LMFDB - Embedded newform 927.2.f.f.46.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(46,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("927.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.6
Character	$\chi$	$=$	927.46
Dual form			927.2.f.f.262.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.609528 - 1.05573i) q^{2} +(0.256951 - 0.445052i) q^{4} +(-1.48540 + 2.57279i) q^{5} +(0.0501933 - 0.0869373i) q^{7} -3.06459 q^{8} +O(q^{10})$	\(q+(-0.609528 - 1.05573i) q^{2} +(0.256951 - 0.445052i) q^{4} +(-1.48540 + 2.57279i) q^{5} +(0.0501933 - 0.0869373i) q^{7} -3.06459 q^{8} +3.62157 q^{10} +(0.856724 - 1.48389i) q^{11} +0.822677 q^{13} -0.122377 q^{14} +(1.35405 + 2.34528i) q^{16} +(-1.04980 + 1.81831i) q^{17} +(-0.333534 - 0.577697i) q^{19} +(0.763350 + 1.32216i) q^{20} -2.08879 q^{22} +4.28723 q^{23} +(-1.91282 - 3.31310i) q^{25} +(-0.501445 - 0.868528i) q^{26} +(-0.0257944 - 0.0446773i) q^{28} +(2.93443 + 5.08257i) q^{29} +6.90867 q^{31} +(-1.41392 + 2.44899i) q^{32} +2.55953 q^{34} +(0.149114 + 0.258273i) q^{35} +9.62862 q^{37} +(-0.406596 + 0.704246i) q^{38} +(4.55214 - 7.88453i) q^{40} +(3.86413 + 6.69287i) q^{41} +(0.963015 + 1.66799i) q^{43} +(-0.440272 - 0.762574i) q^{44} +(-2.61319 - 4.52617i) q^{46} +(1.40506 - 2.43364i) q^{47} +(3.49496 + 6.05345i) q^{49} +(-2.33184 + 4.03886i) q^{50} +(0.211388 - 0.366134i) q^{52} +(0.851291 - 1.47448i) q^{53} +(2.54515 + 4.40834i) q^{55} +(-0.153822 + 0.266427i) q^{56} +(3.57723 - 6.19594i) q^{58} +(2.84358 + 4.92523i) q^{59} -12.5835 q^{61} +(-4.21103 - 7.29372i) q^{62} +8.86351 q^{64} +(-1.22200 + 2.11657i) q^{65} +(-3.36497 + 5.82830i) q^{67} +(0.539495 + 0.934432i) q^{68} +(0.181778 - 0.314849i) q^{70} +(4.27959 - 7.41246i) q^{71} -2.38797 q^{73} +(-5.86892 - 10.1653i) q^{74} -0.342807 q^{76} +(-0.0860036 - 0.148963i) q^{77} +9.93377 q^{79} -8.04522 q^{80} +(4.71059 - 8.15899i) q^{82} +(-6.81177 - 11.7983i) q^{83} +(-3.11875 - 5.40183i) q^{85} +(1.17397 - 2.03337i) q^{86} +(-2.62551 + 4.54751i) q^{88} +0.260223 q^{89} +(0.0412929 - 0.0715213i) q^{91} +(1.10161 - 1.90804i) q^{92} -3.42570 q^{94} +1.98172 q^{95} +(-1.23480 - 2.13873i) q^{97} +(4.26055 - 7.37950i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) $ 32 * q - 18 * q^4 + 8 * q^7	$ 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) $ 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.609528	−	1.05573i	−0.431001	−	0.746516i	0.565958	−	0.824434i	$-0.308506\pi$
$2$	−0.609528	−	1.05573i	−0.431001	−	0.746516i	−0.996960	+	0.0779174i	$0.975173\pi$
$3$		0			0
$3$		0			0
$4$	0.256951	−	0.445052i	0.128476	−	0.222526i
$5$	−1.48540	+	2.57279i	−0.664291	+	1.15059i	0.315186	+	0.949030i	$0.397933\pi$
$5$	−1.48540	+	2.57279i	−0.664291	+	1.15059i	−0.979477	+	0.201555i	$0.935400\pi$
$6$		0			0
$7$	0.0501933	−	0.0869373i	0.0189713	−	0.0328592i	−0.856384	−	0.516340i	$-0.827294\pi$
$7$	0.0501933	−	0.0869373i	0.0189713	−	0.0328592i	0.875355	+	0.483480i	$0.160628\pi$
$8$	−3.06459			−1.08350
$9$		0			0
$10$	3.62157			1.14524
$11$	0.856724	−	1.48389i	0.258312	−	0.447410i	−0.707478	−	0.706736i	$-0.750167\pi$
$11$	0.856724	−	1.48389i	0.258312	−	0.447410i	0.965790	+	0.259326i	$0.0835004\pi$
$12$		0			0
$13$	0.822677			0.228170			0.114085	−	0.993471i	$-0.463606\pi$
$13$	0.822677			0.228170			0.114085	+	0.993471i	$0.463606\pi$
$14$	−0.122377			−0.0327066
$15$		0			0
$16$	1.35405	+	2.34528i	0.338513	+	0.586321i
$17$	−1.04980	+	1.81831i	−0.254614	+	0.441004i	−0.964791	−	0.263019i	$-0.915282\pi$
$17$	−1.04980	+	1.81831i	−0.254614	+	0.441004i	0.710177	+	0.704024i	$0.248615\pi$
$18$		0			0
$19$	−0.333534	−	0.577697i	−0.0765179	−	0.132533i	0.825227	−	0.564801i	$-0.191047\pi$
$19$	−0.333534	−	0.577697i	−0.0765179	−	0.132533i	−0.901745	+	0.432268i	$0.857714\pi$
$20$	0.763350	+	1.32216i	0.170690	+	0.295644i
$21$		0			0
$22$	−2.08879			−0.445331
$23$	4.28723			0.893949			0.446974	−	0.894547i	$-0.352501\pi$
$23$	4.28723			0.893949			0.446974	+	0.894547i	$0.352501\pi$
$24$		0			0
$25$	−1.91282	−	3.31310i	−0.382564	−	0.662621i
$26$	−0.501445	−	0.868528i	−0.0983415	−	0.170332i
$27$		0			0
$28$	−0.0257944	−	0.0446773i	−0.00487469	−	0.00844321i
$29$	2.93443	+	5.08257i	0.544909	+	0.943810i	0.998613	+	0.0526575i	$0.0167692\pi$
$29$	2.93443	+	5.08257i	0.544909	+	0.943810i	−0.453704	+	0.891153i	$0.649897\pi$
$30$		0			0
$31$	6.90867			1.24083			0.620417	−	0.784272i	$-0.286963\pi$
$31$	6.90867			1.24083			0.620417	+	0.784272i	$0.286963\pi$
$32$	−1.41392	+	2.44899i	−0.249949	+	0.432924i
$33$		0			0
$34$	2.55953			0.438956
$35$	0.149114	+	0.258273i	0.0252049	+	0.0436561i
$36$		0			0
$37$	9.62862			1.58294			0.791468	−	0.611210i	$-0.209317\pi$
$37$	9.62862			1.58294			0.791468	+	0.611210i	$0.209317\pi$
$38$	−0.406596	+	0.704246i	−0.0659586	+	0.114244i
$39$		0			0
$40$	4.55214	−	7.88453i	0.719756	−	1.24665i
$41$	3.86413	+	6.69287i	0.603476	+	1.04525i	0.992290	+	0.123935i	$0.0395514\pi$
$41$	3.86413	+	6.69287i	0.603476	+	1.04525i	−0.388814	+	0.921316i	$0.627115\pi$
$42$		0			0
$43$	0.963015	+	1.66799i	0.146858	+	0.254366i	0.930065	−	0.367396i	$-0.119751\pi$
$43$	0.963015	+	1.66799i	0.146858	+	0.254366i	−0.783206	+	0.621762i	$0.786417\pi$
$44$	−0.440272	−	0.762574i	−0.0663735	−	0.114962i
$45$		0			0
$46$	−2.61319	−	4.52617i	−0.385293	−	0.667347i
$47$	1.40506	−	2.43364i	0.204950	−	0.354983i	−0.745167	−	0.666878i	$-0.767630\pi$
$47$	1.40506	−	2.43364i	0.204950	−	0.354983i	0.950117	+	0.311895i	$0.100964\pi$
$48$		0			0
$49$	3.49496	+	6.05345i	0.499280	+	0.864779i
$50$	−2.33184	+	4.03886i	−0.329772	+	0.571181i
$51$		0			0
$52$	0.211388	−	0.366134i	0.0293142	−	0.0507737i
$53$	0.851291	−	1.47448i	0.116934	−	0.202535i	−0.801617	−	0.597838i	$-0.796027\pi$
$53$	0.851291	−	1.47448i	0.116934	−	0.202535i	0.918551	+	0.395302i	$0.129360\pi$
$54$		0			0
$55$	2.54515	+	4.40834i	0.343189	+	0.594420i
$56$	−0.153822	+	0.266427i	−0.0205553	+	0.0356028i
$57$		0			0
$58$	3.57723	−	6.19594i	0.469713	−	0.813567i
$59$	2.84358	+	4.92523i	0.370203	+	0.641211i	0.989597	−	0.143870i	$-0.0459548\pi$
$59$	2.84358	+	4.92523i	0.370203	+	0.641211i	−0.619393	+	0.785081i	$0.712621\pi$
$60$		0			0
$61$	−12.5835			−1.61115			−0.805574	−	0.592496i	$-0.798143\pi$
$61$	−12.5835			−1.61115			−0.805574	+	0.592496i	$0.798143\pi$
$62$	−4.21103	−	7.29372i	−0.534801	−	0.926303i
$63$		0			0
$64$	8.86351			1.10794
$65$	−1.22200	+	2.11657i	−0.151571	+	0.262529i
$66$		0			0
$67$	−3.36497	+	5.82830i	−0.411097	+	0.712041i	−0.995010	−	0.0997756i	$-0.968188\pi$
$67$	−3.36497	+	5.82830i	−0.411097	+	0.712041i	0.583913	+	0.811816i	$0.301521\pi$
$68$	0.539495	+	0.934432i	0.0654233	+	0.113317i
$69$		0			0
$70$	0.181778	−	0.314849i	0.0217267	−	0.0376317i
$71$	4.27959	−	7.41246i	0.507894	−	0.879698i	−0.492065	−	0.870559i	$-0.663758\pi$
$71$	4.27959	−	7.41246i	0.507894	−	0.879698i	0.999958	−	0.00913893i	$-0.00290905\pi$
$72$		0			0
$73$	−2.38797			−0.279491			−0.139745	−	0.990187i	$-0.544628\pi$
$73$	−2.38797			−0.279491			−0.139745	+	0.990187i	$0.544628\pi$
