LMFDB - Embedded newform 600.2.d.g.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(349,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("600.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.2
Root			$-1.08003 - 0.912978i$ of defining polynomial
Character	$\chi$	$=$	600.349
Dual form			600.2.d.g.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41298 + 0.0591148i) q^{2} -1.00000 q^{3} +(1.99301 - 0.167056i) q^{4} +(1.41298 - 0.0591148i) q^{6} +1.33411i q^{7} +(-2.80620 + 0.353863i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.41298 + 0.0591148i) q^{2} -1.00000 q^{3} +(1.99301 - 0.167056i) q^{4} +(1.41298 - 0.0591148i) q^{6} +1.33411i q^{7} +(-2.80620 + 0.353863i) q^{8} +1.00000 q^{9} -2.94418i q^{11} +(-1.99301 + 0.167056i) q^{12} +2.04184 q^{13} +(-0.0788658 - 1.88507i) q^{14} +(3.94418 - 0.665888i) q^{16} +3.61241i q^{17} +(-1.41298 + 0.0591148i) q^{18} +5.35964i q^{19} -1.33411i q^{21} +(0.174045 + 4.16007i) q^{22} -8.59609i q^{23} +(2.80620 - 0.353863i) q^{24} +(-2.88507 + 0.120703i) q^{26} -1.00000 q^{27} +(0.222871 + 2.65890i) q^{28} +5.26432i q^{29} -2.08134 q^{31} +(-5.53368 + 1.17404i) q^{32} +2.94418i q^{33} +(-0.213547 - 5.10425i) q^{34} +(1.99301 - 0.167056i) q^{36} +6.55659 q^{37} +(-0.316834 - 7.57304i) q^{38} -2.04184 q^{39} +7.02786 q^{41} +(0.0788658 + 1.88507i) q^{42} +8.50078 q^{43} +(-0.491843 - 5.86779i) q^{44} +(0.508157 + 12.1461i) q^{46} +9.97204i q^{47} +(-3.94418 + 0.665888i) q^{48} +5.22015 q^{49} -3.61241i q^{51} +(4.06940 - 0.341101i) q^{52} +6.12318 q^{53} +(1.41298 - 0.0591148i) q^{54} +(-0.472092 - 3.74379i) q^{56} -5.35964i q^{57} +(-0.311199 - 7.43836i) q^{58} +4.75190i q^{59} +8.51476i q^{61} +(2.94089 - 0.123038i) q^{62} +1.33411i q^{63} +(7.74956 - 1.98602i) q^{64} +(-0.174045 - 4.16007i) q^{66} +10.6961 q^{67} +(0.603474 + 7.19957i) q^{68} +8.59609i q^{69} -2.62405 q^{71} +(-2.80620 + 0.353863i) q^{72} +15.3875i q^{73} +(-9.26432 + 0.387592i) q^{74} +(0.895358 + 10.6818i) q^{76} +3.92787 q^{77} +(2.88507 - 0.120703i) q^{78} -10.4450 q^{79} +1.00000 q^{81} +(-9.93021 + 0.415451i) q^{82} -1.52708 q^{83} +(-0.222871 - 2.65890i) q^{84} +(-12.0114 + 0.502522i) q^{86} -5.26432i q^{87} +(1.04184 + 8.26198i) q^{88} +12.7193 q^{89} +2.72404i q^{91} +(-1.43603 - 17.1321i) q^{92} +2.08134 q^{93} +(-0.589496 - 14.0903i) q^{94} +(5.53368 - 1.17404i) q^{96} -13.4450i q^{97} +(-7.37595 + 0.308588i) q^{98} -2.94418i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9} + 4 q^{12} + 6 q^{14} + 8 q^{16} - 2 q^{18} + 20 q^{22} + 8 q^{24} - 2 q^{26} - 8 q^{27} + 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} - 4 q^{36} + 14 q^{38} - 6 q^{42} - 8 q^{43} + 12 q^{44} + 20 q^{46} - 8 q^{48} + 24 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{56} - 20 q^{58} + 26 q^{62} + 32 q^{64} - 20 q^{66} + 24 q^{67} + 36 q^{68} - 40 q^{71} - 8 q^{72} - 8 q^{74} - 20 q^{76} - 24 q^{77} + 2 q^{78} + 16 q^{79} + 8 q^{81} - 16 q^{82} - 32 q^{83} - 24 q^{84} - 18 q^{86} - 8 q^{88} + 28 q^{92} - 8 q^{93} + 4 q^{94} + 12 q^{96} - 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9 + 4 * q^12 + 6 * q^14 + 8 * q^16 - 2 * q^18 + 20 * q^22 + 8 * q^24 - 2 * q^26 - 8 * q^27 + 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 - 4 * q^36 + 14 * q^38 - 6 * q^42 - 8 * q^43 + 12 * q^44 + 20 * q^46 - 8 * q^48 + 24 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^56 - 20 * q^58 + 26 * q^62 + 32 * q^64 - 20 * q^66 + 24 * q^67 + 36 * q^68 - 40 * q^71 - 8 * q^72 - 8 * q^74 - 20 * q^76 - 24 * q^77 + 2 * q^78 + 16 * q^79 + 8 * q^81 - 16 * q^82 - 32 * q^83 - 24 * q^84 - 18 * q^86 - 8 * q^88 + 28 * q^92 - 8 * q^93 + 4 * q^94 + 12 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	−1.41298	+	0.0591148i	−0.999126	+	0.0418005i
$2$	−1.41298	+	0.0591148i	−0.999126	+	0.0418005i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.99301	−	0.167056i	0.996505	−	0.0835279i
$5$		0			0
$5$		0			0
$6$	1.41298	−	0.0591148i	0.576846	−	0.0241335i
$7$			1.33411i			0.504247i	0.967695	+	0.252123i	$0.0811289\pi$
$7$			1.33411i			0.504247i	−0.967695	+	0.252123i	$0.918871\pi$
$8$	−2.80620	+	0.353863i	−0.992143	+	0.125109i
$9$	1.00000			0.333333
$10$		0			0
$11$		−	2.94418i		−	0.887705i	−0.896100	−	0.443853i	$-0.853611\pi$
$11$		−	2.94418i		−	0.887705i	0.896100	−	0.443853i	$-0.146389\pi$
$12$	−1.99301	+	0.167056i	−0.575333	+	0.0482249i
$13$	2.04184			0.566304			0.283152	−	0.959075i	$-0.408620\pi$
$13$	2.04184			0.566304			0.283152	+	0.959075i	$0.408620\pi$
$14$	−0.0788658	−	1.88507i	−0.0210778	−	0.503806i
$15$		0			0
$16$	3.94418	−	0.665888i	0.986046	−	0.166472i
$17$			3.61241i			0.876138i	0.898941	+	0.438069i	$0.144337\pi$
$17$			3.61241i			0.876138i	−0.898941	+	0.438069i	$0.855663\pi$
$18$	−1.41298	+	0.0591148i	−0.333042	+	0.0139335i
$19$			5.35964i			1.22958i	0.788689	+	0.614792i	$0.210760\pi$
$19$			5.35964i			1.22958i	−0.788689	+	0.614792i	$0.789240\pi$
$20$		0			0
$21$		−	1.33411i		−	0.291127i
$22$	0.174045	+	4.16007i	0.0371065	+	0.886929i
$23$		−	8.59609i		−	1.79241i	−0.443641	−	0.896205i	$-0.646313\pi$
$23$		−	8.59609i		−	1.79241i	0.443641	−	0.896205i	$-0.353687\pi$
$24$	2.80620	−	0.353863i	0.572814	−	0.0722319i
$25$		0			0
$26$	−2.88507	+	0.120703i	−0.565809	+	0.0236718i
$27$	−1.00000			−0.192450
$28$	0.222871	+	2.65890i	0.0421187	+	0.502485i
$29$			5.26432i			0.977559i	0.872407	+	0.488780i	$0.162558\pi$
$29$			5.26432i			0.977559i	−0.872407	+	0.488780i	$0.837442\pi$
$30$		0			0
$31$	−2.08134			−0.373820			−0.186910	−	0.982377i	$-0.559847\pi$
$31$	−2.08134			−0.373820			−0.186910	+	0.982377i	$0.559847\pi$
$32$	−5.53368	+	1.17404i	−0.978226	+	0.207544i
$33$			2.94418i			0.512517i
$34$	−0.213547	−	5.10425i	−0.0366230	−	0.875372i
$35$		0			0
$36$	1.99301	−	0.167056i	0.332168	−	0.0278426i
$37$	6.55659			1.07790			0.538949	−	0.842339i	$-0.318822\pi$
$37$	6.55659			1.07790			0.538949	+	0.842339i	$0.318822\pi$
$38$	−0.316834	−	7.57304i	−0.0513973	−	1.22851i
$39$	−2.04184			−0.326956
$40$		0			0
$41$	7.02786			1.09757			0.548784	−	0.835964i	$-0.315091\pi$
$41$	7.02786			1.09757			0.548784	+	0.835964i	$0.315091\pi$
$42$	0.0788658	+	1.88507i	0.0121693	+	0.290873i
$43$	8.50078			1.29636			0.648178	−	0.761489i	$-0.275531\pi$
$43$	8.50078			1.29636			0.648178	+	0.761489i	$0.275531\pi$
$44$	−0.491843	−	5.86779i	−0.0741482	−	0.884603i
$45$		0			0
$46$	0.508157	+	12.1461i	0.0749236	+	1.79084i
$47$			9.97204i			1.45457i	0.686334	+	0.727286i	$0.259219\pi$
$47$			9.97204i			1.45457i	−0.686334	+	0.727286i	$0.740781\pi$
$48$	−3.94418	+	0.665888i	−0.569294	+	0.0961127i
$49$	5.22015			0.745735
$50$		0			0
$51$		−	3.61241i		−	0.505838i
$52$	4.06940	−	0.341101i	0.564325	−	0.0473022i
$53$	6.12318			0.841083			0.420541	−	0.907273i	$-0.361840\pi$
$53$	6.12318			0.841083			0.420541	+	0.907273i	$0.361840\pi$
$54$	1.41298	−	0.0591148i	0.192282	−	0.00804451i
$55$		0			0
$56$	−0.472092	−	3.74379i	−0.0630860	−	0.500285i
$57$		−	5.35964i		−	0.709901i
$58$	−0.311199	−	7.43836i	−0.0408625	−	0.976705i
$59$			4.75190i			0.618644i	0.950957	+	0.309322i	$0.100102\pi$
$59$			4.75190i			0.618644i	−0.950957	+	0.309322i	$0.899898\pi$
$60$		0			0
$61$			8.51476i			1.09020i	0.838370	+	0.545101i	$0.183509\pi$
$61$			8.51476i			1.09020i	−0.838370	+	0.545101i	$0.816491\pi$
$62$	2.94089	−	0.123038i	0.373493	−	0.0156258i
$63$			1.33411i			0.168082i
$64$	7.74956	−	1.98602i	0.968695	−	0.248253i
$65$		0			0
$66$	−0.174045	−	4.16007i	−0.0214235	−	0.512069i
$67$	10.6961			1.30673			0.653367	−	0.757041i	$-0.273356\pi$
