LMFDB - Embedded newform 567.3.r.e.512.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,3,Mod(134,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("567.134");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	567.r (of order $6$, degree $2$, 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:	$15.4496309892$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 6 x^{15} + 18 x^{14} - 24 x^{13} + 53 x^{12} - 204 x^{11} + 558 x^{10} - 774 x^{9} + 828 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 24x^13 + 53x^12 - 204x^11 + 558x^10 - 774x^9 + 828x^8 - 1302x^7 + 2718x^6 - 3780x^5 + 3293x^4 - 1656x^3 + 450x^2 - 30*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{12} $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			512.4
Root			$0.806936 + 0.806936i$ of defining polynomial
Character	$\chi$	$=$	567.512
Dual form			567.3.r.e.134.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.625847 - 0.361333i) q^{2} +(-1.73888 - 3.01182i) q^{4} +(6.88081 - 3.97263i) q^{5} +(-1.32288 + 2.29129i) q^{7} +5.40392i q^{8} +O(q^{10})$	\(q+(-0.625847 - 0.361333i) q^{2} +(-1.73888 - 3.01182i) q^{4} +(6.88081 - 3.97263i) q^{5} +(-1.32288 + 2.29129i) q^{7} +5.40392i q^{8} -5.74177 q^{10} +(8.01242 + 4.62598i) q^{11} +(11.0728 + 19.1786i) q^{13} +(1.65584 - 0.955997i) q^{14} +(-5.00290 + 8.66527i) q^{16} +27.2692i q^{17} +31.8633 q^{19} +(-23.9298 - 13.8158i) q^{20} +(-3.34303 - 5.79030i) q^{22} +(-11.7168 + 6.76470i) q^{23} +(19.0637 - 33.0192i) q^{25} -16.0038i q^{26} +9.20127 q^{28} +(-5.83588 - 3.36935i) q^{29} +(-5.96753 - 10.3361i) q^{31} +(24.9818 - 14.4233i) q^{32} +(9.85326 - 17.0663i) q^{34} +21.0212i q^{35} +26.8988 q^{37} +(-19.9415 - 11.5133i) q^{38} +(21.4678 + 37.1833i) q^{40} +(-55.3940 + 31.9817i) q^{41} +(8.10924 - 14.0456i) q^{43} -32.1760i q^{44} +9.77724 q^{46} +(0.448944 + 0.259198i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-23.8619 + 13.7766i) q^{50} +(38.5084 - 66.6985i) q^{52} -71.8912i q^{53} +73.5092 q^{55} +(-12.3819 - 7.14871i) q^{56} +(2.43491 + 4.21739i) q^{58} +(-33.3887 + 19.2770i) q^{59} +(-13.9611 + 24.1814i) q^{61} +8.62506i q^{62} +19.1768 q^{64} +(152.379 + 87.9763i) q^{65} +(-14.7824 - 25.6039i) q^{67} +(82.1300 - 47.4178i) q^{68} +(7.59565 - 13.1561i) q^{70} -39.4892i q^{71} +67.1187 q^{73} +(-16.8345 - 9.71940i) q^{74} +(-55.4064 - 95.9666i) q^{76} +(-21.1989 + 12.2392i) q^{77} +(9.38444 - 16.2543i) q^{79} +79.4987i q^{80} +46.2242 q^{82} +(69.3594 + 40.0446i) q^{83} +(108.331 + 187.634i) q^{85} +(-10.1503 + 5.86027i) q^{86} +(-24.9984 + 43.2985i) q^{88} +62.9293i q^{89} -58.5917 q^{91} +(40.7482 + 23.5260i) q^{92} +(-0.187313 - 0.324436i) q^{94} +(219.245 - 126.581i) q^{95} +(23.3906 - 40.5137i) q^{97} +5.05866i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4}+O(q^{10}) $ 16 * q + 12 * q^4	$ 16 q + 12 q^{4} - 104 q^{10} - 36 q^{13} - 132 q^{16} + 24 q^{19} + 136 q^{22} + 108 q^{25} + 112 q^{28} + 28 q^{31} + 12 q^{34} - 8 q^{37} - 336 q^{40} + 152 q^{43} + 216 q^{46} - 56 q^{49} + 272 q^{52} + 392 q^{55} + 220 q^{58} - 180 q^{61} - 1400 q^{64} + 132 q^{67} - 196 q^{70} + 544 q^{73} - 544 q^{76} - 316 q^{79} + 56 q^{82} + 228 q^{85} - 112 q^{91} + 348 q^{94} + 364 q^{97}+O(q^{100}) $ 16 * q + 12 * q^4 - 104 * q^10 - 36 * q^13 - 132 * q^16 + 24 * q^19 + 136 * q^22 + 108 * q^25 + 112 * q^28 + 28 * q^31 + 12 * q^34 - 8 * q^37 - 336 * q^40 + 152 * q^43 + 216 * q^46 - 56 * q^49 + 272 * q^52 + 392 * q^55 + 220 * q^58 - 180 * q^61 - 1400 * q^64 + 132 * q^67 - 196 * q^70 + 544 * q^73 - 544 * q^76 - 316 * q^79 + 56 * q^82 + 228 * q^85 - 112 * q^91 + 348 * q^94 + 364 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.625847	−	0.361333i	−0.312923	−	0.180666i	0.335311	−	0.942108i	$-0.391159\pi$
$2$	−0.625847	−	0.361333i	−0.312923	−	0.180666i	−0.648234	+	0.761441i	$0.724492\pi$
$3$		0			0
$3$		0			0
$4$	−1.73888	−	3.01182i	−0.434719	−	0.752956i
$5$	6.88081	−	3.97263i	1.37616	−	0.794527i	0.384466	−	0.923139i	$-0.374386\pi$
$5$	6.88081	−	3.97263i	1.37616	−	0.794527i	0.991695	+	0.128612i	$0.0410522\pi$
$6$		0			0
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$8$			5.40392i			0.675490i
$9$		0			0
$10$	−5.74177			−0.574177
$11$	8.01242	+	4.62598i	0.728402	+	0.420543i	0.817837	−	0.575449i	$-0.195173\pi$
$11$	8.01242	+	4.62598i	0.728402	+	0.420543i	−0.0894351	+	0.995993i	$0.528506\pi$
$12$		0			0
$13$	11.0728	+	19.1786i	0.851753	+	1.47528i	0.879625	+	0.475667i	$0.157793\pi$
$13$	11.0728	+	19.1786i	0.851753	+	1.47528i	−0.0278727	+	0.999611i	$0.508873\pi$
$14$	1.65584	−	0.955997i	0.118274	−	0.0682855i
$15$		0			0
$16$	−5.00290	+	8.66527i	−0.312681	+	0.541579i
$17$			27.2692i			1.60407i	0.597277	+	0.802035i	$0.296249\pi$
$17$			27.2692i			1.60407i	−0.597277	+	0.802035i	$0.703751\pi$
$18$		0			0
$19$	31.8633			1.67702			0.838508	−	0.544890i	$-0.183428\pi$
$19$	31.8633			1.67702			0.838508	+	0.544890i	$0.183428\pi$
$20$	−23.9298	−	13.8158i	−1.19649	−	0.690792i
$21$		0			0
$22$	−3.34303	−	5.79030i	−0.151956	−	0.263196i
$23$	−11.7168	+	6.76470i	−0.509427	+	0.294118i	−0.732598	−	0.680662i	$-0.761692\pi$
$23$	−11.7168	+	6.76470i	−0.509427	+	0.294118i	0.223171	+	0.974779i	$0.428359\pi$
$24$		0			0
$25$	19.0637	−	33.0192i	0.762546	−	1.32077i
$26$		−	16.0038i		−	0.615532i
$27$		0			0
$28$	9.20127			0.328617
$29$	−5.83588	−	3.36935i	−0.201237	−	0.116184i	0.395995	−	0.918253i	$-0.370400\pi$
$29$	−5.83588	−	3.36935i	−0.201237	−	0.116184i	−0.597233	+	0.802068i	$0.703733\pi$
$30$		0			0
$31$	−5.96753	−	10.3361i	−0.192501	−	0.333422i	0.753577	−	0.657359i	$-0.228327\pi$
$31$	−5.96753	−	10.3361i	−0.192501	−	0.333422i	−0.946078	+	0.323938i	$0.894993\pi$
$32$	24.9818	−	14.4233i	0.780682	−	0.450727i
$33$		0			0
$34$	9.85326	−	17.0663i	0.289802	−	0.501951i
$35$			21.0212i			0.600606i
$36$		0			0
$37$	26.8988			0.726993			0.363497	−	0.931595i	$-0.381583\pi$
$37$	26.8988			0.726993			0.363497	+	0.931595i	$0.381583\pi$
$38$	−19.9415	−	11.5133i	−0.524777	−	0.302980i
$39$		0			0
$40$	21.4678	+	37.1833i	0.536695	+	0.929582i
$41$	−55.3940	+	31.9817i	−1.35107	+	0.780042i	−0.988400	−	0.151874i	$-0.951469\pi$
$41$	−55.3940	+	31.9817i	−1.35107	+	0.780042i	−0.362673	+	0.931916i	$0.618136\pi$
$42$		0			0
$43$	8.10924	−	14.0456i	0.188587	−	0.326642i	−0.756192	−	0.654349i	$-0.772943\pi$
$43$	8.10924	−	14.0456i	0.188587	−	0.326642i	0.944779	+	0.327707i	$0.106276\pi$
$44$		−	32.1760i		−	0.731273i
$45$		0			0
$46$	9.77724			0.212549
$47$	0.448944	+	0.259198i	0.00955200	+	0.00551485i	0.504768	−	0.863255i	$-0.331578\pi$
$47$	0.448944	+	0.259198i	0.00955200	+	0.00551485i	−0.495216	+	0.868770i	$0.664911\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	−23.8619	+	13.7766i	−0.477237	+	0.275533i
$51$		0			0
$52$	38.5084	−	66.6985i	0.740547	−	1.28266i
$53$		−	71.8912i		−	1.35644i	−0.734860	−	0.678219i	$-0.762752\pi$
$53$		−	71.8912i		−	1.35644i	0.734860	−	0.678219i	$-0.237248\pi$
$54$		0			0
$55$	73.5092			1.33653
$56$	−12.3819	−	7.14871i	−0.221106	−	0.127656i
$57$		0			0
$58$	2.43491	+	4.21739i	0.0419813	+	0.0727137i
$59$	−33.3887	+	19.2770i	−0.565911	+	0.326729i	−0.755514	−	0.655132i	$-0.772613\pi$
$59$	−33.3887	+	19.2770i	−0.565911	+	0.326729i	0.189604	+	0.981861i	$0.439280\pi$
$60$		0			0
