LMFDB - Embedded newform 195.3.d.a.131.14

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			131.14
Character	$\chi$	$=$	195.131
Dual form			195.3.d.a.131.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.858859i q^{2} +(2.44162 - 1.74313i) q^{3} +3.26236 q^{4} +2.23607i q^{5} +(-1.49710 - 2.09701i) q^{6} +2.16867 q^{7} -6.23734i q^{8} +(2.92302 - 8.51211i) q^{9} +1.92047 q^{10} +7.88082i q^{11} +(7.96545 - 5.68671i) q^{12} +3.60555 q^{13} -1.86258i q^{14} +(3.89775 + 5.45963i) q^{15} +7.69245 q^{16} +3.67384i q^{17} +(-7.31070 - 2.51046i) q^{18} -20.8237 q^{19} +7.29486i q^{20} +(5.29507 - 3.78027i) q^{21} +6.76851 q^{22} -6.25251i q^{23} +(-10.8725 - 15.2292i) q^{24} -5.00000 q^{25} -3.09666i q^{26} +(-7.70077 - 25.8785i) q^{27} +7.07498 q^{28} +2.29496i q^{29} +(4.68905 - 3.34762i) q^{30} -24.7051 q^{31} -31.5561i q^{32} +(13.7373 + 19.2420i) q^{33} +3.15531 q^{34} +4.84929i q^{35} +(9.53595 - 27.7696i) q^{36} -16.3579 q^{37} +17.8846i q^{38} +(8.80339 - 6.28493i) q^{39} +13.9471 q^{40} +18.7742i q^{41} +(-3.24671 - 4.54772i) q^{42} +58.4174 q^{43} +25.7101i q^{44} +(19.0336 + 6.53607i) q^{45} -5.37003 q^{46} +6.89606i q^{47} +(18.7820 - 13.4089i) q^{48} -44.2969 q^{49} +4.29429i q^{50} +(6.40397 + 8.97013i) q^{51} +11.7626 q^{52} +34.1678i q^{53} +(-22.2260 + 6.61387i) q^{54} -17.6221 q^{55} -13.5267i q^{56} +(-50.8435 + 36.2983i) q^{57} +1.97104 q^{58} +78.6419i q^{59} +(12.7159 + 17.8113i) q^{60} -98.8756 q^{61} +21.2182i q^{62} +(6.33907 - 18.4599i) q^{63} +3.66755 q^{64} +8.06226i q^{65} +(16.5261 - 11.7984i) q^{66} -55.1753 q^{67} +11.9854i q^{68} +(-10.8989 - 15.2663i) q^{69} +4.16486 q^{70} +67.9447i q^{71} +(-53.0929 - 18.2319i) q^{72} +99.2688 q^{73} +14.0492i q^{74} +(-12.2081 + 8.71563i) q^{75} -67.9343 q^{76} +17.0909i q^{77} +(-5.39787 - 7.56087i) q^{78} +66.9315 q^{79} +17.2008i q^{80} +(-63.9119 - 49.7621i) q^{81} +16.1244 q^{82} +138.095i q^{83} +(17.2744 - 12.3326i) q^{84} -8.21496 q^{85} -50.1723i q^{86} +(4.00040 + 5.60342i) q^{87} +49.1554 q^{88} -34.4200i q^{89} +(5.61356 - 16.3472i) q^{90} +7.81925 q^{91} -20.3980i q^{92} +(-60.3205 + 43.0641i) q^{93} +5.92274 q^{94} -46.5631i q^{95} +(-55.0063 - 77.0480i) q^{96} -3.08056 q^{97} +38.0448i q^{98} +(67.0824 + 23.0358i) 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 $

$2$		−	0.858859i		−	0.429429i	−0.976677	−	0.214715i	$-0.931118\pi$
$2$		−	0.858859i		−	0.429429i	0.976677	−	0.214715i	$-0.0688822\pi$
$3$	2.44162	−	1.74313i	0.813873	−	0.581042i
$3$	2.44162	−	1.74313i	0.813873	−	0.581042i
$4$	3.26236			0.815590
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	−1.49710	−	2.09701i	−0.249517	−	0.349501i
$7$	2.16867			0.309810			0.154905	−	0.987929i	$-0.450493\pi$
$7$	2.16867			0.309810			0.154905	+	0.987929i	$0.450493\pi$
$8$		−	6.23734i		−	0.779668i
$9$	2.92302	−	8.51211i	0.324780	−	0.945790i
$10$	1.92047			0.192047
$11$			7.88082i			0.716438i	0.933637	+	0.358219i	$0.116616\pi$
$11$			7.88082i			0.716438i	−0.933637	+	0.358219i	$0.883384\pi$
$12$	7.96545	−	5.68671i	0.663787	−	0.473892i
$13$	3.60555			0.277350
$13$	3.60555			0.277350
$14$		−	1.86258i		−	0.133042i
$15$	3.89775	+	5.45963i	0.259850	+	0.363975i
$16$	7.69245			0.480778
$17$			3.67384i			0.216108i	0.994145	+	0.108054i	$0.0344620\pi$
$17$			3.67384i			0.216108i	−0.994145	+	0.108054i	$0.965538\pi$
$18$	−7.31070	−	2.51046i	−0.406150	−	0.139470i
$19$	−20.8237			−1.09598			−0.547991	−	0.836484i	$-0.684607\pi$
$19$	−20.8237			−1.09598			−0.547991	+	0.836484i	$0.684607\pi$
$20$			7.29486i			0.364743i
$21$	5.29507	−	3.78027i	0.252146	−	0.180013i
$22$	6.76851			0.307660
$23$		−	6.25251i		−	0.271848i	−0.990719	−	0.135924i	$-0.956600\pi$
$23$		−	6.25251i		−	0.271848i	0.990719	−	0.135924i	$-0.0434004\pi$
$24$	−10.8725	−	15.2292i	−0.453020	−	0.634551i
$25$	−5.00000			−0.200000
$26$		−	3.09666i		−	0.119102i
$27$	−7.70077	−	25.8785i	−0.285214	−	0.958464i
$28$	7.07498			0.252678
$29$			2.29496i			0.0791365i	0.999217	+	0.0395682i	$0.0125982\pi$
$29$			2.29496i			0.0791365i	−0.999217	+	0.0395682i	$0.987402\pi$
$30$	4.68905	−	3.34762i	0.156302	−	0.111587i
$31$	−24.7051			−0.796939			−0.398469	−	0.917182i	$-0.630458\pi$
$31$	−24.7051			−0.796939			−0.398469	+	0.917182i	$0.630458\pi$
$32$		−	31.5561i		−	0.986128i
$33$	13.7373	+	19.2420i	0.416281	+	0.583090i
$34$	3.15531			0.0928033
$35$			4.84929i			0.138551i
$36$	9.53595	−	27.7696i	0.264887	−	0.771377i
$37$	−16.3579			−0.442106			−0.221053	−	0.975262i	$-0.570949\pi$
$37$	−16.3579			−0.442106			−0.221053	+	0.975262i	$0.570949\pi$
$38$			17.8846i			0.470647i
$39$	8.80339	−	6.28493i	0.225728	−	0.161152i
$40$	13.9471			0.348678
$41$			18.7742i			0.457908i	0.973437	+	0.228954i	$0.0735306\pi$
$41$			18.7742i			0.457908i	−0.973437	+	0.228954i	$0.926469\pi$
$42$	−3.24671	−	4.54772i	−0.0773027	−	0.108279i
$43$	58.4174			1.35854			0.679272	−	0.733887i	$-0.262296\pi$
$43$	58.4174			1.35854			0.679272	+	0.733887i	$0.262296\pi$
$44$			25.7101i			0.584320i
$45$	19.0336	+	6.53607i	0.422970	+	0.145246i
$46$	−5.37003			−0.116740
$47$			6.89606i			0.146725i	0.997305	+	0.0733623i	$0.0233730\pi$
$47$			6.89606i			0.146725i	−0.997305	+	0.0733623i	$0.976627\pi$
$48$	18.7820	−	13.4089i	0.391292	−	0.279352i
$49$	−44.2969			−0.904018
$50$			4.29429i			0.0858859i
$51$	6.40397	+	8.97013i	0.125568	+	0.175885i
$52$	11.7626			0.226204
$53$			34.1678i			0.644675i	0.946625	+	0.322338i	$0.104469\pi$
$53$			34.1678i			0.644675i	−0.946625	+	0.322338i	$0.895531\pi$
$54$	−22.2260	+	6.61387i	−0.411593	+	0.122479i
$55$	−17.6221			−0.320401
$56$		−	13.5267i		−	0.241549i
$57$	−50.8435	+	36.2983i	−0.891991	+	0.636812i
$58$	1.97104			0.0339835
$59$			78.6419i			1.33291i	0.745543	+	0.666457i	$0.232190\pi$
$59$			78.6419i			1.33291i	−0.745543	+	0.666457i	$0.767810\pi$
$60$	12.7159	+	17.8113i	0.211931	+	0.296855i
$61$	−98.8756			−1.62091			−0.810456	−	0.585800i	$-0.800781\pi$
$61$	−98.8756			−1.62091			−0.810456	+	0.585800i	$0.800781\pi$
$62$			21.2182i			0.342229i
$63$	6.33907	−	18.4599i	0.100620	−	0.293015i
$64$	3.66755			0.0573055
$65$			8.06226i			0.124035i
$66$	16.5261	−	11.7984i	0.250396	−	0.178763i
$67$	−55.1753			−0.823512			−0.411756	−	0.911294i	$-0.635084\pi$
$67$	−55.1753			−0.823512			−0.411756	+	0.911294i	$0.635084\pi$
$68$			11.9854i			0.176256i
$69$	−10.8989	−	15.2663i	−0.157955	−	0.221250i
$70$	4.16486			0.0594980
$71$			67.9447i			0.956968i	0.878096	+	0.478484i	$0.158814\pi$
$71$			67.9447i			0.956968i	−0.878096	+	0.478484i	$0.841186\pi$
$72$	−53.0929	−	18.2319i	−0.737402	−	0.253221i
$73$	99.2688			1.35985			0.679924	−	0.733283i	$-0.262013\pi$
$73$	99.2688			1.35985			0.679924	+	0.733283i	$0.262013\pi$
$74$			14.0492i			0.189853i
$75$	−12.2081	+	8.71563i	−0.162775	+	0.116208i
$76$	−67.9343			−0.893872
$77$			17.0909i			0.221960i
$78$	−5.39787	−	7.56087i	−0.0692035	−	0.0969342i
$79$	66.9315			0.847235			0.423617	−	0.905841i	$-0.360760\pi$
$79$	66.9315			0.847235			0.423617	+	0.905841i	$0.360760\pi$
$80$			17.2008i			0.215010i
$81$	−63.9119	−	49.7621i	−0.789036	−	0.614347i
$82$	16.1244			0.196639
