LMFDB - Embedded newform 195.3.e.f.194.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,3,Mod(194,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("195.194");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.31336515503$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			194.21
Character	$\chi$	$=$	195.194
Dual form			195.3.e.f.194.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.788299i q^{2} +(-1.53514 - 2.57747i) q^{3} +3.37859 q^{4} +(-1.75492 + 4.68191i) q^{5} +(2.03182 - 1.21015i) q^{6} -10.4924 q^{7} +5.81653i q^{8} +(-4.28669 + 7.91355i) q^{9} +O(q^{10})$	\(q+0.788299i q^{2} +(-1.53514 - 2.57747i) q^{3} +3.37859 q^{4} +(-1.75492 + 4.68191i) q^{5} +(2.03182 - 1.21015i) q^{6} -10.4924 q^{7} +5.81653i q^{8} +(-4.28669 + 7.91355i) q^{9} +(-3.69074 - 1.38340i) q^{10} -3.29821 q^{11} +(-5.18660 - 8.70820i) q^{12} +(5.18183 + 11.9226i) q^{13} -8.27112i q^{14} +(14.7615 - 2.66413i) q^{15} +8.92918 q^{16} +5.61565 q^{17} +(-6.23824 - 3.37919i) q^{18} +22.2852i q^{19} +(-5.92915 + 15.8182i) q^{20} +(16.1073 + 27.0438i) q^{21} -2.59998i q^{22} -42.7496 q^{23} +(14.9919 - 8.92919i) q^{24} +(-18.8405 - 16.4327i) q^{25} +(-9.39858 + 4.08483i) q^{26} +(26.9776 - 1.09959i) q^{27} -35.4494 q^{28} +29.0498i q^{29} +(2.10013 + 11.6365i) q^{30} -24.8148i q^{31} +30.3050i q^{32} +(5.06322 + 8.50104i) q^{33} +4.42681i q^{34} +(18.4133 - 49.1243i) q^{35} +(-14.4830 + 26.7366i) q^{36} +35.6602 q^{37} -17.5674 q^{38} +(22.7753 - 31.6589i) q^{39} +(-27.2325 - 10.2075i) q^{40} -18.1126 q^{41} +(-21.3186 + 12.6973i) q^{42} +21.7412i q^{43} -11.1433 q^{44} +(-29.5277 - 33.9575i) q^{45} -33.6995i q^{46} -57.8488i q^{47} +(-13.7075 - 23.0147i) q^{48} +61.0898 q^{49} +(12.9539 - 14.8520i) q^{50} +(-8.62080 - 14.4742i) q^{51} +(17.5072 + 40.2816i) q^{52} +68.3398 q^{53} +(0.866809 + 21.2664i) q^{54} +(5.78810 - 15.4419i) q^{55} -61.0292i q^{56} +(57.4394 - 34.2109i) q^{57} -22.8999 q^{58} -96.0118 q^{59} +(49.8730 - 9.00099i) q^{60} -38.2340 q^{61} +19.5615 q^{62} +(44.9776 - 83.0319i) q^{63} +11.8273 q^{64} +(-64.9143 + 3.33759i) q^{65} +(-6.70136 + 3.99133i) q^{66} +3.73101 q^{67} +18.9729 q^{68} +(65.6267 + 110.186i) q^{69} +(38.7246 + 14.5152i) q^{70} +42.6346 q^{71} +(-46.0294 - 24.9337i) q^{72} +79.7689 q^{73} +28.1109i q^{74} +(-13.4321 + 73.7874i) q^{75} +75.2924i q^{76} +34.6061 q^{77} +(24.9566 + 17.9538i) q^{78} +61.1362 q^{79} +(-15.6700 + 41.8056i) q^{80} +(-44.2486 - 67.8459i) q^{81} -14.2781i q^{82} -34.8501i q^{83} +(54.4197 + 91.3696i) q^{84} +(-9.85501 + 26.2919i) q^{85} -17.1385 q^{86} +(74.8749 - 44.5955i) q^{87} -19.1841i q^{88} +20.7742 q^{89} +(26.7687 - 23.2767i) q^{90} +(-54.3696 - 125.096i) q^{91} -144.433 q^{92} +(-63.9595 + 38.0942i) q^{93} +45.6021 q^{94} +(-104.337 - 39.1087i) q^{95} +(78.1101 - 46.5224i) q^{96} -93.0425 q^{97} +48.1571i q^{98} +(14.1384 - 26.1006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 88 q^{4} + 28 q^{9}+O(q^{10}) $ 40 * q - 88 * q^4 + 28 * q^9	$ 40 q - 88 q^{4} + 28 q^{9} + 100 q^{10} - 24 q^{16} - 196 q^{25} - 126 q^{30} - 340 q^{36} + 256 q^{39} - 524 q^{40} + 864 q^{49} + 76 q^{51} + 232 q^{55} - 272 q^{61} + 264 q^{64} + 872 q^{66} + 384 q^{69} + 18 q^{75} + 400 q^{79} - 1300 q^{81} + 70 q^{90} - 360 q^{91} + 728 q^{94}+O(q^{100}) $ 40 * q - 88 * q^4 + 28 * q^9 + 100 * q^10 - 24 * q^16 - 196 * q^25 - 126 * q^30 - 340 * q^36 + 256 * q^39 - 524 * q^40 + 864 * q^49 + 76 * q^51 + 232 * q^55 - 272 * q^61 + 264 * q^64 + 872 * q^66 + 384 * q^69 + 18 * q^75 + 400 * q^79 - 1300 * q^81 + 70 * q^90 - 360 * q^91 + 728 * q^94

Display 100 coefficients 10 coefficients

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 $

$2$			0.788299i			0.394149i	0.980388	+	0.197075i	$0.0631441\pi$
$2$			0.788299i			0.394149i	−0.980388	+	0.197075i	$0.936856\pi$
$3$	−1.53514	−	2.57747i	−0.511713	−	0.859156i
$3$	−1.53514	−	2.57747i	−0.511713	−	0.859156i
$4$	3.37859			0.844646
$5$	−1.75492	+	4.68191i	−0.350984	+	0.936381i
$5$	−1.75492	+	4.68191i	−0.350984	+	0.936381i
$6$	2.03182	−	1.21015i	0.338636	−	0.201691i
$7$	−10.4924			−1.49891			−0.749455	−	0.662055i	$-0.769684\pi$
$7$	−10.4924			−1.49891			−0.749455	+	0.662055i	$0.769684\pi$
$8$			5.81653i			0.727066i
$9$	−4.28669	+	7.91355i	−0.476299	+	0.879283i
$10$	−3.69074	−	1.38340i	−0.369074	−	0.138340i
$11$	−3.29821			−0.299837			−0.149919	−	0.988698i	$-0.547901\pi$
$11$	−3.29821			−0.299837			−0.149919	+	0.988698i	$0.547901\pi$
$12$	−5.18660	−	8.70820i	−0.432217	−	0.725683i
$13$	5.18183	+	11.9226i	0.398602	+	0.917124i
$13$	5.18183	+	11.9226i	0.398602	+	0.917124i
$14$		−	8.27112i		−	0.590794i
$15$	14.7615	−	2.66413i	0.984101	−	0.177609i
$16$	8.92918			0.558074
$17$	5.61565			0.330332			0.165166	−	0.986266i	$-0.447184\pi$
$17$	5.61565			0.330332			0.165166	+	0.986266i	$0.447184\pi$
$18$	−6.23824	−	3.37919i	−0.346569	−	0.187733i
$19$			22.2852i			1.17290i	0.809984	+	0.586452i	$0.199476\pi$
$19$			22.2852i			1.17290i	−0.809984	+	0.586452i	$0.800524\pi$
$20$	−5.92915	+	15.8182i	−0.296457	+	0.790911i
$21$	16.1073	+	27.0438i	0.767012	+	1.28780i
$22$		−	2.59998i		−	0.118181i
$23$	−42.7496			−1.85868			−0.929340	−	0.369225i	$-0.879623\pi$
$23$	−42.7496			−1.85868			−0.929340	+	0.369225i	$0.879623\pi$
$24$	14.9919	−	8.92919i	0.624663	−	0.372049i
$25$	−18.8405	−	16.4327i	−0.753620	−	0.657310i
$26$	−9.39858	+	4.08483i	−0.361484	+	0.157109i
$27$	26.9776	−	1.09959i	0.999170	−	0.0407257i
$28$	−35.4494			−1.26605
$29$			29.0498i			1.00172i	0.865529	+	0.500858i	$0.166982\pi$
$29$			29.0498i			1.00172i	−0.865529	+	0.500858i	$0.833018\pi$
$30$	2.10013	+	11.6365i	0.0700044	+	0.387883i
$31$		−	24.8148i		−	0.800479i	−0.916411	−	0.400239i	$-0.868927\pi$
$31$		−	24.8148i		−	0.800479i	0.916411	−	0.400239i	$-0.131073\pi$
$32$			30.3050i			0.947031i
$33$	5.06322	+	8.50104i	0.153431	+	0.257607i
$34$			4.42681i			0.130200i
$35$	18.4133	−	49.1243i	0.526093	−	1.40355i
$36$	−14.4830	+	26.7366i	−0.402304	+	0.742683i
$37$	35.6602			0.963789			0.481895	−	0.876229i	$-0.339949\pi$
$37$	35.6602			0.963789			0.481895	+	0.876229i	$0.339949\pi$
$38$	−17.5674			−0.462299
$39$	22.7753	−	31.6589i	0.583983	−	0.811766i
$40$	−27.2325	−	10.2075i	−0.680811	−	0.255189i
$41$	−18.1126			−0.441770			−0.220885	−	0.975300i	$-0.570894\pi$
$41$	−18.1126			−0.441770			−0.220885	+	0.975300i	$0.570894\pi$
$42$	−21.3186	+	12.6973i	−0.507585	+	0.302317i
$43$			21.7412i			0.505609i	0.967517	+	0.252804i	$0.0813529\pi$
$43$			21.7412i			0.505609i	−0.967517	+	0.252804i	$0.918647\pi$
$44$	−11.1433			−0.253257
$45$	−29.5277	−	33.9575i	−0.656171	−	0.754612i
$46$		−	33.6995i		−	0.732598i
$47$		−	57.8488i		−	1.23082i	−0.788205	−	0.615412i	$-0.788989\pi$
$47$		−	57.8488i		−	1.23082i	0.788205	−	0.615412i	$-0.211011\pi$
$48$	−13.7075	−	23.0147i	−0.285574	−	0.479472i
$49$	61.0898			1.24673
$50$	12.9539	−	14.8520i	0.259078	−	0.297039i
$51$	−8.62080	−	14.4742i	−0.169035	−	0.283807i
$52$	17.5072	+	40.2816i	0.336678	+	0.774645i
$53$	68.3398			1.28943			0.644715	−	0.764423i	$-0.276976\pi$
$53$	68.3398			1.28943			0.644715	+	0.764423i	$0.276976\pi$
$54$	0.866809	+	21.2664i	0.0160520	+	0.393822i
$55$	5.78810	−	15.4419i	0.105238	−	0.280762i
$56$		−	61.0292i		−	1.08981i
$57$	57.4394	−	34.2109i	1.00771	−	0.600191i
$58$	−22.8999			−0.394826
$59$	−96.0118			−1.62732			−0.813660	−	0.581341i	$-0.802528\pi$
$59$	−96.0118			−1.62732			−0.813660	+	0.581341i	$0.802528\pi$
$60$	49.8730	−	9.00099i	0.831217	−	0.150017i
$61$	−38.2340			−0.626787			−0.313394	−	0.949623i	$-0.601466\pi$
$61$	−38.2340			−0.626787			−0.313394	+	0.949623i	$0.601466\pi$
$62$	19.5615			0.315508
$63$	44.9776	−	83.0319i	0.713929	−	1.31797i
$64$	11.8273			0.184802
$65$	−64.9143	+	3.33759i	−0.998681	+	0.0513476i
$66$	−6.70136	+	3.99133i	−0.101536	+	0.0604746i
$67$	3.73101			0.0556867			0.0278433	−	0.999612i	$-0.491136\pi$
