LMFDB - Embedded newform 690.3.b.a.599.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(599,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.599");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.b (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.15
Character	$\chi$	$=$	690.599
Dual form			690.3.b.a.599.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-1.42652 - 2.63914i) q^{3} +2.00000 q^{4} +(-3.84011 - 3.20212i) q^{5} +(2.01740 + 3.73230i) q^{6} +12.7200i q^{7} -2.82843 q^{8} +(-4.93010 + 7.52955i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-1.42652 - 2.63914i) q^{3} +2.00000 q^{4} +(-3.84011 - 3.20212i) q^{5} +(2.01740 + 3.73230i) q^{6} +12.7200i q^{7} -2.82843 q^{8} +(-4.93010 + 7.52955i) q^{9} +(5.43073 + 4.52848i) q^{10} -2.23541i q^{11} +(-2.85303 - 5.27828i) q^{12} -0.635761i q^{13} -17.9888i q^{14} +(-2.97286 + 14.7025i) q^{15} +4.00000 q^{16} -9.66062 q^{17} +(6.97221 - 10.6484i) q^{18} +3.49572 q^{19} +(-7.68021 - 6.40424i) q^{20} +(33.5698 - 18.1453i) q^{21} +3.16135i q^{22} +4.79583 q^{23} +(4.03480 + 7.46461i) q^{24} +(4.49285 + 24.5930i) q^{25} +0.899101i q^{26} +(26.9044 + 2.27017i) q^{27} +25.4400i q^{28} -36.8343i q^{29} +(4.20426 - 20.7924i) q^{30} +38.8991 q^{31} -5.65685 q^{32} +(-5.89957 + 3.18886i) q^{33} +13.6622 q^{34} +(40.7310 - 48.8462i) q^{35} +(-9.86020 + 15.0591i) q^{36} -2.05039i q^{37} -4.94369 q^{38} +(-1.67786 + 0.906924i) q^{39} +(10.8615 + 9.05696i) q^{40} +20.9083i q^{41} +(-47.4749 + 25.6613i) q^{42} -44.3973i q^{43} -4.47083i q^{44} +(43.0426 - 13.1275i) q^{45} -6.78233 q^{46} -12.6819 q^{47} +(-5.70607 - 10.5566i) q^{48} -112.798 q^{49} +(-6.35385 - 34.7797i) q^{50} +(13.7810 + 25.4957i) q^{51} -1.27152i q^{52} -32.1430 q^{53} +(-38.0486 - 3.21051i) q^{54} +(-7.15807 + 8.58423i) q^{55} -35.9776i q^{56} +(-4.98670 - 9.22568i) q^{57} +52.0916i q^{58} -34.6353i q^{59} +(-5.94572 + 29.4049i) q^{60} +15.4050 q^{61} -55.0116 q^{62} +(-95.7759 - 62.7108i) q^{63} +8.00000 q^{64} +(-2.03578 + 2.44139i) q^{65} +(8.34325 - 4.50972i) q^{66} -103.378i q^{67} -19.3212 q^{68} +(-6.84134 - 12.6569i) q^{69} +(-57.6023 + 69.0789i) q^{70} +103.333i q^{71} +(13.9444 - 21.2968i) q^{72} -66.4287i q^{73} +2.89969i q^{74} +(58.4951 - 46.9395i) q^{75} +6.99144 q^{76} +28.4345 q^{77} +(2.37285 - 1.28258i) q^{78} -62.2728 q^{79} +(-15.3604 - 12.8085i) q^{80} +(-32.3883 - 74.2428i) q^{81} -29.5687i q^{82} -21.9860 q^{83} +(67.1397 - 36.2906i) q^{84} +(37.0978 + 30.9345i) q^{85} +62.7873i q^{86} +(-97.2109 + 52.5448i) q^{87} +6.32271i q^{88} -12.4162i q^{89} +(-60.8715 + 18.5651i) q^{90} +8.08687 q^{91} +9.59166 q^{92} +(-55.4902 - 102.660i) q^{93} +17.9349 q^{94} +(-13.4239 - 11.1937i) q^{95} +(8.06960 + 14.9292i) q^{96} -110.069i q^{97} +159.521 q^{98} +(16.8317 + 11.0208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) $ 88 * q + 176 * q^4 + 8 * q^9	$ 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) $ 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−1.42652	−	2.63914i	−0.475506	−	0.879713i
$3$	−1.42652	−	2.63914i	−0.475506	−	0.879713i
$4$	2.00000			0.500000
$5$	−3.84011	−	3.20212i	−0.768021	−	0.640424i
$5$	−3.84011	−	3.20212i	−0.768021	−	0.640424i
$6$	2.01740	+	3.73230i	0.336233	+	0.622051i
$7$			12.7200i			1.81714i	0.417730	+	0.908571i	$0.362826\pi$
$7$			12.7200i			1.81714i	−0.417730	+	0.908571i	$0.637174\pi$
$8$	−2.82843			−0.353553
$9$	−4.93010	+	7.52955i	−0.547789	+	0.836617i
$10$	5.43073	+	4.52848i	0.543073	+	0.452848i
$11$		−	2.23541i		−	0.203219i	−0.994824	−	0.101610i	$-0.967601\pi$
$11$		−	2.23541i		−	0.203219i	0.994824	−	0.101610i	$-0.0323993\pi$
$12$	−2.85303	−	5.27828i	−0.237753	−	0.439856i
$13$		−	0.635761i		−	0.0489047i	−0.999701	−	0.0244523i	$-0.992216\pi$
$13$		−	0.635761i		−	0.0489047i	0.999701	−	0.0244523i	$-0.00778420\pi$
$14$		−	17.9888i		−	1.28491i
$15$	−2.97286	+	14.7025i	−0.198191	+	0.980164i
$16$	4.00000			0.250000
$17$	−9.66062			−0.568272			−0.284136	−	0.958784i	$-0.591707\pi$
$17$	−9.66062			−0.568272			−0.284136	+	0.958784i	$0.591707\pi$
$18$	6.97221	−	10.6484i	0.387345	−	0.591577i
$19$	3.49572			0.183985			0.0919926	−	0.995760i	$-0.470676\pi$
$19$	3.49572			0.183985			0.0919926	+	0.995760i	$0.470676\pi$
$20$	−7.68021	−	6.40424i	−0.384011	−	0.320212i
$21$	33.5698	−	18.1453i	1.59856	−	0.864062i
$22$			3.16135i			0.143698i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$	4.03480	+	7.46461i	0.168117	+	0.311025i
$25$	4.49285	+	24.5930i	0.179714	+	0.983719i
$26$			0.899101i			0.0345808i
$27$	26.9044	+	2.27017i	0.996459	+	0.0840805i
$28$			25.4400i			0.908571i
$29$		−	36.8343i		−	1.27015i	−0.772451	−	0.635075i	$-0.780969\pi$
$29$		−	36.8343i		−	1.27015i	0.772451	−	0.635075i	$-0.219031\pi$
$30$	4.20426	−	20.7924i	0.140142	−	0.693080i
$31$	38.8991			1.25481			0.627405	−	0.778693i	$-0.284117\pi$
$31$	38.8991			1.25481			0.627405	+	0.778693i	$0.284117\pi$
$32$	−5.65685			−0.176777
$33$	−5.89957	+	3.18886i	−0.178775	+	0.0966320i
$34$	13.6622			0.401829
$35$	40.7310	−	48.8462i	1.16374	−	1.39560i
$36$	−9.86020	+	15.0591i	−0.273894	+	0.418308i
$37$		−	2.05039i		−	0.0554160i	−0.999616	−	0.0277080i	$-0.991179\pi$
$37$		−	2.05039i		−	0.0554160i	0.999616	−	0.0277080i	$-0.00882086\pi$
$38$	−4.94369			−0.130097
$39$	−1.67786	+	0.906924i	−0.0430221	+	0.0232544i
$40$	10.8615	+	9.05696i	0.271537	+	0.226424i
$41$			20.9083i			0.509957i	0.966947	+	0.254979i	$0.0820685\pi$
$41$			20.9083i			0.509957i	−0.966947	+	0.254979i	$0.917932\pi$
$42$	−47.4749	+	25.6613i	−1.13035	+	0.610984i
$43$		−	44.3973i		−	1.03250i	−0.856439	−	0.516248i	$-0.827328\pi$
$43$		−	44.3973i		−	1.03250i	0.856439	−	0.516248i	$-0.172672\pi$
$44$		−	4.47083i		−	0.101610i
$45$	43.0426	−	13.1275i	0.956503	−	0.291723i
$46$	−6.78233			−0.147442
$47$	−12.6819			−0.269828			−0.134914	−	0.990857i	$-0.543076\pi$
$47$	−12.6819			−0.269828			−0.134914	+	0.990857i	$0.543076\pi$
$48$	−5.70607	−	10.5566i	−0.118876	−	0.219928i
$49$	−112.798			−2.30201
$50$	−6.35385	−	34.7797i	−0.127077	−	0.695594i
$51$	13.7810	+	25.4957i	0.270217	+	0.499916i
$52$		−	1.27152i		−	0.0244523i
$53$	−32.1430			−0.606472			−0.303236	−	0.952915i	$-0.598067\pi$
$53$	−32.1430			−0.606472			−0.303236	+	0.952915i	$0.598067\pi$
$54$	−38.0486	−	3.21051i	−0.704603	−	0.0594539i
$55$	−7.15807	+	8.58423i	−0.130147	+	0.156077i
$56$		−	35.9776i		−	0.642457i
$57$	−4.98670	−	9.22568i	−0.0874860	−	0.161854i
$58$			52.0916i			0.898131i
$59$		−	34.6353i		−	0.587038i	−0.955953	−	0.293519i	$-0.905174\pi$
$59$		−	34.6353i		−	0.587038i	0.955953	−	0.293519i	$-0.0948264\pi$
$60$	−5.94572	+	29.4049i	−0.0990953	+	0.490082i
$61$	15.4050			0.252541			0.126271	−	0.991996i	$-0.459699\pi$
$61$	15.4050			0.252541			0.126271	+	0.991996i	$0.459699\pi$
$62$	−55.0116			−0.887284
$63$	−95.7759	−	62.7108i	−1.52025	−	0.995410i
$64$	8.00000			0.125000
$65$	−2.03578	+	2.44139i	−0.0313197	+	0.0375598i
$66$	8.34325	−	4.50972i	0.126413	−	0.0683292i
$67$		−	103.378i		−	1.54296i	−0.636255	−	0.771479i	$-0.719517\pi$
$67$		−	103.378i		−	1.54296i	0.636255	−	0.771479i	$-0.280483\pi$
$68$	−19.3212			−0.284136
$69$	−6.84134	−	12.6569i	−0.0991498	−	0.183433i
$70$	−57.6023	+	69.0789i	−0.822890	+	0.986841i
$71$			103.333i			1.45539i	0.685899	+	0.727697i	$0.259409\pi$
$71$			103.333i			1.45539i	−0.685899	+	0.727697i	$0.740591\pi$
$72$	13.9444	−	21.2968i	0.193673	−	0.295789i
$73$		−	66.4287i		−	0.909982i	−0.890496	−	0.454991i	$-0.849642\pi$
$73$		−	66.4287i		−	0.909982i	0.890496	−	0.454991i	$-0.150358\pi$
$74$			2.89969i			0.0391850i
$75$	58.4951	−	46.9395i	0.779935	−	0.625861i
