LMFDB - Embedded newform 1110.2.l.a.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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([0, 3, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.13
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.a.697.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.45560 + 1.69741i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.764053 + 0.764053i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.45560 + 1.69741i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.764053 + 0.764053i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-1.69741 + 1.45560i) q^{10} -4.86540i q^{11} +(-0.707107 + 0.707107i) q^{12} -4.63243i q^{13} +(-0.764053 - 0.764053i) q^{14} +(2.22952 + 0.170986i) q^{15} +1.00000 q^{16} +5.18001 q^{17} +1.00000 q^{18} +(1.84375 - 1.84375i) q^{19} +(-1.45560 - 1.69741i) q^{20} +1.08053i q^{21} +4.86540 q^{22} -4.72007i q^{23} +(-0.707107 - 0.707107i) q^{24} +(-0.762435 + 4.94153i) q^{25} +4.63243 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.764053 - 0.764053i) q^{28} +(6.46705 + 6.46705i) q^{29} +(-0.170986 + 2.22952i) q^{30} +(1.27858 - 1.27858i) q^{31} +1.00000i q^{32} +(-3.44036 - 3.44036i) q^{33} +5.18001i q^{34} +(-2.40907 - 0.184756i) q^{35} +1.00000i q^{36} +(6.03996 - 0.720368i) q^{37} +(1.84375 + 1.84375i) q^{38} +(-3.27562 - 3.27562i) q^{39} +(1.69741 - 1.45560i) q^{40} -3.55371i q^{41} -1.08053 q^{42} +7.49989i q^{43} +4.86540i q^{44} +(1.69741 - 1.45560i) q^{45} +4.72007 q^{46} +(-8.00838 + 8.00838i) q^{47} +(0.707107 - 0.707107i) q^{48} +5.83245i q^{49} +(-4.94153 - 0.762435i) q^{50} +(3.66282 - 3.66282i) q^{51} +4.63243i q^{52} +(-5.64274 - 5.64274i) q^{53} +(0.707107 - 0.707107i) q^{54} +(8.25861 - 7.08210i) q^{55} +(0.764053 + 0.764053i) q^{56} -2.60746i q^{57} +(-6.46705 + 6.46705i) q^{58} +(0.790336 - 0.790336i) q^{59} +(-2.22952 - 0.170986i) q^{60} +(-5.24494 + 5.24494i) q^{61} +(1.27858 + 1.27858i) q^{62} +(0.764053 + 0.764053i) q^{63} -1.00000 q^{64} +(7.86316 - 6.74298i) q^{65} +(3.44036 - 3.44036i) q^{66} +(0.777747 + 0.777747i) q^{67} -5.18001 q^{68} +(-3.33760 - 3.33760i) q^{69} +(0.184756 - 2.40907i) q^{70} +0.599197 q^{71} -1.00000 q^{72} +(1.07198 - 1.07198i) q^{73} +(0.720368 + 6.03996i) q^{74} +(2.95506 + 4.03331i) q^{75} +(-1.84375 + 1.84375i) q^{76} +(3.71743 + 3.71743i) q^{77} +(3.27562 - 3.27562i) q^{78} +(9.56948 - 9.56948i) q^{79} +(1.45560 + 1.69741i) q^{80} -1.00000 q^{81} +3.55371 q^{82} +(-11.2549 - 11.2549i) q^{83} -1.08053i q^{84} +(7.54004 + 8.79263i) q^{85} -7.49989 q^{86} +9.14579 q^{87} -4.86540 q^{88} +(1.70075 + 1.70075i) q^{89} +(1.45560 + 1.69741i) q^{90} +(3.53942 + 3.53942i) q^{91} +4.72007i q^{92} -1.80819i q^{93} +(-8.00838 - 8.00838i) q^{94} +(5.81338 + 0.445840i) q^{95} +(0.707107 + 0.707107i) q^{96} +6.03720 q^{97} -5.83245 q^{98} -4.86540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	1.45560	+	1.69741i	0.650966	+	0.759107i
$5$	1.45560	+	1.69741i	0.650966	+	0.759107i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−0.764053	+	0.764053i	−0.288785	+	0.288785i	−0.836600	−	0.547815i	$-0.815460\pi$
$7$	−0.764053	+	0.764053i	−0.288785	+	0.288785i	0.547815	+	0.836600i	$0.315460\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−1.69741	+	1.45560i	−0.536770	+	0.460302i
$11$		−	4.86540i		−	1.46697i	−0.679703	−	0.733487i	$-0.737891\pi$
$11$		−	4.86540i		−	1.46697i	0.679703	−	0.733487i	$-0.262109\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$		−	4.63243i		−	1.28481i	−0.766367	−	0.642403i	$-0.777938\pi$
$13$		−	4.63243i		−	1.28481i	0.766367	−	0.642403i	$-0.222062\pi$
$14$	−0.764053	−	0.764053i	−0.204202	−	0.204202i
$15$	2.22952	+	0.170986i	0.575660	+	0.0441484i
$16$	1.00000			0.250000
$17$	5.18001			1.25634			0.628169	−	0.778077i	$-0.283805\pi$
$17$	5.18001			1.25634			0.628169	+	0.778077i	$0.283805\pi$
$18$	1.00000			0.235702
$19$	1.84375	−	1.84375i	0.422986	−	0.422986i	−0.463245	−	0.886230i	$-0.653315\pi$
$19$	1.84375	−	1.84375i	0.422986	−	0.422986i	0.886230	+	0.463245i	$0.153315\pi$
$20$	−1.45560	−	1.69741i	−0.325483	−	0.379554i
$21$			1.08053i			0.235792i
$22$	4.86540			1.03731
$23$		−	4.72007i		−	0.984203i	−0.870538	−	0.492102i	$-0.836229\pi$
$23$		−	4.72007i		−	0.984203i	0.870538	−	0.492102i	$-0.163771\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−0.762435	+	4.94153i	−0.152487	+	0.988305i
$26$	4.63243			0.908494
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	0.764053	−	0.764053i	0.144392	−	0.144392i
$29$	6.46705	+	6.46705i	1.20090	+	1.20090i	0.973893	+	0.227008i	$0.0728943\pi$
$29$	6.46705	+	6.46705i	1.20090	+	1.20090i	0.227008	+	0.973893i	$0.427106\pi$
$30$	−0.170986	+	2.22952i	−0.0312177	+	0.407053i
$31$	1.27858	−	1.27858i	0.229640	−	0.229640i	−0.582902	−	0.812542i	$-0.698083\pi$
$31$	1.27858	−	1.27858i	0.229640	−	0.229640i	0.812542	+	0.582902i	$0.198083\pi$
$32$			1.00000i			0.176777i
$33$	−3.44036	−	3.44036i	−0.598890	−	0.598890i
$34$			5.18001i			0.888364i
$35$	−2.40907	−	0.184756i	−0.407208	−	0.0312295i
$36$			1.00000i			0.166667i
$37$	6.03996	−	0.720368i	0.992963	−	0.118428i
$37$	6.03996	−	0.720368i	0.992963	−	0.118428i
$38$	1.84375	+	1.84375i	0.299096	+	0.299096i
$39$	−3.27562	−	3.27562i	−0.524519	−	0.524519i
$40$	1.69741	−	1.45560i	0.268385	−	0.230151i
$41$		−	3.55371i		−	0.554997i	−0.960726	−	0.277498i	$-0.910495\pi$
$41$		−	3.55371i		−	0.554997i	0.960726	−	0.277498i	$-0.0895053\pi$
$42$	−1.08053			−0.166730
$43$			7.49989i			1.14372i	0.820350	+	0.571861i	$0.193779\pi$
$43$			7.49989i			1.14372i	−0.820350	+	0.571861i	$0.806221\pi$
$44$			4.86540i			0.733487i
$45$	1.69741	−	1.45560i	0.253036	−	0.216989i
$46$	4.72007			0.695937
$47$	−8.00838	+	8.00838i	−1.16814	+	1.16814i	−0.185498	+	0.982645i	$0.559390\pi$
$47$	−8.00838	+	8.00838i	−1.16814	+	1.16814i	−0.982645	+	0.185498i	$0.940610\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			5.83245i			0.833207i
$50$	−4.94153	−	0.762435i	−0.698838	−	0.107825i
$51$	3.66282	−	3.66282i	0.512897	−	0.512897i
$52$			4.63243i			0.642403i
$53$	−5.64274	−	5.64274i	−0.775090	−	0.775090i	0.203902	−	0.978991i	$-0.434638\pi$
$53$	−5.64274	−	5.64274i	−0.775090	−	0.775090i	−0.978991	+	0.203902i	$0.934638\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	8.25861	−	7.08210i	1.11359	−	0.954950i
$56$	0.764053	+	0.764053i	0.102101	+	0.102101i
$57$		−	2.60746i		−	0.345366i
$58$	−6.46705	+	6.46705i	−0.849165	+	0.849165i
$59$	0.790336	−	0.790336i	0.102893	−	0.102893i	−0.653786	−	0.756679i	$-0.726820\pi$
$59$	0.790336	−	0.790336i	0.102893	−	0.102893i	0.756679	+	0.653786i	$0.226820\pi$
$60$	−2.22952	−	0.170986i	−0.287830	−	0.0220742i
$61$	−5.24494	+	5.24494i	−0.671545	+	0.671545i	−0.958072	−	0.286527i	$-0.907499\pi$
$61$	−5.24494	+	5.24494i	−0.671545	+	0.671545i	0.286527	+	0.958072i	$0.407499\pi$
$62$	1.27858	+	1.27858i	0.162380	+	0.162380i
$63$	0.764053	+	0.764053i	0.0962616	+	0.0962616i
$64$	−1.00000			−0.125000
$65$	7.86316	−	6.74298i	0.975304	−	0.836364i
$66$	3.44036	−	3.44036i	0.423479	−	0.423479i
$67$	0.777747	+	0.777747i	0.0950169	+	0.0950169i	0.753017	−	0.658001i	$-0.228598\pi$
$67$	0.777747	+	0.777747i	0.0950169	+	0.0950169i	−0.658001	+	0.753017i	$0.728598\pi$
$68$	−5.18001			−0.628169
$69$	−3.33760	−	3.33760i	−0.401799	−	0.401799i
$70$	0.184756	−	2.40907i	0.0220826	−	0.287939i
$71$	0.599197			0.0711117			0.0355558	−	0.999368i	$-0.488680\pi$
$71$	0.599197			0.0711117			0.0355558	+	0.999368i	$0.488680\pi$
$72$	−1.00000			−0.117851
$73$	1.07198	−	1.07198i	0.125466	−	0.125466i	−0.641586	−	0.767051i	$-0.721723\pi$
$73$	1.07198	−	1.07198i	0.125466	−	0.125466i	0.767051	+	0.641586i	$0.221723\pi$
$74$	0.720368	+	6.03996i	0.0837411	+	0.702131i
$75$	2.95506	+	4.03331i	0.341221	+	0.465727i
$76$	−1.84375	+	1.84375i	−0.211493	+	0.211493i
$77$	3.71743	+	3.71743i	0.423640	+	0.423640i
$78$	3.27562	−	3.27562i	0.370891	−	0.370891i
$79$	9.56948	−	9.56948i	1.07665	−	1.07665i	0.0798429	−	0.996807i	$-0.474558\pi$
$79$	9.56948	−	9.56948i	1.07665	−	1.07665i	0.996807	−	0.0798429i	$-0.0254419\pi$
$80$	1.45560	+	1.69741i	0.162741	+	0.189777i
