LMFDB - Embedded newform 600.2.k.e.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(301,600)]

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, 0]))

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

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

chi := DirichletCharacter("600.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.k (of order $2$, degree $1$, 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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			301.3
Root			$-1.08003 + 0.912978i$ of defining polynomial
Character	$\chi$	$=$	600.301
Dual form			600.2.k.e.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0591148 - 1.41298i) q^{2} +1.00000i q^{3} +(-1.99301 + 0.167056i) q^{4} +(1.41298 - 0.0591148i) q^{6} -1.33411 q^{7} +(0.353863 + 2.80620i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.0591148 - 1.41298i) q^{2} +1.00000i q^{3} +(-1.99301 + 0.167056i) q^{4} +(1.41298 - 0.0591148i) q^{6} -1.33411 q^{7} +(0.353863 + 2.80620i) q^{8} -1.00000 q^{9} -2.94418i q^{11} +(-0.167056 - 1.99301i) q^{12} -2.04184i q^{13} +(0.0788658 + 1.88507i) q^{14} +(3.94418 - 0.665888i) q^{16} -3.61241 q^{17} +(0.0591148 + 1.41298i) q^{18} -5.35964i q^{19} -1.33411i q^{21} +(-4.16007 + 0.174045i) q^{22} -8.59609 q^{23} +(-2.80620 + 0.353863i) q^{24} +(-2.88507 + 0.120703i) q^{26} -1.00000i q^{27} +(2.65890 - 0.222871i) q^{28} -5.26432i q^{29} -2.08134 q^{31} +(-1.17404 - 5.53368i) q^{32} +2.94418 q^{33} +(0.213547 + 5.10425i) q^{34} +(1.99301 - 0.167056i) q^{36} +6.55659i q^{37} +(-7.57304 + 0.316834i) q^{38} +2.04184 q^{39} +7.02786 q^{41} +(-1.88507 + 0.0788658i) q^{42} -8.50078i q^{43} +(0.491843 + 5.86779i) q^{44} +(0.508157 + 12.1461i) q^{46} -9.97204 q^{47} +(0.665888 + 3.94418i) q^{48} -5.22015 q^{49} -3.61241i q^{51} +(0.341101 + 4.06940i) q^{52} -6.12318i q^{53} +(-1.41298 + 0.0591148i) q^{54} +(-0.472092 - 3.74379i) q^{56} +5.35964 q^{57} +(-7.43836 + 0.311199i) q^{58} -4.75190i q^{59} +8.51476i q^{61} +(0.123038 + 2.94089i) q^{62} +1.33411 q^{63} +(-7.74956 + 1.98602i) q^{64} +(-0.174045 - 4.16007i) q^{66} +10.6961i q^{67} +(7.19957 - 0.603474i) q^{68} -8.59609i q^{69} -2.62405 q^{71} +(-0.353863 - 2.80620i) q^{72} +15.3875 q^{73} +(9.26432 - 0.387592i) q^{74} +(0.895358 + 10.6818i) q^{76} +3.92787i q^{77} +(-0.120703 - 2.88507i) q^{78} +10.4450 q^{79} +1.00000 q^{81} +(-0.415451 - 9.93021i) q^{82} +1.52708i q^{83} +(0.222871 + 2.65890i) q^{84} +(-12.0114 + 0.502522i) q^{86} +5.26432 q^{87} +(8.26198 - 1.04184i) q^{88} -12.7193 q^{89} +2.72404i q^{91} +(17.1321 - 1.43603i) q^{92} -2.08134i q^{93} +(0.589496 + 14.0903i) q^{94} +(5.53368 - 1.17404i) q^{96} +13.4450 q^{97} +(0.308588 + 7.37595i) q^{98} +2.94418i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9	$ 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} - 2 q^{18} - 12 q^{22} - 8 q^{23} - 8 q^{24} - 2 q^{26} + 4 q^{28} + 8 q^{31} - 28 q^{32} + 12 q^{34} - 4 q^{36} - 30 q^{38} + 6 q^{42} - 12 q^{44} + 20 q^{46} + 8 q^{48} + 20 q^{52} - 2 q^{54} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 30 q^{62} + 8 q^{63} - 32 q^{64} - 20 q^{66} + 28 q^{68} - 40 q^{71} + 4 q^{72} + 16 q^{73} + 8 q^{74} - 20 q^{76} + 22 q^{78} - 16 q^{79} + 8 q^{81} + 24 q^{82} + 24 q^{84} - 18 q^{86} - 24 q^{87} + 8 q^{88} + 36 q^{92} - 4 q^{94} + 12 q^{96} + 8 q^{97} + 48 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 6 * q^14 + 8 * q^16 - 2 * q^18 - 12 * q^22 - 8 * q^23 - 8 * q^24 - 2 * q^26 + 4 * q^28 + 8 * q^31 - 28 * q^32 + 12 * q^34 - 4 * q^36 - 30 * q^38 + 6 * q^42 - 12 * q^44 + 20 * q^46 + 8 * q^48 + 20 * q^52 - 2 * q^54 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 30 * q^62 + 8 * q^63 - 32 * q^64 - 20 * q^66 + 28 * q^68 - 40 * q^71 + 4 * q^72 + 16 * q^73 + 8 * q^74 - 20 * q^76 + 22 * q^78 - 16 * q^79 + 8 * q^81 + 24 * q^82 + 24 * q^84 - 18 * q^86 - 24 * q^87 + 8 * q^88 + 36 * q^92 - 4 * q^94 + 12 * q^96 + 8 * q^97 + 48 * 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 $

$2$	−0.0591148	−	1.41298i	−0.0418005	−	0.999126i
$2$	−0.0591148	−	1.41298i	−0.0418005	−	0.999126i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.99301	+	0.167056i	−0.996505	+	0.0835279i
$5$		0			0
$5$		0			0
$6$	1.41298	−	0.0591148i	0.576846	−	0.0241335i
$7$	−1.33411			−0.504247			−0.252123	−	0.967695i	$-0.581129\pi$
$7$	−1.33411			−0.504247			−0.252123	+	0.967695i	$0.581129\pi$
$8$	0.353863	+	2.80620i	0.125109	+	0.992143i
$9$	−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	$-0.146389\pi$
$12$	−0.167056	−	1.99301i	−0.0482249	−	0.575333i
$13$		−	2.04184i		−	0.566304i	−0.959075	−	0.283152i	$-0.908620\pi$
$13$		−	2.04184i		−	0.566304i	0.959075	−	0.283152i	$-0.0913800\pi$
$14$	0.0788658	+	1.88507i	0.0210778	+	0.503806i
$15$		0			0
$16$	3.94418	−	0.665888i	0.986046	−	0.166472i
$17$	−3.61241			−0.876138			−0.438069	−	0.898941i	$-0.644337\pi$
$17$	−3.61241			−0.876138			−0.438069	+	0.898941i	$0.644337\pi$
$18$	0.0591148	+	1.41298i	0.0139335	+	0.333042i
$19$		−	5.35964i		−	1.22958i	−0.788689	−	0.614792i	$-0.789240\pi$
$19$		−	5.35964i		−	1.22958i	0.788689	−	0.614792i	$-0.210760\pi$
$20$		0			0
$21$		−	1.33411i		−	0.291127i
$22$	−4.16007	+	0.174045i	−0.886929	+	0.0371065i
$23$	−8.59609			−1.79241			−0.896205	−	0.443641i	$-0.853687\pi$
$23$	−8.59609			−1.79241			−0.896205	+	0.443641i	$0.853687\pi$
$24$	−2.80620	+	0.353863i	−0.572814	+	0.0722319i
$25$		0			0
$26$	−2.88507	+	0.120703i	−0.565809	+	0.0236718i
$27$		−	1.00000i		−	0.192450i
$28$	2.65890	−	0.222871i	0.502485	−	0.0421187i
$29$		−	5.26432i		−	0.977559i	−0.872407	−	0.488780i	$-0.837442\pi$
$29$		−	5.26432i		−	0.977559i	0.872407	−	0.488780i	$-0.162558\pi$
$30$		0			0
$31$	−2.08134			−0.373820			−0.186910	−	0.982377i	$-0.559847\pi$
$31$	−2.08134			−0.373820			−0.186910	+	0.982377i	$0.559847\pi$
$32$	−1.17404	−	5.53368i	−0.207544	−	0.978226i
$33$	2.94418			0.512517
$34$	0.213547	+	5.10425i	0.0366230	+	0.875372i
$35$		0			0
$36$	1.99301	−	0.167056i	0.332168	−	0.0278426i
$37$			6.55659i			1.07790i	0.842339	+	0.538949i	$0.181178\pi$
$37$			6.55659i			1.07790i	−0.842339	+	0.538949i	$0.818822\pi$
$38$	−7.57304	+	0.316834i	−1.22851	+	0.0513973i
$39$	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	$0.315091\pi$
$42$	−1.88507	+	0.0788658i	−0.290873	+	0.0121693i
$43$		−	8.50078i		−	1.29636i	−0.761489	−	0.648178i	$-0.775531\pi$
$43$		−	8.50078i		−	1.29636i	0.761489	−	0.648178i	$-0.224469\pi$
$44$	0.491843	+	5.86779i	0.0741482	+	0.884603i
$45$		0			0
$46$	0.508157	+	12.1461i	0.0749236	+	1.79084i
$47$	−9.97204			−1.45457			−0.727286	−	0.686334i	$-0.759219\pi$
$47$	−9.97204			−1.45457			−0.727286	+	0.686334i	$0.759219\pi$
$48$	0.665888	+	3.94418i	0.0961127	+	0.569294i
$49$	−5.22015			−0.745735
$50$		0			0
$51$		−	3.61241i		−	0.505838i
$52$	0.341101	+	4.06940i	0.0473022	+	0.564325i
$53$		−	6.12318i		−	0.841083i	−0.907273	−	0.420541i	$-0.861840\pi$
$53$		−	6.12318i		−	0.841083i	0.907273	−	0.420541i	$-0.138160\pi$
