LMFDB - Embedded newform 300.2.h.b.299.3

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			299.3
Root			$1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	300.299
Dual form			300.2.h.b.299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780776 + 1.17915i) q^{2} +(-0.848071 + 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} -3.02045 q^{7} +(2.78078 + 0.516994i) q^{8} +(-1.56155 - 2.56155i) q^{9} +O(q^{10})$	\(q+(-0.780776 + 1.17915i) q^{2} +(-0.848071 + 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} -3.02045 q^{7} +(2.78078 + 0.516994i) q^{8} +(-1.56155 - 2.56155i) q^{9} -1.32431 q^{11} +(3.44293 + 0.382406i) q^{12} -5.12311i q^{13} +(2.35829 - 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} -2.00000 q^{17} +(4.23967 + 0.158699i) q^{18} -1.32431i q^{19} +(2.56155 - 4.56155i) q^{21} +(1.03399 - 1.56155i) q^{22} -0.371834i q^{23} +(-3.13907 + 3.76115i) 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} +(-3.49737 + 4.87529i) q^{36} -5.12311i q^{37} +(1.56155 + 1.03399i) q^{38} +(7.73704 + 4.34475i) q^{39} +1.12311i q^{41} +(3.37874 + 6.58200i) q^{42} -7.73704 q^{43} +(1.03399 + 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} +3.02045i q^{47} +(-1.98403 - 6.63804i) q^{48} +2.12311 q^{49} +(1.69614 - 3.02045i) q^{51} +(-9.43318 + 4.00000i) q^{52} -12.2462 q^{53} +(-3.83521 + 6.26827i) 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} +(1.48140 + 2.88586i) q^{66} -4.34475 q^{67} +(1.56155 + 3.68260i) q^{68} +(0.561553 + 0.315342i) q^{69} -3.39228 q^{71} +(-3.01802 - 7.93042i) q^{72} +8.24621i q^{73} +(6.04090 + 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} +4.00000 q^{77} +(-11.1640 + 5.73082i) q^{78} -8.10887i q^{79} +(-4.12311 + 8.00000i) q^{81} +(-1.32431 - 0.876894i) q^{82} -15.1022i q^{83} +(-10.3992 - 1.15504i) 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} +(9.37632 + 2.84336i) 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
$6$	−1.11862	−	2.17915i	−0.456676	−	0.889633i
$7$	−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	$-0.563979\pi$
$11$	−1.32431			−0.399294			−0.199647	+	0.979868i	$0.563979\pi$
$12$	3.44293	+	0.382406i	0.993888	+	0.110391i
$13$		−	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	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	4.23967	+	0.158699i	0.999300	+	0.0374058i
$19$		−	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	$-0.987657\pi$
$23$		−	0.371834i		−	0.0775328i	0.999248	−	0.0387664i	$-0.0123428\pi$
$24$	−3.13907	+	3.76115i	−0.640760	+	0.767741i
$25$		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	$0.0936464\pi$
$29$			3.12311i			0.579946i	−0.957035	+	0.289973i	$0.906354\pi$
$30$		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
$36$	−3.49737	+	4.87529i	−0.582894	+	0.812548i
$37$		−	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	$0.0279516\pi$
$41$			1.12311i			0.175400i	−0.996147	+	0.0876998i	$0.972048\pi$
$42$	3.37874	+	6.58200i	0.521351	+	1.01562i
$43$	−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	$0.0707000\pi$
$47$			3.02045i			0.440578i	−0.975435	+	0.220289i	$0.929300\pi$
$48$	−1.98403	−	6.63804i	−0.286371	−	0.958119i
$49$	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	$-0.818076\pi$
$53$	−12.2462			−1.68215			−0.841073	+	0.540921i	$0.818076\pi$
$54$	−3.83521	+	6.26827i	−0.521906	+	0.853003i
$55$		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	$-0.872685\pi$
$59$	−14.1498			−1.84214			−0.921071	+	0.389394i	$0.872685\pi$
$60$		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
$66$	1.48140	+	2.88586i	0.182348	+	0.355225i
$67$	−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	$-0.564515\pi$
$71$	−3.39228			−0.402590			−0.201295	+	0.979531i	$0.564515\pi$
$72$	−3.01802	−	7.93042i	−0.355677	−	0.934609i
$73$			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
$78$	−11.1640	+	5.73082i	−1.26407	+	0.648888i
