LMFDB - Embedded newform 1805.2.b.j.1084.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 $ x^16 + 22x^14 + 190x^12 + 820x^10 + 1862x^8 + 2154x^6 + 1163x^4 + 256*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.14
Root			$1.93600i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.j.1084.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93600i q^{2} -2.41423i q^{3} -1.74811 q^{4} +(-0.825597 - 2.07807i) q^{5} +4.67396 q^{6} -1.46100i q^{7} +0.487655i q^{8} -2.82851 q^{9} +O(q^{10})$	\(q+1.93600i q^{2} -2.41423i q^{3} -1.74811 q^{4} +(-0.825597 - 2.07807i) q^{5} +4.67396 q^{6} -1.46100i q^{7} +0.487655i q^{8} -2.82851 q^{9} +(4.02316 - 1.59836i) q^{10} -2.89488 q^{11} +4.22035i q^{12} +6.12528i q^{13} +2.82851 q^{14} +(-5.01695 + 1.99318i) q^{15} -4.44033 q^{16} +6.29889i q^{17} -5.47600i q^{18} +(1.44324 + 3.63271i) q^{20} -3.52719 q^{21} -5.60450i q^{22} +0.508852i q^{23} +1.17731 q^{24} +(-3.63678 + 3.43130i) q^{25} -11.8586 q^{26} -0.414027i q^{27} +2.55400i q^{28} +1.72159 q^{29} +(-3.85881 - 9.71283i) q^{30} +8.44484 q^{31} -7.62118i q^{32} +6.98890i q^{33} -12.1947 q^{34} +(-3.03607 + 1.20620i) q^{35} +4.94455 q^{36} -3.13569i q^{37} +14.7878 q^{39} +(1.01338 - 0.402607i) q^{40} -7.44400 q^{41} -6.82866i q^{42} +6.90372i q^{43} +5.06057 q^{44} +(2.33521 + 5.87784i) q^{45} -0.985139 q^{46} +0.316851i q^{47} +10.7200i q^{48} +4.86547 q^{49} +(-6.64302 - 7.04082i) q^{50} +15.2070 q^{51} -10.7077i q^{52} +4.34236i q^{53} +0.801557 q^{54} +(2.39000 + 6.01577i) q^{55} +0.712465 q^{56} +3.33300i q^{58} +2.25084 q^{59} +(8.77019 - 3.48431i) q^{60} -6.29374 q^{61} +16.3492i q^{62} +4.13245i q^{63} +5.87399 q^{64} +(12.7288 - 5.05701i) q^{65} -13.5305 q^{66} +10.0324i q^{67} -11.0112i q^{68} +1.22849 q^{69} +(-2.33521 - 5.87784i) q^{70} +6.63567 q^{71} -1.37933i q^{72} +12.9644i q^{73} +6.07070 q^{74} +(8.28396 + 8.78002i) q^{75} +4.22942i q^{77} +28.6293i q^{78} +14.6730 q^{79} +(3.66592 + 9.22733i) q^{80} -9.48507 q^{81} -14.4116i q^{82} -4.94202i q^{83} +6.16593 q^{84} +(13.0896 - 5.20035i) q^{85} -13.3656 q^{86} -4.15631i q^{87} -1.41170i q^{88} -5.35408 q^{89} +(-11.3795 + 4.52097i) q^{90} +8.94904 q^{91} -0.889530i q^{92} -20.3878i q^{93} -0.613425 q^{94} -18.3993 q^{96} -15.9482i q^{97} +9.41958i q^{98} +8.18818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) $ 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9	$ 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} + 16 q^{10} - 22 q^{11} + 6 q^{14} - 10 q^{15} + 8 q^{16} - 14 q^{20} + 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} + 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} - 38 q^{40} - 26 q^{41} + 64 q^{44} - 2 q^{45} - 2 q^{46} + 20 q^{49} + 48 q^{50} + 38 q^{51} + 12 q^{54} - 10 q^{55} - 6 q^{56} + 10 q^{59} + 10 q^{60} - 30 q^{61} + 16 q^{64} + 36 q^{65} + 4 q^{66} + 68 q^{69} + 2 q^{70} + 20 q^{71} + 40 q^{74} + 32 q^{75} + 12 q^{79} + 40 q^{80} - 48 q^{81} - 2 q^{84} - 2 q^{85} + 20 q^{86} - 30 q^{90} + 86 q^{91} - 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) $ 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9 + 16 * q^10 - 22 * q^11 + 6 * q^14 - 10 * q^15 + 8 * q^16 - 14 * q^20 + 20 * q^21 + 14 * q^24 + 4 * q^25 - 16 * q^26 + 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 10 * q^35 + 18 * q^36 + 36 * q^39 - 38 * q^40 - 26 * q^41 + 64 * q^44 - 2 * q^45 - 2 * q^46 + 20 * q^49 + 48 * q^50 + 38 * q^51 + 12 * q^54 - 10 * q^55 - 6 * q^56 + 10 * q^59 + 10 * q^60 - 30 * q^61 + 16 * q^64 + 36 * q^65 + 4 * q^66 + 68 * q^69 + 2 * q^70 + 20 * q^71 + 40 * q^74 + 32 * q^75 + 12 * q^79 + 40 * q^80 - 48 * q^81 - 2 * q^84 - 2 * q^85 + 20 * q^86 - 30 * q^90 + 86 * q^91 - 38 * q^94 + 22 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.93600i			1.36896i	0.729031	+	0.684481i	$0.239971\pi$
$2$			1.93600i			1.36896i	−0.729031	+	0.684481i	$0.760029\pi$
$3$		−	2.41423i		−	1.39386i	−0.717141	−	0.696928i	$-0.754550\pi$
$3$		−	2.41423i		−	1.39386i	0.717141	−	0.696928i	$-0.245450\pi$
$4$	−1.74811			−0.874056
$5$	−0.825597	−	2.07807i	−0.369218	−	0.929343i
$5$	−0.825597	−	2.07807i	−0.369218	−	0.929343i
$6$	4.67396			1.90814
$7$		−	1.46100i		−	0.552207i	−0.961128	−	0.276103i	$-0.910957\pi$
$7$		−	1.46100i		−	0.552207i	0.961128	−	0.276103i	$-0.0890432\pi$
$8$			0.487655i			0.172412i
$9$	−2.82851			−0.942835
$10$	4.02316	−	1.59836i	1.27223	−	0.505446i
$11$	−2.89488			−0.872839			−0.436419	−	0.899743i	$-0.643754\pi$
$11$	−2.89488			−0.872839			−0.436419	+	0.899743i	$0.643754\pi$
$12$			4.22035i			1.21831i
$13$			6.12528i			1.69885i	0.527713	+	0.849423i	$0.323050\pi$
$13$			6.12528i			1.69885i	−0.527713	+	0.849423i	$0.676950\pi$
$14$	2.82851			0.755950
$15$	−5.01695	+	1.99318i	−1.29537	+	0.514637i
$16$	−4.44033			−1.11008
$17$			6.29889i			1.52771i	0.645391	+	0.763853i	$0.276695\pi$
$17$			6.29889i			1.52771i	−0.645391	+	0.763853i	$0.723305\pi$
$18$		−	5.47600i		−	1.29071i
$19$		0			0
$19$		0			0
$20$	1.44324	+	3.63271i	0.322718	+	0.812298i
$21$	−3.52719			−0.769697
$22$		−	5.60450i		−	1.19488i
$23$			0.508852i			0.106103i	0.998592	+	0.0530515i	$0.0168947\pi$
$23$			0.508852i			0.106103i	−0.998592	+	0.0530515i	$0.983105\pi$
$24$	1.17731			0.240318
$25$	−3.63678	+	3.43130i	−0.727356	+	0.686261i
$26$	−11.8586			−2.32565
$27$		−	0.414027i		−	0.0796795i
$28$			2.55400i			0.482660i
$29$	1.72159			0.319691			0.159845	−	0.987142i	$-0.448900\pi$
$29$	1.72159			0.319691			0.159845	+	0.987142i	$0.448900\pi$
$30$	−3.85881	−	9.71283i	−0.704519	−	1.77331i
$31$	8.44484			1.51674			0.758369	−	0.651826i	$-0.225997\pi$
$31$	8.44484			1.51674			0.758369	+	0.651826i	$0.225997\pi$
$32$		−	7.62118i		−	1.34725i
$33$			6.98890i			1.21661i
$34$	−12.1947			−2.09137
$35$	−3.03607	+	1.20620i	−0.513189	+	0.203885i
$36$	4.94455			0.824091
$37$		−	3.13569i		−	0.515504i	−0.966211	−	0.257752i	$-0.917018\pi$
$37$		−	3.13569i		−	0.515504i	0.966211	−	0.257752i	$-0.0829817\pi$
$38$		0			0
$39$	14.7878			2.36795
$40$	1.01338	−	0.402607i	0.160230	−	0.0636577i
$41$	−7.44400			−1.16256			−0.581279	−	0.813704i	$-0.697447\pi$
$41$	−7.44400			−1.16256			−0.581279	+	0.813704i	$0.697447\pi$
$42$		−	6.82866i		−	1.05369i
$43$			6.90372i			1.05281i	0.850235	+	0.526404i	$0.176460\pi$
$43$			6.90372i			1.05281i	−0.850235	+	0.526404i	$0.823540\pi$
$44$	5.06057			0.762910
$45$	2.33521	+	5.87784i	0.348112	+	0.876217i
$46$	−0.985139			−0.145251
$47$			0.316851i			0.0462175i	0.999733	+	0.0231087i	$0.00735640\pi$
$47$			0.316851i			0.0462175i	−0.999733	+	0.0231087i	$0.992644\pi$
$48$			10.7200i			1.54729i
$49$	4.86547			0.695068
$50$	−6.64302	−	7.04082i	−0.939465	−	0.995722i
$51$	15.2070			2.12940
$52$		−	10.7077i		−	1.48489i
$53$			4.34236i			0.596468i	0.954493	+	0.298234i	$0.0963977\pi$
$53$			4.34236i			0.596468i	−0.954493	+	0.298234i	$0.903602\pi$
$54$	0.801557			0.109078
$55$	2.39000	+	6.01577i	0.322268	+	0.811166i
$56$	0.712465			0.0952071
$57$		0			0
$58$			3.33300i			0.437644i
$59$	2.25084			0.293035			0.146517	−	0.989208i	$-0.453194\pi$
