LMFDB - Embedded newform 1805.2.b.i.1084.8

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			1084.8
Root			$-0.317290i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.i.1084.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.317290i q^{2} -2.04300i q^{3} +1.89933 q^{4} +(-1.85074 - 1.25489i) q^{5} -0.648223 q^{6} -3.69961i q^{7} -1.23722i q^{8} -1.17385 q^{9} +O(q^{10})$	\(q-0.317290i q^{2} -2.04300i q^{3} +1.89933 q^{4} +(-1.85074 - 1.25489i) q^{5} -0.648223 q^{6} -3.69961i q^{7} -1.23722i q^{8} -1.17385 q^{9} +(-0.398165 + 0.587221i) q^{10} -5.01076 q^{11} -3.88033i q^{12} -4.59159i q^{13} -1.17385 q^{14} +(-2.56375 + 3.78106i) q^{15} +3.40610 q^{16} +3.21112i q^{17} +0.372450i q^{18} +(-3.51516 - 2.38345i) q^{20} -7.55831 q^{21} +1.58986i q^{22} +0.220987i q^{23} -2.52763 q^{24} +(1.85048 + 4.64497i) q^{25} -1.45686 q^{26} -3.73083i q^{27} -7.02678i q^{28} -3.42114 q^{29} +(1.19969 + 0.813451i) q^{30} +7.89725 q^{31} -3.55515i q^{32} +10.2370i q^{33} +1.01885 q^{34} +(-4.64262 + 6.84702i) q^{35} -2.22952 q^{36} -2.98622i q^{37} -9.38061 q^{39} +(-1.55258 + 2.28977i) q^{40} -0.183247 q^{41} +2.39817i q^{42} +7.30424i q^{43} -9.51707 q^{44} +(2.17249 + 1.47306i) q^{45} +0.0701168 q^{46} +10.8876i q^{47} -6.95866i q^{48} -6.68714 q^{49} +(1.47380 - 0.587138i) q^{50} +6.56032 q^{51} -8.72092i q^{52} -1.93670i q^{53} -1.18375 q^{54} +(9.27362 + 6.28797i) q^{55} -4.57722 q^{56} +1.08549i q^{58} +6.15338 q^{59} +(-4.86940 + 7.18148i) q^{60} +5.02293 q^{61} -2.50572i q^{62} +4.34279i q^{63} +5.68419 q^{64} +(-5.76195 + 8.49783i) q^{65} +3.24809 q^{66} -11.2753i q^{67} +6.09897i q^{68} +0.451476 q^{69} +(2.17249 + 1.47306i) q^{70} +0.851223 q^{71} +1.45230i q^{72} -5.15625i q^{73} -0.947498 q^{74} +(9.48967 - 3.78053i) q^{75} +18.5379i q^{77} +2.97637i q^{78} -9.19657 q^{79} +(-6.30381 - 4.27429i) q^{80} -11.1436 q^{81} +0.0581424i q^{82} -4.53528i q^{83} -14.3557 q^{84} +(4.02961 - 5.94295i) q^{85} +2.31756 q^{86} +6.98938i q^{87} +6.19939i q^{88} +14.8752 q^{89} +(0.467385 - 0.689308i) q^{90} -16.9871 q^{91} +0.419726i q^{92} -16.1341i q^{93} +3.45452 q^{94} -7.26317 q^{96} -1.36602i q^{97} +2.12176i q^{98} +5.88187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.317290i		−	0.224358i	−0.993688	−	0.112179i	$-0.964217\pi$
$2$		−	0.317290i		−	0.224358i	0.993688	−	0.112179i	$-0.0357829\pi$
$3$		−	2.04300i		−	1.17953i	−0.807576	−	0.589763i	$-0.799221\pi$
$3$		−	2.04300i		−	1.17953i	0.807576	−	0.589763i	$-0.200779\pi$
$4$	1.89933			0.949664
$5$	−1.85074	−	1.25489i	−0.827676	−	0.561206i
$5$	−1.85074	−	1.25489i	−0.827676	−	0.561206i
$6$	−0.648223			−0.264636
$7$		−	3.69961i		−	1.39832i	−0.714964	−	0.699161i	$-0.753557\pi$
$7$		−	3.69961i		−	1.39832i	0.714964	−	0.699161i	$-0.246443\pi$
$8$		−	1.23722i		−	0.437422i
$9$	−1.17385			−0.391283
$10$	−0.398165	+	0.587221i	−0.125911	+	0.185695i
$11$	−5.01076			−1.51080			−0.755400	−	0.655263i	$-0.772558\pi$
$11$	−5.01076			−1.51080			−0.755400	+	0.655263i	$0.772558\pi$
$12$		−	3.88033i		−	1.12015i
$13$		−	4.59159i		−	1.27348i	−0.771080	−	0.636738i	$-0.780283\pi$
$13$		−	4.59159i		−	1.27348i	0.771080	−	0.636738i	$-0.219717\pi$
$14$	−1.17385			−0.313724
$15$	−2.56375	+	3.78106i	−0.661957	+	0.976266i
$16$	3.40610			0.851525
$17$			3.21112i			0.778811i	0.921066	+	0.389405i	$0.127319\pi$
$17$			3.21112i			0.778811i	−0.921066	+	0.389405i	$0.872681\pi$
$18$			0.372450i			0.0877873i
$19$		0			0
$19$		0			0
$20$	−3.51516	−	2.38345i	−0.786014	−	0.532957i
$21$	−7.55831			−1.64936
$22$			1.58986i			0.338960i
$23$			0.220987i			0.0460789i	0.999735	+	0.0230395i	$0.00733434\pi$
$23$			0.220987i			0.0460789i	−0.999735	+	0.0230395i	$0.992666\pi$
$24$	−2.52763			−0.515951
$25$	1.85048	+	4.64497i	0.370096	+	0.928993i
$26$	−1.45686			−0.285714
$27$		−	3.73083i		−	0.717998i
$28$		−	7.02678i		−	1.32794i
$29$	−3.42114			−0.635289			−0.317644	−	0.948210i	$-0.602892\pi$
$29$	−3.42114			−0.635289			−0.317644	+	0.948210i	$0.602892\pi$
$30$	1.19969	+	0.813451i	0.219033	+	0.148515i
$31$	7.89725			1.41839			0.709194	−	0.705013i	$-0.249059\pi$
$31$	7.89725			1.41839			0.709194	+	0.705013i	$0.249059\pi$
$32$		−	3.55515i		−	0.628468i
$33$			10.2370i			1.78203i
$34$	1.01885			0.174732
$35$	−4.64262	+	6.84702i	−0.784747	+	1.15736i
$36$	−2.22952			−0.371587
$37$		−	2.98622i		−	0.490932i	−0.969405	−	0.245466i	$-0.921059\pi$
$37$		−	2.98622i		−	0.490932i	0.969405	−	0.245466i	$-0.0789410\pi$
$38$		0			0
$39$	−9.38061			−1.50210
$40$	−1.55258	+	2.28977i	−0.245484	+	0.362044i
$41$	−0.183247			−0.0286184			−0.0143092	−	0.999898i	$-0.504555\pi$
$41$	−0.183247			−0.0286184			−0.0143092	+	0.999898i	$0.504555\pi$
$42$			2.39817i			0.370046i
$43$			7.30424i			1.11389i	0.830551	+	0.556943i	$0.188026\pi$
$43$			7.30424i			1.11389i	−0.830551	+	0.556943i	$0.811974\pi$
$44$	−9.51707			−1.43475
$45$	2.17249	+	1.47306i	0.323856	+	0.219590i
$46$	0.0701168			0.0103382
$47$			10.8876i			1.58812i	0.607840	+	0.794060i	$0.292036\pi$
$47$			10.8876i			1.58812i	−0.607840	+	0.794060i	$0.707964\pi$
$48$		−	6.95866i		−	1.00440i
$49$	−6.68714			−0.955306
$50$	1.47380	−	0.587138i	0.208427	−	0.0830339i
$51$	6.56032			0.918628
$52$		−	8.72092i		−	1.20937i
$53$		−	1.93670i		−	0.266026i	−0.991114	−	0.133013i	$-0.957535\pi$
$53$		−	1.93670i		−	0.266026i	0.991114	−	0.133013i	$-0.0424652\pi$
$54$	−1.18375			−0.161088
$55$	9.27362	+	6.28797i	1.25045	+	0.847870i
$56$	−4.57722			−0.611657
$57$		0			0
$58$			1.08549i			0.142532i
$59$	6.15338			0.801102			0.400551	−	0.916275i	$-0.368819\pi$
$59$	6.15338			0.801102			0.400551	+	0.916275i	$0.368819\pi$
$60$	−4.86940	+	7.18148i	−0.628637	+	0.927125i
$61$	5.02293			0.643121			0.321560	−	0.946889i	$-0.395793\pi$
$61$	5.02293			0.643121			0.321560	+	0.946889i	$0.395793\pi$
$62$		−	2.50572i		−	0.318226i
$63$			4.34279i			0.547140i
$64$	5.68419			0.710523
$65$	−5.76195	+	8.49783i	−0.714682	+	1.05403i
$66$	3.24809			0.399812
$67$		−	11.2753i		−	1.37750i	−0.724998	−	0.688751i	$-0.758159\pi$
$67$		−	11.2753i		−	1.37750i	0.724998	−	0.688751i	$-0.241841\pi$
$68$			6.09897i			0.739608i
$69$	0.451476			0.0543513
$70$	2.17249	+	1.47306i	0.259662	+	0.176064i
$71$	0.851223			0.101022			0.0505108	−	0.998724i	$-0.483915\pi$
$71$	0.851223			0.101022			0.0505108	+	0.998724i	$0.483915\pi$
$72$			1.45230i			0.171156i
$73$		−	5.15625i		−	0.603494i	−0.953388	−	0.301747i	$-0.902430\pi$
$73$		−	5.15625i		−	0.603494i	0.953388	−	0.301747i	$-0.0975698\pi$
$74$	−0.947498			−0.110144
$75$	9.48967	−	3.78053i	1.09577	−	0.436538i
$76$		0			0
$77$			18.5379i			2.11259i
$78$			2.97637i			0.337007i
$79$	−9.19657			−1.03469			−0.517347	−	0.855776i	$-0.673080\pi$
