LMFDB - Embedded newform 1690.2.c.c.1689.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(1689,1690)]

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, 1]))

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

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

chi := DirichletCharacter("1690.1689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.c (of order $2$, degree $1$, not 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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1689.4
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.c.1689.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.539189i q^{3} +1.00000 q^{4} +(-2.17009 + 0.539189i) q^{5} +0.539189i q^{6} -0.709275 q^{7} +1.00000 q^{8} +2.70928 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.539189i q^{3} +1.00000 q^{4} +(-2.17009 + 0.539189i) q^{5} +0.539189i q^{6} -0.709275 q^{7} +1.00000 q^{8} +2.70928 q^{9} +(-2.17009 + 0.539189i) q^{10} -4.51026i q^{11} +0.539189i q^{12} -0.709275 q^{14} +(-0.290725 - 1.17009i) q^{15} +1.00000 q^{16} -3.17009i q^{17} +2.70928 q^{18} -0.120638i q^{19} +(-2.17009 + 0.539189i) q^{20} -0.382433i q^{21} -4.51026i q^{22} +4.97107i q^{23} +0.539189i q^{24} +(4.41855 - 2.34017i) q^{25} +3.07838i q^{27} -0.709275 q^{28} +7.26180 q^{29} +(-0.290725 - 1.17009i) q^{30} -9.66701i q^{31} +1.00000 q^{32} +2.43188 q^{33} -3.17009i q^{34} +(1.53919 - 0.382433i) q^{35} +2.70928 q^{36} +6.95774 q^{37} -0.120638i q^{38} +(-2.17009 + 0.539189i) q^{40} -0.447480i q^{41} -0.382433i q^{42} +2.00000i q^{43} -4.51026i q^{44} +(-5.87936 + 1.46081i) q^{45} +4.97107i q^{46} +4.70928 q^{47} +0.539189i q^{48} -6.49693 q^{49} +(4.41855 - 2.34017i) q^{50} +1.70928 q^{51} -9.58864i q^{53} +3.07838i q^{54} +(2.43188 + 9.78765i) q^{55} -0.709275 q^{56} +0.0650468 q^{57} +7.26180 q^{58} +5.75872i q^{59} +(-0.290725 - 1.17009i) q^{60} +7.06278 q^{61} -9.66701i q^{62} -1.92162 q^{63} +1.00000 q^{64} +2.43188 q^{66} -2.92162 q^{67} -3.17009i q^{68} -2.68035 q^{69} +(1.53919 - 0.382433i) q^{70} +8.18342i q^{71} +2.70928 q^{72} +6.74539 q^{73} +6.95774 q^{74} +(1.26180 + 2.38243i) q^{75} -0.120638i q^{76} +3.19902i q^{77} +16.0072 q^{79} +(-2.17009 + 0.539189i) q^{80} +6.46800 q^{81} -0.447480i q^{82} +0.355771 q^{83} -0.382433i q^{84} +(1.70928 + 6.87936i) q^{85} +2.00000i q^{86} +3.91548i q^{87} -4.51026i q^{88} -3.63090i q^{89} +(-5.87936 + 1.46081i) q^{90} +4.97107i q^{92} +5.21235 q^{93} +4.70928 q^{94} +(0.0650468 + 0.261795i) q^{95} +0.539189i q^{96} -7.90829 q^{97} -6.49693 q^{98} -12.2195i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 6 * q^8 + 2 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{10} + 10 q^{14} - 16 q^{15} + 6 q^{16} + 2 q^{18} - 2 q^{20} - 2 q^{25} + 10 q^{28} + 28 q^{29} - 16 q^{30} + 6 q^{32} - 12 q^{33} + 6 q^{35} + 2 q^{36} + 10 q^{37} - 2 q^{40} - 10 q^{45} + 14 q^{47} - 4 q^{49} - 2 q^{50} - 4 q^{51} - 12 q^{55} + 10 q^{56} - 8 q^{57} + 28 q^{58} - 16 q^{60} + 8 q^{61} - 18 q^{63} + 6 q^{64} - 12 q^{66} - 24 q^{67} + 28 q^{69} + 6 q^{70} + 2 q^{72} - 12 q^{73} + 10 q^{74} - 8 q^{75} + 28 q^{79} - 2 q^{80} - 26 q^{81} + 8 q^{83} - 4 q^{85} - 10 q^{90} + 52 q^{93} + 14 q^{94} - 8 q^{95} - 52 q^{97} - 4 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 6 * q^8 + 2 * q^9 - 2 * q^10 + 10 * q^14 - 16 * q^15 + 6 * q^16 + 2 * q^18 - 2 * q^20 - 2 * q^25 + 10 * q^28 + 28 * q^29 - 16 * q^30 + 6 * q^32 - 12 * q^33 + 6 * q^35 + 2 * q^36 + 10 * q^37 - 2 * q^40 - 10 * q^45 + 14 * q^47 - 4 * q^49 - 2 * q^50 - 4 * q^51 - 12 * q^55 + 10 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^60 + 8 * q^61 - 18 * q^63 + 6 * q^64 - 12 * q^66 - 24 * q^67 + 28 * q^69 + 6 * q^70 + 2 * q^72 - 12 * q^73 + 10 * q^74 - 8 * q^75 + 28 * q^79 - 2 * q^80 - 26 * q^81 + 8 * q^83 - 4 * q^85 - 10 * q^90 + 52 * q^93 + 14 * q^94 - 8 * q^95 - 52 * q^97 - 4 * q^98

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$			0.539189i			0.311301i	0.987812	+	0.155650i	$0.0497473\pi$
$3$			0.539189i			0.311301i	−0.987812	+	0.155650i	$0.950253\pi$
$4$	1.00000			0.500000
$5$	−2.17009	+	0.539189i	−0.970492	+	0.241133i
$5$	−2.17009	+	0.539189i	−0.970492	+	0.241133i
$6$			0.539189i			0.220123i
$7$	−0.709275			−0.268081			−0.134040	−	0.990976i	$-0.542795\pi$
$7$	−0.709275			−0.268081			−0.134040	+	0.990976i	$0.542795\pi$
$8$	1.00000			0.353553
$9$	2.70928			0.903092
$10$	−2.17009	+	0.539189i	−0.686242	+	0.170506i
$11$		−	4.51026i		−	1.35989i	−0.733261	−	0.679947i	$-0.762003\pi$
$11$		−	4.51026i		−	1.35989i	0.733261	−	0.679947i	$-0.237997\pi$
$12$			0.539189i			0.155650i
$13$		0			0
$13$		0			0
$14$	−0.709275			−0.189562
$15$	−0.290725	−	1.17009i	−0.0750648	−	0.302115i
$16$	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	$-0.125602\pi$
$18$	2.70928			0.638582
$19$		−	0.120638i		−	0.0276763i	−0.999904	−	0.0138381i	$-0.995595\pi$
$19$		−	0.120638i		−	0.0276763i	0.999904	−	0.0138381i	$-0.00440496\pi$
$20$	−2.17009	+	0.539189i	−0.485246	+	0.120566i
$21$		−	0.382433i		−	0.0834538i
$22$		−	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	$0.826576\pi$
$24$			0.539189i			0.110061i
$25$	4.41855	−	2.34017i	0.883710	−	0.468035i
$26$		0			0
$27$			3.07838i			0.592434i
$28$	−0.709275			−0.134040
$29$	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
$31$		−	9.66701i		−	1.73625i	−0.496348	−	0.868124i	$-0.665326\pi$
$31$		−	9.66701i		−	1.73625i	0.496348	−	0.868124i	$-0.334674\pi$
$32$	1.00000			0.176777
$33$	2.43188			0.423336
$34$		−	3.17009i		−	0.543665i
$35$	1.53919	−	0.382433i	0.260170	−	0.0646430i
$36$	2.70928			0.451546
$37$	6.95774			1.14385			0.571923	−	0.820308i	$-0.306198\pi$
$37$	6.95774			1.14385			0.571923	+	0.820308i	$0.306198\pi$
$38$		−	0.120638i		−	0.0195701i
$39$		0			0
$40$	−2.17009	+	0.539189i	−0.343121	+	0.0852532i
$41$		−	0.447480i		−	0.0698847i	−0.999389	−	0.0349423i	$-0.988875\pi$
$41$		−	0.447480i		−	0.0698847i	0.999389	−	0.0349423i	$-0.0111248\pi$
$42$		−	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	$0.951268\pi$
$44$		−	4.51026i		−	0.679947i
$45$	−5.87936	+	1.46081i	−0.876444	+	0.217765i
$46$			4.97107i			0.732944i
$47$	4.70928			0.686918			0.343459	−	0.939168i	$-0.388401\pi$
$47$	4.70928			0.686918			0.343459	+	0.939168i	$0.388401\pi$
$48$			0.539189i			0.0778252i
$49$	−6.49693			−0.928133
$50$	4.41855	−	2.34017i	0.624877	−	0.330950i
$51$	1.70928			0.239346
$52$		0			0
$53$		−	9.58864i		−	1.31710i	−0.752537	−	0.658550i	$-0.771170\pi$
$53$		−	9.58864i		−	1.31710i	0.752537	−	0.658550i	$-0.228830\pi$
$54$			3.07838i			0.418914i
$55$	2.43188	+	9.78765i	0.327915	+	1.31977i
$56$	−0.709275			−0.0947809