$67$	3.73101			0.0556867			0.0278433	+	0.999612i	$0.491136\pi$
$68$	18.9729			0.279014
$69$	65.6267	+	110.186i	0.951111	+	1.59690i
$70$	38.7246	+	14.5152i	0.553209	+	0.207359i
$71$	42.6346			0.600488			0.300244	−	0.953862i	$-0.402932\pi$
$71$	42.6346			0.600488			0.300244	+	0.953862i	$0.402932\pi$
$72$	−46.0294	−	24.9337i	−0.639297	−	0.346301i
$73$	79.7689			1.09272			0.546362	−	0.837549i	$-0.316012\pi$
$73$	79.7689			1.09272			0.546362	+	0.837549i	$0.316012\pi$
$74$			28.1109i			0.379877i
$75$	−13.4321	+	73.7874i	−0.179094	+	0.983832i
$76$			75.2924i			0.990689i
$77$	34.6061			0.449429
$78$	24.9566	+	17.9538i	0.319957	+	0.230177i
$79$	61.1362			0.773876			0.386938	−	0.922106i	$-0.373533\pi$
$79$	61.1362			0.773876			0.386938	+	0.922106i	$0.373533\pi$
$80$	−15.6700	+	41.8056i	−0.195875	+	0.522570i
$81$	−44.2486	−	67.8459i	−0.546279	−	0.837604i
$82$		−	14.2781i		−	0.174123i
$83$		−	34.8501i		−	0.419880i	−0.977714	−	0.209940i	$-0.932673\pi$
$83$		−	34.8501i		−	0.419880i	0.977714	−	0.209940i	$-0.0673269\pi$
$84$	54.4197	+	91.3696i	0.647854	+	1.08773i
$85$	−9.85501	+	26.2919i	−0.115941	+	0.309317i
$86$	−17.1385			−0.199285
$87$	74.8749	−	44.5955i	0.860631	−	0.512592i
$88$		−	19.1841i		−	0.218002i
$89$	20.7742			0.233417			0.116709	−	0.993166i	$-0.462766\pi$
$89$	20.7742			0.233417			0.116709	+	0.993166i	$0.462766\pi$
$90$	26.7687	−	23.2767i	0.297430	−	0.258630i
$91$	−54.3696	−	125.096i	−0.597469	−	1.37469i
$92$	−144.433			−1.56993
$93$	−63.9595	+	38.0942i	−0.687736	+	0.409616i
$94$	45.6021			0.485129
$95$	−104.337	−	39.1087i	−1.09829	−	0.411671i
$96$	78.1101	−	46.5224i	0.813647	−	0.484608i
$97$	−93.0425			−0.959201			−0.479601	−	0.877487i	$-0.659218\pi$
$97$	−93.0425			−0.959201			−0.479601	+	0.877487i	$0.659218\pi$
$98$			48.1571i			0.491398i
$99$	14.1384	−	26.1006i	0.142812	−	0.263642i
$100$	−63.6543	−	55.5194i	−0.636543	−	0.555194i
$101$		−	105.682i		−	1.04636i	−0.852222	−	0.523180i	$-0.824746\pi$
$101$		−	105.682i		−	1.04636i	0.852222	−	0.523180i	$-0.175254\pi$
$102$	11.4100	−	6.79577i	0.111862	−	0.0666252i
$103$			95.6050i			0.928204i	0.885782	+	0.464102i	$0.153623\pi$
$103$			95.6050i			0.928204i	−0.885782	+	0.464102i	$0.846377\pi$
$104$	−69.3482	+	30.1402i	−0.666810	+	0.289810i
$105$	−154.883	+	27.9530i	−1.47508	+	0.266220i
$106$			53.8722i			0.508228i
$107$	66.4453			0.620984			0.310492	−	0.950576i	$-0.399506\pi$
$107$	66.4453			0.620984			0.310492	+	0.950576i	$0.399506\pi$
$108$	91.1461	−	3.71507i	0.843946	−	0.0343988i
$109$			142.202i			1.30461i	0.757958	+	0.652304i	$0.226197\pi$
$109$			142.202i			1.30461i	−0.757958	+	0.652304i	$0.773803\pi$
$110$	12.1728	+	4.56275i	0.110662	+	0.0414795i
$111$	−54.7434	−	91.9131i	−0.493184	−	0.828046i
$112$	−93.6882			−0.836502
$113$	24.2707			0.214785			0.107392	−	0.994217i	$-0.465750\pi$
$113$	24.2707			0.214785			0.107392	+	0.994217i	$0.465750\pi$
$114$	26.9684	+	45.2794i	0.236565	+	0.397187i
$115$	75.0222	−	200.150i	0.652367	−	1.74043i
$116$			98.1471i			0.846096i
$117$	−116.563	−	10.1019i	−0.996266	−	0.0863412i
$118$		−	75.6860i		−	0.641407i
$119$	−58.9214			−0.495138
$120$	15.4960	+	85.8608i	0.129133	+	0.715507i
$121$	−110.122			−0.910098
$122$		−	30.1398i		−	0.247048i
$123$	27.8053	+	46.6845i	0.226059	+	0.379549i
$124$		−	83.8390i		−	0.676121i
$125$	110.000	−	59.3714i	0.880001	−	0.474971i
$126$	65.4539	+	35.4557i	0.519476	+	0.281395i
$127$			115.850i			0.912201i	0.889928	+	0.456101i	$0.150754\pi$
$127$			115.850i			0.912201i	−0.889928	+	0.456101i	$0.849246\pi$
$128$			130.543i			1.01987i
$129$	56.0372	−	33.3757i	0.434397	−	0.258727i
$130$	−2.63102	−	51.1718i	−0.0202386	−	0.393629i
$131$			94.9511i			0.724817i	0.932019	+	0.362409i	$0.118046\pi$
$131$			94.9511i			0.724817i	−0.932019	+	0.362409i	$0.881954\pi$
$132$	17.1065	+	28.7215i	0.129595	+	0.217587i
$133$		−	233.824i		−	1.75808i
$134$			2.94115i			0.0219489i
$135$	−42.1953	+	128.236i	−0.312558	+	0.949899i
$136$			32.6636i			0.240173i
$137$			207.305i			1.51317i	0.653893	+	0.756587i	$0.273135\pi$
$137$			207.305i			1.51317i	−0.653893	+	0.756587i	$0.726865\pi$
$138$	−86.8594	+	51.7334i	−0.629416	+	0.374880i
$139$	124.336			0.894504			0.447252	−	0.894408i	$-0.352403\pi$
$139$	124.336			0.894504			0.447252	+	0.894408i	$0.352403\pi$
$140$	62.2108	−	165.971i	0.444363	−	1.18550i
$141$	−149.103	+	88.8060i	−1.05747	+	0.629829i
$142$			33.6088i			0.236682i
$143$	−17.0908	−	39.3233i	−0.119516	−	0.274988i
$144$	−38.2766	+	70.6615i	−0.265810	+	0.490705i
$145$	−136.008	−	50.9800i	−0.937989	−	0.351586i
$146$			62.8817i			0.430697i
$147$	−93.7815	−	157.457i	−0.637969	−	1.07114i
$148$	120.481			0.814061
$149$	245.048			1.64462			0.822309	−	0.569042i	$-0.192686\pi$
$149$	245.048			1.64462			0.822309	+	0.569042i	$0.192686\pi$
$150$	−58.1665	−	10.5885i	−0.387777	−	0.0705899i
$151$			190.934i			1.26446i	0.774780	+	0.632231i	$0.217861\pi$
$151$			190.934i			1.26446i	−0.774780	+	0.632231i	$0.782139\pi$
$152$	−129.622			−0.852779
$153$	−24.0725	+	44.4397i	−0.157337	+	0.290456i
$154$			27.2799i			0.177142i
$155$	116.181	+	43.5481i	0.749553	+	0.280955i
$156$	76.9484	−	106.962i	0.493259	−	0.685655i
$157$			98.3906i			0.626691i	0.949639	+	0.313346i	$0.101450\pi$
$157$			98.3906i			0.626691i	−0.949639	+	0.313346i	$0.898550\pi$
$158$			48.1936i			0.305023i
$159$	−104.911	−	176.144i	−0.659818	−	1.10782i
$160$	−141.885	−	53.1828i	−0.886782	−	0.332393i
$161$	448.545			2.78599
$162$	53.4828	−	34.8811i	0.330141	−	0.215315i
$163$	−181.906			−1.11599			−0.557995	−	0.829845i	$-0.688429\pi$
$163$	−181.906			−1.11599			−0.557995	+	0.829845i	$0.688429\pi$
$164$	−61.1948			−0.373139
$165$	−48.6866	+	8.78687i	−0.295070	+	0.0532537i
$166$	27.4723			0.165496
$167$			6.47501i			0.0387725i	0.999812	+	0.0193863i	$0.00617123\pi$
$167$			6.47501i			0.0387725i	−0.999812	+	0.0193863i	$0.993829\pi$
$168$	−157.301	+	93.6883i	−0.936314	+	0.557669i
$169$	−115.297	+	123.562i	−0.682233	+	0.731135i
$170$	−20.7259	−	7.76869i	−0.121917	−	0.0456982i
$171$	−176.355	−	95.5297i	−1.03132	−	0.558653i
$172$			73.4544i			0.427060i
$173$	39.7693			0.229881			0.114940	−	0.993372i	$-0.463332\pi$
$173$	39.7693			0.229881			0.114940	+	0.993372i	$0.463332\pi$
$174$	35.1546	+	59.0238i	0.202038	+	0.339217i
$175$	197.682	+	172.418i	1.12961	+	0.985248i
$176$	−29.4503			−0.167331
$177$	147.392	+	247.468i	0.832721	+	1.39812i
$178$			16.3762i			0.0920013i
$179$			306.963i			1.71488i	0.514586	+	0.857438i	$0.327945\pi$
$179$			306.963i			1.71488i	−0.514586	+	0.857438i	$0.672055\pi$
$180$	−99.7619	−	114.728i	−0.554233	−	0.637380i
$181$	62.3419			0.344431			0.172215	−	0.985059i	$-0.444908\pi$
$181$	62.3419			0.344431			0.172215	+	0.985059i	$0.444908\pi$
$182$	98.6134	−	42.8595i	0.541832	−	0.235492i
$183$	58.6946	+	98.5470i	0.320735	+	0.538508i
$184$		−	248.655i		−	1.35138i
$185$	−62.5808	+	166.958i	−0.338275	+	0.902475i
$186$	−30.0296	−	50.4192i	−0.161450	−	0.271071i
$187$	−18.5216			−0.0990459
$188$		−	195.447i		−	1.03961i
$189$	−283.059	+	11.5374i	−1.49767	+	0.0610442i
$190$	30.8293	−	82.2488i	0.162260	−	0.432889i
$191$		−	36.2158i		−	0.189612i	−0.995496	−	0.0948058i	$-0.969777\pi$
$191$		−	36.2158i		−	0.189612i	0.995496	−	0.0948058i	$-0.0302230\pi$
$192$	−18.1566	−	30.4846i	−0.0945657	−	0.158774i
$193$	−141.534			−0.733335			−0.366668	−	0.930352i	$-0.619501\pi$
$193$	−141.534			−0.733335			−0.366668	+	0.930352i	$0.619501\pi$
$194$		−	73.3453i		−	0.378069i
$195$	108.255	+	162.191i	0.555154	+	0.831748i
$196$	206.397			1.05305
$197$		−	37.7803i		−	0.191778i	−0.995392	−	0.0958890i	$-0.969431\pi$
$197$		−	37.7803i		−	0.191778i	0.995392	−	0.0958890i	$-0.0305694\pi$
$198$	20.5750	+	11.1453i	0.103914	+	0.0562894i
$199$	110.575			0.555653			0.277827	−	0.960631i	$-0.410386\pi$
$199$	110.575			0.555653			0.277827	+	0.960631i	$0.410386\pi$
$200$	95.5816	−	109.586i	0.477908	−	0.547932i
$201$	−5.72762	−	9.61655i	−0.0284956	−	0.0478435i
