LMFDB - Embedded newform 1805.2.b.i.1084.6

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			1084.6
Root			$-0.805332i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.i.1084.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.805332i q^{2} +1.95838i q^{3} +1.35144 q^{4} +(2.22523 - 0.219874i) q^{5} +1.57714 q^{6} -1.03713i q^{7} -2.69902i q^{8} -0.835236 q^{9} +O(q^{10})$	\(q-0.805332i q^{2} +1.95838i q^{3} +1.35144 q^{4} +(2.22523 - 0.219874i) q^{5} +1.57714 q^{6} -1.03713i q^{7} -2.69902i q^{8} -0.835236 q^{9} +(-0.177072 - 1.79205i) q^{10} +1.80539 q^{11} +2.64663i q^{12} -2.36455i q^{13} -0.835236 q^{14} +(0.430596 + 4.35784i) q^{15} +0.529273 q^{16} +6.49986i q^{17} +0.672642i q^{18} +(3.00727 - 0.297147i) q^{20} +2.03110 q^{21} -1.45394i q^{22} +7.26351i q^{23} +5.28570 q^{24} +(4.90331 - 0.978542i) q^{25} -1.90425 q^{26} +4.23942i q^{27} -1.40162i q^{28} -2.22179 q^{29} +(3.50951 - 0.346773i) q^{30} -5.25331 q^{31} -5.82428i q^{32} +3.53564i q^{33} +5.23455 q^{34} +(-0.228039 - 2.30786i) q^{35} -1.12877 q^{36} -6.67893i q^{37} +4.63069 q^{39} +(-0.593445 - 6.00595i) q^{40} +4.43199 q^{41} -1.63571i q^{42} -6.26252i q^{43} +2.43988 q^{44} +(-1.85859 + 0.183647i) q^{45} +5.84953 q^{46} -8.38928i q^{47} +1.03652i q^{48} +5.92436 q^{49} +(-0.788051 - 3.94879i) q^{50} -12.7292 q^{51} -3.19556i q^{52} +0.0601745i q^{53} +3.41414 q^{54} +(4.01742 - 0.396960i) q^{55} -2.79924 q^{56} +1.78928i q^{58} +12.8100 q^{59} +(0.581925 + 5.88936i) q^{60} -13.4454 q^{61} +4.23066i q^{62} +0.866251i q^{63} -3.63194 q^{64} +(-0.519904 - 5.26168i) q^{65} +2.84736 q^{66} +6.49953i q^{67} +8.78418i q^{68} -14.2247 q^{69} +(-1.85859 + 0.183647i) q^{70} +13.5401 q^{71} +2.25432i q^{72} -8.23357i q^{73} -5.37876 q^{74} +(1.91635 + 9.60253i) q^{75} -1.87243i q^{77} -3.72924i q^{78} +6.11205 q^{79} +(1.17776 - 0.116373i) q^{80} -10.8081 q^{81} -3.56922i q^{82} -4.95287i q^{83} +2.74491 q^{84} +(1.42915 + 14.4637i) q^{85} -5.04341 q^{86} -4.35110i q^{87} -4.87280i q^{88} -13.6216 q^{89} +(0.147897 + 1.49678i) q^{90} -2.45236 q^{91} +9.81620i q^{92} -10.2880i q^{93} -6.75615 q^{94} +11.4061 q^{96} +18.4456i q^{97} -4.77107i q^{98} -1.50793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.805332i		−	0.569456i	−0.958608	−	0.284728i	$-0.908097\pi$
$2$		−	0.805332i		−	0.569456i	0.958608	−	0.284728i	$-0.0919032\pi$
$3$			1.95838i			1.13067i	0.824862	+	0.565334i	$0.191253\pi$
$3$			1.95838i			1.13067i	−0.824862	+	0.565334i	$0.808747\pi$
$4$	1.35144			0.675720
$5$	2.22523	−	0.219874i	0.995154	−	0.0983307i
$5$	2.22523	−	0.219874i	0.995154	−	0.0983307i
$6$	1.57714			0.643866
$7$		−	1.03713i		−	0.391999i	−0.980604	−	0.196000i	$-0.937205\pi$
$7$		−	1.03713i		−	0.391999i	0.980604	−	0.196000i	$-0.0627952\pi$
$8$		−	2.69902i		−	0.954248i
$9$	−0.835236			−0.278412
$10$	−0.177072	−	1.79205i	−0.0559950	−	0.566696i
$11$	1.80539			0.544347			0.272173	−	0.962248i	$-0.412258\pi$
$11$	1.80539			0.544347			0.272173	+	0.962248i	$0.412258\pi$
$12$			2.64663i			0.764016i
$13$		−	2.36455i		−	0.655810i	−0.944711	−	0.327905i	$-0.893657\pi$
$13$		−	2.36455i		−	0.655810i	0.944711	−	0.327905i	$-0.106343\pi$
$14$	−0.835236			−0.223226
$15$	0.430596	+	4.35784i	0.111179	+	1.12519i
$16$	0.529273			0.132318
$17$			6.49986i			1.57645i	0.615388	+	0.788224i	$0.288999\pi$
$17$			6.49986i			1.57645i	−0.615388	+	0.788224i	$0.711001\pi$
$18$			0.672642i			0.158543i
$19$		0			0
$19$		0			0
$20$	3.00727	−	0.297147i	0.672446	−	0.0664440i
$21$	2.03110			0.443222
$22$		−	1.45394i		−	0.309981i
$23$			7.26351i			1.51455i	0.653099	+	0.757273i	$0.273469\pi$
$23$			7.26351i			1.51455i	−0.653099	+	0.757273i	$0.726531\pi$
$24$	5.28570			1.07894
$25$	4.90331	−	0.978542i	0.980662	−	0.195708i
$26$	−1.90425			−0.373454
$27$			4.23942i			0.815877i
$28$		−	1.40162i		−	0.264882i
$29$	−2.22179			−0.412576			−0.206288	−	0.978491i	$-0.566138\pi$
$29$	−2.22179			−0.412576			−0.206288	+	0.978491i	$0.566138\pi$
$30$	3.50951	−	0.346773i	0.640745	−	0.0633118i
$31$	−5.25331			−0.943522			−0.471761	−	0.881727i	$-0.656381\pi$
$31$	−5.25331			−0.943522			−0.471761	+	0.881727i	$0.656381\pi$
$32$		−	5.82428i		−	1.02960i
$33$			3.53564i			0.615476i
$34$	5.23455			0.897717
$35$	−0.228039	−	2.30786i	−0.0385456	−	0.390100i
$36$	−1.12877			−0.188129
$37$		−	6.67893i		−	1.09801i	−0.835819	−	0.549005i	$-0.815007\pi$
$37$		−	6.67893i		−	1.09801i	0.835819	−	0.549005i	$-0.184993\pi$
$38$		0			0
$39$	4.63069			0.741503
$40$	−0.593445	−	6.00595i	−0.0938319	−	0.949624i
$41$	4.43199			0.692161			0.346080	−	0.938205i	$-0.387512\pi$
$41$	4.43199			0.692161			0.346080	+	0.938205i	$0.387512\pi$
$42$		−	1.63571i		−	0.252395i
$43$		−	6.26252i		−	0.955025i	−0.878625	−	0.477513i	$-0.841538\pi$
$43$		−	6.26252i		−	0.955025i	0.878625	−	0.477513i	$-0.158462\pi$
$44$	2.43988			0.367826
$45$	−1.85859	+	0.183647i	−0.277063	+	0.0273765i
$46$	5.84953			0.862467
$47$		−	8.38928i		−	1.22370i	−0.790973	−	0.611851i	$-0.790425\pi$
$47$		−	8.38928i		−	1.22370i	0.790973	−	0.611851i	$-0.209575\pi$
$48$			1.03652i			0.149608i
$49$	5.92436			0.846336
$50$	−0.788051	−	3.94879i	−0.111447	−	0.558444i
$51$	−12.7292			−1.78244
$52$		−	3.19556i		−	0.443144i
$53$			0.0601745i			0.00826560i	0.999991	+	0.00413280i	$0.00131551\pi$
$53$			0.0601745i			0.00826560i	−0.999991	+	0.00413280i	$0.998684\pi$
$54$	3.41414			0.464606
$55$	4.01742	−	0.396960i	0.541709	−	0.0535260i
$56$	−2.79924			−0.374065
$57$		0			0
$58$			1.78928i			0.234944i
$59$	12.8100			1.66772			0.833860	−	0.551976i	$-0.186126\pi$
$59$	12.8100			1.66772			0.833860	+	0.551976i	$0.186126\pi$
$60$	0.581925	+	5.88936i	0.0751262	+	0.760313i
$61$	−13.4454			−1.72151			−0.860753	−	0.509024i	$-0.830007\pi$
$61$	−13.4454			−1.72151			−0.860753	+	0.509024i	$0.830007\pi$
$62$			4.23066i			0.537294i
$63$			0.866251i			0.109137i
$64$	−3.63194			−0.453992
$65$	−0.519904	−	5.26168i	−0.0644862	−	0.652631i
$66$	2.84736			0.350486
$67$			6.49953i			0.794043i	0.917809	+	0.397022i	$0.129956\pi$
$67$			6.49953i			0.794043i	−0.917809	+	0.397022i	$0.870044\pi$
$68$			8.78418i			1.06524i
$69$	−14.2247			−1.71245
$70$	−1.85859	+	0.183647i	−0.222144	+	0.0219500i
$71$	13.5401			1.60692			0.803459	−	0.595361i	$-0.202991\pi$
$71$	13.5401			1.60692			0.803459	+	0.595361i	$0.202991\pi$
$72$			2.25432i			0.265674i
$73$		−	8.23357i		−	0.963666i	−0.876263	−	0.481833i	$-0.839971\pi$
$73$		−	8.23357i		−	0.963666i	0.876263	−	0.481833i	$-0.160029\pi$
$74$	−5.37876			−0.625268
$75$	1.91635	+	9.60253i	0.221281	+	1.10880i
$76$		0			0
$77$		−	1.87243i		−	0.213384i
$78$		−	3.72924i		−	0.422253i
$79$	6.11205			0.687659			0.343830	−	0.939032i	$-0.388276\pi$
