LMFDB - Embedded newform 224.3.s.b.33.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("224.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} + \cdots + 208849 $ x^16 - 26x^14 - 16x^13 + 469x^12 + 144x^11 - 4526x^10 + 4440x^9 + 32608x^8 - 33728x^7 - 49760x^6 + 203528x^5 + 27401x^4 - 156928x^3 + 114964x^2 - 248608x + 208849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			33.5
Root			$0.869658 - 0.314400i$ of defining polynomial
Character	$\chi$	$=$	224.33
Dual form			224.3.s.b.129.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.729881 - 0.421397i) q^{3} +(-1.21685 - 0.702550i) q^{5} +(-1.56553 + 6.82269i) q^{7} +(-4.14485 + 7.17909i) q^{9} +O(q^{10})$	\(q+(0.729881 - 0.421397i) q^{3} +(-1.21685 - 0.702550i) q^{5} +(-1.56553 + 6.82269i) q^{7} +(-4.14485 + 7.17909i) q^{9} +(7.44562 + 12.8962i) q^{11} -2.67477i q^{13} -1.18421 q^{15} +(11.7354 - 6.77544i) q^{17} +(25.2564 + 14.5818i) q^{19} +(1.73241 + 5.63947i) q^{21} +(-11.4367 + 19.8089i) q^{23} +(-11.5128 - 19.9408i) q^{25} +14.5717i q^{27} -3.76543 q^{29} +(-11.4937 + 6.63592i) q^{31} +(10.8688 + 6.27513i) q^{33} +(6.69830 - 7.20235i) q^{35} +(-1.32272 + 2.29102i) q^{37} +(-1.12714 - 1.95227i) q^{39} +45.2712i q^{41} +51.5858 q^{43} +(10.0873 - 5.82393i) q^{45} +(-58.1281 - 33.5603i) q^{47} +(-44.0982 - 21.3623i) q^{49} +(5.71030 - 9.89054i) q^{51} +(-19.9616 - 34.5744i) q^{53} -20.9237i q^{55} +24.5789 q^{57} +(11.0804 - 6.39728i) q^{59} +(67.4084 + 38.9182i) q^{61} +(-42.4918 - 39.5181i) q^{63} +(-1.87916 + 3.25480i) q^{65} +(-22.9199 - 39.6985i) q^{67} +19.2775i q^{69} -40.6812 q^{71} +(55.6834 - 32.1488i) q^{73} +(-16.8060 - 9.70296i) q^{75} +(-99.6431 + 30.6098i) q^{77} +(40.2603 - 69.7329i) q^{79} +(-31.1632 - 53.9762i) q^{81} -121.864i q^{83} -19.0403 q^{85} +(-2.74832 + 1.58674i) q^{87} +(-39.7614 - 22.9562i) q^{89} +(18.2492 + 4.18744i) q^{91} +(-5.59271 + 9.68687i) q^{93} +(-20.4889 - 35.4878i) q^{95} +134.268i q^{97} -123.444 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{9}+O(q^{10}) $ 16 * q + 40 * q^9	$ 16 q + 40 q^{9} - 48 q^{17} - 136 q^{21} + 80 q^{25} - 16 q^{29} - 264 q^{33} + 72 q^{37} + 312 q^{45} + 128 q^{49} + 40 q^{53} + 368 q^{57} + 216 q^{61} - 168 q^{65} - 312 q^{73} + 64 q^{77} - 384 q^{81} - 1072 q^{85} + 24 q^{89} - 168 q^{93}+O(q^{100}) $ 16 * q + 40 * q^9 - 48 * q^17 - 136 * q^21 + 80 * q^25 - 16 * q^29 - 264 * q^33 + 72 * q^37 + 312 * q^45 + 128 * q^49 + 40 * q^53 + 368 * q^57 + 216 * q^61 - 168 * q^65 - 312 * q^73 + 64 * q^77 - 384 * q^81 - 1072 * q^85 + 24 * q^89 - 168 * q^93

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.729881	−	0.421397i	0.243294	−	0.140466i	−0.373396	−	0.927672i	$-0.621807\pi$
$3$	0.729881	−	0.421397i	0.243294	−	0.140466i	0.616690	+	0.787206i	$0.288473\pi$
$4$		0			0
$5$	−1.21685	−	0.702550i	−0.243371	−	0.140510i	0.373354	−	0.927689i	$-0.378208\pi$
$5$	−1.21685	−	0.702550i	−0.243371	−	0.140510i	−0.616725	+	0.787179i	$0.711541\pi$
$6$		0			0
$7$	−1.56553	+	6.82269i	−0.223647	+	0.974670i
$7$	−1.56553	+	6.82269i	−0.223647	+	0.974670i
$8$		0			0
$9$	−4.14485	+	7.17909i	−0.460539	+	0.797677i
$10$		0			0
$11$	7.44562	+	12.8962i	0.676874	+	1.17238i	0.975917	+	0.218141i	$0.0699994\pi$
$11$	7.44562	+	12.8962i	0.676874	+	1.17238i	−0.299043	+	0.954240i	$0.596667\pi$
$12$		0			0
$13$		−	2.67477i		−	0.205752i	−0.994694	−	0.102876i	$-0.967196\pi$
$13$		−	2.67477i		−	0.205752i	0.994694	−	0.102876i	$-0.0328045\pi$
$14$		0			0
$15$	−1.18421			−0.0789474
$16$		0			0
$17$	11.7354	−	6.77544i	0.690318	−	0.398555i	−0.113413	−	0.993548i	$-0.536178\pi$
$17$	11.7354	−	6.77544i	0.690318	−	0.398555i	0.803731	+	0.594993i	$0.202845\pi$
$18$		0			0
$19$	25.2564	+	14.5818i	1.32928	+	0.767462i	0.985189	−	0.171473i	$-0.0548526\pi$
$19$	25.2564	+	14.5818i	1.32928	+	0.767462i	0.344095	+	0.938935i	$0.388186\pi$
$20$		0			0
$21$	1.73241	+	5.63947i	0.0824958	+	0.268546i
$22$		0			0
$23$	−11.4367	+	19.8089i	−0.497247	+	0.861257i	−0.999995	−	0.00317621i	$-0.998989\pi$
$23$	−11.4367	+	19.8089i	−0.497247	+	0.861257i	0.502748	+	0.864433i	$0.332322\pi$
$24$		0			0
$25$	−11.5128	−	19.9408i	−0.460514	−	0.797633i
$26$		0			0
$27$			14.5717i			0.539691i
$28$		0			0
$29$	−3.76543			−0.129843			−0.0649213	−	0.997890i	$-0.520680\pi$
$29$	−3.76543			−0.129843			−0.0649213	+	0.997890i	$0.520680\pi$
$30$		0			0
$31$	−11.4937	+	6.63592i	−0.370766	+	0.214062i	−0.673793	−	0.738920i	$-0.735336\pi$
$31$	−11.4937	+	6.63592i	−0.370766	+	0.214062i	0.303027	+	0.952982i	$0.402003\pi$
$32$		0			0
$33$	10.8688	+	6.27513i	0.329359	+	0.190155i
$34$		0			0
$35$	6.69830	−	7.20235i	0.191380	−	0.205781i
$36$		0			0
$37$	−1.32272	+	2.29102i	−0.0357491	+	0.0619193i	−0.883346	−	0.468721i	$-0.844715\pi$
$37$	−1.32272	+	2.29102i	−0.0357491	+	0.0619193i	0.847597	+	0.530640i	$0.178048\pi$
$38$		0			0
$39$	−1.12714	−	1.95227i	−0.0289011	−	0.0500581i
$40$		0			0
$41$			45.2712i			1.10417i	0.833786	+	0.552087i	$0.186168\pi$
$41$			45.2712i			1.10417i	−0.833786	+	0.552087i	$0.813832\pi$
$42$		0			0
$43$	51.5858			1.19967			0.599834	−	0.800124i	$-0.295233\pi$
$43$	51.5858			1.19967			0.599834	+	0.800124i	$0.295233\pi$
$44$		0			0
$45$	10.0873	−	5.82393i	0.224163	−	0.129421i
$46$		0			0
$47$	−58.1281	−	33.5603i	−1.23677	−	0.714049i	−0.268336	−	0.963325i	$-0.586474\pi$
$47$	−58.1281	−	33.5603i	−1.23677	−	0.714049i	−0.968432	+	0.249276i	$0.919807\pi$
$48$		0			0
$49$	−44.0982	−	21.3623i	−0.899964	−	0.435964i
$50$		0			0
$51$	5.71030	−	9.89054i	0.111967	−	0.193932i
$52$		0			0
$53$	−19.9616	−	34.5744i	−0.376633	−	0.652348i	0.613937	−	0.789355i	$-0.289585\pi$
$53$	−19.9616	−	34.5744i	−0.376633	−	0.652348i	−0.990570	+	0.137007i	$0.956252\pi$
$54$		0			0
$55$		−	20.9237i		−	0.380431i
$56$		0			0
$57$	24.5789			0.431209
$58$		0			0
$59$	11.0804	−	6.39728i	0.187804	−	0.108429i	−0.403150	−	0.915134i	$-0.632085\pi$
$59$	11.0804	−	6.39728i	0.187804	−	0.108429i	0.590954	+	0.806705i	$0.298751\pi$
$60$		0			0
$61$	67.4084	+	38.9182i	1.10506	+	0.638004i	0.937544	−	0.347866i	$-0.113094\pi$
$61$	67.4084	+	38.9182i	1.10506	+	0.638004i	0.167511	+	0.985870i	$0.446427\pi$
$62$		0			0
$63$	−42.4918	−	39.5181i	−0.674473	−	0.627271i
$64$		0			0
$65$	−1.87916	+	3.25480i	−0.0289102	+	0.0500739i
$66$		0			0
$67$	−22.9199	−	39.6985i	−0.342089	−	0.592515i	0.642732	−	0.766091i	$-0.277801\pi$
$67$	−22.9199	−	39.6985i	−0.342089	−	0.592515i	−0.984820	+	0.173576i	$0.944468\pi$
$68$		0			0
$69$			19.2775i			0.279385i
$70$		0			0
