LMFDB - Embedded newform 1110.2.o.a.253.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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			253.6
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	1.69741	−	1.45560i	0.759107	−	0.650966i
$5$	1.69741	−	1.45560i	0.759107	−	0.650966i
$6$	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	$0.315460\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−1.69741	+	1.45560i	−0.536770	+	0.460302i
$11$			4.86540i			1.46697i	0.679703	+	0.733487i	$0.262109\pi$
$11$			4.86540i			1.46697i	−0.679703	+	0.733487i	$0.737891\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−4.63243			−1.28481			−0.642403	−	0.766367i	$-0.722062\pi$
$13$	−4.63243			−1.28481			−0.642403	+	0.766367i	$0.722062\pi$
$14$	0.764053	−	0.764053i	0.204202	−	0.204202i
$15$	−0.170986	+	2.22952i	−0.0441484	+	0.575660i
$16$	1.00000			0.250000
$17$		−	5.18001i		−	1.25634i	−0.778077	−	0.628169i	$-0.783805\pi$
$17$		−	5.18001i		−	1.25634i	0.778077	−	0.628169i	$-0.216195\pi$
$18$			1.00000i			0.235702i
$19$	−1.84375	−	1.84375i	−0.422986	−	0.422986i	0.463245	−	0.886230i	$-0.346685\pi$
$19$	−1.84375	−	1.84375i	−0.422986	−	0.422986i	−0.886230	+	0.463245i	$0.846685\pi$
$20$	1.69741	−	1.45560i	0.379554	−	0.325483i
$21$		−	1.08053i		−	0.235792i
$22$		−	4.86540i		−	1.03731i
$23$	−4.72007			−0.984203			−0.492102	−	0.870538i	$-0.663771\pi$
$23$	−4.72007			−0.984203			−0.492102	+	0.870538i	$0.663771\pi$
$24$	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	−0.227008	+	0.973893i	$0.572894\pi$
$29$	−6.46705	+	6.46705i	−1.20090	+	1.20090i	−0.973893	+	0.227008i	$0.927106\pi$
$30$	0.170986	−	2.22952i	0.0312177	−	0.407053i
$31$	1.27858	+	1.27858i	0.229640	+	0.229640i	0.812542	−	0.582902i	$-0.198083\pi$
$31$	1.27858	+	1.27858i	0.229640	+	0.229640i	−0.582902	+	0.812542i	$0.698083\pi$
$32$	−1.00000			−0.176777
$33$	−3.44036	−	3.44036i	−0.598890	−	0.598890i
$34$			5.18001i			0.888364i
$35$	−0.184756	+	2.40907i	−0.0312295	+	0.407208i
$36$		−	1.00000i		−	0.166667i
$37$	0.720368	−	6.03996i	0.118428	−	0.992963i
$37$	0.720368	−	6.03996i	0.118428	−	0.992963i
$38$	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	$0.0895053\pi$
$41$			3.55371i			0.554997i	−0.960726	+	0.277498i	$0.910495\pi$
$42$			1.08053i			0.166730i
$43$	7.49989			1.14372			0.571861	−	0.820350i	$-0.306221\pi$
$43$	7.49989			1.14372			0.571861	+	0.820350i	$0.306221\pi$
$44$			4.86540i			0.733487i
$45$	−1.45560	−	1.69741i	−0.216989	−	0.253036i
$46$	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
$50$	−0.762435	+	4.94153i	−0.107825	+	0.698838i
$51$	3.66282	+	3.66282i	0.512897	+	0.512897i
$52$	−4.63243			−0.642403
$53$	−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
$55$	7.08210	+	8.25861i	0.954950	+	1.11359i
$56$	0.764053	−	0.764053i	0.102101	−	0.102101i
$57$	2.60746			0.345366
$58$	6.46705	−	6.46705i	0.849165	−	0.849165i
$59$	−0.790336	−	0.790336i	−0.102893	−	0.102893i	0.653786	−	0.756679i	$-0.273180\pi$
$59$	−0.790336	−	0.790336i	−0.102893	−	0.102893i	−0.756679	+	0.653786i	$0.773180\pi$
$60$	−0.170986	+	2.22952i	−0.0220742	+	0.287830i
$61$	−5.24494	−	5.24494i	−0.671545	−	0.671545i	0.286527	−	0.958072i	$-0.407499\pi$
$61$	−5.24494	−	5.24494i	−0.671545	−	0.671545i	−0.958072	+	0.286527i	$0.907499\pi$
$62$	−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	0.658001	−	0.753017i	$-0.271402\pi$
$67$	−0.777747	−	0.777747i	−0.0950169	−	0.0950169i	−0.753017	+	0.658001i	$0.771402\pi$
$68$		−	5.18001i		−	0.628169i
$69$	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	$0.488680\pi$
$72$			1.00000i			0.117851i
$73$	−1.07198	+	1.07198i	−0.125466	+	0.125466i	−0.767051	−	0.641586i	$-0.778277\pi$
$73$	−1.07198	+	1.07198i	−0.125466	+	0.125466i	0.641586	+	0.767051i	$0.278277\pi$
$74$	−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	−0.996807	−	0.0798429i	$-0.974558\pi$
$79$	−9.56948	−	9.56948i	−1.07665	−	1.07665i	−0.0798429	−	0.996807i	$-0.525442\pi$
$80$	1.69741	−	1.45560i	0.189777	−	0.162741i
$81$	−1.00000			−0.111111
$82$		−	3.55371i		−	0.392442i
$83$	−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
$87$		−	9.14579i		−	0.980531i
$88$		−	4.86540i		−	0.518654i
$89$	−1.70075	+	1.70075i	−0.180279	+	0.180279i	−0.791477	−	0.611199i	$-0.790688\pi$
$89$	−1.70075	+	1.70075i	−0.180279	+	0.180279i	0.611199	+	0.791477i	$0.290688\pi$
$90$	1.45560	+	1.69741i	0.153434	+	0.178923i
$91$	3.53942	−	3.53942i	0.371032	−	0.371032i
$92$	−4.72007			−0.492102
$93$	−1.80819			−0.187500
$94$	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
$97$		−	6.03720i		−	0.612985i	−0.951873	−	0.306492i	$-0.900845\pi$
$97$		−	6.03720i		−	0.612985i	0.951873	−	0.306492i	$-0.0991554\pi$
$98$		−	5.83245i		−	0.589166i
$99$	4.86540			0.488991
$100$	0.762435	−	4.94153i	0.0762435	−	0.494153i
$101$			5.63152i			0.560357i	0.959948	+	0.280178i	$0.0903936\pi$
$101$			5.63152i			0.560357i	−0.959948	+	0.280178i	$0.909606\pi$
$102$	−3.66282	−	3.66282i	−0.362673	−	0.362673i
$103$			15.8811i			1.56481i	0.622767	+	0.782407i	$0.286008\pi$
$103$			15.8811i			1.56481i	−0.622767	+	0.782407i	$0.713992\pi$
$104$	4.63243			0.454247
$105$	−1.57283	−	1.83411i	−0.153492	−	0.178991i
$106$	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	$-0.420147\pi$
$109$	−7.52179	−	7.52179i	−0.720457	−	0.720457i	−0.968698	+	0.248241i	$0.920147\pi$
$110$	−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
$113$			4.80474i			0.451991i	0.974128	+	0.225996i	$0.0725635\pi$
