LMFDB - Embedded newform 300.2.h.a.299.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(299,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("300.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.h (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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.5
Root			$-1.17915 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	300.299
Dual form			300.2.h.a.299.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.780776 - 1.17915i) q^{2} +(-0.848071 - 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} -3.02045 q^{7} +(-2.78078 - 0.516994i) q^{8} +(-1.56155 + 2.56155i) q^{9} +O(q^{10})$	\(q+(0.780776 - 1.17915i) q^{2} +(-0.848071 - 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} -3.02045 q^{7} +(-2.78078 - 0.516994i) q^{8} +(-1.56155 + 2.56155i) q^{9} +1.32431 q^{11} +(-2.11862 + 2.74070i) q^{12} -5.12311i q^{13} +(-2.35829 + 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} +2.00000 q^{17} +(1.80122 + 3.84130i) q^{18} -1.32431i q^{19} +(2.56155 + 4.56155i) q^{21} +(1.03399 - 1.56155i) q^{22} +0.371834i q^{23} +(1.57752 + 4.63804i) q^{24} +(-6.04090 - 4.00000i) q^{26} +(5.19283 + 0.185917i) q^{27} +(2.35829 + 5.56155i) q^{28} -3.12311i q^{29} -4.71659i q^{31} +(1.21922 + 5.52390i) q^{32} +(-1.12311 - 2.00000i) q^{33} +(1.56155 - 2.35829i) q^{34} +(5.93581 + 0.875288i) q^{36} -5.12311i q^{37} +(-1.56155 - 1.03399i) q^{38} +(-7.73704 + 4.34475i) q^{39} -1.12311i q^{41} +(7.37874 + 0.541105i) q^{42} -7.73704 q^{43} +(-1.03399 - 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} -3.02045i q^{47} +(6.70062 + 1.76115i) q^{48} +2.12311 q^{49} +(-1.69614 - 3.02045i) q^{51} +(-9.43318 + 4.00000i) q^{52} +12.2462 q^{53} +(4.27366 - 5.97795i) q^{54} +(8.39919 + 1.56155i) q^{56} +(-2.00000 + 1.12311i) q^{57} +(-3.68260 - 2.43845i) q^{58} +14.1498 q^{59} +3.12311 q^{61} +(-5.56155 - 3.68260i) q^{62} +(4.71659 - 7.73704i) q^{63} +(7.46543 + 2.87529i) q^{64} +(-3.23519 - 0.237246i) q^{66} -4.34475 q^{67} +(-1.56155 - 3.68260i) q^{68} +(0.561553 - 0.315342i) q^{69} +3.39228 q^{71} +(5.66664 - 6.31579i) q^{72} +8.24621i q^{73} +(-6.04090 - 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} -4.00000 q^{77} +(-0.917790 + 12.5154i) q^{78} -8.10887i q^{79} +(-4.12311 - 8.00000i) q^{81} +(-1.32431 - 0.876894i) q^{82} +15.1022i q^{83} +(6.39919 - 8.27814i) q^{84} +(-6.04090 + 9.12311i) q^{86} +(-4.71659 + 2.64861i) q^{87} +(-3.68260 - 0.684658i) q^{88} -10.2462i q^{89} +15.4741i q^{91} +(0.684658 - 0.290319i) q^{92} +(-7.12311 + 4.00000i) q^{93} +(-3.56155 - 2.35829i) q^{94} +(7.30834 - 6.52596i) q^{96} +6.00000i q^{97} +(1.65767 - 2.50345i) q^{98} +(-2.06798 + 3.39228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{4} - 6 q^{6} - 14 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^4 - 6 * q^6 - 14 * q^8 + 4 * q^9	$ 8 q - 2 q^{2} + 2 q^{4} - 6 q^{6} - 14 q^{8} + 4 q^{9} - 14 q^{12} - 14 q^{16} + 16 q^{17} - 18 q^{18} + 4 q^{21} + 2 q^{24} + 18 q^{32} + 24 q^{33} - 4 q^{34} + 18 q^{36} + 4 q^{38} + 16 q^{42} + 20 q^{46} + 10 q^{48} - 16 q^{49} + 32 q^{53} + 10 q^{54} - 16 q^{57} - 8 q^{61} - 28 q^{62} + 2 q^{64} - 40 q^{66} + 4 q^{68} - 12 q^{69} + 10 q^{72} - 36 q^{76} - 32 q^{77} + 8 q^{78} - 16 q^{84} - 44 q^{92} - 24 q^{93} - 12 q^{94} + 42 q^{96} + 38 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^4 - 6 * q^6 - 14 * q^8 + 4 * q^9 - 14 * q^12 - 14 * q^16 + 16 * q^17 - 18 * q^18 + 4 * q^21 + 2 * q^24 + 18 * q^32 + 24 * q^33 - 4 * q^34 + 18 * q^36 + 4 * q^38 + 16 * q^42 + 20 * q^46 + 10 * q^48 - 16 * q^49 + 32 * q^53 + 10 * q^54 - 16 * q^57 - 8 * q^61 - 28 * q^62 + 2 * q^64 - 40 * q^66 + 4 * q^68 - 12 * q^69 + 10 * q^72 - 36 * q^76 - 32 * q^77 + 8 * q^78 - 16 * q^84 - 44 * q^92 - 24 * q^93 - 12 * q^94 + 42 * q^96 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	0.780776	−	1.17915i	0.552092	−	0.833783i
$2$	0.780776	−	1.17915i	0.552092	−	0.833783i
$3$	−0.848071	−	1.51022i	−0.489634	−	0.871928i
$3$	−0.848071	−	1.51022i	−0.489634	−	0.871928i
$4$	−0.780776	−	1.84130i	−0.390388	−	0.920650i
$5$		0			0
$5$		0			0
$6$	−2.44293	−	0.179147i	−0.997322	−	0.0731366i
$7$	−3.02045			−1.14162			−0.570811	−	0.821081i	$-0.693371\pi$
$7$	−3.02045			−1.14162			−0.570811	+	0.821081i	$0.693371\pi$
$8$	−2.78078	−	0.516994i	−0.983153	−	0.182785i
$9$	−1.56155	+	2.56155i	−0.520518	+	0.853851i
$10$		0			0
$11$	1.32431			0.399294			0.199647	−	0.979868i	$-0.436021\pi$
$11$	1.32431			0.399294			0.199647	+	0.979868i	$0.436021\pi$
$12$	−2.11862	+	2.74070i	−0.611594	+	0.791172i
$13$		−	5.12311i		−	1.42089i	−0.703751	−	0.710447i	$-0.748493\pi$
$13$		−	5.12311i		−	1.42089i	0.703751	−	0.710447i	$-0.251507\pi$
$14$	−2.35829	+	3.56155i	−0.630281	+	0.951865i
$15$		0			0
$16$	−2.78078	+	2.87529i	−0.695194	+	0.718822i
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	1.80122	+	3.84130i	0.424553	+	0.905403i
$19$		−	1.32431i		−	0.303817i	−0.988395	−	0.151908i	$-0.951458\pi$
$19$		−	1.32431i		−	0.303817i	0.988395	−	0.151908i	$-0.0485419\pi$
$20$		0			0
$21$	2.56155	+	4.56155i	0.558977	+	0.995412i
$22$	1.03399	−	1.56155i	0.220447	−	0.332924i
$23$			0.371834i			0.0775328i	0.999248	+	0.0387664i	$0.0123428\pi$
$23$			0.371834i			0.0775328i	−0.999248	+	0.0387664i	$0.987657\pi$
$24$	1.57752	+	4.63804i	0.322010	+	0.946736i
$25$		0			0
$26$	−6.04090	−	4.00000i	−1.18472	−	0.784465i
$27$	5.19283	+	0.185917i	0.999360	+	0.0357798i
$28$	2.35829	+	5.56155i	0.445676	+	1.05103i
$29$		−	3.12311i		−	0.579946i	−0.957035	−	0.289973i	$-0.906354\pi$
$29$		−	3.12311i		−	0.579946i	0.957035	−	0.289973i	$-0.0936464\pi$
$30$		0			0
$31$		−	4.71659i		−	0.847124i	−0.905867	−	0.423562i	$-0.860780\pi$
$31$		−	4.71659i		−	0.847124i	0.905867	−	0.423562i	$-0.139220\pi$
$32$	1.21922	+	5.52390i	0.215530	+	0.976497i
$33$	−1.12311	−	2.00000i	−0.195508	−	0.348155i
$34$	1.56155	−	2.35829i	0.267804	−	0.404444i
$35$		0			0
$36$	5.93581	+	0.875288i	0.989302	+	0.145881i
$37$		−	5.12311i		−	0.842233i	−0.907006	−	0.421117i	$-0.861638\pi$
$37$		−	5.12311i		−	0.842233i	0.907006	−	0.421117i	$-0.138362\pi$
$38$	−1.56155	−	1.03399i	−0.253317	−	0.167735i
$39$	−7.73704	+	4.34475i	−1.23892	+	0.695718i
$40$		0			0
$41$		−	1.12311i		−	0.175400i	−0.996147	−	0.0876998i	$-0.972048\pi$
$41$		−	1.12311i		−	0.175400i	0.996147	−	0.0876998i	$-0.0279516\pi$
$42$	7.37874	+	0.541105i	1.13856	+	0.0834943i
$43$	−7.73704			−1.17989			−0.589944	−	0.807445i	$-0.700850\pi$
$43$	−7.73704			−1.17989			−0.589944	+	0.807445i	$0.700850\pi$
$44$	−1.03399	−	2.43845i	−0.155879	−	0.367610i
$45$		0			0
$46$	0.438447	+	0.290319i	0.0646455	+	0.0428052i
$47$		−	3.02045i		−	0.440578i	−0.975435	−	0.220289i	$-0.929300\pi$
$47$		−	3.02045i		−	0.440578i	0.975435	−	0.220289i	$-0.0707000\pi$
$48$	6.70062	+	1.76115i	0.967152	+	0.254200i
$49$	2.12311			0.303301
$50$		0			0
$51$	−1.69614	−	3.02045i	−0.237507	−	0.422947i
$52$	−9.43318	+	4.00000i	−1.30815	+	0.554700i
$53$	12.2462			1.68215			0.841073	−	0.540921i	$-0.181924\pi$
$53$	12.2462			1.68215			0.841073	+	0.540921i	$0.181924\pi$
$54$	4.27366	−	5.97795i	0.581571	−	0.813495i
$55$		0			0
$56$	8.39919	+	1.56155i	1.12239	+	0.208671i
$57$	−2.00000	+	1.12311i	−0.264906	+	0.148759i
$58$	−3.68260	−	2.43845i	−0.483549	−	0.320184i
$59$	14.1498			1.84214			0.921071	−	0.389394i	$-0.127315\pi$
$59$	14.1498			1.84214			0.921071	+	0.389394i	$0.127315\pi$
$60$		0			0
$61$	3.12311			0.399873			0.199936	−	0.979809i	$-0.435926\pi$
$61$	3.12311			0.399873			0.199936	+	0.979809i	$0.435926\pi$
$62$	−5.56155	−	3.68260i	−0.706318	−	0.467691i
$63$	4.71659	−	7.73704i	0.594234	−	0.974775i
$64$	7.46543	+	2.87529i	0.933179	+	0.359411i
