LMFDB - Embedded newform 1805.2.b.l.1084.10

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:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.10
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.l.1084.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.449373i q^{2} -1.95684i q^{3} +1.79806 q^{4} +(1.87757 + 1.21438i) q^{5} -0.879352 q^{6} +2.06079i q^{7} -1.70675i q^{8} -0.829224 q^{9} +(0.545709 - 0.843732i) q^{10} -2.30599 q^{11} -3.51852i q^{12} +4.39611i q^{13} +0.926065 q^{14} +(2.37634 - 3.67411i) q^{15} +2.82916 q^{16} +5.47185i q^{17} +0.372631i q^{18} +(3.37600 + 2.18353i) q^{20} +4.03264 q^{21} +1.03625i q^{22} -5.81755i q^{23} -3.33983 q^{24} +(2.05058 + 4.56017i) q^{25} +1.97549 q^{26} -4.24786i q^{27} +3.70544i q^{28} +5.50466 q^{29} +(-1.65105 - 1.06786i) q^{30} -0.757832 q^{31} -4.68485i q^{32} +4.51245i q^{33} +2.45890 q^{34} +(-2.50258 + 3.86929i) q^{35} -1.49100 q^{36} -6.22555i q^{37} +8.60248 q^{39} +(2.07264 - 3.20455i) q^{40} +6.53829 q^{41} -1.81216i q^{42} +3.16680i q^{43} -4.14632 q^{44} +(-1.55693 - 1.00699i) q^{45} -2.61425 q^{46} -6.36116i q^{47} -5.53621i q^{48} +2.75314 q^{49} +(2.04922 - 0.921474i) q^{50} +10.7075 q^{51} +7.90448i q^{52} +3.85028i q^{53} -1.90888 q^{54} +(-4.32967 - 2.80034i) q^{55} +3.51725 q^{56} -2.47365i q^{58} +2.55023 q^{59} +(4.27282 - 6.60629i) q^{60} +9.94010 q^{61} +0.340550i q^{62} -1.70886i q^{63} +3.55308 q^{64} +(-5.33853 + 8.25402i) q^{65} +2.02778 q^{66} +1.70269i q^{67} +9.83874i q^{68} -11.3840 q^{69} +(1.73876 + 1.12459i) q^{70} -9.85909 q^{71} +1.41528i q^{72} +10.2167i q^{73} -2.79760 q^{74} +(8.92352 - 4.01265i) q^{75} -4.75216i q^{77} -3.86572i q^{78} +2.41187 q^{79} +(5.31196 + 3.43567i) q^{80} -10.8001 q^{81} -2.93813i q^{82} -7.06253i q^{83} +7.25095 q^{84} +(-6.64489 + 10.2738i) q^{85} +1.42307 q^{86} -10.7717i q^{87} +3.93574i q^{88} -2.33452 q^{89} +(-0.452514 + 0.699642i) q^{90} -9.05946 q^{91} -10.4603i q^{92} +1.48296i q^{93} -2.85854 q^{94} -9.16749 q^{96} +6.81539i q^{97} -1.23719i q^{98} +1.91218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 + 6 * q^10 + 12 * q^11 + 24 * q^14 + 9 * q^15 + 6 * q^16 + 21 * q^20 - 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 + 36 * q^29 - 18 * q^30 - 42 * q^31 + 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 - 12 * q^40 - 60 * q^41 + 30 * q^44 + 9 * q^45 - 6 * q^46 - 12 * q^49 - 18 * q^50 - 30 * q^51 + 24 * q^54 + 33 * q^55 - 18 * q^56 + 60 * q^59 + 42 * q^60 + 30 * q^61 - 18 * q^65 + 36 * q^66 + 66 * q^69 - 9 * q^70 - 96 * q^71 - 24 * q^74 - 36 * q^75 + 72 * q^79 - 42 * q^80 - 96 * q^81 - 54 * q^84 - 27 * q^85 - 108 * q^86 + 84 * q^89 + 93 * q^90 - 96 * q^91 + 36 * q^94 - 120 * q^96

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 $

$2$		−	0.449373i		−	0.317755i	−0.987298	−	0.158877i	$-0.949213\pi$
$2$		−	0.449373i		−	0.317755i	0.987298	−	0.158877i	$-0.0507875\pi$
$3$		−	1.95684i		−	1.12978i	−0.825165	−	0.564891i	$-0.808918\pi$
$3$		−	1.95684i		−	1.12978i	0.825165	−	0.564891i	$-0.191082\pi$
$4$	1.79806			0.899032
$5$	1.87757	+	1.21438i	0.839677	+	0.543086i
$5$	1.87757	+	1.21438i	0.839677	+	0.543086i
$6$	−0.879352			−0.358994
$7$			2.06079i			0.778906i	0.921046	+	0.389453i	$0.127336\pi$
$7$			2.06079i			0.778906i	−0.921046	+	0.389453i	$0.872664\pi$
$8$		−	1.70675i		−	0.603427i
$9$	−0.829224			−0.276408
$10$	0.545709	−	0.843732i	0.172568	−	0.266811i
$11$	−2.30599			−0.695282			−0.347641	−	0.937628i	$-0.613017\pi$
$11$	−2.30599			−0.695282			−0.347641	+	0.937628i	$0.613017\pi$
$12$		−	3.51852i		−	1.01571i
$13$			4.39611i			1.21926i	0.792686	+	0.609630i	$0.208682\pi$
$13$			4.39611i			1.21926i	−0.792686	+	0.609630i	$0.791318\pi$
$14$	0.926065			0.247501
$15$	2.37634	−	3.67411i	0.613569	−	0.948652i
$16$	2.82916			0.707290
$17$			5.47185i			1.32712i	0.748123	+	0.663560i	$0.230955\pi$
$17$			5.47185i			1.32712i	−0.748123	+	0.663560i	$0.769045\pi$
$18$			0.372631i			0.0878299i
$19$		0			0
$19$		0			0
$20$	3.37600	+	2.18353i	0.754896	+	0.488252i
$21$	4.03264			0.879994
$22$			1.03625i			0.220929i
$23$		−	5.81755i		−	1.21304i	−0.795067	−	0.606522i	$-0.792564\pi$
$23$		−	5.81755i		−	1.21304i	0.795067	−	0.606522i	$-0.207436\pi$
$24$	−3.33983			−0.681741
$25$	2.05058	+	4.56017i	0.410115	+	0.912034i
$26$	1.97549			0.387426
$27$		−	4.24786i		−	0.817502i
$28$			3.70544i			0.700262i
$29$	5.50466			1.02219			0.511095	−	0.859524i	$-0.329240\pi$
$29$	5.50466			1.02219			0.511095	+	0.859524i	$0.329240\pi$
$30$	−1.65105	−	1.06786i	−0.301439	−	0.194965i
$31$	−0.757832			−0.136111			−0.0680553	−	0.997682i	$-0.521679\pi$
$31$	−0.757832			−0.136111			−0.0680553	+	0.997682i	$0.521679\pi$
$32$		−	4.68485i		−	0.828171i
$33$			4.51245i			0.785517i
$34$	2.45890			0.421699
$35$	−2.50258	+	3.86929i	−0.423013	+	0.654030i
$36$	−1.49100			−0.248499
$37$		−	6.22555i		−	1.02347i	−0.859142	−	0.511737i	$-0.829002\pi$
$37$		−	6.22555i		−	1.02347i	0.859142	−	0.511737i	$-0.170998\pi$
$38$		0			0
$39$	8.60248			1.37750
$40$	2.07264	−	3.20455i	0.327713	−	0.506683i
$41$	6.53829			1.02111			0.510554	−	0.859845i	$-0.329440\pi$
$41$	6.53829			1.02111			0.510554	+	0.859845i	$0.329440\pi$
$42$		−	1.81216i		−	0.279623i
$43$			3.16680i			0.482932i	0.970409	+	0.241466i	$0.0776282\pi$
$43$			3.16680i			0.482932i	−0.970409	+	0.241466i	$0.922372\pi$
$44$	−4.14632			−0.625081
$45$	−1.55693	−	1.00699i	−0.232093	−	0.150113i
$46$	−2.61425			−0.385451
$47$		−	6.36116i		−	0.927871i	−0.885869	−	0.463936i	$-0.846437\pi$
$47$		−	6.36116i		−	0.927871i	0.885869	−	0.463936i	$-0.153563\pi$
$48$		−	5.53621i		−	0.799084i
$49$	2.75314			0.393305
$50$	2.04922	−	0.921474i	0.289803	−	0.130316i
$51$	10.7075			1.49936
$52$			7.90448i			1.09615i
$53$			3.85028i			0.528876i	0.964403	+	0.264438i	$0.0851865\pi$
$53$			3.85028i			0.528876i	−0.964403	+	0.264438i	$0.914813\pi$
$54$	−1.90888			−0.259765
$55$	−4.32967	−	2.80034i	−0.583812	−	0.377598i
$56$	3.51725			0.470013
$57$		0			0
$58$		−	2.47365i		−	0.324806i
$59$	2.55023			0.332012			0.166006	−	0.986125i	$-0.446913\pi$
$59$	2.55023			0.332012			0.166006	+	0.986125i	$0.446913\pi$
$60$	4.27282	−	6.60629i	0.551618	−	0.852869i
$61$	9.94010			1.27270			0.636350	−	0.771401i	$-0.280444\pi$
$61$	9.94010			1.27270			0.636350	+	0.771401i	$0.280444\pi$
$62$			0.340550i			0.0432498i
$63$		−	1.70886i		−	0.215296i
$64$	3.55308			0.444135
$65$	−5.33853	+	8.25402i	−0.662163	+	1.02378i
$66$	2.02778			0.249602
$67$			1.70269i			0.208017i	0.994576	+	0.104009i	$0.0331669\pi$
$67$			1.70269i			0.208017i	−0.994576	+	0.104009i	$0.966833\pi$
$68$			9.83874i			1.19312i
$69$	−11.3840			−1.37048
$70$	1.73876	+	1.12459i	0.207821	+	0.134414i
$71$	−9.85909			−1.17006			−0.585029	−	0.811012i	$-0.698917\pi$
$71$	−9.85909			−1.17006			−0.585029	+	0.811012i	$0.698917\pi$
$72$			1.41528i			0.166792i
$73$			10.2167i			1.19577i	0.801581	+	0.597886i	$0.203993\pi$