$113$			4.80474i			0.451991i	−0.974128	+	0.225996i	$0.927436\pi$
$114$	−2.60746			−0.244211
$115$	−8.01192	+	6.87056i	−0.747115	+	0.640683i
$116$	−6.46705	+	6.46705i	−0.600450	+	0.600450i
$117$			4.63243i			0.428268i
$118$	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
$125$	−5.89874	−	9.49763i	−0.527599	−	0.849493i
$126$	−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	$0.154387\pi$
$128$	−1.00000			−0.0883883
$129$	−5.30322	+	5.30322i	−0.466923	+	0.466923i
$130$	7.86316	−	6.74298i	0.689644	−	0.591399i
$131$	−1.70970	−	1.70970i	−0.149377	−	0.149377i	0.628463	−	0.777840i	$-0.283684\pi$
$131$	−1.70970	−	1.70970i	−0.149377	−	0.149377i	−0.777840	+	0.628463i	$0.783684\pi$
$132$	−3.44036	−	3.44036i	−0.299445	−	0.299445i
$133$	2.81745			0.244304
$134$	0.777747	+	0.777747i	0.0671871	+	0.0671871i
$135$	2.22952	+	0.170986i	0.191887	+	0.0147161i
$136$			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	$-0.336671\pi$
$139$	11.5750			0.981782			0.490891	+	0.871221i	$0.336671\pi$
$140$	−0.184756	+	2.40907i	−0.0156148	+	0.203604i
$141$		−	11.3256i		−	0.953785i
$142$	−0.599197			−0.0502835
$143$		−	22.5386i		−	1.88478i
$144$		−	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
$148$	0.720368	−	6.03996i	0.0592139	−	0.496481i
$149$			4.52394i			0.370616i	0.982681	+	0.185308i	$0.0593282\pi$
$149$			4.52394i			0.370616i	−0.982681	+	0.185308i	$0.940672\pi$
$150$	−2.95506	−	4.03331i	−0.241280	−	0.329318i
$151$			6.86682i			0.558814i	0.960173	+	0.279407i	$0.0901378\pi$
$151$			6.86682i			0.558814i	−0.960173	+	0.279407i	$0.909862\pi$
$152$	1.84375	+	1.84375i	0.149548	+	0.149548i
$153$	−5.18001			−0.418779
$154$	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
$162$	1.00000			0.0785674
$163$		−	23.9624i		−	1.87688i	−0.345446	−	0.938439i	$-0.612272\pi$
$163$		−	23.9624i		−	1.87688i	0.345446	−	0.938439i	$-0.387728\pi$
$164$			3.55371i			0.277498i
$165$	−10.8475	−	0.831917i	−0.844478	−	0.0647646i
$166$	11.2549	+	11.2549i	0.873547	+	0.873547i
$167$			15.1621i			1.17328i	0.809849	+	0.586638i	$0.199549\pi$
$167$			15.1621i			1.17328i	−0.809849	+	0.586638i	$0.800451\pi$
$168$			1.08053i			0.0833650i
$169$	8.45941			0.650724
$170$	7.54004	+	8.79263i	0.578295	+	0.674364i
$171$	−1.84375	+	1.84375i	−0.140995	+	0.140995i
$172$	7.49989			0.571861
$173$	−4.54073	+	4.54073i	−0.345225	+	0.345225i	−0.858327	−	0.513102i	$-0.828496\pi$
$173$	−4.54073	+	4.54073i	−0.345225	+	0.345225i	0.513102	+	0.858327i	$0.328496\pi$
$174$			9.14579i			0.693340i
$175$	3.19305	+	4.35813i	0.241372	+	0.329444i
$176$			4.86540i			0.366744i
$177$	1.11770			0.0840117
$178$	1.70075	−	1.70075i	0.127476	−	0.127476i
$179$	3.90880	−	3.90880i	0.292157	−	0.292157i	−0.545775	−	0.837932i	$-0.683765\pi$
$179$	3.90880	−	3.90880i	0.292157	−	0.292157i	0.837932	+	0.545775i	$0.183765\pi$
$180$	−1.45560	−	1.69741i	−0.108494	−	0.126518i
$181$	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
$183$	7.41746			0.548314
$184$	4.72007			0.347968
$185$	−7.56902	−	11.3009i	−0.556485	−	0.830857i
$186$	1.80819			0.132583
$187$	25.2028			1.84301
$188$	−8.00838	+	8.00838i	−0.584071	+	0.584071i
$189$	−1.08053			−0.0785973
$190$	5.81338	+	0.445840i	0.421747	+	0.0323446i
$191$	6.72993	−	6.72993i	0.486961	−	0.486961i	−0.420385	−	0.907346i	$-0.638105\pi$
$191$	6.72993	−	6.72993i	0.486961	−	0.486961i	0.907346	+	0.420385i	$0.138105\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−11.3986			−0.820490			−0.410245	−	0.911975i	$-0.634557\pi$
$193$	−11.3986			−0.820490			−0.410245	+	0.911975i	$0.634557\pi$
$194$			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	$0.427828\pi$
$198$	−4.86540			−0.345769
$199$	−5.10780	+	5.10780i	−0.362082	+	0.362082i	−0.864579	−	0.502497i	$-0.832415\pi$
$199$	−5.10780	+	5.10780i	−0.362082	+	0.362082i	0.502497	+	0.864579i	$0.332415\pi$
$200$	−0.762435	+	4.94153i	−0.0539123	+	0.349419i
$201$	1.09990			0.0775810
$202$		−	5.63152i		−	0.396232i
$203$		−	9.88233i		−	0.693604i
$204$	3.66282	+	3.66282i	0.256449	+	0.256449i
$205$	5.17280	+	6.03212i	0.361284	+	0.421302i
$206$		−	15.8811i		−	1.10649i
$207$			4.72007i			0.328068i
$208$	−4.63243			−0.321201
$209$	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
$217$	−1.95381			−0.132633
$218$	7.52179	+	7.52179i	0.509440	+	0.509440i
$219$		−	1.51601i		−	0.102442i
$220$	7.08210	+	8.25861i	0.477475	+	0.556795i
$221$			23.9960i			1.61415i
$222$	−3.76152	−	4.78027i	−0.252456	−	0.320831i
$223$	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
$227$			10.4498i			0.693577i	0.937943	+	0.346788i	$0.112728\pi$
$227$			10.4498i			0.693577i	−0.937943	+	0.346788i	$0.887272\pi$
$228$	2.60746			0.172683
$229$		−	12.6086i		−	0.833197i	−0.909091	−	0.416598i	$-0.863222\pi$
$229$		−	12.6086i		−	0.833197i	0.909091	−	0.416598i	$-0.136778\pi$
$230$	8.01192	−	6.87056i	0.528290	−	0.453031i
$231$	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	$-0.462904\pi$
$233$	16.9357	−	16.9357i	1.10950	−	1.10950i	0.993217	−	0.116278i	$-0.0370965\pi$
$234$		−	4.63243i		−	0.302831i
$235$	−1.93652	+	25.2506i	−0.126324	+	1.64717i
$236$	−0.790336	−	0.790336i	−0.0514465	−	0.0514465i
$237$	13.5333			0.879081
$238$	−3.95780	−	3.95780i	−0.256546	−	0.256546i
$239$	−2.61342	−	2.61342i	−0.169048	−	0.169048i	0.617513	−	0.786561i	$-0.288140\pi$
$239$	−2.61342	−	2.61342i	−0.169048	−	0.169048i	−0.786561	+	0.617513i	$0.788140\pi$
$240$	−0.170986	+	2.22952i	−0.0110371	+	0.143915i