$79$		−	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	$-0.689000\pi$
$83$		−	15.1022i		−	1.65769i	0.559481	−	0.828843i	$-0.311000\pi$
$84$	−10.3992	−	1.15504i	−1.13464	−	0.126025i
$85$		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	$0.182730\pi$
$89$			10.2462i			1.08610i	−0.839702	+	0.543048i	$0.817270\pi$
$90$		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
$96$	9.37632	+	2.84336i	0.956966	+	0.290199i
$97$			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	$0.0138914\pi$
$101$			0.876894i			0.0872543i	−0.999048	+	0.0436271i	$0.986109\pi$
$102$	2.23725	+	4.35829i	0.221520	+	0.431535i
$103$	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	$-0.953360\pi$
$107$		−	3.02045i		−	0.291998i	0.989285	−	0.145999i	$-0.0466396\pi$
$108$	−4.39676	−	9.41639i	−0.423079	−	0.906093i
$109$	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	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$	−2.88586	+	1.48140i	−0.270286	+	0.138746i
$115$		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
$126$	−12.8057	−	0.479343i	−1.14082	−	0.0427033i
$127$	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	$-0.576666\pi$
$131$	−5.46026			−0.477065			−0.238532	+	0.971135i	$0.576666\pi$
$132$	−4.55950	−	0.506422i	−0.396853	−	0.0440784i
$133$			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	$-0.385413\pi$
$137$	8.24621			0.704521			0.352261	+	0.935902i	$0.385413\pi$
$138$	−0.810281	+	0.415942i	−0.0689757	+	0.0354074i
$139$			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
$144$	11.7075	+	2.63319i	0.975628	+	0.219433i
$145$		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	$-0.805600\pi$
$149$		−	14.0000i		−	1.14692i	0.819232	−	0.573462i	$-0.194400\pi$
$150$		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
$156$	1.95910	−	17.6385i	0.156854	−	1.41221i
$157$			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
$162$	−6.21395	−	11.1080i	−0.488214	−	0.872724i
$163$	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	$-0.885980\pi$
$167$		−	9.06134i		−	0.701188i	0.936528	−	0.350594i	$-0.114020\pi$
$168$	9.48140	−	11.3604i	0.731506	−	0.876470i
$169$	−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	$-0.475776\pi$
$173$	2.00000			0.152057			0.0760286	+	0.997106i	$0.475776\pi$
$174$	6.80571	−	3.49358i	0.515939	−	0.264847i
$175$		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	$-0.622094\pi$
$179$	−10.0138			−0.748468			−0.374234	+	0.927334i	$0.622094\pi$
$180$		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
$186$	−10.2781	+	5.27608i	−0.753630	+	0.386861i
$187$	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	$-0.142752\pi$
$191$	24.9073			1.80223			0.901113	+	0.433585i	$0.142752\pi$
$192$	−10.6735	+	8.83603i	−0.770297	+	0.637686i
$193$		−	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	$-0.548335\pi$
$197$	−4.24621			−0.302530			−0.151265	+	0.988493i	$0.548335\pi$
$198$	−5.61463	−	0.210167i	−0.399014	−	0.0149359i
$199$		−	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
$204$	−6.88586	−	0.764811i	−0.482107	−	0.0535475i
$205$		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
$216$	14.5362	+	2.16766i	0.989063	+	0.147491i
$217$			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
$222$	−11.1640	+	5.73082i	−0.749279	+	0.384628i
$223$	−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	$0.258780\pi$
$227$			21.8868i			1.45268i	−0.687337	+	0.726339i	$0.741220\pi$
$228$	0.506422	−	4.55950i	0.0335386	−	0.301960i
$229$	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	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$	0.813033	−	21.7203i	0.0531497	−	1.41990i
$235$		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	$-0.310002\pi$
$239$	17.3790			1.12416			0.562078	+	0.827084i	$0.310002\pi$
$240$		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
