LMFDB - Embedded newform 195.3.d.a.131.12

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)

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")

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);

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			131.12
Character	$\chi$	$=$	195.131
Dual form			195.3.d.a.131.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.11947i q^{2} +(2.93515 - 0.620391i) q^{3} +2.74679 q^{4} -2.23607i q^{5} +(-0.694509 - 3.28581i) q^{6} -5.59346 q^{7} -7.55282i q^{8} +(8.23023 - 3.64188i) q^{9} -2.50321 q^{10} -6.16296i q^{11} +(8.06224 - 1.70408i) q^{12} -3.60555 q^{13} +6.26171i q^{14} +(-1.38724 - 6.56320i) q^{15} +2.53200 q^{16} +15.1180i q^{17} +(-4.07698 - 9.21349i) q^{18} +20.3138 q^{19} -6.14200i q^{20} +(-16.4177 + 3.47013i) q^{21} -6.89924 q^{22} +33.6359i q^{23} +(-4.68570 - 22.1687i) q^{24} -5.00000 q^{25} +4.03630i q^{26} +(21.8976 - 15.7954i) q^{27} -15.3641 q^{28} -7.19415i q^{29} +(-7.34730 + 1.55297i) q^{30} -24.0139 q^{31} -33.0458i q^{32} +(-3.82344 - 18.0892i) q^{33} +16.9242 q^{34} +12.5074i q^{35} +(22.6067 - 10.0035i) q^{36} +22.3357 q^{37} -22.7407i q^{38} +(-10.5828 + 2.23685i) q^{39} -16.8886 q^{40} -21.1281i q^{41} +(3.88471 + 18.3791i) q^{42} -43.3742 q^{43} -16.9283i q^{44} +(-8.14350 - 18.4034i) q^{45} +37.6544 q^{46} +76.6441i q^{47} +(7.43179 - 1.57083i) q^{48} -17.7132 q^{49} +5.59735i q^{50} +(9.37910 + 44.3737i) q^{51} -9.90368 q^{52} +85.5633i q^{53} +(-17.6825 - 24.5137i) q^{54} -13.7808 q^{55} +42.2464i q^{56} +(59.6242 - 12.6025i) q^{57} -8.05364 q^{58} -16.4722i q^{59} +(-3.81044 - 18.0277i) q^{60} +65.6450 q^{61} +26.8829i q^{62} +(-46.0355 + 20.3707i) q^{63} -26.8658 q^{64} +8.06226i q^{65} +(-20.2503 + 4.28023i) q^{66} +46.7201 q^{67} +41.5260i q^{68} +(20.8674 + 98.7265i) q^{69} +14.0016 q^{70} +91.1773i q^{71} +(-27.5065 - 62.1615i) q^{72} -82.8650 q^{73} -25.0041i q^{74} +(-14.6758 + 3.10196i) q^{75} +55.7978 q^{76} +34.4723i q^{77} +(2.50409 + 11.8472i) q^{78} +60.9960 q^{79} -5.66172i q^{80} +(54.4734 - 59.9471i) q^{81} -23.6523 q^{82} -106.124i q^{83} +(-45.0958 + 9.53172i) q^{84} +33.8050 q^{85} +48.5561i q^{86} +(-4.46319 - 21.1159i) q^{87} -46.5477 q^{88} +89.3690i q^{89} +(-20.6020 + 9.11640i) q^{90} +20.1675 q^{91} +92.3907i q^{92} +(-70.4845 + 14.8980i) q^{93} +85.8008 q^{94} -45.4231i q^{95} +(-20.5013 - 96.9944i) q^{96} -90.4120 q^{97} +19.8294i q^{98} +(-22.4448 - 50.7226i) 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 $

$2$		−	1.11947i		−	0.559735i	−0.960039	−	0.279867i	$-0.909710\pi$
$2$		−	1.11947i		−	0.559735i	0.960039	−	0.279867i	$-0.0902905\pi$
$3$	2.93515	−	0.620391i	0.978384	−	0.206797i
$3$	2.93515	−	0.620391i	0.978384	−	0.206797i
$4$	2.74679			0.686697
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	−0.694509	−	3.28581i	−0.115751	−	0.547635i
$7$	−5.59346			−0.799066			−0.399533	−	0.916719i	$-0.630828\pi$
$7$	−5.59346			−0.799066			−0.399533	+	0.916719i	$0.630828\pi$
$8$		−	7.55282i		−	0.944103i
$9$	8.23023	−	3.64188i	0.914470	−	0.404654i
$10$	−2.50321			−0.250321
$11$		−	6.16296i		−	0.560269i	−0.959961	−	0.280134i	$-0.909621\pi$
$11$		−	6.16296i		−	0.560269i	0.959961	−	0.280134i	$-0.0903791\pi$
$12$	8.06224	−	1.70408i	0.671853	−	0.142007i
$13$	−3.60555			−0.277350
$13$	−3.60555			−0.277350
$14$			6.26171i			0.447265i
$15$	−1.38724	−	6.56320i	−0.0924824	−	0.437547i
$16$	2.53200			0.158250
$17$			15.1180i			0.889296i	0.895705	+	0.444648i	$0.146671\pi$
$17$			15.1180i			0.889296i	−0.895705	+	0.444648i	$0.853329\pi$
$18$	−4.07698	−	9.21349i	−0.226499	−	0.511861i
$19$	20.3138			1.06915			0.534575	−	0.845121i	$-0.320472\pi$
$19$	20.3138			1.06915			0.534575	+	0.845121i	$0.320472\pi$
$20$		−	6.14200i		−	0.307100i
$21$	−16.4177	+	3.47013i	−0.781793	+	0.165244i
$22$	−6.89924			−0.313602
$23$			33.6359i			1.46243i	0.682147	+	0.731215i	$0.261046\pi$
$23$			33.6359i			1.46243i	−0.682147	+	0.731215i	$0.738954\pi$
$24$	−4.68570	−	22.1687i	−0.195238	−	0.923695i
$25$	−5.00000			−0.200000
$26$			4.03630i			0.155242i
$27$	21.8976	−	15.7954i	0.811021	−	0.585016i
$28$	−15.3641			−0.548716
$29$		−	7.19415i		−	0.248074i	−0.992278	−	0.124037i	$-0.960416\pi$
$29$		−	7.19415i		−	0.248074i	0.992278	−	0.124037i	$-0.0395842\pi$
$30$	−7.34730	+	1.55297i	−0.244910	+	0.0517656i
$31$	−24.0139			−0.774643			−0.387322	−	0.921945i	$-0.626600\pi$
$31$	−24.0139			−0.774643			−0.387322	+	0.921945i	$0.626600\pi$
$32$		−	33.0458i		−	1.03268i
$33$	−3.82344	−	18.0892i	−0.115862	−	0.548158i
$34$	16.9242			0.497770
$35$			12.5074i			0.357353i
$36$	22.6067	−	10.0035i	0.627964	−	0.277875i
$37$	22.3357			0.603668			0.301834	−	0.953361i	$-0.402401\pi$
$37$	22.3357			0.603668			0.301834	+	0.953361i	$0.402401\pi$
$38$		−	22.7407i		−	0.598440i
$39$	−10.5828	+	2.23685i	−0.271355	+	0.0573552i
$40$	−16.8886			−0.422216
$41$		−	21.1281i		−	0.515320i	−0.966236	−	0.257660i	$-0.917048\pi$
$41$		−	21.1281i		−	0.515320i	0.966236	−	0.257660i	$-0.0829515\pi$
$42$	3.88471	+	18.3791i	0.0924931	+	0.437597i
$43$	−43.3742			−1.00870			−0.504351	−	0.863499i	$-0.668268\pi$
$43$	−43.3742			−1.00870			−0.504351	+	0.863499i	$0.668268\pi$
$44$		−	16.9283i		−	0.384735i
$45$	−8.14350	−	18.4034i	−0.180967	−	0.408963i
$46$	37.6544			0.818573
$47$			76.6441i			1.63073i	0.578950	+	0.815363i	$0.303463\pi$
$47$			76.6441i			1.63073i	−0.578950	+	0.815363i	$0.696537\pi$
$48$	7.43179	−	1.57083i	0.154829	−	0.0327256i
$49$	−17.7132			−0.361493
$50$			5.59735i			0.111947i
$51$	9.37910	+	44.3737i	0.183904	+	0.870073i
$52$	−9.90368			−0.190455
$53$			85.5633i			1.61440i	0.590277	+	0.807201i	$0.299019\pi$
$53$			85.5633i			1.61440i	−0.590277	+	0.807201i	$0.700981\pi$
$54$	−17.6825	−	24.5137i	−0.327454	−	0.453957i
$55$	−13.7808			−0.250560
$56$			42.2464i			0.754401i
$57$	59.6242	−	12.6025i	1.04604	−	0.221097i
$58$	−8.05364			−0.138856
$59$		−	16.4722i		−	0.279190i	−0.990209	−	0.139595i	$-0.955420\pi$
$59$		−	16.4722i		−	0.279190i	0.990209	−	0.139595i	$-0.0445800\pi$
$60$	−3.81044	−	18.0277i	−0.0635074	−	0.300462i
$61$	65.6450			1.07615			0.538074	−	0.842898i	$-0.319152\pi$
$61$	65.6450			1.07615			0.538074	+	0.842898i	$0.319152\pi$
$62$			26.8829i			0.433595i
$63$	−46.0355	+	20.3707i	−0.730722	+	0.323345i
$64$	−26.8658			−0.419778
$65$			8.06226i			0.124035i
$66$	−20.2503	+	4.28023i	−0.306823	+	0.0648520i
$67$	46.7201			0.697315			0.348657	−	0.937250i	$-0.386638\pi$
$67$	46.7201			0.697315			0.348657	+	0.937250i	$0.386638\pi$
$68$			41.5260i			0.610677i
$69$	20.8674	+	98.7265i	0.302426	+	1.43082i
$70$	14.0016			0.200023
$71$			91.1773i			1.28419i	0.766626	+	0.642094i	$0.221934\pi$
$71$			91.1773i			1.28419i	−0.766626	+	0.642094i	$0.778066\pi$
$72$	−27.5065	−	62.1615i	−0.382035	−	0.863354i
$73$	−82.8650			−1.13514			−0.567568	−	0.823326i	$-0.692116\pi$
$73$	−82.8650			−1.13514			−0.567568	+	0.823326i	$0.692116\pi$
$74$		−	25.0041i		−	0.337894i
$75$	−14.6758	+	3.10196i	−0.195677	+	0.0413594i
$76$	55.7978			0.734182
$77$			34.4723i			0.447692i
$78$	2.50409	+	11.8472i	0.0321037	+	0.151887i
$79$	60.9960			0.772101			0.386050	−	0.922478i	$-0.373839\pi$
