LMFDB - Embedded newform 525.2.t.h.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.h.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94891 - 1.12521i) q^{2} +(-0.742502 - 1.56483i) q^{3} +(1.53217 + 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(-1.42897 + 2.22667i) q^{7} -2.39522i q^{8} +(-1.89738 + 2.32378i) q^{9} +O(q^{10})$	\(q+(-1.94891 - 1.12521i) q^{2} +(-0.742502 - 1.56483i) q^{3} +(1.53217 + 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(-1.42897 + 2.22667i) q^{7} -2.39522i q^{8} +(-1.89738 + 2.32378i) q^{9} +(-1.64925 + 0.952197i) q^{11} +(3.01511 - 4.36805i) q^{12} -5.07948i q^{13} +(5.29039 - 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(2.22839 + 3.85968i) q^{17} +(6.31256 - 2.39390i) q^{18} +(3.85670 + 2.22667i) q^{19} +(4.54537 + 0.582783i) q^{21} +4.28567 q^{22} +(2.46489 + 1.42310i) q^{23} +(-3.74811 + 1.77846i) 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} +(2.71460 + 1.87379i) q^{33} -10.0296i q^{34} +(-9.07397 - 1.47484i) q^{36} +(-2.32292 + 4.02342i) q^{37} +(-5.01092 - 8.67917i) q^{38} +(-7.94852 + 3.77153i) q^{39} +0.250819 q^{41} +(-8.20277 - 6.25027i) 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} +(4.38516 - 6.35287i) q^{51} +(13.4799 - 7.78265i) q^{52} +(2.09711 - 1.21077i) q^{53} +(-8.43313 - 8.10060i) 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} +(-2.46299 - 7.54544i) q^{63} +13.0434 q^{64} +(-3.18212 - 6.70634i) q^{66} +(-4.14868 - 7.18573i) q^{67} +(-6.82855 + 11.8274i) q^{68} +(0.396729 - 4.91379i) q^{69} -9.68436i q^{71} +(5.56596 + 4.54465i) 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} +(-1.79990 - 8.81818i) q^{81} +(-0.488824 - 0.282223i) q^{82} +8.98988 q^{83} +(5.41770 + 12.9554i) q^{84} +(-18.0028 - 10.3939i) q^{86} +(-13.8124 + 6.55388i) q^{87} +(2.28072 + 3.95033i) q^{88} +(-5.43599 + 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} +8.72178i q^{92} +(-7.91972 - 5.46670i) q^{93} +(-5.99548 + 3.46149i) q^{94} +(9.19736 + 6.34861i) 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	$0.959532\pi$
$3$	−0.742502	−	1.56483i	−0.428684	−	0.903455i
$3$	−0.742502	−	1.56483i	−0.428684	−	0.903455i
$4$	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
$9$	−1.89738	+	2.32378i	−0.632460	+	0.774593i
$10$		0			0
$11$	−1.64925	+	0.952197i	−0.497269	+	0.287098i	−0.727585	−	0.686018i	$-0.759357\pi$
$11$	−1.64925	+	0.952197i	−0.497269	+	0.287098i	0.230316	+	0.973116i	$0.426024\pi$
$12$	3.01511	−	4.36805i	0.870386	−	1.26095i
$13$		−	5.07948i		−	1.40879i	−0.709806	−	0.704397i	$-0.751217\pi$
$13$		−	5.07948i		−	1.40879i	0.709806	−	0.704397i	$-0.248783\pi$
$14$	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	$0.651582\pi$
$18$	6.31256	−	2.39390i	1.48788	−	0.564248i
$19$	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
$21$	4.54537	+	0.582783i	0.991880	+	0.127174i
$22$	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	$0.570768\pi$
$24$	−3.74811	+	1.77846i	−0.765080	+	0.363026i
$25$		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	$-0.694227\pi$
$29$		−	8.82675i		−	1.63909i	0.573018	−	0.819543i	$-0.305773\pi$
$30$		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
$33$	2.71460	+	1.87379i	0.472551	+	0.326185i
$34$		−	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	−0.991332	−	0.131382i	$-0.958059\pi$
$37$	−2.32292	+	4.02342i	−0.381886	+	0.661446i	0.609446	+	0.792828i	$0.291392\pi$
$38$	−5.01092	−	8.67917i	−0.812878	−	1.40795i
$39$	−7.94852	+	3.77153i	−1.27278	+	0.603928i
$40$		0			0
$41$	0.250819			0.0391713			0.0195857	−	0.999808i	$-0.493765\pi$
$41$	0.250819			0.0391713			0.0195857	+	0.999808i	$0.493765\pi$
$42$	−8.20277	−	6.25027i	−1.26572	−	0.964437i
$43$	9.23735			1.40868			0.704341	−	0.709862i	$-0.251243\pi$
$43$	9.23735			1.40868			0.704341	+	0.709862i	$0.251243\pi$
$44$	−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
$51$	4.38516	−	6.35287i	0.614045	−	0.889579i
$52$	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	$0.280148\pi$
$54$	−8.43313	−	8.10060i	−1.14760	−	1.10235i
$55$		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	$0.194283\pi$
$59$	6.95983	+	12.0548i	0.906093	+	1.56940i	0.0866494	+	0.996239i	$0.472384\pi$
$60$		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
$63$	−2.46299	−	7.54544i	−0.310308	−	0.950636i
$64$	13.0434			1.63042
$65$		0			0
$66$	−3.18212	−	6.70634i	−0.391692	−	0.825494i
$67$	−4.14868	−	7.18573i	−0.506842	−	0.877876i	−0.999969	−	0.00791862i	$-0.997479\pi$
$67$	−4.14868	−	7.18573i	−0.506842	−	0.877876i	0.493127	−	0.869958i	$-0.335854\pi$
$68$	−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	$-0.805134\pi$
$71$		−	9.68436i		−	1.14932i	0.818392	−	0.574661i	$-0.194866\pi$
$72$	5.56596	+	4.54465i	0.655955	+	0.535592i