$81$	−1.00000			−0.111111
$82$	3.55371			0.392442
$83$	−11.2549	−	11.2549i	−1.23538	−	1.23538i	−0.961868	−	0.273513i	$-0.911814\pi$
$83$	−11.2549	−	11.2549i	−1.23538	−	1.23538i	−0.273513	−	0.961868i	$-0.588186\pi$
$84$		−	1.08053i		−	0.117896i
$85$	7.54004	+	8.79263i	0.817833	+	0.953694i
$86$	−7.49989			−0.808734
$87$	9.14579			0.980531
$88$	−4.86540			−0.518654
$89$	1.70075	+	1.70075i	0.180279	+	0.180279i	0.791477	−	0.611199i	$-0.209312\pi$
$89$	1.70075	+	1.70075i	0.180279	+	0.180279i	−0.611199	+	0.791477i	$0.709312\pi$
$90$	1.45560	+	1.69741i	0.153434	+	0.178923i
$91$	3.53942	+	3.53942i	0.371032	+	0.371032i
$92$			4.72007i			0.492102i
$93$		−	1.80819i		−	0.187500i
$94$	−8.00838	−	8.00838i	−0.826002	−	0.826002i
$95$	5.81338	+	0.445840i	0.596441	+	0.0457422i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	6.03720			0.612985			0.306492	−	0.951873i	$-0.400845\pi$
$97$	6.03720			0.612985			0.306492	+	0.951873i	$0.400845\pi$
$98$	−5.83245			−0.589166
$99$	−4.86540			−0.488991
$100$	0.762435	−	4.94153i	0.0762435	−	0.494153i
$101$		−	5.63152i		−	0.560357i	−0.959948	−	0.280178i	$-0.909606\pi$
$101$		−	5.63152i		−	0.560357i	0.959948	−	0.280178i	$-0.0903936\pi$
$102$	3.66282	+	3.66282i	0.362673	+	0.362673i
$103$	15.8811			1.56481			0.782407	−	0.622767i	$-0.213992\pi$
$103$	15.8811			1.56481			0.782407	+	0.622767i	$0.213992\pi$
$104$	−4.63243			−0.454247
$105$	−1.83411	+	1.57283i	−0.178991	+	0.153492i
$106$	5.64274	−	5.64274i	0.548071	−	0.548071i
$107$	−7.21271	+	7.21271i	−0.697279	+	0.697279i	−0.963823	−	0.266544i	$-0.914118\pi$
$107$	−7.21271	+	7.21271i	−0.697279	+	0.697279i	0.266544	+	0.963823i	$0.414118\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	7.52179	−	7.52179i	0.720457	−	0.720457i	−0.248241	−	0.968698i	$-0.579853\pi$
$109$	7.52179	−	7.52179i	0.720457	−	0.720457i	0.968698	+	0.248241i	$0.0798526\pi$
$110$	7.08210	+	8.25861i	0.675252	+	0.787427i
$111$	3.76152	−	4.78027i	0.357027	−	0.453723i
$112$	−0.764053	+	0.764053i	−0.0721962	+	0.0721962i
$113$	4.80474			0.451991			0.225996	−	0.974128i	$-0.427436\pi$
$113$	4.80474			0.451991			0.225996	+	0.974128i	$0.427436\pi$
$114$	2.60746			0.244211
$115$	8.01192	−	6.87056i	0.747115	−	0.640683i
$116$	−6.46705	−	6.46705i	−0.600450	−	0.600450i
$117$	−4.63243			−0.428268
$118$	0.790336	+	0.790336i	0.0727563	+	0.0727563i
$119$	−3.95780	+	3.95780i	−0.362811	+	0.362811i
$120$	0.170986	−	2.22952i	0.0156088	−	0.203526i
$121$	−12.6722			−1.15201
$122$	−5.24494	−	5.24494i	−0.474854	−	0.474854i
$123$	−2.51285	−	2.51285i	−0.226576	−	0.226576i
$124$	−1.27858	+	1.27858i	−0.114820	+	0.114820i
$125$	−9.49763	+	5.89874i	−0.849493	+	0.527599i
$126$	−0.764053	+	0.764053i	−0.0680672	+	0.0680672i
$127$	4.71555	−	4.71555i	0.418437	−	0.418437i	−0.466227	−	0.884665i	$-0.654387\pi$
$127$	4.71555	−	4.71555i	0.418437	−	0.418437i	0.884665	+	0.466227i	$0.154387\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	5.30322	+	5.30322i	0.466923	+	0.466923i
$130$	6.74298	+	7.86316i	0.591399	+	0.689644i
$131$	−1.70970	+	1.70970i	−0.149377	+	0.149377i	−0.777840	−	0.628463i	$-0.783684\pi$
$131$	−1.70970	+	1.70970i	−0.149377	+	0.149377i	0.628463	+	0.777840i	$0.283684\pi$
$132$	3.44036	+	3.44036i	0.299445	+	0.299445i
$133$			2.81745i			0.244304i
$134$	−0.777747	+	0.777747i	−0.0671871	+	0.0671871i
$135$	0.170986	−	2.22952i	0.0147161	−	0.191887i
$136$		−	5.18001i		−	0.444182i
$137$	−3.74548	+	3.74548i	−0.319998	+	0.319998i	−0.848766	−	0.528768i	$-0.822654\pi$
$137$	−3.74548	+	3.74548i	−0.319998	+	0.319998i	0.528768	+	0.848766i	$0.322654\pi$
$138$	3.33760	−	3.33760i	0.284115	−	0.284115i
$139$	−11.5750			−0.981782			−0.490891	−	0.871221i	$-0.663329\pi$
$139$	−11.5750			−0.981782			−0.490891	+	0.871221i	$0.663329\pi$
$140$	2.40907	+	0.184756i	0.203604	+	0.0156148i
$141$			11.3256i			0.953785i
$142$			0.599197i			0.0502835i
$143$	−22.5386			−1.88478
$144$		−	1.00000i		−	0.0833333i
$145$	−1.56380	+	20.3907i	−0.129867	+	1.69336i
$146$	1.07198	+	1.07198i	0.0887178	+	0.0887178i
$147$	4.12416	+	4.12416i	0.340155	+	0.340155i
$148$	−6.03996	+	0.720368i	−0.496481	+	0.0592139i
$149$			4.52394i			0.370616i	0.982681	+	0.185308i	$0.0593282\pi$
$149$			4.52394i			0.370616i	−0.982681	+	0.185308i	$0.940672\pi$
$150$	−4.03331	+	2.95506i	−0.329318	+	0.241280i
$151$		−	6.86682i		−	0.558814i	−0.960173	−	0.279407i	$-0.909862\pi$
$151$		−	6.86682i		−	0.558814i	0.960173	−	0.279407i	$-0.0901378\pi$
$152$	−1.84375	−	1.84375i	−0.149548	−	0.149548i
$153$		−	5.18001i		−	0.418779i
$154$	−3.71743	+	3.71743i	−0.299559	+	0.299559i
$155$	4.03139	+	0.309175i	0.323809	+	0.0248336i
$156$	3.27562	+	3.27562i	0.262260	+	0.262260i
$157$	−9.23383	+	9.23383i	−0.736940	+	0.736940i	−0.971985	−	0.235044i	$-0.924476\pi$
$157$	−9.23383	+	9.23383i	−0.736940	+	0.736940i	0.235044	+	0.971985i	$0.424476\pi$
$158$	9.56948	+	9.56948i	0.761307	+	0.761307i
$159$	−7.98004			−0.632858
$160$	−1.69741	+	1.45560i	−0.134192	+	0.115076i
$161$	3.60638	+	3.60638i	0.284223	+	0.284223i
$162$		−	1.00000i		−	0.0785674i
$163$	−23.9624			−1.87688			−0.938439	−	0.345446i	$-0.887728\pi$
$163$	−23.9624			−1.87688			−0.938439	+	0.345446i	$0.887728\pi$
$164$			3.55371i			0.277498i
$165$	0.831917	−	10.8475i	0.0647646	−	0.844478i
$166$	11.2549	−	11.2549i	0.873547	−	0.873547i
$167$	−15.1621			−1.17328			−0.586638	−	0.809849i	$-0.699549\pi$
$167$	−15.1621			−1.17328			−0.586638	+	0.809849i	$0.699549\pi$
$168$	1.08053			0.0833650
$169$	−8.45941			−0.650724
$170$	−8.79263	+	7.54004i	−0.674364	+	0.578295i
$171$	−1.84375	−	1.84375i	−0.140995	−	0.140995i
$172$		−	7.49989i		−	0.571861i
$173$	4.54073	−	4.54073i	0.345225	−	0.345225i	−0.513102	−	0.858327i	$-0.671504\pi$
$173$	4.54073	−	4.54073i	0.345225	−	0.345225i	0.858327	+	0.513102i	$0.171504\pi$
$174$			9.14579i			0.693340i
$175$	−3.19305	−	4.35813i	−0.241372	−	0.329444i
$176$		−	4.86540i		−	0.366744i
$177$		−	1.11770i		−	0.0840117i
$178$	−1.70075	+	1.70075i	−0.127476	+	0.127476i
$179$	−3.90880	−	3.90880i	−0.292157	−	0.292157i	0.545775	−	0.837932i	$-0.316235\pi$
$179$	−3.90880	−	3.90880i	−0.292157	−	0.292157i	−0.837932	+	0.545775i	$0.816235\pi$
$180$	−1.69741	+	1.45560i	−0.126518	+	0.108494i
$181$	16.2780			1.20993			0.604967	−	0.796251i	$-0.293186\pi$
$181$	16.2780			1.20993			0.604967	+	0.796251i	$0.293186\pi$
$182$	−3.53942	+	3.53942i	−0.262359	+	0.262359i
$183$			7.41746i			0.548314i
$184$	−4.72007			−0.347968
$185$	10.0145	+	9.20374i	0.736284	+	0.676672i
$186$	1.80819			0.132583
$187$		−	25.2028i		−	1.84301i
$188$	8.00838	−	8.00838i	0.584071	−	0.584071i
$189$	1.08053			0.0785973
$190$	−0.445840	+	5.81338i	−0.0323446	+	0.421747i
$191$	6.72993	+	6.72993i	0.486961	+	0.486961i	0.907346	−	0.420385i	$-0.138105\pi$
$191$	6.72993	+	6.72993i	0.486961	+	0.486961i	−0.420385	+	0.907346i	$0.638105\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$		−	11.3986i		−	0.820490i	−0.911975	−	0.410245i	$-0.865443\pi$
$193$		−	11.3986i		−	0.820490i	0.911975	−	0.410245i	$-0.134557\pi$
$194$			6.03720i			0.433446i
$195$	0.792082	−	10.3281i	0.0567221	−	0.739611i
$196$		−	5.83245i		−	0.416603i
$197$	−10.5213	+	10.5213i	−0.749610	+	0.749610i	−0.974406	−	0.224796i	$-0.927828\pi$
$197$	−10.5213	+	10.5213i	−0.749610	+	0.749610i	0.224796	+	0.974406i	$0.427828\pi$
$198$		−	4.86540i		−	0.345769i
$199$	5.10780	+	5.10780i	0.362082	+	0.362082i	0.864579	−	0.502497i	$-0.167585\pi$
$199$	5.10780	+	5.10780i	0.362082	+	0.362082i	−0.502497	+	0.864579i	$0.667585\pi$
$200$	4.94153	+	0.762435i	0.349419	+	0.0539123i
$201$	1.09990			0.0775810
$202$	5.63152			0.396232
$203$	−9.88233			−0.693604
$204$	−3.66282	+	3.66282i	−0.256449	+	0.256449i
$205$	6.03212	−	5.17280i	0.421302	−	0.361284i
$206$			15.8811i			1.10649i
$207$	−4.72007			−0.328068
$208$		−	4.63243i		−	0.321201i
$209$	−8.97060	−	8.97060i	−0.620509	−	0.620509i
$210$	−1.57283	−	1.83411i	−0.108536	−	0.126566i
$211$	−3.92055			−0.269902			−0.134951	−	0.990852i	$-0.543088\pi$
$211$	−3.92055			−0.269902			−0.134951	+	0.990852i	$0.543088\pi$
$212$	5.64274	+	5.64274i	0.387545	+	0.387545i
$213$	0.423697	−	0.423697i	0.0290312	−	0.0290312i
