LMFDB - Embedded newform 1815.2.c.f.364.8

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:	$8$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.8
Root			$0.228425 + 1.39564i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.f.364.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.18890i q^{2} +1.00000i q^{3} -2.79129 q^{4} +(2.00000 + 1.00000i) q^{5} -2.18890 q^{6} -4.37780i q^{7} -1.73205i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.18890i q^{2} +1.00000i q^{3} -2.79129 q^{4} +(2.00000 + 1.00000i) q^{5} -2.18890 q^{6} -4.37780i q^{7} -1.73205i q^{8} -1.00000 q^{9} +(-2.18890 + 4.37780i) q^{10} -2.79129i q^{12} -4.37780i q^{13} +9.58258 q^{14} +(-1.00000 + 2.00000i) q^{15} -1.79129 q^{16} -3.55945i q^{17} -2.18890i q^{18} +5.29150 q^{19} +(-5.58258 - 2.79129i) q^{20} +4.37780 q^{21} -8.58258i q^{23} +1.73205 q^{24} +(3.00000 + 4.00000i) q^{25} +9.58258 q^{26} -1.00000i q^{27} +12.2197i q^{28} +0.913701 q^{29} +(-4.37780 - 2.18890i) q^{30} -6.58258 q^{31} -7.38505i q^{32} +7.79129 q^{34} +(4.37780 - 8.75560i) q^{35} +2.79129 q^{36} +0.417424i q^{37} +11.5826i q^{38} +4.37780 q^{39} +(1.73205 - 3.46410i) q^{40} +6.92820 q^{41} +9.58258i q^{42} +0.913701i q^{43} +(-2.00000 - 1.00000i) q^{45} +18.7864 q^{46} -2.58258i q^{47} -1.79129i q^{48} -12.1652 q^{49} +(-8.75560 + 6.56670i) q^{50} +3.55945 q^{51} +12.2197i q^{52} -5.00000i q^{53} +2.18890 q^{54} -7.58258 q^{56} +5.29150i q^{57} +2.00000i q^{58} -5.58258 q^{59} +(2.79129 - 5.58258i) q^{60} +8.66025 q^{61} -14.4086i q^{62} +4.37780i q^{63} +12.5826 q^{64} +(4.37780 - 8.75560i) q^{65} +12.7477i q^{67} +9.93545i q^{68} +8.58258 q^{69} +(19.1652 + 9.58258i) q^{70} +9.16515 q^{71} +1.73205i q^{72} -5.10080i q^{73} -0.913701 q^{74} +(-4.00000 + 3.00000i) q^{75} -14.7701 q^{76} +9.58258i q^{78} -2.64575 q^{79} +(-3.58258 - 1.79129i) q^{80} +1.00000 q^{81} +15.1652i q^{82} +1.63670i q^{83} -12.2197 q^{84} +(3.55945 - 7.11890i) q^{85} -2.00000 q^{86} +0.913701i q^{87} +10.7477 q^{89} +(2.18890 - 4.37780i) q^{90} -19.1652 q^{91} +23.9564i q^{92} -6.58258i q^{93} +5.65300 q^{94} +(10.5830 + 5.29150i) q^{95} +7.38505 q^{96} +5.58258i q^{97} -26.6283i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 16 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^4 + 16 * q^5 - 8 * q^9	$ 8 q - 4 q^{4} + 16 q^{5} - 8 q^{9} + 40 q^{14} - 8 q^{15} + 4 q^{16} - 8 q^{20} + 24 q^{25} + 40 q^{26} - 16 q^{31} + 44 q^{34} + 4 q^{36} - 16 q^{45} - 24 q^{49} - 24 q^{56} - 8 q^{59} + 4 q^{60} + 64 q^{64} + 32 q^{69} + 80 q^{70} - 32 q^{75} + 8 q^{80} + 8 q^{81} - 16 q^{86} - 24 q^{89} - 80 q^{91}+O(q^{100}) $ 8 * q - 4 * q^4 + 16 * q^5 - 8 * q^9 + 40 * q^14 - 8 * q^15 + 4 * q^16 - 8 * q^20 + 24 * q^25 + 40 * q^26 - 16 * q^31 + 44 * q^34 + 4 * q^36 - 16 * q^45 - 24 * q^49 - 24 * q^56 - 8 * q^59 + 4 * q^60 + 64 * q^64 + 32 * q^69 + 80 * q^70 - 32 * q^75 + 8 * q^80 + 8 * q^81 - 16 * q^86 - 24 * q^89 - 80 * q^91

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 $

$2$			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
$3$			1.00000i			0.577350i
$4$	−2.79129			−1.39564
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	−2.18890			−0.893615
$7$		−	4.37780i		−	1.65465i	−0.561721	−	0.827327i	$-0.689860\pi$
$7$		−	4.37780i		−	1.65465i	0.561721	−	0.827327i	$-0.310140\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−1.00000			−0.333333
$10$	−2.18890	+	4.37780i	−0.692191	+	1.38438i
$11$		0			0
$11$		0			0
$12$		−	2.79129i		−	0.805775i
$13$		−	4.37780i		−	1.21418i	−0.794632	−	0.607092i	$-0.792336\pi$
$13$		−	4.37780i		−	1.21418i	0.794632	−	0.607092i	$-0.207664\pi$
$14$	9.58258			2.56105
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$	−1.79129			−0.447822
$17$		−	3.55945i		−	0.863294i	−0.902043	−	0.431647i	$-0.857933\pi$
$17$		−	3.55945i		−	0.863294i	0.902043	−	0.431647i	$-0.142067\pi$
$18$		−	2.18890i		−	0.515929i
$19$	5.29150			1.21395			0.606977	−	0.794719i	$-0.292382\pi$
$19$	5.29150			1.21395			0.606977	+	0.794719i	$0.292382\pi$
$20$	−5.58258	−	2.79129i	−1.24830	−	0.624151i
$21$	4.37780			0.955315
$22$		0			0
$23$		−	8.58258i		−	1.78959i	−0.446476	−	0.894795i	$-0.647321\pi$
$23$		−	8.58258i		−	1.78959i	0.446476	−	0.894795i	$-0.352679\pi$
$24$	1.73205			0.353553
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	9.58258			1.87930
$27$		−	1.00000i		−	0.192450i
$28$			12.2197i			2.30931i
$29$	0.913701			0.169670			0.0848350	−	0.996395i	$-0.472964\pi$
$29$	0.913701			0.169670			0.0848350	+	0.996395i	$0.472964\pi$
$30$	−4.37780	−	2.18890i	−0.799274	−	0.399637i
$31$	−6.58258			−1.18227			−0.591133	−	0.806574i	$-0.701319\pi$
$31$	−6.58258			−1.18227			−0.591133	+	0.806574i	$0.701319\pi$
$32$		−	7.38505i		−	1.30551i
$33$		0			0
$34$	7.79129			1.33619
$35$	4.37780	−	8.75560i	0.739984	−	1.47997i
$36$	2.79129			0.465215
$37$			0.417424i			0.0686241i	0.999411	+	0.0343121i	$0.0109240\pi$
$37$			0.417424i			0.0686241i	−0.999411	+	0.0343121i	$0.989076\pi$
$38$			11.5826i			1.87894i
$39$	4.37780			0.701009
$40$	1.73205	−	3.46410i	0.273861	−	0.547723i
$41$	6.92820			1.08200			0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820			1.08200			0.541002	+	0.841021i	$0.318045\pi$
$42$			9.58258i			1.47862i
$43$			0.913701i			0.139338i	0.997570	+	0.0696690i	$0.0221943\pi$
$43$			0.913701i			0.139338i	−0.997570	+	0.0696690i	$0.977806\pi$
$44$		0			0
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$	18.7864			2.76990
$47$		−	2.58258i		−	0.376707i	−0.982101	−	0.188354i	$-0.939685\pi$
$47$		−	2.58258i		−	0.376707i	0.982101	−	0.188354i	$-0.0603151\pi$
$48$		−	1.79129i		−	0.258550i
$49$	−12.1652			−1.73788
$50$	−8.75560	+	6.56670i	−1.23823	+	0.928672i
$51$	3.55945			0.498423
$52$			12.2197i			1.69457i
$53$		−	5.00000i		−	0.686803i	−0.939189	−	0.343401i	$-0.888421\pi$
$53$		−	5.00000i		−	0.686803i	0.939189	−	0.343401i	$-0.111579\pi$
$54$	2.18890			0.297872
$55$		0			0
$56$	−7.58258			−1.01326
$57$			5.29150i			0.700877i
$58$			2.00000i			0.262613i
$59$	−5.58258			−0.726789			−0.363395	−	0.931635i	$-0.618382\pi$
$59$	−5.58258			−0.726789			−0.363395	+	0.931635i	$0.618382\pi$
$60$	2.79129	−	5.58258i	0.360354	−	0.720707i
$61$	8.66025			1.10883			0.554416	−	0.832240i	$-0.312942\pi$
$61$	8.66025			1.10883			0.554416	+	0.832240i	$0.312942\pi$
$62$		−	14.4086i		−	1.82989i
$63$			4.37780i			0.551551i
$64$	12.5826			1.57282
$65$	4.37780	−	8.75560i	0.543000	−	1.08600i
$66$		0			0
$67$			12.7477i			1.55738i	0.627407	+	0.778691i	$0.284116\pi$
$67$			12.7477i			1.55738i	−0.627407	+	0.778691i	$0.715884\pi$
$68$			9.93545i			1.20485i
$69$	8.58258			1.03322
$70$	19.1652	+	9.58258i	2.29067	+	1.14534i
