LMFDB - Embedded newform 338.3.d.g.99.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,3,Mod(99,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.99"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.d (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.612074651904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.4
Root			$4.71318 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.99
Dual form			338.3.d.g.239.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +5.57921 q^{3} +2.00000i q^{4} +(0.323893 + 0.323893i) q^{5} +(5.57921 + 5.57921i) q^{6} +(-5.62134 + 5.62134i) q^{7} +(-2.00000 + 2.00000i) q^{8} +22.1276 q^{9} +0.647786i q^{10} +(3.95787 - 3.95787i) q^{11} +11.1584i q^{12} -11.2427 q^{14} +(1.80707 + 1.80707i) q^{15} -4.00000 q^{16} -2.01247i q^{17} +(22.1276 + 22.1276i) q^{18} +(3.27602 + 3.27602i) q^{19} +(-0.647786 + 0.647786i) q^{20} +(-31.3626 + 31.3626i) q^{21} +7.91574 q^{22} +17.4333i q^{23} +(-11.1584 + 11.1584i) q^{24} -24.7902i q^{25} +73.2415 q^{27} +(-11.2427 - 11.2427i) q^{28} -16.5005 q^{29} +3.61413i q^{30} +(-9.27353 - 9.27353i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(22.0818 - 22.0818i) q^{33} +(2.01247 - 2.01247i) q^{34} -3.64143 q^{35} +44.2552i q^{36} +(24.9264 - 24.9264i) q^{37} +6.55204i q^{38} -1.29557 q^{40} +(-42.9141 - 42.9141i) q^{41} -62.7253 q^{42} -52.2041i q^{43} +(7.91574 + 7.91574i) q^{44} +(7.16697 + 7.16697i) q^{45} +(-17.4333 + 17.4333i) q^{46} +(8.73527 - 8.73527i) q^{47} -22.3168 q^{48} -14.1990i q^{49} +(24.7902 - 24.7902i) q^{50} -11.2280i q^{51} -23.4425 q^{53} +(73.2415 + 73.2415i) q^{54} +2.56385 q^{55} -22.4854i q^{56} +(18.2776 + 18.2776i) q^{57} +(-16.5005 - 16.5005i) q^{58} +(-24.9530 + 24.9530i) q^{59} +(-3.61413 + 3.61413i) q^{60} +27.8841 q^{61} -18.5471i q^{62} +(-124.387 + 124.387i) q^{63} -8.00000i q^{64} +44.1635 q^{66} +(24.2048 + 24.2048i) q^{67} +4.02494 q^{68} +97.2638i q^{69} +(-3.64143 - 3.64143i) q^{70} +(54.0823 + 54.0823i) q^{71} +(-44.2552 + 44.2552i) q^{72} +(-18.9304 + 18.9304i) q^{73} +49.8528 q^{74} -138.310i q^{75} +(-6.55204 + 6.55204i) q^{76} +44.4971i q^{77} -142.837 q^{79} +(-1.29557 - 1.29557i) q^{80} +209.481 q^{81} -85.8281i q^{82} +(-91.7157 - 91.7157i) q^{83} +(-62.7253 - 62.7253i) q^{84} +(0.651824 - 0.651824i) q^{85} +(52.2041 - 52.2041i) q^{86} -92.0599 q^{87} +15.8315i q^{88} +(110.395 - 110.395i) q^{89} +14.3339i q^{90} -34.8665 q^{92} +(-51.7389 - 51.7389i) q^{93} +17.4705 q^{94} +2.12216i q^{95} +(-22.3168 - 22.3168i) q^{96} +(79.6229 + 79.6229i) q^{97} +(14.1990 - 14.1990i) q^{98} +(87.5780 - 87.5780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} + 84 q^{9} + 42 q^{11} + 20 q^{14} + 60 q^{15} - 32 q^{16} + 84 q^{18} + 22 q^{19} - 12 q^{20} - 102 q^{21} + 84 q^{22} + 72 q^{27} + 20 q^{28} + 12 q^{29}+ \cdots + 252 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 + 84 * q^9 + 42 * q^11 + 20 * q^14 + 60 * q^15 - 32 * q^16 + 84 * q^18 + 22 * q^19 - 12 * q^20 - 102 * q^21 + 84 * q^22 + 72 * q^27 + 20 * q^28 + 12 * q^29 + 32 * q^31 - 32 * q^32 + 54 * q^33 - 60 * q^34 + 156 * q^35 + 32 * q^37 - 24 * q^40 - 12 * q^41 - 204 * q^42 + 84 * q^44 - 102 * q^45 - 108 * q^46 + 60 * q^47 - 88 * q^50 - 132 * q^53 + 72 * q^54 + 324 * q^55 - 294 * q^57 + 12 * q^58 + 234 * q^59 - 120 * q^60 - 72 * q^61 - 156 * q^63 + 108 * q^66 - 14 * q^67 - 120 * q^68 + 156 * q^70 + 162 * q^71 - 168 * q^72 + 166 * q^73 + 64 * q^74 - 44 * q^76 - 96 * q^79 - 24 * q^80 + 24 * q^81 - 240 * q^83 - 204 * q^84 - 234 * q^85 + 132 * q^86 - 720 * q^87 + 210 * q^89 - 216 * q^92 - 444 * q^93 + 120 * q^94 + 146 * q^97 - 16 * q^98 + 252 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	5.57921			1.85974			0.929868	−	0.367893i	$-0.119921\pi$
$3$	5.57921			1.85974			0.929868	+	0.367893i	$0.119921\pi$
$4$			2.00000i			0.500000i
$5$	0.323893	+	0.323893i	0.0647786	+	0.0647786i	0.738754	−	0.673975i	$-0.235415\pi$
$5$	0.323893	+	0.323893i	0.0647786	+	0.0647786i	−0.673975	+	0.738754i	$0.735415\pi$
$6$	5.57921	+	5.57921i	0.929868	+	0.929868i
$7$	−5.62134	+	5.62134i	−0.803049	+	0.803049i	−0.983571	−	0.180522i	$-0.942221\pi$
$7$	−5.62134	+	5.62134i	−0.803049	+	0.803049i	0.180522	+	0.983571i	$0.442221\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	22.1276			2.45862
$10$			0.647786i			0.0647786i
$11$	3.95787	−	3.95787i	0.359806	−	0.359806i	−0.503935	−	0.863741i	$-0.668115\pi$
$11$	3.95787	−	3.95787i	0.359806	−	0.359806i	0.863741	+	0.503935i	$0.168115\pi$
$12$			11.1584i			0.929868i
$13$		0			0
$13$		0			0
$14$	−11.2427			−0.803049
$15$	1.80707	+	1.80707i	0.120471	+	0.120471i
$16$	−4.00000			−0.250000
$17$		−	2.01247i		−	0.118380i	−0.998247	−	0.0591902i	$-0.981148\pi$
$17$		−	2.01247i		−	0.118380i	0.998247	−	0.0591902i	$-0.0188519\pi$
$18$	22.1276	+	22.1276i	1.22931	+	1.22931i
$19$	3.27602	+	3.27602i	0.172422	+	0.172422i	0.788043	−	0.615621i	$-0.211095\pi$
$19$	3.27602	+	3.27602i	0.172422	+	0.172422i	−0.615621	+	0.788043i	$0.711095\pi$
$20$	−0.647786	+	0.647786i	−0.0323893	+	0.0323893i
$21$	−31.3626	+	31.3626i	−1.49346	+	1.49346i
$22$	7.91574			0.359806
$23$			17.4333i			0.757968i	0.925403	+	0.378984i	$0.123726\pi$
$23$			17.4333i			0.757968i	−0.925403	+	0.378984i	$0.876274\pi$
$24$	−11.1584	+	11.1584i	−0.464934	+	0.464934i
$25$		−	24.7902i		−	0.991607i
$26$		0			0
$27$	73.2415			2.71265
$28$	−11.2427	−	11.2427i	−0.401524	−	0.401524i
$29$	−16.5005			−0.568983			−0.284492	−	0.958678i	$-0.591825\pi$
$29$	−16.5005			−0.568983			−0.284492	+	0.958678i	$0.591825\pi$
$30$			3.61413i			0.120471i
$31$	−9.27353	−	9.27353i	−0.299146	−	0.299146i	0.541533	−	0.840679i	$-0.317844\pi$
$31$	−9.27353	−	9.27353i	−0.299146	−	0.299146i	−0.840679	+	0.541533i	$0.817844\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	22.0818	−	22.0818i	0.669145	−	0.669145i
$34$	2.01247	−	2.01247i	0.0591902	−	0.0591902i
$35$	−3.64143			−0.104041
$36$			44.2552i			1.22931i
$37$	24.9264	−	24.9264i	0.673687	−	0.673687i	−0.284877	−	0.958564i	$-0.591953\pi$
$37$	24.9264	−	24.9264i	0.673687	−	0.673687i	0.958564	+	0.284877i	$0.0919529\pi$
$38$			6.55204i			0.172422i
$39$		0			0
$40$	−1.29557			−0.0323893
$41$	−42.9141	−	42.9141i	−1.04668	−	1.04668i	−0.998856	−	0.0478289i	$-0.984770\pi$
$41$	−42.9141	−	42.9141i	−1.04668	−	1.04668i	−0.0478289	−	0.998856i	$-0.515230\pi$
$42$	−62.7253			−1.49346
$43$		−	52.2041i		−	1.21405i	−0.794683	−	0.607024i	$-0.792363\pi$
$43$		−	52.2041i		−	1.21405i	0.794683	−	0.607024i	$-0.207637\pi$
$44$	7.91574	+	7.91574i	0.179903	+	0.179903i
$45$	7.16697	+	7.16697i	0.159266	+	0.159266i
$46$	−17.4333	+	17.4333i	−0.378984	+	0.378984i
$47$	8.73527	−	8.73527i	0.185857	−	0.185857i	−0.608045	−	0.793902i	$-0.708046\pi$
$47$	8.73527	−	8.73527i	0.185857	−	0.185857i	0.793902	+	0.608045i	$0.208046\pi$
$48$	−22.3168			−0.464934
$49$		−	14.1990i		−	0.289775i
$50$	24.7902	−	24.7902i	0.495804	−	0.495804i
$51$		−	11.2280i		−	0.220156i
$52$		0			0
$53$	−23.4425			−0.442311			−0.221155	−	0.975239i	$-0.570983\pi$
$53$	−23.4425			−0.442311			−0.221155	+	0.975239i	$0.570983\pi$
$54$	73.2415	+	73.2415i	1.35632	+	1.35632i
$55$	2.56385			0.0466155
$56$		−	22.4854i		−	0.401524i
$57$	18.2776	+	18.2776i	0.320660	+	0.320660i
$58$	−16.5005	−	16.5005i	−0.284492	−	0.284492i
$59$	−24.9530	+	24.9530i	−0.422932	+	0.422932i	−0.886212	−	0.463280i	$-0.846672\pi$
$59$	−24.9530	+	24.9530i	−0.422932	+	0.422932i	0.463280	+	0.886212i	$0.346672\pi$
$60$	−3.61413	+	3.61413i	−0.0602356	+	0.0602356i
$61$	27.8841			0.457117			0.228558	−	0.973530i	$-0.426599\pi$
$61$	27.8841			0.457117			0.228558	+	0.973530i	$0.426599\pi$
$62$		−	18.5471i		−	0.299146i
$63$	−124.387	+	124.387i	−1.97439	+	1.97439i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	44.1635			0.669145
$67$	24.2048	+	24.2048i	0.361265	+	0.361265i	0.864279	−	0.503014i	$-0.167775\pi$
