LMFDB - Embedded newform 912.3.be.f.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.92607408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 94x^2 - 77*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$0.500000 + 0.630453i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.f.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(2.88028 + 4.98878i) q^{5} -1.94451 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(2.88028 + 4.98878i) q^{5} -1.94451 q^{7} +(1.50000 - 2.59808i) q^{9} -8.46561 q^{11} +(-16.7415 - 9.66573i) q^{13} +(8.64083 + 4.98878i) q^{15} +(12.5365 + 21.7138i) q^{17} +(-17.8181 + 6.59651i) q^{19} +(-2.91676 + 1.68399i) q^{21} +(-15.6408 + 27.0907i) q^{23} +(-4.09198 + 7.08751i) q^{25} -5.19615i q^{27} +(13.7071 + 7.91383i) q^{29} +14.4237i q^{31} +(-12.6984 + 7.33143i) q^{33} +(-5.60071 - 9.70072i) q^{35} +41.6423i q^{37} -33.4831 q^{39} +(1.53439 - 0.885881i) q^{41} +(-14.4358 - 25.0035i) q^{43} +17.2817 q^{45} +(-1.70506 + 2.95325i) q^{47} -45.2189 q^{49} +(37.6094 + 21.7138i) q^{51} +(-80.0952 - 46.2430i) q^{53} +(-24.3833 - 42.2331i) q^{55} +(-21.0145 + 25.3257i) q^{57} +(-4.27292 + 2.46697i) q^{59} +(7.45989 - 12.9209i) q^{61} +(-2.91676 + 5.05197i) q^{63} -111.360i q^{65} +(70.4113 + 40.6520i) q^{67} +54.1814i q^{69} +(-52.9948 + 30.5966i) q^{71} +(-38.8299 - 67.2553i) q^{73} +14.1750i q^{75} +16.4614 q^{77} +(-84.0207 + 48.5094i) q^{79} +(-4.50000 - 7.79423i) q^{81} +102.323 q^{83} +(-72.2171 + 125.084i) q^{85} +27.4143 q^{87} +(103.596 + 59.8111i) q^{89} +(32.5540 + 18.7951i) q^{91} +(12.4913 + 21.6355i) q^{93} +(-84.2297 - 69.8911i) q^{95} +(-42.1438 + 24.3318i) q^{97} +(-12.6984 + 21.9943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9	$ 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9 + 36 * q^11 - 3 * q^13 + 12 * q^15 + 38 * q^17 + 10 * q^19 + 33 * q^21 - 54 * q^23 - 21 * q^25 - 102 * q^29 + 54 * q^33 + 24 * q^35 - 6 * q^39 + 96 * q^41 - 107 * q^43 + 24 * q^45 + 50 * q^47 - 48 * q^49 + 114 * q^51 - 90 * q^53 - 148 * q^55 - 3 * q^57 + 27 * q^61 + 33 * q^63 + 39 * q^67 - 84 * q^71 - 77 * q^73 + 260 * q^77 - 9 * q^79 - 27 * q^81 + 348 * q^83 + 68 * q^85 - 204 * q^87 - 72 * q^89 + 393 * q^91 + 129 * q^93 - 104 * q^95 - 228 * q^97 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	2.88028	+	4.98878i	0.576055	+	0.997757i	0.995926	+	0.0901730i	$0.0287420\pi$
$5$	2.88028	+	4.98878i	0.576055	+	0.997757i	−0.419871	+	0.907584i	$0.637925\pi$
$6$		0			0
$7$	−1.94451			−0.277787			−0.138893	−	0.990307i	$-0.544354\pi$
$7$	−1.94451			−0.277787			−0.138893	+	0.990307i	$0.544354\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−8.46561			−0.769601			−0.384800	−	0.923000i	$-0.625730\pi$
$11$	−8.46561			−0.769601			−0.384800	+	0.923000i	$0.625730\pi$
$12$		0			0
$13$	−16.7415	−	9.66573i	−1.28781	−	0.743518i	−0.309547	−	0.950884i	$-0.600178\pi$
$13$	−16.7415	−	9.66573i	−1.28781	−	0.743518i	−0.978263	+	0.207366i	$0.933511\pi$
$14$		0			0
$15$	8.64083	+	4.98878i	0.576055	+	0.332586i
$16$		0			0
$17$	12.5365	+	21.7138i	0.737440	+	1.27728i	0.953644	+	0.300936i	$0.0972990\pi$
$17$	12.5365	+	21.7138i	0.737440	+	1.27728i	−0.216204	+	0.976348i	$0.569368\pi$
$18$		0			0
$19$	−17.8181	+	6.59651i	−0.937797	+	0.347185i
$19$	−17.8181	+	6.59651i	−0.937797	+	0.347185i
$20$		0			0
$21$	−2.91676	+	1.68399i	−0.138893	+	0.0801901i
$22$		0			0
$23$	−15.6408	+	27.0907i	−0.680036	+	1.17786i	0.294933	+	0.955518i	$0.404703\pi$
$23$	−15.6408	+	27.0907i	−0.680036	+	1.17786i	−0.974969	+	0.222339i	$0.928631\pi$
$24$		0			0
$25$	−4.09198	+	7.08751i	−0.163679	+	0.283500i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	13.7071	+	7.91383i	0.472660	+	0.272891i	0.717353	−	0.696710i	$-0.245354\pi$
$29$	13.7071	+	7.91383i	0.472660	+	0.272891i	−0.244692	+	0.969601i	$0.578687\pi$
$30$		0			0
$31$			14.4237i			0.465280i	0.972563	+	0.232640i	$0.0747363\pi$
$31$			14.4237i			0.465280i	−0.972563	+	0.232640i	$0.925264\pi$
$32$		0			0
$33$	−12.6984	+	7.33143i	−0.384800	+	0.222165i
$34$		0			0
$35$	−5.60071	−	9.70072i	−0.160020	−	0.277163i
$36$		0			0
$37$			41.6423i			1.12547i	0.826638	+	0.562734i	$0.190251\pi$
$37$			41.6423i			1.12547i	−0.826638	+	0.562734i	$0.809749\pi$
$38$		0			0
$39$	−33.4831			−0.858541
$40$		0			0
$41$	1.53439	−	0.885881i	0.0374242	−	0.0216069i	−0.481171	−	0.876627i	$-0.659788\pi$
$41$	1.53439	−	0.885881i	0.0374242	−	0.0216069i	0.518595	+	0.855020i	$0.326455\pi$
$42$		0			0
$43$	−14.4358	−	25.0035i	−0.335716	−	0.581476i	0.647906	−	0.761720i	$-0.275645\pi$
$43$	−14.4358	−	25.0035i	−0.335716	−	0.581476i	−0.983622	+	0.180243i	$0.942311\pi$
$44$		0			0
$45$	17.2817			0.384037
$46$		0			0
$47$	−1.70506	+	2.95325i	−0.0362778	+	0.0628350i	−0.883594	−	0.468253i	$-0.844883\pi$
$47$	−1.70506	+	2.95325i	−0.0362778	+	0.0628350i	0.847316	+	0.531088i	$0.178217\pi$
$48$		0			0
$49$	−45.2189			−0.922835
$50$		0			0
$51$	37.6094	+	21.7138i	0.737440	+	0.425761i
$52$		0			0
$53$	−80.0952	−	46.2430i	−1.51123	−	0.872510i	−0.999914	−	0.0131174i	$-0.995824\pi$
$53$	−80.0952	−	46.2430i	−1.51123	−	0.872510i	−0.511317	−	0.859392i	$-0.670842\pi$
$54$		0			0
$55$	−24.3833	−	42.2331i	−0.443333	−	0.767874i
$56$		0			0
$57$	−21.0145	+	25.3257i	−0.368675	+	0.444311i
$58$		0			0
$59$	−4.27292	+	2.46697i	−0.0724224	+	0.0418131i	−0.535774	−	0.844361i	$-0.679980\pi$
$59$	−4.27292	+	2.46697i	−0.0724224	+	0.0418131i	0.463352	+	0.886175i	$0.346647\pi$
$60$		0			0
$61$	7.45989	−	12.9209i	0.122293	−	0.211818i	−0.798378	−	0.602156i	$-0.794309\pi$
$61$	7.45989	−	12.9209i	0.122293	−	0.211818i	0.920672	+	0.390338i	$0.127642\pi$
$62$		0			0
$63$	−2.91676	+	5.05197i	−0.0462978	+	0.0801901i
$64$		0			0
$65$		−	111.360i		−	1.71323i
$66$		0			0
$67$	70.4113	+	40.6520i	1.05091	+	0.606746i	0.922905	−	0.385027i	$-0.125808\pi$
$67$	70.4113	+	40.6520i	1.05091	+	0.606746i	0.128009	+	0.991773i	$0.459141\pi$
$68$		0			0
$69$			54.1814i			0.785238i
$70$		0			0
$71$	−52.9948	+	30.5966i	−0.746406	+	0.430938i	−0.824394	−	0.566017i	$-0.808484\pi$
$71$	−52.9948	+	30.5966i	−0.746406	+	0.430938i	0.0779878	+	0.996954i	$0.475150\pi$
$72$		0			0
$73$	−38.8299	−	67.2553i	−0.531916	−	0.921306i	−0.999306	−	0.0372545i	$-0.988139\pi$
$73$	−38.8299	−	67.2553i	−0.531916	−	0.921306i	0.467390	−	0.884051i	$-0.345195\pi$
$74$		0			0
$75$			14.1750i			0.189000i
$76$		0			0
$77$	16.4614			0.213785
$78$		0			0