$71$	9.16515			1.08770			0.543852	−	0.839181i	$-0.316965\pi$
$71$	9.16515			1.08770			0.543852	+	0.839181i	$0.316965\pi$
$72$			1.73205i			0.204124i
$73$		−	5.10080i		−	0.597004i	−0.954409	−	0.298502i	$-0.903513\pi$
$73$		−	5.10080i		−	0.597004i	0.954409	−	0.298502i	$-0.0964869\pi$
$74$	−0.913701			−0.106216
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$	−14.7701			−1.69425
$77$		0			0
$78$			9.58258i			1.08501i
$79$	−2.64575			−0.297670			−0.148835	−	0.988862i	$-0.547552\pi$
$79$	−2.64575			−0.297670			−0.148835	+	0.988862i	$0.547552\pi$
$80$	−3.58258	−	1.79129i	−0.400544	−	0.200272i
$81$	1.00000			0.111111
$82$			15.1652i			1.67471i
$83$			1.63670i			0.179651i	0.995958	+	0.0898256i	$0.0286310\pi$
$83$			1.63670i			0.179651i	−0.995958	+	0.0898256i	$0.971369\pi$
$84$	−12.2197			−1.33328
$85$	3.55945	−	7.11890i	0.386077	−	0.772154i
$86$	−2.00000			−0.215666
$87$			0.913701i			0.0979590i
$88$		0			0
$89$	10.7477			1.13926			0.569628	−	0.821902i	$-0.307087\pi$
$89$	10.7477			1.13926			0.569628	+	0.821902i	$0.307087\pi$
$90$	2.18890	−	4.37780i	0.230730	−	0.461461i
$91$	−19.1652			−2.00905
$92$			23.9564i			2.49763i
$93$		−	6.58258i		−	0.682581i
$94$	5.65300			0.583063
$95$	10.5830	+	5.29150i	1.08579	+	0.542897i
$96$	7.38505			0.753734
$97$			5.58258i			0.566825i	0.958998	+	0.283412i	$0.0914665\pi$
$97$			5.58258i			0.566825i	−0.958998	+	0.283412i	$0.908534\pi$
$98$		−	26.6283i		−	2.68987i
$99$		0			0
$100$	−8.37386	−	11.1652i	−0.837386	−	1.11652i
$101$	−5.29150			−0.526524			−0.263262	−	0.964724i	$-0.584798\pi$
$101$	−5.29150			−0.526524			−0.263262	+	0.964724i	$0.584798\pi$
$102$			7.79129i			0.771452i
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	−7.58258			−0.743533
$105$	8.75560	+	4.37780i	0.854459	+	0.427230i
$106$	10.9445			1.06302
$107$		−	14.8655i		−	1.43710i	−0.695476	−	0.718549i	$-0.744807\pi$
$107$		−	14.8655i		−	1.43710i	0.695476	−	0.718549i	$-0.255193\pi$
$108$			2.79129i			0.268592i
$109$	−15.6838			−1.50224			−0.751118	−	0.660168i	$-0.770485\pi$
$109$	−15.6838			−1.50224			−0.751118	+	0.660168i	$0.770485\pi$
$110$		0			0
$111$	−0.417424			−0.0396202
$112$			7.84190i			0.740990i
$113$			3.00000i			0.282216i	0.989994	+	0.141108i	$0.0450665\pi$
$113$			3.00000i			0.282216i	−0.989994	+	0.141108i	$0.954933\pi$
$114$	−11.5826			−1.08481
$115$	8.58258	−	17.1652i	0.800329	−	1.60066i
$116$	−2.55040			−0.236799
$117$			4.37780i			0.404728i
$118$		−	12.2197i		−	1.12492i
$119$	−15.5826			−1.42845
$120$	3.46410	+	1.73205i	0.316228	+	0.158114i
$121$		0			0
$122$			18.9564i			1.71624i
$123$			6.92820i			0.624695i
$124$	18.3739			1.65002
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−9.58258			−0.853684
$127$			11.3060i			1.00325i	0.865086	+	0.501623i	$0.167263\pi$
$127$			11.3060i			1.00325i	−0.865086	+	0.501623i	$0.832737\pi$
$128$			12.7719i			1.12889i
$129$	−0.913701			−0.0804468
$130$	19.1652	+	9.58258i	1.68089	+	0.840447i
$131$	−8.75560			−0.764981			−0.382490	−	0.923959i	$-0.624933\pi$
$131$	−8.75560			−0.764981			−0.382490	+	0.923959i	$0.624933\pi$
$132$		0			0
$133$		−	23.1652i		−	2.00867i
$134$	−27.9035			−2.41050
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	−6.16515			−0.528657
$137$			14.1652i			1.21021i	0.796145	+	0.605105i	$0.206869\pi$
$137$			14.1652i			1.21021i	−0.796145	+	0.605105i	$0.793131\pi$
$138$			18.7864i			1.59921i
$139$	−6.30055			−0.534406			−0.267203	−	0.963640i	$-0.586099\pi$
$139$	−6.30055			−0.534406			−0.267203	+	0.963640i	$0.586099\pi$
$140$	−12.2197	+	24.4394i	−1.03275	+	2.06551i
$141$	2.58258			0.217492
$142$			20.0616i			1.68353i
$143$		0			0
$144$	1.79129			0.149274
$145$	1.82740	+	0.913701i	0.151757	+	0.0758787i
$146$	11.1652			0.924035
$147$		−	12.1652i		−	1.00336i
$148$		−	1.16515i		−	0.0957749i
$149$	9.47860			0.776518			0.388259	−	0.921550i	$-0.373077\pi$
$149$	9.47860			0.776518			0.388259	+	0.921550i	$0.373077\pi$
$150$	−6.56670	−	8.75560i	−0.536169	−	0.714892i
$151$	−21.7937			−1.77354			−0.886771	−	0.462208i	$-0.847057\pi$
$151$	−21.7937			−1.77354			−0.886771	+	0.462208i	$0.847057\pi$
$152$		−	9.16515i		−	0.743392i
$153$			3.55945i			0.287765i
$154$		0			0
$155$	−13.1652	−	6.58258i	−1.05745	−	0.528725i
$156$	−12.2197			−0.978359
$157$			21.5826i			1.72248i	0.508201	+	0.861239i	$0.330311\pi$
$157$			21.5826i			1.72248i	−0.508201	+	0.861239i	$0.669689\pi$
$158$		−	5.79129i		−	0.460730i
$159$	5.00000			0.396526
$160$	7.38505	−	14.7701i	0.583840	−	1.16768i
$161$	−37.5728			−2.96115
$162$			2.18890i			0.171976i
$163$		−	8.41742i		−	0.659304i	−0.944103	−	0.329652i	$-0.893069\pi$
$163$		−	8.41742i		−	0.659304i	0.944103	−	0.329652i	$-0.106931\pi$
$164$	−19.3386			−1.51009
$165$		0			0
$166$	−3.58258			−0.278062
$167$		−	2.45505i		−	0.189978i	−0.995478	−	0.0949888i	$-0.969718\pi$
$167$		−	2.45505i		−	0.189978i	0.995478	−	0.0949888i	$-0.0302815\pi$
$168$		−	7.58258i		−	0.585008i
$169$	−6.16515			−0.474242
$170$	15.5826	+	7.79129i	1.19513	+	0.597564i
$171$	−5.29150			−0.404651
$172$		−	2.55040i		−	0.194466i
$173$		−	5.10080i		−	0.387807i	−0.981021	−	0.193903i	$-0.937885\pi$
$173$		−	5.10080i		−	0.387807i	0.981021	−	0.193903i	$-0.0621148\pi$
$174$	−2.00000			−0.151620
$175$	17.5112	−	13.1334i	1.32372	−	0.992792i
$176$		0			0
$177$		−	5.58258i		−	0.419612i
$178$			23.5257i			1.76333i
$179$	−16.7477			−1.25178			−0.625892	−	0.779910i	$-0.715265\pi$
$179$	−16.7477			−1.25178			−0.625892	+	0.779910i	$0.715265\pi$
$180$	5.58258	+	2.79129i	0.416101	+	0.208050i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		−	41.9506i		−	3.10959i
$183$			8.66025i			0.640184i
$184$	−14.8655			−1.09590
$185$	−0.417424	+	0.834849i	−0.0306896	+	0.0613793i
$186$	14.4086			1.05649
$187$		0			0
$188$			7.20871i			0.525749i
$189$	−4.37780			−0.318438
$190$	−11.5826	+	23.1652i	−0.840288	+	1.68058i
$191$	25.9129			1.87499			0.937495	−	0.347999i	$-0.113139\pi$
$191$	25.9129			1.87499			0.937495	+	0.347999i	$0.113139\pi$
$192$			12.5826i			0.908069i
$193$		−	2.74110i		−	0.197309i	−0.995122	−	0.0986544i	$-0.968546\pi$
$193$		−	2.74110i		−	0.197309i	0.995122	−	0.0986544i	$-0.0314538\pi$
$194$	−12.2197			−0.877324
$195$	8.75560	+	4.37780i	0.627002	+	0.313501i
$196$	33.9564			2.42546
$197$			6.92820i			0.493614i	0.969065	+	0.246807i	$0.0793814\pi$
$197$			6.92820i			0.493614i	−0.969065	+	0.246807i	$0.920619\pi$
$198$		0			0
$199$	26.5826			1.88439			0.942194	−	0.335067i	$-0.108759\pi$
$199$	26.5826			1.88439			0.942194	+	0.335067i	$0.108759\pi$
$200$	6.92820	−	5.19615i	0.489898	−	0.367423i
$201$	−12.7477			−0.899155
$202$		−	11.5826i		−	0.814947i
$203$		−	4.00000i		−	0.280745i
$204$	−9.93545			−0.695621
$205$	13.8564	+	6.92820i	0.967773	+	0.483887i
