LMFDB - Embedded newform 195.3.d.a.131.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,3,Mod(131,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.131"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	195.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31336515503$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.2
Character	$\chi$	$=$	195.131
Dual form			195.3.d.a.131.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.82682i q^{2} +(0.963256 + 2.84115i) q^{3} -10.6446 q^{4} +2.23607i q^{5} +(10.8726 - 3.68621i) q^{6} -0.765398 q^{7} +25.4276i q^{8} +(-7.14428 + 5.47351i) q^{9} +8.55704 q^{10} +17.7633i q^{11} +(-10.2535 - 30.2429i) q^{12} -3.60555 q^{13} +2.92904i q^{14} +(-6.35301 + 2.15391i) q^{15} +54.7288 q^{16} +6.19210i q^{17} +(20.9462 + 27.3399i) q^{18} +19.3140 q^{19} -23.8020i q^{20} +(-0.737274 - 2.17461i) q^{21} +67.9769 q^{22} -11.6007i q^{23} +(-72.2438 + 24.4933i) q^{24} -5.00000 q^{25} +13.7978i q^{26} +(-22.4328 - 15.0256i) q^{27} +8.14734 q^{28} +32.5043i q^{29} +(8.24262 + 24.3118i) q^{30} -54.9784 q^{31} -107.727i q^{32} +(-50.4681 + 17.1106i) q^{33} +23.6961 q^{34} -1.71148i q^{35} +(76.0478 - 58.2632i) q^{36} -11.6930 q^{37} -73.9112i q^{38} +(-3.47307 - 10.2439i) q^{39} -56.8579 q^{40} -26.8521i q^{41} +(-8.32186 + 2.82142i) q^{42} +76.6216 q^{43} -189.082i q^{44} +(-12.2391 - 15.9751i) q^{45} -44.3939 q^{46} +62.1944i q^{47} +(52.7178 + 155.493i) q^{48} -48.4142 q^{49} +19.1341i q^{50} +(-17.5927 + 5.96458i) q^{51} +38.3796 q^{52} +54.9052i q^{53} +(-57.5002 + 85.8465i) q^{54} -39.7199 q^{55} -19.4623i q^{56} +(18.6043 + 54.8739i) q^{57} +124.388 q^{58} -67.9132i q^{59} +(67.6251 - 22.9274i) q^{60} +33.2098 q^{61} +210.393i q^{62} +(5.46822 - 4.18942i) q^{63} -193.337 q^{64} -8.06226i q^{65} +(65.4791 + 193.133i) q^{66} -9.24458 q^{67} -65.9124i q^{68} +(32.9594 - 11.1745i) q^{69} -6.54954 q^{70} +9.17544i q^{71} +(-139.179 - 181.662i) q^{72} +56.3779 q^{73} +44.7472i q^{74} +(-4.81628 - 14.2058i) q^{75} -205.589 q^{76} -13.5960i q^{77} +(-39.2017 + 13.2908i) q^{78} +3.07402 q^{79} +122.377i q^{80} +(21.0813 - 78.2085i) q^{81} -102.758 q^{82} -5.35700i q^{83} +(7.84798 + 23.1478i) q^{84} -13.8460 q^{85} -293.217i q^{86} +(-92.3496 + 31.3100i) q^{87} -451.678 q^{88} -73.2637i q^{89} +(-61.1338 + 46.8370i) q^{90} +2.75968 q^{91} +123.485i q^{92} +(-52.9582 - 156.202i) q^{93} +238.007 q^{94} +43.1874i q^{95} +(306.068 - 103.769i) q^{96} +168.185 q^{97} +185.272i q^{98} +(-97.2274 - 126.906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} - 60 q^{4} - 8 q^{6} + 8 q^{9} - 20 q^{10} - 68 q^{12} + 172 q^{16} + 132 q^{18} - 16 q^{19} + 44 q^{21} - 64 q^{22} - 92 q^{24} - 160 q^{25} + 20 q^{27} + 224 q^{28} - 40 q^{30} - 56 q^{31}+ \cdots + 236 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 - 60 * q^4 - 8 * q^6 + 8 * q^9 - 20 * q^10 - 68 * q^12 + 172 * q^16 + 132 * q^18 - 16 * q^19 + 44 * q^21 - 64 * q^22 - 92 * q^24 - 160 * q^25 + 20 * q^27 + 224 * q^28 - 40 * q^30 - 56 * q^31 - 148 * q^33 - 240 * q^34 - 36 * q^36 + 24 * q^37 - 60 * q^40 + 276 * q^42 + 296 * q^43 - 120 * q^45 - 152 * q^46 + 384 * q^48 + 196 * q^49 + 20 * q^51 - 556 * q^54 - 20 * q^55 - 52 * q^57 + 544 * q^58 + 140 * q^60 - 220 * q^61 + 152 * q^63 - 716 * q^64 + 8 * q^66 - 72 * q^67 - 68 * q^69 + 120 * q^70 - 108 * q^72 - 208 * q^73 - 40 * q^75 + 624 * q^76 - 260 * q^78 - 388 * q^79 + 672 * q^81 + 400 * q^82 - 132 * q^84 + 160 * q^85 + 108 * q^87 - 720 * q^88 - 80 * q^90 + 52 * q^91 - 116 * q^93 - 280 * q^94 - 96 * q^96 + 952 * q^97 + 236 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	3.82682i		−	1.91341i	−0.291056	−	0.956706i	$-0.594007\pi$
$2$		−	3.82682i		−	1.91341i	0.291056	−	0.956706i	$-0.405993\pi$
$3$	0.963256	+	2.84115i	0.321085	+	0.947050i
$3$	0.963256	+	2.84115i	0.321085	+	0.947050i
$4$	−10.6446			−2.66115
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	10.8726	−	3.68621i	1.81210	−	0.614369i
$7$	−0.765398			−0.109343			−0.0546713	−	0.998504i	$-0.517411\pi$
$7$	−0.765398			−0.109343			−0.0546713	+	0.998504i	$0.517411\pi$
$8$			25.4276i			3.17846i
$9$	−7.14428	+	5.47351i	−0.793808	+	0.608168i
$10$	8.55704			0.855704
$11$			17.7633i			1.61484i	0.589976	+	0.807421i	$0.299137\pi$
$11$			17.7633i			1.61484i	−0.589976	+	0.807421i	$0.700863\pi$
$12$	−10.2535	−	30.2429i	−0.854455	−	2.52024i
$13$	−3.60555			−0.277350
$13$	−3.60555			−0.277350
$14$			2.92904i			0.209217i
$15$	−6.35301	+	2.15391i	−0.423534	+	0.143594i
$16$	54.7288			3.42055
$17$			6.19210i			0.364241i	0.983276	+	0.182121i	$0.0582962\pi$
$17$			6.19210i			0.364241i	−0.983276	+	0.182121i	$0.941704\pi$
$18$	20.9462	+	27.3399i	1.16368	+	1.51888i
$19$	19.3140			1.01652			0.508262	−	0.861202i	$-0.330288\pi$
$19$	19.3140			1.01652			0.508262	+	0.861202i	$0.330288\pi$
$20$		−	23.8020i		−	1.19010i
$21$	−0.737274	−	2.17461i	−0.0351083	−	0.103553i
$22$	67.9769			3.08986
$23$		−	11.6007i		−	0.504379i	−0.967678	−	0.252189i	$-0.918849\pi$
$23$		−	11.6007i		−	0.504379i	0.967678	−	0.252189i	$-0.0811506\pi$
$24$	−72.2438	+	24.4933i	−3.01016	+	1.02056i
$25$	−5.00000			−0.200000
$26$			13.7978i			0.530685i
$27$	−22.4328	−	15.0256i	−0.830846	−	0.556503i
$28$	8.14734			0.290977
$29$			32.5043i			1.12084i	0.828209	+	0.560419i	$0.189360\pi$
$29$			32.5043i			1.12084i	−0.828209	+	0.560419i	$0.810640\pi$
$30$	8.24262	+	24.3118i	0.274754	+	0.810395i
$31$	−54.9784			−1.77350			−0.886748	−	0.462254i	$-0.847041\pi$
$31$	−54.9784			−1.77350			−0.886748	+	0.462254i	$0.847041\pi$
$32$		−	107.727i		−	3.36647i
$33$	−50.4681	+	17.1106i	−1.52934	+	0.518502i
$34$	23.6961			0.696944
$35$		−	1.71148i		−	0.0488995i
$36$	76.0478	−	58.2632i	2.11244	−	1.61842i
$37$	−11.6930			−0.316028			−0.158014	−	0.987437i	$-0.550509\pi$
$37$	−11.6930			−0.316028			−0.158014	+	0.987437i	$0.550509\pi$
$38$		−	73.9112i		−	1.94503i
$39$	−3.47307	−	10.2439i	−0.0890531	−	0.262664i
$40$	−56.8579			−1.42145
$41$		−	26.8521i		−	0.654929i	−0.944864	−	0.327464i	$-0.893806\pi$
$41$		−	26.8521i		−	0.654929i	0.944864	−	0.327464i	$-0.106194\pi$
$42$	−8.32186	+	2.82142i	−0.198139	+	0.0671767i
$43$	76.6216			1.78190			0.890949	−	0.454103i	$-0.150040\pi$
$43$	76.6216			1.78190			0.890949	+	0.454103i	$0.150040\pi$
$44$		−	189.082i		−	4.29733i
$45$	−12.2391	−	15.9751i	−0.271981	−	0.355002i
$46$	−44.3939			−0.965084
$47$			62.1944i			1.32328i	0.749820	+	0.661642i	$0.230140\pi$
$47$			62.1944i			1.32328i	−0.749820	+	0.661642i	$0.769860\pi$
$48$	52.7178	+	155.493i	1.09829	+	3.23943i
$49$	−48.4142			−0.988044
$50$			19.1341i			0.382682i
$51$	−17.5927	+	5.96458i	−0.344955	+	0.116953i
$52$	38.3796			0.738069
$53$			54.9052i			1.03595i	0.855397	+	0.517973i	$0.173313\pi$
$53$			54.9052i			1.03595i	−0.855397	+	0.517973i	$0.826687\pi$
$54$	−57.5002	+	85.8465i	−1.06482	+	1.58975i
$55$	−39.7199			−0.722179
$56$		−	19.4623i		−	0.347541i
$57$	18.6043	+	54.8739i	0.326391	+	0.962700i
$58$	124.388			2.14463
$59$		−	67.9132i		−	1.15107i	−0.817777	−	0.575536i	$-0.804794\pi$
$59$		−	67.9132i		−	1.15107i	0.817777	−	0.575536i	$-0.195206\pi$
$60$	67.6251	−	22.9274i	1.12708	−	0.382124i
$61$	33.2098			0.544424			0.272212	−	0.962237i	$-0.412245\pi$
$61$	33.2098			0.544424			0.272212	+	0.962237i	$0.412245\pi$
$62$			210.393i			3.39343i
$63$	5.46822	−	4.18942i	0.0867971	−	0.0664987i
$64$	−193.337			−3.02089