$79$	−84.0207	+	48.5094i	−1.06355	+	0.614043i	−0.926413	−	0.376509i	$-0.877125\pi$
$79$	−84.0207	+	48.5094i	−1.06355	+	0.614043i	−0.137140	+	0.990552i	$0.543791\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	102.323			1.23280			0.616401	−	0.787432i	$-0.288590\pi$
$83$	102.323			1.23280			0.616401	+	0.787432i	$0.288590\pi$
$84$		0			0
$85$	−72.2171	+	125.084i	−0.849612	+	1.47157i
$86$		0			0
$87$	27.4143			0.315107
$88$		0			0
$89$	103.596	+	59.8111i	1.16400	+	0.672034i	0.952259	−	0.305292i	$-0.0987540\pi$
$89$	103.596	+	59.8111i	1.16400	+	0.672034i	0.211739	+	0.977326i	$0.432087\pi$
$90$		0			0
$91$	32.5540	+	18.7951i	0.357737	+	0.206539i
$92$		0			0
$93$	12.4913	+	21.6355i	0.134315	+	0.232640i
$94$		0			0
$95$	−84.2297	−	69.8911i	−0.886629	−	0.735695i
$96$		0			0
$97$	−42.1438	+	24.3318i	−0.434473	+	0.250843i	−0.701250	−	0.712915i	$-0.747374\pi$
$97$	−42.1438	+	24.3318i	−0.434473	+	0.250843i	0.266778	+	0.963758i	$0.414041\pi$
$98$		0			0
$99$	−12.6984	+	21.9943i	−0.128267	+	0.222165i
$100$		0			0
$101$	−81.5540	+	141.256i	−0.807465	+	1.39857i	0.107149	+	0.994243i	$0.465828\pi$
$101$	−81.5540	+	141.256i	−0.807465	+	1.39857i	−0.914614	+	0.404327i	$0.867506\pi$
$102$		0			0
$103$			18.2732i			0.177410i	0.996058	+	0.0887050i	$0.0282728\pi$
$103$			18.2732i			0.177410i	−0.996058	+	0.0887050i	$0.971727\pi$
$104$		0			0
$105$	−16.8021	−	9.70072i	−0.160020	−	0.0923878i
$106$		0			0
$107$			55.4789i			0.518494i	0.965811	+	0.259247i	$0.0834744\pi$
$107$			55.4789i			0.518494i	−0.965811	+	0.259247i	$0.916526\pi$
$108$		0			0
$109$	96.4369	−	55.6779i	0.884743	−	0.510806i	0.0125234	−	0.999922i	$-0.496014\pi$
$109$	96.4369	−	55.6779i	0.884743	−	0.510806i	0.872219	+	0.489115i	$0.162680\pi$
$110$		0			0
$111$	36.0633	+	62.4635i	0.324895	+	0.562734i
$112$		0			0
$113$			110.968i			0.982019i	0.871154	+	0.491010i	$0.163372\pi$
$113$			110.968i			0.982019i	−0.871154	+	0.491010i	$0.836628\pi$
$114$		0			0
$115$	−180.200			−1.56695
$116$		0			0
$117$	−50.2246	+	28.9972i	−0.429270	+	0.247839i
$118$		0			0
$119$	−24.3773	−	42.2227i	−0.204851	−	0.354812i
$120$		0			0
$121$	−49.3335			−0.407715
$122$		0			0
$123$	1.53439	−	2.65764i	0.0124747	−	0.0216069i
$124$		0			0
$125$	96.8697			0.774958
$126$		0			0
$127$	209.627	+	121.028i	1.65061	+	0.952979i	0.976822	+	0.214052i	$0.0686661\pi$
$127$	209.627	+	121.028i	1.65061	+	0.952979i	0.673785	+	0.738927i	$0.264667\pi$
$128$		0			0
$129$	−43.3073	−	25.0035i	−0.335716	−	0.193825i
$130$		0			0
$131$	−78.7288	−	136.362i	−0.600983	−	1.04093i	−0.992672	−	0.120836i	$-0.961443\pi$
$131$	−78.7288	−	136.362i	−0.600983	−	1.04093i	0.391689	−	0.920098i	$-0.371891\pi$
$132$		0			0
$133$	34.6475	−	12.8270i	0.260507	−	0.0964433i
$134$		0			0
$135$	25.9225	−	14.9664i	0.192018	−	0.110862i
$136$		0			0
$137$	121.173	−	209.877i	0.884473	−	1.53195i	0.0381558	−	0.999272i	$-0.487852\pi$
$137$	121.173	−	209.877i	0.884473	−	1.53195i	0.846317	−	0.532680i	$-0.178815\pi$
$138$		0			0
$139$	65.0431	−	112.658i	0.467936	−	0.810489i	−0.531392	−	0.847126i	$-0.678331\pi$
$139$	65.0431	−	112.658i	0.467936	−	0.810489i	0.999329	+	0.0366365i	$0.0116644\pi$
$140$		0			0
$141$			5.90649i			0.0418900i
$142$		0			0
$143$	141.727	+	81.8263i	0.991100	+	0.572212i
$144$		0			0
$145$			91.1760i			0.628800i
$146$		0			0
$147$	−67.8283	+	39.1607i	−0.461417	+	0.266399i
$148$		0			0
$149$	−102.368	−	177.306i	−0.687030	−	1.18997i	−0.972794	−	0.231672i	$-0.925581\pi$
$149$	−102.368	−	177.306i	−0.687030	−	1.18997i	0.285764	−	0.958300i	$-0.407753\pi$
$150$		0			0
$151$			234.305i			1.55169i	0.630924	+	0.775845i	$0.282676\pi$
$151$			234.305i			1.55169i	−0.630924	+	0.775845i	$0.717324\pi$
$152$		0			0
$153$	75.2189			0.491627
$154$		0			0
$155$	−71.9566	+	41.5441i	−0.464236	+	0.268027i
$156$		0			0
$157$	44.2955	+	76.7220i	0.282137	+	0.488675i	0.971911	−	0.235349i	$-0.0756234\pi$
$157$	44.2955	+	76.7220i	0.282137	+	0.488675i	−0.689774	+	0.724025i	$0.742290\pi$
$158$		0			0
$159$	−160.190			−1.00749
$160$		0			0
$161$	30.4137	−	52.6780i	0.188905	−	0.327193i
$162$		0			0
$163$	−115.918			−0.711153			−0.355576	−	0.934647i	$-0.615715\pi$
$163$	−115.918			−0.711153			−0.355576	+	0.934647i	$0.615715\pi$
$164$		0			0
$165$	−73.1499	−	42.2331i	−0.443333	−	0.255958i
$166$		0			0
$167$	−78.0426	−	45.0579i	−0.467321	−	0.269808i	0.247797	−	0.968812i	$-0.420293\pi$
$167$	−78.0426	−	45.0579i	−0.467321	−	0.269808i	−0.715118	+	0.699004i	$0.753627\pi$
$168$		0			0
$169$	102.353	+	177.280i	0.605638	+	1.04900i
$170$		0			0
$171$	−9.58896	+	56.1876i	−0.0560758	+	0.328583i
$172$		0			0
$173$	−38.5739	+	22.2707i	−0.222971	+	0.128732i	−0.607325	−	0.794454i	$-0.707757\pi$
$173$	−38.5739	+	22.2707i	−0.222971	+	0.128732i	0.384354	+	0.923186i	$0.374424\pi$
$174$		0			0
$175$	7.95687	−	13.7817i	0.0454678	−	0.0787526i
$176$		0			0
$177$	−4.27292	+	7.40091i	−0.0241408	+	0.0418131i
$178$		0			0
$179$		−	229.632i		−	1.28286i	−0.767181	−	0.641431i	$-0.778341\pi$
$179$		−	229.632i		−	1.28286i	0.767181	−	0.641431i	$-0.221659\pi$
$180$		0			0
$181$	157.070	+	90.6845i	0.867791	+	0.501019i	0.866613	−	0.498980i	$-0.166292\pi$
$181$	157.070	+	90.6845i	0.867791	+	0.501019i	0.00117734	+	0.999999i	$0.499625\pi$
$182$		0			0
$183$		−	25.8418i		−	0.141212i
$184$		0			0
$185$	−207.745	+	119.941i	−1.12294	+	0.648332i
$186$		0			0
$187$	−106.129	−	183.821i	−0.567535	−	0.982999i
$188$		0			0
$189$			10.1039i			0.0534600i
$190$		0			0
$191$	278.704			1.45918			0.729592	−	0.683882i	$-0.239710\pi$
$191$	278.704			1.45918			0.729592	+	0.683882i	$0.239710\pi$
$192$		0			0
$193$	−167.512	+	96.7133i	−0.867939	+	0.501105i	−0.866663	−	0.498894i	$-0.833740\pi$
$193$	−167.512	+	96.7133i	−0.867939	+	0.501105i	−0.00127645	+	0.999999i	$0.500406\pi$
$194$		0			0
$195$	−96.4405	−	167.040i	−0.494567	−	0.856615i
$196$		0			0
$197$	−96.9300			−0.492030			−0.246015	−	0.969266i	$-0.579121\pi$
$197$	−96.9300			−0.492030			−0.246015	+	0.969266i	$0.579121\pi$
$198$		0			0
$199$	−172.893	+	299.460i	−0.868811	+	1.50482i	−0.00559823	+	0.999984i	$0.501782\pi$
$199$	−172.893	+	299.460i	−0.868811	+	1.50482i	−0.863213	+	0.504840i	$0.831551\pi$
$200$		0			0
$201$	140.823			0.700610
$202$		0			0
$203$	−26.6536	−	15.3885i	−0.131299	−	0.0758053i
$204$		0			0
$205$	8.83894	+	5.10316i	0.0431168	+	0.0248935i
$206$		0			0
$207$	46.9225	+	81.2721i	0.226679	+	0.392619i
$208$		0			0
