LMFDB - Embedded newform 224.3.s.b.33.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(33,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("224.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.s (of order $6$, 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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} + \cdots + 208849 $ x^16 - 26x^14 - 16x^13 + 469x^12 + 144x^11 - 4526x^10 + 4440x^9 + 32608x^8 - 33728x^7 - 49760x^6 + 203528x^5 + 27401x^4 - 156928x^3 + 114964x^2 - 248608x + 208849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			33.7
Root			$-2.79414 - 0.796701i$ of defining polynomial
Character	$\chi$	$=$	224.33
Dual form			224.3.s.b.129.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.45151 - 1.99273i) q^{3} +(-7.80961 - 4.50888i) q^{5} +(-5.54917 + 4.26693i) q^{7} +(3.44195 - 5.96164i) q^{9} +O(q^{10})$	\(q+(3.45151 - 1.99273i) q^{3} +(-7.80961 - 4.50888i) q^{5} +(-5.54917 + 4.26693i) q^{7} +(3.44195 - 5.96164i) q^{9} +(-8.28088 - 14.3429i) q^{11} -0.446263i q^{13} -35.9399 q^{15} +(6.02041 - 3.47588i) q^{17} +(-11.0366 - 6.37198i) q^{19} +(-10.6502 + 25.7854i) q^{21} +(13.2871 - 23.0140i) q^{23} +(28.1600 + 48.7745i) q^{25} +8.43362i q^{27} +26.4655 q^{29} +(-21.7635 + 12.5652i) q^{31} +(-57.1631 - 33.0031i) q^{33} +(62.5759 - 8.30251i) q^{35} +(31.6992 - 54.9046i) q^{37} +(-0.889283 - 1.54028i) q^{39} -0.519795i q^{41} -25.5364 q^{43} +(-53.7606 + 31.0387i) q^{45} +(-59.4488 - 34.3228i) q^{47} +(12.5866 - 47.3559i) q^{49} +(13.8530 - 23.9941i) q^{51} +(3.58507 + 6.20953i) q^{53} +149.350i q^{55} -50.7906 q^{57} +(65.3189 - 37.7119i) q^{59} +(39.8855 + 23.0279i) q^{61} +(6.33791 + 47.7687i) q^{63} +(-2.01215 + 3.48514i) q^{65} +(-21.4049 - 37.0743i) q^{67} -105.911i q^{69} +60.0281 q^{71} +(-40.5246 + 23.3969i) q^{73} +(194.389 + 112.230i) q^{75} +(107.152 + 44.2573i) q^{77} +(27.1539 - 47.0319i) q^{79} +(47.7835 + 82.7635i) q^{81} +11.4213i q^{83} -62.6894 q^{85} +(91.3459 - 52.7386i) q^{87} +(53.1854 + 30.7066i) q^{89} +(1.90417 + 2.47639i) q^{91} +(-50.0780 + 86.7377i) q^{93} +(57.4610 + 99.5253i) q^{95} -20.3570i q^{97} -114.010 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{9}+O(q^{10}) $ 16 * q + 40 * q^9	$ 16 q + 40 q^{9} - 48 q^{17} - 136 q^{21} + 80 q^{25} - 16 q^{29} - 264 q^{33} + 72 q^{37} + 312 q^{45} + 128 q^{49} + 40 q^{53} + 368 q^{57} + 216 q^{61} - 168 q^{65} - 312 q^{73} + 64 q^{77} - 384 q^{81} - 1072 q^{85} + 24 q^{89} - 168 q^{93}+O(q^{100}) $ 16 * q + 40 * q^9 - 48 * q^17 - 136 * q^21 + 80 * q^25 - 16 * q^29 - 264 * q^33 + 72 * q^37 + 312 * q^45 + 128 * q^49 + 40 * q^53 + 368 * q^57 + 216 * q^61 - 168 * q^65 - 312 * q^73 + 64 * q^77 - 384 * q^81 - 1072 * q^85 + 24 * q^89 - 168 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	3.45151	−	1.99273i	1.15050	−	0.664244i	0.201494	−	0.979490i	$-0.435420\pi$
$3$	3.45151	−	1.99273i	1.15050	−	0.664244i	0.949010	+	0.315246i	$0.102087\pi$
$4$		0			0
$5$	−7.80961	−	4.50888i	−1.56192	−	0.901776i	−0.997063	−	0.0765879i	$-0.975597\pi$
$5$	−7.80961	−	4.50888i	−1.56192	−	0.901776i	−0.564859	−	0.825188i	$-0.691069\pi$
$6$		0			0
$7$	−5.54917	+	4.26693i	−0.792739	+	0.609562i
$7$	−5.54917	+	4.26693i	−0.792739	+	0.609562i
$8$		0			0
$9$	3.44195	−	5.96164i	0.382439	−	0.662404i
$10$		0			0
$11$	−8.28088	−	14.3429i	−0.752807	−	1.30390i	−0.946457	−	0.322830i	$-0.895366\pi$
$11$	−8.28088	−	14.3429i	−0.752807	−	1.30390i	0.193650	−	0.981071i	$-0.437967\pi$
$12$		0			0
$13$		−	0.446263i		−	0.0343279i	−0.999853	−	0.0171640i	$-0.994536\pi$
$13$		−	0.446263i		−	0.0343279i	0.999853	−	0.0171640i	$-0.00546373\pi$
$14$		0			0
$15$	−35.9399			−2.39599
$16$		0			0
$17$	6.02041	−	3.47588i	0.354142	−	0.204464i	−0.312366	−	0.949962i	$-0.601122\pi$
$17$	6.02041	−	3.47588i	0.354142	−	0.204464i	0.666508	+	0.745498i	$0.267788\pi$
$18$		0			0
$19$	−11.0366	−	6.37198i	−0.580873	−	0.335367i	0.180607	−	0.983555i	$-0.442194\pi$
$19$	−11.0366	−	6.37198i	−0.580873	−	0.335367i	−0.761480	+	0.648188i	$0.775527\pi$
$20$		0			0
$21$	−10.6502	+	25.7854i	−0.507151	+	1.22787i
$22$		0			0
$23$	13.2871	−	23.0140i	0.577701	−	1.00061i	−0.418041	−	0.908428i	$-0.637283\pi$
$23$	13.2871	−	23.0140i	0.577701	−	1.00061i	0.995742	−	0.0921795i	$-0.0293833\pi$
$24$		0			0
$25$	28.1600	+	48.7745i	1.12640	+	1.95098i
$26$		0			0
$27$			8.43362i			0.312356i
$28$		0			0
$29$	26.4655			0.912603			0.456301	−	0.889825i	$-0.349174\pi$
$29$	26.4655			0.912603			0.456301	+	0.889825i	$0.349174\pi$
$30$		0			0
$31$	−21.7635	+	12.5652i	−0.702049	+	0.405328i	−0.808110	−	0.589031i	$-0.799509\pi$
$31$	−21.7635	+	12.5652i	−0.702049	+	0.405328i	0.106061	+	0.994360i	$0.466176\pi$
$32$		0			0
$33$	−57.1631	−	33.0031i	−1.73221	−	1.00009i
$34$		0			0
$35$	62.5759	−	8.30251i	1.78788	−	0.237215i
$36$		0			0
$37$	31.6992	−	54.9046i	0.856735	−	1.48391i	−0.0182908	−	0.999833i	$-0.505822\pi$
$37$	31.6992	−	54.9046i	0.856735	−	1.48391i	0.875026	−	0.484076i	$-0.160844\pi$
$38$		0			0
$39$	−0.889283	−	1.54028i	−0.0228021	−	0.0394944i
$40$		0			0
$41$		−	0.519795i		−	0.0126779i	−0.999980	−	0.00633896i	$-0.997982\pi$
$41$		−	0.519795i		−	0.0126779i	0.999980	−	0.00633896i	$-0.00201777\pi$
$42$		0			0
$43$	−25.5364			−0.593870			−0.296935	−	0.954898i	$-0.595964\pi$
$43$	−25.5364			−0.593870			−0.296935	+	0.954898i	$0.595964\pi$
$44$		0			0
$45$	−53.7606	+	31.0387i	−1.19468	+	0.689749i
$46$		0			0
$47$	−59.4488	−	34.3228i	−1.26487	−	0.730272i	−0.290856	−	0.956767i	$-0.593940\pi$
$47$	−59.4488	−	34.3228i	−1.26487	−	0.730272i	−0.974012	+	0.226495i	$0.927273\pi$
$48$		0			0
$49$	12.5866	−	47.3559i	0.256869	−	0.966446i
$50$		0			0
$51$	13.8530	−	23.9941i	0.271627	−	0.470473i
$52$		0			0
$53$	3.58507	+	6.20953i	0.0676429	+	0.117161i	0.897863	−	0.440274i	$-0.145119\pi$
$53$	3.58507	+	6.20953i	0.0676429	+	0.117161i	−0.830220	+	0.557435i	$0.811785\pi$
$54$		0			0
$55$			149.350i			2.71545i
$56$		0			0
$57$	−50.7906			−0.891062
$58$		0			0
$59$	65.3189	−	37.7119i	1.10710	−	0.639184i	0.169023	−	0.985612i	$-0.445939\pi$
$59$	65.3189	−	37.7119i	1.10710	−	0.639184i	0.938077	+	0.346428i	$0.112605\pi$
$60$		0			0
$61$	39.8855	+	23.0279i	0.653861	+	0.377507i	0.789934	−	0.613192i	$-0.210115\pi$
$61$	39.8855	+	23.0279i	0.653861	+	0.377507i	−0.136073	+	0.990699i	$0.543448\pi$
$62$		0			0
$63$	6.33791	+	47.7687i	0.100602	+	0.758233i
$64$		0			0
$65$	−2.01215	+	3.48514i	−0.0309561	+	0.0536175i
$66$		0			0
$67$	−21.4049	−	37.0743i	−0.319476	−	0.553348i	0.660903	−	0.750471i	$-0.270173\pi$
$67$	−21.4049	−	37.0743i	−0.319476	−	0.553348i	−0.980379	+	0.197123i	$0.936840\pi$