$79$	−9.19657			−1.03469			−0.517347	+	0.855776i	$0.673080\pi$
$80$	−6.30381	−	4.27429i	−0.704787	−	0.477881i
$81$	−11.1436			−1.23818
$82$			0.0581424i			0.00642076i
$83$		−	4.53528i		−	0.497811i	−0.968528	−	0.248906i	$-0.919929\pi$
$83$		−	4.53528i		−	0.497811i	0.968528	−	0.248906i	$-0.0800709\pi$
$84$	−14.3557			−1.56634
$85$	4.02961	−	5.94295i	0.437073	−	0.644603i
$86$	2.31756			0.249909
$87$			6.98938i			0.749340i
$88$			6.19939i			0.660857i
$89$	14.8752			1.57677			0.788385	−	0.615183i	$-0.210918\pi$
$89$	14.8752			1.57677			0.788385	+	0.615183i	$0.210918\pi$
$90$	0.467385	−	0.689308i	0.0492667	−	0.0726595i
$91$	−16.9871			−1.78073
$92$			0.419726i			0.0437595i
$93$		−	16.1341i		−	1.67303i
$94$	3.45452			0.356307
$95$		0			0
$96$	−7.26317			−0.741295
$97$		−	1.36602i		−	0.138698i	−0.997592	−	0.0693490i	$-0.977908\pi$
$97$		−	1.36602i		−	0.138698i	0.997592	−	0.0693490i	$-0.0220922\pi$
$98$			2.12176i			0.214330i
$99$	5.88187			0.591151
$100$	3.51467	+	8.82231i	0.351467	+	0.882231i
$101$	−6.08643			−0.605622			−0.302811	−	0.953051i	$-0.597925\pi$
$101$	−6.08643			−0.605622			−0.302811	+	0.953051i	$0.597925\pi$
$102$		−	2.08152i		−	0.206101i
$103$			13.7063i			1.35052i	0.737579	+	0.675261i	$0.235969\pi$
$103$			13.7063i			1.35052i	−0.737579	+	0.675261i	$0.764031\pi$
$104$	−5.68078			−0.557047
$105$	13.9885	+	9.48488i	1.36513	+	0.925629i
$106$	−0.614494			−0.0596850
$107$		−	17.3036i		−	1.67280i	−0.548119	−	0.836400i	$-0.684656\pi$
$107$		−	17.3036i		−	1.67280i	0.548119	−	0.836400i	$-0.315344\pi$
$108$		−	7.08606i		−	0.681857i
$109$	−13.7511			−1.31712			−0.658561	−	0.752528i	$-0.728834\pi$
$109$	−13.7511			−1.31712			−0.658561	+	0.752528i	$0.728834\pi$
$110$	1.99511	−	2.94242i	0.190226	−	0.280549i
$111$	−6.10086			−0.579068
$112$		−	12.6012i		−	1.19071i
$113$		−	4.15573i		−	0.390938i	−0.980710	−	0.195469i	$-0.937377\pi$
$113$		−	4.15573i		−	0.390938i	0.980710	−	0.195469i	$-0.0626229\pi$
$114$		0			0
$115$	0.277315	−	0.408989i	0.0258598	−	0.0381384i
$116$	−6.49786			−0.603311
$117$			5.38983i			0.498290i
$118$		−	1.95240i		−	0.179733i
$119$	11.8799			1.08903
$120$	4.67799	+	3.17191i	0.427040	+	0.289555i
$121$	14.1077			1.28252
$122$		−	1.59372i		−	0.144289i
$123$			0.374374i			0.0337562i
$124$	14.9995			1.34699
$125$	2.40418	−	10.9188i	0.215037	−	0.976606i
$126$	1.37792			0.122755
$127$			11.9185i			1.05760i	0.848747	+	0.528799i	$0.177357\pi$
$127$			11.9185i			1.05760i	−0.848747	+	0.528799i	$0.822643\pi$
$128$		−	8.91384i		−	0.787879i
$129$	14.9226			1.31386
$130$	2.69627	+	1.82821i	0.236479	+	0.160344i
$131$	−7.58093			−0.662349			−0.331175	−	0.943569i	$-0.607445\pi$
$131$	−7.58093			−0.662349			−0.331175	+	0.943569i	$0.607445\pi$
$132$			19.4434i			1.69233i
$133$		0			0
$134$	−3.57755			−0.309053
$135$	−4.68179	+	6.90479i	−0.402945	+	0.594270i
$136$	3.97285			0.340669
$137$		−	7.98581i		−	0.682274i	−0.940014	−	0.341137i	$-0.889188\pi$
$137$		−	7.98581i		−	0.682274i	0.940014	−	0.341137i	$-0.110812\pi$
$138$		−	0.143249i		−	0.0121941i
$139$	−2.65651			−0.225322			−0.112661	−	0.993633i	$-0.535937\pi$
$139$	−2.65651			−0.225322			−0.112661	+	0.993633i	$0.535937\pi$
$140$	−8.81786	+	13.0047i	−0.745245	+	1.09910i
$141$	22.2434			1.87323
$142$		−	0.270084i		−	0.0226650i
$143$			23.0073i			1.92397i
$144$	−3.99825			−0.333187
$145$	6.33163	+	4.29316i	0.525814	+	0.356528i
$146$	−1.63603			−0.135398
$147$			13.6618i			1.12681i
$148$		−	5.67182i		−	0.466221i
$149$	−8.35153			−0.684184			−0.342092	−	0.939666i	$-0.611135\pi$
$149$	−8.35153			−0.684184			−0.342092	+	0.939666i	$0.611135\pi$
$150$	−1.19952	−	3.01097i	−0.0979407	−	0.245845i
$151$	8.56471			0.696986			0.348493	−	0.937311i	$-0.386694\pi$
$151$	8.56471			0.696986			0.348493	+	0.937311i	$0.386694\pi$
$152$		0			0
$153$		−	3.76937i		−	0.304735i
$154$	5.88187			0.473975
$155$	−14.6158	−	9.91022i	−1.17397	−	0.796008i
$156$	−17.8168			−1.42649
$157$		−	11.3335i		−	0.904510i	−0.891889	−	0.452255i	$-0.850620\pi$
$157$		−	11.3335i		−	0.904510i	0.891889	−	0.452255i	$-0.149380\pi$
$158$			2.91797i			0.232142i
$159$	−3.95668			−0.313785
$160$	−4.46134	+	6.57966i	−0.352700	+	0.520168i
$161$	0.817566			0.0644332
$162$			3.53576i			0.277795i
$163$			4.65048i			0.364254i	0.983275	+	0.182127i	$0.0582982\pi$
$163$			4.65048i			0.364254i	−0.983275	+	0.182127i	$0.941702\pi$
$164$	−0.348046			−0.0271779
$165$	12.8463	−	18.9460i	1.00009	−	1.47494i
$166$	−1.43900			−0.111688
$167$			8.89485i			0.688304i	0.938914	+	0.344152i	$0.111834\pi$
$167$			8.89485i			0.688304i	−0.938914	+	0.344152i	$0.888166\pi$
$168$			9.35126i			0.721466i
$169$	−8.08265			−0.621743
$170$	−1.88564	−	1.27855i	−0.144622	−	0.0980607i
$171$		0			0
$172$			13.8731i			1.05782i
$173$			18.6570i			1.41847i	0.704974	+	0.709233i	$0.250958\pi$
$173$			18.6570i			1.41847i	−0.704974	+	0.709233i	$0.749042\pi$
$174$	2.21766			0.168120
$175$	17.1846	−	6.84606i	1.29903	−	0.517514i
$176$	−17.0671			−1.28648
$177$		−	12.5713i		−	0.944921i
$178$		−	4.71975i		−	0.353760i
$179$	0.224791			0.0168017			0.00840083	−	0.999965i	$-0.497326\pi$
$179$	0.224791			0.0168017			0.00840083	+	0.999965i	$0.497326\pi$
$180$	4.12627	+	2.79782i	0.307554	+	0.208537i
$181$	−24.8780			−1.84917			−0.924583	−	0.380981i	$-0.875586\pi$
$181$	−24.8780			−1.84917			−0.924583	+	0.380981i	$0.875586\pi$
$182$			5.38983i			0.399521i
$183$		−	10.2618i		−	0.758578i
$184$	0.273408			0.0201559
$185$	−3.74740	+	5.52673i	−0.275514	+	0.406333i
$186$	−5.11918			−0.375356
$187$		−	16.0901i		−	1.17663i
$188$			20.6791i			1.50818i
$189$	−13.8026			−1.00399
$190$		0			0
$191$	8.43889			0.610616			0.305308	−	0.952254i	$-0.401241\pi$
$191$	8.43889			0.610616			0.305308	+	0.952254i	$0.401241\pi$
$192$		−	11.6128i		−	0.838081i
$193$			1.60346i			0.115420i	0.998333	+	0.0577098i	$0.0183798\pi$
$193$			1.60346i			0.115420i	−0.998333	+	0.0577098i	$0.981620\pi$
$194$	−0.433423			−0.0311180
$195$	17.3611	+	11.7717i	1.24325	+	0.842987i
$196$	−12.7011			−0.907219
$197$			2.01284i			0.143409i	0.997426	+	0.0717043i	$0.0228438\pi$
$197$			2.01284i			0.143409i	−0.997426	+	0.0717043i	$0.977156\pi$
$198$		−	1.86626i		−	0.132629i
$199$	−5.03693			−0.357059			−0.178529	−	0.983935i	$-0.557134\pi$
$199$	−5.03693			−0.357059			−0.178529	+	0.983935i	$0.557134\pi$
$200$	5.74683	−	2.28944i	0.406362	−	0.161888i
$201$	−23.0355			−1.62480
$202$			1.93116i			0.135876i
$203$			12.6569i			0.888339i
$204$	12.4602			0.872388
$205$	0.339143	+	0.229956i	0.0236868	+	0.0160608i
$206$	4.34886			0.303000
$207$		−	0.259405i		−	0.0180299i
$208$		−	15.6394i		−	1.08440i
$209$		0			0
$210$	3.00945	−	4.43840i	0.207672	−	0.306278i
$211$	4.18849			0.288348			0.144174	−	0.989552i	$-0.453948\pi$
