LMFDB - Embedded newform 1690.2.b.c.339.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(339,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1690.339");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.2
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.c.339.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -0.539189i q^{3} -1.00000 q^{4} +(-0.539189 + 2.17009i) q^{5} -0.539189 q^{6} -0.709275i q^{7} +1.00000i q^{8} +2.70928 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -0.539189i q^{3} -1.00000 q^{4} +(-0.539189 + 2.17009i) q^{5} -0.539189 q^{6} -0.709275i q^{7} +1.00000i q^{8} +2.70928 q^{9} +(2.17009 + 0.539189i) q^{10} -4.51026 q^{11} +0.539189i q^{12} -0.709275 q^{14} +(1.17009 + 0.290725i) q^{15} +1.00000 q^{16} -3.17009i q^{17} -2.70928i q^{18} +0.120638 q^{19} +(0.539189 - 2.17009i) q^{20} -0.382433 q^{21} +4.51026i q^{22} +4.97107i q^{23} +0.539189 q^{24} +(-4.41855 - 2.34017i) q^{25} -3.07838i q^{27} +0.709275i q^{28} +7.26180 q^{29} +(0.290725 - 1.17009i) q^{30} +9.66701 q^{31} -1.00000i q^{32} +2.43188i q^{33} -3.17009 q^{34} +(1.53919 + 0.382433i) q^{35} -2.70928 q^{36} +6.95774i q^{37} -0.120638i q^{38} +(-2.17009 - 0.539189i) q^{40} +0.447480 q^{41} +0.382433i q^{42} +2.00000i q^{43} +4.51026 q^{44} +(-1.46081 + 5.87936i) q^{45} +4.97107 q^{46} +4.70928i q^{47} -0.539189i q^{48} +6.49693 q^{49} +(-2.34017 + 4.41855i) q^{50} -1.70928 q^{51} +9.58864i q^{53} -3.07838 q^{54} +(2.43188 - 9.78765i) q^{55} +0.709275 q^{56} -0.0650468i q^{57} -7.26180i q^{58} +5.75872 q^{59} +(-1.17009 - 0.290725i) q^{60} +7.06278 q^{61} -9.66701i q^{62} -1.92162i q^{63} -1.00000 q^{64} +2.43188 q^{66} +2.92162i q^{67} +3.17009i q^{68} +2.68035 q^{69} +(0.382433 - 1.53919i) q^{70} -8.18342 q^{71} +2.70928i q^{72} +6.74539i q^{73} +6.95774 q^{74} +(-1.26180 + 2.38243i) q^{75} -0.120638 q^{76} +3.19902i q^{77} +16.0072 q^{79} +(-0.539189 + 2.17009i) q^{80} +6.46800 q^{81} -0.447480i q^{82} -0.355771i q^{83} +0.382433 q^{84} +(6.87936 + 1.70928i) q^{85} +2.00000 q^{86} -3.91548i q^{87} -4.51026i q^{88} -3.63090 q^{89} +(5.87936 + 1.46081i) q^{90} -4.97107i q^{92} -5.21235i q^{93} +4.70928 q^{94} +(-0.0650468 + 0.261795i) q^{95} -0.539189 q^{96} +7.90829i q^{97} -6.49693i q^{98} -12.2195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^9	$ 6 q - 6 q^{4} + 2 q^{9} + 2 q^{10} + 6 q^{11} + 10 q^{14} - 4 q^{15} + 6 q^{16} + 26 q^{19} - 12 q^{21} + 2 q^{25} + 28 q^{29} + 16 q^{30} + 12 q^{31} - 8 q^{34} + 6 q^{35} - 2 q^{36} - 2 q^{40} + 4 q^{41} - 6 q^{44} - 12 q^{45} + 4 q^{49} + 8 q^{50} + 4 q^{51} - 12 q^{54} - 12 q^{55} - 10 q^{56} - 16 q^{59} + 4 q^{60} + 8 q^{61} - 6 q^{64} - 12 q^{66} - 28 q^{69} + 12 q^{70} - 40 q^{71} + 10 q^{74} + 8 q^{75} - 26 q^{76} + 28 q^{79} - 26 q^{81} + 12 q^{84} + 16 q^{85} + 12 q^{86} - 14 q^{89} + 10 q^{90} + 14 q^{94} + 8 q^{95} - 26 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^9 + 2 * q^10 + 6 * q^11 + 10 * q^14 - 4 * q^15 + 6 * q^16 + 26 * q^19 - 12 * q^21 + 2 * q^25 + 28 * q^29 + 16 * q^30 + 12 * q^31 - 8 * q^34 + 6 * q^35 - 2 * q^36 - 2 * q^40 + 4 * q^41 - 6 * q^44 - 12 * q^45 + 4 * q^49 + 8 * q^50 + 4 * q^51 - 12 * q^54 - 12 * q^55 - 10 * q^56 - 16 * q^59 + 4 * q^60 + 8 * q^61 - 6 * q^64 - 12 * q^66 - 28 * q^69 + 12 * q^70 - 40 * q^71 + 10 * q^74 + 8 * q^75 - 26 * q^76 + 28 * q^79 - 26 * q^81 + 12 * q^84 + 16 * q^85 + 12 * q^86 - 14 * q^89 + 10 * q^90 + 14 * q^94 + 8 * q^95 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	0.539189i		−	0.311301i	−0.987812	−	0.155650i	$-0.950253\pi$
$3$		−	0.539189i		−	0.311301i	0.987812	−	0.155650i	$-0.0497473\pi$
$4$	−1.00000			−0.500000
$5$	−0.539189	+	2.17009i	−0.241133	+	0.970492i
$5$	−0.539189	+	2.17009i	−0.241133	+	0.970492i
$6$	−0.539189			−0.220123
$7$		−	0.709275i		−	0.268081i	−0.990976	−	0.134040i	$-0.957205\pi$
$7$		−	0.709275i		−	0.268081i	0.990976	−	0.134040i	$-0.0427952\pi$
$8$			1.00000i			0.353553i
$9$	2.70928			0.903092
$10$	2.17009	+	0.539189i	0.686242	+	0.170506i
$11$	−4.51026			−1.35989			−0.679947	−	0.733261i	$-0.737997\pi$
$11$	−4.51026			−1.35989			−0.679947	+	0.733261i	$0.737997\pi$
$12$			0.539189i			0.155650i
$13$		0			0
$13$		0			0
$14$	−0.709275			−0.189562
$15$	1.17009	+	0.290725i	0.302115	+	0.0750648i
$16$	1.00000			0.250000
$17$		−	3.17009i		−	0.768859i	−0.923154	−	0.384429i	$-0.874398\pi$
$17$		−	3.17009i		−	0.768859i	0.923154	−	0.384429i	$-0.125602\pi$
$18$		−	2.70928i		−	0.638582i
$19$	0.120638			0.0276763			0.0138381	−	0.999904i	$-0.495595\pi$
$19$	0.120638			0.0276763			0.0138381	+	0.999904i	$0.495595\pi$
$20$	0.539189	−	2.17009i	0.120566	−	0.485246i
$21$	−0.382433			−0.0834538
$22$			4.51026i			0.961591i
$23$			4.97107i			1.03654i	0.855217	+	0.518270i	$0.173424\pi$
$23$			4.97107i			1.03654i	−0.855217	+	0.518270i	$0.826576\pi$
$24$	0.539189			0.110061
$25$	−4.41855	−	2.34017i	−0.883710	−	0.468035i
$26$		0			0
$27$		−	3.07838i		−	0.592434i
$28$			0.709275i			0.134040i
$29$	7.26180			1.34848			0.674241	−	0.738512i	$-0.264471\pi$
$29$	7.26180			1.34848			0.674241	+	0.738512i	$0.264471\pi$
$30$	0.290725	−	1.17009i	0.0530788	−	0.213628i
$31$	9.66701			1.73625			0.868124	−	0.496348i	$-0.165326\pi$
$31$	9.66701			1.73625			0.868124	+	0.496348i	$0.165326\pi$
$32$		−	1.00000i		−	0.176777i
$33$			2.43188i			0.423336i
$34$	−3.17009			−0.543665
$35$	1.53919	+	0.382433i	0.260170	+	0.0646430i
$36$	−2.70928			−0.451546
$37$			6.95774i			1.14385i	0.820308	+	0.571923i	$0.193802\pi$
$37$			6.95774i			1.14385i	−0.820308	+	0.571923i	$0.806198\pi$
$38$		−	0.120638i		−	0.0195701i
$39$		0			0
$40$	−2.17009	−	0.539189i	−0.343121	−	0.0852532i
$41$	0.447480			0.0698847			0.0349423	−	0.999389i	$-0.488875\pi$
$41$	0.447480			0.0698847			0.0349423	+	0.999389i	$0.488875\pi$
$42$			0.382433i			0.0590108i
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	4.51026			0.679947
$45$	−1.46081	+	5.87936i	−0.217765	+	0.876444i
$46$	4.97107			0.732944
$47$			4.70928i			0.686918i	0.939168	+	0.343459i	$0.111599\pi$
$47$			4.70928i			0.686918i	−0.939168	+	0.343459i	$0.888401\pi$
$48$		−	0.539189i		−	0.0778252i
$49$	6.49693			0.928133
$50$	−2.34017	+	4.41855i	−0.330950	+	0.624877i
$51$	−1.70928			−0.239346
$52$		0			0
$53$			9.58864i			1.31710i	0.752537	+	0.658550i	$0.228830\pi$
$53$			9.58864i			1.31710i	−0.752537	+	0.658550i	$0.771170\pi$
$54$	−3.07838			−0.418914
$55$	2.43188	−	9.78765i	0.327915	−	1.31977i
$56$	0.709275			0.0947809
$57$		−	0.0650468i		−	0.00861565i
$58$		−	7.26180i		−	0.953520i
$59$	5.75872			0.749722			0.374861	−	0.927081i	$-0.377690\pi$
$59$	5.75872			0.749722			0.374861	+	0.927081i	$0.377690\pi$
$60$	−1.17009	−	0.290725i	−0.151058	−	0.0375324i
$61$	7.06278			0.904296			0.452148	−	0.891943i	$-0.350658\pi$
$61$	7.06278			0.904296			0.452148	+	0.891943i	$0.350658\pi$
$62$		−	9.66701i		−	1.22771i
$63$		−	1.92162i		−	0.242102i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.43188			0.299344
$67$			2.92162i			0.356933i	0.983946	+	0.178466i	$0.0571136\pi$
$67$			2.92162i			0.356933i	−0.983946	+	0.178466i	$0.942886\pi$