$61$	−13.9611	+	24.1814i	−0.228871	+	0.396416i	−0.957474	−	0.288521i	$-0.906837\pi$
$61$	−13.9611	+	24.1814i	−0.228871	+	0.396416i	0.728603	+	0.684936i	$0.240170\pi$
$62$			8.62506i			0.139114i
$63$		0			0
$64$	19.1768			0.299637
$65$	152.379	+	87.9763i	2.34430	+	1.35348i
$66$		0			0
$67$	−14.7824	−	25.6039i	−0.220633	−	0.382148i	0.734367	−	0.678752i	$-0.237479\pi$
$67$	−14.7824	−	25.6039i	−0.220633	−	0.382148i	−0.955000	+	0.296604i	$0.904146\pi$
$68$	82.1300	−	47.4178i	1.20779	−	0.697320i
$69$		0			0
$70$	7.59565	−	13.1561i	0.108509	−	0.187944i
$71$		−	39.4892i		−	0.556186i	−0.960554	−	0.278093i	$-0.910298\pi$
$71$		−	39.4892i		−	0.556186i	0.960554	−	0.278093i	$-0.0897023\pi$
$72$		0			0
$73$	67.1187			0.919434			0.459717	−	0.888066i	$-0.347951\pi$
$73$	67.1187			0.919434			0.459717	+	0.888066i	$0.347951\pi$
$74$	−16.8345	−	9.71940i	−0.227493	−	0.131343i
$75$		0			0
$76$	−55.4064	−	95.9666i	−0.729031	−	1.26272i
$77$	−21.1989	+	12.2392i	−0.275310	+	0.158950i
$78$		0			0
$79$	9.38444	−	16.2543i	0.118790	−	0.205751i	−0.800498	−	0.599335i	$-0.795432\pi$
$79$	9.38444	−	16.2543i	0.118790	−	0.205751i	0.919289	+	0.393584i	$0.128765\pi$
$80$			79.4987i			0.993734i
$81$		0			0
$82$	46.2242			0.563710
$83$	69.3594	+	40.0446i	0.835655	+	0.482466i	0.855785	−	0.517332i	$-0.173075\pi$
$83$	69.3594	+	40.0446i	0.835655	+	0.482466i	−0.0201300	+	0.999797i	$0.506408\pi$
$84$		0			0
$85$	108.331	+	187.634i	1.27448	+	2.20746i
$86$	−10.1503	+	5.86027i	−0.118027	+	0.0681427i
$87$		0			0
$88$	−24.9984	+	43.2985i	−0.284073	+	0.492028i
$89$			62.9293i			0.707071i	0.935421	+	0.353535i	$0.115021\pi$
$89$			62.9293i			0.707071i	−0.935421	+	0.353535i	$0.884979\pi$
$90$		0			0
$91$	−58.5917			−0.643864
$92$	40.7482	+	23.5260i	0.442915	+	0.255717i
$93$		0			0
$94$	−0.187313	−	0.324436i	−0.00199270	−	0.00345145i
$95$	219.245	−	126.581i	2.30784	−	1.33243i
$96$		0			0
$97$	23.3906	−	40.5137i	0.241140	−	0.417667i	−0.719899	−	0.694078i	$-0.755812\pi$
$97$	23.3906	−	40.5137i	0.241140	−	0.417667i	0.961039	+	0.276412i	$0.0891454\pi$
$98$			5.05866i			0.0516190i
$99$		0			0
$100$	−132.597			−1.32597
$101$	−90.1149	−	52.0279i	−0.892227	−	0.515128i	−0.0175568	−	0.999846i	$-0.505589\pi$
$101$	−90.1149	−	52.0279i	−0.892227	−	0.515128i	−0.874670	+	0.484718i	$0.838922\pi$
$102$		0			0
$103$	51.9299	+	89.9452i	0.504174	+	0.873255i	0.999988	+	0.00482615i	$0.00153622\pi$
$103$	51.9299	+	89.9452i	0.504174	+	0.873255i	−0.495815	+	0.868428i	$0.665130\pi$
$104$	−103.640	+	59.8364i	−0.996535	+	0.575350i
$105$		0			0
$106$	−25.9767	+	44.9929i	−0.245063	+	0.424461i
$107$		−	116.531i		−	1.08907i	−0.838738	−	0.544536i	$-0.816706\pi$
$107$		−	116.531i		−	1.08907i	0.838738	−	0.544536i	$-0.183294\pi$
$108$		0			0
$109$	−13.9837			−0.128291			−0.0641456	−	0.997941i	$-0.520432\pi$
$109$	−13.9837			−0.128291			−0.0641456	+	0.997941i	$0.520432\pi$
$110$	−46.0055	−	26.5613i	−0.418232	−	0.241466i
$111$		0			0
$112$	−13.2364	−	22.9262i	−0.118182	−	0.204698i
$113$	−45.5281	+	26.2857i	−0.402904	+	0.232617i	−0.687736	−	0.725961i	$-0.741395\pi$
$113$	−45.5281	+	26.2857i	−0.402904	+	0.232617i	0.284832	+	0.958577i	$0.408062\pi$
$114$		0			0
$115$	−53.7474	+	93.0932i	−0.467369	+	0.809506i
$116$			23.4355i			0.202030i
$117$		0			0
$118$	27.8616			0.236116
$119$	−62.4816	−	36.0738i	−0.525055	−	0.303141i
$120$		0			0
$121$	−17.7007	−	30.6585i	−0.146287	−	0.253376i
$122$	17.4750	−	10.0892i	0.143238	−	0.0826985i
$123$		0			0
$124$	−20.7536	+	35.9463i	−0.167368	+	0.289890i
$125$		−	104.300i		−	0.834400i
$126$		0			0
$127$	23.1204			0.182051			0.0910254	−	0.995849i	$-0.470986\pi$
$127$	23.1204			0.182051			0.0910254	+	0.995849i	$0.470986\pi$
$128$	−111.929	−	64.6222i	−0.874445	−	0.504861i
$129$		0			0
$130$	−63.5774	−	110.119i	−0.489057	−	0.847072i
$131$	45.2954	−	26.1513i	0.345766	−	0.199628i	−0.317053	−	0.948408i	$-0.602693\pi$
$131$	45.2954	−	26.1513i	0.345766	−	0.199628i	0.662819	+	0.748780i	$0.269360\pi$
$132$		0			0
$133$	−42.1512	+	73.0080i	−0.316926	+	0.548932i
$134$			21.3655i			0.159444i
$135$		0			0
$136$	−147.360			−1.08353
$137$	−125.826	−	72.6458i	−0.918440	−	0.530261i	−0.0353028	−	0.999377i	$-0.511240\pi$
$137$	−125.826	−	72.6458i	−0.918440	−	0.530261i	−0.883137	+	0.469115i	$0.844573\pi$
$138$		0			0
$139$	−24.3913	−	42.2470i	−0.175477	−	0.303935i	0.764849	−	0.644209i	$-0.222813\pi$
$139$	−24.3913	−	42.2470i	−0.175477	−	0.303935i	−0.940326	+	0.340274i	$0.889480\pi$
$140$	63.3122	−	36.5533i	0.452230	−	0.261095i
$141$		0			0
$142$	−14.2687	+	24.7142i	−0.100484	+	0.174043i
$143$			204.890i			1.43280i
$144$		0			0
$145$	−53.5408			−0.369247
$146$	−42.0060	−	24.2522i	−0.287712	−	0.166111i
$147$		0			0
$148$	−46.7736	−	81.0143i	−0.316038	−	0.547394i
$149$	−191.781	+	110.725i	−1.28712	+	0.743121i	−0.978140	−	0.207946i	$-0.933322\pi$
$149$	−191.781	+	110.725i	−1.28712	+	0.743121i	−0.308984	+	0.951067i	$0.599989\pi$
$150$		0			0
$151$	141.451	−	245.000i	0.936759	−	1.62251i	0.165293	−	0.986245i	$-0.447143\pi$
$151$	141.451	−	245.000i	0.936759	−	1.62251i	0.771467	−	0.636270i	$-0.219523\pi$
$152$			172.187i			1.13281i
$153$		0			0
$154$	17.6897			0.114868
$155$	−82.1229	−	47.4137i	−0.529825	−	0.305895i
$156$		0			0
$157$	−17.1992	−	29.7899i	−0.109549	−	0.189745i	0.806039	−	0.591863i	$-0.201607\pi$
$157$	−17.1992	−	29.7899i	−0.109549	−	0.189745i	−0.915588	+	0.402118i	$0.868274\pi$
$158$	−11.7464	+	6.78182i	−0.0743446	+	0.0429229i
$159$		0			0
$160$	114.597	−	198.487i	0.716229	−	1.24055i
$161$		−	35.7954i		−	0.222332i
$162$		0			0
$163$	−0.514328			−0.00315539			−0.00157769	−	0.999999i	$-0.500502\pi$
$163$	−0.514328			−0.00315539			−0.00157769	+	0.999999i	$0.500502\pi$
$164$	192.647	+	111.225i	1.17468	+	0.678199i
$165$		0			0
$166$	−28.9389	−	50.1236i	−0.174331	−	0.301950i
$167$	135.265	−	78.0955i	0.809972	−	0.467638i	−0.0369741	−	0.999316i	$-0.511772\pi$
$167$	135.265	−	78.0955i	0.809972	−	0.467638i	0.846946	+	0.531679i	$0.178439\pi$
$168$		0			0
$169$	−160.713	+	278.363i	−0.950965	+	1.64712i
$170$		−	156.574i		−	0.921021i
$171$		0			0
$172$	−56.4039			−0.327930
$173$	−66.1401	−	38.1860i	−0.382313	−	0.220728i	0.296511	−	0.955029i	$-0.404177\pi$
$173$	−66.1401	−	38.1860i	−0.382313	−	0.220728i	−0.678824	+	0.734301i	$0.737510\pi$
$174$		0			0
$175$	50.4377	+	87.3606i	0.288215	+	0.499204i
$176$	−80.1707	+	46.2866i	−0.455515	+	0.262992i
$177$		0			0
$178$	22.7384	−	39.3841i	0.127744	−	0.221259i
$179$			92.6544i			0.517622i	0.965928	+	0.258811i	$0.0833307\pi$
$179$			92.6544i			0.517622i	−0.965928	+	0.258811i	$0.916669\pi$
$180$		0			0
$181$	−150.103			−0.829296			−0.414648	−	0.909982i	$-0.636095\pi$
$181$	−150.103			−0.829296			−0.414648	+	0.909982i	$0.636095\pi$
$182$	36.6694	+	21.1711i	0.201480	+	0.116325i
$183$		0			0
$184$	−36.5559	−	63.3167i	−0.198673	−	0.344112i
$185$	185.085	−	106.859i	1.00046	−	0.577616i
$186$		0			0
$187$	−126.147	+	218.492i	−0.674581	+	1.16841i
$188$		−	1.80285i		−	0.00958964i
$189$		0			0
$190$	−182.952			−0.962904
$191$	195.742	+	113.011i	1.02483	+	0.591683i	0.915498	−	0.402323i	$-0.131797\pi$
$191$	195.742	+	113.011i	1.02483	+	0.591683i	0.109327	+	0.994006i	$0.465130\pi$
$192$		0			0
$193$	−17.7094	−	30.6735i	−0.0917583	−	0.158930i	0.816493	−	0.577356i	$-0.195915\pi$
$193$	−17.7094	−	30.6735i	−0.0917583	−	0.158930i	−0.908251	+	0.418426i	$0.862582\pi$