$67$	10.6961			1.30673			0.653367	+	0.757041i	$0.273356\pi$
$68$	0.603474	+	7.19957i	0.0731820	+	0.873076i
$69$			8.59609i			1.03485i
$70$		0			0
$71$	−2.62405			−0.311418			−0.155709	−	0.987803i	$-0.549766\pi$
$71$	−2.62405			−0.311418			−0.155709	+	0.987803i	$0.549766\pi$
$72$	−2.80620	+	0.353863i	−0.330714	+	0.0417031i
$73$			15.3875i			1.80097i	0.434887	+	0.900485i	$0.356788\pi$
$73$			15.3875i			1.80097i	−0.434887	+	0.900485i	$0.643212\pi$
$74$	−9.26432	+	0.387592i	−1.07696	+	0.0450566i
$75$		0			0
$76$	0.895358	+	10.6818i	0.102705	+	1.22529i
$77$	3.92787			0.447622
$78$	2.88507	−	0.120703i	0.326670	−	0.0136669i
$79$	−10.4450			−1.17515			−0.587575	−	0.809170i	$-0.699917\pi$
$79$	−10.4450			−1.17515			−0.587575	+	0.809170i	$0.699917\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−9.93021	+	0.415451i	−1.09661	+	0.0458789i
$83$	−1.52708			−0.167619			−0.0838095	−	0.996482i	$-0.526709\pi$
$83$	−1.52708			−0.167619			−0.0838095	+	0.996482i	$0.526709\pi$
$84$	−0.222871	−	2.65890i	−0.0243172	−	0.290110i
$85$		0			0
$86$	−12.0114	+	0.502522i	−1.29522	+	0.0541883i
$87$		−	5.26432i		−	0.564394i
$88$	1.04184	+	8.26198i	0.111060	+	0.880730i
$89$	12.7193			1.34824			0.674120	−	0.738622i	$-0.264523\pi$
$89$	12.7193			1.34824			0.674120	+	0.738622i	$0.264523\pi$
$90$		0			0
$91$			2.72404i			0.285557i
$92$	−1.43603	−	17.1321i	−0.149716	−	1.78615i
$93$	2.08134			0.215825
$94$	−0.589496	−	14.0903i	−0.0608018	−	1.45330i
$95$		0			0
$96$	5.53368	−	1.17404i	0.564779	−	0.119825i
$97$		−	13.4450i		−	1.36513i	−0.730825	−	0.682565i	$-0.760865\pi$
$97$		−	13.4450i		−	1.36513i	0.730825	−	0.682565i	$-0.239135\pi$
$98$	−7.37595	+	0.308588i	−0.745083	+	0.0311721i
$99$		−	2.94418i		−	0.295902i
$100$		0			0
$101$		−	10.1232i		−	1.00729i	−0.863910	−	0.503647i	$-0.831991\pi$
$101$		−	10.1232i		−	1.00729i	0.863910	−	0.503647i	$-0.168009\pi$
$102$	0.213547	+	5.10425i	0.0211443	+	0.505396i
$103$		−	10.7472i		−	1.05896i	−0.848324	−	0.529478i	$-0.822388\pi$
$103$		−	10.7472i		−	1.05896i	0.848324	−	0.529478i	$-0.177612\pi$
$104$	−5.72981	+	0.722530i	−0.561854	+	0.0708499i
$105$		0			0
$106$	−8.65191	+	0.361971i	−0.840348	+	0.0351577i
$107$	−4.86518			−0.470335			−0.235167	−	0.971955i	$-0.575564\pi$
$107$	−4.86518			−0.470335			−0.235167	+	0.971955i	$0.575564\pi$
$108$	−1.99301	+	0.167056i	−0.191778	+	0.0160750i
$109$		−	15.4573i		−	1.48054i	−0.672310	−	0.740270i	$-0.734698\pi$
$109$		−	15.4573i		−	1.48054i	0.672310	−	0.740270i	$-0.265302\pi$
$110$		0			0
$111$	−6.55659			−0.622324
$112$	0.888369	+	5.26198i	0.0839430	+	0.497211i
$113$			9.88837i			0.930220i	0.885253	+	0.465110i	$0.153985\pi$
$113$			9.88837i			0.930220i	−0.885253	+	0.465110i	$0.846015\pi$
$114$	0.316834	+	7.57304i	0.0296742	+	0.709281i
$115$		0			0
$116$	0.879435	+	10.4918i	0.0816535	+	0.974143i
$117$	2.04184			0.188768
$118$	−0.280908	−	6.71432i	−0.0258596	−	0.618104i
$119$	−4.81936			−0.441790
$120$		0			0
$121$	2.33178			0.211980
$122$	−0.503348	−	12.0312i	−0.0455710	−	1.08925i
$123$	−7.02786			−0.633681
$124$	−4.14813	+	0.347700i	−0.372513	+	0.0312244i
$125$		0			0
$126$	−0.0788658	−	1.88507i	−0.00702592	−	0.167935i
$127$		−	8.75190i		−	0.776605i	−0.921532	−	0.388303i	$-0.873062\pi$
$127$		−	8.75190i		−	0.776605i	0.921532	−	0.388303i	$-0.126938\pi$
$128$	−10.8326	+	3.26432i	−0.957472	+	0.288528i
$129$	−8.50078			−0.748452
$130$		0			0
$131$			0.471266i			0.0411747i	0.999788	+	0.0205874i	$0.00655362\pi$
$131$			0.471266i			0.0411747i	−0.999788	+	0.0205874i	$0.993446\pi$
$132$	0.491843	+	5.86779i	0.0428095	+	0.510726i
$133$	−7.15035			−0.620014
$134$	−15.1133	+	0.632297i	−1.30559	+	0.0546222i
$135$		0			0
$136$	−1.27830	−	10.1372i	−0.109613	−	0.869254i
$137$			1.30382i			0.111393i	0.998448	+	0.0556964i	$0.0177379\pi$
$137$			1.30382i			0.111393i	−0.998448	+	0.0556964i	$0.982262\pi$
$138$	−0.508157	−	12.1461i	−0.0432572	−	1.03394i
$139$			8.74723i			0.741930i	0.928647	+	0.370965i	$0.120973\pi$
$139$			8.74723i			0.741930i	−0.928647	+	0.370965i	$0.879027\pi$
$140$		0			0
$141$		−	9.97204i		−	0.839798i
$142$	3.70773	−	0.155120i	0.311145	−	0.0130174i
$143$		−	6.01155i		−	0.502711i
$144$	3.94418	−	0.665888i	0.328682	−	0.0554907i
$145$		0			0
$146$	−0.909629	−	21.7422i	−0.0752814	−	1.79940i
$147$	−5.22015			−0.430550
$148$	13.0674	−	1.09532i	1.07413	−	0.0900345i
$149$			15.1411i			1.24041i	0.784439	+	0.620205i	$0.212951\pi$
$149$			15.1411i			1.24041i	−0.784439	+	0.620205i	$0.787049\pi$
$150$		0			0
$151$	−23.2782			−1.89435			−0.947176	−	0.320713i	$-0.896078\pi$
$151$	−23.2782			−1.89435			−0.947176	+	0.320713i	$0.896078\pi$
$152$	−1.89657	−	15.0402i	−0.153833	−	1.21992i
$153$			3.61241i			0.292046i
$154$	−5.54999	+	0.232195i	−0.447231	+	0.0187108i
$155$		0			0
$156$	−4.06940	+	0.341101i	−0.325813	+	0.0273099i
$157$	−21.8976			−1.74762			−0.873809	−	0.486270i	$-0.838357\pi$
$157$	−21.8976			−1.74762			−0.873809	+	0.486270i	$0.838357\pi$
$158$	14.7585	−	0.617452i	1.17412	−	0.0491219i
$159$	−6.12318			−0.485599
$160$		0			0
$161$	11.4682			0.903817
$162$	−1.41298	+	0.0591148i	−0.111014	+	0.00464450i
$163$	11.1643			0.874458			0.437229	−	0.899350i	$-0.355960\pi$
$163$	11.1643			0.874458			0.437229	+	0.899350i	$0.355960\pi$
$164$	14.0066	−	1.17404i	1.09373	−	0.0916775i
$165$		0			0
$166$	2.15773	−	0.0902732i	0.167472	−	0.00700656i
$167$			10.0952i			0.781192i	0.920562	+	0.390596i	$0.127731\pi$
$167$			10.0952i			0.781192i	−0.920562	+	0.390596i	$0.872269\pi$
$168$	0.472092	+	3.74379i	0.0364227	+	0.288840i
$169$	−8.83090			−0.679300
$170$		0			0
$171$			5.35964i			0.409862i
$172$	16.9421	−	1.42010i	1.29183	−	0.108282i
$173$	−13.8162			−1.05043			−0.525215	−	0.850970i	$-0.676015\pi$
$173$	−13.8162			−1.05043			−0.525215	+	0.850970i	$0.676015\pi$
$174$	0.311199	+	7.43836i	0.0235920	+	0.563901i
$175$		0			0
$176$	−1.96050	−	11.6124i	−0.147778	−	0.875318i
$177$		−	4.75190i		−	0.357174i
$178$	−17.9720	+	0.751898i	−1.34706	+	0.0563571i
$179$		−	21.9441i		−	1.64018i	−0.572236	−	0.820089i	$-0.693924\pi$
$179$		−	21.9441i		−	1.64018i	0.572236	−	0.820089i	$-0.306076\pi$
$180$		0			0
$181$			1.93021i			0.143471i	0.997424	+	0.0717356i	$0.0228538\pi$
$181$			1.93021i			0.143471i	−0.997424	+	0.0717356i	$0.977146\pi$
$182$	−0.161031	−	3.84901i	−0.0119364	−	0.285307i
$183$		−	8.51476i		−	0.629429i
$184$	3.04184	+	24.1224i	0.224247	+	1.77833i
$185$		0			0
$186$	−2.94089	+	0.123038i	−0.215636	+	0.00902158i
$187$	10.6356			0.777752
$188$	1.66589	+	19.8744i	0.121497	+	1.44949i
$189$		−	1.33411i		−	0.0970423i
$190$		0			0
$191$	12.1232			0.877202			0.438601	−	0.898682i	$-0.355474\pi$
$191$	12.1232			0.877202			0.438601	+	0.898682i	$0.355474\pi$
$192$	−7.74956	+	1.98602i	−0.559276	+	0.143329i
$193$			1.27431i			0.0917267i	0.998948	+	0.0458634i	$0.0146039\pi$
$193$			1.27431i			0.0917267i	−0.998948	+	0.0458634i	$0.985396\pi$
$194$	0.794797	+	18.9974i	0.0570631	+	1.36394i
$195$		0			0
$196$	10.4038	−	0.872056i	0.743129	−	0.0622897i
$197$	−3.30849			−0.235720			−0.117860	−	0.993030i	$-0.537603\pi$
$197$	−3.30849			−0.235720			−0.117860	+	0.993030i	$0.537603\pi$
$198$	0.174045	+	4.16007i	0.0123688	+	0.295643i
$199$	−9.02718			−0.639920			−0.319960	−	0.947431i	$-0.603669\pi$
$199$	−9.02718			−0.639920			−0.319960	+	0.947431i	$0.603669\pi$
$200$		0			0
$201$	−10.6961			−0.754443
$202$	0.598430	+	14.3038i	0.0421054	+	1.00641i
$203$	−7.02319			−0.492931
$204$	−0.603474	−	7.19957i	−0.0422516	−	0.504071i
$205$		0			0