$54$	−1.41298	+	0.0591148i	−0.192282	+	0.00804451i
$55$		0			0
$56$	−0.472092	−	3.74379i	−0.0630860	−	0.500285i
$57$	5.35964			0.709901
$58$	−7.43836	+	0.311199i	−0.976705	+	0.0408625i
$59$		−	4.75190i		−	0.618644i	−0.950957	−	0.309322i	$-0.899898\pi$
$59$		−	4.75190i		−	0.618644i	0.950957	−	0.309322i	$-0.100102\pi$
$60$		0			0
$61$			8.51476i			1.09020i	0.838370	+	0.545101i	$0.183509\pi$
$61$			8.51476i			1.09020i	−0.838370	+	0.545101i	$0.816491\pi$
$62$	0.123038	+	2.94089i	0.0156258	+	0.373493i
$63$	1.33411			0.168082
$64$	−7.74956	+	1.98602i	−0.968695	+	0.248253i
$65$		0			0
$66$	−0.174045	−	4.16007i	−0.0214235	−	0.512069i
$67$			10.6961i			1.30673i	0.757041	+	0.653367i	$0.226644\pi$
$67$			10.6961i			1.30673i	−0.757041	+	0.653367i	$0.773356\pi$
$68$	7.19957	−	0.603474i	0.873076	−	0.0731820i
$69$		−	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	$0.549766\pi$
$72$	−0.353863	−	2.80620i	−0.0417031	−	0.330714i
$73$	15.3875			1.80097			0.900485	−	0.434887i	$-0.143212\pi$
$73$	15.3875			1.80097			0.900485	+	0.434887i	$0.143212\pi$
$74$	9.26432	−	0.387592i	1.07696	−	0.0450566i
$75$		0			0
$76$	0.895358	+	10.6818i	0.102705	+	1.22529i
$77$			3.92787i			0.447622i
$78$	−0.120703	−	2.88507i	−0.0136669	−	0.326670i
$79$	10.4450			1.17515			0.587575	−	0.809170i	$-0.300083\pi$
$79$	10.4450			1.17515			0.587575	+	0.809170i	$0.300083\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−0.415451	−	9.93021i	−0.0458789	−	1.09661i
$83$			1.52708i			0.167619i	0.996482	+	0.0838095i	$0.0267087\pi$
$83$			1.52708i			0.167619i	−0.996482	+	0.0838095i	$0.973291\pi$
$84$	0.222871	+	2.65890i	0.0243172	+	0.290110i
$85$		0			0
$86$	−12.0114	+	0.502522i	−1.29522	+	0.0541883i
$87$	5.26432			0.564394
$88$	8.26198	−	1.04184i	0.880730	−	0.111060i
$89$	−12.7193			−1.34824			−0.674120	−	0.738622i	$-0.735477\pi$
$89$	−12.7193			−1.34824			−0.674120	+	0.738622i	$0.735477\pi$
$90$		0			0
$91$			2.72404i			0.285557i
$92$	17.1321	−	1.43603i	1.78615	−	0.149716i
$93$		−	2.08134i		−	0.215825i
$94$	0.589496	+	14.0903i	0.0608018	+	1.45330i
$95$		0			0
$96$	5.53368	−	1.17404i	0.564779	−	0.119825i
$97$	13.4450			1.36513			0.682565	−	0.730825i	$-0.260865\pi$
$97$	13.4450			1.36513			0.682565	+	0.730825i	$0.260865\pi$
$98$	0.308588	+	7.37595i	0.0311721	+	0.745083i
$99$			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	$-0.168009\pi$
$102$	−5.10425	+	0.213547i	−0.505396	+	0.0211443i
$103$	−10.7472			−1.05896			−0.529478	−	0.848324i	$-0.677612\pi$
$103$	−10.7472			−1.05896			−0.529478	+	0.848324i	$0.677612\pi$
$104$	5.72981	−	0.722530i	0.561854	−	0.0708499i
$105$		0			0
$106$	−8.65191	+	0.361971i	−0.840348	+	0.0351577i
$107$		−	4.86518i		−	0.470335i	−0.971955	−	0.235167i	$-0.924436\pi$
$107$		−	4.86518i		−	0.470335i	0.971955	−	0.235167i	$-0.0755638\pi$
$108$	0.167056	+	1.99301i	0.0160750	+	0.191778i
$109$			15.4573i			1.48054i	0.672310	+	0.740270i	$0.265302\pi$
$109$			15.4573i			1.48054i	−0.672310	+	0.740270i	$0.734698\pi$
$110$		0			0
$111$	−6.55659			−0.622324
$112$	−5.26198	+	0.888369i	−0.497211	+	0.0839430i
$113$	9.88837			0.930220			0.465110	−	0.885253i	$-0.346015\pi$
$113$	9.88837			0.930220			0.465110	+	0.885253i	$0.346015\pi$
$114$	−0.316834	−	7.57304i	−0.0296742	−	0.709281i
$115$		0			0
$116$	0.879435	+	10.4918i	0.0816535	+	0.974143i
$117$			2.04184i			0.188768i
$118$	−6.71432	+	0.280908i	−0.618104	+	0.0258596i
$119$	4.81936			0.441790
$120$		0			0
$121$	2.33178			0.211980
$122$	12.0312	−	0.503348i	1.08925	−	0.0455710i
$123$			7.02786i			0.633681i
$124$	4.14813	−	0.347700i	0.372513	−	0.0312244i
$125$		0			0
$126$	−0.0788658	−	1.88507i	−0.00702592	−	0.167935i
$127$	8.75190			0.776605			0.388303	−	0.921532i	$-0.373062\pi$
$127$	8.75190			0.776605			0.388303	+	0.921532i	$0.373062\pi$
$128$	3.26432	+	10.8326i	0.288528	+	0.957472i
$129$	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	$0.993446\pi$
$132$	−5.86779	+	0.491843i	−0.510726	+	0.0428095i
$133$			7.15035i			0.620014i
$134$	15.1133	−	0.632297i	1.30559	−	0.0546222i
$135$		0			0
$136$	−1.27830	−	10.1372i	−0.109613	−	0.869254i
$137$	−1.30382			−0.111393			−0.0556964	−	0.998448i	$-0.517738\pi$
$137$	−1.30382			−0.111393			−0.0556964	+	0.998448i	$0.517738\pi$
$138$	−12.1461	+	0.508157i	−1.03394	+	0.0432572i
$139$		−	8.74723i		−	0.741930i	−0.928647	−	0.370965i	$-0.879027\pi$
$139$		−	8.74723i		−	0.741930i	0.928647	−	0.370965i	$-0.120973\pi$
$140$		0			0
$141$		−	9.97204i		−	0.839798i
$142$	0.155120	+	3.70773i	0.0130174	+	0.311145i
$143$	−6.01155			−0.502711
$144$	−3.94418	+	0.665888i	−0.328682	+	0.0554907i
$145$		0			0
$146$	−0.909629	−	21.7422i	−0.0752814	−	1.79940i
$147$		−	5.22015i		−	0.430550i
$148$	−1.09532	−	13.0674i	−0.0900345	−	1.07413i
$149$		−	15.1411i		−	1.24041i	−0.784439	−	0.620205i	$-0.787049\pi$
$149$		−	15.1411i		−	1.24041i	0.784439	−	0.620205i	$-0.212951\pi$
$150$		0			0
$151$	−23.2782			−1.89435			−0.947176	−	0.320713i	$-0.896078\pi$
$151$	−23.2782			−1.89435			−0.947176	+	0.320713i	$0.896078\pi$
$152$	15.0402	−	1.89657i	1.21992	−	0.153833i
$153$	3.61241			0.292046
$154$	5.54999	−	0.232195i	0.447231	−	0.0187108i
$155$		0			0
$156$	−4.06940	+	0.341101i	−0.325813	+	0.0273099i
$157$		−	21.8976i		−	1.74762i	−0.486270	−	0.873809i	$-0.661643\pi$
$157$		−	21.8976i		−	1.74762i	0.486270	−	0.873809i	$-0.338357\pi$
$158$	−0.617452	−	14.7585i	−0.0491219	−	1.17412i
$159$	6.12318			0.485599
$160$		0			0
$161$	11.4682			0.903817
$162$	−0.0591148	−	1.41298i	−0.00464450	−	0.111014i
$163$		−	11.1643i		−	0.874458i	−0.899350	−	0.437229i	$-0.855960\pi$
$163$		−	11.1643i		−	0.874458i	0.899350	−	0.437229i	$-0.144040\pi$
$164$	−14.0066	+	1.17404i	−1.09373	+	0.0916775i
$165$		0			0
$166$	2.15773	−	0.0902732i	0.167472	−	0.00700656i
$167$	−10.0952			−0.781192			−0.390596	−	0.920562i	$-0.627731\pi$
$167$	−10.0952			−0.781192			−0.390596	+	0.920562i	$0.627731\pi$
$168$	3.74379	−	0.472092i	0.288840	−	0.0364227i
$169$	8.83090			0.679300
$170$		0			0
$171$			5.35964i			0.409862i
$172$	1.42010	+	16.9421i	0.108282	+	1.29183i
$173$			13.8162i			1.05043i	0.850970	+	0.525215i	$0.176015\pi$
$173$			13.8162i			1.05043i	−0.850970	+	0.525215i	$0.823985\pi$
$174$	−0.311199	−	7.43836i	−0.0235920	−	0.563901i
$175$		0			0
$176$	−1.96050	−	11.6124i	−0.147778	−	0.875318i
$177$	4.75190			0.357174
$178$	0.751898	+	17.9720i	0.0563571	+	1.34706i
$179$			21.9441i			1.64018i	0.572236	+	0.820089i	$0.306076\pi$
$179$			21.9441i			1.64018i	−0.572236	+	0.820089i	$0.693924\pi$
$180$		0			0
$181$			1.93021i			0.143471i	0.997424	+	0.0717356i	$0.0228538\pi$
$181$			1.93021i			0.143471i	−0.997424	+	0.0717356i	$0.977146\pi$
$182$	3.84901	−	0.161031i	0.285307	−	0.0119364i
$183$	−8.51476			−0.629429
$184$	−3.04184	−	24.1224i	−0.224247	−	1.77833i
$185$		0			0
$186$	−2.94089	+	0.123038i	−0.215636	+	0.00902158i
$187$			10.6356i			0.777752i
$188$	19.8744	−	1.66589i	1.44949	−	0.121497i