$57$	0.0650468			0.00861565
$58$	7.26180			0.953520
$59$			5.75872i			0.749722i	0.927081	+	0.374861i	$0.122310\pi$
$59$			5.75872i			0.749722i	−0.927081	+	0.374861i	$0.877690\pi$
$60$	−0.290725	−	1.17009i	−0.0375324	−	0.151058i
$61$	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
$63$	−1.92162			−0.242102
$64$	1.00000			0.125000
$65$		0			0
$66$	2.43188			0.299344
$67$	−2.92162			−0.356933			−0.178466	−	0.983946i	$-0.557114\pi$
$67$	−2.92162			−0.356933			−0.178466	+	0.983946i	$0.557114\pi$
$68$		−	3.17009i		−	0.384429i
$69$	−2.68035			−0.322676
$70$	1.53919	−	0.382433i	0.183968	−	0.0457095i
$71$			8.18342i			0.971193i	0.874183	+	0.485596i	$0.161398\pi$
$71$			8.18342i			0.971193i	−0.874183	+	0.485596i	$0.838602\pi$
$72$	2.70928			0.319291
$73$	6.74539			0.789488			0.394744	−	0.918791i	$-0.370833\pi$
$73$	6.74539			0.789488			0.394744	+	0.918791i	$0.370833\pi$
$74$	6.95774			0.808821
$75$	1.26180	+	2.38243i	0.145700	+	0.275100i
$76$		−	0.120638i		−	0.0138381i
$77$			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	$0.143219\pi$
$80$	−2.17009	+	0.539189i	−0.242623	+	0.0602831i
$81$	6.46800			0.718667
$82$		−	0.447480i		−	0.0494159i
$83$	0.355771			0.0390510			0.0195255	−	0.999809i	$-0.493784\pi$
$83$	0.355771			0.0390510			0.0195255	+	0.999809i	$0.493784\pi$
$84$		−	0.382433i		−	0.0417269i
$85$	1.70928	+	6.87936i	0.185397	+	0.746172i
$86$			2.00000i			0.215666i
$87$			3.91548i			0.419783i
$88$		−	4.51026i		−	0.480795i
$89$		−	3.63090i		−	0.384874i	−0.981309	−	0.192437i	$-0.938361\pi$
$89$		−	3.63090i		−	0.384874i	0.981309	−	0.192437i	$-0.0616392\pi$
$90$	−5.87936	+	1.46081i	−0.619739	+	0.153983i
$91$		0			0
$92$			4.97107i			0.518270i
$93$	5.21235			0.540495
$94$	4.70928			0.485725
$95$	0.0650468	+	0.261795i	0.00667366	+	0.0268596i
$96$			0.539189i			0.0550307i
$97$	−7.90829			−0.802965			−0.401483	−	0.915867i	$-0.631505\pi$
$97$	−7.90829			−0.802965			−0.401483	+	0.915867i	$0.631505\pi$
$98$	−6.49693			−0.656289
$99$		−	12.2195i		−	1.22811i
$100$	4.41855	−	2.34017i	0.441855	−	0.234017i
$101$	−6.14116			−0.611068			−0.305534	−	0.952181i	$-0.598835\pi$
$101$	−6.14116			−0.611068			−0.305534	+	0.952181i	$0.598835\pi$
$102$	1.70928			0.169243
$103$		−	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
$106$		−	9.58864i		−	0.931331i
$107$			0.539189i			0.0521254i	0.999660	+	0.0260627i	$0.00829695\pi$
$107$			0.539189i			0.0521254i	−0.999660	+	0.0260627i	$0.991703\pi$
$108$			3.07838i			0.296217i
$109$		−	11.0205i		−	1.05557i	−0.849377	−	0.527787i	$-0.823022\pi$
$109$		−	11.0205i		−	1.05557i	0.849377	−	0.527787i	$-0.176978\pi$
$110$	2.43188	+	9.78765i	0.231871	+	0.933216i
$111$			3.75154i			0.356080i
$112$	−0.709275			−0.0670202
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$	0.0650468			0.00609219
$115$	−2.68035	−	10.7877i	−0.249944	−	1.00595i
$116$	7.26180			0.674241
$117$		0			0
$118$			5.75872i			0.530133i
$119$			2.24846i			0.206116i
$120$	−0.290725	−	1.17009i	−0.0265394	−	0.106814i
$121$	−9.34244			−0.849313
$122$	7.06278			0.639434
$123$	0.241276			0.0217552
$124$		−	9.66701i		−	0.868124i
$125$	−8.32684	+	7.46081i	−0.744775	+	0.667315i
$126$	−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	$0.818319\pi$
$128$	1.00000			0.0883883
$129$	−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	$0.776034\pi$
$132$	2.43188			0.211668
$133$			0.0855657i			0.00741948i
$134$	−2.92162			−0.252390
$135$	−1.65983	−	6.68035i	−0.142855	−	0.574953i
$136$		−	3.17009i		−	0.271833i
$137$	9.35350			0.799124			0.399562	−	0.916706i	$-0.369162\pi$
$137$	9.35350			0.799124			0.399562	+	0.916706i	$0.369162\pi$
$138$	−2.68035			−0.228166
$139$	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
$141$			2.53919i			0.213838i
$142$			8.18342i			0.686737i
$143$		0			0
$144$	2.70928			0.225773
$145$	−15.7587	+	3.91548i	−1.30869	+	0.325163i
$146$	6.74539			0.558253
$147$		−	3.50307i		−	0.288928i
$148$	6.95774			0.571923
$149$		−	9.23513i		−	0.756572i	−0.925689	−	0.378286i	$-0.876514\pi$
$149$		−	9.23513i		−	0.756572i	0.925689	−	0.378286i	$-0.123486\pi$
$150$	1.26180	+	2.38243i	0.103025	+	0.194525i
$151$		−	9.42574i		−	0.767056i	−0.923529	−	0.383528i	$-0.874709\pi$
$151$		−	9.42574i		−	0.767056i	0.923529	−	0.383528i	$-0.125291\pi$
$152$		−	0.120638i		−	0.00978505i
$153$		−	8.58864i		−	0.694350i
$154$			3.19902i			0.257784i
$155$	5.21235	+	20.9783i	0.418666	+	1.68501i
$156$		0			0
$157$		−	5.77205i		−	0.460660i	−0.973113	−	0.230330i	$-0.926019\pi$
$157$		−	5.77205i		−	0.460660i	0.973113	−	0.230330i	$-0.0739806\pi$
$158$	16.0072			1.27346
$159$	5.17009			0.410015
$160$	−2.17009	+	0.539189i	−0.171560	+	0.0426266i
$161$		−	3.52586i		−	0.277877i
$162$	6.46800			0.508174
$163$	−16.8215			−1.31756			−0.658781	−	0.752335i	$-0.728928\pi$
$163$	−16.8215			−1.31756			−0.658781	+	0.752335i	$0.728928\pi$
$164$		−	0.447480i		−	0.0349423i
$165$	−5.27739	+	1.31124i	−0.410845	+	0.102080i
$166$	0.355771			0.0276132
$167$	−18.1194			−1.40212			−0.701061	−	0.713101i	$-0.747290\pi$
$167$	−18.1194			−1.40212			−0.701061	+	0.713101i	$0.747290\pi$
$168$		−	0.382433i		−	0.0295054i
$169$		0			0
$170$	1.70928	+	6.87936i	0.131095	+	0.527623i
$171$		−	0.326842i		−	0.0249942i
$172$			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	$0.871887\pi$
$174$			3.91548i			0.296832i
$175$	−3.13397	+	1.65983i	−0.236906	+	0.125471i
$176$		−	4.51026i		−	0.339974i
$177$	−3.10504			−0.233389
$178$		−	3.63090i		−	0.272147i
$179$	1.26180			0.0943110			0.0471555	−	0.998888i	$-0.484984\pi$
$179$	1.26180			0.0943110			0.0471555	+	0.998888i	$0.484984\pi$
$180$	−5.87936	+	1.46081i	−0.438222	+	0.108882i
$181$	−2.38243			−0.177085			−0.0885424	−	0.996072i	$-0.528221\pi$
$181$	−2.38243			−0.177085			−0.0885424	+	0.996072i	$0.528221\pi$
$182$		0			0
$183$			3.80817i			0.281508i
$184$			4.97107i			0.366472i
$185$	−15.0989	+	3.75154i	−1.11009	+	0.275818i
$186$	5.21235			0.382188
$187$	−14.2979			−1.04557
$188$	4.70928			0.343459
$189$		−	2.18342i		−	0.158820i
$190$	0.0650468	+	0.261795i	0.00471899	+	0.0189926i
$191$	−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
$193$	−14.0000			−1.00774			−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$	−7.90829			−0.567782
$195$		0			0
$196$	−6.49693			−0.464066
$197$	−8.69368			−0.619399			−0.309699	−	0.950835i	$-0.600228\pi$
$197$	−8.69368			−0.619399			−0.309699	+	0.950835i	$0.600228\pi$
$198$		−	12.2195i		−	0.868405i
$199$	21.5174			1.52533			0.762666	−	0.646793i	$-0.223890\pi$
$199$	21.5174			1.52533			0.762666	+	0.646793i	$0.223890\pi$
$200$	4.41855	−	2.34017i	0.312439	−	0.165475i
$201$		−	1.57531i		−	0.111114i
$202$	−6.14116			−0.432090
