LMFDB - Embedded newform 684.3.g.d.343.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (of order $2$, degree $1$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.2
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98942 + 0.205433i) q^{2} +(3.91559 - 0.817384i) q^{4} -0.0956487 q^{5} -9.56723i q^{7} +(-7.62185 + 2.43051i) q^{8} +O(q^{10})$	\(q+(-1.98942 + 0.205433i) q^{2} +(3.91559 - 0.817384i) q^{4} -0.0956487 q^{5} -9.56723i q^{7} +(-7.62185 + 2.43051i) q^{8} +(0.190286 - 0.0196494i) q^{10} +7.63102i q^{11} +7.83922 q^{13} +(1.96542 + 19.0332i) q^{14} +(14.6638 - 6.40109i) q^{16} +16.6975 q^{17} +4.35890i q^{19} +(-0.374522 + 0.0781817i) q^{20} +(-1.56766 - 15.1813i) q^{22} -6.37991i q^{23} -24.9909 q^{25} +(-15.5955 + 1.61043i) q^{26} +(-7.82010 - 37.4614i) q^{28} +19.5690 q^{29} -57.7824i q^{31} +(-27.8574 + 15.7469i) q^{32} +(-33.2184 + 3.43021i) q^{34} +0.915093i q^{35} +50.5873 q^{37} +(-0.895460 - 8.67169i) q^{38} +(0.729020 - 0.232475i) q^{40} -57.9622 q^{41} +13.2206i q^{43} +(6.23748 + 29.8800i) q^{44} +(1.31064 + 12.6923i) q^{46} +42.0176i q^{47} -42.5319 q^{49} +(49.7173 - 5.13394i) q^{50} +(30.6952 - 6.40766i) q^{52} -40.5786 q^{53} -0.729898i q^{55} +(23.2533 + 72.9200i) q^{56} +(-38.9309 + 4.02010i) q^{58} -89.4572i q^{59} +30.2988 q^{61} +(11.8704 + 114.953i) q^{62} +(52.1852 - 37.0500i) q^{64} -0.749812 q^{65} -61.0526i q^{67} +(65.3807 - 13.6483i) q^{68} +(-0.187990 - 1.82051i) q^{70} -134.657i q^{71} +50.8095 q^{73} +(-100.639 + 10.3923i) q^{74} +(3.56289 + 17.0677i) q^{76} +73.0077 q^{77} -10.4587i q^{79} +(-1.40257 + 0.612256i) q^{80} +(115.311 - 11.9073i) q^{82} -80.3969i q^{83} -1.59709 q^{85} +(-2.71595 - 26.3014i) q^{86} +(-18.5473 - 58.1625i) q^{88} -73.9080 q^{89} -74.9996i q^{91} +(-5.21483 - 24.9811i) q^{92} +(-8.63179 - 83.5908i) q^{94} -0.416923i q^{95} -101.252 q^{97} +(84.6138 - 8.73743i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4}+O(q^{10}) $ 36 * q - 12 * q^4	$ 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) $ 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.98942	+	0.205433i	−0.994711	+	0.102716i
$2$	−1.98942	+	0.205433i	−0.994711	+	0.102716i
$3$		0			0
$3$		0			0
$4$	3.91559	−	0.817384i	0.978899	−	0.204346i
$5$	−0.0956487			−0.0191297			−0.00956487	−	0.999954i	$-0.503045\pi$
$5$	−0.0956487			−0.0191297			−0.00956487	+	0.999954i	$0.503045\pi$
$6$		0			0
$7$		−	9.56723i		−	1.36675i	−0.730069	−	0.683373i	$-0.760512\pi$
$7$		−	9.56723i		−	1.36675i	0.730069	−	0.683373i	$-0.239488\pi$
$8$	−7.62185	+	2.43051i	−0.952731	+	0.303814i
$9$		0			0
$10$	0.190286	−	0.0196494i	0.0190286	−	0.00196494i
$11$			7.63102i			0.693729i	0.937915	+	0.346865i	$0.112754\pi$
$11$			7.63102i			0.693729i	−0.937915	+	0.346865i	$0.887246\pi$
$12$		0			0
$13$	7.83922			0.603017			0.301509	−	0.953463i	$-0.402510\pi$
$13$	7.83922			0.603017			0.301509	+	0.953463i	$0.402510\pi$
$14$	1.96542	+	19.0332i	0.140387	+	1.35952i
$15$		0			0
$16$	14.6638	−	6.40109i	0.916485	−	0.400068i
$17$	16.6975			0.982206			0.491103	−	0.871102i	$-0.336594\pi$
$17$	16.6975			0.982206			0.491103	+	0.871102i	$0.336594\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−0.374522	+	0.0781817i	−0.0187261	+	0.00390909i
$21$		0			0
$22$	−1.56766	−	15.1813i	−0.0712573	−	0.690060i
$23$		−	6.37991i		−	0.277387i	−0.990335	−	0.138694i	$-0.955710\pi$
$23$		−	6.37991i		−	0.277387i	0.990335	−	0.138694i	$-0.0442903\pi$
$24$		0			0
$25$	−24.9909			−0.999634
$26$	−15.5955	+	1.61043i	−0.599828	+	0.0619397i
$27$		0			0
$28$	−7.82010	−	37.4614i	−0.279289	−	1.33791i
$29$	19.5690			0.674792			0.337396	−	0.941363i	$-0.390454\pi$
$29$	19.5690			0.674792			0.337396	+	0.941363i	$0.390454\pi$
$30$		0			0
$31$		−	57.7824i		−	1.86395i	−0.362526	−	0.931973i	$-0.618086\pi$
$31$		−	57.7824i		−	1.86395i	0.362526	−	0.931973i	$-0.381914\pi$
$32$	−27.8574	+	15.7469i	−0.870544	+	0.492090i
$33$		0			0
$34$	−33.2184	+	3.43021i	−0.977011	+	0.100889i
$35$			0.915093i			0.0261455i
$36$		0			0
$37$	50.5873			1.36722			0.683612	−	0.729846i	$-0.260408\pi$
$37$	50.5873			1.36722			0.683612	+	0.729846i	$0.260408\pi$
$38$	−0.895460	−	8.67169i	−0.0235647	−	0.228202i
$39$		0			0
$40$	0.729020	−	0.232475i	0.0182255	−	0.00581189i
$41$	−57.9622			−1.41371			−0.706857	−	0.707357i	$-0.749887\pi$
$41$	−57.9622			−1.41371			−0.706857	+	0.707357i	$0.749887\pi$
$42$		0			0
$43$			13.2206i			0.307457i	0.988113	+	0.153728i	$0.0491280\pi$
$43$			13.2206i			0.307457i	−0.988113	+	0.153728i	$0.950872\pi$
$44$	6.23748	+	29.8800i	0.141761	+	0.679091i
$45$		0			0
$46$	1.31064	+	12.6923i	0.0284922	+	0.275920i
$47$			42.0176i			0.893992i	0.894536	+	0.446996i	$0.147506\pi$
$47$			42.0176i			0.893992i	−0.894536	+	0.446996i	$0.852494\pi$
$48$		0			0
$49$	−42.5319			−0.867997
$50$	49.7173	−	5.13394i	0.994347	−	0.102679i
$51$		0			0
$52$	30.6952	−	6.40766i	0.590293	−	0.123224i
$53$	−40.5786			−0.765634			−0.382817	−	0.923824i	$-0.625046\pi$
$53$	−40.5786			−0.765634			−0.382817	+	0.923824i	$0.625046\pi$
$54$		0			0
$55$		−	0.729898i		−	0.0132709i
$56$	23.2533	+	72.9200i	0.415237	+	1.30214i
$57$		0			0
$58$	−38.9309	+	4.02010i	−0.671222	+	0.0693121i
$59$		−	89.4572i		−	1.51622i	−0.652124	−	0.758112i	$-0.726122\pi$
$59$		−	89.4572i		−	1.51622i	0.652124	−	0.758112i	$-0.273878\pi$
$60$		0			0
$61$	30.2988			0.496701			0.248350	−	0.968670i	$-0.420112\pi$
$61$	30.2988			0.496701			0.248350	+	0.968670i	$0.420112\pi$
$62$	11.8704	+	114.953i	0.191458	+	1.85409i
$63$		0			0
$64$	52.1852	−	37.0500i	0.815394	−	0.578906i
$65$	−0.749812			−0.0115356
$66$		0			0
$67$		−	61.0526i		−	0.911233i	−0.890176	−	0.455616i	$-0.849419\pi$
$67$		−	61.0526i		−	0.911233i	0.890176	−	0.455616i	$-0.150581\pi$
$68$	65.3807	−	13.6483i	0.961480	−	0.200710i
$69$		0			0
$70$	−0.187990	−	1.82051i	−0.00268557	−	0.0260072i
$71$		−	134.657i		−	1.89658i	−0.317411	−	0.948288i	$-0.602813\pi$
$71$		−	134.657i		−	1.89658i	0.317411	−	0.948288i	$-0.397187\pi$
$72$		0			0
$73$	50.8095			0.696021			0.348010	−	0.937491i	$-0.386857\pi$
$73$	50.8095			0.696021			0.348010	+	0.937491i	$0.386857\pi$
$74$	−100.639	+	10.3923i	−1.35999	+	0.140436i
$75$		0			0
$76$	3.56289	+	17.0677i	0.0468802	+	0.224575i
$77$	73.0077			0.948152
$78$		0			0
$79$		−	10.4587i		−	0.132388i	−0.997807	−	0.0661941i	$-0.978914\pi$
$79$		−	10.4587i		−	0.132388i	0.997807	−	0.0661941i	$-0.0210857\pi$
$80$	−1.40257	+	0.612256i	−0.0175321	+	0.00765320i