$74$	−5.86892	−	10.1653i	−0.682248	−	1.18169i
$75$		0			0
$76$	−0.342807			−0.0393227
$77$	−0.0860036	−	0.148963i	−0.00980102	−	0.0169759i
$78$		0			0
$79$	9.93377			1.11764			0.558818	−	0.829290i	$-0.311255\pi$
$79$	9.93377			1.11764			0.558818	+	0.829290i	$0.311255\pi$
$80$	−8.04522			−0.899483
$81$		0			0
$82$	4.71059	−	8.15899i	0.520198	−	0.901009i
$83$	−6.81177	−	11.7983i	−0.747689	−	1.29504i	−0.948928	−	0.315494i	$-0.897830\pi$
$83$	−6.81177	−	11.7983i	−0.747689	−	1.29504i	0.201238	−	0.979542i	$-0.435503\pi$
$84$		0			0
$85$	−3.11875	−	5.40183i	−0.338275	−	0.585910i
$86$	1.17397	−	2.03337i	0.126592	−	0.219264i
$87$		0			0
$88$	−2.62551	+	4.54751i	−0.279880	+	0.484766i
$89$	0.260223			0.0275836			0.0137918	−	0.999905i	$-0.495610\pi$
$89$	0.260223			0.0275836			0.0137918	+	0.999905i	$0.495610\pi$
$90$		0			0
$91$	0.0412929	−	0.0715213i	0.00432867	−	0.00749747i
$92$	1.10161	−	1.90804i	0.114851	−	0.198927i
$93$		0			0
$94$	−3.42570			−0.353334
$95$	1.98172			0.203320
$96$		0			0
$97$	−1.23480	−	2.13873i	−0.125375	−	0.217155i	0.796505	−	0.604632i	$-0.206680\pi$
$97$	−1.23480	−	2.13873i	−0.125375	−	0.217155i	−0.921879	+	0.387477i	$0.873347\pi$
$98$	4.26055	−	7.37950i	0.430381	−	0.745442i
$99$		0			0
$100$	−1.96601			−0.196601
$101$	−0.406416	−	0.703934i	−0.0404399	−	0.0700440i	0.845097	−	0.534613i	$-0.179543\pi$
$101$	−0.406416	−	0.703934i	−0.0404399	−	0.0700440i	−0.885537	+	0.464569i	$0.846209\pi$
$102$		0			0
$103$	−10.1205	+	0.759069i	−0.997199	+	0.0747933i
$103$	−10.1205	+	0.759069i	−0.997199	+	0.0747933i
$104$	−2.52117			−0.247221
$105$		0			0
$106$	−2.07554			−0.201595
$107$	5.39349	−	9.34180i	0.521409	−	0.903106i	−0.478281	−	0.878207i	$-0.658740\pi$
$107$	5.39349	−	9.34180i	0.521409	−	0.903106i	0.999690	−	0.0248995i	$-0.00792658\pi$
$108$		0			0
$109$	6.64933	+	11.5170i	0.636890	+	1.10313i	0.986111	+	0.166086i	$0.0531129\pi$
$109$	6.64933	+	11.5170i	0.636890	+	1.10313i	−0.349221	+	0.937040i	$0.613554\pi$
$110$	3.10269	−	5.37401i	0.295830	−	0.512392i
$111$		0			0
$112$	0.271857			0.0256881
$113$	5.31069			0.499588			0.249794	−	0.968299i	$-0.419637\pi$
$113$	5.31069			0.499588			0.249794	+	0.968299i	$0.419637\pi$
$114$		0			0
$115$	−6.36825	+	11.0301i	−0.593842	+	1.02856i
$116$	3.01601			0.280030
$117$		0			0
$118$	3.46649	−	6.00413i	0.319116	−	0.552725i
$119$	0.105386	+	0.182534i	0.00966070	+	0.0167328i
$120$		0			0
$121$	4.03205	+	6.98371i	0.366550	+	0.634883i
$122$	7.66997	+	13.2848i	0.694407	+	1.20275i
$123$		0			0
$124$	1.77519	−	3.07472i	0.159417	−	0.276118i
$125$	−3.48878			−0.312046
$126$		0			0
$127$	−3.38834			−0.300667			−0.150333	−	0.988635i	$-0.548035\pi$
$127$	−3.38834			−0.300667			−0.150333	+	0.988635i	$0.548035\pi$
$128$	−2.57471	−	4.45952i	−0.227574	−	0.394170i
$129$		0			0
$130$	2.97938			0.261309
$131$	−1.32893	−	2.30178i	−0.116109	−	0.201107i	0.802113	−	0.597172i	$-0.203709\pi$
$131$	−1.32893	−	2.30178i	−0.116109	−	0.201107i	−0.918223	+	0.396065i	$0.870376\pi$
$132$		0			0
$133$	−0.0669646			−0.00580657
$134$	8.20418			0.708733
$135$		0			0
$136$	3.21721	−	5.57236i	0.275873	−	0.477826i
$137$	−1.41962			−0.121286			−0.0606431	−	0.998160i	$-0.519315\pi$
$137$	−1.41962			−0.121286			−0.0606431	+	0.998160i	$0.519315\pi$
$138$		0			0
$139$	3.90192	−	6.75832i	0.330956	−	0.573233i	−0.651743	−	0.758440i	$-0.725962\pi$
$139$	3.90192	−	6.75832i	0.330956	−	0.573233i	0.982700	+	0.185206i	$0.0592954\pi$
$140$	0.153260			0.0129528
$141$		0			0
$142$	−10.4341			−0.875612
$143$	0.704808	−	1.22076i	0.0589390	−	0.102085i
$144$		0			0
$145$	−17.4352			−1.44791
$146$	1.45554	+	2.52106i	0.120461	+	0.208644i
$147$		0			0
$148$	2.47409	−	4.28524i	0.203369	−	0.352245i
$149$	−0.403468	−	0.698827i	−0.0330534	−	0.0572502i	0.849025	−	0.528352i	$-0.177190\pi$
$149$	−0.403468	−	0.698827i	−0.0330534	−	0.0572502i	−0.882079	+	0.471102i	$0.843856\pi$
$150$		0			0
$151$	4.51468	+	7.81965i	0.367399	+	0.636354i	0.989158	−	0.146855i	$-0.0469149\pi$
$151$	4.51468	+	7.81965i	0.367399	+	0.636354i	−0.621759	+	0.783209i	$0.713582\pi$
$152$	1.02214	+	1.77040i	0.0829068	+	0.143599i
$153$		0			0
$154$	−0.104843	+	0.181594i	−0.00844850	+	0.0146332i
$155$	−10.2621	+	17.7745i	−0.824274	+	1.42769i
$156$		0			0
$157$	0.0771173	+	0.133571i	0.00615463	+	0.0106601i	0.869086	−	0.494660i	$-0.164708\pi$
$157$	0.0771173	+	0.133571i	0.00615463	+	0.0106601i	−0.862932	+	0.505321i	$0.831374\pi$
$158$	−6.05491	−	10.4874i	−0.481703	−	0.834334i
$159$		0			0
$160$	−4.20048	−	7.27545i	−0.332077	−	0.575175i
$161$	0.215190	−	0.372720i	0.0169593	−	0.0293745i
$162$		0			0
$163$	5.41735	+	9.38313i	0.424320	+	0.734943i	0.996357	−	0.0852847i	$-0.0271800\pi$
$163$	5.41735	+	9.38313i	0.424320	+	0.734943i	−0.572037	+	0.820228i	$0.693847\pi$
$164$	3.97157			0.310128
$165$		0			0
$166$	−8.30394	+	14.3828i	−0.644510	+	1.11632i
$167$	−9.65224			−0.746913			−0.373456	−	0.927648i	$-0.621827\pi$
$167$	−9.65224			−0.746913			−0.373456	+	0.927648i	$0.621827\pi$
$168$		0			0
$169$	−12.3232			−0.947939
$170$	−3.80193	+	6.58513i	−0.291594	+	0.505056i
$171$		0			0
$172$	0.989791			0.0754708
$173$	0.378938	−	0.656340i	0.0288101	−	0.0499006i	−0.851261	−	0.524743i	$-0.824162\pi$
$173$	0.378938	−	0.656340i	0.0288101	−	0.0499006i	0.880071	+	0.474842i	$0.157495\pi$
$174$		0			0
$175$	−0.384043			−0.0290309
$176$	4.64019			0.349767
$177$		0			0
$178$	−0.158613	−	0.274726i	−0.0118886	−	0.0205916i
$179$	22.5589			1.68613			0.843066	−	0.537811i	$-0.180749\pi$
$179$	22.5589			1.68613			0.843066	+	0.537811i	$0.180749\pi$
$180$		0			0
$181$	−8.27071	−	14.3253i	−0.614757	−	1.06479i	−0.990427	−	0.138037i	$-0.955921\pi$
$181$	−8.27071	−	14.3253i	−0.614757	−	1.06479i	0.375670	−	0.926753i	$-0.377413\pi$
$182$	−0.100677			−0.00746265
$183$		0			0
$184$	−13.1386			−0.968589
$185$	−14.3024	+	24.7724i	−1.05153	+	1.82130i
$186$		0			0
$187$	1.79878	+	3.11558i	0.131540	+	0.227833i
$188$	−0.722065	−	1.25065i	−0.0526620	−	0.0912133i
$189$		0			0
$190$	−1.20792	−	2.09217i	−0.0876314	−	0.151782i
$191$	−3.26333	+	5.65226i	−0.236126	+	0.408983i	−0.959599	−	0.281370i	$-0.909211\pi$
$191$	−3.26333	+	5.65226i	−0.236126	+	0.408983i	0.723473	+	0.690353i	$0.242545\pi$
$192$		0			0
$193$	−11.2420			−0.809213			−0.404607	−	0.914491i	$-0.632592\pi$
$193$	−11.2420			−0.809213			−0.404607	+	0.914491i	$0.632592\pi$
$194$	−1.50529	+	2.60723i	−0.108073	+	0.187189i
$195$		0			0
$196$	3.59214			0.256581
$197$	−8.95738			−0.638187			−0.319094	−	0.947723i	$-0.603378\pi$
$197$	−8.95738			−0.638187			−0.319094	+	0.947723i	$0.603378\pi$
$198$		0			0
$199$	−2.25138	+	3.89950i	−0.159596	+	0.276428i	−0.934723	−	0.355377i	$-0.884352\pi$
$199$	−2.25138	+	3.89950i	−0.159596	+	0.276428i	0.775127	+	0.631805i	$0.217686\pi$
$200$	5.86201	+	10.1533i	0.414507	+	0.717947i
$201$		0			0
$202$	−0.495444	+	0.858135i	−0.0348594	+	0.0603782i
$203$	0.589154			0.0413505
$204$		0			0
$205$	−22.9591			−1.60353
$206$	6.97008	+	10.2218i	0.485629	+	0.712189i
$207$		0			0
$208$	1.11395	+	1.92941i	0.0772383	+	0.133781i
$209$	−1.14299			−0.0790620
$210$		0			0