$206$	13.1334			0.915048
$207$			8.58258i			0.596530i
$208$			7.84190i			0.543738i
$209$		0			0
$210$	−9.58258	+	19.1652i	−0.661261	+	1.32252i
$211$	−20.1570			−1.38766			−0.693831	−	0.720138i	$-0.744079\pi$
$211$	−20.1570			−1.38766			−0.693831	+	0.720138i	$0.744079\pi$
$212$			13.9564i			0.958532i
$213$			9.16515i			0.627986i
$214$	32.5390			2.22432
$215$	−0.913701	+	1.82740i	−0.0623139	+	0.124628i
$216$	−1.73205			−0.117851
$217$			28.8172i			1.95624i
$218$		−	34.3303i		−	2.32514i
$219$	5.10080			0.344680
$220$		0			0
$221$	−15.5826			−1.04820
$222$		−	0.913701i		−	0.0613236i
$223$		−	4.83485i		−	0.323765i	−0.986810	−	0.161883i	$-0.948243\pi$
$223$		−	4.83485i		−	0.323765i	0.986810	−	0.161883i	$-0.0517566\pi$
$224$	−32.3303			−2.16016
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	−6.56670			−0.436811
$227$			2.45505i			0.162947i	0.996675	+	0.0814737i	$0.0259627\pi$
$227$			2.45505i			0.162947i	−0.996675	+	0.0814737i	$0.974037\pi$
$228$		−	14.7701i		−	0.978174i
$229$	3.83485			0.253414			0.126707	−	0.991940i	$-0.459559\pi$
$229$	3.83485			0.253414			0.126707	+	0.991940i	$0.459559\pi$
$230$	37.5728	+	18.7864i	2.47748	+	1.23874i
$231$		0			0
$232$		−	1.58258i		−	0.103901i
$233$		−	21.0707i		−	1.38038i	−0.723626	−	0.690192i	$-0.757526\pi$
$233$		−	21.0707i		−	1.38038i	0.723626	−	0.690192i	$-0.242474\pi$
$234$	−9.58258			−0.626433
$235$	2.58258	−	5.16515i	0.168469	−	0.336937i
$236$	15.5826			1.01434
$237$		−	2.64575i		−	0.171860i
$238$		−	34.1087i		−	2.21094i
$239$	−0.723000			−0.0467670			−0.0233835	−	0.999727i	$-0.507444\pi$
$239$	−0.723000			−0.0467670			−0.0233835	+	0.999727i	$0.507444\pi$
$240$	1.79129	−	3.58258i	0.115627	−	0.231254i
$241$	24.7255			1.59271			0.796354	−	0.604831i	$-0.206760\pi$
$241$	24.7255			1.59271			0.796354	+	0.604831i	$0.206760\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	−24.1733			−1.54753
$245$	−24.3303	−	12.1652i	−1.55441	−	0.777203i
$246$	−15.1652			−0.966895
$247$		−	23.1652i		−	1.47396i
$248$			11.4014i			0.723987i
$249$	−1.63670			−0.103722
$250$	−24.0779	+	4.37780i	−1.52282	+	0.276877i
$251$	7.58258			0.478608			0.239304	−	0.970945i	$-0.423081\pi$
$251$	7.58258			0.478608			0.239304	+	0.970945i	$0.423081\pi$
$252$		−	12.2197i		−	0.769769i
$253$		0			0
$254$	−24.7477			−1.55281
$255$	7.11890	+	3.55945i	0.445803	+	0.222902i
$256$	−2.79129			−0.174455
$257$			13.0000i			0.810918i	0.914113	+	0.405459i	$0.132888\pi$
$257$			13.0000i			0.810918i	−0.914113	+	0.405459i	$0.867112\pi$
$258$		−	2.00000i		−	0.124515i
$259$	1.82740			0.113549
$260$	−12.2197	+	24.4394i	−0.757834	+	1.51567i
$261$	−0.913701			−0.0565566
$262$		−	19.1652i		−	1.18403i
$263$			4.47315i			0.275826i	0.990444	+	0.137913i	$0.0440395\pi$
$263$			4.47315i			0.275826i	−0.990444	+	0.137913i	$0.955961\pi$
$264$		0			0
$265$	5.00000	−	10.0000i	0.307148	−	0.614295i
$266$	50.7062			3.10900
$267$			10.7477i			0.657750i
$268$		−	35.5826i		−	2.17355i
$269$	−0.834849			−0.0509016			−0.0254508	−	0.999676i	$-0.508102\pi$
$269$	−0.834849			−0.0509016			−0.0254508	+	0.999676i	$0.508102\pi$
$270$	4.37780	+	2.18890i	0.266425	+	0.133212i
$271$	18.1389			1.10186			0.550929	−	0.834552i	$-0.314274\pi$
$271$	18.1389			1.10186			0.550929	+	0.834552i	$0.314274\pi$
$272$			6.37600i			0.386602i
$273$		−	19.1652i		−	1.15993i
$274$	−31.0061			−1.87315
$275$		0			0
$276$	−23.9564			−1.44201
$277$		−	15.4931i		−	0.930891i	−0.885077	−	0.465445i	$-0.845894\pi$
$277$		−	15.4931i		−	0.930891i	0.885077	−	0.465445i	$-0.154106\pi$
$278$		−	13.7913i		−	0.827146i
$279$	6.58258			0.394088
$280$	−15.1652	−	7.58258i	−0.906291	−	0.453146i
$281$	22.0797			1.31717			0.658583	−	0.752508i	$-0.271156\pi$
$281$	22.0797			1.31717			0.658583	+	0.752508i	$0.271156\pi$
$282$			5.65300i			0.336631i
$283$		−	18.9572i		−	1.12689i	−0.826154	−	0.563445i	$-0.809476\pi$
$283$		−	18.9572i		−	1.12689i	0.826154	−	0.563445i	$-0.190524\pi$
$284$	−25.5826			−1.51805
$285$	−5.29150	+	10.5830i	−0.313442	+	0.626883i
$286$		0			0
$287$		−	30.3303i		−	1.79034i
$288$			7.38505i			0.435168i
$289$	4.33030			0.254724
$290$	−2.00000	+	4.00000i	−0.117444	+	0.234888i
$291$	−5.58258			−0.327256
$292$			14.2378i			0.833205i
$293$		−	3.75015i		−	0.219086i	−0.993982	−	0.109543i	$-0.965061\pi$
$293$		−	3.75015i		−	0.219086i	0.993982	−	0.109543i	$-0.0349388\pi$
$294$	26.6283			1.55299
$295$	−11.1652	−	5.58258i	−0.650060	−	0.325030i
$296$	0.723000			0.0420235
$297$		0			0
$298$			20.7477i			1.20188i
$299$	−37.5728			−2.17289
$300$	11.1652	−	8.37386i	0.644620	−	0.483465i
$301$	4.00000			0.230556
$302$		−	47.7042i		−	2.74507i
$303$		−	5.29150i		−	0.303989i
$304$	−9.47860			−0.543635
$305$	17.3205	+	8.66025i	0.991769	+	0.495885i
$306$	−7.79129			−0.445398
$307$			6.92820i			0.395413i	0.980261	+	0.197707i	$0.0633494\pi$
$307$			6.92820i			0.395413i	−0.980261	+	0.197707i	$0.936651\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$	14.4086	−	28.8172i	0.818354	−	1.63671i
$311$	−6.41742			−0.363899			−0.181949	−	0.983308i	$-0.558241\pi$
$311$	−6.41742			−0.363899			−0.181949	+	0.983308i	$0.558241\pi$
$312$		−	7.58258i		−	0.429279i
$313$		−	2.41742i		−	0.136641i	−0.997663	−	0.0683205i	$-0.978236\pi$
$313$		−	2.41742i		−	0.136641i	0.997663	−	0.0683205i	$-0.0217640\pi$
$314$	−47.2421			−2.66603
$315$	−4.37780	+	8.75560i	−0.246661	+	0.493322i
$316$	7.38505			0.415442
$317$			26.1652i			1.46958i	0.678294	+	0.734791i	$0.262720\pi$
$317$			26.1652i			1.46958i	−0.678294	+	0.734791i	$0.737280\pi$
$318$			10.9445i			0.613737i
$319$		0			0
$320$	25.1652	+	12.5826i	1.40677	+	0.703387i
$321$	14.8655			0.829709
$322$		−	82.2432i		−	4.58323i
$323$		−	18.8348i		−	1.04800i
$324$	−2.79129			−0.155072
$325$	17.5112	−	13.1334i	0.971347	−	0.728510i
$326$	18.4249			1.02046
$327$		−	15.6838i		−	0.867317i
$328$		−	12.0000i		−	0.662589i
$329$	−11.3060			−0.623320
$330$		0			0
$331$	14.5826			0.801531			0.400765	−	0.916181i	$-0.368744\pi$
$331$	14.5826			0.801531			0.400765	+	0.916181i	$0.368744\pi$
$332$		−	4.56850i		−	0.250729i
$333$		−	0.417424i		−	0.0228747i
$334$	5.37386			0.294045
$335$	−12.7477	+	25.4955i	−0.696483	+	1.39297i
$336$	−7.84190			−0.427811
$337$			20.9753i			1.14260i	0.820742	+	0.571299i	$0.193560\pi$
$337$			20.9753i			1.14260i	−0.820742	+	0.571299i	$0.806440\pi$
$338$		−	13.4949i		−	0.734026i
$339$	−3.00000			−0.162938
$340$	−9.93545	+	19.8709i	−0.538826	+	1.07765i
$341$		0			0
$342$		−	11.5826i		−	0.626314i
$343$			22.6120i			1.22093i
$344$	1.58258			0.0853268
$345$	17.1652	+	8.58258i	0.924141	+	0.462070i
$346$	11.1652			0.600242
$347$			4.47315i			0.240131i	0.992766	+	0.120066i	$0.0383105\pi$
