LMFDB - Embedded newform 224.3.r.d.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(95,224)]

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([3, 0, 4]))

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

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

chi := DirichletCharacter("224.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.r (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.4
Root			$-2.23871 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	224.191
Dual form			224.3.r.d.95.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.100242 - 0.0578747i) q^{3} +(-0.761802 + 1.31948i) q^{5} +(-6.66292 - 2.14605i) q^{7} +(-4.49330 + 7.78263i) q^{9} +O(q^{10})$	\(q+(0.100242 - 0.0578747i) q^{3} +(-0.761802 + 1.31948i) q^{5} +(-6.66292 - 2.14605i) q^{7} +(-4.49330 + 7.78263i) q^{9} +(-3.61683 + 2.08818i) q^{11} -8.98660 q^{13} +0.176356i q^{15} +(10.8090 + 18.7218i) q^{17} +(-23.0472 - 13.3063i) q^{19} +(-0.792106 + 0.170490i) q^{21} +(-9.94966 - 5.74444i) q^{23} +(11.3393 + 19.6403i) q^{25} +2.08194i q^{27} -31.6652 q^{29} +(-7.88287 + 4.55118i) q^{31} +(-0.241705 + 0.418646i) q^{33} +(7.90750 - 7.15672i) q^{35} +(-0.513398 + 0.889231i) q^{37} +(-0.900834 + 0.520097i) q^{39} +13.6920 q^{41} +35.9464i q^{43} +(-6.84601 - 11.8576i) q^{45} +(3.47491 + 2.00624i) q^{47} +(39.7889 + 28.5979i) q^{49} +(2.16703 + 1.25114i) q^{51} +(-39.7991 - 68.9341i) q^{53} -6.36312i q^{55} -3.08039 q^{57} +(87.8782 - 50.7365i) q^{59} +(35.6078 - 61.6745i) q^{61} +(46.6404 - 42.2121i) q^{63} +(6.84601 - 11.8576i) q^{65} +(-48.0548 + 27.7444i) q^{67} -1.32983 q^{69} +69.2678i q^{71} +(12.6977 + 21.9930i) q^{73} +(2.27335 + 1.31252i) q^{75} +(28.5800 - 6.15145i) q^{77} +(108.959 + 62.9074i) q^{79} +(-40.3192 - 69.8349i) q^{81} +33.3214i q^{83} -32.9373 q^{85} +(-3.17418 + 1.83262i) q^{87} +(66.5408 - 115.252i) q^{89} +(59.8770 + 19.2857i) q^{91} +(-0.526796 + 0.912437i) q^{93} +(35.1147 - 20.2735i) q^{95} -8.98660 q^{97} -37.5313i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{5}+O(q^{10}) $ 12 * q + 18 * q^5	$ 12 q + 18 q^{5} - 6 q^{17} + 18 q^{21} + 186 q^{33} - 114 q^{37} + 180 q^{49} - 18 q^{53} - 684 q^{57} + 318 q^{61} - 228 q^{69} + 342 q^{73} + 318 q^{77} - 186 q^{81} - 996 q^{85} + 150 q^{89} - 222 q^{93}+O(q^{100}) $ 12 * q + 18 * q^5 - 6 * q^17 + 18 * q^21 + 186 * q^33 - 114 * q^37 + 180 * q^49 - 18 * q^53 - 684 * q^57 + 318 * q^61 - 228 * q^69 + 342 * q^73 + 318 * q^77 - 186 * q^81 - 996 * q^85 + 150 * q^89 - 222 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.100242	−	0.0578747i	0.0334140	−	0.0192916i	−0.483200	−	0.875510i	$-0.660526\pi$
$3$	0.100242	−	0.0578747i	0.0334140	−	0.0192916i	0.516614	+	0.856218i	$0.327192\pi$
$4$		0			0
$5$	−0.761802	+	1.31948i	−0.152360	+	0.263896i	−0.932095	−	0.362214i	$-0.882021\pi$
$5$	−0.761802	+	1.31948i	−0.152360	+	0.263896i	0.779734	+	0.626111i	$0.215354\pi$
$6$		0			0
$7$	−6.66292	−	2.14605i	−0.951845	−	0.306579i
$7$	−6.66292	−	2.14605i	−0.951845	−	0.306579i
$8$		0			0
$9$	−4.49330	+	7.78263i	−0.499256	+	0.864736i
$10$		0			0
$11$	−3.61683	+	2.08818i	−0.328803	+	0.189834i	−0.655309	−	0.755361i	$-0.727462\pi$
$11$	−3.61683	+	2.08818i	−0.328803	+	0.189834i	0.326507	+	0.945195i	$0.394128\pi$
$12$		0			0
$13$	−8.98660			−0.691277			−0.345639	−	0.938368i	$-0.612338\pi$
$13$	−8.98660			−0.691277			−0.345639	+	0.938368i	$0.612338\pi$
$14$		0			0
$15$			0.176356i			0.0117571i
$16$		0			0
$17$	10.8090	+	18.7218i	0.635824	+	1.10128i	0.986340	+	0.164723i	$0.0526730\pi$
$17$	10.8090	+	18.7218i	0.635824	+	1.10128i	−0.350516	+	0.936557i	$0.613994\pi$
$18$		0			0
$19$	−23.0472	−	13.3063i	−1.21301	−	0.700330i	−0.249595	−	0.968350i	$-0.580297\pi$
$19$	−23.0472	−	13.3063i	−1.21301	−	0.700330i	−0.963413	+	0.268020i	$0.913631\pi$
$20$		0			0
$21$	−0.792106	+	0.170490i	−0.0377193	+	0.00811856i
$22$		0			0
$23$	−9.94966	−	5.74444i	−0.432594	−	0.249758i	0.267857	−	0.963459i	$-0.413684\pi$
$23$	−9.94966	−	5.74444i	−0.432594	−	0.249758i	−0.700451	+	0.713700i	$0.747018\pi$
$24$		0			0
$25$	11.3393	+	19.6403i	0.453573	+	0.785611i
$26$		0			0
$27$			2.08194i			0.0771088i
$28$		0			0
$29$	−31.6652			−1.09190			−0.545952	−	0.837816i	$-0.683832\pi$
$29$	−31.6652			−1.09190			−0.545952	+	0.837816i	$0.683832\pi$
$30$		0			0
$31$	−7.88287	+	4.55118i	−0.254286	+	0.146812i	−0.621725	−	0.783235i	$-0.713568\pi$
$31$	−7.88287	+	4.55118i	−0.254286	+	0.146812i	0.367439	+	0.930048i	$0.380235\pi$
$32$		0			0
$33$	−0.241705	+	0.418646i	−0.00732440	+	0.0126862i
$34$		0			0
$35$	7.90750	−	7.15672i	0.225929	−	0.204478i
$36$		0			0
$37$	−0.513398	+	0.889231i	−0.0138756	+	0.0240333i	−0.872880	−	0.487935i	$-0.837750\pi$
$37$	−0.513398	+	0.889231i	−0.0138756	+	0.0240333i	0.859004	+	0.511969i	$0.171084\pi$
$38$		0			0
$39$	−0.900834	+	0.520097i	−0.0230983	+	0.0133358i
$40$		0			0
$41$	13.6920			0.333952			0.166976	−	0.985961i	$-0.446600\pi$
$41$	13.6920			0.333952			0.166976	+	0.985961i	$0.446600\pi$
$42$		0			0
$43$			35.9464i			0.835963i	0.908456	+	0.417981i	$0.137262\pi$
$43$			35.9464i			0.835963i	−0.908456	+	0.417981i	$0.862738\pi$
$44$		0			0
$45$	−6.84601	−	11.8576i	−0.152134	−	0.263503i
$46$		0			0
$47$	3.47491	+	2.00624i	0.0739342	+	0.0426860i	0.536511	−	0.843893i	$-0.319742\pi$
$47$	3.47491	+	2.00624i	0.0739342	+	0.0426860i	−0.462577	+	0.886579i	$0.653075\pi$
$48$		0			0
$49$	39.7889	+	28.5979i	0.812019	+	0.583631i
$50$		0			0
$51$	2.16703	+	1.25114i	0.0424908	+	0.0245321i
$52$		0			0
$53$	−39.7991	−	68.9341i	−0.750927	−	1.30064i	−0.947374	−	0.320129i	$-0.896274\pi$
$53$	−39.7991	−	68.9341i	−0.750927	−	1.30064i	0.196447	−	0.980514i	$-0.437060\pi$
$54$		0			0
$55$		−	6.36312i		−	0.115693i
$56$		0			0
$57$	−3.08039			−0.0540419
$58$		0			0
$59$	87.8782	−	50.7365i	1.48946	−	0.859941i	0.489534	−	0.871984i	$-0.337167\pi$
$59$	87.8782	−	50.7365i	1.48946	−	0.859941i	0.999927	+	0.0120437i	$0.00383372\pi$
$60$		0			0
$61$	35.6078	−	61.6745i	0.583735	−	1.01106i	−0.411297	−	0.911501i	$-0.634924\pi$
$61$	35.6078	−	61.6745i	0.583735	−	1.01106i	0.995032	−	0.0995568i	$-0.0317425\pi$
$62$		0			0
$63$	46.6404	−	42.2121i	0.740324	−	0.670034i
$64$		0			0
$65$	6.84601	−	11.8576i	0.105323	−	0.182425i
$66$		0			0
$67$	−48.0548	+	27.7444i	−0.717235	+	0.414096i	−0.813734	−	0.581237i	$-0.802569\pi$
$67$	−48.0548	+	27.7444i	−0.717235	+	0.414096i	0.0964989	+	0.995333i	$0.469236\pi$
$68$		0			0
$69$	−1.32983			−0.0192729
$70$		0			0
$71$			69.2678i			0.975603i	0.872955	+	0.487801i	$0.162201\pi$
$71$			69.2678i			0.975603i	−0.872955	+	0.487801i	$0.837799\pi$