$68$			3.17009i			0.384429i
$69$	2.68035			0.322676
$70$	0.382433	−	1.53919i	0.0457095	−	0.183968i
$71$	−8.18342			−0.971193			−0.485596	−	0.874183i	$-0.661398\pi$
$71$	−8.18342			−0.971193			−0.485596	+	0.874183i	$0.661398\pi$
$72$			2.70928i			0.319291i
$73$			6.74539i			0.789488i	0.918791	+	0.394744i	$0.129167\pi$
$73$			6.74539i			0.789488i	−0.918791	+	0.394744i	$0.870833\pi$
$74$	6.95774			0.808821
$75$	−1.26180	+	2.38243i	−0.145700	+	0.275100i
$76$	−0.120638			−0.0138381
$77$			3.19902i			0.364562i
$78$		0			0
$79$	16.0072			1.80095			0.900475	−	0.434908i	$-0.143219\pi$
$79$	16.0072			1.80095			0.900475	+	0.434908i	$0.143219\pi$
$80$	−0.539189	+	2.17009i	−0.0602831	+	0.242623i
$81$	6.46800			0.718667
$82$		−	0.447480i		−	0.0494159i
$83$		−	0.355771i		−	0.0390510i	−0.999809	−	0.0195255i	$-0.993784\pi$
$83$		−	0.355771i		−	0.0390510i	0.999809	−	0.0195255i	$-0.00621555\pi$
$84$	0.382433			0.0417269
$85$	6.87936	+	1.70928i	0.746172	+	0.185397i
$86$	2.00000			0.215666
$87$		−	3.91548i		−	0.419783i
$88$		−	4.51026i		−	0.480795i
$89$	−3.63090			−0.384874			−0.192437	−	0.981309i	$-0.561639\pi$
$89$	−3.63090			−0.384874			−0.192437	+	0.981309i	$0.561639\pi$
$90$	5.87936	+	1.46081i	0.619739	+	0.153983i
$91$		0			0
$92$		−	4.97107i		−	0.518270i
$93$		−	5.21235i		−	0.540495i
$94$	4.70928			0.485725
$95$	−0.0650468	+	0.261795i	−0.00667366	+	0.0268596i
$96$	−0.539189			−0.0550307
$97$			7.90829i			0.802965i	0.915867	+	0.401483i	$0.131505\pi$
$97$			7.90829i			0.802965i	−0.915867	+	0.401483i	$0.868495\pi$
$98$		−	6.49693i		−	0.656289i
$99$	−12.2195			−1.22811
$100$	4.41855	+	2.34017i	0.441855	+	0.234017i
$101$	6.14116			0.611068			0.305534	−	0.952181i	$-0.401165\pi$
$101$	6.14116			0.611068			0.305534	+	0.952181i	$0.401165\pi$
$102$			1.70928i			0.169243i
$103$		−	17.6803i		−	1.74210i	−0.491198	−	0.871048i	$-0.663441\pi$
$103$		−	17.6803i		−	1.74210i	0.491198	−	0.871048i	$-0.336559\pi$
$104$		0			0
$105$	0.206204	−	0.829914i	0.0201234	−	0.0809913i
$106$	9.58864			0.931331
$107$		−	0.539189i		−	0.0521254i	−0.999660	−	0.0260627i	$-0.991703\pi$
$107$		−	0.539189i		−	0.0521254i	0.999660	−	0.0260627i	$-0.00829695\pi$
$108$			3.07838i			0.296217i
$109$	11.0205			1.05557			0.527787	−	0.849377i	$-0.323022\pi$
$109$	11.0205			1.05557			0.527787	+	0.849377i	$0.323022\pi$
$110$	−9.78765	−	2.43188i	−0.933216	−	0.231871i
$111$	3.75154			0.356080
$112$		−	0.709275i		−	0.0670202i
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	−0.0650468			−0.00609219
$115$	−10.7877	−	2.68035i	−1.00595	−	0.249944i
$116$	−7.26180			−0.674241
$117$		0			0
$118$		−	5.75872i		−	0.530133i
$119$	−2.24846			−0.206116
$120$	−0.290725	+	1.17009i	−0.0265394	+	0.106814i
$121$	9.34244			0.849313
$122$		−	7.06278i		−	0.639434i
$123$		−	0.241276i		−	0.0217552i
$124$	−9.66701			−0.868124
$125$	7.46081	−	8.32684i	0.667315	−	0.744775i
$126$	−1.92162			−0.171192
$127$			12.1773i			1.08056i	0.841486	+	0.540279i	$0.181681\pi$
$127$			12.1773i			1.08056i	−0.841486	+	0.540279i	$0.818319\pi$
$128$			1.00000i			0.0883883i
$129$	1.07838			0.0949459
$130$		0			0
$131$	−17.4547			−1.52502			−0.762511	−	0.646976i	$-0.776034\pi$
$131$	−17.4547			−1.52502			−0.762511	+	0.646976i	$0.776034\pi$
$132$		−	2.43188i		−	0.211668i
$133$		−	0.0855657i		−	0.00741948i
$134$	2.92162			0.252390
$135$	6.68035	+	1.65983i	0.574953	+	0.142855i
$136$	3.17009			0.271833
$137$			9.35350i			0.799124i	0.916706	+	0.399562i	$0.130838\pi$
$137$			9.35350i			0.799124i	−0.916706	+	0.399562i	$0.869162\pi$
$138$		−	2.68035i		−	0.228166i
$139$	2.64423			0.224281			0.112140	−	0.993692i	$-0.464229\pi$
$139$	2.64423			0.224281			0.112140	+	0.993692i	$0.464229\pi$
$140$	−1.53919	−	0.382433i	−0.130085	−	0.0323215i
$141$	2.53919			0.213838
$142$			8.18342i			0.686737i
$143$		0			0
$144$	2.70928			0.225773
$145$	−3.91548	+	15.7587i	−0.325163	+	1.30869i
$146$	6.74539			0.558253
$147$		−	3.50307i		−	0.288928i
$148$		−	6.95774i		−	0.571923i
$149$	9.23513			0.756572			0.378286	−	0.925689i	$-0.376514\pi$
$149$	9.23513			0.756572			0.378286	+	0.925689i	$0.376514\pi$
$150$	2.38243	+	1.26180i	0.194525	+	0.103025i
$151$	−9.42574			−0.767056			−0.383528	−	0.923529i	$-0.625291\pi$
$151$	−9.42574			−0.767056			−0.383528	+	0.923529i	$0.625291\pi$
$152$			0.120638i			0.00978505i
$153$		−	8.58864i		−	0.694350i
$154$	3.19902			0.257784
$155$	−5.21235	+	20.9783i	−0.418666	+	1.68501i
$156$		0			0
$157$			5.77205i			0.460660i	0.973113	+	0.230330i	$0.0739806\pi$
$157$			5.77205i			0.460660i	−0.973113	+	0.230330i	$0.926019\pi$
$158$		−	16.0072i		−	1.27346i
$159$	5.17009			0.410015
$160$	2.17009	+	0.539189i	0.171560	+	0.0426266i
$161$	3.52586			0.277877
$162$		−	6.46800i		−	0.508174i
$163$		−	16.8215i		−	1.31756i	−0.752335	−	0.658781i	$-0.771072\pi$
$163$		−	16.8215i		−	1.31756i	0.752335	−	0.658781i	$-0.228928\pi$
$164$	−0.447480			−0.0349423
$165$	−5.27739	−	1.31124i	−0.410845	−	0.102080i
$166$	−0.355771			−0.0276132
$167$		−	18.1194i		−	1.40212i	−0.713101	−	0.701061i	$-0.752710\pi$
$167$		−	18.1194i		−	1.40212i	0.713101	−	0.701061i	$-0.247290\pi$
$168$		−	0.382433i		−	0.0295054i
$169$		0			0
$170$	1.70928	−	6.87936i	0.131095	−	0.527623i
$171$	0.326842			0.0249942
$172$		−	2.00000i		−	0.152499i
$173$			10.3041i			0.783403i	0.920092	+	0.391701i	$0.128113\pi$
$173$			10.3041i			0.783403i	−0.920092	+	0.391701i	$0.871887\pi$
$174$	−3.91548			−0.296832
$175$	−1.65983	+	3.13397i	−0.125471	+	0.236906i
$176$	−4.51026			−0.339974
$177$		−	3.10504i		−	0.233389i
$178$			3.63090i			0.272147i
$179$	−1.26180			−0.0943110			−0.0471555	−	0.998888i	$-0.515016\pi$
$179$	−1.26180			−0.0943110			−0.0471555	+	0.998888i	$0.515016\pi$
$180$	1.46081	−	5.87936i	0.108882	−	0.438222i
$181$	2.38243			0.177085			0.0885424	−	0.996072i	$-0.471779\pi$
$181$	2.38243			0.177085			0.0885424	+	0.996072i	$0.471779\pi$
$182$		0			0
$183$		−	3.80817i		−	0.281508i
$184$	−4.97107			−0.366472
$185$	−15.0989	−	3.75154i	−1.11009	−	0.275818i
$186$	−5.21235			−0.382188
$187$			14.2979i			1.04557i
$188$		−	4.70928i		−	0.343459i
$189$	−2.18342			−0.158820
$190$	0.261795	+	0.0650468i	0.0189926	+	0.00471899i
$191$	−11.0856			−0.802123			−0.401062	−	0.916051i	$-0.631359\pi$
$191$	−11.0856			−0.802123			−0.401062	+	0.916051i	$0.631359\pi$
$192$			0.539189i			0.0389126i
$193$		−	14.0000i		−	1.00774i	−0.863779	−	0.503871i	$-0.831909\pi$
$193$		−	14.0000i		−	1.00774i	0.863779	−	0.503871i	$-0.168091\pi$
$194$	7.90829			0.567782
$195$		0			0
$196$	−6.49693			−0.464066
$197$			8.69368i			0.619399i	0.950835	+	0.309699i	$0.100228\pi$
$197$			8.69368i			0.619399i	−0.950835	+	0.309699i	$0.899772\pi$
$198$			12.2195i			0.868405i
$199$	−21.5174			−1.52533			−0.762666	−	0.646793i	$-0.776110\pi$
$199$	−21.5174			−1.52533			−0.762666	+	0.646793i	$0.776110\pi$
$200$	2.34017	−	4.41855i	0.165475	−	0.312439i
$201$	1.57531			0.111114
$202$		−	6.14116i		−	0.432090i
$203$		−	5.15061i		−	0.361502i
$204$	1.70928			0.119673
$205$	−0.241276	+	0.971071i	−0.0168515	+	0.0678225i
$206$	−17.6803			−1.23185
$207$			13.4680i			0.936091i
$208$		0			0
$209$	−0.544109			−0.0376368