$65$		−	8.06226i		−	0.124035i
$66$	65.4791	+	193.133i	0.992108	+	2.92625i
$67$	−9.24458			−0.137979			−0.0689894	−	0.997617i	$-0.521977\pi$
$67$	−9.24458			−0.137979			−0.0689894	+	0.997617i	$0.521977\pi$
$68$		−	65.9124i		−	0.969299i
$69$	32.9594	−	11.1745i	0.477672	−	0.161949i
$70$	−6.54954			−0.0935649
$71$			9.17544i			0.129232i	0.997910	+	0.0646158i	$0.0205822\pi$
$71$			9.17544i			0.129232i	−0.997910	+	0.0646158i	$0.979418\pi$
$72$	−139.179	−	181.662i	−1.93303	−	2.52308i
$73$	56.3779			0.772300			0.386150	−	0.922436i	$-0.373805\pi$
$73$	56.3779			0.772300			0.386150	+	0.922436i	$0.373805\pi$
$74$			44.7472i			0.604692i
$75$	−4.81628	−	14.2058i	−0.0642171	−	0.189410i
$76$	−205.589			−2.70512
$77$		−	13.5960i		−	0.176571i
$78$	−39.2017	+	13.2908i	−0.502585	+	0.170395i
$79$	3.07402			0.0389116			0.0194558	−	0.999811i	$-0.493807\pi$
$79$	3.07402			0.0389116			0.0194558	+	0.999811i	$0.493807\pi$
$80$			122.377i			1.52972i
$81$	21.0813	−	78.2085i	0.260264	−	0.965538i
$82$	−102.758			−1.25315
$83$		−	5.35700i		−	0.0645422i	−0.999479	−	0.0322711i	$-0.989726\pi$
$83$		−	5.35700i		−	0.0645422i	0.999479	−	0.0322711i	$-0.0102740\pi$
$84$	7.84798	+	23.1478i	0.0934283	+	0.275569i
$85$	−13.8460			−0.162894
$86$		−	293.217i		−	3.40950i
$87$	−92.3496	+	31.3100i	−1.06149	+	0.359885i
$88$	−451.678			−5.13270
$89$		−	73.2637i		−	0.823187i	−0.911367	−	0.411594i	$-0.864972\pi$
$89$		−	73.2637i		−	0.823187i	0.911367	−	0.411594i	$-0.135028\pi$
$90$	−61.1338	+	46.8370i	−0.679265	+	0.520412i
$91$	2.75968			0.0303262
$92$			123.485i			1.34223i
$93$	−52.9582	−	156.202i	−0.569443	−	1.67959i
$94$	238.007			2.53199
$95$			43.1874i			0.454604i
$96$	306.068	−	103.769i	3.18821	−	1.08092i
$97$	168.185			1.73386			0.866931	−	0.498428i	$-0.166089\pi$
$97$	168.185			1.73386			0.866931	+	0.498428i	$0.166089\pi$
$98$			185.272i			1.89054i
$99$	−97.2274	−	126.906i	−0.982095	−	1.28188i
$100$	53.2229			0.532229
$101$			158.775i			1.57203i	0.618205	+	0.786017i	$0.287860\pi$
$101$			158.775i			1.57203i	−0.618205	+	0.786017i	$0.712140\pi$
$102$	22.8254	+	67.3242i	0.223778	+	0.660041i
$103$	−3.57477			−0.0347065			−0.0173532	−	0.999849i	$-0.505524\pi$
$103$	−3.57477			−0.0347065			−0.0173532	+	0.999849i	$0.505524\pi$
$104$		−	91.6807i		−	0.881545i
$105$	4.86258	−	1.64860i	0.0463103	−	0.0157009i
$106$	210.112			1.98219
$107$		−	64.4315i		−	0.602164i	−0.953598	−	0.301082i	$-0.902652\pi$
$107$		−	64.4315i		−	0.602164i	0.953598	−	0.301082i	$-0.0973477\pi$
$108$	238.788	+	159.941i	2.21100	+	1.48093i
$109$	−10.4148			−0.0955490			−0.0477745	−	0.998858i	$-0.515213\pi$
$109$	−10.4148			−0.0955490			−0.0477745	+	0.998858i	$0.515213\pi$
$110$			152.001i			1.38183i
$111$	−11.2634	−	33.2217i	−0.101472	−	0.299294i
$112$	−41.8893			−0.374012
$113$			39.1592i			0.346542i	0.984874	+	0.173271i	$0.0554336\pi$
$113$			39.1592i			0.346542i	−0.984874	+	0.173271i	$0.944566\pi$
$114$	209.993	−	71.1954i	1.84204	−	0.624521i
$115$	25.9400			0.225565
$116$		−	345.995i		−	2.98271i
$117$	25.7591	−	19.7350i	0.220163	−	0.168675i
$118$	−259.892			−2.20247
$119$		−	4.73942i		−	0.0398271i
$120$	−54.7688	−	161.542i	−0.456406	−	1.34618i
$121$	−194.533			−1.60771
$122$		−	127.088i		−	1.04171i
$123$	76.2908	−	25.8654i	0.620250	−	0.210288i
$124$	585.222			4.71953
$125$		−	11.1803i		−	0.0894427i
$126$	−16.0322	−	20.9259i	−0.127239	−	0.166079i
$127$	171.074			1.34704			0.673521	−	0.739168i	$-0.264781\pi$
$127$	171.074			1.34704			0.673521	+	0.739168i	$0.264781\pi$
$128$			308.958i			2.41373i
$129$	73.8062	+	217.694i	0.572141	+	1.68755i
$130$	−30.8528			−0.237330
$131$		−	141.606i		−	1.08096i	−0.841357	−	0.540480i	$-0.818242\pi$
$131$		−	141.606i		−	1.08096i	0.841357	−	0.540480i	$-0.181758\pi$
$132$	537.212	−	182.135i	4.06979	−	1.37981i
$133$	−14.7829			−0.111149
$134$			35.3774i			0.264010i
$135$	33.5982	−	50.1614i	0.248876	−	0.371566i
$136$	−157.451			−1.15773
$137$		−	122.452i		−	0.893808i	−0.894582	−	0.446904i	$-0.852527\pi$
$137$		−	122.452i		−	0.893808i	0.894582	−	0.446904i	$-0.147473\pi$
$138$	−42.7627	−	126.130i	−0.309874	−	0.913983i
$139$	83.8739			0.603410			0.301705	−	0.953401i	$-0.402444\pi$
$139$	83.8739			0.603410			0.301705	+	0.953401i	$0.402444\pi$
$140$			18.2180i			0.130129i
$141$	−176.704	+	59.9091i	−1.25322	+	0.424887i
$142$	35.1128			0.247273
$143$		−	64.0463i		−	0.447877i
$144$	−390.998	+	299.559i	−2.71526	+	2.08027i
$145$	−72.6818			−0.501254
$146$		−	215.748i		−	1.47773i
$147$	−46.6352	−	137.552i	−0.317247	−	0.935728i
$148$	124.467			0.840996
$149$			37.6863i			0.252928i	0.991971	+	0.126464i	$0.0403628\pi$
$149$			37.6863i			0.252928i	−0.991971	+	0.126464i	$0.959637\pi$
$150$	−54.3629	+	18.4311i	−0.362419	+	0.122874i
$151$	−263.787			−1.74693			−0.873465	−	0.486887i	$-0.838133\pi$
$151$	−263.787			−1.74693			−0.873465	+	0.486887i	$0.838133\pi$
$152$			491.109i			3.23098i
$153$	−33.8926	−	44.2381i	−0.221520	−	0.289138i
$154$	−52.0294			−0.337853
$155$		−	122.935i		−	0.793131i
$156$	36.9694	+	109.042i	0.236983	+	0.698988i
$157$	273.013			1.73893			0.869467	−	0.493991i	$-0.164462\pi$
$157$	273.013			1.73893			0.869467	+	0.493991i	$0.164462\pi$
$158$		−	11.7637i		−	0.0744539i
$159$	−155.994	+	52.8877i	−0.981093	+	0.332627i
$160$	240.885			1.50553
$161$			8.87916i			0.0551501i
$162$	−299.290	−	80.6746i	−1.84747	−	0.497991i
$163$	0.545700			0.00334785			0.00167393	−	0.999999i	$-0.499467\pi$
$163$	0.545700			0.00334785			0.00167393	+	0.999999i	$0.499467\pi$
$164$			285.829i			1.74286i
$165$	−38.2604	−	112.850i	−0.231881	−	0.683940i
$166$	−20.5003			−0.123496
$167$			16.1321i			0.0965996i	0.998833	+	0.0482998i	$0.0153803\pi$
$167$			16.1321i			0.0965996i	−0.998833	+	0.0482998i	$0.984620\pi$
$168$	55.2953	−	18.7472i	0.329138	−	0.111590i
$169$	13.0000			0.0769231
$170$			52.9861i			0.311683i
$171$	−137.984	+	105.715i	−0.806926	+	0.618218i
$172$	−815.605			−4.74189
$173$			210.494i			1.21673i	0.793659	+	0.608363i	$0.208174\pi$
$173$			210.494i			1.21673i	−0.793659	+	0.608363i	$0.791826\pi$
$174$	119.818	+	353.406i	0.688608	+	2.03107i
$175$	3.82699			0.0218685
$176$			972.162i			5.52365i
$177$	192.952	−	65.4178i	1.09012	−	0.369592i
$178$	−280.367			−1.57510
$179$			71.0064i			0.396684i	0.980133	+	0.198342i	$0.0635557\pi$
$179$			71.0064i			0.396684i	−0.980133	+	0.198342i	$0.936444\pi$
$180$	130.281	+	170.048i	0.723781	+	0.944712i
$181$	205.491			1.13531			0.567655	−	0.823267i	$-0.307851\pi$
$181$	205.491			1.13531			0.567655	+	0.823267i	$0.307851\pi$
$182$		−	10.5608i		−	0.0580265i
$183$	31.9896	+	94.3542i	0.174806	+	0.515596i
$184$	294.979			1.60315
$185$		−	26.1464i		−	0.141332i
$186$	−597.757	+	202.662i	−3.21375	+	1.08958i
$187$	−109.992			−0.588192
$188$		−	662.033i		−	3.52145i
$189$	17.1701	+	11.5005i	0.0908468	+	0.0608494i
$190$	165.270			0.869844
$191$		−	304.175i		−	1.59254i	−0.604942	−	0.796270i	$-0.706804\pi$
$191$		−	304.175i		−	1.59254i	0.604942	−	0.796270i	$-0.293196\pi$
$192$	−186.233	−	549.299i	−0.969962	−	2.86093i
$193$	116.871			0.605548			0.302774	−	0.953062i	$-0.402087\pi$
$193$	116.871			0.605548			0.302774	+	0.953062i	$0.402087\pi$
$194$		−	643.613i		−	3.31759i
$195$	22.9061	−	7.76602i	0.117467	−	0.0398257i
$196$	515.349			2.62933
$197$			105.775i			0.536931i	0.963289	+	0.268466i	$0.0865166\pi$
$197$			105.775i			0.536931i	−0.963289	+	0.268466i	$0.913483\pi$