$76$	6.99144			0.0919926
$77$	28.4345			0.369279
$78$	2.37285	−	1.28258i	0.0304212	−	0.0164434i
$79$	−62.2728			−0.788263			−0.394131	−	0.919054i	$-0.628955\pi$
$79$	−62.2728			−0.788263			−0.394131	+	0.919054i	$0.628955\pi$
$80$	−15.3604	−	12.8085i	−0.192005	−	0.160106i
$81$	−32.3883	−	74.2428i	−0.399855	−	0.916578i
$82$		−	29.5687i		−	0.360594i
$83$	−21.9860			−0.264892			−0.132446	−	0.991190i	$-0.542283\pi$
$83$	−21.9860			−0.264892			−0.132446	+	0.991190i	$0.542283\pi$
$84$	67.1397	−	36.2906i	0.799282	−	0.432031i
$85$	37.0978	+	30.9345i	0.436445	+	0.363935i
$86$			62.7873i			0.730085i
$87$	−97.2109	+	52.5448i	−1.11737	+	0.603963i
$88$			6.32271i			0.0718489i
$89$		−	12.4162i		−	0.139507i	−0.997564	−	0.0697537i	$-0.977779\pi$
$89$		−	12.4162i		−	0.139507i	0.997564	−	0.0697537i	$-0.0222213\pi$
$90$	−60.8715	+	18.5651i	−0.676350	+	0.206279i
$91$	8.08687			0.0888668
$92$	9.59166			0.104257
$93$	−55.4902	−	102.660i	−0.596669	−	1.10387i
$94$	17.9349			0.190797
$95$	−13.4239	−	11.1937i	−0.141305	−	0.117829i
$96$	8.06960	+	14.9292i	0.0840583	+	0.155513i
$97$		−	110.069i		−	1.13473i	−0.823467	−	0.567364i	$-0.807963\pi$
$97$		−	110.069i		−	1.13473i	0.823467	−	0.567364i	$-0.192037\pi$
$98$	159.521			1.62776
$99$	16.8317	+	11.0208i	0.170017	+	0.111321i
$100$	8.98570	+	49.1859i	0.0898570	+	0.491859i
$101$		−	64.4166i		−	0.637788i	−0.947790	−	0.318894i	$-0.896689\pi$
$101$		−	64.4166i		−	0.637788i	0.947790	−	0.318894i	$-0.103311\pi$
$102$	−19.4893	−	36.0564i	−0.191072	−	0.353494i
$103$		−	144.898i		−	1.40677i	−0.710808	−	0.703386i	$-0.751671\pi$
$103$		−	144.898i		−	1.40677i	0.710808	−	0.703386i	$-0.248329\pi$
$104$			1.79820i			0.0172904i
$105$	−187.015	−	37.8147i	−1.78110	−	0.360140i
$106$	45.4571			0.428841
$107$	166.897			1.55979			0.779893	−	0.625912i	$-0.215273\pi$
$107$	166.897			1.55979			0.779893	+	0.625912i	$0.215273\pi$
$108$	53.8088	+	4.54035i	0.498229	+	0.0420403i
$109$	69.4580			0.637229			0.318615	−	0.947884i	$-0.396782\pi$
$109$	69.4580			0.637229			0.318615	+	0.947884i	$0.396782\pi$
$110$	10.1230	−	12.1399i	0.0920276	−	0.110363i
$111$	−5.41127	+	2.92492i	−0.0487502	+	0.0263506i
$112$			50.8800i			0.454286i
$113$	96.8045			0.856677			0.428339	−	0.903618i	$-0.359099\pi$
$113$	96.8045			0.856677			0.428339	+	0.903618i	$0.359099\pi$
$114$	7.05226	+	13.0471i	0.0618619	+	0.114448i
$115$	−18.4165	−	15.3568i	−0.160144	−	0.133538i
$116$		−	73.6687i		−	0.635075i
$117$	4.78699	+	3.13436i	0.0409145	+	0.0267894i
$118$			48.9816i			0.415099i
$119$		−	122.883i		−	1.03263i
$120$	8.40851	−	41.5848i	0.0700709	−	0.346540i
$121$	116.003			0.958702
$122$	−21.7860			−0.178573
$123$	55.1798	−	29.8260i	0.448616	−	0.242488i
$124$	77.7982			0.627405
$125$	61.4966	−	108.826i	0.491973	−	0.870610i
$126$	135.448	+	88.6865i	1.07498	+	0.703861i
$127$			122.722i			0.966313i	0.875534	+	0.483156i	$0.160510\pi$
$127$			122.722i			0.966313i	−0.875534	+	0.483156i	$0.839490\pi$
$128$	−11.3137			−0.0883883
$129$	−117.171	+	63.3336i	−0.908300	+	0.490958i
$130$	2.87903	−	3.45265i	0.0221464	−	0.0265588i
$131$		−	217.468i		−	1.66006i	−0.557719	−	0.830030i	$-0.688323\pi$
$131$		−	217.468i		−	1.66006i	0.557719	−	0.830030i	$-0.311677\pi$
$132$	−11.7991	+	6.37771i	−0.0893874	+	0.0483160i
$133$			44.4655i			0.334327i
$134$			146.199i			1.09104i
$135$	−96.0464	−	94.8688i	−0.711455	−	0.702732i
$136$	27.3244			0.200914
$137$	−89.8051			−0.655512			−0.327756	−	0.944762i	$-0.606292\pi$
$137$	−89.8051			−0.655512			−0.327756	+	0.944762i	$0.606292\pi$
$138$	9.67511	+	17.8995i	0.0701095	+	0.129707i
$139$	−250.096			−1.79925			−0.899626	−	0.436661i	$-0.856161\pi$
$139$	−250.096			−1.79925			−0.899626	+	0.436661i	$0.856161\pi$
$140$	81.4619	−	97.6923i	0.581871	−	0.697802i
$141$	18.0910	+	33.4693i	0.128305	+	0.237371i
$142$		−	146.135i		−	1.02912i
$143$	−1.42119			−0.00993838
$144$	−19.7204	+	30.1182i	−0.136947	+	0.209154i
$145$	−117.948	+	141.448i	−0.813434	+	0.975502i
$146$			93.9444i			0.643455i
$147$	160.909	+	297.690i	1.09462	+	2.02510i
$148$		−	4.10078i		−	0.0277080i
$149$			252.216i			1.69272i	0.532609	+	0.846361i	$0.321212\pi$
$149$			252.216i			1.69272i	−0.532609	+	0.846361i	$0.678788\pi$
$150$	−82.7246	+	66.3825i	−0.551497	+	0.442550i
$151$	−209.187			−1.38535			−0.692673	−	0.721252i	$-0.743567\pi$
$151$	−209.187			−1.38535			−0.692673	+	0.721252i	$0.743567\pi$
$152$	−9.88738			−0.0650486
$153$	47.6278	−	72.7402i	0.311293	−	0.475426i
$154$	−40.2124			−0.261120
$155$	−149.377	−	124.560i	−0.963721	−	0.803610i
$156$	−3.35572	+	1.81385i	−0.0215110	+	0.0116272i
$157$		−	159.472i		−	1.01574i	−0.861433	−	0.507872i	$-0.830432\pi$
$157$		−	159.472i		−	1.01574i	0.861433	−	0.507872i	$-0.169568\pi$
$158$	88.0670			0.557386
$159$	45.8526	+	84.8299i	0.288381	+	0.533521i
$160$	21.7229	+	18.1139i	0.135768	+	0.113212i
$161$			61.0030i			0.378900i
$162$	45.8039	+	104.995i	0.282740	+	0.648119i
$163$		−	55.1297i		−	0.338219i	−0.985597	−	0.169110i	$-0.945911\pi$
$163$		−	55.1297i		−	0.338219i	0.985597	−	0.169110i	$-0.0540892\pi$
$164$			41.8165i			0.254979i
$165$	32.8661	+	6.64557i	0.199188	+	0.0402762i
$166$	31.0929			0.187307
$167$	303.620			1.81808			0.909042	−	0.416704i	$-0.136815\pi$
$167$	303.620			1.81808			0.909042	+	0.416704i	$0.136815\pi$
$168$	−94.9498	+	51.3226i	−0.565177	+	0.305492i
$169$	168.596			0.997608
$170$	−52.4643	−	43.7480i	−0.308613	−	0.257341i
$171$	−17.2342	+	26.3212i	−0.100785	+	0.153925i
$172$		−	88.7947i		−	0.516248i
$173$	−88.9298			−0.514045			−0.257022	−	0.966405i	$-0.582741\pi$
$173$	−88.9298			−0.514045			−0.257022	+	0.966405i	$0.582741\pi$
$174$	137.477	−	74.3096i	0.790097	−	0.427067i
$175$	−312.823	+	57.1491i	−1.78756	+	0.326566i
$176$		−	8.94166i		−	0.0508049i
$177$	−91.4072	+	49.4078i	−0.516425	+	0.279140i
$178$			17.5591i			0.0986467i
$179$		−	40.6656i		−	0.227182i	−0.993528	−	0.113591i	$-0.963765\pi$
$179$		−	40.6656i		−	0.227182i	0.993528	−	0.113591i	$-0.0362354\pi$
$180$	86.0853	−	26.2550i	0.478251	−	0.145861i
$181$	210.241			1.16155			0.580776	−	0.814064i	$-0.302749\pi$
$181$	210.241			1.16155			0.580776	+	0.814064i	$0.302749\pi$
$182$	−11.4366			−0.0628383
$183$	−21.9755	−	40.6559i	−0.120085	−	0.222164i
$184$	−13.5647			−0.0737210
$185$	−6.56560	+	7.87373i	−0.0354897	+	0.0425607i
$186$	78.4750	+	145.183i	0.421909	+	0.780555i
$187$			21.5955i			0.115484i
$188$	−25.3638			−0.134914
$189$	−28.8766	+	342.224i	−0.152786	+	1.81071i
$190$	18.9843	+	15.8303i	0.0999174	+	0.0833174i
$191$		−	318.625i		−	1.66820i	−0.551617	−	0.834098i	$-0.685989\pi$
$191$		−	318.625i		−	1.66820i	0.551617	−	0.834098i	$-0.314011\pi$
$192$	−11.4121	−	21.1131i	−0.0594382	−	0.109964i
$193$			113.876i			0.590032i	0.955492	+	0.295016i	$0.0953249\pi$
$193$			113.876i			0.590032i	−0.955492	+	0.295016i	$0.904675\pi$
$194$			155.660i			0.802373i
$195$	9.34724	+	1.89003i	0.0479346	+	0.00969244i
$196$	−225.597			−1.15100
$197$	116.479			0.591265			0.295633	−	0.955302i	$-0.404470\pi$
$197$	116.479			0.591265			0.295633	+	0.955302i	$0.404470\pi$
$198$	−23.8036	−	15.5858i	−0.120220	−	0.0787161i
$199$	370.323			1.86092			0.930460	−	0.366393i	$-0.119407\pi$
$199$	370.323			1.86092			0.930460	+	0.366393i	$0.119407\pi$
$200$	−12.7077	−	69.5594i	−0.0635385	−	0.347797i
$201$	−272.829	+	147.471i	−1.35736	+	0.733686i
$202$			91.0988i			0.450984i
$203$	468.533			2.30804
$204$	27.5621	+	50.9914i	0.135108	+	0.249958i
$205$	66.9507	−	80.2899i	0.326589	−	0.391658i
$206$			204.916i			0.994738i
$207$	−23.6439	+	36.1105i	−0.114222	+	0.174447i
$208$		−	2.54304i		−	0.0122262i
$209$		−	7.81438i		−	0.0373894i
