LMFDB - Embedded newform 1815.2.c.e.364.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.3
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.e.364.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.311108i q^{2} -1.00000i q^{3} +1.90321 q^{4} +(0.311108 + 2.21432i) q^{5} -0.311108 q^{6} +0.903212i q^{7} -1.21432i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.311108i q^{2} -1.00000i q^{3} +1.90321 q^{4} +(0.311108 + 2.21432i) q^{5} -0.311108 q^{6} +0.903212i q^{7} -1.21432i q^{8} -1.00000 q^{9} +(0.688892 - 0.0967881i) q^{10} -1.90321i q^{12} +2.90321i q^{13} +0.280996 q^{14} +(2.21432 - 0.311108i) q^{15} +3.42864 q^{16} -2.28100i q^{17} +0.311108i q^{18} +2.42864 q^{19} +(0.592104 + 4.21432i) q^{20} +0.903212 q^{21} -4.00000i q^{23} -1.21432 q^{24} +(-4.80642 + 1.37778i) q^{25} +0.903212 q^{26} +1.00000i q^{27} +1.71900i q^{28} +7.05086 q^{29} +(-0.0967881 - 0.688892i) q^{30} -2.62222 q^{31} -3.49532i q^{32} -0.709636 q^{34} +(-2.00000 + 0.280996i) q^{35} -1.90321 q^{36} +5.80642i q^{37} -0.755569i q^{38} +2.90321 q^{39} +(2.68889 - 0.377784i) q^{40} +10.6637 q^{41} -0.280996i q^{42} +10.7096i q^{43} +(-0.311108 - 2.21432i) q^{45} -1.24443 q^{46} +0.949145i q^{47} -3.42864i q^{48} +6.18421 q^{49} +(0.428639 + 1.49532i) q^{50} -2.28100 q^{51} +5.52543i q^{52} -0.815792i q^{53} +0.311108 q^{54} +1.09679 q^{56} -2.42864i q^{57} -2.19358i q^{58} +1.67307 q^{59} +(4.21432 - 0.592104i) q^{60} +7.24443 q^{61} +0.815792i q^{62} -0.903212i q^{63} +5.76986 q^{64} +(-6.42864 + 0.903212i) q^{65} +12.8573i q^{67} -4.34122i q^{68} -4.00000 q^{69} +(0.0874201 + 0.622216i) q^{70} +9.28592 q^{71} +1.21432i q^{72} -5.65878i q^{73} +1.80642 q^{74} +(1.37778 + 4.80642i) q^{75} +4.62222 q^{76} -0.903212i q^{78} -16.5303 q^{79} +(1.06668 + 7.59210i) q^{80} +1.00000 q^{81} -3.31756i q^{82} +7.76049i q^{83} +1.71900 q^{84} +(5.05086 - 0.709636i) q^{85} +3.33185 q^{86} -7.05086i q^{87} -6.13335 q^{89} +(-0.688892 + 0.0967881i) q^{90} -2.62222 q^{91} -7.61285i q^{92} +2.62222i q^{93} +0.295286 q^{94} +(0.755569 + 5.37778i) q^{95} -3.49532 q^{96} -12.4701i q^{97} -1.92396i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9	$ 6 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9} + 4 q^{10} - 12 q^{14} - 6 q^{16} - 12 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{24} - 2 q^{25} - 8 q^{26} + 16 q^{29} - 14 q^{30} - 16 q^{31} + 36 q^{34} - 12 q^{35} + 2 q^{36} + 4 q^{39} + 16 q^{40} - 16 q^{41} - 2 q^{45} - 8 q^{46} + 10 q^{49} - 24 q^{50} + 2 q^{54} + 20 q^{56} - 16 q^{59} + 12 q^{60} + 44 q^{61} + 22 q^{64} - 12 q^{65} - 24 q^{69} - 40 q^{70} - 24 q^{71} - 16 q^{74} + 8 q^{75} + 28 q^{76} - 20 q^{79} + 6 q^{80} + 6 q^{81} + 24 q^{84} + 4 q^{85} - 20 q^{86} - 36 q^{89} - 4 q^{90} - 16 q^{91} - 24 q^{94} + 4 q^{95} + 6 q^{96}+O(q^{100}) $ 6 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9 + 4 * q^10 - 12 * q^14 - 6 * q^16 - 12 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^24 - 2 * q^25 - 8 * q^26 + 16 * q^29 - 14 * q^30 - 16 * q^31 + 36 * q^34 - 12 * q^35 + 2 * q^36 + 4 * q^39 + 16 * q^40 - 16 * q^41 - 2 * q^45 - 8 * q^46 + 10 * q^49 - 24 * q^50 + 2 * q^54 + 20 * q^56 - 16 * q^59 + 12 * q^60 + 44 * q^61 + 22 * q^64 - 12 * q^65 - 24 * q^69 - 40 * q^70 - 24 * q^71 - 16 * q^74 + 8 * q^75 + 28 * q^76 - 20 * q^79 + 6 * q^80 + 6 * q^81 + 24 * q^84 + 4 * q^85 - 20 * q^86 - 36 * q^89 - 4 * q^90 - 16 * q^91 - 24 * q^94 + 4 * q^95 + 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	0.311108i		−	0.219986i	−0.993932	−	0.109993i	$-0.964917\pi$
$2$		−	0.311108i		−	0.219986i	0.993932	−	0.109993i	$-0.0350829\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.90321			0.951606
$5$	0.311108	+	2.21432i	0.139132	+	0.990274i
$5$	0.311108	+	2.21432i	0.139132	+	0.990274i
$6$	−0.311108			−0.127009
$7$			0.903212i			0.341382i	0.985325	+	0.170691i	$0.0546000\pi$
$7$			0.903212i			0.341382i	−0.985325	+	0.170691i	$0.945400\pi$
$8$		−	1.21432i		−	0.429327i
$9$	−1.00000			−0.333333
$10$	0.688892	−	0.0967881i	0.217847	−	0.0306071i
$11$		0			0
$11$		0			0
$12$		−	1.90321i		−	0.549410i
$13$			2.90321i			0.805206i	0.915375	+	0.402603i	$0.131894\pi$
$13$			2.90321i			0.805206i	−0.915375	+	0.402603i	$0.868106\pi$
$14$	0.280996			0.0750994
$15$	2.21432	−	0.311108i	0.571735	−	0.0803277i
$16$	3.42864			0.857160
$17$		−	2.28100i		−	0.553223i	−0.960982	−	0.276611i	$-0.910789\pi$
$17$		−	2.28100i		−	0.553223i	0.960982	−	0.276611i	$-0.0892115\pi$
$18$			0.311108i			0.0733288i
$19$	2.42864			0.557168			0.278584	−	0.960412i	$-0.410135\pi$
$19$	2.42864			0.557168			0.278584	+	0.960412i	$0.410135\pi$
$20$	0.592104	+	4.21432i	0.132399	+	0.942351i
$21$	0.903212			0.197097
$22$		0			0
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−1.21432			−0.247872
$25$	−4.80642	+	1.37778i	−0.961285	+	0.275557i
$26$	0.903212			0.177134
$27$			1.00000i			0.192450i
$28$			1.71900i			0.324861i
$29$	7.05086			1.30931			0.654655	−	0.755927i	$-0.272814\pi$
$29$	7.05086			1.30931			0.654655	+	0.755927i	$0.272814\pi$
$30$	−0.0967881	−	0.688892i	−0.0176710	−	0.125774i
$31$	−2.62222			−0.470964			−0.235482	−	0.971879i	$-0.575667\pi$
$31$	−2.62222			−0.470964			−0.235482	+	0.971879i	$0.575667\pi$
$32$		−	3.49532i		−	0.617890i
$33$		0			0
$34$	−0.709636			−0.121702
$35$	−2.00000	+	0.280996i	−0.338062	+	0.0474970i
$36$	−1.90321			−0.317202
$37$			5.80642i			0.954570i	0.878749	+	0.477285i	$0.158379\pi$
$37$			5.80642i			0.954570i	−0.878749	+	0.477285i	$0.841621\pi$
$38$		−	0.755569i		−	0.122569i
$39$	2.90321			0.464886
$40$	2.68889	−	0.377784i	0.425151	−	0.0597330i
$41$	10.6637			1.66539			0.832695	−	0.553731i	$-0.186797\pi$
$41$	10.6637			1.66539			0.832695	+	0.553731i	$0.186797\pi$
$42$		−	0.280996i		−	0.0433587i
$43$			10.7096i			1.63320i	0.577201	+	0.816602i	$0.304145\pi$
$43$			10.7096i			1.63320i	−0.577201	+	0.816602i	$0.695855\pi$
$44$		0			0
$45$	−0.311108	−	2.21432i	−0.0463772	−	0.330091i
$46$	−1.24443			−0.183481
$47$			0.949145i			0.138447i	0.997601	+	0.0692235i	$0.0220522\pi$
$47$			0.949145i			0.138447i	−0.997601	+	0.0692235i	$0.977948\pi$
$48$		−	3.42864i		−	0.494881i
$49$	6.18421			0.883458
$50$	0.428639	+	1.49532i	0.0606188	+	0.211470i
$51$	−2.28100			−0.319403
$52$			5.52543i			0.766239i
$53$		−	0.815792i		−	0.112058i	−0.998429	−	0.0560288i	$-0.982156\pi$
$53$		−	0.815792i		−	0.112058i	0.998429	−	0.0560288i	$-0.0178439\pi$
$54$	0.311108			0.0423364
$55$		0			0
$56$	1.09679			0.146564
$57$		−	2.42864i		−	0.321681i
$58$		−	2.19358i		−	0.288031i
$59$	1.67307			0.217815			0.108908	−	0.994052i	$-0.465265\pi$
$59$	1.67307			0.217815			0.108908	+	0.994052i	$0.465265\pi$
$60$	4.21432	−	0.592104i	0.544066	−	0.0764403i
$61$	7.24443			0.927554			0.463777	−	0.885952i	$-0.346494\pi$
$61$	7.24443			0.927554			0.463777	+	0.885952i	$0.346494\pi$
$62$			0.815792i			0.103606i
$63$		−	0.903212i		−	0.113794i
$64$	5.76986			0.721232