$214$	−7.21271	−	7.21271i	−0.493051	−	0.493051i
$215$	−12.7304	+	10.9169i	−0.868208	+	0.744525i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$			1.95381i			0.132633i
$218$	7.52179	+	7.52179i	0.509440	+	0.509440i
$219$		−	1.51601i		−	0.102442i
$220$	−8.25861	+	7.08210i	−0.556795	+	0.477475i
$221$		−	23.9960i		−	1.61415i
$222$	4.78027	+	3.76152i	0.320831	+	0.252456i
$223$	13.0140	+	13.0140i	0.871480	+	0.871480i	0.992634	−	0.121153i	$-0.0386593\pi$
$223$	13.0140	+	13.0140i	0.871480	+	0.871480i	−0.121153	+	0.992634i	$0.538659\pi$
$224$	−0.764053	−	0.764053i	−0.0510504	−	0.0510504i
$225$	4.94153	+	0.762435i	0.329435	+	0.0508290i
$226$			4.80474i			0.319606i
$227$	−10.4498			−0.693577			−0.346788	−	0.937943i	$-0.612728\pi$
$227$	−10.4498			−0.693577			−0.346788	+	0.937943i	$0.612728\pi$
$228$			2.60746i			0.172683i
$229$		−	12.6086i		−	0.833197i	−0.909091	−	0.416598i	$-0.863222\pi$
$229$		−	12.6086i		−	0.833197i	0.909091	−	0.416598i	$-0.136778\pi$
$230$	6.87056	+	8.01192i	0.453031	+	0.528290i
$231$	5.25723			0.345901
$232$	6.46705	−	6.46705i	0.424583	−	0.424583i
$233$	−16.9357	+	16.9357i	−1.10950	+	1.10950i	−0.116278	+	0.993217i	$0.537096\pi$
$233$	−16.9357	+	16.9357i	−1.10950	+	1.10950i	−0.993217	+	0.116278i	$0.962904\pi$
$234$		−	4.63243i		−	0.302831i
$235$	−25.2506	−	1.93652i	−1.64717	−	0.126324i
$236$	−0.790336	+	0.790336i	−0.0514465	+	0.0514465i
$237$		−	13.5333i		−	0.879081i
$238$	−3.95780	−	3.95780i	−0.256546	−	0.256546i
$239$	2.61342	−	2.61342i	0.169048	−	0.169048i	−0.617513	−	0.786561i	$-0.711860\pi$
$239$	2.61342	−	2.61342i	0.169048	−	0.169048i	0.786561	+	0.617513i	$0.211860\pi$
$240$	2.22952	+	0.170986i	0.143915	+	0.0110371i
$241$	14.3186	+	14.3186i	0.922340	+	0.922340i	0.997194	−	0.0748547i	$-0.0238493\pi$
$241$	14.3186	+	14.3186i	0.922340	+	0.922340i	−0.0748547	+	0.997194i	$0.523849\pi$
$242$		−	12.6722i		−	0.814597i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	5.24494	−	5.24494i	0.335773	−	0.335773i
$245$	−9.90008	+	8.48973i	−0.632493	+	0.542389i
$246$	2.51285	−	2.51285i	0.160214	−	0.160214i
$247$	−8.54105	−	8.54105i	−0.543454	−	0.543454i
$248$	−1.27858	−	1.27858i	−0.0811901	−	0.0811901i
$249$	−15.9168			−1.00868
$250$	−5.89874	−	9.49763i	−0.373069	−	0.600683i
$251$	5.64176	−	5.64176i	0.356105	−	0.356105i	−0.506270	−	0.862375i	$-0.668976\pi$
$251$	5.64176	−	5.64176i	0.356105	−	0.356105i	0.862375	+	0.506270i	$0.168976\pi$
$252$	−0.764053	−	0.764053i	−0.0481308	−	0.0481308i
$253$	−22.9651			−1.44380
$254$	4.71555	+	4.71555i	0.295880	+	0.295880i
$255$	11.5489	+	0.885710i	0.723223	+	0.0554653i
$256$	1.00000			0.0625000
$257$	−23.3521			−1.45666			−0.728331	−	0.685226i	$-0.759704\pi$
$257$	−23.3521			−1.45666			−0.728331	+	0.685226i	$0.759704\pi$
$258$	−5.30322	+	5.30322i	−0.330164	+	0.330164i
$259$	−4.06445	+	5.16525i	−0.252552	+	0.320953i
$260$	−7.86316	+	6.74298i	−0.487652	+	0.418182i
$261$	6.46705	−	6.46705i	0.400300	−	0.400300i
$262$	−1.70970	−	1.70970i	−0.105625	−	0.105625i
$263$	9.20714	−	9.20714i	0.567737	−	0.567737i	−0.363757	−	0.931494i	$-0.618506\pi$
$263$	9.20714	−	9.20714i	0.567737	−	0.567737i	0.931494	+	0.363757i	$0.118506\pi$
$264$	−3.44036	+	3.44036i	−0.211740	+	0.211740i
$265$	1.36448	−	17.7917i	0.0838191	−	1.09293i
$266$	−2.81745			−0.172749
$267$	2.40522			0.147197
$268$	−0.777747	−	0.777747i	−0.0475084	−	0.0475084i
$269$		−	19.2094i		−	1.17122i	−0.810593	−	0.585610i	$-0.800855\pi$
$269$		−	19.2094i		−	1.17122i	0.810593	−	0.585610i	$-0.199145\pi$
$270$	2.22952	+	0.170986i	0.135684	+	0.0104059i
$271$	14.4883			0.880103			0.440052	−	0.897972i	$-0.354960\pi$
$271$	14.4883			0.880103			0.440052	+	0.897972i	$0.354960\pi$
$272$	5.18001			0.314084
$273$	5.00550			0.302947
$274$	−3.74548	−	3.74548i	−0.226272	−	0.226272i
$275$	24.0425	+	3.70955i	1.44982	+	0.223694i
$276$	3.33760	+	3.33760i	0.200900	+	0.200900i
$277$			29.6974i			1.78434i	0.451696	+	0.892172i	$0.350819\pi$
$277$			29.6974i			1.78434i	−0.451696	+	0.892172i	$0.649181\pi$
$278$		−	11.5750i		−	0.694225i
$279$	−1.27858	−	1.27858i	−0.0765467	−	0.0765467i
$280$	−0.184756	+	2.40907i	−0.0110413	+	0.143970i
$281$	3.49186	+	3.49186i	0.208307	+	0.208307i	0.803548	−	0.595240i	$-0.202943\pi$
$281$	3.49186	+	3.49186i	0.208307	+	0.208307i	−0.595240	+	0.803548i	$0.702943\pi$
$282$	−11.3256			−0.674428
$283$	−14.7733			−0.878182			−0.439091	−	0.898442i	$-0.644700\pi$
$283$	−14.7733			−0.878182			−0.439091	+	0.898442i	$0.644700\pi$
$284$	−0.599197			−0.0355558
$285$	4.42594	−	3.79543i	0.262170	−	0.224822i
$286$		−	22.5386i		−	1.33274i
$287$	2.71522	+	2.71522i	0.160275	+	0.160275i
$288$	1.00000			0.0589256
$289$	9.83251			0.578383
$290$	−20.3907	−	1.56380i	−1.19738	−	0.0918297i
$291$	4.26895	−	4.26895i	0.250250	−	0.250250i
$292$	−1.07198	+	1.07198i	−0.0627329	+	0.0627329i
$293$	23.9405	+	23.9405i	1.39862	+	1.39862i	0.804034	+	0.594583i	$0.202683\pi$
$293$	23.9405	+	23.9405i	1.39862	+	1.39862i	0.594583	+	0.804034i	$0.297317\pi$
$294$	−4.12416	+	4.12416i	−0.240526	+	0.240526i
$295$	2.49194	+	0.191112i	0.145087	+	0.0111270i
$296$	−0.720368	−	6.03996i	−0.0418705	−	0.351065i
$297$	−3.44036	+	3.44036i	−0.199630	+	0.199630i
$298$	−4.52394			−0.262065
$299$	−21.8654			−1.26451
$300$	−2.95506	−	4.03331i	−0.170611	−	0.232863i
$301$	−5.73031	−	5.73031i	−0.330290	−	0.330290i
$302$	6.86682			0.395141
$303$	−3.98208	−	3.98208i	−0.228765	−	0.228765i
$304$	1.84375	−	1.84375i	0.105746	−	0.105746i
$305$	−16.5374	−	1.26828i	−0.946928	−	0.0726217i
$306$	5.18001			0.296121
$307$	23.3965	+	23.3965i	1.33531	+	1.33531i	0.900543	+	0.434767i	$0.143169\pi$
$307$	23.3965	+	23.3965i	1.33531	+	1.33531i	0.434767	+	0.900543i	$0.356831\pi$
$308$	−3.71743	−	3.71743i	−0.211820	−	0.211820i
$309$	11.2297	−	11.2297i	0.638833	−	0.638833i
$310$	−0.309175	+	4.03139i	−0.0175600	+	0.228968i
$311$	18.7483	−	18.7483i	1.06312	−	1.06312i	0.0652489	−	0.997869i	$-0.479216\pi$
$311$	18.7483	−	18.7483i	1.06312	−	1.06312i	0.997869	−	0.0652489i	$-0.0207841\pi$
$312$	−3.27562	+	3.27562i	−0.185446	+	0.185446i
$313$			26.7290i			1.51081i	0.655255	+	0.755407i	$0.272561\pi$
$313$			26.7290i			1.51081i	−0.655255	+	0.755407i	$0.727439\pi$
$314$	−9.23383	−	9.23383i	−0.521095	−	0.521095i
$315$	−0.184756	+	2.40907i	−0.0104098	+	0.135736i
$316$	−9.56948	+	9.56948i	−0.538325	+	0.538325i
$317$	−18.5839	−	18.5839i	−1.04378	−	1.04378i	−0.998997	−	0.0447783i	$-0.985742\pi$
$317$	−18.5839	−	18.5839i	−1.04378	−	1.04378i	−0.0447783	−	0.998997i	$-0.514258\pi$
$318$		−	7.98004i		−	0.447498i
$319$	31.4648	−	31.4648i	1.76169	−	1.76169i
$320$	−1.45560	−	1.69741i	−0.0813707	−	0.0948884i
$321$			10.2003i			0.569326i
$322$	−3.60638	+	3.60638i	−0.200976	+	0.200976i
$323$	9.55065	−	9.55065i	0.531413	−	0.531413i
$324$	1.00000			0.0555556
$325$	22.8913	+	3.53193i	1.26978	+	0.195916i
$326$		−	23.9624i		−	1.32715i
$327$		−	10.6374i		−	0.588251i
$328$	−3.55371			−0.196221
$329$		−	12.2377i		−	0.674684i
$330$	10.8475	+	0.831917i	0.597136	+	0.0457955i
$331$	−4.72692	−	4.72692i	−0.259815	−	0.259815i	0.565164	−	0.824979i	$-0.308813\pi$
$331$	−4.72692	−	4.72692i	−0.259815	−	0.259815i	−0.824979	+	0.565164i	$0.808813\pi$
$332$	11.2549	+	11.2549i	0.617691	+	0.617691i
$333$	−0.720368	−	6.03996i	−0.0394759	−	0.330988i
$334$		−	15.1621i		−	0.829631i
$335$	−0.188068	+	2.45225i	−0.0102752	+	0.133981i
$336$			1.08053i			0.0589480i
$337$	−13.9016	−	13.9016i	−0.757270	−	0.757270i	0.218555	−	0.975825i	$-0.429866\pi$
$337$	−13.9016	−	13.9016i	−0.757270	−	0.757270i	−0.975825	+	0.218555i	$0.929866\pi$
$338$		−	8.45941i		−	0.460131i
$339$	3.39746	−	3.39746i	0.184525	−	0.184525i
$340$	−7.54004	−	8.79263i	−0.408916	−	0.476847i
$341$	−6.22082	−	6.22082i	−0.336876	−	0.336876i
$342$	1.84375	−	1.84375i	0.0996987	−	0.0996987i
$343$	−9.80467	−	9.80467i	−0.529402	−	0.529402i
$344$	7.49989			0.404367
$345$	0.807067	−	10.5235i	0.0434510	−	0.566566i
$346$	4.54073	+	4.54073i	0.244111	+	0.244111i
$347$		−	0.651438i		−	0.0349710i	−0.999847	−	0.0174855i	$-0.994434\pi$
$347$		−	0.651438i		−	0.0349710i	0.999847	−	0.0174855i	$-0.00556609\pi$