$79$	60.9960			0.772101			0.386050	+	0.922478i	$0.373839\pi$
$80$		−	5.66172i		−	0.0707714i
$81$	54.4734	−	59.9471i	0.672511	−	0.740087i
$82$	−23.6523			−0.288443
$83$		−	106.124i		−	1.27860i	−0.768959	−	0.639298i	$-0.779225\pi$
$83$		−	106.124i		−	1.27860i	0.768959	−	0.639298i	$-0.220775\pi$
$84$	−45.0958	+	9.53172i	−0.536855	+	0.113473i
$85$	33.8050			0.397705
$86$			48.5561i			0.564605i
$87$	−4.46319	−	21.1159i	−0.0513010	−	0.242712i
$88$	−46.5477			−0.528952
$89$			89.3690i			1.00415i	0.864825	+	0.502073i	$0.167429\pi$
$89$			89.3690i			1.00415i	−0.864825	+	0.502073i	$0.832571\pi$
$90$	−20.6020	+	9.11640i	−0.228911	+	0.101293i
$91$	20.1675			0.221621
$92$			92.3907i			1.00425i
$93$	−70.4845	+	14.8980i	−0.757898	+	0.160194i
$94$	85.8008			0.912774
$95$		−	45.4231i		−	0.478138i
$96$	−20.5013	−	96.9944i	−0.213555	−	1.01036i
$97$	−90.4120			−0.932083			−0.466041	−	0.884763i	$-0.654320\pi$
$97$	−90.4120			−0.932083			−0.466041	+	0.884763i	$0.654320\pi$
$98$			19.8294i			0.202340i
$99$	−22.4448	−	50.7226i	−0.226715	−	0.512349i
$100$	−13.7339			−0.137339
$101$		−	11.8910i		−	0.117733i	−0.998266	−	0.0588663i	$-0.981251\pi$
$101$		−	11.8910i		−	0.117733i	0.998266	−	0.0588663i	$-0.0187486\pi$
$102$	49.6750	−	10.4996i	0.487010	−	0.102937i
$103$	−175.477			−1.70366			−0.851828	−	0.523822i	$-0.824506\pi$
$103$	−175.477			−1.70366			−0.851828	+	0.523822i	$0.824506\pi$
$104$			27.2321i			0.261847i
$105$	7.75946	+	36.7110i	0.0738996	+	0.349629i
$106$	95.7855			0.903637
$107$		−	43.4800i		−	0.406355i	−0.979142	−	0.203178i	$-0.934873\pi$
$107$		−	43.4800i		−	0.406355i	0.979142	−	0.203178i	$-0.0651269\pi$
$108$	60.1480	−	43.3867i	0.556926	−	0.401729i
$109$	−14.9421			−0.137084			−0.0685418	−	0.997648i	$-0.521835\pi$
$109$	−14.9421			−0.137084			−0.0685418	+	0.997648i	$0.521835\pi$
$110$			15.4272i			0.140247i
$111$	65.5587	−	13.8569i	0.590619	−	0.124837i
$112$	−14.1626			−0.126452
$113$		−	171.981i		−	1.52195i	−0.648779	−	0.760977i	$-0.724720\pi$
$113$		−	171.981i		−	1.52195i	0.648779	−	0.760977i	$-0.275280\pi$
$114$	−14.1081	−	66.7475i	−0.123756	−	0.585504i
$115$	75.2121			0.654019
$116$		−	19.7608i		−	0.170352i
$117$	−29.6745	+	13.1310i	−0.253628	+	0.112231i
$118$	−18.4401			−0.156272
$119$		−	84.5622i		−	0.710607i
$120$	−49.5707	+	10.4776i	−0.413089	+	0.0873129i
$121$	83.0179			0.686099
$122$		−	73.4876i		−	0.602357i
$123$	−13.1077	−	62.0143i	−0.106567	−	0.504181i
$124$	−65.9612			−0.531945
$125$			11.1803i			0.0894427i
$126$	22.8044	+	51.5353i	0.180987	+	0.409010i
$127$	170.795			1.34484			0.672422	−	0.740168i	$-0.265254\pi$
$127$	170.795			1.34484			0.672422	+	0.740168i	$0.265254\pi$
$128$		−	102.108i		−	0.797717i
$129$	−127.310	+	26.9089i	−0.986897	+	0.208596i
$130$	9.02545			0.0694266
$131$		−	49.4560i		−	0.377526i	−0.982023	−	0.188763i	$-0.939552\pi$
$131$		−	49.4560i		−	0.377526i	0.982023	−	0.188763i	$-0.0604479\pi$
$132$	−10.5022	−	49.6872i	−0.0795621	−	0.376419i
$133$	−113.625			−0.854322
$134$		−	52.3017i		−	0.390311i
$135$	−35.3197	−	48.9645i	−0.261627	−	0.362700i
$136$	114.184			0.839587
$137$		−	66.2896i		−	0.483866i	−0.970293	−	0.241933i	$-0.922219\pi$
$137$		−	66.2896i		−	0.483866i	0.970293	−	0.241933i	$-0.0777814\pi$
$138$	110.521	−	23.3604i	0.800879	−	0.169278i
$139$	12.2888			0.0884086			0.0442043	−	0.999023i	$-0.485925\pi$
$139$	12.2888			0.0884086			0.0442043	+	0.999023i	$0.485925\pi$
$140$			34.3551i			0.245393i
$141$	47.5493	+	224.962i	0.337229	+	1.59548i
$142$	102.070			0.718805
$143$			22.2209i			0.155391i
$144$	20.8389	−	9.22124i	0.144715	−	0.0640364i
$145$	−16.0866			−0.110942
$146$			92.7648i			0.635376i
$147$	−51.9908	+	10.9891i	−0.353679	+	0.0747557i
$148$	61.3514			0.414537
$149$		−	153.598i		−	1.03086i	−0.856932	−	0.515430i	$-0.827632\pi$
$149$		−	153.598i		−	1.03086i	0.856932	−	0.515430i	$-0.172368\pi$
$150$	3.47254	+	16.4291i	0.0231503	+	0.109527i
$151$	−191.330			−1.26709			−0.633543	−	0.773708i	$-0.718400\pi$
$151$	−191.330			−1.26709			−0.633543	+	0.773708i	$0.718400\pi$
$152$		−	153.427i		−	1.00939i
$153$	55.0581	+	124.425i	0.359857	+	0.813235i
$154$	38.5907			0.250589
$155$			53.6968i			0.346431i
$156$	−29.0688	+	6.14416i	−0.186339	+	0.0393856i
$157$	−100.744			−0.641681			−0.320840	−	0.947133i	$-0.603965\pi$
$157$	−100.744			−0.641681			−0.320840	+	0.947133i	$0.603965\pi$
$158$		−	68.2831i		−	0.432172i
$159$	53.0827	+	251.141i	0.333853	+	1.57950i
$160$	−73.8926			−0.461829
$161$		−	188.141i		−	1.16858i
$162$	−67.1089	−	60.9813i	−0.414253	−	0.376428i
$163$	−32.8559			−0.201570			−0.100785	−	0.994908i	$-0.532135\pi$
$163$	−32.8559			−0.201570			−0.100785	+	0.994908i	$0.532135\pi$
$164$		−	58.0345i		−	0.353869i
$165$	−40.4487	+	8.54948i	−0.245144	+	0.0518150i
$166$	−118.802			−0.715675
$167$			261.495i			1.56584i	0.622125	+	0.782918i	$0.286269\pi$
$167$			261.495i			1.56584i	−0.622125	+	0.782918i	$0.713731\pi$
$168$	26.2093	+	124.000i	0.156008	+	0.738093i
$169$	13.0000			0.0769231
$170$		−	37.8436i		−	0.222610i
$171$	167.188	−	73.9807i	0.977706	−	0.432636i
$172$	−119.140			−0.692672
$173$		−	263.381i		−	1.52243i	−0.648499	−	0.761215i	$-0.724603\pi$
$173$		−	263.381i		−	1.52243i	0.648499	−	0.761215i	$-0.275397\pi$
$174$	−23.6386	+	4.99640i	−0.135854	+	0.0287150i
$175$	27.9673			0.159813
$176$		−	15.6046i		−	0.0886624i
$177$	−10.2192	−	48.3484i	−0.0577356	−	0.273155i
$178$	100.046			0.562056
$179$			219.780i			1.22782i	0.789375	+	0.613911i	$0.210405\pi$
$179$			219.780i			1.22782i	−0.789375	+	0.613911i	$0.789595\pi$
$180$	−22.3685	−	50.5501i	−0.124269	−	0.280834i
$181$	77.9617			0.430727			0.215364	−	0.976534i	$-0.430906\pi$
$181$	77.9617			0.430727			0.215364	+	0.976534i	$0.430906\pi$
$182$		−	22.5769i		−	0.124049i
$183$	192.678	−	40.7256i	1.05289	−	0.222544i
$184$	254.046			1.38068
$185$		−	49.9442i		−	0.269968i
$186$	16.6779	+	78.9053i	0.0896661	+	0.424222i
$187$	93.1718			0.498245
$188$			210.525i			1.11982i
$189$	−122.483	+	88.3512i	−0.648060	+	0.467467i
$190$	−50.8498			−0.267631
$191$		−	360.429i		−	1.88706i	−0.331284	−	0.943531i	$-0.607482\pi$
$191$		−	360.429i		−	1.88706i	0.331284	−	0.943531i	$-0.392518\pi$
$192$	−78.8551	+	16.6673i	−0.410704	+	0.0868088i
$193$	39.8730			0.206596			0.103298	−	0.994650i	$-0.467060\pi$
$193$	39.8730			0.206596			0.103298	+	0.994650i	$0.467060\pi$
$194$			101.214i			0.521719i
$195$	5.00175	+	23.6639i	0.0256500	+	0.121354i
$196$	−48.6543			−0.248236
$197$		−	178.477i		−	0.905973i	−0.891517	−	0.452986i	$-0.850359\pi$
$197$		−	178.477i		−	0.905973i	0.891517	−	0.452986i	$-0.149641\pi$
$198$	−56.7824	+	25.1262i	−0.286780	+	0.126900i
$199$	156.078			0.784312			0.392156	−	0.919899i	$-0.371729\pi$
$199$	156.078			0.784312			0.392156	+	0.919899i	$0.371729\pi$
$200$			37.7641i			0.188821i
$201$	137.131	−	28.9847i	0.682241	−	0.144203i
$202$	−13.3116			−0.0658991
$203$			40.2402i			0.198228i
$204$	25.7624	+	121.885i	0.126286	+	0.597477i
$205$	−47.2440			−0.230458
$206$			196.441i			0.953595i
$207$	122.498	+	276.831i	0.591778	+	1.33735i
$208$	−9.12924			−0.0438906
$209$		−	125.193i		−	0.599012i
