LMFDB - Embedded newform 1205.2.b.d.724.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.11
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.d.724.56

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20997i q^{2} +2.26852i q^{3} -2.88397 q^{4} +(-2.23543 - 0.0532972i) q^{5} +5.01336 q^{6} +0.372373i q^{7} +1.95355i q^{8} -2.14617 q^{9} +O(q^{10})$	\(q-2.20997i q^{2} +2.26852i q^{3} -2.88397 q^{4} +(-2.23543 - 0.0532972i) q^{5} +5.01336 q^{6} +0.372373i q^{7} +1.95355i q^{8} -2.14617 q^{9} +(-0.117785 + 4.94024i) q^{10} +3.78368 q^{11} -6.54234i q^{12} -3.03526i q^{13} +0.822934 q^{14} +(0.120906 - 5.07112i) q^{15} -1.45065 q^{16} +0.702265i q^{17} +4.74298i q^{18} -4.26314 q^{19} +(6.44693 + 0.153708i) q^{20} -0.844736 q^{21} -8.36182i q^{22} +7.07928i q^{23} -4.43167 q^{24} +(4.99432 + 0.238285i) q^{25} -6.70783 q^{26} +1.93692i q^{27} -1.07391i q^{28} -2.22462 q^{29} +(-11.2070 - 0.267198i) q^{30} +8.12419 q^{31} +7.11300i q^{32} +8.58334i q^{33} +1.55199 q^{34} +(0.0198465 - 0.832416i) q^{35} +6.18950 q^{36} +0.768032i q^{37} +9.42143i q^{38} +6.88553 q^{39} +(0.104119 - 4.36703i) q^{40} +11.3969 q^{41} +1.86684i q^{42} +10.1749i q^{43} -10.9120 q^{44} +(4.79762 + 0.114385i) q^{45} +15.6450 q^{46} +5.84261i q^{47} -3.29083i q^{48} +6.86134 q^{49} +(0.526602 - 11.0373i) q^{50} -1.59310 q^{51} +8.75359i q^{52} -7.70807i q^{53} +4.28054 q^{54} +(-8.45816 - 0.201659i) q^{55} -0.727451 q^{56} -9.67102i q^{57} +4.91634i q^{58} -14.0213 q^{59} +(-0.348688 + 14.6250i) q^{60} +10.5586 q^{61} -17.9542i q^{62} -0.799178i q^{63} +12.8182 q^{64} +(-0.161771 + 6.78511i) q^{65} +18.9689 q^{66} +12.7576i q^{67} -2.02531i q^{68} -16.0595 q^{69} +(-1.83961 - 0.0438601i) q^{70} -0.694776 q^{71} -4.19266i q^{72} +9.45754i q^{73} +1.69733 q^{74} +(-0.540553 + 11.3297i) q^{75} +12.2948 q^{76} +1.40894i q^{77} -15.2168i q^{78} -4.15383 q^{79} +(3.24283 + 0.0773156i) q^{80} -10.8325 q^{81} -25.1868i q^{82} -11.0345i q^{83} +2.43619 q^{84} +(0.0374288 - 1.56987i) q^{85} +22.4862 q^{86} -5.04658i q^{87} +7.39161i q^{88} +17.5969 q^{89} +(0.252787 - 10.6026i) q^{90} +1.13025 q^{91} -20.4165i q^{92} +18.4299i q^{93} +12.9120 q^{94} +(9.52997 + 0.227214i) q^{95} -16.1360 q^{96} +16.6822i q^{97} -15.1634i q^{98} -8.12043 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 78 q^{4} + 16 q^{6} - 90 q^{9}+O(q^{10}) $ 66 * q - 78 * q^4 + 16 * q^6 - 90 * q^9	$ 66 q - 78 q^{4} + 16 q^{6} - 90 q^{9} + q^{10} + 48 q^{11} - 30 q^{14} - 3 q^{15} + 98 q^{16} - 12 q^{19} - 10 q^{20} + 18 q^{21} - 42 q^{24} + 6 q^{25} + 48 q^{26} - 56 q^{29} - 5 q^{30} + 48 q^{31} - 8 q^{34} + 3 q^{35} + 158 q^{36} - 84 q^{39} - 6 q^{40} + 56 q^{41} - 144 q^{44} - 13 q^{45} + 36 q^{46} - 98 q^{49} + 2 q^{50} + 44 q^{51} - 86 q^{54} + 3 q^{55} + 104 q^{56} - 108 q^{59} + 7 q^{60} + 22 q^{61} - 136 q^{64} + 15 q^{65} + 74 q^{66} - 20 q^{69} - 32 q^{70} + 212 q^{71} - 84 q^{74} - 9 q^{75} + 6 q^{76} - 66 q^{79} - 21 q^{80} + 162 q^{81} + 52 q^{84} - 48 q^{85} + 100 q^{86} - 54 q^{89} - 155 q^{90} + 72 q^{91} + 96 q^{94} - 5 q^{95} + 122 q^{96} - 112 q^{99}+O(q^{100}) $ 66 * q - 78 * q^4 + 16 * q^6 - 90 * q^9 + q^10 + 48 * q^11 - 30 * q^14 - 3 * q^15 + 98 * q^16 - 12 * q^19 - 10 * q^20 + 18 * q^21 - 42 * q^24 + 6 * q^25 + 48 * q^26 - 56 * q^29 - 5 * q^30 + 48 * q^31 - 8 * q^34 + 3 * q^35 + 158 * q^36 - 84 * q^39 - 6 * q^40 + 56 * q^41 - 144 * q^44 - 13 * q^45 + 36 * q^46 - 98 * q^49 + 2 * q^50 + 44 * q^51 - 86 * q^54 + 3 * q^55 + 104 * q^56 - 108 * q^59 + 7 * q^60 + 22 * q^61 - 136 * q^64 + 15 * q^65 + 74 * q^66 - 20 * q^69 - 32 * q^70 + 212 * q^71 - 84 * q^74 - 9 * q^75 + 6 * q^76 - 66 * q^79 - 21 * q^80 + 162 * q^81 + 52 * q^84 - 48 * q^85 + 100 * q^86 - 54 * q^89 - 155 * q^90 + 72 * q^91 + 96 * q^94 - 5 * q^95 + 122 * q^96 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.20997i		−	1.56269i	−0.624102	−	0.781343i	$-0.714535\pi$
$2$		−	2.20997i		−	1.56269i	0.624102	−	0.781343i	$-0.285465\pi$
$3$			2.26852i			1.30973i	0.755746	+	0.654865i	$0.227274\pi$
$3$			2.26852i			1.30973i	−0.755746	+	0.654865i	$0.772726\pi$
$4$	−2.88397			−1.44199
$5$	−2.23543	−	0.0532972i	−0.999716	−	0.0238352i
$5$	−2.23543	−	0.0532972i	−0.999716	−	0.0238352i
$6$	5.01336			2.04669
$7$			0.372373i			0.140744i	0.997521	+	0.0703720i	$0.0224186\pi$
$7$			0.372373i			0.140744i	−0.997521	+	0.0703720i	$0.977581\pi$
$8$			1.95355i			0.690685i
$9$	−2.14617			−0.715391
$10$	−0.117785	+	4.94024i	−0.0372470	+	1.56224i
$11$	3.78368			1.14082			0.570411	−	0.821359i	$-0.306784\pi$
$11$	3.78368			1.14082			0.570411	+	0.821359i	$0.306784\pi$
$12$		−	6.54234i		−	1.88861i
$13$		−	3.03526i		−	0.841828i	−0.907100	−	0.420914i	$-0.861709\pi$
$13$		−	3.03526i		−	0.841828i	0.907100	−	0.420914i	$-0.138291\pi$
$14$	0.822934			0.219938
$15$	0.120906	−	5.07112i	0.0312177	−	1.30936i
$16$	−1.45065			−0.362663
$17$			0.702265i			0.170324i	0.996367	+	0.0851622i	$0.0271408\pi$
$17$			0.702265i			0.170324i	−0.996367	+	0.0851622i	$0.972859\pi$
$18$			4.74298i			1.11793i
$19$	−4.26314			−0.978033			−0.489016	−	0.872275i	$-0.662644\pi$
$19$	−4.26314			−0.978033			−0.489016	+	0.872275i	$0.662644\pi$
$20$	6.44693	+	0.153708i	1.44158	+	0.0343701i
$21$	−0.844736			−0.184336
$22$		−	8.36182i		−	1.78275i
$23$			7.07928i			1.47613i	0.674728	+	0.738066i	$0.264261\pi$
$23$			7.07928i			1.47613i	−0.674728	+	0.738066i	$0.735739\pi$
$24$	−4.43167			−0.904610
$25$	4.99432	+	0.238285i	0.998864	+	0.0476569i
$26$	−6.70783			−1.31551
$27$			1.93692i			0.372761i
$28$		−	1.07391i		−	0.202951i
$29$	−2.22462			−0.413101			−0.206551	−	0.978436i	$-0.566224\pi$
$29$	−2.22462			−0.413101			−0.206551	+	0.978436i	$0.566224\pi$
$30$	−11.2070	−	0.267198i	−2.04611	−	0.0487834i
$31$	8.12419			1.45915			0.729573	−	0.683902i	$-0.239719\pi$
$31$	8.12419			1.45915			0.729573	+	0.683902i	$0.239719\pi$
$32$			7.11300i			1.25741i
$33$			8.58334i			1.49417i
$34$	1.55199			0.266163
$35$	0.0198465	−	0.832416i	0.00335466	−	0.140704i
$36$	6.18950			1.03158
$37$			0.768032i			0.126264i	0.998005	+	0.0631319i	$0.0201089\pi$
$37$			0.768032i			0.126264i	−0.998005	+	0.0631319i	$0.979891\pi$
$38$			9.42143i			1.52836i
$39$	6.88553			1.10257
$40$	0.104119	−	4.36703i	0.0164626	−	0.690489i
$41$	11.3969			1.77990			0.889949	−	0.456061i	$-0.150740\pi$
$41$	11.3969			1.77990			0.889949	+	0.456061i	$0.150740\pi$
$42$			1.86684i			0.288060i
$43$			10.1749i			1.55165i	0.630946	+	0.775827i	$0.282667\pi$
$43$			10.1749i			1.55165i	−0.630946	+	0.775827i	$0.717333\pi$
$44$	−10.9120			−1.64505
$45$	4.79762	+	0.114385i	0.715188	+	0.0170515i
$46$	15.6450			2.30673
$47$			5.84261i			0.852233i	0.904668	+	0.426116i	$0.140119\pi$
$47$			5.84261i			0.852233i	−0.904668	+	0.426116i	$0.859881\pi$
$48$		−	3.29083i		−	0.474990i
$49$	6.86134			0.980191
$50$	0.526602	−	11.0373i	0.0744728	−	1.56091i
$51$	−1.59310			−0.223079
$52$			8.75359i			1.21390i
$53$		−	7.70807i		−	1.05878i	−0.848377	−	0.529392i	$-0.822420\pi$
$53$		−	7.70807i		−	1.05878i	0.848377	−	0.529392i	$-0.177580\pi$
$54$	4.28054			0.582508
$55$	−8.45816	−	0.201659i	−1.14050	−	0.0271918i
$56$	−0.727451			−0.0972097
$57$		−	9.67102i		−	1.28096i
$58$			4.91634i			0.645547i