$73$			10.2167i			1.19577i	−0.801581	+	0.597886i	$0.796007\pi$
$74$	−2.79760			−0.325214
$75$	8.92352	−	4.01265i	1.03040	−	0.463341i
$76$		0			0
$77$		−	4.75216i		−	0.541559i
$78$		−	3.86572i		−	0.437707i
$79$	2.41187			0.271357			0.135679	−	0.990753i	$-0.456679\pi$
$79$	2.41187			0.271357			0.135679	+	0.990753i	$0.456679\pi$
$80$	5.31196	+	3.43567i	0.593895	+	0.384119i
$81$	−10.8001			−1.20001
$82$		−	2.93813i		−	0.324462i
$83$		−	7.06253i		−	0.775213i	−0.921825	−	0.387607i	$-0.873302\pi$
$83$		−	7.06253i		−	0.775213i	0.921825	−	0.387607i	$-0.126698\pi$
$84$	7.25095			0.791143
$85$	−6.64489	+	10.2738i	−0.720740	+	1.11435i
$86$	1.42307			0.153454
$87$		−	10.7717i		−	1.15485i
$88$			3.93574i			0.419552i
$89$	−2.33452			−0.247458			−0.123729	−	0.992316i	$-0.539485\pi$
$89$	−2.33452			−0.247458			−0.123729	+	0.992316i	$0.539485\pi$
$90$	−0.452514	+	0.699642i	−0.0476992	+	0.0737488i
$91$	−9.05946			−0.949689
$92$		−	10.4603i		−	1.09056i
$93$			1.48296i			0.153775i
$94$	−2.85854			−0.294836
$95$		0			0
$96$	−9.16749			−0.935653
$97$			6.81539i			0.691998i	0.938235	+	0.345999i	$0.112460\pi$
$97$			6.81539i			0.691998i	−0.938235	+	0.345999i	$0.887540\pi$
$98$		−	1.23719i		−	0.124975i
$99$	1.91218			0.192181
$100$	3.68706	+	8.19947i	0.368706	+	0.819947i
$101$	12.1976			1.21370			0.606851	−	0.794816i	$-0.292433\pi$
$101$	12.1976			1.21370			0.606851	+	0.794816i	$0.292433\pi$
$102$		−	4.81168i		−	0.476428i
$103$			12.9197i			1.27302i	0.771269	+	0.636509i	$0.219622\pi$
$103$			12.9197i			1.27302i	−0.771269	+	0.636509i	$0.780378\pi$
$104$	7.50304			0.735734
$105$	7.57159	+	4.89715i	0.738911	+	0.477913i
$106$	1.73021			0.168053
$107$			15.1729i			1.46682i	0.679785	+	0.733412i	$0.262073\pi$
$107$			15.1729i			1.46682i	−0.679785	+	0.733412i	$0.737927\pi$
$108$		−	7.63793i		−	0.734960i
$109$	−19.1794			−1.83705			−0.918527	−	0.395359i	$-0.870620\pi$
$109$	−19.1794			−1.83705			−0.918527	+	0.395359i	$0.870620\pi$
$110$	−1.25840	+	1.94564i	−0.119984	+	0.185509i
$111$	−12.1824			−1.15630
$112$			5.83031i			0.550913i
$113$		−	1.91146i		−	0.179815i	−0.995950	−	0.0899075i	$-0.971343\pi$
$113$		−	1.91146i		−	0.179815i	0.995950	−	0.0899075i	$-0.0286571\pi$
$114$		0			0
$115$	7.06470	−	10.9229i	0.658787	−	1.01856i
$116$	9.89773			0.918981
$117$		−	3.64535i		−	0.337013i
$118$		−	1.14601i		−	0.105498i
$119$	−11.2764			−1.03370
$120$	−6.27079	−	4.05582i	−0.572442	−	0.370244i
$121$	−5.68241			−0.516583
$122$		−	4.46682i		−	0.404406i
$123$		−	12.7944i		−	1.15363i
$124$	−1.36263			−0.122368
$125$	−1.68766	+	11.0522i	−0.150949	+	0.988542i
$126$	−0.767915			−0.0684113
$127$		−	21.2359i		−	1.88438i	−0.335077	−	0.942191i	$-0.608762\pi$
$127$		−	21.2359i		−	1.88438i	0.335077	−	0.942191i	$-0.391238\pi$
$128$		−	10.9663i		−	0.969297i
$129$	6.19692			0.545608
$130$	3.70913	+	2.39899i	0.325313	+	0.210406i
$131$	−1.67271			−0.146146			−0.0730728	−	0.997327i	$-0.523281\pi$
$131$	−1.67271			−0.146146			−0.0730728	+	0.997327i	$0.523281\pi$
$132$			8.11368i			0.706205i
$133$		0			0
$134$	0.765145			0.0660984
$135$	5.15851	−	7.97568i	0.443974	−	0.686437i
$136$	9.33908			0.800819
$137$		−	17.2880i		−	1.47701i	−0.674247	−	0.738506i	$-0.735532\pi$
$137$		−	17.2880i		−	1.47701i	0.674247	−	0.738506i	$-0.264468\pi$
$138$			5.11567i			0.435475i
$139$	−12.3265			−1.04552			−0.522761	−	0.852479i	$-0.675098\pi$
$139$	−12.3265			−1.04552			−0.522761	+	0.852479i	$0.675098\pi$
$140$	−4.49980	+	6.95723i	−0.380302	+	0.587994i
$141$	−12.4478			−1.04829
$142$			4.43041i			0.371792i
$143$		−	10.1374i		−	0.847730i
$144$	−2.34601			−0.195501
$145$	10.3354	+	6.68473i	0.858309	+	0.555137i
$146$	4.59111			0.379963
$147$		−	5.38745i		−	0.444349i
$148$		−	11.1939i		−	0.920136i
$149$	−4.35901			−0.357104			−0.178552	−	0.983930i	$-0.557141\pi$
$149$	−4.35901			−0.357104			−0.178552	+	0.983930i	$0.557141\pi$
$150$	−1.80318	−	4.00999i	−0.147229	−	0.327414i
$151$	−4.44628			−0.361833			−0.180917	−	0.983498i	$-0.557906\pi$
$151$	−4.44628			−0.361833			−0.180917	+	0.983498i	$0.557906\pi$
$152$		0			0
$153$		−	4.53739i		−	0.366826i
$154$	−2.13550			−0.172083
$155$	−1.42289	−	0.920294i	−0.114289	−	0.0739198i
$156$	15.4678			1.23841
$157$		−	19.8432i		−	1.58366i	−0.610740	−	0.791831i	$-0.709128\pi$
$157$		−	19.8432i		−	1.58366i	0.610740	−	0.791831i	$-0.290872\pi$
$158$		−	1.08383i		−	0.0862250i
$159$	7.53438			0.597515
$160$	5.68917	−	8.79615i	0.449768	−	0.695397i
$161$	11.9888			0.944847
$162$			4.85326i			0.381308i
$163$		−	1.28088i		−	0.100326i	−0.998741	−	0.0501632i	$-0.984026\pi$
$163$		−	1.28088i		−	0.100326i	0.998741	−	0.0501632i	$-0.0159742\pi$
$164$	11.7563			0.918009
$165$	−5.47982	+	8.47247i	−0.426603	+	0.659581i
$166$	−3.17371			−0.246328
$167$		−	8.03589i		−	0.621836i	−0.950437	−	0.310918i	$-0.899364\pi$
$167$		−	8.03589i		−	0.621836i	0.950437	−	0.310918i	$-0.100636\pi$
$168$		−	6.88270i		−	0.531012i
$169$	−6.32574			−0.486595
$170$	4.61678	+	2.98604i	0.354091	+	0.229019i
$171$		0			0
$172$			5.69410i			0.434171i
$173$		−	2.65910i		−	0.202167i	−0.994878	−	0.101084i	$-0.967769\pi$
$173$		−	2.65910i		−	0.202167i	0.994878	−	0.101084i	$-0.0322310\pi$
$174$	−4.84053			−0.366960
$175$	−9.39756	+	4.22581i	−0.710389	+	0.319441i
$176$	−6.52401			−0.491766
$177$		−	4.99040i		−	0.375101i
$178$			1.04907i			0.0786311i
$179$	8.10201			0.605572			0.302786	−	0.953059i	$-0.402083\pi$
$179$	8.10201			0.605572			0.302786	+	0.953059i	$0.402083\pi$
$180$	−2.79946	−	1.81063i	−0.208659	−	0.134957i
$181$	−21.5023			−1.59826			−0.799128	−	0.601161i	$-0.794705\pi$
$181$	−21.5023			−1.59826			−0.799128	+	0.601161i	$0.794705\pi$
$182$			4.07108i			0.301768i
$183$		−	19.4512i		−	1.43787i
$184$	−9.92910			−0.731983
$185$	7.56017	−	11.6889i	0.555835	−	0.859388i
$186$	0.666401			0.0488629
$187$		−	12.6180i		−	0.922722i
$188$		−	11.4378i		−	0.834186i
$189$	8.75396			0.636757
$190$		0			0
$191$	−19.5939			−1.41777			−0.708884	−	0.705326i	$-0.750801\pi$
$191$	−19.5939			−1.41777			−0.708884	+	0.705326i	$0.750801\pi$
$192$		−	6.95280i		−	0.501775i
$193$		−	0.483357i		−	0.0347928i	−0.999849	−	0.0173964i	$-0.994462\pi$
$193$		−	0.483357i		−	0.0347928i	0.999849	−	0.0173964i	$-0.00553773\pi$
$194$	3.06265			0.219886
$195$	16.1518	+	10.4467i	1.15665	+	0.748100i
$196$	4.95031			0.353594
$197$			1.26189i			0.0899060i	0.998989	+	0.0449530i	$0.0143138\pi$
$197$			1.26189i			0.0899060i	−0.998989	+	0.0449530i	$0.985686\pi$
$198$		−	0.859283i		−	0.0610666i
$199$	−20.6554			−1.46423			−0.732113	−	0.681183i	$-0.761466\pi$
$199$	−20.6554			−1.46423			−0.732113	+	0.681183i	$0.761466\pi$
$200$	7.78306	−	3.49982i	0.550345	−	0.247474i
$201$	3.33190			0.235014
$202$		−	5.48125i		−	0.385660i
$203$			11.3440i			0.796190i
$204$	19.2528			1.34797
$205$	12.2761	+	7.93995i	0.857402	+	0.554550i
$206$	5.80578			0.404508
$207$			4.82405i			0.335295i
$208$			12.4373i			0.862371i
$209$		0			0
$210$	2.20065	−	3.40247i	0.151859	−	0.234793i