$72$		0			0
$73$	12.6977	+	21.9930i	0.173941	+	0.301275i	0.939794	−	0.341741i	$-0.111016\pi$
$73$	12.6977	+	21.9930i	0.173941	+	0.301275i	−0.765853	+	0.643015i	$0.777683\pi$
$74$		0			0
$75$	2.27335	+	1.31252i	0.0303113	+	0.0175003i
$76$		0			0
$77$	28.5800	−	6.15145i	0.371169	−	0.0798889i
$78$		0			0
$79$	108.959	+	62.9074i	1.37923	+	0.796296i	0.992066	−	0.125717i	$-0.0401230\pi$
$79$	108.959	+	62.9074i	1.37923	+	0.796296i	0.387159	+	0.922013i	$0.373456\pi$
$80$		0			0
$81$	−40.3192	−	69.8349i	−0.497768	−	0.862160i
$82$		0			0
$83$			33.3214i			0.401462i	0.979646	+	0.200731i	$0.0643318\pi$
$83$			33.3214i			0.401462i	−0.979646	+	0.200731i	$0.935668\pi$
$84$		0			0
$85$	−32.9373			−0.387498
$86$		0			0
$87$	−3.17418	+	1.83262i	−0.0364849	+	0.0210645i
$88$		0			0
$89$	66.5408	−	115.252i	0.747650	−	1.29497i	−0.201297	−	0.979530i	$-0.564516\pi$
$89$	66.5408	−	115.252i	0.747650	−	1.29497i	0.948947	−	0.315437i	$-0.102151\pi$
$90$		0			0
$91$	59.8770	+	19.2857i	0.657989	+	0.211931i
$92$		0			0
$93$	−0.526796	+	0.912437i	−0.00566447	+	0.00981115i
$94$		0			0
$95$	35.1147	−	20.2735i	0.369629	−	0.213405i
$96$		0			0
$97$	−8.98660			−0.0926454			−0.0463227	−	0.998927i	$-0.514750\pi$
$97$	−8.98660			−0.0926454			−0.0463227	+	0.998927i	$0.514750\pi$
$98$		0			0
$99$		−	37.5313i		−	0.379104i
$100$		0			0
$101$	39.1170	+	67.7526i	0.387297	+	0.670818i	0.992085	−	0.125569i	$-0.0400755\pi$
$101$	39.1170	+	67.7526i	0.387297	+	0.670818i	−0.604788	+	0.796386i	$0.706742\pi$
$102$		0			0
$103$	−146.265	−	84.4459i	−1.42005	−	0.819864i	−0.423743	−	0.905782i	$-0.639284\pi$
$103$	−146.265	−	84.4459i	−1.42005	−	0.819864i	−0.996302	+	0.0859188i	$0.972617\pi$
$104$		0			0
$105$	0.378470	−	1.17505i	0.00360448	−	0.0111909i
$106$		0			0
$107$	24.0807	+	13.9030i	0.225053	+	0.129934i	0.608288	−	0.793717i	$-0.291857\pi$
$107$	24.0807	+	13.9030i	0.225053	+	0.129934i	−0.383235	+	0.923651i	$0.625190\pi$
$108$		0			0
$109$	54.5915	+	94.5553i	0.500840	+	0.867480i	1.00000		0.000970038i	$0.000308773\pi$
$109$	54.5915	+	94.5553i	0.500840	+	0.867480i	−0.499160	+	0.866510i	$0.666358\pi$
$110$		0			0
$111$			0.118851i			0.00107073i
$112$		0			0
$113$	−130.397			−1.15396			−0.576980	−	0.816758i	$-0.695769\pi$
$113$	−130.397			−1.15396			−0.576980	+	0.816758i	$0.695769\pi$
$114$		0			0
$115$	15.1593	−	8.75225i	0.131820	−	0.0761065i
$116$		0			0
$117$	40.3795	−	69.9394i	0.345124	−	0.597772i
$118$		0			0
$119$	−31.8417	−	147.938i	−0.267577	−	1.24318i
$120$		0			0
$121$	−51.7790	+	89.6839i	−0.427926	+	0.741189i
$122$		0			0
$123$	1.37252	−	0.792422i	0.0111587	−	0.00644245i
$124$		0			0
$125$	−72.6434			−0.581147
$126$		0			0
$127$			190.679i			1.50141i	0.660640	+	0.750703i	$0.270285\pi$
$127$			190.679i			1.50141i	−0.660640	+	0.750703i	$0.729715\pi$
$128$		0			0
$129$	2.08039	+	3.60334i	0.0161270	+	0.0279328i
$130$		0			0
$131$	−184.540	−	106.544i	−1.40870	−	0.813315i	−0.413440	−	0.910531i	$-0.635673\pi$
$131$	−184.540	−	106.544i	−1.40870	−	0.813315i	−0.995263	+	0.0972163i	$0.969006\pi$
$132$		0			0
$133$	125.005	+	138.119i	0.939889	+	1.03849i
$134$		0			0
$135$	−2.74708	−	1.58603i	−0.0203487	−	0.0117483i
$136$		0			0
$137$	−33.0380	−	57.2236i	−0.241154	−	0.417690i	0.719890	−	0.694089i	$-0.244192\pi$
$137$	−33.0380	−	57.2236i	−0.241154	−	0.417690i	−0.961043	+	0.276398i	$0.910859\pi$
$138$		0			0
$139$			159.982i			1.15095i	0.817819	+	0.575476i	$0.195183\pi$
$139$			159.982i			1.15095i	−0.817819	+	0.575476i	$0.804817\pi$
$140$		0			0
$141$	0.464442			0.00329392
$142$		0			0
$143$	32.5030	−	18.7656i	0.227294	−	0.131228i
$144$		0			0
$145$	24.1226	−	41.7816i	0.166363	−	0.288149i
$146$		0			0
$147$	5.64361	+	0.563941i	0.0383919	+	0.00383633i
$148$		0			0
$149$	−78.6497	+	136.225i	−0.527850	+	0.914263i	0.471623	+	0.881800i	$0.343668\pi$
$149$	−78.6497	+	136.225i	−0.527850	+	0.914263i	−0.999473	+	0.0324629i	$0.989665\pi$
$150$		0			0
$151$	−159.471	+	92.0705i	−1.05610	+	0.609738i	−0.924350	−	0.381545i	$-0.875392\pi$
$151$	−159.471	+	92.0705i	−1.05610	+	0.609738i	−0.131747	+	0.991283i	$0.542059\pi$
$152$		0			0
$153$	−194.273			−1.26976
$154$		0			0
$155$		−	13.8684i		−	0.0894734i
$156$		0			0
$157$	112.979	+	195.686i	0.719612	+	1.24640i	0.961154	+	0.276014i	$0.0890137\pi$
$157$	112.979	+	195.686i	0.719612	+	1.24640i	−0.241541	+	0.970391i	$0.577653\pi$
$158$		0			0
$159$	−7.97908	−	4.60672i	−0.0501829	−	0.0289731i
$160$		0			0
$161$	53.9659	+	59.6272i	0.335192	+	0.370355i
$162$		0			0
$163$	−247.705	−	143.012i	−1.51966	−	0.877377i	−0.999732	−	0.0231682i	$-0.992625\pi$
$163$	−247.705	−	143.012i	−1.51966	−	0.877377i	−0.519930	−	0.854209i	$-0.674042\pi$
$164$		0			0
$165$	−0.368263	−	0.637851i	−0.00223190	−	0.00386576i
$166$		0			0
$167$		−	130.019i		−	0.778558i	−0.921120	−	0.389279i	$-0.872724\pi$
$167$		−	130.019i		−	0.778558i	0.921120	−	0.389279i	$-0.127276\pi$
$168$		0			0
$169$	−88.2410			−0.522136
$170$		0			0
$171$	207.116	−	119.578i	1.21120	−	0.699288i
$172$		0			0
$173$	−25.7942	+	44.6768i	−0.149099	+	0.258248i	−0.930895	−	0.365287i	$-0.880971\pi$
$173$	−25.7942	+	44.6768i	−0.149099	+	0.258248i	0.781796	+	0.623535i	$0.214304\pi$
$174$		0			0
$175$	−33.4039	−	155.196i	−0.190879	−	0.886836i
$176$		0			0
$177$	5.87272	−	10.1718i	0.0331792	−	0.0574681i
$178$		0			0
$179$	−176.636	+	101.981i	−0.986795	+	0.569726i	−0.904315	−	0.426866i	$-0.859617\pi$
$179$	−176.636	+	101.981i	−0.986795	+	0.569726i	−0.0824801	+	0.996593i	$0.526284\pi$
$180$		0			0
$181$	205.070			1.13299			0.566493	−	0.824067i	$-0.308300\pi$
$181$	205.070			1.13299			0.566493	+	0.824067i	$0.308300\pi$
$182$		0			0
$183$		−	8.24317i		−	0.0450446i
$184$		0			0
$185$	−0.782215	−	1.35484i	−0.00422819	−	0.00732344i
$186$		0			0
$187$	−78.1887	−	45.1423i	−0.418122	−	0.241403i
$188$		0			0
$189$	4.46795	−	13.8718i	0.0236399	−	0.0733957i
$190$		0			0
$191$	235.376	+	135.894i	1.23233	+	0.711488i	0.967516	−	0.252811i	$-0.0813551\pi$
$191$	235.376	+	135.894i	1.23233	+	0.711488i	0.264817	+	0.964299i	$0.414688\pi$
$192$		0			0
$193$	−17.6092	−	30.5001i	−0.0912396	−	0.158032i	0.816793	−	0.576930i	$-0.195750\pi$
$193$	−17.6092	−	30.5001i	−0.0912396	−	0.158032i	−0.908033	+	0.418899i	$0.862416\pi$
$194$		0			0
$195$		−	1.58484i		−	0.00812740i
$196$		0			0
$197$	−179.612			−0.911734			−0.455867	−	0.890048i	$-0.650671\pi$
$197$	−179.612			−0.911734			−0.455867	+	0.890048i	$0.650671\pi$
$198$		0			0
$199$	−283.774	+	163.837i	−1.42600	+	0.823301i	−0.996802	−	0.0799099i	$-0.974537\pi$
$199$	−283.774	+	163.837i	−1.42600	+	0.823301i	−0.429197	+	0.903211i	$0.641203\pi$
$200$		0			0
