LMFDB - Embedded newform 195.3.d.a.131.18

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			131.18
Character	$\chi$	$=$	195.131
Dual form			195.3.d.a.131.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.848705i q^{2} +(1.45000 - 2.62631i) q^{3} +3.27970 q^{4} -2.23607i q^{5} +(2.22896 + 1.23062i) q^{6} +5.71525 q^{7} +6.17832i q^{8} +(-4.79500 - 7.61630i) q^{9} +1.89776 q^{10} +0.158221i q^{11} +(4.75556 - 8.61351i) q^{12} -3.60555 q^{13} +4.85056i q^{14} +(-5.87261 - 3.24230i) q^{15} +7.87524 q^{16} -0.500131i q^{17} +(6.46399 - 4.06954i) q^{18} -7.38194 q^{19} -7.33363i q^{20} +(8.28711 - 15.0100i) q^{21} -0.134283 q^{22} -27.1571i q^{23} +(16.2262 + 8.95856i) q^{24} -5.00000 q^{25} -3.06005i q^{26} +(-26.9555 + 1.54954i) q^{27} +18.7443 q^{28} +43.5267i q^{29} +(2.75175 - 4.98411i) q^{30} +60.8642 q^{31} +31.3970i q^{32} +(0.415537 + 0.229420i) q^{33} +0.424464 q^{34} -12.7797i q^{35} +(-15.7262 - 24.9792i) q^{36} -16.3052 q^{37} -6.26509i q^{38} +(-5.22805 + 9.46929i) q^{39} +13.8151 q^{40} +38.8939i q^{41} +(12.7391 + 7.03331i) q^{42} -33.5312 q^{43} +0.518917i q^{44} +(-17.0306 + 10.7220i) q^{45} +23.0483 q^{46} +10.7438i q^{47} +(11.4191 - 20.6828i) q^{48} -16.3359 q^{49} -4.24352i q^{50} +(-1.31350 - 0.725190i) q^{51} -11.8251 q^{52} -35.9526i q^{53} +(-1.31510 - 22.8773i) q^{54} +0.353792 q^{55} +35.3106i q^{56} +(-10.7038 + 19.3873i) q^{57} -36.9413 q^{58} +58.0013i q^{59} +(-19.2604 - 10.6338i) q^{60} -49.4053 q^{61} +51.6558i q^{62} +(-27.4046 - 43.5290i) q^{63} +4.85415 q^{64} +8.06226i q^{65} +(-0.194710 + 0.352668i) q^{66} -0.886312 q^{67} -1.64028i q^{68} +(-71.3229 - 39.3778i) q^{69} +10.8462 q^{70} +70.9978i q^{71} +(47.0559 - 29.6250i) q^{72} -91.7472 q^{73} -13.8383i q^{74} +(-7.25000 + 13.1315i) q^{75} -24.2105 q^{76} +0.904271i q^{77} +(-8.03663 - 4.43707i) q^{78} -99.0881 q^{79} -17.6096i q^{80} +(-35.0159 + 73.0403i) q^{81} -33.0095 q^{82} -7.11823i q^{83} +(27.1792 - 49.2283i) q^{84} -1.11833 q^{85} -28.4581i q^{86} +(114.315 + 63.1137i) q^{87} -0.977538 q^{88} -38.6312i q^{89} +(-9.09977 - 14.4539i) q^{90} -20.6066 q^{91} -89.0671i q^{92} +(88.2531 - 159.848i) q^{93} -9.11829 q^{94} +16.5065i q^{95} +(82.4583 + 45.5257i) q^{96} +143.364 q^{97} -13.8644i q^{98} +(1.20506 - 0.758669i) 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 $

$2$			0.848705i			0.424352i	0.977231	+	0.212176i	$0.0680551\pi$
$2$			0.848705i			0.424352i	−0.977231	+	0.212176i	$0.931945\pi$
$3$	1.45000	−	2.62631i	0.483333	−	0.875436i
$3$	1.45000	−	2.62631i	0.483333	−	0.875436i
$4$	3.27970			0.819925
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	2.22896	+	1.23062i	0.371494	+	0.205104i
$7$	5.71525			0.816464			0.408232	−	0.912878i	$-0.366145\pi$
$7$	5.71525			0.816464			0.408232	+	0.912878i	$0.366145\pi$
$8$			6.17832i			0.772289i
$9$	−4.79500	−	7.61630i	−0.532778	−	0.846255i
$10$	1.89776			0.189776
$11$			0.158221i			0.0143837i	0.999974	+	0.00719185i	$0.00228926\pi$
$11$			0.158221i			0.0143837i	−0.999974	+	0.00719185i	$0.997711\pi$
$12$	4.75556	−	8.61351i	0.396297	−	0.717792i
$13$	−3.60555			−0.277350
$13$	−3.60555			−0.277350
$14$			4.85056i			0.346469i
$15$	−5.87261	−	3.24230i	−0.391507	−	0.216153i
$16$	7.87524			0.492202
$17$		−	0.500131i		−	0.0294195i	−0.999892	−	0.0147097i	$-0.995318\pi$
$17$		−	0.500131i		−	0.0294195i	0.999892	−	0.0147097i	$-0.00468242\pi$
$18$	6.46399	−	4.06954i	0.359110	−	0.226086i
$19$	−7.38194			−0.388523			−0.194262	−	0.980950i	$-0.562231\pi$
$19$	−7.38194			−0.388523			−0.194262	+	0.980950i	$0.562231\pi$
$20$		−	7.33363i		−	0.366682i
$21$	8.28711	−	15.0100i	0.394624	−	0.714763i
$22$	−0.134283			−0.00610376
$23$		−	27.1571i		−	1.18074i	−0.807132	−	0.590371i	$-0.798981\pi$
$23$		−	27.1571i		−	1.18074i	0.807132	−	0.590371i	$-0.201019\pi$
$24$	16.2262	+	8.95856i	0.676090	+	0.373273i
$25$	−5.00000			−0.200000
$26$		−	3.06005i		−	0.117694i
$27$	−26.9555	+	1.54954i	−0.998352	+	0.0573902i
$28$	18.7443			0.669439
$29$			43.5267i			1.50092i	0.660915	+	0.750461i	$0.270168\pi$
$29$			43.5267i			1.50092i	−0.660915	+	0.750461i	$0.729832\pi$
$30$	2.75175	−	4.98411i	0.0917251	−	0.166137i
$31$	60.8642			1.96336			0.981681	−	0.190532i	$-0.0610213\pi$
$31$	60.8642			1.96336			0.981681	+	0.190532i	$0.0610213\pi$
$32$			31.3970i			0.981157i
$33$	0.415537	+	0.229420i	0.0125920	+	0.00695212i
$34$	0.424464			0.0124842
$35$		−	12.7797i		−	0.365134i
$36$	−15.7262	−	24.9792i	−0.436838	−	0.693866i
$37$	−16.3052			−0.440682			−0.220341	−	0.975423i	$-0.570717\pi$
$37$	−16.3052			−0.440682			−0.220341	+	0.975423i	$0.570717\pi$
$38$		−	6.26509i		−	0.164871i
$39$	−5.22805	+	9.46929i	−0.134053	+	0.242802i
$40$	13.8151			0.345378
$41$			38.8939i			0.948632i	0.880355	+	0.474316i	$0.157305\pi$
$41$			38.8939i			0.948632i	−0.880355	+	0.474316i	$0.842695\pi$
$42$	12.7391	+	7.03331i	0.303311	+	0.167460i
$43$	−33.5312			−0.779796			−0.389898	−	0.920858i	$-0.627490\pi$
$43$	−33.5312			−0.779796			−0.389898	+	0.920858i	$0.627490\pi$
$44$			0.518917i			0.0117936i
$45$	−17.0306	+	10.7220i	−0.378457	+	0.238266i
$46$	23.0483			0.501051
$47$			10.7438i			0.228591i	0.993447	+	0.114296i	$0.0364611\pi$
$47$			10.7438i			0.228591i	−0.993447	+	0.114296i	$0.963539\pi$
$48$	11.4191	−	20.6828i	0.237898	−	0.430892i
$49$	−16.3359			−0.333386
$50$		−	4.24352i		−	0.0848705i
$51$	−1.31350	−	0.725190i	−0.0257549	−	0.0142194i
$52$	−11.8251			−0.227406
$53$		−	35.9526i		−	0.678350i	−0.940723	−	0.339175i	$-0.889852\pi$
$53$		−	35.9526i		−	0.678350i	0.940723	−	0.339175i	$-0.110148\pi$
$54$	−1.31510	−	22.8773i	−0.0243537	−	0.423653i
$55$	0.353792			0.00643259
$56$			35.3106i			0.630547i
$57$	−10.7038	+	19.3873i	−0.187786	+	0.340127i
$58$	−36.9413			−0.636920
$59$			58.0013i			0.983072i	0.870857	+	0.491536i	$0.163564\pi$
$59$			58.0013i			0.983072i	−0.870857	+	0.491536i	$0.836436\pi$
$60$	−19.2604	−	10.6338i	−0.321006	−	0.177229i
$61$	−49.4053			−0.809923			−0.404961	−	0.914334i	$-0.632715\pi$
$61$	−49.4053			−0.809923			−0.404961	+	0.914334i	$0.632715\pi$
$62$			51.6558i			0.833157i
$63$	−27.4046	−	43.5290i	−0.434994	−	0.690937i
$64$	4.85415			0.0758461
$65$			8.06226i			0.124035i
$66$	−0.194710	+	0.352668i	−0.00295015	+	0.00534345i
$67$	−0.886312			−0.0132285			−0.00661427	−	0.999978i	$-0.502105\pi$
$67$	−0.886312			−0.0132285			−0.00661427	+	0.999978i	$0.502105\pi$
$68$		−	1.64028i		−	0.0241218i
$69$	−71.3229	−	39.3778i	−1.03367	−	0.570692i
$70$	10.8462			0.154945
$71$			70.9978i			0.999969i	0.866034	+	0.499985i	$0.166661\pi$
$71$			70.9978i			0.999969i	−0.866034	+	0.499985i	$0.833339\pi$
$72$	47.0559	−	29.6250i	0.653554	−	0.411459i
$73$	−91.7472			−1.25681			−0.628405	−	0.777886i	$-0.716292\pi$
$73$	−91.7472			−1.25681			−0.628405	+	0.777886i	$0.716292\pi$
$74$		−	13.8383i		−	0.187005i
$75$	−7.25000	+	13.1315i	−0.0966666	+	0.175087i
$76$	−24.2105			−0.318560
$77$			0.904271i			0.0117438i
$78$	−8.03663	−	4.43707i	−0.103034	−	0.0568855i
$79$	−99.0881			−1.25428			−0.627140	−	0.778907i	$-0.715775\pi$
$79$	−99.0881			−1.25428			−0.627140	+	0.778907i	$0.715775\pi$
$80$		−	17.6096i		−	0.220120i
$81$	−35.0159	+	73.0403i	−0.432295	+	0.901732i