$211$	4.18849			0.288348			0.144174	+	0.989552i	$0.453948\pi$
$212$		−	3.67842i		−	0.252635i
$213$		−	1.73905i		−	0.119158i
$214$	−5.49025			−0.375306
$215$	9.16604	−	13.5182i	0.625119	−	0.921937i
$216$	−4.61584			−0.314068
$217$		−	29.2168i		−	1.98336i
$218$			4.36310i			0.295506i
$219$	−10.5342			−0.711837
$220$	17.6136	+	11.9429i	1.18751	+	0.805192i
$221$	14.7441			0.991797
$222$			1.93574i			0.129918i
$223$		−	5.32967i		−	0.356901i	−0.983949	−	0.178451i	$-0.942892\pi$
$223$		−	5.32967i		−	0.356901i	0.983949	−	0.178451i	$-0.0571084\pi$
$224$	−13.1527			−0.878801
$225$	−2.17219	−	5.45249i	−0.144812	−	0.363499i
$226$	−1.31857			−0.0877099
$227$		−	5.17899i		−	0.343741i	−0.985120	−	0.171871i	$-0.945019\pi$
$227$		−	5.17899i		−	0.343741i	0.985120	−	0.171871i	$-0.0549811\pi$
$228$		0			0
$229$	17.0790			1.12861			0.564306	−	0.825566i	$-0.309144\pi$
$229$	17.0790			1.12861			0.564306	+	0.825566i	$0.309144\pi$
$230$	−0.129768	−	0.0879892i	−0.00855665	−	0.00580183i
$231$	37.8729			2.49185
$232$			4.23268i			0.277889i
$233$		−	15.8503i		−	1.03839i	−0.854656	−	0.519195i	$-0.826232\pi$
$233$		−	15.8503i		−	1.03839i	0.854656	−	0.519195i	$-0.173768\pi$
$234$	1.71014			0.111795
$235$	13.6628	−	20.1501i	0.891262	−	1.31445i
$236$	11.6873			0.760777
$237$			18.7886i			1.22045i
$238$		−	3.76937i		−	0.244332i
$239$	17.7688			1.14937			0.574685	−	0.818375i	$-0.305125\pi$
$239$	17.7688			1.14937			0.574685	+	0.818375i	$0.305125\pi$
$240$	−8.73238	+	12.8787i	−0.563673	+	0.831315i
$241$	−27.3823			−1.76385			−0.881925	−	0.471390i	$-0.843753\pi$
$241$	−27.3823			−1.76385			−0.881925	+	0.471390i	$0.843753\pi$
$242$		−	4.47623i		−	0.287743i
$243$			11.5739i			0.742469i
$244$	9.54019			0.610748
$245$	12.3762	+	8.39165i	0.790684	+	0.536123i
$246$	0.118785			0.00757345
$247$		0			0
$248$		−	9.77061i		−	0.620434i
$249$	−9.26557			−0.587182
$250$	−3.46442	−	0.762822i	−0.219109	−	0.0482451i
$251$	−8.50216			−0.536651			−0.268326	−	0.963328i	$-0.586470\pi$
$251$	−8.50216			−0.536651			−0.268326	+	0.963328i	$0.586470\pi$
$252$			8.24837i			0.519599i
$253$		−	1.10731i		−	0.0696161i
$254$	3.78162			0.237280
$255$	−12.1414	−	8.23250i	−0.760327	−	0.515539i
$256$	8.54010			0.533756
$257$		−	20.9865i		−	1.30910i	−0.756017	−	0.654552i	$-0.772857\pi$
$257$		−	20.9865i		−	1.30910i	0.756017	−	0.654552i	$-0.227143\pi$
$258$		−	4.73477i		−	0.294774i
$259$	−11.0479			−0.686482
$260$	−10.9438	+	16.1402i	−0.678708	+	1.00097i
$261$	4.01590			0.248578
$262$			2.40535i			0.148603i
$263$			11.7173i			0.722522i	0.932465	+	0.361261i	$0.117654\pi$
$263$			11.7173i			0.722522i	−0.932465	+	0.361261i	$0.882346\pi$
$264$	12.6654			0.779499
$265$	−2.43035	+	3.58433i	−0.149295	+	0.220183i
$266$		0			0
$267$		−	30.3901i		−	1.85984i
$268$		−	21.4156i		−	1.30816i
$269$	13.1743			0.803253			0.401626	−	0.915804i	$-0.368445\pi$
$269$	13.1743			0.803253			0.401626	+	0.915804i	$0.368445\pi$
$270$	2.19082	+	1.48548i	0.133329	+	0.0904037i
$271$	−25.7363			−1.56337			−0.781683	−	0.623676i	$-0.785639\pi$
$271$	−25.7363			−1.56337			−0.781683	+	0.623676i	$0.785639\pi$
$272$			10.9374i			0.663177i
$273$			34.7046i			2.10042i
$274$	−2.53381			−0.153073
$275$	−9.27232	−	23.2748i	−0.559142	−	1.40352i
$276$	0.857501			0.0516155
$277$		−	5.11697i		−	0.307449i	−0.988114	−	0.153724i	$-0.950873\pi$
$277$		−	5.11697i		−	0.307449i	0.988114	−	0.153724i	$-0.0491268\pi$
$278$			0.842882i			0.0505527i
$279$	−9.27018			−0.554991
$280$	8.47125	+	5.74393i	0.506254	+	0.343265i
$281$	−1.80790			−0.107850			−0.0539251	−	0.998545i	$-0.517173\pi$
$281$	−1.80790			−0.107850			−0.0539251	+	0.998545i	$0.517173\pi$
$282$		−	7.05759i		−	0.420273i
$283$			18.6741i			1.11006i	0.831831	+	0.555029i	$0.187293\pi$
$283$			18.6741i			1.11006i	−0.831831	+	0.555029i	$0.812707\pi$
$284$	1.61675			0.0959366
$285$		0			0
$286$	7.29999			0.431657
$287$			0.677944i			0.0400178i
$288$			4.17321i			0.245909i
$289$	6.68871			0.393454
$290$	1.36218	−	2.00896i	0.0799897	−	0.117970i
$291$	−2.79077			−0.163598
$292$		−	9.79341i		−	0.573116i
$293$			0.150745i			0.00880664i	0.999990	+	0.00440332i	$0.00140163\pi$
$293$			0.150745i			0.00880664i	−0.999990	+	0.00440332i	$0.998598\pi$
$294$	4.33475			0.252808
$295$	−11.3883	−	7.72184i	−0.663053	−	0.449583i
$296$	−3.69461			−0.214745
$297$			18.6943i			1.08475i
$298$			2.64985i			0.153502i
$299$	1.01468			0.0586804
$300$	18.0240	−	7.18047i	1.04062	−	0.414565i
$301$	27.0228			1.55757
$302$		−	2.71749i		−	0.156374i
$303$			12.4346i			0.714347i
$304$		0			0
$305$	−9.29614	−	6.30325i	−0.532296	−	0.360923i
$306$	−1.19598			−0.0683697
$307$		−	4.94936i		−	0.282475i	−0.989976	−	0.141237i	$-0.954892\pi$
$307$		−	4.94936i		−	0.282475i	0.989976	−	0.141237i	$-0.0451081\pi$
$308$			35.2095i			2.00625i
$309$	28.0020			1.59298
$310$	−3.14441	+	4.63743i	−0.178590	+	0.263388i
$311$	−23.6262			−1.33972			−0.669859	−	0.742489i	$-0.733645\pi$
$311$	−23.6262			−1.33972			−0.669859	+	0.742489i	$0.733645\pi$
$312$			11.6058i			0.657051i
$313$		−	8.89248i		−	0.502632i	−0.967905	−	0.251316i	$-0.919137\pi$
$313$		−	8.89248i		−	0.502632i	0.967905	−	0.251316i	$-0.0808634\pi$
$314$	−3.59600			−0.202934
$315$	5.44974	−	8.03737i	0.307058	−	0.452855i
$316$	−17.4673			−0.982612
$317$		−	29.5976i		−	1.66237i	−0.555996	−	0.831185i	$-0.687663\pi$
$317$		−	29.5976i		−	1.66237i	0.555996	−	0.831185i	$-0.312337\pi$
$318$			1.25541i			0.0704000i
$319$	17.1425			0.959795
$320$	−10.5200	−	7.13305i	−0.588083	−	0.398750i
$321$	−35.3512			−1.97311
$322$		−	0.259405i		−	0.0144561i
$323$		0			0
$324$	−21.1654			−1.17586
$325$	21.3278	−	8.49664i	1.18305	−	0.471309i
$326$	1.47555			0.0817232
$327$			28.0936i			1.55358i
$328$			0.226716i			0.0125183i
$329$	40.2799			2.22070
$330$	−6.01137	−	4.07601i	−0.330915	−	0.224377i
$331$	25.8866			1.42285			0.711427	−	0.702760i	$-0.248049\pi$
$331$	25.8866			1.42285			0.711427	+	0.702760i	$0.248049\pi$
$332$		−	8.61397i		−	0.472753i
$333$			3.50538i			0.192093i
$334$	2.82224			0.154426
$335$	−14.1494	+	20.8677i	−0.773062	+	1.14013i
$336$	−25.7444			−1.40447
$337$		−	6.08960i		−	0.331721i	−0.986149	−	0.165861i	$-0.946960\pi$
$337$		−	6.08960i		−	0.331721i	0.986149	−	0.165861i	$-0.0530402\pi$
$338$			2.56454i			0.139493i
$339$	−8.49015			−0.461122
$340$	7.65356	−	11.2876i	0.415072	−	0.612156i
$341$	−39.5712			−2.14290
$342$		0			0
$343$		−	1.15747i		−	0.0624972i
$344$	9.03692			0.487238
$345$	−0.835565	−	0.566555i	−0.0449853	−	0.0305023i
$346$	5.91967			0.318244
$347$			6.60514i			0.354582i	0.984158	+	0.177291i	$0.0567334\pi$
$347$			6.60514i			0.354582i	−0.984158	+	0.177291i	$0.943267\pi$
$348$			13.2751i			0.711621i
$349$	−19.6123			−1.04982			−0.524912	−	0.851156i	$-0.675902\pi$
