LMFDB - Embedded newform 224.3.s.b.129.7

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			129.7
Root			$-2.79414 + 0.796701i$ of defining polynomial
Character	$\chi$	$=$	224.129
Dual form			224.3.s.b.33.7

$q$-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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

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

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	0.949010	−	0.315246i	$-0.102087\pi$
$3$	3.45151	+	1.99273i	1.15050	+	0.664244i	0.201494	+	0.979490i	$0.435420\pi$
$4$		0			0
$5$	−7.80961	+	4.50888i	−1.56192	+	0.901776i	−0.564859	+	0.825188i	$0.691069\pi$
$5$	−7.80961	+	4.50888i	−1.56192	+	0.901776i	−0.997063	+	0.0765879i	$0.975597\pi$
$6$		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	0.193650	+	0.981071i	$0.437967\pi$
$11$	−8.28088	+	14.3429i	−0.752807	+	1.30390i	−0.946457	+	0.322830i	$0.895366\pi$
$12$		0			0
$13$			0.446263i			0.0343279i	0.999853	+	0.0171640i	$0.00546373\pi$
$13$			0.446263i			0.0343279i	−0.999853	+	0.0171640i	$0.994536\pi$
$14$		0			0
$15$	−35.9399			−2.39599
$16$		0			0
$17$	6.02041	+	3.47588i	0.354142	+	0.204464i	0.666508	−	0.745498i	$-0.267788\pi$
$17$	6.02041	+	3.47588i	0.354142	+	0.204464i	−0.312366	+	0.949962i	$0.601122\pi$
$18$		0			0
$19$	−11.0366	+	6.37198i	−0.580873	+	0.335367i	−0.761480	−	0.648188i	$-0.775527\pi$
$19$	−11.0366	+	6.37198i	−0.580873	+	0.335367i	0.180607	+	0.983555i	$0.442194\pi$
$20$		0			0
$21$	−10.6502	−	25.7854i	−0.507151	−	1.22787i
$22$		0			0
$23$	13.2871	+	23.0140i	0.577701	+	1.00061i	0.995742	+	0.0921795i	$0.0293833\pi$
$23$	13.2871	+	23.0140i	0.577701	+	1.00061i	−0.418041	+	0.908428i	$0.637283\pi$
$24$		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	0.106061	−	0.994360i	$-0.466176\pi$
$31$	−21.7635	−	12.5652i	−0.702049	−	0.405328i	−0.808110	+	0.589031i	$0.799509\pi$
$32$		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	0.875026	+	0.484076i	$0.160844\pi$
$37$	31.6992	+	54.9046i	0.856735	+	1.48391i	−0.0182908	+	0.999833i	$0.505822\pi$
$38$		0			0
$39$	−0.889283	+	1.54028i	−0.0228021	+	0.0394944i
$40$		0			0
$41$			0.519795i			0.0126779i	0.999980	+	0.00633896i	$0.00201777\pi$
$41$			0.519795i			0.0126779i	−0.999980	+	0.00633896i	$0.997982\pi$
$42$		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	−0.974012	−	0.226495i	$-0.927273\pi$
$47$	−59.4488	+	34.3228i	−1.26487	+	0.730272i	−0.290856	+	0.956767i	$0.593940\pi$
$48$		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	−0.830220	−	0.557435i	$-0.811785\pi$
$53$	3.58507	−	6.20953i	0.0676429	−	0.117161i	0.897863	+	0.440274i	$0.145119\pi$
$54$		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	0.938077	−	0.346428i	$-0.112605\pi$
$59$	65.3189	+	37.7119i	1.10710	+	0.639184i	0.169023	+	0.985612i	$0.445939\pi$
$60$		0			0
$61$	39.8855	−	23.0279i	0.653861	−	0.377507i	−0.136073	−	0.990699i	$-0.543448\pi$
$61$	39.8855	−	23.0279i	0.653861	−	0.377507i	0.789934	+	0.613192i	$0.210115\pi$
$62$		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	−0.980379	−	0.197123i	$-0.936840\pi$
$67$	−21.4049	+	37.0743i	−0.319476	+	0.553348i	0.660903	+	0.750471i	$0.270173\pi$
$68$		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	0.196058	−	0.980592i	$-0.437186\pi$
$73$	−40.5246	−	23.3969i	−0.555132	−	0.320505i	−0.751189	+	0.660087i	$0.770519\pi$