$59$	2.25084			0.293035			0.146517	+	0.989208i	$0.453194\pi$
$60$	8.77019	−	3.48431i	1.13223	−	0.449822i
$61$	−6.29374			−0.805831			−0.402916	−	0.915237i	$-0.632003\pi$
$61$	−6.29374			−0.805831			−0.402916	+	0.915237i	$0.632003\pi$
$62$			16.3492i			2.07636i
$63$			4.13245i			0.520640i
$64$	5.87399			0.734249
$65$	12.7288	−	5.05701i	1.57881	−	0.627245i
$66$	−13.5305			−1.66549
$67$			10.0324i			1.22565i	0.790217	+	0.612827i	$0.209968\pi$
$67$			10.0324i			1.22565i	−0.790217	+	0.612827i	$0.790032\pi$
$68$		−	11.0112i		−	1.33530i
$69$	1.22849			0.147892
$70$	−2.33521	−	5.87784i	−0.279111	−	0.702537i
$71$	6.63567			0.787509			0.393754	−	0.919216i	$-0.371176\pi$
$71$	6.63567			0.787509			0.393754	+	0.919216i	$0.371176\pi$
$72$		−	1.37933i		−	0.162556i
$73$			12.9644i			1.51737i	0.651458	+	0.758685i	$0.274158\pi$
$73$			12.9644i			1.51737i	−0.651458	+	0.758685i	$0.725842\pi$
$74$	6.07070			0.705705
$75$	8.28396	+	8.78002i	0.956549	+	1.01383i
$76$		0			0
$77$			4.22942i			0.481987i
$78$			28.6293i			3.24163i
$79$	14.6730			1.65084			0.825420	−	0.564519i	$-0.190938\pi$
$79$	14.6730			1.65084			0.825420	+	0.564519i	$0.190938\pi$
$80$	3.66592	+	9.22733i	0.409863	+	1.03165i
$81$	−9.48507			−1.05390
$82$		−	14.4116i		−	1.59150i
$83$		−	4.94202i		−	0.542458i	−0.962515	−	0.271229i	$-0.912570\pi$
$83$		−	4.94202i		−	0.542458i	0.962515	−	0.271229i	$-0.0874300\pi$
$84$	6.16593			0.672758
$85$	13.0896	−	5.20035i	1.41976	−	0.564057i
$86$	−13.3656			−1.44125
$87$		−	4.15631i		−	0.445603i
$88$		−	1.41170i		−	0.150488i
$89$	−5.35408			−0.567532			−0.283766	−	0.958894i	$-0.591584\pi$
$89$	−5.35408			−0.567532			−0.283766	+	0.958894i	$0.591584\pi$
$90$	−11.3795	+	4.52097i	−1.19951	+	0.476552i
$91$	8.94904			0.938114
$92$		−	0.889530i		−	0.0927400i
$93$		−	20.3878i		−	2.11411i
$94$	−0.613425			−0.0632700
$95$		0			0
$96$	−18.3993			−1.87787
$97$		−	15.9482i		−	1.61929i	−0.586918	−	0.809646i	$-0.699659\pi$
$97$		−	15.9482i		−	1.61929i	0.586918	−	0.809646i	$-0.300341\pi$
$98$			9.41958i			0.951521i
$99$	8.18818			0.822943
$100$	6.35750	−	5.99830i	0.635750	−	0.599830i
$101$	−6.24001			−0.620904			−0.310452	−	0.950589i	$-0.600480\pi$
$101$	−6.24001			−0.620904			−0.310452	+	0.950589i	$0.600480\pi$
$102$			29.4408i			2.91507i
$103$			7.93296i			0.781658i	0.920463	+	0.390829i	$0.127812\pi$
$103$			7.93296i			0.781658i	−0.920463	+	0.390829i	$0.872188\pi$
$104$	−2.98702			−0.292902
$105$	2.91204	+	7.32977i	0.284186	+	0.715312i
$106$	−8.40682			−0.816543
$107$			17.3832i			1.68050i	0.542200	+	0.840250i	$0.317592\pi$
$107$			17.3832i			1.68050i	−0.542200	+	0.840250i	$0.682408\pi$
$108$			0.723765i			0.0696443i
$109$	8.66544			0.829999			0.414999	−	0.909822i	$-0.363782\pi$
$109$	8.66544			0.829999			0.414999	+	0.909822i	$0.363782\pi$
$110$	−11.6466	+	4.62706i	−1.11046	+	0.441173i
$111$	−7.57027			−0.718538
$112$			6.48733i			0.612995i
$113$		−	9.86985i		−	0.928477i	−0.885710	−	0.464239i	$-0.846328\pi$
$113$		−	9.86985i		−	0.928477i	0.885710	−	0.464239i	$-0.153672\pi$
$114$		0			0
$115$	1.05743	−	0.420107i	0.0986060	−	0.0391752i
$116$	−3.00953			−0.279428
$117$		−	17.3254i		−	1.60173i
$118$			4.35764i			0.401153i
$119$	9.20269			0.843609
$120$	−0.971985	−	2.44654i	−0.0887297	−	0.223337i
$121$	−2.61968			−0.238153
$122$		−	12.1847i		−	1.10315i
$123$			17.9715i			1.62044i
$124$	−14.7625			−1.32571
$125$	10.1330	+	4.72462i	0.906324	+	0.422583i
$126$	−8.00044			−0.712736
$127$			11.9797i			1.06303i	0.847049	+	0.531515i	$0.178377\pi$
$127$			11.9797i			1.06303i	−0.847049	+	0.531515i	$0.821623\pi$
$128$		−	3.87030i		−	0.342089i
$129$	16.6672			1.46746
$130$	9.79039	+	24.6430i	0.858674	+	2.16133i
$131$	−8.04755			−0.703118			−0.351559	−	0.936166i	$-0.614348\pi$
$131$	−8.04755			−0.703118			−0.351559	+	0.936166i	$0.614348\pi$
$132$		−	12.2174i		−	1.06339i
$133$		0			0
$134$	−19.4228			−1.67787
$135$	−0.860378	+	0.341819i	−0.0740495	+	0.0294191i
$136$	−3.07169			−0.263395
$137$			3.13952i			0.268227i	0.990966	+	0.134113i	$0.0428187\pi$
$137$			3.13952i			0.268227i	−0.990966	+	0.134113i	$0.957181\pi$
$138$			2.37835i			0.202459i
$139$	−18.7439			−1.58983			−0.794917	−	0.606719i	$-0.792485\pi$
$139$	−18.7439			−1.58983			−0.794917	+	0.606719i	$0.792485\pi$
$140$	5.30739	−	2.10857i	0.448556	−	0.178207i
$141$	0.764951			0.0644205
$142$			12.8467i			1.07807i
$143$		−	17.7319i		−	1.48282i
$144$	12.5595			1.04662
$145$	−1.42134	−	3.57758i	−0.118036	−	0.297102i
$146$	−25.0992			−2.07722
$147$		−	11.7464i		−	0.968824i
$148$			5.48153i			0.450579i
$149$	8.91189			0.730090			0.365045	−	0.930990i	$-0.381054\pi$
$149$	8.91189			0.730090			0.365045	+	0.930990i	$0.381054\pi$
$150$	−16.9982	+	16.0378i	−1.38789	+	1.30948i
$151$	1.41610			0.115241			0.0576204	−	0.998339i	$-0.481649\pi$
$151$	1.41610			0.115241			0.0576204	+	0.998339i	$0.481649\pi$
$152$		0			0
$153$		−	17.8164i		−	1.44037i
$154$	−8.18818			−0.659822
$155$	−6.97203	−	17.5490i	−0.560007	−	1.40957i
$156$	−25.8508			−2.06972
$157$			4.37921i			0.349499i	0.984613	+	0.174750i	$0.0559116\pi$
$157$			4.37921i			0.349499i	−0.984613	+	0.174750i	$0.944088\pi$
$158$			28.4070i			2.25994i
$159$	10.4834			0.831391
$160$	−15.8374	+	6.29203i	−1.25205	+	0.497428i
$161$	0.743434			0.0585908
$162$		−	18.3631i		−	1.44274i
$163$		−	3.09759i		−	0.242622i	−0.992615	−	0.121311i	$-0.961290\pi$
$163$		−	3.09759i		−	0.242622i	0.992615	−	0.121311i	$-0.0387098\pi$
$164$	13.0130			1.01614
$165$	14.5234	−	5.77002i	1.13065	−	0.449195i
$166$	9.56778			0.742604
$167$			3.25702i			0.252036i	0.992028	+	0.126018i	$0.0402197\pi$
$167$			3.25702i			0.252036i	−0.992028	+	0.126018i	$0.959780\pi$
$168$		−	1.72005i		−	0.132705i
$169$	−24.5190			−1.88608
$170$	10.0679	+	25.3414i	0.772172	+	1.94360i
$171$		0			0
$172$		−	12.0685i		−	0.920213i
$173$			10.5204i			0.799848i	0.916548	+	0.399924i	$0.130964\pi$
$173$			10.5204i			0.799848i	−0.916548	+	0.399924i	$0.869036\pi$
$174$	8.04663			0.610013
$175$	5.01314	+	5.31334i	0.378958	+	0.401651i
$176$	12.8542			0.968922
$177$		−	5.43405i		−	0.408448i
$178$		−	10.3655i		−	0.776929i
$179$	−14.3853			−1.07521			−0.537605	−	0.843197i	$-0.680671\pi$
$179$	−14.3853			−1.07521			−0.537605	+	0.843197i	$0.680671\pi$
$180$	−4.08220	−	10.2751i	−0.304270	−	0.765863i
$181$	−8.13512			−0.604679			−0.302339	−	0.953200i	$-0.597768\pi$
$181$	−8.13512			−0.604679			−0.302339	+	0.953200i	$0.597768\pi$
$182$			17.3254i			1.28424i
$183$			15.1945i			1.12321i
$184$	−0.248144			−0.0182934
$185$	−6.51618	+	2.58881i	−0.479079	+	0.190333i
$186$	39.4708			2.89414
$187$		−	18.2345i		−	1.33344i
$188$		−	0.553891i		−	0.0403967i
$189$	−0.604894			−0.0439995
$190$		0			0
$191$	−6.19452			−0.448220			−0.224110	−	0.974564i	$-0.571947\pi$
$191$	−6.19452			−0.448220			−0.224110	+	0.974564i	$0.571947\pi$
$192$		−	14.1812i		−	1.02344i
$193$			12.5560i			0.903798i	0.892069	+	0.451899i	$0.149253\pi$
$193$			12.5560i			0.903798i	−0.892069	+	0.451899i	$0.850747\pi$
$194$	30.8758			2.21675
$195$	−12.2088	−	30.7302i	−0.874289	−	2.20063i