$65$	−6.42864	+	0.903212i	−0.797375	+	0.112030i
$66$		0			0
$67$			12.8573i			1.57077i	0.619010	+	0.785383i	$0.287534\pi$
$67$			12.8573i			1.57077i	−0.619010	+	0.785383i	$0.712466\pi$
$68$		−	4.34122i		−	0.526450i
$69$	−4.00000			−0.481543
$70$	0.0874201	+	0.622216i	0.0104487	+	0.0743690i
$71$	9.28592			1.10204			0.551018	−	0.834493i	$-0.314240\pi$
$71$	9.28592			1.10204			0.551018	+	0.834493i	$0.314240\pi$
$72$			1.21432i			0.143109i
$73$		−	5.65878i		−	0.662310i	−0.943576	−	0.331155i	$-0.892562\pi$
$73$		−	5.65878i		−	0.662310i	0.943576	−	0.331155i	$-0.107438\pi$
$74$	1.80642			0.209993
$75$	1.37778	+	4.80642i	0.159093	+	0.554998i
$76$	4.62222			0.530204
$77$		0			0
$78$		−	0.903212i		−	0.102269i
$79$	−16.5303			−1.85981			−0.929905	−	0.367800i	$-0.880111\pi$
$79$	−16.5303			−1.85981			−0.929905	+	0.367800i	$0.880111\pi$
$80$	1.06668	+	7.59210i	0.119258	+	0.848823i
$81$	1.00000			0.111111
$82$		−	3.31756i		−	0.366363i
$83$			7.76049i			0.851825i	0.904764	+	0.425912i	$0.140047\pi$
$83$			7.76049i			0.851825i	−0.904764	+	0.425912i	$0.859953\pi$
$84$	1.71900			0.187559
$85$	5.05086	−	0.709636i	0.547842	−	0.0769708i
$86$	3.33185			0.359283
$87$		−	7.05086i		−	0.755931i
$88$		0			0
$89$	−6.13335			−0.650134			−0.325067	−	0.945691i	$-0.605387\pi$
$89$	−6.13335			−0.650134			−0.325067	+	0.945691i	$0.605387\pi$
$90$	−0.688892	+	0.0967881i	−0.0726156	+	0.0102024i
$91$	−2.62222			−0.274883
$92$		−	7.61285i		−	0.793694i
$93$			2.62222i			0.271911i
$94$	0.295286			0.0304565
$95$	0.755569	+	5.37778i	0.0775197	+	0.551749i
$96$	−3.49532			−0.356739
$97$		−	12.4701i		−	1.26615i	−0.774091	−	0.633075i	$-0.781793\pi$
$97$		−	12.4701i		−	1.26615i	0.774091	−	0.633075i	$-0.218207\pi$
$98$		−	1.92396i		−	0.194349i
$99$		0			0
$100$	−9.14764	+	2.62222i	−0.914764	+	0.262222i
$101$	−16.1748			−1.60946			−0.804728	−	0.593643i	$-0.797689\pi$
$101$	−16.1748			−1.60946			−0.804728	+	0.593643i	$0.797689\pi$
$102$			0.709636i			0.0702644i
$103$			17.1526i			1.69009i	0.534693	+	0.845046i	$0.320427\pi$
$103$			17.1526i			1.69009i	−0.534693	+	0.845046i	$0.679573\pi$
$104$	3.52543			0.345697
$105$	0.280996	+	2.00000i	0.0274224	+	0.195180i
$106$	−0.253799			−0.0246512
$107$			13.5669i			1.31156i	0.754951	+	0.655782i	$0.227661\pi$
$107$			13.5669i			1.31156i	−0.754951	+	0.655782i	$0.772339\pi$
$108$			1.90321i			0.183137i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$	5.80642			0.551121
$112$			3.09679i			0.292619i
$113$		−	14.2351i		−	1.33912i	−0.742757	−	0.669561i	$-0.766482\pi$
$113$		−	14.2351i		−	1.33912i	0.742757	−	0.669561i	$-0.233518\pi$
$114$	−0.755569			−0.0707655
$115$	8.85728	−	1.24443i	0.825946	−	0.116044i
$116$	13.4193			1.24595
$117$		−	2.90321i		−	0.268402i
$118$		−	0.520505i		−	0.0479164i
$119$	2.06022			0.188860
$120$	−0.377784	−	2.68889i	−0.0344868	−	0.245461i
$121$		0			0
$122$		−	2.25380i		−	0.204049i
$123$		−	10.6637i		−	0.961514i
$124$	−4.99063			−0.448172
$125$	−4.54617	−	10.2143i	−0.406622	−	0.913597i
$126$	−0.280996			−0.0250331
$127$		−	11.0049i		−	0.976529i	−0.872696	−	0.488264i	$-0.837630\pi$
$127$		−	11.0049i		−	0.976529i	0.872696	−	0.488264i	$-0.162370\pi$
$128$		−	8.78568i		−	0.776552i
$129$	10.7096			0.942931
$130$	0.280996	+	2.00000i	0.0246450	+	0.175412i
$131$	−1.24443			−0.108726			−0.0543632	−	0.998521i	$-0.517313\pi$
$131$	−1.24443			−0.108726			−0.0543632	+	0.998521i	$0.517313\pi$
$132$		0			0
$133$			2.19358i			0.190207i
$134$	4.00000			0.345547
$135$	−2.21432	+	0.311108i	−0.190578	+	0.0267759i
$136$	−2.76986			−0.237513
$137$		−	4.42864i		−	0.378364i	−0.981942	−	0.189182i	$-0.939416\pi$
$137$		−	4.42864i		−	0.378364i	0.981942	−	0.189182i	$-0.0605836\pi$
$138$			1.24443i			0.105933i
$139$	0.917502			0.0778215			0.0389108	−	0.999243i	$-0.487611\pi$
$139$	0.917502			0.0778215			0.0389108	+	0.999243i	$0.487611\pi$
$140$	−3.80642	+	0.534795i	−0.321702	+	0.0451985i
$141$	0.949145			0.0799324
$142$		−	2.88892i		−	0.242433i
$143$		0			0
$144$	−3.42864			−0.285720
$145$	2.19358	+	15.6128i	0.182167	+	1.29658i
$146$	−1.76049			−0.145699
$147$		−	6.18421i		−	0.510065i
$148$			11.0509i			0.908375i
$149$	2.19358			0.179705			0.0898524	−	0.995955i	$-0.471360\pi$
$149$	2.19358			0.179705			0.0898524	+	0.995955i	$0.471360\pi$
$150$	1.49532	−	0.428639i	0.122092	−	0.0349983i
$151$	10.4286			0.848671			0.424335	−	0.905505i	$-0.360508\pi$
$151$	10.4286			0.848671			0.424335	+	0.905505i	$0.360508\pi$
$152$		−	2.94914i		−	0.239207i
$153$			2.28100i			0.184408i
$154$		0			0
$155$	−0.815792	−	5.80642i	−0.0655260	−	0.466383i
$156$	5.52543			0.442388
$157$			5.80642i			0.463403i	0.972787	+	0.231702i	$0.0744293\pi$
$157$			5.80642i			0.463403i	−0.972787	+	0.231702i	$0.925571\pi$
$158$			5.14272i			0.409133i
$159$	−0.815792			−0.0646965
$160$	7.73975	−	1.08742i	0.611881	−	0.0859681i
$161$	3.61285			0.284732
$162$		−	0.311108i		−	0.0244429i
$163$		−	11.0509i		−	0.865570i	−0.901497	−	0.432785i	$-0.857531\pi$
$163$		−	11.0509i		−	0.865570i	0.901497	−	0.432785i	$-0.142469\pi$
$164$	20.2953			1.58480
$165$		0			0
$166$	2.41435			0.187390
$167$		−	13.9541i		−	1.07980i	−0.841730	−	0.539899i	$-0.818462\pi$
$167$		−	13.9541i		−	1.07980i	0.841730	−	0.539899i	$-0.181538\pi$
$168$		−	1.09679i		−	0.0846190i
$169$	4.57136			0.351643
$170$	−0.220773	−	1.57136i	−0.0169325	−	0.120518i
$171$	−2.42864			−0.185723
$172$			20.3827i			1.55417i
$173$		−	18.8430i		−	1.43261i	−0.697789	−	0.716303i	$-0.745833\pi$
$173$		−	18.8430i		−	1.43261i	0.697789	−	0.716303i	$-0.254167\pi$
$174$	−2.19358			−0.166295
$175$	−1.24443	−	4.34122i	−0.0940702	−	0.328165i
$176$		0			0
$177$		−	1.67307i		−	0.125756i
$178$			1.90813i			0.143021i
$179$	−4.85728			−0.363050			−0.181525	−	0.983386i	$-0.558103\pi$
$179$	−4.85728			−0.363050			−0.181525	+	0.983386i	$0.558103\pi$
$180$	−0.592104	−	4.21432i	−0.0441328	−	0.314117i
$181$	−16.7971			−1.24852			−0.624258	−	0.781219i	$-0.714598\pi$
$181$	−16.7971			−1.24852			−0.624258	+	0.781219i	$0.714598\pi$
$182$			0.815792i			0.0604705i
$183$		−	7.24443i		−	0.535524i
$184$	−4.85728			−0.358083
$185$	−12.8573	+	1.80642i	−0.945286	+	0.132811i
$186$	0.815792			0.0598168
$187$		0			0
$188$			1.80642i			0.131747i
$189$	−0.903212			−0.0656990
$190$	1.67307	−	0.235063i	0.121377	−	0.0170533i
$191$	16.8573			1.21975			0.609875	−	0.792498i	$-0.291220\pi$
$191$	16.8573			1.21975			0.609875	+	0.792498i	$0.291220\pi$
$192$		−	5.76986i		−	0.416404i
$193$		−	24.6178i		−	1.77203i	−0.463661	−	0.886013i	$-0.653464\pi$
$193$		−	24.6178i		−	1.77203i	0.463661	−	0.886013i	$-0.346536\pi$
$194$	−3.87955			−0.278536
$195$	0.903212	+	6.42864i	0.0646803	+	0.460364i
$196$	11.7699			0.840704
$197$		−	14.8716i		−	1.05956i	−0.848137	−	0.529778i	$-0.822275\pi$
$197$		−	14.8716i		−	1.05956i	0.848137	−	0.529778i	$-0.177725\pi$
$198$		0			0
$199$	11.2257			0.795768			0.397884	−	0.917436i	$-0.369745\pi$
$199$	11.2257			0.795768			0.397884	+	0.917436i	$0.369745\pi$