$71$	−40.6812			−0.572975			−0.286487	−	0.958084i	$-0.592488\pi$
$71$	−40.6812			−0.572975			−0.286487	+	0.958084i	$0.592488\pi$
$72$		0			0
$73$	55.6834	−	32.1488i	0.762786	−	0.440395i	−0.0675092	−	0.997719i	$-0.521505\pi$
$73$	55.6834	−	32.1488i	0.762786	−	0.440395i	0.830295	+	0.557324i	$0.188172\pi$
$74$		0			0
$75$	−16.8060	−	9.70296i	−0.224080	−	0.129373i
$76$		0			0
$77$	−99.6431	+	30.6098i	−1.29407	+	0.397530i
$78$		0			0
$79$	40.2603	−	69.7329i	0.509624	−	0.882695i	−0.490314	−	0.871546i	$-0.663118\pi$
$79$	40.2603	−	69.7329i	0.509624	−	0.882695i	0.999938	−	0.0111488i	$-0.00354885\pi$
$80$		0			0
$81$	−31.1632	−	53.9762i	−0.384731	−	0.666373i
$82$		0			0
$83$		−	121.864i		−	1.46824i	−0.679021	−	0.734118i	$-0.737596\pi$
$83$		−	121.864i		−	1.46824i	0.679021	−	0.734118i	$-0.262404\pi$
$84$		0			0
$85$	−19.0403			−0.224004
$86$		0			0
$87$	−2.74832	+	1.58674i	−0.0315899	+	0.0182384i
$88$		0			0
$89$	−39.7614	−	22.9562i	−0.446757	−	0.257935i	0.259703	−	0.965689i	$-0.416375\pi$
$89$	−39.7614	−	22.9562i	−0.446757	−	0.257935i	−0.706460	+	0.707753i	$0.749709\pi$
$90$		0			0
$91$	18.2492	+	4.18744i	0.200540	+	0.0460158i
$92$		0			0
$93$	−5.59271	+	9.68687i	−0.0601367	+	0.104160i
$94$		0			0
$95$	−20.4889	−	35.4878i	−0.215672	−	0.373555i
$96$		0			0
$97$			134.268i			1.38421i	0.721798	+	0.692104i	$0.243316\pi$
$97$			134.268i			1.38421i	−0.721798	+	0.692104i	$0.756684\pi$
$98$		0			0
$99$	−123.444			−1.24691
$100$		0			0
$101$	170.810	−	98.6169i	1.69118	−	0.976405i	0.737619	−	0.675218i	$-0.235950\pi$
$101$	170.810	−	98.6169i	1.69118	−	0.976405i	0.953565	−	0.301188i	$-0.0973831\pi$
$102$		0			0
$103$	121.371	+	70.0736i	1.17836	+	0.680326i	0.955635	−	0.294555i	$-0.0951714\pi$
$103$	121.371	+	70.0736i	1.17836	+	0.680326i	0.222725	+	0.974881i	$0.428505\pi$
$104$		0			0
$105$	1.85392	−	8.07950i	0.0176564	−	0.0769477i
$106$		0			0
$107$	−53.0099	+	91.8159i	−0.495420	+	0.858093i	−0.999986	−	0.00528051i	$-0.998319\pi$
$107$	−53.0099	+	91.8159i	−0.495420	+	0.858093i	0.504566	+	0.863373i	$0.331652\pi$
$108$		0			0
$109$	−71.3762	−	123.627i	−0.654828	−	1.13419i	−0.981937	−	0.189208i	$-0.939408\pi$
$109$	−71.3762	−	123.627i	−0.654828	−	1.13419i	0.327109	−	0.944986i	$-0.393925\pi$
$110$		0			0
$111$			2.22956i			0.0200861i
$112$		0			0
$113$	108.519			0.960344			0.480172	−	0.877174i	$-0.340574\pi$
$113$	108.519			0.960344			0.480172	+	0.877174i	$0.340574\pi$
$114$		0			0
$115$	27.8335	−	16.0697i	0.242030	−	0.139736i
$116$		0			0
$117$	19.2024	+	11.0865i	0.164123	+	0.0947567i
$118$		0			0
$119$	27.8546	+	90.6742i	0.234072	+	0.761968i
$120$		0			0
$121$	−50.3745	+	87.2512i	−0.416318	+	0.721084i
$122$		0			0
$123$	19.0771	+	33.0426i	0.155099	+	0.268639i
$124$		0			0
$125$			67.4809i			0.539847i
$126$		0			0
$127$	139.789			1.10070			0.550351	−	0.834934i	$-0.314494\pi$
$127$	139.789			1.10070			0.550351	+	0.834934i	$0.314494\pi$
$128$		0			0
$129$	37.6515	−	21.7381i	0.291872	−	0.168512i
$130$		0			0
$131$	−82.2943	−	47.5126i	−0.628200	−	0.362692i	0.151854	−	0.988403i	$-0.451476\pi$
$131$	−82.2943	−	47.5126i	−0.628200	−	0.362692i	−0.780055	+	0.625711i	$0.784809\pi$
$132$		0			0
$133$	−139.027	+	149.488i	−1.04531	+	1.12397i
$134$		0			0
$135$	10.2373	−	17.7316i	0.0758320	−	0.131345i
$136$		0			0
$137$	−76.7845	−	132.995i	−0.560471	−	0.970764i	−0.997455	−	0.0712949i	$-0.977287\pi$
$137$	−76.7845	−	132.995i	−0.560471	−	0.970764i	0.436984	−	0.899469i	$-0.356046\pi$
$138$		0			0
$139$			217.529i			1.56496i	0.622676	+	0.782480i	$0.286046\pi$
$139$			217.529i			1.56496i	−0.622676	+	0.782480i	$0.713954\pi$
$140$		0			0
$141$	−56.5689			−0.401198
$142$		0			0
$143$	34.4944	−	19.9153i	0.241219	−	0.139268i
$144$		0			0
$145$	4.58198	+	2.64541i	0.0315998	+	0.0182442i
$146$		0			0
$147$	−41.1885	+	2.99096i	−0.280194	+	0.0203467i
$148$		0			0
$149$	−32.0451	+	55.5037i	−0.215068	+	0.372508i	−0.953294	−	0.302045i	$-0.902331\pi$
$149$	−32.0451	+	55.5037i	−0.215068	+	0.372508i	0.738226	+	0.674554i	$0.235664\pi$
$150$		0			0
$151$	136.023	+	235.598i	0.900813	+	1.56025i	0.826440	+	0.563024i	$0.190362\pi$
$151$	136.023	+	235.598i	0.900813	+	1.56025i	0.0743729	+	0.997230i	$0.476304\pi$
$152$		0			0
$153$			112.333i			0.734201i
$154$		0			0
$155$	18.6483			0.120311
$156$		0			0
$157$	187.295	−	108.135i	1.19296	−	0.688757i	0.233984	−	0.972240i	$-0.424824\pi$
$157$	187.295	−	108.135i	1.19296	−	0.688757i	0.958977	+	0.283484i	$0.0914902\pi$
$158$		0			0
$159$	−29.1391	−	16.8235i	−0.183265	−	0.105808i
$160$		0			0
$161$	−117.246	−	109.040i	−0.728233	−	0.677269i
$162$		0			0
$163$	27.3465	−	47.3655i	0.167770	−	0.290586i	−0.769866	−	0.638206i	$-0.779677\pi$
$163$	27.3465	−	47.3655i	0.167770	−	0.290586i	0.937635	+	0.347620i	$0.113010\pi$
$164$		0			0
$165$	−8.81718	−	15.2718i	−0.0534375	−	0.0925564i
$166$		0			0
$167$			248.098i			1.48562i	0.669504	+	0.742809i	$0.266507\pi$
$167$			248.098i			1.48562i	−0.669504	+	0.742809i	$0.733493\pi$
$168$		0			0
$169$	161.846			0.957666
$170$		0			0
$171$	−209.368	+	120.879i	−1.22437	+	0.706892i
$172$		0			0
$173$	224.883	+	129.836i	1.29990	+	0.750499i	0.980387	−	0.197082i	$-0.0631467\pi$
$173$	224.883	+	129.836i	1.29990	+	0.750499i	0.319515	+	0.947581i	$0.396480\pi$
$174$		0			0
$175$	154.074	−	47.3306i	0.880422	−	0.270461i
$176$		0			0
$177$	5.39159	−	9.33851i	0.0304610	−	0.0527600i
$178$		0			0
$179$	−69.0883	−	119.664i	−0.385968	−	0.668516i	0.605935	−	0.795514i	$-0.292799\pi$
$179$	−69.0883	−	119.664i	−0.385968	−	0.668516i	−0.991903	+	0.126998i	$0.959466\pi$
$180$		0			0
$181$		−	114.497i		−	0.632579i	−0.948663	−	0.316290i	$-0.897563\pi$
$181$		−	114.497i		−	0.632579i	0.948663	−	0.316290i	$-0.102437\pi$
$182$		0			0
$183$	65.6001			0.358471
$184$		0			0
$185$	3.21911	−	1.85855i	0.0174006	−	0.0100462i
$186$		0			0
$187$	174.755	+	100.895i	0.934517	+	0.539544i
$188$		0			0
$189$	−99.4180	−	22.8124i	−0.526021	−	0.120700i
$190$		0			0
$191$	−76.2145	+	132.007i	−0.399029	+	0.691138i	−0.993606	−	0.112900i	$-0.963986\pi$
$191$	−76.2145	+	132.007i	−0.399029	+	0.691138i	0.594578	+	0.804038i	$0.297319\pi$
$192$		0			0
$193$	−121.156	−	209.848i	−0.627749	−	1.08729i	−0.988002	−	0.154439i	$-0.950643\pi$
$193$	−121.156	−	209.848i	−0.627749	−	1.08729i	0.360253	−	0.932855i	$-0.382690\pi$
$194$		0			0
$195$			3.16750i			0.0162436i
$196$		0			0
$197$	−197.518			−1.00263			−0.501314	−	0.865265i	$-0.667150\pi$
$197$	−197.518			−1.00263			−0.501314	+	0.865265i	$0.667150\pi$
$198$		0			0
