LMFDB - Embedded newform 845.2.b.f.339.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(339,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.339"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.8
Root			$-0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	845.339
Dual form			845.2.b.f.339.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.18890i q^{2} +1.00000i q^{3} -2.79129 q^{4} +(2.18890 + 0.456850i) q^{5} -2.18890 q^{6} -1.73205i q^{7} -1.73205i q^{8} +2.00000 q^{9} +(-1.00000 + 4.79129i) q^{10} +2.64575 q^{11} -2.79129i q^{12} +3.79129 q^{14} +(-0.456850 + 2.18890i) q^{15} -1.79129 q^{16} +4.58258i q^{17} +4.37780i q^{18} -1.73205 q^{19} +(-6.10985 - 1.27520i) q^{20} +1.73205 q^{21} +5.79129i q^{22} +4.58258i q^{23} +1.73205 q^{24} +(4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +4.83465i q^{28} +4.58258 q^{29} +(-4.79129 - 1.00000i) q^{30} -9.66930 q^{31} -7.38505i q^{32} +2.64575i q^{33} -10.0308 q^{34} +(0.791288 - 3.79129i) q^{35} -5.58258 q^{36} -7.93725i q^{37} -3.79129i q^{38} +(0.791288 - 3.79129i) q^{40} +2.64575 q^{41} +3.79129i q^{42} -1.41742i q^{43} -7.38505 q^{44} +(4.37780 + 0.913701i) q^{45} -10.0308 q^{46} +8.75560i q^{47} -1.79129i q^{48} +4.00000 q^{49} +(-4.37780 + 10.0308i) q^{50} -4.58258 q^{51} -1.58258i q^{53} -10.9445 q^{54} +(5.79129 + 1.20871i) q^{55} -3.00000 q^{56} -1.73205i q^{57} +10.0308i q^{58} +3.36875 q^{59} +(1.27520 - 6.10985i) q^{60} -10.5826 q^{61} -21.1652i q^{62} -3.46410i q^{63} +12.5826 q^{64} -5.79129 q^{66} -14.8655i q^{67} -12.7913i q^{68} -4.58258 q^{69} +(8.29875 + 1.73205i) q^{70} -3.55945 q^{71} -3.46410i q^{72} +17.3739 q^{74} +(-2.00000 + 4.58258i) q^{75} +4.83465 q^{76} -4.58258i q^{77} +6.00000 q^{79} +(-3.92095 - 0.818350i) q^{80} +1.00000 q^{81} +5.79129i q^{82} -11.3060i q^{83} -4.83465 q^{84} +(-2.09355 + 10.0308i) q^{85} +3.10260 q^{86} +4.58258i q^{87} -4.58258i q^{88} +4.28245 q^{89} +(-2.00000 + 9.58258i) q^{90} -12.7913i q^{92} -9.66930i q^{93} -19.1652 q^{94} +(-3.79129 - 0.791288i) q^{95} +7.38505 q^{96} -4.47315i q^{97} +8.75560i q^{98} +5.29150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 16 q^{9} - 8 q^{10} + 12 q^{14} + 4 q^{16} - 20 q^{30} - 12 q^{35} - 8 q^{36} - 12 q^{40} + 32 q^{49} + 28 q^{55} - 24 q^{56} - 48 q^{61} + 64 q^{64} - 28 q^{66} + 84 q^{74} - 16 q^{75}+ \cdots - 12 q^{95}+O(q^{100}) $ 8 * q - 4 * q^4 + 16 * q^9 - 8 * q^10 + 12 * q^14 + 4 * q^16 - 20 * q^30 - 12 * q^35 - 8 * q^36 - 12 * q^40 + 32 * q^49 + 28 * q^55 - 24 * q^56 - 48 * q^61 + 64 * q^64 - 28 * q^66 + 84 * q^74 - 16 * q^75 + 48 * q^79 + 8 * q^81 - 16 * q^90 - 80 * q^94 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$1$	$-1$

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 $

$2$			2.18890i			1.54779i	0.633316	+	0.773893i	$0.281693\pi$
$2$			2.18890i			1.54779i	−0.633316	+	0.773893i	$0.718307\pi$
$3$			1.00000i			0.577350i	0.957427	+	0.288675i	$0.0932147\pi$
$3$			1.00000i			0.577350i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	−2.79129			−1.39564
$5$	2.18890	+	0.456850i	0.978906	+	0.204310i
$5$	2.18890	+	0.456850i	0.978906	+	0.204310i
$6$	−2.18890			−0.893615
$7$		−	1.73205i		−	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$		−	1.73205i		−	0.654654i	0.944911	−	0.327327i	$-0.106148\pi$
$8$		−	1.73205i		−	0.612372i
$9$	2.00000			0.666667
$10$	−1.00000	+	4.79129i	−0.316228	+	1.51514i
$11$	2.64575			0.797724			0.398862	−	0.917011i	$-0.369405\pi$
$11$	2.64575			0.797724			0.398862	+	0.917011i	$0.369405\pi$
$12$		−	2.79129i		−	0.805775i
$13$		0			0
$13$		0			0
$14$	3.79129			1.01326
$15$	−0.456850	+	2.18890i	−0.117958	+	0.565172i
$16$	−1.79129			−0.447822
$17$			4.58258i			1.11144i	0.831370	+	0.555719i	$0.187557\pi$
$17$			4.58258i			1.11144i	−0.831370	+	0.555719i	$0.812443\pi$
$18$			4.37780i			1.03186i
$19$	−1.73205			−0.397360			−0.198680	−	0.980064i	$-0.563665\pi$
$19$	−1.73205			−0.397360			−0.198680	+	0.980064i	$0.563665\pi$
$20$	−6.10985	−	1.27520i	−1.36620	−	0.285144i
$21$	1.73205			0.377964
$22$			5.79129i			1.23471i
$23$			4.58258i			0.955533i	0.878487	+	0.477767i	$0.158554\pi$
$23$			4.58258i			0.955533i	−0.878487	+	0.477767i	$0.841446\pi$
$24$	1.73205			0.353553
$25$	4.58258	+	2.00000i	0.916515	+	0.400000i
$26$		0			0
$27$			5.00000i			0.962250i
$28$			4.83465i			0.913663i
$29$	4.58258			0.850963			0.425481	−	0.904967i	$-0.360105\pi$
$29$	4.58258			0.850963			0.425481	+	0.904967i	$0.360105\pi$
$30$	−4.79129	−	1.00000i	−0.874765	−	0.182574i
$31$	−9.66930			−1.73666			−0.868329	−	0.495988i	$-0.834806\pi$
$31$	−9.66930			−1.73666			−0.868329	+	0.495988i	$0.834806\pi$
$32$		−	7.38505i		−	1.30551i
$33$			2.64575i			0.460566i
$34$	−10.0308			−1.72027
$35$	0.791288	−	3.79129i	0.133752	−	0.640845i
$36$	−5.58258			−0.930429
$37$		−	7.93725i		−	1.30488i	−0.757842	−	0.652438i	$-0.773746\pi$
$37$		−	7.93725i		−	1.30488i	0.757842	−	0.652438i	$-0.226254\pi$
$38$		−	3.79129i		−	0.615028i
$39$		0			0
$40$	0.791288	−	3.79129i	0.125114	−	0.599455i
$41$	2.64575			0.413197			0.206598	−	0.978426i	$-0.433761\pi$
$41$	2.64575			0.413197			0.206598	+	0.978426i	$0.433761\pi$
$42$			3.79129i			0.585008i
$43$		−	1.41742i		−	0.216155i	−0.994142	−	0.108078i	$-0.965531\pi$
$43$		−	1.41742i		−	0.216155i	0.994142	−	0.108078i	$-0.0344695\pi$
$44$	−7.38505			−1.11334
$45$	4.37780	+	0.913701i	0.652604	+	0.136206i
$46$	−10.0308			−1.47896
$47$			8.75560i			1.27714i	0.769565	+	0.638568i	$0.220473\pi$
$47$			8.75560i			1.27714i	−0.769565	+	0.638568i	$0.779527\pi$
$48$		−	1.79129i		−	0.258550i
$49$	4.00000			0.571429
$50$	−4.37780	+	10.0308i	−0.619115	+	1.41857i
$51$	−4.58258			−0.641689
$52$		0			0
$53$		−	1.58258i		−	0.217383i	−0.994076	−	0.108692i	$-0.965334\pi$
$53$		−	1.58258i		−	0.217383i	0.994076	−	0.108692i	$-0.0346661\pi$
$54$	−10.9445			−1.48936
$55$	5.79129	+	1.20871i	0.780897	+	0.162983i
$56$	−3.00000			−0.400892
$57$		−	1.73205i		−	0.229416i
$58$			10.0308i			1.31711i
$59$	3.36875			0.438574			0.219287	−	0.975660i	$-0.429627\pi$
$59$	3.36875			0.438574			0.219287	+	0.975660i	$0.429627\pi$
$60$	1.27520	−	6.10985i	0.164628	−	0.788779i
$61$	−10.5826			−1.35496			−0.677480	−	0.735541i	$-0.736928\pi$
$61$	−10.5826			−1.35496			−0.677480	+	0.735541i	$0.736928\pi$
$62$		−	21.1652i		−	2.68798i
$63$		−	3.46410i		−	0.436436i
$64$	12.5826			1.57282
$65$		0			0
$66$	−5.79129			−0.712858
$67$		−	14.8655i		−	1.81610i	−0.418857	−	0.908052i	$-0.637569\pi$
$67$		−	14.8655i		−	1.81610i	0.418857	−	0.908052i	$-0.362431\pi$
$68$		−	12.7913i		−	1.55117i
$69$	−4.58258			−0.551677
$70$	8.29875	+	1.73205i	0.991891	+	0.207020i
$71$	−3.55945			−0.422429			−0.211215	−	0.977440i	$-0.567742\pi$
$71$	−3.55945			−0.422429			−0.211215	+	0.977440i	$0.567742\pi$
$72$		−	3.46410i		−	0.408248i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	17.3739			2.01967
$75$	−2.00000	+	4.58258i	−0.230940	+	0.529150i