$79$	6.11205			0.687659			0.343830	+	0.939032i	$0.388276\pi$
$80$	1.17776	−	0.116373i	0.131677	−	0.0130109i
$81$	−10.8081			−1.20090
$82$		−	3.56922i		−	0.394155i
$83$		−	4.95287i		−	0.543648i	−0.962347	−	0.271824i	$-0.912373\pi$
$83$		−	4.95287i		−	0.543648i	0.962347	−	0.271824i	$-0.0876269\pi$
$84$	2.74491			0.299494
$85$	1.42915	+	14.4637i	0.155013	+	1.56881i
$86$	−5.04341			−0.543845
$87$		−	4.35110i		−	0.466487i
$88$		−	4.87280i		−	0.519442i
$89$	−13.6216			−1.44389			−0.721945	−	0.691951i	$-0.756751\pi$
$89$	−13.6216			−1.44389			−0.721945	+	0.691951i	$0.756751\pi$
$90$	0.147897	+	1.49678i	0.0155897	+	0.157775i
$91$	−2.45236			−0.257077
$92$			9.81620i			1.02341i
$93$		−	10.2880i		−	1.06681i
$94$	−6.75615			−0.696844
$95$		0			0
$96$	11.4061			1.16413
$97$			18.4456i			1.87287i	0.350841	+	0.936435i	$0.385896\pi$
$97$			18.4456i			1.87287i	−0.350841	+	0.936435i	$0.614104\pi$
$98$		−	4.77107i		−	0.481951i
$99$	−1.50793			−0.151553
$100$	6.62653	−	1.32244i	0.662653	−	0.132244i
$101$	−5.68380			−0.565559			−0.282780	−	0.959185i	$-0.591257\pi$
$101$	−5.68380			−0.565559			−0.282780	+	0.959185i	$0.591257\pi$
$102$			10.2512i			1.01502i
$103$			6.57772i			0.648122i	0.946036	+	0.324061i	$0.105048\pi$
$103$			6.57772i			0.648122i	−0.946036	+	0.324061i	$0.894952\pi$
$104$	−6.38199			−0.625805
$105$	4.51966	−	0.446586i	0.441074	−	0.0435823i
$106$	0.0484604			0.00470689
$107$			12.0277i			1.16276i	0.813631	+	0.581382i	$0.197488\pi$
$107$			12.0277i			1.16276i	−0.813631	+	0.581382i	$0.802512\pi$
$108$			5.72933i			0.551305i
$109$	2.78067			0.266340			0.133170	−	0.991093i	$-0.457484\pi$
$109$	2.78067			0.266340			0.133170	+	0.991093i	$0.457484\pi$
$110$	−0.319684	−	3.23536i	−0.0304807	−	0.308479i
$111$	13.0799			1.24149
$112$		−	0.548927i		−	0.0518687i
$113$		−	5.86007i		−	0.551269i	−0.961262	−	0.275635i	$-0.911112\pi$
$113$		−	5.86007i		−	0.551269i	0.961262	−	0.275635i	$-0.0888880\pi$
$114$		0			0
$115$	1.59706	+	16.1630i	0.148926	+	1.50721i
$116$	−3.00262			−0.278786
$117$			1.97496i			0.182585i
$118$		−	10.3163i		−	0.949692i
$119$	6.74122			0.617967
$120$	11.7619	−	1.16219i	1.07371	−	0.106093i
$121$	−7.74055			−0.703686
$122$			10.8280i			0.980321i
$123$			8.67951i			0.782605i
$124$	−7.09953			−0.637557
$125$	10.6958	−	3.25559i	0.956666	−	0.291189i
$126$	0.697620			0.0621489
$127$			10.5530i			0.936428i	0.883615	+	0.468214i	$0.155102\pi$
$127$			10.5530i			0.936428i	−0.883615	+	0.468214i	$0.844898\pi$
$128$		−	8.72366i		−	0.771069i
$129$	12.2644			1.07982
$130$	−4.23740	+	0.418696i	−0.371645	+	0.0367220i
$131$	−13.6545			−1.19300			−0.596501	−	0.802612i	$-0.703443\pi$
$131$	−13.6545			−1.19300			−0.596501	+	0.802612i	$0.703443\pi$
$132$			4.77821i			0.415890i
$133$		0			0
$134$	5.23427			0.452172
$135$	0.932139	+	9.43369i	0.0802258	+	0.811923i
$136$	17.5433			1.50432
$137$		−	15.6619i		−	1.33809i	−0.743224	−	0.669043i	$-0.766704\pi$
$137$		−	15.6619i		−	1.33809i	0.743224	−	0.669043i	$-0.233296\pi$
$138$			11.4556i			0.975164i
$139$	2.37339			0.201308			0.100654	−	0.994921i	$-0.467906\pi$
$139$	2.37339			0.201308			0.100654	+	0.994921i	$0.467906\pi$
$140$	−0.308181	−	3.11894i	−0.0260460	−	0.263598i
$141$	16.4294			1.38360
$142$		−	10.9043i		−	0.915068i
$143$		−	4.26895i		−	0.356988i
$144$	−0.442068			−0.0368390
$145$	−4.94399	+	0.488514i	−0.410576	+	0.0405689i
$146$	−6.63075			−0.548765
$147$			11.6021i			0.956926i
$148$		−	9.02618i		−	0.741947i
$149$	−3.19551			−0.261786			−0.130893	−	0.991396i	$-0.541784\pi$
$149$	−3.19551			−0.261786			−0.130893	+	0.991396i	$0.541784\pi$
$150$	7.73322	−	1.54330i	0.631415	−	0.126010i
$151$	−14.4241			−1.17382			−0.586908	−	0.809654i	$-0.699655\pi$
$151$	−14.4241			−1.17382			−0.586908	+	0.809654i	$0.699655\pi$
$152$		0			0
$153$		−	5.42892i		−	0.438902i
$154$	−1.50793			−0.121513
$155$	−11.6898	+	1.15507i	−0.938949	+	0.0927772i
$156$	6.25810			0.501049
$157$			10.0688i			0.803574i	0.915733	+	0.401787i	$0.131611\pi$
$157$			10.0688i			0.803574i	−0.915733	+	0.401787i	$0.868389\pi$
$158$		−	4.92223i		−	0.391591i
$159$	−0.117844			−0.00934565
$160$	−1.28061	−	12.9604i	−0.101241	−	1.02461i
$161$	7.53322			0.593701
$162$			8.70410i			0.683859i
$163$			4.33397i			0.339462i	0.985490	+	0.169731i	$0.0542899\pi$
$163$			4.33397i			0.339462i	−0.985490	+	0.169731i	$0.945710\pi$
$164$	5.98958			0.467707
$165$	0.777396	+	7.86762i	0.0605202	+	0.612493i
$166$	−3.98870			−0.309583
$167$		−	6.45124i		−	0.499212i	−0.968348	−	0.249606i	$-0.919699\pi$
$167$		−	6.45124i		−	0.499212i	0.968348	−	0.249606i	$-0.0803010\pi$
$168$		−	5.48197i		−	0.422943i
$169$	7.40888			0.569914
$170$	11.6481	−	1.15094i	0.893367	−	0.0882732i
$171$		0			0
$172$		−	8.46342i		−	0.645330i
$173$		−	6.89080i		−	0.523898i	−0.965082	−	0.261949i	$-0.915635\pi$
$173$		−	6.89080i		−	0.523898i	0.965082	−	0.261949i	$-0.0843652\pi$
$174$	−3.50408			−0.265643
$175$	−1.01488	−	5.08539i	−0.0767176	−	0.384419i
$176$	0.955547			0.0720271
$177$			25.0868i			1.88564i
$178$			10.9699i			0.822231i
$179$	−14.2092			−1.06205			−0.531023	−	0.847357i	$-0.678192\pi$
$179$	−14.2092			−1.06205			−0.531023	+	0.847357i	$0.678192\pi$
$180$	−2.51178	+	0.248188i	−0.187217	+	0.0184988i
$181$	−5.08595			−0.378036			−0.189018	−	0.981974i	$-0.560530\pi$
$181$	−5.08595			−0.378036			−0.189018	+	0.981974i	$0.560530\pi$
$182$			1.97496i			0.146394i
$183$		−	26.3311i		−	1.94645i
$184$	19.6044			1.44525
$185$	−1.46852	−	14.8622i	−0.107968	−	1.09269i
$186$	−8.28521			−0.607501
$187$			11.7348i			0.858135i
$188$		−	11.3376i		−	0.826880i
$189$	4.39684			0.319823
$190$		0			0
$191$	6.63072			0.479782			0.239891	−	0.970800i	$-0.422888\pi$
$191$	6.63072			0.479782			0.239891	+	0.970800i	$0.422888\pi$
$192$		−	7.11269i		−	0.513314i
$193$		−	13.7686i		−	0.991088i	−0.868583	−	0.495544i	$-0.834969\pi$
$193$		−	13.7686i		−	0.991088i	0.868583	−	0.495544i	$-0.165031\pi$
$194$	14.8549			1.06652
$195$	10.3044	−	1.01817i	0.737910	−	0.0729125i
$196$	8.00641			0.571887
$197$			0.729726i			0.0519908i	0.999662	+	0.0259954i	$0.00827552\pi$
$197$			0.729726i			0.0519908i	−0.999662	+	0.0259954i	$0.991724\pi$
$198$			1.21438i			0.0863026i
$199$	−5.72434			−0.405787			−0.202894	−	0.979201i	$-0.565035\pi$
$199$	−5.72434			−0.405787			−0.202894	+	0.979201i	$0.565035\pi$
$200$	−2.64111	−	13.2341i	−0.186754	−	0.935795i
$201$	−12.7285			−0.897800
$202$			4.57735i			0.322061i
$203$			2.30429i			0.161729i
$204$	−17.2027			−1.20443
$205$	9.86221	−	0.974481i	0.688807	−	0.0680607i
$206$	5.29725			0.369077
$207$		−	6.06674i		−	0.421668i
$208$		−	1.25150i		−	0.0867756i
$209$		0			0
$210$	−0.359650	−	3.63983i	−0.0248182	−	0.251172i
$211$	−18.4265			−1.26853			−0.634267	−	0.773114i	$-0.718698\pi$
