LMFDB - Embedded newform 308.2.j.a.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(113,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("308.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	308.141
Dual form			308.2.j.a.225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 0.726543i) q^{3} +(0.618034 + 1.90211i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-0.454915 + 1.40008i) q^{9} +O(q^{10})$	\(q+(1.00000 - 0.726543i) q^{3} +(0.618034 + 1.90211i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-0.454915 + 1.40008i) q^{9} +(3.30902 + 0.224514i) q^{11} +(-0.381966 + 1.17557i) q^{13} +(2.00000 + 1.45309i) q^{15} +(-1.23607 - 3.80423i) q^{17} +(1.61803 - 1.17557i) q^{19} +1.23607 q^{21} -1.61803 q^{23} +(0.809017 - 0.587785i) q^{25} +(1.70820 + 5.25731i) q^{27} +(-4.73607 - 3.44095i) q^{29} +(1.38197 - 4.25325i) q^{31} +(3.47214 - 2.17963i) q^{33} +(-0.618034 + 1.90211i) q^{35} +(-2.54508 - 1.84911i) q^{37} +(0.472136 + 1.45309i) q^{39} +(1.38197 - 1.00406i) q^{41} +4.14590 q^{43} -2.94427 q^{45} +(-8.09017 + 5.87785i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-4.00000 - 2.90617i) q^{51} +(-2.28115 + 7.02067i) q^{53} +(1.61803 + 6.43288i) q^{55} +(0.763932 - 2.35114i) q^{57} +(-7.85410 - 5.70634i) q^{59} +(-2.61803 - 8.05748i) q^{61} +(-1.19098 + 0.865300i) q^{63} -2.47214 q^{65} +2.61803 q^{67} +(-1.61803 + 1.17557i) q^{69} +(4.04508 + 12.4495i) q^{71} +(-13.4721 - 9.78808i) q^{73} +(0.381966 - 1.17557i) q^{75} +(2.54508 + 2.12663i) q^{77} +(1.57295 - 4.84104i) q^{79} +(1.95492 + 1.42033i) q^{81} +(-0.909830 - 2.80017i) q^{83} +(6.47214 - 4.70228i) q^{85} -7.23607 q^{87} -11.2361 q^{89} +(-1.00000 + 0.726543i) q^{91} +(-1.70820 - 5.25731i) q^{93} +(3.23607 + 2.35114i) q^{95} +(3.52786 - 10.8576i) q^{97} +(-1.81966 + 4.53077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 2 q^{5} + q^{7} - 13 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 2 * q^5 + q^7 - 13 * q^9	$ 4 q + 4 q^{3} - 2 q^{5} + q^{7} - 13 q^{9} + 11 q^{11} - 6 q^{13} + 8 q^{15} + 4 q^{17} + 2 q^{19} - 4 q^{21} - 2 q^{23} + q^{25} - 20 q^{27} - 10 q^{29} + 10 q^{31} - 4 q^{33} + 2 q^{35} + q^{37} - 16 q^{39} + 10 q^{41} + 30 q^{43} + 24 q^{45} - 10 q^{47} - q^{49} - 16 q^{51} + 11 q^{53} + 2 q^{55} + 12 q^{57} - 18 q^{59} - 6 q^{61} - 7 q^{63} + 8 q^{65} + 6 q^{67} - 2 q^{69} + 5 q^{71} - 36 q^{73} + 6 q^{75} - q^{77} + 13 q^{79} + 19 q^{81} - 26 q^{83} + 8 q^{85} - 20 q^{87} - 36 q^{89} - 4 q^{91} + 20 q^{93} + 4 q^{95} + 32 q^{97} - 52 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 2 * q^5 + q^7 - 13 * q^9 + 11 * q^11 - 6 * q^13 + 8 * q^15 + 4 * q^17 + 2 * q^19 - 4 * q^21 - 2 * q^23 + q^25 - 20 * q^27 - 10 * q^29 + 10 * q^31 - 4 * q^33 + 2 * q^35 + q^37 - 16 * q^39 + 10 * q^41 + 30 * q^43 + 24 * q^45 - 10 * q^47 - q^49 - 16 * q^51 + 11 * q^53 + 2 * q^55 + 12 * q^57 - 18 * q^59 - 6 * q^61 - 7 * q^63 + 8 * q^65 + 6 * q^67 - 2 * q^69 + 5 * q^71 - 36 * q^73 + 6 * q^75 - q^77 + 13 * q^79 + 19 * q^81 - 26 * q^83 + 8 * q^85 - 20 * q^87 - 36 * q^89 - 4 * q^91 + 20 * q^93 + 4 * q^95 + 32 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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			0
$2$		0			0
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	−0.260418	−	0.965496i	$-0.583860\pi$
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	0.837768	+	0.546027i	$0.183860\pi$
$4$		0			0
$5$	0.618034	+	1.90211i	0.276393	+	0.850651i	0.988847	+	0.148932i	$0.0475836\pi$
$5$	0.618034	+	1.90211i	0.276393	+	0.850651i	−0.712454	+	0.701719i	$0.752416\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$		0			0
$9$	−0.454915	+	1.40008i	−0.151638	+	0.466695i
$10$		0			0
$11$	3.30902	+	0.224514i	0.997706	+	0.0676935i
$11$	3.30902	+	0.224514i	0.997706	+	0.0676935i
$12$		0			0
$13$	−0.381966	+	1.17557i	−0.105938	+	0.326045i	−0.989950	−	0.141421i	$-0.954833\pi$
$13$	−0.381966	+	1.17557i	−0.105938	+	0.326045i	0.884011	+	0.467466i	$0.154833\pi$
$14$		0			0
$15$	2.00000	+	1.45309i	0.516398	+	0.375185i
$16$		0			0
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	−0.981570	−	0.191103i	$-0.938794\pi$
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	0.681780	−	0.731558i	$-0.261206\pi$
$18$		0			0
$19$	1.61803	−	1.17557i	0.371202	−	0.269694i	−0.386507	−	0.922287i	$-0.626318\pi$
$19$	1.61803	−	1.17557i	0.371202	−	0.269694i	0.757709	+	0.652592i	$0.226318\pi$
$20$		0			0
$21$	1.23607			0.269732
$22$		0			0
$23$	−1.61803			−0.337383			−0.168692	−	0.985669i	$-0.553954\pi$
$23$	−1.61803			−0.337383			−0.168692	+	0.985669i	$0.553954\pi$
$24$		0			0
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$		0			0
$27$	1.70820	+	5.25731i	0.328744	+	1.01177i
$28$		0			0
$29$	−4.73607	−	3.44095i	−0.879466	−	0.638969i	0.0536443	−	0.998560i	$-0.482916\pi$
$29$	−4.73607	−	3.44095i	−0.879466	−	0.638969i	−0.933110	+	0.359591i	$0.882916\pi$
$30$		0			0
$31$	1.38197	−	4.25325i	0.248208	−	0.763907i	−0.746884	−	0.664955i	$-0.768451\pi$
$31$	1.38197	−	4.25325i	0.248208	−	0.763907i	0.995092	−	0.0989523i	$-0.0315491\pi$
$32$		0			0
$33$	3.47214	−	2.17963i	0.604421	−	0.379424i
$34$		0			0
$35$	−0.618034	+	1.90211i	−0.104467	+	0.321516i
$36$		0			0
$37$	−2.54508	−	1.84911i	−0.418409	−	0.303992i	0.358588	−	0.933496i	$-0.383258\pi$
$37$	−2.54508	−	1.84911i	−0.418409	−	0.303992i	−0.776998	+	0.629504i	$0.783258\pi$
$38$		0			0
$39$	0.472136	+	1.45309i	0.0756023	+	0.232680i
$40$		0			0
$41$	1.38197	−	1.00406i	0.215827	−	0.156807i	−0.474619	−	0.880191i	$-0.657414\pi$
$41$	1.38197	−	1.00406i	0.215827	−	0.156807i	0.690446	+	0.723384i	$0.257414\pi$
$42$		0			0
$43$	4.14590			0.632244			0.316122	−	0.948719i	$-0.397619\pi$
$43$	4.14590			0.632244			0.316122	+	0.948719i	$0.397619\pi$
$44$		0			0
$45$	−2.94427			−0.438906
$46$		0			0
$47$	−8.09017	+	5.87785i	−1.18007	+	0.857373i	−0.992180	−	0.124817i	$-0.960166\pi$
$47$	−8.09017	+	5.87785i	−1.18007	+	0.857373i	−0.187893	+	0.982190i	$0.560166\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	−4.00000	−	2.90617i	−0.560112	−	0.406945i
$52$		0			0
$53$	−2.28115	+	7.02067i	−0.313340	+	0.964363i	0.663092	+	0.748538i	$0.269244\pi$
$53$	−2.28115	+	7.02067i	−0.313340	+	0.964363i	−0.976432	+	0.215825i	$0.930756\pi$
$54$		0			0
$55$	1.61803	+	6.43288i	0.218176	+	0.867410i
$56$		0			0
$57$	0.763932	−	2.35114i	0.101185	−	0.311416i
$58$		0			0
$59$	−7.85410	−	5.70634i	−1.02252	−	0.742902i	−0.0557197	−	0.998446i	$-0.517745\pi$
$59$	−7.85410	−	5.70634i	−1.02252	−	0.742902i	−0.966797	+	0.255544i	$0.917745\pi$
$60$		0			0
$61$	−2.61803	−	8.05748i	−0.335205	−	1.03165i	−0.966621	−	0.256210i	$-0.917526\pi$
$61$	−2.61803	−	8.05748i	−0.335205	−	1.03165i	0.631416	−	0.775444i	$-0.282474\pi$
$62$		0			0
$63$	−1.19098	+	0.865300i	−0.150050	+	0.109018i
$64$		0			0