$76$	4.83465			0.554573
$77$		−	4.58258i		−	0.522233i
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	−3.92095	−	0.818350i	−0.438376	−	0.0914943i
$81$	1.00000			0.111111
$82$			5.79129i			0.639541i
$83$		−	11.3060i		−	1.24100i	−0.784208	−	0.620498i	$-0.786931\pi$
$83$		−	11.3060i		−	1.24100i	0.784208	−	0.620498i	$-0.213069\pi$
$84$	−4.83465			−0.527504
$85$	−2.09355	+	10.0308i	−0.227077	+	1.08799i
$86$	3.10260			0.334562
$87$			4.58258i			0.491304i
$88$		−	4.58258i		−	0.488504i
$89$	4.28245			0.453939			0.226969	−	0.973902i	$-0.427118\pi$
$89$	4.28245			0.453939			0.226969	+	0.973902i	$0.427118\pi$
$90$	−2.00000	+	9.58258i	−0.210819	+	1.01009i
$91$		0			0
$92$		−	12.7913i		−	1.33358i
$93$		−	9.66930i		−	1.00266i
$94$	−19.1652			−1.97673
$95$	−3.79129	−	0.791288i	−0.388978	−	0.0811844i
$96$	7.38505			0.753734
$97$		−	4.47315i		−	0.454180i	−0.973874	−	0.227090i	$-0.927079\pi$
$97$		−	4.47315i		−	0.454180i	0.973874	−	0.227090i	$-0.0729211\pi$
$98$			8.75560i			0.884450i
$99$	5.29150			0.531816
$100$	−12.7913	−	5.58258i	−1.27913	−	0.558258i
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$		−	10.0308i		−	0.993198i
$103$			15.1652i			1.49427i	0.664674	+	0.747133i	$0.268570\pi$
$103$			15.1652i			1.49427i	−0.664674	+	0.747133i	$0.731430\pi$
$104$		0			0
$105$	3.79129	+	0.791288i	0.369992	+	0.0772218i
$106$	3.46410			0.336463
$107$			1.41742i			0.137028i	0.997650	+	0.0685138i	$0.0218257\pi$
$107$			1.41742i			0.137028i	−0.997650	+	0.0685138i	$0.978174\pi$
$108$		−	13.9564i		−	1.34296i
$109$	2.74110			0.262550			0.131275	−	0.991346i	$-0.458093\pi$
$109$	2.74110			0.262550			0.131275	+	0.991346i	$0.458093\pi$
$110$	−2.64575	+	12.6766i	−0.252262	+	1.20866i
$111$	7.93725			0.753371
$112$			3.10260i			0.293168i
$113$		−	16.5826i		−	1.55996i	−0.625806	−	0.779979i	$-0.715230\pi$
$113$		−	16.5826i		−	1.55996i	0.625806	−	0.779979i	$-0.284770\pi$
$114$	3.79129			0.355087
$115$	−2.09355	+	10.0308i	−0.195225	+	0.935377i
$116$	−12.7913			−1.18764
$117$		0			0
$118$			7.37386i			0.678819i
$119$	7.93725			0.727607
$120$	3.79129	+	0.791288i	0.346096	+	0.0722344i
$121$	−4.00000			−0.363636
$122$		−	23.1642i		−	2.09719i
$123$			2.64575i			0.238559i
$124$	26.9898			2.42376
$125$	9.11710	+	6.47135i	0.815459	+	0.578815i
$126$	7.58258			0.675510
$127$		−	9.74773i		−	0.864971i	−0.901641	−	0.432485i	$-0.857637\pi$
$127$		−	9.74773i		−	0.864971i	0.901641	−	0.432485i	$-0.142363\pi$
$128$			12.7719i			1.12889i
$129$	1.41742			0.124797
$130$		0			0
$131$	1.58258			0.138270			0.0691351	−	0.997607i	$-0.477976\pi$
$131$	1.58258			0.138270			0.0691351	+	0.997607i	$0.477976\pi$
$132$		−	7.38505i		−	0.642786i
$133$			3.00000i			0.260133i
$134$	32.5390			2.81094
$135$	−2.28425	+	10.9445i	−0.196597	+	0.941953i
$136$	7.93725			0.680614
$137$		−	0.0953502i		−	0.00814632i	−0.999992	−	0.00407316i	$-0.998703\pi$
$137$		−	0.0953502i		−	0.00814632i	0.999992	−	0.00407316i	$-0.00129653\pi$
$138$		−	10.0308i		−	0.853879i
$139$	−5.74773			−0.487516			−0.243758	−	0.969836i	$-0.578380\pi$
$139$	−5.74773			−0.487516			−0.243758	+	0.969836i	$0.578380\pi$
$140$	−2.20871	+	10.5826i	−0.186670	+	0.894391i
$141$	−8.75560			−0.737355
$142$		−	7.79129i		−	0.653830i
$143$		0			0
$144$	−3.58258			−0.298548
$145$	10.0308	+	2.09355i	0.833013	+	0.173860i
$146$		0			0
$147$			4.00000i			0.329914i
$148$			22.1552i			1.82114i
$149$	9.76465			0.799952			0.399976	−	0.916526i	$-0.369019\pi$
$149$	9.76465			0.799952			0.399976	+	0.916526i	$0.369019\pi$
$150$	−10.0308	−	4.37780i	−0.819012	−	0.357446i
$151$	−6.20520			−0.504972			−0.252486	−	0.967601i	$-0.581248\pi$
$151$	−6.20520			−0.504972			−0.252486	+	0.967601i	$0.581248\pi$
$152$			3.00000i			0.243332i
$153$			9.16515i			0.740959i
$154$	10.0308			0.808305
$155$	−21.1652	−	4.41742i	−1.70003	−	0.354816i
$156$		0			0
$157$			9.16515i			0.731459i	0.930721	+	0.365729i	$0.119180\pi$
$157$			9.16515i			0.731459i	−0.930721	+	0.365729i	$0.880820\pi$
$158$			13.1334i			1.04484i
$159$	1.58258			0.125506
$160$	3.37386	−	16.1652i	0.266727	−	1.27797i
$161$	7.93725			0.625543
$162$			2.18890i			0.171976i
$163$		−	10.6784i		−	0.836393i	−0.908357	−	0.418197i	$-0.862662\pi$
$163$		−	10.6784i		−	0.836393i	0.908357	−	0.418197i	$-0.137338\pi$
$164$	−7.38505			−0.576676
$165$	−1.20871	+	5.79129i	−0.0940981	+	0.450851i
$166$	24.7477			1.92080
$167$		−	4.28245i		−	0.331386i	−0.986177	−	0.165693i	$-0.947014\pi$
$167$		−	4.28245i		−	0.331386i	0.986177	−	0.165693i	$-0.0529861\pi$
$168$		−	3.00000i		−	0.231455i
$169$		0			0
$170$	−21.9564	−	4.58258i	−1.68398	−	0.351468i
$171$	−3.46410			−0.264906
$172$			3.95644i			0.301676i
$173$			7.41742i			0.563936i	0.959424	+	0.281968i	$0.0909873\pi$
$173$			7.41742i			0.563936i	−0.959424	+	0.281968i	$0.909013\pi$
$174$	−10.0308			−0.760433
$175$	3.46410	−	7.93725i	0.261861	−	0.600000i
$176$	−4.73930			−0.357238
$177$			3.36875i			0.253211i
$178$			9.37386i			0.702601i
$179$	−0.165151			−0.0123440			−0.00617200	−	0.999981i	$-0.501965\pi$
$179$	−0.165151			−0.0123440			−0.00617200	+	0.999981i	$0.501965\pi$
$180$	−12.2197	−	2.55040i	−0.910803	−	0.190096i
$181$	18.7477			1.39351			0.696754	−	0.717310i	$-0.254627\pi$
$181$	18.7477			1.39351			0.696754	+	0.717310i	$0.254627\pi$
$182$		0			0
$183$		−	10.5826i		−	0.782287i
$184$	7.93725			0.585142
$185$	3.62614	−	17.3739i	0.266599	−	1.27735i
$186$	21.1652			1.55190
$187$			12.1244i			0.886621i
$188$		−	24.4394i		−	1.78243i
$189$	8.66025			0.629941
$190$	1.73205	−	8.29875i	0.125656	−	0.602055i
$191$	−7.41742			−0.536706			−0.268353	−	0.963321i	$-0.586479\pi$
$191$	−7.41742			−0.536706			−0.268353	+	0.963321i	$0.586479\pi$
$192$			12.5826i			0.908069i
$193$		−	1.00905i		−	0.0726331i	−0.999340	−	0.0363165i	$-0.988438\pi$
$193$		−	1.00905i		−	0.0726331i	0.999340	−	0.0363165i	$-0.0115625\pi$
$194$	9.79129			0.702973
$195$		0			0
$196$	−11.1652			−0.797511
$197$			19.9663i			1.42254i	0.702920	+	0.711269i	$0.251879\pi$
$197$			19.9663i			1.42254i	−0.702920	+	0.711269i	$0.748121\pi$
$198$			11.5826i			0.823138i
$199$	1.41742			0.100479			0.0502393	−	0.998737i	$-0.484002\pi$
$199$	1.41742			0.100479			0.0502393	+	0.998737i	$0.484002\pi$
$200$	3.46410	−	7.93725i	0.244949	−	0.561249i
$201$	14.8655			1.04853
$202$		−	19.7001i		−	1.38609i
$203$		−	7.93725i		−	0.557086i
$204$	12.7913			0.895569
$205$	5.79129	+	1.20871i	0.404481	+	0.0844201i
$206$	−33.1950			−2.31281
$207$			9.16515i			0.637022i
$208$		0			0
$209$	−4.58258			−0.316983
$210$	−1.73205	+	8.29875i	−0.119523	+	0.572668i
$211$	18.1652			1.25054			0.625270	−	0.780408i	$-0.284989\pi$
$211$	18.1652			1.25054			0.625270	+	0.780408i	$0.284989\pi$
$212$			4.41742i			0.303390i
$213$		−	3.55945i		−	0.243890i
$214$	−3.10260			−0.212089
$215$	0.647551	−	3.10260i	0.0441626	−	0.211596i
$216$	8.66025			0.589256
$217$			16.7477i			1.13691i
$218$			6.00000i			0.406371i