$198$	−485.646	+	372.072i	−2.45276	+	1.87915i
$199$	−31.9034			−0.160319			−0.0801594	−	0.996782i	$-0.525543\pi$
$199$	−31.9034			−0.160319			−0.0801594	+	0.996782i	$0.525543\pi$
$200$		−	127.138i		−	0.635691i
$201$	−8.90490	−	26.2653i	−0.0443030	−	0.130673i
$202$	607.606			3.00795
$203$		−	24.8787i		−	0.122555i
$204$	187.267	−	63.4905i	0.917975	−	0.311228i
$205$	60.0431			0.292893
$206$			13.6800i			0.0664078i
$207$	63.4966	+	82.8787i	0.306747	+	0.400380i
$208$	−197.327			−0.948690
$209$			343.079i			1.64153i
$210$	−6.30889	−	18.6082i	−0.0300423	−	0.0886106i
$211$	142.077			0.673349			0.336674	−	0.941621i	$-0.390698\pi$
$211$	142.077			0.673349			0.336674	+	0.941621i	$0.390698\pi$
$212$		−	584.442i		−	2.75680i
$213$	−26.0688	+	8.83830i	−0.122389	+	0.0414944i
$214$	−246.568			−1.15219
$215$			171.331i			0.796889i
$216$	382.065	−	570.414i	1.76882	−	2.64081i
$217$	42.0803			0.193919
$218$			39.8557i			0.182825i
$219$	54.3064	+	160.178i	0.247974	+	0.731407i
$220$	422.801			1.92182
$221$		−	22.3259i		−	0.101022i
$222$	−127.133	+	43.1030i	−0.572673	+	0.194158i
$223$	−118.080			−0.529506			−0.264753	−	0.964316i	$-0.585290\pi$
$223$	−118.080			−0.529506			−0.264753	+	0.964316i	$0.585290\pi$
$224$			82.4540i			0.368098i
$225$	35.7214	−	27.3676i	0.158762	−	0.121634i
$226$	149.855			0.663077
$227$		−	345.242i		−	1.52089i	−0.649403	−	0.760444i	$-0.724981\pi$
$227$		−	345.242i		−	1.52089i	0.649403	−	0.760444i	$-0.275019\pi$
$228$	−198.035	−	584.110i	−0.868575	−	2.56189i
$229$	−30.4509			−0.132973			−0.0664866	−	0.997787i	$-0.521179\pi$
$229$	−30.4509			−0.132973			−0.0664866	+	0.997787i	$0.521179\pi$
$230$		−	99.2677i		−	0.431599i
$231$	38.6282	−	13.0964i	0.167222	−	0.0566944i
$232$	−826.508			−3.56253
$233$			413.657i			1.77535i	0.460470	+	0.887675i	$0.347681\pi$
$233$			413.657i			1.77535i	−0.460470	+	0.887675i	$0.652319\pi$
$234$	−75.5225	−	98.5754i	−0.322746	−	0.421262i
$235$	−139.071			−0.591791
$236$			722.908i			3.06317i
$237$	2.96107	+	8.73375i	0.0124939	+	0.0368512i
$238$	−18.1369			−0.0762057
$239$			338.502i			1.41633i	0.706048	+	0.708164i	$0.250476\pi$
$239$			338.502i			1.41633i	−0.706048	+	0.708164i	$0.749524\pi$
$240$	−347.692	+	117.881i	−1.44872	+	0.491170i
$241$	91.5757			0.379982			0.189991	−	0.981786i	$-0.439154\pi$
$241$	91.5757			0.379982			0.189991	+	0.981786i	$0.439154\pi$
$242$			744.445i			3.07622i
$243$	242.509	−	15.4396i	0.997979	−	0.0635373i
$244$	−353.505			−1.44879
$245$		−	108.257i		−	0.441867i
$246$	−98.9824	−	291.951i	−0.402368	−	1.18679i
$247$	−69.6375			−0.281933
$248$		−	1397.97i		−	5.63698i
$249$	15.2200	−	5.16016i	0.0611247	−	0.0207235i
$250$	−42.7852			−0.171141
$251$			343.765i			1.36958i	0.728739	+	0.684791i	$0.240107\pi$
$251$			343.765i			1.36958i	−0.728739	+	0.684791i	$0.759893\pi$
$252$	−58.2069	+	44.5946i	−0.230980	+	0.176963i
$253$	206.066			0.814492
$254$		−	654.672i		−	2.57745i
$255$	−13.3372	−	39.3385i	−0.0523028	−	0.154269i
$256$	408.980			1.59758
$257$			346.896i			1.34979i	0.737913	+	0.674896i	$0.235811\pi$
$257$			346.896i			1.34979i	−0.737913	+	0.674896i	$0.764189\pi$
$258$	833.075	−	282.443i	3.22897	−	1.09474i
$259$	8.94983			0.0345553
$260$			85.8194i			0.330074i
$261$	−177.913	−	232.220i	−0.681658	−	0.889731i
$262$	−541.901			−2.06832
$263$			216.012i			0.821339i	0.911784	+	0.410670i	$0.134705\pi$
$263$			216.012i			0.821339i	−0.911784	+	0.410670i	$0.865295\pi$
$264$	−435.081	−	1283.29i	−1.64804	−	4.86093i
$265$	−122.772			−0.463289
$266$			56.5715i			0.212675i
$267$	208.153	−	70.5717i	0.779600	−	0.264313i
$268$	98.4047			0.367182
$269$		−	31.1404i		−	0.115764i	−0.998323	−	0.0578818i	$-0.981565\pi$
$269$		−	31.1404i		−	0.115764i	0.998323	−	0.0578818i	$-0.0184347\pi$
$270$	−191.959	−	128.574i	−0.710958	−	0.476201i
$271$	−152.262			−0.561854			−0.280927	−	0.959729i	$-0.590642\pi$
$271$	−152.262			−0.561854			−0.280927	+	0.959729i	$0.590642\pi$
$272$			338.886i			1.24591i
$273$	2.65828	+	7.84067i	0.00973729	+	0.0287204i
$274$	−468.601			−1.71022
$275$		−	88.8163i		−	0.322968i
$276$	−350.839	+	118.947i	−1.27115	+	0.430969i
$277$	445.171			1.60711			0.803557	−	0.595227i	$-0.202938\pi$
$277$	445.171			1.60711			0.803557	+	0.595227i	$0.202938\pi$
$278$		−	320.971i		−	1.15457i
$279$	392.781	−	300.925i	1.40782	−	1.07858i
$280$	43.5190			0.155425
$281$		−	140.762i		−	0.500934i	−0.968125	−	0.250467i	$-0.919416\pi$
$281$		−	140.762i		−	0.500934i	0.968125	−	0.250467i	$-0.0805842\pi$
$282$	229.262	+	676.213i	0.812984	+	2.39792i
$283$	−288.863			−1.02072			−0.510359	−	0.859962i	$-0.670487\pi$
$283$	−288.863			−1.02072			−0.510359	+	0.859962i	$0.670487\pi$
$284$		−	97.6687i		−	0.343904i
$285$	−122.702	+	41.6005i	−0.430533	+	0.145967i
$286$	−245.094			−0.856972
$287$			20.5525i			0.0716116i
$288$	589.644	+	769.631i	2.04738	+	2.67233i
$289$	250.658			0.867328
$290$			278.141i			0.959106i
$291$	162.005	+	477.838i	0.556718	+	1.64205i
$292$	−600.119			−2.05520
$293$			214.754i			0.732950i	0.930428	+	0.366475i	$0.119435\pi$
$293$			214.754i			0.732950i	−0.930428	+	0.366475i	$0.880565\pi$
$294$	−526.387	+	178.465i	−1.79043	+	0.607023i
$295$	151.859			0.514775
$296$		−	297.326i		−	1.00448i
$297$	266.903	−	398.480i	0.898664	−	1.34168i
$298$	144.219			0.483955
$299$			41.8270i			0.139889i
$300$	51.2673	+	151.214i	0.170891	+	0.504048i
$301$	−58.6460			−0.194837
$302$			1009.46i			3.34260i
$303$	−451.105	+	152.941i	−1.48880	+	0.504757i
$304$	1057.03			3.47707
$305$			74.2595i			0.243474i
$306$	−169.291	+	129.701i	−0.553240	+	0.423859i
$307$	−180.482			−0.587888			−0.293944	−	0.955823i	$-0.594968\pi$
$307$	−180.482			−0.587888			−0.293944	+	0.955823i	$0.594968\pi$
$308$			144.723i			0.469881i
$309$	−3.44342	−	10.1565i	−0.0111437	−	0.0328688i
$310$	−470.452			−1.51759
$311$			338.091i			1.08711i	0.839374	+	0.543555i	$0.182922\pi$
$311$			338.091i			1.08711i	−0.839374	+	0.543555i	$0.817078\pi$
$312$	260.479	−	88.3120i	0.834867	−	0.283051i
$313$	−39.2269			−0.125326			−0.0626628	−	0.998035i	$-0.519959\pi$
$313$	−39.2269			−0.125326			−0.0626628	+	0.998035i	$0.519959\pi$
$314$		−	1044.77i		−	3.32730i
$315$	9.36782	+	12.2273i	0.0297391	+	0.0388168i
$316$	−32.7216			−0.103549
$317$		−	82.9715i		−	0.261740i	−0.991400	−	0.130870i	$-0.958223\pi$
$317$		−	82.9715i		−	0.261740i	0.991400	−	0.130870i	$-0.0417770\pi$
$318$	202.392	+	596.961i	0.636453	+	1.87724i
$319$	−577.383			−1.80998
$320$		−	432.314i		−	1.35098i
$321$	183.060	−	62.0640i	0.570279	−	0.193346i
$322$	33.9790			0.105525
$323$			119.594i			0.370260i
$324$	−224.402	+	832.497i	−0.692599	+	2.56944i
$325$	18.0278			0.0554700
$326$		−	2.08830i		−	0.00640582i
$327$	−10.0322	−	29.5901i	−0.0306794	−	0.0904897i
$328$	682.785			2.08166
$329$		−	47.6034i		−	0.144691i
$330$	−431.858	+	146.416i	−1.30866	+	0.443684i
$331$	−486.716			−1.47044			−0.735220	−	0.677828i	$-0.762921\pi$
$331$	−486.716			−1.47044			−0.735220	+	0.677828i	$0.762921\pi$
$332$			57.0230i			0.171756i
$333$	83.5382	−	64.0019i	0.250866	−	0.192198i
$334$	61.7348			0.184835
$335$		−	20.6715i		−	0.0617060i
$336$	−40.3501	−	119.014i	−0.120090	−	0.354208i
$337$	74.5562			0.221235			0.110617	−	0.993863i	$-0.464717\pi$
$337$	74.5562			0.221235			0.110617	+	0.993863i	$0.464717\pi$
$338$		−	49.7487i		−	0.147186i
$339$	−111.257	+	37.7204i	−0.328192	+	0.111269i
$340$	147.385			0.433484
$341$		−	976.595i		−	2.86391i