$211$	−7.01196			−0.482723			−0.241361	−	0.970435i	$-0.577594\pi$
$211$	−7.01196			−0.482723			−0.241361	+	0.970435i	$0.577594\pi$
$212$			6.92305i			0.475477i
$213$			19.2927i			1.32191i
$214$	6.81831			0.466090
$215$	−3.84569	+	5.94590i	−0.262274	+	0.405507i
$216$	−7.25003			−0.493302
$217$		−	1.56173i		−	0.106017i
$218$			8.61871i			0.583733i
$219$	19.9924			1.35096
$220$	−7.78502	−	5.03519i	−0.524866	−	0.339473i
$221$	−24.0548			−1.61810
$222$			5.47445i			0.367421i
$223$			19.4374i			1.30162i	0.759239	+	0.650812i	$0.225571\pi$
$223$			19.4374i			1.30162i	−0.759239	+	0.650812i	$0.774429\pi$
$224$	9.65449			0.645068
$225$	−1.70039	−	3.78140i	−0.113359	−	0.252093i
$226$	−0.858959			−0.0571371
$227$		−	6.53998i		−	0.434074i	−0.976163	−	0.217037i	$-0.930361\pi$
$227$		−	6.53998i		−	0.434074i	0.976163	−	0.217037i	$-0.0696392\pi$
$228$		0			0
$229$	20.4005			1.34810			0.674052	−	0.738684i	$-0.264552\pi$
$229$	20.4005			1.34810			0.674052	+	0.738684i	$0.264552\pi$
$230$	−4.90846	−	3.17469i	−0.323654	−	0.209333i
$231$	−9.29923			−0.611844
$232$		−	9.39507i		−	0.616816i
$233$		−	12.0490i		−	0.789357i	−0.918819	−	0.394679i	$-0.870856\pi$
$233$		−	12.0490i		−	0.789357i	0.918819	−	0.394679i	$-0.129144\pi$
$234$	−1.63812			−0.107088
$235$	7.72485	−	11.9436i	0.503914	−	0.779112i
$236$	4.58548			0.298489
$237$		−	4.71965i		−	0.306574i
$238$			5.06729i			0.328464i
$239$	6.12499			0.396193			0.198096	−	0.980183i	$-0.436524\pi$
$239$	6.12499			0.396193			0.198096	+	0.980183i	$0.436524\pi$
$240$	6.72305	−	10.3947i	0.433971	−	0.670972i
$241$	7.27309			0.468501			0.234250	−	0.972176i	$-0.424736\pi$
$241$	7.27309			0.468501			0.234250	+	0.972176i	$0.424736\pi$
$242$			2.55352i			0.164147i
$243$			8.39040i			0.538244i
$244$	17.8729			1.14420
$245$	5.16922	+	3.34335i	0.330249	+	0.213598i
$246$	−5.74945			−0.366572
$247$		0			0
$248$			1.29343i			0.0821328i
$249$	−13.8202			−0.875822
$250$	4.96658	+	0.758388i	0.314114	+	0.0479647i
$251$	−24.1866			−1.52664			−0.763321	−	0.646019i	$-0.776433\pi$
$251$	−24.1866			−1.52664			−0.763321	+	0.646019i	$0.776433\pi$
$252$		−	3.07263i		−	0.193558i
$253$			13.4152i			0.843407i
$254$	−9.54285			−0.598771
$255$	20.1042	+	13.0030i	1.25897	+	0.814279i
$256$	2.17817			0.136136
$257$		−	12.2379i		−	0.763382i	−0.924290	−	0.381691i	$-0.875342\pi$
$257$		−	12.2379i		−	0.763382i	0.924290	−	0.381691i	$-0.124658\pi$
$258$		−	2.78473i		−	0.173370i
$259$	12.8296			0.797191
$260$	−9.59902	+	14.8412i	−0.595306	+	0.920415i
$261$	−4.56459			−0.282541
$262$			0.751673i			0.0464385i
$263$			12.3859i			0.763746i	0.924215	+	0.381873i	$0.124721\pi$
$263$			12.3859i			0.763746i	−0.924215	+	0.381873i	$0.875279\pi$
$264$	7.70162			0.474002
$265$	−4.67569	+	7.22919i	−0.287225	+	0.444085i
$266$		0			0
$267$			4.56828i			0.279574i
$268$			3.06155i			0.187014i
$269$	−4.93880			−0.301124			−0.150562	−	0.988601i	$-0.548108\pi$
$269$	−4.93880			−0.301124			−0.150562	+	0.988601i	$0.548108\pi$
$270$	−3.58406	−	2.31810i	−0.218119	−	0.141075i
$271$	−6.90194			−0.419263			−0.209631	−	0.977780i	$-0.567226\pi$
$271$	−6.90194			−0.419263			−0.209631	+	0.977780i	$0.567226\pi$
$272$			15.4808i			0.938658i
$273$			17.7279i			1.07294i
$274$	−7.76876			−0.469328
$275$	−4.72860	−	10.5157i	−0.285146	−	0.634121i
$276$	−20.4692			−1.23210
$277$		−	3.96325i		−	0.238129i	−0.992887	−	0.119064i	$-0.962011\pi$
$277$		−	3.96325i		−	0.238129i	0.992887	−	0.119064i	$-0.0379895\pi$
$278$			5.53921i			0.332220i
$279$	0.628412			0.0376221
$280$	6.60391	+	4.27127i	0.394659	+	0.255257i
$281$	−31.1993			−1.86119			−0.930597	−	0.366045i	$-0.880711\pi$
$281$	−31.1993			−1.86119			−0.930597	+	0.366045i	$0.880711\pi$
$282$			5.59370i			0.333100i
$283$		−	10.6270i		−	0.631711i	−0.948807	−	0.315855i	$-0.897709\pi$
$283$		−	10.6270i		−	0.631711i	0.948807	−	0.315855i	$-0.102291\pi$
$284$	−17.7273			−1.05192
$285$		0			0
$286$	−4.55546			−0.269370
$287$			13.4741i			0.795348i
$288$			3.88478i			0.228913i
$289$	−12.9412			−0.761246
$290$	3.00394	−	4.64446i	0.176397	−	0.272732i
$291$	13.3366			0.781807
$292$			18.3703i			1.07504i
$293$		−	19.6263i		−	1.14658i	−0.819353	−	0.573289i	$-0.805667\pi$
$293$		−	19.6263i		−	1.14658i	0.819353	−	0.573289i	$-0.194333\pi$
$294$	−2.42097			−0.141194
$295$	4.78825	+	3.09695i	0.278783	+	0.180311i
$296$	−10.6255			−0.617592
$297$			9.79553i			0.568394i
$298$			1.95882i			0.113472i
$299$	25.5746			1.47902
$300$	16.0451	−	7.21500i	0.926362	−	0.416558i
$301$	−6.52611			−0.376159
$302$			1.99804i			0.114974i
$303$		−	23.8687i		−	1.37122i
$304$		0			0
$305$	18.6633	+	12.0710i	1.06866	+	0.691185i
$306$	−2.03898			−0.116561
$307$			22.6258i			1.29132i	0.763623	+	0.645662i	$0.223419\pi$
$307$			22.6258i			1.29132i	−0.763623	+	0.645662i	$0.776581\pi$
$308$		−	8.54469i		−	0.486879i
$309$	25.2818			1.43823
$310$	−0.413556	+	0.639407i	−0.0234884	+	0.0363159i
$311$	24.8577			1.40955			0.704776	−	0.709430i	$-0.251047\pi$
$311$	24.8577			1.40955			0.704776	+	0.709430i	$0.251047\pi$
$312$		−	14.6823i		−	0.831219i
$313$			22.2026i			1.25497i	0.778630	+	0.627484i	$0.215915\pi$
$313$			22.2026i			1.25497i	−0.778630	+	0.627484i	$0.784085\pi$
$314$	−8.91701			−0.503216
$315$	2.07520	−	3.20851i	0.116924	−	0.180779i
$316$	4.33670			0.243959
$317$			2.03957i			0.114554i	0.998358	+	0.0572769i	$0.0182418\pi$
$317$			2.03957i			0.114554i	−0.998358	+	0.0572769i	$0.981758\pi$
$318$		−	3.38575i		−	0.189863i
$319$	−12.6937			−0.710710
$320$	6.67117	+	4.31478i	0.372930	+	0.241203i
$321$	29.6910			1.65719
$322$		−	5.38743i		−	0.300230i
$323$		0			0
$324$	−19.4192			−1.07884
$325$	−20.0470	+	9.01454i	−1.11201	+	0.500037i
$326$	−0.575594			−0.0318792
$327$			37.5310i			2.07547i
$328$		−	11.1592i		−	0.616164i
$329$	13.1090			0.722725
$330$	3.80730	+	2.46248i	0.209585	+	0.135555i
$331$	−33.6525			−1.84971			−0.924855	−	0.380321i	$-0.875814\pi$
$331$	−33.6525			−1.84971			−0.924855	+	0.380321i	$0.875814\pi$
$332$		−	12.6989i		−	0.696941i
$333$			5.16237i			0.282896i
$334$	−3.61111			−0.197591
$335$	−2.06771	+	3.19693i	−0.112971	+	0.174667i
$336$	11.4090			0.622411
$337$		−	2.58877i		−	0.141019i	−0.997511	−	0.0705096i	$-0.977537\pi$
$337$		−	2.58877i		−	0.141019i	0.997511	−	0.0705096i	$-0.0224625\pi$
$338$			2.84262i			0.154618i
$339$	−3.74042			−0.203152
$340$	−11.9479	+	18.4730i	−0.647968	+	1.00184i
$341$	1.74755			0.0946353
$342$		0			0
$343$			20.0992i			1.08525i
$344$	5.40493			0.291414
$345$	−21.3744	−	13.8245i	−1.15076	−	0.744286i
$346$	−1.19493			−0.0642397
$347$			23.8033i			1.27783i	0.769279	+	0.638913i	$0.220616\pi$
$347$			23.8033i			1.27783i	−0.769279	+	0.638913i	$0.779384\pi$
$348$		−	19.3683i		−	1.03825i
$349$	2.48241			0.132880			0.0664402	−	0.997790i	$-0.478836\pi$
$349$	2.48241			0.132880			0.0664402	+	0.997790i	$0.478836\pi$
$350$	1.89897	+	4.22301i	0.101504	+	0.225730i
$351$	18.6741			0.996747
$352$			10.8032i			0.575813i