$67$	24.2048	+	24.2048i	0.361265	+	0.361265i	−0.503014	+	0.864279i	$0.667775\pi$
$68$	4.02494			0.0591902
$69$			97.2638i			1.40962i
$70$	−3.64143	−	3.64143i	−0.0520204	−	0.0520204i
$71$	54.0823	+	54.0823i	0.761723	+	0.761723i	0.976634	−	0.214911i	$-0.0689462\pi$
$71$	54.0823	+	54.0823i	0.761723	+	0.761723i	−0.214911	+	0.976634i	$0.568946\pi$
$72$	−44.2552	+	44.2552i	−0.614655	+	0.614655i
$73$	−18.9304	+	18.9304i	−0.259320	+	0.259320i	−0.824778	−	0.565457i	$-0.808700\pi$
$73$	−18.9304	+	18.9304i	−0.259320	+	0.259320i	0.565457	+	0.824778i	$0.308700\pi$
$74$	49.8528			0.673687
$75$		−	138.310i		−	1.84413i
$76$	−6.55204	+	6.55204i	−0.0862110	+	0.0862110i
$77$			44.4971i			0.577884i
$78$		0			0
$79$	−142.837			−1.80806			−0.904029	−	0.427471i	$-0.859404\pi$
$79$	−142.837			−1.80806			−0.904029	+	0.427471i	$0.859404\pi$
$80$	−1.29557	−	1.29557i	−0.0161947	−	0.0161947i
$81$	209.481			2.58619
$82$		−	85.8281i		−	1.04668i
$83$	−91.7157	−	91.7157i	−1.10501	−	1.10501i	−0.993797	−	0.111212i	$-0.964527\pi$
$83$	−91.7157	−	91.7157i	−1.10501	−	1.10501i	−0.111212	−	0.993797i	$-0.535473\pi$
$84$	−62.7253	−	62.7253i	−0.746730	−	0.746730i
$85$	0.651824	−	0.651824i	0.00766852	−	0.00766852i
$86$	52.2041	−	52.2041i	0.607024	−	0.607024i
$87$	−92.0599			−1.05816
$88$			15.8315i			0.179903i
$89$	110.395	−	110.395i	1.24039	−	1.24039i	0.280550	−	0.959839i	$-0.409483\pi$
$89$	110.395	−	110.395i	1.24039	−	1.24039i	0.959839	−	0.280550i	$-0.0905168\pi$
$90$			14.3339i			0.159266i
$91$		0			0
$92$	−34.8665			−0.378984
$93$	−51.7389	−	51.7389i	−0.556333	−	0.556333i
$94$	17.4705			0.185857
$95$			2.12216i			0.0223385i
$96$	−22.3168	−	22.3168i	−0.232467	−	0.232467i
$97$	79.6229	+	79.6229i	0.820855	+	0.820855i	0.986231	−	0.165376i	$-0.0528837\pi$
$97$	79.6229	+	79.6229i	0.820855	+	0.820855i	−0.165376	+	0.986231i	$0.552884\pi$
$98$	14.1990	−	14.1990i	0.144887	−	0.144887i
$99$	87.5780	−	87.5780i	0.884626	−	0.884626i
$100$	49.5804			0.495804
$101$			97.6994i			0.967320i	0.875256	+	0.483660i	$0.160693\pi$
$101$			97.6994i			0.967320i	−0.875256	+	0.483660i	$0.839307\pi$
$102$	11.2280	−	11.2280i	0.110078	−	0.110078i
$103$			108.442i			1.05284i	0.850226	+	0.526418i	$0.176465\pi$
$103$			108.442i			1.05284i	−0.850226	+	0.526418i	$0.823535\pi$
$104$		0			0
$105$	−20.3163			−0.193488
$106$	−23.4425	−	23.4425i	−0.221155	−	0.221155i
$107$	−75.2986			−0.703725			−0.351863	−	0.936052i	$-0.614452\pi$
$107$	−75.2986			−0.703725			−0.351863	+	0.936052i	$0.614452\pi$
$108$			146.483i			1.35632i
$109$	5.83660	+	5.83660i	0.0535468	+	0.0535468i	0.733373	−	0.679826i	$-0.237945\pi$
$109$	5.83660	+	5.83660i	0.0535468	+	0.0535468i	−0.679826	+	0.733373i	$0.737945\pi$
$110$	2.56385	+	2.56385i	0.0233077	+	0.0233077i
$111$	139.070	−	139.070i	1.25288	−	1.25288i
$112$	22.4854	−	22.4854i	0.200762	−	0.200762i
$113$	−114.487			−1.01316			−0.506580	−	0.862193i	$-0.669090\pi$
$113$	−114.487			−1.01316			−0.506580	+	0.862193i	$0.669090\pi$
$114$			36.5552i			0.320660i
$115$	−5.64651	+	5.64651i	−0.0491001	+	0.0491001i
$116$		−	33.0010i		−	0.284492i
$117$		0			0
$118$	−49.9060			−0.422932
$119$	11.3128	+	11.3128i	0.0950653	+	0.0950653i
$120$	−7.22827			−0.0602356
$121$			89.6706i			0.741079i
$122$	27.8841	+	27.8841i	0.228558	+	0.228558i
$123$	−239.427	−	239.427i	−1.94656	−	1.94656i
$124$	18.5471	−	18.5471i	0.149573	−	0.149573i
$125$	16.1267	−	16.1267i	0.129014	−	0.129014i
$126$	−248.773			−1.97439
$127$		−	96.7733i		−	0.761994i	−0.924576	−	0.380997i	$-0.875581\pi$
$127$		−	96.7733i		−	0.761994i	0.924576	−	0.380997i	$-0.124419\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	291.258i		−	2.25781i
$130$		0			0
$131$	159.613			1.21842			0.609212	−	0.793008i	$-0.291486\pi$
$131$	159.613			1.21842			0.609212	+	0.793008i	$0.291486\pi$
$132$	44.1635	+	44.1635i	0.334572	+	0.334572i
$133$	−36.8312			−0.276927
$134$			48.4095i			0.361265i
$135$	23.7224	+	23.7224i	0.175722	+	0.175722i
$136$	4.02494	+	4.02494i	0.0295951	+	0.0295951i
$137$	89.4742	−	89.4742i	0.653096	−	0.653096i	−0.300641	−	0.953737i	$-0.597201\pi$
$137$	89.4742	−	89.4742i	0.653096	−	0.653096i	0.953737	+	0.300641i	$0.0972007\pi$
$138$	−97.2638	+	97.2638i	−0.704810	+	0.704810i
$139$	60.4469			0.434870			0.217435	−	0.976075i	$-0.430231\pi$
$139$	60.4469			0.434870			0.217435	+	0.976075i	$0.430231\pi$
$140$		−	7.28285i		−	0.0520204i
$141$	48.7359	−	48.7359i	0.345645	−	0.345645i
$142$			108.165i			0.761723i
$143$		0			0
$144$	−88.5103			−0.614655
$145$	−5.34441	−	5.34441i	−0.0368580	−	0.0368580i
$146$	−37.8608			−0.259320
$147$		−	79.2190i		−	0.538905i
$148$	49.8528	+	49.8528i	0.336843	+	0.336843i
$149$	−154.374	−	154.374i	−1.03607	−	1.03607i	−0.999325	−	0.0367407i	$-0.988302\pi$
$149$	−154.374	−	154.374i	−1.03607	−	1.03607i	−0.0367407	−	0.999325i	$-0.511698\pi$
$150$	138.310	−	138.310i	0.922064	−	0.922064i
$151$	73.7140	−	73.7140i	0.488172	−	0.488172i	−0.419557	−	0.907729i	$-0.637815\pi$
$151$	73.7140	−	73.7140i	0.488172	−	0.488172i	0.907729	+	0.419557i	$0.137815\pi$
$152$	−13.1041			−0.0862110
$153$		−	44.5310i		−	0.291053i
$154$	−44.4971	+	44.4971i	−0.288942	+	0.288942i
$155$		−	6.00726i		−	0.0387565i
$156$		0			0
$157$	−127.109			−0.809611			−0.404805	−	0.914403i	$-0.632661\pi$
$157$	−127.109			−0.809611			−0.404805	+	0.914403i	$0.632661\pi$
$158$	−142.837	−	142.837i	−0.904029	−	0.904029i
$159$	−130.790			−0.822581
$160$		−	2.59114i		−	0.0161947i
$161$	−97.9983	−	97.9983i	−0.608685	−	0.608685i
$162$	209.481	+	209.481i	1.29310	+	1.29310i
$163$	−119.548	+	119.548i	−0.733426	+	0.733426i	−0.971297	−	0.237871i	$-0.923551\pi$
$163$	−119.548	+	119.548i	−0.733426	+	0.733426i	0.237871	+	0.971297i	$0.423551\pi$
$164$	85.8281	−	85.8281i	0.523342	−	0.523342i
$165$	14.3043			0.0866925
$166$		−	183.431i		−	1.10501i
$167$	117.897	−	117.897i	0.705971	−	0.705971i	−0.259714	−	0.965686i	$-0.583628\pi$
$167$	117.897	−	117.897i	0.705971	−	0.705971i	0.965686	+	0.259714i	$0.0836283\pi$
$168$		−	125.451i		−	0.746730i
$169$		0			0
$170$	1.30365			0.00766852
$171$	72.4904	+	72.4904i	0.423920	+	0.423920i
$172$	104.408			0.607024
$173$		−	140.484i		−	0.812045i	−0.913863	−	0.406023i	$-0.866915\pi$
$173$		−	140.484i		−	0.812045i	0.913863	−	0.406023i	$-0.133085\pi$
$174$	−92.0599	−	92.0599i	−0.529080	−	0.529080i
$175$	139.354	+	139.354i	0.796309	+	0.796309i
$176$	−15.8315	+	15.8315i	−0.0899515	+	0.0899515i
$177$	−139.218	+	139.218i	−0.786543	+	0.786543i
$178$	220.789			1.24039
$179$			316.003i			1.76538i	0.469955	+	0.882691i	$0.344270\pi$
$179$			316.003i			1.76538i	−0.469955	+	0.882691i	$0.655730\pi$
$180$	−14.3339	+	14.3339i	−0.0796330	+	0.0796330i
$181$			83.6580i			0.462199i	0.972930	+	0.231099i	$0.0742323\pi$
$181$			83.6580i			0.462199i	−0.972930	+	0.231099i	$0.925768\pi$
$182$		0			0
$183$	155.571			0.850116
$184$	−34.8665	−	34.8665i	−0.189492	−	0.189492i
$185$	16.1470			0.0872810
$186$		−	103.478i		−	0.556333i
$187$	−7.96508	−	7.96508i	−0.0425940	−	0.0425940i
$188$	17.4705	+	17.4705i	0.0929284	+	0.0929284i
$189$	−411.715	+	411.715i	−2.17839	+	2.17839i
$190$	−2.12216	+	2.12216i	−0.0111693	+	0.0111693i
$191$	69.1133			0.361850			0.180925	−	0.983497i	$-0.442091\pi$
$191$	69.1133			0.361850			0.180925	+	0.983497i	$0.442091\pi$
$192$		−	44.6337i		−	0.232467i
$193$	−229.573	+	229.573i	−1.18950	+	1.18950i	−0.212293	+	0.977206i	$0.568093\pi$
$193$	−229.573	+	229.573i	−1.18950	+	1.18950i	−0.977206	+	0.212293i	$0.931907\pi$
$194$			159.246i			0.820855i
$195$		0			0
$196$	28.3979			0.144887
$197$	226.374	+	226.374i	1.14911	+	1.14911i	0.986729	+	0.162377i	$0.0519160\pi$
$197$	226.374	+	226.374i	1.14911	+	1.14911i	0.162377	+	0.986729i	$0.448084\pi$
$198$	175.156			0.884626
$199$			172.820i			0.868443i	0.900806	+	0.434221i	$0.142976\pi$
$199$			172.820i			0.868443i	−0.900806	+	0.434221i	$0.857024\pi$
$200$	49.5804	+	49.5804i	0.247902	+	0.247902i