$68$		0			0
$69$		−	105.911i		−	1.53494i
$70$		0			0
$71$	60.0281			0.845466			0.422733	−	0.906254i	$-0.361071\pi$
$71$	60.0281			0.845466			0.422733	+	0.906254i	$0.361071\pi$
$72$		0			0
$73$	−40.5246	+	23.3969i	−0.555132	+	0.320505i	−0.751189	−	0.660087i	$-0.770519\pi$
$73$	−40.5246	+	23.3969i	−0.555132	+	0.320505i	0.196058	+	0.980592i	$0.437186\pi$
$74$		0			0
$75$	194.389	+	112.230i	2.59185	+	1.49641i
$76$		0			0
$77$	107.152	+	44.2573i	1.39159	+	0.574770i
$78$		0			0
$79$	27.1539	−	47.0319i	0.343720	−	0.595340i	−0.641401	−	0.767206i	$-0.721646\pi$
$79$	27.1539	−	47.0319i	0.343720	−	0.595340i	0.985120	+	0.171866i	$0.0549796\pi$
$80$		0			0
$81$	47.7835	+	82.7635i	0.589920	+	1.02177i
$82$		0			0
$83$			11.4213i			0.137606i	0.997630	+	0.0688028i	$0.0219179\pi$
$83$			11.4213i			0.137606i	−0.997630	+	0.0688028i	$0.978082\pi$
$84$		0			0
$85$	−62.6894			−0.737522
$86$		0			0
$87$	91.3459	−	52.7386i	1.04995	−	0.606190i
$88$		0			0
$89$	53.1854	+	30.7066i	0.597589	+	0.345018i	0.768092	−	0.640339i	$-0.221206\pi$
$89$	53.1854	+	30.7066i	0.597589	+	0.345018i	−0.170504	+	0.985357i	$0.554539\pi$
$90$		0			0
$91$	1.90417	+	2.47639i	0.0209250	+	0.0272131i
$92$		0			0
$93$	−50.0780	+	86.7377i	−0.538473	+	0.932663i
$94$		0			0
$95$	57.4610	+	99.5253i	0.604852	+	1.04763i
$96$		0			0
$97$		−	20.3570i		−	0.209866i	−0.994479	−	0.104933i	$-0.966537\pi$
$97$		−	20.3570i		−	0.209866i	0.994479	−	0.104933i	$-0.0334629\pi$
$98$		0			0
$99$	−114.010			−1.15161
$100$		0			0
$101$	−155.237	+	89.6260i	−1.53700	+	0.887386i	−0.537985	+	0.842954i	$0.680814\pi$
$101$	−155.237	+	89.6260i	−1.53700	+	0.887386i	−0.999012	+	0.0444318i	$0.985852\pi$
$102$		0			0
$103$	−59.0242	−	34.0777i	−0.573051	−	0.330851i	0.185316	−	0.982679i	$-0.440669\pi$
$103$	−59.0242	−	34.0777i	−0.573051	−	0.330851i	−0.758367	+	0.651828i	$0.774002\pi$
$104$		0			0
$105$	199.437	−	153.353i	1.89940	−	1.46051i
$106$		0			0
$107$	−63.5657	+	110.099i	−0.594072	+	1.02896i	0.399605	+	0.916688i	$0.369147\pi$
$107$	−63.5657	+	110.099i	−0.594072	+	1.02896i	−0.993677	+	0.112276i	$0.964186\pi$
$108$		0			0
$109$	10.7852	+	18.6805i	0.0989468	+	0.171381i	0.911249	−	0.411856i	$-0.135119\pi$
$109$	10.7852	+	18.6805i	0.0989468	+	0.171381i	−0.812302	+	0.583237i	$0.801786\pi$
$110$		0			0
$111$		−	252.672i		−	2.27632i
$112$		0			0
$113$	82.1812			0.727267			0.363634	−	0.931542i	$-0.381536\pi$
$113$	82.1812			0.727267			0.363634	+	0.931542i	$0.381536\pi$
$114$		0			0
$115$	−207.534	+	119.820i	−1.80465	+	1.04191i
$116$		0			0
$117$	−2.66046	−	1.53602i	−0.0227390	−	0.0131283i
$118$		0			0
$119$	−18.5769	+	44.9769i	−0.156109	+	0.377957i
$120$		0			0
$121$	−76.6459	+	132.755i	−0.633437	+	1.09715i
$122$		0			0
$123$	−1.03581	−	1.79408i	−0.00842123	−	0.0145860i
$124$		0			0
$125$		−	282.436i		−	2.25949i
$126$		0			0
$127$	42.9545			0.338225			0.169112	−	0.985597i	$-0.445910\pi$
$127$	42.9545			0.338225			0.169112	+	0.985597i	$0.445910\pi$
$128$		0			0
$129$	−88.1392	+	50.8872i	−0.683249	+	0.394474i
$130$		0			0
$131$	−166.980	−	96.4062i	−1.27466	−	0.735925i	−0.298798	−	0.954316i	$-0.596586\pi$
$131$	−166.980	−	96.4062i	−1.27466	−	0.735925i	−0.975861	+	0.218391i	$0.929919\pi$
$132$		0			0
$133$	88.4327	−	11.7332i	0.664908	−	0.0882193i
$134$		0			0
$135$	38.0262	−	65.8633i	0.281675	−	0.487876i
$136$		0			0
$137$	−73.1244	−	126.655i	−0.533754	−	0.924490i	−0.999223	−	0.0394252i	$-0.987447\pi$
$137$	−73.1244	−	126.655i	−0.533754	−	0.924490i	0.465468	−	0.885065i	$-0.345886\pi$
$138$		0			0
$139$		−	101.042i		−	0.726921i	−0.931610	−	0.363460i	$-0.881595\pi$
$139$		−	101.042i		−	0.726921i	0.931610	−	0.363460i	$-0.118405\pi$
$140$		0			0
$141$	−273.584			−1.94031
$142$		0			0
$143$	−6.40071	+	3.69545i	−0.0447602	+	0.0258423i
$144$		0			0
$145$	−206.685	−	119.330i	−1.42541	−	0.822963i
$146$		0			0
$147$	−50.9247	−	188.531i	−0.346426	−	1.28252i
$148$		0			0
$149$	95.5542	−	165.505i	0.641303	−	1.11077i	−0.343839	−	0.939029i	$-0.611727\pi$
$149$	95.5542	−	165.505i	0.641303	−	1.11077i	0.985142	−	0.171741i	$-0.0549393\pi$
$150$		0			0
$151$	14.3585	+	24.8696i	0.0950893	+	0.164700i	0.909646	−	0.415385i	$-0.136353\pi$
$151$	14.3585	+	24.8696i	0.0950893	+	0.164700i	−0.814557	+	0.580084i	$0.803020\pi$
$152$		0			0
$153$		−	47.8553i		−	0.312780i
$154$		0			0
$155$	226.619			1.46206
$156$		0			0
$157$	109.235	−	63.0666i	0.695762	−	0.401698i	−0.110005	−	0.993931i	$-0.535087\pi$
$157$	109.235	−	63.0666i	0.695762	−	0.401698i	0.805767	+	0.592233i	$0.201753\pi$
$158$		0			0
$159$	24.7478	+	14.2882i	0.155647	+	0.0898627i
$160$		0			0
$161$	24.4665	+	184.404i	0.151966	+	1.14536i
$162$		0			0
$163$	−127.126	+	220.188i	−0.779911	+	1.35085i	0.152081	+	0.988368i	$0.451403\pi$
$163$	−127.126	+	220.188i	−0.779911	+	1.35085i	−0.931992	+	0.362478i	$0.881931\pi$
$164$		0			0
$165$	297.614	+	515.483i	1.80372	+	3.12414i
$166$		0			0
$167$		−	1.71028i		−	0.0102412i	−0.999987	−	0.00512059i	$-0.998370\pi$
$167$		−	1.71028i		−	0.0102412i	0.999987	−	0.00512059i	$-0.00162994\pi$
$168$		0			0
$169$	168.801			0.998822
$170$		0			0
$171$	−75.9748	+	43.8641i	−0.444297	+	0.256515i
$172$		0			0
$173$	87.1688	+	50.3270i	0.503866	+	0.290907i	0.730309	−	0.683117i	$-0.239376\pi$
$173$	87.1688	+	50.3270i	0.503866	+	0.290907i	−0.226443	+	0.974025i	$0.572710\pi$
$174$		0			0
$175$	−364.382	−	150.501i	−2.08218	−	0.860008i
$176$		0			0
$177$	150.299	−	260.326i	0.849148	−	1.47077i
$178$		0			0
$179$	−113.642	−	196.834i	−0.634872	−	1.09963i	−0.986542	−	0.163506i	$-0.947720\pi$
$179$	−113.642	−	196.834i	−0.634872	−	1.09963i	0.351670	−	0.936124i	$-0.385614\pi$
$180$		0			0
$181$			27.1608i			0.150060i	0.997181	+	0.0750298i	$0.0239052\pi$
$181$			27.1608i			0.150060i	−0.997181	+	0.0750298i	$0.976095\pi$
$182$		0			0
$183$	183.554			1.00303
$184$		0			0
$185$	−495.117	+	285.856i	−2.67631	+	1.54517i
$186$		0			0
$187$	−99.7085	−	57.5667i	−0.533201	−	0.307844i
$188$		0			0
$189$	−35.9857	−	46.7996i	−0.190400	−	0.247617i
$190$		0			0
$191$	−27.6562	+	47.9019i	−0.144797	+	0.250795i	−0.929297	−	0.369333i	$-0.879586\pi$
$191$	−27.6562	+	47.9019i	−0.144797	+	0.250795i	0.784500	+	0.620128i	$0.212919\pi$
$192$		0			0
$193$	111.283	+	192.747i	0.576594	+	0.998689i	0.995866	+	0.0908292i	$0.0289517\pi$
$193$	111.283	+	192.747i	0.576594	+	0.998689i	−0.419273	+	0.907860i	$0.637715\pi$
$194$		0			0
$195$			16.0387i			0.0822496i
$196$		0			0
$197$	−15.2516			−0.0774191			−0.0387095	−	0.999251i	$-0.512325\pi$
$197$	−15.2516			−0.0774191			−0.0387095	+	0.999251i	$0.512325\pi$
