LMFDB - Embedded newform 1110.2.u.e.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (of order $4$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.4
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.878679 + 1.49262i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.434124 - 1.67676i) q^{6} +2.38487 q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.45585 + 2.62307i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.878679 + 1.49262i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.434124 - 1.67676i) q^{6} +2.38487 q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.45585 + 2.62307i) q^{9} +1.00000 q^{10} -5.76715 q^{11} +(-1.49262 + 0.878679i) q^{12} +(-1.58054 - 1.58054i) q^{13} +(-1.68635 - 1.68635i) q^{14} +(-1.67676 - 0.434124i) q^{15} -1.00000 q^{16} +(0.766912 - 0.766912i) q^{17} +(2.88423 - 0.825355i) q^{18} +(4.27127 + 4.27127i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(2.09553 + 3.55970i) q^{21} +(4.07799 + 4.07799i) q^{22} +(-5.87049 + 5.87049i) q^{23} +(1.67676 + 0.434124i) q^{24} -1.00000i q^{25} +2.23522i q^{26} +(-5.19448 + 0.131812i) q^{27} +2.38487i q^{28} +(0.666860 + 0.666860i) q^{29} +(0.878679 + 1.49262i) q^{30} +(-4.93081 + 4.93081i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.06748 - 8.60819i) q^{33} -1.08458 q^{34} +(-1.68635 + 1.68635i) q^{35} +(-2.62307 - 1.45585i) q^{36} +(5.79440 + 1.85066i) q^{37} -6.04049i q^{38} +(0.970360 - 3.74793i) q^{39} +1.00000i q^{40} -2.85384 q^{41} +(1.03533 - 3.99886i) q^{42} +(-6.47528 - 6.47528i) q^{43} -5.76715i q^{44} +(-0.825355 - 2.88423i) q^{45} +8.30212 q^{46} -8.44283i q^{47} +(-0.878679 - 1.49262i) q^{48} -1.31242 q^{49} +(-0.707107 + 0.707107i) q^{50} +(1.81858 + 0.470841i) q^{51} +(1.58054 - 1.58054i) q^{52} +7.21707i q^{53} +(3.76626 + 3.57985i) q^{54} +(4.07799 - 4.07799i) q^{55} +(1.68635 - 1.68635i) q^{56} +(-2.62232 + 10.1285i) q^{57} -0.943082i q^{58} +(5.63841 - 5.63841i) q^{59} +(0.434124 - 1.67676i) q^{60} +(-8.82247 + 8.82247i) q^{61} +6.97322 q^{62} +(-3.47200 + 6.25568i) q^{63} -1.00000i q^{64} +2.23522 q^{65} +(-2.50366 + 9.67016i) q^{66} +2.96422i q^{67} +(0.766912 + 0.766912i) q^{68} +(-13.9207 - 3.60415i) q^{69} +2.38487 q^{70} -10.2106i q^{71} +(0.825355 + 2.88423i) q^{72} +1.48258i q^{73} +(-2.78864 - 5.40587i) q^{74} +(1.49262 - 0.878679i) q^{75} +(-4.27127 + 4.27127i) q^{76} -13.7539 q^{77} +(-3.33634 + 1.96404i) q^{78} +(-3.85057 - 3.85057i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-4.76103 - 7.63758i) q^{81} +(2.01797 + 2.01797i) q^{82} +16.2511i q^{83} +(-3.55970 + 2.09553i) q^{84} +1.08458i q^{85} +9.15744i q^{86} +(-0.409414 + 1.58133i) q^{87} +(-4.07799 + 4.07799i) q^{88} +(3.88764 + 3.88764i) q^{89} +(-1.45585 + 2.62307i) q^{90} +(-3.76937 - 3.76937i) q^{91} +(-5.87049 - 5.87049i) q^{92} +(-11.6924 - 3.02724i) q^{93} +(-5.96998 + 5.96998i) q^{94} -6.04049 q^{95} +(-0.434124 + 1.67676i) q^{96} +(11.4270 + 11.4270i) q^{97} +(0.928018 + 0.928018i) q^{98} +(8.39609 - 15.1277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.878679	+	1.49262i	0.507306	+	0.861766i
$3$	0.878679	+	1.49262i	0.507306	+	0.861766i
$4$			1.00000i			0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.434124	−	1.67676i	0.177230	−	0.684536i
$7$	2.38487			0.901395			0.450697	−	0.892677i	$-0.351175\pi$
$7$	2.38487			0.901395			0.450697	+	0.892677i	$0.351175\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.45585	+	2.62307i	−0.485282	+	0.874358i
$10$	1.00000			0.316228
$11$	−5.76715			−1.73886			−0.869431	−	0.494054i	$-0.835515\pi$
$11$	−5.76715			−1.73886			−0.869431	+	0.494054i	$0.835515\pi$
$12$	−1.49262	+	0.878679i	−0.430883	+	0.253653i
$13$	−1.58054	−	1.58054i	−0.438362	−	0.438362i	0.453098	−	0.891460i	$-0.350319\pi$
$13$	−1.58054	−	1.58054i	−0.438362	−	0.438362i	−0.891460	+	0.453098i	$0.850319\pi$
$14$	−1.68635	−	1.68635i	−0.450697	−	0.450697i
$15$	−1.67676	−	0.434124i	−0.432939	−	0.112090i
$16$	−1.00000			−0.250000
$17$	0.766912	−	0.766912i	0.186003	−	0.186003i	−0.607962	−	0.793966i	$-0.708013\pi$
$17$	0.766912	−	0.766912i	0.186003	−	0.186003i	0.793966	+	0.607962i	$0.208013\pi$
$18$	2.88423	−	0.825355i	0.679820	−	0.194538i
$19$	4.27127	+	4.27127i	0.979898	+	0.979898i	0.999802	−	0.0199043i	$-0.00633614\pi$
$19$	4.27127	+	4.27127i	0.979898	+	0.979898i	−0.0199043	+	0.999802i	$0.506336\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	2.09553	+	3.55970i	0.457283	+	0.776791i
$22$	4.07799	+	4.07799i	0.869431	+	0.869431i
$23$	−5.87049	+	5.87049i	−1.22408	+	1.22408i	−0.257913	+	0.966168i	$0.583035\pi$
$23$	−5.87049	+	5.87049i	−1.22408	+	1.22408i	−0.966168	+	0.257913i	$0.916965\pi$
$24$	1.67676	+	0.434124i	0.342268	+	0.0886151i
$25$		−	1.00000i		−	0.200000i
$26$			2.23522i			0.438362i
$27$	−5.19448	+	0.131812i	−0.999678	+	0.0253671i
$28$			2.38487i			0.450697i
$29$	0.666860	+	0.666860i	0.123833	+	0.123833i	0.766307	−	0.642474i	$-0.222092\pi$
$29$	0.666860	+	0.666860i	0.123833	+	0.123833i	−0.642474	+	0.766307i	$0.722092\pi$
$30$	0.878679	+	1.49262i	0.160424	+	0.272514i
$31$	−4.93081	+	4.93081i	−0.885599	+	0.885599i	−0.994097	−	0.108497i	$-0.965396\pi$
$31$	−4.93081	+	4.93081i	−0.885599	+	0.885599i	0.108497	+	0.994097i	$0.465396\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−5.06748	−	8.60819i	−0.882135	−	1.49849i
$34$	−1.08458			−0.186003
$35$	−1.68635	+	1.68635i	−0.285046	+	0.285046i
$36$	−2.62307	−	1.45585i	−0.437179	−	0.242641i
$37$	5.79440	+	1.85066i	0.952593	+	0.304247i
$37$	5.79440	+	1.85066i	0.952593	+	0.304247i
$38$		−	6.04049i		−	0.979898i
$39$	0.970360	−	3.74793i	0.155382	−	0.600149i
$40$			1.00000i			0.158114i
$41$	−2.85384			−0.445695			−0.222847	−	0.974853i	$-0.571535\pi$
$41$	−2.85384			−0.445695			−0.222847	+	0.974853i	$0.571535\pi$
$42$	1.03533	−	3.99886i	0.159754	−	0.617037i
$43$	−6.47528	−	6.47528i	−0.987472	−	0.987472i	0.0124508	−	0.999922i	$-0.496037\pi$
$43$	−6.47528	−	6.47528i	−0.987472	−	0.987472i	−0.999922	+	0.0124508i	$0.996037\pi$
$44$		−	5.76715i		−	0.869431i
$45$	−0.825355	−	2.88423i	−0.123037	−	0.429956i
$46$	8.30212			1.22408
$47$		−	8.44283i		−	1.23151i	−0.787936	−	0.615757i	$-0.788850\pi$
$47$		−	8.44283i		−	1.23151i	0.787936	−	0.615757i	$-0.211150\pi$
$48$	−0.878679	−	1.49262i	−0.126826	−	0.215442i
$49$	−1.31242			−0.187488
$50$	−0.707107	+	0.707107i	−0.100000	+	0.100000i
$51$	1.81858	+	0.470841i	0.254652	+	0.0659309i
$52$	1.58054	−	1.58054i	0.219181	−	0.219181i
$53$			7.21707i			0.991341i	0.868511	+	0.495670i	$0.165078\pi$
$53$			7.21707i			0.991341i	−0.868511	+	0.495670i	$0.834922\pi$
$54$	3.76626	+	3.57985i	0.512523	+	0.487156i
$55$	4.07799	−	4.07799i	0.549877	−	0.549877i
$56$	1.68635	−	1.68635i	0.225349	−	0.225349i
$57$	−2.62232	+	10.1285i	−0.347335	+	1.34155i
$58$		−	0.943082i		−	0.123833i
$59$	5.63841	−	5.63841i	0.734059	−	0.734059i	−0.237362	−	0.971421i	$-0.576283\pi$
$59$	5.63841	−	5.63841i	0.734059	−	0.734059i	0.971421	+	0.237362i	$0.0762829\pi$
$60$	0.434124	−	1.67676i	0.0560451	−	0.216469i
$61$	−8.82247	+	8.82247i	−1.12960	+	1.12960i	−0.139360	+	0.990242i	$0.544504\pi$
$61$	−8.82247	+	8.82247i	−1.12960	+	1.12960i	−0.990242	+	0.139360i	$0.955496\pi$
$62$	6.97322			0.885599
$63$	−3.47200	+	6.25568i	−0.437430	+	0.788141i
$64$		−	1.00000i		−	0.125000i
$65$	2.23522			0.277244
$66$	−2.50366	+	9.67016i	−0.308179	+	1.19031i
$67$			2.96422i			0.362137i	0.983471	+	0.181068i	$0.0579555\pi$
$67$			2.96422i			0.362137i	−0.983471	+	0.181068i	$0.942045\pi$
$68$	0.766912	+	0.766912i	0.0930017	+	0.0930017i
$69$	−13.9207	−	3.60415i	−1.67585	−	0.433888i
$70$	2.38487			0.285046
$71$		−	10.2106i		−	1.21177i	−0.795552	−	0.605886i	$-0.792819\pi$
$71$		−	10.2106i		−	1.21177i	0.795552	−	0.605886i	$-0.207181\pi$
$72$	0.825355	+	2.88423i	0.0972690	+	0.339910i
$73$			1.48258i			0.173523i	0.996229	+	0.0867615i	$0.0276518\pi$
$73$			1.48258i			0.173523i	−0.996229	+	0.0867615i	$0.972348\pi$
$74$	−2.78864	−	5.40587i	−0.324173	−	0.628420i
$75$	1.49262	−	0.878679i	0.172353	−	0.101461i
$76$	−4.27127	+	4.27127i	−0.489949	+	0.489949i
$77$	−13.7539			−1.56740
$78$	−3.33634	+	1.96404i	−0.377766	+	0.222384i
$79$	−3.85057	−	3.85057i	−0.433223	−	0.433223i	0.456500	−	0.889723i	$-0.349103\pi$
$79$	−3.85057	−	3.85057i	−0.433223	−	0.433223i	−0.889723	+	0.456500i	$0.849103\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	−4.76103	−	7.63758i	−0.529003	−	0.848620i
