LMFDB - Embedded newform 1110.2.u.f.401.7

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			401.7
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.f.191.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.70946 - 0.278802i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.01163 + 1.40592i) q^{6} -0.348034 q^{7} +(0.707107 + 0.707107i) q^{8} +(2.84454 - 0.953204i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.70946 - 0.278802i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.01163 + 1.40592i) q^{6} -0.348034 q^{7} +(0.707107 + 0.707107i) q^{8} +(2.84454 - 0.953204i) q^{9} -1.00000 q^{10} -3.72020 q^{11} +(-0.278802 - 1.70946i) q^{12} +(0.586358 - 0.586358i) q^{13} +(0.246097 - 0.246097i) q^{14} +(1.40592 + 1.01163i) q^{15} -1.00000 q^{16} +(2.90814 + 2.90814i) q^{17} +(-1.33738 + 2.68541i) q^{18} +(3.00391 - 3.00391i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-0.594951 + 0.0970324i) q^{21} +(2.63058 - 2.63058i) q^{22} +(6.48575 + 6.48575i) q^{23} +(1.40592 + 1.01163i) q^{24} +1.00000i q^{25} +0.829235i q^{26} +(4.59688 - 2.42253i) q^{27} +0.348034i q^{28} +(-0.289070 + 0.289070i) q^{29} +(-1.70946 + 0.278802i) q^{30} +(4.18795 + 4.18795i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.35955 + 1.03720i) q^{33} -4.11273 q^{34} +(-0.246097 - 0.246097i) q^{35} +(-0.953204 - 2.84454i) q^{36} +(2.18867 - 5.67536i) q^{37} +4.24816i q^{38} +(0.838880 - 1.16584i) q^{39} +1.00000i q^{40} +9.94709 q^{41} +(0.352082 - 0.489306i) q^{42} +(-4.12802 + 4.12802i) q^{43} +3.72020i q^{44} +(2.68541 + 1.33738i) q^{45} -9.17224 q^{46} -7.55524i q^{47} +(-1.70946 + 0.278802i) q^{48} -6.87887 q^{49} +(-0.707107 - 0.707107i) q^{50} +(5.78215 + 4.16056i) q^{51} +(-0.586358 - 0.586358i) q^{52} -0.164161i q^{53} +(-1.53750 + 4.96348i) q^{54} +(-2.63058 - 2.63058i) q^{55} +(-0.246097 - 0.246097i) q^{56} +(4.29758 - 5.97257i) q^{57} -0.408806i q^{58} +(6.51580 + 6.51580i) q^{59} +(1.01163 - 1.40592i) q^{60} +(-8.60550 - 8.60550i) q^{61} -5.92266 q^{62} +(-0.989995 + 0.331747i) q^{63} +1.00000i q^{64} +0.829235 q^{65} +(3.76347 - 5.23029i) q^{66} +14.1406i q^{67} +(2.90814 - 2.90814i) q^{68} +(12.8954 + 9.27892i) q^{69} +0.348034 q^{70} +0.738626i q^{71} +(2.68541 + 1.33738i) q^{72} -15.9210i q^{73} +(2.46547 + 5.56071i) q^{74} +(0.278802 + 1.70946i) q^{75} +(-3.00391 - 3.00391i) q^{76} +1.29475 q^{77} +(0.231192 + 1.41755i) q^{78} +(6.84427 - 6.84427i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(7.18281 - 5.42285i) q^{81} +(-7.03365 + 7.03365i) q^{82} +9.66311i q^{83} +(0.0970324 + 0.594951i) q^{84} +4.11273i q^{85} -5.83790i q^{86} +(-0.413561 + 0.574747i) q^{87} +(-2.63058 - 2.63058i) q^{88} +(-5.63114 + 5.63114i) q^{89} +(-2.84454 + 0.953204i) q^{90} +(-0.204072 + 0.204072i) q^{91} +(6.48575 - 6.48575i) q^{92} +(8.32676 + 5.99154i) q^{93} +(5.34236 + 5.34236i) q^{94} +4.24816 q^{95} +(1.01163 - 1.40592i) q^{96} +(11.0221 - 11.0221i) q^{97} +(4.86410 - 4.86410i) q^{98} +(-10.5823 + 3.54611i) 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} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) $ 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.70946	−	0.278802i	0.986960	−	0.160966i
$3$	1.70946	−	0.278802i	0.986960	−	0.160966i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−1.01163	+	1.40592i	−0.412997	+	0.573963i
$7$	−0.348034			−0.131544			−0.0657722	−	0.997835i	$-0.520951\pi$
$7$	−0.348034			−0.131544			−0.0657722	+	0.997835i	$0.520951\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.84454	−	0.953204i	0.948180	−	0.317735i
$10$	−1.00000			−0.316228
$11$	−3.72020			−1.12168			−0.560841	−	0.827923i	$-0.689522\pi$
$11$	−3.72020			−1.12168			−0.560841	+	0.827923i	$0.689522\pi$
$12$	−0.278802	−	1.70946i	−0.0804832	−	0.493480i
$13$	0.586358	−	0.586358i	0.162626	−	0.162626i	−0.621103	−	0.783729i	$-0.713315\pi$
$13$	0.586358	−	0.586358i	0.162626	−	0.162626i	0.783729	+	0.621103i	$0.213315\pi$
$14$	0.246097	−	0.246097i	0.0657722	−	0.0657722i
$15$	1.40592	+	1.01163i	0.363006	+	0.261202i
$16$	−1.00000			−0.250000
$17$	2.90814	+	2.90814i	0.705327	+	0.705327i	0.965549	−	0.260222i	$-0.0837957\pi$
$17$	2.90814	+	2.90814i	0.705327	+	0.705327i	−0.260222	+	0.965549i	$0.583796\pi$
$18$	−1.33738	+	2.68541i	−0.315223	+	0.632957i
$19$	3.00391	−	3.00391i	0.689143	−	0.689143i	−0.272899	−	0.962043i	$-0.587983\pi$
$19$	3.00391	−	3.00391i	0.689143	−	0.689143i	0.962043	+	0.272899i	$0.0879826\pi$
$20$	0.707107	−	0.707107i	0.158114	−	0.158114i
$21$	−0.594951	+	0.0970324i	−0.129829	+	0.0211742i
$22$	2.63058	−	2.63058i	0.560841	−	0.560841i
$23$	6.48575	+	6.48575i	1.35237	+	1.35237i	0.883000	+	0.469372i	$0.155520\pi$
$23$	6.48575	+	6.48575i	1.35237	+	1.35237i	0.469372	+	0.883000i	$0.344480\pi$
$24$	1.40592	+	1.01163i	0.286982	+	0.206498i
$25$			1.00000i			0.200000i
$26$			0.829235i			0.162626i
$27$	4.59688	−	2.42253i	0.884671	−	0.466216i
$28$			0.348034i			0.0657722i
$29$	−0.289070	+	0.289070i	−0.0536789	+	0.0536789i	−0.733437	−	0.679758i	$-0.762085\pi$
$29$	−0.289070	+	0.289070i	−0.0536789	+	0.0536789i	0.679758	+	0.733437i	$0.262085\pi$
$30$	−1.70946	+	0.278802i	−0.312104	+	0.0509020i
$31$	4.18795	+	4.18795i	0.752178	+	0.752178i	0.974885	−	0.222707i	$-0.0714894\pi$
$31$	4.18795	+	4.18795i	0.752178	+	0.752178i	−0.222707	+	0.974885i	$0.571489\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−6.35955	+	1.03720i	−1.10706	+	0.180553i
$34$	−4.11273			−0.705327
$35$	−0.246097	−	0.246097i	−0.0415980	−	0.0415980i
$36$	−0.953204	−	2.84454i	−0.158867	−	0.474090i
$37$	2.18867	−	5.67536i	0.359815	−	0.933024i
$37$	2.18867	−	5.67536i	0.359815	−	0.933024i
$38$			4.24816i			0.689143i
$39$	0.838880	−	1.16584i	0.134328	−	0.186683i
$40$			1.00000i			0.158114i
$41$	9.94709			1.55347			0.776737	−	0.629825i	$-0.216873\pi$
$41$	9.94709			1.55347			0.776737	+	0.629825i	$0.216873\pi$
$42$	0.352082	−	0.489306i	0.0543274	−	0.0755016i
$43$	−4.12802	+	4.12802i	−0.629517	+	0.629517i	−0.947946	−	0.318430i	$-0.896844\pi$
$43$	−4.12802	+	4.12802i	−0.629517	+	0.629517i	0.318430	+	0.947946i	$0.396844\pi$
$44$			3.72020i			0.560841i
$45$	2.68541	+	1.33738i	0.400317	+	0.199364i
$46$	−9.17224			−1.35237
$47$		−	7.55524i		−	1.10205i	−0.834490	−	0.551023i	$-0.814238\pi$
$47$		−	7.55524i		−	1.10205i	0.834490	−	0.551023i	$-0.185762\pi$
$48$	−1.70946	+	0.278802i	−0.246740	+	0.0402416i
$49$	−6.87887			−0.982696
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	5.78215	+	4.16056i	0.809663	+	0.582596i
$52$	−0.586358	−	0.586358i	−0.0813132	−	0.0813132i
$53$		−	0.164161i		−	0.0225492i	−0.999936	−	0.0112746i	$-0.996411\pi$
$53$		−	0.164161i		−	0.0225492i	0.999936	−	0.0112746i	$-0.00358889\pi$
$54$	−1.53750	+	4.96348i	−0.209227	+	0.675444i
$55$	−2.63058	−	2.63058i	−0.354707	−	0.354707i
$56$	−0.246097	−	0.246097i	−0.0328861	−	0.0328861i
$57$	4.29758	−	5.97257i	0.569228	−	0.791086i
$58$		−	0.408806i		−	0.0536789i
$59$	6.51580	+	6.51580i	0.848285	+	0.848285i	0.989919	−	0.141634i	$-0.0452355\pi$
$59$	6.51580	+	6.51580i	0.848285	+	0.848285i	−0.141634	+	0.989919i	$0.545236\pi$
$60$	1.01163	−	1.40592i	0.130601	−	0.181503i
$61$	−8.60550	−	8.60550i	−1.10182	−	1.10182i	−0.994191	−	0.107630i	$-0.965674\pi$
$61$	−8.60550	−	8.60550i	−1.10182	−	1.10182i	−0.107630	−	0.994191i	$-0.534326\pi$
$62$	−5.92266			−0.752178
$63$	−0.989995	+	0.331747i	−0.124728	+	0.0417962i
$64$			1.00000i			0.125000i
$65$	0.829235			0.102854
$66$	3.76347	−	5.23029i	0.463251	−	0.643804i
$67$			14.1406i			1.72755i	0.503879	+	0.863774i	$0.331906\pi$
$67$			14.1406i			1.72755i	−0.503879	+	0.863774i	$0.668094\pi$
$68$	2.90814	−	2.90814i	0.352664	−	0.352664i
$69$	12.8954	+	9.27892i	1.55242	+	1.11705i
$70$	0.348034			0.0415980
$71$			0.738626i			0.0876587i	0.999039	+	0.0438294i	$0.0139558\pi$
$71$			0.738626i			0.0876587i	−0.999039	+	0.0438294i	$0.986044\pi$
$72$	2.68541	+	1.33738i	0.316479	+	0.157611i
$73$		−	15.9210i		−	1.86341i	−0.363210	−	0.931707i	$-0.618319\pi$
$73$		−	15.9210i		−	1.86341i	0.363210	−	0.931707i	$-0.381681\pi$
$74$	2.46547	+	5.56071i	0.286605	+	0.646419i
$75$	0.278802	+	1.70946i	0.0321933	+	0.197392i
$76$	−3.00391	−	3.00391i	−0.344572	−	0.344572i
$77$	1.29475			0.147551
$78$	0.231192	+	1.41755i	0.0261774	+	0.160506i
$79$	6.84427	−	6.84427i	0.770041	−	0.770041i	−0.208073	−	0.978113i	$-0.566719\pi$
