LMFDB - Embedded newform 525.2.t.i.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 $ x^20 - 3x^19 + 8x^18 - 15x^17 + 18x^16 - 45x^15 + 59x^14 - 147x^13 + 271x^12 - 330x^11 + 879x^10 - 990x^9 + 2439x^8 - 3969x^7 + 4779x^6 - 10935x^5 + 13122x^4 - 32805x^3 + 52488x^2 - 59049*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.2
Root			$0.742502 + 1.56483i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.i.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94891 - 1.12521i) q^{2} +(-0.983931 - 1.42544i) q^{3} +(1.53217 + 2.65380i) q^{4} +(0.313682 + 3.88518i) q^{6} +(1.42897 - 2.22667i) q^{7} -2.39522i q^{8} +(-1.06376 + 2.80507i) q^{9} +O(q^{10})$	\(q+(-1.94891 - 1.12521i) q^{2} +(-0.983931 - 1.42544i) q^{3} +(1.53217 + 2.65380i) q^{4} +(0.313682 + 3.88518i) q^{6} +(1.42897 - 2.22667i) q^{7} -2.39522i q^{8} +(-1.06376 + 2.80507i) q^{9} +(1.64925 - 0.952197i) q^{11} +(2.27529 - 4.79518i) q^{12} +5.07948i q^{13} +(-5.29039 + 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(2.22839 + 3.85968i) q^{17} +(5.22946 - 4.26988i) q^{18} +(3.85670 + 2.22667i) q^{19} +(-4.57999 + 0.153979i) q^{21} -4.28567 q^{22} +(2.46489 + 1.42310i) q^{23} +(-3.41425 + 2.35673i) q^{24} +(5.71546 - 9.89947i) q^{26} +(5.04513 - 1.24366i) q^{27} +(8.09857 + 0.380555i) q^{28} +8.82675i q^{29} +(4.81162 - 2.77799i) q^{31} +(-5.58785 + 3.22615i) q^{32} +(-2.98005 - 1.41402i) q^{33} -10.0296i q^{34} +(-9.07397 + 1.47484i) q^{36} +(2.32292 - 4.02342i) q^{37} +(-5.01092 - 8.67917i) q^{38} +(7.24050 - 4.99786i) q^{39} -0.250819 q^{41} +(9.09926 + 4.85334i) q^{42} -9.23735 q^{43} +(5.05389 + 2.91786i) q^{44} +(-3.20257 - 5.54701i) q^{46} +(1.53816 - 2.66417i) q^{47} +(-1.27491 + 0.102934i) q^{48} +(-2.91610 - 6.36367i) q^{49} +(3.30916 - 6.97409i) q^{51} +(-13.4799 + 7.78265i) q^{52} +(2.09711 - 1.21077i) q^{53} +(-11.2319 - 3.25301i) q^{54} +(-5.33336 - 3.42269i) q^{56} +(-0.620744 - 7.68839i) q^{57} +(9.93190 - 17.2026i) q^{58} +(-6.95983 - 12.0548i) q^{59} +(-1.51554 - 0.874995i) q^{61} -12.5032 q^{62} +(4.72588 + 6.37700i) q^{63} +13.0434 q^{64} +(4.21680 + 6.10897i) q^{66} +(4.14868 + 7.18573i) q^{67} +(-6.82855 + 11.8274i) q^{68} +(-0.396729 - 4.91379i) q^{69} +9.68436i q^{71} +(6.71876 + 2.54794i) q^{72} +(5.47076 - 3.15855i) q^{73} +(-9.05434 + 5.22752i) q^{74} +13.6466i q^{76} +(0.236503 - 5.03300i) q^{77} +(-19.7347 + 1.59334i) q^{78} +(1.59436 - 2.76150i) q^{79} +(-6.73682 - 5.96785i) q^{81} +(0.488824 + 0.282223i) q^{82} +8.98988 q^{83} +(-7.42597 - 11.9185i) q^{84} +(18.0028 + 10.3939i) q^{86} +(12.5820 - 8.68491i) q^{87} +(-2.28072 - 3.95033i) q^{88} +(5.43599 - 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} +8.72178i q^{92} +(-8.69416 - 4.12533i) q^{93} +(-5.99548 + 3.46149i) q^{94} +(10.0967 + 4.79084i) q^{96} +8.94486i q^{97} +(-1.47721 + 15.6835i) q^{98} +(0.916566 + 5.63918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) $ 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9	$ 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) $ 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9 - 21 * q^12 - 18 * q^16 + 14 * q^18 - 9 * q^21 + 20 * q^22 + 18 * q^24 - 10 * q^28 + 42 * q^31 + 12 * q^33 - 36 * q^36 + 24 * q^37 + 33 * q^42 + 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 - 84 * q^52 - 75 * q^54 + 6 * q^57 - 4 * q^58 - 90 * q^61 - 5 * q^63 - 120 * q^64 + 6 * q^66 + 20 * q^67 - 35 * q^72 - 48 * q^73 - 108 * q^78 + 46 * q^79 + 29 * q^81 + 36 * q^82 + 75 * q^84 + 69 * q^87 + 4 * q^88 - 30 * q^91 - 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.94891	−	1.12521i	−1.37809	−	0.795640i	−0.386160	−	0.922432i	$-0.626199\pi$
$2$	−1.94891	−	1.12521i	−1.37809	−	0.795640i	−0.991929	+	0.126791i	$0.959532\pi$
$3$	−0.983931	−	1.42544i	−0.568073	−	0.822978i
$3$	−0.983931	−	1.42544i	−0.568073	−	0.822978i
$4$	1.53217	+	2.65380i	0.766087	+	1.32690i
$5$		0			0
$5$		0			0
$6$	0.313682	+	3.88518i	0.128060	+	1.58612i
$7$	1.42897	−	2.22667i	0.540099	−	0.841602i
$7$	1.42897	−	2.22667i	0.540099	−	0.841602i
$8$		−	2.39522i		−	0.846839i
$9$	−1.06376	+	2.80507i	−0.354587	+	0.935023i
$10$		0			0
$11$	1.64925	−	0.952197i	0.497269	−	0.287098i	−0.230316	−	0.973116i	$-0.573976\pi$
$11$	1.64925	−	0.952197i	0.497269	−	0.287098i	0.727585	+	0.686018i	$0.240643\pi$
$12$	2.27529	−	4.79518i	0.656819	−	1.38425i
$13$			5.07948i			1.40879i	0.709806	+	0.704397i	$0.248783\pi$
$13$			5.07948i			1.40879i	−0.709806	+	0.704397i	$0.751217\pi$
$14$	−5.29039	+	2.73170i	−1.41392	+	0.730078i
$15$		0			0
$16$	0.369233	−	0.639530i	0.0923082	−	0.159882i
$17$	2.22839	+	3.85968i	0.540463	+	0.936110i	0.998877	+	0.0473710i	$0.0150843\pi$
$17$	2.22839	+	3.85968i	0.540463	+	0.936110i	−0.458414	+	0.888739i	$0.651582\pi$
$18$	5.22946	−	4.26988i	1.23259	−	1.00642i
$19$	3.85670	+	2.22667i	0.884788	+	0.510833i	0.872234	−	0.489088i	$-0.162670\pi$
$19$	3.85670	+	2.22667i	0.884788	+	0.510833i	0.0125541	+	0.999921i	$0.496004\pi$
$20$		0			0
$21$	−4.57999	+	0.153979i	−0.999435	+	0.0336010i
$22$	−4.28567			−0.913708
$23$	2.46489	+	1.42310i	0.513965	+	0.296738i	0.734462	−	0.678650i	$-0.237435\pi$
$23$	2.46489	+	1.42310i	0.513965	+	0.296738i	−0.220497	+	0.975388i	$0.570768\pi$
$24$	−3.41425	+	2.35673i	−0.696930	+	0.481066i
$25$		0			0
$26$	5.71546	−	9.89947i	1.12089	−	1.94145i
$27$	5.04513	−	1.24366i	0.970935	−	0.239343i
$28$	8.09857	+	0.380555i	1.53049	+	0.0719181i
$29$			8.82675i			1.63909i	0.573018	+	0.819543i	$0.305773\pi$
$29$			8.82675i			1.63909i	−0.573018	+	0.819543i	$0.694227\pi$
$30$		0			0
$31$	4.81162	−	2.77799i	0.864193	−	0.498942i	−0.00122124	−	0.999999i	$-0.500389\pi$
$31$	4.81162	−	2.77799i	0.864193	−	0.498942i	0.865414	+	0.501057i	$0.167055\pi$
$32$	−5.58785	+	3.22615i	−0.987802	+	0.570308i
$33$	−2.98005	−	1.41402i	−0.518761	−	0.246149i
$34$		−	10.0296i		−	1.72006i
$35$		0			0
$36$	−9.07397	+	1.47484i	−1.51233	+	0.245807i
$37$	2.32292	−	4.02342i	0.381886	−	0.661446i	−0.609446	−	0.792828i	$-0.708608\pi$
$37$	2.32292	−	4.02342i	0.381886	−	0.661446i	0.991332	+	0.131382i	$0.0419414\pi$
$38$	−5.01092	−	8.67917i	−0.812878	−	1.40795i
$39$	7.24050	−	4.99786i	1.15941	−	0.800298i
$40$		0			0
$41$	−0.250819			−0.0391713			−0.0195857	−	0.999808i	$-0.506235\pi$
$41$	−0.250819			−0.0391713			−0.0195857	+	0.999808i	$0.506235\pi$
$42$	9.09926	+	4.85334i	1.40405	+	0.748886i
$43$	−9.23735			−1.40868			−0.704341	−	0.709862i	$-0.748757\pi$
$43$	−9.23735			−1.40868			−0.704341	+	0.709862i	$0.748757\pi$
$44$	5.05389	+	2.91786i	0.761902	+	0.439885i
$45$		0			0
$46$	−3.20257	−	5.54701i	−0.472193	−	0.817863i
$47$	1.53816	−	2.66417i	0.224364	−	0.388610i	−0.731765	−	0.681557i	$-0.761303\pi$
$47$	1.53816	−	2.66417i	0.224364	−	0.388610i	0.956128	+	0.292948i	$0.0946363\pi$
$48$	−1.27491	+	0.102934i	−0.184018	+	0.0148572i
$49$	−2.91610	−	6.36367i	−0.416586	−	0.909096i
$50$		0			0
$51$	3.30916	−	6.97409i	0.463376	−	0.976568i
$52$	−13.4799	+	7.78265i	−1.86933	+	1.07926i
$53$	2.09711	−	1.21077i	0.288060	−	0.166312i	−0.349007	−	0.937120i	$-0.613481\pi$
$53$	2.09711	−	1.21077i	0.288060	−	0.166312i	0.637067	+	0.770809i	$0.280148\pi$
$54$	−11.2319	−	3.25301i	−1.52847	−	0.442679i
$55$		0			0
$56$	−5.33336	−	3.42269i	−0.712701	−	0.457377i
$57$	−0.620744	−	7.68839i	−0.0822196	−	1.01835i
$58$	9.93190	−	17.2026i	1.30412	−	2.25881i
$59$	−6.95983	−	12.0548i	−0.906093	−	1.56940i	−0.819443	−	0.573160i	$-0.805717\pi$
$59$	−6.95983	−	12.0548i	−0.906093	−	1.56940i	−0.0866494	−	0.996239i	$-0.527616\pi$
$60$		0			0
$61$	−1.51554	−	0.874995i	−0.194044	−	0.112032i	0.399830	−	0.916589i	$-0.369069\pi$
$61$	−1.51554	−	0.874995i	−0.194044	−	0.112032i	−0.593875	+	0.804558i	$0.702402\pi$
$62$	−12.5032			−1.58791
$63$	4.72588	+	6.37700i	0.595405	+	0.803426i
$64$	13.0434			1.63042
$65$		0			0
$66$	4.21680	+	6.10897i	0.519052	+	0.751962i
$67$	4.14868	+	7.18573i	0.506842	+	0.877876i	0.999969	+	0.00791862i	$0.00252060\pi$
$67$	4.14868	+	7.18573i	0.506842	+	0.877876i	−0.493127	+	0.869958i	$0.664146\pi$
$68$	−6.82855	+	11.8274i	−0.828084	+	1.43428i
$69$	−0.396729	−	4.91379i	−0.0477606	−	0.591551i
$70$		0			0