$65$		0			0
$66$	−3.23519	−	0.237246i	−0.398224	−	0.0292030i
$67$	−4.34475			−0.530796			−0.265398	−	0.964139i	$-0.585503\pi$
$67$	−4.34475			−0.530796			−0.265398	+	0.964139i	$0.585503\pi$
$68$	−1.56155	−	3.68260i	−0.189366	−	0.446581i
$69$	0.561553	−	0.315342i	0.0676030	−	0.0379627i
$70$		0			0
$71$	3.39228			0.402590			0.201295	−	0.979531i	$-0.435485\pi$
$71$	3.39228			0.402590			0.201295	+	0.979531i	$0.435485\pi$
$72$	5.66664	−	6.31579i	0.667819	−	0.744323i
$73$			8.24621i			0.965146i	0.875856	+	0.482573i	$0.160298\pi$
$73$			8.24621i			0.965146i	−0.875856	+	0.482573i	$0.839702\pi$
$74$	−6.04090	−	4.00000i	−0.702240	−	0.464991i
$75$		0			0
$76$	−2.43845	+	1.03399i	−0.279709	+	0.118607i
$77$	−4.00000			−0.455842
$78$	−0.917790	+	12.5154i	−0.103919	+	1.41709i
$79$		−	8.10887i		−	0.912319i	−0.889898	−	0.456160i	$-0.849225\pi$
$79$		−	8.10887i		−	0.912319i	0.889898	−	0.456160i	$-0.150775\pi$
$80$		0			0
$81$	−4.12311	−	8.00000i	−0.458123	−	0.888889i
$82$	−1.32431	−	0.876894i	−0.146245	−	0.0968368i
$83$			15.1022i			1.65769i	0.559481	+	0.828843i	$0.311000\pi$
$83$			15.1022i			1.65769i	−0.559481	+	0.828843i	$0.689000\pi$
$84$	6.39919	−	8.27814i	0.698209	−	0.903219i
$85$		0			0
$86$	−6.04090	+	9.12311i	−0.651407	+	0.983770i
$87$	−4.71659	+	2.64861i	−0.505671	+	0.283961i
$88$	−3.68260	−	0.684658i	−0.392567	−	0.0729848i
$89$		−	10.2462i		−	1.08610i	−0.839702	−	0.543048i	$-0.817270\pi$
$89$		−	10.2462i		−	1.08610i	0.839702	−	0.543048i	$-0.182730\pi$
$90$		0			0
$91$			15.4741i			1.62212i
$92$	0.684658	−	0.290319i	0.0713806	−	0.0302679i
$93$	−7.12311	+	4.00000i	−0.738632	+	0.414781i
$94$	−3.56155	−	2.35829i	−0.367346	−	0.243240i
$95$		0			0
$96$	7.30834	−	6.52596i	0.745904	−	0.666053i
$97$			6.00000i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$			6.00000i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$	1.65767	−	2.50345i	0.167450	−	0.252887i
$99$	−2.06798	+	3.39228i	−0.207839	+	0.340937i
$100$		0			0
$101$		−	0.876894i		−	0.0872543i	−0.999048	−	0.0436271i	$-0.986109\pi$
$101$		−	0.876894i		−	0.0872543i	0.999048	−	0.0436271i	$-0.0138914\pi$
$102$	−4.88586	−	0.358294i	−0.483772	−	0.0354764i
$103$	9.80501			0.966117			0.483058	−	0.875588i	$-0.339526\pi$
$103$	9.80501			0.966117			0.483058	+	0.875588i	$0.339526\pi$
$104$	−2.64861	+	14.2462i	−0.259718	+	1.39696i
$105$		0			0
$106$	9.56155	−	14.4401i	0.928700	−	1.40255i
$107$			3.02045i			0.291998i	0.989285	+	0.145999i	$0.0466396\pi$
$107$			3.02045i			0.291998i	−0.989285	+	0.145999i	$0.953360\pi$
$108$	−3.71211	−	9.70671i	−0.357198	−	0.934029i
$109$	0.876894			0.0839912			0.0419956	−	0.999118i	$-0.486628\pi$
$109$	0.876894			0.0839912			0.0419956	+	0.999118i	$0.486628\pi$
$110$		0			0
$111$	−7.73704	+	4.34475i	−0.734367	+	0.412386i
$112$	8.39919	−	8.68466i	0.793649	−	0.820623i
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$	−0.237246	+	3.23519i	−0.0222201	+	0.303003i
$115$		0			0
$116$	−5.75058	+	2.43845i	−0.533928	+	0.226404i
$117$	13.1231	+	8.00000i	1.21323	+	0.739600i
$118$	11.0478	−	16.6847i	1.01703	−	1.53595i
$119$	−6.04090			−0.553768
$120$		0			0
$121$	−9.24621			−0.840565
$122$	2.43845	−	3.68260i	0.220767	−	0.333407i
$123$	−1.69614	+	0.952473i	−0.152936	+	0.0858816i
$124$	−8.68466	+	3.68260i	−0.779905	+	0.330707i
$125$		0			0
$126$	−5.44050	−	11.6024i	−0.484679	−	1.03363i
$127$	15.1022			1.34011			0.670054	−	0.742313i	$-0.266271\pi$
$127$	15.1022			1.34011			0.670054	+	0.742313i	$0.266271\pi$
$128$	9.21922	−	6.55789i	0.814872	−	0.579641i
$129$	6.56155	+	11.6847i	0.577713	+	1.02878i
$130$		0			0
$131$	5.46026			0.477065			0.238532	−	0.971135i	$-0.423334\pi$
$131$	5.46026			0.477065			0.238532	+	0.971135i	$0.423334\pi$
$132$	−2.80571	+	3.62953i	−0.244205	+	0.315910i
$133$			4.00000i			0.346844i
$134$	−3.39228	+	5.12311i	−0.293049	+	0.442569i
$135$		0			0
$136$	−5.56155	−	1.03399i	−0.476899	−	0.0886637i
$137$	−8.24621			−0.704521			−0.352261	−	0.935902i	$-0.614587\pi$
$137$	−8.24621			−0.704521			−0.352261	+	0.935902i	$0.614587\pi$
$138$	0.0666131	−	0.908365i	0.00567048	−	0.0773251i
$139$			17.5420i			1.48790i	0.668237	+	0.743949i	$0.267049\pi$
$139$			17.5420i			1.48790i	−0.668237	+	0.743949i	$0.732951\pi$
$140$		0			0
$141$	−4.56155	+	2.56155i	−0.384152	+	0.215722i
$142$	2.64861	−	4.00000i	0.222267	−	0.335673i
$143$		−	6.78456i		−	0.567354i
$144$	−3.02287	−	11.6130i	−0.251906	−	0.967752i
$145$		0			0
$146$	9.72350	+	6.43845i	0.804722	+	0.532850i
$147$	−1.80054	−	3.20636i	−0.148506	−	0.264457i
$148$	−9.43318	+	4.00000i	−0.775402	+	0.328798i
$149$			14.0000i			1.14692i	0.819232	+	0.573462i	$0.194400\pi$
$149$			14.0000i			1.14692i	−0.819232	+	0.573462i	$0.805600\pi$
$150$		0			0
$151$		−	7.36520i		−	0.599372i	−0.954038	−	0.299686i	$-0.903118\pi$
$151$		−	7.36520i		−	0.599372i	0.954038	−	0.299686i	$-0.0968819\pi$
$152$	−0.684658	+	3.68260i	−0.0555331	+	0.298698i
$153$	−3.12311	+	5.12311i	−0.252488	+	0.414179i
$154$	−3.12311	+	4.71659i	−0.251667	+	0.380074i
$155$		0			0
$156$	14.0409	+	10.8539i	1.12417	+	0.869010i
$157$			3.36932i			0.268901i	0.990920	+	0.134450i	$0.0429269\pi$
$157$			3.36932i			0.268901i	−0.990920	+	0.134450i	$0.957073\pi$
$158$	−9.56155	−	6.33122i	−0.760676	−	0.503684i
$159$	−10.3857	−	18.4945i	−0.823636	−	1.46671i
$160$		0			0
$161$		−	1.12311i		−	0.0885131i
$162$	−12.6524	−	1.38446i	−0.994067	−	0.108774i
$163$	15.6829			1.22838			0.614189	−	0.789159i	$-0.289483\pi$
$163$	15.6829			1.22838			0.614189	+	0.789159i	$0.289483\pi$
$164$	−2.06798	+	0.876894i	−0.161482	+	0.0684739i
$165$		0			0
$166$	17.8078	+	11.7915i	1.38215	+	0.915196i
$167$			9.06134i			0.701188i	0.936528	+	0.350594i	$0.114020\pi$
$167$			9.06134i			0.701188i	−0.936528	+	0.350594i	$0.885980\pi$
$168$	−4.76481	−	14.0090i	−0.367613	−	1.08082i
$169$	−13.2462			−1.01894
$170$		0			0
$171$	3.39228	+	2.06798i	0.259414	+	0.158142i
$172$	6.04090	+	14.2462i	0.460614	+	1.08626i
$173$	−2.00000			−0.152057			−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000			−0.152057			−0.0760286	+	0.997106i	$0.524224\pi$
$174$	−0.559496	+	7.62953i	−0.0424153	+	0.578393i
$175$		0			0
$176$	−3.68260	+	3.80776i	−0.277587	+	0.287021i
$177$	−12.0000	−	21.3693i	−0.901975	−	1.60622i
$178$	−12.0818	−	8.00000i	−0.905569	−	0.599625i
$179$	10.0138			0.748468			0.374234	−	0.927334i	$-0.377906\pi$
$179$	10.0138			0.748468			0.374234	+	0.927334i	$0.377906\pi$
$180$		0			0
$181$	−12.2462			−0.910254			−0.455127	−	0.890427i	$-0.650406\pi$
$181$	−12.2462			−0.910254			−0.455127	+	0.890427i	$0.650406\pi$
$182$	18.2462	+	12.0818i	1.35250	+	0.895562i
$183$	−2.64861	−	4.71659i	−0.195791	−	0.348660i
$184$	0.192236	−	1.03399i	0.0141718	−	0.0762266i
$185$		0			0
$186$	−0.844964	+	11.5223i	−0.0619558	+	0.844856i
$187$	2.64861			0.193686
$188$	−5.56155	+	2.35829i	−0.405618	+	0.171996i
$189$	−15.6847	−	0.561553i	−1.14089	−	0.0408470i
$190$		0			0
$191$	−24.9073			−1.80223			−0.901113	−	0.433585i	$-0.857248\pi$
$191$	−24.9073			−1.80223			−0.901113	+	0.433585i	$0.857248\pi$
$192$	−1.98889	−	13.7129i	−0.143535	−	0.989645i
$193$		−	0.246211i		−	0.0177227i	−0.999961	−	0.00886134i	$-0.997179\pi$
$193$		−	0.246211i		−	0.0177227i	0.999961	−	0.00886134i	$-0.00282069\pi$
$194$	7.07488	+	4.68466i	0.507947	+	0.336339i
$195$		0			0
$196$	−1.65767	−	3.90928i	−0.118405	−	0.279234i
$197$	4.24621			0.302530			0.151265	−	0.988493i	$-0.451665\pi$
$197$	4.24621			0.302530			0.151265	+	0.988493i	$0.451665\pi$
$198$	2.38537	+	5.08706i	0.169521	+	0.361522i
$199$		−	5.46026i		−	0.387067i	−0.981094	−	0.193534i	$-0.938005\pi$
$199$		−	5.46026i		−	0.387067i	0.981094	−	0.193534i	$-0.0619949\pi$