$210$	−0.829914	−	0.206204i	−0.0572695	−	0.0142294i
$211$	−5.58864			−0.384738			−0.192369	−	0.981323i	$-0.561617\pi$
$211$	−5.58864			−0.384738			−0.192369	+	0.981323i	$0.561617\pi$
$212$		−	9.58864i		−	0.658550i
$213$			4.41241i			0.302333i
$214$	−0.539189			−0.0368582
$215$	−4.34017	−	1.07838i	−0.295997	−	0.0735448i
$216$	3.07838			0.209457
$217$		−	6.85658i		−	0.465455i
$218$		−	11.0205i		−	0.746404i
$219$	3.63704			0.245768
$220$	−2.43188	+	9.78765i	−0.163957	+	0.659883i
$221$		0			0
$222$		−	3.75154i		−	0.251787i
$223$		−	24.7093i		−	1.65466i	−0.561720	−	0.827328i	$-0.689860\pi$
$223$		−	24.7093i		−	1.65466i	0.561720	−	0.827328i	$-0.310140\pi$
$224$	−0.709275			−0.0473905
$225$	−11.9711	−	6.34017i	−0.798071	−	0.422678i
$226$	−14.0000			−0.931266
$227$			28.6947i			1.90454i	0.305264	+	0.952268i	$0.401255\pi$
$227$			28.6947i			1.90454i	−0.305264	+	0.952268i	$0.598745\pi$
$228$			0.0650468i			0.00430783i
$229$	1.89988			0.125548			0.0627738	−	0.998028i	$-0.480005\pi$
$229$	1.89988			0.125548			0.0627738	+	0.998028i	$0.480005\pi$
$230$	−2.68035	+	10.7877i	−0.176737	+	0.711317i
$231$	1.72487			0.113488
$232$			7.26180i			0.476760i
$233$		−	22.2485i		−	1.45755i	−0.684756	−	0.728773i	$-0.740091\pi$
$233$		−	22.2485i		−	1.45755i	0.684756	−	0.728773i	$-0.259909\pi$
$234$		0			0
$235$	−10.2195	−	2.53919i	−0.666649	−	0.165638i
$236$	−5.75872			−0.374861
$237$		−	8.63090i		−	0.560637i
$238$			2.24846i			0.145746i
$239$	−24.8710			−1.60877			−0.804384	−	0.594110i	$-0.797505\pi$
$239$	−24.8710			−1.60877			−0.804384	+	0.594110i	$0.797505\pi$
$240$	1.17009	+	0.290725i	0.0755288	+	0.0187662i
$241$	−2.95055			−0.190062			−0.0950309	−	0.995474i	$-0.530295\pi$
$241$	−2.95055			−0.190062			−0.0950309	+	0.995474i	$0.530295\pi$
$242$		−	9.34244i		−	0.600555i
$243$		−	12.7226i		−	0.816156i
$244$	−7.06278			−0.452148
$245$	−3.50307	+	14.0989i	−0.223803	+	0.900745i
$246$	−0.241276			−0.0153832
$247$		0			0
$248$			9.66701i			0.613856i
$249$	−0.191828			−0.0121566
$250$	−8.32684	−	7.46081i	−0.526636	−	0.471863i
$251$	16.5597			1.04524			0.522620	−	0.852566i	$-0.324955\pi$
$251$	16.5597			1.04524			0.522620	+	0.852566i	$0.324955\pi$
$252$			1.92162i			0.121051i
$253$		−	22.4208i		−	1.40958i
$254$	12.1773			0.764070
$255$	0.921622	−	3.70928i	0.0577142	−	0.232284i
$256$	1.00000			0.0625000
$257$		−	0.523590i		−	0.0326607i	−0.999867	−	0.0163303i	$-0.994802\pi$
$257$		−	0.523590i		−	0.0326607i	0.999867	−	0.0163303i	$-0.00519834\pi$
$258$		−	1.07838i		−	0.0671369i
$259$	4.93495			0.306643
$260$		0			0
$261$	19.6742			1.21780
$262$			17.4547i			1.07835i
$263$			28.7815i			1.77474i	0.461054	+	0.887372i	$0.347471\pi$
$263$			28.7815i			1.77474i	−0.461054	+	0.887372i	$0.652529\pi$
$264$	−2.43188			−0.149672
$265$	−20.8082	−	5.17009i	−1.27824	−	0.317596i
$266$	−0.0855657			−0.00524637
$267$			1.95774i			0.119812i
$268$		−	2.92162i		−	0.178466i
$269$	−10.0566			−0.613164			−0.306582	−	0.951844i	$-0.599185\pi$
$269$	−10.0566			−0.613164			−0.306582	+	0.951844i	$0.599185\pi$
$270$	1.65983	−	6.68035i	0.101014	−	0.406553i
$271$	18.1256			1.10105			0.550525	−	0.834819i	$-0.314428\pi$
$271$	18.1256			1.10105			0.550525	+	0.834819i	$0.314428\pi$
$272$		−	3.17009i		−	0.192215i
$273$		0			0
$274$	9.35350			0.565066
$275$	19.9288	+	10.5548i	1.20175	+	0.636478i
$276$	−2.68035			−0.161338
$277$			24.7165i			1.48507i	0.669808	+	0.742534i	$0.266376\pi$
$277$			24.7165i			1.48507i	−0.669808	+	0.742534i	$0.733624\pi$
$278$		−	2.64423i		−	0.158590i
$279$	26.1906			1.56799
$280$	−0.382433	+	1.53919i	−0.0228548	+	0.0919841i
$281$	22.9854			1.37120			0.685598	−	0.727980i	$-0.259541\pi$
$281$	22.9854			1.37120			0.685598	+	0.727980i	$0.259541\pi$
$282$		−	2.53919i		−	0.151206i
$283$			18.0989i			1.07587i	0.842987	+	0.537934i	$0.180795\pi$
$283$			18.0989i			1.07587i	−0.842987	+	0.537934i	$0.819205\pi$
$284$	8.18342			0.485596
$285$	0.141157	+	0.0350725i	0.00836142	+	0.00207751i
$286$		0			0
$287$		−	0.317387i		−	0.0187347i
$288$		−	2.70928i		−	0.159646i
$289$	6.95055			0.408856
$290$	15.7587	+	3.91548i	0.925384	+	0.229925i
$291$	4.26406			0.249964
$292$		−	6.74539i		−	0.394744i
$293$			17.8443i			1.04247i	0.853412	+	0.521237i	$0.174529\pi$
$293$			17.8443i			1.04247i	−0.853412	+	0.521237i	$0.825471\pi$
$294$	−3.50307			−0.204303
$295$	−3.10504	+	12.4969i	−0.180782	+	0.727599i
$296$	−6.95774			−0.404410
$297$			13.8843i			0.805648i
$298$		−	9.23513i		−	0.534977i
$299$		0			0
$300$	1.26180	−	2.38243i	0.0728498	−	0.137550i
$301$	1.41855			0.0817639
$302$			9.42574i			0.542390i
$303$		−	3.31124i		−	0.190226i
$304$	0.120638			0.00691907
$305$	−3.80817	+	15.3268i	−0.218055	+	0.877612i
$306$	−8.58864			−0.490980
$307$		−	3.44521i		−	0.196629i	−0.995155	−	0.0983143i	$-0.968655\pi$
$307$		−	3.44521i		−	0.196629i	0.995155	−	0.0983143i	$-0.0313451\pi$
$308$		−	3.19902i		−	0.182281i
$309$	−9.53305			−0.542316
$310$	20.9783	+	5.21235i	1.19149	+	0.296041i
$311$	17.8238			1.01069			0.505347	−	0.862916i	$-0.331365\pi$
$311$	17.8238			1.01069			0.505347	+	0.862916i	$0.331365\pi$
$312$		0			0
$313$			32.2245i			1.82143i	0.413031	+	0.910717i	$0.364470\pi$
$313$			32.2245i			1.82143i	−0.413031	+	0.910717i	$0.635530\pi$
$314$	5.77205			0.325736
$315$	4.17009	+	1.03612i	0.234958	+	0.0583786i
$316$	−16.0072			−0.900475
$317$		−	1.90602i		−	0.107053i	−0.998566	−	0.0535265i	$-0.982954\pi$
$317$		−	1.90602i		−	0.107053i	0.998566	−	0.0535265i	$-0.0170462\pi$
$318$		−	5.17009i		−	0.289924i
$319$	−32.7526			−1.83379
$320$	0.539189	−	2.17009i	0.0301416	−	0.121312i
$321$	−0.290725			−0.0162267
$322$		−	3.52586i		−	0.196488i
$323$		−	0.382433i		−	0.0212792i
$324$	−6.46800			−0.359333
$325$		0			0
$326$	−16.8215			−0.931657
$327$		−	5.94214i		−	0.328601i
$328$			0.447480i			0.0247080i
$329$	3.34017			0.184150
$330$	−1.31124	+	5.27739i	−0.0721816	+	0.290511i
$331$	−0.711543			−0.0391099			−0.0195550	−	0.999809i	$-0.506225\pi$
$331$	−0.711543			−0.0391099			−0.0195550	+	0.999809i	$0.506225\pi$
$332$			0.355771i			0.0195255i
$333$			18.8504i			1.03300i
$334$	−18.1194			−0.991450
$335$	−6.34017	−	1.57531i	−0.346401	−	0.0860682i
$336$	−0.382433			−0.0208635
$337$		−	9.85043i		−	0.536587i	−0.963337	−	0.268294i	$-0.913540\pi$
$337$		−	9.85043i		−	0.536587i	0.963337	−	0.268294i	$-0.0864597\pi$
$338$		0			0
$339$	−7.54864			−0.409986
$340$	−6.87936	−	1.70928i	−0.373086	−	0.0926985i
$341$	−43.6007			−2.36111
$342$		−	0.326842i		−	0.0176736i
$343$		−	9.57304i		−	0.516896i
$344$	−2.00000			−0.107833
$345$	−1.44521	+	5.81658i	−0.0778076	+	0.313154i
$346$	10.3041			0.553949
$347$			25.5330i			1.37069i	0.728221	+	0.685343i	$0.240348\pi$
$347$			25.5330i			1.37069i	−0.728221	+	0.685343i	$0.759652\pi$
$348$			3.91548i			0.209892i
$349$	18.0566			0.966550			0.483275	−	0.875469i	$-0.339447\pi$
$349$	18.0566			0.966550			0.483275	+	0.875469i	$0.339447\pi$
$350$	3.13397	+	1.65983i	0.167518	+	0.0887215i
$351$		0			0
$352$			4.51026i			0.240398i
$353$		−	14.6465i		−	0.779554i	−0.920909	−	0.389777i	$-0.872552\pi$
$353$		−	14.6465i		−	0.779554i	0.920909	−	0.389777i	$-0.127448\pi$
