LMFDB - Embedded newform 525.2.b.i.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(251,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("525.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.b (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.624529833984.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} - 2x^{4} - 18x^{2} + 81 $ x^8 - 2x^6 - 2x^4 - 18*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.7
Root			$-0.777403 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	525.251
Dual form			525.2.b.i.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.40651i q^{2} +(-0.777403 - 1.54779i) q^{3} -3.79129 q^{4} +(3.72476 - 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} -4.31075i q^{8} +(-1.79129 + 2.40651i) q^{9} +O(q^{10})$	\(q+2.40651i q^{2} +(-0.777403 - 1.54779i) q^{3} -3.79129 q^{4} +(3.72476 - 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} -4.31075i q^{8} +(-1.79129 + 2.40651i) q^{9} +4.31075i q^{11} +(2.94736 + 5.86811i) q^{12} +2.44949i q^{13} +(5.89472 + 2.40651i) q^{14} +2.79129 q^{16} -5.89472 q^{17} +(-5.79129 - 4.31075i) q^{18} +6.83723i q^{19} +(-4.56869 + 0.356455i) q^{21} -10.3739 q^{22} +0.502268i q^{23} +(-6.67212 + 3.35119i) q^{24} -5.89472 q^{26} +(5.11732 + 0.901703i) q^{27} +(-3.79129 + 9.28672i) q^{28} +0.502268i q^{29} +4.38774i q^{31} -1.90424i q^{32} +(6.67212 - 3.35119i) q^{33} -14.1857i q^{34} +(6.79129 - 9.12377i) q^{36} +0.582576 q^{37} -16.4539 q^{38} +(3.79129 - 1.90424i) q^{39} +4.66442 q^{41} +(-0.857812 - 10.9946i) q^{42} -2.58258 q^{43} -16.3433i q^{44} -1.20871 q^{46} -5.89472 q^{47} +(-2.16996 - 4.32032i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(4.58258 + 9.12377i) q^{51} -9.28672i q^{52} +13.4345i q^{53} +(-2.16996 + 12.3149i) q^{54} +(-10.5591 - 4.31075i) q^{56} +(10.5826 - 5.31529i) q^{57} -1.20871 q^{58} -10.5591 q^{59} -4.38774i q^{61} -10.5591 q^{62} +(4.10343 + 6.79425i) q^{63} +10.1652 q^{64} +(8.06468 + 16.0565i) q^{66} +14.1652 q^{67} +22.3486 q^{68} +(0.777403 - 0.390465i) q^{69} +4.31075i q^{71} +(10.3739 + 7.72180i) q^{72} -6.32599i q^{73} +1.40197i q^{74} -25.9219i q^{76} +(10.5591 + 4.31075i) q^{77} +(4.58258 + 9.12377i) q^{78} -8.58258 q^{79} +(-2.58258 - 8.62150i) q^{81} +11.2250i q^{82} -7.12502 q^{83} +(17.3212 - 1.35142i) q^{84} -6.21499i q^{86} +(0.777403 - 0.390465i) q^{87} +18.5826 q^{88} +10.5591 q^{89} +(6.00000 + 2.44949i) q^{91} -1.90424i q^{92} +(6.79129 - 3.41105i) q^{93} -14.1857i q^{94} +(-2.94736 + 1.48036i) q^{96} -0.511238i q^{97} +(11.7894 - 12.0325i) q^{98} +(-10.3739 - 7.72180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 12 * q^4 + 8 * q^7 + 4 * q^9	$ 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9} + 4 q^{16} - 28 q^{18} - 12 q^{21} - 28 q^{22} - 12 q^{28} + 36 q^{36} - 32 q^{37} + 12 q^{39} + 16 q^{43} - 28 q^{46} - 40 q^{49} + 48 q^{57} - 28 q^{58} + 4 q^{63} + 8 q^{64} + 40 q^{67} + 28 q^{72} - 32 q^{79} + 16 q^{81} + 60 q^{84} + 112 q^{88} + 48 q^{91} + 36 q^{93} - 28 q^{99}+O(q^{100}) $ 8 * q - 12 * q^4 + 8 * q^7 + 4 * q^9 + 4 * q^16 - 28 * q^18 - 12 * q^21 - 28 * q^22 - 12 * q^28 + 36 * q^36 - 32 * q^37 + 12 * q^39 + 16 * q^43 - 28 * q^46 - 40 * q^49 + 48 * q^57 - 28 * q^58 + 4 * q^63 + 8 * q^64 + 40 * q^67 + 28 * q^72 - 32 * q^79 + 16 * q^81 + 60 * q^84 + 112 * q^88 + 48 * q^91 + 36 * q^93 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$			2.40651i			1.70166i	0.525442	+	0.850830i	$0.323900\pi$
$2$			2.40651i			1.70166i	−0.525442	+	0.850830i	$0.676100\pi$
$3$	−0.777403	−	1.54779i	−0.448834	−	0.893615i
$3$	−0.777403	−	1.54779i	−0.448834	−	0.893615i
$4$	−3.79129			−1.89564
$5$		0			0
$5$		0			0
$6$	3.72476	−	1.87083i	1.52063	−	0.763763i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$		−	4.31075i		−	1.52408i
$9$	−1.79129	+	2.40651i	−0.597096	+	0.802170i
$10$		0			0
$11$			4.31075i			1.29974i	0.760045	+	0.649870i	$0.225177\pi$
$11$			4.31075i			1.29974i	−0.760045	+	0.649870i	$0.774823\pi$
$12$	2.94736	+	5.86811i	0.850830	+	1.69398i
$13$			2.44949i			0.679366i	0.940540	+	0.339683i	$0.110320\pi$
$13$			2.44949i			0.679366i	−0.940540	+	0.339683i	$0.889680\pi$
$14$	5.89472	+	2.40651i	1.57543	+	0.643167i
$15$		0			0
$16$	2.79129			0.697822
$17$	−5.89472			−1.42968			−0.714840	−	0.699288i	$-0.753500\pi$
$17$	−5.89472			−1.42968			−0.714840	+	0.699288i	$0.753500\pi$
$18$	−5.79129	−	4.31075i	−1.36502	−	1.01605i
$19$			6.83723i			1.56857i	0.620402	+	0.784284i	$0.286970\pi$
$19$			6.83723i			1.56857i	−0.620402	+	0.784284i	$0.713030\pi$
$20$		0			0
$21$	−4.56869	+	0.356455i	−0.996970	+	0.0777848i
$22$	−10.3739			−2.21172
$23$			0.502268i			0.104730i	0.998628	+	0.0523650i	$0.0166759\pi$
$23$			0.502268i			0.104730i	−0.998628	+	0.0523650i	$0.983324\pi$
$24$	−6.67212	+	3.35119i	−1.36194	+	0.684059i
$25$		0			0
$26$	−5.89472			−1.15605
$27$	5.11732	+	0.901703i	0.984828	+	0.173533i
$28$	−3.79129	+	9.28672i	−0.716486	+	1.75503i
$29$			0.502268i			0.0932688i	0.998912	+	0.0466344i	$0.0148496\pi$
$29$			0.502268i			0.0932688i	−0.998912	+	0.0466344i	$0.985150\pi$
$30$		0			0
$31$			4.38774i			0.788062i	0.919097	+	0.394031i	$0.128920\pi$
$31$			4.38774i			0.788062i	−0.919097	+	0.394031i	$0.871080\pi$
$32$		−	1.90424i		−	0.336626i
$33$	6.67212	−	3.35119i	1.16147	−	0.583368i
$34$		−	14.1857i		−	2.43283i
$35$		0			0
$36$	6.79129	−	9.12377i	1.13188	−	1.52063i
$37$	0.582576			0.0957749			0.0478874	−	0.998853i	$-0.484751\pi$
$37$	0.582576			0.0957749			0.0478874	+	0.998853i	$0.484751\pi$
$38$	−16.4539			−2.66917
$39$	3.79129	−	1.90424i	0.607092	−	0.304923i
$40$		0			0
$41$	4.66442			0.728460			0.364230	−	0.931309i	$-0.381332\pi$
$41$	4.66442			0.728460			0.364230	+	0.931309i	$0.381332\pi$
$42$	−0.857812	−	10.9946i	−0.132363	−	1.69650i
$43$	−2.58258			−0.393839			−0.196920	−	0.980420i	$-0.563094\pi$
$43$	−2.58258			−0.393839			−0.196920	+	0.980420i	$0.563094\pi$
$44$		−	16.3433i		−	2.46384i
$45$		0			0
$46$	−1.20871			−0.178215
$47$	−5.89472			−0.859833			−0.429917	−	0.902869i	$-0.641457\pi$
$47$	−5.89472			−0.859833			−0.429917	+	0.902869i	$0.641457\pi$
$48$	−2.16996	−	4.32032i	−0.313206	−	0.623584i
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		0			0
$51$	4.58258	+	9.12377i	0.641689	+	1.27758i
$52$		−	9.28672i		−	1.28784i
$53$			13.4345i			1.84537i	0.385551	+	0.922687i	$0.374012\pi$
$53$			13.4345i			1.84537i	−0.385551	+	0.922687i	$0.625988\pi$
$54$	−2.16996	+	12.3149i	−0.295294	+	1.67584i
$55$		0			0
$56$	−10.5591	−	4.31075i	−1.41102	−	0.576048i
$57$	10.5826	−	5.31529i	1.40170	−	0.704027i
$58$	−1.20871			−0.158712
$59$	−10.5591			−1.37468			−0.687342	−	0.726334i	$-0.741222\pi$
$59$	−10.5591			−1.37468			−0.687342	+	0.726334i	$0.741222\pi$
$60$		0			0
$61$		−	4.38774i		−	0.561793i	−0.959738	−	0.280896i	$-0.909368\pi$
$61$		−	4.38774i		−	0.561793i	0.959738	−	0.280896i	$-0.0906317\pi$
$62$	−10.5591			−1.34101
$63$	4.10343	+	6.79425i	0.516984	+	0.855995i
$64$	10.1652			1.27064
$65$		0			0
$66$	8.06468	+	16.0565i	0.992693	+	1.97642i