$196$	−8.50540			−0.607528
$197$		−	3.43662i		−	0.244849i	−0.992478	−	0.122425i	$-0.960933\pi$
$197$		−	3.43662i		−	0.244849i	0.992478	−	0.122425i	$-0.0390670\pi$
$198$			15.8523i			1.12658i
$199$	0.866118			0.0613975			0.0306987	−	0.999529i	$-0.490227\pi$
$199$	0.866118			0.0613975			0.0306987	+	0.999529i	$0.490227\pi$
$200$	−1.67329	−	1.77349i	−0.118320	−	0.125405i
$201$	24.2205			1.70839
$202$		−	12.0807i		−	0.849994i
$203$		−	2.51524i		−	0.176535i
$204$	−26.5835			−1.86122
$205$	6.14575	+	15.4692i	0.429238	+	1.08041i
$206$	−15.3582			−1.07006
$207$		−	1.43929i		−	0.100038i
$208$		−	27.1982i		−	1.88586i
$209$		0			0
$210$	−14.1905	+	5.63773i	−0.979235	+	0.389040i
$211$	7.97947			0.549329			0.274665	−	0.961540i	$-0.411433\pi$
$211$	7.97947			0.549329			0.274665	+	0.961540i	$0.411433\pi$
$212$		−	7.59093i		−	0.521347i
$213$		−	16.0200i		−	1.09767i
$214$	−33.6540			−2.30054
$215$	14.3464	−	5.69969i	0.978419	−	0.388716i
$216$	0.201902			0.0137377
$217$		−	12.3379i		−	0.837553i
$218$			16.7763i			1.13624i
$219$	31.2991			2.11500
$220$	−4.17799	−	10.5162i	−0.281680	−	0.709005i
$221$	−38.5824			−2.59534
$222$		−	14.6561i		−	0.983651i
$223$			15.2911i			1.02397i	0.858995	+	0.511985i	$0.171089\pi$
$223$			15.2911i			1.02397i	−0.858995	+	0.511985i	$0.828911\pi$
$224$	−11.1346			−0.743959
$225$	10.2866	−	9.70546i	0.685777	−	0.647031i
$226$	19.1081			1.27105
$227$			7.39075i			0.490541i	0.969455	+	0.245271i	$0.0788769\pi$
$227$			7.39075i			0.490541i	−0.969455	+	0.245271i	$0.921123\pi$
$228$		0			0
$229$	1.00545			0.0664417			0.0332209	−	0.999448i	$-0.489424\pi$
$229$	1.00545			0.0664417			0.0332209	+	0.999448i	$0.489424\pi$
$230$	0.813328	+	2.04719i	0.0536293	+	0.134988i
$231$	10.2108			0.671821
$232$			0.839541i			0.0551185i
$233$			17.0150i			1.11469i	0.830281	+	0.557344i	$0.188180\pi$
$233$			17.0150i			1.11469i	−0.830281	+	0.557344i	$0.811820\pi$
$234$	33.5420			2.19271
$235$	0.658440	−	0.261591i	0.0429519	−	0.0170643i
$236$	−3.93473			−0.256129
$237$		−	35.4240i		−	2.30103i
$238$			17.8164i			1.15487i
$239$	−8.40908			−0.543938			−0.271969	−	0.962306i	$-0.587675\pi$
$239$	−8.40908			−0.543938			−0.271969	+	0.962306i	$0.587675\pi$
$240$	22.2769	−	8.85038i	1.43797	−	0.571289i
$241$	13.0814			0.842648			0.421324	−	0.906910i	$-0.361566\pi$
$241$	13.0814			0.842648			0.421324	+	0.906910i	$0.361566\pi$
$242$		−	5.07171i		−	0.326022i
$243$			21.6571i			1.38930i
$244$	11.0022			0.704342
$245$	−4.01692	−	10.1108i	−0.256632	−	0.645956i
$246$	−34.7930			−2.21832
$247$		0			0
$248$			4.11817i			0.261504i
$249$	−11.9312			−0.756108
$250$	−9.14688	+	19.6176i	−0.578500	+	1.24072i
$251$	13.6747			0.863137			0.431568	−	0.902080i	$-0.357960\pi$
$251$	13.6747			0.863137			0.431568	+	0.902080i	$0.357960\pi$
$252$		−	7.22399i		−	0.455069i
$253$		−	1.47306i		−	0.0926107i
$254$	−23.1928			−1.45525
$255$	−12.5548	−	31.6012i	−0.786214	−	1.97894i
$256$	19.2409			1.20256
$257$		−	2.94446i		−	0.183670i	−0.995774	−	0.0918352i	$-0.970727\pi$
$257$		−	2.94446i		−	0.183670i	0.995774	−	0.0918352i	$-0.0292733\pi$
$258$			32.2677i			2.00890i
$259$	−4.58124			−0.284665
$260$	−22.2513	+	8.84022i	−1.37997	+	0.548247i
$261$	−4.86952			−0.301416
$262$		−	15.5801i		−	0.962541i
$263$		−	13.1907i		−	0.813370i	−0.913568	−	0.406685i	$-0.866685\pi$
$263$		−	13.1907i		−	0.813370i	0.913568	−	0.406685i	$-0.133315\pi$
$264$	−3.40817			−0.209759
$265$	9.02374	−	3.58504i	0.554324	−	0.220227i
$266$		0			0
$267$			12.9260i			0.791058i
$268$		−	17.5378i		−	1.07129i
$269$	−30.9906			−1.88953			−0.944765	−	0.327749i	$-0.893710\pi$
$269$	−30.9906			−1.88953			−0.944765	+	0.327749i	$0.893710\pi$
$270$	−0.661764	−	1.66570i	−0.0402737	−	0.101371i
$271$	−7.50772			−0.456062			−0.228031	−	0.973654i	$-0.573229\pi$
$271$	−7.50772			−0.456062			−0.228031	+	0.973654i	$0.573229\pi$
$272$		−	27.9691i		−	1.69588i
$273$		−	21.6050i		−	1.30760i
$274$	−6.07812			−0.367192
$275$	10.5280	−	9.93320i	0.634864	−	0.598995i
$276$	−2.14753			−0.129266
$277$		−	9.58988i		−	0.576200i	−0.957600	−	0.288100i	$-0.906976\pi$
$277$		−	9.58988i		−	0.576200i	0.957600	−	0.288100i	$-0.0930236\pi$
$278$		−	36.2882i		−	2.17642i
$279$	−23.8863			−1.43003
$280$	−0.588209	−	1.48055i	−0.0351522	−	0.0884800i
$281$	−16.4874			−0.983555			−0.491778	−	0.870721i	$-0.663653\pi$
$281$	−16.4874			−0.983555			−0.491778	+	0.870721i	$0.663653\pi$
$282$			1.48095i			0.0881892i
$283$		−	29.3679i		−	1.74574i	−0.487951	−	0.872871i	$-0.662256\pi$
$283$		−	29.3679i		−	1.74574i	0.487951	−	0.872871i	$-0.337744\pi$
$284$	−11.5999			−0.688327
$285$		0			0
$286$	34.3291			2.02992
$287$			10.8757i			0.641972i
$288$			21.5566i			1.27023i
$289$	−22.6760			−1.33388
$290$	6.92622	−	2.75172i	0.406722	−	0.161586i
$291$	−38.5026			−2.25706
$292$		−	22.6633i		−	1.32627i
$293$			0.995738i			0.0581717i	0.999577	+	0.0290858i	$0.00925961\pi$
$293$			0.995738i			0.0581717i	−0.999577	+	0.0290858i	$0.990740\pi$
$294$	22.7410			1.32628
$295$	−1.85829	−	4.67742i	−0.108194	−	0.272330i
$296$	1.52913			0.0888790
$297$			1.19856i			0.0695473i
$298$			17.2535i			0.999466i
$299$	−3.11686			−0.180253
$300$	−14.4813	−	15.3485i	−0.836077	−	0.886144i
$301$	10.0864			0.581368
$302$			2.74158i			0.157760i
$303$			15.0648i			0.865451i
$304$		0			0
$305$	5.19610	+	13.0789i	0.297528	+	0.748893i
$306$	34.4927			1.97182
$307$			9.86517i			0.563035i	0.959556	+	0.281518i	$0.0908378\pi$
$307$			9.86517i			0.563035i	−0.959556	+	0.281518i	$0.909162\pi$
$308$		−	7.39351i		−	0.421284i
$309$	19.1520			1.08952
$310$	33.9749	−	13.4979i	1.92965	−	0.766629i
$311$	0.418188			0.0237133			0.0118566	−	0.999930i	$-0.496226\pi$
$311$	0.418188			0.0237133			0.0118566	+	0.999930i	$0.496226\pi$
$312$			7.21136i			0.408263i
$313$		−	6.86188i		−	0.387856i	−0.981016	−	0.193928i	$-0.937877\pi$
$313$		−	6.86188i		−	0.387856i	0.981016	−	0.193928i	$-0.0621228\pi$
$314$	−8.47817			−0.478451
$315$	8.58754	−	3.41174i	0.483853	−	0.192230i
$316$	−25.6500			−1.44293
$317$		−	11.9255i		−	0.669804i	−0.942253	−	0.334902i	$-0.891297\pi$
$317$		−	11.9255i		−	0.669804i	0.942253	−	0.334902i	$-0.108703\pi$
$318$			20.2960i			1.13814i
$319$	−4.98378			−0.279038
$320$	−4.84955	−	12.2066i	−0.271098	−	0.682369i
$321$	41.9671			2.34237
$322$			1.43929i			0.0802085i
$323$		0			0
$324$	16.5810			0.921165
$325$	−21.0177	−	22.2763i	−1.16585	−	1.23567i
$326$	5.99694			0.332140
$327$		−	20.9204i		−	1.15690i
$328$		−	3.63010i		−	0.200439i
$329$	0.462920			0.0255216
$330$	11.1708	+	28.1175i	0.614931	+	1.54782i
$331$	7.96898			0.438015			0.219007	−	0.975723i	$-0.429718\pi$
$331$	7.96898			0.438015			0.219007	+	0.975723i	$0.429718\pi$
$332$			8.63922i			0.474139i
$333$			8.86930i			0.486035i
$334$	−6.30561			−0.345028
$335$	20.8481	−	8.28273i	1.13905	−	0.452534i
$336$	15.6619			0.854427
$337$			4.04620i			0.220410i	0.993909	+	0.110205i	$0.0351508\pi$
$337$			4.04620i			0.220410i	−0.993909	+	0.110205i	$0.964849\pi$
$338$		−	47.4689i		−	2.58197i
$339$	−23.8281			−1.29416