$353$		−	35.7434i		−	1.90243i	−0.308527	−	0.951216i	$-0.599836\pi$
$353$		−	35.7434i		−	1.90243i	0.308527	−	0.951216i	$-0.400164\pi$
$354$	−2.24255			−0.119190
$355$	−18.5112	−	11.9727i	−0.982471	−	0.635442i
$356$	−4.19761			−0.222473
$357$			22.0660i			1.16786i
$358$		−	3.64082i		−	0.192424i
$359$	5.76436			0.304231			0.152116	−	0.988363i	$-0.451391\pi$
$359$	5.76436			0.304231			0.152116	+	0.988363i	$0.451391\pi$
$360$	−1.71868	+	2.65729i	−0.0905823	+	0.140051i
$361$		0			0
$362$			9.66258i			0.507854i
$363$			11.1196i			0.583626i
$364$	−16.2895			−0.853801
$365$	−12.4069	+	19.1826i	−0.649407	+	1.00406i
$366$	−8.74084			−0.456891
$367$		−	5.95729i		−	0.310968i	−0.987838	−	0.155484i	$-0.950306\pi$
$367$		−	5.95729i		−	0.310968i	0.987838	−	0.155484i	$-0.0496937\pi$
$368$		−	16.4588i		−	0.857974i
$369$	−5.42170			−0.282243
$370$	−5.25270	−	3.39734i	−0.273075	−	0.176619i
$371$	−7.93462			−0.411945
$372$			2.66645i			0.138249i
$373$		−	4.46841i		−	0.231365i	−0.993286	−	0.115683i	$-0.963094\pi$
$373$		−	4.46841i		−	0.231365i	0.993286	−	0.115683i	$-0.0369056\pi$
$374$	−5.67021			−0.293199
$375$	21.6274	+	3.30248i	1.11684	+	0.170539i
$376$	−10.8569			−0.559902
$377$			24.1991i			1.24631i
$378$		−	3.93380i		−	0.202333i
$379$	13.3179			0.684095			0.342047	−	0.939683i	$-0.388880\pi$
$379$	13.3179			0.684095			0.342047	+	0.939683i	$0.388880\pi$
$380$		0			0
$381$	−41.5553			−2.12894
$382$			8.80499i			0.450502i
$383$			10.1737i			0.519849i	0.965629	+	0.259925i	$0.0836977\pi$
$383$			10.1737i			0.519849i	−0.965629	+	0.259925i	$0.916302\pi$
$384$	−21.4594			−1.09509
$385$	5.77092	−	8.92255i	0.294113	−	0.454735i
$386$	−0.217208			−0.0110556
$387$		−	2.62598i		−	0.133486i
$388$			12.2545i			0.622128i
$389$	11.4104			0.578530			0.289265	−	0.957249i	$-0.406589\pi$
$389$	11.4104			0.578530			0.289265	+	0.957249i	$0.406589\pi$
$390$	4.69445	−	7.25818i	0.237712	−	0.367532i
$391$	31.8328			1.60985
$392$		−	4.69891i		−	0.237331i
$393$			3.27323i			0.165113i
$394$	0.567060			0.0285681
$395$	4.52848	+	2.92893i	0.227852	+	0.147370i
$396$	3.43822			0.172777
$397$			5.14253i			0.258096i	0.991638	+	0.129048i	$0.0411921\pi$
$397$			5.14253i			0.258096i	−0.991638	+	0.129048i	$0.958808\pi$
$398$			9.28201i			0.465265i
$399$		0			0
$400$	5.80141	+	12.9014i	0.290070	+	0.645072i
$401$	−17.0822			−0.853043			−0.426522	−	0.904477i	$-0.640261\pi$
$401$	−17.0822			−0.853043			−0.426522	+	0.904477i	$0.640261\pi$
$402$		−	1.49727i		−	0.0746768i
$403$		−	3.33151i		−	0.165954i
$404$	21.9320			1.09116
$405$	−20.2779	−	13.1153i	−1.00762	−	0.651707i
$406$	5.09767			0.252993
$407$			14.3561i			0.711603i
$408$		−	18.2751i		−	0.904751i
$409$	−26.0696			−1.28906			−0.644529	−	0.764580i	$-0.722947\pi$
$409$	−26.0696			−1.28906			−0.644529	+	0.764580i	$0.722947\pi$
$410$	3.56800	−	5.51656i	0.176211	−	0.272444i
$411$	−33.8298			−1.66870
$412$			23.2305i			1.14448i
$413$			5.25550i			0.258606i
$414$	2.16780			0.106542
$415$	8.57657	−	13.2604i	0.421007	−	0.650929i
$416$	20.5951			1.00976
$417$			24.1211i			1.18121i
$418$		0			0
$419$	−5.77281			−0.282020			−0.141010	−	0.990008i	$-0.545035\pi$
$419$	−5.77281			−0.282020			−0.141010	+	0.990008i	$0.545035\pi$
$420$	13.6142	+	8.80538i	0.664305	+	0.429659i
$421$	−25.3007			−1.23308			−0.616540	−	0.787323i	$-0.711466\pi$
$421$	−25.3007			−1.23308			−0.616540	+	0.787323i	$0.711466\pi$
$422$			3.15099i			0.153388i
$423$			5.27483i			0.256471i
$424$	6.57146			0.319138
$425$	−24.9526	+	11.2204i	−1.21038	+	0.544272i
$426$	8.66960			0.420044
$427$			20.4845i			0.991314i
$428$			27.2819i			1.31872i
$429$	−19.8372			−0.957750
$430$	2.67193	+	1.72815i	0.128852	+	0.0833387i
$431$	18.7629			0.903777			0.451888	−	0.892074i	$-0.350751\pi$
$431$	18.7629			0.903777			0.451888	+	0.892074i	$0.350751\pi$
$432$		−	12.0179i		−	0.578211i
$433$		−	8.51298i		−	0.409108i	−0.978855	−	0.204554i	$-0.934426\pi$
$433$		−	8.51298i		−	0.409108i	0.978855	−	0.204554i	$-0.0655743\pi$
$434$	−0.701802			−0.0336876
$435$	13.0810	−	20.2247i	0.627184	−	0.969702i
$436$	−34.4858			−1.65157
$437$		0			0
$438$		−	8.98406i		−	0.429275i
$439$	−2.05530			−0.0980941			−0.0490470	−	0.998796i	$-0.515618\pi$
$439$	−2.05530			−0.0980941			−0.0490470	+	0.998796i	$0.515618\pi$
$440$	−4.77948	+	7.38965i	−0.227853	+	0.352288i
$441$	−2.28296			−0.108713
$442$			10.8096i			0.514160i
$443$		−	12.0403i		−	0.572054i	−0.958222	−	0.286027i	$-0.907665\pi$
$443$		−	12.0403i		−	0.572054i	0.958222	−	0.286027i	$-0.0923347\pi$
$444$	−21.9048			−1.03955
$445$	−4.38323	−	2.83498i	−0.207785	−	0.134391i
$446$	8.73464			0.413597
$447$			8.52989i			0.403450i
$448$			7.32215i			0.345939i
$449$	7.49400			0.353664			0.176832	−	0.984241i	$-0.443415\pi$
$449$	7.49400			0.353664			0.176832	+	0.984241i	$0.443415\pi$
$450$	−1.69926	+	0.764108i	−0.0801039	+	0.0360204i
$451$	−15.0772			−0.709959
$452$		−	3.43693i		−	0.161659i
$453$			8.70066i			0.408793i
$454$	−2.93889			−0.137929
$455$	−17.0098	−	11.0016i	−0.797432	−	0.515763i
$456$		0			0
$457$		−	14.0052i		−	0.655137i	−0.944827	−	0.327568i	$-0.893771\pi$
$457$		−	14.0052i		−	0.655137i	0.944827	−	0.327568i	$-0.106229\pi$
$458$		−	9.16745i		−	0.428367i
$459$	23.2437			1.08492
$460$	12.7028	−	19.6401i	0.592271	−	0.915722i
$461$	−17.6751			−0.823210			−0.411605	−	0.911362i	$-0.635032\pi$
$461$	−17.6751			−0.823210			−0.411605	+	0.911362i	$0.635032\pi$
$462$			4.17882i			0.194416i
$463$		−	16.5926i		−	0.771123i	−0.922682	−	0.385562i	$-0.874008\pi$
$463$		−	16.5926i		−	0.771123i	0.922682	−	0.385562i	$-0.125992\pi$
$464$	15.5736			0.722984
$465$	−1.80087	+	2.78436i	−0.0835133	+	0.129122i
$466$	−5.41451			−0.250822
$467$			15.9904i			0.739949i	0.929042	+	0.369975i	$0.120634\pi$
$467$			15.9904i			0.739949i	−0.929042	+	0.369975i	$0.879366\pi$
$468$		−	6.55458i		−	0.302985i
$469$	−3.50890			−0.162026
$470$	−5.36712	−	3.47134i	−0.247567	−	0.160121i
$471$	−38.8300			−1.78919
$472$		−	4.35261i		−	0.200345i
$473$		−	7.30260i		−	0.335774i
$474$	−2.12089			−0.0974155
$475$		0			0
$476$	−20.2756			−0.929331
$477$		−	3.19274i		−	0.146186i
$478$		−	2.75241i		−	0.125892i
$479$	−7.39591			−0.337928			−0.168964	−	0.985622i	$-0.554042\pi$
$479$	−7.39591			−0.337928			−0.168964	+	0.985622i	$0.554042\pi$
$480$	−17.2127	−	11.1328i	−0.785647	−	0.508140i
$481$	27.3682			1.24788
$482$		−	3.26833i		−	0.148868i
$483$		−	23.4601i		−	1.06747i
$484$	−10.2173			−0.464425
$485$	−8.27645	+	12.7964i	−0.375814	+	0.581055i
$486$	3.77042			0.171030
$487$		−	20.1881i		−	0.914811i	−0.889258	−	0.457406i	$-0.848779\pi$
$487$		−	20.1881i		−	0.914811i	0.889258	−	0.457406i	$-0.151221\pi$
$488$		−	16.9652i		−	0.767981i
$489$	−2.50648			−0.113347
$490$	1.50241	−	2.32291i	0.0678720	−	0.104938i
$491$	9.33307			0.421195			0.210598	−	0.977573i	$-0.432459\pi$
$491$	9.33307			0.421195			0.210598	+	0.977573i	$0.432459\pi$
$492$		−	23.0051i		−	1.03715i
$493$			30.1207i			1.35657i