$246$	2.44741	−	1.25633i	0.156041	−	0.0801008i
$247$	−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	$-0.700979\pi$
$251$	−18.7033			−1.18054			−0.590272	+	0.807205i	$0.700979\pi$
$252$	10.5636	−	14.7256i	0.665445	−	0.927623i
$253$			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	$-0.899975\pi$
$257$	−30.4924			−1.90207			−0.951033	+	0.309091i	$0.899975\pi$
$258$	8.65483	+	16.8601i	0.538826	+	1.04967i
$259$			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	$0.262129\pi$
$263$			23.7917i			1.46706i	−0.679656	+	0.733531i	$0.737871\pi$
$264$	4.15709	−	4.98091i	0.255851	−	0.306554i
$265$		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	$0.140358\pi$
$269$			14.0000i			0.853595i	−0.904347	+	0.426798i	$0.859642\pi$
$270$		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
$276$	0.142191	−	1.28020i	0.00855892	−	0.0770589i
$277$		−	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	$-0.866882\pi$
$281$		−	13.6155i		−	0.812234i	0.913821	−	0.406117i	$-0.133118\pi$
$282$	6.58200	−	3.37874i	0.391952	−	0.201201i
$283$	−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
$288$	−12.2459	+	11.7490i	−0.721596	+	0.692315i
$289$	−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	$-0.476805\pi$
$293$	2.49242			0.145609			0.0728044	+	0.997346i	$0.476805\pi$
$294$	−2.37495	−	4.62656i	−0.138510	−	0.269826i
$295$		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
$306$	−8.47934	−	0.317399i	−0.484732	−	0.0181445i
$307$	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	$-0.700445\pi$
$311$	−20.7713			−1.17783			−0.588916	+	0.808194i	$0.700445\pi$
$312$	19.2688	+	16.0818i	1.09088	+	0.910452i
$313$		−	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	$-0.344230\pi$
$317$	16.7386			0.940135			0.470068	+	0.882630i	$0.344230\pi$
$318$	13.6989	+	26.6863i	0.768196	+	1.49649i
$319$		−	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
$324$	17.9496	+	1.34567i	0.997202	+	0.0747592i
$325$		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
$336$	5.99267	+	20.0499i	0.326927	+	1.09381i
$337$			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
$342$	0.210167	−	5.61463i	0.0113645	−	0.303604i
$343$	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	$-0.792199\pi$
$347$		−	22.6305i		−	1.21487i	0.794370	−	0.607434i	$-0.207801\pi$
$348$	−1.19429	+	10.7526i	−0.0640208	+	0.576402i
$349$	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	$-0.681122\pi$
$353$	−20.2462			−1.07760			−0.538799	+	0.842435i	$0.681122\pi$
$354$	15.8283	+	30.8344i	0.841262	+	1.63883i
$355$		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	$-0.307811\pi$
$359$	21.5150			1.13552			0.567758	+	0.823195i	$0.307811\pi$
$360$		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
$366$	−3.49358	−	6.80571i	−0.182612	−	0.355740i
$367$	−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
$372$	1.80365	−	16.2389i	0.0935149	−	0.841947i
$373$		−	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
$378$	11.5841	−	18.9330i	0.595820	−	0.973807i
$379$		−	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	$0.126090\pi$
$383$			15.1022i			0.771688i	−0.922564	+	0.385844i	$0.873910\pi$
$384$	−2.08533	−	19.4846i	−0.106417	−	0.994322i
$385$		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	$-0.823787\pi$
$389$		−	20.7386i		−	1.05149i	0.850642	−	0.525745i	$-0.176213\pi$
$390$		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
$396$	4.63159	−	6.45638i	0.232746	−	0.324445i
$397$		−	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	$-0.795465\pi$
$401$		−	24.0000i		−	1.19850i	0.800561	−	0.599251i	$-0.204535\pi$
$402$	4.86014	+	9.46786i	0.242402	+	0.472214i
$403$	−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
$408$	6.27814	−	7.52230i	0.310814	−	0.372409i
$409$	−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
$414$	0.0590098	−	1.57645i	0.00290017	−	0.0774785i