$210$	264.479	+	53.4781i	1.25943	+	0.254658i
$211$	−224.564			−1.06429			−0.532143	−	0.846654i	$-0.678613\pi$
$211$	−224.564			−1.06429			−0.532143	+	0.846654i	$0.678613\pi$
$212$	−64.2860			−0.303236
$213$	272.710	−	147.406i	1.28033	−	0.692048i
$214$	−236.028			−1.10294
$215$	−142.166	+	170.491i	−0.661236	+	0.792980i
$216$	−76.0971	−	6.42102i	−0.352301	−	0.0297270i
$217$			494.796i			2.28017i
$218$	−98.2285			−0.450589
$219$	−175.314	+	94.7617i	−0.800523	+	0.432702i
$220$	−14.3161	+	17.1685i	−0.0650733	+	0.0780385i
$221$			6.14184i			0.0277912i
$222$	7.65269	−	4.13646i	0.0344716	−	0.0186327i
$223$		−	197.151i		−	0.884087i	−0.896994	−	0.442043i	$-0.854254\pi$
$223$		−	197.151i		−	0.884087i	0.896994	−	0.442043i	$-0.145746\pi$
$224$		−	71.9552i		−	0.321228i
$225$	−207.324	−	87.4166i	−0.921441	−	0.388518i
$226$	−136.902			−0.605762
$227$	−128.576			−0.566413			−0.283206	−	0.959059i	$-0.591398\pi$
$227$	−128.576			−0.566413			−0.283206	+	0.959059i	$0.591398\pi$
$228$	−9.97340	−	18.4514i	−0.0437430	−	0.0809270i
$229$	105.653			0.461366			0.230683	−	0.973029i	$-0.425904\pi$
$229$	105.653			0.461366			0.230683	+	0.973029i	$0.425904\pi$
$230$	26.0449	+	21.7178i	0.113239	+	0.0944254i
$231$	−40.5623	−	75.0425i	−0.175594	−	0.324859i
$232$			104.183i			0.449066i
$233$	198.584			0.852292			0.426146	−	0.904654i	$-0.359871\pi$
$233$	198.584			0.852292			0.426146	+	0.904654i	$0.359871\pi$
$234$	−6.76983	−	4.43266i	−0.0289309	−	0.0189430i
$235$	48.6999	+	40.6090i	0.207233	+	0.172804i
$236$		−	69.2705i		−	0.293519i
$237$	88.8332	+	164.346i	0.374824	+	0.693445i
$238$			173.783i			0.730180i
$239$		−	91.1474i		−	0.381370i	−0.981651	−	0.190685i	$-0.938929\pi$
$239$		−	91.1474i		−	0.381370i	0.981651	−	0.190685i	$-0.0610709\pi$
$240$	−11.8914	+	58.8098i	−0.0495476	+	0.245041i
$241$	347.855			1.44338			0.721691	−	0.692215i	$-0.243365\pi$
$241$	347.855			1.44338			0.721691	+	0.692215i	$0.243365\pi$
$242$	−164.053			−0.677905
$243$	−149.735	+	191.386i	−0.616192	+	0.787596i
$244$	30.8100			0.126271
$245$	433.158	+	361.194i	1.76799	+	1.47426i
$246$	−78.0360	+	42.1803i	−0.317219	+	0.171465i
$247$		−	2.22244i		−	0.00899773i
$248$	−110.023			−0.443642
$249$	31.3634	+	58.0241i	0.125957	+	0.233028i
$250$	−86.9694	+	153.904i	−0.347877	+	0.615615i
$251$			34.9738i			0.139338i	0.997570	+	0.0696689i	$0.0221943\pi$
$251$			34.9738i			0.139338i	−0.997570	+	0.0696689i	$0.977806\pi$
$252$	−191.552	−	125.422i	−0.760126	−	0.497705i
$253$		−	10.7207i		−	0.0423742i
$254$		−	173.555i		−	0.683286i
$255$	28.7197	−	142.035i	0.112626	−	0.556999i
$256$	16.0000			0.0625000
$257$	−386.706			−1.50469			−0.752347	−	0.658767i	$-0.771078\pi$
$257$	−386.706			−1.50469			−0.752347	+	0.658767i	$0.771078\pi$
$258$	165.704	−	89.5672i	0.642265	−	0.347160i
$259$	26.0810			0.100699
$260$	−4.07156	+	4.88278i	−0.0156599	+	0.0187799i
$261$	277.346	+	181.597i	1.06263	+	0.695773i
$262$			307.546i			1.17384i
$263$	194.450			0.739353			0.369676	−	0.929161i	$-0.379469\pi$
$263$	194.450			0.739353			0.369676	+	0.929161i	$0.379469\pi$
$264$	16.6865	−	9.01945i	0.0632064	−	0.0341646i
$265$	123.433	+	102.926i	0.465784	+	0.388399i
$266$		−	62.8838i		−	0.236405i
$267$	−32.7680	+	17.7119i	−0.122726	+	0.0663366i
$268$		−	206.756i		−	0.771479i
$269$			218.046i			0.810578i	0.914189	+	0.405289i	$0.132829\pi$
$269$			218.046i			0.810578i	−0.914189	+	0.405289i	$0.867171\pi$
$270$	135.830	+	134.165i	0.503074	+	0.496907i
$271$	71.7319			0.264693			0.132347	−	0.991203i	$-0.457749\pi$
$271$	71.7319			0.264693			0.132347	+	0.991203i	$0.457749\pi$
$272$	−38.6425			−0.142068
$273$	−11.5361	−	21.3424i	−0.0422566	−	0.0781772i
$274$	127.004			0.463517
$275$	54.9755	−	10.0434i	0.199911	−	0.0365214i
$276$	−13.6827	−	25.3137i	−0.0495749	−	0.0917164i
$277$		−	349.558i		−	1.26194i	−0.775807	−	0.630971i	$-0.782657\pi$
$277$		−	349.558i		−	1.26194i	0.775807	−	0.630971i	$-0.217343\pi$
$278$	353.689			1.27226
$279$	−191.776	+	292.893i	−0.687371	+	1.04979i
$280$	−115.205	+	138.158i	−0.411445	+	0.493421i
$281$			211.507i			0.752695i	0.926479	+	0.376348i	$0.122820\pi$
$281$			211.507i			0.752695i	−0.926479	+	0.376348i	$0.877180\pi$
$282$	−25.5845	−	47.3327i	−0.0907251	−	0.167847i
$283$		−	372.989i		−	1.31798i	−0.752151	−	0.658991i	$-0.770983\pi$
$283$		−	372.989i		−	1.31798i	0.752151	−	0.658991i	$-0.229017\pi$
$284$			206.666i			0.727697i
$285$	−10.3923	+	51.3956i	−0.0364641	+	0.180336i
$286$	2.00986			0.00702750
$287$	−265.953			−0.926665
$288$	27.8888	−	42.5936i	0.0968363	−	0.147894i
$289$	−195.672			−0.677067
$290$	166.804	−	200.037i	0.575185	−	0.689784i
$291$	−290.486	+	157.015i	−0.998234	+	0.539569i
$292$		−	132.857i		−	0.454991i
$293$	396.910			1.35464			0.677321	−	0.735688i	$-0.263141\pi$
$293$	396.910			1.35464			0.677321	+	0.735688i	$0.263141\pi$
$294$	−227.559	−	420.998i	−0.774011	−	1.43197i
$295$	−110.906	+	133.003i	−0.375953	+	0.450858i
$296$			5.79939i			0.0195925i
$297$	5.07478	−	60.1425i	0.0170868	−	0.202500i
$298$		−	356.687i		−	1.19694i
$299$		−	3.04900i		−	0.0101973i
$300$	116.990	−	93.8791i	0.389967	−	0.312930i
$301$	564.734			1.87619
$302$	295.835			0.979587
$303$	−170.004	+	91.8914i	−0.561070	+	0.303272i
$304$	13.9829			0.0459963
$305$	−59.1569	−	49.3287i	−0.193957	−	0.161733i
$306$	−67.3559	+	102.870i	−0.220117	+	0.336177i
$307$			286.658i			0.933738i	0.884326	+	0.466869i	$0.154618\pi$
$307$			286.658i			0.933738i	−0.884326	+	0.466869i	$0.845382\pi$
$308$	56.8689			0.184639
$309$	−382.405	+	206.699i	−1.23756	+	0.668928i
$310$	211.251	+	176.154i	0.681454	+	0.568238i
$311$		−	97.0383i		−	0.312020i	−0.987755	−	0.156010i	$-0.950137\pi$
$311$		−	97.0383i		−	0.312020i	0.987755	−	0.156010i	$-0.0498632\pi$
$312$	4.74571	−	2.56517i	0.0152106	−	0.00822169i
$313$			250.556i			0.800497i	0.916407	+	0.400249i	$0.131076\pi$
$313$			250.556i			0.800497i	−0.916407	+	0.400249i	$0.868924\pi$
$314$			225.527i			0.718239i
$315$	166.982	+	547.502i	0.530102	+	1.73810i
$316$	−124.546			−0.394131
$317$	−375.250			−1.18375			−0.591877	−	0.806029i	$-0.701613\pi$
$317$	−375.250			−1.18375			−0.591877	+	0.806029i	$0.701613\pi$
$318$	−64.8453	−	119.968i	−0.203916	−	0.377256i
$319$	−82.3400			−0.258119
$320$	−30.7209	−	25.6170i	−0.0960027	−	0.0800530i
$321$	−238.082	−	440.465i	−0.741687	−	1.37216i
$322$		−	86.2712i		−	0.267923i
$323$	−33.7708			−0.104554
$324$	−64.7765	−	148.486i	−0.199928	−	0.458289i
$325$	15.6352	−	2.85638i	0.0481084	−	0.00878886i
$326$			77.9652i			0.239157i
$327$	−99.0830	−	183.309i	−0.303006	−	0.560579i
$328$		−	59.1375i		−	0.180297i
$329$		−	161.314i		−	0.490315i
$330$	−46.4797	−	9.39825i	−0.140847	−	0.0284796i
$331$	−388.785			−1.17458			−0.587288	−	0.809378i	$-0.699804\pi$
$331$	−388.785			−1.17458			−0.587288	+	0.809378i	$0.699804\pi$
$332$	−43.9720			−0.132446
$333$	15.4385	+	10.1086i	0.0463620	+	0.0303563i
$334$	−429.384			−1.28558
$335$	−331.029	+	396.983i	−0.988148	+	1.18503i
$336$	134.279	−	72.5812i	0.399641	−	0.216015i
$337$		−	12.3879i		−	0.0367594i	−0.999831	−	0.0183797i	$-0.994149\pi$
$337$		−	12.3879i		−	0.0367594i	0.999831	−	0.0183797i	$-0.00585077\pi$
$338$	−238.430			−0.705416
$339$	−138.093	−	255.480i	−0.407355	−	0.753630i
$340$	74.1957	+	61.8690i	0.218223	+	0.181968i
$341$		−	86.9556i		−	0.255002i
$342$	24.3729	−	37.2238i	0.0712657	−	0.108841i
$343$		−	811.515i		−	2.36593i
$344$			125.575i			0.365043i
$345$	−14.2573	+	70.5105i	−0.0413256	+	0.204378i
$346$	125.766			0.363485
$347$	229.016			0.659989			0.329995	−	0.943983i	$-0.392953\pi$
$347$	229.016			0.659989			0.329995	+	0.943983i	$0.392953\pi$