$71$			9.68436i			1.14932i	0.818392	+	0.574661i	$0.194866\pi$
$71$			9.68436i			1.14932i	−0.818392	+	0.574661i	$0.805134\pi$
$72$	6.71876	+	2.54794i	0.791814	+	0.300278i
$73$	5.47076	−	3.15855i	0.640304	−	0.369680i	−0.144427	−	0.989515i	$-0.546134\pi$
$73$	5.47076	−	3.15855i	0.640304	−	0.369680i	0.784732	+	0.619835i	$0.212801\pi$
$74$	−9.05434	+	5.22752i	−1.05255	+	0.607687i
$75$		0			0
$76$			13.6466i			1.56537i
$77$	0.236503	−	5.03300i	0.0269520	−	0.573564i
$78$	−19.7347	+	1.59334i	−2.23452	+	0.180410i
$79$	1.59436	−	2.76150i	0.179379	−	0.310694i	−0.762289	−	0.647237i	$-0.775924\pi$
$79$	1.59436	−	2.76150i	0.179379	−	0.310694i	0.941668	+	0.336543i	$0.109258\pi$
$80$		0			0
$81$	−6.73682	−	5.96785i	−0.748536	−	0.663094i
$82$	0.488824	+	0.282223i	0.0539816	+	0.0311663i
$83$	8.98988			0.986768			0.493384	−	0.869812i	$-0.335760\pi$
$83$	8.98988			0.986768			0.493384	+	0.869812i	$0.335760\pi$
$84$	−7.42597	−	11.9185i	−0.810240	−	1.30041i
$85$		0			0
$86$	18.0028	+	10.3939i	1.94129	+	1.12080i
$87$	12.5820	−	8.68491i	1.34893	−	0.931120i
$88$	−2.28072	−	3.95033i	−0.243126	−	0.421106i
$89$	5.43599	−	9.41541i	0.576213	−	0.998031i	−0.419695	−	0.907665i	$-0.637863\pi$
$89$	5.43599	−	9.41541i	0.576213	−	0.998031i	0.995909	−	0.0903658i	$-0.0288036\pi$
$90$		0			0
$91$	11.3103	+	7.25841i	1.18564	+	0.760889i
$92$			8.72178i			0.909308i
$93$	−8.69416	−	4.12533i	−0.901543	−	0.427777i
$94$	−5.99548	+	3.46149i	−0.618387	+	0.357026i
$95$		0			0
$96$	10.0967	+	4.79084i	1.03049	+	0.488963i
$97$			8.94486i			0.908213i	0.890947	+	0.454107i	$0.150041\pi$
$97$			8.94486i			0.908213i	−0.890947	+	0.454107i	$0.849959\pi$
$98$	−1.47721	+	15.6835i	−0.149220	+	1.58427i
$99$	0.916566	+	5.63918i	0.0921184	+	0.566759i
$100$		0			0
$101$	−4.71346	−	8.16395i	−0.469007	−	0.812344i	0.530365	−	0.847769i	$-0.322055\pi$
$101$	−4.71346	−	8.16395i	−0.469007	−	0.812344i	−0.999372	+	0.0354254i	$0.988721\pi$
$102$	−14.2966	+	9.86840i	−1.41557	+	0.977117i
$103$	−5.45692	−	3.15056i	−0.537686	−	0.310433i	0.206454	−	0.978456i	$-0.433808\pi$
$103$	−5.45692	−	3.15056i	−0.537686	−	0.310433i	−0.744141	+	0.668023i	$0.767141\pi$
$104$	12.1665			1.19302
$105$		0			0
$106$	−5.44944			−0.529297
$107$	14.3818	+	8.30336i	1.39034	+	0.802716i	0.993353	−	0.115107i	$-0.0367210\pi$
$107$	14.3818	+	8.30336i	1.39034	+	0.802716i	0.396991	+	0.917822i	$0.370054\pi$
$108$	11.0305	+	11.4833i	1.06141	+	1.10498i
$109$	9.20177	+	15.9379i	0.881370	+	1.52658i	0.849818	+	0.527076i	$0.176712\pi$
$109$	9.20177	+	15.9379i	0.881370	+	1.52658i	0.0315518	+	0.999502i	$0.489955\pi$
$110$		0			0
$111$	−8.02073	+	0.647577i	−0.761294	+	0.0614653i
$112$	−0.896399	−	1.73603i	−0.0847018	−	0.164039i
$113$			4.37678i			0.411733i	0.978580	+	0.205866i	$0.0660012\pi$
$113$			4.37678i			0.411733i	−0.978580	+	0.205866i	$0.933999\pi$
$114$	−7.44124	+	15.6825i	−0.696936	+	1.46880i
$115$		0			0
$116$	−23.4245	+	13.5241i	−2.17491	+	1.25568i
$117$	−14.2483	−	5.40336i	−1.31726	−	0.499540i
$118$			31.3250i			2.88370i
$119$	11.7785	+	0.553477i	1.07973	+	0.0507372i
$120$		0			0
$121$	−3.68664	+	6.38545i	−0.335149	+	0.580495i
$122$	1.96910	+	3.41058i	0.178274	+	0.308779i
$123$	0.246788	+	0.357528i	0.0222522	+	0.0322372i
$124$	14.7445	+	8.51273i	1.32409	+	0.764466i
$125$		0			0
$126$	−2.03489	−	17.7458i	−0.181283	−	1.58092i
$127$	−12.7846			−1.13445			−0.567223	−	0.823564i	$-0.691982\pi$
$127$	−12.7846			−1.13445			−0.567223	+	0.823564i	$0.691982\pi$
$128$	−14.2447	−	8.22419i	−1.25907	−	0.726922i
$129$	9.08891	+	13.1673i	0.800234	+	1.15932i
$130$		0			0
$131$	−2.59617	+	4.49669i	−0.226828	+	0.392878i	−0.956866	−	0.290528i	$-0.906169\pi$
$131$	−2.59617	+	4.49669i	−0.226828	+	0.392878i	0.730038	+	0.683406i	$0.239502\pi$
$132$	−0.813434	−	10.0750i	−0.0708003	−	0.876916i
$133$	10.4692	−	5.40576i	0.907791	−	0.468739i
$134$		−	18.6725i		−	1.61306i
$135$		0			0
$136$	9.24478	−	5.33748i	0.792734	−	0.457685i
$137$	11.6770	−	6.74170i	0.997630	−	0.575982i	0.0900838	−	0.995934i	$-0.471287\pi$
$137$	11.6770	−	6.74170i	0.997630	−	0.575982i	0.907546	+	0.419952i	$0.137953\pi$
$138$	−4.75583	+	10.0229i	−0.404843	+	0.853210i
$139$		−	2.02188i		−	0.171493i	−0.996317	−	0.0857466i	$-0.972672\pi$
$139$		−	2.02188i		−	0.171493i	0.996317	−	0.0857466i	$-0.0273276\pi$
$140$		0			0
$141$	−5.31106	+	0.428804i	−0.447272	+	0.0361118i
$142$	10.8969	−	18.8740i	0.914447	−	1.58387i
$143$	4.83667	+	8.37736i	0.404463	+	0.700550i
$144$	1.40115	+	1.71603i	0.116762	+	0.143003i
$145$		0			0
$146$	−14.2161			−1.17653
$147$	−6.20179	+	10.4181i	−0.511515	+	0.859274i
$148$	14.2365			1.17023
$149$	1.11049	+	0.641143i	0.0909750	+	0.0525244i	0.544797	−	0.838568i	$-0.316607\pi$
$149$	1.11049	+	0.641143i	0.0909750	+	0.0525244i	−0.453822	+	0.891092i	$0.649940\pi$
$150$		0			0
$151$	−3.50501	−	6.07085i	−0.285233	−	0.494039i	0.687432	−	0.726248i	$-0.258738\pi$
$151$	−3.50501	−	6.07085i	−0.285233	−	0.494039i	−0.972666	+	0.232210i	$0.925404\pi$
$152$	5.33336	−	9.23766i	0.432593	−	0.749273i
$153$	−13.1971	+	2.14500i	−1.06693	+	0.173413i
$154$	−6.12408	+	9.54277i	−0.493493	+	0.768978i
$155$		0			0
$156$	24.3570	+	11.5573i	1.95012	+	0.925323i
$157$	2.17668	−	1.25671i	0.173718	−	0.100296i	−0.410620	−	0.911807i	$-0.634688\pi$
$157$	2.17668	−	1.25671i	0.173718	−	0.100296i	0.584338	+	0.811511i	$0.301354\pi$
$158$	−6.21452	+	3.58795i	−0.494401	+	0.285442i
$159$	−3.78928	−	1.79799i	−0.300510	−	0.142590i
$160$		0			0
$161$	6.69103	−	3.45492i	0.527327	−	0.272286i
$162$	6.41443	+	19.2111i	0.503965	+	1.50937i
$163$	−1.73224	+	3.00033i	−0.135680	+	0.235004i	−0.925857	−	0.377874i	$-0.876655\pi$
$163$	−1.73224	+	3.00033i	−0.135680	+	0.235004i	0.790177	+	0.612879i	$0.209989\pi$
$164$	−0.384298	−	0.665624i	−0.0300087	−	0.0519765i
$165$		0			0
$166$	−17.5205	−	10.1155i	−1.35985	−	0.785112i
$167$	3.29851			0.255246			0.127623	−	0.991823i	$-0.459265\pi$
$167$	3.29851			0.255246			0.127623	+	0.991823i	$0.459265\pi$
$168$	0.368814	+	10.9701i	0.0284546	+	0.846360i
$169$	−12.8011			−0.984703
$170$		0			0
$171$	−10.3486	+	8.44967i	−0.791375	+	0.646163i
$172$	−14.1532	−	24.5141i	−1.07917	−	1.86918i
$173$	8.72018	−	15.1038i	0.662983	−	1.14832i	−0.316845	−	0.948477i	$-0.602624\pi$
$173$	8.72018	−	15.1038i	0.662983	−	1.14832i	0.979828	−	0.199843i	$-0.0640431\pi$
$174$	−34.2935	+	2.76879i	−2.59979	+	0.209901i
$175$		0			0
$176$		−	1.40633i		−	0.106006i
$177$	−10.3354	+	21.7819i	−0.776855	+	1.63723i
$178$	−21.1885	+	12.2332i	−1.58815	+	0.916917i
$179$	−19.5347	+	11.2784i	−1.46009	+	0.842985i	−0.999015	−	0.0443755i	$-0.985870\pi$
$179$	−19.5347	+	11.2784i	−1.46009	+	0.842985i	−0.461077	+	0.887360i	$0.652537\pi$
$180$		0			0
$181$			3.48204i			0.258818i	0.991591	+	0.129409i	$0.0413080\pi$
$181$			3.48204i			0.258818i	−0.991591	+	0.129409i	$0.958692\pi$
$182$	−13.8756	−	26.8725i	−1.02853	−	1.99192i
$183$	0.243929	+	3.02124i	0.0180317	+	0.223336i
$184$	3.40865	−	5.90396i	0.251289	−	0.435245i
$185$		0			0
$186$	12.3023	+	17.8226i	0.902050	+	1.30682i
$187$	7.35035	+	4.24373i	0.537511	+	0.310332i
$188$	9.42692			0.687529
$189$	4.44009	−	13.0110i	0.322969	−	0.946409i
$190$		0			0
$191$	8.27801	+	4.77931i	0.598976	+	0.345819i	0.768638	−	0.639683i	$-0.220935\pi$
$191$	8.27801	+	4.77931i	0.598976	+	0.345819i	−0.169663	+	0.985502i	$0.554268\pi$
$192$	−12.8338	−	18.5926i	−0.926198	−	1.34180i
$193$	−2.88510	−	4.99714i	−0.207674	−	0.359702i	0.743307	−	0.668950i	$-0.233256\pi$
$193$	−2.88510	−	4.99714i	−0.207674	−	0.359702i	−0.950981	+	0.309248i	$0.899923\pi$
$194$	10.0648	−	17.4328i	0.722611	−	1.25160i
$195$		0			0
$196$	12.4200	−	17.4890i	0.887140	−	1.24922i
$197$		−	4.34500i		−	0.309568i	−0.987948	−	0.154784i	$-0.950532\pi$
$197$		−	4.34500i		−	0.309568i	0.987948	−	0.154784i	$-0.0494682\pi$
$198$	4.55893	−	12.0216i	0.323989	−	0.854338i
$199$	7.53338	−	4.34940i	0.534027	−	0.308321i	−0.208628	−	0.977995i	$-0.566900\pi$
$199$	7.53338	−	4.34940i	0.534027	−	0.308321i	0.742655	+	0.669674i	$0.233566\pi$
$200$		0			0
$201$	6.16081	−	12.9840i	0.434550	−	0.915817i
$202$			21.2144i			1.49264i
$203$	19.6542	+	12.6131i	1.37946	+	0.885269i