$201$	−3.21140	+	5.56231i	−0.0159771	+	0.0276732i
$202$		0			0
$203$	210.983	+	67.9553i	1.03932	+	0.334755i
$204$		0			0
$205$	−10.4306	+	18.0664i	−0.0508811	+	0.0881286i
$206$		0			0
$207$	89.4136	−	51.6230i	0.431950	−	0.249386i
$208$		0			0
$209$	111.144			0.531787
$210$		0			0
$211$			220.000i			1.04266i	0.853356	+	0.521328i	$0.174563\pi$
$211$			220.000i			1.04266i	−0.853356	+	0.521328i	$0.825437\pi$
$212$		0			0
$213$	4.00885	+	6.94354i	0.0188209	+	0.0325988i
$214$		0			0
$215$	−47.4306	−	27.3841i	−0.220607	−	0.127368i
$216$		0			0
$217$	62.2900	−	13.4071i	0.287050	−	0.0617837i
$218$		0			0
$219$	2.54568	+	1.46975i	0.0116241	+	0.00671119i
$220$		0			0
$221$	−97.1363	−	168.245i	−0.439531	−	0.761289i
$222$		0			0
$223$		−	154.732i		−	0.693866i	−0.937890	−	0.346933i	$-0.887223\pi$
$223$		−	154.732i		−	0.693866i	0.937890	−	0.346933i	$-0.112777\pi$
$224$		0			0
$225$	−203.804			−0.905795
$226$		0			0
$227$	319.784	−	184.627i	1.40874	−	0.813336i	0.413473	−	0.910516i	$-0.364316\pi$
$227$	319.784	−	184.627i	1.40874	−	0.813336i	0.995267	+	0.0971799i	$0.0309822\pi$
$228$		0			0
$229$	107.229	−	185.727i	0.468250	−	0.811034i	−0.531091	−	0.847315i	$-0.678218\pi$
$229$	107.229	−	185.727i	0.468250	−	0.811034i	0.999342	+	0.0362811i	$0.0115512\pi$
$230$		0			0
$231$	2.50890	−	2.27069i	0.0108610	−	0.00982983i
$232$		0			0
$233$	64.9799	−	112.548i	0.278884	−	0.483041i	−0.692224	−	0.721683i	$-0.743369\pi$
$233$	64.9799	−	112.548i	0.278884	−	0.483041i	0.971108	+	0.238642i	$0.0767023\pi$
$234$		0			0
$235$	−5.29439	+	3.05672i	−0.0225293	+	0.0130073i
$236$		0			0
$237$	14.5630			0.0614472
$238$		0			0
$239$			108.527i			0.454087i	0.973885	+	0.227043i	$0.0729059\pi$
$239$			108.527i			0.454087i	−0.973885	+	0.227043i	$0.927094\pi$
$240$		0			0
$241$	75.2603	+	130.355i	0.312283	+	0.540891i	0.978856	−	0.204549i	$-0.0655728\pi$
$241$	75.2603	+	130.355i	0.312283	+	0.540891i	−0.666573	+	0.745440i	$0.732240\pi$
$242$		0			0
$243$	−24.3105	−	14.0356i	−0.100043	−	0.0577599i
$244$		0			0
$245$	−68.0457	+	30.7147i	−0.277738	+	0.125366i
$246$		0			0
$247$	207.116	+	119.578i	0.838525	+	0.484122i
$248$		0			0
$249$	1.92846	+	3.34020i	0.00774484	+	0.0134145i
$250$		0			0
$251$			171.358i			0.682702i	0.939936	+	0.341351i	$0.110885\pi$
$251$			171.358i			0.682702i	−0.939936	+	0.341351i	$0.889115\pi$
$252$		0			0
$253$	47.9816			0.189651
$254$		0			0
$255$	−3.30170	+	1.90624i	−0.0129478	+	0.00747544i
$256$		0			0
$257$	168.939	−	292.611i	0.657351	−	1.13857i	−0.323947	−	0.946075i	$-0.605010\pi$
$257$	168.939	−	292.611i	0.657351	−	1.13857i	0.981299	−	0.192491i	$-0.0616566\pi$
$258$		0			0
$259$	5.32906	−	4.82309i	0.0205755	−	0.0186220i
$260$		0			0
$261$	142.281	−	246.439i	0.545140	−	0.944209i
$262$		0			0
$263$	222.965	−	128.729i	0.847774	−	0.489463i	−0.0121250	−	0.999926i	$-0.503860\pi$
$263$	222.965	−	128.729i	0.847774	−	0.489463i	0.859899	+	0.510464i	$0.170526\pi$
$264$		0			0
$265$	121.276			0.457646
$266$		0			0
$267$		−	15.4041i		−	0.0576933i
$268$		0			0
$269$	−152.762	−	264.592i	−0.567889	−	0.983612i	−0.996775	−	0.0802532i	$-0.974427\pi$
$269$	−152.762	−	264.592i	−0.567889	−	0.983612i	0.428886	−	0.903359i	$-0.358906\pi$
$270$		0			0
$271$	277.268	+	160.081i	1.02313	+	0.590705i	0.915009	−	0.403433i	$-0.132183\pi$
$271$	277.268	+	160.081i	1.02313	+	0.590705i	0.108121	+	0.994138i	$0.465516\pi$
$272$		0			0
$273$	7.11834	−	1.53212i	0.0260745	−	0.00561218i
$274$		0			0
$275$	−82.0248	−	47.3570i	−0.298272	−	0.172207i
$276$		0			0
$277$	−26.5313	−	45.9536i	−0.0957810	−	0.165898i	0.814153	−	0.580650i	$-0.197202\pi$
$277$	−26.5313	−	45.9536i	−0.0957810	−	0.165898i	−0.909934	+	0.414752i	$0.863868\pi$
$278$		0			0
$279$		−	81.7992i		−	0.293187i
$280$		0			0
$281$	478.835			1.70404			0.852020	−	0.523509i	$-0.175377\pi$
$281$	478.835			1.70404			0.852020	+	0.523509i	$0.175377\pi$
$282$		0			0
$283$	167.472	−	96.6898i	0.591773	−	0.341660i	−0.174025	−	0.984741i	$-0.555678\pi$
$283$	167.472	−	96.6898i	0.591773	−	0.341660i	0.765798	+	0.643081i	$0.222344\pi$
$284$		0			0
$285$	2.34665	−	4.06451i	0.00823385	−	0.0142614i
$286$		0			0
$287$	−91.2288	−	29.3838i	−0.317871	−	0.102383i
$288$		0			0
$289$	−89.1694	+	154.446i	−0.308545	+	0.534415i
$290$		0			0
$291$	−0.900834	+	0.520097i	−0.00309565	+	0.00178727i
$292$		0			0
$293$	−552.115			−1.88435			−0.942176	−	0.335118i	$-0.891224\pi$
$293$	−552.115			−1.88435			−0.942176	+	0.335118i	$0.891224\pi$
$294$		0			0
$295$			154.605i			0.524084i
$296$		0			0
$297$	−4.34746	−	7.53002i	−0.0146379	−	0.0253536i
$298$		0			0
$299$	89.4136	+	51.6230i	0.299042	+	0.172652i
$300$		0			0
$301$	77.1429	−	239.508i	0.256289	−	0.795707i
$302$		0			0
$303$	7.84232	+	4.52777i	0.0258823	+	0.0149431i
$304$		0			0
$305$	54.2522	+	93.9676i	0.177876	+	0.308091i
$306$		0			0
$307$			391.857i			1.27641i	0.769867	+	0.638204i	$0.220322\pi$
$307$			391.857i			1.27641i	−0.769867	+	0.638204i	$0.779678\pi$
$308$		0			0
$309$	−19.5491			−0.0632658
$310$		0			0
$311$	−163.764	+	94.5492i	−0.526573	+	0.304017i	−0.739620	−	0.673025i	$-0.764995\pi$
$311$	−163.764	+	94.5492i	−0.526573	+	0.304017i	0.213047	+	0.977042i	$0.431661\pi$
$312$		0			0
$313$	−209.995	+	363.722i	−0.670910	+	1.16205i	0.306736	+	0.951795i	$0.400763\pi$
$313$	−209.995	+	363.722i	−0.670910	+	1.16205i	−0.977646	+	0.210256i	$0.932570\pi$
$314$		0			0
$315$	20.1673	+	93.6984i	0.0640231	+	0.297455i
$316$		0			0
$317$	22.0846	−	38.2517i	0.0696675	−	0.120668i	−0.829087	−	0.559119i	$-0.811139\pi$
$317$	22.0846	−	38.2517i	0.0696675	−	0.120668i	0.898755	+	0.438451i	$0.144473\pi$
$318$		0			0
$319$	114.528	−	66.1226i	0.359021	−	0.207281i
$320$		0			0
$321$	3.21852			0.0100265
$322$		0			0
$323$		−	575.311i		−	1.78115i
$324$		0			0
$325$	−101.902	−	176.499i	−0.313544	−	0.543075i
$326$		0			0
$327$	10.9447	+	6.31894i	0.0334701	+	0.0193240i
$328$		0			0
$329$	−18.8475	−	20.8247i	−0.0572873	−	0.0632971i
$330$		0			0
$331$	−50.0956	−	28.9227i	−0.151346	−	0.0873799i	0.422414	−	0.906403i	$-0.361183\pi$
$331$	−50.0956	−	28.9227i	−0.151346	−	0.0873799i	−0.573761	+	0.819023i	$0.694516\pi$
$332$		0			0
$333$	−4.61370	−	7.99117i	−0.0138550	−	0.0239975i
$334$		0			0
$335$		−	84.5431i		−	0.252367i
$336$		0			0
$337$	28.3530			0.0841334			0.0420667	−	0.999115i	$-0.486606\pi$
$337$	28.3530			0.0841334			0.0420667	+	0.999115i	$0.486606\pi$
$338$		0			0
$339$	−13.0713	+	7.54671i	−0.0385584	+	0.0222617i
$340$		0			0
$341$	19.0073	−	32.9217i	0.0557400	−	0.0965445i
$342$		0			0
$343$	−203.738	−	275.935i	−0.593987	−	0.804475i
$344$		0			0