$342$	404.554	+	528.042i	1.18291	+	1.54398i
$343$	74.5606			0.217378
$344$			1948.31i			5.66368i
$345$	24.9868	+	73.6994i	0.0724256	+	0.213621i
$346$	805.522			2.32810
$347$		−	485.549i		−	1.39928i	−0.714497	−	0.699638i	$-0.753344\pi$
$347$		−	485.549i		−	1.39928i	0.714497	−	0.699638i	$-0.246656\pi$
$348$	983.023	−	333.282i	2.82478	−	0.957706i
$349$	359.820			1.03100			0.515501	−	0.856889i	$-0.327606\pi$
$349$	359.820			1.03100			0.515501	+	0.856889i	$0.327606\pi$
$350$		−	14.6452i		−	0.0418435i
$351$	80.8827	+	54.1755i	0.230435	+	0.154346i
$352$	1913.58			5.43631
$353$		−	4.19941i		−	0.0118964i	−0.999982	−	0.00594818i	$-0.998107\pi$
$353$		−	4.19941i		−	0.0118964i	0.999982	−	0.00594818i	$-0.00189337\pi$
$354$	−250.342	−	738.392i	−0.707182	−	2.08585i
$355$	−20.5169			−0.0577941
$356$			779.861i			2.19062i
$357$	13.4654	−	4.56528i	0.0377183	−	0.0127879i
$358$	271.729			0.759020
$359$			257.908i			0.718406i	0.933259	+	0.359203i	$0.116951\pi$
$359$			257.908i			0.718406i	−0.933259	+	0.359203i	$0.883049\pi$
$360$	406.209	−	311.213i	1.12836	−	0.864479i
$361$	12.0295			0.0333227
$362$		−	786.378i		−	2.17232i
$363$	−187.386	−	552.699i	−0.516214	−	1.52259i
$364$	−29.3757			−0.0807024
$365$			126.065i			0.345383i
$366$	361.077	−	122.418i	0.986548	−	0.334477i
$367$	−148.301			−0.404089			−0.202045	−	0.979376i	$-0.564759\pi$
$367$	−148.301			−0.404089			−0.202045	+	0.979376i	$0.564759\pi$
$368$		−	634.893i		−	1.72525i
$369$	146.975	+	191.839i	0.398307	+	0.519888i
$370$	−100.058			−0.270426
$371$		−	42.0243i		−	0.113273i
$372$	563.718	+	1662.70i	1.51537	+	4.46963i
$373$	−112.412			−0.301374			−0.150687	−	0.988582i	$-0.548149\pi$
$373$	−112.412			−0.301374			−0.150687	+	0.988582i	$0.548149\pi$
$374$			420.920i			1.12545i
$375$	31.7650	−	10.7695i	0.0847068	−	0.0287187i
$376$	−1581.46			−4.20600
$377$		−	117.196i		−	0.310865i
$378$	44.0106	−	65.7068i	0.116430	−	0.173827i
$379$	−268.973			−0.709691			−0.354845	−	0.934925i	$-0.615467\pi$
$379$	−268.973			−0.709691			−0.354845	+	0.934925i	$0.615467\pi$
$380$		−	459.711i		−	1.20977i
$381$	164.788	+	486.048i	0.432516	+	1.27572i
$382$	−1164.02			−3.04718
$383$		−	165.919i		−	0.433210i	−0.976259	−	0.216605i	$-0.930502\pi$
$383$		−	165.919i		−	0.433210i	0.976259	−	0.216605i	$-0.0694983\pi$
$384$	−877.796	+	297.605i	−2.28593	+	0.775014i
$385$	30.4015			0.0789650
$386$		−	447.244i		−	1.15866i
$387$	−547.406	+	419.389i	−1.41449	+	1.08369i
$388$	−1790.26			−4.61406
$389$		−	68.1098i		−	0.175090i	−0.996161	−	0.0875448i	$-0.972098\pi$
$389$		−	68.1098i		−	0.175090i	0.996161	−	0.0875448i	$-0.0279021\pi$
$390$	−29.7192	−	87.6576i	−0.0762030	−	0.224763i
$391$	71.8328			0.183716
$392$		−	1231.06i		−	3.14045i
$393$	402.324	−	136.403i	1.02372	−	0.347081i
$394$	404.784			1.02737
$395$			6.87371i			0.0174018i
$396$	1034.95	+	1350.86i	2.61350	+	3.41126i
$397$	−227.675			−0.573490			−0.286745	−	0.958007i	$-0.592573\pi$
$397$	−227.675			−0.573490			−0.286745	+	0.958007i	$0.592573\pi$
$398$			122.089i			0.306756i
$399$	−14.2397	−	42.0004i	−0.0356885	−	0.105264i
$400$	−273.644			−0.684110
$401$			102.824i			0.256418i	0.991747	+	0.128209i	$0.0409229\pi$
$401$			102.824i			0.256418i	−0.991747	+	0.128209i	$0.959077\pi$
$402$	−100.513	+	34.0775i	−0.250031	+	0.0847699i
$403$	198.227			0.491879
$404$		−	1690.10i		−	4.18341i
$405$	174.880	+	47.1393i	0.431802	+	0.116393i
$406$	−95.2066			−0.234499
$407$		−	207.706i		−	0.510335i
$408$	−151.665	−	447.341i	−0.371729	−	1.09642i
$409$	−98.8897			−0.241784			−0.120892	−	0.992666i	$-0.538575\pi$
$409$	−98.8897			−0.241784			−0.120892	+	0.992666i	$0.538575\pi$
$410$		−	229.774i		−	0.560425i
$411$	347.904	−	117.952i	0.846481	−	0.286989i
$412$	38.0519			0.0923590
$413$			51.9806i			0.125861i
$414$	317.162	−	242.990i	0.766092	−	0.586933i
$415$	11.9786			0.0288641
$416$			388.415i			0.933689i
$417$	80.7921	+	238.299i	0.193746	+	0.571459i
$418$	1312.90			3.14092
$419$			600.336i			1.43278i	0.697699	+	0.716391i	$0.254207\pi$
$419$			600.336i			1.43278i	−0.697699	+	0.716391i	$0.745793\pi$
$420$	−51.7601	+	17.5486i	−0.123238	+	0.0417824i
$421$	−565.415			−1.34303			−0.671514	−	0.740992i	$-0.734356\pi$
$421$	−565.415			−1.34303			−0.671514	+	0.740992i	$0.734356\pi$
$422$		−	543.702i		−	1.28839i
$423$	−340.422	−	444.334i	−0.804779	−	1.05043i
$424$	−1396.11			−3.29271
$425$		−	30.9605i		−	0.0728483i
$426$	33.8226	+	99.7607i	0.0793958	+	0.234180i
$427$	−25.4187			−0.0595287
$428$			685.846i			1.60244i
$429$	181.965	−	61.6930i	0.424162	−	0.143807i
$430$	655.654			1.52478
$431$		−	335.903i		−	0.779356i	−0.920951	−	0.389678i	$-0.872586\pi$
$431$		−	335.903i		−	0.779356i	0.920951	−	0.389678i	$-0.127414\pi$
$432$	−1227.72	−	822.331i	−2.84195	−	1.90354i
$433$	373.117			0.861701			0.430851	−	0.902423i	$-0.358214\pi$
$433$	373.117			0.861701			0.430851	+	0.902423i	$0.358214\pi$
$434$		−	161.034i		−	0.371046i
$435$	−70.0112	−	206.500i	−0.160945	−	0.474713i
$436$	110.862			0.254270
$437$		−	224.056i		−	0.512714i
$438$	612.973	−	207.821i	1.39948	−	0.474477i
$439$	−132.713			−0.302308			−0.151154	−	0.988510i	$-0.548299\pi$
$439$	−132.713			−0.302308			−0.151154	+	0.988510i	$0.548299\pi$
$440$		−	1009.98i		−	2.29541i
$441$	345.884	−	264.995i	0.784318	−	0.600897i
$442$	−85.4375			−0.193297
$443$			243.325i			0.549267i	0.961549	+	0.274633i	$0.0885565\pi$
$443$			243.325i			0.549267i	−0.961549	+	0.274633i	$0.911444\pi$
$444$	119.894	+	353.631i	0.270032	+	0.796466i
$445$	163.823			0.368141
$446$			451.871i			1.01316i
$447$	−107.072	+	36.3015i	−0.239535	+	0.0812114i
$448$	147.980			0.330311
$449$		−	257.697i		−	0.573936i	−0.957940	−	0.286968i	$-0.907353\pi$
$449$		−	257.697i		−	0.573936i	0.957940	−	0.286968i	$-0.0926473\pi$
$450$	−104.731	−	136.699i	−0.232735	−	0.303776i
$451$	476.980			1.05761
$452$		−	416.834i		−	0.922198i
$453$	−254.094	−	749.457i	−0.560914	−	1.65443i
$454$	−1321.18			−2.91009
$455$			6.17084i			0.0135623i
$456$	−1395.31	+	473.064i	−3.05990	+	1.03742i
$457$	657.168			1.43800			0.719002	−	0.695008i	$-0.244599\pi$
$457$	657.168			1.43800			0.719002	+	0.695008i	$0.244599\pi$
$458$			116.530i			0.254432i
$459$	93.0399	−	138.906i	0.202701	−	0.302628i
$460$	−276.120			−0.600261
$461$		−	288.831i		−	0.626531i	−0.949666	−	0.313265i	$-0.898577\pi$
$461$		−	288.831i		−	0.626531i	0.949666	−	0.313265i	$-0.101423\pi$
$462$	−50.1176	−	147.823i	−0.108480	−	0.319964i
$463$	−676.522			−1.46117			−0.730586	−	0.682821i	$-0.760753\pi$
$463$	−676.522			−1.46117			−0.730586	+	0.682821i	$0.760753\pi$
$464$			1778.92i			3.83388i
$465$	349.278	−	118.418i	0.751135	−	0.254663i
$466$	1582.99			3.39698
$467$			73.8083i			0.158048i	0.996873	+	0.0790239i	$0.0251804\pi$
$467$			73.8083i			0.158048i	−0.996873	+	0.0790239i	$0.974820\pi$
$468$	−274.194	+	210.071i	−0.585885	+	0.448870i
$469$	7.07579			0.0150870
$470$			532.200i			1.13234i
$471$	262.981	+	775.670i	0.558346	+	1.64686i
$472$	1726.87			3.65863
$473$			1361.05i			2.87748i
$474$	33.4225	−	11.3315i	0.0705116	−	0.0239061i
$475$	−96.5699			−0.203305
$476$			50.4492i			0.105986i
$477$	−300.524	−	392.258i	−0.630029	−	0.822343i
$478$	1295.39			2.71002
$479$		−	575.041i		−	1.20050i	−0.799811	−	0.600252i	$-0.795067\pi$
$479$		−	575.041i		−	1.20050i	0.799811	−	0.600252i	$-0.204933\pi$
$480$	232.034	+	684.390i	0.483403	+	1.42581i
$481$	42.1598			0.0876504