$206$	0.635321	+	15.1856i	0.0442649	+	1.05803i
$207$		−	8.59609i		−	0.597470i
$208$	8.05338	−	1.35964i	0.558402	−	0.0942738i
$209$	15.7798			1.09151
$210$		0			0
$211$		−	6.61241i		−	0.455217i	−0.973753	−	0.227608i	$-0.926909\pi$
$211$		−	6.61241i		−	0.455217i	0.973753	−	0.227608i	$-0.0730906\pi$
$212$	12.2036	−	1.02291i	0.838144	−	0.0702539i
$213$	2.62405			0.179797
$214$	6.87439	−	0.287604i	0.469924	−	0.0196602i
$215$		0			0
$216$	2.80620	−	0.353863i	0.190938	−	0.0240773i
$217$		−	2.77674i		−	0.188497i
$218$	0.913755	+	21.8408i	0.0618873	+	1.47925i
$219$		−	15.3875i		−	1.03979i
$220$		0			0
$221$			7.37595i			0.496160i
$222$	9.26432	−	0.387592i	0.621780	−	0.0260135i
$223$		−	0.833237i		−	0.0557976i	−0.999611	−	0.0278988i	$-0.991118\pi$
$223$		−	0.833237i		−	0.0557976i	0.999611	−	0.0278988i	$-0.00888162\pi$
$224$	−1.56631	−	7.38255i	−0.104653	−	0.493267i
$225$		0			0
$226$	−0.584549	−	13.9720i	−0.0388836	−	0.929407i
$227$	−10.9999			−0.730089			−0.365045	−	0.930990i	$-0.618946\pi$
$227$	−10.9999			−0.730089			−0.365045	+	0.930990i	$0.618946\pi$
$228$	−0.895358	−	10.6818i	−0.0592966	−	0.707420i
$229$		−	15.2061i		−	1.00485i	−0.864622	−	0.502423i	$-0.832442\pi$
$229$		−	15.2061i		−	1.00485i	0.864622	−	0.502423i	$-0.167558\pi$
$230$		0			0
$231$	−3.92787			−0.258435
$232$	−1.86285	−	14.7728i	−0.122302	−	0.969879i
$233$		−	2.47594i		−	0.162204i	−0.996706	−	0.0811020i	$-0.974156\pi$
$233$		−	2.47594i		−	0.162204i	0.996706	−	0.0811020i	$-0.0258439\pi$
$234$	−2.88507	+	0.120703i	−0.188603	+	0.00789059i
$235$		0			0
$236$	0.793832	+	9.47058i	0.0516741	+	0.616482i
$237$	10.4450			0.678473
$238$	6.80964	−	0.284895i	0.441404	−	0.0184670i
$239$	21.0737			1.36314			0.681572	−	0.731751i	$-0.261297\pi$
$239$	21.0737			1.36314			0.681572	+	0.731751i	$0.261297\pi$
$240$		0			0
$241$	−6.10852			−0.393484			−0.196742	−	0.980455i	$-0.563036\pi$
$241$	−6.10852			−0.393484			−0.196742	+	0.980455i	$0.563036\pi$
$242$	−3.29475	+	0.137843i	−0.211794	+	0.00886086i
$243$	−1.00000			−0.0641500
$244$	1.42244	+	16.9700i	0.0910624	+	1.08639i
$245$		0			0
$246$	9.93021	−	0.415451i	0.633127	−	0.0264882i
$247$			10.9435i			0.696318i
$248$	5.84066	−	0.736508i	0.370882	−	0.0467683i
$249$	1.52708			0.0967748
$250$		0			0
$251$			22.5286i			1.42199i	0.703195	+	0.710997i	$0.251756\pi$
$251$			22.5286i			1.42199i	−0.703195	+	0.710997i	$0.748244\pi$
$252$	0.222871	+	2.65890i	0.0140396	+	0.167495i
$253$	−25.3085			−1.59113
$254$	0.517367	+	12.3662i	0.0324625	+	0.775927i
$255$		0			0
$256$	15.1132	−	5.25277i	0.944574	−	0.328298i
$257$			14.5286i			0.906271i	0.891442	+	0.453136i	$0.149695\pi$
$257$			14.5286i			0.906271i	−0.891442	+	0.453136i	$0.850305\pi$
$258$	12.0114	−	0.502522i	0.747798	−	0.0312857i
$259$			8.74723i			0.543526i
$260$		0			0
$261$			5.26432i			0.325853i
$262$	−0.0278588	−	0.665888i	−0.00172112	−	0.0411387i
$263$		−	5.29694i		−	0.326624i	−0.986575	−	0.163312i	$-0.947782\pi$
$263$		−	5.29694i		−	0.326624i	0.986575	−	0.163312i	$-0.0522177\pi$
$264$	−1.04184	−	8.26198i	−0.0641206	−	0.508490i
$265$		0			0
$266$	10.1033	−	0.422692i	0.619472	−	0.0259169i
$267$	−12.7193			−0.778407
$268$	21.3174	−	1.78684i	1.30217	−	0.109149i
$269$		−	27.0737i		−	1.65071i	−0.564613	−	0.825356i	$-0.690975\pi$
$269$		−	27.0737i		−	1.65071i	0.564613	−	0.825356i	$-0.309025\pi$
$270$		0			0
$271$	15.8604			0.963451			0.481726	−	0.876322i	$-0.340010\pi$
$271$	15.8604			0.963451			0.481726	+	0.876322i	$0.340010\pi$
$272$	2.40546	+	14.2480i	0.145852	+	0.863912i
$273$		−	2.72404i		−	0.164866i
$274$	−0.0770751	−	1.84227i	−0.00465628	−	0.111296i
$275$		0			0
$276$	1.43603	+	17.1321i	0.0864387	+	1.03123i
$277$	−9.98592			−0.599996			−0.299998	−	0.953940i	$-0.596986\pi$
$277$	−9.98592			−0.599996			−0.299998	+	0.953940i	$0.596986\pi$
$278$	−0.517091	−	12.3596i	−0.0310130	−	0.741282i
$279$	−2.08134			−0.124607
$280$		0			0
$281$	13.4218			0.800676			0.400338	−	0.916368i	$-0.368893\pi$
$281$	13.4218			0.800676			0.400338	+	0.916368i	$0.368893\pi$
$282$	0.589496	+	14.0903i	0.0351040	+	0.839064i
$283$	−3.83722			−0.228099			−0.114050	−	0.993475i	$-0.536382\pi$
$283$	−3.83722			−0.228099			−0.114050	+	0.993475i	$0.536382\pi$
$284$	−5.22976	+	0.438363i	−0.310329	+	0.0260121i
$285$		0			0
$286$	0.355372	+	8.49418i	0.0210136	+	0.502271i
$287$			9.37595i			0.553445i
$288$	−5.53368	+	1.17404i	−0.326075	+	0.0691813i
$289$	3.95051			0.232383
$290$		0			0
$291$			13.4450i			0.788158i
$292$	2.57057	+	30.6674i	0.150431	+	1.79468i
$293$	26.4450			1.54493			0.772466	−	0.635057i	$-0.219023\pi$
$293$	26.4450			1.54493			0.772466	+	0.635057i	$0.219023\pi$
$294$	7.37595	−	0.308588i	0.430174	−	0.0179972i
$295$		0			0
$296$	−18.3991	+	2.32013i	−1.06943	+	0.134855i
$297$			2.94418i			0.170839i
$298$	−0.895066	−	21.3941i	−0.0518498	−	1.23933i
$299$		−	17.5518i		−	1.01505i
$300$		0			0
$301$			11.3410i			0.653684i
$302$	32.8916	−	1.37609i	1.89270	−	0.0791849i
$303$			10.1232i			0.581561i
$304$	3.56892	+	21.1394i	0.204692	+	1.21243i
$305$		0			0
$306$	−0.213547	−	5.10425i	−0.0122077	−	0.291791i
$307$	1.27596			0.0728230			0.0364115	−	0.999337i	$-0.488407\pi$
$307$	1.27596			0.0728230			0.0364115	+	0.999337i	$0.488407\pi$
$308$	7.82829	−	0.656174i	0.446058	−	0.0373890i
$309$			10.7472i			0.611388i
$310$		0			0
$311$	2.44496			0.138641			0.0693205	−	0.997594i	$-0.477917\pi$
$311$	2.44496			0.138641			0.0693205	+	0.997594i	$0.477917\pi$
$312$	5.72981	−	0.722530i	0.324387	−	0.0409052i
$313$		−	22.8325i		−	1.29057i	−0.763943	−	0.645283i	$-0.776739\pi$
$313$		−	22.8325i		−	1.29057i	0.763943	−	0.645283i	$-0.223261\pi$
$314$	30.9408	−	1.29447i	1.74609	−	0.0730513i
$315$		0			0
$316$	−20.8169	+	1.74489i	−1.17104	+	0.0981579i
$317$	−2.11163			−0.118601			−0.0593005	−	0.998240i	$-0.518887\pi$
$317$	−2.11163			−0.118601			−0.0593005	+	0.998240i	$0.518887\pi$
$318$	8.65191	−	0.361971i	0.485175	−	0.0202983i
$319$	15.4991			0.867784
$320$		0			0
$321$	4.86518			0.271548
$322$	−16.2042	+	0.677938i	−0.903027	+	0.0377800i
$323$	−19.3612			−1.07729
$324$	1.99301	−	0.167056i	0.110723	−	0.00928088i
$325$		0			0
$326$	−15.7749	+	0.659978i	−0.873694	+	0.0365528i
$327$			15.4573i			0.854790i
$328$	−19.7216	+	2.48690i	−1.08894	+	0.137316i
$329$	−13.3038			−0.733463
$330$		0			0
$331$		−	23.2248i		−	1.27655i	−0.769808	−	0.638276i	$-0.779648\pi$
$331$		−	23.2248i		−	1.27655i	0.769808	−	0.638276i	$-0.220352\pi$
$332$	−3.04349	+	0.255108i	−0.167033	+	0.0140009i
$333$	6.55659			0.359299
$334$	−0.596777	−	14.2643i	−0.0326542	−	0.780509i
$335$		0			0
$336$	−0.888369	−	5.26198i	−0.0484645	−	0.287065i
$337$			12.8884i			0.702074i	0.936362	+	0.351037i	$0.114171\pi$
$337$			12.8884i			0.702074i	−0.936362	+	0.351037i	$0.885829\pi$
$338$	12.4779	−	0.522037i	0.678706	−	0.0283951i
$339$		−	9.88837i		−	0.537063i
$340$		0			0
$341$			6.12785i			0.331841i
$342$	−0.316834	−	7.57304i	−0.0171324	−	0.409503i
$343$			16.3030i			0.880281i
$344$	−23.8549	+	3.00811i	−1.28617	+	0.162186i
$345$		0			0
$346$	19.5220	−	0.816745i	1.04951	−	0.0439085i
$347$	−6.79827			−0.364951			−0.182475	−	0.983210i	$-0.558411\pi$
$347$	−6.79827			−0.364951			−0.182475	+	0.983210i	$0.558411\pi$
$348$	−0.879435	−	10.4918i	−0.0471427	−	0.562422i
$349$		−	34.6076i		−	1.85250i	−0.376904	−	0.926252i	$-0.623011\pi$
$349$		−	34.6076i		−	1.85250i	0.376904	−	0.926252i	$-0.376989\pi$
$350$		0			0
$351$	−2.04184			−0.108985
$352$	3.45661	+	16.2922i	0.184238	+	0.868376i
$353$		−	12.2433i		−	0.651647i	−0.945431	−	0.325823i	$-0.894358\pi$