$354$	−3.10504			−0.165031
$355$	4.41241	−	17.7587i	0.234186	−	0.942535i
$356$	3.63090			0.192437
$357$			1.21235i			0.0641642i
$358$			1.26180i			0.0666879i
$359$	13.4186			0.708204			0.354102	−	0.935207i	$-0.384787\pi$
$359$	13.4186			0.708204			0.354102	+	0.935207i	$0.384787\pi$
$360$	−5.87936	−	1.46081i	−0.309870	−	0.0769915i
$361$	−18.9854			−0.999234
$362$		−	2.38243i		−	0.125218i
$363$		−	5.03734i		−	0.264392i
$364$		0			0
$365$	−14.6381	−	3.63704i	−0.766192	−	0.190371i
$366$	−3.80817			−0.199056
$367$		−	21.5441i		−	1.12459i	−0.826936	−	0.562297i	$-0.809918\pi$
$367$		−	21.5441i		−	1.12459i	0.826936	−	0.562297i	$-0.190082\pi$
$368$			4.97107i			0.259135i
$369$	1.21235			0.0631123
$370$	−3.75154	+	15.0989i	−0.195033	+	0.784954i
$371$	6.80098			0.353090
$372$			5.21235i			0.270248i
$373$		−	21.3340i		−	1.10463i	−0.833634	−	0.552317i	$-0.813744\pi$
$373$		−	21.3340i		−	1.10463i	0.833634	−	0.552317i	$-0.186256\pi$
$374$	14.2979			0.739327
$375$	−4.48974	−	4.02279i	−0.231849	−	0.207736i
$376$	−4.70928			−0.242862
$377$		0			0
$378$			2.18342i			0.112303i
$379$	−8.11223			−0.416697			−0.208349	−	0.978055i	$-0.566809\pi$
$379$	−8.11223			−0.416697			−0.208349	+	0.978055i	$0.566809\pi$
$380$	0.0650468	−	0.261795i	0.00333683	−	0.0134298i
$381$	6.56585			0.336379
$382$			11.0856i			0.567187i
$383$		−	24.9399i		−	1.27437i	−0.770712	−	0.637184i	$-0.780099\pi$
$383$		−	24.9399i		−	1.27437i	0.770712	−	0.637184i	$-0.219901\pi$
$384$	0.539189			0.0275154
$385$	−6.94214	−	1.72487i	−0.353804	−	0.0879077i
$386$	−14.0000			−0.712581
$387$			5.41855i			0.275440i
$388$		−	7.90829i		−	0.401483i
$389$	−13.5330			−0.686153			−0.343076	−	0.939308i	$-0.611469\pi$
$389$	−13.5330			−0.686153			−0.343076	+	0.939308i	$0.611469\pi$
$390$		0			0
$391$	15.7587			0.796953
$392$			6.49693i			0.328144i
$393$			9.41136i			0.474740i
$394$	8.69368			0.437981
$395$	−8.63090	+	34.7370i	−0.434268	+	1.74781i
$396$	12.2195			0.614055
$397$		−	4.59478i		−	0.230605i	−0.993330	−	0.115303i	$-0.963216\pi$
$397$		−	4.59478i		−	0.230605i	0.993330	−	0.115303i	$-0.0367838\pi$
$398$			21.5174i			1.07857i
$399$	−0.0461361			−0.00230969
$400$	−4.41855	−	2.34017i	−0.220928	−	0.117009i
$401$	29.7031			1.48330			0.741652	−	0.670785i	$-0.234043\pi$
$401$	29.7031			1.48330			0.741652	+	0.670785i	$0.234043\pi$
$402$		−	1.57531i		−	0.0785691i
$403$		0			0
$404$	−6.14116			−0.305534
$405$	−3.48747	+	14.0361i	−0.173294	+	0.697460i
$406$	−5.15061			−0.255621
$407$		−	31.3812i		−	1.55551i
$408$		−	1.70928i		−	0.0846217i
$409$	10.3112			0.509858			0.254929	−	0.966960i	$-0.417948\pi$
$409$	10.3112			0.509858			0.254929	+	0.966960i	$0.417948\pi$
$410$	0.971071	+	0.241276i	0.0479578	+	0.0119158i
$411$	5.04331			0.248768
$412$			17.6803i			0.871048i
$413$		−	4.08452i		−	0.200986i
$414$	13.4680			0.661916
$415$	0.772055	+	0.191828i	0.0378987	+	0.00941646i
$416$		0			0
$417$		−	1.42574i		−	0.0698187i
$418$			0.544109i			0.0266133i
$419$	−38.0905			−1.86084			−0.930421	−	0.366492i	$-0.880559\pi$
$419$	−38.0905			−1.86084			−0.930421	+	0.366492i	$0.880559\pi$
$420$	−0.206204	+	0.829914i	−0.0100617	+	0.0404956i
$421$	−26.7103			−1.30178			−0.650891	−	0.759171i	$-0.725604\pi$
$421$	−26.7103			−1.30178			−0.650891	+	0.759171i	$0.725604\pi$
$422$			5.58864i			0.272051i
$423$			12.7587i			0.620350i
$424$	−9.58864			−0.465665
$425$	−7.41855	+	14.0072i	−0.359853	+	0.679448i
$426$	4.41241			0.213782
$427$		−	5.00946i		−	0.242425i
$428$			0.539189i			0.0260627i
$429$		0			0
$430$	−1.07838	+	4.34017i	−0.0520040	+	0.209302i
$431$	−20.7187			−0.997986			−0.498993	−	0.866606i	$-0.666297\pi$
$431$	−20.7187			−0.997986			−0.498993	+	0.866606i	$0.666297\pi$
$432$		−	3.07838i		−	0.148109i
$433$			15.8576i			0.762069i	0.924561	+	0.381034i	$0.124432\pi$
$433$			15.8576i			0.762069i	−0.924561	+	0.381034i	$0.875568\pi$
$434$	−6.85658			−0.329126
$435$	8.49693	+	2.11118i	0.407397	+	0.101223i
$436$	−11.0205			−0.527787
$437$			0.599701i			0.0286876i
$438$		−	3.63704i		−	0.173785i
$439$	9.73925			0.464829			0.232415	−	0.972617i	$-0.425337\pi$
$439$	9.73925			0.464829			0.232415	+	0.972617i	$0.425337\pi$
$440$	9.78765	+	2.43188i	0.466608	+	0.115935i
$441$	17.6020			0.838189
$442$		0			0
$443$		−	9.23060i		−	0.438559i	−0.975662	−	0.219279i	$-0.929629\pi$
$443$		−	9.23060i		−	0.438559i	0.975662	−	0.219279i	$-0.0703707\pi$
$444$	−3.75154			−0.178040
$445$	1.95774	−	7.87936i	0.0928058	−	0.373518i
$446$	−24.7093			−1.17002
$447$		−	4.97948i		−	0.235521i
$448$			0.709275i			0.0335101i
$449$	2.92389			0.137987			0.0689934	−	0.997617i	$-0.478021\pi$
$449$	2.92389			0.137987			0.0689934	+	0.997617i	$0.478021\pi$
$450$	−6.34017	+	11.9711i	−0.298879	+	0.564322i
$451$	−2.01825			−0.0950358
$452$			14.0000i			0.658505i
$453$			5.08225i			0.238785i
$454$	28.6947			1.34671
$455$		0			0
$456$	0.0650468			0.00304609
$457$			11.6526i			0.545087i	0.962143	+	0.272544i	$0.0878649\pi$
$457$			11.6526i			0.545087i	−0.962143	+	0.272544i	$0.912135\pi$
$458$		−	1.89988i		−	0.0887756i
$459$	−9.75872			−0.455498
$460$	10.7877	+	2.68035i	0.502977	+	0.124972i
$461$	−30.2979			−1.41111			−0.705557	−	0.708653i	$-0.749303\pi$
$461$	−30.2979			−1.41111			−0.705557	+	0.708653i	$0.749303\pi$
$462$		−	1.72487i		−	0.0802484i
$463$		−	7.04331i		−	0.327330i	−0.986516	−	0.163665i	$-0.947668\pi$
$463$		−	7.04331i		−	0.327330i	0.986516	−	0.163665i	$-0.0523316\pi$
$464$	7.26180			0.337120
$465$	11.3112	+	2.81044i	0.524546	+	0.130331i
$466$	−22.2485			−1.03064
$467$			3.90110i			0.180522i	0.995918	+	0.0902608i	$0.0287700\pi$
$467$			3.90110i			0.180522i	−0.995918	+	0.0902608i	$0.971230\pi$
$468$		0			0
$469$	2.07223			0.0956869
$470$	−2.53919	+	10.2195i	−0.117124	+	0.471392i
$471$	3.11223			0.143404
$472$			5.75872i			0.265067i
$473$		−	9.02052i		−	0.414764i
$474$	−8.63090			−0.396430
$475$	−0.533046	−	0.282314i	−0.0244578	−	0.0129535i
$476$	2.24846			0.103058
$477$			25.9783i			1.18946i
$478$			24.8710i			1.13757i
$479$	−17.5103			−0.800064			−0.400032	−	0.916501i	$-0.631001\pi$
$479$	−17.5103			−0.800064			−0.400032	+	0.916501i	$0.631001\pi$
$480$	0.290725	−	1.17009i	0.0132697	−	0.0534069i
$481$		0			0
$482$			2.95055i			0.134394i
$483$		−	1.90110i		−	0.0865032i
$484$	−9.34244			−0.424656
$485$	−17.1617	−	4.26406i	−0.779272	−	0.193621i
$486$	−12.7226			−0.577109
$487$		−	38.5318i		−	1.74604i	−0.487681	−	0.873022i	$-0.662157\pi$
$487$		−	38.5318i		−	1.74604i	0.487681	−	0.873022i	$-0.337843\pi$
$488$			7.06278i			0.319717i
$489$	−9.06997			−0.410158
$490$	14.0989	+	3.50307i	0.636923	+	0.158253i
$491$	6.82377			0.307952			0.153976	−	0.988075i	$-0.450792\pi$
$491$	6.82377			0.307952			0.153976	+	0.988075i	$0.450792\pi$
$492$			0.241276i			0.0108776i
$493$		−	23.0205i		−	1.03679i
$494$		0			0
$495$	6.58864	−	26.5174i	0.296137	−	1.19187i
$496$	9.66701			0.434062
$497$			5.80430i			0.260358i
$498$			0.191828i			0.00859602i
$499$	−9.57918			−0.428823			−0.214412	−	0.976743i	$-0.568783\pi$
$499$	−9.57918			−0.428823			−0.214412	+	0.976743i	$0.568783\pi$