$345$	1.01307	−	1.75468i	0.00293643	−	0.00508604i
$346$		0			0
$347$	−116.595	+	67.3163i	−0.336009	+	0.193995i	−0.658506	−	0.752576i	$-0.728811\pi$
$347$	−116.595	+	67.3163i	−0.336009	+	0.193995i	0.322497	+	0.946571i	$0.395478\pi$
$348$		0			0
$349$	165.799			0.475069			0.237535	−	0.971379i	$-0.423661\pi$
$349$	165.799			0.475069			0.237535	+	0.971379i	$0.423661\pi$
$350$		0			0
$351$		−	18.7096i		−	0.0533036i
$352$		0			0
$353$	147.961	+	256.276i	0.419152	+	0.725993i	0.995854	−	0.0909615i	$-0.0289940\pi$
$353$	147.961	+	256.276i	0.419152	+	0.725993i	−0.576702	+	0.816954i	$0.695661\pi$
$354$		0			0
$355$	−91.3975	−	52.7683i	−0.257458	−	0.148643i
$356$		0			0
$357$	−11.7537	−	12.9868i	−0.0329237	−	0.0363775i
$358$		0			0
$359$	74.9132	+	43.2511i	0.208672	+	0.120477i	0.600694	−	0.799479i	$-0.294891\pi$
$359$	74.9132	+	43.2511i	0.208672	+	0.120477i	−0.392022	+	0.919956i	$0.628224\pi$
$360$		0			0
$361$	173.614	+	300.708i	0.480926	+	0.832987i
$362$		0			0
$363$			11.9868i			0.0330214i
$364$		0			0
$365$	−38.6925			−0.106007
$366$		0			0
$367$	−472.255	+	272.657i	−1.28680	+	0.742934i	−0.978082	−	0.208220i	$-0.933233\pi$
$367$	−472.255	+	272.657i	−1.28680	+	0.742934i	−0.308717	+	0.951154i	$0.599900\pi$
$368$		0			0
$369$	−61.5224	+	106.560i	−0.166727	+	0.288780i
$370$		0			0
$371$	117.242	+	544.713i	0.316016	+	1.46823i
$372$		0			0
$373$	−169.755	+	294.024i	−0.455106	+	0.788267i	−0.998694	−	0.0510850i	$-0.983732\pi$
$373$	−169.755	+	294.024i	−0.455106	+	0.788267i	0.543588	+	0.839352i	$0.317065\pi$
$374$		0			0
$375$	−7.28191	+	4.20421i	−0.0194184	+	0.0112112i
$376$		0			0
$377$	284.563			0.754809
$378$		0			0
$379$		−	340.706i		−	0.898960i	−0.893291	−	0.449480i	$-0.851609\pi$
$379$		−	340.706i		−	0.898960i	0.893291	−	0.449480i	$-0.148391\pi$
$380$		0			0
$381$	11.0355	+	19.1140i	0.0289645	+	0.0501680i
$382$		0			0
$383$	−230.878	−	133.298i	−0.602815	−	0.348036i	0.167333	−	0.985900i	$-0.446485\pi$
$383$	−230.878	−	133.298i	−0.602815	−	0.348036i	−0.770148	+	0.637865i	$0.779818\pi$
$384$		0			0
$385$	−13.6556	+	42.3969i	−0.0354690	+	0.110122i
$386$		0			0
$387$	−279.757	−	161.518i	−0.722887	−	0.417359i
$388$		0			0
$389$	66.8506	+	115.789i	0.171853	+	0.297657i	0.939068	−	0.343733i	$-0.111691\pi$
$389$	66.8506	+	115.789i	0.171853	+	0.297657i	−0.767215	+	0.641390i	$0.778358\pi$
$390$		0			0
$391$		−	248.367i		−	0.635209i
$392$		0			0
$393$	−24.6649			−0.0627605
$394$		0			0
$395$	−166.010	+	95.8460i	−0.420279	+	0.242648i
$396$		0			0
$397$	−291.181	+	504.341i	−0.733454	+	1.27038i	0.221944	+	0.975059i	$0.428760\pi$
$397$	−291.181	+	504.341i	−0.733454	+	1.27038i	−0.955398	+	0.295321i	$0.904574\pi$
$398$		0			0
$399$	20.5244	+	6.61067i	0.0514395	+	0.0165681i
$400$		0			0
$401$	11.8282	−	20.4870i	0.0294967	−	0.0510897i	−0.850900	−	0.525327i	$-0.823943\pi$
$401$	11.8282	−	20.4870i	0.0294967	−	0.0510897i	0.880397	+	0.474238i	$0.157276\pi$
$402$		0			0
$403$	70.8402	−	40.8996i	0.175782	−	0.101488i
$404$		0			0
$405$	122.861			0.303361
$406$		0			0
$407$		−	4.28827i		−	0.0105363i
$408$		0			0
$409$	−315.709	−	546.824i	−0.771904	−	1.33698i	−0.936518	−	0.350619i	$-0.885971\pi$
$409$	−315.709	−	546.824i	−0.771904	−	1.33698i	0.164614	−	0.986358i	$-0.447362\pi$
$410$		0			0
$411$	−6.62359	−	3.82413i	−0.0161158	−	0.00930446i
$412$		0			0
$413$	−694.408	+	149.462i	−1.68138	+	0.361893i
$414$		0			0
$415$	−43.9669	−	25.3843i	−0.105944	−	0.0611670i
$416$		0			0
$417$	9.25893	+	16.0369i	0.0222037	+	0.0384579i
$418$		0			0
$419$		−	366.411i		−	0.874490i	−0.899343	−	0.437245i	$-0.855954\pi$
$419$		−	366.411i		−	0.874490i	0.899343	−	0.437245i	$-0.144046\pi$
$420$		0			0
$421$	262.549			0.623632			0.311816	−	0.950142i	$-0.399063\pi$
$421$	262.549			0.623632			0.311816	+	0.950142i	$0.399063\pi$
$422$		0			0
$423$	−31.2276	+	18.0293i	−0.0738242	+	0.0426224i
$424$		0			0
$425$	−245.134	+	424.584i	−0.576785	+	0.999021i
$426$		0			0
$427$	−369.609	+	334.516i	−0.865594	+	0.783410i
$428$		0			0
$429$	2.17211	−	3.76220i	0.00506319	−	0.00876971i
$430$		0			0
$431$	−221.469	+	127.865i	−0.513848	+	0.296670i	−0.734414	−	0.678702i	$-0.762543\pi$
$431$	−221.469	+	127.865i	−0.513848	+	0.296670i	0.220566	+	0.975372i	$0.429210\pi$
$432$		0			0
$433$	−363.523			−0.839545			−0.419773	−	0.907629i	$-0.637890\pi$
$433$	−363.523			−0.839545			−0.419773	+	0.907629i	$0.637890\pi$
$434$		0			0
$435$		−	5.58436i		−	0.0128376i
$436$		0			0
$437$	152.874	+	264.786i	0.349826	+	0.605917i
$438$		0			0
$439$	459.468	+	265.274i	1.04663	+	0.604269i	0.921703	−	0.387897i	$-0.126798\pi$
$439$	459.468	+	265.274i	1.04663	+	0.604269i	0.124923	+	0.992166i	$0.460132\pi$
$440$		0			0
$441$	−401.351	+	181.163i	−0.910092	+	0.410801i
$442$		0			0
$443$	−752.435	−	434.418i	−1.69850	−	0.980629i	−0.947187	−	0.320680i	$-0.896088\pi$
$443$	−752.435	−	434.418i	−1.69850	−	0.980629i	−0.751311	−	0.659948i	$-0.770578\pi$
$444$		0			0
$445$	101.382	+	175.599i	0.227824	+	0.394604i
$446$		0			0
$447$			18.2073i			0.0407322i
$448$		0			0
$449$	260.067			0.579213			0.289607	−	0.957146i	$-0.406475\pi$
$449$	260.067			0.579213			0.289607	+	0.957146i	$0.406475\pi$
$450$		0			0
$451$	−49.5217	+	28.5914i	−0.109804	+	0.0633955i
$452$		0			0
$453$	−10.6571	+	18.4586i	−0.0235256	+	0.0407476i
$454$		0			0
$455$	−71.0615	+	64.3146i	−0.156179	+	0.141351i
$456$		0			0
$457$	121.598	−	210.614i	0.266079	−	0.460863i	−0.701767	−	0.712407i	$-0.747605\pi$
$457$	121.598	−	210.614i	0.266079	−	0.460863i	0.967846	+	0.251544i	$0.0809384\pi$
$458$		0			0
$459$	−38.9775	+	22.5037i	−0.0849184	+	0.0490277i
$460$		0			0
$461$	468.031			1.01525			0.507626	−	0.861577i	$-0.330523\pi$
$461$	468.031			1.01525			0.507626	+	0.861577i	$0.330523\pi$
$462$		0			0
$463$		−	451.876i		−	0.975973i	−0.872851	−	0.487987i	$-0.837731\pi$
$463$		−	451.876i		−	0.975973i	0.872851	−	0.487987i	$-0.162269\pi$
$464$		0			0
$465$	−0.802629	−	1.39019i	−0.00172608	−	0.00298966i
$466$		0			0
$467$	750.567	+	433.340i	1.60721	+	0.927923i	0.989991	+	0.141132i	$0.0450743\pi$
$467$	750.567	+	433.340i	1.60721	+	0.927923i	0.617219	+	0.786791i	$0.288259\pi$
$468$		0			0
$469$	379.726	−	81.7308i	0.809650	−	0.174266i
$470$		0			0
$471$	22.6505	+	13.0773i	0.0480902	+	0.0277649i
$472$		0			0
$473$	−75.0625	−	130.012i	−0.158695	−	0.274867i
$474$		0			0
$475$		−	603.536i		−	1.27060i
$476$		0			0
$477$	715.318			1.49962
$478$		0			0
$479$	−365.780	+	211.183i	−0.763633	+	0.440884i	−0.830599	−	0.556871i	$-0.812002\pi$
$479$	−365.780	+	211.183i	−0.763633	+	0.440884i	0.0669655	+	0.997755i	$0.478668\pi$
$480$		0			0
$481$	4.61370	−	7.99117i	0.00959190	−	0.0166137i