$203$	−5.15061			−0.361502
$204$	1.70928			0.119673
$205$	0.241276	+	0.971071i	0.0168515	+	0.0678225i
$206$		−	17.6803i		−	1.23185i
$207$			13.4680i			0.936091i
$208$		0			0
$209$	−0.544109			−0.0376368
$210$	0.206204	+	0.829914i	0.0142294	+	0.0572695i
$211$	−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
$213$	−4.41241			−0.302333
$214$			0.539189i			0.0368582i
$215$	−1.07838	−	4.34017i	−0.0735448	−	0.295997i
$216$			3.07838i			0.209457i
$217$			6.85658i			0.465455i
$218$		−	11.0205i		−	0.746404i
$219$			3.63704i			0.245768i
$220$	2.43188	+	9.78765i	0.163957	+	0.659883i
$221$		0			0
$222$			3.75154i			0.251787i
$223$	24.7093			1.65466			0.827328	−	0.561720i	$-0.189860\pi$
$223$	24.7093			1.65466			0.827328	+	0.561720i	$0.189860\pi$
$224$	−0.709275			−0.0473905
$225$	11.9711	−	6.34017i	0.798071	−	0.422678i
$226$			14.0000i			0.931266i
$227$	−28.6947			−1.90454			−0.952268	−	0.305264i	$-0.901255\pi$
$227$	−28.6947			−1.90454			−0.952268	+	0.305264i	$0.901255\pi$
$228$	0.0650468			0.00430783
$229$			1.89988i			0.125548i	0.998028	+	0.0627738i	$0.0199947\pi$
$229$			1.89988i			0.125548i	−0.998028	+	0.0627738i	$0.980005\pi$
$230$	−2.68035	−	10.7877i	−0.176737	−	0.711317i
$231$	−1.72487			−0.113488
$232$	7.26180			0.476760
$233$		−	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
$236$			5.75872i			0.374861i
$237$			8.63090i			0.560637i
$238$			2.24846i			0.145746i
$239$			24.8710i			1.60877i	0.594110	+	0.804384i	$0.297505\pi$
$239$			24.8710i			1.60877i	−0.594110	+	0.804384i	$0.702495\pi$
$240$	−0.290725	−	1.17009i	−0.0187662	−	0.0755288i
$241$		−	2.95055i		−	0.190062i	−0.995474	−	0.0950309i	$-0.969705\pi$
$241$		−	2.95055i		−	0.190062i	0.995474	−	0.0950309i	$-0.0302950\pi$
$242$	−9.34244			−0.600555
$243$			12.7226i			0.816156i
$244$	7.06278			0.452148
$245$	14.0989	−	3.50307i	0.900745	−	0.223803i
$246$	0.241276			0.0153832
$247$		0			0
$248$		−	9.66701i		−	0.613856i
$249$			0.191828i			0.0121566i
$250$	−8.32684	+	7.46081i	−0.526636	+	0.471863i
$251$	−16.5597			−1.04524			−0.522620	−	0.852566i	$-0.675045\pi$
$251$	−16.5597			−1.04524			−0.522620	+	0.852566i	$0.675045\pi$
$252$	−1.92162			−0.121051
$253$	22.4208			1.40958
$254$			12.1773i			0.764070i
$255$	−3.70928	+	0.921622i	−0.232284	+	0.0577142i
$256$	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	$-0.00519834\pi$
$258$	−1.07838			−0.0671369
$259$	−4.93495			−0.306643
$260$		0			0
$261$	19.6742			1.21780
$262$	−17.4547			−1.07835
$263$		−	28.7815i		−	1.77474i	−0.461054	−	0.887372i	$-0.652529\pi$
$263$		−	28.7815i		−	1.77474i	0.461054	−	0.887372i	$-0.347471\pi$
$264$	2.43188			0.149672
$265$	5.17009	+	20.8082i	0.317596	+	1.27824i
$266$			0.0855657i			0.00524637i
$267$	1.95774			0.119812
$268$	−2.92162			−0.178466
$269$	−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
$271$			18.1256i			1.10105i	0.834819	+	0.550525i	$0.185572\pi$
$271$			18.1256i			1.10105i	−0.834819	+	0.550525i	$0.814428\pi$
$272$		−	3.17009i		−	0.192215i
$273$		0			0
$274$	9.35350			0.565066
$275$	−10.5548	−	19.9288i	−0.636478	−	1.20175i
$276$	−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	$0.733624\pi$
$278$	2.64423			0.158590
$279$		−	26.1906i		−	1.56799i
$280$	1.53919	−	0.382433i	0.0919841	−	0.0228548i
$281$			22.9854i			1.37120i	0.727980	+	0.685598i	$0.240459\pi$
$281$			22.9854i			1.37120i	−0.727980	+	0.685598i	$0.759541\pi$
$282$			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	$0.819205\pi$
$284$			8.18342i			0.485596i
$285$	−0.141157	+	0.0350725i	−0.00836142	+	0.00207751i
$286$		0			0
$287$			0.317387i			0.0187347i
$288$	2.70928			0.159646
$289$	6.95055			0.408856
$290$	−15.7587	+	3.91548i	−0.925384	+	0.229925i
$291$		−	4.26406i		−	0.249964i
$292$	6.74539			0.394744
$293$	17.8443			1.04247			0.521237	−	0.853412i	$-0.325471\pi$
$293$	17.8443			1.04247			0.521237	+	0.853412i	$0.325471\pi$
$294$		−	3.50307i		−	0.204303i
$295$	−3.10504	−	12.4969i	−0.180782	−	0.727599i
$296$	6.95774			0.404410
$297$	13.8843			0.805648
$298$		−	9.23513i		−	0.534977i
$299$		0			0
$300$	1.26180	+	2.38243i	0.0728498	+	0.137550i
$301$		−	1.41855i		−	0.0817639i
$302$		−	9.42574i		−	0.542390i
$303$		−	3.31124i		−	0.190226i
$304$		−	0.120638i		−	0.00691907i
$305$	−15.3268	+	3.80817i	−0.877612	+	0.218055i
$306$		−	8.58864i		−	0.490980i
$307$	−3.44521			−0.196629			−0.0983143	−	0.995155i	$-0.531345\pi$
$307$	−3.44521			−0.196629			−0.0983143	+	0.995155i	$0.531345\pi$
$308$			3.19902i			0.182281i
$309$	9.53305			0.542316
$310$	5.21235	+	20.9783i	0.296041	+	1.19149i
$311$	−17.8238			−1.01069			−0.505347	−	0.862916i	$-0.668635\pi$
$311$	−17.8238			−1.01069			−0.505347	+	0.862916i	$0.668635\pi$
$312$		0			0
$313$		−	32.2245i		−	1.82143i	−0.413031	−	0.910717i	$-0.635530\pi$
$313$		−	32.2245i		−	1.82143i	0.413031	−	0.910717i	$-0.364470\pi$
$314$		−	5.77205i		−	0.325736i
$315$	4.17009	−	1.03612i	0.234958	−	0.0583786i
$316$	16.0072			0.900475
$317$	1.90602			0.107053			0.0535265	−	0.998566i	$-0.482954\pi$
$317$	1.90602			0.107053			0.0535265	+	0.998566i	$0.482954\pi$
$318$	5.17009			0.289924
$319$		−	32.7526i		−	1.83379i
$320$	−2.17009	+	0.539189i	−0.121312	+	0.0301416i
$321$	−0.290725			−0.0162267
$322$		−	3.52586i		−	0.196488i
$323$	−0.382433			−0.0212792
$324$	6.46800			0.359333
$325$		0			0
$326$	−16.8215			−0.931657
$327$	5.94214			0.328601
$328$		−	0.447480i		−	0.0247080i
$329$	−3.34017			−0.184150
$330$	−5.27739	+	1.31124i	−0.290511	+	0.0721816i
$331$			0.711543i			0.0391099i	0.999809	+	0.0195550i	$0.00622494\pi$
$331$			0.711543i			0.0391099i	−0.999809	+	0.0195550i	$0.993775\pi$
$332$	0.355771			0.0195255
$333$	18.8504			1.03300
$334$	−18.1194			−0.991450
$335$	6.34017	−	1.57531i	0.346401	−	0.0860682i
$336$		−	0.382433i		−	0.0208635i
$337$		−	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
$340$	1.70928	+	6.87936i	0.0926985	+	0.373086i
$341$	−43.6007			−2.36111
$342$		−	0.326842i		−	0.0176736i
$343$	9.57304			0.516896
$344$			2.00000i			0.107833i
$345$	5.81658	−	1.44521i	0.313154	−	0.0778076i
$346$			10.3041i			0.553949i
$347$		−	25.5330i		−	1.37069i	−0.728221	−	0.685343i	$-0.759652\pi$
$347$		−	25.5330i		−	1.37069i	0.728221	−	0.685343i	$-0.240348\pi$
$348$			3.91548i			0.209892i
$349$			18.0566i			0.966550i	0.875469	+	0.483275i	$0.160553\pi$
$349$			18.0566i			0.966550i	−0.875469	+	0.483275i	$0.839447\pi$
$350$	−3.13397	+	1.65983i	−0.167518	+	0.0887215i
$351$		0			0
$352$		−	4.51026i		−	0.240398i
$353$	14.6465			0.779554			0.389777	−	0.920909i	$-0.372552\pi$
$353$	14.6465			0.779554			0.389777	+	0.920909i	$0.372552\pi$
$354$	−3.10504			−0.165031
$355$	−4.41241	−	17.7587i	−0.234186	−	0.942535i