$202$	83.3092			0.412422
$203$		−	304.801i		−	1.50148i
$204$	−29.1261	−	48.9022i	−0.142775	−	0.239716i
$205$	31.7861	−	84.8013i	0.155054	−	0.413665i
$206$	−75.3653			−0.365851
$207$	183.254	−	338.301i	0.885287	−	1.63431i
$208$	46.2694	+	106.459i	0.222449	+	0.511823i
$209$		−	73.5012i		−	0.351681i
$210$	−22.0354	−	122.094i	−0.104930	−	0.581402i
$211$	−34.7057			−0.164482			−0.0822410	−	0.996612i	$-0.526208\pi$
$211$	−34.7057			−0.164482			−0.0822410	+	0.996612i	$0.526208\pi$
$212$	230.892			1.08911
$213$	−65.4501	−	109.889i	−0.307278	−	0.515913i
$214$			52.3787i			0.244760i
$215$	−101.790	−	38.1540i	−0.473443	−	0.177461i
$216$	6.39582	+	156.916i	0.0296103	+	0.726463i
$217$			260.366i			1.19985i
$218$	−112.098			−0.514210
$219$	−122.456	−	205.602i	−0.559162	−	0.938821i
$220$	19.5556	−	52.1718i	0.0888890	−	0.237145i
$221$	29.0993	+	66.9532i	0.131671	+	0.302956i
$222$	72.4550	−	43.1542i	0.326374	−	0.194388i
$223$	356.523			1.59876			0.799379	−	0.600827i	$-0.205162\pi$
$223$	356.523			1.59876			0.799379	+	0.600827i	$0.205162\pi$
$224$		−	317.971i		−	1.41951i
$225$	210.805	−	78.6532i	0.936910	−	0.349570i
$226$			19.1325i			0.0846572i
$227$		−	236.049i		−	1.03986i	−0.854208	−	0.519931i	$-0.825957\pi$
$227$		−	236.049i		−	1.03986i	0.854208	−	0.519931i	$-0.174043\pi$
$228$	194.064	−	115.584i	0.851157	−	0.506949i
$229$		−	138.716i		−	0.605747i	−0.953031	−	0.302874i	$-0.902054\pi$
$229$		−	138.716i		−	0.605747i	0.953031	−	0.302874i	$-0.0979460\pi$
$230$	157.778	+	59.1399i	0.685991	+	0.257130i
$231$	−53.1251	−	89.1960i	−0.229979	−	0.386130i
$232$	−168.969			−0.728314
$233$	−293.157			−1.25818			−0.629092	−	0.777331i	$-0.716573\pi$
$233$	−293.157			−1.25818			−0.629092	+	0.777331i	$0.716573\pi$
$234$	7.96333	−	91.8865i	0.0340313	−	0.392677i
$235$	270.843	+	101.520i	1.15252	+	0.432000i
$236$	−324.384			−1.37451
$237$	−93.8526	−	157.577i	−0.396003	−	0.664880i
$238$		−	46.4477i		−	0.195158i
$239$	415.493			1.73847			0.869233	−	0.494404i	$-0.164613\pi$
$239$	415.493			1.73847			0.869233	+	0.494404i	$0.164613\pi$
$240$	131.808	−	23.7885i	0.549201	−	0.0991187i
$241$		−	387.712i		−	1.60876i	−0.594112	−	0.804382i	$-0.702496\pi$
$241$		−	387.712i		−	1.60876i	0.594112	−	0.804382i	$-0.297504\pi$
$242$		−	86.8089i		−	0.358714i
$243$	−106.943	+	218.202i	−0.440094	+	0.897952i
$244$	−129.177			−0.529413
$245$	−107.208	+	286.017i	−0.437583	+	1.16742i
$246$	−36.8014	+	21.9189i	−0.149599	+	0.0891012i
$247$	−265.698	+	115.478i	−1.07570	+	0.467522i
$248$	144.336			0.582001
$249$	−89.8250	+	53.4997i	−0.360743	+	0.214858i
$250$	46.8024	+	86.7130i	0.187210	+	0.346852i
$251$			12.5975i			0.0501892i	0.999685	+	0.0250946i	$0.00798869\pi$
$251$			12.5975i			0.0501892i	−0.999685	+	0.0250946i	$0.992011\pi$
$252$	151.960	−	280.530i	0.603018	−	1.11322i
$253$	140.997			0.557302
$254$	−91.3240			−0.359543
$255$	82.8955	−	14.9608i	0.325080	−	0.0586699i
$256$	−55.5978			−0.217179
$257$	−161.272			−0.627516			−0.313758	−	0.949503i	$-0.601588\pi$
$257$	−161.272			−0.627516			−0.313758	+	0.949503i	$0.601588\pi$
$258$	26.3101	+	44.1741i	0.101977	+	0.171217i
$259$	−374.160			−1.44463
$260$	−219.318	+	11.2763i	−0.843532	+	0.0433706i
$261$	−229.887	−	124.527i	−0.880793	−	0.477117i
$262$	−74.8498			−0.285686
$263$	150.861			0.573616			0.286808	−	0.957988i	$-0.407406\pi$
$263$	150.861			0.573616			0.286808	+	0.957988i	$0.407406\pi$
$264$	−49.4465	+	29.4503i	−0.187297	+	0.111554i
$265$	−119.931	+	319.961i	−0.452569	+	1.20740i
$266$	184.323			0.692945
$267$	−31.8912	−	53.5447i	−0.119443	−	0.200542i
$268$	12.6055			0.0470355
$269$			69.7813i			0.259410i	0.991553	+	0.129705i	$0.0414031\pi$
$269$			69.7813i			0.259410i	−0.991553	+	0.129705i	$0.958597\pi$
$270$	−101.089	−	33.2625i	−0.374402	−	0.123195i
$271$			160.605i			0.592639i	0.955089	+	0.296319i	$0.0957593\pi$
$271$			160.605i			0.592639i	−0.955089	+	0.296319i	$0.904241\pi$
$272$	50.1431			0.184350
$273$	−238.967	+	332.177i	−0.875338	+	1.21676i
$274$	−163.418			−0.596417
$275$	62.1400	+	54.1987i	0.225964	+	0.197086i
$276$	221.725	+	372.272i	0.803353	+	1.34881i
$277$			182.405i			0.658503i	0.944242	+	0.329251i	$0.106796\pi$
$277$			182.405i			0.658503i	−0.944242	+	0.329251i	$0.893204\pi$
$278$			98.0140i			0.352568i
$279$	196.373	+	106.374i	0.703848	+	0.381267i
$280$	285.733	+	107.101i	1.02047	+	0.382505i
$281$	−43.0075			−0.153052			−0.0765258	−	0.997068i	$-0.524383\pi$
$281$	−43.0075			−0.153052			−0.0765258	+	0.997068i	$0.524383\pi$
$282$	−70.0056	−	117.538i	−0.248247	−	0.416802i
$283$		−	344.538i		−	1.21745i	−0.793382	−	0.608724i	$-0.791682\pi$
$283$		−	344.538i		−	1.21745i	0.793382	−	0.608724i	$-0.208318\pi$
$284$	144.045			0.507200
$285$	59.3706	+	328.963i	0.208318	+	1.15426i
$286$	30.9985	−	13.4726i	0.108386	−	0.0471071i
$287$	190.044			0.662173
$288$	−239.820	−	129.908i	−0.832708	−	0.451070i
$289$	−257.465			−0.890881
$290$	40.1875	−	107.215i	0.138578	−	0.369708i
$291$	142.833	+	239.814i	0.490836	+	0.824104i
$292$	269.506			0.922966
$293$			198.500i			0.677474i	0.940881	+	0.338737i	$0.110000\pi$
$293$			198.500i			0.677474i	−0.940881	+	0.338737i	$0.890000\pi$
$294$	124.123	−	73.9278i	0.422188	−	0.251455i
$295$	168.493	−	449.519i	0.571163	−	1.52379i
$296$			207.419i			0.700739i
$297$	−88.9778	+	3.62669i	−0.299589	+	0.0122111i
$298$			193.171i			0.648225i
$299$	−221.521	−	509.687i	−0.740873	−	1.70464i
$300$	−45.3814	+	249.297i	−0.151271	+	0.830990i
$301$		−	228.116i		−	0.757862i
$302$	−150.513			−0.498387
$303$	−272.393	+	162.237i	−0.898986	+	0.535436i
$304$			198.988i			0.654567i
$305$	67.0976	−	179.008i	0.219992	−	0.586912i
$306$	−35.0318	−	18.9764i	−0.114483	−	0.0620142i
$307$	−77.3922			−0.252092			−0.126046	−	0.992024i	$-0.540229\pi$
$307$	−77.3922			−0.252092			−0.126046	+	0.992024i	$0.540229\pi$
$308$	116.919			0.379609
$309$	246.419	−	146.767i	0.797472	−	0.474974i
$310$	−34.3289	+	91.5852i	−0.110738	+	0.295436i
$311$		−	235.951i		−	0.758684i	−0.925256	−	0.379342i	$-0.876150\pi$
$311$		−	235.951i		−	0.758684i	0.925256	−	0.379342i	$-0.123850\pi$
$312$	184.145	+	132.473i	0.590208	+	0.424594i
$313$		−	449.108i		−	1.43485i	−0.696635	−	0.717425i	$-0.745320\pi$
$313$		−	449.108i		−	1.43485i	0.696635	−	0.717425i	$-0.254680\pi$
$314$	−77.5612			−0.247010
$315$	309.816	+	356.295i	0.983542	+	1.13110i
$316$	206.554			0.653651
$317$			363.093i			1.14540i	0.819764	+	0.572702i	$0.194105\pi$
$317$			363.093i			1.14540i	−0.819764	+	0.572702i	$0.805895\pi$
$318$	138.854	−	82.7013i	0.436647	−	0.260067i
$319$		−	95.8123i		−	0.300352i
$320$	−20.7560	+	55.3745i	−0.0648626	+	0.173045i
$321$	−102.003	−	171.261i	−0.317766	−	0.533522i
$322$			353.588i			1.09810i
$323$			125.146i			0.387448i
$324$	−149.498	−	229.223i	−0.461412	−	0.707479i
$325$	98.2930	−	309.780i	0.302440	−	0.953168i
$326$		−	143.396i		−	0.439867i
$327$	366.522	−	218.300i	1.12086	−	0.667585i
$328$		−	105.352i		−	0.321196i
$329$			606.971i			1.84490i
$330$	−6.92668	−	38.3796i	−0.0209899	−	0.116302i
$331$			0.262782i			0.000793904i	1.00000		0.000396952i	$0.000126354\pi$
$331$			0.262782i			0.000793904i	−1.00000		0.000396952i	$0.999874\pi$
$332$		−	117.744i		−	0.354650i
$333$	−152.864	+	282.199i	−0.459052	+	0.847444i
$334$	−5.10424			−0.0152822
$335$	−6.54762	+	17.4682i	−0.0195451	+	0.0521439i
$336$	143.825	+	241.479i	0.428049	+	0.718686i
$337$		−	353.820i		−	1.04991i	−0.851130	−	0.524956i	$-0.824082\pi$
$337$		−	353.820i		−	1.04991i	0.851130	−	0.524956i	$-0.175918\pi$
$338$	−97.4036	−	90.8888i	−0.288176	−	0.268902i
$339$	−37.2589	−	62.5569i	−0.109908	−	0.184534i
$340$	−33.2960	+	88.8295i	−0.0979294	+	0.261263i
$341$			81.8446i			0.240013i
$342$	75.3059	−	139.020i	0.220193	−	0.406492i
$343$	−126.851			−0.369828
$344$	−126.458			−0.367611
$345$	−631.050	+	113.891i	−1.82913	+	0.330118i
$346$			31.3501i			0.0906073i
$347$	−60.2016			−0.173492			−0.0867458	−	0.996230i	$-0.527647\pi$