$211$	−3.49169	+	6.04778i	−0.240378	+	0.416346i	−0.960822	−	0.277167i	$-0.910605\pi$
$211$	−3.49169	+	6.04778i	−0.240378	+	0.416346i	0.720444	+	0.693513i	$0.243938\pi$
$212$	−0.437480	−	0.757738i	−0.0300463	−	0.0520417i
$213$		0			0
$214$	−13.1499			−0.898911
$215$	−5.72185			−0.390227
$216$		0			0
$217$	0.346769	−	0.600621i	0.0235402	−	0.0407728i
$218$	8.10591	−	14.0398i	0.549001	−	0.950898i
$219$		0			0
$220$	2.61592			0.176365
$221$	−0.863647	+	1.49588i	−0.0580952	+	0.100624i
$222$		0			0
$223$	−7.80352	+	13.5161i	−0.522562	+	0.905105i	0.477093	+	0.878853i	$0.341690\pi$
$223$	−7.80352	+	13.5161i	−0.522562	+	0.905105i	−0.999655	+	0.0262518i	$0.991643\pi$
$224$	0.141939	+	0.245846i	0.00948370	+	0.0164262i
$225$		0			0
$226$	−3.23702	−	5.60667i	−0.215323	−	0.372950i
$227$	−8.70968	+	15.0856i	−0.578082	+	1.00127i	0.417617	+	0.908623i	$0.362865\pi$
$227$	−8.70968	+	15.0856i	−0.578082	+	1.00127i	−0.995699	+	0.0926444i	$0.970468\pi$
$228$		0			0
$229$	5.36526			0.354546			0.177273	−	0.984162i	$-0.443272\pi$
$229$	5.36526			0.354546			0.177273	+	0.984162i	$0.443272\pi$
$230$	15.5265			1.02379
$231$		0			0
$232$	−8.99280	−	15.5760i	−0.590406	−	1.02261i
$233$	8.57563			0.561808			0.280904	−	0.959736i	$-0.409366\pi$
$233$	8.57563			0.561808			0.280904	+	0.959736i	$0.409366\pi$
$234$		0			0
$235$	4.17416	+	7.22986i	0.272292	+	0.471624i
$236$	2.92265			0.190248
$237$		0			0
$238$	0.128471	−	0.222519i	0.00832755	−	0.0144237i
$239$	8.43241	−	14.6054i	0.545447	−	0.944742i	−0.453131	−	0.891444i	$-0.649693\pi$
$239$	8.43241	−	14.6054i	0.545447	−	0.944742i	0.998579	−	0.0532986i	$-0.0169735\pi$
$240$		0			0
$241$	1.96648	+	3.40604i	0.126672	+	0.219402i	0.922385	−	0.386271i	$-0.126237\pi$
$241$	1.96648	+	3.40604i	0.126672	+	0.219402i	−0.795713	+	0.605673i	$0.792904\pi$
$242$	4.91529	−	8.51354i	0.315967	−	0.547271i
$243$		0			0
$244$	−3.23333	+	5.60030i	−0.206993	+	0.358522i
$245$	−20.7657			−1.32667
$246$		0			0
$247$	−0.274391	−	0.475259i	−0.0174591	−	0.0302400i
$248$	−21.1722			−1.34444
$249$		0			0
$250$	2.12651	+	3.68322i	0.134492	+	0.232947i
$251$	2.95986	−	5.12663i	0.186825	−	0.323590i	−0.757365	−	0.652992i	$-0.773514\pi$
$251$	2.95986	−	5.12663i	0.186825	−	0.323590i	0.944190	+	0.329402i	$0.106847\pi$
$252$		0			0
$253$	3.67297	−	6.36177i	0.230918	−	0.399961i
$254$	2.06529	+	3.57719i	0.129588	+	0.224453i
$255$		0			0
$256$	5.72479	−	9.91563i	0.357800	−	0.619727i
$257$	−9.30479	+	16.1164i	−0.580417	+	1.00531i	0.415013	+	0.909815i	$0.363777\pi$
$257$	−9.30479	+	16.1164i	−0.580417	+	1.00531i	−0.995430	+	0.0954958i	$0.969556\pi$
$258$		0			0
$259$	0.483292	−	0.837087i	0.0300303	−	0.0520140i
$260$	0.627991	+	1.08771i	0.0389463	+	0.0674570i
$261$		0			0
$262$	−1.62004	+	2.80599i	−0.100087	+	0.173355i
$263$	3.63895	+	6.30284i	0.224387	+	0.388650i	0.956135	−	0.292925i	$-0.0946287\pi$
$263$	3.63895	+	6.30284i	0.224387	+	0.388650i	−0.731748	+	0.681575i	$0.761295\pi$
$264$		0			0
$265$	2.52901	+	4.38038i	0.155356	+	0.269085i
$266$	0.0408168	+	0.0706968i	0.00250264	+	0.00433470i
$267$		0			0
$268$	1.72927	+	2.99518i	0.105632	+	0.182960i
$269$	7.62284	−	13.2032i	0.464773	−	0.805010i	−0.534418	−	0.845220i	$-0.679469\pi$
$269$	7.62284	−	13.2032i	0.464773	−	0.805010i	0.999191	+	0.0402098i	$0.0128026\pi$
$270$		0			0
$271$	−0.604529	+	1.04707i	−0.0367225	+	0.0636052i	−0.883803	−	0.467860i	$-0.845025\pi$
$271$	−0.604529	+	1.04707i	−0.0367225	+	0.0636052i	0.847080	+	0.531465i	$0.178358\pi$
$272$	−5.68593			−0.344760
$273$		0			0
$274$	0.865298	+	1.49874i	0.0522746	+	0.0905422i
$275$	−6.55504			−0.395284
$276$		0			0
$277$	0.570536	−	0.988198i	0.0342802	−	0.0593751i	−0.848376	−	0.529394i	$-0.822419\pi$
$277$	0.570536	−	0.988198i	0.0342802	−	0.0593751i	0.882657	+	0.470019i	$0.155753\pi$
$278$	−9.51332			−0.570571
$279$		0			0
$280$	−0.456973	−	0.791501i	−0.0273094	−	0.0473012i
$281$	8.80824	+	15.2563i	0.525456	+	0.910116i	0.999560	+	0.0296473i	$0.00943840\pi$
$281$	8.80824	+	15.2563i	0.525456	+	0.910116i	−0.474105	+	0.880468i	$0.657228\pi$
$282$		0			0
$283$	−12.0987	−	20.9556i	−0.719193	−	1.24568i	−0.961320	−	0.275434i	$-0.911178\pi$
$283$	−12.0987	−	20.9556i	−0.719193	−	1.24568i	0.242127	−	0.970245i	$-0.422155\pi$
$284$	−2.19929	−	3.80928i	−0.130504	−	0.226039i
$285$		0			0
$286$	−1.71840			−0.101611
$287$	0.775813			0.0457948
$288$		0			0
$289$	6.29584	+	10.9047i	0.370343	+	0.641454i
$290$	10.6272	+	18.4069i	0.624052	+	1.08089i
$291$		0			0
$292$	−0.613592	+	1.06277i	−0.0359077	+	0.0621940i
$293$	−4.77857	−	8.27673i	−0.279167	−	0.483532i	0.692011	−	0.721887i	$-0.256725\pi$
$293$	−4.77857	−	8.27673i	−0.279167	−	0.483532i	−0.971178	+	0.238355i	$0.923392\pi$
$294$		0			0
$295$	−16.8954			−0.983690
$296$	−29.5078			−1.71510
$297$		0			0
$298$	−0.491850	+	0.851910i	−0.0284921	+	0.0493498i
$299$	3.52701			0.203972
$300$		0			0
$301$	0.193347			0.0111444
$302$	5.50365	−	9.53260i	0.316699	−	0.548539i
$303$		0			0
$304$	0.903243	−	1.56446i	0.0518045	−	0.0897281i
$305$	18.6915	−	32.3746i	1.07027	−	1.85376i
$306$		0			0
$307$	10.2890	+	17.8210i	0.587223	+	1.01710i	0.994594	+	0.103837i	$0.0331120\pi$
$307$	10.2890	+	17.8210i	0.587223	+	1.01710i	−0.407372	+	0.913262i	$0.633555\pi$
$308$	−0.0883948			−0.00503676
$309$		0			0
$310$	25.0202			1.42105
$311$	−4.60489	−	7.97590i	−0.261119	−	0.452272i	0.705420	−	0.708789i	$-0.250758\pi$
$311$	−4.60489	−	7.97590i	−0.261119	−	0.452272i	−0.966540	+	0.256517i	$0.917425\pi$
$312$		0			0
$313$	8.29495	−	14.3673i	0.468858	−	0.812086i	−0.530508	−	0.847680i	$-0.677999\pi$
$313$	8.29495	−	14.3673i	0.468858	−	0.812086i	0.999366	+	0.0355935i	$0.0113322\pi$
$314$	0.0940103	−	0.162831i	0.00530531	−	0.00918906i
$315$		0			0
$316$	2.55249	−	4.42104i	0.143589	−	0.248703i
$317$	−16.6939			−0.937622			−0.468811	−	0.883298i	$-0.655317\pi$
$317$	−16.6939			−0.937622			−0.468811	+	0.883298i	$0.655317\pi$
$318$		0			0
$319$	10.0560			0.563026
$320$	−13.1658	+	22.8039i	−0.735993	+	1.27478i
$321$		0			0
$322$	−0.524657			−0.0292380
$323$	1.40058			0.0779301
$324$		0			0
$325$	−1.57364	−	2.72562i	−0.0872896	−	0.151190i
$326$	6.60405	−	11.4386i	0.365765	−	0.633523i
$327$		0			0
$328$	−11.8420	−	20.5109i	−0.653863	−	1.13252i
$329$	−0.141049	−	0.244305i	−0.00777631	−	0.0134690i
$330$		0			0
$331$	−10.3223			−0.567363			−0.283682	−	0.958919i	$-0.591556\pi$
$331$	−10.3223			−0.567363			−0.283682	+	0.958919i	$0.591556\pi$
$332$	−7.00117			−0.384239
$333$		0			0
$334$	5.88331	+	10.1902i	0.321920	+	0.557582i
$335$	−9.99665	−	17.3147i	−0.546176	−	0.946004i
$336$		0			0
$337$	4.50587	+	7.80439i	0.245450	+	0.425132i	0.962258	−	0.272139i	$-0.0877309\pi$
$337$	4.50587	+	7.80439i	0.245450	+	0.425132i	−0.716808	+	0.697271i	$0.754398\pi$
$338$	7.51134	+	13.0100i	0.408563	+	0.707652i
$339$		0			0
$340$	−3.20546			−0.173840
$341$	5.91882	−	10.2517i	0.320522	−	0.555161i
$342$		0			0
$343$	1.40440			0.0758305
$344$	−2.95124	−	5.11170i	−0.159120	−	0.275605i
$345$		0			0
$346$	−0.923894			−0.0496688