$82$	−33.0095			−0.402554
$83$		−	7.11823i		−	0.0857618i	−0.999080	−	0.0428809i	$-0.986346\pi$
$83$		−	7.11823i		−	0.0857618i	0.999080	−	0.0428809i	$-0.0136536\pi$
$84$	27.1792	−	49.2283i	0.323562	−	0.586052i
$85$	−1.11833			−0.0131568
$86$		−	28.4581i		−	0.330908i
$87$	114.315	+	63.1137i	1.31396	+	0.725445i
$88$	−0.977538			−0.0111084
$89$		−	38.6312i		−	0.434059i	−0.976165	−	0.217029i	$-0.930363\pi$
$89$		−	38.6312i		−	0.434059i	0.976165	−	0.217029i	$-0.0696368\pi$
$90$	−9.09977	−	14.4539i	−0.101109	−	0.160599i
$91$	−20.6066			−0.226446
$92$		−	89.0671i		−	0.968121i
$93$	88.2531	−	159.848i	0.948958	−	1.71880i
$94$	−9.11829			−0.0970031
$95$			16.5065i			0.173753i
$96$	82.4583	+	45.5257i	0.858940	+	0.474226i
$97$	143.364			1.47798			0.738990	−	0.673716i	$-0.235303\pi$
$97$	143.364			1.47798			0.738990	+	0.673716i	$0.235303\pi$
$98$		−	13.8644i		−	0.141473i
$99$	1.20506	−	0.758669i	0.0121723	−	0.00766332i
$100$	−16.3985			−0.163985
$101$			118.950i			1.17772i	0.808234	+	0.588861i	$0.200424\pi$
$101$			118.950i			1.17772i	−0.808234	+	0.588861i	$0.799576\pi$
$102$	0.615472	−	1.11477i	0.00603404	−	0.0109291i
$103$	−12.7154			−0.123451			−0.0617253	−	0.998093i	$-0.519660\pi$
$103$	−12.7154			−0.123451			−0.0617253	+	0.998093i	$0.519660\pi$
$104$		−	22.2762i		−	0.214195i
$105$	−33.5634	−	18.5305i	−0.319652	−	0.176481i
$106$	30.5131			0.287860
$107$			124.695i			1.16538i	0.812695	+	0.582689i	$0.197999\pi$
$107$			124.695i			1.16538i	−0.812695	+	0.582689i	$0.802001\pi$
$108$	−88.4060	+	5.08201i	−0.818574	+	0.0470557i
$109$	162.228			1.48833			0.744165	−	0.667996i	$-0.232848\pi$
$109$	162.228			1.48833			0.744165	+	0.667996i	$0.232848\pi$
$110$			0.300265i			0.00272968i
$111$	−23.6426	+	42.8226i	−0.212996	+	0.385789i
$112$	45.0089			0.401866
$113$		−	138.982i		−	1.22993i	−0.788553	−	0.614966i	$-0.789170\pi$
$113$		−	138.982i		−	1.22993i	0.788553	−	0.614966i	$-0.210830\pi$
$114$	−16.4541	−	9.08437i	−0.144334	−	0.0796875i
$115$	−60.7251			−0.528044
$116$			142.755i			1.23064i
$117$	17.2886	+	27.4609i	0.147766	+	0.234709i
$118$	−49.2260			−0.417169
$119$		−	2.85837i		−	0.0240199i
$120$	20.0319	−	36.2828i	0.166933	−	0.302357i
$121$	120.975			0.999793
$122$		−	41.9305i		−	0.343693i
$123$	102.147	+	56.3962i	0.830467	+	0.458505i
$124$	199.616			1.60981
$125$			11.1803i			0.0894427i
$126$	36.9433	−	23.2584i	0.293201	−	0.184591i
$127$	−176.155			−1.38705			−0.693523	−	0.720434i	$-0.743943\pi$
$127$	−176.155			−1.38705			−0.693523	+	0.720434i	$0.743943\pi$
$128$			129.708i			1.01334i
$129$	−48.6203	+	88.0634i	−0.376901	+	0.682662i
$130$	−6.84248			−0.0526344
$131$			6.93895i			0.0529691i	0.999649	+	0.0264845i	$0.00843128\pi$
$131$			6.93895i			0.0529691i	−0.999649	+	0.0264845i	$0.991569\pi$
$132$	1.36284	+	0.752429i	0.0103245	+	0.00570022i
$133$	−42.1896			−0.317215
$134$		−	0.752217i		−	0.00561356i
$135$	3.46487	+	60.2743i	0.0256657	+	0.446477i
$136$	3.08997			0.0227203
$137$		−	234.452i		−	1.71133i	−0.517532	−	0.855664i	$-0.673149\pi$
$137$		−	234.452i		−	1.71133i	0.517532	−	0.855664i	$-0.326851\pi$
$138$	33.4201	−	60.5321i	0.242175	−	0.438638i
$139$	241.111			1.73461			0.867304	−	0.497778i	$-0.165851\pi$
$139$	241.111			1.73461			0.867304	+	0.497778i	$0.165851\pi$
$140$		−	41.9135i		−	0.299382i
$141$	28.2165	+	15.5785i	0.200117	+	0.110486i
$142$	−60.2562			−0.424339
$143$		−	0.570473i		−	0.00398932i
$144$	−37.7618	−	59.9801i	−0.262235	−	0.416529i
$145$	97.3287			0.671233
$146$		−	77.8663i		−	0.533331i
$147$	−23.6871	+	42.9032i	−0.161137	+	0.291858i
$148$	−53.4763			−0.361326
$149$		−	53.9977i		−	0.362401i	−0.983446	−	0.181200i	$-0.942002\pi$
$149$		−	53.9977i		−	0.362401i	0.983446	−	0.181200i	$-0.0579982\pi$
$150$	−11.1448	−	6.15311i	−0.0742987	−	0.0410207i
$151$	10.3411			0.0684844			0.0342422	−	0.999414i	$-0.489098\pi$
$151$	10.3411			0.0684844			0.0342422	+	0.999414i	$0.489098\pi$
$152$		−	45.6079i		−	0.300052i
$153$	−3.80915	+	2.39813i	−0.0248964	+	0.0156740i
$154$	−0.767459			−0.00498350
$155$		−	136.097i		−	0.878042i
$156$	−17.1464	+	31.0564i	−0.109913	+	0.199080i
$157$	113.076			0.720229			0.360114	−	0.932908i	$-0.382738\pi$
$157$	113.076			0.720229			0.360114	+	0.932908i	$0.382738\pi$
$158$		−	84.0965i		−	0.532257i
$159$	−94.4226	−	52.1312i	−0.593853	−	0.327869i
$160$	70.2059			0.438787
$161$		−	155.210i		−	0.964034i
$162$	−61.9897	−	29.7182i	−0.382652	−	0.183445i
$163$	−50.7567			−0.311391			−0.155696	−	0.987805i	$-0.549762\pi$
$163$	−50.7567			−0.311391			−0.155696	+	0.987805i	$0.549762\pi$
$164$			127.560i			0.777807i
$165$	0.512999	−	0.929168i	0.00310908	−	0.00563132i
$166$	6.04128			0.0363932
$167$		−	16.9502i		−	0.101498i	−0.998711	−	0.0507492i	$-0.983839\pi$
$167$		−	16.9502i		−	0.101498i	0.998711	−	0.0507492i	$-0.0161609\pi$
$168$	92.7366	+	51.2004i	0.552004	+	0.304764i
$169$	13.0000			0.0769231
$170$		−	0.949129i		−	0.00558311i
$171$	35.3964	+	56.2230i	0.206997	+	0.328790i
$172$	−109.972			−0.639375
$173$		−	254.399i		−	1.47052i	−0.677787	−	0.735259i	$-0.737061\pi$
$173$		−	254.399i		−	1.47052i	0.677787	−	0.735259i	$-0.262939\pi$
$174$	−53.5649	+	97.0194i	−0.307844	+	0.557583i
$175$	−28.5762			−0.163293
$176$			1.24603i			0.00707969i
$177$	152.329	+	84.1018i	0.860617	+	0.475151i
$178$	32.7865			0.184194
$179$		−	85.6497i		−	0.478490i	−0.970959	−	0.239245i	$-0.923100\pi$
$179$		−	85.6497i		−	0.478490i	0.970959	−	0.239245i	$-0.0768999\pi$
$180$	−55.8551	+	35.1648i	−0.310306	+	0.195360i
$181$	−270.553			−1.49477			−0.747384	−	0.664393i	$-0.768690\pi$
$181$	−270.553			−1.49477			−0.747384	+	0.664393i	$0.768690\pi$
$182$		−	17.4889i		−	0.0960931i
$183$	−71.6376	+	129.754i	−0.391462	+	0.709036i
$184$	167.785			0.911875
$185$			36.4596i			0.197079i
$186$	135.664	+	74.9008i	0.729376	+	0.402693i
$187$	0.0791311			0.000423161
$188$			35.2364i			0.187428i
$189$	−154.057	+	8.85599i	−0.815119	+	0.0468571i
$190$	−14.0092			−0.0737324
$191$		−	363.679i		−	1.90408i	−0.305973	−	0.952040i	$-0.598982\pi$
$191$		−	363.679i		−	1.90408i	0.305973	−	0.952040i	$-0.401018\pi$
$192$	7.03851	−	12.7485i	0.0366589	−	0.0663984i
$193$	−289.833			−1.50173			−0.750864	−	0.660457i	$-0.770363\pi$
$193$	−289.833			−1.50173			−0.750864	+	0.660457i	$0.770363\pi$
$194$			121.674i			0.627185i
$195$	21.1740	+	11.6903i	0.108585	+	0.0599501i
$196$	−53.5769			−0.273352
$197$			16.2644i			0.0825606i	0.999148	+	0.0412803i	$0.0131437\pi$
$197$			16.2644i			0.0825606i	−0.999148	+	0.0412803i	$0.986856\pi$
$198$	0.643886	+	1.02274i	0.00325195	+	0.00516534i
$199$	3.23910			0.0162769			0.00813845	−	0.999967i	$-0.497409\pi$
$199$	3.23910			0.0162769			0.00813845	+	0.999967i	$0.497409\pi$
$200$		−	30.8916i		−	0.154458i
$201$	−1.28515	+	2.32773i	−0.00639379	+	0.0115807i
$202$	−100.953			−0.499770
$203$			248.766i			1.22545i
$204$	−4.30788	−	2.37840i	−0.0211171	−	0.0116588i
$205$	86.9694			0.424241
$206$		−	10.7916i		−	0.0523866i
$207$	−206.836	+	130.218i	−0.999209	+	0.629074i
$208$	−28.3946			−0.136512
$209$		−	1.16798i		−	0.00558840i
$210$	15.7270	−	28.4854i	0.0748903	−	0.135645i
$211$	−293.051			−1.38887			−0.694435	−	0.719556i	$-0.744345\pi$