$65$	−2.47214			−0.306631
$66$		0			0
$67$	2.61803			0.319844			0.159922	−	0.987130i	$-0.448876\pi$
$67$	2.61803			0.319844			0.159922	+	0.987130i	$0.448876\pi$
$68$		0			0
$69$	−1.61803	+	1.17557i	−0.194788	+	0.141522i
$70$		0			0
$71$	4.04508	+	12.4495i	0.480063	+	1.47748i	0.839005	+	0.544123i	$0.183138\pi$
$71$	4.04508	+	12.4495i	0.480063	+	1.47748i	−0.358942	+	0.933360i	$0.616862\pi$
$72$		0			0
$73$	−13.4721	−	9.78808i	−1.57679	−	1.14561i	−0.920257	−	0.391314i	$-0.872020\pi$
$73$	−13.4721	−	9.78808i	−1.57679	−	1.14561i	−0.656537	−	0.754294i	$-0.727980\pi$
$74$		0			0
$75$	0.381966	−	1.17557i	0.0441056	−	0.135743i
$76$		0			0
$77$	2.54508	+	2.12663i	0.290039	+	0.242352i
$78$		0			0
$79$	1.57295	−	4.84104i	0.176971	−	0.544659i	−0.822747	−	0.568407i	$-0.807560\pi$
$79$	1.57295	−	4.84104i	0.176971	−	0.544659i	0.999718	+	0.0237477i	$0.00755984\pi$
$80$		0			0
$81$	1.95492	+	1.42033i	0.217213	+	0.157814i
$82$		0			0
$83$	−0.909830	−	2.80017i	−0.0998668	−	0.307358i	0.888625	−	0.458635i	$-0.151662\pi$
$83$	−0.909830	−	2.80017i	−0.0998668	−	0.307358i	−0.988491	+	0.151277i	$0.951662\pi$
$84$		0			0
$85$	6.47214	−	4.70228i	0.702002	−	0.510034i
$86$		0			0
$87$	−7.23607			−0.775788
$88$		0			0
$89$	−11.2361			−1.19102			−0.595510	−	0.803348i	$-0.703050\pi$
$89$	−11.2361			−1.19102			−0.595510	+	0.803348i	$0.703050\pi$
$90$		0			0
$91$	−1.00000	+	0.726543i	−0.104828	+	0.0761624i
$92$		0			0
$93$	−1.70820	−	5.25731i	−0.177132	−	0.545158i
$94$		0			0
$95$	3.23607	+	2.35114i	0.332014	+	0.241222i
$96$		0			0
$97$	3.52786	−	10.8576i	0.358200	−	1.10243i	−0.595930	−	0.803036i	$-0.703217\pi$
$97$	3.52786	−	10.8576i	0.358200	−	1.10243i	0.954131	−	0.299391i	$-0.0967835\pi$
$98$		0			0
$99$	−1.81966	+	4.53077i	−0.182883	+	0.455359i
$100$		0			0
$101$	1.61803	−	4.97980i	0.161000	−	0.495508i	−0.837719	−	0.546102i	$-0.816111\pi$
$101$	1.61803	−	4.97980i	0.161000	−	0.495508i	0.998719	+	0.0505933i	$0.0161112\pi$
$102$		0			0
$103$	3.00000	+	2.17963i	0.295599	+	0.214765i	0.725693	−	0.688019i	$-0.241520\pi$
$103$	3.00000	+	2.17963i	0.295599	+	0.214765i	−0.430094	+	0.902784i	$0.641520\pi$
$104$		0			0
$105$	0.763932	+	2.35114i	0.0745521	+	0.229448i
$106$		0			0
$107$	8.39919	−	6.10237i	0.811980	−	0.589938i	−0.102424	−	0.994741i	$-0.532660\pi$
$107$	8.39919	−	6.10237i	0.811980	−	0.589938i	0.914404	+	0.404803i	$0.132660\pi$
$108$		0			0
$109$	−14.3820			−1.37754			−0.688771	−	0.724979i	$-0.741850\pi$
$109$	−14.3820			−1.37754			−0.688771	+	0.724979i	$0.741850\pi$
$110$		0			0
$111$	−3.88854			−0.369084
$112$		0			0
$113$	−2.50000	+	1.81636i	−0.235180	+	0.170868i	−0.699133	−	0.714991i	$-0.746431\pi$
$113$	−2.50000	+	1.81636i	−0.235180	+	0.170868i	0.463953	+	0.885860i	$0.346431\pi$
$114$		0			0
$115$	−1.00000	−	3.07768i	−0.0932505	−	0.286995i
$116$		0			0
$117$	−1.47214	−	1.06957i	−0.136099	−	0.0988817i
$118$		0			0
$119$	1.23607	−	3.80423i	0.113310	−	0.348733i
$120$		0			0
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$		0			0
$123$	0.652476	−	2.00811i	0.0588318	−	0.181066i
$124$		0			0
$125$	9.70820	+	7.05342i	0.868328	+	0.630877i
$126$		0			0
$127$	5.97214	+	18.3803i	0.529941	+	1.63099i	0.754332	+	0.656493i	$0.227961\pi$
$127$	5.97214	+	18.3803i	0.529941	+	1.63099i	−0.224391	+	0.974499i	$0.572039\pi$
$128$		0			0
$129$	4.14590	−	3.01217i	0.365026	−	0.265207i
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$	2.00000			0.173422
$134$		0			0
$135$	−8.94427	+	6.49839i	−0.769800	+	0.559293i
$136$		0			0
$137$	6.50000	+	20.0049i	0.555332	+	1.70914i	0.695064	+	0.718948i	$0.255376\pi$
$137$	6.50000	+	20.0049i	0.555332	+	1.70914i	−0.139731	+	0.990189i	$0.544624\pi$
$138$		0			0
$139$	2.61803	+	1.90211i	0.222059	+	0.161335i	0.693253	−	0.720694i	$-0.256177\pi$
$139$	2.61803	+	1.90211i	0.222059	+	0.161335i	−0.471194	+	0.882030i	$0.656177\pi$
$140$		0			0
$141$	−3.81966	+	11.7557i	−0.321673	+	0.990009i
$142$		0			0
$143$	−1.52786	+	3.80423i	−0.127766	+	0.318125i
$144$		0			0
$145$	3.61803	−	11.1352i	0.300461	−	0.924725i
$146$		0			0
$147$	1.00000	+	0.726543i	0.0824786	+	0.0599242i
$148$		0			0
$149$	0.145898	+	0.449028i	0.0119524	+	0.0367858i	0.956855	−	0.290566i	$-0.0938437\pi$
$149$	0.145898	+	0.449028i	0.0119524	+	0.0367858i	−0.944902	+	0.327352i	$0.893844\pi$
$150$		0			0
$151$	19.6353	−	14.2658i	1.59789	−	1.16094i	0.706497	−	0.707716i	$-0.250275\pi$
$151$	19.6353	−	14.2658i	1.59789	−	1.16094i	0.891398	−	0.453222i	$-0.149725\pi$
$152$		0			0
$153$	5.88854			0.476061
$154$		0			0
$155$	8.94427			0.718421
$156$		0			0
$157$	−5.00000	+	3.63271i	−0.399043	+	0.289922i	−0.769151	−	0.639067i	$-0.779321\pi$
$157$	−5.00000	+	3.63271i	−0.399043	+	0.289922i	0.370108	+	0.928989i	$0.379321\pi$
$158$		0			0
$159$	2.81966	+	8.67802i	0.223614	+	0.688212i
$160$		0			0
$161$	−1.30902	−	0.951057i	−0.103165	−	0.0749538i
$162$		0			0
$163$	6.26393	−	19.2784i	0.490629	−	1.51000i	−0.333030	−	0.942916i	$-0.608071\pi$
$163$	6.26393	−	19.2784i	0.490629	−	1.51000i	0.823659	−	0.567085i	$-0.191929\pi$
$164$		0			0
$165$	6.29180	+	5.25731i	0.489816	+	0.409281i
$166$		0			0
$167$	−0.944272	+	2.90617i	−0.0730700	+	0.224886i	−0.980921	−	0.194407i	$-0.937722\pi$
$167$	−0.944272	+	2.90617i	−0.0730700	+	0.224886i	0.907851	+	0.419293i	$0.137722\pi$
$168$		0			0
$169$	9.28115	+	6.74315i	0.713935	+	0.518704i
$170$		0			0
$171$	0.909830	+	2.80017i	0.0695764	+	0.214134i
$172$		0			0
$173$	3.00000	−	2.17963i	0.228086	−	0.165714i	−0.467873	−	0.883796i	$-0.654980\pi$
$173$	3.00000	−	2.17963i	0.228086	−	0.165714i	0.695959	+	0.718082i	$0.254980\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	−12.0000			−0.901975
$178$		0			0
$179$	−1.92705	+	1.40008i	−0.144035	+	0.104647i	−0.657469	−	0.753482i	$-0.728373\pi$
$179$	−1.92705	+	1.40008i	−0.144035	+	0.104647i	0.513434	+	0.858129i	$0.328373\pi$
$180$		0			0
$181$	0.944272	+	2.90617i	0.0701872	+	0.216014i	0.979997	−	0.199011i	$-0.0637729\pi$
$181$	0.944272	+	2.90617i	0.0701872	+	0.216014i	−0.909810	+	0.415025i	$0.863773\pi$
$182$		0			0
$183$	−8.47214	−	6.15537i	−0.626278	−	0.455018i
$184$		0			0
$185$	1.94427	−	5.98385i	0.142946	−	0.439942i
$186$		0			0
$187$	−3.23607	−	12.8658i	−0.236645	−	0.940838i
$188$		0			0
$189$	−1.70820	+	5.25731i	−0.124254	+	0.382413i
$190$		0			0
$191$	−4.35410	−	3.16344i	−0.315052	−	0.228899i	0.419009	−	0.907982i	$-0.362377\pi$
$191$	−4.35410	−	3.16344i	−0.315052	−	0.228899i	−0.734061	+	0.679083i	$0.762377\pi$
$192$		0			0
$193$	4.37132	+	13.4535i	0.314655	+	0.968408i	0.975896	+	0.218235i	$0.0700298\pi$
$193$	4.37132	+	13.4535i	0.314655	+	0.968408i	−0.661242	+	0.750173i	$0.729970\pi$
$194$		0			0
$195$	−2.47214	+	1.79611i	−0.177033	+	0.128622i
$196$		0			0
$197$	5.79837			0.413117			0.206559	−	0.978434i	$-0.433774\pi$
$197$	5.79837			0.413117			0.206559	+	0.978434i	$0.433774\pi$