$211$	−18.4265			−1.26853			−0.634267	+	0.773114i	$0.718698\pi$
$212$			0.0813222i			0.00558523i
$213$			26.5167i			1.81689i
$214$	9.68631			0.662143
$215$	−1.37697	−	13.9356i	−0.0939083	−	0.950397i
$216$	11.4423			0.778549
$217$			5.44838i			0.369860i
$218$		−	2.23937i		−	0.151669i
$219$	16.1244			1.08959
$220$	5.42931	−	0.536467i	0.366044	−	0.0361686i
$221$	15.3693			1.03385
$222$		−	10.5336i		−	0.706971i
$223$			5.88051i			0.393788i	0.980425	+	0.196894i	$0.0630855\pi$
$223$			5.88051i			0.393788i	−0.980425	+	0.196894i	$0.936914\pi$
$224$	−6.04056			−0.403602
$225$	−4.09542	+	0.817313i	−0.273028	+	0.0544876i
$226$	−4.71930			−0.313923
$227$			5.89316i			0.391143i	0.980689	+	0.195571i	$0.0626561\pi$
$227$			5.89316i			0.391143i	−0.980689	+	0.195571i	$0.937344\pi$
$228$		0			0
$229$	−16.2890			−1.07641			−0.538205	−	0.842814i	$-0.680897\pi$
$229$	−16.2890			−1.07641			−0.538205	+	0.842814i	$0.680897\pi$
$230$	13.0166	−	1.28616i	0.858287	−	0.0848069i
$231$	3.66693			0.241266
$232$			5.99666i			0.393700i
$233$		−	22.9771i		−	1.50528i	−0.658432	−	0.752640i	$-0.728780\pi$
$233$		−	22.9771i		−	1.50528i	0.658432	−	0.752640i	$-0.271220\pi$
$234$	1.59050			0.103974
$235$	−1.84458	−	18.6681i	−0.120327	−	1.21777i
$236$	17.3120			1.12691
$237$			11.9697i			0.777515i
$238$		−	5.42892i		−	0.351905i
$239$	4.58060			0.296294			0.148147	−	0.988965i	$-0.452669\pi$
$239$	4.58060			0.296294			0.148147	+	0.988965i	$0.452669\pi$
$240$	0.227903	+	2.30649i	0.0147111	+	0.148883i
$241$	8.67191			0.558607			0.279303	−	0.960203i	$-0.409896\pi$
$241$	8.67191			0.558607			0.279303	+	0.960203i	$0.409896\pi$
$242$			6.23371i			0.400718i
$243$		−	8.44804i		−	0.541942i
$244$	−18.1706			−1.16326
$245$	13.1831	−	1.30261i	0.842235	−	0.0832208i
$246$	6.98988			0.445659
$247$		0			0
$248$			14.1788i			0.900354i
$249$	9.69958			0.614686
$250$	−2.62183	−	8.61370i	−0.165819	−	0.544779i
$251$	2.98418			0.188360			0.0941800	−	0.995555i	$-0.469977\pi$
$251$	2.98418			0.188360			0.0941800	+	0.995555i	$0.469977\pi$
$252$			1.17069i			0.0737464i
$253$			13.1135i			0.824438i
$254$	8.49867			0.533254
$255$	−28.3254	+	2.79882i	−1.77380	+	0.175269i
$256$	−14.2893			−0.893082
$257$		−	5.09001i		−	0.317506i	−0.987318	−	0.158753i	$-0.949253\pi$
$257$		−	5.09001i		−	0.317506i	0.987318	−	0.158753i	$-0.0507474\pi$
$258$		−	9.87689i		−	0.614908i
$259$	−6.92694			−0.430419
$260$	−0.702620	−	7.11085i	−0.0435746	−	0.440996i
$261$	1.85572			0.114866
$262$			10.9964i			0.679362i
$263$			15.5925i			0.961472i	0.876865	+	0.480736i	$0.159630\pi$
$263$			15.5925i			0.961472i	−0.876865	+	0.480736i	$0.840370\pi$
$264$	9.54277			0.587317
$265$	0.0132308	+	0.133902i	0.000812762	+	0.00822554i
$266$		0			0
$267$		−	26.6763i		−	1.63256i
$268$			8.78372i			0.536551i
$269$	−19.2926			−1.17629			−0.588145	−	0.808756i	$-0.700141\pi$
$269$	−19.2926			−1.17629			−0.588145	+	0.808756i	$0.700141\pi$
$270$	7.59725	−	0.750681i	0.462354	−	0.0456850i
$271$	−27.4796			−1.66927			−0.834635	−	0.550804i	$-0.814321\pi$
$271$	−27.4796			−1.66927			−0.834635	+	0.550804i	$0.814321\pi$
$272$			3.44020i			0.208593i
$273$		−	4.80264i		−	0.290669i
$274$	−12.6130			−0.761981
$275$	8.85241	−	1.76665i	0.533820	−	0.106533i
$276$	−19.2238			−1.15714
$277$		−	16.9570i		−	1.01885i	−0.860516	−	0.509424i	$-0.829858\pi$
$277$		−	16.9570i		−	1.01885i	0.860516	−	0.509424i	$-0.170142\pi$
$278$		−	1.91137i		−	0.114636i
$279$	4.38775			0.262688
$280$	−6.22897	+	0.615481i	−0.372252	+	0.0367821i
$281$	−12.4942			−0.745339			−0.372670	−	0.927964i	$-0.621558\pi$
$281$	−12.4942			−0.745339			−0.372670	+	0.927964i	$0.621558\pi$
$282$		−	13.2311i		−	0.787900i
$283$			30.8774i			1.83547i	0.397189	+	0.917737i	$0.369986\pi$
$283$			30.8774i			1.83547i	−0.397189	+	0.917737i	$0.630014\pi$
$284$	18.2987			1.08583
$285$		0			0
$286$	−3.43793			−0.203289
$287$		−	4.59657i		−	0.271327i
$288$			4.86465i			0.286652i
$289$	−25.2482			−1.48519
$290$	0.393416	+	3.98156i	0.0231022	+	0.233805i
$291$	−36.1235			−2.11760
$292$		−	11.1272i		−	0.651169i
$293$		−	25.1823i		−	1.47117i	−0.677434	−	0.735583i	$-0.736908\pi$
$293$		−	25.1823i		−	1.47117i	0.677434	−	0.735583i	$-0.263092\pi$
$294$	9.34355			0.544927
$295$	28.5052	−	2.81659i	1.65964	−	0.163988i
$296$	−18.0266			−1.04777
$297$			7.65383i			0.444120i
$298$			2.57344i			0.149076i
$299$	17.1750			0.993254
$300$	2.58984	+	12.9772i	0.149524	+	0.749242i
$301$	−6.49507			−0.374369
$302$			11.6162i			0.668436i
$303$		−	11.1310i		−	0.639460i
$304$		0			0
$305$	−29.9191	+	2.95629i	−1.71316	+	0.169277i
$306$	−4.37208			−0.249935
$307$			6.07770i			0.346873i	0.984845	+	0.173436i	$0.0554871\pi$
$307$			6.07770i			0.346873i	−0.984845	+	0.173436i	$0.944513\pi$
$308$		−	2.53048i		−	0.144188i
$309$	−12.8817			−0.732812
$310$	0.930212	+	9.41419i	0.0528325	+	0.534690i
$311$	8.22815			0.466576			0.233288	−	0.972408i	$-0.425052\pi$
$311$	8.22815			0.466576			0.233288	+	0.972408i	$0.425052\pi$
$312$		−	12.4983i		−	0.707578i
$313$		−	28.7995i		−	1.62784i	−0.580975	−	0.813922i	$-0.697329\pi$
$313$		−	28.7995i		−	1.62784i	0.580975	−	0.813922i	$-0.302671\pi$
$314$	8.10868			0.457600
$315$	0.190466	+	1.92761i	0.0107316	+	0.108608i
$316$	8.26007			0.464665
$317$		−	13.0478i		−	0.732840i	−0.930450	−	0.366420i	$-0.880583\pi$
$317$		−	13.0478i		−	0.732840i	0.930450	−	0.366420i	$-0.119417\pi$
$318$			0.0949037i			0.00532193i
$319$	−4.01120			−0.224584
$320$	−8.08190	+	0.798569i	−0.451792	+	0.0446413i
$321$	−23.5548			−1.31470
$322$		−	6.06674i		−	0.338086i
$323$		0			0
$324$	−14.6065			−0.811472
$325$	−2.31382	−	11.5941i	−0.128347	−	0.643128i
$326$	3.49028			0.193309
$327$			5.44561i			0.301143i
$328$		−	11.9620i		−	0.660493i
$329$	−8.70080			−0.479690
$330$	6.33605	−	0.626062i	0.348788	−	0.0344636i
$331$	4.28808			0.235694			0.117847	−	0.993032i	$-0.462401\pi$
$331$	4.28808			0.235694			0.117847	+	0.993032i	$0.462401\pi$
$332$		−	6.69351i		−	0.367354i
$333$			5.57849i			0.305699i
$334$	−5.19539			−0.284279
$335$	1.42908	+	14.4629i	0.0780788	+	0.790195i
$336$	1.07500			0.0586463
$337$		−	5.26898i		−	0.287020i	−0.989649	−	0.143510i	$-0.954161\pi$
$337$		−	5.26898i		−	0.287020i	0.989649	−	0.143510i	$-0.0458389\pi$
$338$		−	5.96661i		−	0.324541i
$339$	11.4762			0.623303
$340$	1.93141	+	19.5468i	0.104746	+	1.06008i
$341$	−9.48429			−0.513603
$342$		0			0
$343$		−	13.4043i		−	0.723763i
$344$	−16.9027			−0.911331
$345$	−31.6532	+	3.12764i	−1.70415	+	0.168386i
$346$	−5.54938			−0.298337
$347$			9.78768i			0.525430i	0.964873	+	0.262715i	$0.0846179\pi$
$347$			9.78768i			0.525430i	−0.964873	+	0.262715i	$0.915382\pi$
$348$		−	5.88025i		−	0.315214i
$349$	−13.6788			−0.732211			−0.366106	−	0.930573i	$-0.619309\pi$