$209$	150.841	−	55.8435i	0.721729	−	0.267194i
$210$		0			0
$211$	11.1758	−	6.45233i	0.0529657	−	0.0305798i	−0.473283	−	0.880910i	$-0.656931\pi$
$211$	11.1758	−	6.45233i	0.0529657	−	0.0305798i	0.526249	+	0.850330i	$0.323598\pi$
$212$		0			0
$213$	−52.9948	+	91.7897i	−0.248802	+	0.430938i
$214$		0			0
$215$	83.1580	−	144.034i	0.386781	−	0.669925i
$216$		0			0
$217$		−	28.0469i		−	0.129248i
$218$		0			0
$219$	−116.490	−	67.2553i	−0.531916	−	0.307102i
$220$		0			0
$221$		−	484.697i		−	2.19320i
$222$		0			0
$223$	80.3821	−	46.4086i	0.360458	−	0.208110i	−0.308824	−	0.951119i	$-0.599935\pi$
$223$	80.3821	−	46.4086i	0.360458	−	0.208110i	0.669282	+	0.743009i	$0.266602\pi$
$224$		0			0
$225$	12.2759	+	21.2625i	0.0545597	+	0.0945002i
$226$		0			0
$227$		−	280.870i		−	1.23731i	−0.785662	−	0.618656i	$-0.787677\pi$
$227$		−	280.870i		−	1.23731i	0.785662	−	0.618656i	$-0.212323\pi$
$228$		0			0
$229$	137.541			0.600615			0.300308	−	0.953842i	$-0.402911\pi$
$229$	137.541			0.600615			0.300308	+	0.953842i	$0.402911\pi$
$230$		0			0
$231$	24.6921	−	14.2560i	0.106892	−	0.0617143i
$232$		0			0
$233$	−183.683	−	318.148i	−0.788339	−	1.36544i	−0.926984	−	0.375101i	$-0.877608\pi$
$233$	−183.683	−	318.148i	−0.788339	−	1.36544i	0.138645	−	0.990342i	$-0.455725\pi$
$234$		0			0
$235$	−19.6441			−0.0835921
$236$		0			0
$237$	−84.0207	+	145.528i	−0.354518	+	0.614043i
$238$		0			0
$239$	196.388			0.821707			0.410854	−	0.911701i	$-0.365231\pi$
$239$	196.388			0.821707			0.410854	+	0.911701i	$0.365231\pi$
$240$		0			0
$241$	−118.225	−	68.2572i	−0.490560	−	0.283225i	0.234247	−	0.972177i	$-0.424738\pi$
$241$	−118.225	−	68.2572i	−0.490560	−	0.283225i	−0.724807	+	0.688952i	$0.758071\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−130.243	−	225.587i	−0.531604	−	0.920765i
$246$		0			0
$247$	362.063	+	61.7896i	1.46584	+	0.250160i
$248$		0			0
$249$	153.484	−	88.6140i	0.616401	−	0.355879i
$250$		0			0
$251$	23.3322	−	40.4126i	0.0929571	−	0.161006i	−0.815797	−	0.578338i	$-0.803701\pi$
$251$	23.3322	−	40.4126i	0.0929571	−	0.161006i	0.908754	+	0.417332i	$0.137035\pi$
$252$		0			0
$253$	132.409	−	229.339i	0.523356	−	0.906480i
$254$		0			0
$255$			250.167i			0.981048i
$256$		0			0
$257$	4.73878	+	2.73593i	0.0184388	+	0.0106457i	0.509191	−	0.860653i	$-0.329945\pi$
$257$	4.73878	+	2.73593i	0.0184388	+	0.0106457i	−0.490752	+	0.871299i	$0.663278\pi$
$258$		0			0
$259$		−	80.9737i		−	0.312640i
$260$		0			0
$261$	41.1214	−	23.7415i	0.157553	−	0.0909635i
$262$		0			0
$263$	−37.1071	−	64.2713i	−0.141091	−	0.244378i	0.786816	−	0.617187i	$-0.211728\pi$
$263$	−37.1071	−	64.2713i	−0.141091	−	0.244378i	−0.927908	+	0.372809i	$0.878394\pi$
$264$		0			0
$265$		−	532.770i		−	2.01045i
$266$		0			0
$267$	207.192			0.775998
$268$		0			0
$269$	−64.2197	+	37.0772i	−0.238735	+	0.137834i	−0.614595	−	0.788843i	$-0.710681\pi$
$269$	−64.2197	+	37.0772i	−0.238735	+	0.137834i	0.375860	+	0.926676i	$0.377347\pi$
$270$		0			0
$271$	−48.0380	−	83.2043i	−0.177262	−	0.307027i	0.763680	−	0.645595i	$-0.223391\pi$
$271$	−48.0380	−	83.2043i	−0.177262	−	0.307027i	−0.940942	+	0.338568i	$0.890057\pi$
$272$		0			0
$273$	65.1080			0.238491
$274$		0			0
$275$	34.6411	−	60.0001i	0.125968	−	0.218182i
$276$		0			0
$277$	123.007			0.444068			0.222034	−	0.975039i	$-0.428730\pi$
$277$	123.007			0.444068			0.222034	+	0.975039i	$0.428730\pi$
$278$		0			0
$279$	37.4738	+	21.6355i	0.134315	+	0.0775466i
$280$		0			0
$281$	352.110	+	203.291i	1.25306	+	0.723454i	0.971716	−	0.236153i	$-0.0758866\pi$
$281$	352.110	+	203.291i	1.25306	+	0.723454i	0.281344	+	0.959607i	$0.409220\pi$
$282$		0			0
$283$	92.7689	+	160.680i	0.327805	+	0.567776i	0.982076	−	0.188485i	$-0.0603576\pi$
$283$	92.7689	+	160.680i	0.327805	+	0.567776i	−0.654271	+	0.756260i	$0.727024\pi$
$284$		0			0
$285$	−186.872	−	31.8915i	−0.655691	−	0.111900i
$286$		0			0
$287$	−2.98363	+	1.72260i	−0.0103959	+	0.00600209i
$288$		0			0
$289$	−169.827	+	294.149i	−0.587636	+	1.01782i
$290$		0			0
$291$	−42.1438	+	72.9953i	−0.144824	+	0.250843i
$292$		0			0
$293$			360.407i			1.23006i	0.788505	+	0.615028i	$0.210855\pi$
$293$			360.407i			1.23006i	−0.788505	+	0.615028i	$0.789145\pi$
$294$		0			0
$295$	−24.6144	−	14.2111i	−0.0834385	−	0.0481733i
$296$		0			0
$297$			43.9886i			0.148110i
$298$		0			0
$299$	523.703	−	302.360i	1.75152	−	1.01124i
$300$		0			0
$301$	28.0704	+	48.6194i	0.0932573	+	0.161526i
$302$		0			0
$303$			282.511i			0.932380i
$304$		0			0
$305$	85.9461			0.281791
$306$		0			0
$307$	233.152	−	134.610i	0.759453	−	0.438470i	−0.0696463	−	0.997572i	$-0.522187\pi$
$307$	233.152	−	134.610i	0.759453	−	0.438470i	0.829099	+	0.559101i	$0.188854\pi$
$308$		0			0
$309$	15.8251	+	27.4098i	0.0512139	+	0.0887050i
$310$		0			0
$311$	−53.4530			−0.171874			−0.0859372	−	0.996301i	$-0.527388\pi$
$311$	−53.4530			−0.171874			−0.0859372	+	0.996301i	$0.527388\pi$
$312$		0			0
$313$	−119.760	+	207.430i	−0.382618	+	0.662715i	−0.991436	−	0.130596i	$-0.958311\pi$
$313$	−119.760	+	207.430i	−0.382618	+	0.662715i	0.608817	+	0.793310i	$0.291644\pi$
$314$		0			0
$315$	−33.6043			−0.106680
$316$		0			0
$317$	391.754	+	226.179i	1.23582	+	0.713499i	0.968236	−	0.250036i	$-0.0804426\pi$
$317$	391.754	+	226.179i	1.23582	+	0.713499i	0.267580	+	0.963536i	$0.413776\pi$
$318$		0			0
$319$	−116.039	−	66.9954i	−0.363760	−	0.210017i
$320$		0			0
$321$	48.0461	+	83.2184i	0.149676	+	0.259247i
$322$		0			0
$323$	−366.612	−	304.203i	−1.13502	−	0.941805i
$324$		0			0
$325$	137.012	−	79.1039i	0.421575	−	0.243397i
$326$		0			0
$327$	96.4369	−	167.034i	0.294914	−	0.510806i
$328$		0			0
$329$	3.31549	−	5.74260i	0.0100775	−	0.0174547i
$330$		0			0
$331$		−	95.4707i		−	0.288431i	−0.989546	−	0.144216i	$-0.953934\pi$
$331$		−	95.4707i		−	0.288431i	0.989546	−	0.144216i	$-0.0460659\pi$
$332$		0			0
$333$	108.190	+	62.4635i	0.324895	+	0.187578i
$334$		0			0
$335$			468.356i			1.39808i
$336$		0			0
$337$	−82.2367	+	47.4794i	−0.244026	+	0.140888i	−0.617026	−	0.786943i	$-0.711663\pi$
$337$	−82.2367	+	47.4794i	−0.244026	+	0.140888i	0.373000	+	0.927831i	$0.378329\pi$
$338$		0			0
$339$	96.1013	+	166.452i	0.283485	+	0.491010i
$340$		0			0
$341$		−	122.105i		−	0.358080i
$342$		0			0
$343$	183.209			0.534138
$344$		0			0
$345$	−270.299	+	156.057i	−0.783476	+	0.452340i
$346$		0			0
$347$	−115.221	−	199.568i	−0.332048	−	0.575124i	0.650865	−	0.759193i	$-0.274406\pi$
