i	−0.0196053	−	0.0142441i	0.577939	−	0.816080i	$-0.303857\pi$
$773$	−0.545085	−	0.396027i	−0.0196053	−	0.0142441i	−0.597545	+	0.801836i	$0.703857\pi$
$774$		0			0
$775$	20.3435	−	17.7926i	0.730759	−	0.639128i
$776$		0			0
$777$	2.01064	+	1.46082i	0.0721314	+	0.0524065i
$778$		0			0
$779$	−21.7082	−	66.8110i	−0.777777	−	2.39375i
$780$		0			0
$781$	−16.1803			−0.578978
$782$		0			0
$783$	3.88197	−	11.9475i	0.138730	−	0.426967i
$784$		0			0
$785$	6.09017	+	4.42477i	0.217367	+	0.157927i
$786$		0			0
$787$	−20.0451	−	14.5636i	−0.714530	−	0.519137i	0.170102	−	0.985426i	$-0.445590\pi$
$787$	−20.0451	−	14.5636i	−0.714530	−	0.519137i	−0.884632	+	0.466290i	$0.845590\pi$
$788$		0			0
$789$	−19.8607	+	61.1249i	−0.707059	+	2.17610i
$790$		0			0
$791$	−1.51064	+	1.09755i	−0.0537123	+	0.0390243i
$792$		0			0
$793$	−7.47214	+	5.42882i	−0.265343	+	0.192783i
$794$		0			0
$795$	−2.42299	−	7.45718i	−0.0859344	−	0.264479i
$796$		0			0
$797$	−13.8541	+	42.6385i	−0.490737	+	1.51033i	0.332758	+	0.943012i	$0.392021\pi$
$797$	−13.8541	+	42.6385i	−0.490737	+	1.51033i	−0.823496	+	0.567322i	$0.807979\pi$
$798$		0			0
$799$	−5.91641	−	18.2088i	−0.209307	−	0.644182i
$800$		0			0
$801$	−32.0689			−1.13310
$802$		0			0
$803$	0.145898	−	0.106001i	0.00514863	−	0.00374070i
$804$		0			0
$805$	0.159054			0.00560590
$806$		0			0
$807$	−27.6869			−0.974626
$808$		0			0
$809$	−20.7254	+	15.0579i	−0.728667	+	0.529408i	−0.889142	−	0.457632i	$-0.848698\pi$
$809$	−20.7254	+	15.0579i	−0.728667	+	0.529408i	0.160474	+	0.987040i	$0.448698\pi$
$810$		0			0
$811$	−17.2918			−0.607197			−0.303599	−	0.952800i	$-0.598188\pi$
$811$	−17.2918			−0.607197			−0.303599	+	0.952800i	$0.598188\pi$
$812$		0			0
$813$	−13.0279	−	40.0956i	−0.456907	−	1.40622i
$814$		0			0
$815$	0.937694	−	2.88593i	0.0328460	−	0.101090i
$816$		0			0
$817$	−2.37539	−	7.31069i	−0.0831043	−	0.255769i
$818$		0			0
$819$	−1.76393	+	1.28157i	−0.0616368	+	0.0447817i
$820$		0			0
$821$	18.8541	−	13.6983i	0.658013	−	0.478074i	−0.207979	−	0.978133i	$-0.566688\pi$
$821$	18.8541	−	13.6983i	0.658013	−	0.478074i	0.865991	+	0.500059i	$0.166688\pi$
$822$		0			0
$823$	−0.489357	+	1.50609i	−0.0170579	+	0.0524988i	−0.959223	−	0.282650i	$-0.908787\pi$
$823$	−0.489357	+	1.50609i	−0.0170579	+	0.0524988i	0.942165	+	0.335149i	$0.108787\pi$
$824$		0			0
$825$	10.8541	+	7.88597i	0.377891	+	0.274554i
$826$		0			0
$827$	15.5000	+	11.2614i	0.538988	+	0.391598i	0.823709	−	0.567013i	$-0.191901\pi$
$827$	15.5000	+	11.2614i	0.538988	+	0.391598i	−0.284721	+	0.958610i	$0.591901\pi$
$828$		0			0
$829$	2.56231	−	7.88597i	0.0889926	−	0.273891i	−0.896649	−	0.442742i	$-0.854006\pi$
$829$	2.56231	−	7.88597i	0.0889926	−	0.273891i	0.985642	+	0.168851i	$0.0540057\pi$
$830$		0			0