$200$	1.67307	+	5.83654i	0.118304	+	0.412705i
$201$	12.8573			0.906883
$202$			5.03212i			0.354059i
$203$			6.36842i			0.446975i
$204$	−4.34122			−0.303946
$205$	3.31756	+	23.6128i	0.231709	+	1.64919i
$206$	5.33630			0.371797
$207$			4.00000i			0.278019i
$208$			9.95407i			0.690190i
$209$		0			0
$210$	0.622216	−	0.0874201i	0.0429370	−	0.00603256i
$211$	11.9398			0.821968			0.410984	−	0.911643i	$-0.365185\pi$
$211$	11.9398			0.821968			0.410984	+	0.911643i	$0.365185\pi$
$212$		−	1.55262i		−	0.106635i
$213$		−	9.28592i		−	0.636261i
$214$	4.22077			0.288526
$215$	−23.7146	+	3.33185i	−1.61732	+	0.227230i
$216$	1.21432			0.0826240
$217$		−	2.36842i		−	0.160779i
$218$			3.11108i			0.210709i
$219$	−5.65878			−0.382385
$220$		0			0
$221$	6.62222			0.445458
$222$		−	1.80642i		−	0.121239i
$223$		−	21.8064i		−	1.46027i	−0.683305	−	0.730133i	$-0.739458\pi$
$223$		−	21.8064i		−	1.46027i	0.683305	−	0.730133i	$-0.260542\pi$
$224$	3.15701			0.210937
$225$	4.80642	−	1.37778i	0.320428	−	0.0918523i
$226$	−4.42864			−0.294589
$227$		−	3.19850i		−	0.212292i	−0.994351	−	0.106146i	$-0.966149\pi$
$227$		−	3.19850i		−	0.212292i	0.994351	−	0.106146i	$-0.0338511\pi$
$228$		−	4.62222i		−	0.306114i
$229$	−7.12399			−0.470766			−0.235383	−	0.971903i	$-0.575634\pi$
$229$	−7.12399			−0.470766			−0.235383	+	0.971903i	$0.575634\pi$
$230$	−0.387152	−	2.75557i	−0.0255281	−	0.181697i
$231$		0			0
$232$		−	8.56199i		−	0.562122i
$233$		−	19.5254i		−	1.27915i	−0.768727	−	0.639577i	$-0.779110\pi$
$233$		−	19.5254i		−	1.27915i	0.768727	−	0.639577i	$-0.220890\pi$
$234$	−0.903212			−0.0590448
$235$	−2.10171	+	0.295286i	−0.137100	+	0.0192624i
$236$	3.18421			0.207274
$237$			16.5303i			1.07376i
$238$		−	0.640951i		−	0.0415467i
$239$	−21.9813			−1.42185			−0.710925	−	0.703268i	$-0.751723\pi$
$239$	−21.9813			−1.42185			−0.710925	+	0.703268i	$0.751723\pi$
$240$	7.59210	−	1.06668i	0.490068	−	0.0688537i
$241$	−5.34614			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$241$	−5.34614			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	13.7877			0.882666
$245$	1.92396	+	13.6938i	0.122917	+	0.874866i
$246$	−3.31756			−0.211520
$247$			7.05086i			0.448635i
$248$			3.18421i			0.202197i
$249$	7.76049			0.491801
$250$	−3.17775	+	1.41435i	−0.200979	+	0.0894513i
$251$	−23.7748			−1.50065			−0.750325	−	0.661069i	$-0.770103\pi$
$251$	−23.7748			−1.50065			−0.750325	+	0.661069i	$0.770103\pi$
$252$		−	1.71900i		−	0.108287i
$253$		0			0
$254$	−3.42372			−0.214823
$255$	−0.709636	−	5.05086i	−0.0444391	−	0.316297i
$256$	8.80642			0.550401
$257$		−	8.13335i		−	0.507345i	−0.967290	−	0.253672i	$-0.918362\pi$
$257$		−	8.13335i		−	0.507345i	0.967290	−	0.253672i	$-0.0816385\pi$
$258$		−	3.33185i		−	0.207432i
$259$	−5.24443			−0.325873
$260$	−12.2351	+	1.71900i	−0.758786	+	0.106608i
$261$	−7.05086			−0.436437
$262$			0.387152i			0.0239183i
$263$			22.9032i			1.41227i	0.708076	+	0.706136i	$0.249563\pi$
$263$			22.9032i			1.41227i	−0.708076	+	0.706136i	$0.750437\pi$
$264$		0			0
$265$	1.80642	−	0.253799i	0.110968	−	0.0155908i
$266$	0.682439			0.0418430
$267$			6.13335i			0.375355i
$268$			24.4701i			1.49475i
$269$	−11.8350			−0.721593			−0.360796	−	0.932645i	$-0.617495\pi$
$269$	−11.8350			−0.721593			−0.360796	+	0.932645i	$0.617495\pi$
$270$	0.0967881	+	0.688892i	0.00589033	+	0.0419246i
$271$	−14.8988			−0.905036			−0.452518	−	0.891755i	$-0.649474\pi$
$271$	−14.8988			−0.905036			−0.452518	+	0.891755i	$0.649474\pi$
$272$		−	7.82071i		−	0.474200i
$273$			2.62222i			0.158704i
$274$	−1.37778			−0.0832350
$275$		0			0
$276$	−7.61285			−0.458240
$277$			27.6686i			1.66245i	0.555939	+	0.831223i	$0.312359\pi$
$277$			27.6686i			1.66245i	−0.555939	+	0.831223i	$0.687641\pi$
$278$		−	0.285442i		−	0.0171197i
$279$	2.62222			0.156988
$280$	0.341219	+	2.42864i	0.0203918	+	0.145139i
$281$	−9.80642			−0.585002			−0.292501	−	0.956265i	$-0.594488\pi$
$281$	−9.80642			−0.585002			−0.292501	+	0.956265i	$0.594488\pi$
$282$		−	0.295286i		−	0.0175840i
$283$		−	19.0049i		−	1.12973i	−0.825185	−	0.564863i	$-0.808929\pi$
$283$		−	19.0049i		−	1.12973i	0.825185	−	0.564863i	$-0.191071\pi$
$284$	17.6731			1.04870
$285$	5.37778	−	0.755569i	0.318552	−	0.0447560i
$286$		0			0
$287$			9.63158i			0.568534i
$288$			3.49532i			0.205963i
$289$	11.7971			0.693944
$290$	4.85728	−	0.682439i	0.285229	−	0.0400742i
$291$	−12.4701			−0.731012
$292$		−	10.7699i		−	0.630258i
$293$		−	30.7511i		−	1.79650i	−0.439485	−	0.898250i	$-0.644839\pi$
$293$		−	30.7511i		−	1.79650i	0.439485	−	0.898250i	$-0.355161\pi$
$294$	−1.92396			−0.112207
$295$	0.520505	+	3.70471i	0.0303050	+	0.215697i
$296$	7.05086			0.409823
$297$		0			0
$298$		−	0.682439i		−	0.0395326i
$299$	11.6128			0.671588
$300$	2.62222	+	9.14764i	0.151394	+	0.528139i
$301$	−9.67307			−0.557547
$302$		−	3.24443i		−	0.186696i
$303$			16.1748i			0.929220i
$304$	8.32693			0.477582
$305$	2.25380	+	16.0415i	0.129052	+	0.918533i
$306$	0.709636			0.0405672
$307$			13.4938i			0.770131i	0.922889	+	0.385065i	$0.125821\pi$
$307$			13.4938i			0.770131i	−0.922889	+	0.385065i	$0.874179\pi$
$308$		0			0
$309$	17.1526			0.975775
$310$	−1.80642	+	0.253799i	−0.102598	+	0.0144148i
$311$	−17.5526			−0.995318			−0.497659	−	0.867373i	$-0.665807\pi$
$311$	−17.5526			−0.995318			−0.497659	+	0.867373i	$0.665807\pi$
$312$		−	3.52543i		−	0.199588i
$313$		−	14.3970i		−	0.813766i	−0.913480	−	0.406883i	$-0.866616\pi$
$313$		−	14.3970i		−	0.813766i	0.913480	−	0.406883i	$-0.133384\pi$
$314$	1.80642			0.101942
$315$	2.00000	−	0.280996i	0.112687	−	0.0158323i
$316$	−31.4608			−1.76981
$317$			29.4608i			1.65468i	0.561701	+	0.827341i	$0.310147\pi$
$317$			29.4608i			1.65468i	−0.561701	+	0.827341i	$0.689853\pi$
$318$			0.253799i			0.0142324i
$319$		0			0
$320$	1.79505	+	12.7763i	0.100346	+	0.714218i
$321$	13.5669			0.757231
$322$		−	1.12399i		−	0.0626372i
$323$		−	5.53972i		−	0.308238i
$324$	1.90321			0.105734
$325$	−4.00000	−	13.9541i	−0.221880	−	0.774032i
$326$	−3.43801			−0.190414
$327$			10.0000i			0.553001i
$328$		−	12.9491i		−	0.714997i
$329$	−0.857279			−0.0472633
$330$		0			0
$331$	−2.62222			−0.144130			−0.0720650	−	0.997400i	$-0.522959\pi$
$331$	−2.62222			−0.144130			−0.0720650	+	0.997400i	$0.522959\pi$
$332$			14.7699i			0.810601i
$333$		−	5.80642i		−	0.318190i
$334$	−4.34122			−0.237541
$335$	−28.4701	+	4.00000i	−1.55549	+	0.218543i
$336$	3.09679			0.168944
$337$			5.00492i			0.272635i	0.990665	+	0.136318i	$0.0435268\pi$
$337$			5.00492i			0.272635i	−0.990665	+	0.136318i	$0.956473\pi$
$338$		−	1.42219i		−	0.0773567i
$339$	−14.2351			−0.773143
$340$	9.61285	−	1.35059i	0.521330	−	0.0732459i
$341$		0			0
$342$			0.755569i			0.0408565i
$343$			11.9081i			0.642979i
$344$	13.0049			0.701178
$345$	−1.24443	−	8.85728i	−0.0669979	−	0.476860i
$346$	−5.86220			−0.315154
$347$			22.8113i			1.22458i	0.790634	+	0.612289i	$0.209751\pi$
$347$			22.8113i			1.22458i	−0.790634	+	0.612289i	$0.790249\pi$