$348$	−9.14579			−0.490266
$349$			25.5234i			1.36624i	0.730308	+	0.683118i	$0.239376\pi$
$349$			25.5234i			1.36624i	−0.730308	+	0.683118i	$0.760624\pi$
$350$	4.35813	−	3.19305i	0.232952	−	0.170676i
$351$	−3.27562	+	3.27562i	−0.174840	+	0.174840i
$352$	4.86540			0.259327
$353$	−34.3501			−1.82827			−0.914136	−	0.405408i	$-0.867130\pi$
$353$	−34.3501			−1.82827			−0.914136	+	0.405408i	$0.867130\pi$
$354$	1.11770			0.0594053
$355$	0.872194	+	1.01709i	0.0462913	+	0.0539814i
$356$	−1.70075	−	1.70075i	−0.0901394	−	0.0901394i
$357$			5.59718i			0.296234i
$358$	3.90880	−	3.90880i	0.206586	−	0.206586i
$359$		−	17.0122i		−	0.897868i	−0.893565	−	0.448934i	$-0.851804\pi$
$359$		−	17.0122i		−	0.897868i	0.893565	−	0.448934i	$-0.148196\pi$
$360$	−1.45560	−	1.69741i	−0.0767171	−	0.0894616i
$361$			12.2012i			0.642166i
$362$			16.2780i			0.855552i
$363$	−8.96057	+	8.96057i	−0.470308	+	0.470308i
$364$	−3.53942	−	3.53942i	−0.185516	−	0.185516i
$365$	3.37998	+	0.259217i	0.176916	+	0.0135680i
$366$	−7.41746			−0.387717
$367$	−10.2747	+	10.2747i	−0.536335	+	0.536335i	−0.922451	−	0.386115i	$-0.873817\pi$
$367$	−10.2747	+	10.2747i	−0.536335	+	0.536335i	0.386115	+	0.922451i	$0.373817\pi$
$368$		−	4.72007i		−	0.246051i
$369$	−3.55371			−0.184999
$370$	−9.20374	+	10.0145i	−0.478480	+	0.520632i
$371$	8.62270			0.447668
$372$			1.80819i			0.0937502i
$373$	−6.19992	+	6.19992i	−0.321020	+	0.321020i	−0.849158	−	0.528139i	$-0.822890\pi$
$373$	−6.19992	+	6.19992i	−0.321020	+	0.321020i	0.528139	+	0.849158i	$0.322890\pi$
$374$	25.2028			1.30321
$375$	−2.54480	+	10.8869i	−0.131413	+	0.562196i
$376$	8.00838	+	8.00838i	0.413001	+	0.413001i
$377$	29.9582	−	29.9582i	1.54292	−	1.54292i
$378$			1.08053i			0.0555767i
$379$			31.3961i			1.61271i	0.591433	+	0.806354i	$0.298562\pi$
$379$			31.3961i			1.61271i	−0.591433	+	0.806354i	$0.701438\pi$
$380$	−5.81338	−	0.445840i	−0.298220	−	0.0228711i
$381$		−	6.66879i		−	0.341653i
$382$	−6.72993	+	6.72993i	−0.344333	+	0.344333i
$383$			17.9026i			0.914778i	0.889267	+	0.457389i	$0.151215\pi$
$383$			17.9026i			0.914778i	−0.889267	+	0.457389i	$0.848785\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−0.898915	+	11.7211i	−0.0458129	+	0.597363i
$386$	11.3986			0.580174
$387$	7.49989			0.381241
$388$	−6.03720			−0.306492
$389$	−7.54313	+	7.54313i	−0.382452	+	0.382452i	−0.871985	−	0.489533i	$-0.837167\pi$
$389$	−7.54313	+	7.54313i	−0.382452	+	0.382452i	0.489533	+	0.871985i	$0.337167\pi$
$390$	10.3281	+	0.792082i	0.522984	+	0.0401086i
$391$		−	24.4500i		−	1.23649i
$392$	5.83245			0.294583
$393$			2.41788i			0.121966i
$394$	−10.5213	−	10.5213i	−0.530054	−	0.530054i
$395$	30.1727	+	2.31401i	1.51816	+	0.116430i
$396$	4.86540			0.244496
$397$	−11.1198	−	11.1198i	−0.558087	−	0.558087i	0.370676	−	0.928762i	$-0.379126\pi$
$397$	−11.1198	−	11.1198i	−0.558087	−	0.558087i	−0.928762	+	0.370676i	$0.879126\pi$
$398$	−5.10780	+	5.10780i	−0.256031	+	0.256031i
$399$	1.99224	+	1.99224i	0.0997366	+	0.0997366i
$400$	−0.762435	+	4.94153i	−0.0381217	+	0.247076i
$401$	−22.3136	+	22.3136i	−1.11429	+	1.11429i	−0.121725	+	0.992564i	$0.538843\pi$
$401$	−22.3136	+	22.3136i	−1.11429	+	1.11429i	−0.992564	+	0.121725i	$0.961157\pi$
$402$			1.09990i			0.0548580i
$403$	−5.92294	−	5.92294i	−0.295043	−	0.295043i
$404$			5.63152i			0.280178i
$405$	−1.45560	−	1.69741i	−0.0723295	−	0.0843452i
$406$		−	9.88233i		−	0.490452i
$407$	−3.50488	−	29.3868i	−0.173731	−	1.45665i
$408$	−3.66282	−	3.66282i	−0.181337	−	0.181337i
$409$	−16.7999	−	16.7999i	−0.830701	−	0.830701i	0.156912	−	0.987613i	$-0.449846\pi$
$409$	−16.7999	−	16.7999i	−0.830701	−	0.830701i	−0.987613	+	0.156912i	$0.949846\pi$
$410$	5.17280	+	6.03212i	0.255466	+	0.297905i
$411$			5.29690i			0.261277i
$412$	−15.8811			−0.782407
$413$			1.20772i			0.0594279i
$414$		−	4.72007i		−	0.231979i
$415$	2.72155	−	35.4868i	0.133596	−	1.74198i
$416$	4.63243			0.227124
$417$	−8.18479	+	8.18479i	−0.400811	+	0.400811i
$418$	8.97060	−	8.97060i	0.438766	−	0.438766i
$419$			3.07947i			0.150442i	0.997167	+	0.0752210i	$0.0239662\pi$
$419$			3.07947i			0.150442i	−0.997167	+	0.0752210i	$0.976034\pi$
$420$	1.83411	−	1.57283i	0.0894956	−	0.0767462i
$421$	−2.58223	+	2.58223i	−0.125850	+	0.125850i	−0.767227	−	0.641376i	$-0.778364\pi$
$421$	−2.58223	+	2.58223i	−0.125850	+	0.125850i	0.641376	+	0.767227i	$0.278364\pi$
$422$		−	3.92055i		−	0.190849i
$423$	8.00838	+	8.00838i	0.389381	+	0.389381i
$424$	−5.64274	+	5.64274i	−0.274036	+	0.274036i
$425$	−3.94942	+	25.5972i	−0.191575	+	1.24164i
$426$	0.423697	+	0.423697i	0.0205282	+	0.0205282i
$427$		−	8.01482i		−	0.387864i
$428$	7.21271	−	7.21271i	0.348639	−	0.348639i
$429$	−15.9372	+	15.9372i	−0.769457	+	0.769457i
$430$	−10.9169	−	12.7304i	−0.526458	−	0.613916i
$431$	−9.94058	+	9.94058i	−0.478821	+	0.478821i	−0.904754	−	0.425934i	$-0.859946\pi$
$431$	−9.94058	+	9.94058i	−0.478821	+	0.478821i	0.425934	+	0.904754i	$0.359946\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	13.7642	+	13.7642i	0.661465	+	0.661465i	0.955725	−	0.294260i	$-0.0950732\pi$
$433$	13.7642	+	13.7642i	0.661465	+	0.661465i	−0.294260	+	0.955725i	$0.595073\pi$
$434$	−1.95381			−0.0937859
$435$	13.3126	+	15.5242i	0.638292	+	0.744328i
$436$	−7.52179	+	7.52179i	−0.360228	+	0.360228i
$437$	−8.70264	−	8.70264i	−0.416304	−	0.416304i
$438$	1.51601			0.0724377
$439$	21.9903	+	21.9903i	1.04954	+	1.04954i	0.998707	+	0.0508336i	$0.0161878\pi$
$439$	21.9903	+	21.9903i	1.04954	+	1.04954i	0.0508336	+	0.998707i	$0.483812\pi$
$440$	−7.08210	−	8.25861i	−0.337626	−	0.393714i
$441$	5.83245			0.277736
$442$	23.9960			1.14138
$443$	−17.2453	+	17.2453i	−0.819348	+	0.819348i	−0.986014	−	0.166665i	$-0.946700\pi$
$443$	−17.2453	+	17.2453i	−0.819348	+	0.819348i	0.166665	+	0.986014i	$0.446700\pi$
$444$	−3.76152	+	4.78027i	−0.178514	+	0.226862i
$445$	−0.411259	+	5.36248i	−0.0194956	+	0.254206i
$446$	−13.0140	+	13.0140i	−0.616230	+	0.616230i
$447$	3.19891	+	3.19891i	0.151303	+	0.151303i
$448$	0.764053	−	0.764053i	0.0360981	−	0.0360981i
$449$	0.574002	−	0.574002i	0.0270888	−	0.0270888i	−0.693433	−	0.720521i	$-0.743902\pi$
$449$	0.574002	−	0.574002i	0.0270888	−	0.0270888i	0.720521	+	0.693433i	$0.243902\pi$
$450$	−0.762435	+	4.94153i	−0.0359415	+	0.232946i
$451$	−17.2902			−0.814166
$452$	−4.80474			−0.225996
$453$	−4.85557	−	4.85557i	−0.228135	−	0.228135i
$454$		−	10.4498i		−	0.490433i
$455$	−0.855871	+	11.1599i	−0.0401239	+	0.523182i
$456$	−2.60746			−0.122105
$457$	12.9457			0.605574			0.302787	−	0.953058i	$-0.402083\pi$
$457$	12.9457			0.605574			0.302787	+	0.953058i	$0.402083\pi$
$458$	12.6086			0.589159
$459$	−3.66282	−	3.66282i	−0.170966	−	0.170966i
$460$	−8.01192	+	6.87056i	−0.373558	+	0.320341i
$461$	21.0318	+	21.0318i	0.979548	+	0.979548i	0.999795	−	0.0202466i	$-0.00644514\pi$
$461$	21.0318	+	21.0318i	0.979548	+	0.979548i	−0.0202466	+	0.999795i	$0.506445\pi$
$462$			5.25723i			0.244589i
$463$			14.6765i			0.682076i	0.940050	+	0.341038i	$0.110778\pi$
$463$			14.6765i			0.682076i	−0.940050	+	0.341038i	$0.889222\pi$
$464$	6.46705	+	6.46705i	0.300225	+	0.300225i
$465$	3.06925	−	2.63201i	0.142333	−	0.122056i
$466$	−16.9357	−	16.9357i	−0.784531	−	0.784531i
$467$	−12.6925			−0.587341			−0.293670	−	0.955907i	$-0.594877\pi$
$467$	−12.6925			−0.587341			−0.293670	+	0.955907i	$0.594877\pi$
$468$	4.63243			0.214134
$469$	−1.18848			−0.0548789
$470$	1.93652	−	25.2506i	0.0893248	−	1.16472i
$471$			13.0586i			0.601709i
$472$	−0.790336	−	0.790336i	−0.0363782	−	0.0363782i
$473$	36.4900			1.67781
$474$	13.5333			0.621604
$475$	7.70521	+	10.5167i	0.353539	+	0.482539i
$476$	3.95780	−	3.95780i	0.181406	−	0.181406i
$477$	−5.64274	+	5.64274i	−0.258363	+	0.258363i
$478$	2.61342	+	2.61342i	0.119535	+	0.119535i
$479$	−17.3000	+	17.3000i	−0.790459	+	0.790459i	−0.981569	−	0.191110i	$-0.938791\pi$
$479$	−17.3000	+	17.3000i	−0.790459	+	0.790459i	0.191110	+	0.981569i	$0.438791\pi$
$480$	−0.170986	+	2.22952i	−0.00780442	+	0.101763i
$481$	−3.33706	−	27.9797i	−0.152157	−	1.27576i
$482$	−14.3186	+	14.3186i	−0.652193	+	0.652193i
$483$	5.10020			0.232067
$484$	12.6722			0.576007