$74$		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	0.985120	−	0.171866i	$-0.0549796\pi$
$79$	27.1539	+	47.0319i	0.343720	+	0.595340i	−0.641401	+	0.767206i	$0.721646\pi$
$80$		0			0
$81$	47.7835	−	82.7635i	0.589920	−	1.02177i
$82$		0			0
$83$		−	11.4213i		−	0.137606i	−0.997630	−	0.0688028i	$-0.978082\pi$
$83$		−	11.4213i		−	0.137606i	0.997630	−	0.0688028i	$-0.0219179\pi$
$84$		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	−0.170504	−	0.985357i	$-0.554539\pi$
$89$	53.1854	−	30.7066i	0.597589	−	0.345018i	0.768092	+	0.640339i	$0.221206\pi$
$90$		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	$0.0334629\pi$
$97$			20.3570i			0.209866i	−0.994479	+	0.104933i	$0.966537\pi$
$98$		0			0
$99$	−114.010			−1.15161
$100$		0			0
$101$	−155.237	−	89.6260i	−1.53700	−	0.887386i	−0.999012	−	0.0444318i	$-0.985852\pi$
$101$	−155.237	−	89.6260i	−1.53700	−	0.887386i	−0.537985	−	0.842954i	$-0.680814\pi$
$102$		0			0
$103$	−59.0242	+	34.0777i	−0.573051	+	0.330851i	−0.758367	−	0.651828i	$-0.774002\pi$
$103$	−59.0242	+	34.0777i	−0.573051	+	0.330851i	0.185316	+	0.982679i	$0.440669\pi$
$104$		0			0
$105$	199.437	+	153.353i	1.89940	+	1.46051i
$106$		0			0
$107$	−63.5657	−	110.099i	−0.594072	−	1.02896i	−0.993677	−	0.112276i	$-0.964186\pi$
$107$	−63.5657	−	110.099i	−0.594072	−	1.02896i	0.399605	−	0.916688i	$-0.369147\pi$
$108$		0			0
$109$	10.7852	−	18.6805i	0.0989468	−	0.171381i	−0.812302	−	0.583237i	$-0.801786\pi$
$109$	10.7852	−	18.6805i	0.0989468	−	0.171381i	0.911249	+	0.411856i	$0.135119\pi$
$110$		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	−0.975861	−	0.218391i	$-0.929919\pi$
$131$	−166.980	+	96.4062i	−1.27466	+	0.735925i	−0.298798	+	0.954316i	$0.596586\pi$
$132$		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	0.465468	+	0.885065i	$0.345886\pi$
$137$	−73.1244	+	126.655i	−0.533754	+	0.924490i	−0.999223	+	0.0394252i	$0.987447\pi$
$138$		0			0
$139$			101.042i			0.726921i	0.931610	+	0.363460i	$0.118405\pi$
$139$			101.042i			0.726921i	−0.931610	+	0.363460i	$0.881595\pi$
$140$		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	0.985142	+	0.171741i	$0.0549393\pi$
$149$	95.5542	+	165.505i	0.641303	+	1.11077i	−0.343839	+	0.939029i	$0.611727\pi$
$150$		0			0
$151$	14.3585	−	24.8696i	0.0950893	−	0.164700i	−0.814557	−	0.580084i	$-0.803020\pi$
$151$	14.3585	−	24.8696i	0.0950893	−	0.164700i	0.909646	+	0.415385i	$0.136353\pi$
$152$		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	0.805767	−	0.592233i	$-0.201753\pi$
$157$	109.235	+	63.0666i	0.695762	+	0.401698i	−0.110005	+	0.993931i	$0.535087\pi$
$158$		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	−0.931992	−	0.362478i	$-0.881931\pi$
$163$	−127.126	−	220.188i	−0.779911	−	1.35085i	0.152081	−	0.988368i	$-0.451403\pi$
$164$		0			0
$165$	297.614	−	515.483i	1.80372	−	3.12414i
$166$		0			0
$167$			1.71028i			0.0102412i	0.999987	+	0.00512059i	$0.00162994\pi$
$167$			1.71028i			0.0102412i	−0.999987	+	0.00512059i	$0.998370\pi$
$168$		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	−0.226443	−	0.974025i	$-0.572710\pi$
$173$	87.1688	−	50.3270i	0.503866	−	0.290907i	0.730309	+	0.683117i	$0.239376\pi$
$174$		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	0.351670	+	0.936124i	$0.385614\pi$
$179$	−113.642	+	196.834i	−0.634872	+	1.09963i	−0.986542	+	0.163506i	$0.947720\pi$