$81$		0			0
$82$	115.311	−	11.9073i	1.40624	−	0.145211i
$83$		−	80.3969i		−	0.968638i	−0.874892	−	0.484319i	$-0.839068\pi$
$83$		−	80.3969i		−	0.968638i	0.874892	−	0.484319i	$-0.160932\pi$
$84$		0			0
$85$	−1.59709			−0.0187894
$86$	−2.71595	−	26.3014i	−0.0315808	−	0.305830i
$87$		0			0
$88$	−18.5473	−	58.1625i	−0.210765	−	0.660938i
$89$	−73.9080			−0.830427			−0.415214	−	0.909724i	$-0.636293\pi$
$89$	−73.9080			−0.830427			−0.415214	+	0.909724i	$0.636293\pi$
$90$		0			0
$91$		−	74.9996i		−	0.824172i
$92$	−5.21483	−	24.9811i	−0.0566830	−	0.271534i
$93$		0			0
$94$	−8.63179	−	83.5908i	−0.0918276	−	0.889263i
$95$		−	0.416923i		−	0.00438866i
$96$		0			0
$97$	−101.252			−1.04383			−0.521916	−	0.852997i	$-0.674783\pi$
$97$	−101.252			−1.04383			−0.521916	+	0.852997i	$0.674783\pi$
$98$	84.6138	−	8.73743i	0.863406	−	0.0891575i
$99$		0			0
$100$	−97.8540	+	20.4271i	−0.978540	+	0.204271i
$101$	73.2306			0.725056			0.362528	−	0.931973i	$-0.381914\pi$
$101$	73.2306			0.725056			0.362528	+	0.931973i	$0.381914\pi$
$102$		0			0
$103$		−	16.6014i		−	0.161179i	−0.996747	−	0.0805895i	$-0.974320\pi$
$103$		−	16.6014i		−	0.161179i	0.996747	−	0.0805895i	$-0.0256803\pi$
$104$	−59.7494	+	19.0533i	−0.574513	+	0.183205i
$105$		0			0
$106$	80.7280	−	8.33617i	0.761584	−	0.0786431i
$107$		−	135.797i		−	1.26913i	−0.772871	−	0.634563i	$-0.781180\pi$
$107$		−	135.797i		−	1.26913i	0.772871	−	0.634563i	$-0.218820\pi$
$108$		0			0
$109$	−21.3010			−0.195422			−0.0977109	−	0.995215i	$-0.531152\pi$
$109$	−21.3010			−0.195422			−0.0977109	+	0.995215i	$0.531152\pi$
$110$	0.149945	+	1.45207i	0.00136313	+	0.0132007i
$111$		0			0
$112$	−61.2407	−	140.292i	−0.546792	−	1.25260i
$113$	46.7834			0.414013			0.207006	−	0.978340i	$-0.433628\pi$
$113$	46.7834			0.414013			0.207006	+	0.978340i	$0.433628\pi$
$114$		0			0
$115$			0.610230i			0.00530635i
$116$	76.6241	−	15.9954i	0.660553	−	0.137891i
$117$		0			0
$118$	18.3774	+	177.968i	0.155741	+	1.50820i
$119$		−	159.749i		−	1.34243i
$120$		0			0
$121$	62.7675			0.518740
$122$	−60.2770	+	6.22435i	−0.494074	+	0.0510193i
$123$		0			0
$124$	−47.2304	−	226.252i	−0.380890	−	1.82462i
$125$	4.78156			0.0382525
$126$		0			0
$127$			81.0214i			0.637964i	0.947761	+	0.318982i	$0.103341\pi$
$127$			81.0214i			0.637964i	−0.947761	+	0.318982i	$0.896659\pi$
$128$	−96.2071	+	84.4286i	−0.751618	+	0.659599i
$129$		0			0
$130$	1.49169	−	0.154036i	0.0114745	−	0.00118489i
$131$		−	189.253i		−	1.44468i	−0.691540	−	0.722339i	$-0.743067\pi$
$131$		−	189.253i		−	1.44468i	0.691540	−	0.722339i	$-0.256933\pi$
$132$		0			0
$133$	41.7026			0.313553
$134$	12.5422	+	121.459i	0.0935985	+	0.906413i
$135$		0			0
$136$	−127.266	+	40.5835i	−0.935778	+	0.298408i
$137$	237.261			1.73183			0.865916	−	0.500189i	$-0.166736\pi$
$137$	237.261			1.73183			0.865916	+	0.500189i	$0.166736\pi$
$138$		0			0
$139$		−	189.051i		−	1.36008i	−0.733176	−	0.680039i	$-0.761963\pi$
$139$		−	189.051i		−	1.36008i	0.733176	−	0.680039i	$-0.238037\pi$
$140$	0.747983	+	3.58313i	0.00534273	+	0.0255938i
$141$		0			0
$142$	27.6629	+	267.889i	0.194809	+	1.88654i
$143$			59.8213i			0.418331i
$144$		0			0
$145$	−1.87175			−0.0129086
$146$	−101.082	+	10.4379i	−0.692339	+	0.0714927i
$147$		0			0
$148$	198.079	−	41.3492i	1.33837	−	0.279387i
$149$	85.9682			0.576968			0.288484	−	0.957485i	$-0.406849\pi$
$149$	85.9682			0.576968			0.288484	+	0.957485i	$0.406849\pi$
$150$		0			0
$151$		−	69.8538i		−	0.462608i	−0.972882	−	0.231304i	$-0.925701\pi$
$151$		−	69.8538i		−	0.462608i	0.972882	−	0.231304i	$-0.0742991\pi$
$152$	−10.5944	−	33.2229i	−0.0696997	−	0.218572i
$153$		0			0
$154$	−145.243	+	14.9982i	−0.943137	+	0.0973907i
$155$			5.52681i			0.0356568i
$156$		0			0
$157$	66.1082			0.421071			0.210536	−	0.977586i	$-0.432479\pi$
$157$	66.1082			0.421071			0.210536	+	0.977586i	$0.432479\pi$
$158$	2.14855	+	20.8067i	0.0135984	+	0.131688i
$159$		0			0
$160$	2.66453	−	1.50617i	0.0166533	−	0.00941356i
$161$	−61.0380			−0.379118
$162$		0			0
$163$			209.537i			1.28550i	0.766075	+	0.642752i	$0.222207\pi$
$163$			209.537i			1.28550i	−0.766075	+	0.642752i	$0.777793\pi$
$164$	−226.957	+	47.3774i	−1.38388	+	0.288887i
$165$		0			0
$166$	16.5161	+	159.943i	0.0994949	+	0.963514i
$167$		−	94.6876i		−	0.566992i	−0.958973	−	0.283496i	$-0.908506\pi$
$167$		−	94.6876i		−	0.566992i	0.958973	−	0.283496i	$-0.0914942\pi$
$168$		0			0
$169$	−107.547			−0.636370
$170$	3.17729	−	0.328095i	0.0186900	−	0.00192997i
$171$		0			0
$172$	10.8063	+	51.7666i	0.0628275	+	0.300969i
$173$	−107.114			−0.619156			−0.309578	−	0.950874i	$-0.600188\pi$
$173$	−107.114			−0.619156			−0.309578	+	0.950874i	$0.600188\pi$
$174$		0			0
$175$			239.093i			1.36625i
$176$	48.8469	+	111.900i	0.277539	+	0.635793i
$177$		0			0
$178$	147.034	−	15.1831i	0.826035	−	0.0852984i
$179$			202.586i			1.13176i	0.824486	+	0.565882i	$0.191464\pi$
$179$			202.586i			1.13176i	−0.824486	+	0.565882i	$0.808536\pi$
$180$		0			0
$181$	189.134			1.04494			0.522471	−	0.852657i	$-0.325010\pi$
$181$	189.134			1.04494			0.522471	+	0.852657i	$0.325010\pi$
$182$	15.4074	+	149.206i	0.0846559	+	0.819812i
$183$		0			0
$184$	15.5064	+	48.6267i	0.0842741	+	0.264275i
$185$	−4.83861			−0.0261546
$186$		0			0
$187$			127.419i			0.681385i
$188$	34.3445	+	164.524i	0.182684	+	0.875128i
$189$		0			0
$190$	0.0856496	+	0.829436i	0.000450787	+	0.00436545i
$191$		−	236.358i		−	1.23748i	−0.785597	−	0.618739i	$-0.787644\pi$
$191$		−	236.358i		−	1.23748i	0.785597	−	0.618739i	$-0.212356\pi$
$192$		0			0
$193$	−7.36645			−0.0381681			−0.0190841	−	0.999818i	$-0.506075\pi$
$193$	−7.36645			−0.0381681			−0.0190841	+	0.999818i	$0.506075\pi$
$194$	201.432	−	20.8004i	1.03831	−	0.107219i
$195$		0			0
$196$	−166.538	+	34.7649i	−0.849681	+	0.177372i
$197$	−247.192			−1.25478			−0.627391	−	0.778705i	$-0.715877\pi$
$197$	−247.192			−1.25478			−0.627391	+	0.778705i	$0.715877\pi$
$198$		0			0
$199$			174.589i			0.877330i	0.898651	+	0.438665i	$0.144548\pi$
$199$			174.589i			0.877330i	−0.898651	+	0.438665i	$0.855452\pi$
$200$	190.477	−	60.7406i	0.952383	−	0.303703i
$201$		0			0
$202$	−145.687	+	15.0440i	−0.721221	+	0.0744751i
$203$		−	187.221i		−	0.922269i
$204$		0			0
$205$	5.54401			0.0270440
$206$	3.41048	+	33.0272i	0.0165557	+	0.160326i
$207$		0			0
$208$	114.953	−	50.1796i	0.552656	−	0.241248i
$209$	−33.2629			−0.159152
$210$		0			0
$211$			234.077i			1.10937i	0.832061	+	0.554684i	$0.187161\pi$