$347$	−115.221	−	199.568i	−0.332048	−	0.575124i	−0.982913	+	0.184069i	$0.941073\pi$
$348$		0			0
$349$	−209.160			−0.599312			−0.299656	−	0.954047i	$-0.596872\pi$
$349$	−209.160			−0.599312			−0.299656	+	0.954047i	$0.596872\pi$
$350$		0			0
$351$	−50.2246	+	86.9916i	−0.143090	+	0.247839i
$352$		0			0
$353$	326.125			0.923866			0.461933	−	0.886915i	$-0.347156\pi$
$353$	326.125			0.923866			0.461933	+	0.886915i	$0.347156\pi$
$354$		0			0
$355$	−305.279	−	176.253i	−0.859942	−	0.496488i
$356$		0			0
$357$	−73.1318	−	42.2227i	−0.204851	−	0.118271i
$358$		0			0
$359$	268.735	+	465.463i	0.748566	+	1.29655i	0.948510	+	0.316747i	$0.102590\pi$
$359$	268.735	+	465.463i	0.748566	+	1.29655i	−0.199945	+	0.979807i	$0.564076\pi$
$360$		0			0
$361$	273.972	−	235.075i	0.758925	−	0.651178i
$362$		0			0
$363$	−74.0002	+	42.7240i	−0.203857	+	0.117697i
$364$		0			0
$365$	223.682	−	387.428i	0.612826	−	1.06145i
$366$		0			0
$367$	181.274	−	313.976i	0.493935	−	0.855520i	−0.506041	−	0.862509i	$-0.668892\pi$
$367$	181.274	−	313.976i	0.493935	−	0.855520i	0.999976	+	0.00698970i	$0.00222491\pi$
$368$		0			0
$369$		−	5.31529i		−	0.0144046i
$370$		0			0
$371$	155.746	+	89.9198i	0.419800	+	0.242371i
$372$		0			0
$373$		−	336.486i		−	0.902108i	−0.892497	−	0.451054i	$-0.851048\pi$
$373$		−	336.486i		−	0.902108i	0.892497	−	0.451054i	$-0.148952\pi$
$374$		0			0
$375$	145.305	−	83.8916i	0.387479	−	0.223711i
$376$		0			0
$377$	−152.986	−	264.979i	−0.405798	−	0.702863i
$378$		0			0
$379$			336.744i			0.888507i	0.895901	+	0.444253i	$0.146531\pi$
$379$			336.744i			0.888507i	−0.895901	+	0.444253i	$0.853469\pi$
$380$		0			0
$381$	419.254			1.10041
$382$		0			0
$383$	193.755	−	111.865i	0.505888	−	0.292075i	−0.225254	−	0.974300i	$-0.572321\pi$
$383$	193.755	−	111.865i	0.505888	−	0.292075i	0.731142	+	0.682226i	$0.238988\pi$
$384$		0			0
$385$	47.4134	+	82.1225i	0.123152	+	0.213305i
$386$		0			0
$387$	−86.6146			−0.223810
$388$		0			0
$389$	100.458	−	173.998i	0.258246	−	0.447295i	−0.707526	−	0.706687i	$-0.750189\pi$
$389$	100.458	−	173.998i	0.258246	−	0.447295i	0.965772	+	0.259392i	$0.0835221\pi$
$390$		0			0
$391$	−784.324			−2.00594
$392$		0			0
$393$	−236.186	−	136.362i	−0.600983	−	0.346978i
$394$		0			0
$395$	−484.006	−	279.441i	−1.22533	−	0.707445i
$396$		0			0
$397$	−53.1506	−	92.0595i	−0.133880	−	0.231888i	0.791289	−	0.611443i	$-0.209410\pi$
$397$	−53.1506	−	92.0595i	−0.133880	−	0.231888i	−0.925169	+	0.379555i	$0.876077\pi$
$398$		0			0
$399$	40.8627	−	49.2460i	0.102413	−	0.123424i
$400$		0			0
$401$	185.008	−	106.815i	0.461368	−	0.266371i	−0.251252	−	0.967922i	$-0.580842\pi$
$401$	185.008	−	106.815i	0.461368	−	0.266371i	0.712619	+	0.701551i	$0.247509\pi$
$402$		0			0
$403$	139.415	−	241.474i	0.345944	−	0.599192i
$404$		0			0
$405$	25.9225	−	44.8991i	0.0640061	−	0.110862i
$406$		0			0
$407$		−	352.528i		−	0.866161i
$408$		0			0
$409$	−46.6112	−	26.9110i	−0.113964	−	0.0657970i	0.441935	−	0.897047i	$-0.354292\pi$
$409$	−46.6112	−	26.9110i	−0.113964	−	0.0657970i	−0.555898	+	0.831250i	$0.687626\pi$
$410$		0			0
$411$		−	419.755i		−	1.02130i
$412$		0			0
$413$	8.30872	−	4.79704i	0.0201180	−	0.0116151i
$414$		0			0
$415$	294.717	+	510.465i	0.710162	+	1.23004i
$416$		0			0
$417$		−	225.316i		−	0.540326i
$418$		0			0
$419$	808.890			1.93052			0.965262	−	0.261282i	$-0.0841454\pi$
$419$	808.890			1.93052			0.965262	+	0.261282i	$0.0841454\pi$
$420$		0			0
$421$	−309.086	+	178.451i	−0.734171	+	0.423874i	−0.819946	−	0.572441i	$-0.805997\pi$
$421$	−309.086	+	178.451i	−0.734171	+	0.423874i	0.0857753	+	0.996315i	$0.472663\pi$
$422$		0			0
$423$	5.11517	+	8.85974i	0.0120926	+	0.0209450i
$424$		0			0
$425$	−205.196			−0.482814
$426$		0			0
$427$	−14.5058	+	25.1248i	−0.0339714	+	0.0588402i
$428$		0			0
$429$	283.455			0.660733
$430$		0			0
$431$	36.3673	+	20.9967i	0.0843789	+	0.0487162i	0.541596	−	0.840639i	$-0.317820\pi$
$431$	36.3673	+	20.9967i	0.0843789	+	0.0487162i	−0.457217	+	0.889355i	$0.651154\pi$
$432$		0			0
$433$	533.602	+	308.075i	1.23234	+	0.711491i	0.967517	−	0.252807i	$-0.0813538\pi$
$433$	533.602	+	308.075i	1.23234	+	0.711491i	0.264821	+	0.964298i	$0.414687\pi$
$434$		0			0
$435$	78.9607	+	136.764i	0.181519	+	0.314400i
$436$		0			0
$437$	99.9862	−	585.881i	0.228801	−	1.34069i
$438$		0			0
$439$	408.012	−	235.566i	0.929413	−	0.536597i	0.0427870	−	0.999084i	$-0.486376\pi$
$439$	408.012	−	235.566i	0.929413	−	0.536597i	0.886626	+	0.462487i	$0.153043\pi$
$440$		0			0
$441$	−67.8283	+	117.482i	−0.153806	+	0.266399i
$442$		0			0
$443$	−52.2697	+	90.5338i	−0.117990	+	0.204365i	−0.918971	−	0.394325i	$-0.870979\pi$
$443$	−52.2697	+	90.5338i	−0.117990	+	0.204365i	0.800981	+	0.598690i	$0.204312\pi$
$444$		0			0
$445$			689.089i			1.54852i
$446$		0			0
$447$	−307.103	−	177.306i	−0.687030	−	0.396657i
$448$		0			0
$449$			713.259i			1.58855i	0.607559	+	0.794275i	$0.292149\pi$
$449$			713.259i			1.58855i	−0.607559	+	0.794275i	$0.707851\pi$
$450$		0			0
$451$	−12.9896	+	7.49952i	−0.0288017	+	0.0166287i
$452$		0			0
$453$	202.914	+	351.458i	0.447934	+	0.775845i
$454$		0			0
$455$			216.540i			0.475912i
$456$		0			0
$457$	−5.29457			−0.0115855			−0.00579275	−	0.999983i	$-0.501844\pi$
$457$	−5.29457			−0.0115855			−0.00579275	+	0.999983i	$0.501844\pi$
$458$		0			0
$459$	112.828	−	65.1415i	0.245813	−	0.141920i
$460$		0			0
$461$	−93.4120	−	161.794i	−0.202629	−	0.350964i	0.746746	−	0.665110i	$-0.231615\pi$
$461$	−93.4120	−	161.794i	−0.202629	−	0.350964i	−0.949375	+	0.314146i	$0.898282\pi$
$462$		0			0
$463$	−718.582			−1.55201			−0.776007	−	0.630725i	$-0.782758\pi$
$463$	−718.582			−1.55201			−0.776007	+	0.630725i	$0.782758\pi$
$464$		0			0
$465$	−71.9566	+	124.632i	−0.154745	+	0.268027i
$466$		0			0
$467$	−864.548			−1.85128			−0.925641	−	0.378404i	$-0.876473\pi$
$467$	−864.548			−1.85128			−0.925641	+	0.378404i	$0.876473\pi$
$468$		0			0
$469$	−136.915	−	79.0480i	−0.291930	−	0.168546i
$470$		0			0
$471$	132.886	+	76.7220i	0.282137	+	0.162892i
$472$		0			0
$473$	122.208	+	211.670i	0.258367	+	0.447505i
$474$		0			0
$475$	26.1585	−	153.279i	0.0550706	−	0.322693i
$476$		0			0
$477$	−240.286	+	138.729i	−0.503744	+	0.290837i
$478$		0			0
$479$	−63.1395	+	109.361i	−0.131815	+	0.228311i	−0.924376	−	0.381482i	$-0.875414\pi$
$479$	−63.1395	+	109.361i	−0.131815	+	0.228311i	0.792561	+	0.609793i	$0.208747\pi$
$480$		0			0
$481$	402.504	−	697.157i	0.836806	−	1.44939i