$82$	2.01797	+	2.01797i	0.222847	+	0.222847i
$83$			16.2511i			1.78378i	0.452248	+	0.891892i	$0.350622\pi$
$83$			16.2511i			1.78378i	−0.452248	+	0.891892i	$0.649378\pi$
$84$	−3.55970	+	2.09553i	−0.388396	+	0.228641i
$85$			1.08458i			0.117639i
$86$			9.15744i			0.987472i
$87$	−0.409414	+	1.58133i	−0.0438938	+	0.169536i
$88$	−4.07799	+	4.07799i	−0.434716	+	0.434716i
$89$	3.88764	+	3.88764i	0.412089	+	0.412089i	0.882466	−	0.470377i	$-0.155882\pi$
$89$	3.88764	+	3.88764i	0.412089	+	0.412089i	−0.470377	+	0.882466i	$0.655882\pi$
$90$	−1.45585	+	2.62307i	−0.153460	+	0.276496i
$91$	−3.76937	−	3.76937i	−0.395137	−	0.395137i
$92$	−5.87049	−	5.87049i	−0.612040	−	0.612040i
$93$	−11.6924	−	3.02724i	−1.21245	−	0.313910i
$94$	−5.96998	+	5.96998i	−0.615757	+	0.615757i
$95$	−6.04049			−0.619742
$96$	−0.434124	+	1.67676i	−0.0443076	+	0.171134i
$97$	11.4270	+	11.4270i	1.16024	+	1.16024i	0.984423	+	0.175815i	$0.0562561\pi$
$97$	11.4270	+	11.4270i	1.16024	+	1.16024i	0.175815	+	0.984423i	$0.443744\pi$
$98$	0.928018	+	0.928018i	0.0937440	+	0.0937440i
$99$	8.39609	−	15.1277i	0.843838	−	1.52039i
$100$	1.00000			0.100000
$101$	2.32729			0.231574			0.115787	−	0.993274i	$-0.463061\pi$
$101$	2.32729			0.231574			0.115787	+	0.993274i	$0.463061\pi$
$102$	−0.952995	−	1.61886i	−0.0943606	−	0.160291i
$103$	3.07081	−	3.07081i	0.302576	−	0.302576i	−0.539445	−	0.842021i	$-0.681366\pi$
$103$	3.07081	−	3.07081i	0.302576	−	0.302576i	0.842021	+	0.539445i	$0.181366\pi$
$104$	−2.23522			−0.219181
$105$	−3.99886	−	1.03533i	−0.390248	−	0.101038i
$106$	5.10324	−	5.10324i	0.495670	−	0.495670i
$107$			10.7333i			1.03762i	0.854888	+	0.518812i	$0.173625\pi$
$107$			10.7333i			1.03762i	−0.854888	+	0.518812i	$0.826375\pi$
$108$	−0.131812	−	5.19448i	−0.0126836	−	0.499839i
$109$	−6.01820	−	6.01820i	−0.576439	−	0.576439i	0.357481	−	0.933920i	$-0.383636\pi$
$109$	−6.01820	−	6.01820i	−0.576439	−	0.576439i	−0.933920	+	0.357481i	$0.883636\pi$
$110$	−5.76715			−0.549877
$111$	2.32908	+	10.2750i	0.221066	+	0.975259i
$112$	−2.38487			−0.225349
$113$	−12.0416	−	12.0416i	−1.13278	−	1.13278i	−0.989713	−	0.143069i	$-0.954303\pi$
$113$	−12.0416	−	12.0416i	−1.13278	−	1.13278i	−0.143069	−	0.989713i	$-0.545697\pi$
$114$	9.01618	−	5.30766i	0.844443	−	0.497108i
$115$		−	8.30212i		−	0.774177i
$116$	−0.666860	+	0.666860i	−0.0619164	+	0.0619164i
$117$	6.44688	−	1.84485i	0.596014	−	0.170556i
$118$	−7.97392			−0.734059
$119$	1.82898	−	1.82898i	0.167662	−	0.167662i
$120$	−1.49262	+	0.878679i	−0.136257	+	0.0802121i
$121$	22.2601			2.02364
$122$	12.4769			1.12960
$123$	−2.50761	−	4.25971i	−0.226104	−	0.384085i
$124$	−4.93081	−	4.93081i	−0.442800	−	0.442800i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	6.87850	−	1.96836i	0.612786	−	0.175355i
$127$	−10.6143			−0.941868			−0.470934	−	0.882169i	$-0.656083\pi$
$127$	−10.6143			−0.941868			−0.470934	+	0.882169i	$0.656083\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	3.97546	−	15.3549i	0.350020	−	1.35192i
$130$	−1.58054	−	1.58054i	−0.138622	−	0.138622i
$131$	4.84087	+	4.84087i	0.422949	+	0.422949i	0.886218	−	0.463269i	$-0.153324\pi$
$131$	4.84087	+	4.84087i	0.422949	+	0.422949i	−0.463269	+	0.886218i	$0.653324\pi$
$132$	8.60819	−	5.06748i	0.749246	−	0.441067i
$133$	10.1864	+	10.1864i	0.883274	+	0.883274i
$134$	2.09602	−	2.09602i	0.181068	−	0.181068i
$135$	3.57985	−	3.76626i	0.308104	−	0.324148i
$136$		−	1.08458i		−	0.0930017i
$137$			22.0782i			1.88627i	0.332415	+	0.943133i	$0.392136\pi$
$137$			22.0782i			1.88627i	−0.332415	+	0.943133i	$0.607864\pi$
$138$	7.29490	+	12.3919i	0.620983	+	1.05487i
$139$			4.31292i			0.365817i	0.983130	+	0.182909i	$0.0585512\pi$
$139$			4.31292i			0.365817i	−0.983130	+	0.182909i	$0.941449\pi$
$140$	−1.68635	−	1.68635i	−0.142523	−	0.142523i
$141$	12.6020	−	7.41854i	1.06128	−	0.624754i
$142$	−7.21996	+	7.21996i	−0.605886	+	0.605886i
$143$	9.11520	+	9.11520i	0.762251	+	0.762251i
$144$	1.45585	−	2.62307i	0.121320	−	0.218589i
$145$	−0.943082			−0.0783187
$146$	1.04834	−	1.04834i	0.0867615	−	0.0867615i
$147$	−1.15319	−	1.95894i	−0.0951137	−	0.161571i
$148$	−1.85066	+	5.79440i	−0.152123	+	0.476297i
$149$		−	19.4968i		−	1.59724i	−0.601837	−	0.798619i	$-0.705564\pi$
$149$		−	19.4968i		−	1.59724i	0.601837	−	0.798619i	$-0.294436\pi$
$150$	−1.67676	−	0.434124i	−0.136907	−	0.0354460i
$151$			3.98542i			0.324329i	0.986764	+	0.162165i	$0.0518476\pi$
$151$			3.98542i			0.324329i	−0.986764	+	0.162165i	$0.948152\pi$
$152$	6.04049			0.489949
$153$	0.895161	+	3.12817i	0.0723695	+	0.252898i
$154$	9.72547	+	9.72547i	0.783701	+	0.783701i
$155$		−	6.97322i		−	0.560102i
$156$	3.74793	+	0.970360i	0.300075	+	0.0776910i
$157$	22.7620			1.81661			0.908305	−	0.418310i	$-0.137377\pi$
$157$	22.7620			1.81661			0.908305	+	0.418310i	$0.137377\pi$
$158$			5.44553i			0.433223i
$159$	−10.7724	+	6.34149i	−0.854304	+	0.502913i
$160$	−1.00000			−0.0790569
$161$	−14.0003	+	14.0003i	−1.10338	+	1.10338i
$162$	−2.03403	+	8.76714i	−0.159808	+	0.688811i
$163$	−7.51726	+	7.51726i	−0.588798	+	0.588798i	−0.937306	−	0.348508i	$-0.886688\pi$
$163$	−7.51726	+	7.51726i	−0.588798	+	0.588798i	0.348508	+	0.937306i	$0.386688\pi$
$164$		−	2.85384i		−	0.222847i
$165$	9.67016	+	2.50366i	0.752821	+	0.194910i
$166$	11.4912	−	11.4912i	0.891892	−	0.891892i
$167$	−12.5348	+	12.5348i	−0.969973	+	0.969973i	−0.999562	−	0.0295892i	$-0.990580\pi$
$167$	−12.5348	+	12.5348i	−0.969973	+	0.969973i	0.0295892	+	0.999562i	$0.490580\pi$
$168$	3.99886	+	1.03533i	0.308518	+	0.0798772i
$169$		−	8.00381i		−	0.615677i
$170$	0.766912	−	0.766912i	0.0588195	−	0.0588195i
$171$	−17.4222	+	4.98555i	−1.33231	+	0.381255i
$172$	6.47528	−	6.47528i	0.493736	−	0.493736i
$173$	15.9099			1.20960			0.604802	−	0.796376i	$-0.293252\pi$
$173$	15.9099			1.20960			0.604802	+	0.796376i	$0.293252\pi$
$174$	1.40767	−	0.828666i	0.106715	−	0.0628210i
$175$		−	2.38487i		−	0.180279i
$176$	5.76715			0.434716
$177$	13.3704	+	3.46167i	1.00498	+	0.260195i
$178$		−	5.49796i		−	0.412089i
$179$	9.10948	+	9.10948i	0.680875	+	0.680875i	0.960197	−	0.279322i	$-0.0901098\pi$
$179$	9.10948	+	9.10948i	0.680875	+	0.680875i	−0.279322	+	0.960197i	$0.590110\pi$
$180$	2.88423	−	0.825355i	0.214978	−	0.0615183i
$181$	4.67113			0.347202			0.173601	−	0.984816i	$-0.444460\pi$
$181$	4.67113			0.347202			0.173601	+	0.984816i	$0.444460\pi$
$182$			5.33069i			0.395137i
$183$	−20.9207	−	5.41650i	−1.54651	−	0.400399i
$184$			8.30212i			0.612040i
$185$	−5.40587	+	2.78864i	−0.397448	+	0.205025i
$186$	6.12722	+	10.4084i	0.449270	+	0.763180i
$187$	−4.42290	+	4.42290i	−0.323434	+	0.323434i
$188$	8.44283			0.615757
$189$	−12.3881	+	0.314353i	−0.901104	+	0.0228658i
$190$	4.27127	+	4.27127i	0.309871	+	0.309871i
$191$	2.51857	−	2.51857i	0.182237	−	0.182237i	−0.610093	−	0.792330i	$-0.708868\pi$
$191$	2.51857	−	2.51857i	0.182237	−	0.182237i	0.792330	+	0.610093i	$0.208868\pi$
$192$	1.49262	−	0.878679i	0.107721	−	0.0634132i
$193$	−4.71089	−	4.71089i	−0.339098	−	0.339098i	0.516930	−	0.856028i	$-0.327075\pi$
$193$	−4.71089	−	4.71089i	−0.339098	−	0.339098i	−0.856028	+	0.516930i	$0.827075\pi$
$194$		−	16.1603i		−	1.16024i
$195$	1.96404	+	3.33634i	0.140648	+	0.238920i
$196$		−	1.31242i		−	0.0937440i
$197$			10.7908i			0.768811i	0.923164	+	0.384406i	$0.125594\pi$
$197$			10.7908i			0.768811i	−0.923164	+	0.384406i	$0.874406\pi$
$198$	−16.6338	+	4.75995i	−1.18211	+	0.338275i
$199$	4.64611	−	4.64611i	0.329354	−	0.329354i	−0.522987	−	0.852341i	$-0.675182\pi$
$199$	4.64611	−	4.64611i	0.329354	−	0.329354i	0.852341	+	0.522987i	$0.175182\pi$
$200$	−0.707107	−	0.707107i	−0.0500000	−	0.0500000i
$201$	−4.42446	+	2.60459i	−0.312077	+	0.183714i
$202$	−1.64564	−	1.64564i	−0.115787	−	0.115787i
$203$	1.59037	+	1.59037i	0.111622	+	0.111622i
$204$	−0.470841	+	1.81858i	−0.0329654	+	0.127326i
$205$	2.01797	−	2.01797i	0.140941	−	0.140941i
$206$	−4.34279			−0.302576
$207$	−6.85219	−	23.9452i	−0.476260	−	1.66431i
$208$	1.58054	+	1.58054i	0.109591	+	0.109591i
$209$	−24.6331	−	24.6331i	−1.70391	−	1.70391i
$210$	2.09553	+	3.55970i	0.144605	+	0.245643i
$211$	3.92953			0.270520			0.135260	−	0.990810i	$-0.456813\pi$
$211$	3.92953			0.270520			0.135260	+	0.990810i	$0.456813\pi$
$212$	−7.21707			−0.495670