$347$	−4.68975	+	8.12289i	−0.251759	+	0.436059i	−0.964010	−	0.265865i	$-0.914342\pi$
$347$	−4.68975	+	8.12289i	−0.251759	+	0.436059i	0.712251	+	0.701925i	$0.247676\pi$
$348$		0			0
$349$	−15.9115	+	27.5594i	−0.851721	+	1.47522i	0.0279336	+	0.999610i	$0.491107\pi$
$349$	−15.9115	+	27.5594i	−0.851721	+	1.47522i	−0.879654	+	0.475614i	$0.842226\pi$
$350$	0.234085	+	0.405447i	0.0125124	+	0.0216721i
$351$		0			0
$352$	2.42269	+	4.19622i	0.129130	+	0.223659i
$353$	10.1724	+	17.6191i	0.541422	+	0.937771i	0.998823	+	0.0485101i	$0.0154473\pi$
$353$	10.1724	+	17.6191i	0.541422	+	0.937771i	−0.457400	+	0.889261i	$0.651219\pi$
$354$		0			0
$355$	12.7138	+	22.0209i	0.674778	+	1.16875i
$356$	0.0668646	−	0.115813i	0.00354382	−	0.00613807i
$357$		0			0
$358$	−13.7503	−	23.8162i	−0.726725	−	1.25872i
$359$	1.15455	−	1.99974i	0.0609349	−	0.105542i	−0.833949	−	0.551842i	$-0.813925\pi$
$359$	1.15455	−	1.99974i	0.0609349	−	0.105542i	0.894884	+	0.446300i	$0.147258\pi$
$360$		0			0
$361$	9.27751	−	16.0691i	0.488290	−	0.845743i
$362$	−10.0825	+	17.4633i	−0.529922	+	0.917852i
$363$		0			0
$364$	−0.0212205	−	0.0367550i	−0.00111226	−	0.00192648i
$365$	3.54709	−	6.14374i	0.185663	−	0.321578i
$366$		0			0
$367$	−10.3239	+	17.8816i	−0.538906	+	0.933412i	0.460058	+	0.887889i	$0.347829\pi$
$367$	−10.3239	+	17.8816i	−0.538906	+	0.933412i	−0.998963	+	0.0455228i	$0.985505\pi$
$368$	5.80512	+	10.0548i	0.302613	+	0.524141i
$369$		0			0
$370$	34.8707			1.81284
$371$	−0.0854582	−	0.148018i	−0.00443677	−	0.00768471i
$372$		0			0
$373$	−21.3483			−1.10537			−0.552686	−	0.833390i	$-0.686397\pi$
$373$	−21.3483			−1.10537			−0.552686	+	0.833390i	$0.686397\pi$
$374$	2.19281	−	3.79806i	0.113388	−	0.196393i
$375$		0			0
$376$	−4.30594	+	7.45811i	−0.222062	+	0.384623i
$377$	2.41409	+	4.18132i	0.124332	+	0.215349i
$378$		0			0
$379$	11.7557	−	20.3615i	0.603850	−	1.04590i	−0.388382	−	0.921499i	$-0.626966\pi$
$379$	11.7557	−	20.3615i	0.603850	−	1.04590i	0.992232	−	0.124401i	$-0.0397009\pi$
$380$	0.509206	−	0.881970i	0.0261217	−	0.0452441i
$381$		0			0
$382$	7.95637			0.407083
$383$	−8.64539	−	14.9743i	−0.441759	−	0.765149i	0.556061	−	0.831141i	$-0.312312\pi$
$383$	−8.64539	−	14.9743i	−0.441759	−	0.765149i	−0.997820	+	0.0659924i	$0.978979\pi$
$384$		0			0
$385$	0.510998			0.0260429
$386$	6.85228	+	11.8685i	0.348772	+	0.604091i
$387$		0			0
$388$	−1.26913			−0.0644303
$389$	25.6404			1.30002			0.650010	−	0.759926i	$-0.274765\pi$
$389$	25.6404			1.30002			0.650010	+	0.759926i	$0.274765\pi$
$390$		0			0
$391$	−4.50073	+	7.79550i	−0.227612	+	0.394235i
$392$	−10.7106	−	18.5513i	−0.540968	−	0.936984i
$393$		0			0
$394$	5.45978	+	9.45661i	0.275060	+	0.476417i
$395$	−14.7556	+	25.5575i	−0.742435	+	1.28594i
$396$		0			0
$397$	11.0238	−	19.0937i	0.553268	−	0.958288i	−0.444768	−	0.895646i	$-0.646714\pi$
$397$	11.0238	−	19.0937i	0.553268	−	0.958288i	0.998036	−	0.0626422i	$-0.0199527\pi$
$398$	5.48911			0.275144
$399$		0			0
$400$	5.18011	−	8.97222i	0.259006	−	0.448611i
$401$	13.5807	−	23.5224i	0.678186	−	1.17465i	−0.297340	−	0.954772i	$-0.596100\pi$
$401$	13.5807	−	23.5224i	0.678186	−	1.17465i	0.975527	−	0.219881i	$-0.0705671\pi$
$402$		0			0
$403$	5.68361			0.283121
$404$	−0.417717			−0.0207822
$405$		0			0
$406$	−0.359106	−	0.621989i	−0.0178221	−	0.0308688i
$407$	8.24907	−	14.2878i	0.408891	−	0.708221i
$408$		0			0
$409$	7.18375			0.355214			0.177607	−	0.984102i	$-0.443164\pi$
$409$	7.18375			0.355214			0.177607	+	0.984102i	$0.443164\pi$
$410$	13.9942	+	24.2387i	0.691125	+	1.19706i
$411$		0			0
$412$	−2.26264	+	4.69918i	−0.111472	+	0.231512i
$413$	0.570915			0.0280929
$414$		0			0
$415$	40.4728			1.98673
$416$	−1.16320	+	2.01473i	−0.0570308	+	0.0987802i
$417$		0			0
$418$	0.696682	+	1.20669i	0.0340758	+	0.0590210i
$419$	15.3467	−	26.5813i	0.749736	−	1.29858i	−0.198212	−	0.980159i	$-0.563514\pi$
$419$	15.3467	−	26.5813i	0.749736	−	1.29858i	0.947949	−	0.318423i	$-0.103153\pi$
$420$		0			0
$421$	−35.8903			−1.74919			−0.874593	−	0.484858i	$-0.838871\pi$
$421$	−35.8903			−1.74919			−0.874593	+	0.484858i	$0.838871\pi$
$422$	8.51313			0.414413
$423$		0			0
$424$	−2.60886	+	4.51867i	−0.126697	+	0.219446i
$425$	8.03232			0.389625
$426$		0			0
$427$	−0.631605	+	1.09397i	−0.0305655	+	0.0529410i
$428$	−2.77173	−	4.80077i	−0.133976	−	0.232054i
$429$		0			0
$430$	3.48763	+	6.04075i	0.168188	+	0.291311i
$431$	12.1956	+	21.1235i	0.587443	+	1.01748i	0.994566	+	0.104108i	$0.0331987\pi$
$431$	12.1956	+	21.1235i	0.587443	+	1.01748i	−0.407123	+	0.913373i	$0.633468\pi$
$432$		0			0
$433$	19.1579	−	33.1824i	0.920669	−	1.59465i	0.122288	−	0.992495i	$-0.460977\pi$
$433$	19.1579	−	33.1824i	0.920669	−	1.59465i	0.798382	−	0.602152i	$-0.205690\pi$
$434$	−0.845461			−0.0405834
$435$		0			0
$436$	6.83421			0.327299
$437$	−1.42994	−	2.47672i	−0.0684031	−	0.118478i
$438$		0			0
$439$	33.0672			1.57821			0.789105	−	0.614259i	$-0.210545\pi$
$439$	33.0672			1.57821			0.789105	+	0.614259i	$0.210545\pi$
$440$	−7.79985	−	13.5097i	−0.371843	−	0.644051i
$441$		0			0
$442$	2.10567			0.100156
$443$	28.5308			1.35554			0.677769	−	0.735275i	$-0.262947\pi$
$443$	28.5308			1.35554			0.677769	+	0.735275i	$0.262947\pi$
$444$		0			0
$445$	−0.386535	+	0.669498i	−0.0183235	+	0.0317373i
$446$	19.0259			0.900901
$447$		0			0
$448$	0.444888	−	0.770569i	0.0210190	−	0.0364060i
$449$	13.3904			0.631933			0.315967	−	0.948770i	$-0.397671\pi$
$449$	13.3904			0.631933			0.315967	+	0.948770i	$0.397671\pi$
$450$		0			0
$451$	13.2420			0.623540
$452$	1.36459	−	2.36353i	0.0641848	−	0.111171i
$453$		0			0
$454$	21.2352			0.996617
$455$	0.122673	+	0.212475i	0.00575099	+	0.00996100i
$456$		0			0
$457$	15.6526	−	27.1110i	0.732196	−	1.26820i	−0.223747	−	0.974647i	$-0.571829\pi$
$457$	15.6526	−	27.1110i	0.732196	−	1.26820i	0.955943	−	0.293553i	$-0.0948378\pi$
$458$	−3.27027	−	5.66428i	−0.152810	−	0.264674i
$459$		0			0
$460$	3.27265	+	5.66840i	0.152588	+	0.264291i
$461$	−13.4854	−	23.3574i	−0.628077	−	1.08786i	−0.987937	−	0.154855i	$-0.950509\pi$
$461$	−13.4854	−	23.3574i	−0.628077	−	1.08786i	0.359860	−	0.933006i	$-0.382825\pi$
$462$		0			0
$463$	2.14255	−	3.71100i	0.0995727	−	0.172465i	−0.811935	−	0.583748i	$-0.801586\pi$
$463$	2.14255	−	3.71100i	0.0995727	−	0.172465i	0.911508	+	0.411283i	$0.134919\pi$
$464$	−7.94672	+	13.7641i	−0.368917	+	0.638983i
$465$		0			0
$466$	−5.22709	−	9.05358i	−0.242140	−	0.419399i
$467$	−14.7415	−	25.5330i	−0.682155	−	1.18153i	−0.974322	−	0.225159i	$-0.927710\pi$
$467$	−14.7415	−	25.5330i	−0.682155	−	1.18153i	0.292167	−	0.956367i	$-0.405624\pi$
$468$		0			0
$469$	0.337798	+	0.585083i	0.0155981	+	0.0270166i
$470$	5.08854	−	8.81360i	0.234717	−	0.406541i
$471$		0			0
$472$	−8.71441	−	15.0938i	−0.401113	−	0.694749i
$473$	3.30015			0.151741
$474$		0			0
$475$	−1.27598	+	2.21006i	−0.0585460	+	0.101405i
$476$	0.108316			0.00496466
$477$		0			0
$478$	−20.5592			−0.940354
$479$	−19.0222	+	32.9473i	−0.869145	+	1.50540i	−0.00627247	+	0.999980i	$0.501997\pi$
$479$	−19.0222	+	32.9473i	−0.869145	+	1.50540i	−0.862872	+	0.505422i	$0.831337\pi$
$480$		0			0