$201$	135.043	+	135.043i	0.671858	+	0.671858i
$202$	−97.6994	+	97.6994i	−0.483660	+	0.483660i
$203$	92.7551	−	92.7551i	0.456922	−	0.456922i
$204$	22.4560			0.110078
$205$		−	27.7991i		−	0.135606i
$206$	−108.442	+	108.442i	−0.526418	+	0.526418i
$207$			385.756i			1.86355i
$208$		0			0
$209$	25.9321			0.124077
$210$	−20.3163	−	20.3163i	−0.0967442	−	0.0967442i
$211$	230.179			1.09089			0.545447	−	0.838145i	$-0.316360\pi$
$211$	230.179			1.09089			0.545447	+	0.838145i	$0.316360\pi$
$212$		−	46.8849i		−	0.221155i
$213$	301.736	+	301.736i	1.41660	+	1.41660i
$214$	−75.2986	−	75.2986i	−0.351863	−	0.351863i
$215$	16.9085	−	16.9085i	0.0786444	−	0.0786444i
$216$	−146.483	+	146.483i	−0.678162	+	0.678162i
$217$	104.259			0.480458
$218$			11.6732i			0.0535468i
$219$	−105.617	+	105.617i	−0.482268	+	0.482268i
$220$			5.12770i			0.0233077i
$221$		0			0
$222$	278.139			1.25288
$223$	186.092	+	186.092i	0.834493	+	0.834493i	0.988128	−	0.153635i	$-0.0490980\pi$
$223$	186.092	+	186.092i	0.834493	+	0.834493i	−0.153635	+	0.988128i	$0.549098\pi$
$224$	44.9707			0.200762
$225$		−	548.547i		−	2.43799i
$226$	−114.487	−	114.487i	−0.506580	−	0.506580i
$227$	84.2608	+	84.2608i	0.371193	+	0.371193i	0.867912	−	0.496719i	$-0.165462\pi$
$227$	84.2608	+	84.2608i	0.371193	+	0.371193i	−0.496719	+	0.867912i	$0.665462\pi$
$228$	−36.5552	+	36.5552i	−0.160330	+	0.160330i
$229$	−224.372	+	224.372i	−0.979791	+	0.979791i	−0.999800	−	0.0200093i	$-0.993630\pi$
$229$	−224.372	+	224.372i	−0.979791	+	0.979791i	0.0200093	+	0.999800i	$0.493630\pi$
$230$	−11.2930			−0.0491001
$231$			248.258i			1.07471i
$232$	33.0010	−	33.0010i	0.142246	−	0.142246i
$233$		−	230.683i		−	0.990054i	−0.868878	−	0.495027i	$-0.835158\pi$
$233$		−	230.683i		−	0.990054i	0.868878	−	0.495027i	$-0.164842\pi$
$234$		0			0
$235$	5.65859			0.0240791
$236$	−49.9060	−	49.9060i	−0.211466	−	0.211466i
$237$	−796.915			−3.36251
$238$			22.6255i			0.0950653i
$239$	184.518	+	184.518i	0.772041	+	0.772041i	0.978463	−	0.206422i	$-0.0661820\pi$
$239$	184.518	+	184.518i	0.772041	+	0.772041i	−0.206422	+	0.978463i	$0.566182\pi$
$240$	−7.22827	−	7.22827i	−0.0301178	−	0.0301178i
$241$	−157.292	+	157.292i	−0.652665	+	0.652665i	−0.953634	−	0.300969i	$-0.902690\pi$
$241$	−157.292	+	157.292i	−0.652665	+	0.652665i	0.300969	+	0.953634i	$0.402690\pi$
$242$	−89.6706	+	89.6706i	−0.370540	+	0.370540i
$243$	509.567			2.09698
$244$			55.7682i			0.228558i
$245$	4.59895	−	4.59895i	0.0187712	−	0.0187712i
$246$		−	478.853i		−	1.94656i
$247$		0			0
$248$	37.0941			0.149573
$249$	−511.701	−	511.701i	−2.05502	−	2.05502i
$250$	32.2534			0.129014
$251$			251.968i			1.00386i	0.864909	+	0.501929i	$0.167376\pi$
$251$			251.968i			1.00386i	−0.864909	+	0.501929i	$0.832624\pi$
$252$	−248.773	−	248.773i	−0.987196	−	0.987196i
$253$	68.9985	+	68.9985i	0.272721	+	0.272721i
$254$	96.7733	−	96.7733i	0.380997	−	0.380997i
$255$	3.63666	−	3.63666i	0.0142614	−	0.0142614i
$256$	16.0000			0.0625000
$257$		−	290.290i		−	1.12953i	−0.825251	−	0.564767i	$-0.808966\pi$
$257$		−	290.290i		−	1.12953i	0.825251	−	0.564767i	$-0.191034\pi$
$258$	291.258	−	291.258i	1.12891	−	1.12891i
$259$			280.240i			1.08201i
$260$		0			0
$261$	−365.117			−1.39891
$262$	159.613	+	159.613i	0.609212	+	0.609212i
$263$	−107.867			−0.410143			−0.205071	−	0.978747i	$-0.565743\pi$
$263$	−107.867			−0.410143			−0.205071	+	0.978747i	$0.565743\pi$
$264$			88.3271i			0.334572i
$265$	−7.59285	−	7.59285i	−0.0286523	−	0.0286523i
$266$	−36.8312	−	36.8312i	−0.138463	−	0.138463i
$267$	615.915	−	615.915i	2.30680	−	2.30680i
$268$	−48.4095	+	48.4095i	−0.180632	+	0.180632i
$269$	−435.423			−1.61867			−0.809337	−	0.587345i	$-0.800173\pi$
$269$	−435.423			−1.61867			−0.809337	+	0.587345i	$0.800173\pi$
$270$			47.4448i			0.175722i
$271$	59.4776	−	59.4776i	0.219475	−	0.219475i	−0.588802	−	0.808277i	$-0.700400\pi$
$271$	59.4776	−	59.4776i	0.219475	−	0.219475i	0.808277	+	0.588802i	$0.200400\pi$
$272$			8.04987i			0.0295951i
$273$		0			0
$274$	178.948			0.653096
$275$	−98.1163	−	98.1163i	−0.356786	−	0.356786i
$276$	−194.528			−0.704810
$277$		−	36.8115i		−	0.132893i	−0.997790	−	0.0664467i	$-0.978834\pi$
$277$		−	36.8115i		−	0.132893i	0.997790	−	0.0664467i	$-0.0211662\pi$
$278$	60.4469	+	60.4469i	0.217435	+	0.217435i
$279$	−205.201	−	205.201i	−0.735486	−	0.735486i
$280$	7.28285	−	7.28285i	0.0260102	−	0.0260102i
$281$	−30.1080	+	30.1080i	−0.107146	+	0.107146i	−0.758647	−	0.651501i	$-0.774139\pi$
$281$	−30.1080	+	30.1080i	−0.107146	+	0.107146i	0.651501	+	0.758647i	$0.274139\pi$
$282$	97.4718			0.345645
$283$			104.960i			0.370882i	0.982655	+	0.185441i	$0.0593714\pi$
$283$			104.960i			0.370882i	−0.982655	+	0.185441i	$0.940629\pi$
$284$	−108.165	+	108.165i	−0.380861	+	0.380861i
$285$			11.8400i			0.0415438i
$286$		0			0
$287$	482.469			1.68108
$288$	−88.5103	−	88.5103i	−0.307327	−	0.307327i
$289$	284.950			0.985986
$290$		−	10.6888i		−	0.0368580i
$291$	444.233	+	444.233i	1.52657	+	1.52657i
$292$	−37.8608	−	37.8608i	−0.129660	−	0.129660i
$293$	−88.8706	+	88.8706i	−0.303313	+	0.303313i	−0.842308	−	0.538996i	$-0.818804\pi$
$293$	−88.8706	+	88.8706i	−0.303313	+	0.303313i	0.538996	+	0.842308i	$0.318804\pi$
$294$	79.2190	−	79.2190i	0.269452	−	0.269452i
$295$	−16.1642			−0.0547939
$296$			99.7056i			0.336843i
$297$	289.880	−	289.880i	0.976027	−	0.976027i
$298$		−	308.748i		−	1.03607i
$299$		0			0
$300$	276.619			0.922064
$301$	293.457	+	293.457i	0.974940	+	0.974940i
$302$	147.428			0.488172
$303$			545.085i			1.79896i
$304$	−13.1041	−	13.1041i	−0.0431055	−	0.0431055i
$305$	9.03147	+	9.03147i	0.0296114	+	0.0296114i
$306$	44.5310	−	44.5310i	0.145526	−	0.145526i
$307$	−159.407	+	159.407i	−0.519242	+	0.519242i	−0.917342	−	0.398100i	$-0.869670\pi$
$307$	−159.407	+	159.407i	−0.519242	+	0.519242i	0.398100	+	0.917342i	$0.369670\pi$
$308$	−88.9941			−0.288942
$309$			605.022i			1.95800i
$310$	6.00726	−	6.00726i	0.0193783	−	0.0193783i
$311$		−	461.756i		−	1.48475i	−0.669986	−	0.742374i	$-0.733700\pi$
$311$		−	461.756i		−	1.48475i	0.669986	−	0.742374i	$-0.266300\pi$
$312$		0			0
$313$	8.16759			0.0260945			0.0130473	−	0.999915i	$-0.495847\pi$
$313$	8.16759			0.0260945			0.0130473	+	0.999915i	$0.495847\pi$
$314$	−127.109	−	127.109i	−0.404805	−	0.404805i
$315$	−80.5760			−0.255797
$316$		−	285.673i		−	0.904029i
$317$	−91.6127	−	91.6127i	−0.288999	−	0.288999i	0.547685	−	0.836684i	$-0.315509\pi$
$317$	−91.6127	−	91.6127i	−0.288999	−	0.288999i	−0.836684	+	0.547685i	$0.815509\pi$
$318$	−130.790	−	130.790i	−0.411291	−	0.411291i
$319$	−65.3069	+	65.3069i	−0.204724	+	0.204724i
$320$	2.59114	−	2.59114i	0.00809733	−	0.00809733i
$321$	−420.107			−1.30874
$322$		−	195.997i		−	0.608685i
$323$	6.59288	−	6.59288i	0.0204114	−	0.0204114i
$324$			418.963i			1.29310i
$325$		0			0
$326$	−239.097			−0.733426
$327$	32.5636	+	32.5636i	0.0995828	+	0.0995828i
$328$	171.656			0.523342
$329$			98.2079i			0.298504i
$330$	14.3043	+	14.3043i	0.0433463	+	0.0433463i
$331$	105.739	+	105.739i	0.319454	+	0.319454i	0.848557	−	0.529103i	$-0.177472\pi$
$331$	105.739	+	105.739i	0.319454	+	0.319454i	−0.529103	+	0.848557i	$0.677472\pi$
$332$	183.431	−	183.431i	0.552504	−	0.552504i
$333$	551.561	−	551.561i	1.65634	−	1.65634i
$334$	235.794			0.705971
$335$			15.6795i			0.0468045i
$336$	125.451	−	125.451i	0.373365	−	0.373365i
$337$			61.7332i			0.183185i	0.995797	+	0.0915923i	$0.0291956\pi$
$337$			61.7332i			0.183185i	−0.995797	+	0.0915923i	$0.970804\pi$
$338$		0			0
$339$	−638.747			−1.88421
$340$	1.30365	+	1.30365i	0.00383426	+	0.00383426i
$341$	−73.4068			−0.215269
$342$			144.981i			0.423920i
$343$	−195.629	−	195.629i	−0.570346	−	0.570346i
$344$	104.408	+	104.408i	0.303512	+	0.303512i
$345$	−31.5031	+	31.5031i	−0.0913133	+	0.0913133i
$346$	140.484	−	140.484i	0.406023	−	0.406023i
$347$	220.862			0.636490			0.318245	−	0.948009i	$-0.396907\pi$