$347$			4.47315i			0.240131i	−0.992766	+	0.120066i	$0.961689\pi$
$348$		−	2.55040i		−	0.136716i
$349$	12.3151			0.659210			0.329605	−	0.944119i	$-0.393084\pi$
$349$	12.3151			0.659210			0.329605	+	0.944119i	$0.393084\pi$
$350$	28.7477	+	38.3303i	1.53663	+	2.04884i
$351$	−4.37780			−0.233670
$352$		0			0
$353$			21.3303i			1.13530i	0.823271	+	0.567649i	$0.192147\pi$
$353$			21.3303i			1.13530i	−0.823271	+	0.567649i	$0.807853\pi$
$354$	12.2197			0.649470
$355$	18.3303	+	9.16515i	0.972871	+	0.486436i
$356$	−30.0000			−1.59000
$357$		−	15.5826i		−	0.824717i
$358$		−	36.6591i		−	1.93749i
$359$	24.2487			1.27980			0.639899	−	0.768459i	$-0.278976\pi$
$359$	24.2487			1.27980			0.639899	+	0.768459i	$0.278976\pi$
$360$	−1.73205	+	3.46410i	−0.0912871	+	0.182574i
$361$	9.00000			0.473684
$362$		−	21.8890i		−	1.15046i
$363$		0			0
$364$	53.4955			2.80392
$365$	5.10080	−	10.2016i	0.266988	−	0.533976i
$366$	−18.9564			−0.990869
$367$			19.9129i			1.03944i	0.854336	+	0.519722i	$0.173964\pi$
$367$			19.9129i			1.03944i	−0.854336	+	0.519722i	$0.826036\pi$
$368$			15.3739i			0.801418i
$369$	−6.92820			−0.360668
$370$	−1.82740	−	0.913701i	−0.0950021	−	0.0475010i
$371$	−21.8890			−1.13642
$372$			18.3739i			0.952640i
$373$		−	28.0942i		−	1.45466i	−0.686286	−	0.727332i	$-0.740760\pi$
$373$		−	28.0942i		−	1.45466i	0.686286	−	0.727332i	$-0.259240\pi$
$374$		0			0
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$	−4.47315			−0.230685
$377$		−	4.00000i		−	0.206010i
$378$		−	9.58258i		−	0.492875i
$379$	2.58258			0.132658			0.0663290	−	0.997798i	$-0.478871\pi$
$379$	2.58258			0.132658			0.0663290	+	0.997798i	$0.478871\pi$
$380$	−29.5402	−	14.7701i	−1.51538	−	0.757691i
$381$	−11.3060			−0.579224
$382$			56.7207i			2.90208i
$383$			21.4955i			1.09837i	0.835702	+	0.549183i	$0.185061\pi$
$383$			21.4955i			1.09837i	−0.835702	+	0.549183i	$0.814939\pi$
$384$	−12.7719			−0.651764
$385$		0			0
$386$	6.00000			0.305392
$387$		−	0.913701i		−	0.0464460i
$388$		−	15.5826i		−	0.791085i
$389$	−1.58258			−0.0802398			−0.0401199	−	0.999195i	$-0.512774\pi$
$389$	−1.58258			−0.0802398			−0.0401199	+	0.999195i	$0.512774\pi$
$390$	−9.58258	+	19.1652i	−0.485233	+	0.970465i
$391$	−30.5493			−1.54494
$392$			21.0707i			1.06423i
$393$		−	8.75560i		−	0.441662i
$394$	−15.1652			−0.764009
$395$	−5.29150	−	2.64575i	−0.266244	−	0.133122i
$396$		0			0
$397$			2.00000i			0.100377i	0.998740	+	0.0501886i	$0.0159822\pi$
$397$			2.00000i			0.100377i	−0.998740	+	0.0501886i	$0.984018\pi$
$398$			58.1866i			2.91663i
$399$	23.1652			1.15971
$400$	−5.37386	−	7.16515i	−0.268693	−	0.358258i
$401$	−26.3303			−1.31487			−0.657436	−	0.753510i	$-0.728359\pi$
$401$	−26.3303			−1.31487			−0.657436	+	0.753510i	$0.728359\pi$
$402$		−	27.9035i		−	1.39170i
$403$			28.8172i			1.43549i
$404$	14.7701			0.734840
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$	8.75560			0.434533
$407$		0			0
$408$		−	6.16515i		−	0.305220i
$409$	13.9518			0.689870			0.344935	−	0.938627i	$-0.387901\pi$
$409$	13.9518			0.689870			0.344935	+	0.938627i	$0.387901\pi$
$410$	−15.1652	+	30.3303i	−0.748953	+	1.49791i
$411$	−14.1652			−0.698715
$412$			16.7477i			0.825101i
$413$			24.4394i			1.20258i
$414$	−18.7864			−0.923302
$415$	−1.63670	+	3.27340i	−0.0803425	+	0.160685i
$416$	−32.3303			−1.58512
$417$		−	6.30055i		−	0.308539i
$418$		0			0
$419$	4.33030			0.211549			0.105775	−	0.994390i	$-0.466268\pi$
$419$	4.33030			0.211549			0.105775	+	0.994390i	$0.466268\pi$
$420$	−24.4394	−	12.2197i	−1.19252	−	0.596261i
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$		−	44.1216i		−	2.14781i
$423$			2.58258i			0.125569i
$424$	−8.66025			−0.420579
$425$	14.2378	−	10.6784i	0.690635	−	0.517976i
$426$	−20.0616			−0.971988
$427$		−	37.9129i		−	1.83473i
$428$			41.4938i			2.00568i
$429$		0			0
$430$	−4.00000	−	2.00000i	−0.192897	−	0.0964486i
$431$	15.1515			0.729822			0.364911	−	0.931042i	$-0.381099\pi$
$431$	15.1515			0.729822			0.364911	+	0.931042i	$0.381099\pi$
$432$			1.79129i			0.0861834i
$433$			12.7477i			0.612617i	0.951932	+	0.306308i	$0.0990939\pi$
$433$			12.7477i			0.612617i	−0.951932	+	0.306308i	$0.900906\pi$
$434$	−63.0780			−3.02784
$435$	−0.913701	+	1.82740i	−0.0438086	+	0.0876172i
$436$	43.7780			2.09659
$437$		−	45.4147i		−	2.17248i
$438$			11.1652i			0.533492i
$439$	−11.4014			−0.544157			−0.272079	−	0.962275i	$-0.587711\pi$
$439$	−11.4014			−0.544157			−0.272079	+	0.962275i	$0.587711\pi$
$440$		0			0
$441$	12.1652			0.579293
$442$		−	34.1087i		−	1.62239i
$443$		−	36.0000i		−	1.71041i	−0.518289	−	0.855206i	$-0.673431\pi$
$443$		−	36.0000i		−	1.71041i	0.518289	−	0.855206i	$-0.326569\pi$
$444$	1.16515			0.0552956
$445$	21.4955	+	10.7477i	1.01898	+	0.509491i
$446$	10.5830			0.501120
$447$			9.47860i			0.448323i
$448$		−	55.0840i		−	2.60248i
$449$	21.1652			0.998845			0.499423	−	0.866358i	$-0.333546\pi$
$449$	21.1652			0.998845			0.499423	+	0.866358i	$0.333546\pi$
$450$	8.75560	−	6.56670i	0.412743	−	0.309557i
$451$		0			0
$452$		−	8.37386i		−	0.393873i
$453$		−	21.7937i		−	1.02396i
$454$	−5.37386			−0.252208
$455$	−38.3303	−	19.1652i	−1.79695	−	0.898476i
$456$	9.16515			0.429198
$457$			33.5764i			1.57064i	0.619091	+	0.785319i	$0.287501\pi$
$457$			33.5764i			1.57064i	−0.619091	+	0.785319i	$0.712499\pi$
$458$			8.39410i			0.392231i
$459$	−3.55945			−0.166141
$460$	−23.9564	+	47.9129i	−1.11697	+	2.23395i
$461$	7.65120			0.356352			0.178176	−	0.983999i	$-0.442980\pi$
$461$	7.65120			0.356352			0.178176	+	0.983999i	$0.442980\pi$
$462$		0			0
$463$		−	4.00000i		−	0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	−1.63670			−0.0759819
$465$	6.58258	−	13.1652i	0.305260	−	0.610519i
$466$	46.1216			2.13654
$467$		−	13.7477i		−	0.636169i	−0.948062	−	0.318084i	$-0.896960\pi$
$467$		−	13.7477i		−	0.636169i	0.948062	−	0.318084i	$-0.103040\pi$
$468$		−	12.2197i		−	0.564856i
$469$	55.8070			2.57693
$470$	11.3060	+	5.65300i	0.521507	+	0.260754i
$471$	−21.5826			−0.994473
$472$			9.66930i			0.445066i
$473$		0			0
$474$	5.79129			0.266003
$475$	15.8745	+	21.1660i	0.728372	+	0.971163i
$476$	43.4955			1.99361
$477$			5.00000i			0.228934i
$478$		−	1.58258i		−	0.0723853i
$479$	40.8462			1.86631			0.933156	−	0.359472i	$-0.117043\pi$
$479$	40.8462			1.86631			0.933156	+	0.359472i	$0.117043\pi$
$480$	14.7701	+	7.38505i	0.674160	+	0.337080i
$481$	1.82740			0.0833223
$482$			54.1216i			2.46517i
$483$		−	37.5728i		−	1.70962i
$484$		0			0
$485$	−5.58258	+	11.1652i	−0.253492	+	0.506983i
$486$	−2.18890			−0.0992906
$487$		−	23.9129i		−	1.08360i	−0.840509	−	0.541798i	$-0.817744\pi$
$487$		−	23.9129i		−	1.08360i	0.840509	−	0.541798i	$-0.182256\pi$
$488$		−	15.0000i		−	0.679018i