$204$	23.5781	−	1.90364i	1.65080	−	0.133282i
$205$		0			0
$206$	7.09004	+	12.2803i	0.493987	+	0.855610i
$207$	−6.61396	+	5.40034i	−0.459702	+	0.375350i
$208$	3.24848	+	1.87551i	0.225242	+	0.130043i
$209$	8.48091			0.586637
$210$		0			0
$211$	10.6975			0.736446			0.368223	−	0.929737i	$-0.379966\pi$
$211$	10.6975			0.736446			0.368223	+	0.929737i	$0.379966\pi$
$212$	6.42627	+	3.71021i	0.441358	+	0.254818i
$213$	13.8045	−	9.52873i	0.945867	−	0.652898i
$214$	−18.6860	−	32.3650i	−1.27735	−	2.21243i
$215$		0			0
$216$	−2.97885	−	12.0842i	−0.202685	−	0.822225i
$217$	0.689986	−	14.6835i	0.0468393	−	0.996784i
$218$		−	41.4155i		−	2.80501i
$219$	−9.88517	−	4.69046i	−0.667978	−	0.316952i
$220$		0			0
$221$	−19.6052	+	11.3190i	−1.31879	+	0.761402i
$222$	16.3604	+	7.76290i	1.09804	+	0.521012i
$223$		−	16.9483i		−	1.13494i	−0.823394	−	0.567471i	$-0.807922\pi$
$223$		−	16.9483i		−	1.13494i	0.823394	−	0.567471i	$-0.192078\pi$
$224$	−0.801297	+	17.0523i	−0.0535389	+	1.13936i
$225$		0			0
$226$	4.92477	−	8.52996i	0.327591	−	0.567404i
$227$	1.21572	+	2.10568i	0.0806899	+	0.139759i	0.903546	−	0.428490i	$-0.140954\pi$
$227$	1.21572	+	2.10568i	0.0806899	+	0.139759i	−0.822857	+	0.568249i	$0.807621\pi$
$228$	19.4524	−	13.4273i	1.28827	−	0.889244i
$229$	0.204081	+	0.117826i	0.0134861	+	0.00778618i	0.506728	−	0.862106i	$-0.330855\pi$
$229$	0.204081	+	0.117826i	0.0134861	+	0.00778618i	−0.493242	+	0.869892i	$0.664188\pi$
$230$		0			0
$231$	−7.40695	+	4.61500i	−0.487341	+	0.303645i
$232$	21.1420			1.38804
$233$	−9.59675	−	5.54068i	−0.628704	−	0.362982i	0.151546	−	0.988450i	$-0.451575\pi$
$233$	−9.59675	−	5.54068i	−0.628704	−	0.362982i	−0.780250	+	0.625468i	$0.784908\pi$
$234$	21.6888	+	26.5629i	1.41784	+	1.73647i
$235$		0			0
$236$	21.3273	−	36.9401i	1.38829	−	2.40459i
$237$	−5.50510	+	0.444470i	−0.357594	+	0.0288714i
$238$	−22.3325	−	14.3319i	−1.44760	−	0.929001i
$239$		−	9.67610i		−	0.625895i	−0.949770	−	0.312948i	$-0.898684\pi$
$239$		−	9.67610i		−	0.625895i	0.949770	−	0.312948i	$-0.101316\pi$
$240$		0			0
$241$	−13.9240	+	8.03902i	−0.896923	+	0.517839i	−0.876201	−	0.481947i	$-0.839930\pi$
$241$	−13.9240	+	8.03902i	−0.896923	+	0.517839i	−0.0207223	+	0.999785i	$0.506597\pi$
$242$	14.3699	−	8.29646i	0.923731	−	0.533316i
$243$	−1.87825	+	15.4749i	−0.120490	+	0.992715i
$244$		−	5.36258i		−	0.343304i
$245$		0			0
$246$	−0.0786773	−	0.974478i	−0.00501628	−	0.0621304i
$247$	−11.3103	+	19.5901i	−0.719659	+	1.24649i
$248$	−6.65390	−	11.5249i	−0.422523	−	0.731832i
$249$	−8.84542	−	12.8145i	−0.560556	−	0.812089i
$250$		0			0
$251$	14.3809			0.907716			0.453858	−	0.891074i	$-0.350047\pi$
$251$	14.3809			0.907716			0.453858	+	0.891074i	$0.350047\pi$
$252$	−9.68243	+	22.3122i	−0.609936	+	1.40554i
$253$	5.42031			0.340772
$254$	24.9160	+	14.3852i	1.56337	+	0.902611i
$255$		0			0
$256$	5.46442	+	9.46465i	0.341526	+	0.591541i
$257$	−2.37985	+	4.12202i	−0.148451	+	0.257125i	−0.930655	−	0.365898i	$-0.880762\pi$
$257$	−2.37985	+	4.12202i	−0.148451	+	0.257125i	0.782204	+	0.623022i	$0.214095\pi$
$258$	−2.89759	−	35.8888i	−0.180396	−	2.23434i
$259$	−5.63944	−	10.9217i	−0.350417	−	0.678642i
$260$		0			0
$261$	−24.7596	−	9.38955i	−1.53258	−	0.581199i
$262$	10.1194	−	5.84244i	0.625179	−	0.360947i
$263$	−4.89251	+	2.82469i	−0.301685	+	0.174178i	−0.643200	−	0.765698i	$-0.722393\pi$
$263$	−4.89251	+	2.82469i	−0.301685	+	0.174178i	0.341514	+	0.939877i	$0.389060\pi$
$264$	−3.38689	+	7.13788i	−0.208448	+	0.439306i
$265$		0			0
$266$	−26.4861	−	1.24459i	−1.62396	−	0.0763108i
$267$	−18.7697	+	1.51543i	−1.14869	+	0.0927427i
$268$	−12.7130	+	22.0196i	−0.776570	+	1.34506i
$269$	0.356044	+	0.616686i	0.0217084	+	0.0376000i	0.876676	−	0.481082i	$-0.159756\pi$
$269$	0.356044	+	0.616686i	0.0217084	+	0.0376000i	−0.854967	+	0.518682i	$0.826423\pi$
$270$		0			0
$271$	2.80074	+	1.61701i	0.170133	+	0.0982264i	0.582649	−	0.812724i	$-0.302016\pi$
$271$	2.80074	+	1.61701i	0.170133	+	0.0982264i	−0.412516	+	0.910951i	$0.635350\pi$
$272$	3.29117			0.199557
$273$	−0.782133	−	23.2640i	−0.0473369	−	1.40800i
$274$	−30.3432			−1.83310
$275$		0			0
$276$	12.4324	−	8.58162i	0.748341	−	0.516553i
$277$	11.4567	+	19.8435i	0.688364	+	1.19228i	0.972367	+	0.233459i	$0.0750043\pi$
$277$	11.4567	+	19.8435i	0.688364	+	1.19228i	−0.284002	+	0.958824i	$0.591662\pi$
$278$	−2.27503	+	3.94046i	−0.136447	+	0.236333i
$279$	2.67404	+	16.4521i	0.160091	+	0.984959i
$280$		0			0
$281$		−	12.0342i		−	0.717900i	−0.933357	−	0.358950i	$-0.883135\pi$
$281$		−	12.0342i		−	0.717900i	0.933357	−	0.358950i	$-0.116865\pi$
$282$	10.8333	+	5.14034i	0.645113	+	0.306102i
$283$	15.5030	−	8.95065i	0.921556	−	0.532061i	0.0374249	−	0.999299i	$-0.488084\pi$
$283$	15.5030	−	8.95065i	0.921556	−	0.532061i	0.884131	+	0.467239i	$0.154751\pi$
$284$	−25.7004	+	14.8381i	−1.52504	+	0.880481i
$285$		0			0
$286$		−	21.7690i		−	1.28723i
$287$	−0.358412	+	0.558491i	−0.0211564	+	0.0329667i
$288$	−3.10542	−	19.1062i	−0.182989	−	1.12584i
$289$	−1.43141	+	2.47928i	−0.0842008	+	0.145840i
$290$		0			0
$291$	12.7504	−	8.80112i	0.747440	−	0.515931i
$292$	16.7643	+	9.67889i	0.981058	+	0.566414i
$293$	8.87318			0.518377			0.259188	−	0.965827i	$-0.416545\pi$
$293$	8.87318			0.518377			0.259188	+	0.965827i	$0.416545\pi$
$294$	23.8093	−	13.3258i	1.38859	−	0.777174i
$295$		0			0
$296$	−9.63697	−	5.56391i	−0.560138	−	0.323396i
$297$	7.13648	−	6.85507i	0.414101	−	0.397772i
$298$	−1.44283	−	2.49906i	−0.0835811	−	0.144767i
$299$	−7.22863	+	12.5204i	−0.418043	+	0.724071i
$300$		0			0
$301$	−13.1999	+	20.5685i	−0.760828	+	1.18555i
$302$			15.7754i			0.907773i
$303$	−6.99951	+	14.7515i	−0.402111	+	0.847453i
$304$	2.84804	−	1.64432i	0.163346	−	0.0943081i
$305$		0			0
$306$	28.1336	+	10.6691i	1.60829	+	0.609910i
$307$		−	8.99889i		−	0.513594i	−0.966465	−	0.256797i	$-0.917333\pi$
$307$		−	8.99889i		−	0.513594i	0.966465	−	0.256797i	$-0.0826671\pi$
$308$	13.7190	−	7.08380i	0.781710	−	0.403637i
$309$	0.878303	+	10.8784i	0.0499649	+	0.618853i
$310$		0			0
$311$	3.29851	+	5.71318i	0.187041	+	0.323965i	0.944262	−	0.329194i	$-0.106777\pi$
$311$	3.29851	+	5.71318i	0.187041	+	0.323965i	−0.757221	+	0.653159i	$0.773444\pi$
$312$	−11.9710	−	17.3426i	−0.677723	−	0.981831i
$313$	−16.7007	−	9.64215i	−0.943979	−	0.545007i	−0.0527736	−	0.998607i	$-0.516806\pi$
$313$	−16.7007	−	9.64215i	−0.943979	−	0.545007i	−0.891205	+	0.453600i	$0.850139\pi$
$314$	−5.65621			−0.319198
$315$		0			0
$316$	9.77132			0.549680
$317$	−16.6152	−	9.59278i	−0.933202	−	0.538784i	−0.0453790	−	0.998970i	$-0.514450\pi$
$317$	−16.6152	−	9.59278i	−0.933202	−	0.538784i	−0.887823	+	0.460186i	$0.847783\pi$
$318$	5.36187	+	7.76786i	0.300679	+	0.435600i
$319$	8.40481	+	14.5576i	0.470579	+	0.815066i
$320$		0			0
$321$	−2.31479	−	28.6704i	−0.129199	−	1.60022i
$322$	−16.9277	−	0.795441i	−0.943345	−	0.0443282i
$323$			19.8475i			1.10435i
$324$	5.51551	−	27.0220i	0.306417	−	1.50122i
$325$		0			0
$326$	6.75198	−	3.89826i	0.373958	−	0.215905i
$327$	13.6647	−	28.7984i	0.755659	−	1.59256i
$328$			0.600767i			0.0331718i
$329$	−3.73425	−	7.23199i	−0.205876	−	0.398713i
$330$		0			0
$331$	−5.98753	+	10.3707i	−0.329104	+	0.570026i	−0.982334	−	0.187134i	$-0.940080\pi$
$331$	−5.98753	+	10.3707i	−0.329104	+	0.570026i	0.653230	+	0.757160i	$0.273413\pi$
$332$	13.7741	+	23.8574i	0.755950	+	1.30934i
$333$	8.81493	+	10.7959i	0.483055	+	0.591612i
$334$	−6.42851	−	3.71150i	−0.351752	−	0.203084i
$335$		0			0
$336$	−1.59261	+	2.98589i	−0.0868839	+	0.162894i
$337$	12.6992			0.691769			0.345885	−	0.938277i	$-0.387579\pi$
$337$	12.6992			0.691769			0.345885	+	0.938277i	$0.387579\pi$
$338$	24.9483	+	14.4039i	1.35701	+	0.783469i
$339$	6.23884	−	4.30644i	0.338847	−	0.233894i
$340$		0			0
$341$	5.29039	−	9.16323i	0.286491	−	0.496217i
$342$	29.6761	−	4.82341i	1.60470	−	0.260820i
$343$	−18.3368	−	2.60028i	−0.990095	−	0.140402i
$344$			22.1255i			1.19293i
$345$		0			0
$346$	−33.9897	+	19.6240i	−1.82730	+	1.05499i
$347$	−4.85815	+	2.80486i	−0.260799	+	0.150573i	−0.624699	−	0.780866i	$-0.714778\pi$
$347$	−4.85815	+	2.80486i	−0.260799	+	0.150573i	0.363900	+	0.931438i	$0.381445\pi$