$347$	220.862			0.636490			0.318245	+	0.948009i	$0.396907\pi$
$348$		−	184.120i		−	0.529080i
$349$	−205.786	+	205.786i	−0.589645	+	0.589645i	−0.937535	−	0.347890i	$-0.886898\pi$
$349$	−205.786	+	205.786i	−0.589645	+	0.589645i	0.347890	+	0.937535i	$0.386898\pi$
$350$			278.708i			0.796309i
$351$		0			0
$352$	−31.6629			−0.0899515
$353$	−13.9392	−	13.9392i	−0.0394877	−	0.0394877i	0.687087	−	0.726575i	$-0.258889\pi$
$353$	−13.9392	−	13.9392i	−0.0394877	−	0.0394877i	−0.726575	+	0.687087i	$0.758889\pi$
$354$	−278.436			−0.786543
$355$			35.0338i			0.0986867i
$356$	220.789	+	220.789i	0.620195	+	0.620195i
$357$	63.1163	+	63.1163i	0.176796	+	0.176796i
$358$	−316.003	+	316.003i	−0.882691	+	0.882691i
$359$	−275.618	+	275.618i	−0.767738	+	0.767738i	−0.977708	−	0.209970i	$-0.932663\pi$
$359$	−275.618	+	275.618i	−0.767738	+	0.767738i	0.209970	+	0.977708i	$0.432663\pi$
$360$	−28.6679			−0.0796330
$361$		−	339.535i		−	0.940541i
$362$	−83.6580	+	83.6580i	−0.231099	+	0.231099i
$363$			500.291i			1.37821i
$364$		0			0
$365$	−12.2628			−0.0335968
$366$	155.571	+	155.571i	0.425058	+	0.425058i
$367$	468.735			1.27721			0.638603	−	0.769536i	$-0.279513\pi$
$367$	468.735			1.27721			0.638603	+	0.769536i	$0.279513\pi$
$368$		−	69.7330i		−	0.189492i
$369$	−949.584	−	949.584i	−2.57340	−	2.57340i
$370$	16.1470	+	16.1470i	0.0436405	+	0.0436405i
$371$	131.778	−	131.778i	0.355197	−	0.355197i
$372$	103.478	−	103.478i	0.278166	−	0.278166i
$373$	260.814			0.699234			0.349617	−	0.936893i	$-0.386312\pi$
$373$	260.814			0.699234			0.349617	+	0.936893i	$0.386312\pi$
$374$		−	15.9302i		−	0.0425940i
$375$	89.9742	−	89.9742i	0.239931	−	0.239931i
$376$			34.9411i			0.0929284i
$377$		0			0
$378$	−823.431			−2.17839
$379$	−151.457	−	151.457i	−0.399622	−	0.399622i	0.478478	−	0.878100i	$-0.341189\pi$
$379$	−151.457	−	151.457i	−0.399622	−	0.399622i	−0.878100	+	0.478478i	$0.841189\pi$
$380$	−4.24432			−0.0111693
$381$		−	539.918i		−	1.41711i
$382$	69.1133	+	69.1133i	0.180925	+	0.180925i
$383$	−485.035	−	485.035i	−1.26641	−	1.26641i	−0.947929	−	0.318482i	$-0.896827\pi$
$383$	−485.035	−	485.035i	−1.26641	−	1.26641i	−0.318482	−	0.947929i	$-0.603173\pi$
$384$	44.6337	−	44.6337i	0.116234	−	0.116234i
$385$	−14.4123	+	14.4123i	−0.0374345	+	0.0374345i
$386$	−459.147			−1.18950
$387$		−	1155.15i		−	2.98488i
$388$	−159.246	+	159.246i	−0.410427	+	0.410427i
$389$		−	374.691i		−	0.963216i	−0.876387	−	0.481608i	$-0.840053\pi$
$389$		−	374.691i		−	0.963216i	0.876387	−	0.481608i	$-0.159947\pi$
$390$		0			0
$391$	35.0839			0.0897286
$392$	28.3979	+	28.3979i	0.0724437	+	0.0724437i
$393$	890.517			2.26595
$394$			452.748i			1.14911i
$395$	−46.2638	−	46.2638i	−0.117123	−	0.117123i
$396$	175.156	+	175.156i	0.442313	+	0.442313i
$397$	−461.388	+	461.388i	−1.16219	+	1.16219i	−0.178191	+	0.983996i	$0.557024\pi$
$397$	−461.388	+	461.388i	−1.16219	+	1.16219i	−0.983996	+	0.178191i	$0.942976\pi$
$398$	−172.820	+	172.820i	−0.434221	+	0.434221i
$399$	−205.489			−0.515011
$400$			99.1607i			0.247902i
$401$	−305.660	+	305.660i	−0.762244	+	0.762244i	−0.976728	−	0.214483i	$-0.931193\pi$
$401$	−305.660	+	305.660i	−0.762244	+	0.762244i	0.214483	+	0.976728i	$0.431193\pi$
$402$			270.087i			0.671858i
$403$		0			0
$404$	−195.399			−0.483660
$405$	67.8496	+	67.8496i	0.167530	+	0.167530i
$406$	185.510			0.456922
$407$		−	197.311i		−	0.484793i
$408$	22.4560	+	22.4560i	0.0550391	+	0.0550391i
$409$	197.379	+	197.379i	0.482588	+	0.482588i	0.905957	−	0.423369i	$-0.139153\pi$
$409$	197.379	+	197.379i	0.482588	+	0.482588i	−0.423369	+	0.905957i	$0.639153\pi$
$410$	27.7991	−	27.7991i	0.0678028	−	0.0678028i
$411$	499.195	−	499.195i	1.21459	−	1.21459i
$412$	−216.884			−0.526418
$413$		−	280.539i		−	0.679270i
$414$	−385.756	+	385.756i	−0.931777	+	0.931777i
$415$		−	59.4122i		−	0.143162i
$416$		0			0
$417$	337.246			0.808743
$418$	25.9321	+	25.9321i	0.0620385	+	0.0620385i
$419$	187.590			0.447709			0.223855	−	0.974623i	$-0.428136\pi$
$419$	187.590			0.447709			0.223855	+	0.974623i	$0.428136\pi$
$420$		−	40.6326i		−	0.0967442i
$421$	410.480	+	410.480i	0.975013	+	0.975013i	0.999695	−	0.0246826i	$-0.00785752\pi$
$421$	410.480	+	410.480i	0.975013	+	0.975013i	−0.0246826	+	0.999695i	$0.507858\pi$
$422$	230.179	+	230.179i	0.545447	+	0.545447i
$423$	193.290	−	193.290i	0.456951	−	0.456951i
$424$	46.8849	−	46.8849i	0.110578	−	0.110578i
$425$	−49.8895			−0.117387
$426$			603.473i			1.41660i
$427$	−156.746	+	156.746i	−0.367087	+	0.367087i
$428$		−	150.597i		−	0.351863i
$429$		0			0
$430$	33.8171			0.0786444
$431$	378.330	+	378.330i	0.877795	+	0.877795i	0.993306	−	0.115511i	$-0.0368507\pi$
$431$	378.330	+	378.330i	0.877795	+	0.877795i	−0.115511	+	0.993306i	$0.536851\pi$
$432$	−292.966			−0.678162
$433$			161.880i			0.373857i	0.982374	+	0.186928i	$0.0598532\pi$
$433$			161.880i			0.373857i	−0.982374	+	0.186928i	$0.940147\pi$
$434$	104.259	+	104.259i	0.240229	+	0.240229i
$435$	−29.8176	−	29.8176i	−0.0685461	−	0.0685461i
$436$	−11.6732	+	11.6732i	−0.0267734	+	0.0267734i
$437$	−57.1117	+	57.1117i	−0.130690	+	0.130690i
$438$	−211.233			−0.482268
$439$			164.262i			0.374172i	0.982344	+	0.187086i	$0.0599043\pi$
$439$			164.262i			0.374172i	−0.982344	+	0.187086i	$0.940096\pi$
$440$	−5.12770	+	5.12770i	−0.0116539	+	0.0116539i
$441$		−	314.189i		−	0.712446i
$442$		0			0
$443$	309.912			0.699575			0.349788	−	0.936829i	$-0.386254\pi$
$443$	309.912			0.699575			0.349788	+	0.936829i	$0.386254\pi$
$444$	278.139	+	278.139i	0.626440	+	0.626440i
$445$	71.5121			0.160701
$446$			372.184i			0.834493i
$447$	−861.284	−	861.284i	−1.92681	−	1.92681i
$448$	44.9707	+	44.9707i	0.100381	+	0.100381i
$449$	96.2206	−	96.2206i	0.214300	−	0.214300i	−0.591791	−	0.806091i	$-0.701579\pi$
$449$	96.2206	−	96.2206i	0.214300	−	0.214300i	0.806091	+	0.591791i	$0.201579\pi$
$450$	548.547	−	548.547i	1.21899	−	1.21899i
$451$	−339.696			−0.753207
$452$		−	228.974i		−	0.506580i
$453$	411.266	−	411.266i	0.907871	−	0.907871i
$454$			168.522i			0.371193i
$455$		0			0
$456$	−73.1104			−0.160330
$457$	−160.576	−	160.576i	−0.351371	−	0.351371i	0.509249	−	0.860619i	$-0.329923\pi$
$457$	−160.576	−	160.576i	−0.351371	−	0.351371i	−0.860619	+	0.509249i	$0.829923\pi$
$458$	−448.744			−0.979791
$459$		−	147.396i		−	0.321124i
$460$	−11.2930	−	11.2930i	−0.0245501	−	0.0245501i
$461$	−483.636	−	483.636i	−1.04910	−	1.04910i	−0.998731	−	0.0503703i	$-0.983960\pi$
$461$	−483.636	−	483.636i	−1.04910	−	1.04910i	−0.0503703	−	0.998731i	$-0.516040\pi$
$462$	−248.258	+	248.258i	−0.537356	+	0.537356i
$463$	557.281	−	557.281i	1.20363	−	1.20363i	0.230575	−	0.973055i	$-0.425939\pi$
$463$	557.281	−	557.281i	1.20363	−	1.20363i	0.973055	−	0.230575i	$-0.0740607\pi$
$464$	66.0021			0.142246
$465$		−	33.5158i		−	0.0720769i
$466$	230.683	−	230.683i	0.495027	−	0.495027i
$467$		−	91.0355i		−	0.194937i	−0.995239	−	0.0974684i	$-0.968926\pi$
$467$		−	91.0355i		−	0.194937i	0.995239	−	0.0974684i	$-0.0310745\pi$
$468$		0			0
$469$	−272.126			−0.580227
$470$	5.65859	+	5.65859i	0.0120395	+	0.0120395i
$471$	−709.167			−1.50566
$472$		−	99.8120i		−	0.211466i
$473$	−206.617	−	206.617i	−0.436822	−	0.436822i
$474$	−796.915	−	796.915i	−1.68126	−	1.68126i
$475$	81.2131	−	81.2131i	0.170975	−	0.170975i
$476$	−22.6255	+	22.6255i	−0.0475326	+	0.0475326i
$477$	−518.725			−1.08747
$478$			369.036i			0.772041i
$479$	522.586	−	522.586i	1.09099	−	1.09099i	0.0955700	−	0.995423i	$-0.469533\pi$
$479$	522.586	−	522.586i	1.09099	−	1.09099i	0.995423	−	0.0955700i	$-0.0304674\pi$
$480$		−	14.4565i		−	0.0301178i
$481$		0			0
$482$	−314.584			−0.652665
$483$	−546.753	−	546.753i	−1.13199	−	1.13199i
$484$	−179.341			−0.370540
$485$			51.5786i			0.106348i
$486$	509.567	+	509.567i	1.04849	+	1.04849i
$487$	424.789	+	424.789i	0.872257	+	0.872257i	0.992718	−	0.120461i	$-0.0384372\pi$
$487$	424.789	+	424.789i	0.872257	+	0.872257i	−0.120461	+	0.992718i	$0.538437\pi$