$348$	−194.422	+	105.090i	−0.558683	+	0.301982i
$349$	319.299			0.914896			0.457448	−	0.889236i	$-0.348764\pi$
$349$	319.299			0.914896			0.457448	+	0.889236i	$0.348764\pi$
$350$	442.398	−	80.8210i	1.26399	−	0.230917i
$351$	1.44329	−	17.1048i	0.00411193	−	0.0487315i
$352$			12.6454i			0.0359245i
$353$	570.384			1.61582			0.807909	−	0.589308i	$-0.200599\pi$
$353$	570.384			1.61582			0.807909	+	0.589308i	$0.200599\pi$
$354$	129.269	−	69.8732i	0.365168	−	0.197382i
$355$	330.885	−	396.810i	0.932069	−	1.11777i
$356$		−	24.8323i		−	0.0697537i
$357$	−324.305	+	175.295i	−0.908419	+	0.491022i
$358$			57.5099i			0.160642i
$359$		−	589.158i		−	1.64111i	−0.571569	−	0.820554i	$-0.693665\pi$
$359$		−	589.158i		−	1.64111i	0.571569	−	0.820554i	$-0.306335\pi$
$360$	−121.743	+	37.1302i	−0.338175	+	0.103140i
$361$	−348.780			−0.966149
$362$	−297.325			−0.821341
$363$	−165.480	−	306.148i	−0.455868	−	0.843382i
$364$	16.1737			0.0444334
$365$	−212.713	+	255.093i	−0.582774	+	0.698886i
$366$	31.0781	+	57.4962i	0.0849127	+	0.157093i
$367$			306.861i			0.836134i	0.908416	+	0.418067i	$0.137292\pi$
$367$			306.861i			0.836134i	−0.908416	+	0.418067i	$0.862708\pi$
$368$	19.1833			0.0521286
$369$	−157.430	−	103.080i	−0.426639	−	0.279349i
$370$	9.28516	−	11.1351i	0.0250950	−	0.0300950i
$371$		−	408.859i		−	1.10205i
$372$	−110.980	−	205.320i	−0.298335	−	0.551936i
$373$		−	543.484i		−	1.45706i	−0.685013	−	0.728531i	$-0.740204\pi$
$373$		−	543.484i		−	1.45706i	0.685013	−	0.728531i	$-0.259796\pi$
$374$		−	30.5406i		−	0.0816595i
$375$	−374.934	−	7.05548i	−0.999823	−	0.0188146i
$376$	35.8698			0.0953985
$377$	−23.4178			−0.0621162
$378$	40.8377	−	483.978i	0.108036	−	1.28036i
$379$	−73.5844			−0.194154			−0.0970770	−	0.995277i	$-0.530949\pi$
$379$	−73.5844			−0.194154			−0.0970770	+	0.995277i	$0.530949\pi$
$380$	−26.8479	−	22.3874i	−0.0706523	−	0.0589143i
$381$	323.880	−	175.065i	0.850078	−	0.459487i
$382$			450.604i			1.17959i
$383$	20.0331			0.0523056			0.0261528	−	0.999658i	$-0.491674\pi$
$383$	20.0331			0.0523056			0.0261528	+	0.999658i	$0.491674\pi$
$384$	16.1392	+	29.8584i	0.0420292	+	0.0777563i
$385$	−109.191	−	91.0506i	−0.283614	−	0.236495i
$386$		−	161.045i		−	0.417215i
$387$	334.292	+	218.883i	0.863804	+	0.565590i
$388$		−	220.137i		−	0.567364i
$389$		−	209.712i		−	0.539105i	−0.962986	−	0.269552i	$-0.913124\pi$
$389$		−	209.712i		−	0.539105i	0.962986	−	0.269552i	$-0.0868758\pi$
$390$	−13.2190	−	2.67290i	−0.0338949	−	0.00685359i
$391$	−46.3307			−0.118493
$392$	319.042			0.813882
$393$	−573.928	+	310.222i	−1.46038	+	0.789368i
$394$	−164.727			−0.418088
$395$	239.134	+	199.405i	0.605403	+	0.504823i
$396$	33.6633	+	22.0416i	0.0850084	+	0.0556607i
$397$			157.646i			0.397094i	0.980091	+	0.198547i	$0.0636222\pi$
$397$			157.646i			0.397094i	−0.980091	+	0.198547i	$0.936378\pi$
$398$	−523.716			−1.31587
$399$	117.351	−	63.4308i	0.294112	−	0.158975i
$400$	17.9714	+	98.3719i	0.0449285	+	0.245930i
$401$		−	322.191i		−	0.803469i	−0.915756	−	0.401735i	$-0.868407\pi$
$401$		−	322.191i		−	0.803469i	0.915756	−	0.401735i	$-0.131593\pi$
$402$	385.839	−	208.555i	0.959798	−	0.518794i
$403$		−	24.7305i		−	0.0613661i
$404$		−	128.833i		−	0.318894i
$405$	−113.360	+	388.812i	−0.279901	+	0.960029i
$406$	−662.605			−1.63203
$407$	−4.58348			−0.0112616
$408$	−38.9787	−	72.1128i	−0.0955360	−	0.176747i
$409$	435.863			1.06568			0.532839	−	0.846216i	$-0.321125\pi$
$409$	435.863			1.06568			0.532839	+	0.846216i	$0.321125\pi$
$410$	−94.6827	+	113.547i	−0.230933	+	0.276944i
$411$	128.109	+	237.008i	0.311700	+	0.576662i
$412$		−	289.795i		−	0.703386i
$413$	440.560			1.06673
$414$	33.4375	−	51.0679i	0.0807670	−	0.123352i
$415$	84.4286	+	70.4018i	0.203442	+	0.169643i
$416$			3.59641i			0.00864521i
$417$	356.766	+	660.038i	0.855555	+	1.58283i
$418$			11.0512i			0.0264383i
$419$			80.0264i			0.190994i	0.995430	+	0.0954970i	$0.0304440\pi$
$419$			80.0264i			0.190994i	−0.995430	+	0.0954970i	$0.969556\pi$
$420$	−374.030	−	75.6295i	−0.890548	−	0.180070i
$421$	374.853			0.890388			0.445194	−	0.895434i	$-0.353135\pi$
$421$	374.853			0.890388			0.445194	+	0.895434i	$0.353135\pi$
$422$	317.582			0.752564
$423$	62.5230	−	95.4890i	0.147809	−	0.225742i
$424$	90.9142			0.214420
$425$	−43.4037	−	237.583i	−0.102126	−	0.559020i
$426$	−385.670	+	208.464i	−0.905329	+	0.489352i
$427$			195.952i			0.458903i
$428$	333.794			0.779893
$429$	2.02735	+	3.75071i	0.00472576	+	0.00874292i
$430$	201.053	−	241.110i	0.467564	−	0.560721i
$431$		−	773.014i		−	1.79354i	−0.442501	−	0.896768i	$-0.645909\pi$
$431$		−	773.014i		−	1.79354i	0.442501	−	0.896768i	$-0.354091\pi$
$432$	107.618	+	9.08070i	0.249115	+	0.0210201i
$433$			415.396i			0.959344i	0.877448	+	0.479672i	$0.159244\pi$
$433$			415.396i			0.959344i	−0.877448	+	0.479672i	$0.840756\pi$
$434$		−	699.748i		−	1.61232i
$435$	541.555	+	109.503i	1.24495	+	0.251732i
$436$	138.916			0.318615
$437$	16.7649			0.0383636
$438$	247.932	−	134.013i	0.566055	−	0.305966i
$439$	−262.230			−0.597335			−0.298668	−	0.954357i	$-0.596542\pi$
$439$	−262.230			−0.597335			−0.298668	+	0.954357i	$0.596542\pi$
$440$	20.2461	−	24.2799i	0.0460138	−	0.0551815i
$441$	556.107	−	849.321i	1.26101	−	1.92590i
$442$		−	8.68588i		−	0.0196513i
$443$	−771.627			−1.74182			−0.870910	−	0.491442i	$-0.836470\pi$
$443$	−771.627			−1.74182			−0.870910	+	0.491442i	$0.836470\pi$
$444$	−10.8225	+	5.84984i	−0.0243751	+	0.0131753i
$445$	−39.7580	+	47.6794i	−0.0893439	+	0.107145i
$446$			278.814i			0.625144i
$447$	665.632	−	359.790i	1.48911	−	0.804899i
$448$			101.760i			0.227143i
$449$			166.554i			0.370943i	0.982650	+	0.185472i	$0.0593813\pi$
$449$			166.554i			0.370943i	−0.982650	+	0.185472i	$0.940619\pi$
$450$	293.201	+	123.626i	0.651557	+	0.274724i
$451$	46.7386			0.103633
$452$	193.609			0.428339
$453$	298.409	+	552.074i	0.658740	+	1.21871i
$454$	181.833			0.400514
$455$	−31.0545	−	25.8951i	−0.0682516	−	0.0569124i
$456$	14.1045	+	26.0942i	0.0309310	+	0.0572241i
$457$			324.543i			0.710159i	0.934836	+	0.355079i	$0.115546\pi$
$457$			324.543i			0.710159i	−0.934836	+	0.355079i	$0.884454\pi$
$458$	−149.416			−0.326235
$459$	−259.913	−	21.9313i	−0.566260	−	0.0477806i
$460$	−36.8330	−	30.7137i	−0.0800718	−	0.0667688i
$461$			575.072i			1.24744i	0.781646	+	0.623722i	$0.214380\pi$
$461$			575.072i			1.24744i	−0.781646	+	0.623722i	$0.785620\pi$
$462$	57.3637	+	106.126i	0.124164	+	0.229710i
$463$		−	768.386i		−	1.65958i	−0.558074	−	0.829791i	$-0.688460\pi$
$463$		−	768.386i		−	1.65958i	0.558074	−	0.829791i	$-0.311540\pi$
$464$		−	147.337i		−	0.317537i
$465$	−115.642	+	571.912i	−0.248691	+	1.22992i
$466$	−280.840			−0.602662
$467$	619.812			1.32722			0.663610	−	0.748079i	$-0.269023\pi$
$467$	619.812			1.32722			0.663610	+	0.748079i	$0.269023\pi$
$468$	9.57398	+	6.26872i	0.0204572	+	0.0133947i
$469$	1314.97			2.80378
$470$	−68.8720	−	57.4298i	−0.146536	−	0.122191i
$471$	−420.868	+	227.489i	−0.893563	+	0.482992i
$472$			97.9633i			0.207549i
$473$	−99.2465			−0.209823
$474$	−125.629	−	232.421i	−0.265040	−	0.490340i
$475$	15.7057	+	85.9701i	0.0330647	+	0.180990i
$476$		−	245.766i		−	0.516316i
$477$	158.468	−	242.023i	0.332219	−	0.507385i
$478$			128.902i			0.269669i
$479$			330.303i			0.689568i	0.938682	+	0.344784i	$0.112048\pi$
$479$			330.303i			0.689568i	−0.938682	+	0.344784i	$0.887952\pi$
$480$	16.8170	−	83.1696i	0.0350355	−	0.173270i
$481$	−1.30356			−0.00271010
$482$	−491.942			−1.02063
$483$	160.995	−	87.0218i	0.333323	−	0.180169i
$484$	232.006			0.479351
$485$	−352.453	+	422.675i	−0.726707	+	0.871495i
$486$	211.757	−	270.660i	0.435714	−	0.556914i