$347$	−60.2016			−0.173492			−0.0867458	+	0.996230i	$0.527647\pi$
$348$	252.971	−	150.670i	0.726929	−	0.432959i
$349$		−	115.662i		−	0.331410i	−0.986175	−	0.165705i	$-0.947010\pi$
$349$		−	115.662i		−	0.331410i	0.986175	−	0.165705i	$-0.0529899\pi$
$350$	−135.917	+	155.832i	−0.388335	+	0.445235i
$351$	152.903	+	315.946i	0.435622	+	0.900130i
$352$		−	99.9522i		−	0.283955i
$353$			429.392i			1.21641i	0.793781	+	0.608204i	$0.208110\pi$
$353$			429.392i			1.21641i	−0.793781	+	0.608204i	$0.791890\pi$
$354$	−195.078	+	116.189i	−0.551069	+	0.328216i
$355$	−74.8204	+	199.611i	−0.210762	+	0.562286i
$356$	70.1872			0.197155
$357$	90.4527	+	151.868i	0.253369	+	0.425401i
$358$	−241.979			−0.675918
$359$	238.641			0.664738			0.332369	−	0.943149i	$-0.392152\pi$
$359$	238.641			0.664738			0.332369	+	0.943149i	$0.392152\pi$
$360$	197.515	−	171.749i	0.548653	−	0.477080i
$361$	−135.629			−0.375704
$362$			49.1441i			0.135757i
$363$	169.052	+	283.836i	0.465709	+	0.781916i
$364$	−183.692	−	422.649i	−0.504650	−	1.16112i
$365$	−139.988	+	373.471i	−0.383529	+	1.02321i
$366$	−77.6845	+	46.2689i	−0.212253	+	0.126418i
$367$			601.968i			1.64024i	0.572191	+	0.820120i	$0.306093\pi$
$367$			601.968i			1.64024i	−0.572191	+	0.820120i	$0.693907\pi$
$368$	−381.719			−1.03728
$369$	77.6429	−	143.335i	0.210414	−	0.388441i
$370$	−131.613	−	49.3324i	−0.355710	−	0.133331i
$371$	−717.046			−1.93274
$372$	−216.093	+	128.705i	−0.580894	+	0.345980i
$373$		−	130.814i		−	0.350709i	−0.984505	−	0.175355i	$-0.943893\pi$
$373$		−	130.814i		−	0.350709i	0.984505	−	0.175355i	$-0.0561072\pi$
$374$		−	14.6005i		−	0.0390389i
$375$	−321.894	−	192.379i	−0.858383	−	0.513010i
$376$	336.479			0.894891
$377$	−346.349	+	150.531i	−0.918698	+	0.399286i
$378$	−9.09488	−	223.135i	−0.0240605	−	0.590304i
$379$			206.905i			0.545923i	0.962025	+	0.272962i	$0.0880032\pi$
$379$			206.905i			0.545923i	−0.962025	+	0.272962i	$0.911997\pi$
$380$	−352.512	−	132.132i	−0.927663	−	0.347716i
$381$	298.599	−	177.845i	0.783723	−	0.466785i
$382$	28.5489			0.0747353
$383$		−	101.681i		−	0.265486i	−0.991151	−	0.132743i	$-0.957622\pi$
$383$		−	101.681i		−	0.265486i	0.991151	−	0.132743i	$-0.0423784\pi$
$384$	336.471	−	200.402i	0.876228	−	0.521881i
$385$	−60.7309	+	162.022i	−0.157742	+	0.420837i
$386$		−	111.571i		−	0.289044i
$387$	−172.050	−	93.1977i	−0.444573	−	0.240821i
$388$	−314.352			−0.810186
$389$		−	401.438i		−	1.03198i	−0.856596	−	0.515988i	$-0.827425\pi$
$389$		−	401.438i		−	1.03198i	0.856596	−	0.515988i	$-0.172575\pi$
$390$	−127.855	+	85.3373i	−0.327833	+	0.218814i
$391$	−240.067			−0.613982
$392$			355.331i			0.906456i
$393$	244.733	−	145.763i	0.622731	−	0.370899i
$394$	29.7821			0.0755892
$395$	−107.289	+	286.234i	−0.271618	+	0.724643i
$396$	47.7678	−	88.1830i	0.120626	−	0.222684i
$397$	−219.669			−0.553322			−0.276661	−	0.960968i	$-0.589228\pi$
$397$	−219.669			−0.553322			−0.276661	+	0.960968i	$0.589228\pi$
$398$			87.1662i			0.219010i
$399$	−602.675	+	358.953i	−1.51046	+	0.899632i
$400$	−168.230	−	146.731i	−0.420576	−	0.366827i
$401$	435.514			1.08607			0.543035	−	0.839710i	$-0.317275\pi$
$401$	435.514			1.08607			0.543035	+	0.839710i	$0.317275\pi$
$402$	7.58071	−	4.51507i	0.0188575	−	0.0112315i
$403$	295.858	−	128.586i	0.734138	−	0.319072i
$404$		−	357.057i		−	0.883804i
$405$	395.301	−	88.1035i	0.976051	−	0.217540i
$406$	240.274			0.591809
$407$	−117.615			−0.288980
$408$	84.1893	−	50.1432i	0.206346	−	0.122900i
$409$		−	183.444i		−	0.448519i	−0.974529	−	0.224259i	$-0.928004\pi$
$409$		−	183.444i		−	0.448519i	0.974529	−	0.224259i	$-0.0719963\pi$
$410$	66.8488	+	25.0569i	0.163046	+	0.0611145i
$411$	534.322	−	318.242i	1.30005	−	0.774311i
$412$			323.009i			0.784004i
$413$	1007.39			2.43921
$414$	266.683	+	144.459i	0.644161	+	0.348935i
$415$	163.165	+	61.1591i	0.393168	+	0.147371i
$416$	−361.314	+	157.035i	−0.868544	+	0.377488i
$417$	−190.873	−	320.472i	−0.457730	−	0.768519i
$418$	57.9409			0.138615
$419$		−	476.017i		−	1.13608i	−0.823002	−	0.568039i	$-0.807702\pi$
$419$		−	476.017i		−	1.13608i	0.823002	−	0.568039i	$-0.192298\pi$
$420$	−523.286	+	94.4418i	−1.24592	+	0.224861i
$421$			341.776i			0.811819i	0.913913	+	0.405910i	$0.133045\pi$
$421$			341.776i			0.811819i	−0.913913	+	0.405910i	$0.866955\pi$
$422$		−	27.3584i		−	0.0648304i
$423$	457.789	+	247.980i	1.08224	+	0.586241i
$424$			397.500i			0.937501i
$425$	−105.802	−	92.2805i	−0.248945	−	0.217131i
$426$	86.6257	−	51.5943i	0.203347	−	0.121113i
$427$	401.165			0.939498
$428$	224.491			0.524512
$429$	−75.1179	+	104.418i	−0.175100	+	0.243398i
$430$	30.0768	−	80.2411i	0.0699460	−	0.186607i
$431$	195.792			0.454274			0.227137	−	0.973863i	$-0.427064\pi$
$431$	195.792			0.454274			0.227137	+	0.973863i	$0.427064\pi$
$432$	240.888	−	9.81847i	0.557611	−	0.0227280i
$433$			300.629i			0.694293i	0.937811	+	0.347147i	$0.112849\pi$
$433$			300.629i			0.694293i	−0.937811	+	0.347147i	$0.887151\pi$
$434$	−205.247			−0.472918
$435$	77.3924	+	428.819i	0.177914	+	0.985790i
$436$			480.442i			1.10193i
$437$		−	952.683i		−	2.18005i
$438$	162.076	−	96.5323i	0.370036	−	0.220393i
$439$	−152.725			−0.347893			−0.173947	−	0.984755i	$-0.555652\pi$
$439$	−152.725			−0.347893			−0.173947	+	0.984755i	$0.555652\pi$
$440$	89.8184	+	33.6666i	0.204133	+	0.0765151i
$441$	−261.873	+	483.438i	−0.593817	+	1.09623i
$442$	−52.7791	+	22.9389i	−0.119410	+	0.0518981i
$443$	−561.260			−1.26695			−0.633477	−	0.773762i	$-0.718373\pi$
$443$	−561.260			−1.26695			−0.633477	+	0.773762i	$0.718373\pi$
$444$	−184.955	−	310.536i	−0.416566	−	0.699406i
$445$	−36.4570	+	97.2627i	−0.0819258	+	0.218568i
$446$			281.047i			0.630149i
$447$	−376.183	−	631.603i	−0.841572	−	1.41298i
$448$	−124.097			−0.277002
$449$	−269.134			−0.599408			−0.299704	−	0.954032i	$-0.596888\pi$
$449$	−269.134			−0.599408			−0.299704	+	0.954032i	$0.596888\pi$
$450$	62.0022	+	166.177i	0.137783	+	0.369283i
$451$	59.7390			0.132459
$452$	82.0005			0.181417
$453$	492.126	−	293.110i	1.08637	−	0.647042i
$454$	186.077			0.409861
$455$	681.104	−	35.0193i	1.49693	−	0.0769655i
$456$	198.989	+	334.098i	0.436378	+	0.732670i
$457$	−390.643			−0.854800			−0.427400	−	0.904063i	$-0.640570\pi$
$457$	−390.643			−0.854800			−0.427400	+	0.904063i	$0.640570\pi$
$458$	109.350			0.238755
$459$	151.497	−	6.17493i	0.330058	−	0.0134530i
$460$	253.469	−	676.223i	0.551019	−	1.47005i
$461$	−662.005			−1.43602			−0.718009	−	0.696033i	$-0.754947\pi$
$461$	−662.005			−1.43602			−0.718009	+	0.696033i	$0.754947\pi$
$462$	70.3131	−	41.8785i	0.152193	−	0.0906461i
$463$	671.016			1.44928			0.724639	−	0.689129i	$-0.242006\pi$
$463$	671.016			1.44928			0.724639	+	0.689129i	$0.242006\pi$
$464$			259.391i			0.559032i
$465$	−66.1100	−	366.305i	−0.142172	−	0.787752i
$466$		−	231.095i		−	0.495913i
$467$	608.959			1.30398			0.651991	−	0.758227i	$-0.273934\pi$
$467$	608.959			1.30398			0.651991	+	0.758227i	$0.273934\pi$
$468$	−393.818	−	34.1302i	−0.841492	−	0.0729278i
$469$	−39.1471			−0.0834693
$470$	−80.0281	+	213.505i	−0.170272	+	0.454266i
$471$	253.599	−	151.043i	0.538426	−	0.320686i
$472$		−	558.456i		−	1.18317i
$473$		−	71.7070i		−	0.151600i
$474$	124.217	−	73.9839i	0.262062	−	0.156084i
$475$	366.207	−	419.864i	0.770961	−	0.883925i
$476$	−199.071			−0.418217
$477$	−292.952	+	540.810i	−0.614154	+	1.13377i
$478$			327.533i			0.685215i
$479$	−690.829			−1.44223			−0.721116	−	0.692814i	$-0.756371\pi$
$479$	−690.829			−1.44223			−0.721116	+	0.692814i	$0.756371\pi$
$480$	80.7364	+	447.347i	0.168201	+	0.931974i
$481$	184.785	+	425.163i	0.384168	+	0.883914i
$482$	305.633			0.634094
$483$	−688.579	−	1156.11i	−1.42563	−	2.39360i
$484$	−372.056			−0.768711
$485$	163.282	−	435.616i	0.336664	−	0.898178i
$486$	−172.009	−	84.3030i	−0.353927	−	0.173463i
$487$	−124.032			−0.254687			−0.127343	−	0.991859i	$-0.540645\pi$