$340$	−22.8820	+	9.09079i	−1.24095	+	0.493017i
$341$	−24.4468			−1.32387
$342$		0			0
$343$		−	17.3355i		−	0.936028i
$344$	−3.36664			−0.181517
$345$	−1.01423	−	2.55288i	−0.0546045	−	0.137443i
$346$	−20.3675			−1.09496
$347$		−	3.26228i		−	0.175129i	−0.996159	−	0.0875643i	$-0.972092\pi$
$347$		−	3.26228i		−	0.175129i	0.996159	−	0.0875643i	$-0.0279083\pi$
$348$			7.26569i			0.389482i
$349$	6.32235			0.338428			0.169214	−	0.985579i	$-0.445877\pi$
$349$	6.32235			0.338428			0.169214	+	0.985579i	$0.445877\pi$
$350$	−10.2866	+	9.70546i	−0.549844	+	0.518779i
$351$	2.53603			0.135363
$352$			22.0624i			1.17593i
$353$			6.35500i			0.338242i	0.985595	+	0.169121i	$0.0540929\pi$
$353$			6.35500i			0.338242i	−0.985595	+	0.169121i	$0.945907\pi$
$354$	10.5203			0.559150
$355$	−5.47839	−	13.7894i	−0.290763	−	0.731866i
$356$	9.35954			0.496055
$357$		−	22.2174i		−	1.17587i
$358$		−	27.8500i		−	1.47192i
$359$	2.70761			0.142902			0.0714512	−	0.997444i	$-0.477237\pi$
$359$	2.70761			0.142902			0.0714512	+	0.997444i	$0.477237\pi$
$360$	−2.86636	+	1.13878i	−0.151070	+	0.0600187i
$361$		0			0
$362$		−	15.7496i		−	0.827782i
$363$			6.32451i			0.331951i
$364$	−15.6439			−0.819965
$365$	26.9410	−	10.7034i	1.41016	−	0.560241i
$366$	−29.4167			−1.53764
$367$			23.2443i			1.21334i	0.794953	+	0.606671i	$0.207495\pi$
$367$			23.2443i			1.21334i	−0.794953	+	0.606671i	$0.792505\pi$
$368$		−	2.25947i		−	0.117783i
$369$	21.0554			1.09610
$370$	−5.01195	−	12.6154i	−0.260559	−	0.655841i
$371$	6.34419			0.329374
$372$			35.6401i			1.84785i
$373$			6.24784i			0.323501i	0.986832	+	0.161750i	$0.0517140\pi$
$373$			6.24784i			0.323501i	−0.986832	+	0.161750i	$0.948286\pi$
$374$	35.3021			1.82543
$375$	11.4063	−	24.4634i	0.589020	−	1.26329i
$376$	−0.154514			−0.00796845
$377$			10.5452i			0.543105i
$378$		−	1.17108i		−	0.0602337i
$379$	13.0469			0.670176			0.335088	−	0.942187i	$-0.391234\pi$
$379$	13.0469			0.670176			0.335088	+	0.942187i	$0.391234\pi$
$380$		0			0
$381$	28.9219			1.48171
$382$		−	11.9926i		−	0.613596i
$383$			1.83744i			0.0938889i	0.998898	+	0.0469445i	$0.0149484\pi$
$383$			1.83744i			0.0938889i	−0.998898	+	0.0469445i	$0.985052\pi$
$384$	−9.34379			−0.476823
$385$	8.78905	−	3.49180i	0.447931	−	0.177959i
$386$	−24.3084			−1.23726
$387$		−	19.5272i		−	0.992624i
$388$			27.8792i			1.41535i
$389$	−18.6941			−0.947828			−0.473914	−	0.880571i	$-0.657159\pi$
$389$	−18.6941			−0.947828			−0.473914	+	0.880571i	$0.657159\pi$
$390$	59.4938	−	23.6363i	3.01258	−	1.19687i
$391$	−3.20520			−0.162094
$392$			2.37267i			0.119838i
$393$			19.4286i			0.980045i
$394$	6.65332			0.335189
$395$	−12.1140	−	30.4916i	−0.609521	−	1.53420i
$396$	−14.3139			−0.719298
$397$			24.9631i			1.25286i	0.779477	+	0.626431i	$0.215485\pi$
$397$			24.9631i			1.25286i	−0.779477	+	0.626431i	$0.784515\pi$
$398$			1.67681i			0.0840508i
$399$		0			0
$400$	16.1485	−	15.2361i	0.807424	−	0.761806i
$401$	25.4399			1.27041			0.635203	−	0.772345i	$-0.280916\pi$
$401$	25.4399			1.27041			0.635203	+	0.772345i	$0.280916\pi$
$402$			46.8911i			2.33871i
$403$			51.7270i			2.57670i
$404$	10.9082			0.542705
$405$	7.83085	+	19.7107i	0.389118	+	0.979431i
$406$	4.86952			0.241670
$407$			9.07743i			0.449951i
$408$			7.41575i			0.367135i
$409$	26.8692			1.32859			0.664297	−	0.747468i	$-0.268731\pi$
$409$	26.8692			1.32859			0.664297	+	0.747468i	$0.268731\pi$
$410$	−29.9484	+	11.8982i	−1.47905	+	0.587610i
$411$	7.57951			0.373870
$412$		−	13.8677i		−	0.683213i
$413$		−	3.28849i		−	0.161816i
$414$	2.78647			0.136948
$415$	−10.2699	+	4.08012i	−0.504129	+	0.200285i
$416$	46.6818			2.28877
$417$			45.2520i			2.21600i
$418$		0			0
$419$	−21.0428			−1.02801			−0.514004	−	0.857788i	$-0.671838\pi$
$419$	−21.0428			−1.02801			−0.514004	+	0.857788i	$0.671838\pi$
$420$	−5.09058	−	12.8133i	−0.248395	−	0.625223i
$421$	2.52939			0.123275			0.0616376	−	0.998099i	$-0.480368\pi$
$421$	2.52939			0.123275			0.0616376	+	0.998099i	$0.480368\pi$
$422$			15.4483i			0.752011i
$423$		−	0.896215i		−	0.0435755i
$424$	−2.11757			−0.102838
$425$	−21.6134	−	22.9077i	−1.04840	−	1.11119i
$426$	31.0148			1.50267
$427$			9.19517i			0.444985i
$428$		−	30.3878i		−	1.46885i
$429$	−42.8089			−2.06684
$430$	11.0346	+	27.7748i	0.532137	+	1.33942i
$431$	−30.2212			−1.45570			−0.727852	−	0.685734i	$-0.759481\pi$
$431$	−30.2212			−1.45570			−0.727852	+	0.685734i	$0.759481\pi$
$432$			1.83841i			0.0884507i
$433$			13.0760i			0.628392i	0.949358	+	0.314196i	$0.101735\pi$
$433$			13.0760i			0.628392i	−0.949358	+	0.314196i	$0.898265\pi$
$434$	23.8863			1.14658
$435$	−8.63711	+	3.43144i	−0.414118	+	0.164525i
$436$	−15.1482			−0.725466
$437$		0			0
$438$			60.5952i			2.89535i
$439$	38.3642			1.83102			0.915512	−	0.402290i	$-0.131786\pi$
$439$	38.3642			1.83102			0.915512	+	0.402290i	$0.131786\pi$
$440$	−2.93362	+	1.16550i	−0.139855	+	0.0555629i
$441$	−13.7620			−0.655334
$442$		−	74.6958i		−	3.55292i
$443$			11.5357i			0.548079i	0.961718	+	0.274039i	$0.0883599\pi$
$443$			11.5357i			0.548079i	−0.961718	+	0.274039i	$0.911640\pi$
$444$	13.2337			0.628043
$445$	4.42032	+	11.1262i	0.209543	+	0.527431i
$446$	−29.6037			−1.40177
$447$		−	21.5153i		−	1.01764i
$448$		−	8.58191i		−	0.405457i
$449$	−20.1918			−0.952909			−0.476455	−	0.879199i	$-0.658078\pi$
$449$	−20.1918			−0.952909			−0.476455	+	0.879199i	$0.658078\pi$
$450$	18.7898	+	19.9150i	0.885760	+	0.938802i
$451$	21.5495			1.01473
$452$			17.2536i			0.811541i
$453$		−	3.41880i		−	0.160629i
$454$	−14.3085			−0.671533
$455$	−7.38830	−	18.5968i	−0.346369	−	0.871830i
$456$		0			0
$457$			17.6887i			0.827442i	0.910404	+	0.413721i	$0.135771\pi$
$457$			17.6887i			0.827442i	−0.910404	+	0.413721i	$0.864229\pi$
$458$			1.94655i			0.0909562i
$459$	2.60791			0.121727
$460$	−1.84851	+	0.734394i	−0.0861872	+	0.0342413i
$461$	24.9640			1.16269			0.581345	−	0.813657i	$-0.302527\pi$
$461$	24.9640			1.16269			0.581345	+	0.813657i	$0.302527\pi$
$462$			19.7681i			0.919697i
$463$			17.4046i			0.808860i	0.914569	+	0.404430i	$0.132530\pi$
$463$			17.4046i			0.808860i	−0.914569	+	0.404430i	$0.867470\pi$
$464$	−7.64441			−0.354883
$465$	−42.3673	+	16.8321i	−1.96474	+	0.780570i
$466$	−32.9411			−1.52597
$467$		−	14.6807i		−	0.679342i	−0.940544	−	0.339671i	$-0.889684\pi$
$467$		−	14.6807i		−	0.679342i	0.940544	−	0.339671i	$-0.110316\pi$
$468$			30.2867i			1.40000i
$469$	14.6574			0.676814
$470$	0.506442	+	1.27474i	0.0233604	+	0.0587995i
$471$	10.5724			0.487151
$472$			1.09763i			0.0505227i
$473$		−	19.9854i		−	0.918931i
$474$	68.5810			3.15003
$475$		0			0
$476$	−16.0873			−0.737362
$477$		−	12.2824i		−	0.562372i
$478$		−	16.2800i		−	0.744631i
$479$	−2.88202			−0.131683			−0.0658415	−	0.997830i	$-0.520973\pi$
$479$	−2.88202			−0.131683			−0.0658415	+	0.997830i	$0.520973\pi$
$480$	15.1904	+	38.2351i	0.693344	+	1.74518i
$481$	19.2069			0.875761
$482$			25.3257i			1.15355i
$483$		−	1.79482i		−	0.0816671i
$484$	4.57950			0.208159
$485$	−33.1415	+	13.1668i	−1.50488	+	0.597873i
$486$	−41.9282			−1.90190