$482$		0			0
$483$		−	105.356i		−	0.218129i
$484$		0			0
$485$	−242.772	−	140.164i	−0.500560	−	0.288999i
$486$		0			0
$487$		−	12.1199i		−	0.0248868i	−0.999923	−	0.0124434i	$-0.996039\pi$
$487$		−	12.1199i		−	0.0248868i	0.999923	−	0.0124434i	$-0.00396097\pi$
$488$		0			0
$489$	−173.877	+	100.388i	−0.355576	+	0.205292i
$490$		0			0
$491$	−246.271	−	426.554i	−0.501570	−	0.868745i	−0.999998	−	0.00181372i	$-0.999423\pi$
$491$	−246.271	−	426.554i	−0.501570	−	0.868745i	0.498428	−	0.866931i	$-0.333911\pi$
$492$		0			0
$493$			396.846i			0.804962i
$494$		0			0
$495$	−146.300			−0.295555
$496$		0			0
$497$	103.049	−	59.4952i	0.207342	−	0.119709i
$498$		0			0
$499$	−173.134	−	299.877i	−0.346962	−	0.600956i	0.638746	−	0.769417i	$-0.279453\pi$
$499$	−173.134	−	299.877i	−0.346962	−	0.600956i	−0.985708	+	0.168462i	$0.946120\pi$
$500$		0			0
$501$	−156.085			−0.311547
$502$		0			0
$503$	−166.249	+	287.952i	−0.330516	+	0.572470i	−0.982613	−	0.185665i	$-0.940556\pi$
$503$	−166.249	+	287.952i	−0.330516	+	0.572470i	0.652098	+	0.758135i	$0.273889\pi$
$504$		0			0
$505$	−939.592			−1.86058
$506$		0			0
$507$	307.058	+	177.280i	0.605638	+	0.349665i
$508$		0			0
$509$	−461.493	−	266.443i	−0.906666	−	0.523464i	−0.0273090	−	0.999627i	$-0.508694\pi$
$509$	−461.493	−	266.443i	−0.906666	−	0.523464i	−0.879357	+	0.476163i	$0.842027\pi$
$510$		0			0
$511$	75.5049	+	130.778i	0.147759	+	0.255926i
$512$		0			0
$513$	34.2765	+	92.5858i	0.0668158	+	0.180479i
$514$		0			0
$515$	−91.1612	+	52.6319i	−0.177012	+	0.102198i
$516$		0			0
$517$	14.4343	−	25.0010i	0.0279194	−	0.0483579i
$518$		0			0
$519$	−38.5739	+	66.8120i	−0.0743235	+	0.128732i
$520$		0			0
$521$		−	74.3056i		−	0.142621i	−0.997454	−	0.0713106i	$-0.977282\pi$
$521$		−	74.3056i		−	0.142621i	0.997454	−	0.0713106i	$-0.0227181\pi$
$522$		0			0
$523$	−25.3191	−	14.6180i	−0.0484113	−	0.0279503i	0.475599	−	0.879662i	$-0.342231\pi$
$523$	−25.3191	−	14.6180i	−0.0484113	−	0.0279503i	−0.524010	+	0.851712i	$0.675565\pi$
$524$		0			0
$525$		−	27.5634i		−	0.0525017i
$526$		0			0
$527$	−313.193	+	180.822i	−0.594294	+	0.343116i
$528$		0			0
$529$	−224.771	−	389.315i	−0.424898	−	0.735945i
$530$		0			0
$531$			14.8018i			0.0278754i
$532$		0			0
$533$	−34.2508			−0.0642603
$534$		0			0
$535$	−276.772	+	159.795i	−0.517331	+	0.298681i
$536$		0			0
$537$	−198.867	−	344.448i	−0.370330	−	0.641431i
$538$		0			0
$539$	382.805			0.710214
$540$		0			0
$541$	109.055	−	188.889i	0.201580	−	0.349147i	−0.747458	−	0.664310i	$-0.768726\pi$
$541$	109.055	−	188.889i	0.201580	−	0.349147i	0.949038	+	0.315163i	$0.102059\pi$
$542$		0			0
$543$	314.140			0.578527
$544$		0			0
$545$	555.530	+	320.735i	1.01932	+	0.588505i
$546$		0			0
$547$	465.237	+	268.605i	0.850525	+	0.491051i	0.860828	−	0.508896i	$-0.169946\pi$
$547$	465.237	+	268.605i	0.850525	+	0.491051i	−0.0103027	+	0.999947i	$0.503279\pi$
$548$		0			0
$549$	−22.3797	−	38.7627i	−0.0407644	−	0.0706060i
$550$		0			0
$551$	−296.440	−	50.5903i	−0.538003	−	0.0918154i
$552$		0			0
$553$	163.379	−	94.3268i	0.295441	−	0.170573i
$554$		0			0
$555$	−207.745	+	359.824i	−0.374315	+	0.648332i
$556$		0			0
$557$	−158.164	+	273.947i	−0.283956	+	0.491826i	−0.972355	−	0.233505i	$-0.924980\pi$
$557$	−158.164	+	273.947i	−0.283956	+	0.491826i	0.688399	+	0.725332i	$0.258314\pi$
$558$		0			0
$559$			558.129i			0.998442i
$560$		0			0
$561$	−318.387	−	183.821i	−0.567535	−	0.327666i
$562$		0			0
$563$			595.272i			1.05732i	0.848833	+	0.528661i	$0.177306\pi$
$563$			595.272i			1.05732i	−0.848833	+	0.528661i	$0.822694\pi$
$564$		0			0
$565$	−553.596	+	319.619i	−0.979816	+	0.565697i
$566$		0			0
$567$	8.75028	+	15.1559i	0.0154326	+	0.0267300i
$568$		0			0
$569$			536.213i			0.942377i	0.882032	+	0.471189i	$0.156175\pi$
$569$			536.213i			0.942377i	−0.882032	+	0.471189i	$0.843825\pi$
$570$		0			0
$571$	84.5912			0.148146			0.0740729	−	0.997253i	$-0.476400\pi$
$571$	84.5912			0.148146			0.0740729	+	0.997253i	$0.476400\pi$
$572$		0			0
$573$	418.056	−	241.365i	0.729592	−	0.421230i
$574$		0			0
$575$	−128.004	−	221.709i	−0.222615	−	0.385581i
$576$		0			0
$577$	−850.008			−1.47315			−0.736575	−	0.676356i	$-0.763558\pi$
$577$	−850.008			−1.47315			−0.736575	+	0.676356i	$0.763558\pi$
$578$		0			0
$579$	−167.512	+	290.140i	−0.289313	+	0.501105i
$580$		0			0
$581$	−198.967			−0.342456
$582$		0			0
$583$	678.055	+	391.475i	1.16304	+	0.671484i
$584$		0			0
$585$	−289.322	−	167.040i	−0.494567	−	0.285538i
$586$		0			0
$587$	−229.370	−	397.281i	−0.390750	−	0.676798i	0.601799	−	0.798648i	$-0.294451\pi$
$587$	−229.370	−	397.281i	−0.390750	−	0.676798i	−0.992549	+	0.121849i	$0.961117\pi$
$588$		0			0
$589$	−95.1459	−	257.003i	−0.161538	−	0.436338i
$590$		0			0
$591$	−145.395	+	83.9438i	−0.246015	+	0.142037i
$592$		0			0
$593$	−51.3293	+	88.9049i	−0.0865586	+	0.149924i	−0.906054	−	0.423161i	$-0.860920\pi$
$593$	−51.3293	+	88.9049i	−0.0865586	+	0.149924i	0.819496	+	0.573085i	$0.194254\pi$
$594$		0			0
$595$	140.426	−	243.226i	0.236011	−	0.408783i
$596$		0			0
$597$			598.920i			1.00322i
$598$		0			0
$599$	−322.250	−	186.051i	−0.537980	−	0.310603i	0.206280	−	0.978493i	$-0.433864\pi$
$599$	−322.250	−	186.051i	−0.537980	−	0.310603i	−0.744260	+	0.667890i	$0.767198\pi$
$600$		0			0
$601$			850.837i			1.41570i	0.706362	+	0.707851i	$0.250335\pi$
$601$			850.837i			1.41570i	−0.706362	+	0.707851i	$0.749665\pi$
$602$		0			0
$603$	211.234	−	121.956i	0.350305	−	0.202249i
$604$		0			0
$605$	−142.094	−	246.114i	−0.234866	−	0.406800i
$606$		0			0
$607$			314.498i			0.518119i	0.965861	+	0.259060i	$0.0834126\pi$
$607$			314.498i			0.518119i	−0.965861	+	0.259060i	$0.916587\pi$
$608$		0			0
$609$	−53.3073			−0.0875324
$610$		0			0
$611$	57.0906	−	32.9613i	0.0934379	−	0.0539464i
$612$		0			0
$613$	146.198	+	253.222i	0.238495	+	0.413086i	0.960283	−	0.279029i	$-0.0900125\pi$
$613$	146.198	+	253.222i	0.238495	+	0.413086i	−0.721787	+	0.692115i	$0.756679\pi$
$614$		0			0
$615$	17.6779			0.0287445
$616$		0			0
$617$	−438.183	+	758.955i	−0.710183	+	1.23007i	0.254605	+	0.967045i	$0.418055\pi$
$617$	−438.183	+	758.955i	−0.710183	+	1.23007i	−0.964788	+	0.263028i	$0.915279\pi$
$618$		0			0
$619$	166.847			0.269542			0.134771	−	0.990877i	$-0.456970\pi$
$619$	166.847			0.269542			0.134771	+	0.990877i	$0.456970\pi$
$620$		0			0
$621$	140.767	+	81.2721i	0.226679	+	0.130873i
$622$		0			0