$194$	−29.2778	+	16.9036i	−0.150917	+	0.0871318i
$195$		0			0
$196$	−12.1721	+	21.0828i	−0.0621028	+	0.107565i
$197$		−	93.8848i		−	0.476572i	−0.971195	−	0.238286i	$-0.923414\pi$
$197$		−	93.8848i		−	0.476572i	0.971195	−	0.238286i	$-0.0765856\pi$
$198$		0			0
$199$	−20.0037			−0.100521			−0.0502607	−	0.998736i	$-0.516005\pi$
$199$	−20.0037			−0.100521			−0.0502607	+	0.998736i	$0.516005\pi$
$200$	178.433	+	103.018i	0.892166	+	0.515092i
$201$		0			0
$202$	37.5988	+	65.1230i	0.186133	+	0.322391i
$203$	15.4403	−	8.91446i	0.0760606	−	0.0439136i
$204$		0			0
$205$	−254.104	+	440.120i	−1.23953	+	2.14693i
$206$		−	75.0559i		−	0.364349i
$207$		0			0
$208$	−221.584			−1.06531
$209$	255.302	+	147.399i	1.22154	+	0.705257i
$210$		0			0
$211$	−120.501	−	208.714i	−0.571095	−	0.989166i	−0.996454	−	0.0841413i	$-0.973185\pi$
$211$	−120.501	−	208.714i	−0.571095	−	0.989166i	0.425358	−	0.905025i	$-0.360148\pi$
$212$	−216.524	+	125.010i	−1.02134	+	0.589670i
$213$		0			0
$214$	−42.1063	+	72.9303i	−0.196759	+	0.340796i
$215$		−	128.860i		−	0.599350i
$216$		0			0
$217$	31.5772			0.145517
$218$	8.75167	+	5.05278i	0.0401453	+	0.0231779i
$219$		0			0
$220$	−127.824	−	221.397i	−0.581016	−	1.00635i
$221$	−522.986	+	301.946i	−2.36645	+	1.36627i
$222$		0			0
$223$	179.333	−	310.614i	0.804185	−	1.39289i	−0.112655	−	0.993634i	$-0.535936\pi$
$223$	179.333	−	310.614i	0.804185	−	1.39289i	0.916840	−	0.399255i	$-0.130731\pi$
$224$			76.3207i			0.340717i
$225$		0			0
$226$	37.9915			0.168104
$227$	−109.914	−	63.4591i	−0.484205	−	0.279556i	0.237962	−	0.971274i	$-0.423520\pi$
$227$	−109.914	−	63.4591i	−0.484205	−	0.279556i	−0.722167	+	0.691719i	$0.756854\pi$
$228$		0			0
$229$	120.002	+	207.849i	0.524024	+	0.907637i	0.999609	+	0.0279666i	$0.00890322\pi$
$229$	120.002	+	207.849i	0.524024	+	0.907637i	−0.475585	+	0.879670i	$0.657763\pi$
$230$	67.2753	−	38.8414i	0.292501	−	0.168876i
$231$		0			0
$232$	18.2077	−	31.5366i	0.0784814	−	0.135934i
$233$			353.670i			1.51790i	0.651150	+	0.758949i	$0.274287\pi$
$233$			353.670i			1.51790i	−0.651150	+	0.758949i	$0.725713\pi$
$234$		0			0
$235$	4.11879			0.0175268
$236$	116.118	+	67.0406i	0.492025	+	0.284071i
$237$		0			0
$238$	26.0693	+	45.1533i	0.109535	+	0.189720i
$239$	399.227	−	230.494i	1.67041	−	0.964410i	0.702997	−	0.711193i	$-0.251845\pi$
$239$	399.227	−	230.494i	1.67041	−	0.964410i	0.967410	−	0.253216i	$-0.0814884\pi$
$240$		0			0
$241$	143.140	−	247.927i	0.593944	−	1.02874i	−0.399751	−	0.916624i	$-0.630904\pi$
$241$	143.140	−	247.927i	0.593944	−	1.02874i	0.993695	−	0.112117i	$-0.0357632\pi$
$242$			25.5834i			0.105716i
$243$		0			0
$244$	97.1067			0.397978
$245$	−48.1656	−	27.8084i	−0.196594	−	0.113504i
$246$		0			0
$247$	352.815	+	611.094i	1.42840	+	2.47407i
$248$	55.8553	−	32.2480i	0.225223	−	0.130032i
$249$		0			0
$250$	−37.6870	+	65.2758i	−0.150748	+	0.261103i
$251$		−	171.893i		−	0.684834i	−0.939548	−	0.342417i	$-0.888754\pi$
$251$		−	171.893i		−	0.684834i	0.939548	−	0.342417i	$-0.111246\pi$
$252$		0			0
$253$	−125.173			−0.494757
$254$	−14.4699	−	8.35417i	−0.0569679	−	0.0328904i
$255$		0			0
$256$	8.34668	+	14.4569i	0.0326042	+	0.0564721i
$257$	−413.188	+	238.554i	−1.60774	+	0.928227i	−0.617860	+	0.786288i	$0.712000\pi$
$257$	−413.188	+	238.554i	−1.60774	+	0.928227i	−0.989875	+	0.141939i	$0.954666\pi$
$258$		0			0
$259$	−35.5837	+	61.6328i	−0.137389	+	0.237964i
$260$		−	611.920i		−	2.35354i
$261$		0			0
$262$	−37.7973			−0.144264
$263$	−268.227	−	154.861i	−1.01988	−	0.588826i	−0.105808	−	0.994387i	$-0.533743\pi$
$263$	−268.227	−	154.861i	−1.01988	−	0.588826i	−0.914068	+	0.405561i	$0.867076\pi$
$264$		0			0
$265$	−285.598	−	494.670i	−1.07773	−	1.86668i
$266$	52.7604	−	30.4612i	0.198347	−	0.114516i
$267$		0			0
$268$	−51.4096	+	89.0441i	−0.191827	+	0.332254i
$269$		−	2.34739i		−	0.00872637i	−0.999990	−	0.00436318i	$-0.998611\pi$
$269$		−	2.34739i		−	0.00872637i	0.999990	−	0.00436318i	$-0.00138885\pi$
$270$		0			0
$271$	13.0921			0.0483105			0.0241553	−	0.999708i	$-0.492310\pi$
$271$	13.0921			0.0483105			0.0241553	+	0.999708i	$0.492310\pi$
$272$	−236.295	−	136.425i	−0.868731	−	0.501562i
$273$		0			0
$274$	52.4986	+	90.9303i	0.191601	+	0.331862i
$275$	305.492	−	176.376i	1.11088	−	0.641367i
$276$		0			0
$277$	−111.622	+	193.335i	−0.402968	+	0.697962i	−0.994083	−	0.108626i	$-0.965355\pi$
$277$	−111.622	+	193.335i	−0.402968	+	0.697962i	0.591114	+	0.806588i	$0.298688\pi$
$278$			35.2535i			0.126811i
$279$		0			0
$280$	−113.597			−0.405703
$281$	−36.9327	−	21.3231i	−0.131433	−	0.0758830i	0.432842	−	0.901470i	$-0.357511\pi$
$281$	−36.9327	−	21.3231i	−0.131433	−	0.0758830i	−0.564275	+	0.825587i	$0.690844\pi$
$282$		0			0
$283$	51.8436	+	89.7958i	0.183193	+	0.317300i	0.942966	−	0.332889i	$-0.108023\pi$
$283$	51.8436	+	89.7958i	0.183193	+	0.317300i	−0.759773	+	0.650188i	$0.774690\pi$
$284$	−118.934	+	68.6668i	−0.418783	+	0.241785i
$285$		0			0
$286$	74.0334	−	128.230i	0.258858	−	0.448355i
$287$		−	169.231i		−	0.589657i
$288$		0			0
$289$	−454.609			−1.57304
$290$	33.5083	+	19.3460i	0.115546	+	0.0667105i
$291$		0			0
$292$	−116.711	−	202.150i	−0.399696	−	0.692293i
$293$	279.657	−	161.460i	0.954460	−	0.551058i	0.0599964	−	0.998199i	$-0.480891\pi$
$293$	279.657	−	161.460i	0.954460	−	0.551058i	0.894464	+	0.447141i	$0.147558\pi$
$294$		0			0
$295$	−153.161	+	265.282i	−0.519190	+	0.899263i
$296$			145.359i			0.491076i
$297$		0			0
$298$	160.034			0.537028
$299$	−259.475	−	149.808i	−0.867811	−	0.501031i
$300$		0			0
$301$	21.4550	+	37.1612i	0.0712792	+	0.123459i
$302$	−177.053	+	102.222i	−0.586268	+	0.338482i
$303$		0			0
$304$	−159.409	+	276.104i	−0.524371	+	0.908237i
$305$			221.850i			0.727376i
$306$		0			0
$307$	553.767			1.80380			0.901901	−	0.431943i	$-0.142172\pi$
$307$	553.767			1.80380			0.901901	+	0.431943i	$0.142172\pi$
$308$	73.7245	+	42.5649i	0.239365	+	0.138198i
$309$		0			0
$310$	34.2642	+	59.3474i	0.110530	+	0.191443i
$311$	−244.116	+	140.941i	−0.784940	+	0.453185i	−0.838178	−	0.545397i	$-0.816379\pi$
$311$	−244.116	+	140.941i	−0.784940	+	0.453185i	0.0532384	+	0.998582i	$0.483046\pi$
$312$		0			0
$313$	211.588	−	366.480i	0.675999	−	1.17086i	−0.300177	−	0.953883i	$-0.597046\pi$
$313$	211.588	−	366.480i	0.675999	−	1.17086i	0.976176	−	0.216981i	$-0.0696208\pi$
$314$			24.8586i			0.0791674i
$315$		0			0
$316$	−65.2736			−0.206562
$317$	141.183	+	81.5121i	0.445372	+	0.257136i	0.705874	−	0.708338i	$-0.250555\pi$
$317$	141.183	+	81.5121i	0.445372	+	0.257136i	−0.260501	+	0.965473i	$0.583888\pi$
$318$		0			0
$319$	−31.1730	−	53.9933i	−0.0977212	−	0.169258i
$320$	131.952	−	76.1824i	0.412349	−	0.238070i
$321$		0			0
$322$	−12.9341	+	22.4025i	−0.0401679	+	0.0695729i
$323$			868.886i			2.69005i
$324$		0			0
$325$	844.351			2.59800
$326$	0.321891	+	0.185844i	0.000987395	+	0.000570073i
$327$		0			0
$328$	−172.827	−	299.345i	−0.526911	−	0.912636i
$329$	−1.18779	+	0.685773i	−0.00361032	+	0.00208442i
$330$		0			0
$331$	−2.84512	+	4.92789i	−0.00859553	+	0.0148879i	−0.870291	−	0.492538i	$-0.836069\pi$
$331$	−2.84512	+	4.92789i	−0.00859553	+	0.0148879i	0.861696	+	0.507425i	$0.169403\pi$
$332$		−	278.531i		−	0.838948i
$333$		0			0
$334$	−112.874			−0.337946
$335$	−203.430	−	117.450i	−0.607254	−	0.350598i
$336$		0			0