$59$	−14.0213			−1.82541			−0.912706	−	0.408616i	$-0.866012\pi$
$59$	−14.0213			−1.82541			−0.912706	+	0.408616i	$0.866012\pi$
$60$	−0.348688	+	14.6250i	−0.0450155	+	1.88807i
$61$	10.5586			1.35188			0.675942	−	0.736955i	$-0.263737\pi$
$61$	10.5586			1.35188			0.675942	+	0.736955i	$0.263737\pi$
$62$		−	17.9542i		−	2.28019i
$63$		−	0.799178i		−	0.100687i
$64$	12.8182			1.60228
$65$	−0.161771	+	6.78511i	−0.0200652	+	0.841589i
$66$	18.9689			2.33491
$67$			12.7576i			1.55859i	0.626656	+	0.779296i	$0.284423\pi$
$67$			12.7576i			1.55859i	−0.626656	+	0.779296i	$0.715577\pi$
$68$		−	2.02531i		−	0.245605i
$69$	−16.0595			−1.93333
$70$	−1.83961	−	0.0438601i	−0.219876	−	0.00524228i
$71$	−0.694776			−0.0824547			−0.0412274	−	0.999150i	$-0.513127\pi$
$71$	−0.694776			−0.0824547			−0.0412274	+	0.999150i	$0.513127\pi$
$72$		−	4.19266i		−	0.494110i
$73$			9.45754i			1.10692i	0.832875	+	0.553460i	$0.186693\pi$
$73$			9.45754i			1.10692i	−0.832875	+	0.553460i	$0.813307\pi$
$74$	1.69733			0.197311
$75$	−0.540553	+	11.3297i	−0.0624177	+	1.30824i
$76$	12.2948			1.41031
$77$			1.40894i			0.160564i
$78$		−	15.2168i		−	1.72297i
$79$	−4.15383			−0.467342			−0.233671	−	0.972316i	$-0.575074\pi$
$79$	−4.15383			−0.467342			−0.233671	+	0.972316i	$0.575074\pi$
$80$	3.24283	+	0.0773156i	0.362559	+	0.00864414i
$81$	−10.8325			−1.20361
$82$		−	25.1868i		−	2.78142i
$83$		−	11.0345i		−	1.21120i	−0.795770	−	0.605599i	$-0.792934\pi$
$83$		−	11.0345i		−	1.21120i	0.795770	−	0.605599i	$-0.207066\pi$
$84$	2.43619			0.265811
$85$	0.0374288	−	1.56987i	0.00405972	−	0.170276i
$86$	22.4862			2.42475
$87$		−	5.04658i		−	0.541051i
$88$			7.39161i			0.787949i
$89$	17.5969			1.86527			0.932633	−	0.360827i	$-0.117506\pi$
$89$	17.5969			1.86527			0.932633	+	0.360827i	$0.117506\pi$
$90$	0.252787	−	10.6026i	0.0266461	−	1.11761i
$91$	1.13025			0.118482
$92$		−	20.4165i		−	2.12856i
$93$			18.4299i			1.91109i
$94$	12.9120			1.33177
$95$	9.52997	+	0.227214i	0.977755	+	0.0233116i
$96$	−16.1360			−1.64687
$97$			16.6822i			1.69382i	0.531734	+	0.846911i	$0.321540\pi$
$97$			16.6822i			1.69382i	−0.531734	+	0.846911i	$0.678460\pi$
$98$		−	15.1634i		−	1.53173i
$99$	−8.12043			−0.816134
$100$	−14.4035	−	0.687206i	−1.44035	−	0.0687206i
$101$	13.7376			1.36694			0.683470	−	0.729979i	$-0.260470\pi$
$101$	13.7376			1.36694			0.683470	+	0.729979i	$0.260470\pi$
$102$			3.52071i			0.348602i
$103$		−	1.25499i		−	0.123658i	−0.998087	−	0.0618290i	$-0.980307\pi$
$103$		−	1.25499i		−	0.123658i	0.998087	−	0.0618290i	$-0.0196933\pi$
$104$	5.92953			0.581438
$105$	1.88835	+	0.0450220i	0.184284	+	0.00439370i
$106$	−17.0346			−1.65455
$107$		−	1.64792i		−	0.159310i	−0.996822	−	0.0796552i	$-0.974618\pi$
$107$		−	1.64792i		−	0.159310i	0.996822	−	0.0796552i	$-0.0253819\pi$
$108$		−	5.58603i		−	0.537516i
$109$	9.08309			0.870002			0.435001	−	0.900430i	$-0.356748\pi$
$109$	9.08309			0.870002			0.435001	+	0.900430i	$0.356748\pi$
$110$	−0.445661	+	18.6923i	−0.0424922	+	1.78224i
$111$	−1.74230			−0.165371
$112$		−	0.540183i		−	0.0510425i
$113$		−	8.30222i		−	0.781007i	−0.920601	−	0.390504i	$-0.872301\pi$
$113$		−	8.30222i		−	0.781007i	0.920601	−	0.390504i	$-0.127699\pi$
$114$	−21.3727			−2.00173
$115$	0.377306	−	15.8253i	0.0351840	−	1.47571i
$116$	6.41573			0.595686
$117$			6.51418i			0.602236i
$118$			30.9866i			2.85255i
$119$	−0.261505			−0.0239721
$120$	9.90669	+	0.236195i	0.904353	+	0.0215616i
$121$	3.31622			0.301475
$122$		−	23.3341i		−	2.11257i
$123$			25.8541i			2.33118i
$124$	−23.4299			−2.10407
$125$	−11.1518	−	0.798852i	−0.997444	−	0.0714515i
$126$	−1.76616			−0.157342
$127$			6.19396i			0.549625i	0.961498	+	0.274813i	$0.0886158\pi$
$127$			6.19396i			0.549625i	−0.961498	+	0.274813i	$0.911384\pi$
$128$		−	14.1019i		−	1.24644i
$129$	−23.0819			−2.03225
$130$	14.9949	+	0.357508i	1.31514	+	0.0313556i
$131$	−12.0088			−1.04922			−0.524609	−	0.851344i	$-0.675788\pi$
$131$	−12.0088			−1.04922			−0.524609	+	0.851344i	$0.675788\pi$
$132$		−	24.7541i		−	2.15457i
$133$		−	1.58748i		−	0.137652i
$134$	28.1940			2.43559
$135$	0.103233	−	4.32986i	0.00888484	−	0.372655i
$136$	−1.37191			−0.117640
$137$			2.38223i			0.203527i	0.994809	+	0.101764i	$0.0324485\pi$
$137$			2.38223i			0.203527i	−0.994809	+	0.101764i	$0.967551\pi$
$138$			35.4910i			3.02119i
$139$	−3.03084			−0.257073			−0.128536	−	0.991705i	$-0.541028\pi$
$139$	−3.03084			−0.257073			−0.128536	+	0.991705i	$0.541028\pi$
$140$	−0.0572366	+	2.40066i	−0.00483738	+	0.202893i
$141$	−13.2541			−1.11619
$142$			1.53543i			0.128851i
$143$		−	11.4844i		−	0.960376i
$144$	3.11335			0.259445
$145$	4.97298	+	0.118566i	0.412984	+	0.00984636i
$146$	20.9009			1.72977
$147$			15.5651i			1.28379i
$148$		−	2.21498i		−	0.182071i
$149$	−13.9560			−1.14332			−0.571659	−	0.820491i	$-0.693700\pi$
$149$	−13.9560			−1.14332			−0.571659	+	0.820491i	$0.693700\pi$
$150$	25.0383	+	1.19461i	2.04437	+	0.0975392i
$151$	−19.8038			−1.61161			−0.805804	−	0.592182i	$-0.798267\pi$
$151$	−19.8038			−1.61161			−0.805804	+	0.592182i	$0.798267\pi$
$152$		−	8.32828i		−	0.675512i
$153$		−	1.50718i		−	0.121848i
$154$	3.11372			0.250911
$155$	−18.1611	−	0.432996i	−1.45873	−	0.0347791i
$156$	−19.8577			−1.58989
$157$		−	4.69657i		−	0.374827i	−0.982281	−	0.187414i	$-0.939990\pi$
$157$		−	4.69657i		−	0.374827i	0.982281	−	0.187414i	$-0.0600105\pi$
$158$			9.17984i			0.730309i
$159$	17.4859			1.38672
$160$	0.379103	−	15.9006i	0.0299707	−	1.25706i
$161$	−2.63614			−0.207757
$162$			23.9394i			1.88086i
$163$			12.2047i			0.955943i	0.878375	+	0.477972i	$0.158628\pi$
$163$			12.2047i			0.955943i	−0.878375	+	0.477972i	$0.841372\pi$
$164$	−32.8684			−2.56659
$165$	0.457468	−	19.1875i	0.0356138	−	1.49374i
$166$	−24.3860			−1.89272
$167$			8.56021i			0.662409i	0.943559	+	0.331204i	$0.107455\pi$
$167$			8.56021i			0.662409i	−0.943559	+	0.331204i	$0.892545\pi$
$168$		−	1.65024i		−	0.127318i
$169$	3.78722			0.291325
$170$	−3.46936	−	0.0827165i	−0.266088	−	0.00634406i
$171$	9.14944			0.699675
$172$		−	29.3440i		−	2.23746i
$173$		−	11.8122i		−	0.898063i	−0.893516	−	0.449032i	$-0.851769\pi$
$173$		−	11.8122i		−	0.898063i	0.893516	−	0.449032i	$-0.148231\pi$
$174$	−11.1528			−0.845492
$175$	−0.0887308	+	1.85975i	−0.00670742	+	0.140584i
$176$	−5.48879			−0.413733
$177$		−	31.8075i		−	2.39080i
$178$		−	38.8886i		−	2.91482i
$179$	10.2287			0.764527			0.382263	−	0.924053i	$-0.375145\pi$
$179$	10.2287			0.764527			0.382263	+	0.924053i	$0.375145\pi$
$180$	−13.8362	−	0.329883i	−1.03129	−	0.0245880i
$181$	3.35297			0.249224			0.124612	−	0.992206i	$-0.460231\pi$
$181$	3.35297			0.249224			0.124612	+	0.992206i	$0.460231\pi$
$182$		−	2.49782i		−	0.185150i
$183$			23.9523i			1.77060i
$184$	−13.8298			−1.01954
$185$	0.0409340	−	1.71688i	0.00300953	−	0.126228i
$186$	40.7295			2.98643
$187$			2.65715i			0.194310i
$188$		−	16.8499i		−	1.22891i
$189$	−0.721259			−0.0524638
$190$	0.502136	−	21.0610i	0.0364287	−	1.52792i
$191$	−20.1631			−1.45895			−0.729477	−	0.684006i	$-0.760236\pi$
$191$	−20.1631			−1.45895			−0.729477	+	0.684006i	$0.760236\pi$
$192$			29.0784i			2.09855i
$193$		−	18.7859i		−	1.35224i	−0.736793	−	0.676118i	$-0.763661\pi$