$198$		0			0
$199$	14.1803			1.00522			0.502609	−	0.864514i	$-0.332374\pi$
$199$	14.1803			1.00522			0.502609	+	0.864514i	$0.332374\pi$
$200$		0			0
$201$	2.61803	−	1.90211i	0.184662	−	0.134165i
$202$		0			0
$203$	−1.80902	−	5.56758i	−0.126968	−	0.390768i
$204$		0			0
$205$	2.76393	+	2.00811i	0.193041	+	0.140253i
$206$		0			0
$207$	0.736068	−	2.26538i	0.0511603	−	0.157455i
$208$		0			0
$209$	5.61803	−	3.52671i	0.388608	−	0.243948i
$210$		0			0
$211$	5.26393	−	16.2007i	0.362384	−	1.11530i	−0.589219	−	0.807973i	$-0.700564\pi$
$211$	5.26393	−	16.2007i	0.362384	−	1.11530i	0.951603	−	0.307330i	$-0.0994355\pi$
$212$		0			0
$213$	13.0902	+	9.51057i	0.896924	+	0.651653i
$214$		0			0
$215$	2.56231	+	7.88597i	0.174748	+	0.537818i
$216$		0			0
$217$	3.61803	−	2.62866i	0.245608	−	0.178445i
$218$		0			0
$219$	−20.5836			−1.39091
$220$		0			0
$221$	4.94427			0.332588
$222$		0			0
$223$	−12.4721	+	9.06154i	−0.835196	+	0.606805i	−0.921025	−	0.389505i	$-0.872646\pi$
$223$	−12.4721	+	9.06154i	−0.835196	+	0.606805i	0.0858286	+	0.996310i	$0.472646\pi$
$224$		0			0
$225$	0.454915	+	1.40008i	0.0303277	+	0.0933390i
$226$		0			0
$227$	−15.7082	−	11.4127i	−1.04259	−	0.757486i	−0.0718007	−	0.997419i	$-0.522875\pi$
$227$	−15.7082	−	11.4127i	−1.04259	−	0.757486i	−0.970789	+	0.239933i	$0.922875\pi$
$228$		0			0
$229$	4.56231	−	14.0413i	0.301486	−	0.927877i	−0.679480	−	0.733694i	$-0.737794\pi$
$229$	4.56231	−	14.0413i	0.301486	−	0.927877i	0.980965	−	0.194183i	$-0.0622056\pi$
$230$		0			0
$231$	4.09017	+	0.277515i	0.269113	+	0.0182591i
$232$		0			0
$233$	−8.79837	+	27.0786i	−0.576401	+	1.77398i	0.0549590	+	0.998489i	$0.482497\pi$
$233$	−8.79837	+	27.0786i	−0.576401	+	1.77398i	−0.631360	+	0.775490i	$0.717503\pi$
$234$		0			0
$235$	−16.1803	−	11.7557i	−1.05549	−	0.766858i
$236$		0			0
$237$	−1.94427	−	5.98385i	−0.126294	−	0.388693i
$238$		0			0
$239$	−16.2984	+	11.8415i	−1.05425	+	0.765960i	−0.973017	−	0.230734i	$-0.925887\pi$
$239$	−16.2984	+	11.8415i	−1.05425	+	0.765960i	−0.0812374	+	0.996695i	$0.525887\pi$
$240$		0			0
$241$	−6.47214			−0.416907			−0.208453	−	0.978032i	$-0.566843\pi$
$241$	−6.47214			−0.416907			−0.208453	+	0.978032i	$0.566843\pi$
$242$		0			0
$243$	−13.5967			−0.872232
$244$		0			0
$245$	−1.61803	+	1.17557i	−0.103372	+	0.0751044i
$246$		0			0
$247$	0.763932	+	2.35114i	0.0486078	+	0.149600i
$248$		0			0
$249$	−2.94427	−	2.13914i	−0.186586	−	0.135562i
$250$		0			0
$251$	5.14590	−	15.8374i	0.324806	−	0.999651i	−0.646722	−	0.762726i	$-0.723861\pi$
$251$	5.14590	−	15.8374i	0.324806	−	0.999651i	0.971528	−	0.236925i	$-0.0761395\pi$
$252$		0			0
$253$	−5.35410	−	0.363271i	−0.336610	−	0.0228387i
$254$		0			0
$255$	3.05573	−	9.40456i	0.191357	−	0.588937i
$256$		0			0
$257$	−8.85410	−	6.43288i	−0.552304	−	0.401272i	0.276330	−	0.961063i	$-0.410882\pi$
$257$	−8.85410	−	6.43288i	−0.552304	−	0.401272i	−0.828634	+	0.559791i	$0.810882\pi$
$258$		0			0
$259$	−0.972136	−	2.99193i	−0.0604056	−	0.185909i
$260$		0			0
$261$	6.97214	−	5.06555i	0.431564	−	0.313550i
$262$		0			0
$263$	−14.0344			−0.865401			−0.432700	−	0.901538i	$-0.642439\pi$
$263$	−14.0344			−0.865401			−0.432700	+	0.901538i	$0.642439\pi$
$264$		0			0
$265$	−14.7639			−0.906941
$266$		0			0
$267$	−11.2361	+	8.16348i	−0.687636	+	0.499597i
$268$		0			0
$269$	1.76393	+	5.42882i	0.107549	+	0.331001i	0.990320	−	0.138802i	$-0.0443250\pi$
$269$	1.76393	+	5.42882i	0.107549	+	0.331001i	−0.882771	+	0.469803i	$0.844325\pi$
$270$		0			0
$271$	21.1803	+	15.3884i	1.28661	+	0.934780i	0.999731	−	0.0231859i	$-0.00738095\pi$
$271$	21.1803	+	15.3884i	1.28661	+	0.934780i	0.286883	+	0.957966i	$0.407381\pi$
$272$		0			0
$273$	−0.472136	+	1.45309i	−0.0285750	+	0.0879447i
$274$		0			0
$275$	2.80902	−	1.76336i	0.169390	−	0.106334i
$276$		0			0
$277$	−3.55573	+	10.9434i	−0.213643	+	0.657526i	0.785604	+	0.618729i	$0.212352\pi$
$277$	−3.55573	+	10.9434i	−0.213643	+	0.657526i	−0.999247	+	0.0387961i	$0.987648\pi$
$278$		0			0
$279$	5.32624	+	3.86974i	0.318874	+	0.231675i
$280$		0			0
$281$	−3.42705	−	10.5474i	−0.204441	−	0.629204i	−0.999736	−	0.0229814i	$-0.992684\pi$
$281$	−3.42705	−	10.5474i	−0.204441	−	0.629204i	0.795295	−	0.606222i	$-0.207316\pi$
$282$		0			0
$283$	−4.00000	+	2.90617i	−0.237775	+	0.172754i	−0.700292	−	0.713857i	$-0.746947\pi$
$283$	−4.00000	+	2.90617i	−0.237775	+	0.172754i	0.462516	+	0.886611i	$0.346947\pi$
$284$		0			0
$285$	4.94427			0.292873
$286$		0			0
$287$	1.70820			0.100832
$288$		0			0
$289$	0.809017	−	0.587785i	0.0475892	−	0.0345756i
$290$		0			0
$291$	−4.36068	−	13.4208i	−0.255628	−	0.786741i
$292$		0			0
$293$	−7.23607	−	5.25731i	−0.422736	−	0.307135i	0.356002	−	0.934485i	$-0.384140\pi$
$293$	−7.23607	−	5.25731i	−0.422736	−	0.307135i	−0.778738	+	0.627350i	$0.784140\pi$
$294$		0			0
$295$	6.00000	−	18.4661i	0.349334	−	1.07514i
$296$		0			0
$297$	4.47214	+	17.7800i	0.259500	+	1.03170i
$298$		0			0
$299$	0.618034	−	1.90211i	0.0357418	−	0.110002i
$300$		0			0
$301$	3.35410	+	2.43690i	0.193327	+	0.140460i
$302$		0			0
$303$	−2.00000	−	6.15537i	−0.114897	−	0.353617i
$304$		0			0
$305$	13.7082	−	9.95959i	0.784929	−	0.570285i
$306$		0			0
$307$	−14.9443			−0.852915			−0.426457	−	0.904508i	$-0.640239\pi$
$307$	−14.9443			−0.852915			−0.426457	+	0.904508i	$0.640239\pi$
$308$		0			0
$309$	4.58359			0.260751
$310$		0			0
$311$	−0.236068	+	0.171513i	−0.0133862	+	0.00972563i	−0.594458	−	0.804126i	$-0.702633\pi$
$311$	−0.236068	+	0.171513i	−0.0133862	+	0.00972563i	0.581072	+	0.813852i	$0.302633\pi$
$312$		0			0
$313$	7.61803	+	23.4459i	0.430597	+	1.32524i	0.897532	+	0.440949i	$0.145358\pi$
$313$	7.61803	+	23.4459i	0.430597	+	1.32524i	−0.466935	+	0.884291i	$0.654642\pi$
$314$		0			0
$315$	−2.38197	−	1.73060i	−0.134209	−	0.0975082i
$316$		0			0
$317$	−6.57295	+	20.2295i	−0.369174	+	1.13620i	0.578152	+	0.815929i	$0.303774\pi$
$317$	−6.57295	+	20.2295i	−0.369174	+	1.13620i	−0.947326	+	0.320271i	$0.896226\pi$
$318$		0			0
$319$	−14.8992	−	12.4495i	−0.834194	−	0.697038i
$320$		0			0
$321$	3.96556	−	12.2047i	0.221336	−	0.681202i
$322$		0			0
$323$	−6.47214	−	4.70228i	−0.360119	−	0.261642i
$324$		0			0
$325$	0.381966	+	1.17557i	0.0211877	+	0.0652089i
$326$		0			0
$327$	−14.3820	+	10.4491i	−0.795325	+	0.577837i
$328$		0			0
$329$	−10.0000			−0.551318
$330$		0			0
$331$	32.2705			1.77375			0.886874	−	0.462012i	$-0.152872\pi$
$331$	32.2705			1.77375			0.886874	+	0.462012i	$0.152872\pi$
$332$		0			0
$333$	3.74671	−	2.72214i	0.205319	−	0.149173i
$334$		0			0
$335$	1.61803	+	4.97980i	0.0884026	+	0.272075i
$336$		0			0
$337$	−19.0172	−	13.8168i	−1.03593	−	0.752650i	−0.0664463	−	0.997790i	$-0.521166\pi$
$337$	−19.0172	−	13.8168i	−1.03593	−	0.752650i	−0.969488	+	0.245140i	$0.921166\pi$
$338$		0			0
$339$	−1.18034	+	3.63271i	−0.0641073	+	0.197302i