$356$		−	3.63090i		−	0.192437i
$357$	−1.21235			−0.0641642
$358$	1.26180			0.0666879
$359$			13.4186i			0.708204i	0.935207	+	0.354102i	$0.115213\pi$
$359$			13.4186i			0.708204i	−0.935207	+	0.354102i	$0.884787\pi$
$360$	−5.87936	+	1.46081i	−0.309870	+	0.0769915i
$361$	18.9854			0.999234
$362$	−2.38243			−0.125218
$363$		−	5.03734i		−	0.264392i
$364$		0			0
$365$	−14.6381	+	3.63704i	−0.766192	+	0.190371i
$366$			3.80817i			0.199056i
$367$			21.5441i			1.12459i	0.826936	+	0.562297i	$0.190082\pi$
$367$			21.5441i			1.12459i	−0.826936	+	0.562297i	$0.809918\pi$
$368$			4.97107i			0.259135i
$369$		−	1.21235i		−	0.0631123i
$370$	−15.0989	+	3.75154i	−0.784954	+	0.195033i
$371$			6.80098i			0.353090i
$372$	5.21235			0.270248
$373$			21.3340i			1.10463i	0.833634	+	0.552317i	$0.186256\pi$
$373$			21.3340i			1.10463i	−0.833634	+	0.552317i	$0.813744\pi$
$374$	−14.2979			−0.739327
$375$	−4.02279	−	4.48974i	−0.207736	−	0.231849i
$376$	4.70928			0.242862
$377$		0			0
$378$		−	2.18342i		−	0.112303i
$379$			8.11223i			0.416697i	0.978055	+	0.208349i	$0.0668088\pi$
$379$			8.11223i			0.416697i	−0.978055	+	0.208349i	$0.933191\pi$
$380$	0.0650468	+	0.261795i	0.00333683	+	0.0134298i
$381$	−6.56585			−0.336379
$382$	−11.0856			−0.567187
$383$	24.9399			1.27437			0.637184	−	0.770712i	$-0.280099\pi$
$383$	24.9399			1.27437			0.637184	+	0.770712i	$0.280099\pi$
$384$			0.539189i			0.0275154i
$385$	−1.72487	−	6.94214i	−0.0879077	−	0.353804i
$386$	−14.0000			−0.712581
$387$			5.41855i			0.275440i
$388$	−7.90829			−0.401483
$389$	13.5330			0.686153			0.343076	−	0.939308i	$-0.388531\pi$
$389$	13.5330			0.686153			0.343076	+	0.939308i	$0.388531\pi$
$390$		0			0
$391$	15.7587			0.796953
$392$	−6.49693			−0.328144
$393$		−	9.41136i		−	0.474740i
$394$	−8.69368			−0.437981
$395$	−34.7370	+	8.63090i	−1.74781	+	0.434268i
$396$		−	12.2195i		−	0.614055i
$397$	−4.59478			−0.230605			−0.115303	−	0.993330i	$-0.536784\pi$
$397$	−4.59478			−0.230605			−0.115303	+	0.993330i	$0.536784\pi$
$398$	21.5174			1.07857
$399$	−0.0461361			−0.00230969
$400$	4.41855	−	2.34017i	0.220928	−	0.117009i
$401$			29.7031i			1.48330i	0.670785	+	0.741652i	$0.265957\pi$
$401$			29.7031i			1.48330i	−0.670785	+	0.741652i	$0.734043\pi$
$402$		−	1.57531i		−	0.0785691i
$403$		0			0
$404$	−6.14116			−0.305534
$405$	−14.0361	+	3.48747i	−0.697460	+	0.173294i
$406$	−5.15061			−0.255621
$407$		−	31.3812i		−	1.55551i
$408$	1.70928			0.0846217
$409$		−	10.3112i		−	0.509858i	−0.966960	−	0.254929i	$-0.917948\pi$
$409$		−	10.3112i		−	0.509858i	0.966960	−	0.254929i	$-0.0820521\pi$
$410$	0.241276	+	0.971071i	0.0119158	+	0.0479578i
$411$			5.04331i			0.248768i
$412$		−	17.6803i		−	0.871048i
$413$		−	4.08452i		−	0.200986i
$414$			13.4680i			0.661916i
$415$	−0.772055	+	0.191828i	−0.0378987	+	0.00941646i
$416$		0			0
$417$			1.42574i			0.0698187i
$418$	−0.544109			−0.0266133
$419$	−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
$421$			26.7103i			1.30178i	0.759171	+	0.650891i	$0.225604\pi$
$421$			26.7103i			1.30178i	−0.759171	+	0.650891i	$0.774396\pi$
$422$	−5.58864			−0.272051
$423$	12.7587			0.620350
$424$		−	9.58864i		−	0.465665i
$425$	−7.41855	−	14.0072i	−0.359853	−	0.679448i
$426$	−4.41241			−0.213782
$427$	−5.00946			−0.242425
$428$			0.539189i			0.0260627i
$429$		0			0
$430$	−1.07838	−	4.34017i	−0.0520040	−	0.209302i
$431$			20.7187i			0.997986i	0.866606	+	0.498993i	$0.166297\pi$
$431$			20.7187i			0.997986i	−0.866606	+	0.498993i	$0.833703\pi$
$432$			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	$0.875568\pi$
$434$			6.85658i			0.329126i
$435$	−2.11118	−	8.49693i	−0.101223	−	0.407397i
$436$		−	11.0205i		−	0.527787i
$437$	0.599701			0.0286876
$438$			3.63704i			0.173785i
$439$	−9.73925			−0.464829			−0.232415	−	0.972617i	$-0.574663\pi$
$439$	−9.73925			−0.464829			−0.232415	+	0.972617i	$0.574663\pi$
$440$	2.43188	+	9.78765i	0.115935	+	0.466608i
$441$	−17.6020			−0.838189
$442$		0			0
$443$			9.23060i			0.438559i	0.975662	+	0.219279i	$0.0703707\pi$
$443$			9.23060i			0.438559i	−0.975662	+	0.219279i	$0.929629\pi$
$444$			3.75154i			0.178040i
$445$	1.95774	+	7.87936i	0.0928058	+	0.373518i
$446$	24.7093			1.17002
$447$	4.97948			0.235521
$448$	−0.709275			−0.0335101
$449$			2.92389i			0.137987i	0.997617	+	0.0689934i	$0.0219788\pi$
$449$			2.92389i			0.137987i	−0.997617	+	0.0689934i	$0.978021\pi$
$450$	11.9711	−	6.34017i	0.564322	−	0.298879i
$451$	−2.01825			−0.0950358
$452$			14.0000i			0.658505i
$453$	5.08225			0.238785
$454$	−28.6947			−1.34671
$455$		0			0
$456$	0.0650468			0.00304609
$457$	−11.6526			−0.545087			−0.272544	−	0.962143i	$-0.587865\pi$
$457$	−11.6526			−0.545087			−0.272544	+	0.962143i	$0.587865\pi$
$458$			1.89988i			0.0887756i
$459$	9.75872			0.455498
$460$	−2.68035	−	10.7877i	−0.124972	−	0.502977i
$461$			30.2979i			1.41111i	0.708653	+	0.705557i	$0.249303\pi$
$461$			30.2979i			1.41111i	−0.708653	+	0.705557i	$0.750697\pi$
$462$	−1.72487			−0.0802484
$463$	−7.04331			−0.327330			−0.163665	−	0.986516i	$-0.552332\pi$
$463$	−7.04331			−0.327330			−0.163665	+	0.986516i	$0.552332\pi$
$464$	7.26180			0.337120
$465$	−11.3112	+	2.81044i	−0.524546	+	0.130331i
$466$		−	22.2485i		−	1.03064i
$467$			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
$470$	−10.2195	+	2.53919i	−0.471392	+	0.117124i
$471$	3.11223			0.143404
$472$			5.75872i			0.265067i
$473$	9.02052			0.414764
$474$			8.63090i			0.396430i
$475$	−0.282314	−	0.533046i	−0.0129535	−	0.0244578i
$476$			2.24846i			0.103058i
$477$		−	25.9783i		−	1.18946i
$478$			24.8710i			1.13757i
$479$		−	17.5103i		−	0.800064i	−0.916501	−	0.400032i	$-0.868999\pi$
$479$		−	17.5103i		−	0.800064i	0.916501	−	0.400032i	$-0.131001\pi$
$480$	−0.290725	−	1.17009i	−0.0132697	−	0.0534069i
$481$		0			0
$482$		−	2.95055i		−	0.134394i
$483$	1.90110			0.0865032
$484$	−9.34244			−0.424656
$485$	17.1617	−	4.26406i	0.779272	−	0.193621i
$486$			12.7226i			0.577109i
$487$	38.5318			1.74604			0.873022	−	0.487681i	$-0.162157\pi$
$487$	38.5318			1.74604			0.873022	+	0.487681i	$0.162157\pi$
$488$	7.06278			0.319717
$489$		−	9.06997i		−	0.410158i
$490$	14.0989	−	3.50307i	0.636923	−	0.158253i
$491$	−6.82377			−0.307952			−0.153976	−	0.988075i	$-0.549208\pi$
$491$	−6.82377			−0.307952			−0.153976	+	0.988075i	$0.549208\pi$
$492$	0.241276			0.0108776
$493$		−	23.0205i		−	1.03679i
$494$		0			0
$495$	6.58864	+	26.5174i	0.296137	+	1.19187i
$496$		−	9.66701i		−	0.434062i
$497$		−	5.80430i		−	0.260358i
$498$			0.191828i			0.00859602i
$499$			9.57918i			0.428823i	0.976743	+	0.214412i	$0.0687834\pi$
$499$			9.57918i			0.428823i	−0.976743	+	0.214412i	$0.931217\pi$