$349$	−13.6788			−0.732211			−0.366106	+	0.930573i	$0.619309\pi$
$350$	−4.09542	+	0.817313i	−0.218910	+	0.0436872i
$351$	10.0243			0.535060
$352$		−	10.5151i		−	0.560458i
$353$			16.9726i			0.903363i	0.892179	+	0.451681i	$0.149176\pi$
$353$			16.9726i			0.903363i	−0.892179	+	0.451681i	$0.850824\pi$
$354$	20.2032			1.07379
$355$	30.1299	−	2.97712i	1.59913	−	0.158009i
$356$	−18.4088			−0.975665
$357$			13.2018i			0.698716i
$358$			11.4431i			0.604789i
$359$	10.2829			0.542713			0.271356	−	0.962479i	$-0.412528\pi$
$359$	10.2829			0.542713			0.271356	+	0.962479i	$0.412528\pi$
$360$	0.495667	+	5.01639i	0.0261239	+	0.264387i
$361$		0			0
$362$			4.09588i			0.215275i
$363$		−	15.1589i		−	0.795636i
$364$	−3.31422			−0.173712
$365$	−1.81035	−	18.3216i	−0.0947580	−	0.958996i
$366$	−21.2053			−1.10842
$367$		−	36.2545i		−	1.89247i	−0.323480	−	0.946235i	$-0.604853\pi$
$367$		−	36.2545i		−	1.89247i	0.323480	−	0.946235i	$-0.395147\pi$
$368$			3.84438i			0.200402i
$369$	−3.70176			−0.192706
$370$	−11.9690	+	1.18265i	−0.622237	+	0.0614830i
$371$	0.0624089			0.00324011
$372$		−	13.9036i		−	0.720866i
$373$			20.9496i			1.08473i	0.840143	+	0.542365i	$0.182471\pi$
$373$			20.9496i			1.08473i	−0.840143	+	0.542365i	$0.817529\pi$
$374$	9.45042			0.488670
$375$	6.37567	+	20.9465i	0.329238	+	1.08167i
$376$	−22.6428			−1.16772
$377$			5.25354i			0.270571i
$378$		−	3.54092i		−	0.182125i
$379$	−12.7015			−0.652434			−0.326217	−	0.945295i	$-0.605774\pi$
$379$	−12.7015			−0.652434			−0.326217	+	0.945295i	$0.605774\pi$
$380$		0			0
$381$	−20.6668			−1.05879
$382$		−	5.33993i		−	0.273214i
$383$			8.28673i			0.423432i	0.977331	+	0.211716i	$0.0679052\pi$
$383$			8.28673i			0.423432i	−0.977331	+	0.211716i	$0.932095\pi$
$384$	17.0842			0.871824
$385$	−0.411700	−	4.16660i	−0.0209822	−	0.212350i
$386$	−11.0883			−0.564381
$387$			5.23068i			0.265891i
$388$			24.9282i			1.26554i
$389$	15.0072			0.760898			0.380449	−	0.924802i	$-0.375769\pi$
$389$	15.0072			0.760898			0.380449	+	0.924802i	$0.375769\pi$
$390$	−0.819963	−	8.29842i	−0.0415205	−	0.420207i
$391$	−47.2118			−2.38760
$392$		−	15.9900i		−	0.807615i
$393$		−	26.7407i		−	1.34889i
$394$	0.587671			0.0296064
$395$	13.6007	−	1.34388i	0.684327	−	0.0676180i
$396$	−2.03788			−0.102407
$397$		−	9.68332i		−	0.485992i	−0.970027	−	0.242996i	$-0.921870\pi$
$397$		−	9.68332i		−	0.485992i	0.970027	−	0.242996i	$-0.0781302\pi$
$398$			4.60999i			0.231078i
$399$		0			0
$400$	2.59519	−	0.517916i	0.129760	−	0.0258958i
$401$	−17.3572			−0.866775			−0.433387	−	0.901208i	$-0.642682\pi$
$401$	−17.3572			−0.866775			−0.433387	+	0.901208i	$0.642682\pi$
$402$			10.2507i			0.511257i
$403$			12.4217i			0.618771i
$404$	−7.68132			−0.382160
$405$	−24.0505	+	2.37642i	−1.19508	+	0.118085i
$406$	1.85572			0.0920977
$407$		−	12.0581i		−	0.597698i
$408$			34.3563i			1.70089i
$409$	15.3330			0.758167			0.379083	−	0.925363i	$-0.376239\pi$
$409$	15.3330			0.758167			0.379083	+	0.925363i	$0.376239\pi$
$410$	−0.784780	−	7.94235i	−0.0387575	−	0.392245i
$411$	30.6719			1.51293
$412$			8.88940i			0.437949i
$413$		−	13.2857i		−	0.653745i
$414$	−4.88574			−0.240121
$415$	−1.08901	−	11.0213i	−0.0534573	−	0.541013i
$416$	−13.7718			−0.675220
$417$			4.64799i			0.227613i
$418$		0			0
$419$	−1.03847			−0.0507326			−0.0253663	−	0.999678i	$-0.508075\pi$
$419$	−1.03847			−0.0507326			−0.0253663	+	0.999678i	$0.508075\pi$
$420$	6.10805	−	0.603534i	0.298042	−	0.0294494i
$421$	31.9823			1.55872			0.779360	−	0.626577i	$-0.215544\pi$
$421$	31.9823			1.55872			0.779360	+	0.626577i	$0.215544\pi$
$422$			14.8395i			0.722374i
$423$			7.00703i			0.340693i
$424$	0.162412			0.00788743
$425$	6.36039	+	31.8708i	0.308524	+	1.54596i
$426$	21.3547			1.03464
$427$			13.9447i			0.674829i
$428$			16.2548i			0.785704i
$429$	8.36022			0.403635
$430$	−11.2227	+	1.10891i	−0.541209	+	0.0534766i
$431$	9.65878			0.465247			0.232624	−	0.972567i	$-0.425269\pi$
$431$	9.65878			0.465247			0.232624	+	0.972567i	$0.425269\pi$
$432$			2.24381i			0.107955i
$433$			22.4423i			1.07851i	0.842143	+	0.539254i	$0.181294\pi$
$433$			22.4423i			1.07851i	−0.842143	+	0.539254i	$0.818706\pi$
$434$	4.38775			0.210619
$435$	−0.956694	−	9.68220i	−0.0458699	−	0.464226i
$436$	3.75792			0.179972
$437$		0			0
$438$		−	12.9855i		−	0.620472i
$439$	−20.8661			−0.995884			−0.497942	−	0.867210i	$-0.665911\pi$
$439$	−20.8661			−0.995884			−0.497942	+	0.867210i	$0.665911\pi$
$440$	−1.07140	−	10.8431i	−0.0510771	−	0.516925i
$441$	−4.94824			−0.235630
$442$		−	12.3774i		−	0.588732i
$443$		−	0.0662795i		−	0.00314903i	−0.999999	−	0.00157452i	$-0.999499\pi$
$443$		−	0.0662795i		−	0.00314903i	0.999999	−	0.00157452i	$-0.000501184\pi$
$444$	17.6767			0.838897
$445$	−30.3113	+	2.99504i	−1.43689	+	0.141979i
$446$	4.73576			0.224245
$447$		−	6.25800i		−	0.295993i
$448$			3.76680i			0.177965i
$449$	0.575177			0.0271443			0.0135721	−	0.999908i	$-0.495680\pi$
$449$	0.575177			0.0271443			0.0135721	+	0.999908i	$0.495680\pi$
$450$	0.658209	+	3.29817i	0.0310282	+	0.155477i
$451$	8.00150			0.376776
$452$		−	7.91954i		−	0.372504i
$453$		−	28.2478i		−	1.32720i
$454$	4.74595			0.222738
$455$	−5.45706	+	0.539210i	−0.255831	+	0.0252786i
$456$		0			0
$457$			41.2016i			1.92733i	0.267113	+	0.963665i	$0.413930\pi$
$457$			41.2016i			1.92733i	−0.267113	+	0.963665i	$0.586070\pi$
$458$			13.1181i			0.612967i
$459$	−27.5557			−1.28619
$460$	2.15833	+	21.8433i	0.100633	+	1.01845i
$461$	−32.5041			−1.51387			−0.756933	−	0.653492i	$-0.773303\pi$
$461$	−32.5041			−1.51387			−0.756933	+	0.653492i	$0.773303\pi$
$462$		−	2.95310i		−	0.137390i
$463$		−	6.59889i		−	0.306676i	−0.988174	−	0.153338i	$-0.950998\pi$
$463$		−	6.59889i		−	0.306676i	0.988174	−	0.153338i	$-0.0490024\pi$
$464$	−1.17593			−0.0545913
$465$	−2.26205	−	22.8931i	−0.104900	−	1.06164i
$466$	−18.5042			−0.857190
$467$			37.3500i			1.72835i	0.503190	+	0.864176i	$0.332160\pi$
$467$			37.3500i			1.72835i	−0.503190	+	0.864176i	$0.667840\pi$
$468$			2.66904i			0.123377i
$469$	6.74087			0.311265
$470$	−15.0340	+	1.48550i	−0.693467	+	0.0685211i
$471$	−19.7184			−0.908576
$472$		−	34.5745i		−	1.59142i
$473$		−	11.3063i		−	0.519865i
$474$	9.63957			0.442760
$475$		0			0
$476$	9.11036			0.417573
$477$		−	0.0502599i		−	0.00230124i
$478$		−	3.68890i		−	0.168726i
$479$	12.7086			0.580672			0.290336	−	0.956925i	$-0.406233\pi$
$479$	12.7086			0.580672			0.290336	+	0.956925i	$0.406233\pi$
$480$	25.3813	−	2.50791i	1.15849	−	0.114470i
$481$	−15.7927			−0.720085
$482$		−	6.98376i		−	0.318102i
$483$			14.7529i			0.671279i
$484$	−10.4609			−0.475495
$485$	4.05572	+	41.0458i	0.184161	+	1.86379i
$486$	−6.80347			−0.308612