$83$			138.095i			1.66380i	0.554928	+	0.831898i	$0.312746\pi$
$83$			138.095i			1.66380i	−0.554928	+	0.831898i	$0.687254\pi$
$84$	17.2744	−	12.3326i	0.205648	−	0.146817i
$85$	−8.21496			−0.0966466
$86$		−	50.1723i		−	0.583399i
$87$	4.00040	+	5.60342i	0.0459816	+	0.0644071i
$88$	49.1554			0.558584
$89$		−	34.4200i		−	0.386742i	−0.981126	−	0.193371i	$-0.938058\pi$
$89$		−	34.4200i		−	0.386742i	0.981126	−	0.193371i	$-0.0619421\pi$
$90$	5.61356	−	16.3472i	0.0623729	−	0.181636i
$91$	7.81925			0.0859258
$92$		−	20.3980i		−	0.221717i
$93$	−60.3205	+	43.0641i	−0.648607	+	0.463055i
$94$	5.92274			0.0630079
$95$		−	46.5631i		−	0.490138i
$96$	−55.0063	−	77.0480i	−0.572982	−	0.802584i
$97$	−3.08056			−0.0317584			−0.0158792	−	0.999874i	$-0.505055\pi$
$97$	−3.08056			−0.0317584			−0.0158792	+	0.999874i	$0.505055\pi$
$98$			38.0448i			0.388212i
$99$	67.0824	+	23.0358i	0.677600	+	0.232685i
$100$	−16.3118			−0.163118
$101$		−	161.574i		−	1.59975i	−0.600169	−	0.799873i	$-0.704900\pi$
$101$		−	161.574i		−	1.59975i	0.600169	−	0.799873i	$-0.295100\pi$
$102$	7.70407	−	5.50011i	0.0755301	−	0.0539226i
$103$	98.9611			0.960787			0.480393	−	0.877053i	$-0.340494\pi$
$103$	98.9611			0.960787			0.480393	+	0.877053i	$0.340494\pi$
$104$		−	22.4891i		−	0.216241i
$105$	8.45293	+	11.8401i	0.0805041	+	0.112763i
$106$	29.3453			0.276843
$107$		−	79.3997i		−	0.742053i	−0.928622	−	0.371027i	$-0.879006\pi$
$107$		−	79.3997i		−	0.742053i	0.928622	−	0.371027i	$-0.120994\pi$
$108$	−25.1227	−	84.4251i	−0.232618	−	0.781714i
$109$	−55.4375			−0.508601			−0.254301	−	0.967125i	$-0.581845\pi$
$109$	−55.4375			−0.508601			−0.254301	+	0.967125i	$0.581845\pi$
$110$			15.1349i			0.137590i
$111$	−39.9399	+	28.5139i	−0.359819	+	0.256882i
$112$	16.6824			0.148950
$113$			141.110i			1.24876i	0.781120	+	0.624381i	$0.214649\pi$
$113$			141.110i			1.24876i	−0.781120	+	0.624381i	$0.785351\pi$
$114$	31.1751	+	43.6674i	0.273466	+	0.383047i
$115$	13.9810			0.121574
$116$			7.48698i			0.0645429i
$117$	10.5391	−	30.6908i	0.0900778	−	0.262315i
$118$	67.5423			0.572393
$119$			7.96735i			0.0669525i
$120$	34.0536	−	24.3116i	0.283780	−	0.202597i
$121$	58.8926			0.486716
$122$			84.9202i			0.696067i
$123$	32.7259	+	45.8396i	0.266064	+	0.372680i
$124$	−80.5970			−0.649975
$125$		−	11.1803i		−	0.0894427i
$126$	−15.8545	−	5.44436i	−0.125829	−	0.0432092i
$127$	61.8511			0.487017			0.243508	−	0.969899i	$-0.421702\pi$
$127$	61.8511			0.487017			0.243508	+	0.969899i	$0.421702\pi$
$128$		−	129.374i		−	1.01074i
$129$	142.633	−	101.829i	1.10568	−	0.789371i
$130$	6.92434			0.0532642
$131$		−	195.560i		−	1.49282i	−0.665485	−	0.746411i	$-0.731775\pi$
$131$		−	195.560i		−	1.49282i	0.665485	−	0.746411i	$-0.268225\pi$
$132$	44.8159	+	62.7743i	0.339515	+	0.475563i
$133$	−45.1596			−0.339546
$134$			47.3878i			0.353640i
$135$	57.8661	−	17.2194i	0.428638	−	0.127551i
$136$	22.9150			0.168493
$137$		−	196.564i		−	1.43477i	−0.696676	−	0.717386i	$-0.745338\pi$
$137$		−	196.564i		−	1.43477i	0.696676	−	0.717386i	$-0.254662\pi$
$138$	−13.1116	+	9.36064i	−0.0950114	+	0.0678307i
$139$	−159.050			−1.14424			−0.572121	−	0.820169i	$-0.693879\pi$
$139$	−159.050			−1.14424			−0.572121	+	0.820169i	$0.693879\pi$
$140$			15.8201i			0.113001i
$141$	12.0207	+	16.8376i	0.0852532	+	0.119415i
$142$	58.3549			0.410950
$143$			28.4147i			0.198704i
$144$	22.4852	−	65.4789i	0.156147	−	0.454715i
$145$	−5.13168			−0.0353909
$146$		−	85.2579i		−	0.583958i
$147$	−108.156	+	77.2150i	−0.735756	+	0.525272i
$148$	−53.3655			−0.360578
$149$		−	130.652i		−	0.876860i	−0.898765	−	0.438430i	$-0.855535\pi$
$149$		−	130.652i		−	0.876860i	0.898765	−	0.438430i	$-0.144465\pi$
$150$	7.48550	+	10.4850i	0.0499033	+	0.0699002i
$151$	−183.626			−1.21607			−0.608033	−	0.793912i	$-0.708041\pi$
$151$	−183.626			−1.21607			−0.608033	+	0.793912i	$0.708041\pi$
$152$			129.884i			0.854502i
$153$	31.2721	+	10.7387i	0.204393	+	0.0701877i
$154$	14.6787			0.0953161
$155$		−	55.2423i		−	0.356402i
$156$	28.7198	−	20.5037i	0.184101	−	0.131434i
$157$	−105.599			−0.672606			−0.336303	−	0.941754i	$-0.609177\pi$
$157$	−105.599			−0.672606			−0.336303	+	0.941754i	$0.609177\pi$
$158$		−	57.4847i		−	0.363827i
$159$	59.5588	+	83.4248i	0.374584	+	0.524684i
$160$	70.5616			0.441010
$161$		−	13.5596i		−	0.0842213i
$162$	−42.7386	+	54.8913i	−0.263819	+	0.338835i
$163$	168.274			1.03236			0.516179	−	0.856481i	$-0.327354\pi$
$163$	168.274			1.03236			0.516179	+	0.856481i	$0.327354\pi$
$164$			61.2484i			0.373466i
$165$	−43.0264	+	30.7175i	−0.260766	+	0.186166i
$166$	118.604			0.714483
$167$		−	219.443i		−	1.31403i	−0.753877	−	0.657015i	$-0.771819\pi$
$167$		−	219.443i		−	1.31403i	0.753877	−	0.657015i	$-0.228181\pi$
$168$	−23.5788	−	33.0272i	−0.140350	−	0.196590i
$169$	13.0000			0.0769231
$170$			7.05549i			0.0415029i
$171$	−60.8680	+	177.253i	−0.355953	+	1.03657i
$172$	190.579			1.10802
$173$		−	106.638i		−	0.616406i	−0.951321	−	0.308203i	$-0.900272\pi$
$173$		−	106.638i		−	0.616406i	0.951321	−	0.308203i	$-0.0997276\pi$
$174$	4.81254	−	3.43578i	0.0276583	−	0.0197459i
$175$	−10.8433			−0.0619620
$176$			60.6228i			0.344448i
$177$	137.083	+	192.014i	0.774479	+	1.08482i
$178$	−29.5619			−0.166078
$179$		−	185.383i		−	1.03566i	−0.855483	−	0.517830i	$-0.826740\pi$
$179$		−	185.383i		−	1.03566i	0.855483	−	0.517830i	$-0.173260\pi$
$180$	62.0946	+	21.3230i	0.344970	+	0.118461i
$181$	116.307			0.642580			0.321290	−	0.946981i	$-0.395884\pi$
$181$	116.307			0.642580			0.321290	+	0.946981i	$0.395884\pi$
$182$		−	6.71563i		−	0.0368991i
$183$	−241.417	+	172.353i	−1.31922	+	0.941818i
$184$	−38.9991			−0.211951
$185$		−	36.5774i		−	0.197716i
$186$	36.9860	+	51.8068i	0.198849	+	0.278531i
$187$	−28.9529			−0.154828
$188$			22.4974i			0.119667i
$189$	−16.7004	−	56.1220i	−0.0883620	−	0.296942i
$190$	−39.9911			−0.210480
$191$			304.954i			1.59662i	0.602247	+	0.798310i	$0.294272\pi$
$191$			304.954i			1.59662i	−0.602247	+	0.798310i	$0.705728\pi$
$192$	8.95478	−	6.39301i	0.0466395	−	0.0332969i
$193$	171.435			0.888266			0.444133	−	0.895961i	$-0.353512\pi$
$193$	171.435			0.888266			0.444133	+	0.895961i	$0.353512\pi$
$194$			2.64577i			0.0136380i
$195$	14.0535	+	19.6850i	0.0720694	+	0.100949i
$196$	−144.512			−0.737308
$197$			77.1378i			0.391562i	0.980648	+	0.195781i	$0.0627242\pi$
$197$			77.1378i			0.391562i	−0.980648	+	0.195781i	$0.937276\pi$
$198$	19.7845	−	57.6143i	0.0999218	−	0.290981i
$199$	−207.306			−1.04174			−0.520870	−	0.853636i	$-0.674392\pi$
$199$	−207.306			−1.04174			−0.520870	+	0.853636i	$0.674392\pi$
$200$			31.1867i			0.155934i
$201$	−134.717	+	96.1775i	−0.670234	+	0.478495i
$202$	−138.770			−0.686978
$203$			4.97700i			0.0245173i
$204$	20.8921	+	29.2638i	0.102412	+	0.143450i
$205$	−41.9805			−0.204783
$206$		−	84.9936i		−	0.412590i
$207$	−53.2221	−	18.2762i	−0.257111	−	0.0882909i
$208$	27.7355			0.133344
$209$		−	164.108i		−	0.785204i
$210$	10.1690	−	7.25987i	0.0484238	−	0.0345708i
$211$	131.933			0.625276			0.312638	−	0.949872i	$-0.398787\pi$
$211$	131.933			0.625276			0.312638	+	0.949872i	$0.398787\pi$
$212$			111.468i			0.525791i