$189$			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	$0.355474\pi$
$192$	−1.98602	−	7.74956i	−0.143329	−	0.559276i
$193$	1.27431			0.0917267			0.0458634	−	0.998948i	$-0.485396\pi$
$193$	1.27431			0.0917267			0.0458634	+	0.998948i	$0.485396\pi$
$194$	−0.794797	−	18.9974i	−0.0570631	−	1.36394i
$195$		0			0
$196$	10.4038	−	0.872056i	0.743129	−	0.0622897i
$197$		−	3.30849i		−	0.235720i	−0.993030	−	0.117860i	$-0.962397\pi$
$197$		−	3.30849i		−	0.235720i	0.993030	−	0.117860i	$-0.0376034\pi$
$198$	4.16007	−	0.174045i	0.295643	−	0.0123688i
$199$	9.02718			0.639920			0.319960	−	0.947431i	$-0.396331\pi$
$199$	9.02718			0.639920			0.319960	+	0.947431i	$0.396331\pi$
$200$		0			0
$201$	−10.6961			−0.754443
$202$	−14.3038	+	0.598430i	−1.00641	+	0.0421054i
$203$			7.02319i			0.492931i
$204$	0.603474	+	7.19957i	0.0422516	+	0.504071i
$205$		0			0
$206$	0.635321	+	15.1856i	0.0442649	+	1.05803i
$207$	8.59609			0.597470
$208$	−1.35964	−	8.05338i	−0.0942738	−	0.558402i
$209$	−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	$-0.0730906\pi$
$212$	1.02291	+	12.2036i	0.0702539	+	0.838144i
$213$		−	2.62405i		−	0.179797i
$214$	−6.87439	+	0.287604i	−0.469924	+	0.0196602i
$215$		0			0
$216$	2.80620	−	0.353863i	0.190938	−	0.0240773i
$217$	2.77674			0.188497
$218$	21.8408	−	0.913755i	1.47925	−	0.0618873i
$219$			15.3875i			1.03979i
$220$		0			0
$221$			7.37595i			0.496160i
$222$	0.387592	+	9.26432i	0.0260135	+	0.621780i
$223$	−0.833237			−0.0557976			−0.0278988	−	0.999611i	$-0.508882\pi$
$223$	−0.833237			−0.0557976			−0.0278988	+	0.999611i	$0.508882\pi$
$224$	1.56631	+	7.38255i	0.104653	+	0.493267i
$225$		0			0
$226$	−0.584549	−	13.9720i	−0.0388836	−	0.929407i
$227$		−	10.9999i		−	0.730089i	−0.930990	−	0.365045i	$-0.881054\pi$
$227$		−	10.9999i		−	0.730089i	0.930990	−	0.365045i	$-0.118946\pi$
$228$	−10.6818	+	0.895358i	−0.707420	+	0.0592966i
$229$			15.2061i			1.00485i	0.864622	+	0.502423i	$0.167558\pi$
$229$			15.2061i			1.00485i	−0.864622	+	0.502423i	$0.832442\pi$
$230$		0			0
$231$	−3.92787			−0.258435
$232$	14.7728	−	1.86285i	0.969879	−	0.122302i
$233$	−2.47594			−0.162204			−0.0811020	−	0.996706i	$-0.525844\pi$
$233$	−2.47594			−0.162204			−0.0811020	+	0.996706i	$0.525844\pi$
$234$	2.88507	−	0.120703i	0.188603	−	0.00789059i
$235$		0			0
$236$	0.793832	+	9.47058i	0.0516741	+	0.616482i
$237$			10.4450i			0.678473i
$238$	−0.284895	−	6.80964i	−0.0184670	−	0.441404i
$239$	−21.0737			−1.36314			−0.681572	−	0.731751i	$-0.738703\pi$
$239$	−21.0737			−1.36314			−0.681572	+	0.731751i	$0.738703\pi$
$240$		0			0
$241$	−6.10852			−0.393484			−0.196742	−	0.980455i	$-0.563036\pi$
$241$	−6.10852			−0.393484			−0.196742	+	0.980455i	$0.563036\pi$
$242$	−0.137843	−	3.29475i	−0.00886086	−	0.211794i
$243$			1.00000i			0.0641500i
$244$	−1.42244	−	16.9700i	−0.0910624	−	1.08639i
$245$		0			0
$246$	9.93021	−	0.415451i	0.633127	−	0.0264882i
$247$	−10.9435			−0.696318
$248$	−0.736508	−	5.84066i	−0.0467683	−	0.370882i
$249$	−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	$0.748244\pi$
$252$	−2.65890	+	0.222871i	−0.167495	+	0.0140396i
$253$			25.3085i			1.59113i
$254$	−0.517367	−	12.3662i	−0.0324625	−	0.775927i
$255$		0			0
$256$	15.1132	−	5.25277i	0.944574	−	0.328298i
$257$	−14.5286			−0.906271			−0.453136	−	0.891442i	$-0.649695\pi$
$257$	−14.5286			−0.906271			−0.453136	+	0.891442i	$0.649695\pi$
$258$	−0.502522	−	12.0114i	−0.0312857	−	0.747798i
$259$		−	8.74723i		−	0.543526i
$260$		0			0
$261$			5.26432i			0.325853i
$262$	0.665888	−	0.0278588i	0.0411387	−	0.00172112i
$263$	−5.29694			−0.326624			−0.163312	−	0.986575i	$-0.552218\pi$
$263$	−5.29694			−0.326624			−0.163312	+	0.986575i	$0.552218\pi$
$264$	1.04184	+	8.26198i	0.0641206	+	0.508490i
$265$		0			0
$266$	10.1033	−	0.422692i	0.619472	−	0.0259169i
$267$		−	12.7193i		−	0.778407i
$268$	−1.78684	−	21.3174i	−0.109149	−	1.30217i
$269$			27.0737i			1.65071i	0.564613	+	0.825356i	$0.309025\pi$
$269$			27.0737i			1.65071i	−0.564613	+	0.825356i	$0.690975\pi$
$270$		0			0
$271$	15.8604			0.963451			0.481726	−	0.876322i	$-0.340010\pi$
$271$	15.8604			0.963451			0.481726	+	0.876322i	$0.340010\pi$
$272$	−14.2480	+	2.40546i	−0.863912	+	0.145852i
$273$	−2.72404			−0.164866
$274$	0.0770751	+	1.84227i	0.00465628	+	0.111296i
$275$		0			0
$276$	1.43603	+	17.1321i	0.0864387	+	1.03123i
$277$		−	9.98592i		−	0.599996i	−0.953940	−	0.299998i	$-0.903014\pi$
$277$		−	9.98592i		−	0.599996i	0.953940	−	0.299998i	$-0.0969860\pi$
$278$	−12.3596	+	0.517091i	−0.741282	+	0.0310130i
$279$	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	$0.368893\pi$
$282$	−14.0903	+	0.589496i	−0.839064	+	0.0351040i
$283$			3.83722i			0.228099i	0.993475	+	0.114050i	$0.0363823\pi$
$283$			3.83722i			0.228099i	−0.993475	+	0.114050i	$0.963618\pi$
$284$	5.22976	−	0.438363i	0.310329	−	0.0260121i
$285$		0			0
$286$	0.355372	+	8.49418i	0.0210136	+	0.502271i
$287$	−9.37595			−0.553445
$288$	1.17404	+	5.53368i	0.0691813	+	0.326075i
$289$	−3.95051			−0.232383
$290$		0			0
$291$			13.4450i			0.788158i
$292$	−30.6674	+	2.57057i	−1.79468	+	0.150431i
$293$		−	26.4450i		−	1.54493i	−0.635057	−	0.772466i	$-0.719023\pi$
$293$		−	26.4450i		−	1.54493i	0.635057	−	0.772466i	$-0.280977\pi$
$294$	−7.37595	+	0.308588i	−0.430174	+	0.0179972i
$295$		0			0
$296$	−18.3991	+	2.32013i	−1.06943	+	0.134855i
$297$	−2.94418			−0.170839
$298$	−21.3941	+	0.895066i	−1.23933	+	0.0518498i
$299$			17.5518i			1.01505i
$300$		0			0
$301$			11.3410i			0.653684i
$302$	1.37609	+	32.8916i	0.0791849	+	1.89270i
$303$	10.1232			0.581561
$304$	−3.56892	−	21.1394i	−0.204692	−	1.21243i
$305$		0			0
$306$	−0.213547	−	5.10425i	−0.0122077	−	0.291791i
$307$			1.27596i			0.0728230i	0.999337	+	0.0364115i	$0.0115927\pi$
$307$			1.27596i			0.0728230i	−0.999337	+	0.0364115i	$0.988407\pi$
$308$	−0.656174	−	7.82829i	−0.0373890	−	0.446058i
$309$		−	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	$0.477917\pi$
$312$	0.722530	+	5.72981i	0.0409052	+	0.324387i
$313$	−22.8325			−1.29057			−0.645283	−	0.763943i	$-0.723261\pi$
$313$	−22.8325			−1.29057			−0.645283	+	0.763943i	$0.723261\pi$
$314$	−30.9408	+	1.29447i	−1.74609	+	0.0730513i
$315$		0			0
$316$	−20.8169	+	1.74489i	−1.17104	+	0.0981579i
$317$		−	2.11163i		−	0.118601i	−0.998240	−	0.0593005i	$-0.981113\pi$
$317$		−	2.11163i		−	0.118601i	0.998240	−	0.0593005i	$-0.0188870\pi$
$318$	−0.361971	−	8.65191i	−0.0202983	−	0.485175i
$319$	−15.4991			−0.867784
$320$		0			0
$321$	4.86518			0.271548
$322$	−0.677938	−	16.2042i	−0.0377800	−	0.903027i
$323$			19.3612i			1.07729i
$324$	−1.99301	+	0.167056i	−0.110723	+	0.00928088i
$325$		0			0
$326$	−15.7749	+	0.659978i	−0.873694	+	0.0365528i
$327$	−15.4573			−0.854790
$328$	2.48690	+	19.7216i	0.137316	+	1.08894i
$329$	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	$-0.220352\pi$
$332$	−0.255108	−	3.04349i	−0.0140009	−	0.167033i
$333$		−	6.55659i		−	0.359299i
$334$	0.596777	+	14.2643i	0.0326542	+	0.780509i
$335$		0			0