$200$		0			0
$201$	3.68466	+	6.56155i	0.259896	+	0.462816i
$202$	−1.03399	−	0.684658i	−0.0727511	−	0.0481724i
$203$			9.43318i			0.662079i
$204$	−4.23725	+	5.48140i	−0.296667	+	0.383775i
$205$		0			0
$206$	7.65552	−	11.5616i	0.533385	−	0.805532i
$207$	−0.952473	−	0.580639i	−0.0662014	−	0.0403572i
$208$	14.7304	+	14.2462i	1.02137	+	0.987797i
$209$		−	1.75379i		−	0.121312i
$210$		0			0
$211$		−	16.7984i		−	1.15645i	−0.815878	−	0.578224i	$-0.803746\pi$
$211$		−	16.7984i		−	1.15645i	0.815878	−	0.578224i	$-0.196254\pi$
$212$	−9.56155	−	22.5490i	−0.656690	−	1.54867i
$213$	−2.87689	−	5.12311i	−0.197122	−	0.351029i
$214$	3.56155	+	2.35829i	0.243463	+	0.161210i
$215$		0			0
$216$	−14.3440	−	3.20165i	−0.975983	−	0.217845i
$217$			14.2462i			0.967096i
$218$	0.684658	−	1.03399i	0.0463709	−	0.0700305i
$219$	12.4536	−	6.99337i	0.841538	−	0.472568i
$220$		0			0
$221$		−	10.2462i		−	0.689235i
$222$	−0.917790	+	12.5154i	−0.0615980	+	0.839978i
$223$	−8.31768			−0.556993			−0.278496	−	0.960437i	$-0.589836\pi$
$223$	−8.31768			−0.556993			−0.278496	+	0.960437i	$0.589836\pi$
$224$	−3.68260	−	16.6847i	−0.246054	−	1.11479i
$225$		0			0
$226$	−10.9309	+	16.5081i	−0.727111	+	1.09810i
$227$		−	21.8868i		−	1.45268i	−0.687337	−	0.726339i	$-0.741220\pi$
$227$		−	21.8868i		−	1.45268i	0.687337	−	0.726339i	$-0.258780\pi$
$228$	3.62953	+	2.80571i	0.240371	+	0.185812i
$229$	16.2462			1.07358			0.536790	−	0.843716i	$-0.319637\pi$
$229$	16.2462			1.07358			0.536790	+	0.843716i	$0.319637\pi$
$230$		0			0
$231$	3.39228	+	6.04090i	0.223196	+	0.397462i
$232$	−1.61463	+	8.68466i	−0.106005	+	0.570176i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$	19.6794	−	9.22786i	1.28648	−	0.603244i
$235$		0			0
$236$	−11.0478	−	26.0540i	−0.719151	−	1.69597i
$237$	−12.2462	+	6.87689i	−0.795477	+	0.446702i
$238$	−4.71659	+	7.12311i	−0.305731	+	0.461722i
$239$	−17.3790			−1.12416			−0.562078	−	0.827084i	$-0.689998\pi$
$239$	−17.3790			−1.12416			−0.562078	+	0.827084i	$0.689998\pi$
$240$		0			0
$241$	13.3693			0.861193			0.430597	−	0.902544i	$-0.358303\pi$
$241$	13.3693			0.861193			0.430597	+	0.902544i	$0.358303\pi$
$242$	−7.21922	+	10.9026i	−0.464069	+	0.700849i
$243$	−8.58511	+	13.0114i	−0.550735	+	0.834680i
$244$	−2.43845	−	5.75058i	−0.156106	−	0.368143i
$245$		0			0
$246$	−0.201201	+	2.74367i	−0.0128281	+	0.174930i
$247$	−6.78456			−0.431691
$248$	−2.43845	+	13.1158i	−0.154842	+	0.832853i
$249$	22.8078	−	12.8078i	1.44538	−	0.811659i
$250$		0			0
$251$	18.7033			1.18054			0.590272	−	0.807205i	$-0.299021\pi$
$251$	18.7033			1.18054			0.590272	+	0.807205i	$0.299021\pi$
$252$	−17.9288	−	2.64376i	−1.12941	−	0.166541i
$253$			0.492423i			0.0309583i
$254$	11.7915	−	17.8078i	0.739863	−	1.11736i
$255$		0			0
$256$	−0.534565	−	15.9911i	−0.0334103	−	0.999442i
$257$	30.4924			1.90207			0.951033	−	0.309091i	$-0.100025\pi$
$257$	30.4924			1.90207			0.951033	+	0.309091i	$0.100025\pi$
$258$	18.9010	+	1.38607i	1.17673	+	0.0862929i
$259$			15.4741i			0.961512i
$260$		0			0
$261$	8.00000	+	4.87689i	0.495188	+	0.301872i
$262$	4.26324	−	6.43845i	0.263384	−	0.397769i
$263$		−	23.7917i		−	1.46706i	−0.679656	−	0.733531i	$-0.737871\pi$
$263$		−	23.7917i		−	1.46706i	0.679656	−	0.733531i	$-0.262129\pi$
$264$	2.08912	+	6.14219i	0.128576	+	0.378026i
$265$		0			0
$266$	4.71659	+	3.12311i	0.289193	+	0.191490i
$267$	−15.4741	+	8.68951i	−0.946998	+	0.531789i
$268$	3.39228	+	8.00000i	0.207217	+	0.488678i
$269$		−	14.0000i		−	0.853595i	−0.904347	−	0.426798i	$-0.859642\pi$
$269$		−	14.0000i		−	0.853595i	0.904347	−	0.426798i	$-0.140358\pi$
$270$		0			0
$271$			15.3110i			0.930080i	0.885290	+	0.465040i	$0.153960\pi$
$271$			15.3110i			0.930080i	−0.885290	+	0.465040i	$0.846040\pi$
$272$	−5.56155	+	5.75058i	−0.337219	+	0.348680i
$273$	23.3693	−	13.1231i	1.41438	−	0.794246i
$274$	−6.43845	+	9.72350i	−0.388961	+	0.587418i
$275$		0			0
$276$	−1.01909	−	0.787776i	−0.0613418	−	0.0474186i
$277$		−	23.3693i		−	1.40413i	−0.712115	−	0.702063i	$-0.752262\pi$
$277$		−	23.3693i		−	1.40413i	0.712115	−	0.702063i	$-0.247738\pi$
$278$	20.6847	+	13.6964i	1.24058	+	0.821457i
$279$	12.0818	+	7.36520i	0.723318	+	0.440943i
$280$		0			0
$281$			13.6155i			0.812234i	0.913821	+	0.406117i	$0.133118\pi$
$281$			13.6155i			0.812234i	−0.913821	+	0.406117i	$0.866882\pi$
$282$	−0.541105	+	7.37874i	−0.0322223	+	0.439398i
$283$	−23.2111			−1.37976			−0.689879	−	0.723925i	$-0.742336\pi$
$283$	−23.2111			−1.37976			−0.689879	+	0.723925i	$0.742336\pi$
$284$	−2.64861	−	6.24621i	−0.157166	−	0.370644i
$285$		0			0
$286$	−8.00000	−	5.29723i	−0.473050	−	0.313232i
$287$			3.39228i			0.200240i
$288$	−16.0536	−	5.50276i	−0.945970	−	0.324253i
$289$	−13.0000			−0.764706
$290$		0			0
$291$	9.06134	−	5.08842i	0.531185	−	0.298289i
$292$	15.1838	−	6.43845i	0.888562	−	0.376782i
$293$	−2.49242			−0.145609			−0.0728044	−	0.997346i	$-0.523195\pi$
$293$	−2.49242			−0.145609			−0.0728044	+	0.997346i	$0.523195\pi$
$294$	−5.18660	−	0.380349i	−0.302489	−	0.0221824i
$295$		0			0
$296$	−2.64861	+	14.2462i	−0.153948	+	0.828044i
$297$	6.87689	+	0.246211i	0.399038	+	0.0142866i
$298$	16.5081	+	10.9309i	0.956286	+	0.633208i
$299$	1.90495			0.110166
$300$		0			0
$301$	23.3693			1.34699
$302$	−8.68466	−	5.75058i	−0.499746	−	0.330908i
$303$	−1.32431	+	0.743668i	−0.0760794	+	0.0427226i
$304$	3.80776	+	3.68260i	0.218390	+	0.211212i
$305$		0			0
$306$	3.60245	+	7.68260i	0.205938	+	0.439185i
$307$	11.1293			0.635184			0.317592	−	0.948227i	$-0.397126\pi$
$307$	11.1293			0.635184			0.317592	+	0.948227i	$0.397126\pi$
$308$	3.12311	+	7.36520i	0.177955	+	0.419671i
$309$	−8.31534	−	14.8078i	−0.473043	−	0.842384i
$310$		0			0
$311$	20.7713			1.17783			0.588916	−	0.808194i	$-0.299555\pi$
$311$	20.7713			1.17783			0.588916	+	0.808194i	$0.299555\pi$
$312$	23.7612	−	8.08179i	1.34521	−	0.457541i
$313$		−	22.4924i		−	1.27135i	−0.771958	−	0.635673i	$-0.780722\pi$
$313$		−	22.4924i		−	1.27135i	0.771958	−	0.635673i	$-0.219278\pi$
$314$	3.97292	+	2.63068i	0.224205	+	0.148458i
$315$		0			0
$316$	−14.9309	+	6.33122i	−0.839927	+	0.356159i
$317$	−16.7386			−0.940135			−0.470068	−	0.882630i	$-0.655770\pi$
$317$	−16.7386			−0.940135			−0.470068	+	0.882630i	$0.655770\pi$
$318$	−29.9166	−	2.19387i	−1.67764	−	0.123026i
$319$		−	4.13595i		−	0.231569i
$320$		0			0
$321$	4.56155	−	2.56155i	0.254601	−	0.142972i
$322$	−1.32431	−	0.876894i	−0.0738007	−	0.0488674i
$323$		−	2.64861i		−	0.147373i
$324$	−11.5112	+	13.8381i	−0.639510	+	0.768783i
$325$		0			0
$326$	12.2448	−	18.4924i	0.678178	−	1.02420i
$327$	−0.743668	−	1.32431i	−0.0411249	−	0.0732343i
$328$	−0.580639	+	3.12311i	−0.0320604	+	0.172445i
$329$			9.12311i			0.502973i
$330$		0			0
$331$		−	3.22925i		−	0.177496i	−0.996054	−	0.0887479i	$-0.971713\pi$
$331$		−	3.22925i		−	0.177496i	0.996054	−	0.0887479i	$-0.0282865\pi$
$332$	27.8078	−	11.7915i	1.52615	−	0.647141i
$333$	13.1231	+	8.00000i	0.719142	+	0.438397i
$334$	10.6847	+	7.07488i	0.584638	+	0.387120i
$335$		0			0
$336$	−20.2389	−	5.31946i	−1.10412	−	0.290200i
$337$			1.50758i			0.0821230i	0.999157	+	0.0410615i	$0.0130740\pi$
$337$			1.50758i			0.0821230i	−0.999157	+	0.0410615i	$0.986926\pi$
$338$	−10.3423	+	15.6192i	−0.562549	+	0.849574i
$339$	11.8730	+	21.1431i	0.644852	+	1.14834i
$340$		0			0
$341$		−	6.24621i		−	0.338251i
$342$	5.08706	−	2.38537i	0.275077	−	0.128986i
$343$	14.7304			0.795367
$344$	21.5150	+	4.00000i	1.16001	+	0.215666i
$345$		0			0
$346$	−1.56155	+	2.35829i	−0.0839496	+	0.126783i
$347$			22.6305i			1.21487i	0.794370	+	0.607434i	$0.207801\pi$
$347$			22.6305i			1.21487i	−0.794370	+	0.607434i	$0.792199\pi$