$500$	−8.32684	+	7.46081i	−0.372388	+	0.333658i
$501$		−	9.76979i		−	0.436482i
$502$	−16.5597			−0.739096
$503$		−	16.6742i		−	0.743466i	−0.928340	−	0.371733i	$-0.878764\pi$
$503$		−	16.6742i		−	0.743466i	0.928340	−	0.371733i	$-0.121236\pi$
$504$	−1.92162			−0.0855959
$505$	13.3268	−	3.31124i	0.593037	−	0.147348i
$506$	22.4208			0.996727
$507$		0			0
$508$			12.1773i			0.540279i
$509$		−	23.6598i		−	1.04870i	−0.851502	−	0.524352i	$-0.824308\pi$
$509$		−	23.6598i		−	1.04870i	0.851502	−	0.524352i	$-0.175692\pi$
$510$	−3.70928	+	0.921622i	−0.164249	+	0.0408101i
$511$	−4.78434			−0.211647
$512$	1.00000			0.0441942
$513$	0.371370			0.0163964
$514$		−	0.523590i		−	0.0230946i
$515$	9.53305	+	38.3679i	0.420076	+	1.69069i
$516$	−1.07838			−0.0474729
$517$		−	21.2401i		−	0.934136i
$518$	−4.93495			−0.216829
$519$	−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	$0.676594\pi$
$522$	19.6742			0.861116
$523$		−	23.3340i		−	1.02033i	−0.860078	−	0.510163i	$-0.829585\pi$
$523$		−	23.3340i		−	1.02033i	0.860078	−	0.510163i	$-0.170415\pi$
$524$	−17.4547			−0.762511
$525$	−0.894960	−	1.68980i	−0.0390593	−	0.0737490i
$526$		−	28.7815i		−	1.25493i
$527$	−30.6453			−1.33493
$528$	2.43188			0.105834
$529$	−1.71154			−0.0744149
$530$	5.17009	+	20.8082i	0.224574	+	0.903849i
$531$			15.6020i			0.677068i
$532$			0.0855657i			0.00370974i
$533$		0			0
$534$	1.95774			0.0847197
$535$	−0.290725	−	1.17009i	−0.0125691	−	0.0505873i
$536$	−2.92162			−0.126195
$537$			0.680346i			0.0293591i
$538$	−10.0566			−0.433572
$539$			29.3028i			1.26216i
$540$	−1.65983	−	6.68035i	−0.0714276	−	0.287476i
$541$		−	33.1494i		−	1.42520i	−0.701569	−	0.712602i	$-0.747517\pi$
$541$		−	33.1494i		−	1.42520i	0.701569	−	0.712602i	$-0.252483\pi$
$542$			18.1256i			0.778559i
$543$		−	1.28458i		−	0.0551267i
$544$		−	3.17009i		−	0.135916i
$545$	5.94214	+	23.9155i	0.254533	+	1.02443i
$546$		0			0
$547$			43.6742i			1.86737i	0.358090	+	0.933687i	$0.383428\pi$
$547$			43.6742i			1.86737i	−0.358090	+	0.933687i	$0.616572\pi$
$548$	9.35350			0.399562
$549$	19.1350			0.816662
$550$	−10.5548	−	19.9288i	−0.450058	−	0.849767i
$551$		−	0.876050i		−	0.0373210i
$552$	−2.68035			−0.114083
$553$	−11.3535			−0.482800
$554$			24.7165i			1.05010i
$555$	−2.02279	−	8.14116i	−0.0858625	−	0.345573i
$556$	2.64423			0.112140
$557$	22.3991			0.949079			0.474540	−	0.880234i	$-0.342615\pi$
$557$	22.3991			0.949079			0.474540	+	0.880234i	$0.342615\pi$
$558$		−	26.1906i		−	1.10874i
$559$		0			0
$560$	1.53919	−	0.382433i	0.0650426	−	0.0161608i
$561$		−	7.70928i		−	0.325486i
$562$			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	$0.998382\pi$
$564$			2.53919i			0.106919i
$565$	−7.54864	−	30.3812i	−0.317574	−	1.27815i
$566$			18.0989i			0.760753i
$567$	−4.58759			−0.192661
$568$			8.18342i			0.343369i
$569$	27.1711			1.13907			0.569537	−	0.821966i	$-0.307123\pi$
$569$	27.1711			1.13907			0.569537	+	0.821966i	$0.307123\pi$
$570$	−0.141157	+	0.0350725i	−0.00591242	+	0.00146902i
$571$	−2.25461			−0.0943524			−0.0471762	−	0.998887i	$-0.515022\pi$
$571$	−2.25461			−0.0943524			−0.0471762	+	0.998887i	$0.515022\pi$
$572$		0			0
$573$		−	5.97721i		−	0.249702i
$574$			0.317387i			0.0132475i
$575$	11.6332	+	21.9649i	0.485137	+	0.916001i
$576$	2.70928			0.112886
$577$	7.86481			0.327416			0.163708	−	0.986509i	$-0.447654\pi$
$577$	7.86481			0.327416			0.163708	+	0.986509i	$0.447654\pi$
$578$	6.95055			0.289105
$579$		−	7.54864i		−	0.313711i
$580$	−15.7587	+	3.91548i	−0.654345	+	0.162581i
$581$	−0.252340			−0.0104688
$582$		−	4.26406i		−	0.176751i
$583$	−43.2472			−1.79112
$584$	6.74539			0.279126
$585$		0			0
$586$	17.8443			0.737141
$587$	−11.2039			−0.462436			−0.231218	−	0.972902i	$-0.574271\pi$
$587$	−11.2039			−0.462436			−0.231218	+	0.972902i	$0.574271\pi$
$588$		−	3.50307i		−	0.144464i
$589$	−1.16621			−0.0480529
$590$	−3.10504	−	12.4969i	−0.127832	−	0.514490i
$591$		−	4.68753i		−	0.192819i
$592$	6.95774			0.285961
$593$	13.4186			0.551034			0.275517	−	0.961296i	$-0.411151\pi$
$593$	13.4186			0.551034			0.275517	+	0.961296i	$0.411151\pi$
$594$	13.8843			0.569679
$595$	−1.21235	−	4.87936i	−0.0497014	−	0.200034i
$596$		−	9.23513i		−	0.378286i
$597$			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	$0.706510\pi$
$600$	1.26180	+	2.38243i	0.0515126	+	0.0972624i
$601$	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
$603$	−7.91548			−0.322343
$604$		−	9.42574i		−	0.383528i
$605$	20.2739	−	5.03734i	0.824251	−	0.204797i
$606$		−	3.31124i		−	0.134510i
$607$			10.3919i			0.421794i	0.977508	+	0.210897i	$0.0676384\pi$
$607$			10.3919i			0.421794i	−0.977508	+	0.210897i	$0.932362\pi$
$608$		−	0.120638i		−	0.00489252i
$609$		−	2.77715i		−	0.112536i
$610$	−15.3268	+	3.80817i	−0.620566	+	0.154188i
$611$		0			0
$612$		−	8.58864i		−	0.347175i
$613$	30.5285			1.23303			0.616517	−	0.787341i	$-0.288543\pi$
$613$	30.5285			1.23303			0.616517	+	0.787341i	$0.288543\pi$
$614$	−3.44521			−0.139037
$615$	−0.523590	+	0.130094i	−0.0211132	+	0.00524588i
$616$			3.19902i			0.128892i
$617$	7.30283			0.294001			0.147000	−	0.989136i	$-0.453038\pi$
$617$	7.30283			0.294001			0.147000	+	0.989136i	$0.453038\pi$
$618$	9.53305			0.383475
$619$			24.5103i			0.985151i	0.870270	+	0.492575i	$0.163944\pi$
$619$			24.5103i			0.985151i	−0.870270	+	0.492575i	$0.836056\pi$
$620$	5.21235	+	20.9783i	0.209333	+	0.842507i
$621$	−15.3028			−0.614082
$622$	−17.8238			−0.714668
$623$			2.57531i			0.103177i
$624$		0			0
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$		−	32.2245i		−	1.28795i
$627$		−	0.293378i		−	0.0117164i
$628$		−	5.77205i		−	0.230330i
$629$		−	22.0566i		−	0.879456i
$630$	4.17009	−	1.03612i	0.166140	−	0.0412799i
$631$		−	3.07838i		−	0.122548i	−0.998121	−	0.0612741i	$-0.980484\pi$
$631$		−	3.07838i		−	0.122548i	0.998121	−	0.0612741i	$-0.0195164\pi$
$632$	16.0072			0.636732
$633$		−	3.01333i		−	0.119769i
$634$	1.90602			0.0756979
$635$	−6.56585	−	26.4257i	−0.260558	−	1.04867i
$636$	5.17009			0.205007
$637$		0			0
$638$		−	32.7526i		−	1.29669i
$639$			22.1711i			0.877076i
$640$	−2.17009	+	0.539189i	−0.0857802	+	0.0213133i
$641$	2.46800			0.0974801			0.0487401	−	0.998811i	$-0.484479\pi$
$641$	2.46800			0.0974801			0.0487401	+	0.998811i	$0.484479\pi$
$642$	−0.290725			−0.0114740
$643$	18.8215			0.742248			0.371124	−	0.928583i	$-0.378973\pi$
$643$	18.8215			0.742248			0.371124	+	0.928583i	$0.378973\pi$
$644$		−	3.52586i		−	0.138938i
$645$	2.34017	−	0.581449i	0.0921442	−	0.0228945i
$646$	−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	$0.926111\pi$
$648$	6.46800			0.254087
$649$	25.9733			1.01954
$650$		0			0
$651$	−3.69699			−0.144896
$652$	−16.8215			−0.658781