$73$	−5.47076	+	3.15855i	−0.640304	+	0.369680i	−0.784732	−	0.619835i	$-0.787199\pi$
$73$	−5.47076	+	3.15855i	−0.640304	+	0.369680i	0.144427	+	0.989515i	$0.453866\pi$
$74$	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
$81$	−1.79990	−	8.81818i	−0.199988	−	0.979798i
$82$	−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	$0.335760\pi$
$84$	5.41770	+	12.9554i	0.591120	+	1.41355i
$85$		0			0
$86$	−18.0028	−	10.3939i	−1.94129	−	1.12080i
$87$	−13.8124	+	6.55388i	−1.48084	+	0.702650i
$88$	2.28072	+	3.95033i	0.243126	+	0.421106i
$89$	−5.43599	+	9.41541i	−0.576213	+	0.998031i	0.419695	+	0.907665i	$0.362137\pi$
$89$	−5.43599	+	9.41541i	−0.576213	+	0.998031i	−0.995909	+	0.0903658i	$0.971196\pi$
$90$		0			0
$91$	11.3103	+	7.25841i	1.18564	+	0.760889i
$92$			8.72178i			0.909308i
$93$	−7.91972	−	5.46670i	−0.821237	−	0.566871i
$94$	−5.99548	+	3.46149i	−0.618387	+	0.357026i
$95$		0			0
$96$	9.19736	+	6.34861i	0.938702	+	0.647952i
$97$		−	8.94486i		−	0.908213i	−0.890947	−	0.454107i	$-0.849959\pi$
$97$		−	8.94486i		−	0.908213i	0.890947	−	0.454107i	$-0.150041\pi$
$98$	−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	0.999372	−	0.0354254i	$-0.0112786\pi$
$101$	4.71346	+	8.16395i	0.469007	+	0.812344i	−0.530365	+	0.847769i	$0.677945\pi$
$102$	−15.6946	+	7.44698i	−1.55399	+	0.737361i
$103$	5.45692	+	3.15056i	0.537686	+	0.310433i	0.744141	−	0.668023i	$-0.232859\pi$
$103$	5.45692	+	3.15056i	0.537686	+	0.310433i	−0.206454	+	0.978456i	$0.566192\pi$
$104$	−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	$0.370054\pi$
$108$	4.42957	+	15.2943i	0.426236	+	1.47169i
$109$	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	$0.933999\pi$
$114$	−9.86079	+	14.2855i	−0.923548	+	1.33796i
$115$		0			0
$116$	23.4245	−	13.5241i	2.17491	−	1.25568i
$117$	11.8036	+	9.63771i	1.09124	+	0.891007i
$118$		−	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
$123$	−0.186234	−	0.392489i	−0.0167921	−	0.0353895i
$124$	14.7445	+	8.51273i	1.32409	+	0.764466i
$125$		0			0
$126$	−3.69002	+	17.4768i	−0.328733	+	1.55696i
$127$	12.7846			1.13445			0.567223	−	0.823564i	$-0.308018\pi$
$127$	12.7846			1.13445			0.567223	+	0.823564i	$0.308018\pi$
$128$	−14.2447	−	8.22419i	−1.25907	−	0.726922i
$129$	−6.85875	−	14.4549i	−0.603880	−	1.27268i
$130$		0			0
$131$	2.59617	−	4.49669i	0.226828	−	0.392878i	−0.730038	−	0.683406i	$-0.760498\pi$
$131$	2.59617	−	4.49669i	0.226828	−	0.392878i	0.956866	+	0.290528i	$0.0938311\pi$
$132$	−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	$0.137953\pi$
$138$	−6.30221	+	9.13015i	−0.536480	+	0.777210i
$139$		−	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
$144$	0.785551	+	2.07145i	0.0654626	+	0.172621i
$145$		0			0
$146$	14.2161			1.17653
$147$	−7.79285	+	9.28825i	−0.642743	+	0.766082i
$148$	−14.2365			−1.17023
$149$	−1.11049	−	0.641143i	−0.0909750	−	0.0525244i	0.453822	−	0.891092i	$-0.350060\pi$
$149$	−1.11049	−	0.641143i	−0.0909750	−	0.0525244i	−0.544797	+	0.838568i	$0.683393\pi$
$150$		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
$156$	−22.1874	−	15.3152i	−1.77641	−	1.22620i
$157$	−2.17668	+	1.25671i	−0.173718	+	0.100296i	−0.584338	−	0.811511i	$-0.698646\pi$
$157$	−2.17668	+	1.25671i	−0.173718	+	0.100296i	0.410620	+	0.911807i	$0.365312\pi$
$158$	−6.21452	+	3.58795i	−0.494401	+	0.285442i
$159$	−3.45175	−	2.38262i	−0.273742	−	0.188954i
$160$		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	−0.790177	−	0.612879i	$-0.790011\pi$
$163$	1.73224	−	3.00033i	0.135680	−	0.235004i	0.925857	+	0.377874i	$0.123345\pi$
$164$	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	$0.459265\pi$
$168$	1.39589	−	10.8872i	0.107696	−	0.839963i
$169$	−12.8011			−0.984703
$170$		0			0
$171$	−12.4919	+	4.73729i	−0.955281	+	0.362269i
$172$	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
$177$	13.6960	−	19.8417i	1.02945	−	1.49139i
$178$	21.1885	−	12.2332i	1.58815	−	0.916917i
$179$	19.5347	−	11.2784i	1.46009	−	0.842985i	0.461077	−	0.887360i	$-0.347463\pi$
$179$	19.5347	−	11.2784i	1.46009	−	0.842985i	0.999015	+	0.0443755i	$0.0141298\pi$
$180$		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
$186$	9.28369	+	19.5654i	0.680713	+	1.43461i
$187$	−7.35035	−	4.24373i	−0.537511	−	0.310332i
$188$	9.42692			0.687529
$189$	−9.97855	+	9.45667i	−0.725833	+	0.687871i
$190$		0			0
$191$	−8.27801	−	4.77931i	−0.598976	−	0.345819i	0.169663	−	0.985502i	$-0.445732\pi$
$191$	−8.27801	−	4.77931i	−0.598976	−	0.345819i	−0.768638	+	0.639683i	$0.779065\pi$
$192$	−9.68474	−	20.4107i	−0.698936	−	1.47301i
$193$	2.88510	+	4.99714i	0.207674	+	0.359702i	0.950981	−	0.309248i	$-0.100077\pi$
$193$	2.88510	+	4.99714i	0.207674	+	0.359702i	−0.743307	+	0.668950i	$0.766744\pi$
$194$	−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	$-0.0494682\pi$