$487$		−	766.837i		−	1.57461i	−0.616562	−	0.787307i	$-0.711475\pi$
$487$		−	766.837i		−	1.57461i	0.616562	−	0.787307i	$-0.288525\pi$
$488$	−43.5719			−0.0892867
$489$	−145.495	+	78.6435i	−0.297536	+	0.160825i
$490$	−612.578	−	510.805i	−1.25016	−	1.04246i
$491$			171.008i			0.348286i	0.984720	+	0.174143i	$0.0557154\pi$
$491$			171.008i			0.348286i	−0.984720	+	0.174143i	$0.944285\pi$
$492$	110.360	−	59.6520i	0.224308	−	0.121244i
$493$			355.843i			0.721790i
$494$			3.14301i			0.00636236i
$495$	−29.3454	−	96.2181i	−0.0592837	−	0.194380i
$496$	155.596			0.313702
$497$	−1314.39			−2.64466
$498$	−44.3546	−	82.0585i	−0.0890654	−	0.164776i
$499$	659.800			1.32224			0.661122	−	0.750278i	$-0.270081\pi$
$499$	659.800			1.32224			0.661122	+	0.750278i	$0.270081\pi$
$500$	122.993	−	217.653i	0.245987	−	0.435305i
$501$	−433.119	−	801.295i	−0.864509	−	1.59939i
$502$		−	49.4604i		−	0.0985268i
$503$	−398.315			−0.791879			−0.395939	−	0.918277i	$-0.629581\pi$
$503$	−398.315			−0.791879			−0.395939	+	0.918277i	$0.629581\pi$
$504$	270.895	+	177.373i	0.537490	+	0.351931i
$505$	−206.270	+	247.367i	−0.408455	+	0.489835i
$506$			15.1613i			0.0299631i
$507$	−240.505	−	444.948i	−0.474368	−	0.877609i
$508$			245.443i			0.483156i
$509$		−	380.104i		−	0.746765i	−0.927677	−	0.373383i	$-0.878198\pi$
$509$		−	380.104i		−	0.746765i	0.927677	−	0.373383i	$-0.121802\pi$
$510$	−40.6157	+	200.868i	−0.0796387	+	0.393858i
$511$	844.973			1.65357
$512$	−22.6274			−0.0441942
$513$	94.0502	+	7.93589i	0.183334	+	0.0154696i
$514$	546.885			1.06398
$515$	−463.979	+	556.422i	−0.900931	+	1.08043i
$516$	−234.341	+	126.667i	−0.454150	+	0.245479i
$517$			28.3493i			0.0548343i
$518$	−36.8841			−0.0712048
$519$	126.860	+	234.698i	0.244431	+	0.452212i
$520$	5.75806	−	6.90529i	0.0110732	−	0.0132794i
$521$			66.7813i			0.128179i	0.997944	+	0.0640895i	$0.0204143\pi$
$521$			66.7813i			0.128179i	−0.997944	+	0.0640895i	$0.979586\pi$
$522$	−392.226	−	256.817i	−0.751392	−	0.491986i
$523$		−	496.177i		−	0.948713i	−0.880333	−	0.474357i	$-0.842681\pi$
$523$		−	496.177i		−	0.948713i	0.880333	−	0.474357i	$-0.157319\pi$
$524$		−	434.936i		−	0.830030i
$525$	597.071	+	744.058i	1.13728	+	1.41725i
$526$	−274.993			−0.522801
$527$	−375.790			−0.713073
$528$	−23.5983	+	12.7554i	−0.0446937	+	0.0241580i
$529$	23.0000			0.0434783
$530$	−174.560	−	145.559i	−0.329359	−	0.274640i
$531$	260.788	+	170.755i	0.491126	+	0.321573i
$532$			88.9311i			0.167164i
$533$	13.2926			0.0249393
$534$	46.3409	−	25.0484i	0.0867807	−	0.0469071i
$535$	−640.903	−	534.425i	−1.19795	−	0.998925i
$536$			292.398i			0.545518i
$537$	−107.322	+	58.0102i	−0.199855	+	0.108026i
$538$		−	308.363i		−	0.573166i
$539$			252.151i			0.467813i
$540$	−192.093	−	189.738i	−0.355727	−	0.351366i
$541$	−146.067			−0.269994			−0.134997	−	0.990846i	$-0.543102\pi$
$541$	−146.067			−0.269994			−0.134997	+	0.990846i	$0.543102\pi$
$542$	−101.444			−0.187167
$543$	−299.912	−	554.854i	−0.552324	−	1.02183i
$544$	54.6487			0.100457
$545$	−266.726	−	222.413i	−0.489406	−	0.408097i
$546$	16.3145	+	30.1827i	0.0298800	+	0.0552796i
$547$			243.641i			0.445414i	0.974885	+	0.222707i	$0.0714893\pi$
$547$			243.641i			0.445414i	−0.974885	+	0.222707i	$0.928511\pi$
$548$	−179.610			−0.327756
$549$	−75.9482	+	115.993i	−0.138339	+	0.211280i
$550$	−77.7471	+	14.2035i	−0.141358	+	0.0258245i
$551$		−	128.762i		−	0.233689i
$552$	19.3502	+	35.7990i	0.0350547	+	0.0648533i
$553$		−	792.110i		−	1.43239i
$554$			494.349i			0.892327i
$555$	30.1458	+	6.09553i	0.0543168	+	0.0109829i
$556$	−500.192			−0.899626
$557$	−994.901			−1.78618			−0.893089	−	0.449880i	$-0.851467\pi$
$557$	−994.901			−1.78618			−0.893089	+	0.449880i	$0.851467\pi$
$558$	271.213	−	414.213i	0.486044	−	0.742317i
$559$	−28.2261			−0.0504939
$560$	162.924	−	195.385i	0.290935	−	0.348901i
$561$	56.9935	−	30.8063i	0.101593	−	0.0549133i
$562$		−	299.117i		−	0.532236i
$563$	290.294			0.515620			0.257810	−	0.966196i	$-0.416999\pi$
$563$	290.294			0.515620			0.257810	+	0.966196i	$0.416999\pi$
$564$	36.1819	+	66.9386i	0.0641523	+	0.118685i
$565$	−371.740	−	309.980i	−0.657946	−	0.548637i
$566$			527.486i			0.931954i
$567$	944.369	−	411.979i	1.66555	−	0.726594i
$568$		−	292.270i		−	0.514559i
$569$		−	20.8696i		−	0.0366777i	−0.999832	−	0.0183388i	$-0.994162\pi$
$569$		−	20.8696i		−	0.0366777i	0.999832	−	0.0183388i	$-0.00583776\pi$
$570$	14.6969	−	72.6844i	0.0257840	−	0.127516i
$571$	296.178			0.518700			0.259350	−	0.965783i	$-0.416492\pi$
$571$	296.178			0.518700			0.259350	+	0.965783i	$0.416492\pi$
$572$	−2.84238			−0.00496919
$573$	−840.896	+	454.525i	−1.46753	+	0.793237i
$574$	376.114			0.655251
$575$	21.5470	+	117.944i	0.0374730	+	0.205120i
$576$	−39.4408	+	60.2364i	−0.0684736	+	0.104577i
$577$			48.7618i			0.0845093i	0.999107	+	0.0422546i	$0.0134541\pi$
$577$			48.7618i			0.0845093i	−0.999107	+	0.0422546i	$0.986546\pi$
$578$	276.723			0.478759
$579$	300.535	−	162.446i	0.519058	−	0.280563i
$580$	−235.896	+	282.896i	−0.406717	+	0.487751i
$581$		−	279.662i		−	0.481346i
$582$	410.809	−	222.052i	0.705858	−	0.381533i
$583$			71.8530i			0.123247i
$584$			187.889i			0.321727i
$585$	−8.34596	−	27.3648i	−0.0142666	−	0.0467775i
$586$	−561.316			−0.957876
$587$	−151.973			−0.258897			−0.129448	−	0.991586i	$-0.541321\pi$
$587$	−151.973			−0.258897			−0.129448	+	0.991586i	$0.541321\pi$
$588$	321.818	+	595.381i	0.547309	+	1.01255i
$589$	135.980			0.230866
$590$	156.845	−	188.095i	0.265839	−	0.318805i
$591$	−166.160	−	307.405i	−0.281150	−	0.520144i
$592$		−	8.20157i		−	0.0138540i
$593$	−392.414			−0.661744			−0.330872	−	0.943676i	$-0.607343\pi$
$593$	−392.414			−0.661744			−0.330872	+	0.943676i	$0.607343\pi$
$594$	−7.17682	+	85.0543i	−0.0120822	+	0.143189i
$595$	−393.486	+	471.884i	−0.661322	+	0.793083i
$596$			504.431i			0.846361i
$597$	−528.272	−	977.334i	−0.884878	−	1.63708i
$598$			4.31194i			0.00721060i
$599$			569.828i			0.951298i	0.879635	+	0.475649i	$0.157787\pi$
$599$			569.828i			0.951298i	−0.879635	+	0.475649i	$0.842213\pi$
$600$	−165.449	+	132.765i	−0.275749	+	0.221275i
$601$	−1040.37			−1.73107			−0.865536	−	0.500846i	$-0.833022\pi$
$601$	−1040.37			−1.73107			−0.865536	+	0.500846i	$0.833022\pi$
$602$	−798.655			−1.32667
$603$	778.392	+	509.665i	1.29086	+	0.845215i
$604$	−418.374			−0.692673
$605$	−445.464	−	371.455i	−0.736304	−	0.613976i
$606$	240.422	−	129.954i	0.396737	−	0.214446i
$607$			835.820i			1.37697i	0.725252	+	0.688484i	$0.241723\pi$
$607$			835.820i			1.37697i	−0.725252	+	0.688484i	$0.758277\pi$
$608$	−19.7748			−0.0325243
$609$	−668.370	−	1236.52i	−1.09749	−	2.03041i
$610$	83.6604	+	69.7613i	0.137148	+	0.114363i
$611$			8.06265i			0.0131958i
$612$	95.2556	−	145.480i	0.155646	−	0.237713i
$613$			254.053i			0.414442i	0.978294	+	0.207221i	$0.0664419\pi$
$613$			254.053i			0.414442i	−0.978294	+	0.207221i	$0.933558\pi$
$614$		−	405.395i		−	0.660253i
$615$	−307.403	−	62.1573i	−0.499842	−	0.101069i
$616$	−80.4248			−0.130560
$617$	−1014.01			−1.64345			−0.821727	−	0.569882i	$-0.806989\pi$
$617$	−1014.01			−1.64345			−0.821727	+	0.569882i	$0.806989\pi$
$618$	540.802	−	292.316i	0.875084	−	0.473004i
$619$	334.784			0.540846			0.270423	−	0.962742i	$-0.412836\pi$
$619$	334.784			0.540846			0.270423	+	0.962742i	$0.412836\pi$
$620$	−298.753	−	249.119i	−0.481860	−	0.401805i
$621$	129.029	+	10.8874i	0.207776	+	0.0175320i
$622$			137.233i			0.220632i
$623$	157.934			0.253505
$624$	−6.71144	+	3.62769i	−0.0107555	+	0.00581361i
$625$	−584.629	+	220.985i	−0.935406	+	0.353576i
$626$		−	354.339i		−	0.566037i