$198$		0			0
$199$	−38.3544	+	22.1439i	−0.192736	+	0.111276i	−0.593263	−	0.805009i	$-0.702160\pi$
$199$	−38.3544	+	22.1439i	−0.192736	+	0.111276i	0.400527	+	0.916285i	$0.368827\pi$
$200$		0			0
$201$	−147.758	−	85.3083i	−0.735116	−	0.424419i
$202$		0			0
$203$	−146.861	+	112.926i	−0.723455	+	0.556287i
$204$		0			0
$205$	−2.34369	+	4.05939i	−0.0114326	+	0.0198019i
$206$		0			0
$207$	−91.4673	−	158.426i	−0.441871	−	0.765343i
$208$		0			0
$209$			211.062i			1.00987i
$210$		0			0
$211$	−138.721			−0.657446			−0.328723	−	0.944426i	$-0.606618\pi$
$211$	−138.721			−0.657446			−0.328723	+	0.944426i	$0.606618\pi$
$212$		0			0
$213$	207.188	−	119.620i	0.972712	−	0.561596i
$214$		0			0
$215$	199.429	+	115.141i	0.927578	+	0.535537i
$216$		0			0
$217$	67.1548	−	162.590i	0.309469	−	0.749261i
$218$		0			0
$219$	−93.2474	+	161.509i	−0.425787	+	0.737485i
$220$		0			0
$221$	−1.55116	−	2.68669i	−0.00701882	−	0.0121570i
$222$		0			0
$223$		−	53.1564i		−	0.238370i	−0.992872	−	0.119185i	$-0.961972\pi$
$223$		−	53.1564i		−	0.238370i	0.992872	−	0.119185i	$-0.0380281\pi$
$224$		0			0
$225$	387.701			1.72312
$226$		0			0
$227$	346.938	−	200.305i	1.52836	−	0.882399i	0.528930	−	0.848666i	$-0.322594\pi$
$227$	346.938	−	200.305i	1.52836	−	0.882399i	0.999431	−	0.0337337i	$-0.0107398\pi$
$228$		0			0
$229$	−329.566	−	190.275i	−1.43915	−	0.830895i	−0.441361	−	0.897330i	$-0.645504\pi$
$229$	−329.566	−	190.275i	−1.43915	−	0.830895i	−0.997791	+	0.0664348i	$0.978838\pi$
$230$		0			0
$231$	458.030	−	60.7710i	1.98281	−	0.263078i
$232$		0			0
$233$	166.501	−	288.389i	0.714598	−	1.23772i	−0.248516	−	0.968628i	$-0.579943\pi$
$233$	166.501	−	288.389i	0.714598	−	1.23772i	0.963114	−	0.269093i	$-0.0867238\pi$
$234$		0			0
$235$	309.514	+	536.095i	1.31708	+	2.28125i
$236$		0			0
$237$		−	216.441i		−	0.913255i
$238$		0			0
$239$	123.781			0.517912			0.258956	−	0.965889i	$-0.416622\pi$
$239$	123.781			0.517912			0.258956	+	0.965889i	$0.416622\pi$
$240$		0			0
$241$	−72.1258	+	41.6418i	−0.299277	+	0.172788i	−0.642118	−	0.766606i	$-0.721944\pi$
$241$	−72.1258	+	41.6418i	−0.299277	+	0.172788i	0.342841	+	0.939393i	$0.388611\pi$
$242$		0			0
$243$	264.117	+	152.488i	1.08690	+	0.627523i
$244$		0			0
$245$	−311.818	+	313.079i	−1.27273	+	1.27787i
$246$		0			0
$247$	−2.84358	+	4.92523i	−0.0115125	+	0.0199402i
$248$		0			0
$249$	22.7595	+	39.4206i	0.0914036	+	0.158316i
$250$		0			0
$251$		−	403.749i		−	1.60856i	−0.594250	−	0.804281i	$-0.702551\pi$
$251$		−	403.749i		−	1.60856i	0.594250	−	0.804281i	$-0.297449\pi$
$252$		0			0
$253$	−440.116			−1.73959
$254$		0			0
$255$	−216.373	+	124.923i	−0.848521	+	0.489894i
$256$		0			0
$257$	−223.667	−	129.134i	−0.870298	−	0.502467i	−0.00285088	−	0.999996i	$-0.500907\pi$
$257$	−223.667	−	129.134i	−0.870298	−	0.502467i	−0.867447	+	0.497529i	$0.834241\pi$
$258$		0			0
$259$	58.3699	+	439.933i	0.225367	+	1.69858i
$260$		0			0
$261$	91.0929	−	157.778i	0.349015	−	0.604512i
$262$		0			0
$263$	196.929	+	341.090i	0.748778	+	1.29692i	0.948409	+	0.317050i	$0.102692\pi$
$263$	196.929	+	341.090i	0.748778	+	1.29692i	−0.199631	+	0.979871i	$0.563974\pi$
$264$		0			0
$265$		−	64.6586i		−	0.243995i
$266$		0			0
$267$	244.760			0.916704
$268$		0			0
$269$	46.6236	−	26.9181i	0.173322	−	0.100067i	−0.410829	−	0.911712i	$-0.634761\pi$
$269$	46.6236	−	26.9181i	0.173322	−	0.100067i	0.584151	+	0.811645i	$0.301427\pi$
$270$		0			0
$271$	−41.1477	−	23.7567i	−0.151837	−	0.0876629i	0.422157	−	0.906523i	$-0.361273\pi$
$271$	−41.1477	−	23.7567i	−0.151837	−	0.0876629i	−0.573993	+	0.818860i	$0.694607\pi$
$272$		0			0
$273$	11.5071	+	4.75278i	0.0421504	+	0.0174095i
$274$		0			0
$275$	466.379	−	807.791i	1.69592	−	2.93742i
$276$		0			0
$277$	121.959	+	211.239i	0.440285	+	0.762595i	0.997710	−	0.0676314i	$-0.0215442\pi$
$277$	121.959	+	211.239i	0.440285	+	0.762595i	−0.557426	+	0.830227i	$0.688211\pi$
$278$		0			0
$279$			172.995i			0.620053i
$280$		0			0
$281$	173.857			0.618709			0.309355	−	0.950947i	$-0.399887\pi$
$281$	173.857			0.618709			0.309355	+	0.950947i	$0.399887\pi$
$282$		0			0
$283$	−45.5040	+	26.2717i	−0.160792	+	0.0928330i	−0.578237	−	0.815869i	$-0.696259\pi$
$283$	−45.5040	+	26.2717i	−0.160792	+	0.0928330i	0.417445	+	0.908702i	$0.362926\pi$
$284$		0			0
$285$	396.654	+	229.008i	1.39177	+	0.803539i
$286$		0			0
$287$	2.21793	+	2.88443i	0.00772797	+	0.0100503i
$288$		0			0
$289$	−120.336	+	208.429i	−0.416389	+	0.721207i
$290$		0			0
$291$	−40.5661	−	70.2625i	−0.139402	−	0.241452i
$292$		0			0
$293$		−	321.060i		−	1.09577i	−0.836554	−	0.547885i	$-0.815433\pi$
$293$		−	321.060i		−	1.09577i	0.836554	−	0.547885i	$-0.184567\pi$
$294$		0			0
$295$	−680.153			−2.30560
$296$		0			0
$297$	120.963	−	69.8378i	0.407282	−	0.235144i
$298$		0			0
$299$	−10.2703	−	5.92955i	−0.0343488	−	0.0198313i
$300$		0			0
$301$	141.706	−	108.962i	0.470784	−	0.362000i
$302$		0			0
$303$	−357.201	+	618.690i	−1.17888	+	2.04188i
$304$		0			0
$305$	−207.660	−	359.678i	−0.680853	−	1.17927i
$306$		0			0
$307$			568.177i			1.85074i	0.379066	+	0.925370i	$0.376245\pi$
$307$			568.177i			1.85074i	−0.379066	+	0.925370i	$0.623755\pi$
$308$		0			0
$309$	−271.630			−0.879063
$310$		0			0
$311$	41.7405	−	24.0989i	0.134214	−	0.0774884i	−0.431390	−	0.902166i	$-0.641977\pi$
$311$	41.7405	−	24.0989i	0.134214	−	0.0774884i	0.565604	+	0.824677i	$0.308643\pi$
$312$		0			0
$313$	70.5536	+	40.7341i	0.225411	+	0.130141i	0.608453	−	0.793590i	$-0.291790\pi$
$313$	70.5536	+	40.7341i	0.225411	+	0.130141i	−0.383042	+	0.923731i	$0.625124\pi$
$314$		0			0
$315$	165.887	−	401.632i	0.526625	−	1.27502i
$316$		0			0
$317$	−198.291	+	343.449i	−0.625522	+	1.08344i	0.362917	+	0.931821i	$0.381781\pi$
$317$	−198.291	+	343.449i	−0.625522	+	1.08344i	−0.988440	+	0.151615i	$0.951553\pi$
$318$		0			0
$319$	−219.157	−	379.592i	−0.687014	−	1.18994i
$320$		0			0
$321$			506.678i			1.57844i
$322$		0			0
$323$	−88.5930			−0.274282
$324$		0			0
$325$	21.7663	−	12.5668i	0.0669731	−	0.0386670i
$326$		0			0
$327$	74.4505	+	42.9840i	0.227677	+	0.131450i
$328$		0			0
$329$	476.344	−	63.2009i	1.44786	−	0.192100i
$330$		0			0
$331$	237.118	−	410.701i	0.716369	−	1.24079i	−0.246060	−	0.969255i	$-0.579136\pi$
$331$	237.118	−	410.701i	0.716369	−	1.24079i	0.962429	−	0.271533i	$-0.0875305\pi$
$332$		0			0
$333$	−218.214	−	377.958i	−0.655298	−	1.13501i
$334$		0			0
$335$			386.048i			1.15238i
$336$		0			0
$337$	234.392			0.695526			0.347763	−	0.937583i	$-0.386941\pi$
$337$	234.392			0.695526			0.347763	+	0.937583i	$0.386941\pi$
$338$		0			0
$339$	283.649	−	163.765i	0.836724	−	0.483083i
