LMFDB - Embedded newform 525.2.g.f.524.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(524,525)]

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, 1, 1]))

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

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

chi := DirichletCharacter("525.524");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.g (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 32x^{14} + 386x^{12} + 2208x^{10} + 6263x^{8} + 8496x^{6} + 4790x^{4} + 704x^{2} + 25 $ x^16 + 32x^14 + 386x^12 + 2208x^10 + 6263x^8 + 8496x^6 + 4790x^4 + 704*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			524.3
Root			$-1.32519i$ of defining polynomial
Character	$\chi$	$=$	525.524
Dual form			525.2.g.f.524.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40651 q^{2} +(1.54779 - 0.777403i) q^{3} +3.79129 q^{4} +(-3.72476 + 1.87083i) q^{6} +(-2.44949 + 1.00000i) q^{7} -4.31075 q^{8} +(1.79129 - 2.40651i) q^{9} +O(q^{10})$	\(q-2.40651 q^{2} +(1.54779 - 0.777403i) q^{3} +3.79129 q^{4} +(-3.72476 + 1.87083i) q^{6} +(-2.44949 + 1.00000i) q^{7} -4.31075 q^{8} +(1.79129 - 2.40651i) q^{9} +4.31075i q^{11} +(5.86811 - 2.94736i) q^{12} -2.44949 q^{13} +(5.89472 - 2.40651i) q^{14} +2.79129 q^{16} +5.89472i q^{17} +(-4.31075 + 5.79129i) q^{18} +6.83723i q^{19} +(-3.01388 + 3.45203i) q^{21} -10.3739i q^{22} +0.502268 q^{23} +(-6.67212 + 3.35119i) q^{24} +5.89472 q^{26} +(0.901703 - 5.11732i) q^{27} +(-9.28672 + 3.79129i) q^{28} -0.502268i q^{29} -4.38774i q^{31} +1.90424 q^{32} +(3.35119 + 6.67212i) q^{33} -14.1857i q^{34} +(6.79129 - 9.12377i) q^{36} +0.582576i q^{37} -16.4539i q^{38} +(-3.79129 + 1.90424i) q^{39} -4.66442 q^{41} +(7.25294 - 8.30734i) q^{42} +2.58258i q^{43} +16.3433i q^{44} -1.20871 q^{46} +5.89472i q^{47} +(4.32032 - 2.16996i) q^{48} +(5.00000 - 4.89898i) q^{49} +(4.58258 + 9.12377i) q^{51} -9.28672 q^{52} +13.4345 q^{53} +(-2.16996 + 12.3149i) q^{54} +(10.5591 - 4.31075i) q^{56} +(5.31529 + 10.5826i) q^{57} +1.20871i q^{58} -10.5591 q^{59} +4.38774i q^{61} +10.5591i q^{62} +(-1.98123 + 7.68601i) q^{63} -10.1652 q^{64} +(-8.06468 - 16.0565i) q^{66} +14.1652i q^{67} +22.3486i q^{68} +(0.777403 - 0.390465i) q^{69} +4.31075i q^{71} +(-7.72180 + 10.3739i) q^{72} +6.32599 q^{73} -1.40197i q^{74} +25.9219i q^{76} +(-4.31075 - 10.5591i) q^{77} +(9.12377 - 4.58258i) q^{78} +8.58258 q^{79} +(-2.58258 - 8.62150i) q^{81} +11.2250 q^{82} -7.12502i q^{83} +(-11.4265 + 13.0876i) q^{84} -6.21499i q^{86} +(-0.390465 - 0.777403i) q^{87} -18.5826i q^{88} +10.5591 q^{89} +(6.00000 - 2.44949i) q^{91} +1.90424 q^{92} +(-3.41105 - 6.79129i) q^{93} -14.1857i q^{94} +(2.94736 - 1.48036i) q^{96} -0.511238 q^{97} +(-12.0325 + 11.7894i) q^{98} +(10.3739 + 7.72180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 24 * q^4 - 8 * q^9	$ 16 q + 24 q^{4} - 8 q^{9} + 8 q^{16} - 24 q^{21} + 72 q^{36} - 24 q^{39} - 56 q^{46} + 80 q^{49} - 16 q^{64} + 64 q^{79} + 32 q^{81} - 120 q^{84} + 96 q^{91} + 56 q^{99}+O(q^{100}) $ 16 * q + 24 * q^4 - 8 * q^9 + 8 * q^16 - 24 * q^21 + 72 * q^36 - 24 * q^39 - 56 * q^46 + 80 * q^49 - 16 * q^64 + 64 * q^79 + 32 * q^81 - 120 * q^84 + 96 * q^91 + 56 * 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 $

$2$	−2.40651			−1.70166			−0.850830	−	0.525442i	$-0.823900\pi$
$2$	−2.40651			−1.70166			−0.850830	+	0.525442i	$0.823900\pi$
$3$	1.54779	−	0.777403i	0.893615	−	0.448834i
$3$	1.54779	−	0.777403i	0.893615	−	0.448834i
$4$	3.79129			1.89564
$5$		0			0
$5$		0			0
$6$	−3.72476	+	1.87083i	−1.52063	+	0.763763i
$7$	−2.44949	+	1.00000i	−0.925820	+	0.377964i
$7$	−2.44949	+	1.00000i	−0.925820	+	0.377964i
$8$	−4.31075			−1.52408
$9$	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	$0.774823\pi$
$12$	5.86811	−	2.94736i	1.69398	−	0.850830i
$13$	−2.44949			−0.679366			−0.339683	−	0.940540i	$-0.610320\pi$
$13$	−2.44949			−0.679366			−0.339683	+	0.940540i	$0.610320\pi$
$14$	5.89472	−	2.40651i	1.57543	−	0.643167i
$15$		0			0
$16$	2.79129			0.697822
$17$			5.89472i			1.42968i	0.699288	+	0.714840i	$0.253500\pi$
$17$			5.89472i			1.42968i	−0.699288	+	0.714840i	$0.746500\pi$
$18$	−4.31075	+	5.79129i	−1.01605	+	1.36502i
$19$			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
$21$	−3.01388	+	3.45203i	−0.657684	+	0.753294i
$22$		−	10.3739i		−	2.21172i
$23$	0.502268			0.104730			0.0523650	−	0.998628i	$-0.483324\pi$
$23$	0.502268			0.104730			0.0523650	+	0.998628i	$0.483324\pi$
$24$	−6.67212	+	3.35119i	−1.36194	+	0.684059i
$25$		0			0
$26$	5.89472			1.15605
$27$	0.901703	−	5.11732i	0.173533	−	0.984828i
$28$	−9.28672	+	3.79129i	−1.75503	+	0.716486i
$29$		−	0.502268i		−	0.0932688i	−0.998912	−	0.0466344i	$-0.985150\pi$
$29$		−	0.502268i		−	0.0932688i	0.998912	−	0.0466344i	$-0.0148496\pi$
$30$		0			0
$31$		−	4.38774i		−	0.788062i	−0.919097	−	0.394031i	$-0.871080\pi$
$31$		−	4.38774i		−	0.788062i	0.919097	−	0.394031i	$-0.128920\pi$
$32$	1.90424			0.336626
$33$	3.35119	+	6.67212i	0.583368	+	1.16147i
$34$		−	14.1857i		−	2.43283i
$35$		0			0
$36$	6.79129	−	9.12377i	1.13188	−	1.52063i
$37$			0.582576i			0.0957749i	0.998853	+	0.0478874i	$0.0152489\pi$
$37$			0.582576i			0.0957749i	−0.998853	+	0.0478874i	$0.984751\pi$
$38$		−	16.4539i		−	2.66917i
$39$	−3.79129	+	1.90424i	−0.607092	+	0.304923i
$40$		0			0
$41$	−4.66442			−0.728460			−0.364230	−	0.931309i	$-0.618668\pi$
$41$	−4.66442			−0.728460			−0.364230	+	0.931309i	$0.618668\pi$
$42$	7.25294	−	8.30734i	1.11915	−	1.28185i
$43$			2.58258i			0.393839i	0.980420	+	0.196920i	$0.0630938\pi$
$43$			2.58258i			0.393839i	−0.980420	+	0.196920i	$0.936906\pi$
$44$			16.3433i			2.46384i
$45$		0			0
$46$	−1.20871			−0.178215
$47$			5.89472i			0.859833i	0.902869	+	0.429917i	$0.141457\pi$
$47$			5.89472i			0.859833i	−0.902869	+	0.429917i	$0.858543\pi$
$48$	4.32032	−	2.16996i	0.623584	−	0.313206i
$49$	5.00000	−	4.89898i	0.714286	−	0.699854i
$50$		0			0
$51$	4.58258	+	9.12377i	0.641689	+	1.27758i
$52$	−9.28672			−1.28784
$53$	13.4345			1.84537			0.922687	−	0.385551i	$-0.125988\pi$
$53$	13.4345			1.84537			0.922687	+	0.385551i	$0.125988\pi$
$54$	−2.16996	+	12.3149i	−0.295294	+	1.67584i
$55$		0			0
$56$	10.5591	−	4.31075i	1.41102	−	0.576048i
$57$	5.31529	+	10.5826i	0.704027	+	1.40170i
$58$			1.20871i			0.158712i
$59$	−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	$0.0906317\pi$
$61$			4.38774i			0.561793i	−0.959738	+	0.280896i	$0.909368\pi$