$627$	−20.6232	+	11.1473i	−0.0328919	+	0.0177789i
$628$		−	318.944i		−	0.507872i
$629$			19.8081i			0.0314914i
$630$	−236.148	−	774.285i	−0.374838	−	1.22902i
$631$	936.585			1.48429			0.742144	−	0.670241i	$-0.233809\pi$
$631$	936.585			1.48429			0.742144	+	0.670241i	$0.233809\pi$
$632$	176.134			0.278693
$633$	320.345	+	592.656i	0.506074	+	0.936266i
$634$	530.683			0.837040
$635$	392.970	−	471.265i	0.618850	−	0.742149i
$636$	91.7051	+	169.660i	0.144190	+	0.266761i
$637$			71.7127i			0.112579i
$638$	116.446			0.182518
$639$	−778.051	−	509.442i	−1.21761	−	0.797248i
$640$	43.4459	+	36.2279i	0.0678842	+	0.0566060i
$641$			247.737i			0.386486i	0.981151	+	0.193243i	$0.0619005\pi$
$641$			247.737i			0.386486i	−0.981151	+	0.193243i	$0.938100\pi$
$642$	336.698	+	622.911i	0.524452	+	0.970266i
$643$			721.358i			1.12186i	0.827862	+	0.560932i	$0.189557\pi$
$643$			721.358i			1.12186i	−0.827862	+	0.560932i	$0.810443\pi$
$644$			122.006i			0.189450i
$645$	652.750	+	131.987i	1.01202	+	0.204631i
$646$	47.7591			0.0739306
$647$	−505.748			−0.781682			−0.390841	−	0.920458i	$-0.627816\pi$
$647$	−505.748			−0.781682			−0.390841	+	0.920458i	$0.627816\pi$
$648$	91.6079	+	209.990i	0.141370	+	0.324059i
$649$	−77.4241			−0.119298
$650$	−22.1116	+	4.03953i	−0.0340178	+	0.00621466i
$651$	1305.84	−	705.836i	2.00589	−	1.08423i
$652$		−	110.259i		−	0.169110i
$653$	−937.577			−1.43580			−0.717900	−	0.696146i	$-0.754896\pi$
$653$	−937.577			−1.43580			−0.717900	+	0.696146i	$0.754896\pi$
$654$	140.125	+	259.238i	0.214258	+	0.396389i
$655$	−696.358	+	835.100i	−1.06314	+	1.27496i
$656$			83.6330i			0.127489i
$657$	500.178	+	327.500i	0.761306	+	0.498478i
$658$			228.132i			0.346705i
$659$			194.845i			0.295668i	0.989012	+	0.147834i	$0.0472301\pi$
$659$			194.845i			0.295668i	−0.989012	+	0.147834i	$0.952770\pi$
$660$	65.7322	+	13.2911i	0.0995942	+	0.0201381i
$661$	−1079.58			−1.63325			−0.816627	−	0.577166i	$-0.804159\pi$
$661$	−1079.58			−1.63325			−0.816627	+	0.577166i	$0.804159\pi$
$662$	549.824			0.830551
$663$	16.2092	−	8.76145i	0.0244482	−	0.0132149i
$664$	62.1858			0.0936533
$665$	142.384	−	170.752i	0.214111	−	0.256771i
$666$	−21.8334	−	14.2958i	−0.0327829	−	0.0214651i
$667$		−	176.651i		−	0.264844i
$668$	607.240			0.909042
$669$	−520.310	+	281.240i	−0.777742	+	0.420388i
$670$	468.146	−	561.419i	0.698726	−	0.837939i
$671$		−	34.4366i		−	0.0513213i
$672$	−189.900	+	102.645i	−0.282589	+	0.152746i
$673$			1017.14i			1.51135i	0.654949	+	0.755673i	$0.272690\pi$
$673$			1017.14i			1.51135i	−0.654949	+	0.755673i	$0.727310\pi$
$674$			17.5192i			0.0259928i
$675$	65.0471	+	671.859i	0.0963661	+	0.995346i
$676$	337.192			0.498804
$677$	1006.78			1.48712			0.743560	−	0.668669i	$-0.233136\pi$
$677$	1006.78			1.48712			0.743560	+	0.668669i	$0.233136\pi$
$678$	195.293	+	361.304i	0.288043	+	0.532897i
$679$	1400.07			2.06196
$680$	−104.929	−	87.4959i	−0.154307	−	0.128670i
$681$	183.415	+	339.329i	0.269332	+	0.498280i
$682$			122.974i			0.180314i
$683$	75.4398			0.110454			0.0552268	−	0.998474i	$-0.482412\pi$
$683$	75.4398			0.110454			0.0552268	+	0.998474i	$0.482412\pi$
$684$	−34.4685	+	52.6424i	−0.0503925	+	0.0769625i
$685$	344.861	+	287.567i	0.503447	+	0.419805i
$686$			1147.66i			1.67297i
$687$	−150.715	−	278.832i	−0.219382	−	0.405869i
$688$		−	177.589i		−	0.258124i
$689$			20.4353i			0.0296593i
$690$	20.1629	−	99.7169i	0.0292216	−	0.144517i
$691$	−983.980			−1.42399			−0.711997	−	0.702182i	$-0.752209\pi$
$691$	−983.980			−1.42399			−0.711997	+	0.702182i	$0.752209\pi$
$692$	−177.860			−0.257022
$693$	−140.185	+	214.099i	−0.202287	+	0.308945i
$694$	−323.878			−0.466683
$695$	960.396	+	800.838i	1.38186	+	1.15228i
$696$	274.954	−	148.619i	0.395049	−	0.213533i
$697$		−	201.987i		−	0.289795i
$698$	−451.556			−0.646929
$699$	−283.284	−	524.091i	−0.405270	−	0.749772i
$700$	−625.645	+	114.298i	−0.893779	+	0.163283i
$701$			667.926i			0.952819i	0.879224	+	0.476409i	$0.158062\pi$
$701$			667.926i			0.952819i	−0.879224	+	0.476409i	$0.841938\pi$
$702$	−2.04112	+	24.1898i	−0.00290757	+	0.0344584i
$703$		−	7.16759i		−	0.0101957i
$704$		−	17.8833i		−	0.0254024i
$705$	37.7015	−	186.455i	0.0534773	−	0.264475i
$706$	−806.644			−1.14256
$707$	819.379			1.15895
$708$	−182.814	+	98.8156i	−0.258212	+	0.139570i
$709$	−322.487			−0.454848			−0.227424	−	0.973796i	$-0.573030\pi$
$709$	−322.487			−0.454848			−0.227424	+	0.973796i	$0.573030\pi$
$710$	−467.941	+	561.174i	−0.659072	+	0.790385i
$711$	307.011	−	468.886i	0.431801	−	0.659474i
$712$			35.1182i			0.0493233i
$713$	186.554			0.261646
$714$	458.637	−	247.904i	0.642349	−	0.347205i
$715$	5.45752	+	4.55082i	0.00763289	+	0.00636478i
$716$		−	81.3313i		−	0.113591i
$717$	−240.551	+	130.023i	−0.335496	+	0.181344i
$718$			833.195i			1.16044i
$719$		−	787.862i		−	1.09577i	−0.836552	−	0.547887i	$-0.815432\pi$
$719$		−	787.862i		−	1.09577i	0.836552	−	0.547887i	$-0.184568\pi$
$720$	172.171	−	52.5101i	0.239126	−	0.0729307i
$721$	1843.10			2.55631
$722$	493.249			0.683171
$723$	−496.221	−	918.038i	−0.686337	−	1.26976i
$724$	420.482			0.580776
$725$	905.866	−	165.491i	1.24947	−	0.228264i
$726$	234.024	+	432.958i	0.322347	+	0.596361i
$727$		−	518.452i		−	0.713139i	−0.934269	−	0.356569i	$-0.883946\pi$
$727$		−	518.452i		−	0.713139i	0.934269	−	0.356569i	$-0.116054\pi$
$728$	−22.8731			−0.0314191
$729$	718.693	+	122.155i	0.985861	+	0.167566i
$730$	300.821	−	360.756i	0.412084	−	0.494187i
$731$			428.906i			0.586739i
$732$	−43.9510	−	81.3119i	−0.0600424	−	0.111082i
$733$			541.297i			0.738468i	0.929336	+	0.369234i	$0.120380\pi$
$733$			541.297i			0.738468i	−0.929336	+	0.369234i	$0.879620\pi$
$734$		−	433.967i		−	0.591236i
$735$	335.333	−	1658.41i	0.456236	−	2.25634i
$736$	−27.1293			−0.0368605
$737$	−231.093			−0.313559
$738$	222.639	+	145.777i	0.301679	+	0.197529i
$739$	−1010.45			−1.36732			−0.683661	−	0.729799i	$-0.739613\pi$
$739$	−1010.45			−1.36732			−0.683661	+	0.729799i	$0.739613\pi$
$740$	−13.1312	+	15.7475i	−0.0177449	+	0.0212803i
$741$	−5.86533	+	3.17035i	−0.00791542	+	0.00427847i
$742$			578.214i			0.779264i
$743$	630.503			0.848591			0.424296	−	0.905524i	$-0.360522\pi$
$743$	630.503			0.848591			0.424296	+	0.905524i	$0.360522\pi$
$744$	156.950	+	290.367i	0.210954	+	0.390278i
$745$	807.625	−	968.535i	1.08406	−	1.30005i
$746$			768.602i			1.03030i
$747$	108.393	−	165.545i	0.145105	−	0.221613i
$748$			43.1910i			0.0577420i
$749$			2122.93i			2.83435i
$750$	530.236	+	9.97796i	0.706982	+	0.0133039i
$751$	−1188.40			−1.58243			−0.791213	−	0.611540i	$-0.790550\pi$
$751$	−1188.40			−1.58243			−0.791213	+	0.611540i	$0.790550\pi$
$752$	−50.7276			−0.0674569
$753$	92.3007	−	49.8907i	0.122577	−	0.0662560i
$754$	33.1178			0.0439228
$755$	803.301	+	669.842i	1.06397	+	0.887208i
$756$	−57.7532	+	684.448i	−0.0763932	+	0.905354i
$757$		−	319.200i		−	0.421665i	−0.977522	−	0.210832i	$-0.932383\pi$
$757$		−	319.200i		−	0.421665i	0.977522	−	0.210832i	$-0.0676174\pi$
$758$	104.064			0.137288
$759$	−28.2933	+	15.2932i	−0.0372771	+	0.0201492i
$760$	37.9686	+	31.6606i	0.0499587	+	0.0416587i
$761$			124.010i			0.162956i	0.996675	+	0.0814782i	$0.0259641\pi$
$761$			124.010i			0.162956i	−0.996675	+	0.0814782i	$0.974036\pi$
$762$	−458.035	+	247.579i	−0.601096	+	0.324907i
$763$			883.506i			1.15794i
$764$		−	637.251i		−	0.834098i
$765$	−415.819	+	126.820i	−0.543554	+	0.165778i
$766$	−28.3310			−0.0369857
$767$	−22.0197			−0.0287089
$768$	−22.8243	−	42.2262i	−0.0297191	−	0.0549820i
$769$	1004.95			1.30683			0.653413	−	0.757002i	$-0.273337\pi$
$769$	1004.95			1.30683			0.653413	+	0.757002i	$0.273337\pi$