$219$		0			0
$220$	−16.1652	−	3.37386i	−1.08985	−	0.227466i
$221$		0			0
$222$			17.3739i			1.16606i
$223$			8.66025i			0.579934i	0.957037	+	0.289967i	$0.0936443\pi$
$223$			8.66025i			0.579934i	−0.957037	+	0.289967i	$0.906356\pi$
$224$	−12.7913			−0.854654
$225$	9.16515	+	4.00000i	0.611010	+	0.266667i
$226$	36.2976			2.41448
$227$		−	6.10985i		−	0.405525i	−0.979228	−	0.202763i	$-0.935008\pi$
$227$		−	6.10985i		−	0.405525i	0.979228	−	0.202763i	$-0.0649920\pi$
$228$			4.83465i			0.320183i
$229$	5.48220			0.362274			0.181137	−	0.983458i	$-0.442022\pi$
$229$	5.48220			0.362274			0.181137	+	0.983458i	$0.442022\pi$
$230$	−21.9564	−	4.58258i	−1.44776	−	0.302166i
$231$	4.58258			0.301511
$232$		−	7.93725i		−	0.521106i
$233$		−	21.1652i		−	1.38658i	−0.720661	−	0.693288i	$-0.756162\pi$
$233$		−	21.1652i		−	1.38658i	0.720661	−	0.693288i	$-0.243838\pi$
$234$		0			0
$235$	−4.00000	+	19.1652i	−0.260931	+	1.25020i
$236$	−9.40315			−0.612093
$237$			6.00000i			0.389742i
$238$			17.3739i			1.12618i
$239$	−20.9753			−1.35678			−0.678390	−	0.734702i	$-0.737322\pi$
$239$	−20.9753			−1.35678			−0.678390	+	0.734702i	$0.737322\pi$
$240$	0.818350	−	3.92095i	0.0528243	−	0.253096i
$241$	1.73205			0.111571			0.0557856	−	0.998443i	$-0.482234\pi$
$241$	1.73205			0.111571			0.0557856	+	0.998443i	$0.482234\pi$
$242$		−	8.75560i		−	0.562832i
$243$			16.0000i			1.02640i
$244$	29.5390			1.89104
$245$	8.75560	+	1.82740i	0.559375	+	0.116748i
$246$	−5.79129			−0.369239
$247$		0			0
$248$			16.7477i			1.06348i
$249$	11.3060			0.716489
$250$	−14.1652	+	19.9564i	−0.895883	+	1.26216i
$251$	−18.1652			−1.14657			−0.573287	−	0.819355i	$-0.694332\pi$
$251$	−18.1652			−1.14657			−0.573287	+	0.819355i	$0.694332\pi$
$252$			9.66930i			0.609109i
$253$			12.1244i			0.762252i
$254$	21.3368			1.33879
$255$	−10.0308	−	2.09355i	−0.628153	−	0.131103i
$256$	−2.79129			−0.174455
$257$			0.165151i			0.0103019i	0.999987	+	0.00515093i	$0.00163960\pi$
$257$			0.165151i			0.0103019i	−0.999987	+	0.00515093i	$0.998360\pi$
$258$			3.10260i			0.193160i
$259$	−13.7477			−0.854242
$260$		0			0
$261$	9.16515			0.567309
$262$			3.46410i			0.214013i
$263$			9.00000i			0.554964i	0.960731	+	0.277482i	$0.0894999\pi$
$263$			9.00000i			0.554964i	−0.960731	+	0.277482i	$0.910500\pi$
$264$	4.58258			0.282038
$265$	0.723000	−	3.46410i	0.0444135	−	0.212798i
$266$	−6.56670			−0.402630
$267$			4.28245i			0.262082i
$268$			41.4938i			2.53464i
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$	−23.9564	−	5.00000i	−1.45794	−	0.304290i
$271$	8.66025			0.526073			0.263036	−	0.964786i	$-0.415276\pi$
$271$	8.66025			0.526073			0.263036	+	0.964786i	$0.415276\pi$
$272$		−	8.20871i		−	0.497726i
$273$		0			0
$274$	0.208712			0.0126088
$275$	12.1244	+	5.29150i	0.731126	+	0.319090i
$276$	12.7913			0.769945
$277$		−	16.5826i		−	0.996350i	−0.867076	−	0.498175i	$-0.834004\pi$
$277$		−	16.5826i		−	0.996350i	0.867076	−	0.498175i	$-0.165996\pi$
$278$		−	12.5812i		−	0.754571i
$279$	−19.3386			−1.15777
$280$	−6.56670	−	1.37055i	−0.392436	−	0.0819061i
$281$	17.5112			1.04463			0.522316	−	0.852752i	$-0.325068\pi$
$281$	17.5112			1.04463			0.522316	+	0.852752i	$0.325068\pi$
$282$		−	19.1652i		−	1.14127i
$283$			0.252273i			0.0149961i	0.999972	+	0.00749803i	$0.00238672\pi$
$283$			0.252273i			0.0149961i	−0.999972	+	0.00749803i	$0.997613\pi$
$284$	9.93545			0.589561
$285$	0.791288	−	3.79129i	0.0468718	−	0.224577i
$286$		0			0
$287$		−	4.58258i		−	0.270501i
$288$		−	14.7701i		−	0.870337i
$289$	−4.00000			−0.235294
$290$	−4.58258	+	21.9564i	−0.269098	+	1.28933i
$291$	4.47315			0.262221
$292$		0			0
$293$		−	23.4304i		−	1.36882i	−0.729099	−	0.684408i	$-0.760061\pi$
$293$		−	23.4304i		−	1.36882i	0.729099	−	0.684408i	$-0.239939\pi$
$294$	−8.75560			−0.510637
$295$	7.37386	+	1.53901i	0.429323	+	0.0896049i
$296$	−13.7477			−0.799070
$297$			13.2288i			0.767610i
$298$			21.3739i			1.23815i
$299$		0			0
$300$	5.58258	−	12.7913i	0.322310	−	0.738505i
$301$	−2.45505			−0.141507
$302$		−	13.5826i		−	0.781589i
$303$		−	9.00000i		−	0.517036i
$304$	3.10260			0.177946
$305$	−23.1642	−	4.83465i	−1.32638	−	0.276831i
$306$	−20.0616			−1.14685
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$			12.7913i			0.728851i
$309$	−15.1652			−0.862715
$310$	9.66930	−	46.3284i	0.549180	−	2.63128i
$311$	1.58258			0.0897396			0.0448698	−	0.998993i	$-0.485713\pi$
$311$	1.58258			0.0897396			0.0448698	+	0.998993i	$0.485713\pi$
$312$		0			0
$313$		−	30.7477i		−	1.73796i	−0.494843	−	0.868982i	$-0.664775\pi$
$313$		−	30.7477i		−	1.73796i	0.494843	−	0.868982i	$-0.335225\pi$
$314$	−20.0616			−1.13214
$315$	1.58258	−	7.58258i	0.0891680	−	0.427230i
$316$	−16.7477			−0.942133
$317$			20.9753i			1.17809i	0.808100	+	0.589045i	$0.200496\pi$
$317$			20.9753i			1.17809i	−0.808100	+	0.589045i	$0.799504\pi$
$318$			3.46410i			0.194257i
$319$	12.1244			0.678834
$320$	27.5420	+	5.74835i	1.53965	+	0.321343i
$321$	−1.41742			−0.0791129
$322$			17.3739i			0.968208i
$323$		−	7.93725i		−	0.441641i
$324$	−2.79129			−0.155072
$325$		0			0
$326$	23.3739			1.29456
$327$			2.74110i			0.151583i
$328$		−	4.58258i		−	0.253030i
$329$	15.1652			0.836082
$330$	−12.6766	−	2.64575i	−0.697821	−	0.145644i
$331$	11.4014			0.626675			0.313338	−	0.949642i	$-0.398553\pi$
$331$	11.4014			0.626675			0.313338	+	0.949642i	$0.398553\pi$
$332$			31.5583i			1.73199i
$333$		−	15.8745i		−	0.869918i
$334$	9.37386			0.512915
$335$	6.79129	−	32.5390i	0.371048	−	1.77780i
$336$	−3.10260			−0.169261
$337$			3.25227i			0.177163i	0.996069	+	0.0885813i	$0.0282333\pi$
$337$			3.25227i			0.177163i	−0.996069	+	0.0885813i	$0.971767\pi$
$338$		0			0
$339$	16.5826			0.900642
$340$	5.84370	−	27.9989i	0.316919	−	1.51845i
$341$	−25.5826			−1.38537
$342$		−	7.58258i		−	0.410019i
$343$		−	19.0526i		−	1.02874i
$344$	−2.45505			−0.132367
$345$	−10.0308	−	2.09355i	−0.540040	−	0.112713i
$346$	−16.2360			−0.872853
$347$		−	15.3303i		−	0.822974i	−0.911416	−	0.411487i	$-0.865010\pi$
$347$		−	15.3303i		−	0.822974i	0.911416	−	0.411487i	$-0.134990\pi$
$348$		−	12.7913i		−	0.685685i
$349$	18.3296			0.981159			0.490579	−	0.871396i	$-0.336785\pi$
$349$	18.3296			0.981159			0.490579	+	0.871396i	$0.336785\pi$
$350$	17.3739	+	7.58258i	0.928672	+	0.405306i
$351$		0			0
$352$		−	19.5390i		−	1.04143i
$353$		−	17.4159i		−	0.926953i	−0.886109	−	0.463476i	$-0.846602\pi$
$353$		−	17.4159i		−	0.926953i	0.886109	−	0.463476i	$-0.153398\pi$
$354$	−7.37386			−0.391916
$355$	−7.79129	−	1.62614i	−0.413519	−	0.0863064i
$356$	−11.9536			−0.633537
$357$			7.93725i			0.420084i
$358$		−	0.361500i		−	0.0191059i
$359$	−33.3857			−1.76203			−0.881015	−	0.473088i	$-0.843139\pi$
$359$	−33.3857			−1.76203			−0.881015	+	0.473088i	$0.843139\pi$
$360$	1.58258	−	7.58258i	0.0834091	−	0.399637i
$361$	−16.0000			−0.842105
$362$			41.0369i			2.15685i
$363$		−	4.00000i		−	0.209946i
$364$		0			0
$365$		0			0