$349$	−19.6123			−1.04982			−0.524912	+	0.851156i	$0.675902\pi$
$350$	−2.17219	−	5.45249i	−0.116108	−	0.291448i
$351$	−17.1304			−0.914354
$352$			17.8140i			0.949490i
$353$		−	19.2599i		−	1.02510i	−0.858657	−	0.512551i	$-0.828701\pi$
$353$		−	19.2599i		−	1.02510i	0.858657	−	0.512551i	$-0.171299\pi$
$354$	−3.98876			−0.212000
$355$	−1.57539	−	1.06820i	−0.0836132	−	0.0566939i
$356$	28.2529			1.49740
$357$		−	24.2706i		−	1.28454i
$358$		−	0.0713238i		−	0.00376958i
$359$	35.7362			1.88609			0.943043	−	0.332671i	$-0.107950\pi$
$359$	35.7362			1.88609			0.943043	+	0.332671i	$0.107950\pi$
$360$	1.82249	−	2.68784i	0.0960536	−	0.141662i
$361$		0			0
$362$			7.89352i			0.414874i
$363$		−	28.8221i		−	1.51277i
$364$	−32.2640			−1.69110
$365$	−6.47055	+	9.54289i	−0.338684	+	0.499498i
$366$	−3.25598			−0.170193
$367$		−	13.8593i		−	0.723450i	−0.932285	−	0.361725i	$-0.882188\pi$
$367$		−	13.8593i		−	0.723450i	0.932285	−	0.361725i	$-0.117812\pi$
$368$			0.752703i			0.0392373i
$369$	0.215105			0.0111979
$370$	1.75357	+	1.18901i	0.0911639	+	0.0618137i
$371$	−7.16504			−0.371990
$372$		−	30.6439i		−	1.58881i
$373$		−	23.6819i		−	1.22620i	−0.790005	−	0.613101i	$-0.789922\pi$
$373$		−	23.6819i		−	1.22620i	0.790005	−	0.613101i	$-0.210078\pi$
$374$	−5.10524			−0.263985
$375$	−22.3071	−	4.91174i	−1.15193	−	0.253641i
$376$	13.4703			0.694678
$377$			15.7084i			0.809026i
$378$			4.37943i			0.225253i
$379$	33.7504			1.73364			0.866820	−	0.498622i	$-0.166160\pi$
$379$	33.7504			1.73364			0.866820	+	0.498622i	$0.166160\pi$
$380$		0			0
$381$	24.3495			1.24746
$382$		−	2.67757i		−	0.136996i
$383$		−	15.9027i		−	0.812588i	−0.913742	−	0.406294i	$-0.866821\pi$
$383$		−	15.9027i		−	0.812588i	0.913742	−	0.406294i	$-0.133179\pi$
$384$	−18.2110			−0.929325
$385$	23.2631	−	34.3088i	1.18560	−	1.74854i
$386$	0.508761			0.0258953
$387$		−	8.57407i		−	0.435844i
$388$		−	2.59451i		−	0.131716i
$389$	0.715535			0.0362791			0.0181395	−	0.999835i	$-0.494226\pi$
$389$	0.715535			0.0362791			0.0181395	+	0.999835i	$0.494226\pi$
$390$	3.73503	−	5.50849i	0.189131	−	0.278933i
$391$	−0.709615			−0.0358868
$392$			8.27344i			0.417872i
$393$			15.4878i			0.781259i
$394$	0.638652			0.0321748
$395$	17.0205	+	11.5407i	0.856392	+	0.580676i
$396$	11.1716			0.561394
$397$			14.3593i			0.720671i	0.932823	+	0.360336i	$0.117338\pi$
$397$			14.3593i			0.720671i	−0.932823	+	0.360336i	$0.882662\pi$
$398$			1.59817i			0.0801088i
$399$		0			0
$400$	6.30292	+	15.8212i	0.315146	+	0.791061i
$401$	−34.5791			−1.72680			−0.863398	−	0.504524i	$-0.831668\pi$
$401$	−34.5791			−1.72680			−0.863398	+	0.504524i	$0.831668\pi$
$402$			7.30893i			0.364536i
$403$		−	36.2609i		−	1.80628i
$404$	−11.5601			−0.575137
$405$	20.6240	+	13.9841i	1.02481	+	0.694874i
$406$	4.01590			0.199306
$407$			14.9633i			0.741701i
$408$		−	8.11653i		−	0.401828i
$409$	18.4355			0.911575			0.455788	−	0.890089i	$-0.349358\pi$
$409$	18.4355			0.911575			0.455788	+	0.890089i	$0.349358\pi$
$410$	0.0729626	−	0.107607i	0.00360337	−	0.00531431i
$411$	−16.3150			−0.804760
$412$			26.0327i			1.28254i
$413$		−	22.7651i		−	1.12020i
$414$	−0.0823065			−0.00404514
$415$	−5.69129	+	8.39362i	−0.279375	+	0.412027i
$416$	−16.3238			−0.800339
$417$			5.42725i			0.265773i
$418$		0			0
$419$	34.3437			1.67780			0.838901	−	0.544285i	$-0.183199\pi$
$419$	34.3437			1.67780			0.838901	+	0.544285i	$0.183199\pi$
$420$	26.5687	+	18.0149i	1.29642	+	0.879037i
$421$	−0.225020			−0.0109668			−0.00548340	−	0.999985i	$-0.501745\pi$
$421$	−0.225020			−0.0109668			−0.00548340	+	0.999985i	$0.501745\pi$
$422$		−	1.32897i		−	0.0646930i
$423$		−	12.7804i		−	0.621404i
$424$	−2.39611			−0.116366
$425$	−14.9155	+	5.94211i	−0.723510	+	0.288235i
$426$	−0.551782			−0.0267339
$427$		−	18.5829i		−	0.899290i
$428$		−	32.8652i		−	1.58860i
$429$	47.0040			2.26937
$430$	−4.28920	−	2.90829i	−0.206844	−	0.140250i
$431$	13.3531			0.643198			0.321599	−	0.946876i	$-0.395780\pi$
$431$	13.3531			0.643198			0.321599	+	0.946876i	$0.395780\pi$
$432$		−	12.7076i		−	0.611393i
$433$		−	21.4161i		−	1.02919i	−0.857433	−	0.514595i	$-0.827942\pi$
$433$		−	21.4161i		−	1.02919i	0.857433	−	0.514595i	$-0.172058\pi$
$434$	−9.27018			−0.444983
$435$	8.77093	−	12.9355i	0.420534	−	0.620211i
$436$	−26.1179			−1.25082
$437$		0			0
$438$			3.34240i			0.159706i
$439$	7.21678			0.344438			0.172219	−	0.985059i	$-0.444906\pi$
$439$	7.21678			0.344438			0.172219	+	0.985059i	$0.444906\pi$
$440$	7.77958	−	11.4735i	0.370877	−	0.546976i
$441$	7.84969			0.373795
$442$		−	4.67816i		−	0.222517i
$443$		−	34.6591i		−	1.64671i	−0.567530	−	0.823353i	$-0.692101\pi$
$443$		−	34.6591i		−	1.64671i	0.567530	−	0.823353i	$-0.307899\pi$
$444$	−11.5875			−0.549920
$445$	−27.5302	−	18.6668i	−1.30505	−	0.884892i
$446$	−1.69105			−0.0800735
$447$			17.0622i			0.807013i
$448$		−	21.0293i		−	0.993540i
$449$	−5.09006			−0.240215			−0.120107	−	0.992761i	$-0.538324\pi$
$449$	−5.09006			−0.240215			−0.120107	+	0.992761i	$0.538324\pi$
$450$	−1.73002	+	0.689212i	−0.0815538	+	0.0324898i
$451$	0.918208			0.0432367
$452$		−	7.89309i		−	0.371260i
$453$		−	17.4977i		−	0.822113i
$454$	−1.64324			−0.0771210
$455$	31.4387	+	21.3170i	1.47387	+	0.999356i
$456$		0			0
$457$		−	39.9916i		−	1.87073i	−0.353686	−	0.935364i	$-0.615072\pi$
$457$		−	39.9916i		−	1.87073i	0.353686	−	0.935364i	$-0.384928\pi$
$458$		−	5.41899i		−	0.253213i
$459$	11.9801			0.559185
$460$	0.526712	−	0.776804i	0.0245581	−	0.0362187i
$461$	26.4955			1.23402			0.617009	−	0.786956i	$-0.288344\pi$
$461$	26.4955			1.23402			0.617009	+	0.786956i	$0.288344\pi$
$462$		−	12.0167i		−	0.559066i
$463$		−	9.68844i		−	0.450260i	−0.974329	−	0.225130i	$-0.927719\pi$
$463$		−	9.68844i		−	0.450260i	0.974329	−	0.225130i	$-0.0722807\pi$
$464$	−11.6527			−0.540964
$465$	−20.2466	+	29.8600i	−0.938912	+	1.38472i
$466$	−5.02915			−0.232971
$467$			5.78310i			0.267610i	0.991008	+	0.133805i	$0.0427195\pi$
$467$			5.78310i			0.267610i	−0.991008	+	0.133805i	$0.957280\pi$
$468$			10.2370i			0.473208i
$469$	−41.7144			−1.92619
$470$	−6.39342	−	4.33506i	−0.294907	−	0.199961i
$471$	−23.1543			−1.06689
$472$		−	7.61306i		−	0.350419i
$473$		−	36.5998i		−	1.68286i
$474$	5.96142			0.273817
$475$		0			0
$476$	22.5638			1.03421
$477$			2.27339i			0.104091i
$478$		−	5.63786i		−	0.257870i
$479$	−1.77194			−0.0809620			−0.0404810	−	0.999180i	$-0.512889\pi$
$479$	−1.77194			−0.0809620			−0.0404810	+	0.999180i	$0.512889\pi$
$480$	13.4423	+	9.11452i	0.613552	+	0.416019i
$481$	−13.7115			−0.625191
$482$			8.68812i			0.395733i
$483$		−	1.67029i		−	0.0760007i
$484$	26.7952			1.21796
$485$	−1.71421	+	2.52814i	−0.0778381	+	0.114797i
$486$	3.67229			0.166579
