LMFDB - Embedded newform 825.2.bs.b.299.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(74,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("825.74");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bs (of order $10$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			299.2
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	825.299
Dual form			825.2.bs.b.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11803 + 0.363271i) q^{2} +(0.451057 + 1.67229i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.103198 + 2.03353i) q^{6} +(-3.07768 - 2.23607i) q^{7} +(-1.80902 - 2.48990i) q^{8} +(-2.59310 + 1.50859i) q^{9} +O(q^{10})$	\(q+(1.11803 + 0.363271i) q^{2} +(0.451057 + 1.67229i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.103198 + 2.03353i) q^{6} +(-3.07768 - 2.23607i) q^{7} +(-1.80902 - 2.48990i) q^{8} +(-2.59310 + 1.50859i) q^{9} +(-0.726543 - 3.23607i) q^{11} +(0.381966 - 1.00000i) q^{12} +(-2.62866 - 3.61803i) q^{14} +(-0.736068 - 2.26538i) q^{16} +(1.38197 - 0.449028i) q^{17} +(-3.44720 + 0.744661i) q^{18} +(-3.19098 - 4.39201i) q^{19} +(2.35114 - 6.15537i) q^{21} +(0.363271 - 3.88197i) q^{22} +9.09017 q^{23} +(3.34786 - 4.14828i) q^{24} +(-3.69244 - 3.65594i) q^{27} +(0.726543 + 2.23607i) q^{28} +(-7.83297 - 5.69098i) q^{29} +(-1.54508 + 4.75528i) q^{31} +3.35520i q^{32} +(5.08393 - 2.67464i) q^{33} +1.70820 q^{34} +(1.84458 + 0.187701i) q^{36} +(-5.11855 + 7.04508i) q^{37} +(-1.97214 - 6.06961i) q^{38} +(-2.48990 + 1.80902i) q^{41} +(4.86472 - 6.02781i) q^{42} -3.35520 q^{43} +(-0.812299 + 1.88197i) q^{44} +(10.1631 + 3.30220i) q^{46} +(4.92705 - 3.57971i) q^{47} +(3.45637 - 2.25273i) q^{48} +(2.30902 + 7.10642i) q^{49} +(1.37425 + 2.10851i) q^{51} +(1.66312 - 5.11855i) q^{53} +(-2.80017 - 5.42882i) q^{54} +11.7082i q^{56} +(5.90540 - 7.31729i) q^{57} +(-6.69015 - 9.20820i) q^{58} +(2.04087 - 2.80902i) q^{59} +(-7.39919 + 2.40414i) q^{61} +(-3.45492 + 4.75528i) q^{62} +(11.3540 + 1.15537i) q^{63} +(-2.69098 + 8.28199i) q^{64} +(6.65562 - 1.14349i) q^{66} -3.32624i q^{67} +(-0.854102 - 0.277515i) q^{68} +(4.10018 + 15.2014i) q^{69} +(1.62460 - 0.527864i) q^{71} +(8.44720 + 3.72747i) q^{72} +(-2.48990 - 1.80902i) q^{73} +(-8.28199 + 6.01722i) q^{74} +3.35520i q^{76} +(-5.00000 + 11.5842i) q^{77} +(-4.04508 - 1.31433i) q^{79} +(4.44829 - 7.82385i) q^{81} +(-3.44095 + 1.11803i) q^{82} +(0.527864 - 0.171513i) q^{83} +(-3.41164 + 2.22358i) q^{84} +(-3.75123 - 1.21885i) q^{86} +(5.98385 - 15.6659i) q^{87} +(-6.74315 + 7.66312i) q^{88} -5.85410i q^{89} +(-4.54508 - 3.30220i) q^{92} +(-8.64912 - 0.438926i) q^{93} +(6.80902 - 2.21238i) q^{94} +(-5.61086 + 1.51338i) q^{96} +(16.1680 + 5.25329i) q^{97} +8.78402i q^{98} +(6.76590 + 7.29538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{4} - 10 q^{6} - 10 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 4 * q^4 - 10 * q^6 - 10 * q^8 - 10 * q^9	$ 8 q - 4 q^{3} - 4 q^{4} - 10 q^{6} - 10 q^{8} - 10 q^{9} + 12 q^{12} + 12 q^{16} + 20 q^{17} + 10 q^{18} - 30 q^{19} + 28 q^{23} + 10 q^{24} + 2 q^{27} + 10 q^{31} + 6 q^{33} - 40 q^{34} + 20 q^{38} + 50 q^{46} + 26 q^{47} + 14 q^{48} + 14 q^{49} - 40 q^{51} - 18 q^{53} + 30 q^{57} - 10 q^{61} - 50 q^{62} - 26 q^{64} + 30 q^{66} + 20 q^{68} - 14 q^{69} + 30 q^{72} - 40 q^{77} - 10 q^{79} - 2 q^{81} + 40 q^{83} - 14 q^{92} - 30 q^{93} + 50 q^{94} - 50 q^{96} + 4 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^4 - 10 * q^6 - 10 * q^8 - 10 * q^9 + 12 * q^12 + 12 * q^16 + 20 * q^17 + 10 * q^18 - 30 * q^19 + 28 * q^23 + 10 * q^24 + 2 * q^27 + 10 * q^31 + 6 * q^33 - 40 * q^34 + 20 * q^38 + 50 * q^46 + 26 * q^47 + 14 * q^48 + 14 * q^49 - 40 * q^51 - 18 * q^53 + 30 * q^57 - 10 * q^61 - 50 * q^62 - 26 * q^64 + 30 * q^66 + 20 * q^68 - 14 * q^69 + 30 * q^72 - 40 * q^77 - 10 * q^79 - 2 * q^81 + 40 * q^83 - 14 * q^92 - 30 * q^93 + 50 * q^94 - 50 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.11803	+	0.363271i	0.790569	+	0.256872i	0.676347	−	0.736584i	$-0.263562\pi$
$2$	1.11803	+	0.363271i	0.790569	+	0.256872i	0.114223	+	0.993455i	$0.463562\pi$
$3$	0.451057	+	1.67229i	0.260418	+	0.965496i
$3$	0.451057	+	1.67229i	0.260418	+	0.965496i
$4$	−0.500000	−	0.363271i	−0.250000	−	0.181636i
$5$		0			0
$5$		0			0
$6$	−0.103198	+	2.03353i	−0.0421303	+	0.830186i
$7$	−3.07768	−	2.23607i	−1.16326	−	0.845154i	−0.173069	−	0.984910i	$-0.555368\pi$
$7$	−3.07768	−	2.23607i	−1.16326	−	0.845154i	−0.990186	+	0.139755i	$0.955368\pi$
$8$	−1.80902	−	2.48990i	−0.639584	−	0.880312i
$9$	−2.59310	+	1.50859i	−0.864365	+	0.502864i
$10$		0			0
$11$	−0.726543	−	3.23607i	−0.219061	−	0.975711i
$11$	−0.726543	−	3.23607i	−0.219061	−	0.975711i
$12$	0.381966	−	1.00000i	0.110264	−	0.288675i
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$	−2.62866	−	3.61803i	−0.702538	−	0.966960i
$15$		0			0
$16$	−0.736068	−	2.26538i	−0.184017	−	0.566346i
$17$	1.38197	−	0.449028i	0.335176	−	0.108905i	−0.136594	−	0.990627i	$-0.543615\pi$
$17$	1.38197	−	0.449028i	0.335176	−	0.108905i	0.471770	+	0.881722i	$0.343615\pi$
$18$	−3.44720	+	0.744661i	−0.812512	+	0.175518i
$19$	−3.19098	−	4.39201i	−0.732062	−	1.00760i	−0.999036	−	0.0438929i	$-0.986024\pi$
$19$	−3.19098	−	4.39201i	−0.732062	−	1.00760i	0.266975	−	0.963704i	$-0.413976\pi$
$20$		0			0
$21$	2.35114	−	6.15537i	0.513061	−	1.34321i
$22$	0.363271	−	3.88197i	0.0774497	−	0.827638i
$23$	9.09017			1.89543			0.947716	−	0.319116i	$-0.103386\pi$
$23$	9.09017			1.89543			0.947716	+	0.319116i	$0.103386\pi$
$24$	3.34786	−	4.14828i	0.683379	−	0.846765i
$25$		0			0
$26$		0			0
$27$	−3.69244	−	3.65594i	−0.710610	−	0.703587i
$28$	0.726543	+	2.23607i	0.137304	+	0.422577i
$29$	−7.83297	−	5.69098i	−1.45455	−	1.05679i	−0.984743	−	0.174018i	$-0.944325\pi$
$29$	−7.83297	−	5.69098i	−1.45455	−	1.05679i	−0.469803	−	0.882771i	$-0.655675\pi$
$30$		0			0
$31$	−1.54508	+	4.75528i	−0.277505	+	0.854074i	0.711040	+	0.703151i	$0.248224\pi$
$31$	−1.54508	+	4.75528i	−0.277505	+	0.854074i	−0.988546	+	0.150923i	$0.951776\pi$
$32$			3.35520i			0.593121i
$33$	5.08393	−	2.67464i	0.884998	−	0.465595i
$34$	1.70820			0.292955
$35$		0			0
$36$	1.84458	+	0.187701i	0.307429	+	0.0312835i
$37$	−5.11855	+	7.04508i	−0.841485	+	1.15820i	0.144190	+	0.989550i	$0.453942\pi$
$37$	−5.11855	+	7.04508i	−0.841485	+	1.15820i	−0.985675	+	0.168655i	$0.946058\pi$
$38$	−1.97214	−	6.06961i	−0.319923	−	0.984621i
$39$		0			0
$40$		0			0
$41$	−2.48990	+	1.80902i	−0.388857	+	0.282521i	−0.764987	−	0.644046i	$-0.777255\pi$
$41$	−2.48990	+	1.80902i	−0.388857	+	0.282521i	0.376130	+	0.926567i	$0.377255\pi$
$42$	4.86472	−	6.02781i	0.750643	−	0.930111i
$43$	−3.35520			−0.511663			−0.255831	−	0.966721i	$-0.582349\pi$
$43$	−3.35520			−0.511663			−0.255831	+	0.966721i	$0.582349\pi$
$44$	−0.812299	+	1.88197i	−0.122459	+	0.283717i
$45$		0			0
$46$	10.1631	+	3.30220i	1.49847	+	0.486882i
$47$	4.92705	−	3.57971i	0.718684	−	0.522155i	−0.167279	−	0.985910i	$-0.553498\pi$
$47$	4.92705	−	3.57971i	0.718684	−	0.522155i	0.885964	+	0.463755i	$0.153498\pi$
$48$	3.45637	−	2.25273i	0.498884	−	0.325154i
$49$	2.30902	+	7.10642i	0.329860	+	1.01520i
$50$		0			0
$51$	1.37425	+	2.10851i	0.192433	+	0.295250i
$52$		0			0
$53$	1.66312	−	5.11855i	0.228447	−	0.703087i	−0.769476	−	0.638675i	$-0.779483\pi$
$53$	1.66312	−	5.11855i	0.228447	−	0.703087i	0.997923	−	0.0644122i	$-0.0205173\pi$
$54$	−2.80017	−	5.42882i	−0.381055	−	0.738769i
$55$		0			0
$56$			11.7082i			1.56457i
$57$	5.90540	−	7.31729i	0.782189	−	0.969199i
$58$	−6.69015	−	9.20820i	−0.878460	−	1.20910i
$59$	2.04087	−	2.80902i	0.265699	−	0.365703i	−0.655233	−	0.755427i	$-0.727430\pi$
$59$	2.04087	−	2.80902i	0.265699	−	0.365703i	0.920932	+	0.389724i	$0.127430\pi$
$60$		0			0
$61$	−7.39919	+	2.40414i	−0.947369	+	0.307819i	−0.741646	−	0.670792i	$-0.765955\pi$
$61$	−7.39919	+	2.40414i	−0.947369	+	0.307819i	−0.205723	+	0.978610i	$0.565955\pi$
$62$	−3.45492	+	4.75528i	−0.438775	+	0.603921i
$63$	11.3540	+	1.15537i	1.43048	+	0.145563i
$64$	−2.69098	+	8.28199i	−0.336373	+	1.03525i
$65$		0			0
$66$	6.65562	−	1.14349i	0.819250	−	0.140754i
$67$		−	3.32624i		−	0.406365i	−0.979141	−	0.203182i	$-0.934872\pi$