$831$	29.9230			1.03802
$832$		0			0
$833$	−4.79837	−	14.7679i	−0.166254	−	0.511677i
$834$		0			0
$835$	5.76393	+	4.18774i	0.199469	+	0.144923i
$836$		0			0
$837$	−10.6910	−	6.37988i	−0.369534	−	0.220521i
$838$		0			0
$839$	−23.3713	−	16.9803i	−0.806868	−	0.586224i	0.106053	−	0.994360i	$-0.466179\pi$
$839$	−23.3713	−	16.9803i	−0.806868	−	0.586224i	−0.912921	+	0.408137i	$0.866179\pi$
$840$		0			0
$841$	0.791796	+	2.43690i	0.0273033	+	0.0840310i
$842$		0			0
$843$	9.27051			0.319293
$844$		0			0
$845$	−0.982779	+	3.02468i	−0.0338086	+	0.104052i
$846$		0			0
$847$	1.80902	+	1.31433i	0.0621586	+	0.0451608i
$848$		0			0
$849$	34.3328	+	24.9443i	1.17830	+	0.856084i
$850$		0			0
$851$	−2.56637	+	7.89848i	−0.0879741	+	0.270756i
$852$		0			0
$853$	−13.7082	+	9.95959i	−0.469360	+	0.341010i	−0.797192	−	0.603726i	$-0.793682\pi$
$853$	−13.7082	+	9.95959i	−0.469360	+	0.341010i	0.327832	+	0.944736i	$0.393682\pi$
$854$		0			0
$855$	−4.14590	+	3.01217i	−0.141787	+	0.103014i
$856$		0			0
$857$	10.0902	+	31.0543i	0.344674	+	1.06080i	0.961758	+	0.273900i	$0.0883136\pi$
$857$	10.0902	+	31.0543i	0.344674	+	1.06080i	−0.617085	+	0.786897i	$0.711686\pi$
$858$		0			0
$859$	7.07295	−	21.7683i	0.241326	−	0.742725i	−0.754893	−	0.655848i	$-0.772311\pi$
$859$	7.07295	−	21.7683i	0.241326	−	0.742725i	0.996219	−	0.0868770i	$-0.0276887\pi$
$860$		0			0
$861$	−1.70820	−	5.25731i	−0.0582154	−	0.179169i
$862$		0			0
$863$	−40.6180			−1.38265			−0.691327	−	0.722542i	$-0.742974\pi$
$863$	−40.6180			−1.38265			−0.691327	+	0.722542i	$0.742974\pi$
$864$		0			0
$865$	2.97214	−	2.15938i	0.101056	−	0.0734212i
$866$		0			0
$867$	26.8328			0.911290
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−11.2082	+	8.14324i	−0.379776	+	0.275923i
$872$		0			0
$873$	9.41641			0.318697
$874$		0			0
$875$	0.274575	+	0.845055i	0.00928233	+	0.0285681i
$876$		0			0
$877$	3.18034	−	9.78808i	0.107392	−	0.330520i	−0.882892	−	0.469576i	$-0.844407\pi$
$877$	3.18034	−	9.78808i	0.107392	−	0.330520i	0.990285	+	0.139056i	$0.0444068\pi$
$878$		0			0
$879$	−18.7041	−	57.5654i	−0.630875	−	1.94163i
$880$		0			0
$881$	13.1910	−	9.58381i	0.444416	−	0.322887i	−0.342971	−	0.939346i	$-0.611433\pi$
$881$	13.1910	−	9.58381i	0.444416	−	0.322887i	0.787387	+	0.616459i	$0.211433\pi$
$882$		0			0
$883$	37.4058	−	27.1769i	1.25880	−	0.914575i	0.260106	−	0.965580i	$-0.416243\pi$
$883$	37.4058	−	27.1769i	1.25880	−	0.914575i	0.998698	+	0.0510053i	$0.0162425\pi$
$884$		0			0
$885$	−3.35410	+	10.3229i	−0.112747	+	0.346999i
$886$		0			0
$887$	2.59017	+	1.88187i	0.0869694	+	0.0631870i	0.630420	−	0.776254i	$-0.282883\pi$
$887$	2.59017	+	1.88187i	0.0869694	+	0.0631870i	−0.543451	+	0.839441i	$0.682883\pi$
$888$		0			0
$889$	1.71885	+	1.24882i	0.0576483	+	0.0418839i