$199$	142.172	−	82.0833i	0.714435	−	0.412479i	−0.0982663	−	0.995160i	$-0.531330\pi$
$199$	142.172	−	82.0833i	0.714435	−	0.412479i	0.812701	+	0.582681i	$0.197996\pi$
$200$		0			0
$201$	−33.4577	−	19.3168i	−0.166456	−	0.0961035i
$202$		0			0
$203$	5.89490	−	25.6904i	0.0290389	−	0.126554i
$204$		0			0
$205$	31.8053	−	55.0883i	0.155148	−	0.268724i
$206$		0			0
$207$	−94.8066	−	164.210i	−0.458003	−	0.793284i
$208$		0			0
$209$			434.282i			2.07790i
$210$		0			0
$211$	−53.1445			−0.251870			−0.125935	−	0.992039i	$-0.540193\pi$
$211$	−53.1445			−0.251870			−0.125935	+	0.992039i	$0.540193\pi$
$212$		0			0
$213$	−29.6925	+	17.1429i	−0.139401	+	0.0804833i
$214$		0			0
$215$	−62.7723	−	36.2416i	−0.291964	−	0.168565i
$216$		0			0
$217$	−27.2810	−	88.8070i	−0.125719	−	0.409249i
$218$		0			0
$219$	27.0948	−	46.9296i	0.123721	−	0.214291i
$220$		0			0
$221$	−18.1228	−	31.3896i	−0.0820035	−	0.142034i
$222$		0			0
$223$		−	310.755i		−	1.39352i	−0.717303	−	0.696761i	$-0.754624\pi$
$223$		−	310.755i		−	1.39352i	0.717303	−	0.696761i	$-0.245376\pi$
$224$		0			0
$225$	190.876			0.848338
$226$		0			0
$227$	43.2131	−	24.9491i	0.190366	−	0.109908i	−0.401788	−	0.915733i	$-0.631611\pi$
$227$	43.2131	−	24.9491i	0.190366	−	0.109908i	0.592154	+	0.805825i	$0.298278\pi$
$228$		0			0
$229$	182.833	+	105.559i	0.798398	+	0.460955i	0.842911	−	0.538054i	$-0.180840\pi$
$229$	182.833	+	105.559i	0.798398	+	0.460955i	−0.0445127	+	0.999009i	$0.514174\pi$
$230$		0			0
$231$	−59.8287	+	64.3308i	−0.258999	+	0.278488i
$232$		0			0
$233$	−37.7274	+	65.3457i	−0.161920	+	0.280454i	−0.935557	−	0.353175i	$-0.885102\pi$
$233$	−37.7274	+	65.3457i	−0.161920	+	0.280454i	0.773637	+	0.633629i	$0.218435\pi$
$234$		0			0
$235$	47.1556	+	81.6759i	0.200662	+	0.347557i
$236$		0			0
$237$		−	67.8623i		−	0.286339i
$238$		0			0
$239$	−310.396			−1.29873			−0.649365	−	0.760477i	$-0.724965\pi$
$239$	−310.396			−1.29873			−0.649365	+	0.760477i	$0.724965\pi$
$240$		0			0
$241$	93.7200	−	54.1093i	0.388880	−	0.224520i	−0.292795	−	0.956175i	$-0.594585\pi$
$241$	93.7200	−	54.1093i	0.388880	−	0.224520i	0.681675	+	0.731656i	$0.261252\pi$
$242$		0			0
$243$	−159.066	−	91.8366i	−0.654591	−	0.377929i
$244$		0			0
$245$	38.6530	+	56.9759i	0.157767	+	0.232555i
$246$		0			0
$247$	39.0030	−	67.5551i	0.157907	−	0.273502i
$248$		0			0
$249$	−51.3530	−	88.9460i	−0.206237	−	0.357213i
$250$		0			0
$251$		−	302.023i		−	1.20328i	−0.798768	−	0.601639i	$-0.794515\pi$
$251$		−	302.023i		−	1.20328i	0.798768	−	0.601639i	$-0.205485\pi$
$252$		0			0
$253$	−340.613			−1.34629
$254$		0			0
$255$	−13.8972	+	8.02355i	−0.0544988	+	0.0314649i
$256$		0			0
$257$	−89.8068	−	51.8500i	−0.349443	−	0.201751i	0.314997	−	0.949093i	$-0.397996\pi$
$257$	−89.8068	−	51.8500i	−0.349443	−	0.201751i	−0.664440	+	0.747342i	$0.731330\pi$
$258$		0			0
$259$	−13.5601	−	12.6112i	−0.0523557	−	0.0486917i
$260$		0			0
$261$	15.6072	−	27.0324i	0.0597975	−	0.103572i
$262$		0			0
$263$	−128.972	−	223.386i	−0.490387	−	0.849375i	0.509552	−	0.860440i	$-0.329811\pi$
$263$	−128.972	−	223.386i	−0.490387	−	0.849375i	−0.999939	+	0.0110651i	$0.996478\pi$
$264$		0			0
$265$			56.0960i			0.211683i
$266$		0			0
$267$	−38.6948			−0.144924
$268$		0			0
$269$	140.523	−	81.1310i	0.522390	−	0.301602i	−0.215522	−	0.976499i	$-0.569145\pi$
$269$	140.523	−	81.1310i	0.522390	−	0.301602i	0.737912	+	0.674897i	$0.235812\pi$
$270$		0			0
$271$	−54.3429	−	31.3749i	−0.200527	−	0.115775i	0.396374	−	0.918089i	$-0.370268\pi$
$271$	−54.3429	−	31.3749i	−0.200527	−	0.115775i	−0.596901	+	0.802315i	$0.703602\pi$
$272$		0			0
$273$	15.0843	−	4.63381i	0.0552538	−	0.0169737i
$274$		0			0
$275$	171.441	−	296.944i	0.623420	−	1.07980i
$276$		0			0
$277$	128.576	+	222.701i	0.464175	+	0.803974i	0.999164	−	0.0408848i	$-0.0130177\pi$
$277$	128.576	+	222.701i	0.464175	+	0.803974i	−0.534989	+	0.844859i	$0.679684\pi$
$278$		0			0
$279$		−	110.019i		−	0.394335i
$280$		0			0
$281$	230.243			0.819369			0.409685	−	0.912227i	$-0.365639\pi$
$281$	230.243			0.819369			0.409685	+	0.912227i	$0.365639\pi$
$282$		0			0
$283$	354.637	−	204.750i	1.25313	−	0.723497i	0.281402	−	0.959590i	$-0.409200\pi$
$283$	354.637	−	204.750i	1.25313	−	0.723497i	0.971730	+	0.236093i	$0.0758671\pi$
$284$		0			0
$285$	−29.9089	−	17.2679i	−0.104943	−	0.0605891i
$286$		0			0
$287$	−308.871	−	70.8733i	−1.07621	−	0.246945i
$288$		0			0
$289$	−52.6868	+	91.2562i	−0.182307	+	0.315765i
$290$		0			0
$291$	56.5803	+	97.9999i	0.194434	+	0.336769i
$292$		0			0
$293$		−	438.106i		−	1.49524i	−0.664126	−	0.747621i	$-0.731196\pi$
$293$		−	438.106i		−	1.49524i	0.664126	−	0.747621i	$-0.268804\pi$
$294$		0			0
$295$	−17.9776			−0.0609412
$296$		0			0
$297$	−187.919	+	108.495i	−0.632724	+	0.365303i
$298$		0			0
$299$	52.9843	+	30.5905i	0.177205	+	0.102309i
$300$		0			0
$301$	−80.7590	+	351.954i	−0.268302	+	1.16928i
$302$		0			0
$303$	83.1138	−	143.957i	0.274303	−	0.475107i
$304$		0			0
$305$	−54.6840	−	94.7155i	−0.179292	−	0.310543i
$306$		0			0
$307$			136.514i			0.444672i	0.974970	+	0.222336i	$0.0713682\pi$
$307$			136.514i			0.444672i	−0.974970	+	0.222336i	$0.928632\pi$
$308$		0			0
$309$	118.115			0.382250
$310$		0			0
$311$	−503.092	+	290.461i	−1.61766	+	0.933957i	−0.630138	+	0.776484i	$0.717001\pi$
$311$	−503.092	+	290.461i	−1.61766	+	0.933957i	−0.987523	+	0.157473i	$0.949665\pi$
$312$		0			0
$313$	−162.118	−	93.5987i	−0.517948	−	0.299037i	0.218147	−	0.975916i	$-0.429999\pi$
$313$	−162.118	−	93.5987i	−0.517948	−	0.299037i	−0.736095	+	0.676879i	$0.763332\pi$
$314$		0			0
$315$	23.9428	+	77.9403i	0.0760090	+	0.247430i
$316$		0			0
$317$	−82.9440	+	143.663i	−0.261653	+	0.453196i	−0.966681	−	0.255983i	$-0.917601\pi$
$317$	−82.9440	+	143.663i	−0.261653	+	0.453196i	0.705028	+	0.709179i	$0.250934\pi$
$318$		0			0
$319$	−28.0360	−	48.5597i	−0.0878871	−	0.152225i
$320$		0			0
$321$			89.3530i			0.278358i
$322$		0			0
$323$	395.192			1.22350
$324$		0			0
$325$	−53.3372	+	30.7943i	−0.164115	+	0.0947516i
$326$		0			0
$327$	−104.192	−	60.1555i	−0.318631	−	0.183962i
$328$		0			0
$329$	319.973	−	344.051i	0.972562	−	1.04575i
$330$		0			0
$331$	−209.099	+	362.170i	−0.631719	+	1.09417i	0.355481	+	0.934683i	$0.384317\pi$
$331$	−209.099	+	362.170i	−0.631719	+	1.09417i	−0.987200	+	0.159486i	$0.949016\pi$
$332$		0			0
$333$	−10.9649	−	18.9918i	−0.0329277	−	0.0570325i
$334$		0			0
$335$			64.4096i			0.192268i
$336$		0			0
$337$	104.000			0.308607			0.154303	−	0.988024i	$-0.450687\pi$
$337$	104.000			0.308607			0.154303	+	0.988024i	$0.450687\pi$
$338$		0			0