$211$	−293.051			−1.38887			−0.694435	+	0.719556i	$0.744345\pi$
$212$		−	117.914i		−	0.556196i
$213$	186.462	+	102.947i	0.875409	+	0.483318i
$214$	−105.830			−0.494531
$215$			74.9781i			0.348736i
$216$	−9.57353	−	166.540i	−0.0443219	−	0.771017i
$217$	347.854			1.60301
$218$			137.684i			0.631576i
$219$	−133.033	+	240.957i	−0.607458	+	1.10026i
$220$	1.16033			0.00527424
$221$			1.80325i			0.00815949i
$222$	−36.3438	−	20.0656i	−0.163711	−	0.0903855i
$223$	234.429			1.05125			0.525624	−	0.850717i	$-0.323832\pi$
$223$	234.429			1.05125			0.525624	+	0.850717i	$0.323832\pi$
$224$			179.442i			0.801079i
$225$	23.9750	+	38.0815i	0.106556	+	0.169251i
$226$	117.955			0.521925
$227$			109.658i			0.483076i	0.970391	+	0.241538i	$0.0776518\pi$
$227$			109.658i			0.483076i	−0.970391	+	0.241538i	$0.922348\pi$
$228$	−35.1053	+	63.5844i	−0.153971	+	0.278879i
$229$	73.4865			0.320902			0.160451	−	0.987044i	$-0.448705\pi$
$229$	73.4865			0.320902			0.160451	+	0.987044i	$0.448705\pi$
$230$		−	51.5377i		−	0.224077i
$231$	2.37490	+	1.31119i	0.0102809	+	0.00567616i
$232$	−268.922			−1.15915
$233$		−	32.6938i		−	0.140317i	−0.997536	−	0.0701583i	$-0.977650\pi$
$233$		−	32.6938i		−	0.140317i	0.997536	−	0.0701583i	$-0.0223504\pi$
$234$	−23.3062	+	14.6729i	−0.0995993	+	0.0627049i
$235$	24.0238			0.102229
$236$			190.227i			0.806046i
$237$	−143.678	+	260.236i	−0.606235	+	1.09804i
$238$	2.42592			0.0101929
$239$		−	303.835i		−	1.27128i	−0.771987	−	0.635638i	$-0.780737\pi$
$239$		−	303.835i		−	1.27128i	0.771987	−	0.635638i	$-0.219263\pi$
$240$	−46.2482	−	25.5339i	−0.192701	−	0.106391i
$241$	223.844			0.928814			0.464407	−	0.885622i	$-0.346268\pi$
$241$	223.844			0.928814			0.464407	+	0.885622i	$0.346268\pi$
$242$			102.672i			0.424265i
$243$	141.053	+	197.871i	0.580467	+	0.814284i
$244$	−162.035			−0.664076
$245$			36.5282i			0.149095i
$246$	−47.8637	+	86.6930i	−0.194568	+	0.352411i
$247$	26.6160			0.107757
$248$			376.038i			1.51628i
$249$	−18.6947	−	10.3214i	−0.0750790	−	0.0414515i
$250$	−9.48881			−0.0379552
$251$			105.280i			0.419441i	0.977761	+	0.209721i	$0.0672554\pi$
$251$			105.280i			0.419441i	−0.977761	+	0.209721i	$0.932745\pi$
$252$	−89.8790	−	142.762i	−0.356663	−	0.566517i
$253$	4.29681			0.0169835
$254$		−	149.504i		−	0.588597i
$255$	−1.62157	+	2.93707i	−0.00635911	+	0.0115179i
$256$	−90.6670			−0.354168
$257$			36.7130i			0.142852i	0.997446	+	0.0714260i	$0.0227550\pi$
$257$			36.7130i			0.142852i	−0.997446	+	0.0714260i	$0.977245\pi$
$258$	−74.7398	−	41.2643i	−0.289689	−	0.159939i
$259$	−93.1885			−0.359801
$260$			26.4418i			0.101699i
$261$	331.512	−	208.711i	1.27016	−	0.799658i
$262$	−5.88912			−0.0224776
$263$		−	419.283i		−	1.59423i	−0.603827	−	0.797116i	$-0.706358\pi$
$263$		−	419.283i		−	1.59423i	0.603827	−	0.797116i	$-0.293642\pi$
$264$	−1.41743	+	2.56732i	−0.00536905	+	0.00972468i
$265$	−80.3924			−0.303367
$266$		−	35.8065i		−	0.134611i
$267$	−101.458	−	56.0153i	−0.379991	−	0.209795i
$268$	−2.90684			−0.0108464
$269$		−	249.344i		−	0.926931i	−0.886115	−	0.463465i	$-0.846606\pi$
$269$		−	249.344i		−	0.926931i	0.886115	−	0.463465i	$-0.153394\pi$
$270$	−51.1551	+	2.94065i	−0.189463	+	0.0108913i
$271$	−358.799			−1.32398			−0.661990	−	0.749513i	$-0.730288\pi$
$271$	−358.799			−1.32398			−0.661990	+	0.749513i	$0.730288\pi$
$272$		−	3.93865i		−	0.0144803i
$273$	−29.8796	+	54.1194i	−0.109449	+	0.198239i
$274$	198.980			0.726206
$275$		−	0.791104i		−	0.00287674i
$276$	−233.918	−	129.147i	−0.847528	−	0.467925i
$277$	188.529			0.680612			0.340306	−	0.940315i	$-0.389469\pi$
$277$	188.529			0.680612			0.340306	+	0.940315i	$0.389469\pi$
$278$			204.632i			0.736085i
$279$	−291.844	−	463.560i	−1.04604	−	1.66150i
$280$	78.9569			0.281989
$281$		−	411.696i		−	1.46511i	−0.680708	−	0.732555i	$-0.738328\pi$
$281$		−	411.696i		−	1.46511i	0.680708	−	0.732555i	$-0.261672\pi$
$282$	−13.2215	+	23.9475i	−0.0468848	+	0.0849201i
$283$	−264.059			−0.933071			−0.466536	−	0.884502i	$-0.654498\pi$
$283$	−264.059			−0.933071			−0.466536	+	0.884502i	$0.654498\pi$
$284$			232.852i			0.819900i
$285$	43.3512	+	23.9344i	0.152110	+	0.0839805i
$286$	0.484163			0.00169288
$287$			222.288i			0.774524i
$288$	239.129	−	150.549i	0.830309	−	0.522739i
$289$	288.750			0.999134
$290$			82.6033i			0.284839i
$291$	207.878	−	376.519i	0.714357	−	1.29388i
$292$	−300.903			−1.03049
$293$			291.057i			0.993368i	0.867931	+	0.496684i	$0.165449\pi$
$293$			291.057i			0.993368i	−0.867931	+	0.496684i	$0.834551\pi$
$294$	−36.4121	−	20.1033i	−0.123851	−	0.0683787i
$295$	129.695			0.439643
$296$		−	100.739i		−	0.340334i
$297$	−0.245169	−	4.26492i	−0.000825484	−	0.0143600i
$298$	45.8281			0.153786
$299$			97.9163i			0.327479i
$300$	−23.7778	+	43.0675i	−0.0792594	+	0.143558i
$301$	−191.639			−0.636676
$302$			8.77657i			0.0290615i
$303$	312.400	+	172.477i	1.03102	+	0.569233i
$304$	−58.1345			−0.191232
$305$			110.474i			0.362208i
$306$	−2.03530	−	3.23284i	−0.00665132	−	0.0105648i
$307$	131.664			0.428871			0.214436	−	0.976738i	$-0.431209\pi$
$307$	131.664			0.428871			0.214436	+	0.976738i	$0.431209\pi$
$308$			2.96574i			0.00962902i
$309$	−18.4374	+	33.3946i	−0.0596678	+	0.108073i
$310$	115.506			0.372599
$311$			73.9535i			0.237792i	0.992907	+	0.118896i	$0.0379356\pi$
$311$			73.9535i			0.237792i	−0.992907	+	0.118896i	$0.962064\pi$
$312$	−58.5043	−	32.3005i	−0.187514	−	0.103527i
$313$	243.959			0.779421			0.389710	−	0.920937i	$-0.372575\pi$
$313$	243.959			0.779421			0.389710	+	0.920937i	$0.372575\pi$
$314$			95.9680i			0.305631i
$315$	−97.3339	+	61.2786i	−0.308996	+	0.194535i
$316$	−324.979			−1.02842
$317$		−	251.630i		−	0.793784i	−0.917865	−	0.396892i	$-0.870089\pi$
$317$		−	251.630i		−	0.793784i	0.917865	−	0.396892i	$-0.129911\pi$
$318$	44.2440	−	80.1369i	0.139132	−	0.252003i
$319$	−6.88683			−0.0215888
$320$		−	10.8542i		−	0.0339194i
$321$	327.489	+	180.808i	1.02021	+	0.563266i
$322$	131.727			0.409090
$323$			3.69194i			0.0114301i
$324$	−114.842	+	239.550i	−0.354450	+	0.739353i
$325$	18.0278			0.0554700
$326$		−	43.0775i		−	0.132140i
$327$	235.230	−	426.061i	0.719359	−	1.30294i
$328$	−240.299			−0.732619
$329$			61.4034i			0.186636i
$330$	0.788589	+	0.435384i	0.00238966	+	0.00131935i
$331$	304.896			0.921136			0.460568	−	0.887624i	$-0.347646\pi$
$331$	304.896			0.921136			0.460568	+	0.887624i	$0.347646\pi$
$332$		−	23.3457i		−	0.0703183i
$333$	78.1837	+	124.186i	0.234786	+	0.372930i
$334$	14.3858			0.0430711
$335$			1.98185i			0.00591598i
$336$	65.2629	−	118.207i	0.194235	−	0.351808i
$337$	321.388			0.953672			0.476836	−	0.878992i	$-0.341784\pi$
$337$	321.388			0.953672			0.476836	+	0.878992i	$0.341784\pi$
$338$			11.0332i			0.0326425i
$339$	−365.011	−	201.524i	−1.07673	−	0.594467i
$340$	−3.66778			−0.0107876
$341$			9.62998i			0.0282404i
$342$	−47.7167	+	30.0411i	−0.139523	+	0.0878395i
$343$	−373.411			−1.08866
$344$		−	207.167i		−	0.602229i
$345$	−88.0513	+	159.483i	−0.255221	+	0.462269i
$346$	215.910			0.624017
$347$			157.727i			0.454546i	0.973831	+	0.227273i	$0.0729810\pi$
$347$			157.727i			0.454546i	−0.973831	+	0.227273i	$0.927019\pi$
$348$	374.918	+	206.994i	1.07735	+	0.594811i