$485$	8.78777	+	10.2476i	0.399032	+	0.465321i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−25.7666			−1.16760			−0.583798	−	0.811899i	$-0.698434\pi$
$487$	−25.7666			−1.16760			−0.583798	+	0.811899i	$0.698434\pi$
$488$	5.24494	+	5.24494i	0.237427	+	0.237427i
$489$	−16.9440	+	16.9440i	−0.766232	+	0.766232i
$490$	−8.48973	−	9.90008i	−0.383527	−	0.447240i
$491$	−4.97935			−0.224715			−0.112358	−	0.993668i	$-0.535840\pi$
$491$	−4.97935			−0.224715			−0.112358	+	0.993668i	$0.535840\pi$
$492$	2.51285	+	2.51285i	0.113288	+	0.113288i
$493$	33.4994	+	33.4994i	1.50874	+	1.50874i
$494$	8.54105	−	8.54105i	0.384280	−	0.384280i
$495$	−7.08210	−	8.25861i	−0.318317	−	0.371197i
$496$	1.27858	−	1.27858i	0.0574101	−	0.0574101i
$497$	−0.457819	+	0.457819i	−0.0205360	+	0.0205360i
$498$		−	15.9168i		−	0.713248i
$499$	−19.1310	−	19.1310i	−0.856423	−	0.856423i	0.134492	−	0.990915i	$-0.457060\pi$
$499$	−19.1310	−	19.1310i	−0.856423	−	0.856423i	−0.990915	+	0.134492i	$0.957060\pi$
$500$	9.49763	−	5.89874i	0.424747	−	0.263800i
$501$	−10.7212	+	10.7212i	−0.478988	+	0.478988i
$502$	5.64176	+	5.64176i	0.251804	+	0.251804i
$503$			12.4777i			0.556353i	0.960530	+	0.278177i	$0.0897301\pi$
$503$			12.4777i			0.556353i	−0.960530	+	0.278177i	$0.910270\pi$
$504$	0.764053	−	0.764053i	0.0340336	−	0.0340336i
$505$	9.55902	−	8.19726i	0.425371	−	0.364773i
$506$		−	22.9651i		−	1.02092i
$507$	−5.98171	+	5.98171i	−0.265657	+	0.265657i
$508$	−4.71555	+	4.71555i	−0.209219	+	0.209219i
$509$	31.1191			1.37933			0.689665	−	0.724129i	$-0.257758\pi$
$509$	31.1191			1.37933			0.689665	+	0.724129i	$0.257758\pi$
$510$	−0.885710	+	11.5489i	−0.0392199	+	0.511396i
$511$			1.63810i			0.0724653i
$512$			1.00000i			0.0441942i
$513$	−2.60746			−0.115122
$514$		−	23.3521i		−	1.03002i
$515$	23.1166	+	26.9569i	1.01864	+	1.18786i
$516$	−5.30322	−	5.30322i	−0.233461	−	0.233461i
$517$	38.9640	+	38.9640i	1.71364	+	1.71364i
$518$	−5.16525	−	4.06445i	−0.226948	−	0.178582i
$519$		−	6.42156i		−	0.281875i
$520$	−6.74298	−	7.86316i	−0.295699	−	0.344822i
$521$		−	11.3207i		−	0.495967i	−0.968764	−	0.247983i	$-0.920232\pi$
$521$		−	11.3207i		−	0.495967i	0.968764	−	0.247983i	$-0.0797679\pi$
$522$	6.46705	+	6.46705i	0.283055	+	0.283055i
$523$			2.09242i			0.0914952i	0.998953	+	0.0457476i	$0.0145670\pi$
$523$			2.09242i			0.0914952i	−0.998953	+	0.0457476i	$0.985433\pi$
$524$	1.70970	−	1.70970i	0.0746884	−	0.0746884i
$525$	−5.33949	−	0.823837i	−0.233034	−	0.0359552i
$526$	9.20714	+	9.20714i	0.401450	+	0.401450i
$527$	6.62307	−	6.62307i	0.288506	−	0.288506i
$528$	−3.44036	−	3.44036i	−0.149722	−	0.149722i
$529$	0.720919			0.0313443
$530$	17.7917	+	1.36448i	0.772821	+	0.0592691i
$531$	−0.790336	−	0.790336i	−0.0342977	−	0.0342977i
$532$		−	2.81745i		−	0.122152i
$533$	−16.4623			−0.713062
$534$			2.40522i			0.104084i
$535$	−22.7418	−	1.74411i	−0.983214	−	0.0754045i
$536$	0.777747	−	0.777747i	0.0335935	−	0.0335935i
$537$	−5.52788			−0.238545
$538$	19.2094			0.828178
$539$	28.3772			1.22229
$540$	−0.170986	+	2.22952i	−0.00735807	+	0.0959433i
$541$	−6.92733	−	6.92733i	−0.297829	−	0.297829i	0.542334	−	0.840163i	$-0.317541\pi$
$541$	−6.92733	−	6.92733i	−0.297829	−	0.297829i	−0.840163	+	0.542334i	$0.817541\pi$
$542$			14.4883i			0.622327i
$543$	11.5103	−	11.5103i	0.493953	−	0.493953i
$544$			5.18001i			0.222091i
$545$	23.7163	+	1.81885i	1.01590	+	0.0779110i
$546$			5.00550i			0.214216i
$547$		−	4.89932i		−	0.209480i	−0.994500	−	0.104740i	$-0.966599\pi$
$547$		−	4.89932i		−	0.209480i	0.994500	−	0.104740i	$-0.0334010\pi$
$548$	3.74548	−	3.74548i	0.159999	−	0.159999i
$549$	5.24494	+	5.24494i	0.223848	+	0.223848i
$550$	−3.70955	+	24.0425i	−0.158176	+	1.02518i
$551$	23.8473			1.01593
$552$	−3.33760	+	3.33760i	−0.142057	+	0.142057i
$553$			14.6232i			0.621841i
$554$	−29.6974			−1.26172
$555$	13.5894	−	0.573327i	0.576837	−	0.0243364i
$556$	11.5750			0.490891
$557$			31.8866i			1.35108i	0.737324	+	0.675539i	$0.236089\pi$
$557$			31.8866i			1.35108i	−0.737324	+	0.675539i	$0.763911\pi$
$558$	1.27858	−	1.27858i	0.0541267	−	0.0541267i
$559$	34.7427			1.46946
$560$	−2.40907	−	0.184756i	−0.101802	−	0.00780738i
$561$	−17.8211	−	17.8211i	−0.752407	−	0.752407i
$562$	−3.49186	+	3.49186i	−0.147295	+	0.147295i
$563$		−	43.4484i		−	1.83113i	−0.402170	−	0.915565i	$-0.631744\pi$
$563$		−	43.4484i		−	1.83113i	0.402170	−	0.915565i	$-0.368256\pi$
$564$		−	11.3256i		−	0.476892i
$565$	6.99379	+	8.15563i	0.294231	+	0.343110i
$566$		−	14.7733i		−	0.620969i
$567$	0.764053	−	0.764053i	0.0320872	−	0.0320872i
$568$		−	0.599197i		−	0.0251418i
$569$	19.9460	+	19.9460i	0.836180	+	0.836180i	0.988354	−	0.152174i	$-0.0486274\pi$
$569$	19.9460	+	19.9460i	0.836180	+	0.836180i	−0.152174	+	0.988354i	$0.548627\pi$
$570$	3.79543	+	4.42594i	0.158973	+	0.185382i
$571$	7.76992			0.325161			0.162581	−	0.986695i	$-0.448018\pi$
$571$	7.76992			0.325161			0.162581	+	0.986695i	$0.448018\pi$
$572$	22.5386			0.942388
$573$	9.51756			0.397602
$574$	−2.71522	+	2.71522i	−0.113331	+	0.113331i
$575$	23.3244	+	3.59875i	0.972693	+	0.150078i
$576$			1.00000i			0.0416667i
$577$	10.9161			0.454442			0.227221	−	0.973843i	$-0.427036\pi$
$577$	10.9161			0.454442			0.227221	+	0.973843i	$0.427036\pi$
$578$			9.83251i			0.408978i
$579$	−8.06003	−	8.06003i	−0.334964	−	0.334964i
$580$	1.56380	−	20.3907i	0.0649334	−	0.846679i
$581$	17.1986			0.713519
$582$	4.26895	+	4.26895i	0.176954	+	0.176954i
$583$	−27.4542	+	27.4542i	−1.13704	+	1.13704i
$584$	−1.07198	−	1.07198i	−0.0443589	−	0.0443589i
$585$	−6.74298	−	7.86316i	−0.278788	−	0.325101i
$586$	−23.9405	+	23.9405i	−0.988972	+	0.988972i
$587$		−	22.1879i		−	0.915793i	−0.889005	−	0.457897i	$-0.848603\pi$
$587$		−	22.1879i		−	0.915793i	0.889005	−	0.457897i	$-0.151397\pi$
$588$	−4.12416	−	4.12416i	−0.170078	−	0.170078i
$589$		−	4.71478i		−	0.194269i
$590$	−0.191112	+	2.49194i	−0.00786795	+	0.102592i
$591$			14.8793i			0.612054i
$592$	6.03996	−	0.720368i	0.248241	−	0.0296069i
$593$	−24.0835	−	24.0835i	−0.988991	−	0.988991i	0.0109487	−	0.999940i	$-0.496515\pi$
$593$	−24.0835	−	24.0835i	−0.988991	−	0.988991i	−0.999940	+	0.0109487i	$0.996515\pi$
$594$	−3.44036	−	3.44036i	−0.141160	−	0.141160i
$595$	−12.4790	−	0.957040i	−0.511590	−	0.0392348i
$596$		−	4.52394i		−	0.185308i
$597$	7.22351			0.295639
$598$		−	21.8654i		−	0.894143i
$599$		−	43.9186i		−	1.79446i	−0.441560	−	0.897232i	$-0.645575\pi$
$599$		−	43.9186i		−	1.79446i	0.441560	−	0.897232i	$-0.354425\pi$
$600$	4.03331	−	2.95506i	0.164659	−	0.120640i
$601$	−32.0175			−1.30602			−0.653010	−	0.757349i	$-0.726494\pi$
$601$	−32.0175			−1.30602			−0.653010	+	0.757349i	$0.726494\pi$
$602$	5.73031	−	5.73031i	0.233550	−	0.233550i
$603$	0.777747	−	0.777747i	0.0316723	−	0.0316723i
$604$			6.86682i			0.279407i
$605$	−18.4456	−	21.5099i	−0.749922	−	0.874502i
$606$	3.98208	−	3.98208i	0.161761	−	0.161761i
$607$			44.7940i			1.81813i	0.416651	+	0.909067i	$0.363204\pi$
$607$			44.7940i			1.81813i	−0.416651	+	0.909067i	$0.636796\pi$
$608$	1.84375	+	1.84375i	0.0747740	+	0.0747740i
$609$	−6.98787	+	6.98787i	−0.283163	+	0.283163i
$610$	1.26828	−	16.5374i	0.0513513	−	0.669579i
$611$	37.0983	+	37.0983i	1.50084	+	1.50084i
$612$			5.18001i			0.209390i
$613$	−30.3408	+	30.3408i	−1.22545	+	1.22545i	−0.259787	+	0.965666i	$0.583652\pi$
$613$	−30.3408	+	30.3408i	−1.22545	+	1.22545i	−0.965666	+	0.259787i	$0.916348\pi$
$614$	−23.3965	+	23.3965i	−0.944207	+	0.944207i
$615$	0.607636	−	7.92308i	0.0245022	−	0.319489i
$616$	3.71743	−	3.71743i	0.149779	−	0.149779i
$617$	24.4682	+	24.4682i	0.985053	+	0.985053i	0.999890	−	0.0148372i	$-0.00472301\pi$
$617$	24.4682	+	24.4682i	0.985053	+	0.985053i	−0.0148372	+	0.999890i	$0.504723\pi$
$618$	11.2297	+	11.2297i	0.451723	+	0.451723i
$619$	−18.8165			−0.756299			−0.378150	−	0.925745i	$-0.623439\pi$
$619$	−18.8165			−0.756299			−0.378150	+	0.925745i	$0.623439\pi$
$620$	−4.03139	−	0.309175i	−0.161905	−	0.0124168i
$621$	−3.33760	+	3.33760i	−0.133933	+	0.133933i
$622$	18.7483	+	18.7483i	0.751738	+	0.751738i
$623$	−2.59892			−0.104124
$624$	−3.27562	−	3.27562i	−0.131130	−	0.131130i