$489$	8.41742			0.380649
$490$	26.6283	−	53.2566i	1.20294	−	2.40589i
$491$	−22.8027			−1.02907			−0.514536	−	0.857469i	$-0.672036\pi$
$491$	−22.8027			−1.02907			−0.514536	+	0.857469i	$0.672036\pi$
$492$		−	19.3386i		−	0.871852i
$493$		−	3.25227i		−	0.146475i
$494$	50.7062			2.28138
$495$		0			0
$496$	11.7913			0.529444
$497$		−	40.1232i		−	1.79977i
$498$		−	3.58258i		−	0.160539i
$499$	−24.0000			−1.07439			−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000			−1.07439			−0.537194	+	0.843459i	$0.680516\pi$
$500$	−5.58258	−	30.7042i	−0.249660	−	1.37313i
$501$	2.45505			0.109684
$502$			16.5975i			0.740783i
$503$		−	19.7756i		−	0.881749i	−0.897569	−	0.440874i	$-0.854668\pi$
$503$		−	19.7756i		−	0.881749i	0.897569	−	0.440874i	$-0.145332\pi$
$504$	7.58258			0.337755
$505$	−10.5830	−	5.29150i	−0.470938	−	0.235469i
$506$		0			0
$507$		−	6.16515i		−	0.273804i
$508$		−	31.5583i		−	1.40017i
$509$	41.9129			1.85776			0.928878	−	0.370386i	$-0.120775\pi$
$509$	41.9129			1.85776			0.928878	+	0.370386i	$0.120775\pi$
$510$	−7.79129	+	15.5826i	−0.345004	+	0.690008i
$511$	−22.3303			−0.987834
$512$			19.4340i			0.858868i
$513$		−	5.29150i		−	0.233626i
$514$	−28.4557			−1.25513
$515$	6.00000	−	12.0000i	0.264392	−	0.528783i
$516$	2.55040			0.112275
$517$		0			0
$518$			4.00000i			0.175750i
$519$	5.10080			0.223900
$520$	−15.1652	−	7.58258i	−0.665036	−	0.332518i
$521$	35.5826			1.55890			0.779450	−	0.626464i	$-0.215498\pi$
$521$	35.5826			1.55890			0.779450	+	0.626464i	$0.215498\pi$
$522$		−	2.00000i		−	0.0875376i
$523$			11.1153i			0.486038i	0.970021	+	0.243019i	$0.0781378\pi$
$523$			11.1153i			0.486038i	−0.970021	+	0.243019i	$0.921862\pi$
$524$	24.4394			1.06764
$525$	13.1334	+	17.5112i	0.573189	+	0.764252i
$526$	−9.79129			−0.426920
$527$			23.4304i			1.02064i
$528$		0			0
$529$	−50.6606			−2.20264
$530$	21.8890	+	10.9445i	0.950798	+	0.475399i
$531$	5.58258			0.242263
$532$			64.6606i			2.80339i
$533$		−	30.3303i		−	1.31375i
$534$	−23.5257			−1.01806
$535$	14.8655	−	29.7309i	0.642690	−	1.28538i
$536$	22.0797			0.953698
$537$		−	16.7477i		−	0.722718i
$538$		−	1.82740i		−	0.0787849i
$539$		0			0
$540$	−2.79129	+	5.58258i	−0.120118	+	0.240236i
$541$	−17.1298			−0.736468			−0.368234	−	0.929733i	$-0.620037\pi$
$541$	−17.1298			−0.736468			−0.368234	+	0.929733i	$0.620037\pi$
$542$			39.7042i			1.70544i
$543$		−	10.0000i		−	0.429141i
$544$	−26.2867			−1.12703
$545$	−31.3676	−	15.6838i	−1.34364	−	0.671820i
$546$	41.9506			1.79532
$547$		−	18.2342i		−	0.779638i	−0.920891	−	0.389819i	$-0.872537\pi$
$547$		−	18.2342i		−	0.779638i	0.920891	−	0.389819i	$-0.127463\pi$
$548$		−	39.5390i		−	1.68902i
$549$	−8.66025			−0.369611
$550$		0			0
$551$	4.83485			0.205971
$552$		−	14.8655i		−	0.632716i
$553$			11.5826i			0.492541i
$554$	33.9129			1.44082
$555$	−0.834849	−	0.417424i	−0.0354373	−	0.0177187i
$556$	17.5867			0.745840
$557$			3.36875i			0.142739i	0.997450	+	0.0713693i	$0.0227369\pi$
$557$			3.36875i			0.142739i	−0.997450	+	0.0713693i	$0.977263\pi$
$558$			14.4086i			0.609965i
$559$	4.00000			0.169182
$560$	−7.84190	+	15.6838i	−0.331381	+	0.662762i
$561$		0			0
$562$			48.3303i			2.03869i
$563$			4.91010i			0.206936i	0.994633	+	0.103468i	$0.0329940\pi$
$563$			4.91010i			0.206936i	−0.994633	+	0.103468i	$0.967006\pi$
$564$	−7.20871			−0.303542
$565$	−3.00000	+	6.00000i	−0.126211	+	0.252422i
$566$	41.4955			1.74418
$567$		−	4.37780i		−	0.183850i
$568$		−	15.8745i		−	0.666080i
$569$	−7.84190			−0.328750			−0.164375	−	0.986398i	$-0.552561\pi$
$569$	−7.84190			−0.328750			−0.164375	+	0.986398i	$0.552561\pi$
$570$	−23.1652	−	11.5826i	−0.970281	−	0.485141i
$571$	7.55585			0.316203			0.158101	−	0.987423i	$-0.449463\pi$
$571$	7.55585			0.316203			0.158101	+	0.987423i	$0.449463\pi$
$572$		0			0
$573$			25.9129i			1.08253i
$574$	66.3900			2.77107
$575$	34.3303	−	25.7477i	1.43167	−	1.07375i
$576$	−12.5826			−0.524274
$577$			24.0000i			0.999133i	0.866276	+	0.499567i	$0.166507\pi$
$577$			24.0000i			0.999133i	−0.866276	+	0.499567i	$0.833493\pi$
$578$			9.47860i			0.394258i
$579$	2.74110			0.113916
$580$	−5.10080	−	2.55040i	−0.211799	−	0.105900i
$581$	7.16515			0.297261
$582$		−	12.2197i		−	0.506523i
$583$		0			0
$584$	−8.83485			−0.365589
$585$	−4.37780	+	8.75560i	−0.181000	+	0.362000i
$586$	8.20871			0.339099
$587$		−	31.7477i		−	1.31037i	−0.755469	−	0.655184i	$-0.772591\pi$
$587$		−	31.7477i		−	1.31037i	0.755469	−	0.655184i	$-0.227409\pi$
$588$			33.9564i			1.40034i
$589$	−34.8317			−1.43522
$590$	12.2197	−	24.4394i	0.503077	−	1.00615i
$591$	−6.92820			−0.284988
$592$		−	0.747727i		−	0.0307314i
$593$			3.65480i			0.150085i	0.997180	+	0.0750424i	$0.0239092\pi$
$593$			3.65480i			0.150085i	−0.997180	+	0.0750424i	$0.976091\pi$
$594$		0			0
$595$	−31.1652	−	15.5826i	−1.27765	−	0.638823i
$596$	−26.4575			−1.08374
$597$			26.5826i			1.08795i
$598$		−	82.2432i		−	3.36317i
$599$	13.9129			0.568465			0.284232	−	0.958755i	$-0.408261\pi$
$599$	13.9129			0.568465			0.284232	+	0.958755i	$0.408261\pi$
$600$	5.19615	+	6.92820i	0.212132	+	0.282843i
$601$	−3.65480			−0.149082			−0.0745412	−	0.997218i	$-0.523749\pi$
$601$	−3.65480			−0.149082			−0.0745412	+	0.997218i	$0.523749\pi$
$602$			8.75560i			0.356852i
$603$		−	12.7477i		−	0.519128i
$604$	60.8324			2.47523
$605$		0			0
$606$	11.5826			0.470510
$607$		−	44.6917i		−	1.81398i	−0.421151	−	0.906991i	$-0.638374\pi$
$607$		−	44.6917i		−	1.81398i	0.421151	−	0.906991i	$-0.361626\pi$
$608$		−	39.0780i		−	1.58482i
$609$	4.00000			0.162088
$610$	−18.9564	+	37.9129i	−0.767524	+	1.53505i
$611$	−11.3060			−0.457392
$612$		−	9.93545i		−	0.401617i
$613$			33.1950i			1.34073i	0.742030	+	0.670367i	$0.233863\pi$
$613$			33.1950i			1.34073i	−0.742030	+	0.670367i	$0.766137\pi$
$614$	−15.1652			−0.612016
$615$	−6.92820	+	13.8564i	−0.279372	+	0.558744i
$616$		0			0
$617$		−	19.4955i		−	0.784857i	−0.919782	−	0.392429i	$-0.871635\pi$
$617$		−	19.4955i		−	0.784857i	0.919782	−	0.392429i	$-0.128365\pi$
$618$			13.1334i			0.528303i
$619$	−45.4955			−1.82862			−0.914308	−	0.405019i	$-0.867265\pi$
$619$	−45.4955			−1.82862			−0.914308	+	0.405019i	$0.867265\pi$
$620$	36.7477	+	18.3739i	1.47582	+	0.737912i
$621$	−8.58258			−0.344407
$622$		−	14.0471i		−	0.563238i
$623$		−	47.0514i		−	1.88508i
$624$	−7.84190			−0.313927
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	5.29150			0.211491
$627$		0			0
$628$		−	60.2432i		−	2.40396i
$629$	1.48580			0.0592428
$630$	−19.1652	−	9.58258i	−0.763558	−	0.381779i
$631$	−11.4174			−0.454520			−0.227260	−	0.973834i	$-0.572977\pi$
$631$	−11.4174			−0.454520			−0.227260	+	0.973834i	$0.572977\pi$
$632$			4.58258i			0.182285i