$500$	−7.46081	+	8.32684i	−0.333658	+	0.372388i
$501$	−9.76979			−0.436482
$502$		−	16.5597i		−	0.739096i
$503$			16.6742i			0.743466i	0.928340	+	0.371733i	$0.121236\pi$
$503$			16.6742i			0.743466i	−0.928340	+	0.371733i	$0.878764\pi$
$504$	1.92162			0.0855959
$505$	−3.31124	+	13.3268i	−0.147348	+	0.593037i
$506$	−22.4208			−0.996727
$507$		0			0
$508$		−	12.1773i		−	0.540279i
$509$	23.6598			1.04870			0.524352	−	0.851502i	$-0.324308\pi$
$509$	23.6598			1.04870			0.524352	+	0.851502i	$0.324308\pi$
$510$	−3.70928	−	0.921622i	−0.164249	−	0.0408101i
$511$	4.78434			0.211647
$512$		−	1.00000i		−	0.0441942i
$513$		−	0.371370i		−	0.0163964i
$514$	−0.523590			−0.0230946
$515$	38.3679	+	9.53305i	1.69069	+	0.420076i
$516$	−1.07838			−0.0474729
$517$		−	21.2401i		−	0.934136i
$518$		−	4.93495i		−	0.216829i
$519$	5.55583			0.243874
$520$		0			0
$521$	−24.0472			−1.05353			−0.526763	−	0.850012i	$-0.676594\pi$
$521$	−24.0472			−1.05353			−0.526763	+	0.850012i	$0.676594\pi$
$522$		−	19.6742i		−	0.861116i
$523$			23.3340i			1.02033i	0.860078	+	0.510163i	$0.170415\pi$
$523$			23.3340i			1.02033i	−0.860078	+	0.510163i	$0.829585\pi$
$524$	17.4547			0.762511
$525$	1.68980	+	0.894960i	0.0737490	+	0.0390593i
$526$	28.7815			1.25493
$527$		−	30.6453i		−	1.33493i
$528$			2.43188i			0.105834i
$529$	−1.71154			−0.0744149
$530$	−5.17009	+	20.8082i	−0.224574	+	0.903849i
$531$	15.6020			0.677068
$532$			0.0855657i			0.00370974i
$533$		0			0
$534$	1.95774			0.0847197
$535$	1.17009	+	0.290725i	0.0505873	+	0.0125691i
$536$	−2.92162			−0.126195
$537$			0.680346i			0.0293591i
$538$			10.0566i			0.433572i
$539$	−29.3028			−1.26216
$540$	−6.68035	−	1.65983i	−0.287476	−	0.0714276i
$541$	−33.1494			−1.42520			−0.712602	−	0.701569i	$-0.752483\pi$
$541$	−33.1494			−1.42520			−0.712602	+	0.701569i	$0.752483\pi$
$542$		−	18.1256i		−	0.778559i
$543$		−	1.28458i		−	0.0551267i
$544$	−3.17009			−0.135916
$545$	−5.94214	+	23.9155i	−0.254533	+	1.02443i
$546$		0			0
$547$		−	43.6742i		−	1.86737i	−0.358090	−	0.933687i	$-0.616572\pi$
$547$		−	43.6742i		−	1.86737i	0.358090	−	0.933687i	$-0.383428\pi$
$548$		−	9.35350i		−	0.399562i
$549$	19.1350			0.816662
$550$	10.5548	−	19.9288i	0.450058	−	0.849767i
$551$	0.876050			0.0373210
$552$			2.68035i			0.114083i
$553$		−	11.3535i		−	0.482800i
$554$	24.7165			1.05010
$555$	−2.02279	+	8.14116i	−0.0858625	+	0.345573i
$556$	−2.64423			−0.112140
$557$			22.3991i			0.949079i	0.880234	+	0.474540i	$0.157385\pi$
$557$			22.3991i			0.949079i	−0.880234	+	0.474540i	$0.842615\pi$
$558$		−	26.1906i		−	1.10874i
$559$		0			0
$560$	1.53919	+	0.382433i	0.0650426	+	0.0161608i
$561$	7.70928			0.325486
$562$		−	22.9854i		−	0.969583i
$563$			0.241276i			0.0101686i	0.999987	+	0.00508429i	$0.00161839\pi$
$563$			0.241276i			0.0101686i	−0.999987	+	0.00508429i	$0.998382\pi$
$564$	−2.53919			−0.106919
$565$	30.3812	+	7.54864i	1.27815	+	0.317574i
$566$	18.0989			0.760753
$567$		−	4.58759i		−	0.192661i
$568$		−	8.18342i		−	0.343369i
$569$	−27.1711			−1.13907			−0.569537	−	0.821966i	$-0.692877\pi$
$569$	−27.1711			−1.13907			−0.569537	+	0.821966i	$0.692877\pi$
$570$	0.0350725	−	0.141157i	0.00146902	−	0.00591242i
$571$	2.25461			0.0943524			0.0471762	−	0.998887i	$-0.484978\pi$
$571$	2.25461			0.0943524			0.0471762	+	0.998887i	$0.484978\pi$
$572$		0			0
$573$			5.97721i			0.249702i
$574$	−0.317387			−0.0132475
$575$	11.6332	−	21.9649i	0.485137	−	0.916001i
$576$	−2.70928			−0.112886
$577$		−	7.86481i		−	0.327416i	−0.986509	−	0.163708i	$-0.947654\pi$
$577$		−	7.86481i		−	0.327416i	0.986509	−	0.163708i	$-0.0523455\pi$
$578$		−	6.95055i		−	0.289105i
$579$	−7.54864			−0.313711
$580$	3.91548	−	15.7587i	0.162581	−	0.654345i
$581$	−0.252340			−0.0104688
$582$		−	4.26406i		−	0.176751i
$583$		−	43.2472i		−	1.79112i
$584$	−6.74539			−0.279126
$585$		0			0
$586$	17.8443			0.737141
$587$			11.2039i			0.462436i	0.972902	+	0.231218i	$0.0742711\pi$
$587$			11.2039i			0.462436i	−0.972902	+	0.231218i	$0.925729\pi$
$588$			3.50307i			0.144464i
$589$	1.16621			0.0480529
$590$	12.4969	+	3.10504i	0.514490	+	0.127832i
$591$	4.68753			0.192819
$592$			6.95774i			0.285961i
$593$			13.4186i			0.551034i	0.961296	+	0.275517i	$0.0888490\pi$
$593$			13.4186i			0.551034i	−0.961296	+	0.275517i	$0.911151\pi$
$594$	13.8843			0.569679
$595$	1.21235	−	4.87936i	0.0497014	−	0.200034i
$596$	−9.23513			−0.378286
$597$			11.6020i			0.474837i
$598$		0			0
$599$	−29.5753			−1.20841			−0.604207	−	0.796827i	$-0.706510\pi$
$599$	−29.5753			−1.20841			−0.604207	+	0.796827i	$0.706510\pi$
$600$	−2.38243	−	1.26180i	−0.0972624	−	0.0515126i
$601$	24.9832			1.01909			0.509543	−	0.860445i	$-0.329815\pi$
$601$	24.9832			1.01909			0.509543	+	0.860445i	$0.329815\pi$
$602$		−	1.41855i		−	0.0578158i
$603$			7.91548i			0.322343i
$604$	9.42574			0.383528
$605$	−5.03734	+	20.2739i	−0.204797	+	0.824251i
$606$	−3.31124			−0.134510
$607$		−	10.3919i		−	0.421794i	−0.977508	−	0.210897i	$-0.932362\pi$
$607$		−	10.3919i		−	0.421794i	0.977508	−	0.210897i	$-0.0676384\pi$
$608$		−	0.120638i		−	0.00489252i
$609$	−2.77715			−0.112536
$610$	15.3268	+	3.80817i	0.620566	+	0.154188i
$611$		0			0
$612$			8.58864i			0.347175i
$613$		−	30.5285i		−	1.23303i	−0.787341	−	0.616517i	$-0.788543\pi$
$613$		−	30.5285i		−	1.23303i	0.787341	−	0.616517i	$-0.211457\pi$
$614$	−3.44521			−0.139037
$615$	0.523590	+	0.130094i	0.0211132	+	0.00524588i
$616$	−3.19902			−0.128892
$617$		−	7.30283i		−	0.294001i	−0.989136	−	0.147000i	$-0.953038\pi$
$617$		−	7.30283i		−	0.294001i	0.989136	−	0.147000i	$-0.0469619\pi$
$618$			9.53305i			0.383475i
$619$	24.5103			0.985151			0.492575	−	0.870270i	$-0.336056\pi$
$619$	24.5103			0.985151			0.492575	+	0.870270i	$0.336056\pi$
$620$	5.21235	−	20.9783i	0.209333	−	0.842507i
$621$	15.3028			0.614082
$622$		−	17.8238i		−	0.714668i
$623$			2.57531i			0.103177i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	32.2245			1.28795
$627$			0.293378i			0.0117164i
$628$		−	5.77205i		−	0.230330i
$629$	22.0566			0.879456
$630$	1.03612	−	4.17009i	0.0412799	−	0.166140i
$631$	−3.07838			−0.122548			−0.0612741	−	0.998121i	$-0.519516\pi$
$631$	−3.07838			−0.122548			−0.0612741	+	0.998121i	$0.519516\pi$
$632$			16.0072i			0.636732i
$633$			3.01333i			0.119769i
$634$	−1.90602			−0.0756979
$635$	−26.4257	−	6.56585i	−1.04867	−	0.260558i
$636$	−5.17009			−0.205007
$637$		0			0
$638$			32.7526i			1.29669i
$639$	−22.1711			−0.877076
$640$	−2.17009	−	0.539189i	−0.0857802	−	0.0213133i
$641$	−2.46800			−0.0974801			−0.0487401	−	0.998811i	$-0.515521\pi$
$641$	−2.46800			−0.0974801			−0.0487401	+	0.998811i	$0.515521\pi$
$642$			0.290725i			0.0114740i
$643$		−	18.8215i		−	0.742248i	−0.928583	−	0.371124i	$-0.878973\pi$
$643$		−	18.8215i		−	0.742248i	0.928583	−	0.371124i	$-0.121027\pi$
$644$	−3.52586			−0.138938
$645$	−0.581449	+	2.34017i	−0.0228945	+	0.0921442i
$646$	−0.382433			−0.0150466
$647$			11.7031i			0.460098i	0.973179	+	0.230049i	$0.0738886\pi$
$647$			11.7031i			0.460098i	−0.973179	+	0.230049i	$0.926111\pi$
$648$			6.46800i			0.254087i
$649$	−25.9733			−1.01954
$650$		0			0