$348$	8.55950	+	6.61668i	0.458837	+	0.354691i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	0.952473	−	26.6034i	0.0508392	−	1.41998i
$352$	1.61463	+	7.31534i	0.0860599	+	0.389909i
$353$	20.2462			1.07760			0.538799	−	0.842435i	$-0.318878\pi$
$353$	20.2462			1.07760			0.538799	+	0.842435i	$0.318878\pi$
$354$	−34.5669	−	2.53489i	−1.83721	−	0.134728i
$355$		0			0
$356$	−18.8664	+	8.00000i	−0.999915	+	0.423999i
$357$	5.12311	+	9.12311i	0.271144	+	0.482846i
$358$	7.81855	−	11.8078i	0.413223	−	0.624060i
$359$	−21.5150			−1.13552			−0.567758	−	0.823195i	$-0.692189\pi$
$359$	−21.5150			−1.13552			−0.567758	+	0.823195i	$0.692189\pi$
$360$		0			0
$361$	17.2462			0.907695
$362$	−9.56155	+	14.4401i	−0.502544	+	0.758954i
$363$	7.84144	+	13.9638i	0.411569	+	0.732912i
$364$	28.4924	−	12.0818i	1.49341	−	0.633258i
$365$		0			0
$366$	−7.62953	−	0.559496i	−0.398802	−	0.0292453i
$367$	−10.9663			−0.572436			−0.286218	−	0.958165i	$-0.592398\pi$
$367$	−10.9663			−0.572436			−0.286218	+	0.958165i	$0.592398\pi$
$368$	−1.06913	−	1.03399i	−0.0557323	−	0.0539003i
$369$	2.87689	+	1.75379i	0.149765	+	0.0912986i
$370$		0			0
$371$	−36.9890			−1.92038
$372$	12.9268	+	9.99267i	0.670221	+	0.518096i
$373$		−	9.12311i		−	0.472377i	−0.971707	−	0.236188i	$-0.924102\pi$
$373$		−	9.12311i		−	0.472377i	0.971707	−	0.236188i	$-0.0758982\pi$
$374$	2.06798	−	3.12311i	0.106932	−	0.161492i
$375$		0			0
$376$	−1.56155	+	8.39919i	−0.0805309	+	0.433155i
$377$	−16.0000			−0.824042
$378$	−12.9084	+	18.0561i	−0.663935	+	0.928704i
$379$		−	18.7033i		−	0.960725i	−0.877070	−	0.480363i	$-0.840505\pi$
$379$		−	18.7033i		−	0.960725i	0.877070	−	0.480363i	$-0.159495\pi$
$380$		0			0
$381$	−12.8078	−	22.8078i	−0.656162	−	1.16848i
$382$	−19.4470	+	29.3693i	−0.994995	+	1.50266i
$383$		−	15.1022i		−	0.771688i	−0.922564	−	0.385844i	$-0.873910\pi$
$383$		−	15.1022i		−	0.771688i	0.922564	−	0.385844i	$-0.126090\pi$
$384$	−17.7224	−	8.36154i	−0.904394	−	0.426698i
$385$		0			0
$386$	−0.290319	−	0.192236i	−0.0147769	−	0.00978455i
$387$	12.0818	−	19.8188i	0.614152	−	1.00745i
$388$	11.0478	−	4.68466i	0.560867	−	0.237827i
$389$			20.7386i			1.05149i	0.850642	+	0.525745i	$0.176213\pi$
$389$			20.7386i			1.05149i	−0.850642	+	0.525745i	$0.823787\pi$
$390$		0			0
$391$			0.743668i			0.0376089i
$392$	−5.90388	−	1.09763i	−0.298191	−	0.0554388i
$393$	−4.63068	−	8.24621i	−0.233587	−	0.415966i
$394$	3.31534	−	5.00691i	0.167024	−	0.252244i
$395$		0			0
$396$	7.86084	+	1.15915i	0.395022	+	0.0582495i
$397$		−	14.8769i		−	0.746650i	−0.927701	−	0.373325i	$-0.878218\pi$
$397$		−	14.8769i		−	0.746650i	0.927701	−	0.373325i	$-0.121782\pi$
$398$	−6.43845	−	4.26324i	−0.322730	−	0.213697i
$399$	6.04090	−	3.39228i	0.302423	−	0.169827i
$400$		0			0
$401$			24.0000i			1.19850i	0.800561	+	0.599251i	$0.204535\pi$
$401$			24.0000i			1.19850i	−0.800561	+	0.599251i	$0.795465\pi$
$402$	10.6139	+	0.778351i	0.529375	+	0.0388206i
$403$	−24.1636			−1.20367
$404$	−1.61463	+	0.684658i	−0.0803307	+	0.0340630i
$405$		0			0
$406$	11.1231	+	7.36520i	0.552030	+	0.365529i
$407$		−	6.78456i		−	0.336298i
$408$	3.15504	+	9.27608i	0.156198	+	0.459235i
$409$	−25.3693			−1.25443			−0.627216	−	0.778845i	$-0.715806\pi$
$409$	−25.3693			−1.25443			−0.627216	+	0.778845i	$0.715806\pi$
$410$		0			0
$411$	6.99337	+	12.4536i	0.344957	+	0.614292i
$412$	−7.65552	−	18.0540i	−0.377161	−	0.889456i
$413$	−42.7386			−2.10303
$414$	−1.42833	+	0.669757i	−0.0701984	+	0.0329167i
$415$		0			0
$416$	28.2995	−	6.24621i	1.38750	−	0.306246i
$417$	26.4924	−	14.8769i	1.29734	−	0.728525i
$418$	−2.06798	−	1.36932i	−0.101148	−	0.0669755i
$419$	−7.36520			−0.359814			−0.179907	−	0.983684i	$-0.557580\pi$
$419$	−7.36520			−0.359814			−0.179907	+	0.983684i	$0.557580\pi$
$420$		0			0
$421$	−25.3693			−1.23642			−0.618212	−	0.786011i	$-0.712143\pi$
$421$	−25.3693			−1.23642			−0.618212	+	0.786011i	$0.712143\pi$
$422$	−19.8078	−	13.1158i	−0.964227	−	0.638466i
$423$	7.73704	+	4.71659i	0.376188	+	0.229328i
$424$	−34.0540	−	6.33122i	−1.65381	−	0.307471i
$425$		0			0
$426$	−8.28711	−	0.607718i	−0.401512	−	0.0294440i
$427$	−9.43318			−0.456503
$428$	5.56155	−	2.35829i	0.268828	−	0.113992i
$429$	−10.2462	+	5.75379i	−0.494692	+	0.277796i
$430$		0			0
$431$	−16.6354			−0.801297			−0.400648	−	0.916232i	$-0.631215\pi$
$431$	−16.6354			−0.801297			−0.400648	+	0.916232i	$0.631215\pi$
$432$	−14.9747	+	14.4139i	−0.720468	+	0.693488i
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$	16.7984	+	11.1231i	0.806348	+	0.533926i
$435$		0			0
$436$	−0.684658	−	1.61463i	−0.0327892	−	0.0773266i
$437$	0.492423			0.0235558
$438$	1.47729	−	20.1449i	0.0705875	−	0.962561i
$439$		−	9.27015i		−	0.442440i	−0.975224	−	0.221220i	$-0.928996\pi$
$439$		−	9.27015i		−	0.442440i	0.975224	−	0.221220i	$-0.0710039\pi$
$440$		0			0
$441$	−3.31534	+	5.43845i	−0.157873	+	0.258974i
$442$	−12.0818	−	8.00000i	−0.574672	−	0.380521i
$443$		−	16.5896i		−	0.788195i	−0.919069	−	0.394097i	$-0.871057\pi$
$443$		−	16.5896i		−	0.788195i	0.919069	−	0.394097i	$-0.128943\pi$
$444$	14.0409	+	10.8539i	0.666351	+	0.515105i
$445$		0			0
$446$	−6.49424	+	9.80776i	−0.307511	+	0.464411i
$447$	21.1431	−	11.8730i	1.00004	−	0.561573i
$448$	−22.5490	−	8.68466i	−1.06534	−	0.410312i
$449$			27.3693i			1.29164i	0.763491	+	0.645819i	$0.223484\pi$
$449$			27.3693i			1.29164i	−0.763491	+	0.645819i	$0.776516\pi$
$450$		0			0
$451$		−	1.48734i		−	0.0700359i
$452$	10.9309	+	25.7782i	0.514145	+	1.21250i
$453$	−11.1231	+	6.24621i	−0.522609	+	0.293473i
$454$	−25.8078	−	17.0887i	−1.21122	−	0.802012i
$455$		0			0
$456$	6.14219	−	2.08912i	0.287634	−	0.0978319i
$457$			10.0000i			0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$			10.0000i			0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	12.6847	−	19.1567i	0.592715	−	0.895133i
$459$	10.3857	+	0.371834i	0.484761	+	0.0173557i
$460$		0			0
$461$			41.8617i			1.94970i	0.222872	+	0.974848i	$0.428457\pi$
$461$			41.8617i			1.94970i	−0.222872	+	0.974848i	$0.571543\pi$
$462$	9.77172	+	0.716589i	0.454622	+	0.0333387i
$463$	−3.02045			−0.140372			−0.0701861	−	0.997534i	$-0.522359\pi$
$463$	−3.02045			−0.140372			−0.0701861	+	0.997534i	$0.522359\pi$
$464$	8.97983	+	8.68466i	0.416878	+	0.403175i
$465$		0			0
$466$	7.80776	−	11.7915i	0.361688	−	0.546229i
$467$		−	2.27678i		−	0.105357i	−0.998612	−	0.0526784i	$-0.983224\pi$
$467$		−	2.27678i		−	0.105357i	0.998612	−	0.0526784i	$-0.0167758\pi$
$468$	4.48419	−	30.4098i	0.207282	−	1.40569i
$469$	13.1231			0.605969
$470$		0			0
$471$	5.08842	−	2.85742i	0.234462	−	0.131663i
$472$	−39.3473	−	7.31534i	−1.81111	−	0.336716i
$473$	−10.2462			−0.471121
$474$	−1.45268	+	19.8094i	−0.0667239	+	0.909876i
$475$		0			0
$476$	4.71659	+	11.1231i	0.216184	+	0.509827i
$477$	−19.1231	+	31.3693i	−0.875587	+	1.43630i
$478$	−13.5691	+	20.4924i	−0.620637	+	0.937302i
$479$	−25.6509			−1.17202			−0.586010	−	0.810304i	$-0.699302\pi$
$479$	−25.6509			−1.17202			−0.586010	+	0.810304i	$0.699302\pi$
$480$		0			0
$481$	−26.2462			−1.19672
$482$	10.4384	−	15.7644i	0.475458	−	0.718048i
$483$	−1.69614	+	0.952473i	−0.0771771	+	0.0433390i
$484$	7.21922	+	17.0251i	0.328147	+	0.773866i
$485$		0			0
$486$	8.63928	+	20.2821i	0.391886	+	0.920014i
$487$	−25.2791			−1.14550			−0.572752	−	0.819728i	$-0.694124\pi$
$487$	−25.2791			−1.14550			−0.572752	+	0.819728i	$0.694124\pi$
$488$	−8.68466	−	1.61463i	−0.393136	−	0.0730907i
$489$	−13.3002	−	23.6847i	−0.601455	−	1.07106i
$490$		0			0
$491$	26.9752			1.21737			0.608687	−	0.793410i	$-0.291696\pi$
$491$	26.9752			1.21737			0.608687	+	0.793410i	$0.291696\pi$
$492$	3.07810	+	2.37944i	0.138771	+	0.107273i
$493$		−	6.24621i		−	0.281315i
$494$	−5.29723	+	8.00000i	−0.238334	+	0.359937i