$633$		−	20.1570i		−	0.801167i
$634$	−57.2729			−2.27460
$635$	−11.3060	+	22.6120i	−0.448665	+	0.897330i
$636$	−13.9564			−0.553409
$637$			53.2566i			2.11010i
$638$		0			0
$639$	−9.16515			−0.362568
$640$	−12.7719	+	25.5438i	−0.504854	+	1.00971i
$641$	14.4174			0.569454			0.284727	−	0.958609i	$-0.408097\pi$
$641$	14.4174			0.569454			0.284727	+	0.958609i	$0.408097\pi$
$642$			32.5390i			1.28421i
$643$			18.3303i			0.722877i	0.932396	+	0.361438i	$0.117714\pi$
$643$			18.3303i			0.722877i	−0.932396	+	0.361438i	$0.882286\pi$
$644$	104.877			4.13272
$645$	−1.82740	−	0.913701i	−0.0719538	−	0.0359769i
$646$	41.2276			1.62208
$647$		−	23.4174i		−	0.920634i	−0.887755	−	0.460317i	$-0.847736\pi$
$647$		−	23.4174i		−	0.920634i	0.887755	−	0.460317i	$-0.152264\pi$
$648$		−	1.73205i		−	0.0680414i
$649$		0			0
$650$	28.7477	+	38.3303i	1.12758	+	1.50344i
$651$	−28.8172			−1.12944
$652$			23.4955i			0.920153i
$653$		−	28.3303i		−	1.10865i	−0.832300	−	0.554325i	$-0.812976\pi$
$653$		−	28.3303i		−	1.10865i	0.832300	−	0.554325i	$-0.187024\pi$
$654$	34.3303			1.34242
$655$	−17.5112	−	8.75560i	−0.684220	−	0.342110i
$656$	−12.4104			−0.484545
$657$			5.10080i			0.199001i
$658$		−	24.7477i		−	0.964767i
$659$	11.6874			0.455277			0.227638	−	0.973746i	$-0.426900\pi$
$659$	11.6874			0.455277			0.227638	+	0.973746i	$0.426900\pi$
$660$		0			0
$661$	−2.83485			−0.110263			−0.0551314	−	0.998479i	$-0.517558\pi$
$661$	−2.83485			−0.110263			−0.0551314	+	0.998479i	$0.517558\pi$
$662$			31.9198i			1.24060i
$663$		−	15.5826i		−	0.605177i
$664$	2.83485			0.110013
$665$	23.1652	−	46.3303i	0.898306	−	1.79661i
$666$	0.913701			0.0354052
$667$		−	7.84190i		−	0.303640i
$668$			6.85275i			0.265141i
$669$	4.83485			0.186926
$670$	−55.8070	−	27.9035i	−2.15601	−	1.07801i
$671$		0			0
$672$		−	32.3303i		−	1.24717i
$673$			44.5010i			1.71539i	0.514160	+	0.857694i	$0.328104\pi$
$673$			44.5010i			1.71539i	−0.514160	+	0.857694i	$0.671896\pi$
$674$	−45.9129			−1.76850
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	17.2087			0.661874
$677$			15.6838i			0.602778i	0.953501	+	0.301389i	$0.0974502\pi$
$677$			15.6838i			0.602778i	−0.953501	+	0.301389i	$0.902550\pi$
$678$		−	6.56670i		−	0.252193i
$679$	24.4394			0.937899
$680$	−12.3303	−	6.16515i	−0.472846	−	0.236423i
$681$	−2.45505			−0.0940778
$682$		0			0
$683$			26.3303i			1.00750i	0.863849	+	0.503751i	$0.168047\pi$
$683$			26.3303i			1.00750i	−0.863849	+	0.503751i	$0.831953\pi$
$684$	14.7701			0.564749
$685$	−14.1652	+	28.3303i	−0.541223	+	1.08245i
$686$	−49.4955			−1.88975
$687$			3.83485i			0.146309i
$688$		−	1.63670i		−	0.0623986i
$689$	−21.8890			−0.833905
$690$	−18.7864	+	37.5728i	−0.715186	+	1.43037i
$691$	−30.5826			−1.16342			−0.581708	−	0.813398i	$-0.697615\pi$
$691$	−30.5826			−1.16342			−0.581708	+	0.813398i	$0.697615\pi$
$692$			14.2378i			0.541240i
$693$		0			0
$694$	−9.79129			−0.371672
$695$	−12.6011	−	6.30055i	−0.477987	−	0.238994i
$696$	1.58258			0.0599874
$697$		−	24.6606i		−	0.934087i
$698$			26.9564i			1.02032i
$699$	21.0707			0.796966
$700$	−48.8788	+	36.6591i	−1.84745	+	1.38558i
$701$	−1.29510			−0.0489153			−0.0244577	−	0.999701i	$-0.507786\pi$
$701$	−1.29510			−0.0489153			−0.0244577	+	0.999701i	$0.507786\pi$
$702$		−	9.58258i		−	0.361671i
$703$			2.20880i			0.0833065i
$704$		0			0
$705$	5.16515	+	2.58258i	0.194531	+	0.0972654i
$706$	−46.6899			−1.75720
$707$			23.1652i			0.871215i
$708$			15.5826i			0.585629i
$709$	−11.0000			−0.413114			−0.206557	−	0.978435i	$-0.566226\pi$
$709$	−11.0000			−0.413114			−0.206557	+	0.978435i	$0.566226\pi$
$710$	−20.0616	+	40.1232i	−0.752899	+	1.50580i
$711$	2.64575			0.0992234
$712$		−	18.6156i		−	0.697649i
$713$			56.4955i			2.11577i
$714$	34.1087			1.27649
$715$		0			0
$716$	46.7477			1.74704
$717$		−	0.723000i		−	0.0270009i
$718$			53.0780i			1.98085i
$719$	−9.49545			−0.354121			−0.177060	−	0.984200i	$-0.556659\pi$
$719$	−9.49545			−0.354121			−0.177060	+	0.984200i	$0.556659\pi$
$720$	3.58258	+	1.79129i	0.133515	+	0.0667574i
$721$	−26.2668			−0.978227
$722$			19.7001i			0.733162i
$723$			24.7255i			0.919550i
$724$	27.9129			1.03737
$725$	2.74110	+	3.65480i	0.101802	+	0.135736i
$726$		0			0
$727$			31.4955i			1.16810i	0.811717	+	0.584051i	$0.198533\pi$
$727$			31.4955i			1.16810i	−0.811717	+	0.584051i	$0.801467\pi$
$728$			33.1950i			1.23029i
$729$	−1.00000			−0.0370370
$730$	22.3303	+	11.1652i	0.826482	+	0.413241i
$731$	3.25227			0.120290
$732$		−	24.1733i		−	0.893469i
$733$			24.6301i			0.909734i	0.890559	+	0.454867i	$0.150313\pi$
$733$			24.6301i			0.909734i	−0.890559	+	0.454867i	$0.849687\pi$
$734$	−43.5873			−1.60884
$735$	12.1652	−	24.3303i	0.448718	−	0.897437i
$736$	−63.3828			−2.33632
$737$		0			0
$738$		−	15.1652i		−	0.558237i
$739$	23.4304			0.861900			0.430950	−	0.902376i	$-0.358179\pi$
$739$	23.4304			0.861900			0.430950	+	0.902376i	$0.358179\pi$
$740$	1.16515	−	2.33030i	0.0428318	−	0.0856636i
$741$	23.1652			0.850993
$742$		−	47.9129i		−	1.75894i
$743$			48.0605i			1.76317i	0.472027	+	0.881584i	$0.343522\pi$
$743$			48.0605i			1.76317i	−0.472027	+	0.881584i	$0.656478\pi$
$744$	−11.4014			−0.417994
$745$	18.9572	+	9.47860i	0.694538	+	0.347269i
$746$	61.4955			2.25151
$747$		−	1.63670i		−	0.0598837i
$748$		0			0
$749$	−65.0780			−2.37790
$750$	−4.37780	−	24.0779i	−0.159855	−	0.879201i
$751$	15.7477			0.574643			0.287321	−	0.957834i	$-0.407235\pi$
$751$	15.7477			0.574643			0.287321	+	0.957834i	$0.407235\pi$
$752$			4.62614i			0.168698i
$753$			7.58258i			0.276324i
$754$	8.75560			0.318860
$755$	−43.5873	−	21.7937i	−1.58631	−	0.793153i
$756$	12.2197			0.444426
$757$		−	21.4955i		−	0.781266i	−0.920547	−	0.390633i	$-0.872256\pi$
$757$		−	21.4955i		−	0.781266i	0.920547	−	0.390633i	$-0.127744\pi$
$758$			5.65300i			0.205326i
$759$		0			0
$760$	9.16515	−	18.3303i	0.332455	−	0.664910i
$761$	−31.0260			−1.12469			−0.562346	−	0.826902i	$-0.690101\pi$
$761$	−31.0260			−1.12469			−0.562346	+	0.826902i	$0.690101\pi$
$762$		−	24.7477i		−	0.896516i
$763$			68.6606i			2.48568i
$764$	−72.3303			−2.61682
$765$	−3.55945	+	7.11890i	−0.128692	+	0.257385i
$766$	−47.0514			−1.70004
$767$			24.4394i			0.882456i
$768$		−	2.79129i		−	0.100722i
$769$	−19.4340			−0.700807			−0.350403	−	0.936599i	$-0.613955\pi$
$769$	−19.4340			−0.700807			−0.350403	+	0.936599i	$0.613955\pi$
$770$		0			0
$771$	−13.0000			−0.468184
$772$			7.65120i			0.275373i
$773$			12.1652i			0.437550i	0.975775	+	0.218775i	$0.0702061\pi$
$773$			12.1652i			0.437550i	−0.975775	+	0.218775i	$0.929794\pi$
$774$	2.00000			0.0718885
$775$	−19.7477	−	26.3303i	−0.709359	−	0.945812i
$776$	9.66930			0.347108
$777$			1.82740i			0.0655576i