$340$		0			0
$341$	5.52786	−	13.7638i	0.299351	−	0.745353i
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$		0			0
$345$	−3.23607	−	2.35114i	−0.174224	−	0.126581i
$346$		0			0
$347$	−4.80902	−	14.8006i	−0.258162	−	0.794540i	−0.993190	−	0.116504i	$-0.962831\pi$
$347$	−4.80902	−	14.8006i	−0.258162	−	0.794540i	0.735029	−	0.678036i	$-0.237169\pi$
$348$		0			0
$349$	−23.5623	+	17.1190i	−1.26126	+	0.916360i	−0.998819	−	0.0485877i	$-0.984528\pi$
$349$	−23.5623	+	17.1190i	−1.26126	+	0.916360i	−0.262442	+	0.964948i	$0.584528\pi$
$350$		0			0
$351$	−6.83282			−0.364709
$352$		0			0
$353$	17.4164			0.926982			0.463491	−	0.886102i	$-0.346597\pi$
$353$	17.4164			0.926982			0.463491	+	0.886102i	$0.346597\pi$
$354$		0			0
$355$	−21.1803	+	15.3884i	−1.12414	+	0.816732i
$356$		0			0
$357$	−1.52786	−	4.70228i	−0.0808631	−	0.248871i
$358$		0			0
$359$	3.30902	+	2.40414i	0.174643	+	0.126886i	0.671673	−	0.740848i	$-0.265576\pi$
$359$	3.30902	+	2.40414i	0.174643	+	0.126886i	−0.497030	+	0.867734i	$0.665576\pi$
$360$		0			0
$361$	−4.63525	+	14.2658i	−0.243961	+	0.750834i
$362$		0			0
$363$	11.9787	−	6.43288i	0.628719	−	0.337639i
$364$		0			0
$365$	10.2918	−	31.6749i	0.538697	−	1.65794i
$366$		0			0
$367$	1.85410	+	1.34708i	0.0967833	+	0.0703172i	0.635124	−	0.772410i	$-0.280949\pi$
$367$	1.85410	+	1.34708i	0.0967833	+	0.0703172i	−0.538341	+	0.842727i	$0.680949\pi$
$368$		0			0
$369$	0.777088	+	2.39163i	0.0404536	+	0.124503i
$370$		0			0
$371$	−5.97214	+	4.33901i	−0.310058	+	0.225270i
$372$		0			0
$373$	15.5279			0.804002			0.402001	−	0.915639i	$-0.368315\pi$
$373$	15.5279			0.804002			0.402001	+	0.915639i	$0.368315\pi$
$374$		0			0
$375$	14.8328			0.765963
$376$		0			0
$377$	5.85410	−	4.25325i	0.301502	−	0.219054i
$378$		0			0
$379$	2.02786	+	6.24112i	0.104164	+	0.320585i	0.989533	−	0.144304i	$-0.0460943\pi$
$379$	2.02786	+	6.24112i	0.104164	+	0.320585i	−0.885369	+	0.464889i	$0.846094\pi$
$380$		0			0
$381$	19.3262	+	14.0413i	0.990113	+	0.719359i
$382$		0			0
$383$	−2.00000	+	6.15537i	−0.102195	+	0.314525i	−0.989062	−	0.147501i	$-0.952877\pi$
$383$	−2.00000	+	6.15537i	−0.102195	+	0.314525i	0.886867	+	0.462025i	$0.152877\pi$
$384$		0			0
$385$	−2.47214	+	6.15537i	−0.125992	+	0.313707i
$386$		0			0
$387$	−1.88603	+	5.80461i	−0.0958724	+	0.295065i
$388$		0			0
$389$	−29.1976	−	21.2133i	−1.48038	−	1.07556i	−0.977436	−	0.211234i	$-0.932252\pi$
$389$	−29.1976	−	21.2133i	−1.48038	−	1.07556i	−0.502940	−	0.864322i	$-0.667748\pi$
$390$		0			0
$391$	2.00000	+	6.15537i	0.101144	+	0.311290i
$392$		0			0
$393$	4.00000	−	2.90617i	0.201773	−	0.146597i
$394$		0			0
$395$	10.1803			0.512228
$396$		0			0
$397$	−34.6525			−1.73916			−0.869579	−	0.493794i	$-0.835610\pi$
$397$	−34.6525			−1.73916			−0.869579	+	0.493794i	$0.835610\pi$
$398$		0			0
$399$	2.00000	−	1.45309i	0.100125	−	0.0727452i
$400$		0			0
$401$	0.500000	+	1.53884i	0.0249688	+	0.0768461i	0.962764	−	0.270342i	$-0.0871367\pi$
$401$	0.500000	+	1.53884i	0.0249688	+	0.0768461i	−0.937796	+	0.347188i	$0.887137\pi$
$402$		0			0
$403$	4.47214	+	3.24920i	0.222773	+	0.161854i
$404$		0			0
$405$	−1.49342	+	4.59628i	−0.0742087	+	0.228391i
$406$		0			0
$407$	−8.00658	−	6.69015i	−0.396871	−	0.331619i
$408$		0			0
$409$	−11.4164	+	35.1361i	−0.564505	+	1.73737i	0.104912	+	0.994481i	$0.466544\pi$
$409$	−11.4164	+	35.1361i	−0.564505	+	1.73737i	−0.669418	+	0.742886i	$0.733456\pi$
$410$		0			0
$411$	21.0344	+	15.2824i	1.03755	+	0.753826i
$412$		0			0
$413$	−3.00000	−	9.23305i	−0.147620	−	0.454329i
$414$		0			0
$415$	4.76393	−	3.46120i	0.233852	−	0.169904i
$416$		0			0
$417$	4.00000			0.195881
$418$		0			0
$419$	16.4721			0.804717			0.402358	−	0.915482i	$-0.368191\pi$
$419$	16.4721			0.804717			0.402358	+	0.915482i	$0.368191\pi$
$420$		0			0
$421$	22.7254	−	16.5110i	1.10757	−	0.804696i	0.125290	−	0.992120i	$-0.460014\pi$
$421$	22.7254	−	16.5110i	1.10757	−	0.804696i	0.982279	+	0.187424i	$0.0600138\pi$
$422$		0			0
$423$	−4.54915	−	14.0008i	−0.221187	−	0.680744i
$424$		0			0
$425$	−3.23607	−	2.35114i	−0.156972	−	0.114047i
$426$		0			0
$427$	2.61803	−	8.05748i	0.126696	−	0.389929i
$428$		0			0
$429$	1.23607	+	4.91428i	0.0596779	+	0.237264i
$430$		0			0
$431$	−7.26393	+	22.3561i	−0.349891	+	1.07685i	0.609022	+	0.793154i	$0.291562\pi$
$431$	−7.26393	+	22.3561i	−0.349891	+	1.07685i	−0.958913	+	0.283701i	$0.908438\pi$
$432$		0			0
$433$	4.00000	+	2.90617i	0.192228	+	0.139662i	0.679736	−	0.733457i	$-0.262094\pi$
$433$	4.00000	+	2.90617i	0.192228	+	0.139662i	−0.487509	+	0.873118i	$0.662094\pi$
$434$		0			0
$435$	−4.47214	−	13.7638i	−0.214423	−	0.659925i
$436$		0			0
$437$	−2.61803	+	1.90211i	−0.125238	+	0.0909904i
$438$		0			0
$439$	28.6525			1.36751			0.683754	−	0.729713i	$-0.260346\pi$
$439$	28.6525			1.36751			0.683754	+	0.729713i	$0.260346\pi$
$440$		0			0
$441$	−1.47214			−0.0701017
$442$		0			0
$443$	14.0623	−	10.2169i	0.668120	−	0.485418i	−0.201275	−	0.979535i	$-0.564509\pi$
$443$	14.0623	−	10.2169i	0.668120	−	0.485418i	0.869395	+	0.494117i	$0.164509\pi$
$444$		0			0
$445$	−6.94427	−	21.3723i	−0.329190	−	1.01314i
$446$		0			0
$447$	0.472136	+	0.343027i	0.0223313	+	0.0162246i
$448$		0			0
$449$	−1.73607	+	5.34307i	−0.0819301	+	0.252155i	−0.983628	−	0.180212i	$-0.942322\pi$
$449$	−1.73607	+	5.34307i	−0.0819301	+	0.252155i	0.901698	+	0.432367i	$0.142322\pi$
$450$		0			0
$451$	4.79837	−	3.01217i	0.225947	−	0.141838i
$452$		0			0
$453$	9.27051	−	28.5317i	0.435567	−	1.34054i
$454$		0			0
$455$	−2.00000	−	1.45309i	−0.0937614	−	0.0681217i
$456$		0			0
$457$	5.02786	+	15.4742i	0.235194	+	0.723851i	0.997096	+	0.0761592i	$0.0242657\pi$
$457$	5.02786	+	15.4742i	0.235194	+	0.723851i	−0.761902	+	0.647692i	$0.775734\pi$
$458$		0			0
$459$	17.8885	−	12.9968i	0.834966	−	0.606638i
$460$		0			0
$461$	38.1803			1.77824			0.889118	−	0.457678i	$-0.151319\pi$
$461$	38.1803			1.77824			0.889118	+	0.457678i	$0.151319\pi$
$462$		0			0
$463$	−17.4508			−0.811010			−0.405505	−	0.914093i	$-0.632904\pi$
$463$	−17.4508			−0.811010			−0.405505	+	0.914093i	$0.632904\pi$
$464$		0			0
$465$	8.94427	−	6.49839i	0.414781	−	0.301356i
$466$		0			0
$467$	11.4164	+	35.1361i	0.528288	+	1.62590i	0.757720	+	0.652580i	$0.226313\pi$
$467$	11.4164	+	35.1361i	0.528288	+	1.62590i	−0.229432	+	0.973325i	$0.573687\pi$
$468$		0			0
$469$	2.11803	+	1.53884i	0.0978017	+	0.0710571i
$470$		0			0
$471$	−2.36068	+	7.26543i	−0.108774	+	0.334773i
$472$		0			0
$473$	13.7188	+	0.930812i	0.630793	+	0.0427988i
$474$		0			0
$475$	0.618034	−	1.90211i	0.0283573	−	0.0872749i
$476$		0			0
$477$	−8.79180	−	6.38761i	−0.402549	−	0.292469i
$478$		0			0
$479$	8.85410	+	27.2501i	0.404554	+	1.24509i	0.921267	+	0.388931i	$0.127156\pi$
$479$	8.85410	+	27.2501i	0.404554	+	1.24509i	−0.516713	+	0.856159i	$0.672844\pi$