$336$	−0.888369	−	5.26198i	−0.0484645	−	0.287065i
$337$	−12.8884			−0.702074			−0.351037	−	0.936362i	$-0.614171\pi$
$337$	−12.8884			−0.702074			−0.351037	+	0.936362i	$0.614171\pi$
$338$	−0.522037	−	12.4779i	−0.0283951	−	0.678706i
$339$			9.88837i			0.537063i
$340$		0			0
$341$			6.12785i			0.331841i
$342$	7.57304	−	0.316834i	0.409503	−	0.0171324i
$343$	16.3030			0.880281
$344$	23.8549	−	3.00811i	1.28617	−	0.162186i
$345$		0			0
$346$	19.5220	−	0.816745i	1.04951	−	0.0439085i
$347$		−	6.79827i		−	0.364951i	−0.983210	−	0.182475i	$-0.941589\pi$
$347$		−	6.79827i		−	0.364951i	0.983210	−	0.182475i	$-0.0584109\pi$
$348$	−10.4918	+	0.879435i	−0.562422	+	0.0471427i
$349$			34.6076i			1.85250i	0.376904	+	0.926252i	$0.376989\pi$
$349$			34.6076i			1.85250i	−0.376904	+	0.926252i	$0.623011\pi$
$350$		0			0
$351$	−2.04184			−0.108985
$352$	−16.2922	+	3.45661i	−0.868376	+	0.184238i
$353$	−12.2433			−0.651647			−0.325823	−	0.945431i	$-0.605642\pi$
$353$	−12.2433			−0.651647			−0.325823	+	0.945431i	$0.605642\pi$
$354$	−0.280908	−	6.71432i	−0.0149301	−	0.356862i
$355$		0			0
$356$	25.3496	−	2.12483i	1.34353	−	0.112616i
$357$			4.81936i			0.255067i
$358$	31.0065	−	1.29722i	1.63874	−	0.0685603i
$359$	−2.01622			−0.106412			−0.0532059	−	0.998584i	$-0.516944\pi$
$359$	−2.01622			−0.106412			−0.0532059	+	0.998584i	$0.516944\pi$
$360$		0			0
$361$	−9.72569			−0.511878
$362$	2.72734	−	0.114104i	0.143346	−	0.00599716i
$363$			2.33178i			0.122387i
$364$	−0.455067	−	5.42904i	−0.0238520	−	0.284559i
$365$		0			0
$366$	0.503348	+	12.0312i	0.0263104	+	0.628879i
$367$	13.4131			0.700159			0.350079	−	0.936720i	$-0.386155\pi$
$367$	13.4131			0.700159			0.350079	+	0.936720i	$0.386155\pi$
$368$	−33.9046	+	5.72404i	−1.76740	+	0.298386i
$369$	−7.02786			−0.365856
$370$		0			0
$371$			8.16900i			0.424113i
$372$	0.347700	+	4.14813i	0.0180274	+	0.215071i
$373$			10.0976i			0.522832i	0.965226	+	0.261416i	$0.0841894\pi$
$373$			10.0976i			0.522832i	−0.965226	+	0.261416i	$0.915811\pi$
$374$	15.0279	−	0.628722i	0.777072	−	0.0325104i
$375$		0			0
$376$	−3.52873	−	27.9836i	−0.181981	−	1.44314i
$377$	−10.7489			−0.553595
$378$	1.88507	−	0.0788658i	0.0969575	−	0.00405642i
$379$		−	18.2775i		−	0.938853i	−0.882972	−	0.469426i	$-0.844461\pi$
$379$		−	18.2775i		−	0.938853i	0.882972	−	0.469426i	$-0.155539\pi$
$380$		0			0
$381$			8.75190i			0.448373i
$382$	−0.716660	−	17.1298i	−0.0366675	−	0.876436i
$383$	11.7734			0.601594			0.300797	−	0.953688i	$-0.402747\pi$
$383$	11.7734			0.601594			0.300797	+	0.953688i	$0.402747\pi$
$384$	−10.8326	+	3.26432i	−0.552796	+	0.166582i
$385$		0			0
$386$	−0.0753305	−	1.80057i	−0.00383422	−	0.0916466i
$387$			8.50078i			0.432119i
$388$	−26.7960	+	2.24606i	−1.36036	+	0.114026i
$389$		−	33.4270i		−	1.69482i	−0.530942	−	0.847408i	$-0.678162\pi$
$389$		−	33.4270i		−	1.69482i	0.530942	−	0.847408i	$-0.321838\pi$
$390$		0			0
$391$	31.0526			1.57040
$392$	−1.84721	−	14.6488i	−0.0932984	−	0.739876i
$393$	−0.471266			−0.0237722
$394$	−4.67482	+	0.195581i	−0.235514	+	0.00985322i
$395$		0			0
$396$	−0.491843	−	5.86779i	−0.0247161	−	0.294868i
$397$		−	39.0434i		−	1.95953i	−0.200147	−	0.979766i	$-0.564142\pi$
$397$		−	39.0434i		−	1.95953i	0.200147	−	0.979766i	$-0.435858\pi$
$398$	−0.533640	−	12.7552i	−0.0267490	−	0.639360i
$399$	−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	$0.710675\pi$
$402$	0.632297	+	15.1133i	0.0315361	+	0.753784i
$403$			4.24976i			0.211695i
$404$	1.69114	+	20.1756i	0.0841372	+	1.00377i
$405$		0			0
$406$	9.92361	−	0.415175i	0.492500	−	0.0206048i
$407$	19.3038			0.956855
$408$	10.1372	−	1.27830i	0.501864	−	0.0632851i
$409$	−14.5024			−0.717099			−0.358550	−	0.933511i	$-0.616729\pi$
$409$	−14.5024			−0.717099			−0.358550	+	0.933511i	$0.616729\pi$
$410$		0			0
$411$		−	1.30382i		−	0.0643127i
$412$	21.4193	−	1.79539i	1.05526	−	0.0884524i
$413$			6.33956i			0.311949i
$414$	−0.508157	−	12.1461i	−0.0249745	−	0.596948i
$415$		0			0
$416$	−11.2989	+	2.39721i	−0.553973	+	0.117533i
$417$	8.74723			0.428354
$418$	0.932818	+	22.2964i	0.0456256	+	1.09055i
$419$		−	12.6419i		−	0.617598i	−0.951127	−	0.308799i	$-0.900073\pi$
$419$		−	12.6419i		−	0.617598i	0.951127	−	0.308799i	$-0.0999271\pi$
$420$		0			0
$421$		−	16.8389i		−	0.820677i	−0.911933	−	0.410338i	$-0.865411\pi$
$421$		−	16.8389i		−	0.820677i	0.911933	−	0.410338i	$-0.134589\pi$
$422$	−9.34318	+	0.390891i	−0.454819	+	0.0190283i
$423$	9.97204			0.484857
$424$	17.1829	−	2.16676i	0.834474	−	0.105227i
$425$		0			0
$426$	−3.70773	+	0.155120i	−0.179640	+	0.00751561i
$427$		−	11.3596i		−	0.549731i
$428$	0.812757	+	9.69636i	0.0392861	+	0.468691i
$429$		−	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	$0.453930\pi$
$432$	−0.665888	−	3.94418i	−0.0320376	−	0.189765i
$433$	2.22482			0.106918			0.0534589	−	0.998570i	$-0.482975\pi$
$433$	2.22482			0.106918			0.0534589	+	0.998570i	$0.482975\pi$
$434$	−0.164146	−	3.92347i	−0.00787928	−	0.188333i
$435$		0			0
$436$	−2.58223	−	30.8065i	−0.123666	−	1.47537i
$437$			46.0719i			2.20392i
$438$	21.7422	−	0.909629i	1.03888	−	0.0434638i
$439$	−2.30460			−0.109993			−0.0549963	−	0.998487i	$-0.517515\pi$
$439$	−2.30460			−0.109993			−0.0549963	+	0.998487i	$0.517515\pi$
$440$		0			0
$441$	5.22015			0.248578
$442$	10.4220	−	0.436028i	0.495726	−	0.0207397i
$443$		−	22.1347i		−	1.05165i	−0.850592	−	0.525826i	$-0.823756\pi$
$443$		−	22.1347i		−	1.05165i	0.850592	−	0.525826i	$-0.176244\pi$
$444$	13.0674	−	1.09532i	0.620149	−	0.0519815i
$445$		0			0
$446$	0.0492566	+	1.17734i	0.00233237	+	0.0557489i
$447$	15.1411			0.716151
$448$	10.3388	−	2.64957i	0.488462	−	0.125181i
$449$	21.5861			1.01871			0.509356	−	0.860556i	$-0.329884\pi$
$449$	21.5861			1.01871			0.509356	+	0.860556i	$0.329884\pi$
$450$		0			0
$451$		−	20.6913i		−	0.974316i
$452$	−19.7076	+	1.65191i	−0.926969	+	0.0776993i
$453$		−	23.2782i		−	1.09371i
$454$	−15.5426	+	0.650257i	−0.729451	+	0.0305181i
$455$		0			0
$456$	1.89657	+	15.0402i	0.0888153	+	0.704323i
$457$	2.50088			0.116986			0.0584930	−	0.998288i	$-0.481370\pi$
$457$	2.50088			0.116986			0.0584930	+	0.998288i	$0.481370\pi$
$458$	21.4858	−	0.898904i	1.00397	−	0.0420030i
$459$			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	$-0.0192555\pi$
$462$	0.232195	+	5.54999i	0.0108027	+	0.258209i
$463$	27.8604			1.29478			0.647392	−	0.762158i	$-0.275860\pi$
$463$	27.8604			1.29478			0.647392	+	0.762158i	$0.275860\pi$
$464$	−3.50545	−	20.7634i	−0.162736	−	0.963919i
$465$		0			0
$466$	0.146365	+	3.49844i	0.00678021	+	0.162062i
$467$		−	5.75200i		−	0.266171i	−0.991105	−	0.133085i	$-0.957512\pi$
$467$		−	5.75200i		−	0.266171i	0.991105	−	0.133085i	$-0.0424884\pi$
$468$	−0.341101	−	4.06940i	−0.0157674	−	0.188108i
$469$		−	14.2698i		−	0.658917i
$470$		0			0
$471$	21.8976			1.00899
$472$	13.3348	−	1.68152i	0.613784	−	0.0773982i
$473$	−25.0279			−1.15078
$474$	14.7585	−	0.617452i	0.677880	−	0.0283605i
$475$		0			0
$476$	−9.60503	+	0.805102i	−0.440246	+	0.0369018i