$79$	6.84427	−	6.84427i	0.770041	−	0.770041i	0.978113	+	0.208073i	$0.0667191\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	7.18281	−	5.42285i	0.798089	−	0.602539i
$82$	−7.03365	+	7.03365i	−0.776737	+	0.776737i
$83$			9.66311i			1.06066i	0.847790	+	0.530332i	$0.177933\pi$
$83$			9.66311i			1.06066i	−0.847790	+	0.530332i	$0.822067\pi$
$84$	0.0970324	+	0.594951i	0.0105871	+	0.0649145i
$85$			4.11273i			0.446088i
$86$		−	5.83790i		−	0.629517i
$87$	−0.413561	+	0.574747i	−0.0443384	+	0.0616194i
$88$	−2.63058	−	2.63058i	−0.280421	−	0.280421i
$89$	−5.63114	+	5.63114i	−0.596900	+	0.596900i	−0.939486	−	0.342586i	$-0.888697\pi$
$89$	−5.63114	+	5.63114i	−0.596900	+	0.596900i	0.342586	+	0.939486i	$0.388697\pi$
$90$	−2.84454	+	0.953204i	−0.299841	+	0.100476i
$91$	−0.204072	+	0.204072i	−0.0213926	+	0.0213926i
$92$	6.48575	−	6.48575i	0.676186	−	0.676186i
$93$	8.32676	+	5.99154i	0.863445	+	0.621294i
$94$	5.34236	+	5.34236i	0.551023	+	0.551023i
$95$	4.24816			0.435852
$96$	1.01163	−	1.40592i	0.103249	−	0.143491i
$97$	11.0221	−	11.0221i	1.11913	−	1.11913i	0.127257	−	0.991870i	$-0.459383\pi$
$97$	11.0221	−	11.0221i	1.11913	−	1.11913i	0.991870	−	0.127257i	$-0.0406171\pi$
$98$	4.86410	−	4.86410i	0.491348	−	0.491348i
$99$	−10.5823	+	3.54611i	−1.06356	+	0.356397i
$100$	1.00000			0.100000
$101$	−16.0733			−1.59936			−0.799678	−	0.600429i	$-0.794997\pi$
$101$	−16.0733			−1.59936			−0.799678	+	0.600429i	$0.794997\pi$
$102$	−7.03056	+	1.14664i	−0.696129	+	0.113534i
$103$	−6.58533	−	6.58533i	−0.648872	−	0.648872i	0.303848	−	0.952720i	$-0.401728\pi$
$103$	−6.58533	−	6.58533i	−0.648872	−	0.648872i	−0.952720	+	0.303848i	$0.901728\pi$
$104$	0.829235			0.0813132
$105$	−0.489306	−	0.352082i	−0.0477514	−	0.0343597i
$106$	0.116079	+	0.116079i	0.0112746	+	0.0112746i
$107$		−	9.53842i		−	0.922114i	−0.887371	−	0.461057i	$-0.847470\pi$
$107$		−	9.53842i		−	0.922114i	0.887371	−	0.461057i	$-0.152530\pi$
$108$	−2.42253	−	4.59688i	−0.233108	−	0.442335i
$109$	−9.32002	+	9.32002i	−0.892696	+	0.892696i	−0.994776	−	0.102080i	$-0.967450\pi$
$109$	−9.32002	+	9.32002i	−0.892696	+	0.892696i	0.102080	+	0.994776i	$0.467450\pi$
$110$	3.72020			0.354707
$111$	2.15915	−	10.3120i	0.204937	−	0.978775i
$112$	0.348034			0.0328861
$113$	−5.27517	+	5.27517i	−0.496247	+	0.496247i	−0.910267	−	0.414021i	$-0.864124\pi$
$113$	−5.27517	+	5.27517i	−0.496247	+	0.496247i	0.414021	+	0.910267i	$0.364124\pi$
$114$	1.18440	+	7.26209i	0.110929	+	0.680157i
$115$			9.17224i			0.855316i
$116$	0.289070	+	0.289070i	0.0268394	+	0.0268394i
$117$	1.10900	−	2.22684i	0.102527	−	0.205871i
$118$	−9.21474			−0.848285
$119$	−1.01213	−	1.01213i	−0.0927818	−	0.0927818i
$120$	0.278802	+	1.70946i	0.0254510	+	0.156052i
$121$	2.83989			0.258172
$122$	12.1700			1.10182
$123$	17.0042	−	2.77327i	1.53322	−	0.250057i
$124$	4.18795	−	4.18795i	0.376089	−	0.376089i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	0.465452	−	0.934613i	0.0414657	−	0.0832619i
$127$	6.85581			0.608355			0.304178	−	0.952615i	$-0.401618\pi$
$127$	6.85581			0.608355			0.304178	+	0.952615i	$0.401618\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−5.90580	+	8.20760i	−0.519977	+	0.722639i
$130$	−0.586358	+	0.586358i	−0.0514270	+	0.0514270i
$131$	−3.32864	+	3.32864i	−0.290824	+	0.290824i	−0.837406	−	0.546582i	$-0.815929\pi$
$131$	−3.32864	+	3.32864i	−0.290824	+	0.290824i	0.546582	+	0.837406i	$0.315929\pi$
$132$	1.03720	+	6.35955i	0.0902766	+	0.553528i
$133$	−1.04546	+	1.04546i	−0.0906529	+	0.0906529i
$134$	−9.99891	−	9.99891i	−0.863774	−	0.863774i
$135$	4.96348	+	1.53750i	0.427188	+	0.132327i
$136$			4.11273i			0.352664i
$137$			2.18171i			0.186396i	0.995648	+	0.0931980i	$0.0297089\pi$
$137$			2.18171i			0.186396i	−0.995648	+	0.0931980i	$0.970291\pi$
$138$	−15.6796	+	2.55724i	−1.33474	+	0.217686i
$139$			3.77025i			0.319788i	0.987134	+	0.159894i	$0.0511153\pi$
$139$			3.77025i			0.319788i	−0.987134	+	0.159894i	$0.948885\pi$
$140$	−0.246097	+	0.246097i	−0.0207990	+	0.0207990i
$141$	−2.10642	−	12.9154i	−0.177392	−	1.08767i
$142$	−0.522287	−	0.522287i	−0.0438294	−	0.0438294i
$143$	−2.18137	+	2.18137i	−0.182415	+	0.182415i
$144$	−2.84454	+	0.953204i	−0.237045	+	0.0794336i
$145$	−0.408806			−0.0339495
$146$	11.2579	+	11.2579i	0.931707	+	0.931707i
$147$	−11.7592	+	1.91784i	−0.969882	+	0.158181i
$148$	−5.67536	−	2.18867i	−0.466512	−	0.179907i
$149$			14.7936i			1.21194i	0.795489	+	0.605968i	$0.207214\pi$
$149$			14.7936i			1.21194i	−0.795489	+	0.605968i	$0.792786\pi$
$150$	−1.40592	−	1.01163i	−0.114793	−	0.0825994i
$151$			2.35718i			0.191825i	0.995390	+	0.0959124i	$0.0305769\pi$
$151$			2.35718i			0.191825i	−0.995390	+	0.0959124i	$0.969423\pi$
$152$	4.24816			0.344572
$153$	11.0444	+	5.50026i	0.892884	+	0.444670i
$154$	−0.915530	+	0.915530i	−0.0737755	+	0.0737755i
$155$			5.92266i			0.475719i
$156$	−1.16584	−	0.838880i	−0.0933415	−	0.0671642i
$157$	−17.5824			−1.40323			−0.701616	−	0.712555i	$-0.747538\pi$
$157$	−17.5824			−1.40323			−0.701616	+	0.712555i	$0.747538\pi$
$158$			9.67926i			0.770041i
$159$	−0.0457683	−	0.280627i	−0.00362966	−	0.0222552i
$160$	1.00000			0.0790569
$161$	−2.25726	−	2.25726i	−0.177897	−	0.177897i
$162$	−1.24448	+	8.91354i	−0.0977753	+	0.700314i
$163$	2.83898	+	2.83898i	0.222366	+	0.222366i	0.809494	−	0.587128i	$-0.199742\pi$
$163$	2.83898	+	2.83898i	0.222366	+	0.222366i	−0.587128	+	0.809494i	$0.699742\pi$
$164$		−	9.94709i		−	0.776737i
$165$	−5.23029	−	3.76347i	−0.407178	−	0.292986i
$166$	−6.83285	−	6.83285i	−0.530332	−	0.530332i
$167$	−8.73935	−	8.73935i	−0.676272	−	0.676272i	0.282883	−	0.959154i	$-0.408709\pi$
$167$	−8.73935	−	8.73935i	−0.676272	−	0.676272i	−0.959154	+	0.282883i	$0.908709\pi$
$168$	−0.489306	−	0.352082i	−0.0377508	−	0.0271637i
$169$			12.3124i			0.947105i
$170$	−2.90814	−	2.90814i	−0.223044	−	0.223044i
$171$	5.68139	−	11.4081i	0.434467	−	0.872396i
$172$	4.12802	+	4.12802i	0.314758	+	0.314758i
$173$	19.5438			1.48588			0.742942	−	0.669356i	$-0.233430\pi$
$173$	19.5438			1.48588			0.742942	+	0.669356i	$0.233430\pi$
$174$	−0.113976	−	0.698840i	−0.00864049	−	0.0529789i
$175$		−	0.348034i		−	0.0263089i
$176$	3.72020			0.280421
$177$	12.9552	+	9.32192i	0.973769	+	0.700678i
$178$		−	7.96364i		−	0.596900i
$179$	−4.09892	+	4.09892i	−0.306368	+	0.306368i	−0.843499	−	0.537131i	$-0.819508\pi$
$179$	−4.09892	+	4.09892i	−0.306368	+	0.306368i	0.537131	+	0.843499i	$0.319508\pi$
$180$	1.33738	−	2.68541i	0.0996821	−	0.200159i
$181$	−10.8868			−0.809211			−0.404605	−	0.914491i	$-0.632591\pi$
$181$	−10.8868			−0.809211			−0.404605	+	0.914491i	$0.632591\pi$
$182$		−	0.288602i		−	0.0213926i
$183$	−17.1100	−	12.3116i	−1.26481	−	0.910097i
$184$			9.17224i			0.676186i
$185$	5.56071	−	2.46547i	0.408831	−	0.181265i
$186$	−10.1246	+	1.65125i	−0.742370	+	0.121075i
$187$	−10.8189	−	10.8189i	−0.791153	−	0.791153i
$188$	−7.55524			−0.551023
$189$	−1.59987	+	0.843122i	−0.116373	+	0.0613281i
$190$	−3.00391	+	3.00391i	−0.217926	+	0.217926i
$191$	−14.0022	−	14.0022i	−1.01316	−	1.01316i	−0.999912	−	0.0132497i	$-0.995782\pi$
$191$	−14.0022	−	14.0022i	−1.01316	−	1.01316i	−0.0132497	−	0.999912i	$-0.504218\pi$
$192$	0.278802	+	1.70946i	0.0201208	+	0.123370i
$193$	11.7248	−	11.7248i	0.843971	−	0.843971i	−0.145401	−	0.989373i	$-0.546447\pi$
$193$	11.7248	−	11.7248i	0.843971	−	0.843971i	0.989373	+	0.145401i	$0.0464473\pi$
$194$			15.5876i			1.11913i
$195$	1.41755	−	0.231192i	0.101513	−	0.0165560i
$196$			6.87887i			0.491348i
$197$		−	1.38691i		−	0.0988132i	−0.998779	−	0.0494066i	$-0.984267\pi$
$197$		−	1.38691i		−	0.0988132i	0.998779	−	0.0494066i	$-0.0157330\pi$
$198$	4.97531	−	9.99026i	0.353580	−	0.709977i
$199$	12.9450	+	12.9450i	0.917647	+	0.917647i	0.996858	−	0.0792111i	$-0.0252401\pi$
$199$	12.9450	+	12.9450i	0.917647	+	0.917647i	−0.0792111	+	0.996858i	$0.525240\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$	3.94242	+	24.1728i	0.278077	+	1.70502i
$202$	11.3656	−	11.3656i	0.799678	−	0.799678i
$203$	0.100606	−	0.100606i	0.00706115	−	0.00706115i
$204$	4.16056	−	5.78215i	0.291298	−	0.404832i
$205$	7.03365	+	7.03365i	0.491252	+	0.491252i
$206$	9.31307			0.648872
$207$	24.6312	+	12.2667i	1.71199	+	0.852597i
$208$	−0.586358	+	0.586358i	−0.0406566	+	0.0406566i
$209$	−11.1751	+	11.1751i	−0.773000	+	0.773000i
$210$	0.594951	−	0.0970324i	0.0410555	−	0.00669587i
$211$	16.2108			1.11600			0.557999	−	0.829841i	$-0.311569\pi$
$211$	16.2108			1.11600			0.557999	+	0.829841i	$0.311569\pi$
$212$	−0.164161			−0.0112746