$480$		0			0
$481$	3.14590	−	2.28563i	0.143441	−	0.104216i
$482$		0			0
$483$	−2.00000			−0.0910032
$484$		0			0
$485$	22.8328			1.03678
$486$		0			0
$487$	−2.11803	+	1.53884i	−0.0959773	+	0.0697316i	−0.634739	−	0.772727i	$-0.718892\pi$
$487$	−2.11803	+	1.53884i	−0.0959773	+	0.0697316i	0.538762	+	0.842458i	$0.318892\pi$
$488$		0			0
$489$	−7.74265	−	23.8294i	−0.350135	−	1.07760i
$490$		0			0
$491$	5.70820	+	4.14725i	0.257608	+	0.187163i	0.709092	−	0.705116i	$-0.249105\pi$
$491$	5.70820	+	4.14725i	0.257608	+	0.187163i	−0.451484	+	0.892279i	$0.649105\pi$
$492$		0			0
$493$	−7.23607	+	22.2703i	−0.325896	+	1.00301i
$494$		0			0
$495$	−9.74265	−	0.661030i	−0.437899	−	0.0297111i
$496$		0			0
$497$	−4.04508	+	12.4495i	−0.181447	+	0.558436i
$498$		0			0
$499$	12.1180	+	8.80427i	0.542478	+	0.394133i	0.825004	−	0.565126i	$-0.191173\pi$
$499$	12.1180	+	8.80427i	0.542478	+	0.394133i	−0.282527	+	0.959259i	$0.591173\pi$
$500$		0			0
$501$	1.16718	+	3.59222i	0.0521459	+	0.160489i
$502$		0			0
$503$	−7.23607	+	5.25731i	−0.322640	+	0.234412i	−0.737301	−	0.675564i	$-0.763900\pi$
$503$	−7.23607	+	5.25731i	−0.322640	+	0.234412i	0.414661	+	0.909976i	$0.363900\pi$
$504$		0			0
$505$	10.4721			0.466004
$506$		0			0
$507$	14.1803			0.629771
$508$		0			0
$509$	14.3262	−	10.4086i	0.634999	−	0.461354i	−0.223129	−	0.974789i	$-0.571627\pi$
$509$	14.3262	−	10.4086i	0.634999	−	0.461354i	0.858129	+	0.513435i	$0.171627\pi$
$510$		0			0
$511$	−5.14590	−	15.8374i	−0.227641	−	0.700607i
$512$		0			0
$513$	8.94427	+	6.49839i	0.394899	+	0.286911i
$514$		0			0
$515$	−2.29180	+	7.05342i	−0.100989	+	0.310811i
$516$		0			0
$517$	−28.0902	+	17.6336i	−1.23540	+	0.775523i
$518$		0			0
$519$	1.41641	−	4.35926i	0.0621734	−	0.191350i
$520$		0			0
$521$	17.4721	+	12.6942i	0.765468	+	0.556145i	0.900583	−	0.434685i	$-0.143140\pi$
$521$	17.4721	+	12.6942i	0.765468	+	0.556145i	−0.135114	+	0.990830i	$0.543140\pi$
$522$		0			0
$523$	2.67376	+	8.22899i	0.116915	+	0.359829i	0.992342	−	0.123523i	$-0.0394192\pi$
$523$	2.67376	+	8.22899i	0.116915	+	0.359829i	−0.875426	+	0.483352i	$0.839419\pi$
$524$		0			0
$525$	1.00000	−	0.726543i	0.0436436	−	0.0317089i
$526$		0			0
$527$	−17.8885			−0.779237
$528$		0			0
$529$	−20.3820			−0.886172
$530$		0			0
$531$	11.5623	−	8.40051i	0.501761	−	0.364551i
$532$		0			0
$533$	0.652476	+	2.00811i	0.0282619	+	0.0869811i
$534$		0			0
$535$	16.7984	+	12.2047i	0.726257	+	0.527657i
$536$		0			0
$537$	−0.909830	+	2.80017i	−0.0392621	+	0.120836i
$538$		0			0
$539$	0.809017	+	3.21644i	0.0348468	+	0.138542i
$540$		0			0
$541$	−4.02786	+	12.3965i	−0.173171	+	0.532967i	−0.999545	−	0.0301551i	$-0.990400\pi$
$541$	−4.02786	+	12.3965i	−0.173171	+	0.532967i	0.826374	+	0.563122i	$0.190400\pi$
$542$		0			0
$543$	3.05573	+	2.22012i	0.131134	+	0.0952743i
$544$		0			0
$545$	−8.88854	−	27.3561i	−0.380743	−	1.17181i
$546$		0			0
$547$	−15.4164	+	11.2007i	−0.659158	+	0.478906i	−0.866378	−	0.499388i	$-0.833558\pi$
$547$	−15.4164	+	11.2007i	−0.659158	+	0.478906i	0.207220	+	0.978294i	$0.433558\pi$
$548$		0			0
$549$	12.4721			0.532298
$550$		0			0
$551$	−11.7082			−0.498786
$552$		0			0
$553$	4.11803	−	2.99193i	0.175117	−	0.127230i
$554$		0			0
$555$	−2.40325	−	7.39645i	−0.102012	−	0.313962i
$556$		0			0
$557$	3.97214	+	2.88593i	0.168305	+	0.122281i	0.668749	−	0.743488i	$-0.266830\pi$
$557$	3.97214	+	2.88593i	0.168305	+	0.122281i	−0.500444	+	0.865769i	$0.666830\pi$
$558$		0			0
$559$	−1.58359	+	4.87380i	−0.0669788	+	0.206140i
$560$		0			0
$561$	−12.5836	−	10.5146i	−0.531280	−	0.443928i
$562$		0			0
$563$	−4.74265	+	14.5964i	−0.199879	+	0.615163i	0.800006	+	0.599992i	$0.204829\pi$
$563$	−4.74265	+	14.5964i	−0.199879	+	0.615163i	−0.999885	+	0.0151716i	$0.995171\pi$
$564$		0			0
$565$	−5.00000	−	3.63271i	−0.210352	−	0.152829i
$566$		0			0
$567$	0.746711	+	2.29814i	0.0313589	+	0.0965128i
$568$		0			0
$569$	−3.61803	+	2.62866i	−0.151676	+	0.110199i	−0.661035	−	0.750355i	$-0.729883\pi$
$569$	−3.61803	+	2.62866i	−0.151676	+	0.110199i	0.509359	+	0.860554i	$0.329883\pi$
$570$		0			0
$571$	−41.9787			−1.75675			−0.878377	−	0.477968i	$-0.841373\pi$
$571$	−41.9787			−1.75675			−0.878377	+	0.477968i	$0.841373\pi$
$572$		0			0
$573$	−6.65248			−0.277911
$574$		0			0
$575$	−1.30902	+	0.951057i	−0.0545898	+	0.0396618i
$576$		0			0
$577$	−1.29180	−	3.97574i	−0.0537782	−	0.165512i	0.920560	−	0.390601i	$-0.127733\pi$
$577$	−1.29180	−	3.97574i	−0.0537782	−	0.165512i	−0.974338	+	0.225089i	$0.927733\pi$
$578$		0			0
$579$	14.1459	+	10.2776i	0.587883	+	0.427122i
$580$		0			0
$581$	0.909830	−	2.80017i	0.0377461	−	0.116171i
$582$		0			0
$583$	−9.12461	+	22.7194i	−0.377903	+	0.940940i
$584$		0			0
$585$	1.12461	−	3.46120i	0.0464970	−	0.143103i
$586$		0			0
$587$	−15.0902	−	10.9637i	−0.622838	−	0.452518i	0.231074	−	0.972936i	$-0.425776\pi$
$587$	−15.0902	−	10.9637i	−0.622838	−	0.452518i	−0.853912	+	0.520418i	$0.825776\pi$
$588$		0			0
$589$	−2.76393	−	8.50651i	−0.113886	−	0.350505i
$590$		0			0
$591$	5.79837	−	4.21277i	0.238513	−	0.173290i
$592$		0			0
$593$	31.2361			1.28271			0.641356	−	0.767244i	$-0.278372\pi$
$593$	31.2361			1.28271			0.641356	+	0.767244i	$0.278372\pi$
$594$		0			0
$595$	8.00000			0.327968
$596$		0			0
$597$	14.1803	−	10.3026i	0.580363	−	0.421658i
$598$		0			0
$599$	−12.5000	−	38.4710i	−0.510736	−	1.57188i	−0.790908	−	0.611935i	$-0.790392\pi$
$599$	−12.5000	−	38.4710i	−0.510736	−	1.57188i	0.280172	−	0.959950i	$-0.409608\pi$
$600$		0			0
$601$	−33.2705	−	24.1724i	−1.35713	−	0.986014i	−0.998622	−	0.0524889i	$-0.983285\pi$
$601$	−33.2705	−	24.1724i	−1.35713	−	0.986014i	−0.358511	−	0.933526i	$-0.616715\pi$
$602$		0			0
$603$	−1.19098	+	3.66547i	−0.0485006	+	0.149269i
$604$		0			0
$605$	3.90983	+	21.6498i	0.158957	+	0.880189i
$606$		0			0
$607$	10.3820	−	31.9524i	0.421391	−	1.29691i	−0.485017	−	0.874505i	$-0.661187\pi$
$607$	10.3820	−	31.9524i	0.421391	−	1.29691i	0.906408	−	0.422403i	$-0.138813\pi$
$608$		0			0
$609$	−5.85410	−	4.25325i	−0.237220	−	0.172351i
$610$		0			0
$611$	−3.81966	−	11.7557i	−0.154527	−	0.475585i
$612$		0			0
$613$	−9.97214	+	7.24518i	−0.402771	+	0.292630i	−0.770669	−	0.637236i	$-0.780078\pi$
$613$	−9.97214	+	7.24518i	−0.402771	+	0.292630i	0.367898	+	0.929866i	$0.380078\pi$
$614$		0			0
$615$	4.22291			0.170284
$616$		0			0
$617$	−38.5066			−1.55022			−0.775108	−	0.631828i	$-0.782305\pi$
$617$	−38.5066			−1.55022			−0.775108	+	0.631828i	$0.782305\pi$
$618$		0			0
$619$	12.3262	−	8.95554i	0.495433	−	0.359953i	−0.311837	−	0.950136i	$-0.600944\pi$
$619$	12.3262	−	8.95554i	0.495433	−	0.359953i	0.807270	+	0.590182i	$0.200944\pi$
$620$		0			0
$621$	−2.76393	−	8.50651i	−0.110913	−	0.341354i
$622$		0			0
$623$	−9.09017	−	6.60440i	−0.364190	−	0.264600i
$624$		0			0
$625$	−5.87132	+	18.0701i	−0.234853	+	0.722803i