$653$		−	14.6937i		−	0.575008i	−0.957779	−	0.287504i	$-0.907175\pi$
$653$		−	14.6937i		−	0.575008i	0.957779	−	0.287504i	$-0.0928255\pi$
$654$	5.94214			0.232356
$655$	37.8781	−	9.41136i	1.48002	−	0.367732i
$656$		−	0.447480i		−	0.0174712i
$657$	18.2751			0.712981
$658$	−3.34017			−0.130213
$659$	−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
$661$		−	5.84202i		−	0.227228i	−0.993525	−	0.113614i	$-0.963757\pi$
$661$		−	5.84202i		−	0.227228i	0.993525	−	0.113614i	$-0.0362428\pi$
$662$			0.711543i			0.0276549i
$663$		0			0
$664$	0.355771			0.0138066
$665$	−0.0461361	−	0.185685i	−0.00178908	−	0.00720055i
$666$	18.8504			0.730439
$667$			36.0989i			1.39775i
$668$	−18.1194			−0.701061
$669$			13.3230i			0.515096i
$670$	6.34017	−	1.57531i	0.244942	−	0.0608594i
$671$		−	31.8550i		−	1.22975i
$672$		−	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	$-0.288958\pi$
$674$		−	9.85043i		−	0.379424i
$675$	7.20394	+	13.6020i	0.277280	+	0.523540i
$676$		0			0
$677$		−	28.2700i		−	1.08651i	−0.839569	−	0.543253i	$-0.817193\pi$
$677$		−	28.2700i		−	1.08651i	0.839569	−	0.543253i	$-0.182807\pi$
$678$	−7.54864			−0.289904
$679$	5.60916			0.215260
$680$	1.70928	+	6.87936i	0.0655477	+	0.263811i
$681$		−	15.4719i		−	0.592884i
$682$	−43.6007			−1.66956
$683$	−41.5052			−1.58815			−0.794075	−	0.607819i	$-0.792045\pi$
$683$	−41.5052			−1.58815			−0.794075	+	0.607819i	$0.792045\pi$
$684$		−	0.326842i		−	0.0124971i
$685$	−20.2979	+	5.04331i	−0.775543	+	0.192695i
$686$	9.57304			0.365500
$687$	−1.02439			−0.0390831
$688$			2.00000i			0.0762493i
$689$		0			0
$690$	5.81658	−	1.44521i	0.221434	−	0.0550183i
$691$			24.1084i			0.917125i	0.888662	+	0.458562i	$0.151635\pi$
$691$			24.1084i			0.917125i	−0.888662	+	0.458562i	$0.848365\pi$
$692$			10.3041i			0.391701i
$693$			8.66701i			0.329233i
$694$		−	25.5330i		−	0.969221i
$695$	−5.73820	+	1.42574i	−0.217663	+	0.0540813i
$696$			3.91548i			0.148416i
$697$	−1.41855			−0.0537314
$698$			18.0566i			0.683454i
$699$	11.9961			0.453735
$700$	−3.13397	+	1.65983i	−0.118453	+	0.0627356i
$701$	14.1822			0.535654			0.267827	−	0.963467i	$-0.413694\pi$
$701$	14.1822			0.535654			0.267827	+	0.963467i	$0.413694\pi$
$702$		0			0
$703$		−	0.839369i		−	0.0316574i
$704$		−	4.51026i		−	0.169987i
$705$	−1.36910	−	5.51026i	−0.0515634	−	0.207528i
$706$	14.6465			0.551228
$707$	4.35577			0.163816
$708$	−3.10504			−0.116695
$709$			46.4957i			1.74618i	0.487556	+	0.873091i	$0.337888\pi$
$709$			46.4957i			1.74618i	−0.487556	+	0.873091i	$0.662112\pi$
$710$	−4.41241	−	17.7587i	−0.165595	−	0.666473i
$711$	43.3679			1.62642
$712$		−	3.63090i		−	0.136074i
$713$	48.0554			1.79969
$714$	−1.21235			−0.0453709
$715$		0			0
$716$	1.26180			0.0471555
$717$	−13.4101			−0.500811
$718$			13.4186i			0.500776i
$719$	−12.7214			−0.474428			−0.237214	−	0.971457i	$-0.576234\pi$
$719$	−12.7214			−0.474428			−0.237214	+	0.971457i	$0.576234\pi$
$720$	−5.87936	+	1.46081i	−0.219111	+	0.0544412i
$721$			12.5402i			0.467023i
$722$	18.9854			0.706565
$723$	1.59090			0.0591664
$724$	−2.38243			−0.0885424
$725$	32.0866	−	16.9939i	1.19167	−	0.631136i
$726$		−	5.03734i		−	0.186953i
$727$			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
$730$	−14.6381	+	3.63704i	−0.541780	+	0.134613i
$731$	6.34017			0.234500
$732$			3.80817i			0.140754i
$733$	31.5848			1.16661			0.583305	−	0.812253i	$-0.301759\pi$
$733$	31.5848			1.16661			0.583305	+	0.812253i	$0.301759\pi$
$734$			21.5441i			0.795208i
$735$	1.88882	+	7.60197i	0.0696701	+	0.280403i
$736$			4.97107i			0.183236i
$737$			13.1773i			0.485391i
$738$		−	1.21235i		−	0.0446271i
$739$		−	2.83218i		−	0.104183i	−0.998642	−	0.0520917i	$-0.983411\pi$
$739$		−	2.83218i		−	0.104183i	0.998642	−	0.0520917i	$-0.0165888\pi$
$740$	−15.0989	+	3.75154i	−0.555046	+	0.137909i
$741$		0			0
$742$			6.80098i			0.249672i
$743$	20.8020			0.763152			0.381576	−	0.924337i	$-0.375381\pi$
$743$	20.8020			0.763152			0.381576	+	0.924337i	$0.375381\pi$
$744$	5.21235			0.191094
$745$	4.97948	+	20.0410i	0.182434	+	0.734247i
$746$			21.3340i			0.781094i
$747$	0.963883			0.0352666
$748$	−14.2979			−0.522783
$749$		−	0.382433i		−	0.0139738i
$750$	−4.02279	−	4.48974i	−0.146891	−	0.163942i
$751$	−36.2823			−1.32396			−0.661980	−	0.749521i	$-0.730284\pi$
$751$	−36.2823			−1.32396			−0.661980	+	0.749521i	$0.730284\pi$
$752$	4.70928			0.171730
$753$		−	8.92881i		−	0.325384i
$754$		0			0
$755$	5.08225	+	20.4547i	0.184962	+	0.744422i
$756$		−	2.18342i		−	0.0794101i
$757$		−	40.8687i		−	1.48540i	−0.669626	−	0.742699i	$-0.733545\pi$
$757$		−	40.8687i		−	1.48540i	0.669626	−	0.742699i	$-0.266455\pi$
$758$			8.11223i			0.294649i
$759$			12.0891i			0.438805i
$760$	0.0650468	+	0.261795i	0.00235949	+	0.00949631i
$761$			35.6225i			1.29131i	0.763627	+	0.645657i	$0.223416\pi$
$761$			35.6225i			1.29131i	−0.763627	+	0.645657i	$0.776584\pi$
$762$	−6.56585			−0.237856
$763$			7.81658i			0.282979i
$764$	−11.0856			−0.401062
$765$	4.63090	+	18.6381i	0.167430	+	0.673861i
$766$	24.9399			0.901114
$767$		0			0
$768$			0.539189i			0.0194563i
$769$			3.36910i			0.121493i	0.998153	+	0.0607465i	$0.0193481\pi$
$769$			3.36910i			0.121493i	−0.998153	+	0.0607465i	$0.980652\pi$
$770$	−1.72487	−	6.94214i	−0.0621601	−	0.250177i
$771$	0.282314			0.0101673
$772$	−14.0000			−0.503871
$773$	−11.0794			−0.398499			−0.199250	−	0.979949i	$-0.563850\pi$
$773$	−11.0794			−0.398499			−0.199250	+	0.979949i	$0.563850\pi$
$774$			5.41855i			0.194766i
$775$	−22.6225	−	42.7142i	−0.812624	−	1.53434i
$776$	−7.90829			−0.283891
$777$		−	2.66087i		−	0.0954582i
$778$	13.5330			0.485183
$779$	−0.0539832			−0.00193415
$780$		0			0
$781$	36.9093			1.32072
$782$	15.7587			0.563531
$783$			22.3545i			0.798886i
$784$	−6.49693			−0.232033
$785$	3.11223	+	12.5259i	0.111080	+	0.447067i
$786$		−	9.41136i		−	0.335692i
$787$	−5.67089			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$787$	−5.67089			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$788$	−8.69368			−0.309699
$789$	15.5187			0.552479
$790$	−34.7370	+	8.63090i	−1.23589	+	0.307074i
$791$		−	9.92986i		−	0.353065i
$792$		−	12.2195i		−	0.434202i
$793$		0			0
$794$	−4.59478			−0.163063
$795$	−11.2195	+	2.78765i	−0.397916	+	0.0988679i
$796$	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	$-0.160911\pi$
$798$	−0.0461361			−0.00163320
$799$		−	14.9288i		−	0.528143i
$800$	4.41855	−	2.34017i	0.156219	−	0.0827376i
$801$		−	9.83710i		−	0.347577i
$802$			29.7031i			1.04885i
$803$		−	30.4235i		−	1.07362i
$804$		−	1.57531i		−	0.0555568i
$805$	1.90110	+	7.65142i	0.0670051	+	0.269677i
$806$		0			0
$807$		−	5.42243i		−	0.190878i
$808$	−6.14116			−0.216045