$198$	−8.13155	+	9.95895i	−0.577884	+	0.707752i
$199$	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
$201$	−8.16403	+	11.8274i	−0.575846	+	0.834240i
$202$		−	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
$207$	−7.98381	+	3.02769i	−0.554913	+	0.210439i
$208$	−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
$213$	−15.1544	+	7.19066i	−1.03836	+	0.492696i
$214$	−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
$219$	9.00464	+	6.21558i	0.608477	+	0.420010i
$220$		0			0
$221$	19.6052	−	11.3190i	1.31879	−	0.761402i
$222$	−14.9031	−	10.2870i	−1.00023	−	0.690421i
$223$			16.9483i			1.13494i	0.823394	+	0.567471i	$0.192078\pi$
$223$			16.9483i			1.13494i	−0.823394	+	0.567471i	$0.807922\pi$
$224$	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	$0.807621\pi$
$228$	21.3546	−	10.1326i	1.41424	−	0.671049i
$229$	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
$231$	−8.05139	+	3.36693i	−0.529743	+	0.221528i
$232$	−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	$0.784908\pi$
$234$	−12.1598	−	32.0645i	−0.794909	−	2.09612i
$235$		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	$0.101316\pi$
$239$			9.67610i			0.625895i	−0.949770	+	0.312948i	$0.898684\pi$
$240$		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
$243$	−12.4625	+	9.36405i	−0.799471	+	0.600704i
$244$		−	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
$249$	−6.67501	−	14.0676i	−0.423012	−	0.891500i
$250$		0			0
$251$	−14.3809			−0.907716			−0.453858	−	0.891074i	$-0.649953\pi$
$251$	−14.3809			−0.907716			−0.453858	+	0.891074i	$0.649953\pi$
$252$	16.2504	−	18.0972i	1.02368	−	1.14002i
$253$	−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
$261$	20.5114	+	16.7477i	1.26962	+	1.03666i
$262$	−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	$0.389060\pi$
$264$	4.48815	−	6.50207i	0.276226	−	0.400175i
$265$		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	0.854967	−	0.518682i	$-0.173577\pi$
$269$	−0.356044	−	0.616686i	−0.0217084	−	0.0376000i	−0.876676	+	0.481082i	$0.840244\pi$
$270$		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
$273$	2.96024	−	23.0881i	0.179162	−	1.39736i
$274$	−30.3432			−1.83310
$275$		0			0
$276$	13.6481	−	6.47594i	0.821518	−	0.389806i
$277$	−11.4567	−	19.8435i	−0.688364	−	1.19228i	−0.972367	−	0.233459i	$-0.924996\pi$
$277$	−11.4567	−	19.8435i	−0.688364	−	1.19228i	0.284002	−	0.958824i	$-0.408338\pi$
$278$	−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	$0.116865\pi$
$281$			12.0342i			0.717900i	−0.933357	+	0.358950i	$0.883135\pi$
$282$	9.86831	+	6.81174i	0.587649	+	0.405633i
$283$	−15.5030	+	8.95065i	−0.921556	+	0.532061i	−0.884131	−	0.467239i	$-0.845249\pi$
$283$	−15.5030	+	8.95065i	−0.921556	+	0.532061i	−0.0374249	+	0.999299i	$0.511916\pi$
$284$	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
$291$	−13.9972	+	6.64158i	−0.820529	+	0.389336i
$292$	−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	$0.416545\pi$
$294$	25.6388	−	9.33343i	1.49528	−	0.544337i
$295$		0			0
$296$	9.63697	+	5.56391i	0.560138	+	0.323396i
$297$	−9.50491	+	2.75284i	−0.551531	+	0.159736i
$298$	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
$303$	9.27544	−	13.4375i	0.532860	−	0.771965i
$304$	2.84804	−	1.64432i	0.163346	−	0.0943081i
$305$		0			0
$306$	23.3065	+	19.0299i	1.33234	+	1.08787i
$307$			8.99889i			0.513594i	0.966465	+	0.256797i	$0.0826671\pi$
$307$			8.99889i			0.513594i	−0.966465	+	0.256797i	$0.917333\pi$
$308$	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	0.757221	−	0.653159i	$-0.226556\pi$
$311$	−3.29851	−	5.71318i	−0.187041	−	0.323965i	−0.944262	+	0.329194i	$0.893223\pi$
$312$	9.03364	+	19.0385i	0.511429	+	1.07784i
$313$	16.7007	+	9.64215i	0.943979	+	0.545007i	0.891205	−	0.453600i	$-0.149861\pi$
$313$	16.7007	+	9.64215i	0.943979	+	0.545007i	0.0527736	+	0.998607i	$0.483194\pi$
$314$	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	$0.847783\pi$
$318$	4.04622	+	8.52745i	0.226901	+	0.478195i
$319$	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
$324$	20.6440	−	18.2876i	1.14689	−	1.01598i
$325$		0			0
$326$	−6.75198	+	3.89826i	−0.373958	+	0.215905i
$327$	18.1078	−	26.2332i	1.00136	−	1.45070i
$328$		−	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
$333$	−4.94207	−	13.0319i	−0.270824	−	0.714144i
$334$	−6.42851	−	3.71150i	−0.351752	−	0.203084i
$335$		0			0
$336$	2.05101	−	2.69172i	0.111892	−	0.146845i
$337$	−12.6992			−0.691769			−0.345885	−	0.938277i	$-0.612421\pi$
$337$	−12.6992			−0.691769			−0.345885	+	0.938277i	$0.612421\pi$
$338$	24.9483	+	14.4039i	1.35701	+	0.783469i
$339$	6.84891	−	3.24977i	0.371982	−	0.176503i
$340$		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	$0.381445\pi$