$494$		0			0
$495$	3.59026	+	2.32211i	0.161370	+	0.104371i
$496$	−2.14403			−0.0962697
$497$		−	20.3175i		−	0.911366i
$498$			6.21044i			0.278297i
$499$	23.9612			1.07265			0.536326	−	0.844011i	$-0.319812\pi$
$499$	23.9612			1.07265			0.536326	+	0.844011i	$0.319812\pi$
$500$	−3.03452	+	19.8726i	−0.135708	+	0.888730i
$501$	−15.7249			−0.702539
$502$			10.8688i			0.485098i
$503$		−	10.3338i		−	0.460763i	−0.973100	−	0.230382i	$-0.926003\pi$
$503$		−	10.3338i		−	0.460763i	0.973100	−	0.230382i	$-0.0739974\pi$
$504$	−2.91659			−0.129915
$505$	22.9018	+	14.8124i	1.01912	+	0.659144i
$506$	6.02844			0.267997
$507$			12.3785i			0.549747i
$508$		−	38.1835i		−	1.69412i
$509$	27.7116			1.22829			0.614147	−	0.789192i	$-0.289500\pi$
$509$	27.7116			1.22829			0.614147	+	0.789192i	$0.289500\pi$
$510$	5.84320	−	9.03430i	0.258741	−	0.400045i
$511$	−21.0545			−0.931395
$512$		−	22.9115i		−	1.01256i
$513$		0			0
$514$	−5.49940			−0.242568
$515$	−15.6894	+	24.2577i	−0.691358	+	1.06892i
$516$	11.1424			0.490519
$517$			14.6688i			0.645132i
$518$		−	5.76527i		−	0.253311i
$519$	−5.20343			−0.228405
$520$	14.0875	+	9.11153i	0.617779	+	0.399567i
$521$	10.5729			0.463209			0.231604	−	0.972810i	$-0.425602\pi$
$521$	10.5729			0.463209			0.231604	+	0.972810i	$0.425602\pi$
$522$			2.05121i			0.0897788i
$523$		−	18.1596i		−	0.794065i	−0.917805	−	0.397032i	$-0.870040\pi$
$523$		−	18.1596i		−	0.794065i	0.917805	−	0.397032i	$-0.129960\pi$
$524$	−3.00765			−0.131390
$525$	8.26923	+	18.3895i	0.360899	+	0.802585i
$526$	5.56588			0.242684
$527$		−	4.14675i		−	0.180635i
$528$			12.7665i			0.555588i
$529$	−10.8439			−0.471475
$530$	3.24860	+	2.10113i	0.141110	+	0.0912673i
$531$	−2.11471			−0.0917707
$532$		0			0
$533$			28.7430i			1.24500i
$534$	2.05286			0.0888360
$535$	−18.4257	+	28.4883i	−0.796612	+	1.23166i
$536$	2.90607			0.125523
$537$		−	15.8543i		−	0.684165i
$538$			2.21936i			0.0956835i
$539$	−6.34870			−0.273458
$540$	9.27533	−	14.3408i	0.399147	−	0.617129i
$541$	6.10507			0.262478			0.131239	−	0.991351i	$-0.458105\pi$
$541$	6.10507			0.262478			0.131239	+	0.991351i	$0.458105\pi$
$542$			3.10155i			0.133223i
$543$			42.0766i			1.80568i
$544$	25.6348			1.09908
$545$	−36.0108	−	23.2910i	−1.54253	−	0.997678i
$546$	7.96645			0.340933
$547$		−	10.9019i		−	0.466132i	−0.972461	−	0.233066i	$-0.925124\pi$
$547$		−	10.9019i		−	0.466132i	0.972461	−	0.233066i	$-0.0748759\pi$
$548$		−	31.0849i		−	1.32788i
$549$	−8.24256			−0.351784
$550$	−4.72547	+	2.12491i	−0.201495	+	0.0906064i
$551$		0			0
$552$			19.4297i			0.826981i
$553$			4.97037i			0.211362i
$554$	−1.78098			−0.0756665
$555$	−22.8734	−	14.7940i	−0.970921	−	0.627972i
$556$	−22.1639			−0.939958
$557$		−	12.2157i		−	0.517595i	−0.965932	−	0.258798i	$-0.916674\pi$
$557$		−	12.2157i		−	0.517595i	0.965932	−	0.258798i	$-0.0833263\pi$
$558$		−	0.282392i		−	0.0119546i
$559$	−13.9216			−0.588820
$560$	−7.08020	+	10.9468i	−0.299193	+	0.462589i
$561$	−24.6915			−1.04247
$562$			14.0201i			0.591403i
$563$			18.3200i			0.772095i	0.922479	+	0.386048i	$0.126160\pi$
$563$			18.3200i			0.772095i	−0.922479	+	0.386048i	$0.873840\pi$
$564$	−22.3819			−0.942448
$565$	2.32123	−	3.58891i	0.0976550	−	0.150987i
$566$	−4.77550			−0.200729
$567$		−	22.2567i		−	0.934693i
$568$			16.8270i			0.706044i
$569$	32.3240			1.35509			0.677546	−	0.735480i	$-0.263043\pi$
$569$	32.3240			1.35509			0.677546	+	0.735480i	$0.263043\pi$
$570$		0			0
$571$	−13.2641			−0.555083			−0.277542	−	0.960714i	$-0.589520\pi$
$571$	−13.2641			−0.555083			−0.277542	+	0.960714i	$0.589520\pi$
$572$		−	18.2276i		−	0.762136i
$573$			38.3422i			1.60177i
$574$	6.05488			0.252726
$575$	26.5290	−	11.9293i	1.10634	−	0.497487i
$576$	−2.94629			−0.122762
$577$		−	21.7627i		−	0.905993i	−0.891512	−	0.452996i	$-0.850355\pi$
$577$		−	21.7627i		−	0.905993i	0.891512	−	0.452996i	$-0.149645\pi$
$578$			5.81542i			0.241890i
$579$	−0.945853			−0.0393083
$580$	18.5837	+	12.0196i	0.771647	+	0.499086i
$581$	14.5544			0.603818
$582$		−	5.99312i		−	0.248423i
$583$		−	8.87870i		−	0.367718i
$584$	17.4373			0.721561
$585$	4.42684	−	6.84442i	0.183027	−	0.282982i
$586$	−8.81952			−0.364331
$587$		−	41.5762i		−	1.71604i	−0.513620	−	0.858018i	$-0.671696\pi$
$587$		−	41.5762i		−	1.71604i	0.513620	−	0.858018i	$-0.328304\pi$
$588$		−	9.68697i		−	0.399484i
$589$		0			0
$590$	1.39168	−	2.15171i	0.0572947	−	0.0885846i
$591$	2.46932			0.101574
$592$		−	17.6131i		−	0.723893i
$593$		−	8.58712i		−	0.352631i	−0.984334	−	0.176315i	$-0.943582\pi$
$593$		−	8.58712i		−	0.352631i	0.984334	−	0.176315i	$-0.0564179\pi$
$594$	4.40185			0.180610
$595$	−21.1722	−	13.6937i	−0.867975	−	0.561389i
$596$	−7.83778			−0.321048
$597$			40.4194i			1.65426i
$598$		−	11.4925i		−	0.469964i
$599$	41.2980			1.68739			0.843696	−	0.536822i	$-0.180375\pi$
$599$	41.2980			1.68739			0.843696	+	0.536822i	$0.180375\pi$
$600$	−6.84858	−	15.2302i	−0.279592	−	0.621771i
$601$	1.60121			0.0653145			0.0326573	−	0.999467i	$-0.489603\pi$
$601$	1.60121			0.0653145			0.0326573	+	0.999467i	$0.489603\pi$
$602$			2.93266i			0.119526i
$603$		−	1.41191i		−	0.0574975i
$604$	−7.99470			−0.325300
$605$	−10.6692	−	6.90060i	−0.433763	−	0.280549i
$606$	−10.7259			−0.435711
$607$			32.4708i			1.31795i	0.752165	+	0.658975i	$0.229010\pi$
$607$			32.4708i			1.31795i	−0.752165	+	0.658975i	$0.770990\pi$
$608$		0			0
$609$	22.1983			0.899521
$610$	5.42440	−	8.38678i	0.219628	−	0.339571i
$611$	27.9643			1.13132
$612$		−	8.15852i		−	0.329788i
$613$			13.9352i			0.562839i	0.959585	+	0.281420i	$0.0908053\pi$
$613$			13.9352i			0.562839i	−0.959585	+	0.281420i	$0.909195\pi$
$614$	10.1674			0.410325
$615$	15.5372	−	24.0224i	0.626521	−	0.968677i
$616$	−8.11075			−0.326791
$617$			14.4224i			0.580625i	0.956932	+	0.290313i	$0.0937593\pi$
$617$			14.4224i			0.580625i	−0.956932	+	0.290313i	$0.906241\pi$
$618$		−	11.3610i		−	0.457005i
$619$	4.71305			0.189434			0.0947168	−	0.995504i	$-0.469805\pi$
$619$	4.71305			0.189434			0.0947168	+	0.995504i	$0.469805\pi$
$620$	−2.55844	−	1.65475i	−0.102749	−	0.0664563i
$621$	−24.7122			−0.991665
$622$		−	11.1704i		−	0.447892i
$623$		−	4.81095i		−	0.192747i
$624$	24.3378			0.974291
$625$	−16.5903	+	18.7019i	−0.663611	+	0.748078i
$626$	9.97728			0.398772
$627$		0			0
$628$		−	35.6794i		−	1.42376i
$629$	34.0653			1.35827
$630$	−1.44182	−	0.932538i	−0.0574434	−	0.0371532i
$631$	3.31273			0.131878			0.0659388	−	0.997824i	$-0.478996\pi$
$631$	3.31273			0.131878			0.0659388	+	0.997824i	$0.478996\pi$
$632$		−	4.11646i		−	0.163744i
$633$			13.7213i			0.545372i
$634$	0.916530			0.0364000
$635$	25.7884	−	39.8720i	1.02338	−	1.58227i
$636$	13.5473			0.537185
$637$			12.1031i			0.479541i
$638$			5.70420i			0.225831i
$639$	8.17539			0.323413
$640$	13.3173	−	20.5901i	0.526412	−	0.813897i
$641$	0.0491989			0.00194324			0.000971620	−	1.00000i	$-0.499691\pi$
$641$	0.0491989			0.00194324			0.000971620		1.00000i	$0.499691\pi$