$241$	14.3186	−	14.3186i	0.922340	−	0.922340i	−0.0748547	−	0.997194i	$-0.523849\pi$
$241$	14.3186	−	14.3186i	0.922340	−	0.922340i	0.997194	+	0.0748547i	$0.0238493\pi$
$242$	12.6722			0.814597
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−5.24494	−	5.24494i	−0.335773	−	0.335773i
$245$	8.48973	+	9.90008i	0.542389	+	0.632493i
$246$	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	0.862375	−	0.506270i	$-0.168976\pi$
$251$	5.64176	+	5.64176i	0.356105	+	0.356105i	−0.506270	+	0.862375i	$0.668976\pi$
$252$	0.764053	+	0.764053i	0.0481308	+	0.0481308i
$253$		−	22.9651i		−	1.44380i
$254$	−4.71555	+	4.71555i	−0.295880	+	0.295880i
$255$	11.5489	+	0.885710i	0.723223	+	0.0554653i
$256$	1.00000			0.0625000
$257$			23.3521i			1.45666i	0.685226	+	0.728331i	$0.259704\pi$
$257$			23.3521i			1.45666i	−0.685226	+	0.728331i	$0.740296\pi$
$258$	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	−0.931494	−	0.363757i	$-0.881494\pi$
$263$	−9.20714	+	9.20714i	−0.567737	+	0.567737i	0.363757	+	0.931494i	$0.381494\pi$
$264$	3.44036	+	3.44036i	0.211740	+	0.211740i
$265$	−17.7917	−	1.36448i	−1.09293	−	0.0838191i
$266$	−2.81745			−0.172749
$267$		−	2.40522i		−	0.147197i
$268$	−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	$0.354960\pi$
$272$		−	5.18001i		−	0.314084i
$273$			5.00550i			0.302947i
$274$	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
$277$	−29.6974			−1.78434			−0.892172	−	0.451696i	$-0.850819\pi$
$277$	−29.6974			−1.78434			−0.892172	+	0.451696i	$0.850819\pi$
$278$	−11.5750			−0.694225
$279$	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	−0.595240	−	0.803548i	$-0.702943\pi$
$281$	3.49186	−	3.49186i	0.208307	−	0.208307i	0.803548	+	0.595240i	$0.202943\pi$
$282$			11.3256i			0.674428i
$283$		−	14.7733i		−	0.878182i	−0.898442	−	0.439091i	$-0.855300\pi$
$283$		−	14.7733i		−	0.878182i	0.898442	−	0.439091i	$-0.144700\pi$
$284$	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
$288$			1.00000i			0.0589256i
$289$	−9.83251			−0.578383
$290$	1.56380	−	20.3907i	0.0918297	−	1.19738i
$291$	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
$298$		−	4.52394i		−	0.262065i
$299$	21.8654			1.26451
$300$	2.95506	+	4.03331i	0.170611	+	0.232863i
$301$	−5.73031	+	5.73031i	−0.330290	+	0.330290i
$302$		−	6.86682i		−	0.395141i
$303$	−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	$-0.856831\pi$
$307$	−23.3965	−	23.3965i	−1.33531	−	1.33531i	−0.434767	−	0.900543i	$-0.643169\pi$
$308$	−3.71743	−	3.71743i	−0.211820	−	0.211820i
$309$	−11.2297	−	11.2297i	−0.638833	−	0.638833i
$310$	−4.03139	−	0.309175i	−0.228968	−	0.0175600i
$311$	18.7483	+	18.7483i	1.06312	+	1.06312i	0.997869	+	0.0652489i	$0.0207841\pi$
$311$	18.7483	+	18.7483i	1.06312	+	1.06312i	0.0652489	+	0.997869i	$0.479216\pi$
$312$	−3.27562	+	3.27562i	−0.185446	+	0.185446i
$313$	26.7290			1.51081			0.755407	−	0.655255i	$-0.227439\pi$
$313$	26.7290			1.51081			0.755407	+	0.655255i	$0.227439\pi$
$314$	9.23383	−	9.23383i	0.521095	−	0.521095i
$315$	2.40907	+	0.184756i	0.135736	+	0.0104098i
$316$	−9.56948	−	9.56948i	−0.538325	−	0.538325i
$317$	18.5839	+	18.5839i	1.04378	+	1.04378i	0.998997	+	0.0447783i	$0.0142581\pi$
$317$	18.5839	+	18.5839i	1.04378	+	1.04378i	0.0447783	+	0.998997i	$0.485742\pi$
$318$	−7.98004			−0.447498
$319$	−31.4648	−	31.4648i	−1.76169	−	1.76169i
$320$	1.69741	−	1.45560i	0.0948884	−	0.0813707i
$321$		−	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
$325$	−3.53193	+	22.8913i	−0.195916	+	1.26978i
$326$			23.9624i			1.32715i
$327$	10.6374			0.588251
$328$		−	3.55371i		−	0.196221i
$329$		−	12.2377i		−	0.674684i
$330$	10.8475	+	0.831917i	0.597136	+	0.0457955i
$331$	−4.72692	+	4.72692i	−0.259815	+	0.259815i	−0.824979	−	0.565164i	$-0.808813\pi$
$331$	−4.72692	+	4.72692i	−0.259815	+	0.259815i	0.565164	+	0.824979i	$0.308813\pi$
$332$	−11.2549	−	11.2549i	−0.617691	−	0.617691i
$333$	−6.03996	−	0.720368i	−0.330988	−	0.0394759i
$334$		−	15.1621i		−	0.829631i
$335$	−2.45225	−	0.188068i	−0.133981	−	0.0102752i
$336$		−	1.08053i		−	0.0589480i
$337$	13.9016	+	13.9016i	0.757270	+	0.757270i	0.975825	−	0.218555i	$-0.0701343\pi$
$337$	13.9016	+	13.9016i	0.757270	+	0.757270i	−0.218555	+	0.975825i	$0.570134\pi$
$338$	−8.45941			−0.460131
$339$	−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
$347$	0.651438			0.0349710			0.0174855	−	0.999847i	$-0.494434\pi$
$347$	0.651438			0.0349710			0.0174855	+	0.999847i	$0.494434\pi$
$348$		−	9.14579i		−	0.490266i
$349$			25.5234i			1.36624i	0.730308	+	0.683118i	$0.239376\pi$
$349$			25.5234i			1.36624i	−0.730308	+	0.683118i	$0.760624\pi$
$350$	−3.19305	−	4.35813i	−0.170676	−	0.232952i
$351$	−3.27562	−	3.27562i	−0.174840	−	0.174840i
$352$		−	4.86540i		−	0.259327i
$353$		−	34.3501i		−	1.82827i	−0.405408	−	0.914136i	$-0.632870\pi$
$353$		−	34.3501i		−	1.82827i	0.405408	−	0.914136i	$-0.367130\pi$
$354$	−1.11770			−0.0594053
$355$	1.01709	−	0.872194i	0.0539814	−	0.0462913i
$356$	−1.70075	+	1.70075i	−0.0901394	+	0.0901394i
$357$	−5.59718			−0.296234
$358$	−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
$362$	−16.2780			−0.855552
$363$	8.96057	−	8.96057i	0.470308	−	0.470308i
$364$	3.53942	−	3.53942i	0.185516	−	0.185516i
$365$	−0.259217	+	3.37998i	−0.0135680	+	0.176916i
$366$	−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	$0.373817\pi$
$368$	−4.72007			−0.246051
$369$	3.55371			0.184999
$370$	7.56902	+	11.3009i	0.393495	+	0.587505i
$371$	8.62270			0.447668
$372$	−1.80819			−0.0937502