$487$	−124.032			−0.254687			−0.127343	+	0.991859i	$0.540645\pi$
$488$		−	222.389i		−	0.455716i
$489$	279.252	+	468.858i	0.571067	+	0.958809i
$490$	−225.467	−	84.5118i	−0.460136	−	0.172473i
$491$		−	518.858i		−	1.05674i	−0.849015	−	0.528369i	$-0.822804\pi$
$491$		−	518.858i		−	1.05674i	0.849015	−	0.528369i	$-0.177196\pi$
$492$	93.9426	+	157.728i	0.190940	+	0.320585i
$493$			163.133i			0.330899i
$494$	−91.0311	−	209.449i	−0.184273	−	0.423986i
$495$	97.3886	+	111.999i	0.196745	+	0.226261i
$496$		−	221.576i		−	0.446726i
$497$	−447.338			−0.900077
$498$	−42.1738	−	70.8089i	−0.0846863	−	0.142187i
$499$		−	612.065i		−	1.22658i	−0.789857	−	0.613292i	$-0.789845\pi$
$499$		−	612.065i		−	1.22658i	0.789857	−	0.613292i	$-0.210155\pi$
$500$	371.645	−	200.591i	0.743290	−	0.401182i
$501$	16.6891	−	9.94005i	0.0333117	−	0.0198404i
$502$	−9.93058			−0.0197820
$503$	−441.737			−0.878205			−0.439103	−	0.898437i	$-0.644704\pi$
$503$	−441.737			−0.878205			−0.439103	+	0.898437i	$0.644704\pi$
$504$	482.958	+	261.613i	0.958249	+	0.519074i
$505$	494.795	+	185.464i	0.979792	+	0.367256i
$506$			111.148i			0.219660i
$507$	495.474	+	107.491i	0.977267	+	0.212013i
$508$			391.408i			0.770487i
$509$	739.372			1.45260			0.726299	−	0.687379i	$-0.241239\pi$
$509$	739.372			1.45260			0.726299	+	0.687379i	$0.241239\pi$
$510$	11.7936	+	65.3464i	0.0231247	+	0.128130i
$511$	−836.965			−1.63790
$512$			478.346i			0.934269i
$513$	24.5047	+	601.201i	0.0477674	+	1.17193i
$514$		−	127.130i		−	0.247335i
$515$	−447.614	−	167.779i	−0.869153	−	0.325785i
$516$	189.326	−	112.763i	0.366912	−	0.218533i
$517$			190.797i			0.369047i
$518$		−	294.950i		−	0.569401i
$519$	−61.0515	−	102.504i	−0.117633	−	0.197503i
$520$	−19.4132	−	377.576i	−0.0373331	−	0.726107i
$521$		−	300.845i		−	0.577438i	−0.957414	−	0.288719i	$-0.906771\pi$
$521$		−	300.845i		−	0.577438i	0.957414	−	0.288719i	$-0.0932293\pi$
$522$	98.1648	−	181.220i	0.188055	−	0.347164i
$523$			205.401i			0.392735i	0.980530	+	0.196368i	$0.0629146\pi$
$523$			205.401i			0.392735i	−0.980530	+	0.196368i	$0.937085\pi$
$524$			320.800i			0.612214i
$525$	140.934	−	774.205i	0.268446	−	1.47468i
$526$			118.924i			0.226091i
$527$		−	139.351i		−	0.264424i
$528$	45.2103	+	75.9073i	0.0856257	+	0.143764i
$529$	1298.53			2.45469
$530$	−252.224	−	94.5413i	−0.475895	−	0.178380i
$531$	411.573	−	759.795i	0.775091	−	1.43087i
$532$		−	789.996i		−	1.48495i
$533$	−93.8561	−	215.949i	−0.176090	−	0.405158i
$534$	42.2092	−	25.1398i	0.0790435	−	0.0470783i
$535$	−116.606	+	311.091i	−0.217955	+	0.581478i
$536$			21.7015i			0.0404879i
$537$	791.188	−	471.231i	1.47335	−	0.877525i
$538$	−55.0085			−0.102246
$539$	−201.487			−0.373817
$540$	−142.561	+	433.257i	−0.264001	+	0.802328i
$541$		−	368.781i		−	0.681666i	−0.940124	−	0.340833i	$-0.889291\pi$
$541$		−	368.781i		−	0.681666i	0.940124	−	0.340833i	$-0.110709\pi$
$542$	−126.605			−0.233588
$543$	−95.7036	−	160.684i	−0.176250	−	0.295920i
$544$			170.182i			0.312835i
$545$	−665.778	−	249.554i	−1.22161	−	0.457896i
$546$	−261.854	−	188.378i	−0.479587	−	0.345014i
$547$			5.41064i			0.00989148i	0.999988	+	0.00494574i	$0.00157428\pi$
$547$			5.41064i			0.00989148i	−0.999988	+	0.00494574i	$0.998426\pi$
$548$			700.397i			1.27810i
$549$	163.897	−	302.567i	0.298538	−	0.551124i
$550$	−42.7247	+	48.9849i	−0.0776813	+	0.0890634i
$551$	−647.380			−1.17492
$552$	−640.899	+	381.719i	−1.16105	+	0.691521i
$553$	−641.464			−1.15997
$554$	−143.790			−0.259548
$555$	526.399	−	95.0035i	0.948466	−	0.171177i
$556$	420.080			0.755540
$557$		−	386.944i		−	0.694693i	−0.937737	−	0.347347i	$-0.887083\pi$
$557$		−	386.944i		−	0.694693i	0.937737	−	0.347347i	$-0.112917\pi$
$558$	−83.8541	+	154.801i	−0.150276	+	0.277421i
$559$	−259.212	+	112.659i	−0.463706	+	0.201537i
$560$	164.415	−	438.640i	0.293599	−	0.783285i
$561$	28.4332	+	47.7388i	0.0506831	+	0.0850959i
$562$		−	33.9028i		−	0.0603252i
$563$	338.364			0.601002			0.300501	−	0.953781i	$-0.402846\pi$
$563$	338.364			0.601002			0.300501	+	0.953781i	$0.402846\pi$
$564$	−503.759	+	300.038i	−0.893189	+	0.531983i
$565$	−42.5931	+	113.633i	−0.0753860	+	0.201120i
$566$	271.599			0.479857
$567$	464.272	+	711.864i	0.818822	+	1.25549i
$568$			247.986i			0.436594i
$569$			660.133i			1.16016i	0.814558	+	0.580082i	$0.196980\pi$
$569$			660.133i			1.16016i	−0.814558	+	0.580082i	$0.803020\pi$
$570$	−259.321	+	46.8018i	−0.454949	+	0.0821084i
$571$	69.4601			0.121646			0.0608232	−	0.998149i	$-0.480627\pi$
$571$	69.4601			0.121646			0.0608232	+	0.998149i	$0.480627\pi$
$572$	−57.7426	−	132.857i	−0.100949	−	0.232268i
$573$	−93.3451	+	55.5963i	−0.162906	+	0.0970268i
$574$			149.811i			0.260995i
$575$	805.425	+	702.494i	1.40074	+	1.22173i
$576$	−50.7001	+	93.5962i	−0.0880211	+	0.162493i
$577$	278.605			0.482851			0.241426	−	0.970419i	$-0.422385\pi$
$577$	278.605			0.482851			0.241426	+	0.970419i	$0.422385\pi$
$578$		−	202.959i		−	0.351140i
$579$	217.274	+	364.799i	0.375257	+	0.630050i
$580$	−459.516	−	172.240i	−0.792269	−	0.296966i
$581$			365.660i			0.629363i
$582$	−189.045	+	112.595i	−0.324820	+	0.193463i
$583$	−225.399			−0.386619
$584$			463.978i			0.794483i
$585$	251.855	−	528.009i	0.430522	−	0.902580i
$586$	−156.477			−0.267026
$587$			930.344i			1.58491i	0.609929	+	0.792456i	$0.291198\pi$
$587$			930.344i			1.58491i	−0.609929	+	0.792456i	$0.708802\pi$
$588$	−316.849	−	531.982i	−0.538858	−	0.904732i
$589$	553.003			0.938885
$590$	354.355	+	132.823i	0.600602	+	0.225124i
$591$	−97.3775	+	57.9980i	−0.164767	+	0.0981354i
$592$	318.416			0.537865
$593$		−	529.268i		−	0.892527i	−0.894902	−	0.446263i	$-0.852754\pi$
$593$		−	529.268i		−	0.892527i	0.894902	−	0.446263i	$-0.147246\pi$
$594$	−2.85892	−	70.1411i	−0.00481300	−	0.118083i
$595$	103.402	−	275.865i	0.173786	−	0.463638i
$596$	827.915			1.38912
$597$	−169.748	−	285.004i	−0.284335	−	0.477393i
$598$	401.786	−	174.625i	0.671883	−	0.292015i
$599$			862.676i			1.44019i	0.693873	+	0.720097i	$0.255903\pi$
$599$			862.676i			1.44019i	−0.693873	+	0.720097i	$0.744097\pi$
$600$	−429.187	−	78.1280i	−0.715311	−	0.130213i
$601$	−732.710			−1.21915			−0.609576	−	0.792728i	$-0.708660\pi$
$601$	−732.710			−1.21915			−0.609576	+	0.792728i	$0.708660\pi$
$602$	179.824			0.298711
$603$	−15.9937	+	29.5255i	−0.0265235	+	0.0489643i
$604$			645.086i			1.06802i
$605$	193.255	−	515.580i	0.319430	−	0.852198i
$606$	−127.891	−	214.727i	−0.211042	−	0.354335i
$607$			571.266i			0.941130i	0.882365	+	0.470565i	$0.155950\pi$
$607$			571.266i			0.941130i	−0.882365	+	0.470565i	$0.844050\pi$
$608$	−675.352			−1.11078
$609$	−785.615	+	467.912i	−1.29001	+	0.768329i
$610$	141.112	+	52.8930i	0.231331	+	0.0867098i
$611$	689.708	−	299.762i	1.12882	−	0.490609i
$612$	−81.3311	+	150.143i	−0.132894	+	0.245332i
$613$	562.680			0.917911			0.458956	−	0.888459i	$-0.348224\pi$
$613$	562.680			0.917911			0.458956	+	0.888459i	$0.348224\pi$
$614$		−	61.0081i		−	0.0993618i
$615$	−267.369	+	48.2542i	−0.434746	+	0.0784621i
$616$			201.287i			0.326765i
$617$		−	21.3170i		−	0.0345494i	−0.999851	−	0.0172747i	$-0.994501\pi$
$617$		−	21.3170i		−	0.0345494i	0.999851	−	0.0172747i	$-0.00549899\pi$
$618$	115.696	+	194.252i	0.187211	+	0.314323i
$619$		−	6.34749i		−	0.0102544i	−0.999987	−	0.00512721i	$-0.998368\pi$
$619$		−	6.34749i		−	0.0102544i	0.999987	−	0.00512721i	$-0.00163205\pi$
$620$	392.527	+	147.131i	0.633107	+	0.237308i
$621$	−1153.28	+	47.0073i	−1.85714	+	0.0756961i
$622$	186.000			0.299035
$623$	−217.970			−0.349872
$624$	203.365	−	282.688i	0.325905	−	0.453025i
$625$	84.9297	+	619.203i	0.135888	+	0.990724i
$626$	354.032			0.565546
$627$	−189.447	+	112.835i	−0.302149	+	0.179960i
$628$			332.421i			0.529333i
$629$	200.255			0.318371
$630$	−280.867	+	244.227i	−0.445821	+	0.387662i
$631$			146.759i			0.232581i	0.993215	+	0.116291i	$0.0371004\pi$
$631$			146.759i			0.232581i	−0.993215	+	0.116291i	$0.962900\pi$
$632$			355.601i			0.562659i