$651$	−3.69699			−0.144896
$652$			16.8215i			0.658781i
$653$			14.6937i			0.575008i	0.957779	+	0.287504i	$0.0928255\pi$
$653$			14.6937i			0.575008i	−0.957779	+	0.287504i	$0.907175\pi$
$654$	−5.94214			−0.232356
$655$	9.41136	−	37.8781i	0.367732	−	1.48002i
$656$	0.447480			0.0174712
$657$			18.2751i			0.712981i
$658$		−	3.34017i		−	0.130213i
$659$	−18.7877			−0.731863			−0.365932	−	0.930642i	$-0.619250\pi$
$659$	−18.7877			−0.731863			−0.365932	+	0.930642i	$0.619250\pi$
$660$	5.27739	+	1.31124i	0.205422	+	0.0510401i
$661$	−5.84202			−0.227228			−0.113614	−	0.993525i	$-0.536243\pi$
$661$	−5.84202			−0.227228			−0.113614	+	0.993525i	$0.536243\pi$
$662$			0.711543i			0.0276549i
$663$		0			0
$664$	0.355771			0.0138066
$665$	0.185685	+	0.0461361i	0.00720055	+	0.00178908i
$666$	18.8504			0.730439
$667$			36.0989i			1.39775i
$668$			18.1194i			0.701061i
$669$	−13.3230			−0.515096
$670$	−1.57531	+	6.34017i	−0.0608594	+	0.244942i
$671$	−31.8550			−1.22975
$672$			0.382433i			0.0147527i
$673$		−	40.8925i		−	1.57629i	−0.615489	−	0.788145i	$-0.711042\pi$
$673$		−	40.8925i		−	1.57629i	0.615489	−	0.788145i	$-0.288958\pi$
$674$	−9.85043			−0.379424
$675$	−7.20394	+	13.6020i	−0.277280	+	0.523540i
$676$		0			0
$677$			28.2700i			1.08651i	0.839569	+	0.543253i	$0.182807\pi$
$677$			28.2700i			1.08651i	−0.839569	+	0.543253i	$0.817193\pi$
$678$			7.54864i			0.289904i
$679$	5.60916			0.215260
$680$	−1.70928	+	6.87936i	−0.0655477	+	0.263811i
$681$	15.4719			0.592884
$682$			43.6007i			1.66956i
$683$		−	41.5052i		−	1.58815i	−0.607819	−	0.794075i	$-0.707955\pi$
$683$		−	41.5052i		−	1.58815i	0.607819	−	0.794075i	$-0.292045\pi$
$684$	−0.326842			−0.0124971
$685$	−20.2979	−	5.04331i	−0.775543	−	0.192695i
$686$	−9.57304			−0.365500
$687$		−	1.02439i		−	0.0390831i
$688$			2.00000i			0.0762493i
$689$		0			0
$690$	5.81658	+	1.44521i	0.221434	+	0.0550183i
$691$	−24.1084			−0.917125			−0.458562	−	0.888662i	$-0.651635\pi$
$691$	−24.1084			−0.917125			−0.458562	+	0.888662i	$0.651635\pi$
$692$		−	10.3041i		−	0.391701i
$693$			8.66701i			0.329233i
$694$	25.5330			0.969221
$695$	−1.42574	+	5.73820i	−0.0540813	+	0.217663i
$696$	3.91548			0.148416
$697$		−	1.41855i		−	0.0537314i
$698$		−	18.0566i		−	0.683454i
$699$	−11.9961			−0.453735
$700$	1.65983	−	3.13397i	0.0627356	−	0.118453i
$701$	−14.1822			−0.535654			−0.267827	−	0.963467i	$-0.586306\pi$
$701$	−14.1822			−0.535654			−0.267827	+	0.963467i	$0.586306\pi$
$702$		0			0
$703$			0.839369i			0.0316574i
$704$	4.51026			0.169987
$705$	−1.36910	+	5.51026i	−0.0515634	+	0.207528i
$706$	−14.6465			−0.551228
$707$		−	4.35577i		−	0.163816i
$708$			3.10504i			0.116695i
$709$	46.4957			1.74618			0.873091	−	0.487556i	$-0.162112\pi$
$709$	46.4957			1.74618			0.873091	+	0.487556i	$0.162112\pi$
$710$	−17.7587	−	4.41241i	−0.666473	−	0.165595i
$711$	43.3679			1.62642
$712$		−	3.63090i		−	0.136074i
$713$			48.0554i			1.79969i
$714$	1.21235			0.0453709
$715$		0			0
$716$	1.26180			0.0471555
$717$			13.4101i			0.500811i
$718$		−	13.4186i		−	0.500776i
$719$	12.7214			0.474428			0.237214	−	0.971457i	$-0.423766\pi$
$719$	12.7214			0.474428			0.237214	+	0.971457i	$0.423766\pi$
$720$	−1.46081	+	5.87936i	−0.0544412	+	0.219111i
$721$	−12.5402			−0.467023
$722$			18.9854i			0.706565i
$723$			1.59090i			0.0591664i
$724$	−2.38243			−0.0885424
$725$	−32.0866	−	16.9939i	−1.19167	−	0.631136i
$726$	−5.03734			−0.186953
$727$			13.2595i			0.491769i	0.969299	+	0.245884i	$0.0790783\pi$
$727$			13.2595i			0.491769i	−0.969299	+	0.245884i	$0.920922\pi$
$728$		0			0
$729$	12.5441			0.464597
$730$	−3.63704	+	14.6381i	−0.134613	+	0.541780i
$731$	6.34017			0.234500
$732$			3.80817i			0.140754i
$733$		−	31.5848i		−	1.16661i	−0.812253	−	0.583305i	$-0.801759\pi$
$733$		−	31.5848i		−	1.16661i	0.812253	−	0.583305i	$-0.198241\pi$
$734$	−21.5441			−0.795208
$735$	7.60197	+	1.88882i	0.280403	+	0.0696701i
$736$	4.97107			0.183236
$737$		−	13.1773i		−	0.485391i
$738$		−	1.21235i		−	0.0446271i
$739$	−2.83218			−0.104183			−0.0520917	−	0.998642i	$-0.516589\pi$
$739$	−2.83218			−0.104183			−0.0520917	+	0.998642i	$0.516589\pi$
$740$	15.0989	+	3.75154i	0.555046	+	0.137909i
$741$		0			0
$742$		−	6.80098i		−	0.249672i
$743$		−	20.8020i		−	0.763152i	−0.924337	−	0.381576i	$-0.875381\pi$
$743$		−	20.8020i		−	0.763152i	0.924337	−	0.381576i	$-0.124619\pi$
$744$	5.21235			0.191094
$745$	−4.97948	+	20.0410i	−0.182434	+	0.734247i
$746$	−21.3340			−0.781094
$747$		−	0.963883i		−	0.0352666i
$748$		−	14.2979i		−	0.522783i
$749$	−0.382433			−0.0139738
$750$	−4.02279	+	4.48974i	−0.146891	+	0.163942i
$751$	36.2823			1.32396			0.661980	−	0.749521i	$-0.269716\pi$
$751$	36.2823			1.32396			0.661980	+	0.749521i	$0.269716\pi$
$752$			4.70928i			0.171730i
$753$		−	8.92881i		−	0.325384i
$754$		0			0
$755$	5.08225	−	20.4547i	0.184962	−	0.744422i
$756$	2.18342			0.0794101
$757$			40.8687i			1.48540i	0.669626	+	0.742699i	$0.266455\pi$
$757$			40.8687i			1.48540i	−0.669626	+	0.742699i	$0.733545\pi$
$758$			8.11223i			0.294649i
$759$	−12.0891			−0.438805
$760$	−0.261795	−	0.0650468i	−0.00949631	−	0.00235949i
$761$	35.6225			1.29131			0.645657	−	0.763627i	$-0.276584\pi$
$761$	35.6225			1.29131			0.645657	+	0.763627i	$0.276584\pi$
$762$		−	6.56585i		−	0.237856i
$763$		−	7.81658i		−	0.282979i
$764$	11.0856			0.401062
$765$	18.6381	+	4.63090i	0.673861	+	0.167430i
$766$	−24.9399			−0.901114
$767$		0			0
$768$		−	0.539189i		−	0.0194563i
$769$	−3.36910			−0.121493			−0.0607465	−	0.998153i	$-0.519348\pi$
$769$	−3.36910			−0.121493			−0.0607465	+	0.998153i	$0.519348\pi$
$770$	−1.72487	+	6.94214i	−0.0621601	+	0.250177i
$771$	−0.282314			−0.0101673
$772$			14.0000i			0.503871i
$773$			11.0794i			0.398499i	0.979949	+	0.199250i	$0.0638504\pi$
$773$			11.0794i			0.398499i	−0.979949	+	0.199250i	$0.936150\pi$
$774$	5.41855			0.194766
$775$	−42.7142	−	22.6225i	−1.53434	−	0.812624i
$776$	−7.90829			−0.283891
$777$		−	2.66087i		−	0.0954582i
$778$			13.5330i			0.485183i
$779$	0.0539832			0.00193415
$780$		0			0
$781$	36.9093			1.32072
$782$		−	15.7587i		−	0.563531i
$783$		−	22.3545i		−	0.798886i
$784$	6.49693			0.232033
$785$	−12.5259	−	3.11223i	−0.447067	−	0.111080i
$786$	9.41136			0.335692
$787$		−	5.67089i		−	0.202145i	−0.994879	−	0.101073i	$-0.967773\pi$
$787$		−	5.67089i		−	0.202145i	0.994879	−	0.101073i	$-0.0322275\pi$
$788$		−	8.69368i		−	0.309699i
$789$	15.5187			0.552479
$790$	34.7370	+	8.63090i	1.23589	+	0.307074i
$791$	−9.92986			−0.353065
$792$		−	12.2195i		−	0.434202i
$793$		0			0
$794$	−4.59478			−0.163063
$795$	−2.78765	+	11.2195i	−0.0988679	+	0.397916i
$796$	21.5174			0.762666
$797$		−	27.3424i		−	0.968519i	−0.874924	−	0.484259i	$-0.839089\pi$
$797$		−	27.3424i		−	0.968519i	0.874924	−	0.484259i	$-0.160911\pi$
$798$			0.0461361i			0.00163320i
$799$	14.9288			0.528143
$800$	−2.34017	+	4.41855i	−0.0827376	+	0.156219i
$801$	−9.83710			−0.347577
$802$		−	29.7031i		−	1.04885i
$803$		−	30.4235i		−	1.07362i
$804$	−1.57531			−0.0555568
$805$	−1.90110	+	7.65142i	−0.0670051	+	0.269677i
$806$		0			0
$807$			5.42243i			0.190878i
$808$			6.14116i			0.216045i