$213$	15.2405	−	8.97181i	1.04426	−	0.614738i
$214$	7.58956	−	7.58956i	0.518812	−	0.518812i
$215$	9.15744			0.624532
$216$	−3.57985	+	3.76626i	−0.243578	+	0.256261i
$217$	−11.7593	+	11.7593i	−0.798275	+	0.798275i
$218$			8.51102i			0.576439i
$219$	−2.21293	+	1.30271i	−0.149536	+	0.0880292i
$220$	4.07799	+	4.07799i	0.274938	+	0.274938i
$221$	−2.42426			−0.163074
$222$	5.61861	−	8.91242i	0.377096	−	0.598163i
$223$	15.8876			1.06391			0.531956	−	0.846772i	$-0.321457\pi$
$223$	15.8876			1.06391			0.531956	+	0.846772i	$0.321457\pi$
$224$	1.68635	+	1.68635i	0.112674	+	0.112674i
$225$	2.62307	+	1.45585i	0.174872	+	0.0970564i
$226$			17.0294i			1.13278i
$227$	−2.98325	+	2.98325i	−0.198005	+	0.198005i	−0.799144	−	0.601139i	$-0.794714\pi$
$227$	−2.98325	+	2.98325i	−0.198005	+	0.198005i	0.601139	+	0.799144i	$0.294714\pi$
$228$	−10.1285	−	2.62232i	−0.670775	−	0.173667i
$229$	23.9167			1.58046			0.790229	−	0.612812i	$-0.209962\pi$
$229$	23.9167			1.58046			0.790229	+	0.612812i	$0.209962\pi$
$230$	−5.87049	+	5.87049i	−0.387088	+	0.387088i
$231$	−12.0853	−	20.5294i	−0.795152	−	1.35073i
$232$	0.943082			0.0619164
$233$	25.6460			1.68013			0.840063	−	0.542489i	$-0.182518\pi$
$233$	25.6460			1.68013			0.840063	+	0.542489i	$0.182518\pi$
$234$	−5.86314	−	3.25413i	−0.383285	−	0.212729i
$235$	5.96998	+	5.96998i	0.389439	+	0.389439i
$236$	5.63841	+	5.63841i	0.367029	+	0.367029i
$237$	2.36403	−	9.13087i	0.153561	−	0.593114i
$238$	−2.58657			−0.167662
$239$	−11.0015	+	11.0015i	−0.711626	+	0.711626i	−0.966875	−	0.255249i	$-0.917843\pi$
$239$	−11.0015	+	11.0015i	−0.711626	+	0.711626i	0.255249	+	0.966875i	$0.417843\pi$
$240$	1.67676	+	0.434124i	0.108235	+	0.0280226i
$241$	−20.6461	−	20.6461i	−1.32993	−	1.32993i	−0.905427	−	0.424503i	$-0.860449\pi$
$241$	−20.6461	−	20.6461i	−1.32993	−	1.32993i	−0.424503	−	0.905427i	$-0.639551\pi$
$242$	−15.7402	−	15.7402i	−1.01182	−	1.01182i
$243$	7.21661	−	13.8174i	0.462946	−	0.886387i
$244$	−8.82247	−	8.82247i	−0.564801	−	0.564801i
$245$	0.928018	−	0.928018i	0.0592889	−	0.0592889i
$246$	−1.23892	+	4.78521i	−0.0789906	+	0.305094i
$247$		−	13.5018i		−	0.859100i
$248$			6.97322i			0.442800i
$249$	−24.2567	+	14.2795i	−1.53721	+	0.904924i
$250$		−	1.00000i		−	0.0632456i
$251$	3.73539	+	3.73539i	0.235776	+	0.235776i	0.815098	−	0.579323i	$-0.196683\pi$
$251$	3.73539	+	3.73539i	0.235776	+	0.235776i	−0.579323	+	0.815098i	$0.696683\pi$
$252$	−6.25568	−	3.47200i	−0.394071	−	0.218715i
$253$	33.8560	−	33.8560i	2.12851	−	2.12851i
$254$	7.50545	+	7.50545i	0.470934	+	0.470934i
$255$	−1.61886	+	0.952995i	−0.101377	+	0.0596789i
$256$	1.00000			0.0625000
$257$	9.24794	−	9.24794i	0.576870	−	0.576870i	−0.357169	−	0.934040i	$-0.616258\pi$
$257$	9.24794	−	9.24794i	0.576870	−	0.576870i	0.934040	+	0.357169i	$0.116258\pi$
$258$	−13.6686	+	8.04645i	−0.850970	+	0.500950i
$259$	13.8189	+	4.41358i	0.858662	+	0.274246i
$260$			2.23522i			0.138622i
$261$	−2.72007	+	0.778377i	−0.168368	+	0.0481803i
$262$		−	6.84602i		−	0.422949i
$263$	13.9407			0.859620			0.429810	−	0.902919i	$-0.358581\pi$
$263$	13.9407			0.859620			0.429810	+	0.902919i	$0.358581\pi$
$264$	−9.67016	−	2.50366i	−0.595157	−	0.154090i
$265$	−5.10324	−	5.10324i	−0.313489	−	0.313489i
$266$		−	14.4058i		−	0.883274i
$267$	−2.38679	+	9.21878i	−0.146069	+	0.564180i
$268$	−2.96422			−0.181068
$269$		−	10.1133i		−	0.616617i	−0.951287	−	0.308308i	$-0.900237\pi$
$269$		−	10.1133i		−	0.616617i	0.951287	−	0.308308i	$-0.0997628\pi$
$270$	−5.19448	+	0.131812i	−0.316126	+	0.00802180i
$271$	29.2907			1.77928			0.889640	−	0.456662i	$-0.150955\pi$
$271$	29.2907			1.77928			0.889640	+	0.456662i	$0.150955\pi$
$272$	−0.766912	+	0.766912i	−0.0465009	+	0.0465009i
$273$	2.31418	−	8.93831i	0.140060	−	0.540971i
$274$	15.6116	−	15.6116i	0.943133	−	0.943133i
$275$			5.76715i			0.347773i
$276$	3.60415	−	13.9207i	0.216944	−	0.837927i
$277$	−11.9085	+	11.9085i	−0.715514	+	0.715514i	−0.967683	−	0.252169i	$-0.918856\pi$
$277$	−11.9085	+	11.9085i	−0.715514	+	0.715514i	0.252169	+	0.967683i	$0.418856\pi$
$278$	3.04969	−	3.04969i	0.182909	−	0.182909i
$279$	−5.75538	−	20.1124i	−0.344565	−	1.20410i
$280$			2.38487i			0.142523i
$281$	3.54960	−	3.54960i	0.211751	−	0.211751i	−0.593260	−	0.805011i	$-0.702159\pi$
$281$	3.54960	−	3.54960i	0.211751	−	0.211751i	0.805011	+	0.593260i	$0.202159\pi$
$282$	−14.1566	−	3.66523i	−0.843015	−	0.218261i
$283$	−9.57331	+	9.57331i	−0.569074	+	0.569074i	−0.931869	−	0.362795i	$-0.881823\pi$
$283$	−9.57331	+	9.57331i	−0.569074	+	0.569074i	0.362795	+	0.931869i	$0.381823\pi$
$284$	10.2106			0.605886
$285$	−5.30766	−	9.01618i	−0.314398	−	0.534072i
$286$		−	12.8908i		−	0.762251i
$287$	−6.80602			−0.401747
$288$	−2.88423	+	0.825355i	−0.169955	+	0.0486345i
$289$			15.8237i			0.930805i
$290$	0.666860	+	0.666860i	0.0391593	+	0.0391593i
$291$	−7.01555	+	27.0969i	−0.411259	+	1.58845i
$292$	−1.48258			−0.0867615
$293$		−	4.08873i		−	0.238866i	−0.992842	−	0.119433i	$-0.961892\pi$
$293$		−	4.08873i		−	0.238866i	0.992842	−	0.119433i	$-0.0381077\pi$
$294$	−0.569751	+	2.20061i	−0.0332285	+	0.128342i
$295$			7.97392i			0.464259i
$296$	5.40587	−	2.78864i	0.314210	−	0.162087i
$297$	29.9574	−	0.760178i	1.73830	−	0.0441100i
$298$	−13.7863	+	13.7863i	−0.798619	+	0.798619i
$299$	18.5570			1.07318
$300$	0.878679	+	1.49262i	0.0507306	+	0.0861766i
$301$	−15.4427	−	15.4427i	−0.890102	−	0.890102i
$302$	2.81812	−	2.81812i	0.162165	−	0.162165i
$303$	2.04494	+	3.47376i	0.117479	+	0.199563i
$304$	−4.27127	−	4.27127i	−0.244974	−	0.244974i
$305$		−	12.4769i		−	0.714423i
$306$	1.57898	−	2.84493i	0.0902641	−	0.162634i
$307$			2.82576i			0.161275i	0.996744	+	0.0806373i	$0.0256956\pi$
$307$			2.82576i			0.161275i	−0.996744	+	0.0806373i	$0.974304\pi$
$308$		−	13.7539i		−	0.783701i
$309$	7.28183	+	1.88531i	0.414249	+	0.107251i
$310$	−4.93081	+	4.93081i	−0.280051	+	0.280051i
$311$	9.24050	+	9.24050i	0.523981	+	0.523981i	0.918771	−	0.394790i	$-0.129183\pi$
$311$	9.24050	+	9.24050i	0.523981	+	0.523981i	−0.394790	+	0.918771i	$0.629183\pi$
$312$	−1.96404	−	3.33634i	−0.111192	−	0.188883i
$313$	−3.34887	−	3.34887i	−0.189290	−	0.189290i	0.606099	−	0.795389i	$-0.292733\pi$
$313$	−3.34887	−	3.34887i	−0.189290	−	0.189290i	−0.795389	+	0.606099i	$0.792733\pi$
$314$	−16.0952	−	16.0952i	−0.908305	−	0.908305i
$315$	−1.96836	−	6.87850i	−0.110905	−	0.387560i
$316$	3.85057	−	3.85057i	0.216612	−	0.216612i
$317$	25.0019			1.40425			0.702123	−	0.712056i	$-0.252236\pi$
$317$	25.0019			1.40425			0.702123	+	0.712056i	$0.252236\pi$
$318$	12.1013	+	3.13310i	0.678608	+	0.175696i
$319$	−3.84588	−	3.84588i	−0.215328	−	0.215328i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	−16.0207	+	9.43109i	−0.894189	+	0.526392i
$322$	19.7994			1.10338
$323$	6.55138			0.364529
$324$	7.63758	−	4.76103i	0.424310	−	0.264501i
$325$	−1.58054	+	1.58054i	−0.0876724	+	0.0876724i
$326$	10.6310			0.588798
$327$	3.69484	−	14.2710i	0.204325	−	0.789187i
$328$	−2.01797	+	2.01797i	−0.111424	+	0.111424i
$329$		−	20.1350i		−	1.11008i
$330$	−5.06748	−	8.60819i	−0.278956	−	0.473865i
$331$	−16.1922	−	16.1922i	−0.890002	−	0.890002i	0.104520	−	0.994523i	$-0.466669\pi$
$331$	−16.1922	−	16.1922i	−0.890002	−	0.890002i	−0.994523	+	0.104520i	$0.966669\pi$
$332$	−16.2511			−0.891892
$333$	−13.2902	+	12.5049i	−0.728297	+	0.685262i
$334$	17.7269			0.969973
$335$	−2.09602	−	2.09602i	−0.114518	−	0.114518i
$336$	−2.09553	−	3.55970i	−0.114321	−	0.194198i
$337$		−	11.4390i		−	0.623121i	−0.950226	−	0.311560i	$-0.899148\pi$
$337$		−	11.4390i		−	0.623121i	0.950226	−	0.311560i	$-0.100852\pi$
$338$	−5.65955	+	5.65955i	−0.307839	+	0.307839i
$339$	7.39289	−	28.5544i	0.401526	−	1.55086i
$340$	−1.08458			−0.0588195
$341$	28.4367	−	28.4367i	1.53994	−	1.53994i
$342$	15.8447	+	8.79403i	0.856781	+	0.475527i
$343$	−19.8240			−1.07040
$344$	−9.15744			−0.493736
$345$	12.3919	−	7.29490i	0.667159	−	0.392744i
$346$	−11.2500	−	11.2500i	−0.604802	−	0.604802i
$347$	5.80793	+	5.80793i	0.311786	+	0.311786i	0.845601	−	0.533815i	$-0.179242\pi$
$347$	5.80793	+	5.80793i	0.311786	+	0.311786i	−0.533815	+	0.845601i	$0.679242\pi$
$348$	−1.58133	−	0.409414i	−0.0847679	−	0.0219469i
$349$	11.5690			0.619277			0.309638	−	0.950854i	$-0.399792\pi$
$349$	11.5690			0.619277			0.309638	+	0.950854i	$0.399792\pi$
$350$	−1.68635	+	1.68635i	−0.0901395	+	0.0901395i