$211$			234.077i			1.10937i	−0.832061	+	0.554684i	$0.812839\pi$
$212$	−158.889	+	33.1683i	−0.749478	+	0.156454i
$213$		0			0
$214$	27.8970	+	270.157i	0.130360	+	1.26241i
$215$		−	1.26454i		−	0.00588156i
$216$		0			0
$217$	−552.817			−2.54754
$218$	42.3766	−	4.37592i	0.194388	−	0.0200730i
$219$		0			0
$220$	−0.596607	−	2.85798i	−0.00271185	−	0.0129908i
$221$	130.895			0.592287
$222$		0			0
$223$			142.738i			0.640082i	0.947404	+	0.320041i	$0.103697\pi$
$223$			142.738i			0.640082i	−0.947404	+	0.320041i	$0.896303\pi$
$224$	150.654	+	266.518i	0.672563	+	1.18981i
$225$		0			0
$226$	−93.0719	+	9.61084i	−0.411823	+	0.0425258i
$227$			338.494i			1.49116i	0.666414	+	0.745582i	$0.267828\pi$
$227$			338.494i			1.49116i	−0.666414	+	0.745582i	$0.732172\pi$
$228$		0			0
$229$	−104.649			−0.456981			−0.228491	−	0.973546i	$-0.573379\pi$
$229$	−104.649			−0.456981			−0.228491	+	0.973546i	$0.573379\pi$
$230$	−0.125361	−	1.21400i	−0.000545048	−	0.00527828i
$231$		0			0
$232$	−149.152	+	47.5626i	−0.642895	+	0.205011i
$233$	−106.731			−0.458075			−0.229037	−	0.973418i	$-0.573558\pi$
$233$	−106.731			−0.458075			−0.229037	+	0.973418i	$0.573558\pi$
$234$		0			0
$235$		−	4.01893i		−	0.0171018i
$236$	−73.1209	−	350.278i	−0.309834	−	1.48423i
$237$		0			0
$238$	32.8176	+	317.808i	0.137889	+	1.33533i
$239$		−	246.219i		−	1.03020i	−0.857129	−	0.515102i	$-0.827754\pi$
$239$		−	246.219i		−	1.03020i	0.857129	−	0.515102i	$-0.172246\pi$
$240$		0			0
$241$	95.2425			0.395197			0.197599	−	0.980283i	$-0.436686\pi$
$241$	95.2425			0.395197			0.197599	+	0.980283i	$0.436686\pi$
$242$	−124.871	+	12.8945i	−0.515996	+	0.0532830i
$243$		0			0
$244$	118.638	−	24.7657i	0.486220	−	0.101499i
$245$	4.06812			0.0166046
$246$		0			0
$247$			34.1704i			0.138342i
$248$	140.441	+	440.408i	0.566293	+	1.77584i
$249$		0			0
$250$	−9.51254	+	0.982289i	−0.0380502	+	0.00392915i
$251$			478.257i			1.90541i	0.303903	+	0.952703i	$0.401710\pi$
$251$			478.257i			1.90541i	−0.303903	+	0.952703i	$0.598290\pi$
$252$		0			0
$253$	48.6852			0.192432
$254$	−16.6444	−	161.186i	−0.0655293	−	0.634589i
$255$		0			0
$256$	174.052	−	187.728i	0.679891	−	0.733313i
$257$	−395.469			−1.53879			−0.769395	−	0.638773i	$-0.779442\pi$
$257$	−395.469			−1.53879			−0.769395	+	0.638773i	$0.779442\pi$
$258$		0			0
$259$		−	483.980i		−	1.86865i
$260$	−2.93596	+	0.612884i	−0.0112921	+	0.00235725i
$261$		0			0
$262$	38.8787	+	376.503i	0.148392	+	1.43704i
$263$			105.268i			0.400260i	0.979769	+	0.200130i	$0.0641365\pi$
$263$			105.268i			0.400260i	−0.979769	+	0.200130i	$0.935863\pi$
$264$		0			0
$265$	3.88129			0.0146464
$266$	−82.9640	+	8.56707i	−0.311895	+	0.0322070i
$267$		0			0
$268$	−49.9034	−	239.057i	−0.186207	−	0.892005i
$269$	27.1446			0.100909			0.0504546	−	0.998726i	$-0.483933\pi$
$269$	27.1446			0.100909			0.0504546	+	0.998726i	$0.483933\pi$
$270$		0			0
$271$			228.783i			0.844218i	0.906545	+	0.422109i	$0.138710\pi$
$271$			228.783i			0.844218i	−0.906545	+	0.422109i	$0.861290\pi$
$272$	244.848	−	106.882i	0.900177	−	0.392949i
$273$		0			0
$274$	−472.012	+	48.7412i	−1.72267	+	0.177887i
$275$		−	190.706i		−	0.693475i
$276$		0			0
$277$	−3.16335			−0.0114200			−0.00571002	−	0.999984i	$-0.501818\pi$
$277$	−3.16335			−0.0114200			−0.00571002	+	0.999984i	$0.501818\pi$
$278$	38.8372	+	376.102i	0.139702	+	1.35288i
$279$		0			0
$280$	−2.22415	−	6.97470i	−0.00794338	−	0.0249097i
$281$	228.667			0.813763			0.406881	−	0.913481i	$-0.366616\pi$
$281$	228.667			0.813763			0.406881	+	0.913481i	$0.366616\pi$
$282$		0			0
$283$			86.7931i			0.306690i	0.988173	+	0.153345i	$0.0490045\pi$
$283$			86.7931i			0.306690i	−0.988173	+	0.153345i	$0.950995\pi$
$284$	−110.066	−	527.262i	−0.387558	−	1.85656i
$285$		0			0
$286$	−12.2892	−	119.010i	−0.0429694	−	0.416118i
$287$			554.538i			1.93219i
$288$		0			0
$289$	−10.1934			−0.0352714
$290$	3.72369	−	0.384518i	0.0128403	−	0.00132592i
$291$		0			0
$292$	198.949	−	41.5309i	0.681334	−	0.142229i
$293$	−423.581			−1.44567			−0.722835	−	0.691021i	$-0.757161\pi$
$293$	−423.581			−1.44567			−0.722835	+	0.691021i	$0.757161\pi$
$294$		0			0
$295$			8.55647i			0.0290050i
$296$	−385.569	+	122.953i	−1.30260	+	0.415382i
$297$		0			0
$298$	−171.027	+	17.6607i	−0.573916	+	0.0592640i
$299$		−	50.0135i		−	0.167269i
$300$		0			0
$301$	126.485			0.420215
$302$	14.3502	+	138.969i	0.0475174	+	0.460161i
$303$		0			0
$304$	27.9017	+	63.9179i	0.0917819	+	0.210256i
$305$	−2.89804			−0.00950176
$306$		0			0
$307$		−	130.373i		−	0.424669i	−0.977197	−	0.212335i	$-0.931893\pi$
$307$		−	130.373i		−	0.424669i	0.977197	−	0.212335i	$-0.0681067\pi$
$308$	285.869	−	59.6754i	0.928145	−	0.193751i
$309$		0			0
$310$	−1.13539	−	10.9952i	−0.00366254	−	0.0354682i
$311$			355.493i			1.14306i	0.820580	+	0.571532i	$0.193651\pi$
$311$			355.493i			1.14306i	−0.820580	+	0.571532i	$0.806349\pi$
$312$		0			0
$313$	190.194			0.607648			0.303824	−	0.952728i	$-0.401736\pi$
$313$	190.194			0.607648			0.303824	+	0.952728i	$0.401736\pi$
$314$	−131.517	+	13.5808i	−0.418844	+	0.0432509i
$315$		0			0
$316$	−8.54875	−	40.9519i	−0.0270530	−	0.129595i
$317$	268.849			0.848105			0.424053	−	0.905638i	$-0.360607\pi$
$317$	268.849			0.848105			0.424053	+	0.905638i	$0.360607\pi$
$318$		0			0
$319$			149.331i			0.468123i
$320$	−4.99145	+	3.54379i	−0.0155983	+	0.0110743i
$321$		0			0
$322$	121.430	−	12.5392i	0.377113	−	0.0389416i
$323$			72.7827i			0.225334i
$324$		0			0
$325$	−195.909			−0.602796
$326$	−43.0457	−	416.857i	−0.132042	−	1.27870i
$327$		0			0
$328$	441.780	−	140.878i	1.34689	−	0.429506i
$329$	401.992			1.22186
$330$		0			0
$331$		−	372.121i		−	1.12423i	−0.827059	−	0.562116i	$-0.809988\pi$
$331$		−	372.121i		−	1.12423i	0.827059	−	0.562116i	$-0.190012\pi$
$332$	−65.7152	−	314.802i	−0.197937	−	0.948198i
$333$		0			0
$334$	19.4519	+	188.374i	0.0582393	+	0.563993i
$335$			5.83960i			0.0174317i
$336$		0			0
$337$	589.875			1.75037			0.875186	−	0.483787i	$-0.160739\pi$
$337$	589.875			1.75037			0.875186	+	0.483787i	$0.160739\pi$
$338$	213.955	−	22.0936i	0.633004	−	0.0653656i
$339$		0			0
$340$	−6.25358	+	1.30544i	−0.0183929	+	0.00383953i
$341$	440.938			1.29307
$342$		0			0
$343$		−	61.8822i		−	0.180415i
$344$	−32.1329	−	100.766i	−0.0934096	−	0.292923i
$345$		0			0
$346$	213.095	−	22.0047i	0.615881	−	0.0635974i
$347$		−	496.275i		−	1.43019i	−0.699028	−	0.715094i	$-0.746384\pi$
$347$		−	496.275i		−	1.43019i	0.699028	−	0.715094i	$-0.253616\pi$