$348$		−	13.4193i		−	0.719348i
$349$	21.2257			1.13619			0.568093	−	0.822965i	$-0.307681\pi$
$349$	21.2257			1.13619			0.568093	+	0.822965i	$0.307681\pi$
$350$	−1.35059	+	0.387152i	−0.0721919	+	0.0206942i
$351$	−2.90321			−0.154962
$352$		0			0
$353$		−	7.18421i		−	0.382377i	−0.981553	−	0.191188i	$-0.938766\pi$
$353$		−	7.18421i		−	0.382377i	0.981553	−	0.191188i	$-0.0612341\pi$
$354$	−0.520505			−0.0276645
$355$	2.88892	+	20.5620i	0.153328	+	1.09132i
$356$	−11.6731			−0.618672
$357$		−	2.06022i		−	0.109039i
$358$			1.51114i			0.0798661i
$359$	−14.1017			−0.744260			−0.372130	−	0.928181i	$-0.621372\pi$
$359$	−14.1017			−0.744260			−0.372130	+	0.928181i	$0.621372\pi$
$360$	−2.68889	+	0.377784i	−0.141717	+	0.0199110i
$361$	−13.1017			−0.689564
$362$			5.22570i			0.274656i
$363$		0			0
$364$	−4.99063			−0.261580
$365$	12.5303	−	1.76049i	0.655868	−	0.0921483i
$366$	−2.25380			−0.117808
$367$		−	3.90813i		−	0.204003i	−0.994784	−	0.102001i	$-0.967475\pi$
$367$		−	3.90813i		−	0.204003i	0.994784	−	0.102001i	$-0.0325246\pi$
$368$		−	13.7146i		−	0.714921i
$369$	−10.6637			−0.555130
$370$	0.561993	+	4.00000i	0.0292166	+	0.207950i
$371$	0.736833			0.0382545
$372$			4.99063i			0.258752i
$373$			12.9763i			0.671890i	0.941882	+	0.335945i	$0.109056\pi$
$373$			12.9763i			0.671890i	−0.941882	+	0.335945i	$0.890944\pi$
$374$		0			0
$375$	−10.2143	+	4.54617i	−0.527465	+	0.234763i
$376$	1.15257			0.0594390
$377$			20.4701i			1.05427i
$378$			0.280996i			0.0144529i
$379$	−36.0830			−1.85346			−0.926729	−	0.375731i	$-0.877392\pi$
$379$	−36.0830			−1.85346			−0.926729	+	0.375731i	$0.877392\pi$
$380$	1.43801	+	10.2351i	0.0737682	+	0.525048i
$381$	−11.0049			−0.563799
$382$		−	5.24443i		−	0.268328i
$383$		−	20.2953i		−	1.03704i	−0.855065	−	0.518520i	$-0.826483\pi$
$383$		−	20.2953i		−	1.03704i	0.855065	−	0.518520i	$-0.173517\pi$
$384$	−8.78568			−0.448342
$385$		0			0
$386$	−7.65878			−0.389822
$387$		−	10.7096i		−	0.544401i
$388$		−	23.7333i		−	1.20488i
$389$	−30.4701			−1.54490			−0.772448	−	0.635078i	$-0.780968\pi$
$389$	−30.4701			−1.54490			−0.772448	+	0.635078i	$0.780968\pi$
$390$	2.00000	−	0.280996i	0.101274	−	0.0142288i
$391$	−9.12399			−0.461420
$392$		−	7.50961i		−	0.379292i
$393$			1.24443i			0.0627733i
$394$	−4.62666			−0.233088
$395$	−5.14272	−	36.6035i	−0.258758	−	1.84172i
$396$		0			0
$397$			4.97773i			0.249825i	0.992168	+	0.124912i	$0.0398650\pi$
$397$			4.97773i			0.249825i	−0.992168	+	0.124912i	$0.960135\pi$
$398$		−	3.49240i		−	0.175058i
$399$	2.19358			0.109816
$400$	−16.4795	+	4.72393i	−0.823975	+	0.236196i
$401$	−1.86665			−0.0932159			−0.0466079	−	0.998913i	$-0.514841\pi$
$401$	−1.86665			−0.0932159			−0.0466079	+	0.998913i	$0.514841\pi$
$402$		−	4.00000i		−	0.199502i
$403$		−	7.61285i		−	0.379223i
$404$	−30.7841			−1.53157
$405$	0.311108	+	2.21432i	0.0154591	+	0.110030i
$406$	1.98126			0.0983285
$407$		0			0
$408$			2.76986i			0.137128i
$409$	−3.63158			−0.179570			−0.0897851	−	0.995961i	$-0.528618\pi$
$409$	−3.63158			−0.179570			−0.0897851	+	0.995961i	$0.528618\pi$
$410$	7.34614	−	1.03212i	0.362800	−	0.0509727i
$411$	−4.42864			−0.218449
$412$			32.6450i			1.60830i
$413$			1.51114i			0.0743582i
$414$	1.24443			0.0611605
$415$	−17.1842	+	2.41435i	−0.843540	+	0.118516i
$416$	10.1476			0.497529
$417$		−	0.917502i		−	0.0449303i
$418$		0			0
$419$	−4.85728			−0.237294			−0.118647	−	0.992937i	$-0.537856\pi$
$419$	−4.85728			−0.237294			−0.118647	+	0.992937i	$0.537856\pi$
$420$	0.534795	+	3.80642i	0.0260953	+	0.185734i
$421$	22.6321			1.10302			0.551510	−	0.834169i	$-0.314052\pi$
$421$	22.6321			1.10302			0.551510	+	0.834169i	$0.314052\pi$
$422$		−	3.71456i		−	0.180822i
$423$		−	0.949145i		−	0.0461490i
$424$	−0.990632			−0.0481093
$425$	3.14272	+	10.9634i	0.152444	+	0.531805i
$426$	−2.88892			−0.139969
$427$			6.54326i			0.316650i
$428$			25.8207i			1.24809i
$429$		0			0
$430$	1.03657	+	7.37778i	0.0499876	+	0.355788i
$431$	−1.24443			−0.0599421			−0.0299711	−	0.999551i	$-0.509542\pi$
$431$	−1.24443			−0.0599421			−0.0299711	+	0.999551i	$0.509542\pi$
$432$			3.42864i			0.164960i
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$	−0.736833			−0.0353691
$435$	15.6128	−	2.19358i	0.748579	−	0.105174i
$436$	−19.0321			−0.911473
$437$		−	9.71456i		−	0.464710i
$438$			1.76049i			0.0841195i
$439$	−2.42864			−0.115913			−0.0579563	−	0.998319i	$-0.518458\pi$
$439$	−2.42864			−0.115913			−0.0579563	+	0.998319i	$0.518458\pi$
$440$		0			0
$441$	−6.18421			−0.294486
$442$		−	2.06022i		−	0.0979948i
$443$		−	31.0509i		−	1.47527i	−0.675199	−	0.737635i	$-0.735942\pi$
$443$		−	31.0509i		−	1.47527i	0.675199	−	0.737635i	$-0.264058\pi$
$444$	11.0509			0.524450
$445$	−1.90813	−	13.5812i	−0.0904542	−	0.643811i
$446$	−6.78415			−0.321239
$447$		−	2.19358i		−	0.103753i
$448$			5.21141i			0.246216i
$449$	37.3590			1.76308			0.881541	−	0.472107i	$-0.156506\pi$
$449$	37.3590			1.76308			0.881541	+	0.472107i	$0.156506\pi$
$450$	−0.428639	−	1.49532i	−0.0202063	−	0.0704899i
$451$		0			0
$452$		−	27.0923i		−	1.27432i
$453$		−	10.4286i		−	0.489980i
$454$	−0.995078			−0.0467013
$455$	−0.815792	−	5.80642i	−0.0382449	−	0.272209i
$456$	−2.94914			−0.138106
$457$		−	8.73822i		−	0.408757i	−0.978892	−	0.204378i	$-0.934483\pi$
$457$		−	8.73822i		−	0.408757i	0.978892	−	0.204378i	$-0.0655172\pi$
$458$			2.21633i			0.103562i
$459$	2.28100			0.106468
$460$	16.8573	−	2.36842i	0.785975	−	0.110428i
$461$	−31.7877			−1.48050			−0.740250	−	0.672332i	$-0.765293\pi$
$461$	−31.7877			−1.48050			−0.740250	+	0.672332i	$0.765293\pi$
$462$		0			0
$463$		−	12.0919i		−	0.561957i	−0.959714	−	0.280978i	$-0.909341\pi$
$463$		−	12.0919i		−	0.561957i	0.959714	−	0.280978i	$-0.0906589\pi$
$464$	24.1748			1.12229
$465$	−5.80642	+	0.815792i	−0.269266	+	0.0378314i
$466$	−6.07451			−0.281396
$467$		−	15.3461i		−	0.710135i	−0.934841	−	0.355067i	$-0.884458\pi$
$467$		−	15.3461i		−	0.710135i	0.934841	−	0.355067i	$-0.115542\pi$
$468$		−	5.52543i		−	0.255413i
$469$	−11.6128			−0.536231
$470$	0.0918659	+	0.653858i	0.00423746	+	0.0301602i
$471$	5.80642			0.267546
$472$		−	2.03164i		−	0.0935139i
$473$		0			0
$474$	5.14272			0.236213
$475$	−11.6731	+	3.34614i	−0.535597	+	0.153532i
$476$	3.92104			0.179721
$477$			0.815792i			0.0373525i
$478$			6.83854i			0.312788i
$479$	5.89829			0.269500			0.134750	−	0.990880i	$-0.456977\pi$
$479$	5.89829			0.269500			0.134750	+	0.990880i	$0.456977\pi$
$480$	−1.08742	−	7.73975i	−0.0496337	−	0.353270i
$481$	−16.8573			−0.768626
$482$			1.66323i			0.0757579i
$483$		−	3.61285i		−	0.164390i
$484$		0			0
$485$	27.6128	−	3.87955i	1.25383	−	0.176161i
$486$	−0.311108			−0.0141121
$487$			31.3461i			1.42043i	0.703985	+	0.710215i	$0.251402\pi$
$487$			31.3461i			1.42043i	−0.703985	+	0.710215i	$0.748598\pi$
$488$		−	8.79706i		−	0.398224i
$489$	−11.0509			−0.499737
$490$	4.26025	−	0.598558i	0.192459	−	0.0270401i