$481$	7.92125			0.361178
$482$	2.39725	−	4.15215i	0.109192	−	0.189125i
$483$		0			0
$484$	4.14416			0.188371
$485$	7.33667			0.333141
$486$		0			0
$487$	−12.6047	−	21.8320i	−0.571173	−	0.989300i	−0.996446	−	0.0842353i	$-0.973155\pi$
$487$	−12.6047	−	21.8320i	−0.571173	−	0.989300i	0.425273	−	0.905065i	$-0.360178\pi$
$488$	38.5631			1.74567
$489$		0			0
$490$	12.6572	+	21.9230i	0.571796	+	0.990380i
$491$	−19.6543			−0.886988			−0.443494	−	0.896277i	$-0.646261\pi$
$491$	−19.6543			−0.886988			−0.443494	+	0.896277i	$0.646261\pi$
$492$		0			0
$493$	−12.3222			−0.554966
$494$	−0.334498	+	0.579367i	−0.0150498	+	0.0260669i
$495$		0			0
$496$	9.35469	+	16.2028i	0.420038	+	0.727527i
$497$	−0.429613	−	0.744112i	−0.0192708	−	0.0333780i
$498$		0			0
$499$	16.1143	+	27.9109i	0.721377	+	1.24946i	0.960448	+	0.278460i	$0.0898238\pi$
$499$	16.1143	+	27.9109i	0.721377	+	1.24946i	−0.239071	+	0.971002i	$0.576843\pi$
$500$	−0.896445	+	1.55269i	−0.0400902	+	0.0694383i
$501$		0			0
$502$	−7.21647			−0.322087
$503$	−9.59255	+	16.6148i	−0.427711	+	0.740816i	−0.996669	−	0.0815496i	$-0.974013\pi$
$503$	−9.59255	+	16.6148i	−0.427711	+	0.740816i	0.568959	+	0.822366i	$0.307346\pi$
$504$		0			0
$505$	2.41476			0.107456
$506$	−8.95512			−0.398104
$507$		0			0
$508$	−0.870638	+	1.50799i	−0.0386283	+	0.0669062i
$509$	−17.5969	−	30.4788i	−0.779970	−	1.35095i	−0.931958	−	0.362566i	$-0.881901\pi$
$509$	−17.5969	−	30.4788i	−0.779970	−	1.35095i	0.151988	−	0.988382i	$-0.451432\pi$
$510$		0			0
$511$	−0.119860	+	0.207604i	−0.00530230	+	0.00918385i
$512$	−24.2565			−1.07200
$513$		0			0
$514$	22.6861			1.00064
$515$	13.0800	−	27.1653i	0.576374	−	1.19705i
$516$		0			0
$517$	−2.40750	−	4.16992i	−0.105882	−	0.183393i
$518$	−1.17832			−0.0517724
$519$		0			0
$520$	3.74494	−	6.48643i	0.164226	−	0.284449i
$521$	−19.8020	−	34.2981i	−0.867543	−	1.50263i	−0.864500	−	0.502633i	$-0.832365\pi$
$521$	−19.8020	−	34.2981i	−0.867543	−	1.50263i	−0.00304340	−	0.999995i	$-0.500969\pi$
$522$		0			0
$523$	27.6546			1.20925			0.604625	−	0.796510i	$-0.293323\pi$
$523$	27.6546			1.20925			0.604625	+	0.796510i	$0.293323\pi$
$524$	−1.36588			−0.0596688
$525$		0			0
$526$	4.43608	−	7.68352i	0.193422	−	0.335017i
$527$	−7.25273	+	12.5621i	−0.315934	+	0.547213i
$528$		0			0
$529$	−4.61967			−0.200855
$530$	3.08301	−	5.33993i	0.133917	−	0.231952i
$531$		0			0
$532$	−0.0172066	+	0.0298027i	−0.000746002	+	0.00129211i
$533$	3.17893	+	5.50607i	0.137695	+	0.238495i
$534$		0			0
$535$	16.0230	+	27.7526i	0.692734	+	1.19985i
$536$	10.3123	−	17.8613i	0.445422	−	0.771493i
$537$		0			0
$538$	−18.5853			−0.801271
$539$	11.9769			0.515880
$540$		0			0
$541$	−8.17216	−	14.1546i	−0.351349	−	0.608553i	0.635137	−	0.772399i	$-0.280943\pi$
$541$	−8.17216	−	14.1546i	−0.351349	−	0.608553i	−0.986486	+	0.163846i	$0.947610\pi$
$542$	1.47391			0.0633098
$543$		0			0
$544$	−2.96868	−	5.14190i	−0.127281	−	0.220457i
$545$	−39.5076			−1.69232
$546$		0			0
$547$	8.37438	−	14.5048i	0.358063	−	0.620183i	−0.629575	−	0.776940i	$-0.716771\pi$
$547$	8.37438	−	14.5048i	0.358063	−	0.620183i	0.987637	+	0.156757i	$0.0501041\pi$
$548$	−0.364773	+	0.631805i	−0.0155823	+	0.0269894i
$549$		0			0
$550$	3.99548	+	6.92038i	0.170368	+	0.295086i
$551$	1.95746	−	3.39042i	0.0833906	−	0.144437i
$552$		0			0
$553$	0.498608	−	0.863615i	0.0212030	−	0.0367246i
$554$	−1.39103			−0.0590993
$555$		0			0
$556$	−2.00520	−	3.47312i	−0.0850396	−	0.147293i
$557$	−24.7342			−1.04802			−0.524011	−	0.851712i	$-0.675565\pi$
$557$	−24.7342			−1.04802			−0.524011	+	0.851712i	$0.675565\pi$
$558$		0			0
$559$	0.792251	+	1.37222i	0.0335086	+	0.0580387i
$560$	−0.403816	+	0.699430i	−0.0170643	+	0.0295563i
$561$		0			0
$562$	10.7377	−	18.5983i	0.452944	−	0.784522i
$563$	9.30960	+	16.1247i	0.392353	+	0.679575i	0.992759	−	0.120120i	$-0.0383279\pi$
$563$	9.30960	+	16.1247i	0.392353	+	0.679575i	−0.600406	+	0.799695i	$0.704995\pi$
$564$		0			0
$565$	−7.88850	+	13.6633i	−0.331872	+	0.574818i
$566$	−14.7490	+	25.5460i	−0.619947	+	1.07378i
$567$		0			0
$568$	−13.1152	+	22.7161i	−0.550300	+	0.953148i
$569$	1.10187	+	1.90849i	0.0461927	+	0.0800080i	0.888197	−	0.459462i	$-0.151958\pi$
$569$	1.10187	+	1.90849i	0.0461927	+	0.0800080i	−0.842005	+	0.539470i	$0.818625\pi$
$570$		0			0
$571$	10.8971	−	18.8744i	0.456031	−	0.789869i	−0.542716	−	0.839916i	$-0.682604\pi$
$571$	10.8971	−	18.8744i	0.456031	−	0.789869i	0.998747	+	0.0500474i	$0.0159372\pi$
$572$	−0.362202	−	0.627352i	−0.0151444	−	0.0262309i
$573$		0			0
$574$	−0.472880	−	0.819052i	−0.0197376	−	0.0341866i
$575$	−8.20070	−	14.2040i	−0.341993	−	0.592349i
$576$		0			0
$577$	−23.5599	−	40.8070i	−0.980812	−	1.69882i	−0.659242	−	0.751931i	$-0.729123\pi$
$577$	−23.5599	−	40.8070i	−0.980812	−	1.69882i	−0.321571	−	0.946886i	$-0.604211\pi$
$578$	7.67498	−	13.2935i	0.319237	−	0.552935i
$579$		0			0
$580$	−4.47999	+	7.75956i	−0.186021	+	0.322198i
$581$	−1.36762			−0.0567385
$582$		0			0
$583$	−1.45864	−	2.52644i	−0.0604108	−	0.104635i
$584$	7.31815			0.302827
$585$		0			0
$586$	−5.82535	+	10.0898i	−0.240643	+	0.416806i
$587$	−27.6042			−1.13935			−0.569674	−	0.821871i	$-0.692930\pi$
$587$	−27.6042			−1.13935			−0.569674	+	0.821871i	$0.692930\pi$
$588$		0			0
$589$	−2.30427	−	3.99112i	−0.0949460	−	0.164451i
$590$	10.2982	+	17.8371i	0.423972	+	0.734341i
$591$		0			0
$592$	13.0376	+	22.5819i	0.535844	+	0.928109i
$593$	19.4462	+	33.6819i	0.798561	+	1.38315i	0.920553	+	0.390617i	$0.127738\pi$
$593$	19.4462	+	33.6819i	0.798561	+	1.38315i	−0.121993	+	0.992531i	$0.538928\pi$
$594$		0			0
$595$	−0.626160			−0.0256701
$596$	−0.414686			−0.0169862
$597$		0			0
$598$	−2.14981	−	3.72358i	−0.0879122	−	0.152268i
$599$	−12.8731	−	22.2968i	−0.525979	−	0.911022i	−0.999542	−	0.0302621i	$-0.990366\pi$
$599$	−12.8731	−	22.2968i	−0.525979	−	0.911022i	0.473563	−	0.880760i	$-0.342968\pi$
$600$		0			0
$601$	4.23930	−	7.34269i	0.172925	−	0.299514i	−0.766516	−	0.642225i	$-0.778012\pi$
$601$	4.23930	−	7.34269i	0.172925	−	0.299514i	0.939441	+	0.342710i	$0.111345\pi$
$602$	−0.117851	−	0.204123i	−0.00480324	−	0.00831945i
$603$		0			0
$604$	4.64021			0.188807
$605$	−23.9568			−0.973983
$606$		0			0
$607$	−0.158531	+	0.274583i	−0.00643456	+	0.0111450i	−0.869225	−	0.494417i	$-0.835382\pi$
$607$	−0.158531	+	0.274583i	−0.00643456	+	0.0111450i	0.862790	+	0.505562i	$0.168715\pi$
$608$	1.88637			0.0765022
$609$		0			0
$610$	−45.5719			−1.84515
$611$	1.15591	−	2.00210i	0.0467633	−	0.0809964i
$612$		0			0
$613$	2.38871	−	4.13737i	0.0964791	−	0.167107i	−0.813746	−	0.581221i	$-0.802575\pi$
$613$	2.38871	−	4.13737i	0.0964791	−	0.167107i	0.910225	+	0.414114i	$0.135909\pi$
$614$	12.5428	−	21.7248i	0.506188	−	0.876743i
$615$		0			0
$616$	0.263565	+	0.456509i	0.0106194	+	0.0183933i
$617$	−0.924396			−0.0372148			−0.0186074	−	0.999827i	$-0.505923\pi$
$617$	−0.924396			−0.0372148			−0.0186074	+	0.999827i	$0.505923\pi$
$618$		0			0
$619$	−13.7873			−0.554158			−0.277079	−	0.960847i	$-0.589366\pi$
$619$	−13.7873			−0.554158			−0.277079	+	0.960847i	$0.589366\pi$