$337$	321.138	+	556.228i	0.952933	+	1.65053i	0.739029	+	0.673673i	$0.235284\pi$
$337$	321.138	+	556.228i	0.952933	+	1.65053i	0.213903	+	0.976855i	$0.431382\pi$
$338$	201.164	−	116.142i	0.595158	−	0.343615i
$339$		0			0
$340$	376.747	−	652.545i	1.10808	−	1.91925i
$341$		−	110.423i		−	0.323820i
$342$		0			0
$343$	18.5203			0.0539949
$344$	75.9013	+	43.8217i	0.220643	+	0.127389i
$345$		0			0
$346$	27.5957	+	47.7972i	0.0797564	+	0.138142i
$347$	−26.2047	+	15.1293i	−0.0755178	+	0.0436002i	−0.537283	−	0.843402i	$-0.680549\pi$
$347$	−26.2047	+	15.1293i	−0.0755178	+	0.0436002i	0.461766	+	0.887002i	$0.347216\pi$
$348$		0			0
$349$	220.179	−	381.361i	0.630884	−	1.09272i	−0.356487	−	0.934300i	$-0.616026\pi$
$349$	220.179	−	381.361i	0.630884	−	1.09272i	0.987371	−	0.158423i	$-0.0506411\pi$
$350$		−	72.8992i		−	0.208283i
$351$		0			0
$352$	266.886			0.758200
$353$	232.207	+	134.065i	0.657810	+	0.379787i	0.791442	−	0.611244i	$-0.209331\pi$
$353$	232.207	+	134.065i	0.657810	+	0.379787i	−0.133632	+	0.991031i	$0.542664\pi$
$354$		0			0
$355$	−156.876	−	271.717i	−0.441904	−	0.765401i
$356$	189.532	−	109.426i	0.532393	−	0.307377i
$357$		0			0
$358$	33.4791	−	57.9874i	0.0935169	−	0.161976i
$359$			226.280i			0.630307i	0.949041	+	0.315153i	$0.102056\pi$
$359$			226.280i			0.630307i	−0.949041	+	0.315153i	$0.897944\pi$
$360$		0			0
$361$	654.269			1.81238
$362$	93.9413	+	54.2370i	0.259506	+	0.149826i
$363$		0			0
$364$	101.884	+	176.468i	0.279900	+	0.484802i
$365$	461.830	−	266.638i	1.26529	−	0.730515i
$366$		0			0
$367$	273.088	−	473.003i	0.744110	−	1.28884i	−0.206500	−	0.978447i	$-0.566207\pi$
$367$	273.088	−	473.003i	0.744110	−	1.28884i	0.950610	−	0.310389i	$-0.100459\pi$
$368$		−	135.372i		−	0.367860i
$369$		0			0
$370$	−154.447			−0.417423
$371$	164.723	+	95.1032i	0.443999	+	0.256343i
$372$		0			0
$373$	52.5120	+	90.9535i	0.140783	+	0.243843i	0.927792	−	0.373099i	$-0.121705\pi$
$373$	52.5120	+	90.9535i	0.140783	+	0.243843i	−0.787009	+	0.616942i	$0.788371\pi$
$374$	157.897	−	91.1618i	0.422184	−	0.243748i
$375$		0			0
$376$	−1.40068	+	2.42606i	−0.00372522	+	0.00645227i
$377$		−	149.232i		−	0.395842i
$378$		0			0
$379$	101.586			0.268037			0.134019	−	0.990979i	$-0.457212\pi$
$379$	101.586			0.268037			0.134019	+	0.990979i	$0.457212\pi$
$380$	−762.481	−	440.218i	−2.00653	−	1.15847i
$381$		0			0
$382$	−81.6695	−	141.456i	−0.213794	−	0.370303i
$383$	202.404	−	116.858i	0.528469	−	0.305112i	−0.211924	−	0.977286i	$-0.567973\pi$
$383$	202.404	−	116.858i	0.528469	−	0.305112i	0.740393	+	0.672175i	$0.234640\pi$
$384$		0			0
$385$	−97.2436	+	168.431i	−0.252581	+	0.437483i
$386$			25.5959i			0.0663106i
$387$		0			0
$388$	−162.693			−0.419313
$389$	−62.6150	−	36.1508i	−0.160964	−	0.0929326i	0.417354	−	0.908744i	$-0.362957\pi$
$389$	−62.6150	−	36.1508i	−0.160964	−	0.0929326i	−0.578318	+	0.815811i	$0.696291\pi$
$390$		0			0
$391$	−184.468	−	319.508i	−0.471785	−	0.817156i
$392$	32.7595	−	18.9137i	0.0835702	−	0.0482493i
$393$		0			0
$394$	−33.9236	+	58.7575i	−0.0861006	+	0.149131i
$395$		−	149.124i		−	0.377529i
$396$		0			0
$397$	−423.076			−1.06568			−0.532842	−	0.846215i	$-0.678876\pi$
$397$	−423.076			−1.06568			−0.532842	+	0.846215i	$0.678876\pi$
$398$	12.5193	+	7.22801i	0.0314555	+	0.0181608i
$399$		0			0
$400$	190.747	+	330.383i	0.476867	+	0.825959i
$401$	314.754	−	181.723i	0.784923	−	0.453176i	−0.0532491	−	0.998581i	$-0.516958\pi$
$401$	314.754	−	181.723i	0.784923	−	0.453176i	0.838172	+	0.545406i	$0.183624\pi$
$402$		0			0
$403$	132.154	−	228.898i	0.327927	−	0.567985i
$404$			361.880i			0.895744i
$405$		0			0
$406$	−12.8843			−0.0317348
$407$	215.524	+	124.433i	0.529544	+	0.305732i
$408$		0			0
$409$	284.082	+	492.044i	0.694577	+	1.20304i	0.970323	+	0.241812i	$0.0777417\pi$
$409$	284.082	+	492.044i	0.694577	+	1.20304i	−0.275746	+	0.961230i	$0.588925\pi$
$410$	318.060	−	183.632i	0.775756	−	0.447883i
$411$		0			0
$412$	180.599	−	312.807i	0.438348	−	0.759241i
$413$		−	102.004i		−	0.246984i
$414$		0			0
$415$	636.331			1.53333
$416$	553.236	+	319.411i	1.32989	+	0.767815i
$417$		0			0
$418$	−106.520	−	184.498i	−0.254833	−	0.441383i
$419$	−552.701	+	319.102i	−1.31910	+	0.761580i	−0.983583	−	0.180456i	$-0.942243\pi$
$419$	−552.701	+	319.102i	−1.31910	+	0.761580i	−0.335512	+	0.942036i	$0.608909\pi$
$420$		0			0
$421$	−123.304	+	213.569i	−0.292883	+	0.507289i	−0.974490	−	0.224430i	$-0.927948\pi$
$421$	−123.304	+	213.569i	−0.292883	+	0.507289i	0.681607	+	0.731718i	$0.261281\pi$
$422$			174.164i			0.412711i
$423$		0			0
$424$	388.494			0.916260
$425$	900.408	+	519.851i	2.11861	+	1.22318i
$426$		0			0
$427$	−36.9376	−	63.9779i	−0.0865050	−	0.149831i
$428$	−350.970	+	202.632i	−0.820022	+	0.473440i
$429$		0			0
$430$	−46.5614	+	80.6468i	−0.108282	+	0.187551i
$431$		−	138.307i		−	0.320898i	−0.987044	−	0.160449i	$-0.948706\pi$
$431$		−	138.307i		−	0.320898i	0.987044	−	0.160449i	$-0.0512942\pi$
$432$		0			0
$433$	209.792			0.484507			0.242254	−	0.970213i	$-0.422113\pi$
$433$	209.792			0.484507			0.242254	+	0.970213i	$0.422113\pi$
$434$	−19.7625	−	11.4099i	−0.0455357	−	0.0262901i
$435$		0			0
$436$	24.3160	+	42.1165i	0.0557706	+	0.0965976i
$437$	−373.336	+	215.546i	−0.854316	+	0.493240i
$438$		0			0
$439$	−357.212	+	618.710i	−0.813696	+	1.40936i	0.0965650	+	0.995327i	$0.469214\pi$
$439$	−357.212	+	618.710i	−0.813696	+	1.40936i	−0.910261	+	0.414036i	$0.864119\pi$
$440$			397.238i			0.902813i
$441$		0			0
$442$	436.412			0.987357
$443$	−453.192	−	261.651i	−1.02301	−	0.590634i	−0.108034	−	0.994147i	$-0.534456\pi$
$443$	−453.192	−	261.651i	−1.02301	−	0.590634i	−0.914974	+	0.403513i	$0.867789\pi$
$444$		0			0
$445$	249.995	+	433.004i	0.561787	+	0.973043i
$446$	−224.470	+	129.598i	−0.503296	+	0.290578i
$447$		0			0
$448$	−25.3685	+	43.9395i	−0.0566261	+	0.0980793i
$449$		−	453.325i		−	1.00963i	−0.863227	−	0.504816i	$-0.831560\pi$
$449$		−	453.325i		−	1.00963i	0.863227	−	0.504816i	$-0.168440\pi$
$450$		0			0
$451$	−591.787			−1.31217
$452$	158.336	+	91.4151i	0.350300	+	0.202246i
$453$		0			0
$454$	45.8597	+	79.4314i	0.101013	+	0.174959i
$455$	−403.158	+	232.763i	−0.886061	+	0.511568i
$456$		0			0
$457$	−170.193	+	294.783i	−0.372413	+	0.645039i	−0.989936	−	0.141514i	$-0.954803\pi$
$457$	−170.193	+	294.783i	−0.372413	+	0.645039i	0.617523	+	0.786553i	$0.288136\pi$
$458$		−	173.442i		−	0.378694i
$459$		0			0
$460$	373.841			0.812697
$461$	−171.784	−	99.1795i	−0.372633	−	0.215140i	0.301975	−	0.953316i	$-0.402354\pi$
$461$	−171.784	−	99.1795i	−0.372633	−	0.215140i	−0.674608	+	0.738176i	$0.735687\pi$
$462$		0			0
$463$	−289.171	−	500.858i	−0.624559	−	1.08177i	−0.988626	−	0.150395i	$-0.951946\pi$
$463$	−289.171	−	500.858i	−0.624559	−	1.08177i	0.364067	−	0.931373i	$-0.381388\pi$
$464$	58.3926	−	33.7130i	0.125846	−	0.0726573i
$465$		0			0
$466$	127.793	−	221.344i	0.274233	−	0.474986i
$467$		−	867.984i		−	1.85864i	−0.369277	−	0.929319i	$-0.620395\pi$
$467$		−	867.984i		−	1.85864i	0.369277	−	0.929319i	$-0.379605\pi$
$468$		0			0
$469$	78.2212			0.166783
$470$	−2.57773	−	1.48826i	−0.00548454	−	0.00316650i
$471$		0			0
$472$	−104.171	−	180.430i	−0.220702	−	0.382267i
$473$	129.949	−	75.0263i	0.274734	−	0.158618i
$474$		0			0
$475$	607.431	−	1052.10i	1.27880	−	2.21495i
$476$			250.911i			0.527125i
$477$		0			0