$210$	41.0969	−	8.68647i	0.195699	−	0.0413642i
$211$	−371.766			−1.76192			−0.880961	−	0.473189i	$-0.843103\pi$
$211$	−371.766			−1.76192			−0.880961	+	0.473189i	$0.843103\pi$
$212$			235.024i			1.10860i
$213$	56.5656	+	267.619i	0.265566	+	1.25643i
$214$	−48.6745			−0.227451
$215$			96.9876i			0.451105i
$216$	−119.300	−	165.389i	−0.552316	−	0.765688i
$217$	134.321			0.618991
$218$			16.7272i			0.0767305i
$219$	−243.221	+	51.4087i	−1.11060	+	0.234743i
$220$	−37.8529			−0.172059
$221$		−	54.5089i		−	0.246646i
$222$	−15.5123	−	73.3909i	−0.0698754	−	0.330590i
$223$	−424.523			−1.90369			−0.951846	−	0.306576i	$-0.900817\pi$
$223$	−424.523			−1.90369			−0.951846	+	0.306576i	$0.900817\pi$
$224$			184.840i			0.825180i
$225$	−41.1511	+	18.2094i	−0.182894	+	0.0809307i
$226$	−192.527			−0.851890
$227$			5.89221i			0.0259569i	0.999916	+	0.0129784i	$0.00413128\pi$
$227$			5.89221i			0.0259569i	−0.999916	+	0.0129784i	$0.995869\pi$
$228$	163.775	−	34.6165i	0.718312	−	0.151827i
$229$	227.275			0.992469			0.496234	−	0.868189i	$-0.334716\pi$
$229$	227.275			0.992469			0.496234	+	0.868189i	$0.334716\pi$
$230$		−	84.1977i		−	0.366077i
$231$	21.3863	+	101.181i	0.0925814	+	0.438015i
$232$	−54.3362			−0.234208
$233$		−	108.338i		−	0.464969i	−0.972600	−	0.232484i	$-0.925315\pi$
$233$		−	108.338i		−	0.464969i	0.972600	−	0.232484i	$-0.0746854\pi$
$234$	14.6998	+	33.2197i	0.0628195	+	0.141965i
$235$	171.382			0.729283
$236$		−	45.2456i		−	0.191719i
$237$	179.032	−	37.8413i	0.755411	−	0.159668i
$238$	−94.6648			−0.397751
$239$			112.150i			0.469247i	0.972086	+	0.234623i	$0.0753857\pi$
$239$			112.150i			0.469247i	−0.972086	+	0.234623i	$0.924614\pi$
$240$	−3.51248	−	16.6180i	−0.0146353	−	0.0692416i
$241$	−246.300			−1.02199			−0.510996	−	0.859583i	$-0.670723\pi$
$241$	−246.300			−1.02199			−0.510996	+	0.859583i	$0.670723\pi$
$242$		−	92.9361i		−	0.384033i
$243$	122.697	−	209.749i	0.504926	−	0.863163i
$244$	180.313			0.738987
$245$			39.6079i			0.161665i
$246$	−69.4231	+	14.6737i	−0.282208	+	0.0596491i
$247$	−73.2426			−0.296529
$248$			181.373i			0.731343i
$249$	−65.8381	−	311.489i	−0.264410	−	1.25096i
$250$	12.5160			0.0500642
$251$		−	67.6636i		−	0.269576i	−0.990874	−	0.134788i	$-0.956965\pi$
$251$		−	67.6636i		−	0.269576i	0.990874	−	0.134788i	$-0.0430353\pi$
$252$	−126.450	+	55.9541i	−0.501785	+	0.222040i
$253$	207.297			0.819354
$254$		−	191.200i		−	0.752756i
$255$	99.2227	−	20.9723i	0.389109	−	0.0822443i
$256$	−221.770			−0.866287
$257$			113.536i			0.441772i	0.975300	+	0.220886i	$0.0708950\pi$
$257$			113.536i			0.441772i	−0.975300	+	0.220886i	$0.929105\pi$
$258$	30.1237	+	142.519i	0.116759	+	0.552401i
$259$	−124.934			−0.482370
$260$			22.1453i			0.0851743i
$261$	−26.2003	−	59.2095i	−0.100384	−	0.226856i
$262$	−55.3644			−0.211315
$263$			380.049i			1.44505i	0.691343	+	0.722527i	$0.257019\pi$
$263$			380.049i			1.44505i	−0.691343	+	0.722527i	$0.742981\pi$
$264$	−136.625	+	28.8778i	−0.517518	+	0.109386i
$265$	191.325			0.721982
$266$			127.199i			0.478193i
$267$	55.4437	+	262.312i	0.207654	+	0.982441i
$268$	128.330			0.478844
$269$		−	427.314i		−	1.58853i	−0.607573	−	0.794264i	$-0.707857\pi$
$269$		−	427.314i		−	1.58853i	0.607573	−	0.794264i	$-0.292143\pi$
$270$	−54.8142	+	39.5393i	−0.203016	+	0.146442i
$271$	−349.256			−1.28877			−0.644383	−	0.764703i	$-0.722886\pi$
$271$	−349.256			−1.28877			−0.644383	+	0.764703i	$0.722886\pi$
$272$			38.2788i			0.140731i
$273$	59.1947	−	12.5117i	0.216830	−	0.0458306i
$274$	−74.2092			−0.270837
$275$			30.8148i			0.112054i
$276$	57.3183	+	271.181i	0.207675	+	0.982539i
$277$	−43.5813			−0.157333			−0.0786666	−	0.996901i	$-0.525066\pi$
$277$	−43.5813			−0.157333			−0.0786666	+	0.996901i	$0.525066\pi$
$278$		−	13.7569i		−	0.0494854i
$279$	−197.640	+	87.4560i	−0.708388	+	0.313462i
$280$	94.4659			0.337378
$281$		−	7.43666i		−	0.0264650i	−0.999912	−	0.0132325i	$-0.995788\pi$
$281$		−	7.43666i		−	0.0264650i	0.999912	−	0.0132325i	$-0.00421215\pi$
$282$	251.838	−	53.2300i	0.893044	−	0.188759i
$283$	433.546			1.53196			0.765982	−	0.642862i	$-0.222253\pi$
$283$	433.546			1.53196			0.765982	+	0.642862i	$0.222253\pi$
$284$			250.445i			0.881848i
$285$	−28.1801	−	133.324i	−0.0988776	−	0.467803i
$286$	24.8756			0.0869775
$287$			118.179i			0.411775i
$288$	−120.349	−	271.974i	−0.417878	−	0.944356i
$289$	60.4449			0.209152
$290$			18.0085i			0.0620982i
$291$	−265.373	+	56.0908i	−0.911935	+	0.192752i
$292$	−227.613			−0.779495
$293$		−	221.584i		−	0.756260i	−0.925753	−	0.378130i	$-0.876567\pi$
$293$		−	221.584i		−	0.756260i	0.925753	−	0.378130i	$-0.123433\pi$
$294$	12.3020	+	58.2022i	0.0418434	+	0.197967i
$295$	−36.8330			−0.124857
$296$		−	168.698i		−	0.569924i
$297$	−97.3467	−	134.954i	−0.327766	−	0.454390i
$298$	−171.948			−0.577008
$299$		−	121.276i		−	0.405605i
$300$	−40.3112	+	8.52041i	−0.134371	+	0.0284014i
$301$	242.612			0.806019
$302$			214.188i			0.709232i
$303$	−7.37707	−	34.9019i	−0.0243468	−	0.115188i
$304$	51.4346			0.169193
$305$		−	146.787i		−	0.481268i
$306$	139.290	−	61.6359i	0.455196	−	0.201425i
$307$	365.472			1.19046			0.595232	−	0.803554i	$-0.297060\pi$
$307$	365.472			1.19046			0.595232	+	0.803554i	$0.297060\pi$
$308$			94.6880i			0.307429i
$309$	−515.050	+	108.864i	−1.66683	+	0.352311i
$310$	60.1119			0.193909
$311$			353.621i			1.13705i	0.822668	+	0.568523i	$0.192485\pi$
$311$			353.621i			1.13705i	−0.822668	+	0.568523i	$0.807515\pi$
$312$	16.8945	+	79.9303i	0.0541492	+	0.256187i
$313$	180.686			0.577271			0.288636	−	0.957439i	$-0.406798\pi$
$313$	180.686			0.577271			0.288636	+	0.957439i	$0.406798\pi$
$314$			112.780i			0.359171i
$315$	45.5504	+	102.938i	0.144604	+	0.326789i
$316$	167.543			0.530199
$317$		−	500.949i		−	1.58028i	−0.612926	−	0.790140i	$-0.710008\pi$
$317$		−	500.949i		−	1.58028i	0.612926	−	0.790140i	$-0.289992\pi$
$318$	281.145	−	59.4245i	0.884104	−	0.186869i
$319$	−44.3373			−0.138988
$320$			60.0737i			0.187730i
$321$	−26.9746	−	127.620i	−0.0840331	−	0.397571i
$322$	−210.618			−0.654094
$323$			307.106i			0.950791i
$324$	149.627	−	164.662i	0.461811	−	0.508216i
$325$	18.0278			0.0554700
$326$			36.7811i			0.112826i
$327$	−43.8574	+	9.26996i	−0.134120	+	0.0283485i
$328$	−159.577			−0.486516
$329$		−	428.706i		−	1.30306i
$330$	9.57088	+	45.2811i	0.0290027	+	0.137215i
$331$	−202.405			−0.611495			−0.305747	−	0.952113i	$-0.598906\pi$
$331$	−202.405			−0.611495			−0.305747	+	0.952113i	$0.598906\pi$
$332$		−	291.499i		−	0.878009i
$333$	183.828	−	81.3440i	0.552036	−	0.244276i
$334$	292.735			0.876453
$335$		−	104.469i		−	0.311849i
$336$	−41.5695	+	8.78637i	−0.123719	+	0.0261499i
$337$	158.743			0.471047			0.235523	−	0.971869i	$-0.424320\pi$
$337$	158.743			0.471047			0.235523	+	0.971869i	$0.424320\pi$
$338$		−	14.5531i		−	0.0430565i
$339$	−106.695	−	504.789i	−0.314735	−	1.48905i
$340$	92.8551			0.273103
$341$			147.997i			0.434008i
$342$	−82.8191	−	187.161i	−0.242161	−	0.547256i
$343$	373.158			1.08792
$344$			327.597i			0.952318i
$345$	220.759	−	46.6609i	0.639881	−	0.135249i
$346$	−294.846			−0.852157
$347$		−	295.158i		−	0.850600i	−0.905052	−	0.425300i	$-0.860169\pi$