$487$			16.2131i			0.734688i	0.930085	+	0.367344i	$0.119733\pi$
$487$			16.2131i			0.734688i	−0.930085	+	0.367344i	$0.880267\pi$
$488$		−	6.21445i		−	0.281315i
$489$	9.50094			0.429647
$490$	2.66258	−	3.92683i	0.120283	−	0.177396i
$491$	18.4869			0.834300			0.417150	−	0.908838i	$-0.363029\pi$
$491$	18.4869			0.834300			0.417150	+	0.908838i	$0.363029\pi$
$492$			0.711059i			0.0320570i
$493$		−	10.9857i		−	0.494770i
$494$		0			0
$495$	−10.8858	−	7.38113i	−0.489281	−	0.331757i
$496$	26.8988			1.20779
$497$		−	3.14920i		−	0.141261i
$498$			2.93987i			0.131739i
$499$	17.2843			0.773751			0.386875	−	0.922132i	$-0.373554\pi$
$499$	17.2843			0.773751			0.386875	+	0.922132i	$0.373554\pi$
$500$	4.56633	−	20.7384i	0.204212	−	0.927447i
$501$	18.1722			0.811873
$502$			2.69765i			0.120402i
$503$			40.7325i			1.81617i	0.418782	+	0.908087i	$0.362457\pi$
$503$			40.7325i			1.81617i	−0.418782	+	0.908087i	$0.637543\pi$
$504$	5.37297			0.239331
$505$	11.2644	+	7.63782i	0.501259	+	0.339879i
$506$	−0.351338			−0.0156189
$507$			16.5129i			0.733362i
$508$			22.6372i			1.00436i
$509$	−21.2017			−0.939747			−0.469873	−	0.882734i	$-0.655700\pi$
$509$	−21.2017			−0.939747			−0.469873	+	0.882734i	$0.655700\pi$
$510$	−2.61209	+	3.85235i	−0.115665	+	0.170585i
$511$	−19.0761			−0.843879
$512$		−	20.5374i		−	0.907632i
$513$		0			0
$514$	−6.65881			−0.293707
$515$	17.1999	−	25.3668i	0.757920	−	1.11779i
$516$	28.3428			1.24772
$517$		−	54.5551i		−	2.39933i
$518$			3.50538i			0.154017i
$519$	38.1163			1.67312
$520$	10.5137	+	7.12878i	0.461054	+	0.312618i
$521$	19.2704			0.844251			0.422125	−	0.906538i	$-0.361284\pi$
$521$	19.2704			0.844251			0.422125	+	0.906538i	$0.361284\pi$
$522$		−	1.27420i		−	0.0557703i
$523$			24.4971i			1.07118i	0.844477	+	0.535591i	$0.179911\pi$
$523$			24.4971i			1.07118i	−0.844477	+	0.535591i	$0.820089\pi$
$524$	−14.3987			−0.629009
$525$	−13.9865	−	35.1081i	−0.610421	−	1.53224i
$526$	3.71779			0.162103
$527$			25.3590i			1.10466i
$528$			34.8682i			1.51744i
$529$	22.9512			0.997877
$530$	1.13727	+	0.771125i	0.0493998	+	0.0334955i
$531$	−7.22313			−0.313457
$532$		0			0
$533$			0.841395i			0.0364449i
$534$	−9.64245			−0.417270
$535$	−21.7142	+	32.0244i	−0.938785	+	1.38454i
$536$	−13.9500			−0.602550
$537$		−	0.459248i		−	0.0198180i
$538$		−	4.18008i		−	0.180216i
$539$	33.5076			1.44328
$540$	−8.89226	+	13.1145i	−0.382662	+	0.564357i
$541$	30.5029			1.31142			0.655711	−	0.755012i	$-0.272369\pi$
$541$	30.5029			1.31142			0.655711	+	0.755012i	$0.272369\pi$
$542$			8.16585i			0.350753i
$543$			50.8257i			2.18114i
$544$	11.4160			0.489458
$545$	25.4498	+	17.2562i	1.09015	+	0.739176i
$546$	11.0114			0.471245
$547$		−	3.16224i		−	0.135207i	−0.997712	−	0.0676037i	$-0.978465\pi$
$547$		−	3.16224i		−	0.135207i	0.997712	−	0.0676037i	$-0.0215354\pi$
$548$		−	15.1677i		−	0.647931i
$549$	−5.89616			−0.251642
$550$	−7.38486	+	2.94201i	−0.314891	+	0.125448i
$551$		0			0
$552$		−	0.558573i		−	0.0237745i
$553$			34.0237i			1.44684i
$554$	−1.62356			−0.0689785
$555$	11.2911	+	7.65593i	0.479281	+	0.324976i
$556$	−5.04558			−0.213980
$557$			33.8886i			1.43591i	0.696092	+	0.717953i	$0.254921\pi$
$557$			33.8886i			1.43591i	−0.696092	+	0.717953i	$0.745079\pi$
$558$			2.94133i			0.124517i
$559$	33.5380			1.41851
$560$	−15.8132	+	23.3216i	−0.668231	+	0.985519i
$561$	−32.8722			−1.38786
$562$			0.573627i			0.0241970i
$563$			36.5457i			1.54022i	0.637911	+	0.770110i	$0.279799\pi$
$563$			36.5457i			1.54022i	−0.637911	+	0.770110i	$0.720201\pi$
$564$	42.2474			1.77894
$565$	−5.21500	+	7.69117i	−0.219397	+	0.323570i
$566$	5.92509			0.249050
$567$			41.2271i			1.73138i
$568$		−	1.05315i		−	0.0441891i
$569$	1.31802			0.0552543			0.0276272	−	0.999618i	$-0.491205\pi$
$569$	1.31802			0.0552543			0.0276272	+	0.999618i	$0.491205\pi$
$570$		0			0
$571$	−17.0771			−0.714656			−0.357328	−	0.933979i	$-0.616312\pi$
$571$	−17.0771			−0.714656			−0.357328	+	0.933979i	$0.616312\pi$
$572$			43.6985i			1.82712i
$573$		−	17.2406i		−	0.720238i
$574$	0.215105			0.00897829
$575$	−1.02648	+	0.408932i	−0.0428070	+	0.0170536i
$576$	−6.67237			−0.278016
$577$			47.2699i			1.96787i	0.178517	+	0.983937i	$0.442870\pi$
$577$			47.2699i			1.96787i	−0.178517	+	0.983937i	$0.557130\pi$
$578$		−	2.12226i		−	0.0882744i
$579$	3.27587			0.136140
$580$	12.0258	+	8.15412i	0.499346	+	0.338581i
$581$	−16.7788			−0.696101
$582$			0.885483i			0.0367045i
$583$			9.70433i			0.401912i
$584$	−6.37940			−0.263981
$585$	6.76366	−	9.97517i	0.279643	−	0.412423i
$586$	0.0478300			0.00197584
$587$		−	0.620087i		−	0.0255937i	−0.999918	−	0.0127969i	$-0.995927\pi$
$587$		−	0.620087i		−	0.0255937i	0.999918	−	0.0127969i	$-0.00407348\pi$
$588$			25.9483i			1.07009i
$589$		0			0
$590$	−2.45006	+	3.61339i	−0.100867	+	0.148761i
$591$	4.11222			0.169154
$592$		−	10.1714i		−	0.418041i
$593$		−	8.96071i		−	0.367972i	−0.982929	−	0.183986i	$-0.941100\pi$
$593$		−	8.96071i		−	0.367972i	0.982929	−	0.183986i	$-0.0589002\pi$
$594$	5.93150			0.243372
$595$	−21.9866	−	14.9080i	−0.901363	−	0.611169i
$596$	−15.8623			−0.649745
$597$			10.2905i			0.421160i
$598$		−	0.321947i		−	0.0131654i
$599$	−0.338212			−0.0138190			−0.00690948	−	0.999976i	$-0.502199\pi$
$599$	−0.338212			−0.0138190			−0.00690948	+	0.999976i	$0.502199\pi$
$600$	−4.67734	−	11.7408i	−0.190951	−	0.479315i
$601$	39.7523			1.62153			0.810766	−	0.585370i	$-0.199051\pi$
$601$	39.7523			1.62153			0.810766	+	0.585370i	$0.199051\pi$
$602$		−	8.57407i		−	0.349453i
$603$			13.2355i			0.538993i
$604$	16.2672			0.661902
$605$	−26.1097	−	17.7037i	−1.06151	−	0.719757i
$606$	3.94536			0.160269
$607$		−	22.5614i		−	0.915738i	−0.889020	−	0.457869i	$-0.848613\pi$
$607$		−	22.5614i		−	0.915738i	0.889020	−	0.457869i	$-0.151387\pi$
$608$		0			0
$609$	25.8580			1.04782
$610$	−1.99996	+	2.94957i	−0.0809758	+	0.119425i
$611$	49.9913			2.02243
$612$		−	7.15926i		−	0.289396i
$613$			32.5953i			1.31651i	0.752794	+	0.658257i	$0.228706\pi$
$613$			32.5953i			1.31651i	−0.752794	+	0.658257i	$0.771294\pi$
$614$	−1.57038			−0.0633754
$615$	0.469800	−	0.692869i	0.0189442	−	0.0279392i
$616$	22.9354			0.924092
$617$		−	29.4270i		−	1.18469i	−0.805686	−	0.592343i	$-0.798203\pi$
$617$		−	29.4270i		−	1.18469i	0.805686	−	0.592343i	$-0.201797\pi$
$618$		−	8.88473i		−	0.357396i
$619$	24.9940			1.00459			0.502297	−	0.864695i	$-0.332488\pi$
$619$	24.9940			1.00459			0.502297	+	0.864695i	$0.332488\pi$
$620$	−27.7601	−	18.8227i	−1.11487	−	0.755940i
$621$	0.824463			0.0330846
$622$			7.49634i			0.300576i
$623$		−	55.0325i		−	2.20483i
$624$	−31.9513			−1.27907
$625$	−18.1514	+	17.1908i	−0.726058	+	0.687634i
$626$	−2.82149			−0.112769
$627$		0			0
$628$		−	21.5260i		−	0.858981i