$349$	142.635			0.408697			0.204349	−	0.978898i	$-0.434492\pi$
$349$	142.635			0.408697			0.204349	+	0.978898i	$0.434492\pi$
$350$		−	24.2528i		−	0.0692937i
$351$	97.1894	−	5.58693i	0.276893	−	0.0159172i
$352$	−4.96766			−0.0141127
$353$		−	513.946i		−	1.45594i	−0.685610	−	0.727969i	$-0.740465\pi$
$353$		−	513.946i		−	1.45594i	0.685610	−	0.727969i	$-0.259535\pi$
$354$	−71.3776	+	129.283i	−0.201632	+	0.365205i
$355$	158.756			0.447200
$356$		−	126.699i		−	0.355896i
$357$	−7.50697	−	4.14464i	−0.0210279	−	0.0116096i
$358$	72.6913			0.203048
$359$			333.243i			0.928254i	0.885769	+	0.464127i	$0.153632\pi$
$359$			333.243i			0.928254i	−0.885769	+	0.464127i	$0.846368\pi$
$360$	−66.2436	−	105.220i	−0.184010	−	0.292278i
$361$	−306.507			−0.849050
$362$		−	229.620i		−	0.634308i
$363$	175.414	−	317.718i	0.483233	−	0.875255i
$364$	−67.5836			−0.185669
$365$			205.153i			0.562063i
$366$	−110.122	−	60.7992i	−0.300881	−	0.166118i
$367$	−301.086			−0.820399			−0.410199	−	0.911996i	$-0.634541\pi$
$367$	−301.086			−0.820399			−0.410199	+	0.911996i	$0.634541\pi$
$368$		−	213.868i		−	0.581164i
$369$	296.228	−	186.496i	0.802785	−	0.505410i
$370$	−30.9435			−0.0836310
$371$		−	205.478i		−	0.553849i
$372$	289.444	−	524.254i	0.778074	−	1.40929i
$373$	564.877			1.51442			0.757208	−	0.653174i	$-0.226563\pi$
$373$	564.877			1.51442			0.757208	+	0.653174i	$0.226563\pi$
$374$			0.0671589i			0.000179569i
$375$	29.3630	+	16.2115i	0.0783014	+	0.0432306i
$376$	−66.3785			−0.176538
$377$		−	156.938i		−	0.416281i
$378$	−7.51612	−	130.749i	−0.0198839	−	0.345897i
$379$	199.618			0.526696			0.263348	−	0.964701i	$-0.415173\pi$
$379$	199.618			0.526696			0.263348	+	0.964701i	$0.415173\pi$
$380$			54.1364i			0.142464i
$381$	−255.425	+	462.637i	−0.670406	+	1.21427i
$382$	308.656			0.808001
$383$			722.487i			1.88639i	0.332242	+	0.943194i	$0.392195\pi$
$383$			722.487i			1.88639i	−0.332242	+	0.943194i	$0.607805\pi$
$384$	340.653	+	188.076i	0.887117	+	0.489782i
$385$	2.02201			0.00525198
$386$		−	245.983i		−	0.637262i
$387$	160.782	+	255.384i	0.415458	+	0.659907i
$388$	470.191			1.21183
$389$		−	689.844i		−	1.77338i	−0.462366	−	0.886689i	$-0.652999\pi$
$389$		−	689.844i		−	1.77338i	0.462366	−	0.886689i	$-0.347001\pi$
$390$	−9.92159	+	17.9705i	−0.0254400	+	0.0460781i
$391$	−13.5821			−0.0347368
$392$		−	100.928i		−	0.257471i
$393$	18.2238	+	10.0615i	0.0463711	+	0.0256017i
$394$	−13.8037			−0.0350348
$395$			221.568i			0.560931i
$396$	3.95222	−	2.48821i	0.00998036	−	0.00628335i
$397$	86.4994			0.217883			0.108941	−	0.994048i	$-0.465254\pi$
$397$	86.4994			0.217883			0.108941	+	0.994048i	$0.465254\pi$
$398$			2.74904i			0.00690714i
$399$	−61.1749	+	110.803i	−0.153321	+	0.277702i
$400$	−39.3762			−0.0984404
$401$			421.345i			1.05074i	0.850875	+	0.525368i	$0.176072\pi$
$401$			421.345i			1.05074i	−0.850875	+	0.525368i	$0.823928\pi$
$402$	−1.97556	−	1.09071i	−0.00491432	−	0.00271322i
$403$	−219.449			−0.544539
$404$			390.120i			0.965645i
$405$	163.323	+	78.2979i	0.403267	+	0.193328i
$406$	−211.129			−0.520022
$407$		−	2.57983i		−	0.00633864i
$408$	4.48045	−	8.11521i	0.0109815	−	0.0198902i
$409$	150.527			0.368036			0.184018	−	0.982923i	$-0.441090\pi$
$409$	150.527			0.368036			0.184018	+	0.982923i	$0.441090\pi$
$410$			73.8114i			0.180028i
$411$	−615.743	−	339.955i	−1.49816	−	0.827141i
$412$	−41.7028			−0.101220
$413$			331.492i			0.802643i
$414$	−110.517	−	175.543i	−0.266949	−	0.424017i
$415$	−15.9168			−0.0383538
$416$		−	113.204i		−	0.272124i
$417$	349.610	−	633.231i	0.838394	−	1.51854i
$418$	0.991266			0.00237145
$419$			125.374i			0.299221i	0.988745	+	0.149610i	$0.0478020\pi$
$419$			125.374i			0.299221i	−0.988745	+	0.149610i	$0.952198\pi$
$420$	−110.078	−	60.7746i	−0.262090	−	0.144701i
$421$	−389.483			−0.925138			−0.462569	−	0.886583i	$-0.653072\pi$
$421$	−389.483			−0.925138			−0.462569	+	0.886583i	$0.653072\pi$
$422$		−	248.714i		−	0.589370i
$423$	81.8278	−	51.5164i	0.193446	−	0.121788i
$424$	222.126			0.523883
$425$			2.50065i			0.00588389i
$426$	−87.3714	+	158.251i	−0.205097	+	0.371482i
$427$	−282.364			−0.661273
$428$			408.964i			0.955523i
$429$	−1.49824	−	0.827186i	−0.00349240	−	0.00192817i
$430$	−63.6343			−0.147987
$431$			200.331i			0.464806i	0.972620	+	0.232403i	$0.0746588\pi$
$431$			200.331i			0.464806i	−0.972620	+	0.232403i	$0.925341\pi$
$432$	−212.281	+	12.2030i	−0.491391	+	0.0282476i
$433$	83.6825			0.193262			0.0966310	−	0.995320i	$-0.469193\pi$
$433$	83.6825			0.193262			0.0966310	+	0.995320i	$0.469193\pi$
$434$			295.226i			0.680243i
$435$	141.127	−	255.615i	0.324429	−	0.587621i
$436$	532.059			1.22032
$437$			200.472i			0.458746i
$438$	−204.501	−	112.906i	−0.466897	−	0.257776i
$439$	−496.717			−1.13147			−0.565737	−	0.824586i	$-0.691408\pi$
$439$	−496.717			−1.13147			−0.565737	+	0.824586i	$0.691408\pi$
$440$			2.18584i			0.00496782i
$441$	78.3308	+	124.419i	0.177621	+	0.282130i
$442$	−1.53043			−0.00346250
$443$			752.790i			1.69930i	0.527348	+	0.849650i	$0.323187\pi$
$443$			752.790i			1.69930i	−0.527348	+	0.849650i	$0.676813\pi$
$444$	−77.5406	+	140.445i	−0.174641	+	0.316318i
$445$	−86.3821			−0.194117
$446$			198.961i			0.446100i
$447$	−141.815	−	78.2966i	−0.317259	−	0.175160i
$448$	27.7427			0.0619256
$449$		−	838.131i		−	1.86666i	−0.359019	−	0.933330i	$-0.616889\pi$
$449$		−	838.131i		−	1.86666i	0.359019	−	0.933330i	$-0.383111\pi$
$450$	−32.3199	+	20.3477i	−0.0718221	+	0.0452171i
$451$	−6.15382			−0.0136448
$452$		−	455.821i		−	1.00845i
$453$	14.9946	−	27.1590i	0.0331008	−	0.0599537i
$454$	−93.0675			−0.204994
$455$			46.0778i			0.101270i
$456$	−119.781	−	66.1315i	−0.262677	−	0.145025i
$457$	−508.996			−1.11378			−0.556889	−	0.830587i	$-0.688005\pi$
$457$	−508.996			−1.11378			−0.556889	+	0.830587i	$0.688005\pi$
$458$			62.3684i			0.136175i
$459$	0.774971	+	13.4813i	0.00168839	+	0.0293710i
$460$	−199.160			−0.432957
$461$			525.881i			1.14074i	0.821388	+	0.570370i	$0.193200\pi$
$461$			525.881i			1.14074i	−0.821388	+	0.570370i	$0.806800\pi$
$462$	−1.11282	+	2.01558i	−0.00240869	+	0.00436274i
$463$	−798.637			−1.72492			−0.862458	−	0.506128i	$-0.831076\pi$
$463$	−798.637			−1.72492			−0.862458	+	0.506128i	$0.831076\pi$
$464$			342.783i			0.738757i
$465$	−357.432	−	197.340i	−0.768670	−	0.424387i
$466$	27.7474			0.0595437
$467$			340.538i			0.729203i	0.931164	+	0.364602i	$0.118795\pi$
$467$			340.538i			0.729203i	−0.931164	+	0.364602i	$0.881205\pi$
$468$	56.7015	+	90.0637i	0.121157	+	0.192444i
$469$	−5.06550			−0.0108006
$470$			20.3891i			0.0433811i
$471$	163.960	−	296.972i	0.348110	−	0.630514i
$472$	−358.350			−0.759216
$473$		−	5.30534i		−	0.0112164i
$474$	−220.864	−	121.940i	−0.465957	−	0.257257i
$475$	36.9097			0.0777046
$476$		−	9.37461i		−	0.0196946i
$477$	−273.825	+	172.393i	−0.574057	+	0.361410i
$478$	257.866			0.539469
$479$		−	155.200i		−	0.324008i	−0.986790	−	0.162004i	$-0.948204\pi$
$479$		−	155.200i		−	0.324008i	0.986790	−	0.162004i	$-0.0517958\pi$
$480$	101.798	−	184.382i	0.212080	−	0.384130i
$481$	58.7894			0.122223
$482$			189.978i			0.394144i
$483$	−407.628	−	225.054i	−0.843951	−	0.465950i