$347$		−	295.158i		−	0.850600i	0.905052	−	0.425300i	$-0.139831\pi$
$348$	−12.2594	−	58.0010i	−0.0352283	−	0.166669i
$349$	256.538			0.735066			0.367533	−	0.930010i	$-0.380202\pi$
$349$	256.538			0.735066			0.367533	+	0.930010i	$0.380202\pi$
$350$		−	31.3086i		−	0.0894530i
$351$	−78.9528	+	56.9513i	−0.224937	+	0.162254i
$352$	−203.660			−0.578579
$353$		−	153.321i		−	0.434337i	−0.976134	−	0.217169i	$-0.930318\pi$
$353$		−	153.321i		−	0.434337i	0.976134	−	0.217169i	$-0.0696822\pi$
$354$	−54.1246	+	11.4401i	−0.152894	+	0.0323166i
$355$	203.879			0.574306
$356$			245.478i			0.689544i
$357$	−52.4616	−	248.203i	−0.146951	−	0.695246i
$358$	246.037			0.687254
$359$		−	169.182i		−	0.471260i	−0.971843	−	0.235630i	$-0.924285\pi$
$359$		−	169.182i		−	0.471260i	0.971843	−	0.235630i	$-0.0757154\pi$
$360$	−138.997	+	61.5064i	−0.386104	+	0.170851i
$361$	51.6525			0.143082
$362$		−	87.2757i		−	0.241093i
$363$	243.670	−	51.5036i	0.671268	−	0.141883i
$364$	55.3959			0.152187
$365$			185.292i			0.507649i
$366$	−45.5910	−	215.697i	−0.124566	−	0.589336i
$367$	319.768			0.871303			0.435651	−	0.900116i	$-0.356518\pi$
$367$	319.768			0.871303			0.435651	+	0.900116i	$0.356518\pi$
$368$			85.1660i			0.231429i
$369$	−76.9462	−	173.889i	−0.208526	−	0.471245i
$370$	−55.9110			−0.151111
$371$		−	478.595i		−	1.29001i
$372$	−193.606	+	40.9217i	−0.520446	+	0.110005i
$373$	−68.2799			−0.183056			−0.0915280	−	0.995803i	$-0.529175\pi$
$373$	−68.2799			−0.183056			−0.0915280	+	0.995803i	$0.529175\pi$
$374$		−	104.303i		−	0.278885i
$375$	6.93618	+	32.8160i	0.0184965	+	0.0875093i
$376$	578.880			1.53957
$377$			25.9389i			0.0688034i
$378$	98.9065	+	137.116i	0.261657	+	0.362742i
$379$	361.468			0.953742			0.476871	−	0.878973i	$-0.341771\pi$
$379$	361.468			0.953742			0.476871	+	0.878973i	$0.341771\pi$
$380$		−	124.768i		−	0.328336i
$381$	501.310	−	105.960i	1.31577	−	0.278110i
$382$	−403.489			−1.05625
$383$			578.493i			1.51043i	0.655479	+	0.755213i	$0.272467\pi$
$383$			578.493i			1.51043i	−0.655479	+	0.755213i	$0.727533\pi$
$384$	−63.3467	−	299.702i	−0.164965	−	0.780473i
$385$	77.0824			0.200214
$386$		−	44.6366i		−	0.115639i
$387$	−356.979	+	157.964i	−0.922427	+	0.408175i
$388$	−248.343			−0.640059
$389$		−	98.5631i		−	0.253376i	−0.991943	−	0.126688i	$-0.959565\pi$
$389$		−	98.5631i		−	0.253376i	0.991943	−	0.126688i	$-0.0404346\pi$
$390$	26.4911	−	5.59931i	0.0679258	−	0.0143572i
$391$	−508.509			−1.30053
$392$			133.784i			0.341287i
$393$	−30.6820	−	145.161i	−0.0780713	−	0.369366i
$394$	−199.799			−0.507104
$395$		−	136.391i		−	0.345294i
$396$	−61.6510	−	139.324i	−0.155684	−	0.351829i
$397$	−412.726			−1.03961			−0.519806	−	0.854284i	$-0.673996\pi$
$397$	−412.726			−1.03961			−0.519806	+	0.854284i	$0.673996\pi$
$398$		−	174.725i		−	0.439007i
$399$	−333.506	+	70.4918i	−0.835854	+	0.176671i
$400$	−12.6600			−0.0316500
$401$		−	586.192i		−	1.46182i	−0.682472	−	0.730912i	$-0.739095\pi$
$401$		−	586.192i		−	1.46182i	0.682472	−	0.730912i	$-0.260905\pi$
$402$	−32.4475	−	153.513i	−0.0807152	−	0.381874i
$403$	86.5835			0.214847
$404$		−	32.6621i		−	0.0808467i
$405$	−134.046	−	121.806i	−0.330977	−	0.300756i
$406$	45.0477			0.110955
$407$		−	137.654i		−	0.338216i
$408$	335.147	−	70.8387i	0.821439	−	0.173624i
$409$	−426.519			−1.04283			−0.521417	−	0.853302i	$-0.674596\pi$
$409$	−426.519			−1.04283			−0.521417	+	0.853302i	$0.674596\pi$
$410$			52.8882i			0.128996i
$411$	−41.1255	−	194.570i	−0.100062	−	0.473407i
$412$	−481.997			−1.16990
$413$			92.1366i			0.223091i
$414$	309.904	−	137.133i	0.748560	−	0.331239i
$415$	−237.299			−0.571806
$416$			119.148i			0.286414i
$417$	36.0695	−	7.62386i	0.0864976	−	0.0182826i
$418$	−140.150			−0.335288
$419$			549.373i			1.31115i	0.755128	+	0.655577i	$0.227574\pi$
$419$			549.373i			1.31115i	−0.755128	+	0.655577i	$0.772426\pi$
$420$	21.3136	+	100.837i	0.0507466	+	0.240089i
$421$	437.822			1.03996			0.519978	−	0.854179i	$-0.325940\pi$
$421$	437.822			1.03996			0.519978	+	0.854179i	$0.325940\pi$
$422$			416.180i			0.986209i
$423$	279.129	+	630.799i	0.659880	+	1.49125i
$424$	646.244			1.52416
$425$		−	75.5902i		−	0.177859i
$426$	299.592	−	63.3235i	0.703267	−	0.148647i
$427$	−367.183			−0.859913
$428$		−	119.430i		−	0.279043i
$429$	13.7856	+	65.2216i	0.0321343	+	0.152032i
$430$	108.575			0.252499
$431$			807.375i			1.87326i	0.350320	+	0.936630i	$0.386073\pi$
$431$			807.375i			1.87326i	−0.350320	+	0.936630i	$0.613927\pi$
$432$	55.4446	−	39.9940i	0.128344	−	0.0925787i
$433$	−553.350			−1.27795			−0.638973	−	0.769230i	$-0.720640\pi$
$433$	−553.350			−1.27795			−0.638973	+	0.769230i	$0.720640\pi$
$434$		−	150.368i		−	0.346471i
$435$	−47.2167	+	9.97999i	−0.108544	+	0.0229425i
$436$	−41.0428			−0.0941349
$437$			683.275i			1.56356i
$438$	57.5505	+	272.279i	0.131394	+	0.621641i
$439$	−713.121			−1.62442			−0.812211	−	0.583364i	$-0.801736\pi$
$439$	−713.121			−1.62442			−0.812211	+	0.583364i	$0.801736\pi$
$440$			104.084i			0.236554i
$441$	−145.783	+	64.5093i	−0.330575	+	0.146280i
$442$	−61.0210			−0.138057
$443$			69.1318i			0.156054i	0.996951	+	0.0780268i	$0.0248620\pi$
$443$			69.1318i			0.156054i	−0.996951	+	0.0780268i	$0.975138\pi$
$444$	180.076	−	38.0619i	0.405576	−	0.0857250i
$445$	199.835			0.449068
$446$			475.241i			1.06556i
$447$	−95.2909	−	450.834i	−0.213179	−	1.00858i
$448$	150.273			0.335430
$449$			782.570i			1.74292i	0.490468	+	0.871459i	$0.336826\pi$
$449$			782.570i			1.74292i	−0.490468	+	0.871459i	$0.663174\pi$
$450$	20.3849	+	46.0675i	0.0452998	+	0.102372i
$451$	−130.212			−0.288718
$452$		−	472.395i		−	1.04512i
$453$	−561.582	+	118.699i	−1.23970	+	0.262030i
$454$	6.59615			0.0145290
$455$		−	45.0959i		−	0.0991120i
$456$	−95.1847	−	450.331i	−0.208738	−	0.987569i
$457$	308.581			0.675231			0.337616	−	0.941284i	$-0.390380\pi$
$457$	308.581			0.675231			0.337616	+	0.941284i	$0.390380\pi$
$458$		−	254.428i		−	0.555519i
$459$	238.796	+	331.048i	0.520253	+	0.721239i
$460$	206.592			0.449113
$461$			71.0626i			0.154149i	0.997025	+	0.0770744i	$0.0245579\pi$
$461$			71.0626i			0.154149i	−0.997025	+	0.0770744i	$0.975442\pi$
$462$	113.269	−	23.9413i	0.245172	−	0.0518210i
$463$	−66.9585			−0.144619			−0.0723094	−	0.997382i	$-0.523037\pi$
$463$	−66.9585			−0.144619			−0.0723094	+	0.997382i	$0.523037\pi$
$464$		−	18.2156i		−	0.0392577i
$465$	33.3130	+	157.608i	0.0716409	+	0.338942i
$466$	−121.281			−0.260259
$467$			489.508i			1.04820i	0.851658	+	0.524098i	$0.175597\pi$
$467$			489.508i			1.04820i	−0.851658	+	0.524098i	$0.824403\pi$
$468$	−81.5096	+	36.0681i	−0.174166	+	0.0770685i
$469$	−261.327			−0.557201
$470$		−	191.856i		−	0.408205i
$471$	−295.698	+	62.5006i	−0.627810	+	0.132698i
$472$	−124.412			−0.263584
$473$			267.313i			0.565144i
$474$	−42.3622	−	200.421i	−0.0893718	−	0.422830i
$475$	−101.569			−0.213830
$476$		−	232.274i		−	0.487971i
$477$	311.612	+	704.206i	0.653274	+	1.47632i
$478$	125.549			0.262654
$479$			208.858i			0.436028i	0.975946	+	0.218014i	$0.0699579\pi$
$479$			208.858i			0.436028i	−0.975946	+	0.218014i	$0.930042\pi$
$480$	−216.886	+	45.8423i	−0.451846	+	0.0955048i