$629$	9.58912			0.382343
$630$	−2.55017	−	1.72915i	−0.101601	−	0.0688908i
$631$	−28.3101			−1.12701			−0.563504	−	0.826113i	$-0.690547\pi$
$631$	−28.3101			−1.12701			−0.563504	+	0.826113i	$0.690547\pi$
$632$			11.3781i			0.452598i
$633$		−	8.55709i		−	0.340114i
$634$	−9.39103			−0.372965
$635$	14.9565	−	22.0581i	0.593530	−	0.875348i
$636$	−7.51502			−0.297990
$637$			30.7046i			1.21656i
$638$		−	5.43913i		−	0.215337i
$639$	−0.999208			−0.0395280
$640$	−11.1859	+	16.4972i	−0.442162	+	0.652109i
$641$	−28.7741			−1.13651			−0.568254	−	0.822853i	$-0.692381\pi$
$641$	−28.7741			−1.13651			−0.568254	+	0.822853i	$0.692381\pi$
$642$			11.2166i			0.442683i
$643$		−	10.0599i		−	0.396722i	−0.980129	−	0.198361i	$-0.936438\pi$
$643$		−	10.0599i		−	0.396722i	0.980129	−	0.198361i	$-0.0635618\pi$
$644$	1.55282			0.0611899
$645$	−27.6178	−	18.7262i	−1.08745	−	0.737344i
$646$		0			0
$647$			18.9903i			0.746586i	0.927714	+	0.373293i	$0.121771\pi$
$647$			18.9903i			0.746586i	−0.927714	+	0.373293i	$0.878229\pi$
$648$			13.7871i			0.541607i
$649$	−30.8331			−1.21030
$650$	−2.69590	−	6.76708i	−0.105742	−	0.265427i
$651$	−59.6899			−2.33943
$652$			8.83279i			0.345919i
$653$		−	42.6940i		−	1.67074i	−0.549685	−	0.835372i	$-0.685252\pi$
$653$		−	42.6940i		−	1.67074i	0.549685	−	0.835372i	$-0.314748\pi$
$654$	8.91381			0.348557
$655$	14.0303	+	9.51327i	0.548211	+	0.371714i
$656$	−0.624158			−0.0243693
$657$			6.05266i			0.236137i
$658$		−	12.7804i		−	0.498232i
$659$	−14.4043			−0.561111			−0.280556	−	0.959838i	$-0.590519\pi$
$659$	−14.4043			−0.561111			−0.280556	+	0.959838i	$0.590519\pi$
$660$	24.3994	−	35.9847i	0.949745	−	1.40070i
$661$	−8.24176			−0.320567			−0.160284	−	0.987071i	$-0.551241\pi$
$661$	−8.24176			−0.320567			−0.160284	+	0.987071i	$0.551241\pi$
$662$		−	8.21354i		−	0.319228i
$663$		−	30.1222i		−	1.16985i
$664$	−5.61112			−0.217754
$665$		0			0
$666$	1.11222			0.0430976
$667$		−	0.756026i		−	0.0292734i
$668$			16.8942i			0.653657i
$669$	−10.8885			−0.420974
$670$	6.62111	+	4.48944i	0.255796	+	0.173442i
$671$	−25.1687			−0.971627
$672$			26.8709i			1.03657i
$673$		−	37.9246i		−	1.46189i	−0.682438	−	0.730944i	$-0.739080\pi$
$673$		−	37.9246i		−	1.46189i	0.682438	−	0.730944i	$-0.260920\pi$
$674$	−1.93217			−0.0744242
$675$	17.3296	−	6.90382i	0.667015	−	0.265728i
$676$	−15.3516			−0.590446
$677$			8.17207i			0.314078i	0.987592	+	0.157039i	$0.0501949\pi$
$677$			8.17207i			0.314078i	−0.987592	+	0.157039i	$0.949805\pi$
$678$			2.69384i			0.103456i
$679$	−5.05374			−0.193945
$680$	−7.35271	−	4.98550i	−0.281964	−	0.191185i
$681$	−10.5807			−0.405452
$682$			12.5555i			0.480777i
$683$			16.4611i			0.629868i	0.949114	+	0.314934i	$0.101982\pi$
$683$			16.4611i			0.629868i	−0.949114	+	0.314934i	$0.898018\pi$
$684$		0			0
$685$	−10.0213	+	14.7797i	−0.382896	+	0.564702i
$686$	−0.367252			−0.0140217
$687$		−	34.8924i		−	1.33123i
$688$			24.8789i			0.948501i
$689$	−8.89252			−0.338778
$690$	−0.179762	+	0.265116i	−0.00684342	+	0.0100928i
$691$	11.9386			0.454166			0.227083	−	0.973875i	$-0.427081\pi$
$691$	11.9386			0.454166			0.227083	+	0.973875i	$0.427081\pi$
$692$			35.4358i			1.34707i
$693$		−	21.7607i		−	0.826619i
$694$	2.09574			0.0795532
$695$	4.91651	+	3.33364i	0.186494	+	0.126452i
$696$	8.64737			0.327778
$697$		−	0.588429i		−	0.0222883i
$698$			6.22279i			0.235536i
$699$	−32.3822			−1.22481
$700$	32.6391	−	13.0029i	1.23364	−	0.491464i
$701$	−15.7112			−0.593404			−0.296702	−	0.954970i	$-0.595887\pi$
$701$	−15.7112			−0.593404			−0.296702	+	0.954970i	$0.595887\pi$
$702$			5.43530i			0.205142i
$703$		0			0
$704$	−28.4821			−1.07346
$705$	−41.1667	−	27.9131i	−1.55043	−	1.05127i
$706$	−6.11097			−0.229989
$707$			22.5174i			0.846855i
$708$		−	23.8771i		−	0.897357i
$709$	0.810620			0.0304435			0.0152217	−	0.999884i	$-0.495155\pi$
$709$	0.810620			0.0304435			0.0152217	+	0.999884i	$0.495155\pi$
$710$	−0.338927	+	0.499856i	−0.0127197	+	0.0187593i
$711$	10.7954			0.404858
$712$		−	18.4039i		−	0.689713i
$713$			1.74519i			0.0653578i
$714$	−7.70082			−0.288196
$715$	28.8718	−	42.5806i	1.07974	−	1.59242i
$716$	0.426951			0.0159559
$717$		−	36.3017i		−	1.35571i
$718$		−	11.3387i		−	0.423158i
$719$	13.4593			0.501948			0.250974	−	0.967994i	$-0.419249\pi$
$719$	13.4593			0.501948			0.250974	+	0.967994i	$0.419249\pi$
$720$	7.39971	+	5.01737i	0.275771	+	0.186987i
$721$	50.7080			1.88846
$722$		0			0
$723$			55.9421i			2.08051i
$724$	−47.2514			−1.75609
$725$	−6.33075	−	15.8911i	−0.235118	−	0.590179i
$726$	−9.14494			−0.339401
$727$			2.13941i			0.0793464i	0.999213	+	0.0396732i	$0.0126317\pi$
$727$			2.13941i			0.0793464i	−0.999213	+	0.0396732i	$0.987368\pi$
$728$			21.0167i			0.778931i
$729$	−9.78531			−0.362419
$730$	3.02786	+	2.05304i	0.112066	+	0.0759864i
$731$	−23.4548			−0.867506
$732$		−	19.4906i		−	0.720394i
$733$		−	0.353890i		−	0.0130712i	−0.999979	−	0.00653561i	$-0.997920\pi$
$733$		−	0.353890i		−	0.0130712i	0.999979	−	0.00653561i	$-0.00208036\pi$
$734$	−4.39741			−0.162311
$735$	17.1441	−	25.2845i	0.632371	−	0.932633i
$736$	0.785641			0.0289591
$737$			56.4980i			2.08113i
$738$		−	0.0682504i		−	0.00251233i
$739$	−0.530279			−0.0195066			−0.00975332	−	0.999952i	$-0.503105\pi$
$739$	−0.530279			−0.0195066			−0.00975332	+	0.999952i	$0.503105\pi$
$740$	−7.11753	+	10.4971i	−0.261646	+	0.385880i
$741$		0			0
$742$			2.27339i			0.0834588i
$743$		−	10.9210i		−	0.400654i	−0.979729	−	0.200327i	$-0.935800\pi$
$743$		−	10.9210i		−	0.400654i	0.979729	−	0.200327i	$-0.0642004\pi$
$744$	−19.9614			−0.731819
$745$	15.4565	+	10.4803i	0.566283	+	0.383968i
$746$	−7.51402			−0.275108
$747$			5.32373i			0.194785i
$748$		−	30.5605i		−	1.11740i
$749$	−64.0166			−2.33911
$750$	−1.55845	+	7.07780i	−0.0569064	+	0.258445i
$751$	−8.00460			−0.292092			−0.146046	−	0.989278i	$-0.546655\pi$
$751$	−8.00460			−0.292092			−0.146046	+	0.989278i	$0.546655\pi$
$752$			37.0842i			1.35232i
$753$			17.3699i			0.632995i
$754$	4.98412			0.181511
$755$	−15.8510	−	10.7478i	−0.576879	−	0.391153i
$756$	−26.2157			−0.953455
$757$			30.1904i			1.09729i	0.836056	+	0.548645i	$0.184856\pi$
$757$			30.1904i			1.09729i	−0.836056	+	0.548645i	$0.815144\pi$
$758$		−	10.7086i		−	0.388955i
$759$	−2.26224			−0.0821140
$760$		0			0
$761$	−0.399315			−0.0144751			−0.00723757	−	0.999974i	$-0.502304\pi$
$761$	−0.399315			−0.0144751			−0.00723757	+	0.999974i	$0.502304\pi$
$762$		−	7.72585i		−	0.279878i
$763$			50.8739i			1.84176i
$764$	16.0282			0.579880
$765$	−4.73016	+	6.97612i	−0.171019	+	0.252222i
$766$	−5.04575			−0.182310
$767$		−	28.2538i		−	1.02018i
$768$		−	17.4474i		−	0.629580i
$769$	6.52791			0.235403			0.117701	−	0.993049i	$-0.462447\pi$