$180$		0			0
$181$		−	27.1608i		−	0.150060i	−0.997181	−	0.0750298i	$-0.976095\pi$
$181$		−	27.1608i		−	0.150060i	0.997181	−	0.0750298i	$-0.0239052\pi$
$182$		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	0.784500	−	0.620128i	$-0.212919\pi$
$191$	−27.6562	−	47.9019i	−0.144797	−	0.250795i	−0.929297	+	0.369333i	$0.879586\pi$
$192$		0			0
$193$	111.283	−	192.747i	0.576594	−	0.998689i	−0.419273	−	0.907860i	$-0.637715\pi$
$193$	111.283	−	192.747i	0.576594	−	0.998689i	0.995866	−	0.0908292i	$-0.0289517\pi$
$194$		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	0.400527	−	0.916285i	$-0.368827\pi$
$199$	−38.3544	−	22.1439i	−0.192736	−	0.111276i	−0.593263	+	0.805009i	$0.702160\pi$
$200$		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	$0.0380281\pi$
$223$			53.1564i			0.238370i	−0.992872	+	0.119185i	$0.961972\pi$
$224$		0			0
$225$	387.701			1.72312
$226$		0			0
$227$	346.938	+	200.305i	1.52836	+	0.882399i	0.999431	+	0.0337337i	$0.0107398\pi$
$227$	346.938	+	200.305i	1.52836	+	0.882399i	0.528930	+	0.848666i	$0.322594\pi$
$228$		0			0
$229$	−329.566	+	190.275i	−1.43915	+	0.830895i	−0.997791	−	0.0664348i	$-0.978838\pi$
$229$	−329.566	+	190.275i	−1.43915	+	0.830895i	−0.441361	+	0.897330i	$0.645504\pi$
$230$		0			0
$231$	458.030	+	60.7710i	1.98281	+	0.263078i
$232$		0			0
$233$	166.501	+	288.389i	0.714598	+	1.23772i	0.963114	+	0.269093i	$0.0867238\pi$
$233$	166.501	+	288.389i	0.714598	+	1.23772i	−0.248516	+	0.968628i	$0.579943\pi$
$234$		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	0.342841	−	0.939393i	$-0.388611\pi$
$241$	−72.1258	−	41.6418i	−0.299277	−	0.172788i	−0.642118	+	0.766606i	$0.721944\pi$
$242$		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	$0.297449\pi$
$251$			403.749i			1.60856i	−0.594250	+	0.804281i	$0.702551\pi$
$252$		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	−0.867447	−	0.497529i	$-0.834241\pi$
$257$	−223.667	+	129.134i	−0.870298	+	0.502467i	−0.00285088	+	0.999996i	$0.500907\pi$
$258$		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	−0.199631	−	0.979871i	$-0.563974\pi$
$263$	196.929	−	341.090i	0.748778	−	1.29692i	0.948409	−	0.317050i	$-0.102692\pi$
$264$		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	0.584151	−	0.811645i	$-0.301427\pi$
$269$	46.6236	+	26.9181i	0.173322	+	0.100067i	−0.410829	+	0.911712i	$0.634761\pi$
$270$		0			0
$271$	−41.1477	+	23.7567i	−0.151837	+	0.0876629i	−0.573993	−	0.818860i	$-0.694607\pi$
$271$	−41.1477	+	23.7567i	−0.151837	+	0.0876629i	0.422157	+	0.906523i	$0.361273\pi$
$272$		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	−0.557426	−	0.830227i	$-0.688211\pi$
$277$	121.959	−	211.239i	0.440285	−	0.762595i	0.997710	+	0.0676314i	$0.0215442\pi$
$278$		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	0.417445	−	0.908702i	$-0.362926\pi$
$283$	−45.5040	−	26.2717i	−0.160792	−	0.0928330i	−0.578237	+	0.815869i	$0.696259\pi$
$284$		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	$0.184567\pi$
$293$			321.060i			1.09577i	−0.836554	+	0.547885i	$0.815433\pi$
$294$		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	$-0.623755\pi$
$307$		−	568.177i		−	1.85074i	0.379066	−	0.925370i	$-0.376245\pi$
$308$		0			0
$309$	−271.630			−0.879063
$310$		0			0
$311$	41.7405	+	24.0989i	0.134214	+	0.0774884i	0.565604	−	0.824677i	$-0.308643\pi$