$487$		−	21.6054i		−	0.979033i	−0.871994	−	0.489517i	$-0.837173\pi$
$487$		−	21.6054i		−	0.979033i	0.871994	−	0.489517i	$-0.162827\pi$
$488$			36.2894i			1.64274i
$489$	−8.48753			−0.383820
$490$	−1.04904	−	10.6167i	−0.0473906	−	0.479615i
$491$	34.0900			1.53846			0.769229	−	0.638973i	$-0.220641\pi$
$491$	34.0900			1.53846			0.769229	+	0.638973i	$0.220641\pi$
$492$			11.7298i			0.528822i
$493$		−	14.4413i		−	0.650404i
$494$		0			0
$495$	−3.35550	+	0.331555i	−0.150818	+	0.0149023i
$496$	−2.78043			−0.124845
$497$		−	14.0429i		−	0.629911i
$498$		−	7.81138i		−	0.350036i
$499$	11.1398			0.498684			0.249342	−	0.968415i	$-0.419786\pi$
$499$	11.1398			0.498684			0.249342	+	0.968415i	$0.419786\pi$
$500$	14.4548	−	4.39974i	0.646438	−	0.196762i
$501$	12.6339			0.564443
$502$		−	2.40326i		−	0.107263i
$503$		−	13.2039i		−	0.588735i	−0.955692	−	0.294367i	$-0.904891\pi$
$503$		−	13.2039i		−	0.588735i	0.955692	−	0.294367i	$-0.0951089\pi$
$504$	2.33803			0.104144
$505$	−12.6478	+	1.24972i	−0.562819	+	0.0556119i
$506$	10.5607			0.469481
$507$			14.5094i			0.644384i
$508$			14.2618i			0.632763i
$509$	−9.19539			−0.407579			−0.203789	−	0.979015i	$-0.565326\pi$
$509$	−9.19539			−0.407579			−0.203789	+	0.979015i	$0.565326\pi$
$510$	2.25398	+	22.8113i	0.0998077	+	1.01010i
$511$	−8.53931			−0.377757
$512$		−	5.93968i		−	0.262499i
$513$		0			0
$514$	−4.09915			−0.180806
$515$	1.44627	+	14.6370i	0.0637303	+	0.644981i
$516$	16.5746			0.729655
$517$		−	15.1460i		−	0.666118i
$518$			5.57849i			0.245105i
$519$	13.4948			0.592355
$520$	−14.2014	+	1.40323i	−0.622772	+	0.0615359i
$521$	21.4325			0.938973			0.469486	−	0.882940i	$-0.344439\pi$
$521$	21.4325			0.938973			0.469486	+	0.882940i	$0.344439\pi$
$522$		−	1.49447i		−	0.0654111i
$523$			9.04219i			0.395387i	0.980264	+	0.197694i	$0.0633452\pi$
$523$			9.04219i			0.395387i	−0.980264	+	0.197694i	$0.936655\pi$
$524$	−18.4533			−0.806136
$525$	9.95910	−	1.98751i	0.434651	−	0.0867422i
$526$	12.5571			0.547516
$527$		−	34.1458i		−	1.48741i
$528$			1.87132i			0.0814388i
$529$	−29.7585			−1.29385
$530$	0.107836	−	0.0106552i	0.00468408	−	0.000462832i
$531$	−10.6994			−0.464313
$532$		0			0
$533$		−	10.4797i		−	0.453926i
$534$	−21.4832			−0.929671
$535$	2.64459	+	26.7645i	0.114335	+	1.15713i
$536$	17.5424			0.757715
$537$		−	27.8270i		−	1.20082i
$538$			15.5369i			0.669845i
$539$	10.6958			0.460701
$540$	1.25973	+	12.7491i	0.0542102	+	0.548633i
$541$	−23.9095			−1.02795			−0.513976	−	0.857805i	$-0.671828\pi$
$541$	−23.9095			−1.02795			−0.513976	+	0.857805i	$0.671828\pi$
$542$			22.1302i			0.950575i
$543$		−	9.96020i		−	0.427433i
$544$	37.8570			1.62311
$545$	6.18764	−	0.611398i	0.265050	−	0.0261894i
$546$	−3.86772			−0.165523
$547$		−	38.3031i		−	1.63772i	−0.573992	−	0.818861i	$-0.694606\pi$
$547$		−	38.3031i		−	1.63772i	0.573992	−	0.818861i	$-0.305394\pi$
$548$		−	21.1661i		−	0.904172i
$549$	11.2301			0.479288
$550$	−1.42274	−	7.12913i	−0.0606659	−	0.303987i
$551$		0			0
$552$			38.3927i			1.63410i
$553$		−	6.33901i		−	0.269562i
$554$	−13.6560			−0.580189
$555$	29.1057	−	2.87592i	1.23547	−	0.122076i
$556$	3.20750			0.136028
$557$		−	10.7640i		−	0.456084i	−0.973651	−	0.228042i	$-0.926768\pi$
$557$		−	10.7640i		−	0.456084i	0.973651	−	0.228042i	$-0.0732323\pi$
$558$		−	3.53360i		−	0.149589i
$559$	−14.8081			−0.626315
$560$	−0.120695	−	1.22149i	−0.00510029	−	0.0516173i
$561$	−22.9812			−0.970266
$562$			10.0619i			0.424438i
$563$			12.0769i			0.508981i	0.967075	+	0.254490i	$0.0819077\pi$
$563$			12.0769i			0.508981i	−0.967075	+	0.254490i	$0.918092\pi$
$564$	22.2033			0.934928
$565$	−1.28848	−	13.0400i	−0.0542067	−	0.548598i
$566$	24.8666			1.04522
$567$			11.2094i			0.470752i
$568$		−	36.5451i		−	1.53340i
$569$	41.3125			1.73191			0.865954	−	0.500123i	$-0.166712\pi$
$569$	41.3125			1.73191			0.865954	+	0.500123i	$0.166712\pi$
$570$		0			0
$571$	0.646103			0.0270385			0.0135193	−	0.999909i	$-0.495697\pi$
$571$	0.646103			0.0270385			0.0135193	+	0.999909i	$0.495697\pi$
$572$		−	5.76924i		−	0.241224i
$573$			12.9854i			0.542474i
$574$	−3.70176			−0.154509
$575$	7.10764	+	35.6152i	0.296409	+	1.48526i
$576$	3.03352			0.126397
$577$			9.70295i			0.403939i	0.979392	+	0.201969i	$0.0647342\pi$
$577$			9.70295i			0.403939i	−0.979392	+	0.201969i	$0.935266\pi$
$578$			20.3332i			0.845749i
$579$	26.9642			1.12059
$580$	−6.68151	+	0.660197i	−0.277435	+	0.0274132i
$581$	−5.13678			−0.213110
$582$			29.0914i			1.20588i
$583$			0.108639i			0.00449935i
$584$	−22.2226			−0.919577
$585$	0.434243	+	4.39475i	0.0179537	+	0.181700i
$586$	−20.2801			−0.837764
$587$		−	19.2787i		−	0.795716i	−0.917447	−	0.397858i	$-0.869754\pi$
$587$		−	19.2787i		−	0.795716i	0.917447	−	0.397858i	$-0.130246\pi$
$588$			15.6796i			0.646615i
$589$		0			0
$590$	−2.26829	−	22.9562i	−0.0933839	−	0.945090i
$591$	−1.42908			−0.0587844
$592$		−	3.53498i		−	0.145287i
$593$		−	35.2446i		−	1.44732i	−0.690156	−	0.723660i	$-0.742458\pi$
$593$		−	35.2446i		−	1.44732i	0.690156	−	0.723660i	$-0.257542\pi$
$594$	6.16387			0.252907
$595$	15.0008	−	1.48222i	0.614972	−	0.0607651i
$596$	−4.31854			−0.176894
$597$		−	11.2104i		−	0.458811i
$598$		−	13.8315i		−	0.565614i
$599$	0.181646			0.00742186			0.00371093	−	0.999993i	$-0.498819\pi$
$599$	0.181646			0.00742186			0.00371093	+	0.999993i	$0.498819\pi$
$600$	25.9174	−	5.17228i	1.05807	−	0.211157i
$601$	−29.0186			−1.18369			−0.591847	−	0.806050i	$-0.701601\pi$
$601$	−29.0186			−1.18369			−0.591847	+	0.806050i	$0.701601\pi$
$602$			5.23068i			0.213187i
$603$		−	5.42864i		−	0.221071i
$604$	−19.4933			−0.793172
$605$	−17.2245	+	1.70195i	−0.700276	+	0.0691940i
$606$	−8.96417			−0.364144
$607$			31.8804i			1.29398i	0.762497	+	0.646992i	$0.223973\pi$
$607$			31.8804i			1.29398i	−0.762497	+	0.646992i	$0.776027\pi$
$608$		0			0
$609$	−4.51267			−0.182862
$610$	2.38080	+	24.0948i	0.0963956	+	0.975570i
$611$	−19.8369			−0.802515
$612$		−	7.33686i		−	0.296575i
$613$			26.1763i			1.05725i	0.848855	+	0.528626i	$0.177293\pi$
$613$			26.1763i			1.05725i	−0.848855	+	0.528626i	$0.822707\pi$
$614$	4.89457			0.197529
$615$	1.90840	+	19.3139i	0.0769541	+	0.778812i
$616$	−5.05374			−0.203621
$617$			30.4273i			1.22496i	0.790487	+	0.612479i	$0.209828\pi$
$617$			30.4273i			1.22496i	−0.790487	+	0.612479i	$0.790172\pi$
$618$			10.3740i			0.417304i
$619$	25.1588			1.01122			0.505609	−	0.862763i	$-0.331268\pi$
$619$	25.1588			1.01122			0.505609	+	0.862763i	$0.331268\pi$
$620$	−15.7981	+	1.56100i	−0.634467	+	0.0626914i
$621$	−30.7931			−1.23568
$622$		−	6.62639i		−	0.265694i
$623$			14.1274i			0.566004i
$624$	2.45090			0.0981145
$625$	23.0849	−	9.59619i	0.923397	−	0.383847i
$626$	−23.1931			−0.926984
$627$		0			0