$213$	0.205930	+	1.26265i	0.0141101	+	0.0865157i
$214$	6.74468	+	6.74468i	0.461057	+	0.461057i
$215$	−5.83790			−0.398141
$216$	4.96348	+	1.53750i	0.337722	+	0.104614i
$217$	−1.45755	−	1.45755i	−0.0989448	−	0.0989448i
$218$		−	13.1805i		−	0.892696i
$219$	−4.43881	−	27.2164i	−0.299947	−	1.83912i
$220$	−2.63058	+	2.63058i	−0.177354	+	0.177354i
$221$	3.41042			0.229410
$222$	5.76496	+	8.81846i	0.386919	+	0.591856i
$223$	−5.18177			−0.346997			−0.173498	−	0.984834i	$-0.555507\pi$
$223$	−5.18177			−0.346997			−0.173498	+	0.984834i	$0.555507\pi$
$224$	−0.246097	+	0.246097i	−0.0164430	+	0.0164430i
$225$	0.953204	+	2.84454i	0.0635469	+	0.189636i
$226$		−	7.46022i		−	0.496247i
$227$	−14.9028	−	14.9028i	−0.989133	−	0.989133i	0.0108088	−	0.999942i	$-0.496559\pi$
$227$	−14.9028	−	14.9028i	−0.989133	−	0.989133i	−0.999942	+	0.0108088i	$0.996559\pi$
$228$	−5.97257	−	4.29758i	−0.395543	−	0.284614i
$229$	−15.8227			−1.04559			−0.522796	−	0.852458i	$-0.675111\pi$
$229$	−15.8227			−1.04559			−0.522796	+	0.852458i	$0.675111\pi$
$230$	−6.48575	−	6.48575i	−0.427658	−	0.427658i
$231$	2.21334	−	0.360980i	0.145627	−	0.0237507i
$232$	−0.408806			−0.0268394
$233$	−17.2520			−1.13022			−0.565109	−	0.825016i	$-0.691166\pi$
$233$	−17.2520			−1.13022			−0.565109	+	0.825016i	$0.691166\pi$
$234$	0.790430	+	2.35879i	0.0516720	+	0.154199i
$235$	5.34236	−	5.34236i	0.348497	−	0.348497i
$236$	6.51580	−	6.51580i	0.424143	−	0.424143i
$237$	9.79184	−	13.6082i	0.636049	−	0.883950i
$238$	1.43137			0.0927818
$239$	−8.68104	−	8.68104i	−0.561530	−	0.561530i	0.368212	−	0.929742i	$-0.379970\pi$
$239$	−8.68104	−	8.68104i	−0.561530	−	0.561530i	−0.929742	+	0.368212i	$0.879970\pi$
$240$	−1.40592	−	1.01163i	−0.0907515	−	0.0653005i
$241$	11.6905	−	11.6905i	0.753050	−	0.753050i	−0.221997	−	0.975047i	$-0.571258\pi$
$241$	11.6905	−	11.6905i	0.753050	−	0.753050i	0.975047	+	0.221997i	$0.0712576\pi$
$242$	−2.00811	+	2.00811i	−0.129086	+	0.129086i
$243$	10.7669	−	11.2728i	0.690694	−	0.723147i
$244$	−8.60550	+	8.60550i	−0.550911	+	0.550911i
$245$	−4.86410	−	4.86410i	−0.310756	−	0.310756i
$246$	−10.0628	+	13.9848i	−0.641580	+	0.891637i
$247$		−	3.52273i		−	0.224146i
$248$			5.92266i			0.376089i
$249$	2.69409	+	16.5187i	0.170731	+	1.04683i
$250$		−	1.00000i		−	0.0632456i
$251$	−5.17135	+	5.17135i	−0.326413	+	0.326413i	−0.851221	−	0.524808i	$-0.824137\pi$
$251$	−5.17135	+	5.17135i	−0.326413	+	0.326413i	0.524808	+	0.851221i	$0.324137\pi$
$252$	0.331747	+	0.989995i	0.0208981	+	0.0623638i
$253$	−24.1283	−	24.1283i	−1.51693	−	1.51693i
$254$	−4.84779	+	4.84779i	−0.304178	+	0.304178i
$255$	1.14664	+	7.03056i	0.0718051	+	0.440271i
$256$	1.00000			0.0625000
$257$	−20.9443	−	20.9443i	−1.30647	−	1.30647i	−0.923947	−	0.382520i	$-0.875056\pi$
$257$	−20.9443	−	20.9443i	−1.30647	−	1.30647i	−0.382520	−	0.923947i	$-0.624944\pi$
$258$	−1.62762	−	9.97968i	−0.101331	−	0.621308i
$259$	−0.761730	+	1.97522i	−0.0473316	+	0.122734i
$260$		−	0.829235i		−	0.0514270i
$261$	−0.546728	+	1.09781i	−0.0338416	+	0.0679529i
$262$		−	4.70740i		−	0.290824i
$263$	−0.826816			−0.0509837			−0.0254918	−	0.999675i	$-0.508115\pi$
$263$	−0.826816			−0.0509837			−0.0254918	+	0.999675i	$0.508115\pi$
$264$	−5.23029	−	3.76347i	−0.321902	−	0.231626i
$265$	0.116079	−	0.116079i	0.00713068	−	0.00713068i
$266$		−	1.47850i		−	0.0906529i
$267$	−8.05627	+	11.1962i	−0.493035	+	0.685197i
$268$	14.1406			0.863774
$269$		−	22.9891i		−	1.40167i	−0.713323	−	0.700835i	$-0.752811\pi$
$269$		−	22.9891i		−	1.40167i	0.713323	−	0.700835i	$-0.247189\pi$
$270$	−4.59688	+	2.42253i	−0.279757	+	0.147431i
$271$	−8.57848			−0.521105			−0.260553	−	0.965460i	$-0.583905\pi$
$271$	−8.57848			−0.521105			−0.260553	+	0.965460i	$0.583905\pi$
$272$	−2.90814	−	2.90814i	−0.176332	−	0.176332i
$273$	−0.291959	+	0.405750i	−0.0176701	+	0.0245571i
$274$	−1.54270	−	1.54270i	−0.0931980	−	0.0931980i
$275$		−	3.72020i		−	0.224337i
$276$	9.27892	−	12.8954i	0.558526	−	0.776212i
$277$	−12.4445	−	12.4445i	−0.747719	−	0.747719i	0.226332	−	0.974050i	$-0.427327\pi$
$277$	−12.4445	−	12.4445i	−0.747719	−	0.747719i	−0.974050	+	0.226332i	$0.927327\pi$
$278$	−2.66597	−	2.66597i	−0.159894	−	0.159894i
$279$	15.9048	+	7.92082i	0.952193	+	0.474207i
$280$		−	0.348034i		−	0.0207990i
$281$	0.971269	+	0.971269i	0.0579410	+	0.0579410i	0.735484	−	0.677543i	$-0.236955\pi$
$281$	0.971269	+	0.971269i	0.0579410	+	0.0579410i	−0.677543	+	0.735484i	$0.736955\pi$
$282$	10.6220	+	7.64312i	0.632533	+	0.455141i
$283$	−1.46923	−	1.46923i	−0.0873364	−	0.0873364i	0.662089	−	0.749425i	$-0.269670\pi$
$283$	−1.46923	−	1.46923i	−0.0873364	−	0.0873364i	−0.749425	+	0.662089i	$0.769670\pi$
$284$	0.738626			0.0438294
$285$	7.26209	−	1.18440i	0.430169	−	0.0701576i
$286$		−	3.08492i		−	0.182415i
$287$	−3.46192			−0.204351
$288$	1.33738	−	2.68541i	0.0788056	−	0.158239i
$289$		−	0.0854698i		−	0.00502764i
$290$	0.289070	−	0.289070i	0.0169748	−	0.0169748i
$291$	15.7689	−	21.9149i	0.924391	−	1.28467i
$292$	−15.9210			−0.931707
$293$			1.74107i			0.101715i	0.998706	+	0.0508573i	$0.0161954\pi$
$293$			1.74107i			0.101715i	−0.998706	+	0.0508573i	$0.983805\pi$
$294$	6.95888	−	9.67112i	0.405850	−	0.564031i
$295$			9.21474i			0.536503i
$296$	5.56071	−	2.46547i	0.323210	−	0.143302i
$297$	−17.1013	+	9.01230i	−0.992320	+	0.522947i
$298$	−10.4606	−	10.4606i	−0.605968	−	0.605968i
$299$	7.60594			0.439863
$300$	1.70946	−	0.278802i	0.0986960	−	0.0160966i
$301$	1.43669	−	1.43669i	0.0828093	−	0.0828093i
$302$	−1.66678	−	1.66678i	−0.0959124	−	0.0959124i
$303$	−27.4768	+	4.48127i	−1.57850	+	0.257442i
$304$	−3.00391	+	3.00391i	−0.172286	+	0.172286i
$305$		−	12.1700i		−	0.696853i
$306$	−11.6988	+	3.92027i	−0.668777	+	0.224107i
$307$		−	9.43400i		−	0.538427i	−0.963081	−	0.269213i	$-0.913236\pi$
$307$		−	9.43400i		−	0.538427i	0.963081	−	0.269213i	$-0.0867637\pi$
$308$		−	1.29475i		−	0.0737755i
$309$	−13.0934	−	9.42139i	−0.744857	−	0.535964i
$310$	−4.18795	−	4.18795i	−0.237860	−	0.237860i
$311$	−17.4484	+	17.4484i	−0.989408	+	0.989408i	−0.999944	−	0.0105370i	$-0.996646\pi$
$311$	−17.4484	+	17.4484i	−0.989408	+	0.989408i	0.0105370	+	0.999944i	$0.496646\pi$
$312$	1.41755	−	0.231192i	0.0802529	−	0.0130887i
$313$	7.61657	−	7.61657i	0.430514	−	0.430514i	−0.458289	−	0.888803i	$-0.651538\pi$
$313$	7.61657	−	7.61657i	0.430514	−	0.430514i	0.888803	+	0.458289i	$0.151538\pi$
$314$	12.4327	−	12.4327i	0.701616	−	0.701616i
$315$	−0.934613	−	0.465452i	−0.0526595	−	0.0262252i
$316$	−6.84427	−	6.84427i	−0.385020	−	0.385020i
$317$	−20.5090			−1.15190			−0.575951	−	0.817485i	$-0.695368\pi$
$317$	−20.5090			−1.15190			−0.575951	+	0.817485i	$0.695368\pi$
$318$	0.230796	+	0.166070i	0.0129424	+	0.00931275i
$319$	1.07540	−	1.07540i	0.0602107	−	0.0602107i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$	−2.65933	−	16.3056i	−0.148429	−	0.910089i
$322$	3.19225			0.177897
$323$	17.4715			0.972143
$324$	−5.42285	−	7.18281i	−0.301269	−	0.399045i
$325$	0.586358	+	0.586358i	0.0325253	+	0.0325253i
$326$	−4.01492			−0.222366
$327$	−13.3338	+	18.5307i	−0.737362	+	1.02475i
$328$	7.03365	+	7.03365i	0.388369	+	0.388369i
$329$			2.62948i			0.144968i
$330$	6.35955	−	1.03720i	0.350082	−	0.0570959i
$331$	−1.37048	+	1.37048i	−0.0753283	+	0.0753283i	−0.743767	−	0.668439i	$-0.766963\pi$
$331$	−1.37048	+	1.37048i	−0.0753283	+	0.0753283i	0.668439	+	0.743767i	$0.266963\pi$
$332$	9.66311			0.530332
$333$	0.815972	−	18.2300i	0.0447150	−	0.999000i
$334$	12.3593			0.676272
$335$	−9.99891	+	9.99891i	−0.546299	+	0.546299i
$336$	0.594951	−	0.0970324i	0.0324572	−	0.00529355i
$337$		−	33.5414i		−	1.82711i	−0.406711	−	0.913557i	$-0.633324\pi$
$337$		−	33.5414i		−	1.82711i	0.406711	−	0.913557i	$-0.366676\pi$
$338$	−8.70616	−	8.70616i	−0.473553	−	0.473553i
$339$	−7.54699	+	10.4884i	−0.409896	+	0.569654i
$340$	4.11273			0.223044
$341$	−15.5800	−	15.5800i	−0.843705	−	0.843705i
$342$	4.04937	+	12.0841i	0.218965	+	0.653432i
$343$	4.83031			0.260812
$344$	−5.83790			−0.314758
$345$	2.55724	+	15.6796i	0.137677	+	0.844162i
$346$	−13.8195	+	13.8195i	−0.742942	+	0.742942i
$347$	14.2780	−	14.2780i	0.766484	−	0.766484i	−0.211002	−	0.977486i	$-0.567673\pi$
$347$	14.2780	−	14.2780i	0.766484	−	0.766484i	0.977486	+	0.211002i	$0.0676727\pi$
$348$	0.574747	+	0.413561i	0.0308097	+	0.0221692i
$349$	6.56028			0.351164			0.175582	−	0.984465i	$-0.443819\pi$
$349$	6.56028			0.351164			0.175582	+	0.984465i	$0.443819\pi$