$366$	23.1642			1.21081
$367$		−	25.7477i		−	1.34402i	−0.740542	−	0.672010i	$-0.765431\pi$
$367$		−	25.7477i		−	1.34402i	0.740542	−	0.672010i	$-0.234569\pi$
$368$		−	8.20871i		−	0.427909i
$369$	5.29150			0.275465
$370$	38.0297	+	7.93725i	1.97707	+	0.412638i
$371$	−2.74110			−0.142311
$372$			26.9898i			1.39936i
$373$		−	13.0000i		−	0.673114i	−0.941663	−	0.336557i	$-0.890737\pi$
$373$		−	13.0000i		−	0.673114i	0.941663	−	0.336557i	$-0.109263\pi$
$374$	−26.5390			−1.37230
$375$	−6.47135	+	9.11710i	−0.334179	+	0.470805i
$376$	15.1652			0.782083
$377$		0			0
$378$			18.9564i			0.975014i
$379$	−21.0707			−1.08233			−0.541164	−	0.840917i	$-0.682016\pi$
$379$	−21.0707			−1.08233			−0.541164	+	0.840917i	$0.682016\pi$
$380$	10.5826	+	2.20871i	0.542875	+	0.113305i
$381$	9.74773			0.499391
$382$		−	16.2360i		−	0.830706i
$383$			2.83645i			0.144936i	0.997371	+	0.0724680i	$0.0230875\pi$
$383$			2.83645i			0.144936i	−0.997371	+	0.0724680i	$0.976912\pi$
$384$	−12.7719			−0.651764
$385$	2.09355	−	10.0308i	0.106697	−	0.511217i
$386$	2.20871			0.112420
$387$		−	2.83485i		−	0.144103i
$388$			12.4859i			0.633873i
$389$	15.1652			0.768904			0.384452	−	0.923145i	$-0.374390\pi$
$389$	15.1652			0.768904			0.384452	+	0.923145i	$0.374390\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$		−	6.92820i		−	0.349927i
$393$			1.58258i			0.0798304i
$394$	−43.7042			−2.20178
$395$	13.1334	+	2.74110i	0.660813	+	0.137920i
$396$	−14.7701			−0.742226
$397$			27.2759i			1.36894i	0.729043	+	0.684468i	$0.239966\pi$
$397$			27.2759i			1.36894i	−0.729043	+	0.684468i	$0.760034\pi$
$398$			3.10260i			0.155519i
$399$	−3.00000			−0.150188
$400$	−8.20871	−	3.58258i	−0.410436	−	0.179129i
$401$	12.5058			0.624508			0.312254	−	0.949999i	$-0.398916\pi$
$401$	12.5058			0.624508			0.312254	+	0.949999i	$0.398916\pi$
$402$			32.5390i			1.62290i
$403$		0			0
$404$	25.1216			1.24985
$405$	2.18890	+	0.456850i	0.108767	+	0.0227011i
$406$	17.3739			0.862250
$407$		−	21.0000i		−	1.04093i
$408$			7.93725i			0.392953i
$409$	8.66025			0.428222			0.214111	−	0.976809i	$-0.431315\pi$
$409$	8.66025			0.428222			0.214111	+	0.976809i	$0.431315\pi$
$410$	−2.64575	+	12.6766i	−0.130664	+	0.626050i
$411$	0.0953502			0.00470328
$412$		−	42.3303i		−	2.08546i
$413$		−	5.83485i		−	0.287114i
$414$	−20.0616			−0.985974
$415$	5.16515	−	24.7477i	0.253547	−	1.21482i
$416$		0			0
$417$		−	5.74773i		−	0.281467i
$418$		−	10.0308i		−	0.490623i
$419$	24.1652			1.18054			0.590272	−	0.807204i	$-0.299020\pi$
$419$	24.1652			1.18054			0.590272	+	0.807204i	$0.299020\pi$
$420$	−10.5826	−	2.20871i	−0.516377	−	0.107774i
$421$	−26.2668			−1.28017			−0.640083	−	0.768306i	$-0.721100\pi$
$421$	−26.2668			−1.28017			−0.640083	+	0.768306i	$0.721100\pi$
$422$			39.7617i			1.93557i
$423$			17.5112i			0.851424i
$424$	−2.74110			−0.133120
$425$	−9.16515	+	21.0000i	−0.444575	+	1.01865i
$426$	7.79129			0.377489
$427$			18.3296i			0.887030i
$428$		−	3.95644i		−	0.191242i
$429$		0			0
$430$	6.79129	+	1.41742i	0.327505	+	0.0683543i
$431$	−29.6356			−1.42749			−0.713747	−	0.700403i	$-0.753004\pi$
$431$	−29.6356			−1.42749			−0.713747	+	0.700403i	$0.753004\pi$
$432$		−	8.95644i		−	0.430917i
$433$			17.7477i			0.852901i	0.904511	+	0.426451i	$0.140236\pi$
$433$			17.7477i			0.852901i	−0.904511	+	0.426451i	$0.859764\pi$
$434$	−36.6591			−1.75969
$435$	−2.09355	+	10.0308i	−0.100378	+	0.480940i
$436$	−7.65120			−0.366426
$437$		−	7.93725i		−	0.379690i
$438$		0			0
$439$	40.4955			1.93274			0.966371	−	0.257151i	$-0.0827837\pi$
$439$	40.4955			1.93274			0.966371	+	0.257151i	$0.0827837\pi$
$440$	2.09355	−	10.0308i	0.0998061	−	0.478200i
$441$	8.00000			0.380952
$442$		0			0
$443$		−	25.9129i		−	1.23116i	−0.788075	−	0.615579i	$-0.788922\pi$
$443$		−	25.9129i		−	1.23116i	0.788075	−	0.615579i	$-0.211078\pi$
$444$	−22.1552			−1.05144
$445$	9.37386	+	1.95644i	0.444364	+	0.0927441i
$446$	−18.9564			−0.897613
$447$			9.76465i			0.461852i
$448$		−	21.7937i		−	1.02965i
$449$	−37.4775			−1.76867			−0.884336	−	0.466852i	$-0.845388\pi$
$449$	−37.4775			−1.76867			−0.884336	+	0.466852i	$0.845388\pi$
$450$	−8.75560	+	20.0616i	−0.412743	+	0.945713i
$451$	7.00000			0.329617
$452$			46.2867i			2.17715i
$453$		−	6.20520i		−	0.291546i
$454$	13.3739			0.627667
$455$		0			0
$456$	−3.00000			−0.140488
$457$		−	1.73205i		−	0.0810219i	−0.999179	−	0.0405110i	$-0.987101\pi$
$457$		−	1.73205i		−	0.0810219i	0.999179	−	0.0405110i	$-0.0128986\pi$
$458$			12.0000i			0.560723i
$459$	−22.9129			−1.06948
$460$	5.84370	−	27.9989i	0.272464	−	1.30545i
$461$	−1.19975			−0.0558780			−0.0279390	−	0.999610i	$-0.508894\pi$
$461$	−1.19975			−0.0558780			−0.0279390	+	0.999610i	$0.508894\pi$
$462$			10.0308i			0.466675i
$463$			8.22330i			0.382169i	0.981574	+	0.191085i	$0.0612005\pi$
$463$			8.22330i			0.382169i	−0.981574	+	0.191085i	$0.938799\pi$
$464$	−8.20871			−0.381080
$465$	4.41742	−	21.1652i	0.204853	−	0.981510i
$466$	46.3284			2.14612
$467$			12.3303i			0.570578i	0.958441	+	0.285289i	$0.0920896\pi$
$467$			12.3303i			0.570578i	−0.958441	+	0.285289i	$0.907910\pi$
$468$		0			0
$469$	−25.7477			−1.18892
$470$	−41.9506	−	8.75560i	−1.93504	−	0.403866i
$471$	−9.16515			−0.422308
$472$		−	5.83485i		−	0.268571i
$473$		−	3.75015i		−	0.172432i
$474$	−13.1334			−0.603237
$475$	−7.93725	−	3.46410i	−0.364186	−	0.158944i
$476$	−22.1552			−1.01548
$477$		−	3.16515i		−	0.144922i
$478$		−	45.9129i		−	2.10001i
$479$	−32.3767			−1.47933			−0.739664	−	0.672977i	$-0.765015\pi$
$479$	−32.3767			−1.47933			−0.739664	+	0.672977i	$0.765015\pi$
$480$	16.1652	+	3.37386i	0.737835	+	0.153995i
$481$		0			0
$482$			3.79129i			0.172688i
$483$			7.93725i			0.361158i
$484$	11.1652			0.507507
$485$	2.04356	−	9.79129i	0.0927933	−	0.444599i
$486$	−35.0224			−1.58865
$487$			21.0707i			0.954803i	0.878685	+	0.477401i	$0.158421\pi$
$487$			21.0707i			0.954803i	−0.878685	+	0.477401i	$0.841579\pi$
$488$			18.3296i			0.829740i
$489$	10.6784			0.482892
$490$	−4.00000	+	19.1652i	−0.180702	+	0.865793i
$491$	−28.5826			−1.28991			−0.644957	−	0.764219i	$-0.723125\pi$
$491$	−28.5826			−1.28991			−0.644957	+	0.764219i	$0.723125\pi$
$492$		−	7.38505i		−	0.332944i
$493$			21.0000i			0.945792i
$494$		0			0
$495$	11.5826	+	2.41742i	0.520598	+	0.108655i
$496$	17.3205			0.777714
$497$			6.16515i			0.276545i
$498$			24.7477i			1.10897i
$499$	16.5975			0.743006			0.371503	−	0.928432i	$-0.378842\pi$
$499$	16.5975			0.743006			0.371503	+	0.928432i	$0.378842\pi$
$500$	−25.4485	−	18.0634i	−1.13809	−	0.807820i
$501$	4.28245			0.191326
$502$		−	39.7617i		−	1.77465i
$503$		−	18.1652i		−	0.809944i	−0.914329	−	0.404972i	$-0.867281\pi$
$503$		−	18.1652i		−	0.809944i	0.914329	−	0.404972i	$-0.132719\pi$
$504$	−6.00000			−0.267261
$505$	−19.7001	−	4.11165i	−0.876643	−	0.182966i
$506$	−26.5390			−1.17980
$507$		0			0
$508$			27.2087i			1.20719i
$509$	29.6356			1.31357			0.656787	−	0.754076i	$-0.271915\pi$