$67$	14.1652			1.73055			0.865274	−	0.501299i	$-0.167144\pi$
$67$	14.1652			1.73055			0.865274	+	0.501299i	$0.167144\pi$
$68$	22.3486			2.71016
$69$	0.777403	−	0.390465i	0.0935884	−	0.0470064i
$70$		0			0
$71$			4.31075i			0.511592i	0.966731	+	0.255796i	$0.0823375\pi$
$71$			4.31075i			0.511592i	−0.966731	+	0.255796i	$0.917662\pi$
$72$	10.3739	+	7.72180i	1.22257	+	0.910022i
$73$		−	6.32599i		−	0.740401i	−0.928952	−	0.370201i	$-0.879289\pi$
$73$		−	6.32599i		−	0.740401i	0.928952	−	0.370201i	$-0.120711\pi$
$74$			1.40197i			0.162976i
$75$		0			0
$76$		−	25.9219i		−	2.97345i
$77$	10.5591	+	4.31075i	1.20333	+	0.491256i
$78$	4.58258	+	9.12377i	0.518875	+	1.03306i
$79$	−8.58258			−0.965615			−0.482808	−	0.875726i	$-0.660383\pi$
$79$	−8.58258			−0.965615			−0.482808	+	0.875726i	$0.660383\pi$
$80$		0			0
$81$	−2.58258	−	8.62150i	−0.286953	−	0.957945i
$82$			11.2250i			1.23959i
$83$	−7.12502			−0.782073			−0.391036	−	0.920375i	$-0.627883\pi$
$83$	−7.12502			−0.782073			−0.391036	+	0.920375i	$0.627883\pi$
$84$	17.3212	−	1.35142i	1.88990	−	0.147452i
$85$		0			0
$86$		−	6.21499i		−	0.670180i
$87$	0.777403	−	0.390465i	0.0833464	−	0.0418622i
$88$	18.5826			1.98091
$89$	10.5591			1.11927			0.559633	−	0.828740i	$-0.310942\pi$
$89$	10.5591			1.11927			0.559633	+	0.828740i	$0.310942\pi$
$90$		0			0
$91$	6.00000	+	2.44949i	0.628971	+	0.256776i
$92$		−	1.90424i		−	0.198531i
$93$	6.79129	−	3.41105i	0.704224	−	0.353709i
$94$		−	14.1857i		−	1.46314i
$95$		0			0
$96$	−2.94736	+	1.48036i	−0.300814	+	0.151089i
$97$		−	0.511238i		−	0.0519084i	−0.999663	−	0.0259542i	$-0.991738\pi$
$97$		−	0.511238i		−	0.0519084i	0.999663	−	0.0259542i	$-0.00826240\pi$
$98$	11.7894	−	12.0325i	1.19091	−	1.21547i
$99$	−10.3739	−	7.72180i	−1.04261	−	0.776070i
$100$		0			0
$101$	13.0197			1.29551			0.647756	−	0.761848i	$-0.275708\pi$
$101$	13.0197			1.29551			0.647756	+	0.761848i	$0.275708\pi$
$102$	−21.9564	+	11.0280i	−2.17401	+	1.09194i
$103$			6.83723i			0.673692i	0.941560	+	0.336846i	$0.109360\pi$
$103$			6.83723i			0.673692i	−0.941560	+	0.336846i	$0.890640\pi$
$104$	10.5591			1.03541
$105$		0			0
$106$	−32.3303			−3.14020
$107$		−	1.00454i		−	0.0971121i	−0.998820	−	0.0485561i	$-0.984538\pi$
$107$		−	1.00454i		−	0.0971121i	0.998820	−	0.0485561i	$-0.0154620\pi$
$108$	−19.4012	−	3.41862i	−1.86688	−	0.328956i
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$		0			0
$111$	−0.452896	−	0.901703i	−0.0429870	−	0.0855859i
$112$	2.79129	−	6.83723i	0.263752	−	0.646058i
$113$		−	6.31982i		−	0.594519i	−0.954797	−	0.297259i	$-0.903927\pi$
$113$		−	6.31982i		−	0.594519i	0.954797	−	0.297259i	$-0.0960726\pi$
$114$	12.7913	+	25.4671i	1.19801	+	2.38521i
$115$		0			0
$116$		−	1.90424i		−	0.176804i
$117$	−5.89472	−	4.38774i	−0.544967	−	0.405647i
$118$		−	25.4107i		−	2.33924i
$119$	−5.89472	+	14.4391i	−0.540368	+	1.32363i
$120$		0			0
$121$	−7.58258			−0.689325
$122$	10.5591			0.955980
$123$	−3.62614	−	7.21953i	−0.326958	−	0.650963i
$124$		−	16.6352i		−	1.49388i
$125$		0			0
$126$	−16.3504	+	9.87495i	−1.45661	+	0.879730i
$127$	−10.1652			−0.902011			−0.451006	−	0.892521i	$-0.648935\pi$
$127$	−10.1652			−0.902011			−0.451006	+	0.892521i	$0.648935\pi$
$128$			20.6540i			1.82558i
$129$	2.00770	+	3.99728i	0.176768	+	0.351941i
$130$		0			0
$131$	−5.89472			−0.515024			−0.257512	−	0.966275i	$-0.582903\pi$
$131$	−5.89472			−0.515024			−0.257512	+	0.966275i	$0.582903\pi$
$132$	−25.2959	+	12.7053i	−2.20173	+	1.10586i
$133$	16.7477	+	6.83723i	1.45221	+	0.592863i
$134$			34.0886i			2.94480i
$135$		0			0
$136$			25.4107i			2.17895i
$137$		−	1.00454i		−	0.0858233i	−0.999079	−	0.0429116i	$-0.986337\pi$
$137$		−	1.00454i		−	0.0858233i	0.999079	−	0.0429116i	$-0.0136634\pi$
$138$	0.939657	+	1.87083i	0.0799889	+	0.159256i
$139$			2.44949i			0.207763i	0.994590	+	0.103882i	$0.0331263\pi$
$139$			2.44949i			0.207763i	−0.994590	+	0.103882i	$0.966874\pi$
$140$		0			0
$141$	4.58258	+	9.12377i	0.385922	+	0.768360i
$142$	−10.3739			−0.870555
$143$	−10.5591			−0.883000
$144$	−5.00000	+	6.71726i	−0.416667	+	0.559772i
$145$		0			0
$146$	15.2236			1.25991
$147$	−3.69556	+	11.5474i	−0.304805	+	0.952415i
$148$	−2.20871			−0.181555
$149$		−	6.31982i		−	0.517740i	−0.965912	−	0.258870i	$-0.916650\pi$
$149$		−	6.31982i		−	0.517740i	0.965912	−	0.258870i	$-0.0833501\pi$
$150$		0			0
$151$	14.1652			1.15274			0.576372	−	0.817188i	$-0.304468\pi$
$151$	14.1652			1.15274			0.576372	+	0.817188i	$0.304468\pi$
$152$	29.4736			2.39062
$153$	10.5591	−	14.1857i	0.853656	−	1.14685i
$154$	−10.3739	+	25.4107i	−0.835950	+	2.04765i
$155$		0			0
$156$	−14.3739	+	7.21953i	−1.15083	+	0.578025i
$157$		−	9.28672i		−	0.741161i	−0.928800	−	0.370580i	$-0.879159\pi$
$157$		−	9.28672i		−	0.741161i	0.928800	−	0.370580i	$-0.120841\pi$
$158$		−	20.6540i		−	1.64315i
$159$	20.7938	−	10.4440i	1.64905	−	0.828266i
$160$		0			0
$161$	1.23030	+	0.502268i	0.0969612	+	0.0395842i
$162$	20.7477	−	6.21499i	1.63010	−	0.488296i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−17.6842			−1.38090
$165$		0			0
$166$		−	17.1464i		−	1.33082i
$167$	13.0197			1.00750			0.503749	−	0.863850i	$-0.331954\pi$
$167$	13.0197			1.00750			0.503749	+	0.863850i	$0.331954\pi$
$168$	1.53659	+	19.6945i	0.118550	+	1.51946i
$169$	7.00000			0.538462
$170$		0			0
$171$	−16.4539	−	12.2474i	−1.25826	−	0.936586i
$172$	9.79129			0.746579
$173$	−17.6842			−1.34450			−0.672251	−	0.740323i	$-0.734672\pi$
$173$	−17.6842			−1.34450			−0.672251	+	0.740323i	$0.734672\pi$
$174$	0.939657	+	1.87083i	0.0712352	+	0.141827i
$175$		0			0
$176$			12.0325i			0.906987i
$177$	8.20871	+	16.3433i	0.617005	+	1.22844i
$178$			25.4107i			1.90461i
$179$		−	12.4300i		−	0.929061i	−0.885557	−	0.464530i	$-0.846223\pi$
$179$		−	12.4300i		−	0.929061i	0.885557	−	0.464530i	$-0.153777\pi$
$180$		0			0
$181$			12.2474i			0.910346i	0.890403	+	0.455173i	$0.150423\pi$
$181$			12.2474i			0.910346i	−0.890403	+	0.455173i	$0.849577\pi$
$182$	−5.89472	+	14.4391i	−0.436946	+	1.07029i
$183$	−6.79129	+	3.41105i	−0.502026	+	0.252152i
$184$	2.16515			0.159617
$185$		0			0
$186$	8.20871	+	16.3433i	0.601892	+	1.19835i
$187$		−	25.4107i		−	1.85821i
$188$	22.3486			1.62994
$189$	7.32603	−	11.6331i	0.532890	−	0.846184i
$190$		0			0
$191$		−	15.4436i		−	1.11746i	−0.829350	−	0.558730i	$-0.811289\pi$
$191$		−	15.4436i		−	1.11746i	0.829350	−	0.558730i	$-0.188711\pi$
$192$	−7.90242	−	15.7335i	−0.570308	−	1.13547i
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	1.23030			0.0883304
$195$		0			0
$196$	18.9564	+	18.5734i	1.35403	+	1.32667i
$197$			18.7498i			1.33587i	0.744220	+	0.667934i	$0.232821\pi$
$197$			18.7498i			1.33587i	−0.744220	+	0.667934i	$0.767179\pi$
$198$	18.5826	−	24.9648i	1.32061	−	1.77417i
$199$			19.0847i			1.35288i	0.736499	+	0.676439i	$0.236478\pi$
$199$			19.0847i			1.35288i	−0.736499	+	0.676439i	$0.763522\pi$
$200$		0			0
$201$	−11.0120	−	21.9246i	−0.776729	−	1.54644i
$202$			31.3321i			2.20452i
$203$	1.23030	+	0.502268i	0.0863501	+	0.0352523i