$340$		0			0
$341$	360.442	+	208.101i	1.05702	+	0.610268i
$342$		0			0
$343$	132.219	+	316.492i	0.385478	+	0.922717i
$344$		0			0
$345$	−477.538	+	827.120i	−1.38417	+	2.39745i
$346$		0			0
$347$	−112.495	−	194.846i	−0.324192	−	0.561517i	0.657156	−	0.753754i	$-0.271759\pi$
$347$	−112.495	−	194.846i	−0.324192	−	0.561517i	−0.981349	+	0.192237i	$0.938426\pi$
$348$		0			0
$349$			414.621i			1.18802i	0.804456	+	0.594012i	$0.202457\pi$
$349$			414.621i			1.18802i	−0.804456	+	0.594012i	$0.797543\pi$
$350$		0			0
$351$	3.76362			0.0107226
$352$		0			0
$353$	173.723	−	100.299i	0.492134	−	0.284134i	−0.233325	−	0.972399i	$-0.574961\pi$
$353$	173.723	−	100.299i	0.492134	−	0.284134i	0.725459	+	0.688265i	$0.241627\pi$
$354$		0			0
$355$	−468.796	−	270.659i	−1.32055	−	0.762421i
$356$		0			0
$357$	25.5085	+	192.257i	0.0714524	+	0.538536i
$358$		0			0
$359$	74.9646	−	129.842i	0.208815	−	0.361678i	−0.742527	−	0.669817i	$-0.766373\pi$
$359$	74.9646	−	129.842i	0.208815	−	0.361678i	0.951342	+	0.308139i	$0.0997060\pi$
$360$		0			0
$361$	−99.2957	−	171.985i	−0.275057	−	0.476413i
$362$		0			0
$363$			610.939i			1.68303i
$364$		0			0
$365$	421.975			1.15610
$366$		0			0
$367$	420.745	−	242.917i	1.14644	−	0.661900i	0.198426	−	0.980116i	$-0.436417\pi$
$367$	420.745	−	242.917i	1.14644	−	0.661900i	0.948018	+	0.318216i	$0.103084\pi$
$368$		0			0
$369$	−3.09883	−	1.78911i	−0.00839790	−	0.00484853i
$370$		0			0
$371$	−46.3898	−	19.1605i	−0.125040	−	0.0516455i
$372$		0			0
$373$	81.0234	−	140.337i	0.217221	−	0.376238i	−0.736736	−	0.676180i	$-0.763634\pi$
$373$	81.0234	−	140.337i	0.217221	−	0.376238i	0.953957	+	0.299942i	$0.0969674\pi$
$374$		0			0
$375$	−562.818	−	974.830i	−1.50085	−	2.59955i
$376$		0			0
$377$		−	11.8106i		−	0.0313278i
$378$		0			0
$379$	388.817			1.02590			0.512951	−	0.858418i	$-0.328552\pi$
$379$	388.817			1.02590			0.512951	+	0.858418i	$0.328552\pi$
$380$		0			0
$381$	148.258	−	85.5968i	0.389129	−	0.224664i
$382$		0			0
$383$	−24.4796	−	14.1333i	−0.0639153	−	0.0369015i	0.467702	−	0.883886i	$-0.345082\pi$
$383$	−24.4796	−	14.1333i	−0.0639153	−	0.0369015i	−0.531617	+	0.846985i	$0.678415\pi$
$384$		0			0
$385$	−637.266	−	828.768i	−1.65524	−	2.15264i
$386$		0			0
$387$	−87.8951	+	152.239i	−0.227119	+	0.393382i
$388$		0			0
$389$	−303.146	−	525.065i	−0.779296	−	1.34978i	−0.932348	−	0.361562i	$-0.882244\pi$
$389$	−303.146	−	525.065i	−0.779296	−	1.34978i	0.153052	−	0.988218i	$-0.451090\pi$
$390$		0			0
$391$		−	184.738i		−	0.472476i
$392$		0			0
$393$	−768.446			−1.95533
$394$		0			0
$395$	−424.122	+	244.867i	−1.07373	+	0.619916i
$396$		0			0
$397$	528.942	+	305.385i	1.33235	+	0.769231i	0.985659	−	0.168750i	$-0.0539729\pi$
$397$	528.942	+	305.385i	1.33235	+	0.769231i	0.346688	+	0.937980i	$0.387306\pi$
$398$		0			0
$399$	281.846	−	216.720i	0.706380	−	0.543157i
$400$		0			0
$401$	107.055	−	185.424i	0.266969	−	0.462404i	−0.701109	−	0.713054i	$-0.747311\pi$
$401$	107.055	−	185.424i	0.266969	−	0.462404i	0.968078	+	0.250651i	$0.0806446\pi$
$402$		0			0
$403$	5.60738	+	9.71226i	0.0139141	+	0.0240999i
$404$		0			0
$405$		−	861.800i		−	2.12790i
$406$		0			0
$407$	−1049.99			−2.57983
$408$		0			0
$409$	206.544	−	119.248i	0.504996	−	0.291560i	−0.225778	−	0.974179i	$-0.572492\pi$
$409$	206.544	−	119.248i	0.504996	−	0.291560i	0.730774	+	0.682619i	$0.239159\pi$
$410$		0			0
$411$	−504.779	−	291.434i	−1.22817	−	0.709086i
$412$		0			0
$413$	−201.552	+	487.981i	−0.488019	+	1.18155i
$414$		0			0
$415$	51.4971	−	89.1955i	0.124089	−	0.214929i
$416$		0			0
$417$	−201.349	−	348.748i	−0.482852	−	0.836325i
$418$		0			0
$419$			126.446i			0.301779i	0.988551	+	0.150890i	$0.0482138\pi$
$419$			126.446i			0.301779i	−0.988551	+	0.150890i	$0.951786\pi$
$420$		0			0
$421$	−113.097			−0.268639			−0.134319	−	0.990938i	$-0.542885\pi$
$421$	−113.097			−0.268639			−0.134319	+	0.990938i	$0.542885\pi$
$422$		0			0
$423$	−409.240	+	236.275i	−0.967470	+	0.558569i
$424$		0			0
$425$	339.069	+	195.762i	0.797809	+	0.460615i
$426$		0			0
$427$	−319.590	+	42.4029i	−0.748455	+	0.0993043i
$428$		0			0
$429$	−14.7281	+	25.5098i	−0.0343312	+	0.0594634i
$430$		0			0
$431$	344.592	+	596.851i	0.799517	+	1.38480i	0.919931	+	0.392081i	$0.128245\pi$
$431$	344.592	+	596.851i	0.799517	+	1.38480i	−0.120413	+	0.992724i	$0.538422\pi$
$432$		0			0
$433$			600.031i			1.38575i	0.721057	+	0.692876i	$0.243657\pi$
$433$			600.031i			1.38575i	−0.721057	+	0.692876i	$0.756343\pi$
$434$		0			0
$435$	−951.167			−2.18659
$436$		0			0
$437$	−293.289	+	169.331i	−0.671142	+	0.387484i
$438$		0			0
$439$	−143.073	−	82.6032i	−0.325906	−	0.188162i	0.328116	−	0.944637i	$-0.393586\pi$
$439$	−143.073	−	82.6032i	−0.325906	−	0.188162i	−0.654022	+	0.756475i	$0.726920\pi$
$440$		0			0
$441$	−238.996	−	238.033i	−0.541941	−	0.539758i
$442$		0			0
$443$	102.417	−	177.391i	0.231189	−	0.400431i	−0.726969	−	0.686670i	$-0.759072\pi$
$443$	102.417	−	177.391i	0.231189	−	0.400431i	0.958158	+	0.286239i	$0.0924052\pi$
$444$		0			0
$445$	−276.905	−	479.613i	−0.622258	−	1.07778i
$446$		0			0
$447$		−	761.655i		−	1.70393i
$448$		0			0
$449$	−112.007			−0.249458			−0.124729	−	0.992191i	$-0.539806\pi$
$449$	−112.007			−0.249458			−0.124729	+	0.992191i	$0.539806\pi$
$450$		0			0
$451$	−7.45536	+	4.30436i	−0.0165307	+	0.00954403i
$452$		0			0
$453$	99.1169	+	57.2252i	0.218801	+	0.126325i
$454$		0			0
$455$	−3.70511	−	27.9253i	−0.00814309	−	0.0613744i
$456$		0			0
$457$	−82.6173	+	143.097i	−0.180782	+	0.313123i	−0.942147	−	0.335200i	$-0.891196\pi$
$457$	−82.6173	+	143.097i	−0.180782	+	0.313123i	0.761365	+	0.648323i	$0.224529\pi$
$458$		0			0
$459$	29.3143	+	50.7738i	0.0638655	+	0.110618i
$460$		0			0
$461$			187.790i			0.407353i	0.979038	+	0.203677i	$0.0652891\pi$
$461$			187.790i			0.407353i	−0.979038	+	0.203677i	$0.934711\pi$
$462$		0			0
$463$	678.682			1.46584			0.732918	−	0.680317i	$-0.238158\pi$
$463$	678.682			1.46584			0.732918	+	0.680317i	$0.238158\pi$
$464$		0			0
$465$	782.179	−	451.591i	1.68211	−	0.971164i
$466$		0			0
$467$	−13.7799	−	7.95581i	−0.0295072	−	0.0170360i	0.485174	−	0.874418i	$-0.338756\pi$
$467$	−13.7799	−	7.95581i	−0.0295072	−	0.0170360i	−0.514681	+	0.857382i	$0.672090\pi$
$468$		0			0
$469$	276.973	+	114.399i	0.590560	+	0.243920i
$470$		0			0
$471$	251.350	−	435.350i	0.533651	−	0.924311i
$472$		0			0
$473$	211.464	+	366.266i	0.447069	+	0.774347i
$474$		0			0
$475$		−	717.739i		−	1.51103i
$476$		0			0
$477$	49.3586			0.103477
$478$		0			0
$479$	−479.556	+	276.872i	−1.00116	+	0.578020i	−0.908591	−	0.417686i	$-0.862841\pi$
