LMFDB - Embedded newform 1110.2.u.e.401.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.18
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.e.191.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(0.952541 + 1.44660i) q^{6} +2.97676 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.75590 - 1.18533i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(0.952541 + 1.44660i) q^{6} +2.97676 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.75590 - 1.18533i) q^{9} +1.00000 q^{10} -2.43854 q^{11} +(1.69645 + 0.349356i) q^{12} +(3.37975 - 3.37975i) q^{13} +(2.10489 - 2.10489i) q^{14} +(-1.44660 + 0.952541i) q^{15} -1.00000 q^{16} +(2.64124 + 2.64124i) q^{17} +(-2.78687 + 1.11056i) q^{18} +(5.18614 - 5.18614i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-1.03995 + 5.04993i) q^{21} +(-1.72431 + 1.72431i) q^{22} +(4.56924 + 4.56924i) q^{23} +(1.44660 - 0.952541i) q^{24} +1.00000i q^{25} -4.77969i q^{26} +(2.97365 - 4.26115i) q^{27} -2.97676i q^{28} +(-2.17706 + 2.17706i) q^{29} +(-0.349356 + 1.69645i) q^{30} +(-1.20146 - 1.20146i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.851919 - 4.13687i) q^{33} +3.73527 q^{34} +(2.10489 + 2.10489i) q^{35} +(-1.18533 + 2.75590i) q^{36} +(5.17502 + 3.19675i) q^{37} -7.33431i q^{38} +(4.55285 + 6.91433i) q^{39} -1.00000i q^{40} -7.04761 q^{41} +(2.83549 + 4.30620i) q^{42} +(-3.83120 + 3.83120i) q^{43} +2.43854i q^{44} +(-1.11056 - 2.78687i) q^{45} +6.46188 q^{46} +6.56942i q^{47} +(0.349356 - 1.69645i) q^{48} +1.86110 q^{49} +(0.707107 + 0.707107i) q^{50} +(-5.40347 + 3.55800i) q^{51} +(-3.37975 - 3.37975i) q^{52} +0.00856748i q^{53} +(-0.910402 - 5.11578i) q^{54} +(-1.72431 - 1.72431i) q^{55} +(-2.10489 - 2.10489i) q^{56} +(6.98623 + 10.6098i) q^{57} +3.07883i q^{58} +(3.57544 + 3.57544i) q^{59} +(0.952541 + 1.44660i) q^{60} +(8.28937 + 8.28937i) q^{61} -1.69913 q^{62} +(-8.20365 - 3.52845i) q^{63} +1.00000i q^{64} +4.77969 q^{65} +(-2.32281 - 3.52760i) q^{66} +3.64813i q^{67} +(2.64124 - 2.64124i) q^{68} +(-9.34779 + 6.15521i) q^{69} +2.97676 q^{70} -9.63129i q^{71} +(1.11056 + 2.78687i) q^{72} -5.75117i q^{73} +(5.91973 - 1.39885i) q^{74} +(-1.69645 - 0.349356i) q^{75} +(-5.18614 - 5.18614i) q^{76} -7.25895 q^{77} +(8.10852 + 1.66982i) q^{78} +(6.34989 - 6.34989i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(6.18998 + 6.53331i) q^{81} +(-4.98341 + 4.98341i) q^{82} -16.7962i q^{83} +(5.04993 + 1.03995i) q^{84} +3.73527i q^{85} +5.41814i q^{86} +(-2.93271 - 4.45385i) q^{87} +(1.72431 + 1.72431i) q^{88} +(1.72334 - 1.72334i) q^{89} +(-2.75590 - 1.18533i) q^{90} +(10.0607 - 10.0607i) q^{91} +(4.56924 - 4.56924i) q^{92} +(2.45796 - 1.61849i) q^{93} +(4.64528 + 4.64528i) q^{94} +7.33431 q^{95} +(-0.952541 - 1.44660i) q^{96} +(-4.30682 + 4.30682i) q^{97} +(1.31599 - 1.31599i) q^{98} +(6.72037 + 2.89048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.349356	+	1.69645i	−0.201701	+	0.979447i
$3$	−0.349356	+	1.69645i	−0.201701	+	0.979447i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	0.952541	+	1.44660i	0.388873	+	0.590574i