$213$	118.436	+	165.895i	0.556039	+	0.778851i
$214$	−68.1931			−0.318659
$215$			130.625i			0.607559i
$216$	−161.413	+	48.0323i	−0.747284	+	0.222372i
$217$	−53.5772			−0.246900
$218$			47.6130i			0.218408i
$219$	242.377	−	173.038i	1.10674	−	0.790128i
$220$	−57.4895			−0.261316
$221$			13.2462i			0.0599377i
$222$	24.4894	+	34.3027i	0.110313	+	0.154517i
$223$	−392.472			−1.75996			−0.879982	−	0.475007i	$-0.842445\pi$
$223$	−392.472			−1.75996			−0.879982	+	0.475007i	$0.842445\pi$
$224$		−	68.4348i		−	0.305512i
$225$	−14.6151	+	42.5605i	−0.0649560	+	0.189158i
$226$	121.194			0.536255
$227$		−	212.311i		−	0.935293i	−0.883916	−	0.467646i	$-0.845102\pi$
$227$		−	212.311i		−	0.935293i	0.883916	−	0.467646i	$-0.154898\pi$
$228$	−165.870	+	118.418i	−0.727499	+	0.519377i
$229$	83.1407			0.363060			0.181530	−	0.983385i	$-0.441895\pi$
$229$	83.1407			0.363060			0.181530	+	0.983385i	$0.441895\pi$
$230$		−	12.0077i		−	0.0522076i
$231$	29.7916	+	41.7295i	0.128968	+	0.180647i
$232$	14.3144			0.0617002
$233$		−	410.058i		−	1.75991i	−0.475061	−	0.879953i	$-0.657574\pi$
$233$		−	410.058i		−	1.75991i	0.475061	−	0.879953i	$-0.342426\pi$
$234$	−26.3591	−	9.05160i	−0.112646	−	0.0386821i
$235$	−15.4201			−0.0656173
$236$			256.558i			1.08711i
$237$	163.421	−	116.670i	0.689542	−	0.492279i
$238$	6.84283			0.0287514
$239$			262.360i			1.09774i	0.835907	+	0.548871i	$0.184942\pi$
$239$			262.360i			1.09774i	−0.835907	+	0.548871i	$0.815058\pi$
$240$	29.9832	+	41.9979i	0.124930	+	0.174991i
$241$	360.621			1.49635			0.748176	−	0.663500i	$-0.230930\pi$
$241$	360.621			1.49635			0.748176	+	0.663500i	$0.230930\pi$
$242$		−	50.5805i		−	0.209010i
$243$	−242.790	−	10.0937i	−0.999137	−	0.0415378i
$244$	−322.568			−1.32200
$245$		−	99.0508i		−	0.404289i
$246$	39.3697	−	28.1069i	0.160040	−	0.114256i
$247$	−75.0808			−0.303971
$248$			154.094i			0.621347i
$249$	240.717	+	337.176i	0.966736	+	1.35412i
$250$	−9.60233			−0.0384093
$251$			451.867i			1.80027i	0.435613	+	0.900134i	$0.356532\pi$
$251$			451.867i			1.80027i	−0.435613	+	0.900134i	$0.643468\pi$
$252$	20.6803	−	60.2230i	0.0820648	−	0.238980i
$253$	49.2750			0.194763
$254$		−	53.1214i		−	0.209139i
$255$	−20.0578	+	14.3197i	−0.0786581	+	0.0561557i
$256$	−96.4441			−0.376735
$257$		−	89.1222i		−	0.346779i	−0.984853	−	0.173390i	$-0.944528\pi$
$257$		−	89.1222i		−	0.346779i	0.984853	−	0.173390i	$-0.0554720\pi$
$258$	−87.4566	−	122.502i	−0.338979	−	0.474813i
$259$	−35.4749			−0.136969
$260$			26.3020i			0.101162i
$261$	19.5349	+	6.70821i	0.0748464	+	0.0257019i
$262$	−167.958			−0.641062
$263$		−	315.624i		−	1.20009i	−0.799966	−	0.600046i	$-0.795149\pi$
$263$		−	315.624i		−	1.20009i	0.799966	−	0.600046i	$-0.204851\pi$
$264$	120.019	−	85.6841i	0.454617	−	0.324561i
$265$	−76.4015			−0.288308
$266$			38.7857i			0.145811i
$267$	−59.9985	−	84.0406i	−0.224713	−	0.314759i
$268$	−180.002			−0.671648
$269$			284.707i			1.05839i	0.848500	+	0.529195i	$0.177506\pi$
$269$			284.707i			1.05839i	−0.848500	+	0.529195i	$0.822494\pi$
$270$	−14.7891	−	49.6989i	−0.0547743	−	0.184070i
$271$	270.051			0.996498			0.498249	−	0.867034i	$-0.333976\pi$
$271$	270.051			0.996498			0.498249	+	0.867034i	$0.333976\pi$
$272$			28.2608i			0.103900i
$273$	19.0916	−	13.6299i	0.0699327	−	0.0499265i
$274$	−168.821			−0.616133
$275$		−	39.4041i		−	0.143288i
$276$	−35.5562	−	49.8041i	−0.128827	−	0.180450i
$277$	−287.075			−1.03637			−0.518186	−	0.855268i	$-0.673393\pi$
$277$	−287.075			−1.03637			−0.518186	+	0.855268i	$0.673393\pi$
$278$			136.601i			0.491372i
$279$	−72.2135	+	210.292i	−0.258830	+	0.753736i
$280$	30.2467			0.108024
$281$		−	338.918i		−	1.20611i	−0.797698	−	0.603057i	$-0.793949\pi$
$281$		−	338.918i		−	1.20611i	0.797698	−	0.603057i	$-0.206051\pi$
$282$	14.4611	−	10.3241i	0.0512805	−	0.0366102i
$283$	157.483			0.556479			0.278239	−	0.960512i	$-0.410249\pi$
$283$	157.483			0.556479			0.278239	+	0.960512i	$0.410249\pi$
$284$			221.660i			0.780494i
$285$	−81.1654	−	113.689i	−0.284791	−	0.398910i
$286$	24.4042			0.0853295
$287$			40.7151i			0.141865i
$288$	−268.609	−	92.2391i	−0.932670	−	0.320275i
$289$	275.503			0.953297
$290$			4.40739i			0.0151979i
$291$	−7.52157	+	5.36981i	−0.0258473	+	0.0184530i
$292$	323.851			1.10908
$293$			24.6805i			0.0842337i	0.999113	+	0.0421169i	$0.0134102\pi$
$293$			24.6805i			0.0842337i	−0.999113	+	0.0421169i	$0.986590\pi$
$294$	66.3168	+	92.8909i	0.225567	+	0.315955i
$295$	−175.849			−0.596097
$296$			102.030i			0.344696i
$297$	203.944	−	60.6884i	0.686680	−	0.204338i
$298$	−112.212			−0.376550
$299$		−	22.5438i		−	0.0753972i
$300$	−39.8272	+	28.4335i	−0.132757	+	0.0947785i
$301$	126.688			0.420890
$302$			157.709i			0.522214i
$303$	−281.645	−	394.503i	−0.929520	−	1.30199i
$304$	−160.185			−0.526924
$305$		−	221.093i		−	0.724894i
$306$	9.22304	−	26.8583i	0.0301407	−	0.0877724i
$307$	−169.717			−0.552823			−0.276412	−	0.961039i	$-0.589145\pi$
$307$	−169.717			−0.552823			−0.276412	+	0.961039i	$0.589145\pi$
$308$			55.7567i			0.181028i
$309$	241.625	−	172.502i	0.781959	−	0.558258i
$310$	−47.4453			−0.153049
$311$			189.448i			0.609157i	0.952487	+	0.304579i	$0.0985156\pi$
$311$			189.448i			0.609157i	−0.952487	+	0.304579i	$0.901484\pi$
$312$	−39.2013	−	54.9098i	−0.125645	−	0.175993i
$313$	386.249			1.23402			0.617011	−	0.786954i	$-0.288343\pi$
$313$	386.249			1.23402			0.617011	+	0.786954i	$0.288343\pi$
$314$			90.6948i			0.288837i
$315$	41.2777	+	14.1746i	0.131040	+	0.0449987i
$316$	218.355			0.690996
$317$		−	355.768i		−	1.12230i	−0.827715	−	0.561148i	$-0.810360\pi$
$317$		−	355.768i		−	1.12230i	0.827715	−	0.561148i	$-0.189640\pi$
$318$	71.6501	−	51.1526i	0.225315	−	0.160857i
$319$	−18.0862			−0.0566964
$320$			8.20090i			0.0256278i
$321$	−138.404	−	193.864i	−0.431164	−	0.603937i
$322$	−11.6458			−0.0361671
$323$		−	76.5028i		−	0.236851i
$324$	−208.504	−	162.342i	−0.643530	−	0.501056i
$325$	−18.0278			−0.0554700
$326$		−	144.524i		−	0.443325i
$327$	−135.357	+	96.6346i	−0.413937	+	0.295519i
$328$	117.101			0.357017
$329$			14.9553i			0.0454568i
$330$	26.3820	+	36.9536i	0.0799454	+	0.111981i
$331$	584.473			1.76578			0.882890	−	0.469579i	$-0.155594\pi$
$331$	584.473			1.76578			0.882890	+	0.469579i	$0.155594\pi$
$332$			450.516i			1.35698i
$333$	−47.8146	+	139.240i	−0.143587	+	0.418139i
$334$	−188.471			−0.564284
$335$		−	123.376i		−	0.368286i
$336$	40.7320	−	29.0795i	0.121226	−	0.0865461i
$337$	259.709			0.770649			0.385324	−	0.922781i	$-0.374090\pi$
$337$	259.709			0.770649			0.385324	+	0.922781i	$0.374090\pi$
$338$		−	11.1652i		−	0.0330330i
$339$	245.973	+	344.537i	0.725583	+	1.01633i
$340$	−26.8002			−0.0788240
$341$		−	194.697i		−	0.570957i
$342$	152.235	+	52.2770i	0.445133	+	0.152857i
$343$	−202.330			−0.589884
$344$		−	364.369i		−	1.05921i
$345$	34.1364	−	24.3707i	0.0989461	−	0.0706398i
$346$	−91.5872			−0.264703
$347$			607.556i			1.75088i	0.483326	+	0.875440i	$0.339429\pi$
$347$			607.556i			1.75088i	−0.483326	+	0.875440i	$0.660571\pi$
$348$	13.0508	+	18.2804i	0.0375022	+	0.0525298i
$349$	90.4877			0.259277			0.129639	−	0.991561i	$-0.458618\pi$