$809$	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
$811$		−	47.3390i		−	1.66230i	−0.556052	−	0.831148i	$-0.687684\pi$
$811$		−	47.3390i		−	1.66230i	0.556052	−	0.831148i	$-0.312316\pi$
$812$	−5.15061			−0.180751
$813$	−9.77310			−0.342758
$814$		−	31.3812i		−	1.09991i
$815$	36.5041	−	9.06997i	1.27868	−	0.317707i
$816$	1.70928			0.0598366
$817$	0.241276			0.00844119
$818$		−	10.3112i		−	0.360524i
$819$		0			0
$820$	0.241276	+	0.971071i	0.00842573	+	0.0339113i
$821$			20.6816i			0.721792i	0.932606	+	0.360896i	$0.117529\pi$
$821$			20.6816i			0.721792i	−0.932606	+	0.360896i	$0.882471\pi$
$822$			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	$-0.112372\pi$
$824$		−	17.6803i		−	0.615924i
$825$	10.7454	−	5.69102i	0.374107	−	0.198136i
$826$		−	4.08452i		−	0.142119i
$827$	−39.6730			−1.37956			−0.689782	−	0.724017i	$-0.742294\pi$
$827$	−39.6730			−1.37956			−0.689782	+	0.724017i	$0.742294\pi$
$828$			13.4680i			0.468045i
$829$	−25.3874			−0.881739			−0.440870	−	0.897571i	$-0.645330\pi$
$829$	−25.3874			−0.881739			−0.440870	+	0.897571i	$0.645330\pi$
$830$	−0.772055	+	0.191828i	−0.0267984	+	0.00665845i
$831$	−13.3268			−0.462303
$832$		0			0
$833$			20.5958i			0.713603i
$834$			1.42574i			0.0493693i
$835$	39.3207	−	9.76979i	1.36075	−	0.338097i
$836$	−0.544109			−0.0188184
$837$	29.7587			1.02861
$838$	−38.0905			−1.31581
$839$			23.0277i			0.795005i	0.917601	+	0.397502i	$0.130123\pi$
$839$			23.0277i			0.795005i	−0.917601	+	0.397502i	$0.869877\pi$
$840$	0.206204	+	0.829914i	0.00711471	+	0.0286347i
$841$	23.7337			0.818402
$842$			26.7103i			0.920498i
$843$	−12.3935			−0.426855
$844$	−5.58864			−0.192369
$845$		0			0
$846$	12.7587			0.438654
$847$	6.62636			0.227685
$848$		−	9.58864i		−	0.329275i
$849$	−9.75872			−0.334919
$850$	−7.41855	−	14.0072i	−0.254454	−	0.480443i
$851$			34.5874i			1.18564i
$852$	−4.41241			−0.151167
$853$	−13.7047			−0.469241			−0.234621	−	0.972087i	$-0.575385\pi$
$853$	−13.7047			−0.469241			−0.234621	+	0.972087i	$0.575385\pi$
$854$	−5.00946			−0.171420
$855$	0.176230	+	0.709275i	0.00602692	+	0.0242567i
$856$			0.539189i			0.0184291i
$857$			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	$0.575194\pi$
$860$	−1.07838	−	4.34017i	−0.0367724	−	0.147999i
$861$	−0.171131			−0.00583214
$862$			20.7187i			0.705683i
$863$	19.9383			0.678706			0.339353	−	0.940659i	$-0.389792\pi$
$863$	19.9383			0.678706			0.339353	+	0.940659i	$0.389792\pi$
$864$			3.07838i			0.104729i
$865$	−5.55583	−	22.3607i	−0.188904	−	0.760286i
$866$			15.8576i			0.538864i
$867$			3.74766i			0.127277i
$868$			6.85658i			0.232727i
$869$		−	72.1966i		−	2.44910i
$870$	−2.11118	−	8.49693i	−0.0715758	−	0.288073i
$871$		0			0
$872$		−	11.0205i		−	0.373202i
$873$	−21.4257			−0.725151
$874$	0.599701			0.0202852
$875$	5.90602	−	5.29177i	0.199660	−	0.178894i
$876$			3.63704i			0.122884i
$877$	−21.6163			−0.729932			−0.364966	−	0.931021i	$-0.618919\pi$
$877$	−21.6163			−0.729932			−0.364966	+	0.931021i	$0.618919\pi$
$878$	−9.73925			−0.328684
$879$			9.62144i			0.324523i
$880$	2.43188	+	9.78765i	0.0819787	+	0.329942i
$881$	7.99386			0.269320			0.134660	−	0.990892i	$-0.457006\pi$
$881$	7.99386			0.269320			0.134660	+	0.990892i	$0.457006\pi$
$882$	−17.6020			−0.592689
$883$			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
$886$			9.23060i			0.310108i
$887$			17.1627i			0.576268i	0.957590	+	0.288134i	$0.0930348\pi$
$887$			17.1627i			0.576268i	−0.957590	+	0.288134i	$0.906965\pi$
$888$			3.75154i			0.125893i
$889$		−	8.63704i		−	0.289677i
$890$	1.95774	+	7.87936i	0.0656236	+	0.264117i
$891$		−	29.1724i		−	0.977311i
$892$	24.7093			0.827328
$893$		−	0.568118i		−	0.0190114i
$894$	4.97948			0.166539
$895$	−2.73820	+	0.680346i	−0.0915281	+	0.0227415i
$896$	−0.709275			−0.0236952
$897$		0			0
$898$			2.92389i			0.0975715i
$899$		−	70.1999i		−	2.34130i
$900$	11.9711	−	6.34017i	0.399036	−	0.211339i
$901$	−30.3968			−1.01266
$902$	−2.01825			−0.0672004
$903$	0.764867			0.0254532
$904$			14.0000i			0.465633i
$905$	5.17009	−	1.28458i	0.171859	−	0.0427009i
$906$	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	$-0.0878514\pi$
$908$	−28.6947			−0.952268
$909$	−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	$0.523875\pi$
$912$	0.0650468			0.00215391
$913$		−	1.60462i		−	0.0531052i
$914$	−11.6526			−0.385435
$915$	−2.05332	−	8.26406i	−0.0678808	−	0.273201i
$916$			1.89988i			0.0627738i
$917$	12.3802			0.408829
$918$	9.75872			0.322086
$919$	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
$921$		−	1.85762i		−	0.0612107i
$922$			30.2979i			0.997809i
$923$		0			0
$924$	−1.72487			−0.0567442
$925$	30.7431	−	16.2823i	1.01083	−	0.535359i
$926$	−7.04331			−0.231457
$927$		−	47.9009i		−	1.57327i
$928$	7.26180			0.238380
$929$			59.3295i			1.94654i	0.229669	+	0.973269i	$0.426236\pi$
$929$			59.3295i			1.94654i	−0.229669	+	0.973269i	$0.573764\pi$
$930$	−11.3112	+	2.81044i	−0.370910	+	0.0921579i
$931$			0.783777i			0.0256873i
$932$		−	22.2485i		−	0.728773i
$933$		−	9.61038i		−	0.314630i
$934$			3.90110i			0.127648i
$935$	31.0277	−	7.70928i	1.01471	−	0.252120i
$936$		0			0
$937$			1.75872i			0.0574550i	0.999587	+	0.0287275i	$0.00914551\pi$
$937$			1.75872i			0.0574550i	−0.999587	+	0.0287275i	$0.990854\pi$
$938$	2.07223			0.0676609
$939$	17.3751			0.567014
$940$	−10.2195	+	2.53919i	−0.333324	+	0.0828192i
$941$		−	42.2967i		−	1.37883i	−0.724365	−	0.689416i	$-0.757867\pi$
$941$		−	42.2967i		−	1.37883i	0.724365	−	0.689416i	$-0.242133\pi$
$942$	3.11223			0.101402
$943$	2.22446			0.0724382
$944$			5.75872i			0.187430i
$945$	1.17727	+	4.73820i	0.0382967	+	0.154134i
$946$	9.02052			0.293282
$947$	−4.83832			−0.157224			−0.0786122	−	0.996905i	$-0.525049\pi$
$947$	−4.83832			−0.157224			−0.0786122	+	0.996905i	$0.525049\pi$
$948$			8.63090i			0.280319i
$949$		0			0
$950$	−0.282314	−	0.533046i	−0.00915948	−	0.0172943i
$951$			1.02771i			0.0333257i
$952$			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	$0.861902\pi$
$954$		−	25.9783i		−	0.841077i
$955$	24.0566	−	5.97721i	0.778454	−	0.193418i
$956$			24.8710i			0.804384i
$957$	17.6598			0.570861
$958$		−	17.5103i		−	0.565731i
$959$	−6.63421			−0.214230
$960$	−0.290725	−	1.17009i	−0.00938310	−	0.0377644i
$961$	−62.4512			−2.01455
$962$		0			0
$963$			1.46081i			0.0470740i
$964$		−	2.95055i		−	0.0950309i
$965$	30.3812	−	7.54864i	0.978006	−	0.242999i
$966$	1.90110			0.0611670
$967$	−29.9939			−0.964537			−0.482269	−	0.876023i	$-0.660187\pi$
$967$	−29.9939			−0.964537			−0.482269	+	0.876023i	$0.660187\pi$
$968$	−9.34244			−0.300277
$969$		−	0.206204i		−	0.00662422i
$970$	17.1617	−	4.26406i	0.551028	−	0.136911i