$348$	42.3259	+	20.0834i	2.26890	+	1.07658i
$349$			33.8725i			1.81315i	0.422041	+	0.906577i	$0.361314\pi$
$349$			33.8725i			1.81315i	−0.422041	+	0.906577i	$0.638686\pi$
$350$		0			0
$351$	6.31717	+	25.6266i	0.337186	+	1.36785i
$352$	−6.14386	+	10.6415i	−0.327469	+	0.567192i
$353$	−18.3706	−	31.8188i	−0.977767	−	1.69354i	−0.670485	−	0.741923i	$-0.733914\pi$
$353$	−18.3706	−	31.8188i	−0.977767	−	1.69354i	−0.307281	−	0.951619i	$-0.599419\pi$
$354$	44.6519	−	30.8216i	2.37322	−	1.63815i
$355$		0			0
$356$	33.3155			1.76572
$357$	−10.8003	−	17.3342i	−0.571612	−	0.917421i
$358$	50.7619			2.68285
$359$	−21.1388	−	12.2045i	−1.11566	−	0.644127i	−0.175371	−	0.984502i	$-0.556113\pi$
$359$	−21.1388	−	12.2045i	−1.11566	−	0.644127i	−0.940290	+	0.340375i	$0.889446\pi$
$360$		0			0
$361$	0.416104	+	0.720714i	0.0219002	+	0.0379323i
$362$	3.91801	−	6.78619i	0.205926	−	0.356674i
$363$	12.7295	−	1.02775i	0.668124	−	0.0539429i
$364$	−1.93302	+	41.1365i	−0.101318	+	2.15614i
$365$		0			0
$366$	2.92412	−	6.16260i	0.152846	−	0.322124i
$367$	17.8968	−	10.3327i	0.934203	−	0.539362i	0.0460646	−	0.998938i	$-0.485332\pi$
$367$	17.8968	−	10.3327i	0.934203	−	0.539362i	0.888138	+	0.459576i	$0.151999\pi$
$368$	1.82024	−	1.05091i	0.0948864	−	0.0547827i
$369$	0.266812	−	0.703565i	0.0138897	−	0.0366261i
$370$		0			0
$371$	0.300725	−	6.39971i	0.0156129	−	0.332256i
$372$	−2.37316	−	29.3933i	−0.123042	−	1.52397i
$373$	−10.4361	+	18.0759i	−0.540363	+	0.935936i	0.458520	+	0.888684i	$0.348380\pi$
$373$	−10.4361	+	18.0759i	−0.540363	+	0.935936i	−0.998883	+	0.0472520i	$0.984954\pi$
$374$	−9.55013	−	16.5413i	−0.493825	−	0.855331i
$375$		0			0
$376$	−6.38128	−	3.68424i	−0.329090	−	0.190000i
$377$	−44.8353			−2.30914
$378$	−23.2934	+	20.3612i	−1.19808	+	1.04727i
$379$	−27.0384			−1.38887			−0.694435	−	0.719556i	$-0.744345\pi$
$379$	−27.0384			−1.38887			−0.694435	+	0.719556i	$0.744345\pi$
$380$		0			0
$381$	12.5791	+	18.2236i	0.644447	+	0.933624i
$382$	−10.7554	−	18.6289i	−0.550295	−	0.953138i
$383$	−3.16723	+	5.48580i	−0.161838	+	0.280311i	−0.935528	−	0.353253i	$-0.885076\pi$
$383$	−3.16723	+	5.48580i	−0.161838	+	0.280311i	0.773690	+	0.633564i	$0.218409\pi$
$384$	2.29272	+	28.3970i	0.117000	+	1.44913i
$385$		0			0
$386$			12.9853i			0.660936i
$387$	9.82633	−	25.9114i	0.499501	−	1.31715i
$388$	−23.7379	+	13.7051i	−1.20511	+	0.695770i
$389$	−10.7869	+	6.22784i	−0.546919	+	0.315764i	−0.747879	−	0.663836i	$-0.768927\pi$
$389$	−10.7869	+	6.22784i	−0.546919	+	0.315764i	0.200959	+	0.979600i	$0.435594\pi$
$390$		0			0
$391$			12.6849i			0.641503i
$392$	−15.2424	+	6.98471i	−0.769858	+	0.352781i
$393$	8.96422	−	0.723752i	0.452185	−	0.0365085i
$394$	−4.88902	+	8.46803i	−0.246305	+	0.426613i
$395$		0			0
$396$	−13.5609	+	11.0726i	−0.681463	+	0.556419i
$397$	−24.6611	−	14.2381i	−1.23771	−	0.714591i	−0.269082	−	0.963117i	$-0.586720\pi$
$397$	−24.6611	−	14.2381i	−1.23771	−	0.714591i	−0.968625	+	0.248527i	$0.920054\pi$
$398$	−19.5759			−0.981250
$399$	−18.0065	−	9.60426i	−0.901453	−	0.480815i
$400$		0			0
$401$	12.7515	+	7.36207i	0.636779	+	0.367644i	0.783373	−	0.621552i	$-0.213498\pi$
$401$	12.7515	+	7.36207i	0.636779	+	0.367644i	−0.146594	+	0.989197i	$0.546831\pi$
$402$	−26.6165	+	18.3724i	−1.32751	+	0.916333i
$403$	14.1108	+	24.4405i	0.702907	+	1.21747i
$404$	14.4437	−	25.0172i	0.718600	−	1.24465i
$405$		0			0
$406$	−24.1120	−	46.6970i	−1.19666	−	2.31753i
$407$		−	8.84751i		−	0.438555i
$408$	−16.7045	−	7.92618i	−0.826995	−	0.392404i
$409$	−0.810609	+	0.468005i	−0.0400820	+	0.0231414i	−0.519907	−	0.854223i	$-0.674033\pi$
$409$	−0.810609	+	0.468005i	−0.0400820	+	0.0231414i	0.479825	+	0.877364i	$0.340700\pi$
$410$		0			0
$411$	−21.0992	−	10.0115i	−1.04075	−	0.493828i
$412$		−	19.3088i		−	0.951276i
$413$	−36.7874	−	1.72865i	−1.81019	−	0.0850615i
$414$	18.9665	−	3.08273i	0.932154	−	0.151508i
$415$		0			0
$416$	−16.3872	−	28.3834i	−0.803446	−	1.39161i
$417$	−2.88206	+	1.98939i	−0.141135	+	0.0974206i
$418$	−16.5286	−	9.54277i	−0.808438	−	0.466752i
$419$	30.1515			1.47299			0.736497	−	0.676440i	$-0.236478\pi$
$419$	30.1515			1.47299			0.736497	+	0.676440i	$0.236478\pi$
$420$		0			0
$421$	36.3685			1.77249			0.886245	−	0.463217i	$-0.153305\pi$
$421$	36.3685			1.77249			0.886245	+	0.463217i	$0.153305\pi$
$422$	−20.8485	−	12.0369i	−1.01489	−	0.585946i
$423$	5.83695	+	7.14869i	0.283802	+	0.347581i
$424$	−2.90005	−	5.02304i	−0.140839	−	0.243940i
$425$		0			0
$426$	−37.6255	+	3.03780i	−1.82296	+	0.147182i
$427$	−4.11397	+	2.12426i	−0.199089	+	0.102800i
$428$			50.8887i			2.45980i
$429$	7.18248	−	15.1371i	0.346773	−	0.730827i
$430$		0			0
$431$	11.9349	−	6.89063i	0.574885	−	0.331910i	−0.184213	−	0.982886i	$-0.558974\pi$
$431$	11.9349	−	6.89063i	0.574885	−	0.331910i	0.759098	+	0.650976i	$0.225640\pi$
$432$	1.06747	−	3.68571i	0.0513584	−	0.177329i
$433$			1.16840i			0.0561499i	0.999606	+	0.0280750i	$0.00893771\pi$
$433$			1.16840i			0.0561499i	−0.999606	+	0.0280750i	$0.991062\pi$
$434$	−17.8667	+	27.8406i	−0.857630	+	1.33639i
$435$		0			0
$436$	−28.1974	+	48.8394i	−1.35041	+	2.33898i
$437$	6.33756	+	10.9770i	0.303167	+	0.525100i
$438$	13.9876	+	20.2641i	0.668354	+	0.968258i
$439$	2.50353	+	1.44541i	0.119487	+	0.0689858i	0.558552	−	0.829469i	$-0.311357\pi$
$439$	2.50353	+	1.44541i	0.119487	+	0.0689858i	−0.439065	+	0.898455i	$0.644690\pi$
$440$		0			0
$441$	20.9526	−	1.41044i	0.997742	−	0.0671640i
$442$	50.9450			2.42321
$443$	−14.2948	−	8.25313i	−0.679169	−	0.392118i	0.120373	−	0.992729i	$-0.461591\pi$
$443$	−14.2948	−	8.25313i	−0.679169	−	0.392118i	−0.799542	+	0.600611i	$0.794924\pi$
$444$	−14.0077	−	20.2932i	−0.664776	−	0.963075i
$445$		0			0
$446$	−19.0703	+	33.0307i	−0.903005	+	1.56405i
$447$	−0.178736	−	2.21378i	−0.00845392	−	0.104708i
$448$	18.6386	−	29.0433i	0.880589	−	1.37217i
$449$			25.9824i			1.22618i	0.790012	+	0.613092i	$0.210075\pi$
$449$			25.9824i			1.22618i	−0.790012	+	0.613092i	$0.789925\pi$
$450$		0			0
$451$	−0.413664	+	0.238829i	−0.0194787	+	0.0112460i
$452$	−11.6151	+	6.70598i	−0.546329	+	0.315423i
$453$	−5.20495	+	10.9695i	−0.244550	+	0.515391i
$454$		−	5.47172i		−	0.256801i
$455$		0			0
$456$	−18.4154	+	1.48682i	−0.862380	+	0.0696267i
$457$	0.750953	−	1.30069i	0.0351281	−	0.0608436i	−0.847927	−	0.530113i	$-0.822149\pi$
$457$	0.750953	−	1.30069i	0.0351281	−	0.0608436i	0.883055	+	0.469270i	$0.155483\pi$
$458$	−0.265158	−	0.459266i	−0.0123900	−	0.0214601i
$459$	16.0426	+	16.7012i	0.748806	+	0.779545i
$460$		0			0
$461$	1.40468			0.0654225			0.0327113	−	0.999465i	$-0.489586\pi$
$461$	1.40468			0.0654225			0.0327113	+	0.999465i	$0.489586\pi$
$462$	19.6283	−	0.659903i	0.913192	−	0.0307015i
$463$	20.2056			0.939033			0.469516	−	0.882924i	$-0.344428\pi$
$463$	20.2056			0.939033			0.469516	+	0.882924i	$0.344428\pi$
$464$	5.64497	+	3.25912i	0.262061	+	0.151301i
$465$		0			0
$466$	12.4688	+	21.5966i	0.577607	+	1.00044i
$467$	−19.3296	+	33.4798i	−0.894467	+	1.54926i	−0.0600041	+	0.998198i	$0.519111\pi$
$467$	−19.3296	+	33.4798i	−0.894467	+	1.54926i	−0.834463	+	0.551064i	$0.814222\pi$
$468$	−7.49143	−	46.0911i	−0.346291	−	2.13056i
$469$	21.9286	+	1.03043i	1.01257	+	0.0475809i
$470$		0			0
$471$	−3.93306	−	1.86621i	−0.181226	−	0.0859906i
$472$	−28.8739	+	16.6703i	−1.32903	+	0.767314i
$473$	−15.2347	+	8.79578i	−0.700494	+	0.404430i
$474$	11.2291	+	5.32813i	0.515768	+	0.244729i
$475$		0			0
$476$	16.5779	+	32.1059i	0.759848	+	1.47157i
$477$	1.16546	+	7.17050i	0.0533627	+	0.328315i
$478$	−10.8876	+	18.8579i	−0.497987	+	0.862539i
$479$	−15.3467	−	26.5813i	−0.701210	−	1.21453i	−0.968042	−	0.250788i	$-0.919310\pi$
$479$	−15.3467	−	26.5813i	−0.701210	−	1.21453i	0.266832	−	0.963743i	$-0.414023\pi$
$480$		0			0
$481$	20.4369	+	11.7992i	0.931841	+	0.537999i
$482$	36.1822			1.64805
$483$	−11.5083	−	6.13826i	−0.523645	−	0.279301i
$484$	−22.5943			−1.02701
$485$		0			0
$486$	21.0730	−	28.0458i	0.955889	−	1.27218i
$487$	14.8500	+	25.7209i	0.672915	+	1.16552i	0.977074	+	0.212902i	$0.0682916\pi$
$487$	14.8500	+	25.7209i	0.672915	+	1.16552i	−0.304158	+	0.952622i	$0.598375\pi$
$488$	−2.09581	+	3.63004i	−0.0948727	+	0.164324i