$62$			10.5591i			1.34101i
$63$	−1.98123	+	7.68601i	−0.249612	+	0.968346i
$64$	−10.1652			−1.27064
$65$		0			0
$66$	−8.06468	−	16.0565i	−0.992693	−	1.97642i
$67$			14.1652i			1.73055i	0.501299	+	0.865274i	$0.332856\pi$
$67$			14.1652i			1.73055i	−0.501299	+	0.865274i	$0.667144\pi$
$68$			22.3486i			2.71016i
$69$	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	$0.917662\pi$
$72$	−7.72180	+	10.3739i	−0.910022	+	1.22257i
$73$	6.32599			0.740401			0.370201	−	0.928952i	$-0.379289\pi$
$73$	6.32599			0.740401			0.370201	+	0.928952i	$0.379289\pi$
$74$		−	1.40197i		−	0.162976i
$75$		0			0
$76$			25.9219i			2.97345i
$77$	−4.31075	−	10.5591i	−0.491256	−	1.20333i
$78$	9.12377	−	4.58258i	1.03306	−	0.518875i
$79$	8.58258			0.965615			0.482808	−	0.875726i	$-0.339617\pi$
$79$	8.58258			0.965615			0.482808	+	0.875726i	$0.339617\pi$
$80$		0			0
$81$	−2.58258	−	8.62150i	−0.286953	−	0.957945i
$82$	11.2250			1.23959
$83$		−	7.12502i		−	0.782073i	−0.920375	−	0.391036i	$-0.872117\pi$
$83$		−	7.12502i		−	0.782073i	0.920375	−	0.391036i	$-0.127883\pi$
$84$	−11.4265	+	13.0876i	−1.24673	+	1.42798i
$85$		0			0
$86$		−	6.21499i		−	0.670180i
$87$	−0.390465	−	0.777403i	−0.0418622	−	0.0833464i
$88$		−	18.5826i		−	1.98091i
$89$	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
$92$	1.90424			0.198531
$93$	−3.41105	−	6.79129i	−0.353709	−	0.704224i
$94$		−	14.1857i		−	1.46314i
$95$		0			0
$96$	2.94736	−	1.48036i	0.300814	−	0.151089i
$97$	−0.511238			−0.0519084			−0.0259542	−	0.999663i	$-0.508262\pi$
$97$	−0.511238			−0.0519084			−0.0259542	+	0.999663i	$0.508262\pi$
$98$	−12.0325	+	11.7894i	−1.21547	+	1.19091i
$99$	10.3739	+	7.72180i	1.04261	+	0.776070i
$100$		0			0
$101$	−13.0197			−1.29551			−0.647756	−	0.761848i	$-0.724292\pi$
$101$	−13.0197			−1.29551			−0.647756	+	0.761848i	$0.724292\pi$
$102$	−11.0280	−	21.9564i	−1.09194	−	2.17401i
$103$	−6.83723			−0.673692			−0.336846	−	0.941560i	$-0.609360\pi$
$103$	−6.83723			−0.673692			−0.336846	+	0.941560i	$0.609360\pi$
$104$	10.5591			1.03541
$105$		0			0
$106$	−32.3303			−3.14020
$107$	1.00454			0.0971121			0.0485561	−	0.998820i	$-0.484538\pi$
$107$	1.00454			0.0971121			0.0485561	+	0.998820i	$0.484538\pi$
$108$	3.41862	−	19.4012i	0.328956	−	1.86688i
$109$	−5.00000			−0.478913			−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000			−0.478913			−0.239457	+	0.970907i	$0.576969\pi$
$110$		0			0
$111$	0.452896	+	0.901703i	0.0429870	+	0.0855859i
$112$	−6.83723	+	2.79129i	−0.646058	+	0.263752i
$113$	−6.31982			−0.594519			−0.297259	−	0.954797i	$-0.596073\pi$
$113$	−6.31982			−0.594519			−0.297259	+	0.954797i	$0.596073\pi$
$114$	−12.7913	−	25.4671i	−1.19801	−	2.38521i
$115$		0			0
$116$		−	1.90424i		−	0.176804i
$117$	−4.38774	+	5.89472i	−0.405647	+	0.544967i
$118$	25.4107			2.33924
$119$	−5.89472	−	14.4391i	−0.540368	−	1.32363i
$120$		0			0
$121$	−7.58258			−0.689325
$122$		−	10.5591i		−	0.955980i
$123$	−7.21953	+	3.62614i	−0.650963	+	0.326958i
$124$		−	16.6352i		−	1.49388i
$125$		0			0
$126$	4.76785	−	18.4965i	0.424754	−	1.64779i
$127$		−	10.1652i		−	0.902011i	−0.892521	−	0.451006i	$-0.851065\pi$
$127$		−	10.1652i		−	0.902011i	0.892521	−	0.451006i	$-0.148935\pi$
$128$	20.6540			1.82558
$129$	2.00770	+	3.99728i	0.176768	+	0.351941i
$130$		0			0
$131$	5.89472			0.515024			0.257512	−	0.966275i	$-0.417097\pi$
$131$	5.89472			0.515024			0.257512	+	0.966275i	$0.417097\pi$
$132$	12.7053	+	25.2959i	1.10586	+	2.20173i
$133$	−6.83723	−	16.7477i	−0.592863	−	1.45221i
$134$		−	34.0886i		−	2.94480i
$135$		0			0
$136$		−	25.4107i		−	2.17895i
$137$	1.00454			0.0858233			0.0429116	−	0.999079i	$-0.486337\pi$
$137$	1.00454			0.0858233			0.0429116	+	0.999079i	$0.486337\pi$
$138$	−1.87083	+	0.939657i	−0.159256	+	0.0799889i
$139$			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
$142$		−	10.3739i		−	0.870555i
$143$		−	10.5591i		−	0.883000i
$144$	5.00000	−	6.71726i	0.416667	−	0.559772i
$145$		0			0
$146$	−15.2236			−1.25991
$147$	3.93045	−	11.4696i	0.324178	−	0.945996i
$148$			2.20871i			0.181555i
$149$			6.31982i			0.517740i	0.965912	+	0.258870i	$0.0833501\pi$
$149$			6.31982i			0.517740i	−0.965912	+	0.258870i	$0.916650\pi$
$150$		0			0
$151$	14.1652			1.15274			0.576372	−	0.817188i	$-0.304468\pi$
$151$	14.1652			1.15274			0.576372	+	0.817188i	$0.304468\pi$
$152$		−	29.4736i		−	2.39062i
$153$	14.1857	+	10.5591i	1.14685	+	0.853656i
$154$	10.3739	+	25.4107i	0.835950	+	2.04765i
$155$		0			0
$156$	−14.3739	+	7.21953i	−1.15083	+	0.578025i
$157$	−9.28672			−0.741161			−0.370580	−	0.928800i	$-0.620841\pi$
$157$	−9.28672			−0.741161			−0.370580	+	0.928800i	$0.620841\pi$
$158$	−20.6540			−1.64315
$159$	20.7938	−	10.4440i	1.64905	−	0.828266i
$160$		0			0
$161$	−1.23030	+	0.502268i	−0.0969612	+	0.0395842i
$162$	6.21499	+	20.7477i	0.488296	+	1.63010i
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	−17.6842			−1.38090
$165$		0			0
$166$			17.1464i			1.33082i
$167$		−	13.0197i		−	1.00750i	−0.863850	−	0.503749i	$-0.831954\pi$
$167$		−	13.0197i		−	1.00750i	0.863850	−	0.503749i	$-0.168046\pi$
$168$	12.9921	−	14.8808i	1.00236	−	1.14808i
$169$	−7.00000			−0.538462
$170$		0			0
$171$	16.4539	+	12.2474i	1.25826	+	0.936586i
$172$			9.79129i			0.746579i
$173$		−	17.6842i		−	1.34450i	−0.740323	−	0.672251i	$-0.765328\pi$
$173$		−	17.6842i		−	1.34450i	0.740323	−	0.672251i	$-0.234672\pi$
$174$	0.939657	+	1.87083i	0.0712352	+	0.141827i
$175$		0			0
$176$			12.0325i			0.906987i
$177$	−16.3433	+	8.20871i	−1.22844	+	0.617005i
$178$	−25.4107			−1.90461
$179$			12.4300i			0.929061i	0.885557	+	0.464530i	$0.153777\pi$
$179$			12.4300i			0.929061i	−0.885557	+	0.464530i	$0.846223\pi$
$180$		0			0
$181$		−	12.2474i		−	0.910346i	−0.890403	−	0.455173i	$-0.849577\pi$
$181$		−	12.2474i		−	0.910346i	0.890403	−	0.455173i	$-0.150423\pi$
$182$	−14.4391	+	5.89472i	−1.07029	+	0.436946i
$183$	3.41105	+	6.79129i	0.252152	+	0.502026i
$184$	−2.16515			−0.159617
$185$		0			0
$186$	8.20871	+	16.3433i	0.601892	+	1.19835i
$187$	−25.4107			−1.85821
$188$			22.3486i			1.62994i
$189$	2.90860	+	13.4365i	0.211570	+	0.977363i
$190$		0			0
$191$		−	15.4436i		−	1.11746i	−0.829350	−	0.558730i	$-0.811289\pi$
$191$		−	15.4436i		−	1.11746i	0.829350	−	0.558730i	$-0.188711\pi$
$192$	−15.7335	+	7.90242i	−1.13547	+	0.570308i
$193$		−	11.0000i		−	0.791797i	−0.918294	−	0.395899i	$-0.870433\pi$