$193$		−	18.7859i		−	1.35224i	0.736793	−	0.676118i	$-0.236339\pi$
$194$	36.8672			2.64691
$195$	−15.3921	−	0.366979i	−1.10225	−	0.0262799i
$196$	−19.7879			−1.41342
$197$		−	22.2950i		−	1.58845i	−0.607624	−	0.794225i	$-0.707877\pi$
$197$		−	22.2950i		−	1.58845i	0.607624	−	0.794225i	$-0.292123\pi$
$198$			17.9459i			1.27536i
$199$	8.52382			0.604237			0.302119	−	0.953270i	$-0.402306\pi$
$199$	8.52382			0.604237			0.302119	+	0.953270i	$0.402306\pi$
$200$	−0.465501	+	9.75666i	−0.0329159	+	0.689900i
$201$	−28.9409			−2.04133
$202$		−	30.3596i		−	2.13610i
$203$		−	0.828388i		−	0.0581415i
$204$	4.59446			0.321676
$205$	−25.4770	−	0.607423i	−1.77939	−	0.0424243i
$206$	−2.77349			−0.193239
$207$		−	15.1934i		−	1.05601i
$208$			4.40309i			0.305300i
$209$	−16.1304			−1.11576
$210$	0.0994974	−	4.17320i	0.00686597	−	0.287978i
$211$	−14.3197			−0.985807			−0.492903	−	0.870084i	$-0.664064\pi$
$211$	−14.3197			−0.985807			−0.492903	+	0.870084i	$0.664064\pi$
$212$			22.2299i			1.52675i
$213$		−	1.57611i		−	0.107993i
$214$	−3.64185			−0.248952
$215$	0.542292	−	22.7452i	0.0369840	−	1.55121i
$216$	−3.78388			−0.257460
$217$			3.02523i			0.205366i
$218$		−	20.0734i		−	1.35954i
$219$	−21.4546			−1.44977
$220$	24.3931	+	0.581580i	1.64458	+	0.0392101i
$221$	2.13155			0.143384
$222$			3.85042i			0.258423i
$223$			6.98392i			0.467678i	0.972275	+	0.233839i	$0.0751289\pi$
$223$			6.98392i			0.467678i	−0.972275	+	0.233839i	$0.924871\pi$
$224$	−2.64869			−0.176973
$225$	−10.7187	−	0.511400i	−0.714578	−	0.0340933i
$226$	−18.3477			−1.22047
$227$		−	3.06063i		−	0.203141i	−0.994828	−	0.101571i	$-0.967613\pi$
$227$		−	3.06063i		−	0.203141i	0.994828	−	0.101571i	$-0.0323868\pi$
$228$			27.8909i			1.84712i
$229$	2.01475			0.133139			0.0665694	−	0.997782i	$-0.478795\pi$
$229$	2.01475			0.133139			0.0665694	+	0.997782i	$0.478795\pi$
$230$	−34.9734	−	0.833835i	−2.30608	−	0.0549815i
$231$	−3.19621			−0.210295
$232$		−	4.34591i		−	0.285323i
$233$			1.73468i			0.113642i	0.998384	+	0.0568212i	$0.0180965\pi$
$233$			1.73468i			0.113642i	−0.998384	+	0.0568212i	$0.981904\pi$
$234$	14.3962			0.941106
$235$	0.311395	−	13.0608i	0.0203132	−	0.851991i
$236$	40.4369			2.63222
$237$		−	9.42303i		−	0.612092i
$238$			0.577918i			0.0374609i
$239$	−0.0847133			−0.00547965			−0.00273982	−	0.999996i	$-0.500872\pi$
$239$	−0.0847133			−0.00547965			−0.00273982	+	0.999996i	$0.500872\pi$
$240$	−0.175392	+	7.35642i	−0.0113215	+	0.474855i
$241$	−1.00000			−0.0644157
$241$	−1.00000			−0.0644157
$242$		−	7.32875i		−	0.471110i
$243$		−	18.7629i		−	1.20364i
$244$	−30.4506			−1.94940
$245$	−15.3381	−	0.365690i	−0.979913	−	0.0233631i
$246$	57.1368			3.64291
$247$			12.9397i			0.823336i
$248$			15.8710i			1.00781i
$249$	25.0320			1.58634
$250$	−1.76544	+	24.6451i	−0.111656	+	1.55869i
$251$	24.0806			1.51995			0.759976	−	0.649951i	$-0.225211\pi$
$251$	24.0806			1.51995			0.759976	+	0.649951i	$0.225211\pi$
$252$			2.30481i			0.145189i
$253$			26.7857i			1.68400i
$254$	13.6885			0.858891
$255$	3.56127	+	0.0849078i	0.223015	+	0.00531713i
$256$	−5.52835			−0.345522
$257$			6.09887i			0.380437i	0.981742	+	0.190219i	$0.0609197\pi$
$257$			6.09887i			0.380437i	−0.981742	+	0.190219i	$0.939080\pi$
$258$			51.0103i			3.17576i
$259$	−0.285995			−0.0177709
$260$	0.466542	−	19.5681i	0.0289337	−	1.21356i
$261$	4.77441			0.295529
$262$			26.5392i			1.63960i
$263$		−	10.2746i		−	0.633562i	−0.948499	−	0.316781i	$-0.897398\pi$
$263$		−	10.2746i		−	0.633562i	0.948499	−	0.316781i	$-0.102602\pi$
$264$	−16.7680			−1.03200
$265$	−0.410818	+	17.2309i	−0.0252364	+	1.05848i
$266$	−3.50829			−0.215107
$267$			39.9188i			2.44299i
$268$		−	36.7926i		−	2.24747i
$269$	19.5761			1.19358			0.596788	−	0.802399i	$-0.296443\pi$
$269$	19.5761			1.19358			0.596788	+	0.802399i	$0.296443\pi$
$270$	−9.56887	−	0.228141i	−0.582343	−	0.0138842i
$271$	14.7957			0.898773			0.449386	−	0.893337i	$-0.351643\pi$
$271$	14.7957			0.898773			0.449386	+	0.893337i	$0.351643\pi$
$272$		−	1.01874i		−	0.0617703i
$273$			2.56399i			0.155180i
$274$	5.26465			0.318049
$275$	18.8969	+	0.901592i	1.13953	+	0.0543681i
$276$	46.3151			2.78784
$277$		−	10.5979i		−	0.636763i	−0.947963	−	0.318382i	$-0.896861\pi$
$277$		−	10.5979i		−	0.636763i	0.947963	−	0.318382i	$-0.103139\pi$
$278$			6.69807i			0.401724i
$279$	−17.4359			−1.04386
$280$	1.62617	+	0.0387711i	0.0971821	+	0.00231702i
$281$	−19.7017			−1.17531			−0.587653	−	0.809113i	$-0.699948\pi$
$281$	−19.7017			−1.17531			−0.587653	+	0.809113i	$0.699948\pi$
$282$			29.2911i			1.74426i
$283$		−	17.1408i		−	1.01892i	−0.860495	−	0.509459i	$-0.829846\pi$
$283$		−	17.1408i		−	1.01892i	0.860495	−	0.509459i	$-0.170154\pi$
$284$	2.00371			0.118899
$285$	−0.515438	+	21.6189i	−0.0305319	+	1.28059i
$286$	−25.3803			−1.50077
$287$			4.24390i			0.250510i
$288$		−	15.2657i		−	0.899541i
$289$	16.5068			0.970990
$290$	0.262027	−	10.9901i	0.0153868	−	0.645364i
$291$	−37.8439			−2.21845
$292$		−	27.2753i		−	1.59616i
$293$		−	3.80087i		−	0.222049i	−0.993818	−	0.111025i	$-0.964587\pi$
$293$		−	3.80087i		−	0.222049i	0.993818	−	0.111025i	$-0.0354133\pi$
$294$	34.3983			2.00615
$295$	31.3436	+	0.747294i	1.82489	+	0.0435091i
$296$	−1.50039			−0.0872085
$297$			7.32869i			0.425254i
$298$			30.8423i			1.78665i
$299$	21.4874			1.24265
$300$	1.55894	−	32.6745i	0.0900054	−	1.88647i
$301$	−3.78885			−0.218386
$302$			43.7658i			2.51844i
$303$			31.1639i			1.79032i
$304$	6.18433			0.354696
$305$	−23.6029	−	0.562741i	−1.35150	−	0.0322225i
$306$	−3.33083			−0.190411
$307$			14.5018i			0.827664i	0.910353	+	0.413832i	$0.135810\pi$
$307$			14.5018i			0.827664i	−0.910353	+	0.413832i	$0.864190\pi$
$308$		−	4.06335i		−	0.231531i
$309$	2.84697			0.161958
$310$	−0.956909	+	40.1354i	−0.0543488	+	2.27954i
$311$	−5.65261			−0.320530			−0.160265	−	0.987074i	$-0.551235\pi$
$311$	−5.65261			−0.320530			−0.160265	+	0.987074i	$0.551235\pi$
$312$			13.4512i			0.761527i
$313$			23.3042i			1.31723i	0.752479	+	0.658616i	$0.228858\pi$
$313$			23.3042i			1.31723i	−0.752479	+	0.658616i	$0.771142\pi$
$314$	−10.3793			−0.585737
$315$	−0.0425939	+	1.78651i	−0.00239990	+	0.100658i
$316$	11.9795			0.673901
$317$		−	17.3855i		−	0.976465i	−0.872714	−	0.488232i	$-0.837642\pi$
$317$		−	17.3855i		−	0.976465i	0.872714	−	0.488232i	$-0.162358\pi$
$318$		−	38.6433i		−	2.16701i
$319$	−8.41724			−0.471275
$320$	−28.6543	−	0.683175i	−1.60182	−	0.0381907i
$321$	3.73833			0.208653
$322$			5.82579i			0.324658i
$323$		−	2.99386i		−	0.166583i
$324$	31.2405			1.73558
$325$	0.723255	−	15.1590i	0.0401189	−	0.840872i
$326$	26.9720			1.49384
$327$			20.6052i			1.13947i
$328$			22.2644i			1.22935i
$329$	−2.17563			−0.119947
$330$	−42.4038	−	1.01099i	−2.33425	−	0.0556532i
$331$	5.19902			0.285764			0.142882	−	0.989740i	$-0.454363\pi$
$331$	5.19902			0.285764			0.142882	+	0.989740i	$0.454363\pi$
$332$			31.8233i			1.74653i
$333$		−	1.64833i		−	0.0903279i
$334$	18.9178			1.03514
$335$	0.679946	−	28.5188i	0.0371494	−	1.55815i
$336$	1.22542			0.0668519
$337$		−	17.0208i		−	0.927183i	−0.886049	−	0.463591i	$-0.846561\pi$
$337$		−	17.0208i		−	0.927183i	0.886049	−	0.463591i	$-0.153439\pi$
$338$		−	8.36965i		−	0.455249i
$339$	18.8337			1.02291