$481$	−80.5325			−0.167427
$482$			275.725i			0.572044i
$483$	−116.721	−	552.223i	−0.241659	−	1.14332i
$484$	228.033			0.471142
$485$			202.167i			0.416840i
$486$	−234.807	−	137.356i	−0.483142	−	0.282624i
$487$	891.523			1.83064			0.915321	−	0.402725i	$-0.131937\pi$
$487$	891.523			1.83064			0.915321	+	0.402725i	$0.131937\pi$
$488$		−	495.805i		−	1.01599i
$489$	−96.4369	+	20.3835i	−0.197213	+	0.0416840i
$490$	44.3398			0.0904894
$491$			570.781i			1.16249i	0.813729	+	0.581244i	$0.197434\pi$
$491$			570.781i			1.16249i	−0.813729	+	0.581244i	$0.802566\pi$
$492$	−36.0041	−	170.340i	−0.0731791	−	0.346220i
$493$	108.761			0.220612
$494$			81.9929i			0.165978i
$495$	−113.419	+	50.1880i	−0.229129	+	0.101390i
$496$	−60.8032			−0.122587
$497$		−	509.997i		−	1.02615i
$498$	−348.702	+	73.7037i	−0.700205	+	0.147999i
$499$	115.129			0.230720			0.115360	−	0.993324i	$-0.463198\pi$
$499$	115.129			0.230720			0.115360	+	0.993324i	$0.463198\pi$
$500$			30.7100i			0.0614200i
$501$	162.229	+	767.526i	0.323810	+	1.53199i
$502$	−75.7473			−0.150891
$503$		−	179.212i		−	0.356287i	−0.984005	−	0.178143i	$-0.942991\pi$
$503$		−	179.212i		−	0.356287i	0.984005	−	0.178143i	$-0.0570091\pi$
$504$	153.857	+	347.698i	0.305271	+	0.689877i
$505$	−26.5891			−0.0526517
$506$		−	232.062i		−	0.458621i
$507$	38.1570	−	8.06508i	0.0752603	−	0.0159075i
$508$	469.138			0.923500
$509$			551.465i			1.08343i	0.840563	+	0.541714i	$0.182224\pi$
$509$			551.465i			1.08343i	−0.840563	+	0.541714i	$0.817776\pi$
$510$	−23.4778	−	111.077i	−0.0460350	−	0.217798i
$511$	463.502			0.907049
$512$		−	160.167i		−	0.312826i
$513$	444.824	−	320.866i	0.867104	−	0.625470i
$514$	127.100			0.247275
$515$			392.377i			0.761898i
$516$	−349.693	+	73.9132i	−0.677699	+	0.143243i
$517$	472.355			0.913645
$518$			139.860i			0.270000i
$519$	−163.399	−	773.062i	−0.314834	−	1.48952i
$520$	60.8928			0.117102
$521$			462.639i			0.887982i	0.896031	+	0.443991i	$0.146438\pi$
$521$			462.639i			0.887982i	−0.896031	+	0.443991i	$0.853562\pi$
$522$	−66.2833	+	29.3304i	−0.126979	+	0.0561885i
$523$	−1005.90			−1.92332			−0.961661	−	0.274240i	$-0.911574\pi$
$523$	−1005.90			−1.92332			−0.961661	+	0.274240i	$0.911574\pi$
$524$		−	135.845i		−	0.259246i
$525$	82.0883	−	17.3507i	0.156359	−	0.0330489i
$526$	425.453			0.808847
$527$		−	363.044i		−	0.688887i
$528$	−9.68095	−	45.8018i	−0.0183351	−	0.0867459i
$529$	−602.373			−1.13870
$530$		−	214.183i		−	0.404119i
$531$	−59.9898	−	135.570i	−0.112975	−	0.255311i
$532$	−312.103			−0.586660
$533$			76.1786i			0.142924i
$534$	293.650	−	62.0676i	0.549906	−	0.116231i
$535$	−97.2243			−0.181728
$536$		−	352.869i		−	0.658337i
$537$	136.350	+	645.088i	0.253910	+	1.20128i
$538$	−478.365			−0.889154
$539$			109.166i			0.202533i
$540$	−97.0157	−	134.495i	−0.179659	−	0.249065i
$541$	−638.887			−1.18094			−0.590469	−	0.807061i	$-0.701057\pi$
$541$	−638.887			−1.18094			−0.590469	+	0.807061i	$0.701057\pi$
$542$			390.981i			0.721368i
$543$	228.829	−	48.3667i	0.421417	−	0.0890731i
$544$	499.588			0.918359
$545$			33.4116i			0.0613057i
$546$	−14.0065	−	66.2667i	−0.0256530	−	0.121368i
$547$	−306.558			−0.560435			−0.280218	−	0.959937i	$-0.590407\pi$
$547$	−306.558			−0.560435			−0.280218	+	0.959937i	$0.590407\pi$
$548$		−	182.084i		−	0.332269i
$549$	540.273	−	239.071i	0.984104	−	0.435467i
$550$	34.4962			0.0627204
$551$		−	146.141i		−	0.265229i
$552$	745.663	−	157.608i	1.35084	−	0.285521i
$553$	−341.179			−0.616959
$554$			48.7879i			0.0880648i
$555$	−30.9849	−	146.594i	−0.0558287	−	0.264133i
$556$	33.7547			0.0607099
$557$		−	478.312i		−	0.858729i	−0.903131	−	0.429365i	$-0.858738\pi$
$557$		−	478.312i		−	0.858729i	0.903131	−	0.429365i	$-0.141262\pi$
$558$	97.9043	+	221.252i	0.175456	+	0.396509i
$559$	156.388			0.279764
$560$			31.6686i			0.0565511i
$561$	273.473	−	57.8030i	0.487475	−	0.103036i
$562$	−8.32511			−0.0148134
$563$			336.935i			0.598463i	0.954180	+	0.299232i	$0.0967304\pi$
$563$			336.935i			0.598463i	−0.954180	+	0.299232i	$0.903270\pi$
$564$	130.608	+	617.923i	0.231574	+	1.09561i
$565$	−384.561			−0.680638
$566$		−	485.341i		−	0.857493i
$567$	−304.695	+	335.312i	−0.537381	+	0.591379i
$568$	688.646			1.21241
$569$		−	885.531i		−	1.55629i	−0.628082	−	0.778147i	$-0.716160\pi$
$569$		−	885.531i		−	1.55629i	0.628082	−	0.778147i	$-0.283840\pi$
$570$	−149.252	+	31.5468i	−0.261846	+	0.0553452i
$571$	579.884			1.01556			0.507779	−	0.861487i	$-0.330467\pi$
$571$	579.884			1.01556			0.507779	+	0.861487i	$0.330467\pi$
$572$			61.0360i			0.106706i
$573$	−223.607	−	1057.91i	−0.390239	−	1.84627i
$574$	132.298			0.230485
$575$		−	168.179i		−	0.292486i
$576$	−221.111	+	97.8420i	−0.383874	+	0.169865i
$577$	326.531			0.565912			0.282956	−	0.959133i	$-0.408685\pi$
$577$	326.531			0.565912			0.282956	+	0.959133i	$0.408685\pi$
$578$		−	67.6662i		−	0.117070i
$579$	117.033	−	24.7369i	0.202130	−	0.0427234i
$580$	−44.1865			−0.0761837
$581$			593.598i			1.02168i
$582$	62.7920	+	297.077i	0.107890	+	0.510442i
$583$	527.323			0.904499
$584$			625.865i			1.07169i
$585$	29.3618	+	66.3542i	0.0501911	+	0.113426i
$586$	−248.057			−0.423305
$587$			226.579i			0.385995i	0.981199	+	0.192998i	$0.0618210\pi$
$587$			226.579i			0.385995i	−0.981199	+	0.192998i	$0.938179\pi$
$588$	−142.808	+	30.1847i	−0.242870	+	0.0513345i
$589$	−487.815			−0.828210
$590$			41.2334i			0.0698871i
$591$	−110.725	−	523.856i	−0.187352	−	0.886389i
$592$	56.5539			0.0955303
$593$			725.233i			1.22299i	0.791248	+	0.611495i	$0.209432\pi$
$593$			725.233i			1.22299i	−0.791248	+	0.611495i	$0.790568\pi$
$594$	−151.077	+	108.977i	−0.254338	+	0.183462i
$595$	−189.087			−0.317793
$596$		−	421.902i		−	0.707889i
$597$	458.113	−	96.8295i	0.767358	−	0.162193i
$598$	−135.765			−0.227031
$599$			910.888i			1.52068i	0.649524	+	0.760341i	$0.274968\pi$
$599$			910.888i			1.52068i	−0.649524	+	0.760341i	$0.725032\pi$
$600$	23.4285	+	110.843i	0.0390475	+	0.184739i
$601$	366.944			0.610557			0.305278	−	0.952263i	$-0.401251\pi$
$601$	366.944			0.610557			0.305278	+	0.952263i	$0.401251\pi$
$602$		−	271.597i		−	0.451157i
$603$	384.517	−	170.149i	0.637673	−	0.282171i
$604$	−525.543			−0.870104
$605$		−	185.634i		−	0.306833i
$606$	−39.0716	+	8.25841i	−0.0644746	+	0.0136277i
$607$	592.791			0.976591			0.488295	−	0.872678i	$-0.337619\pi$
$607$	592.791			0.976591			0.488295	+	0.872678i	$0.337619\pi$
$608$		−	671.287i		−	1.10409i
$609$	24.9647	+	118.111i	0.0409929	+	0.193943i
$610$	−164.323			−0.269382
$611$		−	276.344i		−	0.452282i
$612$	151.233	+	341.769i	0.247113	+	0.558446i
$613$	−1151.53			−1.87852			−0.939261	−	0.343202i	$-0.888488\pi$
$613$	−1151.53			−1.87852			−0.939261	+	0.343202i	$0.888488\pi$
$614$		−	409.135i		−	0.666344i
$615$	−138.668	+	29.3097i	−0.225477	+	0.0476581i
$616$	260.363			0.422667
$617$		−	737.148i		−	1.19473i	−0.801970	−	0.597364i	$-0.796215\pi$
$617$		−	737.148i		−	1.19473i	0.801970	−	0.597364i	$-0.203785\pi$
$618$	121.870	+	576.583i	0.197201	+	0.932982i
$619$	105.331			0.170164			0.0850819	−	0.996374i	$-0.472885\pi$
$619$	105.331			0.170164			0.0850819	+	0.996374i	$0.472885\pi$