$809$	5.02893			0.176808			0.0884039	−	0.996085i	$-0.471823\pi$
$809$	5.02893			0.176808			0.0884039	+	0.996085i	$0.471823\pi$
$810$	14.0361	+	3.48747i	0.493179	+	0.122537i
$811$	47.3390			1.66230			0.831148	−	0.556052i	$-0.187684\pi$
$811$	47.3390			1.66230			0.831148	+	0.556052i	$0.187684\pi$
$812$			5.15061i			0.180751i
$813$		−	9.77310i		−	0.342758i
$814$	−31.3812			−1.09991
$815$	36.5041	+	9.06997i	1.27868	+	0.317707i
$816$	−1.70928			−0.0598366
$817$			0.241276i			0.00844119i
$818$		−	10.3112i		−	0.360524i
$819$		0			0
$820$	0.241276	−	0.971071i	0.00842573	−	0.0339113i
$821$	−20.6816			−0.721792			−0.360896	−	0.932606i	$-0.617529\pi$
$821$	−20.6816			−0.721792			−0.360896	+	0.932606i	$0.617529\pi$
$822$		−	5.04331i		−	0.175905i
$823$		−	19.8371i		−	0.691478i	−0.938331	−	0.345739i	$-0.887628\pi$
$823$		−	19.8371i		−	0.691478i	0.938331	−	0.345739i	$-0.112372\pi$
$824$	17.6803			0.615924
$825$	5.69102	−	10.7454i	0.198136	−	0.374107i
$826$	−4.08452			−0.142119
$827$		−	39.6730i		−	1.37956i	−0.724017	−	0.689782i	$-0.757706\pi$
$827$		−	39.6730i		−	1.37956i	0.724017	−	0.689782i	$-0.242294\pi$
$828$		−	13.4680i		−	0.468045i
$829$	25.3874			0.881739			0.440870	−	0.897571i	$-0.354670\pi$
$829$	25.3874			0.881739			0.440870	+	0.897571i	$0.354670\pi$
$830$	0.191828	−	0.772055i	0.00665845	−	0.0267984i
$831$	13.3268			0.462303
$832$		0			0
$833$		−	20.5958i		−	0.713603i
$834$	−1.42574			−0.0493693
$835$	39.3207	+	9.76979i	1.36075	+	0.338097i
$836$	0.544109			0.0188184
$837$		−	29.7587i		−	1.02861i
$838$			38.0905i			1.31581i
$839$	23.0277			0.795005			0.397502	−	0.917601i	$-0.369877\pi$
$839$	23.0277			0.795005			0.397502	+	0.917601i	$0.369877\pi$
$840$	0.829914	+	0.206204i	0.0286347	+	0.00711471i
$841$	23.7337			0.818402
$842$			26.7103i			0.920498i
$843$		−	12.3935i		−	0.426855i
$844$	5.58864			0.192369
$845$		0			0
$846$	12.7587			0.438654
$847$		−	6.62636i		−	0.227685i
$848$			9.58864i			0.329275i
$849$	9.75872			0.334919
$850$	14.0072	+	7.41855i	0.480443	+	0.254454i
$851$	−34.5874			−1.18564
$852$		−	4.41241i		−	0.151167i
$853$		−	13.7047i		−	0.469241i	−0.972087	−	0.234621i	$-0.924615\pi$
$853$		−	13.7047i		−	0.469241i	0.972087	−	0.234621i	$-0.0753848\pi$
$854$	−5.00946			−0.171420
$855$	−0.176230	+	0.709275i	−0.00602692	+	0.0242567i
$856$	0.539189			0.0184291
$857$			17.8648i			0.610250i	0.952312	+	0.305125i	$0.0986983\pi$
$857$			17.8648i			0.610250i	−0.952312	+	0.305125i	$0.901302\pi$
$858$		0			0
$859$	−13.7187			−0.468077			−0.234039	−	0.972227i	$-0.575194\pi$
$859$	−13.7187			−0.468077			−0.234039	+	0.972227i	$0.575194\pi$
$860$	4.34017	+	1.07838i	0.147999	+	0.0367724i
$861$	−0.171131			−0.00583214
$862$			20.7187i			0.705683i
$863$		−	19.9383i		−	0.678706i	−0.940659	−	0.339353i	$-0.889792\pi$
$863$		−	19.9383i		−	0.678706i	0.940659	−	0.339353i	$-0.110208\pi$
$864$	−3.07838			−0.104729
$865$	−22.3607	−	5.55583i	−0.760286	−	0.188904i
$866$	15.8576			0.538864
$867$		−	3.74766i		−	0.127277i
$868$			6.85658i			0.232727i
$869$	−72.1966			−2.44910
$870$	2.11118	−	8.49693i	0.0715758	−	0.288073i
$871$		0			0
$872$			11.0205i			0.373202i
$873$			21.4257i			0.725151i
$874$	0.599701			0.0202852
$875$	−5.90602	−	5.29177i	−0.199660	−	0.178894i
$876$	−3.63704			−0.122884
$877$			21.6163i			0.729932i	0.931021	+	0.364966i	$0.118919\pi$
$877$			21.6163i			0.729932i	−0.931021	+	0.364966i	$0.881081\pi$
$878$		−	9.73925i		−	0.328684i
$879$	9.62144			0.324523
$880$	2.43188	−	9.78765i	0.0819787	−	0.329942i
$881$	−7.99386			−0.269320			−0.134660	−	0.990892i	$-0.542994\pi$
$881$	−7.99386			−0.269320			−0.134660	+	0.990892i	$0.542994\pi$
$882$		−	17.6020i		−	0.592689i
$883$			26.2713i			0.884098i	0.896991	+	0.442049i	$0.145748\pi$
$883$			26.2713i			0.884098i	−0.896991	+	0.442049i	$0.854252\pi$
$884$		0			0
$885$	6.73820	+	1.67420i	0.226502	+	0.0562777i
$886$	−9.23060			−0.310108
$887$		−	17.1627i		−	0.576268i	−0.957590	−	0.288134i	$-0.906965\pi$
$887$		−	17.1627i		−	0.576268i	0.957590	−	0.288134i	$-0.0930348\pi$
$888$			3.75154i			0.125893i
$889$	8.63704			0.289677
$890$	−7.87936	−	1.95774i	−0.264117	−	0.0656236i
$891$	−29.1724			−0.977311
$892$			24.7093i			0.827328i
$893$			0.568118i			0.0190114i
$894$	−4.97948			−0.166539
$895$	0.680346	−	2.73820i	0.0227415	−	0.0915281i
$896$	0.709275			0.0236952
$897$		0			0
$898$		−	2.92389i		−	0.0975715i
$899$	70.1999			2.34130
$900$	11.9711	+	6.34017i	0.399036	+	0.211339i
$901$	30.3968			1.01266
$902$			2.01825i			0.0672004i
$903$		−	0.764867i		−	0.0254532i
$904$	14.0000			0.465633
$905$	−1.28458	+	5.17009i	−0.0427009	+	0.171859i
$906$	5.08225			0.168847
$907$		−	16.4136i		−	0.545006i	−0.962155	−	0.272503i	$-0.912149\pi$
$907$		−	16.4136i		−	0.545006i	0.962155	−	0.272503i	$-0.0878514\pi$
$908$		−	28.6947i		−	0.952268i
$909$	16.6381			0.551850
$910$		0			0
$911$	−4.52359			−0.149873			−0.0749366	−	0.997188i	$-0.523875\pi$
$911$	−4.52359			−0.149873			−0.0749366	+	0.997188i	$0.523875\pi$
$912$		−	0.0650468i		−	0.00215391i
$913$			1.60462i			0.0531052i
$914$	11.6526			0.385435
$915$	8.26406	+	2.05332i	0.273201	+	0.0678808i
$916$	−1.89988			−0.0627738
$917$			12.3802i			0.408829i
$918$			9.75872i			0.322086i
$919$	7.64301			0.252120			0.126060	−	0.992023i	$-0.459767\pi$
$919$	7.64301			0.252120			0.126060	+	0.992023i	$0.459767\pi$
$920$	2.68035	−	10.7877i	0.0883684	−	0.355658i
$921$	−1.85762			−0.0612107
$922$			30.2979i			0.997809i
$923$		0			0
$924$	−1.72487			−0.0567442
$925$	16.2823	−	30.7431i	0.535359	−	1.01083i
$926$	−7.04331			−0.231457
$927$		−	47.9009i		−	1.57327i
$928$		−	7.26180i		−	0.238380i
$929$	−59.3295			−1.94654			−0.973269	−	0.229669i	$-0.926236\pi$
$929$	−59.3295			−1.94654			−0.973269	+	0.229669i	$0.926236\pi$
$930$	2.81044	−	11.3112i	0.0921579	−	0.370910i
$931$	0.783777			0.0256873
$932$			22.2485i			0.728773i
$933$		−	9.61038i		−	0.314630i
$934$	3.90110			0.127648
$935$	−31.0277	−	7.70928i	−1.01471	−	0.252120i
$936$		0			0
$937$		−	1.75872i		−	0.0574550i	−0.999587	−	0.0287275i	$-0.990854\pi$
$937$		−	1.75872i		−	0.0574550i	0.999587	−	0.0287275i	$-0.00914551\pi$
$938$		−	2.07223i		−	0.0676609i
$939$	17.3751			0.567014
$940$	10.2195	+	2.53919i	0.333324	+	0.0828192i
$941$	42.2967			1.37883			0.689416	−	0.724365i	$-0.257867\pi$
$941$	42.2967			1.37883			0.689416	+	0.724365i	$0.257867\pi$
$942$		−	3.11223i		−	0.101402i
$943$			2.22446i			0.0724382i
$944$	5.75872			0.187430
$945$	1.17727	−	4.73820i	0.0382967	−	0.154134i
$946$	−9.02052			−0.293282
$947$		−	4.83832i		−	0.157224i	−0.996905	−	0.0786122i	$-0.974951\pi$
$947$		−	4.83832i		−	0.157224i	0.996905	−	0.0786122i	$-0.0250489\pi$
$948$			8.63090i			0.280319i
$949$		0			0
$950$	−0.282314	+	0.533046i	−0.00915948	+	0.0172943i
$951$	−1.02771			−0.0333257
$952$		−	2.24846i		−	0.0728731i
$953$			25.9539i			0.840728i	0.907356	+	0.420364i	$0.138098\pi$
$953$			25.9539i			0.840728i	−0.907356	+	0.420364i	$0.861902\pi$
$954$	25.9783			0.841077
$955$	5.97721	−	24.0566i	0.193418	−	0.778454i
$956$	24.8710			0.804384
$957$			17.6598i			0.570861i
$958$			17.5103i			0.565731i