$351$	8.41840	+	8.00173i	0.449341	+	0.427101i
$352$	−4.07799	−	4.07799i	−0.217358	−	0.217358i
$353$	8.48939	+	8.48939i	0.451845	+	0.451845i	0.895966	−	0.444122i	$-0.146484\pi$
$353$	8.48939	+	8.48939i	0.451845	+	0.451845i	−0.444122	+	0.895966i	$0.646484\pi$
$354$	−7.00652	−	11.9021i	−0.372392	−	0.632587i
$355$	7.21996	+	7.21996i	0.383196	+	0.383196i
$356$	−3.88764	+	3.88764i	−0.206045	+	0.206045i
$357$	4.33707	+	1.12289i	0.229542	+	0.0594297i
$358$		−	12.8828i		−	0.680875i
$359$			22.1081i			1.16682i	0.812177	+	0.583411i	$0.198282\pi$
$359$			22.1081i			1.16682i	−0.812177	+	0.583411i	$0.801718\pi$
$360$	−2.62307	−	1.45585i	−0.138248	−	0.0767298i
$361$			17.4876i			0.920399i
$362$	−3.30299	−	3.30299i	−0.173601	−	0.173601i
$363$	19.5595	+	33.2259i	1.02661	+	1.74391i
$364$	3.76937	−	3.76937i	0.197569	−	0.197569i
$365$	−1.04834	−	1.04834i	−0.0548728	−	0.0548728i
$366$	10.9632	+	18.6232i	0.573053	+	0.973452i
$367$	−21.8077			−1.13835			−0.569176	−	0.822216i	$-0.692738\pi$
$367$	−21.8077			−1.13835			−0.569176	+	0.822216i	$0.692738\pi$
$368$	5.87049	−	5.87049i	0.306020	−	0.306020i
$369$	4.15475	−	7.48583i	0.216288	−	0.389697i
$370$	5.79440	+	1.85066i	0.301236	+	0.0962113i
$371$			17.2117i			0.893589i
$372$	3.02724	−	11.6924i	0.156955	−	0.606225i
$373$			18.7132i			0.968931i	0.874810	+	0.484465i	$0.160986\pi$
$373$			18.7132i			0.968931i	−0.874810	+	0.484465i	$0.839014\pi$
$374$	6.25492			0.323434
$375$	−0.434124	+	1.67676i	−0.0224180	+	0.0865877i
$376$	−5.96998	−	5.96998i	−0.307878	−	0.307878i
$377$		−	2.10799i		−	0.108567i
$378$	8.98202	+	8.53746i	0.461985	+	0.439119i
$379$	−5.00400			−0.257038			−0.128519	−	0.991707i	$-0.541022\pi$
$379$	−5.00400			−0.257038			−0.128519	+	0.991707i	$0.541022\pi$
$380$		−	6.04049i		−	0.309871i
$381$	−9.32657	−	15.8432i	−0.477815	−	0.811670i
$382$	−3.56179			−0.182237
$383$	−7.07401	+	7.07401i	−0.361465	+	0.361465i	−0.864352	−	0.502887i	$-0.832271\pi$
$383$	−7.07401	+	7.07401i	−0.361465	+	0.361465i	0.502887	+	0.864352i	$0.332271\pi$
$384$	−1.67676	−	0.434124i	−0.0855670	−	0.0221538i
$385$	9.72547	−	9.72547i	0.495656	−	0.495656i
$386$			6.66221i			0.339098i
$387$	26.4122	−	7.55813i	1.34261	−	0.384201i
$388$	−11.4270	+	11.4270i	−0.580119	+	0.580119i
$389$	8.14631	−	8.14631i	0.413034	−	0.413034i	−0.469760	−	0.882794i	$-0.655660\pi$
$389$	8.14631	−	8.14631i	0.413034	−	0.413034i	0.882794	+	0.469760i	$0.155660\pi$
$390$	0.970360	−	3.74793i	0.0491361	−	0.189784i
$391$			9.00429i			0.455367i
$392$	−0.928018	+	0.928018i	−0.0468720	+	0.0468720i
$393$	−2.97202	+	11.4792i	−0.149919	+	0.579047i
$394$	7.63023	−	7.63023i	0.384406	−	0.384406i
$395$	5.44553			0.273994
$396$	15.1277	+	8.39609i	0.760194	+	0.421919i
$397$		−	24.1303i		−	1.21106i	−0.795821	−	0.605532i	$-0.792960\pi$
$397$		−	24.1303i		−	1.21106i	0.795821	−	0.605532i	$-0.207040\pi$
$398$	−6.57059			−0.329354
$399$	−6.25389	+	24.1551i	−0.313086	+	1.20927i
$400$			1.00000i			0.0500000i
$401$	2.25525	+	2.25525i	0.112622	+	0.112622i	0.761172	−	0.648550i	$-0.224624\pi$
$401$	2.25525	+	2.25525i	0.112622	+	0.112622i	−0.648550	+	0.761172i	$0.724624\pi$
$402$	4.97029	+	1.28684i	0.247895	+	0.0641815i
$403$	15.5867			0.776426
$404$			2.32729i			0.115787i
$405$	8.76714	+	2.03403i	0.435643	+	0.101072i
$406$		−	2.24912i		−	0.111622i
$407$	−33.4172	−	10.6730i	−1.65643	−	0.529043i
$408$	1.61886	−	0.952995i	0.0801457	−	0.0471803i
$409$	0.672279	−	0.672279i	0.0332420	−	0.0332420i	−0.690290	−	0.723532i	$-0.742517\pi$
$409$	0.672279	−	0.672279i	0.0332420	−	0.0332420i	0.723532	+	0.690290i	$0.242517\pi$
$410$	−2.85384			−0.140941
$411$	−32.9544	+	19.3996i	−1.62552	+	0.956914i
$412$	3.07081	+	3.07081i	0.151288	+	0.151288i
$413$	13.4469	−	13.4469i	0.661676	−	0.661676i
$414$	−12.0866	+	21.7771i	−0.594024	+	1.07028i
$415$	−11.4912	−	11.4912i	−0.564082	−	0.564082i
$416$		−	2.23522i		−	0.109591i
$417$	−6.43756	+	3.78967i	−0.315249	+	0.185581i
$418$			34.8365i			1.70391i
$419$			8.78968i			0.429404i	0.976680	+	0.214702i	$0.0688780\pi$
$419$			8.78968i			0.429404i	−0.976680	+	0.214702i	$0.931122\pi$
$420$	1.03533	−	3.99886i	0.0505188	−	0.195124i
$421$	−22.8305	+	22.8305i	−1.11269	+	1.11269i	−0.119903	+	0.992786i	$0.538258\pi$
$421$	−22.8305	+	22.8305i	−1.11269	+	1.11269i	−0.992786	+	0.119903i	$0.961742\pi$
$422$	−2.77860	−	2.77860i	−0.135260	−	0.135260i
$423$	22.1462	+	12.2915i	1.07678	+	0.597631i
$424$	5.10324	+	5.10324i	0.247835	+	0.247835i
$425$	−0.766912	−	0.766912i	−0.0372007	−	0.0372007i
$426$	−17.1207	−	4.43265i	−0.829501	−	0.214762i
$427$	−21.0404	+	21.0404i	−1.01822	+	1.01822i
$428$	−10.7333			−0.518812
$429$	−5.59622	+	21.6149i	−0.270188	+	1.04358i
$430$	−6.47528	−	6.47528i	−0.312266	−	0.312266i
$431$	−21.2557	−	21.2557i	−1.02385	−	1.02385i	−0.999709	−	0.0241401i	$-0.992315\pi$
$431$	−21.2557	−	21.2557i	−1.02385	−	1.02385i	−0.0241401	−	0.999709i	$-0.507685\pi$
$432$	5.19448	−	0.131812i	0.249920	−	0.00634179i
$433$	−20.9909			−1.00876			−0.504379	−	0.863483i	$-0.668278\pi$
$433$	−20.9909			−1.00876			−0.504379	+	0.863483i	$0.668278\pi$
$434$	16.6302			0.798275
$435$	−0.828666	−	1.40767i	−0.0397315	−	0.0674924i
$436$	6.01820	−	6.01820i	0.288220	−	0.288220i
$437$	−50.1489			−2.39895
$438$	2.48594	+	0.643624i	0.118783	+	0.0307535i
$439$	−1.49381	+	1.49381i	−0.0712955	+	0.0712955i	−0.741855	−	0.670560i	$-0.766054\pi$
$439$	−1.49381	+	1.49381i	−0.0712955	+	0.0712955i	0.670560	+	0.741855i	$0.266054\pi$
$440$		−	5.76715i		−	0.274938i
$441$	1.91067	−	3.44256i	0.0909845	−	0.163932i
$442$	1.71421	+	1.71421i	0.0815369	+	0.0815369i
$443$	−5.07352			−0.241050			−0.120525	−	0.992710i	$-0.538458\pi$
$443$	−5.07352			−0.241050			−0.120525	+	0.992710i	$0.538458\pi$
$444$	−10.2750	+	2.32908i	−0.487629	+	0.110533i
$445$	−5.49796			−0.260628
$446$	−11.2342	−	11.2342i	−0.531956	−	0.531956i
$447$	29.1013	−	17.1314i	1.37645	−	0.810288i
$448$		−	2.38487i		−	0.112674i
$449$	3.64509	−	3.64509i	0.172022	−	0.172022i	−0.615845	−	0.787867i	$-0.711185\pi$
$449$	3.64509	−	3.64509i	0.172022	−	0.172022i	0.787867	+	0.615845i	$0.211185\pi$
$450$	−0.825355	−	2.88423i	−0.0389076	−	0.135964i
$451$	16.4585			0.775002
$452$	12.0416	−	12.0416i	0.566391	−	0.566391i
$453$	−5.94873	+	3.50191i	−0.279496	+	0.164534i
$454$	4.21895			0.198005
$455$	5.33069			0.249907
$456$	5.30766	+	9.01618i	0.248554	+	0.422221i
$457$	−14.4628	−	14.4628i	−0.676539	−	0.676539i	0.282676	−	0.959215i	$-0.408778\pi$
$457$	−14.4628	−	14.4628i	−0.676539	−	0.676539i	−0.959215	+	0.282676i	$0.908778\pi$
$458$	−16.9116	−	16.9116i	−0.790229	−	0.790229i
$459$	−3.88262	+	4.08480i	−0.181225	+	0.190662i
$460$	8.30212			0.387088
$461$	3.48415	−	3.48415i	0.162273	−	0.162273i	−0.621300	−	0.783573i	$-0.713395\pi$
$461$	3.48415	−	3.48415i	0.162273	−	0.162273i	0.783573	+	0.621300i	$0.213395\pi$
$462$	−5.97089	+	23.0620i	−0.277791	+	1.07294i
$463$	13.8483	+	13.8483i	0.643586	+	0.643586i	0.951435	−	0.307849i	$-0.0996091\pi$
$463$	13.8483	+	13.8483i	0.643586	+	0.643586i	−0.307849	+	0.951435i	$0.599609\pi$
$464$	−0.666860	−	0.666860i	−0.0309582	−	0.0309582i
$465$	10.4084	−	6.12722i	0.482677	−	0.284143i
$466$	−18.1345	−	18.1345i	−0.840063	−	0.840063i
$467$	4.04485	−	4.04485i	0.187173	−	0.187173i	−0.607300	−	0.794473i	$-0.707747\pi$
$467$	4.04485	−	4.04485i	0.187173	−	0.187173i	0.794473	+	0.607300i	$0.207747\pi$
$468$	1.84485	+	6.44688i	0.0852780	+	0.298007i
$469$			7.06926i			0.326428i
$470$		−	8.44283i		−	0.389439i
$471$	20.0005	+	33.9751i	0.921576	+	1.56549i
$472$		−	7.97392i		−	0.367029i
$473$	37.3440	+	37.3440i	1.71708	+	1.71708i
$474$	−8.12813	+	4.78488i	−0.373337	+	0.219777i
$475$	4.27127	−	4.27127i	0.195980	−	0.195980i
$476$	1.82898	+	1.82898i	0.0838312	+	0.0838312i
$477$	−18.9309	−	10.5069i	−0.866786	−	0.481080i
$478$	15.5584			0.711626
$479$	4.03608	−	4.03608i	0.184413	−	0.184413i	−0.608862	−	0.793276i	$-0.708374\pi$
$479$	4.03608	−	4.03608i	0.184413	−	0.184413i	0.793276	+	0.608862i	$0.208374\pi$
$480$	−0.878679	−	1.49262i	−0.0401060	−	0.0681286i
$481$	−6.23322	−	12.0833i	−0.284211	−	0.550951i
$482$			29.1979i			1.32993i
$483$	−33.1990	−	8.59541i	−1.51061	−	0.391105i
$484$			22.2601i			1.01182i
$485$	−16.1603			−0.733799
$486$	−14.8733	+	4.66746i	−0.674666	+	0.211720i
$487$	5.50666	+	5.50666i	0.249531	+	0.249531i	0.820778	−	0.571247i	$-0.193540\pi$