$67$		−	3.32624i		−	0.406365i	0.979141	−	0.203182i	$-0.0651284\pi$
$68$	−0.854102	−	0.277515i	−0.103575	−	0.0336536i
$69$	4.10018	+	15.2014i	0.493604	+	1.83003i
$70$		0			0
$71$	1.62460	−	0.527864i	0.192804	−	0.0626459i	−0.211023	−	0.977481i	$-0.567680\pi$
$71$	1.62460	−	0.527864i	0.192804	−	0.0626459i	0.403828	+	0.914835i	$0.367680\pi$
$72$	8.44720	+	3.72747i	0.995512	+	0.439287i
$73$	−2.48990	−	1.80902i	−0.291421	−	0.211729i	0.432463	−	0.901652i	$-0.357645\pi$
$73$	−2.48990	−	1.80902i	−0.291421	−	0.211729i	−0.723883	+	0.689922i	$0.757645\pi$
$74$	−8.28199	+	6.01722i	−0.962762	+	0.699488i
$75$		0			0
$76$			3.35520i			0.384868i
$77$	−5.00000	+	11.5842i	−0.569803	+	1.32014i
$78$		0			0
$79$	−4.04508	−	1.31433i	−0.455108	−	0.147873i	0.0724876	−	0.997369i	$-0.476906\pi$
$79$	−4.04508	−	1.31433i	−0.455108	−	0.147873i	−0.527595	+	0.849496i	$0.676906\pi$
$80$		0			0
$81$	4.44829	−	7.82385i	0.494255	−	0.869317i
$82$	−3.44095	+	1.11803i	−0.379990	+	0.123466i
$83$	0.527864	−	0.171513i	0.0579406	−	0.0188260i	−0.279903	−	0.960028i	$-0.590302\pi$
$83$	0.527864	−	0.171513i	0.0579406	−	0.0188260i	0.337844	+	0.941202i	$0.390302\pi$
$84$	−3.41164	+	2.22358i	−0.372240	+	0.242613i
$85$		0			0
$86$	−3.75123	−	1.21885i	−0.404505	−	0.131432i
$87$	5.98385	−	15.6659i	0.641536	−	1.67956i
$88$	−6.74315	+	7.66312i	−0.718822	+	0.816891i
$89$		−	5.85410i		−	0.620534i	−0.950650	−	0.310267i	$-0.899582\pi$
$89$		−	5.85410i		−	0.620534i	0.950650	−	0.310267i	$-0.100418\pi$
$90$		0			0
$91$		0			0
$92$	−4.54508	−	3.30220i	−0.473858	−	0.344278i
$93$	−8.64912	−	0.438926i	−0.896872	−	0.0455145i
$94$	6.80902	−	2.21238i	0.702296	−	0.228190i
$95$		0			0
$96$	−5.61086	+	1.51338i	−0.572656	+	0.154459i
$97$	16.1680	+	5.25329i	1.64161	+	0.533391i	0.976897	−	0.213710i	$-0.0685548\pi$
$97$	16.1680	+	5.25329i	1.64161	+	0.533391i	0.664711	+	0.747101i	$0.268555\pi$
$98$			8.78402i			0.887320i
$99$	6.76590	+	7.29538i	0.679999	+	0.733213i
$100$		0			0
$101$	2.76741	−	8.51722i	0.275368	−	0.847495i	−0.713754	−	0.700397i	$-0.753007\pi$
$101$	2.76741	−	8.51722i	0.275368	−	0.847495i	0.989122	−	0.147099i	$-0.0469935\pi$
$102$	0.770497	+	2.85661i	0.0762905	+	0.282846i
$103$	4.78804	−	6.59017i	0.471779	−	0.649349i	−0.505120	−	0.863049i	$-0.668552\pi$
$103$	4.78804	−	6.59017i	0.471779	−	0.649349i	0.976899	+	0.213701i	$0.0685517\pi$
$104$		0			0
$105$		0			0
$106$	3.71885	−	5.11855i	0.361206	−	0.497158i
$107$	3.35410	+	4.61653i	0.324253	+	0.446296i	0.939760	−	0.341835i	$-0.111049\pi$
$107$	3.35410	+	4.61653i	0.324253	+	0.446296i	−0.615507	+	0.788132i	$0.711049\pi$
$108$	0.518118	+	3.16933i	0.0498560	+	0.304969i
$109$		−	16.7355i		−	1.60297i	−0.598015	−	0.801485i	$-0.704044\pi$
$109$		−	16.7355i		−	1.60297i	0.598015	−	0.801485i	$-0.295956\pi$
$110$		0			0
$111$	−14.0902	−	5.38197i	−1.33738	−	0.510834i
$112$	−2.80017	+	8.61803i	−0.264591	+	0.814328i
$113$	−4.42705	+	3.21644i	−0.416462	+	0.302577i	−0.776213	−	0.630471i	$-0.782862\pi$
$113$	−4.42705	+	3.21644i	−0.416462	+	0.302577i	0.359751	+	0.933048i	$0.382862\pi$
$114$	9.26059	−	6.03572i	0.867334	−	0.565297i
$115$		0			0
$116$	1.84911	+	5.69098i	0.171686	+	0.528395i
$117$		0			0
$118$	3.30220	−	2.39919i	0.303992	−	0.220863i
$119$	−5.25731	−	1.70820i	−0.481937	−	0.156591i
$120$		0			0
$121$	−9.94427	+	4.70228i	−0.904025	+	0.427480i
$122$	−9.14590			−0.828031
$123$	−4.14828	−	3.34786i	−0.374038	−	0.301866i
$124$	2.50000	−	1.81636i	0.224507	−	0.163114i
$125$		0			0
$126$	12.2745	+	5.41634i	1.09350	+	0.482526i
$127$	−0.779543	−	2.39919i	−0.0691733	−	0.212893i	0.910494	−	0.413522i	$-0.135702\pi$
$127$	−0.779543	−	2.39919i	−0.0691733	−	0.212893i	−0.979667	+	0.200629i	$0.935702\pi$
$128$	−2.07295	+	2.85317i	−0.183225	+	0.252187i
$129$	−1.51338	−	5.61086i	−0.133246	−	0.494009i
$130$		0			0
$131$	−9.78808			−0.855188			−0.427594	−	0.903971i	$-0.640639\pi$
$131$	−9.78808			−0.855188			−0.427594	+	0.903971i	$0.640639\pi$
$132$	−3.51358	−	0.509525i	−0.305818	−	0.0443485i
$133$			20.6525i			1.79080i
$134$	1.20833	−	3.71885i	0.104384	−	0.321259i
$135$		0			0
$136$	−3.61803	−	2.62866i	−0.310244	−	0.225405i
$137$	1.45492	+	4.47777i	0.124302	+	0.382562i	0.993773	−	0.111422i	$-0.0355404\pi$
$137$	1.45492	+	4.47777i	0.124302	+	0.382562i	−0.869471	+	0.493983i	$0.835540\pi$
$138$	−0.938085	+	18.4851i	−0.0798551	+	1.57356i
$139$	−2.66312	+	3.66547i	−0.225883	+	0.310901i	−0.906883	−	0.421382i	$-0.861545\pi$
$139$	−2.66312	+	3.66547i	−0.225883	+	0.310901i	0.681000	+	0.732283i	$0.261545\pi$
$140$		0			0
$141$	8.20869	+	6.62480i	0.691296	+	0.557909i
$142$	2.00811			0.168517
$143$		0			0
$144$	5.32624	+	4.76393i	0.443853	+	0.396994i
$145$		0			0
$146$	−2.12663	−	2.92705i	−0.176001	−	0.242244i
$147$	−10.8425	+	7.06674i	−0.894274	+	0.582855i
$148$	5.11855	−	1.66312i	0.420743	−	0.136708i
$149$	6.37988	+	19.6353i	0.522660	+	1.60858i	0.768897	+	0.639373i	$0.220806\pi$
$149$	6.37988	+	19.6353i	0.522660	+	1.60858i	−0.246237	+	0.969210i	$0.579194\pi$
$150$		0			0
$151$	8.41641	+	11.5842i	0.684918	+	0.942708i	0.999980	−	0.00636288i	$-0.00202538\pi$
$151$	8.41641	+	11.5842i	0.684918	+	0.942708i	−0.315062	+	0.949071i	$0.602025\pi$
$152$	−5.16312	+	15.8904i	−0.418784	+	1.28889i
$153$	−2.90617	+	3.24920i	−0.234950	+	0.262682i
$154$	−9.79837	+	11.1352i	−0.789575	+	0.897297i
$155$		0			0
$156$		0			0
$157$	−10.1514	−	13.9721i	−0.810166	−	1.11510i	−0.991298	−	0.131639i	$-0.957976\pi$
$157$	−10.1514	−	13.9721i	−0.810166	−	1.11510i	0.181132	−	0.983459i	$-0.442024\pi$
$158$	−4.04508	−	2.93893i	−0.321810	−	0.233808i
$159$	9.30986	+	0.472457i	0.738320	+	0.0374683i
$160$		0			0
$161$	−27.9767	−	20.3262i	−2.20487	−	1.60193i
$162$	7.81553	−	7.13140i	0.614046	−	0.560295i
$163$	15.0251	+	4.88197i	1.17686	+	0.382385i	0.831199	−	0.555974i	$-0.187655\pi$
$163$	15.0251	+	4.88197i	1.17686	+	0.382385i	0.345661	+	0.938359i	$0.387655\pi$
$164$	1.90211			0.148530
$165$		0			0
$166$	0.652476			0.0506419
$167$	15.0623	+	4.89404i	1.16556	+	0.378712i	0.826982	−	0.562228i	$-0.190056\pi$
$167$	15.0623	+	4.89404i	1.16556	+	0.378712i	0.338574	+	0.940940i	$0.390056\pi$
$168$	−19.5795	+	5.28106i	−1.51059	+	0.407443i
$169$	10.5172	+	7.64121i	0.809017	+	0.587785i
$170$		0			0
$171$	14.9003	+	6.57501i	1.13945	+	0.502804i
$172$	1.67760	+	1.21885i	0.127916	+	0.0929362i
$173$	−13.2533	−	18.2416i	−1.00763	−	1.38688i	−0.920525	−	0.390683i	$-0.872239\pi$
$173$	−13.2533	−	18.2416i	−1.00763	−	1.38688i	−0.0871036	−	0.996199i	$-0.527761\pi$
$174$	12.3811	−	15.3413i	0.938611	−	1.16302i
$175$		0			0
$176$	−6.79615	+	4.02786i	−0.512279	+	0.303612i
$177$	5.61803	+	2.14590i	0.422277	+	0.161296i
$178$	2.12663	−	6.54508i	0.159397	−	0.490575i
$179$	1.93487	+	2.66312i	0.144619	+	0.199051i	0.875181	−	0.483795i	$-0.160742\pi$
$179$	1.93487	+	2.66312i	0.144619	+	0.199051i	−0.730562	+	0.682846i	$0.760742\pi$
$180$		0			0
$181$	−5.00000	−	15.3884i	−0.371647	−	1.14381i	−0.945713	−	0.325003i	$-0.894635\pi$
$181$	−5.00000	−	15.3884i	−0.371647	−	1.14381i	0.574066	−	0.818809i	$-0.305365\pi$
$182$		0			0
$183$	−7.35787	−	11.2892i	−0.543909	−	0.834519i
$184$	−16.4443	−	22.6336i	−1.21229	−	1.66857i
$185$		0			0
$186$	−9.51057	−	3.63271i	−0.697348	−	0.266363i
$187$	−2.45714	−	4.14590i	−0.179684	−	0.303178i
$188$	−3.76393			−0.274513
$189$	3.18921	+	19.5084i	0.231981	+	1.41903i
$190$		0			0
$191$	8.36775	−	11.5172i	0.605469	−	0.833357i	−0.390726	−	0.920507i	$-0.627776\pi$
$191$	8.36775	−	11.5172i	0.605469	−	0.833357i	0.996195	+	0.0871502i	$0.0277760\pi$
$192$	−15.0637	−	0.764452i	−1.08713	−	0.0551696i
$193$	1.03681	+	3.19098i	0.0746314	+	0.229692i	0.981413	−	0.191910i	$-0.0614681\pi$
$193$	1.03681	+	3.19098i	0.0746314	+	0.229692i	−0.906781	+	0.421602i	$0.861468\pi$
$194$	16.1680	+	11.7467i	1.16079	+	0.843365i
$195$		0			0
$196$	1.42705	−	4.39201i	0.101932	−	0.313715i
$197$		−	1.06957i		−	0.0762037i	−0.999274	−	0.0381018i	$-0.987869\pi$
$197$		−	1.06957i		−	0.0762037i	0.999274	−	0.0381018i	$-0.0121311\pi$
$198$	4.91431	+	10.6143i	0.349245	+	0.754328i
$199$	11.3820			0.806846			0.403423	−	0.915014i	$-0.367820\pi$
$199$	11.3820			0.806846			0.403423	+	0.915014i	$0.367820\pi$
$200$		0			0
$201$	5.56243	−	1.50032i	0.392343	−	0.105825i