$482$		−	350.444i		−	0.727062i
$483$	−25.2270	+	8.55291i	−0.0522299	+	0.0177079i
$484$	2070.73			4.27836
$485$			376.072i			0.775407i
$486$	−59.0845	−	928.039i	−0.121573	−	1.90955i
$487$	288.720			0.592855			0.296427	−	0.955055i	$-0.404205\pi$
$487$	288.720			0.592855			0.296427	+	0.955055i	$0.404205\pi$
$488$			844.448i			1.73043i
$489$	0.525649	+	1.55042i	0.00107495	+	0.00317058i
$490$	−414.282			−0.845473
$491$		−	724.099i		−	1.47474i	−0.675487	−	0.737372i	$-0.736067\pi$
$491$		−	724.099i		−	1.47474i	0.675487	−	0.737372i	$-0.263933\pi$
$492$	−812.084	+	275.327i	−1.65058	+	0.559607i
$493$	−201.270			−0.408256
$494$			266.491i			0.539454i
$495$	283.770	−	217.407i	0.573272	−	0.439206i
$496$	−3008.90			−6.06633
$497$		−	7.02287i		−	0.0141305i
$498$	−19.7470	−	58.2444i	−0.0396527	−	0.116957i
$499$	293.062			0.587298			0.293649	−	0.955913i	$-0.405130\pi$
$499$	293.062			0.587298			0.293649	+	0.955913i	$0.405130\pi$
$500$			119.010i			0.238020i
$501$	−45.8338	+	15.5394i	−0.0914846	+	0.0310167i
$502$	1315.53			2.62058
$503$		−	548.696i		−	1.09085i	−0.838160	−	0.545424i	$-0.816369\pi$
$503$		−	548.696i		−	1.09085i	0.838160	−	0.545424i	$-0.183631\pi$
$504$	106.527	+	139.044i	0.211363	+	0.275881i
$505$	−355.033			−0.703035
$506$		−	788.580i		−	1.55846i
$507$	12.5223	+	36.9350i	0.0246989	+	0.0728500i
$508$	−1821.02			−3.58468
$509$			700.782i			1.37678i	0.725340	+	0.688391i	$0.241683\pi$
$509$			700.782i			1.37678i	−0.725340	+	0.688391i	$0.758317\pi$
$510$	−150.541	+	51.0392i	−0.295179	+	0.100077i
$511$	−43.1515			−0.0844453
$512$		−	329.265i		−	0.643096i
$513$	−433.267	−	290.203i	−0.844575	−	0.565699i
$514$	1327.51			2.58271
$515$		−	7.99342i		−	0.0155212i
$516$	−785.636	−	2317.26i	−1.52255	−	4.49081i
$517$	−1104.77			−2.13689
$518$		−	34.2494i		−	0.0661185i
$519$	−598.044	+	202.759i	−1.15230	+	0.390673i
$520$	205.004			0.394239
$521$			154.996i			0.297497i	0.988875	+	0.148748i	$0.0475244\pi$
$521$			154.996i			0.297497i	−0.988875	+	0.148748i	$0.952476\pi$
$522$	−888.664	+	680.841i	−1.70242	+	1.30429i
$523$	420.807			0.804602			0.402301	−	0.915508i	$-0.368211\pi$
$523$	420.807			0.804602			0.402301	+	0.915508i	$0.368211\pi$
$524$			1507.34i			2.87659i
$525$	3.68637	+	10.8731i	0.00702166	+	0.0207106i
$526$	826.641			1.57156
$527$		−	340.432i		−	0.645980i
$528$	−2762.06	+	936.441i	−5.23117	+	1.77356i
$529$	394.423			0.745602
$530$			469.826i			0.886463i
$531$	371.724	+	485.191i	0.700045	+	0.913730i
$532$	157.358			0.295785
$533$			96.8165i			0.181645i
$534$	−270.065	−	796.565i	−0.505740	−	1.49170i
$535$	144.073			0.269296
$536$		−	235.068i		−	0.438560i
$537$	−201.740	+	68.3974i	−0.375680	+	0.127369i
$538$	−119.169			−0.221503
$539$		−	859.993i		−	1.59554i
$540$	−357.639	+	533.947i	−0.662294	+	0.988790i
$541$	−961.104			−1.77653			−0.888267	−	0.459328i	$-0.848090\pi$
$541$	−961.104			−1.77653			−0.888267	+	0.459328i	$0.848090\pi$
$542$			582.681i			1.07506i
$543$	197.941	+	583.831i	0.364531	+	1.07520i
$544$	667.056			1.22621
$545$		−	23.2883i		−	0.0427308i
$546$	30.0049	−	10.1728i	0.0549540	−	0.0186315i
$547$	−412.803			−0.754667			−0.377334	−	0.926077i	$-0.623159\pi$
$547$	−412.803			−0.754667			−0.377334	+	0.926077i	$0.623159\pi$
$548$			1303.45i			2.37855i
$549$	−237.260	+	181.774i	−0.432168	+	0.331101i
$550$	−339.884			−0.617972
$551$			627.787i			1.13936i
$552$	284.140	+	838.079i	0.514747	+	1.51826i
$553$	−2.35285			−0.00425470
$554$		−	1703.59i		−	3.07507i
$555$	74.2859	−	25.1857i	0.133848	−	0.0453796i
$556$	−892.803			−1.60576
$557$		−	61.5448i		−	0.110493i	−0.998473	−	0.0552467i	$-0.982405\pi$
$557$		−	61.5448i		−	0.110493i	0.998473	−	0.0552467i	$-0.0175945\pi$
$558$	−1151.59	−	1503.10i	−2.06377	−	2.69373i
$559$	−276.263			−0.494210
$560$		−	93.6674i		−	0.167263i
$561$	−105.950	−	312.504i	−0.188860	−	0.557048i
$562$	−538.673			−0.958493
$563$		−	820.428i		−	1.45724i	−0.684916	−	0.728622i	$-0.740161\pi$
$563$		−	820.428i		−	1.45724i	0.684916	−	0.728622i	$-0.259839\pi$
$564$	1880.94	−	637.707i	3.33499	−	1.13069i
$565$	−87.5627			−0.154978
$566$			1105.43i			1.95305i
$567$	−16.1356	+	59.8607i	−0.0284579	+	0.105574i
$568$	−233.310			−0.410757
$569$		−	228.404i		−	0.401413i	−0.979651	−	0.200707i	$-0.935676\pi$
$569$		−	228.404i		−	0.401413i	0.979651	−	0.200707i	$-0.0643238\pi$
$570$	159.198	+	469.558i	0.279294	+	0.823786i
$571$	−121.969			−0.213606			−0.106803	−	0.994280i	$-0.534061\pi$
$571$	−121.969			−0.213606			−0.106803	+	0.994280i	$0.534061\pi$
$572$			681.747i			1.19186i
$573$	864.207	−	292.998i	1.50821	−	0.511341i
$574$	78.6509			0.137022
$575$			58.0036i			0.100876i
$576$	1381.25	−	1058.23i	2.39800	−	1.83721i
$577$	−377.617			−0.654448			−0.327224	−	0.944947i	$-0.606113\pi$
$577$	−377.617			−0.654448			−0.327224	+	0.944947i	$0.606113\pi$
$578$		−	959.223i		−	1.65956i
$579$	112.576	+	332.047i	0.194433	+	0.573484i
$580$	773.668			1.33391
$581$			4.10024i			0.00705721i
$582$	1828.60	−	619.964i	3.14193	−	1.06523i
$583$	−975.295			−1.67289
$584$			1433.56i			2.45472i
$585$	44.1289	+	57.5990i	0.0754339	+	0.0984598i
$586$	821.827			1.40243
$587$		−	57.5337i		−	0.0980132i	−0.998798	−	0.0490066i	$-0.984394\pi$
$587$		−	57.5337i		−	0.0980132i	0.998798	−	0.0490066i	$-0.0156055\pi$
$588$	496.413	+	1464.18i	0.844239	+	2.49011i
$589$	−1061.85			−1.80280
$590$		−	581.136i		−	0.984976i
$591$	−300.524	+	101.889i	−0.508501	+	0.172401i
$592$	−639.946			−1.08099
$593$			116.547i			0.196538i	0.995160	+	0.0982691i	$0.0313306\pi$
$593$			116.547i			0.196538i	−0.995160	+	0.0982691i	$0.968669\pi$
$594$	−1524.91	−	1021.39i	−2.56720	−	1.71951i
$595$	10.5977			0.0178112
$596$		−	401.154i		−	0.673078i
$597$	−30.7312	−	90.6424i	−0.0514760	−	0.151830i
$598$	160.064			0.267666
$599$			11.4502i			0.0191156i	0.999954	+	0.00955779i	$0.00304239\pi$
$599$			11.4502i			0.0191156i	−0.999954	+	0.00955779i	$0.996958\pi$
$600$	361.219	−	122.467i	0.602031	−	0.204111i
$601$	−48.0256			−0.0799094			−0.0399547	−	0.999201i	$-0.512721\pi$
$601$	−48.0256			−0.0799094			−0.0399547	+	0.999201i	$0.512721\pi$
$602$			224.428i			0.372804i
$603$	66.0459	−	50.6003i	0.109529	−	0.0839143i
$604$	2807.90			4.64884
$605$		−	434.990i		−	0.718992i
$606$	585.280	+	1726.30i	0.965808	+	2.84868i
$607$	−96.6498			−0.159225			−0.0796127	−	0.996826i	$-0.525368\pi$
$607$	−96.6498			−0.159225			−0.0796127	+	0.996826i	$0.525368\pi$
$608$		−	2080.63i		−	3.42210i
$609$	70.6843	−	23.9646i	0.116066	−	0.0393507i
$610$	284.178			0.465865
$611$		−	224.245i		−	0.367013i
$612$	360.772	+	470.896i	0.589497	+	0.769438i
$613$	166.005			0.270807			0.135404	−	0.990791i	$-0.456767\pi$
$613$	166.005			0.270807			0.135404	+	0.990791i	$0.456767\pi$
$614$			690.671i			1.12487i
$615$	57.8368	+	170.591i	0.0940437	+	0.277384i
$616$	345.713			0.561223
$617$		−	810.007i		−	1.31282i	−0.754406	−	0.656408i	$-0.772075\pi$
$617$		−	810.007i		−	1.31282i	0.754406	−	0.656408i	$-0.227925\pi$
$618$	−38.8670	+	13.1774i	−0.0628915	+	0.0213226i
$619$	556.769			0.899465			0.449733	−	0.893163i	$-0.351519\pi$
$619$	556.769			0.899465			0.449733	+	0.893163i	$0.351519\pi$
$620$			1308.60i			2.11064i
$621$	−174.307	+	260.237i	−0.280688	+	0.419061i
$622$	1293.82			2.08009
$623$			56.0759i			0.0900094i
$624$	−190.077	−	560.637i	−0.304610	−	0.898457i
$625$	25.0000			0.0400000
$626$			150.115i			0.239800i
$627$	−974.740	+	330.473i	−1.55461	+	0.527070i