$626$		0			0
$627$	3.05573	−	7.60845i	0.122034	−	0.303852i
$628$		0			0
$629$	−3.88854	+	11.9677i	−0.155046	+	0.477184i
$630$		0			0
$631$	30.5795	+	22.2173i	1.21735	+	0.884458i	0.995877	−	0.0907084i	$-0.0289131\pi$
$631$	30.5795	+	22.2173i	1.21735	+	0.884458i	0.221474	+	0.975166i	$0.428913\pi$
$632$		0			0
$633$	−6.50658	−	20.0252i	−0.258613	−	0.795930i
$634$		0			0
$635$	−31.2705	+	22.7194i	−1.24093	+	0.901590i
$636$		0			0
$637$	−1.23607			−0.0489748
$638$		0			0
$639$	−19.2705			−0.762330
$640$		0			0
$641$	37.1525	−	26.9929i	1.46743	−	1.06615i	0.486087	−	0.873910i	$-0.338424\pi$
$641$	37.1525	−	26.9929i	1.46743	−	1.06615i	0.981347	−	0.192243i	$-0.0615763\pi$
$642$		0			0
$643$	−5.43769	−	16.7355i	−0.214442	−	0.659984i	−0.999193	−	0.0401726i	$-0.987209\pi$
$643$	−5.43769	−	16.7355i	−0.214442	−	0.659984i	0.784751	−	0.619811i	$-0.212791\pi$
$644$		0			0
$645$	8.29180	+	6.02434i	0.326489	+	0.237208i
$646$		0			0
$647$	1.41641	−	4.35926i	0.0556847	−	0.171380i	−0.919346	−	0.393450i	$-0.871281\pi$
$647$	1.41641	−	4.35926i	0.0556847	−	0.171380i	0.975031	+	0.222070i	$0.0712814\pi$
$648$		0			0
$649$	−24.7082	−	20.6457i	−0.969882	−	0.810416i
$650$		0			0
$651$	1.70820	−	5.25731i	0.0669498	−	0.206050i
$652$		0			0
$653$	−31.9615	−	23.2214i	−1.25075	−	0.908723i	−0.252485	−	0.967601i	$-0.581248\pi$
$653$	−31.9615	−	23.2214i	−1.25075	−	0.908723i	−0.998265	+	0.0588779i	$0.981248\pi$
$654$		0			0
$655$	2.47214	+	7.60845i	0.0965943	+	0.297287i
$656$		0			0
$657$	19.8328	−	14.4094i	0.773752	−	0.562164i
$658$		0			0
$659$	25.8885			1.00847			0.504237	−	0.863565i	$-0.331774\pi$
$659$	25.8885			1.00847			0.504237	+	0.863565i	$0.331774\pi$
$660$		0			0
$661$	−22.4721			−0.874065			−0.437032	−	0.899446i	$-0.643970\pi$
$661$	−22.4721			−0.874065			−0.437032	+	0.899446i	$0.643970\pi$
$662$		0			0
$663$	4.94427	−	3.59222i	0.192020	−	0.139510i
$664$		0			0
$665$	1.23607	+	3.80423i	0.0479327	+	0.147522i
$666$		0			0
$667$	7.66312	+	5.56758i	0.296717	+	0.215578i
$668$		0			0
$669$	−5.88854	+	18.1231i	−0.227664	+	0.700679i
$670$		0			0
$671$	−6.85410	−	27.2501i	−0.264600	−	1.05198i
$672$		0			0
$673$	−6.01064	+	18.4989i	−0.231693	+	0.713079i	0.765850	+	0.643020i	$0.222319\pi$
$673$	−6.01064	+	18.4989i	−0.231693	+	0.713079i	−0.997543	+	0.0700588i	$0.977681\pi$
$674$		0			0
$675$	4.47214	+	3.24920i	0.172133	+	0.125062i
$676$		0			0
$677$	−14.7639	−	45.4387i	−0.567424	−	1.74635i	−0.660637	−	0.750705i	$-0.729714\pi$
$677$	−14.7639	−	45.4387i	−0.567424	−	1.74635i	0.0932132	−	0.995646i	$-0.470286\pi$
$678$		0			0
$679$	9.23607	−	6.71040i	0.354448	−	0.257521i
$680$		0			0
$681$	−24.0000			−0.919682
$682$		0			0
$683$	23.3262			0.892554			0.446277	−	0.894895i	$-0.352750\pi$
$683$	23.3262			0.892554			0.446277	+	0.894895i	$0.352750\pi$
$684$		0			0
$685$	−34.0344	+	24.7275i	−1.30039	+	0.944788i
$686$		0			0
$687$	−5.63932	−	17.3560i	−0.215153	−	0.662174i
$688$		0			0
$689$	−7.38197	−	5.36331i	−0.281231	−	0.204326i
$690$		0			0
$691$	−8.88854	+	27.3561i	−0.338136	+	1.04068i	0.627020	+	0.779003i	$0.284274\pi$
$691$	−8.88854	+	27.3561i	−0.338136	+	1.04068i	−0.965157	+	0.261673i	$0.915726\pi$
$692$		0			0
$693$	−4.13525	+	2.59590i	−0.157085	+	0.0986101i
$694$		0			0
$695$	−2.00000	+	6.15537i	−0.0758643	+	0.233486i
$696$		0			0
$697$	−5.52786	−	4.01623i	−0.209383	−	0.152125i
$698$		0			0
$699$	10.8754	+	33.4710i	0.411345	+	1.26599i
$700$		0			0
$701$	−30.2533	+	21.9803i	−1.14265	+	0.830185i	−0.987486	−	0.157704i	$-0.949591\pi$
$701$	−30.2533	+	21.9803i	−1.14265	+	0.830185i	−0.155165	+	0.987889i	$0.549591\pi$
$702$		0			0
$703$	−6.29180			−0.237300
$704$		0			0
$705$	−24.7214			−0.931060
$706$		0			0
$707$	4.23607	−	3.07768i	0.159314	−	0.115748i
$708$		0			0
$709$	−12.5517	−	38.6300i	−0.471388	−	1.45078i	−0.850768	−	0.525541i	$-0.823863\pi$
$709$	−12.5517	−	38.6300i	−0.471388	−	1.45078i	0.379381	−	0.925241i	$-0.376137\pi$
$710$		0			0
$711$	6.06231	+	4.40452i	0.227354	+	0.165183i
$712$		0			0
$713$	−2.23607	+	6.88191i	−0.0837414	+	0.257730i
$714$		0			0
$715$	−8.18034	−	0.555029i	−0.305927	−	0.0207569i
$716$		0			0
$717$	−7.69505	+	23.6829i	−0.287377	+	0.884455i
$718$		0			0
$719$	21.7082	+	15.7719i	0.809579	+	0.588194i	0.913709	−	0.406370i	$-0.133206\pi$
$719$	21.7082	+	15.7719i	0.809579	+	0.588194i	−0.104129	+	0.994564i	$0.533206\pi$
$720$		0			0
$721$	1.14590	+	3.52671i	0.0426755	+	0.131342i
$722$		0			0
$723$	−6.47214	+	4.70228i	−0.240701	+	0.174880i
$724$		0			0
$725$	−5.85410			−0.217416
$726$		0			0
$727$	−32.4721			−1.20432			−0.602162	−	0.798374i	$-0.705694\pi$
$727$	−32.4721			−1.20432			−0.602162	+	0.798374i	$0.705694\pi$
$728$		0			0
$729$	−19.4615	+	14.1396i	−0.720796	+	0.523689i
$730$		0			0
$731$	−5.12461	−	15.7719i	−0.189541	−	0.583346i
$732$		0			0
$733$	40.2705	+	29.2582i	1.48743	+	1.08068i	0.975068	+	0.221905i	$0.0712275\pi$
$733$	40.2705	+	29.2582i	1.48743	+	1.08068i	0.512357	+	0.858773i	$0.328772\pi$
$734$		0			0
$735$	−0.763932	+	2.35114i	−0.0281781	+	0.0867231i
$736$		0			0
$737$	8.66312	+	0.587785i	0.319110	+	0.0216513i
$738$		0			0
$739$	−6.13525	+	18.8824i	−0.225689	+	0.694599i	0.772532	+	0.634976i	$0.218990\pi$
$739$	−6.13525	+	18.8824i	−0.225689	+	0.694599i	−0.998221	+	0.0596234i	$0.981010\pi$
$740$		0			0
$741$	2.47214	+	1.79611i	0.0908162	+	0.0659818i
$742$		0			0
$743$	−0.538507	−	1.65735i	−0.0197559	−	0.0608024i	0.940693	−	0.339260i	$-0.110177\pi$
$743$	−0.538507	−	1.65735i	−0.0197559	−	0.0608024i	−0.960448	+	0.278458i	$0.910177\pi$
$744$		0			0
$745$	−0.763932	+	0.555029i	−0.0279883	+	0.0203347i
$746$		0			0
$747$	4.33437			0.158586
$748$		0			0
$749$	10.3820			0.379349
$750$		0			0
$751$	16.5451	−	12.0207i	0.603739	−	0.438642i	−0.243465	−	0.969910i	$-0.578284\pi$
$751$	16.5451	−	12.0207i	0.603739	−	0.438642i	0.847204	+	0.531268i	$0.178284\pi$
$752$		0			0
$753$	−6.36068	−	19.5762i	−0.231796	−	0.713395i
$754$		0			0
$755$	39.2705	+	28.5317i	1.42920	+	1.03837i
$756$		0			0
$757$	4.68441	−	14.4171i	0.170258	−	0.523999i	−0.829128	−	0.559059i	$-0.811162\pi$
$757$	4.68441	−	14.4171i	0.170258	−	0.523999i	0.999385	+	0.0350604i	$0.0111624\pi$
$758$		0			0
$759$	−5.61803	+	3.52671i	−0.203922	+	0.128012i
$760$		0			0
$761$	11.6525	−	35.8626i	0.422402	−	1.30002i	−0.483058	−	0.875588i	$-0.660474\pi$
$761$	11.6525	−	35.8626i	0.422402	−	1.30002i	0.905460	−	0.424431i	$-0.139526\pi$
$762$		0			0
$763$	−11.6353	−	8.45351i	−0.421225	−	0.306038i
$764$		0			0
$765$	3.63932	+	11.2007i	0.131580	+	0.404961i
$766$		0			0
$767$	9.70820	−	7.05342i	0.350543	−	0.254684i
$768$		0			0
$769$	42.5410			1.53407			0.767034	−	0.641606i	$-0.221732\pi$
$769$	42.5410			1.53407			0.767034	+	0.641606i	$0.221732\pi$
$770$		0			0
$771$	−13.5279			−0.487194
$772$		0			0
$773$	5.09017	−	3.69822i	0.183081	−	0.133016i	−0.492470	−	0.870329i	$-0.663906\pi$