$623$	−201.443	−	116.303i	−0.323343	−	0.186682i
$624$		0			0
$625$	381.311	+	660.450i	0.610097	+	1.05672i
$626$		0			0
$627$	177.900	−	214.398i	0.283732	−	0.341942i
$628$		0			0
$629$	−904.214	+	522.048i	−1.43754	+	0.829965i
$630$		0			0
$631$	−464.592	+	804.698i	−0.736280	+	1.27527i	0.217880	+	0.975976i	$0.430086\pi$
$631$	−464.592	+	804.698i	−0.736280	+	1.27527i	−0.954160	+	0.299298i	$0.903248\pi$
$632$		0			0
$633$	11.1758	−	19.3570i	0.0176552	−	0.0305798i
$634$		0			0
$635$			1394.38i			2.19587i
$636$		0			0
$637$	757.034	+	437.074i	1.18844	+	0.686144i
$638$		0			0
$639$			183.579i			0.287292i
$640$		0			0
$641$	425.692	−	245.773i	0.664106	−	0.383422i	−0.129734	−	0.991549i	$-0.541412\pi$
$641$	425.692	−	245.773i	0.664106	−	0.383422i	0.793840	+	0.608127i	$0.208079\pi$
$642$		0			0
$643$	−175.770	−	304.442i	−0.273359	−	0.473472i	0.696361	−	0.717692i	$-0.254801\pi$
$643$	−175.770	−	304.442i	−0.273359	−	0.473472i	−0.969720	+	0.244220i	$0.921468\pi$
$644$		0			0
$645$		−	288.068i		−	0.446617i
$646$		0			0
$647$	−767.027			−1.18551			−0.592757	−	0.805381i	$-0.701961\pi$
$647$	−767.027			−1.18551			−0.592757	+	0.805381i	$0.701961\pi$
$648$		0			0
$649$	36.1729	−	20.8844i	0.0557363	−	0.0321794i
$650$		0			0
$651$	−24.2893	−	42.0704i	−0.0373108	−	0.0646242i
$652$		0			0
$653$	−254.877			−0.390317			−0.195159	−	0.980772i	$-0.562522\pi$
$653$	−254.877			−0.390317			−0.195159	+	0.980772i	$0.562522\pi$
$654$		0			0
$655$	453.521	−	785.522i	0.692399	−	1.19927i
$656$		0			0
$657$	−232.979			−0.354611
$658$		0			0
$659$	427.502	+	246.818i	0.648713	+	0.374535i	0.787963	−	0.615723i	$-0.211136\pi$
$659$	427.502	+	246.818i	0.648713	+	0.374535i	−0.139250	+	0.990257i	$0.544469\pi$
$660$		0			0
$661$	−1110.75	−	641.292i	−1.68041	−	0.970185i	−0.961388	−	0.275197i	$-0.911257\pi$
$661$	−1110.75	−	641.292i	−1.68041	−	0.970185i	−0.719021	−	0.694988i	$-0.755410\pi$
$662$		0			0
$663$	−419.760	−	727.046i	−0.633122	−	1.09660i
$664$		0			0
$665$	163.785	+	135.904i	0.246294	+	0.204366i
$666$		0			0
$667$	−428.782	+	247.558i	−0.642852	+	0.371151i
$668$		0			0
$669$	80.3821	−	139.226i	0.120153	−	0.208110i
$670$		0			0
$671$	−63.1525	+	109.383i	−0.0941169	+	0.163015i
$672$		0			0
$673$		−	337.649i		−	0.501707i	−0.968025	−	0.250853i	$-0.919289\pi$
$673$		−	337.649i		−	0.501707i	0.968025	−	0.250853i	$-0.0807112\pi$
$674$		0			0
$675$	36.8278	+	21.2625i	0.0545597	+	0.0315001i
$676$		0			0
$677$		−	394.197i		−	0.582270i	−0.956682	−	0.291135i	$-0.905967\pi$
$677$		−	394.197i		−	0.582270i	0.956682	−	0.291135i	$-0.0940329\pi$
$678$		0			0
$679$	81.9489	−	47.3132i	0.120691	−	0.0696808i
$680$		0			0
$681$	−243.240	−	421.305i	−0.357181	−	0.618656i
$682$		0			0
$683$			612.782i			0.897192i	0.893735	+	0.448596i	$0.148076\pi$
$683$			612.782i			0.897192i	−0.893735	+	0.448596i	$0.851924\pi$
$684$		0			0
$685$	1396.04			2.03802
$686$		0			0
$687$	206.311	−	119.114i	0.300308	−	0.173383i
$688$		0			0
$689$	893.945	+	1548.36i	1.29745	+	2.24725i
$690$		0			0
$691$	−254.757			−0.368678			−0.184339	−	0.982863i	$-0.559014\pi$
$691$	−254.757			−0.368678			−0.184339	+	0.982863i	$0.559014\pi$
$692$		0			0
$693$	24.6921	−	42.7680i	0.0356308	−	0.0617143i
$694$		0			0
$695$	749.369			1.07823
$696$		0			0
$697$	38.4717	+	22.2117i	0.0551962	+	0.0318675i
$698$		0			0
$699$	−551.049	−	318.148i	−0.788339	−	0.455148i
$700$		0			0
$701$	−3.62864	−	6.28499i	−0.00517638	−	0.00896576i	0.863426	−	0.504476i	$-0.168314\pi$
$701$	−3.62864	−	6.28499i	−0.00517638	−	0.00896576i	−0.868602	+	0.495510i	$0.834981\pi$
$702$		0			0
$703$	−274.694	−	741.989i	−0.390746	−	1.05546i
$704$		0			0
$705$	−29.4662	+	17.0123i	−0.0417960	+	0.0241310i
$706$		0			0
$707$	158.582	−	274.672i	0.224303	−	0.388504i
$708$		0			0
$709$	−522.280	+	904.615i	−0.736643	+	1.27590i	0.217356	+	0.976092i	$0.430257\pi$
$709$	−522.280	+	904.615i	−0.736643	+	1.27590i	−0.953999	+	0.299810i	$0.903077\pi$
$710$		0			0
$711$			291.056i			0.409362i
$712$		0			0
$713$	−390.747	−	225.598i	−0.548033	−	0.316407i
$714$		0			0
$715$			942.729i			1.31850i
$716$		0			0
$717$	294.582	−	170.077i	0.410854	−	0.237207i
$718$		0			0
$719$	658.810	+	1141.09i	0.916286	+	1.58705i	0.805007	+	0.593265i	$0.202161\pi$
$719$	658.810	+	1141.09i	0.916286	+	1.58705i	0.111279	+	0.993789i	$0.464505\pi$
$720$		0			0
$721$		−	35.5324i		−	0.0492821i
$722$		0			0
$723$	−236.450			−0.327040
$724$		0			0
$725$	−112.179	+	64.7664i	−0.154729	+	0.0893330i
$726$		0			0
$727$	88.8280	+	153.855i	0.122184	+	0.211630i	0.920629	−	0.390439i	$-0.127677\pi$
$727$	88.8280	+	153.855i	0.122184	+	0.211630i	−0.798444	+	0.602068i	$0.794343\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	361.948	−	626.912i	0.495140	−	0.857608i
$732$		0			0
$733$	321.795			0.439011			0.219505	−	0.975611i	$-0.429556\pi$
$733$	321.795			0.439011			0.219505	+	0.975611i	$0.429556\pi$
$734$		0			0
$735$	−390.729	−	225.587i	−0.531604	−	0.306922i
$736$		0			0
$737$	−596.074	−	344.144i	−0.808785	−	0.466952i
$738$		0			0
$739$	−85.7034	−	148.443i	−0.115972	−	0.200870i	0.802196	−	0.597061i	$-0.203665\pi$
$739$	−85.7034	−	148.443i	−0.115972	−	0.200870i	−0.918168	+	0.396191i	$0.870332\pi$
$740$		0			0
$741$	596.606	−	220.872i	0.805136	−	0.298072i
$742$		0			0
$743$	257.044	−	148.405i	0.345955	−	0.199737i	−0.316947	−	0.948443i	$-0.602658\pi$
$743$	257.044	−	148.405i	0.345955	−	0.199737i	0.662902	+	0.748706i	$0.269325\pi$
$744$		0			0
$745$	589.693	−	1021.38i	0.791535	−	1.37098i
$746$		0			0
$747$	153.484	−	265.842i	0.205467	−	0.355879i
$748$		0			0
$749$		−	107.879i		−	0.144031i
$750$		0			0
$751$	117.403	+	67.7829i	0.156329	+	0.0902568i	0.576124	−	0.817362i	$-0.304565\pi$
$751$	117.403	+	67.7829i	0.156329	+	0.0902568i	−0.419795	+	0.907619i	$0.637898\pi$
$752$		0			0
$753$		−	80.8252i		−	0.107338i
$754$		0			0
$755$	−1168.90	+	674.864i	−1.54821	+	0.893859i
$756$		0			0
$757$	4.71078	+	8.15931i	0.00622296	+	0.0107785i	0.869120	−	0.494601i	$-0.164686\pi$
$757$	4.71078	+	8.15931i	0.00622296	+	0.0107785i	−0.862897	+	0.505380i	$0.831352\pi$
$758$		0			0
$759$		−	458.679i		−	0.604320i
$760$		0			0
$761$	−501.946			−0.659587			−0.329794	−	0.944053i	$-0.606979\pi$
$761$	−501.946			−0.659587			−0.329794	+	0.944053i	$0.606979\pi$
$762$		0			0
$763$	−187.522	+	108.266i	−0.245770	+	0.141895i
$764$		0			0
$765$	216.651	+	375.251i	0.283204	+	0.490524i
$766$		0			0