$489$	5.98120	−	0.482910i	0.270479	−	0.0218379i
$490$		0			0
$491$		−	7.13665i		−	0.322073i	−0.986948	−	0.161036i	$-0.948516\pi$
$491$		−	7.13665i		−	0.322073i	0.986948	−	0.161036i	$-0.0514836\pi$
$492$	−0.570685	+	1.20272i	−0.0257285	+	0.0542229i
$493$	−34.0684	+	19.6694i	−1.53436	+	0.885866i
$494$	44.0857	−	25.4529i	1.98351	−	1.14518i
$495$		0			0
$496$		−	4.10290i		−	0.184226i
$497$	21.5639	+	13.8386i	0.967271	+	0.620747i
$498$	2.81996	+	34.9273i	0.126365	+	1.56513i
$499$	6.67079	−	11.5541i	0.298626	−	0.517235i	−0.677196	−	0.735802i	$-0.736805\pi$
$499$	6.67079	−	11.5541i	0.298626	−	0.517235i	0.975822	+	0.218568i	$0.0701385\pi$
$500$		0			0
$501$	−3.24550	−	4.70183i	−0.144998	−	0.210062i
$502$	−28.0272	−	16.1815i	−1.25091	−	0.722216i
$503$	30.4353			1.35704			0.678522	−	0.734580i	$-0.262621\pi$
$503$	30.4353			1.35704			0.678522	+	0.734580i	$0.262621\pi$
$504$	15.2743	−	11.3195i	0.680372	−	0.504212i
$505$		0			0
$506$	−10.5637	−	6.09896i	−0.469614	−	0.271132i
$507$	12.5954	+	18.2473i	0.559383	+	0.810389i
$508$	−19.5882	−	33.9277i	−0.869084	−	1.50530i
$509$	−16.4870	+	28.5563i	−0.730774	+	1.26574i	0.225779	+	0.974179i	$0.427507\pi$
$509$	−16.4870	+	28.5563i	−0.730774	+	1.26574i	−0.956553	+	0.291559i	$0.905826\pi$
$510$		0			0
$511$	0.784506	−	16.6950i	0.0347045	−	0.738545i
$512$			8.30237i			0.366916i
$513$	22.2268	+	6.43738i	0.981336	+	0.284217i
$514$	9.27624	−	5.35564i	0.409157	−	0.236227i
$515$		0			0
$516$	−21.0176	+	44.2948i	−0.925249	+	1.94997i
$517$		−	5.85853i		−	0.257658i
$518$	−1.29839	+	27.6310i	−0.0570480	+	1.21404i
$519$	−30.1096	+	2.43099i	−1.32167	+	0.106708i
$520$		0			0
$521$	−12.7254	−	22.0411i	−0.557511	−	0.965638i	−0.997703	−	0.0677342i	$-0.978423\pi$
$521$	−12.7254	−	22.0411i	−0.557511	−	0.965638i	0.440192	−	0.897904i	$-0.354910\pi$
$522$	37.6892	+	46.1591i	1.64961	+	2.02033i
$523$	−20.9524	−	12.0969i	−0.916184	−	0.528959i	−0.0337685	−	0.999430i	$-0.510751\pi$
$523$	−20.9524	−	12.0969i	−0.916184	−	0.528959i	−0.882416	+	0.470470i	$0.844084\pi$
$524$	−15.9111			−0.695081
$525$		0			0
$526$	12.7134			0.554332
$527$	21.4443	+	12.3809i	0.934129	+	0.539320i
$528$	−2.00464	+	1.38373i	−0.0872407	+	0.0602192i
$529$	−7.44955	−	12.9030i	−0.323893	−	0.561000i
$530$		0			0
$531$	41.2181	−	6.69940i	1.78871	−	0.290729i
$532$	30.3864	+	19.5005i	1.31742	+	0.845454i
$533$		−	1.27403i		−	0.0551844i
$534$	38.2857	+	18.1664i	1.65679	+	0.786136i
$535$		0			0
$536$	17.2114	−	9.93701i	0.743419	−	0.429213i
$537$	35.2974	+	16.7484i	1.52320	+	0.722748i
$538$		−	1.60249i		−	0.0690882i
$539$	−10.8689	−	7.71861i	−0.468155	−	0.332464i
$540$		0			0
$541$	17.8529	−	30.9222i	0.767557	−	1.32945i	−0.171328	−	0.985214i	$-0.554806\pi$
$541$	17.8529	−	30.9222i	0.767557	−	1.32945i	0.938884	−	0.344233i	$-0.111861\pi$
$542$	−3.63894	−	6.30282i	−0.156306	−	0.270729i
$543$	4.96344	−	3.42609i	0.213002	−	0.147027i
$544$	−24.9038	−	14.3782i	−1.06774	−	0.616460i
$545$		0			0
$546$	−24.6524	+	46.2195i	−1.05503	+	1.97801i
$547$	−14.1119			−0.603380			−0.301690	−	0.953406i	$-0.597551\pi$
$547$	−14.1119			−0.603380			−0.301690	+	0.953406i	$0.597551\pi$
$548$	35.7823	+	20.6589i	1.52854	+	0.882505i
$549$	4.06659	−	3.32040i	0.173558	−	0.141711i
$550$		0			0
$551$	−19.6542	+	34.0421i	−0.837299	+	1.45024i
$552$	−11.7696	+	0.950254i	−0.500948	+	0.0404455i
$553$	−3.87067	−	7.49620i	−0.164598	−	0.318771i
$554$		−	51.5644i		−	2.19076i
$555$		0			0
$556$	5.36566	−	3.09787i	0.227555	−	0.131379i
$557$	−27.2162	+	15.7133i	−1.15319	+	0.665792i	−0.949661	−	0.313278i	$-0.898573\pi$
$557$	−27.2162	+	15.7133i	−1.15319	+	0.665792i	−0.203524	+	0.979070i	$0.565240\pi$
$558$	13.3005	−	35.0725i	0.563054	−	1.48474i
$559$		−	46.9209i		−	1.98454i
$560$		0			0
$561$	−1.18305	−	14.6530i	−0.0499486	−	0.618651i
$562$	−13.5409	+	23.4536i	−0.571190	+	0.989330i
$563$	16.0333	+	27.7705i	0.675723	+	1.17039i	0.976257	+	0.216615i	$0.0695016\pi$
$563$	16.0333	+	27.7705i	0.675723	+	1.17039i	−0.300535	+	0.953771i	$0.597165\pi$
$564$	−9.27544	−	13.4375i	−0.390566	−	0.565822i
$565$		0			0
$566$	−40.2853			−1.69332
$567$	−22.9151	+	6.47281i	−0.962345	+	0.271833i
$568$	23.1962			0.973290
$569$	17.1344	+	9.89257i	0.718313	+	0.414718i	0.814131	−	0.580681i	$-0.197214\pi$
$569$	17.1344	+	9.89257i	0.718313	+	0.414718i	−0.0958187	+	0.995399i	$0.530547\pi$
$570$		0			0
$571$	−12.9459	−	22.4229i	−0.541768	−	0.938370i	−0.998803	−	0.0489208i	$-0.984422\pi$
$571$	−12.9459	−	22.4229i	−0.541768	−	0.938370i	0.457035	−	0.889449i	$-0.348912\pi$
$572$	−14.8212	+	25.6711i	−0.619707	+	1.07336i
$573$	−1.33236	−	16.5023i	−0.0556602	−	0.689394i
$574$	1.32693	−	0.685162i	0.0553850	−	0.0285981i
$575$		0			0
$576$	−13.8750	+	36.5876i	−0.578127	+	1.52448i
$577$	20.3323	−	11.7388i	0.846443	−	0.488694i	−0.0130060	−	0.999915i	$-0.504140\pi$
$577$	20.3323	−	11.7388i	0.846443	−	0.488694i	0.859449	+	0.511221i	$0.170807\pi$
$578$	5.57940	−	3.22127i	0.232073	−	0.133987i
$579$	−4.28439	+	9.02938i	−0.178053	+	0.375248i
$580$		0			0
$581$	12.8463	−	20.0175i	0.532952	−	0.830465i
$582$	−34.7524	+	2.80584i	−1.44053	+	0.116306i
$583$	2.30578	−	3.99372i	0.0954955	−	0.165403i
$584$	−7.56542	−	13.1037i	−0.313059	−	0.542234i
$585$		0			0
$586$	−17.2930	−	9.98415i	−0.714369	−	0.412441i
$587$	−36.1962			−1.49398			−0.746988	−	0.664837i	$-0.768501\pi$
$587$	−36.1962			−1.49398			−0.746988	+	0.664837i	$0.768501\pi$
$588$	−37.1499	−	0.495928i	−1.53204	−	0.0204517i
$589$	24.7427			1.01950
$590$		0			0
$591$	−6.19354	+	4.27518i	−0.254768	+	0.175857i
$592$	−1.71540	−	2.97115i	−0.0705024	−	0.122114i
$593$	−7.50446	+	12.9981i	−0.308171	+	0.533768i	−0.977962	−	0.208781i	$-0.933050\pi$
$593$	−7.50446	+	12.9981i	−0.308171	+	0.533768i	0.669791	+	0.742550i	$0.266384\pi$
$594$	−21.6217	+	5.32994i	−0.887151	+	0.218690i
$595$		0			0
$596$			3.92937i			0.160953i
$597$	−13.6121	−	6.45888i	−0.557108	−	0.264344i
$598$	28.1760	−	16.2674i	1.15220	−	0.665223i
$599$	11.3793	−	6.56986i	0.464947	−	0.268437i	−0.249175	−	0.968458i	$-0.580159\pi$
$599$	11.3793	−	6.56986i	0.464947	−	0.268437i	0.714122	+	0.700021i	$0.246826\pi$
$600$		0			0
$601$		−	17.2898i		−	0.705267i	−0.935762	−	0.352633i	$-0.885286\pi$
$601$		−	17.2898i		−	0.705267i	0.935762	−	0.352633i	$-0.114714\pi$
$602$	48.8692	−	25.2337i	1.99176	−	1.02845i
$603$	−24.5697	+	3.99344i	−1.00055	+	0.162625i
$604$	10.7406	−	18.6032i	0.437027	−	0.756954i
$605$		0			0
$606$	30.2399	−	20.8735i	1.22841	−	0.847930i
$607$	−0.391428	−	0.225991i	−0.0158876	−	0.00917270i	0.492035	−	0.870575i	$-0.336253\pi$
$607$	−0.391428	−	0.225991i	−0.0158876	−	0.00917270i	−0.507923	+	0.861403i	$0.669586\pi$
$608$	−28.7342			−1.16533
$609$	−1.35913	−	40.4264i	−0.0550749	−	1.63816i
$610$		0			0
$611$	13.5326	+	7.81306i	0.547471	+	0.316083i
$612$	−25.9127	−	31.7361i	−1.04746	−	1.28286i
$613$	0.774834	+	1.34205i	0.0312953	+	0.0542050i	0.881249	−	0.472653i	$-0.156703\pi$
$613$	0.774834	+	1.34205i	0.0312953	+	0.0542050i	−0.849954	+	0.526858i	$0.823370\pi$
$614$	−10.1256	+	17.5380i	−0.408636	+	0.707778i
$615$		0			0
$616$	−12.0552	−	0.566476i	−0.485716	−	0.0228240i
$617$		−	42.6618i		−	1.71750i	−0.512394	−	0.858751i	$-0.671241\pi$
$617$		−	42.6618i		−	1.71750i	0.512394	−	0.858751i	$-0.328759\pi$
$618$	10.5287	−	22.1894i	0.423528	−	0.892589i
$619$	21.8956	−	12.6414i	0.880058	−	0.508102i	0.00938032	−	0.999956i	$-0.497014\pi$
$619$	21.8956	−	12.6414i	0.880058	−	0.508102i	0.870677	+	0.491854i	$0.163681\pi$
$620$		0			0
$621$	14.2055	+	4.11425i	0.570049	+	0.165099i
$622$		−	14.8460i		−	0.595270i
$623$	−13.1971	−	25.5584i	−0.528732	−	1.02398i
$624$	−0.522850	−	6.47589i	−0.0209307	−	0.259243i
$625$		0			0
$626$	21.6988	+	37.5834i	0.867258	+	1.50214i
$627$	−8.34463	−	12.0890i	−0.333252	−	0.482790i
$628$	6.67010	+	3.85098i	0.266166	+	0.153671i
$629$	20.7055			0.825581
$630$		0			0
$631$	4.91791			0.195779			0.0978895	−	0.995197i	$-0.468791\pi$
$631$	4.91791			0.195779			0.0978895	+	0.995197i	$0.468791\pi$
$632$	−6.61441	−	3.81883i	−0.263107	−	0.151905i
$633$	−10.5256	−	15.2487i	−0.418355	−	0.606079i
$634$	21.5877	+	37.3910i	0.857357	+	1.48499i