$350$	0.246097	+	0.246097i	0.0131544	+	0.0131544i
$351$	1.27495	−	4.11589i	0.0680517	−	0.219690i
$352$	−2.63058	+	2.63058i	−0.140210	+	0.140210i
$353$	25.6324	−	25.6324i	1.36427	−	1.36427i	0.495889	−	0.868386i	$-0.334842\pi$
$353$	25.6324	−	25.6324i	1.36427	−	1.36427i	0.868386	−	0.495889i	$-0.165158\pi$
$354$	−15.7523	+	2.56909i	−0.837224	+	0.136545i
$355$	−0.522287	+	0.522287i	−0.0277201	+	0.0277201i
$356$	5.63114	+	5.63114i	0.298450	+	0.298450i
$357$	−2.01238	−	1.44802i	−0.106507	−	0.0766372i
$358$		−	5.79675i		−	0.306368i
$359$			18.5723i			0.980209i	0.871664	+	0.490104i	$0.163041\pi$
$359$			18.5723i			0.980209i	−0.871664	+	0.490104i	$0.836959\pi$
$360$	0.953204	+	2.84454i	0.0502382	+	0.149920i
$361$			0.953098i			0.0501631i
$362$	7.69814	−	7.69814i	0.404605	−	0.404605i
$363$	4.85470	−	0.791767i	0.254805	−	0.0415570i
$364$	0.204072	+	0.204072i	0.0106963	+	0.0106963i
$365$	11.2579	−	11.2579i	0.589263	−	0.589263i
$366$	20.8042	−	3.39302i	1.08745	−	0.177356i
$367$	−10.8985			−0.568898			−0.284449	−	0.958691i	$-0.591811\pi$
$367$	−10.8985			−0.568898			−0.284449	+	0.958691i	$0.591811\pi$
$368$	−6.48575	−	6.48575i	−0.338093	−	0.338093i
$369$	28.2949	−	9.48160i	1.47297	−	0.493592i
$370$	−2.18867	+	5.67536i	−0.113783	+	0.295048i
$371$			0.0571334i			0.00296622i
$372$	5.99154	−	8.32676i	0.310647	−	0.431722i
$373$			27.5555i			1.42677i	0.700772	+	0.713385i	$0.252839\pi$
$373$			27.5555i			1.42677i	−0.700772	+	0.713385i	$0.747161\pi$
$374$	15.3002			0.791153
$375$	−1.01163	+	1.40592i	−0.0522404	+	0.0726012i
$376$	5.34236	−	5.34236i	0.275511	−	0.275511i
$377$			0.338996i			0.0174592i
$378$	0.535102	−	1.72746i	0.0275227	−	0.0888508i
$379$	5.24130			0.269228			0.134614	−	0.990898i	$-0.457021\pi$
$379$	5.24130			0.269228			0.134614	+	0.990898i	$0.457021\pi$
$380$		−	4.24816i		−	0.217926i
$381$	11.7198	−	1.91141i	0.600422	−	0.0979247i
$382$	19.8021			1.01316
$383$	20.0864	+	20.0864i	1.02637	+	1.02637i	0.999643	+	0.0267254i	$0.00850796\pi$
$383$	20.0864	+	20.0864i	1.02637	+	1.02637i	0.0267254	+	0.999643i	$0.491492\pi$
$384$	−1.40592	−	1.01163i	−0.0717454	−	0.0516246i
$385$	0.915530	+	0.915530i	0.0466597	+	0.0466597i
$386$			16.5814i			0.843971i
$387$	−7.80746	+	15.6771i	−0.396876	+	0.796914i
$388$	−11.0221	−	11.0221i	−0.559563	−	0.559563i
$389$	5.94620	+	5.94620i	0.301484	+	0.301484i	0.841594	−	0.540110i	$-0.181617\pi$
$389$	5.94620	+	5.94620i	0.301484	+	0.301484i	−0.540110	+	0.841594i	$0.681617\pi$
$390$	−0.838880	+	1.16584i	−0.0424784	+	0.0590344i
$391$			37.7229i			1.90773i
$392$	−4.86410	−	4.86410i	−0.245674	−	0.245674i
$393$	−4.76216	+	6.61822i	−0.240219	+	0.333845i
$394$	0.980693	+	0.980693i	0.0494066	+	0.0494066i
$395$	9.67926			0.487016
$396$	3.54611	+	10.5823i	0.178199	+	0.531778i
$397$			12.6809i			0.636435i	0.948018	+	0.318218i	$0.103084\pi$
$397$			12.6809i			0.636435i	−0.948018	+	0.318218i	$0.896916\pi$
$398$	−18.3070			−0.917647
$399$	−1.49570	+	2.07865i	−0.0748787	+	0.104063i
$400$		−	1.00000i		−	0.0500000i
$401$	−21.8657	+	21.8657i	−1.09192	+	1.09192i	−0.0965961	+	0.995324i	$0.530796\pi$
$401$	−21.8657	+	21.8657i	−1.09192	+	1.09192i	−0.995324	+	0.0965961i	$0.969204\pi$
$402$	−19.8805	−	14.3051i	−0.991549	−	0.713472i
$403$	4.91127			0.244648
$404$			16.0733i			0.799678i
$405$	8.91354	+	1.24448i	0.442918	+	0.0618385i
$406$			0.142278i			0.00706115i
$407$	−8.14228	+	21.1135i	−0.403598	+	1.04656i
$408$	1.14664	+	7.03056i	0.0567669	+	0.348065i
$409$	−19.3828	−	19.3828i	−0.958419	−	0.958419i	0.0407505	−	0.999169i	$-0.487025\pi$
$409$	−19.3828	−	19.3828i	−0.958419	−	0.958419i	−0.999169	+	0.0407505i	$0.987025\pi$
$410$	−9.94709			−0.491252
$411$	0.608264	+	3.72955i	0.0300035	+	0.183965i
$412$	−6.58533	+	6.58533i	−0.324436	+	0.324436i
$413$	−2.26772	−	2.26772i	−0.111587	−	0.111587i
$414$	−26.0908	+	8.74301i	−1.28229	+	0.429696i
$415$	−6.83285	+	6.83285i	−0.335411	+	0.335411i
$416$		−	0.829235i		−	0.0406566i
$417$	1.05115	+	6.44510i	0.0514751	+	0.315618i
$418$		−	15.8040i		−	0.773000i
$419$			24.4184i			1.19292i	0.802643	+	0.596459i	$0.203426\pi$
$419$			24.4184i			1.19292i	−0.802643	+	0.596459i	$0.796574\pi$
$420$	−0.352082	+	0.489306i	−0.0171798	+	0.0238757i
$421$	1.06044	+	1.06044i	0.0516825	+	0.0516825i	0.732476	−	0.680793i	$-0.238365\pi$
$421$	1.06044	+	1.06044i	0.0516825	+	0.0516825i	−0.680793	+	0.732476i	$0.738365\pi$
$422$	−11.4628	+	11.4628i	−0.557999	+	0.557999i
$423$	−7.20169	−	21.4912i	−0.350158	−	1.04494i
$424$	0.116079	−	0.116079i	0.00563730	−	0.00563730i
$425$	−2.90814	+	2.90814i	−0.141065	+	0.141065i
$426$	−1.03845	−	0.747217i	−0.0503129	−	0.0362028i
$427$	2.99500	+	2.99500i	0.144938	+	0.144938i
$428$	−9.53842			−0.461057
$429$	−3.12080	+	4.33714i	−0.150674	+	0.209399i
$430$	4.12802	−	4.12802i	0.199071	−	0.199071i
$431$	10.7838	−	10.7838i	0.519437	−	0.519437i	−0.397964	−	0.917401i	$-0.630283\pi$
$431$	10.7838	−	10.7838i	0.519437	−	0.519437i	0.917401	+	0.397964i	$0.130283\pi$
$432$	−4.59688	+	2.42253i	−0.221168	+	0.116554i
$433$	15.8953			0.763879			0.381940	−	0.924187i	$-0.375256\pi$
$433$	15.8953			0.763879			0.381940	+	0.924187i	$0.375256\pi$
$434$	2.06128			0.0989448
$435$	−0.698840	+	0.113976i	−0.0335068	+	0.00546473i
$436$	9.32002	+	9.32002i	0.446348	+	0.446348i
$437$	38.9652			1.86396
$438$	22.3836	+	16.1062i	1.06953	+	0.769584i
$439$	−9.33981	−	9.33981i	−0.445765	−	0.445765i	0.448179	−	0.893944i	$-0.352073\pi$
$439$	−9.33981	−	9.33981i	−0.445765	−	0.445765i	−0.893944	+	0.448179i	$0.852073\pi$
$440$		−	3.72020i		−	0.177354i
$441$	−19.5672	+	6.55697i	−0.931772	+	0.312237i
$442$	−2.41153	+	2.41153i	−0.114705	+	0.114705i
$443$	−9.89122			−0.469946			−0.234973	−	0.972002i	$-0.575500\pi$
$443$	−9.89122			−0.469946			−0.234973	+	0.972002i	$0.575500\pi$
$444$	−10.3120	−	2.15915i	−0.489388	−	0.102469i
$445$	−7.96364			−0.377513
$446$	3.66406	−	3.66406i	0.173498	−	0.173498i
$447$	4.12447	+	25.2891i	0.195081	+	1.19613i
$448$		−	0.348034i		−	0.0164430i
$449$	−6.81279	−	6.81279i	−0.321516	−	0.321516i	0.527833	−	0.849348i	$-0.323005\pi$
$449$	−6.81279	−	6.81279i	−0.321516	−	0.321516i	−0.849348	+	0.527833i	$0.823005\pi$
$450$	−2.68541	−	1.33738i	−0.126591	−	0.0630445i
$451$	−37.0052			−1.74251
$452$	5.27517	+	5.27517i	0.248123	+	0.248123i
$453$	0.657187	+	4.02952i	0.0308773	+	0.189323i
$454$	21.0757			0.989133
$455$	−0.288602			−0.0135299
$456$	7.26209	−	1.18440i	0.340078	−	0.0554644i
$457$	17.0996	−	17.0996i	0.799888	−	0.799888i	−0.183190	−	0.983078i	$-0.558642\pi$
$457$	17.0996	−	17.0996i	0.799888	−	0.799888i	0.983078	+	0.183190i	$0.0586423\pi$
$458$	11.1883	−	11.1883i	0.522796	−	0.522796i
$459$	20.4134	+	6.32332i	0.952817	+	0.295147i
$460$	9.17224			0.427658
$461$	−0.729355	−	0.729355i	−0.0339694	−	0.0339694i	0.689918	−	0.723887i	$-0.257647\pi$
$461$	−0.729355	−	0.729355i	−0.0339694	−	0.0339694i	−0.723887	+	0.689918i	$0.757647\pi$
$462$	−1.30981	+	1.82032i	−0.0609381	+	0.0846888i
$463$	6.28322	−	6.28322i	0.292006	−	0.292006i	−0.545866	−	0.837872i	$-0.683799\pi$
$463$	6.28322	−	6.28322i	0.292006	−	0.292006i	0.837872	+	0.545866i	$0.183799\pi$
$464$	0.289070	−	0.289070i	0.0134197	−	0.0134197i
$465$	1.65125	+	10.1246i	0.0765748	+	0.469516i
$466$	12.1990	−	12.1990i	0.565109	−	0.565109i
$467$	−8.64673	−	8.64673i	−0.400123	−	0.400123i	0.478153	−	0.878276i	$-0.341306\pi$
$467$	−8.64673	−	8.64673i	−0.400123	−	0.400123i	−0.878276	+	0.478153i	$0.841306\pi$
$468$	−2.22684	−	1.10900i	−0.102936	−	0.0512635i
$469$		−	4.92140i		−	0.227249i
$470$			7.55524i			0.348497i
$471$	−30.0566	+	4.90202i	−1.38493	+	0.225873i
$472$			9.21474i			0.424143i
$473$	15.3570	−	15.3570i	0.706118	−	0.706118i
$474$	2.69860	+	16.5464i	0.123951	+	0.759999i
$475$	3.00391	+	3.00391i	0.137829	+	0.137829i
$476$	−1.01213	+	1.01213i	−0.0463909	+	0.0463909i
$477$	−0.156479	−	0.466961i	−0.00716466	−	0.0213807i
$478$	12.2768			0.561530
$479$	−4.52948	−	4.52948i	−0.206957	−	0.206957i	0.596016	−	0.802973i	$-0.296750\pi$
$479$	−4.52948	−	4.52948i	−0.206957	−	0.206957i	−0.802973	+	0.596016i	$0.796750\pi$
$480$	1.70946	−	0.278802i	0.0780260	−	0.0127255i
$481$	−2.04445	−	4.61113i	−0.0932189	−	0.210250i
$482$			16.5328i			0.753050i
$483$	−4.48803	−	3.22938i	−0.204213	−	0.146942i
$484$		−	2.83989i		−	0.129086i
$485$	15.5876			0.707798
$486$	0.357725	+	15.5844i	0.0162267	+	0.706921i
$487$	3.72320	−	3.72320i	0.168714	−	0.168714i	−0.617700	−	0.786414i	$-0.711935\pi$