$348$	−38.5556	−	26.6136i	−2.06680	−	1.42664i
$349$			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	$-0.599419\pi$
$354$	−49.0182	+	23.2589i	−2.60529	+	1.23619i
$355$		0			0
$356$	−33.3155			−1.76572
$357$	7.87948	+	18.8423i	0.417026	+	0.997242i
$358$	−50.7619			−2.68285
$359$	21.1388	+	12.2045i	1.11566	+	0.644127i	0.940290	−	0.340375i	$-0.110554\pi$
$359$	21.1388	+	12.2045i	1.11566	+	0.644127i	0.175371	+	0.984502i	$0.443887\pi$
$360$		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
$366$	3.87491	−	5.61366i	0.202545	−	0.293431i
$367$	−17.8968	+	10.3327i	−0.934203	+	0.539362i	−0.888138	−	0.459576i	$-0.848001\pi$
$367$	−17.8968	+	10.3327i	−0.934203	+	0.539362i	−0.0460646	+	0.998938i	$0.514668\pi$
$368$	1.82024	−	1.05091i	0.0948864	−	0.0547827i
$369$	−0.475899	+	0.582848i	−0.0247743	+	0.0303418i
$370$		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	$-0.651620\pi$
$373$	10.4361	−	18.0759i	0.540363	−	0.935936i	0.998883	−	0.0472520i	$-0.0150464\pi$
$374$	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
$378$	30.0880	−	7.20230i	1.54756	−	0.370446i
$379$	−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
$381$	−9.49256	−	20.0056i	−0.486319	−	1.02492i
$382$	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
$387$	−17.5268	+	21.4656i	−0.890935	+	1.09116i
$388$	23.7379	−	13.7051i	1.20511	−	0.695770i
$389$	10.7869	−	6.22784i	0.546919	−	0.315764i	−0.200959	−	0.979600i	$-0.564406\pi$
$389$	10.7869	−	6.22784i	0.546919	−	0.315764i	0.747879	+	0.663836i	$0.231073\pi$
$390$		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
$396$	16.3696	−	6.20782i	0.822604	−	0.311955i
$397$	24.6611	+	14.2381i	1.23771	+	0.714591i	0.968625	−	0.248527i	$-0.0799463\pi$
$397$	24.6611	+	14.2381i	1.23771	+	0.714591i	0.269082	+	0.963117i	$0.413280\pi$
$398$	−19.5759			−0.981250
$399$	16.2325	+	12.3686i	0.812640	+	0.619207i
$400$		0			0
$401$	−12.7515	−	7.36207i	−0.636779	−	0.367644i	0.146594	−	0.989197i	$-0.453169\pi$
$401$	−12.7515	−	7.36207i	−0.636779	−	0.367644i	−0.783373	+	0.621552i	$0.786502\pi$
$402$	29.2192	−	13.8644i	1.45732	−	0.691491i
$403$	−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
$408$	−15.2165	−	10.5034i	−0.753330	−	0.519997i
$409$	−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
$411$	−19.2198	−	13.2667i	−0.948041	−	0.654399i
$412$			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
$417$	−3.16389	+	1.50125i	−0.154936	+	0.0735164i
$418$	16.5286	+	9.54277i	0.808438	+	0.466752i
$419$	−30.1515			−1.47299			−0.736497	−	0.676440i	$-0.763522\pi$
$419$	−30.1515			−1.47299			−0.736497	+	0.676440i	$0.763522\pi$
$420$		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
$423$	3.27247	+	8.62929i	0.159113	+	0.419571i
$424$	−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
$429$	9.51789	−	13.7888i	0.459528	−	0.665728i
$430$		0			0
$431$	−11.9349	+	6.89063i	−0.574885	+	0.331910i	−0.759098	−	0.650976i	$-0.774360\pi$
$431$	−11.9349	+	6.89063i	−0.574885	+	0.331910i	0.184213	+	0.982886i	$0.441026\pi$
$432$	2.65819	−	2.76731i	0.127892	−	0.133142i
$433$		−	1.16840i		−	0.0561499i	−0.999606	−	0.0280750i	$-0.991062\pi$
$433$		−	1.16840i		−	0.0561499i	0.999606	−	0.0280750i	$-0.00893771\pi$
$434$	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
$438$	−10.5555	−	22.2457i	−0.504359	−	1.06294i
$439$	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
$441$	20.3207	+	5.29793i	0.967654	+	0.252282i
$442$	−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	$0.794924\pi$
$444$	10.5706	+	22.2776i	0.501659	+	1.05725i
$445$		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	$-0.789925\pi$
$449$		−	25.9824i		−	1.22618i	0.790012	−	0.613092i	$-0.210075\pi$
$450$		0			0
$451$	−0.413664	+	0.238829i	−0.0194787	+	0.0112460i
$452$	−11.6151	+	6.70598i	−0.546329	+	0.315423i
$453$	−6.89737	+	9.99236i	−0.324067	+	0.469482i
$454$		−	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	−0.883055	−	0.469270i	$-0.844517\pi$
$457$	−0.750953	+	1.30069i	−0.0351281	+	0.0608436i	0.847927	+	0.530113i	$0.177851\pi$
$458$	−0.265158	−	0.459266i	−0.0123900	−	0.0214601i
$459$	6.44235	+	22.2439i	0.300703	+	1.03826i
$460$		0			0
$461$	−1.40468			−0.0654225			−0.0327113	−	0.999465i	$-0.510414\pi$
$461$	−1.40468			−0.0654225			−0.0327113	+	0.999465i	$0.510414\pi$
$462$	19.4799	+	2.49762i	0.906289	+	0.116200i
$463$	−20.2056			−0.939033			−0.469516	−	0.882924i	$-0.655572\pi$
$463$	−20.2056			−0.939033			−0.469516	+	0.882924i	$0.655572\pi$
$464$	−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
$471$	3.58272	+	2.47302i	0.165083	+	0.113951i
$472$	28.8739	−	16.6703i	1.32903	−	0.767314i
$473$	−15.2347	+	8.79578i	−0.700494	+	0.404430i
$474$	10.2288	+	7.06060i	0.469826	+	0.324304i
$475$		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	$0.0806898\pi$