$488$	−55.7682	+	55.7682i	−0.114279	+	0.114279i
$489$	−666.986	+	666.986i	−1.36398	+	1.36398i
$490$	9.19789			0.0187712
$491$			557.000i			1.13442i	0.823573	+	0.567210i	$0.191977\pi$
$491$			557.000i			1.13442i	−0.823573	+	0.567210i	$0.808023\pi$
$492$	478.853	−	478.853i	0.973279	−	0.973279i
$493$			33.2068i			0.0673565i
$494$		0			0
$495$	56.7318			0.114610
$496$	37.0941	+	37.0941i	0.0747865	+	0.0747865i
$497$	−608.030			−1.22340
$498$		−	1023.40i		−	2.05502i
$499$	92.7376	+	92.7376i	0.185847	+	0.185847i	0.793898	−	0.608051i	$-0.208048\pi$
$499$	92.7376	+	92.7376i	0.185847	+	0.185847i	−0.608051	+	0.793898i	$0.708048\pi$
$500$	32.2534	+	32.2534i	0.0645068	+	0.0645068i
$501$	657.773	−	657.773i	1.31292	−	1.31292i
$502$	−251.968	+	251.968i	−0.501929	+	0.501929i
$503$	−136.856			−0.272079			−0.136039	−	0.990703i	$-0.543437\pi$
$503$	−136.856			−0.272079			−0.136039	+	0.990703i	$0.543437\pi$
$504$		−	497.547i		−	0.987196i
$505$	−31.6441	+	31.6441i	−0.0626617	+	0.0626617i
$506$			137.997i			0.272721i
$507$		0			0
$508$	193.547			0.380997
$509$	−119.875	−	119.875i	−0.235511	−	0.235511i	0.579478	−	0.814988i	$-0.303257\pi$
$509$	−119.875	−	119.875i	−0.235511	−	0.235511i	−0.814988	+	0.579478i	$0.803257\pi$
$510$	7.27333			0.0142614
$511$		−	212.828i		−	0.416494i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	239.940	+	239.940i	0.467720	+	0.467720i
$514$	290.290	−	290.290i	0.564767	−	0.564767i
$515$	−35.1237	+	35.1237i	−0.0682013	+	0.0682013i
$516$	582.515			1.12891
$517$		−	69.1461i		−	0.133745i
$518$	−280.240	+	280.240i	−0.541003	+	0.541003i
$519$		−	783.789i		−	1.51019i
$520$		0			0
$521$	161.073			0.309161			0.154580	−	0.987980i	$-0.450597\pi$
$521$	161.073			0.309161			0.154580	+	0.987980i	$0.450597\pi$
$522$	−365.117	−	365.117i	−0.699457	−	0.699457i
$523$	135.412			0.258915			0.129457	−	0.991585i	$-0.458676\pi$
$523$	135.412			0.258915			0.129457	+	0.991585i	$0.458676\pi$
$524$			319.227i			0.609212i
$525$	777.486	+	777.486i	1.48093	+	1.48093i
$526$	−107.867	−	107.867i	−0.205071	−	0.205071i
$527$	−18.6627	+	18.6627i	−0.0354130	+	0.0354130i
$528$	−88.3271	+	88.3271i	−0.167286	+	0.167286i
$529$	225.081			0.425485
$530$		−	15.1857i		−	0.0286523i
$531$	−552.149	+	552.149i	−1.03983	+	1.03983i
$532$		−	73.6625i		−	0.138463i
$533$		0			0
$534$	1231.83			2.30680
$535$	−24.3887	−	24.3887i	−0.0455864	−	0.0455864i
$536$	−96.8190			−0.180632
$537$			1763.05i			3.28314i
$538$	−435.423	−	435.423i	−0.809337	−	0.809337i
$539$	−56.1976	−	56.1976i	−0.104263	−	0.104263i
$540$	−47.4448	+	47.4448i	−0.0878608	+	0.0878608i
$541$	−127.802	+	127.802i	−0.236233	+	0.236233i	−0.815288	−	0.579055i	$-0.803422\pi$
$541$	−127.802	+	127.802i	−0.236233	+	0.236233i	0.579055	+	0.815288i	$0.303422\pi$
$542$	118.955			0.219475
$543$			466.745i			0.859568i
$544$	−8.04987	+	8.04987i	−0.0147976	+	0.0147976i
$545$			3.78087i			0.00693737i
$546$		0			0
$547$	−161.504			−0.295254			−0.147627	−	0.989043i	$-0.547163\pi$
$547$	−161.504			−0.295254			−0.147627	+	0.989043i	$0.547163\pi$
$548$	178.948	+	178.948i	0.326548	+	0.326548i
$549$	617.008			1.12388
$550$		−	196.233i		−	0.356786i
$551$	−54.0560	−	54.0560i	−0.0981053	−	0.0981053i
$552$	−194.528	−	194.528i	−0.352405	−	0.352405i
$553$	802.933	−	802.933i	1.45196	−	1.45196i
$554$	36.8115	−	36.8115i	0.0664467	−	0.0664467i
$555$	90.0874			0.162320
$556$			120.894i			0.217435i
$557$	−420.771	+	420.771i	−0.755423	+	0.755423i	−0.975486	−	0.220063i	$-0.929374\pi$
$557$	−420.771	+	420.771i	−0.755423	+	0.755423i	0.220063	+	0.975486i	$0.429374\pi$
$558$		−	410.401i		−	0.735486i
$559$		0			0
$560$	14.5657			0.0260102
$561$	−44.4389	−	44.4389i	−0.0792136	−	0.0792136i
$562$	−60.2161			−0.107146
$563$		−	622.301i		−	1.10533i	−0.833403	−	0.552665i	$-0.813611\pi$
$563$		−	622.301i		−	1.10533i	0.833403	−	0.552665i	$-0.186389\pi$
$564$	97.4718	+	97.4718i	0.172822	+	0.172822i
$565$	−37.0815	−	37.0815i	−0.0656310	−	0.0656310i
$566$	−104.960	+	104.960i	−0.185441	+	0.185441i
$567$	−1177.57	+	1177.57i	−2.07684	+	2.07684i
$568$	−216.329			−0.380861
$569$		−	779.992i		−	1.37081i	−0.728161	−	0.685406i	$-0.759625\pi$
$569$		−	779.992i		−	1.37081i	0.728161	−	0.685406i	$-0.240375\pi$
$570$	−11.8400	+	11.8400i	−0.0207719	+	0.0207719i
$571$			556.142i			0.973980i	0.873408	+	0.486990i	$0.161905\pi$
$571$			556.142i			0.973980i	−0.873408	+	0.486990i	$0.838095\pi$
$572$		0			0
$573$	385.598			0.672945
$574$	482.469	+	482.469i	0.840539	+	0.840539i
$575$	432.174			0.751606
$576$		−	177.021i		−	0.307327i
$577$	401.975	+	401.975i	0.696663	+	0.696663i	0.963689	−	0.267026i	$-0.0860409\pi$
$577$	401.975	+	401.975i	0.696663	+	0.696663i	−0.267026	+	0.963689i	$0.586041\pi$
$578$	284.950	+	284.950i	0.492993	+	0.492993i
$579$	−1280.84	+	1280.84i	−2.21215	+	2.21215i
$580$	10.6888	−	10.6888i	0.0184290	−	0.0184290i
$581$	1031.13			1.77475
$582$			888.466i			1.52657i
$583$	−92.7822	+	92.7822i	−0.159146	+	0.159146i
$584$		−	75.7216i		−	0.129660i
$585$		0			0
$586$	−177.741			−0.303313
$587$	−474.205	−	474.205i	−0.807845	−	0.807845i	0.176462	−	0.984307i	$-0.443535\pi$
$587$	−474.205	−	474.205i	−0.807845	−	0.807845i	−0.984307	+	0.176462i	$0.943535\pi$
$588$	158.438			0.269452
$589$		−	60.7605i		−	0.103159i
$590$	−16.1642	−	16.1642i	−0.0273970	−	0.0273970i
$591$	1262.99	+	1262.99i	2.13703	+	2.13703i
$592$	−99.7056	+	99.7056i	−0.168422	+	0.168422i
$593$	−185.442	+	185.442i	−0.312719	+	0.312719i	−0.845962	−	0.533243i	$-0.820973\pi$
$593$	−185.442	+	185.442i	−0.312719	+	0.312719i	0.533243	+	0.845962i	$0.320973\pi$
$594$	579.760			0.976027
$595$			7.32826i			0.0123164i
$596$	308.748	−	308.748i	0.518033	−	0.518033i
$597$			964.199i			1.61507i
$598$		0			0
$599$	−171.466			−0.286254			−0.143127	−	0.989704i	$-0.545716\pi$
$599$	−171.466			−0.286254			−0.143127	+	0.989704i	$0.545716\pi$
$600$	276.619	+	276.619i	0.461032	+	0.461032i
$601$	107.652			0.179121			0.0895606	−	0.995981i	$-0.471454\pi$
$601$	107.652			0.179121			0.0895606	+	0.995981i	$0.471454\pi$
$602$			586.914i			0.974940i
$603$	535.593	+	535.593i	0.888213	+	0.888213i
$604$	147.428	+	147.428i	0.244086	+	0.244086i
$605$	−29.0437	+	29.0437i	−0.0480061	+	0.0480061i
$606$	−545.085	+	545.085i	−0.899480	+	0.899480i
$607$	433.595			0.714324			0.357162	−	0.934042i	$-0.383744\pi$
$607$	433.595			0.714324			0.357162	+	0.934042i	$0.383744\pi$
$608$		−	26.2081i		−	0.0431055i
$609$	517.500	−	517.500i	0.849754	−	0.849754i
$610$			18.0629i			0.0296114i
$611$		0			0
$612$	89.0621			0.145526
$613$	−454.202	−	454.202i	−0.740949	−	0.740949i	0.231812	−	0.972761i	$-0.425535\pi$
$613$	−454.202	−	454.202i	−0.740949	−	0.740949i	−0.972761	+	0.231812i	$0.925535\pi$
$614$	−318.815			−0.519242
$615$		−	155.097i		−	0.252191i
$616$	−88.9941	−	88.9941i	−0.144471	−	0.144471i
$617$	−292.823	−	292.823i	−0.474592	−	0.474592i	0.428805	−	0.903397i	$-0.358935\pi$
$617$	−292.823	−	292.823i	−0.474592	−	0.474592i	−0.903397	+	0.428805i	$0.858935\pi$
$618$	−605.022	+	605.022i	−0.978999	+	0.978999i
$619$	693.205	−	693.205i	1.11988	−	1.11988i	0.128120	−	0.991759i	$-0.459106\pi$
$619$	693.205	−	693.205i	1.11988	−	1.11988i	0.991759	−	0.128120i	$-0.0408943\pi$
$620$	12.0145			0.0193783
$621$			1276.84i			2.05610i
$622$	461.756	−	461.756i	0.742374	−	0.742374i
$623$			1241.13i			1.99219i
$624$		0			0
$625$	−609.308			−0.974893
$626$	8.16759	+	8.16759i	0.0130473	+	0.0130473i
$627$	144.681			0.230751
$628$		−	254.218i		−	0.404805i
$629$	−50.1636	−	50.1636i	−0.0797513	−	0.0797513i
$630$	−80.5760	−	80.5760i	−0.127898	−	0.127898i
$631$	−371.741	+	371.741i	−0.589130	+	0.589130i	−0.937396	−	0.348266i	$-0.886771\pi$
$631$	−371.741	+	371.741i	−0.589130	+	0.589130i	0.348266	+	0.937396i	$0.386771\pi$
$632$	285.673	−	285.673i	0.452014	−	0.452014i
$633$	1284.22			2.02878
$634$		−	183.225i		−	0.288999i
$635$	31.3442	−	31.3442i	0.0493609	−	0.0493609i