$482$		0			0
$483$	8.86055	+	2.85389i	0.0183448	+	0.00590867i
$484$		0			0
$485$	6.84601	−	11.8576i	0.0141155	−	0.0244487i
$486$		0			0
$487$	367.916	−	212.417i	0.755475	−	0.436174i	−0.0721938	−	0.997391i	$-0.523000\pi$
$487$	367.916	−	212.417i	0.755475	−	0.436174i	0.827669	+	0.561217i	$0.189667\pi$
$488$		0			0
$489$	−33.1072			−0.0677039
$490$		0			0
$491$			165.938i			0.337959i	0.985620	+	0.168980i	$0.0540472\pi$
$491$			165.938i			0.337959i	−0.985620	+	0.168980i	$0.945953\pi$
$492$		0			0
$493$	−342.270	−	592.829i	−0.694259	−	1.20249i
$494$		0			0
$495$	49.5217	+	28.5914i	0.100044	+	0.0577604i
$496$		0			0
$497$	148.652	−	461.525i	0.299099	−	0.928623i
$498$		0			0
$499$	663.092	+	382.836i	1.32884	+	0.767207i	0.985121	−	0.171865i	$-0.0549792\pi$
$499$	663.092	+	382.836i	1.32884	+	0.767207i	0.343721	+	0.939072i	$0.388313\pi$
$500$		0			0
$501$	−7.52482	−	13.0334i	−0.0150196	−	0.0260147i
$502$		0			0
$503$			175.410i			0.348728i	0.984681	+	0.174364i	$0.0557869\pi$
$503$			175.410i			0.348728i	−0.984681	+	0.174364i	$0.944213\pi$
$504$		0			0
$505$	−119.198			−0.236035
$506$		0			0
$507$	−8.84545	+	5.10692i	−0.0174466	+	0.0100728i
$508$		0			0
$509$	−370.012	+	640.879i	−0.726939	+	1.25910i	0.231232	+	0.972899i	$0.425724\pi$
$509$	−370.012	+	640.879i	−0.726939	+	1.25910i	−0.958171	+	0.286196i	$0.907609\pi$
$510$		0			0
$511$	−37.4054	−	173.788i	−0.0732004	−	0.340093i
$512$		0			0
$513$	27.7029	−	47.9827i	0.0540017	−	0.0935336i
$514$		0			0
$515$	222.850	−	128.662i	0.432718	−	0.249830i
$516$		0			0
$517$	−16.7575			−0.0324130
$518$		0			0
$519$			5.97132i			0.0115054i
$520$		0			0
$521$	−125.990	−	218.221i	−0.241823	−	0.418850i	0.719411	−	0.694585i	$-0.244412\pi$
$521$	−125.990	−	218.221i	−0.241823	−	0.418850i	−0.961234	+	0.275735i	$0.911079\pi$
$522$		0			0
$523$	124.579	+	71.9256i	0.238200	+	0.137525i	0.614349	−	0.789034i	$-0.289419\pi$
$523$	124.579	+	71.9256i	0.238200	+	0.137525i	−0.376149	+	0.926559i	$0.622752\pi$
$524$		0			0
$525$	−12.3304	−	13.6239i	−0.0234865	−	0.0259503i
$526$		0			0
$527$	−170.412	−	98.3874i	−0.323362	−	0.186693i
$528$		0			0
$529$	−198.503	−	343.817i	−0.375242	−	0.649938i
$530$		0			0
$531$			911.898i			1.71732i
$532$		0			0
$533$	−123.045			−0.230853
$534$		0			0
$535$	−36.6894	+	21.1826i	−0.0685783	+	0.0395937i
$536$		0			0
$537$	−11.8042	+	20.4455i	−0.0219818	+	0.0380736i
$538$		0			0
$539$	−203.627	−	20.3476i	−0.377787	−	0.0377506i
$540$		0			0
$541$	461.627	−	799.562i	0.853286	−	1.47793i	−0.0249409	−	0.999689i	$-0.507940\pi$
$541$	461.627	−	799.562i	0.853286	−	1.47793i	0.878226	−	0.478245i	$-0.158727\pi$
$542$		0			0
$543$	20.5566	−	11.8684i	0.0378575	−	0.0218571i
$544$		0			0
$545$	−166.352			−0.305233
$546$		0			0
$547$		−	472.616i		−	0.864015i	−0.901870	−	0.432007i	$-0.857805\pi$
$547$		−	472.616i		−	0.864015i	0.901870	−	0.432007i	$-0.142195\pi$
$548$		0			0
$549$	319.993	+	554.245i	0.582866	+	1.00955i
$550$		0			0
$551$	729.793	+	421.346i	1.32449	+	0.764694i
$552$		0			0
$553$	−590.981	−	652.978i	−1.06868	−	1.18079i
$554$		0			0
$555$	−0.156822	−	0.0905410i	−0.000282561	−	0.000163137i
$556$		0			0
$557$	395.538	+	685.092i	0.710122	+	1.22997i	0.964811	+	0.262944i	$0.0846934\pi$
$557$	395.538	+	685.092i	0.710122	+	1.22997i	−0.254689	+	0.967023i	$0.581973\pi$
$558$		0			0
$559$		−	323.036i		−	0.577882i
$560$		0			0
$561$	−10.4504			−0.0186281
$562$		0			0
$563$	296.714	−	171.308i	0.527024	−	0.304277i	−0.212780	−	0.977100i	$-0.568252\pi$
$563$	296.714	−	171.308i	0.527024	−	0.304277i	0.739804	+	0.672823i	$0.234918\pi$
$564$		0			0
$565$	99.3371	−	172.057i	0.175818	−	0.304525i
$566$		0			0
$567$	118.774	+	551.832i	0.209478	+	0.973248i
$568$		0			0
$569$	287.438	−	497.858i	0.505164	−	0.874969i	−0.494818	−	0.868996i	$-0.664765\pi$
$569$	287.438	−	497.858i	0.505164	−	0.874969i	0.999982	−	0.00597297i	$-0.00190127\pi$
$570$		0			0
$571$	348.438	−	201.171i	0.610225	−	0.352313i	−0.162829	−	0.986654i	$-0.552062\pi$
$571$	348.438	−	201.171i	0.610225	−	0.352313i	0.773053	+	0.634341i	$0.218728\pi$
$572$		0			0
$573$	31.4593			0.0549028
$574$		0			0
$575$		−	260.552i		−	0.453134i
$576$		0			0
$577$	−428.455	−	742.105i	−0.742556	−	1.28614i	−0.951328	−	0.308180i	$-0.900280\pi$
$577$	−428.455	−	742.105i	−0.742556	−	1.28614i	0.208773	−	0.977964i	$-0.433053\pi$
$578$		0			0
$579$	−3.53037	−	2.03826i	−0.00609736	−	0.00352031i
$580$		0			0
$581$	71.5094	−	222.018i	0.123080	−	0.382130i
$582$		0			0
$583$	287.893	+	166.215i	0.493814	+	0.285103i
$584$		0			0
$585$	61.5224	+	106.560i	0.105166	+	0.182154i
$586$		0			0
$587$			517.144i			0.880995i	0.897754	+	0.440497i	$0.145198\pi$
$587$			517.144i			0.880995i	−0.897754	+	0.440497i	$0.854802\pi$
$588$		0			0
$589$	242.237			0.411268
$590$		0			0
$591$	−18.0046	+	10.3950i	−0.0304647	+	0.0175888i
$592$		0			0
$593$	153.278	−	265.485i	0.258479	−	0.447699i	−0.707356	−	0.706858i	$-0.750112\pi$
$593$	153.278	−	265.485i	0.258479	−	0.447699i	0.965835	+	0.259159i	$0.0834454\pi$
$594$		0			0
$595$	219.459	+	70.6852i	0.368838	+	0.118799i
$596$		0			0
$597$	−18.9640	+	32.8466i	−0.0317655	+	0.0550195i
$598$		0			0
$599$	697.268	−	402.568i	1.16405	−	0.672067i	0.211782	−	0.977317i	$-0.432073\pi$
$599$	697.268	−	402.568i	1.16405	−	0.672067i	0.952272	+	0.305250i	$0.0987400\pi$
$600$		0			0
$601$	389.495			0.648079			0.324039	−	0.946044i	$-0.394959\pi$
$601$	389.495			0.648079			0.324039	+	0.946044i	$0.394959\pi$
$602$		0			0
$603$		−	498.656i		−	0.826959i
$604$		0			0
$605$	−78.8908	−	136.643i	−0.130398	−	0.225856i
$606$		0			0
$607$	230.342	+	132.988i	0.379476	+	0.219091i	0.677590	−	0.735439i	$-0.263024\pi$
$607$	230.342	+	132.988i	0.379476	+	0.219091i	−0.298114	+	0.954530i	$0.596358\pi$
$608$		0			0
$609$	25.0822	−	5.39860i	0.0411859	−	0.00886470i
$610$		0			0
$611$	−31.2276	−	18.0293i	−0.0511090	−	0.0295078i
$612$		0			0
$613$	2.51977	+	4.36436i	0.00411055	+	0.00711968i	0.868073	−	0.496436i	$-0.165358\pi$
$613$	2.51977	+	4.36436i	0.00411055	+	0.00711968i	−0.863963	+	0.503556i	$0.832025\pi$
$614$		0			0
$615$			2.41468i			0.00392630i
$616$		0			0
$617$	742.316			1.20311			0.601553	−	0.798833i	$-0.294549\pi$
$617$	742.316			1.20311			0.601553	+	0.798833i	$0.294549\pi$
$618$		0			0
$619$	−368.239	+	212.603i	−0.594893	+	0.343462i	−0.767030	−	0.641611i	$-0.778266\pi$
$619$	−368.239	+	212.603i	−0.594893	+	0.343462i	0.172137	+	0.985073i	$0.444933\pi$
$620$		0			0
$621$	11.9596	−	20.7146i	0.0192586	−	0.0333568i
$622$		0			0
$623$	−690.693	+	625.115i	−1.10866	+	1.00339i
$624$		0			0
$625$	−228.143	+	395.155i	−0.365029	+	0.632248i