$628$	−2906.11			−4.62756
$629$		−	72.4045i		−	0.115110i
$630$	46.7917	−	35.8490i	0.0742726	−	0.0569032i
$631$	832.682			1.31962			0.659811	−	0.751432i	$-0.270636\pi$
$631$	832.682			1.31962			0.659811	+	0.751432i	$0.270636\pi$
$632$			78.1650i			0.123679i
$633$	136.856	+	403.661i	0.216202	+	0.637695i
$634$	−317.517			−0.500816
$635$			382.534i			0.602416i
$636$	1660.49	−	562.968i	2.61083	−	0.885169i
$637$	174.560			0.274034
$638$			2209.54i			3.46323i
$639$	−50.2219	−	65.5519i	−0.0785945	−	0.102585i
$640$	−690.851			−1.07945
$641$			385.612i			0.601578i	0.953691	+	0.300789i	$0.0972500\pi$
$641$			385.612i			0.601578i	−0.953691	+	0.300789i	$0.902750\pi$
$642$	−237.508	−	700.537i	−0.369950	−	1.09118i
$643$	590.422			0.918230			0.459115	−	0.888377i	$-0.348167\pi$
$643$	590.422			0.918230			0.459115	+	0.888377i	$0.348167\pi$
$644$		−	94.5150i		−	0.146762i
$645$	−486.778	+	165.036i	−0.754694	+	0.255869i
$646$	457.666			0.708461
$647$		−	670.561i		−	1.03642i	−0.855255	−	0.518208i	$-0.826599\pi$
$647$		−	670.561i		−	1.03642i	0.855255	−	0.518208i	$-0.173401\pi$
$648$	1988.66	+	536.049i	3.06892	+	0.827236i
$649$	1206.36			1.85880
$650$		−	68.9891i		−	0.106137i
$651$	40.5341	+	119.557i	0.0622644	+	0.183651i
$652$	−5.80875			−0.00890912
$653$		−	161.297i		−	0.247009i	−0.992344	−	0.123505i	$-0.960587\pi$
$653$		−	161.297i		−	0.247009i	0.992344	−	0.123505i	$-0.0394133\pi$
$654$	−113.236	+	38.3913i	−0.173144	+	0.0587023i
$655$	316.640			0.483420
$656$		−	1469.58i		−	2.24022i
$657$	−402.779	+	308.585i	−0.613058	+	0.469688i
$658$	−182.170			−0.276854
$659$		−	34.9635i		−	0.0530555i	−0.999648	−	0.0265277i	$-0.991555\pi$
$659$		−	34.9635i		−	0.0530555i	0.999648	−	0.0265277i	$-0.00844503\pi$
$660$	407.266	+	1201.24i	0.617070	+	1.82006i
$661$	773.240			1.16980			0.584902	−	0.811104i	$-0.301133\pi$
$661$	773.240			1.16980			0.584902	+	0.811104i	$0.301133\pi$
$662$			1862.58i			2.81356i
$663$	63.4314	−	21.5056i	0.0956733	−	0.0324368i
$664$	136.216			0.205144
$665$		−	33.0555i		−	0.0497076i
$666$	−244.924	−	319.686i	−0.367754	−	0.480009i
$667$	377.073			0.565327
$668$		−	171.720i		−	0.257065i
$669$	−113.741	−	335.483i	−0.170017	−	0.501469i
$670$	−79.1063			−0.118069
$671$			589.915i			0.879158i
$672$	−234.264	+	79.4243i	−0.348607	+	0.118191i
$673$	−962.003			−1.42942			−0.714712	−	0.699419i	$-0.753442\pi$
$673$	−962.003			−1.42942			−0.714712	+	0.699419i	$0.753442\pi$
$674$		−	285.313i		−	0.423314i
$675$	112.164	+	75.1279i	0.166169	+	0.111301i
$676$	−138.380			−0.204703
$677$			639.211i			0.944182i	0.881550	+	0.472091i	$0.156501\pi$
$677$			639.211i			0.944182i	−0.881550	+	0.472091i	$0.843499\pi$
$678$	144.349	+	425.762i	0.212904	+	0.627967i
$679$	−128.728			−0.189585
$680$		−	352.070i		−	0.517750i
$681$	980.883	−	332.556i	1.44036	−	0.488335i
$682$	−3737.26			−5.47985
$683$		−	1045.15i		−	1.53023i	−0.643891	−	0.765117i	$-0.722681\pi$
$683$		−	1045.15i		−	1.53023i	0.643891	−	0.765117i	$-0.277319\pi$
$684$	1468.79	−	1125.29i	2.14735	−	1.64517i
$685$	273.810			0.399723
$686$		−	285.330i		−	0.415933i
$687$	−29.3320	−	86.5155i	−0.0426957	−	0.125932i
$688$	4193.41			6.09507
$689$		−	197.963i		−	0.287320i
$690$	282.035	−	95.6202i	0.408746	−	0.138580i
$691$	1007.15			1.45753			0.728765	−	0.684764i	$-0.240095\pi$
$691$	1007.15			1.45753			0.728765	+	0.684764i	$0.240095\pi$
$692$		−	2240.62i		−	3.23788i
$693$	74.4177	+	97.1333i	0.107385	+	0.140164i
$694$	−1858.11			−2.67739
$695$			187.548i			0.269853i
$696$	−796.139	−	2348.23i	−1.14388	−	3.37390i
$697$	166.271			0.238552
$698$		−	1376.97i		−	1.97273i
$699$	−1175.26	+	398.457i	−1.68135	+	0.570039i
$700$	−40.7367			−0.0581953
$701$			131.829i			0.188058i	0.995569	+	0.0940292i	$0.0299747\pi$
$701$			131.829i			0.188058i	−0.995569	+	0.0940292i	$0.970025\pi$
$702$	207.320	−	309.524i	0.295328	−	0.440917i
$703$	−225.839			−0.321250
$704$		−	3434.29i		−	4.87825i
$705$	−133.961	−	395.121i	−0.190015	−	0.560456i
$706$	−16.0704			−0.0227626
$707$		−	121.526i		−	0.171890i
$708$	−2053.89	+	696.345i	−2.90097	+	0.983538i
$709$	−800.698			−1.12933			−0.564667	−	0.825319i	$-0.690995\pi$
$709$	−800.698			−1.12933			−0.564667	+	0.825319i	$0.690995\pi$
$710$			78.5146i			0.110584i
$711$	−21.9616	+	16.8257i	−0.0308884	+	0.0236648i
$712$	1862.92			2.61646
$713$			637.788i			0.894513i
$714$	−17.4705	−	51.5298i	−0.0244685	−	0.0721706i
$715$	143.212			0.200296
$716$		−	755.834i		−	1.05563i
$717$	−961.736	+	326.064i	−1.34133	+	0.454762i
$718$	986.968			1.37461
$719$			1133.64i			1.57668i	0.615237	+	0.788342i	$0.289060\pi$
$719$			1133.64i			1.57668i	−0.615237	+	0.788342i	$0.710940\pi$
$720$	−669.834	−	874.297i	−0.930324	−	1.21430i
$721$	2.73612			0.00379490
$722$		−	46.0348i		−	0.0637601i
$723$	88.2108	+	260.180i	0.122007	+	0.359862i
$724$	−2187.37			−3.02123
$725$		−	162.522i		−	0.224168i
$726$	−2115.08	+	717.091i	−2.91334	+	0.987729i
$727$	623.805			0.858053			0.429027	−	0.903292i	$-0.358857\pi$
$727$	623.805			0.858053			0.429027	+	0.903292i	$0.358857\pi$
$728$			70.1722i			0.0963904i
$729$	277.464	+	674.132i	0.380610	+	0.924736i
$730$	482.428			0.660860
$731$			474.449i			0.649041i
$732$	−340.516	−	1004.36i	−0.465185	−	1.37208i
$733$	−452.753			−0.617672			−0.308836	−	0.951115i	$-0.599939\pi$
$733$	−452.753			−0.617672			−0.308836	+	0.951115i	$0.599939\pi$
$734$			567.521i			0.773189i
$735$	307.575	−	104.280i	0.418470	−	0.141877i
$736$	−1249.71			−1.69797
$737$		−	164.214i		−	0.222814i
$738$	734.133	−	562.448i	0.994760	−	0.762125i
$739$	392.901			0.531666			0.265833	−	0.964019i	$-0.414353\pi$
$739$	392.901			0.531666			0.265833	+	0.964019i	$0.414353\pi$
$740$			278.318i			0.376105i
$741$	−67.0788	−	197.851i	−0.0905246	−	0.267005i
$742$	−160.820			−0.216738
$743$		−	119.313i		−	0.160583i	−0.996771	−	0.0802915i	$-0.974415\pi$
$743$		−	119.313i		−	0.160583i	0.996771	−	0.0802915i	$-0.0255851\pi$
$744$	3971.84	−	1346.60i	5.33850	−	1.80995i
$745$	−84.2690			−0.113113
$746$			430.183i			0.576652i
$747$	29.3216	+	38.2719i	0.0392525	+	0.0512341i
$748$	1170.82			1.56527
$749$			49.3157i			0.0658421i
$750$	−41.2131	−	121.559i	−0.0549508	−	0.162079i
$751$	64.5944			0.0860112			0.0430056	−	0.999075i	$-0.486307\pi$
$751$	64.5944			0.0860112			0.0430056	+	0.999075i	$0.486307\pi$
$752$			3403.82i			4.52636i
$753$	−976.689	+	331.134i	−1.29706	+	0.439753i
$754$	−448.488			−0.594812
$755$		−	589.845i		−	0.781251i
$756$	−182.768	−	122.418i	−0.241757	−	0.161929i
$757$	−676.373			−0.893491			−0.446746	−	0.894661i	$-0.647417\pi$
$757$	−676.373			−0.893491			−0.446746	+	0.894661i	$0.647417\pi$
$758$			1029.31i			1.35793i
$759$	198.495	+	585.466i	0.261521	+	0.771365i
$760$	−1098.15			−1.44494
$761$			148.782i			0.195509i	0.995211	+	0.0977545i	$0.0311660\pi$
$761$			148.782i			0.195509i	−0.995211	+	0.0977545i	$0.968834\pi$
$762$	1860.02	−	630.616i	2.44097	−	0.827581i
$763$	7.97150			0.0104476
$764$			3237.82i			4.23798i
$765$	98.9194	−	75.7860i	0.129306	−	0.0990667i
$766$	−634.944			−0.828909
$767$			244.865i			0.319250i
$768$	393.953	+	1161.98i	0.512960	+	1.51299i
$769$	−106.923			−0.139042			−0.0695209	−	0.997580i	$-0.522147\pi$
$769$	−106.923			−0.139042			−0.0695209	+	0.997580i	$0.522147\pi$
$770$		−	116.341i		−	0.151092i
$771$	−985.585	+	334.150i	−1.27832	+	0.433398i
$772$	−1244.04			−1.61145
$773$			1140.76i			1.47576i	0.674932	+	0.737880i	$0.264173\pi$