$959$	6.63421			0.214230
$960$	−1.17009	−	0.290725i	−0.0377644	−	0.00938310i
$961$	62.4512			2.01455
$962$		0			0
$963$		−	1.46081i		−	0.0470740i
$964$	2.95055			0.0950309
$965$	30.3812	+	7.54864i	0.978006	+	0.242999i
$966$	−1.90110			−0.0611670
$967$			29.9939i			0.964537i	0.876023	+	0.482269i	$0.160187\pi$
$967$			29.9939i			0.964537i	−0.876023	+	0.482269i	$0.839813\pi$
$968$			9.34244i			0.300277i
$969$	−0.206204			−0.00662422
$970$	−4.26406	+	17.1617i	−0.136911	+	0.551028i
$971$	15.7286			0.504754			0.252377	−	0.967629i	$-0.418788\pi$
$971$	15.7286			0.504754			0.252377	+	0.967629i	$0.418788\pi$
$972$			12.7226i			0.408078i
$973$		−	1.87549i		−	0.0601253i
$974$	−38.5318			−1.23464
$975$		0			0
$976$	7.06278			0.226074
$977$		−	27.5441i		−	0.881214i	−0.897700	−	0.440607i	$-0.854763\pi$
$977$		−	27.5441i		−	0.881214i	0.897700	−	0.440607i	$-0.145237\pi$
$978$			9.06997i			0.290026i
$979$	16.3763			0.523389
$980$	3.50307	−	14.0989i	0.111902	−	0.450373i
$981$	29.8576			0.953280
$982$		−	6.82377i		−	0.217755i
$983$		−	18.0289i		−	0.575034i	−0.957776	−	0.287517i	$-0.907170\pi$
$983$		−	18.0289i		−	0.575034i	0.957776	−	0.287517i	$-0.0928297\pi$
$984$	0.241276			0.00769161
$985$	−18.8660	−	4.68753i	−0.601122	−	0.149357i
$986$	−23.0205			−0.733123
$987$		−	1.80098i		−	0.0573260i
$988$		0			0
$989$	−9.94214			−0.316142
$990$	−26.5174	−	6.58864i	−0.842780	−	0.209401i
$991$	11.6332			0.369540			0.184770	−	0.982782i	$-0.440846\pi$
$991$	11.6332			0.369540			0.184770	+	0.982782i	$0.440846\pi$
$992$		−	9.66701i		−	0.306928i
$993$			0.383656i			0.0121750i
$994$	5.80430			0.184101
$995$	11.6020	−	46.6947i	0.367807	−	1.48032i
$996$	0.191828			0.00607830
$997$		−	28.8648i		−	0.914158i	−0.889426	−	0.457079i	$-0.848896\pi$
$997$		−	28.8648i		−	0.914158i	0.889426	−	0.457079i	$-0.151104\pi$
$998$			9.57918i			0.303224i
$999$	21.4186			0.677653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.c.339.2		6
5.2	odd	4		8450.2.a.cb.1.2		3
5.3	odd	4		8450.2.a.bu.1.2		3
5.4	even	2	inner	1690.2.b.c.339.5		6
13.3	even	3		130.2.n.a.9.5	yes	12
13.5	odd	4		1690.2.c.b.1689.3		6
13.8	odd	4		1690.2.c.c.1689.3		6
13.9	even	3		130.2.n.a.29.2	yes	12
13.12	even	2		1690.2.b.b.339.5		6
39.29	odd	6		1170.2.bp.h.919.2		12
39.35	odd	6		1170.2.bp.h.289.5		12
52.3	odd	6		1040.2.dh.b.529.3		12
52.35	odd	6		1040.2.dh.b.289.4		12
65.3	odd	12		650.2.e.k.451.2		6
65.9	even	6		130.2.n.a.29.5	yes	12
65.12	odd	4		8450.2.a.bt.1.2		3
65.22	odd	12		650.2.e.j.601.2		6
65.29	even	6		130.2.n.a.9.2	✓	12
65.34	odd	4		1690.2.c.b.1689.4		6
65.38	odd	4		8450.2.a.ca.1.2		3
65.42	odd	12		650.2.e.j.451.2		6
65.44	odd	4		1690.2.c.c.1689.4		6
65.48	odd	12		650.2.e.k.601.2		6
65.64	even	2		1690.2.b.b.339.2		6
195.29	odd	6		1170.2.bp.h.919.5		12
195.74	odd	6		1170.2.bp.h.289.2		12
260.139	odd	6		1040.2.dh.b.289.3		12
260.159	odd	6		1040.2.dh.b.529.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.2	✓	12	65.29	even	6
130.2.n.a.9.5	yes	12	13.3	even	3
130.2.n.a.29.2	yes	12	13.9	even	3
130.2.n.a.29.5	yes	12	65.9	even	6
650.2.e.j.451.2		6	65.42	odd	12
650.2.e.j.601.2		6	65.22	odd	12
650.2.e.k.451.2		6	65.3	odd	12
650.2.e.k.601.2		6	65.48	odd	12
1040.2.dh.b.289.3		12	260.139	odd	6
1040.2.dh.b.289.4		12	52.35	odd	6
1040.2.dh.b.529.3		12	52.3	odd	6
1040.2.dh.b.529.4		12	260.159	odd	6
1170.2.bp.h.289.2		12	195.74	odd	6
1170.2.bp.h.289.5		12	39.35	odd	6
1170.2.bp.h.919.2		12	39.29	odd	6
1170.2.bp.h.919.5		12	195.29	odd	6
1690.2.b.b.339.2		6	65.64	even	2
1690.2.b.b.339.5		6	13.12	even	2
1690.2.b.c.339.2		6	1.1	even	1	trivial
1690.2.b.c.339.5		6	5.4	even	2	inner
1690.2.c.b.1689.3		6	13.5	odd	4
1690.2.c.b.1689.4		6	65.34	odd	4
1690.2.c.c.1689.3		6	13.8	odd	4
1690.2.c.c.1689.4		6	65.44	odd	4
8450.2.a.bt.1.2		3	65.12	odd	4
8450.2.a.bu.1.2		3	5.3	odd	4
8450.2.a.ca.1.2		3	65.38	odd	4
8450.2.a.cb.1.2		3	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.539189i q^{3} -1.00000 q^{4} +(-0.539189 + 2.17009i) q^{5} -0.539189 q^{6} -0.709275i q^{7} +1.00000i q^{8} +2.70928 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -0.539189i q^{3} -1.00000 q^{4} +(-0.539189 + 2.17009i) q^{5} -0.539189 q^{6} -0.709275i q^{7} +1.00000i q^{8} +2.70928 q^{9} +(2.17009 + 0.539189i) q^{10} -4.51026 q^{11} +0.539189i q^{12} -0.709275 q^{14} +(1.17009 + 0.290725i) q^{15} +1.00000 q^{16} -3.17009i q^{17} -2.70928i q^{18} +0.120638 q^{19} +(0.539189 - 2.17009i) q^{20} -0.382433 q^{21} +4.51026i q^{22} +4.97107i q^{23} +0.539189 q^{24} +(-4.41855 - 2.34017i) q^{25} -3.07838i q^{27} +0.709275i q^{28} +7.26180 q^{29} +(0.290725 - 1.17009i) q^{30} +9.66701 q^{31} -1.00000i q^{32} +2.43188i q^{33} -3.17009 q^{34} +(1.53919 + 0.382433i) q^{35} -2.70928 q^{36} +6.95774i q^{37} -0.120638i q^{38} +(-2.17009 - 0.539189i) q^{40} +0.447480 q^{41} +0.382433i q^{42} +2.00000i q^{43} +4.51026 q^{44} +(-1.46081 + 5.87936i) q^{45} +4.97107 q^{46} +4.70928i q^{47} -0.539189i q^{48} +6.49693 q^{49} +(-2.34017 + 4.41855i) q^{50} -1.70928 q^{51} +9.58864i q^{53} -3.07838 q^{54} +(2.43188 - 9.78765i) q^{55} +0.709275 q^{56} -0.0650468i q^{57} -7.26180i q^{58} +5.75872 q^{59} +(-1.17009 - 0.290725i) q^{60} +7.06278 q^{61} -9.66701i q^{62} -1.92162i q^{63} -1.00000 q^{64} +2.43188 q^{66} +2.92162i q^{67} +3.17009i q^{68} +2.68035 q^{69} +(0.382433 - 1.53919i) q^{70} -8.18342 q^{71} +2.70928i q^{72} +6.74539i q^{73} +6.95774 q^{74} +(-1.26180 + 2.38243i) q^{75} -0.120638 q^{76} +3.19902i q^{77} +16.0072 q^{79} +(-0.539189 + 2.17009i) q^{80} +6.46800 q^{81} -0.447480i q^{82} -0.355771i q^{83} +0.382433 q^{84} +(6.87936 + 1.70928i) q^{85} +2.00000 q^{86} -3.91548i q^{87} -4.51026i q^{88} -3.63090 q^{89} +(5.87936 + 1.46081i) q^{90} -4.97107i q^{92} -5.21235i q^{93} +4.70928 q^{94} +(-0.0650468 + 0.261795i) q^{95} -0.539189 q^{96} +7.90829i q^{97} -6.49693i q^{98} -12.2195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^9	\( 6 q - 6 q^{4} + 2 q^{9} + 2 q^{10} + 6 q^{11} + 10 q^{14} - 4 q^{15} + 6 q^{16} + 26 q^{19} - 12 q^{21} + 2 q^{25} + 28 q^{29} + 16 q^{30} + 12 q^{31} - 8 q^{34} + 6 q^{35} - 2 q^{36} - 2 q^{40} + 4 q^{41} - 6 q^{44} - 12 q^{45} + 4 q^{49} + 8 q^{50} + 4 q^{51} - 12 q^{54} - 12 q^{55} - 10 q^{56} - 16 q^{59} + 4 q^{60} + 8 q^{61} - 6 q^{64} - 12 q^{66} - 28 q^{69} + 12 q^{70} - 40 q^{71} + 10 q^{74} + 8 q^{75} - 26 q^{76} + 28 q^{79} - 26 q^{81} + 12 q^{84} + 16 q^{85} + 12 q^{86} - 14 q^{89} + 10 q^{90} + 14 q^{94} + 8 q^{95} - 26 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^9 + 2 * q^10 + 6 * q^11 + 10 * q^14 - 4 * q^15 + 6 * q^16 + 26 * q^19 - 12 * q^21 + 2 * q^25 + 28 * q^29 + 16 * q^30 + 12 * q^31 - 8 * q^34 + 6 * q^35 - 2 * q^36 - 2 * q^40 + 4 * q^41 - 6 * q^44 - 12 * q^45 + 4 * q^49 + 8 * q^50 + 4 * q^51 - 12 * q^54 - 12 * q^55 - 10 * q^56 - 16 * q^59 + 4 * q^60 + 8 * q^61 - 6 * q^64 - 12 * q^66 - 28 * q^69 + 12 * q^70 - 40 * q^71 + 10 * q^74 + 8 * q^75 - 26 * q^76 + 28 * q^79 - 26 * q^81 + 12 * q^84 + 16 * q^85 + 12 * q^86 - 14 * q^89 + 10 * q^90 + 14 * q^94 + 8 * q^95 - 26 * q^99

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