$415$		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	$-0.442420\pi$
$419$	7.36520			0.359814			0.179907	+	0.983684i	$0.442420\pi$
$420$		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
$426$	3.79468	+	7.39228i	0.183853	+	0.358157i
$427$	−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	$-0.368785\pi$
$431$	16.6354			0.801297			0.400648	+	0.916232i	$0.368785\pi$
$432$	−13.9055	+	15.4479i	−0.669030	+	0.743236i
$433$			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
$438$	17.9697	−	9.22440i	0.858626	−	0.440759i
$439$		−	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	$0.128943\pi$
$443$			16.5896i			0.788195i	−0.919069	+	0.394097i	$0.871057\pi$
$444$	1.95910	−	17.6385i	0.0929750	−	0.837086i
$445$		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	$-0.776516\pi$
$449$		−	27.3693i		−	1.29164i	0.763491	−	0.645819i	$-0.223484\pi$
$450$		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
$456$	4.98091	+	4.15709i	0.233253	+	0.194674i
$457$			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	$-0.571543\pi$
$461$		−	41.8617i		−	1.94970i	0.222872	−	0.974848i	$-0.428457\pi$
$462$	−4.47449	−	8.71659i	−0.208172	−	0.405532i
$463$	−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	$0.0167758\pi$
$467$			2.27678i			0.105357i	−0.998612	+	0.0526784i	$0.983224\pi$
$468$	24.9766	+	17.9174i	1.15454	+	0.828231i
$469$	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
$474$	−17.6704	+	9.07077i	−0.811629	+	0.416634i
$475$		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	$-0.300698\pi$
$479$	25.6509			1.17202			0.586010	+	0.810304i	$0.300698\pi$
$480$		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
$486$	22.0454	+	0.0358705i	0.999999	+	0.00162712i
$487$	−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	$-0.708304\pi$
$491$	−26.9752			−1.21737			−0.608687	+	0.793410i	$0.708304\pi$
$492$	−0.429482	+	3.86677i	−0.0193625	+	0.174328i
$493$		−	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
$498$	−32.9100	+	16.8937i	−1.47473	+	0.757025i
$499$		−	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	$-0.896281\pi$
$503$		−	14.3586i		−	0.640217i	0.947381	−	0.320109i	$-0.103719\pi$
$504$	9.11578	+	23.9534i	0.406049	+	1.06697i
$505$		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	$0.0792843\pi$
$509$			11.1231i			0.493023i	−0.969140	+	0.246511i	$0.920716\pi$
$510$		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
$516$	−26.6381	−	2.95869i	−1.17268	−	0.130249i
$517$		−	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	$0.316158\pi$
$521$			38.2462i			1.67560i	−0.545980	+	0.837798i	$0.683842\pi$
$522$	−0.495635	+	13.2409i	−0.0216933	+	0.579540i
$523$	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
$528$	2.62747	+	8.79081i	0.114346	+	0.382571i
$529$	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
$534$	22.3280	−	11.4616i	0.966227	−	0.495994i
$535$		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
$546$	33.7203	−	17.3097i	1.44309	−	0.740785i
$547$	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
$552$	1.39852	+	1.16721i	0.0595251	+	0.0496799i
$553$			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	$-0.778699\pi$
$557$	−36.2462			−1.53580			−0.767901	+	0.640569i	$0.778699\pi$
$558$	0.748519	−	19.9968i	0.0316874	−	0.846532i
$559$			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	$0.0532382\pi$
$563$			7.90007i			0.332948i	−0.986046	+	0.166474i	$0.946762\pi$
$564$	−1.15504	+	10.3992i	−0.0486358	+	0.437885i
$565$		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	$-0.911297\pi$
$569$		−	13.1231i		−	0.550149i	0.961423	−	0.275075i	$-0.0887026\pi$
$570$		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
$576$	−4.29247	−	23.6130i	−0.178853	−	0.983876i
$577$			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
$582$	13.0749	−	6.71174i	0.541971	−	0.278210i
$583$	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	$0.0122159\pi$