$348$		0			0
$349$	483.924			1.38660			0.693302	−	0.720648i	$-0.256155\pi$
$349$	483.924			1.38660			0.693302	+	0.720648i	$0.256155\pi$
$350$	−49.1175	−	475.657i	−0.140336	−	1.35902i
$351$		0			0
$352$	−120.165	−	212.581i	−0.341377	−	0.603922i
$353$	29.0531			0.0823034			0.0411517	−	0.999153i	$-0.486897\pi$
$353$	29.0531			0.0823034			0.0411517	+	0.999153i	$0.486897\pi$
$354$		0			0
$355$			12.8798i			0.0362810i
$356$	−289.394	+	60.4113i	−0.812904	+	0.169695i
$357$		0			0
$358$	−41.6177	−	403.028i	−0.116251	−	1.12578i
$359$		−	332.143i		−	0.925191i	−0.886570	−	0.462595i	$-0.846918\pi$
$359$		−	332.143i		−	0.925191i	0.886570	−	0.462595i	$-0.153082\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−376.268	+	38.8544i	−1.03941	+	0.107333i
$363$		0			0
$364$	−61.3035	−	293.668i	−0.168416	−	0.806781i
$365$	−4.85986			−0.0133147
$366$		0			0
$367$			250.955i			0.683801i	0.939736	+	0.341900i	$0.111071\pi$
$367$			250.955i			0.683801i	−0.939736	+	0.341900i	$0.888929\pi$
$368$	−40.8383	−	93.5534i	−0.110974	−	0.254221i
$369$		0			0
$370$	9.62603	−	0.994008i	0.0260163	−	0.00268651i
$371$			388.225i			1.04643i
$372$		0			0
$373$	−451.339			−1.21002			−0.605012	−	0.796217i	$-0.706832\pi$
$373$	−451.339			−1.21002			−0.605012	+	0.796217i	$0.706832\pi$
$374$	−26.1760	−	253.490i	−0.0699894	−	0.677781i
$375$		0			0
$376$	−102.124	−	320.252i	−0.271607	−	0.851734i
$377$	153.405			0.406911
$378$		0			0
$379$			244.546i			0.645241i	0.946528	+	0.322620i	$0.104564\pi$
$379$			244.546i			0.645241i	−0.946528	+	0.322620i	$0.895436\pi$
$380$	−0.340786	−	1.63250i	−0.000896806	−	0.00429606i
$381$		0			0
$382$	48.5557	+	470.216i	0.127109	+	1.23093i
$383$			176.792i			0.461599i	0.973001	+	0.230799i	$0.0741341\pi$
$383$			176.792i			0.461599i	−0.973001	+	0.230799i	$0.925866\pi$
$384$		0			0
$385$	−6.98310			−0.0181379
$386$	14.6550	−	1.51331i	0.0379662	−	0.00392049i
$387$		0			0
$388$	−396.461	+	82.7616i	−1.02181	+	0.213303i
$389$	−209.991			−0.539822			−0.269911	−	0.962885i	$-0.586994\pi$
$389$	−209.991			−0.539822			−0.269911	+	0.962885i	$0.586994\pi$
$390$		0			0
$391$		−	106.528i		−	0.272451i
$392$	324.171	−	103.374i	0.826968	−	0.263710i
$393$		0			0
$394$	491.769	−	50.7813i	1.24814	−	0.128887i
$395$			1.00036i			0.00253255i
$396$		0			0
$397$	−435.374			−1.09666			−0.548329	−	0.836262i	$-0.684736\pi$
$397$	−435.374			−1.09666			−0.548329	+	0.836262i	$0.684736\pi$
$398$	−35.8662	−	347.330i	−0.0901161	−	0.872689i
$399$		0			0
$400$	−366.460	+	159.969i	−0.916150	+	0.399922i
$401$	694.395			1.73166			0.865830	−	0.500339i	$-0.166791\pi$
$401$	694.395			1.73166			0.865830	+	0.500339i	$0.166791\pi$
$402$		0			0
$403$		−	452.969i		−	1.12399i
$404$	286.742	−	59.8576i	0.709756	−	0.148162i
$405$		0			0
$406$	38.4612	+	372.461i	0.0947321	+	0.917391i
$407$			386.033i			0.948483i
$408$		0			0
$409$	−587.460			−1.43633			−0.718166	−	0.695871i	$-0.755018\pi$
$409$	−587.460			−1.43633			−0.718166	+	0.695871i	$0.755018\pi$
$410$	−11.0294	+	1.13892i	−0.0269009	+	0.00277786i
$411$		0			0
$412$	−13.5697	−	65.0045i	−0.0329363	−	0.157778i
$413$	−855.858			−2.07229
$414$		0			0
$415$			7.68986i			0.0185298i
$416$	−218.380	+	123.443i	−0.524953	+	0.296739i
$417$		0			0
$418$	66.1738	−	6.83328i	0.158311	−	0.0163475i
$419$		−	485.542i		−	1.15881i	−0.815040	−	0.579405i	$-0.803285\pi$
$419$		−	485.542i		−	1.15881i	0.815040	−	0.579405i	$-0.196715\pi$
$420$		0			0
$421$	−450.385			−1.06980			−0.534900	−	0.844916i	$-0.679651\pi$
$421$	−450.385			−1.06980			−0.534900	+	0.844916i	$0.679651\pi$
$422$	−48.0870	−	465.677i	−0.113950	−	1.10350i
$423$		0			0
$424$	309.284	−	98.6268i	0.729444	−	0.232610i
$425$	−417.285			−0.981847
$426$		0			0
$427$		−	289.875i		−	0.678864i
$428$	−110.998	−	531.724i	−0.259341	−	1.24235i
$429$		0			0
$430$	0.259777	+	2.51570i	0.000604133	+	0.00585046i
$431$			241.465i			0.560244i	0.959964	+	0.280122i	$0.0903750\pi$
$431$			241.465i			0.560244i	−0.959964	+	0.280122i	$0.909625\pi$
$432$		0			0
$433$	650.587			1.50251			0.751255	−	0.660012i	$-0.229449\pi$
$433$	650.587			1.50251			0.751255	+	0.660012i	$0.229449\pi$
$434$	1099.79	−	113.567i	2.53407	−	0.261674i
$435$		0			0
$436$	−83.4060	+	17.4111i	−0.191298	+	0.0399337i
$437$	27.8094			0.0636370
$438$		0			0
$439$		−	624.375i		−	1.42227i	−0.703057	−	0.711134i	$-0.748182\pi$
$439$		−	624.375i		−	1.42227i	0.703057	−	0.711134i	$-0.251818\pi$
$440$	1.77402	+	5.56317i	0.00403187	+	0.0126436i
$441$		0			0
$442$	−260.406	+	26.8902i	−0.589154	+	0.0608375i
$443$			502.356i			1.13399i	0.823722	+	0.566994i	$0.191894\pi$
$443$			502.356i			1.13399i	−0.823722	+	0.566994i	$0.808106\pi$
$444$		0			0
$445$	7.06921			0.0158859
$446$	−29.3231	−	283.967i	−0.0657469	−	0.636697i
$447$		0			0
$448$	−354.466	−	499.268i	−0.791218	−	1.11444i
$449$	134.312			0.299136			0.149568	−	0.988751i	$-0.452212\pi$
$449$	134.312			0.299136			0.149568	+	0.988751i	$0.452212\pi$
$450$		0			0
$451$		−	442.311i		−	0.980734i
$452$	183.185	−	38.2400i	0.405276	−	0.0846018i
$453$		0			0
$454$	−69.5377	−	673.407i	−0.153167	−	1.48328i
$455$			7.17362i			0.0157662i
$456$		0			0
$457$	330.353			0.722873			0.361437	−	0.932397i	$-0.382286\pi$
$457$	330.353			0.722873			0.361437	+	0.932397i	$0.382286\pi$
$458$	208.190	−	21.4983i	0.454564	−	0.0469394i
$459$		0			0
$460$	0.498792	+	2.38941i	0.00108433	+	0.00519438i
$461$	285.670			0.619674			0.309837	−	0.950790i	$-0.399725\pi$
$461$	285.670			0.619674			0.309837	+	0.950790i	$0.399725\pi$
$462$		0			0
$463$			455.529i			0.983864i	0.870634	+	0.491932i	$0.163709\pi$
$463$			455.529i			0.983864i	−0.870634	+	0.491932i	$0.836291\pi$
$464$	286.955	−	125.263i	0.618437	−	0.269963i
$465$		0			0
$466$	212.334	−	21.9261i	0.455652	−	0.0470517i
$467$			236.094i			0.505556i	0.967524	+	0.252778i	$0.0813442\pi$
$467$			236.094i			0.505556i	−0.967524	+	0.252778i	$0.918656\pi$
$468$		0			0
$469$	−584.104			−1.24542
$470$	0.825620	+	7.99535i	0.00175664	+	0.0170114i
$471$		0			0
$472$	217.427	+	681.830i	0.460650	+	1.44455i
$473$	−100.887			−0.213292
$474$		0			0
$475$		−	108.933i		−	0.229332i
$476$	−130.576	−	625.512i	−0.274320	−	1.31410i
$477$		0			0
$478$	50.5813	+	489.833i	0.105819	+	1.02475i
$479$			426.197i			0.889765i	0.895589	+	0.444882i	$0.146755\pi$
$479$			426.197i			0.889765i	−0.895589	+	0.444882i	$0.853245\pi$
$480$		0			0
$481$	396.565			0.824459
$482$	−189.478	+	19.5659i	−0.393107	+	0.0405932i