$479$	15.3467	+	26.5813i	0.701210	+	1.21453i	−0.266832	+	0.963743i	$0.585977\pi$
$480$		0			0
$481$	20.4369	+	11.7992i	0.931841	+	0.537999i
$482$	36.1822			1.64805
$483$	10.3745	+	7.90503i	0.472055	+	0.359691i
$484$	−22.5943			−1.02701
$485$		0			0
$486$	34.8249	−	4.22682i	1.57969	−	0.191733i
$487$	−14.8500	−	25.7209i	−0.672915	−	1.16552i	−0.977074	−	0.212902i	$-0.931708\pi$
$487$	−14.8500	−	25.7209i	−0.672915	−	1.16552i	0.304158	−	0.952622i	$-0.401625\pi$
$488$	−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	$0.0514836\pi$
$491$			7.13665i			0.322073i	−0.986948	+	0.161036i	$0.948516\pi$
$492$	0.756246	−	1.09559i	0.0340942	−	0.0493930i
$493$	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
$501$	−2.44915	−	5.16160i	−0.109420	−	0.230603i
$502$	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	$0.262621\pi$
$504$	−18.0730	+	5.89941i	−0.805035	+	0.262780i
$505$		0			0
$506$	10.5637	+	6.09896i	0.469614	+	0.271132i
$507$	9.50488	+	20.0316i	0.422126	+	0.889634i
$508$	19.5882	+	33.9277i	0.869084	+	1.50530i
$509$	16.4870	−	28.5563i	0.730774	−	1.26574i	−0.225779	−	0.974179i	$-0.572493\pi$
$509$	16.4870	−	28.5563i	0.730774	−	1.26574i	0.956553	−	0.291559i	$-0.0941740\pi$
$510$		0			0
$511$	0.784506	−	16.6950i	0.0347045	−	0.738545i
$512$			8.30237i			0.366916i
$513$	16.6883	+	16.0303i	0.736808	+	0.707754i
$514$	9.27624	−	5.35564i	0.409157	−	0.236227i
$515$		0			0
$516$	27.8516	−	40.3492i	1.22610	−	1.77627i
$517$			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	$0.0215770\pi$
$521$	12.7254	+	22.0411i	0.557511	+	0.965638i	−0.440192	+	0.897904i	$0.645090\pi$
$522$	−21.1304	−	55.7194i	−0.924850	−	2.43877i
$523$	20.9524	+	12.0969i	0.916184	+	0.528959i	0.882416	−	0.470470i	$-0.155916\pi$
$523$	20.9524	+	12.0969i	0.916184	+	0.528959i	0.0337685	+	0.999430i	$0.489249\pi$
$524$	15.9111			0.695081
$525$		0			0
$526$	12.7134			0.554332
$527$	21.4443	+	12.3809i	0.934129	+	0.539320i
$528$	2.20067	−	1.04420i	0.0957717	−	0.0454431i
$529$	−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
$534$	−34.8754	−	24.0732i	−1.50921	−	1.04175i
$535$		0			0
$536$	−17.2114	+	9.93701i	−0.743419	+	0.429213i
$537$	−32.1533	−	22.1943i	−1.38752	−	0.957753i
$538$			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
$543$	5.44880	−	2.58542i	0.233830	−	0.110951i
$544$	−24.9038	−	14.3782i	−1.06774	−	0.616460i
$545$		0			0
$546$	−31.7481	+	41.6658i	−1.35869	+	1.78313i
$547$	14.1119			0.603380			0.301690	−	0.953406i	$-0.402449\pi$
$547$	14.1119			0.603380			0.301690	+	0.953406i	$0.402449\pi$
$548$	35.7823	+	20.6589i	1.52854	+	0.882505i
$549$	4.90884	−	1.86157i	0.209504	−	0.0794499i
$550$		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	$0.565240\pi$
$558$	23.7234	−	29.0548i	1.00429	−	1.22999i
$559$		−	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	$0.597165\pi$
$564$	−6.99951	−	14.7515i	−0.294733	−	0.621151i
$565$		0			0
$566$	40.2853			1.69332
$567$	22.2072	+	8.59313i	0.932613	+	0.360877i
$568$	−23.1962			−0.973290
$569$	−17.1344	−	9.89257i	−0.718313	−	0.414718i	0.0958187	−	0.995399i	$-0.469453\pi$
$569$	−17.1344	−	9.89257i	−0.718313	−	0.414718i	−0.814131	+	0.580681i	$0.802786\pi$
$570$		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
$576$	−24.7482	+	30.3099i	−1.03118	+	1.26291i
$577$	−20.3323	+	11.7388i	−0.846443	+	0.488694i	−0.859449	−	0.511221i	$-0.829193\pi$
$577$	−20.3323	+	11.7388i	−0.846443	+	0.488694i	0.0130060	+	0.999915i	$0.495860\pi$
$578$	5.57940	−	3.22127i	0.232073	−	0.133987i
$579$	5.67748	−	8.22508i	0.235948	−	0.341823i
$580$		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	$0.768501\pi$
$588$	−36.5892	−	6.44947i	−1.50891	−	0.265972i
$589$	24.7427			1.01950
$590$		0			0
$591$	−6.79918	+	3.22617i	−0.279681	+	0.132707i
$592$	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
$597$	−12.3996	−	8.55901i	−0.507483	−	0.350297i
$598$	−28.1760	+	16.2674i	−1.15220	+	0.665223i
$599$	−11.3793	+	6.56986i	−0.464947	+	0.268437i	−0.714122	−	0.700021i	$-0.753174\pi$
$599$	−11.3793	+	6.56986i	−0.464947	+	0.268437i	0.249175	+	0.968458i	$0.419841\pi$
$600$		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
$606$	−33.1970	+	15.7518i	−1.34854	+	0.639872i
$607$	0.391428	+	0.225991i	0.0158876	+	0.00917270i	0.507923	−	0.861403i	$-0.330414\pi$
$607$	0.391428	+	0.225991i	0.0158876	+	0.00917270i	−0.492035	+	0.870575i	$0.663747\pi$
$608$	−28.7342			−1.16533
$609$	5.14408	−	40.1208i	0.208449	−	1.62578i
$610$		0			0
$611$	−13.5326	−	7.81306i	−0.547471	−	0.316083i
$612$	−14.5279	−	38.3091i	−0.587256	−	1.54855i
$613$	−0.774834	−	1.34205i	−0.0312953	−	0.0542050i	0.849954	−	0.526858i	$-0.176630\pi$
$613$	−0.774834	−	1.34205i	−0.0312953	−	0.0542050i	−0.881249	+	0.472653i	$0.843297\pi$