$487$			22.9093i			1.03812i	0.854737	+	0.519061i	$0.173718\pi$
$487$			22.9093i			1.03812i	−0.854737	+	0.519061i	$0.826282\pi$
$488$		−	3.06918i		−	0.138935i
$489$	−7.47828			−0.338180
$490$	19.5746	−	7.77678i	0.884289	−	0.351319i
$491$	−21.2033			−0.956889			−0.478445	−	0.878118i	$-0.658799\pi$
$491$	−21.2033			−0.956889			−0.478445	+	0.878118i	$0.658799\pi$
$492$		−	31.4163i		−	1.41635i
$493$			10.8441i			0.488393i
$494$		0			0
$495$	−6.76014	−	17.0156i	−0.303846	−	0.764796i
$496$	−37.4978			−1.68370
$497$		−	9.69472i		−	0.434868i
$498$		−	23.0988i		−	1.03508i
$499$	36.5201			1.63487			0.817433	−	0.576024i	$-0.195396\pi$
$499$	36.5201			1.63487			0.817433	+	0.576024i	$0.195396\pi$
$500$	−17.7137	−	8.25916i	−0.792179	−	0.369361i
$501$	7.86320			0.351302
$502$			26.4742i			1.18160i
$503$		−	32.6315i		−	1.45497i	−0.686125	−	0.727483i	$-0.740690\pi$
$503$		−	32.6315i		−	1.45497i	0.686125	−	0.727483i	$-0.259310\pi$
$504$	−2.01521			−0.0897646
$505$	5.15173	+	12.9672i	0.229249	+	0.577033i
$506$	2.85186			0.126781
$507$			59.1945i			2.62892i
$508$		−	20.9419i		−	0.929148i
$509$	−43.2651			−1.91769			−0.958846	−	0.283927i	$-0.908363\pi$
$509$	−43.2651			−1.91769			−0.958846	+	0.283927i	$0.908363\pi$
$510$	61.1801	−	24.3062i	2.70910	−	1.07630i
$511$	18.9410			0.837902
$512$			29.5099i			1.30416i
$513$		0			0
$514$	5.70049			0.251438
$515$	16.4853	−	6.54943i	0.726428	−	0.288602i
$516$	−29.1361			−1.28265
$517$		−	0.917245i		−	0.0403404i
$518$		−	8.86930i		−	0.389695i
$519$	25.3986			1.11487
$520$	2.46608	+	6.20725i	0.108145	+	0.272206i
$521$	38.7647			1.69831			0.849156	−	0.528142i	$-0.177111\pi$
$521$	38.7647			1.69831			0.849156	+	0.528142i	$0.177111\pi$
$522$		−	9.42741i		−	0.412627i
$523$		−	27.6586i		−	1.20943i	−0.796443	−	0.604714i	$-0.793288\pi$
$523$		−	27.6586i		−	1.20943i	0.796443	−	0.604714i	$-0.206712\pi$
$524$	14.0680			0.614564
$525$	12.8276	−	12.1029i	0.559843	−	0.528213i
$526$	25.5372			1.11347
$527$			53.1931i			2.31713i
$528$		−	31.0330i		−	1.35054i
$529$	22.7411			0.988742
$530$	6.94065	+	17.4700i	0.301482	+	0.758848i
$531$	−6.36652			−0.276284
$532$		0			0
$533$		−	45.5966i		−	1.97501i
$534$	−25.0248			−1.08293
$535$	36.1236	−	14.3515i	1.56176	−	0.620471i
$536$	−4.89235			−0.211318
$537$			34.7295i			1.49869i
$538$		−	59.9979i		−	2.58669i
$539$	−14.0850			−0.606682
$540$	1.50404	−	0.597539i	0.0647235	−	0.0257140i
$541$	−4.19755			−0.180467			−0.0902335	−	0.995921i	$-0.528761\pi$
$541$	−4.19755			−0.180467			−0.0902335	+	0.995921i	$0.528761\pi$
$542$		−	14.5350i		−	0.624331i
$543$			19.6400i			0.842835i
$544$	48.0050			2.05820
$545$	−7.15417	−	18.0074i	−0.306451	−	0.771353i
$546$	41.8274			1.79005
$547$		−	14.4970i		−	0.619848i	−0.950761	−	0.309924i	$-0.899696\pi$
$547$		−	14.4970i		−	0.619848i	0.950761	−	0.309924i	$-0.100304\pi$
$548$		−	5.48823i		−	0.234445i
$549$	17.8019			0.759766
$550$	19.2307	+	20.3823i	0.820001	+	0.869105i
$551$		0			0
$552$			0.599077i			0.0254984i
$553$		−	21.4373i		−	0.911605i
$554$	18.5661			0.788796
$555$	6.24999	+	15.7316i	0.265297	+	0.667768i
$556$	32.7664			1.38960
$557$			28.9192i			1.22535i	0.790337	+	0.612673i	$0.209906\pi$
$557$			28.9192i			1.22535i	−0.790337	+	0.612673i	$0.790094\pi$
$558$		−	46.2439i		−	1.95766i
$559$	−42.2872			−1.78856
$560$	13.4811	−	5.35592i	0.569682	−	0.226329i
$561$	−44.0223			−1.85862
$562$		−	31.9197i		−	1.34645i
$563$			24.5426i			1.03435i	0.855880	+	0.517174i	$0.173016\pi$
$563$			24.5426i			1.03435i	−0.855880	+	0.517174i	$0.826984\pi$
$564$	−1.33722			−0.0563072
$565$	−20.5103	+	8.14852i	−0.862874	+	0.342811i
$566$	56.8564			2.38985
$567$			13.8577i			0.581969i
$568$			3.23592i			0.135776i
$569$	−0.454757			−0.0190644			−0.00953221	−	0.999955i	$-0.503034\pi$
$569$	−0.454757			−0.0190644			−0.00953221	+	0.999955i	$0.503034\pi$
$570$		0			0
$571$	−24.0492			−1.00643			−0.503213	−	0.864162i	$-0.667849\pi$
$571$	−24.0492			−1.00643			−0.503213	+	0.864162i	$0.667849\pi$
$572$			30.9974i			1.29607i
$573$			14.9550i			0.624754i
$574$	−21.0554			−0.878835
$575$	−1.74603	−	1.85058i	−0.0728143	−	0.0771746i
$576$	−16.6146			−0.692275
$577$		−	31.5181i		−	1.31211i	−0.754711	−	0.656057i	$-0.772223\pi$
$577$		−	31.5181i		−	1.31211i	0.754711	−	0.656057i	$-0.227777\pi$
$578$		−	43.9009i		−	1.82604i
$579$	30.3130			1.25976
$580$	2.48466	+	6.25402i	0.103170	+	0.259684i
$581$	−7.22031			−0.299549
$582$		−	74.5412i		−	3.08983i
$583$		−	12.5706i		−	0.520621i
$584$	−6.32216			−0.261613
$585$	−36.0034	+	14.3038i	−1.48856	+	0.591389i
$586$	−1.92775			−0.0796348
$587$			0.243299i			0.0100420i	0.999987	+	0.00502101i	$0.00159824\pi$
$587$			0.243299i			0.0100420i	−0.999987	+	0.00502101i	$0.998402\pi$
$588$			20.5340i			0.846807i
$589$		0			0
$590$	9.05550	−	3.59766i	0.372809	−	0.148113i
$591$	−8.29680			−0.341285
$592$			13.9235i			0.572251i
$593$		−	38.5061i		−	1.58126i	−0.612296	−	0.790628i	$-0.709754\pi$
$593$		−	38.5061i		−	1.58126i	0.612296	−	0.790628i	$-0.290246\pi$
$594$	−2.32041			−0.0952076
$595$	−7.59772	−	19.1239i	−0.311476	−	0.784002i
$596$	−15.5790			−0.638140
$597$		−	2.09101i		−	0.0855792i
$598$		−	6.03425i		−	0.246759i
$599$	−14.3109			−0.584728			−0.292364	−	0.956307i	$-0.594442\pi$
$599$	−14.3109			−0.584728			−0.292364	+	0.956307i	$0.594442\pi$
$600$	−4.28162	+	4.03971i	−0.174796	+	0.164921i
$601$	36.8537			1.50329			0.751647	−	0.659566i	$-0.229260\pi$
$601$	36.8537			1.50329			0.751647	+	0.659566i	$0.229260\pi$
$602$			19.5272i			0.795870i
$603$		−	28.3767i		−	1.15559i
$604$	−2.47551			−0.100727
$605$	2.16280	+	5.44389i	0.0879304	+	0.221326i
$606$	−29.1656			−1.18477
$607$		−	45.1585i		−	1.83293i	−0.400119	−	0.916463i	$-0.631031\pi$
$607$		−	45.1585i		−	1.83293i	0.400119	−	0.916463i	$-0.368969\pi$
$608$		0			0
$609$	−6.07237			−0.246065
$610$	−25.3207	+	10.0597i	−1.02521	+	0.407304i
$611$	−1.94080			−0.0785164
$612$			31.1452i			1.25897i
$613$			12.8540i			0.519167i	0.965721	+	0.259583i	$0.0835852\pi$
$613$			12.8540i			0.519167i	−0.965721	+	0.259583i	$0.916415\pi$
$614$	−19.0990			−0.770774
$615$	37.3462	−	14.8372i	1.50594	−	0.598295i
$616$	−2.06250			−0.0831004
$617$		−	42.2758i		−	1.70196i	−0.525199	−	0.850979i	$-0.676009\pi$
$617$		−	42.2758i		−	1.70196i	0.525199	−	0.850979i	$-0.323991\pi$
$618$			37.0783i			1.49151i
$619$	−25.2048			−1.01307			−0.506533	−	0.862221i	$-0.669073\pi$
$619$	−25.2048			−1.01307			−0.506533	+	0.862221i	$0.669073\pi$
$620$	12.1879	+	30.6776i	0.489478	+	1.23204i
$621$	0.210678			0.00845423
$622$			0.809614i			0.0324626i
$623$			7.82233i			0.313395i
$624$	−65.6628			−2.62861
$625$	1.45231	−	24.9578i	0.0580926	−	0.998311i
$626$	13.2846			0.530960
$627$		0			0
$628$		−	7.65535i		−	0.305482i
$629$	19.7513			0.787538
$630$	6.60514	+	16.6255i	0.263155	+	0.662376i
$631$	1.49432			0.0594880			0.0297440	−	0.999558i	$-0.490531\pi$
$631$	1.49432			0.0594880			0.0297440	+	0.999558i	$0.490531\pi$
$632$			7.15536i			0.284625i
$633$		−	19.2643i		−	0.765686i
$634$	23.0878			0.916936