$628$			13.6073i			0.542991i
$629$	43.4121			1.73096
$630$	1.55237	−	0.153388i	0.0618477	−	0.00611114i
$631$	−22.4203			−0.892539			−0.446269	−	0.894899i	$-0.647248\pi$
$631$	−22.4203			−0.892539			−0.446269	+	0.894899i	$0.647248\pi$
$632$		−	16.4965i		−	0.656198i
$633$		−	36.0861i		−	1.43429i
$634$	−10.5078			−0.417320
$635$	2.32033	+	23.4829i	0.0920796	+	0.931890i
$636$	−0.159259			−0.00631505
$637$		−	14.0085i		−	0.555035i
$638$			3.23035i			0.127891i
$639$	−11.3092			−0.447385
$640$	−1.91811	−	19.4122i	−0.0758198	−	0.767333i
$641$	−0.599952			−0.0236967			−0.0118483	−	0.999930i	$-0.503772\pi$
$641$	−0.599952			−0.0236967			−0.0118483	+	0.999930i	$0.503772\pi$
$642$			18.9694i			0.748664i
$643$			28.0144i			1.10478i	0.833586	+	0.552390i	$0.186284\pi$
$643$			28.0144i			1.10478i	−0.833586	+	0.552390i	$0.813716\pi$
$644$	10.1807			0.401176
$645$	27.2911	−	2.69662i	1.07458	−	0.106179i
$646$		0			0
$647$			14.5244i			0.571013i	0.958377	+	0.285506i	$0.0921618\pi$
$647$			14.5244i			0.571013i	−0.958377	+	0.285506i	$0.907838\pi$
$648$			29.1713i			1.14596i
$649$	23.1271			0.907818
$650$	−9.33714	+	1.86339i	−0.366233	+	0.0730881i
$651$	−10.6700			−0.418189
$652$			5.85710i			0.229382i
$653$			22.9792i			0.899247i	0.893218	+	0.449623i	$0.148442\pi$
$653$			22.9792i			0.899247i	−0.893218	+	0.449623i	$0.851558\pi$
$654$	4.38552			0.171487
$655$	−30.3845	+	3.00228i	−1.18722	+	0.117309i
$656$	2.34573			0.0915856
$657$			6.87697i			0.268296i
$658$			7.00703i			0.273162i
$659$	−29.7896			−1.16044			−0.580219	−	0.814460i	$-0.697033\pi$
$659$	−29.7896			−1.16044			−0.580219	+	0.814460i	$0.697033\pi$
$660$	1.05060	+	10.6326i	0.0408947	+	0.413874i
$661$	−25.1870			−0.979660			−0.489830	−	0.871818i	$-0.662941\pi$
$661$	−25.1870			−0.979660			−0.489830	+	0.871818i	$0.662941\pi$
$662$		−	3.45333i		−	0.134217i
$663$			30.0988i			1.16894i
$664$	−13.3679			−0.518775
$665$		0			0
$666$	4.49253			0.174082
$667$		−	16.1380i		−	0.624865i
$668$		−	8.71846i		−	0.337327i
$669$	−11.5163			−0.445244
$670$	11.6475	−	1.15088i	0.449981	−	0.0444624i
$671$	−24.2742			−0.937096
$672$		−	11.8297i		−	0.456340i
$673$		−	20.9432i		−	0.807302i	−0.914913	−	0.403651i	$-0.867741\pi$
$673$		−	20.9432i		−	0.807302i	0.914913	−	0.403651i	$-0.132259\pi$
$674$	−4.24328			−0.163445
$675$	4.14845	+	20.7872i	0.159674	+	0.800100i
$676$	10.0127			0.385102
$677$		−	33.8768i		−	1.30199i	−0.759082	−	0.650995i	$-0.774352\pi$
$677$		−	33.8768i		−	1.30199i	0.759082	−	0.650995i	$-0.225648\pi$
$678$		−	9.24217i		−	0.354943i
$679$	19.1306			0.734164
$680$	39.0378	−	3.85731i	1.49703	−	0.147921i
$681$	−11.5410			−0.442253
$682$			7.63800i			0.292474i
$683$			30.3942i			1.16300i	0.813546	+	0.581501i	$0.197534\pi$
$683$			30.3942i			1.16300i	−0.813546	+	0.581501i	$0.802466\pi$
$684$		0			0
$685$	−3.44365	−	34.8513i	−0.131575	−	1.33160i
$686$	−10.7949			−0.412151
$687$		−	31.9000i		−	1.21706i
$688$		−	3.31458i		−	0.126367i
$689$	0.142286			0.00542066
$690$	2.51879	+	25.4913i	0.0958886	+	0.970438i
$691$	−9.00959			−0.342741			−0.171371	−	0.985207i	$-0.554820\pi$
$691$	−9.00959			−0.342741			−0.171371	+	0.985207i	$0.554820\pi$
$692$		−	9.31251i		−	0.354009i
$693$			1.56393i			0.0594086i
$694$	7.88233			0.299209
$695$	5.28135	−	0.521847i	0.200333	−	0.0197948i
$696$	−11.7437			−0.445144
$697$			28.8073i			1.09116i
$698$			11.0160i			0.416962i
$699$	44.9978			1.70197
$700$	−1.37155	−	6.87260i	−0.0518396	−	0.259760i
$701$	1.50058			0.0566762			0.0283381	−	0.999598i	$-0.490978\pi$
$701$	1.50058			0.0566762			0.0283381	+	0.999598i	$0.490978\pi$
$702$		−	8.07292i		−	0.304693i
$703$		0			0
$704$	−6.55708			−0.247129
$705$	36.5591	−	3.61239i	1.37690	−	0.136051i
$706$	13.6686			0.514425
$707$			5.89486i			0.221699i
$708$			33.9033i			1.27416i
$709$	40.6894			1.52812			0.764061	−	0.645144i	$-0.223202\pi$
$709$	40.6894			1.52812			0.764061	+	0.645144i	$0.223202\pi$
$710$	−2.39757	−	24.2646i	−0.0899793	−	0.910633i
$711$	−5.10500			−0.191453
$712$			36.7651i			1.37783i
$713$		−	38.1574i		−	1.42901i
$714$	10.6319			0.397888
$715$	−0.938633	−	9.49941i	−0.0351029	−	0.355258i
$716$	−19.2029			−0.717647
$717$			8.97053i			0.335011i
$718$		−	8.28117i		−	0.309051i
$719$	18.5007			0.689959			0.344980	−	0.938610i	$-0.387886\pi$
$719$	18.5007			0.689959			0.344980	+	0.938610i	$0.387886\pi$
$720$	−0.983704	+	0.0971993i	−0.0366605	+	0.00362241i
$721$	6.82197			0.254064
$722$		0			0
$723$			16.9829i			0.631599i
$724$	−6.87336			−0.255446
$725$	−10.8941	+	2.17411i	−0.404597	+	0.0807445i
$726$	−12.2080			−0.453080
$727$			0.175782i			0.00651939i	0.999995	+	0.00325970i	$0.00103760\pi$
$727$			0.175782i			0.00651939i	−0.999995	+	0.00325970i	$0.998962\pi$
$728$			6.61897i			0.245315i
$729$	−15.8798			−0.588142
$730$	−14.7550	+	1.45793i	−0.546106	+	0.0539605i
$731$	40.7055			1.50555
$732$		−	35.5849i		−	1.31526i
$733$		−	31.7823i		−	1.17390i	−0.809621	−	0.586952i	$-0.800328\pi$
$733$		−	31.7823i		−	1.17390i	0.809621	−	0.586952i	$-0.199672\pi$
$734$	−29.1969			−1.07768
$735$	2.55100	+	25.8174i	0.0940952	+	0.952289i
$736$	42.3047			1.55937
$737$			11.7342i			0.432235i
$738$			2.98115i			0.109738i
$739$	−1.60789			−0.0591473			−0.0295737	−	0.999563i	$-0.509415\pi$
$739$	−1.60789			−0.0591473			−0.0295737	+	0.999563i	$0.509415\pi$
$740$	−1.98462	−	20.0853i	−0.0729562	−	0.738352i
$741$		0			0
$742$		−	0.0502599i		−	0.00184510i
$743$		−	13.7363i		−	0.503935i	−0.967736	−	0.251968i	$-0.918922\pi$
$743$		−	13.7363i		−	0.503935i	0.967736	−	0.251968i	$-0.0810777\pi$
$744$	−27.7674			−1.01800
$745$	−7.11074	+	0.702609i	−0.260517	+	0.0257416i
$746$	16.8714			0.617706
$747$			4.13682i			0.151358i
$748$			15.8589i			0.579859i
$749$	12.4744			0.455803
$750$	16.8689	−	5.13453i	0.615964	−	0.187487i
$751$	44.1497			1.61104			0.805522	−	0.592565i	$-0.201885\pi$
$751$	44.1497			1.61104			0.805522	+	0.592565i	$0.201885\pi$
$752$		−	4.44022i		−	0.161918i
$753$			5.84415i			0.212973i
$754$	4.23084			0.154078
$755$	−32.0970	+	3.17149i	−1.16813	+	0.115422i
$756$	5.94207			0.216111
$757$		−	25.5242i		−	0.927693i	−0.885916	−	0.463846i	$-0.846469\pi$
$757$		−	25.5242i		−	0.927693i	0.885916	−	0.463846i	$-0.153531\pi$
$758$			10.2289i			0.371532i
$759$	−25.6812			−0.932167
$760$		0			0
$761$	−1.51764			−0.0550143			−0.0275072	−	0.999622i	$-0.508757\pi$
$761$	−1.51764			−0.0550143			−0.0275072	+	0.999622i	$0.508757\pi$
$762$			16.6436i			0.602934i
$763$		−	2.88393i		−	0.104405i
$764$	8.96102			0.324198
$765$	−1.19368	−	12.0806i	−0.0431576	−	0.436775i
$766$	6.67357			0.241126
$767$		−	30.2899i		−	1.09371i
$768$		−	27.9838i		−	1.00978i
$769$	−34.9179			−1.25917			−0.629586	−	0.776931i	$-0.716776\pi$