$487$	3.72320	−	3.72320i	0.168714	−	0.168714i	0.786414	+	0.617700i	$0.211935\pi$
$488$		−	12.1700i		−	0.550911i
$489$	5.64465	+	4.06162i	0.255260	+	0.183673i
$490$	6.87887			0.310756
$491$			4.21252i			0.190108i	0.995472	+	0.0950542i	$0.0303024\pi$
$491$			4.21252i			0.190108i	−0.995472	+	0.0950542i	$0.969698\pi$
$492$	−2.77327	−	17.0042i	−0.125028	−	0.766608i
$493$	−1.68131			−0.0757223
$494$	2.49094	+	2.49094i	0.112073	+	0.112073i
$495$	−9.99026	−	4.97531i	−0.449029	−	0.223623i
$496$	−4.18795	−	4.18795i	−0.188045	−	0.188045i
$497$		−	0.257067i		−	0.0115310i
$498$	−13.5855	−	9.77550i	−0.608782	−	0.438051i
$499$	14.6597	+	14.6597i	0.656259	+	0.656259i	0.954493	−	0.298234i	$-0.0963975\pi$
$499$	14.6597	+	14.6597i	0.656259	+	0.656259i	−0.298234	+	0.954493i	$0.596398\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$	−17.3762	−	12.5031i	−0.776310	−	0.558596i
$502$		−	7.31340i		−	0.326413i
$503$	−17.8082	−	17.8082i	−0.794028	−	0.794028i	0.188118	−	0.982146i	$-0.439761\pi$
$503$	−17.8082	−	17.8082i	−0.794028	−	0.794028i	−0.982146	+	0.188118i	$0.939761\pi$
$504$	−0.934613	−	0.465452i	−0.0416310	−	0.0207329i
$505$	−11.3656	−	11.3656i	−0.505761	−	0.505761i
$506$	34.1226			1.51693
$507$	3.43271	+	21.0476i	0.152452	+	0.934755i
$508$		−	6.85581i		−	0.304178i
$509$	−29.2452			−1.29627			−0.648136	−	0.761525i	$-0.724451\pi$
$509$	−29.2452			−1.29627			−0.648136	+	0.761525i	$0.724451\pi$
$510$	−5.78215	−	4.16056i	−0.256038	−	0.184233i
$511$			5.54105i			0.245122i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	6.53155	−	21.0857i	0.288375	−	0.930955i
$514$	29.6197			1.30647
$515$		−	9.31307i		−	0.410383i
$516$	8.20760	+	5.90580i	0.361319	+	0.259988i
$517$			28.1070i			1.23615i
$518$	−0.858065	−	1.93531i	−0.0377012	−	0.0850328i
$519$	33.4094	−	5.44883i	1.46651	−	0.239177i
$520$	0.586358	+	0.586358i	0.0257135	+	0.0257135i
$521$	43.3318			1.89840			0.949201	−	0.314670i	$-0.101894\pi$
$521$	43.3318			1.89840			0.949201	+	0.314670i	$0.101894\pi$
$522$	−0.389676	−	1.16287i	−0.0170556	−	0.0508972i
$523$	−28.8478	+	28.8478i	−1.26143	+	1.26143i	−0.311025	+	0.950402i	$0.600672\pi$
$523$	−28.8478	+	28.8478i	−1.26143	+	1.26143i	−0.950402	+	0.311025i	$0.899328\pi$
$524$	3.32864	+	3.32864i	0.145412	+	0.145412i
$525$	−0.0970324	−	0.594951i	−0.00423484	−	0.0259658i
$526$	0.584647	−	0.584647i	0.0254918	−	0.0254918i
$527$			24.3583i			1.06106i
$528$	6.35955	−	1.03720i	0.276764	−	0.0451383i
$529$			61.1299i			2.65782i
$530$			0.164161i			0.00713068i
$531$	24.7453	+	12.3236i	1.07386	+	0.534797i
$532$	1.04546	+	1.04546i	0.0453265	+	0.0453265i
$533$	5.83255	−	5.83255i	0.252636	−	0.252636i
$534$	−2.22028	−	13.6136i	−0.0960808	−	0.589116i
$535$	6.74468	−	6.74468i	0.291598	−	0.291598i
$536$	−9.99891	+	9.99891i	−0.431887	+	0.431887i
$537$	−5.86418	+	8.14975i	−0.253058	+	0.351688i
$538$	16.2557	+	16.2557i	0.700835	+	0.700835i
$539$	25.5908			1.10227
$540$	1.53750	−	4.96348i	0.0661635	−	0.213594i
$541$	−8.31534	+	8.31534i	−0.357504	+	0.357504i	−0.862892	−	0.505388i	$-0.831349\pi$
$541$	−8.31534	+	8.31534i	−0.357504	+	0.357504i	0.505388	+	0.862892i	$0.331349\pi$
$542$	6.06590	−	6.06590i	0.260553	−	0.260553i
$543$	−18.6106	+	3.03526i	−0.798658	+	0.130256i
$544$	4.11273			0.176332
$545$	−13.1805			−0.564591
$546$	−0.0804627	−	0.493354i	−0.00344348	−	0.0211136i
$547$	23.2358	+	23.2358i	0.993489	+	0.993489i	0.999979	−	0.00648976i	$-0.00206577\pi$
$547$	23.2358	+	23.2358i	0.993489	+	0.993489i	−0.00648976	+	0.999979i	$0.502066\pi$
$548$	2.18171			0.0931980
$549$	−32.6815	−	16.2759i	−1.39481	−	0.694638i
$550$	2.63058	+	2.63058i	0.112168	+	0.112168i
$551$			1.73668i			0.0739849i
$552$	2.55724	+	15.6796i	0.108843	+	0.667369i
$553$	−2.38204	+	2.38204i	−0.101294	+	0.101294i
$554$	17.5992			0.747719
$555$	8.81846	−	5.76496i	0.374323	−	0.244709i
$556$	3.77025			0.159894
$557$	12.9487	−	12.9487i	0.548653	−	0.548653i	−0.377398	−	0.926051i	$-0.623181\pi$
$557$	12.9487	−	12.9487i	0.548653	−	0.548653i	0.926051	+	0.377398i	$0.123181\pi$
$558$	−16.8472	+	5.64550i	−0.713200	+	0.238993i
$559$			4.84099i			0.204752i
$560$	0.246097	+	0.246097i	0.0103995	+	0.0103995i
$561$	−21.5108	−	15.4781i	−0.908185	−	0.653487i
$562$	−1.37358			−0.0579410
$563$	−13.8676	−	13.8676i	−0.584452	−	0.584452i	0.351672	−	0.936123i	$-0.385613\pi$
$563$	−13.8676	−	13.8676i	−0.584452	−	0.584452i	−0.936123	+	0.351672i	$0.885613\pi$
$564$	−12.9154	+	2.10642i	−0.543837	+	0.0886961i
$565$	−7.46022			−0.313854
$566$	2.07780			0.0873364
$567$	−2.49986	+	1.88733i	−0.104984	+	0.0792606i
$568$	−0.522287	+	0.522287i	−0.0219147	+	0.0219147i
$569$	−4.33445	+	4.33445i	−0.181710	+	0.181710i	−0.792100	−	0.610391i	$-0.791012\pi$
$569$	−4.33445	+	4.33445i	−0.181710	+	0.181710i	0.610391	+	0.792100i	$0.291012\pi$
$570$	−4.29758	+	5.97257i	−0.180006	+	0.250163i
$571$	−2.93311			−0.122747			−0.0613734	−	0.998115i	$-0.519548\pi$
$571$	−2.93311			−0.122747			−0.0613734	+	0.998115i	$0.519548\pi$
$572$	2.18137	+	2.18137i	0.0912076	+	0.0912076i
$573$	−27.8401	−	20.0324i	−1.16304	−	0.836865i
$574$	2.44795	−	2.44795i	0.102175	−	0.102175i
$575$	−6.48575	+	6.48575i	−0.270475	+	0.270475i
$576$	0.953204	+	2.84454i	0.0397168	+	0.118522i
$577$	9.36579	−	9.36579i	0.389903	−	0.389903i	−0.484750	−	0.874653i	$-0.661089\pi$
$577$	9.36579	−	9.36579i	0.389903	−	0.389903i	0.874653	+	0.484750i	$0.161089\pi$
$578$	0.0604363	+	0.0604363i	0.00251382	+	0.00251382i
$579$	16.7743	−	23.3121i	0.697115	−	0.968817i
$580$			0.408806i			0.0169748i
$581$		−	3.36309i		−	0.139524i
$582$	4.34586	+	26.6465i	0.180142	+	1.10453i
$583$			0.610710i			0.0252930i
$584$	11.2579	−	11.2579i	0.465854	−	0.465854i
$585$	2.35879	−	0.790430i	0.0975240	−	0.0326803i
$586$	−1.23113	−	1.23113i	−0.0508573	−	0.0508573i
$587$	−18.1736	+	18.1736i	−0.750105	+	0.750105i	−0.974499	−	0.224394i	$-0.927960\pi$
$587$	−18.1736	+	18.1736i	−0.750105	+	0.750105i	0.224394	+	0.974499i	$0.427960\pi$
$588$	1.91784	+	11.7592i	0.0790905	+	0.484941i
$589$	25.1604			1.03672
$590$	−6.51580	−	6.51580i	−0.268251	−	0.268251i
$591$	−0.386673	−	2.37087i	−0.0159056	−	0.0975247i
$592$	−2.18867	+	5.67536i	−0.0899537	+	0.233256i
$593$			43.6579i			1.79282i	0.443229	+	0.896408i	$0.353833\pi$
$593$			43.6579i			1.79282i	−0.443229	+	0.896408i	$0.646167\pi$
$594$	5.71981	−	18.4651i	0.234687	−	0.757633i
$595$		−	1.43137i		−	0.0586803i
$596$	14.7936			0.605968
$597$	25.7381	+	18.5199i	1.05339	+	0.757970i
$598$	−5.37821	+	5.37821i	−0.219931	+	0.219931i
$599$			10.4813i			0.428254i	0.976806	+	0.214127i	$0.0686907\pi$
$599$			10.4813i			0.428254i	−0.976806	+	0.214127i	$0.931309\pi$
$600$	−1.01163	+	1.40592i	−0.0412997	+	0.0573963i
$601$	31.5992			1.28896			0.644480	−	0.764621i	$-0.277074\pi$
$601$	31.5992			1.28896			0.644480	+	0.764621i	$0.277074\pi$
$602$			2.03178i			0.0828093i
$603$	13.4789	+	40.2235i	0.548902	+	1.63803i
$604$	2.35718			0.0959124
$605$	2.00811	+	2.00811i	0.0816412	+	0.0816412i
$606$	16.2603	−	22.5978i	0.660529	−	0.917972i
$607$	14.2922	+	14.2922i	0.580101	+	0.580101i	0.934931	−	0.354830i	$-0.115461\pi$
$607$	14.2922	+	14.2922i	0.580101	+	0.580101i	−0.354830	+	0.934931i	$0.615461\pi$
$608$		−	4.24816i		−	0.172286i
$609$	0.143933	−	0.200031i	0.00583247	−	0.00810568i
$610$	8.60550	+	8.60550i	0.348426	+	0.348426i
$611$	−4.43008	−	4.43008i	−0.179222	−	0.179222i
$612$	5.50026	−	11.0444i	0.222335	−	0.446442i
$613$		−	0.137392i		−	0.00554922i	−0.999996	−	0.00277461i	$-0.999117\pi$
$613$		−	0.137392i		−	0.00554922i	0.999996	−	0.00277461i	$-0.000883187\pi$
$614$	6.67084	+	6.67084i	0.269213	+	0.269213i
$615$	13.9848	+	10.0628i	0.563921	+	0.405771i
$616$	0.915530	+	0.915530i	0.0368878	+	0.0368878i
$617$	−28.1830			−1.13461			−0.567303	−	0.823509i	$-0.692013\pi$
$617$	−28.1830			−1.13461			−0.567303	+	0.823509i	$0.692013\pi$
$618$	15.9204	−	2.59650i	0.640411	−	0.104447i
$619$			19.2838i			0.775080i	0.921853	+	0.387540i	$0.126675\pi$
$619$			19.2838i			0.775080i	−0.921853	+	0.387540i	$0.873325\pi$
$620$	5.92266			0.237860
$621$	45.5262	+	14.1023i	1.82690	+	0.565906i
$622$		−	24.6758i		−	0.989408i
$623$	1.95983	−	1.95983i	0.0785188	−	0.0785188i
$624$	−0.838880	+	1.16584i	−0.0335821	+	0.0466708i
$625$	−1.00000			−0.0400000
$626$			10.7714i			0.430514i
$627$	−15.9878	+	22.2191i	−0.638493	+	0.887347i
$628$			17.5824i			0.701616i
$629$	22.8697	−	10.1398i	0.911874	−	0.404300i