$642$		−	13.3424i		−	0.526581i
$643$		−	12.0003i		−	0.473246i	−0.971602	−	0.236623i	$-0.923959\pi$
$643$		−	12.0003i		−	0.473246i	0.971602	−	0.236623i	$-0.0760406\pi$
$644$	21.5566			0.849448
$645$	11.6352	+	7.52539i	0.458135	+	0.296312i
$646$		0			0
$647$		−	36.3971i		−	1.43092i	−0.698656	−	0.715458i	$-0.746218\pi$
$647$		−	36.3971i		−	1.43092i	0.698656	−	0.715458i	$-0.253782\pi$
$648$			18.4330i			0.724116i
$649$	−5.88081			−0.230842
$650$	4.05089	+	9.00858i	0.158889	+	0.353345i
$651$	−3.05607			−0.119777
$652$		−	2.30311i		−	0.0901967i
$653$			31.7999i			1.24443i	0.782847	+	0.622214i	$0.213767\pi$
$653$			31.7999i			1.24443i	−0.782847	+	0.622214i	$0.786233\pi$
$654$	16.8654			0.659491
$655$	−3.14065	−	2.03131i	−0.122715	−	0.0793697i
$656$	18.4979			0.722220
$657$		−	8.47192i		−	0.330521i
$658$		−	5.89085i		−	0.229649i
$659$	26.8414			1.04559			0.522796	−	0.852458i	$-0.324889\pi$
$659$	26.8414			1.04559			0.522796	+	0.852458i	$0.324889\pi$
$660$	−9.85307	+	15.2340i	−0.383530	+	0.592984i
$661$	34.2970			1.33400			0.667000	−	0.745057i	$-0.267578\pi$
$661$	34.2970			1.33400			0.667000	+	0.745057i	$0.267578\pi$
$662$			15.1225i			0.587754i
$663$			47.0715i			1.82810i
$664$	−12.0540			−0.467784
$665$		0			0
$666$	2.31983			0.0898917
$667$		−	32.0236i		−	1.23996i
$668$		−	14.4490i		−	0.559050i
$669$	38.0358			1.47055
$670$	1.43662	+	0.929174i	0.0555013	+	0.0358971i
$671$	−22.9218			−0.884885
$672$		−	18.8923i		−	0.728786i
$673$			21.7196i			0.837230i	0.908164	+	0.418615i	$0.137484\pi$
$673$			21.7196i			0.837230i	−0.908164	+	0.418615i	$0.862516\pi$
$674$	−1.16332			−0.0448096
$675$	19.3710	−	8.71056i	0.745589	−	0.335270i
$676$	−11.3741			−0.437465
$677$		−	8.53064i		−	0.327859i	−0.986472	−	0.163930i	$-0.947583\pi$
$677$		−	8.53064i		−	0.327859i	0.986472	−	0.163930i	$-0.0524170\pi$
$678$			1.68085i			0.0645525i
$679$	−14.0451			−0.539001
$680$	17.5348	+	11.3412i	0.672429	+	0.434914i
$681$	−12.7977			−0.490409
$682$		−	0.785303i		−	0.0300708i
$683$		−	17.3190i		−	0.662695i	−0.943509	−	0.331347i	$-0.892497\pi$
$683$		−	17.3190i		−	0.662695i	0.943509	−	0.331347i	$-0.107503\pi$
$684$		0			0
$685$	20.9941	−	32.4595i	0.802145	−	1.24021i
$686$	9.03204			0.344845
$687$		−	39.9206i		−	1.52306i
$688$			8.95938i			0.341573i
$689$	−16.9262			−0.644838
$690$	−6.21236	+	9.60506i	−0.236500	+	0.365658i
$691$	17.2709			0.657014			0.328507	−	0.944501i	$-0.393454\pi$
$691$	17.2709			0.657014			0.328507	+	0.944501i	$0.393454\pi$
$692$		−	4.78122i		−	0.181755i
$693$			3.94061i			0.149691i
$694$	10.6966			0.406036
$695$	−23.1440	−	14.9691i	−0.877902	−	0.567809i
$696$	−18.3846			−0.696868
$697$			35.7765i			1.35513i
$698$		−	1.11553i		−	0.0422234i
$699$	−23.5780			−0.891802
$700$	−16.8974	+	7.59827i	−0.638662	+	0.287188i
$701$	21.8816			0.826457			0.413228	−	0.910627i	$-0.364401\pi$
$701$	21.8816			0.826457			0.413228	+	0.910627i	$0.364401\pi$
$702$		−	8.39162i		−	0.316721i
$703$		0			0
$704$	−8.19336			−0.308799
$705$	−23.3716	−	15.1163i	−0.880227	−	0.569313i
$706$	−16.0621			−0.604507
$707$			25.1366i			0.945360i
$708$		−	8.97305i		−	0.337228i
$709$	−20.5621			−0.772224			−0.386112	−	0.922452i	$-0.626182\pi$
$709$	−20.5621			−0.772224			−0.386112	+	0.922452i	$0.626182\pi$
$710$	−5.38019	+	8.31843i	−0.201915	+	0.312185i
$711$	−1.99998			−0.0750052
$712$			3.98443i			0.149323i
$713$			4.40873i			0.165108i
$714$	9.91588			0.371092
$715$	12.3106	−	19.0337i	0.460390	−	0.711819i
$716$	14.5679			0.544429
$717$		−	11.9856i		−	0.447612i
$718$		−	2.59035i		−	0.0966709i
$719$	−15.6722			−0.584473			−0.292237	−	0.956346i	$-0.594400\pi$
$719$	−15.6722			−0.584473			−0.292237	+	0.956346i	$0.594400\pi$
$720$	−4.40480	−	2.84894i	−0.164157	−	0.106174i
$721$	−26.6249			−0.991561
$722$		0			0
$723$		−	14.2323i		−	0.529304i
$724$	−38.6626			−1.43688
$725$	11.2877	+	25.1022i	0.419215	+	0.932271i
$726$	4.99684			0.185450
$727$			43.5233i			1.61419i	0.590421	+	0.807095i	$0.298962\pi$
$727$			43.5233i			1.61419i	−0.590421	+	0.807095i	$0.701038\pi$
$728$			15.4622i			0.573068i
$729$	−15.9815			−0.591907
$730$	8.62014	+	5.57533i	0.319046	+	0.206352i
$731$	−17.3282			−0.640908
$732$		−	34.9745i		−	1.29269i
$733$		−	12.6904i		−	0.468729i	−0.972149	−	0.234364i	$-0.924699\pi$
$733$		−	12.6904i		−	0.468729i	0.972149	−	0.234364i	$-0.0753009\pi$
$734$	−2.67705			−0.0988116
$735$	6.54239	−	10.1153i	0.241320	−	0.373110i
$736$	−27.2543			−1.00461
$737$		−	3.92639i		−	0.144630i
$738$			2.43637i			0.0896839i
$739$	−28.1664			−1.03612			−0.518059	−	0.855345i	$-0.673345\pi$
$739$	−28.1664			−1.03612			−0.518059	+	0.855345i	$0.673345\pi$
$740$	13.5937	−	21.0175i	0.499713	−	0.772617i
$741$		0			0
$742$			3.56561i			0.130898i
$743$			25.5639i			0.937849i	0.883238	+	0.468924i	$0.155358\pi$
$743$			25.5639i			0.937849i	−0.883238	+	0.468924i	$0.844642\pi$
$744$	2.53103			0.0927922
$745$	−8.18437	−	5.29348i	−0.299852	−	0.193938i
$746$	−2.00798			−0.0735175
$747$			5.85641i			0.214275i
$748$		−	22.6880i		−	0.829557i
$749$	−31.2683			−1.14252
$750$	1.48404	−	9.71880i	0.0541896	−	0.354880i
$751$	−34.6687			−1.26508			−0.632539	−	0.774529i	$-0.717987\pi$
$751$	−34.6687			−1.26508			−0.632539	+	0.774529i	$0.717987\pi$
$752$		−	17.9968i		−	0.656274i
$753$			47.3293i			1.72477i
$754$	10.8744			0.396023
$755$	−8.34823	−	5.39946i	−0.303823	−	0.196507i
$756$	15.7402			0.572465
$757$			45.7467i			1.66269i	0.555755	+	0.831346i	$0.312429\pi$
$757$			45.7467i			1.66269i	−0.555755	+	0.831346i	$0.687571\pi$
$758$		−	5.98471i		−	0.217374i
$759$	26.2514			0.952867
$760$		0			0
$761$	2.85442			0.103472			0.0517362	−	0.998661i	$-0.483524\pi$
$761$	2.85442			0.103472			0.0517362	+	0.998661i	$0.483524\pi$
$762$			18.6738i			0.676481i
$763$		−	39.5248i		−	1.43089i
$764$	−35.2311			−1.27462
$765$	5.51010	−	8.51929i	0.199218	−	0.308016i
$766$	4.57177			0.165185
$767$			11.2111i			0.404809i
$768$		−	4.26233i		−	0.153804i
$769$	−19.5208			−0.703937			−0.351969	−	0.936012i	$-0.614488\pi$
$769$	−19.5208			−0.703937			−0.351969	+	0.936012i	$0.614488\pi$
$770$	−4.00955	−	2.59330i	−0.144494	−	0.0934560i
$771$	−23.9477			−0.862455
$772$		−	0.869107i		−	0.0312798i
$773$			7.24881i			0.260722i	0.991467	+	0.130361i	$0.0416136\pi$
$773$			7.24881i			0.260722i	−0.991467	+	0.130361i	$0.958386\pi$
$774$	−1.18005			−0.0424159
$775$	−1.55399	−	3.45584i	−0.0558210	−	0.124138i
$776$	11.6322			0.417570
$777$		−	25.1054i		−	0.900652i
$778$		−	5.12753i		−	0.183831i
$779$		0			0
$780$	29.0419	+	18.7837i	1.03987	+	0.672566i
$781$	22.7349			0.813520
$782$		−	14.3048i		−	0.511539i
$783$		−	23.3830i		−	0.835641i
$784$	7.78906			0.278181
$785$	24.0972	−	37.2571i	0.860065	−	1.32976i
$786$	1.47090			0.0524654
$787$		−	4.20711i		−	0.149967i	−0.997185	−	0.0749837i	$-0.976110\pi$
$787$		−	4.20711i		−	0.149967i	0.997185	−	0.0749837i	$-0.0238905\pi$
$788$			2.26896i			0.0808283i
$789$	24.2372			0.862867