$202$	6.18812	−	8.51722i	0.435395	−	0.599270i
$203$	11.3820	+	35.0301i	0.798857	+	2.45863i
$204$	0.0788361	−	1.55348i	0.00551963	−	0.108765i
$205$		0			0
$206$	7.74721	−	5.62868i	0.539774	−	0.392169i
$207$	−23.5717	+	13.7134i	−1.63835	+	0.953145i
$208$		0			0
$209$	−11.8945	+	13.5172i	−0.822757	+	0.935006i
$210$		0			0
$211$	−1.64590	−	0.534785i	−0.113308	−	0.0368161i	0.251814	−	0.967776i	$-0.418973\pi$
$211$	−1.64590	−	0.534785i	−0.113308	−	0.0368161i	−0.365122	+	0.930960i	$0.618973\pi$
$212$	−2.69098	+	1.95511i	−0.184817	+	0.134278i
$213$	1.61553	+	2.47870i	0.110694	+	0.169838i
$214$	2.07295	+	6.37988i	0.141704	+	0.436120i
$215$		0			0
$216$	−2.42325	+	15.8075i	−0.164881	+	1.07556i
$217$	15.3884	−	11.1803i	1.04463	−	0.758971i
$218$	6.07953	−	18.7109i	0.411758	−	1.26726i
$219$	1.90211	−	4.97980i	0.128533	−	0.336503i
$220$		0			0
$221$		0			0
$222$	−13.7982	−	11.1358i	−0.926073	−	0.747384i
$223$	3.85723	+	5.30902i	0.258299	+	0.355518i	0.918396	−	0.395662i	$-0.129485\pi$
$223$	3.85723	+	5.30902i	0.258299	+	0.355518i	−0.660097	+	0.751180i	$0.729485\pi$
$224$	7.50245	−	10.3262i	0.501279	−	0.689951i
$225$		0			0
$226$	−6.11803	+	1.98787i	−0.406966	+	0.132231i
$227$	−10.9549	+	15.0781i	−0.727103	+	1.00077i	0.272155	+	0.962254i	$0.412264\pi$
$227$	−10.9549	+	15.0781i	−0.727103	+	1.00077i	−0.999258	+	0.0385182i	$0.987736\pi$
$228$	−5.61086	+	1.51338i	−0.371588	+	0.100226i
$229$	5.10081	−	15.6987i	0.337071	−	1.03740i	−0.628622	−	0.777711i	$-0.716381\pi$
$229$	5.10081	−	15.6987i	0.337071	−	1.03740i	0.965693	−	0.259687i	$-0.0836195\pi$
$230$		0			0
$231$	−21.6274	−	3.13632i	−1.42298	−	0.206354i
$232$			29.7984i			1.95636i
$233$	−5.59017	−	1.81636i	−0.366224	−	0.118993i	0.120123	−	0.992759i	$-0.461671\pi$
$233$	−5.59017	−	1.81636i	−0.366224	−	0.118993i	−0.486347	+	0.873766i	$0.661671\pi$
$234$		0			0
$235$		0			0
$236$	−2.04087	+	0.663119i	−0.132849	+	0.0431654i
$237$	0.373373	−	7.35738i	0.0242532	−	0.477913i
$238$	−5.25731	−	3.81966i	−0.340781	−	0.247592i
$239$	−8.42075	+	6.11803i	−0.544693	+	0.395743i	−0.825825	−	0.563926i	$-0.809290\pi$
$239$	−8.42075	+	6.11803i	−0.544693	+	0.395743i	0.281132	+	0.959669i	$0.409290\pi$
$240$		0			0
$241$		−	9.85359i		−	0.634726i	−0.948304	−	0.317363i	$-0.897203\pi$
$241$		−	9.85359i		−	0.634726i	0.948304	−	0.317363i	$-0.102797\pi$
$242$	−12.8262	+	1.64484i	−0.824502	+	0.105735i
$243$	15.0902	+	3.90983i	0.968035	+	0.250816i
$244$	4.57295	+	1.48584i	0.292753	+	0.0951212i
$245$		0			0
$246$	−3.42174	−	5.24997i	−0.218162	−	0.334726i
$247$		0			0
$248$	14.6353	−	4.75528i	0.929340	−	0.301961i
$249$	0.524916	+	0.805379i	0.0332652	+	0.0510388i
$250$		0			0
$251$	−10.5146	−	3.41641i	−0.663677	−	0.215642i	−0.0422420	−	0.999107i	$-0.513450\pi$
$251$	−10.5146	−	3.41641i	−0.663677	−	0.215642i	−0.621435	+	0.783466i	$0.713450\pi$
$252$	−5.25731	−	4.70228i	−0.331179	−	0.296216i
$253$	−6.60440	−	29.4164i	−0.415215	−	1.84939i
$254$		−	2.96556i		−	0.186076i
$255$		0			0
$256$	10.7361	−	7.80021i	0.671004	−	0.487513i
$257$	−19.8262	−	14.4046i	−1.23673	−	0.898535i	−0.239351	−	0.970933i	$-0.576935\pi$
$257$	−19.8262	−	14.4046i	−1.23673	−	0.898535i	−0.997376	+	0.0723985i	$0.976935\pi$
$258$	0.346249	−	6.82290i	0.0215565	−	0.424775i
$259$	31.5066	−	10.2371i	1.95772	−	0.636103i
$260$		0			0
$261$	28.8970	+	2.94051i	1.78868	+	0.182013i
$262$	−10.9434	−	3.55573i	−0.676086	−	0.219674i
$263$			14.2128i			0.876402i	0.898877	+	0.438201i	$0.144384\pi$
$263$			14.2128i			0.876402i	−0.898877	+	0.438201i	$0.855616\pi$
$264$	−15.8565	−	7.81999i	−0.975899	−	0.481287i
$265$		0			0
$266$	−7.50245	+	23.0902i	−0.460005	+	1.41575i
$267$	9.78975	−	2.64053i	0.599123	−	0.161598i
$268$	−1.20833	+	1.66312i	−0.0738103	+	0.101591i
$269$	15.7517	−	5.11803i	0.960397	−	0.312052i	0.213464	−	0.976951i	$-0.431525\pi$
$269$	15.7517	−	5.11803i	0.960397	−	0.312052i	0.746933	+	0.664899i	$0.231525\pi$
$270$		0			0
$271$	11.8713	−	16.3395i	0.721132	−	0.992552i	−0.278354	−	0.960479i	$-0.589789\pi$
$271$	11.8713	−	16.3395i	0.721132	−	0.992552i	0.999486	−	0.0320738i	$-0.0102112\pi$
$272$	−2.03444	−	2.80017i	−0.123356	−	0.169785i
$273$		0			0
$274$			5.53483i			0.334371i
$275$		0			0
$276$	3.47214	−	9.09017i	0.208998	−	0.547164i
$277$	−8.16348	+	25.1246i	−0.490496	+	1.50959i	0.333364	+	0.942798i	$0.391816\pi$
$277$	−8.16348	+	25.1246i	−0.490496	+	1.50959i	−0.823860	+	0.566793i	$0.808184\pi$
$278$	−4.30902	+	3.13068i	−0.258438	+	0.187766i
$279$	−3.16723	−	14.6618i	−0.189617	−	0.877780i
$280$		0			0
$281$	−0.759299	−	2.33688i	−0.0452960	−	0.139407i	0.925851	−	0.377889i	$-0.123350\pi$
$281$	−0.759299	−	2.33688i	−0.0452960	−	0.139407i	−0.971147	+	0.238483i	$0.923350\pi$
$282$	6.77099	+	10.3887i	0.403207	+	0.618640i
$283$	8.86978	−	6.44427i	0.527254	−	0.383072i	−0.292076	−	0.956395i	$-0.594346\pi$
$283$	8.86978	−	6.44427i	0.527254	−	0.383072i	0.819329	+	0.573323i	$0.194346\pi$
$284$	−1.00406	−	0.326238i	−0.0595798	−	0.0193587i
$285$		0			0
$286$		0			0
$287$	11.7082			0.691113
$288$	−5.06163	−	8.70035i	−0.298259	−	0.512673i
$289$	−12.0451	+	8.75127i	−0.708534	+	0.514780i
$290$		0			0
$291$	−1.49235	+	29.4070i	−0.0874831	+	1.72387i
$292$	0.587785	+	1.80902i	0.0343975	+	0.105865i
$293$	6.80902	−	9.37181i	0.397787	−	0.547507i	−0.562400	−	0.826865i	$-0.690122\pi$
$293$	6.80902	−	9.37181i	0.397787	−	0.547507i	0.960187	+	0.279359i	$0.0901218\pi$
$294$	−14.6894	+	3.96209i	−0.856704	+	0.231074i
$295$		0			0
$296$	26.8011			1.55778
$297$	−9.14817	+	14.6052i	−0.530831	+	0.847478i
$298$			24.2705i			1.40595i
$299$		0			0
$300$		0			0
$301$	10.3262	+	7.50245i	0.595194	+	0.432434i
$302$	5.20163	+	16.0090i	0.299320	+	0.921212i
$303$	15.4915	+	0.786164i	0.889964	+	0.0451639i
$304$	−7.60081	+	10.4616i	−0.435937	+	0.600015i
$305$		0			0
$306$	−4.42954	+	2.57698i	−0.253220	+	0.147316i
$307$	26.4581			1.51004			0.755021	−	0.655701i	$-0.227627\pi$
$307$	26.4581			1.51004			0.755021	+	0.655701i	$0.227627\pi$
$308$	6.70820	−	3.97574i	0.382235	−	0.226539i
$309$	13.1803	+	5.03444i	0.749803	+	0.286399i
$310$		0			0
$311$	10.2044	+	14.0451i	0.578636	+	0.796424i	0.993545	−	0.113439i	$-0.0361867\pi$
$311$	10.2044	+	14.0451i	0.578636	+	0.796424i	−0.414909	+	0.909863i	$0.636187\pi$
$312$		0			0
$313$	2.07363	−	0.673762i	0.117208	−	0.0380833i	−0.249826	−	0.968291i	$-0.580373\pi$
$313$	2.07363	−	0.673762i	0.117208	−	0.0380833i	0.367034	+	0.930208i	$0.380373\pi$
$314$	−6.27388	−	19.3090i	−0.354056	−	1.08967i
$315$		0			0
$316$	1.54508	+	2.12663i	0.0869178	+	0.119632i
$317$	5.72542	−	17.6210i	0.321572	−	0.989697i	−0.651392	−	0.758741i	$-0.725815\pi$
$317$	5.72542	−	17.6210i	0.321572	−	0.989697i	0.972964	−	0.230956i	$-0.0741852\pi$
$318$	10.2371	+	3.91023i	0.574068	+	0.219275i
$319$	−12.7254	+	29.4828i	−0.712487	+	1.65072i
$320$		0			0
$321$	−6.20727	+	7.69134i	−0.346456	+	0.429289i
$322$	−23.8949	−	32.8885i	−1.33161	−	1.83281i
$323$	−6.38197	−	4.63677i	−0.355102	−	0.257997i
$324$	−5.06633	+	2.29599i	−0.281463	+	0.127555i
$325$		0			0
$326$	15.0251	+	10.9164i	0.832166	+	0.604604i
$327$	27.9866	−	7.54866i	1.54766	−	0.417442i
$328$	9.00854	+	2.92705i	0.497413	+	0.161619i
$329$	−23.1684			−1.27731
$330$		0			0
$331$	−25.1246			−1.38097			−0.690487	−	0.723345i	$-0.742604\pi$
$331$	−25.1246			−1.38097			−0.690487	+	0.723345i	$0.742604\pi$
$332$	−0.326238	−	0.106001i	−0.0179046	−	0.00581757i
$333$	2.64474	−	25.9904i	0.144931	−	1.42426i
$334$	15.0623	+	10.9434i	0.824173	+	0.598797i
$335$		0			0
$336$	−15.6749	−	0.795469i	−0.855134	−	0.0433964i
$337$	2.12663	+	1.54508i	0.115845	+	0.0841661i	0.644199	−	0.764858i	$-0.277191\pi$
$337$	2.12663	+	1.54508i	0.115845	+	0.0841661i	−0.528354	+	0.849024i	$0.677191\pi$
$338$	8.98278	+	12.3637i	0.488599	+	0.672499i
$339$	−7.37567	−	5.95251i	−0.400591	−	0.323296i
$340$		0			0
$341$	16.5110	+	1.54508i	0.894120	+	0.0836710i
$342$	14.2705	+	12.7639i	0.771661	+	0.690194i
$343$	0.555029	−	1.70820i	0.0299688	−	0.0922343i
$344$	6.06961	+	8.35410i	0.327251	+	0.450423i
$345$		0			0
$346$	−8.19098	−	25.2093i	−0.440350	−	1.35526i
$347$	29.2705	−	9.51057i	1.57132	−	0.510554i	0.611520	−	0.791229i	$-0.290558\pi$