$349$	90.4877			0.259277			0.129639	+	0.991561i	$0.458618\pi$
$350$			9.31291i			0.0266083i
$351$	−27.7655	−	93.3064i	−0.0791040	−	0.265830i
$352$	248.688			0.706500
$353$		−	701.372i		−	1.98689i	−0.114318	−	0.993444i	$-0.536468\pi$
$353$		−	701.372i		−	1.98689i	0.114318	−	0.993444i	$-0.463532\pi$
$354$	164.913	−	117.735i	0.465855	−	0.332584i
$355$	−151.929			−0.427969
$356$		−	112.291i		−	0.315423i
$357$	13.8881	+	19.4532i	0.0389022	+	0.0544909i
$358$	−159.218			−0.444743
$359$		−	197.298i		−	0.549576i	−0.961505	−	0.274788i	$-0.911392\pi$
$359$		−	197.298i		−	0.549576i	0.961505	−	0.274788i	$-0.0886076\pi$
$360$	40.7677	−	118.719i	0.113244	−	0.329776i
$361$	72.6246			0.201176
$362$		−	99.8912i		−	0.275943i
$363$	143.793	−	102.657i	0.396125	−	0.282802i
$364$	25.5092			0.0700803
$365$			221.972i			0.608142i
$366$	148.027	+	207.343i	0.404444	+	0.566511i
$367$	447.535			1.21944			0.609720	−	0.792617i	$-0.291282\pi$
$367$	447.535			1.21944			0.609720	+	0.792617i	$0.291282\pi$
$368$		−	48.0971i		−	0.130699i
$369$	159.808	+	54.8775i	0.433085	+	0.148720i
$370$	−31.4149			−0.0849050
$371$			74.0987i			0.199727i
$372$	−196.787	+	140.491i	−0.528998	+	0.377663i
$373$	464.809			1.24614			0.623068	−	0.782168i	$-0.285886\pi$
$373$	464.809			1.24614			0.623068	+	0.782168i	$0.285886\pi$
$374$			24.8664i			0.0664878i
$375$	−19.4887	−	27.2981i	−0.0519700	−	0.0727951i
$376$	43.0131			0.114397
$377$			8.27459i			0.0219485i
$378$	−48.2009	+	14.3433i	−0.127515	+	0.0379453i
$379$	176.321			0.465226			0.232613	−	0.972569i	$-0.425273\pi$
$379$	176.321			0.465226			0.232613	+	0.972569i	$0.425273\pi$
$380$		−	151.906i		−	0.399752i
$381$	151.017	−	107.814i	0.396370	−	0.282977i
$382$	261.913			0.685636
$383$			388.263i			1.01374i	0.862022	+	0.506871i	$0.169198\pi$
$383$			388.263i			1.01374i	−0.862022	+	0.506871i	$0.830802\pi$
$384$	−225.516	−	315.883i	−0.587281	−	0.822612i
$385$	−38.2164			−0.0992634
$386$		−	147.239i		−	0.381448i
$387$	170.755	−	497.255i	0.441228	−	1.28490i
$388$	−10.0499			−0.0259018
$389$			177.598i			0.456551i	0.973597	+	0.228275i	$0.0733086\pi$
$389$			177.598i			0.456551i	−0.973597	+	0.228275i	$0.926691\pi$
$390$	16.9066	−	12.0700i	0.0433503	−	0.0309487i
$391$	22.9707			0.0587487
$392$			276.295i			0.704834i
$393$	−340.885	−	477.483i	−0.867393	−	1.21497i
$394$	66.2505			0.168148
$395$			149.663i			0.378895i
$396$	218.847	+	75.1511i	0.552644	+	0.189776i
$397$	−24.5812			−0.0619173			−0.0309587	−	0.999521i	$-0.509856\pi$
$397$	−24.5812			−0.0619173			−0.0309587	+	0.999521i	$0.509856\pi$
$398$			178.047i			0.447354i
$399$	−110.263	+	78.7189i	−0.276348	+	0.197291i
$400$	−38.4622			−0.0961556
$401$		−	249.018i		−	0.620993i	−0.950575	−	0.310497i	$-0.899505\pi$
$401$		−	249.018i		−	0.620993i	0.950575	−	0.310497i	$-0.100495\pi$
$402$	82.6029	+	115.703i	0.205480	+	0.287818i
$403$	−89.0755			−0.221031
$404$		−	527.114i		−	1.30474i
$405$	111.271	−	142.911i	0.274744	−	0.352868i
$406$	4.27454			0.0105284
$407$		−	128.914i		−	0.316742i
$408$	55.9498	−	39.9438i	0.137132	−	0.0979014i
$409$	−630.799			−1.54230			−0.771148	−	0.636656i	$-0.780317\pi$
$409$	−630.799			−1.54230			−0.771148	+	0.636656i	$0.780317\pi$
$410$			36.0553i			0.0879398i
$411$	−342.636	−	479.934i	−0.833663	−	1.16772i
$412$	322.847			0.783609
$413$			170.548i			0.412950i
$414$	−15.6967	+	45.7102i	−0.0379147	+	0.110411i
$415$	−308.790			−0.744072
$416$		−	113.777i		−	0.273503i
$417$	−388.339	+	277.244i	−0.931269	+	0.664853i
$418$	−140.945			−0.337190
$419$			441.990i			1.05487i	0.849596	+	0.527434i	$0.176846\pi$
$419$			441.990i			1.05487i	−0.849596	+	0.527434i	$0.823154\pi$
$420$	27.5765	+	38.6268i	0.0656584	+	0.0919685i
$421$	−589.061			−1.39919			−0.699597	−	0.714537i	$-0.746637\pi$
$421$	−589.061			−1.39919			−0.699597	+	0.714537i	$0.746637\pi$
$422$		−	113.312i		−	0.268512i
$423$	58.7000	+	20.1573i	0.138771	+	0.0476532i
$424$	213.116			0.502633
$425$		−	18.3692i		−	0.0432217i
$426$	142.481	−	101.720i	0.334461	−	0.238779i
$427$	−214.429			−0.502175
$428$		−	259.030i		−	0.605211i
$429$	49.5304	+	69.3779i	0.115456	+	0.161720i
$430$	112.189			0.260904
$431$			435.952i			1.01149i	0.862683	+	0.505745i	$0.168782\pi$
$431$			435.952i			1.01149i	−0.862683	+	0.505745i	$0.831218\pi$
$432$	−59.2378	−	199.069i	−0.137124	−	0.460808i
$433$	−151.516			−0.349921			−0.174960	−	0.984575i	$-0.555980\pi$
$433$	−151.516			−0.349921			−0.174960	+	0.984575i	$0.555980\pi$
$434$			46.0152i			0.106026i
$435$	−12.5296	+	8.94517i	−0.0288037	+	0.0205636i
$436$	−180.857			−0.414810
$437$			130.200i			0.297941i
$438$	−148.615	−	208.167i	−0.339304	−	0.475268i
$439$	−98.5022			−0.224379			−0.112189	−	0.993687i	$-0.535786\pi$
$439$	−98.5022			−0.224379			−0.112189	+	0.993687i	$0.535786\pi$
$440$			109.915i			0.249806i
$441$	−129.481	+	377.060i	−0.293607	+	0.855011i
$442$	11.3766			0.0257390
$443$		−	437.508i		−	0.987602i	−0.869575	−	0.493801i	$-0.835607\pi$
$443$		−	437.508i		−	0.987602i	0.869575	−	0.493801i	$-0.164393\pi$
$444$	−130.298	+	93.0228i	−0.293465	+	0.209511i
$445$	76.9655			0.172956
$446$			337.078i			0.755780i
$447$	−227.743	−	319.003i	−0.509493	−	0.713653i
$448$	7.95371			0.0177538
$449$			483.200i			1.07617i	0.842891	+	0.538084i	$0.180852\pi$
$449$			483.200i			1.07617i	−0.842891	+	0.538084i	$0.819148\pi$
$450$	36.5535	+	12.5523i	0.0812300	+	0.0278940i
$451$	−147.957			−0.328063
$452$			460.352i			1.01848i
$453$	−448.345	+	320.083i	−0.989723	+	0.706585i
$454$	−182.346			−0.401642
$455$			17.4844i			0.0384272i
$456$	226.405	+	317.128i	0.496502	+	0.695456i
$457$	−192.388			−0.420981			−0.210490	−	0.977596i	$-0.567506\pi$
$457$	−192.388			−0.420981			−0.210490	+	0.977596i	$0.567506\pi$
$458$		−	71.4061i		−	0.155909i
$459$	95.0736	−	28.2914i	0.207132	−	0.0616370i
$460$	45.6112			0.0991548
$461$		−	492.440i		−	1.06820i	−0.845421	−	0.534100i	$-0.820651\pi$
$461$		−	492.440i		−	1.06820i	0.845421	−	0.534100i	$-0.179349\pi$
$462$	35.8397	−	25.5868i	0.0775752	−	0.0553826i
$463$	−352.360			−0.761037			−0.380519	−	0.924773i	$-0.624255\pi$
$463$	−352.360			−0.761037			−0.380519	+	0.924773i	$0.624255\pi$
$464$			17.6538i			0.0380471i
$465$	−96.2943	−	134.881i	−0.207084	−	0.290066i
$466$	−352.182			−0.755755
$467$			663.046i			1.41980i	0.704304	+	0.709899i	$0.251259\pi$
$467$			663.046i			1.41980i	−0.704304	+	0.709899i	$0.748741\pi$
$468$	34.3824	−	100.125i	0.0734666	−	0.213941i
$469$	−119.657			−0.255132
$470$			13.2437i			0.0281780i
$471$	−257.833	+	184.073i	−0.547416	+	0.390812i
$472$	490.517			1.03923
$473$			460.377i			0.973313i
$474$	−100.203	−	140.356i	−0.211399	−	0.296110i
$475$	104.118			0.219196
$476$			25.9924i			0.0546058i
$477$	290.840	+	99.8732i	0.609727	+	0.209378i
$478$	225.330			0.471403
$479$			632.137i			1.31970i	0.751397	+	0.659851i	$0.229380\pi$
$479$			632.137i			1.31970i	−0.751397	+	0.659851i	$0.770620\pi$
$480$	172.285	−	122.998i	0.358926	−	0.256245i
$481$	−58.9794			−0.122618
$482$		−	309.723i		−	0.642578i
$483$	−23.6362	−	33.1075i	−0.0489361	−	0.0685455i
$484$	192.129			0.396961
$485$		−	6.88835i		−	0.0142028i