$495$		0			0
$496$	13.5616	+	13.1158i	0.608932	+	0.588916i
$497$	−10.2462			−0.459605
$498$	2.70552	−	36.8937i	0.121237	−	1.65325i
$499$		−	32.2725i		−	1.44471i	−0.691521	−	0.722357i	$-0.743059\pi$
$499$		−	32.2725i		−	1.44471i	0.691521	−	0.722357i	$-0.256941\pi$
$500$		0			0
$501$	13.6847	−	7.68466i	0.611385	−	0.343325i
$502$	14.6031	−	22.0540i	0.651769	−	0.984317i
$503$			14.3586i			0.640217i	0.947381	+	0.320109i	$0.103719\pi$
$503$			14.3586i			0.640217i	−0.947381	+	0.320109i	$0.896281\pi$
$504$	−17.1158	+	19.0765i	−0.762397	+	0.849736i
$505$		0			0
$506$	0.580639	+	0.384472i	0.0258125	+	0.0170919i
$507$	11.2337	+	20.0047i	0.498907	+	0.888442i
$508$	−11.7915	−	27.8078i	−0.523162	−	1.23377i
$509$		−	11.1231i		−	0.493023i	−0.969140	−	0.246511i	$-0.920716\pi$
$509$		−	11.1231i		−	0.493023i	0.969140	−	0.246511i	$-0.0792843\pi$
$510$		0			0
$511$		−	24.9073i		−	1.10183i
$512$	−19.2732	−	11.8551i	−0.851763	−	0.523927i
$513$	0.246211	−	6.87689i	0.0108705	−	0.303622i
$514$	23.8078	−	35.9551i	1.05012	−	1.58591i
$515$		0			0
$516$	16.3919	−	21.2049i	0.721612	−	0.933494i
$517$		−	4.00000i		−	0.175920i
$518$	18.2462	+	12.0818i	0.801692	+	0.530843i
$519$	1.69614	+	3.02045i	0.0744523	+	0.132583i
$520$		0			0
$521$		−	38.2462i		−	1.67560i	−0.545980	−	0.837798i	$-0.683842\pi$
$521$		−	38.2462i		−	1.67560i	0.545980	−	0.837798i	$-0.316158\pi$
$522$	11.9968	−	5.62541i	0.525085	−	0.246218i
$523$	35.2929			1.54325			0.771625	−	0.636077i	$-0.219444\pi$
$523$	35.2929			1.54325			0.771625	+	0.636077i	$0.219444\pi$
$524$	−4.26324	−	10.0540i	−0.186241	−	0.439210i
$525$		0			0
$526$	−28.0540	−	18.5760i	−1.22321	−	0.809954i
$527$		−	9.43318i		−	0.410916i
$528$	8.87368	+	2.33230i	0.386177	+	0.101500i
$529$	22.8617			0.993989
$530$		0			0
$531$	−22.0956	+	36.2454i	−0.958868	+	1.57292i
$532$	7.36520	−	3.12311i	0.319322	−	0.135404i
$533$	−5.75379			−0.249224
$534$	−1.83558	+	25.0308i	−0.0794333	+	1.08319i
$535$		0			0
$536$	12.0818	+	2.24621i	0.521854	+	0.0970215i
$537$	−8.49242	−	15.1231i	−0.366475	−	0.652610i
$538$	−16.5081	−	10.9309i	−0.711713	−	0.471263i
$539$	2.81164			0.121106
$540$		0			0
$541$	−26.9848			−1.16017			−0.580085	−	0.814556i	$-0.696980\pi$
$541$	−26.9848			−1.16017			−0.580085	+	0.814556i	$0.696980\pi$
$542$	18.0540	+	11.9545i	0.775485	+	0.513490i
$543$	10.3857	+	18.4945i	0.445691	+	0.793676i
$544$	2.43845	+	11.0478i	0.104548	+	0.473671i
$545$		0			0
$546$	2.77214	−	37.8021i	0.118637	−	1.61778i
$547$	5.83209			0.249362			0.124681	−	0.992197i	$-0.460209\pi$
$547$	5.83209			0.249362			0.124681	+	0.992197i	$0.460209\pi$
$548$	6.43845	+	15.1838i	0.275037	+	0.648618i
$549$	−4.87689	+	8.00000i	−0.208141	+	0.341432i
$550$		0			0
$551$	−4.13595			−0.176197
$552$	−1.72458	+	0.586575i	−0.0734031	+	0.0249663i
$553$			24.4924i			1.04152i
$554$	−27.5559	−	18.2462i	−1.17074	−	0.775207i
$555$		0			0
$556$	32.3002	−	13.6964i	1.36983	−	0.580858i
$557$	36.2462			1.53580			0.767901	−	0.640569i	$-0.221301\pi$
$557$	36.2462			1.53580			0.767901	+	0.640569i	$0.221301\pi$
$558$	18.1178	−	8.49563i	0.766989	−	0.359649i
$559$			39.6377i			1.67649i
$560$		0			0
$561$	−2.24621	−	4.00000i	−0.0948351	−	0.168880i
$562$	16.0547	+	10.6307i	0.677227	+	0.448428i
$563$		−	7.90007i		−	0.332948i	−0.986046	−	0.166474i	$-0.946762\pi$
$563$		−	7.90007i		−	0.332948i	0.986046	−	0.166474i	$-0.0532382\pi$
$564$	8.27814	+	6.39919i	0.348573	+	0.269455i
$565$		0			0
$566$	−18.1227	+	27.3693i	−0.761753	+	1.15042i
$567$	12.4536	+	24.1636i	0.523003	+	1.01478i
$568$	−9.43318	−	1.75379i	−0.395807	−	0.0735873i
$569$			13.1231i			0.550149i	0.961423	+	0.275075i	$0.0887026\pi$
$569$			13.1231i			0.550149i	−0.961423	+	0.275075i	$0.911297\pi$
$570$		0			0
$571$			33.0161i			1.38168i	0.723007	+	0.690841i	$0.242759\pi$
$571$			33.0161i			1.38168i	−0.723007	+	0.690841i	$0.757241\pi$
$572$	−12.4924	+	5.29723i	−0.522334	+	0.221488i
$573$	21.1231	+	37.6155i	0.882430	+	1.57141i
$574$	4.00000	+	2.64861i	0.166957	+	0.110551i
$575$		0			0
$576$	−19.0229	+	14.6332i	−0.792620	+	0.609716i
$577$			32.2462i			1.34243i	0.741264	+	0.671214i	$0.234227\pi$
$577$			32.2462i			1.34243i	−0.741264	+	0.671214i	$0.765773\pi$
$578$	−10.1501	+	15.3289i	−0.422188	+	0.637599i
$579$	−0.371834	+	0.208805i	−0.0154529	+	0.00867762i
$580$		0			0
$581$		−	45.6155i		−	1.89245i
$582$	1.07488	−	14.6576i	0.0445554	−	0.607576i
$583$	16.2177			0.671670
$584$	4.26324	−	22.9309i	0.176414	−	0.948886i
$585$		0			0
$586$	−1.94602	+	2.93893i	−0.0803895	+	0.121406i
$587$		−	1.85917i		−	0.0767362i	−0.999264	−	0.0383681i	$-0.987784\pi$
$587$		−	1.85917i		−	0.0767362i	0.999264	−	0.0383681i	$-0.0122159\pi$
$588$	−4.49806	+	5.81880i	−0.185497	+	0.239963i
$589$	−6.24621			−0.257371
$590$		0			0
$591$	−3.60109	−	6.41273i	−0.148129	−	0.263784i
$592$	14.7304	+	14.2462i	0.605416	+	0.585516i
$593$	−8.24621			−0.338631			−0.169316	−	0.985562i	$-0.554156\pi$
$593$	−8.24621			−0.338631			−0.169316	+	0.985562i	$0.554156\pi$
$594$	5.65964	−	7.91664i	0.232218	−	0.324823i
$595$		0			0
$596$	25.7782	−	10.9309i	1.05592	−	0.447746i
$597$	−8.24621	+	4.63068i	−0.337495	+	0.189521i
$598$	1.48734	−	2.24621i	0.0608217	−	0.0918544i
$599$	44.1912			1.80560			0.902802	−	0.430056i	$-0.141506\pi$
$599$	44.1912			1.80560			0.902802	+	0.430056i	$0.141506\pi$
$600$		0			0
$601$	23.1231			0.943211			0.471606	−	0.881810i	$-0.343675\pi$
$601$	23.1231			0.943211			0.471606	+	0.881810i	$0.343675\pi$
$602$	18.2462	−	27.5559i	0.743660	−	1.12309i
$603$	6.78456	−	11.1293i	0.276289	−	0.453221i
$604$	−13.5616	+	5.75058i	−0.551812	+	0.233988i
$605$		0			0
$606$	−0.157093	+	2.14219i	−0.00638148	+	0.0870206i
$607$	4.50778			0.182965			0.0914827	−	0.995807i	$-0.470839\pi$
$607$	4.50778			0.182965			0.0914827	+	0.995807i	$0.470839\pi$
$608$	7.31534	−	1.61463i	0.296676	−	0.0654817i
$609$	14.2462	−	8.00000i	0.577286	−	0.324176i
$610$		0			0
$611$	−15.4741			−0.626014
$612$	11.8716	+	1.75058i	0.479882	+	0.0707629i
$613$			9.12311i			0.368479i	0.982881	+	0.184239i	$0.0589822\pi$
$613$			9.12311i			0.368479i	−0.982881	+	0.184239i	$0.941018\pi$
$614$	8.68951	−	13.1231i	0.350680	−	0.529605i
$615$		0			0
$616$	11.1231	+	2.06798i	0.448163	+	0.0833211i
$617$	−14.0000			−0.563619			−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000			−0.563619			−0.281809	+	0.959470i	$0.590935\pi$
$618$	−23.9530	−	1.75654i	−0.963529	−	0.0706584i
$619$			28.1365i			1.13090i	0.824782	+	0.565451i	$0.191298\pi$
$619$			28.1365i			1.13090i	−0.824782	+	0.565451i	$0.808702\pi$
$620$		0			0
$621$	−0.0691303	+	1.93087i	−0.00277410	+	0.0774831i
$622$	16.2177	−	24.4924i	0.650272	−	0.982057i
$623$			30.9481i			1.23991i
$624$	9.02255	−	34.3280i	0.361191	−	1.37422i
$625$		0			0
$626$	−26.5219	−	17.5616i	−1.06003	−	0.701901i
$627$	−2.64861	+	1.48734i	−0.105775	+	0.0593985i
$628$	6.20393	−	2.63068i	0.247564	−	0.104976i
$629$		−	10.2462i		−	0.408543i
$630$		0			0
$631$			39.8007i			1.58444i	0.610235	+	0.792220i	$0.291075\pi$
$631$			39.8007i			1.58444i	−0.610235	+	0.792220i	$0.708925\pi$
$632$	−4.19224	+	22.5490i	−0.166758	+	0.896949i
$633$	−25.3693	+	14.2462i	−1.00834	+	0.566236i
$634$	−13.0691	+	19.7373i	−0.519041	+	0.783869i
$635$		0			0
$636$	−25.9451	+	33.5632i	−1.02879	+	1.33087i
$637$		−	10.8769i		−	0.430958i
$638$	−4.87689	−	3.22925i	−0.193078	−	0.127847i
$639$	−5.29723	+	8.68951i	−0.209555	+	0.343752i
$640$		0			0
$641$		−	6.38447i		−	0.252171i	−0.992019	−	0.126086i	$-0.959759\pi$
$641$		−	6.38447i		−	0.252171i	0.992019	−	0.126086i	$-0.0402414\pi$
$642$	0.541105	−	7.37874i	0.0213557	−	0.291216i
$643$	−3.60109			−0.142013			−0.0710065	−	0.997476i	$-0.522621\pi$