$778$		−	3.46410i		−	0.124194i
$779$	36.6606			1.31350
$780$	−24.4394	−	12.2197i	−0.875071	−	0.437536i
$781$		0			0
$782$		−	66.8693i		−	2.39124i
$783$		−	0.913701i		−	0.0326530i
$784$	21.7913			0.778260
$785$	−21.5826	+	43.1652i	−0.770315	+	1.54063i
$786$	19.1652			0.683598
$787$			36.2777i			1.29316i	0.762846	+	0.646580i	$0.223802\pi$
$787$			36.2777i			1.29316i	−0.762846	+	0.646580i	$0.776198\pi$
$788$		−	19.3386i		−	0.688909i
$789$	−4.47315			−0.159248
$790$	5.79129	−	11.5826i	0.206045	−	0.412090i
$791$	13.1334			0.466970
$792$		0			0
$793$		−	37.9129i		−	1.34633i
$794$	−4.37780			−0.155362
$795$	10.0000	+	5.00000i	0.354663	+	0.177332i
$796$	−74.1996			−2.62994
$797$			9.16515i			0.324646i	0.986738	+	0.162323i	$0.0518987\pi$
$797$			9.16515i			0.324646i	−0.986738	+	0.162323i	$0.948101\pi$
$798$			50.7062i			1.79498i
$799$	−9.19255			−0.325209
$800$	29.5402	−	22.1552i	1.04440	−	0.783303i
$801$	−10.7477			−0.379752
$802$		−	57.6344i		−	2.03514i
$803$		0			0
$804$	35.5826			1.25490
$805$	−75.1456	−	37.5728i	−2.64854	−	1.32427i
$806$	−63.0780			−2.22183
$807$		−	0.834849i		−	0.0293881i
$808$			9.16515i			0.322429i
$809$	−47.4328			−1.66765			−0.833825	−	0.552029i	$-0.813854\pi$
$809$	−47.4328			−1.66765			−0.833825	+	0.552029i	$0.813854\pi$
$810$	−2.18890	+	4.37780i	−0.0769101	+	0.153820i
$811$	−46.2331			−1.62346			−0.811731	−	0.584031i	$-0.801475\pi$
$811$	−46.2331			−1.62346			−0.811731	+	0.584031i	$0.801475\pi$
$812$			11.1652i			0.391820i
$813$			18.1389i			0.636158i
$814$		0			0
$815$	8.41742	−	16.8348i	0.294850	−	0.589699i
$816$	−6.37600			−0.223205
$817$			4.83485i			0.169150i
$818$			30.5390i			1.06777i
$819$	19.1652			0.669685
$820$	−38.6772	−	19.3386i	−1.35067	−	0.675334i
$821$	−22.6120			−0.789165			−0.394582	−	0.918861i	$-0.629111\pi$
$821$	−22.6120			−0.789165			−0.394582	+	0.918861i	$0.629111\pi$
$822$		−	31.0061i		−	1.08146i
$823$		−	23.1652i		−	0.807486i	−0.914872	−	0.403743i	$-0.867709\pi$
$823$		−	23.1652i		−	0.807486i	0.914872	−	0.403743i	$-0.132291\pi$
$824$	−10.3923			−0.362033
$825$		0			0
$826$	−53.4955			−1.86134
$827$			31.5583i			1.09739i	0.836023	+	0.548695i	$0.184875\pi$
$827$			31.5583i			1.09739i	−0.836023	+	0.548695i	$0.815125\pi$
$828$		−	23.9564i		−	0.832544i
$829$	8.16515			0.283587			0.141794	−	0.989896i	$-0.454713\pi$
$829$	8.16515			0.283587			0.141794	+	0.989896i	$0.454713\pi$
$830$	−7.16515	−	3.58258i	−0.248706	−	0.124353i
$831$	15.4931			0.537450
$832$		−	55.0840i		−	1.90970i
$833$			43.3013i			1.50030i
$834$	13.7913			0.477553
$835$	2.45505	−	4.91010i	0.0849605	−	0.169921i
$836$		0			0
$837$			6.58258i			0.227527i
$838$			9.47860i			0.327433i
$839$	−17.1652			−0.592607			−0.296303	−	0.955094i	$-0.595754\pi$
$839$	−17.1652			−0.592607			−0.296303	+	0.955094i	$0.595754\pi$
$840$	7.58258	−	15.1652i	0.261624	−	0.523247i
$841$	−28.1652			−0.971212
$842$		−	2.18890i		−	0.0754345i
$843$			22.0797i			0.760466i
$844$	56.2639			1.93668
$845$	−12.3303	−	6.16515i	−0.424175	−	0.212088i
$846$	−5.65300			−0.194354
$847$		0			0
$848$			8.95644i			0.307565i
$849$	18.9572			0.650610
$850$	23.3739	+	31.1652i	0.801717	+	1.06896i
$851$	3.58258			0.122809
$852$		−	25.5826i		−	0.876445i
$853$		−	38.6772i		−	1.32428i	−0.749379	−	0.662141i	$-0.769648\pi$
$853$		−	38.6772i		−	1.32428i	0.749379	−	0.662141i	$-0.230352\pi$
$854$	82.9875			2.83978
$855$	−10.5830	−	5.29150i	−0.361931	−	0.180966i
$856$	−25.7477			−0.880039
$857$		−	15.7792i		−	0.539006i	−0.963000	−	0.269503i	$-0.913141\pi$
$857$		−	15.7792i		−	0.539006i	0.963000	−	0.269503i	$-0.0868594\pi$
$858$		0			0
$859$	−10.3303			−0.352465			−0.176233	−	0.984349i	$-0.556391\pi$
$859$	−10.3303			−0.352465			−0.176233	+	0.984349i	$0.556391\pi$
$860$	2.55040	−	5.10080i	0.0869680	−	0.173936i
$861$	30.3303			1.03365
$862$			33.1652i			1.12961i
$863$		−	18.3303i		−	0.623971i	−0.950087	−	0.311985i	$-0.899006\pi$
$863$		−	18.3303i		−	0.623971i	0.950087	−	0.311985i	$-0.100994\pi$
$864$	−7.38505			−0.251245
$865$	5.10080	−	10.2016i	0.173432	−	0.346865i
$866$	−27.9035			−0.948200
$867$			4.33030i			0.147065i
$868$		−	80.4371i		−	2.73021i
$869$		0			0
$870$	−4.00000	−	2.00000i	−0.135613	−	0.0678064i
$871$	55.8070			1.89095
$872$			27.1652i			0.919928i
$873$		−	5.58258i		−	0.188942i
$874$	99.4083			3.36254
$875$	48.1558	−	8.75560i	1.62796	−	0.295993i
$876$	−14.2378			−0.481051
$877$			17.7019i			0.597751i	0.954292	+	0.298875i	$0.0966115\pi$
$877$			17.7019i			0.597751i	−0.954292	+	0.298875i	$0.903388\pi$
$878$		−	24.9564i		−	0.842239i
$879$	3.75015			0.126489
$880$		0			0
$881$	51.4955			1.73493			0.867463	−	0.497502i	$-0.165749\pi$
$881$	51.4955			1.73493			0.867463	+	0.497502i	$0.165749\pi$
$882$			26.6283i			0.896622i
$883$			5.25227i			0.176753i	0.996087	+	0.0883765i	$0.0281679\pi$
$883$			5.25227i			0.176753i	−0.996087	+	0.0883765i	$0.971832\pi$
$884$	43.4955			1.46291
$885$	5.58258	−	11.1652i	0.187656	−	0.375312i
$886$	78.8004			2.64735
$887$			5.67290i			0.190477i	0.995454	+	0.0952387i	$0.0303614\pi$
$887$			5.67290i			0.190477i	−0.995454	+	0.0952387i	$0.969639\pi$
$888$			0.723000i			0.0242623i
$889$	49.4955			1.66002
$890$	−23.5257	+	47.0514i	−0.788584	+	1.57717i
$891$		0			0
$892$			13.4955i			0.451861i
$893$		−	13.6657i		−	0.457305i
$894$	−20.7477			−0.693908
$895$	−33.4955	−	16.7477i	−1.11963	−	0.559815i
$896$	55.9129			1.86792
$897$		−	37.5728i		−	1.25452i
$898$			46.3284i			1.54600i
$899$	−6.01450			−0.200595
$900$	8.37386	+	11.1652i	0.279129	+	0.372172i
$901$	−17.7973			−0.592913
$902$		0			0
$903$			4.00000i			0.133112i
$904$	5.19615			0.172821
$905$	−20.0000	−	10.0000i	−0.664822	−	0.332411i
$906$	47.7042			1.58486
$907$			29.1652i			0.968413i	0.874954	+	0.484206i	$0.160892\pi$
$907$			29.1652i			0.968413i	−0.874954	+	0.484206i	$0.839108\pi$
$908$		−	6.85275i		−	0.227417i
$909$	5.29150			0.175508
$910$	41.9506	−	83.9012i	1.39065	−	2.78130i
$911$	16.4174			0.543934			0.271967	−	0.962307i	$-0.412326\pi$
$911$	16.4174			0.543934			0.271967	+	0.962307i	$0.412326\pi$
$912$		−	9.47860i		−	0.313868i
$913$		0			0
$914$	−73.4955			−2.43101
$915$	−8.66025	+	17.3205i	−0.286299	+	0.572598i
$916$	−10.7042			−0.353676
$917$			38.3303i			1.26578i
$918$		−	7.79129i		−	0.257151i
$919$	21.3567			0.704493			0.352246	−	0.935907i	$-0.385418\pi$
$919$	21.3567			0.704493			0.352246	+	0.935907i	$0.385418\pi$
$920$	−29.7309	−	14.8655i	−0.980199	−	0.490100i
$921$	−6.92820			−0.228292
$922$			16.7477i			0.551557i
$923$		−	40.1232i		−	1.32067i
$924$		0			0
$925$	−1.66970	+	1.25227i	−0.0548993	+	0.0411745i
$926$	8.75560			0.287727
$927$			6.00000i			0.197066i
$928$		−	6.74773i		−	0.221505i