$625$	−23.8374	−	7.53518i	−0.953495	−	0.301407i
$626$	−26.7290			−1.06831
$627$	−12.6863			−0.506644
$628$	9.23383	−	9.23383i	0.368470	−	0.368470i
$629$	31.2870	−	3.73151i	1.24750	−	0.148785i
$630$	−2.40907	−	0.184756i	−0.0959798	−	0.00736087i
$631$	−5.74618	+	5.74618i	−0.228752	+	0.228752i	−0.812171	−	0.583419i	$-0.801714\pi$
$631$	−5.74618	+	5.74618i	−0.228752	+	0.228752i	0.583419	+	0.812171i	$0.301714\pi$
$632$	−9.56948	−	9.56948i	−0.380653	−	0.380653i
$633$	−2.77225	+	2.77225i	−0.110187	+	0.110187i
$634$	18.5839	−	18.5839i	0.738061	−	0.738061i
$635$	14.8682	+	1.14027i	0.590027	+	0.0452503i
$636$	7.98004			0.316429
$637$	27.0184			1.07051
$638$	31.4648	+	31.4648i	1.24570	+	1.24570i
$639$		−	0.599197i		−	0.0237039i
$640$	1.69741	−	1.45560i	0.0670962	−	0.0575378i
$641$	9.84764			0.388958			0.194479	−	0.980907i	$-0.437698\pi$
$641$	9.84764			0.388958			0.194479	+	0.980907i	$0.437698\pi$
$642$	−10.2003			−0.402574
$643$	45.3302			1.78765			0.893825	−	0.448417i	$-0.148012\pi$
$643$	45.3302			1.78765			0.893825	+	0.448417i	$0.148012\pi$
$644$	−3.60638	−	3.60638i	−0.142111	−	0.142111i
$645$	−1.28238	+	16.7212i	−0.0504936	+	0.658395i
$646$	9.55065	+	9.55065i	0.375765	+	0.375765i
$647$		−	48.2835i		−	1.89822i	−0.314942	−	0.949111i	$-0.601985\pi$
$647$		−	48.2835i		−	1.89822i	0.314942	−	0.949111i	$-0.398015\pi$
$648$			1.00000i			0.0392837i
$649$	−3.84530	−	3.84530i	−0.150941	−	0.150941i
$650$	−3.53193	+	22.8913i	−0.138534	+	0.897870i
$651$	1.38155	+	1.38155i	0.0541473	+	0.0541473i
$652$	23.9624			0.938439
$653$	−23.4562			−0.917912			−0.458956	−	0.888459i	$-0.651776\pi$
$653$	−23.4562			−0.917912			−0.458956	+	0.888459i	$0.651776\pi$
$654$	10.6374			0.415956
$655$	−5.39071	−	0.413423i	−0.210632	−	0.0161538i
$656$		−	3.55371i		−	0.138749i
$657$	−1.07198	−	1.07198i	−0.0418219	−	0.0418219i
$658$	12.2377			0.477074
$659$	42.8689			1.66993			0.834967	−	0.550300i	$-0.185487\pi$
$659$	42.8689			1.66993			0.834967	+	0.550300i	$0.185487\pi$
$660$	−0.831917	+	10.8475i	−0.0323823	+	0.422239i
$661$	−11.0362	+	11.0362i	−0.429259	+	0.429259i	−0.888376	−	0.459117i	$-0.848166\pi$
$661$	−11.0362	+	11.0362i	−0.429259	+	0.429259i	0.459117	+	0.888376i	$0.348166\pi$
$662$	4.72692	−	4.72692i	0.183717	−	0.183717i
$663$	−16.9678	−	16.9678i	−0.658973	−	0.658973i
$664$	−11.2549	+	11.2549i	−0.436773	+	0.436773i
$665$	−4.78238	+	4.10109i	−0.185453	+	0.159033i
$666$	6.03996	−	0.720368i	0.234044	−	0.0279137i
$667$	30.5249	−	30.5249i	1.18193	−	1.18193i
$668$	15.1621			0.586638
$669$	18.4045			0.711561
$670$	−2.45225	−	0.188068i	−0.0947387	−	0.00726569i
$671$	25.5187	+	25.5187i	0.985140	+	0.985140i
$672$	−1.08053			−0.0416825
$673$	17.9122	+	17.9122i	0.690463	+	0.690463i	0.962334	−	0.271870i	$-0.0876422\pi$
$673$	17.9122	+	17.9122i	0.690463	+	0.690463i	−0.271870	+	0.962334i	$0.587642\pi$
$674$	13.9016	−	13.9016i	0.535470	−	0.535470i
$675$	4.03331	−	2.95506i	0.155242	−	0.113740i
$676$	8.45941			0.325362
$677$	11.1599	+	11.1599i	0.428909	+	0.428909i	0.888257	−	0.459347i	$-0.151917\pi$
$677$	11.1599	+	11.1599i	0.428909	+	0.428909i	−0.459347	+	0.888257i	$0.651917\pi$
$678$	3.39746	+	3.39746i	0.130479	+	0.130479i
$679$	−4.61274	+	4.61274i	−0.177021	+	0.177021i
$680$	8.79263	−	7.54004i	0.337182	−	0.289147i
$681$	−7.38911	+	7.38911i	−0.283151	+	0.283151i
$682$	6.22082	−	6.22082i	0.238208	−	0.238208i
$683$		−	28.1871i		−	1.07855i	−0.842130	−	0.539274i	$-0.818699\pi$
$683$		−	28.1871i		−	1.07855i	0.842130	−	0.539274i	$-0.181301\pi$
$684$	1.84375	+	1.84375i	0.0704976	+	0.0704976i
$685$	−11.8096	−	0.905697i	−0.451220	−	0.0346049i
$686$	9.80467	−	9.80467i	0.374344	−	0.374344i
$687$	−8.91559	−	8.91559i	−0.340151	−	0.340151i
$688$			7.49989i			0.285931i
$689$	−26.1396	+	26.1396i	−0.995839	+	0.995839i
$690$	10.5235	+	0.807067i	0.400623	+	0.0307245i
$691$			13.7497i			0.523063i	0.965195	+	0.261531i	$0.0842275\pi$
$691$			13.7497i			0.523063i	−0.965195	+	0.261531i	$0.915773\pi$
$692$	−4.54073	+	4.54073i	−0.172612	+	0.172612i
$693$	3.71743	−	3.71743i	0.141213	−	0.141213i
$694$	0.651438			0.0247282
$695$	−16.8487	−	19.6476i	−0.639107	−	0.745278i
$696$		−	9.14579i		−	0.346670i
$697$		−	18.4083i		−	0.697263i
$698$	−25.5234			−0.966074
$699$			23.9507i			0.905899i
$700$	3.19305	+	4.35813i	0.120686	+	0.164722i
$701$	7.09322	+	7.09322i	0.267907	+	0.267907i	0.828257	−	0.560349i	$-0.189333\pi$
$701$	7.09322	+	7.09322i	0.267907	+	0.267907i	−0.560349	+	0.828257i	$0.689333\pi$
$702$	−3.27562	−	3.27562i	−0.123630	−	0.123630i
$703$	9.80800	−	12.4644i	0.369916	−	0.470102i
$704$			4.86540i			0.183372i
$705$	−19.2242	+	16.4855i	−0.724025	+	0.620881i
$706$		−	34.3501i		−	1.29278i
$707$	4.30278	+	4.30278i	0.161823	+	0.161823i
$708$			1.11770i			0.0420059i
$709$	30.9530	−	30.9530i	1.16247	−	1.16247i	0.178531	−	0.983934i	$-0.442865\pi$
$709$	30.9530	−	30.9530i	1.16247	−	1.16247i	0.983934	−	0.178531i	$-0.0571345\pi$
$710$	−1.01709	+	0.872194i	−0.0381706	+	0.0327329i
$711$	−9.56948	−	9.56948i	−0.358883	−	0.358883i
$712$	1.70075	−	1.70075i	0.0637382	−	0.0637382i
$713$	−6.03500	−	6.03500i	−0.226013	−	0.226013i
$714$	−5.59718			−0.209469
$715$	−32.8073	−	38.2574i	−1.22692	−	1.43075i
$716$	3.90880	+	3.90880i	0.146079	+	0.146079i
$717$		−	3.69593i		−	0.138027i
$718$	17.0122			0.634889
$719$			16.8010i			0.626571i	0.949659	+	0.313285i	$0.101430\pi$
$719$			16.8010i			0.626571i	−0.949659	+	0.313285i	$0.898570\pi$
$720$	1.69741	−	1.45560i	0.0632589	−	0.0542472i
$721$	−12.1340	+	12.1340i	−0.451895	+	0.451895i
$722$	−12.2012			−0.454080
$723$	20.2495			0.753087
$724$	−16.2780			−0.604967
$725$	−36.8878	+	27.0264i	−1.36998	+	1.00374i
$726$	−8.96057	−	8.96057i	−0.332558	−	0.332558i
$727$		−	21.2760i		−	0.789085i	−0.918878	−	0.394542i	$-0.870903\pi$
$727$		−	21.2760i		−	0.789085i	0.918878	−	0.394542i	$-0.129097\pi$
$728$	3.53942	−	3.53942i	0.131180	−	0.131180i
$729$			1.00000i			0.0370370i
$730$	−0.259217	+	3.37998i	−0.00959404	+	0.125098i
$731$			38.8495i			1.43690i
$732$		−	7.41746i		−	0.274157i
$733$	36.8126	−	36.8126i	1.35970	−	1.35970i	0.485428	−	0.874277i	$-0.338664\pi$
$733$	36.8126	−	36.8126i	1.35970	−	1.35970i	0.874277	−	0.485428i	$-0.161336\pi$
$734$	−10.2747	−	10.2747i	−0.379246	−	0.379246i
$735$	−0.997268	+	13.0036i	−0.0367848	+	0.479644i
$736$	4.72007			0.173984
$737$	3.78405	−	3.78405i	0.139387	−	0.139387i
$738$		−	3.55371i		−	0.130814i
$739$	9.01878			0.331761			0.165881	−	0.986146i	$-0.446953\pi$
$739$	9.01878			0.331761			0.165881	+	0.986146i	$0.446953\pi$
$740$	−10.0145	−	9.20374i	−0.368142	−	0.338336i
$741$	−12.0789			−0.443728
$742$			8.62270i			0.316549i
$743$	35.3819	−	35.3819i	1.29803	−	1.29803i	0.368345	−	0.929689i	$-0.379924\pi$
$743$	35.3819	−	35.3819i	1.29803	−	1.29803i	0.929689	−	0.368345i	$-0.120076\pi$
$744$	−1.80819			−0.0662914
$745$	−7.67901	+	6.58507i	−0.281337	+	0.241258i
$746$	−6.19992	−	6.19992i	−0.226995	−	0.226995i
$747$	−11.2549	+	11.2549i	−0.411794	+	0.411794i
$748$			25.2028i			0.921507i
$749$		−	11.0218i		−	0.402727i
$750$	−10.8869	−	2.54480i	−0.397532	−	0.0929228i
$751$		−	20.1864i		−	0.736613i	−0.929704	−	0.368307i	$-0.879938\pi$
$751$		−	20.1864i		−	0.736613i	0.929704	−	0.368307i	$-0.120062\pi$
$752$	−8.00838	+	8.00838i	−0.292036	+	0.292036i
$753$		−	7.97866i		−	0.290759i
$754$	29.9582	+	29.9582i	1.09101	+	1.09101i
$755$	11.6558	−	9.99537i	0.424199	−	0.363769i
$756$	−1.08053			−0.0392986
$757$	−23.3149			−0.847394			−0.423697	−	0.905804i	$-0.639268\pi$
$757$	−23.3149			−0.847394			−0.423697	+	0.905804i	$0.639268\pi$
$758$	−31.3961			−1.14036
$759$	−16.2387	+	16.2387i	−0.589429	+	0.589429i
$760$	0.445840	−	5.81338i	0.0161723	−	0.210874i
$761$		−	14.6952i		−	0.532702i	−0.963876	−	0.266351i	$-0.914182\pi$
$761$		−	14.6952i		−	0.532702i	0.963876	−	0.266351i	$-0.0858180\pi$
$762$	6.66879			0.241585
$763$			11.4941i			0.416114i
$764$	−6.72993	−	6.72993i	−0.243480	−	0.243480i
$765$	8.79263	−	7.54004i	0.317898	−	0.272611i
$766$	−17.9026			−0.646846
$767$	−3.66118	−	3.66118i	−0.132197	−	0.132197i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−18.5881	−	18.5881i	−0.670304	−	0.670304i	0.287482	−	0.957786i	$-0.407182\pi$