$587$			1.85917i			0.0767362i	−0.999264	+	0.0383681i	$0.987784\pi$
$588$	7.30970	+	0.811887i	0.301447	+	0.0334817i
$589$	−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	$-0.445844\pi$
$593$	8.24621			0.338631			0.169316	+	0.985562i	$0.445844\pi$
$594$	5.07900	−	8.30111i	0.208394	−	0.340599i
$595$		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	$-0.858494\pi$
$599$	−44.1912			−1.80560			−0.902802	+	0.430056i	$0.858494\pi$
$600$		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
$606$	1.91088	−	0.980914i	0.0776243	−	0.0398469i
$607$	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
$612$	6.99473	−	9.75058i	0.282745	−	0.394144i
$613$			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	$-0.409065\pi$
$617$	14.0000			0.563619			0.281809	+	0.959470i	$0.409065\pi$
$618$	−10.9681	−	21.3666i	−0.441202	−	0.859489i
$619$			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
$624$	−34.0074	+	10.1644i	−1.36139	+	0.406902i
$625$		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
$636$	−42.1628	−	4.68302i	−1.67187	−	0.185694i
$637$		−	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	$0.0402414\pi$
$641$			6.38447i			0.252171i	−0.992019	+	0.126086i	$0.959759\pi$
$642$	−6.58200	+	3.37874i	−0.259771	+	0.133348i
$643$	−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	$-0.744240\pi$
$647$		−	36.6172i		−	1.43957i	0.694197	−	0.719786i	$-0.255760\pi$
$648$	−15.6014	+	20.1146i	−0.612880	+	0.790176i
$649$	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	$-0.776175\pi$
$653$	−38.9848			−1.52559			−0.762797	+	0.646638i	$0.776175\pi$
$654$	−0.980914	−	1.91088i	−0.0383568	−	0.0747214i
$655$		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	$-0.339929\pi$
$659$	24.7442			0.963898			0.481949	+	0.876199i	$0.339929\pi$
$660$		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
$666$	0.813033	−	21.7203i	0.0315044	−	0.841644i
$667$	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
$672$	−28.3207	−	8.58821i	−1.09249	−	0.331298i
$673$			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	$-0.509223\pi$
$677$	−1.50758			−0.0579409			−0.0289705	+	0.999580i	$0.509223\pi$
$678$	−15.6607	−	30.5081i	−0.601446	−	1.17166i
$679$		−	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	$-0.951704\pi$
$683$		−	7.90007i		−	0.302288i	0.988512	−	0.151144i	$-0.0482957\pi$
$684$	6.45638	+	4.63159i	0.246866	+	0.177093i
$685$		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
$696$	−11.7465	−	9.80365i	−0.445249	−	0.371606i
$697$		−	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	$-0.892740\pi$
$701$		−	17.5076i		−	0.661252i	0.943762	−	0.330626i	$-0.107260\pi$
$702$	32.1130	+	19.6482i	1.21203	+	0.741573i
$703$	−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
$708$	−48.7167	−	5.41095i	−1.83088	−	0.203356i
$709$	−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
$714$	−6.75748	−	13.1640i	−0.252893	−	0.492650i
$715$		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	$-0.695810\pi$
$719$	−30.9481			−1.15417			−0.577086	+	0.816684i	$0.695810\pi$
$720$		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
$726$	10.3430	+	20.1489i	0.383866	+	0.747794i
$727$	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
$732$	10.7526	+	1.19429i	0.397429	+	0.0441423i
$733$		−	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
$738$	−0.178236	+	4.76160i	−0.00656096	+	0.175277i
$739$		−	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	$0.0575630\pi$
$743$			9.80501i			0.359711i	−0.983693	+	0.179856i	$0.942437\pi$
$744$	17.7398	+	14.8057i	0.650372	+	0.542804i
$745$		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
$756$	13.2802	+	28.4417i	0.482996	+	1.03442i
$757$		−	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	$0.191534\pi$
$761$			31.2311i			1.13212i	−0.824362	+	0.566062i	$0.808466\pi$
$762$	−16.8937	−	32.9100i	−0.611995	−	1.19220i