$773$	5.09017	−	3.69822i	0.183081	−	0.133016i	0.675551	+	0.737313i	$0.263906\pi$
$774$		0			0
$775$	−1.38197	−	4.25325i	−0.0496417	−	0.152781i
$776$		0			0
$777$	−3.14590	−	2.28563i	−0.112858	−	0.0819965i
$778$		0			0
$779$	1.05573	−	3.24920i	0.0378254	−	0.116415i
$780$		0			0
$781$	10.5902	+	42.1038i	0.378946	+	1.50659i
$782$		0			0
$783$	10.0000	−	30.7768i	0.357371	−	1.09987i
$784$		0			0
$785$	−10.0000	−	7.26543i	−0.356915	−	0.259314i
$786$		0			0
$787$	9.43769	+	29.0462i	0.336417	+	1.03539i	0.966020	+	0.258469i	$0.0832179\pi$
$787$	9.43769	+	29.0462i	0.336417	+	1.03539i	−0.629602	+	0.776918i	$0.716782\pi$
$788$		0			0
$789$	−14.0344	+	10.1966i	−0.499639	+	0.363009i
$790$		0			0
$791$	−3.09017			−0.109874
$792$		0			0
$793$	10.4721			0.371876
$794$		0			0
$795$	−14.7639	+	10.7266i	−0.523623	+	0.380434i
$796$		0			0
$797$	2.81966	+	8.67802i	0.0998775	+	0.307391i	0.988494	−	0.151259i	$-0.0483329\pi$
$797$	2.81966	+	8.67802i	0.0998775	+	0.307391i	−0.888617	+	0.458651i	$0.848333\pi$
$798$		0			0
$799$	32.3607	+	23.5114i	1.14484	+	0.831774i
$800$		0			0
$801$	5.11146	−	15.7314i	0.180604	−	0.555843i
$802$		0			0
$803$	−42.3820	−	35.4136i	−1.49563	−	1.24972i
$804$		0			0
$805$	1.00000	−	3.07768i	0.0352454	−	0.108474i
$806$		0			0
$807$	5.70820	+	4.14725i	0.200938	+	0.145990i
$808$		0			0
$809$	−5.84752	−	17.9968i	−0.205588	−	0.632735i	−0.999689	−	0.0249486i	$-0.992058\pi$
$809$	−5.84752	−	17.9968i	−0.205588	−	0.632735i	0.794101	−	0.607786i	$-0.207942\pi$
$810$		0			0
$811$	−22.6525	+	16.4580i	−0.795436	+	0.577918i	−0.909572	−	0.415547i	$-0.863590\pi$
$811$	−22.6525	+	16.4580i	−0.795436	+	0.577918i	0.114136	+	0.993465i	$0.463590\pi$
$812$		0			0
$813$	32.3607			1.13494
$814$		0			0
$815$	40.5410			1.42009
$816$		0			0
$817$	6.70820	−	4.87380i	0.234690	−	0.170513i
$818$		0			0
$819$	−0.562306	−	1.73060i	−0.0196486	−	0.0604720i
$820$		0			0
$821$	0.854102	+	0.620541i	0.0298084	+	0.0216570i	0.602590	−	0.798051i	$-0.294136\pi$
$821$	0.854102	+	0.620541i	0.0298084	+	0.0216570i	−0.572781	+	0.819708i	$0.694136\pi$
$822$		0			0
$823$	−7.57295	+	23.3071i	−0.263976	+	0.812436i	0.727951	+	0.685629i	$0.240473\pi$
$823$	−7.57295	+	23.3071i	−0.263976	+	0.812436i	−0.991927	+	0.126807i	$0.959527\pi$
$824$		0			0
$825$	1.52786	−	3.80423i	0.0531934	−	0.132446i
$826$		0			0
$827$	−10.4721	+	32.2299i	−0.364152	+	1.12074i	0.586359	+	0.810052i	$0.300561\pi$
$827$	−10.4721	+	32.2299i	−0.364152	+	1.12074i	−0.950510	+	0.310693i	$0.899439\pi$
$828$		0			0
$829$	−41.8885	−	30.4338i	−1.45485	−	1.05701i	−0.984668	−	0.174440i	$-0.944188\pi$
$829$	−41.8885	−	30.4338i	−1.45485	−	1.05701i	−0.470181	−	0.882570i	$-0.655812\pi$
$830$		0			0
$831$	4.39512	+	13.5268i	0.152465	+	0.469239i
$832$		0			0
$833$	3.23607	−	2.35114i	0.112123	−	0.0814622i
$834$		0			0
$835$	−6.11146			−0.211496
$836$		0			0
$837$	24.7214			0.854495
$838$		0			0
$839$	27.7082	−	20.1312i	0.956593	−	0.695006i	0.00423635	−	0.999991i	$-0.498652\pi$
$839$	27.7082	−	20.1312i	0.956593	−	0.695006i	0.952357	+	0.304985i	$0.0986515\pi$
$840$		0			0
$841$	1.62868	+	5.01255i	0.0561613	+	0.172847i
$842$		0			0
$843$	−11.0902	−	8.05748i	−0.381966	−	0.277514i
$844$		0			0
$845$	−7.09017	+	21.8213i	−0.243909	+	0.750676i
$846$		0			0
$847$	7.94427	+	7.60845i	0.272968	+	0.261430i
$848$		0			0
$849$	−1.88854	+	5.81234i	−0.0648147	+	0.199479i
$850$		0			0
$851$	4.11803	+	2.99193i	0.141164	+	0.102562i
$852$		0			0
$853$	−1.87539	−	5.77185i	−0.0642121	−	0.197624i	0.913803	−	0.406157i	$-0.133131\pi$
$853$	−1.87539	−	5.77185i	−0.0642121	−	0.197624i	−0.978015	+	0.208532i	$0.933131\pi$
$854$		0			0
$855$	−4.76393	+	3.46120i	−0.162923	+	0.118371i
$856$		0			0
$857$	6.11146			0.208763			0.104382	−	0.994537i	$-0.466714\pi$
$857$	6.11146			0.208763			0.104382	+	0.994537i	$0.466714\pi$
$858$		0			0
$859$	19.5967			0.668632			0.334316	−	0.942461i	$-0.391495\pi$
$859$	19.5967			0.668632			0.334316	+	0.942461i	$0.391495\pi$
$860$		0			0
$861$	1.70820	−	1.24108i	0.0582154	−	0.0422960i
$862$		0			0
$863$	−6.87539	−	21.1603i	−0.234041	−	0.720304i	−0.997247	−	0.0741490i	$-0.976376\pi$
$863$	−6.87539	−	21.1603i	−0.234041	−	0.720304i	0.763206	−	0.646155i	$-0.223624\pi$
$864$		0			0
$865$	6.00000	+	4.35926i	0.204006	+	0.148219i
$866$		0			0
$867$	0.381966	−	1.17557i	0.0129722	−	0.0399245i
$868$		0			0
$869$	6.29180	−	15.6659i	0.213435	−	0.531430i
$870$		0			0
$871$	−1.00000	+	3.07768i	−0.0338837	+	0.104283i
$872$		0			0
$873$	13.5967	+	9.87862i	0.460180	+	0.334340i
$874$		0			0
$875$	3.70820	+	11.4127i	0.125360	+	0.385819i
$876$		0			0
$877$	37.3328	−	27.1239i	1.26064	−	0.915908i	0.261851	−	0.965108i	$-0.415667\pi$
$877$	37.3328	−	27.1239i	1.26064	−	0.915908i	0.998789	+	0.0492001i	$0.0156672\pi$
$878$		0			0
$879$	−11.0557			−0.372900
$880$		0			0
$881$	41.0132			1.38177			0.690884	−	0.722965i	$-0.257221\pi$
$881$	41.0132			1.38177			0.690884	+	0.722965i	$0.257221\pi$
$882$		0			0
$883$	26.6525	−	19.3642i	0.896927	−	0.651656i	−0.0407477	−	0.999169i	$-0.512974\pi$
$883$	26.6525	−	19.3642i	0.896927	−	0.651656i	0.937675	+	0.347514i	$0.112974\pi$
$884$		0			0
$885$	−7.41641	−	22.8254i	−0.249300	−	0.767266i
$886$		0			0
$887$	−40.1246	−	29.1522i	−1.34725	−	0.978836i	−0.999143	−	0.0413823i	$-0.986824\pi$
$887$	−40.1246	−	29.1522i	−1.34725	−	0.978836i	−0.348109	−	0.937454i	$-0.613176\pi$
$888$		0			0
$889$	−5.97214	+	18.3803i	−0.200299	+	0.616457i
$890$		0			0
$891$	6.14996	+	5.13880i	0.206032	+	0.172156i
$892$		0			0
$893$	−6.18034	+	19.0211i	−0.206817	+	0.636518i
$894$		0			0
$895$	−3.85410	−	2.80017i	−0.128828	−	0.0935993i
$896$		0			0
$897$	−0.763932	−	2.35114i	−0.0255069	−	0.0785023i
$898$		0			0
$899$	−21.1803	+	15.3884i	−0.706404	+	0.513232i
$900$		0			0
$901$	29.5279			0.983716
$902$		0			0
$903$	5.12461			0.170536
$904$		0			0
$905$	−4.94427	+	3.59222i	−0.164353	+	0.119410i
$906$		0			0
$907$	3.66312	+	11.2739i	0.121632	+	0.374344i	0.993272	−	0.115801i	$-0.0369436\pi$
$907$	3.66312	+	11.2739i	0.121632	+	0.374344i	−0.871641	+	0.490146i	$0.836944\pi$
$908$		0			0
$909$	6.23607	+	4.53077i	0.206837	+	0.150276i
$910$		0			0
$911$	9.88854	−	30.4338i	0.327622	−	1.00832i	−0.642621	−	0.766184i	$-0.722153\pi$
$911$	9.88854	−	30.4338i	0.327622	−	1.00832i	0.970243	−	0.242133i	$-0.0778470\pi$
$912$		0			0
$913$	−2.38197	−	9.47008i	−0.0788316	−	0.313414i
$914$		0			0
$915$	6.47214	−	19.9192i	0.213962	−	0.658508i
$916$		0			0
$917$	3.23607	+	2.35114i	0.106864	+	0.0776415i
$918$		0			0
$919$	−5.28115	−	16.2537i	−0.174209	−	0.536161i	0.825387	−	0.564567i	$-0.190957\pi$
$919$	−5.28115	−	16.2537i	−0.174209	−	0.536161i	−0.999596	+	0.0284063i	$0.990957\pi$
$920$		0			0
$921$	−14.9443	+	10.8576i	−0.492431	+	0.357772i
$922$		0			0
$923$	−16.1803			−0.532582