$636$		−	261.581i		−	0.411291i
$637$		0			0
$638$	−130.614			−0.204724
$639$	1196.71	+	1196.71i	1.87279	+	1.87279i
$640$	5.18229			0.00809733
$641$		−	1081.26i		−	1.68683i	−0.537260	−	0.843416i	$-0.680541\pi$
$641$		−	1081.26i		−	1.68683i	0.537260	−	0.843416i	$-0.319459\pi$
$642$	−420.107	−	420.107i	−0.654372	−	0.654372i
$643$	−279.195	−	279.195i	−0.434207	−	0.434207i	0.455850	−	0.890057i	$-0.349335\pi$
$643$	−279.195	−	279.195i	−0.434207	−	0.434207i	−0.890057	+	0.455850i	$0.849335\pi$
$644$	195.997	−	195.997i	0.304343	−	0.304343i
$645$	94.3363	−	94.3363i	0.146258	−	0.146258i
$646$	13.1858			0.0204114
$647$		−	318.067i		−	0.491603i	−0.969320	−	0.245801i	$-0.920949\pi$
$647$		−	318.067i		−	0.491603i	0.969320	−	0.245801i	$-0.0790511\pi$
$648$	−418.963	+	418.963i	−0.646548	+	0.646548i
$649$			197.521i			0.304347i
$650$		0			0
$651$	581.685			0.893525
$652$	−239.097	−	239.097i	−0.366713	−	0.366713i
$653$	−402.230			−0.615972			−0.307986	−	0.951391i	$-0.599655\pi$
$653$	−402.230			−0.615972			−0.307986	+	0.951391i	$0.599655\pi$
$654$			65.1272i			0.0995828i
$655$	51.6977	+	51.6977i	0.0789278	+	0.0789278i
$656$	171.656	+	171.656i	0.261671	+	0.261671i
$657$	−418.884	+	418.884i	−0.637570	+	0.637570i
$658$	−98.2079	+	98.2079i	−0.149252	+	0.149252i
$659$	585.747			0.888842			0.444421	−	0.895818i	$-0.353409\pi$
$659$	585.747			0.888842			0.444421	+	0.895818i	$0.353409\pi$
$660$			28.6085i			0.0433463i
$661$	571.835	−	571.835i	0.865105	−	0.865105i	−0.126821	−	0.991926i	$-0.540477\pi$
$661$	571.835	−	571.835i	0.865105	−	0.865105i	0.991926	+	0.126821i	$0.0404772\pi$
$662$			211.479i			0.319454i
$663$		0			0
$664$	366.863			0.552504
$665$	−11.9294	−	11.9294i	−0.0179389	−	0.0179389i
$666$	1103.12			1.65634
$667$		−	287.658i		−	0.431271i
$668$	235.794	+	235.794i	0.352986	+	0.352986i
$669$	1038.25	+	1038.25i	1.55194	+	1.55194i
$670$	−15.6795	+	15.6795i	−0.0234022	+	0.0234022i
$671$	110.362	−	110.362i	0.164473	−	0.164473i
$672$	250.901			0.373365
$673$			431.251i			0.640788i	0.947284	+	0.320394i	$0.103815\pi$
$673$			431.251i			0.640788i	−0.947284	+	0.320394i	$0.896185\pi$
$674$	−61.7332	+	61.7332i	−0.0915923	+	0.0915923i
$675$		−	1815.67i		−	2.68988i
$676$		0			0
$677$	6.72056			0.00992697			0.00496348	−	0.999988i	$-0.498420\pi$
$677$	6.72056			0.00992697			0.00496348	+	0.999988i	$0.498420\pi$
$678$	−638.747	−	638.747i	−0.942104	−	0.942104i
$679$	−895.175			−1.31837
$680$			2.60730i			0.00383426i
$681$	470.109	+	470.109i	0.690321	+	0.690321i
$682$	−73.4068	−	73.4068i	−0.107635	−	0.107635i
$683$	−86.6845	+	86.6845i	−0.126917	+	0.126917i	−0.767712	−	0.640795i	$-0.778605\pi$
$683$	−86.6845	+	86.6845i	−0.126917	+	0.126917i	0.640795	+	0.767712i	$0.278605\pi$
$684$	−144.981	+	144.981i	−0.211960	+	0.211960i
$685$	57.9601			0.0846133
$686$		−	391.257i		−	0.570346i
$687$	−1251.82	+	1251.82i	−1.82215	+	1.82215i
$688$			208.816i			0.303512i
$689$		0			0
$690$	−63.0061			−0.0913133
$691$	−66.5361	−	66.5361i	−0.0962896	−	0.0962896i	0.657321	−	0.753611i	$-0.271690\pi$
$691$	−66.5361	−	66.5361i	−0.0962896	−	0.0962896i	−0.753611	+	0.657321i	$0.771690\pi$
$692$	280.968			0.406023
$693$			984.612i			1.42080i
$694$	220.862	+	220.862i	0.318245	+	0.318245i
$695$	19.5783	+	19.5783i	0.0281703	+	0.0281703i
$696$	184.120	−	184.120i	0.264540	−	0.264540i
$697$	−86.3632	+	86.3632i	−0.123907	+	0.123907i
$698$	−411.572			−0.589645
$699$		−	1287.03i		−	1.84124i
$700$	−278.708	+	278.708i	−0.398155	+	0.398155i
$701$		−	716.506i		−	1.02212i	−0.859545	−	0.511060i	$-0.829253\pi$
$701$		−	716.506i		−	1.02212i	0.859545	−	0.511060i	$-0.170747\pi$
$702$		0			0
$703$	163.319			0.232317
$704$	−31.6629	−	31.6629i	−0.0449758	−	0.0449758i
$705$	31.5704			0.0447808
$706$		−	27.8783i		−	0.0394877i
$707$	−549.201	−	549.201i	−0.776805	−	0.776805i
$708$	−278.436	−	278.436i	−0.393271	−	0.393271i
$709$	700.605	−	700.605i	0.988160	−	0.988160i	−0.0117707	−	0.999931i	$-0.503747\pi$
$709$	700.605	−	700.605i	0.988160	−	0.988160i	0.999931	+	0.0117707i	$0.00374682\pi$
$710$	−35.0338	+	35.0338i	−0.0493433	+	0.0493433i
$711$	−3160.63			−4.44533
$712$			441.579i			0.620195i
$713$	161.668	−	161.668i	0.226743	−	0.226743i
$714$			126.233i			0.176796i
$715$		0			0
$716$	−632.006			−0.882691
$717$	1029.46	+	1029.46i	1.43579	+	1.43579i
$718$	−551.236			−0.767738
$719$			173.887i			0.241846i	0.992662	+	0.120923i	$0.0385854\pi$
$719$			173.887i			0.241846i	−0.992662	+	0.120923i	$0.961415\pi$
$720$	−28.6679	−	28.6679i	−0.0398165	−	0.0398165i
$721$	−609.591	−	609.591i	−0.845479	−	0.845479i
$722$	339.535	−	339.535i	0.470271	−	0.470271i
$723$	−877.566	+	877.566i	−1.21378	+	1.21378i
$724$	−167.316			−0.231099
$725$			409.051i			0.564208i
$726$	−500.291	+	500.291i	−0.689106	+	0.689106i
$727$		−	729.011i		−	1.00277i	−0.865225	−	0.501383i	$-0.832825\pi$
$727$		−	729.011i		−	1.00277i	0.865225	−	0.501383i	$-0.167175\pi$
$728$		0			0
$729$	957.649			1.31365
$730$	−12.2628	−	12.2628i	−0.0167984	−	0.0167984i
$731$	−105.059			−0.143720
$732$			311.143i			0.425058i
$733$	−762.465	−	762.465i	−1.04020	−	1.04020i	−0.999157	−	0.0410404i	$-0.986933\pi$
$733$	−762.465	−	762.465i	−1.04020	−	1.04020i	−0.0410404	−	0.999157i	$-0.513067\pi$
$734$	468.735	+	468.735i	0.638603	+	0.638603i
$735$	25.6585	−	25.6585i	0.0349095	−	0.0349095i
$736$	69.7330	−	69.7330i	0.0947460	−	0.0947460i
$737$	191.598			0.259971
$738$		−	1899.17i		−	2.57340i
$739$	433.888	−	433.888i	0.587129	−	0.587129i	−0.349724	−	0.936853i	$-0.613725\pi$
$739$	433.888	−	433.888i	0.587129	−	0.587129i	0.936853	+	0.349724i	$0.113725\pi$
$740$			32.2940i			0.0436405i
$741$		0			0
$742$	263.556			0.355197
$743$	−117.752	−	117.752i	−0.158482	−	0.158482i	0.623412	−	0.781894i	$-0.285746\pi$
$743$	−117.752	−	117.752i	−0.158482	−	0.158482i	−0.781894	+	0.623412i	$0.785746\pi$
$744$	206.956			0.278166
$745$		−	100.001i		−	0.134230i
$746$	260.814	+	260.814i	0.349617	+	0.349617i
$747$	−2029.45	−	2029.45i	−2.71680	−	2.71680i
$748$	15.9302	−	15.9302i	0.0212970	−	0.0212970i
$749$	423.279	−	423.279i	0.565126	−	0.565126i
$750$	179.948			0.239931
$751$			134.259i			0.178774i	0.995997	+	0.0893871i	$0.0284908\pi$
$751$			134.259i			0.178774i	−0.995997	+	0.0893871i	$0.971509\pi$
$752$	−34.9411	+	34.9411i	−0.0464642	+	0.0464642i
$753$			1405.78i			1.86691i
$754$		0			0
$755$	47.7509			0.0632462
$756$	−823.431	−	823.431i	−1.08919	−	1.08919i
$757$	−1196.43			−1.58049			−0.790247	−	0.612788i	$-0.790048\pi$
$757$	−1196.43			−1.58049			−0.790247	+	0.612788i	$0.790048\pi$
$758$		−	302.913i		−	0.399622i
$759$	384.957	+	384.957i	0.507190	+	0.507190i
$760$	−4.24432	−	4.24432i	−0.00558463	−	0.00558463i
$761$	24.7365	−	24.7365i	0.0325053	−	0.0325053i	−0.690667	−	0.723173i	$-0.742683\pi$
$761$	24.7365	−	24.7365i	0.0325053	−	0.0325053i	0.723173	+	0.690667i	$0.242683\pi$
$762$	539.918	−	539.918i	0.708554	−	0.708554i
$763$	−65.6190			−0.0860013
$764$			138.227i			0.180925i
$765$	14.4233	−	14.4233i	0.0188540	−	0.0188540i
$766$		−	970.071i		−	1.26641i
$767$		0			0
$768$	89.2673			0.116234
$769$	−176.417	−	176.417i	−0.229410	−	0.229410i	0.583036	−	0.812446i	$-0.301865\pi$
$769$	−176.417	−	176.417i	−0.229410	−	0.229410i	−0.812446	+	0.583036i	$0.801865\pi$
$770$	−28.8246			−0.0374345
$771$		−	1619.59i		−	2.10063i
$772$	−459.147	−	459.147i	−0.594750	−	0.594750i
$773$	−390.198	−	390.198i	−0.504784	−	0.504784i	0.408137	−	0.912921i	$-0.366179\pi$
$773$	−390.198	−	390.198i	−0.504784	−	0.504784i	−0.912921	+	0.408137i	$0.866179\pi$
$774$	1155.15	−	1155.15i	1.49244	−	1.49244i
$775$	−229.892	+	229.892i	−0.296635	+	0.296635i
$776$	−318.492			−0.410427
$777$			1563.52i			2.01225i
$778$	374.691	−	374.691i	0.481608	−	0.481608i
$779$		−	281.175i		−	0.360943i
$780$		0			0
$781$	428.101			0.548145
$782$	35.0839	+	35.0839i	0.0448643	+	0.0448643i
$783$	−1208.52			−1.54345