$763$	−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
$768$	24.6034	+	12.7542i	0.887800	+	0.460229i
$769$	−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	$-0.501409\pi$
$773$	−0.246211			−0.00885560			−0.00442780	+	0.999990i	$0.501409\pi$
$774$	−32.8025	−	1.22786i	−1.17906	−	0.0441346i
$775$		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
$786$	6.10797	+	11.8987i	0.217864	+	0.424413i
$787$	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
$792$	3.99679	+	10.5023i	0.142020	+	0.373183i
$793$		−	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	$-0.572438\pi$
$797$	−12.7386			−0.451226			−0.225613	+	0.974217i	$0.572438\pi$
$798$	8.71659	−	4.47449i	0.308564	−	0.158395i
$799$		−	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
$804$	−14.9587	−	1.66146i	−0.527552	−	0.0585951i
$805$		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	$-0.824796\pi$
$809$		−	29.7538i		−	1.04609i	0.852306	−	0.523044i	$-0.175204\pi$
$810$		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
$816$	3.96807	+	13.2761i	0.138910	+	0.464756i
$817$			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	$-0.620766\pi$
$821$		−	53.2311i		−	1.85778i	0.370360	−	0.928888i	$-0.379234\pi$
$822$	−9.22440	−	17.9697i	−0.321738	−	0.626766i
$823$	−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	$-0.900130\pi$
$827$		−	17.7509i		−	0.617258i	0.951183	−	0.308629i	$-0.0998701\pi$
$828$	1.81280	+	1.30044i	0.0629991	+	0.0451934i
$829$	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
$834$	38.2267	−	19.6229i	1.32368	−	0.679487i
$835$		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	$-0.598865\pi$
$839$	−17.7051			−0.611247			−0.305624	+	0.952152i	$0.598865\pi$
$840$		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
$846$	−0.479343	+	12.8057i	−0.0164802	+	0.440269i
$847$	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
$852$	−11.6794	−	1.29723i	−0.400129	−	0.0444423i
$853$		−	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	$-0.384750\pi$
$857$	20.7386			0.708418			0.354209	+	0.935166i	$0.384750\pi$
$858$	14.7846	−	7.58937i	0.504737	−	0.259097i
$859$			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	$-0.942539\pi$
$863$		−	10.5487i		−	0.359081i	0.983751	−	0.179541i	$-0.0574611\pi$
$864$	−7.35820	−	28.4580i	−0.250331	−	0.968160i
$865$		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
$876$	−3.15340	+	28.3911i	−0.106543	+	0.959247i
$877$		−	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	$-0.996618\pi$
$881$		−	0.630683i		−	0.0212483i	0.999944	−	0.0106241i	$-0.00338183\pi$
$882$	9.00127	+	0.336935i	0.303089	+	0.0113452i
$883$	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	$-0.665715\pi$
$887$		−	51.6737i		−	1.73503i	0.497409	−	0.867516i	$-0.334285\pi$
$888$	19.2688	+	16.0818i	0.646617	+	0.539670i
$889$	−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
$894$	−30.5081	+	15.6607i	−1.02034	+	0.523773i
$895$		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
$906$	−16.0499	+	8.23888i	−0.533221	+	0.273719i
$907$	−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	$-0.423802\pi$
$911$	14.3128			0.474204			0.237102	+	0.971485i	$0.423802\pi$
$912$	−8.79081	+	2.62747i	−0.291093	+	0.0870043i
$913$			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
$918$	7.67042	−	12.5365i	0.253162	−	0.413767i
$919$			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
$924$	13.7717	+	1.52962i	0.453056	+	0.0503209i
$925$		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	$-0.817149\pi$
$929$		−	33.1231i		−	1.08673i	0.839495	−	0.543367i	$-0.182851\pi$
$930$		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
$936$	−40.6284	+	15.4616i	−1.32798	+	0.505380i
$937$			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	$-0.995450\pi$
$941$		−	0.876894i		−	0.0285859i	0.999898	−	0.0142930i	$-0.00454975\pi$