$478$	−333.140			−0.696946
$479$	−626.878	−	361.928i	−1.30872	−	0.755591i	−0.326840	−	0.945080i	$-0.605984\pi$
$479$	−626.878	−	361.928i	−1.30872	−	0.755591i	−0.981883	+	0.189489i	$0.939317\pi$
$480$		0			0
$481$	297.844	+	515.881i	0.619219	+	1.07252i
$482$	−179.168	+	103.443i	−0.371718	+	0.214611i
$483$		0			0
$484$	−61.5587	+	106.623i	−0.127187	+	0.220295i
$485$		−	371.689i		−	0.766369i
$486$		0			0
$487$	−881.932			−1.81095			−0.905474	−	0.424401i	$-0.860485\pi$
$487$	−881.932			−1.81095			−0.905474	+	0.424401i	$0.860485\pi$
$488$	−130.674	−	75.4447i	−0.267775	−	0.154600i
$489$		0			0
$490$	20.0962	+	34.8077i	0.0410127	+	0.0710360i
$491$	−651.247	+	375.998i	−1.32637	+	0.765779i	−0.984736	−	0.174054i	$-0.944313\pi$
$491$	−651.247	+	375.998i	−1.32637	+	0.765779i	−0.341633	+	0.939833i	$0.610980\pi$
$492$		0			0
$493$	91.8794	−	159.140i	0.186368	−	0.322799i
$494$		−	509.935i		−	1.03226i
$495$		0			0
$496$	119.420			0.240766
$497$	90.4811	+	52.2393i	0.182054	+	0.105109i
$498$		0			0
$499$	−13.7680	−	23.8468i	−0.0275911	−	0.0477892i	0.851900	−	0.523704i	$-0.175450\pi$
$499$	−13.7680	−	23.8468i	−0.0275911	−	0.0477892i	−0.879491	+	0.475915i	$0.842117\pi$
$500$	−314.133	+	181.365i	−0.628267	+	0.362730i
$501$		0			0
$502$	−62.1107	+	107.579i	−0.123727	+	0.214301i
$503$			820.917i			1.63204i	0.578022	+	0.816021i	$0.303825\pi$
$503$			820.917i			1.63204i	−0.578022	+	0.816021i	$0.696175\pi$
$504$		0			0
$505$	−826.751			−1.63713
$506$	78.3394	+	45.2293i	0.154821	+	0.0893859i
$507$		0			0
$508$	−40.2036	−	69.6347i	−0.0791410	−	0.137076i
$509$	−424.587	+	245.135i	−0.834159	+	0.481602i	−0.855274	−	0.518175i	$-0.826611\pi$
$509$	−424.587	+	245.135i	−0.834159	+	0.481602i	0.0211158	+	0.999777i	$0.493278\pi$
$510$		0			0
$511$	−88.7896	+	153.788i	−0.173757	+	0.300955i
$512$			504.914i			0.986160i
$513$		0			0
$514$	344.790			0.670798
$515$	714.639	+	412.597i	1.38765	+	0.801159i
$516$		0			0
$517$	2.39809	+	4.15361i	0.00463846	+	0.00803406i
$518$	44.5399	−	25.7151i	0.0859844	−	0.0496431i
$519$		0			0
$520$	−475.416	+	823.445i	−0.914262	+	1.58355i
$521$		−	424.710i		−	0.815182i	−0.913164	−	0.407591i	$-0.866369\pi$
$521$		−	424.710i		−	0.815182i	0.913164	−	0.407591i	$-0.133631\pi$
$522$		0			0
$523$	745.325			1.42510			0.712548	−	0.701624i	$-0.247541\pi$
$523$	745.325			1.42510			0.712548	+	0.701624i	$0.247541\pi$
$524$	−157.526	−	90.9478i	−0.300622	−	0.173564i
$525$		0			0
$526$	111.913	+	193.839i	0.212762	+	0.368515i
$527$	281.856	−	162.730i	0.534832	−	0.308785i
$528$		0			0
$529$	−172.978	+	299.606i	−0.326990	+	0.566363i
$530$			412.783i			0.778836i
$531$		0			0
$532$	293.183			0.551096
$533$	−1226.73	−	708.254i	−2.30156	−	1.32881i
$534$		0			0
$535$	−462.934	−	801.824i	−0.865296	−	1.49874i
$536$	138.361	−	79.8830i	0.258137	−	0.149035i
$537$		0			0
$538$	−0.848190	+	1.46911i	−0.00157656	+	0.00273068i
$539$		−	64.7637i		−	0.120155i
$540$		0			0
$541$	−2.11927			−0.00391732			−0.00195866	−	0.999998i	$-0.500623\pi$
$541$	−2.11927			−0.00391732			−0.00195866	+	0.999998i	$0.500623\pi$
$542$	−8.19368	−	4.73062i	−0.0151175	−	0.00872809i
$543$		0			0
$544$	393.311	+	681.234i	0.722997	+	1.25227i
$545$	−96.2193	+	55.5523i	−0.176549	+	0.101931i
$546$		0			0
$547$	86.0063	−	148.967i	0.157233	−	0.272335i	−0.776637	−	0.629948i	$-0.783076\pi$
$547$	86.0063	−	148.967i	0.157233	−	0.272335i	0.933870	+	0.357613i	$0.116409\pi$
$548$			505.289i			0.922059i
$549$		0			0
$550$	−254.922			−0.463494
$551$	−185.950	−	107.359i	−0.337478	−	0.194843i
$552$		0			0
$553$	24.8289	+	43.0049i	0.0448986	+	0.0777666i
$554$	139.717	−	80.6656i	0.252197	−	0.145606i
$555$		0			0
$556$	−84.8270	+	146.925i	−0.152567	+	0.264253i
$557$		−	866.241i		−	1.55519i	−0.628765	−	0.777595i	$-0.716439\pi$
$557$		−	866.241i		−	1.55519i	0.628765	−	0.777595i	$-0.283561\pi$
$558$		0			0
$559$	359.168			0.642518
$560$	−182.154	−	105.167i	−0.325276	−	0.187798i
$561$		0			0
$562$	15.4095	+	26.6900i	0.0274190	+	0.0474911i
$563$	−428.587	+	247.445i	−0.761256	+	0.439511i	−0.829746	−	0.558140i	$-0.811515\pi$
$563$	−428.587	+	247.445i	−0.761256	+	0.439511i	0.0684906	+	0.997652i	$0.478182\pi$
$564$		0			0
$565$	−208.847	+	361.733i	−0.369640	+	0.640236i
$566$		−	74.9312i		−	0.132387i
$567$		0			0
$568$	213.396			0.375697
$569$	412.906	+	238.392i	0.725670	+	0.418966i	0.816836	−	0.576870i	$-0.195726\pi$
$569$	412.906	+	238.392i	0.725670	+	0.418966i	−0.0911657	+	0.995836i	$0.529059\pi$
$570$		0			0
$571$	−362.318	−	627.553i	−0.634532	−	1.09904i	−0.986614	−	0.163073i	$-0.947859\pi$
$571$	−362.318	−	627.553i	−0.634532	−	1.09904i	0.352082	−	0.935969i	$-0.385474\pi$
$572$	617.092	−	356.278i	1.07883	−	0.622864i
$573$		0			0
$574$	−61.1489	+	105.913i	−0.106531	+	0.184517i
$575$			515.840i			0.897113i
$576$		0			0
$577$	74.4585			0.129044			0.0645221	−	0.997916i	$-0.479448\pi$
$577$	74.4585			0.129044			0.0645221	+	0.997916i	$0.479448\pi$
$578$	284.516	+	164.265i	0.492242	+	0.284196i
$579$		0			0
$580$	93.1008	+	161.255i	0.160519	+	0.278026i
$581$	−183.508	+	105.948i	−0.315848	+	0.182355i
$582$		0			0
$583$	332.567	−	576.023i	0.570441	−	0.988033i
$584$			362.704i			0.621068i
$585$		0			0
$586$	−233.363			−0.398230
$587$	649.543	+	375.014i	1.10655	+	0.638865i	0.937933	−	0.346817i	$-0.112738\pi$
$587$	649.543	+	375.014i	1.10655	+	0.638865i	0.168614	+	0.985682i	$0.446071\pi$
$588$		0			0
$589$	−190.145	−	329.341i	−0.322827	−	0.559153i
$590$	191.711	−	110.684i	0.324933	−	0.187600i
$591$		0			0
$592$	−134.572	+	233.085i	−0.227317	+	0.393725i
$593$		−	830.097i		−	1.39983i	−0.714228	−	0.699913i	$-0.753222\pi$
$593$		−	830.097i		−	1.39983i	0.714228	−	0.699913i	$-0.246778\pi$
$594$		0			0
$595$	−573.231			−0.963414
$596$	666.969	+	385.075i	1.11908	+	0.646098i
$597$		0			0
$598$	108.261	+	187.514i	0.181039	+	0.313569i
$599$	546.791	−	315.690i	0.912840	−	0.527029i	0.0314964	−	0.999504i	$-0.489973\pi$
$599$	546.791	−	315.690i	0.912840	−	0.527029i	0.881344	+	0.472475i	$0.156639\pi$
$600$		0			0
$601$	−272.658	+	472.257i	−0.453674	+	0.785786i	−0.998611	−	0.0526910i	$-0.983220\pi$
$601$	−272.658	+	472.257i	−0.453674	+	0.785786i	0.544937	+	0.838477i	$0.316553\pi$
$602$		−	31.0096i		−	0.0515110i
$603$		0			0
$604$	−983.861			−1.62891
$605$	−243.590	−	140.637i	−0.402628	−	0.232458i
$606$		0			0
$607$	−2.63026	−	4.55575i	−0.00433321	−	0.00750535i	0.863851	−	0.503748i	$-0.168046\pi$
$607$	−2.63026	−	4.55575i	−0.00433321	−	0.00750535i	−0.868184	+	0.496243i	$0.834713\pi$
$608$	796.003	−	459.572i	1.30921	−	0.755876i
$609$		0			0
$610$	80.1616	−	138.844i	0.131412	−	0.227613i
$611$			11.4802i			0.0187891i
$612$		0			0
$613$	−428.462			−0.698959			−0.349480	−	0.936944i	$-0.613642\pi$
$613$	−428.462			−0.698959			−0.349480	+	0.936944i	$0.613642\pi$
$614$	−346.573	−	200.094i	−0.564452	−	0.325886i
$615$		0			0
$616$	−66.1395	−	114.557i	−0.107369	−	0.185969i
$617$	905.611	−	522.855i	1.46777	−	0.847415i	0.468417	−	0.883508i	$-0.344825\pi$
$617$	905.611	−	522.855i	1.46777	−	0.847415i	0.999348	+	0.0360927i	$0.0114912\pi$
$618$		0			0
$619$	349.652	−	605.615i	0.564866	−	0.978377i	−0.432196	−	0.901780i	$-0.642261\pi$
$619$	349.652	−	605.615i	0.564866	−	0.978377i	0.997062	−	0.0765973i	$-0.0244056\pi$
$620$			329.786i			0.531913i
$621$		0			0
$622$	203.706			0.327501