$509$	29.6356			1.31357			0.656787	+	0.754076i	$0.271915\pi$
$510$	4.58258	−	21.9564i	0.202920	−	0.972247i
$511$		0			0
$512$			19.4340i			0.858868i
$513$		−	8.66025i		−	0.382360i
$514$	−0.361500			−0.0159451
$515$	−6.92820	+	33.1950i	−0.305293	+	1.46275i
$516$	−3.95644			−0.174173
$517$			23.1652i			1.01880i
$518$		−	30.0924i		−	1.32218i
$519$	−7.41742			−0.325589
$520$		0			0
$521$	−27.4955			−1.20460			−0.602299	−	0.798271i	$-0.705748\pi$
$521$	−27.4955			−1.20460			−0.602299	+	0.798271i	$0.705748\pi$
$522$			20.0616i			0.878073i
$523$		−	18.1652i		−	0.794307i	−0.917752	−	0.397153i	$-0.869998\pi$
$523$		−	18.1652i		−	0.794307i	0.917752	−	0.397153i	$-0.130002\pi$
$524$	−4.41742			−0.192976
$525$	7.93725	+	3.46410i	0.346410	+	0.151186i
$526$	−19.7001			−0.858966
$527$		−	44.3103i		−	1.93019i
$528$		−	4.73930i		−	0.206252i
$529$	2.00000			0.0869565
$530$	7.58258	+	1.58258i	0.329366	+	0.0687427i
$531$	6.73750			0.292383
$532$		−	8.37386i		−	0.363053i
$533$		0			0
$534$	−9.37386			−0.405647
$535$	−0.647551	+	3.10260i	−0.0279961	+	0.134137i
$536$	−25.7477			−1.11213
$537$		−	0.165151i		−	0.00712681i
$538$			32.8335i			1.41555i
$539$	10.5830			0.455842
$540$	6.37600	−	30.5493i	0.274379	−	1.31463i
$541$	10.3923			0.446800			0.223400	−	0.974727i	$-0.428284\pi$
$541$	10.3923			0.446800			0.223400	+	0.974727i	$0.428284\pi$
$542$			18.9564i			0.814249i
$543$			18.7477i			0.804542i
$544$	33.8426			1.45099
$545$	6.00000	+	1.25227i	0.257012	+	0.0536415i
$546$		0			0
$547$		−	1.25227i		−	0.0535433i	−0.999642	−	0.0267717i	$-0.991477\pi$
$547$		−	1.25227i		−	0.0535433i	0.999642	−	0.0267717i	$-0.00852270\pi$
$548$			0.266150i			0.0113694i
$549$	−21.1652			−0.903307
$550$	−11.5826	+	26.5390i	−0.493883	+	1.13163i
$551$	−7.93725			−0.338138
$552$			7.93725i			0.337832i
$553$		−	10.3923i		−	0.441926i
$554$	36.2976			1.54214
$555$	17.3739	+	3.62614i	0.737479	+	0.153921i
$556$	16.0436			0.680399
$557$			13.0381i			0.552440i	0.961094	+	0.276220i	$0.0890819\pi$
$557$			13.0381i			0.552440i	−0.961094	+	0.276220i	$0.910918\pi$
$558$		−	42.3303i		−	1.79198i
$559$		0			0
$560$	−1.41742	+	6.79129i	−0.0598971	+	0.286984i
$561$	−12.1244			−0.511891
$562$			38.3303i			1.61687i
$563$			9.00000i			0.379305i	0.981851	+	0.189652i	$0.0607361\pi$
$563$			9.00000i			0.379305i	−0.981851	+	0.189652i	$0.939264\pi$
$564$	24.4394			1.02908
$565$	7.57575	−	36.2976i	0.318714	−	1.52705i
$566$	−0.552200			−0.0232107
$567$		−	1.73205i		−	0.0727393i
$568$			6.16515i			0.258684i
$569$	−19.7477			−0.827868			−0.413934	−	0.910307i	$-0.635846\pi$
$569$	−19.7477			−0.827868			−0.413934	+	0.910307i	$0.635846\pi$
$570$	8.29875	+	1.73205i	0.347597	+	0.0725476i
$571$	−29.0780			−1.21688			−0.608439	−	0.793601i	$-0.708204\pi$
$571$	−29.0780			−1.21688			−0.608439	+	0.793601i	$0.708204\pi$
$572$		0			0
$573$		−	7.41742i		−	0.309867i
$574$	10.0308			0.418678
$575$	−9.16515	+	21.0000i	−0.382213	+	0.875761i
$576$	25.1652			1.04855
$577$		−	6.92820i		−	0.288425i	−0.989547	−	0.144212i	$-0.953935\pi$
$577$		−	6.92820i		−	0.288425i	0.989547	−	0.144212i	$-0.0460649\pi$
$578$		−	8.75560i		−	0.364185i
$579$	1.00905			0.0419347
$580$	−27.9989	−	5.84370i	−1.16259	−	0.242647i
$581$	−19.5826			−0.812422
$582$			9.79129i			0.405862i
$583$		−	4.18710i		−	0.173412i
$584$		0			0
$585$		0			0
$586$	51.2867			2.11864
$587$			18.7110i			0.772284i	0.922439	+	0.386142i	$0.126193\pi$
$587$			18.7110i			0.772284i	−0.922439	+	0.386142i	$0.873807\pi$
$588$		−	11.1652i		−	0.460443i
$589$	16.7477			0.690078
$590$	−3.36875	+	16.1407i	−0.138689	+	0.664500i
$591$	−19.9663			−0.821302
$592$			14.2179i			0.584352i
$593$		−	21.1660i		−	0.869184i	−0.900627	−	0.434592i	$-0.856893\pi$
$593$		−	21.1660i		−	0.869184i	0.900627	−	0.434592i	$-0.143107\pi$
$594$	−28.9564			−1.18810
$595$	17.3739	+	3.62614i	0.712259	+	0.148657i
$596$	−27.2560			−1.11645
$597$			1.41742i			0.0580113i
$598$		0			0
$599$	39.4955			1.61374			0.806870	−	0.590729i	$-0.201160\pi$
$599$	39.4955			1.61374			0.806870	+	0.590729i	$0.201160\pi$
$600$	7.93725	+	3.46410i	0.324037	+	0.141421i
$601$	−28.9129			−1.17938			−0.589690	−	0.807629i	$-0.700750\pi$
$601$	−28.9129			−1.17938			−0.589690	+	0.807629i	$0.700750\pi$
$602$		−	5.37386i		−	0.219022i
$603$		−	29.7309i		−	1.21074i
$604$	17.3205			0.704761
$605$	−8.75560	−	1.82740i	−0.355966	−	0.0742944i
$606$	19.7001			0.800262
$607$			19.7477i			0.801536i	0.916180	+	0.400768i	$0.131257\pi$
$607$			19.7477i			0.801536i	−0.916180	+	0.400768i	$0.868743\pi$
$608$			12.7913i			0.518755i
$609$	7.93725			0.321634
$610$	10.5826	−	50.7042i	0.428476	−	2.05295i
$611$		0			0
$612$		−	25.5826i		−	1.03411i
$613$			21.7937i			0.880238i	0.897940	+	0.440119i	$0.145064\pi$
$613$			21.7937i			0.880238i	−0.897940	+	0.440119i	$0.854936\pi$
$614$	53.0780			2.14205
$615$	−1.20871	+	5.79129i	−0.0487400	+	0.233527i
$616$	−7.93725			−0.319801
$617$			3.36875i			0.135621i	0.997698	+	0.0678104i	$0.0216013\pi$
$617$			3.36875i			0.135621i	−0.997698	+	0.0678104i	$0.978399\pi$
$618$		−	33.1950i		−	1.33530i
$619$	−2.01810			−0.0811143			−0.0405572	−	0.999177i	$-0.512913\pi$
$619$	−2.01810			−0.0811143			−0.0405572	+	0.999177i	$0.512913\pi$
$620$	59.0780	+	12.3303i	2.37263	+	0.495197i
$621$	−22.9129			−0.919462
$622$			3.46410i			0.138898i
$623$		−	7.41742i		−	0.297173i
$624$		0			0
$625$	17.0000	+	18.3303i	0.680000	+	0.733212i
$626$	67.3037			2.69000
$627$		−	4.58258i		−	0.183010i
$628$		−	25.5826i		−	1.02086i
$629$	36.3731			1.45029
$630$	16.5975	+	3.46410i	0.661261	+	0.138013i
$631$	21.7937			0.867592			0.433796	−	0.901011i	$-0.357174\pi$
$631$	21.7937			0.867592			0.433796	+	0.901011i	$0.357174\pi$
$632$		−	10.3923i		−	0.413384i
$633$			18.1652i			0.722000i
$634$	−45.9129			−1.82343
$635$	4.45325	−	21.3368i	0.176722	−	0.846725i
$636$	−4.41742			−0.175162
$637$		0			0
$638$			26.5390i			1.05069i
$639$	−7.11890			−0.281619
$640$	−5.83485	+	27.9564i	−0.230643	+	1.10508i
$641$	0.165151			0.00652309			0.00326154	−	0.999995i	$-0.498962\pi$
$641$	0.165151			0.00652309			0.00326154	+	0.999995i	$0.498962\pi$
$642$		−	3.10260i		−	0.122450i
$643$			5.91915i			0.233429i	0.993166	+	0.116714i	$0.0372362\pi$
$643$			5.91915i			0.233429i	−0.993166	+	0.116714i	$0.962764\pi$
$644$	−22.1552			−0.873036
$645$	3.10260	+	0.647551i	0.122165	+	0.0254973i
$646$	17.3739			0.683566
$647$			27.0000i			1.06148i	0.847535	+	0.530740i	$0.178086\pi$
$647$			27.0000i			1.06148i	−0.847535	+	0.530740i	$0.821914\pi$
$648$		−	1.73205i		−	0.0680414i
$649$	8.91288			0.349861
$650$		0			0
$651$	−16.7477			−0.656395
$652$			29.8064i			1.16731i
$653$			48.8258i			1.91070i	0.295477	+	0.955350i	$0.404521\pi$
$653$			48.8258i			1.91070i	−0.295477	+	0.955350i	$0.595479\pi$
$654$	−6.00000			−0.234619
$655$	3.46410	+	0.723000i	0.135354	+	0.0282500i
$656$	−4.73930			−0.185039
$657$		0			0