$487$	5.50666	+	5.50666i	0.249531	+	0.249531i	−0.571247	+	0.820778i	$0.693540\pi$
$488$			12.4769i			0.564801i
$489$	−17.8257	−	4.61518i	−0.806106	−	0.208705i
$490$	−1.31242			−0.0592889
$491$			14.6275i			0.660132i	0.943958	+	0.330066i	$0.107071\pi$
$491$			14.6275i			0.660132i	−0.943958	+	0.330066i	$0.892929\pi$
$492$	4.25971	−	2.50761i	0.192042	−	0.113052i
$493$	1.02285			0.0460666
$494$	−9.54722	+	9.54722i	−0.429550	+	0.429550i
$495$	4.75995	+	16.6338i	0.213944	+	0.747634i
$496$	4.93081	−	4.93081i	0.221400	−	0.221400i
$497$		−	24.3508i		−	1.09228i
$498$	27.2492	+	7.05497i	1.22106	+	0.316141i
$499$	−3.49525	+	3.49525i	−0.156469	+	0.156469i	−0.781000	−	0.624531i	$-0.785290\pi$
$499$	−3.49525	+	3.49525i	−0.156469	+	0.156469i	0.624531	+	0.781000i	$0.285290\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	−29.7238	−	7.69567i	−1.32796	−	0.343817i
$502$		−	5.28264i		−	0.235776i
$503$	−22.0215	+	22.0215i	−0.981892	+	0.981892i	−0.999839	−	0.0179468i	$-0.994287\pi$
$503$	−22.0215	+	22.0215i	−0.981892	+	0.981892i	0.0179468	+	0.999839i	$0.494287\pi$
$504$	1.96836	+	6.87850i	0.0876777	+	0.306393i
$505$	−1.64564	+	1.64564i	−0.0732301	+	0.0732301i
$506$	−47.8796			−2.12851
$507$	11.9467	−	7.03278i	0.530570	−	0.312337i
$508$		−	10.6143i		−	0.470934i
$509$	31.9079			1.41429			0.707147	−	0.707067i	$-0.249982\pi$
$509$	31.9079			1.41429			0.707147	+	0.707067i	$0.249982\pi$
$510$	1.81858	+	0.470841i	0.0805281	+	0.0208492i
$511$			3.53576i			0.156413i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−22.7501	−	21.6240i	−1.00444	−	0.954725i
$514$	−13.0786			−0.576870
$515$			4.34279i			0.191366i
$516$	15.3549	+	3.97546i	0.675960	+	0.175010i
$517$			48.6911i			2.14143i
$518$	−6.65054	−	12.8923i	−0.292208	−	0.566454i
$519$	13.9797	+	23.7474i	0.613639	+	1.04240i
$520$	1.58054	−	1.58054i	0.0693111	−	0.0693111i
$521$	9.90496			0.433944			0.216972	−	0.976178i	$-0.430382\pi$
$521$	9.90496			0.433944			0.216972	+	0.976178i	$0.430382\pi$
$522$	2.47377	+	1.37298i	0.108274	+	0.0600938i
$523$	13.6371	+	13.6371i	0.596307	+	0.596307i	0.939328	−	0.343021i	$-0.111450\pi$
$523$	13.6371	+	13.6371i	0.596307	+	0.596307i	−0.343021	+	0.939328i	$0.611450\pi$
$524$	−4.84087	+	4.84087i	−0.211474	+	0.211474i
$525$	3.55970	−	2.09553i	0.155358	−	0.0914565i
$526$	−9.85756	−	9.85756i	−0.429810	−	0.429810i
$527$			7.56299i			0.329449i
$528$	5.06748	+	8.60819i	0.220534	+	0.374623i
$529$		−	45.9252i		−	1.99675i
$530$			7.21707i			0.313489i
$531$	6.58131	+	22.9986i	0.285605	+	0.998055i
$532$	−10.1864	+	10.1864i	−0.441637	+	0.441637i
$533$	4.51060	+	4.51060i	0.195376	+	0.195376i
$534$	8.20638	−	4.83094i	0.355125	−	0.209055i
$535$	−7.58956	−	7.58956i	−0.328125	−	0.328125i
$536$	2.09602	+	2.09602i	0.0905341	+	0.0905341i
$537$	−5.59271	+	21.6013i	−0.241343	+	0.932167i
$538$	−7.15116	+	7.15116i	−0.308308	+	0.308308i
$539$	7.56890			0.326016
$540$	3.76626	+	3.57985i	0.162074	+	0.154052i
$541$	19.1072	+	19.1072i	0.821484	+	0.821484i	0.986321	−	0.164837i	$-0.0527099\pi$
$541$	19.1072	+	19.1072i	0.821484	+	0.821484i	−0.164837	+	0.986321i	$0.552710\pi$
$542$	−20.7116	−	20.7116i	−0.889640	−	0.889640i
$543$	4.10442	+	6.97223i	0.176138	+	0.299207i
$544$	1.08458			0.0465009
$545$	8.51102			0.364572
$546$	−7.95671	+	4.68397i	−0.340516	+	0.200455i
$547$	−27.2486	+	27.2486i	−1.16507	+	1.16507i	−0.181714	+	0.983351i	$0.558164\pi$
$547$	−27.2486	+	27.2486i	−1.16507	+	1.16507i	−0.983351	+	0.181714i	$0.941836\pi$
$548$	−22.0782			−0.943133
$549$	−10.2978	−	35.9861i	−0.439501	−	1.53585i
$550$	4.07799	−	4.07799i	0.173886	−	0.173886i
$551$			5.69668i			0.242687i
$552$	−12.3919	+	7.29490i	−0.527436	+	0.310492i
$553$	−9.18310	−	9.18310i	−0.390505	−	0.390505i
$554$	16.8412			0.715514
$555$	−8.91242	−	5.61861i	−0.378311	−	0.238497i
$556$	−4.31292			−0.182909
$557$	2.90028	+	2.90028i	0.122889	+	0.122889i	0.765876	−	0.642988i	$-0.222305\pi$
$557$	2.90028	+	2.90028i	0.122889	+	0.122889i	−0.642988	+	0.765876i	$0.722305\pi$
$558$	−10.1519	+	18.2913i	−0.429765	+	0.774331i
$559$			20.4689i			0.865740i
$560$	1.68635	−	1.68635i	0.0712615	−	0.0712615i
$561$	−10.4880	−	2.71541i	−0.442805	−	0.114645i
$562$	−5.01989			−0.211751
$563$	2.02165	−	2.02165i	0.0852024	−	0.0852024i	−0.663221	−	0.748424i	$-0.730811\pi$
$563$	2.02165	−	2.02165i	0.0852024	−	0.0852024i	0.748424	+	0.663221i	$0.230811\pi$
$564$	7.41854	+	12.6020i	0.312377	+	0.530638i
$565$	17.0294			0.716434
$566$	13.5387			0.569074
$567$	−11.3544	−	18.2146i	−0.476840	−	0.764941i
$568$	−7.21996	−	7.21996i	−0.302943	−	0.302943i
$569$	1.16582	+	1.16582i	0.0488736	+	0.0488736i	0.731121	−	0.682248i	$-0.238997\pi$
$569$	1.16582	+	1.16582i	0.0488736	+	0.0488736i	−0.682248	+	0.731121i	$0.738997\pi$
$570$	−2.62232	+	10.1285i	−0.109837	+	0.424235i
$571$	2.10782			0.0882095			0.0441048	−	0.999027i	$-0.485956\pi$
$571$	2.10782			0.0882095			0.0441048	+	0.999027i	$0.485956\pi$
$572$	−9.11520	+	9.11520i	−0.381126	+	0.381126i
$573$	5.97228	+	1.54626i	0.249496	+	0.0645958i
$574$	4.81259	+	4.81259i	0.200873	+	0.200873i
$575$	5.87049	+	5.87049i	0.244816	+	0.244816i
$576$	2.62307	+	1.45585i	0.109295	+	0.0606602i
$577$	−10.2491	−	10.2491i	−0.426674	−	0.426674i	0.460820	−	0.887494i	$-0.347555\pi$
$577$	−10.2491	−	10.2491i	−0.426674	−	0.426674i	−0.887494	+	0.460820i	$0.847555\pi$
$578$	11.1890	−	11.1890i	0.465403	−	0.465403i
$579$	2.89222	−	11.1710i	0.120197	−	0.464249i
$580$		−	0.943082i		−	0.0391593i
$581$			38.7566i			1.60789i
$582$	24.1212	−	14.1997i	0.999854	−	0.588596i
$583$		−	41.6219i		−	1.72381i
$584$	1.04834	+	1.04834i	0.0433808	+	0.0433808i
$585$	−3.25413	+	5.86314i	−0.134542	+	0.242411i
$586$	−2.89117	+	2.89117i	−0.119433	+	0.119433i
$587$	19.4626	+	19.4626i	0.803309	+	0.803309i	0.983611	−	0.180303i	$-0.0577077\pi$
$587$	19.4626	+	19.4626i	0.803309	+	0.803309i	−0.180303	+	0.983611i	$0.557708\pi$
$588$	1.95894	−	1.15319i	0.0807854	−	0.0475568i
$589$	−42.1217			−1.73559
$590$	5.63841	−	5.63841i	0.232130	−	0.232130i
$591$	−16.1066	+	9.48163i	−0.662535	+	0.390022i
$592$	−5.79440	−	1.85066i	−0.238148	−	0.0760617i
$593$			19.0894i			0.783909i	0.919985	+	0.391954i	$0.128201\pi$
$593$			19.0894i			0.783909i	−0.919985	+	0.391954i	$0.871799\pi$
$594$	−21.7206	−	20.6455i	−0.891206	−	0.847097i
$595$			2.58657i			0.106039i
$596$	19.4968			0.798619
$597$	11.0173	+	2.85245i	0.450909	+	0.116743i
$598$	−13.1218	−	13.1218i	−0.536591	−	0.536591i
$599$		−	6.46972i		−	0.264346i	−0.991227	−	0.132173i	$-0.957805\pi$
$599$		−	6.46972i		−	0.264346i	0.991227	−	0.132173i	$-0.0421954\pi$
$600$	0.434124	−	1.67676i	0.0177230	−	0.0684536i
$601$	7.19361			0.293433			0.146717	−	0.989179i	$-0.453129\pi$
$601$	7.19361			0.293433			0.146717	+	0.989179i	$0.453129\pi$
$602$			21.8393i			0.890102i
$603$	−7.77535	−	4.31544i	−0.316637	−	0.175738i
$604$	−3.98542			−0.162165
$605$	−15.7402	+	15.7402i	−0.639932	+	0.639932i
$606$	1.01033	−	3.90231i	0.0410419	−	0.158521i
$607$	10.2240	−	10.2240i	0.414978	−	0.414978i	−0.468491	−	0.883468i	$-0.655202\pi$
$607$	10.2240	−	10.2240i	0.414978	−	0.414978i	0.883468	+	0.468491i	$0.155202\pi$
$608$			6.04049i			0.244974i
$609$	−0.976398	+	3.77125i	−0.0395656	+	0.152819i
$610$	−8.82247	+	8.82247i	−0.357211	+	0.357211i
$611$	−13.3442	+	13.3442i	−0.539849	+	0.539849i
$612$	−3.12817	+	0.895161i	−0.126449	+	0.0361847i
$613$			10.1511i			0.409999i	0.978762	+	0.205000i	$0.0657193\pi$
$613$			10.1511i			0.409999i	−0.978762	+	0.205000i	$0.934281\pi$
$614$	1.99811	−	1.99811i	0.0806373	−	0.0806373i
$615$	4.78521	+	1.23892i	0.192958	+	0.0499580i
$616$	−9.72547	+	9.72547i	−0.391850	+	0.391850i
$617$	−37.4403			−1.50729			−0.753646	−	0.657281i	$-0.771706\pi$
$617$	−37.4403			−1.50729			−0.753646	+	0.657281i	$0.771706\pi$
$618$	−3.81592	−	6.48214i	−0.153499	−	0.260750i
$619$			9.57027i			0.384661i	0.981330	+	0.192331i	$0.0616046\pi$
$619$			9.57027i			0.384661i	−0.981330	+	0.192331i	$0.938395\pi$
$620$	6.97322			0.280051
$621$	29.7203	−	31.2679i	1.19264	−	1.25474i
$622$		−	13.0680i		−	0.523981i
$623$	9.27151	+	9.27151i	0.371455	+	0.371455i
$624$	−0.970360	+	3.74793i	−0.0388455	+	0.150037i
$625$	−1.00000			−0.0400000
$626$			4.73602i			0.189290i
$627$	15.1233	−	58.4125i	0.603968	−	2.33277i
$628$			22.7620i			0.908305i
$629$	5.86309	−	3.02450i	0.233777	−	0.120595i