$477$			6.12318i			0.280361i
$478$	1.24577	+	29.7766i	0.0569801	+	1.36195i
$479$	−12.5473			−0.573299			−0.286649	−	0.958036i	$-0.592541\pi$
$479$	−12.5473			−0.573299			−0.286649	+	0.958036i	$0.592541\pi$
$480$		0			0
$481$	13.3875			0.610417
$482$	0.361104	+	8.63119i	0.0164478	+	0.393140i
$483$			11.4682i			0.521819i
$484$	−4.64726	+	0.389537i	−0.211239	+	0.0177062i
$485$		0			0
$486$	1.41298	−	0.0591148i	0.0640940	−	0.00268150i
$487$	8.60530			0.389944			0.194972	−	0.980809i	$-0.437538\pi$
$487$	8.60530			0.389944			0.194972	+	0.980809i	$0.437538\pi$
$488$	−23.8941	+	3.01305i	−1.08164	+	0.136395i
$489$	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	$-0.312996\pi$
$492$	−1.17404	−	14.0066i	−0.0529300	−	0.631466i
$493$			19.0169i			0.856477i
$494$	0.646923	+	15.4629i	0.0291065	+	0.695710i
$495$		0			0
$496$	−8.20919	+	1.38594i	−0.368603	+	0.0622305i
$497$	3.50078			0.157031
$498$	0.0902732	+	2.15773i	0.00404524	+	0.0966903i
$499$		−	36.2496i		−	1.62275i	−0.584524	−	0.811377i	$-0.698719\pi$
$499$		−	36.2496i		−	1.62275i	0.584524	−	0.811377i	$-0.301281\pi$
$500$		0			0
$501$		−	10.0952i		−	0.451021i
$502$	31.8325	−	1.33178i	1.42075	−	0.0594401i
$503$	23.3527			1.04124			0.520622	−	0.853787i	$-0.325700\pi$
$503$	23.3527			1.04124			0.520622	+	0.853787i	$0.325700\pi$
$504$	0.472092	+	3.74379i	0.0210287	+	0.166762i
$505$		0			0
$506$	35.7603	−	1.49611i	1.58974	−	0.0665101i
$507$			8.83090i			0.392194i
$508$	−17.4426	+	1.46206i	−0.773891	+	0.0648682i
$509$			3.35506i			0.148711i	0.997232	+	0.0743553i	$0.0236899\pi$
$509$			3.35506i			0.148711i	−0.997232	+	0.0743553i	$0.976310\pi$
$510$		0			0
$511$	−20.5286			−0.908133
$512$	−8.31546	−	21.0441i	−0.367495	−	0.930025i
$513$	−5.35964			−0.236634
$514$	0.858858	+	20.5286i	0.0378826	+	0.905479i
$515$		0			0
$516$	−16.9421	+	1.42010i	−0.745836	+	0.0625166i
$517$			29.3595i			1.29123i
$518$	−12.3596	+	0.517091i	−0.543051	+	0.0227197i
$519$	−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	$0.763327\pi$
$522$	7.43836	−	0.311199i	0.325568	−	0.0136208i
$523$		−	0.965721i		−	0.0422280i	−0.999777	−	0.0211140i	$-0.993279\pi$
$523$		−	0.965721i		−	0.0422280i	0.999777	−	0.0211140i	$-0.00672130\pi$
$524$	−0.0787277	−	0.939238i	−0.00343924	−	0.0410308i
$525$		0			0
$526$	0.313128	+	7.48446i	0.0136530	+	0.326338i
$527$	7.51865			0.327517
$528$	11.6124	−	1.96050i	0.505365	−	0.0853197i
$529$	50.8928			2.21273
$530$		0			0
$531$			4.75190i			0.206215i
$532$	−1.19451	−	14.2507i	−0.0517885	−	0.617848i
$533$		−	14.3497i		−	0.621556i
$534$	−17.9720	+	0.751898i	−0.777726	+	0.0325378i
$535$		0			0
$536$	−30.0154	+	3.78494i	−1.29647	+	0.163485i
$537$	−21.9441			−0.946957
$538$	38.2545	−	1.60046i	1.64927	−	0.0690006i
$539$			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	$0.956422\pi$
$542$	−0.937586	−	22.4104i	−0.0402728	−	0.962609i
$543$	−1.93021			−0.0828331
$544$	4.24113	+	19.9899i	0.181837	+	0.857060i
$545$		0			0
$546$	0.161031	+	3.84901i	0.00689149	+	0.164722i
$547$			2.07433i			0.0886921i	0.999016	+	0.0443460i	$0.0141204\pi$
$547$			2.07433i			0.0886921i	−0.999016	+	0.0443460i	$0.985880\pi$
$548$	2.59853	−	0.217811i	0.111004	−	0.00930442i
$549$		−	8.51476i		−	0.363401i
$550$		0			0
$551$	−28.2148			−1.20199
$552$	24.1224	−	3.04184i	1.02672	−	0.129469i
$553$	−13.9347			−0.592566
$554$	−14.1099	+	0.590316i	−0.599472	+	0.0250801i
$555$		0			0
$556$	1.46128	+	17.4333i	0.0619719	+	0.739337i
$557$		−	27.6931i		−	1.17339i	−0.809807	−	0.586696i	$-0.800428\pi$
$557$		−	27.6931i		−	1.17339i	0.809807	−	0.586696i	$-0.199572\pi$
$558$	−0.123038	−	2.94089i	−0.00520861	−	0.124498i
$559$	−17.3572			−0.734131
$560$		0			0
$561$	−10.6356			−0.449035
$562$	−0.793426	−	18.9647i	−0.0334687	−	0.799976i
$563$		−	3.80771i		−	0.160476i	−0.996776	−	0.0802380i	$-0.974432\pi$
$563$		−	3.80771i		−	0.160476i	0.996776	−	0.0802380i	$-0.0255680\pi$
$564$	1.66589	+	19.8744i	0.0701466	+	0.836863i
$565$		0			0
$566$	5.42191	−	0.226837i	0.227900	−	0.00953467i
$567$	−1.33411			−0.0560274
$568$	−0.928554	−	7.36362i	−0.0389613	−	0.308971i
$569$	38.6371			1.61975			0.809875	−	0.586603i	$-0.199535\pi$
$569$	38.6371			1.61975			0.809875	+	0.586603i	$0.199535\pi$
$570$		0			0
$571$			6.24976i			0.261544i	0.991412	+	0.130772i	$0.0417456\pi$
$571$			6.24976i			0.261544i	−0.991412	+	0.130772i	$0.958254\pi$
$572$	11.9811	−	1.00426i	0.500954	−	0.0419904i
$573$			12.1232i			0.506453i
$574$	0.554258	+	13.2480i	0.0231343	+	0.552961i
$575$		0			0
$576$	7.74956	−	1.98602i	0.322898	−	0.0827509i
$577$	2.17377			0.0904952			0.0452476	−	0.998976i	$-0.485592\pi$
$577$	2.17377			0.0904952			0.0452476	+	0.998976i	$0.485592\pi$
$578$	0.233534	+	5.58198i	0.00971372	+	0.232180i
$579$			1.27431i			0.0529585i
$580$		0			0
$581$		−	2.03730i		−	0.0845213i
$582$	18.9974	−	0.794797i	0.787469	−	0.0329454i
$583$	−18.0278			−0.746634
$584$	5.44506	+	43.1804i	0.225318	+	1.78682i
$585$		0			0
$586$	−37.3661	+	1.56329i	−1.54358	+	0.0645789i
$587$			34.1688i			1.41030i	0.709059	+	0.705149i	$0.249120\pi$
$587$			34.1688i			1.41030i	−0.709059	+	0.705149i	$0.750880\pi$
$588$	0.872056	+	10.4038i	0.0359630	+	0.429046i
$589$			11.1552i			0.459643i
$590$		0			0
$591$	3.30849			0.136093
$592$	4.36596	+	25.8604i	0.179440	+	1.06286i
$593$	−12.9952			−0.533650			−0.266825	−	0.963745i	$-0.585975\pi$
$593$	−12.9952			−0.533650			−0.266825	+	0.963745i	$0.585975\pi$
$594$	0.174045	+	4.16007i	0.00714115	+	0.170690i
$595$		0			0
$596$	2.52942	+	30.1765i	0.103609	+	1.23608i
$597$			9.02718i			0.369458i
$598$	24.8003	−	1.03757i	1.01416	−	0.0424295i
$599$	47.2572			1.93088			0.965439	−	0.260628i	$-0.0839295\pi$
$599$	47.2572			1.93088			0.965439	+	0.260628i	$0.0839295\pi$
$600$		0			0
$601$	−23.5007			−0.958613			−0.479306	−	0.877648i	$-0.659112\pi$
$601$	−23.5007			−0.958613			−0.479306	+	0.877648i	$0.659112\pi$
$602$	16.0246	−	0.670421i	0.653112	−	0.0273243i
$603$		−	10.6961i		−	0.435578i
$604$	46.3937	−	3.88876i	1.88773	−	0.158231i
$605$		0			0
$606$	−0.598430	−	14.3038i	−0.0243096	−	0.581053i
$607$	0.218591			0.00887233			0.00443617	−	0.999990i	$-0.498588\pi$
$607$	0.218591			0.00887233			0.00443617	+	0.999990i	$0.498588\pi$
$608$	−29.6585	+	6.29245i	−1.20281	+	0.255193i
$609$	−7.02319			−0.284594
$610$		0			0
$611$			20.3613i			0.823730i
$612$	−7.19957	+	0.603474i	−0.291025	+	0.0243940i
$613$		−	35.7488i		−	1.44388i	−0.691956	−	0.721940i	$-0.743251\pi$
$613$		−	35.7488i		−	1.44388i	0.691956	−	0.721940i	$-0.256749\pi$
$614$	1.80290	−	0.0754282i	0.0727593	−	0.00304404i
$615$		0			0
$616$	−11.0224	+	1.38993i	−0.444105	+	0.0560018i
$617$	33.0836			1.33189			0.665947	−	0.745999i	$-0.268028\pi$
$617$	33.0836			1.33189			0.665947	+	0.745999i	$0.268028\pi$
$618$	−15.1856	+	0.635321i	−0.610854	+	0.0255563i
$619$		−	25.1084i		−	1.00919i	−0.863355	−	0.504596i	$-0.831641\pi$
$619$		−	25.1084i		−	1.00919i	0.863355	−	0.504596i	$-0.168359\pi$
$620$		0			0
$621$			8.59609i			0.344949i