$339$	79.2059	−	45.7295i	0.233646	−	0.134895i
$340$		0			0
$341$	−171.156	−	98.8170i	−0.501924	−	0.289786i
$342$		0			0
$343$	214.785	−	267.425i	0.626196	−	0.779666i
$344$		0			0
$345$	13.5434	−	23.4579i	0.0392563	−	0.0679940i
$346$		0			0
$347$	48.9796	+	84.8352i	0.141152	+	0.244482i	0.927931	−	0.372753i	$-0.121586\pi$
$347$	48.9796	+	84.8352i	0.141152	+	0.244482i	−0.786779	+	0.617235i	$0.788253\pi$
$348$		0			0
$349$		−	248.606i		−	0.712339i	−0.934421	−	0.356169i	$-0.884083\pi$
$349$		−	248.606i		−	0.712339i	0.934421	−	0.356169i	$-0.115917\pi$
$350$		0			0
$351$	38.9759			0.111042
$352$		0			0
$353$	−113.804	+	65.7047i	−0.322390	+	0.186132i	−0.652458	−	0.757825i	$-0.726262\pi$
$353$	−113.804	+	65.7047i	−0.322390	+	0.186132i	0.330067	+	0.943957i	$0.392929\pi$
$354$		0			0
$355$	49.5030	+	28.5806i	0.139445	+	0.0805087i
$356$		0			0
$357$	58.5404	+	54.4436i	0.163979	+	0.152503i
$358$		0			0
$359$	−176.634	+	305.939i	−0.492016	+	0.852196i	−0.999958	−	0.00919491i	$-0.997073\pi$
$359$	−176.634	+	305.939i	−0.492016	+	0.852196i	0.507942	+	0.861391i	$0.330406\pi$
$360$		0			0
$361$	244.757	+	423.931i	0.677996	+	1.17432i
$362$		0			0
$363$			84.9107i			0.233914i
$364$		0			0
$365$	−90.3446			−0.247519
$366$		0			0
$367$	−105.306	+	60.7983i	−0.286937	+	0.165663i	−0.636560	−	0.771228i	$-0.719643\pi$
$367$	−105.306	+	60.7983i	−0.286937	+	0.165663i	0.349623	+	0.936891i	$0.386310\pi$
$368$		0			0
$369$	−325.006	−	187.642i	−0.880774	−	0.508515i
$370$		0			0
$371$	267.141	−	82.0642i	0.720057	−	0.221197i
$372$		0			0
$373$	245.458	−	425.145i	0.658063	−	1.13980i	−0.323053	−	0.946381i	$-0.604709\pi$
$373$	245.458	−	425.145i	0.658063	−	1.13980i	0.981116	−	0.193418i	$-0.0619573\pi$
$374$		0			0
$375$	28.4363	+	49.2531i	0.0758301	+	0.131342i
$376$		0			0
$377$			10.0717i			0.0267153i
$378$		0			0
$379$	325.094			0.857768			0.428884	−	0.903360i	$-0.358907\pi$
$379$	325.094			0.857768			0.428884	+	0.903360i	$0.358907\pi$
$380$		0			0
$381$	102.029	−	58.9067i	0.267794	−	0.154611i
$382$		0			0
$383$	385.028	+	222.296i	1.00529	+	0.580407i	0.909810	−	0.415024i	$-0.136227\pi$
$383$	385.028	+	222.296i	1.00529	+	0.580407i	0.0954837	+	0.995431i	$0.469560\pi$
$384$		0			0
$385$	142.756	+	32.7567i	0.370794	+	0.0850822i
$386$		0			0
$387$	−213.815	+	370.339i	−0.552494	+	0.956948i
$388$		0			0
$389$	209.219	+	362.379i	0.537839	+	0.931565i	0.999020	+	0.0442585i	$0.0140925\pi$
$389$	209.219	+	362.379i	0.537839	+	0.931565i	−0.461181	+	0.887306i	$0.652574\pi$
$390$		0			0
$391$			309.954i			0.792721i
$392$		0			0
$393$	−80.0867			−0.203783
$394$		0			0
$395$	−97.9817	+	56.5698i	−0.248055	+	0.143215i
$396$		0			0
$397$	378.814	+	218.708i	0.954192	+	0.550903i	0.894381	−	0.447307i	$-0.147617\pi$
$397$	378.814	+	218.708i	0.954192	+	0.550903i	0.0598112	+	0.998210i	$0.480950\pi$
$398$		0			0
$399$	−38.4790	+	167.694i	−0.0964385	+	0.420286i
$400$		0			0
$401$	45.2362	−	78.3513i	0.112808	−	0.195390i	−0.804093	−	0.594503i	$-0.797349\pi$
$401$	45.2362	−	78.3513i	0.112808	−	0.195390i	0.916902	+	0.399113i	$0.130682\pi$
$402$		0			0
$403$	17.7496	+	30.7432i	0.0440436	+	0.0762858i
$404$		0			0
$405$			87.5748i			0.216234i
$406$		0			0
$407$	−39.3938			−0.0967907
$408$		0			0
$409$	−607.126	+	350.524i	−1.48442	+	0.857028i	−0.999843	−	0.0177233i	$-0.994358\pi$
$409$	−607.126	+	350.524i	−1.48442	+	0.857028i	−0.484573	+	0.874751i	$0.661025\pi$
$410$		0			0
$411$	−112.087	−	64.7136i	−0.272718	−	0.157454i
$412$		0			0
$413$	26.3000	+	85.6134i	0.0636803	+	0.207296i
$414$		0			0
$415$	−85.6153	+	148.290i	−0.206302	+	0.357326i
$416$		0			0
$417$	91.6663	+	158.771i	0.219823	+	0.380745i
$418$		0			0
$419$			374.252i			0.893202i	0.894733	+	0.446601i	$0.147366\pi$
$419$			374.252i			0.893202i	−0.894733	+	0.446601i	$0.852634\pi$
$420$		0			0
$421$	−733.801			−1.74299			−0.871497	−	0.490400i	$-0.836851\pi$
$421$	−733.801			−1.74299			−0.871497	+	0.490400i	$0.836851\pi$
$422$		0			0
$423$	481.865	−	278.205i	1.13916	−	0.657694i
$424$		0			0
$425$	−270.216	−	156.009i	−0.635802	−	0.367081i
$426$		0			0
$427$	−371.057	+	398.979i	−0.868986	+	0.934376i
$428$		0			0
$429$	16.7845	−	29.0717i	0.0391248	−	0.0677662i
$430$		0			0
$431$	416.503	+	721.405i	0.966365	+	1.67379i	0.705903	+	0.708308i	$0.250541\pi$
$431$	416.503	+	721.405i	0.966365	+	1.67379i	0.260462	+	0.965484i	$0.416125\pi$
$432$		0			0
$433$		−	414.085i		−	0.956316i	−0.878274	−	0.478158i	$-0.841305\pi$
$433$		−	414.085i		−	0.956316i	0.878274	−	0.478158i	$-0.158695\pi$
$434$		0			0
$435$	4.45907			0.0102507
$436$		0			0
$437$	−577.698	+	333.534i	−1.32196	+	0.763236i
$438$		0			0
$439$	−61.9802	−	35.7843i	−0.141185	−	0.0815132i	0.427744	−	0.903900i	$-0.359309\pi$
$439$	−61.9802	−	35.7843i	−0.141185	−	0.0815132i	−0.568929	+	0.822387i	$0.692642\pi$
$440$		0			0
$441$	336.142	−	228.042i	0.762227	−	0.517102i
$442$		0			0
$443$	414.628	−	718.157i	0.935956	−	1.62112i	0.163035	−	0.986620i	$-0.447872\pi$
$443$	414.628	−	718.157i	0.935956	−	1.62112i	0.772921	−	0.634503i	$-0.218795\pi$
$444$		0			0
$445$	32.2558	+	55.8687i	0.0724850	+	0.125548i
$446$		0			0
$447$			54.0149i			0.120839i
$448$		0			0
$449$	247.153			0.550452			0.275226	−	0.961380i	$-0.411247\pi$
$449$	247.153			0.550452			0.275226	+	0.961380i	$0.411247\pi$
$450$		0			0
$451$	−583.825	+	337.072i	−1.29451	+	0.747388i
$452$		0			0
$453$	198.561	+	114.639i	0.438325	+	0.253067i
$454$		0			0
$455$	−19.2646	−	17.9164i	−0.0423399	−	0.0393768i
$456$		0			0
$457$	240.746	−	416.984i	0.526796	−	0.912437i	−0.472717	−	0.881214i	$-0.656727\pi$
$457$	240.746	−	416.984i	0.526796	−	0.912437i	0.999512	−	0.0312226i	$-0.00994009\pi$
$458$		0			0
$459$	98.7294	+	171.004i	0.215097	+	0.372559i
$460$		0			0
$461$		−	256.190i		−	0.555727i	−0.960621	−	0.277863i	$-0.910374\pi$
$461$		−	256.190i		−	0.555727i	0.960621	−	0.277863i	$-0.0896263\pi$
$462$		0			0
$463$	142.004			0.306705			0.153353	−	0.988172i	$-0.450993\pi$
$463$	142.004			0.306705			0.153353	+	0.988172i	$0.450993\pi$
$464$		0			0
$465$	13.6110	−	7.85832i	0.0292710	−	0.0168996i
$466$		0			0
$467$	375.153	+	216.594i	0.803324	+	0.463800i	0.844632	−	0.535347i	$-0.179819\pi$
$467$	375.153	+	216.594i	0.803324	+	0.463800i	−0.0413078	+	0.999146i	$0.513152\pi$
$468$		0			0
$469$	306.732	−	94.2265i	0.654014	−	0.200909i
$470$		0			0
$471$	91.1354	−	157.851i	0.193493	−	0.335140i
$472$		0			0
$473$	384.088	+	665.260i	0.812025	+	1.40647i
$474$		0			0
$475$		−	671.511i		−	1.41371i
$476$		0			0
$477$	330.950			0.693816