$623$	−144.189	−	83.2476i	−0.231443	−	0.133624i
$624$		0			0
$625$	62.2454	+	107.812i	0.0995927	+	0.172500i
$626$	−264.843	+	152.907i	−0.423072	+	0.244261i
$627$		0			0
$628$	−59.8147	+	103.602i	−0.0952463	+	0.164971i
$629$			733.507i			1.16615i
$630$		0			0
$631$	−748.642			−1.18644			−0.593218	−	0.805042i	$-0.702143\pi$
$631$	−748.642			−1.18644			−0.593218	+	0.805042i	$0.702143\pi$
$632$	87.8371	+	50.7127i	0.138983	+	0.0802417i
$633$		0			0
$634$	−58.9060	−	102.028i	−0.0929116	−	0.160928i
$635$	159.087	−	91.8491i	0.250531	−	0.144644i
$636$		0			0
$637$	77.5095	−	134.250i	0.121679	−	0.210754i
$638$			45.0554i			0.0706197i
$639$		0			0
$640$	−1026.88			−1.60450
$641$	57.2317	+	33.0427i	0.0892850	+	0.0515487i	0.543978	−	0.839100i	$-0.316918\pi$
$641$	57.2317	+	33.0427i	0.0892850	+	0.0515487i	−0.454693	+	0.890648i	$0.650251\pi$
$642$		0			0
$643$	−381.603	−	660.956i	−0.593473	−	1.02792i	−0.993760	−	0.111535i	$-0.964423\pi$
$643$	−381.603	−	660.956i	−0.593473	−	1.02792i	0.400288	−	0.916389i	$-0.368910\pi$
$644$	−107.810	+	62.2439i	−0.167406	+	0.0966520i
$645$		0			0
$646$	313.957	−	543.790i	0.486002	−	0.841780i
$647$			522.507i			0.807585i	0.914851	+	0.403792i	$0.132308\pi$
$647$			522.507i			0.807585i	−0.914851	+	0.403792i	$0.867692\pi$
$648$		0			0
$649$	−356.700			−0.549614
$650$	−528.434	−	305.092i	−0.812976	−	0.469372i
$651$		0			0
$652$	0.894354	+	1.54907i	0.00137171	+	0.00237587i
$653$	−33.3856	+	19.2752i	−0.0511266	+	0.0295179i	−0.525345	−	0.850889i	$-0.676064\pi$
$653$	−33.3856	+	19.2752i	−0.0511266	+	0.0295179i	0.474219	+	0.880407i	$0.342731\pi$
$654$		0			0
$655$	207.779	−	359.884i	0.317220	−	0.549441i
$656$		−	640.005i		−	0.975618i
$657$		0			0
$658$	0.991169			0.00150634
$659$	648.715	+	374.536i	0.984393	+	0.568339i	0.903594	−	0.428391i	$-0.140919\pi$
$659$	648.715	+	374.536i	0.984393	+	0.568339i	0.0807994	+	0.996730i	$0.474253\pi$
$660$		0			0
$661$	−302.683	−	524.263i	−0.457917	−	0.793135i	0.540934	−	0.841065i	$-0.318071\pi$
$661$	−302.683	−	524.263i	−0.457917	−	0.793135i	−0.998851	+	0.0479297i	$0.984738\pi$
$662$	3.56122	−	2.05607i	0.00537948	−	0.00310585i
$663$		0			0
$664$	−216.398	+	374.812i	−0.325900	+	0.564476i
$665$			669.805i			1.00723i
$666$		0			0
$667$	91.1706			0.136688
$668$	−470.420	−	271.597i	−0.704221	−	0.406582i
$669$		0			0
$670$	84.8773	+	147.012i	0.126683	+	0.219421i
$671$	−223.725	+	129.168i	−0.333420	+	0.192500i
$672$		0			0
$673$	−521.052	+	902.488i	−0.774222	+	1.34099i	0.161008	+	0.986953i	$0.448525\pi$
$673$	−521.052	+	902.488i	−0.774222	+	1.34099i	−0.935231	+	0.354039i	$0.884808\pi$
$674$		−	464.151i		−	0.688652i
$675$		0			0
$676$	1117.84			1.65361
$677$	37.1218	+	21.4323i	0.0548328	+	0.0316577i	0.527166	−	0.849762i	$-0.323255\pi$
$677$	37.1218	+	21.4323i	0.0548328	+	0.0316577i	−0.472333	+	0.881420i	$0.656588\pi$
$678$		0			0
$679$	61.8856	+	107.189i	0.0911423	+	0.157863i
$680$	−1013.96	+	585.409i	−1.49112	+	0.860896i
$681$		0			0
$682$	−39.8993	+	69.1077i	−0.0585034	+	0.101331i
$683$			1041.21i			1.52446i	0.647305	+	0.762231i	$0.275896\pi$
$683$			1041.21i			1.52446i	−0.647305	+	0.762231i	$0.724104\pi$
$684$		0			0
$685$	−1154.38			−1.68523
$686$	−11.5908	−	6.69198i	−0.0168963	−	0.00975507i
$687$		0			0
$688$	81.1394	+	140.538i	0.117935	+	0.204270i
$689$	1378.77	−	796.036i	2.00112	−	1.15535i
$690$		0			0
$691$	260.512	−	451.219i	0.377007	−	0.652995i	−0.613618	−	0.789603i	$-0.710287\pi$
$691$	260.512	−	451.219i	0.377007	−	0.652995i	0.990625	+	0.136608i	$0.0436200\pi$
$692$			265.603i			0.383819i
$693$		0			0
$694$	21.8668			0.0315084
$695$	−335.664	−	193.796i	−0.482969	−	0.278843i
$696$		0			0
$697$	−872.116	−	1510.55i	−1.25124	−	2.16722i
$698$	−275.596	+	159.116i	−0.394837	+	0.227959i
$699$		0			0
$700$	175.410	−	303.819i	0.250586	−	0.434027i
$701$			249.669i			0.356161i	0.984016	+	0.178080i	$0.0569887\pi$
$701$			249.669i			0.356161i	−0.984016	+	0.178080i	$0.943011\pi$
$702$		0			0
$703$	857.083			1.21918
$704$	153.653	+	88.7114i	0.218257	+	0.126010i
$705$		0			0
$706$	−96.8840	−	167.808i	−0.137229	−	0.237688i
$707$	238.422	−	137.653i	0.337230	−	0.194700i
$708$		0			0
$709$	−525.086	+	909.476i	−0.740601	+	1.28276i	0.211621	+	0.977352i	$0.432126\pi$
$709$	−525.086	+	909.476i	−0.740601	+	1.28276i	−0.952222	+	0.305407i	$0.901208\pi$
$710$			226.738i			0.319349i
$711$		0			0
$712$	−340.065			−0.477619
$713$	139.841	+	80.7372i	0.196130	+	0.113236i
$714$		0			0
$715$	813.952	+	1409.81i	1.13839	+	1.97176i
$716$	279.059	−	161.115i	0.389747	−	0.225020i
$717$		0			0
$718$	81.7624	−	141.617i	0.113875	−	0.197238i
$719$			121.143i			0.168488i	0.996445	+	0.0842441i	$0.0268476\pi$
$719$			121.143i			0.168488i	−0.996445	+	0.0842441i	$0.973152\pi$
$720$		0			0
$721$	−274.787			−0.381120
$722$	−409.472	−	236.409i	−0.567136	−	0.327436i
$723$		0			0
$724$	261.010	+	452.083i	0.360511	+	0.624424i
$725$	−222.507	+	128.464i	−0.306906	+	0.177192i
$726$		0			0
$727$	−480.719	+	832.629i	−0.661236	+	1.14529i	0.319055	+	0.947736i	$0.396635\pi$
$727$	−480.719	+	832.629i	−0.661236	+	1.14529i	−0.980291	+	0.197559i	$0.936699\pi$
$728$		−	316.624i		−	0.434924i
$729$		0			0
$730$	−385.380			−0.527918
$731$	383.013	+	221.132i	0.523957	+	0.302507i
$732$		0			0
$733$	−80.5916	−	139.589i	−0.109948	−	0.190435i	0.805801	−	0.592186i	$-0.201735\pi$
$733$	−80.5916	−	139.589i	−0.109948	−	0.190435i	−0.915749	+	0.401751i	$0.868402\pi$
$734$	−341.823	+	197.352i	−0.465699	+	0.268871i
$735$		0			0
$736$	−195.138	+	337.989i	−0.265133	+	0.459224i
$737$		−	273.533i		−	0.371143i
$738$		0			0
$739$	−643.023			−0.870126			−0.435063	−	0.900400i	$-0.643274\pi$
$739$	−643.023			−0.870126			−0.435063	+	0.900400i	$0.643274\pi$
$740$	−643.681	−	371.629i	−0.869839	−	0.502202i
$741$		0			0
$742$	−68.7278	−	119.040i	−0.0926250	−	0.160431i
$743$	−43.0660	+	24.8642i	−0.0579623	+	0.0334646i	−0.528701	−	0.848808i	$-0.677321\pi$
$743$	−43.0660	+	24.8642i	−0.0579623	+	0.0334646i	0.470739	+	0.882273i	$0.343987\pi$
$744$		0			0
$745$	−879.741	+	1523.76i	−1.18086	+	2.04531i
$746$		−	75.8973i		−	0.101739i
$747$		0			0
$748$	877.414			1.17301
$749$	267.005	+	154.155i	0.356482	+	0.205815i
$750$		0			0
$751$	−483.069	−	836.700i	−0.643235	−	1.11412i	−0.984706	−	0.174223i	$-0.944259\pi$
$751$	−483.069	−	836.700i	−0.643235	−	1.11412i	0.341472	−	0.939892i	$-0.389075\pi$
$752$	−4.49204	+	2.59348i	−0.00597346	+	0.00344878i
$753$		0			0
$754$	−53.9225	+	93.3965i	−0.0715153	+	0.123868i
$755$		−	2247.73i		−	2.97712i
$756$		0			0
$757$	136.110			0.179802			0.0899009	−	0.995951i	$-0.471345\pi$
$757$	136.110			0.179802			0.0899009	+	0.995951i	$0.471345\pi$
$758$	−63.5773	−	36.7064i	−0.0838751	−	0.0484253i
$759$		0			0
$760$	684.034	+	1184.78i	0.900045	+	1.55892i
$761$	1161.18	−	670.408i	1.52586	−	0.880957i	0.526333	−	0.850278i	$-0.323566\pi$
$761$	1161.18	−	670.408i	1.52586	−	0.880957i	0.999529	−	0.0306790i	$-0.00976695\pi$
$762$		0			0
$763$	18.4987	−	32.0408i	0.0242447	−	0.0419931i
$764$		−	786.052i		−	1.02886i
$765$		0			0
$766$	−168.898			−0.220494
$767$	−739.412	−	426.900i	−0.964032	−	0.556584i
$768$		0			0
$769$	286.095	+	495.530i	0.372035	+	0.644383i	0.989878	−	0.141918i	$-0.0453269\pi$
$769$	286.095	+	495.530i	0.372035	+	0.644383i	−0.617844	+	0.786301i	$0.711994\pi$