$769$	6.52791			0.235403			0.117701	+	0.993049i	$0.462447\pi$
$770$	−10.8858	−	7.38113i	−0.392298	−	0.265997i
$771$	−42.8755			−1.54412
$772$			3.04550i			0.109610i
$773$		−	29.2223i		−	1.05105i	−0.850777	−	0.525527i	$-0.823868\pi$
$773$		−	29.2223i		−	1.05105i	0.850777	−	0.525527i	$-0.176132\pi$
$774$	−2.72046			−0.0977850
$775$	14.6137	+	36.6825i	0.524940	+	1.31767i
$776$	−1.69006			−0.0606696
$777$			22.5708i			0.809723i
$778$		−	0.227032i		−	0.00813949i
$779$		0			0
$780$	32.9744	+	22.3583i	1.18067	+	0.800554i
$781$	−4.26528			−0.152624
$782$			0.225153i			0.00805147i
$783$			12.7637i			0.456136i
$784$	−22.7771			−0.813466
$785$	−14.2223	+	20.9753i	−0.507616	+	0.748642i
$786$	4.91413			0.175281
$787$			43.2638i			1.54219i	0.636722	+	0.771093i	$0.280290\pi$
$787$			43.2638i			1.54219i	−0.636722	+	0.771093i	$0.719710\pi$
$788$			3.82303i			0.136190i
$789$	23.9385			0.852234
$790$	3.66175	−	5.40041i	0.130279	−	0.192138i
$791$	−15.3746			−0.546657
$792$		−	7.27715i		−	0.258582i
$793$		−	23.0632i		−	0.818999i
$794$	4.55605			0.161688
$795$	7.32278	+	4.96521i	0.259712	+	0.176098i
$796$	−9.56678			−0.339086
$797$			27.5833i			0.977050i	0.872550	+	0.488525i	$0.162465\pi$
$797$			27.5833i			0.977050i	−0.872550	+	0.488525i	$0.837535\pi$
$798$		0			0
$799$	−34.9614			−1.23684
$800$	16.5136	−	6.57874i	0.583843	−	0.232594i
$801$	−17.4613			−0.616963
$802$			10.9716i			0.387420i
$803$			25.8368i			0.911759i
$804$	−43.7520			−1.54301
$805$	−1.51310	−	1.02596i	−0.0533298	−	0.0361603i
$806$	−11.5052			−0.405254
$807$		−	26.9151i		−	0.947458i
$808$			7.53023i			0.264912i
$809$	−47.2870			−1.66252			−0.831262	−	0.555881i	$-0.812381\pi$
$809$	−47.2870			−1.66252			−0.831262	+	0.555881i	$0.812381\pi$
$810$	4.43700	−	6.54377i	0.155900	−	0.229925i
$811$	−35.1587			−1.23459			−0.617294	−	0.786733i	$-0.711771\pi$
$811$	−35.1587			−1.23459			−0.617294	+	0.786733i	$0.711771\pi$
$812$			24.0396i			0.843623i
$813$			52.5792i			1.84403i
$814$	4.74769			0.166406
$815$	5.83586	−	8.60684i	0.204421	−	0.301484i
$816$	22.3451			0.782234
$817$		0			0
$818$		−	5.84938i		−	0.204519i
$819$	19.9403			0.696770
$820$	0.644144	+	0.436761i	0.0224945	+	0.0152524i
$821$	32.1078			1.12057			0.560285	−	0.828300i	$-0.310692\pi$
$821$	32.1078			1.12057			0.560285	+	0.828300i	$0.310692\pi$
$822$			5.17658i			0.180554i
$823$			24.6481i			0.859180i	0.903024	+	0.429590i	$0.141342\pi$
$823$			24.6481i			0.859180i	−0.903024	+	0.429590i	$0.858658\pi$
$824$	16.9576			0.590748
$825$	−47.5504	+	18.9433i	−1.65549	+	0.659523i
$826$	−7.22313			−0.251325
$827$			4.29867i			0.149479i	0.997203	+	0.0747397i	$0.0238126\pi$
$827$			4.29867i			0.149479i	−0.997203	+	0.0747397i	$0.976187\pi$
$828$		−	0.492695i		−	0.0171223i
$829$	11.2729			0.391524			0.195762	−	0.980651i	$-0.437282\pi$
$829$	11.2729			0.391524			0.195762	+	0.980651i	$0.437282\pi$
$830$	2.66321	+	1.80579i	0.0924413	+	0.0626798i
$831$	−10.4540			−0.362644
$832$		−	26.0994i		−	0.904835i
$833$		−	21.4732i		−	0.744002i
$834$	1.72201			0.0596283
$835$	11.1621	−	16.4621i	0.386280	−	0.569693i
$836$		0			0
$837$		−	29.4633i		−	1.01840i
$838$		−	10.8969i		−	0.376427i
$839$	36.5388			1.26146			0.630730	−	0.776003i	$-0.282756\pi$
$839$	36.5388			1.26146			0.630730	+	0.776003i	$0.282756\pi$
$840$	11.7348	−	17.3068i	0.404891	−	0.597140i
$841$	−17.2958			−0.596408
$842$			0.0713965i			0.00246049i
$843$			3.69353i			0.127212i
$844$	7.95532			0.273833
$845$	14.9589	+	10.1429i	0.514602	+	0.348926i
$846$	−4.05509			−0.139417
$847$		−	52.1931i		−	1.79338i
$848$		−	6.59659i		−	0.226528i
$849$	38.1511			1.30934
$850$	1.88537	+	4.73255i	0.0646677	+	0.162325i
$851$	0.659916			0.0226216
$852$		−	3.30302i		−	0.113160i
$853$			13.5898i			0.465306i	0.972560	+	0.232653i	$0.0747407\pi$
$853$			13.5898i			0.465306i	−0.972560	+	0.232653i	$0.925259\pi$
$854$	−5.89616			−0.201763
$855$		0			0
$856$	−21.4083			−0.731720
$857$		−	5.85278i		−	0.199927i	−0.994991	−	0.0999637i	$-0.968127\pi$
$857$		−	5.85278i		−	0.199927i	0.994991	−	0.0999637i	$-0.0318727\pi$
$858$		−	14.9139i		−	0.509151i
$859$	20.2569			0.691157			0.345579	−	0.938390i	$-0.387683\pi$
$859$	20.2569			0.691157			0.345579	+	0.938390i	$0.387683\pi$
$860$	17.4093	−	25.6756i	0.593653	−	0.875530i
$861$	1.38504			0.0472020
$862$		−	4.23681i		−	0.144306i
$863$			5.65447i			0.192481i	0.995358	+	0.0962403i	$0.0306817\pi$
$863$			5.65447i			0.192481i	−0.995358	+	0.0962403i	$0.969318\pi$
$864$	−13.2637			−0.451239
$865$	23.4126	−	34.5293i	0.796051	−	1.17403i
$866$	−6.79509			−0.230907
$867$		−	13.6650i		−	0.464089i
$868$		−	55.4922i		−	1.88353i
$869$	46.0818			1.56322
$870$	−4.10431	−	2.78293i	−0.139149	−	0.0943500i
$871$	−51.7717			−1.75422
$872$			17.0131i			0.576138i
$873$			1.60350i			0.0542702i
$874$		0			0
$875$	−40.3953	−	8.89454i	−1.36561	−	0.300690i
$876$	−20.0079			−0.676006
$877$			57.4540i			1.94008i	0.242939	+	0.970041i	$0.421888\pi$
$877$			57.4540i			1.94008i	−0.242939	+	0.970041i	$0.578112\pi$
$878$		−	2.28981i		−	0.0772773i
$879$	0.307973			0.0103877
$880$	31.5869	+	21.4175i	1.06479	+	0.721982i
$881$	8.46121			0.285065			0.142533	−	0.989790i	$-0.454475\pi$
$881$	8.46121			0.285065			0.142533	+	0.989790i	$0.454475\pi$
$882$		−	2.49063i		−	0.0838637i
$883$			12.8839i			0.433578i	0.976218	+	0.216789i	$0.0695584\pi$
$883$			12.8839i			0.433578i	−0.976218	+	0.216789i	$0.930442\pi$
$884$	28.0039			0.941874
$885$	−15.7757	+	23.2663i	−0.530295	+	0.782088i
$886$	−10.9970			−0.369451
$887$		−	32.9290i		−	1.10565i	−0.833298	−	0.552823i	$-0.813550\pi$
$887$		−	32.9290i		−	1.10565i	0.833298	−	0.552823i	$-0.186450\pi$
$888$			7.54808i			0.253297i
$889$	44.0939			1.47886
$890$	−5.92279	+	8.73503i	−0.198532	+	0.292799i
$891$	55.8380			1.87064
$892$		−	10.1228i		−	0.338936i
$893$		0			0
$894$	5.41365			0.181060
$895$	−0.416030	−	0.282089i	−0.0139063	−	0.00942919i
$896$	−32.9777			−1.10171
$897$		−	2.07299i		−	0.0692151i
$898$			1.61502i			0.0538940i
$899$	−27.0176			−0.901087
$900$	−4.12569	−	10.3561i	−0.137523	−	0.345202i
$901$	6.21897			0.207184
$902$		−	0.291338i		−	0.00970049i
$903$		−	55.2077i		−	1.83720i
$904$	−5.14153			−0.171005
$905$	46.0427	+	31.2192i	1.53051	+	1.03776i
$906$	−5.55184			−0.184447
$907$			34.1251i			1.13311i	0.824025	+	0.566553i	$0.191723\pi$
$907$			34.1251i			1.13311i	−0.824025	+	0.566553i	$0.808277\pi$
$908$		−	9.83659i		−	0.326439i
$909$	7.14455			0.236970
$910$	6.76366	−	9.97517i	0.224213	−	0.330674i
$911$	−27.5938			−0.914222			−0.457111	−	0.889410i	$-0.651116\pi$
$911$	−27.5938			−0.914222			−0.457111	+	0.889410i	$0.651116\pi$
$912$		0			0
$913$			22.7252i			0.752094i
$914$	−12.6889			−0.419712
$915$	−12.8775	+	18.9920i	−0.425718	+	0.627857i