$204$	−17.3739	−	34.5908i	−1.21641	−	2.42184i
$205$		0			0
$206$	−16.4539			−1.14639
$207$	−1.20871	−	0.899706i	−0.0840113	−	0.0625339i
$208$			6.83723i			0.474077i
$209$	−29.4736			−2.03873
$210$		0			0
$211$	12.7477			0.877590			0.438795	−	0.898587i	$-0.355405\pi$
$211$	12.7477			0.877590			0.438795	+	0.898587i	$0.355405\pi$
$212$		−	50.9341i		−	3.49817i
$213$	6.67212	−	3.35119i	0.457166	−	0.229620i
$214$	2.41742			0.165252
$215$		0			0
$216$	3.88702	−	22.0595i	0.264478	−	1.50096i
$217$	10.7477	+	4.38774i	0.729603	+	0.297859i
$218$			12.0325i			0.814947i
$219$	−9.79129	+	4.91785i	−0.661634	+	0.332317i
$220$		0			0
$221$		−	14.4391i		−	0.971276i
$222$	2.16996	−	1.08990i	0.145638	−	0.0731493i
$223$			2.44949i			0.164030i	0.996631	+	0.0820150i	$0.0261355\pi$
$223$			2.44949i			0.164030i	−0.996631	+	0.0820150i	$0.973864\pi$
$224$	−4.66442	−	1.90424i	−0.311655	−	0.127233i
$225$		0			0
$226$	15.2087			1.01167
$227$	−5.89472			−0.391246			−0.195623	−	0.980679i	$-0.562673\pi$
$227$	−5.89472			−0.391246			−0.195623	+	0.980679i	$0.562673\pi$
$228$	−40.1216	+	20.1518i	−2.65712	+	1.33458i
$229$		−	18.5734i		−	1.22737i	−0.789552	−	0.613684i	$-0.789687\pi$
$229$		−	18.5734i		−	1.22737i	0.789552	−	0.613684i	$-0.210313\pi$
$230$		0			0
$231$	−1.53659	−	19.6945i	−0.101100	−	1.29580i
$232$	2.16515			0.142149
$233$			0.502268i			0.0329047i	0.999865	+	0.0164523i	$0.00523717\pi$
$233$			0.502268i			0.0329047i	−0.999865	+	0.0164523i	$0.994763\pi$
$234$	10.5591	−	14.1857i	0.690273	−	0.927348i
$235$		0			0
$236$	40.0327			2.60591
$237$	6.67212	+	13.2840i	0.433401	+	0.862888i
$238$	−34.7477	−	14.1857i	−2.25236	−	0.919522i
$239$		−	12.4300i		−	0.804029i	−0.915633	−	0.402014i	$-0.868310\pi$
$239$		−	12.4300i		−	0.804029i	0.915633	−	0.402014i	$-0.131690\pi$
$240$		0			0
$241$			7.85971i			0.506288i	0.967429	+	0.253144i	$0.0814647\pi$
$241$			7.85971i			0.506288i	−0.967429	+	0.253144i	$0.918535\pi$
$242$		−	18.2475i		−	1.17300i
$243$	−11.3365	+	10.6997i	−0.727240	+	0.686384i
$244$			16.6352i			1.06496i
$245$		0			0
$246$	17.3739	−	8.72633i	1.10772	−	0.556371i
$247$	−16.7477			−1.06563
$248$	18.9145			1.20107
$249$	5.53901	+	11.0280i	0.351021	+	0.698872i
$250$		0			0
$251$	15.2236			0.960903			0.480451	−	0.877021i	$-0.340473\pi$
$251$	15.2236			0.960903			0.480451	+	0.877021i	$0.340473\pi$
$252$	−15.5573	−	25.7590i	−0.980017	−	1.62266i
$253$	−2.16515			−0.136122
$254$		−	24.4625i		−	1.53492i
$255$		0			0
$256$	−29.3739			−1.83587
$257$	−16.4539			−1.02636			−0.513182	−	0.858280i	$-0.671533\pi$
$257$	−16.4539			−1.02636			−0.513182	+	0.858280i	$0.671533\pi$
$258$	−9.61948	+	4.83156i	−0.598883	+	0.300800i
$259$	0.582576	−	1.42701i	0.0361995	−	0.0886703i
$260$		0			0
$261$	−1.20871	−	0.899706i	−0.0748174	−	0.0556904i
$262$		−	14.1857i		−	0.876395i
$263$			7.32436i			0.451639i	0.974169	+	0.225820i	$0.0725060\pi$
$263$			7.32436i			0.451639i	−0.974169	+	0.225820i	$0.927494\pi$
$264$	−14.4462	−	28.7619i	−0.889100	−	1.77017i
$265$		0			0
$266$	−16.4539	+	40.3036i	−1.00885	+	2.47117i
$267$	−8.20871	−	16.3433i	−0.502365	−	1.00019i
$268$	−53.7042			−3.28050
$269$	18.9145			1.15324			0.576618	−	0.817014i	$-0.304372\pi$
$269$	18.9145			1.15324			0.576618	+	0.817014i	$0.304372\pi$
$270$		0			0
$271$			3.47197i			0.210907i	0.994424	+	0.105453i	$0.0336294\pi$
$271$			3.47197i			0.210907i	−0.994424	+	0.105453i	$0.966371\pi$
$272$	−16.4539			−0.997662
$273$	−0.873133	−	11.1910i	−0.0528444	−	0.677308i
$274$	2.41742			0.146042
$275$		0			0
$276$	−2.94736	+	1.48036i	−0.177410	+	0.0891074i
$277$	−8.74773			−0.525600			−0.262800	−	0.964850i	$-0.584646\pi$
$277$	−8.74773			−0.525600			−0.262800	+	0.964850i	$0.584646\pi$
$278$	−5.89472			−0.353542
$279$	−10.5591	−	7.85971i	−0.632159	−	0.470548i
$280$		0			0
$281$		−	21.5538i		−	1.28579i	−0.765955	−	0.642895i	$-0.777733\pi$
$281$		−	21.5538i		−	1.28579i	0.765955	−	0.642895i	$-0.222267\pi$
$282$	−21.9564	+	11.0280i	−1.30749	+	0.656709i
$283$		−	1.02248i		−	0.0607799i	−0.999538	−	0.0303900i	$-0.990325\pi$
$283$		−	1.02248i		−	0.0607799i	0.999538	−	0.0303900i	$-0.00967491\pi$
$284$		−	16.3433i		−	0.969796i
$285$		0			0
$286$		−	25.4107i		−	1.50256i
$287$	4.66442	−	11.4255i	0.275332	−	0.674423i
$288$	4.58258	+	3.41105i	0.270031	+	0.200998i
$289$	17.7477			1.04398
$290$		0			0
$291$	−0.791288	+	0.397438i	−0.0463861	+	0.0232983i
$292$			23.9837i			1.40354i
$293$	22.3486			1.30562			0.652809	−	0.757523i	$-0.273590\pi$
$293$	22.3486			1.30562			0.652809	+	0.757523i	$0.273590\pi$
$294$	−27.7890	−	8.89340i	−1.62069	−	0.518673i
$295$		0			0
$296$		−	2.51134i		−	0.145969i
$297$	−3.88702	+	22.0595i	−0.225548	+	1.28002i
$298$	15.2087			0.881017
$299$	−1.23030			−0.0711501
$300$		0			0
$301$	−2.58258	+	6.32599i	−0.148857	+	0.364624i
$302$			34.0886i			1.96158i
$303$	−10.1216	−	20.1518i	−0.581470	−	1.15769i
$304$			19.0847i			1.09458i
$305$		0			0
$306$	34.1380	+	25.4107i	1.95154	+	1.45263i
$307$			20.5117i			1.17066i	0.810794	+	0.585332i	$0.199036\pi$
$307$			20.5117i			1.17066i	−0.810794	+	0.585332i	$0.800964\pi$
$308$	−40.0327	−	16.3433i	−2.28108	−	0.931246i
$309$	10.5826	−	5.31529i	0.602022	−	0.302376i
$310$		0			0
$311$	−27.0130			−1.53177			−0.765883	−	0.642979i	$-0.777698\pi$
$311$	−27.0130			−1.53177			−0.765883	+	0.642979i	$0.777698\pi$
$312$	−8.20871	−	16.3433i	−0.464727	−	0.925257i
$313$		−	10.7137i		−	0.605576i	−0.953058	−	0.302788i	$-0.902083\pi$
$313$		−	10.7137i		−	0.605576i	0.953058	−	0.302788i	$-0.0979174\pi$
$314$	22.3486			1.26120
$315$		0			0
$316$	32.5390			1.83046
$317$		−	13.9368i		−	0.782768i	−0.920227	−	0.391384i	$-0.871996\pi$
$317$		−	13.9368i		−	0.782768i	0.920227	−	0.391384i	$-0.128004\pi$
$318$	25.1337	+	50.0404i	1.40943	+	2.80613i
$319$	−2.16515			−0.121225
$320$		0			0
$321$	−1.55481	+	0.780929i	−0.0867809	+	0.0435872i
$322$	−1.20871	+	2.96073i	−0.0673589	+	0.164995i
$323$		−	40.3036i		−	2.24255i
$324$	9.79129	+	32.6866i	0.543960	+	1.81592i
$325$		0			0
$326$		−	9.62604i		−	0.533137i
$327$	−3.88702	−	7.73893i	−0.214953	−	0.427964i
$328$		−	20.1072i		−	1.11023i
$329$	−5.89472	+	14.4391i	−0.324986	+	0.796051i
$330$		0			0
$331$	17.0000			0.934405			0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000			0.934405			0.467202	+	0.884150i	$0.345262\pi$
$332$	27.0130			1.48253
$333$	−1.04356	+	1.40197i	−0.0571868	+	0.0768277i
$334$			31.3321i			1.71442i
$335$		0			0
$336$	−12.7525	+	0.994968i	−0.695708	+	0.0542800i
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$			16.8456i			0.916278i
$339$	−9.78174	+	4.91305i	−0.531271	+	0.266840i
$340$		0			0
$341$	−18.9145			−1.02428
$342$	29.4736	−	39.5964i	1.59375	−	2.14113i
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$			11.1328i			0.600243i
$345$		0			0
$346$		−	42.5571i		−	2.28788i
$347$			18.7498i			1.00654i	0.864129	+	0.503271i	$0.167870\pi$
$347$			18.7498i			1.00654i	−0.864129	+	0.503271i	$0.832130\pi$
$348$	−2.94736	+	1.48036i	−0.157995	+	0.0793558i
$349$		−	1.93825i		−	0.103752i	−0.998654	−	0.0518761i	$-0.983480\pi$