$311$	41.7405	+	24.0989i	0.134214	+	0.0774884i	−0.431390	+	0.902166i	$0.641977\pi$
$312$		0			0
$313$	70.5536	−	40.7341i	0.225411	−	0.130141i	−0.383042	−	0.923731i	$-0.625124\pi$
$313$	70.5536	−	40.7341i	0.225411	−	0.130141i	0.608453	+	0.793590i	$0.291790\pi$
$314$		0			0
$315$	165.887	+	401.632i	0.526625	+	1.27502i
$316$		0			0
$317$	−198.291	−	343.449i	−0.625522	−	1.08344i	−0.988440	−	0.151615i	$-0.951553\pi$
$317$	−198.291	−	343.449i	−0.625522	−	1.08344i	0.362917	−	0.931821i	$-0.381781\pi$
$318$		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	0.962429	+	0.271533i	$0.0875305\pi$
$331$	237.118	+	410.701i	0.716369	+	1.24079i	−0.246060	+	0.969255i	$0.579136\pi$
$332$		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	−0.981349	−	0.192237i	$-0.938426\pi$
$347$	−112.495	+	194.846i	−0.324192	+	0.561517i	0.657156	+	0.753754i	$0.271759\pi$
$348$		0			0
$349$		−	414.621i		−	1.18802i	−0.804456	−	0.594012i	$-0.797543\pi$
$349$		−	414.621i		−	1.18802i	0.804456	−	0.594012i	$-0.202457\pi$
$350$		0			0
$351$	3.76362			0.0107226
$352$		0			0
$353$	173.723	+	100.299i	0.492134	+	0.284134i	0.725459	−	0.688265i	$-0.241627\pi$
$353$	173.723	+	100.299i	0.492134	+	0.284134i	−0.233325	+	0.972399i	$0.574961\pi$
$354$		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	0.951342	−	0.308139i	$-0.0997060\pi$
$359$	74.9646	+	129.842i	0.208815	+	0.361678i	−0.742527	+	0.669817i	$0.766373\pi$
$360$		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	0.948018	−	0.318216i	$-0.103084\pi$
$367$	420.745	+	242.917i	1.14644	+	0.661900i	0.198426	+	0.980116i	$0.436417\pi$
$368$		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	0.953957	−	0.299942i	$-0.0969674\pi$
$373$	81.0234	+	140.337i	0.217221	+	0.376238i	−0.736736	+	0.676180i	$0.763634\pi$
$374$		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	−0.531617	−	0.846985i	$-0.678415\pi$
$383$	−24.4796	+	14.1333i	−0.0639153	+	0.0369015i	0.467702	+	0.883886i	$0.345082\pi$
$384$		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	0.153052	+	0.988218i	$0.451090\pi$
$389$	−303.146	+	525.065i	−0.779296	+	1.34978i	−0.932348	+	0.361562i	$0.882244\pi$
$390$		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	0.346688	−	0.937980i	$-0.387306\pi$
$397$	528.942	−	305.385i	1.33235	−	0.769231i	0.985659	+	0.168750i	$0.0539729\pi$
$398$		0			0
$399$	281.846	+	216.720i	0.706380	+	0.543157i
$400$		0			0
$401$	107.055	+	185.424i	0.266969	+	0.462404i	0.968078	−	0.250651i	$-0.0806446\pi$
$401$	107.055	+	185.424i	0.266969	+	0.462404i	−0.701109	+	0.713054i	$0.747311\pi$
$402$		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	0.730774	−	0.682619i	$-0.239159\pi$
$409$	206.544	+	119.248i	0.504996	+	0.291560i	−0.225778	+	0.974179i	$0.572492\pi$
$410$		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	$-0.951786\pi$
$419$		−	126.446i		−	0.301779i	0.988551	−	0.150890i	$-0.0482138\pi$
$420$		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	−0.120413	−	0.992724i	$-0.538422\pi$
$431$	344.592	−	596.851i	0.799517	−	1.38480i	0.919931	−	0.392081i	$-0.128245\pi$
$432$		0			0
$433$		−	600.031i		−	1.38575i	−0.721057	−	0.692876i	$-0.756343\pi$
$433$		−	600.031i		−	1.38575i	0.721057	−	0.692876i	$-0.243657\pi$
$434$		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	−0.654022	−	0.756475i	$-0.726920\pi$