$626$		0			0
$627$	11.1412	−	6.43240i	0.0177691	−	0.0102590i
$628$		0			0
$629$	−22.1973			−0.0352898
$630$		0			0
$631$			122.339i			0.193881i	0.995290	+	0.0969405i	$0.0309057\pi$
$631$			122.339i			0.193881i	−0.995290	+	0.0969405i	$0.969094\pi$
$632$		0			0
$633$	12.7325	+	22.0533i	0.0201145	+	0.0348393i
$634$		0			0
$635$	−251.597	−	145.259i	−0.396215	−	0.228755i
$636$		0			0
$637$	−357.567	−	256.998i	−0.561330	−	0.403451i
$638$		0			0
$639$	−539.085	−	311.241i	−0.843639	−	0.487075i
$640$		0			0
$641$	106.313	+	184.139i	0.165855	+	0.287269i	0.936959	−	0.349441i	$-0.113628\pi$
$641$	106.313	+	184.139i	0.165855	+	0.287269i	−0.771104	+	0.636710i	$0.780295\pi$
$642$		0			0
$643$		−	1002.79i		−	1.55954i	−0.626063	−	0.779772i	$-0.715335\pi$
$643$		−	1002.79i		−	1.55954i	0.626063	−	0.779772i	$-0.284665\pi$
$644$		0			0
$645$	−6.33938			−0.00982849
$646$		0			0
$647$	435.448	−	251.406i	0.673027	−	0.388572i	−0.124196	−	0.992258i	$-0.539635\pi$
$647$	435.448	−	251.406i	0.673027	−	0.388572i	0.797223	+	0.603685i	$0.206302\pi$
$648$		0			0
$649$	−211.894	+	367.011i	−0.326493	+	0.565502i
$650$		0			0
$651$	5.46814	−	4.94896i	0.00839959	−	0.00760209i
$652$		0			0
$653$	−118.693	+	205.582i	−0.181765	+	0.314826i	−0.942482	−	0.334258i	$-0.891514\pi$
$653$	−118.693	+	205.582i	−0.181765	+	0.314826i	0.760717	+	0.649084i	$0.224848\pi$
$654$		0			0
$655$	281.166	−	162.331i	0.429261	−	0.247834i
$656$		0			0
$657$	−228.218			−0.347364
$658$		0			0
$659$			795.143i			1.20659i	0.797518	+	0.603295i	$0.206146\pi$
$659$			795.143i			1.20659i	−0.797518	+	0.603295i	$0.793854\pi$
$660$		0			0
$661$	−323.075	−	559.582i	−0.488767	−	0.846569i	0.511150	−	0.859492i	$-0.329220\pi$
$661$	−323.075	−	559.582i	−0.488767	−	0.846569i	−0.999917	+	0.0129226i	$0.995887\pi$
$662$		0			0
$663$	−19.4743	−	11.2435i	−0.0293729	−	0.0169585i
$664$		0			0
$665$	−277.475	+	59.7226i	−0.417255	+	0.0898084i
$666$		0			0
$667$	315.058	+	181.899i	0.472351	+	0.272712i
$668$		0			0
$669$	−8.95508	−	15.5107i	−0.0133858	−	0.0231848i
$670$		0			0
$671$			297.422i			0.443252i
$672$		0			0
$673$	−714.773			−1.06207			−0.531035	−	0.847350i	$-0.678197\pi$
$673$	−714.773			−1.06207			−0.531035	+	0.847350i	$0.678197\pi$
$674$		0			0
$675$	−40.8898	+	23.6078i	−0.0605775	+	0.0349745i
$676$		0			0
$677$	165.452	−	286.572i	0.244390	−	0.423297i	−0.717570	−	0.696487i	$-0.754745\pi$
$677$	165.452	−	286.572i	0.244390	−	0.423297i	0.961960	+	0.273190i	$0.0880788\pi$
$678$		0			0
$679$	59.8770	+	19.2857i	0.0881841	+	0.0284031i
$680$		0			0
$681$	21.3705	−	37.0148i	0.0313811	−	0.0543536i
$682$		0			0
$683$	−746.868	+	431.205i	−1.09351	+	0.631339i	−0.934509	−	0.355939i	$-0.884161\pi$
$683$	−746.868	+	431.205i	−1.09351	+	0.631339i	−0.159002	+	0.987278i	$0.550828\pi$
$684$		0			0
$685$	100.674			0.146969
$686$		0			0
$687$		−	24.8235i		−	0.0361331i
$688$		0			0
$689$	357.659	+	619.483i	0.519098	+	0.899105i
$690$		0			0
$691$	530.380	+	306.215i	0.767555	+	0.443148i	0.832002	−	0.554773i	$-0.187195\pi$
$691$	530.380	+	306.215i	0.767555	+	0.443148i	−0.0644469	+	0.997921i	$0.520528\pi$
$692$		0			0
$693$	−80.5441	+	250.068i	−0.116225	+	0.360848i
$694$		0			0
$695$	−211.093	−	121.875i	−0.303732	−	0.175360i
$696$		0			0
$697$	147.997	+	256.339i	0.212335	+	0.367774i
$698$		0			0
$699$		−	15.0428i		−	0.0215204i
$700$		0			0
$701$	564.644			0.805483			0.402742	−	0.915314i	$-0.368057\pi$
$701$	564.644			0.805483			0.402742	+	0.915314i	$0.368057\pi$
$702$		0			0
$703$	23.6647	−	13.6628i	0.0336625	−	0.0194350i
$704$		0			0
$705$	−0.353813	+	0.612822i	−0.000501862	+	0.000869251i
$706$		0			0
$707$	−115.233	−	535.377i	−0.162988	−	0.757252i
$708$		0			0
$709$	−481.996	+	834.842i	−0.679825	+	1.17749i	0.295208	+	0.955433i	$0.404611\pi$
$709$	−481.996	+	834.842i	−0.679825	+	1.17749i	−0.975033	+	0.222059i	$0.928722\pi$
$710$		0			0
$711$	−979.169	+	565.324i	−1.37717	+	0.795111i
$712$		0			0
$713$	104.576			0.146670
$714$		0			0
$715$			57.1828i			0.0799759i
$716$		0			0
$717$	6.28095	+	10.8789i	0.00876004	+	0.0151728i
$718$		0			0
$719$	−567.664	−	327.741i	−0.789519	−	0.455829i	0.0502743	−	0.998735i	$-0.483990\pi$
$719$	−567.664	−	327.741i	−0.789519	−	0.455829i	−0.839793	+	0.542907i	$0.817324\pi$
$720$		0			0
$721$	793.324	+	876.548i	1.10031	+	1.21574i
$722$		0			0
$723$	15.0885	+	8.71133i	0.0208693	+	0.0120489i
$724$		0			0
$725$	−359.062	−	621.914i	−0.495258	−	0.857812i
$726$		0			0
$727$		−	141.161i		−	0.194169i	−0.995276	−	0.0970843i	$-0.969048\pi$
$727$		−	141.161i		−	0.194169i	0.995276	−	0.0970843i	$-0.0309516\pi$
$728$		0			0
$729$	722.497			0.991079
$730$		0			0
$731$	−672.980	+	388.545i	−0.920629	+	0.531525i
$732$		0			0
$733$	−391.259	+	677.680i	−0.533777	+	0.924529i	0.465444	+	0.885077i	$0.345895\pi$
$733$	−391.259	+	677.680i	−0.533777	+	0.924529i	−0.999221	+	0.0394519i	$0.987439\pi$
$734$		0			0
$735$	−5.04343	+	7.01703i	−0.00686181	+	0.00954697i
$736$		0			0
$737$	115.871	−	200.694i	0.157219	−	0.272312i
$738$		0			0
$739$	654.934	−	378.126i	0.886243	−	0.511673i	0.0135312	−	0.999908i	$-0.495693\pi$
$739$	654.934	−	378.126i	0.886243	−	0.511673i	0.872712	+	0.488236i	$0.162359\pi$
$740$		0			0
$741$	27.6822			0.0373579
$742$		0			0
$743$		−	1219.39i		−	1.64118i	−0.571520	−	0.820588i	$-0.693646\pi$
$743$		−	1219.39i		−	1.64118i	0.571520	−	0.820588i	$-0.306354\pi$
$744$		0			0
$745$	−119.831	−	207.553i	−0.160847	−	0.278595i
$746$		0			0
$747$	−259.328	−	149.723i	−0.347159	−	0.200432i
$748$		0			0
$749$	−130.611	−	144.313i	−0.174380	−	0.192674i
$750$		0			0
$751$	−318.014	−	183.605i	−0.423454	−	0.244481i	0.273100	−	0.961986i	$-0.411951\pi$
$751$	−318.014	−	183.605i	−0.423454	−	0.244481i	−0.696554	+	0.717504i	$0.745284\pi$
$752$		0			0
$753$	9.91731	+	17.1773i	0.0131704	+	0.0228118i
$754$		0			0
$755$		−	280.558i		−	0.371600i
$756$		0			0
$757$	−1243.95			−1.64326			−0.821632	−	0.570018i	$-0.806936\pi$
$757$	−1243.95			−1.64326			−0.821632	+	0.570018i	$0.806936\pi$
$758$		0			0
$759$	4.80977	−	2.77692i	0.00633698	−	0.00365866i
$760$		0			0
$761$	−687.446	+	1190.69i	−0.903345	+	1.56464i	−0.0802214	+	0.996777i	$0.525563\pi$
$761$	−687.446	+	1190.69i	−0.903345	+	1.56464i	−0.823124	+	0.567862i	$0.807771\pi$
$762$		0			0
$763$	−160.818	−	747.171i	−0.210771	−	0.979254i
$764$		0			0
$765$	147.997	−	256.339i	0.193460	−	0.335083i
$766$		0			0
$767$	−789.726	+	455.949i	−1.02963	+	0.594457i
$768$		0			0
$769$	414.353			0.538820			0.269410	−	0.963026i	$-0.413171\pi$
$769$	414.353			0.538820			0.269410	+	0.963026i	$0.413171\pi$
$770$		0			0