$373$	6.19992	−	6.19992i	0.321020	−	0.321020i	−0.528139	−	0.849158i	$-0.677110\pi$
$373$	6.19992	−	6.19992i	0.321020	−	0.321020i	0.849158	+	0.528139i	$0.177110\pi$
$374$	−25.2028			−1.30321
$375$	10.8869	+	2.54480i	0.562196	+	0.131413i
$376$	8.00838	−	8.00838i	0.413001	−	0.413001i
$377$	29.9582	−	29.9582i	1.54292	−	1.54292i
$378$	1.08053			0.0555767
$379$			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
$383$	17.9026			0.914778			0.457389	−	0.889267i	$-0.348785\pi$
$383$	17.9026			0.914778			0.457389	+	0.889267i	$0.348785\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−11.7211	−	0.898915i	−0.597363	−	0.0458129i
$386$	11.3986			0.580174
$387$		−	7.49989i		−	0.381241i
$388$		−	6.03720i		−	0.306492i
$389$	7.54313	+	7.54313i	0.382452	+	0.382452i	0.871985	−	0.489533i	$-0.162833\pi$
$389$	7.54313	+	7.54313i	0.382452	+	0.382452i	−0.489533	+	0.871985i	$0.662833\pi$
$390$	−0.792082	+	10.3281i	−0.0401086	+	0.522984i
$391$			24.4500i			1.23649i
$392$		−	5.83245i		−	0.294583i
$393$	2.41788			0.121966
$394$	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	0.928762	−	0.370676i	$-0.120874\pi$
$397$	11.1198	+	11.1198i	0.558087	+	0.558087i	−0.370676	+	0.928762i	$0.620874\pi$
$398$	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	−0.992564	−	0.121725i	$-0.961157\pi$
$401$	−22.3136	−	22.3136i	−1.11429	−	1.11429i	−0.121725	−	0.992564i	$-0.538843\pi$
$402$	−1.09990			−0.0548580
$403$	−5.92294	−	5.92294i	−0.295043	−	0.295043i
$404$			5.63152i			0.280178i
$405$	−1.69741	+	1.45560i	−0.0843452	+	0.0723295i
$406$			9.88233i			0.490452i
$407$	29.3868	+	3.50488i	1.45665	+	0.173731i
$408$	−3.66282	−	3.66282i	−0.181337	−	0.181337i
$409$	16.7999	−	16.7999i	0.830701	−	0.830701i	−0.156912	−	0.987613i	$-0.550154\pi$
$409$	16.7999	−	16.7999i	0.830701	−	0.830701i	0.987613	+	0.156912i	$0.0501538\pi$
$410$	−5.17280	−	6.03212i	−0.255466	−	0.297905i
$411$		−	5.29690i		−	0.261277i
$412$			15.8811i			0.782407i
$413$	1.20772			0.0594279
$414$		−	4.72007i		−	0.231979i
$415$	−35.4868	−	2.72155i	−1.74198	−	0.133596i
$416$	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	$0.976034\pi$
$420$	−1.57283	−	1.83411i	−0.0767462	−	0.0894956i
$421$	−2.58223	−	2.58223i	−0.125850	−	0.125850i	0.641376	−	0.767227i	$-0.278364\pi$
$421$	−2.58223	−	2.58223i	−0.125850	−	0.125850i	−0.767227	+	0.641376i	$0.778364\pi$
$422$	3.92055			0.190849
$423$	8.00838	+	8.00838i	0.389381	+	0.389381i
$424$	5.64274	+	5.64274i	0.274036	+	0.274036i
$425$	−25.5972	−	3.94942i	−1.24164	−	0.191575i
$426$	0.423697	−	0.423697i	0.0205282	−	0.0205282i
$427$	8.01482			0.387864
$428$	−7.21271	+	7.21271i	−0.348639	+	0.348639i
$429$	15.9372	+	15.9372i	0.769457	+	0.769457i
$430$	−12.7304	+	10.9169i	−0.613916	+	0.526458i
$431$	−9.94058	−	9.94058i	−0.478821	−	0.478821i	0.425934	−	0.904754i	$-0.359946\pi$
$431$	−9.94058	−	9.94058i	−0.478821	−	0.478821i	−0.904754	+	0.425934i	$0.859946\pi$
$432$	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
$438$			1.51601i			0.0724377i
$439$	−21.9903	+	21.9903i	−1.04954	+	1.04954i	−0.0508336	+	0.998707i	$0.516188\pi$
$439$	−21.9903	+	21.9903i	−1.04954	+	1.04954i	−0.998707	+	0.0508336i	$0.983812\pi$
$440$	−7.08210	−	8.25861i	−0.337626	−	0.393714i
$441$	5.83245			0.277736
$442$		−	23.9960i		−	1.14138i
$443$	17.2453	−	17.2453i	0.819348	−	0.819348i	−0.166665	−	0.986014i	$-0.553300\pi$
$443$	17.2453	−	17.2453i	0.819348	−	0.819348i	0.986014	+	0.166665i	$0.0533000\pi$
$444$	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	$-0.256098\pi$
$449$	−0.574002	−	0.574002i	−0.0270888	−	0.0270888i	−0.720521	+	0.693433i	$0.756098\pi$
$450$	4.94153	+	0.762435i	0.232946	+	0.0359415i
$451$	−17.2902			−0.814166
$452$			4.80474i			0.225996i
$453$	−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
$457$		−	12.9457i		−	0.605574i	−0.953058	−	0.302787i	$-0.902083\pi$
$457$		−	12.9457i		−	0.605574i	0.953058	−	0.302787i	$-0.0979171\pi$
$458$			12.6086i			0.589159i
$459$	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	−0.0202466	−	0.999795i	$-0.506445\pi$
$461$	21.0318	−	21.0318i	0.979548	−	0.979548i	0.999795	+	0.0202466i	$0.00644514\pi$
$462$	−5.25723			−0.244589
$463$	14.6765			0.682076			0.341038	−	0.940050i	$-0.389222\pi$
$463$	14.6765			0.682076			0.341038	+	0.940050i	$0.389222\pi$
$464$	−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
$467$			12.6925i			0.587341i	0.955907	+	0.293670i	$0.0948768\pi$
$467$			12.6925i			0.587341i	−0.955907	+	0.293670i	$0.905123\pi$
$468$			4.63243i			0.214134i
$469$	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
$473$			36.4900i			1.67781i
$474$	−13.5333			−0.621604
$475$	−10.5167	+	7.70521i	−0.482539	+	0.353539i
$476$	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	$-0.0612086\pi$
$479$	17.3000	+	17.3000i	0.790459	+	0.790459i	−0.191110	+	0.981569i	$0.561209\pi$
$480$	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
$483$			5.10020i			0.232067i
$484$	−12.6722			−0.576007
$485$	−8.78777	−	10.2476i	−0.399032	−	0.465321i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$			25.7666i			1.16760i	0.811899	+	0.583798i	$0.198434\pi$
$487$			25.7666i			1.16760i	−0.811899	+	0.583798i	$0.801566\pi$
$488$	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
$495$	8.25861	−	7.08210i	0.371197	−	0.318317i
$496$	1.27858	+	1.27858i	0.0574101	+	0.0574101i
$497$	−0.457819	+	0.457819i	−0.0205360	+	0.0205360i
$498$	−15.9168			−0.713248
$499$	19.1310	−	19.1310i	0.856423	−	0.856423i	−0.134492	−	0.990915i	$-0.542940\pi$