$349$		−	1.93825i		−	0.103752i	0.998654	−	0.0518761i	$-0.0165201\pi$
$350$		0			0
$351$	−2.20871	+	12.5348i	−0.117892	+	0.669059i
$352$	8.20871			0.437526
$353$	13.9933			0.744786			0.372393	−	0.928075i	$-0.378537\pi$
$353$	13.9933			0.744786			0.372393	+	0.928075i	$0.378537\pi$
$354$	−39.3303	+	19.7543i	−2.09038	+	1.04993i
$355$		0			0
$356$	−40.0327			−2.12173
$357$	26.9312	−	2.10120i	1.42535	−	0.111207i
$358$	29.9129			1.58094
$359$		−	6.31982i		−	0.333547i	−0.985995	−	0.166774i	$-0.946665\pi$
$359$		−	6.31982i		−	0.333547i	0.985995	−	0.166774i	$-0.0533349\pi$
$360$		0			0
$361$	−27.7477			−1.46041
$362$	−29.4736			−1.54910
$363$	5.89472	+	11.7362i	0.309393	+	0.615991i
$364$	−22.7477	−	9.28672i	−1.19230	−	0.486756i
$365$		0			0
$366$	−8.20871	−	16.3433i	−0.429076	−	0.854278i
$367$			32.7591i			1.71001i	0.518617	+	0.855007i	$0.326447\pi$
$367$			32.7591i			1.71001i	−0.518617	+	0.855007i	$0.673553\pi$
$368$			1.40197i			0.0730829i
$369$	−8.35532	+	11.2250i	−0.434961	+	0.584349i
$370$		0			0
$371$	32.9077	+	13.4345i	1.70848	+	0.697486i
$372$	−25.7477	+	12.9323i	−1.33496	+	0.670506i
$373$	18.9129			0.979272			0.489636	−	0.871927i	$-0.337130\pi$
$373$	18.9129			0.979272			0.489636	+	0.871927i	$0.337130\pi$
$374$	61.1510			3.16204
$375$		0			0
$376$			25.4107i			1.31046i
$377$	−1.23030			−0.0633637
$378$	27.9952	+	17.6302i	1.43992	+	0.906797i
$379$	−19.3303			−0.992931			−0.496465	−	0.868056i	$-0.665369\pi$
$379$	−19.3303			−0.992931			−0.496465	+	0.868056i	$0.665369\pi$
$380$		0			0
$381$	7.90242	+	15.7335i	0.404853	+	0.806051i
$382$	37.1652			1.90153
$383$	−19.8880			−1.01623			−0.508114	−	0.861290i	$-0.669657\pi$
$383$	−19.8880			−1.01623			−0.508114	+	0.861290i	$0.669657\pi$
$384$	31.9681	−	16.0565i	1.63136	−	0.819381i
$385$		0			0
$386$			26.4716i			1.34737i
$387$	4.62614	−	6.21499i	0.235160	−	0.315926i
$388$			1.93825i			0.0983998i
$389$			26.3668i			1.33685i	0.743780	+	0.668424i	$0.233031\pi$
$389$			26.3668i			1.33685i	−0.743780	+	0.668424i	$0.766969\pi$
$390$		0			0
$391$		−	2.96073i		−	0.149730i
$392$	−21.1183	+	21.5538i	−1.06663	+	1.08863i
$393$	4.58258	+	9.12377i	0.231160	+	0.460233i
$394$	−45.1216			−2.27319
$395$		0			0
$396$	39.3303	+	29.2756i	1.97642	+	1.47115i
$397$		−	13.6745i		−	0.686302i	−0.939280	−	0.343151i	$-0.888506\pi$
$397$		−	13.6745i		−	0.686302i	0.939280	−	0.343151i	$-0.111494\pi$
$398$	−45.9275			−2.30214
$399$	−2.43716	−	31.2372i	−0.122011	−	1.56382i
$400$		0			0
$401$			11.1328i			0.555948i	0.960589	+	0.277974i	$0.0896628\pi$
$401$			11.1328i			0.555948i	−0.960589	+	0.277974i	$0.910337\pi$
$402$	52.7618	−	26.5006i	2.63152	−	1.32173i
$403$	−10.7477			−0.535382
$404$	−49.3616			−2.45583
$405$		0			0
$406$	−1.20871	+	2.96073i	−0.0599874	+	0.146938i
$407$			2.51134i			0.124482i
$408$	39.3303	−	19.7543i	1.94714	−	0.977986i
$409$			24.3882i			1.20592i	0.797772	+	0.602959i	$0.206012\pi$
$409$			24.3882i			1.20592i	−0.797772	+	0.602959i	$0.793988\pi$
$410$		0			0
$411$	−1.55481	+	0.780929i	−0.0766930	+	0.0385204i
$412$		−	25.9219i		−	1.27708i
$413$	−10.5591	+	25.8645i	−0.519581	+	1.27271i
$414$	2.16515	−	2.90878i	0.106411	−	0.142959i
$415$		0			0
$416$	4.66442			0.228692
$417$	3.79129	−	1.90424i	0.185660	−	0.0932511i
$418$		−	70.9285i		−	3.46923i
$419$	18.9145			0.924032			0.462016	−	0.886872i	$-0.347126\pi$
$419$	18.9145			0.924032			0.462016	+	0.886872i	$0.347126\pi$
$420$		0			0
$421$	−10.1652			−0.495419			−0.247710	−	0.968834i	$-0.579678\pi$
$421$	−10.1652			−0.495419			−0.247710	+	0.968834i	$0.579678\pi$
$422$			30.6775i			1.49336i
$423$	10.5591	−	14.1857i	0.513403	−	0.689732i
$424$	57.9129			2.81250
$425$		0			0
$426$	8.06468	+	16.0565i	0.390735	+	0.777941i
$427$	−10.7477	−	4.38774i	−0.520119	−	0.212338i
$428$			3.80848i			0.184090i
$429$	8.20871	+	16.3433i	0.396320	+	0.789062i
$430$		0			0
$431$			30.8872i			1.48778i	0.668300	+	0.743892i	$0.267022\pi$
$431$			30.8872i			1.48778i	−0.668300	+	0.743892i	$0.732978\pi$
$432$	14.2839	+	2.51691i	0.687235	+	0.121095i
$433$			23.4724i			1.12801i	0.825770	+	0.564006i	$0.190741\pi$
$433$			23.4724i			1.12801i	−0.825770	+	0.564006i	$0.809259\pi$
$434$	−10.5591	+	25.8645i	−0.506855	+	1.24154i
$435$		0			0
$436$	−18.9564			−0.907849
$437$	−3.43412			−0.164276
$438$	−11.8348	−	23.5628i	−0.565491	−	1.12588i
$439$			26.9444i			1.28599i	0.765872	+	0.642993i	$0.222307\pi$
$439$			26.9444i			1.28599i	−0.765872	+	0.642993i	$0.777693\pi$
$440$		0			0
$441$	20.7459	−	3.25706i	0.987899	−	0.155098i
$442$	34.7477			1.65278
$443$			13.4345i			0.638293i	0.947705	+	0.319147i	$0.103396\pi$
$443$			13.4345i			0.638293i	−0.947705	+	0.319147i	$0.896604\pi$
$444$	1.71706	+	3.41862i	0.0814881	+	0.162240i
$445$		0			0
$446$	−5.89472			−0.279123
$447$	−9.78174	+	4.91305i	−0.462660	+	0.232379i
$448$	10.1652	−	24.8994i	0.480258	−	1.17639i
$449$			19.5447i			0.922371i	0.887304	+	0.461185i	$0.152576\pi$
$449$			19.5447i			0.922371i	−0.887304	+	0.461185i	$0.847424\pi$
$450$		0			0
$451$			20.1072i			0.946809i
$452$			23.9603i			1.12700i
$453$	−11.0120	−	21.9246i	−0.517391	−	1.03011i
$454$		−	14.1857i		−	0.665768i
$455$		0			0
$456$	−22.9129	−	45.6189i	−1.07299	−	2.13630i
$457$	−15.8348			−0.740723			−0.370361	−	0.928888i	$-0.620766\pi$
$457$	−15.8348			−0.740723			−0.370361	+	0.928888i	$0.620766\pi$
$458$	44.6972			2.08856
$459$	−30.1652	−	5.31529i	−1.40799	−	0.248096i
$460$		0			0
$461$	−8.09854			−0.377187			−0.188593	−	0.982055i	$-0.560393\pi$
$461$	−8.09854			−0.377187			−0.188593	+	0.982055i	$0.560393\pi$
$462$	47.3950	−	3.69781i	2.20501	−	0.172038i
$463$	−14.7477			−0.685385			−0.342693	−	0.939448i	$-0.611339\pi$
$463$	−14.7477			−0.685385			−0.342693	+	0.939448i	$0.611339\pi$
$464$			1.40197i			0.0650850i
$465$		0			0
$466$	−1.20871			−0.0559925
$467$	−35.3683			−1.63665			−0.818325	−	0.574755i	$-0.805097\pi$
$467$	−35.3683			−1.63665			−0.818325	+	0.574755i	$0.805097\pi$
$468$	22.3486	+	16.6352i	1.03306	+	0.768962i
$469$	14.1652	−	34.6974i	0.654086	−	1.60218i
$470$		0			0
$471$	−14.3739	+	7.21953i	−0.662313	+	0.332658i
$472$			45.5178i			2.09513i
$473$		−	11.1328i		−	0.511889i
$474$	−31.9681	+	16.0565i	−1.46834	+	0.737501i
$475$		0			0
$476$	22.3486	−	54.7426i	1.02435	−	2.50912i
$477$	−32.3303	−	24.0651i	−1.48030	−	1.10186i
$478$	29.9129			1.36818
$479$	−10.5591			−0.482459			−0.241230	−	0.970468i	$-0.577551\pi$
$479$	−10.5591			−0.482459			−0.241230	+	0.970468i	$0.577551\pi$
$480$		0			0
$481$			1.42701i			0.0650662i
$482$	−18.9145			−0.861530
$483$	−0.179036	−	2.29471i	−0.00814641	−	0.104413i
$484$	28.7477			1.30671
$485$		0			0
$486$	−25.7488	−	27.2815i	−1.16799	−	1.23751i
$487$	−40.1652			−1.82006			−0.910028	−	0.414546i	$-0.863940\pi$
$487$	−40.1652			−1.82006			−0.910028	+	0.414546i	$0.863940\pi$
$488$	−18.9145			−0.856217
$489$	3.10961	+	6.19115i	0.140622	+	0.279973i
$490$		0			0
$491$		−	2.51134i		−	0.113335i	−0.998393	−	0.0566676i	$-0.981952\pi$