$771$		−	39.1092i		−	0.0507254i
$772$		0			0
$773$	390.465	+	676.305i	0.505130	+	0.874910i	0.999982	+	0.00593327i	$0.00188863\pi$
$773$	390.465	+	676.305i	0.505130	+	0.874910i	−0.494853	+	0.868977i	$0.664778\pi$
$774$		0			0
$775$	−178.773	−	103.214i	−0.230674	−	0.133180i
$776$		0			0
$777$	0.255061	−	0.791894i	0.000328263	−	0.00101917i
$778$		0			0
$779$	−315.562	−	182.190i	−0.405086	−	0.233877i
$780$		0			0
$781$	−144.643	−	250.530i	−0.185203	−	0.320781i
$782$		0			0
$783$		−	65.9251i		−	0.0841955i
$784$		0			0
$785$	−344.271			−0.438562
$786$		0			0
$787$	−944.208	+	545.139i	−1.19976	+	0.692679i	−0.960501	−	0.278277i	$-0.910237\pi$
$787$	−944.208	+	545.139i	−1.19976	+	0.692679i	−0.239255	+	0.970957i	$0.576903\pi$
$788$		0			0
$789$	14.9003	−	25.8080i	0.0188850	−	0.0327098i
$790$		0			0
$791$	868.827	+	279.840i	1.09839	+	0.353780i
$792$		0			0
$793$	−319.993	+	554.245i	−0.403522	+	0.698921i
$794$		0			0
$795$	12.1570	−	7.01883i	0.0152918	−	0.00882871i
$796$		0			0
$797$	−915.987			−1.14929			−0.574647	−	0.818402i	$-0.694861\pi$
$797$	−915.987			−1.14929			−0.574647	+	0.818402i	$0.694861\pi$
$798$		0			0
$799$			86.7419i			0.108563i
$800$		0			0
$801$	597.976	+	1035.72i	0.746537	+	1.29304i
$802$		0			0
$803$	−91.8508	−	53.0301i	−0.114385	−	0.0660399i
$804$		0			0
$805$	−119.788	+	25.7828i	−0.148805	+	0.0320283i
$806$		0			0
$807$	−30.6263	−	17.6821i	−0.0379508	−	0.0219109i
$808$		0			0
$809$	279.786	+	484.604i	0.345842	+	0.599016i	0.985506	−	0.169638i	$-0.0542600\pi$
$809$	279.786	+	484.604i	0.345842	+	0.599016i	−0.639664	+	0.768654i	$0.720927\pi$
$810$		0			0
$811$		−	387.982i		−	0.478399i	−0.970970	−	0.239200i	$-0.923115\pi$
$811$		−	387.982i		−	0.478399i	0.970970	−	0.239200i	$-0.0768850\pi$
$812$		0			0
$813$	37.0586			0.0455825
$814$		0			0
$815$	377.404	−	217.894i	0.463073	−	0.267355i
$816$		0			0
$817$	478.313	−	828.462i	0.585450	−	1.01403i
$818$		0			0
$819$	−419.139	+	379.344i	−0.511769	+	0.463179i
$820$		0			0
$821$	545.092	−	944.127i	0.663937	−	1.14997i	−0.315636	−	0.948881i	$-0.602218\pi$
$821$	545.092	−	944.127i	0.663937	−	1.14997i	0.979572	−	0.201092i	$-0.0644490\pi$
$822$		0			0
$823$	−233.432	+	134.772i	−0.283635	+	0.163757i	−0.635068	−	0.772456i	$-0.719028\pi$
$823$	−233.432	+	134.772i	−0.283635	+	0.163757i	0.351433	+	0.936213i	$0.385695\pi$
$824$		0			0
$825$	−10.9631			−0.0132886
$826$		0			0
$827$			165.679i			0.200337i	0.994970	+	0.100169i	$0.0319382\pi$
$827$			165.679i			0.200337i	−0.994970	+	0.100169i	$0.968062\pi$
$828$		0			0
$829$	−453.089	−	784.773i	−0.546549	−	0.946650i	−0.998508	−	0.0546116i	$-0.982608\pi$
$829$	−453.089	−	784.773i	−0.546549	−	0.946650i	0.451959	−	0.892039i	$-0.350725\pi$
$830$		0			0
$831$	−5.31911	−	3.07099i	−0.00640085	−	0.00369553i
$832$		0			0
$833$	−105.325	+	1054.03i	−0.126440	+	1.26535i
$834$		0			0
$835$	171.558	+	99.0489i	0.205458	+	0.118621i
$836$		0			0
$837$	−9.47527	−	16.4116i	−0.0113205	−	0.0196077i
$838$		0			0
$839$			1383.82i			1.64937i	0.565592	+	0.824685i	$0.308648\pi$
$839$			1383.82i			1.64937i	−0.565592	+	0.824685i	$0.691352\pi$
$840$		0			0
$841$	161.687			0.192256
$842$		0			0
$843$	47.9994	−	27.7125i	0.0569388	−	0.0328736i
$844$		0			0
$845$	67.2222	−	116.432i	0.0795529	−	0.137790i
$846$		0			0
$847$	537.466	−	486.436i	0.634552	−	0.574304i
$848$		0			0
$849$	11.1918	−	19.3847i	0.0131823	−	0.0228324i
$850$		0			0
$851$	10.2163	−	5.89836i	0.0120050	−	0.00693110i
$852$		0			0
$853$	197.566			0.231613			0.115807	−	0.993272i	$-0.463055\pi$
$853$	197.566			0.231613			0.115807	+	0.993272i	$0.463055\pi$
$854$		0			0
$855$			364.380i			0.426175i
$856$		0			0
$857$	58.9830	+	102.162i	0.0688250	+	0.119208i	0.898384	−	0.439210i	$-0.144742\pi$
$857$	58.9830	+	102.162i	0.0688250	+	0.119208i	−0.829559	+	0.558419i	$0.811408\pi$
$858$		0			0
$859$	−286.768	−	165.565i	−0.333839	−	0.192742i	0.323705	−	0.946158i	$-0.395071\pi$
$859$	−286.768	−	165.565i	−0.333839	−	0.192742i	−0.657544	+	0.753416i	$0.728405\pi$
$860$		0			0
$861$	−10.8455	+	2.33435i	−0.0125964	+	0.00271121i
$862$		0			0
$863$	43.0945	+	24.8806i	0.0499356	+	0.0288304i	0.524760	−	0.851250i	$-0.324155\pi$
$863$	43.0945	+	24.8806i	0.0499356	+	0.0288304i	−0.474824	+	0.880081i	$0.657488\pi$
$864$		0			0
$865$	−39.3001	−	68.0698i	−0.0454337	−	0.0786934i
$866$		0			0
$867$			20.6426i			0.0238092i
$868$		0			0
$869$	−525.447			−0.604658
$870$		0			0
$871$	431.849	−	249.328i	0.495808	−	0.286255i
$872$		0			0
$873$	40.3795	−	69.9394i	0.0462537	−	0.0801138i
$874$		0			0
$875$	484.017	+	155.897i	0.553162	+	0.178167i
$876$		0			0
$877$	−444.043	+	769.105i	−0.506320	+	0.876972i	0.493653	+	0.869659i	$0.335661\pi$
$877$	−444.043	+	769.105i	−0.506320	+	0.876972i	−0.999973	+	0.00731339i	$0.997672\pi$
$878$		0			0
$879$	−55.3451	+	31.9535i	−0.0629637	+	0.0363521i
$880$		0			0
$881$	90.4266			0.102641			0.0513204	−	0.998682i	$-0.483657\pi$
$881$	90.4266			0.102641			0.0513204	+	0.998682i	$0.483657\pi$
$882$		0			0
$883$			1292.66i			1.46394i	0.681336	+	0.731971i	$0.261399\pi$
$883$			1292.66i			1.46394i	−0.681336	+	0.731971i	$0.738601\pi$
$884$		0			0
$885$	8.94770	+	15.4979i	0.0101104	+	0.0175117i
$886$		0			0
$887$	−1299.69	−	750.378i	−1.46527	−	0.845973i	−0.466020	−	0.884774i	$-0.654313\pi$
$887$	−1299.69	−	750.378i	−1.46527	−	0.845973i	−0.999247	+	0.0388014i	$0.987646\pi$
$888$		0			0
$889$	409.206	−	1270.48i	0.460300	−	1.42911i
$890$		0			0
$891$	291.656	+	168.387i	0.327335	+	0.188987i
$892$		0			0
$893$	−53.3912	−	92.4762i	−0.0597885	−	0.103557i
$894$		0			0
$895$		−	310.757i		−	0.347215i
$896$		0			0
$897$	11.9507			0.0133229
$898$		0			0
$899$	249.613	−	144.114i	0.277656	−	0.160305i
$900$		0			0
$901$	860.378	−	1490.22i	0.954915	−	1.65396i
$902$		0			0
$903$	−6.12850	−	28.4734i	−0.00678682	−	0.0315320i
$904$		0			0
$905$	−156.223	+	270.586i	−0.172622	+	0.298990i
$906$		0			0
$907$	1138.88	−	657.533i	1.25566	−	0.724953i	0.283429	−	0.958993i	$-0.408528\pi$
$907$	1138.88	−	657.533i	1.25566	−	0.724953i	0.972227	+	0.234040i	$0.0751946\pi$
$908$		0			0
$909$	−703.058			−0.773441
$910$		0			0
$911$			536.125i			0.588501i	0.955728	+	0.294251i	$0.0950700\pi$
$911$			536.125i			0.588501i	−0.955728	+	0.294251i	$0.904930\pi$
$912$		0			0
$913$	−69.5810	−	120.518i	−0.0762113	−	0.132002i
$914$		0			0
$915$	10.8767	+	6.27966i	0.0118871	+	0.00686302i
$916$		0			0
$917$	1000.93	+	1105.93i	1.09152	+	1.20603i
$918$		0			0
$919$	45.7786	+	26.4303i	0.0498135	+	0.0287598i	0.524700	−	0.851287i	$-0.324178\pi$
$919$	45.7786	+	26.4303i	0.0498135	+	0.0287598i	−0.474886	+	0.880047i	$0.657511\pi$