$658$			33.1950i			1.29408i
$659$	24.4955			0.954207			0.477104	−	0.878847i	$-0.341687\pi$
$659$	24.4955			0.954207			0.477104	+	0.878847i	$0.341687\pi$
$660$	3.37386	−	16.1652i	0.131327	−	0.629228i
$661$	2.45505			0.0954904			0.0477452	−	0.998860i	$-0.484796\pi$
$661$	2.45505			0.0954904			0.0477452	+	0.998860i	$0.484796\pi$
$662$			24.9564i			0.969960i
$663$		0			0
$664$	−19.5826			−0.759951
$665$	−1.37055	+	6.56670i	−0.0531477	+	0.254646i
$666$	34.7477			1.34645
$667$			21.0000i			0.813123i
$668$			11.9536i			0.462497i
$669$	−8.66025			−0.334825
$670$	71.2247	+	14.8655i	2.75165	+	0.574303i
$671$	−27.9989			−1.08088
$672$		−	12.7913i		−	0.493435i
$673$			5.83485i			0.224917i	0.993656	+	0.112458i	$0.0358725\pi$
$673$			5.83485i			0.224917i	−0.993656	+	0.112458i	$0.964127\pi$
$674$	−7.11890			−0.274210
$675$	−10.0000	+	22.9129i	−0.384900	+	0.881917i
$676$		0			0
$677$			21.1652i			0.813443i	0.913552	+	0.406721i	$0.133328\pi$
$677$			21.1652i			0.813443i	−0.913552	+	0.406721i	$0.866672\pi$
$678$			36.2976i			1.39400i
$679$	−7.74773			−0.297330
$680$	17.3739	+	3.62614i	0.666257	+	0.139056i
$681$	6.10985			0.234130
$682$		−	55.9977i		−	2.14426i
$683$			11.9337i			0.456629i	0.973587	+	0.228314i	$0.0733214\pi$
$683$			11.9337i			0.456629i	−0.973587	+	0.228314i	$0.926679\pi$
$684$	9.66930			0.369715
$685$	0.0435608	−	0.208712i	0.00166437	−	0.00797448i
$686$	41.7042			1.59227
$687$			5.48220i			0.209159i
$688$			2.53901i			0.0967990i
$689$		0			0
$690$	4.58258	−	21.9564i	0.174456	−	0.835867i
$691$	−35.6501			−1.35619			−0.678096	−	0.734973i	$-0.737195\pi$
$691$	−35.6501			−1.35619			−0.678096	+	0.734973i	$0.737195\pi$
$692$		−	20.7042i		−	0.787054i
$693$		−	9.16515i		−	0.348155i
$694$	33.5565			1.27379
$695$	−12.5812	−	2.62585i	−0.477232	−	0.0996042i
$696$	7.93725			0.300861
$697$			12.1244i			0.459243i
$698$			40.1216i			1.51862i
$699$	21.1652			0.800540
$700$	−9.66930	+	22.1552i	−0.365465	+	0.837386i
$701$	2.83485			0.107071			0.0535354	−	0.998566i	$-0.482951\pi$
$701$	2.83485			0.107071			0.0535354	+	0.998566i	$0.482951\pi$
$702$		0			0
$703$			13.7477i			0.518505i
$704$	33.2904			1.25468
$705$	−19.1652	−	4.00000i	−0.721801	−	0.150649i
$706$	38.1216			1.43472
$707$			15.5885i			0.586264i
$708$		−	9.40315i		−	0.353392i
$709$	−36.3731			−1.36602			−0.683010	−	0.730409i	$-0.739329\pi$
$709$	−36.3731			−1.36602			−0.683010	+	0.730409i	$0.739329\pi$
$710$	3.55945	−	17.0544i	0.133584	−	0.640039i
$711$	12.0000			0.450035
$712$		−	7.41742i		−	0.277980i
$713$		−	44.3103i		−	1.65943i
$714$	−17.3739			−0.650201
$715$		0			0
$716$	0.460985			0.0172278
$717$		−	20.9753i		−	0.783337i
$718$		−	73.0780i		−	2.72725i
$719$	30.4955			1.13729			0.568644	−	0.822584i	$-0.307468\pi$
$719$	30.4955			1.13729			0.568644	+	0.822584i	$0.307468\pi$
$720$	−7.84190	−	1.63670i	−0.292250	−	0.0609962i
$721$	26.2668			0.978227
$722$		−	35.0224i		−	1.30340i
$723$			1.73205i			0.0644157i
$724$	−52.3303			−1.94484
$725$	21.0000	+	9.16515i	0.779920	+	0.340385i
$726$	8.75560			0.324951
$727$		−	42.7477i		−	1.58543i	−0.609595	−	0.792713i	$-0.708668\pi$
$727$		−	42.7477i		−	1.58543i	0.609595	−	0.792713i	$-0.291332\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	6.49545			0.240243
$732$			29.5390i			1.09179i
$733$		−	8.94630i		−	0.330439i	−0.986257	−	0.165220i	$-0.947167\pi$
$733$		−	8.94630i		−	0.330439i	0.986257	−	0.165220i	$-0.0528333\pi$
$734$	56.3592			2.08026
$735$	−1.82740	+	8.75560i	−0.0674047	+	0.322955i
$736$	33.8426			1.24745
$737$		−	39.3303i		−	1.44875i
$738$			11.5826i			0.426361i
$739$	−48.7835			−1.79453			−0.897265	−	0.441493i	$-0.854449\pi$
$739$	−48.7835			−1.79453			−0.897265	+	0.441493i	$0.854449\pi$
$740$	−10.1216	+	48.4955i	−0.372077	+	1.78273i
$741$		0			0
$742$		−	6.00000i		−	0.220267i
$743$		−	42.7690i		−	1.56904i	−0.620103	−	0.784521i	$-0.712909\pi$
$743$		−	42.7690i		−	1.56904i	0.620103	−	0.784521i	$-0.287091\pi$
$744$	−16.7477			−0.614001
$745$	21.3739	+	4.46099i	0.783078	+	0.163438i
$746$	28.4557			1.04184
$747$		−	22.6120i		−	0.827330i
$748$		−	33.8426i		−	1.23741i
$749$	2.45505			0.0897056
$750$	−19.9564	−	14.1652i	−0.728706	−	0.517238i
$751$	15.7477			0.574643			0.287321	−	0.957834i	$-0.407235\pi$
$751$	15.7477			0.574643			0.287321	+	0.957834i	$0.407235\pi$
$752$		−	15.6838i		−	0.571930i
$753$		−	18.1652i		−	0.661975i
$754$		0			0
$755$	−13.5826	−	2.83485i	−0.494321	−	0.103171i
$756$	−24.1733			−0.879173
$757$			17.7477i			0.645052i	0.946561	+	0.322526i	$0.104532\pi$
$757$			17.7477i			0.645052i	−0.946561	+	0.322526i	$0.895468\pi$
$758$		−	46.1216i		−	1.67521i
$759$	−12.1244			−0.440086
$760$	−1.37055	+	6.56670i	−0.0497151	+	0.238199i
$761$	40.7509			1.47722			0.738609	−	0.674134i	$-0.235483\pi$
$761$	40.7509			1.47722			0.738609	+	0.674134i	$0.235483\pi$
$762$			21.3368i			0.772951i
$763$		−	4.74773i		−	0.171879i
$764$	20.7042			0.749050
$765$	−4.18710	+	20.0616i	−0.151385	+	0.725329i
$766$	−6.20871			−0.224330
$767$		0			0
$768$		−	2.79129i		−	0.100722i
$769$	15.5885			0.562134			0.281067	−	0.959688i	$-0.409312\pi$
$769$	15.5885			0.562134			0.281067	+	0.959688i	$0.409312\pi$
$770$	21.9564	+	4.58258i	0.791255	+	0.165145i
$771$	−0.165151			−0.00594778
$772$			2.81655i			0.101370i
$773$			34.7364i			1.24938i	0.780873	+	0.624690i	$0.214775\pi$
$773$			34.7364i			1.24938i	−0.780873	+	0.624690i	$0.785225\pi$
$774$	6.20520			0.223041
$775$	−44.3103	−	19.3386i	−1.59167	−	0.694663i
$776$	−7.74773			−0.278127
$777$		−	13.7477i		−	0.493197i
$778$			33.1950i			1.19010i
$779$	−4.58258			−0.164188
$780$		0			0
$781$	−9.41742			−0.336982
$782$		−	45.9669i		−	1.64377i
$783$			22.9129i			0.818839i
$784$	−7.16515			−0.255898
$785$	−4.18710	+	20.0616i	−0.149444	+	0.716030i
$786$	−3.46410			−0.123560
$787$			32.1860i			1.14731i	0.819099	+	0.573653i	$0.194474\pi$
$787$			32.1860i			1.14731i	−0.819099	+	0.573653i	$0.805526\pi$
$788$		−	55.7316i		−	1.98536i
$789$	−9.00000			−0.320408
$790$	−6.00000	+	28.7477i	−0.213470	+	1.02280i
$791$	−28.7219			−1.02123
$792$		−	9.16515i		−	0.325669i
$793$		0			0
$794$	−59.7042			−2.11882
$795$	3.46410	+	0.723000i	0.122859	+	0.0256422i
$796$	−3.95644			−0.140232
$797$		−	20.0780i		−	0.711200i	−0.934638	−	0.355600i	$-0.884276\pi$
$797$		−	20.0780i		−	0.711200i	0.934638	−	0.355600i	$-0.115724\pi$
$798$		−	6.56670i		−	0.232459i
$799$	−40.1232			−1.41946
$800$	14.7701	−	33.8426i	0.522202	−	1.19652i
$801$	8.56490			0.302626
$802$			27.3739i			0.966605i
$803$		0			0
$804$	−41.4938			−1.46337
$805$	17.3739	+	3.62614i	0.612348	+	0.127805i
$806$		0			0
$807$			15.0000i			0.528025i
$808$			15.5885i			0.548400i
$809$	−36.8258			−1.29472			−0.647362	−	0.762182i	$-0.724128\pi$
$809$	−36.8258			−1.29472			−0.647362	+	0.762182i	$0.724128\pi$
$810$	−1.00000	+	4.79129i	−0.0351364	+	0.168349i
$811$	−18.7665			−0.658981			−0.329491	−	0.944159i	$-0.606877\pi$