$483$		0			0
$484$	245.772	−	51.3052i	0.507794	−	0.106002i
$485$	9.68460			0.0199683
$486$		0			0
$487$			929.716i			1.90907i	0.298103	+	0.954534i	$0.403646\pi$
$487$			929.716i			1.90907i	−0.298103	+	0.954534i	$0.596354\pi$
$488$	−230.933	+	73.6415i	−0.473222	+	0.150905i
$489$		0			0
$490$	−8.09320	+	0.835724i	−0.0165167	+	0.00170556i
$491$			770.529i			1.56931i	0.619935	+	0.784653i	$0.287159\pi$
$491$			770.529i			1.56931i	−0.619935	+	0.784653i	$0.712841\pi$
$492$		0			0
$493$	326.753			0.662784
$494$	−7.01971	−	67.9793i	−0.0142099	−	0.137610i
$495$		0			0
$496$	−369.870	−	847.307i	−0.745706	−	1.70828i
$497$	−1288.29			−2.59214
$498$		0			0
$499$		−	701.981i		−	1.40677i	−0.710807	−	0.703387i	$-0.751670\pi$
$499$		−	701.981i		−	1.40677i	0.710807	−	0.703387i	$-0.248330\pi$
$500$	18.7227	−	3.90837i	0.0374453	−	0.00781674i
$501$		0			0
$502$	−98.2496	−	951.455i	−0.195716	−	1.89533i
$503$			766.313i			1.52348i	0.647880	+	0.761742i	$0.275656\pi$
$503$			766.313i			1.52348i	−0.647880	+	0.761742i	$0.724344\pi$
$504$		0			0
$505$	−7.00442			−0.0138701
$506$	−96.8554	+	10.0015i	−0.191414	+	0.0197659i
$507$		0			0
$508$	66.2256	+	317.247i	0.130365	+	0.624502i
$509$	576.596			1.13280			0.566401	−	0.824130i	$-0.308335\pi$
$509$	576.596			1.13280			0.566401	+	0.824130i	$0.308335\pi$
$510$		0			0
$511$		−	486.106i		−	0.951284i
$512$	−307.697	+	409.226i	−0.600972	+	0.799270i
$513$		0			0
$514$	786.755	−	81.2423i	1.53065	−	0.158059i
$515$			1.58791i			0.00308331i
$516$		0			0
$517$	−320.637			−0.620188
$518$	99.4253	+	962.840i	0.191941	+	1.85876i
$519$		0			0
$520$	5.71495	−	1.82243i	0.0109903	−	0.00350467i
$521$	−278.971			−0.535453			−0.267727	−	0.963495i	$-0.586272\pi$
$521$	−278.971			−0.535453			−0.267727	+	0.963495i	$0.586272\pi$
$522$		0			0
$523$		−	15.9961i		−	0.0305854i	−0.999883	−	0.0152927i	$-0.995132\pi$
$523$		−	15.9961i		−	0.0305854i	0.999883	−	0.0152927i	$-0.00486800\pi$
$524$	−154.692	−	741.037i	−0.295214	−	1.41419i
$525$		0			0
$526$	−21.6256	−	209.423i	−0.0411133	−	0.398143i
$527$		−	964.821i		−	1.83078i
$528$		0			0
$529$	488.297			0.923056
$530$	−7.72153	+	0.797344i	−0.0145689	+	0.00150442i
$531$		0			0
$532$	163.290	−	34.0870i	0.306937	−	0.0640734i
$533$	−454.379			−0.852493
$534$		0			0
$535$			12.9888i			0.0242781i
$536$	148.389	+	465.334i	0.276845	+	0.868160i
$537$		0			0
$538$	−54.0020	+	5.57638i	−0.100375	+	0.0103650i
$539$		−	324.562i		−	0.602155i
$540$		0			0
$541$	973.220			1.79893			0.899464	−	0.436995i	$-0.143957\pi$
$541$	973.220			1.79893			0.899464	+	0.436995i	$0.143957\pi$
$542$	−46.9995	−	455.146i	−0.0867149	−	0.839752i
$543$		0			0
$544$	−465.149	+	262.934i	−0.855054	+	0.483334i
$545$	2.03741			0.00373837
$546$		0			0
$547$		−	266.112i		−	0.486494i	−0.969964	−	0.243247i	$-0.921787\pi$
$547$		−	266.112i		−	0.486494i	0.969964	−	0.243247i	$-0.0782126\pi$
$548$	929.018	−	193.933i	1.69529	−	0.353893i
$549$		0			0
$550$	39.1772	+	379.394i	0.0712312	+	0.689807i
$551$			85.2991i			0.154808i
$552$		0			0
$553$	−100.061			−0.180941
$554$	6.29323	−	0.649855i	0.0113596	−	0.00117302i
$555$		0			0
$556$	−154.527	−	740.247i	−0.277927	−	1.33138i
$557$	470.329			0.844398			0.422199	−	0.906503i	$-0.361258\pi$
$557$	470.329			0.844398			0.422199	+	0.906503i	$0.361258\pi$
$558$		0			0
$559$			103.639i			0.185402i
$560$	5.85759	+	13.4187i	0.0104600	+	0.0239620i
$561$		0			0
$562$	−454.916	+	46.9757i	−0.809459	+	0.0835867i
$563$			146.073i			0.259455i	0.991550	+	0.129728i	$0.0414103\pi$
$563$			146.073i			0.259455i	−0.991550	+	0.129728i	$0.958590\pi$
$564$		0			0
$565$	−4.47477			−0.00791995
$566$	−17.8301	−	172.668i	−0.0315020	−	0.305067i
$567$		0			0
$568$	327.285	+	1026.33i	0.576206	+	1.80693i
$569$	−485.326			−0.852945			−0.426472	−	0.904501i	$-0.640244\pi$
$569$	−485.326			−0.852945			−0.426472	+	0.904501i	$0.640244\pi$
$570$		0			0
$571$		−	162.231i		−	0.284118i	−0.989858	−	0.142059i	$-0.954628\pi$
$571$		−	162.231i		−	0.284118i	0.989858	−	0.142059i	$-0.0453722\pi$
$572$	48.8970	+	234.236i	0.0854842	+	0.409503i
$573$		0			0
$574$	−113.920	−	1103.21i	−0.198467	−	1.92197i
$575$			159.439i			0.277286i
$576$		0			0
$577$	126.190			0.218700			0.109350	−	0.994003i	$-0.465123\pi$
$577$	126.190			0.218700			0.109350	+	0.994003i	$0.465123\pi$
$578$	20.2790	−	2.09406i	0.0350848	−	0.00362295i
$579$		0			0
$580$	−7.32900	+	1.52994i	−0.0126362	+	0.00263782i
$581$	−769.176			−1.32388
$582$		0			0
$583$		−	309.656i		−	0.531143i
$584$	−387.262	+	123.493i	−0.663121	+	0.211461i
$585$		0			0
$586$	842.682	−	87.0174i	1.43802	−	0.148494i
$587$			358.563i			0.610839i	0.952218	+	0.305420i	$0.0987967\pi$
$587$			358.563i			0.610839i	−0.952218	+	0.305420i	$0.901203\pi$
$588$		0			0
$589$	251.867			0.427619
$590$	−1.75778	−	17.0224i	−0.00297928	−	0.0288516i
$591$		0			0
$592$	741.800	−	323.814i	1.25304	−	0.546982i
$593$	684.571			1.15442			0.577210	−	0.816596i	$-0.304141\pi$
$593$	684.571			1.15442			0.577210	+	0.816596i	$0.304141\pi$
$594$		0			0
$595$			15.2798i			0.0256803i
$596$	336.617	−	70.2690i	0.564793	−	0.117901i
$597$		0			0
$598$	10.2744	+	99.4979i	0.0171813	+	0.166384i
$599$			126.965i			0.211961i	0.994368	+	0.105981i	$0.0337981\pi$
$599$			126.965i			0.211961i	−0.994368	+	0.105981i	$0.966202\pi$
$600$		0			0
$601$	−613.265			−1.02041			−0.510204	−	0.860054i	$-0.670430\pi$
$601$	−613.265			−1.02041			−0.510204	+	0.860054i	$0.670430\pi$
$602$	−251.632	+	25.9841i	−0.417993	+	0.0431630i
$603$		0			0
$604$	−57.0974	−	273.519i	−0.0945320	−	0.452846i
$605$	−6.00363			−0.00992336
$606$		0			0
$607$			177.313i			0.292114i	0.989276	+	0.146057i	$0.0466583\pi$
$607$			177.313i			0.292114i	−0.989276	+	0.146057i	$0.953342\pi$
$608$	−68.6391	−	121.428i	−0.112893	−	0.199717i
$609$		0			0
$610$	5.76542	−	0.595351i	0.00945150	−	0.000975986i
$611$			329.385i			0.539092i
$612$		0			0
$613$	−529.686			−0.864087			−0.432044	−	0.901853i	$-0.642207\pi$
$613$	−529.686			−0.864087			−0.432044	+	0.901853i	$0.642207\pi$
$614$	26.7830	+	259.368i	0.0436205	+	0.422423i
$615$		0			0
$616$	−556.454	+	177.446i	−0.903334	+	0.288062i
$617$	1003.40			1.62625			0.813125	−	0.582090i	$-0.197765\pi$
$617$	1003.40			1.62625			0.813125	+	0.582090i	$0.197765\pi$
$618$		0			0
$619$		−	563.776i		−	0.910784i	−0.890291	−	0.455392i	$-0.849499\pi$
$619$		−	563.776i		−	0.910784i	0.890291	−	0.455392i	$-0.150501\pi$