$340$	−0.107944	+	4.52745i	−0.00585406	+	0.245536i
$341$	30.7393			1.66463
$342$		−	20.2200i		−	1.09337i
$343$			5.16159i			0.278700i
$344$	−19.8771			−1.07170
$345$	35.8999	+	0.855925i	1.93279	+	0.0460815i
$346$	−26.1046			−1.40339
$347$			3.82926i			0.205565i	0.994704	+	0.102783i	$0.0327746\pi$
$347$			3.82926i			0.205565i	−0.994704	+	0.102783i	$0.967225\pi$
$348$			14.5542i			0.780187i
$349$	12.6129			0.675151			0.337576	−	0.941298i	$-0.390393\pi$
$349$	12.6129			0.675151			0.337576	+	0.941298i	$0.390393\pi$
$350$	4.11000	+	0.196093i	0.219689	+	0.0104816i
$351$	5.87906			0.313801
$352$			26.9133i			1.43448i
$353$			18.6132i			0.990680i	0.868699	+	0.495340i	$0.164956\pi$
$353$			18.6132i			0.990680i	−0.868699	+	0.495340i	$0.835044\pi$
$354$	−70.2936			−3.73606
$355$	1.55312	+	0.0370296i	0.0824313	+	0.00196533i
$356$	−50.7489			−2.68969
$357$		−	0.593228i		−	0.0313970i
$358$		−	22.6051i		−	1.19471i
$359$	−1.47759			−0.0779841			−0.0389921	−	0.999240i	$-0.512415\pi$
$359$	−1.47759			−0.0779841			−0.0389921	+	0.999240i	$0.512415\pi$
$360$	−0.223457	+	9.37241i	−0.0117772	+	0.493969i
$361$	−0.825596			−0.0434524
$362$		−	7.40997i		−	0.389459i
$363$			7.52291i			0.394850i
$364$	−3.25960			−0.170850
$365$	0.504060	−	21.1417i	0.0263837	−	1.10661i
$366$	52.9338			2.76689
$367$		−	15.9466i		−	0.832408i	−0.909271	−	0.416204i	$-0.863360\pi$
$367$		−	15.9466i		−	0.832408i	0.909271	−	0.416204i	$-0.136640\pi$
$368$		−	10.2696i		−	0.535338i
$369$	−24.4597			−1.27332
$370$	−3.79427	−	0.0904629i	−0.197254	−	0.00470294i
$371$	2.87028			0.149018
$372$		−	53.1512i		−	2.75576i
$373$			35.9531i			1.86158i	0.365551	+	0.930791i	$0.380881\pi$
$373$			35.9531i			1.86158i	−0.365551	+	0.930791i	$0.619119\pi$
$374$	5.87222			0.303645
$375$	1.81221	−	25.2980i	0.0935821	−	1.30638i
$376$	−11.4139			−0.588624
$377$			6.75228i			0.347760i
$378$			1.59396i			0.0819845i
$379$	−16.8578			−0.865927			−0.432963	−	0.901411i	$-0.642532\pi$
$379$	−16.8578			−0.865927			−0.432963	+	0.901411i	$0.642532\pi$
$380$	−27.4842	−	0.655278i	−1.40991	−	0.0336150i
$381$	−14.0511			−0.719860
$382$			44.5600i			2.27989i
$383$			10.3324i			0.527963i	0.964528	+	0.263982i	$0.0850358\pi$
$383$			10.3324i			0.527963i	−0.964528	+	0.263982i	$0.914964\pi$
$384$	31.9904			1.63250
$385$	0.0750926	−	3.14959i	0.00382707	−	0.160518i
$386$	−41.5162			−2.11312
$387$		−	21.8370i		−	1.11004i
$388$		−	48.1110i		−	2.44247i
$389$	−35.3884			−1.79426			−0.897131	−	0.441764i	$-0.854353\pi$
$389$	−35.3884			−1.79426			−0.897131	+	0.441764i	$0.854353\pi$
$390$	−0.811014	+	34.0162i	−0.0410673	+	1.72248i
$391$	−4.97154			−0.251421
$392$			13.4040i			0.677003i
$393$		−	27.2423i		−	1.37419i
$394$	−49.2712			−2.48225
$395$	9.28560	+	0.221387i	0.467209	+	0.0111392i
$396$	23.4191			1.17685
$397$		−	6.32475i		−	0.317430i	−0.987324	−	0.158715i	$-0.949265\pi$
$397$		−	6.32475i		−	0.317430i	0.987324	−	0.158715i	$-0.0507351\pi$
$398$		−	18.8374i		−	0.944233i
$399$	3.60123			0.180287
$400$	−7.24501	−	0.345668i	−0.362250	−	0.0172834i
$401$	−29.2556			−1.46095			−0.730477	−	0.682937i	$-0.760702\pi$
$401$	−29.2556			−1.46095			−0.730477	+	0.682937i	$0.760702\pi$
$402$			63.9586i			3.18996i
$403$		−	24.6590i		−	1.22835i
$404$	−39.6188			−1.97111
$405$	24.2152	+	0.577340i	1.20326	+	0.0286882i
$406$	−1.83071			−0.0908568
$407$			2.90599i			0.144044i
$408$		−	3.11221i		−	0.154077i
$409$	6.96607			0.344450			0.172225	−	0.985058i	$-0.444904\pi$
$409$	6.96607			0.344450			0.172225	+	0.985058i	$0.444904\pi$
$410$	−1.34239	+	56.3035i	−0.0662958	+	2.78063i
$411$	−5.40412			−0.266566
$412$			3.61936i			0.178313i
$413$		−	5.22114i		−	0.256916i
$414$	−33.5769			−1.65021
$415$	−0.588110	+	24.6670i	−0.0288692	+	1.21085i
$416$	21.5898			1.05853
$417$		−	6.87552i		−	0.336696i
$418$			35.6476i			1.74358i
$419$	11.9149			0.582079			0.291039	−	0.956711i	$-0.405999\pi$
$419$	11.9149			0.582079			0.291039	+	0.956711i	$0.405999\pi$
$420$	−5.44595	−	0.129842i	−0.265735	−	0.00633565i
$421$	30.4399			1.48355			0.741776	−	0.670648i	$-0.233984\pi$
$421$	30.4399			1.48355			0.741776	+	0.670648i	$0.233984\pi$
$422$			31.6461i			1.54051i
$423$		−	12.5393i		−	0.609680i
$424$	15.0581			0.731287
$425$	−0.167339	+	3.50734i	−0.00811713	+	0.170131i
$426$	−3.48316			−0.168760
$427$			3.93172i			0.190269i
$428$			4.75255i			0.229723i
$429$	26.0526			1.25783
$430$	−50.2663	−	1.19845i	−2.42406	−	0.0577944i
$431$	16.3542			0.787756			0.393878	−	0.919163i	$-0.371133\pi$
$431$	16.3542			0.787756			0.393878	+	0.919163i	$0.371133\pi$
$432$		−	2.80980i		−	0.135186i
$433$			3.31562i			0.159338i	0.996821	+	0.0796692i	$0.0253864\pi$
$433$			3.31562i			0.159338i	−0.996821	+	0.0796692i	$0.974614\pi$
$434$	6.68567			0.320923
$435$	−0.268969	+	11.2813i	−0.0128961	+	0.540897i
$436$	−26.1954			−1.25453
$437$		−	30.1800i		−	1.44371i
$438$			47.4140i			2.26553i
$439$	1.51016			0.0720759			0.0360379	−	0.999350i	$-0.488526\pi$
$439$	1.51016			0.0720759			0.0360379	+	0.999350i	$0.488526\pi$
$440$	0.393952	−	16.5235i	0.0187809	−	0.787725i
$441$	−14.7256			−0.701220
$442$		−	4.71067i		−	0.224064i
$443$		−	36.1571i		−	1.71787i	−0.512082	−	0.858937i	$-0.671125\pi$
$443$		−	36.1571i		−	1.71787i	0.512082	−	0.858937i	$-0.328875\pi$
$444$	5.02473			0.238463
$445$	−39.3366	−	0.937864i	−1.86474	−	0.0444590i
$446$	15.4343			0.730834
$447$		−	31.6594i		−	1.49744i
$448$			4.77316i			0.225511i
$449$	−9.67351			−0.456521			−0.228260	−	0.973600i	$-0.573304\pi$
$449$	−9.67351			−0.456521			−0.228260	+	0.973600i	$0.573304\pi$
$450$	−1.13018	+	23.6879i	−0.0532771	+	1.11666i
$451$	43.1222			2.03055
$452$			23.9434i			1.12620i
$453$		−	44.9252i		−	2.11077i
$454$	−6.76391			−0.317446
$455$	−2.52659	−	0.0602391i	−0.118449	−	0.00282405i
$456$	18.8928			0.884738
$457$		−	28.9905i		−	1.35612i	−0.735007	−	0.678060i	$-0.762821\pi$
$457$		−	28.9905i		−	1.35612i	0.735007	−	0.678060i	$-0.237179\pi$
$458$		−	4.45255i		−	0.208054i
$459$	−1.36023			−0.0634903
$460$	−1.08814	+	45.6396i	−0.0507348	+	2.12796i
$461$	−14.7354			−0.686295			−0.343148	−	0.939281i	$-0.611493\pi$
$461$	−14.7354			−0.686295			−0.343148	+	0.939281i	$0.611493\pi$
$462$			7.06353i			0.328625i
$463$			28.9590i			1.34584i	0.739715	+	0.672921i	$0.234960\pi$
$463$			28.9590i			1.34584i	−0.739715	+	0.672921i	$0.765040\pi$
$464$	3.22714			0.149816
$465$	0.982260	−	41.1987i	0.0455512	−	1.91054i
$466$	3.83358			0.177587
$467$			36.7827i			1.70210i	0.525084	+	0.851051i	$0.324034\pi$
$467$			36.7827i			1.70210i	−0.525084	+	0.851051i	$0.675966\pi$
$468$		−	18.7867i		−	0.868416i
$469$	−4.75060			−0.219362
$470$	−28.8639	−	0.688174i	−1.33139	−	0.0317431i
$471$	10.6543			0.490922
$472$		−	27.3913i		−	1.26079i
$473$			38.4984i			1.77016i
$474$	−20.8246			−0.956507
$475$	−21.2915	−	1.01584i	−0.976921	−	0.0466100i
$476$	0.754173			0.0345675
$477$			16.5428i			0.757445i
$478$			0.187214i			0.00856297i
$479$	−5.89590			−0.269390			−0.134695	−	0.990887i	$-0.543006\pi$
$479$	−5.89590			−0.269390			−0.134695	+	0.990887i	$0.543006\pi$
$480$	36.0709	+	0.860002i	1.64640	+	0.0392535i
$481$	2.33117			0.106292
$482$			2.20997i			0.100661i
$483$		−	5.98012i		−	0.272105i
$484$	−9.56389			−0.434722