$635$	24.8948	−	9.89044i	0.987919	−	0.392490i
$636$	−18.3262			−0.726683
$637$			29.8024i			1.18081i
$638$		−	9.64863i		−	0.381993i
$639$	−18.7690			−0.742491
$640$	−8.04277	+	3.19531i	−0.317918	+	0.126306i
$641$	−6.57587			−0.259731			−0.129866	−	0.991532i	$-0.541455\pi$
$641$	−6.57587			−0.259731			−0.129866	+	0.991532i	$0.541455\pi$
$642$			81.2485i			3.20662i
$643$			4.60673i			0.181672i	0.995866	+	0.0908359i	$0.0289539\pi$
$643$			4.60673i			0.181672i	−0.995866	+	0.0908359i	$0.971046\pi$
$644$	−1.29961			−0.0512116
$645$	−13.7604	−	34.6356i	−0.541814	−	1.36378i
$646$		0			0
$647$		−	3.53706i		−	0.139056i	−0.997580	−	0.0695281i	$-0.977851\pi$
$647$		−	3.53706i		−	0.139056i	0.997580	−	0.0695281i	$-0.0221494\pi$
$648$		−	4.62544i		−	0.181705i
$649$	−6.51592			−0.255772
$650$	43.1270	−	40.6903i	1.69158	−	1.59601i
$651$	−29.7866			−1.16743
$652$			5.41493i			0.212065i
$653$			48.6489i			1.90378i	0.306444	+	0.951889i	$0.400861\pi$
$653$			48.6489i			1.90378i	−0.306444	+	0.951889i	$0.599139\pi$
$654$	40.5019			1.58375
$655$	6.64403	+	16.7234i	0.259604	+	0.653437i
$656$	33.0538			1.29053
$657$		−	36.6699i		−	1.43063i
$658$			0.896215i			0.0349381i
$659$	21.2450			0.827588			0.413794	−	0.910371i	$-0.364203\pi$
$659$	21.2450			0.827588			0.413794	+	0.910371i	$0.364203\pi$
$660$	−25.3886	+	10.0866i	−0.988251	+	0.392622i
$661$	14.7872			0.575154			0.287577	−	0.957757i	$-0.407150\pi$
$661$	14.7872			0.575154			0.287577	+	0.957757i	$0.407150\pi$
$662$			15.4280i			0.599625i
$663$			93.1469i			3.61753i
$664$	2.41000			0.0935262
$665$		0			0
$666$	−17.1710			−0.665363
$667$			0.876033i			0.0339201i
$668$		−	5.69364i		−	0.220294i
$669$	36.9163			1.42727
$670$	16.0354	+	40.3620i	0.619501	+	1.55932i
$671$	18.2196			0.703361
$672$			26.8814i			1.03697i
$673$			6.36313i			0.245280i	0.992451	+	0.122640i	$0.0391361\pi$
$673$			6.36313i			0.245280i	−0.992451	+	0.122640i	$0.960864\pi$
$674$	−7.83345			−0.301733
$675$	1.42065	+	1.50572i	0.0546809	+	0.0579553i
$676$	42.8620			1.64854
$677$		−	45.6873i		−	1.75591i	−0.478746	−	0.877953i	$-0.658909\pi$
$677$		−	45.6873i		−	1.75591i	0.478746	−	0.877953i	$-0.341091\pi$
$678$		−	46.1313i		−	1.77166i
$679$	−23.3003			−0.894184
$680$	2.53598	+	6.38319i	0.0972502	+	0.244784i
$681$	17.8430			0.683744
$682$		−	47.3291i		−	1.81232i
$683$		−	15.8141i		−	0.605109i	−0.953132	−	0.302554i	$-0.902161\pi$
$683$		−	15.8141i		−	0.605109i	0.953132	−	0.302554i	$-0.0978394\pi$
$684$		0			0
$685$	6.52415	−	2.59198i	0.249275	−	0.0990343i
$686$	33.5616			1.28139
$687$		−	2.42738i		−	0.0926102i
$688$		−	30.6548i		−	1.16870i
$689$	−26.5981			−1.01331
$690$	4.94239	−	1.96356i	0.188154	−	0.0747515i
$691$	−35.2478			−1.34089			−0.670444	−	0.741960i	$-0.733896\pi$
$691$	−35.2478			−1.34089			−0.670444	+	0.741960i	$0.733896\pi$
$692$		−	18.3908i		−	0.699113i
$693$		−	11.9629i		−	0.454435i
$694$	6.31580			0.239744
$695$	15.4749	+	38.9511i	0.586996	+	1.47750i
$696$	2.02684			0.0768273
$697$		−	46.8890i		−	1.77605i
$698$			12.2401i			0.463295i
$699$	41.0781			1.55372
$700$	−8.76353	−	9.28832i	−0.331230	−	0.351065i
$701$	−51.0439			−1.92790			−0.963951	−	0.266079i	$-0.914272\pi$
$701$	−51.0439			−1.92790			−0.963951	+	0.266079i	$0.914272\pi$
$702$			4.90976i			0.185307i
$703$		0			0
$704$	−17.0045			−0.640880
$705$	−0.631542	−	1.58963i	−0.0237852	−	0.0598688i
$706$	−12.3033			−0.463041
$707$			9.11667i			0.342867i
$708$			9.49934i			0.357007i
$709$	−1.76418			−0.0662552			−0.0331276	−	0.999451i	$-0.510547\pi$
$709$	−1.76418			−0.0662552			−0.0331276	+	0.999451i	$0.510547\pi$
$710$	26.6963	−	10.6062i	1.00190	−	0.398043i
$711$	−41.5026			−1.55647
$712$		−	2.61095i		−	0.0978493i
$713$			4.29717i			0.160930i
$714$	43.0130			1.60972
$715$	−36.8482	+	14.6394i	−1.37805	+	0.547484i
$716$	25.1472			0.939793
$717$			20.3015i			0.758172i
$718$			5.24195i			0.195628i
$719$	51.5725			1.92333			0.961665	−	0.274227i	$-0.0884220\pi$
$719$	51.5725			1.92333			0.961665	+	0.274227i	$0.0884220\pi$
$720$	−10.3691	−	26.0995i	−0.386433	−	0.972673i
$721$	11.5901			0.431637
$722$		0			0
$723$		−	31.5815i		−	1.17453i
$724$	14.2211			0.528523
$725$	−6.26103	+	5.90729i	−0.232529	+	0.219391i
$726$	−12.2443			−0.454428
$727$		−	39.7695i		−	1.47497i	−0.675364	−	0.737484i	$-0.736014\pi$
$727$		−	39.7695i		−	1.47497i	0.675364	−	0.737484i	$-0.263986\pi$
$728$			4.36404i			0.161742i
$729$	23.8299			0.882589
$730$	20.7218	+	52.1579i	0.766948	+	1.93045i
$731$	−43.4858			−1.60838
$732$		−	26.5618i		−	0.981751i
$733$		−	32.2476i		−	1.19109i	−0.803321	−	0.595547i	$-0.796935\pi$
$733$		−	32.2476i		−	1.19109i	0.803321	−	0.595547i	$-0.203065\pi$
$734$	−45.0010			−1.66102
$735$	−24.4098	+	9.69777i	−0.900370	+	0.357708i
$736$	3.87805			0.142947
$737$		−	29.0426i		−	1.06980i
$738$			40.7633i			1.50052i
$739$	33.2127			1.22175			0.610875	−	0.791727i	$-0.290818\pi$
$739$	33.2127			1.22175			0.610875	+	0.791727i	$0.290818\pi$
$740$	11.3910	−	4.52554i	0.418742	−	0.166362i
$741$		0			0
$742$			12.2824i			0.450900i
$743$		−	21.0511i		−	0.772290i	−0.922438	−	0.386145i	$-0.873806\pi$
$743$		−	21.0511i		−	0.772290i	0.922438	−	0.386145i	$-0.126194\pi$
$744$	9.94220			0.364499
$745$	−7.35763	−	18.5196i	−0.269563	−	0.678504i
$746$	−12.0958			−0.442860
$747$			13.9785i			0.511448i
$748$			31.8760i			1.16550i
$749$	25.3969			0.927983
$750$	47.3613	+	22.0827i	1.72939	+	0.806345i
$751$	−9.54033			−0.348132			−0.174066	−	0.984734i	$-0.555691\pi$
$751$	−9.54033			−0.348132			−0.174066	+	0.984734i	$0.555691\pi$
$752$		−	1.40692i		−	0.0513052i
$753$		−	33.0138i		−	1.20309i
$754$	−20.4155			−0.743490
$755$	−1.16913	−	2.94277i	−0.0425490	−	0.107098i
$756$	1.05742			0.0384581
$757$		−	36.0653i		−	1.31082i	−0.755275	−	0.655408i	$-0.772497\pi$
$757$		−	36.0653i		−	1.31082i	0.755275	−	0.655408i	$-0.227503\pi$
$758$			25.2589i			0.917445i
$759$	−3.55632			−0.129086
$760$		0			0
$761$	−13.0993			−0.474848			−0.237424	−	0.971406i	$-0.576303\pi$
$761$	−13.0993			−0.474848			−0.237424	+	0.971406i	$0.576303\pi$
$762$			55.9928i			2.02841i
$763$		−	12.6602i		−	0.458331i
$764$	10.8287			0.391769
$765$	−37.0239	+	14.7092i	−1.33860	+	0.531813i
$766$	−3.55730			−0.128530
$767$			13.7870i			0.497821i
$768$		−	46.4519i		−	1.67619i
$769$	43.3213			1.56221			0.781103	−	0.624402i	$-0.214657\pi$
$769$	43.3213			1.56221			0.781103	+	0.624402i	$0.214657\pi$
$770$	6.76014	+	17.0156i	0.243618	+	0.613201i
$771$	−7.10861			−0.256010
$772$		−	21.9492i		−	0.789970i
$773$		−	2.58122i		−	0.0928401i	−0.998922	−	0.0464200i	$-0.985219\pi$
$773$		−	2.58122i		−	0.0928401i	0.998922	−	0.0464200i	$-0.0147813\pi$
$774$	37.8048			1.35886
$775$	−30.7120	+	28.9768i	−1.10321	+	1.04088i
$776$	7.77721			0.279186
$777$			11.0602i			0.396781i
$778$		−	36.1918i		−	1.29754i
$779$		0			0
$780$	21.3423	+	53.7198i	0.764178	+	1.92348i
$781$	−19.2094			−0.687368
$782$		−	6.20529i		−	0.221901i
$783$		−	0.712783i		−	0.0254728i
$784$	−21.6043			−0.771582
$785$	9.10032	−	3.61546i	0.324804	−	0.129041i
$786$	−37.6139			−1.34164