$890$		0			0
$891$	4.20163	−	12.9313i	0.140760	−	0.433214i
$892$		0			0
$893$	57.4377			1.92208
$894$		0			0
$895$	−0.871323	−	2.68166i	−0.0291251	−	0.0896379i
$896$		0			0
$897$	−14.7361	−	10.7064i	−0.492023	−	0.357476i
$898$		0			0
$899$	31.1525	−	2.82041i	1.03899	−	0.0940661i
$900$		0			0
$901$	16.6074	+	12.0660i	0.553272	+	0.401976i
$902$		0			0
$903$	−0.186918	−	0.575274i	−0.00622023	−	0.0191439i
$904$		0			0
$905$	−6.27051			−0.208439
$906$		0			0
$907$	15.7877	−	48.5896i	0.524223	−	1.61339i	−0.241624	−	0.970370i	$-0.577680\pi$
$907$	15.7877	−	48.5896i	0.524223	−	1.61339i	0.765847	−	0.643023i	$-0.222320\pi$
$908$		0			0
$909$	14.9443	+	10.8576i	0.495670	+	0.360125i
$910$		0			0
$911$	8.23607	+	5.98385i	0.272873	+	0.198254i	0.715803	−	0.698302i	$-0.246061\pi$
$911$	8.23607	+	5.98385i	0.272873	+	0.198254i	−0.442930	+	0.896556i	$0.646061\pi$
$912$		0			0
$913$	−3.00000	+	9.23305i	−0.0992855	+	0.305569i
$914$		0			0
$915$	−1.38197	+	1.00406i	−0.0456864	+	0.0331931i
$916$		0			0
$917$	−2.68034	+	1.94738i	−0.0885126	+	0.0643082i
$918$		0			0
$919$	8.16312	+	25.1235i	0.269276	+	0.828748i	0.990677	+	0.136230i	$0.0434986\pi$
$919$	8.16312	+	25.1235i	0.269276	+	0.828748i	−0.721401	+	0.692518i	$0.756501\pi$
$920$		0			0
$921$	17.8647	−	54.9820i	0.588663	−	1.81172i
$922$		0			0
$923$	18.6803	+	57.4922i	0.614871	+	1.89238i
$924$		0			0
$925$	−22.8541			−0.751438
$926$		0			0
$927$	−11.5623	+	8.40051i	−0.379756	+	0.275909i
$928$		0			0
$929$	22.8197			0.748689			0.374344	−	0.927290i	$-0.377868\pi$
$929$	22.8197			0.748689			0.374344	+	0.927290i	$0.377868\pi$
$930$		0			0
$931$	46.5836			1.52672
$932$		0			0
$933$	34.2705	−	24.8990i	1.12197	−	0.815156i
$934$		0			0
$935$	1.05573			0.0345260
$936$		0			0
$937$	−16.9828	−	52.2676i	−0.554803	−	1.70751i	−0.696462	−	0.717593i	$-0.745244\pi$
$937$	−16.9828	−	52.2676i	−0.554803	−	1.70751i	0.141659	−	0.989915i	$-0.454756\pi$
$938$		0			0
$939$	−9.87539	+	30.3933i	−0.322271	+	0.991849i
$940$		0			0
$941$	17.1246	+	52.7041i	0.558246	+	1.71811i	0.687212	+	0.726457i	$0.258834\pi$
$941$	17.1246	+	52.7041i	0.558246	+	1.71811i	−0.128966	+	0.991649i	$0.541166\pi$
$942$		0			0
$943$	14.9443	−	10.8576i	0.486652	−	0.353574i
$944$		0			0
$945$	0.163119	−	0.118513i	0.00530626	−	0.00385522i
$946$		0			0
$947$	−0.742646	+	2.28563i	−0.0241327	+	0.0742730i	−0.962398	−	0.271645i	$-0.912432\pi$
$947$	−0.742646	+	2.28563i	−0.0241327	+	0.0742730i	0.938265	+	0.345918i	$0.112432\pi$
$948$		0			0
$949$	−0.545085	−	0.396027i	−0.0176942	−	0.0128556i
$950$		0			0
$951$	8.94427	+	6.49839i	0.290038	+	0.210725i
$952$		0			0
$953$	1.73607	−	5.34307i	0.0562368	−	0.173079i	−0.918993	−	0.394275i	$-0.870996\pi$
$953$	1.73607	−	5.34307i	0.0562368	−	0.173079i	0.975229	+	0.221196i	$0.0709959\pi$