$499$	19.1310	−	19.1310i	0.856423	−	0.856423i	0.990915	+	0.134492i	$0.0429403\pi$
$500$	−5.89874	−	9.49763i	−0.263800	−	0.424747i
$501$	−10.7212	−	10.7212i	−0.478988	−	0.478988i
$502$	−5.64176	−	5.64176i	−0.251804	−	0.251804i
$503$	12.4777			0.556353			0.278177	−	0.960530i	$-0.410270\pi$
$503$	12.4777			0.556353			0.278177	+	0.960530i	$0.410270\pi$
$504$	−0.764053	−	0.764053i	−0.0340336	−	0.0340336i
$505$	8.19726	+	9.55902i	0.364773	+	0.425371i
$506$			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	$-0.742242\pi$
$509$	−31.1191			−1.37933			−0.689665	+	0.724129i	$0.742242\pi$
$510$	−11.5489	−	0.885710i	−0.511396	−	0.0392199i
$511$		−	1.63810i		−	0.0724653i
$512$	−1.00000			−0.0441942
$513$		−	2.60746i		−	0.115122i
$514$		−	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
$518$	−4.06445	−	5.16525i	−0.178582	−	0.226948i
$519$		−	6.42156i		−	0.281875i
$520$	7.86316	−	6.74298i	0.344822	−	0.295699i
$521$			11.3207i			0.495967i	0.968764	+	0.247983i	$0.0797679\pi$
$521$			11.3207i			0.495967i	−0.968764	+	0.247983i	$0.920232\pi$
$522$	−6.46705	−	6.46705i	−0.283055	−	0.283055i
$523$	2.09242			0.0914952			0.0457476	−	0.998953i	$-0.485433\pi$
$523$	2.09242			0.0914952			0.0457476	+	0.998953i	$0.485433\pi$
$524$	−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
$532$	2.81745			0.122152
$533$		−	16.4623i		−	0.713062i
$534$			2.40522i			0.104084i
$535$	−1.74411	+	22.7418i	−0.0754045	+	0.983214i
$536$	0.777747	+	0.777747i	0.0335935	+	0.0335935i
$537$			5.52788i			0.238545i
$538$			19.2094i			0.828178i
$539$	−28.3772			−1.22229
$540$	2.22952	+	0.170986i	0.0959433	+	0.00735807i
$541$	−6.92733	+	6.92733i	−0.297829	+	0.297829i	−0.840163	−	0.542334i	$-0.817541\pi$
$541$	−6.92733	+	6.92733i	−0.297829	+	0.297829i	0.542334	+	0.840163i	$0.317541\pi$
$542$	−14.4883			−0.622327
$543$	−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
$547$	4.89932			0.209480			0.104740	−	0.994500i	$-0.466599\pi$
$547$	4.89932			0.209480			0.104740	+	0.994500i	$0.466599\pi$
$548$	−3.74548	+	3.74548i	−0.159999	+	0.159999i
$549$	−5.24494	+	5.24494i	−0.223848	+	0.223848i
$550$	−24.0425	−	3.70955i	−1.02518	−	0.158176i
$551$	23.8473			1.01593
$552$	−3.33760	+	3.33760i	−0.142057	+	0.142057i
$553$	14.6232			0.621841
$554$	29.6974			1.26172
$555$	13.3430	+	2.63883i	0.566380	+	0.112012i
$556$	11.5750			0.490891
$557$	−31.8866			−1.35108			−0.675539	−	0.737324i	$-0.736089\pi$
$557$	−31.8866			−1.35108			−0.675539	+	0.737324i	$0.736089\pi$
$558$	−1.27858	+	1.27858i	−0.0541267	+	0.0541267i
$559$	−34.7427			−1.46946
$560$	−0.184756	+	2.40907i	−0.00780738	+	0.101802i
$561$	−17.8211	+	17.8211i	−0.752407	+	0.752407i
$562$	−3.49186	+	3.49186i	−0.147295	+	0.147295i
$563$	−43.4484			−1.83113			−0.915565	−	0.402170i	$-0.868256\pi$
$563$	−43.4484			−1.83113			−0.915565	+	0.402170i	$0.868256\pi$
$564$		−	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
$568$	−0.599197			−0.0251418
$569$	−19.9460	+	19.9460i	−0.836180	+	0.836180i	−0.988354	−	0.152174i	$-0.951373\pi$
$569$	−19.9460	+	19.9460i	−0.836180	+	0.836180i	0.152174	+	0.988354i	$0.451373\pi$
$570$	−4.42594	+	3.79543i	−0.185382	+	0.158973i
$571$	7.76992			0.325161			0.162581	−	0.986695i	$-0.448018\pi$
$571$	7.76992			0.325161			0.162581	+	0.986695i	$0.448018\pi$
$572$		−	22.5386i		−	0.942388i
$573$			9.51756i			0.397602i
$574$	2.71522	+	2.71522i	0.113331	+	0.113331i
$575$	−3.59875	+	23.3244i	−0.150078	+	0.972693i
$576$		−	1.00000i		−	0.0416667i
$577$		−	10.9161i		−	0.454442i	−0.973843	−	0.227221i	$-0.927036\pi$
$577$		−	10.9161i		−	0.454442i	0.973843	−	0.227221i	$-0.0729640\pi$
$578$	9.83251			0.408978
$579$	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
$587$	22.1879			0.915793			0.457897	−	0.889005i	$-0.348603\pi$
$587$	22.1879			0.915793			0.457897	+	0.889005i	$0.348603\pi$
$588$	−4.12416	−	4.12416i	−0.170078	−	0.170078i
$589$		−	4.71478i		−	0.194269i
$590$	2.49194	+	0.191112i	0.102592	+	0.00786795i
$591$		−	14.8793i		−	0.612054i
$592$	0.720368	−	6.03996i	0.0296069	−	0.248241i
$593$	−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
$597$		−	7.22351i		−	0.295639i
$598$	−21.8654			−0.894143
$599$		−	43.9186i		−	1.79446i	−0.441560	−	0.897232i	$-0.645575\pi$
$599$		−	43.9186i		−	1.79446i	0.441560	−	0.897232i	$-0.354425\pi$
$600$	−2.95506	−	4.03331i	−0.120640	−	0.164659i
$601$	−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
$605$	−21.5099	+	18.4456i	−0.874502	+	0.749922i
$606$	3.98208	+	3.98208i	0.161761	+	0.161761i
$607$	−44.7940			−1.81813			−0.909067	−	0.416651i	$-0.863204\pi$
$607$	−44.7940			−1.81813			−0.909067	+	0.416651i	$0.863204\pi$
$608$	1.84375	+	1.84375i	0.0747740	+	0.0747740i
$609$	6.98787	+	6.98787i	0.283163	+	0.283163i
$610$	16.5374	+	1.26828i	0.669579	+	0.0513513i
$611$	37.0983	−	37.0983i	1.50084	−	1.50084i
$612$	−5.18001			−0.209390
$613$	30.3408	−	30.3408i	1.22545	−	1.22545i	0.259787	−	0.965666i	$-0.416348\pi$
$613$	30.3408	−	30.3408i	1.22545	−	1.22545i	0.965666	−	0.259787i	$-0.0836524\pi$
$614$	23.3965	+	23.3965i	0.944207	+	0.944207i
$615$	−7.92308	−	0.607636i	−0.319489	−	0.0245022i
$616$	3.71743	+	3.71743i	0.149779	+	0.149779i
$617$	−24.4682	−	24.4682i	−0.985053	−	0.985053i	0.0148372	−	0.999890i	$-0.495277\pi$
$617$	−24.4682	−	24.4682i	−0.985053	−	0.985053i	−0.999890	+	0.0148372i	$0.995277\pi$
$618$	11.2297	+	11.2297i	0.451723	+	0.451723i
$619$	18.8165			0.756299			0.378150	−	0.925745i	$-0.376561\pi$