$193$		−	11.0000i		−	0.791797i	0.918294	−	0.395899i	$-0.129567\pi$
$194$	1.23030			0.0883304
$195$		0			0
$196$	18.9564	−	18.5734i	1.35403	−	1.32667i
$197$	−18.7498			−1.33587			−0.667934	−	0.744220i	$-0.732821\pi$
$197$	−18.7498			−1.33587			−0.667934	+	0.744220i	$0.732821\pi$
$198$	−24.9648	−	18.5826i	−1.77417	−	1.32061i
$199$			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
$202$	31.3321			2.20452
$203$	0.502268	+	1.23030i	0.0352523	+	0.0863501i
$204$	17.3739	+	34.5908i	1.21641	+	2.42184i
$205$		0			0
$206$	16.4539			1.14639
$207$	0.899706	−	1.20871i	0.0625339	−	0.0840113i
$208$	−6.83723			−0.474077
$209$	−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	$0.355405\pi$
$212$	50.9341			3.49817
$213$	3.35119	+	6.67212i	0.229620	+	0.457166i
$214$	−2.41742			−0.165252
$215$		0			0
$216$	−3.88702	+	22.0595i	−0.264478	+	1.50096i
$217$	4.38774	+	10.7477i	0.297859	+	0.729603i
$218$	12.0325			0.814947
$219$	9.79129	−	4.91785i	0.661634	−	0.332317i
$220$		0			0
$221$		−	14.4391i		−	0.971276i
$222$	−1.08990	−	2.16996i	−0.0731493	−	0.145638i
$223$	−2.44949			−0.164030			−0.0820150	−	0.996631i	$-0.526136\pi$
$223$	−2.44949			−0.164030			−0.0820150	+	0.996631i	$0.526136\pi$
$224$	−4.66442	+	1.90424i	−0.311655	+	0.127233i
$225$		0			0
$226$	15.2087			1.01167
$227$			5.89472i			0.391246i	0.980679	+	0.195623i	$0.0626729\pi$
$227$			5.89472i			0.391246i	−0.980679	+	0.195623i	$0.937327\pi$
$228$	20.1518	+	40.1216i	1.33458	+	2.65712i
$229$		−	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
$231$	−14.8808	−	12.9921i	−0.979087	−	0.854818i
$232$			2.16515i			0.142149i
$233$	0.502268			0.0329047			0.0164523	−	0.999865i	$-0.494763\pi$
$233$	0.502268			0.0329047			0.0164523	+	0.999865i	$0.494763\pi$
$234$	10.5591	−	14.1857i	0.690273	−	0.927348i
$235$		0			0
$236$	−40.0327			−2.60591
$237$	13.2840	−	6.67212i	0.862888	−	0.433401i
$238$	14.1857	+	34.7477i	0.919522	+	2.25236i
$239$			12.4300i			0.804029i	0.915633	+	0.402014i	$0.131690\pi$
$239$			12.4300i			0.804029i	−0.915633	+	0.402014i	$0.868310\pi$
$240$		0			0
$241$		−	7.85971i		−	0.506288i	−0.967429	−	0.253144i	$-0.918535\pi$
$241$		−	7.85971i		−	0.506288i	0.967429	−	0.253144i	$-0.0814647\pi$
$242$	18.2475			1.17300
$243$	−10.6997	−	11.3365i	−0.686384	−	0.727240i
$244$			16.6352i			1.06496i
$245$		0			0
$246$	17.3739	−	8.72633i	1.10772	−	0.556371i
$247$		−	16.7477i		−	1.06563i
$248$			18.9145i			1.20107i
$249$	−5.53901	−	11.0280i	−0.351021	−	0.698872i
$250$		0			0
$251$	−15.2236			−0.960903			−0.480451	−	0.877021i	$-0.659527\pi$
$251$	−15.2236			−0.960903			−0.480451	+	0.877021i	$0.659527\pi$
$252$	−7.51142	+	29.1399i	−0.473175	+	1.83564i
$253$			2.16515i			0.136122i
$254$			24.4625i			1.53492i
$255$		0			0
$256$	−29.3739			−1.83587
$257$			16.4539i			1.02636i	0.858280	+	0.513182i	$0.171533\pi$
$257$			16.4539i			1.02636i	−0.858280	+	0.513182i	$0.828467\pi$
$258$	−4.83156	−	9.61948i	−0.300800	−	0.598883i
$259$	−0.582576	−	1.42701i	−0.0361995	−	0.0886703i
$260$		0			0
$261$	−1.20871	−	0.899706i	−0.0748174	−	0.0556904i
$262$	−14.1857			−0.876395
$263$	7.32436			0.451639			0.225820	−	0.974169i	$-0.427494\pi$
$263$	7.32436			0.451639			0.225820	+	0.974169i	$0.427494\pi$
$264$	−14.4462	−	28.7619i	−0.889100	−	1.77017i
$265$		0			0
$266$	16.4539	+	40.3036i	1.00885	+	2.47117i
$267$	16.3433	−	8.20871i	1.00019	−	0.502365i
$268$			53.7042i			3.28050i
$269$	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	$-0.966371\pi$
$271$		−	3.47197i		−	0.210907i	0.994424	−	0.105453i	$-0.0336294\pi$
$272$			16.4539i			0.997662i
$273$	7.38248	−	8.45571i	0.446808	−	0.511763i
$274$	−2.41742			−0.146042
$275$		0			0
$276$	2.94736	−	1.48036i	0.177410	−	0.0891074i
$277$		−	8.74773i		−	0.525600i	−0.964850	−	0.262800i	$-0.915354\pi$
$277$		−	8.74773i		−	0.525600i	0.964850	−	0.262800i	$-0.0846459\pi$
$278$		−	5.89472i		−	0.353542i
$279$	−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	$-0.222267\pi$
$282$	−11.0280	−	21.9564i	−0.656709	−	1.30749i
$283$	1.02248			0.0607799			0.0303900	−	0.999538i	$-0.490325\pi$
$283$	1.02248			0.0607799			0.0303900	+	0.999538i	$0.490325\pi$
$284$			16.3433i			0.969796i
$285$		0			0
$286$			25.4107i			1.50256i
$287$	11.4255	−	4.66442i	0.674423	−	0.275332i
$288$	3.41105	−	4.58258i	0.200998	−	0.270031i
$289$	−17.7477			−1.04398
$290$		0			0
$291$	−0.791288	+	0.397438i	−0.0463861	+	0.0232983i
$292$	23.9837			1.40354
$293$			22.3486i			1.30562i	0.757523	+	0.652809i	$0.226410\pi$
$293$			22.3486i			1.30562i	−0.757523	+	0.652809i	$0.773590\pi$
$294$	−9.45867	+	27.6017i	−0.551641	+	1.60976i
$295$		0			0
$296$		−	2.51134i		−	0.145969i
$297$	22.0595	+	3.88702i	1.28002	+	0.225548i
$298$		−	15.2087i		−	0.881017i
$299$	−1.23030			−0.0711501
$300$		0			0
$301$	−2.58258	−	6.32599i	−0.148857	−	0.364624i
$302$	−34.0886			−1.96158
$303$	−20.1518	+	10.1216i	−1.15769	+	0.581470i
$304$			19.0847i			1.09458i
$305$		0			0
$306$	−34.1380	−	25.4107i	−1.95154	−	1.45263i
$307$	20.5117			1.17066			0.585332	−	0.810794i	$-0.300964\pi$
$307$	20.5117			1.17066			0.585332	+	0.810794i	$0.300964\pi$
$308$	−16.3433	−	40.0327i	−0.931246	−	2.28108i
$309$	−10.5826	+	5.31529i	−0.602022	+	0.302376i
$310$		0			0
$311$	27.0130			1.53177			0.765883	−	0.642979i	$-0.222302\pi$
$311$	27.0130			1.53177			0.765883	+	0.642979i	$0.222302\pi$
$312$	16.3433	−	8.20871i	0.925257	−	0.464727i
$313$	10.7137			0.605576			0.302788	−	0.953058i	$-0.402083\pi$
$313$	10.7137			0.605576			0.302788	+	0.953058i	$0.402083\pi$
$314$	22.3486			1.26120
$315$		0			0
$316$	32.5390			1.83046
$317$	13.9368			0.782768			0.391384	−	0.920227i	$-0.371996\pi$
$317$	13.9368			0.782768			0.391384	+	0.920227i	$0.371996\pi$
$318$	−50.0404	+	25.1337i	−2.80613	+	1.40943i
$319$	2.16515			0.121225
$320$		0			0
$321$	1.55481	−	0.780929i	0.0867809	−	0.0435872i
$322$	2.96073	−	1.20871i	0.164995	−	0.0673589i
$323$	−40.3036			−2.24255
$324$	−9.79129	−	32.6866i	−0.543960	−	1.81592i
$325$		0			0
$326$		−	9.62604i		−	0.533137i
$327$	−7.73893	+	3.88702i	−0.427964	+	0.214953i
$328$	20.1072			1.11023
$329$	−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	$0.345262\pi$
$332$		−	27.0130i		−	1.48253i
$333$	1.40197	+	1.04356i	0.0768277	+	0.0571868i
$334$			31.3321i			1.71442i
$335$		0			0
$336$	−8.41262	+	9.63561i	−0.458946	+	0.525665i
$337$			2.00000i			0.108947i	0.998515	+	0.0544735i	$0.0173480\pi$