$347$	29.2705	−	9.51057i	1.57132	−	0.510554i	0.959803	+	0.280675i	$0.0905582\pi$
$348$	−8.68291	+	5.65920i	−0.465453	+	0.303365i
$349$	−2.01064	−	2.76741i	−0.107627	−	0.148136i	0.751806	−	0.659385i	$-0.229183\pi$
$349$	−2.01064	−	2.76741i	−0.107627	−	0.148136i	−0.859433	+	0.511249i	$0.829183\pi$
$350$		0			0
$351$		0			0
$352$	10.8576	−	2.43769i	0.578715	−	0.129930i
$353$	−33.3607			−1.77561			−0.887805	−	0.460220i	$-0.847771\pi$
$353$	−33.3607			−1.77561			−0.887805	+	0.460220i	$0.847771\pi$
$354$	5.50161	+	4.44006i	0.292407	+	0.235986i
$355$		0			0
$356$	−2.12663	+	2.92705i	−0.112711	+	0.155133i
$357$	0.485265	−	9.56224i	0.0256829	−	0.506087i
$358$	1.19581	+	3.68034i	0.0632008	+	0.194512i
$359$	0.865300	+	0.628677i	0.0456688	+	0.0331803i	0.610385	−	0.792105i	$-0.291015\pi$
$359$	0.865300	+	0.628677i	0.0456688	+	0.0331803i	−0.564717	+	0.825285i	$0.691015\pi$
$360$		0			0
$361$	−3.23607	+	9.95959i	−0.170319	+	0.524189i
$362$		−	19.0211i		−	0.999728i
$363$	−12.3490	−	14.5087i	−0.648154	−	0.761509i
$364$		0			0
$365$		0			0
$366$	−4.12532	−	15.2946i	−0.215634	−	0.799460i
$367$	−7.36369	+	10.1353i	−0.384382	+	0.529056i	−0.956739	−	0.290949i	$-0.906029\pi$
$367$	−7.36369	+	10.1353i	−0.384382	+	0.529056i	0.572357	+	0.820005i	$0.306029\pi$
$368$	−6.69098	−	20.5927i	−0.348792	−	1.07347i
$369$	3.72747	−	8.44720i	0.194045	−	0.439744i
$370$		0			0
$371$	−16.5640	+	12.0344i	−0.859959	+	0.624797i
$372$	4.16511	+	3.36144i	0.215951	+	0.174283i
$373$	−4.63677			−0.240083			−0.120041	−	0.992769i	$-0.538303\pi$
$373$	−4.63677			−0.240083			−0.120041	+	0.992769i	$0.538303\pi$
$374$	−1.24108	−	5.52786i	−0.0641749	−	0.285839i
$375$		0			0
$376$	−17.8262	−	5.79210i	−0.919318	−	0.298705i
$377$		0			0
$378$	−3.52119	+	22.9696i	−0.181110	+	1.18143i
$379$	−4.10739	−	12.6412i	−0.210982	−	0.649337i	−0.999414	−	0.0342154i	$-0.989107\pi$
$379$	−4.10739	−	12.6412i	−0.210982	−	0.649337i	0.788432	−	0.615122i	$-0.210893\pi$
$380$		0			0
$381$	3.66051	−	2.38579i	0.187534	−	0.122228i
$382$	13.5393	−	9.83688i	0.692731	−	0.503299i
$383$	−2.78115	+	8.55951i	−0.142110	+	0.437370i	−0.996628	−	0.0820516i	$-0.973853\pi$
$383$	−2.78115	+	8.55951i	−0.142110	+	0.437370i	0.854518	+	0.519422i	$0.173853\pi$
$384$	−5.70634	−	2.17963i	−0.291200	−	0.111229i
$385$		0			0
$386$			3.94427i			0.200758i
$387$	8.70035	−	5.06163i	0.442264	−	0.257297i
$388$	−6.17561	−	8.50000i	−0.313519	−	0.431522i
$389$	11.4127	−	15.7082i	0.578646	−	0.796438i	−0.414900	−	0.909867i	$-0.636184\pi$
$389$	11.4127	−	15.7082i	0.578646	−	0.796438i	0.993546	+	0.113429i	$0.0361835\pi$
$390$		0			0
$391$	12.5623	−	4.08174i	0.635303	−	0.206422i
$392$	13.5172	−	18.6049i	0.682723	−	0.939687i
$393$	−4.41498	−	16.3685i	−0.222706	−	0.825681i
$394$	0.388544	−	1.19581i	0.0195746	−	0.0602443i
$395$		0			0
$396$	−0.732751	−	6.10555i	−0.0368221	−	0.306815i
$397$		−	9.38197i		−	0.470867i	−0.971890	−	0.235434i	$-0.924349\pi$
$397$		−	9.38197i		−	0.470867i	0.971890	−	0.235434i	$-0.0756510\pi$
$398$	12.7254	+	4.13474i	0.637868	+	0.207256i
$399$	−34.5369	+	9.31543i	−1.72901	+	0.466355i
$400$		0			0
$401$	15.9964	−	5.19756i	0.798824	−	0.259554i	0.118967	−	0.992898i	$-0.462042\pi$
$401$	15.9964	−	5.19756i	0.798824	−	0.259554i	0.679857	+	0.733344i	$0.262042\pi$
$402$	6.76401	+	0.343260i	0.337358	+	0.0171203i
$403$		0			0
$404$	−4.47777	+	3.25329i	−0.222777	+	0.161857i
$405$		0			0
$406$			43.2996i			2.14892i
$407$	26.5172	+	11.4454i	1.31441	+	0.567329i
$408$	2.76393	−	7.23607i	0.136835	−	0.358239i
$409$	−34.9615	−	11.3597i	−1.72873	−	0.561700i	−0.735469	−	0.677559i	$-0.763038\pi$
$409$	−34.9615	−	11.3597i	−1.72873	−	0.561700i	−0.993266	+	0.115859i	$0.963038\pi$
$410$		0			0
$411$	−6.83187	+	4.45276i	−0.336991	+	0.219639i
$412$	−4.78804	+	1.55573i	−0.235890	+	0.0766452i
$413$	−12.5623	+	4.08174i	−0.618151	+	0.200849i
$414$	−31.3356	+	6.76910i	−1.54006	+	0.332683i
$415$		0			0
$416$		0			0
$417$	−7.33094	−	2.80017i	−0.358998	−	0.137125i
$418$	−18.2088	+	10.7918i	−0.890623	+	0.527844i
$419$		−	30.7771i		−	1.50356i	−0.659415	−	0.751780i	$-0.729196\pi$
$419$		−	30.7771i		−	1.50356i	0.659415	−	0.751780i	$-0.270804\pi$
$420$		0			0
$421$	12.8262	−	9.31881i	0.625113	−	0.454171i	−0.229591	−	0.973287i	$-0.573739\pi$
$421$	12.8262	−	9.31881i	0.625113	−	0.454171i	0.854704	+	0.519116i	$0.173739\pi$
$422$	−1.64590	−	1.19581i	−0.0801211	−	0.0582114i
$423$	−7.37599	+	16.7155i	−0.358633	+	0.812733i
$424$	−15.7533	+	5.11855i	−0.765047	+	0.248579i
$425$		0			0
$426$	0.905773	+	3.35815i	0.0438848	+	0.162703i
$427$	28.1482	+	9.14590i	1.36219	+	0.442601i
$428$		−	3.52671i		−	0.170470i
$429$		0			0
$430$		0			0
$431$	9.51057	−	29.2705i	0.458108	−	1.40991i	−0.409340	−	0.912382i	$-0.634241\pi$
$431$	9.51057	−	29.2705i	0.458108	−	1.40991i	0.867447	−	0.497529i	$-0.165759\pi$
$432$	−5.56423	+	11.0558i	−0.267709	+	0.531923i
$433$	−12.3637	+	17.0172i	−0.594163	+	0.817795i	−0.995158	−	0.0982847i	$-0.968664\pi$
$433$	−12.3637	+	17.0172i	−0.594163	+	0.817795i	0.400995	+	0.916080i	$0.368664\pi$
$434$	21.2663	−	6.90983i	1.02081	−	0.331682i
$435$		0			0
$436$	−6.07953	+	8.36775i	−0.291157	+	0.400743i
$437$	−29.0066	−	39.9241i	−1.38757	−	1.90983i
$438$	3.93564	−	4.87660i	0.188052	−	0.233013i
$439$			2.62866i			0.125459i	0.998031	+	0.0627294i	$0.0199805\pi$
$439$			2.62866i			0.125459i	−0.998031	+	0.0627294i	$0.980019\pi$
$440$		0			0
$441$	−16.7082	−	14.9443i	−0.795629	−	0.711632i
$442$		0			0
$443$	2.78115	−	2.02063i	0.132137	−	0.0960028i	−0.519754	−	0.854316i	$-0.673976\pi$
$443$	2.78115	−	2.02063i	0.132137	−	0.0960028i	0.651890	+	0.758313i	$0.273976\pi$
$444$	5.08997	+	7.80954i	0.241559	+	0.370624i
$445$		0			0
$446$	2.38390	+	7.33688i	0.112881	+	0.347411i
$447$	−29.9581	+	19.5256i	−1.41697	+	0.923530i
$448$	26.8011	−	19.4721i	1.26623	−	0.919972i
$449$	−14.5761	−	4.73607i	−0.687890	−	0.223509i	−0.0558433	−	0.998440i	$-0.517785\pi$
$449$	−14.5761	−	4.73607i	−0.687890	−	0.223509i	−0.632046	+	0.774931i	$0.717785\pi$
$450$		0			0
$451$	7.66312	+	6.74315i	0.360842	+	0.317523i
$452$	3.38197			0.159074
$453$	−15.5758	+	19.2998i	−0.731816	+	0.906783i
$454$	−17.7254	+	12.8783i	−0.831895	+	0.604407i
$455$		0			0
$456$	−28.9023	−	1.46673i	−1.35347	−	0.0686861i
$457$	4.30625	+	13.2533i	0.201438	+	0.619963i	0.999841	+	0.0178390i	$0.00567862\pi$
$457$	4.30625	+	13.2533i	0.201438	+	0.619963i	−0.798403	+	0.602124i	$0.794321\pi$
$458$	11.4058	−	15.6987i	0.532956	−	0.733552i
$459$	−6.74444	−	3.39438i	−0.314804	−	0.158436i
$460$		0			0
$461$	23.5519			1.09692			0.548461	−	0.836176i	$-0.315214\pi$
$461$	23.5519			1.09692			0.548461	+	0.836176i	$0.315214\pi$
$462$	−23.0408	−	11.3631i	−1.07196	−	0.528660i
$463$		−	22.0902i		−	1.02662i	−0.858204	−	0.513309i	$-0.828420\pi$
$463$		−	22.0902i		−	1.02662i	0.858204	−	0.513309i	$-0.171580\pi$
$464$	−7.12667	+	21.9336i	−0.330847	+	1.01824i
$465$		0			0
$466$	−5.59017	−	4.06150i	−0.258960	−	0.188145i
$467$	−9.01722	−	27.7522i	−0.417267	−	1.28422i	−0.910207	−	0.414153i	$-0.864078\pi$
$467$	−9.01722	−	27.7522i	−0.417267	−	1.28422i	0.492940	−	0.870063i	$-0.335922\pi$
$468$		0			0
$469$	−7.43769	+	10.2371i	−0.343441	+	0.472706i
$470$		0			0
$471$	18.7866	−	23.2782i	0.865641	−	1.07260i
$472$	−10.6861			−0.491869
$473$	2.43769	+	10.8576i	0.112085	+	0.499235i
$474$	3.09017	−	8.09017i	0.141936	−	0.371594i
$475$		0			0
$476$	2.00811	+	2.76393i	0.0920418	+	0.126685i
$477$	3.40919	+	15.7819i	0.156096	+	0.722602i
$478$	−11.6372	+	3.78115i	−0.532273	+	0.172946i
$479$	−9.40456	−	28.9443i	−0.429705	−	1.32250i	−0.898416	−	0.439146i	$-0.855281\pi$
$479$	−9.40456	−	28.9443i	−0.429705	−	1.32250i	0.468710	−	0.883352i	$-0.344719\pi$
$480$		0			0
$481$		0			0
$482$	3.57953	−	11.0167i	0.163043	−	0.501795i
$483$	21.3723	−	55.9533i	0.972472	−	2.54596i
$484$	6.68034	+	1.26133i	0.303652	+	0.0573331i
$485$		0			0
$486$	15.4510	+	9.85315i	0.700871	+	0.446948i
$487$	−1.17557	−	1.61803i	−0.0532702	−	0.0733201i	0.781551	−	0.623842i	$-0.214429\pi$
$487$	−1.17557	−	1.61803i	−0.0532702	−	0.0733201i	−0.834821	+	0.550521i	$0.814429\pi$
$488$	19.3713	+	14.0741i	0.876899	+	0.637104i
$489$	−1.38686	+	27.3284i	−0.0627162	+	1.23583i
$490$		0			0