$620$			147.494i			0.237893i
$621$	531.294	+	736.545i	0.855546	+	1.18606i
$622$	395.868			0.636444
$623$		−	499.882i		−	0.802379i
$624$	−26.7957	+	5.66370i	−0.0429418	+	0.00907644i
$625$	25.0000			0.0400000
$626$		−	202.272i		−	0.323119i
$627$	−77.6689	−	367.462i	−0.123874	−	0.586063i
$628$	−276.722			−0.440640
$629$			337.672i			0.536840i
$630$	115.236	−	50.9922i	0.182915	−	0.0809401i
$631$	−574.340			−0.910206			−0.455103	−	0.890439i	$-0.650398\pi$
$631$	−574.340			−0.910206			−0.455103	+	0.890439i	$0.650398\pi$
$632$		−	460.692i		−	0.728943i
$633$	−1091.19	+	230.640i	−1.72384	+	0.364360i
$634$	−560.797			−0.884538
$635$		−	381.910i		−	0.601432i
$636$	145.807	+	689.832i	0.229256	+	1.08464i
$637$	63.8658			0.100260
$638$			49.6342i			0.0777966i
$639$	332.057	+	750.410i	0.519651	+	1.17435i
$640$	−228.320			−0.356750
$641$		−	682.520i		−	1.06477i	−0.846501	−	0.532387i	$-0.821295\pi$
$641$		−	682.520i		−	1.06477i	0.846501	−	0.532387i	$-0.178705\pi$
$642$	−142.867	+	30.1973i	−0.222535	+	0.0470362i
$643$	298.380			0.464044			0.232022	−	0.972711i	$-0.425466\pi$
$643$	298.380			0.464044			0.232022	+	0.972711i	$0.425466\pi$
$644$		−	516.784i		−	0.802459i
$645$	60.1702	+	284.673i	0.0932872	+	0.441354i
$646$	343.795			0.532191
$647$			40.4589i			0.0625331i	0.999511	+	0.0312666i	$0.00995408\pi$
$647$			40.4589i			0.0625331i	−0.999511	+	0.0312666i	$0.990046\pi$
$648$	−452.770	−	411.428i	−0.698719	−	0.634919i
$649$	−101.517			−0.156421
$650$		−	20.1815i		−	0.0310485i
$651$	394.253	−	83.3316i	0.605611	−	0.128006i
$652$	−90.2481			−0.138417
$653$		−	927.349i		−	1.42014i	−0.704133	−	0.710068i	$-0.748664\pi$
$653$		−	927.349i		−	1.42014i	0.704133	−	0.710068i	$-0.251336\pi$
$654$	10.3774	+	49.0970i	0.0158676	+	0.0750719i
$655$	−110.587			−0.168835
$656$		−	53.4964i		−	0.0815493i
$657$	−681.998	+	301.785i	−1.03805	+	0.459337i
$658$	−479.924			−0.729367
$659$		−	712.210i		−	1.08074i	−0.841426	−	0.540372i	$-0.818284\pi$
$659$		−	712.210i		−	1.08074i	0.841426	−	0.540372i	$-0.181716\pi$
$660$	−111.104	+	23.4836i	−0.168339	+	0.0355812i
$661$	390.806			0.591234			0.295617	−	0.955306i	$-0.404475\pi$
$661$	390.806			0.591234			0.295617	+	0.955306i	$0.404475\pi$
$662$			226.586i			0.342275i
$663$	−33.8168	−	159.992i	−0.0510058	−	0.241315i
$664$	−801.532			−1.20713
$665$			254.073i			0.382064i
$666$	−91.0622	−	205.790i	−0.136730	−	0.308994i
$667$	241.982			0.362791
$668$			718.270i			1.07525i
$669$	−1246.04	+	263.371i	−1.86254	+	0.393678i
$670$	−116.950			−0.174552
$671$		−	404.567i		−	0.602932i
$672$	114.673	+	542.535i	0.170645	+	0.807343i
$673$	710.679			1.05599			0.527993	−	0.849249i	$-0.322945\pi$
$673$	710.679			1.05599			0.527993	+	0.849249i	$0.322945\pi$
$674$		−	177.708i		−	0.263661i
$675$	−109.488	+	78.9772i	−0.162204	+	0.117003i
$676$	35.7082			0.0528228
$677$			711.445i			1.05088i	0.850831	+	0.525440i	$0.176099\pi$
$677$			711.445i			1.05088i	−0.850831	+	0.525440i	$0.823901\pi$
$678$	−565.096	+	119.442i	−0.833476	+	0.176168i
$679$	505.716			0.744796
$680$		−	255.323i		−	0.375475i
$681$	3.65547	+	17.2945i	0.00536780	+	0.0253958i
$682$	165.678			0.242930
$683$		−	44.5787i		−	0.0652690i	−0.999467	−	0.0326345i	$-0.989610\pi$
$683$		−	44.5787i		−	0.0652690i	0.999467	−	0.0326345i	$-0.0103897\pi$
$684$	459.229	−	203.209i	0.671387	−	0.297090i
$685$	−148.228			−0.216391
$686$		−	417.739i		−	0.608948i
$687$	667.088	−	141.000i	0.971016	−	0.205240i
$688$	−109.823			−0.159627
$689$		−	308.503i		−	0.447754i
$690$	−52.2355	−	247.133i	−0.0757036	−	0.358164i
$691$	−324.404			−0.469471			−0.234735	−	0.972059i	$-0.575422\pi$
$691$	−324.404			−0.469471			−0.234735	+	0.972059i	$0.575422\pi$
$692$		−	723.451i		−	1.04545i
$693$	125.544	+	283.715i	0.181160	+	0.409401i
$694$	−330.421			−0.476110
$695$		−	27.4786i		−	0.0395375i
$696$	−159.485	+	33.7097i	−0.229145	+	0.0484334i
$697$	319.416			0.458273
$698$		−	287.187i		−	0.411442i
$699$	−67.2117	−	317.988i	−0.0961541	−	0.454918i
$700$	76.8203			0.109743
$701$		−	964.757i		−	1.37626i	−0.725589	−	0.688129i	$-0.758432\pi$
$701$		−	964.757i		−	1.37626i	0.725589	−	0.688129i	$-0.241568\pi$
$702$	63.7552	+	88.3853i	0.0908194	+	0.125905i
$703$	453.724			0.645411
$704$			165.573i			0.235188i
$705$	503.031	−	106.324i	0.713519	−	0.150814i
$706$	−171.638			−0.243114
$707$			66.5119i			0.0940762i
$708$	−28.0700	−	132.803i	−0.0396469	−	0.187575i
$709$	1242.13			1.75195			0.875974	−	0.482358i	$-0.160220\pi$
$709$	1242.13			1.75195			0.875974	+	0.482358i	$0.160220\pi$
$710$		−	228.236i		−	0.321459i
$711$	502.011	−	222.140i	0.706063	−	0.312433i
$712$	674.989			0.948018
$713$		−	807.730i		−	1.13286i
$714$	−277.856	+	58.7292i	−0.389153	+	0.0822538i
$715$	49.6874			0.0694928
$716$			603.689i			0.843141i
$717$	69.5769	+	329.177i	0.0970389	+	0.459104i
$718$	−189.395			−0.263781
$719$		−	711.793i		−	0.989977i	−0.868900	−	0.494988i	$-0.835172\pi$
$719$		−	711.793i		−	0.989977i	0.868900	−	0.494988i	$-0.164828\pi$
$720$	−20.6193	−	46.5972i	−0.0286379	−	0.0647184i
$721$	981.522			1.36133
$722$		−	57.8234i		−	0.0800878i
$723$	−722.927	+	152.802i	−0.999900	+	0.211345i
$724$	214.144			0.295779
$725$			35.9708i			0.0496148i
$726$	−57.6567	−	272.781i	−0.0794169	−	0.375732i
$727$	−613.120			−0.843356			−0.421678	−	0.906746i	$-0.638559\pi$
$727$	−613.120			−0.843356			−0.421678	+	0.906746i	$0.638559\pi$
$728$		−	152.322i		−	0.209233i
$729$	230.008	−	691.764i	0.315512	−	0.948922i
$730$	207.428			0.284149
$731$		−	655.732i		−	0.897035i
$732$	529.246	−	111.864i	0.723013	−	0.152820i
$733$	−861.754			−1.17565			−0.587827	−	0.808987i	$-0.700016\pi$
$733$	−861.754			−1.17565			−0.587827	+	0.808987i	$0.700016\pi$
$734$		−	357.971i		−	0.487698i
$735$	24.5724	+	116.255i	0.0334318	+	0.158170i
$736$	1111.52			1.51022
$737$		−	287.934i		−	0.390684i
$738$	−194.664	+	86.1389i	−0.263772	+	0.116719i
$739$	−6.37973			−0.00863293			−0.00431646	−	0.999991i	$-0.501374\pi$
$739$	−6.37973			−0.00863293			−0.00431646	+	0.999991i	$0.501374\pi$
$740$		−	137.186i		−	0.185387i
$741$	−214.978	+	45.4391i	−0.290119	+	0.0613213i
$742$	−535.773			−0.722066
$743$			320.955i			0.431971i	0.976397	+	0.215986i	$0.0692964\pi$
$743$			320.955i			0.431971i	−0.976397	+	0.215986i	$0.930704\pi$
$744$	112.522	+	532.357i	0.151240	+	0.715534i
$745$	−343.456			−0.461015
$746$			76.4373i			0.102463i
$747$	−386.490	−	873.421i	−0.517389	−	1.16924i
$748$	255.923			0.342143
$749$			243.204i			0.324705i
$750$	36.7365	−	7.76485i	0.0489820	−	0.0103531i
$751$	−250.805			−0.333962			−0.166981	−	0.985960i	$-0.553402\pi$
$751$	−250.805			−0.333962			−0.166981	+	0.985960i	$0.553402\pi$
$752$			194.063i			0.258062i
$753$	−41.9779	−	198.603i	−0.0557475	−	0.263749i
$754$	29.0378			0.0385117
$755$			427.827i			0.566658i
$756$	−336.436	+	242.682i	−0.445021	+	0.321008i
$757$	461.728			0.609945			0.304972	−	0.952361i	$-0.401353\pi$
$757$	461.728			0.609945			0.304972	+	0.952361i	$0.401353\pi$
$758$		−	404.653i		−	0.533843i
$759$	608.447	−	128.605i	0.801643	−	0.169440i
$760$	−343.073			−0.451412
$761$			849.179i			1.11587i	0.829884	+	0.557937i	$0.188407\pi$