$478$		0			0
$479$	227.894	−	131.575i	0.475770	−	0.274686i	−0.242882	−	0.970056i	$-0.578093\pi$
$479$	227.894	−	131.575i	0.475770	−	0.274686i	0.718652	+	0.695370i	$0.244759\pi$
$480$		0			0
$481$	6.12795	+	3.53797i	0.0127400	+	0.00735545i
$482$		0			0
$483$	−131.525	−	30.1796i	−0.272308	−	0.0624836i
$484$		0			0
$485$	94.3302	−	163.385i	0.194495	−	0.336876i
$486$		0			0
$487$	−338.504	−	586.307i	−0.695081	−	1.20392i	−0.970153	−	0.242492i	$-0.922035\pi$
$487$	−338.504	−	586.307i	−0.695081	−	1.20392i	0.275072	−	0.961424i	$-0.411298\pi$
$488$		0			0
$489$		−	46.0950i		−	0.0942637i
$490$		0			0
$491$	−807.748			−1.64511			−0.822554	−	0.568686i	$-0.807452\pi$
$491$	−807.748			−1.64511			−0.822554	+	0.568686i	$0.807452\pi$
$492$		0			0
$493$	−44.1889	+	25.5125i	−0.0896326	+	0.0517494i
$494$		0			0
$495$	150.213	+	86.7255i	0.303461	+	0.175203i
$496$		0			0
$497$	63.6876	−	277.555i	0.128144	−	0.558461i
$498$		0			0
$499$	−78.2519	+	135.536i	−0.156817	+	0.271616i	−0.933719	−	0.358006i	$-0.883457\pi$
$499$	−78.2519	+	135.536i	−0.156817	+	0.271616i	0.776902	+	0.629622i	$0.216790\pi$
$500$		0			0
$501$	104.548	+	181.082i	0.208678	+	0.361441i
$502$		0			0
$503$		−	499.753i		−	0.993545i	−0.867881	−	0.496773i	$-0.834518\pi$
$503$		−	499.753i		−	0.993545i	0.867881	−	0.496773i	$-0.165482\pi$
$504$		0			0
$505$	−277.133			−0.548779
$506$		0			0
$507$	118.128	−	68.2013i	0.232994	−	0.134519i
$508$		0			0
$509$	−462.478	−	267.012i	−0.908602	−	0.524582i	−0.0286209	−	0.999590i	$-0.509112\pi$
$509$	−462.478	−	267.012i	−0.908602	−	0.524582i	−0.879981	+	0.475009i	$0.842445\pi$
$510$		0			0
$511$	132.167	+	430.240i	0.258645	+	0.841958i
$512$		0			0
$513$	−212.481	+	368.027i	−0.414193	+	0.717403i
$514$		0			0
$515$	−98.4604	−	170.538i	−0.191185	−	0.331143i
$516$		0			0
$517$		−	999.509i		−	1.93329i
$518$		0			0
$519$	218.851			0.421677
$520$		0			0
$521$	−623.856	+	360.184i	−1.19742	+	0.691331i	−0.959979	−	0.280070i	$-0.909642\pi$
$521$	−623.856	+	360.184i	−1.19742	+	0.691331i	−0.237442	+	0.971402i	$0.576309\pi$
$522$		0			0
$523$	−523.499	−	302.243i	−1.00095	−	0.577902i	−0.0924242	−	0.995720i	$-0.529462\pi$
$523$	−523.499	−	302.243i	−1.00095	−	0.577902i	−0.908531	+	0.417818i	$0.862795\pi$
$524$		0			0
$525$	92.5107	−	99.4721i	0.176211	−	0.189471i
$526$		0			0
$527$	−89.9225	+	155.750i	−0.170631	+	0.295542i
$528$		0			0
$529$	2.90487	+	5.03138i	0.00549125	+	0.00951112i
$530$		0			0
$531$			106.063i			0.199742i
$532$		0			0
$533$	121.090			0.227186
$534$		0			0
$535$	129.011	−	74.4843i	0.241141	−	0.139223i
$536$		0			0
$537$	−100.853	−	58.2272i	−0.187807	−	0.108431i
$538$		0			0
$539$	−52.8470	−	727.754i	−0.0980463	−	1.35019i
$540$		0			0
$541$	−177.344	+	307.168i	−0.327807	+	0.567779i	−0.982077	−	0.188483i	$-0.939643\pi$
$541$	−177.344	+	307.168i	−0.327807	+	0.567779i	0.654269	+	0.756262i	$0.272976\pi$
$542$		0			0
$543$	−48.2487	−	83.5692i	−0.0888557	−	0.153903i
$544$		0			0
$545$			200.581i			0.368039i
$546$		0			0
$547$	−867.407			−1.58575			−0.792877	−	0.609382i	$-0.791417\pi$
$547$	−867.407			−1.58575			−0.792877	+	0.609382i	$0.791417\pi$
$548$		0			0
$549$	−558.795	+	322.620i	−1.01784	+	0.587651i
$550$		0			0
$551$	−95.1012	−	54.9067i	−0.172597	−	0.0996492i
$552$		0			0
$553$	412.737	+	383.853i	0.746360	+	0.694128i
$554$		0			0
$555$	1.56638	−	2.71304i	0.00282230	−	0.00488837i
$556$		0			0
$557$	67.3674	+	116.684i	0.120947	+	0.209486i	0.920141	−	0.391586i	$-0.128074\pi$
$557$	67.3674	+	116.684i	0.120947	+	0.209486i	−0.799194	+	0.601073i	$0.794740\pi$
$558$		0			0
$559$		−	137.980i		−	0.246834i
$560$		0			0
$561$	170.067			0.303150
$562$		0			0
$563$	413.611	−	238.798i	0.734655	−	0.424153i	−0.0854680	−	0.996341i	$-0.527239\pi$
$563$	413.611	−	238.798i	0.734655	−	0.424153i	0.820123	+	0.572188i	$0.193905\pi$
$564$		0			0
$565$	−132.051	−	76.2399i	−0.233719	−	0.134938i
$566$		0			0
$567$	417.050	−	128.115i	0.735538	−	0.225953i
$568$		0			0
$569$	166.341	−	288.110i	0.292338	−	0.506345i	−0.682024	−	0.731330i	$-0.738900\pi$
$569$	166.341	−	288.110i	0.292338	−	0.506345i	0.974362	+	0.224985i	$0.0722333\pi$
$570$		0			0
$571$	−525.564	−	910.304i	−0.920427	−	1.59423i	−0.798755	−	0.601657i	$-0.794508\pi$
$571$	−525.564	−	910.304i	−0.920427	−	1.59423i	−0.121672	−	0.992570i	$-0.538826\pi$
$572$		0			0
$573$			128.466i			0.224199i
$574$		0			0
$575$	526.675			0.915956
$576$		0			0
$577$	350.366	−	202.284i	0.607221	−	0.350579i	−0.164656	−	0.986351i	$-0.552651\pi$
$577$	350.366	−	202.284i	0.607221	−	0.350579i	0.771877	+	0.635772i	$0.219318\pi$
$578$		0			0
$579$	−176.858	−	102.109i	−0.305455	−	0.176355i
$580$		0			0
$581$	831.438	+	190.781i	1.43105	+	0.328367i
$582$		0			0
$583$	297.252	−	514.856i	0.509867	−	0.883115i
$584$		0			0
$585$	−15.5777	−	26.9813i	−0.0266285	−	0.0461220i
$586$		0			0
$587$			64.6639i			0.110160i	0.998482	+	0.0550800i	$0.0175414\pi$
$587$			64.6639i			0.110160i	−0.998482	+	0.0550800i	$0.982459\pi$
$588$		0			0
$589$	−387.054			−0.657137
$590$		0			0
$591$	−144.165	+	83.2335i	−0.243933	+	0.140835i
$592$		0			0
$593$	36.0843	+	20.8333i	0.0608504	+	0.0351320i	0.530117	−	0.847925i	$-0.322148\pi$
$593$	36.0843	+	20.8333i	0.0608504	+	0.0351320i	−0.469266	+	0.883057i	$0.655482\pi$
$594$		0			0
$595$	29.8082	−	129.906i	0.0500979	−	0.218330i
$596$		0			0
$597$	69.1794	−	119.822i	0.115878	−	0.200707i
$598$		0			0
$599$	−60.0025	−	103.927i	−0.100171	−	0.173502i	0.811584	−	0.584236i	$-0.198606\pi$
$599$	−60.0025	−	103.927i	−0.100171	−	0.173502i	−0.911755	+	0.410734i	$0.865272\pi$
$600$		0			0
$601$		−	1120.08i		−	1.86369i	−0.362858	−	0.931844i	$-0.618199\pi$
$601$		−	1120.08i		−	1.86369i	0.362858	−	0.931844i	$-0.381801\pi$
$602$		0			0
$603$	379.999			0.630180
$604$		0			0
$605$	122.597	−	70.7812i	0.202639	−	0.116994i
$606$		0			0
$607$	−383.831	−	221.605i	−0.632342	−	0.365083i	0.149317	−	0.988789i	$-0.452293\pi$
$607$	−383.831	−	221.605i	−0.632342	−	0.365083i	−0.781658	+	0.623707i	$0.785626\pi$
$608$		0			0
$609$	−6.52328	−	21.2350i	−0.0107115	−	0.0348687i
$610$		0			0
$611$	−89.7662	+	155.480i	−0.146917	+	0.254467i
$612$		0			0
$613$	568.642	+	984.916i	0.927637	+	1.60672i	0.787264	+	0.616617i	$0.211497\pi$
$613$	568.642	+	984.916i	0.927637	+	1.60672i	0.140374	+	0.990099i	$0.455170\pi$
$614$		0			0
$615$		−	53.6106i		−	0.0871717i
$616$		0			0
$617$	−357.454			−0.579343			−0.289671	−	0.957126i	$-0.593546\pi$
$617$	−357.454			−0.579343			−0.289671	+	0.957126i	$0.593546\pi$
$618$		0			0