$439$	−143.073	+	82.6032i	−0.325906	+	0.188162i	0.328116	+	0.944637i	$0.393586\pi$
$440$		0			0
$441$	−238.996	+	238.033i	−0.541941	+	0.539758i
$442$		0			0
$443$	102.417	+	177.391i	0.231189	+	0.400431i	0.958158	−	0.286239i	$-0.0924052\pi$
$443$	102.417	+	177.391i	0.231189	+	0.400431i	−0.726969	+	0.686670i	$0.759072\pi$
$444$		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	0.761365	−	0.648323i	$-0.224529\pi$
$457$	−82.6173	−	143.097i	−0.180782	−	0.313123i	−0.942147	+	0.335200i	$0.891196\pi$
$458$		0			0
$459$	29.3143	−	50.7738i	0.0638655	−	0.110618i
$460$		0			0
$461$		−	187.790i		−	0.407353i	−0.979038	−	0.203677i	$-0.934711\pi$
$461$		−	187.790i		−	0.407353i	0.979038	−	0.203677i	$-0.0652891\pi$
$462$		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	−0.514681	−	0.857382i	$-0.672090\pi$
$467$	−13.7799	+	7.95581i	−0.0295072	+	0.0170360i	0.485174	+	0.874418i	$0.338756\pi$
$468$		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	−0.0925686	−	0.995706i	$-0.529508\pi$
$479$	−479.556	−	276.872i	−1.00116	−	0.578020i	−0.908591	+	0.417686i	$0.862841\pi$
$480$		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	−0.590148	−	0.807295i	$-0.700930\pi$
$487$	196.779	−	340.832i	0.404065	−	0.699860i	0.994212	+	0.107435i	$0.0342638\pi$
$488$		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	0.933126	−	0.359551i	$-0.117070\pi$
$499$	77.4362	+	134.123i	0.155183	+	0.268784i	−0.777943	+	0.628335i	$0.783737\pi$
$500$		0			0
$501$	−3.40812	+	5.90304i	−0.00680264	+	0.0117825i
$502$		0			0
$503$		−	710.432i		−	1.41239i	−0.708018	−	0.706194i	$-0.750410\pi$
$503$		−	710.432i		−	1.41239i	0.708018	−	0.706194i	$-0.249590\pi$
$504$		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	−0.570569	−	0.821249i	$-0.693277\pi$
$509$	−73.6172	+	42.5029i	−0.144631	+	0.0835027i	0.425938	+	0.904752i	$0.359944\pi$
$510$		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	0.843123	−	0.537721i	$-0.180715\pi$
$521$	416.281	+	240.340i	0.799004	+	0.461305i	−0.0441190	+	0.999026i	$0.514048\pi$
$522$		0			0
$523$	461.122	−	266.229i	0.881686	−	0.509042i	0.0104722	−	0.999945i	$-0.496667\pi$
$523$	461.122	−	266.229i	0.881686	−	0.509042i	0.871214	+	0.490903i	$0.163333\pi$
$524$		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	0.940366	+	0.340164i	$0.110483\pi$
$541$	413.743	+	716.623i	0.764774	+	1.32463i	−0.175593	+	0.984463i	$0.556184\pi$
$542$		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	−0.857443	−	0.514580i	$-0.827948\pi$
$557$	9.42314	−	16.3214i	0.0169177	−	0.0293023i	0.874360	+	0.485277i	$0.161281\pi$
$558$		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	0.0510945	−	0.998694i	$-0.483729\pi$
$563$	−443.786	−	256.220i	−0.788253	−	0.455098i	−0.839347	+	0.543596i	$0.817062\pi$
$564$		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	0.997891	+	0.0649178i	$0.0206785\pi$
$569$	315.889	+	547.136i	0.555166	+	0.961575i	−0.442725	+	0.896658i	$0.645988\pi$
$570$		0			0
$571$	−458.358	+	793.900i	−0.802729	+	1.39037i	0.115084	+	0.993356i	$0.463286\pi$
$571$	−458.358	+	793.900i	−0.802729	+	1.39037i	−0.917813	+	0.397012i	$0.870047\pi$
$572$		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	0.632210	−	0.774797i	$-0.282148\pi$
$577$	160.014	+	92.3843i	0.277321	+	0.160111i	−0.354889	+	0.934908i	$0.615481\pi$
$578$		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	$-0.961458\pi$