$622$	−0.144534	−	3.45468i	−0.00579527	−	0.138520i
$623$	16.9689			0.679846
$624$	8.05338	−	1.35964i	0.322393	−	0.0544290i
$625$		0			0
$626$	1.34974	+	32.2617i	0.0539463	+	1.28944i
$627$		−	15.7798i		−	0.630183i
$628$	3.65812	+	43.6421i	0.145975	+	1.74151i
$629$		−	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	$0.346616\pi$
$632$	3.69608	+	29.3107i	0.147022	+	1.16592i
$633$	6.61241			0.262820
$634$	−2.98369	+	0.124829i	−0.118497	+	0.00495758i
$635$		0			0
$636$	−12.2036	+	1.02291i	−0.483902	+	0.0405611i
$637$			10.6587i			0.422313i
$638$	0.916228	+	21.8999i	0.0362738	+	0.867026i
$639$	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	$0.773054\pi$
$642$	−0.287604	−	6.87439i	−0.0113508	−	0.271311i
$643$		−	45.8045i		−	1.80635i	−0.429269	−	0.903177i	$-0.641229\pi$
$643$		−	45.8045i		−	1.80635i	0.429269	−	0.903177i	$-0.358771\pi$
$644$	−22.8561	+	1.91582i	−0.900658	+	0.0754940i
$645$		0			0
$646$	27.3569	−	1.14453i	1.07634	−	0.0450311i
$647$	48.1114			1.89146			0.945728	−	0.324960i	$-0.105351\pi$
$647$	48.1114			1.89146			0.945728	+	0.324960i	$0.105351\pi$
$648$	0.353863	+	2.80620i	0.0139010	+	0.110238i
$649$	−13.9905			−0.549174
$650$		0			0
$651$			2.77674i			0.108829i
$652$	1.86507	+	22.2506i	0.0730417	+	0.871402i
$653$		−	38.3331i		−	1.50009i	−0.661386	−	0.750046i	$-0.730031\pi$
$653$		−	38.3331i		−	1.50009i	0.661386	−	0.750046i	$-0.269969\pi$
$654$	0.913755	+	21.8408i	0.0357306	+	0.854043i
$655$		0			0
$656$	27.7192	−	4.67977i	1.08225	−	0.182714i
$657$	−15.3875			−0.600323
$658$	−0.786453	−	18.7980i	−0.0306591	−	0.732822i
$659$		−	5.03253i		−	0.196040i	−0.995184	−	0.0980198i	$-0.968749\pi$
$659$		−	5.03253i		−	0.196040i	0.995184	−	0.0980198i	$-0.0312508\pi$
$660$		0			0
$661$		−	17.4665i		−	0.679368i	−0.940540	−	0.339684i	$-0.889680\pi$
$661$		−	17.4665i		−	0.679368i	0.940540	−	0.339684i	$-0.110320\pi$
$662$	−32.8161	+	1.37293i	−1.27544	+	0.0533605i
$663$	−7.37595			−0.286458
$664$	−4.28530	+	0.540377i	−0.166302	+	0.0209707i
$665$		0			0
$666$	−9.26432	+	0.387592i	−0.358985	+	0.0150189i
$667$			45.2526i			1.75219i
$668$	20.1199	−	1.68647i	0.778462	−	0.0652513i
$669$		−	0.833237i		−	0.0322148i
$670$		0			0
$671$	25.0690			0.967779
$672$	−7.38255	+	1.56631i	−0.284788	+	0.0604216i
$673$	−32.4448			−1.25065			−0.625327	−	0.780363i	$-0.715034\pi$
$673$	−32.4448			−1.25065			−0.625327	+	0.780363i	$0.715034\pi$
$674$	0.761894	+	18.2110i	0.0293471	+	0.701461i
$675$		0			0
$676$	−17.6001	+	1.47525i	−0.676926	+	0.0567405i
$677$			8.07213i			0.310237i	0.987896	+	0.155119i	$0.0495760\pi$
$677$			8.07213i			0.310237i	−0.987896	+	0.155119i	$0.950424\pi$
$678$	13.9720	−	0.584549i	0.536593	−	0.0224495i
$679$	−17.9371			−0.688362
$680$		0			0
$681$	10.9999			0.421517
$682$	8.65851	−	0.362247i	0.331551	−	0.0138711i
$683$			36.3380i			1.39043i	0.718799	+	0.695217i	$0.244692\pi$
$683$			36.3380i			1.39043i	−0.718799	+	0.695217i	$0.755308\pi$
$684$	−0.895358	−	10.6818i	−0.0342349	−	0.408429i
$685$		0			0
$686$	−0.963751	−	23.0358i	−0.0367962	−	0.879512i
$687$	−15.2061			−0.580148
$688$	−5.66057	−	33.5286i	−0.215807	−	1.27827i
$689$	−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	$0.907892\pi$
$692$	−2.30808	−	27.5359i	−0.0877402	−	1.04676i
$693$		−	3.92787i		−	0.149207i
$694$	−9.60581	+	0.401879i	−0.364632	+	0.0152551i
$695$		0			0
$696$	1.86285	+	14.7728i	0.0706110	+	0.559960i
$697$	−25.3875			−0.961620
$698$	48.8998	−	2.04582i	1.85089	−	0.0774356i
$699$		−	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	$-0.0807362\pi$
$702$	0.120703	+	2.88507i	0.00455564	+	0.108890i
$703$	35.1409			1.32537
$704$	5.84721	+	22.8161i	0.220375	+	0.859916i
$705$		0			0
$706$	0.723763	+	17.2996i	0.0272392	+	0.651077i
$707$			13.5054i			0.507925i
$708$	−9.47058	+	0.793832i	−0.355926	+	0.0298340i
$709$		−	37.8976i		−	1.42327i	−0.702548	−	0.711637i	$-0.747954\pi$
$709$		−	37.8976i		−	1.42327i	0.702548	−	0.711637i	$-0.252046\pi$
$710$		0			0
$711$	−10.4450			−0.391717
$712$	−4.50088	−	35.6929i	−0.168677	−	1.33765i
$713$	17.8914			0.670038
$714$	6.80964	−	0.284895i	0.254844	−	0.0106619i
$715$		0			0
$716$	−3.66589	−	43.7348i	−0.137001	−	1.63445i
$717$		−	21.0737i		−	0.787011i
$718$	0.119188	+	2.84887i	0.00444807	+	0.106319i
$719$	−4.17909			−0.155854			−0.0779269	−	0.996959i	$-0.524830\pi$
$719$	−4.17909			−0.155854			−0.0779269	+	0.996959i	$0.524830\pi$
$720$		0			0
$721$	14.3380			0.533975
$722$	0.574933	+	13.7422i	0.0213968	+	0.511431i
$723$		−	6.10852i		−	0.227178i
$724$	−0.322452	−	3.84692i	−0.0119838	−	0.142970i
$725$		0			0
$726$	3.29475	−	0.137843i	0.122280	−	0.00511582i
$727$	−26.7727			−0.992943			−0.496471	−	0.868053i	$-0.665371\pi$
$727$	−26.7727			−0.992943			−0.496471	+	0.868053i	$0.665371\pi$
$728$	−7.64421	+	0.963936i	−0.283313	+	0.0357258i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$			30.7083i			1.13579i
$732$	16.9700	−	1.42244i	0.627229	−	0.0525749i
$733$			21.3364i			0.788080i	0.919093	+	0.394040i	$0.128923\pi$
$733$			21.3364i			0.788080i	−0.919093	+	0.394040i	$0.871077\pi$
$734$	−0.792914	−	18.9524i	−0.0292670	−	0.699547i
$735$		0			0
$736$	10.0922	+	47.5680i	0.372003	+	1.75338i
$737$	31.4912			1.15999
$738$	0.415451	+	9.93021i	0.0152930	+	0.365536i
$739$			13.1038i			0.482033i	0.970521	+	0.241016i	$0.0774807\pi$
$739$			13.1038i			0.482033i	−0.970521	+	0.241016i	$0.922519\pi$
$740$		0			0
$741$		−	10.9435i		−	0.402020i
$742$	11.5426	−	0.482909i	0.423743	−	0.0177282i
$743$	33.3595			1.22384			0.611921	−	0.790919i	$-0.290397\pi$
$743$	33.3595			1.22384			0.611921	+	0.790919i	$0.290397\pi$
$744$	5.84066	−	0.736508i	0.214129	−	0.0270017i
$745$		0			0
$746$	14.2676	−	0.596915i	0.522375	−	0.0218546i
$747$		−	1.52708i		−	0.0558730i
$748$	−1.77674	−	21.1969i	−0.0649640	−	0.775034i
$749$			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	$0.511159\pi$
$752$	−39.3316	+	6.64027i	−1.43428	+	0.242146i
$753$	−22.5286			−0.820989
$754$	0.635418	+	15.1879i	0.0231406	+	0.553112i
$755$		0			0
$756$	−0.222871	−	2.65890i	−0.00810575	−	0.0967032i
$757$			13.9908i			0.508504i	0.967138	+	0.254252i	$0.0818292\pi$
$757$			13.9908i			0.508504i	−0.967138	+	0.254252i	$0.918171\pi$
$758$	−25.8257	+	1.08047i	−0.938032	+	0.0392445i
$759$	−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	$0.346011\pi$
$762$	12.3662	−	0.517367i	0.447981	−	0.0187422i
$763$		−	20.6217i		−	0.746557i
$764$	−24.1616	+	2.02525i	−0.874137	+	0.0732709i
$765$		0			0
$766$	−0.695985	−	16.6356i	−0.0251469	−	0.601069i
$767$	−9.70260			−0.350341
$768$	5.25277	+	15.1132i	0.189543	+	0.545350i
$769$	−12.3922			−0.446873			−0.223436	−	0.974719i	$-0.571728\pi$
$769$	−12.3922			−0.446873			−0.223436	+	0.974719i	$0.571728\pi$
$770$		0			0
$771$		−	14.5286i		−	0.523236i
$772$	−2.53971	+	0.212881i	−0.0914062	+	0.00766174i
$773$			38.4843i			1.38418i	0.721810	+	0.692091i	$0.243311\pi$
$773$			38.4843i			1.38418i	−0.721810	+	0.692091i	$0.756689\pi$