$619$	−686.616	+	396.418i	−1.10923	+	0.640416i	−0.938631	−	0.344923i	$-0.887905\pi$
$619$	−686.616	+	396.418i	−1.10923	+	0.640416i	−0.170603	+	0.985340i	$0.554572\pi$
$620$		0			0
$621$	−288.649	−	166.651i	−0.464813	−	0.268360i
$622$		0			0
$623$	218.871	−	235.341i	0.351318	−	0.377754i
$624$		0			0
$625$	−240.412	+	416.407i	−0.384660	+	0.666250i
$626$		0			0
$627$	183.005	+	316.974i	0.291874	+	0.505541i
$628$		0			0
$629$			35.8480i			0.0569920i
$630$		0			0
$631$	−587.326			−0.930786			−0.465393	−	0.885104i	$-0.654087\pi$
$631$	−587.326			−0.930786			−0.465393	+	0.885104i	$0.654087\pi$
$632$		0			0
$633$	−38.7892	+	22.3950i	−0.0612783	+	0.0353791i
$634$		0			0
$635$	−170.103	−	98.2088i	−0.267878	−	0.154660i
$636$		0			0
$637$	−57.1392	+	117.953i	−0.0897004	+	0.185169i
$638$		0			0
$639$	168.617	−	292.054i	0.263877	−	0.457048i
$640$		0			0
$641$	−229.349	−	397.244i	−0.357798	−	0.619725i	0.629794	−	0.776762i	$-0.283139\pi$
$641$	−229.349	−	397.244i	−0.357798	−	0.619725i	−0.987593	+	0.157037i	$0.949806\pi$
$642$		0			0
$643$			242.009i			0.376374i	0.982133	+	0.188187i	$0.0602611\pi$
$643$			242.009i			0.376374i	−0.982133	+	0.188187i	$0.939739\pi$
$644$		0			0
$645$	−61.0884			−0.0947107
$646$		0			0
$647$	−68.6970	+	39.6622i	−0.106178	+	0.0613017i	−0.552148	−	0.833746i	$-0.686192\pi$
$647$	−68.6970	+	39.6622i	−0.106178	+	0.0613017i	0.445971	+	0.895048i	$0.352859\pi$
$648$		0			0
$649$	165.001	+	95.2634i	0.254239	+	0.146785i
$650$		0			0
$651$	−57.3349	−	53.3224i	−0.0880721	−	0.0819085i
$652$		0			0
$653$	56.1079	−	97.1817i	0.0859232	−	0.148823i	−0.819861	−	0.572563i	$-0.805949\pi$
$653$	56.1079	−	97.1817i	0.0859232	−	0.148823i	0.905784	+	0.423739i	$0.139283\pi$
$654$		0			0
$655$	66.7600	+	115.632i	0.101924	+	0.176537i
$656$		0			0
$657$			533.008i			0.811275i
$658$		0			0
$659$	811.930			1.23206			0.616032	−	0.787721i	$-0.288739\pi$
$659$	811.930			1.23206			0.616032	+	0.787721i	$0.288739\pi$
$660$		0			0
$661$	−317.842	+	183.506i	−0.480850	+	0.277619i	−0.720771	−	0.693174i	$-0.756212\pi$
$661$	−317.842	+	183.506i	−0.480850	+	0.277619i	0.239921	+	0.970792i	$0.422879\pi$
$662$		0			0
$663$	−26.4549	−	15.2738i	−0.0399019	−	0.0230374i
$664$		0			0
$665$	274.198	−	84.2321i	0.412328	−	0.126665i
$666$		0			0
$667$	43.0640	−	74.5891i	0.0645638	−	0.111828i
$668$		0			0
$669$	−130.952	−	226.815i	−0.195742	−	0.339035i
$670$		0			0
$671$			1159.08i			1.72739i
$672$		0			0
$673$	−504.526			−0.749668			−0.374834	−	0.927092i	$-0.622300\pi$
$673$	−504.526			−0.749668			−0.374834	+	0.927092i	$0.622300\pi$
$674$		0			0
$675$	290.571	−	167.761i	0.430476	−	0.248535i
$676$		0			0
$677$	−519.740	−	300.072i	−0.767710	−	0.443238i	0.0643468	−	0.997928i	$-0.479504\pi$
$677$	−519.740	−	300.072i	−0.767710	−	0.443238i	−0.832057	+	0.554690i	$0.812837\pi$
$678$		0			0
$679$	−916.071	−	210.201i	−1.34915	−	0.309574i
$680$		0			0
$681$	21.0270	−	36.4198i	0.0308766	−	0.0534798i
$682$		0			0
$683$	−105.717	−	183.107i	−0.154783	−	0.268093i	0.778197	−	0.628020i	$-0.216135\pi$
$683$	−105.717	−	183.107i	−0.154783	−	0.268093i	−0.932980	+	0.359928i	$0.882801\pi$
$684$		0			0
$685$			215.780i			0.315007i
$686$		0			0
$687$	177.929			0.258994
$688$		0			0
$689$	−92.4787	+	53.3926i	−0.134222	+	0.0774929i
$690$		0			0
$691$	−16.6678	−	9.62318i	−0.0241213	−	0.0139265i	0.487891	−	0.872905i	$-0.337766\pi$
$691$	−16.6678	−	9.62318i	−0.0241213	−	0.0139265i	−0.512012	+	0.858978i	$0.671100\pi$
$692$		0			0
$693$	193.255	−	842.219i	0.278867	−	1.21532i
$694$		0			0
$695$	152.825	−	264.701i	0.219893	−	0.380865i
$696$		0			0
$697$	306.732	+	531.275i	0.440075	+	0.762232i
$698$		0			0
$699$			63.5928i			0.0909768i
$700$		0			0
$701$	1073.36			1.53119			0.765595	−	0.643323i	$-0.222445\pi$
$701$	1073.36			1.53119			0.765595	+	0.643323i	$0.222445\pi$
$702$		0			0
$703$	−66.8142	+	38.5752i	−0.0950415	+	0.0548722i
$704$		0			0
$705$	68.8360	+	39.7425i	0.0976397	+	0.0563723i
$706$		0			0
$707$	405.425	+	1319.77i	0.573445	+	1.86672i
$708$		0			0
$709$	128.799	−	223.086i	0.181663	−	0.314649i	−0.760784	−	0.649005i	$-0.775185\pi$
$709$	128.799	−	223.086i	0.181663	−	0.314649i	0.942447	+	0.334356i	$0.108519\pi$
$710$		0			0
$711$	333.746	+	578.065i	0.469403	+	0.813030i
$712$		0			0
$713$		−	303.571i		−	0.425766i
$714$		0			0
$715$	−55.9661			−0.0782743
$716$		0			0
$717$	−226.553	+	130.800i	−0.315973	+	0.182427i
$718$		0			0
$719$	278.533	+	160.811i	0.387389	+	0.223659i	0.681028	−	0.732257i	$-0.261533\pi$
$719$	278.533	+	160.811i	0.387389	+	0.223659i	−0.293639	+	0.955916i	$0.594866\pi$
$720$		0			0
$721$	−668.101	+	718.375i	−0.926630	+	0.996359i
$722$		0			0
$723$	45.6030	−	78.9867i	0.0630747	−	0.109249i
$724$		0			0
$725$	43.3509	+	75.0859i	0.0597943	+	0.103567i
$726$		0			0
$727$		−	19.9115i		−	0.0273886i	−0.999906	−	0.0136943i	$-0.995641\pi$
$727$		−	19.9115i		−	0.0273886i	0.999906	−	0.0136943i	$-0.00435917\pi$
$728$		0			0
$729$	406.138			0.557117
$730$		0			0
$731$	605.380	−	349.516i	0.828153	−	0.478134i
$732$		0			0
$733$	514.080	+	296.804i	0.701337	+	0.404917i	0.807845	−	0.589395i	$-0.200634\pi$
$733$	514.080	+	296.804i	0.701337	+	0.404917i	−0.106508	+	0.994312i	$0.533967\pi$
$734$		0			0
$735$	52.2216	+	25.2974i	0.0710498	+	0.0344182i
$736$		0			0
$737$	341.306	−	591.160i	0.463102	−	0.802116i
$738$		0			0
$739$	505.499	+	875.550i	0.684031	+	1.18478i	0.973740	+	0.227662i	$0.0731080\pi$
$739$	505.499	+	875.550i	0.684031	+	1.18478i	−0.289709	+	0.957115i	$0.593559\pi$
$740$		0			0
$741$		−	65.7430i		−	0.0887219i
$742$		0			0
$743$	−581.910			−0.783189			−0.391595	−	0.920138i	$-0.628076\pi$
$743$	−581.910			−0.783189			−0.391595	+	0.920138i	$0.628076\pi$
$744$		0			0
$745$	77.9883	−	45.0266i	0.104682	−	0.0604383i
$746$		0			0
$747$	874.870	+	505.106i	1.17118	+	0.676180i
$748$		0			0
$749$	−543.443	−	505.411i	−0.725558	−	0.674781i
$750$		0			0
$751$	−605.277	+	1048.37i	−0.805962	+	1.39597i	0.109678	+	0.993967i	$0.465018\pi$
$751$	−605.277	+	1048.37i	−0.805962	+	1.39597i	−0.915640	+	0.402000i	$0.868315\pi$
$752$		0			0
$753$	−127.272	−	220.441i	−0.169019	−	0.292750i
$754$		0			0
$755$		−	382.251i		−	0.506293i
$756$		0			0
$757$	−245.833			−0.324746			−0.162373	−	0.986729i	$-0.551915\pi$
$757$	−245.833			−0.324746			−0.162373	+	0.986729i	$0.551915\pi$
$758$		0			0
$759$	−248.607	+	143.533i	−0.327545	+	0.189108i
$760$		0			0
$761$	59.4109	+	34.3009i	0.0780694	+	0.0450734i	0.538527	−	0.842609i	$-0.318981\pi$
$761$	59.4109	+	34.3009i	0.0780694	+	0.0450734i	−0.460457	+	0.887682i	$0.652314\pi$