$620$	4.51753	+	21.6407i	0.00728633	+	0.0349044i
$621$		0			0
$622$	−73.0298	−	707.225i	−0.117411	−	1.13702i
$623$			707.095i			1.13498i
$624$		0			0
$625$	624.314			0.998902
$626$	−378.376	+	39.0720i	−0.604434	+	0.0624154i
$627$		0			0
$628$	258.853	−	54.0358i	0.412186	−	0.0860442i
$629$	844.681			1.34289
$630$		0			0
$631$			31.1937i			0.0494354i	0.999694	+	0.0247177i	$0.00786868\pi$
$631$			31.1937i			0.0494354i	−0.999694	+	0.0247177i	$0.992131\pi$
$632$	25.4199	+	79.7144i	0.0402214	+	0.126130i
$633$		0			0
$634$	−534.855	+	55.2304i	−0.843620	+	0.0871143i
$635$		−	7.74959i		−	0.0122041i
$636$		0			0
$637$	−333.417			−0.523417
$638$	−30.6775	−	297.083i	−0.0480838	−	0.465647i
$639$		0			0
$640$	9.20209	−	8.07549i	0.0143783	−	0.0126180i
$641$	122.049			0.190403			0.0952017	−	0.995458i	$-0.469650\pi$
$641$	122.049			0.190403			0.0952017	+	0.995458i	$0.469650\pi$
$642$		0			0
$643$			167.907i			0.261130i	0.991440	+	0.130565i	$0.0416792\pi$
$643$			167.907i			0.261130i	−0.991440	+	0.130565i	$0.958321\pi$
$644$	−239.000	+	49.8915i	−0.371118	+	0.0774713i
$645$		0			0
$646$	−14.9519	−	144.796i	−0.0231454	−	0.224142i
$647$			185.483i			0.286682i	0.989673	+	0.143341i	$0.0457846\pi$
$647$			185.483i			0.286682i	−0.989673	+	0.143341i	$0.954215\pi$
$648$		0			0
$649$	682.650			1.05185
$650$	389.745	−	40.2461i	0.599608	−	0.0619170i
$651$		0			0
$652$	171.272	+	820.462i	0.262687	+	1.25838i
$653$	−759.904			−1.16371			−0.581856	−	0.813292i	$-0.697673\pi$
$653$	−759.904			−1.16371			−0.581856	+	0.813292i	$0.697673\pi$
$654$		0			0
$655$			18.1018i			0.0276363i
$656$	−849.945	+	371.021i	−1.29565	+	0.565582i
$657$		0			0
$658$	−799.732	+	82.5823i	−1.21540	+	0.125505i
$659$			443.323i			0.672721i	0.941733	+	0.336360i	$0.109196\pi$
$659$			443.323i			0.672721i	−0.941733	+	0.336360i	$0.890804\pi$
$660$		0			0
$661$	−826.457			−1.25031			−0.625157	−	0.780499i	$-0.714965\pi$
$661$	−826.457			−1.25031			−0.625157	+	0.780499i	$0.714965\pi$
$662$	76.4457	+	740.305i	0.115477	+	1.11829i
$663$		0			0
$664$	195.406	+	612.773i	0.294286	+	0.922851i
$665$	−3.98880			−0.00599819
$666$		0			0
$667$		−	124.848i		−	0.187179i
$668$	−77.3962	−	370.758i	−0.115863	−	0.555028i
$669$		0			0
$670$	−1.19964	−	11.6174i	−0.00179051	−	0.0173394i
$671$			231.210i			0.344576i
$672$		0			0
$673$	−853.769			−1.26860			−0.634301	−	0.773086i	$-0.718712\pi$
$673$	−853.769			−1.26860			−0.634301	+	0.773086i	$0.718712\pi$
$674$	−1173.51	+	121.180i	−1.74111	+	0.179792i
$675$		0			0
$676$	−421.109	+	87.9069i	−0.622942	+	0.130040i
$677$	1219.09			1.80072			0.900360	−	0.435146i	$-0.143303\pi$
$677$	1219.09			1.80072			0.900360	+	0.435146i	$0.143303\pi$
$678$		0			0
$679$			968.699i			1.42665i
$680$	12.1728	−	3.88176i	0.0179012	−	0.00570847i
$681$		0			0
$682$	−877.212	+	90.5831i	−1.28624	+	0.132820i
$683$		−	218.976i		−	0.320610i	−0.987068	−	0.160305i	$-0.948752\pi$
$683$		−	218.976i		−	0.320610i	0.987068	−	0.160305i	$-0.0512477\pi$
$684$		0			0
$685$	−22.6937			−0.0331295
$686$	12.7126	+	123.110i	0.0185315	+	0.179460i
$687$		0			0
$688$	84.6264	+	193.864i	0.123004	+	0.281779i
$689$	−318.105			−0.461690
$690$		0			0
$691$		−	211.157i		−	0.305582i	−0.988259	−	0.152791i	$-0.951174\pi$
$691$		−	211.157i		−	0.305582i	0.988259	−	0.152791i	$-0.0488261\pi$
$692$	−419.415	+	87.5532i	−0.606091	+	0.126522i
$693$		0			0
$694$	101.951	+	987.301i	0.146904	+	1.42262i
$695$			18.0825i			0.0260180i
$696$		0			0
$697$	−967.825			−1.38856
$698$	−962.730	+	99.4139i	−1.37927	+	0.142427i
$699$		0			0
$700$	195.431	+	936.192i	0.279187	+	1.33742i
$701$	119.133			0.169947			0.0849737	−	0.996383i	$-0.472919\pi$
$701$	119.133			0.169947			0.0849737	+	0.996383i	$0.472919\pi$
$702$		0			0
$703$			220.505i			0.313663i
$704$	282.729	+	398.227i	0.401604	+	0.565663i
$705$		0			0
$706$	−57.7989	+	5.96845i	−0.0818681	+	0.00845390i
$707$		−	700.614i		−	0.990968i
$708$		0			0
$709$	678.269			0.956656			0.478328	−	0.878181i	$-0.341243\pi$
$709$	678.269			0.956656			0.478328	+	0.878181i	$0.341243\pi$
$710$	−2.64592	−	25.6233i	−0.00372665	−	0.0360891i
$711$		0			0
$712$	563.316	−	179.634i	0.791174	−	0.252296i
$713$	−368.646			−0.517035
$714$		0			0
$715$		−	5.72183i		−	0.00800256i
$716$	165.590	+	793.243i	0.231271	+	1.10788i
$717$		0			0
$718$	68.2331	+	660.773i	0.0950322	+	0.920297i
$719$		−	553.637i		−	0.770010i	−0.922914	−	0.385005i	$-0.874200\pi$
$719$		−	553.637i		−	0.770010i	0.922914	−	0.385005i	$-0.125800\pi$
$720$		0			0
$721$	−158.830			−0.220291
$722$	37.7990	−	3.90322i	0.0523532	−	0.00540612i
$723$		0			0
$724$	740.574	−	154.596i	1.02289	−	0.213530i
$725$	−489.045			−0.674545
$726$		0			0
$727$			179.368i			0.246724i	0.992362	+	0.123362i	$0.0393676\pi$
$727$			179.368i			0.246724i	−0.992362	+	0.123362i	$0.960632\pi$
$728$	182.288	+	571.636i	0.250395	+	0.785214i
$729$		0			0
$730$	9.66832	−	0.998375i	0.0132443	−	0.00136764i
$731$			220.751i			0.301986i
$732$		0			0
$733$	−681.854			−0.930224			−0.465112	−	0.885252i	$-0.653986\pi$
$733$	−681.854			−0.930224			−0.465112	+	0.885252i	$0.653986\pi$
$734$	−51.5543	−	499.255i	−0.0702375	−	0.680184i
$735$		0			0
$736$	100.464	+	177.728i	0.136499	+	0.241478i
$737$	465.894			0.632149
$738$		0			0
$739$			900.871i			1.21904i	0.792770	+	0.609520i	$0.208638\pi$
$739$			900.871i			1.21904i	−0.792770	+	0.609520i	$0.791362\pi$
$740$	−18.9460	+	3.95500i	−0.0256027	+	0.00534460i
$741$		0			0
$742$	−79.7540	−	772.343i	−0.107485	−	1.04089i
$743$		−	832.140i		−	1.11997i	−0.828502	−	0.559987i	$-0.810806\pi$
$743$		−	832.140i		−	1.11997i	0.828502	−	0.559987i	$-0.189194\pi$
$744$		0			0
$745$	−8.22275			−0.0110372
$746$	897.903	−	92.7197i	1.20362	−	0.124289i
$747$		0			0
$748$	104.150	+	498.921i	0.139238	+	0.667007i
$749$	−1299.20			−1.73457
$750$		0			0
$751$			947.298i			1.26138i	0.776034	+	0.630691i	$0.217228\pi$
$751$			947.298i			1.26138i	−0.776034	+	0.630691i	$0.782772\pi$
$752$	268.959	+	616.137i	0.357658	+	0.819331i
$753$		0			0
$754$	−305.188	+	31.5145i	−0.404759	+	0.0417964i
$755$			6.68142i			0.00884957i
$756$		0			0
$757$	494.147			0.652770			0.326385	−	0.945237i	$-0.394169\pi$
$757$	494.147			0.652770			0.326385	+	0.945237i	$0.394169\pi$
$758$	−50.2378	−	486.506i	−0.0662768	−	0.641828i
$759$		0			0
$760$	1.01334	+	3.17773i	0.00133334	+	0.00418122i
$761$	−768.733			−1.01016			−0.505081	−	0.863072i	$-0.668537\pi$
$761$	−768.733			−1.01016			−0.505081	+	0.863072i	$0.668537\pi$