$485$	0.889115	−	37.2920i	0.0403726	−	1.69334i
$486$	−41.4654			−1.88091
$487$			21.8628i			0.990700i	0.868694	+	0.495350i	$0.164960\pi$
$487$			21.8628i			0.990700i	−0.868694	+	0.495350i	$0.835040\pi$
$488$			20.6267i			0.933726i
$489$	−27.6865			−1.25203
$490$	−0.808164	+	33.8967i	−0.0365091	+	1.53130i
$491$	18.4329			0.831863			0.415931	−	0.909396i	$-0.363456\pi$
$491$	18.4329			0.831863			0.415931	+	0.909396i	$0.363456\pi$
$492$		−	74.5624i		−	3.36153i
$493$		−	1.56227i		−	0.0703612i
$494$	28.5964			1.28661
$495$	18.1527	+	0.432796i	0.815902	+	0.0194527i
$496$	−11.7854			−0.529178
$497$		−	0.258716i		−	0.0116050i
$498$		−	55.3201i		−	2.47895i
$499$	−4.73483			−0.211960			−0.105980	−	0.994368i	$-0.533798\pi$
$499$	−4.73483			−0.211960			−0.105980	+	0.994368i	$0.533798\pi$
$500$	32.1614	+	2.30387i	1.43830	+	0.103032i
$501$	−19.4190			−0.867576
$502$		−	53.2173i		−	2.37521i
$503$		−	29.0515i		−	1.29534i	−0.761921	−	0.647670i	$-0.775743\pi$
$503$		−	29.0515i		−	1.29534i	0.761921	−	0.647670i	$-0.224257\pi$
$504$	1.56123			0.0695429
$505$	−30.7094	−	0.732174i	−1.36655	−	0.0325813i
$506$	59.1957			2.63157
$507$			8.59138i			0.381557i
$508$		−	17.8632i		−	0.792552i
$509$	−5.09179			−0.225690			−0.112845	−	0.993613i	$-0.535996\pi$
$509$	−5.09179			−0.225690			−0.112845	+	0.993613i	$0.535996\pi$
$510$	0.187644	−	7.87030i	0.00830901	−	0.348503i
$511$	−3.52173			−0.155792
$512$		−	15.9863i		−	0.706502i
$513$		−	8.25738i		−	0.364572i
$514$	13.4783			0.594504
$515$	−0.0668875	+	2.80545i	−0.00294742	+	0.123623i
$516$	66.5675			2.93047
$517$			22.1066i			0.972246i
$518$			0.632040i			0.0277703i
$519$	26.7961			1.17622
$520$	−13.2551	−	0.316027i	−0.581273	−	0.0138587i
$521$	18.0399			0.790342			0.395171	−	0.918608i	$-0.370685\pi$
$521$	18.0399			0.790342			0.395171	+	0.918608i	$0.370685\pi$
$522$		−	10.5513i		−	0.461818i
$523$			19.6243i			0.858111i	0.903278	+	0.429056i	$0.141154\pi$
$523$			19.6243i			0.858111i	−0.903278	+	0.429056i	$0.858846\pi$
$524$	34.6332			1.51296
$525$	−4.21888	−	0.201287i	−0.184127	−	0.00878490i
$526$	−22.7067			−0.990058
$527$			5.70533i			0.248528i
$528$		−	12.4514i		−	0.541879i
$529$	−27.1163			−1.17897
$530$	38.0797	+	0.907897i	1.65408	+	0.0394365i
$531$	30.0920			1.30588
$532$			4.57825i			0.198492i
$533$		−	34.5925i		−	1.49837i
$534$	88.2194			3.81763
$535$	−0.0878295	+	3.68381i	−0.00379720	+	0.159265i
$536$	−24.9227			−1.07650
$537$			23.2039i			1.00132i
$538$		−	43.2627i		−	1.86519i
$539$	25.9611			1.11822
$540$	−0.297720	+	12.4872i	−0.0128118	+	0.537363i
$541$	20.5064			0.881639			0.440820	−	0.897596i	$-0.354688\pi$
$541$	20.5064			0.881639			0.440820	+	0.897596i	$0.354688\pi$
$542$		−	32.6980i		−	1.40450i
$543$			7.60628i			0.326417i
$544$	−4.99521			−0.214168
$545$	−20.3046	−	0.484103i	−0.869755	−	0.0207367i
$546$	5.66634			0.242497
$547$			2.72035i			0.116314i	0.998307	+	0.0581568i	$0.0185223\pi$
$547$			2.72035i			0.116314i	−0.998307	+	0.0581568i	$0.981478\pi$
$548$		−	6.87027i		−	0.293484i
$549$	−22.6605			−0.967125
$550$	1.99249	−	41.7616i	0.0849602	−	1.78072i
$551$	9.48387			0.404026
$552$		−	31.3730i		−	1.33533i
$553$		−	1.54678i		−	0.0657756i
$554$	−23.4209			−0.995061
$555$	3.89478	+	0.0928594i	0.165324	+	0.00394166i
$556$	8.74086			0.370695
$557$		−	21.3629i		−	0.905175i	−0.891720	−	0.452588i	$-0.850501\pi$
$557$		−	21.3629i		−	0.905175i	0.891720	−	0.452588i	$-0.149499\pi$
$558$			38.5328i			1.63123i
$559$	30.8833			1.30623
$560$	−0.0287903	+	1.20754i	−0.00121661	+	0.0510280i
$561$	−6.02778			−0.254493
$562$			43.5402i			1.83663i
$563$		−	39.4767i		−	1.66374i	−0.554967	−	0.831872i	$-0.687269\pi$
$563$		−	39.4767i		−	1.66374i	0.554967	−	0.831872i	$-0.312731\pi$
$564$	38.2244			1.60954
$565$	−0.442485	+	18.5591i	−0.0186155	+	0.780785i
$566$	−37.8808			−1.59225
$567$		−	4.03372i		−	0.169400i
$568$		−	1.35728i		−	0.0569502i
$569$	−46.0974			−1.93250			−0.966252	−	0.257598i	$-0.917069\pi$
$569$	−46.0974			−1.93250			−0.966252	+	0.257598i	$0.917069\pi$
$570$	47.7772	+	1.13910i	2.00117	+	0.0477118i
$571$	5.50019			0.230176			0.115088	−	0.993355i	$-0.463285\pi$
$571$	5.50019			0.230176			0.115088	+	0.993355i	$0.463285\pi$
$572$			33.1208i			1.38485i
$573$		−	45.7404i		−	1.91083i
$574$	9.37891			0.391468
$575$	−1.68688	+	35.3562i	−0.0703479	+	1.47446i
$576$	−27.5101			−1.14625
$577$			18.5505i			0.772266i	0.922443	+	0.386133i	$0.126189\pi$
$577$			18.5505i			0.772266i	−0.922443	+	0.386133i	$0.873811\pi$
$578$		−	36.4796i		−	1.51735i
$579$	42.6161			1.77106
$580$	−14.3419	−	0.341941i	−0.595517	−	0.0141983i
$581$	4.10897			0.170469
$582$			83.6339i			3.46674i
$583$		−	29.1649i		−	1.20788i
$584$	−18.4758			−0.764534
$585$	0.347188	−	14.5620i	0.0143544	−	0.602065i
$586$	−8.39982			−0.346993
$587$			20.0073i			0.825789i	0.910779	+	0.412895i	$0.135482\pi$
$587$			20.0073i			0.825789i	−0.910779	+	0.412895i	$0.864518\pi$
$588$		−	44.8892i		−	1.85120i
$589$	−34.6346			−1.42709
$590$	1.65150	−	69.2684i	0.0679911	−	2.85174i
$591$	50.5765			2.08044
$592$		−	1.11415i		−	0.0457911i
$593$		−	25.2242i		−	1.03583i	−0.855432	−	0.517916i	$-0.826708\pi$
$593$		−	25.2242i		−	1.03583i	0.855432	−	0.517916i	$-0.173292\pi$
$594$	16.1962			0.664538
$595$	0.584577	+	0.0139375i	0.0239653	+	0.000571381i
$596$	40.2487			1.64865
$597$			19.3364i			0.791387i
$598$		−	47.4866i		−	1.94187i
$599$	20.8882			0.853469			0.426735	−	0.904377i	$-0.359664\pi$
$599$	20.8882			0.853469			0.426735	+	0.904377i	$0.359664\pi$
$600$	−22.1332	−	1.05600i	−0.903583	−	0.0431109i
$601$	12.6800			0.517227			0.258614	−	0.965981i	$-0.416734\pi$
$601$	12.6800			0.517227			0.258614	+	0.965981i	$0.416734\pi$
$602$			8.37325i			0.341268i
$603$		−	27.3801i		−	1.11500i
$604$	57.1135			2.32392
$605$	−7.41319	−	0.176745i	−0.301389	−	0.00718572i
$606$	68.8714			2.79771
$607$			7.80257i			0.316697i	0.987383	+	0.158348i	$0.0506169\pi$
$607$			7.80257i			0.316697i	−0.987383	+	0.158348i	$0.949383\pi$
$608$		−	30.3237i		−	1.22979i
$609$	1.87921			0.0761496
$610$	−1.24364	+	52.1618i	−0.0503536	+	2.11197i
$611$	17.7338			0.717434
$612$			4.34667i			0.175704i
$613$		−	11.9022i		−	0.480724i	−0.970683	−	0.240362i	$-0.922734\pi$
$613$		−	11.9022i		−	0.480724i	0.970683	−	0.240362i	$-0.0772662\pi$
$614$	32.0487			1.29338
$615$	1.37795	−	57.7951i	0.0555643	−	2.33052i
$616$	−2.75244			−0.110899
$617$			44.3848i			1.78686i	0.449199	+	0.893432i	$0.351709\pi$
$617$			44.3848i			1.78686i	−0.449199	+	0.893432i	$0.648291\pi$
$618$		−	6.29172i		−	0.253090i
$619$	−15.8942			−0.638842			−0.319421	−	0.947613i	$-0.603488\pi$
$619$	−15.8942			−0.638842			−0.319421	+	0.947613i	$0.603488\pi$
$620$	52.3760	+	1.24875i	2.10347	+	0.0501510i
$621$	−13.7120			−0.550245
$622$			12.4921i			0.500888i
$623$			6.55261i			0.262525i
$624$	−9.98850			−0.399860
$625$	24.8864	+	2.38014i	0.995458	+	0.0952055i
$626$	51.5017			2.05842
$627$		−	36.5920i		−	1.46134i
$628$			13.5448i			0.540496i
$629$	−0.539362			−0.0215058
$630$	3.94813	+	0.0941313i	0.157297	+	0.00375028i
$631$	−38.0169			−1.51343			−0.756714	−	0.653746i	$-0.773196\pi$
$631$	−38.0169			−1.51343			−0.756714	+	0.653746i	$0.773196\pi$
$632$		−	8.11472i		−	0.322786i