$762$		0			0
$763$	955.212	−	293.436i	1.25192	−	0.384582i
$764$		0			0
$765$	78.9194	−	136.692i	0.103163	−	0.178683i
$766$		0			0
$767$	−17.1113	−	29.6376i	−0.0223094	−	0.0386409i
$768$		0			0
$769$		−	540.953i		−	0.703450i	−0.936103	−	0.351725i	$-0.885595\pi$
$769$		−	540.953i		−	0.703450i	0.936103	−	0.351725i	$-0.114405\pi$
$770$		0			0
$771$	−87.3977			−0.113356
$772$		0			0
$773$	−223.462	+	129.016i	−0.289085	+	0.166903i	−0.637529	−	0.770426i	$-0.720043\pi$
$773$	−223.462	+	129.016i	−0.289085	+	0.166903i	0.348444	+	0.937329i	$0.386710\pi$
$774$		0			0
$775$	264.651	+	152.797i	0.341486	+	0.197157i
$776$		0			0
$777$	−15.2116	−	3.49044i	−0.0195773	−	0.00449220i
$778$		0			0
$779$	−660.134	+	1143.39i	−0.847412	+	1.46776i
$780$		0			0
$781$	−302.897	−	524.633i	−0.387832	−	0.671745i
$782$		0			0
$783$		−	54.8686i		−	0.0700749i
$784$		0			0
$785$	−303.880			−0.387109
$786$		0			0
$787$	−156.307	+	90.2438i	−0.198611	+	0.114668i	−0.596007	−	0.802979i	$-0.703247\pi$
$787$	−156.307	+	90.2438i	−0.198611	+	0.114668i	0.397396	+	0.917647i	$0.369914\pi$
$788$		0			0
$789$	−188.268	−	108.697i	−0.238616	−	0.137765i
$790$		0			0
$791$	−169.889	+	740.391i	−0.214778	+	0.936018i
$792$		0			0
$793$	104.097	−	180.302i	0.131270	−	0.227367i
$794$		0			0
$795$	23.6387	+	40.9434i	0.0297342	+	0.0515011i
$796$		0			0
$797$			1387.83i			1.74132i	0.491886	+	0.870660i	$0.336308\pi$
$797$			1387.83i			1.74132i	−0.491886	+	0.870660i	$0.663692\pi$
$798$		0			0
$799$	−909.543			−1.13835
$800$		0			0
$801$	329.610	−	190.300i	0.411498	−	0.237578i
$802$		0			0
$803$	829.194	+	478.736i	1.03262	+	0.596184i
$804$		0			0
$805$	66.0643	+	215.057i	0.0820674	+	0.267151i
$806$		0			0
$807$	68.3767	−	118.432i	0.0847295	−	0.146756i
$808$		0			0
$809$	354.447	+	613.920i	0.438130	+	0.758863i	0.997545	−	0.0700243i	$-0.0223077\pi$
$809$	354.447	+	613.920i	0.438130	+	0.758863i	−0.559415	+	0.828887i	$0.688974\pi$
$810$		0			0
$811$			281.652i			0.347289i	0.984808	+	0.173645i	$0.0555544\pi$
$811$			281.652i			0.347289i	−0.984808	+	0.173645i	$0.944446\pi$
$812$		0			0
$813$	−52.8852			−0.0650495
$814$		0			0
$815$	−66.5533	+	38.4246i	−0.0816605	+	0.0471467i
$816$		0			0
$817$	1302.87	+	752.212i	1.59470	+	0.920700i
$818$		0			0
$819$	−105.702	+	113.656i	−0.129062	+	0.138774i
$820$		0			0
$821$	−610.722	+	1057.80i	−0.743876	+	1.28843i	0.206842	+	0.978374i	$0.433681\pi$
$821$	−610.722	+	1057.80i	−0.743876	+	1.28843i	−0.950718	+	0.310057i	$0.899652\pi$
$822$		0			0
$823$	−41.7002	−	72.2268i	−0.0506685	−	0.0877604i	0.839579	−	0.543238i	$-0.182802\pi$
$823$	−41.7002	−	72.2268i	−0.0506685	−	0.0877604i	−0.890247	+	0.455478i	$0.849469\pi$
$824$		0			0
$825$		−	288.978i		−	0.350277i
$826$		0			0
$827$	804.602			0.972916			0.486458	−	0.873704i	$-0.338289\pi$
$827$	804.602			0.972916			0.486458	+	0.873704i	$0.338289\pi$
$828$		0			0
$829$	891.302	−	514.593i	1.07515	−	0.620740i	0.145568	−	0.989348i	$-0.453499\pi$
$829$	891.302	−	514.593i	1.07515	−	0.620740i	0.929585	+	0.368608i	$0.120166\pi$
$830$		0			0
$831$	187.691	+	108.363i	0.225862	+	0.130401i
$832$		0			0
$833$	−662.249	+	48.0902i	−0.795017	+	0.0577314i
$834$		0			0
$835$	174.301	−	301.899i	0.208744	−	0.361555i
$836$		0			0
$837$	−96.6963	−	167.483i	−0.115527	−	0.200099i
$838$		0			0
$839$		−	864.563i		−	1.03047i	−0.857049	−	0.515234i	$-0.827705\pi$
$839$		−	864.563i		−	1.03047i	0.857049	−	0.515234i	$-0.172295\pi$
$840$		0			0
$841$	−826.822			−0.983141
$842$		0			0
$843$	168.050	−	97.0237i	0.199348	−	0.115093i
$844$		0			0
$845$	−196.942	−	113.705i	−0.233068	−	0.134562i
$846$		0			0
$847$	−516.425	−	480.284i	−0.609711	−	0.567041i
$848$		0			0
$849$	172.562	−	298.886i	0.203253	−	0.352044i
$850$		0			0
$851$	−30.2550	−	52.4032i	−0.0355523	−	0.0615784i
$852$		0			0
$853$			285.568i			0.334781i	0.985891	+	0.167391i	$0.0535341\pi$
$853$			285.568i			0.334781i	−0.985891	+	0.167391i	$0.946466\pi$
$854$		0			0
$855$	339.693			0.397302
$856$		0			0
$857$	−565.510	+	326.497i	−0.659872	+	0.380977i	−0.792228	−	0.610225i	$-0.791079\pi$
$857$	−565.510	+	326.497i	−0.659872	+	0.380977i	0.132356	+	0.991202i	$0.457746\pi$
$858$		0			0
$859$	−75.6507	−	43.6770i	−0.0880683	−	0.0508463i	0.455319	−	0.890328i	$-0.349525\pi$
$859$	−75.6507	−	43.6770i	−0.0880683	−	0.0508463i	−0.543387	+	0.839482i	$0.682859\pi$
$860$		0			0
$861$	−255.305	+	78.4283i	−0.296522	+	0.0910898i
$862$		0			0
$863$	213.639	−	370.034i	0.247554	−	0.428776i	−0.715293	−	0.698825i	$-0.753707\pi$
$863$	213.639	−	370.034i	0.247554	−	0.428776i	0.962847	+	0.270049i	$0.0870399\pi$
$864$		0			0
$865$	−182.433	−	315.983i	−0.210905	−	0.365299i
$866$		0			0
$867$			88.8083i			0.102432i
$868$		0			0
$869$	1199.05			1.37981
$870$		0			0
$871$	−106.184	+	61.3056i	−0.121911	+	0.0703853i
$872$		0			0
$873$	−963.923	−	556.521i	−1.10415	−	0.637482i
$874$		0			0
$875$	−460.401	−	105.643i	−0.526173	−	0.120735i
$876$		0			0
$877$	290.651	−	503.422i	0.331415	−	0.574028i	−0.651374	−	0.758756i	$-0.725807\pi$
$877$	290.651	−	503.422i	0.331415	−	0.574028i	0.982790	+	0.184729i	$0.0591406\pi$
$878$		0			0
$879$	−184.617	−	319.765i	−0.210030	−	0.363783i
$880$		0			0
$881$			617.976i			0.701448i	0.936479	+	0.350724i	$0.114064\pi$
$881$			617.976i			0.701448i	−0.936479	+	0.350724i	$0.885936\pi$
$882$		0			0
$883$	−150.782			−0.170761			−0.0853807	−	0.996348i	$-0.527211\pi$
$883$	−150.782			−0.170761			−0.0853807	+	0.996348i	$0.527211\pi$
$884$		0			0
$885$	−13.1215	+	7.57573i	−0.0148266	+	0.00856015i
$886$		0			0
$887$	−1158.00	−	668.569i	−1.30552	−	0.753742i	−0.324174	−	0.945997i	$-0.605086\pi$
$887$	−1158.00	−	668.569i	−1.30552	−	0.753742i	−0.981345	+	0.192256i	$0.938420\pi$
$888$		0			0
$889$	−218.844	+	953.737i	−0.246169	+	1.07282i
$890$		0			0
$891$	464.058	−	803.773i	0.520829	−	0.902102i
$892$		0			0
$893$	−978.738	−	1695.22i	−1.09601	−	1.89835i
$894$		0			0
$895$			194.152i			0.216930i
$896$		0			0
$897$	51.5630			0.0574839
$898$		0			0
$899$	43.2789	−	24.9871i	0.0481412	−	0.0277943i
$900$		0			0
$901$	−468.514	−	270.497i	−0.519993	−	0.300218i
$902$		0			0
$903$	89.3678	+	290.916i	0.0989677	+	0.322166i
$904$		0			0
$905$	−80.4398	+	139.326i	−0.0888838	+	0.153951i
$906$		0			0
$907$	322.677	+	558.894i	0.355763	+	0.616200i	0.987248	−	0.159188i	$-0.0508876\pi$
$907$	322.677	+	558.894i	0.355763	+	0.616200i	−0.631485	+	0.775388i	$0.717554\pi$
$908$		0			0
$909$			1635.01i			1.79869i
$910$		0			0
$911$	865.195			0.949720			0.474860	−	0.880061i	$-0.342499\pi$