$761$			849.179i			1.11587i	−0.829884	+	0.557937i	$0.811593\pi$
$762$	−118.619	−	561.201i	−0.155668	−	0.736484i
$763$	83.5782			0.109539
$764$		−	990.022i		−	1.29584i
$765$	278.223	−	123.114i	0.363690	−	0.160933i
$766$	647.606			0.845438
$767$			59.3914i			0.0774333i
$768$	−650.927	+	137.584i	−0.847562	+	0.179146i
$769$	1244.44			1.61826			0.809131	−	0.587628i	$-0.199938\pi$
$769$	1244.44			1.61826			0.809131	+	0.587628i	$0.199938\pi$
$770$		−	86.2914i		−	0.112067i
$771$	70.4364	+	333.244i	0.0913572	+	0.432223i
$772$	109.523			0.141869
$773$			808.965i			1.04653i	0.852171	+	0.523263i	$0.175286\pi$
$773$			808.965i			1.04653i	−0.852171	+	0.523263i	$0.824714\pi$
$774$	176.836	+	399.628i	0.228470	+	0.516315i
$775$	120.070			0.154929
$776$			682.866i			0.879982i
$777$	−366.700	+	77.5079i	−0.471943	+	0.0997528i
$778$	−110.338			−0.141823
$779$		−	429.194i		−	0.550955i
$780$	13.7388	+	64.9999i	0.0176138	+	0.0833331i
$781$	561.922			0.719491
$782$			569.260i			0.727954i
$783$	−113.635	−	157.535i	−0.145127	−	0.201194i
$784$	−44.8497			−0.0572062
$785$			225.270i			0.286968i
$786$	−162.503	+	34.3476i	−0.206747	+	0.0436992i
$787$	−8.98060			−0.0114112			−0.00570559	−	0.999984i	$-0.501816\pi$
$787$	−8.98060			−0.0114112			−0.00570559	+	0.999984i	$0.501816\pi$
$788$		−	490.237i		−	0.622129i
$789$	235.779	+	1115.50i	0.298833	+	1.41382i
$790$	−152.686			−0.193273
$791$			961.968i			1.21614i
$792$	−383.099	+	169.521i	−0.483710	+	0.214042i
$793$	−236.686			−0.298470
$794$			462.034i			0.581907i
$795$	561.569	−	118.697i	0.706376	−	0.149304i
$796$	428.714			0.538585
$797$			413.956i			0.519392i	0.965690	+	0.259696i	$0.0836224\pi$
$797$			413.956i			0.519392i	−0.965690	+	0.259696i	$0.916378\pi$
$798$	78.9134	+	373.350i	0.0988890	+	0.467857i
$799$	−1158.71			−1.45020
$800$			165.229i			0.206536i
$801$	325.472	+	735.528i	0.406332	+	0.918262i
$802$	−656.224			−0.818234
$803$			510.694i			0.635982i
$804$	376.668	−	79.6149i	0.468493	−	0.0990235i
$805$	−420.696			−0.522604
$806$		−	96.9276i		−	0.120258i
$807$	−265.102	−	1254.23i	−0.328503	−	1.55419i
$808$	−89.8106			−0.111152
$809$			406.692i			0.502709i	0.967895	+	0.251355i	$0.0808760\pi$
$809$			406.692i			0.502709i	−0.967895	+	0.251355i	$0.919124\pi$
$810$	−136.358	+	150.060i	−0.168344	+	0.185259i
$811$	−516.312			−0.636636			−0.318318	−	0.947984i	$-0.603118\pi$
$811$	−516.312			−0.636636			−0.318318	+	0.947984i	$0.603118\pi$
$812$			110.531i			0.136122i
$813$	−1025.12	+	216.675i	−1.26091	+	0.266513i
$814$	−154.099			−0.189311
$815$			73.4679i			0.0901447i
$816$	23.7478	+	112.354i	0.0291027	+	0.137689i
$817$	−881.096			−1.07845
$818$			477.475i			0.583710i
$819$	165.983	−	73.4478i	0.202666	−	0.0896798i
$820$	−129.769			−0.158255
$821$			1324.66i			1.61348i	0.590910	+	0.806738i	$0.298769\pi$
$821$			1324.66i			1.61348i	−0.590910	+	0.806738i	$0.701231\pi$
$822$	−217.815	+	46.0387i	−0.264982	+	0.0560082i
$823$	430.499			0.523086			0.261543	−	0.965192i	$-0.415769\pi$
$823$	430.499			0.523086			0.261543	+	0.965192i	$0.415769\pi$
$824$			1325.34i			1.60843i
$825$	19.1172	+	90.4461i	0.0231724	+	0.109632i
$826$	103.144			0.124872
$827$			1237.94i			1.49691i	0.663186	+	0.748455i	$0.269204\pi$
$827$			1237.94i			1.49691i	−0.663186	+	0.748455i	$0.730796\pi$
$828$	336.476	+	760.396i	0.406372	+	0.918353i
$829$	−540.995			−0.652588			−0.326294	−	0.945268i	$-0.605800\pi$
$829$	−540.995			−0.652588			−0.326294	+	0.945268i	$0.605800\pi$
$830$			265.649i			0.320060i
$831$	−127.918	+	27.0374i	−0.153932	+	0.0325360i
$832$	96.8659			0.116425
$833$		−	267.788i		−	0.321475i
$834$	−8.53468	−	40.3787i	−0.0102334	−	0.0484157i
$835$	584.720			0.700263
$836$		−	343.880i		−	0.411339i
$837$	−525.847	+	379.311i	−0.628252	+	0.453179i
$838$	615.007			0.733898
$839$		−	565.476i		−	0.673988i	−0.941507	−	0.336994i	$-0.890590\pi$
$839$		−	565.476i		−	0.673988i	0.941507	−	0.336994i	$-0.109410\pi$
$840$	277.272	−	58.6058i	0.330085	−	0.0697688i
$841$	789.244			0.938459
$842$		−	490.128i		−	0.582100i
$843$	−4.61364	−	21.8277i	−0.00547288	−	0.0258929i
$844$	−1021.16			−1.20991
$845$		−	29.0689i		−	0.0344010i
$846$	706.160	−	312.476i	0.834705	−	0.369358i
$847$	−464.358			−0.548238
$848$			216.646i			0.255479i
$849$	1272.52	−	268.968i	1.49885	−	0.316805i
$850$	−84.6209			−0.0995540
$851$			751.281i			0.882822i
$852$	155.374	+	735.094i	0.182364	+	0.862786i
$853$	−849.646			−0.996069			−0.498034	−	0.867157i	$-0.665945\pi$
$853$	−849.646			−0.996069			−0.498034	+	0.867157i	$0.665945\pi$
$854$			411.050i			0.481323i
$855$	−165.426	−	373.843i	−0.193480	−	0.437243i
$856$	−328.397			−0.383641
$857$		−	1021.50i		−	1.19195i	−0.803001	−	0.595977i	$-0.796765\pi$
$857$		−	1021.50i		−	1.19195i	0.803001	−	0.595977i	$-0.203235\pi$
$858$	73.0136	−	15.4326i	0.0850974	−	0.0179867i
$859$	1141.94			1.32939			0.664693	−	0.747117i	$-0.268562\pi$
$859$	1141.94			1.32939			0.664693	+	0.747117i	$0.268562\pi$
$860$			266.404i			0.309773i
$861$	73.3175	+	346.875i	0.0851539	+	0.402874i
$862$	903.832			1.04853
$863$		−	504.249i		−	0.584298i	−0.956373	−	0.292149i	$-0.905630\pi$
$863$		−	504.249i		−	0.584298i	0.956373	−	0.292149i	$-0.0943703\pi$
$864$	−521.973	−	723.623i	−0.604135	−	0.837526i
$865$	−588.937			−0.680852
$866$			619.459i			0.715310i
$867$	177.415	−	37.4995i	0.204631	−	0.0432520i
$868$	368.951			0.425059
$869$		−	375.916i		−	0.432584i
$870$	11.1723	+	52.8576i	0.0128417	+	0.0607559i
$871$	−168.452			−0.193400
$872$			112.855i			0.129421i
$873$	−744.112	+	329.270i	−0.852362	+	0.377171i
$874$	764.905			0.875177
$875$		−	62.5368i		−	0.0714706i
$876$	−668.077	+	141.209i	−0.762645	+	0.161197i
$877$	−1191.38			−1.35847			−0.679235	−	0.733920i	$-0.737688\pi$
$877$	−1191.38			−1.35847			−0.679235	+	0.733920i	$0.737688\pi$
$878$			798.318i			0.909245i
$879$	−137.469	−	650.383i	−0.156392	−	0.739912i
$880$	−34.8929			−0.0396510
$881$		−	1179.42i		−	1.33873i	−0.742932	−	0.669367i	$-0.766566\pi$
$881$		−	1179.42i		−	1.33873i	0.742932	−	0.669367i	$-0.233434\pi$
$882$	72.2162	+	163.200i	0.0818778	+	0.185034i
$883$	1650.28			1.86895			0.934474	−	0.356031i	$-0.115870\pi$
$883$	1650.28			1.86895			0.934474	+	0.356031i	$0.115870\pi$
$884$		−	149.724i		−	0.169371i
$885$	−108.110	+	22.8508i	−0.122159	+	0.0258202i
$886$	77.3909			0.0873486
$887$		−	482.665i		−	0.544154i	−0.962275	−	0.272077i	$-0.912289\pi$
$887$		−	482.665i		−	0.544154i	0.962275	−	0.272077i	$-0.0877105\pi$
$888$	−104.659	−	495.153i	−0.117859	−	0.557605i
$889$	−955.336			−1.07462
$890$		−	223.709i		−	0.251359i
$891$	−369.451	−	335.717i	−0.414648	−	0.376787i
$892$	−1166.08			−1.30726
$893$			1556.94i			1.74349i
$894$	−504.695	+	106.675i	−0.564536	+	0.119324i
$895$	491.443			0.549099
$896$			571.136i			0.637428i
$897$	−75.2385	−	355.963i	−0.0838779	−	0.396838i
$898$	876.064			0.975572
$899$			172.760i			0.192169i
$900$	−113.033	+	50.0174i	−0.125593	+	0.0555749i
$901$	−1293.55			−1.43568
$902$			145.768i			0.161606i
$903$	712.102	−	150.514i	0.788596	−	0.166682i
$904$	−1298.94			−1.43688
$905$		−	174.328i		−	0.192627i
$906$	132.880	+	628.674i	0.146667	+	0.693901i