$619$	18.8165			0.756299			0.378150	+	0.925745i	$0.376561\pi$
$620$	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
$623$		−	2.59892i		−	0.104124i
$624$	3.27562	−	3.27562i	0.131130	−	0.131130i
$625$	−23.8374	−	7.53518i	−0.953495	−	0.301407i
$626$	−26.7290			−1.06831
$627$			12.6863i			0.506644i
$628$	−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	0.583419	−	0.812171i	$-0.301714\pi$
$631$	−5.74618	−	5.74618i	−0.228752	−	0.228752i	−0.812171	+	0.583419i	$0.801714\pi$
$632$	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
$635$	1.14027	−	14.8682i	0.0452503	−	0.590027i
$636$	7.98004			0.316429
$637$		−	27.0184i		−	1.07051i
$638$	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	$0.437698\pi$
$642$			10.2003i			0.402574i
$643$			45.3302i			1.78765i	0.448417	+	0.893825i	$0.351988\pi$
$643$			45.3302i			1.78765i	−0.448417	+	0.893825i	$0.648012\pi$
$644$	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
$647$	48.2835			1.89822			0.949111	−	0.314942i	$-0.101985\pi$
$647$	48.2835			1.89822			0.949111	+	0.314942i	$0.101985\pi$
$648$	1.00000			0.0392837
$649$	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
$652$		−	23.9624i		−	0.938439i
$653$		−	23.4562i		−	0.917912i	−0.888459	−	0.458956i	$-0.848224\pi$
$653$		−	23.4562i		−	0.917912i	0.888459	−	0.458956i	$-0.151776\pi$
$654$	−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
$658$			12.2377i			0.477074i
$659$	−42.8689			−1.66993			−0.834967	−	0.550300i	$-0.814513\pi$
$659$	−42.8689			−1.66993			−0.834967	+	0.550300i	$0.814513\pi$
$660$	−10.8475	−	0.831917i	−0.422239	−	0.0323823i
$661$	−11.0362	−	11.0362i	−0.429259	−	0.429259i	0.459117	−	0.888376i	$-0.348166\pi$
$661$	−11.0362	−	11.0362i	−0.429259	−	0.429259i	−0.888376	+	0.459117i	$0.848166\pi$
$662$	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
$668$			15.1621i			0.586638i
$669$	−18.4045			−0.711561
$670$	2.45225	+	0.188068i	0.0947387	+	0.00726569i
$671$	25.5187	−	25.5187i	0.985140	−	0.985140i
$672$			1.08053i			0.0416825i
$673$	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	0.459347	−	0.888257i	$-0.348083\pi$
$677$	−11.1599	−	11.1599i	−0.428909	−	0.428909i	−0.888257	+	0.459347i	$0.848083\pi$
$678$	3.39746	+	3.39746i	0.130479	+	0.130479i
$679$	4.61274	+	4.61274i	0.177021	+	0.177021i
$680$	7.54004	+	8.79263i	0.289147	+	0.337182i
$681$	−7.38911	−	7.38911i	−0.283151	−	0.283151i
$682$	6.22082	−	6.22082i	0.238208	−	0.238208i
$683$	−28.1871			−1.07855			−0.539274	−	0.842130i	$-0.681301\pi$
$683$	−28.1871			−1.07855			−0.539274	+	0.842130i	$0.681301\pi$
$684$	−1.84375	+	1.84375i	−0.0704976	+	0.0704976i
$685$	−0.905697	+	11.8096i	−0.0346049	+	0.451220i
$686$	9.80467	+	9.80467i	0.374344	+	0.374344i
$687$	8.91559	+	8.91559i	0.340151	+	0.340151i
$688$	7.49989			0.285931
$689$	26.1396	+	26.1396i	0.995839	+	0.995839i
$690$	−0.807067	+	10.5235i	−0.0307245	+	0.400623i
$691$		−	13.7497i		−	0.523063i	−0.965195	−	0.261531i	$-0.915773\pi$
$691$		−	13.7497i		−	0.523063i	0.965195	−	0.261531i	$-0.0842275\pi$
$692$	−4.54073	+	4.54073i	−0.172612	+	0.172612i
$693$	−3.71743	+	3.71743i	−0.141213	+	0.141213i
$694$	−0.651438			−0.0247282
$695$	19.6476	−	16.8487i	0.745278	−	0.639107i
$696$			9.14579i			0.346670i
$697$	18.4083			0.697263
$698$		−	25.5234i		−	0.966074i
$699$			23.9507i			0.905899i
$700$	3.19305	+	4.35813i	0.120686	+	0.164722i
$701$	7.09322	−	7.09322i	0.267907	−	0.267907i	−0.560349	−	0.828257i	$-0.689333\pi$
$701$	7.09322	−	7.09322i	0.267907	−	0.267907i	0.828257	+	0.560349i	$0.189333\pi$
$702$	3.27562	+	3.27562i	0.123630	+	0.123630i
$703$	−12.4644	+	9.80800i	−0.470102	+	0.369916i
$704$			4.86540i			0.183372i
$705$	−16.4855	−	19.2242i	−0.620881	−	0.724025i
$706$			34.3501i			1.29278i
$707$	−4.30278	−	4.30278i	−0.161823	−	0.161823i
$708$	1.11770			0.0420059
$709$	−30.9530	−	30.9530i	−1.16247	−	1.16247i	−0.983934	−	0.178531i	$-0.942865\pi$
$709$	−30.9530	−	30.9530i	−1.16247	−	1.16247i	−0.178531	−	0.983934i	$-0.557135\pi$
$710$	−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
$717$	3.69593			0.138027
$718$			17.0122i			0.634889i
$719$			16.8010i			0.626571i	0.949659	+	0.313285i	$0.101430\pi$
$719$			16.8010i			0.626571i	−0.949659	+	0.313285i	$0.898570\pi$
$720$	−1.45560	−	1.69741i	−0.0542472	−	0.0632589i
$721$	−12.1340	−	12.1340i	−0.451895	−	0.451895i
$722$			12.2012i			0.454080i
$723$			20.2495i			0.753087i
$724$	16.2780			0.604967
$725$	27.0264	+	36.8878i	1.00374	+	1.36998i
$726$	−8.96057	+	8.96057i	−0.332558	+	0.332558i
$727$	21.2760			0.789085			0.394542	−	0.918878i	$-0.370903\pi$
$727$	21.2760			0.789085			0.394542	+	0.918878i	$0.370903\pi$
$728$	−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
$732$	7.41746			0.274157
$733$	−36.8126	+	36.8126i	−1.35970	+	1.35970i	−0.485428	+	0.874277i	$0.661336\pi$
$733$	−36.8126	+	36.8126i	−1.35970	+	1.35970i	−0.874277	+	0.485428i	$0.838664\pi$
$734$	10.2747	−	10.2747i	0.379246	−	0.379246i
$735$	−13.0036	−	0.997268i	−0.479644	−	0.0367848i
$736$	4.72007			0.173984
$737$	3.78405	−	3.78405i	0.139387	−	0.139387i
$738$	−3.55371			−0.130814
$739$	−9.01878			−0.331761			−0.165881	−	0.986146i	$-0.553047\pi$
$739$	−9.01878			−0.331761			−0.165881	+	0.986146i	$0.553047\pi$
$740$	−7.56902	−	11.3009i	−0.278243	−	0.415429i
$741$	−12.0789			−0.443728
$742$	−8.62270			−0.316549
$743$	−35.3819	+	35.3819i	−1.29803	+	1.29803i	−0.368345	+	0.929689i	$0.620076\pi$
$743$	−35.3819	+	35.3819i	−1.29803	+	1.29803i	−0.929689	+	0.368345i	$0.879924\pi$