$614$	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	$-0.328759\pi$
$618$	−13.9522	+	20.2129i	−0.561241	+	0.813081i
$619$	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
$621$	10.6658	+	10.2452i	0.428004	+	0.411127i
$622$			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
$627$	6.29710	+	13.2712i	0.251482	+	0.530000i
$628$	−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
$633$	−7.94292	−	16.7398i	−0.315703	−	0.665346i
$634$	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
$639$	22.5043	+	18.3749i	0.890256	+	0.726900i
$640$		0			0
$641$	11.0323	−	6.36950i	0.435750	−	0.251580i	−0.266043	−	0.963961i	$-0.585716\pi$
$641$	11.0323	−	6.36950i	0.435750	−	0.251580i	0.701793	+	0.712381i	$0.252383\pi$
$642$	−36.7714	+	53.2714i	−1.45125	+	2.10246i
$643$			2.51652i			0.0992419i	0.998768	+	0.0496210i	$0.0158013\pi$
$643$			2.51652i			0.0992419i	−0.998768	+	0.0496210i	$0.984199\pi$
$644$	−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	$-0.458866\pi$
$648$	−21.1215	+	4.31115i	−0.829731	+	0.169358i
$649$	−22.9571	−	13.2543i	−0.901143	−	0.520275i
$650$		0			0
$651$	23.4896	−	9.82286i	0.920628	−	0.384988i
$652$	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	$0.981391\pi$
$654$	−64.8082	+	30.7511i	−2.53420	+	1.20246i
$655$		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	$-0.987054\pi$
$659$		−	2.08754i		−	0.0813192i	0.999173	−	0.0406596i	$-0.0129459\pi$
$660$		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
$663$	−32.2693	−	22.2743i	−1.25323	−	0.865063i
$664$		−	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
$669$	26.5212	−	12.5841i	1.02537	−	0.486531i
$670$		0			0
$671$	3.33267			0.128656
$672$	−27.2790	+	11.4075i	−1.05231	+	0.440054i
$673$	29.6317			1.14222			0.571108	−	0.820875i	$-0.306514\pi$
$673$	29.6317			1.14222			0.571108	+	0.820875i	$0.306514\pi$
$674$	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
$681$	2.39236	−	3.46586i	0.0916755	−	0.132812i
$682$	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	$0.456143\pi$
$684$	−31.7116	−	25.8927i	−1.21252	−	0.990034i
$685$		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
$693$	11.2468	+	10.0991i	0.427232	+	0.383633i
$694$	12.6242			0.479206
$695$		0			0
$696$	15.6980	+	33.0836i	0.595031	+	1.25403i
$697$	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	$-0.998759\pi$
$701$		−	0.206478i		−	0.00779858i	0.999992	−	0.00389929i	$-0.00124119\pi$
$702$	−41.1468	+	42.8359i	−1.55299	+	1.61674i
$703$	−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
$711$	3.39203	+	8.94455i	0.127211	+	0.335447i
$712$	22.5520	+	13.0204i	0.845171	+	0.487960i
$713$	15.8135			0.592220
$714$	5.84506	−	45.5881i	0.218746	−	1.70609i
$715$		0			0
$716$	59.8611	+	34.5608i	2.23712	+	1.29160i
$717$	15.1414	−	7.18453i	0.565468	−	0.268311i
$718$	−27.4651	−	47.5709i	−1.02499	−	1.77533i
$719$	−4.36496	+	7.56034i	−0.162786	+	0.281953i	−0.935867	−	0.352354i	$-0.885381\pi$
$719$	−4.36496	+	7.56034i	−0.162786	+	0.281953i	0.773081	+	0.634307i	$0.218715\pi$
$720$		0			0
$721$	−14.8130	+	7.64871i	−0.551665	+	0.284853i
$722$		−	1.87281i		−	0.0696988i
$723$	22.9183	+	15.8197i	0.852340	+	0.588340i
$724$	−9.24065	+	5.33509i	−0.343426	+	0.198277i
$725$		0			0
$726$	−23.6522	−	16.3263i	−0.877816	−	0.605925i
$727$			26.6400i			0.988024i	0.869455	+	0.494012i	$0.164470\pi$
$727$			26.6400i			0.988024i	−0.869455	+	0.494012i	$0.835530\pi$
$728$	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
$732$	−8.39152	+	3.98173i	−0.310159	+	0.147169i
$733$	−27.1888	−	15.6975i	−1.00424	−	0.579800i	−0.0947418	−	0.995502i	$-0.530203\pi$
$733$	−27.1888	−	15.6975i	−1.00424	−	0.579800i	−0.909501	+	0.415702i	$0.863536\pi$
$734$	46.5056			1.71655
$735$		0			0
$736$	−18.3646			−0.676927
$737$	13.6845	+	7.90073i	0.504074	+	0.291027i
$738$	1.58331	−	0.600436i	0.0582824	−	0.0221023i
$739$	−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	$-0.125526\pi$
$744$	−13.0940	+	18.9695i	−0.480048	+	0.695455i
$745$		0			0
$746$	−40.6783	+	23.4856i	−1.48934	+	0.859869i
$747$	−17.0572	+	20.8905i	−0.624091	+	0.764343i
$748$		−	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
$753$	10.6779	+	22.5037i	0.389123	+	0.820080i
$754$	87.3801	+	50.4489i	3.18220	+	1.83724i
$755$		0			0
$756$	−40.3850	−	11.9918i	−1.46879	−	0.436139i
$757$	0.401257			0.0145839			0.00729196	−	0.999973i	$-0.497679\pi$
$757$	0.401257			0.0145839			0.00729196	+	0.999973i	$0.497679\pi$
$758$	52.6955	+	30.4238i	1.91399	+	1.10504i
$759$	4.02459	+	8.48185i	0.146083	+	0.307872i
$760$		0			0
$761$	21.1371	−	36.6105i	0.766219	−	1.32713i	−0.173381	−	0.984855i	$-0.555469\pi$
$761$	21.1371	−	36.6105i	0.766219	−	1.32713i	0.939600	−	0.342275i	$-0.111197\pi$
$762$	−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