$954$		0			0
$955$	−8.16718			−0.264284
$956$		0			0
$957$	4.79837	+	14.7679i	0.155109	+	0.477378i
$958$		0			0
$959$	−2.00000	−	1.45309i	−0.0645834	−	0.0469226i
$960$		0			0
$961$	4.12868	−	30.7238i	0.133183	−	0.991091i
$962$		0			0
$963$	6.61803	+	4.80828i	0.213263	+	0.154945i
$964$		0			0
$965$	−1.34346	−	4.13474i	−0.0432475	−	0.133102i
$966$		0			0
$967$	−13.1115			−0.421636			−0.210818	−	0.977525i	$-0.567613\pi$
$967$	−13.1115			−0.421636			−0.210818	+	0.977525i	$0.567613\pi$
$968$		0			0
$969$	10.3647	−	31.8994i	0.332964	−	1.02476i
$970$		0			0
$971$	2.02786	+	1.47333i	0.0650773	+	0.0472814i	0.619848	−	0.784722i	$-0.287194\pi$
$971$	2.02786	+	1.47333i	0.0650773	+	0.0472814i	−0.554771	+	0.832003i	$0.687194\pi$
$972$		0			0
$973$	−2.69098	−	1.95511i	−0.0862690	−	0.0626781i
$974$		0			0
$975$	15.4894	−	47.6713i	0.496056	−	1.52670i
$976$		0			0
$977$	22.7082	−	16.4985i	0.726500	−	0.527833i	−0.161954	−	0.986798i	$-0.551780\pi$
$977$	22.7082	−	16.4985i	0.726500	−	0.527833i	0.888454	+	0.458965i	$0.151780\pi$
$978$		0			0
$979$	−16.0344	+	11.6497i	−0.512463	+	0.372326i
$980$		0			0
$981$	4.32624	+	13.3148i	0.138126	+	0.425109i
$982$		0			0
$983$	−15.3713	+	47.3081i	−0.490269	+	1.50889i	0.333933	+	0.942597i	$0.391624\pi$
$983$	−15.3713	+	47.3081i	−0.490269	+	1.50889i	−0.824202	+	0.566296i	$0.808376\pi$
$984$		0			0
$985$	−3.17376	−	9.76784i	−0.101124	−	0.311229i
$986$		0			0
$987$	4.51973			0.143865
$988$		0			0
$989$	1.63525	−	1.18808i	0.0519981	−	0.0377788i
$990$		0			0
$991$	−15.9787			−0.507581			−0.253790	−	0.967259i	$-0.581677\pi$
$991$	−15.9787			−0.507581			−0.253790	+	0.967259i	$0.581677\pi$
$992$		0			0
$993$	−34.6738			−1.10034
$994$		0			0
$995$	−6.78115	+	4.92680i	−0.214977	+	0.156190i
$996$		0			0
$997$	−42.8885			−1.35829			−0.679147	−	0.734002i	$-0.737650\pi$
$997$	−42.8885			−1.35829			−0.679147	+	0.734002i	$0.737650\pi$
$998$		0			0
$999$	3.25329	+	10.0126i	0.102930	+	0.316784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.2.f.b.33.1	✓	4
3.2	odd	2		1116.2.m.c.901.1		4
4.3	odd	2		496.2.n.a.33.1		4
31.4	even	5		3844.2.a.g.1.1		2
31.16	even	5	inner	124.2.f.b.109.1	yes	4
31.27	odd	10		3844.2.a.f.1.2		2
93.47	odd	10		1116.2.m.c.109.1		4
124.47	odd	10		496.2.n.a.481.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.2.f.b.33.1	✓	4	1.1	even	1	trivial
124.2.f.b.109.1	yes	4	31.16	even	5	inner
496.2.n.a.33.1		4	4.3	odd	2
496.2.n.a.481.1		4	124.47	odd	10
1116.2.m.c.109.1		4	93.47	odd	10
1116.2.m.c.901.1		4	3.2	odd	2
3844.2.a.f.1.2		2	31.27	odd	10
3844.2.a.g.1.1		2	31.4	even	5