$774$	12.0114	−	0.502522i	0.431741	−	0.0180628i
$775$		0			0
$776$	4.75767	+	37.7293i	0.170790	+	1.35440i
$777$	8.74723			0.313805
$778$	−47.2316	+	1.97603i	−1.69333	+	0.0708442i
$779$		−	37.6668i		−	1.34955i
$780$		0			0
$781$			7.72569i			0.276447i
$782$	−1.83567	−	43.8766i	−0.0656434	−	1.56903i
$783$	−5.26432			−0.188131
$784$	−20.5892	+	3.47603i	−0.735329	+	0.124144i
$785$		0			0
$786$	0.0278588	+	0.665888i	0.000993691	+	0.0237514i
$787$			0.389147i			0.0138716i	0.999976	+	0.00693579i	$0.00220775\pi$
$787$			0.389147i			0.0138716i	−0.999976	+	0.00693579i	$0.997792\pi$
$788$	0.552703	+	6.59386i	0.0196892	+	0.234896i
$789$		−	5.29694i		−	0.188576i
$790$		0			0
$791$	−13.1922			−0.469060
$792$	−8.26198	+	1.04184i	−0.293577	+	0.0370201i
$793$	17.3857			0.617386
$794$	−55.1674	+	2.30804i	−1.95782	+	0.0819094i
$795$		0			0
$796$	−17.9913	+	1.50804i	−0.637683	+	0.0534512i
$797$		−	0.854188i		−	0.0302569i	−0.999886	−	0.0151284i	$-0.995184\pi$
$797$		−	0.854188i		−	0.0302569i	0.999886	−	0.0151284i	$-0.00481572\pi$
$798$	0.422692	+	10.1033i	0.0149631	+	0.357652i
$799$	36.0231			1.27441
$800$		0			0
$801$	12.7193			0.449413
$802$	1.45505	+	34.7790i	0.0513796	+	1.22809i
$803$		−	45.3036i		−	1.59873i
$804$	21.3174	−	1.78684i	0.751807	−	0.0630171i
$805$		0			0
$806$	6.00481	−	0.251224i	0.211510	−	0.00884897i
$807$	−27.0737			−0.953039
$808$	28.4077	−	3.58221i	0.999379	−	0.126022i
$809$	−10.4107			−0.366020			−0.183010	−	0.983111i	$-0.558584\pi$
$809$	−10.4107			−0.366020			−0.183010	+	0.983111i	$0.558584\pi$
$810$		0			0
$811$			6.08825i			0.213787i	0.994270	+	0.106894i	$0.0340904\pi$
$811$			6.08825i			0.213787i	−0.994270	+	0.106894i	$0.965910\pi$
$812$	−1.17326	−	13.9973i	−0.0411735	−	0.491209i
$813$			15.8604i			0.556249i
$814$	−1.14114	−	27.2759i	−0.0399970	−	0.956019i
$815$		0			0
$816$	−2.40546	−	14.2480i	−0.0842080	−	0.498780i
$817$	−45.5611			−1.59398
$818$	0.857309	+	20.4916i	0.0299751	+	0.716472i
$819$		−	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	$-0.211884\pi$
$822$	−1.84227	+	0.0770751i	−0.0642565	+	0.00268830i
$823$	−16.2846			−0.567646			−0.283823	−	0.958877i	$-0.591603\pi$
$823$	−16.2846			−0.567646			−0.283823	+	0.958877i	$0.591603\pi$
$824$	−3.80304	−	30.1589i	−0.132485	−	1.05064i
$825$		0			0
$826$	8.95766	−	0.374762i	0.311677	−	0.0130396i
$827$		−	32.1362i		−	1.11748i	−0.829341	−	0.558742i	$-0.811284\pi$
$827$		−	32.1362i		−	1.11748i	0.829341	−	0.558742i	$-0.188716\pi$
$828$	−17.1321	+	1.43603i	−0.595382	+	0.0499054i
$829$			22.4682i			0.780355i	0.920740	+	0.390177i	$0.127586\pi$
$829$			22.4682i			0.780355i	−0.920740	+	0.390177i	$0.872414\pi$
$830$		0			0
$831$	9.98592			0.346408
$832$	4.05513	+	15.8233i	0.140586	+	0.548576i
$833$	18.8573			0.653367
$834$	−0.517091	−	12.3596i	−0.0179054	−	0.427979i
$835$		0			0
$836$	31.4492	−	2.63610i	1.08769	−	0.0911715i
$837$			2.08134i			0.0719416i
$838$	−17.8627	+	0.747325i	−0.617058	+	0.0258159i
$839$	−16.1358			−0.557070			−0.278535	−	0.960426i	$-0.589849\pi$
$839$	−16.1358			−0.557070			−0.278535	+	0.960426i	$0.589849\pi$
$840$		0			0
$841$	1.28695			0.0443777
$842$	−23.7930	+	0.995427i	−0.819959	+	0.0343047i
$843$			13.4218i			0.462270i
$844$	1.10464	+	13.1786i	0.0380233	+	0.453626i
$845$		0			0
$846$	−0.589496	−	14.0903i	−0.0202673	−	0.484434i
$847$	−3.11085			−0.106890
$848$	−4.07735	−	24.1509i	−0.140017	−	0.829347i
$849$	−3.83722			−0.131693
$850$		0			0
$851$		−	56.3611i		−	1.93203i
$852$	0.438363	+	5.22976i	0.0150181	+	0.179169i
$853$		−	44.6262i		−	1.52797i	−0.645233	−	0.763986i	$-0.723240\pi$
$853$		−	44.6262i		−	1.52797i	0.645233	−	0.763986i	$-0.276760\pi$
$854$	−16.0509	+	0.671523i	−0.549251	+	0.0229790i
$855$		0			0
$856$	13.6527	−	1.72161i	0.466639	−	0.0588433i
$857$	−4.52553			−0.154589			−0.0772945	−	0.997008i	$-0.524628\pi$
$857$	−4.52553			−0.154589			−0.0772945	+	0.997008i	$0.524628\pi$
$858$	−8.49418	+	0.355372i	−0.289986	+	0.0121322i
$859$			42.7783i			1.45958i	0.683673	+	0.729788i	$0.260381\pi$
$859$			42.7783i			1.45958i	−0.683673	+	0.729788i	$0.739619\pi$
$860$		0			0
$861$		−	9.37595i		−	0.319531i
$862$	−0.354006	−	8.46155i	−0.0120575	−	0.288202i
$863$	−23.7734			−0.809257			−0.404629	−	0.914481i	$-0.632599\pi$
$863$	−23.7734			−0.809257			−0.404629	+	0.914481i	$0.632599\pi$
$864$	−5.53368	+	1.17404i	−0.188260	+	0.0399418i
$865$		0			0
$866$	−0.131520	−	3.14362i	−0.00446922	−	0.106824i
$867$		−	3.95051i		−	0.134166i
$868$	−5.53407	+	0.463870i	−0.187839	+	0.0157448i
$869$		−	30.7519i		−	1.04319i
$870$		0			0
$871$	21.8397			0.740009
$872$	−43.3763	+	5.46976i	−1.46891	+	0.185229i
$873$	−13.4450			−0.455043
$874$	65.0986	−	2.72353i	2.20199	−	0.0921249i
$875$		0			0
$876$	−2.57057	−	30.6674i	−0.0868515	−	1.03616i
$877$		−	13.1470i		−	0.443944i	−0.975053	−	0.221972i	$-0.928751\pi$
$877$		−	13.1470i		−	0.443944i	0.975053	−	0.221972i	$-0.0712494\pi$
$878$	0.136236	+	3.25635i	0.00459774	+	0.109896i
$879$	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	$0.272454\pi$
$882$	−0.308588	−	7.37595i	−0.0103907	−	0.248361i
$883$			44.5843i			1.50038i	0.661223	+	0.750190i	$0.270038\pi$
$883$			44.5843i			1.50038i	−0.661223	+	0.750190i	$0.729962\pi$
$884$	−1.23220	−	14.7003i	−0.0414432	−	0.494426i
$885$		0			0
$886$	−31.2759	+	1.30849i	−1.05073	+	0.0439596i
$887$	32.3240			1.08533			0.542667	−	0.839948i	$-0.317415\pi$
$887$	32.3240			1.08533			0.542667	+	0.839948i	$0.317415\pi$
$888$	−2.32013	−	18.3991i	−0.0778586	−	0.617435i
$889$	−11.6760			−0.391601
$890$		0			0
$891$		−	2.94418i		−	0.0986339i
$892$	1.66065	−	0.139197i	0.0556027	−	0.00466066i
$893$			53.4465i			1.78852i
$894$	−0.895066	−	21.3941i	−0.0299355	−	0.715526i
$895$		0			0
$896$	−4.35497	−	14.4518i	−0.145489	−	0.482802i
$897$	−17.5518			−0.586038
$898$	−1.27606	−	30.5007i	−0.0425826	−	1.01782i
$899$			10.9568i			0.365431i
$900$		0			0
$901$			22.1194i			0.736904i
$902$	−29.2364	+	1.22316i	−0.973464	+	0.0407269i
$903$	−11.3410			−0.377404
$904$	3.49912	+	27.7488i	0.116379	+	0.922911i
$905$		0			0
$906$	−32.8916	+	1.37609i	−1.09275	+	0.0457174i
$907$		−	14.8309i		−	0.492452i	−0.969212	−	0.246226i	$-0.920809\pi$
$907$		−	14.8309i		−	0.492452i	0.969212	−	0.246226i	$-0.0791905\pi$
$908$	1.83760	+	21.9229i	0.0609828	+	0.727538i
$909$			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	$0.438392\pi$
$912$	21.1394	−	3.56892i	0.699995	−	0.118179i
$913$	4.49601			0.148796
$914$	−0.147839	−	3.53368i	−0.00489007	−	0.116884i
$915$		0			0
$916$	−2.54026	−	30.3059i	−0.0839327	−	1.00133i
$917$		−	0.628722i		−	0.0207622i
$918$	5.10425	−	0.213547i	0.168465	−	0.00704810i
$919$	−58.2518			−1.92155			−0.960775	−	0.277330i	$-0.910550\pi$
$919$	−58.2518			−1.92155			−0.960775	+	0.277330i	$0.910550\pi$
$920$		0			0
$921$	−1.27596			−0.0420444
$922$	−3.66822	+	0.153468i	−0.120807	+	0.00505419i
$923$			5.35789i			0.176357i
$924$	7.82829	−	0.656174i	0.257532	−	0.0215865i
$925$		0			0
$926$	−1.64696	−	39.3661i	−0.0541226	−	1.29365i