$769$	−18.5881	−	18.5881i	−0.670304	−	0.670304i	−0.957786	+	0.287482i	$0.907182\pi$
$770$	−11.7211	−	0.898915i	−0.422400	−	0.0323946i
$771$	−16.5124	+	16.5124i	−0.594680	+	0.594680i
$772$			11.3986i			0.410245i
$773$	−21.3379	−	21.3379i	−0.767471	−	0.767471i	0.210190	−	0.977661i	$-0.432592\pi$
$773$	−21.3379	−	21.3379i	−0.767471	−	0.767471i	−0.977661	+	0.210190i	$0.932592\pi$
$774$			7.49989i			0.269578i
$775$	5.34332	+	7.29299i	0.191938	+	0.261972i
$776$		−	6.03720i		−	0.216723i
$777$	0.778382	+	6.52638i	0.0279243	+	0.234133i
$778$	−7.54313	−	7.54313i	−0.270434	−	0.270434i
$779$	−6.55216	−	6.55216i	−0.234756	−	0.234756i
$780$	−0.792082	+	10.3281i	−0.0283611	+	0.369805i
$781$		−	2.91534i		−	0.104319i
$782$	24.4500			0.874331
$783$		−	9.14579i		−	0.326844i
$784$			5.83245i			0.208302i
$785$	−29.1144	−	2.23284i	−1.03914	−	0.0796936i
$786$	−2.41788			−0.0862428
$787$	13.4957	−	13.4957i	0.481069	−	0.481069i	−0.424404	−	0.905473i	$-0.639516\pi$
$787$	13.4957	−	13.4957i	0.481069	−	0.481069i	0.905473	+	0.424404i	$0.139516\pi$
$788$	10.5213	−	10.5213i	0.374805	−	0.374805i
$789$		−	13.0209i		−	0.463555i
$790$	−2.31401	+	30.1727i	−0.0823286	+	1.07350i
$791$	−3.67107	+	3.67107i	−0.130528	+	0.130528i
$792$			4.86540i			0.172885i
$793$	24.2968	+	24.2968i	0.862805	+	0.862805i
$794$	11.1198	−	11.1198i	0.394627	−	0.394627i
$795$	−11.6158	−	13.5454i	−0.411969	−	0.480407i
$796$	−5.10780	−	5.10780i	−0.181041	−	0.181041i
$797$		−	37.4922i		−	1.32804i	−0.747715	−	0.664020i	$-0.768849\pi$
$797$		−	37.4922i		−	1.32804i	0.747715	−	0.664020i	$-0.231151\pi$
$798$	−1.99224	+	1.99224i	−0.0705244	+	0.0705244i
$799$	−41.4835	+	41.4835i	−1.46758	+	1.46758i
$800$	−4.94153	−	0.762435i	−0.174709	−	0.0269561i
$801$	1.70075	−	1.70075i	0.0600929	−	0.0600929i
$802$	−22.3136	−	22.3136i	−0.787921	−	0.787921i
$803$	−5.21562	−	5.21562i	−0.184055	−	0.184055i
$804$	−1.09990			−0.0387905
$805$	−0.872064	+	11.3710i	−0.0307362	+	0.400775i
$806$	5.92294	−	5.92294i	0.208627	−	0.208627i
$807$	−13.5831	−	13.5831i	−0.478149	−	0.478149i
$808$	−5.63152			−0.198116
$809$	−1.36538	−	1.36538i	−0.0480041	−	0.0480041i	0.682697	−	0.730701i	$-0.260807\pi$
$809$	−1.36538	−	1.36538i	−0.0480041	−	0.0480041i	−0.730701	+	0.682697i	$0.760807\pi$
$810$	1.69741	−	1.45560i	0.0596411	−	0.0511447i
$811$	−31.6407			−1.11105			−0.555527	−	0.831498i	$-0.687484\pi$
$811$	−31.6407			−1.11105			−0.555527	+	0.831498i	$0.687484\pi$
$812$	9.88233			0.346802
$813$	10.2448	−	10.2448i	0.359301	−	0.359301i
$814$	29.3868	−	3.50488i	1.03001	−	0.122846i
$815$	−34.8797	−	40.6741i	−1.22178	−	1.42475i
$816$	3.66282	−	3.66282i	0.128224	−	0.128224i
$817$	13.8279	+	13.8279i	0.483778	+	0.483778i
$818$	16.7999	−	16.7999i	0.587394	−	0.587394i
$819$	3.53942	−	3.53942i	0.123677	−	0.123677i
$820$	−6.03212	+	5.17280i	−0.210651	+	0.180642i
$821$	10.9084			0.380707			0.190353	−	0.981716i	$-0.439037\pi$
$821$	10.9084			0.380707			0.190353	+	0.981716i	$0.439037\pi$
$822$	−5.29690			−0.184751
$823$	−16.6842	−	16.6842i	−0.581574	−	0.581574i	0.353762	−	0.935336i	$-0.384902\pi$
$823$	−16.6842	−	16.6842i	−0.581574	−	0.581574i	−0.935336	+	0.353762i	$0.884902\pi$
$824$		−	15.8811i		−	0.553246i
$825$	19.6237	−	14.3776i	0.683209	−	0.500563i
$826$	−1.20772			−0.0420218
$827$	−26.9666			−0.937722			−0.468861	−	0.883272i	$-0.655335\pi$
$827$	−26.9666			−0.937722			−0.468861	+	0.883272i	$0.655335\pi$
$828$	4.72007			0.164034
$829$	−6.05887	−	6.05887i	−0.210433	−	0.210433i	0.594018	−	0.804452i	$-0.297541\pi$
$829$	−6.05887	−	6.05887i	−0.210433	−	0.210433i	−0.804452	+	0.594018i	$0.797541\pi$
$830$	35.4868	+	2.72155i	1.23176	+	0.0944663i
$831$	20.9992	+	20.9992i	0.728455	+	0.728455i
$832$			4.63243i			0.160601i
$833$			30.2121i			1.04679i
$834$	−8.18479	−	8.18479i	−0.283416	−	0.283416i
$835$	−22.0700	−	25.7363i	−0.763762	−	0.890642i
$836$	8.97060	+	8.97060i	0.310255	+	0.310255i
$837$	−1.80819			−0.0625001
$838$	−3.07947			−0.106379
$839$	−48.1268			−1.66152			−0.830761	−	0.556630i	$-0.812094\pi$
$839$	−48.1268			−1.66152			−0.830761	+	0.556630i	$0.812094\pi$
$840$	1.57283	+	1.83411i	0.0542678	+	0.0632830i
$841$			54.6454i			1.88433i
$842$	−2.58223	−	2.58223i	−0.0889897	−	0.0889897i
$843$	4.93824			0.170082
$844$	3.92055			0.134951
$845$	−12.3136	−	14.3591i	−0.423599	−	0.493969i
$846$	−8.00838	+	8.00838i	−0.275334	+	0.275334i
$847$	9.68220	−	9.68220i	0.332684	−	0.332684i
$848$	−5.64274	−	5.64274i	−0.193772	−	0.193772i
$849$	−10.4463	+	10.4463i	−0.358516	+	0.358516i
$850$	−25.5972	−	3.94942i	−0.877975	−	0.135464i
$851$	−3.40019	−	28.5090i	−0.116557	−	0.977277i
$852$	−0.423697	+	0.423697i	−0.0145156	+	0.0145156i
$853$	−0.209022			−0.00715677			−0.00357838	−	0.999994i	$-0.501139\pi$
$853$	−0.209022			−0.00715677			−0.00357838	+	0.999994i	$0.501139\pi$
$854$	8.01482			0.274261
$855$	0.445840	−	5.81338i	0.0152474	−	0.198814i
$856$	7.21271	+	7.21271i	0.246525	+	0.246525i
$857$	−27.1503			−0.927437			−0.463718	−	0.885983i	$-0.653485\pi$
$857$	−27.1503			−0.927437			−0.463718	+	0.885983i	$0.653485\pi$
$858$	−15.9372	−	15.9372i	−0.544088	−	0.544088i
$859$	0.741722	−	0.741722i	0.0253072	−	0.0253072i	−0.694340	−	0.719647i	$-0.744304\pi$
$859$	0.741722	−	0.741722i	0.0253072	−	0.0253072i	0.719647	+	0.694340i	$0.244304\pi$
$860$	12.7304	−	10.9169i	0.434104	−	0.372262i
$861$	3.83991			0.130864
$862$	−9.94058	−	9.94058i	−0.338578	−	0.338578i
$863$	18.9404	+	18.9404i	0.644738	+	0.644738i	0.951717	−	0.306978i	$-0.0993179\pi$
$863$	18.9404	+	18.9404i	0.644738	+	0.644738i	−0.306978	+	0.951717i	$0.599318\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	14.3170	+	1.09800i	0.486792	+	0.0373330i
$866$	−13.7642	+	13.7642i	−0.467727	+	0.467727i
$867$	6.95263	−	6.95263i	0.236124	−	0.236124i
$868$		−	1.95381i		−	0.0663166i
$869$	−46.5594	−	46.5594i	−1.57942	−	1.57942i
$870$	−15.5242	+	13.3126i	−0.526320	+	0.451341i
$871$	3.60286	−	3.60286i	0.122078	−	0.122078i
$872$	−7.52179	−	7.52179i	−0.254720	−	0.254720i
$873$		−	6.03720i		−	0.204328i
$874$	8.70264	−	8.70264i	0.294371	−	0.294371i
$875$	2.74974	−	11.7636i	0.0929582	−	0.397684i
$876$			1.51601i			0.0512212i
$877$	23.7859	−	23.7859i	0.803194	−	0.803194i	−0.180400	−	0.983593i	$-0.557739\pi$
$877$	23.7859	−	23.7859i	0.803194	−	0.803194i	0.983593	+	0.180400i	$0.0577391\pi$
$878$	−21.9903	+	21.9903i	−0.742137	+	0.742137i
$879$	33.8569			1.14197
$880$	8.25861	−	7.08210i	0.278398	−	0.238738i
$881$		−	25.7820i		−	0.868617i	−0.900764	−	0.434308i	$-0.856993\pi$
$881$		−	25.7820i		−	0.868617i	0.900764	−	0.434308i	$-0.143007\pi$
$882$			5.83245i			0.196389i
$883$	41.2363			1.38771			0.693856	−	0.720114i	$-0.255910\pi$
$883$	41.2363			1.38771			0.693856	+	0.720114i	$0.255910\pi$
$884$			23.9960i			0.807074i
$885$	1.89721	−	1.62693i	0.0637739	−	0.0546888i
$886$	−17.2453	−	17.2453i	−0.579367	−	0.579367i
$887$	12.6972	+	12.6972i	0.426330	+	0.426330i	0.887376	−	0.461046i	$-0.152526\pi$
$887$	12.6972	+	12.6972i	0.426330	+	0.426330i	−0.461046	+	0.887376i	$0.652526\pi$
$888$	−4.78027	−	3.76152i	−0.160415	−	0.126228i
$889$			7.20586i			0.241677i
$890$	−5.36248	−	0.411259i	−0.179751	−	0.0137854i
$891$			4.86540i			0.162997i
$892$	−13.0140	−	13.0140i	−0.435740	−	0.435740i
$893$			29.5309i			0.988215i
$894$	−3.19891	+	3.19891i	−0.106988	+	0.106988i
$895$	0.945190	−	12.3245i	0.0315942	−	0.411963i
$896$	0.764053	+	0.764053i	0.0255252	+	0.0255252i
$897$	−15.4612	+	15.4612i	−0.516234	+	0.516234i
$898$	0.574002	+	0.574002i	0.0191547	+	0.0191547i
$899$	16.5373			0.551550
$900$	−4.94153	−	0.762435i	−0.164718	−	0.0254145i
$901$	−29.2294	−	29.2294i	−0.973774	−	0.973774i
$902$		−	17.2902i		−	0.575702i
$903$	−8.10389			−0.269681
$904$		−	4.80474i		−	0.159803i
$905$	23.6943	+	27.6305i	0.787626	+	0.918469i
$906$	4.85557	−	4.85557i	0.161316	−	0.161316i
$907$	−34.2793			−1.13822			−0.569112	−	0.822260i	$-0.692713\pi$
$907$	−34.2793			−1.13822			−0.569112	+	0.822260i	$0.692713\pi$
$908$	10.4498			0.346788
$909$	−5.63152			−0.186786
$910$	−11.1599	−	0.855871i	−0.369946	−	0.0283719i