$7$	2.97676			1.12511			0.562555	−	0.826760i	$-0.309819\pi$
$7$	2.97676			1.12511			0.562555	+	0.826760i	$0.309819\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.75590	−	1.18533i	−0.918634	−	0.395111i
$10$	1.00000			0.316228
$11$	−2.43854			−0.735247			−0.367624	−	0.929975i	$-0.619829\pi$
$11$	−2.43854			−0.735247			−0.367624	+	0.929975i	$0.619829\pi$
$12$	1.69645	+	0.349356i	0.489724	+	0.100850i
$13$	3.37975	−	3.37975i	0.937375	−	0.937375i	−0.0607761	−	0.998151i	$-0.519358\pi$
$13$	3.37975	−	3.37975i	0.937375	−	0.937375i	0.998151	+	0.0607761i	$0.0193576\pi$
$14$	2.10489	−	2.10489i	0.562555	−	0.562555i
$15$	−1.44660	+	0.952541i	−0.373512	+	0.245945i
$16$	−1.00000			−0.250000
$17$	2.64124	+	2.64124i	0.640594	+	0.640594i	0.950702	−	0.310107i	$-0.100365\pi$
$17$	2.64124	+	2.64124i	0.640594	+	0.640594i	−0.310107	+	0.950702i	$0.600365\pi$
$18$	−2.78687	+	1.11056i	−0.656872	+	0.261762i
$19$	5.18614	−	5.18614i	1.18978	−	1.18978i	0.212654	−	0.977128i	$-0.431789\pi$
$19$	5.18614	−	5.18614i	1.18978	−	1.18978i	0.977128	−	0.212654i	$-0.0682108\pi$
$20$	0.707107	−	0.707107i	0.158114	−	0.158114i
$21$	−1.03995	+	5.04993i	−0.226935	+	1.10199i
$22$	−1.72431	+	1.72431i	−0.367624	+	0.367624i
$23$	4.56924	+	4.56924i	0.952753	+	0.952753i	0.998933	−	0.0461806i	$-0.0147050\pi$
$23$	4.56924	+	4.56924i	0.952753	+	0.952753i	−0.0461806	+	0.998933i	$0.514705\pi$
$24$	1.44660	−	0.952541i	0.295287	−	0.194437i
$25$			1.00000i			0.200000i
$26$		−	4.77969i		−	0.937375i
$27$	2.97365	−	4.26115i	0.572279	−	0.820059i
$28$		−	2.97676i		−	0.562555i
$29$	−2.17706	+	2.17706i	−0.404270	+	0.404270i	−0.879735	−	0.475465i	$-0.842280\pi$
$29$	−2.17706	+	2.17706i	−0.404270	+	0.404270i	0.475465	+	0.879735i	$0.342280\pi$
$30$	−0.349356	+	1.69645i	−0.0637834	+	0.309728i
$31$	−1.20146	−	1.20146i	−0.215789	−	0.215789i	0.590932	−	0.806721i	$-0.298760\pi$
$31$	−1.20146	−	1.20146i	−0.215789	−	0.215789i	−0.806721	+	0.590932i	$0.798760\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.851919	−	4.13687i	0.148300	−	0.720136i
$34$	3.73527			0.640594
$35$	2.10489	+	2.10489i	0.355791	+	0.355791i
$36$	−1.18533	+	2.75590i	−0.197555	+	0.459317i
$37$	5.17502	+	3.19675i	0.850767	+	0.525542i
$37$	5.17502	+	3.19675i	0.850767	+	0.525542i
$38$		−	7.33431i		−	1.18978i
$39$	4.55285	+	6.91433i	0.729040	+	1.10718i
$40$		−	1.00000i		−	0.158114i
$41$	−7.04761			−1.10065			−0.550326	−	0.834950i	$-0.685496\pi$
$41$	−7.04761			−1.10065			−0.550326	+	0.834950i	$0.685496\pi$
$42$	2.83549	+	4.30620i	0.437525	+	0.664460i
$43$	−3.83120	+	3.83120i	−0.584253	+	0.584253i	−0.936069	−	0.351816i	$-0.885564\pi$
$43$	−3.83120	+	3.83120i	−0.584253	+	0.584253i	0.351816	+	0.936069i	$0.385564\pi$
$44$			2.43854i			0.367624i
$45$	−1.11056	−	2.78687i	−0.165553	−	0.415442i
$46$	6.46188			0.952753
$47$			6.56942i			0.958249i	0.877747	+	0.479124i	$0.159046\pi$
$47$			6.56942i			0.958249i	−0.877747	+	0.479124i	$0.840954\pi$
$48$	0.349356	−	1.69645i	0.0504252	−	0.244862i