$630$	−3.47200	+	6.25568i	−0.138328	+	0.249232i
$631$	31.7177	−	31.7177i	1.26266	−	1.26266i	0.312862	−	0.949799i	$-0.398712\pi$
$631$	31.7177	−	31.7177i	1.26266	−	1.26266i	0.949799	−	0.312862i	$-0.101288\pi$
$632$	−5.44553			−0.216612
$633$	3.45280	+	5.86530i	0.137236	+	0.233125i
$634$	−17.6790	−	17.6790i	−0.702123	−	0.702123i
$635$	7.50545	−	7.50545i	0.297845	−	0.297845i
$636$	−6.34149	−	10.7724i	−0.251456	−	0.427152i
$637$	2.07432	+	2.07432i	0.0821876	+	0.0821876i
$638$			5.43890i			0.215328i
$639$	26.7831	+	14.8650i	1.05952	+	0.588051i
$640$		−	1.00000i		−	0.0395285i
$641$		−	5.24179i		−	0.207038i	−0.994627	−	0.103519i	$-0.966990\pi$
$641$		−	5.24179i		−	0.207038i	0.994627	−	0.103519i	$-0.0330103\pi$
$642$	17.9971	+	4.65956i	0.710291	+	0.183898i
$643$	−33.1809	+	33.1809i	−1.30853	+	1.30853i	−0.386049	+	0.922478i	$0.626161\pi$
$643$	−33.1809	+	33.1809i	−1.30853	+	1.30853i	−0.922478	+	0.386049i	$0.873839\pi$
$644$	−14.0003	−	14.0003i	−0.551690	−	0.551690i
$645$	8.04645	+	13.6686i	0.316829	+	0.538200i
$646$	−4.63253	−	4.63253i	−0.182264	−	0.182264i
$647$	4.39581	+	4.39581i	0.172817	+	0.172817i	0.788216	−	0.615399i	$-0.211005\pi$
$647$	4.39581	+	4.39581i	0.172817	+	0.172817i	−0.615399	+	0.788216i	$0.711005\pi$
$648$	−8.76714	−	2.03403i	−0.344406	−	0.0799042i
$649$	−32.5176	+	32.5176i	−1.27643	+	1.27643i
$650$	2.23522			0.0876724
$651$	−27.8849	−	7.21956i	−1.09290	−	0.282957i
$652$	−7.51726	−	7.51726i	−0.294399	−	0.294399i
$653$	13.7401	+	13.7401i	0.537690	+	0.537690i	0.922850	−	0.385160i	$-0.125854\pi$
$653$	13.7401	+	13.7401i	0.537690	+	0.537690i	−0.385160	+	0.922850i	$0.625854\pi$
$654$	−12.7037	+	7.47846i	−0.496756	+	0.292431i
$655$	−6.84602			−0.267496
$656$	2.85384			0.111424
$657$	−3.88892	−	2.15841i	−0.151721	−	0.0842076i
$658$	−14.2376	+	14.2376i	−0.555040	+	0.555040i
$659$	−6.94050			−0.270364			−0.135182	−	0.990821i	$-0.543162\pi$
$659$	−6.94050			−0.270364			−0.135182	+	0.990821i	$0.543162\pi$
$660$	−2.50366	+	9.67016i	−0.0974548	+	0.376410i
$661$	−7.92259	+	7.92259i	−0.308153	+	0.308153i	−0.844193	−	0.536040i	$-0.819920\pi$
$661$	−7.92259	+	7.92259i	−0.308153	+	0.308153i	0.536040	+	0.844193i	$0.319920\pi$
$662$			22.8992i			0.890002i
$663$	−2.13015	−	3.61851i	−0.0827282	−	0.140531i
$664$	11.4912	+	11.4912i	0.445946	+	0.445946i
$665$	−14.4058			−0.558632
$666$	18.2398	+	0.555300i	0.706779	+	0.0215174i
$667$	−7.82958			−0.303163
$668$	−12.5348	−	12.5348i	−0.484986	−	0.484986i
$669$	13.9601	+	23.7142i	0.539729	+	0.916843i
$670$			2.96422i			0.114518i
$671$	50.8806	−	50.8806i	1.96422	−	1.96422i
$672$	−1.03533	+	3.99886i	−0.0399386	+	0.154259i
$673$	34.0773			1.31358			0.656791	−	0.754073i	$-0.271913\pi$
$673$	34.0773			1.31358			0.656791	+	0.754073i	$0.271913\pi$
$674$	−8.08858	+	8.08858i	−0.311560	+	0.311560i
$675$	0.131812	+	5.19448i	0.00507343	+	0.199936i
$676$	8.00381			0.307839
$677$	−6.68405			−0.256889			−0.128444	−	0.991717i	$-0.540998\pi$
$677$	−6.68405			−0.256889			−0.128444	+	0.991717i	$0.540998\pi$
$678$	−25.4185	+	14.9634i	−0.976193	+	0.574667i
$679$	27.2519	+	27.2519i	1.04583	+	1.04583i
$680$	0.766912	+	0.766912i	0.0294097	+	0.0294097i
$681$	−7.07419	−	1.83155i	−0.271083	−	0.0701850i
$682$	−40.2156			−1.53994
$683$	20.8898	−	20.8898i	0.799324	−	0.799324i	−0.183665	−	0.982989i	$-0.558796\pi$
$683$	20.8898	−	20.8898i	0.799324	−	0.799324i	0.982989	+	0.183665i	$0.0587961\pi$
$684$	−4.98555	−	17.4222i	−0.190627	−	0.666154i
$685$	−15.6116	−	15.6116i	−0.596490	−	0.596490i
$686$	14.0177	+	14.0177i	0.535198	+	0.535198i
$687$	21.0151	+	35.6985i	0.801775	+	1.36198i
$688$	6.47528	+	6.47528i	0.246868	+	0.246868i
$689$	11.4068	−	11.4068i	0.434566	−	0.434566i
$690$	−13.9207	−	3.60415i	−0.529952	−	0.137208i
$691$			24.1662i			0.919324i	0.888094	+	0.459662i	$0.152029\pi$
$691$			24.1662i			0.919324i	−0.888094	+	0.459662i	$0.847971\pi$
$692$			15.9099i			0.604802i
$693$	20.0235	−	36.0775i	0.760631	−	1.37047i
$694$		−	8.21366i		−	0.311786i
$695$	−3.04969	−	3.04969i	−0.115682	−	0.115682i
$696$	0.828666	+	1.40767i	0.0314105	+	0.0533574i
$697$	−2.18864	+	2.18864i	−0.0829008	+	0.0829008i
$698$	−8.18055	−	8.18055i	−0.309638	−	0.309638i
$699$	22.5346	+	38.2798i	0.852338	+	1.44788i
$700$	2.38487			0.0901395
$701$	−4.73203	+	4.73203i	−0.178726	+	0.178726i	−0.790800	−	0.612074i	$-0.790335\pi$
$701$	−4.73203	+	4.73203i	−0.178726	+	0.178726i	0.612074	+	0.790800i	$0.290335\pi$
$702$	−0.294627	−	11.6108i	−0.0111200	−	0.438221i
$703$	16.8448	+	32.6541i	0.635313	+	1.23157i
$704$			5.76715i			0.217358i
$705$	−3.66523	+	14.1566i	−0.138041	+	0.533170i
$706$		−	12.0058i		−	0.451845i
$707$	5.55027			0.208739
$708$	−3.46167	+	13.3704i	−0.130097	+	0.502490i
$709$	−2.36375	−	2.36375i	−0.0887727	−	0.0887727i	0.661326	−	0.750099i	$-0.269994\pi$
$709$	−2.36375	−	2.36375i	−0.0887727	−	0.0887727i	−0.750099	+	0.661326i	$0.769994\pi$
$710$		−	10.2106i		−	0.383196i
$711$	15.7062	−	4.49449i	0.589028	−	0.168557i
$712$	5.49796			0.206045
$713$		−	57.8925i		−	2.16809i
$714$	−2.27277	−	3.86077i	−0.0850561	−	0.144486i
$715$	−12.8908			−0.482090
$716$	−9.10948	+	9.10948i	−0.340437	+	0.340437i
$717$	−26.0878	−	6.75429i	−0.974268	−	0.252243i
$718$	15.6328	−	15.6328i	0.583411	−	0.583411i
$719$		−	20.6295i		−	0.769349i	−0.923052	−	0.384675i	$-0.874314\pi$
$719$		−	20.6295i		−	0.769349i	0.923052	−	0.384675i	$-0.125686\pi$
$720$	0.825355	+	2.88423i	0.0307591	+	0.107489i
$721$	7.32348	−	7.32348i	0.272741	−	0.272741i
$722$	12.3656	−	12.3656i	0.460199	−	0.460199i
$723$	12.6755	−	48.9580i	0.471407	−	1.82077i
$724$			4.67113i			0.173601i
$725$	0.666860	−	0.666860i	0.0247665	−	0.0247665i
$726$	9.66362	−	37.3249i	0.358651	−	1.38526i
$727$	4.87778	−	4.87778i	0.180907	−	0.180907i	−0.610844	−	0.791751i	$-0.709170\pi$
$727$	4.87778	−	4.87778i	0.180907	−	0.180907i	0.791751	+	0.610844i	$0.209170\pi$
$728$	−5.33069			−0.197569
$729$	26.9653	−	1.36939i	0.998713	−	0.0507180i
$730$			1.48258i			0.0548728i
$731$	−9.93195			−0.367346
$732$	5.41650	−	20.9207i	0.200200	−	0.773253i
$733$		−	27.2107i		−	1.00505i	−0.864563	−	0.502525i	$-0.832405\pi$
$733$		−	27.2107i		−	1.00505i	0.864563	−	0.502525i	$-0.167595\pi$
$734$	15.4204	+	15.4204i	0.569176	+	0.569176i
$735$	2.20061	+	0.569751i	0.0811708	+	0.0210156i
$736$	−8.30212			−0.306020
$737$		−	17.0951i		−	0.629706i
$738$	−8.23113	+	2.35543i	−0.302992	+	0.0867045i
$739$		−	21.1878i		−	0.779406i	−0.920941	−	0.389703i	$-0.872578\pi$
$739$		−	21.1878i		−	0.779406i	0.920941	−	0.389703i	$-0.127422\pi$
$740$	−2.78864	−	5.40587i	−0.102513	−	0.198724i
$741$	20.1531	−	11.8638i	0.740343	−	0.435826i
$742$	12.1705	−	12.1705i	0.446794	−	0.446794i
$743$	−30.3326			−1.11279			−0.556397	−	0.830917i	$-0.687817\pi$
$743$	−30.3326			−1.11279			−0.556397	+	0.830917i	$0.687817\pi$
$744$	−10.4084	+	6.12722i	−0.381590	+	0.224635i
$745$	13.7863	+	13.7863i	0.505091	+	0.505091i
$746$	13.2322	−	13.2322i	0.484465	−	0.484465i
$747$	−42.6277	−	23.6590i	−1.55967	−	0.865638i
$748$	−4.42290	−	4.42290i	−0.161717	−	0.161717i
$749$			25.5974i			0.935308i
$750$	1.49262	−	0.878679i	0.0545029	−	0.0320848i
$751$		−	14.3381i		−	0.523204i	−0.965176	−	0.261602i	$-0.915749\pi$
$751$		−	14.3381i		−	0.523204i	0.965176	−	0.261602i	$-0.0842508\pi$
$752$			8.44283i			0.307878i
$753$	−2.29332	+	8.85774i	−0.0835732	+	0.322794i
$754$	−1.49058	+	1.49058i	−0.0542836	+	0.0542836i
$755$	−2.81812	−	2.81812i	−0.102562	−	0.102562i
$756$	−0.314353	−	12.3881i	−0.0114329	−	0.450552i
$757$	23.3542	+	23.3542i	0.848822	+	0.848822i	0.989986	−	0.141164i	$-0.0450845\pi$
$757$	23.3542	+	23.3542i	0.848822	+	0.848822i	−0.141164	+	0.989986i	$0.545084\pi$
$758$	3.53836	+	3.53836i	0.128519	+	0.128519i
$759$	80.2828	+	20.7857i	2.91408	+	0.754472i
$760$	−4.27127	+	4.27127i	−0.154935	+	0.154935i
$761$	−41.2576			−1.49559			−0.747794	−	0.663931i	$-0.768887\pi$
$761$	−41.2576			−1.49559			−0.747794	+	0.663931i	$0.768887\pi$
$762$	−4.60792	+	17.7977i	−0.166927	+	0.644742i
$763$	−14.3526	−	14.3526i	−0.519599	−	0.519599i
$764$	2.51857	+	2.51857i	0.0911185	+	0.0911185i
$765$	−2.84493	−	1.57898i	−0.102858	−	0.0570880i
$766$	10.0042			0.361465
$767$	−17.8234			−0.643567
$768$	0.878679	+	1.49262i	0.0317066	+	0.0538604i
$769$	−6.65238	+	6.65238i	−0.239891	+	0.239891i	−0.816805	−	0.576914i	$-0.804257\pi$