$620$	5.27373	+	9.13437i	0.211798	+	0.366845i
$621$		0			0
$622$	−5.61362	+	9.72307i	−0.225085	+	0.389860i
$623$	0.0130614	−	0.0226231i	0.000523296	−	0.000906375i
$624$		0			0
$625$	14.7463	−	25.5414i	0.589853	−	1.02166i
$626$	−20.2240			−0.808314
$627$		0			0
$628$	0.0792615			0.00316288
$629$	−10.1081	+	17.5078i	−0.403038	+	0.698082i
$630$		0			0
$631$	25.6687			1.02185			0.510927	−	0.859624i	$-0.329302\pi$
$631$	25.6687			1.02185			0.510927	+	0.859624i	$0.329302\pi$
$632$	−30.4429			−1.21095
$633$		0			0
$634$	10.1754	+	17.6243i	0.404116	+	0.699950i
$635$	5.03304	−	8.71748i	0.199730	−	0.345943i
$636$		0			0
$637$	2.87523	+	4.98004i	0.113921	+	0.197316i
$638$	−6.12940	−	10.6164i	−0.242665	−	0.420308i
$639$		0			0
$640$	15.2979			0.604702
$641$	38.7167			1.52922			0.764608	−	0.644495i	$-0.222932\pi$
$641$	38.7167			1.52922			0.764608	+	0.644495i	$0.222932\pi$
$642$		0			0
$643$	3.88683	+	6.73218i	0.153282	+	0.265491i	0.932432	−	0.361346i	$-0.117683\pi$
$643$	3.88683	+	6.73218i	0.153282	+	0.265491i	−0.779150	+	0.626837i	$0.784349\pi$
$644$	−0.110587	−	0.191542i	−0.00435772	−	0.00754780i
$645$		0			0
$646$	−0.853690	−	1.47863i	−0.0335880	−	0.0581761i
$647$	23.7011	+	41.0516i	0.931787	+	1.61390i	0.780265	+	0.625449i	$0.215084\pi$
$647$	23.7011	+	41.0516i	0.931787	+	1.61390i	0.151523	+	0.988454i	$0.451582\pi$
$648$		0			0
$649$	9.74467			0.382512
$650$	−1.91835	+	3.32268i	−0.0752439	+	0.130326i
$651$		0			0
$652$	5.56798			0.218059
$653$	13.5783	+	23.5183i	0.531361	+	0.920343i	0.999330	+	0.0365989i	$0.0116524\pi$
$653$	13.5783	+	23.5183i	0.531361	+	0.920343i	−0.467969	+	0.883745i	$0.655014\pi$
$654$		0			0
$655$	7.89597			0.308521
$656$	−10.4645	+	18.1250i	−0.408568	+	0.707661i
$657$		0			0
$658$	−0.171947	+	0.297821i	−0.00670320	+	0.0116103i
$659$	23.3541	+	40.4505i	0.909746	+	1.57573i	0.814416	+	0.580281i	$0.197057\pi$
$659$	23.3541	+	40.4505i	0.909746	+	1.57573i	0.0953297	+	0.995446i	$0.469609\pi$
$660$		0			0
$661$	−17.4629	−	30.2466i	−0.679228	−	1.17646i	−0.975214	−	0.221265i	$-0.928981\pi$
$661$	−17.4629	−	30.2466i	−0.679228	−	1.17646i	0.295986	−	0.955192i	$-0.404352\pi$
$662$	6.29171	+	10.8976i	0.244534	+	0.423546i
$663$		0			0
$664$	20.8753	+	36.1570i	0.810118	+	1.40317i
$665$	0.0994692	−	0.172286i	0.00385725	−	0.00668095i
$666$		0			0
$667$	12.5806	+	21.7902i	0.487121	+	0.843718i
$668$	−2.48015	+	4.29575i	−0.0959600	+	0.166208i
$669$		0			0
$670$	−12.1865	+	21.1076i	−0.470805	+	0.815458i
$671$	−10.7806	+	18.6725i	−0.416179	+	0.720843i
$672$		0			0
$673$	−3.92627	−	6.80051i	−0.151347	−	0.262140i	0.780376	−	0.625311i	$-0.215028\pi$
$673$	−3.92627	−	6.80051i	−0.151347	−	0.262140i	−0.931723	+	0.363170i	$0.881694\pi$
$674$	5.49290	−	9.51399i	0.211579	−	0.366465i
$675$		0			0
$676$	−3.16646	+	5.48447i	−0.121787	+	0.210941i
$677$	−8.33389	−	14.4347i	−0.320298	−	0.554772i	0.660252	−	0.751044i	$-0.270450\pi$
$677$	−8.33389	−	14.4347i	−0.320298	−	0.554772i	−0.980549	+	0.196273i	$0.937116\pi$
$678$		0			0
$679$	−0.247914			−0.00951407
$680$	9.55767	+	16.5544i	0.366520	+	0.634831i
$681$		0			0
$682$	−14.4308			−0.552582
$683$	−15.4000	+	26.6737i	−0.589266	+	1.02064i	0.405062	+	0.914289i	$0.367250\pi$
$683$	−15.4000	+	26.6737i	−0.589266	+	1.02064i	−0.994329	+	0.106350i	$0.966083\pi$
$684$		0			0
$685$	2.10870	−	3.65238i	0.0805693	−	0.139550i
$686$	−0.856021	−	1.48267i	−0.0326830	−	0.0566087i
$687$		0			0
$688$	−2.60794	+	4.51709i	−0.0994268	+	0.172212i
$689$	0.700338	−	1.21302i	0.0266808	−	0.0462124i
$690$		0			0
$691$	−5.53904			−0.210715			−0.105358	−	0.994434i	$-0.533599\pi$
$691$	−5.53904			−0.210715			−0.105358	+	0.994434i	$0.533599\pi$
$692$	−0.194737	−	0.337295i	−0.00740279	−	0.0128220i
$693$		0			0
$694$	11.4341			0.434034
$695$	11.5918	+	20.0776i	0.439703	+	0.761587i
$696$		0			0
$697$	−16.2263			−0.614614
$698$	38.7939			1.46837
$699$		0			0
$700$	−0.0986803	+	0.170919i	−0.00372976	+	0.00646014i
$701$	−14.7369	−	25.5251i	−0.556605	−	0.964068i	−0.997777	−	0.0666456i	$-0.978770\pi$
$701$	−14.7369	−	25.5251i	−0.556605	−	0.964068i	0.441172	−	0.897423i	$-0.354563\pi$
$702$		0			0
$703$	−3.21147	−	5.56243i	−0.121123	−	0.209791i
$704$	7.59358	−	13.1525i	0.286194	−	0.495702i
$705$		0			0
$706$	12.4007	−	21.4787i	0.466708	−	0.808361i
$707$	−0.0815975			−0.00306879
$708$		0			0
$709$	4.42280	−	7.66052i	0.166102	−	0.287697i	−0.770944	−	0.636903i	$-0.780215\pi$
$709$	4.42280	−	7.66052i	0.166102	−	0.287697i	0.937046	+	0.349206i	$0.113549\pi$
$710$	15.4988	−	26.8448i	0.581661	−	1.00747i
$711$		0			0
$712$	−0.797476			−0.0298867
$713$	29.6190			1.10924
$714$		0			0
$715$	2.09384	+	3.62664i	0.0783052	+	0.135629i
$716$	5.79653	−	10.0399i	0.216627	−	0.375208i
$717$		0			0
$718$	−2.81493			−0.105052
$719$	13.6652	+	23.6688i	0.509625	+	0.882696i	0.999938	+	0.0111496i	$0.00354909\pi$
$719$	13.6652	+	23.6688i	0.509625	+	0.882696i	−0.490313	+	0.871546i	$0.663118\pi$
$720$		0			0
$721$	−0.441988	+	0.917946i	−0.0164605	+	0.0341861i
$722$	−22.6196			−0.841815
$723$		0			0
$724$	−8.50067			−0.315925
$725$	11.2261	−	19.4441i	0.416926	−	0.722136i
$726$		0			0
$727$	1.20782	+	2.09201i	0.0447957	+	0.0775884i	0.887554	−	0.460704i	$-0.152403\pi$
$727$	1.20782	+	2.09201i	0.0447957	+	0.0775884i	−0.842758	+	0.538292i	$0.819070\pi$
$728$	−0.126546	+	0.219183i	−0.00469009	+	0.00812348i
$729$		0			0
$730$	−8.64820			−0.320084
$731$	−4.04389			−0.149569
$732$		0			0
$733$	3.50332	−	6.06792i	0.129398	−	0.224124i	−0.794046	−	0.607858i	$-0.792029\pi$
$733$	3.50332	−	6.06792i	0.129398	−	0.224124i	0.923443	+	0.383735i	$0.125362\pi$
$734$	25.1709			0.929076
$735$		0			0
$736$	−6.06182	+	10.4994i	−0.223442	+	0.387012i
$737$	5.76571	+	9.98650i	0.212383	+	0.367857i
$738$		0			0
$739$	−6.45602	−	11.1822i	−0.237489	−	0.411342i	0.722504	−	0.691366i	$-0.242991\pi$
$739$	−6.45602	−	11.1822i	−0.237489	−	0.411342i	−0.959993	+	0.280024i	$0.909658\pi$
$740$	7.35001	+	12.7306i	0.270192	+	0.467986i
$741$		0			0
$742$	−0.104178	+	0.180442i	−0.00382451	+	0.00662424i
$743$	−17.4799			−0.641276			−0.320638	−	0.947202i	$-0.603897\pi$
$743$	−17.4799			−0.641276			−0.320638	+	0.947202i	$0.603897\pi$
$744$		0			0
$745$	2.39725			0.0878283
$746$	13.0124	+	22.5381i	0.476417	+	0.825178i
$747$		0			0
$748$	1.84879			0.0675985
$749$	−0.541434	−	0.937791i	−0.0197836	−	0.0342661i
$750$		0			0
$751$	−38.6142			−1.40905			−0.704526	−	0.709678i	$-0.748840\pi$
$751$	−38.6142			−1.40905			−0.704526	+	0.709678i	$0.748840\pi$
$752$	7.61011			0.277512
$753$		0			0
$754$	2.94291	−	5.09726i	0.107174	−	0.185631i
$755$	−26.8244			−0.976240
$756$		0			0
$757$	−22.5326	+	39.0276i	−0.818960	+	1.41848i	0.0874887	+	0.996166i	$0.472116\pi$
$757$	−22.5326	+	39.0276i	−0.818960	+	1.41848i	−0.906449	+	0.422315i	$0.861217\pi$
$758$	−28.6618			−1.04104
$759$		0			0
$760$	−6.07316			−0.220297
$761$	−4.54384	+	7.87017i	−0.164714	+	0.285293i	−0.936554	−	0.350524i	$-0.886004\pi$
$761$	−4.54384	+	7.87017i	−0.164714	+	0.285293i	0.771840	+	0.635817i	$0.219337\pi$
$762$		0			0
$763$	1.33501			0.0483305