$635$		0			0
$636$	−1.03432	−	12.8109i	−0.0410135	−	0.507983i
$637$	32.3242	−	14.8123i	1.28073	−	0.586885i
$638$		−	37.8285i		−	1.49765i
$639$	−27.1653	−	10.3018i	−1.07464	−	0.407535i
$640$		0			0
$641$	−11.0323	+	6.36950i	−0.435750	+	0.251580i	−0.701793	−	0.712381i	$-0.747617\pi$
$641$	−11.0323	+	6.36950i	−0.435750	+	0.251580i	0.266043	+	0.963961i	$0.414284\pi$
$642$	−27.7487	+	58.4807i	−1.09516	+	2.30805i
$643$		−	2.51652i		−	0.0992419i	−0.998768	−	0.0496210i	$-0.984199\pi$
$643$		−	2.51652i		−	0.0992419i	0.998768	−	0.0496210i	$-0.0158013\pi$
$644$	19.4205	+	12.4631i	0.765275	+	0.491116i
$645$		0			0
$646$	22.3325	−	38.6811i	0.878662	−	1.52189i
$647$	−20.2058	−	34.9974i	−0.794371	−	1.37589i	−0.923238	−	0.384230i	$-0.874467\pi$
$647$	−20.2058	−	34.9974i	−0.794371	−	1.37589i	0.128866	−	0.991662i	$-0.458866\pi$
$648$	−14.2943	+	16.1362i	−0.561534	+	0.633889i
$649$	−22.9571	−	13.2543i	−0.901143	−	0.520275i
$650$		0			0
$651$	−21.6094	+	13.4641i	−0.846940	+	0.527698i
$652$	−10.6164			−0.415770
$653$	−36.9723	−	21.3460i	−1.44684	−	0.835332i	−0.448546	−	0.893760i	$-0.648058\pi$
$653$	−36.9723	−	21.3460i	−1.44684	−	0.835332i	−0.998292	+	0.0584277i	$0.981391\pi$
$654$	−59.0354	+	40.7500i	−2.30847	+	1.59345i
$655$		0			0
$656$	−0.0926106	+	0.160406i	−0.00361584	+	0.00626281i
$657$	3.04035	+	18.7058i	0.118616	+	0.729783i
$658$	−0.859751	+	18.2963i	−0.0335166	+	0.713265i
$659$			2.08754i			0.0813192i	0.999173	+	0.0406596i	$0.0129459\pi$
$659$			2.08754i			0.0813192i	−0.999173	+	0.0406596i	$0.987054\pi$
$660$		0			0
$661$	20.5058	−	11.8391i	0.797585	−	0.460486i	−0.0450412	−	0.998985i	$-0.514342\pi$
$661$	20.5058	−	11.8391i	0.797585	−	0.460486i	0.842626	+	0.538499i	$0.181009\pi$
$662$	23.3384	−	13.4744i	0.907071	−	0.523698i
$663$	35.4248	+	16.8088i	1.37578	+	0.652801i
$664$		−	21.5328i		−	0.835633i
$665$		0			0
$666$	−5.03191	−	30.9589i	−0.194983	−	1.19963i
$667$	−12.5614	+	21.7570i	−0.486379	+	0.842433i
$668$	5.05389	+	8.75359i	0.195541	+	0.338687i
$669$	−24.1588	+	16.6759i	−0.934032	+	0.644729i
$670$		0			0
$671$	−3.33267			−0.128656
$672$	25.0955	−	15.6361i	0.968081	−	0.603177i
$673$	−29.6317			−1.14222			−0.571108	−	0.820875i	$-0.693486\pi$
$673$	−29.6317			−1.14222			−0.571108	+	0.820875i	$0.693486\pi$
$674$	−24.7496	−	14.2892i	−0.953320	−	0.550400i
$675$		0			0
$676$	−19.6136	−	33.9717i	−0.754368	−	1.30660i
$677$	17.0667	−	29.5604i	0.655927	−	1.13610i	−0.325734	−	0.945462i	$-0.605611\pi$
$677$	17.0667	−	29.5604i	0.655927	−	1.13610i	0.981661	−	0.190637i	$-0.0610554\pi$
$678$	−17.0046	+	1.37291i	−0.653057	+	0.0527265i
$679$	19.9172	+	12.7819i	0.764354	+	0.490525i
$680$		0			0
$681$	1.80534	−	3.80478i	0.0691809	−	0.145799i
$682$	−20.6210	+	11.9056i	−0.789620	+	0.455887i
$683$	−17.0344	+	9.83481i	−0.651803	+	0.376319i	−0.789147	−	0.614205i	$-0.789477\pi$
$683$	−17.0344	+	9.83481i	−0.651803	+	0.376319i	0.137344	+	0.990523i	$0.456143\pi$
$684$	−38.2796	−	14.5167i	−1.46366	−	0.555060i
$685$		0			0
$686$	32.8110	+	25.7004i	1.25273	+	0.981246i
$687$	−0.0328473	−	0.406838i	−0.00125320	−	0.0155219i
$688$	−3.41073	+	5.90756i	−0.130033	+	0.225224i
$689$	6.15006	+	10.6522i	0.234299	+	0.405817i
$690$		0			0
$691$	−0.800772	−	0.462326i	−0.0304628	−	0.0175877i	0.484691	−	0.874685i	$-0.338932\pi$
$691$	−0.800772	−	0.462326i	−0.0304628	−	0.0175877i	−0.515154	+	0.857098i	$0.672265\pi$
$692$	53.4433			2.03161
$693$	13.8663	+	6.01732i	0.526738	+	0.228579i
$694$	12.6242			0.479206
$695$		0			0
$696$	−20.8023	−	30.1367i	−0.788508	−	1.14233i
$697$	−0.558922	−	0.968081i	−0.0211707	−	0.0366687i
$698$	38.1135	−	66.0145i	1.44262	−	2.49869i
$699$	1.54462	+	19.1312i	0.0584228	+	0.723610i
$700$		0			0
$701$			0.206478i			0.00779858i	0.999992	+	0.00389929i	$0.00124119\pi$
$701$			0.206478i			0.00779858i	−0.999992	+	0.00389929i	$0.998759\pi$
$702$	16.5236	−	57.0522i	0.623643	−	2.15330i
$703$	17.9176	−	10.3447i	0.675776	−	0.390160i
$704$	21.5118	−	12.4199i	0.810758	−	0.468091i
$705$		0			0
$706$			82.6826i			3.11180i
$707$	−24.9138	−	1.17071i	−0.936980	−	0.0440291i
$708$	−73.6405	+	5.94558i	−2.76758	+	0.223449i
$709$	−20.5452	+	35.5852i	−0.771589	+	1.33643i	0.165102	+	0.986276i	$0.447205\pi$
$709$	−20.5452	+	35.5852i	−0.771589	+	1.33643i	−0.936692	+	0.350156i	$0.886129\pi$
$710$		0			0
$711$	6.05020	+	7.40986i	0.226900	+	0.277891i
$712$	−22.5520	−	13.0204i	−0.845171	−	0.487960i
$713$	15.8135			0.592220
$714$	1.54434	+	45.9353i	0.0577956	+	1.71909i
$715$		0			0
$716$	−59.8611	−	34.5608i	−2.23712	−	1.29160i
$717$	−13.7927	+	9.52061i	−0.515098	+	0.355554i
$718$	27.4651	+	47.5709i	1.02499	+	1.77533i
$719$	4.36496	−	7.56034i	0.162786	−	0.281953i	−0.773081	−	0.634307i	$-0.781285\pi$
$719$	4.36496	−	7.56034i	0.162786	−	0.281953i	0.935867	+	0.352354i	$0.114619\pi$
$720$		0			0
$721$	−14.8130	+	7.64871i	−0.551665	+	0.284853i
$722$		−	1.87281i		−	0.0696988i
$723$	25.1594	+	11.9380i	0.935687	+	0.443978i
$724$	−9.24065	+	5.33509i	−0.343426	+	0.198277i
$725$		0			0
$726$	−25.9651	−	12.3203i	−0.963654	−	0.457248i
$727$		−	26.6400i		−	0.988024i	−0.869455	−	0.494012i	$-0.835530\pi$
$727$		−	26.6400i		−	0.988024i	0.869455	−	0.494012i	$-0.164470\pi$
$728$	17.3855	−	27.0907i	0.644350	−	1.00405i
$729$	23.9066	−	12.5489i	0.885430	−	0.464774i
$730$		0			0
$731$	−20.5844	−	35.6532i	−0.761341	−	1.31868i
$732$	−7.64404	+	5.27640i	−0.282532	+	0.195022i
$733$	27.1888	+	15.6975i	1.00424	+	0.579800i	0.909501	−	0.415702i	$-0.136464\pi$
$733$	27.1888	+	15.6975i	1.00424	+	0.579800i	0.0947418	+	0.995502i	$0.469797\pi$
$734$	−46.5056			−1.71655
$735$		0			0
$736$	−18.3646			−0.676927
$737$	13.6845	+	7.90073i	0.504074	+	0.291027i
$738$	−1.31165	+	1.07097i	−0.0482824	+	0.0394229i
$739$	−6.49377	−	11.2475i	−0.238877	−	0.413747i	0.721515	−	0.692399i	$-0.243446\pi$
$739$	−6.49377	−	11.2475i	−0.238877	−	0.413747i	−0.960392	+	0.278651i	$0.910113\pi$
$740$		0			0
$741$	39.0530	−	3.15306i	1.43465	−	0.115831i
$742$	−7.78708	+	12.1341i	−0.285873	+	0.445457i
$743$		−	20.9456i		−	0.768419i	−0.923246	−	0.384209i	$-0.874474\pi$
$743$		−	20.9456i		−	0.768419i	0.923246	−	0.384209i	$-0.125526\pi$
$744$	−9.88108	+	20.8244i	−0.362258	+	0.763461i
$745$		0			0
$746$	40.6783	−	23.4856i	1.48934	−	0.859869i
$747$	−9.56309	+	25.2172i	−0.349895	+	0.922651i
$748$			26.0085i			0.950966i
$749$	39.0400	−	20.1583i	1.42649	−	0.736570i
$750$		0			0
$751$	−2.17046	+	3.75935i	−0.0792014	+	0.137181i	−0.902906	−	0.429839i	$-0.858570\pi$
$751$	−2.17046	+	3.75935i	−0.0792014	+	0.137181i	0.823704	+	0.567020i	$0.191904\pi$
$752$	−1.13588	−	1.96740i	−0.0414212	−	0.0717437i
$753$	−14.1498	−	20.4992i	−0.515649	−	0.747031i
$754$	87.3801	+	50.4489i	3.18220	+	1.83724i
$755$		0			0
$756$	41.3316	−	8.15195i	1.50321	−	0.296484i
$757$	−0.401257			−0.0145839			−0.00729196	−	0.999973i	$-0.502321\pi$
$757$	−0.401257			−0.0145839			−0.00729196	+	0.999973i	$0.502321\pi$
$758$	52.6955	+	30.4238i	1.91399	+	1.10504i
$759$	−5.33320	−	7.72632i	−0.193583	−	0.280448i
$760$		0			0
$761$	−21.1371	+	36.6105i	−0.766219	+	1.32713i	0.173381	+	0.984855i	$0.444531\pi$
$761$	−21.1371	+	36.6105i	−0.766219	+	1.32713i	−0.939600	+	0.342275i	$0.888803\pi$
$762$	−4.01028	−	49.6703i	−0.145277	−	1.79937i
$763$	48.6375	+	2.28550i	1.76080	+	0.0827406i
$764$			29.2909i			1.05971i
$765$		0			0
$766$	12.3453	−	7.12757i	0.446054	−	0.257530i
$767$	61.2320	−	35.3523i	2.21096	−	1.27650i
$768$	8.11469	−	17.1018i	0.292814	−	0.617107i
$769$			0.306962i			0.0110693i	0.999985	+	0.00553466i	$0.00176175\pi$
$769$			0.306962i			0.0110693i	−0.999985	+	0.00553466i	$0.998238\pi$
$770$		0			0
$771$	8.21730	−	0.663448i	0.295939	−	0.0238935i
$772$	8.84096	−	15.3130i	0.318193	−	0.551126i
$773$	1.06021	+	1.83633i	0.0381330	+	0.0660483i	0.884462	−	0.466612i	$-0.154526\pi$
$773$	1.06021	+	1.83633i	0.0381330	+	0.0660483i	−0.846329	+	0.532661i	$0.821192\pi$
$774$	−48.3063	+	39.4424i	−1.73633	+	1.41773i
$775$		0			0
$776$	21.4249			0.769110
$777$	−10.0194	+	18.7849i	−0.359445	+	0.673904i
$778$	28.0304			1.00494
$779$	−0.967334	−	0.558491i	−0.0346583	−	0.0200100i
$780$		0			0