$491$		−	2.51134i		−	0.113335i	0.998393	−	0.0566676i	$-0.0180475\pi$
$492$	13.7477	+	27.3713i	0.619795	+	1.23399i
$493$		−	2.96073i		−	0.133344i
$494$		−	40.3036i		−	1.81334i
$495$		0			0
$496$			12.2474i			0.549927i
$497$	10.5591	+	4.31075i	0.473642	+	0.193364i
$498$	−26.5390	+	13.3297i	−1.18924	+	0.597318i
$499$	30.7477			1.37646			0.688229	−	0.725494i	$-0.258389\pi$
$499$	30.7477			1.37646			0.688229	+	0.725494i	$0.258389\pi$
$500$		0			0
$501$	−10.1216	−	20.1518i	−0.452199	−	0.900315i
$502$			36.6356i			1.63513i
$503$	11.7894			0.525665			0.262833	−	0.964841i	$-0.415343\pi$
$503$	11.7894			0.525665			0.262833	+	0.964841i	$0.415343\pi$
$504$	29.2883	−	17.6889i	1.30461	−	0.787925i
$505$		0			0
$506$		−	5.21046i		−	0.231633i
$507$	−5.44182	−	10.8345i	−0.241680	−	0.481177i
$508$	38.5390			1.70989
$509$	31.6774			1.40408			0.702039	−	0.712139i	$-0.252273\pi$
$509$	31.6774			1.40408			0.702039	+	0.712139i	$0.252273\pi$
$510$		0			0
$511$	−15.4955	−	6.32599i	−0.685479	−	0.279845i
$512$		−	29.3804i		−	1.29844i
$513$	−6.16515	+	34.9883i	−0.272198	+	1.54477i
$514$		−	39.5964i		−	1.74652i
$515$		0			0
$516$	−7.61178	−	15.1548i	−0.335090	−	0.667154i
$517$		−	25.4107i		−	1.11756i
$518$	3.43412	+	1.40197i	0.150887	+	0.0615992i
$519$	13.7477	+	27.3713i	0.603458	+	1.20147i
$520$		0			0
$521$	−35.3683			−1.54951			−0.774757	−	0.632259i	$-0.782128\pi$
$521$	−35.3683			−1.54951			−0.774757	+	0.632259i	$0.782128\pi$
$522$	2.16515	−	2.90878i	0.0947661	−	0.127314i
$523$			14.6969i			0.642652i	0.946969	+	0.321326i	$0.104129\pi$
$523$			14.6969i			0.642652i	−0.946969	+	0.321326i	$0.895871\pi$
$524$	22.3486			0.976302
$525$		0			0
$526$	−17.6261			−0.768536
$527$		−	25.8645i		−	1.12668i
$528$	18.6238	−	9.35414i	0.810498	−	0.407087i
$529$	22.7477			0.989032
$530$		0			0
$531$	18.9145	−	25.4107i	0.820818	−	1.10273i
$532$	−63.4955	−	25.9219i	−2.75288	−	1.12386i
$533$			11.4255i			0.494891i
$534$	39.3303	−	19.7543i	1.70199	−	0.854854i
$535$		0			0
$536$		−	61.0624i		−	2.63750i
$537$	−19.2390	+	9.66311i	−0.830223	+	0.416994i
$538$			45.5178i			1.96241i
$539$	21.1183	−	21.5538i	0.909629	−	0.928386i
$540$		0			0
$541$	0.582576			0.0250469			0.0125234	−	0.999922i	$-0.496014\pi$
$541$	0.582576			0.0250469			0.0125234	+	0.999922i	$0.496014\pi$
$542$	−8.35532			−0.358892
$543$	18.9564	−	9.52121i	0.813499	−	0.408594i
$544$			11.2250i			0.481267i
$545$		0			0
$546$	26.9312	−	2.10120i	1.15255	−	0.0899231i
$547$	41.3303			1.76716			0.883578	−	0.468284i	$-0.155128\pi$
$547$	41.3303			1.76716			0.883578	+	0.468284i	$0.155128\pi$
$548$			3.80848i			0.162690i
$549$	10.5591	+	7.85971i	0.450653	+	0.335444i
$550$		0			0
$551$	−3.43412			−0.146298
$552$	−1.68320	−	3.35119i	−0.0716416	−	0.142636i
$553$	−8.58258	+	21.0229i	−0.364968	+	0.893986i
$554$		−	21.0515i		−	0.894392i
$555$		0			0
$556$		−	9.28672i		−	0.393845i
$557$		−	46.6234i		−	1.97550i	−0.156056	−	0.987748i	$-0.549878\pi$
$557$		−	46.6234i		−	1.97550i	0.156056	−	0.987748i	$-0.450122\pi$
$558$	18.9145	−	25.4107i	0.800713	−	1.07572i
$559$		−	6.32599i		−	0.267561i
$560$		0			0
$561$	−39.3303	+	19.7543i	−1.66053	+	0.834029i
$562$	51.8693			2.18798
$563$	32.9077			1.38690			0.693448	−	0.720507i	$-0.256091\pi$
$563$	32.9077			1.38690			0.693448	+	0.720507i	$0.256091\pi$
$564$	−17.3739	−	34.5908i	−0.731572	−	1.45654i
$565$		0			0
$566$	2.46060			0.103427
$567$	−23.7009	−	2.29551i	−0.995342	−	0.0964023i
$568$	18.5826			0.779708
$569$		−	32.1843i		−	1.34924i	−0.738166	−	0.674619i	$-0.764308\pi$
$569$		−	32.1843i		−	1.34924i	0.738166	−	0.674619i	$-0.235692\pi$
$570$		0			0
$571$	−2.25227			−0.0942547			−0.0471273	−	0.998889i	$-0.515007\pi$
$571$	−2.25227			−0.0942547			−0.0471273	+	0.998889i	$0.515007\pi$
$572$	40.0327			1.67385
$573$	−23.9034	+	12.0059i	−0.998578	+	0.501554i
$574$	27.4955	+	11.2250i	1.14764	+	0.468521i
$575$		0			0
$576$	−18.2087	+	24.4625i	−0.758696	+	1.01927i
$577$		−	12.7587i		−	0.531151i	−0.964090	−	0.265576i	$-0.914438\pi$
$577$		−	12.7587i		−	0.531151i	0.964090	−	0.265576i	$-0.0855620\pi$
$578$			42.7101i			1.77650i
$579$	−8.55144	−	17.0257i	−0.355386	−	0.707562i
$580$		0			0
$581$	−7.12502	+	17.4527i	−0.295596	+	0.724058i
$582$	−0.956439	−	1.90424i	−0.0396457	−	0.0789334i
$583$	−57.9129			−2.39851
$584$	−27.2698			−1.12843
$585$		0			0
$586$			53.7821i			2.22172i
$587$	34.1380			1.40903			0.704513	−	0.709691i	$-0.251165\pi$
$587$	34.1380			1.40903			0.704513	+	0.709691i	$0.251165\pi$
$588$	14.0109	−	43.7796i	0.577801	−	1.80544i
$589$	−30.0000			−1.23613
$590$		0			0
$591$	29.0207	−	14.5762i	1.19375	−	0.599583i
$592$	1.62614			0.0668338
$593$	11.7894			0.484134			0.242067	−	0.970259i	$-0.422175\pi$
$593$	11.7894			0.484134			0.242067	+	0.970259i	$0.422175\pi$
$594$	−53.0863	−	9.35414i	−2.17816	−	0.383805i
$595$		0			0
$596$			23.9603i			0.981451i
$597$	29.5390	−	14.8365i	1.20895	−	0.607217i
$598$		−	2.96073i		−	0.121073i
$599$			19.5447i			0.798574i	0.916826	+	0.399287i	$0.130742\pi$
$599$			19.5447i			0.798574i	−0.916826	+	0.399287i	$0.869258\pi$
$600$		0			0
$601$			42.0459i			1.71509i	0.514412	+	0.857543i	$0.328010\pi$
$601$			42.0459i			1.71509i	−0.514412	+	0.857543i	$0.671990\pi$
$602$	−15.2236	−	6.21499i	−0.620466	−	0.253304i
$603$	−25.3739	+	34.0886i	−1.03330	+	1.38819i
$604$	−53.7042			−2.18519
$605$		0			0
$606$	48.4955	−	24.3577i	1.96999	−	0.989464i
$607$		−	1.42701i		−	0.0579207i	−0.999581	−	0.0289603i	$-0.990780\pi$
$607$		−	1.42701i		−	0.0579207i	0.999581	−	0.0289603i	$-0.00921965\pi$
$608$	13.0197			0.528020
$609$	−0.179036	−	2.29471i	−0.00725490	−	0.0929862i
$610$		0			0
$611$		−	14.4391i		−	0.584142i
$612$	−40.0327	+	53.7821i	−1.61823	+	2.17401i
$613$	27.4174			1.10738			0.553690	−	0.832723i	$-0.313219\pi$
$613$	27.4174			1.10738			0.553690	+	0.832723i	$0.313219\pi$
$614$	−49.3616			−1.99207
$615$		0			0
$616$	18.5826	−	45.5178i	0.748713	−	1.83397i
$617$		−	13.9368i		−	0.561074i	−0.959843	−	0.280537i	$-0.909487\pi$
$617$		−	13.9368i		−	0.561074i	0.959843	−	0.280537i	$-0.0905125\pi$
$618$	12.7913	+	25.4671i	0.514541	+	1.02444i
$619$			35.7199i			1.43570i	0.696196	+	0.717851i	$0.254874\pi$
$619$			35.7199i			1.43570i	−0.696196	+	0.717851i	$0.745126\pi$
$620$		0			0
$621$	−0.452896	+	2.57026i	−0.0181741	+	0.103141i
$622$		−	65.0070i		−	2.60655i
$623$	10.5591	−	25.8645i	0.423043	−	1.03624i
$624$	10.5826	−	5.31529i	0.423642	−	0.212782i
$625$		0			0
$626$	25.7827			1.03048
$627$	22.9129	+	45.6189i	0.915052	+	1.82184i
$628$			35.2086i			1.40498i
$629$	−3.43412			−0.136927
$630$		0			0
$631$	6.25227			0.248899			0.124450	−	0.992226i	$-0.460284\pi$
$631$	6.25227			0.248899			0.124450	+	0.992226i	$0.460284\pi$
$632$			36.9973i			1.47168i
$633$	−9.91013	−	19.7308i	−0.393892	−	0.784227i
$634$	33.5390			1.33200
$635$		0			0
$636$	−78.8352	+	39.5964i	−3.12602	+	1.57010i
$637$	12.0000	−	12.2474i	0.475457	−	0.485262i
$638$		−	5.21046i		−	0.206284i
$639$	−10.3739	−	7.72180i	−0.410384	−	0.305470i
$640$		0			0
$641$			36.9973i			1.46131i	0.682748	+	0.730654i	$0.260785\pi$