$811$	−18.7665			−0.658981			−0.329491	+	0.944159i	$0.606877\pi$
$812$			22.1552i			0.777494i
$813$			8.66025i			0.303728i
$814$	45.9669			1.61114
$815$	4.87841	−	23.3739i	0.170883	−	0.818751i
$816$	8.20871			0.287362
$817$			2.45505i			0.0858914i
$818$			18.9564i			0.662796i
$819$		0			0
$820$	−16.1652	−	3.37386i	−0.564512	−	0.117820i
$821$	−23.4304			−0.817725			−0.408863	−	0.912596i	$-0.634074\pi$
$821$	−23.4304			−0.817725			−0.408863	+	0.912596i	$0.634074\pi$
$822$			0.208712i			0.00727967i
$823$			40.5826i			1.41462i	0.706904	+	0.707310i	$0.250091\pi$
$823$			40.5826i			1.41462i	−0.706904	+	0.707310i	$0.749909\pi$
$824$	26.2668			0.915048
$825$	−5.29150	+	12.1244i	−0.184226	+	0.422116i
$826$	12.7719			0.444391
$827$			31.5583i			1.09739i	0.836023	+	0.548695i	$0.184875\pi$
$827$			31.5583i			1.09739i	−0.836023	+	0.548695i	$0.815125\pi$
$828$		−	25.5826i		−	0.889056i
$829$	3.33030			0.115666			0.0578331	−	0.998326i	$-0.481581\pi$
$829$	3.33030			0.115666			0.0578331	+	0.998326i	$0.481581\pi$
$830$	54.1703	+	11.3060i	1.88028	+	0.392437i
$831$	16.5826			0.575243
$832$		0			0
$833$			18.3303i			0.635107i
$834$	12.5812			0.435652
$835$	1.95644	−	9.37386i	0.0677054	−	0.324396i
$836$	12.7913			0.442396
$837$		−	48.3465i		−	1.67110i
$838$			52.8951i			1.82723i
$839$	−1.35065			−0.0466296			−0.0233148	−	0.999728i	$-0.507422\pi$
$839$	−1.35065			−0.0466296			−0.0233148	+	0.999728i	$0.507422\pi$
$840$	1.37055	−	6.56670i	0.0472885	−	0.226573i
$841$	−8.00000			−0.275862
$842$		−	57.4955i		−	1.98142i
$843$			17.5112i			0.603118i
$844$	−50.7042			−1.74531
$845$		0			0
$846$	−38.3303			−1.31782
$847$			6.92820i			0.238056i
$848$			2.83485i			0.0973491i
$849$	−0.252273			−0.00865798
$850$	−45.9669	−	20.0616i	−1.57665	−	0.688108i
$851$	36.3731			1.24685
$852$			9.93545i			0.340383i
$853$			53.2566i			1.82347i	0.410777	+	0.911736i	$0.365258\pi$
$853$			53.2566i			1.82347i	−0.410777	+	0.911736i	$0.634742\pi$
$854$	−40.1216			−1.37293
$855$	−7.58258	−	1.58258i	−0.259319	−	0.0541229i
$856$	2.45505			0.0839119
$857$			22.7477i			0.777048i	0.921439	+	0.388524i	$0.127015\pi$
$857$			22.7477i			0.777048i	−0.921439	+	0.388524i	$0.872985\pi$
$858$		0			0
$859$	−38.2432			−1.30484			−0.652420	−	0.757857i	$-0.726246\pi$
$859$	−38.2432			−1.30484			−0.652420	+	0.757857i	$0.726246\pi$
$860$	−1.80750	+	8.66025i	−0.0616352	+	0.295312i
$861$	4.58258			0.156174
$862$		−	64.8693i		−	2.20946i
$863$			34.8317i			1.18569i	0.805318	+	0.592843i	$0.201994\pi$
$863$			34.8317i			1.18569i	−0.805318	+	0.592843i	$0.798006\pi$
$864$	36.9253			1.25622
$865$	−3.38865	+	16.2360i	−0.115218	+	0.552041i
$866$	−38.8480			−1.32011
$867$		−	4.00000i		−	0.135847i
$868$		−	46.7477i		−	1.58672i
$869$	15.8745			0.538506
$870$	−21.9564	−	4.58258i	−0.744393	−	0.155364i
$871$		0			0
$872$		−	4.74773i		−	0.160778i
$873$		−	8.94630i		−	0.302787i
$874$	17.3739			0.587680
$875$	11.2087	−	15.7913i	0.378924	−	0.533843i
$876$		0			0
$877$		−	7.93725i		−	0.268022i	−0.990980	−	0.134011i	$-0.957214\pi$
$877$		−	7.93725i		−	0.268022i	0.990980	−	0.134011i	$-0.0427858\pi$
$878$			88.6405i			2.99147i
$879$	23.4304			0.790286
$880$	−10.3739	−	2.16515i	−0.349703	−	0.0729872i
$881$	18.4955			0.623128			0.311564	−	0.950225i	$-0.399147\pi$
$881$	18.4955			0.623128			0.311564	+	0.950225i	$0.399147\pi$
$882$			17.5112i			0.589633i
$883$			46.2432i			1.55621i	0.628136	+	0.778103i	$0.283818\pi$
$883$			46.2432i			1.55621i	−0.628136	+	0.778103i	$0.716182\pi$
$884$		0			0
$885$	−1.53901	+	7.37386i	−0.0517334	+	0.247870i
$886$	56.7207			1.90557
$887$			0.495454i			0.0166357i	0.999965	+	0.00831786i	$0.00264769\pi$
$887$			0.495454i			0.0166357i	−0.999965	+	0.00831786i	$0.997352\pi$
$888$		−	13.7477i		−	0.461344i
$889$	−16.8836			−0.566256
$890$	−4.28245	+	20.5185i	−0.143548	+	0.687780i
$891$	2.64575			0.0886360
$892$		−	24.1733i		−	0.809381i
$893$		−	15.1652i		−	0.507482i
$894$	−21.3739			−0.714849
$895$	−0.361500	−	0.0754495i	−0.0120836	−	0.00252200i
$896$	22.1216			0.739030
$897$		0			0
$898$		−	82.0345i		−	2.73753i
$899$	−44.3103			−1.47783
$900$	−25.5826	−	11.1652i	−0.852753	−	0.372172i
$901$	7.25227			0.241608
$902$			15.3223i			0.510177i
$903$		−	2.45505i		−	0.0816990i
$904$	−28.7219			−0.955275
$905$	41.0369	+	8.56490i	1.36411	+	0.284707i
$906$	13.5826			0.451251
$907$		−	33.7477i		−	1.12057i	−0.828298	−	0.560287i	$-0.810691\pi$
$907$		−	33.7477i		−	1.12057i	0.828298	−	0.560287i	$-0.189309\pi$
$908$			17.0544i			0.565969i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	37.9129			1.25611			0.628055	−	0.778169i	$-0.283851\pi$
$911$	37.9129			1.25611			0.628055	+	0.778169i	$0.283851\pi$
$912$			3.10260i			0.102737i
$913$		−	29.9129i		−	0.989972i
$914$	3.79129			0.125405
$915$	4.83465	−	23.1642i	0.159829	−	0.765785i
$916$	−15.3024			−0.505606
$917$		−	2.74110i		−	0.0905191i
$918$		−	50.1540i		−	1.65533i
$919$	−35.8348			−1.18208			−0.591041	−	0.806641i	$-0.701283\pi$
$919$	−35.8348			−1.18208			−0.591041	+	0.806641i	$0.701283\pi$
$920$	17.3739	+	3.62614i	0.572799	+	0.119550i
$921$	24.2487			0.799022
$922$		−	2.62614i		−	0.0864872i
$923$		0			0
$924$	−12.7913			−0.420802
$925$	15.8745	−	36.3731i	0.521951	−	1.19594i
$926$	−18.0000			−0.591517
$927$			30.3303i			0.996178i
$928$		−	33.8426i		−	1.11094i
$929$	−15.9699			−0.523954			−0.261977	−	0.965074i	$-0.584374\pi$
$929$	−15.9699			−0.523954			−0.261977	+	0.965074i	$0.584374\pi$
$930$	46.3284	+	9.66930i	1.51917	+	0.317069i
$931$	−6.92820			−0.227063
$932$			59.0780i			1.93517i
$933$			1.58258i			0.0518112i
$934$	−26.9898			−0.883134
$935$	−5.53901	+	26.5390i	−0.181145	+	0.867919i
$936$		0			0
$937$			23.4955i			0.767563i	0.923424	+	0.383782i	$0.125378\pi$
$937$			23.4955i			0.767563i	−0.923424	+	0.383782i	$0.874622\pi$
$938$		−	56.3592i		−	1.84019i
$939$	30.7477			1.00341
$940$	11.1652	−	53.4955i	0.364167	−	1.74483i
$941$	26.4575			0.862490			0.431245	−	0.902235i	$-0.358074\pi$
$941$	26.4575			0.862490			0.431245	+	0.902235i	$0.358074\pi$
$942$		−	20.0616i		−	0.653643i
$943$			12.1244i			0.394823i
$944$	−6.03440			−0.196403
$945$	18.9564	+	3.95644i	0.616653	+	0.128703i
$946$	8.20871			0.266888
$947$		−	38.5819i		−	1.25374i	−0.779123	−	0.626871i	$-0.784335\pi$
$947$		−	38.5819i		−	1.25374i	0.779123	−	0.626871i	$-0.215665\pi$
$948$		−	16.7477i		−	0.543941i
$949$		0			0
$950$	7.58258	−	17.3739i	0.246011	−	0.563683i
$951$	−20.9753			−0.680171
$952$		−	13.7477i		−	0.445566i
$953$		−	56.0780i		−	1.81655i	−0.418378	−	0.908273i	$-0.637401\pi$
$953$		−	56.0780i		−	1.81655i	0.418378	−	0.908273i	$-0.362599\pi$
$954$	6.92820			0.224309
$955$	−16.2360	−	3.38865i	−0.525385	−	0.109654i
$956$	58.5481			1.89358
$957$			12.1244i			0.391925i
$958$		−	70.8693i		−	2.28968i
$959$	−0.165151			−0.00533302
$960$	−5.74835	+	27.5420i	−0.185527	+	0.888915i
$961$	62.4955			2.01598
$962$		0			0
$963$			2.83485i			0.0913517i
$964$	−4.83465			−0.155714