$49$	1.86110			0.265871
$50$	0.707107	+	0.707107i	0.100000	+	0.100000i
$51$	−5.40347	+	3.55800i	−0.756637	+	0.498220i
$52$	−3.37975	−	3.37975i	−0.468688	−	0.468688i
$53$			0.00856748i			0.00117683i	1.00000		0.000588417i	$0.000187299\pi$
$53$			0.00856748i			0.00117683i	−1.00000		0.000588417i	$0.999813\pi$
$54$	−0.910402	−	5.11578i	−0.123890	−	0.696169i
$55$	−1.72431	−	1.72431i	−0.232506	−	0.232506i
$56$	−2.10489	−	2.10489i	−0.281277	−	0.281277i
$57$	6.98623	+	10.6098i	0.925348	+	1.40531i
$58$			3.07883i			0.404270i
$59$	3.57544	+	3.57544i	0.465483	+	0.465483i	0.900447	−	0.434965i	$-0.143239\pi$
$59$	3.57544	+	3.57544i	0.465483	+	0.465483i	−0.434965	+	0.900447i	$0.643239\pi$
$60$	0.952541	+	1.44660i	0.122973	+	0.186756i
$61$	8.28937	+	8.28937i	1.06135	+	1.06135i	0.997991	+	0.0633543i	$0.0201798\pi$
$61$	8.28937	+	8.28937i	1.06135	+	1.06135i	0.0633543	+	0.997991i	$0.479820\pi$
$62$	−1.69913			−0.215789
$63$	−8.20365	−	3.52845i	−1.03356	−	0.444543i
$64$			1.00000i			0.125000i
$65$	4.77969			0.592848
$66$	−2.32281	−	3.52760i	−0.285918	−	0.434218i
$67$			3.64813i			0.445689i	0.974854	+	0.222845i	$0.0715343\pi$
$67$			3.64813i			0.445689i	−0.974854	+	0.222845i	$0.928466\pi$
$68$	2.64124	−	2.64124i	0.320297	−	0.320297i
$69$	−9.34779	+	6.15521i	−1.12534	+	0.741000i
$70$	2.97676			0.355791
$71$		−	9.63129i		−	1.14302i	−0.820594	−	0.571512i	$-0.806357\pi$
$71$		−	9.63129i		−	1.14302i	0.820594	−	0.571512i	$-0.193643\pi$
$72$	1.11056	+	2.78687i	0.130881	+	0.328436i
$73$		−	5.75117i		−	0.673123i	−0.941661	−	0.336561i	$-0.890736\pi$
$73$		−	5.75117i		−	0.673123i	0.941661	−	0.336561i	$-0.109264\pi$
$74$	5.91973	−	1.39885i	0.688155	−	0.162613i
$75$	−1.69645	−	0.349356i	−0.195889	−	0.0403402i
$76$	−5.18614	−	5.18614i	−0.594891	−	0.594891i
$77$	−7.25895			−0.827234
$78$	8.10852	+	1.66982i	0.918110	+	0.189069i
$79$	6.34989	−	6.34989i	0.714419	−	0.714419i	−0.253038	−	0.967456i	$-0.581430\pi$
$79$	6.34989	−	6.34989i	0.714419	−	0.714419i	0.967456	+	0.253038i	$0.0814296\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	6.18998	+	6.53331i	0.687775	+	0.725924i
$82$	−4.98341	+	4.98341i	−0.550326	+	0.550326i
$83$		−	16.7962i		−	1.84362i	−0.387640	−	0.921811i	$-0.626710\pi$
$83$		−	16.7962i		−	1.84362i	0.387640	−	0.921811i	$-0.373290\pi$
$84$	5.04993	+	1.03995i	0.550993	+	0.113468i
$85$			3.73527i			0.405147i
$86$			5.41814i			0.584253i
$87$	−2.93271	−	4.45385i	−0.314420	−	0.477503i
$88$	1.72431	+	1.72431i	0.183812	+	0.183812i
$89$	1.72334	−	1.72334i	0.182674	−	0.182674i	−0.609846	−	0.792520i	$-0.708769\pi$
$89$	1.72334	−	1.72334i	0.182674	−	0.182674i	0.792520	+	0.609846i	$0.208769\pi$
$90$	−2.75590	−	1.18533i	−0.290497	−	0.124945i
$91$	10.0607	−	10.0607i	1.05465	−	1.05465i
$92$	4.56924	−	4.56924i	0.476376	−	0.476376i
$93$	2.45796	−	1.61849i	0.254879	−	0.167829i
$94$	4.64528	+	4.64528i	0.479124	+	0.479124i
$95$	7.33431			0.752484
$96$	−0.952541	−	1.44660i	−0.0972183	−	0.147643i
$97$	−4.30682	+	4.30682i	−0.437291	+	0.437291i	−0.891099	−	0.453808i	$-0.850065\pi$