$633$		−	32.4844i		−	1.29114i
$634$	−38.4214			−1.52591
$635$	0.330121	−	13.8462i	0.0131004	−	0.549469i
$636$	−50.4288			−1.99963
$637$		−	20.8259i		−	0.825153i
$638$			18.6018i			0.736454i
$639$	1.49111			0.0589874
$640$	−0.751592	+	31.5238i	−0.0297093	+	1.24609i
$641$	−0.557890			−0.0220353			−0.0110177	−	0.999939i	$-0.503507\pi$
$641$	−0.557890			−0.0220353			−0.0110177	+	0.999939i	$0.503507\pi$
$642$		−	8.26161i		−	0.326060i
$643$		−	29.3830i		−	1.15875i	−0.815060	−	0.579377i	$-0.803296\pi$
$643$		−	29.3830i		−	1.15875i	0.815060	−	0.579377i	$-0.196704\pi$
$644$	7.60255			0.299582
$645$	51.5980	+	1.23020i	2.03167	+	0.0484390i
$646$	−6.61634			−0.260316
$647$		−	2.00527i		−	0.0788355i	−0.999223	−	0.0394177i	$-0.987450\pi$
$647$		−	2.00527i		−	0.0788355i	0.999223	−	0.0394177i	$-0.0125503\pi$
$648$		−	21.1618i		−	0.831313i
$649$	−53.0519			−2.08247
$650$	−33.5010	−	1.59837i	−1.31402	−	0.0626933i
$651$	−6.86279			−0.268974
$652$		−	35.1979i		−	1.37846i
$653$			14.6250i			0.572319i	0.958182	+	0.286160i	$0.0923788\pi$
$653$			14.6250i			0.572319i	−0.958182	+	0.286160i	$0.907621\pi$
$654$	45.5368			1.78063
$655$	26.8449	+	0.640037i	1.04892	+	0.0250083i
$656$	−16.5329			−0.645502
$657$		−	20.2975i		−	0.791881i
$658$			4.80809i			0.187439i
$659$	18.2521			0.710999			0.355500	−	0.934676i	$-0.384311\pi$
$659$	18.2521			0.710999			0.355500	+	0.934676i	$0.384311\pi$
$660$	−1.31932	+	55.3362i	−0.0513546	+	2.15396i
$661$	16.5367			0.643203			0.321602	−	0.946875i	$-0.395779\pi$
$661$	16.5367			0.643203			0.321602	+	0.946875i	$0.395779\pi$
$662$		−	11.4897i		−	0.446559i
$663$			4.83547i			0.187794i
$664$	21.5565			0.836556
$665$	−0.0846083	+	3.54871i	−0.00328097	+	0.137613i
$666$	−3.64276			−0.141154
$667$		−	15.7487i		−	0.609792i
$668$		−	24.6874i		−	0.955184i
$669$	−15.8431			−0.612531
$670$	−63.0258	−	1.50266i	−2.43490	−	0.0580528i
$671$	39.9502			1.54226
$672$		−	6.00860i		−	0.231787i
$673$			37.1550i			1.43222i	0.697988	+	0.716110i	$0.254079\pi$
$673$			37.1550i			1.43222i	−0.697988	+	0.716110i	$0.745921\pi$
$674$	−37.6155			−1.44889
$675$	−0.461539	+	9.67361i	−0.0177646	+	0.372337i
$676$	−10.9222			−0.420086
$677$			50.4114i			1.93747i	0.248104	+	0.968733i	$0.420193\pi$
$677$			50.4114i			1.93747i	−0.248104	+	0.968733i	$0.579807\pi$
$678$		−	41.6220i		−	1.59848i
$679$	−6.21201			−0.238395
$680$	3.06682	+	0.0731190i	0.117607	+	0.00280399i
$681$	6.94310			0.266060
$682$		−	67.9330i		−	2.60129i
$683$			27.1344i			1.03827i	0.854692	+	0.519135i	$0.173746\pi$
$683$			27.1344i			1.03827i	−0.854692	+	0.519135i	$0.826254\pi$
$684$	−26.3867			−1.00892
$685$	0.126966	−	5.32531i	0.00485112	−	0.203469i
$686$	11.4070			0.435520
$687$			4.57051i			0.174376i
$688$		−	14.7602i		−	0.562727i
$689$	−23.3960			−0.891315
$690$	1.89157	−	79.3377i	0.0720108	−	3.02034i
$691$	−42.9496			−1.63388			−0.816939	−	0.576724i	$-0.804331\pi$
$691$	−42.9496			−1.63388			−0.816939	+	0.576724i	$0.804331\pi$
$692$			34.0660i			1.29499i
$693$		−	3.02383i		−	0.114866i
$694$	8.46255			0.321234
$695$	6.77524	+	0.161535i	0.257000	+	0.00612739i
$696$	9.85877			0.373696
$697$			8.00365i			0.303160i
$698$		−	27.8741i		−	1.05505i
$699$	−3.93514			−0.148841
$700$	0.255897	−	5.36347i	0.00967201	−	0.202720i
$701$	23.2165			0.876875			0.438437	−	0.898762i	$-0.355532\pi$
$701$	23.2165			0.876875			0.438437	+	0.898762i	$0.355532\pi$
$702$		−	12.9925i		−	0.490372i
$703$		−	3.27423i		−	0.123490i
$704$	48.5000			1.82791
$705$	29.6286	+	0.706405i	1.11588	+	0.0266047i
$706$	41.1346			1.54812
$707$			5.11551i			0.192388i
$708$			91.7319i			3.44749i
$709$	35.9993			1.35198			0.675991	−	0.736910i	$-0.263716\pi$
$709$	35.9993			1.35198			0.675991	+	0.736910i	$0.263716\pi$
$710$	0.0818343	−	3.43236i	0.00307119	−	0.128814i
$711$	8.91483			0.334332
$712$			34.3764i			1.28831i
$713$			57.5134i			2.15389i
$714$	−1.31102			−0.0490636
$715$	−0.612088	+	25.6727i	−0.0228908	+	0.960103i
$716$	−29.4992			−1.10244
$717$		−	0.192174i		−	0.00717686i
$718$			3.26543i			0.121865i
$719$	−30.5664			−1.13993			−0.569967	−	0.821668i	$-0.693044\pi$
$719$	−30.5664			−1.13993			−0.569967	+	0.821668i	$0.693044\pi$
$720$	−6.95967	−	0.165933i	−0.259372	−	0.00618394i
$721$	0.467325			0.0174041
$722$			1.82454i			0.0679025i
$723$		−	2.26852i		−	0.0843671i
$724$	−9.66988			−0.359378
$725$	−11.1104	−	0.530092i	−0.412632	−	0.0196871i
$726$	16.6254			0.617027
$727$		−	37.2636i		−	1.38203i	−0.722840	−	0.691015i	$-0.757164\pi$
$727$		−	37.2636i		−	1.38203i	0.722840	−	0.691015i	$-0.242836\pi$
$728$			2.20800i			0.0818339i
$729$	10.0665			0.372833
$730$	−46.7225	−	1.11396i	−1.72928	−	0.0412294i
$731$	−7.14546			−0.264284
$732$		−	69.0776i		−	2.55318i
$733$		−	22.9111i		−	0.846243i	−0.906073	−	0.423121i	$-0.860934\pi$
$733$		−	22.9111i		−	0.846243i	0.906073	−	0.423121i	$-0.139066\pi$
$734$	−35.2416			−1.30079
$735$	0.829574	−	34.7947i	0.0305993	−	1.28342i
$736$	−50.3549			−1.85611
$737$			48.2708i			1.77808i
$738$			54.0553i			1.98980i
$739$	−49.9652			−1.83800			−0.919000	−	0.394258i	$-0.871002\pi$
$739$	−49.9652			−1.83800			−0.919000	+	0.394258i	$0.871002\pi$
$740$	−0.118052	+	4.95145i	−0.00433969	+	0.182019i
$741$	−29.3540			−1.07835
$742$		−	6.34324i		−	0.232868i
$743$			6.00868i			0.220437i	0.993907	+	0.110218i	$0.0351551\pi$
$743$			6.00868i			0.220437i	−0.993907	+	0.110218i	$0.964845\pi$
$744$	−36.0037			−1.31996
$745$	31.1977	+	0.743815i	1.14299	+	0.0272513i
$746$	79.4554			2.90907
$747$			23.6820i			0.866479i
$748$		−	7.66313i		−	0.280192i
$749$	0.613641			0.0224220
$750$	−55.9078	−	4.00493i	−2.04146	−	0.146239i
$751$	4.02821			0.146992			0.0734958	−	0.997296i	$-0.476584\pi$
$751$	4.02821			0.146992			0.0734958	+	0.997296i	$0.476584\pi$
$752$		−	8.47559i		−	0.309073i
$753$			54.6272i			1.99073i
$754$	14.9223			0.543440
$755$	44.2700	+	1.05549i	1.61115	+	0.0384131i
$756$	2.08009			0.0756521
$757$		−	35.6364i		−	1.29523i	−0.761969	−	0.647614i	$-0.775767\pi$
$757$		−	35.6364i		−	1.29523i	0.761969	−	0.647614i	$-0.224233\pi$
$758$			37.2552i			1.35317i
$759$	−60.7639			−2.20559
$760$	−0.443874	+	18.6173i	−0.0161010	+	0.675320i
$761$	−33.5375			−1.21573			−0.607867	−	0.794039i	$-0.707975\pi$
$761$	−33.5375			−1.21573			−0.607867	+	0.794039i	$0.707975\pi$
$762$			31.0526i			1.12492i
$763$			3.38230i			0.122448i
$764$	58.1499			2.10379
$765$	−0.0803286	+	3.36920i	−0.00290429	+	0.121814i
$766$	22.8344			0.825040
$767$			42.5581i			1.53668i
$768$		−	12.5412i		−	0.452540i
$769$	43.4481			1.56678			0.783389	−	0.621532i	$-0.213489\pi$
$769$	43.4481			1.56678			0.783389	+	0.621532i	$0.213489\pi$
$770$	−6.96051	−	0.165952i	−0.250839	−	0.00598051i
$771$	−13.8354			−0.498270
$772$			54.1779i			1.94991i
$773$		−	23.6950i		−	0.852248i	−0.904665	−	0.426124i	$-0.859879\pi$
$773$		−	23.6950i		−	0.852248i	0.904665	−	0.426124i	$-0.140121\pi$
$774$	−48.2592			−1.73464
$775$	40.5748	+	1.93587i	1.45749	+	0.0695384i
$776$	−32.5896			−1.16990
$777$		−	0.648784i		−	0.0232750i
$778$			78.2073i			2.80387i
$779$	−48.5867			−1.74080
$780$	44.3905	+	1.05836i	1.58943	+	0.0378953i
$781$	−2.62881			−0.0940662
$782$			10.9869i			0.392893i
$783$		−	4.30891i		−	0.153988i