$643$	−3.60109			−0.142013			−0.0710065	+	0.997476i	$0.522621\pi$
$644$	−2.06798	+	0.876894i	−0.0814896	+	0.0345545i
$645$		0			0
$646$	−3.12311	−	2.06798i	−0.122877	−	0.0813634i
$647$			36.6172i			1.43957i	0.694197	+	0.719786i	$0.255760\pi$
$647$			36.6172i			1.43957i	−0.694197	+	0.719786i	$0.744240\pi$
$648$	7.32948	+	24.3778i	0.287929	+	0.957652i
$649$	18.7386			0.735556
$650$		0			0
$651$	21.5150	−	12.0818i	0.843238	−	0.473523i
$652$	−12.2448	−	28.8769i	−0.479544	−	1.13091i
$653$	38.9848			1.52559			0.762797	−	0.646638i	$-0.223825\pi$
$653$	38.9848			1.52559			0.762797	+	0.646638i	$0.223825\pi$
$654$	−2.14219	−	0.157093i	−0.0837663	−	0.00614283i
$655$		0			0
$656$	3.22925	+	3.12311i	0.126081	+	0.121937i
$657$	−21.1231	−	12.8769i	−0.824091	−	0.502375i
$658$	10.7575	+	7.12311i	0.419370	+	0.277688i
$659$	−24.7442			−0.963898			−0.481949	−	0.876199i	$-0.660071\pi$
$659$	−24.7442			−0.963898			−0.481949	+	0.876199i	$0.660071\pi$
$660$		0			0
$661$	28.1080			1.09327			0.546636	−	0.837370i	$-0.315908\pi$
$661$	28.1080			1.09327			0.546636	+	0.837370i	$0.315908\pi$
$662$	−3.80776	−	2.52132i	−0.147993	−	0.0979940i
$663$	−15.4741	+	8.68951i	−0.600963	+	0.337473i
$664$	7.80776	−	41.9960i	0.303000	−	1.62976i
$665$		0			0
$666$	19.6794	−	9.22786i	0.762561	−	0.357572i
$667$	1.16128			0.0449648
$668$	16.6847	−	7.07488i	0.645549	−	0.273735i
$669$	7.05398	+	12.5616i	0.272722	+	0.485658i
$670$		0			0
$671$	4.13595			0.159667
$672$	−22.0745	+	19.7113i	−0.851541	+	0.760381i
$673$			22.4924i			0.867019i	0.901149	+	0.433510i	$0.142725\pi$
$673$			22.4924i			0.867019i	−0.901149	+	0.433510i	$0.857275\pi$
$674$	1.77766	+	1.17708i	0.0684727	+	0.0453395i
$675$		0			0
$676$	10.3423	+	24.3903i	0.397782	+	0.938087i
$677$	1.50758			0.0579409			0.0289705	−	0.999580i	$-0.490777\pi$
$677$	1.50758			0.0579409			0.0289705	+	0.999580i	$0.490777\pi$
$678$	34.2010	+	2.50806i	1.31348	+	0.0963215i
$679$		−	18.1227i		−	0.695485i
$680$		0			0
$681$	−33.0540	+	18.5616i	−1.26663	+	0.711280i
$682$	−7.36520	−	4.87689i	−0.282028	−	0.186746i
$683$			7.90007i			0.302288i	0.988512	+	0.151144i	$0.0482957\pi$
$683$			7.90007i			0.302288i	−0.988512	+	0.151144i	$0.951704\pi$
$684$	1.15915	−	7.86084i	0.0443212	−	0.300567i
$685$		0			0
$686$	11.5012	−	17.3693i	0.439116	−	0.663164i
$687$	−13.7779	−	24.5354i	−0.525661	−	0.936085i
$688$	21.5150	−	22.2462i	0.820251	−	0.848129i
$689$		−	62.7386i		−	2.39015i
$690$		0			0
$691$		−	18.2857i		−	0.695621i	−0.937565	−	0.347811i	$-0.886925\pi$
$691$		−	18.2857i		−	0.695621i	0.937565	−	0.347811i	$-0.113075\pi$
$692$	1.56155	+	3.68260i	0.0593613	+	0.139991i
$693$	6.24621	−	10.2462i	0.237274	−	0.389221i
$694$	26.6847	+	17.6693i	1.01294	+	0.670719i
$695$		0			0
$696$	14.4851	−	4.92676i	0.549056	−	0.186748i
$697$		−	2.24621i		−	0.0850813i
$698$	10.9309	−	16.5081i	0.413740	−	0.624839i
$699$	−8.48071	−	15.1022i	−0.320770	−	0.571219i
$700$		0			0
$701$			17.5076i			0.661252i	0.943762	+	0.330626i	$0.107260\pi$
$701$			17.5076i			0.661252i	−0.943762	+	0.330626i	$0.892740\pi$
$702$	−30.6256	−	21.8944i	−1.15589	−	0.826351i
$703$	−6.78456			−0.255885
$704$	9.88653	+	3.80776i	0.372612	+	0.143511i
$705$		0			0
$706$	15.8078	−	23.8733i	0.594933	−	0.898482i
$707$			2.64861i			0.0996114i
$708$	−29.9780	+	38.7803i	−1.12664	+	1.45745i
$709$	−6.49242			−0.243828			−0.121914	−	0.992541i	$-0.538903\pi$
$709$	−6.49242			−0.243828			−0.121914	+	0.992541i	$0.538903\pi$
$710$		0			0
$711$	20.7713	+	12.6624i	0.778985	+	0.474878i
$712$	−5.29723	+	28.4924i	−0.198522	+	1.06780i
$713$	1.75379			0.0656799
$714$	14.7575	+	1.08221i	0.552285	+	0.0405007i
$715$		0			0
$716$	−7.81855	−	18.4384i	−0.292193	−	0.689077i
$717$	14.7386	+	26.2462i	0.550424	+	0.980183i
$718$	−16.7984	+	25.3693i	−0.626910	+	0.946774i
$719$	30.9481			1.15417			0.577086	−	0.816684i	$-0.304190\pi$
$719$	30.9481			1.15417			0.577086	+	0.816684i	$0.304190\pi$
$720$		0			0
$721$	−29.6155			−1.10294
$722$	13.4654	−	20.3358i	0.501132	−	0.756821i
$723$	−11.3381	−	20.1907i	−0.421669	−	0.750899i
$724$	9.56155	+	22.5490i	0.355352	+	0.838025i
$725$		0			0
$726$	22.5878	+	1.65643i	0.838314	+	0.0614760i
$727$	10.9663			0.406717			0.203359	−	0.979104i	$-0.434814\pi$
$727$	10.9663			0.406717			0.203359	+	0.979104i	$0.434814\pi$
$728$	8.00000	−	43.0299i	0.296500	−	1.59480i
$729$	26.9309	+	1.93087i	0.997440	+	0.0715137i
$730$		0			0
$731$	−15.4741			−0.572329
$732$	−6.61668	+	8.55950i	−0.244560	+	0.316368i
$733$		−	26.8769i		−	0.992721i	−0.868117	−	0.496360i	$-0.834669\pi$
$733$		−	26.8769i		−	0.992721i	0.868117	−	0.496360i	$-0.165331\pi$
$734$	−8.56222	+	12.9309i	−0.316037	+	0.477287i
$735$		0			0
$736$	−2.05398	+	0.453349i	−0.0757105	+	0.0167107i
$737$	−5.75379			−0.211944
$738$	4.31419	−	2.02297i	0.158807	−	0.0744664i
$739$		−	26.9752i		−	0.992300i	−0.868237	−	0.496150i	$-0.834747\pi$
$739$		−	26.9752i		−	0.992300i	0.868237	−	0.496150i	$-0.165253\pi$
$740$		0			0
$741$	5.75379	+	10.2462i	0.211371	+	0.376404i
$742$	−28.8802	+	43.6155i	−1.06022	+	1.60118i
$743$		−	9.80501i		−	0.359711i	−0.983693	−	0.179856i	$-0.942437\pi$
$743$		−	9.80501i		−	0.359711i	0.983693	−	0.179856i	$-0.0575630\pi$
$744$	21.8757	−	7.44050i	0.802004	−	0.272782i
$745$		0			0
$746$	−10.7575	−	7.12311i	−0.393860	−	0.260795i
$747$	−38.6852	−	23.5829i	−1.41542	−	0.862855i
$748$	−2.06798	−	4.87689i	−0.0756127	−	0.178317i
$749$		−	9.12311i		−	0.333351i
$750$		0			0
$751$		−	11.5012i		−	0.419683i	−0.977735	−	0.209842i	$-0.932705\pi$
$751$		−	11.5012i		−	0.419683i	0.977735	−	0.209842i	$-0.0672948\pi$
$752$	8.68466	+	8.39919i	0.316697	+	0.306287i
$753$	−15.8617	−	28.2462i	−0.578034	−	1.02935i
$754$	−12.4924	+	18.8664i	−0.454947	+	0.687072i
$755$		0			0
$756$	11.2122	+	29.3186i	0.407785	+	1.06631i
$757$		−	10.8769i		−	0.395327i	−0.980270	−	0.197664i	$-0.936665\pi$
$757$		−	10.8769i		−	0.395327i	0.980270	−	0.197664i	$-0.0633354\pi$
$758$	−22.0540	−	14.6031i	−0.801036	−	0.530409i
$759$	0.743668	−	0.417609i	0.0269934	−	0.0151582i
$760$		0			0
$761$		−	31.2311i		−	1.13212i	−0.824362	−	0.566062i	$-0.808466\pi$
$761$		−	31.2311i		−	1.13212i	0.824362	−	0.566062i	$-0.191534\pi$
$762$	−36.8937	−	2.70552i	−1.33652	−	0.0980108i
$763$	−2.64861			−0.0958863
$764$	19.4470	+	45.8617i	0.703568	+	1.65922i
$765$		0			0
$766$	−17.8078	−	11.7915i	−0.643421	−	0.426043i
$767$		−	72.4908i		−	2.61749i
$768$	−23.6967	+	14.3689i	−0.855083	+	0.518492i
$769$	−38.9848			−1.40583			−0.702915	−	0.711274i	$-0.748118\pi$
$769$	−38.9848			−1.40583			−0.702915	+	0.711274i	$0.748118\pi$
$770$		0			0
$771$	−25.8597	−	46.0504i	−0.931315	−	1.65846i
$772$	−0.453349	+	0.192236i	−0.0163164	+	0.00691872i
$773$	0.246211			0.00885560			0.00442780	−	0.999990i	$-0.498591\pi$
$773$	0.246211			0.00885560			0.00442780	+	0.999990i	$0.498591\pi$
$774$	−13.9361	−	29.7203i	−0.500924	−	1.06827i
$775$		0			0
$776$	3.10196	−	16.6847i	0.111354	−	0.598944i
$777$	23.3693	−	13.1231i	0.838370	−	0.470789i
$778$	24.4539	+	16.1922i	0.876715	+	0.580520i
$779$	−1.48734			−0.0532894
$780$		0			0
$781$	4.49242			0.160752
$782$	0.876894	+	0.580639i	0.0313577	+	0.0207636i
$783$	0.580639	−	16.2177i	0.0207503	−	0.579575i
$784$	−5.90388	+	6.10454i	−0.210853	+	0.218019i
$785$		0			0
$786$	−13.3390	−	0.978190i	−0.475787	−	0.0348909i
$787$	42.0775			1.49990			0.749950	−	0.661495i	$-0.230078\pi$
$787$	42.0775			1.49990			0.749950	+	0.661495i	$0.230078\pi$
$788$	−3.31534	−	7.81855i	−0.118104	−	0.278524i
$789$	−35.9309	+	20.1771i	−1.27917	+	0.718323i
$790$		0			0
$791$	42.2863			1.50353
$792$	7.50437	−	8.36405i	0.266656	−	0.297203i
$793$		−	16.0000i		−	0.568177i
$794$	−17.5420	−	11.6155i	−0.622544	−	0.412220i
$795$		0			0