$630$	0.989995	−	0.331747i	0.0394424	−	0.0132171i
$631$	−1.01625	−	1.01625i	−0.0404564	−	0.0404564i	0.686589	−	0.727046i	$-0.259107\pi$
$631$	−1.01625	−	1.01625i	−0.0404564	−	0.0404564i	−0.727046	+	0.686589i	$0.759107\pi$
$632$	9.67926			0.385020
$633$	27.7118	−	4.51961i	1.10145	−	0.179638i
$634$	14.5021	−	14.5021i	0.575951	−	0.575951i
$635$	4.84779	+	4.84779i	0.192379	+	0.192379i
$636$	−0.280627	+	0.0457683i	−0.0111276	+	0.00181483i
$637$	−4.03348	+	4.03348i	−0.159812	+	0.159812i
$638$			1.52084i			0.0602107i
$639$	0.704061	+	2.10105i	0.0278522	+	0.0831162i
$640$		−	1.00000i		−	0.0395285i
$641$		−	15.8819i		−	0.627297i	−0.949539	−	0.313648i	$-0.898449\pi$
$641$		−	15.8819i		−	0.627297i	0.949539	−	0.313648i	$-0.101551\pi$
$642$	13.4102	+	9.64937i	0.529259	+	0.380830i
$643$	29.9979	+	29.9979i	1.18300	+	1.18300i	0.978963	+	0.204037i	$0.0654064\pi$
$643$	29.9979	+	29.9979i	1.18300	+	1.18300i	0.204037	+	0.978963i	$0.434594\pi$
$644$	−2.25726	+	2.25726i	−0.0889485	+	0.0889485i
$645$	−9.97968	+	1.62762i	−0.392949	+	0.0640873i
$646$	−12.3542	+	12.3542i	−0.486071	+	0.486071i
$647$	−2.08271	+	2.08271i	−0.0818800	+	0.0818800i	−0.746861	−	0.664981i	$-0.768440\pi$
$647$	−2.08271	+	2.08271i	−0.0818800	+	0.0818800i	0.664981	+	0.746861i	$0.268440\pi$
$648$	8.91354	+	1.24448i	0.350157	+	0.0488876i
$649$	−24.2401	−	24.2401i	−0.951507	−	0.951507i
$650$	−0.829235			−0.0325253
$651$	−2.89799	−	2.08526i	−0.113581	−	0.0817277i
$652$	2.83898	−	2.83898i	0.111183	−	0.111183i
$653$	18.6146	−	18.6146i	0.728447	−	0.728447i	−0.241863	−	0.970310i	$-0.577759\pi$
$653$	18.6146	−	18.6146i	0.728447	−	0.728447i	0.970310	+	0.241863i	$0.0777586\pi$
$654$	−3.67475	−	22.5316i	−0.143694	−	0.881056i
$655$	−4.70740			−0.183933
$656$	−9.94709			−0.388369
$657$	−15.1760	−	45.2880i	−0.592071	−	1.76685i
$658$	−1.85932	−	1.85932i	−0.0724839	−	0.0724839i
$659$	6.86347			0.267363			0.133681	−	0.991024i	$-0.457320\pi$
$659$	6.86347			0.267363			0.133681	+	0.991024i	$0.457320\pi$
$660$	−3.76347	+	5.23029i	−0.146493	+	0.203589i
$661$	−20.0138	−	20.0138i	−0.778446	−	0.778446i	0.201121	−	0.979566i	$-0.435542\pi$
$661$	−20.0138	−	20.0138i	−0.778446	−	0.778446i	−0.979566	+	0.201121i	$0.935542\pi$
$662$		−	1.93815i		−	0.0753283i
$663$	5.82999	−	0.950831i	0.226418	−	0.0369272i
$664$	−6.83285	+	6.83285i	−0.265166	+	0.265166i
$665$	−1.47850			−0.0573339
$666$	12.3136	+	13.4676i	0.477142	+	0.521857i
$667$	−3.74967			−0.145188
$668$	−8.73935	+	8.73935i	−0.338136	+	0.338136i
$669$	−8.85804	+	1.44469i	−0.342472	+	0.0558548i
$670$		−	14.1406i		−	0.546299i
$671$	32.0142	+	32.0142i	1.23589	+	1.23589i
$672$	−0.352082	+	0.489306i	−0.0135818	+	0.0188754i
$673$	37.7218			1.45407			0.727034	−	0.686601i	$-0.240898\pi$
$673$	37.7218			1.45407			0.727034	+	0.686601i	$0.240898\pi$
$674$	23.7173	+	23.7173i	0.913557	+	0.913557i
$675$	2.42253	+	4.59688i	0.0932433	+	0.176934i
$676$	12.3124			0.473553
$677$	−26.3889			−1.01421			−0.507104	−	0.861885i	$-0.669284\pi$
$677$	−26.3889			−1.01421			−0.507104	+	0.861885i	$0.669284\pi$
$678$	−2.07992	−	12.7530i	−0.0798790	−	0.489775i
$679$	−3.83607	+	3.83607i	−0.147215	+	0.147215i
$680$	−2.90814	+	2.90814i	−0.111522	+	0.111522i
$681$	−29.6307	−	21.3209i	−1.13545	−	0.817017i
$682$	22.0335			0.843705
$683$	30.4848	+	30.4848i	1.16647	+	1.16647i	0.983032	+	0.183435i	$0.0587218\pi$
$683$	30.4848	+	30.4848i	1.16647	+	1.16647i	0.183435	+	0.983032i	$0.441278\pi$
$684$	−11.4081	−	5.68139i	−0.436198	−	0.217234i
$685$	−1.54270	+	1.54270i	−0.0589436	+	0.0589436i
$686$	−3.41555	+	3.41555i	−0.130406	+	0.130406i
$687$	−27.0483	+	4.41140i	−1.03196	+	0.168305i
$688$	4.12802	−	4.12802i	0.157379	−	0.157379i
$689$	−0.0962569	−	0.0962569i	−0.00366709	−	0.00366709i
$690$	−12.8954	−	9.27892i	−0.490920	−	0.353243i
$691$		−	14.1593i		−	0.538646i	−0.963050	−	0.269323i	$-0.913200\pi$
$691$		−	14.1593i		−	0.538646i	0.963050	−	0.269323i	$-0.0867998\pi$
$692$		−	19.5438i		−	0.742942i
$693$	3.68298	−	1.23417i	0.139905	−	0.0468821i
$694$			20.1922i			0.766484i
$695$	−2.66597	+	2.66597i	−0.101126	+	0.101126i
$696$	−0.698840	+	0.113976i	−0.0264895	+	0.00432025i
$697$	28.9275	+	28.9275i	1.09571	+	1.09571i
$698$	−4.63882	+	4.63882i	−0.175582	+	0.175582i
$699$	−29.4917	+	4.80990i	−1.11548	+	0.181927i
$700$	−0.348034			−0.0131544
$701$	−18.6242	−	18.6242i	−0.703428	−	0.703428i	0.261717	−	0.965145i	$-0.415711\pi$
$701$	−18.6242	−	18.6242i	−0.703428	−	0.703428i	−0.965145	+	0.261717i	$0.915711\pi$
$702$	2.00885	+	3.81190i	0.0758191	+	0.143871i
$703$	−10.4737	−	23.6228i	−0.395023	−	0.890951i
$704$		−	3.72020i		−	0.140210i
$705$	7.64312	−	10.6220i	0.287857	−	0.400049i
$706$			36.2497i			1.36427i
$707$	5.59406			0.210386
$708$	9.32192	−	12.9552i	0.350339	−	0.486885i
$709$	16.5635	−	16.5635i	0.622054	−	0.622054i	−0.324002	−	0.946056i	$-0.605029\pi$
$709$	16.5635	−	16.5635i	0.622054	−	0.622054i	0.946056	+	0.324002i	$0.105029\pi$
$710$		−	0.738626i		−	0.0277201i
$711$	12.9448	−	25.9928i	0.485468	−	0.974805i
$712$	−7.96364			−0.298450
$713$			54.3240i			2.03445i
$714$	2.44687	−	0.399068i	0.0915719	−	0.0149347i
$715$	−3.08492			−0.115370
$716$	4.09892	+	4.09892i	0.153184	+	0.153184i
$717$	−17.2602	−	12.4196i	−0.644595	−	0.463820i
$718$	−13.1326	−	13.1326i	−0.490104	−	0.490104i
$719$		−	12.6073i		−	0.470174i	−0.971974	−	0.235087i	$-0.924462\pi$
$719$		−	12.6073i		−	0.470174i	0.971974	−	0.235087i	$-0.0755376\pi$
$720$	−2.68541	−	1.33738i	−0.100079	−	0.0498411i
$721$	2.29192	+	2.29192i	0.0853555	+	0.0853555i
$722$	−0.673942	−	0.673942i	−0.0250815	−	0.0250815i
$723$	16.7251	−	23.2438i	0.622014	−	0.864446i
$724$			10.8868i			0.404605i
$725$	−0.289070	−	0.289070i	−0.0107358	−	0.0107358i
$726$	−2.87292	+	3.99265i	−0.106624	+	0.148181i
$727$	−16.6603	−	16.6603i	−0.617895	−	0.617895i	0.327096	−	0.944991i	$-0.393930\pi$
$727$	−16.6603	−	16.6603i	−0.617895	−	0.617895i	−0.944991	+	0.327096i	$0.893930\pi$
$728$	−0.288602			−0.0106963
$729$	15.2627	−	22.2722i	0.565285	−	0.824896i
$730$			15.9210i			0.589263i
$731$	−24.0097			−0.888030
$732$	−12.3116	+	17.1100i	−0.455049	+	0.632405i
$733$		−	19.0725i		−	0.704460i	−0.935913	−	0.352230i	$-0.885423\pi$
$733$		−	19.0725i		−	0.704460i	0.935913	−	0.352230i	$-0.114577\pi$
$734$	7.70642	−	7.70642i	0.284449	−	0.284449i
$735$	−9.67112	−	6.95888i	−0.356725	−	0.256682i
$736$	9.17224			0.338093
$737$		−	52.6058i		−	1.93776i
$738$	−13.3030	+	26.7120i	−0.489690	+	0.983283i
$739$		−	39.6325i		−	1.45791i	−0.684563	−	0.728953i	$-0.740007\pi$
$739$		−	39.6325i		−	1.45791i	0.684563	−	0.728953i	$-0.259993\pi$
$740$	−2.46547	−	5.56071i	−0.0906323	−	0.204416i
$741$	−0.982143	−	6.02198i	−0.0360799	−	0.221223i
$742$	−0.0403994	−	0.0403994i	−0.00148311	−	0.00148311i
$743$	4.80447			0.176259			0.0881295	−	0.996109i	$-0.471911\pi$
$743$	4.80447			0.176259			0.0881295	+	0.996109i	$0.471911\pi$
$744$	1.65125	+	10.1246i	0.0605377	+	0.371185i
$745$	−10.4606	+	10.4606i	−0.383248	+	0.383248i
$746$	−19.4847	−	19.4847i	−0.713385	−	0.713385i
$747$	9.21091	+	27.4871i	0.337010	+	1.00570i
$748$	−10.8189	+	10.8189i	−0.395577	+	0.395577i
$749$			3.31969i			0.121299i
$750$	−0.278802	−	1.70946i	−0.0101804	−	0.0624208i
$751$			4.63856i			0.169264i	0.996412	+	0.0846318i	$0.0269714\pi$
$751$			4.63856i			0.169264i	−0.996412	+	0.0846318i	$0.973029\pi$
$752$			7.55524i			0.275511i
$753$	−7.39847	+	10.2820i	−0.269615	+	0.374698i
$754$	−0.239707	−	0.239707i	−0.00872960	−	0.00872960i
$755$	−1.66678	+	1.66678i	−0.0606603	+	0.0606603i
$756$	0.843122	+	1.59987i	0.0306641	+	0.0581867i
$757$	−24.2357	+	24.2357i	−0.880861	+	0.880861i	−0.993622	−	0.112761i	$-0.964030\pi$
$757$	−24.2357	+	24.2357i	−0.880861	+	0.880861i	0.112761	+	0.993622i	$0.464030\pi$
$758$	−3.70616	+	3.70616i	−0.134614	+	0.134614i
$759$	−47.9735	−	34.5195i	−1.74133	−	1.25298i
$760$	3.00391	+	3.00391i	0.108963	+	0.108963i
$761$	1.10162			0.0399339			0.0199669	−	0.999801i	$-0.493644\pi$
$761$	1.10162			0.0399339			0.0199669	+	0.999801i	$0.493644\pi$
$762$	−6.93556	+	9.63870i	−0.251249	+	0.349173i
$763$	3.24368	−	3.24368i	0.117429	−	0.117429i
$764$	−14.0022	+	14.0022i	−0.506581	+	0.506581i
$765$	3.92027	+	11.6988i	0.141738	+	0.422972i
$766$	−28.4065			−1.02637
$767$	7.64119			0.275907
$768$	1.70946	−	0.278802i	0.0616850	−	0.0100604i
$769$	−4.38921	−	4.38921i	−0.158279	−	0.158279i	0.623525	−	0.781804i	$-0.285700\pi$
$769$	−4.38921	−	4.38921i	−0.158279	−	0.158279i	−0.781804	+	0.623525i	$0.785700\pi$