$633$	53.2781	+	89.4528i	0.0841676	+	0.141316i
$634$	−286.226			−0.451460
$635$	−542.397	−	203.307i	−0.854168	−	0.320168i
$636$	−354.451	−	595.116i	−0.557313	−	0.935718i
$637$	316.557	+	728.351i	0.496950	+	1.14341i
$638$	75.5287			0.118384
$639$	−182.762	+	337.391i	−0.286012	+	0.527999i
$640$	−611.192	−	229.093i	−0.954988	−	0.357958i
$641$		−	1175.54i		−	1.83392i	−0.398985	−	0.916958i	$-0.630637\pi$
$641$		−	1175.54i		−	1.83392i	0.398985	−	0.916958i	$-0.369363\pi$
$642$	135.004	−	80.4086i	0.210287	−	0.125247i
$643$	−1235.57			−1.92158			−0.960788	−	0.277283i	$-0.910566\pi$
$643$	−1235.57			−1.92158			−0.960788	+	0.277283i	$0.910566\pi$
$644$	1515.45			2.35318
$645$	57.9213	+	320.933i	0.0898005	+	0.497570i
$646$	−98.6522			−0.152712
$647$	−766.318			−1.18442			−0.592208	−	0.805785i	$-0.701744\pi$
$647$	−766.318			−1.18442			−0.592208	+	0.805785i	$0.701744\pi$
$648$	394.628	−	257.373i	0.608993	−	0.397181i
$649$	316.667			0.487931
$650$	244.199	+	77.4843i	0.375691	+	0.119207i
$651$	671.087	−	399.699i	1.03085	−	0.613977i
$652$	−614.586			−0.942616
$653$	−115.606			−0.177038			−0.0885189	−	0.996074i	$-0.528213\pi$
$653$	−115.606			−0.177038			−0.0885189	+	0.996074i	$0.528213\pi$
$654$	172.086	+	288.929i	0.263128	+	0.441787i
$655$	−444.552	−	166.632i	−0.678706	−	0.254399i
$656$	−161.730			−0.246540
$657$	−341.945	+	631.255i	−0.520464	+	0.960815i
$658$	−478.474			−0.727165
$659$		−	387.286i		−	0.587688i	−0.955853	−	0.293844i	$-0.905065\pi$
$659$		−	387.286i		−	0.587688i	0.955853	−	0.293844i	$-0.0949346\pi$
$660$	−164.492	+	29.6872i	−0.249230	+	0.0449806i
$661$		−	540.989i		−	0.818441i	−0.912436	−	0.409220i	$-0.865801\pi$
$661$		−	540.989i		−	0.818441i	0.912436	−	0.409220i	$-0.134199\pi$
$662$	−0.207151			−0.000312917
$663$	127.898	−	177.785i	0.192908	−	0.268152i
$664$	202.706			0.305281
$665$	1094.74	+	410.343i	1.64623	+	0.617057i
$666$	−222.457	−	120.503i	−0.334020	−	0.180935i
$667$		−	1241.87i		−	1.86187i
$668$			21.8764i			0.0327491i
$669$	−547.313	−	918.927i	−0.818105	−	1.37358i
$670$	−13.7702	−	5.16148i	−0.0205525	−	0.00770370i
$671$	126.104			0.187934
$672$	−819.560	+	488.130i	−1.21958	+	0.726384i
$673$		−	884.578i		−	1.31438i	−0.753725	−	0.657190i	$-0.771745\pi$
$673$		−	884.578i		−	1.31438i	0.753725	−	0.657190i	$-0.228255\pi$
$674$	278.916			0.413822
$675$	−526.341	−	422.599i	−0.779765	−	0.626073i
$676$	−389.542	+	417.464i	−0.576246	+	0.617550i
$677$	701.777			1.03660			0.518299	−	0.855199i	$-0.326565\pi$
$677$	701.777			1.03660			0.518299	+	0.855199i	$0.326565\pi$
$678$	49.3135	−	29.3711i	0.0727338	−	0.0433202i
$679$	976.237			1.43776
$680$	−152.928	−	57.3220i	−0.224894	−	0.0842970i
$681$	−608.409	+	362.368i	−0.893405	+	0.532112i
$682$	−64.5180			−0.0946011
$683$		−	599.528i		−	0.877786i	−0.898539	−	0.438893i	$-0.855371\pi$
$683$		−	599.528i		−	0.877786i	0.898539	−	0.438893i	$-0.144629\pi$
$684$	−595.830	−	322.755i	−0.871097	−	0.471864i
$685$	−970.582	−	363.803i	−1.41691	−	0.531100i
$686$		−	99.9966i		−	0.145768i
$687$	−357.536	+	212.949i	−0.520431	+	0.309969i
$688$			194.131i			0.282167i
$689$	354.125	+	814.789i	0.513969	+	1.18257i
$690$	−89.7798	−	497.456i	−0.130116	−	0.720950i
$691$		−	56.9097i		−	0.0823585i	−0.999152	−	0.0411792i	$-0.986889\pi$
$691$		−	56.9097i		−	0.0823585i	0.999152	−	0.0411792i	$-0.0131115\pi$
$692$	134.364			0.194168
$693$	−148.345	+	273.857i	−0.214063	+	0.395176i
$694$		−	47.4569i		−	0.0683816i
$695$	−218.200	+	582.130i	−0.313957	+	0.837597i
$696$	259.391	+	435.512i	0.372688	+	0.625736i
$697$	−101.714			−0.145931
$698$	91.1762			0.130625
$699$	450.037	+	755.603i	0.643830	+	1.08098i
$700$	667.884	+	582.530i	0.954120	+	0.832186i
$701$			923.569i			1.31750i	0.752361	+	0.658751i	$0.228915\pi$
$701$			923.569i			1.31750i	−0.752361	+	0.658751i	$0.771085\pi$
$702$	−249.059	+	120.533i	−0.354786	+	0.171700i
$703$			794.694i			1.13043i
$704$	−39.0090			−0.0554106
$705$	−154.117	−	853.936i	−0.218605	−	1.21126i
$706$	−338.489			−0.479446
$707$			1108.86i			1.56840i
$708$	497.975	+	836.090i	0.703355	+	1.18092i
$709$			1214.52i			1.71300i	0.516149	+	0.856499i	$0.327365\pi$
$709$			1214.52i			1.71300i	−0.516149	+	0.856499i	$0.672635\pi$
$710$	−157.353	−	58.9808i	−0.221625	−	0.0830716i
$711$	−262.072	+	483.804i	−0.368596	+	0.680456i
$712$			120.833i			0.169710i
$713$			1060.83i			1.48783i
$714$	−119.718	+	71.3037i	−0.167672	+	0.0998652i
$715$	214.101	−	11.0081i	0.299442	−	0.0153959i
$716$			1037.10i			1.44846i
$717$	−637.840	−	1070.92i	−0.889596	−	1.49361i
$718$			188.120i			0.262006i
$719$		−	251.260i		−	0.349458i	−0.984617	−	0.174729i	$-0.944095\pi$
$719$		−	251.260i		−	0.349458i	0.984617	−	0.174729i	$-0.0559049\pi$
$720$	−263.658	−	303.213i	−0.366192	−	0.421129i
$721$		−	1003.12i		−	1.39129i
$722$		−	106.916i		−	0.148084i
$723$	−999.316	+	595.193i	−1.38218	+	0.823226i
$724$	210.627			0.290922
$725$	477.368	−	547.313i	0.658438	−	0.754914i
$726$	−223.747	+	133.264i	−0.308192	+	0.183559i
$727$		−	1049.06i		−	1.44299i	−0.692419	−	0.721496i	$-0.743455\pi$
$727$		−	1049.06i		−	1.44299i	0.692419	−	0.721496i	$-0.256545\pi$
$728$	727.627	−	316.243i	0.999488	−	0.434399i
$729$	726.582	−	59.3288i	0.996683	−	0.0813839i
$730$	−294.406	−	110.352i	−0.403296	−	0.151168i
$731$			122.091i			0.167019i
$732$	198.305	+	332.949i	0.270908	+	0.454849i
$733$	851.692			1.16193			0.580963	−	0.813930i	$-0.302676\pi$
$733$	851.692			1.16193			0.580963	+	0.813930i	$0.302676\pi$
$734$	−474.531			−0.646500
$735$	901.779	−	162.751i	1.22691	−	0.221430i
$736$		−	1295.53i		−	1.76023i
$737$	−12.3056			−0.0166969
$738$	112.990	+	61.2058i	0.153104	+	0.0829347i
$739$		−	742.028i		−	1.00410i	−0.864839	−	0.502049i	$-0.832580\pi$
$739$		−	742.028i		−	1.00410i	0.864839	−	0.502049i	$-0.167420\pi$
$740$	−211.435	+	564.081i	−0.285722	+	0.762272i
$741$	705.524	+	507.552i	0.952124	+	0.684956i
$742$		−	565.247i		−	0.761788i
$743$			594.550i			0.800202i	0.916471	+	0.400101i	$0.131025\pi$
$743$			594.550i			0.800202i	−0.916471	+	0.400101i	$0.868975\pi$
$744$	−221.576	−	372.022i	−0.297818	−	0.500030i
$745$	−430.040	+	1147.29i	−0.577234	+	1.53999i
$746$	103.121			0.138232
$747$	275.788	+	149.391i	0.369194	+	0.199989i
$748$	−62.5768			−0.0836588
$749$	−697.168			−0.930799
$750$	151.652	−	253.748i	0.202203	−	0.338331i
$751$	888.030			1.18246			0.591232	−	0.806502i	$-0.298642\pi$
$751$	888.030			1.18246			0.591232	+	0.806502i	$0.298642\pi$
$752$		−	516.542i		−	0.686891i
$753$	32.4696	−	19.3389i	0.0431203	−	0.0256825i
$754$	−118.663	−	273.027i	−0.157378	−	0.362104i
$755$	−893.934	−	335.073i	−1.18402	−	0.443806i
$756$	−956.339	+	38.9799i	−1.26500	+	0.0515608i
$757$		−	788.965i		−	1.04223i	−0.853488	−	0.521113i	$-0.825517\pi$
$757$		−	788.965i		−	1.04223i	0.853488	−	0.521113i	$-0.174483\pi$
$758$	−163.103			−0.215175
$759$	−216.451	−	363.416i	−0.285179	−	0.478809i
$760$	227.477	−	606.880i	0.299312	−	0.798526i
$761$	274.957			0.361311			0.180655	−	0.983546i	$-0.442178\pi$
$761$	274.957			0.361311			0.180655	+	0.983546i	$0.442178\pi$
$762$	140.195	+	235.385i	0.183983	+	0.308904i
$763$		−	1492.04i		−	1.95549i
$764$		−	122.358i		−	0.160155i
$765$	−165.817	−	190.694i	−0.216754	−	0.249273i
$766$	80.1550			0.104641
$767$	−497.517	−	1144.71i	−0.648653	−	1.49245i
$768$	85.3505	+	143.302i	0.111133	+	0.186591i
$769$			1483.77i			1.92948i	0.263203	+	0.964741i	$0.415221\pi$
$769$			1483.77i			1.92948i	−0.263203	+	0.964741i	$0.584779\pi$
$770$	−127.722	−	47.8741i	−0.165873	−	0.0621741i
$771$	247.575	+	415.673i	0.321108	+	0.539135i
$772$	−478.184			−0.619409
$773$		−	622.090i		−	0.804774i	−0.915470	−	0.402387i	$-0.868181\pi$
$773$		−	622.090i		−	0.804774i	0.915470	−	0.402387i	$-0.131819\pi$
$774$	73.4676	−	135.627i	0.0949194	−	0.175228i
$775$	−407.776	+	467.524i	−0.526163	+	0.603257i
$776$		−	541.184i		−	0.697403i
$777$	574.388	+	964.386i	0.739238	+	1.24117i