$337$			2.00000i			0.108947i	−0.998515	+	0.0544735i	$0.982652\pi$
$338$	16.8456			0.916278
$339$	−9.78174	+	4.91305i	−0.531271	+	0.266840i
$340$		0			0
$341$	18.9145			1.02428
$342$	−39.5964	−	29.4736i	−2.14113	−	1.59375i
$343$	−7.34847	+	17.0000i	−0.396780	+	0.917914i
$344$		−	11.1328i		−	0.600243i
$345$		0			0
$346$			42.5571i			2.28788i
$347$	−18.7498			−1.00654			−0.503271	−	0.864129i	$-0.667870\pi$
$347$	−18.7498			−1.00654			−0.503271	+	0.864129i	$0.667870\pi$
$348$	−1.48036	−	2.94736i	−0.0793558	−	0.157995i
$349$		−	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
$352$			8.20871i			0.437526i
$353$			13.9933i			0.744786i	0.928075	+	0.372393i	$0.121463\pi$
$353$			13.9933i			0.744786i	−0.928075	+	0.372393i	$0.878537\pi$
$354$	39.3303	−	19.7543i	2.09038	−	1.04993i
$355$		0			0
$356$	40.0327			2.12173
$357$	−20.3487	−	17.7660i	−1.07697	−	0.940277i
$358$		−	29.9129i		−	1.58094i
$359$			6.31982i			0.333547i	0.985995	+	0.166774i	$0.0533349\pi$
$359$			6.31982i			0.333547i	−0.985995	+	0.166774i	$0.946665\pi$
$360$		0			0
$361$	−27.7477			−1.46041
$362$			29.4736i			1.54910i
$363$	−11.7362	+	5.89472i	−0.615991	+	0.309393i
$364$	22.7477	−	9.28672i	1.19230	−	0.486756i
$365$		0			0
$366$	−8.20871	−	16.3433i	−0.429076	−	0.854278i
$367$	32.7591			1.71001			0.855007	−	0.518617i	$-0.173553\pi$
$367$	32.7591			1.71001			0.855007	+	0.518617i	$0.173553\pi$
$368$	1.40197			0.0730829
$369$	−8.35532	+	11.2250i	−0.434961	+	0.584349i
$370$		0			0
$371$	−32.9077	+	13.4345i	−1.70848	+	0.697486i
$372$	−12.9323	−	25.7477i	−0.670506	−	1.33496i
$373$		−	18.9129i		−	0.979272i	−0.871927	−	0.489636i	$-0.837130\pi$
$373$		−	18.9129i		−	0.979272i	0.871927	−	0.489636i	$-0.162870\pi$
$374$	61.1510			3.16204
$375$		0			0
$376$		−	25.4107i		−	1.31046i
$377$			1.23030i			0.0633637i
$378$	−6.99958	−	32.3351i	−0.360020	−	1.66314i
$379$	19.3303			0.992931			0.496465	−	0.868056i	$-0.334631\pi$
$379$	19.3303			0.992931			0.496465	+	0.868056i	$0.334631\pi$
$380$		0			0
$381$	−7.90242	−	15.7335i	−0.404853	−	0.806051i
$382$			37.1652i			1.90153i
$383$		−	19.8880i		−	1.01623i	−0.861290	−	0.508114i	$-0.830343\pi$
$383$		−	19.8880i		−	1.01623i	0.861290	−	0.508114i	$-0.169657\pi$
$384$	31.9681	−	16.0565i	1.63136	−	0.819381i
$385$		0			0
$386$			26.4716i			1.34737i
$387$	6.21499	+	4.62614i	0.315926	+	0.235160i
$388$	−1.93825			−0.0983998
$389$		−	26.3668i		−	1.33685i	−0.743780	−	0.668424i	$-0.766969\pi$
$389$		−	26.3668i		−	1.33685i	0.743780	−	0.668424i	$-0.233031\pi$
$390$		0			0
$391$			2.96073i			0.149730i
$392$	−21.5538	+	21.1183i	−1.08863	+	1.06663i
$393$	9.12377	−	4.58258i	0.460233	−	0.231160i
$394$	45.1216			2.27319
$395$		0			0
$396$	39.3303	+	29.2756i	1.97642	+	1.47115i
$397$	−13.6745			−0.686302			−0.343151	−	0.939280i	$-0.611494\pi$
$397$	−13.6745			−0.686302			−0.343151	+	0.939280i	$0.611494\pi$
$398$		−	45.9275i		−	2.30214i
$399$	−23.6023	−	20.6066i	−1.18159	−	1.03162i
$400$		0			0
$401$			11.1328i			0.555948i	0.960589	+	0.277974i	$0.0896628\pi$
$401$			11.1328i			0.555948i	−0.960589	+	0.277974i	$0.910337\pi$
$402$	−26.5006	−	52.7618i	−1.32173	−	2.63152i
$403$			10.7477i			0.535382i
$404$	−49.3616			−2.45583
$405$		0			0
$406$	−1.20871	−	2.96073i	−0.0599874	−	0.146938i
$407$	−2.51134			−0.124482
$408$	−19.7543	−	39.3303i	−0.977986	−	1.94714i
$409$			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
$412$	−25.9219			−1.27708
$413$	25.8645	−	10.5591i	1.27271	−	0.519581i
$414$	−2.16515	+	2.90878i	−0.106411	+	0.142959i
$415$		0			0
$416$	−4.66442			−0.228692
$417$	1.90424	+	3.79129i	0.0932511	+	0.185660i
$418$	70.9285			3.46923
$419$	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	$0.579678\pi$
$422$	−30.6775			−1.49336
$423$	14.1857	+	10.5591i	0.689732	+	0.513403i
$424$	−57.9129			−2.81250
$425$		0			0
$426$	−8.06468	−	16.0565i	−0.390735	−	0.777941i
$427$	−4.38774	−	10.7477i	−0.212338	−	0.520119i
$428$	3.80848			0.184090
$429$	−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	$0.732978\pi$
$432$	2.51691	−	14.2839i	0.121095	−	0.687235i
$433$	−23.4724			−1.12801			−0.564006	−	0.825770i	$-0.690741\pi$
$433$	−23.4724			−1.12801			−0.564006	+	0.825770i	$0.690741\pi$
$434$	−10.5591	−	25.8645i	−0.506855	−	1.24154i
$435$		0			0
$436$	−18.9564			−0.907849
$437$			3.43412i			0.164276i
$438$	−23.5628	+	11.8348i	−1.12588	+	0.565491i
$439$			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
$441$	−2.83300	−	20.8080i	−0.134905	−	0.990859i
$442$			34.7477i			1.65278i
$443$	13.4345			0.638293			0.319147	−	0.947705i	$-0.396604\pi$
$443$	13.4345			0.638293			0.319147	+	0.947705i	$0.396604\pi$
$444$	1.71706	+	3.41862i	0.0814881	+	0.162240i
$445$		0			0
$446$	5.89472			0.279123
$447$	4.91305	+	9.78174i	0.232379	+	0.462660i
$448$	24.8994	−	10.1652i	1.17639	−	0.480258i
$449$		−	19.5447i		−	0.922371i	−0.887304	−	0.461185i	$-0.847424\pi$
$449$		−	19.5447i		−	0.922371i	0.887304	−	0.461185i	$-0.152576\pi$
$450$		0			0
$451$		−	20.1072i		−	0.946809i
$452$	−23.9603			−1.12700
$453$	21.9246	−	11.0120i	1.03011	−	0.517391i
$454$		−	14.1857i		−	0.665768i
$455$		0			0
$456$	−22.9129	−	45.6189i	−1.07299	−	2.13630i
$457$		−	15.8348i		−	0.740723i	−0.928888	−	0.370361i	$-0.879234\pi$
$457$		−	15.8348i		−	0.740723i	0.928888	−	0.370361i	$-0.120766\pi$
$458$			44.6972i			2.08856i
$459$	30.1652	+	5.31529i	1.40799	+	0.248096i
$460$		0			0
$461$	8.09854			0.377187			0.188593	−	0.982055i	$-0.439607\pi$
$461$	8.09854			0.377187			0.188593	+	0.982055i	$0.439607\pi$
$462$	35.8109	+	31.2656i	1.66607	+	1.45461i
$463$			14.7477i			0.685385i	0.939448	+	0.342693i	$0.111339\pi$
$463$			14.7477i			0.685385i	−0.939448	+	0.342693i	$0.888661\pi$
$464$		−	1.40197i		−	0.0650850i
$465$		0			0
$466$	−1.20871			−0.0559925
$467$			35.3683i			1.63665i	0.574755	+	0.818325i	$0.305097\pi$
$467$			35.3683i			1.63665i	−0.574755	+	0.818325i	$0.694903\pi$
$468$	−16.6352	+	22.3486i	−0.768962	+	1.03306i
$469$	−14.1652	−	34.6974i	−0.654086	−	1.60218i
$470$		0			0
$471$	−14.3739	+	7.21953i	−0.662313	+	0.332658i
$472$	45.5178			2.09513
$473$	−11.1328			−0.511889
$474$	−31.9681	+	16.0565i	−1.46834	+	0.737501i
$475$		0			0
$476$	−22.3486	−	54.7426i	−1.02435	−	2.50912i
$477$	24.0651	−	32.3303i	1.10186	−	1.48030i
$478$		−	29.9129i		−	1.36818i
$479$	−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
$482$			18.9145i			0.861530i
$483$	−1.51378	+	1.73384i	−0.0688792	+	0.0788926i