$907$	489.647			0.539853			0.269927	−	0.962881i	$-0.413001\pi$
$907$	489.647			0.539853			0.269927	+	0.962881i	$0.413001\pi$
$908$			16.1846i			0.0178245i
$909$	−43.3056	−	97.8657i	−0.0476410	−	0.107663i
$910$	−50.4835			−0.0554764
$911$		−	1192.85i		−	1.30939i	−0.755894	−	0.654694i	$-0.772798\pi$
$911$		−	1192.85i		−	1.30939i	0.755894	−	0.654694i	$-0.227202\pi$
$912$	150.968	−	31.9096i	0.165535	−	0.0349886i
$913$	−654.035			−0.716358
$914$		−	345.447i		−	0.377951i
$915$	−91.0651	−	430.841i	−0.0995247	−	0.470865i
$916$	624.277			0.681525
$917$			276.630i			0.301669i
$918$	370.599	−	267.325i	0.403702	−	0.291204i
$919$	−1193.58			−1.29879			−0.649393	−	0.760453i	$-0.724977\pi$
$919$	−1193.58			−1.29879			−0.649393	+	0.760453i	$0.724977\pi$
$920$		−	568.064i		−	0.617461i
$921$	1072.72	−	226.736i	1.16473	−	0.246184i
$922$	79.5524			0.0862825
$923$		−	328.745i		−	0.356170i
$924$	58.7436	+	277.924i	0.0635753	+	0.300783i
$925$	−111.679			−0.120734
$926$			74.9580i			0.0809481i
$927$	−1444.21	+	639.065i	−1.55794	+	0.689391i
$928$	−237.736			−0.256182
$929$			1014.16i			1.09167i	0.837893	+	0.545835i	$0.183788\pi$
$929$			1014.16i			1.09167i	−0.837893	+	0.545835i	$0.816212\pi$
$930$	176.438	−	37.2929i	0.189718	−	0.0400999i
$931$	−359.823			−0.386491
$932$		−	297.581i		−	0.319293i
$933$	219.383	+	1037.93i	0.235138	+	1.11247i
$934$	547.989			0.586712
$935$		−	208.339i		−	0.222822i
$936$	99.1761	+	224.126i	0.105957	+	0.239451i
$937$	1161.83			1.23994			0.619971	−	0.784625i	$-0.287144\pi$
$937$	1161.83			1.23994			0.619971	+	0.784625i	$0.287144\pi$
$938$			292.548i			0.311884i
$939$	530.340	−	112.096i	0.564793	−	0.119378i
$940$	470.749			0.500797
$941$			1114.52i			1.18440i	0.805792	+	0.592199i	$0.201740\pi$
$941$			1114.52i			1.18440i	−0.805792	+	0.592199i	$0.798260\pi$
$942$	69.9675	+	331.025i	0.0742755	+	0.351407i
$943$	710.664			0.753620
$944$		−	41.7076i		−	0.0441817i
$945$	197.559	+	273.881i	0.209057	+	0.289821i
$946$	299.249			0.316331
$947$		−	530.572i		−	0.560266i	−0.959961	−	0.280133i	$-0.909621\pi$
$947$		−	530.572i		−	0.560266i	0.959961	−	0.280133i	$-0.0903785\pi$
$948$	491.764	−	103.942i	0.518738	−	0.109644i
$949$	298.774			0.314830
$950$			113.704i			0.119688i
$951$	−310.784	−	1470.36i	−0.326797	−	1.54612i
$952$	−638.683			−0.670886
$953$		−	703.897i		−	0.738612i	−0.929308	−	0.369306i	$-0.879595\pi$
$953$		−	703.897i		−	0.738612i	0.929308	−	0.369306i	$-0.120405\pi$
$954$	788.337	−	348.840i	0.826349	−	0.365660i
$955$	−805.943			−0.843920
$956$			308.052i			0.322230i
$957$	−130.137	+	27.5064i	−0.135984	+	0.0287424i
$958$	233.810			0.244060
$959$			370.789i			0.386641i
$960$	37.2692	+	176.325i	0.0388221	+	0.183672i
$961$	−384.331			−0.399928
$962$			90.1537i			0.0937149i
$963$	−158.349	−	357.850i	−0.164433	−	0.371600i
$964$	−676.533			−0.701798
$965$		−	89.1587i		−	0.0923925i
$966$	−618.197	+	130.666i	−0.639955	+	0.135265i
$967$	1328.41			1.37374			0.686871	−	0.726779i	$-0.258984\pi$
$967$	1328.41			1.37374			0.686871	+	0.726779i	$0.258984\pi$
$968$		−	627.020i		−	0.647748i
$969$	190.526	+	901.401i	0.196621	+	0.930239i
$970$	226.320			0.233320
$971$			729.823i			0.751620i	0.926697	+	0.375810i	$0.122635\pi$
$971$			729.823i			0.751620i	−0.926697	+	0.375810i	$0.877365\pi$
$972$	337.023	−	576.135i	0.346731	−	0.592731i
$973$	−68.7369			−0.0706443
$974$		−	998.033i		−	1.02467i
$975$	52.9142	−	11.1843i	0.0542710	−	0.0114710i
$976$	166.213			0.170300
$977$			329.511i			0.337268i	0.985679	+	0.168634i	$0.0539356\pi$
$977$			329.511i			0.337268i	−0.985679	+	0.168634i	$0.946064\pi$
$978$	22.8187	+	107.958i	0.0233320	+	0.110387i
$979$	550.778			0.562592
$980$			108.794i			0.111015i
$981$	−122.977	+	54.4175i	−0.125359	+	0.0554714i
$982$	638.972			0.650685
$983$		−	1084.63i		−	1.10339i	−0.834047	−	0.551693i	$-0.813982\pi$
$983$		−	1084.63i		−	1.10339i	0.834047	−	0.551693i	$-0.186018\pi$
$984$	−468.383	+	99.0002i	−0.475999	+	0.100610i
$985$	−399.086			−0.405163
$986$		−	121.755i		−	0.123484i
$987$	−265.965	−	1258.32i	−0.269469	−	1.27489i
$988$	−201.182			−0.203625
$989$		−	1458.93i		−	1.47516i
$990$	56.1840	+	126.969i	0.0567515	+	0.128252i
$991$	−1663.40			−1.67850			−0.839251	−	0.543744i	$-0.817006\pi$
$991$	−1663.40			−1.67850			−0.839251	+	0.543744i	$0.817006\pi$
$992$			793.559i			0.799959i
$993$	−594.089	+	125.570i	−0.598277	+	0.126455i
$994$	−570.926			−0.574372
$995$		−	349.001i		−	0.350755i
$996$	−180.843	−	855.593i	−0.181570	−	0.859029i
$997$	−1238.84			−1.24256			−0.621282	−	0.783587i	$-0.713388\pi$
$997$	−1238.84			−1.24256			−0.621282	+	0.783587i	$0.713388\pi$
$998$		−	128.884i		−	0.129142i
$999$	489.098	−	352.802i	0.489588	−	0.353156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.3.d.a.131.12	✓	32
3.2	odd	2	inner	195.3.d.a.131.21	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.3.d.a.131.12	✓	32	1.1	even	1	trivial
195.3.d.a.131.21	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-1.11947i q^{2} +(2.93515 - 0.620391i) q^{3} +2.74679 q^{4} -2.23607i q^{5} +(-0.694509 - 3.28581i) q^{6} -5.59346 q^{7} -7.55282i q^{8} +(8.23023 - 3.64188i) q^{9} -2.50321 q^{10} -6.16296i q^{11} +(8.06224 - 1.70408i) q^{12} -3.60555 q^{13} +6.26171i q^{14} +(-1.38724 - 6.56320i) q^{15} +2.53200 q^{16} +15.1180i q^{17} +(-4.07698 - 9.21349i) q^{18} +20.3138 q^{19} -6.14200i q^{20} +(-16.4177 + 3.47013i) q^{21} -6.89924 q^{22} +33.6359i q^{23} +(-4.68570 - 22.1687i) q^{24} -5.00000 q^{25} +4.03630i q^{26} +(21.8976 - 15.7954i) q^{27} -15.3641 q^{28} -7.19415i q^{29} +(-7.34730 + 1.55297i) q^{30} -24.0139 q^{31} -33.0458i q^{32} +(-3.82344 - 18.0892i) q^{33} +16.9242 q^{34} +12.5074i q^{35} +(22.6067 - 10.0035i) q^{36} +22.3357 q^{37} -22.7407i q^{38} +(-10.5828 + 2.23685i) q^{39} -16.8886 q^{40} -21.1281i q^{41} +(3.88471 + 18.3791i) q^{42} -43.3742 q^{43} -16.9283i q^{44} +(-8.14350 - 18.4034i) q^{45} +37.6544 q^{46} +76.6441i q^{47} +(7.43179 - 1.57083i) q^{48} -17.7132 q^{49} +5.59735i q^{50} +(9.37910 + 44.3737i) q^{51} -9.90368 q^{52} +85.5633i q^{53} +(-17.6825 - 24.5137i) q^{54} -13.7808 q^{55} +42.2464i q^{56} +(59.6242 - 12.6025i) q^{57} -8.05364 q^{58} -16.4722i q^{59} +(-3.81044 - 18.0277i) q^{60} +65.6450 q^{61} +26.8829i q^{62} +(-46.0355 + 20.3707i) q^{63} -26.8658 q^{64} +8.06226i q^{65} +(-20.2503 + 4.28023i) q^{66} +46.7201 q^{67} +41.5260i q^{68} +(20.8674 + 98.7265i) q^{69} +14.0016 q^{70} +91.1773i q^{71} +(-27.5065 - 62.1615i) q^{72} -82.8650 q^{73} -25.0041i q^{74} +(-14.6758 + 3.10196i) q^{75} +55.7978 q^{76} +34.4723i q^{77} +(2.50409 + 11.8472i) q^{78} +60.9960 q^{79} -5.66172i q^{80} +(54.4734 - 59.9471i) q^{81} -23.6523 q^{82} -106.124i q^{83} +(-45.0958 + 9.53172i) q^{84} +33.8050 q^{85} +48.5561i q^{86} +(-4.46319 - 21.1159i) q^{87} -46.5477 q^{88} +89.3690i q^{89} +(-20.6020 + 9.11640i) q^{90} +20.1675 q^{91} +92.3907i q^{92} +(-70.4845 + 14.8980i) q^{93} +85.8008 q^{94} -45.4231i q^{95} +(-20.5013 - 96.9944i) q^{96} -90.4120 q^{97} +19.8294i q^{98} +(-22.4448 - 50.7226i) 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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