$796$	−10.0540	+	4.26324i	−0.356354	+	0.151107i
$797$	12.7386			0.451226			0.225613	−	0.974217i	$-0.427562\pi$
$797$	12.7386			0.451226			0.225613	+	0.974217i	$0.427562\pi$
$798$	0.716589	−	9.77172i	0.0253670	−	0.345915i
$799$		−	6.04090i		−	0.213712i
$800$		0			0
$801$	26.2462	+	16.0000i	0.927364	+	0.565332i
$802$	28.2995	+	18.7386i	0.999291	+	0.661684i
$803$			10.9205i			0.385377i
$804$	9.20490	−	11.9077i	0.324632	−	0.419951i
$805$		0			0
$806$	−18.8664	+	28.4924i	−0.664539	+	1.00360i
$807$	−21.1431	+	11.8730i	−0.744274	+	0.417949i
$808$	−0.453349	+	2.43845i	−0.0159488	+	0.0857843i
$809$			29.7538i			1.04609i	0.852306	+	0.523044i	$0.175204\pi$
$809$			29.7538i			1.04609i	−0.852306	+	0.523044i	$0.824796\pi$
$810$		0			0
$811$		−	46.2592i		−	1.62438i	−0.583393	−	0.812190i	$-0.698275\pi$
$811$		−	46.2592i		−	1.62438i	0.583393	−	0.812190i	$-0.301725\pi$
$812$	17.3693	−	7.36520i	0.609544	−	0.258468i
$813$	23.1231	−	12.9848i	0.810963	−	0.455398i
$814$	−8.00000	−	5.29723i	−0.280400	−	0.185668i
$815$		0			0
$816$	13.4012	+	3.52230i	0.469137	+	0.123305i
$817$			10.2462i			0.358470i
$818$	−19.8078	+	29.9142i	−0.692562	+	1.04592i
$819$	−39.6377	−	24.1636i	−1.38505	−	0.844344i
$820$		0			0
$821$			53.2311i			1.85778i	0.370360	+	0.928888i	$0.379234\pi$
$821$			53.2311i			1.85778i	−0.370360	+	0.928888i	$0.620766\pi$
$822$	20.1449	+	1.47729i	0.702635	+	0.0515263i
$823$	−48.2814			−1.68298			−0.841492	−	0.540270i	$-0.818322\pi$
$823$	−48.2814			−1.68298			−0.841492	+	0.540270i	$0.818322\pi$
$824$	−27.2655	−	5.06913i	−0.949840	−	0.176592i
$825$		0			0
$826$	−33.3693	+	50.3951i	−1.16107	+	1.75347i
$827$			17.7509i			0.617258i	0.951183	+	0.308629i	$0.0998701\pi$
$827$			17.7509i			0.617258i	−0.951183	+	0.308629i	$0.900130\pi$
$828$	−0.325462	+	2.20714i	−0.0113106	+	0.0767033i
$829$	8.87689			0.308307			0.154154	−	0.988047i	$-0.450735\pi$
$829$	8.87689			0.308307			0.154154	+	0.988047i	$0.450735\pi$
$830$		0			0
$831$	−35.2929	+	19.8188i	−1.22430	+	0.687508i
$832$	14.7304	−	38.2462i	0.510685	−	1.32595i
$833$	4.24621			0.147122
$834$	3.14261	−	42.8540i	0.108820	−	1.48391i
$835$		0			0
$836$	−3.22925	+	1.36932i	−0.111686	+	0.0473588i
$837$	0.876894	−	24.4924i	0.0303099	−	0.846582i
$838$	−5.75058	+	8.68466i	−0.198650	+	0.300007i
$839$	17.7051			0.611247			0.305624	−	0.952152i	$-0.401135\pi$
$839$	17.7051			0.611247			0.305624	+	0.952152i	$0.401135\pi$
$840$		0			0
$841$	19.2462			0.663662
$842$	−19.8078	+	29.9142i	−0.682621	+	1.03091i
$843$	20.5625	−	11.5469i	0.708210	−	0.397697i
$844$	−30.9309	+	13.1158i	−1.06468	+	0.451464i
$845$		0			0
$846$	11.6024	−	5.44050i	0.398900	−	0.187048i
$847$	27.9277			0.959607
$848$	−34.0540	+	35.2114i	−1.16942	+	1.20916i
$849$	19.6847	+	35.0540i	0.675576	+	1.20305i
$850$		0			0
$851$	1.90495			0.0653007
$852$	−7.18697	+	9.29723i	−0.246221	+	0.318518i
$853$		−	7.86174i		−	0.269181i	−0.990901	−	0.134590i	$-0.957028\pi$
$853$		−	7.86174i		−	0.269181i	0.990901	−	0.134590i	$-0.0429719\pi$
$854$	−7.36520	+	11.1231i	−0.252032	+	0.380625i
$855$		0			0
$856$	1.56155	−	8.39919i	0.0533728	−	0.287078i
$857$	−20.7386			−0.708418			−0.354209	−	0.935166i	$-0.615250\pi$
$857$	−20.7386			−0.708418			−0.354209	+	0.935166i	$0.615250\pi$
$858$	−1.21544	+	16.5742i	−0.0414943	+	0.565834i
$859$			33.4337i			1.14074i	0.821386	+	0.570372i	$0.193201\pi$
$859$			33.4337i			1.14074i	−0.821386	+	0.570372i	$0.806799\pi$
$860$		0			0
$861$	5.12311	−	2.87689i	0.174595	−	0.0980443i
$862$	−12.9885	+	19.6155i	−0.442390	+	0.668108i
$863$			10.5487i			0.359081i	0.983751	+	0.179541i	$0.0574611\pi$
$863$			10.5487i			0.359081i	−0.983751	+	0.179541i	$0.942539\pi$
$864$	5.30423	+	28.9113i	0.180453	+	0.983584i
$865$		0			0
$866$	21.2247	+	14.0540i	0.721243	+	0.477574i
$867$	11.0249	+	19.6329i	0.374426	+	0.666769i
$868$	26.2316	−	11.1231i	0.890357	−	0.377543i
$869$		−	10.7386i		−	0.364283i
$870$		0			0
$871$			22.2586i			0.754205i
$872$	−2.43845	−	0.453349i	−0.0825762	−	0.0153523i
$873$	−15.3693	−	9.36932i	−0.520173	−	0.317103i
$874$	0.384472	−	0.580639i	0.0130050	−	0.0196404i
$875$		0			0
$876$	−22.6004	−	17.4706i	−0.763596	−	0.590277i
$877$		−	37.6155i		−	1.27019i	−0.772436	−	0.635093i	$-0.780962\pi$
$877$		−	37.6155i		−	1.27019i	0.772436	−	0.635093i	$-0.219038\pi$
$878$	−10.9309	−	7.23791i	−0.368899	−	0.244268i
$879$	2.11375	+	3.76412i	0.0712950	+	0.126960i
$880$		0			0
$881$			0.630683i			0.0212483i	0.999944	+	0.0106241i	$0.00338183\pi$
$881$			0.630683i			0.0212483i	−0.999944	+	0.0106241i	$0.996618\pi$
$882$	3.82419	+	8.15549i	0.128767	+	0.274610i
$883$	22.4674			0.756090			0.378045	−	0.925787i	$-0.376597\pi$
$883$	22.4674			0.756090			0.378045	+	0.925787i	$0.376597\pi$
$884$	−18.8664	+	8.00000i	−0.634544	+	0.269069i
$885$		0			0
$886$	−19.5616	−	12.9527i	−0.657183	−	0.435156i
$887$			51.6737i			1.73503i	0.497409	+	0.867516i	$0.334285\pi$
$887$			51.6737i			1.73503i	−0.497409	+	0.867516i	$0.665715\pi$
$888$	23.7612	−	8.08179i	0.797373	−	0.271207i
$889$	−45.6155			−1.52990
$890$		0			0
$891$	−5.46026	−	10.5945i	−0.182925	−	0.354928i
$892$	6.49424	+	15.3153i	0.217443	+	0.512796i
$893$	−4.00000			−0.133855
$894$	2.50806	−	34.2010i	0.0838821	−	1.14385i
$895$		0			0
$896$	−27.8462	+	19.8078i	−0.930276	+	0.661731i
$897$	−1.61553	−	2.87689i	−0.0539409	−	0.0960567i
$898$	32.2725	+	21.3693i	1.07695	+	0.713103i
$899$	−14.7304			−0.491287
$900$		0			0
$901$	24.4924			0.815961
$902$	−1.75379	−	1.16128i	−0.0583948	−	0.0386663i
$903$	−19.8188	−	35.2929i	−0.659529	−	1.17447i
$904$	38.9309	+	7.23791i	1.29482	+	0.240729i
$905$		0			0
$906$	−1.31946	+	17.9927i	−0.0438360	+	0.597767i
$907$	−46.2134			−1.53449			−0.767246	−	0.641353i	$-0.778373\pi$
$907$	−46.2134			−1.53449			−0.767246	+	0.641353i	$0.778373\pi$
$908$	−40.3002	+	17.0887i	−1.33741	+	0.567108i
$909$	2.24621	+	1.36932i	0.0745021	+	0.0454174i
$910$		0			0
$911$	−14.3128			−0.474204			−0.237102	−	0.971485i	$-0.576198\pi$
$911$	−14.3128			−0.474204			−0.237102	+	0.971485i	$0.576198\pi$
$912$	2.33230	−	8.87368i	0.0772302	−	0.293837i
$913$			20.0000i			0.661903i
$914$	11.7915	+	7.80776i	0.390027	+	0.258258i
$915$		0			0
$916$	−12.6847	−	29.9142i	−0.419113	−	0.988392i
$917$	−16.4924			−0.544628
$918$	8.54732	−	11.9559i	0.282104	−	0.394603i
$919$			49.9775i			1.64861i	0.566148	+	0.824303i	$0.308433\pi$
$919$			49.9775i			1.64861i	−0.566148	+	0.824303i	$0.691567\pi$
$920$		0			0
$921$	−9.43845	−	16.8078i	−0.311007	−	0.553835i
$922$	49.3612	+	32.6847i	1.62562	+	1.07641i
$923$		−	17.3790i		−	0.572037i
$924$	8.47449	−	10.9628i	0.278790	−	0.360650i
$925$		0			0
$926$	−2.35829	+	3.56155i	−0.0774984	+	0.117040i
$927$	−15.3110	+	25.1161i	−0.502881	+	0.824920i
$928$	17.2517	−	3.80776i	0.566316	−	0.124996i
$929$			33.1231i			1.08673i	0.839495	+	0.543367i	$0.182851\pi$
$929$			33.1231i			1.08673i	−0.839495	+	0.543367i	$0.817149\pi$
$930$		0			0
$931$		−	2.81164i		−	0.0921479i
$932$	−7.80776	−	18.4130i	−0.255752	−	0.603138i
$933$	−17.6155	−	31.3693i	−0.576707	−	1.02699i
$934$	−2.68466	−	1.77766i	−0.0878447	−	0.0581667i
$935$		0			0
$936$	−32.3565	−	29.0308i	−1.05760	−	0.948901i
$937$			22.4924i			0.734795i	0.930064	+	0.367398i	$0.119751\pi$
$937$			22.4924i			0.734795i	−0.930064	+	0.367398i	$0.880249\pi$
$938$	10.2462	−	15.4741i	0.334551	−	0.505246i
$939$	−33.9686	+	19.0752i	−1.10852	+	0.622494i
$940$		0			0
$941$			0.876894i			0.0285859i	0.999898	+	0.0142930i	$0.00454975\pi$
$941$			0.876894i			0.0285859i	−0.999898	+	0.0142930i	$0.995450\pi$
$942$	0.603604	−	8.23100i	0.0196665	−	0.268181i
$943$	0.417609			0.0135992
$944$	−39.3473	+	40.6847i	−1.28065	+	1.32417i
$945$		0			0