$770$	121.719	−	70.2746i	0.158077	−	0.0912657i
$771$		0			0
$772$	−61.5888	+	106.675i	−0.0797782	+	0.138180i
$773$		−	628.925i		−	0.813616i	−0.913514	−	0.406808i	$-0.866642\pi$
$773$		−	628.925i		−	0.813616i	0.913514	−	0.406808i	$-0.133358\pi$
$774$		0			0
$775$	−455.052			−0.587164
$776$	218.932	+	126.401i	0.282129	+	0.162887i
$777$		0			0
$778$	26.1249	+	45.2497i	0.0335796	+	0.0581616i
$779$	−1765.04	+	1019.04i	−2.26577	+	1.30814i
$780$		0			0
$781$	182.676	−	316.404i	0.233900	−	0.405127i
$782$			266.617i			0.340943i
$783$		0			0
$784$	70.0405			0.0893374
$785$	−236.689	−	136.652i	−0.301515	−	0.174080i
$786$		0			0
$787$	133.061	+	230.469i	0.169074	+	0.292845i	0.938095	−	0.346379i	$-0.112589\pi$
$787$	133.061	+	230.469i	0.169074	+	0.292845i	−0.769020	+	0.639224i	$0.779256\pi$
$788$	−282.764	+	163.254i	−0.358838	+	0.207175i
$789$		0			0
$790$	−53.8834	+	93.3287i	−0.0682068	+	0.118138i
$791$		−	139.091i		−	0.175842i
$792$		0			0
$793$	−618.354			−0.779765
$794$	264.781	+	152.871i	0.333477	+	0.192533i
$795$		0			0
$796$	34.7841	+	60.2477i	0.0436986	+	0.0756881i
$797$	−620.719	+	358.372i	−0.778819	+	0.449651i	−0.836012	−	0.548712i	$-0.815118\pi$
$797$	−620.719	+	358.372i	−0.778819	+	0.449651i	0.0571926	+	0.998363i	$0.481785\pi$
$798$		0			0
$799$	−7.06812	+	12.2423i	−0.00884620	+	0.0153221i
$800$		−	1099.84i		−	1.37480i
$801$		0			0
$802$	−262.651			−0.327494
$803$	537.783	+	310.489i	0.669718	+	0.386662i
$804$		0			0
$805$	−142.202	−	246.302i	−0.176649	−	0.305965i
$806$	−165.417	+	95.5034i	−0.205232	+	0.118491i
$807$		0			0
$808$	281.154	−	486.974i	0.347963	−	0.602690i
$809$			591.782i			0.731498i	0.930713	+	0.365749i	$0.119187\pi$
$809$			591.782i			0.731498i	−0.930713	+	0.365749i	$0.880813\pi$
$810$		0			0
$811$	−1308.23			−1.61311			−0.806555	−	0.591159i	$-0.798670\pi$
$811$	−1308.23			−1.61311			−0.806555	+	0.591159i	$0.798670\pi$
$812$	−53.6976	−	31.0023i	−0.0661300	−	0.0381802i
$813$		0			0
$814$	−89.9235	−	155.752i	−0.110471	−	0.191342i
$815$	−3.53899	+	2.04324i	−0.00434232	+	0.00250704i
$816$		0			0
$817$	258.387	−	447.540i	0.316263	−	0.547784i
$818$		−	410.593i		−	0.501947i
$819$		0			0
$820$	1767.42			2.15539
$821$	123.467	+	71.2835i	0.150386	+	0.0868252i	0.573305	−	0.819342i	$-0.305661\pi$
$821$	123.467	+	71.2835i	0.150386	+	0.0868252i	−0.422919	+	0.906168i	$0.638995\pi$
$822$		0			0
$823$	−56.5030	−	97.8661i	−0.0686550	−	0.118914i	0.829655	−	0.558277i	$-0.188537\pi$
$823$	−56.5030	−	97.8661i	−0.0686550	−	0.118914i	−0.898309	+	0.439363i	$0.855204\pi$
$824$	−486.056	+	280.625i	−0.589874	+	0.340564i
$825$		0			0
$826$	−36.8575	+	63.8390i	−0.0446217	+	0.0772870i
$827$		−	69.0940i		−	0.0835477i	−0.999127	−	0.0417739i	$-0.986699\pi$
$827$		−	69.0940i		−	0.0835477i	0.999127	−	0.0417739i	$-0.0133009\pi$
$828$		0			0
$829$	−107.675			−0.129885			−0.0649426	−	0.997889i	$-0.520686\pi$
$829$	−107.675			−0.129885			−0.0649426	+	0.997889i	$0.520686\pi$
$830$	−398.246	−	229.927i	−0.479814	−	0.277021i
$831$		0			0
$832$	212.340	+	367.784i	0.255217	+	0.442049i
$833$	165.311	−	95.4422i	0.198452	−	0.114576i
$834$		0			0
$835$	620.490	−	1074.72i	0.743101	−	1.28709i
$836$		−	1025.23i		−	1.22636i
$837$		0			0
$838$	461.208			0.550368
$839$	400.896	+	231.457i	0.477825	+	0.275873i	0.719510	−	0.694482i	$-0.244367\pi$
$839$	400.896	+	231.457i	0.477825	+	0.275873i	−0.241684	+	0.970355i	$0.577700\pi$
$840$		0			0
$841$	−397.795	−	689.001i	−0.473002	−	0.819264i
$842$	154.339	−	89.1075i	0.183300	−	0.105828i
$843$		0			0
$844$	−419.073	+	725.856i	−0.496532	+	0.860019i
$845$			2553.82i			3.02227i
$846$		0			0
$847$	93.6633			0.110582
$848$	622.957	+	359.664i	0.734619	+	0.424132i
$849$		0			0
$850$	−375.678	−	650.694i	−0.441974	−	0.765522i
$851$	−315.168	+	181.962i	−0.370350	+	0.213822i
$852$		0			0
$853$	445.477	−	771.589i	0.522247	−	0.904559i	−0.477418	−	0.878676i	$-0.658427\pi$
$853$	445.477	−	771.589i	0.522247	−	0.904559i	0.999665	−	0.0258823i	$-0.00823951\pi$
$854$			53.3871i			0.0625142i
$855$		0			0
$856$	629.722			0.735656
$857$	−532.608	−	307.501i	−0.621479	−	0.358811i	0.155965	−	0.987763i	$-0.450151\pi$
$857$	−532.608	−	307.501i	−0.621479	−	0.358811i	−0.777445	+	0.628951i	$0.783485\pi$
$858$		0			0
$859$	−17.2489	−	29.8760i	−0.0200802	−	0.0347800i	0.855811	−	0.517289i	$-0.173059\pi$
$859$	−17.2489	−	29.8760i	−0.0200802	−	0.0347800i	−0.875891	+	0.482509i	$0.839725\pi$
$860$	−388.104	+	224.072i	−0.451284	+	0.260549i
$861$		0			0
$862$	−49.9748	+	86.5589i	−0.0579754	+	0.100416i
$863$		−	588.277i		−	0.681665i	−0.940124	−	0.340832i	$-0.889291\pi$
$863$		−	588.277i		−	0.681665i	0.940124	−	0.340832i	$-0.110709\pi$
$864$		0			0
$865$	−606.796			−0.701498
$866$	−131.297	−	75.8046i	−0.151614	−	0.0875341i
$867$		0			0
$868$	−54.9089	−	95.1050i	−0.0632591	−	0.109568i
$869$	150.384	−	86.8244i	0.173054	−	0.0999130i
$870$		0			0
$871$	327.365	−	567.013i	0.375850	−	0.650991i
$872$		−	75.5669i		−	0.0866593i
$873$		0			0
$874$	311.535			0.356447
$875$	238.981	+	137.976i	0.273122	+	0.157687i
$876$		0			0
$877$	−33.2143	−	57.5288i	−0.0378726	−	0.0655972i	0.846468	−	0.532440i	$-0.178725\pi$
$877$	−33.2143	−	57.5288i	−0.0378726	−	0.0655972i	−0.884340	+	0.466843i	$0.845391\pi$
$878$	447.120	−	258.145i	0.509249	−	0.294015i
$879$		0			0
$880$	−367.759	+	636.978i	−0.417908	+	0.723838i
$881$			1060.27i			1.20349i	0.798689	+	0.601744i	$0.205527\pi$
$881$			1060.27i			1.20349i	−0.798689	+	0.601744i	$0.794473\pi$
$882$		0			0
$883$	828.431			0.938201			0.469100	−	0.883145i	$-0.344578\pi$
$883$	828.431			0.938201			0.469100	+	0.883145i	$0.344578\pi$
$884$	1818.82	+	1050.09i	2.05748	+	1.18789i
$885$		0			0
$886$	189.086	+	327.507i	0.213415	+	0.369646i
$887$	−247.317	+	142.788i	−0.278824	+	0.160979i	−0.632891	−	0.774241i	$-0.718132\pi$
$887$	−247.317	+	142.788i	−0.278824	+	0.160979i	0.354067	+	0.935220i	$0.384798\pi$
$888$		0			0
$889$	−30.5855	+	52.9756i	−0.0344044	+	0.0595901i
$890$		−	361.326i		−	0.405984i
$891$		0			0
$892$	−1247.35			−1.39838
$893$	14.3048	+	8.25890i	0.0160188	+	0.00924849i
$894$		0			0
$895$	368.082	+	637.537i	0.411265	+	0.712332i
$896$	296.136	−	170.974i	0.330509	−	0.190820i
$897$		0			0
$898$	−163.801	+	283.712i	−0.182407	+	0.315938i
$899$			80.4268i			0.0894625i
$900$		0			0
$901$	1960.42			2.17582
$902$	370.368	+	213.832i	0.410608	+	0.237064i
$903$		0			0
$904$	−142.046	−	246.030i	−0.157130	−	0.272157i
$905$	−1032.83	+	596.303i	−1.14125	+	0.658898i
$906$		0			0
$907$	−383.301	+	663.897i	−0.422604	+	0.731971i	−0.996193	−	0.0871720i	$-0.972217\pi$
$907$	−383.301	+	663.897i	−0.422604	+	0.731971i	0.573590	+	0.819143i	$0.305550\pi$
$908$			441.391i			0.486113i
$909$		0			0
$910$	336.420			0.369692
$911$	952.587	+	549.976i	1.04565	+	0.603706i	0.921428	−	0.388549i	$-0.127023\pi$
$911$	952.587	+	549.976i	1.04565	+	0.603706i	0.124221	+	0.992255i	$0.460357\pi$
$912$		0			0
$913$	370.491	+	641.709i	0.405795	+	0.702858i
$914$	213.029	−	122.993i	0.233074	−	0.134565i
$915$		0			0
$916$	417.336	−	722.847i	0.455607	−	0.789134i
$917$			138.380i			0.150905i
$918$		0			0
$919$	411.489			0.447757			0.223879	−	0.974617i	$-0.428128\pi$
$919$	411.489			0.447757			0.223879	+	0.974617i	$0.428128\pi$
$920$	−503.068	−	290.446i	−0.546813	−	0.315703i
$921$		0			0
$922$	71.6736	+	124.142i	0.0777371	+	0.134645i