$916$	32.4386			1.07180
$917$			28.0465i			0.926178i
$918$		−	3.80117i		−	0.125457i
$919$	−13.1572			−0.434017			−0.217009	−	0.976170i	$-0.569630\pi$
$919$	−13.1572			−0.434017			−0.217009	+	0.976170i	$0.569630\pi$
$920$	−0.506008	−	0.343099i	−0.0166826	−	0.0113116i
$921$	−10.1115			−0.333186
$922$		−	8.40674i		−	0.276861i
$923$		−	3.90846i		−	0.128649i
$924$	71.9330			2.36642
$925$	13.8709	−	5.52595i	0.456073	−	0.181692i
$926$	−3.07404			−0.101019
$927$		−	16.0891i		−	0.528436i
$928$			12.1627i			0.399259i
$929$	23.5599			0.772975			0.386487	−	0.922295i	$-0.373688\pi$
$929$	23.5599			0.772975			0.386487	+	0.922295i	$0.373688\pi$
$930$	9.47427	+	6.42403i	0.310674	+	0.210652i
$931$		0			0
$932$		−	30.1050i		−	0.986121i
$933$			48.2683i			1.58023i
$934$	1.83492			0.0600403
$935$	−20.1914	+	29.7787i	−0.660330	+	0.973867i
$936$	6.66838			0.217963
$937$			35.9997i			1.17606i	0.808839	+	0.588030i	$0.200096\pi$
$937$			35.9997i			1.17606i	−0.808839	+	0.588030i	$0.799904\pi$
$938$			13.2355i			0.432156i
$939$	−18.1673			−0.592868
$940$	25.9501	−	38.2717i	0.846399	−	1.24828i
$941$	41.8515			1.36432			0.682160	−	0.731203i	$-0.261041\pi$
$941$	41.8515			1.36432			0.682160	+	0.731203i	$0.261041\pi$
$942$			7.34662i			0.239366i
$943$		−	0.0404952i		−	0.00131871i
$944$	20.9590			0.682158
$945$	25.5451	+	17.3208i	0.830981	+	0.563446i
$946$	−11.6127			−0.377562
$947$		−	3.63656i		−	0.118172i	−0.998253	−	0.0590861i	$-0.981181\pi$
$947$		−	3.63656i		−	0.118172i	0.998253	−	0.0590861i	$-0.0188187\pi$
$948$			35.6857i			1.15902i
$949$	−23.6754			−0.768535
$950$		0			0
$951$	−60.4680			−1.96081
$952$		−	14.6980i		−	0.476365i
$953$		−	10.7543i		−	0.348366i	−0.984713	−	0.174183i	$-0.944272\pi$
$953$		−	10.7543i		−	0.348366i	0.984713	−	0.174183i	$-0.0557284\pi$
$954$	0.721324			0.0233537
$955$	−15.6182	−	10.5899i	−0.505393	−	0.342681i
$956$	33.7488			1.09151
$957$		−	35.0221i		−	1.13210i
$958$			0.562218i			0.0181644i
$959$	−29.5444			−0.954039
$960$	−14.5728	+	21.4923i	−0.470336	+	0.693660i
$961$	31.3666			1.01183
$962$			4.35052i			0.140266i
$963$			20.3118i			0.654538i
$964$	−52.0080			−1.67506
$965$	2.01217	−	2.96759i	0.0647741	−	0.0955301i
$966$	−0.529964			−0.0170513
$967$		−	18.7666i		−	0.603493i	−0.953388	−	0.301747i	$-0.902430\pi$
$967$		−	18.7666i		−	0.603493i	0.953388	−	0.301747i	$-0.0975696\pi$
$968$		−	17.4543i		−	0.561002i
$969$		0			0
$970$	0.802154	+	0.543900i	0.0257556	+	0.0174636i
$971$	−38.4930			−1.23530			−0.617650	−	0.786453i	$-0.711915\pi$
$971$	−38.4930			−1.23530			−0.617650	+	0.786453i	$0.711915\pi$
$972$			21.9827i			0.705096i
$973$			9.82805i			0.315073i
$974$	5.14426			0.164833
$975$	−17.3586	−	43.5726i	−0.555921	−	1.39544i
$976$	17.1086			0.547633
$977$		−	21.7651i		−	0.696328i	−0.937434	−	0.348164i	$-0.886805\pi$
$977$		−	21.7651i		−	0.696328i	0.937434	−	0.348164i	$-0.113195\pi$
$978$		−	3.01455i		−	0.0963946i
$979$	−74.5361			−2.38218
$980$	23.5064	+	15.9385i	0.750884	+	0.509137i
$981$	16.1418			0.515367
$982$		−	5.86569i		−	0.187182i
$983$			32.9796i			1.05189i	0.850520	+	0.525943i	$0.176288\pi$
$983$			32.9796i			1.05189i	−0.850520	+	0.525943i	$0.823712\pi$
$984$	0.463182			0.0147657
$985$	2.52590	−	3.72524i	0.0804817	−	0.118696i
$986$	−3.48564			−0.111005
$987$		−	82.2918i		−	2.61938i
$988$		0			0
$989$	−1.61414			−0.0513266
$990$	−2.34196	+	3.45396i	−0.0744322	+	0.109774i
$991$	−44.9400			−1.42757			−0.713783	−	0.700367i	$-0.753020\pi$
$991$	−44.9400			−1.42757			−0.713783	+	0.700367i	$0.753020\pi$
$992$		−	28.0759i		−	0.891412i
$993$		−	52.8862i		−	1.67829i
$994$	−0.999208			−0.0316929
$995$	9.32205	+	6.32082i	0.295529	+	0.200383i
$996$	−17.5983			−0.557625
$997$		−	1.52970i		−	0.0484462i	−0.999707	−	0.0242231i	$-0.992289\pi$
$997$		−	1.52970i		−	0.0484462i	0.999707	−	0.0242231i	$-0.00771120\pi$
$998$		−	5.48412i		−	0.173597i
$999$	−11.1411			−0.352488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.i.1084.8	✓	16
5.2	odd	4		9025.2.a.cl.1.9		16
5.3	odd	4		9025.2.a.cl.1.8		16
5.4	even	2	inner	1805.2.b.i.1084.9	yes	16
19.18	odd	2		1805.2.b.j.1084.9	yes	16
95.18	even	4		9025.2.a.ck.1.9		16
95.37	even	4		9025.2.a.ck.1.8		16
95.94	odd	2		1805.2.b.j.1084.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.i.1084.8	✓	16	1.1	even	1	trivial
1805.2.b.i.1084.9	yes	16	5.4	even	2	inner
1805.2.b.j.1084.8	yes	16	95.94	odd	2
1805.2.b.j.1084.9	yes	16	19.18	odd	2
9025.2.a.ck.1.8		16	95.37	even	4
9025.2.a.ck.1.9		16	95.18	even	4
9025.2.a.cl.1.8		16	5.3	odd	4
9025.2.a.cl.1.9		16	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.317290i q^{2} -2.04300i q^{3} +1.89933 q^{4} +(-1.85074 - 1.25489i) q^{5} -0.648223 q^{6} -3.69961i q^{7} -1.23722i q^{8} -1.17385 q^{9} +O(q^{10})\)	\(q-0.317290i q^{2} -2.04300i q^{3} +1.89933 q^{4} +(-1.85074 - 1.25489i) q^{5} -0.648223 q^{6} -3.69961i q^{7} -1.23722i q^{8} -1.17385 q^{9} +(-0.398165 + 0.587221i) q^{10} -5.01076 q^{11} -3.88033i q^{12} -4.59159i q^{13} -1.17385 q^{14} +(-2.56375 + 3.78106i) q^{15} +3.40610 q^{16} +3.21112i q^{17} +0.372450i q^{18} +(-3.51516 - 2.38345i) q^{20} -7.55831 q^{21} +1.58986i q^{22} +0.220987i q^{23} -2.52763 q^{24} +(1.85048 + 4.64497i) q^{25} -1.45686 q^{26} -3.73083i q^{27} -7.02678i q^{28} -3.42114 q^{29} +(1.19969 + 0.813451i) q^{30} +7.89725 q^{31} -3.55515i q^{32} +10.2370i q^{33} +1.01885 q^{34} +(-4.64262 + 6.84702i) q^{35} -2.22952 q^{36} -2.98622i q^{37} -9.38061 q^{39} +(-1.55258 + 2.28977i) q^{40} -0.183247 q^{41} +2.39817i q^{42} +7.30424i q^{43} -9.51707 q^{44} +(2.17249 + 1.47306i) q^{45} +0.0701168 q^{46} +10.8876i q^{47} -6.95866i q^{48} -6.68714 q^{49} +(1.47380 - 0.587138i) q^{50} +6.56032 q^{51} -8.72092i q^{52} -1.93670i q^{53} -1.18375 q^{54} +(9.27362 + 6.28797i) q^{55} -4.57722 q^{56} +1.08549i q^{58} +6.15338 q^{59} +(-4.86940 + 7.18148i) q^{60} +5.02293 q^{61} -2.50572i q^{62} +4.34279i q^{63} +5.68419 q^{64} +(-5.76195 + 8.49783i) q^{65} +3.24809 q^{66} -11.2753i q^{67} +6.09897i q^{68} +0.451476 q^{69} +(2.17249 + 1.47306i) q^{70} +0.851223 q^{71} +1.45230i q^{72} -5.15625i q^{73} -0.947498 q^{74} +(9.48967 - 3.78053i) q^{75} +18.5379i q^{77} +2.97637i q^{78} -9.19657 q^{79} +(-6.30381 - 4.27429i) q^{80} -11.1436 q^{81} +0.0581424i q^{82} -4.53528i q^{83} -14.3557 q^{84} +(4.02961 - 5.94295i) q^{85} +2.31756 q^{86} +6.98938i q^{87} +6.19939i q^{88} +14.8752 q^{89} +(0.467385 - 0.689308i) q^{90} -16.9871 q^{91} +0.419726i q^{92} -16.1341i q^{93} +3.45452 q^{94} -7.26317 q^{96} -1.36602i q^{97} +2.12176i q^{98} +5.88187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 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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