$587$		−	141.805i		−	0.241575i	0.992678	−	0.120788i	$-0.0385420\pi$
$588$		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	−0.0247264	−	0.999694i	$-0.507871\pi$
$593$	491.402	−	283.711i	0.828671	−	0.478433i	0.853397	+	0.521261i	$0.174538\pi$
$594$		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	−0.990284	−	0.139059i	$-0.955592\pi$
$599$	−224.453	+	388.764i	−0.374713	+	0.649022i	0.615571	+	0.788081i	$0.288925\pi$
$600$		0			0
$601$			939.633i			1.56345i	0.623623	+	0.781725i	$0.285660\pi$
$601$			939.633i			1.56345i	−0.623623	+	0.781725i	$0.714340\pi$
$602$		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	−0.647835	−	0.761781i	$-0.724325\pi$
$607$	−189.403	+	109.352i	−0.312031	+	0.180151i	0.335804	+	0.941932i	$0.390992\pi$
$608$		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	−0.958107	−	0.286411i	$-0.907538\pi$
$613$	−141.612	+	245.279i	−0.231014	+	0.400128i	0.727093	+	0.686539i	$0.240871\pi$
$614$		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	0.0191078	−	0.999817i	$-0.493917\pi$
$619$	−518.230	−	299.200i	−0.837206	−	0.483361i	−0.856313	+	0.516457i	$0.827251\pi$
$620$		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	−0.999298	−	0.0374621i	$-0.988073\pi$
$641$	−299.479	+	518.713i	−0.467206	+	0.809224i	0.532092	+	0.846686i	$0.321406\pi$
$642$		0			0
$643$		−	707.781i		−	1.10075i	−0.834918	−	0.550374i	$-0.814485\pi$
$643$		−	707.781i		−	1.10075i	0.834918	−	0.550374i	$-0.185515\pi$
$644$		0			0
$645$	917.776			1.42291
$646$		0			0
$647$	422.678	+	244.033i	0.653289	+	0.377177i	0.789715	−	0.613474i	$-0.210228\pi$
$647$	422.678	+	244.033i	0.653289	+	0.377177i	−0.136426	+	0.990650i	$0.543562\pi$
$648$		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	0.696939	−	0.717131i	$-0.254545\pi$
$653$	−177.997	−	308.300i	−0.272584	−	0.472129i	−0.969523	+	0.245001i	$0.921212\pi$
$654$		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	0.441331	−	0.897344i	$-0.354506\pi$
$661$	−76.0985	−	43.9355i	−0.115126	−	0.0664682i	−0.556457	+	0.830876i	$0.687840\pi$
$662$		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	−0.444750	−	0.895655i	$-0.646707\pi$
$677$	73.4780	−	42.4226i	0.108535	−	0.0626626i	0.553285	+	0.832992i	$0.313374\pi$
$678$		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	−0.955377	−	0.295389i	$-0.904551\pi$
$683$	−151.540	+	262.475i	−0.221874	+	0.384297i	0.733503	+	0.679686i	$0.237884\pi$
$684$		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	−0.331307	−	0.943523i	$-0.607490\pi$
$691$	221.226	−	127.725i	0.320154	−	0.184841i	0.651461	+	0.758682i	$0.274156\pi$
$692$		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	−0.995454	−	0.0952436i	$-0.969637\pi$
$709$	−411.369	−	712.512i	−0.580210	−	1.00495i	0.415244	−	0.909710i	$-0.363696\pi$
$710$		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	−0.999995	−	0.00330501i	$-0.998948\pi$
$719$	−1076.44	+	621.481i	−1.49713	+	0.864368i	−0.497135	+	0.867673i	$0.665615\pi$
$720$		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	$0.249076\pi$
$727$			1025.14i			1.41010i	−0.709156	+	0.705052i	$0.750924\pi$
$728$		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	−0.879749	−	0.475439i	$-0.842289\pi$
$733$	−665.476	+	384.213i	−0.907880	+	0.524165i	−0.0281317	+	0.999604i	$0.508956\pi$