$787$			32.3874i			1.15449i	0.816572	+	0.577243i	$0.195872\pi$
$787$			32.3874i			1.15449i	−0.816572	+	0.577243i	$0.804128\pi$
$788$			6.00761i			0.214012i
$789$	−31.8453			−1.13372
$790$	59.0318	−	23.4527i	2.10026	−	0.834410i
$791$	−14.4199			−0.512711
$792$			3.99301i			0.141885i
$793$		−	38.5509i		−	1.36898i
$794$	−48.3286			−1.71512
$795$	−8.65510	−	21.7854i	−0.306965	−	0.772647i
$796$	−1.51407			−0.0536648
$797$			0.660265i			0.0233878i	0.999932	+	0.0116939i	$0.00372236\pi$
$797$			0.660265i			0.0233878i	−0.999932	+	0.0116939i	$0.996278\pi$
$798$		0			0
$799$	−1.99581			−0.0706067
$800$	26.1506	+	27.7166i	0.924563	+	0.979928i
$801$	15.1441			0.535089
$802$			49.2517i			1.73914i
$803$		−	37.5304i		−	1.32442i
$804$	−42.3402			−1.49322
$805$	−0.613777	−	1.54491i	−0.0216328	−	0.0544509i
$806$	−100.144			−3.52741
$807$			74.8184i			2.63373i
$808$		−	3.04297i		−	0.107051i
$809$	39.0366			1.37246			0.686228	−	0.727387i	$-0.259265\pi$
$809$	39.0366			1.37246			0.686228	+	0.727387i	$0.259265\pi$
$810$	−38.1600	+	15.1606i	−1.34080	+	0.532688i
$811$	−29.9982			−1.05338			−0.526690	−	0.850057i	$-0.676567\pi$
$811$	−29.9982			−1.05338			−0.526690	+	0.850057i	$0.676567\pi$
$812$			4.39693i			0.154302i
$813$			18.1254i			0.635684i
$814$	−17.5739			−0.615966
$815$	−6.43701	+	2.55736i	−0.225479	+	0.0895803i
$816$	−67.5239			−2.36381
$817$		0			0
$818$			52.0188i			1.81880i
$819$	−25.3124			−0.884487
$820$	−10.7435	−	27.0419i	−0.375178	−	0.944343i
$821$	−36.5733			−1.27642			−0.638208	−	0.769864i	$-0.720324\pi$
$821$	−36.5733			−1.27642			−0.638208	+	0.769864i	$0.720324\pi$
$822$			14.6740i			0.511814i
$823$			1.19784i			0.0417542i	0.999782	+	0.0208771i	$0.00664588\pi$
$823$			1.19784i			0.0417542i	−0.999782	+	0.0208771i	$0.993354\pi$
$824$	−3.86855			−0.134767
$825$	−23.9810	−	25.4171i	−0.834913	−	0.884909i
$826$	6.36652			0.221520
$827$		−	0.0989534i		−	0.00344095i	−0.999999	−	0.00172047i	$-0.999452\pi$
$827$		−	0.0989534i		−	0.00344095i	0.999999	−	0.00172047i	$-0.000547644\pi$
$828$			2.51604i			0.0874385i
$829$	−3.38031			−0.117403			−0.0587015	−	0.998276i	$-0.518696\pi$
$829$	−3.38031			−0.117403			−0.0587015	+	0.998276i	$0.518696\pi$
$830$	−7.89913	−	19.8826i	−0.274183	−	0.690133i
$831$	−23.1522			−0.803140
$832$			35.9798i			1.24738i
$833$			30.6471i			1.06186i
$834$	−87.6080			−3.03362
$835$	6.76833	−	2.68899i	0.234228	−	0.0930563i
$836$		0			0
$837$		−	3.49639i		−	0.120853i
$838$		−	40.7389i		−	1.40730i
$839$	11.7241			0.404759			0.202380	−	0.979307i	$-0.435133\pi$
$839$	11.7241			0.404759			0.202380	+	0.979307i	$0.435133\pi$
$840$	−3.57440	+	1.42007i	−0.123328	+	0.0489971i
$841$	−26.0361			−0.897798
$842$			4.89692i			0.168759i
$843$			39.8043i			1.37093i
$844$	−13.9490			−0.480145
$845$	20.2428	+	50.9523i	0.696374	+	1.75281i
$846$	1.73508			0.0596532
$847$			3.82736i			0.131510i
$848$		−	19.2815i		−	0.662129i
$849$	−70.9009			−2.43331
$850$	44.3493	−	41.8436i	1.52117	−	1.43523i
$851$	1.59560			0.0546964
$852$			28.0048i			0.959429i
$853$		−	11.8398i		−	0.405389i	−0.979242	−	0.202694i	$-0.935030\pi$
$853$		−	11.8398i		−	0.405389i	0.979242	−	0.202694i	$-0.0649698\pi$
$854$	−17.8019			−0.609168
$855$		0			0
$856$	−8.47701			−0.289738
$857$			52.7265i			1.80110i	0.434749	+	0.900552i	$0.356837\pi$
$857$			52.7265i			1.80110i	−0.434749	+	0.900552i	$0.643163\pi$
$858$		−	82.8783i		−	2.82942i
$859$	5.72563			0.195356			0.0976779	−	0.995218i	$-0.468858\pi$
$859$	5.72563			0.195356			0.0976779	+	0.995218i	$0.468858\pi$
$860$	−25.0792	+	9.96371i	−0.855194	+	0.339760i
$861$	26.2564			0.894817
$862$		−	58.5084i		−	1.99280i
$863$		−	10.4374i		−	0.355293i	−0.984094	−	0.177646i	$-0.943152\pi$
$863$		−	10.4374i		−	0.355293i	0.984094	−	0.177646i	$-0.0568483\pi$
$864$	−3.15537			−0.107348
$865$	21.8621	−	8.68558i	0.743333	−	0.295319i
$866$	−25.3152			−0.860244
$867$			54.7451i			1.85924i
$868$			21.5681i			0.732068i
$869$	−42.4765			−1.44092
$870$	−6.64327	−	16.7215i	−0.225228	−	0.566911i
$871$	−61.4513			−2.08220
$872$			4.22575i			0.143102i
$873$			45.1095i			1.52673i
$874$		0			0
$875$	6.90268	−	14.8044i	0.233353	−	0.500478i
$876$	−54.7143			−1.84863
$877$		−	16.9211i		−	0.571386i	−0.958321	−	0.285693i	$-0.907776\pi$
$877$		−	16.9211i		−	0.571386i	0.958321	−	0.285693i	$-0.0922238\pi$
$878$			74.2733i			2.50660i
$879$	2.40394			0.0810829
$880$	−10.6124	−	26.7120i	−0.357744	−	0.900461i
$881$	−28.2082			−0.950360			−0.475180	−	0.879889i	$-0.657617\pi$
$881$	−28.2082			−0.950360			−0.475180	+	0.879889i	$0.657617\pi$
$882$		−	26.6433i		−	0.897128i
$883$			2.89071i			0.0972800i	0.998816	+	0.0486400i	$0.0154887\pi$
$883$			2.89071i			0.0972800i	−0.998816	+	0.0486400i	$0.984511\pi$
$884$	67.4465			2.26847
$885$	−11.2924	+	4.48634i	−0.379589	+	0.150807i
$886$	−22.3332			−0.750299
$887$			32.9315i			1.10573i	0.833270	+	0.552866i	$0.186466\pi$
$887$			32.9315i			1.10573i	−0.833270	+	0.552866i	$0.813534\pi$
$888$		−	3.69168i		−	0.123885i
$889$	17.5024			0.587013
$890$	−21.5403	+	8.55775i	−0.722034	+	0.286857i
$891$	27.4581			0.919882
$892$		−	26.7306i		−	0.895007i
$893$		0			0
$894$	41.6538			1.39311
$895$	11.8765	+	29.8937i	0.396987	+	0.999238i
$896$	−5.65451			−0.188904
$897$			7.52481i			0.251246i
$898$		−	39.0914i		−	1.30450i
$899$	14.5385			0.484887
$900$	−17.9822	+	16.9662i	−0.599407	+	0.565541i
$901$	−27.3520			−0.911228
$902$			41.7199i			1.38912i
$903$		−	24.3508i		−	0.810343i
$904$	4.81308			0.160081
$905$	6.71633	+	16.9054i	0.223258	+	0.561954i
$906$	6.61881			0.219895
$907$		−	22.8800i		−	0.759717i	−0.925045	−	0.379859i	$-0.875973\pi$
$907$		−	22.8800i		−	0.759717i	0.925045	−	0.379859i	$-0.124027\pi$
$908$		−	12.9199i		−	0.428761i
$909$	17.6499			0.585410
$910$	36.0034	−	14.3038i	1.19350	−	0.474166i
$911$	11.6167			0.384880			0.192440	−	0.981309i	$-0.438360\pi$
$911$	11.6167			0.384880			0.192440	+	0.981309i	$0.438360\pi$
$912$		0			0
$913$			14.3066i			0.473478i
$914$	−34.2454			−1.13274
$915$	31.5754	−	12.5446i	1.04385	−	0.414711i
$916$	−1.75763			−0.0580738
$917$			11.7575i			0.388266i
$918$			5.04892i			0.166639i
$919$	12.4353			0.410203			0.205101	−	0.978741i	$-0.434248\pi$
$919$	12.4353			0.410203			0.205101	+	0.978741i	$0.434248\pi$
$920$	0.204867	+	0.515662i	0.00675427	+	0.0170009i
$921$	23.8168			0.784790
$922$			48.3305i			1.59168i
$923$			40.6453i			1.33786i
$924$	−17.8496			−0.587209
$925$	10.7595	+	11.4038i	0.353770	+	0.374954i
$926$	−33.6954			−1.10730
$927$		−	22.4384i		−	0.736974i
$928$		−	13.1205i		−	0.430703i
$929$	15.7247			0.515910			0.257955	−	0.966157i	$-0.416951\pi$
$929$	15.7247			0.515910			0.257955	+	0.966157i	$0.416951\pi$
$930$	−32.5870	−	82.0233i	−1.06857	−	2.68965i
$931$		0			0
$932$		−	29.7441i		−	0.974301i
$933$		−	1.00960i		−	0.0330529i
$934$	28.4219			0.929993
$935$	−37.8927	+	15.0544i	−1.23922	+	0.492331i
$936$	8.44881			0.276158
$937$			16.4857i			0.538563i	0.963061	+	0.269282i	$0.0867862\pi$
$937$			16.4857i			0.538563i	−0.963061	+	0.269282i	$0.913214\pi$
$938$			28.3767i			0.926533i