$744$	1.80819			0.0662914
$745$	6.58507	+	7.67901i	0.241258	+	0.281337i
$746$	−6.19992	+	6.19992i	−0.226995	+	0.226995i
$747$	−11.2549	+	11.2549i	−0.411794	+	0.411794i
$748$	25.2028			0.921507
$749$		−	11.0218i		−	0.402727i
$750$	−10.8869	−	2.54480i	−0.397532	−	0.0929228i
$751$			20.1864i			0.736613i	0.929704	+	0.368307i	$0.120062\pi$
$751$			20.1864i			0.736613i	−0.929704	+	0.368307i	$0.879938\pi$
$752$	−8.00838	+	8.00838i	−0.292036	+	0.292036i
$753$	−7.97866			−0.290759
$754$	−29.9582	+	29.9582i	−1.09101	+	1.09101i
$755$	9.99537	+	11.6558i	0.363769	+	0.424199i
$756$	−1.08053			−0.0392986
$757$			23.3149i			0.847394i	0.905804	+	0.423697i	$0.139268\pi$
$757$			23.3149i			0.847394i	−0.905804	+	0.423697i	$0.860732\pi$
$758$		−	31.3961i		−	1.14036i
$759$	16.2387	+	16.2387i	0.589429	+	0.589429i
$760$	5.81338	+	0.445840i	0.210874	+	0.0161723i
$761$			14.6952i			0.532702i	0.963876	+	0.266351i	$0.0858180\pi$
$761$			14.6952i			0.532702i	−0.963876	+	0.266351i	$0.914182\pi$
$762$		−	6.66879i		−	0.241585i
$763$	11.4941			0.416114
$764$	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	$-0.592818\pi$
$769$	18.5881	−	18.5881i	0.670304	−	0.670304i	0.957786	+	0.287482i	$0.0928181\pi$
$770$	11.7211	+	0.898915i	0.422400	+	0.0323946i
$771$	−16.5124	−	16.5124i	−0.594680	−	0.594680i
$772$	−11.3986			−0.410245
$773$	−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
$775$	7.29299	−	5.34332i	0.261972	−	0.191938i
$776$			6.03720i			0.216723i
$777$	−6.52638	−	0.778382i	−0.234133	−	0.0279243i
$778$	−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
$782$		−	24.4500i		−	0.874331i
$783$	−9.14579			−0.326844
$784$			5.83245i			0.208302i
$785$	−2.23284	+	29.1144i	−0.0796936	+	1.03914i
$786$	−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
$790$	30.1727	+	2.31401i	1.07350	+	0.0823286i
$791$	−3.67107	−	3.67107i	−0.130528	−	0.130528i
$792$	−4.86540			−0.172885
$793$	24.2968	+	24.2968i	0.862805	+	0.862805i
$794$	−11.1198	−	11.1198i	−0.394627	−	0.394627i
$795$	13.5454	−	11.6158i	0.480407	−	0.411969i
$796$	−5.10780	+	5.10780i	−0.181041	+	0.181041i
$797$	37.4922			1.32804			0.664020	−	0.747715i	$-0.268849\pi$
$797$	37.4922			1.32804			0.664020	+	0.747715i	$0.268849\pi$
$798$	1.99224	−	1.99224i	0.0705244	−	0.0705244i
$799$	41.4835	+	41.4835i	1.46758	+	1.46758i
$800$	−0.762435	+	4.94153i	−0.0269561	+	0.174709i
$801$	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
$808$		−	5.63152i		−	0.198116i
$809$	1.36538	−	1.36538i	0.0480041	−	0.0480041i	−0.682697	−	0.730701i	$-0.739193\pi$
$809$	1.36538	−	1.36538i	0.0480041	−	0.0480041i	0.730701	+	0.682697i	$0.239193\pi$
$810$	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	$0.687484\pi$
$812$		−	9.88233i		−	0.346802i
$813$	−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
$820$	5.17280	+	6.03212i	0.180642	+	0.210651i
$821$	10.9084			0.380707			0.190353	−	0.981716i	$-0.439037\pi$
$821$	10.9084			0.380707			0.190353	+	0.981716i	$0.439037\pi$
$822$			5.29690i			0.184751i
$823$	−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
$827$			26.9666i			0.937722i	0.883272	+	0.468861i	$0.155335\pi$
$827$			26.9666i			0.937722i	−0.883272	+	0.468861i	$0.844665\pi$
$828$			4.72007i			0.164034i
$829$	6.05887	−	6.05887i	0.210433	−	0.210433i	−0.594018	−	0.804452i	$-0.702459\pi$
$829$	6.05887	−	6.05887i	0.210433	−	0.210433i	0.804452	+	0.594018i	$0.202459\pi$
$830$	35.4868	+	2.72155i	1.23176	+	0.0944663i
$831$	20.9992	−	20.9992i	0.728455	−	0.728455i
$832$	−4.63243			−0.160601
$833$	30.2121			1.04679
$834$	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
$837$			1.80819i			0.0625001i
$838$		−	3.07947i		−	0.106379i
$839$	48.1268			1.66152			0.830761	−	0.556630i	$-0.187906\pi$
$839$	48.1268			1.66152			0.830761	+	0.556630i	$0.187906\pi$
$840$	1.57283	+	1.83411i	0.0542678	+	0.0632830i
$841$		−	54.6454i		−	1.88433i
$842$	2.58223	+	2.58223i	0.0889897	+	0.0889897i
$843$			4.93824i			0.170082i
$844$	−3.92055			−0.134951
$845$	14.3591	−	12.3136i	0.493969	−	0.423599i
$846$	−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
$853$		−	0.209022i		−	0.00715677i	−0.999994	−	0.00357838i	$-0.998861\pi$
$853$		−	0.209022i		−	0.00715677i	0.999994	−	0.00357838i	$-0.00113904\pi$
$854$	−8.01482			−0.274261
$855$	−0.445840	+	5.81338i	−0.0152474	+	0.198814i
$856$	7.21271	−	7.21271i	0.246525	−	0.246525i
$857$			27.1503i			0.927437i	0.885983	+	0.463718i	$0.153485\pi$
$857$			27.1503i			0.927437i	−0.885983	+	0.463718i	$0.846515\pi$
$858$	−15.9372	−	15.9372i	−0.544088	−	0.544088i
$859$	−0.741722	−	0.741722i	−0.0253072	−	0.0253072i	0.694340	−	0.719647i	$-0.255696\pi$
$859$	−0.741722	−	0.741722i	−0.0253072	−	0.0253072i	−0.719647	+	0.694340i	$0.755696\pi$
$860$	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
$865$	−1.09800	+	14.3170i	−0.0373330	+	0.486792i
$866$	−13.7642	−	13.7642i	−0.467727	−	0.467727i
$867$	6.95263	−	6.95263i	0.236124	−	0.236124i
$868$	−1.95381			−0.0663166
$869$	46.5594	−	46.5594i	1.57942	−	1.57942i
$870$	13.3126	+	15.5242i	0.451341	+	0.526320i
$871$	3.60286	+	3.60286i	0.122078	+	0.122078i
$872$	7.52179	+	7.52179i	0.254720	+	0.254720i
$873$	−6.03720			−0.204328
$874$	−8.70264	−	8.70264i	−0.294371	−	0.294371i
$875$	11.7636	+	2.74974i	0.397684	+	0.0929582i
$876$		−	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
$880$	7.08210	+	8.25861i	0.238738	+	0.278398i
$881$			25.7820i			0.868617i	0.900764	+	0.434308i	$0.143007\pi$