$927$	10.7472			0.352985
$928$	−29.1311	+	6.18055i	−0.956274	+	0.202886i
$929$	18.4433			0.605105			0.302553	−	0.953133i	$-0.402161\pi$
$929$	18.4433			0.605105			0.302553	+	0.953133i	$0.402161\pi$
$930$		0			0
$931$			27.9781i			0.916944i
$932$	4.93457	−	0.413620i	0.161637	−	0.0135486i
$933$			2.44496i			0.0800445i
$934$	−8.12744	+	0.340028i	−0.265938	+	0.0111261i
$935$		0			0
$936$	−5.72981	+	0.722530i	−0.187285	+	0.0236166i
$937$	16.1005			0.525982			0.262991	−	0.964798i	$-0.415291\pi$
$937$	16.1005			0.525982			0.262991	+	0.964798i	$0.415291\pi$
$938$	−20.1629	+	0.843555i	−0.658341	+	0.0275430i
$939$		−	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	$0.824748\pi$
$942$	−1.29447	−	30.9408i	−0.0421762	−	1.00811i
$943$	−60.4121			−1.96729
$944$	−3.16423	−	18.7424i	−0.102987	−	0.610012i
$945$		0			0
$946$	1.47952	+	35.3638i	0.0481033	+	1.14978i
$947$			4.10998i			0.133556i	0.997768	+	0.0667782i	$0.0212720\pi$
$947$			4.10998i			0.133556i	−0.997768	+	0.0667782i	$0.978728\pi$
$948$	−1.74489	−	20.8169i	−0.0566715	−	0.676102i
$949$		−	31.4188i		−	1.01990i
$950$		0			0
$951$	2.11163			0.0684743
$952$	1.70539	+	13.5241i	0.0552720	+	0.438318i
$953$	31.7208			1.02754			0.513769	−	0.857928i	$-0.328249\pi$
$953$	31.7208			1.02754			0.513769	+	0.857928i	$0.328249\pi$
$954$	8.65191	−	0.361971i	0.280116	−	0.0117192i
$955$		0			0
$956$	42.0001	−	3.52048i	1.35838	−	0.113861i
$957$		−	15.4991i		−	0.501016i
$958$	0.741729	+	17.7290i	0.0239642	+	0.572798i
$959$	1.73944			0.0561695
$960$		0			0
$961$	−26.6680			−0.860259
$962$	−0.791399	−	18.9162i	−0.0255157	−	0.609884i
$963$			4.86518i			0.156778i
$964$	12.1743	−	1.02046i	0.392109	−	0.0328669i
$965$		0			0
$966$	16.2042	−	0.677938i	0.521363	−	0.0218123i
$967$	−26.9936			−0.868055			−0.434027	−	0.900900i	$-0.642908\pi$
$967$	−26.9936			−0.868055			−0.434027	+	0.900900i	$0.642908\pi$
$968$	0.825129	+	6.54344i	0.0265206	+	0.210314i
$969$	−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	$-0.0724139\pi$
$972$	−0.167056	−	1.99301i	−0.00535832	−	0.0639259i
$973$			11.6698i			0.374116i
$974$	−0.508701	−	12.1591i	−0.0162998	−	0.389603i
$975$		0			0
$976$	5.66988	+	33.5838i	0.181488	+	1.07499i
$977$	1.14251			0.0365520			0.0182760	−	0.999833i	$-0.494182\pi$
$977$	1.14251			0.0365520			0.0182760	+	0.999833i	$0.494182\pi$
$978$	−0.659978	−	15.7749i	−0.0211038	−	0.504427i
$979$			37.4479i			1.19684i
$980$		0			0
$981$		−	15.4573i		−	0.493513i
$982$	−52.1200	+	2.18055i	−1.66321	+	0.0695840i
$983$	6.41720			0.204677			0.102338	−	0.994750i	$-0.467368\pi$
$983$	6.41720			0.204677			0.102338	+	0.994750i	$0.467368\pi$
$984$	−19.7216	+	2.48690i	−0.628702	+	0.0792794i
$985$		0			0
$986$	26.8704	−	1.12418i	0.855728	−	0.0358011i
$987$			13.3038i			0.423465i
$988$	21.8105	−	1.82818i	0.693885	−	0.0581620i
$989$			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	$0.537472\pi$
$992$	2.44359	+	11.5175i	0.0775839	+	0.365680i
$993$	23.2248			0.737017
$994$	−0.206948	−	4.94652i	−0.00656399	−	0.156894i
$995$		0			0
$996$	3.04349	−	0.255108i	0.0964367	−	0.00808340i
$997$		−	31.6649i		−	1.00284i	−0.865205	−	0.501419i	$-0.832812\pi$
$997$		−	31.6649i		−	1.00284i	0.865205	−	0.501419i	$-0.167188\pi$
$998$	−51.2198	+	2.14289i	−1.62133	+	0.0678319i
$999$	6.55659			0.207441

Twists

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

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

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.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0591148 - 1.41298i) q^{2} +1.00000i q^{3} +(-1.99301 + 0.167056i) q^{4} +(1.41298 - 0.0591148i) q^{6} -1.33411 q^{7} +(0.353863 + 2.80620i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.0591148 - 1.41298i) q^{2} +1.00000i q^{3} +(-1.99301 + 0.167056i) q^{4} +(1.41298 - 0.0591148i) q^{6} -1.33411 q^{7} +(0.353863 + 2.80620i) q^{8} -1.00000 q^{9} -2.94418i q^{11} +(-0.167056 - 1.99301i) q^{12} -2.04184i q^{13} +(0.0788658 + 1.88507i) q^{14} +(3.94418 - 0.665888i) q^{16} -3.61241 q^{17} +(0.0591148 + 1.41298i) q^{18} -5.35964i q^{19} -1.33411i q^{21} +(-4.16007 + 0.174045i) q^{22} -8.59609 q^{23} +(-2.80620 + 0.353863i) q^{24} +(-2.88507 + 0.120703i) q^{26} -1.00000i q^{27} +(2.65890 - 0.222871i) q^{28} -5.26432i q^{29} -2.08134 q^{31} +(-1.17404 - 5.53368i) q^{32} +2.94418 q^{33} +(0.213547 + 5.10425i) q^{34} +(1.99301 - 0.167056i) q^{36} +6.55659i q^{37} +(-7.57304 + 0.316834i) q^{38} +2.04184 q^{39} +7.02786 q^{41} +(-1.88507 + 0.0788658i) q^{42} -8.50078i q^{43} +(0.491843 + 5.86779i) q^{44} +(0.508157 + 12.1461i) q^{46} -9.97204 q^{47} +(0.665888 + 3.94418i) q^{48} -5.22015 q^{49} -3.61241i q^{51} +(0.341101 + 4.06940i) q^{52} -6.12318i q^{53} +(-1.41298 + 0.0591148i) q^{54} +(-0.472092 - 3.74379i) q^{56} +5.35964 q^{57} +(-7.43836 + 0.311199i) q^{58} -4.75190i q^{59} +8.51476i q^{61} +(0.123038 + 2.94089i) q^{62} +1.33411 q^{63} +(-7.74956 + 1.98602i) q^{64} +(-0.174045 - 4.16007i) q^{66} +10.6961i q^{67} +(7.19957 - 0.603474i) q^{68} -8.59609i q^{69} -2.62405 q^{71} +(-0.353863 - 2.80620i) q^{72} +15.3875 q^{73} +(9.26432 - 0.387592i) q^{74} +(0.895358 + 10.6818i) q^{76} +3.92787i q^{77} +(-0.120703 - 2.88507i) q^{78} +10.4450 q^{79} +1.00000 q^{81} +(-0.415451 - 9.93021i) q^{82} +1.52708i q^{83} +(0.222871 + 2.65890i) q^{84} +(-12.0114 + 0.502522i) q^{86} +5.26432 q^{87} +(8.26198 - 1.04184i) q^{88} -12.7193 q^{89} +2.72404i q^{91} +(17.1321 - 1.43603i) q^{92} -2.08134i q^{93} +(0.589496 + 14.0903i) q^{94} +(5.53368 - 1.17404i) q^{96} +13.4450 q^{97} +(0.308588 + 7.37595i) q^{98} +2.94418i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9	\( 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} - 2 q^{18} - 12 q^{22} - 8 q^{23} - 8 q^{24} - 2 q^{26} + 4 q^{28} + 8 q^{31} - 28 q^{32} + 12 q^{34} - 4 q^{36} - 30 q^{38} + 6 q^{42} - 12 q^{44} + 20 q^{46} + 8 q^{48} + 20 q^{52} - 2 q^{54} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 30 q^{62} + 8 q^{63} - 32 q^{64} - 20 q^{66} + 28 q^{68} - 40 q^{71} + 4 q^{72} + 16 q^{73} + 8 q^{74} - 20 q^{76} + 22 q^{78} - 16 q^{79} + 8 q^{81} + 24 q^{82} + 24 q^{84} - 18 q^{86} - 24 q^{87} + 8 q^{88} + 36 q^{92} - 4 q^{94} + 12 q^{96} + 8 q^{97} + 48 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^4 + 2 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 6 * q^14 + 8 * q^16 - 2 * q^18 - 12 * q^22 - 8 * q^23 - 8 * q^24 - 2 * q^26 + 4 * q^28 + 8 * q^31 - 28 * q^32 + 12 * q^34 - 4 * q^36 - 30 * q^38 + 6 * q^42 - 12 * q^44 + 20 * q^46 + 8 * q^48 + 20 * q^52 - 2 * q^54 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 30 * q^62 + 8 * q^63 - 32 * q^64 - 20 * q^66 + 28 * q^68 - 40 * q^71 + 4 * q^72 + 16 * q^73 + 8 * q^74 - 20 * q^76 + 22 * q^78 - 16 * q^79 + 8 * q^81 + 24 * q^82 + 24 * q^84 - 18 * q^86 - 24 * q^87 + 8 * q^88 + 36 * q^92 - 4 * q^94 + 12 * q^96 + 8 * q^97 + 48 * q^98

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