$491$	−10.3229	−	7.50000i	−0.465864	−	0.338470i	0.329963	−	0.943994i	$-0.392964\pi$
$491$	−10.3229	−	7.50000i	−0.465864	−	0.338470i	−0.795827	+	0.605524i	$0.792964\pi$
$492$	0.857960	+	3.18088i	0.0386798	+	0.143405i
$493$	−13.3803	−	4.34752i	−0.602619	−	0.195803i
$494$		0			0
$495$		0			0
$496$	11.9098			0.534767
$497$	−6.18034	−	2.00811i	−0.277226	−	0.0900762i
$498$	0.294303	+	1.09113i	0.0131881	+	0.0488946i
$499$	−7.66312	−	5.56758i	−0.343048	−	0.249239i	0.402899	−	0.915245i	$-0.368003\pi$
$499$	−7.66312	−	5.56758i	−0.343048	−	0.249239i	−0.745947	+	0.666005i	$0.768003\pi$
$500$		0			0
$501$	−1.39029	+	27.3960i	−0.0621138	+	1.22396i
$502$	−10.5146	−	7.63932i	−0.469291	−	0.340960i
$503$	−2.03444	−	2.80017i	−0.0907113	−	0.124853i	0.761249	−	0.648459i	$-0.224586\pi$
$503$	−2.03444	−	2.80017i	−0.0907113	−	0.124853i	−0.851961	+	0.523606i	$0.824586\pi$
$504$	−17.6629	−	30.3605i	−0.786769	−	1.35236i
$505$		0			0
$506$	3.30220	−	35.2877i	0.146801	−	1.56873i
$507$	−8.03444	+	21.0344i	−0.356822	+	0.934172i
$508$	−0.481784	+	1.48278i	−0.0213757	+	0.0657877i
$509$	10.7189	+	14.7533i	0.475107	+	0.653928i	0.977555	−	0.210679i	$-0.0675675\pi$
$509$	10.7189	+	14.7533i	0.475107	+	0.653928i	−0.502449	+	0.864607i	$0.667567\pi$
$510$		0			0
$511$	3.61803	+	11.1352i	0.160052	+	0.492591i
$512$	21.5451	−	7.00042i	0.952167	−	0.309378i
$513$	−4.27445	+	27.8833i	−0.188721	+	1.23108i
$514$	−16.9336	−	23.3071i	−0.746910	−	1.02803i
$515$		0			0
$516$	−1.28157	+	3.35520i	−0.0564180	+	0.147704i
$517$	−15.1639	−	13.3435i	−0.666908	−	0.586845i
$518$	38.9443			1.71111
$519$	24.5272	−	30.3913i	1.07663	−	1.33403i
$520$		0			0
$521$	−10.3759	+	14.2812i	−0.454575	+	0.625669i	−0.973373	−	0.229228i	$-0.926380\pi$
$521$	−10.3759	+	14.2812i	−0.454575	+	0.625669i	0.518798	+	0.854897i	$0.326380\pi$
$522$	31.2396	+	13.7850i	1.36732	+	0.603355i
$523$	−3.85723	−	11.8713i	−0.168665	−	0.519097i	0.830623	−	0.556835i	$-0.187985\pi$
$523$	−3.85723	−	11.8713i	−0.168665	−	0.519097i	−0.999288	+	0.0377386i	$0.987985\pi$
$524$	4.89404	+	3.55573i	0.213797	+	0.155333i
$525$		0			0
$526$	−5.16312	+	15.8904i	−0.225123	+	0.692856i
$527$			7.26543i			0.316487i
$528$	−9.80120	−	9.54833i	−0.426542	−	0.415538i
$529$	59.6312			2.59266
$530$		0			0
$531$	−1.05451	+	10.3629i	−0.0457618	+	0.449711i
$532$	7.50245	−	10.3262i	0.325273	−	0.447699i
$533$		0			0
$534$	11.9045	+	0.604130i	0.515158	+	0.0261433i
$535$		0			0
$536$	−8.28199	+	6.01722i	−0.357728	+	0.259904i
$537$	−3.58077	+	4.43688i	−0.154522	+	0.191465i
$538$	19.4702			0.839418
$539$	21.3193	−	12.6353i	0.918286	−	0.544239i
$540$		0			0
$541$	−15.3885	−	5.00004i	−0.661605	−	0.214969i	−0.0410809	−	0.999156i	$-0.513080\pi$
$541$	−15.3885	−	5.00004i	−0.661605	−	0.214969i	−0.620524	+	0.784187i	$0.713080\pi$
$542$	19.2082	−	13.9556i	0.825063	−	0.599443i
$543$	23.4786	−	15.3025i	1.00756	−	0.656693i
$544$	1.50658	+	4.63677i	0.0645940	+	0.198800i
$545$		0			0
$546$		0			0
$547$	−10.5474	+	7.66312i	−0.450973	+	0.327651i	−0.789980	−	0.613133i	$-0.789909\pi$
$547$	−10.5474	+	7.66312i	−0.450973	+	0.327651i	0.339007	+	0.940784i	$0.389909\pi$
$548$	0.899187	−	2.76741i	0.0384114	−	0.118218i
$549$	15.5599	−	17.3965i	0.664082	−	0.742466i
$550$		0			0
$551$			52.5623i			2.23923i
$552$	30.4326	−	37.7086i	1.29530	−	1.60498i
$553$	9.51057	+	13.0902i	0.404430	+	0.556651i
$554$	−18.2541	+	25.1246i	−0.775542	+	1.06744i
$555$		0			0
$556$	2.66312	−	0.865300i	0.112941	−	0.0366969i
$557$	14.7361	−	20.2825i	0.624387	−	0.859395i	−0.373276	−	0.927720i	$-0.621766\pi$
$557$	14.7361	−	20.2825i	0.624387	−	0.859395i	0.997663	+	0.0683251i	$0.0217655\pi$
$558$	1.78514	−	17.5430i	0.0755710	−	0.742653i
$559$		0			0
$560$		0			0
$561$	5.82483	−	5.97908i	0.245924	−	0.252437i
$562$		−	2.88854i		−	0.121846i
$563$	11.9721	+	3.88998i	0.504565	+	0.163943i	0.550229	−	0.835014i	$-0.314540\pi$
$563$	11.9721	+	3.88998i	0.504565	+	0.163943i	−0.0456639	+	0.998957i	$0.514540\pi$
$564$	−1.69775	−	6.29438i	−0.0714880	−	0.265041i
$565$		0			0
$566$	12.2577	−	3.98278i	0.515231	−	0.167409i
$567$	−31.1851	+	14.1327i	−1.30965	+	0.593516i
$568$	−4.25325	−	3.09017i	−0.178463	−	0.129661i
$569$	3.02468	−	2.19756i	0.126801	−	0.0921265i	−0.522577	−	0.852592i	$-0.675029\pi$
$569$	3.02468	−	2.19756i	0.126801	−	0.0921265i	0.649378	+	0.760466i	$0.275029\pi$
$570$		0			0
$571$		−	10.9637i		−	0.458814i	−0.973331	−	0.229407i	$-0.926321\pi$
$571$		−	10.9637i		−	0.458814i	0.973331	−	0.229407i	$-0.0736788\pi$
$572$		0			0
$573$	23.0344	+	8.79837i	0.962278	+	0.367557i
$574$	13.0902	+	4.25325i	0.546373	+	0.177527i
$575$		0			0
$576$	−5.51618	−	25.5356i	−0.229841	−	1.06398i
$577$	−36.4302	+	11.8369i	−1.51661	+	0.492776i	−0.944810	−	0.327619i	$-0.893754\pi$
$577$	−36.4302	+	11.8369i	−1.51661	+	0.492776i	−0.571798	+	0.820394i	$0.693754\pi$
$578$	−16.6459	+	5.40858i	−0.692378	+	0.224967i
$579$	−4.86858	+	3.17316i	−0.202331	+	0.131872i
$580$		0			0
$581$	−2.00811	−	0.652476i	−0.0833106	−	0.0270693i
$582$	−12.3512	+	32.3359i	−0.511975	+	1.34037i
$583$	−17.7723	−	1.66312i	−0.736054	−	0.0688793i
$584$			9.47214i			0.391960i
$585$		0			0
$586$	11.0172	−	8.00448i	0.455117	−	0.330662i
$587$	28.8713	+	20.9762i	1.19165	+	0.865782i	0.993437	−	0.114377i	$-0.0364873\pi$
$587$	28.8713	+	20.9762i	1.19165	+	0.865782i	0.198210	+	0.980160i	$0.436487\pi$
$588$	7.98839	+	0.405395i	0.329436	+	0.0167182i
$589$	25.8156	−	8.38800i	1.06371	−	0.345621i
$590$		0			0
$591$	1.78863	−	0.482436i	0.0735743	−	0.0198448i
$592$	19.7274	+	6.40983i	0.810792	+	0.263442i
$593$		−	24.2380i		−	0.995333i	−0.867368	−	0.497667i	$-0.834190\pi$
$593$		−	24.2380i		−	0.995333i	0.867368	−	0.497667i	$-0.165810\pi$
$594$	−15.5336	+	13.0058i	−0.637351	+	0.533635i
$595$		0			0
$596$	3.94298	−	12.1353i	0.161511	−	0.497079i
$597$	5.13391	+	19.0339i	0.210117	+	0.779007i
$598$		0			0
$599$	−33.9075	+	11.0172i	−1.38542	+	0.450151i	−0.904449	−	0.426583i	$-0.859717\pi$
$599$	−33.9075	+	11.0172i	−1.38542	+	0.450151i	−0.480975	+	0.876734i	$0.659717\pi$
$600$		0			0
$601$	2.76393	−	3.80423i	0.112743	−	0.155178i	−0.748916	−	0.662665i	$-0.769425\pi$
$601$	2.76393	−	3.80423i	0.112743	−	0.155178i	0.861659	+	0.507487i	$0.169425\pi$
$602$	8.81966	+	12.1392i	0.359463	+	0.494758i
$603$	5.01794	+	8.62525i	0.204346	+	0.351248i
$604$		−	8.84953i		−	0.360082i
$605$		0			0
$606$	17.0344	+	6.50658i	0.691977	+	0.264312i
$607$	−0.673542	+	2.07295i	−0.0273382	+	0.0841384i	−0.963795	−	0.266645i	$-0.914085\pi$
$607$	−0.673542	+	2.07295i	−0.0273382	+	0.0841384i	0.936456	+	0.350784i	$0.114085\pi$
$608$	14.7361	−	10.7064i	0.597626	−	0.434201i
$609$	−53.4465	+	34.8345i	−2.16576	+	1.41156i
$610$		0			0
$611$		0			0
$612$	2.63342	−	0.568870i	0.106450	−	0.0229952i
$613$	2.48990	−	1.80902i	0.100566	−	0.0730655i	−0.536366	−	0.843986i	$-0.680203\pi$
$613$	2.48990	−	1.80902i	0.100566	−	0.0730655i	0.636932	+	0.770920i	$0.280203\pi$
$614$	29.5810	+	9.61146i	1.19379	+	0.387887i
$615$		0			0
$616$	37.8885	−	8.50651i	1.52657	−	0.342737i
$617$	−41.5967			−1.67462			−0.837311	−	0.546727i	$-0.815874\pi$
$617$	−41.5967			−1.67462			−0.837311	+	0.546727i	$0.815874\pi$
$618$	12.9072	+	10.4167i	0.519204	+	0.419022i
$619$	−0.809017	+	0.587785i	−0.0325171	+	0.0236251i	−0.603925	−	0.797041i	$-0.706397\pi$
$619$	−0.809017	+	0.587785i	−0.0325171	+	0.0236251i	0.571408	+	0.820666i	$0.306397\pi$
$620$		0			0
$621$	−33.5649	−	33.2331i	−1.34691	−	1.33360i
$622$	6.30664	+	19.4098i	0.252873	+	0.778263i
$623$	−13.0902	+	18.0171i	−0.524447	+	0.721839i
$624$		0			0
$625$		0			0
$626$	2.56314			0.102444
$627$	−27.9698	−	13.7939i	−1.11700	−	0.550877i
$628$			10.6738i			0.425929i
$629$	−3.91023	+	12.0344i	−0.155911	+	0.479845i
$630$		0			0
$631$	2.20820	+	1.60435i	0.0879072	+	0.0638683i	0.630871	−	0.775888i	$-0.282698\pi$
$631$	2.20820	+	1.60435i	0.0879072	+	0.0638683i	−0.542964	+	0.839756i	$0.682698\pi$
$632$	4.04508	+	12.4495i	0.160905	+	0.495214i
$633$	0.151921	−	2.99363i	0.00603832	−	0.118986i
$634$	12.8024	−	17.6210i	0.508450	−	0.699821i
$635$		0			0
$636$	−4.48330	−	3.61823i	−0.177774	−	0.143472i
$637$		0			0
$638$	−24.9377	+	28.3399i	−0.987293	+	1.12199i
$639$	−3.41641	+	3.81966i	−0.135151	+	0.151103i
$640$		0			0