$971$	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
$973$	−1.87549			−0.0601253
$974$	38.5318			1.23464
$975$		0			0
$976$	7.06278			0.226074
$977$	27.5441			0.881214			0.440607	−	0.897700i	$-0.354763\pi$
$977$	27.5441			0.881214			0.440607	+	0.897700i	$0.354763\pi$
$978$		−	9.06997i		−	0.290026i
$979$	−16.3763			−0.523389
$980$	14.0989	−	3.50307i	0.450373	−	0.111902i
$981$		−	29.8576i		−	0.953280i
$982$	−6.82377			−0.217755
$983$	−18.0289			−0.575034			−0.287517	−	0.957776i	$-0.592830\pi$
$983$	−18.0289			−0.575034			−0.287517	+	0.957776i	$0.592830\pi$
$984$	0.241276			0.00769161
$985$	18.8660	−	4.68753i	0.601122	−	0.149357i
$986$		−	23.0205i		−	0.733123i
$987$		−	1.80098i		−	0.0573260i
$988$		0			0
$989$	−9.94214			−0.316142
$990$	6.58864	+	26.5174i	0.209401	+	0.842780i
$991$	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
$993$	−0.383656			−0.0121750
$994$		−	5.80430i		−	0.184101i
$995$	−46.6947	+	11.6020i	−1.48032	+	0.367807i
$996$			0.191828i			0.00607830i
$997$			28.8648i			0.914158i	0.889426	+	0.457079i	$0.151104\pi$
$997$			28.8648i			0.914158i	−0.889426	+	0.457079i	$0.848896\pi$
$998$			9.57918i			0.303224i
$999$			21.4186i			0.677653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.c.1689.4		6
5.4	even	2		1690.2.c.b.1689.3		6
13.5	odd	4		1690.2.b.b.339.2		6
13.7	odd	12		130.2.n.a.29.5	yes	12
13.8	odd	4		1690.2.b.c.339.5		6
13.11	odd	12		130.2.n.a.9.2	✓	12
13.12	even	2		1690.2.c.b.1689.4		6
39.11	even	12		1170.2.bp.h.919.5		12
39.20	even	12		1170.2.bp.h.289.2		12
52.7	even	12		1040.2.dh.b.289.3		12
52.11	even	12		1040.2.dh.b.529.4		12
65.7	even	12		650.2.e.k.601.2		6
65.8	even	4		8450.2.a.cb.1.2		3
65.18	even	4		8450.2.a.bt.1.2		3
65.24	odd	12		130.2.n.a.9.5	yes	12
65.33	even	12		650.2.e.j.601.2		6
65.34	odd	4		1690.2.b.c.339.2		6
65.37	even	12		650.2.e.k.451.2		6
65.44	odd	4		1690.2.b.b.339.5		6
65.47	even	4		8450.2.a.bu.1.2		3
65.57	even	4		8450.2.a.ca.1.2		3
65.59	odd	12		130.2.n.a.29.2	yes	12
65.63	even	12		650.2.e.j.451.2		6
65.64	even	2	inner	1690.2.c.c.1689.3		6
195.59	even	12		1170.2.bp.h.289.5		12
195.89	even	12		1170.2.bp.h.919.2		12
260.59	even	12		1040.2.dh.b.289.4		12
260.219	even	12		1040.2.dh.b.529.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.2	✓	12	13.11	odd	12
130.2.n.a.9.5	yes	12	65.24	odd	12
130.2.n.a.29.2	yes	12	65.59	odd	12
130.2.n.a.29.5	yes	12	13.7	odd	12
650.2.e.j.451.2		6	65.63	even	12
650.2.e.j.601.2		6	65.33	even	12
650.2.e.k.451.2		6	65.37	even	12
650.2.e.k.601.2		6	65.7	even	12
1040.2.dh.b.289.3		12	52.7	even	12
1040.2.dh.b.289.4		12	260.59	even	12
1040.2.dh.b.529.3		12	260.219	even	12
1040.2.dh.b.529.4		12	52.11	even	12
1170.2.bp.h.289.2		12	39.20	even	12
1170.2.bp.h.289.5		12	195.59	even	12
1170.2.bp.h.919.2		12	195.89	even	12
1170.2.bp.h.919.5		12	39.11	even	12
1690.2.b.b.339.2		6	13.5	odd	4
1690.2.b.b.339.5		6	65.44	odd	4
1690.2.b.c.339.2		6	65.34	odd	4
1690.2.b.c.339.5		6	13.8	odd	4
1690.2.c.b.1689.3		6	5.4	even	2
1690.2.c.b.1689.4		6	13.12	even	2
1690.2.c.c.1689.3		6	65.64	even	2	inner
1690.2.c.c.1689.4		6	1.1	even	1	trivial
8450.2.a.bt.1.2		3	65.18	even	4
8450.2.a.bu.1.2		3	65.47	even	4
8450.2.a.ca.1.2		3	65.57	even	4
8450.2.a.cb.1.2		3	65.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.539189i q^{3} +1.00000 q^{4} +(-2.17009 + 0.539189i) q^{5} +0.539189i q^{6} -0.709275 q^{7} +1.00000 q^{8} +2.70928 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.539189i q^{3} +1.00000 q^{4} +(-2.17009 + 0.539189i) q^{5} +0.539189i q^{6} -0.709275 q^{7} +1.00000 q^{8} +2.70928 q^{9} +(-2.17009 + 0.539189i) q^{10} -4.51026i q^{11} +0.539189i q^{12} -0.709275 q^{14} +(-0.290725 - 1.17009i) q^{15} +1.00000 q^{16} -3.17009i q^{17} +2.70928 q^{18} -0.120638i q^{19} +(-2.17009 + 0.539189i) q^{20} -0.382433i q^{21} -4.51026i q^{22} +4.97107i q^{23} +0.539189i q^{24} +(4.41855 - 2.34017i) q^{25} +3.07838i q^{27} -0.709275 q^{28} +7.26180 q^{29} +(-0.290725 - 1.17009i) q^{30} -9.66701i q^{31} +1.00000 q^{32} +2.43188 q^{33} -3.17009i q^{34} +(1.53919 - 0.382433i) q^{35} +2.70928 q^{36} +6.95774 q^{37} -0.120638i q^{38} +(-2.17009 + 0.539189i) q^{40} -0.447480i q^{41} -0.382433i q^{42} +2.00000i q^{43} -4.51026i q^{44} +(-5.87936 + 1.46081i) q^{45} +4.97107i q^{46} +4.70928 q^{47} +0.539189i q^{48} -6.49693 q^{49} +(4.41855 - 2.34017i) q^{50} +1.70928 q^{51} -9.58864i q^{53} +3.07838i q^{54} +(2.43188 + 9.78765i) q^{55} -0.709275 q^{56} +0.0650468 q^{57} +7.26180 q^{58} +5.75872i q^{59} +(-0.290725 - 1.17009i) q^{60} +7.06278 q^{61} -9.66701i q^{62} -1.92162 q^{63} +1.00000 q^{64} +2.43188 q^{66} -2.92162 q^{67} -3.17009i q^{68} -2.68035 q^{69} +(1.53919 - 0.382433i) q^{70} +8.18342i q^{71} +2.70928 q^{72} +6.74539 q^{73} +6.95774 q^{74} +(1.26180 + 2.38243i) q^{75} -0.120638i q^{76} +3.19902i q^{77} +16.0072 q^{79} +(-2.17009 + 0.539189i) q^{80} +6.46800 q^{81} -0.447480i q^{82} +0.355771 q^{83} -0.382433i q^{84} +(1.70928 + 6.87936i) q^{85} +2.00000i q^{86} +3.91548i q^{87} -4.51026i q^{88} -3.63090i q^{89} +(-5.87936 + 1.46081i) q^{90} +4.97107i q^{92} +5.21235 q^{93} +4.70928 q^{94} +(0.0650468 + 0.261795i) q^{95} +0.539189i q^{96} -7.90829 q^{97} -6.49693 q^{98} -12.2195i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 6 * q^8 + 2 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 10 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{10} + 10 q^{14} - 16 q^{15} + 6 q^{16} + 2 q^{18} - 2 q^{20} - 2 q^{25} + 10 q^{28} + 28 q^{29} - 16 q^{30} + 6 q^{32} - 12 q^{33} + 6 q^{35} + 2 q^{36} + 10 q^{37} - 2 q^{40} - 10 q^{45} + 14 q^{47} - 4 q^{49} - 2 q^{50} - 4 q^{51} - 12 q^{55} + 10 q^{56} - 8 q^{57} + 28 q^{58} - 16 q^{60} + 8 q^{61} - 18 q^{63} + 6 q^{64} - 12 q^{66} - 24 q^{67} + 28 q^{69} + 6 q^{70} + 2 q^{72} - 12 q^{73} + 10 q^{74} - 8 q^{75} + 28 q^{79} - 2 q^{80} - 26 q^{81} + 8 q^{83} - 4 q^{85} - 10 q^{90} + 52 q^{93} + 14 q^{94} - 8 q^{95} - 52 q^{97} - 4 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 10 * q^7 + 6 * q^8 + 2 * q^9 - 2 * q^10 + 10 * q^14 - 16 * q^15 + 6 * q^16 + 2 * q^18 - 2 * q^20 - 2 * q^25 + 10 * q^28 + 28 * q^29 - 16 * q^30 + 6 * q^32 - 12 * q^33 + 6 * q^35 + 2 * q^36 + 10 * q^37 - 2 * q^40 - 10 * q^45 + 14 * q^47 - 4 * q^49 - 2 * q^50 - 4 * q^51 - 12 * q^55 + 10 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^60 + 8 * q^61 - 18 * q^63 + 6 * q^64 - 12 * q^66 - 24 * q^67 + 28 * q^69 + 6 * q^70 + 2 * q^72 - 12 * q^73 + 10 * q^74 - 8 * q^75 + 28 * q^79 - 2 * q^80 - 26 * q^81 + 8 * q^83 - 4 * q^85 - 10 * q^90 + 52 * q^93 + 14 * q^94 - 8 * q^95 - 52 * q^97 - 4 * q^98

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