$97$	−4.30682	+	4.30682i	−0.437291	+	0.437291i	0.453808	+	0.891099i	$0.350065\pi$
$98$	1.31599	−	1.31599i	0.132936	−	0.132936i
$99$	6.72037	+	2.89048i	0.675423	+	0.290504i
$100$	1.00000			0.100000
$101$	0.223998			0.0222886			0.0111443	−	0.999938i	$-0.496453\pi$
$101$	0.223998			0.0222886			0.0111443	+	0.999938i	$0.496453\pi$
$102$	−1.30494	+	6.33672i	−0.129208	+	0.627428i
$103$	−0.790994	−	0.790994i	−0.0779389	−	0.0779389i	0.667063	−	0.745002i	$-0.267551\pi$
$103$	−0.790994	−	0.790994i	−0.0779389	−	0.0779389i	−0.745002	+	0.667063i	$0.767551\pi$
$104$	−4.77969			−0.468688
$105$	−4.30620	+	2.83549i	−0.420242	+	0.276715i
$106$	0.00605812	+	0.00605812i	0.000588417	+	0.000588417i
$107$		−	13.3421i		−	1.28983i	−0.764256	−	0.644914i	$-0.776893\pi$
$107$		−	13.3421i		−	1.28983i	0.764256	−	0.644914i	$-0.223107\pi$
$108$	−4.26115	−	2.97365i	−0.410029	−	0.286140i
$109$	−8.23612	+	8.23612i	−0.788877	+	0.788877i	−0.981310	−	0.192433i	$-0.938362\pi$
$109$	−8.23612	+	8.23612i	−0.788877	+	0.788877i	0.192433	+	0.981310i	$0.438362\pi$
$110$	−2.43854			−0.232506
$111$	−7.23106	+	7.66236i	−0.686341	+	0.727279i
$112$	−2.97676			−0.281277
$113$	1.62412	−	1.62412i	0.152784	−	0.152784i	−0.626576	−	0.779360i	$-0.715544\pi$
$113$	1.62412	−	1.62412i	0.152784	−	0.152784i	0.779360	+	0.626576i	$0.215544\pi$
$114$	12.4423	+	2.56228i	1.16533	+	0.239980i
$115$			6.46188i			0.602574i
$116$	2.17706	+	2.17706i	0.202135	+	0.202135i
$117$	−13.3204	+	5.30814i	−1.23147	+	0.490738i
$118$	5.05644			0.465483
$119$	7.86233	+	7.86233i	0.720739	+	0.720739i
$120$	1.69645	+	0.349356i	0.154864	+	0.0318917i
$121$	−5.05352			−0.459411
$122$	11.7229			1.06135
$123$	2.46212	−	11.9559i	0.222002	−	1.07803i
$124$	−1.20146	+	1.20146i	−0.107895	+	0.107895i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−8.29585	+	3.30587i	−0.739053	+	0.294510i
$127$	−0.265733			−0.0235800			−0.0117900	−	0.999930i	$-0.503753\pi$
$127$	−0.265733			−0.0235800			−0.0117900	+	0.999930i	$0.503753\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−5.16100	−	7.83791i	−0.454401	−	0.690090i
$130$	3.37975	−	3.37975i	0.296424	−	0.296424i
$131$	−5.37214	+	5.37214i	−0.469366	+	0.469366i	−0.901709	−	0.432343i	$-0.857687\pi$
$131$	−5.37214	+	5.37214i	−0.469366	+	0.469366i	0.432343	+	0.901709i	$0.357687\pi$
$132$	−4.13687	−	0.851919i	−0.360068	−	0.0741500i
$133$	15.4379	−	15.4379i	1.33863	−	1.33863i
$134$	2.57961	+	2.57961i	0.222845	+	0.222845i
$135$	5.11578	−	0.910402i	0.440296	−	0.0783549i
$136$		−	3.73527i		−	0.320297i
$137$		−	7.45566i		−	0.636980i	−0.947926	−	0.318490i	$-0.896824\pi$
$137$		−	7.45566i		−	0.636980i	0.947926	−	0.318490i	$-0.103176\pi$
$138$	−2.25750	+	10.9623i	−0.192171	+	0.933171i
$139$		−	18.3826i		−	1.55920i	−0.626281	−	0.779598i	$-0.715424\pi$
$139$		−	18.3826i		−	1.55920i	0.626281	−	0.779598i	$-0.284576\pi$
$140$	2.10489	−	2.10489i	0.177895	−	0.177895i
$141$	−11.1447	−	2.29507i	−0.938554	−	0.193280i
$142$	−6.81035	−	6.81035i	−0.571512	−	0.571512i
$143$	−8.24167	+	8.24167i	−0.689203	+	0.689203i