$773$			1140.76i			1.47576i	−0.674932	+	0.737880i	$0.735827\pi$
$774$	1604.93	+	2094.83i	2.07355	+	2.70649i
$775$	274.892			0.354699
$776$			4276.54i			5.51101i
$777$	8.62097	+	25.4278i	0.0110952	+	0.0327256i
$778$	−260.644			−0.335018
$779$		−	518.620i		−	0.665751i
$780$	−243.826	+	82.6660i	−0.312597	+	0.105982i
$781$	−162.986			−0.208689
$782$		−	274.892i		−	0.351524i
$783$	488.396	−	729.164i	0.623749	−	0.931244i
$784$	−2649.65			−3.37965
$785$			610.475i			0.777675i
$786$	−521.989	−	1539.62i	−0.664108	−	1.95881i
$787$	203.210			0.258209			0.129104	−	0.991631i	$-0.458790\pi$
$787$	203.210			0.258209			0.129104	+	0.991631i	$0.458790\pi$
$788$		−	1125.94i		−	1.42885i
$789$	−613.723	+	208.075i	−0.777849	+	0.263720i
$790$	26.3045			0.0332968
$791$		−	29.9724i		−	0.0378918i
$792$	3226.91	−	2472.26i	4.07438	−	3.12155i
$793$	−119.740			−0.150996
$794$			871.274i			1.09732i
$795$	−118.261	−	348.813i	−0.148755	−	0.438758i
$796$	339.599			0.426631
$797$			187.116i			0.234775i	0.993086	+	0.117387i	$0.0374519\pi$
$797$			187.116i			0.234775i	−0.993086	+	0.117387i	$0.962548\pi$
$798$	−160.728	+	54.4928i	−0.201414	+	0.0682867i
$799$	−385.114			−0.481995
$800$			538.634i			0.673293i
$801$	401.010	+	523.416i	0.500636	+	0.653453i
$802$	393.489			0.490634
$803$			1001.46i			1.24714i
$804$	94.7890	+	279.583i	0.117897	+	0.347740i
$805$	−19.8544			−0.0246639
$806$		−	758.581i		−	0.941167i
$807$	88.4746	−	29.9962i	0.109634	−	0.0371700i
$808$	−4037.29			−4.99664
$809$			339.771i			0.419988i	0.977703	+	0.209994i	$0.0673445\pi$
$809$			339.771i			0.419988i	−0.977703	+	0.209994i	$0.932655\pi$
$810$	180.394	−	669.234i	0.222709	−	0.826214i
$811$	685.419			0.845152			0.422576	−	0.906327i	$-0.361126\pi$
$811$	685.419			0.845152			0.422576	+	0.906327i	$0.361126\pi$
$812$			264.824i			0.326138i
$813$	−146.668	−	432.600i	−0.180403	−	0.532104i
$814$	−794.856			−0.976481
$815$			1.22022i			0.00149720i
$816$	−962.827	+	326.434i	−1.17994	+	0.400042i
$817$	1479.87			1.81134
$818$			378.434i			0.462633i
$819$	−19.7159	+	15.1052i	−0.0240732	+	0.0184434i
$820$	−639.133			−0.779431
$821$		−	1189.70i		−	1.44909i	−0.689230	−	0.724543i	$-0.742051\pi$
$821$		−	1189.70i		−	1.44909i	0.689230	−	0.724543i	$-0.257949\pi$
$822$	−451.383	−	1331.37i	−0.549128	−	1.61967i
$823$	1383.79			1.68140			0.840699	−	0.541503i	$-0.182144\pi$
$823$	1383.79			1.68140			0.840699	+	0.541503i	$0.182144\pi$
$824$		−	90.8979i		−	0.110313i
$825$	252.341	−	85.5528i	0.305867	−	0.103700i
$826$	198.921			0.240824
$827$		−	1369.76i		−	1.65630i	−0.560505	−	0.828151i	$-0.689393\pi$
$827$		−	1369.76i		−	1.65630i	0.560505	−	0.828151i	$-0.310607\pi$
$828$	−675.895	−	882.209i	−0.816298	−	1.06547i
$829$	34.2053			0.0412610			0.0206305	−	0.999787i	$-0.493433\pi$
$829$	34.2053			0.0412610			0.0206305	+	0.999787i	$0.493433\pi$
$830$		−	45.8400i		−	0.0552290i
$831$	428.813	+	1264.80i	0.516021	+	1.52202i
$832$	697.085			0.837843
$833$		−	299.786i		−	0.359887i
$834$	911.926	−	309.177i	1.09344	−	0.370716i
$835$	−36.0725			−0.0432006
$836$		−	3651.93i		−	4.36834i
$837$	1233.32	+	826.081i	1.47350	+	0.986955i
$838$	2297.38			2.74150
$839$		−	154.593i		−	0.184258i	−0.995747	−	0.0921290i	$-0.970633\pi$
$839$		−	154.593i		−	0.184258i	0.995747	−	0.0921290i	$-0.0293672\pi$
$840$	41.9199	+	123.644i	0.0499047	+	0.147195i
$841$	−215.530			−0.256279
$842$			2163.74i			2.56977i
$843$	399.927	−	135.590i	0.474410	−	0.160843i
$844$	−1512.35			−1.79188
$845$			29.0689i			0.0344010i
$846$	−1700.39	+	1302.73i	−2.00991	+	1.53987i
$847$	148.896			0.175792
$848$			3004.89i			3.54351i
$849$	−278.249	−	820.703i	−0.327737	−	0.966670i
$850$	−118.480			−0.139389
$851$			135.648i			0.159398i
$852$	277.492	−	94.0800i	0.325694	−	0.110423i
$853$	940.577			1.10267			0.551335	−	0.834284i	$-0.314119\pi$
$853$	940.577			1.10267			0.551335	+	0.834284i	$0.314119\pi$
$854$			97.2731i			0.113903i
$855$	−236.386	−	308.542i	−0.276475	−	0.360868i
$856$	1638.34			1.91395
$857$		−	721.525i		−	0.841919i	−0.907079	−	0.420960i	$-0.861693\pi$
$857$		−	721.525i		−	0.841919i	0.907079	−	0.420960i	$-0.138307\pi$
$858$	−236.088	−	696.349i	−0.275161	−	0.811596i
$859$	−984.953			−1.14663			−0.573314	−	0.819336i	$-0.694342\pi$
$859$	−984.953			−1.14663			−0.573314	+	0.819336i	$0.694342\pi$
$860$		−	1823.75i		−	2.12064i
$861$	−58.3928	+	19.7973i	−0.0678198	+	0.0229934i
$862$	−1285.44			−1.49123
$863$		−	268.705i		−	0.311361i	−0.987807	−	0.155681i	$-0.950243\pi$
$863$		−	268.705i		−	0.311361i	0.987807	−	0.155681i	$-0.0497570\pi$
$864$	−1618.66	+	2416.62i	−1.87345	+	2.79701i
$865$	−470.678			−0.544136
$866$		−	1427.85i		−	1.64879i
$867$	241.448	+	712.157i	0.278486	+	0.821403i
$868$	−447.928			−0.516046
$869$			54.6046i			0.0628361i
$870$	−790.240	+	267.921i	−0.908321	+	0.307955i
$871$	33.3318			0.0382685
$872$		−	264.825i		−	0.303698i
$873$	−1201.56	+	920.561i	−1.37635	+	1.05448i
$874$	−857.422			−0.981032
$875$			8.55741i			0.00977990i
$876$	−578.068	−	1705.03i	−0.659895	−	1.94638i
$877$	−400.930			−0.457160			−0.228580	−	0.973525i	$-0.573408\pi$
$877$	−400.930			−0.457160			−0.228580	+	0.973525i	$0.573408\pi$
$878$			507.870i			0.578439i
$879$	−610.149	+	206.863i	−0.694140	+	0.235339i
$880$	−2173.82			−2.47025
$881$		−	1310.86i		−	1.48792i	−0.668223	−	0.743961i	$-0.732945\pi$
$881$		−	1310.86i		−	1.48792i	0.668223	−	0.743961i	$-0.267055\pi$
$882$	−1014.09	−	1323.64i	−1.14976	−	1.50072i
$883$	974.612			1.10375			0.551876	−	0.833926i	$-0.313912\pi$
$883$	974.612			1.10375			0.551876	+	0.833926i	$0.313912\pi$
$884$			237.650i			0.268835i
$885$	146.279	+	431.453i	0.165287	+	0.487518i
$886$	931.162			1.05097
$887$		−	472.071i		−	0.532211i	−0.963944	−	0.266105i	$-0.914263\pi$
$887$		−	472.071i		−	0.532211i	0.963944	−	0.266105i	$-0.0857369\pi$
$888$	844.749	−	286.401i	0.951294	−	0.322524i
$889$	−130.940			−0.147289
$890$		−	626.920i		−	0.704405i
$891$	1389.24	+	374.473i	1.55919	+	0.420284i
$892$	1256.91			1.40909
$893$			1201.22i			1.34515i
$894$	138.919	+	409.747i	0.155391	+	0.458330i
$895$	−158.775			−0.177402
$896$		−	236.476i		−	0.263924i
$897$	−118.837	+	40.2901i	−0.132482	+	0.0449165i
$898$	−986.161			−1.09818
$899$		−	1787.03i		−	1.98780i
$900$	−380.239	+	291.316i	−0.422488	+	0.323685i
$901$	−339.978			−0.377335
$902$		−	1825.32i		−	2.02364i
$903$	−56.4912	−	166.622i	−0.0625594	−	0.184521i
$904$	−995.727			−1.10147
$905$			459.492i			0.507726i
$906$	−2868.04	+	972.373i	−3.16561	+	1.07326i
$907$	−1079.15			−1.18980			−0.594899	−	0.803801i	$-0.702808\pi$
$907$	−1079.15			−1.18980			−0.594899	+	0.803801i	$0.702808\pi$
$908$			3674.95i			4.04730i
$909$	−869.059	−	1134.34i	−0.956061	−	1.24789i
$910$	23.6147			0.0259502
$911$		−	230.412i		−	0.252922i	−0.991972	−	0.126461i	$-0.959638\pi$
$911$		−	230.412i		−	0.252922i	0.991972	−	0.126461i	$-0.0403618\pi$
$912$	1018.19	+	3003.18i	1.11644	+	3.29296i
$913$	95.1578			0.104225
$914$		−	2514.87i		−	2.75150i
$915$	−210.982	+	71.5309i	−0.230582	+	0.0781758i
$916$	324.137			0.353861
$917$			108.385i			0.118195i
$918$	−531.571	−	356.047i	−0.579053	−	0.387851i
$919$	1000.28			1.08845			0.544224	−	0.838940i	$-0.316824\pi$
$919$	1000.28			1.08845			0.544224	+	0.838940i	$0.316824\pi$
$920$			659.593i			0.716948i
$921$	−173.850	−	512.775i	−0.188762	−	0.556759i
$922$	−1105.30			−1.19881
$923$		−	33.0825i		−	0.0358424i