$641$			36.9973i			1.46131i	−0.682748	+	0.730654i	$0.739215\pi$
$642$	−1.87931	−	3.74166i	−0.0741706	−	0.147671i
$643$		−	43.0683i		−	1.69845i	−0.528032	−	0.849225i	$-0.677070\pi$
$643$		−	43.0683i		−	1.69845i	0.528032	−	0.849225i	$-0.322930\pi$
$644$	−4.66442	−	1.90424i	−0.183804	−	0.0750376i
$645$		0			0
$646$	96.9909			3.81606
$647$	−18.6577			−0.733509			−0.366755	−	0.930318i	$-0.619531\pi$
$647$	−18.6577			−0.733509			−0.366755	+	0.930318i	$0.619531\pi$
$648$	−37.1652	+	11.1328i	−1.45999	+	0.437339i
$649$		−	45.5178i		−	1.78673i
$650$		0			0
$651$	−1.56403	−	20.0462i	−0.0612992	−	0.785674i
$652$	15.1652			0.593913
$653$		−	12.4300i		−	0.486423i	−0.969973	−	0.243211i	$-0.921799\pi$
$653$		−	12.4300i		−	0.486423i	0.969973	−	0.243211i	$-0.0782009\pi$
$654$	18.6238	−	9.35414i	0.728249	−	0.365776i
$655$		0			0
$656$	13.0197			0.508335
$657$	15.2236	+	11.3317i	0.593928	+	0.442091i
$658$	−34.7477	−	14.1857i	−1.35461	−	0.553016i
$659$		−	12.4300i		−	0.484203i	−0.970251	−	0.242102i	$-0.922163\pi$
$659$		−	12.4300i		−	0.484203i	0.970251	−	0.242102i	$-0.0778368\pi$
$660$		0			0
$661$		−	32.3546i		−	1.25845i	−0.777224	−	0.629224i	$-0.783373\pi$
$661$		−	32.3546i		−	1.25845i	0.777224	−	0.629224i	$-0.216627\pi$
$662$			40.9107i			1.59004i
$663$	−22.3486	+	11.2250i	−0.867947	+	0.435942i
$664$			30.7142i			1.19194i
$665$		0			0
$666$	−3.37386	−	2.51134i	−0.130735	−	0.0973124i
$667$	−0.252273			−0.00976805
$668$	−49.3616			−1.90986
$669$	3.79129	−	1.90424i	0.146580	−	0.0736222i
$670$		0			0
$671$	18.9145			0.730185
$672$	0.678776	+	8.69989i	0.0261844	+	0.335606i
$673$	47.4955			1.83082			0.915408	−	0.402528i	$-0.131868\pi$
$673$	47.4955			1.83082			0.915408	+	0.402528i	$0.131868\pi$
$674$			4.81302i			0.185391i
$675$		0			0
$676$	−26.5390			−1.02073
$677$	23.5789			0.906210			0.453105	−	0.891457i	$-0.350316\pi$
$677$	23.5789			0.906210			0.453105	+	0.891457i	$0.350316\pi$
$678$	−11.8233	−	23.5398i	−0.454071	−	0.904042i
$679$	−1.25227	−	0.511238i	−0.0480578	−	0.0196195i
$680$		0			0
$681$	4.58258	+	9.12377i	0.175605	+	0.349624i
$682$		−	45.5178i		−	1.74297i
$683$			33.1889i			1.26994i	0.772538	+	0.634968i	$0.218987\pi$
$683$			33.1889i			1.26994i	−0.772538	+	0.634968i	$0.781013\pi$
$684$	62.3813	+	46.4336i	2.38521	+	1.77543i
$685$		0			0
$686$	−17.6842	−	40.9107i	−0.675184	−	1.56198i
$687$	−28.7477	+	14.4391i	−1.09679	+	0.550884i
$688$	−7.20871			−0.274830
$689$	−32.9077			−1.25368
$690$		0			0
$691$		−	4.38774i		−	0.166918i	−0.996511	−	0.0834588i	$-0.973403\pi$
$691$		−	4.38774i		−	0.166918i	0.996511	−	0.0834588i	$-0.0265967\pi$
$692$	67.0457			2.54870
$693$	−29.2883	+	17.6889i	−1.11257	+	0.671945i
$694$	−45.1216			−1.71279
$695$		0			0
$696$	−1.68320	−	3.35119i	−0.0638014	−	0.127027i
$697$	−27.4955			−1.04146
$698$	4.66442			0.176551
$699$	0.777403	−	0.390465i	0.0294041	−	0.0147687i
$700$		0			0
$701$		−	15.4436i		−	0.583296i	−0.956526	−	0.291648i	$-0.905796\pi$
$701$		−	15.4436i		−	0.583296i	0.956526	−	0.291648i	$-0.0942037\pi$
$702$	−30.1652	−	5.31529i	−1.13851	−	0.200613i
$703$			3.98320i			0.150229i
$704$			43.8194i			1.65151i
$705$		0			0
$706$			33.6749i			1.26737i
$707$	13.0197	−	31.8917i	0.489658	−	1.19941i
$708$	−31.1216	−	61.9621i	−1.16962	−	2.32868i
$709$	−31.4955			−1.18284			−0.591418	−	0.806365i	$-0.701432\pi$
$709$	−31.4955			−1.18284			−0.591418	+	0.806365i	$0.701432\pi$
$710$		0			0
$711$	15.3739	−	20.6540i	0.576565	−	0.774587i
$712$		−	45.5178i		−	1.70585i
$713$	−2.20382			−0.0825337
$714$	5.05656	+	64.8101i	0.189237	+	2.42546i
$715$		0			0
$716$			47.1257i			1.76117i
$717$	−19.2390	+	9.66311i	−0.718492	+	0.360876i
$718$	15.2087			0.567584
$719$	40.0327			1.49297			0.746485	−	0.665403i	$-0.231740\pi$
$719$	40.0327			1.49297			0.746485	+	0.665403i	$0.231740\pi$
$720$		0			0
$721$	16.7477	+	6.83723i	0.623718	+	0.254632i
$722$		−	66.7752i		−	2.48511i
$723$	12.1652	−	6.11016i	0.452427	−	0.227239i
$724$		−	46.4336i		−	1.72569i
$725$		0			0
$726$	−28.2433	+	14.1857i	−1.04821	+	0.526481i
$727$			45.0066i			1.66920i	0.550855	+	0.834601i	$0.314302\pi$
$727$			45.0066i			1.66920i	−0.550855	+	0.834601i	$0.685698\pi$
$728$	10.5591	−	25.8645i	0.391348	−	0.958602i
$729$	25.3739	+	9.22860i	0.939773	+	0.341800i
$730$		0			0
$731$	15.2236			0.563064
$732$	25.7477	−	12.9323i	0.951663	−	0.477990i
$733$			32.2479i			1.19110i	0.803317	+	0.595552i	$0.203067\pi$
$733$			32.2479i			1.19110i	−0.803317	+	0.595552i	$0.796933\pi$
$734$	−78.8352			−2.90986
$735$		0			0
$736$	0.956439			0.0352548
$737$			61.0624i			2.24926i
$738$	−27.0130	−	20.1072i	−0.994362	−	0.740155i
$739$	−40.8258			−1.50180			−0.750900	−	0.660416i	$-0.770380\pi$
$739$	−40.8258			−1.50180			−0.750900	+	0.660416i	$0.770380\pi$
$740$		0			0
$741$	13.0197	+	25.9219i	0.478292	+	0.952265i
$742$	−32.3303	+	79.1927i	−1.18688	+	2.90726i
$743$		−	12.4300i		−	0.456012i	−0.973660	−	0.228006i	$-0.926779\pi$
$743$		−	12.4300i		−	0.456012i	0.973660	−	0.228006i	$-0.0732206\pi$
$744$	−14.7042	−	29.2756i	−0.539081	−	1.07329i
$745$		0			0
$746$			45.5140i			1.66639i
$747$	12.7630	−	17.1464i	0.466972	−	0.627355i
$748$			96.3392i			3.52251i
$749$	−2.46060	−	1.00454i	−0.0899083	−	0.0367049i
$750$		0			0
$751$	−38.7477			−1.41392			−0.706962	−	0.707251i	$-0.749935\pi$
$751$	−38.7477			−1.41392			−0.706962	+	0.707251i	$0.749935\pi$
$752$	−16.4539			−0.600011
$753$	−11.8348	−	23.5628i	−0.431286	−	0.858677i
$754$		−	2.96073i		−	0.107823i
$755$		0			0
$756$	−27.7751	+	44.1045i	−1.01017	+	1.60406i
$757$	6.25227			0.227243			0.113621	−	0.993524i	$-0.463755\pi$
$757$	6.25227			0.227243			0.113621	+	0.993524i	$0.463755\pi$
$758$		−	46.5186i		−	1.68963i
$759$	1.68320	+	3.35119i	0.0610961	+	0.121641i
$760$		0			0
$761$	44.6972			1.62027			0.810135	−	0.586243i	$-0.199394\pi$
$761$	44.6972			1.62027			0.810135	+	0.586243i	$0.199394\pi$
$762$	−37.8628	+	19.0173i	−1.37162	+	0.688923i
$763$	5.00000	−	12.2474i	0.181012	−	0.443387i
$764$			58.5511i			2.11830i
$765$		0			0
$766$		−	47.8606i		−	1.72927i
$767$		−	25.8645i		−	0.933913i
$768$	22.8353	+	45.4645i	0.823999	+	1.64056i
$769$			3.36526i			0.121355i	0.998157	+	0.0606773i	$0.0193260\pi$
$769$			3.36526i			0.121355i	−0.998157	+	0.0606773i	$0.980674\pi$
$770$		0			0
$771$	12.7913	+	25.4671i	0.460667	+	0.917174i
$772$	−41.7042			−1.50097
$773$	−7.12502			−0.256269			−0.128135	−	0.991757i	$-0.540899\pi$
$773$	−7.12502			−0.256269			−0.128135	+	0.991757i	$0.540899\pi$
$774$	14.9564	+	11.1328i	0.537598	+	0.400162i
$775$		0			0
$776$	−2.20382			−0.0791126
$777$	−2.66161	+	0.207662i	−0.0954847	+	0.00744983i
$778$	−63.4519			−2.27486
$779$			31.8917i			1.14264i
$780$		0			0
$781$	−18.5826			−0.664937
$782$	7.12502			0.254790
$783$	−0.452896	+	2.57026i	−0.0161852	+	0.0918537i
$784$	−13.9564	−	13.6745i	−0.498444	−	0.488374i
$785$		0			0
$786$	−21.9564	+	11.0280i	−0.783160	+	0.393356i
$787$			16.1240i			0.574757i	0.957817	+	0.287378i	$0.0927837\pi$
$787$			16.1240i			0.574757i	−0.957817	+	0.287378i	$0.907216\pi$