$923$	757.348	−	437.255i	0.820529	−	0.473732i
$924$		0			0
$925$	512.789	−	888.176i	0.554366	−	0.960190i
$926$			417.947i			0.451347i
$927$		0			0
$928$	−194.388			−0.209470
$929$	188.407	+	108.777i	0.202806	+	0.117090i	0.597964	−	0.801523i	$-0.295977\pi$
$929$	188.407	+	108.777i	0.202806	+	0.117090i	−0.395158	+	0.918613i	$0.629310\pi$
$930$		0			0
$931$	−111.522	−	193.161i	−0.119787	−	0.207477i
$932$	1065.19	−	614.989i	1.14291	−	0.659860i
$933$		0			0
$934$	−313.631	+	543.225i	−0.335794	+	0.581611i
$935$			2004.54i			2.14389i
$936$		0			0
$937$	−674.025			−0.719344			−0.359672	−	0.933079i	$-0.617111\pi$
$937$	−674.025			−0.719344			−0.359672	+	0.933079i	$0.617111\pi$
$938$	−48.9545	−	28.2639i	−0.0521903	−	0.0301321i
$939$		0			0
$940$	−7.16208	−	12.4051i	−0.00761923	−	0.0131969i
$941$	1329.99	−	767.870i	1.41338	−	0.816015i	0.417675	−	0.908597i	$-0.362845\pi$
$941$	1329.99	−	767.870i	1.41338	−	0.816015i	0.995705	+	0.0925814i	$0.0295118\pi$
$942$		0			0
$943$	432.694	−	749.448i	0.458848	−	0.794749i
$944$		−	385.763i		−	0.408647i
$945$		0			0
$946$	−108.438			−0.114628
$947$	−270.500	−	156.173i	−0.285639	−	0.164914i	0.350334	−	0.936625i	$-0.386068\pi$
$947$	−270.500	−	156.173i	−0.285639	−	0.164914i	−0.635974	+	0.771711i	$0.719401\pi$
$948$		0			0
$949$	743.190	+	1287.24i	0.783130	+	1.35642i
$950$	−760.317	+	438.969i	−0.800334	+	0.462073i
$951$		0			0
$952$	194.940	−	337.645i	0.204768	−	0.354669i
$953$		−	842.068i		−	0.883597i	−0.897114	−	0.441798i	$-0.854341\pi$
$953$		−	842.068i		−	0.883597i	0.897114	−	0.441798i	$-0.145659\pi$
$954$		0			0
$955$	1795.81			1.88043
$956$	−1388.41	−	801.601i	−1.45232	−	0.838495i
$957$		0			0
$958$	261.553	+	453.023i	0.273020	+	0.472884i
$959$	332.905	−	192.203i	0.347138	−	0.200420i
$960$		0			0
$961$	409.277	−	708.889i	0.425887	−	0.737657i
$962$		−	430.483i		−	0.447488i
$963$		0			0
$964$	−995.615			−1.03280
$965$	−243.709	−	140.706i	−0.252548	−	0.145809i
$966$		0			0
$967$	−635.238	−	1100.26i	−0.656916	−	1.13781i	−0.981410	−	0.191924i	$-0.938527\pi$
$967$	−635.238	−	1100.26i	−0.656916	−	1.13781i	0.324494	−	0.945888i	$-0.394806\pi$
$968$	165.676	−	95.6531i	0.171153	−	0.0988152i
$969$		0			0
$970$	−134.303	+	232.620i	−0.138457	+	0.239815i
$971$			140.610i			0.144810i	0.997375	+	0.0724048i	$0.0230673\pi$
$971$			140.610i			0.144810i	−0.997375	+	0.0724048i	$0.976933\pi$
$972$		0			0
$973$	129.067			0.132648
$974$	551.954	+	318.671i	0.566688	+	0.327178i
$975$		0			0
$976$	−139.692	−	241.954i	−0.143127	−	0.247903i
$977$	−713.685	+	412.046i	−0.730486	+	0.421747i	−0.818600	−	0.574364i	$-0.805249\pi$
$977$	−713.685	+	412.046i	−0.730486	+	0.421747i	0.0881137	+	0.996110i	$0.471916\pi$
$978$		0			0
$979$	−291.109	+	504.216i	−0.297354	+	0.515032i
$980$			193.422i			0.197369i
$981$		0			0
$982$	543.441			0.553403
$983$	166.240	+	95.9789i	0.169115	+	0.0976387i	0.582169	−	0.813068i	$-0.302204\pi$
$983$	166.240	+	95.9789i	0.169115	+	0.0976387i	−0.413053	+	0.910707i	$0.635538\pi$
$984$		0			0
$985$	−372.970	−	646.003i	−0.378650	−	0.655840i
$986$	−115.005	+	66.3981i	−0.116638	+	0.0673409i
$987$		0			0
$988$	1227.01	−	2125.24i	1.24191	−	2.15105i
$989$			219.426i			0.221867i
$990$		0			0
$991$	1913.96			1.93135			0.965673	−	0.259761i	$-0.0836438\pi$
$991$	1913.96			1.93135			0.965673	+	0.259761i	$0.0836438\pi$
$992$	−298.160	−	172.142i	−0.300564	−	0.173531i
$993$		0			0
$994$	−37.7515	−	65.3876i	−0.0379794	−	0.0657822i
$995$	−137.642	+	79.4676i	−0.138334	+	0.0798669i
$996$		0			0
$997$	843.132	−	1460.35i	0.845669	−	1.46474i	−0.0393706	−	0.999225i	$-0.512535\pi$
$997$	843.132	−	1460.35i	0.845669	−	1.46474i	0.885039	−	0.465516i	$-0.154131\pi$
$998$			19.8993i			0.0199391i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.3.r.e.512.4		16
3.2	odd	2	inner	567.3.r.e.512.5		16
9.2	odd	6		189.3.b.c.134.4	✓	8
9.4	even	3	inner	567.3.r.e.134.5		16
9.5	odd	6	inner	567.3.r.e.134.4		16
9.7	even	3		189.3.b.c.134.5	yes	8
36.7	odd	6		3024.3.d.j.1457.8		8
36.11	even	6		3024.3.d.j.1457.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.3.b.c.134.4	✓	8	9.2	odd	6
189.3.b.c.134.5	yes	8	9.7	even	3
567.3.r.e.134.4		16	9.5	odd	6	inner
567.3.r.e.134.5		16	9.4	even	3	inner
567.3.r.e.512.4		16	1.1	even	1	trivial
567.3.r.e.512.5		16	3.2	odd	2	inner
3024.3.d.j.1457.1		8	36.11	even	6
3024.3.d.j.1457.8		8	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	567.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.625847 - 0.361333i) q^{2} +(-1.73888 - 3.01182i) q^{4} +(6.88081 - 3.97263i) q^{5} +(-1.32288 + 2.29129i) q^{7} +5.40392i q^{8} +O(q^{10})\)	\(q+(-0.625847 - 0.361333i) q^{2} +(-1.73888 - 3.01182i) q^{4} +(6.88081 - 3.97263i) q^{5} +(-1.32288 + 2.29129i) q^{7} +5.40392i q^{8} -5.74177 q^{10} +(8.01242 + 4.62598i) q^{11} +(11.0728 + 19.1786i) q^{13} +(1.65584 - 0.955997i) q^{14} +(-5.00290 + 8.66527i) q^{16} +27.2692i q^{17} +31.8633 q^{19} +(-23.9298 - 13.8158i) q^{20} +(-3.34303 - 5.79030i) q^{22} +(-11.7168 + 6.76470i) q^{23} +(19.0637 - 33.0192i) q^{25} -16.0038i q^{26} +9.20127 q^{28} +(-5.83588 - 3.36935i) q^{29} +(-5.96753 - 10.3361i) q^{31} +(24.9818 - 14.4233i) q^{32} +(9.85326 - 17.0663i) q^{34} +21.0212i q^{35} +26.8988 q^{37} +(-19.9415 - 11.5133i) q^{38} +(21.4678 + 37.1833i) q^{40} +(-55.3940 + 31.9817i) q^{41} +(8.10924 - 14.0456i) q^{43} -32.1760i q^{44} +9.77724 q^{46} +(0.448944 + 0.259198i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-23.8619 + 13.7766i) q^{50} +(38.5084 - 66.6985i) q^{52} -71.8912i q^{53} +73.5092 q^{55} +(-12.3819 - 7.14871i) q^{56} +(2.43491 + 4.21739i) q^{58} +(-33.3887 + 19.2770i) q^{59} +(-13.9611 + 24.1814i) q^{61} +8.62506i q^{62} +19.1768 q^{64} +(152.379 + 87.9763i) q^{65} +(-14.7824 - 25.6039i) q^{67} +(82.1300 - 47.4178i) q^{68} +(7.59565 - 13.1561i) q^{70} -39.4892i q^{71} +67.1187 q^{73} +(-16.8345 - 9.71940i) q^{74} +(-55.4064 - 95.9666i) q^{76} +(-21.1989 + 12.2392i) q^{77} +(9.38444 - 16.2543i) q^{79} +79.4987i q^{80} +46.2242 q^{82} +(69.3594 + 40.0446i) q^{83} +(108.331 + 187.634i) q^{85} +(-10.1503 + 5.86027i) q^{86} +(-24.9984 + 43.2985i) q^{88} +62.9293i q^{89} -58.5917 q^{91} +(40.7482 + 23.5260i) q^{92} +(-0.187313 - 0.324436i) q^{94} +(219.245 - 126.581i) q^{95} +(23.3906 - 40.5137i) q^{97} +5.05866i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4}+O(q^{10}) \) 16 * q + 12 * q^4	\( 16 q + 12 q^{4} - 104 q^{10} - 36 q^{13} - 132 q^{16} + 24 q^{19} + 136 q^{22} + 108 q^{25} + 112 q^{28} + 28 q^{31} + 12 q^{34} - 8 q^{37} - 336 q^{40} + 152 q^{43} + 216 q^{46} - 56 q^{49} + 272 q^{52} + 392 q^{55} + 220 q^{58} - 180 q^{61} - 1400 q^{64} + 132 q^{67} - 196 q^{70} + 544 q^{73} - 544 q^{76} - 316 q^{79} + 56 q^{82} + 228 q^{85} - 112 q^{91} + 348 q^{94} + 364 q^{97}+O(q^{100}) \) 16 * q + 12 * q^4 - 104 * q^10 - 36 * q^13 - 132 * q^16 + 24 * q^19 + 136 * q^22 + 108 * q^25 + 112 * q^28 + 28 * q^31 + 12 * q^34 - 8 * q^37 - 336 * q^40 + 152 * q^43 + 216 * q^46 - 56 * q^49 + 272 * q^52 + 392 * q^55 + 220 * q^58 - 180 * q^61 - 1400 * q^64 + 132 * q^67 - 196 * q^70 + 544 * q^73 - 544 * q^76 - 316 * q^79 + 56 * q^82 + 228 * q^85 - 112 * q^91 + 348 * q^94 + 364 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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