$769$	−34.9179			−1.25917			−0.629586	+	0.776931i	$0.716776\pi$
$770$	−3.35550	+	0.331555i	−0.120924	+	0.0119484i
$771$	9.96815			0.358994
$772$		−	18.6075i		−	0.669698i
$773$		−	44.5250i		−	1.60145i	−0.599031	−	0.800726i	$-0.704447\pi$
$773$		−	44.5250i		−	1.60145i	0.599031	−	0.800726i	$-0.295553\pi$
$774$	4.21244			0.151413
$775$	−25.7586	+	5.14058i	−0.925276	+	0.184655i
$776$	49.7852			1.78718
$777$		−	13.5656i		−	0.486661i
$778$		−	12.0858i		−	0.433297i
$779$		0			0
$780$	13.9257	−	1.37599i	0.498621	−	0.0492685i
$781$	24.4453			0.874720
$782$			38.0212i			1.35963i
$783$		−	9.41910i		−	0.336611i
$784$	3.13560			0.111986
$785$	2.21386	+	22.4053i	0.0790160	+	0.799679i
$786$	−21.5351			−0.768133
$787$		−	23.3866i		−	0.833643i	−0.908988	−	0.416822i	$-0.863144\pi$
$787$		−	23.3866i		−	0.833643i	0.908988	−	0.416822i	$-0.136856\pi$
$788$			0.986181i			0.0351312i
$789$	−30.5359			−1.08711
$790$	−1.08227	−	10.9531i	−0.0385054	−	0.389694i
$791$	−6.07768			−0.216097
$792$			4.06994i			0.144619i
$793$			31.7924i			1.12898i
$794$	−7.79829			−0.276751
$795$	−0.262231	+	0.0259109i	−0.00930036	+	0.000918965i
$796$	−7.73610			−0.274199
$797$		−	19.6099i		−	0.694618i	−0.937751	−	0.347309i	$-0.887095\pi$
$797$		−	19.6099i		−	0.694618i	0.937751	−	0.347309i	$-0.112905\pi$
$798$		0			0
$799$	54.5292			1.92910
$800$	−5.69930	−	28.5583i	−0.201501	−	1.00969i
$801$	11.3773			0.401996
$802$			13.9783i			0.493590i
$803$		−	14.8648i		−	0.524569i
$804$	−17.2018			−0.606662
$805$	16.7632	−	1.65636i	0.590824	−	0.0583790i
$806$	10.0036			0.352362
$807$		−	37.7821i		−	1.32999i
$808$			15.3407i			0.539684i
$809$	28.1670			0.990298			0.495149	−	0.868808i	$-0.335113\pi$
$809$	28.1670			0.990298			0.495149	+	0.868808i	$0.335113\pi$
$810$	1.91381	+	19.3686i	0.0672443	+	0.680544i
$811$	−3.22068			−0.113093			−0.0565467	−	0.998400i	$-0.518009\pi$
$811$	−3.22068			−0.113093			−0.0565467	+	0.998400i	$0.518009\pi$
$812$			3.11411i			0.109284i
$813$		−	53.8155i		−	1.88739i
$814$	−9.71078			−0.340363
$815$	0.952927	+	9.64408i	0.0333796	+	0.337817i
$816$	−6.73721			−0.235850
$817$		0			0
$818$		−	12.3481i		−	0.431742i
$819$	2.04830			0.0715733
$820$	13.3282	−	1.31695i	0.465441	−	0.0459900i
$821$	−8.81189			−0.307537			−0.153768	−	0.988107i	$-0.549141\pi$
$821$	−8.81189			−0.307537			−0.153768	+	0.988107i	$0.549141\pi$
$822$		−	24.7010i		−	0.861548i
$823$			12.2640i			0.427497i	0.976889	+	0.213748i	$0.0685672\pi$
$823$			12.2640i			0.427497i	−0.976889	+	0.213748i	$0.931433\pi$
$824$	17.7534			0.618470
$825$	3.45977	+	17.3363i	0.120454	+	0.603574i
$826$	−10.6994			−0.372279
$827$		−	45.8102i		−	1.59298i	−0.604653	−	0.796489i	$-0.706688\pi$
$827$		−	45.8102i		−	1.59298i	0.604653	−	0.796489i	$-0.293312\pi$
$828$		−	8.19884i		−	0.284930i
$829$	−46.7917			−1.62514			−0.812572	−	0.582861i	$-0.801933\pi$
$829$	−46.7917			−1.62514			−0.812572	+	0.582861i	$0.801933\pi$
$830$	−8.87579	+	0.877013i	−0.308083	+	0.0304416i
$831$	33.2082			1.15198
$832$			8.58791i			0.297732i
$833$			38.5075i			1.33421i
$834$	3.74318			0.129616
$835$	−1.41846	−	14.3555i	−0.0490878	−	0.496792i
$836$		0			0
$837$		−	22.2710i		−	0.769798i
$838$			0.836314i			0.0288900i
$839$	40.7277			1.40608			0.703038	−	0.711152i	$-0.251826\pi$
$839$	40.7277			1.40608			0.703038	+	0.711152i	$0.251826\pi$
$840$	−1.20534	−	12.1987i	−0.0415883	−	0.420894i
$841$	−24.0637			−0.829781
$842$		−	25.7563i		−	0.887622i
$843$		−	24.4683i		−	0.842732i
$844$	−24.9024			−0.857174
$845$	16.4865	−	1.62902i	0.567152	−	0.0560400i
$846$	5.64298			0.194010
$847$			8.02798i			0.275845i
$848$			0.0318487i			0.00109369i
$849$	−60.4696			−2.07531
$850$	25.6666	−	5.12222i	0.880357	−	0.175691i
$851$	48.5125			1.66299
$852$			35.8357i			1.22771i
$853$			28.2038i			0.965678i	0.875709	+	0.482839i	$0.160394\pi$
$853$			28.2038i			0.965678i	−0.875709	+	0.482839i	$0.839606\pi$
$854$	11.2301			0.384285
$855$		0			0
$856$	32.4631			1.10957
$857$		−	8.80423i		−	0.300747i	−0.988629	−	0.150373i	$-0.951952\pi$
$857$		−	8.80423i		−	0.300747i	0.988629	−	0.150373i	$-0.0480476\pi$
$858$		−	6.73275i		−	0.229852i
$859$	−19.9249			−0.679830			−0.339915	−	0.940456i	$-0.610398\pi$
$859$	−19.9249			−0.679830			−0.339915	+	0.940456i	$0.610398\pi$
$860$	−1.86089	−	18.8331i	−0.0634558	−	0.642203i
$861$	9.00180			0.306781
$862$		−	7.77852i		−	0.264938i
$863$			1.20780i			0.0411141i	0.999789	+	0.0205571i	$0.00654398\pi$
$863$			1.20780i			0.0411141i	−0.999789	+	0.0205571i	$0.993456\pi$
$864$	24.6916			0.840025
$865$	−1.51511	−	15.3336i	−0.0515153	−	0.521359i
$866$	18.0735			0.614162
$867$		−	49.4455i		−	1.67926i
$868$			7.36316i			0.249922i
$869$	11.0347			0.374325
$870$	−7.79738	+	0.770456i	−0.264356	+	0.0261209i
$871$	15.3685			0.520741
$872$		−	7.50510i		−	0.254155i
$873$		−	15.4065i		−	0.521430i
$874$		0			0
$875$	−3.37648	−	11.0930i	−0.114146	−	0.375012i
$876$	21.7912			0.736256
$877$		−	8.95984i		−	0.302552i	−0.988492	−	0.151276i	$-0.951662\pi$
$877$		−	8.95984i		−	0.302552i	0.988492	−	0.151276i	$-0.0483383\pi$
$878$			16.8041i			0.567112i
$879$	49.3164			1.66340
$880$	2.12631	−	0.210100i	0.0716780	−	0.00708247i
$881$	−3.13906			−0.105758			−0.0528789	−	0.998601i	$-0.516840\pi$
$881$	−3.13906			−0.105758			−0.0528789	+	0.998601i	$0.516840\pi$
$882$			3.98497i			0.134181i
$883$		−	12.3080i		−	0.414197i	−0.978320	−	0.207099i	$-0.933598\pi$
$883$		−	12.3080i		−	0.414197i	0.978320	−	0.207099i	$-0.0664021\pi$
$884$	20.7707			0.698593
$885$	5.51594	+	55.8239i	0.185416	+	1.87650i
$886$	−0.0533770			−0.00179323
$887$		−	29.3370i		−	0.985041i	−0.870301	−	0.492521i	$-0.836076\pi$
$887$		−	29.3370i		−	0.985041i	0.870301	−	0.492521i	$-0.163924\pi$
$888$		−	35.3028i		−	1.18469i
$889$	10.9449			0.367079
$890$	2.41200	+	24.4106i	0.0808505	+	0.818246i
$891$	−19.5129			−0.653706
$892$			7.94716i			0.266091i
$893$		0			0
$894$	−5.03977			−0.168555
$895$	−31.6188	+	3.12424i	−1.05690	+	0.104432i
$896$	−9.04759			−0.302259
$897$			33.6350i			1.12304i
$898$		−	0.463209i		−	0.0154575i
$899$	11.6717			0.389274
$900$	−5.53472	+	1.10455i	−0.184491	+	0.0368184i
$901$	−0.391126			−0.0130303
$902$		−	6.44386i		−	0.214557i
$903$		−	12.7198i		−	0.423288i
$904$	−15.8165			−0.526048
$905$	−11.3174	+	1.11827i	−0.376204	+	0.0371725i
$906$	−22.7489			−0.755780
$907$		−	1.85256i		−	0.0615131i	−0.999527	−	0.0307566i	$-0.990208\pi$
$907$		−	1.85256i		−	0.0615131i	0.999527	−	0.0307566i	$-0.00979166\pi$
$908$			7.96426i			0.264303i
$909$	4.74732			0.157459
$910$	0.434243	+	4.39475i	0.0143950	+	0.145684i
$911$	−33.0581			−1.09526			−0.547632	−	0.836720i	$-0.684470\pi$
$911$	−33.0581			−1.09526			−0.547632	+	0.836720i	$0.684470\pi$
$912$		0			0
$913$		−	8.94188i		−	0.295933i