$784$	−9.95340			−0.355479
$785$	−0.250314	+	10.4989i	−0.00893409	+	0.374721i
$786$	−60.2046			−2.14743
$787$			18.5145i			0.659969i	0.943986	+	0.329985i	$0.107044\pi$
$787$			18.5145i			0.659969i	−0.943986	+	0.329985i	$0.892956\pi$
$788$			64.2980i			2.29052i
$789$	23.3082			0.829794
$790$	0.489260	−	20.5209i	0.0174071	−	0.730101i
$791$	3.09153			0.109922
$792$		−	15.8637i		−	0.563691i
$793$		−	32.0479i		−	1.13805i
$794$	−13.9775			−0.496043
$795$	−39.0885	−	0.931949i	−1.38633	−	0.0330528i
$796$	−24.5824			−0.871302
$797$		−	46.9694i		−	1.66374i	−0.554970	−	0.831871i	$-0.687270\pi$
$797$		−	46.9694i		−	1.66374i	0.554970	−	0.831871i	$-0.312730\pi$
$798$		−	7.95861i		−	0.281732i
$799$	−4.10306			−0.145156
$800$	−1.69492	+	35.5246i	−0.0599244	+	1.25598i
$801$	−37.7659			−1.33439
$802$			64.6540i			2.28301i
$803$			35.7843i			1.26280i
$804$	83.4648			2.94358
$805$	5.89291	+	0.140499i	0.207698	+	0.00495193i
$806$	−54.4956			−1.91953
$807$			44.4088i			1.56326i
$808$			26.8371i			0.944125i
$809$	0.668110			0.0234895			0.0117448	−	0.999931i	$-0.496261\pi$
$809$	0.668110			0.0234895			0.0117448	+	0.999931i	$0.496261\pi$
$810$	1.27590	−	53.5150i	0.0448307	−	1.88032i
$811$	20.2312			0.710414			0.355207	−	0.934788i	$-0.384410\pi$
$811$	20.2312			0.710414			0.355207	+	0.934788i	$0.384410\pi$
$812$			2.38905i			0.0838392i
$813$			33.5642i			1.17715i
$814$	6.42215			0.225096
$815$	0.650474	−	27.2827i	0.0227851	−	0.955672i
$816$	2.31103			0.0809023
$817$		−	43.3770i		−	1.51757i
$818$		−	15.3948i		−	0.538267i
$819$	−2.42571			−0.0847611
$820$	73.4750	+	1.75179i	2.56586	+	0.0611752i
$821$	−14.4859			−0.505563			−0.252781	−	0.967523i	$-0.581345\pi$
$821$	−14.4859			−0.505563			−0.252781	+	0.967523i	$0.581345\pi$
$822$			11.9430i			0.416558i
$823$		−	16.6518i		−	0.580445i	−0.956959	−	0.290223i	$-0.906271\pi$
$823$		−	16.6518i		−	0.580445i	0.956959	−	0.290223i	$-0.0937293\pi$
$824$	2.45169			0.0854087
$825$	−2.04528	+	42.8679i	−0.0712074	+	1.49247i
$826$	−11.5386			−0.401478
$827$		−	7.02125i		−	0.244153i	−0.992521	−	0.122076i	$-0.961045\pi$
$827$		−	7.02125i		−	0.244153i	0.992521	−	0.122076i	$-0.0389553\pi$
$828$			43.8172i			1.52275i
$829$	16.9465			0.588576			0.294288	−	0.955717i	$-0.404917\pi$
$829$	16.9465			0.588576			0.294288	+	0.955717i	$0.404917\pi$
$830$	54.5133	+	1.29971i	1.89218	+	0.0451134i
$831$	24.0414			0.833987
$832$		−	38.9066i		−	1.34884i
$833$			4.81848i			0.166950i
$834$	−15.1947			−0.526149
$835$	0.456235	−	19.1358i	0.0157887	−	0.662220i
$836$	46.5195			1.60891
$837$			15.7359i			0.543913i
$838$		−	26.3315i		−	0.909606i
$839$	4.22287			0.145790			0.0728949	−	0.997340i	$-0.476776\pi$
$839$	4.22287			0.145790			0.0728949	+	0.997340i	$0.476776\pi$
$840$	−0.0879529	+	3.68899i	−0.00303466	+	0.127282i
$841$	−24.0511			−0.829347
$842$		−	67.2714i		−	2.31833i
$843$		−	44.6937i		−	1.53933i
$844$	41.2975			1.42152
$845$	−8.46608	−	0.201848i	−0.291242	−	0.00694379i
$846$	−27.7114			−0.952737
$847$			1.23487i			0.0424307i
$848$			11.1817i			0.383982i
$849$	38.8843			1.33451
$850$	7.75111	+	0.369814i	0.265861	+	0.0126845i
$851$	−5.43712			−0.186382
$852$			4.54546i			0.155725i
$853$			13.6874i			0.468648i	0.972159	+	0.234324i	$0.0752876\pi$
$853$			13.6874i			0.468648i	−0.972159	+	0.234324i	$0.924712\pi$
$854$	8.68899			0.297331
$855$	−20.4530	−	0.487640i	−0.699477	−	0.0166769i
$856$	3.21930			0.110033
$857$			16.7973i			0.573786i	0.957963	+	0.286893i	$0.0926224\pi$
$857$			16.7973i			0.573786i	−0.957963	+	0.286893i	$0.907378\pi$
$858$		−	57.5756i		−	1.96560i
$859$	−2.95778			−0.100918			−0.0504591	−	0.998726i	$-0.516068\pi$
$859$	−2.95778			−0.100918			−0.0504591	+	0.998726i	$0.516068\pi$
$860$	−1.56396	+	65.5966i	−0.0533304	+	2.23683i
$861$	−9.62737			−0.328100
$862$		−	36.1424i		−	1.23102i
$863$			28.1942i			0.959741i	0.877339	+	0.479871i	$0.159316\pi$
$863$			28.1942i			0.959741i	−0.877339	+	0.479871i	$0.840684\pi$
$864$	−13.7773			−0.468714
$865$	−0.629556	+	26.4053i	−0.0214055	+	0.897808i
$866$	7.32742			0.248996
$867$			37.4460i			1.27173i
$868$		−	8.72468i		−	0.296135i
$869$	−15.7168			−0.533154
$870$	24.9313	+	0.594413i	0.845252	+	0.0201525i
$871$	38.7227			1.31207
$872$			17.7443i			0.600898i
$873$		−	35.8029i		−	1.21174i
$874$	−66.6970			−2.25606
$875$	0.297471	−	4.15262i	0.0100564	−	0.140384i
$876$	61.8744			2.09054
$877$			21.7682i			0.735059i	0.930012	+	0.367529i	$0.119796\pi$
$877$			21.7682i			0.735059i	−0.930012	+	0.367529i	$0.880204\pi$
$878$		−	3.33740i		−	0.112632i
$879$	8.62235			0.290825
$880$	12.2698	+	0.292537i	0.413616	+	0.00986143i
$881$	17.4794			0.588897			0.294449	−	0.955667i	$-0.404864\pi$
$881$	17.4794			0.588897			0.294449	+	0.955667i	$0.404864\pi$
$882$			32.5432i			1.09579i
$883$		−	1.08094i		−	0.0363766i	−0.999835	−	0.0181883i	$-0.994210\pi$
$883$		−	1.08094i		−	0.0363766i	0.999835	−	0.0181883i	$-0.00578984\pi$
$884$	−6.14734			−0.206758
$885$	−1.69525	+	71.1035i	−0.0569852	+	2.39012i
$886$	−79.9061			−2.68450
$887$		−	27.8526i		−	0.935200i	−0.883940	−	0.467600i	$-0.845119\pi$
$887$		−	27.8526i		−	0.935200i	0.883940	−	0.467600i	$-0.154881\pi$
$888$		−	3.40366i		−	0.114219i
$889$	−2.30647			−0.0773564
$890$	−2.07265	+	86.9328i	−0.0694755	+	2.91399i
$891$	−40.9865			−1.37310
$892$		−	20.1414i		−	0.674385i
$893$		−	24.9079i		−	0.833511i
$894$	−69.9663			−2.34002
$895$	−22.8655	−	0.545159i	−0.764309	−	0.0182227i
$896$	5.25117			0.175429
$897$			48.7446i			1.62754i
$898$			21.3782i			0.713399i
$899$	−18.0732			−0.602775
$900$	30.9123	+	1.47486i	1.03041	+	0.0491621i
$901$	5.41311			0.180337
$902$		−	95.2989i		−	3.17310i
$903$		−	8.59508i		−	0.286026i
$904$	16.2188			0.539430
$905$	−7.49534	−	0.178704i	−0.249154	−	0.00594032i
$906$	−99.2834			−3.29847
$907$		−	26.3979i		−	0.876529i	−0.898846	−	0.438265i	$-0.855593\pi$
$907$		−	26.3979i		−	0.876529i	0.898846	−	0.438265i	$-0.144407\pi$
$908$			8.82678i			0.292927i
$909$	−29.4832			−0.977896
$910$	−0.133127	+	5.58370i	−0.00441310	+	0.185098i
$911$	0.713573			0.0236417			0.0118209	−	0.999930i	$-0.496237\pi$
$911$	0.713573			0.0236417			0.0118209	+	0.999930i	$0.496237\pi$
$912$			14.0293i			0.464555i
$913$		−	41.7511i		−	1.38176i
$914$	−64.0682			−2.11919
$915$	1.27659	−	53.5437i	0.0422027	−	1.77010i
$916$	−5.81049			−0.191984
$917$		−	4.47177i		−	0.147671i
$918$			3.00608i			0.0992153i
$919$	−43.1004			−1.42175			−0.710876	−	0.703317i	$-0.751701\pi$
$919$	−43.1004			−1.42175			−0.710876	+	0.703317i	$0.751701\pi$
$920$	30.9155	+	0.737087i	1.01925	+	0.0243010i
$921$	−32.8977			−1.08402
$922$			32.5648i			1.07246i
$923$			2.10882i			0.0694127i
$924$	9.21777			0.303242
$925$	−0.183010	+	3.83580i	−0.00601734	+	0.126120i
$926$	63.9987			2.10313
$927$			2.69343i			0.0884638i
$928$		−	15.8237i		−	0.519438i
$929$	−6.29923			−0.206671			−0.103336	−	0.994647i	$-0.532952\pi$
$929$	−6.29923			−0.206671			−0.103336	+	0.994647i	$0.532952\pi$
$930$	−91.0480	−	2.17077i	−2.98558	−	0.0711822i
$931$	−29.2509			−0.958659
$932$		−	5.00276i		−	0.163871i
$933$		−	12.8231i		−	0.419808i
$934$	81.2887			2.65985
$935$	0.141618	−	5.93987i	0.00463142	−	0.194255i
$936$	−12.7258			−0.415956
$937$		−	17.1954i		−	0.561751i	−0.959744	−	0.280875i	$-0.909375\pi$