$484$	396.762			0.819755
$485$		−	320.572i		−	0.660973i
$486$	−167.934	+	119.713i	−0.345543	+	0.246322i
$487$	−693.409			−1.42384			−0.711919	−	0.702262i	$-0.752174\pi$
$487$	−693.409			−1.42384			−0.711919	+	0.702262i	$0.752174\pi$
$488$		−	305.241i		−	0.625495i
$489$	−73.5972	+	133.303i	−0.150506	+	0.272603i
$490$	−31.0017			−0.0632687
$491$		−	170.137i		−	0.346512i	−0.984877	−	0.173256i	$-0.944571\pi$
$491$		−	170.137i		−	0.346512i	0.984877	−	0.173256i	$-0.0554287\pi$
$492$	335.013	+	184.963i	0.680921	+	0.375940i
$493$	21.7691			0.0441563
$494$			22.5891i			0.0457269i
$495$	−1.69644	−	2.69459i	−0.00342714	−	0.00544361i
$496$	479.320			0.966371
$497$			405.770i			0.816439i
$498$	8.75985	−	15.8663i	0.0175901	−	0.0318600i
$499$	478.723			0.959364			0.479682	−	0.877442i	$-0.340752\pi$
$499$	478.723			0.959364			0.479682	+	0.877442i	$0.340752\pi$
$500$			36.6682i			0.0733363i
$501$	−44.5166	−	24.5779i	−0.0888555	−	0.0490576i
$502$	−89.3514			−0.177991
$503$			33.3554i			0.0663130i	0.999450	+	0.0331565i	$0.0105560\pi$
$503$			33.3554i			0.0663130i	−0.999450	+	0.0331565i	$0.989444\pi$
$504$	268.936	−	169.315i	0.533603	−	0.335941i
$505$	265.980			0.526694
$506$			3.64673i			0.00720697i
$507$	18.8500	−	34.1420i	0.0371795	−	0.0673413i
$508$	−577.735			−1.13727
$509$			1011.65i			1.98753i	0.111495	+	0.993765i	$0.464436\pi$
$509$			1011.65i			1.98753i	−0.111495	+	0.993765i	$0.535564\pi$
$510$	−2.49271	−	1.37624i	−0.00488766	−	0.00269850i
$511$	−524.358			−1.02614
$512$			441.882i			0.863050i
$513$	198.984	−	11.4386i	0.387883	−	0.0222974i
$514$	−31.1585			−0.0606196
$515$			28.4325i			0.0552088i
$516$	−159.460	+	288.822i	−0.309031	+	0.559732i
$517$	−1.69989			−0.00328799
$518$		−	79.0895i		−	0.152683i
$519$	−668.132	−	368.879i	−1.28734	−	0.710750i
$520$	−49.8112			−0.0957907
$521$			297.809i			0.571611i	0.958288	+	0.285806i	$0.0922612\pi$
$521$			297.809i			0.571611i	−0.958288	+	0.285806i	$0.907739\pi$
$522$	177.134	+	281.356i	0.339337	+	0.538996i
$523$	516.262			0.987118			0.493559	−	0.869712i	$-0.335696\pi$
$523$	516.262			0.987118			0.493559	+	0.869712i	$0.335696\pi$
$524$			22.7577i			0.0434307i
$525$	−41.4355	+	75.0501i	−0.0789249	+	0.142953i
$526$	355.847			0.676516
$527$		−	30.4401i		−	0.0577611i
$528$	3.27245	+	1.80674i	0.00619782	+	0.00342185i
$529$	−208.507			−0.394153
$530$		−	68.2294i		−	0.128735i
$531$	441.755	−	278.116i	0.831930	−	0.523759i
$532$	−138.369			−0.260093
$533$		−	140.234i		−	0.263103i
$534$	47.5404	−	86.1075i	0.0890270	−	0.161250i
$535$	278.827			0.521173
$536$		−	5.47592i		−	0.0102163i
$537$	−224.943	−	124.192i	−0.418888	−	0.231270i
$538$	211.620			0.393345
$539$		−	2.58468i		−	0.00479533i
$540$	11.3637	+	197.682i	0.0210439	+	0.366077i
$541$	−95.5619			−0.176639			−0.0883197	−	0.996092i	$-0.528150\pi$
$541$	−95.5619			−0.176639			−0.0883197	+	0.996092i	$0.528150\pi$
$542$		−	304.514i		−	0.561834i
$543$	−392.302	+	710.556i	−0.722471	+	1.30857i
$544$	15.7026			0.0288651
$545$		−	362.753i		−	0.665601i
$546$	−45.9314	−	25.3590i	−0.0841234	−	0.0464450i
$547$	471.826			0.862570			0.431285	−	0.902216i	$-0.358060\pi$
$547$	471.826			0.862570			0.431285	+	0.902216i	$0.358060\pi$
$548$		−	768.932i		−	1.40316i
$549$	236.898	+	376.285i	0.431509	+	0.685401i
$550$	0.671413			0.00122075
$551$		−	321.312i		−	0.583143i
$552$	243.288	−	440.655i	0.440740	−	0.798289i
$553$	−566.313			−1.02407
$554$			160.006i			0.288819i
$555$	95.7543	+	52.8664i	0.172530	+	0.0952549i
$556$	790.771			1.42225
$557$			774.466i			1.39042i	0.718805	+	0.695212i	$0.244689\pi$
$557$			774.466i			1.39042i	−0.718805	+	0.695212i	$0.755311\pi$
$558$	393.425	−	247.689i	0.705064	−	0.443888i
$559$	120.899			0.216277
$560$		−	100.643i		−	0.179720i
$561$	0.114740	−	0.207823i	0.000204528	−	0.000370451i
$562$	349.408			0.621723
$563$		−	627.725i		−	1.11496i	−0.830189	−	0.557482i	$-0.811768\pi$
$563$		−	627.725i		−	1.11496i	0.830189	−	0.557482i	$-0.188232\pi$
$564$	92.5416	+	51.0927i	0.164081	+	0.0905899i
$565$	−310.774			−0.550043
$566$		−	224.108i		−	0.395951i
$567$	−200.125	+	417.444i	−0.352953	+	0.736232i
$568$	−438.647			−0.772266
$569$		−	958.228i		−	1.68406i	−0.539434	−	0.842028i	$-0.681362\pi$
$569$		−	958.228i		−	1.68406i	0.539434	−	0.842028i	$-0.318638\pi$
$570$	−20.3133	+	36.7924i	−0.0356373	+	0.0645480i
$571$	308.205			0.539764			0.269882	−	0.962893i	$-0.413015\pi$
$571$	308.205			0.539764			0.269882	+	0.962893i	$0.413015\pi$
$572$		−	1.87098i		−	0.00327094i
$573$	−955.134	−	527.335i	−1.66690	−	0.920305i
$574$	−188.657			−0.328671
$575$			135.785i			0.236149i
$576$	−23.2757	−	36.9706i	−0.0404091	−	0.0641851i
$577$	572.896			0.992888			0.496444	−	0.868069i	$-0.334639\pi$
$577$	572.896			0.992888			0.496444	+	0.868069i	$0.334639\pi$
$578$			245.063i			0.423985i
$579$	−420.258	+	761.192i	−0.725835	+	1.31467i
$580$	319.209			0.550360
$581$		−	40.6825i		−	0.0700214i
$582$	319.553	+	176.427i	0.549060	+	0.303139i
$583$	5.68844			0.00975719
$584$		−	566.843i		−	0.970622i
$585$	61.4045	−	38.6585i	0.104965	−	0.0660830i
$586$	−247.021			−0.421538
$587$			962.019i			1.63887i	0.573169	+	0.819437i	$0.305714\pi$
$587$			962.019i			1.63887i	−0.573169	+	0.819437i	$0.694286\pi$
$588$	−77.6865	+	140.710i	−0.132120	+	0.239302i
$589$	−449.296			−0.762811
$590$			110.073i			0.186564i
$591$	42.7154	+	23.5834i	0.0722765	+	0.0399043i
$592$	−128.408			−0.216905
$593$		−	897.607i		−	1.51367i	−0.653605	−	0.756836i	$-0.726744\pi$
$593$		−	897.607i		−	1.51367i	0.653605	−	0.756836i	$-0.273256\pi$
$594$	3.61966	−	0.208076i	0.00609370	−	0.000350296i
$595$	−6.39152			−0.0107420
$596$		−	177.096i		−	0.297141i
$597$	4.69670	−	8.50689i	0.00786717	−	0.0142494i
$598$	−83.1020			−0.138967
$599$			49.7559i			0.0830649i	0.999137	+	0.0415324i	$0.0132240\pi$
$599$			49.7559i			0.0830649i	−0.999137	+	0.0415324i	$0.986776\pi$
$600$	−81.1308	−	44.7928i	−0.135218	−	0.0746546i
$601$	878.878			1.46236			0.731180	−	0.682185i	$-0.238970\pi$
$601$	878.878			1.46236			0.731180	+	0.682185i	$0.238970\pi$
$602$		−	162.645i		−	0.270175i
$603$	4.24987	+	6.75041i	0.00704788	+	0.0111947i
$604$	33.9158			0.0561521
$605$		−	270.508i		−	0.447121i
$606$	−146.382	+	265.135i	−0.241555	+	0.437516i
$607$	−617.541			−1.01737			−0.508683	−	0.860954i	$-0.669868\pi$
$607$	−617.541			−1.01737			−0.508683	+	0.860954i	$0.669868\pi$
$608$		−	231.771i		−	0.381202i
$609$	653.337	+	360.711i	1.07280	+	0.592300i
$610$	−93.7594			−0.153704
$611$		−	38.7372i		−	0.0633997i
$612$	−12.4929	+	7.86515i	−0.0204132	+	0.0128515i
$613$	−769.368			−1.25509			−0.627543	−	0.778582i	$-0.715939\pi$
$613$	−769.368			−1.25509			−0.627543	+	0.778582i	$0.715939\pi$
$614$			111.743i			0.181993i
$615$	126.106	−	228.409i	0.205050	−	0.371396i
$616$	−5.58687			−0.00906960
$617$			550.095i			0.891564i	0.895142	+	0.445782i	$0.147074\pi$
$617$			550.095i			0.891564i	−0.895142	+	0.445782i	$0.852926\pi$
$618$	−28.3422	−	15.6479i	−0.0458611	−	0.0253202i
$619$	−442.627			−0.715069			−0.357534	−	0.933900i	$-0.616382\pi$
$619$	−442.627			−0.715069			−0.357534	+	0.933900i	$0.616382\pi$
$620$		−	446.356i		−	0.719929i
$621$	42.0809	+	732.033i	0.0677631	+	1.17880i