$781$	9.22142	+	15.9720i	0.329968	+	0.571522i
$782$	14.2731	−	24.7218i	0.510406	−	0.884049i
$783$	10.9775	+	44.5321i	0.392304	+	1.59145i
$784$	−5.14648	−	0.484741i	−0.183803	−	0.0173122i
$785$		0			0
$786$	−18.2849	−	8.67606i	−0.652199	−	0.309465i
$787$	−17.7119	+	10.2260i	−0.631360	+	0.364516i	−0.781279	−	0.624183i	$-0.785432\pi$
$787$	−17.7119	+	10.2260i	−0.631360	+	0.364516i	0.149919	+	0.988698i	$0.452099\pi$
$788$	11.5308	−	6.65730i	0.410767	−	0.237156i
$789$	8.84032	+	4.19468i	0.314724	+	0.149335i
$790$		0			0
$791$	9.74563	+	6.25427i	0.346515	+	0.222376i
$792$	13.5071	−	2.19538i	0.479954	−	0.0780094i
$793$	4.44452	−	7.69814i	0.157830	−	0.273369i
$794$	32.0416	+	55.4977i	1.13711	+	1.96954i
$795$		0			0
$796$	23.0849	+	13.3281i	0.818223	+	0.472401i
$797$	21.2684			0.753365			0.376682	−	0.926342i	$-0.377065\pi$
$797$	21.2684			0.753365			0.376682	+	0.926342i	$0.377065\pi$
$798$	24.2864	+	38.9789i	0.859728	+	1.37984i
$799$	13.7105			0.485042
$800$		0			0
$801$	20.6283	+	25.2641i	0.728864	+	0.892662i
$802$	−16.5677	−	28.6961i	−0.585025	−	1.01329i
$803$	6.01512	−	10.4185i	0.212269	−	0.367661i
$804$	43.8963	−	3.54410i	1.54810	−	0.124991i
$805$		0			0
$806$		−	63.5100i		−	2.23704i
$807$	0.528726	−	1.11429i	0.0186121	−	0.0392250i
$808$	−19.5545	+	11.2898i	−0.687924	+	0.397173i
$809$	−19.3311	+	11.1608i	−0.679646	+	0.392394i	−0.799722	−	0.600371i	$-0.795020\pi$
$809$	−19.3311	+	11.1608i	−0.679646	+	0.392394i	0.120075	+	0.992765i	$0.461686\pi$
$810$		0			0
$811$			39.7633i			1.39628i	0.715962	+	0.698139i	$0.245988\pi$
$811$			39.7633i			1.39628i	−0.715962	+	0.698139i	$0.754012\pi$
$812$	−3.35906	+	71.4840i	−0.117880	+	2.50860i
$813$	−0.450786	−	5.58332i	−0.0158097	−	0.195816i
$814$	−9.95527	+	17.2430i	−0.348932	+	0.604368i
$815$		0			0
$816$	−3.23829	−	4.69137i	−0.113363	−	0.164231i
$817$	−35.6257	−	20.5685i	−1.24639	−	0.719601i
$818$	2.10641			0.0736488
$819$	−32.3918	+	24.0050i	−1.13186	+	0.838803i
$820$		0			0
$821$	−34.1580	−	19.7211i	−1.19212	−	0.688272i	−0.233335	−	0.972397i	$-0.574964\pi$
$821$	−34.1580	−	19.7211i	−1.19212	−	0.688272i	−0.958787	+	0.284125i	$0.908297\pi$
$822$	29.8556	+	43.2524i	1.04133	+	1.50860i
$823$	−23.8993	−	41.3948i	−0.833077	−	1.44293i	−0.895587	−	0.444887i	$-0.853244\pi$
$823$	−23.8993	−	41.3948i	−0.833077	−	1.44293i	0.0625104	−	0.998044i	$-0.480089\pi$
$824$	−7.54628	+	13.0705i	−0.262887	+	0.455334i
$825$		0			0
$826$	69.7503	+	44.7623i	2.42692	+	1.55748i
$827$			40.7367i			1.41655i	0.705935	+	0.708277i	$0.250527\pi$
$827$			40.7367i			1.41655i	−0.705935	+	0.708277i	$0.749473\pi$
$828$	−24.4652	−	9.27789i	−0.850224	−	0.322429i
$829$	−18.8083	+	10.8590i	−0.653238	+	0.377147i	−0.789696	−	0.613499i	$-0.789762\pi$
$829$	−18.8083	+	10.8590i	−0.653238	+	0.377147i	0.136458	+	0.990646i	$0.456428\pi$
$830$		0			0
$831$	17.0132	−	35.8555i	0.590182	−	1.24381i
$832$			66.2536i			2.29693i
$833$	18.0635	−	25.4360i	0.625864	−	0.881303i
$834$	7.85536	−	0.634225i	0.272009	−	0.0219614i
$835$		0			0
$836$	12.9942	+	22.5067i	0.449415	+	0.778410i
$837$	20.8204	−	19.9994i	0.719657	−	0.691279i
$838$	−58.7626	−	33.9266i	−2.02992	−	1.17197i
$839$	9.40638			0.324744			0.162372	−	0.986730i	$-0.448085\pi$
$839$	9.40638			0.324744			0.162372	+	0.986730i	$0.448085\pi$
$840$		0			0
$841$	−48.9115			−1.68660
$842$	−70.8790	−	40.9220i	−2.44265	−	1.41026i
$843$	−17.1540	+	11.8408i	−0.590816	+	0.407819i
$844$	16.3904	+	28.3891i	0.564182	+	0.977192i
$845$		0			0
$846$	−3.33197	−	20.4999i	−0.114555	−	0.704803i
$847$	8.95019	+	17.3335i	0.307532	+	0.595587i
$848$		−	1.78822i		−	0.0614077i
$849$	−28.0125	−	13.2918i	−0.961385	−	0.456172i
$850$		0			0
$851$	11.4515	−	6.61152i	0.392552	−	0.226640i
$852$	46.4382	+	22.0347i	1.59095	+	0.754896i
$853$			28.2296i			0.966562i	0.875465	+	0.483281i	$0.160555\pi$
$853$			28.2296i			0.966562i	−0.875465	+	0.483281i	$0.839445\pi$
$854$	10.4080	+	0.489076i	0.356154	+	0.0167358i
$855$		0			0
$856$	19.8884	−	34.4477i	0.679771	−	1.17740i
$857$	−8.37845	−	14.5119i	−0.286202	−	0.495717i	0.686698	−	0.726943i	$-0.259060\pi$
$857$	−8.37845	−	14.5119i	−0.286202	−	0.495717i	−0.972900	+	0.231226i	$0.925726\pi$
$858$	−31.0304	+	21.4192i	−1.05936	+	0.731238i
$859$	8.38608	+	4.84171i	0.286129	+	0.165197i	0.636195	−	0.771528i	$-0.280507\pi$
$859$	8.38608	+	4.84171i	0.286129	+	0.165197i	−0.350066	+	0.936725i	$0.613841\pi$
$860$		0			0
$861$	1.14875	−	0.0386209i	0.0391492	−	0.00131620i
$862$	−31.0135			−1.05632
$863$	−19.0593	−	11.0039i	−0.648785	−	0.374576i	0.139206	−	0.990263i	$-0.455545\pi$
$863$	−19.0593	−	11.0039i	−0.648785	−	0.374576i	−0.787990	+	0.615687i	$0.788878\pi$
$864$	−24.1792	+	23.2257i	−0.822592	+	0.790155i
$865$		0			0
$866$	1.31469	−	2.27712i	0.0446751	−	0.0773796i
$867$	4.94248	−	0.399046i	0.167855	−	0.0135523i
$868$	40.0244	−	20.6667i	1.35852	−	0.701472i
$869$		−	6.07256i		−	0.205998i
$870$		0			0
$871$	−36.4998	+	21.0732i	−1.23675	+	0.714036i
$872$	38.1749	−	22.0403i	1.29276	−	0.746378i
$873$	−25.0910	−	9.51520i	−0.849200	−	0.322041i
$874$		−	28.5242i		−	0.964847i
$875$		0			0
$876$	−2.69825	−	33.4199i	−0.0911655	−	1.12915i
$877$	10.5609	−	18.2921i	0.356617	−	0.617679i	−0.630776	−	0.775965i	$-0.717263\pi$
$877$	10.5609	−	18.2921i	0.356617	−	0.617679i	0.987393	+	0.158286i	$0.0505968\pi$
$878$	−3.25277	−	5.63397i	−0.109776	−	0.190137i
$879$	−8.73059	−	12.6482i	−0.294475	−	0.426613i
$880$		0			0
$881$	−44.3021			−1.49258			−0.746288	−	0.665623i	$-0.768166\pi$
$881$	−44.3021			−1.49258			−0.746288	+	0.665623i	$0.768166\pi$
$882$	−42.4218	−	20.8271i	−1.42842	−	0.701286i
$883$	5.12282			0.172397			0.0861984	−	0.996278i	$-0.472528\pi$
$883$	5.12282			0.172397			0.0861984	+	0.996278i	$0.472528\pi$
$884$	−60.0771	−	34.6855i	−2.02061	−	1.16660i
$885$		0			0
$886$	18.5729	+	32.1693i	0.623970	+	1.08075i
$887$	3.87397	−	6.70992i	0.130075	−	0.225297i	−0.793630	−	0.608401i	$-0.791811\pi$
$887$	3.87397	−	6.70992i	0.130075	−	0.225297i	0.923705	+	0.383104i	$0.125145\pi$
$888$	1.55109	+	19.2114i	0.0520512	+	0.644693i
$889$	−18.2687	+	28.4670i	−0.612713	+	0.954751i
$890$		0			0
$891$	−16.7933	−	3.42771i	−0.562597	−	0.114833i
$892$	44.9774	−	25.9677i	1.50596	−	0.869464i
$893$	11.8645	−	6.84995i	0.397029	−	0.229225i
$894$	−2.14262	+	4.51558i	−0.0716598	+	0.151024i
$895$		0			0
$896$	−38.6678	+	19.9661i	−1.29180	+	0.667022i
$897$	24.9595	−	2.01518i	0.833374	−	0.0672848i
$898$	29.2355	−	50.6374i	0.975601	−	1.68979i
$899$	24.5206	+	42.4710i	0.817809	+	1.41649i
$900$		0			0
$901$	9.34634	+	5.39611i	0.311372	+	0.179770i
$902$	1.07493			0.0357912
$903$	42.3069	−	1.42236i	1.40789	−	0.0473331i
$904$	10.4833			0.348671
$905$		0			0
$906$	22.4869	−	15.5219i	0.747078	−	0.515681i
$907$	12.2639	+	21.2416i	0.407215	+	0.705316i	0.994576	−	0.104008i	$-0.0331668\pi$
$907$	12.2639	+	21.2416i	0.407215	+	0.705316i	−0.587362	+	0.809324i	$0.699833\pi$
$908$	−3.72538	+	6.45254i	−0.123631	+	0.214135i
$909$	27.9145	−	4.53708i	0.925864	−	0.150486i
$910$		0			0
$911$			43.8824i			1.45389i	0.686697	+	0.726944i	$0.259060\pi$
$911$			43.8824i			1.45389i	−0.686697	+	0.726944i	$0.740940\pi$
$912$	−5.14615	−	2.44182i	−0.170406	−	0.0808567i
$913$	14.8266	−	8.56014i	0.490689	−	0.283299i
$914$	−2.92708	+	1.68995i	−0.0968193	+	0.0558986i
$915$		0			0
$916$			0.722122i			0.0238596i
$917$	6.30281	+	12.2064i	0.208137	+	0.403092i
$918$	−12.4734	−	50.6004i	−0.411684	−	1.67006i
$919$	7.85902	−	13.6122i	0.259245	−	0.449026i	−0.706795	−	0.707419i	$-0.749860\pi$
$919$	7.85902	−	13.6122i	0.259245	−	0.449026i	0.966040	+	0.258393i	$0.0831929\pi$
$920$		0			0
$921$	−12.8274	+	8.85428i	−0.422676	+	0.291758i
$922$	−2.73760	−	1.58056i	−0.0901581	−	0.0520528i
$923$	−49.1915			−1.61916
$924$	−23.5960	−	12.5856i	−0.776253	−	0.414036i
$925$		0			0
$926$	−39.3789	−	22.7354i	−1.29407	−	0.747132i
$927$	14.6424	−	11.9556i	0.480919	−	0.392674i
$928$	−28.4764	−	49.3225i	−0.934783	−	1.61909i
$929$	9.87128	−	17.0976i	0.323866	−	0.560952i	−0.657416	−	0.753528i	$-0.728351\pi$
$929$	9.87128	−	17.0976i	0.323866	−	0.560952i	0.981282	+	0.192575i	$0.0616839\pi$
$930$		0			0
$931$	2.92324	−	31.0360i	0.0958054	−	1.01716i