$937$		−	17.1954i		−	0.561751i	0.959744	−	0.280875i	$-0.0906247\pi$
$938$			10.4987i			0.342794i
$939$	−52.8660			−1.72522
$940$	−0.898054	+	37.6669i	−0.0292913	+	1.22856i
$941$	−15.5318			−0.506322			−0.253161	−	0.967424i	$-0.581470\pi$
$941$	−15.5318			−0.506322			−0.253161	+	0.967424i	$0.581470\pi$
$942$		−	23.5456i		−	0.767157i
$943$			80.6819i			2.62737i
$944$	20.3399			0.662009
$945$	1.61232	+	0.0384411i	0.0524489	+	0.00125049i
$946$	85.0804			2.76620
$947$		−	43.2607i		−	1.40578i	−0.711297	−	0.702892i	$-0.751892\pi$
$947$		−	43.2607i		−	1.40578i	0.711297	−	0.702892i	$-0.248108\pi$
$948$			27.1758i			0.882628i
$949$	28.7060			0.931838
$950$	−2.24498	+	47.0536i	−0.0728368	+	1.52662i
$951$	39.4392			1.27890
$952$		−	0.510863i		−	0.0165572i
$953$			10.3314i			0.334666i	0.985900	+	0.167333i	$0.0535156\pi$
$953$			10.3314i			0.334666i	−0.985900	+	0.167333i	$0.946484\pi$
$954$	36.5592			1.18365
$955$	45.0733	+	1.07464i	1.45854	+	0.0347745i
$956$	0.244311			0.00790158
$957$		−	19.0947i		−	0.617242i
$958$			13.0298i			0.420973i
$959$	−0.887078			−0.0286452
$960$	1.54979	−	65.0027i	0.0500194	−	2.09795i
$961$	35.0024			1.12911
$962$		−	5.15183i		−	0.166102i
$963$			3.53672i			0.113969i
$964$	2.88397			0.0928865
$965$	−1.00123	+	41.9945i	−0.0322309	+	1.35185i
$966$	−13.2159			−0.425215
$967$		−	15.9401i		−	0.512598i	−0.966598	−	0.256299i	$-0.917497\pi$
$967$		−	15.9401i		−	0.512598i	0.966598	−	0.256299i	$-0.0825032\pi$
$968$			6.47841i			0.208224i
$969$	6.79162			0.218178
$970$	−82.4142	−	1.96492i	−2.64616	−	0.0630897i
$971$	21.6770			0.695647			0.347824	−	0.937560i	$-0.386921\pi$
$971$	21.6770			0.695647			0.347824	+	0.937560i	$0.386921\pi$
$972$			54.1116i			1.73563i
$973$		−	1.12861i		−	0.0361814i
$974$	48.3162			1.54815
$975$	34.3885	+	1.64072i	1.10131	+	0.0525450i
$976$	−15.3168			−0.490278
$977$			48.6376i			1.55605i	0.628231	+	0.778027i	$0.283779\pi$
$977$			48.6376i			1.55605i	−0.628231	+	0.778027i	$0.716221\pi$
$978$			61.1864i			1.95652i
$979$	66.5809			2.12794
$980$	44.2345	+	1.05464i	1.41302	+	0.0336892i
$981$	−19.4939			−0.622392
$982$		−	40.7361i		−	1.29994i
$983$		−	53.0177i		−	1.69100i	−0.533975	−	0.845500i	$-0.679302\pi$
$983$		−	53.0177i		−	1.69100i	0.533975	−	0.845500i	$-0.320698\pi$
$984$	−50.5073			−1.61011
$985$	−1.18826	+	49.8389i	−0.0378611	+	1.58800i
$986$	−3.45257			−0.109952
$987$		−	4.93546i		−	0.157098i
$988$		−	37.3178i		−	1.18724i
$989$	−72.0308			−2.29045
$990$	0.956466	−	40.1169i	0.0303985	−	1.27500i
$991$	34.2607			1.08833			0.544164	−	0.838979i	$-0.316847\pi$
$991$	34.2607			1.08833			0.544164	+	0.838979i	$0.316847\pi$
$992$			57.7873i			1.83475i
$993$			11.7941i			0.374273i
$994$	−0.571755			−0.0181350
$995$	−19.0544	−	0.454295i	−0.604066	−	0.0144021i
$996$	−72.1917			−2.28748
$997$			49.2198i			1.55881i	0.626522	+	0.779404i	$0.284478\pi$
$997$			49.2198i			1.55881i	−0.626522	+	0.779404i	$0.715522\pi$
$998$			10.4638i			0.331227i
$999$	−1.48762			−0.0470662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.d.724.11	✓	66
5.2	odd	4		6025.2.a.q.1.56		66
5.3	odd	4		6025.2.a.q.1.11		66
5.4	even	2	inner	1205.2.b.d.724.56	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.d.724.11	✓	66	1.1	even	1	trivial
1205.2.b.d.724.56	yes	66	5.4	even	2	inner
6025.2.a.q.1.11		66	5.3	odd	4
6025.2.a.q.1.56		66	5.2	odd	4

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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.20997i q^{2} +2.26852i q^{3} -2.88397 q^{4} +(-2.23543 - 0.0532972i) q^{5} +5.01336 q^{6} +0.372373i q^{7} +1.95355i q^{8} -2.14617 q^{9} +O(q^{10})\)	\(q-2.20997i q^{2} +2.26852i q^{3} -2.88397 q^{4} +(-2.23543 - 0.0532972i) q^{5} +5.01336 q^{6} +0.372373i q^{7} +1.95355i q^{8} -2.14617 q^{9} +(-0.117785 + 4.94024i) q^{10} +3.78368 q^{11} -6.54234i q^{12} -3.03526i q^{13} +0.822934 q^{14} +(0.120906 - 5.07112i) q^{15} -1.45065 q^{16} +0.702265i q^{17} +4.74298i q^{18} -4.26314 q^{19} +(6.44693 + 0.153708i) q^{20} -0.844736 q^{21} -8.36182i q^{22} +7.07928i q^{23} -4.43167 q^{24} +(4.99432 + 0.238285i) q^{25} -6.70783 q^{26} +1.93692i q^{27} -1.07391i q^{28} -2.22462 q^{29} +(-11.2070 - 0.267198i) q^{30} +8.12419 q^{31} +7.11300i q^{32} +8.58334i q^{33} +1.55199 q^{34} +(0.0198465 - 0.832416i) q^{35} +6.18950 q^{36} +0.768032i q^{37} +9.42143i q^{38} +6.88553 q^{39} +(0.104119 - 4.36703i) q^{40} +11.3969 q^{41} +1.86684i q^{42} +10.1749i q^{43} -10.9120 q^{44} +(4.79762 + 0.114385i) q^{45} +15.6450 q^{46} +5.84261i q^{47} -3.29083i q^{48} +6.86134 q^{49} +(0.526602 - 11.0373i) q^{50} -1.59310 q^{51} +8.75359i q^{52} -7.70807i q^{53} +4.28054 q^{54} +(-8.45816 - 0.201659i) q^{55} -0.727451 q^{56} -9.67102i q^{57} +4.91634i q^{58} -14.0213 q^{59} +(-0.348688 + 14.6250i) q^{60} +10.5586 q^{61} -17.9542i q^{62} -0.799178i q^{63} +12.8182 q^{64} +(-0.161771 + 6.78511i) q^{65} +18.9689 q^{66} +12.7576i q^{67} -2.02531i q^{68} -16.0595 q^{69} +(-1.83961 - 0.0438601i) q^{70} -0.694776 q^{71} -4.19266i q^{72} +9.45754i q^{73} +1.69733 q^{74} +(-0.540553 + 11.3297i) q^{75} +12.2948 q^{76} +1.40894i q^{77} -15.2168i q^{78} -4.15383 q^{79} +(3.24283 + 0.0773156i) q^{80} -10.8325 q^{81} -25.1868i q^{82} -11.0345i q^{83} +2.43619 q^{84} +(0.0374288 - 1.56987i) q^{85} +22.4862 q^{86} -5.04658i q^{87} +7.39161i q^{88} +17.5969 q^{89} +(0.252787 - 10.6026i) q^{90} +1.13025 q^{91} -20.4165i q^{92} +18.4299i q^{93} +12.9120 q^{94} +(9.52997 + 0.227214i) q^{95} -16.1360 q^{96} +16.6822i q^{97} -15.1634i q^{98} -8.12043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 78 q^{4} + 16 q^{6} - 90 q^{9}+O(q^{10}) \) 66 * q - 78 * q^4 + 16 * q^6 - 90 * q^9	\( 66 q - 78 q^{4} + 16 q^{6} - 90 q^{9} + q^{10} + 48 q^{11} - 30 q^{14} - 3 q^{15} + 98 q^{16} - 12 q^{19} - 10 q^{20} + 18 q^{21} - 42 q^{24} + 6 q^{25} + 48 q^{26} - 56 q^{29} - 5 q^{30} + 48 q^{31} - 8 q^{34} + 3 q^{35} + 158 q^{36} - 84 q^{39} - 6 q^{40} + 56 q^{41} - 144 q^{44} - 13 q^{45} + 36 q^{46} - 98 q^{49} + 2 q^{50} + 44 q^{51} - 86 q^{54} + 3 q^{55} + 104 q^{56} - 108 q^{59} + 7 q^{60} + 22 q^{61} - 136 q^{64} + 15 q^{65} + 74 q^{66} - 20 q^{69} - 32 q^{70} + 212 q^{71} - 84 q^{74} - 9 q^{75} + 6 q^{76} - 66 q^{79} - 21 q^{80} + 162 q^{81} + 52 q^{84} - 48 q^{85} + 100 q^{86} - 54 q^{89} - 155 q^{90} + 72 q^{91} + 96 q^{94} - 5 q^{95} + 122 q^{96} - 112 q^{99}+O(q^{100}) \) 66 * q - 78 * q^4 + 16 * q^6 - 90 * q^9 + q^10 + 48 * q^11 - 30 * q^14 - 3 * q^15 + 98 * q^16 - 12 * q^19 - 10 * q^20 + 18 * q^21 - 42 * q^24 + 6 * q^25 + 48 * q^26 - 56 * q^29 - 5 * q^30 + 48 * q^31 - 8 * q^34 + 3 * q^35 + 158 * q^36 - 84 * q^39 - 6 * q^40 + 56 * q^41 - 144 * q^44 - 13 * q^45 + 36 * q^46 - 98 * q^49 + 2 * q^50 + 44 * q^51 - 86 * q^54 + 3 * q^55 + 104 * q^56 - 108 * q^59 + 7 * q^60 + 22 * q^61 - 136 * q^64 + 15 * q^65 + 74 * q^66 - 20 * q^69 - 32 * q^70 + 212 * q^71 - 84 * q^74 - 9 * q^75 + 6 * q^76 - 66 * q^79 - 21 * q^80 + 162 * q^81 + 52 * q^84 - 48 * q^85 + 100 * q^86 - 54 * q^89 - 155 * q^90 + 72 * q^91 + 96 * q^94 - 5 * q^95 + 122 * q^96 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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