$768$	10.7532	−	15.5784i	0.388023	−	0.562137i
$769$			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	$0.821192\pi$
$774$	58.3113	−	22.1133i	2.09596	−	0.794846i
$775$		0			0
$776$	−21.4249			−0.769110
$777$	−12.9033	+	16.9341i	−0.462903	+	0.607509i
$778$	−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
$786$	16.6561	+	11.4971i	0.594104	+	0.410089i
$787$	17.7119	−	10.2260i	0.631360	−	0.364516i	−0.149919	−	0.988698i	$-0.547901\pi$
$787$	17.7119	−	10.2260i	0.631360	−	0.364516i	0.781279	+	0.624183i	$0.214568\pi$
$788$	11.5308	−	6.65730i	0.410767	−	0.237156i
$789$	8.05286	+	5.55860i	0.286690	+	0.197892i
$790$		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	$0.377065\pi$
$798$	−17.7184	−	42.3703i	−0.627224	−	1.49989i
$799$	13.7105			0.485042
$800$		0			0
$801$	−11.5652	−	30.4966i	−0.408636	−	1.07755i
$802$	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
$807$	−0.700644	+	1.01504i	−0.0246638	+	0.0357310i
$808$	19.5545	−	11.2898i	0.687924	−	0.397173i
$809$	19.3311	−	11.1608i	0.679646	−	0.392394i	−0.120075	−	0.992765i	$-0.538314\pi$
$809$	19.3311	−	11.1608i	0.679646	−	0.392394i	0.799722	+	0.600371i	$0.204980\pi$
$810$		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
$816$	−2.44370	−	5.15012i	−0.0855468	−	0.180290i
$817$	35.6257	+	20.5685i	1.24639	+	0.719601i
$818$	2.10641			0.0736488
$819$	−38.3269	+	12.5107i	−1.33925	+	0.437160i
$820$		0			0
$821$	34.1580	+	19.7211i	1.19212	+	0.688272i	0.958787	−	0.284125i	$-0.0917030\pi$
$821$	34.1580	+	19.7211i	1.19212	+	0.688272i	0.233335	+	0.972397i	$0.425036\pi$
$822$	22.5299	+	47.4819i	0.785820	+	1.65612i
$823$	23.8993	+	41.3948i	0.833077	+	1.44293i	0.895587	+	0.444887i	$0.146756\pi$
$823$	23.8993	+	41.3948i	0.833077	+	1.44293i	−0.0625104	+	0.998044i	$0.519911\pi$
$824$	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	$0.749473\pi$
$828$	−20.2675	−	16.5485i	−0.704344	−	0.575101i
$829$	−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
$831$	−22.5451	+	32.6616i	−0.782082	+	1.13302i
$832$		−	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
$837$	27.7301	−	8.03127i	0.958494	−	0.277601i
$838$	58.7626	+	33.9266i	2.02992	+	1.17197i
$839$	−9.40638			−0.324744			−0.162372	−	0.986730i	$-0.551915\pi$
$839$	−9.40638			−0.324744			−0.162372	+	0.986730i	$0.551915\pi$
$840$		0			0
$841$	−48.9115			−1.68660
$842$	−70.8790	−	40.9220i	−2.44265	−	1.41026i
$843$	18.8315	−	8.93542i	0.648590	−	0.307752i
$844$	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
$849$	25.5172	+	17.6136i	0.875749	+	0.604498i
$850$		0			0
$851$	−11.4515	+	6.61152i	−0.392552	+	0.226640i
$852$	−42.3017	−	29.1994i	−1.44923	−	1.00035i
$853$		−	28.2296i		−	0.966562i	−0.875465	−	0.483281i	$-0.839445\pi$
$853$		−	28.2296i		−	0.966562i	0.875465	−	0.483281i	$-0.160555\pi$
$854$	−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	$0.925726\pi$
$858$	−34.0647	+	16.1635i	−1.16295	+	0.551814i
$859$	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
$861$	1.14006	+	0.146173i	0.0388533	+	0.00498157i
$862$	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	$0.788878\pi$
$864$	−32.2037	+	9.32691i	−1.09559	+	0.317308i
$865$		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
$873$	20.7859	+	16.9718i	0.703496	+	0.574409i
$874$		−	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	−0.987393	−	0.158286i	$-0.949403\pi$
$877$	−10.5609	+	18.2921i	−0.356617	+	0.617679i	0.630776	+	0.775965i	$0.282737\pi$
$878$	−3.25277	−	5.63397i	−0.109776	−	0.190137i
$879$	−6.58836	−	13.8850i	−0.222220	−	0.468330i
$880$		0			0
$881$	44.3021			1.49258			0.746288	−	0.665623i	$-0.231834\pi$
$881$	44.3021			1.49258			0.746288	+	0.665623i	$0.231834\pi$
$882$	−33.6421	−	33.1902i	−1.13279	−	1.11757i
$883$	−5.12282			−0.172397			−0.0861984	−	0.996278i	$-0.527472\pi$
$883$	−5.12282			−0.172397			−0.0861984	+	0.996278i	$0.527472\pi$
$884$	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
$891$	11.3651	+	12.8296i	0.380746	+	0.429807i
$892$	−44.9774	+	25.9677i	−1.50596	+	0.869464i
$893$	11.8645	−	6.84995i	0.397029	−	0.229225i
$894$	2.83930	−	4.11335i	0.0949603	−	0.137571i
$895$		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
$903$	41.9871	+	5.38337i	1.39724	+	0.179147i
$904$	10.4833			0.348671
$905$		0			0
$906$	24.6858	−	11.7133i	0.820132	−	0.389148i
$907$	−12.2639	−	21.2416i	−0.407215	−	0.705316i	0.587362	−	0.809324i	$-0.300167\pi$
$907$	−12.2639	−	21.2416i	−0.407215	−	0.705316i	−0.994576	+	0.104008i	$0.966833\pi$
$908$	−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	$-0.740940\pi$
$911$		−	43.8824i		−	1.45389i	0.686697	−	0.726944i	$-0.259060\pi$
$912$	−4.68775	−	3.23579i	−0.155227	−	0.107148i
$913$	−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