$769$	−6.65238	+	6.65238i	−0.239891	+	0.239891i	0.576914	+	0.816805i	$0.304257\pi$
$770$	−13.7539			−0.495656
$771$	21.9297	+	5.67771i	0.789777	+	0.204478i
$772$	4.71089	−	4.71089i	0.169549	−	0.169549i
$773$		−	24.0960i		−	0.866674i	−0.901232	−	0.433337i	$-0.857336\pi$
$773$		−	24.0960i		−	0.866674i	0.901232	−	0.433337i	$-0.142664\pi$
$774$	−24.0206	−	13.3318i	−0.863404	−	0.479202i
$775$	4.93081	+	4.93081i	0.177120	+	0.177120i
$776$	16.1603			0.580119
$777$	5.55454	+	24.5045i	0.199268	+	0.879093i
$778$	−11.5206			−0.413034
$779$	−12.1895	−	12.1895i	−0.436735	−	0.436735i
$780$	−3.33634	+	1.96404i	−0.119460	+	0.0703239i
$781$			58.8859i			2.10710i
$782$	6.36700	−	6.36700i	0.227683	−	0.227683i
$783$	−3.55189	−	3.37609i	−0.126934	−	0.120652i
$784$	1.31242			0.0468720
$785$	−16.0952	+	16.0952i	−0.574462	+	0.574462i
$786$	10.2185	−	6.01546i	0.364483	−	0.214564i
$787$	−20.9015			−0.745058			−0.372529	−	0.928021i	$-0.621509\pi$
$787$	−20.9015			−0.745058			−0.372529	+	0.928021i	$0.621509\pi$
$788$	−10.7908			−0.384406
$789$	12.2494	+	20.8082i	0.436090	+	0.740791i
$790$	−3.85057	−	3.85057i	−0.136997	−	0.136997i
$791$	−28.7177	−	28.7177i	−1.02108	−	1.02108i
$792$	−4.75995	−	16.6338i	−0.169137	−	0.591057i
$793$	27.8885			0.990349
$794$	−17.0627	+	17.0627i	−0.605532	+	0.605532i
$795$	3.13310	−	12.1013i	0.111120	−	0.429190i
$796$	4.64611	+	4.64611i	0.164677	+	0.164677i
$797$	−10.8270	−	10.8270i	−0.383511	−	0.383511i	0.488854	−	0.872366i	$-0.337415\pi$
$797$	−10.8270	−	10.8270i	−0.383511	−	0.383511i	−0.872366	+	0.488854i	$0.837415\pi$
$798$	21.5024	−	12.6580i	0.761176	−	0.448090i
$799$	−6.47491	−	6.47491i	−0.229066	−	0.229066i
$800$	0.707107	−	0.707107i	0.0250000	−	0.0250000i
$801$	−15.8574	+	4.53776i	−0.560293	+	0.160334i
$802$		−	3.18941i		−	0.112622i
$803$		−	8.55027i		−	0.301733i
$804$	−2.60459	−	4.42446i	−0.0918570	−	0.156039i
$805$		−	19.7994i		−	0.697839i
$806$	−11.0214	−	11.0214i	−0.388213	−	0.388213i
$807$	15.0953	−	8.88631i	0.531379	−	0.312813i
$808$	1.64564	−	1.64564i	0.0578935	−	0.0578935i
$809$	−29.1906	−	29.1906i	−1.02629	−	1.02629i	−0.999645	−	0.0266408i	$-0.991519\pi$
$809$	−29.1906	−	29.1906i	−1.02629	−	1.02629i	−0.0266408	−	0.999645i	$-0.508481\pi$
$810$	−4.76103	−	7.63758i	−0.167285	−	0.268357i
$811$	−52.5079			−1.84380			−0.921902	−	0.387424i	$-0.873365\pi$
$811$	−52.5079			−1.84380			−0.921902	+	0.387424i	$0.873365\pi$
$812$	−1.59037	+	1.59037i	−0.0558111	+	0.0558111i
$813$	25.7371	+	43.7199i	0.902639	+	1.53332i
$814$	16.0825	+	31.1765i	0.563693	+	1.09274i
$815$		−	10.6310i		−	0.372388i
$816$	−1.81858	−	0.470841i	−0.0636630	−	0.0164827i
$817$		−	55.3154i		−	1.93524i
$818$	−0.950746			−0.0332420
$819$	15.3749	−	4.39971i	0.537244	−	0.153738i
$820$	2.01797	+	2.01797i	0.0704705	+	0.0704705i
$821$			16.4066i			0.572593i	0.958141	+	0.286297i	$0.0924242\pi$
$821$			16.4066i			0.572593i	−0.958141	+	0.286297i	$0.907576\pi$
$822$	37.0199	+	9.58466i	1.29122	+	0.334303i
$823$	−39.0832			−1.36235			−0.681177	−	0.732118i	$-0.738532\pi$
$823$	−39.0832			−1.36235			−0.681177	+	0.732118i	$0.738532\pi$
$824$		−	4.34279i		−	0.151288i
$825$	−8.60819	+	5.06748i	−0.299699	+	0.176427i
$826$	−19.0167			−0.661676
$827$	−13.5649	+	13.5649i	−0.471699	+	0.471699i	−0.902464	−	0.430765i	$-0.858244\pi$
$827$	−13.5649	+	13.5649i	−0.471699	+	0.471699i	0.430765	+	0.902464i	$0.358244\pi$
$828$	23.9452	−	6.85219i	0.832155	−	0.238130i
$829$	−23.0222	+	23.0222i	−0.799595	+	0.799595i	−0.983032	−	0.183437i	$-0.941278\pi$
$829$	−23.0222	+	23.0222i	−0.799595	+	0.799595i	0.183437	+	0.983032i	$0.441278\pi$
$830$			16.2511i			0.564082i
$831$	−28.2387	−	7.31116i	−0.979590	−	0.253621i
$832$	−1.58054	+	1.58054i	−0.0547953	+	0.0547953i
$833$	−1.00651	+	1.00651i	−0.0348734	+	0.0348734i
$834$	7.23175	+	1.87234i	0.250415	+	0.0648339i
$835$		−	17.7269i		−	0.613465i
$836$	24.6331	−	24.6331i	0.851954	−	0.851954i
$837$	24.9631	−	26.2629i	0.862849	−	0.907780i
$838$	6.21524	−	6.21524i	0.214702	−	0.214702i
$839$	−27.1461			−0.937188			−0.468594	−	0.883414i	$-0.655239\pi$
$839$	−27.1461			−0.937188			−0.468594	+	0.883414i	$0.655239\pi$
$840$	−3.55970	+	2.09553i	−0.122821	+	0.0723027i
$841$		−	28.1106i		−	0.969331i
$842$	32.2872			1.11269
$843$	8.41718	+	2.17925i	0.289903	+	0.0750575i
$844$			3.92953i			0.135260i
$845$	5.65955	+	5.65955i	0.194694	+	0.194694i
$846$	−6.96833	−	24.3511i	−0.239576	−	0.837207i
$847$	53.0873			1.82410
$848$		−	7.21707i		−	0.247835i
$849$	−22.7012	−	5.87747i	−0.779104	−	0.201714i
$850$			1.08458i			0.0372007i
$851$	−44.8802	+	23.1517i	−1.53847	+	0.793629i
$852$	8.97181	+	15.2405i	0.307369	+	0.522132i
$853$	−6.09664	+	6.09664i	−0.208745	+	0.208745i	−0.803734	−	0.594989i	$-0.797156\pi$
$853$	−6.09664	+	6.09664i	−0.208745	+	0.208745i	0.594989	+	0.803734i	$0.297156\pi$
$854$	29.7556			1.01822
$855$	8.79403	−	15.8447i	0.300749	−	0.541876i
$856$	7.58956	+	7.58956i	0.259406	+	0.259406i
$857$	14.1481	−	14.1481i	0.483291	−	0.483291i	−0.422890	−	0.906181i	$-0.638984\pi$
$857$	14.1481	−	14.1481i	0.483291	−	0.483291i	0.906181	+	0.422890i	$0.138984\pi$
$858$	19.2412	−	11.3269i	0.656882	−	0.386694i
$859$	−36.0754	−	36.0754i	−1.23088	−	1.23088i	−0.963628	−	0.267248i	$-0.913886\pi$
$859$	−36.0754	−	36.0754i	−1.23088	−	1.23088i	−0.267248	−	0.963628i	$-0.586114\pi$
$860$			9.15744i			0.312266i
$861$	−5.98031	−	10.1588i	−0.203808	−	0.346212i
$862$			30.0600i			1.02385i
$863$		−	20.6159i		−	0.701775i	−0.936418	−	0.350887i	$-0.885880\pi$
$863$		−	20.6159i		−	0.701775i	0.936418	−	0.350887i	$-0.114120\pi$
$864$	−3.76626	−	3.57985i	−0.128131	−	0.121789i
$865$	−11.2500	+	11.2500i	−0.382510	+	0.382510i
$866$	14.8428	+	14.8428i	0.504379	+	0.504379i
$867$	−23.6188	+	13.9039i	−0.802137	+	0.472203i
$868$	−11.7593	−	11.7593i	−0.399137	−	0.399137i
$869$	22.2068	+	22.2068i	0.753316	+	0.753316i
$870$	−0.409414	+	1.58133i	−0.0138804	+	0.0536119i
$871$	4.68505	−	4.68505i	0.158747	−	0.158747i
$872$	−8.51102			−0.288220
$873$	−46.6099	+	13.3379i	−1.57751	+	0.451421i
$874$	35.4606	+	35.4606i	1.19947	+	1.19947i
$875$	1.68635	+	1.68635i	0.0570092	+	0.0570092i
$876$	−1.30271	−	2.21293i	−0.0440146	−	0.0747681i
$877$	21.2420			0.717291			0.358645	−	0.933474i	$-0.383239\pi$
$877$	21.2420			0.717291			0.358645	+	0.933474i	$0.383239\pi$
$878$	2.11256			0.0712955
$879$	6.10293	−	3.59268i	0.205847	−	0.121178i
$880$	−4.07799	+	4.07799i	−0.137469	+	0.137469i
$881$	8.09375			0.272685			0.136343	−	0.990662i	$-0.456465\pi$
$881$	8.09375			0.272685			0.136343	+	0.990662i	$0.456465\pi$
$882$	−3.78531	+	1.08321i	−0.127458	+	0.0364735i
$883$	38.6040	−	38.6040i	1.29913	−	1.29913i	0.370158	−	0.928969i	$-0.379303\pi$
$883$	38.6040	−	38.6040i	1.29913	−	1.29913i	0.928969	−	0.370158i	$-0.120697\pi$
$884$		−	2.42426i		−	0.0815369i
$885$	−11.9021	+	7.00652i	−0.400083	+	0.235521i
$886$	3.58752	+	3.58752i	0.120525	+	0.120525i
$887$	47.1547			1.58330			0.791649	−	0.610976i	$-0.209223\pi$
$887$	47.1547			1.58330			0.791649	+	0.610976i	$0.209223\pi$
$888$	8.91242	+	5.61861i	0.299081	+	0.188548i
$889$	−25.3137			−0.848994
$890$	3.88764	+	3.88764i	0.130314	+	0.130314i
$891$	27.4576	+	44.0471i	0.919863	+	1.47563i
$892$			15.8876i			0.531956i
$893$	36.0616	−	36.0616i	1.20676	−	1.20676i
$894$	−32.6915	−	8.46401i	−1.09337	−	0.283079i
$895$	−12.8828			−0.430623
$896$	−1.68635	+	1.68635i	−0.0563372	+	0.0563372i
$897$	16.3057	+	27.6987i	0.544431	+	0.924831i
$898$	−5.15494			−0.172022
$899$	−6.57631			−0.219332
$900$	−1.45585	+	2.62307i	−0.0485282	+	0.0874358i
$901$	5.53486	+	5.53486i	0.184393	+	0.184393i
$902$	−11.6379	−	11.6379i	−0.387501	−	0.387501i
$903$	9.48094	−	36.6193i	0.315506	−	1.21861i
$904$	−17.0294			−0.566391
$905$	−3.30299	+	3.30299i	−0.109795	+	0.109795i
$906$	6.68261	+	1.73017i	0.222015	+	0.0574809i
$907$	−25.8953	−	25.8953i	−0.859840	−	0.859840i	0.131479	−	0.991319i	$-0.458027\pi$
$907$	−25.8953	−	25.8953i	−0.859840	−	0.859840i	−0.991319	+	0.131479i	$0.958027\pi$
$908$	−2.98325	−	2.98325i	−0.0990026	−	0.0990026i
$909$	−3.38817	+	6.10465i	−0.112379	+	0.202478i
$910$	−3.76937	−	3.76937i	−0.124953	−	0.124953i
$911$	−0.380958	+	0.380958i	−0.0126217	+	0.0126217i	−0.713389	−	0.700768i	$-0.752841\pi$
$911$	−0.380958	+	0.380958i	−0.0126217	+	0.0126217i	0.700768	+	0.713389i	$0.252841\pi$
$912$	2.62232	−	10.1285i	0.0868337	−	0.335388i