$479$	−479.556	+	276.872i	−1.00116	+	0.578020i	−0.0925686	+	0.995706i	$0.529508\pi$
$480$		0			0
$481$	−24.5019	−	14.1462i	−0.0509395	−	0.0294100i
$482$		0			0
$483$	451.913	+	587.716i	0.935638	+	1.21680i
$484$		0			0
$485$	−91.7874	+	158.980i	−0.189252	+	0.327795i
$486$		0			0
$487$	196.779	+	340.832i	0.404065	+	0.699860i	0.994212	−	0.107435i	$-0.0342638\pi$
$487$	196.779	+	340.832i	0.404065	+	0.699860i	−0.590148	+	0.807295i	$0.700930\pi$
$488$		0			0
$489$			1013.31i			2.07220i
$490$		0			0
$491$	−96.8828			−0.197317			−0.0986586	−	0.995121i	$-0.531455\pi$
$491$	−96.8828			−0.197317			−0.0986586	+	0.995121i	$0.531455\pi$
$492$		0			0
$493$	159.333	−	91.9909i	0.323191	−	0.186594i
$494$		0			0
$495$	890.370	+	514.055i	1.79873	+	1.03850i
$496$		0			0
$497$	−333.106	+	256.136i	−0.670234	+	0.515364i
$498$		0			0
$499$	77.4362	−	134.123i	0.155183	−	0.268784i	−0.777943	−	0.628335i	$-0.783737\pi$
$499$	77.4362	−	134.123i	0.155183	−	0.268784i	0.933126	+	0.359551i	$0.117070\pi$
$500$		0			0
$501$	−3.40812	−	5.90304i	−0.00680264	−	0.0117825i
$502$		0			0
$503$			710.432i			1.41239i	0.708018	+	0.706194i	$0.249590\pi$
$503$			710.432i			1.41239i	−0.708018	+	0.706194i	$0.750410\pi$
$504$		0			0
$505$	1616.45			3.20089
$506$		0			0
$507$	582.618	−	336.375i	1.14915	−	0.663461i
$508$		0			0
$509$	−73.6172	−	42.5029i	−0.144631	−	0.0835027i	0.425938	−	0.904752i	$-0.359944\pi$
$509$	−73.6172	−	42.5029i	−0.144631	−	0.0835027i	−0.570569	+	0.821249i	$0.693277\pi$
$510$		0			0
$511$	125.045	−	302.749i	0.244707	−	0.592464i
$512$		0			0
$513$	53.7389	−	93.0784i	0.104754	−	0.181439i
$514$		0			0
$515$	307.304	+	532.266i	0.596707	+	1.03353i
$516$		0			0
$517$			1136.89i			2.19902i
$518$		0			0
$519$	401.152			0.772933
$520$		0			0
$521$	416.281	−	240.340i	0.799004	−	0.461305i	−0.0441190	−	0.999026i	$-0.514048\pi$
$521$	416.281	−	240.340i	0.799004	−	0.461305i	0.843123	+	0.537721i	$0.180715\pi$
$522$		0			0
$523$	461.122	+	266.229i	0.881686	+	0.509042i	0.871214	−	0.490903i	$-0.163333\pi$
$523$	461.122	+	266.229i	0.881686	+	0.509042i	0.0104722	+	0.999945i	$0.496667\pi$
$524$		0			0
$525$	−1557.58	+	206.658i	−2.96681	+	0.393634i
$526$		0			0
$527$	−87.3502	+	151.295i	−0.165750	+	0.287087i
$528$		0			0
$529$	−88.5952	−	153.451i	−0.167477	−	0.290078i
$530$		0			0
$531$		−	519.210i		−	0.977796i
$532$		0			0
$533$	−0.231965			−0.000435207
$534$		0			0
$535$	992.847	−	573.220i	1.85579	−	1.07144i
$536$		0			0
$537$	−784.474	−	452.916i	−1.46084	−	0.843419i
$538$		0			0
$539$	−783.449	+	211.620i	−1.45352	+	0.392615i
$540$		0			0
$541$	413.743	−	716.623i	0.764774	−	1.32463i	−0.175593	−	0.984463i	$-0.556184\pi$
$541$	413.743	−	716.623i	0.764774	−	1.32463i	0.940366	−	0.340164i	$-0.110483\pi$
$542$		0			0
$543$	54.1241	+	93.7458i	0.0996761	+	0.172644i
$544$		0			0
$545$		−	194.517i		−	0.356911i
$546$		0			0
$547$	665.687			1.21698			0.608489	−	0.793562i	$-0.291776\pi$
$547$	665.687			1.21698			0.608489	+	0.793562i	$0.291776\pi$
$548$		0			0
$549$	274.568	−	158.522i	0.500124	−	0.288747i
$550$		0			0
$551$	−292.089	−	168.637i	−0.530107	−	0.306057i
$552$		0			0
$553$	50.0003	+	376.852i	0.0904165	+	0.681467i
$554$		0			0
$555$	−1139.27	+	1973.27i	−2.05273	+	3.55544i
$556$		0			0
$557$	9.42314	+	16.3214i	0.0169177	+	0.0293023i	0.874360	−	0.485277i	$-0.161281\pi$
$557$	9.42314	+	16.3214i	0.0169177	+	0.0293023i	−0.857443	+	0.514580i	$0.827948\pi$
$558$		0			0
$559$			11.3960i			0.0203863i
$560$		0			0
$561$	−458.860			−0.817932
$562$		0			0
$563$	−443.786	+	256.220i	−0.788253	+	0.455098i	−0.839347	−	0.543596i	$-0.817062\pi$
$563$	−443.786	+	256.220i	−0.788253	+	0.455098i	0.0510945	+	0.998694i	$0.483729\pi$
$564$		0			0
$565$	−641.803	−	370.545i	−1.13593	−	0.655832i
$566$		0			0
$567$	−618.305	−	255.380i	−1.09048	−	0.450405i
$568$		0			0
$569$	315.889	−	547.136i	0.555166	−	0.961575i	−0.442725	−	0.896658i	$-0.645988\pi$
$569$	315.889	−	547.136i	0.555166	−	0.961575i	0.997891	−	0.0649178i	$-0.0206785\pi$
$570$		0			0
$571$	−458.358	−	793.900i	−0.802729	−	1.39037i	−0.917813	−	0.397012i	$-0.870047\pi$
$571$	−458.358	−	793.900i	−0.802729	−	1.39037i	0.115084	−	0.993356i	$-0.463286\pi$
$572$		0			0
$573$			220.445i			0.384721i
$574$		0			0
$575$	1496.66			2.60289
$576$		0			0
$577$	160.014	−	92.3843i	0.277321	−	0.160111i	−0.354889	−	0.934908i	$-0.615481\pi$
$577$	160.014	−	92.3843i	0.277321	−	0.160111i	0.632210	+	0.774797i	$0.282148\pi$
$578$		0			0
$579$	768.186	+	443.512i	1.32675	+	0.765997i
$580$		0			0
$581$	−48.7337	−	63.3785i	−0.0838790	−	0.109085i
$582$		0			0
$583$	59.3751	−	102.841i	0.101844	−	0.176399i
$584$		0			0
$585$	13.8514	+	23.9914i	0.0236776	+	0.0410109i
$586$		0			0
$587$			141.805i			0.241575i	0.992678	+	0.120788i	$0.0385420\pi$
$587$			141.805i			0.241575i	−0.992678	+	0.120788i	$0.961458\pi$
$588$		0			0
$589$	320.260			0.543735
$590$		0			0
$591$	−52.6409	+	30.3923i	−0.0890710	+	0.0514251i
$592$		0			0
$593$	491.402	+	283.711i	0.828671	+	0.478433i	0.853397	−	0.521261i	$-0.174538\pi$
$593$	491.402	+	283.711i	0.828671	+	0.478433i	−0.0247264	+	0.999694i	$0.507871\pi$
$594$		0			0
$595$	347.874	−	267.491i	0.584662	−	0.449565i
$596$		0			0
$597$	−88.2538	+	152.860i	−0.147829	+	0.256047i
$598$		0			0
$599$	−224.453	−	388.764i	−0.374713	−	0.649022i	0.615571	−	0.788081i	$-0.288925\pi$
$599$	−224.453	−	388.764i	−0.374713	−	0.649022i	−0.990284	+	0.139059i	$0.955592\pi$
$600$		0			0
$601$		−	939.633i		−	1.56345i	−0.623623	−	0.781725i	$-0.714340\pi$
$601$		−	939.633i		−	1.56345i	0.623623	−	0.781725i	$-0.285660\pi$
$602$		0			0
$603$	−294.698			−0.488720
$604$		0			0
$605$	1197.15	−	691.174i	1.97876	−	1.14244i
$606$		0			0
$607$	−189.403	−	109.352i	−0.312031	−	0.180151i	0.335804	−	0.941932i	$-0.390992\pi$
$607$	−189.403	−	109.352i	−0.312031	−	0.180151i	−0.647835	+	0.761781i	$0.724325\pi$
$608$		0			0
$609$	−281.862	+	682.422i	−0.462828	+	1.12056i
$610$		0			0
$611$	−15.3170	+	26.5298i	−0.0250687	+	0.0434203i
$612$		0			0
$613$	−141.612	−	245.279i	−0.231014	−	0.400128i	0.727093	−	0.686539i	$-0.240871\pi$
$613$	−141.612	−	245.279i	−0.231014	−	0.400128i	−0.958107	+	0.286411i	$0.907538\pi$
$614$		0			0
$615$			18.6814i			0.0303762i
$616$		0			0
$617$	−1099.79			−1.78247			−0.891236	−	0.453539i	$-0.850161\pi$
$617$	−1099.79			−1.78247			−0.891236	+	0.453539i	$0.850161\pi$
$618$		0			0
$619$	−518.230	+	299.200i	−0.837206	+	0.483361i	−0.856313	−	0.516457i	$-0.827251\pi$
$619$	−518.230	+	299.200i	−0.837206	+	0.483361i	0.0191078	+	0.999817i	$0.493917\pi$
$620$		0			0
$621$	194.091	+	112.059i	0.312546	+	0.180449i