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80902 - 1.31433i) q^{3} -0.381966 q^{5} +(0.0729490 + 0.224514i) q^{7} +(0.618034 - 1.90211i) q^{9} +O(q^{10})\)	\(q+(1.80902 - 1.31433i) q^{3} -0.381966 q^{5} +(0.0729490 + 0.224514i) q^{7} +(0.618034 - 1.90211i) q^{9} +(-0.381966 - 1.17557i) q^{11} +(-3.73607 + 2.71441i) q^{13} +(-0.690983 + 0.502029i) q^{15} +(0.690983 - 2.12663i) q^{17} +(5.42705 + 3.94298i) q^{19} +(0.427051 + 0.310271i) q^{21} +(-0.545085 + 1.67760i) q^{23} -4.85410 q^{25} +(0.690983 + 2.12663i) q^{27} +(-4.54508 - 3.30220i) q^{29} +(-4.19098 + 3.66547i) q^{31} +(-2.23607 - 1.62460i) q^{33} +(-0.0278640 - 0.0857567i) q^{35} +4.70820 q^{37} +(-3.19098 + 9.82084i) q^{39} +(-8.47214 - 6.15537i) q^{41} +(-0.927051 - 0.673542i) q^{43} +(-0.236068 + 0.726543i) q^{45} +(6.92705 - 5.03280i) q^{47} +(5.61803 - 4.08174i) q^{49} +(-1.54508 - 4.75528i) q^{51} +(-2.83688 + 8.73102i) q^{53} +(0.145898 + 0.449028i) q^{55} +15.0000 q^{57} +(10.2812 - 7.46969i) q^{59} +2.00000 q^{61} +0.472136 q^{63} +(1.42705 - 1.03681i) q^{65} +3.00000 q^{67} +(1.21885 + 3.75123i) q^{69} +(4.04508 - 12.4495i) q^{71} +(0.0450850 + 0.138757i) q^{73} +(-8.78115 + 6.37988i) q^{75} +(0.236068 - 0.171513i) q^{77} +(8.89919 + 6.46564i) q^{81} +(-6.35410 - 4.61653i) q^{83} +(-0.263932 + 0.812299i) q^{85} -12.5623 q^{87} +(-4.95492 - 15.2497i) q^{89} +(-0.881966 - 0.640786i) q^{91} +(-2.76393 + 12.1392i) q^{93} +(-2.07295 - 1.50609i) q^{95} +(1.45492 + 4.47777i) q^{97} -2.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{3} - 6 q^{5} + 7 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 5 * q^3 - 6 * q^5 + 7 * q^7 - 2 * q^9	\( 4 q + 5 q^{3} - 6 q^{5} + 7 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{13} - 5 q^{15} + 5 q^{17} + 15 q^{19} - 5 q^{21} + 9 q^{23} - 6 q^{25} + 5 q^{27} - 7 q^{29} - 19 q^{31} - 18 q^{35} - 8 q^{37} - 15 q^{39} - 16 q^{41} + 3 q^{43} + 8 q^{45} + 21 q^{47} + 18 q^{49} + 5 q^{51} - 27 q^{53} + 14 q^{55} + 60 q^{57} + 21 q^{59} + 8 q^{61} - 16 q^{63} - q^{65} + 12 q^{67} + 25 q^{69} + 5 q^{71} - 11 q^{73} - 15 q^{75} - 8 q^{77} + 11 q^{81} - 12 q^{83} - 10 q^{85} - 10 q^{87} - 31 q^{89} - 8 q^{91} - 20 q^{93} - 15 q^{95} + 17 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q + 5 * q^3 - 6 * q^5 + 7 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^13 - 5 * q^15 + 5 * q^17 + 15 * q^19 - 5 * q^21 + 9 * q^23 - 6 * q^25 + 5 * q^27 - 7 * q^29 - 19 * q^31 - 18 * q^35 - 8 * q^37 - 15 * q^39 - 16 * q^41 + 3 * q^43 + 8 * q^45 + 21 * q^47 + 18 * q^49 + 5 * q^51 - 27 * q^53 + 14 * q^55 + 60 * q^57 + 21 * q^59 + 8 * q^61 - 16 * q^63 - q^65 + 12 * q^67 + 25 * q^69 + 5 * q^71 - 11 * q^73 - 15 * q^75 - 8 * q^77 + 11 * q^81 - 12 * q^83 - 10 * q^85 - 10 * q^87 - 31 * q^89 - 8 * q^91 - 20 * q^93 - 15 * q^95 + 17 * q^97 + 8 * q^99

Introduction

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