$778$	316.453			0.406753
$779$		−	403.642i		−	0.518153i
$780$	365.749	+	547.975i	0.468909	+	0.702533i
$781$	−140.618			−0.180049
$782$		−	189.244i		−	0.242001i
$783$	31.9430	+	783.693i	0.0407956	+	1.00089i
$784$	545.482			0.695768
$785$	−460.655	−	172.668i	−0.586822	−	0.219959i
$786$	114.905	+	192.923i	0.146190	+	0.245449i
$787$	688.266			0.874544			0.437272	−	0.899329i	$-0.355945\pi$
$787$	688.266			0.874544			0.437272	+	0.899329i	$0.355945\pi$
$788$		−	127.644i		−	0.161985i
$789$	−231.593	−	388.840i	−0.293527	−	0.492826i
$790$	−225.638	−	84.5759i	−0.285618	−	0.107058i
$791$	−254.657			−0.321943
$792$	151.815	+	82.2365i	0.191685	+	0.103834i
$793$	−198.122	−	455.849i	−0.249839	−	0.574842i
$794$		−	173.165i		−	0.218092i
$795$	1008.80	−	182.066i	1.26893	−	0.229014i
$796$	373.587			0.469331
$797$	277.330			0.347967			0.173984	−	0.984749i	$-0.444336\pi$
$797$	277.330			0.347967			0.173984	+	0.984749i	$0.444336\pi$
$798$	−282.962	−	475.088i	−0.354589	−	0.595348i
$799$		−	324.858i		−	0.406581i
$800$	497.994	−	570.961i	0.622492	−	0.713702i
$801$	−89.0524	+	164.397i	−0.111177	+	0.205240i
$802$			343.315i			0.428074i
$803$	−263.095			−0.327640
$804$	−19.3512	−	32.4903i	−0.0240687	−	0.0404109i
$805$	−787.161	+	2100.05i	−0.977839	+	2.60875i
$806$	101.364	+	233.224i	0.125762	+	0.289360i
$807$	179.859	−	107.124i	0.222874	−	0.132744i
$808$	614.704			0.760773
$809$			1069.05i			1.32144i	0.750631	+	0.660722i	$0.229750\pi$
$809$			1069.05i			1.32144i	−0.750631	+	0.660722i	$0.770250\pi$
$810$	69.4519	+	311.615i	0.0857431	+	0.384710i
$811$			123.734i			0.152570i	0.997086	+	0.0762849i	$0.0243058\pi$
$811$			123.734i			0.152570i	−0.997086	+	0.0762849i	$0.975694\pi$
$812$		−	1029.80i		−	1.26822i
$813$	413.955	−	246.551i	0.509169	−	0.303261i
$814$		−	92.7157i		−	0.113901i
$815$	319.231	−	851.668i	0.391694	−	1.04499i
$816$	−76.9767	−	129.242i	−0.0943342	−	0.158385i
$817$	−484.506			−0.593031
$818$	144.609			0.176783
$819$	1223.02	+	105.993i	1.49331	+	0.129418i
$820$	107.392	−	286.508i	0.130966	−	0.349400i
$821$	1011.50			1.23204			0.616019	−	0.787731i	$-0.288745\pi$
$821$	1011.50			1.23204			0.616019	+	0.787731i	$0.288745\pi$
$822$	250.870	+	421.205i	0.305194	+	0.512415i
$823$		−	134.463i		−	0.163382i	−0.996658	−	0.0816908i	$-0.973968\pi$
$823$		−	134.463i		−	0.163382i	0.996658	−	0.0816908i	$-0.0260320\pi$
$824$	−556.089			−0.674865
$825$	44.3018	−	243.366i	0.0536992	−	0.294990i
$826$			794.126i			0.961411i
$827$		−	438.579i		−	0.530325i	−0.964204	−	0.265162i	$-0.914574\pi$
$827$		−	438.579i		−	0.530325i	0.964204	−	0.265162i	$-0.0854256\pi$
$828$	619.141	−	1142.98i	0.747755	−	1.38041i
$829$	−179.592			−0.216636			−0.108318	−	0.994116i	$-0.534547\pi$
$829$	−179.592			−0.216636			−0.108318	+	0.994116i	$0.534547\pi$
$830$	−48.2116	+	128.623i	−0.0580863	+	0.154967i
$831$	470.144	−	280.018i	0.565757	−	0.336965i
$832$	61.2872	+	141.013i	0.0736625	+	0.169486i
$833$	343.059			0.411836
$834$	252.628	−	150.465i	0.302911	−	0.180414i
$835$	−30.3154	−	11.3631i	−0.0363059	−	0.0136085i
$836$		−	248.330i		−	0.297046i
$837$	−27.2863	−	669.445i	−0.0326001	−	0.799815i
$838$	375.243			0.447784
$839$	−258.511			−0.308118			−0.154059	−	0.988062i	$-0.549235\pi$
$839$	−258.511			−0.308118			−0.154059	+	0.988062i	$0.549235\pi$
$840$	−162.590	−	900.883i	−0.193559	−	1.07248i
$841$	−2.88959			−0.00343590
$842$	−269.422			−0.319978
$843$	66.0225	+	110.851i	0.0783186	+	0.131495i
$844$	−117.256			−0.138929
$845$	−376.167	−	756.653i	−0.445168	−	0.895447i
$846$	−195.482	+	360.875i	−0.231066	+	0.426566i
$847$	1155.44			1.36415
$848$	610.218			0.719597
$849$	−888.036	+	528.914i	−1.04598	+	0.622985i
$850$	72.7446	−	83.4033i	0.0855819	−	0.0981215i
$851$	−1524.46			−1.79138
$852$	−221.129	−	371.271i	−0.259541	−	0.435764i
$853$	397.710			0.466249			0.233124	−	0.972447i	$-0.425105\pi$
$853$	397.710			0.466249			0.233124	+	0.972447i	$0.425105\pi$
$854$			316.238i			0.370302i
$855$	756.750	−	658.030i	0.885088	−	0.769626i
$856$			386.481i			0.451496i
$857$	1161.58			1.35540			0.677700	−	0.735339i	$-0.262977\pi$
$857$	1161.58			1.35540			0.677700	+	0.735339i	$0.262977\pi$
$858$	−82.3123	−	59.2153i	−0.0959351	−	0.0690155i
$859$	−805.574			−0.937804			−0.468902	−	0.883250i	$-0.655350\pi$
$859$	−805.574			−0.937804			−0.468902	+	0.883250i	$0.655350\pi$
$860$	−343.907	−	128.907i	−0.399892	−	0.149891i
$861$	−291.744	−	489.832i	−0.338843	−	0.568910i
$862$			154.343i			0.179052i
$863$			1359.34i			1.57513i	0.616232	+	0.787564i	$0.288658\pi$
$863$			1359.34i			1.57513i	−0.616232	+	0.787564i	$0.711342\pi$
$864$	33.3232	+	817.556i	0.0385685	+	0.946245i
$865$	−69.7920	+	186.196i	−0.0806844	+	0.215256i
$866$	−236.985			−0.273655
$867$	395.244	+	663.607i	0.455875	+	0.765406i
$868$			879.670i			1.01345i
$869$	−201.640			−0.232037
$870$	−338.037	+	61.0083i	−0.388549	+	0.0701245i
$871$	19.3334	+	44.4833i	0.0221968	+	0.0510716i
$872$	−827.123			−0.948536
$873$	398.844	−	736.297i	0.456867	−	0.843410i
$874$	750.999			0.859267
$875$	−1154.16	+	622.946i	−1.31904	+	0.711939i
$876$	−413.729	−	694.643i	−0.472294	−	0.792972i
$877$	468.561			0.534278			0.267139	−	0.963658i	$-0.413922\pi$
$877$	468.561			0.534278			0.267139	+	0.963658i	$0.413922\pi$
$878$		−	120.393i		−	0.137122i
$879$	511.627	−	304.725i	0.582056	−	0.346673i
$880$	51.6829	−	137.884i	0.0587306	−	0.156686i
$881$			557.408i			0.632700i	0.948643	+	0.316350i	$0.102457\pi$
$881$			557.408i			0.632700i	−0.948643	+	0.316350i	$0.897543\pi$
$882$	−381.093	−	206.434i	−0.432079	−	0.234053i
$883$			262.535i			0.297322i	0.988888	+	0.148661i	$0.0474963\pi$
$883$			262.535i			0.297322i	−0.988888	+	0.148661i	$0.952504\pi$
$884$	98.3145	+	226.207i	0.111215	+	0.255890i
$885$	−1417.28	+	255.788i	−1.60145	+	0.289026i
$886$		−	442.441i		−	0.499369i
$887$	644.890			0.727046			0.363523	−	0.931585i	$-0.381574\pi$
$887$	644.890			0.727046			0.363523	+	0.931585i	$0.381574\pi$
$888$	534.615	−	318.417i	0.602044	−	0.358577i
$889$		−	1215.54i		−	1.36731i
$890$	−76.6720	−	28.7390i	−0.0861484	−	0.0322910i
$891$	145.941	+	223.770i	0.163795	+	0.251145i
$892$	1204.54			1.35038
$893$	1289.17			1.44364
$894$	497.892	−	296.544i	0.556926	−	0.331705i
$895$	−1437.17	−	538.695i	−1.60578	−	0.601894i
$896$		−	1369.71i		−	1.52869i
$897$	−973.637	+	1353.41i	−1.08544	+	1.50881i
$898$		−	212.158i		−	0.236256i
$899$	720.866			0.801853
$900$	712.222	−	265.737i	0.791358	−	0.295263i
$901$	383.772			0.425940
$902$			47.0922i			0.0522086i
$903$	−587.963	+	350.191i	−0.651122	+	0.387808i
$904$			141.171i			0.156163i
$905$	−109.405	+	291.879i	−0.120890	+	0.322518i
$906$	231.058	+	387.942i	0.255031	+	0.428192i
$907$			1076.51i			1.18689i	0.804873	+	0.593447i	$0.202233\pi$
$907$			1076.51i			1.18689i	−0.804873	+	0.593447i	$0.797767\pi$
$908$		−	797.511i		−	0.878316i
$909$	836.322	+	453.027i	0.920047	+	0.498380i
$910$	27.6057	+	536.914i	0.0303359	+	0.590015i
$911$		−	479.606i		−	0.526461i	−0.964733	−	0.263231i	$-0.915212\pi$
$911$		−	479.606i		−	0.526461i	0.964733	−	0.263231i	$-0.0847880\pi$
$912$	512.886	−	305.475i	0.562375	−	0.334951i
$913$			114.943i			0.125896i
$914$		−	307.944i		−	0.336919i
$915$	−564.392	+	101.860i	−0.616822	+	0.111323i
$916$		−	468.664i		−	0.511642i
$917$		−	996.262i		−	1.08644i
$918$	4.86769	+	119.425i	0.00530250	+	0.130092i
$919$	−1234.15			−1.34292			−0.671462	−	0.741039i	$-0.734333\pi$
$919$	−1234.15			−1.34292			−0.671462	+	0.741039i	$0.734333\pi$
$920$	1164.18	+	436.369i	1.26541	+	0.474314i
$921$	118.808	+	199.476i	0.128999	+	0.216586i
$922$		−	521.857i		−	0.566006i
$923$	220.925	+	508.316i	0.239356	+	0.550722i
$924$	−179.488	−	301.356i	−0.194251	−	0.326143i
$925$	−671.857	−	585.995i	−0.726331	−	0.633508i
$926$			528.961i			0.571232i
$927$	−756.575	−	409.829i	−0.816154	−	0.442102i
$928$	−880.353			−0.948656
$929$	−433.497			−0.466627			−0.233314	−	0.972402i	$-0.574957\pi$