$641$	−14.8661	−	20.4615i	−0.587177	−	0.808180i	0.407282	−	0.913302i	$-0.366477\pi$
$641$	−14.8661	−	20.4615i	−0.587177	−	0.808180i	−0.994459	+	0.105122i	$0.966477\pi$
$642$	−9.73398	+	6.34426i	−0.384170	+	0.250388i
$643$	−22.1316	+	7.19098i	−0.872784	+	0.283585i	−0.710958	−	0.703235i	$-0.751738\pi$
$643$	−22.1316	+	7.19098i	−0.872784	+	0.283585i	−0.161826	+	0.986819i	$0.551738\pi$
$644$	6.60440	+	20.3262i	0.260250	+	0.800966i
$645$		0			0
$646$	−5.45085	−	7.50245i	−0.214461	−	0.295180i
$647$	10.9443	−	33.6830i	0.430264	−	1.32422i	−0.467599	−	0.883941i	$-0.654881\pi$
$647$	10.9443	−	33.6830i	0.430264	−	1.32422i	0.897863	−	0.440275i	$-0.145119\pi$
$648$	−27.5276	+	3.07768i	−1.08139	+	0.120903i
$649$	−10.5729	−	4.56352i	−0.415025	−	0.179134i
$650$		0			0
$651$	25.6378	+	20.6909i	1.00482	+	0.810941i
$652$	−5.73910	−	7.89919i	−0.224760	−	0.309356i
$653$	29.6803	+	21.5640i	1.16148	+	0.843866i	0.989965	−	0.141316i	$-0.0451332\pi$
$653$	29.6803	+	21.5640i	1.16148	+	0.843866i	0.171517	+	0.985181i	$0.445133\pi$
$654$	34.0322	+	1.72707i	1.33076	+	0.0675336i
$655$		0			0
$656$	5.93085	+	4.30902i	0.231561	+	0.168239i
$657$	9.18562	+	0.934712i	0.358365	+	0.0364666i
$658$	−25.9030	−	8.41641i	−1.00981	−	0.328106i
$659$	44.6467			1.73919			0.869593	−	0.493769i	$-0.164381\pi$
$659$	44.6467			1.73919			0.869593	+	0.493769i	$0.164381\pi$
$660$		0			0
$661$	37.8541			1.47235			0.736177	−	0.676789i	$-0.236629\pi$
$661$	37.8541			1.47235			0.736177	+	0.676789i	$0.236629\pi$
$662$	−28.0902	−	9.12705i	−1.09176	−	0.354733i
$663$		0			0
$664$	−1.38197	−	1.00406i	−0.0536307	−	0.0389650i
$665$		0			0
$666$	12.3985	−	28.0974i	0.480431	−	1.08875i
$667$	−71.2030	−	51.7320i	−2.75699	−	2.00307i
$668$	−5.75329	−	7.91872i	−0.222601	−	0.306385i
$669$	−7.13838	+	8.84506i	−0.275986	+	0.341970i
$670$		0			0
$671$	13.1558	+	22.1976i	0.507874	+	0.856927i
$672$	20.6525	+	7.88854i	0.796687	+	0.304307i
$673$	3.18368	−	9.79837i	0.122722	−	0.377700i	−0.870757	−	0.491713i	$-0.836371\pi$
$673$	3.18368	−	9.79837i	0.122722	−	0.377700i	0.993479	+	0.114014i	$0.0363708\pi$
$674$	1.81636	+	2.50000i	0.0699634	+	0.0962964i
$675$		0			0
$676$	−2.48278	−	7.64121i	−0.0954915	−	0.293893i
$677$	−43.0517	+	13.9883i	−1.65461	+	0.537615i	−0.979732	−	0.200314i	$-0.935804\pi$
$677$	−43.0517	+	13.9883i	−1.65461	+	0.537615i	−0.674878	+	0.737929i	$0.735804\pi$
$678$	−6.08387	−	9.33447i	−0.233650	−	0.358488i
$679$	−38.0132	−	52.3206i	−1.45881	−	2.00788i
$680$		0			0
$681$	−30.1563	−	11.5187i	−1.15559	−	0.441397i
$682$	17.8986	+	7.72542i	0.685371	+	0.295822i
$683$	−44.0000			−1.68361			−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000			−1.68361			−0.841807	+	0.539779i	$0.818508\pi$
$684$	−5.06163	−	8.70035i	−0.193536	−	0.332666i
$685$		0			0
$686$	1.24108	−	1.70820i	0.0473848	−	0.0652195i
$687$	28.5535	+	1.44903i	1.08938	+	0.0552841i
$688$	2.46965	+	7.60081i	0.0941547	+	0.289778i
$689$		0			0
$690$		0			0
$691$	−15.5623	+	47.8959i	−0.592018	+	1.82204i	−0.0229755	+	0.999736i	$0.507314\pi$
$691$	−15.5623	+	47.8959i	−0.592018	+	1.82204i	−0.569043	+	0.822308i	$0.692686\pi$
$692$			13.9353i			0.529742i
$693$	−4.51035	−	37.5819i	−0.171334	−	1.42762i
$694$	36.1803			1.37339
$695$		0			0
$696$	−49.8315	+	13.4408i	−1.88886	+	0.509470i
$697$	−2.62866	+	3.61803i	−0.0995674	+	0.137043i
$698$	−1.24265	−	3.82447i	−0.0470348	−	0.144758i
$699$	0.515989	−	10.1677i	0.0195165	−	0.384576i
$700$		0			0
$701$	17.4293	−	12.6631i	0.658295	−	0.478279i	−0.207792	−	0.978173i	$-0.566628\pi$
$701$	17.4293	−	12.6631i	0.658295	−	0.478279i	0.866087	+	0.499894i	$0.166628\pi$
$702$		0			0
$703$	47.2753			1.78302
$704$	28.7562	+	2.69098i	1.08379	+	0.101420i
$705$		0			0
$706$	−37.2984	−	12.1190i	−1.40374	−	0.456104i
$707$	−27.5623	+	20.0252i	−1.03659	+	0.753125i
$708$	−2.02947	−	3.11382i	−0.0762723	−	0.117024i
$709$	9.48936	+	29.2052i	0.356380	+	1.09683i	0.955205	+	0.295945i	$0.0956347\pi$
$709$	9.48936	+	29.2052i	0.356380	+	1.09683i	−0.598825	+	0.800880i	$0.704365\pi$
$710$		0			0
$711$	12.4721	−	2.69421i	0.467740	−	0.101041i
$712$	−14.5761	+	10.5902i	−0.546263	+	0.396883i
$713$	−14.0451	+	43.2263i	−0.525993	+	1.61884i
$714$	4.01623	−	10.5146i	0.150304	−	0.393500i
$715$		0			0
$716$		−	2.03444i		−	0.0760307i
$717$	−14.0294	−	11.3223i	−0.523936	−	0.422841i
$718$	0.739054	+	1.01722i	0.0275813	+	0.0379623i
$719$	9.31881	−	12.8262i	0.347533	−	0.478338i	−0.599090	−	0.800682i	$-0.704471\pi$
$719$	9.31881	−	12.8262i	0.347533	−	0.478338i	0.946623	+	0.322344i	$0.104471\pi$
$720$		0			0
$721$	−29.4721	+	9.57608i	−1.09760	+	0.356632i
$722$	−7.23607	+	9.95959i	−0.269299	+	0.370658i
$723$	16.4780	−	4.44453i	0.612825	−	0.165294i
$724$	−3.09017	+	9.51057i	−0.114845	+	0.353457i
$725$		0			0
$726$	−8.53601	−	20.7072i	−0.316801	−	0.768518i
$727$			0.0344419i			0.00127738i	1.00000		0.000638689i	$0.000203301\pi$
$727$			0.0344419i			0.00127738i	−1.00000		0.000638689i	$0.999797\pi$
$728$		0			0
$729$	0.268157	+	26.9987i	0.00993173	+	0.999951i
$730$		0			0
$731$	−4.63677	+	1.50658i	−0.171497	+	0.0557228i
$732$	−0.422096	+	8.31749i	−0.0156011	+	0.307423i
$733$	28.0297	+	20.3647i	1.03530	+	0.752189i	0.969362	−	0.245635i	$-0.0789964\pi$
$733$	28.0297	+	20.3647i	1.03530	+	0.752189i	0.0659369	+	0.997824i	$0.478996\pi$
$734$	−11.9147	+	8.65654i	−0.439780	+	0.319519i
$735$		0			0
$736$			30.4993i			1.12422i
$737$	−10.7639	+	2.41665i	−0.396495	+	0.0890186i
$738$	7.23607	−	8.09017i	0.266363	−	0.297803i
$739$	−27.0344	−	8.78402i	−0.994478	−	0.323125i	−0.233821	−	0.972280i	$-0.575123\pi$
$739$	−27.0344	−	8.78402i	−0.994478	−	0.323125i	−0.760657	+	0.649154i	$0.775123\pi$
$740$		0			0
$741$		0			0
$742$	−22.8909	+	7.43769i	−0.840350	+	0.273046i
$743$	11.0172	−	3.57971i	0.404183	−	0.131327i	−0.0998686	−	0.995001i	$-0.531842\pi$
$743$	11.0172	−	3.57971i	0.404183	−	0.131327i	0.504051	+	0.863674i	$0.331842\pi$
$744$	14.5535	+	22.3295i	0.533558	+	0.818638i
$745$		0			0
$746$	−5.18407	−	1.68441i	−0.189802	−	0.0616705i
$747$	−1.11006	+	1.24108i	−0.0406149	+	0.0454088i
$748$	−0.277515	+	2.96556i	−0.0101469	+	0.108432i
$749$		−	21.7082i		−	0.793201i
$750$		0			0
$751$	6.94427	−	5.04531i	0.253400	−	0.184106i	−0.453832	−	0.891087i	$-0.649943\pi$
$751$	6.94427	−	5.04531i	0.253400	−	0.184106i	0.707232	+	0.706981i	$0.249943\pi$
$752$	−11.7361	−	8.52675i	−0.427970	−	0.310939i
$753$	0.970530	−	19.1245i	0.0353681	−	0.696935i
$754$		0			0
$755$		0			0
$756$	5.49223	−	10.9127i	0.199750	−	0.396892i
$757$	19.3642	+	6.29180i	0.703802	+	0.228679i	0.638986	−	0.769218i	$-0.279354\pi$
$757$	19.3642	+	6.29180i	0.703802	+	0.228679i	0.0648159	+	0.997897i	$0.479354\pi$
$758$		−	15.6254i		−	0.567542i
$759$	46.2138	−	24.3129i	1.67745	−	0.882503i
$760$		0			0
$761$	−5.29007	+	16.2812i	−0.191765	+	0.590191i	0.808234	+	0.588861i	$0.200423\pi$
$761$	−5.29007	+	16.2812i	−0.191765	+	0.590191i	−0.999999	+	0.00133034i	$0.999577\pi$
$762$	4.95927	−	1.33763i	0.179655	−	0.0484574i
$763$	−37.4217	+	51.5066i	−1.35476	+	1.86466i
$764$	−8.36775	+	2.71885i	−0.302735	+	0.0983644i
$765$		0			0
$766$	−6.21885	+	8.55951i	−0.224696	+	0.309268i
$767$		0			0
$768$	17.8868	+	14.4355i	0.645433	+	0.520895i
$769$			40.1814i			1.44898i	0.689286	+	0.724489i	$0.257924\pi$
$769$			40.1814i			1.44898i	−0.689286	+	0.724489i	$0.742076\pi$
$770$		0			0
$771$	15.1459	−	39.6525i	0.545466	−	1.42805i
$772$	0.640786	−	1.97214i	0.0230624	−	0.0709787i
$773$	−26.4894	+	19.2456i	−0.952756	+	0.692218i	−0.951457	−	0.307781i	$-0.900413\pi$
$773$	−26.4894	+	19.2456i	−0.952756	+	0.692218i	−0.00129886	+	0.999999i	$0.500413\pi$
$774$	11.5660	−	2.49849i	0.415732	−	0.0898062i
$775$		0			0
$776$	−16.1680	−	49.7599i	−0.580396	−	1.78628i
$777$	31.3306	+	48.0706i	1.12398	+	1.72452i
$778$	18.4661	−	13.4164i	0.662042	−	0.481002i
$779$	15.8904	+	5.16312i	0.569334	+	0.184988i
$780$		0			0
$781$	−2.88854	−	4.87380i	−0.103360	−	0.174398i
$782$	15.5279			0.555275
$783$	8.11681	+	49.6505i	0.290071	+	1.77436i
$784$	14.3992	−	10.4616i	0.514257	−	0.373629i
$785$		0			0
$786$	1.01011	−	19.9044i	0.0360294	−	0.709965i
$787$	8.53926	+	26.2812i	0.304392	+	0.936822i	0.979903	+	0.199473i	$0.0639229\pi$