$942$	7.34224	−	3.76900i	0.239223	−	0.122800i
$943$	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	$0.176964\pi$
$947$			32.4813i			1.05550i	−0.849400	+	0.527750i	$0.823036\pi$
$948$	3.10088	−	27.9183i	0.100712	−	0.906743i
$949$	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	$-0.618692\pi$
$953$	−22.4924			−0.728601			−0.364301	+	0.931281i	$0.618692\pi$
$954$	−51.9199	−	1.94347i	−1.68097	−	0.0629220i
$955$		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
$966$	2.44741	−	1.25633i	0.0787442	−	0.0404218i
$967$	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	$-0.820059\pi$
$971$	−52.6261			−1.68885			−0.844427	+	0.535671i	$0.820059\pi$
$972$	−17.2548	+	25.9667i	−0.553448	+	0.832884i
$973$		−	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	$-0.669595\pi$
$977$	−31.7538			−1.01589			−0.507947	+	0.861388i	$0.669595\pi$
$978$	−17.5432	−	34.1753i	−0.560971	−	1.09281i
$979$		−	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	$-0.779740\pi$
$983$		−	40.0095i		−	1.27610i	0.769993	−	0.638052i	$-0.220260\pi$
$984$	−4.22417	−	3.52551i	−0.134662	−	0.112389i
$985$		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
$996$	5.77518	−	51.9960i	0.182994	−	1.64755i
$997$			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.b.299.3		8
3.2	odd	2		300.2.h.a.299.5		8
4.3	odd	2	inner	300.2.h.b.299.2		8
5.2	odd	4		60.2.e.a.11.1	✓	8
5.3	odd	4		300.2.e.c.251.8		8
5.4	even	2		300.2.h.a.299.6		8
12.11	even	2		300.2.h.a.299.8		8
15.2	even	4		60.2.e.a.11.8	yes	8
15.8	even	4		300.2.e.c.251.1		8
15.14	odd	2	inner	300.2.h.b.299.4		8
20.3	even	4		300.2.e.c.251.2		8
20.7	even	4		60.2.e.a.11.7	yes	8
20.19	odd	2		300.2.h.a.299.7		8
40.27	even	4		960.2.h.g.191.8		8
40.37	odd	4		960.2.h.g.191.1		8
60.23	odd	4		300.2.e.c.251.7		8
60.47	odd	4		60.2.e.a.11.2	yes	8
60.59	even	2	inner	300.2.h.b.299.1		8
120.77	even	4		960.2.h.g.191.7		8
120.107	odd	4		960.2.h.g.191.2		8

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

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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)

\(f(q)\)	\(=\)	\(q+(-0.780776 + 1.17915i) q^{2} +(-0.848071 + 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} -3.02045 q^{7} +(2.78078 + 0.516994i) q^{8} +(-1.56155 - 2.56155i) q^{9} +O(q^{10})\)	\(q+(-0.780776 + 1.17915i) q^{2} +(-0.848071 + 1.51022i) q^{3} +(-0.780776 - 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} -3.02045 q^{7} +(2.78078 + 0.516994i) q^{8} +(-1.56155 - 2.56155i) q^{9} -1.32431 q^{11} +(3.44293 + 0.382406i) q^{12} -5.12311i q^{13} +(2.35829 - 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} -2.00000 q^{17} +(4.23967 + 0.158699i) q^{18} -1.32431i q^{19} +(2.56155 - 4.56155i) q^{21} +(1.03399 - 1.56155i) q^{22} -0.371834i q^{23} +(-3.13907 + 3.76115i) 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} +(-3.49737 + 4.87529i) q^{36} -5.12311i q^{37} +(1.56155 + 1.03399i) q^{38} +(7.73704 + 4.34475i) q^{39} +1.12311i q^{41} +(3.37874 + 6.58200i) q^{42} -7.73704 q^{43} +(1.03399 + 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} +3.02045i q^{47} +(-1.98403 - 6.63804i) q^{48} +2.12311 q^{49} +(1.69614 - 3.02045i) q^{51} +(-9.43318 + 4.00000i) q^{52} -12.2462 q^{53} +(-3.83521 + 6.26827i) 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} +(1.48140 + 2.88586i) q^{66} -4.34475 q^{67} +(1.56155 + 3.68260i) q^{68} +(0.561553 + 0.315342i) q^{69} -3.39228 q^{71} +(-3.01802 - 7.93042i) q^{72} +8.24621i q^{73} +(6.04090 + 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} +4.00000 q^{77} +(-11.1640 + 5.73082i) q^{78} -8.10887i q^{79} +(-4.12311 + 8.00000i) q^{81} +(-1.32431 - 0.876894i) q^{82} -15.1022i q^{83} +(-10.3992 - 1.15504i) 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} +(9.37632 + 2.84336i) 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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