$924$		0			0
$925$	−3.14590			−0.103436
$926$		0			0
$927$	−4.41641	+	3.20871i	−0.145054	+	0.105388i
$928$		0			0
$929$	14.7082	+	45.2672i	0.482561	+	1.48517i	0.835483	+	0.549516i	$0.185188\pi$
$929$	14.7082	+	45.2672i	0.482561	+	1.48517i	−0.352923	+	0.935653i	$0.614812\pi$
$930$		0			0
$931$	1.61803	+	1.17557i	0.0530289	+	0.0385278i
$932$		0			0
$933$	−0.111456	+	0.343027i	−0.00364891	+	0.0112302i
$934$		0			0
$935$	22.4721	−	14.1068i	0.734917	−	0.461343i
$936$		0			0
$937$	−0.965558	+	2.97168i	−0.0315434	+	0.0970806i	−0.965589	−	0.260074i	$-0.916253\pi$
$937$	−0.965558	+	2.97168i	−0.0315434	+	0.0970806i	0.934045	+	0.357155i	$0.116253\pi$
$938$		0			0
$939$	24.6525	+	17.9111i	0.804503	+	0.584506i
$940$		0			0
$941$	−11.0557	−	34.0260i	−0.360406	−	1.10922i	−0.952808	−	0.303574i	$-0.901820\pi$
$941$	−11.0557	−	34.0260i	−0.360406	−	1.10922i	0.592401	−	0.805643i	$-0.298180\pi$
$942$		0			0
$943$	−2.23607	+	1.62460i	−0.0728164	+	0.0529042i
$944$		0			0
$945$	−11.0557			−0.359643
$946$		0			0
$947$	38.8328			1.26190			0.630948	−	0.775825i	$-0.282666\pi$
$947$	38.8328			1.26190			0.630948	+	0.775825i	$0.282666\pi$
$948$		0			0
$949$	16.6525	−	12.0987i	0.540562	−	0.392741i
$950$		0			0
$951$	8.12461	+	25.0050i	0.263459	+	0.810842i
$952$		0			0
$953$	46.4336	+	33.7360i	1.50413	+	1.09282i	0.968699	+	0.248239i	$0.0798520\pi$
$953$	46.4336	+	33.7360i	1.50413	+	1.09282i	0.535434	+	0.844577i	$0.320148\pi$
$954$		0			0
$955$	3.32624	−	10.2371i	0.107635	−	0.331265i
$956$		0			0
$957$	−23.9443	−	1.62460i	−0.774008	−	0.0525158i
$958$		0			0
$959$	−6.50000	+	20.0049i	−0.209896	+	0.645993i
$960$		0			0
$961$	8.89919	+	6.46564i	0.287071	+	0.208569i
$962$		0			0
$963$	4.72291	+	14.5356i	0.152194	+	0.468404i
$964$		0			0
$965$	−22.8885	+	16.6295i	−0.736808	+	0.535323i
$966$		0			0
$967$	12.0902			0.388794			0.194397	−	0.980923i	$-0.437725\pi$
$967$	12.0902			0.388794			0.194397	+	0.980923i	$0.437725\pi$
$968$		0			0
$969$	−9.88854			−0.317666
$970$		0			0
$971$	−27.8885	+	20.2622i	−0.894986	+	0.650245i	−0.937173	−	0.348864i	$-0.886567\pi$
$971$	−27.8885	+	20.2622i	−0.894986	+	0.650245i	0.0421873	+	0.999110i	$0.486567\pi$
$972$		0			0
$973$	1.00000	+	3.07768i	0.0320585	+	0.0986660i
$974$		0			0
$975$	1.23607	+	0.898056i	0.0395859	+	0.0287608i
$976$		0			0
$977$	10.7918	−	33.2137i	0.345260	−	1.06260i	−0.616184	−	0.787602i	$-0.711322\pi$
$977$	10.7918	−	33.2137i	0.345260	−	1.06260i	0.961444	−	0.274999i	$-0.0886777\pi$
$978$		0			0
$979$	−37.1803	−	2.52265i	−1.18829	−	0.0806244i
$980$		0			0
$981$	6.54257	−	20.1360i	0.208888	−	0.642892i
$982$		0			0
$983$	−35.1246	−	25.5195i	−1.12030	−	0.813946i	−0.136046	−	0.990702i	$-0.543440\pi$
$983$	−35.1246	−	25.5195i	−1.12030	−	0.813946i	−0.984255	+	0.176756i	$0.943440\pi$
$984$		0			0
$985$	3.58359	+	11.0292i	0.114183	+	0.351418i
$986$		0			0
$987$	−10.0000	+	7.26543i	−0.318304	+	0.231261i
$988$		0			0
$989$	−6.70820			−0.213308
$990$		0			0
$991$	21.8885			0.695313			0.347656	−	0.937622i	$-0.386978\pi$
$991$	21.8885			0.695313			0.347656	+	0.937622i	$0.386978\pi$
$992$		0			0
$993$	32.2705	−	23.4459i	1.02407	−	0.744033i
$994$		0			0
$995$	8.76393	+	26.9726i	0.277835	+	0.855089i
$996$		0			0
$997$	10.8541	+	7.88597i	0.343753	+	0.249751i	0.746244	−	0.665673i	$-0.231855\pi$
$997$	10.8541	+	7.88597i	0.343753	+	0.249751i	−0.402491	+	0.915424i	$0.631855\pi$
$998$		0			0
$999$	5.37384	−	16.5390i	0.170021	−	0.523270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.j.a.141.1	✓	4
11.4	even	5		3388.2.a.k.1.1		2
11.5	even	5	inner	308.2.j.a.225.1	yes	4
11.7	odd	10		3388.2.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.j.a.141.1	✓	4	1.1	even	1	trivial
308.2.j.a.225.1	yes	4	11.5	even	5	inner
3388.2.a.k.1.1		2	11.4	even	5
3388.2.a.l.1.1		2	11.7	odd	10

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 0.726543i) q^{3} +(0.618034 + 1.90211i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-0.454915 + 1.40008i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 0.726543i) q^{3} +(0.618034 + 1.90211i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-0.454915 + 1.40008i) q^{9} +(3.30902 + 0.224514i) q^{11} +(-0.381966 + 1.17557i) q^{13} +(2.00000 + 1.45309i) q^{15} +(-1.23607 - 3.80423i) q^{17} +(1.61803 - 1.17557i) q^{19} +1.23607 q^{21} -1.61803 q^{23} +(0.809017 - 0.587785i) q^{25} +(1.70820 + 5.25731i) q^{27} +(-4.73607 - 3.44095i) q^{29} +(1.38197 - 4.25325i) q^{31} +(3.47214 - 2.17963i) q^{33} +(-0.618034 + 1.90211i) q^{35} +(-2.54508 - 1.84911i) q^{37} +(0.472136 + 1.45309i) q^{39} +(1.38197 - 1.00406i) q^{41} +4.14590 q^{43} -2.94427 q^{45} +(-8.09017 + 5.87785i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-4.00000 - 2.90617i) q^{51} +(-2.28115 + 7.02067i) q^{53} +(1.61803 + 6.43288i) q^{55} +(0.763932 - 2.35114i) q^{57} +(-7.85410 - 5.70634i) q^{59} +(-2.61803 - 8.05748i) q^{61} +(-1.19098 + 0.865300i) q^{63} -2.47214 q^{65} +2.61803 q^{67} +(-1.61803 + 1.17557i) q^{69} +(4.04508 + 12.4495i) q^{71} +(-13.4721 - 9.78808i) q^{73} +(0.381966 - 1.17557i) q^{75} +(2.54508 + 2.12663i) q^{77} +(1.57295 - 4.84104i) q^{79} +(1.95492 + 1.42033i) q^{81} +(-0.909830 - 2.80017i) q^{83} +(6.47214 - 4.70228i) q^{85} -7.23607 q^{87} -11.2361 q^{89} +(-1.00000 + 0.726543i) q^{91} +(-1.70820 - 5.25731i) q^{93} +(3.23607 + 2.35114i) q^{95} +(3.52786 - 10.8576i) q^{97} +(-1.81966 + 4.53077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 2 q^{5} + q^{7} - 13 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 2 * q^5 + q^7 - 13 * q^9	\( 4 q + 4 q^{3} - 2 q^{5} + q^{7} - 13 q^{9} + 11 q^{11} - 6 q^{13} + 8 q^{15} + 4 q^{17} + 2 q^{19} - 4 q^{21} - 2 q^{23} + q^{25} - 20 q^{27} - 10 q^{29} + 10 q^{31} - 4 q^{33} + 2 q^{35} + q^{37} - 16 q^{39} + 10 q^{41} + 30 q^{43} + 24 q^{45} - 10 q^{47} - q^{49} - 16 q^{51} + 11 q^{53} + 2 q^{55} + 12 q^{57} - 18 q^{59} - 6 q^{61} - 7 q^{63} + 8 q^{65} + 6 q^{67} - 2 q^{69} + 5 q^{71} - 36 q^{73} + 6 q^{75} - q^{77} + 13 q^{79} + 19 q^{81} - 26 q^{83} + 8 q^{85} - 20 q^{87} - 36 q^{89} - 4 q^{91} + 20 q^{93} + 4 q^{95} + 32 q^{97} - 52 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 2 * q^5 + q^7 - 13 * q^9 + 11 * q^11 - 6 * q^13 + 8 * q^15 + 4 * q^17 + 2 * q^19 - 4 * q^21 - 2 * q^23 + q^25 - 20 * q^27 - 10 * q^29 + 10 * q^31 - 4 * q^33 + 2 * q^35 + q^37 - 16 * q^39 + 10 * q^41 + 30 * q^43 + 24 * q^45 - 10 * q^47 - q^49 - 16 * q^51 + 11 * q^53 + 2 * q^55 + 12 * q^57 - 18 * q^59 - 6 * q^61 - 7 * q^63 + 8 * q^65 + 6 * q^67 - 2 * q^69 + 5 * q^71 - 36 * q^73 + 6 * q^75 - q^77 + 13 * q^79 + 19 * q^81 - 26 * q^83 + 8 * q^85 - 20 * q^87 - 36 * q^89 - 4 * q^91 + 20 * q^93 + 4 * q^95 + 32 * q^97 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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