$770$	−1.29475			−0.0466597
$771$	−41.6428	−	29.9642i	−1.49973	−	1.07913i
$772$	−11.7248	−	11.7248i	−0.421986	−	0.421986i
$773$			36.7986i			1.32355i	0.749701	+	0.661777i	$0.230197\pi$
$773$			36.7986i			1.32355i	−0.749701	+	0.661777i	$0.769803\pi$
$774$	−5.56470	−	16.6061i	−0.200019	−	0.596895i
$775$	−4.18795	+	4.18795i	−0.150436	+	0.150436i
$776$	15.5876			0.559563
$777$	−0.751456	+	3.58894i	−0.0269583	+	0.128752i
$778$	−8.40919			−0.301484
$779$	29.8801	−	29.8801i	1.07057	−	1.07057i
$780$	−0.231192	−	1.41755i	−0.00827801	−	0.0507564i
$781$		−	2.74784i		−	0.0983253i
$782$	−26.6741	−	26.6741i	−0.953865	−	0.953865i
$783$	−0.628540	+	2.02910i	−0.0224622	+	0.0725141i
$784$	6.87887			0.245674
$785$	−12.4327	−	12.4327i	−0.443741	−	0.443741i
$786$	−1.31243	−	8.04714i	−0.0468129	−	0.287032i
$787$	2.73413			0.0974614			0.0487307	−	0.998812i	$-0.484482\pi$
$787$	2.73413			0.0974614			0.0487307	+	0.998812i	$0.484482\pi$
$788$	−1.38691			−0.0494066
$789$	−1.41341	+	0.230518i	−0.0503188	+	0.00820665i
$790$	−6.84427	+	6.84427i	−0.243508	+	0.243508i
$791$	1.83594	−	1.83594i	0.0652784	−	0.0652784i
$792$	−9.99026	−	4.97531i	−0.354989	−	0.176790i
$793$	−10.0918			−0.358370
$794$	−8.96674	−	8.96674i	−0.318218	−	0.318218i
$795$	0.166070	−	0.230796i	0.00588990	−	0.00818550i
$796$	12.9450	−	12.9450i	0.458823	−	0.458823i
$797$	9.60816	−	9.60816i	0.340338	−	0.340338i	−0.516156	−	0.856495i	$-0.672638\pi$
$797$	9.60816	−	9.60816i	0.340338	−	0.340338i	0.856495	+	0.516156i	$0.172638\pi$
$798$	−0.412210	−	2.52745i	−0.0145921	−	0.0894708i
$799$	21.9717	−	21.9717i	0.777302	−	0.777302i
$800$	0.707107	+	0.707107i	0.0250000	+	0.0250000i
$801$	−10.6504	+	21.3856i	−0.376313	+	0.755624i
$802$		−	30.9227i		−	1.09192i
$803$			59.2294i			2.09016i
$804$	24.1728	−	3.94242i	0.852511	−	0.139039i
$805$		−	3.19225i		−	0.112512i
$806$	−3.47280	+	3.47280i	−0.122324	+	0.122324i
$807$	−6.40940	−	39.2991i	−0.225622	−	1.38339i
$808$	−11.3656	−	11.3656i	−0.399839	−	0.399839i
$809$	−15.3138	+	15.3138i	−0.538405	+	0.538405i	−0.923060	−	0.384656i	$-0.874320\pi$
$809$	−15.3138	+	15.3138i	−0.538405	+	0.538405i	0.384656	+	0.923060i	$0.374320\pi$
$810$	−7.18281	+	5.42285i	−0.252378	+	0.190540i
$811$	−8.02200			−0.281690			−0.140845	−	0.990032i	$-0.544982\pi$
$811$	−8.02200			−0.281690			−0.140845	+	0.990032i	$0.544982\pi$
$812$	−0.100606	−	0.100606i	−0.00353058	−	0.00353058i
$813$	−14.6646	+	2.39169i	−0.514310	+	0.0838804i
$814$	−9.17203	−	20.6870i	−0.321479	−	0.725077i
$815$			4.01492i			0.140637i
$816$	−5.78215	−	4.16056i	−0.202416	−	0.145649i
$817$			24.8003i			0.867654i
$818$	27.4114			0.958419
$819$	−0.385969	+	0.775014i	−0.0134868	+	0.0270812i
$820$	7.03365	−	7.03365i	0.245626	−	0.245626i
$821$		−	17.6701i		−	0.616691i	−0.951274	−	0.308346i	$-0.900225\pi$
$821$		−	17.6701i		−	0.616691i	0.951274	−	0.308346i	$-0.0997753\pi$
$822$	−3.06730	−	2.20708i	−0.106984	−	0.0769809i
$823$	−47.3923			−1.65199			−0.825996	−	0.563676i	$-0.809387\pi$
$823$	−47.3923			−1.65199			−0.825996	+	0.563676i	$0.809387\pi$
$824$		−	9.31307i		−	0.324436i
$825$	−1.03720	−	6.35955i	−0.0361106	−	0.221411i
$826$	3.20704			0.111587
$827$	23.8439	+	23.8439i	0.829133	+	0.829133i	0.987397	−	0.158264i	$-0.0505896\pi$
$827$	23.8439	+	23.8439i	0.829133	+	0.829133i	−0.158264	+	0.987397i	$0.550590\pi$
$828$	12.2667	−	24.6312i	0.426298	−	0.855994i
$829$	−18.4809	−	18.4809i	−0.641867	−	0.641867i	0.309147	−	0.951014i	$-0.399956\pi$
$829$	−18.4809	−	18.4809i	−0.641867	−	0.641867i	−0.951014	+	0.309147i	$0.899956\pi$
$830$		−	9.66311i		−	0.335411i
$831$	−24.7430	−	17.8039i	−0.858326	−	0.617611i
$832$	0.586358	+	0.586358i	0.0203283	+	0.0203283i
$833$	−20.0047	−	20.0047i	−0.693122	−	0.693122i
$834$	−5.30065	−	3.81410i	−0.183547	−	0.132072i
$835$		−	12.3593i		−	0.427712i
$836$	11.1751	+	11.1751i	0.386500	+	0.386500i
$837$	29.3970	+	9.10608i	1.01611	+	0.314752i
$838$	−17.2664	−	17.2664i	−0.596459	−	0.596459i
$839$	33.1366			1.14400			0.572000	−	0.820253i	$-0.306168\pi$
$839$	33.1366			1.14400			0.572000	+	0.820253i	$0.306168\pi$
$840$	−0.0970324	−	0.594951i	−0.00334794	−	0.0205278i
$841$			28.8329i			0.994237i
$842$	−1.49968			−0.0516825
$843$	1.93114	+	1.38956i	0.0665120	+	0.0478589i
$844$		−	16.2108i		−	0.557999i
$845$	−8.70616	+	8.70616i	−0.299501	+	0.299501i
$846$	20.2889	+	10.1042i	0.697548	+	0.347390i
$847$	−0.988378			−0.0339611
$848$			0.164161i			0.00563730i
$849$	−2.92121	−	2.10197i	−0.100256	−	0.0721393i
$850$		−	4.11273i		−	0.141065i
$851$	51.0041	−	22.6138i	1.74840	−	0.775192i
$852$	1.26265	−	0.205930i	0.0432578	−	0.00705505i
$853$	−3.14167	−	3.14167i	−0.107569	−	0.107569i	0.651274	−	0.758843i	$-0.274235\pi$
$853$	−3.14167	−	3.14167i	−0.107569	−	0.107569i	−0.758843	+	0.651274i	$0.774235\pi$
$854$	−4.23557			−0.144938
$855$	12.0841	−	4.04937i	0.413266	−	0.138485i
$856$	6.74468	−	6.74468i	0.230528	−	0.230528i
$857$	−6.44238	−	6.44238i	−0.220067	−	0.220067i	0.588459	−	0.808527i	$-0.299735\pi$
$857$	−6.44238	−	6.44238i	−0.220067	−	0.220067i	−0.808527	+	0.588459i	$0.799735\pi$
$858$	−0.860082	−	5.27356i	−0.0293627	−	0.180036i
$859$	7.97483	−	7.97483i	0.272098	−	0.272098i	−0.557846	−	0.829944i	$-0.688372\pi$
$859$	7.97483	−	7.97483i	0.272098	−	0.272098i	0.829944	+	0.557846i	$0.188372\pi$
$860$			5.83790i			0.199071i
$861$	−5.91803	+	0.965190i	−0.201686	+	0.0328936i
$862$			15.2506i			0.519437i
$863$			13.3993i			0.456119i	0.973647	+	0.228060i	$0.0732381\pi$
$863$			13.3993i			0.456119i	−0.973647	+	0.228060i	$0.926762\pi$
$864$	1.53750	−	4.96348i	0.0523068	−	0.168861i
$865$	13.8195	+	13.8195i	0.469878	+	0.469878i
$866$	−11.2397	+	11.2397i	−0.381940	+	0.381940i
$867$	−0.0238291	−	0.146108i	−0.000809280	−	0.00496207i
$868$	−1.45755	+	1.45755i	−0.0494724	+	0.0494724i
$869$	−25.4621	+	25.4621i	−0.863741	+	0.863741i
$870$	0.413561	−	0.574747i	0.0140210	−	0.0194858i
$871$	8.29145	+	8.29145i	0.280945	+	0.280945i
$872$	−13.1805			−0.446348
$873$	20.8465	−	41.8592i	0.705548	−	1.41672i
$874$	−27.5525	+	27.5525i	−0.931979	+	0.931979i
$875$	0.246097	−	0.246097i	0.00831959	−	0.00831959i
$876$	−27.2164	+	4.43881i	−0.919558	+	0.149973i
$877$	26.2075			0.884965			0.442483	−	0.896777i	$-0.354098\pi$
$877$	26.2075			0.884965			0.442483	+	0.896777i	$0.354098\pi$
$878$	13.2085			0.445765
$879$	0.485415	+	2.97630i	0.0163726	+	0.100388i
$880$	2.63058	+	2.63058i	0.0886768	+	0.0886768i
$881$	−16.8777			−0.568623			−0.284312	−	0.958732i	$-0.591765\pi$
$881$	−16.8777			−0.568623			−0.284312	+	0.958732i	$0.591765\pi$
$882$	9.19964	−	18.4726i	0.309768	−	0.622004i
$883$	38.5237	+	38.5237i	1.29643	+	1.29643i	0.930737	+	0.365690i	$0.119167\pi$
$883$	38.5237	+	38.5237i	1.29643	+	1.29643i	0.365690	+	0.930737i	$0.380833\pi$
$884$		−	3.41042i		−	0.114705i
$885$	2.56909	+	15.7523i	0.0863589	+	0.529507i
$886$	6.99415	−	6.99415i	0.234973	−	0.234973i
$887$	−30.2782			−1.01664			−0.508321	−	0.861168i	$-0.669734\pi$
$887$	−30.2782			−1.01664			−0.508321	+	0.861168i	$0.669734\pi$
$888$	8.81846	−	5.76496i	0.295928	−	0.193459i
$889$	−2.38605			−0.0800257
$890$	5.63114	−	5.63114i	0.188756	−	0.188756i
$891$	−26.7215	+	20.1741i	−0.895203	+	0.675857i
$892$			5.18177i			0.173498i
$893$	−22.6952	−	22.6952i	−0.759467	−	0.759467i
$894$	−20.7985	−	14.9656i	−0.695606	−	0.500525i
$895$	−5.79675			−0.193764
$896$	0.246097	+	0.246097i	0.00822152	+	0.00822152i
$897$	13.0021	−	2.12055i	0.434127	−	0.0708031i
$898$	9.63475			0.321516
$899$	−2.42122			−0.0807522
$900$	2.84454	−	0.953204i	0.0948180	−	0.0317735i
$901$	0.477402	−	0.477402i	0.0159046	−	0.0159046i
$902$	26.1666	−	26.1666i	0.871253	−	0.871253i
$903$	2.05542	−	2.85652i	0.0684000	−	0.0950590i
$904$	−7.46022			−0.248123
$905$	−7.69814	−	7.69814i	−0.255895	−	0.255895i
$906$	−3.31400	−	2.38460i	−0.110100	−	0.0792230i
$907$	32.4218	−	32.4218i	1.07655	−	1.07655i	0.0797310	−	0.996816i	$-0.474594\pi$
$907$	32.4218	−	32.4218i	1.07655	−	1.07655i	0.996816	−	0.0797310i	$-0.0254061\pi$
$908$	−14.9028	+	14.9028i	−0.494566	+	0.494566i
$909$	−45.7212	+	15.3212i	−1.51648	+	0.508171i
$910$	0.204072	−	0.204072i	0.00676493	−	0.00676493i
$911$	−4.77098	−	4.77098i	−0.158069	−	0.158069i	0.623641	−	0.781711i	$-0.285653\pi$
$911$	−4.77098	−	4.77098i	−0.158069	−	0.158069i	−0.781711	+	0.623641i	$0.785653\pi$
$912$	−4.29758	+	5.97257i	−0.142307	+	0.197771i
$913$		−	35.9487i		−	1.18973i