$144$	2.75590	+	1.18533i	0.229658	+	0.0987776i
$145$	−3.07883			−0.255683
$146$	−4.06669	−	4.06669i	−0.336561	−	0.336561i
$147$	−0.650186	+	3.15726i	−0.0536264	+	0.260407i
$148$	3.19675	−	5.17502i	0.262771	−	0.425384i
$149$			10.3217i			0.845589i	0.906226	+	0.422795i	$0.138951\pi$
$149$			10.3217i			0.845589i	−0.906226	+	0.422795i	$0.861049\pi$
$150$	−1.44660	+	0.952541i	−0.118115	+	0.0777746i
$151$			21.8379i			1.77714i	0.458741	+	0.888570i	$0.348301\pi$
$151$			21.8379i			1.77714i	−0.458741	+	0.888570i	$0.651699\pi$
$152$	−7.33431			−0.594891
$153$	−4.14825	−	10.4097i	−0.335366	−	0.841577i
$154$	−5.13285	+	5.13285i	−0.413617	+	0.413617i
$155$		−	1.69913i		−	0.136477i
$156$	6.91433	−	4.55285i	0.553589	−	0.364520i
$157$	−6.37842			−0.509053			−0.254527	−	0.967066i	$-0.581920\pi$
$157$	−6.37842			−0.509053			−0.254527	+	0.967066i	$0.581920\pi$
$158$		−	8.98011i		−	0.714419i
$159$	−0.0145343	−	0.00299310i	−0.00115265	−	0.000237368i
$160$	−1.00000			−0.0790569
$161$	13.6015	+	13.6015i	1.07195	+	1.07195i
$162$	8.99672	+	0.242774i	0.706849	+	0.0190742i
$163$	−13.2027	−	13.2027i	−1.03412	−	1.03412i	−0.999397	−	0.0347202i	$-0.988946\pi$
$163$	−13.2027	−	13.2027i	−1.03412	−	1.03412i	−0.0347202	−	0.999397i	$-0.511054\pi$
$164$			7.04761i			0.550326i
$165$	3.52760	−	2.32281i	0.274624	−	0.180830i
$166$	−11.8767	−	11.8767i	−0.921811	−	0.921811i
$167$	−11.4214	−	11.4214i	−0.883817	−	0.883817i	0.110103	−	0.993920i	$-0.464882\pi$
$167$	−11.4214	−	11.4214i	−0.883817	−	0.883817i	−0.993920	+	0.110103i	$0.964882\pi$
$168$	4.30620	−	2.83549i	0.332230	−	0.218762i
$169$		−	9.84548i		−	0.757345i
$170$	2.64124	+	2.64124i	0.202574	+	0.202574i
$171$	−20.4398	+	8.14519i	−1.56307	+	0.622878i
$172$	3.83120	+	3.83120i	0.292127	+	0.292127i
$173$	−18.3766			−1.39715			−0.698573	−	0.715539i	$-0.746181\pi$
$173$	−18.3766			−1.39715			−0.698573	+	0.715539i	$0.746181\pi$
$174$	−5.22309	−	1.07561i	−0.395961	−	0.0815417i
$175$			2.97676i			0.225022i
$176$	2.43854			0.183812
$177$	−7.31466	+	4.81646i	−0.549804	+	0.362027i
$178$		−	2.43717i		−	0.182674i
$179$	−14.5304	+	14.5304i	−1.08606	+	1.08606i	−0.0901264	+	0.995930i	$0.528727\pi$
$179$	−14.5304	+	14.5304i	−1.08606	+	1.08606i	−0.995930	+	0.0901264i	$0.971273\pi$
$180$	−2.78687	+	1.11056i	−0.207721	+	0.0827763i
$181$	−2.29142			−0.170320			−0.0851599	−	0.996367i	$-0.527140\pi$
$181$	−2.29142			−0.170320			−0.0851599	+	0.996367i	$0.527140\pi$
$182$		−	14.2280i		−	1.05465i
$183$	−16.9585	+	11.1666i	−1.25361	+	0.825458i
$184$		−	6.46188i		−	0.476376i
$185$	1.39885	+	5.91973i	0.102845	+	0.435227i
$186$	0.593600	−	2.88249i	0.0435248	−	0.211354i
$187$	−6.44076	−	6.44076i	−0.470995	−	0.470995i
$188$	6.56942			0.479124
$189$	8.85184	−	12.6844i	0.643876	−	0.922656i
$190$	5.18614	−	5.18614i	0.376242	−	0.376242i
$191$	−5.55986	−	5.55986i	−0.402297	−	0.402297i	0.476745	−	0.879042i	$-0.341817\pi$
$191$	−5.55986	−	5.55986i	−0.402297	−	0.402297i	−0.879042	+	0.476745i	$0.841817\pi$
$192$	−1.69645	−	0.349356i	−0.122431	−	0.0252126i