$734$		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	0.397725	+	0.917505i	$0.369800\pi$
$739$	−440.237	+	762.513i	−0.595720	+	1.03182i	−0.993445	+	0.114312i	$0.963534\pi$
$740$		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	0.955521	−	0.294924i	$-0.0952943\pi$
$751$	166.984	+	289.224i	0.222349	+	0.385119i	−0.733172	+	0.680043i	$0.761961\pi$
$752$		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	0.0975611	−	0.995230i	$-0.468896\pi$
$761$	767.267	−	442.982i	1.00824	−	0.582105i	0.910675	+	0.413124i	$0.135563\pi$
$762$		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	$0.0873503\pi$
$769$			416.779i			0.541976i	−0.962583	+	0.270988i	$0.912650\pi$
$770$		0			0
$771$	−1029.32			−1.33504
$772$		0			0
$773$	−57.9458	−	33.4550i	−0.0749623	−	0.0432795i	0.462050	−	0.886854i	$-0.347114\pi$
$773$	−57.9458	−	33.4550i	−0.0749623	−	0.0432795i	−0.537013	+	0.843574i	$0.680447\pi$
$774$		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	0.987701	−	0.156355i	$-0.0499745\pi$
$787$	1059.42	+	611.654i	1.34614	+	0.777196i	0.358443	+	0.933552i	$0.383308\pi$
$788$		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	$0.118279\pi$
$797$			578.768i			0.726184i	−0.931753	+	0.363092i	$0.881721\pi$
$798$		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	−0.446799	−	0.894635i	$-0.647436\pi$
$809$	446.064	−	772.605i	0.551377	−	0.955013i	0.998176	−	0.0603783i	$-0.0192307\pi$
$810$		0			0
$811$		−	200.724i		−	0.247502i	−0.992313	−	0.123751i	$-0.960508\pi$
$811$		−	200.724i		−	0.247502i	0.992313	−	0.123751i	$-0.0394925\pi$
$812$		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	0.606528	−	0.795062i	$-0.292562\pi$
$821$	−316.315	−	547.873i	−0.385280	−	0.667324i	−0.991808	+	0.127738i	$0.959228\pi$
$822$		0			0
$823$	1.90823	−	3.30515i	0.00231863	−	0.00401598i	−0.864864	−	0.502007i	$-0.832595\pi$
$823$	1.90823	−	3.30515i	0.00231863	−	0.00401598i	0.867182	+	0.497991i	$0.165929\pi$
$824$		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	0.0576632	−	0.998336i	$-0.481635\pi$
$829$	−645.036	−	372.412i	−0.778090	−	0.449230i	−0.835753	+	0.549106i	$0.814968\pi$
$830$		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	$-0.766353\pi$
$839$		−	1124.03i		−	1.33973i	0.742485	−	0.669863i	$-0.233647\pi$
$840$		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	$-0.982041\pi$
$853$		−	96.2021i		−	0.112781i	0.998409	−	0.0563905i	$-0.0179592\pi$
$854$		0			0
$855$	791.112			0.925277
$856$		0			0
$857$	741.679	+	428.208i	0.865436	+	0.499660i	0.865829	−	0.500340i	$-0.166792\pi$
$857$	741.679	+	428.208i	0.865436	+	0.499660i	−0.000392914		1.00000i	$0.500125\pi$
$858$		0			0
$859$	1451.57	−	838.062i	1.68983	−	0.975625i	0.735195	−	0.677856i	$-0.237091\pi$
$859$	1451.57	−	838.062i	1.68983	−	0.975625i	0.954638	−	0.297769i	$-0.0962427\pi$
$860$		0			0
$861$	13.4031	−	5.53591i	0.0155669	−	0.00642962i
$862$		0			0
$863$	141.625	+	245.301i	0.164107	+	0.284242i	0.936338	−	0.351100i	$-0.114192\pi$
$863$	141.625	+	245.301i	0.164107	+	0.284242i	−0.772231	+	0.635342i	$0.780859\pi$
$864$		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	0.999578	−	0.0290568i	$-0.00925037\pi$
$877$	416.246	+	720.959i	0.474625	+	0.822075i	−0.524953	+	0.851131i	$0.675917\pi$
$878$		0			0
$879$	−639.787	+	1108.14i	−0.727858	+	1.26069i
$880$		0			0
$881$		−	890.282i		−	1.01054i	−0.862962	−	0.505268i	$-0.831394\pi$