$787$	8.53926	+	26.2812i	0.304392	+	0.936822i	−0.675512	+	0.737349i	$0.736077\pi$
$788$	−0.388544	+	0.534785i	−0.0138413	+	0.0190509i
$789$	−23.7680	+	6.41080i	−0.846162	+	0.228230i
$790$		0			0
$791$	20.8172			0.740176
$792$	5.92511	−	30.0439i	0.210540	−	1.06756i
$793$		0			0
$794$	3.40820	−	10.4894i	0.120952	−	0.372253i
$795$		0			0
$796$	−5.69098	−	4.13474i	−0.201712	−	0.146552i
$797$	−4.87132	−	14.9924i	−0.172551	−	0.531058i	0.826962	−	0.562258i	$-0.190067\pi$
$797$	−4.87132	−	14.9924i	−0.172551	−	0.531058i	−0.999513	+	0.0312000i	$0.990067\pi$
$798$	−41.9974	−	2.13129i	−1.48669	−	0.0754468i
$799$	5.20163	−	7.15942i	0.184020	−	0.253282i
$800$		0			0
$801$	8.83146	+	15.1802i	0.312044	+	0.536368i
$802$	19.7727			0.698198
$803$	−4.04508	+	9.37181i	−0.142748	+	0.330724i
$804$	−3.32624	−	1.27051i	−0.117307	−	0.0448074i
$805$		0			0
$806$		0			0
$807$	15.6637	+	24.0328i	0.551389	+	0.845996i
$808$	−26.2133	+	8.51722i	−0.922181	+	0.299635i
$809$	0.244758	+	0.753289i	0.00860525	+	0.0264842i	0.955267	−	0.295745i	$-0.0955678\pi$
$809$	0.244758	+	0.753289i	0.00860525	+	0.0264842i	−0.946662	+	0.322229i	$0.895568\pi$
$810$		0			0
$811$	−11.7705	−	16.2007i	−0.413319	−	0.568884i	0.550705	−	0.834700i	$-0.314359\pi$
$811$	−11.7705	−	16.2007i	−0.413319	−	0.568884i	−0.964024	+	0.265816i	$0.914359\pi$
$812$	7.03444	−	21.6498i	0.246861	−	0.759759i
$813$	32.6789	+	12.4822i	1.14610	+	0.437772i
$814$	25.4894	+	22.4293i	0.893401	+	0.786148i
$815$		0			0
$816$	3.76504	−	4.66521i	0.131803	−	0.163315i
$817$	10.7064	+	14.7361i	0.374569	+	0.515550i
$818$	−34.9615	−	25.4010i	−1.22240	−	0.888126i
$819$		0			0
$820$		0			0
$821$	3.38795	+	2.46149i	0.118240	+	0.0859067i	0.645334	−	0.763901i	$-0.276718\pi$
$821$	3.38795	+	2.46149i	0.118240	+	0.0859067i	−0.527094	+	0.849807i	$0.676718\pi$
$822$	−9.25582	+	2.49652i	−0.322834	+	0.0870761i
$823$	−5.82485	−	1.89261i	−0.203042	−	0.0659722i	0.205731	−	0.978609i	$-0.434043\pi$
$823$	−5.82485	−	1.89261i	−0.203042	−	0.0659722i	−0.408772	+	0.912636i	$0.634043\pi$
$824$	−25.0705			−0.873372
$825$		0			0
$826$	−15.5279			−0.540283
$827$	23.9443	+	7.77997i	0.832624	+	0.270536i	0.694150	−	0.719830i	$-0.255780\pi$
$827$	23.9443	+	7.77997i	0.832624	+	0.270536i	0.138474	+	0.990366i	$0.455780\pi$
$828$	16.7675	+	1.70623i	0.582711	+	0.0592957i
$829$	10.0451	+	7.29818i	0.348880	+	0.253476i	0.748399	−	0.663249i	$-0.230823\pi$
$829$	10.0451	+	7.29818i	0.348880	+	0.253476i	−0.399519	+	0.916725i	$0.630823\pi$
$830$		0			0
$831$	−45.6978	−	2.31907i	−1.58524	−	0.0804478i
$832$		0			0
$833$	6.38197	+	8.78402i	0.221122	+	0.304348i
$834$	−7.17902	−	5.79380i	−0.248589	−	0.200623i
$835$		0			0
$836$	10.8576	−	2.43769i	0.375520	−	0.0843094i
$837$	23.0902	−	11.9098i	0.798113	−	0.411664i
$838$	11.1804	−	34.4098i	0.386222	−	1.18867i
$839$	21.9196	+	30.1697i	0.756748	+	1.04157i	0.997478	+	0.0709815i	$0.0226131\pi$
$839$	21.9196	+	30.1697i	0.756748	+	1.04157i	−0.240730	+	0.970592i	$0.577387\pi$
$840$		0			0
$841$	20.0066	+	61.5739i	0.689882	+	2.12324i
$842$	17.7254	−	5.75934i	0.610858	−	0.198480i
$843$	3.56545	−	2.32383i	0.122801	−	0.0800370i
$844$	0.628677	+	0.865300i	0.0216400	+	0.0297848i
$845$		0			0
$846$	−14.3188	+	16.0090i	−0.492292	+	0.550399i
$847$	41.1199	+	7.76393i	1.41290	+	0.266772i
$848$	−12.8197			−0.440229
$849$	14.7775	+	11.9261i	0.507161	+	0.409303i
$850$		0			0
$851$	−46.5285	+	64.0410i	−1.59498	+	2.19530i
$852$	0.0926774	−	1.82622i	0.00317507	−	0.0625654i
$853$	9.28605	+	28.5795i	0.317948	+	0.978544i	0.974524	+	0.224284i	$0.0720043\pi$
$853$	9.28605	+	28.5795i	0.317948	+	0.978544i	−0.656575	+	0.754260i	$0.727996\pi$
$854$	28.1482	+	20.4508i	0.963211	+	0.699814i
$855$		0			0
$856$	5.42705	−	16.7027i	0.185493	−	0.570888i
$857$			23.1684i			0.791417i	0.918376	+	0.395708i	$0.129501\pi$
$857$			23.1684i			0.791417i	−0.918376	+	0.395708i	$0.870499\pi$
$858$		0			0
$859$	−45.6312			−1.55692			−0.778458	−	0.627697i	$-0.783998\pi$
$859$	−45.6312			−1.55692			−0.778458	+	0.627697i	$0.783998\pi$
$860$		0			0
$861$	5.28106	+	19.5795i	0.179978	+	0.667267i
$862$	21.2663	−	29.2705i	0.724332	−	0.996958i
$863$	5.40983	+	16.6497i	0.184153	+	0.566764i	0.999933	−	0.0115985i	$-0.00369199\pi$
$863$	5.40983	+	16.6497i	0.184153	+	0.566764i	−0.815780	+	0.578362i	$0.803692\pi$
$864$	12.2664	−	12.3889i	0.417312	−	0.421477i
$865$		0			0
$866$	−20.0049	+	14.5344i	−0.679796	+	0.493900i
$867$	−20.0677	−	16.1955i	−0.681533	−	0.550029i
$868$	−11.7557			−0.399015
$869$	−1.31433	+	14.0451i	−0.0445855	+	0.476447i
$870$		0			0
$871$		0			0
$872$	−41.6697	+	30.2748i	−1.41111	+	1.02523i
$873$	−49.8502	+	10.7686i	−1.68717	+	0.364462i
$874$	−17.9271	−	55.1738i	−0.606392	−	1.86628i
$875$		0			0
$876$	−2.76007	+	1.79892i	−0.0932542	+	0.0607797i
$877$	7.88597	−	5.72949i	0.266290	−	0.193471i	−0.446625	−	0.894721i	$-0.647374\pi$
$877$	7.88597	−	5.72949i	0.266290	−	0.193471i	0.712916	+	0.701250i	$0.247374\pi$
$878$	−0.954915	+	2.93893i	−0.0322268	+	0.0991840i
$879$	18.7436	+	7.15942i	0.632206	+	0.241481i
$880$		0			0
$881$		−	34.9230i		−	1.17659i	−0.808648	−	0.588293i	$-0.799800\pi$
$881$		−	34.9230i		−	1.17659i	0.808648	−	0.588293i	$-0.200200\pi$
$882$	−13.2515	−	22.7778i	−0.446202	−	0.766969i
$883$	−9.85359	−	13.5623i	−0.331600	−	0.456408i	0.610365	−	0.792121i	$-0.291023\pi$
$883$	−9.85359	−	13.5623i	−0.331600	−	0.456408i	−0.941964	+	0.335713i	$0.891023\pi$
$884$		0			0
$885$		0			0
$886$	3.84346	−	1.24882i	0.129124	−	0.0419548i
$887$	24.0451	−	33.0952i	0.807355	−	1.11123i	−0.184371	−	0.982857i	$-0.559025\pi$
$887$	24.0451	−	33.0952i	0.807355	−	1.11123i	0.991726	−	0.128372i	$-0.0409752\pi$
$888$	12.0888	+	44.8192i	0.405674	+	1.50403i
$889$	−2.96556	+	9.12705i	−0.0994616	+	0.306111i
$890$		0			0
$891$	−28.5504	−	8.71062i	−0.956474	−	0.291817i
$892$		−	4.05573i		−	0.135796i
$893$	−31.4443	−	10.2169i	−1.05224	−	0.341894i
$894$	−40.5873	+	10.9474i	−1.35744	+	0.366135i
$895$		0			0
$896$	12.7598	−	4.14590i	0.426274	−	0.138505i
$897$		0			0
$898$	−14.5761	−	10.5902i	−0.486411	−	0.353399i
$899$	39.1648	−	28.4549i	1.30622	−	0.949025i
$900$		0			0
$901$		−	7.82045i		−	0.260537i
$902$	6.11803	+	10.3229i	0.203708	+	0.343714i
$903$	−7.88854	+	20.6525i	−0.262514	+	0.687271i
$904$	16.0172	+	5.20431i	0.532725	+	0.173093i
$905$		0			0
$906$	−24.4254	+	15.9196i	−0.811478	+	0.528892i
$907$	12.9188	−	4.19756i	0.428961	−	0.139378i	−0.0865762	−	0.996245i	$-0.527593\pi$
$907$	12.9188	−	4.19756i	0.428961	−	0.139378i	0.515537	+	0.856868i	$0.327593\pi$
$908$	10.9549	−	3.55947i	0.363552	−	0.118125i
$909$	5.67285	+	26.2609i	0.188157	+	0.871018i
$910$		0			0
$911$	5.98385	+	1.94427i	0.198254	+	0.0644166i	0.406461	−	0.913668i	$-0.366763\pi$
$911$	5.98385	+	1.94427i	0.198254	+	0.0644166i	−0.208207	+	0.978085i	$0.566763\pi$
$912$	−20.9232	−	7.99197i	−0.692838	−	0.264640i
$913$	−0.938545	−	1.58359i	−0.0310613	−	0.0524093i
$914$			16.3820i			0.541867i
$915$		0			0
$916$	−8.25329	+	5.99637i	−0.272696	+	0.198125i
$917$	30.1246	+	21.8868i	0.994802	+	0.722766i
$918$	−6.30743	−	6.24510i	−0.208176	−	0.206119i
$919$	−4.83688	+	1.57160i	−0.159554	+	0.0518422i	−0.387705	−	0.921784i	$-0.626732\pi$
$919$	−4.83688	+	1.57160i	−0.159554	+	0.0518422i	0.228151	+	0.973626i	$0.426732\pi$
$920$		0			0
$921$	11.9341	+	44.2455i	0.393241	+	1.45794i
$922$	26.3318	+	8.55573i	0.867192	+	0.281768i
$923$		0			0
$924$	9.67436	+	9.42477i	0.318263	+	0.310052i
$925$		0			0
$926$	8.02472	−	24.6976i	0.263709	−	0.811612i
$927$	−2.47396	+	24.3121i	−0.0812555	+	0.798516i
$928$	19.0944	−	26.2812i	0.626804	−	0.862721i
$929$	−42.2753	+	13.7361i	−1.38701	+	0.450666i	−0.904966	−	0.425483i	$-0.860104\pi$
$929$	−42.2753	+	13.7361i	−1.38701	+	0.450666i	−0.482040	+	0.876149i	$0.660104\pi$
$930$		0			0
$931$	23.8435	−	32.8177i	0.781438	−	1.07556i
$932$	2.13525	+	2.93893i	0.0699426	+	0.0962677i
$933$	−18.8847	+	23.3997i	−0.618257	+	0.766073i
$934$		−	34.3035i		−	1.12245i
$935$		0			0
$936$		0			0
$937$	−6.01661	+	18.5172i	−0.196554	+	0.604931i	0.803401	+	0.595439i	$0.203022\pi$
$937$	−6.01661	+	18.5172i	−0.196554	+	0.604931i	−0.999955	+	0.00949271i	$0.996978\pi$
$938$	−12.0344	+	8.74353i	−0.392938	+	0.285486i