$762$		0			0
$763$			203.791i			0.267092i
$764$	−193.195	−	925.483i	−0.252874	−	1.21137i
$765$		0			0
$766$	−36.3189	−	351.715i	−0.0474137	−	0.459157i
$767$		−	701.275i		−	0.914309i
$768$		0			0
$769$	412.161			0.535970			0.267985	−	0.963423i	$-0.413642\pi$
$769$	412.161			0.535970			0.267985	+	0.963423i	$0.413642\pi$
$770$	13.8923	−	1.43456i	0.0180420	−	0.00186306i
$771$		0			0
$772$	−28.8440	+	6.02122i	−0.0373627	+	0.00779951i
$773$	267.935			0.346617			0.173309	−	0.984868i	$-0.444554\pi$
$773$	267.935			0.346617			0.173309	+	0.984868i	$0.444554\pi$
$774$		0			0
$775$			1444.03i			1.86326i
$776$	771.726	−	246.094i	0.994492	−	0.317131i
$777$		0			0
$778$	417.760	−	43.1390i	0.536967	−	0.0554485i
$779$		−	252.652i		−	0.324328i
$780$		0			0
$781$	1027.57			1.31571
$782$	21.8844	+	211.930i	0.0279852	+	0.271010i
$783$		0			0
$784$	−623.677	+	272.250i	−0.795507	+	0.347258i
$785$	−6.32316			−0.00805498
$786$		0			0
$787$			110.453i			0.140346i	0.997535	+	0.0701731i	$0.0223552\pi$
$787$			110.453i			0.140346i	−0.997535	+	0.0701731i	$0.977645\pi$
$788$	−967.904	+	202.051i	−1.22830	+	0.256410i
$789$		0			0
$790$	−0.205506	−	1.99014i	−0.000260135	−	0.00251916i
$791$		−	447.588i		−	0.565850i
$792$		0			0
$793$	237.519			0.299519
$794$	866.141	−	89.4399i	1.09086	−	0.112645i
$795$		0			0
$796$	142.706	+	683.618i	0.179279	+	0.858817i
$797$	1548.70			1.94317			0.971583	−	0.236701i	$-0.0760660\pi$
$797$	1548.70			1.94317			0.971583	+	0.236701i	$0.0760660\pi$
$798$		0			0
$799$			701.589i			0.878084i
$800$	696.181	−	393.528i	0.870226	−	0.491910i
$801$		0			0
$802$	−1381.44	+	142.651i	−1.72250	+	0.177870i
$803$			387.728i			0.482850i
$804$		0			0
$805$	5.83821			0.00725243
$806$	93.0546	+	901.146i	0.115452	+	1.11805i
$807$		0			0
$808$	−558.153	+	177.988i	−0.690784	+	0.220282i
$809$	728.020			0.899901			0.449950	−	0.893054i	$-0.351442\pi$
$809$	728.020			0.899901			0.449950	+	0.893054i	$0.351442\pi$
$810$		0			0
$811$		−	954.297i		−	1.17669i	−0.808609	−	0.588346i	$-0.799779\pi$
$811$		−	954.297i		−	1.17669i	0.808609	−	0.588346i	$-0.200221\pi$
$812$	−153.031	−	733.080i	−0.188462	−	0.902808i
$813$		0			0
$814$	−79.3037	−	767.981i	−0.0974247	−	0.943466i
$815$		−	20.0420i		−	0.0245914i
$816$		0			0
$817$	−57.6274			−0.0705354
$818$	1168.71	−	120.683i	1.42874	−	0.147535i
$819$		0			0
$820$	21.7081	−	4.53159i	0.0264733	−	0.00552633i
$821$	721.057			0.878267			0.439133	−	0.898422i	$-0.355286\pi$
$821$	721.057			0.878267			0.439133	+	0.898422i	$0.355286\pi$
$822$		0			0
$823$			1434.21i			1.74266i	0.490699	+	0.871329i	$0.336741\pi$
$823$			1434.21i			1.74266i	−0.490699	+	0.871329i	$0.663259\pi$
$824$	40.3500	+	126.534i	0.0489684	+	0.153560i
$825$		0			0
$826$	1702.66	−	175.821i	2.06133	−	0.212858i
$827$		−	1384.86i		−	1.67456i	−0.546774	−	0.837280i	$-0.684144\pi$
$827$		−	1384.86i		−	1.67456i	0.546774	−	0.837280i	$-0.315856\pi$
$828$		0			0
$829$	−671.349			−0.809829			−0.404915	−	0.914354i	$-0.632699\pi$
$829$	−671.349			−0.809829			−0.404915	+	0.914354i	$0.632699\pi$
$830$	−1.57975	−	15.2984i	−0.00190331	−	0.0184318i
$831$		0			0
$832$	409.092	−	290.443i	0.491697	−	0.349090i
$833$	−710.176			−0.852552
$834$		0			0
$835$			9.05675i			0.0108464i
$836$	−130.244	+	27.1885i	−0.155794	+	0.0325222i
$837$		0			0
$838$	99.7461	+	965.947i	0.119029	+	1.15268i
$839$		−	1429.20i		−	1.70346i	−0.523983	−	0.851729i	$-0.675554\pi$
$839$		−	1429.20i		−	1.70346i	0.523983	−	0.851729i	$-0.324446\pi$
$840$		0			0
$841$	−458.056			−0.544656
$842$	896.006	−	92.5239i	1.06414	−	0.109886i
$843$		0			0
$844$	191.330	+	916.549i	0.226695	+	1.08596i
$845$	10.2867			0.0121736
$846$		0			0
$847$		−	600.511i		−	0.708986i
$848$	−595.035	+	259.747i	−0.701693	+	0.306306i
$849$		0			0
$850$	830.155	−	85.7239i	0.976653	−	0.100852i
$851$		−	322.742i		−	0.379250i
$852$		0			0
$853$	−399.859			−0.468768			−0.234384	−	0.972144i	$-0.575307\pi$
$853$	−399.859			−0.468768			−0.234384	+	0.972144i	$0.575307\pi$
$854$	59.5498	+	576.684i	0.0697304	+	0.675274i
$855$		0			0
$856$	330.055	+	1035.02i	0.385578	+	1.20914i
$857$	86.5773			0.101024			0.0505118	−	0.998723i	$-0.483915\pi$
$857$	86.5773			0.101024			0.0505118	+	0.998723i	$0.483915\pi$
$858$		0			0
$859$		−	1144.17i		−	1.33198i	−0.745960	−	0.665991i	$-0.768009\pi$
$859$		−	1144.17i		−	1.33198i	0.745960	−	0.665991i	$-0.231991\pi$
$860$	−1.03361	−	4.95141i	−0.00120187	−	0.00575746i
$861$		0			0
$862$	−49.6048	−	480.376i	−0.0575462	−	0.557281i
$863$		−	1121.50i		−	1.29954i	−0.760130	−	0.649771i	$-0.774865\pi$
$863$		−	1121.50i		−	1.29954i	0.760130	−	0.649771i	$-0.225135\pi$
$864$		0			0
$865$	10.2453			0.0118443
$866$	−1294.29	+	133.652i	−1.49456	+	0.154332i
$867$		0			0
$868$	−2164.61	+	451.864i	−2.49379	+	0.520580i
$869$	79.8104			0.0918416
$870$		0			0
$871$		−	478.605i		−	0.549489i
$872$	162.353	−	51.7723i	0.186185	−	0.0593719i
$873$		0			0
$874$	−55.3245	+	5.71295i	−0.0633004	+	0.00653656i
$875$		−	45.7463i		−	0.0522815i
$876$		0			0
$877$	1460.55			1.66540			0.832698	−	0.553727i	$-0.186795\pi$
$877$	1460.55			1.66540			0.832698	+	0.553727i	$0.186795\pi$
$878$	128.267	+	1242.15i	0.146090	+	1.41474i
$879$		0			0
$880$	−4.67214	−	10.7030i	−0.00530925	−	0.0121626i
$881$	−1514.46			−1.71902			−0.859512	−	0.511116i	$-0.829232\pi$
$881$	−1514.46			−1.71902			−0.859512	+	0.511116i	$0.829232\pi$
$882$		0			0
$883$			715.217i			0.809986i	0.914320	+	0.404993i	$0.132726\pi$
$883$			715.217i			0.809986i	−0.914320	+	0.404993i	$0.867274\pi$
$884$	512.533	−	106.992i	0.579789	−	0.121031i
$885$		0			0
$886$	−103.200	−	999.399i	−0.116479	−	1.12799i
$887$		−	922.246i		−	1.03974i	−0.854247	−	0.519868i	$-0.825981\pi$
$887$		−	922.246i		−	1.03974i	0.854247	−	0.519868i	$-0.174019\pi$
$888$		0			0
$889$	775.150			0.871935
$890$	−14.0636	+	1.45225i	−0.0158018	+	0.00163174i
$891$		0			0
$892$	116.672	+	558.906i	0.130798	+	0.626576i
$893$	−183.151			−0.205096
$894$		0			0
$895$		−	19.3771i		−	0.0216503i
$896$	807.748	+	920.435i	0.901504	+	1.02727i
$897$		0			0
$898$	−267.204	+	27.5921i	−0.297554	+	0.0307262i
$899$		−	1130.74i		−	1.25778i
$900$		0			0
$901$	−677.561			−0.752010
$902$	90.8651	+	879.943i	0.100737	+	0.975547i
$903$		0			0
$904$	−356.576	+	113.708i	−0.394443	+	0.125783i
$905$	−18.0905			−0.0199895
$906$		0			0
$907$		−	467.193i		−	0.515098i	−0.966265	−	0.257549i	$-0.917085\pi$
$907$		−	467.193i		−	0.515098i	0.966265	−	0.257549i	$-0.0829148\pi$