$770$	154.420	+	128.765i	0.200545	+	0.167227i
$771$	551.643	+	1020.57i	0.715491	+	1.32370i
$772$			227.752i			0.295016i
$773$	−943.044			−1.21998			−0.609990	−	0.792409i	$-0.708826\pi$
$773$	−943.044			−1.21998			−0.609990	+	0.792409i	$0.708826\pi$
$774$	−472.760	−	309.548i	−0.610802	−	0.399932i
$775$	174.768	+	956.645i	0.225507	+	1.23438i
$776$			311.321i			0.401187i
$777$	−37.2050	−	68.8313i	−0.0478828	−	0.0885860i
$778$			296.577i			0.381205i
$779$			73.0894i			0.0938246i
$780$	18.6945	+	3.78005i	0.0239673	+	0.00484622i
$781$	230.992			0.295764
$782$	65.5215			0.0837871
$783$	83.6204	−	991.005i	0.106795	−	1.26565i
$784$	−451.193			−0.575502
$785$	−510.648	+	612.389i	−0.650507	+	0.780113i
$786$	811.656	−	438.720i	1.03264	−	0.558167i
$787$		−	672.308i		−	0.854266i	−0.904189	−	0.427133i	$-0.859524\pi$
$787$		−	672.308i		−	0.854266i	0.904189	−	0.427133i	$-0.140476\pi$
$788$	232.959			0.295633
$789$	−277.386	−	513.180i	−0.351566	−	0.650418i
$790$	−338.187	−	282.001i	−0.428084	−	0.356963i
$791$			1231.35i			1.55670i
$792$	−47.6071	−	31.1716i	−0.0601100	−	0.0393580i
$793$		−	9.79390i		−	0.0123504i
$794$		−	222.945i		−	0.280788i
$795$	95.5566	−	472.581i	0.120197	−	0.594442i
$796$	740.646			0.930460
$797$	170.910			0.214442			0.107221	−	0.994235i	$-0.465805\pi$
$797$	170.910			0.214442			0.107221	+	0.994235i	$0.465805\pi$
$798$	−165.959	+	89.7048i	−0.207969	+	0.112412i
$799$	122.515			0.153336
$800$	−25.4154	−	139.119i	−0.0317693	−	0.173899i
$801$	93.4881	+	61.2129i	0.116714	+	0.0764206i
$802$			455.647i			0.568138i
$803$	−148.496			−0.184926
$804$	−545.659	+	294.942i	−0.678680	+	0.366843i
$805$	195.339	−	234.258i	0.242657	−	0.291004i
$806$			34.9742i			0.0433924i
$807$	575.452	−	311.046i	0.713076	−	0.385435i
$808$			182.198i			0.225492i
$809$		−	152.854i		−	0.188942i	−0.995528	−	0.0944711i	$-0.969884\pi$
$809$		−	152.854i		−	0.188942i	0.995528	−	0.0944711i	$-0.0301160\pi$
$810$	160.315	−	549.863i	0.197920	−	0.678843i
$811$	−98.8175			−0.121846			−0.0609232	−	0.998142i	$-0.519404\pi$
$811$	−98.8175			−0.121846			−0.0609232	+	0.998142i	$0.519404\pi$
$812$	937.065			1.15402
$813$	−102.327	−	189.310i	−0.125863	−	0.232854i
$814$	6.48202			0.00796316
$815$	−176.532	+	211.704i	−0.216604	+	0.259760i
$816$	55.1242	+	101.983i	0.0675541	+	0.124979i
$817$		−	155.201i		−	0.189964i
$818$	−616.403			−0.753549
$819$	−39.8691	+	60.8905i	−0.0486802	+	0.0743474i
$820$	133.901	−	160.580i	0.163295	−	0.195829i
$821$		−	53.3391i		−	0.0649685i	−0.999472	−	0.0324842i	$-0.989658\pi$
$821$		−	53.3391i		−	0.0649685i	0.999472	−	0.0324842i	$-0.0103419\pi$
$822$	−181.173	−	335.180i	−0.220405	−	0.407762i
$823$			1259.90i			1.53087i	0.643515	+	0.765434i	$0.277476\pi$
$823$			1259.90i			1.53087i	−0.643515	+	0.765434i	$0.722524\pi$
$824$			409.832i			0.497369i
$825$	−104.929	−	130.761i	−0.127187	−	0.158498i
$826$	−623.046			−0.754293
$827$	−756.863			−0.915191			−0.457595	−	0.889161i	$-0.651289\pi$
$827$	−756.863			−0.915191			−0.457595	+	0.889161i	$0.651289\pi$
$828$	−47.2878	+	72.2209i	−0.0571109	+	0.0872233i
$829$	−724.181			−0.873560			−0.436780	−	0.899568i	$-0.643881\pi$
$829$	−724.181			−0.873560			−0.436780	+	0.899568i	$0.643881\pi$
$830$	−119.400	−	99.5632i	−0.143856	−	0.119956i
$831$	−922.531	+	498.650i	−1.11015	+	0.600060i
$832$		−	5.08609i		−	0.00611308i
$833$	1089.70			1.30817
$834$	−504.544	−	933.435i	−0.604969	−	1.11923i
$835$	−1165.93	−	972.228i	−1.39633	−	1.16434i
$836$		−	15.6288i		−	0.0186947i
$837$	1046.56	+	88.3077i	1.25037	+	0.105505i
$838$		−	113.174i		−	0.135053i
$839$			1028.47i			1.22583i	0.790149	+	0.612915i	$0.210003\pi$
$839$			1028.47i			1.22583i	−0.790149	+	0.612915i	$0.789997\pi$
$840$	528.959	+	106.956i	0.629713	+	0.127329i
$841$	−515.768			−0.613280
$842$	−530.123			−0.629599
$843$	558.197	−	301.719i	0.662155	−	0.357911i
$844$	−449.129			−0.532143
$845$	−647.426	−	539.864i	−0.766185	−	0.638892i
$846$	−88.4209	+	135.042i	−0.104516	+	0.159624i
$847$			1475.56i			1.74210i
$848$	−128.572			−0.151618
$849$	−984.369	+	532.075i	−1.15945	+	0.626708i
$850$	61.3822	+	335.994i	0.0722143	+	0.395287i
$851$		−	9.83334i		−	0.0115550i
$852$	545.420	−	294.812i	0.640164	−	0.346024i
$853$			668.115i			0.783254i	0.920124	+	0.391627i	$0.128088\pi$
$853$			668.115i			0.783254i	−0.920124	+	0.391627i	$0.871912\pi$
$854$		−	277.117i		−	0.324493i
$855$	150.465	−	45.8901i	0.175982	−	0.0536726i
$856$	−472.056			−0.551468
$857$	−23.2624			−0.0271439			−0.0135720	−	0.999908i	$-0.504320\pi$
$857$	−23.2624			−0.0271439			−0.0135720	+	0.999908i	$0.504320\pi$
$858$	−2.86711	−	5.30431i	−0.00334162	−	0.00618218i
$859$	−601.480			−0.700209			−0.350105	−	0.936711i	$-0.613854\pi$
$859$	−601.480			−0.700209			−0.350105	+	0.936711i	$0.613854\pi$
$860$	−284.331	+	340.981i	−0.330618	+	0.396490i
$861$	379.386	+	701.887i	0.440635	+	0.815199i
$862$			1093.21i			1.26822i
$863$	619.688			0.718063			0.359031	−	0.933326i	$-0.383107\pi$
$863$	619.688			0.718063			0.359031	+	0.933326i	$0.383107\pi$
$864$	−152.194	−	12.8420i	−0.176151	−	0.0148635i
$865$	341.500	+	284.764i	0.394798	+	0.329207i
$866$		−	587.459i		−	0.678359i
$867$	279.130	+	516.406i	0.321949	+	0.595624i
$868$			989.593i			1.14008i
$869$			139.205i			0.160190i
$870$	−765.874	−	154.861i	−0.880315	−	0.178001i
$871$	−65.7238			−0.0754579
$872$	−196.457			−0.225295
$873$	828.767	+	542.649i	0.949332	+	0.621591i
$874$	−23.7091			−0.0271271
$875$	1384.27	+	782.237i	1.58202	+	0.893985i
$876$	−350.629	+	189.523i	−0.400261	+	0.216351i
$877$		−	1244.05i		−	1.41853i	−0.704943	−	0.709264i	$-0.749027\pi$
$877$		−	1244.05i		−	1.41853i	0.704943	−	0.709264i	$-0.250973\pi$
$878$	370.849			0.422380
$879$	−566.199	−	1047.50i	−0.644140	−	1.19170i
$880$	−28.6323	+	34.3369i	−0.0325367	+	0.0390192i
$881$		−	104.891i		−	0.119059i	−0.998227	−	0.0595293i	$-0.981040\pi$
$881$		−	104.891i		−	0.119059i	0.998227	−	0.0595293i	$-0.0189600\pi$
$882$	−786.454	+	1201.12i	−0.891671	+	1.36182i
$883$		−	1204.44i		−	1.36403i	−0.731339	−	0.682014i	$-0.761104\pi$
$883$		−	1204.44i		−	1.36403i	0.731339	−	0.682014i	$-0.238896\pi$
$884$			12.2837i			0.0138956i
$885$	509.223	+	102.966i	0.575393	+	0.116345i
$886$	1091.24			1.23165
$887$	1206.02			1.35966			0.679831	−	0.733369i	$-0.262053\pi$
$887$	1206.02			1.35966			0.679831	+	0.733369i	$0.262053\pi$
$888$	15.3054	−	8.27292i	0.0172358	−	0.00931635i
$889$	−1561.02			−1.75593
$890$	56.2264	−	67.4289i	0.0631757	−	0.0757628i
$891$	−165.964	+	72.4012i	−0.186267	+	0.0812584i
$892$		−	394.303i		−	0.442043i
$893$	−44.3324			−0.0496443
$894$	−941.346	+	508.820i	−1.05296	+	0.569150i
$895$	−130.216	+	156.160i	−0.145493	+	0.174481i
$896$		−	143.910i		−	0.160614i
$897$	−8.04673	+	4.34945i	−0.00897072	+	0.00484889i
$898$		−	235.542i		−	0.262297i
$899$		−	1432.82i		−	1.59380i
$900$	−414.648	−	174.833i	−0.460721	−	0.194259i
$901$	310.522			0.344641
$902$	−66.0984			−0.0732798
$903$	−805.603	−	1490.41i	−0.892141	−	1.65051i
$904$	−273.805			−0.302881
$905$	−807.347	−	673.216i	−0.892096	−	0.743885i
$906$	−422.014	−	780.750i	−0.465799	−	0.861755i
$907$		−	265.356i		−	0.292565i	−0.989243	−	0.146282i	$-0.953269\pi$
$907$		−	265.356i		−	0.292565i	0.989243	−	0.146282i	$-0.0467308\pi$
$908$	−257.151			−0.283206
$909$	485.028	+	317.580i	0.533584	+	0.349373i
$910$	43.9176	+	36.6213i	0.0482612	+	0.0402431i
$911$		−	1286.84i		−	1.41256i	−0.707933	−	0.706279i	$-0.750372\pi$
$911$		−	1286.84i		−	1.41256i	0.707933	−	0.706279i	$-0.249628\pi$
$912$	−19.9468	−	36.9027i	−0.0218715	−	0.0404635i
$913$			49.1478i			0.0538311i