$913$		−	93.7223i		−	3.10176i
$914$			20.4534i			0.676539i
$915$	18.6232	−	10.9632i	0.615665	−	0.362431i
$916$			23.9167i			0.790229i
$917$	11.5448	+	11.5448i	0.381244	+	0.381244i
$918$	5.63381	−	0.142960i	0.185944	−	0.00471838i
$919$	28.6235	−	28.6235i	0.944201	−	0.944201i	−0.0543226	−	0.998523i	$-0.517300\pi$
$919$	28.6235	−	28.6235i	0.944201	−	0.944201i	0.998523	+	0.0543226i	$0.0172999\pi$
$920$	−5.87049	−	5.87049i	−0.193544	−	0.193544i
$921$	−4.21779	+	2.48294i	−0.138981	+	0.0818156i
$922$	−4.92734			−0.162273
$923$	−16.1382	+	16.1382i	−0.531194	+	0.531194i
$924$	20.5294	−	12.0853i	0.675367	−	0.397576i
$925$	1.85066	−	5.79440i	0.0608493	−	0.190519i
$926$		−	19.5845i		−	0.643586i
$927$	3.58434	+	12.5256i	0.117725	+	0.411395i
$928$			0.943082i			0.0309582i
$929$	−55.7240			−1.82825			−0.914123	−	0.405436i	$-0.867120\pi$
$929$	−55.7240			−1.82825			−0.914123	+	0.405436i	$0.867120\pi$
$930$	−11.6924	−	3.02724i	−0.383410	−	0.0992671i
$931$	−5.60569	−	5.60569i	−0.183719	−	0.183719i
$932$			25.6460i			0.840063i
$933$	−5.67315	+	21.9120i	−0.185730	+	0.717367i
$934$	−5.72028			−0.187173
$935$		−	6.25492i		−	0.204558i
$936$	3.25413	−	5.86314i	0.106365	−	0.191643i
$937$	28.5848			0.933823			0.466912	−	0.884304i	$-0.345367\pi$
$937$	28.5848			0.933823			0.466912	+	0.884304i	$0.345367\pi$
$938$	4.99872	−	4.99872i	0.163214	−	0.163214i
$939$	2.05602	−	7.94119i	0.0670957	−	0.259151i
$940$	−5.96998	+	5.96998i	−0.194719	+	0.194719i
$941$		−	42.0849i		−	1.37193i	−0.727635	−	0.685965i	$-0.759380\pi$
$941$		−	42.0849i		−	1.37193i	0.727635	−	0.685965i	$-0.240620\pi$
$942$	9.88154	−	38.1666i	0.321958	−	1.24353i
$943$	16.7534	−	16.7534i	0.545567	−	0.545567i
$944$	−5.63841	+	5.63841i	−0.183515	+	0.183515i
$945$	8.53746	−	8.98202i	0.277723	−	0.292185i
$946$		−	52.8123i		−	1.71708i
$947$	−26.2598	+	26.2598i	−0.853329	+	0.853329i	−0.990542	−	0.137212i	$-0.956186\pi$
$947$	−26.2598	+	26.2598i	−0.853329	+	0.853329i	0.137212	+	0.990542i	$0.456186\pi$
$948$	9.13087	+	2.36403i	0.296557	+	0.0767803i
$949$	2.34327	−	2.34327i	0.0760659	−	0.0760659i
$950$	−6.04049			−0.195980
$951$	21.9686	+	37.3184i	0.712382	+	1.21013i
$952$		−	2.58657i		−	0.0838312i
$953$	−26.0414			−0.843562			−0.421781	−	0.906698i	$-0.638595\pi$
$953$	−26.0414			−0.843562			−0.421781	+	0.906698i	$0.638595\pi$
$954$	5.95664	+	20.8157i	0.192853	+	0.673933i
$955$			3.56179i			0.115257i
$956$	−11.0015	−	11.0015i	−0.355813	−	0.355813i
$957$	2.36115	−	9.11975i	0.0763253	−	0.294800i
$958$	−5.70788			−0.184413
$959$			52.6535i			1.70027i
$960$	−0.434124	+	1.67676i	−0.0140113	+	0.0541173i
$961$		−	17.6258i		−	0.568573i
$962$	−4.13663	+	12.9517i	−0.133370	+	0.417581i
$963$	−28.1541	−	15.6260i	−0.907254	−	0.503540i
$964$	20.6461	−	20.6461i	0.664965	−	0.664965i
$965$	6.66221			0.214464
$966$	17.3974	+	29.5531i	0.559751	+	0.950855i
$967$	2.52912	+	2.52912i	0.0813311	+	0.0813311i	0.746602	−	0.665271i	$-0.231684\pi$
$967$	2.52912	+	2.52912i	0.0813311	+	0.0813311i	−0.665271	+	0.746602i	$0.731684\pi$
$968$	15.7402	−	15.7402i	0.505911	−	0.505911i
$969$	5.75656	+	9.77874i	0.184927	+	0.314138i
$970$	11.4270	+	11.4270i	0.366900	+	0.366900i
$971$			55.6668i			1.78643i	0.449628	+	0.893216i	$0.351556\pi$
$971$			55.6668i			1.78643i	−0.449628	+	0.893216i	$0.648444\pi$
$972$	13.8174	+	7.21661i	0.443193	+	0.231473i
$973$			10.2857i			0.329746i
$974$		−	7.78760i		−	0.249531i
$975$	−3.74793	−	0.970360i	−0.120030	−	0.0310764i
$976$	8.82247	−	8.82247i	0.282400	−	0.282400i
$977$	−13.3819	−	13.3819i	−0.428126	−	0.428126i	0.459864	−	0.887990i	$-0.347898\pi$
$977$	−13.3819	−	13.3819i	−0.428126	−	0.428126i	−0.887990	+	0.459864i	$0.847898\pi$
$978$	9.34125	+	15.8681i	0.298700	+	0.507406i
$979$	−22.4206	−	22.4206i	−0.716567	−	0.716567i
$980$	0.928018	+	0.928018i	0.0296444	+	0.0296444i
$981$	24.5478	−	7.02461i	0.783750	−	0.224279i
$982$	10.3432	−	10.3432i	0.330066	−	0.330066i
$983$	21.6640			0.690975			0.345488	−	0.938423i	$-0.387714\pi$
$983$	21.6640			0.690975			0.345488	+	0.938423i	$0.387714\pi$
$984$	−4.78521	−	1.23892i	−0.152547	−	0.0394953i
$985$	−7.63023	−	7.63023i	−0.243119	−	0.243119i
$986$	−0.723261	−	0.723261i	−0.0230333	−	0.0230333i
$987$	30.0540	−	17.6922i	0.956629	−	0.563150i
$988$	13.5018			0.429550
$989$	76.0261			2.41749
$990$	8.39609	−	15.1277i	0.266845	−	0.480789i
$991$	8.58660	−	8.58660i	0.272762	−	0.272762i	−0.557449	−	0.830211i	$-0.688220\pi$
$991$	8.58660	−	8.58660i	0.272762	−	0.272762i	0.830211	+	0.557449i	$0.188220\pi$
$992$	−6.97322			−0.221400
$993$	9.94108	−	38.3965i	0.315471	−	1.21848i
$994$	−17.2186	+	17.2186i	−0.546142	+	0.546142i
$995$			6.57059i			0.208302i
$996$	−14.2795	−	24.2567i	−0.452462	−	0.768603i
$997$	−13.9394	−	13.9394i	−0.441465	−	0.441465i	0.451039	−	0.892504i	$-0.351053\pi$
$997$	−13.9394	−	13.9394i	−0.441465	−	0.441465i	−0.892504	+	0.451039i	$0.851053\pi$
$998$	4.94303			0.156469
$999$	−30.3428	−	8.84945i	−0.960005	−	0.279984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.191.4	✓	40
3.2	odd	2	inner	1110.2.u.e.191.20	yes	40
37.31	odd	4	inner	1110.2.u.e.401.20	yes	40
111.68	even	4	inner	1110.2.u.e.401.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.4	✓	40	1.1	even	1	trivial
1110.2.u.e.191.20	yes	40	3.2	odd	2	inner
1110.2.u.e.401.4	yes	40	111.68	even	4	inner
1110.2.u.e.401.20	yes	40	37.31	odd	4	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.878679 + 1.49262i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.434124 - 1.67676i) q^{6} +2.38487 q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.45585 + 2.62307i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.878679 + 1.49262i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.434124 - 1.67676i) q^{6} +2.38487 q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.45585 + 2.62307i) q^{9} +1.00000 q^{10} -5.76715 q^{11} +(-1.49262 + 0.878679i) q^{12} +(-1.58054 - 1.58054i) q^{13} +(-1.68635 - 1.68635i) q^{14} +(-1.67676 - 0.434124i) q^{15} -1.00000 q^{16} +(0.766912 - 0.766912i) q^{17} +(2.88423 - 0.825355i) q^{18} +(4.27127 + 4.27127i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(2.09553 + 3.55970i) q^{21} +(4.07799 + 4.07799i) q^{22} +(-5.87049 + 5.87049i) q^{23} +(1.67676 + 0.434124i) q^{24} -1.00000i q^{25} +2.23522i q^{26} +(-5.19448 + 0.131812i) q^{27} +2.38487i q^{28} +(0.666860 + 0.666860i) q^{29} +(0.878679 + 1.49262i) q^{30} +(-4.93081 + 4.93081i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.06748 - 8.60819i) q^{33} -1.08458 q^{34} +(-1.68635 + 1.68635i) q^{35} +(-2.62307 - 1.45585i) q^{36} +(5.79440 + 1.85066i) q^{37} -6.04049i q^{38} +(0.970360 - 3.74793i) q^{39} +1.00000i q^{40} -2.85384 q^{41} +(1.03533 - 3.99886i) q^{42} +(-6.47528 - 6.47528i) q^{43} -5.76715i q^{44} +(-0.825355 - 2.88423i) q^{45} +8.30212 q^{46} -8.44283i q^{47} +(-0.878679 - 1.49262i) q^{48} -1.31242 q^{49} +(-0.707107 + 0.707107i) q^{50} +(1.81858 + 0.470841i) q^{51} +(1.58054 - 1.58054i) q^{52} +7.21707i q^{53} +(3.76626 + 3.57985i) q^{54} +(4.07799 - 4.07799i) q^{55} +(1.68635 - 1.68635i) q^{56} +(-2.62232 + 10.1285i) q^{57} -0.943082i q^{58} +(5.63841 - 5.63841i) q^{59} +(0.434124 - 1.67676i) q^{60} +(-8.82247 + 8.82247i) q^{61} +6.97322 q^{62} +(-3.47200 + 6.25568i) q^{63} -1.00000i q^{64} +2.23522 q^{65} +(-2.50366 + 9.67016i) q^{66} +2.96422i q^{67} +(0.766912 + 0.766912i) q^{68} +(-13.9207 - 3.60415i) q^{69} +2.38487 q^{70} -10.2106i q^{71} +(0.825355 + 2.88423i) q^{72} +1.48258i q^{73} +(-2.78864 - 5.40587i) q^{74} +(1.49262 - 0.878679i) q^{75} +(-4.27127 + 4.27127i) q^{76} -13.7539 q^{77} +(-3.33634 + 1.96404i) q^{78} +(-3.85057 - 3.85057i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-4.76103 - 7.63758i) q^{81} +(2.01797 + 2.01797i) q^{82} +16.2511i q^{83} +(-3.55970 + 2.09553i) q^{84} +1.08458i q^{85} +9.15744i q^{86} +(-0.409414 + 1.58133i) q^{87} +(-4.07799 + 4.07799i) q^{88} +(3.88764 + 3.88764i) q^{89} +(-1.45585 + 2.62307i) q^{90} +(-3.76937 - 3.76937i) q^{91} +(-5.87049 - 5.87049i) q^{92} +(-11.6924 - 3.02724i) q^{93} +(-5.96998 + 5.96998i) q^{94} -6.04049 q^{95} +(-0.434124 + 1.67676i) q^{96} +(11.4270 + 11.4270i) q^{97} +(0.928018 + 0.928018i) q^{98} +(8.39609 - 15.1277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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