$920$		0			0
$921$	22.6786	+	39.2805i	0.0246239	+	0.0426499i
$922$		0			0
$923$		−	622.482i		−	0.674412i
$924$		0			0
$925$	−23.2863			−0.0251744
$926$		0			0
$927$	1314.42	−	758.882i	1.41793	−	0.818643i
$928$		0			0
$929$	926.773	−	1605.22i	0.997603	−	1.72790i	0.438876	−	0.898548i	$-0.355377\pi$
$929$	926.773	−	1605.22i	0.997603	−	1.72790i	0.558727	−	0.829352i	$-0.311290\pi$
$930$		0			0
$931$	−536.489	−	1188.54i	−0.576250	−	1.27663i
$932$		0			0
$933$	−10.9440	+	18.9556i	−0.0117299	+	0.0203168i
$934$		0			0
$935$	119.129	−	68.7790i	0.127410	−	0.0735604i
$936$		0			0
$937$	82.1362			0.0876587			0.0438294	−	0.999039i	$-0.486044\pi$
$937$	82.1362			0.0876587			0.0438294	+	0.999039i	$0.486044\pi$
$938$		0			0
$939$			48.6136i			0.0517717i
$940$		0			0
$941$	−167.879	−	290.774i	−0.178405	−	0.309006i	0.762930	−	0.646482i	$-0.223760\pi$
$941$	−167.879	−	290.774i	−0.178405	−	0.309006i	−0.941334	+	0.337476i	$0.890427\pi$
$942$		0			0
$943$	−136.231	−	78.6530i	−0.144466	−	0.0834072i
$944$		0			0
$945$	14.8998	+	16.4629i	0.0157670	+	0.0174211i
$946$		0			0
$947$	1029.84	+	594.577i	1.08747	+	0.627853i	0.932903	−	0.360128i	$-0.117267\pi$
$947$	1029.84	+	594.577i	1.08747	+	0.627853i	0.154571	+	0.987982i	$0.450600\pi$
$948$		0			0
$949$	−114.109	−	197.643i	−0.120241	−	0.208264i
$950$		0			0
$951$		−	5.11256i		−	0.00537598i
$952$		0			0
$953$	0.101737			0.000106754			5.33770e−5	−	1.00000i	$-0.499983\pi$
$953$	0.101737			0.000106754			5.33770e−5		1.00000i	$0.499983\pi$
$954$		0			0
$955$	−358.619	+	207.049i	−0.375517	+	0.216805i
$956$		0			0
$957$	7.65366	−	13.2565i	0.00799755	−	0.0138522i
$958$		0			0
$959$	97.3249	+	452.177i	0.101486	+	0.471509i
$960$		0			0
$961$	−439.074	+	760.498i	−0.456892	+	0.791361i
$962$		0			0
$963$	−216.403	+	124.940i	−0.224718	+	0.129741i
$964$		0			0
$965$	53.6591			0.0556052
$966$		0			0
$967$			642.073i			0.663984i	0.943282	+	0.331992i	$0.107721\pi$
$967$			642.073i			0.663984i	−0.943282	+	0.331992i	$0.892279\pi$
$968$		0			0
$969$	−33.2959	−	57.6703i	−0.0343611	−	0.0595152i
$970$		0			0
$971$	747.506	+	431.573i	0.769831	+	0.444462i	0.832814	−	0.553552i	$-0.186728\pi$
$971$	747.506	+	431.573i	0.769831	+	0.444462i	−0.0629831	+	0.998015i	$0.520061\pi$
$972$		0			0
$973$	343.330	−	1065.95i	0.352858	−	1.09553i
$974$		0			0
$975$	−20.4297	−	11.7951i	−0.0209535	−	0.0120975i
$976$		0			0
$977$	−617.289	−	1069.18i	−0.631821	−	1.09435i	−0.987179	−	0.159615i	$-0.948975\pi$
$977$	−617.289	−	1069.18i	−0.631821	−	1.09435i	0.355359	−	0.934730i	$-0.384359\pi$
$978$		0			0
$979$			555.796i			0.567718i
$980$		0			0
$981$	−981.185			−1.00019
$982$		0			0
$983$	1527.89	−	882.128i	1.55431	−	0.897383i	0.556531	−	0.830827i	$-0.312132\pi$
$983$	1527.89	−	882.128i	1.55431	−	0.897383i	0.997783	−	0.0665567i	$-0.0212013\pi$
$984$		0			0
$985$	136.829	−	236.994i	0.138912	−	0.240603i
$986$		0			0
$987$	−3.09454	−	0.996717i	−0.00313530	−	0.00100985i
$988$		0			0
$989$	206.492	−	357.654i	0.208789	−	0.361632i
$990$		0			0
$991$	−196.129	+	113.235i	−0.197910	+	0.114264i	−0.595680	−	0.803222i	$-0.703118\pi$
$991$	−196.129	+	113.235i	−0.197910	+	0.114264i	0.397770	+	0.917485i	$0.369784\pi$
$992$		0			0
$993$	−6.69558			−0.00674278
$994$		0			0
$995$		−	499.245i		−	0.501754i
$996$		0			0
$997$	411.891	+	713.416i	0.413130	+	0.715562i	0.995230	−	0.0975548i	$-0.0311021\pi$
$997$	411.891	+	713.416i	0.413130	+	0.715562i	−0.582100	+	0.813117i	$0.697769\pi$
$998$		0			0
$999$	−1.85132	−	1.06886i	−0.00185318	−	0.00106993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.r.d.191.4	yes	12
4.3	odd	2	inner	224.3.r.d.191.3	yes	12
7.2	even	3		1568.3.d.i.1471.4		6
7.4	even	3	inner	224.3.r.d.95.3	✓	12
7.5	odd	6		1568.3.d.l.1471.3		6
8.3	odd	2		448.3.r.f.191.4		12
8.5	even	2		448.3.r.f.191.3		12
28.11	odd	6	inner	224.3.r.d.95.4	yes	12
28.19	even	6		1568.3.d.l.1471.4		6
28.23	odd	6		1568.3.d.i.1471.3		6
56.11	odd	6		448.3.r.f.319.3		12
56.53	even	6		448.3.r.f.319.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.d.95.3	✓	12	7.4	even	3	inner
224.3.r.d.95.4	yes	12	28.11	odd	6	inner
224.3.r.d.191.3	yes	12	4.3	odd	2	inner
224.3.r.d.191.4	yes	12	1.1	even	1	trivial
448.3.r.f.191.3		12	8.5	even	2
448.3.r.f.191.4		12	8.3	odd	2
448.3.r.f.319.3		12	56.11	odd	6
448.3.r.f.319.4		12	56.53	even	6
1568.3.d.i.1471.3		6	28.23	odd	6
1568.3.d.i.1471.4		6	7.2	even	3
1568.3.d.l.1471.3		6	7.5	odd	6
1568.3.d.l.1471.4		6	28.19	even	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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.100242 - 0.0578747i) q^{3} +(-0.761802 + 1.31948i) q^{5} +(-6.66292 - 2.14605i) q^{7} +(-4.49330 + 7.78263i) q^{9} +O(q^{10})\)	\(q+(0.100242 - 0.0578747i) q^{3} +(-0.761802 + 1.31948i) q^{5} +(-6.66292 - 2.14605i) q^{7} +(-4.49330 + 7.78263i) q^{9} +(-3.61683 + 2.08818i) q^{11} -8.98660 q^{13} +0.176356i q^{15} +(10.8090 + 18.7218i) q^{17} +(-23.0472 - 13.3063i) q^{19} +(-0.792106 + 0.170490i) q^{21} +(-9.94966 - 5.74444i) q^{23} +(11.3393 + 19.6403i) q^{25} +2.08194i q^{27} -31.6652 q^{29} +(-7.88287 + 4.55118i) q^{31} +(-0.241705 + 0.418646i) q^{33} +(7.90750 - 7.15672i) q^{35} +(-0.513398 + 0.889231i) q^{37} +(-0.900834 + 0.520097i) q^{39} +13.6920 q^{41} +35.9464i q^{43} +(-6.84601 - 11.8576i) q^{45} +(3.47491 + 2.00624i) q^{47} +(39.7889 + 28.5979i) q^{49} +(2.16703 + 1.25114i) q^{51} +(-39.7991 - 68.9341i) q^{53} -6.36312i q^{55} -3.08039 q^{57} +(87.8782 - 50.7365i) q^{59} +(35.6078 - 61.6745i) q^{61} +(46.6404 - 42.2121i) q^{63} +(6.84601 - 11.8576i) q^{65} +(-48.0548 + 27.7444i) q^{67} -1.32983 q^{69} +69.2678i q^{71} +(12.6977 + 21.9930i) q^{73} +(2.27335 + 1.31252i) q^{75} +(28.5800 - 6.15145i) q^{77} +(108.959 + 62.9074i) q^{79} +(-40.3192 - 69.8349i) q^{81} +33.3214i q^{83} -32.9373 q^{85} +(-3.17418 + 1.83262i) q^{87} +(66.5408 - 115.252i) q^{89} +(59.8770 + 19.2857i) q^{91} +(-0.526796 + 0.912437i) q^{93} +(35.1147 - 20.2735i) q^{95} -8.98660 q^{97} -37.5313i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{5}+O(q^{10}) \) 12 * q + 18 * q^5	\( 12 q + 18 q^{5} - 6 q^{17} + 18 q^{21} + 186 q^{33} - 114 q^{37} + 180 q^{49} - 18 q^{53} - 684 q^{57} + 318 q^{61} - 228 q^{69} + 342 q^{73} + 318 q^{77} - 186 q^{81} - 996 q^{85} + 150 q^{89} - 222 q^{93}+O(q^{100}) \) 12 * q + 18 * q^5 - 6 * q^17 + 18 * q^21 + 186 * q^33 - 114 * q^37 + 180 * q^49 - 18 * q^53 - 684 * q^57 + 318 * q^61 - 228 * q^69 + 342 * q^73 + 318 * q^77 - 186 * q^81 - 996 * q^85 + 150 * q^89 - 222 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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