$193$	−6.93955	+	6.93955i	−0.499519	+	0.499519i	−0.911288	−	0.411769i	$-0.864911\pi$
$193$	−6.93955	+	6.93955i	−0.499519	+	0.499519i	0.411769	+	0.911288i	$0.364911\pi$
$194$			6.09076i			0.437291i
$195$	−1.66982	+	8.10852i	−0.119578	+	0.580663i
$196$		−	1.86110i		−	0.132936i
$197$			1.08968i			0.0776363i	0.999246	+	0.0388182i	$0.0123593\pi$
$197$			1.08968i			0.0776363i	−0.999246	+	0.0388182i	$0.987641\pi$
$198$	6.79590	−	2.70815i	0.482964	−	0.192459i
$199$	−6.21327	−	6.21327i	−0.440447	−	0.440447i	0.451715	−	0.892162i	$-0.350812\pi$
$199$	−6.21327	−	6.21327i	−0.440447	−	0.440447i	−0.892162	+	0.451715i	$0.850812\pi$
$200$	0.707107	−	0.707107i	0.0500000	−	0.0500000i
$201$	−6.18887	−	1.27449i	−0.436529	−	0.0898959i
$202$	0.158390	−	0.158390i	0.0111443	−	0.0111443i
$203$	−6.48059	+	6.48059i	−0.454848	+	0.454848i
$204$	3.55800	+	5.40347i	0.249110	+	0.378318i
$205$	−4.98341	−	4.98341i	−0.348057	−	0.348057i
$206$	−1.11863			−0.0779389
$207$	−7.17631	−	18.0084i	−0.498788	−	1.25167i
$208$	−3.37975	+	3.37975i	−0.234344	+	0.234344i
$209$	−12.6466	+	12.6466i	−0.874784	+	0.874784i
$210$	−1.03995	+	5.04993i	−0.0717633	+	0.348478i
$211$	19.8475			1.36636			0.683180	−	0.730250i	$-0.260597\pi$
$211$	19.8475			1.36636			0.683180	+	0.730250i	$0.260597\pi$
$212$	0.00856748			0.000588417
$213$	16.3390	+	3.36475i	1.11953	+	0.230549i
$214$	−9.43427	−	9.43427i	−0.644914	−	0.644914i
$215$	−5.41814			−0.369514
$216$	−5.11578	+	0.910402i	−0.348084	+	0.0619450i
$217$	−3.57647	−	3.57647i	−0.242786	−	0.242786i
$218$			11.6476i			0.788877i
$219$	9.75658	+	2.00920i	0.659288	+	0.135769i
$220$	−1.72431	+	1.72431i	−0.116253	+	0.116253i
$221$	17.8535			1.20095
$222$	0.304982	+	10.5312i	0.0204690	+	0.706810i
$223$	−18.7033			−1.25246			−0.626232	−	0.779637i	$-0.715404\pi$
$223$	−18.7033			−1.25246			−0.626232	+	0.779637i	$0.715404\pi$
$224$	−2.10489	+	2.10489i	−0.140639	+	0.140639i
$225$	1.18533	−	2.75590i	0.0790221	−	0.183727i
$226$		−	2.29685i		−	0.152784i
$227$	14.6213	+	14.6213i	0.970449	+	0.970449i	0.999576	−	0.0291269i	$-0.00927268\pi$
$227$	14.6213	+	14.6213i	0.970449	+	0.970449i	−0.0291269	+	0.999576i	$0.509273\pi$
$228$	10.6098	−	6.98623i	0.702654	−	0.462674i
$229$	−6.40334			−0.423145			−0.211572	−	0.977362i	$-0.567858\pi$
$229$	−6.40334			−0.423145			−0.211572	+	0.977362i	$0.567858\pi$
$230$	4.56924	+	4.56924i	0.301287	+	0.301287i
$231$	2.53596	−	12.3145i	0.166854	−	0.810232i
$232$	3.07883			0.202135
$233$	−9.92789			−0.650398			−0.325199	−	0.945646i	$-0.605431\pi$
$233$	−9.92789			−0.650398			−0.325199	+	0.945646i	$0.605431\pi$
$234$	−5.66552	+	13.1724i	−0.370367	+	0.861104i
$235$	−4.64528	+	4.64528i	−0.303025	+	0.303025i
$236$	3.57544	−	3.57544i	0.232741	−	0.232741i
$237$	8.55392	+	12.9907i	0.555637	+	0.843834i
$238$	11.1190			0.720739
$239$	−18.3998	−	18.3998i	−1.19018	−	1.19018i	−0.977016	−	0.213168i	$-0.931622\pi$
$239$	−18.3998	−	18.3998i	−1.19018	−	1.19018i	−0.213168	−	0.977016i	$-0.568378\pi$
$240$	1.44660	−	0.952541i	0.0933779	−	0.0614863i
$241$	18.2602	−	18.2602i	1.17624	−	1.17624i	0.195550	−	0.980694i	$-0.437351\pi$