$622$	−62.7647			−0.100908
$623$		−	220.787i		−	0.354394i
$624$	−41.1721	+	74.5729i	−0.0659809	+	0.119508i
$625$	25.0000			0.0400000
$626$			207.049i			0.330749i
$627$	−3.06747	−	1.69356i	−0.00489229	−	0.00270106i
$628$	370.855			0.590533
$629$			8.15476i			0.0129646i
$630$	−52.0075	−	82.6077i	−0.0825515	−	0.131123i
$631$	−22.6368			−0.0358745			−0.0179372	−	0.999839i	$-0.505710\pi$
$631$	−22.6368			−0.0358745			−0.0179372	+	0.999839i	$0.505710\pi$
$632$		−	612.198i		−	0.968667i
$633$	−424.924	+	769.644i	−0.671287	+	1.21587i
$634$	213.559			0.336844
$635$			393.894i			0.620306i
$636$	−309.678	−	170.975i	−0.486915	−	0.268828i
$637$	58.9000			0.0924647
$638$		−	5.84489i		−	0.00916126i
$639$	540.740	−	340.435i	0.846229	−	0.532762i
$640$	290.035			0.453180
$641$		−	124.181i		−	0.193730i	−0.995298	−	0.0968651i	$-0.969118\pi$
$641$		−	124.181i		−	0.193730i	0.995298	−	0.0968651i	$-0.0308816\pi$
$642$	−153.453	+	277.941i	−0.239023	+	0.432930i
$643$	653.042			1.01562			0.507809	−	0.861470i	$-0.330456\pi$
$643$	653.042			1.01562			0.507809	+	0.861470i	$0.330456\pi$
$644$		−	509.041i		−	0.790436i
$645$	196.916	+	108.718i	0.305296	+	0.168555i
$646$	−3.13336			−0.00485041
$647$			16.5197i			0.0255328i	0.999919	+	0.0127664i	$0.00406378\pi$
$647$			16.5197i			0.0255328i	−0.999919	+	0.0127664i	$0.995936\pi$
$648$	−451.266	−	216.339i	−0.696398	−	0.333857i
$649$	−9.17700			−0.0141402
$650$			15.3002i			0.0235388i
$651$	504.388	−	913.573i	0.774790	−	1.40334i
$652$	−166.467			−0.255317
$653$		−	1109.50i		−	1.69908i	−0.527527	−	0.849538i	$-0.676881\pi$
$653$		−	1109.50i		−	1.69908i	0.527527	−	0.849538i	$-0.323119\pi$
$654$	361.600	+	199.641i	0.552905	+	0.305262i
$655$	15.5160			0.0236885
$656$			306.299i			0.466919i
$657$	439.928	+	698.774i	0.669601	+	1.06358i
$658$	−52.1133			−0.0791996
$659$		−	522.932i		−	0.793524i	−0.917921	−	0.396762i	$-0.870134\pi$
$659$		−	522.932i		−	0.793524i	0.917921	−	0.396762i	$-0.129866\pi$
$660$	1.68248	−	3.04739i	0.00254922	−	0.00461726i
$661$	−33.7392			−0.0510427			−0.0255214	−	0.999674i	$-0.508125\pi$
$661$	−33.7392			−0.0510427			−0.0255214	+	0.999674i	$0.508125\pi$
$662$			258.767i			0.390886i
$663$	4.73589	+	2.61471i	0.00714312	+	0.00394375i
$664$	43.9787			0.0662329
$665$			94.3389i			0.141863i
$666$	−105.397	+	66.3549i	−0.158254	+	0.0996319i
$667$	1182.06			1.77220
$668$		−	55.5917i		−	0.0832212i
$669$	339.921	−	615.682i	0.508103	−	0.920302i
$670$	−1.68201			−0.00251046
$671$		−	7.81694i		−	0.0116497i
$672$	471.270	+	260.190i	0.701294	+	0.387188i
$673$	321.918			0.478333			0.239166	−	0.970979i	$-0.423126\pi$
$673$	321.918			0.478333			0.239166	+	0.970979i	$0.423126\pi$
$674$			272.763i			0.404693i
$675$	134.777	−	7.74768i	0.199670	−	0.0114780i
$676$	42.6361			0.0630712
$677$		−	685.004i		−	1.01182i	−0.862585	−	0.505911i	$-0.831156\pi$
$677$		−	685.004i		−	1.01182i	0.862585	−	0.505911i	$-0.168844\pi$
$678$	171.035	−	309.786i	0.252264	−	0.456912i
$679$	819.362			1.20672
$680$		−	6.90938i		−	0.0101608i
$681$	287.996	+	159.004i	0.422902	+	0.233487i
$682$	−8.17301			−0.0119839
$683$			286.048i			0.418811i	0.977829	+	0.209405i	$0.0671528\pi$
$683$			286.048i			0.418811i	−0.977829	+	0.209405i	$0.932847\pi$
$684$	116.090	+	184.395i	0.169722	+	0.269583i
$685$	−524.250			−0.765329
$686$		−	316.916i		−	0.461976i
$687$	106.555	−	192.998i	0.155103	−	0.280929i
$688$	−264.066			−0.383818
$689$			129.629i			0.188141i
$690$	−135.354	−	74.7296i	−0.196165	−	0.108304i
$691$	−916.742			−1.32669			−0.663344	−	0.748314i	$-0.730863\pi$
$691$	−916.742			−1.32669			−0.663344	+	0.748314i	$0.730863\pi$
$692$		−	834.354i		−	1.20571i
$693$	6.88719	−	4.33598i	0.00993823	−	0.00625683i
$694$	−133.864			−0.192888
$695$		−	539.140i		−	0.775741i
$696$	−389.937	+	706.272i	−0.560254	+	1.01476i
$697$	19.4521			0.0279083
$698$			121.055i			0.173432i
$699$	−85.8640	−	47.4060i	−0.122838	−	0.0678197i
$700$	−93.7215			−0.133888
$701$			1301.07i			1.85601i	0.372564	+	0.928007i	$0.378479\pi$
$701$			1301.07i			1.85601i	−0.372564	+	0.928007i	$0.621521\pi$
$702$	4.74166	+	82.4851i	0.00675450	+	0.117500i
$703$	120.364			0.171215
$704$			0.768027i			0.00109095i
$705$	34.8345	−	63.0940i	0.0494107	−	0.0894950i
$706$	436.188			0.617830
$707$			679.829i			0.961569i
$708$	499.594	+	275.829i	0.705642	+	0.389589i
$709$	−906.182			−1.27811			−0.639056	−	0.769160i	$-0.720675\pi$
$709$	−906.182			−1.27811			−0.639056	+	0.769160i	$0.720675\pi$
$710$			134.737i			0.189770i
$711$	475.128	+	754.684i	0.668253	+	1.06144i
$712$	238.676			0.335219
$713$		−	1652.89i		−	2.31823i
$714$	3.51758	−	6.37120i	0.00492658	−	0.00892325i
$715$	−1.27562			−0.00178408
$716$		−	280.905i		−	0.392326i
$717$	−797.964	−	440.560i	−1.11292	−	0.614450i
$718$	−282.825			−0.393907
$719$			494.323i			0.687515i	0.939059	+	0.343757i	$0.111700\pi$
$719$			494.323i			0.687515i	−0.939059	+	0.343757i	$0.888300\pi$
$720$	−134.120	+	84.4379i	−0.186277	+	0.117275i
$721$	−72.6718			−0.100793
$722$		−	260.134i		−	0.360296i
$723$	324.574	−	587.884i	0.448927	−	0.813117i
$724$	−887.332			−1.22560
$725$		−	217.634i		−	0.300184i
$726$	269.649	+	148.874i	0.371417	+	0.205061i
$727$	1400.10			1.92586			0.962930	−	0.269750i	$-0.0869410\pi$
$727$	1400.10			1.92586			0.962930	+	0.269750i	$0.0869410\pi$
$728$		−	127.314i		−	0.174882i
$729$	724.198	−	83.5371i	0.993413	−	0.114591i
$730$	−174.114			−0.238513
$731$			16.7700i			0.0229412i
$732$	−234.950	+	425.553i	−0.320970	+	0.581356i
$733$	−306.793			−0.418545			−0.209273	−	0.977857i	$-0.567110\pi$
$733$	−306.793			−0.418545			−0.209273	+	0.977857i	$0.567110\pi$
$734$		−	255.533i		−	0.348138i
$735$	95.9344	+	52.9659i	0.130523	+	0.0720625i
$736$	852.651			1.15849
$737$		−	0.140233i		−	0.000190275i
$738$	158.280	+	251.410i	0.214472	+	0.340664i
$739$	752.077			1.01770			0.508848	−	0.860857i	$-0.330072\pi$
$739$	752.077			1.01770			0.508848	+	0.860857i	$0.330072\pi$
$740$			119.577i			0.161590i
$741$	38.5931	−	69.9017i	0.0520825	−	0.0943343i
$742$	174.390			0.235027
$743$			856.194i			1.15235i	0.817327	+	0.576174i	$0.195455\pi$
$743$			856.194i			1.15235i	−0.817327	+	0.576174i	$0.804545\pi$
$744$	987.593	+	545.255i	1.32741	+	0.732870i
$745$	−120.742			−0.162070
$746$			479.414i			0.642646i
$747$	−54.2145	+	34.1319i	−0.0725764	+	0.0456920i
$748$	0.259526			0.000346960
$749$			712.666i			0.951489i
$750$	−13.7588	+	24.9205i	−0.0183450	+	0.0332274i
$751$	637.103			0.848339			0.424170	−	0.905583i	$-0.360566\pi$
$751$	637.103			0.848339			0.424170	+	0.905583i	$0.360566\pi$
$752$			84.6098i			0.112513i
$753$	276.497	+	152.656i	0.367194	+	0.202730i
$754$	133.194			0.176650
$755$		−	23.1235i		−	0.0306271i
$756$	−505.262	+	29.0450i	−0.668336	+	0.0384193i
$757$	−85.9070			−0.113484			−0.0567418	−	0.998389i	$-0.518071\pi$
$757$	−85.9070			−0.113484			−0.0567418	+	0.998389i	$0.518071\pi$
$758$			169.417i			0.223505i
$759$	6.23038	−	11.2848i	0.00820867	−	0.0148679i
$760$	−101.982			−0.134187
$761$		−	8.96052i		−	0.0117747i	−0.999983	−	0.00588734i	$-0.998126\pi$
$761$		−	8.96052i		−	0.0117747i	0.999983	−	0.00588734i	$-0.00187401\pi$