$790$	1.31618	−	2.03498i	0.0468276	−	0.0724012i
$791$	3.93912			0.140059
$792$		−	3.26361i		−	0.115967i
$793$			43.6977i			1.55175i
$794$	2.31091			0.0820113
$795$	14.1464	+	9.14958i	0.501720	+	0.324502i
$796$	−37.1398			−1.31639
$797$		−	25.6411i		−	0.908253i	−0.890937	−	0.454127i	$-0.849951\pi$
$797$		−	25.6411i		−	0.908253i	0.890937	−	0.454127i	$-0.150049\pi$
$798$		0			0
$799$	34.8074			1.23140
$800$	21.3637	−	9.60663i	0.755320	−	0.339646i
$801$	1.93584			0.0683994
$802$			7.67627i			0.271059i
$803$		−	23.5596i		−	0.831399i
$804$	5.99096			0.211285
$805$	22.5098	+	14.5589i	0.793367	+	0.513133i
$806$	−1.49709			−0.0527328
$807$			9.66444i			0.340204i
$808$		−	20.8181i		−	0.732380i
$809$	0.516056			0.0181436			0.00907179	−	0.999959i	$-0.497112\pi$
$809$	0.516056			0.0181436			0.00907179	+	0.999959i	$0.497112\pi$
$810$	−5.89369	+	9.11235i	−0.207083	+	0.320176i
$811$	24.0377			0.844078			0.422039	−	0.906578i	$-0.361315\pi$
$811$	24.0377			0.844078			0.422039	+	0.906578i	$0.361315\pi$
$812$			20.3972i			0.715800i
$813$			13.5060i			0.473676i
$814$	6.45123			0.226115
$815$	1.55547	−	2.40495i	0.0544859	−	0.0842418i
$816$	30.2934			1.06048
$817$		0			0
$818$			11.7150i			0.409605i
$819$	7.51232			0.262502
$820$	22.0733	+	14.2765i	0.770831	+	0.498558i
$821$	38.7573			1.35264			0.676320	−	0.736608i	$-0.263574\pi$
$821$	38.7573			1.35264			0.676320	+	0.736608i	$0.263574\pi$
$822$			15.2022i			0.530238i
$823$			3.48827i			0.121593i	0.998150	+	0.0607967i	$0.0193641\pi$
$823$			3.48827i			0.121593i	−0.998150	+	0.0607967i	$0.980636\pi$
$824$	22.0507			0.768173
$825$	−20.5775	+	9.25312i	−0.716418	+	0.322152i
$826$	2.36168			0.0821734
$827$		−	27.4821i		−	0.955645i	−0.878456	−	0.477823i	$-0.841426\pi$
$827$		−	27.4821i		−	0.955645i	0.878456	−	0.477823i	$-0.158574\pi$
$828$			8.67395i			0.301441i
$829$	−8.60945			−0.299019			−0.149509	−	0.988760i	$-0.547769\pi$
$829$	−8.60945			−0.299019			−0.149509	+	0.988760i	$0.547769\pi$
$830$	−5.95888	−	3.85408i	−0.206836	−	0.133777i
$831$	−7.75545			−0.269034
$832$			15.6197i			0.541516i
$833$			15.0648i			0.521963i
$834$	10.8394			0.375336
$835$	9.75860	−	15.0880i	0.337710	−	0.522141i
$836$		0			0
$837$			3.21917i			0.111271i
$838$			2.59415i			0.0896133i
$839$	11.9397			0.412206			0.206103	−	0.978530i	$-0.433922\pi$
$839$	11.9397			0.412206			0.206103	+	0.978530i	$0.433922\pi$
$840$	8.35820	−	12.9228i	0.288385	−	0.445879i
$841$	1.30126			0.0448710
$842$			11.3695i			0.391817i
$843$			61.0520i			2.10274i
$844$	−12.6079			−0.433983
$845$	−11.8771	−	7.68184i	−0.408583	−	0.264263i
$846$	2.37037			0.0814949
$847$		−	11.7103i		−	0.402370i
$848$			10.8931i			0.374069i
$849$	−20.7954			−0.713695
$850$	5.04217	+	11.2130i	0.172945	+	0.384603i
$851$	−36.2175			−1.24152
$852$			34.6894i			1.18844i
$853$			28.9175i			0.990117i	0.868860	+	0.495059i	$0.164853\pi$
$853$			28.9175i			0.990117i	−0.868860	+	0.495059i	$0.835147\pi$
$854$	9.20518			0.314995
$855$		0			0
$856$	25.8964			0.885121
$857$		−	55.2147i		−	1.88610i	−0.332651	−	0.943050i	$-0.607943\pi$
$857$		−	55.2147i		−	1.88610i	0.332651	−	0.943050i	$-0.392057\pi$
$858$			8.91431i			0.304330i
$859$	26.6572			0.909532			0.454766	−	0.890611i	$-0.349723\pi$
$859$	26.6572			0.909532			0.454766	+	0.890611i	$0.349723\pi$
$860$	−6.91479	+	10.6911i	−0.235792	+	0.364564i
$861$	26.3666			0.898570
$862$		−	8.43154i		−	0.287180i
$863$			1.21123i			0.0412307i	0.999787	+	0.0206154i	$0.00656254\pi$
$863$			1.21123i			0.0412307i	−0.999787	+	0.0206154i	$0.993437\pi$
$864$	−19.9006			−0.677031
$865$	3.22915	−	4.99265i	0.109794	−	0.169755i
$866$	−3.82551			−0.129996
$867$			25.3238i			0.860042i
$868$		−	2.80810i		−	0.0953131i
$869$	−5.56176			−0.188670
$870$	−9.08846	−	5.87823i	−0.308128	−	0.199291i
$871$	−7.48522			−0.253627
$872$			32.7344i			1.10853i
$873$		−	5.65148i		−	0.191274i
$874$		0			0
$875$	−22.7764	−	3.47791i	−0.769981	−	0.117575i
$876$	35.9476			1.21456
$877$			49.5420i			1.67291i	0.548032	+	0.836457i	$0.315377\pi$
$877$			49.5420i			1.67291i	−0.548032	+	0.836457i	$0.684623\pi$
$878$			0.923597i			0.0311699i
$879$	−38.4055			−1.29538
$880$	−12.2493	−	7.92261i	−0.412925	−	0.267071i
$881$	−30.5639			−1.02972			−0.514861	−	0.857273i	$-0.672157\pi$
$881$	−30.5639			−1.02972			−0.514861	+	0.857273i	$0.672157\pi$
$882$			1.02590i			0.0345440i
$883$			5.57841i			0.187729i	0.995585	+	0.0938643i	$0.0299220\pi$
$883$			5.57841i			0.187729i	−0.995585	+	0.0938643i	$0.970078\pi$
$884$	−43.2521			−1.45473
$885$	6.06023	−	9.36985i	0.203712	−	0.314964i
$886$	−5.41061			−0.181773
$887$		−	0.666360i		−	0.0223742i	−0.999937	−	0.0111871i	$-0.996439\pi$
$887$		−	0.666360i		−	0.0223742i	0.999937	−	0.0111871i	$-0.00356104\pi$
$888$			20.7923i			0.697744i
$889$	43.7628			1.46776
$890$	−1.27397	+	1.96971i	−0.0427034	+	0.0660247i
$891$	24.9048			0.834343
$892$			34.9497i			1.17020i
$893$		0			0
$894$	3.83310			0.128198
$895$	15.2121	+	9.83889i	0.508485	+	0.328878i
$896$	22.5994			0.754992
$897$		−	50.0454i		−	1.67097i
$898$		−	3.36760i		−	0.112378i
$899$	−4.17161			−0.139131
$900$	−3.05740	−	6.79920i	−0.101913	−	0.226640i
$901$	−21.0682			−0.701882
$902$			6.77530i			0.225593i
$903$			12.7706i			0.424978i
$904$	−3.26238			−0.108505
$905$	−40.3723	−	26.1120i	−1.34202	−	0.867991i
$906$	3.90984			0.129896
$907$			52.7812i			1.75257i	0.481792	+	0.876286i	$0.339986\pi$
$907$			52.7812i			1.75257i	−0.481792	+	0.876286i	$0.660014\pi$
$908$		−	11.7593i		−	0.390246i
$909$	−10.1145			−0.335477
$910$	−4.94383	+	7.64376i	−0.163886	+	0.253388i
$911$	13.0586			0.432650			0.216325	−	0.976321i	$-0.430593\pi$
$911$	13.0586			0.432650			0.216325	+	0.976321i	$0.430593\pi$
$912$		0			0
$913$			16.2861i			0.538992i
$914$	−6.29357			−0.208173
$915$	23.6211	−	36.5211i	0.780889	−	1.20735i
$916$	36.6814			1.21199
$917$		−	3.44712i		−	0.113834i
$918$		−	10.4451i		−	0.344739i
$919$	46.0539			1.51918			0.759589	−	0.650403i	$-0.225400\pi$
$919$	46.0539			1.51918			0.759589	+	0.650403i	$0.225400\pi$
$920$	−18.6426	−	12.0577i	−0.614629	−	0.397530i
$921$	44.2751			1.45892
$922$			7.94271i			0.261579i
$923$		−	43.3416i		−	1.42661i
$924$	−16.7206			−0.550067
$925$	28.3896	−	12.7660i	0.933443	−	0.419742i
$926$	−7.45627			−0.245028
$927$		−	10.7133i		−	0.351872i
$928$		−	25.7885i		−	0.846548i
$929$	−30.9736			−1.01621			−0.508105	−	0.861295i	$-0.669654\pi$
$929$	−30.9736			−1.01621			−0.508105	+	0.861295i	$0.669654\pi$
$930$	1.25122	+	0.809262i	0.0410290	+	0.0265368i
$931$		0			0
$932$		−	21.6649i		−	0.709657i
$933$		−	48.6426i		−	1.59249i
$934$	7.18568			0.235123
$935$	15.3231	−	23.6913i	0.501118	−	0.774789i
$936$	−6.22170			−0.203363
$937$			34.8133i			1.13730i	0.822580	+	0.568650i	$0.192534\pi$
$937$			34.8133i			1.13730i	−0.822580	+	0.568650i	$0.807466\pi$
$938$			1.57680i			0.0514845i
$939$	43.4470			1.41784
$940$	13.8898	−	21.4753i	0.453035	−	0.700447i