$484$	−28.7477			−1.30671
$485$		0			0
$486$	25.7488	+	27.2815i	1.16799	+	1.23751i
$487$		−	40.1652i		−	1.82006i	−0.414546	−	0.910028i	$-0.636060\pi$
$487$		−	40.1652i		−	1.82006i	0.414546	−	0.910028i	$-0.363940\pi$
$488$		−	18.9145i		−	0.856217i
$489$	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	$-0.0180475\pi$
$492$	−27.3713	+	13.7477i	−1.23399	+	0.619795i
$493$	2.96073			0.133344
$494$			40.3036i			1.81334i
$495$		0			0
$496$		−	12.2474i		−	0.549927i
$497$	−4.31075	−	10.5591i	−0.193364	−	0.473642i
$498$	13.3297	+	26.5390i	0.597318	+	1.18924i
$499$	−30.7477			−1.37646			−0.688229	−	0.725494i	$-0.741611\pi$
$499$	−30.7477			−1.37646			−0.688229	+	0.725494i	$0.741611\pi$
$500$		0			0
$501$	−10.1216	−	20.1518i	−0.452199	−	0.900315i
$502$	36.6356			1.63513
$503$			11.7894i			0.525665i	0.964841	+	0.262833i	$0.0846567\pi$
$503$			11.7894i			0.525665i	−0.964841	+	0.262833i	$0.915343\pi$
$504$	8.54060	−	33.1325i	0.380428	−	1.47584i
$505$		0			0
$506$		−	5.21046i		−	0.231633i
$507$	−10.8345	+	5.44182i	−0.481177	+	0.241680i
$508$		−	38.5390i		−	1.70989i
$509$	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
$512$	29.3804			1.29844
$513$	34.9883	+	6.16515i	1.54477	+	0.272198i
$514$		−	39.5964i		−	1.74652i
$515$		0			0
$516$	7.61178	+	15.1548i	0.335090	+	0.667154i
$517$	−25.4107			−1.11756
$518$	1.40197	+	3.43412i	0.0615992	+	0.150887i
$519$	−13.7477	−	27.3713i	−0.603458	−	1.20147i
$520$		0			0
$521$	35.3683			1.54951			0.774757	−	0.632259i	$-0.217872\pi$
$521$	35.3683			1.54951			0.774757	+	0.632259i	$0.217872\pi$
$522$	2.90878	+	2.16515i	0.127314	+	0.0947661i
$523$	−14.6969			−0.642652			−0.321326	−	0.946969i	$-0.604129\pi$
$523$	−14.6969			−0.642652			−0.321326	+	0.946969i	$0.604129\pi$
$524$	22.3486			0.976302
$525$		0			0
$526$	−17.6261			−0.768536
$527$	25.8645			1.12668
$528$	9.35414	+	18.6238i	0.407087	+	0.810498i
$529$	−22.7477			−0.989032
$530$		0			0
$531$	−18.9145	+	25.4107i	−0.820818	+	1.10273i
$532$	−25.9219	−	63.4955i	−1.12386	−	2.75288i
$533$	11.4255			0.494891
$534$	−39.3303	+	19.7543i	−1.70199	+	0.854854i
$535$		0			0
$536$		−	61.0624i		−	2.63750i
$537$	9.66311	+	19.2390i	0.416994	+	0.830223i
$538$	−45.5178			−1.96241
$539$	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	$0.496014\pi$
$542$			8.35532i			0.358892i
$543$	−9.52121	−	18.9564i	−0.408594	−	0.813499i
$544$			11.2250i			0.481267i
$545$		0			0
$546$	−17.7660	+	20.3487i	−0.760315	+	0.870846i
$547$			41.3303i			1.76716i	0.468284	+	0.883578i	$0.344872\pi$
$547$			41.3303i			1.76716i	−0.468284	+	0.883578i	$0.655128\pi$
$548$	3.80848			0.162690
$549$	10.5591	+	7.85971i	0.450653	+	0.335444i
$550$		0			0
$551$	3.43412			0.146298
$552$	−3.35119	+	1.68320i	−0.142636	+	0.0716416i
$553$	−21.0229	+	8.58258i	−0.893986	+	0.364968i
$554$			21.0515i			0.894392i
$555$		0			0
$556$			9.28672i			0.393845i
$557$	46.6234			1.97550			0.987748	−	0.156056i	$-0.0498782\pi$
$557$	46.6234			1.97550			0.987748	+	0.156056i	$0.0498782\pi$
$558$	25.4107	+	18.9145i	1.07572	+	0.800713i
$559$		−	6.32599i		−	0.267561i
$560$		0			0
$561$	−39.3303	+	19.7543i	−1.66053	+	0.834029i
$562$			51.8693i			2.18798i
$563$			32.9077i			1.38690i	0.720507	+	0.693448i	$0.243909\pi$
$563$			32.9077i			1.38690i	−0.720507	+	0.693448i	$0.756091\pi$
$564$	17.3739	+	34.5908i	0.731572	+	1.45654i
$565$		0			0
$566$	−2.46060			−0.103427
$567$	14.9475	+	18.5357i	0.627736	+	0.778426i
$568$		−	18.5826i		−	0.779708i
$569$			32.1843i			1.34924i	0.738166	+	0.674619i	$0.235692\pi$
$569$			32.1843i			1.34924i	−0.738166	+	0.674619i	$0.764308\pi$
$570$		0			0
$571$	−2.25227			−0.0942547			−0.0471273	−	0.998889i	$-0.515007\pi$
$571$	−2.25227			−0.0942547			−0.0471273	+	0.998889i	$0.515007\pi$
$572$		−	40.0327i		−	1.67385i
$573$	−12.0059	−	23.9034i	−0.501554	−	0.998578i
$574$	−27.4955	+	11.2250i	−1.14764	+	0.468521i
$575$		0			0
$576$	−18.2087	+	24.4625i	−0.758696	+	1.01927i
$577$	−12.7587			−0.531151			−0.265576	−	0.964090i	$-0.585562\pi$
$577$	−12.7587			−0.531151			−0.265576	+	0.964090i	$0.585562\pi$
$578$	42.7101			1.77650
$579$	−8.55144	−	17.0257i	−0.355386	−	0.707562i
$580$		0			0
$581$	7.12502	+	17.4527i	0.295596	+	0.724058i
$582$	1.90424	−	0.956439i	0.0789334	−	0.0396457i
$583$			57.9129i			2.39851i
$584$	−27.2698			−1.12843
$585$		0			0
$586$		−	53.7821i		−	2.22172i
$587$		−	34.1380i		−	1.40903i	−0.709691	−	0.704513i	$-0.751165\pi$
$587$		−	34.1380i		−	1.40903i	0.709691	−	0.704513i	$-0.248835\pi$
$588$	14.9015	−	43.4845i	0.614526	−	1.79327i
$589$	30.0000			1.23613
$590$		0			0
$591$	−29.0207	+	14.5762i	−1.19375	+	0.599583i
$592$			1.62614i			0.0668338i
$593$			11.7894i			0.484134i	0.970259	+	0.242067i	$0.0778254\pi$
$593$			11.7894i			0.484134i	−0.970259	+	0.242067i	$0.922175\pi$
$594$	−53.0863	−	9.35414i	−2.17816	−	0.383805i
$595$		0			0
$596$			23.9603i			0.981451i
$597$	14.8365	+	29.5390i	0.607217	+	1.20895i
$598$	2.96073			0.121073
$599$		−	19.5447i		−	0.798574i	−0.916826	−	0.399287i	$-0.869258\pi$
$599$		−	19.5447i		−	0.798574i	0.916826	−	0.399287i	$-0.130742\pi$
$600$		0			0
$601$		−	42.0459i		−	1.71509i	−0.514412	−	0.857543i	$-0.671990\pi$
$601$		−	42.0459i		−	1.71509i	0.514412	−	0.857543i	$-0.328010\pi$
$602$	6.21499	+	15.2236i	0.253304	+	0.620466i
$603$	34.0886	+	25.3739i	1.38819	+	1.03330i
$604$	53.7042			2.18519
$605$		0			0
$606$	48.4955	−	24.3577i	1.96999	−	0.989464i
$607$	−1.42701			−0.0579207			−0.0289603	−	0.999581i	$-0.509220\pi$
$607$	−1.42701			−0.0579207			−0.0289603	+	0.999581i	$0.509220\pi$
$608$			13.0197i			0.528020i
$609$	1.73384	+	1.51378i	0.0702589	+	0.0613413i
$610$		0			0
$611$		−	14.4391i		−	0.584142i
$612$	53.7821	+	40.0327i	2.17401	+	1.61823i
$613$		−	27.4174i		−	1.10738i	−0.832723	−	0.553690i	$-0.813219\pi$
$613$		−	27.4174i		−	1.10738i	0.832723	−	0.553690i	$-0.186781\pi$
$614$	−49.3616			−1.99207
$615$		0			0
$616$	18.5826	+	45.5178i	0.748713	+	1.83397i
$617$	13.9368			0.561074			0.280537	−	0.959843i	$-0.409487\pi$
$617$	13.9368			0.561074			0.280537	+	0.959843i	$0.409487\pi$
$618$	25.4671	−	12.7913i	1.02444	−	0.514541i
$619$			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
$622$	−65.0070			−2.60655
$623$	−25.8645	+	10.5591i	−1.03624	+	0.423043i
$624$	−10.5826	+	5.31529i	−0.423642	+	0.212782i
$625$		0			0
$626$	−25.7827			−1.03048
$627$	−45.6189	+	22.9129i	−1.82184	+	0.915052i