$486$	−8.66906	+	208.523i	−0.0178376	+	0.429059i
$487$	−605.100			−1.24250			−0.621252	−	0.783611i	$-0.713376\pi$
$487$	−605.100			−1.24250			−0.621252	+	0.783611i	$0.713376\pi$
$488$			616.721i			1.26377i
$489$	410.862	−	293.323i	0.840208	−	0.599843i
$490$	−85.0707			−0.173614
$491$			737.678i			1.50240i	0.660075	+	0.751200i	$0.270524\pi$
$491$			737.678i			1.50240i	−0.660075	+	0.751200i	$0.729476\pi$
$492$	106.764	+	149.545i	0.216999	+	0.303954i
$493$	−8.43131			−0.0171020
$494$			64.4838i			0.130534i
$495$	−51.5096	+	150.001i	−0.104060	+	0.303032i
$496$	−190.043			−0.383151
$497$			147.350i			0.296478i
$498$	289.586	−	206.742i	0.581499	−	0.415145i
$499$	−475.888			−0.953683			−0.476841	−	0.878989i	$-0.658218\pi$
$499$	−475.888			−0.953683			−0.476841	+	0.878989i	$0.658218\pi$
$500$		−	36.4743i		−	0.0729486i
$501$	−382.517	−	535.797i	−0.763507	−	1.06945i
$502$	388.090			0.773088
$503$			508.608i			1.01115i	0.862783	+	0.505574i	$0.168719\pi$
$503$			508.608i			1.01115i	−0.862783	+	0.505574i	$0.831281\pi$
$504$	−115.141	−	39.5389i	−0.228454	−	0.0784503i
$505$	361.291			0.715428
$506$		−	42.3202i		−	0.0836368i
$507$	31.7411	−	22.6606i	0.0626057	−	0.0446955i
$508$	201.781			0.397206
$509$			5.59169i			0.0109856i	0.999985	+	0.00549282i	$0.00174843\pi$
$509$			5.59169i			0.0109856i	−0.999985	+	0.00549282i	$0.998252\pi$
$510$	12.2986	+	17.2268i	0.0241149	+	0.0337781i
$511$	215.281			0.421294
$512$		−	434.665i		−	0.848956i
$513$	160.358	+	538.886i	0.312589	+	1.05046i
$514$	−76.5434			−0.148917
$515$			221.284i			0.429677i
$516$	465.321	−	332.203i	0.901784	−	0.643804i
$517$	−54.3466			−0.105119
$518$			30.4680i			0.0588185i
$519$	−185.884	−	260.370i	−0.358158	−	0.501676i
$520$	50.2871			0.0967059
$521$		−	270.095i		−	0.518417i	−0.965821	−	0.259209i	$-0.916538\pi$
$521$		−	270.095i		−	0.518417i	0.965821	−	0.259209i	$-0.0834617\pi$
$522$	5.76140	−	16.7777i	0.0110372	−	0.0321413i
$523$	−566.082			−1.08238			−0.541188	−	0.840902i	$-0.682025\pi$
$523$	−566.082			−1.08238			−0.541188	+	0.840902i	$0.682025\pi$
$524$		−	637.987i		−	1.21753i
$525$	−26.4753	+	18.9013i	−0.0504292	+	0.0360025i
$526$	−271.076			−0.515354
$527$		−	90.7626i		−	0.172225i
$528$	105.673	+	148.018i	0.200139	+	0.280337i
$529$	489.906			0.926098
$530$			65.6181i			0.123808i
$531$	669.408	+	229.872i	1.26066	+	0.432904i
$532$	−147.327			−0.276931
$533$			67.6915i			0.127001i
$534$	−72.1790	+	51.5302i	−0.135167	+	0.0964985i
$535$	177.543			0.331856
$536$			344.147i			0.642066i
$537$	−323.146	−	452.635i	−0.601762	−	0.842896i
$538$	244.523			0.454504
$539$		−	349.096i		−	0.647673i
$540$	188.780	−	56.1761i	0.349593	−	0.104030i
$541$	661.837			1.22336			0.611680	−	0.791106i	$-0.290494\pi$
$541$	661.837			1.22336			0.611680	+	0.791106i	$0.290494\pi$
$542$		−	231.936i		−	0.427926i
$543$	283.977	−	202.738i	0.522979	−	0.373366i
$544$	115.932			0.213110
$545$		−	123.962i		−	0.227453i
$546$	−11.7062	−	16.3970i	−0.0214399	−	0.0300312i
$547$	−332.280			−0.607460			−0.303730	−	0.952758i	$-0.598232\pi$
$547$	−332.280			−0.607460			−0.303730	+	0.952758i	$0.598232\pi$
$548$		−	641.262i		−	1.17019i
$549$	−289.015	+	841.640i	−0.526440	+	1.53304i
$550$	−33.8426			−0.0615320
$551$		−	47.7894i		−	0.0867321i
$552$	−95.2209	+	67.9803i	−0.172502	+	0.123153i
$553$	145.152			0.262482
$554$			246.557i			0.445049i
$555$	−63.7591	−	89.3082i	−0.114881	−	0.160916i
$556$	−518.878			−0.933233
$557$			238.585i			0.428340i	0.976796	+	0.214170i	$0.0687046\pi$
$557$			238.585i			0.428340i	−0.976796	+	0.214170i	$0.931295\pi$
$558$	180.612	+	62.0212i	0.323677	+	0.111149i
$559$	210.627			0.376792
$560$			37.3029i			0.0666124i
$561$	−70.6920	+	50.4686i	−0.126011	+	0.0899618i
$562$	−291.083			−0.517940
$563$			496.137i			0.881239i	0.897694	+	0.440619i	$0.145241\pi$
$563$			496.137i			0.881239i	−0.897694	+	0.440619i	$0.854759\pi$
$564$	39.2159	+	54.9302i	0.0695317	+	0.0973940i
$565$	−315.532			−0.558463
$566$		−	135.256i		−	0.238968i
$567$	−138.604	−	107.918i	−0.244451	−	0.190331i
$568$	423.795			0.746117
$569$		−	637.580i		−	1.12053i	−0.828315	−	0.560263i	$-0.810700\pi$
$569$		−	637.580i		−	1.12053i	0.828315	−	0.560263i	$-0.189300\pi$
$570$	−97.6432	+	69.7096i	−0.171304	+	0.122298i
$571$	463.764			0.812196			0.406098	−	0.913830i	$-0.366889\pi$
$571$	463.764			0.812196			0.406098	+	0.913830i	$0.366889\pi$
$572$			92.6991i			0.162061i
$573$	531.574	+	744.583i	0.927704	+	1.29945i
$574$	34.9686			0.0609208
$575$			31.2626i			0.0543697i
$576$	10.7203	−	31.2186i	0.0186117	−	0.0541990i
$577$	150.749			0.261264			0.130632	−	0.991431i	$-0.458299\pi$
$577$	150.749			0.261264			0.130632	+	0.991431i	$0.458299\pi$
$578$		−	236.618i		−	0.409374i
$579$	418.580	−	298.834i	0.722936	−	0.516120i
$580$	−16.7414			−0.0288645
$581$			299.483i			0.515461i
$582$	4.61191	+	6.45997i	0.00792425	+	0.0110996i
$583$	−269.270			−0.461870
$584$		−	619.174i		−	1.06023i
$585$	68.6268	+	23.5661i	0.117311	+	0.0402840i
$586$	21.1970			0.0361724
$587$		−	676.321i		−	1.15217i	−0.817391	−	0.576083i	$-0.804581\pi$
$587$		−	676.321i		−	1.15217i	0.817391	−	0.576083i	$-0.195419\pi$
$588$	−352.844	+	251.903i	−0.600076	+	0.428407i
$589$	514.450			0.873430
$590$			151.029i			0.255982i
$591$	134.461	+	188.341i	0.227514	+	0.318682i
$592$	−125.833			−0.212555
$593$		−	364.257i		−	0.614262i	−0.951667	−	0.307131i	$-0.900631\pi$
$593$		−	364.257i		−	0.614262i	0.951667	−	0.307131i	$-0.0993690\pi$
$594$	−52.1228	−	175.159i	−0.0877488	−	0.294881i
$595$	−17.8155			−0.0299421
$596$		−	426.235i		−	0.715159i
$597$	−506.163	+	361.361i	−0.847845	+	0.605295i
$598$	−19.3619			−0.0323778
$599$		−	355.195i		−	0.592979i	−0.955036	−	0.296490i	$-0.904184\pi$
$599$		−	355.195i		−	0.592979i	0.955036	−	0.296490i	$-0.0958160\pi$
$600$	54.3624	+	76.1461i	0.0906040	+	0.126910i
$601$	−899.187			−1.49615			−0.748075	−	0.663614i	$-0.769022\pi$
$601$	−899.187			−1.49615			−0.748075	+	0.663614i	$0.769022\pi$
$602$		−	108.807i		−	0.180743i
$603$	−161.278	+	469.658i	−0.267460	+	0.778869i
$604$	−599.054			−0.991811
$605$			131.688i			0.217666i
$606$	−338.823	+	241.893i	−0.559113	+	0.399163i
$607$	−768.361			−1.26583			−0.632917	−	0.774220i	$-0.718142\pi$
$607$	−768.361			−1.26583			−0.632917	+	0.774220i	$0.718142\pi$
$608$			657.113i			1.08078i
$609$	8.67555	+	12.1520i	0.0142456	+	0.0199540i
$610$	−189.887			−0.311291
$611$			24.8641i			0.0406941i
$612$	102.021	+	35.0336i	0.166701	+	0.0572444i
$613$	258.337			0.421430			0.210715	−	0.977547i	$-0.432421\pi$
$613$	258.337			0.421430			0.210715	+	0.977547i	$0.432421\pi$
$614$			145.763i			0.237399i
$615$	−102.500	+	73.1773i	−0.166667	+	0.118987i
$616$	106.602			0.173055
$617$		−	316.180i		−	0.512448i	−0.966617	−	0.256224i	$-0.917522\pi$
$617$		−	316.180i		−	0.512448i	0.966617	−	0.256224i	$-0.0824784\pi$
$618$	−148.155	−	207.522i	−0.239732	−	0.335796i
$619$	655.788			1.05943			0.529716	−	0.848175i	$-0.322299\pi$
$619$	655.788			1.05943			0.529716	+	0.848175i	$0.322299\pi$
$620$		−	180.220i		−	0.290678i
$621$	−161.806	+	48.1492i	−0.260557	+	0.0775349i
$622$	162.709			0.261590