$914$	33.1810			1.09753
$915$	−5.78953	−	58.5928i	−0.191396	−	1.93702i
$916$	−22.0137			−0.727352
$917$			14.1616i			0.467656i
$918$			22.1914i			0.732427i
$919$	−50.8506			−1.67741			−0.838703	−	0.544590i	$-0.816685\pi$
$919$	−50.8506			−1.67741			−0.838703	+	0.544590i	$0.816685\pi$
$920$	43.6242	−	4.31049i	1.43825	−	0.142113i
$921$	−11.9024			−0.392198
$922$			26.1766i			0.862080i
$923$		−	32.0164i		−	1.05383i
$924$	4.95564			0.163029
$925$	−6.53561	−	32.7489i	−0.214890	−	1.07678i
$926$	−5.31429			−0.174638
$927$		−	5.49395i		−	0.180445i
$928$			12.9403i			0.424787i
$929$	−8.01818			−0.263068			−0.131534	−	0.991312i	$-0.541990\pi$
$929$	−8.01818			−0.263068			−0.131534	+	0.991312i	$0.541990\pi$
$930$	−18.4365	+	1.82170i	−0.604557	+	0.0597360i
$931$		0			0
$932$		−	31.0522i		−	1.01715i
$933$			16.1138i			0.527543i
$934$	30.0791			0.984220
$935$	2.58018	+	26.1127i	0.0843810	+	0.853976i
$936$	5.33047			0.174232
$937$			52.9527i			1.72989i	0.501869	+	0.864944i	$0.332646\pi$
$937$			52.9527i			1.72989i	−0.501869	+	0.864944i	$0.667354\pi$
$938$		−	5.42864i		−	0.177251i
$939$	56.4002			1.84055
$940$	−2.49285	−	25.2288i	−0.0813077	−	0.822873i
$941$	−29.3673			−0.957347			−0.478674	−	0.877993i	$-0.658882\pi$
$941$	−29.3673			−0.957347			−0.478674	+	0.877993i	$0.658882\pi$
$942$			15.8799i			0.517394i
$943$			32.1918i			1.04831i
$944$	6.77999			0.220670
$945$	9.78400	−	0.966752i	0.318273	−	0.0314485i
$946$	−9.10534			−0.296040
$947$		−	0.230323i		−	0.00748449i	−0.999993	−	0.00374225i	$-0.998809\pi$
$947$		−	0.230323i		−	0.00748449i	0.999993	−	0.00374225i	$-0.00119120\pi$
$948$			16.1763i			0.525382i
$949$	−19.4687			−0.631981
$950$		0			0
$951$	25.5526			0.828599
$952$		−	18.1947i		−	0.589694i
$953$			9.62121i			0.311662i	0.987784	+	0.155831i	$0.0498055\pi$
$953$			9.62121i			0.311662i	−0.987784	+	0.155831i	$0.950195\pi$
$954$	−0.0404759			−0.00131046
$955$	14.7549	−	1.45792i	0.477457	−	0.0471773i
$956$	6.19040			0.200212
$957$		−	7.85545i		−	0.253931i
$958$		−	10.2347i		−	0.330667i
$959$	−16.2435			−0.524529
$960$	−1.56390	−	15.8274i	−0.0504746	−	0.510827i
$961$	−3.40276			−0.109767
$962$			12.7184i			0.410056i
$963$		−	10.0460i		−	0.323728i
$964$	11.7196			0.377462
$965$	−3.02737	−	30.6384i	−0.0974544	−	0.986285i
$966$	11.8810			0.382264
$967$		−	21.1871i		−	0.681330i	−0.940185	−	0.340665i	$-0.889348\pi$
$967$		−	21.1871i		−	0.681330i	0.940185	−	0.340665i	$-0.110652\pi$
$968$			20.8919i			0.671492i
$969$		0			0
$970$	33.0555	−	3.26620i	1.06135	−	0.104871i
$971$	−18.2019			−0.584126			−0.292063	−	0.956399i	$-0.594342\pi$
$971$	−18.2019			−0.584126			−0.292063	+	0.956399i	$0.594342\pi$
$972$		−	11.4170i		−	0.366201i
$973$		−	2.46152i		−	0.0789128i
$974$	−17.3995			−0.557516
$975$	22.7057	−	4.53132i	0.727164	−	0.145118i
$976$	−7.11628			−0.227787
$977$		−	12.8125i		−	0.409909i	−0.978771	−	0.204955i	$-0.934295\pi$
$977$		−	12.8125i		−	0.409909i	0.978771	−	0.204955i	$-0.0657047\pi$
$978$			6.83528i			0.218568i
$979$	−24.5924			−0.785977
$980$	17.8161	−	1.76040i	0.569115	−	0.0562340i
$981$	−2.32252			−0.0741524
$982$		−	27.4537i		−	0.876083i
$983$			41.3211i			1.31794i	0.752169	+	0.658970i	$0.229007\pi$
$983$			41.3211i			1.31794i	−0.752169	+	0.658970i	$0.770993\pi$
$984$	23.4262			0.746799
$985$	0.160448	+	1.62381i	0.00511229	+	0.0517388i
$986$	−11.6301			−0.370376
$987$		−	17.0394i		−	0.542371i
$988$		0			0
$989$	45.4879			1.44643
$990$	0.267012	+	2.70229i	0.00848619	+	0.0858843i
$991$	28.2455			0.897249			0.448624	−	0.893720i	$-0.351914\pi$
$991$	28.2455			0.897249			0.448624	+	0.893720i	$0.351914\pi$
$992$			30.5968i			0.971448i
$993$			8.39767i			0.266492i
$994$	−11.3092			−0.358706
$995$	−12.7380	+	1.25863i	−0.403821	+	0.0399014i
$996$	13.1084			0.415356
$997$			34.1678i			1.08211i	0.840988	+	0.541053i	$0.181974\pi$
$997$			34.1678i			1.08211i	−0.840988	+	0.541053i	$0.818026\pi$
$998$		−	8.97120i		−	0.283979i
$999$	28.3148			0.895841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.i.1084.6	✓	16
5.2	odd	4		9025.2.a.cl.1.11		16
5.3	odd	4		9025.2.a.cl.1.6		16
5.4	even	2	inner	1805.2.b.i.1084.11	yes	16
19.18	odd	2		1805.2.b.j.1084.11	yes	16
95.18	even	4		9025.2.a.ck.1.11		16
95.37	even	4		9025.2.a.ck.1.6		16
95.94	odd	2		1805.2.b.j.1084.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.i.1084.6	✓	16	1.1	even	1	trivial
1805.2.b.i.1084.11	yes	16	5.4	even	2	inner
1805.2.b.j.1084.6	yes	16	95.94	odd	2
1805.2.b.j.1084.11	yes	16	19.18	odd	2
9025.2.a.ck.1.6		16	95.37	even	4
9025.2.a.ck.1.11		16	95.18	even	4
9025.2.a.cl.1.6		16	5.3	odd	4
9025.2.a.cl.1.11		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)

\(f(q)\)	\(=\)	\(q-0.805332i q^{2} +1.95838i q^{3} +1.35144 q^{4} +(2.22523 - 0.219874i) q^{5} +1.57714 q^{6} -1.03713i q^{7} -2.69902i q^{8} -0.835236 q^{9} +O(q^{10})\)	\(q-0.805332i q^{2} +1.95838i q^{3} +1.35144 q^{4} +(2.22523 - 0.219874i) q^{5} +1.57714 q^{6} -1.03713i q^{7} -2.69902i q^{8} -0.835236 q^{9} +(-0.177072 - 1.79205i) q^{10} +1.80539 q^{11} +2.64663i q^{12} -2.36455i q^{13} -0.835236 q^{14} +(0.430596 + 4.35784i) q^{15} +0.529273 q^{16} +6.49986i q^{17} +0.672642i q^{18} +(3.00727 - 0.297147i) q^{20} +2.03110 q^{21} -1.45394i q^{22} +7.26351i q^{23} +5.28570 q^{24} +(4.90331 - 0.978542i) q^{25} -1.90425 q^{26} +4.23942i q^{27} -1.40162i q^{28} -2.22179 q^{29} +(3.50951 - 0.346773i) q^{30} -5.25331 q^{31} -5.82428i q^{32} +3.53564i q^{33} +5.23455 q^{34} +(-0.228039 - 2.30786i) q^{35} -1.12877 q^{36} -6.67893i q^{37} +4.63069 q^{39} +(-0.593445 - 6.00595i) q^{40} +4.43199 q^{41} -1.63571i q^{42} -6.26252i q^{43} +2.43988 q^{44} +(-1.85859 + 0.183647i) q^{45} +5.84953 q^{46} -8.38928i q^{47} +1.03652i q^{48} +5.92436 q^{49} +(-0.788051 - 3.94879i) q^{50} -12.7292 q^{51} -3.19556i q^{52} +0.0601745i q^{53} +3.41414 q^{54} +(4.01742 - 0.396960i) q^{55} -2.79924 q^{56} +1.78928i q^{58} +12.8100 q^{59} +(0.581925 + 5.88936i) q^{60} -13.4454 q^{61} +4.23066i q^{62} +0.866251i q^{63} -3.63194 q^{64} +(-0.519904 - 5.26168i) q^{65} +2.84736 q^{66} +6.49953i q^{67} +8.78418i q^{68} -14.2247 q^{69} +(-1.85859 + 0.183647i) q^{70} +13.5401 q^{71} +2.25432i q^{72} -8.23357i q^{73} -5.37876 q^{74} +(1.91635 + 9.60253i) q^{75} -1.87243i q^{77} -3.72924i q^{78} +6.11205 q^{79} +(1.17776 - 0.116373i) q^{80} -10.8081 q^{81} -3.56922i q^{82} -4.95287i q^{83} +2.74491 q^{84} +(1.42915 + 14.4637i) q^{85} -5.04341 q^{86} -4.35110i q^{87} -4.87280i q^{88} -13.6216 q^{89} +(0.147897 + 1.49678i) q^{90} -2.45236 q^{91} +9.81620i q^{92} -10.2880i q^{93} -6.75615 q^{94} +11.4061 q^{96} +18.4456i q^{97} -4.77107i q^{98} -1.50793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more