$908$	276.680	+	1325.41i	0.304713	+	1.45970i
$909$		0			0
$910$	−1.47370	−	14.2714i	−0.00161945	−	0.0156828i
$911$			686.124i			0.753155i	0.926385	+	0.376577i	$0.122899\pi$
$911$			686.124i			0.753155i	−0.926385	+	0.376577i	$0.877101\pi$
$912$		0			0
$913$	613.511			0.671972
$914$	−657.212	+	67.8653i	−0.719050	+	0.0742509i
$915$		0			0
$916$	−409.762	+	85.5382i	−0.447338	+	0.0933823i
$917$	−1810.62			−1.97451
$918$		0			0
$919$			810.952i			0.882429i	0.897402	+	0.441215i	$0.145452\pi$
$919$			810.952i			0.882429i	−0.897402	+	0.441215i	$0.854548\pi$
$920$	−1.48317	−	4.65108i	−0.00161214	−	0.00505552i
$921$		0			0
$922$	−568.318	+	58.6859i	−0.616397	+	0.0636507i
$923$		−	1055.61i		−	1.14367i
$924$		0			0
$925$	−1264.22			−1.36672
$926$	−93.5806	−	906.240i	−0.101059	−	0.978660i
$927$		0			0
$928$	−545.141	+	308.150i	−0.587436	+	0.332058i
$929$	714.900			0.769538			0.384769	−	0.923013i	$-0.374281\pi$
$929$	714.900			0.769538			0.384769	+	0.923013i	$0.374281\pi$
$930$		0			0
$931$		−	185.392i		−	0.199132i
$932$	−417.917	+	87.2406i	−0.448409	+	0.0936057i
$933$		0			0
$934$	−48.5015	−	469.691i	−0.0519288	−	0.502882i
$935$		−	12.1875i		−	0.0130347i
$936$		0			0
$937$	295.227			0.315077			0.157539	−	0.987513i	$-0.449644\pi$
$937$	295.227			0.315077			0.157539	+	0.987513i	$0.449644\pi$
$938$	1162.03	−	119.994i	1.23884	−	0.127925i
$939$		0			0
$940$	−3.28501	−	15.7365i	−0.00349469	−	0.0167410i
$941$	150.067			0.159476			0.0797382	−	0.996816i	$-0.474592\pi$
$941$	150.067			0.159476			0.0797382	+	0.996816i	$0.474592\pi$
$942$		0			0
$943$			369.794i			0.392146i
$944$	−572.624	−	1311.78i	−0.606593	−	1.38960i
$945$		0			0
$946$	200.707	−	20.7255i	0.212163	−	0.0219085i
$947$		−	475.749i		−	0.502374i	−0.967939	−	0.251187i	$-0.919179\pi$
$947$		−	475.749i		−	0.502374i	0.967939	−	0.251187i	$-0.0808210\pi$
$948$		0			0
$949$	398.307			0.419712
$950$	22.3783	+	216.713i	0.0235561	+	0.228119i
$951$		0			0
$952$	388.271	+	1217.58i	0.407848	+	1.27897i
$953$	150.444			0.157863			0.0789317	−	0.996880i	$-0.474849\pi$
$953$	150.444			0.157863			0.0789317	+	0.996880i	$0.474849\pi$
$954$		0			0
$955$			22.6074i			0.0236726i
$956$	−201.255	−	964.092i	−0.210518	−	1.00846i
$957$		0			0
$958$	−87.5548	−	847.886i	−0.0913933	−	0.885058i
$959$		−	2269.93i		−	2.36698i
$960$		0			0
$961$	−2377.80			−2.47430
$962$	−788.935	+	81.4674i	−0.820098	+	0.0846854i
$963$		0			0
$964$	372.931	−	77.8497i	0.386858	−	0.0807570i
$965$	0.704591			0.000730147
$966$		0			0
$967$		−	1359.56i		−	1.40595i	−0.711214	−	0.702976i	$-0.751854\pi$
$967$		−	1359.56i		−	1.40595i	0.711214	−	0.702976i	$-0.248146\pi$
$968$	−478.405	+	152.557i	−0.494220	+	0.157600i
$969$		0			0
$970$	−19.2668	+	1.98953i	−0.0198626	+	0.00205107i
$971$			1070.02i			1.10198i	0.834513	+	0.550989i	$0.185749\pi$
$971$			1070.02i			1.10198i	−0.834513	+	0.550989i	$0.814251\pi$
$972$		0			0
$973$	−1808.69			−1.85888
$974$	−190.994	−	1849.60i	−0.196092	−	1.89897i
$975$		0			0
$976$	444.294	−	193.945i	0.455219	−	0.198714i
$977$	−512.923			−0.524998			−0.262499	−	0.964932i	$-0.584547\pi$
$977$	−512.923			−0.524998			−0.262499	+	0.964932i	$0.584547\pi$
$978$		0			0
$979$		−	563.994i		−	0.576092i
$980$	15.9291	−	3.32521i	0.0162542	−	0.00339308i
$981$		0			0
$982$	−158.292	−	1532.91i	−0.161193	−	1.56101i
$983$			1799.31i			1.83042i	0.402974	+	0.915212i	$0.367977\pi$
$983$			1799.31i			1.83042i	−0.402974	+	0.915212i	$0.632023\pi$
$984$		0			0
$985$	23.6436			0.0240037
$986$	−650.049	+	67.1257i	−0.659279	+	0.0680788i
$987$		0			0
$988$	27.9303	+	133.797i	0.0282696	+	0.135422i
$989$	84.3464			0.0852845
$990$		0			0
$991$			921.947i			0.930320i	0.885227	+	0.465160i	$0.154003\pi$
$991$			921.947i			0.930320i	−0.885227	+	0.465160i	$0.845997\pi$
$992$	909.892	+	1609.67i	0.917230	+	1.62265i
$993$		0			0
$994$	2562.96	−	264.657i	2.57843	−	0.266255i
$995$		−	16.6992i		−	0.0167831i
$996$		0			0
$997$	1642.31			1.64725			0.823625	−	0.567134i	$-0.191948\pi$
$997$	1642.31			1.64725			0.823625	+	0.567134i	$0.191948\pi$
$998$	144.210	+	1396.54i	0.144499	+	1.39933i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.2	yes	36
3.2	odd	2	inner	684.3.g.d.343.35	yes	36
4.3	odd	2	inner	684.3.g.d.343.1	✓	36
12.11	even	2	inner	684.3.g.d.343.36	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.1	✓	36	4.3	odd	2	inner
684.3.g.d.343.2	yes	36	1.1	even	1	trivial
684.3.g.d.343.35	yes	36	3.2	odd	2	inner
684.3.g.d.343.36	yes	36	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98942 + 0.205433i) q^{2} +(3.91559 - 0.817384i) q^{4} -0.0956487 q^{5} -9.56723i q^{7} +(-7.62185 + 2.43051i) q^{8} +O(q^{10})\)	\(q+(-1.98942 + 0.205433i) q^{2} +(3.91559 - 0.817384i) q^{4} -0.0956487 q^{5} -9.56723i q^{7} +(-7.62185 + 2.43051i) q^{8} +(0.190286 - 0.0196494i) q^{10} +7.63102i q^{11} +7.83922 q^{13} +(1.96542 + 19.0332i) q^{14} +(14.6638 - 6.40109i) q^{16} +16.6975 q^{17} +4.35890i q^{19} +(-0.374522 + 0.0781817i) q^{20} +(-1.56766 - 15.1813i) q^{22} -6.37991i q^{23} -24.9909 q^{25} +(-15.5955 + 1.61043i) q^{26} +(-7.82010 - 37.4614i) q^{28} +19.5690 q^{29} -57.7824i q^{31} +(-27.8574 + 15.7469i) q^{32} +(-33.2184 + 3.43021i) q^{34} +0.915093i q^{35} +50.5873 q^{37} +(-0.895460 - 8.67169i) q^{38} +(0.729020 - 0.232475i) q^{40} -57.9622 q^{41} +13.2206i q^{43} +(6.23748 + 29.8800i) q^{44} +(1.31064 + 12.6923i) q^{46} +42.0176i q^{47} -42.5319 q^{49} +(49.7173 - 5.13394i) q^{50} +(30.6952 - 6.40766i) q^{52} -40.5786 q^{53} -0.729898i q^{55} +(23.2533 + 72.9200i) q^{56} +(-38.9309 + 4.02010i) q^{58} -89.4572i q^{59} +30.2988 q^{61} +(11.8704 + 114.953i) q^{62} +(52.1852 - 37.0500i) q^{64} -0.749812 q^{65} -61.0526i q^{67} +(65.3807 - 13.6483i) q^{68} +(-0.187990 - 1.82051i) q^{70} -134.657i q^{71} +50.8095 q^{73} +(-100.639 + 10.3923i) q^{74} +(3.56289 + 17.0677i) q^{76} +73.0077 q^{77} -10.4587i q^{79} +(-1.40257 + 0.612256i) q^{80} +(115.311 - 11.9073i) q^{82} -80.3969i q^{83} -1.59709 q^{85} +(-2.71595 - 26.3014i) q^{86} +(-18.5473 - 58.1625i) q^{88} -73.9080 q^{89} -74.9996i q^{91} +(-5.21483 - 24.9811i) q^{92} +(-8.63179 - 83.5908i) q^{94} -0.416923i q^{95} -101.252 q^{97} +(84.6138 - 8.73743i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 36 * q - 12 * q^4	\( 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) \) 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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