$914$			24.1826i			0.799888i
$915$	−3.39302	−	20.8042i	−0.112170	−	0.687766i
$916$			15.8227i			0.522796i
$917$	1.15848	−	1.15848i	0.0382563	−	0.0382563i
$918$	−18.9057	+	9.96321i	−0.623982	+	0.328835i
$919$	−41.5937	−	41.5937i	−1.37205	−	1.37205i	−0.857400	−	0.514651i	$-0.827922\pi$
$919$	−41.5937	−	41.5937i	−1.37205	−	1.37205i	−0.514651	−	0.857400i	$-0.672078\pi$
$920$	−6.48575	+	6.48575i	−0.213829	+	0.213829i
$921$	−2.63022	−	16.1271i	−0.0866685	−	0.531406i
$922$	1.03146			0.0339694
$923$	0.433099	+	0.433099i	0.0142556	+	0.0142556i
$924$	−0.360980	−	2.21334i	−0.0118754	−	0.0728135i
$925$	5.67536	+	2.18867i	0.186605	+	0.0719629i
$926$			8.88581i			0.292006i
$927$	−25.0094	−	12.4551i	−0.821417	−	0.409078i
$928$			0.408806i			0.0134197i
$929$	26.8594			0.881228			0.440614	−	0.897697i	$-0.354761\pi$
$929$	26.8594			0.881228			0.440614	+	0.897697i	$0.354761\pi$
$930$	−8.32676	−	5.99154i	−0.273045	−	0.196470i
$931$	−20.6635	+	20.6635i	−0.677218	+	0.677218i
$932$			17.2520i			0.565109i
$933$	−24.9628	+	34.6921i	−0.817244	+	1.13577i
$934$	12.2283			0.400123
$935$		−	15.3002i		−	0.500369i
$936$	2.35879	−	0.790430i	0.0770995	−	0.0258360i
$937$	−2.71379			−0.0886557			−0.0443278	−	0.999017i	$-0.514115\pi$
$937$	−2.71379			−0.0886557			−0.0443278	+	0.999017i	$0.514115\pi$
$938$	3.47996	+	3.47996i	0.113625	+	0.113625i
$939$	10.8967	−	15.1438i	0.355602	−	0.494198i
$940$	−5.34236	−	5.34236i	−0.174249	−	0.174249i
$941$		−	5.22310i		−	0.170268i	−0.996369	−	0.0851342i	$-0.972868\pi$
$941$		−	5.22310i		−	0.170268i	0.996369	−	0.0851342i	$-0.0271319\pi$
$942$	17.7870	−	24.7195i	0.579530	−	0.805403i
$943$	64.5143	+	64.5143i	2.10088	+	2.10088i
$944$	−6.51580	−	6.51580i	−0.212071	−	0.212071i
$945$	−1.72746	−	0.535102i	−0.0561942	−	0.0174069i
$946$			21.7181i			0.706118i
$947$	3.68356	+	3.68356i	0.119700	+	0.119700i	0.764419	−	0.644720i	$-0.223026\pi$
$947$	3.68356	+	3.68356i	0.119700	+	0.119700i	−0.644720	+	0.764419i	$0.723026\pi$
$948$	−13.6082	−	9.79184i	−0.441975	−	0.318024i
$949$	−9.33542	−	9.33542i	−0.303040	−	0.303040i
$950$	−4.24816			−0.137829
$951$	−35.0594	+	5.71795i	−1.13688	+	0.185417i
$952$		−	1.43137i		−	0.0463909i
$953$	−9.01908			−0.292157			−0.146078	−	0.989273i	$-0.546665\pi$
$953$	−9.01908			−0.292157			−0.146078	+	0.989273i	$0.546665\pi$
$954$	0.440839	+	0.219544i	0.0142727	+	0.00710802i
$955$		−	19.8021i		−	0.640780i
$956$	−8.68104	+	8.68104i	−0.280765	+	0.280765i
$957$	1.53853	−	2.13818i	0.0497336	−	0.0691174i
$958$	6.40565			0.206957
$959$		−	0.759308i		−	0.0245193i
$960$	−1.01163	+	1.40592i	−0.0326503	+	0.0453758i
$961$			4.07785i			0.131544i
$962$	4.70621	+	1.81492i	0.151734	+	0.0585153i
$963$	−9.09206	−	27.1324i	−0.292987	−	0.874330i
$964$	−11.6905	−	11.6905i	−0.376525	−	0.376525i
$965$	16.5814			0.533774
$966$	5.45703	−	0.890004i	0.175577	−	0.0286354i
$967$	−8.75126	+	8.75126i	−0.281422	+	0.281422i	−0.833676	−	0.552254i	$-0.813768\pi$
$967$	−8.75126	+	8.75126i	−0.281422	+	0.281422i	0.552254	+	0.833676i	$0.313768\pi$
$968$	2.00811	+	2.00811i	0.0645430	+	0.0645430i
$969$	29.8670	−	4.87110i	0.959466	−	0.156482i
$970$	−11.0221	+	11.0221i	−0.353899	+	0.353899i
$971$		−	35.3826i		−	1.13548i	−0.823208	−	0.567740i	$-0.807818\pi$
$971$		−	35.3826i		−	1.13548i	0.823208	−	0.567740i	$-0.192182\pi$
$972$	−11.2728	−	10.7669i	−0.361574	−	0.345347i
$973$		−	1.31217i		−	0.0420663i
$974$			5.26540i			0.168714i
$975$	1.16584	+	0.838880i	0.0373366	+	0.0268657i
$976$	8.60550	+	8.60550i	0.275455	+	0.275455i
$977$	25.2942	−	25.2942i	0.809232	−	0.809232i	−0.175286	−	0.984518i	$-0.556085\pi$
$977$	25.2942	−	25.2942i	0.809232	−	0.809232i	0.984518	+	0.175286i	$0.0560850\pi$
$978$	−6.86337	+	1.11937i	−0.219466	+	0.0357934i
$979$	20.9490	−	20.9490i	0.669532	−	0.669532i
$980$	−4.86410	+	4.86410i	−0.155378	+	0.155378i
$981$	−17.6273	+	35.3951i	−0.562796	+	1.13008i
$982$	−2.97870	−	2.97870i	−0.0950542	−	0.0950542i
$983$	6.06207			0.193350			0.0966750	−	0.995316i	$-0.469179\pi$
$983$	6.06207			0.193350			0.0966750	+	0.995316i	$0.469179\pi$
$984$	13.9848	+	10.0628i	0.445818	+	0.320790i
$985$	0.980693	−	0.980693i	0.0312475	−	0.0312475i
$986$	1.18886	−	1.18886i	0.0378612	−	0.0378612i
$987$	0.733103	+	4.49500i	0.0233349	+	0.143077i
$988$	−3.52273			−0.112073
$989$	−53.5466			−1.70268
$990$	10.5823	−	3.54611i	0.336326	−	0.112703i
$991$	21.7632	+	21.7632i	0.691331	+	0.691331i	0.962525	−	0.271194i	$-0.0874184\pi$
$991$	21.7632	+	21.7632i	0.691331	+	0.691331i	−0.271194	+	0.962525i	$0.587418\pi$
$992$	5.92266			0.188045
$993$	−1.96069	+	2.72487i	−0.0622207	+	0.0864713i
$994$	0.181774	+	0.181774i	0.00576551	+	0.00576551i
$995$			18.3070i			0.580371i
$996$	16.5187	−	2.69409i	0.523416	−	0.0853656i
$997$	27.2352	−	27.2352i	0.862546	−	0.862546i	−0.129087	−	0.991633i	$-0.541205\pi$
$997$	27.2352	−	27.2352i	0.862546	−	0.862546i	0.991633	+	0.129087i	$0.0412048\pi$
$998$	−20.7320			−0.656259
$999$	−3.68769	−	31.3911i	−0.116673	−	0.993170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.401.7	yes	40
3.2	odd	2	inner	1110.2.u.f.401.13	yes	40
37.6	odd	4	inner	1110.2.u.f.191.13	yes	40
111.80	even	4	inner	1110.2.u.f.191.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.7	✓	40	111.80	even	4	inner
1110.2.u.f.191.13	yes	40	37.6	odd	4	inner
1110.2.u.f.401.7	yes	40	1.1	even	1	trivial
1110.2.u.f.401.13	yes	40	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.70946 - 0.278802i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.01163 + 1.40592i) q^{6} -0.348034 q^{7} +(0.707107 + 0.707107i) q^{8} +(2.84454 - 0.953204i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.70946 - 0.278802i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.01163 + 1.40592i) q^{6} -0.348034 q^{7} +(0.707107 + 0.707107i) q^{8} +(2.84454 - 0.953204i) q^{9} -1.00000 q^{10} -3.72020 q^{11} +(-0.278802 - 1.70946i) q^{12} +(0.586358 - 0.586358i) q^{13} +(0.246097 - 0.246097i) q^{14} +(1.40592 + 1.01163i) q^{15} -1.00000 q^{16} +(2.90814 + 2.90814i) q^{17} +(-1.33738 + 2.68541i) q^{18} +(3.00391 - 3.00391i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-0.594951 + 0.0970324i) q^{21} +(2.63058 - 2.63058i) q^{22} +(6.48575 + 6.48575i) q^{23} +(1.40592 + 1.01163i) q^{24} +1.00000i q^{25} +0.829235i q^{26} +(4.59688 - 2.42253i) q^{27} +0.348034i q^{28} +(-0.289070 + 0.289070i) q^{29} +(-1.70946 + 0.278802i) q^{30} +(4.18795 + 4.18795i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.35955 + 1.03720i) q^{33} -4.11273 q^{34} +(-0.246097 - 0.246097i) q^{35} +(-0.953204 - 2.84454i) q^{36} +(2.18867 - 5.67536i) q^{37} +4.24816i q^{38} +(0.838880 - 1.16584i) q^{39} +1.00000i q^{40} +9.94709 q^{41} +(0.352082 - 0.489306i) q^{42} +(-4.12802 + 4.12802i) q^{43} +3.72020i q^{44} +(2.68541 + 1.33738i) q^{45} -9.17224 q^{46} -7.55524i q^{47} +(-1.70946 + 0.278802i) q^{48} -6.87887 q^{49} +(-0.707107 - 0.707107i) q^{50} +(5.78215 + 4.16056i) q^{51} +(-0.586358 - 0.586358i) q^{52} -0.164161i q^{53} +(-1.53750 + 4.96348i) q^{54} +(-2.63058 - 2.63058i) q^{55} +(-0.246097 - 0.246097i) q^{56} +(4.29758 - 5.97257i) q^{57} -0.408806i q^{58} +(6.51580 + 6.51580i) q^{59} +(1.01163 - 1.40592i) q^{60} +(-8.60550 - 8.60550i) q^{61} -5.92266 q^{62} +(-0.989995 + 0.331747i) q^{63} +1.00000i q^{64} +0.829235 q^{65} +(3.76347 - 5.23029i) q^{66} +14.1406i q^{67} +(2.90814 - 2.90814i) q^{68} +(12.8954 + 9.27892i) q^{69} +0.348034 q^{70} +0.738626i q^{71} +(2.68541 + 1.33738i) q^{72} -15.9210i q^{73} +(2.46547 + 5.56071i) q^{74} +(0.278802 + 1.70946i) q^{75} +(-3.00391 - 3.00391i) q^{76} +1.29475 q^{77} +(0.231192 + 1.41755i) q^{78} +(6.84427 - 6.84427i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(7.18281 - 5.42285i) q^{81} +(-7.03365 + 7.03365i) q^{82} +9.66311i q^{83} +(0.0970324 + 0.594951i) q^{84} +4.11273i q^{85} -5.83790i q^{86} +(-0.413561 + 0.574747i) q^{87} +(-2.63058 - 2.63058i) q^{88} +(-5.63114 + 5.63114i) q^{89} +(-2.84454 + 0.953204i) q^{90} +(-0.204072 + 0.204072i) q^{91} +(6.48575 - 6.48575i) q^{92} +(8.32676 + 5.99154i) q^{93} +(5.34236 + 5.34236i) q^{94} +4.24816 q^{95} +(1.01163 - 1.40592i) q^{96} +(11.0221 - 11.0221i) q^{97} +(4.86410 - 4.86410i) q^{98} +(-10.5823 + 3.54611i) 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	\( 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) \) 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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