$767$	95.3803			0.124355
$768$		0			0
$769$	722.257	−	1250.99i	0.939216	−	1.62677i	0.172279	−	0.985048i	$-0.444887\pi$
$769$	722.257	−	1250.99i	0.939216	−	1.62677i	0.766937	−	0.641722i	$-0.221780\pi$
$770$		0			0
$771$	9.47756			0.0122926
$772$		0			0
$773$	−572.771	−	330.690i	−0.740972	−	0.427800i	0.0814506	−	0.996677i	$-0.474045\pi$
$773$	−572.771	−	330.690i	−0.740972	−	0.427800i	−0.822423	+	0.568877i	$0.807378\pi$
$774$		0			0
$775$	−102.228	−	59.0213i	−0.131907	−	0.0761565i
$776$		0			0
$777$	−70.1253	−	121.461i	−0.0902514	−	0.156320i
$778$		0			0
$779$	−21.4963	+	25.9064i	−0.0275947	+	0.0332559i
$780$		0			0
$781$	448.633	−	259.019i	0.574435	−	0.331650i
$782$		0			0
$783$	41.1214	−	71.2244i	0.0525178	−	0.0909635i
$784$		0			0
$785$	−255.166	+	441.961i	−0.325053	+	0.563008i
$786$		0			0
$787$		−	1319.00i		−	1.67598i	−0.545686	−	0.837990i	$-0.683731\pi$
$787$		−	1319.00i		−	1.67598i	0.545686	−	0.837990i	$-0.316269\pi$
$788$		0			0
$789$	−111.321	−	64.2713i	−0.141091	−	0.0814592i
$790$		0			0
$791$		−	215.778i		−	0.272792i
$792$		0			0
$793$	−249.780	+	144.211i	−0.314981	+	0.181854i
$794$		0			0
$795$	−461.393	−	799.156i	−0.580368	−	1.00523i
$796$		0			0
$797$			512.600i			0.643162i	0.946882	+	0.321581i	$0.104214\pi$
$797$			512.600i			0.643162i	−0.946882	+	0.321581i	$0.895786\pi$
$798$		0			0
$799$	−85.5017			−0.107011
$800$		0			0
$801$	310.787	−	179.433i	0.387999	−	0.224011i
$802$		0			0
$803$	328.719	+	569.357i	0.409363	+	0.709038i
$804$		0			0
$805$	350.399			0.435278
$806$		0			0
$807$	−64.2197	+	111.232i	−0.0795783	+	0.137834i
$808$		0			0
$809$	368.489			0.455487			0.227743	−	0.973721i	$-0.426865\pi$
$809$	368.489			0.455487			0.227743	+	0.973721i	$0.426865\pi$
$810$		0			0
$811$	5.72688	+	3.30642i	0.00706150	+	0.00407696i	0.503527	−	0.863980i	$-0.332036\pi$
$811$	5.72688	+	3.30642i	0.00706150	+	0.00407696i	−0.496465	+	0.868057i	$0.665369\pi$
$812$		0			0
$813$	−144.114	−	83.2043i	−0.177262	−	0.102342i
$814$		0			0
$815$	−333.876	−	578.290i	−0.409663	−	0.709558i
$816$		0			0
$817$	422.154	+	350.290i	0.516713	+	0.428751i
$818$		0			0
$819$	97.6621	−	56.3852i	0.119246	−	0.0688464i
$820$		0			0
$821$	−541.742	+	938.324i	−0.659856	+	1.14290i	0.320796	+	0.947148i	$0.396049\pi$
$821$	−541.742	+	938.324i	−0.659856	+	1.14290i	−0.980653	+	0.195756i	$0.937284\pi$
$822$		0			0
$823$	160.542	−	278.067i	0.195069	−	0.337869i	−0.751854	−	0.659329i	$-0.770840\pi$
$823$	160.542	−	278.067i	0.195069	−	0.337869i	0.946923	+	0.321460i	$0.104174\pi$
$824$		0			0
$825$		−	120.000i		−	0.145455i
$826$		0			0
$827$	710.535	+	410.228i	0.859172	+	0.496043i	0.863735	−	0.503946i	$-0.168119\pi$
$827$	710.535	+	410.228i	0.859172	+	0.496043i	−0.00456293	+	0.999990i	$0.501452\pi$
$828$		0			0
$829$			1041.55i			1.25640i	0.778053	+	0.628199i	$0.216208\pi$
$829$			1041.55i			1.25640i	−0.778053	+	0.628199i	$0.783792\pi$
$830$		0			0
$831$	184.510	−	106.527i	0.222034	−	0.128191i
$832$		0			0
$833$	−566.886	−	981.875i	−0.680535	−	1.17872i
$834$		0			0
$835$		−	519.117i		−	0.621697i
$836$		0			0
$837$	74.9476			0.0895431
$838$		0			0
$839$	−791.650	+	457.059i	−0.943564	+	0.544767i	−0.891076	−	0.453855i	$-0.850048\pi$
$839$	−791.650	+	457.059i	−0.943564	+	0.544767i	−0.0524880	+	0.998622i	$0.516715\pi$
$840$		0			0
$841$	−295.243	−	511.375i	−0.351061	−	0.608056i
$842$		0			0
$843$	704.219			0.835373
$844$		0			0
$845$	−589.608	+	1021.23i	−0.697761	+	1.20856i
$846$		0			0
$847$	95.9292			0.113258
$848$		0			0
$849$	278.307	+	160.680i	0.327805	+	0.189259i
$850$		0			0
$851$	−1128.12	−	651.320i	−1.32564	−	0.765359i
$852$		0			0
$853$	−3.45117	−	5.97759i	−0.00404592	−	0.00700773i	0.863995	−	0.503500i	$-0.167955\pi$
$853$	−3.45117	−	5.97759i	−0.00404592	−	0.00700773i	−0.868041	+	0.496492i	$0.834621\pi$
$854$		0			0
$855$	−307.927	+	113.999i	−0.360148	+	0.133332i
$856$		0			0
$857$	543.649	−	313.876i	0.634363	−	0.366250i	−0.148077	−	0.988976i	$-0.547308\pi$
$857$	543.649	−	313.876i	0.634363	−	0.366250i	0.782440	+	0.622726i	$0.213975\pi$
$858$		0			0
$859$	−347.688	+	602.214i	−0.404759	+	0.701064i	−0.994293	−	0.106680i	$-0.965978\pi$
$859$	−347.688	+	602.214i	−0.404759	+	0.701064i	0.589534	+	0.807743i	$0.299311\pi$
$860$		0			0
$861$	−2.98363	+	5.16780i	−0.00346531	+	0.00600209i
$862$		0			0
$863$		−	636.029i		−	0.736998i	−0.929628	−	0.368499i	$-0.879872\pi$
$863$		−	636.029i		−	0.736998i	0.929628	−	0.368499i	$-0.120128\pi$
$864$		0			0
$865$	−222.207	−	128.291i	−0.256887	−	0.148314i
$866$		0			0
$867$			588.297i			0.678544i
$868$		0			0
$869$	711.287	−	410.662i	0.818512	−	0.472568i
$870$		0			0
$871$	−785.862	−	1361.15i	−0.902253	−	1.56275i
$872$		0			0
$873$			145.991i			0.167229i
$874$		0			0
$875$	−188.364			−0.215273
$876$		0			0
$877$	−710.586	+	410.257i	−0.810246	+	0.467796i	−0.847041	−	0.531527i	$-0.821618\pi$
$877$	−710.586	+	410.257i	−0.810246	+	0.467796i	0.0367954	+	0.999323i	$0.488285\pi$
$878$		0			0
$879$	312.121	+	540.610i	0.355087	+	0.615028i
$880$		0			0
$881$	1473.56			1.67260			0.836301	−	0.548271i	$-0.184714\pi$
$881$	1473.56			1.67260			0.836301	+	0.548271i	$0.184714\pi$
$882$		0			0
$883$	−204.732	+	354.606i	−0.231859	+	0.401592i	−0.958355	−	0.285578i	$-0.907814\pi$
$883$	−204.732	+	354.606i	−0.231859	+	0.401592i	0.726496	+	0.687171i	$0.241148\pi$
$884$		0			0
$885$	−49.2287			−0.0556257
$886$		0			0
$887$	1177.32	+	679.728i	1.32731	+	0.766322i	0.984883	−	0.173223i	$-0.0554181\pi$
$887$	1177.32	+	679.728i	1.32731	+	0.766322i	0.342426	+	0.939545i	$0.388751\pi$
$888$		0			0
$889$	−407.621	−	235.340i	−0.458517	−	0.264725i
$890$		0			0
$891$	38.0952	+	65.9829i	0.0427556	+	0.0740549i
$892$		0			0
$893$	10.8998	−	63.8688i	0.0122058	−	0.0715216i
$894$		0			0
$895$	1145.59	−	661.404i	1.27998	−	0.738999i
$896$		0			0
$897$	523.703	−	907.080i	0.583838	−	1.01124i
$898$		0			0
$899$	−114.146	+	197.707i	−0.126970	+	0.219919i
$900$		0			0
$901$		−	2318.90i		−	2.57369i
$902$		0			0
$903$	84.2113	+	48.6194i	0.0932573	+	0.0538421i
$904$		0			0
$905$			1044.79i			1.15446i
$906$		0			0
$907$	−1396.68	+	806.372i	−1.53989	+	0.889054i	−0.541042	+	0.840996i	$0.681970\pi$
$907$	−1396.68	+	806.372i	−1.53989	+	0.889054i	−0.998845	+	0.0480579i	$0.984697\pi$
$908$		0			0
$909$	244.662	+	423.767i	0.269155	+	0.466190i
$910$		0			0
$911$		−	5.81037i		−	0.00637801i	−0.999995	−	0.00318901i	$-0.998985\pi$