$929$	30.3303			0.995105			0.497552	−	0.867434i	$-0.334232\pi$
$929$	30.3303			0.995105			0.497552	+	0.867434i	$0.334232\pi$
$930$	28.8172	+	14.4086i	0.944954	+	0.472477i
$931$	−64.3719			−2.10970
$932$			58.8143i			1.92653i
$933$		−	6.41742i		−	0.210097i
$934$	30.0924			0.984654
$935$		0			0
$936$	7.58258			0.247844
$937$			34.1087i			1.11428i	0.830418	+	0.557142i	$0.188102\pi$
$937$			34.1087i			1.11428i	−0.830418	+	0.557142i	$0.811898\pi$
$938$			122.156i			3.98854i
$939$	2.41742			0.0788897
$940$	−7.20871	+	14.4174i	−0.235122	+	0.470245i
$941$	−34.2994			−1.11813			−0.559065	−	0.829124i	$-0.688840\pi$
$941$	−34.2994			−1.11813			−0.559065	+	0.829124i	$0.688840\pi$
$942$		−	47.2421i		−	1.53923i
$943$		−	59.4618i		−	1.93634i
$944$	10.0000			0.325472
$945$	−8.75560	−	4.37780i	−0.284820	−	0.142410i
$946$		0			0
$947$			8.91288i			0.289630i	0.989459	+	0.144815i	$0.0462586\pi$
$947$			8.91288i			0.289630i	−0.989459	+	0.144815i	$0.953741\pi$
$948$			7.38505i			0.239855i
$949$	−22.3303			−0.724872
$950$	−46.3303	+	34.7477i	−1.50315	+	1.12737i
$951$	−26.1652			−0.848463
$952$			26.9898i			0.874745i
$953$			17.8926i			0.579598i	0.957087	+	0.289799i	$0.0935885\pi$
$953$			17.8926i			0.579598i	−0.957087	+	0.289799i	$0.906411\pi$
$954$	−10.9445			−0.354341
$955$	51.8258	+	25.9129i	1.67704	+	0.838521i
$956$	2.01810			0.0652701
$957$		0			0
$958$			89.4083i			2.88865i
$959$	62.0122			2.00248
$960$	−12.5826	+	25.1652i	−0.406101	+	0.812202i
$961$	12.3303			0.397752
$962$			4.00000i			0.128965i
$963$			14.8655i			0.479033i
$964$	−69.0159			−2.22285
$965$	2.74110	−	5.48220i	0.0882392	−	0.176478i
$966$	82.2432			2.64613
$967$		−	36.8498i		−	1.18501i	−0.805567	−	0.592505i	$-0.798139\pi$
$967$		−	36.8498i		−	1.18501i	0.805567	−	0.592505i	$-0.201861\pi$
$968$		0			0
$969$	18.8348			0.605063
$970$	−24.4394	−	12.2197i	−0.784702	−	0.392351i
$971$	44.4174			1.42542			0.712711	−	0.701457i	$-0.247467\pi$
$971$	44.4174			1.42542			0.712711	+	0.701457i	$0.247467\pi$
$972$		−	2.79129i		−	0.0895306i
$973$			27.5826i			0.884257i
$974$	52.3429			1.67718
$975$	13.1334	+	17.5112i	0.420606	+	0.560807i
$976$	−15.5130			−0.496559
$977$			36.1652i			1.15703i	0.815673	+	0.578513i	$0.196367\pi$
$977$			36.1652i			1.15703i	−0.815673	+	0.578513i	$0.803633\pi$
$978$			18.4249i			0.589164i
$979$		0			0
$980$	67.9129	+	33.9564i	2.16940	+	1.08470i
$981$	15.6838			0.500745
$982$		−	49.9129i		−	1.59278i
$983$		−	40.0780i		−	1.27829i	−0.769086	−	0.639145i	$-0.779288\pi$
$983$		−	40.0780i		−	1.27829i	0.769086	−	0.639145i	$-0.220712\pi$
$984$	12.0000			0.382546
$985$	−6.92820	+	13.8564i	−0.220751	+	0.441502i
$986$	7.11890			0.226712
$987$		−	11.3060i		−	0.359874i
$988$			64.6606i			2.05713i
$989$	7.84190			0.249358
$990$		0			0
$991$	7.74773			0.246115			0.123057	−	0.992400i	$-0.460730\pi$
$991$	7.74773			0.246115			0.123057	+	0.992400i	$0.460730\pi$
$992$			48.6127i			1.54345i
$993$			14.5826i			0.462764i
$994$	87.8258			2.78566
$995$	53.1652	+	26.5826i	1.68545	+	0.842724i
$996$	4.56850			0.144759
$997$		−	9.66930i		−	0.306230i	−0.988208	−	0.153115i	$-0.951070\pi$
$997$		−	9.66930i		−	0.306230i	0.988208	−	0.153115i	$-0.0489305\pi$
$998$		−	52.5336i		−	1.66292i
$999$	0.417424			0.0132067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.f.364.8	yes	8
5.2	odd	4		9075.2.a.cz.1.1		4
5.3	odd	4		9075.2.a.cs.1.4		4
5.4	even	2	inner	1815.2.c.f.364.1	✓	8
11.10	odd	2	inner	1815.2.c.f.364.2	yes	8
55.32	even	4		9075.2.a.cz.1.4		4
55.43	even	4		9075.2.a.cs.1.1		4
55.54	odd	2	inner	1815.2.c.f.364.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.f.364.1	✓	8	5.4	even	2	inner
1815.2.c.f.364.2	yes	8	11.10	odd	2	inner
1815.2.c.f.364.7	yes	8	55.54	odd	2	inner
1815.2.c.f.364.8	yes	8	1.1	even	1	trivial
9075.2.a.cs.1.1		4	55.43	even	4
9075.2.a.cs.1.4		4	5.3	odd	4
9075.2.a.cz.1.1		4	5.2	odd	4
9075.2.a.cz.1.4		4	55.32	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.18890i q^{2} +1.00000i q^{3} -2.79129 q^{4} +(2.00000 + 1.00000i) q^{5} -2.18890 q^{6} -4.37780i q^{7} -1.73205i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.18890i q^{2} +1.00000i q^{3} -2.79129 q^{4} +(2.00000 + 1.00000i) q^{5} -2.18890 q^{6} -4.37780i q^{7} -1.73205i q^{8} -1.00000 q^{9} +(-2.18890 + 4.37780i) q^{10} -2.79129i q^{12} -4.37780i q^{13} +9.58258 q^{14} +(-1.00000 + 2.00000i) q^{15} -1.79129 q^{16} -3.55945i q^{17} -2.18890i q^{18} +5.29150 q^{19} +(-5.58258 - 2.79129i) q^{20} +4.37780 q^{21} -8.58258i q^{23} +1.73205 q^{24} +(3.00000 + 4.00000i) q^{25} +9.58258 q^{26} -1.00000i q^{27} +12.2197i q^{28} +0.913701 q^{29} +(-4.37780 - 2.18890i) q^{30} -6.58258 q^{31} -7.38505i q^{32} +7.79129 q^{34} +(4.37780 - 8.75560i) q^{35} +2.79129 q^{36} +0.417424i q^{37} +11.5826i q^{38} +4.37780 q^{39} +(1.73205 - 3.46410i) q^{40} +6.92820 q^{41} +9.58258i q^{42} +0.913701i q^{43} +(-2.00000 - 1.00000i) q^{45} +18.7864 q^{46} -2.58258i q^{47} -1.79129i q^{48} -12.1652 q^{49} +(-8.75560 + 6.56670i) q^{50} +3.55945 q^{51} +12.2197i q^{52} -5.00000i q^{53} +2.18890 q^{54} -7.58258 q^{56} +5.29150i q^{57} +2.00000i q^{58} -5.58258 q^{59} +(2.79129 - 5.58258i) q^{60} +8.66025 q^{61} -14.4086i q^{62} +4.37780i q^{63} +12.5826 q^{64} +(4.37780 - 8.75560i) q^{65} +12.7477i q^{67} +9.93545i q^{68} +8.58258 q^{69} +(19.1652 + 9.58258i) q^{70} +9.16515 q^{71} +1.73205i q^{72} -5.10080i q^{73} -0.913701 q^{74} +(-4.00000 + 3.00000i) q^{75} -14.7701 q^{76} +9.58258i q^{78} -2.64575 q^{79} +(-3.58258 - 1.79129i) q^{80} +1.00000 q^{81} +15.1652i q^{82} +1.63670i q^{83} -12.2197 q^{84} +(3.55945 - 7.11890i) q^{85} -2.00000 q^{86} +0.913701i q^{87} +10.7477 q^{89} +(2.18890 - 4.37780i) q^{90} -19.1652 q^{91} +23.9564i q^{92} -6.58258i q^{93} +5.65300 q^{94} +(10.5830 + 5.29150i) q^{95} +7.38505 q^{96} +5.58258i q^{97} -26.6283i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 16 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^4 + 16 * q^5 - 8 * q^9	\( 8 q - 4 q^{4} + 16 q^{5} - 8 q^{9} + 40 q^{14} - 8 q^{15} + 4 q^{16} - 8 q^{20} + 24 q^{25} + 40 q^{26} - 16 q^{31} + 44 q^{34} + 4 q^{36} - 16 q^{45} - 24 q^{49} - 24 q^{56} - 8 q^{59} + 4 q^{60} + 64 q^{64} + 32 q^{69} + 80 q^{70} - 32 q^{75} + 8 q^{80} + 8 q^{81} - 16 q^{86} - 24 q^{89} - 80 q^{91}+O(q^{100}) \) 8 * q - 4 * q^4 + 16 * q^5 - 8 * q^9 + 40 * q^14 - 8 * q^15 + 4 * q^16 - 8 * q^20 + 24 * q^25 + 40 * q^26 - 16 * q^31 + 44 * q^34 + 4 * q^36 - 16 * q^45 - 24 * q^49 - 24 * q^56 - 8 * q^59 + 4 * q^60 + 64 * q^64 + 32 * q^69 + 80 * q^70 - 32 * q^75 + 8 * q^80 + 8 * q^81 - 16 * q^86 - 24 * q^89 - 80 * q^91

Introduction

L-functions

Modular forms

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