$939$	2.06205	+	3.16380i	0.0672924	+	0.103247i
$940$		0			0
$941$	0.661030	+	2.03444i	0.0215490	+	0.0663209i	0.961253	−	0.275669i	$-0.0888993\pi$
$941$	0.661030	+	2.03444i	0.0215490	+	0.0663209i	−0.939704	+	0.341990i	$0.888899\pi$
$942$	29.4604	−	19.2012i	0.959871	−	0.625609i
$943$	−22.6336	+	16.4443i	−0.737051	+	0.535499i
$944$	−7.86572	−	2.55573i	−0.256007	−	0.0831819i
$945$		0			0
$946$	−1.21885	+	13.0248i	−0.0396281	+	0.423472i
$947$	5.68692			0.184800			0.0924000	−	0.995722i	$-0.470546\pi$
$947$	5.68692			0.184800			0.0924000	+	0.995722i	$0.470546\pi$
$948$	−2.85941	+	3.54306i	−0.0928694	+	0.115073i
$949$		0			0
$950$		0			0
$951$	32.0500	+	1.62647i	1.03929	+	0.0527420i
$952$	5.25731	+	16.1803i	0.170390	+	0.524408i
$953$	15.1869	−	20.9030i	0.491953	−	0.677115i	−0.488794	−	0.872399i	$-0.662563\pi$
$953$	15.1869	−	20.9030i	0.491953	−	0.677115i	0.980747	+	0.195285i	$0.0625631\pi$
$954$	−1.92151	+	18.8831i	−0.0622113	+	0.611364i
$955$		0			0
$956$	6.43288			0.208054
$957$	−55.0435	−	7.98219i	−1.77931	−	0.258028i
$958$		−	35.7771i		−	1.15591i
$959$	5.53483	−	17.0344i	0.178729	−	0.550071i
$960$		0			0
$961$	4.85410	+	3.52671i	0.156584	+	0.113765i
$962$		0			0
$963$	−15.6620	−	6.91112i	−0.504700	−	0.222708i
$964$	−3.57953	+	4.92680i	−0.115289	+	0.158681i
$965$		0			0
$966$	44.2212	−	54.7938i	1.42279	−	1.76296i
$967$	39.7729			1.27901			0.639504	−	0.768787i	$-0.279140\pi$
$967$	39.7729			1.27901			0.639504	+	0.768787i	$0.279140\pi$
$968$	29.6976	+	16.2537i	0.954516	+	0.522414i
$969$	4.87539	−	12.7639i	0.156620	−	0.410037i
$970$		0			0
$971$	−1.37984	−	1.89919i	−0.0442812	−	0.0609478i	0.786302	−	0.617842i	$-0.211993\pi$
$971$	−1.37984	−	1.89919i	−0.0442812	−	0.0609478i	−0.830583	+	0.556894i	$0.811993\pi$
$972$	−6.12476	−	7.43674i	−0.196452	−	0.238534i
$973$	16.3925	−	5.32624i	0.525519	−	0.170751i
$974$	−0.726543	−	2.23607i	−0.0232799	−	0.0716482i
$975$		0			0
$976$	10.8926	+	14.9924i	0.348664	+	0.479895i
$977$	−12.2082	+	37.5730i	−0.390575	+	1.20207i	0.541779	+	0.840521i	$0.317751\pi$
$977$	−12.2082	+	37.5730i	−0.390575	+	1.20207i	−0.932354	+	0.361546i	$0.882249\pi$
$978$	−11.4782	+	30.0503i	−0.367032	+	0.960902i
$979$	−18.9443	+	4.25325i	−0.605462	+	0.135935i
$980$		0			0
$981$	25.2471	+	43.3968i	0.806077	+	1.38555i
$982$	−8.81678	−	12.1353i	−0.281355	−	0.387252i
$983$	−23.1353	−	16.8087i	−0.737900	−	0.536116i	0.154153	−	0.988047i	$-0.450735\pi$
$983$	−23.1353	−	16.8087i	−0.737900	−	0.536116i	−0.892053	+	0.451931i	$0.850735\pi$
$984$	−0.831514	+	16.3851i	−0.0265077	+	0.522339i
$985$		0			0
$986$	−13.3803	−	9.72136i	−0.426116	−	0.309591i
$987$	−10.4503	−	38.7442i	−0.332635	−	1.23324i
$988$		0			0
$989$	−30.4993			−0.969822
$990$		0			0
$991$	−46.8328			−1.48769			−0.743847	−	0.668350i	$-0.767001\pi$
$991$	−46.8328			−1.48769			−0.743847	+	0.668350i	$0.767001\pi$
$992$	−15.9549	−	5.18407i	−0.506569	−	0.164594i
$993$	−11.3326	−	42.0156i	−0.359630	−	1.33332i
$994$	−6.18034	−	4.49028i	−0.196028	−	0.142423i
$995$		0			0
$996$	0.0301127	−	0.593376i	0.000954157	−	0.0188018i
$997$	−1.86936	−	1.35817i	−0.0592031	−	0.0430136i	0.557790	−	0.829982i	$-0.311649\pi$
$997$	−1.86936	−	1.35817i	−0.0592031	−	0.0430136i	−0.616993	+	0.786968i	$0.711649\pi$
$998$	−6.54508	−	9.00854i	−0.207181	−	0.285160i
$999$	44.6564	−	7.30038i	1.41286	−	0.230974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bs.b.299.2		8
3.2	odd	2		825.2.bs.c.299.2		8
5.2	odd	4		825.2.bi.c.101.1	yes	8
5.3	odd	4		825.2.bi.a.101.2	yes	8
5.4	even	2		825.2.bs.c.299.1		8
11.6	odd	10	inner	825.2.bs.b.149.1		8
15.2	even	4		825.2.bi.c.101.2	yes	8
15.8	even	4		825.2.bi.a.101.1	✓	8
15.14	odd	2	inner	825.2.bs.b.299.1		8
33.17	even	10		825.2.bs.c.149.1		8
55.17	even	20		825.2.bi.c.776.2	yes	8
55.28	even	20		825.2.bi.a.776.1	yes	8
55.39	odd	10		825.2.bs.c.149.2		8
165.17	odd	20		825.2.bi.c.776.1	yes	8
165.83	odd	20		825.2.bi.a.776.2	yes	8
165.149	even	10	inner	825.2.bs.b.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.bi.a.101.1	✓	8	15.8	even	4
825.2.bi.a.101.2	yes	8	5.3	odd	4
825.2.bi.a.776.1	yes	8	55.28	even	20
825.2.bi.a.776.2	yes	8	165.83	odd	20
825.2.bi.c.101.1	yes	8	5.2	odd	4
825.2.bi.c.101.2	yes	8	15.2	even	4
825.2.bi.c.776.1	yes	8	165.17	odd	20
825.2.bi.c.776.2	yes	8	55.17	even	20
825.2.bs.b.149.1		8	11.6	odd	10	inner
825.2.bs.b.149.2		8	165.149	even	10	inner
825.2.bs.b.299.1		8	15.14	odd	2	inner
825.2.bs.b.299.2		8	1.1	even	1	trivial
825.2.bs.c.149.1		8	33.17	even	10
825.2.bs.c.149.2		8	55.39	odd	10
825.2.bs.c.299.1		8	5.4	even	2
825.2.bs.c.299.2		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bs (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11803 + 0.363271i) q^{2} +(0.451057 + 1.67229i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.103198 + 2.03353i) q^{6} +(-3.07768 - 2.23607i) q^{7} +(-1.80902 - 2.48990i) q^{8} +(-2.59310 + 1.50859i) q^{9} +O(q^{10})\)	\(q+(1.11803 + 0.363271i) q^{2} +(0.451057 + 1.67229i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.103198 + 2.03353i) q^{6} +(-3.07768 - 2.23607i) q^{7} +(-1.80902 - 2.48990i) q^{8} +(-2.59310 + 1.50859i) q^{9} +(-0.726543 - 3.23607i) q^{11} +(0.381966 - 1.00000i) q^{12} +(-2.62866 - 3.61803i) q^{14} +(-0.736068 - 2.26538i) q^{16} +(1.38197 - 0.449028i) q^{17} +(-3.44720 + 0.744661i) q^{18} +(-3.19098 - 4.39201i) q^{19} +(2.35114 - 6.15537i) q^{21} +(0.363271 - 3.88197i) q^{22} +9.09017 q^{23} +(3.34786 - 4.14828i) q^{24} +(-3.69244 - 3.65594i) q^{27} +(0.726543 + 2.23607i) q^{28} +(-7.83297 - 5.69098i) q^{29} +(-1.54508 + 4.75528i) q^{31} +3.35520i q^{32} +(5.08393 - 2.67464i) q^{33} +1.70820 q^{34} +(1.84458 + 0.187701i) q^{36} +(-5.11855 + 7.04508i) q^{37} +(-1.97214 - 6.06961i) q^{38} +(-2.48990 + 1.80902i) q^{41} +(4.86472 - 6.02781i) q^{42} -3.35520 q^{43} +(-0.812299 + 1.88197i) q^{44} +(10.1631 + 3.30220i) q^{46} +(4.92705 - 3.57971i) q^{47} +(3.45637 - 2.25273i) q^{48} +(2.30902 + 7.10642i) q^{49} +(1.37425 + 2.10851i) q^{51} +(1.66312 - 5.11855i) q^{53} +(-2.80017 - 5.42882i) q^{54} +11.7082i q^{56} +(5.90540 - 7.31729i) q^{57} +(-6.69015 - 9.20820i) q^{58} +(2.04087 - 2.80902i) q^{59} +(-7.39919 + 2.40414i) q^{61} +(-3.45492 + 4.75528i) q^{62} +(11.3540 + 1.15537i) q^{63} +(-2.69098 + 8.28199i) q^{64} +(6.65562 - 1.14349i) q^{66} -3.32624i q^{67} +(-0.854102 - 0.277515i) q^{68} +(4.10018 + 15.2014i) q^{69} +(1.62460 - 0.527864i) q^{71} +(8.44720 + 3.72747i) q^{72} +(-2.48990 - 1.80902i) q^{73} +(-8.28199 + 6.01722i) q^{74} +3.35520i q^{76} +(-5.00000 + 11.5842i) q^{77} +(-4.04508 - 1.31433i) q^{79} +(4.44829 - 7.82385i) q^{81} +(-3.44095 + 1.11803i) q^{82} +(0.527864 - 0.171513i) q^{83} +(-3.41164 + 2.22358i) q^{84} +(-3.75123 - 1.21885i) q^{86} +(5.98385 - 15.6659i) q^{87} +(-6.74315 + 7.66312i) q^{88} -5.85410i q^{89} +(-4.54508 - 3.30220i) q^{92} +(-8.64912 - 0.438926i) q^{93} +(6.80902 - 2.21238i) q^{94} +(-5.61086 + 1.51338i) q^{96} +(16.1680 + 5.25329i) q^{97} +8.78402i q^{98} +(6.76590 + 7.29538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{4} - 10 q^{6} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 4 * q^4 - 10 * q^6 - 10 * q^8 - 10 * q^9	\( 8 q - 4 q^{3} - 4 q^{4} - 10 q^{6} - 10 q^{8} - 10 q^{9} + 12 q^{12} + 12 q^{16} + 20 q^{17} + 10 q^{18} - 30 q^{19} + 28 q^{23} + 10 q^{24} + 2 q^{27} + 10 q^{31} + 6 q^{33} - 40 q^{34} + 20 q^{38} + 50 q^{46} + 26 q^{47} + 14 q^{48} + 14 q^{49} - 40 q^{51} - 18 q^{53} + 30 q^{57} - 10 q^{61} - 50 q^{62} - 26 q^{64} + 30 q^{66} + 20 q^{68} - 14 q^{69} + 30 q^{72} - 40 q^{77} - 10 q^{79} - 2 q^{81} + 40 q^{83} - 14 q^{92} - 30 q^{93} + 50 q^{94} - 50 q^{96} + 4 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^4 - 10 * q^6 - 10 * q^8 - 10 * q^9 + 12 * q^12 + 12 * q^16 + 20 * q^17 + 10 * q^18 - 30 * q^19 + 28 * q^23 + 10 * q^24 + 2 * q^27 + 10 * q^31 + 6 * q^33 - 40 * q^34 + 20 * q^38 + 50 * q^46 + 26 * q^47 + 14 * q^48 + 14 * q^49 - 40 * q^51 - 18 * q^53 + 30 * q^57 - 10 * q^61 - 50 * q^62 - 26 * q^64 + 30 * q^66 + 20 * q^68 - 14 * q^69 + 30 * q^72 - 40 * q^77 - 10 * q^79 - 2 * q^81 + 40 * q^83 - 14 * q^92 - 30 * q^93 + 50 * q^94 - 50 * q^96 + 4 * q^99

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