$628$	−35.2086			−1.40498
$629$	−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	$0.460284\pi$
$632$	−36.9973			−1.47168
$633$	19.7308	−	9.91013i	0.784227	−	0.393892i
$634$	−33.5390			−1.33200
$635$		0			0
$636$	78.8352	−	39.5964i	3.12602	−	1.57010i
$637$	−12.2474	+	12.0000i	−0.485262	+	0.475457i
$638$	−5.21046			−0.206284
$639$	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	$0.739215\pi$
$642$	−3.74166	+	1.87931i	−0.147671	+	0.0741706i
$643$	43.0683			1.69845			0.849225	−	0.528032i	$-0.177070\pi$
$643$	43.0683			1.69845			0.849225	+	0.528032i	$0.177070\pi$
$644$	−4.66442	+	1.90424i	−0.183804	+	0.0750376i
$645$		0			0
$646$	96.9909			3.81606
$647$			18.6577i			0.733509i	0.930318	+	0.366755i	$0.119531\pi$
$647$			18.6577i			0.733509i	−0.930318	+	0.366755i	$0.880469\pi$
$648$	11.1328	+	37.1652i	0.437339	+	1.45999i
$649$		−	45.5178i		−	1.78673i
$650$		0			0
$651$	15.1466	+	13.2241i	0.593642	+	0.518295i
$652$			15.1652i			0.593913i
$653$	−12.4300			−0.486423			−0.243211	−	0.969973i	$-0.578201\pi$
$653$	−12.4300			−0.486423			−0.243211	+	0.969973i	$0.578201\pi$
$654$	18.6238	−	9.35414i	0.728249	−	0.365776i
$655$		0			0
$656$	−13.0197			−0.508335
$657$	11.3317	−	15.2236i	0.442091	−	0.593928i
$658$	14.1857	+	34.7477i	0.553016	+	1.35461i
$659$			12.4300i			0.484203i	0.970251	+	0.242102i	$0.0778368\pi$
$659$			12.4300i			0.484203i	−0.970251	+	0.242102i	$0.922163\pi$
$660$		0			0
$661$			32.3546i			1.25845i	0.777224	+	0.629224i	$0.216627\pi$
$661$			32.3546i			1.25845i	−0.777224	+	0.629224i	$0.783373\pi$
$662$	−40.9107			−1.59004
$663$	−11.2250	−	22.3486i	−0.435942	−	0.867947i
$664$			30.7142i			1.19194i
$665$		0			0
$666$	−3.37386	−	2.51134i	−0.130735	−	0.0973124i
$667$		−	0.252273i		−	0.00976805i
$668$		−	49.3616i		−	1.90986i
$669$	−3.79129	+	1.90424i	−0.146580	+	0.0736222i
$670$		0			0
$671$	−18.9145			−0.730185
$672$	−5.73916	+	6.57350i	−0.221393	+	0.253578i
$673$		−	47.4955i		−	1.83082i	−0.402528	−	0.915408i	$-0.631868\pi$
$673$		−	47.4955i		−	1.83082i	0.402528	−	0.915408i	$-0.368132\pi$
$674$		−	4.81302i		−	0.185391i
$675$		0			0
$676$	−26.5390			−1.02073
$677$		−	23.5789i		−	0.906210i	−0.891457	−	0.453105i	$-0.850316\pi$
$677$		−	23.5789i		−	0.906210i	0.891457	−	0.453105i	$-0.149684\pi$
$678$	23.5398	−	11.8233i	0.904042	−	0.454071i
$679$	1.25227	−	0.511238i	0.0480578	−	0.0196195i
$680$		0			0
$681$	4.58258	+	9.12377i	0.175605	+	0.349624i
$682$	−45.5178			−1.74297
$683$	33.1889			1.26994			0.634968	−	0.772538i	$-0.281013\pi$
$683$	33.1889			1.26994			0.634968	+	0.772538i	$0.281013\pi$
$684$	62.3813	+	46.4336i	2.38521	+	1.77543i
$685$		0			0
$686$	17.6842	−	40.9107i	0.675184	−	1.56198i
$687$	−14.4391	−	28.7477i	−0.550884	−	1.09679i
$688$			7.20871i			0.274830i
$689$	−32.9077			−1.25368
$690$		0			0
$691$			4.38774i			0.166918i	0.996511	+	0.0834588i	$0.0265967\pi$
$691$			4.38774i			0.166918i	−0.996511	+	0.0834588i	$0.973403\pi$
$692$		−	67.0457i		−	2.54870i
$693$	−33.1325	−	8.54060i	−1.25860	−	0.324430i
$694$	45.1216			1.71279
$695$		0			0
$696$	1.68320	+	3.35119i	0.0638014	+	0.127027i
$697$		−	27.4955i		−	1.04146i
$698$			4.66442i			0.176551i
$699$	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	$-0.0942037\pi$
$702$	5.31529	−	30.1652i	0.200613	−	1.13851i
$703$	−3.98320			−0.150229
$704$		−	43.8194i		−	1.65151i
$705$		0			0
$706$		−	33.6749i		−	1.26737i
$707$	31.8917	−	13.0197i	1.19941	−	0.489658i
$708$	−61.9621	+	31.1216i	−2.32868	+	1.16962i
$709$	31.4955			1.18284			0.591418	−	0.806365i	$-0.298568\pi$
$709$	31.4955			1.18284			0.591418	+	0.806365i	$0.298568\pi$
$710$		0			0
$711$	15.3739	−	20.6540i	0.576565	−	0.774587i
$712$	−45.5178			−1.70585
$713$		−	2.20382i		−	0.0825337i
$714$	48.9694	+	42.7541i	1.83264	+	1.60003i
$715$		0			0
$716$			47.1257i			1.76117i
$717$	9.66311	+	19.2390i	0.360876	+	0.718492i
$718$		−	15.2087i		−	0.567584i
$719$	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
$722$	66.7752			2.48511
$723$	−6.11016	−	12.1652i	−0.227239	−	0.452427i
$724$		−	46.4336i		−	1.72569i
$725$		0			0
$726$	28.2433	−	14.1857i	1.04821	−	0.526481i
$727$	45.0066			1.66920			0.834601	−	0.550855i	$-0.185698\pi$
$727$	45.0066			1.66920			0.834601	+	0.550855i	$0.185698\pi$
$728$	−25.8645	+	10.5591i	−0.958602	+	0.391348i
$729$	−25.3739	−	9.22860i	−0.939773	−	0.341800i
$730$		0			0
$731$	−15.2236			−0.563064
$732$	12.9323	+	25.7477i	0.477990	+	0.951663i
$733$	−32.2479			−1.19110			−0.595552	−	0.803317i	$-0.703067\pi$
$733$	−32.2479			−1.19110			−0.595552	+	0.803317i	$0.703067\pi$
$734$	−78.8352			−2.90986
$735$		0			0
$736$	0.956439			0.0352548
$737$	−61.0624			−2.24926
$738$	20.1072	−	27.0130i	0.740155	−	0.994362i
$739$	40.8258			1.50180			0.750900	−	0.660416i	$-0.229620\pi$
$739$	40.8258			1.50180			0.750900	+	0.660416i	$0.229620\pi$
$740$		0			0
$741$	−13.0197	−	25.9219i	−0.478292	−	0.952265i
$742$	79.1927	−	32.3303i	2.90726	−	1.18688i
$743$	−12.4300			−0.456012			−0.228006	−	0.973660i	$-0.573221\pi$
$743$	−12.4300			−0.456012			−0.228006	+	0.973660i	$0.573221\pi$
$744$	14.7042	+	29.2756i	0.539081	+	1.07329i
$745$		0			0
$746$			45.5140i			1.66639i
$747$	−17.1464	−	12.7630i	−0.627355	−	0.466972i
$748$	−96.3392			−3.52251
$749$	−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	$0.749935\pi$
$752$			16.4539i			0.600011i
$753$	−23.5628	+	11.8348i	−0.858677	+	0.431286i
$754$		−	2.96073i		−	0.107823i
$755$		0			0
$756$	11.0274	+	50.9417i	0.401061	+	1.85273i
$757$			6.25227i			0.227243i	0.993524	+	0.113621i	$0.0362451\pi$
$757$			6.25227i			0.227243i	−0.993524	+	0.113621i	$0.963755\pi$
$758$	−46.5186			−1.68963
$759$	1.68320	+	3.35119i	0.0610961	+	0.121641i
$760$		0			0
$761$	−44.6972			−1.62027			−0.810135	−	0.586243i	$-0.800606\pi$
$761$	−44.6972			−1.62027			−0.810135	+	0.586243i	$0.800606\pi$
$762$	19.0173	+	37.8628i	0.688923	+	1.37162i
$763$	12.2474	−	5.00000i	0.443387	−	0.181012i
$764$		−	58.5511i		−	2.11830i
$765$		0			0
$766$			47.8606i			1.72927i
$767$	25.8645			0.933913
$768$	−45.4645	+	22.8353i	−1.64056	+	0.823999i
$769$			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
$772$		−	41.7042i		−	1.50097i
$773$		−	7.12502i		−	0.256269i	−0.991757	−	0.128135i	$-0.959101\pi$
$773$		−	7.12502i		−	0.256269i	0.991757	−	0.128135i	$-0.0408989\pi$
$774$	−14.9564	−	11.1328i	−0.537598	−	0.400162i
$775$		0			0
$776$	2.20382			0.0791126