$353$		−	12.2433i		−	0.651647i	0.945431	−	0.325823i	$-0.105642\pi$
$354$	0.280908	+	6.71432i	0.0149301	+	0.356862i
$355$		0			0
$356$	25.3496	−	2.12483i	1.34353	−	0.112616i
$357$	4.81936			0.255067
$358$	1.29722	+	31.0065i	0.0685603	+	1.63874i
$359$	2.01622			0.106412			0.0532059	−	0.998584i	$-0.483056\pi$
$359$	2.01622			0.106412			0.0532059	+	0.998584i	$0.483056\pi$
$360$		0			0
$361$	−9.72569			−0.511878
$362$	−0.114104	−	2.72734i	−0.00599716	−	0.143346i
$363$	−2.33178			−0.122387
$364$	0.455067	+	5.42904i	0.0238520	+	0.284559i
$365$		0			0
$366$	0.503348	+	12.0312i	0.0263104	+	0.628879i
$367$		−	13.4131i		−	0.700159i	−0.936720	−	0.350079i	$-0.886155\pi$
$367$		−	13.4131i		−	0.700159i	0.936720	−	0.350079i	$-0.113845\pi$
$368$	−5.72404	−	33.9046i	−0.298386	−	1.76740i
$369$	7.02786			0.365856
$370$		0			0
$371$			8.16900i			0.424113i
$372$	4.14813	−	0.347700i	0.215071	−	0.0180274i
$373$	−10.0976			−0.522832			−0.261416	−	0.965226i	$-0.584189\pi$
$373$	−10.0976			−0.522832			−0.261416	+	0.965226i	$0.584189\pi$
$374$	−15.0279	+	0.628722i	−0.777072	+	0.0325104i
$375$		0			0
$376$	−3.52873	−	27.9836i	−0.181981	−	1.44314i
$377$			10.7489i			0.553595i
$378$	0.0788658	+	1.88507i	0.00405642	+	0.0969575i
$379$			18.2775i			0.938853i	0.882972	+	0.469426i	$0.155539\pi$
$379$			18.2775i			0.938853i	−0.882972	+	0.469426i	$0.844461\pi$
$380$		0			0
$381$			8.75190i			0.448373i
$382$	−17.1298	+	0.716660i	−0.876436	+	0.0366675i
$383$			11.7734i			0.601594i	0.953688	+	0.300797i	$0.0972527\pi$
$383$			11.7734i			0.601594i	−0.953688	+	0.300797i	$0.902747\pi$
$384$	10.8326	−	3.26432i	0.552796	−	0.166582i
$385$		0			0
$386$	−0.0753305	−	1.80057i	−0.00383422	−	0.0916466i
$387$	8.50078			0.432119
$388$	−2.24606	−	26.7960i	−0.114026	−	1.36036i
$389$			33.4270i			1.69482i	0.530942	+	0.847408i	$0.321838\pi$
$389$			33.4270i			1.69482i	−0.530942	+	0.847408i	$0.678162\pi$
$390$		0			0
$391$	31.0526			1.57040
$392$	−14.6488	+	1.84721i	−0.739876	+	0.0932984i
$393$		−	0.471266i		−	0.0237722i
$394$	4.67482	−	0.195581i	0.235514	−	0.00985322i
$395$		0			0
$396$	−0.491843	−	5.86779i	−0.0247161	−	0.294868i
$397$	−39.0434			−1.95953			−0.979766	−	0.200147i	$-0.935858\pi$
$397$	−39.0434			−1.95953			−0.979766	+	0.200147i	$0.935858\pi$
$398$	12.7552	−	0.533640i	0.639360	−	0.0267490i
$399$	7.15035			0.357965
$400$		0			0
$401$	−24.6140			−1.22916			−0.614581	−	0.788853i	$-0.710675\pi$
$401$	−24.6140			−1.22916			−0.614581	+	0.788853i	$0.710675\pi$
$402$	15.1133	−	0.632297i	0.753784	−	0.0315361i
$403$	−4.24976			−0.211695
$404$	−1.69114	−	20.1756i	−0.0841372	−	1.00377i
$405$		0			0
$406$	9.92361	−	0.415175i	0.492500	−	0.0206048i
$407$		−	19.3038i		−	0.956855i
$408$	1.27830	+	10.1372i	0.0632851	+	0.501864i
$409$	14.5024			0.717099			0.358550	−	0.933511i	$-0.383271\pi$
$409$	14.5024			0.717099			0.358550	+	0.933511i	$0.383271\pi$
$410$		0			0
$411$		−	1.30382i		−	0.0643127i
$412$	−1.79539	−	21.4193i	−0.0884524	−	1.05526i
$413$	−6.33956			−0.311949
$414$	0.508157	+	12.1461i	0.0249745	+	0.596948i
$415$		0			0
$416$	−11.2989	+	2.39721i	−0.553973	+	0.117533i
$417$		−	8.74723i		−	0.428354i
$418$	−22.2964	+	0.932818i	−1.09055	+	0.0456256i
$419$			12.6419i			0.617598i	0.951127	+	0.308799i	$0.0999271\pi$
$419$			12.6419i			0.617598i	−0.951127	+	0.308799i	$0.900073\pi$
$420$		0			0
$421$		−	16.8389i		−	0.820677i	−0.911933	−	0.410338i	$-0.865411\pi$
$421$		−	16.8389i		−	0.820677i	0.911933	−	0.410338i	$-0.134589\pi$
$422$	0.390891	+	9.34318i	0.0190283	+	0.454819i
$423$			9.97204i			0.484857i
$424$	−17.1829	+	2.16676i	−0.834474	+	0.105227i
$425$		0			0
$426$	−3.70773	+	0.155120i	−0.179640	+	0.00751561i
$427$	−11.3596			−0.549731
$428$	−9.69636	+	0.812757i	−0.468691	+	0.0392861i
$429$			6.01155i			0.290240i
$430$		0			0
$431$	5.98845			0.288454			0.144227	−	0.989545i	$-0.453930\pi$
$431$	5.98845			0.288454			0.144227	+	0.989545i	$0.453930\pi$
$432$	−3.94418	+	0.665888i	−0.189765	+	0.0320376i
$433$			2.22482i			0.106918i	0.998570	+	0.0534589i	$0.0170246\pi$
$433$			2.22482i			0.106918i	−0.998570	+	0.0534589i	$0.982975\pi$
$434$	0.164146	+	3.92347i	0.00787928	+	0.188333i
$435$		0			0
$436$	−2.58223	−	30.8065i	−0.123666	−	1.47537i
$437$	46.0719			2.20392
$438$	0.909629	+	21.7422i	0.0434638	+	1.03888i
$439$	2.30460			0.109993			0.0549963	−	0.998487i	$-0.482485\pi$
$439$	2.30460			0.109993			0.0549963	+	0.998487i	$0.482485\pi$
$440$		0			0
$441$	5.22015			0.248578
$442$	−0.436028	−	10.4220i	−0.0207397	−	0.495726i
$443$	22.1347			1.05165			0.525826	−	0.850592i	$-0.323756\pi$
$443$	22.1347			1.05165			0.525826	+	0.850592i	$0.323756\pi$
$444$	−13.0674	+	1.09532i	−0.620149	+	0.0519815i
$445$		0			0
$446$	0.0492566	+	1.17734i	0.00233237	+	0.0557489i
$447$		−	15.1411i		−	0.716151i
$448$	2.64957	+	10.3388i	0.125181	+	0.488462i
$449$	−21.5861			−1.01871			−0.509356	−	0.860556i	$-0.670116\pi$
$449$	−21.5861			−1.01871			−0.509356	+	0.860556i	$0.670116\pi$
$450$		0			0
$451$		−	20.6913i		−	0.974316i
$452$	1.65191	+	19.7076i	0.0776993	+	0.926969i
$453$	23.2782			1.09371
$454$	15.5426	−	0.650257i	0.729451	−	0.0305181i
$455$		0			0
$456$	1.89657	+	15.0402i	0.0888153	+	0.704323i
$457$		−	2.50088i		−	0.116986i	−0.998288	−	0.0584930i	$-0.981370\pi$
$457$		−	2.50088i		−	0.116986i	0.998288	−	0.0584930i	$-0.0186295\pi$
$458$	0.898904	+	21.4858i	0.0420030	+	1.00397i
$459$		−	3.61241i		−	0.168613i
$460$		0			0
$461$		−	2.59609i		−	0.120912i	−0.998171	−	0.0604561i	$-0.980744\pi$
$461$		−	2.59609i		−	0.120912i	0.998171	−	0.0604561i	$-0.0192555\pi$
$462$	5.54999	−	0.232195i	0.258209	−	0.0108027i
$463$			27.8604i			1.29478i	0.762158	+	0.647392i	$0.224140\pi$
$463$			27.8604i			1.29478i	−0.762158	+	0.647392i	$0.775860\pi$
$464$	3.50545	+	20.7634i	0.162736	+	0.963919i
$465$		0			0
$466$	0.146365	+	3.49844i	0.00678021	+	0.162062i
$467$	−5.75200			−0.266171			−0.133085	−	0.991105i	$-0.542488\pi$
$467$	−5.75200			−0.266171			−0.133085	+	0.991105i	$0.542488\pi$
$468$	4.06940	−	0.341101i	0.188108	−	0.0157674i
$469$			14.2698i			0.658917i
$470$		0			0
$471$	21.8976			1.00899
$472$	−1.68152	−	13.3348i	−0.0773982	−	0.613784i
$473$		−	25.0279i		−	1.15078i
$474$	−14.7585	+	0.617452i	−0.677880	+	0.0283605i
$475$		0			0
$476$	−9.60503	+	0.805102i	−0.440246	+	0.0369018i
$477$	6.12318			0.280361
$478$	−29.7766	+	1.24577i	−1.36195	+	0.0569801i
$479$	12.5473			0.573299			0.286649	−	0.958036i	$-0.407459\pi$
$479$	12.5473			0.573299			0.286649	+	0.958036i	$0.407459\pi$
$480$		0			0
$481$	13.3875			0.610417
$482$	8.63119	−	0.361104i	0.393140	−	0.0164478i
$483$	−11.4682			−0.521819
$484$	4.64726	−	0.389537i	0.211239	−	0.0177062i
$485$		0			0
$486$	1.41298	−	0.0591148i	0.0640940	−	0.00268150i
$487$		−	8.60530i		−	0.389944i	−0.980809	−	0.194972i	$-0.937538\pi$
$487$		−	8.60530i		−	0.389944i	0.980809	−	0.194972i	$-0.0624615\pi$
$488$	−3.01305	−	23.8941i	−0.136395	−	1.08164i
$489$	−11.1643			−0.504868
$490$		0			0
$491$		−	36.8866i		−	1.66467i	−0.554273	−	0.832335i	$-0.687004\pi$
$491$		−	36.8866i		−	1.66467i	0.554273	−	0.832335i	$-0.312996\pi$
$492$	−14.0066	+	1.17404i	−0.631466	+	0.0529300i
$493$	−19.0169			−0.856477
$494$	−0.646923	−	15.4629i	−0.0291065	−	0.695710i
$495$		0			0
$496$	−8.20919	+	1.38594i	−0.368603	+	0.0622305i
$497$		−	3.50078i		−	0.157031i
$498$	−2.15773	+	0.0902732i	−0.0966903	+	0.00404524i
$499$			36.2496i			1.62275i	0.584524	+	0.811377i	$0.301281\pi$
$499$			36.2496i			1.62275i	−0.584524	+	0.811377i	$0.698719\pi$
$500$		0			0
$501$		−	10.0952i		−	0.451021i