$764$	1.67703	+	2.90471i	0.0606729	+	0.105089i
$765$		0			0
$766$	−10.5392	+	18.2545i	−0.380798	+	0.659561i
$767$	2.33935	+	4.05188i	0.0844691	+	0.146305i
$768$		0			0
$769$	10.8029	+	18.7112i	0.389563	+	0.674743i	0.992391	−	0.123128i	$-0.0392926\pi$
$769$	10.8029	+	18.7112i	0.389563	+	0.674743i	−0.602827	+	0.797872i	$0.705959\pi$
$770$	−0.311468	−	0.539478i	−0.0112245	−	0.0194414i
$771$		0			0
$772$	−2.88863	+	5.00326i	−0.103964	+	0.180071i
$773$	−20.0521	+	34.7312i	−0.721223	+	1.24919i	0.239287	+	0.970949i	$0.423086\pi$
$773$	−20.0521	+	34.7312i	−0.721223	+	1.24919i	−0.960510	+	0.278246i	$0.910247\pi$
$774$		0			0
$775$	−13.2151	−	22.8891i	−0.474699	−	0.822202i
$776$	3.78414	+	6.55433i	0.135843	+	0.235287i
$777$		0			0
$778$	−15.6285	−	27.0694i	−0.560311	−	0.970486i
$779$	2.57764	−	4.46460i	0.0923534	−	0.159961i
$780$		0			0
$781$	−7.33285	−	12.7009i	−0.262390	−	0.454473i
$782$	10.9733			0.392404
$783$		0			0
$784$	−9.46471	+	16.3934i	−0.338025	+	0.585477i
$785$	−0.458200			−0.0163539
$786$		0			0
$787$	−3.87254			−0.138041			−0.0690206	−	0.997615i	$-0.521987\pi$
$787$	−3.87254			−0.138041			−0.0690206	+	0.997615i	$0.521987\pi$
$788$	−2.30161	+	3.98650i	−0.0819914	+	0.142013i
$789$		0			0
$790$	35.9758			1.27996
$791$	0.266561	−	0.461697i	0.00947782	−	0.0164161i
$792$		0			0
$793$	−10.3521			−0.367615
$794$	−26.8772			−0.953837
$795$		0			0
$796$	1.15699	+	2.00396i	0.0410083	+	0.0710285i
$797$	37.6697			1.33433			0.667164	−	0.744911i	$-0.267508\pi$
$797$	37.6697			1.33433			0.667164	+	0.744911i	$0.267508\pi$
$798$		0			0
$799$	2.95007	+	5.10968i	0.104366	+	0.180767i
$800$	10.8183			0.382486
$801$		0			0
$802$	−33.1112			−1.16920
$803$	−2.04583	+	3.54348i	−0.0721958	+	0.125047i
$804$		0			0
$805$	0.639286	+	1.10728i	0.0225319	+	0.0390264i
$806$	−3.46432	−	6.00038i	−0.122025	−	0.211354i
$807$		0			0
$808$	1.24550	+	2.15727i	0.0438165	+	0.0758924i
$809$	−3.70289	+	6.41359i	−0.130187	+	0.225490i	−0.923748	−	0.383000i	$-0.874891\pi$
$809$	−3.70289	+	6.41359i	−0.130187	+	0.225490i	0.793562	+	0.608490i	$0.208224\pi$
$810$		0			0
$811$	−37.6856			−1.32332			−0.661660	−	0.749804i	$-0.730148\pi$
$811$	−37.6856			−1.32332			−0.661660	+	0.749804i	$0.730148\pi$
$812$	0.151384	−	0.262204i	0.00531252	−	0.00920156i
$813$		0			0
$814$	−20.1122			−0.704931
$815$	−32.1877			−1.12749
$816$		0			0
$817$	0.642396	−	1.11266i	0.0224746	−	0.0389271i
$818$	−4.37870	−	7.58412i	−0.153098	−	0.265173i
$819$		0			0
$820$	−5.89937	+	10.2180i	−0.206015	+	0.356828i
$821$	−48.1660			−1.68101			−0.840503	−	0.541807i	$-0.817740\pi$
$821$	−48.1660			−1.68101			−0.840503	+	0.541807i	$0.817740\pi$
$822$		0			0
$823$	−14.8353			−0.517125			−0.258563	−	0.965994i	$-0.583249\pi$
$823$	−14.8353			−0.517125			−0.258563	+	0.965994i	$0.583249\pi$
$824$	31.0151	−	2.32623i	1.08046	−	0.0810382i
$825$		0			0
$826$	−0.347989	−	0.602734i	−0.0121081	−	0.0209718i
$827$	−29.8491			−1.03796			−0.518978	−	0.854787i	$-0.673687\pi$
$827$	−29.8491			−1.03796			−0.518978	+	0.854787i	$0.673687\pi$
$828$		0			0
$829$	5.00876	−	8.67543i	0.173962	−	0.301310i	−0.765840	−	0.643031i	$-0.777676\pi$
$829$	5.00876	−	8.67543i	0.173962	−	0.301310i	0.939801	+	0.341721i	$0.111010\pi$
$830$	−24.6693	−	42.7285i	−0.856285	−	1.48313i
$831$		0			0
$832$	7.29181			0.252798
$833$	−14.6760			−0.508495
$834$		0			0
$835$	14.3374	−	24.8331i	0.496167	−	0.859387i
$836$	−0.293691	+	0.508688i	−0.0101575	+	0.0175934i
$837$		0			0
$838$	−37.4170			−1.29255
$839$	1.39283	−	2.41245i	0.0480858	−	0.0832870i	−0.840981	−	0.541065i	$-0.818021\pi$
$839$	1.39283	−	2.41245i	0.0480858	−	0.0832870i	0.889066	+	0.457778i	$0.151355\pi$
$840$		0			0
$841$	−2.72170	+	4.71413i	−0.0938518	+	0.162556i
$842$	21.8761	+	37.8906i	0.753901	+	1.30580i
$843$		0			0
$844$	1.79439	+	3.10797i	0.0617653	+	0.106981i
$845$	18.3049	−	31.7050i	0.629707	−	1.09068i
$846$		0			0
$847$	0.809527			0.0278157
$848$	4.61076			0.158334
$849$		0			0
$850$	−4.89593	−	8.47999i	−0.167929	−	0.290861i
$851$	41.2801			1.41506
$852$		0			0
$853$	−14.2519	−	24.6850i	−0.487976	−	0.845200i	0.511928	−	0.859028i	$-0.328931\pi$
$853$	−14.2519	−	24.6850i	−0.487976	−	0.845200i	−0.999904	+	0.0138285i	$0.995598\pi$
$854$	1.53992			0.0526951
$855$		0			0
$856$	−16.5288	+	28.6288i	−0.564944	+	0.978511i
$857$	−5.59726	+	9.69474i	−0.191199	+	0.331166i	−0.945648	−	0.325193i	$-0.894571\pi$
$857$	−5.59726	+	9.69474i	−0.191199	+	0.331166i	0.754449	+	0.656359i	$0.227904\pi$
$858$		0			0
$859$	23.8931	+	41.3840i	0.815221	+	1.41200i	0.909169	+	0.416426i	$0.136718\pi$
$859$	23.8931	+	41.3840i	0.815221	+	1.41200i	−0.0939489	+	0.995577i	$0.529949\pi$
$860$	−1.47023	+	2.54652i	−0.0501346	+	0.0868356i
$861$		0			0
$862$	14.8672	−	25.7507i	0.506378	−	0.877072i
$863$	−5.44444			−0.185331			−0.0926654	−	0.995697i	$-0.529539\pi$
$863$	−5.44444			−0.185331			−0.0926654	+	0.995697i	$0.529539\pi$
$864$		0			0
$865$	1.12575	+	1.94985i	0.0382766	+	0.0662970i
$866$	−46.7091			−1.58724
$867$		0			0
$868$	−0.178205	−	0.308660i	−0.00604868	−	0.0104766i
$869$	8.51050	−	14.7406i	0.288699	−	0.500041i
$870$		0			0
$871$	−2.76829	+	4.79481i	−0.0937998	+	0.162466i
$872$	−20.3775	−	35.2948i	−0.690068	−	1.19523i
$873$		0			0
$874$	−1.74317	+	3.01926i	−0.0589636	+	0.102128i
$875$	−0.175113	+	0.303305i	−0.00591990	+	0.0102536i
$876$		0			0
$877$	−13.2126	+	22.8848i	−0.446156	+	0.772765i	−0.998132	−	0.0610950i	$-0.980541\pi$
$877$	−13.2126	+	22.8848i	−0.446156	+	0.772765i	0.551976	+	0.833860i	$0.313874\pi$
$878$	−20.1554	−	34.9101i	−0.680210	−	1.17816i
$879$		0			0
$880$	−6.89253	+	11.9382i	−0.232347	+	0.402437i
$881$	15.4833	+	26.8178i	0.521645	+	0.903516i	0.999683	+	0.0251764i	$0.00801475\pi$
$881$	15.4833	+	26.8178i	0.521645	+	0.903516i	−0.478038	+	0.878339i	$0.658652\pi$
$882$		0			0
$883$	−25.8674	−	44.8037i	−0.870507	−	1.50776i	−0.861473	−	0.507804i	$-0.830458\pi$
$883$	−25.8674	−	44.8037i	−0.870507	−	1.50776i	−0.00903448	−	0.999959i	$-0.502876\pi$
$884$	0.443830	+	0.768736i	0.0149276	+	0.0258554i
$885$		0			0
$886$	−17.3903	−	30.1209i	−0.584239	−	1.01193i
$887$	17.9879	−	31.1560i	0.603975	−	1.04611i	−0.388238	−	0.921559i	$-0.626916\pi$
$887$	17.9879	−	31.1560i	0.603975	−	1.04611i	0.992213	−	0.124556i	$-0.0397505\pi$
$888$		0			0
$889$	−0.170072	+	0.294573i	−0.00570403	+	0.00987967i
$890$	0.942416			0.0315899
$891$		0			0
$892$	4.01025	+	6.94595i	0.134273	+	0.232568i
$893$	−1.87454			−0.0627292
$894$		0			0
$895$	−33.5090	+	58.0392i	−1.12008	+	1.94004i
$896$	−0.516932			−0.0172695
$897$		0			0
$898$	−8.16184	−	14.1367i	−0.272364	−	0.471748i
$899$	20.2730	+	35.1138i	0.676142	+	1.17111i
$900$		0			0
$901$	1.78737	+	3.09582i	0.0595460	+	0.103137i
$902$	−8.07136	−	13.9800i	−0.268747	−	0.465483i
$903$		0			0
$904$	−16.2751			−0.541301
$905$	49.1412			1.63351
$906$		0			0
$907$	9.57873	+	16.5908i	0.318056	+	0.550890i	0.980082	−	0.198591i	$-0.0636365\pi$
$907$	9.57873	+	16.5908i	0.318056	+	0.550890i	−0.662026	+	0.749481i	$0.730303\pi$
$908$	4.47592	+	7.75253i	0.148539	+	0.257277i