$911$	865.195			0.949720			0.474860	+	0.880061i	$0.342499\pi$
$912$		0			0
$913$	1571.58	−	907.350i	1.72133	−	0.993812i
$914$		0			0
$915$	−79.8257	−	46.0874i	−0.0872412	−	0.0503687i
$916$		0			0
$917$	452.998	−	487.086i	0.494000	−	0.531173i
$918$		0			0
$919$	−31.6093	+	54.7489i	−0.0343953	+	0.0595745i	−0.882711	−	0.469917i	$-0.844284\pi$
$919$	−31.6093	+	54.7489i	−0.0343953	+	0.0595745i	0.848315	+	0.529491i	$0.177617\pi$
$920$		0			0
$921$	57.5268	+	99.6393i	0.0624612	+	0.108186i
$922$		0			0
$923$			108.813i			0.117891i
$924$		0			0
$925$	60.9130			0.0658519
$926$		0			0
$927$	−1006.13	+	580.889i	−1.08536	+	0.626633i
$928$		0			0
$929$	1109.30	+	640.454i	1.19408	+	0.689402i	0.959229	−	0.282630i	$-0.0912069\pi$
$929$	1109.30	+	640.454i	1.19408	+	0.689402i	0.234850	+	0.972032i	$0.424540\pi$
$930$		0			0
$931$	−802.262	−	1182.56i	−0.861721	−	1.27021i
$932$		0			0
$933$	−244.799	+	424.004i	−0.262378	+	0.454452i
$934$		0			0
$935$	−141.767	−	245.548i	−0.151623	−	0.262618i
$936$		0			0
$937$		−	1176.84i		−	1.25597i	−0.778227	−	0.627983i	$-0.783881\pi$
$937$		−	1176.84i		−	1.25597i	0.778227	−	0.627983i	$-0.216119\pi$
$938$		0			0
$939$	−157.769			−0.168018
$940$		0			0
$941$	1184.64	−	683.950i	1.25891	−	0.726833i	0.286048	−	0.958215i	$-0.407658\pi$
$941$	1184.64	−	683.950i	1.25891	−	0.726833i	0.972863	+	0.231382i	$0.0743249\pi$
$942$		0			0
$943$	−896.772	−	517.752i	−0.950978	−	0.549047i
$944$		0			0
$945$	104.950	+	97.6054i	0.111058	+	0.103286i
$946$		0			0
$947$	87.6049	−	151.736i	0.0925078	−	0.160228i	−0.816058	−	0.577970i	$-0.803845\pi$
$947$	87.6049	−	151.736i	0.0925078	−	0.160228i	0.908566	+	0.417742i	$0.137178\pi$
$948$		0			0
$949$	−85.9908	−	148.940i	−0.0906120	−	0.156945i
$950$		0			0
$951$			139.809i			0.147013i
$952$		0			0
$953$	89.5669			0.0939842			0.0469921	−	0.998895i	$-0.485036\pi$
$953$	89.5669			0.0939842			0.0469921	+	0.998895i	$0.485036\pi$
$954$		0			0
$955$	185.484	−	107.089i	0.194224	−	0.112135i
$956$		0			0
$957$	−40.9259	−	23.6286i	−0.0427648	−	0.0246903i
$958$		0			0
$959$	1027.59	−	315.670i	1.07152	−	0.329166i
$960$		0			0
$961$	−392.429	+	679.707i	−0.408355	+	0.707292i
$962$		0			0
$963$	−439.436	−	761.126i	−0.456320	−	0.790370i
$964$		0			0
$965$			340.472i			0.352820i
$966$		0			0
$967$	640.201			0.662049			0.331024	−	0.943622i	$-0.392606\pi$
$967$	640.201			0.662049			0.331024	+	0.943622i	$0.392606\pi$
$968$		0			0
$969$	288.443	−	166.533i	0.297671	−	0.171860i
$970$		0			0
$971$	−990.220	−	571.704i	−1.01979	−	0.588779i	−0.105750	−	0.994393i	$-0.533724\pi$
$971$	−990.220	−	571.704i	−1.01979	−	0.588779i	−0.914044	+	0.405614i	$0.867058\pi$
$972$		0			0
$973$	−1484.14	−	340.549i	−1.52532	−	0.349999i
$974$		0			0
$975$	−25.9532	+	44.9523i	−0.0266187	+	0.0461049i
$976$		0			0
$977$	−801.534	−	1388.30i	−0.820403	−	1.42098i	−0.905382	−	0.424597i	$-0.860416\pi$
$977$	−801.534	−	1388.30i	−0.820403	−	1.42098i	0.0849795	−	0.996383i	$-0.472918\pi$
$978$		0			0
$979$		−	683.694i		−	0.698359i
$980$		0			0
$981$	1183.37			1.20629
$982$		0			0
$983$	850.237	−	490.885i	0.864941	−	0.499374i	−0.000722851	−	1.00000i	$-0.500230\pi$
$983$	850.237	−	490.885i	0.864941	−	0.499374i	0.865664	+	0.500626i	$0.166897\pi$
$984$		0			0
$985$	240.350	+	138.766i	0.244010	+	0.140879i
$986$		0			0
$987$	88.5602	−	385.952i	0.0897267	−	0.391035i
$988$		0			0
$989$	−589.970	+	1021.86i	−0.596531	+	1.03322i
$990$		0			0
$991$	−413.854	−	716.817i	−0.417613	−	0.723327i	0.578086	−	0.815976i	$-0.303800\pi$
$991$	−413.854	−	716.817i	−0.417613	−	0.723327i	−0.995699	+	0.0926491i	$0.970467\pi$
$992$		0			0
$993$			352.455i			0.354939i
$994$		0			0
$995$	−230.671			−0.231830
$996$		0			0
$997$	−156.575	+	90.3985i	−0.157046	+	0.0906705i	−0.576463	−	0.817123i	$-0.695568\pi$
$997$	−156.575	+	90.3985i	−0.157046	+	0.0906705i	0.419418	+	0.907793i	$0.362234\pi$
$998$		0			0
$999$	−33.3839	−	19.2742i	−0.0334173	−	0.0192935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.s.b.33.5	yes	16
4.3	odd	2	inner	224.3.s.b.33.4	✓	16
7.2	even	3		1568.3.c.g.97.10		16
7.3	odd	6	inner	224.3.s.b.129.5	yes	16
7.5	odd	6		1568.3.c.g.97.7		16
8.3	odd	2		448.3.s.h.257.5		16
8.5	even	2		448.3.s.h.257.4		16
28.3	even	6	inner	224.3.s.b.129.4	yes	16
28.19	even	6		1568.3.c.g.97.9		16
28.23	odd	6		1568.3.c.g.97.8		16
56.3	even	6		448.3.s.h.129.5		16
56.45	odd	6		448.3.s.h.129.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.b.33.4	✓	16	4.3	odd	2	inner
224.3.s.b.33.5	yes	16	1.1	even	1	trivial
224.3.s.b.129.4	yes	16	28.3	even	6	inner
224.3.s.b.129.5	yes	16	7.3	odd	6	inner
448.3.s.h.129.4		16	56.45	odd	6
448.3.s.h.129.5		16	56.3	even	6
448.3.s.h.257.4		16	8.5	even	2
448.3.s.h.257.5		16	8.3	odd	2
1568.3.c.g.97.7		16	7.5	odd	6
1568.3.c.g.97.8		16	28.23	odd	6
1568.3.c.g.97.9		16	28.19	even	6
1568.3.c.g.97.10		16	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.729881 - 0.421397i) q^{3} +(-1.21685 - 0.702550i) q^{5} +(-1.56553 + 6.82269i) q^{7} +(-4.14485 + 7.17909i) q^{9} +O(q^{10})\)	\(q+(0.729881 - 0.421397i) q^{3} +(-1.21685 - 0.702550i) q^{5} +(-1.56553 + 6.82269i) q^{7} +(-4.14485 + 7.17909i) q^{9} +(7.44562 + 12.8962i) q^{11} -2.67477i q^{13} -1.18421 q^{15} +(11.7354 - 6.77544i) q^{17} +(25.2564 + 14.5818i) q^{19} +(1.73241 + 5.63947i) q^{21} +(-11.4367 + 19.8089i) q^{23} +(-11.5128 - 19.9408i) q^{25} +14.5717i q^{27} -3.76543 q^{29} +(-11.4937 + 6.63592i) q^{31} +(10.8688 + 6.27513i) q^{33} +(6.69830 - 7.20235i) q^{35} +(-1.32272 + 2.29102i) q^{37} +(-1.12714 - 1.95227i) q^{39} +45.2712i q^{41} +51.5858 q^{43} +(10.0873 - 5.82393i) q^{45} +(-58.1281 - 33.5603i) q^{47} +(-44.0982 - 21.3623i) q^{49} +(5.71030 - 9.89054i) q^{51} +(-19.9616 - 34.5744i) q^{53} -20.9237i q^{55} +24.5789 q^{57} +(11.0804 - 6.39728i) q^{59} +(67.4084 + 38.9182i) q^{61} +(-42.4918 - 39.5181i) q^{63} +(-1.87916 + 3.25480i) q^{65} +(-22.9199 - 39.6985i) q^{67} +19.2775i q^{69} -40.6812 q^{71} +(55.6834 - 32.1488i) q^{73} +(-16.8060 - 9.70296i) q^{75} +(-99.6431 + 30.6098i) q^{77} +(40.2603 - 69.7329i) q^{79} +(-31.1632 - 53.9762i) q^{81} -121.864i q^{83} -19.0403 q^{85} +(-2.74832 + 1.58674i) q^{87} +(-39.7614 - 22.9562i) q^{89} +(18.2492 + 4.18744i) q^{91} +(-5.59271 + 9.68687i) q^{93} +(-20.4889 - 35.4878i) q^{95} +134.268i q^{97} -123.444 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{9}+O(q^{10}) \) 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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