$502$	−1.33178	−	31.8325i	−0.0594401	−	1.42075i
$503$			23.3527i			1.04124i	0.853787	+	0.520622i	$0.174300\pi$
$503$			23.3527i			1.04124i	−0.853787	+	0.520622i	$0.825700\pi$
$504$	−0.472092	−	3.74379i	−0.0210287	−	0.166762i
$505$		0			0
$506$	35.7603	−	1.49611i	1.58974	−	0.0665101i
$507$	8.83090			0.392194
$508$	−1.46206	−	17.4426i	−0.0648682	−	0.773891i
$509$		−	3.35506i		−	0.148711i	−0.997232	−	0.0743553i	$-0.976310\pi$
$509$		−	3.35506i		−	0.148711i	0.997232	−	0.0743553i	$-0.0236899\pi$
$510$		0			0
$511$	−20.5286			−0.908133
$512$	−21.0441	+	8.31546i	−0.930025	+	0.367495i
$513$		−	5.35964i		−	0.236634i
$514$	−0.858858	−	20.5286i	−0.0378826	−	0.905479i
$515$		0			0
$516$	−16.9421	+	1.42010i	−0.745836	+	0.0625166i
$517$	29.3595			1.29123
$518$	−0.517091	−	12.3596i	−0.0227197	−	0.543051i
$519$	13.8162			0.606466
$520$		0			0
$521$	−33.6029			−1.47217			−0.736084	−	0.676890i	$-0.763327\pi$
$521$	−33.6029			−1.47217			−0.736084	+	0.676890i	$0.763327\pi$
$522$	−0.311199	−	7.43836i	−0.0136208	−	0.325568i
$523$	0.965721			0.0422280			0.0211140	−	0.999777i	$-0.493279\pi$
$523$	0.965721			0.0422280			0.0211140	+	0.999777i	$0.493279\pi$
$524$	0.0787277	+	0.939238i	0.00343924	+	0.0410308i
$525$		0			0
$526$	0.313128	+	7.48446i	0.0136530	+	0.326338i
$527$		−	7.51865i		−	0.327517i
$528$	1.96050	+	11.6124i	0.0853197	+	0.505365i
$529$	−50.8928			−2.21273
$530$		0			0
$531$			4.75190i			0.206215i
$532$	−14.2507	+	1.19451i	−0.617848	+	0.0517885i
$533$	14.3497			0.621556
$534$	17.9720	−	0.751898i	0.777726	−	0.0325378i
$535$		0			0
$536$	−30.0154	+	3.78494i	−1.29647	+	0.163485i
$537$			21.9441i			0.946957i
$538$	1.60046	+	38.2545i	0.0690006	+	1.64927i
$539$		−	15.3691i		−	0.661993i
$540$		0			0
$541$			6.34877i			0.272955i	0.990643	+	0.136478i	$0.0435781\pi$
$541$			6.34877i			0.272955i	−0.990643	+	0.136478i	$0.956422\pi$
$542$	−22.4104	+	0.937586i	−0.962609	+	0.0402728i
$543$		−	1.93021i		−	0.0828331i
$544$	−4.24113	−	19.9899i	−0.181837	−	0.857060i
$545$		0			0
$546$	0.161031	+	3.84901i	0.00689149	+	0.164722i
$547$	2.07433			0.0886921			0.0443460	−	0.999016i	$-0.485880\pi$
$547$	2.07433			0.0886921			0.0443460	+	0.999016i	$0.485880\pi$
$548$	0.217811	+	2.59853i	0.00930442	+	0.111004i
$549$			8.51476i			0.363401i
$550$		0			0
$551$	−28.2148			−1.20199
$552$	−3.04184	−	24.1224i	−0.129469	−	1.02672i
$553$		−	13.9347i		−	0.592566i
$554$	14.1099	−	0.590316i	0.599472	−	0.0250801i
$555$		0			0
$556$	1.46128	+	17.4333i	0.0619719	+	0.739337i
$557$	−27.6931			−1.17339			−0.586696	−	0.809807i	$-0.699572\pi$
$557$	−27.6931			−1.17339			−0.586696	+	0.809807i	$0.699572\pi$
$558$	2.94089	−	0.123038i	0.124498	−	0.00520861i
$559$	17.3572			0.734131
$560$		0			0
$561$	−10.6356			−0.449035
$562$	−18.9647	+	0.793426i	−0.799976	+	0.0334687i
$563$	3.80771			0.160476			0.0802380	−	0.996776i	$-0.474432\pi$
$563$	3.80771			0.160476			0.0802380	+	0.996776i	$0.474432\pi$
$564$	−1.66589	−	19.8744i	−0.0701466	−	0.836863i
$565$		0			0
$566$	5.42191	−	0.226837i	0.227900	−	0.00953467i
$567$			1.33411i			0.0560274i
$568$	7.36362	−	0.928554i	0.308971	−	0.0389613i
$569$	−38.6371			−1.61975			−0.809875	−	0.586603i	$-0.800465\pi$
$569$	−38.6371			−1.61975			−0.809875	+	0.586603i	$0.800465\pi$
$570$		0			0
$571$			6.24976i			0.261544i	0.991412	+	0.130772i	$0.0417456\pi$
$571$			6.24976i			0.261544i	−0.991412	+	0.130772i	$0.958254\pi$
$572$	−1.00426	−	11.9811i	−0.0419904	−	0.500954i
$573$	−12.1232			−0.506453
$574$	−0.554258	−	13.2480i	−0.0231343	−	0.552961i
$575$		0			0
$576$	7.74956	−	1.98602i	0.322898	−	0.0827509i
$577$		−	2.17377i		−	0.0904952i	−0.998976	−	0.0452476i	$-0.985592\pi$
$577$		−	2.17377i		−	0.0904952i	0.998976	−	0.0452476i	$-0.0144077\pi$
$578$	−5.58198	+	0.233534i	−0.232180	+	0.00971372i
$579$		−	1.27431i		−	0.0529585i
$580$		0			0
$581$		−	2.03730i		−	0.0845213i
$582$	−0.794797	−	18.9974i	−0.0329454	−	0.787469i
$583$		−	18.0278i		−	0.746634i
$584$	−5.44506	−	43.1804i	−0.225318	−	1.78682i
$585$		0			0
$586$	−37.3661	+	1.56329i	−1.54358	+	0.0645789i
$587$	34.1688			1.41030			0.705149	−	0.709059i	$-0.250880\pi$
$587$	34.1688			1.41030			0.705149	+	0.709059i	$0.250880\pi$
$588$	−10.4038	+	0.872056i	−0.429046	+	0.0359630i
$589$		−	11.1552i		−	0.459643i
$590$		0			0
$591$	3.30849			0.136093
$592$	25.8604	−	4.36596i	1.06286	−	0.179440i
$593$		−	12.9952i		−	0.533650i	−0.963745	−	0.266825i	$-0.914025\pi$
$593$		−	12.9952i		−	0.533650i	0.963745	−	0.266825i	$-0.0859746\pi$
$594$	−0.174045	−	4.16007i	−0.00714115	−	0.170690i
$595$		0			0
$596$	2.52942	+	30.1765i	0.103609	+	1.23608i
$597$	9.02718			0.369458
$598$	1.03757	+	24.8003i	0.0424295	+	1.01416i
$599$	−47.2572			−1.93088			−0.965439	−	0.260628i	$-0.916071\pi$
$599$	−47.2572			−1.93088			−0.965439	+	0.260628i	$0.916071\pi$
$600$		0			0
$601$	−23.5007			−0.958613			−0.479306	−	0.877648i	$-0.659112\pi$
$601$	−23.5007			−0.958613			−0.479306	+	0.877648i	$0.659112\pi$
$602$	−0.670421	−	16.0246i	−0.0273243	−	0.653112i
$603$	10.6961			0.435578
$604$	−46.3937	+	3.88876i	−1.88773	+	0.158231i
$605$		0			0
$606$	−0.598430	−	14.3038i	−0.0243096	−	0.581053i
$607$		−	0.218591i		−	0.00887233i	−0.999990	−	0.00443617i	$-0.998588\pi$
$607$		−	0.218591i		−	0.00887233i	0.999990	−	0.00443617i	$-0.00141208\pi$
$608$	−6.29245	−	29.6585i	−0.255193	−	1.20281i
$609$	7.02319			0.284594
$610$		0			0
$611$			20.3613i			0.823730i
$612$	0.603474	+	7.19957i	0.0243940	+	0.291025i
$613$	35.7488			1.44388			0.721940	−	0.691956i	$-0.243251\pi$
$613$	35.7488			1.44388			0.721940	+	0.691956i	$0.243251\pi$
$614$	−1.80290	+	0.0754282i	−0.0727593	+	0.00304404i
$615$		0			0
$616$	−11.0224	+	1.38993i	−0.444105	+	0.0560018i
$617$		−	33.0836i		−	1.33189i	−0.745999	−	0.665947i	$-0.768028\pi$
$617$		−	33.0836i		−	1.33189i	0.745999	−	0.665947i	$-0.231972\pi$
$618$	−0.635321	−	15.1856i	−0.0255563	−	0.610854i
$619$			25.1084i			1.00919i	0.863355	+	0.504596i	$0.168359\pi$
$619$			25.1084i			1.00919i	−0.863355	+	0.504596i	$0.831641\pi$
$620$		0			0
$621$			8.59609i			0.344949i
$622$	−3.45468	+	0.144534i	−0.138520	+	0.00579527i
$623$			16.9689i			0.679846i
$624$	−8.05338	+	1.35964i	−0.322393	+	0.0544290i
$625$		0			0
$626$	1.34974	+	32.2617i	0.0539463	+	1.28944i
$627$	−15.7798			−0.630183
$628$	−43.6421	+	3.65812i	−1.74151	+	0.145975i
$629$			23.6851i			0.944386i
$630$		0			0
$631$	23.2829			0.926876			0.463438	−	0.886129i	$-0.346616\pi$
$631$	23.2829			0.926876			0.463438	+	0.886129i	$0.346616\pi$
$632$	29.3107	−	3.69608i	1.16592	−	0.147022i
$633$			6.61241i			0.262820i
$634$	2.98369	−	0.124829i	0.118497	−	0.00495758i
$635$		0			0
$636$	−12.2036	+	1.02291i	−0.483902	+	0.0405611i
$637$	10.6587			0.422313
$638$	−21.8999	+	0.916228i	−0.867026	+	0.0362738i
$639$	−2.62405			−0.103806
$640$		0			0
$641$	−38.3021			−1.51284			−0.756420	−	0.654086i	$-0.773054\pi$
$641$	−38.3021			−1.51284			−0.756420	+	0.654086i	$0.773054\pi$
$642$	−6.87439	+	0.287604i	−0.271311	+	0.0113508i
$643$	45.8045			1.80635			0.903177	−	0.429269i	$-0.141229\pi$
$643$	45.8045			1.80635			0.903177	+	0.429269i	$0.141229\pi$
$644$	22.8561	−	1.91582i	0.900658	−	0.0754940i
$645$		0			0
$646$	27.3569	−	1.14453i	1.07634	−	0.0450311i
$647$		−	48.1114i		−	1.89146i	−0.324960	−	0.945728i	$-0.605351\pi$
$647$		−	48.1114i		−	1.89146i	0.324960	−	0.945728i	$-0.394649\pi$
$648$	−2.80620	+	0.353863i	−0.110238	+	0.0139010i
$649$	13.9905			0.549174
$650$		0			0
$651$			2.77674i			0.108829i
$652$	22.2506	−	1.86507i	0.871402	−	0.0730417i