$909$		0			0
$910$	0.149545	−	0.259020i	0.00495737	−	0.00858641i
$911$	−9.78296	−	16.9446i	−0.324124	−	0.561399i	0.657211	−	0.753707i	$-0.271736\pi$
$911$	−9.78296	−	16.9446i	−0.324124	−	0.561399i	−0.981335	+	0.192308i	$0.938403\pi$
$912$		0			0
$913$	−23.3432			−0.772549
$914$	−38.1627			−1.26231
$915$		0			0
$916$	1.37861	−	2.38782i	0.0455505	−	0.0788958i
$917$	−0.266814			−0.00881096
$918$		0			0
$919$	20.2701			0.668647			0.334324	−	0.942458i	$-0.391492\pi$
$919$	20.2701			0.668647			0.334324	+	0.942458i	$0.391492\pi$
$920$	19.5160	−	33.8028i	0.643425	−	1.11444i
$921$		0			0
$922$	−16.4395	+	28.4740i	−0.541404	+	0.937740i
$923$	3.52072	−	6.09807i	0.115886	−	0.200720i
$924$		0			0
$925$	−18.4178	−	31.9006i	−0.605575	−	1.04889i
$926$	−5.22378			−0.171664
$927$		0			0
$928$	−16.5962			−0.544798
$929$	−7.31800	−	12.6751i	−0.240096	−	0.415858i	0.720646	−	0.693304i	$-0.243846\pi$
$929$	−7.31800	−	12.6751i	−0.240096	−	0.415858i	−0.960741	+	0.277446i	$0.910512\pi$
$930$		0			0
$931$	2.33137	−	4.03806i	0.0764077	−	0.132342i
$932$	2.20352	−	3.81660i	0.0721786	−	0.125017i
$933$		0			0
$934$	−17.9707	+	31.1262i	−0.588019	+	1.01848i
$935$	−10.6876			−0.349522
$936$		0			0
$937$	−1.51709			−0.0495610			−0.0247805	−	0.999693i	$-0.507889\pi$
$937$	−1.51709			−0.0495610			−0.0247805	+	0.999693i	$0.507889\pi$
$938$	0.411795	−	0.713249i	0.0134456	−	0.0232884i
$939$		0			0
$940$	4.29022			0.139932
$941$	−41.7751			−1.36183			−0.680915	−	0.732362i	$-0.738418\pi$
$941$	−41.7751			−1.36183			−0.680915	+	0.732362i	$0.738418\pi$
$942$		0			0
$943$	16.5664	+	28.6939i	0.539477	+	0.934401i
$944$	−7.70071	+	13.3380i	−0.250637	+	0.434116i
$945$		0			0
$946$	−2.01154	−	3.48408i	−0.0654007	−	0.113277i
$947$	−0.400889	−	0.694360i	−0.0130271	−	0.0225637i	0.859438	−	0.511239i	$-0.170813\pi$
$947$	−0.400889	−	0.694360i	−0.0130271	−	0.0225637i	−0.872465	+	0.488676i	$0.837480\pi$
$948$		0			0
$949$	−1.96453			−0.0637713
$950$	3.11099			0.100934
$951$		0			0
$952$	−0.322964	−	0.559390i	−0.0104673	−	0.0181299i
$953$	−21.6771	−	37.5459i	−0.702192	−	1.21623i	−0.967696	−	0.252122i	$-0.918872\pi$
$953$	−21.6771	−	37.5459i	−0.702192	−	1.21623i	0.265504	−	0.964110i	$-0.414462\pi$
$954$		0			0
$955$	−9.69470	−	16.7917i	−0.313713	−	0.543367i
$956$	−4.33343	−	7.50573i	−0.140153	−	0.242753i
$957$		0			0
$958$	46.3782			1.49841
$959$	−0.0712553	+	0.123418i	−0.00230095	+	0.00398537i
$960$		0			0
$961$	16.7297			0.539669
$962$	−4.82823	−	8.36273i	−0.155668	−	0.269625i
$963$		0			0
$964$	2.02115			0.0650970
$965$	16.6988	−	28.9231i	0.537553	−	0.931069i
$966$		0			0
$967$	27.6775	−	47.9389i	0.890049	−	1.54161i	0.0502345	−	0.998737i	$-0.484003\pi$
$967$	27.6775	−	47.9389i	0.890049	−	1.54161i	0.839815	−	0.542873i	$-0.182664\pi$
$968$	−12.3566	−	21.4022i	−0.397155	−	0.687893i
$969$		0			0
$970$	−4.47191	−	7.74557i	−0.143584	−	0.248695i
$971$	12.9927	+	22.5040i	0.416955	+	0.722187i	0.995631	−	0.0933700i	$-0.0297640\pi$
$971$	12.9927	+	22.5040i	0.416955	+	0.722187i	−0.578677	+	0.815557i	$0.696431\pi$
$972$		0			0
$973$	−0.391700	−	0.678444i	−0.0125573	−	0.0217499i
$974$	−15.3658	+	26.6144i	−0.492353	+	0.852780i
$975$		0			0
$976$	−17.0386	−	29.5118i	−0.545394	−	0.944649i
$977$	2.12158	−	3.67469i	0.0678754	−	0.117564i	−0.830090	−	0.557629i	$-0.811711\pi$
$977$	2.12158	−	3.67469i	0.0678754	−	0.117564i	0.897966	+	0.440065i	$0.145045\pi$
$978$		0			0
$979$	0.222939	−	0.386142i	0.00712517	−	0.0123412i
$980$	−5.33576	+	9.24180i	−0.170444	+	0.295218i
$981$		0			0
$982$	11.9799	+	20.7498i	0.382293	+	0.662151i
$983$	20.7016	−	35.8562i	0.660277	−	1.14363i	−0.320265	−	0.947328i	$-0.603772\pi$
$983$	20.7016	−	35.8562i	0.660277	−	1.14363i	0.980543	−	0.196306i	$-0.0628946\pi$
$984$		0			0
$985$	13.3053	−	23.0454i	0.423942	−	0.734289i
$986$	7.51075	+	13.0090i	0.239191	+	0.414291i
$987$		0			0
$988$	−0.282020			−0.00897225
$989$	4.12866	+	7.15106i	0.131284	+	0.227390i
$990$		0			0
$991$	42.4460			1.34834			0.674171	−	0.738576i	$-0.264501\pi$
$991$	42.4460			1.34834			0.674171	+	0.738576i	$0.264501\pi$
$992$	−9.76834	+	16.9193i	−0.310145	+	0.537187i
$993$		0			0
$994$	−0.523722	+	0.907114i	−0.0166115	+	0.0287719i
$995$	−6.68839	−	11.5846i	−0.212036	−	0.367257i
$996$		0			0
$997$	13.7257	−	23.7737i	0.434698	−	0.752919i	−0.562573	−	0.826748i	$-0.690188\pi$
$997$	13.7257	−	23.7737i	0.434698	−	0.752919i	0.997271	+	0.0738284i	$0.0235217\pi$
$998$	19.6443	−	34.0249i	0.621829	−	1.07704i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.f.f.46.6	✓	32
3.2	odd	2	inner	927.2.f.f.46.11	yes	32
103.56	even	3	inner	927.2.f.f.262.6	yes	32
309.56	odd	6	inner	927.2.f.f.262.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.f.f.46.6	✓	32	1.1	even	1	trivial
927.2.f.f.46.11	yes	32	3.2	odd	2	inner
927.2.f.f.262.6	yes	32	103.56	even	3	inner
927.2.f.f.262.11	yes	32	309.56	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.609528 - 1.05573i) q^{2} +(0.256951 - 0.445052i) q^{4} +(-1.48540 + 2.57279i) q^{5} +(0.0501933 - 0.0869373i) q^{7} -3.06459 q^{8} +O(q^{10})\)	\(q+(-0.609528 - 1.05573i) q^{2} +(0.256951 - 0.445052i) q^{4} +(-1.48540 + 2.57279i) q^{5} +(0.0501933 - 0.0869373i) q^{7} -3.06459 q^{8} +3.62157 q^{10} +(0.856724 - 1.48389i) q^{11} +0.822677 q^{13} -0.122377 q^{14} +(1.35405 + 2.34528i) q^{16} +(-1.04980 + 1.81831i) q^{17} +(-0.333534 - 0.577697i) q^{19} +(0.763350 + 1.32216i) q^{20} -2.08879 q^{22} +4.28723 q^{23} +(-1.91282 - 3.31310i) q^{25} +(-0.501445 - 0.868528i) q^{26} +(-0.0257944 - 0.0446773i) q^{28} +(2.93443 + 5.08257i) q^{29} +6.90867 q^{31} +(-1.41392 + 2.44899i) q^{32} +2.55953 q^{34} +(0.149114 + 0.258273i) q^{35} +9.62862 q^{37} +(-0.406596 + 0.704246i) q^{38} +(4.55214 - 7.88453i) q^{40} +(3.86413 + 6.69287i) q^{41} +(0.963015 + 1.66799i) q^{43} +(-0.440272 - 0.762574i) q^{44} +(-2.61319 - 4.52617i) q^{46} +(1.40506 - 2.43364i) q^{47} +(3.49496 + 6.05345i) q^{49} +(-2.33184 + 4.03886i) q^{50} +(0.211388 - 0.366134i) q^{52} +(0.851291 - 1.47448i) q^{53} +(2.54515 + 4.40834i) q^{55} +(-0.153822 + 0.266427i) q^{56} +(3.57723 - 6.19594i) q^{58} +(2.84358 + 4.92523i) q^{59} -12.5835 q^{61} +(-4.21103 - 7.29372i) q^{62} +8.86351 q^{64} +(-1.22200 + 2.11657i) q^{65} +(-3.36497 + 5.82830i) q^{67} +(0.539495 + 0.934432i) q^{68} +(0.181778 - 0.314849i) q^{70} +(4.27959 - 7.41246i) q^{71} -2.38797 q^{73} +(-5.86892 - 10.1653i) q^{74} -0.342807 q^{76} +(-0.0860036 - 0.148963i) q^{77} +9.93377 q^{79} -8.04522 q^{80} +(4.71059 - 8.15899i) q^{82} +(-6.81177 - 11.7983i) q^{83} +(-3.11875 - 5.40183i) q^{85} +(1.17397 - 2.03337i) q^{86} +(-2.62551 + 4.54751i) q^{88} +0.260223 q^{89} +(0.0412929 - 0.0715213i) q^{91} +(1.10161 - 1.90804i) q^{92} -3.42570 q^{94} +1.98172 q^{95} +(-1.23480 - 2.13873i) q^{97} +(4.26055 - 7.37950i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) \) 32 * q - 18 * q^4 + 8 * q^7	\( 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) \) 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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