$762$	−392.643	−	216.780i	−0.515279	−	0.284488i
$763$	927.173			1.21517
$764$		−	1192.76i		−	1.56120i
$765$	5.36238	+	8.51751i	0.00700965	+	0.0111340i
$766$	−613.178			−0.800493
$767$		−	209.127i		−	0.272655i
$768$	−131.467	+	238.120i	−0.171181	+	0.310052i
$769$	−241.067			−0.313481			−0.156741	−	0.987640i	$-0.550099\pi$
$769$	−241.067			−0.313481			−0.156741	+	0.987640i	$0.550099\pi$
$770$			1.71609i			0.00222869i
$771$	96.4196	+	53.2338i	0.125058	+	0.0690451i
$772$	−950.567			−1.23130
$773$			192.332i			0.248813i	0.992231	+	0.124406i	$0.0397026\pi$
$773$			192.332i			0.248813i	−0.992231	+	0.124406i	$0.960297\pi$
$774$	−216.745	+	136.457i	−0.280033	+	0.176301i
$775$	−304.321			−0.392672
$776$			885.749i			1.14143i
$777$	−135.123	+	244.742i	−0.173904	+	0.314983i
$778$	585.474			0.752537
$779$		−	287.112i		−	0.368565i
$780$	69.4443	+	38.3406i	0.0890312	+	0.0491546i
$781$	−11.2333			−0.0143833
$782$		−	11.5272i		−	0.0147407i
$783$	−67.4462	−	1173.28i	−0.0861382	−	1.49845i
$784$	−128.649			−0.164093
$785$		−	252.845i		−	0.322096i
$786$	−8.53922	+	15.4667i	−0.0108642	+	0.0196777i
$787$	−571.119			−0.725691			−0.362846	−	0.931849i	$-0.618195\pi$
$787$	−571.119			−0.725691			−0.362846	+	0.931849i	$0.618195\pi$
$788$			53.3425i			0.0676935i
$789$	−1101.17	−	607.960i	−1.39565	−	0.770545i
$790$	−188.046			−0.238032
$791$		−	794.319i		−	1.00420i
$792$	4.68730	+	7.44522i	0.00591830	+	0.00940052i
$793$	178.133			0.224632
$794$			73.4124i			0.0924590i
$795$	−116.569	+	211.135i	−0.146628	+	0.265579i
$796$	10.6233			0.0133458
$797$		−	1286.29i		−	1.61391i	−0.590613	−	0.806955i	$-0.701114\pi$
$797$		−	1286.29i		−	1.61391i	0.590613	−	0.806955i	$-0.298886\pi$
$798$	−94.0390	−	51.9194i	−0.117843	−	0.0650620i
$799$	5.37330			0.00672503
$800$		−	156.985i		−	0.196231i
$801$	−294.227	+	185.237i	−0.367325	+	0.231257i
$802$	−357.597			−0.445882
$803$		−	14.5163i		−	0.0180776i
$804$	−4.21491	+	7.63426i	−0.00524243	+	0.00949534i
$805$	−347.059			−0.431129
$806$		−	186.247i		−	0.231076i
$807$	−654.855	−	361.549i	−0.811469	−	0.448016i
$808$	−734.911			−0.909543
$809$			698.286i			0.863147i	0.902078	+	0.431574i	$0.142041\pi$
$809$			698.286i			0.863147i	−0.902078	+	0.431574i	$0.857959\pi$
$810$	−66.4518	+	138.613i	−0.0820393	+	0.171127i
$811$	348.537			0.429762			0.214881	−	0.976640i	$-0.431064\pi$
$811$	348.537			0.429762			0.214881	+	0.976640i	$0.431064\pi$
$812$			815.878i			1.00478i
$813$	−520.258	+	942.316i	−0.639924	+	1.15906i
$814$	2.18951			0.00268982
$815$			113.496i			0.139258i
$816$	−10.3441	−	5.71104i	−0.0126766	−	0.00699882i
$817$	247.526			0.302969
$818$			127.753i			0.156177i
$819$	98.8088	+	156.946i	0.120646	+	0.191631i
$820$	285.234			0.347846
$821$		−	617.371i		−	0.751974i	−0.926625	−	0.375987i	$-0.877304\pi$
$821$		−	617.371i		−	0.751974i	0.926625	−	0.375987i	$-0.122696\pi$
$822$	288.522	−	522.584i	0.350999	−	0.635747i
$823$	16.1089			0.0195733			0.00978667	−	0.999952i	$-0.496885\pi$
$823$	16.1089			0.0195733			0.00978667	+	0.999952i	$0.496885\pi$
$824$		−	78.5599i		−	0.0953397i
$825$	−2.07768	−	1.14710i	−0.00251840	−	0.00139042i
$826$	−281.339			−0.340604
$827$		−	285.662i		−	0.345420i	−0.984973	−	0.172710i	$-0.944748\pi$
$827$		−	285.662i		−	0.345420i	0.984973	−	0.172710i	$-0.0552523\pi$
$828$	−678.361	+	427.077i	−0.819277	+	0.515793i
$829$	−898.304			−1.08360			−0.541800	−	0.840508i	$-0.682257\pi$
$829$	−898.304			−1.08360			−0.541800	+	0.840508i	$0.682257\pi$
$830$		−	13.5087i		−	0.0162755i
$831$	273.368	−	495.137i	0.328962	−	0.595832i
$832$	−17.5019			−0.0210359
$833$			8.17010i			0.00980804i
$834$	537.426	+	296.716i	0.644396	+	0.355774i
$835$	−37.9019			−0.0453915
$836$		−	3.83061i		−	0.00458207i
$837$	−1640.63	+	94.3113i	−1.96013	+	0.112678i
$838$	−106.405			−0.126975
$839$			841.177i			1.00259i	0.865275	+	0.501297i	$0.167144\pi$
$839$			841.177i			1.00259i	−0.865275	+	0.501297i	$0.832856\pi$
$840$	114.488	−	207.365i	0.136295	−	0.246864i
$841$	−1053.58			−1.25277
$842$		−	330.556i		−	0.392585i
$843$	−1081.24	−	596.959i	−1.28261	−	0.708136i
$844$	−961.121			−1.13877
$845$		−	29.0689i		−	0.0344010i
$846$	43.7222	+	69.4476i	0.0516811	+	0.0820894i
$847$	691.402			0.816295
$848$		−	283.135i		−	0.333886i
$849$	−382.886	+	693.501i	−0.450984	+	0.816845i
$850$	−2.12232			−0.00249684
$851$			442.803i			0.520332i
$852$	611.540	+	337.635i	0.717770	+	0.396285i
$853$	−818.451			−0.959497			−0.479748	−	0.877406i	$-0.659272\pi$
$853$	−818.451			−0.959497			−0.479748	+	0.877406i	$0.659272\pi$
$854$		−	239.643i		−	0.280613i
$855$	125.718	−	79.1488i	0.147039	−	0.0925717i
$856$	−770.408			−0.900009
$857$		−	128.481i		−	0.149919i	−0.997187	−	0.0749597i	$-0.976117\pi$
$857$		−	128.481i		−	0.149919i	0.997187	−	0.0749597i	$-0.0238828\pi$
$858$	0.702036	−	1.27156i	0.000818224	−	0.00148201i
$859$	−1622.62			−1.88897			−0.944484	−	0.328558i	$-0.893438\pi$
$859$	−1622.62			−1.88897			−0.944484	+	0.328558i	$0.893438\pi$
$860$			245.906i			0.285937i
$861$	583.798	+	322.318i	0.678047	+	0.374353i
$862$	−170.022			−0.197241
$863$			320.079i			0.370892i	0.982655	+	0.185446i	$0.0593729\pi$
$863$			320.079i			0.370892i	−0.982655	+	0.185446i	$0.940627\pi$
$864$	−48.6508	−	846.322i	−0.0563088	−	0.979540i
$865$	−568.854			−0.657635
$866$			71.0217i			0.0820112i
$867$	418.687	−	758.347i	0.482915	−	0.874679i
$868$	1140.86			1.31435
$869$		−	15.6778i		−	0.0180412i
$870$	216.942	+	119.775i	0.249359	+	0.137672i
$871$	3.19564			0.00366894
$872$			1002.30i			1.14942i
$873$	−687.431	−	1091.90i	−0.787436	−	1.25075i
$874$	−170.141			−0.194670
$875$			63.8984i			0.0730268i
$876$	−436.310	+	790.265i	−0.498070	+	0.902129i
$877$	1031.81			1.17652			0.588260	−	0.808672i	$-0.299813\pi$
$877$	1031.81			1.17652			0.588260	+	0.808672i	$0.299813\pi$
$878$		−	421.566i		−	0.480144i
$879$	764.405	+	422.032i	0.869631	+	0.480128i
$880$	2.78620			0.00316613
$881$			1422.50i			1.61464i	0.590116	+	0.807318i	$0.299082\pi$
$881$			1422.50i			1.61464i	−0.590116	+	0.807318i	$0.700918\pi$
$882$	−105.595	+	66.4797i	−0.119722	+	0.0753738i
$883$	977.285			1.10678			0.553389	−	0.832923i	$-0.313334\pi$
$883$	977.285			1.10678			0.553389	+	0.832923i	$0.313334\pi$
$884$			5.91411i			0.00669017i
$885$	188.057	−	340.619i	0.212494	−	0.384880i
$886$	−638.896			−0.721102
$887$		−	797.224i		−	0.898786i	−0.893334	−	0.449393i	$-0.851640\pi$
$887$		−	797.224i		−	0.898786i	0.893334	−	0.449393i	$-0.148360\pi$
$888$	−264.572	−	146.071i	−0.297941	−	0.164495i
$889$	−1006.77			−1.13247
$890$		−	73.3129i		−	0.0823740i
$891$	−11.5565	−	5.54024i	−0.0129702	−	0.00621800i
$892$	768.855			0.861945
$893$		−	79.3099i		−	0.0888129i
$894$	66.4507	−	120.359i	0.0743297	−	0.134629i
$895$	−191.519			−0.213987
$896$			741.312i			0.827358i
$897$	257.158	+	141.979i	0.286687	+	0.158282i
$898$	711.325			0.792122
$899$			2649.22i			2.94685i
$900$	78.6309	+	124.896i	0.0873676	+	0.138773i
$901$	−17.9810			−0.0199567
$902$		−	5.22278i		−	0.00579022i
$903$	−277.877	+	503.304i	−0.307727	+	0.557369i
$904$	858.677			0.949864
$905$			604.975i			0.668480i
$906$	23.0500	+	12.7260i	0.0254415	+	0.0140464i
$907$	−653.403			−0.720401			−0.360200	−	0.932875i	$-0.617292\pi$