$653$	38.3331			1.50009			0.750046	−	0.661386i	$-0.230031\pi$
$653$	38.3331			1.50009			0.750046	+	0.661386i	$0.230031\pi$
$654$	−0.913755	−	21.8408i	−0.0357306	−	0.854043i
$655$		0			0
$656$	27.7192	−	4.67977i	1.08225	−	0.182714i
$657$			15.3875i			0.600323i
$658$	18.7980	−	0.786453i	0.732822	−	0.0306591i
$659$			5.03253i			0.196040i	0.995184	+	0.0980198i	$0.0312508\pi$
$659$			5.03253i			0.196040i	−0.995184	+	0.0980198i	$0.968749\pi$
$660$		0			0
$661$		−	17.4665i		−	0.679368i	−0.940540	−	0.339684i	$-0.889680\pi$
$661$		−	17.4665i		−	0.679368i	0.940540	−	0.339684i	$-0.110320\pi$
$662$	1.37293	+	32.8161i	0.0533605	+	1.27544i
$663$		−	7.37595i		−	0.286458i
$664$	4.28530	−	0.540377i	0.166302	−	0.0209707i
$665$		0			0
$666$	−9.26432	+	0.387592i	−0.358985	+	0.0150189i
$667$	45.2526			1.75219
$668$	1.68647	+	20.1199i	0.0652513	+	0.778462i
$669$			0.833237i			0.0322148i
$670$		0			0
$671$	25.0690			0.967779
$672$	1.56631	+	7.38255i	0.0604216	+	0.284788i
$673$		−	32.4448i		−	1.25065i	−0.780363	−	0.625327i	$-0.784966\pi$
$673$		−	32.4448i		−	1.25065i	0.780363	−	0.625327i	$-0.215034\pi$
$674$	−0.761894	−	18.2110i	−0.0293471	−	0.701461i
$675$		0			0
$676$	−17.6001	+	1.47525i	−0.676926	+	0.0567405i
$677$	8.07213			0.310237			0.155119	−	0.987896i	$-0.450424\pi$
$677$	8.07213			0.310237			0.155119	+	0.987896i	$0.450424\pi$
$678$	0.584549	+	13.9720i	0.0224495	+	0.536593i
$679$	17.9371			0.688362
$680$		0			0
$681$	10.9999			0.421517
$682$	−0.362247	−	8.65851i	−0.0138711	−	0.331551i
$683$	−36.3380			−1.39043			−0.695217	−	0.718799i	$-0.744692\pi$
$683$	−36.3380			−1.39043			−0.695217	+	0.718799i	$0.744692\pi$
$684$	0.895358	+	10.6818i	0.0342349	+	0.408429i
$685$		0			0
$686$	−0.963751	−	23.0358i	−0.0367962	−	0.879512i
$687$			15.2061i			0.580148i
$688$	33.5286	−	5.66057i	1.27827	−	0.215807i
$689$	12.5025			0.476308
$690$		0			0
$691$			15.0016i			0.570686i	0.958425	+	0.285343i	$0.0921075\pi$
$691$			15.0016i			0.570686i	−0.958425	+	0.285343i	$0.907892\pi$
$692$	−27.5359	+	2.30808i	−1.04676	+	0.0877402i
$693$	3.92787			0.149207
$694$	9.60581	−	0.401879i	0.364632	−	0.0152551i
$695$		0			0
$696$	1.86285	+	14.7728i	0.0706110	+	0.559960i
$697$			25.3875i			0.961620i
$698$	2.04582	+	48.8998i	0.0774356	+	1.85089i
$699$			2.47594i			0.0936485i
$700$		0			0
$701$		−	13.2874i		−	0.501859i	−0.968005	−	0.250929i	$-0.919264\pi$
$701$		−	13.2874i		−	0.501859i	0.968005	−	0.250929i	$-0.0807362\pi$
$702$	2.88507	−	0.120703i	0.108890	−	0.00455564i
$703$			35.1409i			1.32537i
$704$	−5.84721	−	22.8161i	−0.220375	−	0.859916i
$705$		0			0
$706$	0.723763	+	17.2996i	0.0272392	+	0.651077i
$707$	13.5054			0.507925
$708$	−0.793832	−	9.47058i	−0.0298340	−	0.355926i
$709$			37.8976i			1.42327i	0.702548	+	0.711637i	$0.252046\pi$
$709$			37.8976i			1.42327i	−0.702548	+	0.711637i	$0.747954\pi$
$710$		0			0
$711$	−10.4450			−0.391717
$712$	−35.6929	+	4.50088i	−1.33765	+	0.168677i
$713$			17.8914i			0.670038i
$714$	−6.80964	+	0.284895i	−0.254844	+	0.0106619i
$715$		0			0
$716$	−3.66589	−	43.7348i	−0.137001	−	1.63445i
$717$	−21.0737			−0.787011
$718$	−2.84887	+	0.119188i	−0.106319	+	0.00444807i
$719$	4.17909			0.155854			0.0779269	−	0.996959i	$-0.475170\pi$
$719$	4.17909			0.155854			0.0779269	+	0.996959i	$0.475170\pi$
$720$		0			0
$721$	14.3380			0.533975
$722$	13.7422	−	0.574933i	0.511431	−	0.0213968i
$723$	6.10852			0.227178
$724$	0.322452	+	3.84692i	0.0119838	+	0.142970i
$725$		0			0
$726$	3.29475	−	0.137843i	0.122280	−	0.00511582i
$727$			26.7727i			0.992943i	0.868053	+	0.496471i	$0.165371\pi$
$727$			26.7727i			0.992943i	−0.868053	+	0.496471i	$0.834629\pi$
$728$	−0.963936	−	7.64421i	−0.0357258	−	0.283313i
$729$	1.00000			0.0370370
$730$		0			0
$731$			30.7083i			1.13579i
$732$	−1.42244	−	16.9700i	−0.0525749	−	0.627229i
$733$	−21.3364			−0.788080			−0.394040	−	0.919093i	$-0.628923\pi$
$733$	−21.3364			−0.788080			−0.394040	+	0.919093i	$0.628923\pi$
$734$	0.792914	+	18.9524i	0.0292670	+	0.699547i
$735$		0			0
$736$	10.0922	+	47.5680i	0.372003	+	1.75338i
$737$		−	31.4912i		−	1.15999i
$738$	−9.93021	+	0.415451i	−0.365536	+	0.0152930i
$739$		−	13.1038i		−	0.482033i	−0.970521	−	0.241016i	$-0.922519\pi$
$739$		−	13.1038i		−	0.482033i	0.970521	−	0.241016i	$-0.0774807\pi$
$740$		0			0
$741$		−	10.9435i		−	0.402020i
$742$	−0.482909	−	11.5426i	−0.0177282	−	0.423743i
$743$			33.3595i			1.22384i	0.790919	+	0.611921i	$0.209603\pi$
$743$			33.3595i			1.22384i	−0.790919	+	0.611921i	$0.790397\pi$
$744$	−5.84066	+	0.736508i	−0.214129	+	0.0270017i
$745$		0			0
$746$	14.2676	−	0.596915i	0.522375	−	0.0218546i
$747$	−1.52708			−0.0558730
$748$	21.1969	−	1.77674i	0.775034	−	0.0649640i
$749$		−	6.49069i		−	0.237165i
$750$		0			0
$751$	−1.92100			−0.0700981			−0.0350491	−	0.999386i	$-0.511159\pi$
$751$	−1.92100			−0.0700981			−0.0350491	+	0.999386i	$0.511159\pi$
$752$	6.64027	+	39.3316i	0.242146	+	1.43428i
$753$		−	22.5286i		−	0.820989i
$754$	−0.635418	−	15.1879i	−0.0231406	−	0.553112i
$755$		0			0
$756$	−0.222871	−	2.65890i	−0.00810575	−	0.0967032i
$757$	13.9908			0.508504			0.254252	−	0.967138i	$-0.418171\pi$
$757$	13.9908			0.508504			0.254252	+	0.967138i	$0.418171\pi$
$758$	−1.08047	−	25.8257i	−0.0392445	−	0.938032i
$759$	25.3085			0.918640
$760$		0			0
$761$	25.6618			0.930240			0.465120	−	0.885248i	$-0.346011\pi$
$761$	25.6618			0.930240			0.465120	+	0.885248i	$0.346011\pi$
$762$	−0.517367	−	12.3662i	−0.0187422	−	0.447981i
$763$	20.6217			0.746557
$764$	24.1616	−	2.02525i	0.874137	−	0.0732709i
$765$		0			0
$766$	−0.695985	−	16.6356i	−0.0251469	−	0.601069i
$767$			9.70260i			0.350341i
$768$	−15.1132	+	5.25277i	−0.545350	+	0.189543i
$769$	12.3922			0.446873			0.223436	−	0.974719i	$-0.428272\pi$
$769$	12.3922			0.446873			0.223436	+	0.974719i	$0.428272\pi$
$770$		0			0
$771$		−	14.5286i		−	0.523236i
$772$	0.212881	+	2.53971i	0.00766174	+	0.0914062i
$773$	−38.4843			−1.38418			−0.692091	−	0.721810i	$-0.743311\pi$
$773$	−38.4843			−1.38418			−0.692091	+	0.721810i	$0.743311\pi$
$774$	−12.0114	+	0.502522i	−0.431741	+	0.0180628i
$775$		0			0
$776$	4.75767	+	37.7293i	0.170790	+	1.35440i
$777$		−	8.74723i		−	0.313805i
$778$	−1.97603	−	47.2316i	−0.0708442	−	1.69333i
$779$			37.6668i			1.34955i
$780$		0			0
$781$			7.72569i			0.276447i
$782$	−43.8766	+	1.83567i	−1.56903	+	0.0656434i
$783$		−	5.26432i		−	0.188131i
$784$	20.5892	−	3.47603i	0.735329	−	0.124144i
$785$		0			0
$786$	0.0278588	+	0.665888i	0.000993691	+	0.0237514i
$787$	0.389147			0.0138716			0.00693579	−	0.999976i	$-0.497792\pi$
$787$	0.389147			0.0138716			0.00693579	+	0.999976i	$0.497792\pi$
$788$	−6.59386	+	0.552703i	−0.234896	+	0.0196892i
$789$			5.29694i			0.188576i
$790$		0			0
$791$	−13.1922			−0.469060
$792$	1.04184	+	8.26198i	0.0370201	+	0.293577i
$793$			17.3857i			0.617386i
$794$	55.1674	−	2.30804i	1.95782	−	0.0819094i
$795$		0			0
$796$	−17.9913	+	1.50804i	−0.637683	+	0.0534512i
$797$	−0.854188			−0.0302569			−0.0151284	−	0.999886i	$-0.504816\pi$
$797$	−0.854188			−0.0302569			−0.0151284	+	0.999886i	$0.504816\pi$
$798$	−10.1033	+	0.422692i	−0.357652	+	0.0149631i
$799$	−36.0231			−1.27441
$800$		0			0
$801$	12.7193			0.449413
$802$	34.7790	−	1.45505i	1.22809	−	0.0513796i
$803$	45.3036			1.59873
$804$	−21.3174	+	1.78684i	−0.751807	+	0.0630171i
$805$		0			0
$806$	6.00481	−	0.251224i	0.211510	−	0.00884897i
$807$			27.0737i			0.953039i
$808$	3.58221	+	28.4077i	0.126022	+	0.999379i
$809$	10.4107			0.366020			0.183010	−	0.983111i	$-0.441416\pi$