$777$	−2.01107	−	1.75582i	−0.0721467	−	0.0629895i
$778$			63.4519i			2.27486i
$779$		−	31.8917i		−	1.14264i
$780$		0			0
$781$	−18.5826			−0.664937
$782$		−	7.12502i		−	0.254790i
$783$	−2.57026	−	0.452896i	−0.0918537	−	0.0161852i
$784$	13.9564	−	13.6745i	0.498444	−	0.488374i
$785$		0			0
$786$	−21.9564	+	11.0280i	−0.783160	+	0.393356i
$787$	16.1240			0.574757			0.287378	−	0.957817i	$-0.407216\pi$
$787$	16.1240			0.574757			0.287378	+	0.957817i	$0.407216\pi$
$788$	−71.0859			−2.53233
$789$	11.3365	−	5.69398i	0.403592	−	0.202711i
$790$		0			0
$791$	15.4803	−	6.31982i	0.550418	−	0.224707i
$792$	−44.7191	−	33.2867i	−1.58903	−	1.18279i
$793$		−	10.7477i		−	0.381663i
$794$	32.9077			1.16785
$795$		0			0
$796$			72.3555i			2.56457i
$797$		−	15.2236i		−	0.539246i	−0.962966	−	0.269623i	$-0.913101\pi$
$797$		−	15.2236i		−	0.539246i	0.962966	−	0.269623i	$-0.0868991\pi$
$798$	56.7992	+	49.5900i	2.01067	+	1.75547i
$799$	−34.7477			−1.22929
$800$		0			0
$801$	18.9145	−	25.4107i	0.668310	−	0.897842i
$802$		−	26.7913i		−	0.946033i
$803$			27.2698i			0.962330i
$804$	41.7498	+	83.1226i	1.47240	+	2.93151i
$805$		0			0
$806$		−	25.8645i		−	0.911038i
$807$	29.2756	−	14.7042i	1.03055	−	0.517611i
$808$	56.1249			1.97447
$809$		−	7.32436i		−	0.257511i	−0.991676	−	0.128755i	$-0.958902\pi$
$809$		−	7.32436i		−	0.257511i	0.991676	−	0.128755i	$-0.0410982\pi$
$810$		0			0
$811$			8.77548i			0.308149i	0.988059	+	0.154074i	$0.0492396\pi$
$811$			8.77548i			0.308149i	−0.988059	+	0.154074i	$0.950760\pi$
$812$	1.90424	+	4.66442i	0.0668258	+	0.163689i
$813$	−2.69912	−	5.37386i	−0.0946622	−	0.188470i
$814$	6.04356			0.211827
$815$		0			0
$816$	12.7913	+	25.4671i	0.447785	+	0.891526i
$817$	−17.6577			−0.617764
$818$		−	58.6904i		−	2.05206i
$819$	4.85301	−	18.8268i	0.169578	−	0.657862i
$820$		0			0
$821$		−	15.4436i		−	0.538985i	−0.963002	−	0.269493i	$-0.913144\pi$
$821$		−	15.4436i		−	0.538985i	0.963002	−	0.269493i	$-0.0868560\pi$
$822$	−3.74166	+	1.87931i	−0.130505	+	0.0655486i
$823$			29.7477i			1.03694i	0.855096	+	0.518470i	$0.173498\pi$
$823$			29.7477i			1.03694i	−0.855096	+	0.518470i	$0.826502\pi$
$824$	29.4736			1.02676
$825$		0			0
$826$	−62.2432	+	25.4107i	−2.16572	+	0.884150i
$827$	−44.6143			−1.55139			−0.775696	−	0.631107i	$-0.782601\pi$
$827$	−44.6143			−1.55139			−0.775696	+	0.631107i	$0.782601\pi$
$828$	3.41105	−	4.58258i	0.118542	−	0.159256i
$829$		−	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
$832$	24.8994			0.863233
$833$	28.8781	+	29.4736i	1.00057	+	1.02120i
$834$	−4.58258	−	9.12377i	−0.158682	−	0.315930i
$835$		0			0
$836$	−111.743			−3.86471
$837$	−22.4535	−	3.95644i	−0.776105	−	0.136755i
$838$	−45.5178			−1.57239
$839$	−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
$842$	24.4625			0.843035
$843$	−16.7560	−	33.3606i	−0.577106	−	1.14900i
$844$	48.3303			1.66360
$845$		0			0
$846$	−34.1380	−	25.4107i	−1.17369	−	0.873637i
$847$	18.5734	−	7.58258i	0.638191	−	0.260540i
$848$	37.4996			1.28774
$849$	1.58258	−	0.794877i	0.0543139	−	0.0272801i
$850$		0			0
$851$			0.292609i			0.0100305i
$852$	12.7053	+	25.2959i	0.435278	+	0.866625i
$853$	27.3489			0.936409			0.468205	−	0.883620i	$-0.344901\pi$
$853$	27.3489			0.936409			0.468205	+	0.883620i	$0.344901\pi$
$854$	10.5591	+	25.8645i	0.361326	+	0.885065i
$855$		0			0
$856$	−4.33030			−0.148007
$857$		−	21.3751i		−	0.730158i	−0.930977	−	0.365079i	$-0.881042\pi$
$857$		−	21.3751i		−	0.730158i	0.930977	−	0.365079i	$-0.118958\pi$
$858$	19.7543	+	39.3303i	0.674402	+	1.34271i
$859$		−	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
$861$	14.0580	−	16.1017i	0.479096	−	0.548745i
$862$		−	74.3303i		−	2.53170i
$863$	−39.0064			−1.32779			−0.663897	−	0.747824i	$-0.731099\pi$
$863$	−39.0064			−1.32779			−0.663897	+	0.747824i	$0.731099\pi$
$864$	1.71706	−	9.74461i	0.0584156	−	0.331518i
$865$		0			0
$866$	56.4866			1.91949
$867$	−27.4697	+	13.7971i	−0.932920	+	0.468576i
$868$	16.6352	+	40.7477i	0.564635	+	1.38307i
$869$			36.9973i			1.25505i
$870$		0			0
$871$		−	34.6974i		−	1.17568i
$872$	21.5538			0.729902
$873$	−0.915775	+	1.23030i	−0.0309943	+	0.0416393i
$874$		−	8.26424i		−	0.279542i
$875$		0			0
$876$	37.1216	−	18.6450i	1.25422	−	0.629955i
$877$			23.4955i			0.793385i	0.917952	+	0.396693i	$0.129842\pi$
$877$			23.4955i			0.793385i	−0.917952	+	0.396693i	$0.870158\pi$
$878$		−	64.8419i		−	2.18831i
$879$	17.3739	+	34.5908i	0.586006	+	1.16672i
$880$		0			0
$881$	58.6904			1.97733			0.988665	−	0.150136i	$-0.0479712\pi$
$881$	58.6904			1.97733			0.988665	+	0.150136i	$0.0479712\pi$
$882$	6.81764	+	50.0747i	0.229562	+	1.68610i
$883$		−	24.5826i		−	0.827270i	−0.910443	−	0.413635i	$-0.864259\pi$
$883$		−	24.5826i		−	0.827270i	0.910443	−	0.413635i	$-0.135741\pi$
$884$		−	54.7426i		−	1.84119i
$885$		0			0
$886$	−32.3303			−1.08616
$887$		−	46.9010i		−	1.57478i	−0.616455	−	0.787390i	$-0.711432\pi$
$887$		−	46.9010i		−	1.57478i	0.616455	−	0.787390i	$-0.288568\pi$
$888$	−1.95232	−	3.88702i	−0.0655157	−	0.130440i
$889$	10.1652	+	24.8994i	0.340928	+	0.835100i
$890$		0			0
$891$	37.1652	−	11.1328i	1.24508	−	0.372964i
$892$	−9.28672			−0.310942
$893$	−40.3036			−1.34871
$894$	−11.8233	−	23.5398i	−0.395430	−	0.787290i
$895$		0			0
$896$	−50.5919	+	20.6540i	−1.69016	+	0.690003i
$897$	−1.90424	+	0.956439i	−0.0635808	+	0.0319346i
$898$			47.0345i			1.56956i
$899$	−2.20382			−0.0735015
$900$		0			0
$901$			79.1927i			2.63829i
$902$			48.3881i			1.61115i
$903$	−8.91512	−	7.78358i	−0.296677	−	0.259021i
$904$	27.2432			0.906095
$905$		0			0
$906$	−52.7618	+	26.5006i	−1.75289	+	0.880423i
$907$			53.4955i			1.77629i	0.459566	+	0.888144i	$0.348005\pi$
$907$			53.4955i			1.77629i	−0.459566	+	0.888144i	$0.651995\pi$
$908$			22.3486i			0.741664i
$909$	−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	$-0.355365\pi$
$912$	14.8365	+	29.5390i	0.491285	+	0.978135i
$913$	30.7142			1.01649
$914$			38.1067i			1.26046i
$915$		0			0
$916$		−	70.4173i		−	2.32665i
$917$	−14.4391	+	5.89472i	−0.476820	+	0.194661i
$918$	−72.5927	−	12.7913i	−2.39592	−	0.422175i
$919$	−40.0780			−1.32205			−0.661026	−	0.750363i	$-0.729879\pi$
$919$	−40.0780			−1.32205			−0.661026	+	0.750363i	$0.729879\pi$
$920$		0			0
$921$	31.7477	−	15.9459i	1.04612	−	0.525434i
$922$	−19.4892			−0.641843
$923$		−	10.5591i		−	0.347558i
$924$	−56.4175	−	49.2568i	−1.85600	−	1.62043i
$925$		0			0
$926$		−	35.4905i		−	1.16629i