$491$	8.00000			0.361035			0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000			0.361035			0.180517	+	0.983572i	$0.442223\pi$
$492$		−	20.2953i		−	0.914982i
$493$		−	16.0830i		−	0.724341i
$494$	2.19358			0.0986937
$495$		0			0
$496$	−8.99063			−0.403691
$497$			8.38715i			0.376215i
$498$		−	2.41435i		−	0.108190i
$499$	−15.1427			−0.677881			−0.338941	−	0.940808i	$-0.610069\pi$
$499$	−15.1427			−0.677881			−0.338941	+	0.940808i	$0.610069\pi$
$500$	−8.65233	−	19.4400i	−0.386944	−	0.869384i
$501$	−13.9541			−0.623422
$502$			7.39652i			0.330123i
$503$			26.0370i			1.16093i	0.814284	+	0.580467i	$0.197130\pi$
$503$			26.0370i			1.16093i	−0.814284	+	0.580467i	$0.802870\pi$
$504$	−1.09679			−0.0488548
$505$	−5.03212	−	35.8163i	−0.223926	−	1.59380i
$506$		0			0
$507$		−	4.57136i		−	0.203021i
$508$		−	20.9447i		−	0.929271i
$509$	24.5718			1.08913			0.544564	−	0.838719i	$-0.316695\pi$
$509$	24.5718			1.08913			0.544564	+	0.838719i	$0.316695\pi$
$510$	−1.57136	+	0.220773i	−0.0695810	+	0.00977600i
$511$	5.11108			0.226101
$512$		−	20.3111i		−	0.897633i
$513$			2.42864i			0.107227i
$514$	−2.53035			−0.111609
$515$	−37.9813	+	5.33630i	−1.67365	+	0.235145i
$516$	20.3827			0.897299
$517$		0			0
$518$			1.63158i			0.0716877i
$519$	−18.8430			−0.827115
$520$	1.09679	+	7.80642i	0.0480973	+	0.342334i
$521$	−4.88892			−0.214188			−0.107094	−	0.994249i	$-0.534155\pi$
$521$	−4.88892			−0.214188			−0.107094	+	0.994249i	$0.534155\pi$
$522$			2.19358i			0.0960102i
$523$		−	4.22077i		−	0.184562i	−0.995733	−	0.0922808i	$-0.970584\pi$
$523$		−	4.22077i		−	0.184562i	0.995733	−	0.0922808i	$-0.0294157\pi$
$524$	−2.36842			−0.103465
$525$	−4.34122	+	1.24443i	−0.189466	+	0.0543114i
$526$	7.12537			0.310681
$527$			5.98126i			0.260548i
$528$		0			0
$529$	7.00000			0.304348
$530$	−0.0789589	−	0.561993i	−0.00342976	−	0.0244114i
$531$	−1.67307			−0.0726051
$532$			4.17484i			0.181002i
$533$			30.9590i			1.34098i
$534$	1.90813			0.0825730
$535$	−30.0415	+	4.22077i	−1.29881	+	0.182480i
$536$	15.6128			0.674372
$537$			4.85728i			0.209607i
$538$			3.68196i			0.158741i
$539$		0			0
$540$	−4.21432	+	0.592104i	−0.181355	+	0.0254801i
$541$	13.6128			0.585262			0.292631	−	0.956225i	$-0.405469\pi$
$541$	13.6128			0.585262			0.292631	+	0.956225i	$0.405469\pi$
$542$			4.63512i			0.199096i
$543$			16.7971i			0.720831i
$544$	−7.97280			−0.341831
$545$	−3.11108	−	22.1432i	−0.133264	−	0.948510i
$546$	0.815792			0.0349127
$547$			7.48394i			0.319990i	0.987118	+	0.159995i	$0.0511478\pi$
$547$			7.48394i			0.319990i	−0.987118	+	0.159995i	$0.948852\pi$
$548$		−	8.42864i		−	0.360054i
$549$	−7.24443			−0.309185
$550$		0			0
$551$	17.1240			0.729506
$552$			4.85728i			0.206740i
$553$		−	14.9304i		−	0.634906i
$554$	8.60793			0.365716
$555$	1.80642	+	12.8573i	0.0766784	+	0.545761i
$556$	1.74620			0.0740554
$557$			32.2908i			1.36821i	0.729385	+	0.684103i	$0.239806\pi$
$557$			32.2908i			1.36821i	−0.729385	+	0.684103i	$0.760194\pi$
$558$		−	0.815792i		−	0.0345352i
$559$	−31.0923			−1.31507
$560$	−6.85728	+	0.963435i	−0.289773	+	0.0407126i
$561$		0			0
$562$			3.05086i			0.128693i
$563$		−	7.49378i		−	0.315825i	−0.987453	−	0.157913i	$-0.949524\pi$
$563$		−	7.49378i		−	0.315825i	0.987453	−	0.157913i	$-0.0504765\pi$
$564$	1.80642			0.0760642
$565$	31.5210	−	4.42864i	1.32610	−	0.186314i
$566$	−5.91258			−0.248524
$567$			0.903212i			0.0379313i
$568$		−	11.2761i		−	0.473134i
$569$	−12.9491			−0.542856			−0.271428	−	0.962459i	$-0.587496\pi$
$569$	−12.9491			−0.542856			−0.271428	+	0.962459i	$0.587496\pi$
$570$	−0.235063	−	1.67307i	−0.00984572	−	0.0700772i
$571$	15.2859			0.639696			0.319848	−	0.947469i	$-0.396368\pi$
$571$	15.2859			0.639696			0.319848	+	0.947469i	$0.396368\pi$
$572$		0			0
$573$		−	16.8573i		−	0.704223i
$574$	2.99646			0.125070
$575$	5.51114	+	19.2257i	0.229830	+	0.801767i
$576$	−5.76986			−0.240411
$577$		−	28.4415i		−	1.18404i	−0.805924	−	0.592019i	$-0.798331\pi$
$577$		−	28.4415i		−	1.18404i	0.805924	−	0.592019i	$-0.201669\pi$
$578$		−	3.67016i		−	0.152658i
$579$	−24.6178			−1.02308
$580$	4.17484	+	29.7146i	0.173351	+	1.23383i
$581$	−7.00937			−0.290798
$582$			3.87955i			0.160813i
$583$		0			0
$584$	−6.87157			−0.284348
$585$	6.42864	−	0.903212i	0.265792	−	0.0373432i
$586$	−9.56691			−0.395206
$587$			8.47013i			0.349600i	0.984604	+	0.174800i	$0.0559278\pi$
$587$			8.47013i			0.349600i	−0.984604	+	0.174800i	$0.944072\pi$
$588$		−	11.7699i		−	0.485381i
$589$	−6.36842			−0.262406
$590$	1.15257	−	0.161933i	0.0474504	−	0.00666669i
$591$	−14.8716			−0.611735
$592$			19.9081i			0.818219i
$593$		−	26.5763i		−	1.09136i	−0.837995	−	0.545679i	$-0.816272\pi$
$593$		−	26.5763i		−	1.09136i	0.837995	−	0.545679i	$-0.183728\pi$
$594$		0			0
$595$	0.640951	+	4.56199i	0.0262764	+	0.187023i
$596$	4.17484			0.171008
$597$		−	11.2257i		−	0.459437i
$598$		−	3.61285i		−	0.147740i
$599$	8.77430			0.358508			0.179254	−	0.983803i	$-0.442632\pi$
$599$	8.77430			0.358508			0.179254	+	0.983803i	$0.442632\pi$
$600$	5.83654	−	1.67307i	0.238276	−	0.0683028i
$601$	41.8163			1.70572			0.852861	−	0.522139i	$-0.174866\pi$
$601$	41.8163			1.70572			0.852861	+	0.522139i	$0.174866\pi$
$602$			3.00937i			0.122653i
$603$		−	12.8573i		−	0.523589i
$604$	19.8479			0.807600
$605$		0			0
$606$	5.03212			0.204416
$607$			29.9353i			1.21504i	0.794305	+	0.607519i	$0.207835\pi$
$607$			29.9353i			1.21504i	−0.794305	+	0.607519i	$0.792165\pi$
$608$		−	8.48886i		−	0.344269i
$609$	6.36842			0.258061
$610$	4.99063	−	0.701175i	0.202065	−	0.0283897i
$611$	−2.75557			−0.111478
$612$			4.34122i			0.175483i
$613$		−	26.1289i		−	1.05534i	−0.849450	−	0.527668i	$-0.823066\pi$
$613$		−	26.1289i		−	1.05534i	0.849450	−	0.527668i	$-0.176934\pi$
$614$	4.19802			0.169418
$615$	23.6128	−	3.31756i	0.952162	−	0.133777i
$616$		0			0
$617$			3.66323i			0.147476i	0.997278	+	0.0737380i	$0.0234928\pi$
$617$			3.66323i			0.147476i	−0.997278	+	0.0737380i	$0.976507\pi$
$618$		−	5.33630i		−	0.214657i
$619$	−43.2958			−1.74020			−0.870102	−	0.492872i	$-0.835947\pi$
$619$	−43.2958			−1.74020			−0.870102	+	0.492872i	$0.835947\pi$
$620$	−1.55262	−	11.0509i	−0.0623549	−	0.443813i
$621$	4.00000			0.160514
$622$			5.46076i			0.218956i
$623$		−	5.53972i		−	0.221944i
$624$	9.95407			0.398482
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$	−4.47902			−0.179018
$627$		0			0
$628$			11.0509i			0.440977i
$629$	13.2444			0.528090
$630$	−0.0874201	−	0.622216i	−0.00348290	−	0.0247897i
$631$	8.97773			0.357398			0.178699	−	0.983904i	$-0.442811\pi$
$631$	8.97773			0.357398			0.178699	+	0.983904i	$0.442811\pi$
$632$			20.0731i			0.798466i
$633$		−	11.9398i		−	0.474564i
$634$	9.16547			0.364007
$635$	24.3684	−	3.42372i	0.967031	−	0.135866i
$636$	−1.55262			−0.0615656
$637$			17.9541i			0.711366i
$638$		0			0
$639$	−9.28592			−0.367345
$640$	19.4543	−	2.73329i	0.768999	−	0.108043i
$641$	9.21279			0.363883			0.181942	−	0.983309i	$-0.441762\pi$