$809$	10.4107			0.366020			0.183010	+	0.983111i	$0.441416\pi$
$810$		0			0
$811$			6.08825i			0.213787i	0.994270	+	0.106894i	$0.0340904\pi$
$811$			6.08825i			0.213787i	−0.994270	+	0.106894i	$0.965910\pi$
$812$	−13.9973	+	1.17326i	−0.491209	+	0.0411735i
$813$	−15.8604			−0.556249
$814$	1.14114	+	27.2759i	0.0399970	+	0.956019i
$815$		0			0
$816$	−2.40546	−	14.2480i	−0.0842080	−	0.498780i
$817$			45.5611i			1.59398i
$818$	−20.4916	+	0.857309i	−0.716472	+	0.0299751i
$819$			2.72404i			0.0951856i
$820$		0			0
$821$		−	35.3908i		−	1.23515i	−0.786513	−	0.617574i	$-0.788116\pi$
$821$		−	35.3908i		−	1.23515i	0.786513	−	0.617574i	$-0.211884\pi$
$822$	0.0770751	+	1.84227i	0.00268830	+	0.0642565i
$823$		−	16.2846i		−	0.567646i	−0.958877	−	0.283823i	$-0.908397\pi$
$823$		−	16.2846i		−	0.567646i	0.958877	−	0.283823i	$-0.0916028\pi$
$824$	3.80304	+	30.1589i	0.132485	+	1.05064i
$825$		0			0
$826$	8.95766	−	0.374762i	0.311677	−	0.0130396i
$827$	−32.1362			−1.11748			−0.558742	−	0.829341i	$-0.688716\pi$
$827$	−32.1362			−1.11748			−0.558742	+	0.829341i	$0.688716\pi$
$828$	−1.43603	−	17.1321i	−0.0499054	−	0.595382i
$829$		−	22.4682i		−	0.780355i	−0.920740	−	0.390177i	$-0.872414\pi$
$829$		−	22.4682i		−	0.780355i	0.920740	−	0.390177i	$-0.127586\pi$
$830$		0			0
$831$	9.98592			0.346408
$832$	15.8233	−	4.05513i	0.548576	−	0.140586i
$833$			18.8573i			0.653367i
$834$	0.517091	+	12.3596i	0.0179054	+	0.427979i
$835$		0			0
$836$	31.4492	−	2.63610i	1.08769	−	0.0911715i
$837$	2.08134			0.0719416
$838$	−0.747325	−	17.8627i	−0.0258159	−	0.617058i
$839$	16.1358			0.557070			0.278535	−	0.960426i	$-0.410151\pi$
$839$	16.1358			0.557070			0.278535	+	0.960426i	$0.410151\pi$
$840$		0			0
$841$	1.28695			0.0443777
$842$	0.995427	+	23.7930i	0.0343047	+	0.819959i
$843$	−13.4218			−0.462270
$844$	−1.10464	−	13.1786i	−0.0380233	−	0.453626i
$845$		0			0
$846$	−0.589496	−	14.0903i	−0.0202673	−	0.484434i
$847$			3.11085i			0.106890i
$848$	24.1509	−	4.07735i	0.829347	−	0.140017i
$849$	3.83722			0.131693
$850$		0			0
$851$		−	56.3611i		−	1.93203i
$852$	5.22976	−	0.438363i	0.179169	−	0.0150181i
$853$	44.6262			1.52797			0.763986	−	0.645233i	$-0.223240\pi$
$853$	44.6262			1.52797			0.763986	+	0.645233i	$0.223240\pi$
$854$	16.0509	−	0.671523i	0.549251	−	0.0229790i
$855$		0			0
$856$	13.6527	−	1.72161i	0.466639	−	0.0588433i
$857$			4.52553i			0.154589i	0.997008	+	0.0772945i	$0.0246282\pi$
$857$			4.52553i			0.154589i	−0.997008	+	0.0772945i	$0.975372\pi$
$858$	−0.355372	−	8.49418i	−0.0121322	−	0.289986i
$859$		−	42.7783i		−	1.45958i	−0.683673	−	0.729788i	$-0.739619\pi$
$859$		−	42.7783i		−	1.45958i	0.683673	−	0.729788i	$-0.260381\pi$
$860$		0			0
$861$		−	9.37595i		−	0.319531i
$862$	−8.46155	+	0.354006i	−0.288202	+	0.0120575i
$863$		−	23.7734i		−	0.809257i	−0.914481	−	0.404629i	$-0.867401\pi$
$863$		−	23.7734i		−	0.809257i	0.914481	−	0.404629i	$-0.132599\pi$
$864$	5.53368	−	1.17404i	0.188260	−	0.0399418i
$865$		0			0
$866$	−0.131520	−	3.14362i	−0.00446922	−	0.106824i
$867$	−3.95051			−0.134166
$868$	−0.463870	−	5.53407i	−0.0157448	−	0.187839i
$869$			30.7519i			1.04319i
$870$		0			0
$871$	21.8397			0.740009
$872$	5.46976	+	43.3763i	0.185229	+	1.46891i
$873$		−	13.4450i		−	0.455043i
$874$	−65.0986	+	2.72353i	−2.20199	+	0.0921249i
$875$		0			0
$876$	−2.57057	−	30.6674i	−0.0868515	−	1.03616i
$877$	−13.1470			−0.443944			−0.221972	−	0.975053i	$-0.571249\pi$
$877$	−13.1470			−0.443944			−0.221972	+	0.975053i	$0.571249\pi$
$878$	−3.25635	+	0.136236i	−0.109896	+	0.00459774i
$879$	−26.4450			−0.891966
$880$		0			0
$881$	38.9132			1.31102			0.655510	−	0.755187i	$-0.272454\pi$
$881$	38.9132			1.31102			0.655510	+	0.755187i	$0.272454\pi$
$882$	−7.37595	+	0.308588i	−0.248361	+	0.0103907i
$883$	−44.5843			−1.50038			−0.750190	−	0.661223i	$-0.770038\pi$
$883$	−44.5843			−1.50038			−0.750190	+	0.661223i	$0.770038\pi$
$884$	1.23220	+	14.7003i	0.0414432	+	0.494426i
$885$		0			0
$886$	−31.2759	+	1.30849i	−1.05073	+	0.0439596i
$887$		−	32.3240i		−	1.08533i	−0.839948	−	0.542667i	$-0.817415\pi$
$887$		−	32.3240i		−	1.08533i	0.839948	−	0.542667i	$-0.182585\pi$
$888$	18.3991	−	2.32013i	0.617435	−	0.0778586i
$889$	11.6760			0.391601
$890$		0			0
$891$		−	2.94418i		−	0.0986339i
$892$	−0.139197	−	1.66065i	−0.00466066	−	0.0556027i
$893$	−53.4465			−1.78852
$894$	0.895066	+	21.3941i	0.0299355	+	0.715526i
$895$		0			0
$896$	−4.35497	−	14.4518i	−0.145489	−	0.482802i
$897$			17.5518i			0.586038i
$898$	30.5007	−	1.27606i	1.01782	−	0.0425826i
$899$		−	10.9568i		−	0.365431i
$900$		0			0
$901$			22.1194i			0.736904i
$902$	1.22316	+	29.2364i	0.0407269	+	0.973464i
$903$		−	11.3410i		−	0.377404i
$904$	−3.49912	−	27.7488i	−0.116379	−	0.922911i
$905$		0			0
$906$	−32.8916	+	1.37609i	−1.09275	+	0.0457174i
$907$	−14.8309			−0.492452			−0.246226	−	0.969212i	$-0.579191\pi$
$907$	−14.8309			−0.492452			−0.246226	+	0.969212i	$0.579191\pi$
$908$	−21.9229	+	1.83760i	−0.727538	+	0.0609828i
$909$		−	10.1232i		−	0.335765i
$910$		0			0
$911$	11.6108			0.384681			0.192341	−	0.981328i	$-0.438392\pi$
$911$	11.6108			0.384681			0.192341	+	0.981328i	$0.438392\pi$
$912$	−3.56892	−	21.1394i	−0.118179	−	0.699995i
$913$			4.49601i			0.148796i
$914$	0.147839	+	3.53368i	0.00489007	+	0.116884i
$915$		0			0
$916$	−2.54026	−	30.3059i	−0.0839327	−	1.00133i
$917$	−0.628722			−0.0207622
$918$	0.213547	+	5.10425i	0.00704810	+	0.168465i
$919$	58.2518			1.92155			0.960775	−	0.277330i	$-0.0894495\pi$
$919$	58.2518			1.92155			0.960775	+	0.277330i	$0.0894495\pi$
$920$		0			0
$921$	−1.27596			−0.0420444
$922$	0.153468	+	3.66822i	0.00505419	+	0.120807i
$923$	−5.35789			−0.176357
$924$	−7.82829	+	0.656174i	−0.257532	+	0.0215865i
$925$		0			0
$926$	−1.64696	−	39.3661i	−0.0541226	−	1.29365i
$927$		−	10.7472i		−	0.352985i
$928$	−6.18055	−	29.1311i	−0.202886	−	0.956274i
$929$	−18.4433			−0.605105			−0.302553	−	0.953133i	$-0.597839\pi$
$929$	−18.4433			−0.605105			−0.302553	+	0.953133i	$0.597839\pi$
$930$		0			0
$931$			27.9781i			0.916944i
$932$	−0.413620	−	4.93457i	−0.0135486	−	0.161637i
$933$	−2.44496			−0.0800445
$934$	8.12744	−	0.340028i	0.265938	−	0.0111261i
$935$		0			0
$936$	−5.72981	+	0.722530i	−0.187285	+	0.0236166i
$937$		−	16.1005i		−	0.525982i	−0.964798	−	0.262991i	$-0.915291\pi$
$937$		−	16.1005i		−	0.525982i	0.964798	−	0.262991i	$-0.0847089\pi$
$938$	−0.843555	−	20.1629i	−0.0275430	−	0.658341i
$939$			22.8325i			0.745109i
$940$		0			0
$941$			32.0974i			1.04635i	0.852226	+	0.523173i	$0.175252\pi$
$941$			32.0974i			1.04635i	−0.852226	+	0.523173i	$0.824748\pi$
$942$	−30.9408	+	1.29447i	−1.00811	+	0.0421762i
$943$		−	60.4121i		−	1.96729i
$944$	3.16423	+	18.7424i	0.102987	+	0.610012i
$945$		0			0
$946$	1.47952	+	35.3638i	0.0481033	+	1.14978i
$947$	4.10998			0.133556			0.0667782	−	0.997768i	$-0.478728\pi$
$947$	4.10998			0.133556			0.0667782	+	0.997768i	$0.478728\pi$
$948$	20.8169	−	1.74489i	0.676102	−	0.0566715i
$949$			31.4188i			1.01990i
$950$		0			0
$951$	2.11163			0.0684743
$952$	13.5241	−	1.70539i	0.438318	−	0.0552720i
$953$			31.7208i			1.02754i	0.857928	+	0.513769i	$0.171751\pi$
$953$			31.7208i			1.02754i	−0.857928	+	0.513769i	$0.828249\pi$
$954$	−8.65191	+	0.361971i	−0.280116	+	0.0117192i
$955$		0			0
$956$	42.0001	−	3.52048i	1.35838	−	0.113861i
$957$	−15.4991			−0.501016
$958$	−17.7290	+	0.741729i	−0.572798	+	0.0239642i
$959$	−1.73944			−0.0561695
$960$		0			0
$961$	−26.6680			−0.860259
$962$	−18.9162	+	0.791399i	−0.609884	+	0.0255157i
$963$	−4.86518			−0.156778
$964$	−12.1743	+	1.02046i	−0.392109	+	0.0328669i