$921$	14.0817	−	6.68169i	0.464008	−	0.220169i
$922$	2.73760	+	1.58056i	0.0901581	+	0.0520528i
$923$	−49.1915			−1.61916
$924$	−21.2713	−	16.2081i	−0.699774	−	0.533207i
$925$		0			0
$926$	39.3789	+	22.7354i	1.29407	+	0.747132i
$927$	−17.6750	+	6.70288i	−0.580525	+	0.220151i
$928$	28.4764	+	49.3225i	0.934783	+	1.61909i
$929$	−9.87128	+	17.0976i	−0.323866	+	0.560952i	−0.981282	−	0.192575i	$-0.938316\pi$
$929$	−9.87128	+	17.0976i	−0.323866	+	0.560952i	0.657416	+	0.753528i	$0.271649\pi$
$930$		0			0
$931$	2.92324	−	31.0360i	0.0958054	−	1.01716i
$932$		−	33.9572i		−	1.11230i
$933$	−6.49101	+	9.40365i	−0.212506	+	0.307862i
$934$	75.3434	−	43.4995i	2.46531	−	1.42335i
$935$		0			0
$936$	23.0844	−	28.2722i	0.754539	−	0.924106i
$937$		−	37.1538i		−	1.21376i	−0.794793	−	0.606881i	$-0.792420\pi$
$937$		−	37.1538i		−	1.21376i	0.794793	−	0.606881i	$-0.207580\pi$
$938$	−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	$-0.990730\pi$
$941$	−16.1049	−	27.8945i	−0.525005	−	0.909336i	0.474571	−	0.880217i	$-0.342603\pi$
$942$	−4.19975	−	8.85100i	−0.136835	−	0.288381i
$943$	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	$0.514173\pi$
$948$	−7.25523	−	15.2904i	−0.235639	−	0.496611i
$949$	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	$0.847795\pi$
$954$	10.3397	−	12.6633i	0.334759	−	0.409989i
$955$		0			0
$956$	−25.6785	+	14.8255i	−0.830501	+	0.479490i
$957$	16.5395	−	23.9611i	0.534646	−	0.774552i
$958$		−	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
$963$	−46.5830	+	17.6656i	−1.50112	+	0.569265i
$964$	−42.6680	−	24.6344i	−1.37424	−	0.793419i
$965$		0			0
$966$	−11.3241	−	27.0796i	−0.364349	−	0.871272i
$967$	42.3117			1.36065			0.680326	−	0.732909i	$-0.261838\pi$
$967$	42.3117			1.36065			0.680326	+	0.732909i	$0.261838\pi$
$968$	15.2946	+	8.83032i	0.491586	+	0.283817i
$969$	31.0580	−	14.7368i	0.997726	−	0.473415i
$970$		0			0
$971$	−11.7297	+	20.3164i	−0.376424	+	0.651985i	−0.990539	−	0.137231i	$-0.956180\pi$
$971$	−11.7297	+	20.3164i	−0.376424	+	0.651985i	0.614115	+	0.789216i	$0.289513\pi$
$972$	−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	$0.523527\pi$
$978$	11.1135	+	7.67123i	0.355370	+	0.245299i
$979$		−	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	$0.601908\pi$
$984$	−0.940098	+	0.446071i	−0.0299692	+	0.0142202i
$985$		0			0
$986$	−88.5285			−2.81932
$987$	8.54414	−	11.2132i	0.271963	−	0.356921i
$988$	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
$996$	27.1055	−	39.2682i	0.858869	−	1.24426i
$997$	38.6961	−	22.3412i	1.22552	−	0.707552i	0.259428	−	0.965763i	$-0.416466\pi$
$997$	38.6961	−	22.3412i	1.22552	−	0.707552i	0.966089	+	0.258210i	$0.0831327\pi$
$998$	−26.0016	+	15.0120i	−0.823065	+	0.475197i
$999$	−16.7232	+	17.4097i	−0.529099	+	0.550819i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-1.94891 - 1.12521i) q^{2} +(-0.742502 - 1.56483i) q^{3} +(1.53217 + 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(-1.42897 + 2.22667i) q^{7} -2.39522i q^{8} +(-1.89738 + 2.32378i) q^{9} +O(q^{10})\)	\(q+(-1.94891 - 1.12521i) q^{2} +(-0.742502 - 1.56483i) q^{3} +(1.53217 + 2.65380i) q^{4} +(-0.313682 + 3.88518i) q^{6} +(-1.42897 + 2.22667i) q^{7} -2.39522i q^{8} +(-1.89738 + 2.32378i) q^{9} +(-1.64925 + 0.952197i) q^{11} +(3.01511 - 4.36805i) q^{12} -5.07948i q^{13} +(5.29039 - 2.73170i) q^{14} +(0.369233 - 0.639530i) q^{16} +(2.22839 + 3.85968i) q^{17} +(6.31256 - 2.39390i) q^{18} +(3.85670 + 2.22667i) q^{19} +(4.54537 + 0.582783i) q^{21} +4.28567 q^{22} +(2.46489 + 1.42310i) q^{23} +(-3.74811 + 1.77846i) 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} +(2.71460 + 1.87379i) q^{33} -10.0296i q^{34} +(-9.07397 - 1.47484i) q^{36} +(-2.32292 + 4.02342i) q^{37} +(-5.01092 - 8.67917i) q^{38} +(-7.94852 + 3.77153i) q^{39} +0.250819 q^{41} +(-8.20277 - 6.25027i) 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} +(4.38516 - 6.35287i) q^{51} +(13.4799 - 7.78265i) q^{52} +(2.09711 - 1.21077i) q^{53} +(-8.43313 - 8.10060i) 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} +(-2.46299 - 7.54544i) q^{63} +13.0434 q^{64} +(-3.18212 - 6.70634i) q^{66} +(-4.14868 - 7.18573i) q^{67} +(-6.82855 + 11.8274i) q^{68} +(0.396729 - 4.91379i) q^{69} -9.68436i q^{71} +(5.56596 + 4.54465i) 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} +(-1.79990 - 8.81818i) q^{81} +(-0.488824 - 0.282223i) q^{82} +8.98988 q^{83} +(5.41770 + 12.9554i) q^{84} +(-18.0028 - 10.3939i) q^{86} +(-13.8124 + 6.55388i) q^{87} +(2.28072 + 3.95033i) q^{88} +(-5.43599 + 9.41541i) q^{89} +(11.3103 + 7.25841i) q^{91} +8.72178i q^{92} +(-7.91972 - 5.46670i) q^{93} +(-5.99548 + 3.46149i) q^{94} +(9.19736 + 6.34861i) 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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