$788$		−	71.0859i		−	2.53233i
$789$	11.3365	−	5.69398i	0.403592	−	0.202711i
$790$		0			0
$791$	−15.4803	−	6.31982i	−0.550418	−	0.224707i
$792$	−33.2867	+	44.7191i	−1.18279	+	1.58903i
$793$	10.7477			0.381663
$794$	32.9077			1.16785
$795$		0			0
$796$		−	72.3555i		−	2.56457i
$797$	15.2236			0.539246			0.269623	−	0.962966i	$-0.413101\pi$
$797$	15.2236			0.539246			0.269623	+	0.962966i	$0.413101\pi$
$798$	75.1726	−	5.86506i	2.66108	−	0.207621i
$799$	34.7477			1.22929
$800$		0			0
$801$	−18.9145	+	25.4107i	−0.668310	+	0.897842i
$802$	−26.7913			−0.946033
$803$	27.2698			0.962330
$804$	41.7498	+	83.1226i	1.47240	+	2.93151i
$805$		0			0
$806$		−	25.8645i		−	0.911038i
$807$	−14.7042	−	29.2756i	−0.517611	−	1.03055i
$808$		−	56.1249i		−	1.97447i
$809$			7.32436i			0.257511i	0.991676	+	0.128755i	$0.0410982\pi$
$809$			7.32436i			0.257511i	−0.991676	+	0.128755i	$0.958902\pi$
$810$		0			0
$811$		−	8.77548i		−	0.308149i	−0.988059	−	0.154074i	$-0.950760\pi$
$811$		−	8.77548i		−	0.308149i	0.988059	−	0.154074i	$-0.0492396\pi$
$812$	−4.66442	−	1.90424i	−0.163689	−	0.0668258i
$813$	5.37386	−	2.69912i	0.188470	−	0.0946622i
$814$	−6.04356			−0.211827
$815$		0			0
$816$	12.7913	+	25.4671i	0.447785	+	0.891526i
$817$		−	17.6577i		−	0.617764i
$818$	−58.6904			−2.05206
$819$	−16.6424	+	10.0513i	−0.581534	+	0.351221i
$820$		0			0
$821$		−	15.4436i		−	0.538985i	−0.963002	−	0.269493i	$-0.913144\pi$
$821$		−	15.4436i		−	0.538985i	0.963002	−	0.269493i	$-0.0868560\pi$
$822$	−1.87931	−	3.74166i	−0.0655486	−	0.130505i
$823$	−29.7477			−1.03694			−0.518470	−	0.855096i	$-0.673498\pi$
$823$	−29.7477			−1.03694			−0.518470	+	0.855096i	$0.673498\pi$
$824$	29.4736			1.02676
$825$		0			0
$826$	−62.2432	−	25.4107i	−2.16572	−	0.884150i
$827$			44.6143i			1.55139i	0.631107	+	0.775696i	$0.282601\pi$
$827$			44.6143i			1.55139i	−0.631107	+	0.775696i	$0.717399\pi$
$828$	4.58258	+	3.41105i	0.159256	+	0.118542i
$829$		−	26.4331i		−	0.918061i	−0.888420	−	0.459031i	$-0.848197\pi$
$829$		−	26.4331i		−	0.918061i	0.888420	−	0.459031i	$-0.151803\pi$
$830$		0			0
$831$	6.80051	+	13.5396i	0.235907	+	0.469684i
$832$			24.8994i			0.863233i
$833$	29.4736	+	28.8781i	1.02120	+	1.00057i
$834$	4.58258	+	9.12377i	0.158682	+	0.315930i
$835$		0			0
$836$	111.743			3.86471
$837$	−3.95644	+	22.4535i	−0.136755	+	0.776105i
$838$			45.5178i			1.57239i
$839$	−10.5591			−0.364542			−0.182271	−	0.983248i	$-0.558345\pi$
$839$	−10.5591			−0.364542			−0.182271	+	0.983248i	$0.558345\pi$
$840$		0			0
$841$	28.7477			0.991301
$842$		−	24.4625i		−	0.843035i
$843$	−33.3606	+	16.7560i	−1.14900	+	0.577106i
$844$	−48.3303			−1.66360
$845$		0			0
$846$	34.1380	+	25.4107i	1.17369	+	0.873637i
$847$	−7.58258	+	18.5734i	−0.260540	+	0.638191i
$848$			37.4996i			1.28774i
$849$	−1.58258	+	0.794877i	−0.0543139	+	0.0272801i
$850$		0			0
$851$			0.292609i			0.0100305i
$852$	−25.2959	+	12.7053i	−0.866625	+	0.435278i
$853$		−	27.3489i		−	0.936409i	−0.883620	−	0.468205i	$-0.844901\pi$
$853$		−	27.3489i		−	0.936409i	0.883620	−	0.468205i	$-0.155099\pi$
$854$	10.5591	−	25.8645i	0.361326	−	0.885065i
$855$		0			0
$856$	−4.33030			−0.148007
$857$	21.3751			0.730158			0.365079	−	0.930977i	$-0.381042\pi$
$857$	21.3751			0.730158			0.365079	+	0.930977i	$0.381042\pi$
$858$	−39.3303	+	19.7543i	−1.34271	+	0.674402i
$859$		−	25.5174i		−	0.870642i	−0.900275	−	0.435321i	$-0.856635\pi$
$859$		−	25.5174i		−	0.870642i	0.900275	−	0.435321i	$-0.143365\pi$
$860$		0			0
$861$	−21.3103	+	1.66266i	−0.726253	+	0.0566632i
$862$	−74.3303			−2.53170
$863$		−	39.0064i		−	1.32779i	−0.747824	−	0.663897i	$-0.768901\pi$
$863$		−	39.0064i		−	1.32779i	0.747824	−	0.663897i	$-0.231099\pi$
$864$	1.71706	−	9.74461i	0.0584156	−	0.331518i
$865$		0			0
$866$	−56.4866			−1.91949
$867$	−13.7971	−	27.4697i	−0.468576	−	0.932920i
$868$	−40.7477	−	16.6352i	−1.38307	−	0.564635i
$869$		−	36.9973i		−	1.25505i
$870$		0			0
$871$			34.6974i			1.17568i
$872$		−	21.5538i		−	0.729902i
$873$	1.23030	+	0.915775i	0.0416393	+	0.0309943i
$874$		−	8.26424i		−	0.279542i
$875$		0			0
$876$	37.1216	−	18.6450i	1.25422	−	0.629955i
$877$	23.4955			0.793385			0.396693	−	0.917952i	$-0.370158\pi$
$877$	23.4955			0.793385			0.396693	+	0.917952i	$0.370158\pi$
$878$	−64.8419			−2.18831
$879$	−17.3739	−	34.5908i	−0.586006	−	1.16672i
$880$		0			0
$881$	−58.6904			−1.97733			−0.988665	−	0.150136i	$-0.952029\pi$
$881$	−58.6904			−1.97733			−0.988665	+	0.150136i	$0.952029\pi$
$882$	7.83816	+	49.9252i	0.263924	+	1.68107i
$883$	24.5826			0.827270			0.413635	−	0.910443i	$-0.364259\pi$
$883$	24.5826			0.827270			0.413635	+	0.910443i	$0.364259\pi$
$884$			54.7426i			1.84119i
$885$		0			0
$886$	−32.3303			−1.08616
$887$	46.9010			1.57478			0.787390	−	0.616455i	$-0.211432\pi$
$887$	46.9010			1.57478			0.787390	+	0.616455i	$0.211432\pi$
$888$	−3.88702	+	1.95232i	−0.130440	+	0.0655157i
$889$	−10.1652	+	24.8994i	−0.340928	+	0.835100i
$890$		0			0
$891$	37.1652	−	11.1328i	1.24508	−	0.372964i
$892$		−	9.28672i		−	0.310942i
$893$		−	40.3036i		−	1.34871i
$894$	−11.8233	−	23.5398i	−0.395430	−	0.787290i
$895$		0			0
$896$	50.5919	+	20.6540i	1.69016	+	0.690003i
$897$	0.956439	+	1.90424i	0.0319346	+	0.0635808i
$898$	−47.0345			−1.56956
$899$	−2.20382			−0.0735015
$900$		0			0
$901$		−	79.1927i		−	2.63829i
$902$	−48.3881			−1.61115
$903$	11.7990	−	0.920572i	0.392646	−	0.0306347i
$904$	−27.2432			−0.906095
$905$		0			0
$906$	52.7618	−	26.5006i	1.75289	−	0.880423i
$907$	53.4955			1.77629			0.888144	−	0.459566i	$-0.151995\pi$
$907$	53.4955			1.77629			0.888144	+	0.459566i	$0.151995\pi$
$908$	22.3486			0.741664
$909$	−23.3221	+	31.3321i	−0.773545	+	1.03922i
$910$		0			0
$911$		−	54.2404i		−	1.79706i	−0.438909	−	0.898532i	$-0.644635\pi$
$911$		−	54.2404i		−	1.79706i	0.438909	−	0.898532i	$-0.355365\pi$
$912$	29.5390	−	14.8365i	0.978135	−	0.491285i
$913$		−	30.7142i		−	1.01649i
$914$		−	38.1067i		−	1.26046i
$915$		0			0
$916$			70.4173i			2.32665i
$917$	−5.89472	+	14.4391i	−0.194661	+	0.476820i
$918$	12.7913	−	72.5927i	0.422175	−	2.39592i
$919$	40.0780			1.32205			0.661026	−	0.750363i	$-0.270121\pi$
$919$	40.0780			1.32205			0.661026	+	0.750363i	$0.270121\pi$
$920$		0			0
$921$	31.7477	−	15.9459i	1.04612	−	0.525434i
$922$		−	19.4892i		−	0.641843i
$923$	−10.5591			−0.347558
$924$	5.82565	+	74.6675i	0.191650	+	2.45638i
$925$		0			0
$926$		−	35.4905i		−	1.16629i
$927$	−16.4539	−	12.2474i	−0.540416	−	0.402259i
$928$	0.956439			0.0313967
$929$	10.5591			0.346434			0.173217	−	0.984884i	$-0.444584\pi$
$929$	10.5591			0.346434			0.173217	+	0.984884i	$0.444584\pi$
$930$		0			0
$931$	33.4955	−	34.1862i	1.09777	−	1.12041i
$932$		−	1.90424i		−	0.0623755i
$933$	21.0000	+	41.8104i	0.687509	+	1.36881i
$934$		−	85.1142i		−	2.78502i
$935$		0			0
$936$	−18.9145	+	25.4107i	−0.618238	+	0.830574i
$937$		−	25.0061i		−	0.816915i	−0.912777	−	0.408457i	$-0.866067\pi$
$937$		−	25.0061i		−	0.816915i	0.912777	−	0.408457i	$-0.133933\pi$
$938$	83.4996	+	34.0886i	2.72636	+	1.11303i