$784$			56.7958i			0.0724437i
$785$	−41.1697	−	41.1697i	−0.0524455	−	0.0524455i
$786$	890.517	+	890.517i	1.13297	+	1.13297i
$787$	−498.109	+	498.109i	−0.632922	+	0.632922i	−0.948800	−	0.315878i	$-0.897701\pi$
$787$	−498.109	+	498.109i	−0.632922	+	0.632922i	0.315878	+	0.948800i	$0.397701\pi$
$788$	−452.748	+	452.748i	−0.574553	+	0.574553i
$789$	−601.815			−0.762757
$790$		−	92.5276i		−	0.117123i
$791$	643.570	−	643.570i	0.813616	−	0.813616i
$792$			350.312i			0.442313i
$793$		0			0
$794$	−922.776			−1.16219
$795$	−42.3621	−	42.3621i	−0.0532857	−	0.0532857i
$796$	−345.640			−0.434221
$797$			136.438i			0.171189i	0.996330	+	0.0855945i	$0.0272789\pi$
$797$			136.438i			0.171189i	−0.996330	+	0.0855945i	$0.972721\pi$
$798$	−205.489	−	205.489i	−0.257505	−	0.257505i
$799$	−17.5795	−	17.5795i	−0.0220018	−	0.0220018i
$800$	−99.1607	+	99.1607i	−0.123951	+	0.123951i
$801$	2442.77	−	2442.77i	3.04965	−	3.04965i
$802$	−611.320			−0.762244
$803$			149.848i			0.186610i
$804$	−270.087	+	270.087i	−0.335929	+	0.335929i
$805$		−	63.4819i		−	0.0788596i
$806$		0			0
$807$	−2429.32			−3.01031
$808$	−195.399	−	195.399i	−0.241830	−	0.241830i
$809$	−100.101			−0.123735			−0.0618674	−	0.998084i	$-0.519706\pi$
$809$	−100.101			−0.123735			−0.0618674	+	0.998084i	$0.519706\pi$
$810$			135.699i			0.167530i
$811$	−143.367	−	143.367i	−0.176778	−	0.176778i	0.613172	−	0.789950i	$-0.289893\pi$
$811$	−143.367	−	143.367i	−0.176778	−	0.176778i	−0.789950	+	0.613172i	$0.789893\pi$
$812$	185.510	+	185.510i	0.228461	+	0.228461i
$813$	331.838	−	331.838i	0.408165	−	0.408165i
$814$	197.311	−	197.311i	0.242397	−	0.242397i
$815$	−77.4419			−0.0950207
$816$			44.9119i			0.0550391i
$817$	171.022	−	171.022i	0.209329	−	0.209329i
$818$			394.757i			0.482588i
$819$		0			0
$820$	55.5983			0.0678028
$821$	−209.254	−	209.254i	−0.254877	−	0.254877i	0.568090	−	0.822967i	$-0.307683\pi$
$821$	−209.254	−	209.254i	−0.254877	−	0.254877i	−0.822967	+	0.568090i	$0.807683\pi$
$822$	998.390			1.21459
$823$			246.944i			0.300054i	0.988682	+	0.150027i	$0.0479361\pi$
$823$			246.944i			0.300054i	−0.988682	+	0.150027i	$0.952064\pi$
$824$	−216.884	−	216.884i	−0.263209	−	0.263209i
$825$	−547.411	−	547.411i	−0.663529	−	0.663529i
$826$	280.539	−	280.539i	0.339635	−	0.339635i
$827$	450.766	−	450.766i	0.545062	−	0.545062i	−0.379947	−	0.925008i	$-0.624058\pi$
$827$	450.766	−	450.766i	0.545062	−	0.545062i	0.925008	+	0.379947i	$0.124058\pi$
$828$	−771.511			−0.931777
$829$		−	903.915i		−	1.09037i	−0.838316	−	0.545184i	$-0.816460\pi$
$829$		−	903.915i		−	1.09037i	0.838316	−	0.545184i	$-0.183540\pi$
$830$	59.4122	−	59.4122i	0.0715809	−	0.0715809i
$831$		−	205.379i		−	0.247147i
$832$		0			0
$833$	−28.5750			−0.0343037
$834$	337.246	+	337.246i	0.404371	+	0.404371i
$835$	76.3722			0.0914637
$836$			51.8642i			0.0620385i
$837$	−679.207	−	679.207i	−0.811478	−	0.811478i
$838$	187.590	+	187.590i	0.223855	+	0.223855i
$839$	−682.338	+	682.338i	−0.813276	+	0.813276i	−0.985124	−	0.171848i	$-0.945026\pi$
$839$	−682.338	+	682.338i	−0.813276	+	0.813276i	0.171848	+	0.985124i	$0.445026\pi$
$840$	40.6326	−	40.6326i	0.0483721	−	0.0483721i
$841$	−568.733			−0.676258
$842$			820.961i			0.975013i
$843$	−167.979	+	167.979i	−0.199263	+	0.199263i
$844$			460.358i			0.545447i
$845$		0			0
$846$	386.581			0.456951
$847$	−504.069	−	504.069i	−0.595123	−	0.595123i
$848$	93.7699			0.110578
$849$			585.592i			0.689743i
$850$	−49.8895	−	49.8895i	−0.0586935	−	0.0586935i
$851$	434.549	+	434.549i	0.510633	+	0.510633i
$852$	−603.473	+	603.473i	−0.708302	+	0.708302i
$853$	−103.615	+	103.615i	−0.121471	+	0.121471i	−0.765229	−	0.643758i	$-0.777374\pi$
$853$	−103.615	+	103.615i	−0.121471	+	0.121471i	0.643758	+	0.765229i	$0.277374\pi$
$854$	−313.492			−0.367087
$855$			46.9582i			0.0549219i
$856$	150.597	−	150.597i	0.175931	−	0.175931i
$857$			497.605i			0.580636i	0.956930	+	0.290318i	$0.0937612\pi$
$857$			497.605i			0.580636i	−0.956930	+	0.290318i	$0.906239\pi$
$858$		0			0
$859$	763.167			0.888437			0.444218	−	0.895918i	$-0.353481\pi$
$859$	763.167			0.888437			0.444218	+	0.895918i	$0.353481\pi$
$860$	33.8171	+	33.8171i	0.0393222	+	0.0393222i
$861$	2691.80			3.12636
$862$			756.659i			0.877795i
$863$	299.561	+	299.561i	0.347115	+	0.347115i	0.859034	−	0.511919i	$-0.171065\pi$
$863$	299.561	+	299.561i	0.347115	+	0.347115i	−0.511919	+	0.859034i	$0.671065\pi$
$864$	−292.966	−	292.966i	−0.339081	−	0.339081i
$865$	45.5018	−	45.5018i	0.0526032	−	0.0526032i
$866$	−161.880	+	161.880i	−0.186928	+	0.186928i
$867$	1589.80			1.83367
$868$			208.519i			0.240229i
$869$	−565.328	+	565.328i	−0.650550	+	0.650550i
$870$		−	59.6351i		−	0.0685461i
$871$		0			0
$872$	−23.3464			−0.0267734
$873$	1761.86	+	1761.86i	2.01817	+	2.01817i
$874$	−114.223			−0.130690
$875$			181.307i			0.207208i
$876$	−211.233	−	211.233i	−0.241134	−	0.241134i
$877$	−887.711	−	887.711i	−1.01221	−	1.01221i	−0.999924	−	0.0122887i	$-0.996088\pi$
$877$	−887.711	−	887.711i	−1.01221	−	1.01221i	−0.0122887	−	0.999924i	$-0.503912\pi$
$878$	−164.262	+	164.262i	−0.187086	+	0.187086i
$879$	−495.828	+	495.828i	−0.564082	+	0.564082i
$880$	−10.2554			−0.0116539
$881$		−	562.408i		−	0.638374i	−0.947692	−	0.319187i	$-0.896590\pi$
$881$		−	562.408i		−	0.638374i	0.947692	−	0.319187i	$-0.103410\pi$
$882$	314.189	−	314.189i	0.356223	−	0.356223i
$883$		−	325.309i		−	0.368413i	−0.982888	−	0.184207i	$-0.941028\pi$
$883$		−	325.309i		−	0.368413i	0.982888	−	0.184207i	$-0.0589715\pi$
$884$		0			0
$885$	−90.1835			−0.101902
$886$	309.912	+	309.912i	0.349788	+	0.349788i
$887$	1488.80			1.67846			0.839231	−	0.543775i	$-0.183006\pi$
$887$	1488.80			1.67846			0.839231	+	0.543775i	$0.183006\pi$
$888$			556.279i			0.626440i
$889$	543.996	+	543.996i	0.611919	+	0.611919i
$890$	71.5121	+	71.5121i	0.0803507	+	0.0803507i
$891$	829.100	−	829.100i	0.930527	−	0.930527i
$892$	−372.184	+	372.184i	−0.417246	+	0.417246i
$893$	57.2338			0.0640916
$894$		−	1722.57i		−	1.92681i
$895$	−102.351	+	102.351i	−0.114359	+	0.114359i
$896$			89.9415i			0.100381i
$897$		0			0
$898$	192.441			0.214300
$899$	153.018	+	153.018i	0.170209	+	0.170209i
$900$	1097.09			1.21899
$901$			47.1772i			0.0523609i
$902$	−339.696	−	339.696i	−0.376603	−	0.376603i
$903$	1637.26	+	1637.26i	1.81313	+	1.81313i
$904$	228.974	−	228.974i	0.253290	−	0.253290i
$905$	−27.0962	+	27.0962i	−0.0299406	+	0.0299406i
$906$	822.531			0.907871
$907$			262.849i			0.289801i	0.989446	+	0.144900i	$0.0462861\pi$
$907$			262.849i			0.289801i	−0.989446	+	0.144900i	$0.953714\pi$
$908$	−168.522	+	168.522i	−0.185597	+	0.185597i
$909$			2161.85i			2.37827i
$910$		0			0
$911$	−1043.25			−1.14517			−0.572584	−	0.819846i	$-0.694059\pi$
$911$	−1043.25			−1.14517			−0.572584	+	0.819846i	$0.694059\pi$
$912$	−73.1104	−	73.1104i	−0.0801649	−	0.0801649i
$913$	−725.997			−0.795178
$914$		−	321.153i		−	0.351371i
$915$	50.3885	+	50.3885i	0.0550694	+	0.0550694i
$916$	−448.744	−	448.744i	−0.489895	−	0.489895i
$917$	−897.242	+	897.242i	−0.978453	+	0.978453i
$918$	147.396	−	147.396i	0.160562	−	0.160562i
$919$	−816.955			−0.888961			−0.444481	−	0.895788i	$-0.646612\pi$
$919$	−816.955			−0.888961			−0.444481	+	0.895788i	$0.646612\pi$
$920$		−	22.5860i		−	0.0245501i
$921$	−889.367	+	889.367i	−0.965654	+	0.965654i
$922$		−	967.271i		−	1.04910i
$923$		0			0
$924$	−496.517			−0.537356
$925$	−617.930	−	617.930i	−0.668033	−	0.668033i
$926$	1114.56			1.20363
$927$			2399.56i			2.58852i
$928$	66.0021	+	66.0021i	0.0711229	+	0.0711229i
$929$	1058.03	+	1058.03i	1.13889	+	1.13889i	0.988649	+	0.150242i	$0.0480054\pi$
$929$	1058.03	+	1058.03i	1.13889	+	1.13889i	0.150242	+	0.988649i	$0.451995\pi$
$930$	33.5158	−	33.5158i	0.0360385	−	0.0360385i
$931$	46.5161	−	46.5161i	0.0499635	−	0.0499635i
$932$	461.365			0.495027
$933$		−	2576.24i		−	2.76124i
$934$	91.0355	−	91.0355i	0.0974684	−	0.0974684i