$965$	0.460985	−	2.20871i	0.0148396	−	0.0711010i
$966$	−17.3739			−0.558995
$967$		−	21.5076i		−	0.691638i	−0.938301	−	0.345819i	$-0.887601\pi$
$967$		−	21.5076i		−	0.691638i	0.938301	−	0.345819i	$-0.112399\pi$
$968$			6.92820i			0.222681i
$969$	7.93725			0.254981
$970$	21.4322	+	4.47315i	0.688145	+	0.143624i
$971$	36.4955			1.17119			0.585597	−	0.810602i	$-0.300860\pi$
$971$	36.4955			1.17119			0.585597	+	0.810602i	$0.300860\pi$
$972$		−	44.6606i		−	1.43249i
$973$			9.95536i			0.319154i
$974$	−46.1216			−1.47783
$975$		0			0
$976$	18.9564			0.606781
$977$		−	38.7726i		−	1.24044i	−0.784426	−	0.620222i	$-0.787042\pi$
$977$		−	38.7726i		−	1.24044i	0.784426	−	0.620222i	$-0.212958\pi$
$978$			23.3739i			0.747414i
$979$	11.3303			0.362118
$980$	−24.4394	−	5.10080i	−0.780688	−	0.162939i
$981$	5.48220			0.175033
$982$		−	62.5644i		−	1.99651i
$983$			3.12250i			0.0995924i	0.998759	+	0.0497962i	$0.0158572\pi$
$983$			3.12250i			0.0995924i	−0.998759	+	0.0497962i	$0.984143\pi$
$984$	4.58258			0.146087
$985$	−9.12159	+	43.7042i	−0.290638	+	1.39253i
$986$	−45.9669			−1.46389
$987$			15.1652i			0.482712i
$988$		0			0
$989$	6.49545			0.206543
$990$	−5.29150	+	25.3531i	−0.168175	+	0.805775i
$991$	−13.0000			−0.412959			−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000			−0.412959			−0.206479	+	0.978451i	$0.566201\pi$
$992$			71.4083i			2.26722i
$993$			11.4014i			0.361811i
$994$	−13.4949			−0.428032
$995$	3.10260	+	0.647551i	0.0983591	+	0.0205287i
$996$	−31.5583			−0.999963
$997$			18.1652i			0.575296i	0.957736	+	0.287648i	$0.0928733\pi$
$997$			18.1652i			0.575296i	−0.957736	+	0.287648i	$0.907127\pi$
$998$			36.3303i			1.15002i
$999$	39.6863			1.25562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.b.f.339.8		8
5.2	odd	4		4225.2.a.bk.1.1		4
5.3	odd	4		4225.2.a.bj.1.4		4
5.4	even	2	inner	845.2.b.f.339.1		8
13.2	odd	12		845.2.l.c.654.1		8
13.3	even	3		845.2.n.c.529.1		8
13.4	even	6		845.2.n.c.484.2		8
13.5	odd	4		845.2.d.c.844.8		8
13.6	odd	12		65.2.l.a.49.1	yes	8
13.7	odd	12		845.2.l.c.699.4		8
13.8	odd	4		845.2.d.c.844.2		8
13.9	even	3		845.2.n.d.484.4		8
13.10	even	6		845.2.n.d.529.3		8
13.11	odd	12		65.2.l.a.4.4	yes	8
13.12	even	2	inner	845.2.b.f.339.2		8
39.11	even	12		585.2.bf.a.199.1		8
39.32	even	12		585.2.bf.a.244.4		8
52.11	even	12		1040.2.df.b.849.3		8
52.19	even	12		1040.2.df.b.49.2		8
65.4	even	6		845.2.n.d.484.3		8
65.9	even	6		845.2.n.c.484.1		8
65.12	odd	4		4225.2.a.bk.1.4		4
65.19	odd	12		65.2.l.a.49.4	yes	8
65.24	odd	12		65.2.l.a.4.1	✓	8
65.29	even	6		845.2.n.d.529.4		8
65.32	even	12		325.2.n.c.101.2		4
65.34	odd	4		845.2.d.c.844.7		8
65.37	even	12		325.2.n.c.251.2		4
65.38	odd	4		4225.2.a.bj.1.1		4
65.44	odd	4		845.2.d.c.844.1		8
65.49	even	6		845.2.n.c.529.2		8
65.54	odd	12		845.2.l.c.654.4		8
65.58	even	12		325.2.n.b.101.1		4
65.59	odd	12		845.2.l.c.699.1		8
65.63	even	12		325.2.n.b.251.1		4
65.64	even	2	inner	845.2.b.f.339.7		8
195.89	even	12		585.2.bf.a.199.4		8
195.149	even	12		585.2.bf.a.244.1		8
260.19	even	12		1040.2.df.b.49.3		8
260.219	even	12		1040.2.df.b.849.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.1	✓	8	65.24	odd	12
65.2.l.a.4.4	yes	8	13.11	odd	12
65.2.l.a.49.1	yes	8	13.6	odd	12
65.2.l.a.49.4	yes	8	65.19	odd	12
325.2.n.b.101.1		4	65.58	even	12
325.2.n.b.251.1		4	65.63	even	12
325.2.n.c.101.2		4	65.32	even	12
325.2.n.c.251.2		4	65.37	even	12
585.2.bf.a.199.1		8	39.11	even	12
585.2.bf.a.199.4		8	195.89	even	12
585.2.bf.a.244.1		8	195.149	even	12
585.2.bf.a.244.4		8	39.32	even	12
845.2.b.f.339.1		8	5.4	even	2	inner
845.2.b.f.339.2		8	13.12	even	2	inner
845.2.b.f.339.7		8	65.64	even	2	inner
845.2.b.f.339.8		8	1.1	even	1	trivial
845.2.d.c.844.1		8	65.44	odd	4
845.2.d.c.844.2		8	13.8	odd	4
845.2.d.c.844.7		8	65.34	odd	4
845.2.d.c.844.8		8	13.5	odd	4
845.2.l.c.654.1		8	13.2	odd	12
845.2.l.c.654.4		8	65.54	odd	12
845.2.l.c.699.1		8	65.59	odd	12
845.2.l.c.699.4		8	13.7	odd	12
845.2.n.c.484.1		8	65.9	even	6
845.2.n.c.484.2		8	13.4	even	6
845.2.n.c.529.1		8	13.3	even	3
845.2.n.c.529.2		8	65.49	even	6
845.2.n.d.484.3		8	65.4	even	6
845.2.n.d.484.4		8	13.9	even	3
845.2.n.d.529.3		8	13.10	even	6
845.2.n.d.529.4		8	65.29	even	6
1040.2.df.b.49.2		8	52.19	even	12
1040.2.df.b.49.3		8	260.19	even	12
1040.2.df.b.849.2		8	260.219	even	12
1040.2.df.b.849.3		8	52.11	even	12
4225.2.a.bj.1.1		4	65.38	odd	4
4225.2.a.bj.1.4		4	5.3	odd	4
4225.2.a.bk.1.1		4	5.2	odd	4
4225.2.a.bk.1.4		4	65.12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.18890i q^{2} +1.00000i q^{3} -2.79129 q^{4} +(2.18890 + 0.456850i) q^{5} -2.18890 q^{6} -1.73205i q^{7} -1.73205i q^{8} +2.00000 q^{9} +(-1.00000 + 4.79129i) q^{10} +2.64575 q^{11} -2.79129i q^{12} +3.79129 q^{14} +(-0.456850 + 2.18890i) q^{15} -1.79129 q^{16} +4.58258i q^{17} +4.37780i q^{18} -1.73205 q^{19} +(-6.10985 - 1.27520i) q^{20} +1.73205 q^{21} +5.79129i q^{22} +4.58258i q^{23} +1.73205 q^{24} +(4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +4.83465i q^{28} +4.58258 q^{29} +(-4.79129 - 1.00000i) q^{30} -9.66930 q^{31} -7.38505i q^{32} +2.64575i q^{33} -10.0308 q^{34} +(0.791288 - 3.79129i) q^{35} -5.58258 q^{36} -7.93725i q^{37} -3.79129i q^{38} +(0.791288 - 3.79129i) q^{40} +2.64575 q^{41} +3.79129i q^{42} -1.41742i q^{43} -7.38505 q^{44} +(4.37780 + 0.913701i) q^{45} -10.0308 q^{46} +8.75560i q^{47} -1.79129i q^{48} +4.00000 q^{49} +(-4.37780 + 10.0308i) q^{50} -4.58258 q^{51} -1.58258i q^{53} -10.9445 q^{54} +(5.79129 + 1.20871i) q^{55} -3.00000 q^{56} -1.73205i q^{57} +10.0308i q^{58} +3.36875 q^{59} +(1.27520 - 6.10985i) q^{60} -10.5826 q^{61} -21.1652i q^{62} -3.46410i q^{63} +12.5826 q^{64} -5.79129 q^{66} -14.8655i q^{67} -12.7913i q^{68} -4.58258 q^{69} +(8.29875 + 1.73205i) q^{70} -3.55945 q^{71} -3.46410i q^{72} +17.3739 q^{74} +(-2.00000 + 4.58258i) q^{75} +4.83465 q^{76} -4.58258i q^{77} +6.00000 q^{79} +(-3.92095 - 0.818350i) q^{80} +1.00000 q^{81} +5.79129i q^{82} -11.3060i q^{83} -4.83465 q^{84} +(-2.09355 + 10.0308i) q^{85} +3.10260 q^{86} +4.58258i q^{87} -4.58258i q^{88} +4.28245 q^{89} +(-2.00000 + 9.58258i) q^{90} -12.7913i q^{92} -9.66930i q^{93} -19.1652 q^{94} +(-3.79129 - 0.791288i) q^{95} +7.38505 q^{96} -4.47315i q^{97} +8.75560i q^{98} +5.29150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 16 q^{9} - 8 q^{10} + 12 q^{14} + 4 q^{16} - 20 q^{30} - 12 q^{35} - 8 q^{36} - 12 q^{40} + 32 q^{49} + 28 q^{55} - 24 q^{56} - 48 q^{61} + 64 q^{64} - 28 q^{66} + 84 q^{74} - 16 q^{75}+ \cdots - 12 q^{95}+O(q^{100}) \) 8 * q - 4 * q^4 + 16 * q^9 - 8 * q^10 + 12 * q^14 + 4 * q^16 - 20 * q^30 - 12 * q^35 - 8 * q^36 - 12 * q^40 + 32 * q^49 + 28 * q^55 - 24 * q^56 - 48 * q^61 + 64 * q^64 - 28 * q^66 + 84 * q^74 - 16 * q^75 + 48 * q^79 + 8 * q^81 - 16 * q^90 - 80 * q^94 - 12 * q^95

Introduction

L-functions

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