$929$	−433.497			−0.466627			−0.233314	+	0.972402i	$0.574957\pi$
$930$	288.758	−	52.1144i	0.310492	−	0.0560370i
$931$			1361.40i			1.46230i
$932$	−990.456			−1.06272
$933$	−608.156	+	362.217i	−0.651828	+	0.388229i
$934$			480.042i			0.513963i
$935$	32.5039	−	86.7164i	0.0347635	−	0.0927448i
$936$	58.7581	−	677.993i	0.0627758	−	0.724351i
$937$		−	1368.68i		−	1.46070i	−0.683071	−	0.730352i	$-0.739356\pi$
$937$		−	1368.68i		−	1.46070i	0.683071	−	0.730352i	$-0.260644\pi$
$938$		−	30.8596i		−	0.0328994i
$939$	−1157.56	+	689.444i	−1.23276	+	0.734232i
$940$	915.065	+	342.994i	0.973473	+	0.364887i
$941$	−151.925			−0.161450			−0.0807252	−	0.996736i	$-0.525724\pi$
$941$	−151.925			−0.161450			−0.0807252	+	0.996736i	$0.525724\pi$
$942$	119.067	+	199.911i	0.126398	+	0.212220i
$943$	774.305			0.821108
$944$	−857.307			−0.908164
$945$	442.729	−	1345.50i	0.468496	−	1.42381i
$946$	56.5265			0.0597532
$947$			1799.36i			1.90006i	0.312161	+	0.950029i	$0.398947\pi$
$947$			1799.36i			1.90006i	−0.312161	+	0.950029i	$0.601053\pi$
$948$	−317.089	−	532.386i	−0.334482	−	0.561589i
$949$	413.349	+	951.054i	0.435562	+	1.00216i
$950$	330.978	+	288.680i	0.348398	+	0.303874i
$951$	935.861	−	557.398i	0.984081	−	0.586118i
$952$		−	342.718i		−	0.359998i
$953$	−829.668			−0.870586			−0.435293	−	0.900289i	$-0.643355\pi$
$953$	−829.668			−0.870586			−0.435293	+	0.900289i	$0.643355\pi$
$954$	−426.320	−	230.933i	−0.446876	−	0.242068i
$955$	169.559	+	63.5559i	0.177549	+	0.0665506i
$956$	1403.78			1.46839
$957$	−246.953	+	147.085i	−0.258049	+	0.153694i
$958$		−	544.580i		−	0.568455i
$959$		−	2175.12i		−	2.26811i
$960$	174.589	−	31.5096i	0.181864	−	0.0328225i
$961$	345.224			0.359234
$962$	−335.155	+	145.666i	−0.348394	+	0.151420i
$963$	−284.830	+	525.818i	−0.295774	+	0.546021i
$964$		−	1309.92i		−	1.35884i
$965$	248.380	−	662.648i	0.257389	−	0.686681i
$966$	911.361	−	542.806i	0.943438	−	0.561911i
$967$	−1118.92			−1.15711			−0.578553	−	0.815645i	$-0.696382\pi$
$967$	−1118.92			−1.15711			−0.578553	+	0.815645i	$0.696382\pi$
$968$		−	640.527i		−	0.661701i
$969$	322.559	−	192.116i	0.332878	−	0.198262i
$970$	343.396	+	128.715i	0.354016	+	0.132696i
$971$			15.5851i			0.0160506i	0.999968	+	0.00802530i	$0.00255456\pi$
$971$			15.5851i			0.0160506i	−0.999968	+	0.00802530i	$0.997445\pi$
$972$	−361.316	+	737.215i	−0.371724	+	0.758451i
$973$	−1304.58			−1.34078
$974$		−	97.7746i		−	0.100385i
$975$	−949.341	+	222.208i	−0.973683	+	0.227906i
$976$	−341.398			−0.349793
$977$			1.78329i			0.00182527i	1.00000		0.000912635i	$0.000290501\pi$
$977$			1.78329i			0.00182527i	−1.00000		0.000912635i	$0.999709\pi$
$978$	−369.600	+	220.134i	−0.377914	+	0.225086i
$979$	−68.5175			−0.0699873
$980$	−362.211	+	966.333i	−0.369603	+	0.986054i
$981$	−1125.32	−	609.577i	−1.14712	−	0.621383i
$982$	409.015			0.416513
$983$		−	725.440i		−	0.737986i	−0.929432	−	0.368993i	$-0.879703\pi$
$983$		−	725.440i		−	0.737986i	0.929432	−	0.368993i	$-0.120297\pi$
$984$	−271.542	+	161.730i	−0.275957	+	0.164360i
$985$	176.884	+	66.3014i	0.179577	+	0.0673110i
$986$	−128.598			−0.130424
$987$	1564.45	−	931.785i	1.58505	−	0.944058i
$988$	−897.682	+	390.152i	−0.908585	+	0.394891i
$989$		−	929.427i		−	0.939765i
$990$	−88.2888	+	76.7713i	−0.0891806	+	0.0775468i
$991$	498.352			0.502878			0.251439	−	0.967873i	$-0.419096\pi$
$991$	498.352			0.502878			0.251439	+	0.967873i	$0.419096\pi$
$992$	752.013			0.758078
$993$	0.677313	−	0.403408i	0.000682088	−	0.000406251i
$994$		−	352.636i		−	0.354765i
$995$	−194.050	+	517.702i	−0.195025	+	0.520304i
$996$	−303.481	+	180.753i	−0.304700	+	0.181479i
$997$			1020.89i			1.02396i	0.858997	+	0.511981i	$0.171088\pi$
$997$			1020.89i			1.02396i	−0.858997	+	0.511981i	$0.828912\pi$
$998$	482.490			0.483457
$999$	962.027	−	39.2118i	0.962990	−	0.0392510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.3.e.f.194.21	yes	40
3.2	odd	2	inner	195.3.e.f.194.19	yes	40
5.4	even	2	inner	195.3.e.f.194.20	yes	40
13.12	even	2	inner	195.3.e.f.194.17	✓	40
15.14	odd	2	inner	195.3.e.f.194.22	yes	40
39.38	odd	2	inner	195.3.e.f.194.23	yes	40
65.64	even	2	inner	195.3.e.f.194.24	yes	40
195.194	odd	2	inner	195.3.e.f.194.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.3.e.f.194.17	✓	40	13.12	even	2	inner
195.3.e.f.194.18	yes	40	195.194	odd	2	inner
195.3.e.f.194.19	yes	40	3.2	odd	2	inner
195.3.e.f.194.20	yes	40	5.4	even	2	inner
195.3.e.f.194.21	yes	40	1.1	even	1	trivial
195.3.e.f.194.22	yes	40	15.14	odd	2	inner
195.3.e.f.194.23	yes	40	39.38	odd	2	inner
195.3.e.f.194.24	yes	40	65.64	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+0.788299i q^{2} +(-1.53514 - 2.57747i) q^{3} +3.37859 q^{4} +(-1.75492 + 4.68191i) q^{5} +(2.03182 - 1.21015i) q^{6} -10.4924 q^{7} +5.81653i q^{8} +(-4.28669 + 7.91355i) q^{9} +O(q^{10})\)	\(q+0.788299i q^{2} +(-1.53514 - 2.57747i) q^{3} +3.37859 q^{4} +(-1.75492 + 4.68191i) q^{5} +(2.03182 - 1.21015i) q^{6} -10.4924 q^{7} +5.81653i q^{8} +(-4.28669 + 7.91355i) q^{9} +(-3.69074 - 1.38340i) q^{10} -3.29821 q^{11} +(-5.18660 - 8.70820i) q^{12} +(5.18183 + 11.9226i) q^{13} -8.27112i q^{14} +(14.7615 - 2.66413i) q^{15} +8.92918 q^{16} +5.61565 q^{17} +(-6.23824 - 3.37919i) q^{18} +22.2852i q^{19} +(-5.92915 + 15.8182i) q^{20} +(16.1073 + 27.0438i) q^{21} -2.59998i q^{22} -42.7496 q^{23} +(14.9919 - 8.92919i) q^{24} +(-18.8405 - 16.4327i) q^{25} +(-9.39858 + 4.08483i) q^{26} +(26.9776 - 1.09959i) q^{27} -35.4494 q^{28} +29.0498i q^{29} +(2.10013 + 11.6365i) q^{30} -24.8148i q^{31} +30.3050i q^{32} +(5.06322 + 8.50104i) q^{33} +4.42681i q^{34} +(18.4133 - 49.1243i) q^{35} +(-14.4830 + 26.7366i) q^{36} +35.6602 q^{37} -17.5674 q^{38} +(22.7753 - 31.6589i) q^{39} +(-27.2325 - 10.2075i) q^{40} -18.1126 q^{41} +(-21.3186 + 12.6973i) q^{42} +21.7412i q^{43} -11.1433 q^{44} +(-29.5277 - 33.9575i) q^{45} -33.6995i q^{46} -57.8488i q^{47} +(-13.7075 - 23.0147i) q^{48} +61.0898 q^{49} +(12.9539 - 14.8520i) q^{50} +(-8.62080 - 14.4742i) q^{51} +(17.5072 + 40.2816i) q^{52} +68.3398 q^{53} +(0.866809 + 21.2664i) q^{54} +(5.78810 - 15.4419i) q^{55} -61.0292i q^{56} +(57.4394 - 34.2109i) q^{57} -22.8999 q^{58} -96.0118 q^{59} +(49.8730 - 9.00099i) q^{60} -38.2340 q^{61} +19.5615 q^{62} +(44.9776 - 83.0319i) q^{63} +11.8273 q^{64} +(-64.9143 + 3.33759i) q^{65} +(-6.70136 + 3.99133i) q^{66} +3.73101 q^{67} +18.9729 q^{68} +(65.6267 + 110.186i) q^{69} +(38.7246 + 14.5152i) q^{70} +42.6346 q^{71} +(-46.0294 - 24.9337i) q^{72} +79.7689 q^{73} +28.1109i q^{74} +(-13.4321 + 73.7874i) q^{75} +75.2924i q^{76} +34.6061 q^{77} +(24.9566 + 17.9538i) q^{78} +61.1362 q^{79} +(-15.6700 + 41.8056i) q^{80} +(-44.2486 - 67.8459i) q^{81} -14.2781i q^{82} -34.8501i q^{83} +(54.4197 + 91.3696i) q^{84} +(-9.85501 + 26.2919i) q^{85} -17.1385 q^{86} +(74.8749 - 44.5955i) q^{87} -19.1841i q^{88} +20.7742 q^{89} +(26.7687 - 23.2767i) q^{90} +(-54.3696 - 125.096i) q^{91} -144.433 q^{92} +(-63.9595 + 38.0942i) q^{93} +45.6021 q^{94} +(-104.337 - 39.1087i) q^{95} +(78.1101 - 46.5224i) q^{96} -93.0425 q^{97} +48.1571i q^{98} +(14.1384 - 26.1006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 88 q^{4} + 28 q^{9}+O(q^{10}) \) 40 * q - 88 * q^4 + 28 * q^9	\( 40 q - 88 q^{4} + 28 q^{9} + 100 q^{10} - 24 q^{16} - 196 q^{25} - 126 q^{30} - 340 q^{36} + 256 q^{39} - 524 q^{40} + 864 q^{49} + 76 q^{51} + 232 q^{55} - 272 q^{61} + 264 q^{64} + 872 q^{66} + 384 q^{69} + 18 q^{75} + 400 q^{79} - 1300 q^{81} + 70 q^{90} - 360 q^{91} + 728 q^{94}+O(q^{100}) \) 40 * q - 88 * q^4 + 28 * q^9 + 100 * q^10 - 24 * q^16 - 196 * q^25 - 126 * q^30 - 340 * q^36 + 256 * q^39 - 524 * q^40 + 864 * q^49 + 76 * q^51 + 232 * q^55 - 272 * q^61 + 264 * q^64 + 872 * q^66 + 384 * q^69 + 18 * q^75 + 400 * q^79 - 1300 * q^81 + 70 * q^90 - 360 * q^91 + 728 * q^94

Introduction

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