$641$	9.21279			0.363883			0.181942	+	0.983309i	$0.441762\pi$
$642$		−	4.22077i		−	0.166581i
$643$		−	16.3783i		−	0.645896i	−0.946417	−	0.322948i	$-0.895326\pi$
$643$		−	16.3783i		−	0.645896i	0.946417	−	0.322948i	$-0.104674\pi$
$644$	6.87601			0.270953
$645$	3.33185	+	23.7146i	0.131192	+	0.933760i
$646$	−1.72345			−0.0678082
$647$		−	9.80642i		−	0.385530i	−0.981245	−	0.192765i	$-0.938254\pi$
$647$		−	9.80642i		−	0.385530i	0.981245	−	0.192765i	$-0.0617456\pi$
$648$		−	1.21432i		−	0.0477030i
$649$		0			0
$650$	−4.34122	+	1.24443i	−0.170277	+	0.0488106i
$651$	−2.36842			−0.0928256
$652$		−	21.0321i		−	0.823681i
$653$			33.0736i			1.29427i	0.762375	+	0.647135i	$0.224033\pi$
$653$			33.0736i			1.29427i	−0.762375	+	0.647135i	$0.775967\pi$
$654$	3.11108			0.121653
$655$	−0.387152	−	2.75557i	−0.0151273	−	0.107669i
$656$	36.5620			1.42751
$657$			5.65878i			0.220770i
$658$			0.266706i			0.0103973i
$659$	34.1017			1.32841			0.664207	−	0.747549i	$-0.268769\pi$
$659$	34.1017			1.32841			0.664207	+	0.747549i	$0.268769\pi$
$660$		0			0
$661$	−5.40943			−0.210402			−0.105201	−	0.994451i	$-0.533549\pi$
$661$	−5.40943			−0.210402			−0.105201	+	0.994451i	$0.533549\pi$
$662$			0.815792i			0.0317066i
$663$		−	6.62222i		−	0.257186i
$664$	9.42372			0.365711
$665$	−4.85728	+	0.682439i	−0.188357	+	0.0264638i
$666$	−1.80642			−0.0699975
$667$		−	28.2034i		−	1.09204i
$668$		−	26.5575i		−	1.02754i
$669$	−21.8064			−0.843085
$670$	1.24443	+	8.85728i	0.0480766	+	0.342187i
$671$		0			0
$672$		−	3.15701i		−	0.121784i
$673$		−	24.1476i		−	0.930823i	−0.885094	−	0.465412i	$-0.845906\pi$
$673$		−	24.1476i		−	0.930823i	0.885094	−	0.465412i	$-0.154094\pi$
$674$	1.55707			0.0599761
$675$	−1.37778	−	4.80642i	−0.0530309	−	0.184999i
$676$	8.70027			0.334626
$677$			26.2810i			1.01006i	0.863102	+	0.505030i	$0.168519\pi$
$677$			26.2810i			1.01006i	−0.863102	+	0.505030i	$0.831481\pi$
$678$			4.42864i			0.170081i
$679$	11.2632			0.432241
$680$	−0.861725	−	6.13335i	−0.0330456	−	0.235203i
$681$	−3.19850			−0.122567
$682$		0			0
$683$			15.3176i			0.586110i	0.956096	+	0.293055i	$0.0946719\pi$
$683$			15.3176i			0.586110i	−0.956096	+	0.293055i	$0.905328\pi$
$684$	−4.62222			−0.176735
$685$	9.80642	−	1.37778i	0.374684	−	0.0526424i
$686$	3.70471			0.141447
$687$			7.12399i			0.271797i
$688$			36.7195i			1.39992i
$689$	2.36842			0.0902295
$690$	−2.75557	+	0.387152i	−0.104903	+	0.0147386i
$691$	15.0223			0.571474			0.285737	−	0.958308i	$-0.407762\pi$
$691$	15.0223			0.571474			0.285737	+	0.958308i	$0.407762\pi$
$692$		−	35.8622i		−	1.36328i
$693$		0			0
$694$	7.09679			0.269390
$695$	0.285442	+	2.03164i	0.0108274	+	0.0770646i
$696$	−8.56199			−0.324541
$697$		−	24.3239i		−	0.921332i
$698$		−	6.60348i		−	0.249945i
$699$	−19.5254			−0.738519
$700$	−2.36842	−	8.26226i	−0.0895177	−	0.312284i
$701$	19.9081			0.751920			0.375960	−	0.926636i	$-0.377313\pi$
$701$	19.9081			0.751920			0.375960	+	0.926636i	$0.377313\pi$
$702$			0.903212i			0.0340895i
$703$			14.1017i			0.531856i
$704$		0			0
$705$	0.295286	+	2.10171i	0.0111211	+	0.0791550i
$706$	−2.23506			−0.0841177
$707$		−	14.6093i		−	0.549440i
$708$		−	3.18421i		−	0.119670i
$709$	13.5081			0.507306			0.253653	−	0.967295i	$-0.418368\pi$
$709$	13.5081			0.507306			0.253653	+	0.967295i	$0.418368\pi$
$710$	6.39700	−	0.898766i	0.240075	−	0.0337301i
$711$	16.5303			0.619937
$712$			7.44785i			0.279120i
$713$			10.4889i			0.392811i
$714$	−0.640951			−0.0239870
$715$		0			0
$716$	−9.24443			−0.345481
$717$			21.9813i			0.820905i
$718$			4.38715i			0.163727i
$719$	16.0830			0.599794			0.299897	−	0.953972i	$-0.403048\pi$
$719$	16.0830			0.599794			0.299897	+	0.953972i	$0.403048\pi$
$720$	−1.06668	−	7.59210i	−0.0397527	−	0.282941i
$721$	−15.4924			−0.576967
$722$			4.07604i			0.151695i
$723$			5.34614i			0.198825i
$724$	−31.9684			−1.18809
$725$	−33.8894	+	9.71456i	−1.25862	+	0.360790i
$726$		0			0
$727$			23.6128i			0.875752i	0.899035	+	0.437876i	$0.144269\pi$
$727$			23.6128i			0.875752i	−0.899035	+	0.437876i	$0.855731\pi$
$728$			3.18421i			0.118015i
$729$	−1.00000			−0.0370370
$730$	−0.547702	−	3.89829i	−0.0202714	−	0.144282i
$731$	24.4286			0.903526
$732$		−	13.7877i		−	0.509608i
$733$		−	30.0459i		−	1.10977i	−0.831926	−	0.554886i	$-0.812762\pi$
$733$		−	30.0459i		−	1.10977i	0.831926	−	0.554886i	$-0.187238\pi$
$734$	−1.21585			−0.0448779
$735$	13.6938	−	1.92396i	0.505104	−	0.0709662i
$736$	−13.9813			−0.515356
$737$		0			0
$738$			3.31756i			0.122121i
$739$	−24.4099			−0.897933			−0.448966	−	0.893549i	$-0.648208\pi$
$739$	−24.4099			−0.897933			−0.448966	+	0.893549i	$0.648208\pi$
$740$	−24.4701	+	3.43801i	−0.899540	+	0.126384i
$741$	7.05086			0.259020
$742$		−	0.229234i		−	0.00841546i
$743$		−	33.1798i		−	1.21725i	−0.793459	−	0.608624i	$-0.791722\pi$
$743$		−	33.1798i		−	1.21725i	0.793459	−	0.608624i	$-0.208278\pi$
$744$	3.18421			0.116739
$745$	0.682439	+	4.85728i	0.0250026	+	0.177957i
$746$	4.03704			0.147807
$747$		−	7.76049i		−	0.283942i
$748$		0			0
$749$	−12.2538			−0.447744
$750$	1.41435	+	3.17775i	0.0516447	+	0.116035i
$751$	−22.5718			−0.823658			−0.411829	−	0.911261i	$-0.635110\pi$
$751$	−22.5718			−0.823658			−0.411829	+	0.911261i	$0.635110\pi$
$752$			3.25428i			0.118671i
$753$			23.7748i			0.866401i
$754$	6.36842			0.231924
$755$	3.24443	+	23.0923i	0.118077	+	0.840416i
$756$	−1.71900			−0.0625196
$757$		−	4.94914i		−	0.179880i	−0.995947	−	0.0899399i	$-0.971333\pi$
$757$		−	4.94914i		−	0.179880i	0.995947	−	0.0899399i	$-0.0286675\pi$
$758$			11.2257i			0.407736i
$759$		0			0
$760$	6.53035	−	0.917502i	0.236881	−	0.0332813i
$761$	−14.6637			−0.531559			−0.265779	−	0.964034i	$-0.585629\pi$
$761$	−14.6637			−0.531559			−0.265779	+	0.964034i	$0.585629\pi$
$762$			3.42372i			0.124028i
$763$		−	9.03212i		−	0.326985i
$764$	32.0830			1.16072
$765$	−5.05086	+	0.709636i	−0.182614	+	0.0256569i
$766$	−6.31402			−0.228135
$767$			4.85728i			0.175386i
$768$		−	8.80642i		−	0.317774i
$769$	−44.5718			−1.60730			−0.803651	−	0.595101i	$-0.797112\pi$
$769$	−44.5718			−1.60730			−0.803651	+	0.595101i	$0.797112\pi$
$770$		0			0
$771$	−8.13335			−0.292916
$772$		−	46.8528i		−	1.68627i
$773$			17.3145i			0.622759i	0.950286	+	0.311380i	$0.100791\pi$
$773$			17.3145i			0.622759i	−0.950286	+	0.311380i	$0.899209\pi$
$774$	−3.33185			−0.119761
$775$	12.6035	−	3.61285i	0.452730	−	0.129777i
$776$	−15.1427			−0.543592
$777$			5.24443i			0.188143i
$778$			9.47949i			0.339856i
$779$	25.8983			0.927903
$780$	1.71900	+	12.2351i	0.0615502	+	0.438086i
$781$		0			0
$782$			2.83854i			0.101506i
$783$			7.05086i			0.251977i
$784$	21.2034			0.757265
$785$	−12.8573	+	1.80642i	−0.458896	+	0.0644740i
$786$	0.387152			0.0138093
$787$			36.5161i			1.30166i	0.759225	+	0.650828i	$0.225578\pi$
$787$			36.5161i			1.30166i	−0.759225	+	0.650828i	$0.774422\pi$
$788$		−	28.3037i		−	1.00828i
$789$	22.9032			0.815376
$790$	−11.3876	+	1.59994i	−0.405154	+	0.0569233i
$791$	12.8573			0.457152