$622$		0			0
$623$	−426.158	+	56.5422i	−0.684042	+	0.0907580i
$624$		0			0
$625$	−569.469	+	986.349i	−0.911150	+	1.57816i
$626$		0			0
$627$	420.590	+	728.484i	0.670798	+	1.16186i
$628$		0			0
$629$		−	440.731i		−	0.700685i
$630$		0			0
$631$	1056.45			1.67425			0.837127	−	0.547008i	$-0.184233\pi$
$631$	1056.45			1.67425			0.837127	+	0.547008i	$0.184233\pi$
$632$		0			0
$633$	−478.797	+	276.434i	−0.756394	+	0.436704i
$634$		0			0
$635$	−335.458	−	193.677i	−0.528280	−	0.305003i
$636$		0			0
$637$	−21.1332	−	5.61694i	−0.0331761	−	0.00881780i
$638$		0			0
$639$	206.614	−	357.866i	0.323339	−	0.560040i
$640$		0			0
$641$	−299.479	−	518.713i	−0.467206	−	0.809224i	0.532092	−	0.846686i	$-0.321406\pi$
$641$	−299.479	−	518.713i	−0.467206	−	0.809224i	−0.999298	+	0.0374621i	$0.988073\pi$
$642$		0			0
$643$			707.781i			1.10075i	0.834918	+	0.550374i	$0.185515\pi$
$643$			707.781i			1.10075i	−0.834918	+	0.550374i	$0.814485\pi$
$644$		0			0
$645$	917.776			1.42291
$646$		0			0
$647$	422.678	−	244.033i	0.653289	−	0.377177i	−0.136426	−	0.990650i	$-0.543562\pi$
$647$	422.678	−	244.033i	0.653289	−	0.377177i	0.789715	+	0.613474i	$0.210228\pi$
$648$		0			0
$649$	−1081.80	−	624.575i	−1.66686	−	0.962365i
$650$		0			0
$651$	−92.2121	−	695.002i	−0.141647	−	1.06759i
$652$		0			0
$653$	−177.997	+	308.300i	−0.272584	+	0.472129i	−0.969523	−	0.245001i	$-0.921212\pi$
$653$	−177.997	+	308.300i	−0.272584	+	0.472129i	0.696939	+	0.717131i	$0.254545\pi$
$654$		0			0
$655$	869.368	+	1505.79i	1.32728	+	2.29891i
$656$		0			0
$657$			322.124i			0.490295i
$658$		0			0
$659$	1182.36			1.79418			0.897088	−	0.441852i	$-0.145678\pi$
$659$	1182.36			1.79418			0.897088	+	0.441852i	$0.145678\pi$
$660$		0			0
$661$	−76.0985	+	43.9355i	−0.115126	+	0.0664682i	−0.556457	−	0.830876i	$-0.687840\pi$
$661$	−76.0985	+	43.9355i	−0.115126	+	0.0664682i	0.441331	+	0.897344i	$0.354506\pi$
$662$		0			0
$663$	−10.7077	−	6.18209i	−0.0161504	−	0.00932441i
$664$		0			0
$665$	−743.528	−	307.101i	−1.11809	−	0.461806i
$666$		0			0
$667$	351.650	−	609.076i	0.527211	−	0.913157i
$668$		0			0
$669$	−105.926	−	183.470i	−0.158336	−	0.274245i
$670$		0			0
$671$		−	762.766i		−	1.13676i
$672$		0			0
$673$	939.720			1.39631			0.698157	−	0.715944i	$-0.254004\pi$
$673$	939.720			1.39631			0.698157	+	0.715944i	$0.254004\pi$
$674$		0			0
$675$	−411.346	+	237.491i	−0.609401	+	0.351838i
$676$		0			0
$677$	73.4780	+	42.4226i	0.108535	+	0.0626626i	0.553285	−	0.832992i	$-0.313374\pi$
$677$	73.4780	+	42.4226i	0.108535	+	0.0626626i	−0.444750	+	0.895655i	$0.646707\pi$
$678$		0			0
$679$	86.8621	+	112.965i	0.127926	+	0.166369i
$680$		0			0
$681$	798.306	−	1382.71i	1.17226	−	2.03041i
$682$		0			0
$683$	−151.540	−	262.475i	−0.221874	−	0.384297i	0.733503	−	0.679686i	$-0.237884\pi$
$683$	−151.540	−	262.475i	−0.221874	−	0.384297i	−0.955377	+	0.295389i	$0.904551\pi$
$684$		0			0
$685$			1318.84i			1.92531i
$686$		0			0
$687$	−1516.67			−2.20767
$688$		0			0
$689$	2.77108	−	1.59989i	0.00402189	−	0.00232204i
$690$		0			0
$691$	221.226	+	127.725i	0.320154	+	0.184841i	0.651461	−	0.758682i	$-0.274156\pi$
$691$	221.226	+	127.725i	0.320154	+	0.184841i	−0.331307	+	0.943523i	$0.607490\pi$
$692$		0			0
$693$	632.658	−	486.471i	0.912927	−	0.701978i
$694$		0			0
$695$	−455.586	+	789.098i	−0.655519	+	1.13539i
$696$		0			0
$697$	−1.80675	−	3.12938i	−0.00259217	−	0.00448978i
$698$		0			0
$699$		−	1327.17i		−	1.89867i
$700$		0			0
$701$	−560.333			−0.799333			−0.399667	−	0.916661i	$-0.630874\pi$
$701$	−560.333			−0.799333			−0.399667	+	0.916661i	$0.630874\pi$
$702$		0			0
$703$	−699.702	+	403.973i	−0.995309	+	0.574642i
$704$		0			0
$705$	2136.58	+	1233.56i	3.03062	+	1.74973i
$706$		0			0
$707$	479.007	−	1159.73i	0.677521	−	1.64036i
$708$		0			0
$709$	−411.369	+	712.512i	−0.580210	+	1.00495i	0.415244	+	0.909710i	$0.363696\pi$
$709$	−411.369	+	712.512i	−0.580210	+	1.00495i	−0.995454	+	0.0952436i	$0.969637\pi$
$710$		0			0
$711$	−186.925	−	323.763i	−0.262904	−	0.455363i
$712$		0			0
$713$			667.820i			0.936634i
$714$		0			0
$715$	66.6494			0.0932159
$716$		0			0
$717$	427.231	−	246.662i	0.595860	−	0.344020i
$718$		0			0
$719$	−1076.44	−	621.481i	−1.49713	−	0.864368i	−0.497135	−	0.867673i	$-0.665615\pi$
$719$	−1076.44	−	621.481i	−1.49713	−	0.864368i	−0.999995	+	0.00330501i	$0.998948\pi$
$720$		0			0
$721$	472.943	−	62.7496i	0.655954	−	0.0870313i
$722$		0			0
$723$	−165.962	+	287.454i	−0.229546	+	0.397586i
$724$		0			0
$725$	745.267	+	1290.84i	1.02795	+	1.78047i
$726$		0			0
$727$		−	1025.14i		−	1.41010i	−0.709156	−	0.705052i	$-0.750924\pi$
$727$		−	1025.14i		−	1.41010i	0.709156	−	0.705052i	$-0.249076\pi$
$728$		0			0
$729$	355.367			0.487472
$730$		0			0
$731$	−153.740	+	88.7616i	−0.210314	+	0.121425i
$732$		0			0
$733$	−665.476	−	384.213i	−0.907880	−	0.524165i	−0.0281317	−	0.999604i	$-0.508956\pi$
$733$	−665.476	−	384.213i	−0.907880	−	0.524165i	−0.879749	+	0.475439i	$0.842289\pi$
$734$		0			0
$735$	−452.362	+	1701.97i	−0.615458	+	2.31560i
$736$		0			0
$737$	−354.502	+	614.016i	−0.481007	+	0.833129i
$738$		0			0
$739$	−440.237	−	762.513i	−0.595720	−	1.03182i	−0.993445	−	0.114312i	$-0.963534\pi$
$739$	−440.237	−	762.513i	−0.595720	−	1.03182i	0.397725	−	0.917505i	$-0.369800\pi$
$740$		0			0
$741$			22.6660i			0.0305883i
$742$		0			0
$743$	−984.949			−1.32564			−0.662819	−	0.748780i	$-0.730640\pi$
$743$	−984.949			−1.32564			−0.662819	+	0.748780i	$0.730640\pi$
$744$		0			0
$745$	−1492.48	+	861.685i	−2.00333	+	1.15662i
$746$		0			0
$747$	68.0894	+	39.3114i	0.0911504	+	0.0526257i
$748$		0			0
$749$	−117.048	−	882.189i	−0.156272	−	1.17782i
$750$		0			0
$751$	166.984	−	289.224i	0.222349	−	0.385119i	−0.733172	−	0.680043i	$-0.761961\pi$
$751$	166.984	−	289.224i	0.222349	−	0.385119i	0.955521	+	0.294924i	$0.0952943\pi$
$752$		0			0
$753$	−804.563	−	1393.54i	−1.06848	−	1.85066i
$754$		0			0
$755$		−	258.963i		−	0.342997i
$756$		0			0
$757$	−964.869			−1.27460			−0.637298	−	0.770617i	$-0.719948\pi$
$757$	−964.869			−1.27460			−0.637298	+	0.770617i	$0.719948\pi$
$758$		0			0
$759$	−1519.07	+	877.033i	−2.00140	+	1.15551i
$760$		0			0
$761$	767.267	+	442.982i	1.00824	+	0.582105i	0.910675	−	0.413124i	$-0.135563\pi$
$761$	767.267	+	442.982i	1.00824	+	0.582105i	0.0975611	+	0.995230i	$0.468896\pi$
$762$		0			0
$763$	−139.557	−	57.6417i	−0.182906	−	0.0755461i
$764$		0			0
$765$	−215.774	+	373.731i	−0.282057	+	0.488537i
$766$		0			0
$767$	−16.8294	−	29.1494i	−0.0219419	−	0.0380045i
$768$		0			0
$769$		−	416.779i		−	0.541976i	−0.962583	−	0.270988i	$-0.912650\pi$