$924$	−411.181	+	139.406i	−0.445001	+	0.150872i
$925$	58.4652			0.0632056
$926$			2588.93i			2.79582i
$927$	25.5391	−	19.5665i	0.0275503	−	0.0211074i
$928$	3501.59			3.77326
$929$			550.220i			0.592271i	0.955146	+	0.296136i	$0.0956980\pi$
$929$			550.220i			0.592271i	−0.955146	+	0.296136i	$0.904302\pi$
$930$	−453.166	−	1336.62i	−0.487275	−	1.43723i
$931$	−935.070			−1.00437
$932$		−	4403.20i		−	4.72447i
$933$	−960.568	+	325.668i	−1.02955	+	0.349055i
$934$	282.452			0.302411
$935$		−	245.949i		−	0.263048i
$936$	501.815	+	654.992i	0.536127	+	0.699778i
$937$	918.345			0.980091			0.490046	−	0.871697i	$-0.336980\pi$
$937$	918.345			0.980091			0.490046	+	0.871697i	$0.336980\pi$
$938$		−	27.0778i		−	0.0288676i
$939$	−37.7856	−	111.450i	−0.0402402	−	0.118690i
$940$	1480.35			1.57484
$941$			14.6127i			0.0155289i	0.999970	+	0.00776446i	$0.00247153\pi$
$941$			14.6127i			0.0155289i	−0.999970	+	0.00776446i	$0.997528\pi$
$942$	2968.35	−	1006.38i	3.15112	−	1.06835i
$943$	−311.503			−0.330332
$944$		−	3716.81i		−	3.93730i
$945$	−25.7160	+	38.3934i	−0.0272127	+	0.0406279i
$946$	5208.50			5.50581
$947$		−	302.926i		−	0.319880i	−0.987127	−	0.159940i	$-0.948870\pi$
$947$		−	302.926i		−	0.319880i	0.987127	−	0.159940i	$-0.0511301\pi$
$948$	−31.5193	−	92.9671i	−0.0332482	−	0.0980665i
$949$	−203.273			−0.214197
$950$			369.556i			0.389006i
$951$	235.734	−	79.9228i	0.247881	−	0.0840408i
$952$	120.512			0.126589
$953$			1059.71i			1.11197i	0.831191	+	0.555987i	$0.187660\pi$
$953$			1059.71i			1.11197i	−0.831191	+	0.555987i	$0.812340\pi$
$954$	−1501.10	+	1150.05i	−1.57348	+	1.20551i
$955$	680.156			0.712205
$956$		−	3603.22i		−	3.76905i
$957$	−556.167	−	1640.43i	−0.581157	−	1.71414i
$958$	−2200.58			−2.29706
$959$			93.7243i			0.0977313i
$960$	1228.27	−	416.429i	1.27945	−	0.433780i
$961$	2061.62			2.14529
$962$		−	161.338i		−	0.167711i
$963$	352.667	+	460.316i	0.366217	+	0.478002i
$964$	−974.785			−1.01119
$965$			261.331i			0.270809i
$966$	32.7305	+	96.5394i	0.0338825	+	0.0999373i
$967$	1056.74			1.09281			0.546404	−	0.837522i	$-0.315996\pi$
$967$	1056.74			1.09281			0.546404	+	0.837522i	$0.315996\pi$
$968$		−	4946.53i		−	5.11005i
$969$	−339.785	+	115.200i	−0.350655	+	0.118885i
$970$	1439.16			1.48367
$971$			270.764i			0.278851i	0.990233	+	0.139425i	$0.0445255\pi$
$971$			270.764i			0.278851i	−0.990233	+	0.139425i	$0.955474\pi$
$972$	−2581.41	+	164.348i	−2.65577	+	0.169082i
$973$	−64.1970			−0.0659784
$974$		−	1104.88i		−	1.13438i
$975$	17.3653	+	51.2196i	0.0178106	+	0.0525329i
$976$	1817.53			1.86223
$977$			1181.19i			1.20900i	0.796605	+	0.604500i	$0.206627\pi$
$977$			1181.19i			1.20900i	−0.796605	+	0.604500i	$0.793373\pi$
$978$	5.93317	−	2.01156i	0.00606663	−	0.00205681i
$979$	1301.40			1.32932
$980$			1152.35i			1.17587i
$981$	74.4065	−	57.0057i	0.0758476	−	0.0581098i
$982$	−2771.00			−2.82179
$983$		−	964.232i		−	0.980907i	−0.871467	−	0.490453i	$-0.836831\pi$
$983$		−	964.232i		−	0.980907i	0.871467	−	0.490453i	$-0.163169\pi$
$984$	657.697	+	1939.90i	0.668391	+	1.97144i
$985$	−236.521			−0.240123
$986$			770.225i			0.781161i
$987$	135.249	−	45.8543i	0.137030	−	0.0464583i
$988$	741.262			0.750265
$989$		−	888.865i		−	0.898751i
$990$	−831.979	−	1085.94i	−0.840383	−	1.09691i
$991$	−503.550			−0.508123			−0.254062	−	0.967188i	$-0.581767\pi$
$991$	−503.550			−0.508123			−0.254062	+	0.967188i	$0.581767\pi$
$992$			5922.65i			5.97041i
$993$	−468.832	−	1382.83i	−0.472137	−	1.39258i
$994$	−26.8753			−0.0270375
$995$		−	71.3382i		−	0.0716967i
$996$	−162.011	+	54.9278i	−0.162662	+	0.0551484i
$997$	110.384			0.110716			0.0553581	−	0.998467i	$-0.482370\pi$
$997$	110.384			0.110716			0.0553581	+	0.998467i	$0.482370\pi$
$998$		−	1121.50i		−	1.12374i
$999$	262.308	+	175.694i	0.262570	+	0.175870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.3.d.a.131.2	✓	32
3.2	odd	2	inner	195.3.d.a.131.31	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.3.d.a.131.2	✓	32	1.1	even	1	trivial
195.3.d.a.131.31	yes	32	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	195.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.82682i q^{2} +(0.963256 + 2.84115i) q^{3} -10.6446 q^{4} +2.23607i q^{5} +(10.8726 - 3.68621i) q^{6} -0.765398 q^{7} +25.4276i q^{8} +(-7.14428 + 5.47351i) q^{9} +8.55704 q^{10} +17.7633i q^{11} +(-10.2535 - 30.2429i) q^{12} -3.60555 q^{13} +2.92904i q^{14} +(-6.35301 + 2.15391i) q^{15} +54.7288 q^{16} +6.19210i q^{17} +(20.9462 + 27.3399i) q^{18} +19.3140 q^{19} -23.8020i q^{20} +(-0.737274 - 2.17461i) q^{21} +67.9769 q^{22} -11.6007i q^{23} +(-72.2438 + 24.4933i) q^{24} -5.00000 q^{25} +13.7978i q^{26} +(-22.4328 - 15.0256i) q^{27} +8.14734 q^{28} +32.5043i q^{29} +(8.24262 + 24.3118i) q^{30} -54.9784 q^{31} -107.727i q^{32} +(-50.4681 + 17.1106i) q^{33} +23.6961 q^{34} -1.71148i q^{35} +(76.0478 - 58.2632i) q^{36} -11.6930 q^{37} -73.9112i q^{38} +(-3.47307 - 10.2439i) q^{39} -56.8579 q^{40} -26.8521i q^{41} +(-8.32186 + 2.82142i) q^{42} +76.6216 q^{43} -189.082i q^{44} +(-12.2391 - 15.9751i) q^{45} -44.3939 q^{46} +62.1944i q^{47} +(52.7178 + 155.493i) q^{48} -48.4142 q^{49} +19.1341i q^{50} +(-17.5927 + 5.96458i) q^{51} +38.3796 q^{52} +54.9052i q^{53} +(-57.5002 + 85.8465i) q^{54} -39.7199 q^{55} -19.4623i q^{56} +(18.6043 + 54.8739i) q^{57} +124.388 q^{58} -67.9132i q^{59} +(67.6251 - 22.9274i) q^{60} +33.2098 q^{61} +210.393i q^{62} +(5.46822 - 4.18942i) q^{63} -193.337 q^{64} -8.06226i q^{65} +(65.4791 + 193.133i) q^{66} -9.24458 q^{67} -65.9124i q^{68} +(32.9594 - 11.1745i) q^{69} -6.54954 q^{70} +9.17544i q^{71} +(-139.179 - 181.662i) q^{72} +56.3779 q^{73} +44.7472i q^{74} +(-4.81628 - 14.2058i) q^{75} -205.589 q^{76} -13.5960i q^{77} +(-39.2017 + 13.2908i) q^{78} +3.07402 q^{79} +122.377i q^{80} +(21.0813 - 78.2085i) q^{81} -102.758 q^{82} -5.35700i q^{83} +(7.84798 + 23.1478i) q^{84} -13.8460 q^{85} -293.217i q^{86} +(-92.3496 + 31.3100i) q^{87} -451.678 q^{88} -73.2637i q^{89} +(-61.1338 + 46.8370i) q^{90} +2.75968 q^{91} +123.485i q^{92} +(-52.9582 - 156.202i) q^{93} +238.007 q^{94} +43.1874i q^{95} +(306.068 - 103.769i) q^{96} +168.185 q^{97} +185.272i q^{98} +(-97.2274 - 126.906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} - 60 q^{4} - 8 q^{6} + 8 q^{9} - 20 q^{10} - 68 q^{12} + 172 q^{16} + 132 q^{18} - 16 q^{19} + 44 q^{21} - 64 q^{22} - 92 q^{24} - 160 q^{25} + 20 q^{27} + 224 q^{28} - 40 q^{30} - 56 q^{31}+ \cdots + 236 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 - 60 * q^4 - 8 * q^6 + 8 * q^9 - 20 * q^10 - 68 * q^12 + 172 * q^16 + 132 * q^18 - 16 * q^19 + 44 * q^21 - 64 * q^22 - 92 * q^24 - 160 * q^25 + 20 * q^27 + 224 * q^28 - 40 * q^30 - 56 * q^31 - 148 * q^33 - 240 * q^34 - 36 * q^36 + 24 * q^37 - 60 * q^40 + 276 * q^42 + 296 * q^43 - 120 * q^45 - 152 * q^46 + 384 * q^48 + 196 * q^49 + 20 * q^51 - 556 * q^54 - 20 * q^55 - 52 * q^57 + 544 * q^58 + 140 * q^60 - 220 * q^61 + 152 * q^63 - 716 * q^64 + 8 * q^66 - 72 * q^67 - 68 * q^69 + 120 * q^70 - 108 * q^72 - 208 * q^73 - 40 * q^75 + 624 * q^76 - 260 * q^78 - 388 * q^79 + 672 * q^81 + 400 * q^82 - 132 * q^84 + 160 * q^85 + 108 * q^87 - 720 * q^88 - 80 * q^90 + 52 * q^91 - 116 * q^93 - 280 * q^94 - 96 * q^96 + 952 * q^97 + 236 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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