$792$		0			0
$793$			21.0321i			0.746872i
$794$	1.54861			0.0549581
$795$	−0.253799	−	1.80642i	−0.00900133	−	0.0640673i
$796$	21.3649			0.757258
$797$			14.3180i			0.507171i	0.967313	+	0.253585i	$0.0816099\pi$
$797$			14.3180i			0.507171i	−0.967313	+	0.253585i	$0.918390\pi$
$798$		−	0.682439i		−	0.0241581i
$799$	2.16500			0.0765921
$800$	4.81579	+	16.8000i	0.170264	+	0.593969i
$801$	6.13335			0.216711
$802$			0.580728i			0.0205062i
$803$		0			0
$804$	24.4701			0.862995
$805$	1.12399	+	8.00000i	0.0396153	+	0.281963i
$806$	−2.36842			−0.0834239
$807$			11.8350i			0.416612i
$808$			19.6414i			0.690983i
$809$	32.0544			1.12697			0.563486	−	0.826125i	$-0.309460\pi$
$809$	32.0544			1.12697			0.563486	+	0.826125i	$0.309460\pi$
$810$	0.688892	−	0.0967881i	0.0242052	−	0.00340079i
$811$	8.44738			0.296627			0.148314	−	0.988940i	$-0.452615\pi$
$811$	8.44738			0.296627			0.148314	+	0.988940i	$0.452615\pi$
$812$			12.1204i			0.425344i
$813$			14.8988i			0.522523i
$814$		0			0
$815$	24.4701	−	3.43801i	0.857151	−	0.120428i
$816$	−7.82071			−0.273780
$817$			26.0098i			0.909969i
$818$			1.12981i			0.0395030i
$819$	2.62222			0.0916276
$820$	6.31402	+	44.9403i	0.220495	+	1.56938i
$821$	−17.2159			−0.600837			−0.300419	−	0.953807i	$-0.597126\pi$
$821$	−17.2159			−0.600837			−0.300419	+	0.953807i	$0.597126\pi$
$822$			1.37778i			0.0480557i
$823$			12.7654i			0.444974i	0.974936	+	0.222487i	$0.0714175\pi$
$823$			12.7654i			0.444974i	−0.974936	+	0.222487i	$0.928582\pi$
$824$	20.8287			0.725602
$825$		0			0
$826$	0.470127			0.0163578
$827$			8.70964i			0.302864i	0.988468	+	0.151432i	$0.0483884\pi$
$827$			8.70964i			0.302864i	−0.988468	+	0.151432i	$0.951612\pi$
$828$			7.61285i			0.264565i
$829$	8.32693			0.289206			0.144603	−	0.989490i	$-0.453809\pi$
$829$	8.32693			0.289206			0.144603	+	0.989490i	$0.453809\pi$
$830$	0.751123	+	5.34614i	0.0260719	+	0.185567i
$831$	27.6686			0.959814
$832$			16.7511i			0.580741i
$833$		−	14.1062i		−	0.488749i
$834$	−0.285442			−0.00988405
$835$	30.8988	−	4.34122i	1.06930	−	0.150234i
$836$		0			0
$837$		−	2.62222i		−	0.0906370i
$838$			1.51114i			0.0522014i
$839$	−12.8988			−0.445315			−0.222657	−	0.974897i	$-0.571473\pi$
$839$	−12.8988			−0.445315			−0.222657	+	0.974897i	$0.571473\pi$
$840$	2.42864	−	0.341219i	0.0837960	−	0.0117732i
$841$	20.7146			0.714295
$842$		−	7.04101i		−	0.242649i
$843$			9.80642i			0.337751i
$844$	22.7239			0.782190
$845$	1.42219	+	10.1225i	0.0489247	+	0.348223i
$846$	−0.295286			−0.0101522
$847$		0			0
$848$		−	2.79706i		−	0.0960513i
$849$	−19.0049			−0.652247
$850$	3.41081	−	0.977725i	0.116990	−	0.0335357i
$851$	23.2257			0.796167
$852$		−	17.6731i		−	0.605469i
$853$			19.6686i			0.673441i	0.941605	+	0.336720i	$0.109318\pi$
$853$			19.6686i			0.673441i	−0.941605	+	0.336720i	$0.890682\pi$
$854$	2.03566			0.0696588
$855$	−0.755569	−	5.37778i	−0.0258399	−	0.183916i
$856$	16.4746			0.563089
$857$			31.8207i			1.08697i	0.839417	+	0.543487i	$0.182896\pi$
$857$			31.8207i			1.08697i	−0.839417	+	0.543487i	$0.817104\pi$
$858$		0			0
$859$	−27.8292			−0.949519			−0.474760	−	0.880116i	$-0.657465\pi$
$859$	−27.8292			−0.949519			−0.474760	+	0.880116i	$0.657465\pi$
$860$	−45.1338	+	6.34122i	−1.53905	+	0.216234i
$861$	9.63158			0.328243
$862$			0.387152i			0.0131865i
$863$		−	4.82870i		−	0.164371i	−0.996617	−	0.0821854i	$-0.973810\pi$
$863$		−	4.82870i		−	0.164371i	0.996617	−	0.0821854i	$-0.0261900\pi$
$864$	3.49532			0.118913
$865$	41.7244	−	5.86220i	1.41867	−	0.199321i
$866$	4.97773			0.169150
$867$		−	11.7971i		−	0.400649i
$868$		−	4.50760i		−	0.152998i
$869$		0			0
$870$	−0.682439	−	4.85728i	−0.0231368	−	0.164677i
$871$	−37.3274			−1.26479
$872$			12.1432i			0.411221i
$873$			12.4701i			0.422050i
$874$	−3.02227			−0.102230
$875$	9.22570	−	4.10616i	0.311885	−	0.138813i
$876$	−10.7699			−0.363880
$877$			21.9826i			0.742301i	0.928573	+	0.371151i	$0.121037\pi$
$877$			21.9826i			0.742301i	−0.928573	+	0.371151i	$0.878963\pi$
$878$			0.755569i			0.0254992i
$879$	−30.7511			−1.03721
$880$		0			0
$881$	−12.1017			−0.407717			−0.203858	−	0.979000i	$-0.565348\pi$
$881$	−12.1017			−0.407717			−0.203858	+	0.979000i	$0.565348\pi$
$882$			1.92396i			0.0647830i
$883$			8.73683i			0.294018i	0.989135	+	0.147009i	$0.0469646\pi$
$883$			8.73683i			0.294018i	−0.989135	+	0.147009i	$0.953035\pi$
$884$	12.6035			0.423901
$885$	3.70471	−	0.520505i	0.124533	−	0.0174966i
$886$	−9.66016			−0.324540
$887$		−	19.8524i		−	0.666577i	−0.942825	−	0.333288i	$-0.891842\pi$
$887$		−	19.8524i		−	0.666577i	0.942825	−	0.333288i	$-0.108158\pi$
$888$		−	7.05086i		−	0.236611i
$889$	9.93978			0.333369
$890$	−4.22522	+	0.593635i	−0.141630	+	0.0198987i
$891$		0			0
$892$		−	41.5022i		−	1.38960i
$893$			2.30513i			0.0771383i
$894$	−0.682439			−0.0228242
$895$	−1.51114	−	10.7556i	−0.0505118	−	0.359519i
$896$	7.93533			0.265101
$897$		−	11.6128i		−	0.387742i
$898$		−	11.6227i		−	0.387854i
$899$	−18.4889			−0.616638
$900$	9.14764	−	2.62222i	0.304921	−	0.0874072i
$901$	−1.86082			−0.0619928
$902$		0			0
$903$			9.67307i			0.321900i
$904$	−17.2859			−0.574921
$905$	−5.22570	−	37.1941i	−0.173708	−	1.23637i
$906$	−3.24443			−0.107789
$907$		−	32.8287i		−	1.09006i	−0.838417	−	0.545030i	$-0.816518\pi$
$907$		−	32.8287i		−	1.09006i	0.838417	−	0.545030i	$-0.183482\pi$
$908$		−	6.08742i		−	0.202018i
$909$	16.1748			0.536486
$910$	−1.80642	+	0.253799i	−0.0598824	+	0.00841336i
$911$	−16.3497			−0.541689			−0.270845	−	0.962623i	$-0.587303\pi$
$911$	−16.3497			−0.541689			−0.270845	+	0.962623i	$0.587303\pi$
$912$		−	8.32693i		−	0.275732i
$913$		0			0
$914$	−2.71853			−0.0899209
$915$	16.0415	−	2.25380i	0.530315	−	0.0745083i
$916$	−13.5585			−0.447984
$917$		−	1.12399i		−	0.0371173i
$918$		−	0.709636i		−	0.0234215i
$919$	20.0228			0.660490			0.330245	−	0.943895i	$-0.392869\pi$
$919$	20.0228			0.660490			0.330245	+	0.943895i	$0.392869\pi$
$920$	−1.51114	−	10.7556i	−0.0498207	−	0.354601i
$921$	13.4938			0.444635
$922$			9.88940i			0.325690i
$923$			26.9590i			0.887366i
$924$		0			0
$925$	−8.00000	−	27.9081i	−0.263038	−	0.917614i
$926$	−3.76187			−0.123623
$927$		−	17.1526i		−	0.563364i
$928$		−	24.6450i		−	0.809011i
$929$	43.5308			1.42820			0.714100	−	0.700044i	$-0.246836\pi$
$929$	43.5308			1.42820			0.714100	+	0.700044i	$0.246836\pi$
$930$	0.253799	+	1.80642i	0.00832240	+	0.0592350i
$931$	15.0192			0.492235
$932$		−	37.1610i		−	1.21725i
$933$			17.5526i			0.574647i
$934$	−4.77430			−0.156220
$935$		0			0
$936$	−3.52543			−0.115232
$937$		−	43.4563i		−	1.41966i	−0.704375	−	0.709828i	$-0.748773\pi$
$937$		−	43.4563i		−	1.41966i	0.704375	−	0.709828i	$-0.251227\pi$
$938$			3.61285i			0.117964i
$939$	−14.3970			−0.469828
$940$	−4.00000	+	0.561993i	−0.130466	+	0.0183302i
$941$	23.7244			0.773393			0.386697	−	0.922207i	$-0.373616\pi$
$941$	23.7244			0.773393			0.386697	+	0.922207i	$0.373616\pi$
$942$		−	1.80642i		−	0.0588565i