$769$		−	416.779i		−	0.541976i	0.962583	−	0.270988i	$-0.0873503\pi$
$770$		0			0
$771$	−1029.32			−1.33504
$772$		0			0
$773$	−57.9458	+	33.4550i	−0.0749623	+	0.0432795i	−0.537013	−	0.843574i	$-0.680447\pi$
$773$	−57.9458	+	33.4550i	−0.0749623	+	0.0432795i	0.462050	+	0.886854i	$0.347114\pi$
$774$		0			0
$775$	−1225.72	−	707.670i	−1.58157	−	0.913122i
$776$		0			0
$777$	1078.13	+	1402.12i	1.38756	+	1.80453i
$778$		0			0
$779$	−3.31212	+	5.73676i	−0.00425176	+	0.00736426i
$780$		0			0
$781$	−497.085	−	860.977i	−0.636473	−	1.10240i
$782$		0			0
$783$			223.200i			0.285057i
$784$		0			0
$785$	−1137.44			−1.44897
$786$		0			0
$787$	1059.42	−	611.654i	1.34614	−	0.777196i	0.358443	−	0.933552i	$-0.383308\pi$
$787$	1059.42	−	611.654i	1.34614	−	0.777196i	0.987701	+	0.156355i	$0.0499745\pi$
$788$		0			0
$789$	1359.40	+	784.851i	1.72294	+	0.994742i
$790$		0			0
$791$	−456.038	+	350.662i	−0.576533	+	0.443314i
$792$		0			0
$793$	10.2765	−	17.7995i	0.0129590	−	0.0224457i
$794$		0			0
$795$	−128.847	−	223.170i	−0.162072	−	0.280717i
$796$		0			0
$797$		−	578.768i		−	0.726184i	−0.931753	−	0.363092i	$-0.881721\pi$
$797$		−	578.768i		−	0.726184i	0.931753	−	0.363092i	$-0.118279\pi$
$798$		0			0
$799$	−477.208			−0.597256
$800$		0			0
$801$	366.123	−	211.381i	0.457083	−	0.263897i
$802$		0			0
$803$	671.159	+	387.494i	0.835814	+	0.482558i
$804$		0			0
$805$	640.380	−	1550.44i	0.795503	−	1.92601i
$806$		0			0
$807$	107.281	−	185.817i	0.132938	−	0.230256i
$808$		0			0
$809$	446.064	+	772.605i	0.551377	+	0.955013i	0.998176	+	0.0603783i	$0.0192307\pi$
$809$	446.064	+	772.605i	0.551377	+	0.955013i	−0.446799	+	0.894635i	$0.647436\pi$
$810$		0			0
$811$			200.724i			0.247502i	0.992313	+	0.123751i	$0.0394925\pi$
$811$			200.724i			0.247502i	−0.992313	+	0.123751i	$0.960508\pi$
$812$		0			0
$813$	−189.362			−0.232918
$814$		0			0
$815$	1985.60	−	1146.39i	2.43632	−	1.40661i
$816$		0			0
$817$	281.835	+	162.717i	0.344963	+	0.199165i
$818$		0			0
$819$	21.3174	−	2.82837i	0.0260286	−	0.00345345i
$820$		0			0
$821$	−316.315	+	547.873i	−0.385280	+	0.667324i	−0.991808	−	0.127738i	$-0.959228\pi$
$821$	−316.315	+	547.873i	−0.385280	+	0.667324i	0.606528	+	0.795062i	$0.292562\pi$
$822$		0			0
$823$	1.90823	+	3.30515i	0.00231863	+	0.00401598i	0.867182	−	0.497991i	$-0.165929\pi$
$823$	1.90823	+	3.30515i	0.00231863	+	0.00401598i	−0.864864	+	0.502007i	$0.832595\pi$
$824$		0			0
$825$		−	3717.47i		−	4.50602i
$826$		0			0
$827$	−1174.97			−1.42076			−0.710382	−	0.703817i	$-0.751478\pi$
$827$	−1174.97			−1.42076			−0.710382	+	0.703817i	$0.751478\pi$
$828$		0			0
$829$	−645.036	+	372.412i	−0.778090	+	0.449230i	−0.835753	−	0.549106i	$-0.814968\pi$
$829$	−645.036	+	372.412i	−0.778090	+	0.449230i	0.0576632	+	0.998336i	$0.481635\pi$
$830$		0			0
$831$	841.885	+	486.062i	1.01310	+	0.584913i
$832$		0			0
$833$	−88.8270	−	328.851i	−0.106635	−	0.394779i
$834$		0			0
$835$	−7.71143	+	13.3566i	−0.00923525	+	0.0159959i
$836$		0			0
$837$	−105.970	−	183.545i	−0.126607	−	0.219289i
$838$		0			0
$839$			1124.03i			1.33973i	0.742485	+	0.669863i	$0.233647\pi$
$839$			1124.03i			1.33973i	−0.742485	+	0.669863i	$0.766353\pi$
$840$		0			0
$841$	−140.579			−0.167156
$842$		0			0
$843$	600.070	−	346.451i	0.711827	−	0.410974i
$844$		0			0
$845$	−1318.27	−	761.103i	−1.56008	−	0.900713i
$846$		0			0
$847$	−141.133	−	1063.72i	−0.166627	−	1.25587i
$848$		0			0
$849$	−104.705	+	181.354i	−0.123327	+	0.213609i
$850$		0			0
$851$	−842.382	−	1459.05i	−0.989873	−	1.71451i
$852$		0			0
$853$			96.2021i			0.112781i	0.998409	+	0.0563905i	$0.0179592\pi$
$853$			96.2021i			0.112781i	−0.998409	+	0.0563905i	$0.982041\pi$
$854$		0			0
$855$	791.112			0.925277
$856$		0			0
$857$	741.679	−	428.208i	0.865436	−	0.499660i	−0.000392914	−	1.00000i	$-0.500125\pi$
$857$	741.679	−	428.208i	0.865436	−	0.499660i	0.865829	+	0.500340i	$0.166792\pi$
$858$		0			0
$859$	1451.57	+	838.062i	1.68983	+	0.975625i	0.954638	+	0.297769i	$0.0962427\pi$
$859$	1451.57	+	838.062i	1.68983	+	0.975625i	0.735195	+	0.677856i	$0.237091\pi$
$860$		0			0
$861$	13.4031	+	5.53591i	0.0155669	+	0.00642962i
$862$		0			0
$863$	141.625	−	245.301i	0.164107	−	0.284242i	−0.772231	−	0.635342i	$-0.780859\pi$
$863$	141.625	−	245.301i	0.164107	−	0.284242i	0.936338	+	0.351100i	$0.114192\pi$
$864$		0			0
$865$	−453.836	−	786.067i	−0.524666	−	0.908748i
$866$		0			0
$867$			959.193i			1.10634i
$868$		0			0
$869$	−899.431			−1.03502
$870$		0			0
$871$	−16.5449	+	9.55220i	−0.0189953	+	0.0109669i
$872$		0			0
$873$	−121.361	−	70.0679i	−0.139016	−	0.0802611i
$874$		0			0
$875$	1205.13	+	1567.28i	1.37730	+	1.79118i
$876$		0			0
$877$	416.246	−	720.959i	0.474625	−	0.822075i	−0.524953	−	0.851131i	$-0.675917\pi$
$877$	416.246	−	720.959i	0.474625	−	0.822075i	0.999578	+	0.0290568i	$0.00925037\pi$
$878$		0			0
$879$	−639.787	−	1108.14i	−0.727858	−	1.26069i
$880$		0			0
$881$			890.282i			1.01054i	0.862962	+	0.505268i	$0.168606\pi$
$881$			890.282i			1.01054i	−0.862962	+	0.505268i	$0.831394\pi$
$882$		0			0
$883$	322.429			0.365152			0.182576	−	0.983192i	$-0.441556\pi$
$883$	322.429			0.365152			0.182576	+	0.983192i	$0.441556\pi$
$884$		0			0
$885$	−2347.56	+	1355.36i	−2.65260	+	1.53148i
$886$		0			0
$887$	−469.859	−	271.273i	−0.529717	−	0.305832i	0.211184	−	0.977446i	$-0.432268\pi$
$887$	−469.859	−	271.273i	−0.529717	−	0.305832i	−0.740901	+	0.671614i	$0.765601\pi$
$888$		0			0
$889$	−238.362	+	183.284i	−0.268124	+	0.206169i
$890$		0			0
$891$	791.379	−	1370.71i	0.888192	−	1.53839i
$892$		0			0
$893$	437.408	+	757.613i	0.489819	+	0.848391i
$894$		0			0
$895$			2049.59i			2.29005i
$896$		0			0
$897$	−47.2640			−0.0526912
$898$		0			0
$899$	−575.982	+	332.543i	−0.640692	+	0.369904i
$900$		0			0
$901$	43.1672	+	24.9226i	0.0479103	+	0.0276610i
$902$		0			0
$903$	271.967	−	658.465i	0.301182	−	0.729198i
$904$		0			0
$905$	122.465	−	212.115i	0.135320	−	0.234381i
$906$		0			0
$907$	727.975	+	1260.89i	0.802619	+	1.39018i	0.917887	+	0.396842i	$0.129894\pi$
$907$	727.975	+	1260.89i	0.802619	+	1.39018i	−0.115268	+	0.993334i	$0.536773\pi$
$908$		0			0
$909$			1233.95i			1.35748i
$910$		0			0
$911$	−336.756			−0.369655			−0.184828	−	0.982771i	$-0.559173\pi$
$911$	−336.756			−0.369655			−0.184828	+	0.982771i	$0.559173\pi$
$912$		0			0
$913$	163.814	−	94.5780i	0.179424	−	0.103590i
$914$		0			0
$915$	−1433.48	−	827.622i	−1.56665	−	0.904505i
$916$		0			0
$917$	1337.96	−	177.519i	1.45906	−	0.193587i
$918$		0			0
$919$	490.370	−	849.346i	0.533591	−	0.924207i	−0.465639	−	0.884975i	$-0.654176\pi$