$965$		0			0
$966$	16.2042	−	0.677938i	0.521363	−	0.0218123i
$967$			26.9936i			0.868055i	0.900900	+	0.434027i	$0.142908\pi$
$967$			26.9936i			0.868055i	−0.900900	+	0.434027i	$0.857092\pi$
$968$	−6.54344	+	0.825129i	−0.210314	+	0.0265206i
$969$	19.3612			0.621971
$970$		0			0
$971$		−	14.0559i		−	0.451076i	−0.974234	−	0.225538i	$-0.927586\pi$
$971$		−	14.0559i		−	0.451076i	0.974234	−	0.225538i	$-0.0724139\pi$
$972$	−1.99301	+	0.167056i	−0.0639259	+	0.00535832i
$973$	−11.6698			−0.374116
$974$	0.508701	+	12.1591i	0.0162998	+	0.389603i
$975$		0			0
$976$	5.66988	+	33.5838i	0.181488	+	1.07499i
$977$		−	1.14251i		−	0.0365520i	−0.999833	−	0.0182760i	$-0.994182\pi$
$977$		−	1.14251i		−	0.0365520i	0.999833	−	0.0182760i	$-0.00581776\pi$
$978$	15.7749	−	0.659978i	0.504427	−	0.0211038i
$979$		−	37.4479i		−	1.19684i
$980$		0			0
$981$		−	15.4573i		−	0.493513i
$982$	2.18055	+	52.1200i	0.0695840	+	1.66321i
$983$			6.41720i			0.204677i	0.994750	+	0.102338i	$0.0326325\pi$
$983$			6.41720i			0.204677i	−0.994750	+	0.102338i	$0.967368\pi$
$984$	19.7216	−	2.48690i	0.628702	−	0.0792794i
$985$		0			0
$986$	26.8704	−	1.12418i	0.855728	−	0.0358011i
$987$	13.3038			0.423465
$988$	1.82818	+	21.8105i	0.0581620	+	0.693885i
$989$		−	73.0735i		−	2.32360i
$990$		0			0
$991$	−7.39470			−0.234900			−0.117450	−	0.993079i	$-0.537472\pi$
$991$	−7.39470			−0.234900			−0.117450	+	0.993079i	$0.537472\pi$
$992$	11.5175	−	2.44359i	0.365680	−	0.0775839i
$993$			23.2248i			0.737017i
$994$	0.206948	+	4.94652i	0.00656399	+	0.156894i
$995$		0			0
$996$	3.04349	−	0.255108i	0.0964367	−	0.00808340i
$997$	−31.6649			−1.00284			−0.501419	−	0.865205i	$-0.667188\pi$
$997$	−31.6649			−1.00284			−0.501419	+	0.865205i	$0.667188\pi$
$998$	−2.14289	−	51.2198i	−0.0678319	−	1.62133i
$999$	−6.55659			−0.207441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.d.g.349.2		8
3.2	odd	2		1800.2.d.t.1549.7		8
4.3	odd	2		2400.2.d.h.49.3		8
5.2	odd	4		600.2.k.e.301.3	yes	8
5.3	odd	4		600.2.k.d.301.6	yes	8
5.4	even	2		600.2.d.h.349.7		8
8.3	odd	2		2400.2.d.g.49.3		8
8.5	even	2		600.2.d.h.349.8		8
12.11	even	2		7200.2.d.t.2449.3		8
15.2	even	4		1800.2.k.q.901.6		8
15.8	even	4		1800.2.k.t.901.3		8
15.14	odd	2		1800.2.d.s.1549.2		8
20.3	even	4		2400.2.k.d.1201.6		8
20.7	even	4		2400.2.k.e.1201.3		8
20.19	odd	2		2400.2.d.g.49.6		8
24.5	odd	2		1800.2.d.s.1549.1		8
24.11	even	2		7200.2.d.s.2449.3		8
40.3	even	4		2400.2.k.d.1201.2		8
40.13	odd	4		600.2.k.d.301.5	✓	8
40.19	odd	2		2400.2.d.h.49.6		8
40.27	even	4		2400.2.k.e.1201.7		8
40.29	even	2	inner	600.2.d.g.349.1		8
40.37	odd	4		600.2.k.e.301.4	yes	8
60.23	odd	4		7200.2.k.r.3601.3		8
60.47	odd	4		7200.2.k.s.3601.5		8
60.59	even	2		7200.2.d.s.2449.6		8
120.29	odd	2		1800.2.d.t.1549.8		8
120.53	even	4		1800.2.k.t.901.4		8
120.59	even	2		7200.2.d.t.2449.6		8
120.77	even	4		1800.2.k.q.901.5		8
120.83	odd	4		7200.2.k.r.3601.4		8
120.107	odd	4		7200.2.k.s.3601.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.d.g.349.1		8	40.29	even	2	inner
600.2.d.g.349.2		8	1.1	even	1	trivial
600.2.d.h.349.7		8	5.4	even	2
600.2.d.h.349.8		8	8.5	even	2
600.2.k.d.301.5	✓	8	40.13	odd	4
600.2.k.d.301.6	yes	8	5.3	odd	4
600.2.k.e.301.3	yes	8	5.2	odd	4
600.2.k.e.301.4	yes	8	40.37	odd	4
1800.2.d.s.1549.1		8	24.5	odd	2
1800.2.d.s.1549.2		8	15.14	odd	2
1800.2.d.t.1549.7		8	3.2	odd	2
1800.2.d.t.1549.8		8	120.29	odd	2
1800.2.k.q.901.5		8	120.77	even	4
1800.2.k.q.901.6		8	15.2	even	4
1800.2.k.t.901.3		8	15.8	even	4
1800.2.k.t.901.4		8	120.53	even	4
2400.2.d.g.49.3		8	8.3	odd	2
2400.2.d.g.49.6		8	20.19	odd	2
2400.2.d.h.49.3		8	4.3	odd	2
2400.2.d.h.49.6		8	40.19	odd	2
2400.2.k.d.1201.2		8	40.3	even	4
2400.2.k.d.1201.6		8	20.3	even	4
2400.2.k.e.1201.3		8	20.7	even	4
2400.2.k.e.1201.7		8	40.27	even	4
7200.2.d.s.2449.3		8	24.11	even	2
7200.2.d.s.2449.6		8	60.59	even	2
7200.2.d.t.2449.3		8	12.11	even	2
7200.2.d.t.2449.6		8	120.59	even	2
7200.2.k.r.3601.3		8	60.23	odd	4
7200.2.k.r.3601.4		8	120.83	odd	4
7200.2.k.s.3601.5		8	60.47	odd	4
7200.2.k.s.3601.6		8	120.107	odd	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41298 + 0.0591148i) q^{2} -1.00000 q^{3} +(1.99301 - 0.167056i) q^{4} +(1.41298 - 0.0591148i) q^{6} +1.33411i q^{7} +(-2.80620 + 0.353863i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.41298 + 0.0591148i) q^{2} -1.00000 q^{3} +(1.99301 - 0.167056i) q^{4} +(1.41298 - 0.0591148i) q^{6} +1.33411i q^{7} +(-2.80620 + 0.353863i) q^{8} +1.00000 q^{9} -2.94418i q^{11} +(-1.99301 + 0.167056i) q^{12} +2.04184 q^{13} +(-0.0788658 - 1.88507i) q^{14} +(3.94418 - 0.665888i) q^{16} +3.61241i q^{17} +(-1.41298 + 0.0591148i) q^{18} +5.35964i q^{19} -1.33411i q^{21} +(0.174045 + 4.16007i) q^{22} -8.59609i q^{23} +(2.80620 - 0.353863i) q^{24} +(-2.88507 + 0.120703i) q^{26} -1.00000 q^{27} +(0.222871 + 2.65890i) q^{28} +5.26432i q^{29} -2.08134 q^{31} +(-5.53368 + 1.17404i) q^{32} +2.94418i q^{33} +(-0.213547 - 5.10425i) q^{34} +(1.99301 - 0.167056i) q^{36} +6.55659 q^{37} +(-0.316834 - 7.57304i) q^{38} -2.04184 q^{39} +7.02786 q^{41} +(0.0788658 + 1.88507i) q^{42} +8.50078 q^{43} +(-0.491843 - 5.86779i) q^{44} +(0.508157 + 12.1461i) q^{46} +9.97204i q^{47} +(-3.94418 + 0.665888i) q^{48} +5.22015 q^{49} -3.61241i q^{51} +(4.06940 - 0.341101i) q^{52} +6.12318 q^{53} +(1.41298 - 0.0591148i) q^{54} +(-0.472092 - 3.74379i) q^{56} -5.35964i q^{57} +(-0.311199 - 7.43836i) q^{58} +4.75190i q^{59} +8.51476i q^{61} +(2.94089 - 0.123038i) q^{62} +1.33411i q^{63} +(7.74956 - 1.98602i) q^{64} +(-0.174045 - 4.16007i) q^{66} +10.6961 q^{67} +(0.603474 + 7.19957i) q^{68} +8.59609i q^{69} -2.62405 q^{71} +(-2.80620 + 0.353863i) q^{72} +15.3875i q^{73} +(-9.26432 + 0.387592i) q^{74} +(0.895358 + 10.6818i) q^{76} +3.92787 q^{77} +(2.88507 - 0.120703i) q^{78} -10.4450 q^{79} +1.00000 q^{81} +(-9.93021 + 0.415451i) q^{82} -1.52708 q^{83} +(-0.222871 - 2.65890i) q^{84} +(-12.0114 + 0.502522i) q^{86} -5.26432i q^{87} +(1.04184 + 8.26198i) q^{88} +12.7193 q^{89} +2.72404i q^{91} +(-1.43603 - 17.1321i) q^{92} +2.08134 q^{93} +(-0.589496 - 14.0903i) q^{94} +(5.53368 - 1.17404i) q^{96} -13.4450i q^{97} +(-7.37595 + 0.308588i) q^{98} -2.94418i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9} + 4 q^{12} + 6 q^{14} + 8 q^{16} - 2 q^{18} + 20 q^{22} + 8 q^{24} - 2 q^{26} - 8 q^{27} + 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} - 4 q^{36} + 14 q^{38} - 6 q^{42} - 8 q^{43} + 12 q^{44} + 20 q^{46} - 8 q^{48} + 24 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{56} - 20 q^{58} + 26 q^{62} + 32 q^{64} - 20 q^{66} + 24 q^{67} + 36 q^{68} - 40 q^{71} - 8 q^{72} - 8 q^{74} - 20 q^{76} - 24 q^{77} + 2 q^{78} + 16 q^{79} + 8 q^{81} - 16 q^{82} - 32 q^{83} - 24 q^{84} - 18 q^{86} - 8 q^{88} + 28 q^{92} - 8 q^{93} + 4 q^{94} + 12 q^{96} - 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9 + 4 * q^12 + 6 * q^14 + 8 * q^16 - 2 * q^18 + 20 * q^22 + 8 * q^24 - 2 * q^26 - 8 * q^27 + 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 - 4 * q^36 + 14 * q^38 - 6 * q^42 - 8 * q^43 + 12 * q^44 + 20 * q^46 - 8 * q^48 + 24 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^56 - 20 * q^58 + 26 * q^62 + 32 * q^64 - 20 * q^66 + 24 * q^67 + 36 * q^68 - 40 * q^71 - 8 * q^72 - 8 * q^74 - 20 * q^76 - 24 * q^77 + 2 * q^78 + 16 * q^79 + 8 * q^81 - 16 * q^82 - 32 * q^83 - 24 * q^84 - 18 * q^86 - 8 * q^88 + 28 * q^92 - 8 * q^93 + 4 * q^94 + 12 * q^96 - 40 * q^98

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