$914$		−	458.973i		−	0.502158i
$915$	−45.7969	+	226.491i	−0.0500512	+	0.247532i
$916$	211.305			0.230683
$917$	2766.19			3.01657
$918$	367.573	+	31.0155i	0.400406	+	0.0337860i
$919$	318.329			0.346386			0.173193	−	0.984888i	$-0.444592\pi$
$919$	318.329			0.346386			0.173193	+	0.984888i	$0.444592\pi$
$920$	52.0898	+	43.4357i	0.0566193	+	0.0472127i
$921$	756.529	−	408.922i	0.821421	−	0.443998i
$922$		−	813.275i		−	0.882077i
$923$	65.6950			0.0711755
$924$	−81.1245	−	150.085i	−0.0877971	−	0.162430i
$925$	50.4252	−	9.21211i	0.0545138	−	0.00995904i
$926$			1086.66i			1.17350i
$927$	1091.01	+	714.359i	1.17693	+	0.770614i
$928$			208.366i			0.224533i
$929$			513.188i			0.552409i	0.961099	+	0.276205i	$0.0890768\pi$
$929$			513.188i			0.552409i	−0.961099	+	0.276205i	$0.910923\pi$
$930$	163.542	−	808.806i	0.175851	−	0.869684i
$931$	−394.311			−0.423535
$932$	397.168			0.426146
$933$	−256.097	+	138.427i	−0.274488	+	0.148367i
$934$	−876.546			−0.938486
$935$	69.1514	−	82.9290i	0.0739587	−	0.0886941i
$936$	−13.5397	−	8.86532i	−0.0144654	−	0.00947149i
$937$		−	1772.15i		−	1.89130i	−0.325181	−	0.945652i	$-0.605425\pi$
$937$		−	1772.15i		−	1.89130i	0.325181	−	0.945652i	$-0.394575\pi$
$938$	−1859.65			−1.98257
$939$	661.251	−	357.422i	0.704207	−	0.380641i
$940$	97.3997	+	81.2180i	0.103617	+	0.0864021i
$941$		−	818.895i		−	0.870239i	−0.900373	−	0.435120i	$-0.856706\pi$
$941$		−	818.895i		−	0.870239i	0.900373	−	0.435120i	$-0.143294\pi$
$942$	595.197	−	321.718i	0.631844	−	0.341527i
$943$			100.272i			0.106333i
$944$		−	138.541i		−	0.146760i
$945$	1206.73	−	1221.71i	1.27696	−	1.29281i
$946$	140.356			0.148368
$947$	−1576.72			−1.66496			−0.832482	−	0.554051i	$-0.813081\pi$
$947$	−1576.72			−1.66496			−0.832482	+	0.554051i	$0.813081\pi$
$948$	177.666	+	328.693i	0.187412	+	0.346722i
$949$	−42.2328			−0.0445024
$950$	−22.2113	−	121.580i	−0.0233803	−	0.127979i
$951$	535.300	+	990.336i	0.562882	+	1.04136i
$952$			347.566i			0.365090i
$953$	275.660			0.289255			0.144627	−	0.989486i	$-0.453802\pi$
$953$	275.660			0.289255			0.144627	+	0.989486i	$0.453802\pi$
$954$	−224.108	+	342.272i	−0.234914	+	0.358775i
$955$	−1020.28	+	1223.56i	−1.06835	+	1.28121i
$956$		−	182.295i		−	0.190685i
$957$	117.459	+	217.307i	0.122737	+	0.227071i
$958$		−	467.119i		−	0.487598i
$959$		−	1142.32i		−	1.19116i
$960$	−23.7829	+	117.620i	−0.0247738	+	0.122520i
$961$	552.140			0.574547
$962$	1.84351			0.00191633
$963$	−822.819	+	1256.66i	−0.854433	+	1.30494i
$964$	695.711			0.721691
$965$	364.645	−	437.296i	0.377870	−	0.453157i
$966$	−227.682	+	123.067i	−0.235695	+	0.127399i
$967$		−	1032.64i		−	1.06788i	−0.845521	−	0.533942i	$-0.820710\pi$
$967$		−	1032.64i		−	1.06788i	0.845521	−	0.533942i	$-0.179290\pi$
$968$	−328.106			−0.338952
$969$	48.1746	+	89.1258i	0.0497158	+	0.0919771i
$970$	498.443	−	597.753i	0.513859	−	0.616240i
$971$			506.126i			0.521242i	0.965441	+	0.260621i	$0.0839273\pi$
$971$			506.126i			0.521242i	−0.965441	+	0.260621i	$0.916073\pi$
$972$	−299.469	+	382.772i	−0.308096	+	0.393798i
$973$		−	3181.22i		−	3.26950i
$974$			1084.47i			1.11342i
$975$	−29.8423	−	37.1889i	−0.0306075	−	0.0381425i
$976$	61.6200			0.0631353
$977$	−156.675			−0.160363			−0.0801815	−	0.996780i	$-0.525550\pi$
$977$	−156.675			−0.160363			−0.0801815	+	0.996780i	$0.525550\pi$
$978$	205.761	−	111.219i	0.210390	−	0.113721i
$979$	−27.7553			−0.0283506
$980$	866.315	+	722.388i	0.883995	+	0.737130i
$981$	−342.435	+	522.988i	−0.349067	+	0.533117i
$982$		−	241.842i		−	0.246275i
$983$	1322.31			1.34517			0.672587	−	0.740018i	$-0.265183\pi$
$983$	1322.31			1.34517			0.672587	+	0.740018i	$0.265183\pi$
$984$	−156.072	+	84.3606i	−0.158610	+	0.0857323i
$985$	−447.293	−	372.981i	−0.454105	−	0.378661i
$986$		−	503.237i		−	0.510383i
$987$	−425.729	+	230.117i	−0.431337	+	0.233148i
$988$		−	4.44488i		−	0.00449887i
$989$		−	212.922i		−	0.215290i
$990$	41.5007	+	136.073i	0.0419199	+	0.137447i
$991$	−1535.49			−1.54943			−0.774717	−	0.632308i	$-0.782108\pi$
$991$	−1535.49			−1.54943			−0.774717	+	0.632308i	$0.782108\pi$
$992$	−220.047			−0.221821
$993$	554.608	+	1026.06i	0.558518	+	1.03329i
$994$	1858.83			1.87006
$995$	−1422.08	−	1185.82i	−1.42923	−	1.19178i
$996$	62.7268	+	116.048i	0.0629787	+	0.116514i
$997$			1275.00i			1.27883i	0.768861	+	0.639417i	$0.220824\pi$
$997$			1275.00i			1.27883i	−0.768861	+	0.639417i	$0.779176\pi$
$998$	−933.098			−0.934968
$999$	4.65475	−	55.1646i	0.00465941	−	0.0552198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.b.a.599.15	✓	88
3.2	odd	2	inner	690.3.b.a.599.73	yes	88
5.4	even	2	inner	690.3.b.a.599.74	yes	88
15.14	odd	2	inner	690.3.b.a.599.16	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.b.a.599.15	✓	88	1.1	even	1	trivial
690.3.b.a.599.16	yes	88	15.14	odd	2	inner
690.3.b.a.599.73	yes	88	3.2	odd	2	inner
690.3.b.a.599.74	yes	88	5.4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-1.42652 - 2.63914i) q^{3} +2.00000 q^{4} +(-3.84011 - 3.20212i) q^{5} +(2.01740 + 3.73230i) q^{6} +12.7200i q^{7} -2.82843 q^{8} +(-4.93010 + 7.52955i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-1.42652 - 2.63914i) q^{3} +2.00000 q^{4} +(-3.84011 - 3.20212i) q^{5} +(2.01740 + 3.73230i) q^{6} +12.7200i q^{7} -2.82843 q^{8} +(-4.93010 + 7.52955i) q^{9} +(5.43073 + 4.52848i) q^{10} -2.23541i q^{11} +(-2.85303 - 5.27828i) q^{12} -0.635761i q^{13} -17.9888i q^{14} +(-2.97286 + 14.7025i) q^{15} +4.00000 q^{16} -9.66062 q^{17} +(6.97221 - 10.6484i) q^{18} +3.49572 q^{19} +(-7.68021 - 6.40424i) q^{20} +(33.5698 - 18.1453i) q^{21} +3.16135i q^{22} +4.79583 q^{23} +(4.03480 + 7.46461i) q^{24} +(4.49285 + 24.5930i) q^{25} +0.899101i q^{26} +(26.9044 + 2.27017i) q^{27} +25.4400i q^{28} -36.8343i q^{29} +(4.20426 - 20.7924i) q^{30} +38.8991 q^{31} -5.65685 q^{32} +(-5.89957 + 3.18886i) q^{33} +13.6622 q^{34} +(40.7310 - 48.8462i) q^{35} +(-9.86020 + 15.0591i) q^{36} -2.05039i q^{37} -4.94369 q^{38} +(-1.67786 + 0.906924i) q^{39} +(10.8615 + 9.05696i) q^{40} +20.9083i q^{41} +(-47.4749 + 25.6613i) q^{42} -44.3973i q^{43} -4.47083i q^{44} +(43.0426 - 13.1275i) q^{45} -6.78233 q^{46} -12.6819 q^{47} +(-5.70607 - 10.5566i) q^{48} -112.798 q^{49} +(-6.35385 - 34.7797i) q^{50} +(13.7810 + 25.4957i) q^{51} -1.27152i q^{52} -32.1430 q^{53} +(-38.0486 - 3.21051i) q^{54} +(-7.15807 + 8.58423i) q^{55} -35.9776i q^{56} +(-4.98670 - 9.22568i) q^{57} +52.0916i q^{58} -34.6353i q^{59} +(-5.94572 + 29.4049i) q^{60} +15.4050 q^{61} -55.0116 q^{62} +(-95.7759 - 62.7108i) q^{63} +8.00000 q^{64} +(-2.03578 + 2.44139i) q^{65} +(8.34325 - 4.50972i) q^{66} -103.378i q^{67} -19.3212 q^{68} +(-6.84134 - 12.6569i) q^{69} +(-57.6023 + 69.0789i) q^{70} +103.333i q^{71} +(13.9444 - 21.2968i) q^{72} -66.4287i q^{73} +2.89969i q^{74} +(58.4951 - 46.9395i) q^{75} +6.99144 q^{76} +28.4345 q^{77} +(2.37285 - 1.28258i) q^{78} -62.2728 q^{79} +(-15.3604 - 12.8085i) q^{80} +(-32.3883 - 74.2428i) q^{81} -29.5687i q^{82} -21.9860 q^{83} +(67.1397 - 36.2906i) q^{84} +(37.0978 + 30.9345i) q^{85} +62.7873i q^{86} +(-97.2109 + 52.5448i) q^{87} +6.32271i q^{88} -12.4162i q^{89} +(-60.8715 + 18.5651i) q^{90} +8.08687 q^{91} +9.59166 q^{92} +(-55.4902 - 102.660i) q^{93} +17.9349 q^{94} +(-13.4239 - 11.1937i) q^{95} +(8.06960 + 14.9292i) q^{96} -110.069i q^{97} +159.521 q^{98} +(16.8317 + 11.0208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) \) 88 * q + 176 * q^4 + 8 * q^9	\( 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) \) 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

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