$881$		−	890.282i		−	1.01054i	0.862962	−	0.505268i	$-0.168606\pi$
$882$		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	−0.740901	−	0.671614i	$-0.765601\pi$
$887$	−469.859	+	271.273i	−0.529717	+	0.305832i	0.211184	+	0.977446i	$0.432268\pi$
$888$		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	−0.115268	−	0.993334i	$-0.536773\pi$
$907$	727.975	−	1260.89i	0.802619	−	1.39018i	0.917887	−	0.396842i	$-0.129894\pi$
$908$		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	0.999230	+	0.0392319i	$0.0124911\pi$
$919$	490.370	+	849.346i	0.533591	+	0.924207i	−0.465639	+	0.884975i	$0.654176\pi$
$920$		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	−0.680507	−	0.732742i	$-0.738240\pi$
$929$	−358.768	+	207.135i	−0.386188	+	0.222965i	0.294319	+	0.955707i	$0.404907\pi$
$930$		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	$-0.750296\pi$
$937$		−	1323.89i		−	1.41290i	0.707764	−	0.706449i	$-0.249704\pi$
$938$		0			0
$939$	324.689			0.345781
$940$		0			0
$941$	823.269	+	475.315i	0.874888	+	0.505117i	0.868969	−	0.494866i	$-0.164783\pi$
$941$	823.269	+	475.315i	0.874888	+	0.505117i	0.00591840	+	0.999982i	$0.498116\pi$
$942$		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	−0.990780	−	0.135477i	$-0.956743\pi$
$947$	−580.243	−	1005.01i	−0.612717	−	1.06126i	0.378064	−	0.925780i	$-0.376590\pi$
$948$		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	−0.789449	−	0.613816i	$-0.789634\pi$
$971$	−633.669	+	365.849i	−0.652594	+	0.376776i	0.136855	+	0.990591i	$0.456301\pi$
$972$		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	−0.595589	−	0.803289i	$-0.703081\pi$
$977$	388.723	−	673.288i	0.397874	−	0.689138i	0.993463	+	0.114151i	$0.0364147\pi$
$978$		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	−0.237396	−	0.971413i	$-0.576294\pi$
$983$	−1177.01	−	679.546i	−1.19736	−	0.691298i	−0.959966	+	0.280115i	$0.909627\pi$
$984$		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	−0.987246	−	0.159202i	$-0.949108\pi$
$991$	−352.548	+	610.632i	−0.355750	+	0.616177i	0.631496	+	0.775379i	$0.282441\pi$
$992$		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	−0.150631	−	0.988590i	$-0.548131\pi$
$997$	−1078.84	−	622.871i	−1.08209	−	0.624745i	−0.931460	+	0.363845i	$0.881464\pi$
$998$		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.129.7	yes	16
4.3	odd	2	inner	224.3.s.b.129.2	yes	16
7.3	odd	6		1568.3.c.g.97.14		16
7.4	even	3		1568.3.c.g.97.3		16
7.5	odd	6	inner	224.3.s.b.33.7	yes	16
8.3	odd	2		448.3.s.h.129.7		16
8.5	even	2		448.3.s.h.129.2		16
28.3	even	6		1568.3.c.g.97.4		16
28.11	odd	6		1568.3.c.g.97.13		16
28.19	even	6	inner	224.3.s.b.33.2	✓	16
56.5	odd	6		448.3.s.h.257.2		16
56.19	even	6		448.3.s.h.257.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.b.33.2	✓	16	28.19	even	6	inner
224.3.s.b.33.7	yes	16	7.5	odd	6	inner
224.3.s.b.129.2	yes	16	4.3	odd	2	inner
224.3.s.b.129.7	yes	16	1.1	even	1	trivial
448.3.s.h.129.2		16	8.5	even	2
448.3.s.h.129.7		16	8.3	odd	2
448.3.s.h.257.2		16	56.5	odd	6
448.3.s.h.257.7		16	56.19	even	6
1568.3.c.g.97.3		16	7.4	even	3
1568.3.c.g.97.4		16	28.3	even	6
1568.3.c.g.97.13		16	28.11	odd	6
1568.3.c.g.97.14		16	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
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

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