$241$	18.2602	−	18.2602i	1.17624	−	1.17624i	0.980694	−	0.195550i	$-0.0626492\pi$
$242$	−3.57338	+	3.57338i	−0.229706	+	0.229706i
$243$	−13.2460	+	8.21855i	−0.849729	+	0.527220i
$244$	8.28937	−	8.28937i	0.530673	−	0.530673i
$245$	1.31599	+	1.31599i	0.0840758	+	0.0840758i
$246$	−6.71314	−	10.1951i	−0.428014	−	0.650016i
$247$		−	35.0557i		−	2.23054i
$248$			1.69913i			0.107895i
$249$	28.4939	+	5.86785i	1.80573	+	0.371860i
$250$			1.00000i			0.0632456i
$251$	17.3355	−	17.3355i	1.09420	−	1.09420i	0.0991297	−	0.995075i	$-0.468394\pi$
$251$	17.3355	−	17.3355i	1.09420	−	1.09420i	0.995075	−	0.0991297i	$-0.0316059\pi$
$252$	−3.52845	+	8.20365i	−0.222271	+	0.516782i
$253$	−11.1423	−	11.1423i	−0.700509	−	0.700509i
$254$	−0.187902	+	0.187902i	−0.0117900	+	0.0117900i
$255$	−6.33672	−	1.30494i	−0.396821	−	0.0817186i
$256$	1.00000			0.0625000
$257$	21.4622	+	21.4622i	1.33877	+	1.33877i	0.897248	+	0.441526i	$0.145563\pi$
$257$	21.4622	+	21.4622i	1.33877	+	1.33877i	0.441526	+	0.897248i	$0.354437\pi$
$258$	−9.19162	−	1.89286i	−0.572245	−	0.117844i
$259$	15.4048	+	9.51595i	0.957206	+	0.591293i
$260$		−	4.77969i		−	0.296424i
$261$	8.58031	−	3.41923i	0.531108	−	0.211645i
$262$			7.59736i			0.469366i
$263$	7.76918			0.479068			0.239534	−	0.970888i	$-0.423005\pi$
$263$	7.76918			0.479068			0.239534	+	0.970888i	$0.423005\pi$
$264$	−3.52760	+	2.32281i	−0.217109	+	0.142959i
$265$	−0.00605812	+	0.00605812i	−0.000372147	+	0.000372147i
$266$		−	21.8325i		−	1.33863i
$267$	2.32150	+	3.52562i	0.142074	+	0.215764i
$268$	3.64813			0.222845
$269$			25.5891i			1.56019i	0.625659	+	0.780097i	$0.284830\pi$
$269$			25.5891i			1.56019i	−0.625659	+	0.780097i	$0.715170\pi$
$270$	2.97365	−	4.26115i	0.180971	−	0.259325i
$271$	−7.34693			−0.446294			−0.223147	−	0.974785i	$-0.571633\pi$
$271$	−7.34693			−0.446294			−0.223147	+	0.974785i	$0.571633\pi$
$272$	−2.64124	−	2.64124i	−0.160149	−	0.160149i
$273$	13.5528	+	20.5823i	0.820250	+	1.24570i
$274$	−5.27195	−	5.27195i	−0.318490	−	0.318490i
$275$		−	2.43854i		−	0.147049i
$276$	6.15521	+	9.34779i	0.370500	+	0.562671i
$277$	3.64147	+	3.64147i	0.218795	+	0.218795i	0.807990	−	0.589196i	$-0.200555\pi$
$277$	3.64147	+	3.64147i	0.218795	+	0.218795i	−0.589196	+	0.807990i	$0.700555\pi$
$278$	−12.9985	−	12.9985i	−0.779598	−	0.779598i
$279$	1.88698	+	4.73525i	0.112971	+	0.283492i
$280$		−	2.97676i		−	0.177895i
$281$	−16.5786	−	16.5786i	−0.988999	−	0.988999i	0.0109410	−	0.999940i	$-0.496517\pi$
$281$	−16.5786	−	16.5786i	−0.988999	−	0.988999i	−0.999940	+	0.0109410i	$0.996517\pi$
$282$	−9.50336	+	6.25765i	−0.565917	+	0.372637i
$283$	−4.84935	−	4.84935i	−0.288264	−	0.288264i	0.548130	−	0.836393i	$-0.315340\pi$
$283$	−4.84935	−	4.84935i	−0.288264	−	0.288264i	−0.836393	+	0.548130i	$0.815340\pi$
$284$	−9.63129			−0.571512
$285$	−2.56228	+	12.4423i	−0.151777	+	0.737018i
$286$			11.6555i			0.689203i
$287$	−20.9790			−1.23835
$288$	2.78687	−	1.11056i	0.164218	−	0.0654404i
$289$		−	3.04772i		−	0.179278i
$290$	−2.17706	+	2.17706i	−0.127842	+	0.127842i