$907$	−653.403			−0.720401			−0.360200	+	0.932875i	$0.617292\pi$
$908$			359.646i			0.396086i
$909$	905.958	−	570.366i	0.996654	−	0.627465i
$910$	−39.1065			−0.0429741
$911$			1649.26i			1.81038i	0.425002	+	0.905192i	$0.360273\pi$
$911$			1649.26i			1.81038i	−0.425002	+	0.905192i	$0.639727\pi$
$912$	−84.2950	+	152.679i	−0.0924287	+	0.167411i
$913$	1.12625			0.00123357
$914$		−	431.988i		−	0.472634i
$915$	290.138	+	160.187i	0.317090	+	0.175067i
$916$	241.014			0.263116
$917$			39.6578i			0.0432474i
$918$	−11.4416	+	0.657722i	−0.0124636	+	0.000716472i
$919$	757.286			0.824032			0.412016	−	0.911177i	$-0.364825\pi$
$919$	757.286			0.824032			0.412016	+	0.911177i	$0.364825\pi$
$920$		−	375.179i		−	0.407803i
$921$	190.912	−	345.789i	0.207288	−	0.375450i
$922$	−446.318			−0.484075
$923$		−	255.986i		−	0.277342i
$924$	7.78895	+	4.30032i	0.00842959	+	0.00465402i
$925$	81.5262			0.0881364
$926$		−	677.807i		−	0.731973i
$927$	60.9705	+	96.8444i	0.0657718	+	0.104471i
$928$	−1366.61			−1.47264
$929$		−	492.309i		−	0.529935i	−0.964257	−	0.264967i	$-0.914639\pi$
$929$		−	492.309i		−	0.529935i	0.964257	−	0.264967i	$-0.0853612\pi$
$930$	167.483	−	303.354i	0.180090	−	0.326187i
$931$	120.591			0.129528
$932$		−	107.226i		−	0.115049i
$933$	194.225	+	107.232i	0.208172	+	0.114933i
$934$	−289.016			−0.309439
$935$		−	0.176943i		−	0.000189243i
$936$	−169.662	+	106.815i	−0.181263	+	0.114118i
$937$	895.346			0.955546			0.477773	−	0.878483i	$-0.341444\pi$
$937$	895.346			0.955546			0.477773	+	0.878483i	$0.341444\pi$
$938$		−	4.29911i		−	0.00458327i
$939$	353.740	−	640.711i	0.376720	−	0.682333i
$940$	78.7909			0.0838201
$941$		−	963.944i		−	1.02438i	−0.858872	−	0.512191i	$-0.828834\pi$
$941$		−	963.944i		−	1.02438i	0.858872	−	0.512191i	$-0.171166\pi$
$942$	252.042	+	139.154i	0.267560	+	0.147721i
$943$	1056.25			1.12009
$944$			456.774i			0.483870i
$945$	19.8026	+	344.483i	0.0209551	+	0.364532i
$946$	4.50267			0.00475969
$947$		−	1726.05i		−	1.82265i	−0.411691	−	0.911324i	$-0.635062\pi$
$947$		−	1726.05i		−	1.82265i	0.411691	−	0.911324i	$-0.364938\pi$
$948$	−471.220	+	853.496i	−0.497067	+	0.900312i
$949$	330.799			0.348577
$950$			31.3254i			0.0329741i
$951$	−660.857	−	364.863i	−0.694908	−	0.383662i
$952$	17.6599			0.0185504
$953$			716.413i			0.751745i	0.926671	+	0.375873i	$0.122657\pi$
$953$			716.413i			0.751745i	−0.926671	+	0.375873i	$0.877343\pi$
$954$	−146.310	−	232.397i	−0.153365	−	0.243603i
$955$	−813.212			−0.851531
$956$		−	996.487i		−	1.04235i
$957$	−9.98590	+	18.0869i	−0.0104346	+	0.0188996i
$958$	131.719			0.137494
$959$		−	1339.95i		−	1.39724i
$960$	−28.5065	−	15.7386i	−0.0296943	−	0.0163944i
$961$	2743.45			2.85479
$962$			49.8948i			0.0518657i
$963$	949.717	−	597.915i	0.986207	−	0.620888i
$964$	734.142			0.761558
$965$			648.087i			0.671593i
$966$	191.004	−	345.956i	0.197727	−	0.358132i
$967$	252.597			0.261218			0.130609	−	0.991434i	$-0.458307\pi$
$967$	252.597			0.261218			0.130609	+	0.991434i	$0.458307\pi$
$968$			747.422i			0.772130i
$969$	9.69617	+	5.35331i	0.0100064	+	0.00552457i
$970$	272.071			0.280485
$971$		−	476.368i		−	0.490596i	−0.969448	−	0.245298i	$-0.921114\pi$
$971$		−	476.368i		−	0.490596i	0.969448	−	0.245298i	$-0.0788858\pi$
$972$	462.613	+	648.958i	0.475939	+	0.667652i
$973$	1378.01			1.41625
$974$		−	588.500i		−	0.604209i
$975$	26.1402	−	47.3465i	0.0268105	−	0.0485605i
$976$	−389.078			−0.398646
$977$			232.241i			0.237709i	0.992912	+	0.118854i	$0.0379222\pi$
$977$			232.241i			0.237709i	−0.992912	+	0.118854i	$0.962078\pi$
$978$	−113.135	−	62.4623i	−0.115680	−	0.0638674i
$979$	6.11226			0.00624337
$980$			119.802i			0.122247i
$981$	−777.883	−	1235.58i	−0.792949	−	1.25951i
$982$	144.396			0.147043
$983$			774.697i			0.788094i	0.919090	+	0.394047i	$0.128925\pi$
$983$			774.697i			0.788094i	−0.919090	+	0.394047i	$0.871075\pi$
$984$	−348.433	+	631.099i	−0.354099	+	0.641361i
$985$	36.3684			0.0369222
$986$			18.4755i			0.0187378i
$987$	161.264	+	89.0349i	0.163388	+	0.0902076i
$988$	87.2924			0.0883526
$989$			910.611i			0.920739i
$990$	2.28691	−	1.43977i	0.00231001	−	0.00145432i
$991$	−829.027			−0.836556			−0.418278	−	0.908319i	$-0.637366\pi$
$991$	−829.027			−0.836556			−0.418278	+	0.908319i	$0.637366\pi$
$992$			1910.95i			1.92637i
$993$	442.099	−	800.752i	0.445216	−	0.806396i
$994$	−344.379			−0.346458
$995$		−	7.24285i		−	0.00727925i
$996$	−61.3129	−	33.8512i	−0.0615592	−	0.0339871i
$997$	−1721.22			−1.72640			−0.863199	−	0.504864i	$-0.831543\pi$
$997$	−1721.22			−1.72640			−0.863199	+	0.504864i	$0.831543\pi$
$998$			406.294i			0.407108i
$999$	439.516	−	25.2656i	0.439956	−	0.0252909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.3.d.a.131.18	yes	32
3.2	odd	2	inner	195.3.d.a.131.15	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.3.d.a.131.15	✓	32	3.2	odd	2	inner
195.3.d.a.131.18	yes	32	1.1	even	1	trivial

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+0.848705i q^{2} +(1.45000 - 2.62631i) q^{3} +3.27970 q^{4} -2.23607i q^{5} +(2.22896 + 1.23062i) q^{6} +5.71525 q^{7} +6.17832i q^{8} +(-4.79500 - 7.61630i) q^{9} +1.89776 q^{10} +0.158221i q^{11} +(4.75556 - 8.61351i) q^{12} -3.60555 q^{13} +4.85056i q^{14} +(-5.87261 - 3.24230i) q^{15} +7.87524 q^{16} -0.500131i q^{17} +(6.46399 - 4.06954i) q^{18} -7.38194 q^{19} -7.33363i q^{20} +(8.28711 - 15.0100i) q^{21} -0.134283 q^{22} -27.1571i q^{23} +(16.2262 + 8.95856i) q^{24} -5.00000 q^{25} -3.06005i q^{26} +(-26.9555 + 1.54954i) q^{27} +18.7443 q^{28} +43.5267i q^{29} +(2.75175 - 4.98411i) q^{30} +60.8642 q^{31} +31.3970i q^{32} +(0.415537 + 0.229420i) q^{33} +0.424464 q^{34} -12.7797i q^{35} +(-15.7262 - 24.9792i) q^{36} -16.3052 q^{37} -6.26509i q^{38} +(-5.22805 + 9.46929i) q^{39} +13.8151 q^{40} +38.8939i q^{41} +(12.7391 + 7.03331i) q^{42} -33.5312 q^{43} +0.518917i q^{44} +(-17.0306 + 10.7220i) q^{45} +23.0483 q^{46} +10.7438i q^{47} +(11.4191 - 20.6828i) q^{48} -16.3359 q^{49} -4.24352i q^{50} +(-1.31350 - 0.725190i) q^{51} -11.8251 q^{52} -35.9526i q^{53} +(-1.31510 - 22.8773i) q^{54} +0.353792 q^{55} +35.3106i q^{56} +(-10.7038 + 19.3873i) q^{57} -36.9413 q^{58} +58.0013i q^{59} +(-19.2604 - 10.6338i) q^{60} -49.4053 q^{61} +51.6558i q^{62} +(-27.4046 - 43.5290i) q^{63} +4.85415 q^{64} +8.06226i q^{65} +(-0.194710 + 0.352668i) q^{66} -0.886312 q^{67} -1.64028i q^{68} +(-71.3229 - 39.3778i) q^{69} +10.8462 q^{70} +70.9978i q^{71} +(47.0559 - 29.6250i) q^{72} -91.7472 q^{73} -13.8383i q^{74} +(-7.25000 + 13.1315i) q^{75} -24.2105 q^{76} +0.904271i q^{77} +(-8.03663 - 4.43707i) q^{78} -99.0881 q^{79} -17.6096i q^{80} +(-35.0159 + 73.0403i) q^{81} -33.0095 q^{82} -7.11823i q^{83} +(27.1792 - 49.2283i) q^{84} -1.11833 q^{85} -28.4581i q^{86} +(114.315 + 63.1137i) q^{87} -0.977538 q^{88} -38.6312i q^{89} +(-9.09977 - 14.4539i) q^{90} -20.6066 q^{91} -89.0671i q^{92} +(88.2531 - 159.848i) q^{93} -9.11829 q^{94} +16.5065i q^{95} +(82.4583 + 45.5257i) q^{96} +143.364 q^{97} -13.8644i q^{98} +(1.20506 - 0.758669i) 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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