$943$		−	42.6548i		−	1.38903i
$944$	5.73636			0.186703
$945$	−0.280996	−	2.00000i	−0.00914081	−	0.0650600i
$946$		0			0
$947$			11.7047i			0.380352i	0.981750	+	0.190176i	$0.0609059\pi$
$947$			11.7047i			0.380352i	−0.981750	+	0.190176i	$0.939094\pi$
$948$			31.4608i			1.02180i
$949$	16.4286			0.533296
$950$	1.04101	+	3.63158i	0.0337748	+	0.117824i
$951$	29.4608			0.955331
$952$		−	2.50177i		−	0.0810828i
$953$			46.1258i			1.49416i	0.664733	+	0.747081i	$0.268545\pi$
$953$			46.1258i			1.49416i	−0.664733	+	0.747081i	$0.731455\pi$
$954$	0.253799			0.00821705
$955$	5.24443	+	37.3274i	0.169706	+	1.20789i
$956$	−41.8350			−1.35304
$957$		0			0
$958$		−	1.83500i		−	0.0592863i
$959$	4.00000			0.129167
$960$	12.7763	−	1.79505i	0.412354	−	0.0579349i
$961$	−24.1240			−0.778193
$962$			5.24443i			0.169087i
$963$		−	13.5669i		−	0.437188i
$964$	−10.1748			−0.327710
$965$	54.5116	−	7.65878i	1.75479	−	0.246545i
$966$	−1.12399			−0.0361636
$967$		−	17.0495i		−	0.548274i	−0.961691	−	0.274137i	$-0.911608\pi$
$967$		−	17.0495i		−	0.548274i	0.961691	−	0.274137i	$-0.0883922\pi$
$968$		0			0
$969$	−5.53972			−0.177961
$970$	−1.20696	−	8.59057i	−0.0387531	−	0.275827i
$971$	−58.1847			−1.86724			−0.933618	−	0.358271i	$-0.883366\pi$
$971$	−58.1847			−1.86724			−0.933618	+	0.358271i	$0.883366\pi$
$972$		−	1.90321i		−	0.0610456i
$973$			0.828699i			0.0265669i
$974$	9.75203			0.312475
$975$	−13.9541	+	4.00000i	−0.446888	+	0.128103i
$976$	24.8385			0.795062
$977$		−	51.7373i		−	1.65522i	−0.561301	−	0.827612i	$-0.689699\pi$
$977$		−	51.7373i		−	1.65522i	0.561301	−	0.827612i	$-0.310301\pi$
$978$			3.43801i			0.109935i
$979$		0			0
$980$	3.66170	+	26.0622i	0.116969	+	0.832527i
$981$	10.0000			0.319275
$982$		−	2.48886i		−	0.0794228i
$983$			26.3970i			0.841933i	0.907076	+	0.420967i	$0.138309\pi$
$983$			26.3970i			0.841933i	−0.907076	+	0.420967i	$0.861691\pi$
$984$	−12.9491			−0.412804
$985$	32.9304	−	4.62666i	1.04925	−	0.147418i
$986$	−5.00354			−0.159345
$987$			0.857279i			0.0272875i
$988$			13.4193i			0.426924i
$989$	42.8385			1.36219
$990$		0			0
$991$	−23.0923			−0.733552			−0.366776	−	0.930309i	$-0.619539\pi$
$991$	−23.0923			−0.733552			−0.366776	+	0.930309i	$0.619539\pi$
$992$			9.16547i			0.291004i
$993$			2.62222i			0.0832135i
$994$	2.60931			0.0827622
$995$	3.49240	+	24.8573i	0.110717	+	0.788029i
$996$	14.7699			0.468001
$997$		−	12.9131i		−	0.408961i	−0.978871	−	0.204480i	$-0.934450\pi$
$997$		−	12.9131i		−	0.408961i	0.978871	−	0.204480i	$-0.0655504\pi$
$998$			4.71102i			0.149125i
$999$	−5.80642			−0.183707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.e.364.3		6
5.2	odd	4		9075.2.a.ch.1.2		3
5.3	odd	4		9075.2.a.cg.1.2		3
5.4	even	2	inner	1815.2.c.e.364.4		6
11.10	odd	2		165.2.c.b.34.4	yes	6
33.32	even	2		495.2.c.e.199.3		6
44.43	even	2		2640.2.d.h.529.5		6
55.32	even	4		825.2.a.j.1.2		3
55.43	even	4		825.2.a.l.1.2		3
55.54	odd	2		165.2.c.b.34.3	✓	6
165.32	odd	4		2475.2.a.bc.1.2		3
165.98	odd	4		2475.2.a.ba.1.2		3
165.164	even	2		495.2.c.e.199.4		6
220.219	even	2		2640.2.d.h.529.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.c.b.34.3	✓	6	55.54	odd	2
165.2.c.b.34.4	yes	6	11.10	odd	2
495.2.c.e.199.3		6	33.32	even	2
495.2.c.e.199.4		6	165.164	even	2
825.2.a.j.1.2		3	55.32	even	4
825.2.a.l.1.2		3	55.43	even	4
1815.2.c.e.364.3		6	1.1	even	1	trivial
1815.2.c.e.364.4		6	5.4	even	2	inner
2475.2.a.ba.1.2		3	165.98	odd	4
2475.2.a.bc.1.2		3	165.32	odd	4
2640.2.d.h.529.2		6	220.219	even	2
2640.2.d.h.529.5		6	44.43	even	2
9075.2.a.cg.1.2		3	5.3	odd	4
9075.2.a.ch.1.2		3	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.311108i q^{2} -1.00000i q^{3} +1.90321 q^{4} +(0.311108 + 2.21432i) q^{5} -0.311108 q^{6} +0.903212i q^{7} -1.21432i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.311108i q^{2} -1.00000i q^{3} +1.90321 q^{4} +(0.311108 + 2.21432i) q^{5} -0.311108 q^{6} +0.903212i q^{7} -1.21432i q^{8} -1.00000 q^{9} +(0.688892 - 0.0967881i) q^{10} -1.90321i q^{12} +2.90321i q^{13} +0.280996 q^{14} +(2.21432 - 0.311108i) q^{15} +3.42864 q^{16} -2.28100i q^{17} +0.311108i q^{18} +2.42864 q^{19} +(0.592104 + 4.21432i) q^{20} +0.903212 q^{21} -4.00000i q^{23} -1.21432 q^{24} +(-4.80642 + 1.37778i) q^{25} +0.903212 q^{26} +1.00000i q^{27} +1.71900i q^{28} +7.05086 q^{29} +(-0.0967881 - 0.688892i) q^{30} -2.62222 q^{31} -3.49532i q^{32} -0.709636 q^{34} +(-2.00000 + 0.280996i) q^{35} -1.90321 q^{36} +5.80642i q^{37} -0.755569i q^{38} +2.90321 q^{39} +(2.68889 - 0.377784i) q^{40} +10.6637 q^{41} -0.280996i q^{42} +10.7096i q^{43} +(-0.311108 - 2.21432i) q^{45} -1.24443 q^{46} +0.949145i q^{47} -3.42864i q^{48} +6.18421 q^{49} +(0.428639 + 1.49532i) q^{50} -2.28100 q^{51} +5.52543i q^{52} -0.815792i q^{53} +0.311108 q^{54} +1.09679 q^{56} -2.42864i q^{57} -2.19358i q^{58} +1.67307 q^{59} +(4.21432 - 0.592104i) q^{60} +7.24443 q^{61} +0.815792i q^{62} -0.903212i q^{63} +5.76986 q^{64} +(-6.42864 + 0.903212i) q^{65} +12.8573i q^{67} -4.34122i q^{68} -4.00000 q^{69} +(0.0874201 + 0.622216i) q^{70} +9.28592 q^{71} +1.21432i q^{72} -5.65878i q^{73} +1.80642 q^{74} +(1.37778 + 4.80642i) q^{75} +4.62222 q^{76} -0.903212i q^{78} -16.5303 q^{79} +(1.06668 + 7.59210i) q^{80} +1.00000 q^{81} -3.31756i q^{82} +7.76049i q^{83} +1.71900 q^{84} +(5.05086 - 0.709636i) q^{85} +3.33185 q^{86} -7.05086i q^{87} -6.13335 q^{89} +(-0.688892 + 0.0967881i) q^{90} -2.62222 q^{91} -7.61285i q^{92} +2.62222i q^{93} +0.295286 q^{94} +(0.755569 + 5.37778i) q^{95} -3.49532 q^{96} -12.4701i q^{97} -1.92396i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9	\( 6 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9} + 4 q^{10} - 12 q^{14} - 6 q^{16} - 12 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{24} - 2 q^{25} - 8 q^{26} + 16 q^{29} - 14 q^{30} - 16 q^{31} + 36 q^{34} - 12 q^{35} + 2 q^{36} + 4 q^{39} + 16 q^{40} - 16 q^{41} - 2 q^{45} - 8 q^{46} + 10 q^{49} - 24 q^{50} + 2 q^{54} + 20 q^{56} - 16 q^{59} + 12 q^{60} + 44 q^{61} + 22 q^{64} - 12 q^{65} - 24 q^{69} - 40 q^{70} - 24 q^{71} - 16 q^{74} + 8 q^{75} + 28 q^{76} - 20 q^{79} + 6 q^{80} + 6 q^{81} + 24 q^{84} + 4 q^{85} - 20 q^{86} - 36 q^{89} - 4 q^{90} - 16 q^{91} - 24 q^{94} + 4 q^{95} + 6 q^{96}+O(q^{100}) \) 6 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9 + 4 * q^10 - 12 * q^14 - 6 * q^16 - 12 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^24 - 2 * q^25 - 8 * q^26 + 16 * q^29 - 14 * q^30 - 16 * q^31 + 36 * q^34 - 12 * q^35 + 2 * q^36 + 4 * q^39 + 16 * q^40 - 16 * q^41 - 2 * q^45 - 8 * q^46 + 10 * q^49 - 24 * q^50 + 2 * q^54 + 20 * q^56 - 16 * q^59 + 12 * q^60 + 44 * q^61 + 22 * q^64 - 12 * q^65 - 24 * q^69 - 40 * q^70 - 24 * q^71 - 16 * q^74 + 8 * q^75 + 28 * q^76 - 20 * q^79 + 6 * q^80 + 6 * q^81 + 24 * q^84 + 4 * q^85 - 20 * q^86 - 36 * q^89 - 4 * q^90 - 16 * q^91 - 24 * q^94 + 4 * q^95 + 6 * q^96

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