$919$	490.370	−	849.346i	0.533591	−	0.924207i	0.999230	−	0.0392319i	$-0.0124911\pi$
$920$		0			0
$921$	1132.22	+	1961.07i	1.22934	+	2.12928i
$922$		0			0
$923$		−	26.7883i		−	0.0290231i
$924$		0			0
$925$	3570.59			3.86010
$926$		0			0
$927$	−406.317	+	234.587i	−0.438314	+	0.253061i
$928$		0			0
$929$	−358.768	−	207.135i	−0.386188	−	0.222965i	0.294319	−	0.955707i	$-0.404907\pi$
$929$	−358.768	−	207.135i	−0.386188	−	0.222965i	−0.680507	+	0.732742i	$0.738240\pi$
$930$		0			0
$931$	−440.664	+	442.446i	−0.473323	+	0.475237i
$932$		0			0
$933$	96.0452	−	166.355i	0.102942	−	0.178301i
$934$		0			0
$935$	519.123	+	899.147i	0.555212	+	0.961655i
$936$		0			0
$937$			1323.89i			1.41290i	0.707764	+	0.706449i	$0.249704\pi$
$937$			1323.89i			1.41290i	−0.707764	+	0.706449i	$0.750296\pi$
$938$		0			0
$939$	324.689			0.345781
$940$		0			0
$941$	823.269	−	475.315i	0.874888	−	0.505117i	0.00591840	−	0.999982i	$-0.498116\pi$
$941$	823.269	−	475.315i	0.874888	−	0.505117i	0.868969	+	0.494866i	$0.164783\pi$
$942$		0			0
$943$	−11.9625	−	6.90658i	−0.0126856	−	0.00732405i
$944$		0			0
$945$	70.0202	+	527.742i	0.0740955	+	0.558457i
$946$		0			0
$947$	−580.243	+	1005.01i	−0.612717	+	1.06126i	0.378064	+	0.925780i	$0.376590\pi$
$947$	−580.243	+	1005.01i	−0.612717	+	1.06126i	−0.990780	+	0.135477i	$0.956743\pi$
$948$		0			0
$949$	10.4412	+	18.0846i	0.0110023	+	0.0190565i
$950$		0			0
$951$			1580.56i			1.66200i
$952$		0			0
$953$	−1025.81			−1.07640			−0.538201	−	0.842816i	$-0.680896\pi$
$953$	−1025.81			−1.07640			−0.538201	+	0.842816i	$0.680896\pi$
$954$		0			0
$955$	431.968	−	249.397i	0.452322	−	0.261148i
$956$		0			0
$957$	−1512.85	−	873.443i	−1.58082	−	0.912689i
$958$		0			0
$959$	946.208	+	390.814i	0.986661	+	0.407523i
$960$		0			0
$961$	−164.733	+	285.326i	−0.171418	+	0.296905i
$962$		0			0
$963$	437.580	+	757.912i	0.454393	+	0.787032i
$964$		0			0
$965$		−	2007.04i		−	2.07983i
$966$		0			0
$967$	−648.379			−0.670505			−0.335253	−	0.942128i	$-0.608822\pi$
$967$	−648.379			−0.670505			−0.335253	+	0.942128i	$0.608822\pi$
$968$		0			0
$969$	−305.780	+	176.542i	−0.315562	+	0.182190i
$970$		0			0
$971$	−633.669	−	365.849i	−0.652594	−	0.376776i	0.136855	−	0.990591i	$-0.456301\pi$
$971$	−633.669	−	365.849i	−0.652594	−	0.376776i	−0.789449	+	0.613816i	$0.789634\pi$
$972$		0			0
$973$	431.139	+	560.699i	0.443103	+	0.576258i
$974$		0			0
$975$	50.0843	−	86.7486i	0.0513686	−	0.0889729i
$976$		0			0
$977$	388.723	+	673.288i	0.397874	+	0.689138i	0.993463	−	0.114151i	$-0.0364147\pi$
$977$	388.723	+	673.288i	0.397874	+	0.689138i	−0.595589	+	0.803289i	$0.703081\pi$
$978$		0			0
$979$		−	1017.11i		−	1.03893i
$980$		0			0
$981$	148.489			0.151364
$982$		0			0
$983$	−1177.01	+	679.546i	−1.19736	+	0.691298i	−0.959966	−	0.280115i	$-0.909627\pi$
$983$	−1177.01	+	679.546i	−1.19736	+	0.691298i	−0.237396	+	0.971413i	$0.576294\pi$
$984$		0			0
$985$	119.109	+	68.7674i	0.120923	+	0.0698147i
$986$		0			0
$987$	1518.17	−	1167.36i	1.53816	−	1.18274i
$988$		0			0
$989$	−339.305	+	587.694i	−0.343079	+	0.594231i
$990$		0			0
$991$	−352.548	−	610.632i	−0.355750	−	0.616177i	0.631496	−	0.775379i	$-0.282441\pi$
$991$	−352.548	−	610.632i	−0.355750	−	0.616177i	−0.987246	+	0.159202i	$0.949108\pi$
$992$		0			0
$993$		−	1890.05i		−	1.90337i
$994$		0			0
$995$	399.377			0.401384
$996$		0			0
$997$	−1078.84	+	622.871i	−1.08209	+	0.624745i	−0.931460	−	0.363845i	$-0.881464\pi$
$997$	−1078.84	+	622.871i	−1.08209	+	0.624745i	−0.150631	+	0.988590i	$0.548131\pi$
$998$		0			0
$999$	463.045	+	267.339i	0.463508	+	0.267607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.s.b.33.7	yes	16
4.3	odd	2	inner	224.3.s.b.33.2	✓	16
7.2	even	3		1568.3.c.g.97.14		16
7.3	odd	6	inner	224.3.s.b.129.7	yes	16
7.5	odd	6		1568.3.c.g.97.3		16
8.3	odd	2		448.3.s.h.257.7		16
8.5	even	2		448.3.s.h.257.2		16
28.3	even	6	inner	224.3.s.b.129.2	yes	16
28.19	even	6		1568.3.c.g.97.13		16
28.23	odd	6		1568.3.c.g.97.4		16
56.3	even	6		448.3.s.h.129.7		16
56.45	odd	6		448.3.s.h.129.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.b.33.2	✓	16	4.3	odd	2	inner
224.3.s.b.33.7	yes	16	1.1	even	1	trivial
224.3.s.b.129.2	yes	16	28.3	even	6	inner
224.3.s.b.129.7	yes	16	7.3	odd	6	inner
448.3.s.h.129.2		16	56.45	odd	6
448.3.s.h.129.7		16	56.3	even	6
448.3.s.h.257.2		16	8.5	even	2
448.3.s.h.257.7		16	8.3	odd	2
1568.3.c.g.97.3		16	7.5	odd	6
1568.3.c.g.97.4		16	28.23	odd	6
1568.3.c.g.97.13		16	28.19	even	6
1568.3.c.g.97.14		16	7.2	even	3

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.45151 - 1.99273i) q^{3} +(-7.80961 - 4.50888i) q^{5} +(-5.54917 + 4.26693i) q^{7} +(3.44195 - 5.96164i) q^{9} +O(q^{10})\)	\(q+(3.45151 - 1.99273i) q^{3} +(-7.80961 - 4.50888i) q^{5} +(-5.54917 + 4.26693i) q^{7} +(3.44195 - 5.96164i) q^{9} +(-8.28088 - 14.3429i) q^{11} -0.446263i q^{13} -35.9399 q^{15} +(6.02041 - 3.47588i) q^{17} +(-11.0366 - 6.37198i) q^{19} +(-10.6502 + 25.7854i) q^{21} +(13.2871 - 23.0140i) q^{23} +(28.1600 + 48.7745i) q^{25} +8.43362i q^{27} +26.4655 q^{29} +(-21.7635 + 12.5652i) q^{31} +(-57.1631 - 33.0031i) q^{33} +(62.5759 - 8.30251i) q^{35} +(31.6992 - 54.9046i) q^{37} +(-0.889283 - 1.54028i) q^{39} -0.519795i q^{41} -25.5364 q^{43} +(-53.7606 + 31.0387i) q^{45} +(-59.4488 - 34.3228i) q^{47} +(12.5866 - 47.3559i) q^{49} +(13.8530 - 23.9941i) q^{51} +(3.58507 + 6.20953i) q^{53} +149.350i q^{55} -50.7906 q^{57} +(65.3189 - 37.7119i) q^{59} +(39.8855 + 23.0279i) q^{61} +(6.33791 + 47.7687i) q^{63} +(-2.01215 + 3.48514i) q^{65} +(-21.4049 - 37.0743i) q^{67} -105.911i q^{69} +60.0281 q^{71} +(-40.5246 + 23.3969i) q^{73} +(194.389 + 112.230i) q^{75} +(107.152 + 44.2573i) q^{77} +(27.1539 - 47.0319i) q^{79} +(47.7835 + 82.7635i) q^{81} +11.4213i q^{83} -62.6894 q^{85} +(91.3459 - 52.7386i) q^{87} +(53.1854 + 30.7066i) q^{89} +(1.90417 + 2.47639i) q^{91} +(-50.0780 + 86.7377i) q^{93} +(57.4610 + 99.5253i) q^{95} -20.3570i q^{97} -114.010 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{9}+O(q^{10}) \) 16 * q + 40 * q^9	\( 16 q + 40 q^{9} - 48 q^{17} - 136 q^{21} + 80 q^{25} - 16 q^{29} - 264 q^{33} + 72 q^{37} + 312 q^{45} + 128 q^{49} + 40 q^{53} + 368 q^{57} + 216 q^{61} - 168 q^{65} - 312 q^{73} + 64 q^{77} - 384 q^{81} - 1072 q^{85} + 24 q^{89} - 168 q^{93}+O(q^{100}) \) 16 * q + 40 * q^9 - 48 * q^17 - 136 * q^21 + 80 * q^25 - 16 * q^29 - 264 * q^33 + 72 * q^37 + 312 * q^45 + 128 * q^49 + 40 * q^53 + 368 * q^57 + 216 * q^61 - 168 * q^65 - 312 * q^73 + 64 * q^77 - 384 * q^81 - 1072 * q^85 + 24 * q^89 - 168 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more