$623$		−	74.6457i		−	0.119816i
$624$	67.7196	−	48.3465i	0.108525	−	0.0774784i
$625$	25.0000			0.0400000
$626$		−	331.734i		−	0.529926i
$627$	−286.060	−	400.688i	−0.456236	−	0.639056i
$628$	−344.503			−0.548571
$629$		−	60.0964i		−	0.0955428i
$630$	12.1740	−	35.4517i	0.0193238	−	0.0562726i
$631$	−9.22519			−0.0146200			−0.00730998	−	0.999973i	$-0.502327\pi$
$631$	−9.22519			−0.0146200			−0.00730998	+	0.999973i	$0.502327\pi$
$632$		−	417.475i		−	0.660562i
$633$	322.131	−	229.976i	0.508896	−	0.363312i
$634$	−305.555			−0.481947
$635$			138.303i			0.217801i
$636$	194.302	+	272.162i	0.305507	+	0.427927i
$637$	−159.715			−0.250729
$638$			15.5335i			0.0243471i
$639$	578.353	+	198.604i	0.905090	+	0.310804i
$640$	289.290			0.452015
$641$		−	29.5373i		−	0.0460800i	−0.999735	−	0.0230400i	$-0.992665\pi$
$641$		−	29.5373i		−	0.0460800i	0.999735	−	0.0230400i	$-0.00733451\pi$
$642$	−166.502	+	118.869i	−0.259348	+	0.185155i
$643$	982.278			1.52765			0.763825	−	0.645424i	$-0.223319\pi$
$643$	982.278			1.52765			0.763825	+	0.645424i	$0.223319\pi$
$644$		−	44.2364i		−	0.0686901i
$645$	227.696	+	318.937i	0.353018	+	0.494476i
$646$	−65.7051			−0.101711
$647$			428.532i			0.662338i	0.943572	+	0.331169i	$0.107443\pi$
$647$			428.532i			0.662338i	−0.943572	+	0.331169i	$0.892557\pi$
$648$	−310.383	+	398.640i	−0.478987	+	0.615186i
$649$	−619.763			−0.954951
$650$			15.4833i			0.0238205i
$651$	−130.815	+	93.3918i	−0.200945	+	0.143459i
$652$	548.971			0.841980
$653$			314.873i			0.482195i	0.970501	+	0.241097i	$0.0775073\pi$
$653$			314.873i			0.482195i	−0.970501	+	0.241097i	$0.922493\pi$
$654$	82.9955	+	116.253i	0.126904	+	0.177757i
$655$	437.285			0.667611
$656$			144.420i			0.220152i
$657$	290.165	−	844.987i	0.441651	−	1.28613i
$658$	12.8445			0.0195205
$659$		−	1090.81i		−	1.65525i	−0.561282	−	0.827625i	$-0.689692\pi$
$659$		−	1090.81i		−	1.65525i	0.561282	−	0.827625i	$-0.310308\pi$
$660$	−140.368	+	100.211i	−0.212678	+	0.151836i
$661$	−1100.10			−1.66429			−0.832145	−	0.554558i	$-0.812888\pi$
$661$	−1100.10			−1.66429			−0.832145	+	0.554558i	$0.812888\pi$
$662$		−	501.980i		−	0.758278i
$663$	23.0898	+	32.3422i	0.0348263	+	0.0487817i
$664$	861.347			1.29721
$665$		−	100.980i		−	0.151850i
$666$	119.588	+	41.0660i	0.179561	+	0.0616606i
$667$	14.3493			0.0215131
$668$		−	715.903i		−	1.07171i
$669$	−958.267	+	684.128i	−1.43239	+	1.02261i
$670$	−105.962			−0.158153
$671$		−	779.221i		−	1.16128i
$672$	−119.290	−	167.092i	−0.177516	−	0.248648i
$673$	849.550			1.26233			0.631166	−	0.775648i	$-0.282577\pi$
$673$	849.550			1.26233			0.631166	+	0.775648i	$0.282577\pi$
$674$		−	223.053i		−	0.330939i
$675$	38.5038	+	129.393i	0.0570427	+	0.191693i
$676$	42.4107			0.0627377
$677$		−	362.200i		−	0.535008i	−0.963557	−	0.267504i	$-0.913801\pi$
$677$		−	362.200i		−	0.535008i	0.963557	−	0.267504i	$-0.0861988\pi$
$678$	295.909	−	211.256i	0.436444	−	0.311587i
$679$	−6.68073			−0.00983907
$680$			51.2395i			0.0753522i
$681$	−370.086	−	518.384i	−0.543444	−	0.761210i
$682$	−167.217			−0.245186
$683$		−	151.262i		−	0.221466i	−0.993850	−	0.110733i	$-0.964680\pi$
$683$		−	151.262i		−	0.221466i	0.993850	−	0.110733i	$-0.0353199\pi$
$684$	−198.573	+	578.264i	−0.290312	+	0.845415i
$685$	439.530			0.641650
$686$			173.773i			0.253313i
$687$	202.998	−	144.925i	0.295485	−	0.210953i
$688$	449.373			0.653158
$689$			123.194i			0.178801i
$690$	−20.9310	−	29.3184i	−0.0303348	−	0.0424904i
$691$	−57.4985			−0.0832106			−0.0416053	−	0.999134i	$-0.513247\pi$
$691$	−57.4985			−0.0832106			−0.0416053	+	0.999134i	$0.513247\pi$
$692$		−	347.892i		−	0.502735i
$693$	145.480	+	49.9571i	0.209927	+	0.0720881i
$694$	521.805			0.751880
$695$		−	355.646i		−	0.511721i
$696$	34.9504	−	24.9519i	0.0502161	−	0.0358504i
$697$	−68.9736			−0.0989578
$698$		−	77.7162i		−	0.111341i
$699$	−714.783	−	1001.21i	−1.02258	−	1.43234i
$700$	−35.3749			−0.0505356
$701$			100.516i			0.143390i	0.997427	+	0.0716951i	$0.0228408\pi$
$701$			100.516i			0.143390i	−0.997427	+	0.0716951i	$0.977159\pi$
$702$	−80.1370	+	23.8467i	−0.114155	+	0.0339696i
$703$	340.632			0.484540
$704$			28.9033i			0.0410559i
$705$	−37.6499	+	26.8791i	−0.0534042	+	0.0381264i
$706$	−602.379			−0.853228
$707$		−	350.402i		−	0.495617i
$708$	447.214	+	626.418i	0.631658	+	0.884772i
$709$	461.780			0.651311			0.325656	−	0.945488i	$-0.394415\pi$
$709$	461.780			0.651311			0.325656	+	0.945488i	$0.394415\pi$
$710$			130.486i			0.183783i
$711$	195.642	−	569.728i	0.275165	−	0.801306i
$712$	−214.690			−0.301530
$713$			154.469i			0.216647i
$714$	16.7076	−	11.9279i	0.0234000	−	0.0167058i
$715$	−63.5372			−0.0888633
$716$		−	604.787i		−	0.844675i
$717$	457.327	+	640.584i	0.637834	+	0.893423i
$718$	−169.451			−0.236004
$719$			871.834i			1.21256i	0.795249	+	0.606282i	$0.207340\pi$
$719$			871.834i			1.21256i	−0.795249	+	0.606282i	$0.792660\pi$
$720$	146.415	+	50.2784i	0.203355	+	0.0698311i
$721$	214.614			0.297661
$722$		−	62.3743i		−	0.0863910i
$723$	880.500	−	628.608i	1.21784	−	0.869444i
$724$	379.435			0.524082
$725$		−	11.4748i		−	0.0158273i
$726$	−88.1681	−	123.498i	−0.121444	−	0.170108i
$727$	532.393			0.732315			0.366157	−	0.930553i	$-0.380673\pi$
$727$	532.393			0.732315			0.366157	+	0.930553i	$0.380673\pi$
$728$		−	48.7713i		−	0.0669936i
$729$	−610.396	+	398.569i	−0.837306	+	0.546734i
$730$	190.643			0.261154
$731$			214.616i			0.293593i
$732$	−787.589	+	562.277i	−1.07594	+	0.768138i
$733$	−436.449			−0.595429			−0.297714	−	0.954655i	$-0.596224\pi$
$733$	−436.449			−0.595429			−0.297714	+	0.954655i	$0.596224\pi$
$734$		−	384.369i		−	0.523664i
$735$	−172.658	−	241.844i	−0.234909	−	0.329040i
$736$	−197.305			−0.268077
$737$		−	434.827i		−	0.589995i
$738$	47.1320	−	137.253i	0.0638645	−	0.185979i
$739$	140.241			0.189772			0.0948858	−	0.995488i	$-0.469751\pi$
$739$	140.241			0.189772			0.0948858	+	0.995488i	$0.469751\pi$
$740$		−	119.329i		−	0.161255i
$741$	−183.319	+	130.875i	−0.247394	+	0.176620i
$742$	63.6403			0.0857686
$743$		−	1066.05i		−	1.43479i	−0.696665	−	0.717397i	$-0.745334\pi$
$743$		−	1066.05i		−	1.43479i	0.696665	−	0.717397i	$-0.254666\pi$
$744$	268.606	+	376.239i	0.361029	+	0.505698i
$745$	292.147			0.392144
$746$		−	399.205i		−	0.535127i
$747$	1175.48	+	403.655i	1.57360	+	0.540368i
$748$	−94.4548			−0.126276
$749$		−	172.192i		−	0.229895i
$750$	−23.4453	+	16.7381i	−0.0312603	+	0.0223174i
$751$	673.484			0.896783			0.448391	−	0.893837i	$-0.351997\pi$
$751$	673.484			0.896783			0.448391	+	0.893837i	$0.351997\pi$
$752$			53.0476i			0.0705420i
$753$	787.662	+	1103.29i	1.04603	+	1.46519i
$754$	7.10670			0.00942534
$755$		−	410.600i		−	0.543841i
$756$	−54.4828	−	183.090i	−0.0720672	−	0.242183i
$757$	−661.610			−0.873990			−0.436995	−	0.899464i	$-0.643957\pi$
$757$	−661.610			−0.873990			−0.436995	+	0.899464i	$0.643957\pi$
$758$		−	151.434i		−	0.199782i
$759$	120.311	−	85.8925i	0.158512	−	0.113165i
$760$	−290.430			−0.382145
$761$		−	91.8473i		−	0.120693i	−0.998177	−	0.0603464i	$-0.980779\pi$
$761$		−	91.8473i		−	0.120693i	0.998177	−	0.0603464i	$-0.0192205\pi$