$881$			25.7820i			0.868617i	−0.900764	+	0.434308i	$0.856993\pi$
$882$	−5.83245			−0.196389
$883$			41.2363i			1.38771i	0.720114	+	0.693856i	$0.244090\pi$
$883$			41.2363i			1.38771i	−0.720114	+	0.693856i	$0.755910\pi$
$884$			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	0.461046	−	0.887376i	$-0.347474\pi$
$887$	−12.6972	−	12.6972i	−0.426330	−	0.426330i	−0.887376	+	0.461046i	$0.847474\pi$
$888$	−3.76152	−	4.78027i	−0.126228	−	0.160415i
$889$			7.20586i			0.241677i
$890$	0.411259	−	5.36248i	0.0137854	−	0.179751i
$891$		−	4.86540i		−	0.162997i
$892$	13.0140	+	13.0140i	0.435740	+	0.435740i
$893$	29.5309			0.988215
$894$	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
$902$	17.2902			0.575702
$903$		−	8.10389i		−	0.269681i
$904$		−	4.80474i		−	0.159803i
$905$	27.6305	−	23.6943i	0.918469	−	0.787626i
$906$	4.85557	+	4.85557i	0.161316	+	0.161316i
$907$			34.2793i			1.13822i	0.822260	+	0.569112i	$0.192713\pi$
$907$			34.2793i			1.13822i	−0.822260	+	0.569112i	$0.807287\pi$
$908$			10.4498i			0.346788i
$909$	5.63152			0.186786
$910$	−0.855871	+	11.1599i	−0.0283719	+	0.369946i
$911$	23.1995	−	23.1995i	0.768632	−	0.768632i	−0.209234	−	0.977866i	$-0.567097\pi$
$911$	23.1995	−	23.1995i	0.768632	−	0.768632i	0.977866	+	0.209234i	$0.0670969\pi$
$912$	2.60746			0.0863416
$913$	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
$917$	2.61260			0.0862756
$918$	−3.66282	+	3.66282i	−0.120891	+	0.120891i
$919$	−9.82515	+	9.82515i	−0.324102	+	0.324102i	−0.850338	−	0.526236i	$-0.823603\pi$
$919$	−9.82515	+	9.82515i	−0.324102	+	0.324102i	0.526236	+	0.850338i	$0.323603\pi$
$920$	8.01192	−	6.87056i	0.264145	−	0.226516i
$921$	33.0877			1.09028
$922$	−21.0318	+	21.0318i	−0.692645	+	0.692645i
$923$	−2.77574			−0.0913646
$924$	5.25723			0.172950
$925$	−29.2974	−	8.16479i	−0.963292	−	0.268457i
$926$	−14.6765			−0.482301
$927$	15.8811			0.521605
$928$	6.46705	−	6.46705i	0.212291	−	0.212291i
$929$	−23.3283			−0.765378			−0.382689	−	0.923877i	$-0.625002\pi$
$929$	−23.3283			−0.765378			−0.382689	+	0.923877i	$0.625002\pi$
$930$	3.06925	−	2.63201i	0.100645	−	0.0863069i
$931$	10.7536	−	10.7536i	0.352434	−	0.352434i
$932$	16.9357	−	16.9357i	0.554748	−	0.554748i
$933$	−26.5141			−0.868032
$934$		−	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	$0.288464\pi$
$938$	−1.18848			−0.0388052
$939$	−18.9003	+	18.9003i	−0.616788	+	0.616788i
$940$	−1.93652	+	25.2506i	−0.0631622	+	0.823583i
$941$	−37.3652			−1.21807			−0.609035	−	0.793144i	$-0.708443\pi$
$941$	−37.3652			−1.21807			−0.609035	+	0.793144i	$0.708443\pi$
$942$			13.0586i			0.425473i
$943$		−	16.7738i		−	0.546229i
$944$	−0.790336	−	0.790336i	−0.0257232	−	0.0257232i
$945$	−1.83411	+	1.57283i	−0.0596637	+	0.0511641i
$946$		−	36.4900i		−	1.18639i
$947$		−	28.3116i		−	0.920004i	−0.887918	−	0.460002i	$-0.847849\pi$
$947$		−	28.3116i		−	0.920004i	0.887918	−	0.460002i	$-0.152151\pi$
$948$	13.5333			0.439541
$949$	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	−0.591134	−	0.806573i	$-0.701320\pi$
$953$	6.65077	−	6.65077i	0.215440	−	0.215440i	0.806573	+	0.591134i	$0.201320\pi$
$954$	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
$957$	44.4980			1.43841
$958$	−17.3000	−	17.3000i	−0.558939	−	0.558939i
$959$		−	5.72348i		−	0.184821i
$960$	−0.170986	+	2.22952i	−0.00551856	+	0.0719575i
$961$		−	27.7305i		−	0.894531i
$962$	3.33706	−	27.9797i	0.107591	−	0.902101i
$963$	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
$967$		−	1.06824i		−	0.0343524i	−0.999852	−	0.0171762i	$-0.994532\pi$
$967$		−	1.06824i		−	0.0343524i	0.999852	−	0.0171762i	$-0.00546762\pi$
$968$	12.6722			0.407298
$969$		−	13.5067i		−	0.433897i
$970$	8.78777	+	10.2476i	0.282158	+	0.329032i
$971$	−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
$975$	−13.6891	−	18.6840i	−0.438403	−	0.598368i
$976$	−5.24494	−	5.24494i	−0.167886	−	0.167886i
$977$	36.3637			1.16338			0.581688	−	0.813412i	$-0.302392\pi$
$977$	36.3637			1.16338			0.581688	+	0.813412i	$0.302392\pi$
$978$	−16.9440	−	16.9440i	−0.541808	−	0.541808i
$979$	−8.27482	−	8.27482i	−0.264464	−	0.264464i
$980$	8.48973	+	9.90008i	0.271195	+	0.316246i
$981$	−7.52179	+	7.52179i	−0.240152	+	0.240152i
$982$	4.97935			0.158898
$983$	−5.76895	+	5.76895i	−0.184001	+	0.184001i	−0.793097	−	0.609096i	$-0.791533\pi$
$983$	−5.76895	+	5.76895i	−0.184001	+	0.184001i	0.609096	+	0.793097i	$0.291533\pi$
$984$	2.51285	+	2.51285i	0.0801069	+	0.0801069i
$985$	−2.54416	+	33.1738i	−0.0810637	+	1.05700i
$986$	−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	0.881334	−	0.472493i	$-0.156646\pi$
$991$	12.8704	+	12.8704i	0.408841	+	0.408841i	−0.472493	+	0.881334i	$0.656646\pi$
$992$	−1.27858	−	1.27858i	−0.0405950	−	0.0405950i
$993$		−	6.68487i		−	0.212138i
$994$	0.457819	−	0.457819i	0.0145211	−	0.0145211i
$995$	−1.23512	+	16.1050i	−0.0391560	+	0.510562i
$996$	15.9168			0.504342
$997$		−	17.3919i		−	0.550808i	−0.961329	−	0.275404i	$-0.911188\pi$
$997$		−	17.3919i		−	0.550808i	0.961329	−	0.275404i	$-0.0888117\pi$
$998$	−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.o.a.253.6	yes	36
5.2	odd	4		1110.2.l.a.697.13	yes	36
37.6	odd	4		1110.2.l.a.43.13	✓	36
185.117	even	4	inner	1110.2.o.a.487.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.13	✓	36	37.6	odd	4
1110.2.l.a.697.13	yes	36	5.2	odd	4
1110.2.o.a.253.6	yes	36	1.1	even	1	trivial
1110.2.o.a.487.6	yes	36	185.117	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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