$927$	−12.2474	+	16.4539i	−0.402259	+	0.540416i
$928$		−	0.956439i		−	0.0313967i
$929$	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
$932$	1.90424			0.0623755
$933$	41.8104	−	21.0000i	1.36881	−	0.687509i
$934$		−	85.1142i		−	2.78502i
$935$		0			0
$936$	18.9145	−	25.4107i	0.618238	−	0.830574i
$937$	−25.0061			−0.816915			−0.408457	−	0.912777i	$-0.633933\pi$
$937$	−25.0061			−0.816915			−0.408457	+	0.912777i	$0.633933\pi$
$938$	34.0886	+	83.4996i	1.11303	+	2.72636i
$939$	16.5826	−	8.32889i	0.541152	−	0.271803i
$940$		0			0
$941$	−25.7827			−0.840492			−0.420246	−	0.907410i	$-0.638056\pi$
$941$	−25.7827			−0.840492			−0.420246	+	0.907410i	$0.638056\pi$
$942$	34.5908	−	17.3739i	1.12703	−	0.566071i
$943$	−2.34279			−0.0762917
$944$	−29.4736			−0.959284
$945$		0			0
$946$	26.7913			0.871060
$947$	−24.8600			−0.807841			−0.403920	−	0.914794i	$-0.632353\pi$
$947$	−24.8600			−0.807841			−0.403920	+	0.914794i	$0.632353\pi$
$948$	50.3635	−	25.2959i	1.63573	−	0.821574i
$949$	−15.4955			−0.503004
$950$		0			0
$951$	21.5712	−	10.8345i	0.699493	−	0.351333i
$952$	25.4107	+	62.2432i	0.823565	+	2.01731i
$953$	0.502268			0.0162700			0.00813502	−	0.999967i	$-0.497411\pi$
$953$	0.502268			0.0162700			0.00813502	+	0.999967i	$0.497411\pi$
$954$	−57.9129	+	77.8032i	−1.87500	+	2.51897i
$955$		0			0
$956$			47.1257i			1.52415i
$957$	3.35119	−	1.68320i	0.108329	−	0.0544100i
$958$	25.4107			0.820982
$959$	−2.46060	+	1.00454i	−0.0794569	+	0.0324381i
$960$		0			0
$961$	11.7477			0.378959
$962$			3.43412i			0.110720i
$963$	1.79941	−	2.41742i	0.0579853	−	0.0779004i
$964$		−	29.7984i		−	0.959742i
$965$		0			0
$966$	3.64292	−	4.17251i	0.117209	−	0.134248i
$967$			12.7477i			0.409939i	0.978768	+	0.204970i	$0.0657096\pi$
$967$			12.7477i			0.409939i	−0.978768	+	0.204970i	$0.934290\pi$
$968$	32.6866			1.05059
$969$	−62.3813	+	31.3321i	−2.00398	+	1.00653i
$970$		0			0
$971$	48.1313			1.54461			0.772303	−	0.635254i	$-0.219105\pi$
$971$	48.1313			1.54461			0.772303	+	0.635254i	$0.219105\pi$
$972$	−40.5655	−	42.9801i	−1.30114	−	1.37859i
$973$	−2.44949	−	6.00000i	−0.0785270	−	0.192351i
$974$			96.6578i			3.09712i
$975$		0			0
$976$			12.2474i			0.392031i
$977$	13.9368			0.445877			0.222939	−	0.974832i	$-0.428435\pi$
$977$	13.9368			0.445877			0.222939	+	0.974832i	$0.428435\pi$
$978$	−7.48331	−	14.8991i	−0.239290	−	0.476419i
$979$			45.5178i			1.45476i
$980$		0			0
$981$	−8.95644	+	12.0325i	−0.285957	+	0.384170i
$982$			6.04356i			0.192858i
$983$		−	7.12502i		−	0.227253i	−0.993524	−	0.113626i	$-0.963753\pi$
$983$		−	7.12502i		−	0.227253i	0.993524	−	0.113626i	$-0.0362467\pi$
$984$	31.1216	−	15.6314i	0.992120	−	0.498310i
$985$		0			0
$986$	−7.12502			−0.226907
$987$	−20.3487	−	17.7660i	−0.647708	−	0.565498i
$988$		−	63.4955i		−	2.02006i
$989$			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	$0.385955\pi$
$992$		−	8.35532i		−	0.265282i
$993$	26.3124	−	13.2159i	0.834998	−	0.419393i
$994$	10.3739	+	25.4107i	0.329039	+	0.805978i
$995$		0			0
$996$	−21.0000	−	41.8104i	−0.665410	−	1.32481i
$997$	36.2311			1.14745			0.573725	−	0.819048i	$-0.305498\pi$
$997$	36.2311			1.14745			0.573725	+	0.819048i	$0.305498\pi$
$998$	73.9947			2.34226
$999$	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.g.f.524.3		16
3.2	odd	2	inner	525.2.g.f.524.16		16
5.2	odd	4		525.2.b.h.251.1	✓	8
5.3	odd	4		525.2.b.i.251.8	yes	8
5.4	even	2	inner	525.2.g.f.524.14		16
7.6	odd	2	inner	525.2.g.f.524.2		16
15.2	even	4		525.2.b.h.251.8	yes	8
15.8	even	4		525.2.b.i.251.1	yes	8
15.14	odd	2	inner	525.2.g.f.524.1		16
21.20	even	2	inner	525.2.g.f.524.13		16
35.13	even	4		525.2.b.i.251.7	yes	8
35.27	even	4		525.2.b.h.251.2	yes	8
35.34	odd	2	inner	525.2.g.f.524.15		16
105.62	odd	4		525.2.b.h.251.7	yes	8
105.83	odd	4		525.2.b.i.251.2	yes	8
105.104	even	2	inner	525.2.g.f.524.4		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.40651 q^{2} +(1.54779 - 0.777403i) q^{3} +3.79129 q^{4} +(-3.72476 + 1.87083i) q^{6} +(-2.44949 + 1.00000i) q^{7} -4.31075 q^{8} +(1.79129 - 2.40651i) q^{9} +O(q^{10})\)	\(q-2.40651 q^{2} +(1.54779 - 0.777403i) q^{3} +3.79129 q^{4} +(-3.72476 + 1.87083i) q^{6} +(-2.44949 + 1.00000i) q^{7} -4.31075 q^{8} +(1.79129 - 2.40651i) q^{9} +4.31075i q^{11} +(5.86811 - 2.94736i) q^{12} -2.44949 q^{13} +(5.89472 - 2.40651i) q^{14} +2.79129 q^{16} +5.89472i q^{17} +(-4.31075 + 5.79129i) q^{18} +6.83723i q^{19} +(-3.01388 + 3.45203i) q^{21} -10.3739i q^{22} +0.502268 q^{23} +(-6.67212 + 3.35119i) q^{24} +5.89472 q^{26} +(0.901703 - 5.11732i) q^{27} +(-9.28672 + 3.79129i) q^{28} -0.502268i q^{29} -4.38774i q^{31} +1.90424 q^{32} +(3.35119 + 6.67212i) q^{33} -14.1857i q^{34} +(6.79129 - 9.12377i) q^{36} +0.582576i q^{37} -16.4539i q^{38} +(-3.79129 + 1.90424i) q^{39} -4.66442 q^{41} +(7.25294 - 8.30734i) q^{42} +2.58258i q^{43} +16.3433i q^{44} -1.20871 q^{46} +5.89472i q^{47} +(4.32032 - 2.16996i) q^{48} +(5.00000 - 4.89898i) q^{49} +(4.58258 + 9.12377i) q^{51} -9.28672 q^{52} +13.4345 q^{53} +(-2.16996 + 12.3149i) q^{54} +(10.5591 - 4.31075i) q^{56} +(5.31529 + 10.5826i) q^{57} +1.20871i q^{58} -10.5591 q^{59} +4.38774i q^{61} +10.5591i q^{62} +(-1.98123 + 7.68601i) q^{63} -10.1652 q^{64} +(-8.06468 - 16.0565i) q^{66} +14.1652i q^{67} +22.3486i q^{68} +(0.777403 - 0.390465i) q^{69} +4.31075i q^{71} +(-7.72180 + 10.3739i) q^{72} +6.32599 q^{73} -1.40197i q^{74} +25.9219i q^{76} +(-4.31075 - 10.5591i) q^{77} +(9.12377 - 4.58258i) q^{78} +8.58258 q^{79} +(-2.58258 - 8.62150i) q^{81} +11.2250 q^{82} -7.12502i q^{83} +(-11.4265 + 13.0876i) q^{84} -6.21499i q^{86} +(-0.390465 - 0.777403i) q^{87} -18.5826i q^{88} +10.5591 q^{89} +(6.00000 - 2.44949i) q^{91} +1.90424 q^{92} +(-3.41105 - 6.79129i) q^{93} -14.1857i q^{94} +(2.94736 - 1.48036i) q^{96} -0.511238 q^{97} +(-12.0325 + 11.7894i) q^{98} +(10.3739 + 7.72180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 24 * q^4 - 8 * q^9	\( 16 q + 24 q^{4} - 8 q^{9} + 8 q^{16} - 24 q^{21} + 72 q^{36} - 24 q^{39} - 56 q^{46} + 80 q^{49} - 16 q^{64} + 64 q^{79} + 32 q^{81} - 120 q^{84} + 96 q^{91} + 56 q^{99}+O(q^{100}) \) 16 * q + 24 * q^4 - 8 * q^9 + 8 * q^16 - 24 * q^21 + 72 * q^36 - 24 * q^39 - 56 * q^46 + 80 * q^49 - 16 * q^64 + 64 * q^79 + 32 * q^81 - 120 * q^84 + 96 * q^91 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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