$946$	−8.00000	+	12.0818i	−0.260102	+	0.392813i
$947$		−	32.4813i		−	1.05550i	−0.849400	−	0.527750i	$-0.823036\pi$
$947$		−	32.4813i		−	1.05550i	0.849400	−	0.527750i	$-0.176964\pi$
$948$	22.2240	+	17.1796i	0.721801	+	0.557969i
$949$	42.2462			1.37137
$950$		0			0
$951$	14.1955	+	25.2791i	0.460322	+	0.819731i
$952$	16.7984	+	3.12311i	0.544439	+	0.101220i
$953$	22.4924			0.728601			0.364301	−	0.931281i	$-0.381308\pi$
$953$	22.4924			0.728601			0.364301	+	0.931281i	$0.381308\pi$
$954$	22.0582	+	47.0414i	0.714160	+	1.52302i
$955$		0			0
$956$	13.5691	+	32.0000i	0.438857	+	1.03495i
$957$	−6.24621	+	3.50758i	−0.201911	+	0.113384i
$958$	−20.0276	+	30.2462i	−0.647063	+	0.977211i
$959$	24.9073			0.804297
$960$		0			0
$961$	8.75379			0.282380
$962$	−20.4924	+	30.9481i	−0.660702	+	0.997808i
$963$	−7.73704	−	4.71659i	−0.249323	−	0.151990i
$964$	−10.4384	−	24.6169i	−0.336200	−	0.792858i
$965$		0			0
$966$	−0.201201	+	2.74367i	−0.00647354	+	0.0882761i
$967$	26.4404			0.850265			0.425132	−	0.905131i	$-0.360228\pi$
$967$	26.4404			0.850265			0.425132	+	0.905131i	$0.360228\pi$
$968$	25.7116	+	4.78023i	0.826404	+	0.153643i
$969$	−4.00000	+	2.24621i	−0.128499	+	0.0721587i
$970$		0			0
$971$	52.6261			1.68885			0.844427	−	0.535671i	$-0.179941\pi$
$971$	52.6261			1.68885			0.844427	+	0.535671i	$0.179941\pi$
$972$	30.6609	+	5.64879i	0.983449	+	0.181185i
$973$		−	52.9848i		−	1.69862i
$974$	−19.7373	+	29.8078i	−0.632424	+	0.955102i
$975$		0			0
$976$	−8.68466	+	8.97983i	−0.277989	+	0.287437i
$977$	31.7538			1.01589			0.507947	−	0.861388i	$-0.330405\pi$
$977$	31.7538			1.01589			0.507947	+	0.861388i	$0.330405\pi$
$978$	−38.3122	−	2.80954i	−1.22509	−	0.0898393i
$979$		−	13.5691i		−	0.433671i
$980$		0			0
$981$	−1.36932	+	2.24621i	−0.0437189	+	0.0717160i
$982$	21.0616	−	31.8078i	0.672103	−	1.01503i
$983$			40.0095i			1.27610i	0.769993	+	0.638052i	$0.220260\pi$
$983$			40.0095i			1.27610i	−0.769993	+	0.638052i	$0.779740\pi$
$984$	5.20901	−	1.77172i	0.166057	−	0.0564804i
$985$		0			0
$986$	−7.36520	−	4.87689i	−0.234556	−	0.155312i
$987$	13.7779	−	7.73704i	0.438556	−	0.246273i
$988$	5.29723	+	12.4924i	0.168527	+	0.397437i
$989$		−	2.87689i		−	0.0914799i
$990$		0			0
$991$		−	33.0161i		−	1.04879i	−0.851475	−	0.524396i	$-0.824291\pi$
$991$		−	33.0161i		−	1.04879i	0.851475	−	0.524396i	$-0.175709\pi$
$992$	26.0540	−	5.75058i	0.827215	−	0.182581i
$993$	−4.87689	+	2.73863i	−0.154764	+	0.0869079i
$994$	−8.00000	+	12.0818i	−0.253745	+	0.383211i
$995$		0			0
$996$	−41.3907	−	31.9960i	−1.31151	−	1.01383i
$997$			33.6155i			1.06461i	0.846551	+	0.532307i	$0.178675\pi$
$997$			33.6155i			1.06461i	−0.846551	+	0.532307i	$0.821325\pi$
$998$	−38.0540	−	25.1976i	−1.20458	−	0.797615i
$999$	0.952473	−	26.6034i	0.0301349	−	0.841694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.h.a.299.5		8
3.2	odd	2		300.2.h.b.299.3		8
4.3	odd	2	inner	300.2.h.a.299.8		8
5.2	odd	4		60.2.e.a.11.8	yes	8
5.3	odd	4		300.2.e.c.251.1		8
5.4	even	2		300.2.h.b.299.4		8
12.11	even	2		300.2.h.b.299.2		8
15.2	even	4		60.2.e.a.11.1	✓	8
15.8	even	4		300.2.e.c.251.8		8
15.14	odd	2	inner	300.2.h.a.299.6		8
20.3	even	4		300.2.e.c.251.7		8
20.7	even	4		60.2.e.a.11.2	yes	8
20.19	odd	2		300.2.h.b.299.1		8
40.27	even	4		960.2.h.g.191.2		8
40.37	odd	4		960.2.h.g.191.7		8
60.23	odd	4		300.2.e.c.251.2		8
60.47	odd	4		60.2.e.a.11.7	yes	8
60.59	even	2	inner	300.2.h.a.299.7		8
120.77	even	4		960.2.h.g.191.1		8
120.107	odd	4		960.2.h.g.191.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.e.a.11.1	✓	8	15.2	even	4
60.2.e.a.11.2	yes	8	20.7	even	4
60.2.e.a.11.7	yes	8	60.47	odd	4
60.2.e.a.11.8	yes	8	5.2	odd	4
300.2.e.c.251.1		8	5.3	odd	4
300.2.e.c.251.2		8	60.23	odd	4
300.2.e.c.251.7		8	20.3	even	4
300.2.e.c.251.8		8	15.8	even	4
300.2.h.a.299.5		8	1.1	even	1	trivial
300.2.h.a.299.6		8	15.14	odd	2	inner
300.2.h.a.299.7		8	60.59	even	2	inner
300.2.h.a.299.8		8	4.3	odd	2	inner
300.2.h.b.299.1		8	20.19	odd	2
300.2.h.b.299.2		8	12.11	even	2
300.2.h.b.299.3		8	3.2	odd	2
300.2.h.b.299.4		8	5.4	even	2
960.2.h.g.191.1		8	120.77	even	4
960.2.h.g.191.2		8	40.27	even	4
960.2.h.g.191.7		8	40.37	odd	4
960.2.h.g.191.8		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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.780776 - 1.17915i) q^{2} +(-0.848071 - 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} -3.02045 q^{7} +(-2.78078 - 0.516994i) q^{8} +(-1.56155 + 2.56155i) q^{9} +O(q^{10})\)	\(q+(0.780776 - 1.17915i) q^{2} +(-0.848071 - 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} -3.02045 q^{7} +(-2.78078 - 0.516994i) q^{8} +(-1.56155 + 2.56155i) q^{9} +1.32431 q^{11} +(-2.11862 + 2.74070i) q^{12} -5.12311i q^{13} +(-2.35829 + 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} +2.00000 q^{17} +(1.80122 + 3.84130i) q^{18} -1.32431i q^{19} +(2.56155 + 4.56155i) q^{21} +(1.03399 - 1.56155i) q^{22} +0.371834i q^{23} +(1.57752 + 4.63804i) q^{24} +(-6.04090 - 4.00000i) q^{26} +(5.19283 + 0.185917i) q^{27} +(2.35829 + 5.56155i) q^{28} -3.12311i q^{29} -4.71659i q^{31} +(1.21922 + 5.52390i) q^{32} +(-1.12311 - 2.00000i) q^{33} +(1.56155 - 2.35829i) q^{34} +(5.93581 + 0.875288i) q^{36} -5.12311i q^{37} +(-1.56155 - 1.03399i) q^{38} +(-7.73704 + 4.34475i) q^{39} -1.12311i q^{41} +(7.37874 + 0.541105i) q^{42} -7.73704 q^{43} +(-1.03399 - 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} -3.02045i q^{47} +(6.70062 + 1.76115i) q^{48} +2.12311 q^{49} +(-1.69614 - 3.02045i) q^{51} +(-9.43318 + 4.00000i) q^{52} +12.2462 q^{53} +(4.27366 - 5.97795i) q^{54} +(8.39919 + 1.56155i) q^{56} +(-2.00000 + 1.12311i) q^{57} +(-3.68260 - 2.43845i) q^{58} +14.1498 q^{59} +3.12311 q^{61} +(-5.56155 - 3.68260i) q^{62} +(4.71659 - 7.73704i) q^{63} +(7.46543 + 2.87529i) q^{64} +(-3.23519 - 0.237246i) q^{66} -4.34475 q^{67} +(-1.56155 - 3.68260i) q^{68} +(0.561553 - 0.315342i) q^{69} +3.39228 q^{71} +(5.66664 - 6.31579i) q^{72} +8.24621i q^{73} +(-6.04090 - 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} -4.00000 q^{77} +(-0.917790 + 12.5154i) q^{78} -8.10887i q^{79} +(-4.12311 - 8.00000i) q^{81} +(-1.32431 - 0.876894i) q^{82} +15.1022i q^{83} +(6.39919 - 8.27814i) q^{84} +(-6.04090 + 9.12311i) q^{86} +(-4.71659 + 2.64861i) q^{87} +(-3.68260 - 0.684658i) q^{88} -10.2462i q^{89} +15.4741i q^{91} +(0.684658 - 0.290319i) q^{92} +(-7.12311 + 4.00000i) q^{93} +(-3.56155 - 2.35829i) q^{94} +(7.30834 - 6.52596i) q^{96} +6.00000i q^{97} +(1.65767 - 2.50345i) q^{98} +(-2.06798 + 3.39228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{4} - 6 q^{6} - 14 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^4 - 6 * q^6 - 14 * q^8 + 4 * q^9	\( 8 q - 2 q^{2} + 2 q^{4} - 6 q^{6} - 14 q^{8} + 4 q^{9} - 14 q^{12} - 14 q^{16} + 16 q^{17} - 18 q^{18} + 4 q^{21} + 2 q^{24} + 18 q^{32} + 24 q^{33} - 4 q^{34} + 18 q^{36} + 4 q^{38} + 16 q^{42} + 20 q^{46} + 10 q^{48} - 16 q^{49} + 32 q^{53} + 10 q^{54} - 16 q^{57} - 8 q^{61} - 28 q^{62} + 2 q^{64} - 40 q^{66} + 4 q^{68} - 12 q^{69} + 10 q^{72} - 36 q^{76} - 32 q^{77} + 8 q^{78} - 16 q^{84} - 44 q^{92} - 24 q^{93} - 12 q^{94} + 42 q^{96} + 38 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^4 - 6 * q^6 - 14 * q^8 + 4 * q^9 - 14 * q^12 - 14 * q^16 + 16 * q^17 - 18 * q^18 + 4 * q^21 + 2 * q^24 + 18 * q^32 + 24 * q^33 - 4 * q^34 + 18 * q^36 + 4 * q^38 + 16 * q^42 + 20 * q^46 + 10 * q^48 - 16 * q^49 + 32 * q^53 + 10 * q^54 - 16 * q^57 - 8 * q^61 - 28 * q^62 + 2 * q^64 - 40 * q^66 + 4 * q^68 - 12 * q^69 + 10 * q^72 - 36 * q^76 - 32 * q^77 + 8 * q^78 - 16 * q^84 - 44 * q^92 - 24 * q^93 - 12 * q^94 + 42 * q^96 + 38 * q^98

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