$911$	23.1995	+	23.1995i	0.768632	+	0.768632i	0.977866	−	0.209234i	$-0.0670969\pi$
$911$	23.1995	+	23.1995i	0.768632	+	0.768632i	−0.209234	+	0.977866i	$0.567097\pi$
$912$		−	2.60746i		−	0.0863416i
$913$	−54.7594	+	54.7594i	−1.81227	+	1.81227i
$914$			12.9457i			0.428206i
$915$	−12.5905	+	10.7969i	−0.416229	+	0.356934i
$916$			12.6086i			0.416598i
$917$		−	2.61260i		−	0.0862756i
$918$	3.66282	−	3.66282i	0.120891	−	0.120891i
$919$	9.82515	+	9.82515i	0.324102	+	0.324102i	0.850338	−	0.526236i	$-0.176397\pi$
$919$	9.82515	+	9.82515i	0.324102	+	0.324102i	−0.526236	+	0.850338i	$0.676397\pi$
$920$	−6.87056	−	8.01192i	−0.226516	−	0.264145i
$921$	33.0877			1.09028
$922$	−21.0318	+	21.0318i	−0.692645	+	0.692645i
$923$		−	2.77574i		−	0.0913646i
$924$	−5.25723			−0.172950
$925$	−1.04535	+	30.3958i	−0.0343710	+	0.999409i
$926$	−14.6765			−0.482301
$927$		−	15.8811i		−	0.521605i
$928$	−6.46705	+	6.46705i	−0.212291	+	0.212291i
$929$	23.3283			0.765378			0.382689	−	0.923877i	$-0.374998\pi$
$929$	23.3283			0.765378			0.382689	+	0.923877i	$0.374998\pi$
$930$	2.63201	+	3.06925i	0.0863069	+	0.100645i
$931$	10.7536	+	10.7536i	0.352434	+	0.352434i
$932$	16.9357	−	16.9357i	0.554748	−	0.554748i
$933$		−	26.5141i		−	0.868032i
$934$		−	12.6925i		−	0.415312i
$935$	42.7797	−	36.6854i	1.39905	−	1.19974i
$936$			4.63243i			0.151416i
$937$	−5.21829	+	5.21829i	−0.170474	+	0.170474i	−0.787188	−	0.616714i	$-0.788464\pi$
$937$	−5.21829	+	5.21829i	−0.170474	+	0.170474i	0.616714	+	0.787188i	$0.288464\pi$
$938$		−	1.18848i		−	0.0388052i
$939$	18.9003	+	18.9003i	0.616788	+	0.616788i
$940$	25.2506	+	1.93652i	0.823583	+	0.0631622i
$941$	−37.3652			−1.21807			−0.609035	−	0.793144i	$-0.708443\pi$
$941$	−37.3652			−1.21807			−0.609035	+	0.793144i	$0.708443\pi$
$942$	−13.0586			−0.425473
$943$	−16.7738			−0.546229
$944$	0.790336	−	0.790336i	0.0257232	−	0.0257232i
$945$	1.57283	+	1.83411i	0.0511641	+	0.0596637i
$946$			36.4900i			1.18639i
$947$	28.3116			0.920004			0.460002	−	0.887918i	$-0.347849\pi$
$947$	28.3116			0.920004			0.460002	+	0.887918i	$0.347849\pi$
$948$			13.5333i			0.439541i
$949$	−4.96588	−	4.96588i	−0.161199	−	0.161199i
$950$	−10.5167	+	7.70521i	−0.341207	+	0.249990i
$951$	−26.2816			−0.852239
$952$	3.95780	+	3.95780i	0.128273	+	0.128273i
$953$	−6.65077	+	6.65077i	−0.215440	+	0.215440i	−0.806573	−	0.591134i	$-0.798680\pi$
$953$	−6.65077	+	6.65077i	−0.215440	+	0.215440i	0.591134	+	0.806573i	$0.298680\pi$
$954$	−5.64274	−	5.64274i	−0.182690	−	0.182690i
$955$	−1.62737	+	21.2196i	−0.0526605	+	0.686650i
$956$	−2.61342	+	2.61342i	−0.0845240	+	0.0845240i
$957$		−	44.4980i		−	1.43841i
$958$	−17.3000	−	17.3000i	−0.558939	−	0.558939i
$959$		−	5.72348i		−	0.184821i
$960$	−2.22952	−	0.170986i	−0.0719575	−	0.00551856i
$961$			27.7305i			0.894531i
$962$	27.9797	−	3.33706i	0.902101	−	0.107591i
$963$	7.21271	+	7.21271i	0.232426	+	0.232426i
$964$	−14.3186	−	14.3186i	−0.461170	−	0.461170i
$965$	19.3482	−	16.5919i	0.622840	−	0.534111i
$966$			5.10020i			0.164096i
$967$	1.06824			0.0343524			0.0171762	−	0.999852i	$-0.494532\pi$
$967$	1.06824			0.0343524			0.0171762	+	0.999852i	$0.494532\pi$
$968$			12.6722i			0.407298i
$969$		−	13.5067i		−	0.433897i
$970$	−10.2476	+	8.78777i	−0.329032	+	0.282158i
$971$	−41.5880			−1.33462			−0.667312	−	0.744778i	$-0.732555\pi$
$971$	−41.5880			−1.33462			−0.667312	+	0.744778i	$0.732555\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	8.84394	−	8.84394i	0.283524	−	0.283524i
$974$		−	25.7666i		−	0.825615i
$975$	18.6840	−	13.6891i	0.598368	−	0.438403i
$976$	−5.24494	+	5.24494i	−0.167886	+	0.167886i
$977$		−	36.3637i		−	1.16338i	−0.813412	−	0.581688i	$-0.802392\pi$
$977$		−	36.3637i		−	1.16338i	0.813412	−	0.581688i	$-0.197608\pi$
$978$	−16.9440	−	16.9440i	−0.541808	−	0.541808i
$979$	8.27482	−	8.27482i	0.264464	−	0.264464i
$980$	9.90008	−	8.48973i	0.316246	−	0.271195i
$981$	−7.52179	−	7.52179i	−0.240152	−	0.240152i
$982$		−	4.97935i		−	0.158898i
$983$	5.76895	−	5.76895i	0.184001	−	0.184001i	−0.609096	−	0.793097i	$-0.708467\pi$
$983$	5.76895	−	5.76895i	0.184001	−	0.184001i	0.793097	+	0.609096i	$0.208467\pi$
$984$	−2.51285	+	2.51285i	−0.0801069	+	0.0801069i
$985$	−33.1738	−	2.54416i	−1.05700	−	0.0810637i
$986$	−33.4994	+	33.4994i	−1.06684	+	1.06684i
$987$	−8.65333	−	8.65333i	−0.275439	−	0.275439i
$988$	8.54105	+	8.54105i	0.271727	+	0.271727i
$989$	35.4000			1.12566
$990$	8.25861	−	7.08210i	0.262476	−	0.225084i
$991$	12.8704	−	12.8704i	0.408841	−	0.408841i	−0.472493	−	0.881334i	$-0.656646\pi$
$991$	12.8704	−	12.8704i	0.408841	−	0.408841i	0.881334	+	0.472493i	$0.156646\pi$
$992$	1.27858	+	1.27858i	0.0405950	+	0.0405950i
$993$	−6.68487			−0.212138
$994$	−0.457819	−	0.457819i	−0.0145211	−	0.0145211i
$995$	−1.23512	+	16.1050i	−0.0391560	+	0.510562i
$996$	15.9168			0.504342
$997$	17.3919			0.550808			0.275404	−	0.961329i	$-0.411188\pi$
$997$	17.3919			0.550808			0.275404	+	0.961329i	$0.411188\pi$
$998$	19.1310	−	19.1310i	0.605582	−	0.605582i
$999$	−4.78027	−	3.76152i	−0.151241	−	0.119009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.43.13	✓	36
5.2	odd	4		1110.2.o.a.487.6	yes	36
37.31	odd	4		1110.2.o.a.253.6	yes	36
185.142	even	4	inner	1110.2.l.a.697.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.13	✓	36	1.1	even	1	trivial
1110.2.l.a.697.13	yes	36	185.142	even	4	inner
1110.2.o.a.253.6	yes	36	37.31	odd	4
1110.2.o.a.487.6	yes	36	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.45560 + 1.69741i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.764053 + 0.764053i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.45560 + 1.69741i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.764053 + 0.764053i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-1.69741 + 1.45560i) q^{10} -4.86540i q^{11} +(-0.707107 + 0.707107i) q^{12} -4.63243i q^{13} +(-0.764053 - 0.764053i) q^{14} +(2.22952 + 0.170986i) q^{15} +1.00000 q^{16} +5.18001 q^{17} +1.00000 q^{18} +(1.84375 - 1.84375i) q^{19} +(-1.45560 - 1.69741i) q^{20} +1.08053i q^{21} +4.86540 q^{22} -4.72007i q^{23} +(-0.707107 - 0.707107i) q^{24} +(-0.762435 + 4.94153i) q^{25} +4.63243 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.764053 - 0.764053i) q^{28} +(6.46705 + 6.46705i) q^{29} +(-0.170986 + 2.22952i) q^{30} +(1.27858 - 1.27858i) q^{31} +1.00000i q^{32} +(-3.44036 - 3.44036i) q^{33} +5.18001i q^{34} +(-2.40907 - 0.184756i) q^{35} +1.00000i q^{36} +(6.03996 - 0.720368i) q^{37} +(1.84375 + 1.84375i) q^{38} +(-3.27562 - 3.27562i) q^{39} +(1.69741 - 1.45560i) q^{40} -3.55371i q^{41} -1.08053 q^{42} +7.49989i q^{43} +4.86540i q^{44} +(1.69741 - 1.45560i) q^{45} +4.72007 q^{46} +(-8.00838 + 8.00838i) q^{47} +(0.707107 - 0.707107i) q^{48} +5.83245i q^{49} +(-4.94153 - 0.762435i) q^{50} +(3.66282 - 3.66282i) q^{51} +4.63243i q^{52} +(-5.64274 - 5.64274i) q^{53} +(0.707107 - 0.707107i) q^{54} +(8.25861 - 7.08210i) q^{55} +(0.764053 + 0.764053i) q^{56} -2.60746i q^{57} +(-6.46705 + 6.46705i) q^{58} +(0.790336 - 0.790336i) q^{59} +(-2.22952 - 0.170986i) q^{60} +(-5.24494 + 5.24494i) q^{61} +(1.27858 + 1.27858i) q^{62} +(0.764053 + 0.764053i) q^{63} -1.00000 q^{64} +(7.86316 - 6.74298i) q^{65} +(3.44036 - 3.44036i) q^{66} +(0.777747 + 0.777747i) q^{67} -5.18001 q^{68} +(-3.33760 - 3.33760i) q^{69} +(0.184756 - 2.40907i) q^{70} +0.599197 q^{71} -1.00000 q^{72} +(1.07198 - 1.07198i) q^{73} +(0.720368 + 6.03996i) q^{74} +(2.95506 + 4.03331i) q^{75} +(-1.84375 + 1.84375i) q^{76} +(3.71743 + 3.71743i) q^{77} +(3.27562 - 3.27562i) q^{78} +(9.56948 - 9.56948i) q^{79} +(1.45560 + 1.69741i) q^{80} -1.00000 q^{81} +3.55371 q^{82} +(-11.2549 - 11.2549i) q^{83} -1.08053i q^{84} +(7.54004 + 8.79263i) q^{85} -7.49989 q^{86} +9.14579 q^{87} -4.86540 q^{88} +(1.70075 + 1.70075i) q^{89} +(1.45560 + 1.69741i) q^{90} +(3.53942 + 3.53942i) q^{91} +4.72007i q^{92} -1.80819i q^{93} +(-8.00838 - 8.00838i) q^{94} +(5.81338 + 0.445840i) q^{95} +(0.707107 + 0.707107i) q^{96} +6.03720 q^{97} -5.83245 q^{98} -4.86540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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