$939$	−16.5661			−0.540616
$940$	−1.15103	+	0.457291i	−0.0375424	+	0.0149152i
$941$	−13.7308			−0.447611			−0.223806	−	0.974634i	$-0.571848\pi$
$941$	−13.7308			−0.447611			−0.223806	+	0.974634i	$0.571848\pi$
$942$			20.4683i			0.666892i
$943$		−	3.78789i		−	0.123351i
$944$	−9.99448			−0.325293
$945$	0.499399	+	1.25701i	0.0162454	+	0.0408907i
$946$	38.6919			1.25798
$947$			45.7355i			1.48620i	0.669179	+	0.743101i	$0.266646\pi$
$947$			45.7355i			1.48620i	−0.669179	+	0.743101i	$0.733354\pi$
$948$			61.9251i			2.01123i
$949$	−79.4106			−2.57778
$950$		0			0
$951$	−28.7909			−0.933610
$952$			4.48774i			0.145448i
$953$		−	32.7211i		−	1.05994i	−0.848016	−	0.529971i	$-0.822203\pi$
$953$		−	32.7211i		−	1.05994i	0.848016	−	0.529971i	$-0.177797\pi$
$954$	23.7787			0.769865
$955$	5.11418	+	12.8727i	0.165491	+	0.416550i
$956$	14.7000			0.475433
$957$			12.0320i			0.388939i
$958$		−	5.57961i		−	0.180269i
$959$	4.58684			0.148117
$960$	−29.4695	+	11.7079i	−0.951124	+	0.377872i
$961$	40.3153			1.30049
$962$			37.1847i			1.19888i
$963$		−	49.1685i		−	1.58443i
$964$	−22.8678			−0.736522
$965$	26.0922	−	10.3662i	0.839938	−	0.333699i
$966$	3.47478			0.111799
$967$			11.4909i			0.369523i	0.982783	+	0.184761i	$0.0591512\pi$
$967$			11.4909i			0.369523i	−0.982783	+	0.184761i	$0.940849\pi$
$968$		−	1.27750i		−	0.0410604i
$969$		0			0
$970$	−25.4909	−	64.1621i	−0.818465	−	2.06012i
$971$	−54.4334			−1.74685			−0.873425	−	0.486959i	$-0.838106\pi$
$971$	−54.4334			−1.74685			−0.873425	+	0.486959i	$0.838106\pi$
$972$		−	37.8590i		−	1.21433i
$973$			27.3848i			0.877917i
$974$	−44.3526			−1.42115
$975$	−53.7800	+	50.7415i	−1.72234	+	1.62503i
$976$	27.9463			0.894539
$977$			23.6834i			0.757698i	0.925459	+	0.378849i	$0.123680\pi$
$977$			23.6834i			0.757698i	−0.925459	+	0.378849i	$0.876320\pi$
$978$		−	14.4780i		−	0.462955i
$979$	15.4994			0.495364
$980$	7.02203	+	17.6748i	0.224311	+	0.564602i
$981$	−24.5103			−0.782552
$982$		−	41.0496i		−	1.30994i
$983$		−	4.93140i		−	0.157287i	−0.996903	−	0.0786436i	$-0.974941\pi$
$983$		−	4.93140i		−	0.157287i	0.996903	−	0.0786436i	$-0.0250589\pi$
$984$	−8.76391			−0.279383
$985$	−7.14156	+	2.83727i	−0.227549	+	0.0904029i
$986$	−20.9942			−0.668592
$987$		−	1.11760i		−	0.0355735i
$988$		0			0
$989$	−3.51297			−0.111706
$990$	32.9423	−	13.0877i	1.04698	−	0.415953i
$991$	−12.3542			−0.392445			−0.196223	−	0.980559i	$-0.562867\pi$
$991$	−12.3542			−0.392445			−0.196223	+	0.980559i	$0.562867\pi$
$992$		−	64.3596i		−	2.04342i
$993$		−	19.2389i		−	0.610530i
$994$	18.7690			0.595317
$995$	−0.715064	−	1.79986i	−0.0226691	−	0.0570593i
$996$	20.8571			0.660881
$997$		−	33.3639i		−	1.05664i	−0.849044	−	0.528322i	$-0.822821\pi$
$997$		−	33.3639i		−	1.05664i	0.849044	−	0.528322i	$-0.177179\pi$
$998$			70.7032i			2.23807i
$999$	−1.29826			−0.0410750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.j.1084.14	yes	16
5.2	odd	4		9025.2.a.ck.1.3		16
5.3	odd	4		9025.2.a.ck.1.14		16
5.4	even	2	inner	1805.2.b.j.1084.3	yes	16
19.18	odd	2		1805.2.b.i.1084.3	✓	16
95.18	even	4		9025.2.a.cl.1.3		16
95.37	even	4		9025.2.a.cl.1.14		16
95.94	odd	2		1805.2.b.i.1084.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.i.1084.3	✓	16	19.18	odd	2
1805.2.b.i.1084.14	yes	16	95.94	odd	2
1805.2.b.j.1084.3	yes	16	5.4	even	2	inner
1805.2.b.j.1084.14	yes	16	1.1	even	1	trivial
9025.2.a.ck.1.3		16	5.2	odd	4
9025.2.a.ck.1.14		16	5.3	odd	4
9025.2.a.cl.1.3		16	95.18	even	4
9025.2.a.cl.1.14		16	95.37	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.93600i q^{2} -2.41423i q^{3} -1.74811 q^{4} +(-0.825597 - 2.07807i) q^{5} +4.67396 q^{6} -1.46100i q^{7} +0.487655i q^{8} -2.82851 q^{9} +O(q^{10})\)	\(q+1.93600i q^{2} -2.41423i q^{3} -1.74811 q^{4} +(-0.825597 - 2.07807i) q^{5} +4.67396 q^{6} -1.46100i q^{7} +0.487655i q^{8} -2.82851 q^{9} +(4.02316 - 1.59836i) q^{10} -2.89488 q^{11} +4.22035i q^{12} +6.12528i q^{13} +2.82851 q^{14} +(-5.01695 + 1.99318i) q^{15} -4.44033 q^{16} +6.29889i q^{17} -5.47600i q^{18} +(1.44324 + 3.63271i) q^{20} -3.52719 q^{21} -5.60450i q^{22} +0.508852i q^{23} +1.17731 q^{24} +(-3.63678 + 3.43130i) q^{25} -11.8586 q^{26} -0.414027i q^{27} +2.55400i q^{28} +1.72159 q^{29} +(-3.85881 - 9.71283i) q^{30} +8.44484 q^{31} -7.62118i q^{32} +6.98890i q^{33} -12.1947 q^{34} +(-3.03607 + 1.20620i) q^{35} +4.94455 q^{36} -3.13569i q^{37} +14.7878 q^{39} +(1.01338 - 0.402607i) q^{40} -7.44400 q^{41} -6.82866i q^{42} +6.90372i q^{43} +5.06057 q^{44} +(2.33521 + 5.87784i) q^{45} -0.985139 q^{46} +0.316851i q^{47} +10.7200i q^{48} +4.86547 q^{49} +(-6.64302 - 7.04082i) q^{50} +15.2070 q^{51} -10.7077i q^{52} +4.34236i q^{53} +0.801557 q^{54} +(2.39000 + 6.01577i) q^{55} +0.712465 q^{56} +3.33300i q^{58} +2.25084 q^{59} +(8.77019 - 3.48431i) q^{60} -6.29374 q^{61} +16.3492i q^{62} +4.13245i q^{63} +5.87399 q^{64} +(12.7288 - 5.05701i) q^{65} -13.5305 q^{66} +10.0324i q^{67} -11.0112i q^{68} +1.22849 q^{69} +(-2.33521 - 5.87784i) q^{70} +6.63567 q^{71} -1.37933i q^{72} +12.9644i q^{73} +6.07070 q^{74} +(8.28396 + 8.78002i) q^{75} +4.22942i q^{77} +28.6293i q^{78} +14.6730 q^{79} +(3.66592 + 9.22733i) q^{80} -9.48507 q^{81} -14.4116i q^{82} -4.94202i q^{83} +6.16593 q^{84} +(13.0896 - 5.20035i) q^{85} -13.3656 q^{86} -4.15631i q^{87} -1.41170i q^{88} -5.35408 q^{89} +(-11.3795 + 4.52097i) q^{90} +8.94904 q^{91} -0.889530i q^{92} -20.3878i q^{93} -0.613425 q^{94} -18.3993 q^{96} -15.9482i q^{97} +9.41958i q^{98} +8.18818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9	\( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} + 16 q^{10} - 22 q^{11} + 6 q^{14} - 10 q^{15} + 8 q^{16} - 14 q^{20} + 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} + 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} - 38 q^{40} - 26 q^{41} + 64 q^{44} - 2 q^{45} - 2 q^{46} + 20 q^{49} + 48 q^{50} + 38 q^{51} + 12 q^{54} - 10 q^{55} - 6 q^{56} + 10 q^{59} + 10 q^{60} - 30 q^{61} + 16 q^{64} + 36 q^{65} + 4 q^{66} + 68 q^{69} + 2 q^{70} + 20 q^{71} + 40 q^{74} + 32 q^{75} + 12 q^{79} + 40 q^{80} - 48 q^{81} - 2 q^{84} - 2 q^{85} + 20 q^{86} - 30 q^{90} + 86 q^{91} - 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) \) 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9 + 16 * q^10 - 22 * q^11 + 6 * q^14 - 10 * q^15 + 8 * q^16 - 14 * q^20 + 20 * q^21 + 14 * q^24 + 4 * q^25 - 16 * q^26 + 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 10 * q^35 + 18 * q^36 + 36 * q^39 - 38 * q^40 - 26 * q^41 + 64 * q^44 - 2 * q^45 - 2 * q^46 + 20 * q^49 + 48 * q^50 + 38 * q^51 + 12 * q^54 - 10 * q^55 - 6 * q^56 + 10 * q^59 + 10 * q^60 - 30 * q^61 + 16 * q^64 + 36 * q^65 + 4 * q^66 + 68 * q^69 + 2 * q^70 + 20 * q^71 + 40 * q^74 + 32 * q^75 + 12 * q^79 + 40 * q^80 - 48 * q^81 - 2 * q^84 - 2 * q^85 + 20 * q^86 - 30 * q^90 + 86 * q^91 - 38 * q^94 + 22 * q^96 + 32 * q^99

Introduction

L-functions

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Database

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