$935$		−	5.15967i		−	0.00551836i
$936$		0			0
$937$	−1671.65			−1.78404			−0.892020	−	0.451996i	$-0.850712\pi$
$937$	−1671.65			−1.78404			−0.892020	+	0.451996i	$0.850712\pi$
$938$	−272.126	−	272.126i	−0.290113	−	0.290113i
$939$	45.5687			0.0485290
$940$			11.3172i			0.0120395i
$941$	87.2271	+	87.2271i	0.0926962	+	0.0926962i	0.751934	−	0.659238i	$-0.229121\pi$
$941$	87.2271	+	87.2271i	0.0926962	+	0.0926962i	−0.659238	+	0.751934i	$0.729121\pi$
$942$	−709.167	−	709.167i	−0.752831	−	0.752831i
$943$	748.132	−	748.132i	0.793353	−	0.793353i
$944$	99.8120	−	99.8120i	0.105733	−	0.105733i
$945$	−266.704			−0.282226
$946$		−	413.234i		−	0.436822i
$947$	1046.94	−	1046.94i	1.10554	−	1.10554i	0.111806	−	0.993730i	$-0.464336\pi$
$947$	1046.94	−	1046.94i	1.10554	−	1.10554i	0.993730	−	0.111806i	$-0.0356635\pi$
$948$		−	1593.83i		−	1.68126i
$949$		0			0
$950$	162.426			0.170975
$951$	−511.127	−	511.127i	−0.537462	−	0.537462i
$952$	−45.2511			−0.0475326
$953$		−	850.534i		−	0.892481i	−0.894913	−	0.446240i	$-0.852763\pi$
$953$		−	850.534i		−	0.892481i	0.894913	−	0.446240i	$-0.147237\pi$
$954$	−518.725	−	518.725i	−0.543737	−	0.543737i
$955$	22.3853	+	22.3853i	0.0234401	+	0.0234401i
$956$	−369.036	+	369.036i	−0.386021	+	0.386021i
$957$	−364.361	+	364.361i	−0.380732	+	0.380732i
$958$	1045.17			1.09099
$959$			1005.93i			1.04894i
$960$	14.4565	−	14.4565i	0.0150589	−	0.0150589i
$961$		−	789.003i		−	0.821023i
$962$		0			0
$963$	−1666.18			−1.73019
$964$	−314.584	−	314.584i	−0.326332	−	0.326332i
$965$	−148.714			−0.154108
$966$		−	1093.51i		−	1.13199i
$967$	133.506	+	133.506i	0.138062	+	0.138062i	0.772760	−	0.634698i	$-0.218875\pi$
$967$	133.506	+	133.506i	0.138062	+	0.138062i	−0.634698	+	0.772760i	$0.718875\pi$
$968$	−179.341	−	179.341i	−0.185270	−	0.185270i
$969$	36.7831	−	36.7831i	0.0379598	−	0.0379598i
$970$	−51.5786	+	51.5786i	−0.0531738	+	0.0531738i
$971$	1387.44			1.42888			0.714439	−	0.699697i	$-0.246682\pi$
$971$	1387.44			1.42888			0.714439	+	0.699697i	$0.246682\pi$
$972$			1019.13i			1.04849i
$973$	−339.793	+	339.793i	−0.349221	+	0.349221i
$974$			849.579i			0.872257i
$975$		0			0
$976$	−111.536			−0.114279
$977$	990.982	+	990.982i	1.01431	+	1.01431i	0.999896	+	0.0144153i	$0.00458870\pi$
$977$	990.982	+	990.982i	1.01431	+	1.01431i	0.0144153	+	0.999896i	$0.495411\pi$
$978$	−1333.97			−1.36398
$979$		−	873.855i		−	0.892599i
$980$	9.19789	+	9.19789i	0.00938560	+	0.00938560i
$981$	129.150	+	129.150i	0.131651	+	0.131651i
$982$	−557.000	+	557.000i	−0.567210	+	0.567210i
$983$	457.371	−	457.371i	0.465280	−	0.465280i	−0.435101	−	0.900382i	$-0.643287\pi$
$983$	457.371	−	457.371i	0.465280	−	0.465280i	0.900382	+	0.435101i	$0.143287\pi$
$984$	957.706			0.973279
$985$			146.642i			0.148875i
$986$	−33.2068	+	33.2068i	−0.0336783	+	0.0336783i
$987$			547.922i			0.555139i
$988$		0			0
$989$	910.087			0.920210
$990$	56.7318	+	56.7318i	0.0573049	+	0.0573049i
$991$	−151.629			−0.153007			−0.0765033	−	0.997069i	$-0.524376\pi$
$991$	−151.629			−0.153007			−0.0765033	+	0.997069i	$0.524376\pi$
$992$			74.1882i			0.0747865i
$993$	589.942	+	589.942i	0.594100	+	0.594100i
$994$	−608.030	−	608.030i	−0.611700	−	0.611700i
$995$	−55.9752	+	55.9752i	−0.0562565	+	0.0562565i
$996$	1023.40	−	1023.40i	1.02751	−	1.02751i
$997$	−479.802			−0.481245			−0.240623	−	0.970619i	$-0.577352\pi$
$997$	−479.802			−0.481245			−0.240623	+	0.970619i	$0.577352\pi$
$998$			185.475i			0.185847i
$999$	1825.65	−	1825.65i	1.82747	−	1.82747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.d.g.99.4		8
13.2	odd	12		338.3.f.h.19.1		8
13.3	even	3		26.3.f.b.7.1	✓	8
13.4	even	6		338.3.f.j.89.1		8
13.5	odd	4	inner	338.3.d.g.239.4		8
13.6	odd	12		26.3.f.b.15.1	yes	8
13.7	odd	12		338.3.f.i.249.1		8
13.8	odd	4		338.3.d.f.239.4		8
13.9	even	3		338.3.f.h.89.1		8
13.10	even	6		338.3.f.i.319.1		8
13.11	odd	12		338.3.f.j.19.1		8
13.12	even	2		338.3.d.f.99.4		8
39.29	odd	6		234.3.bb.f.163.2		8
39.32	even	12		234.3.bb.f.145.2		8
52.3	odd	6		208.3.bd.f.33.2		8
52.19	even	12		208.3.bd.f.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.7.1	✓	8	13.3	even	3
26.3.f.b.15.1	yes	8	13.6	odd	12
208.3.bd.f.33.2		8	52.3	odd	6
208.3.bd.f.145.2		8	52.19	even	12
234.3.bb.f.145.2		8	39.32	even	12
234.3.bb.f.163.2		8	39.29	odd	6
338.3.d.f.99.4		8	13.12	even	2
338.3.d.f.239.4		8	13.8	odd	4
338.3.d.g.99.4		8	1.1	even	1	trivial
338.3.d.g.239.4		8	13.5	odd	4	inner
338.3.f.h.19.1		8	13.2	odd	12
338.3.f.h.89.1		8	13.9	even	3
338.3.f.i.249.1		8	13.7	odd	12
338.3.f.i.319.1		8	13.10	even	6
338.3.f.j.19.1		8	13.11	odd	12
338.3.f.j.89.1		8	13.4	even	6

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +5.57921 q^{3} +2.00000i q^{4} +(0.323893 + 0.323893i) q^{5} +(5.57921 + 5.57921i) q^{6} +(-5.62134 + 5.62134i) q^{7} +(-2.00000 + 2.00000i) q^{8} +22.1276 q^{9} +0.647786i q^{10} +(3.95787 - 3.95787i) q^{11} +11.1584i q^{12} -11.2427 q^{14} +(1.80707 + 1.80707i) q^{15} -4.00000 q^{16} -2.01247i q^{17} +(22.1276 + 22.1276i) q^{18} +(3.27602 + 3.27602i) q^{19} +(-0.647786 + 0.647786i) q^{20} +(-31.3626 + 31.3626i) q^{21} +7.91574 q^{22} +17.4333i q^{23} +(-11.1584 + 11.1584i) q^{24} -24.7902i q^{25} +73.2415 q^{27} +(-11.2427 - 11.2427i) q^{28} -16.5005 q^{29} +3.61413i q^{30} +(-9.27353 - 9.27353i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(22.0818 - 22.0818i) q^{33} +(2.01247 - 2.01247i) q^{34} -3.64143 q^{35} +44.2552i q^{36} +(24.9264 - 24.9264i) q^{37} +6.55204i q^{38} -1.29557 q^{40} +(-42.9141 - 42.9141i) q^{41} -62.7253 q^{42} -52.2041i q^{43} +(7.91574 + 7.91574i) q^{44} +(7.16697 + 7.16697i) q^{45} +(-17.4333 + 17.4333i) q^{46} +(8.73527 - 8.73527i) q^{47} -22.3168 q^{48} -14.1990i q^{49} +(24.7902 - 24.7902i) q^{50} -11.2280i q^{51} -23.4425 q^{53} +(73.2415 + 73.2415i) q^{54} +2.56385 q^{55} -22.4854i q^{56} +(18.2776 + 18.2776i) q^{57} +(-16.5005 - 16.5005i) q^{58} +(-24.9530 + 24.9530i) q^{59} +(-3.61413 + 3.61413i) q^{60} +27.8841 q^{61} -18.5471i q^{62} +(-124.387 + 124.387i) q^{63} -8.00000i q^{64} +44.1635 q^{66} +(24.2048 + 24.2048i) q^{67} +4.02494 q^{68} +97.2638i q^{69} +(-3.64143 - 3.64143i) q^{70} +(54.0823 + 54.0823i) q^{71} +(-44.2552 + 44.2552i) q^{72} +(-18.9304 + 18.9304i) q^{73} +49.8528 q^{74} -138.310i q^{75} +(-6.55204 + 6.55204i) q^{76} +44.4971i q^{77} -142.837 q^{79} +(-1.29557 - 1.29557i) q^{80} +209.481 q^{81} -85.8281i q^{82} +(-91.7157 - 91.7157i) q^{83} +(-62.7253 - 62.7253i) q^{84} +(0.651824 - 0.651824i) q^{85} +(52.2041 - 52.2041i) q^{86} -92.0599 q^{87} +15.8315i q^{88} +(110.395 - 110.395i) q^{89} +14.3339i q^{90} -34.8665 q^{92} +(-51.7389 - 51.7389i) q^{93} +17.4705 q^{94} +2.12216i q^{95} +(-22.3168 - 22.3168i) q^{96} +(79.6229 + 79.6229i) q^{97} +(14.1990 - 14.1990i) q^{98} +(87.5780 - 87.5780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} + 84 q^{9} + 42 q^{11} + 20 q^{14} + 60 q^{15} - 32 q^{16} + 84 q^{18} + 22 q^{19} - 12 q^{20} - 102 q^{21} + 84 q^{22} + 72 q^{27} + 20 q^{28} + 12 q^{29}+ \cdots + 252 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 + 84 * q^9 + 42 * q^11 + 20 * q^14 + 60 * q^15 - 32 * q^16 + 84 * q^18 + 22 * q^19 - 12 * q^20 - 102 * q^21 + 84 * q^22 + 72 * q^27 + 20 * q^28 + 12 * q^29 + 32 * q^31 - 32 * q^32 + 54 * q^33 - 60 * q^34 + 156 * q^35 + 32 * q^37 - 24 * q^40 - 12 * q^41 - 204 * q^42 + 84 * q^44 - 102 * q^45 - 108 * q^46 + 60 * q^47 - 88 * q^50 - 132 * q^53 + 72 * q^54 + 324 * q^55 - 294 * q^57 + 12 * q^58 + 234 * q^59 - 120 * q^60 - 72 * q^61 - 156 * q^63 + 108 * q^66 - 14 * q^67 - 120 * q^68 + 156 * q^70 + 162 * q^71 - 168 * q^72 + 166 * q^73 + 64 * q^74 - 44 * q^76 - 96 * q^79 - 24 * q^80 + 24 * q^81 - 240 * q^83 - 204 * q^84 - 234 * q^85 + 132 * q^86 - 720 * q^87 + 210 * q^89 - 216 * q^92 - 444 * q^93 + 120 * q^94 + 146 * q^97 - 16 * q^98 + 252 * q^99

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