$939$	−16.5826	+	8.32889i	−0.541152	+	0.271803i
$940$		0			0
$941$	25.7827			0.840492			0.420246	−	0.907410i	$-0.361944\pi$
$941$	25.7827			0.840492			0.420246	+	0.907410i	$0.361944\pi$
$942$	−17.3739	−	34.5908i	−0.566071	−	1.12703i
$943$			2.34279i			0.0762917i
$944$	−29.4736			−0.959284
$945$		0			0
$946$	26.7913			0.871060
$947$			24.8600i			0.807841i	0.914794	+	0.403920i	$0.132353\pi$
$947$			24.8600i			0.807841i	−0.914794	+	0.403920i	$0.867647\pi$
$948$	−25.2959	−	50.3635i	−0.821574	−	1.63573i
$949$	15.4955			0.503004
$950$		0			0
$951$	−21.5712	+	10.8345i	−0.699493	+	0.351333i
$952$	62.2432	+	25.4107i	2.01731	+	0.823565i
$953$			0.502268i			0.0162700i	0.999967	+	0.00813502i	$0.00258949\pi$
$953$			0.502268i			0.0162700i	−0.999967	+	0.00813502i	$0.997411\pi$
$954$	57.9129	−	77.8032i	1.87500	−	2.51897i
$955$		0			0
$956$			47.1257i			1.52415i
$957$	1.68320	+	3.35119i	0.0544100	+	0.108329i
$958$		−	25.4107i		−	0.820982i
$959$	−2.46060	−	1.00454i	−0.0794569	−	0.0324381i
$960$		0			0
$961$	11.7477			0.378959
$962$	−3.43412			−0.110720
$963$	2.41742	+	1.79941i	0.0779004	+	0.0579853i
$964$		−	29.7984i		−	0.959742i
$965$		0			0
$966$	5.52223	−	0.430851i	0.177675	−	0.0138624i
$967$	12.7477			0.409939			0.204970	−	0.978768i	$-0.434290\pi$
$967$	12.7477			0.409939			0.204970	+	0.978768i	$0.434290\pi$
$968$			32.6866i			1.05059i
$969$	−62.3813	+	31.3321i	−2.00398	+	1.00653i
$970$		0			0
$971$	−48.1313			−1.54461			−0.772303	−	0.635254i	$-0.780895\pi$
$971$	−48.1313			−1.54461			−0.772303	+	0.635254i	$0.780895\pi$
$972$	42.9801	−	40.5655i	1.37859	−	1.30114i
$973$	6.00000	+	2.44949i	0.192351	+	0.0785270i
$974$		−	96.6578i		−	3.09712i
$975$		0			0
$976$		−	12.2474i		−	0.392031i
$977$		−	13.9368i		−	0.445877i	−0.974832	−	0.222939i	$-0.928435\pi$
$977$		−	13.9368i		−	0.445877i	0.974832	−	0.222939i	$-0.0715650\pi$
$978$	−14.8991	+	7.48331i	−0.476419	+	0.239290i
$979$			45.5178i			1.45476i
$980$		0			0
$981$	−8.95644	+	12.0325i	−0.285957	+	0.384170i
$982$	6.04356			0.192858
$983$	−7.12502			−0.227253			−0.113626	−	0.993524i	$-0.536247\pi$
$983$	−7.12502			−0.227253			−0.113626	+	0.993524i	$0.536247\pi$
$984$	−31.1216	+	15.6314i	−0.992120	+	0.498310i
$985$		0			0
$986$	7.12502			0.226907
$987$	26.9312	−	2.10120i	0.857228	−	0.0668820i
$988$	63.4955			2.02006
$989$		−	1.29714i		−	0.0412468i
$990$		0			0
$991$	22.0780			0.701332			0.350666	−	0.936501i	$-0.385955\pi$
$991$	22.0780			0.701332			0.350666	+	0.936501i	$0.385955\pi$
$992$	8.35532			0.265282
$993$	−13.2159	−	26.3124i	−0.419393	−	0.834998i
$994$	−10.3739	+	25.4107i	−0.329039	+	0.805978i
$995$		0			0
$996$	−21.0000	−	41.8104i	−0.665410	−	1.32481i
$997$			36.2311i			1.14745i	0.819048	+	0.573725i	$0.194502\pi$
$997$			36.2311i			1.14745i	−0.819048	+	0.573725i	$0.805498\pi$
$998$			73.9947i			2.34226i
$999$	2.98122	+	0.525310i	0.0943218	+	0.0166201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.b.i.251.7	yes	8
3.2	odd	2	inner	525.2.b.i.251.2	yes	8
5.2	odd	4		525.2.g.f.524.2		16
5.3	odd	4		525.2.g.f.524.15		16
5.4	even	2		525.2.b.h.251.2	yes	8
7.6	odd	2	inner	525.2.b.i.251.8	yes	8
15.2	even	4		525.2.g.f.524.13		16
15.8	even	4		525.2.g.f.524.4		16
15.14	odd	2		525.2.b.h.251.7	yes	8
21.20	even	2	inner	525.2.b.i.251.1	yes	8
35.13	even	4		525.2.g.f.524.14		16
35.27	even	4		525.2.g.f.524.3		16
35.34	odd	2		525.2.b.h.251.1	✓	8
105.62	odd	4		525.2.g.f.524.16		16
105.83	odd	4		525.2.g.f.524.1		16
105.104	even	2		525.2.b.h.251.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.b.h.251.1	✓	8	35.34	odd	2
525.2.b.h.251.2	yes	8	5.4	even	2
525.2.b.h.251.7	yes	8	15.14	odd	2
525.2.b.h.251.8	yes	8	105.104	even	2
525.2.b.i.251.1	yes	8	21.20	even	2	inner
525.2.b.i.251.2	yes	8	3.2	odd	2	inner
525.2.b.i.251.7	yes	8	1.1	even	1	trivial
525.2.b.i.251.8	yes	8	7.6	odd	2	inner
525.2.g.f.524.1		16	105.83	odd	4
525.2.g.f.524.2		16	5.2	odd	4
525.2.g.f.524.3		16	35.27	even	4
525.2.g.f.524.4		16	15.8	even	4
525.2.g.f.524.13		16	15.2	even	4
525.2.g.f.524.14		16	35.13	even	4
525.2.g.f.524.15		16	5.3	odd	4
525.2.g.f.524.16		16	105.62	odd	4

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.40651i q^{2} +(-0.777403 - 1.54779i) q^{3} -3.79129 q^{4} +(3.72476 - 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} -4.31075i q^{8} +(-1.79129 + 2.40651i) q^{9} +O(q^{10})\)	\(q+2.40651i q^{2} +(-0.777403 - 1.54779i) q^{3} -3.79129 q^{4} +(3.72476 - 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} -4.31075i q^{8} +(-1.79129 + 2.40651i) q^{9} +4.31075i q^{11} +(2.94736 + 5.86811i) q^{12} +2.44949i q^{13} +(5.89472 + 2.40651i) q^{14} +2.79129 q^{16} -5.89472 q^{17} +(-5.79129 - 4.31075i) q^{18} +6.83723i q^{19} +(-4.56869 + 0.356455i) q^{21} -10.3739 q^{22} +0.502268i q^{23} +(-6.67212 + 3.35119i) q^{24} -5.89472 q^{26} +(5.11732 + 0.901703i) q^{27} +(-3.79129 + 9.28672i) q^{28} +0.502268i q^{29} +4.38774i q^{31} -1.90424i q^{32} +(6.67212 - 3.35119i) q^{33} -14.1857i q^{34} +(6.79129 - 9.12377i) q^{36} +0.582576 q^{37} -16.4539 q^{38} +(3.79129 - 1.90424i) q^{39} +4.66442 q^{41} +(-0.857812 - 10.9946i) q^{42} -2.58258 q^{43} -16.3433i q^{44} -1.20871 q^{46} -5.89472 q^{47} +(-2.16996 - 4.32032i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(4.58258 + 9.12377i) q^{51} -9.28672i q^{52} +13.4345i q^{53} +(-2.16996 + 12.3149i) q^{54} +(-10.5591 - 4.31075i) q^{56} +(10.5826 - 5.31529i) q^{57} -1.20871 q^{58} -10.5591 q^{59} -4.38774i q^{61} -10.5591 q^{62} +(4.10343 + 6.79425i) q^{63} +10.1652 q^{64} +(8.06468 + 16.0565i) q^{66} +14.1652 q^{67} +22.3486 q^{68} +(0.777403 - 0.390465i) q^{69} +4.31075i q^{71} +(10.3739 + 7.72180i) q^{72} -6.32599i q^{73} +1.40197i q^{74} -25.9219i q^{76} +(10.5591 + 4.31075i) q^{77} +(4.58258 + 9.12377i) q^{78} -8.58258 q^{79} +(-2.58258 - 8.62150i) q^{81} +11.2250i q^{82} -7.12502 q^{83} +(17.3212 - 1.35142i) q^{84} -6.21499i q^{86} +(0.777403 - 0.390465i) q^{87} +18.5826 q^{88} +10.5591 q^{89} +(6.00000 + 2.44949i) q^{91} -1.90424i q^{92} +(6.79129 - 3.41105i) q^{93} -14.1857i q^{94} +(-2.94736 + 1.48036i) q^{96} -0.511238i q^{97} +(11.7894 - 12.0325i) q^{98} +(-10.3739 - 7.72180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 12 * q^4 + 8 * q^7 + 4 * q^9	\( 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9} + 4 q^{16} - 28 q^{18} - 12 q^{21} - 28 q^{22} - 12 q^{28} + 36 q^{36} - 32 q^{37} + 12 q^{39} + 16 q^{43} - 28 q^{46} - 40 q^{49} + 48 q^{57} - 28 q^{58} + 4 q^{63} + 8 q^{64} + 40 q^{67} + 28 q^{72} - 32 q^{79} + 16 q^{81} + 60 q^{84} + 112 q^{88} + 48 q^{91} + 36 q^{93} - 28 q^{99}+O(q^{100}) \) 8 * q - 12 * q^4 + 8 * q^7 + 4 * q^9 + 4 * q^16 - 28 * q^18 - 12 * q^21 - 28 * q^22 - 12 * q^28 + 36 * q^36 - 32 * q^37 + 12 * q^39 + 16 * q^43 - 28 * q^46 - 40 * q^49 + 48 * q^57 - 28 * q^58 + 4 * q^63 + 8 * q^64 + 40 * q^67 + 28 * q^72 - 32 * q^79 + 16 * q^81 + 60 * q^84 + 112 * q^88 + 48 * q^91 + 36 * q^93 - 28 * q^99

Introduction

L-functions

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