$911$		−	5.81037i		−	0.00637801i	0.999995	−	0.00318901i	$-0.00101509\pi$
$912$		0			0
$913$	−866.223			−0.948766
$914$		0			0
$915$	128.919	−	74.4315i	0.140895	−	0.0813459i
$916$		0			0
$917$	153.089	+	265.157i	0.166945	+	0.289157i
$918$		0			0
$919$	223.733			0.243452			0.121726	−	0.992564i	$-0.461157\pi$
$919$	223.733			0.243452			0.121726	+	0.992564i	$0.461157\pi$
$920$		0			0
$921$	233.152	−	403.831i	0.253151	−	0.438470i
$922$		0			0
$923$	1182.95			1.28164
$924$		0			0
$925$	−295.140	−	170.399i	−0.319071	−	0.184216i
$926$		0			0
$927$	47.4752	+	27.4098i	0.0512139	+	0.0295683i
$928$		0			0
$929$	−87.0368	−	150.752i	−0.0936887	−	0.162274i	0.815372	−	0.578938i	$-0.196533\pi$
$929$	−87.0368	−	150.752i	−0.0936887	−	0.162274i	−0.909061	+	0.416664i	$0.863199\pi$
$930$		0			0
$931$	805.717	−	298.287i	0.865431	−	0.320394i
$932$		0			0
$933$	−80.1794	+	46.2916i	−0.0859372	+	0.0496159i
$934$		0			0
$935$	611.361	−	1058.91i	0.653862	−	1.13252i
$936$		0			0
$937$	71.6605	−	124.120i	0.0764786	−	0.132465i	−0.825250	−	0.564768i	$-0.808966\pi$
$937$	71.6605	−	124.120i	0.0764786	−	0.132465i	0.901728	+	0.432303i	$0.142299\pi$
$938$		0			0
$939$			414.859i			0.441810i
$940$		0			0
$941$	−133.495	−	77.0732i	−0.141865	−	0.0819057i	0.427388	−	0.904068i	$-0.359434\pi$
$941$	−133.495	−	77.0732i	−0.141865	−	0.0819057i	−0.569252	+	0.822163i	$0.692767\pi$
$942$		0			0
$943$			55.4237i			0.0587738i
$944$		0			0
$945$	−50.4064	+	29.1022i	−0.0533401	+	0.0307959i
$946$		0			0
$947$	79.3787	+	137.488i	0.0838213	+	0.145183i	0.904888	−	0.425649i	$-0.139954\pi$
$947$	79.3787	+	137.488i	0.0838213	+	0.145183i	−0.821067	+	0.570832i	$0.806621\pi$
$948$		0			0
$949$			1501.28i			1.58196i
$950$		0			0
$951$	783.508			0.823878
$952$		0			0
$953$	191.938	−	110.815i	0.201404	−	0.116280i	−0.395906	−	0.918291i	$-0.629570\pi$
$953$	191.938	−	110.815i	0.201404	−	0.116280i	0.597310	+	0.802010i	$0.296236\pi$
$954$		0			0
$955$	802.745	+	1390.40i	0.840571	+	1.45591i
$956$		0			0
$957$	−232.079			−0.242507
$958$		0			0
$959$	−235.621	+	408.108i	−0.245695	+	0.425556i
$960$		0			0
$961$	752.958			0.783515
$962$		0			0
$963$	144.138	+	83.2184i	0.149676	+	0.0864157i
$964$		0			0
$965$	−964.963	−	557.122i	−0.999962	−	0.577328i
$966$		0			0
$967$	252.311	+	437.015i	0.260921	+	0.451929i	0.966487	−	0.256716i	$-0.0826404\pi$
$967$	252.311	+	437.015i	0.260921	+	0.451929i	−0.705566	+	0.708645i	$0.749307\pi$
$968$		0			0
$969$	−813.366	−	138.809i	−0.839387	−	0.143249i
$970$		0			0
$971$	1145.39	−	661.292i	1.17960	−	0.681042i	0.223678	−	0.974663i	$-0.428194\pi$
$971$	1145.39	−	661.292i	1.17960	−	0.681042i	0.955922	+	0.293621i	$0.0948603\pi$
$972$		0			0
$973$	−126.477	+	219.064i	−0.129986	+	0.225143i
$974$		0			0
$975$	137.012	−	237.312i	0.140525	−	0.243397i
$976$		0			0
$977$			1211.93i			1.24046i	0.784419	+	0.620231i	$0.212961\pi$
$977$			1211.93i			1.24046i	−0.784419	+	0.620231i	$0.787039\pi$
$978$		0			0
$979$	−877.001	−	506.337i	−0.895814	−	0.517198i
$980$		0			0
$981$		−	334.067i		−	0.340538i
$982$		0			0
$983$	−924.023	+	533.485i	−0.940003	+	0.542711i	−0.889961	−	0.456036i	$-0.849269\pi$
$983$	−924.023	+	533.485i	−0.940003	+	0.542711i	−0.0500419	+	0.998747i	$0.515935\pi$
$984$		0			0
$985$	−279.185	−	483.563i	−0.283437	−	0.490927i
$986$		0			0
$987$		−	11.4852i		−	0.0116365i
$988$		0			0
$989$	903.150			0.913195
$990$		0			0
$991$	225.943	−	130.448i	0.227995	−	0.131633i	−0.381652	−	0.924306i	$-0.624645\pi$
$991$	225.943	−	130.448i	0.227995	−	0.131633i	0.609647	+	0.792673i	$0.291311\pi$
$992$		0			0
$993$	−82.6800	−	143.206i	−0.0832629	−	0.144216i
$994$		0			0
$995$	−1991.92			−2.00193
$996$		0			0
$997$	361.653	−	626.401i	0.362741	−	0.628286i	−0.625670	−	0.780088i	$-0.715174\pi$
$997$	361.653	−	626.401i	0.362741	−	0.628286i	0.988411	+	0.151802i	$0.0485076\pi$
$998$		0			0
$999$	216.380			0.216596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.f.145.3		6
4.3	odd	2		57.3.g.b.31.2	✓	6
12.11	even	2		171.3.p.c.145.2		6
19.8	odd	6	inner	912.3.be.f.673.3		6
76.27	even	6		57.3.g.b.46.2	yes	6
228.179	odd	6		171.3.p.c.46.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.2	✓	6	4.3	odd	2
57.3.g.b.46.2	yes	6	76.27	even	6
171.3.p.c.46.2		6	228.179	odd	6
171.3.p.c.145.2		6	12.11	even	2
912.3.be.f.145.3		6	1.1	even	1	trivial
912.3.be.f.673.3		6	19.8	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(2.88028 + 4.98878i) q^{5} -1.94451 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(2.88028 + 4.98878i) q^{5} -1.94451 q^{7} +(1.50000 - 2.59808i) q^{9} -8.46561 q^{11} +(-16.7415 - 9.66573i) q^{13} +(8.64083 + 4.98878i) q^{15} +(12.5365 + 21.7138i) q^{17} +(-17.8181 + 6.59651i) q^{19} +(-2.91676 + 1.68399i) q^{21} +(-15.6408 + 27.0907i) q^{23} +(-4.09198 + 7.08751i) q^{25} -5.19615i q^{27} +(13.7071 + 7.91383i) q^{29} +14.4237i q^{31} +(-12.6984 + 7.33143i) q^{33} +(-5.60071 - 9.70072i) q^{35} +41.6423i q^{37} -33.4831 q^{39} +(1.53439 - 0.885881i) q^{41} +(-14.4358 - 25.0035i) q^{43} +17.2817 q^{45} +(-1.70506 + 2.95325i) q^{47} -45.2189 q^{49} +(37.6094 + 21.7138i) q^{51} +(-80.0952 - 46.2430i) q^{53} +(-24.3833 - 42.2331i) q^{55} +(-21.0145 + 25.3257i) q^{57} +(-4.27292 + 2.46697i) q^{59} +(7.45989 - 12.9209i) q^{61} +(-2.91676 + 5.05197i) q^{63} -111.360i q^{65} +(70.4113 + 40.6520i) q^{67} +54.1814i q^{69} +(-52.9948 + 30.5966i) q^{71} +(-38.8299 - 67.2553i) q^{73} +14.1750i q^{75} +16.4614 q^{77} +(-84.0207 + 48.5094i) q^{79} +(-4.50000 - 7.79423i) q^{81} +102.323 q^{83} +(-72.2171 + 125.084i) q^{85} +27.4143 q^{87} +(103.596 + 59.8111i) q^{89} +(32.5540 + 18.7951i) q^{91} +(12.4913 + 21.6355i) q^{93} +(-84.2297 - 69.8911i) q^{95} +(-42.1438 + 24.3318i) q^{97} +(-12.6984 + 21.9943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9	\( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9 + 36 * q^11 - 3 * q^13 + 12 * q^15 + 38 * q^17 + 10 * q^19 + 33 * q^21 - 54 * q^23 - 21 * q^25 - 102 * q^29 + 54 * q^33 + 24 * q^35 - 6 * q^39 + 96 * q^41 - 107 * q^43 + 24 * q^45 + 50 * q^47 - 48 * q^49 + 114 * q^51 - 90 * q^53 - 148 * q^55 - 3 * q^57 + 27 * q^61 + 33 * q^63 + 39 * q^67 - 84 * q^71 - 77 * q^73 + 260 * q^77 - 9 * q^79 - 27 * q^81 + 348 * q^83 + 68 * q^85 - 204 * q^87 - 72 * q^89 + 393 * q^91 + 129 * q^93 - 104 * q^95 - 228 * q^97 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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