$762$	−92.5973	−	129.702i	−0.121519	−	0.170213i
$763$	−120.226			−0.157570
$764$			994.872i			1.30219i
$765$	−24.0125	+	69.9266i	−0.0313889	+	0.0914073i
$766$	333.463			0.435330
$767$			283.548i			0.369684i
$768$	−235.480	+	168.114i	−0.306614	+	0.218899i
$769$	1109.96			1.44338			0.721692	−	0.692214i	$-0.243364\pi$
$769$	1109.96			1.44338			0.721692	+	0.692214i	$0.243364\pi$
$770$			32.8225i			0.0426266i
$771$	−155.351	−	217.603i	−0.201493	−	0.282234i
$772$	559.284			0.724462
$773$			1213.29i			1.56958i	0.619761	+	0.784790i	$0.287229\pi$
$773$			1213.29i			1.56958i	−0.619761	+	0.784790i	$0.712771\pi$
$774$	−427.072	−	146.655i	−0.551772	−	0.189476i
$775$	123.525			0.159388
$776$			19.2145i			0.0247610i
$777$	−86.6163	+	61.8373i	−0.111475	+	0.0795847i
$778$	152.532			0.196056
$779$		−	390.948i		−	0.501859i
$780$	45.8477	+	64.2195i	0.0587791	+	0.0823327i
$781$	−535.460			−0.685609
$782$		−	19.7286i		−	0.0252284i
$783$	59.3901	−	17.6729i	0.0758495	−	0.0225708i
$784$	−340.751			−0.434632
$785$		−	236.127i		−	0.300799i
$786$	−410.090	+	292.772i	−0.521743	+	0.372484i
$787$	−205.750			−0.261436			−0.130718	−	0.991420i	$-0.541728\pi$
$787$	−205.750			−0.261436			−0.130718	+	0.991420i	$0.541728\pi$
$788$			251.651i			0.319355i
$789$	−550.172	−	770.634i	−0.697304	−	0.976722i
$790$	128.540			0.162709
$791$			306.021i			0.386879i
$792$	143.682	−	418.416i	0.181417	−	0.528303i
$793$	−356.501			−0.449560
$794$			21.1118i			0.0265891i
$795$	−186.543	+	133.177i	−0.234646	+	0.167519i
$796$	−676.308			−0.849633
$797$			1101.39i			1.38192i	0.722892	+	0.690961i	$0.242812\pi$
$797$			1101.39i			1.38192i	−0.722892	+	0.690961i	$0.757188\pi$
$798$	67.6085	+	94.7001i	0.0847224	+	0.118672i
$799$	−25.3350			−0.0317084
$800$			157.781i			0.197226i
$801$	−292.987	−	100.610i	−0.365776	−	0.125606i
$802$	−213.872			−0.266673
$803$			782.320i			0.974247i
$804$	−439.496	+	313.766i	−0.546637	+	0.390256i
$805$	30.3203			0.0376649
$806$			76.5033i			0.0949172i
$807$	496.280	+	695.147i	0.614970	+	0.861396i
$808$	−1007.80			−1.24727
$809$			1245.96i			1.54013i	0.637967	+	0.770064i	$0.279776\pi$
$809$			1245.96i			1.54013i	−0.637967	+	0.770064i	$0.720224\pi$
$810$	−122.741	−	95.5665i	−0.151532	−	0.117983i
$811$	313.283			0.386292			0.193146	−	0.981170i	$-0.438131\pi$
$811$	313.283			0.386292			0.193146	+	0.981170i	$0.438131\pi$
$812$			16.2368i			0.0199960i
$813$	659.362	−	470.733i	0.811024	−	0.579008i
$814$	−110.719			−0.136018
$815$			376.273i			0.461684i
$816$	49.2622	+	69.0022i	0.0603703	+	0.0845616i
$817$	−1216.46			−1.48894
$818$			541.767i			0.662307i
$819$	22.8558	−	66.5583i	0.0279070	−	0.0812677i
$820$	−136.956			−0.167019
$821$		−	1561.58i		−	1.90205i	−0.309120	−	0.951023i	$-0.600034\pi$
$821$		−	1561.58i		−	1.90205i	0.309120	−	0.951023i	$-0.399966\pi$
$822$	−412.196	+	294.276i	−0.501455	+	0.357999i
$823$	−71.2864			−0.0866177			−0.0433089	−	0.999062i	$-0.513790\pi$
$823$	−71.2864			−0.0866177			−0.0433089	+	0.999062i	$0.513790\pi$
$824$		−	617.254i		−	0.749095i
$825$	−68.6864	−	96.2099i	−0.0832562	−	0.116618i
$826$	146.477			0.177333
$827$			655.018i			0.792041i	0.918242	+	0.396020i	$0.129609\pi$
$827$			655.018i			0.792041i	−0.918242	+	0.396020i	$0.870391\pi$
$828$	−173.630	−	59.6237i	−0.209698	−	0.0720092i
$829$	−1649.47			−1.98971			−0.994854	−	0.101324i	$-0.967692\pi$
$829$	−1649.47			−1.98971			−0.994854	+	0.101324i	$0.967692\pi$
$830$			265.207i			0.319527i
$831$	−700.929	+	500.408i	−0.843476	+	0.602176i
$832$	13.2236			0.0158937
$833$		−	162.740i		−	0.195366i
$834$	238.113	+	333.529i	0.285508	+	0.399914i
$835$	490.690			0.587652
$836$		−	535.378i		−	0.640404i
$837$	190.248	+	639.332i	0.227298	+	0.763837i
$838$	379.607			0.452992
$839$			750.115i			0.894058i	0.894519	+	0.447029i	$0.147518\pi$
$839$			750.115i			0.894058i	−0.894519	+	0.447029i	$0.852482\pi$
$840$	73.8510	−	52.7238i	0.0879178	−	0.0627665i
$841$	835.733			0.993737
$842$			505.920i			0.600855i
$843$	−590.777	−	827.509i	−0.700803	−	0.981623i
$844$	430.414			0.509969
$845$			29.0689i			0.0344010i
$846$	17.3123	−	50.4150i	0.0204637	−	0.0595922i
$847$	127.719			0.150789
$848$			262.834i			0.309946i
$849$	384.515	−	274.514i	0.452903	−	0.323338i
$850$	−15.7766			−0.0185607
$851$			102.278i			0.120186i
$852$	386.382	+	541.210i	0.453500	+	0.635223i
$853$	−1045.72			−1.22593			−0.612966	−	0.790109i	$-0.710024\pi$
$853$	−1045.72			−1.22593			−0.612966	+	0.790109i	$0.710024\pi$
$854$			184.164i			0.215649i
$855$	−396.350	−	136.105i	−0.463567	−	0.159187i
$856$	−495.243			−0.578555
$857$			1325.06i			1.54616i	0.634307	+	0.773081i	$0.281285\pi$
$857$			1325.06i			1.54616i	−0.634307	+	0.773081i	$0.718715\pi$
$858$	59.5859	−	42.5397i	0.0694474	−	0.0495800i
$859$	−1191.12			−1.38664			−0.693320	−	0.720630i	$-0.743853\pi$
$859$	−1191.12			−1.38664			−0.693320	+	0.720630i	$0.743853\pi$
$860$			426.147i			0.495519i
$861$	70.9716	+	99.4109i	0.0824293	+	0.115460i
$862$	374.421			0.434364
$863$		−	75.6364i		−	0.0876436i	−0.999039	−	0.0438218i	$-0.986047\pi$
$863$		−	75.6364i		−	0.0876436i	0.999039	−	0.0438218i	$-0.0139534\pi$
$864$	−816.625	+	243.006i	−0.945168	+	0.281257i
$865$	238.450			0.275665
$866$			130.131i			0.150266i
$867$	672.673	−	480.236i	0.775863	−	0.553906i
$868$	−174.788			−0.201369
$869$			527.476i			0.606991i
$870$	7.68264	+	10.7612i	0.00883062	+	0.0123692i
$871$	−198.937			−0.228401
$872$			345.783i			0.396540i
$873$	−9.00455	+	26.2221i	−0.0103145	+	0.0300368i
$874$	111.824			0.127945
$875$		−	24.2465i		−	0.0277102i
$876$	790.721	−	564.513i	0.902649	−	0.644421i
$877$	899.812			1.02601			0.513006	−	0.858385i	$-0.328532\pi$
$877$	899.812			1.02601			0.513006	+	0.858385i	$0.328532\pi$
$878$			84.5995i			0.0963548i
$879$	43.0212	+	60.2604i	0.0489433	+	0.0685556i
$880$	−135.557			−0.154042
$881$		−	527.216i		−	0.598429i	−0.954186	−	0.299215i	$-0.903275\pi$
$881$		−	527.216i		−	0.598429i	0.954186	−	0.299215i	$-0.0967246\pi$
$882$	323.841	+	111.206i	0.367167	+	0.126083i
$883$	−699.464			−0.792144			−0.396072	−	0.918219i	$-0.629627\pi$
$883$	−699.464			−0.792144			−0.396072	+	0.918219i	$0.629627\pi$
$884$			43.2140i			0.0488846i
$885$	−429.356	+	306.527i	−0.485148	+	0.346358i
$886$	−375.757			−0.424105
$887$		−	256.112i		−	0.288740i	−0.989524	−	0.144370i	$-0.953884\pi$
$887$		−	256.112i		−	0.288740i	0.989524	−	0.144370i	$-0.0461156\pi$
$888$	177.851	+	249.119i	0.200283	+	0.280539i
$889$	134.135			0.150883
$890$		−	66.1025i		−	0.0742725i
$891$	392.167	−	503.678i	0.440142	−	0.565296i
$892$	−1280.39			−1.43541
$893$		−	143.601i		−	0.160808i
$894$	−273.979	+	195.599i	−0.306464	+	0.218791i
$895$	414.529			0.463161
$896$		−	280.570i		−	0.313136i
$897$	−39.2966	−	55.0433i	−0.0438089	−	0.0613638i
$898$	415.000			0.462138
$899$		−	56.6972i		−	0.0630669i
$900$	−47.6797	+	138.848i	−0.0529775	+	0.154275i
$901$	−125.527			−0.139320
$902$			127.074i			0.140880i
$903$	309.324	−	220.833i	0.342552	−	0.244555i
$904$	880.152			0.973620
$905$			260.070i			0.287370i
$906$	274.906	+	385.065i	0.303429	+	0.425016i
$907$	393.756			0.434130			0.217065	−	0.976157i	$-0.430352\pi$