$941$	16.2153			0.528604			0.264302	−	0.964440i	$-0.414858\pi$
$941$	16.2153			0.528604			0.264302	+	0.964440i	$0.414858\pi$
$942$			17.4492i			0.568525i
$943$		−	38.0368i		−	1.23865i
$944$	7.21502			0.234829
$945$	16.4362	+	10.6306i	0.534670	+	0.345814i
$946$	−3.28159			−0.106694
$947$		−	14.6403i		−	0.475746i	−0.971296	−	0.237873i	$-0.923550\pi$
$947$		−	14.6403i		−	0.475746i	0.971296	−	0.237873i	$-0.0764502\pi$
$948$		−	8.48624i		−	0.275620i
$949$	−44.9136			−1.45796
$950$		0			0
$951$	3.99112			0.129421
$952$			19.2459i			0.623763i
$953$		−	40.8271i		−	1.32252i	−0.750156	−	0.661260i	$-0.770022\pi$
$953$		−	40.8271i		−	1.32252i	0.750156	−	0.661260i	$-0.229978\pi$
$954$	−1.43473			−0.0464512
$955$	−36.7891	−	23.7944i	−1.19047	−	0.769970i
$956$	11.0131			0.356190
$957$			24.8395i			0.802947i
$958$			3.32352i			0.107378i
$959$	35.6269			1.15045
$960$	8.44333	−	13.0544i	0.272507	−	0.421329i
$961$	−30.4257			−0.981474
$962$		−	12.2985i		−	0.396520i
$963$		−	12.5818i		−	0.405442i
$964$	13.0775			0.421197
$965$	0.586978	−	0.907539i	0.0188955	−	0.0292147i
$966$	−10.5423			−0.339194
$967$			24.1608i			0.776958i	0.921458	+	0.388479i	$0.126999\pi$
$967$			24.1608i			0.776958i	−0.921458	+	0.388479i	$0.873001\pi$
$968$			9.69845i			0.311720i
$969$		0			0
$970$	5.75036	+	3.71922i	0.184633	+	0.119417i
$971$	−27.7592			−0.890836			−0.445418	−	0.895323i	$-0.646945\pi$
$971$	−27.7592			−0.890836			−0.445418	+	0.895323i	$0.646945\pi$
$972$			15.0865i			0.483899i
$973$		−	25.4024i		−	0.814364i
$974$	−9.07201			−0.290686
$975$	17.6400	+	39.2287i	0.564933	+	1.25633i
$976$	28.1221			0.900168
$977$		−	3.56499i		−	0.114054i	−0.998373	−	0.0570270i	$-0.981838\pi$
$977$		−	3.56499i		−	0.114054i	0.998373	−	0.0570270i	$-0.0181621\pi$
$978$			1.12635i			0.0360166i
$979$	5.38337			0.172053
$980$	9.29458	+	6.01155i	0.296905	+	0.192032i
$981$	15.9040			0.507776
$982$		−	4.19403i		−	0.133837i
$983$		−	1.63550i		−	0.0521643i	−0.999660	−	0.0260822i	$-0.991697\pi$
$983$		−	1.63550i		−	0.0521643i	0.999660	−	0.0260822i	$-0.00830315\pi$
$984$	−21.8368			−0.696131
$985$	−1.53241	+	2.36929i	−0.0488267	+	0.0754920i
$986$	13.5354			0.431056
$987$		−	25.6523i		−	0.816521i
$988$		0			0
$989$	18.4230			0.585818
$990$	1.04349	−	1.61337i	0.0331644	−	0.0512762i
$991$	−1.50405			−0.0477778			−0.0238889	−	0.999715i	$-0.507605\pi$
$991$	−1.50405			−0.0477778			−0.0238889	+	0.999715i	$0.507605\pi$
$992$			3.55033i			0.112723i
$993$			65.8526i			2.08977i
$994$	−9.13015			−0.289591
$995$	−38.7822	−	25.0835i	−1.22948	−	0.795201i
$996$	−24.8497			−0.787392
$997$		−	51.4138i		−	1.62829i	−0.580660	−	0.814146i	$-0.697205\pi$
$997$		−	51.4138i		−	1.62829i	0.580660	−	0.814146i	$-0.302795\pi$
$998$		−	10.7675i		−	0.340841i
$999$	−26.4453			−0.836692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.l.1084.10		24
5.2	odd	4		9025.2.a.ct.1.15		24
5.3	odd	4		9025.2.a.ct.1.10		24
5.4	even	2	inner	1805.2.b.l.1084.15		24
19.14	odd	18		95.2.p.a.44.5	yes	48
19.15	odd	18		95.2.p.a.54.4	yes	48
19.18	odd	2		1805.2.b.k.1084.15		24
57.14	even	18		855.2.da.b.424.4		48
57.53	even	18		855.2.da.b.244.5		48
95.14	odd	18		95.2.p.a.44.4	✓	48
95.18	even	4		9025.2.a.cu.1.15		24
95.33	even	36		475.2.l.f.101.5		48
95.34	odd	18		95.2.p.a.54.5	yes	48
95.37	even	4		9025.2.a.cu.1.10		24
95.52	even	36		475.2.l.f.101.4		48
95.53	even	36		475.2.l.f.301.5		48
95.72	even	36		475.2.l.f.301.4		48
95.94	odd	2		1805.2.b.k.1084.10		24
285.14	even	18		855.2.da.b.424.5		48
285.224	even	18		855.2.da.b.244.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.4	✓	48	95.14	odd	18
95.2.p.a.44.5	yes	48	19.14	odd	18
95.2.p.a.54.4	yes	48	19.15	odd	18
95.2.p.a.54.5	yes	48	95.34	odd	18
475.2.l.f.101.4		48	95.52	even	36
475.2.l.f.101.5		48	95.33	even	36
475.2.l.f.301.4		48	95.72	even	36
475.2.l.f.301.5		48	95.53	even	36
855.2.da.b.244.4		48	285.224	even	18
855.2.da.b.244.5		48	57.53	even	18
855.2.da.b.424.4		48	57.14	even	18
855.2.da.b.424.5		48	285.14	even	18
1805.2.b.k.1084.10		24	95.94	odd	2
1805.2.b.k.1084.15		24	19.18	odd	2
1805.2.b.l.1084.10		24	1.1	even	1	trivial
1805.2.b.l.1084.15		24	5.4	even	2	inner
9025.2.a.ct.1.10		24	5.3	odd	4
9025.2.a.ct.1.15		24	5.2	odd	4
9025.2.a.cu.1.10		24	95.37	even	4
9025.2.a.cu.1.15		24	95.18	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)

\(f(q)\)	\(=\)	\(q-0.449373i q^{2} -1.95684i q^{3} +1.79806 q^{4} +(1.87757 + 1.21438i) q^{5} -0.879352 q^{6} +2.06079i q^{7} -1.70675i q^{8} -0.829224 q^{9} +(0.545709 - 0.843732i) q^{10} -2.30599 q^{11} -3.51852i q^{12} +4.39611i q^{13} +0.926065 q^{14} +(2.37634 - 3.67411i) q^{15} +2.82916 q^{16} +5.47185i q^{17} +0.372631i q^{18} +(3.37600 + 2.18353i) q^{20} +4.03264 q^{21} +1.03625i q^{22} -5.81755i q^{23} -3.33983 q^{24} +(2.05058 + 4.56017i) q^{25} +1.97549 q^{26} -4.24786i q^{27} +3.70544i q^{28} +5.50466 q^{29} +(-1.65105 - 1.06786i) q^{30} -0.757832 q^{31} -4.68485i q^{32} +4.51245i q^{33} +2.45890 q^{34} +(-2.50258 + 3.86929i) q^{35} -1.49100 q^{36} -6.22555i q^{37} +8.60248 q^{39} +(2.07264 - 3.20455i) q^{40} +6.53829 q^{41} -1.81216i q^{42} +3.16680i q^{43} -4.14632 q^{44} +(-1.55693 - 1.00699i) q^{45} -2.61425 q^{46} -6.36116i q^{47} -5.53621i q^{48} +2.75314 q^{49} +(2.04922 - 0.921474i) q^{50} +10.7075 q^{51} +7.90448i q^{52} +3.85028i q^{53} -1.90888 q^{54} +(-4.32967 - 2.80034i) q^{55} +3.51725 q^{56} -2.47365i q^{58} +2.55023 q^{59} +(4.27282 - 6.60629i) q^{60} +9.94010 q^{61} +0.340550i q^{62} -1.70886i q^{63} +3.55308 q^{64} +(-5.33853 + 8.25402i) q^{65} +2.02778 q^{66} +1.70269i q^{67} +9.83874i q^{68} -11.3840 q^{69} +(1.73876 + 1.12459i) q^{70} -9.85909 q^{71} +1.41528i q^{72} +10.2167i q^{73} -2.79760 q^{74} +(8.92352 - 4.01265i) q^{75} -4.75216i q^{77} -3.86572i q^{78} +2.41187 q^{79} +(5.31196 + 3.43567i) q^{80} -10.8001 q^{81} -2.93813i q^{82} -7.06253i q^{83} +7.25095 q^{84} +(-6.64489 + 10.2738i) q^{85} +1.42307 q^{86} -10.7717i q^{87} +3.93574i q^{88} -2.33452 q^{89} +(-0.452514 + 0.699642i) q^{90} -9.05946 q^{91} -10.4603i q^{92} +1.48296i q^{93} -2.85854 q^{94} -9.16749 q^{96} +6.81539i q^{97} -1.23719i q^{98} +1.91218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 + 6 * q^10 + 12 * q^11 + 24 * q^14 + 9 * q^15 + 6 * q^16 + 21 * q^20 - 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 + 36 * q^29 - 18 * q^30 - 42 * q^31 + 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 - 12 * q^40 - 60 * q^41 + 30 * q^44 + 9 * q^45 - 6 * q^46 - 12 * q^49 - 18 * q^50 - 30 * q^51 + 24 * q^54 + 33 * q^55 - 18 * q^56 + 60 * q^59 + 42 * q^60 + 30 * q^61 - 18 * q^65 + 36 * q^66 + 66 * q^69 - 9 * q^70 - 96 * q^71 - 24 * q^74 - 36 * q^75 + 72 * q^79 - 42 * q^80 - 96 * q^81 - 54 * q^84 - 27 * q^85 - 108 * q^86 + 84 * q^89 + 93 * q^90 - 96 * q^91 + 36 * q^94 - 120 * q^96

Introduction

L-functions

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Database

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