$932$		−	33.9572i		−	1.11230i
$933$	4.89830	−	10.3232i	0.160363	−	0.337967i
$934$	75.3434	−	43.4995i	2.46531	−	1.42335i
$935$		0			0
$936$	−12.9422	+	34.1278i	−0.423030	+	1.11550i
$937$			37.1538i			1.21376i	0.794793	+	0.606881i	$0.207580\pi$
$937$			37.1538i			1.21376i	−0.794793	+	0.606881i	$0.792420\pi$
$938$	−41.5774	−	26.6824i	−1.35755	−	0.871210i
$939$	2.68801	+	33.2930i	0.0877199	+	1.08648i
$940$		0			0
$941$	16.1049	+	27.8945i	0.525005	+	0.909336i	0.999576	+	0.0291183i	$0.00926996\pi$
$941$	16.1049	+	27.8945i	0.525005	+	0.909336i	−0.474571	+	0.880217i	$0.657397\pi$
$942$	5.56532	+	8.06259i	0.181328	+	0.262693i
$943$	−0.618241	−	0.356942i	−0.0201327	−	0.0116236i
$944$	−10.2792			−0.334559
$945$		0			0
$946$	39.5882			1.28712
$947$	24.5694	+	14.1852i	0.798400	+	0.460956i	0.842911	−	0.538053i	$-0.180840\pi$
$947$	24.5694	+	14.1852i	0.798400	+	0.460956i	−0.0445115	+	0.999009i	$0.514173\pi$
$948$	−9.61430	−	13.9284i	−0.312258	−	0.452375i
$949$	16.0438	+	27.7886i	0.520803	+	0.902057i
$950$		0			0
$951$	2.67425	+	33.1226i	0.0867185	+	1.07407i
$952$	1.32570	−	28.2122i	0.0429662	−	0.914361i
$953$			28.4105i			0.920305i	0.887840	+	0.460153i	$0.152205\pi$
$953$			28.4105i			0.920305i	−0.887840	+	0.460153i	$0.847795\pi$
$954$	5.79691	−	15.2861i	0.187682	−	0.494904i
$955$		0			0
$956$	25.6785	−	14.8255i	0.830501	−	0.479490i
$957$	12.4812	−	26.3042i	0.403459	−	0.850293i
$958$			69.0729i			2.23164i
$959$	1.67447	−	35.6344i	0.0540716	−	1.15069i
$960$		0			0
$961$	−0.0655266	+	0.113495i	−0.00211376	+	0.00366114i
$962$	−26.5531	−	45.9913i	−0.856107	−	1.48282i
$963$	−38.5903	+	31.5092i	−1.24356	+	1.01537i
$964$	−42.6680	−	24.6344i	−1.37424	−	0.793419i
$965$		0			0
$966$	15.5219	+	24.9121i	0.499407	+	0.801535i
$967$	−42.3117			−1.36065			−0.680326	−	0.732909i	$-0.738162\pi$
$967$	−42.3117			−1.36065			−0.680326	+	0.732909i	$0.738162\pi$
$968$	15.2946	+	8.83032i	0.491586	+	0.283817i
$969$	28.2914	−	19.5286i	0.908852	−	0.627348i
$970$		0			0
$971$	11.7297	−	20.3164i	0.376424	−	0.651985i	−0.614115	−	0.789216i	$-0.710487\pi$
$971$	11.7297	−	20.3164i	0.376424	−	0.651985i	0.990539	+	0.137231i	$0.0438203\pi$
$972$	−43.9451	+	18.7257i	−1.40954	+	0.600628i
$973$	−4.50205	−	2.88919i	−0.144329	−	0.0926233i
$974$		−	66.8370i		−	2.14159i
$975$		0			0
$976$	−1.11917	+	0.646154i	−0.0358238	+	0.0206829i
$977$	−30.4577	+	17.5848i	−0.974429	+	0.562587i	−0.900584	−	0.434683i	$-0.856861\pi$
$977$	−30.4577	+	17.5848i	−0.974429	+	0.562587i	−0.0738456	+	0.997270i	$0.523527\pi$
$978$	−12.2002	−	5.78893i	−0.390120	−	0.185110i
$979$		−	20.7045i		−	0.661720i
$980$		0			0
$981$	−54.4955	+	8.85745i	−1.73991	+	0.282796i
$982$	−8.03020	+	13.9087i	−0.256254	+	0.443845i
$983$	20.8391	+	36.0944i	0.664665	+	1.15123i	0.979376	+	0.202046i	$0.0647590\pi$
$983$	20.8391	+	36.0944i	0.664665	+	1.15123i	−0.314711	+	0.949187i	$0.601908\pi$
$984$	0.856358	−	0.591113i	0.0272997	−	0.0188440i
$985$		0			0
$986$	88.5285			2.81932
$987$	−6.63453	+	12.4387i	−0.211179	+	0.395929i
$988$	−69.3175			−2.20528
$989$	−22.7690	−	13.1457i	−0.724013	−	0.418009i
$990$		0			0
$991$	−22.1571	−	38.3773i	−0.703844	−	1.21909i	−0.967107	−	0.254370i	$-0.918132\pi$
$991$	−22.1571	−	38.3773i	−0.703844	−	1.21909i	0.263262	−	0.964724i	$-0.415201\pi$
$992$	−17.9244	+	31.0460i	−0.569101	+	0.985711i
$993$	20.6741	−	1.66919i	0.656074	−	0.0529700i
$994$	−26.4548	−	51.2340i	−0.839094	−	1.62505i
$995$		0			0
$996$	20.4546	−	43.1081i	0.648127	−	1.36593i
$997$	−38.6961	+	22.3412i	−1.22552	+	0.707552i	−0.966089	−	0.258210i	$-0.916867\pi$
$997$	−38.6961	+	22.3412i	−1.22552	+	0.707552i	−0.259428	+	0.965763i	$0.583534\pi$
$998$	−26.0016	+	15.0120i	−0.823065	+	0.475197i
$999$	6.71565	−	23.1876i	0.212474	−	0.733622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.i.26.2	yes	20
3.2	odd	2	inner	525.2.t.i.26.9	yes	20
5.2	odd	4		525.2.q.g.299.18		40
5.3	odd	4		525.2.q.g.299.3		40
5.4	even	2		525.2.t.h.26.9	yes	20
7.3	odd	6	inner	525.2.t.i.101.9	yes	20
15.2	even	4		525.2.q.g.299.4		40
15.8	even	4		525.2.q.g.299.17		40
15.14	odd	2		525.2.t.h.26.2	✓	20
21.17	even	6	inner	525.2.t.i.101.2	yes	20
35.3	even	12		525.2.q.g.374.4		40
35.17	even	12		525.2.q.g.374.17		40
35.24	odd	6		525.2.t.h.101.2	yes	20
105.17	odd	12		525.2.q.g.374.3		40
105.38	odd	12		525.2.q.g.374.18		40
105.59	even	6		525.2.t.h.101.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.3		40	5.3	odd	4
525.2.q.g.299.4		40	15.2	even	4
525.2.q.g.299.17		40	15.8	even	4
525.2.q.g.299.18		40	5.2	odd	4
525.2.q.g.374.3		40	105.17	odd	12
525.2.q.g.374.4		40	35.3	even	12
525.2.q.g.374.17		40	35.17	even	12
525.2.q.g.374.18		40	105.38	odd	12
525.2.t.h.26.2	✓	20	15.14	odd	2
525.2.t.h.26.9	yes	20	5.4	even	2
525.2.t.h.101.2	yes	20	35.24	odd	6
525.2.t.h.101.9	yes	20	105.59	even	6
525.2.t.i.26.2	yes	20	1.1	even	1	trivial
525.2.t.i.26.9	yes	20	3.2	odd	2	inner
525.2.t.i.101.2	yes	20	21.17	even	6	inner
525.2.t.i.101.9	yes	20	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94891 - 1.12521i) q^{2} +(-0.983931 - 1.42544i) q^{3} +(1.53217 + 2.65380i) q^{4} +(0.313682 + 3.88518i) q^{6} +(1.42897 - 2.22667i) q^{7} -2.39522i q^{8} +(-1.06376 + 2.80507i) q^{9} +O(q^{10})\)	\(q+(-1.94891 - 1.12521i) q^{2} +(-0.983931 - 1.42544i) q^{3} +(1.53217 + 2.65380i) q^{4} +(0.313682 + 3.88518i) q^{6} +(1.42897 - 2.22667i) q^{7} -2.39522i q^{8} +(-1.06376 + 2.80507i) q^{9} +(1.64925 - 0.952197i) q^{11} +(2.27529 - 4.79518i) q^{12} +5.07948i q^{13} +(-5.29039 + 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(2.22839 + 3.85968i) q^{17} +(5.22946 - 4.26988i) q^{18} +(3.85670 + 2.22667i) q^{19} +(-4.57999 + 0.153979i) q^{21} -4.28567 q^{22} +(2.46489 + 1.42310i) q^{23} +(-3.41425 + 2.35673i) q^{24} +(5.71546 - 9.89947i) q^{26} +(5.04513 - 1.24366i) q^{27} +(8.09857 + 0.380555i) q^{28} +8.82675i q^{29} +(4.81162 - 2.77799i) q^{31} +(-5.58785 + 3.22615i) q^{32} +(-2.98005 - 1.41402i) q^{33} -10.0296i q^{34} +(-9.07397 + 1.47484i) q^{36} +(2.32292 - 4.02342i) q^{37} +(-5.01092 - 8.67917i) q^{38} +(7.24050 - 4.99786i) q^{39} -0.250819 q^{41} +(9.09926 + 4.85334i) q^{42} -9.23735 q^{43} +(5.05389 + 2.91786i) q^{44} +(-3.20257 - 5.54701i) q^{46} +(1.53816 - 2.66417i) q^{47} +(-1.27491 + 0.102934i) q^{48} +(-2.91610 - 6.36367i) q^{49} +(3.30916 - 6.97409i) q^{51} +(-13.4799 + 7.78265i) q^{52} +(2.09711 - 1.21077i) q^{53} +(-11.2319 - 3.25301i) q^{54} +(-5.33336 - 3.42269i) q^{56} +(-0.620744 - 7.68839i) q^{57} +(9.93190 - 17.2026i) q^{58} +(-6.95983 - 12.0548i) q^{59} +(-1.51554 - 0.874995i) q^{61} -12.5032 q^{62} +(4.72588 + 6.37700i) q^{63} +13.0434 q^{64} +(4.21680 + 6.10897i) q^{66} +(4.14868 + 7.18573i) q^{67} +(-6.82855 + 11.8274i) q^{68} +(-0.396729 - 4.91379i) q^{69} +9.68436i q^{71} +(6.71876 + 2.54794i) q^{72} +(5.47076 - 3.15855i) q^{73} +(-9.05434 + 5.22752i) q^{74} +13.6466i q^{76} +(0.236503 - 5.03300i) q^{77} +(-19.7347 + 1.59334i) q^{78} +(1.59436 - 2.76150i) q^{79} +(-6.73682 - 5.96785i) q^{81} +(0.488824 + 0.282223i) q^{82} +8.98988 q^{83} +(-7.42597 - 11.9185i) q^{84} +(18.0028 + 10.3939i) q^{86} +(12.5820 - 8.68491i) q^{87} +(-2.28072 - 3.95033i) q^{88} +(5.43599 - 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} +8.72178i q^{92} +(-8.69416 - 4.12533i) q^{93} +(-5.99548 + 3.46149i) q^{94} +(10.0967 + 4.79084i) q^{96} +8.94486i q^{97} +(-1.47721 + 15.6835i) q^{98} +(0.916566 + 5.63918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9	\( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9 - 21 * q^12 - 18 * q^16 + 14 * q^18 - 9 * q^21 + 20 * q^22 + 18 * q^24 - 10 * q^28 + 42 * q^31 + 12 * q^33 - 36 * q^36 + 24 * q^37 + 33 * q^42 + 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 - 84 * q^52 - 75 * q^54 + 6 * q^57 - 4 * q^58 - 90 * q^61 - 5 * q^63 - 120 * q^64 + 6 * q^66 + 20 * q^67 - 35 * q^72 - 48 * q^73 - 108 * q^78 + 46 * q^79 + 29 * q^81 + 36 * q^82 + 75 * q^84 + 69 * q^87 + 4 * q^88 - 30 * q^91 - 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Introduction

L-functions

Modular forms

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