$907$	393.756			0.434130			0.217065	+	0.976157i	$0.430352\pi$
$908$		−	692.637i		−	0.762816i
$909$	−1375.34	−	472.285i	−1.51302	−	0.519566i
$910$	15.0166			0.0165018
$911$		−	175.594i		−	0.192748i	−0.995345	−	0.0963742i	$-0.969275\pi$
$911$		−	175.594i		−	0.192748i	0.995345	−	0.0963742i	$-0.0307246\pi$
$912$	−391.111	+	279.223i	−0.428849	+	0.306165i
$913$	−1088.30			−1.19201
$914$			165.234i			0.180782i
$915$	−385.392	−	539.824i	−0.421194	−	0.589972i
$916$	271.235			0.296108
$917$		−	424.104i		−	0.462491i
$918$	−24.2983	−	81.6548i	−0.0264688	−	0.0889486i
$919$	−537.127			−0.584469			−0.292234	−	0.956347i	$-0.594399\pi$
$919$	−537.127			−0.584469			−0.292234	+	0.956347i	$0.594399\pi$
$920$		−	87.2046i		−	0.0947876i
$921$	−414.384	+	295.838i	−0.449928	+	0.321214i
$922$	−422.937			−0.458716
$923$			244.978i			0.265415i
$924$	97.1910	+	136.137i	0.105185	+	0.147334i
$925$	81.7896			0.0884212
$926$			302.628i			0.326812i
$927$	289.265	−	842.367i	0.312044	−	0.908702i
$928$	72.4199			0.0780387
$929$		−	857.033i		−	0.922533i	−0.887262	−	0.461267i	$-0.847395\pi$
$929$		−	857.033i		−	0.922533i	0.887262	−	0.461267i	$-0.152605\pi$
$930$	−115.843	+	82.7032i	−0.124563	+	0.0889282i
$931$	922.423			0.990787
$932$		−	1337.76i		−	1.43536i
$933$	330.232	+	462.560i	0.353946	+	0.495777i
$934$	569.463			0.609703
$935$		−	64.7406i		−	0.0692413i
$936$	−191.429	−	65.7360i	−0.204518	−	0.0702308i
$937$	−1038.21			−1.10801			−0.554007	−	0.832512i	$-0.686902\pi$
$937$	−1038.21			−1.10801			−0.554007	+	0.832512i	$0.686902\pi$
$938$			102.768i			0.109561i
$939$	943.074	−	673.281i	1.00434	−	0.717019i
$940$	−50.3058			−0.0535168
$941$			242.533i			0.257739i	0.991662	+	0.128870i	$0.0411349\pi$
$941$			242.533i			0.257739i	−0.991662	+	0.128870i	$0.958865\pi$
$942$	158.092	+	221.442i	0.167826	+	0.235077i
$943$	117.386			0.124482
$944$			604.949i			0.640836i
$945$	125.493	−	37.3433i	0.132796	−	0.0395167i
$946$	395.399			0.417969
$947$			552.868i			0.583810i	0.956447	+	0.291905i	$0.0942890\pi$
$947$			552.868i			0.583810i	−0.956447	+	0.291905i	$0.905711\pi$
$948$	533.140	−	380.620i	0.562384	−	0.401498i
$949$	357.919			0.377154
$950$		−	89.4229i		−	0.0941294i
$951$	−620.149	−	868.650i	−0.652102	−	0.913407i
$952$	49.6951			0.0522007
$953$		−	182.607i		−	0.191613i	−0.995400	−	0.0958064i	$-0.969457\pi$
$953$		−	182.607i		−	0.191613i	0.995400	−	0.0958064i	$-0.0305430\pi$
$954$	85.7770	−	249.790i	0.0899130	−	0.261835i
$955$	−681.899			−0.714030
$956$			855.914i			0.895308i
$957$	−44.1595	+	31.5265i	−0.0461437	+	0.0329430i
$958$	542.916			0.566718
$959$		−	426.282i		−	0.444507i
$960$	14.2952	+	20.0235i	0.0148908	+	0.0208578i
$961$	−350.658			−0.364889
$962$			50.6549i			0.0526559i
$963$	−675.858	−	232.087i	−0.701826	−	0.241004i
$964$	1176.48			1.22041
$965$			383.341i			0.397245i
$966$	−28.4347	+	20.3001i	−0.0294355	+	0.0210146i
$967$	1256.65			1.29953			0.649765	−	0.760135i	$-0.274867\pi$
$967$	1256.65			1.29953			0.649765	+	0.760135i	$0.274867\pi$
$968$		−	367.334i		−	0.379477i
$969$	−133.354	−	186.791i	−0.137620	−	0.192767i
$970$	−5.91612			−0.00609909
$971$			1724.94i			1.77646i	0.459401	+	0.888229i	$0.348064\pi$
$971$			1724.94i			1.77646i	−0.459401	+	0.888229i	$0.651936\pi$
$972$	−792.070	−	32.9293i	−0.814886	−	0.0338779i
$973$	−344.926			−0.354498
$974$			519.695i			0.533568i
$975$	−44.0169	+	31.4247i	−0.0451456	+	0.0322304i
$976$	−760.596			−0.779299
$977$		−	1808.47i		−	1.85104i	−0.378700	−	0.925520i	$-0.623629\pi$
$977$		−	1808.47i		−	1.85104i	0.378700	−	0.925520i	$-0.376371\pi$
$978$	−251.923	−	352.872i	−0.257590	−	0.360810i
$979$	271.258			0.277077
$980$		−	323.140i		−	0.329734i
$981$	−162.045	+	471.890i	−0.165183	+	0.481030i
$982$	633.561			0.645174
$983$		−	1758.03i		−	1.78843i	−0.447639	−	0.894214i	$-0.647735\pi$
$983$		−	1758.03i		−	1.78843i	0.447639	−	0.894214i	$-0.352265\pi$
$984$	285.917	−	204.123i	0.290566	−	0.207442i
$985$	−172.485			−0.175112
$986$			7.24131i			0.00734412i
$987$	26.0689	+	36.5151i	0.0264123	+	0.0369961i
$988$	−244.941			−0.247916
$989$		−	365.255i		−	0.369318i
$990$	128.830	+	44.2395i	0.130131	+	0.0446864i
$991$	1355.64			1.36795			0.683975	−	0.729506i	$-0.260250\pi$
$991$	1355.64			1.36795			0.683975	+	0.729506i	$0.260250\pi$
$992$			779.597i			0.785884i
$993$	1427.06	−	1018.81i	1.43712	−	1.02599i
$994$	126.553			0.127316
$995$		−	463.551i		−	0.465880i
$996$	785.307	+	1099.99i	0.788460	+	1.10441i
$997$	355.215			0.356284			0.178142	−	0.984005i	$-0.442991\pi$
$997$	355.215			0.356284			0.178142	+	0.984005i	$0.442991\pi$
$998$			408.720i			0.409539i
$999$	125.969	+	423.319i	0.126095	+	0.423743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.3.d.a.131.14	✓	32
3.2	odd	2	inner	195.3.d.a.131.19	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.3.d.a.131.14	✓	32	1.1	even	1	trivial
195.3.d.a.131.19	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-0.858859i q^{2} +(2.44162 - 1.74313i) q^{3} +3.26236 q^{4} +2.23607i q^{5} +(-1.49710 - 2.09701i) q^{6} +2.16867 q^{7} -6.23734i q^{8} +(2.92302 - 8.51211i) q^{9} +1.92047 q^{10} +7.88082i q^{11} +(7.96545 - 5.68671i) q^{12} +3.60555 q^{13} -1.86258i q^{14} +(3.89775 + 5.45963i) q^{15} +7.69245 q^{16} +3.67384i q^{17} +(-7.31070 - 2.51046i) q^{18} -20.8237 q^{19} +7.29486i q^{20} +(5.29507 - 3.78027i) q^{21} +6.76851 q^{22} -6.25251i q^{23} +(-10.8725 - 15.2292i) q^{24} -5.00000 q^{25} -3.09666i q^{26} +(-7.70077 - 25.8785i) q^{27} +7.07498 q^{28} +2.29496i q^{29} +(4.68905 - 3.34762i) q^{30} -24.7051 q^{31} -31.5561i q^{32} +(13.7373 + 19.2420i) q^{33} +3.15531 q^{34} +4.84929i q^{35} +(9.53595 - 27.7696i) q^{36} -16.3579 q^{37} +17.8846i q^{38} +(8.80339 - 6.28493i) q^{39} +13.9471 q^{40} +18.7742i q^{41} +(-3.24671 - 4.54772i) q^{42} +58.4174 q^{43} +25.7101i q^{44} +(19.0336 + 6.53607i) q^{45} -5.37003 q^{46} +6.89606i q^{47} +(18.7820 - 13.4089i) q^{48} -44.2969 q^{49} +4.29429i q^{50} +(6.40397 + 8.97013i) q^{51} +11.7626 q^{52} +34.1678i q^{53} +(-22.2260 + 6.61387i) q^{54} -17.6221 q^{55} -13.5267i q^{56} +(-50.8435 + 36.2983i) q^{57} +1.97104 q^{58} +78.6419i q^{59} +(12.7159 + 17.8113i) q^{60} -98.8756 q^{61} +21.2182i q^{62} +(6.33907 - 18.4599i) q^{63} +3.66755 q^{64} +8.06226i q^{65} +(16.5261 - 11.7984i) q^{66} -55.1753 q^{67} +11.9854i q^{68} +(-10.8989 - 15.2663i) q^{69} +4.16486 q^{70} +67.9447i q^{71} +(-53.0929 - 18.2319i) q^{72} +99.2688 q^{73} +14.0492i q^{74} +(-12.2081 + 8.71563i) q^{75} -67.9343 q^{76} +17.0909i q^{77} +(-5.39787 - 7.56087i) q^{78} +66.9315 q^{79} +17.2008i q^{80} +(-63.9119 - 49.7621i) q^{81} +16.1244 q^{82} +138.095i q^{83} +(17.2744 - 12.3326i) q^{84} -8.21496 q^{85} -50.1723i q^{86} +(4.00040 + 5.60342i) q^{87} +49.1554 q^{88} -34.4200i q^{89} +(5.61356 - 16.3472i) q^{90} +7.81925 q^{91} -20.3980i q^{92} +(-60.3205 + 43.0641i) q^{93} +5.92274 q^{94} -46.5631i q^{95} +(-55.0063 - 77.0480i) q^{96} -3.08056 q^{97} +38.0448i q^{98} +(67.0824 + 23.0358i) 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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