$291$	−5.80170	−	8.81093i	−0.340102	−	0.516506i
$292$	−5.75117			−0.336561
$293$		−	16.8721i		−	0.985681i	−0.870120	−	0.492840i	$-0.835959\pi$
$293$		−	16.8721i		−	0.985681i	0.870120	−	0.492840i	$-0.164041\pi$
$294$	1.77277	+	2.69227i	0.103390	+	0.157017i
$295$			5.05644i			0.294397i
$296$	−1.39885	−	5.91973i	−0.0813063	−	0.344077i
$297$	−7.25136	+	10.3910i	−0.420767	+	0.602946i
$298$	7.29857	+	7.29857i	0.422795	+	0.422795i
$299$	30.8858			1.78617
$300$	−0.349356	+	1.69645i	−0.0201701	+	0.0979447i
$301$	−11.4046	+	11.4046i	−0.657349	+	0.657349i
$302$	15.4417	+	15.4417i	0.888570	+	0.888570i
$303$	−0.0782550	+	0.380001i	−0.00449563	+	0.0218305i
$304$	−5.18614	+	5.18614i	−0.297445	+	0.297445i
$305$			11.7229i			0.671254i
$306$	−10.2940	−	4.42754i	−0.588471	−	0.253106i
$307$			2.59584i			0.148153i	0.997253	+	0.0740763i	$0.0236008\pi$
$307$			2.59584i			0.148153i	−0.997253	+	0.0740763i	$0.976399\pi$
$308$			7.25895i			0.413617i
$309$	1.61822	−	1.06554i	0.0920574	−	0.0606167i
$310$	−1.20146	−	1.20146i	−0.0682385	−	0.0682385i
$311$	2.69292	−	2.69292i	0.152702	−	0.152702i	−0.626622	−	0.779323i	$-0.715563\pi$
$311$	2.69292	−	2.69292i	0.152702	−	0.152702i	0.779323	+	0.626622i	$0.215563\pi$
$312$	1.66982	−	8.10852i	0.0945347	−	0.459055i
$313$	−7.66085	+	7.66085i	−0.433017	+	0.433017i	−0.889653	−	0.456636i	$-0.849054\pi$
$313$	−7.66085	+	7.66085i	−0.433017	+	0.433017i	0.456636	+	0.889653i	$0.349054\pi$
$314$	−4.51022	+	4.51022i	−0.254527	+	0.254527i
$315$	−3.30587	−	8.29585i	−0.186265	−	0.467418i
$316$	−6.34989	−	6.34989i	−0.357209	−	0.357209i
$317$	12.5140			0.702854			0.351427	−	0.936215i	$-0.385697\pi$
$317$	12.5140			0.702854			0.351427	+	0.936215i	$0.385697\pi$
$318$	−0.0123938	+	0.00816087i	−0.000695007	+	0.000457639i
$319$	5.30885	−	5.30885i	0.297239	−	0.297239i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$	22.6342	+	4.66113i	1.26332	+	0.260159i
$322$	19.2355			1.07195
$323$	27.3957			1.52433
$324$	6.53331	−	6.18998i	0.362962	−	0.343888i
$325$	3.37975	+	3.37975i	0.187475	+	0.187475i
$326$	−18.6715			−1.03412
$327$	−11.0948	−	16.8495i	−0.613546	−	0.931780i
$328$	4.98341	+	4.98341i	0.275163	+	0.275163i
$329$			19.5556i			1.07813i
$330$	0.851919	−	4.13687i	0.0468966	−	0.227727i
$331$	−5.65251	+	5.65251i	−0.310690	+	0.310690i	−0.845177	−	0.534487i	$-0.820505\pi$
$331$	−5.65251	+	5.65251i	−0.310690	+	0.310690i	0.534487	+	0.845177i	$0.320505\pi$
$332$	−16.7962			−0.921811
$333$	−10.4726	−	14.9440i	−0.573896	−	0.818928i
$334$	−16.1523			−0.883817
$335$	−2.57961	+	2.57961i	−0.140939	+	0.140939i
$336$	1.03995	−	5.04993i	0.0567339	−	0.275496i
$337$		−	6.95275i		−	0.378740i	−0.981906	−	0.189370i	$-0.939355\pi$
$337$		−	6.95275i		−	0.378740i	0.981906	−	0.189370i	$-0.0606446\pi$
$338$	−6.96181	−	6.96181i	−0.378672	−	0.378672i
$339$	2.18784	+	3.32263i	0.118827	+	0.180461i
$340$	3.73527			0.202574
$341$	2.92982	+	2.92982i	0.158658	+	0.158658i
$342$	−8.69359	+	20.2126i	−0.470095	+	1.09297i
$343$	−15.2973			−0.825975
$344$	5.41814			0.292127
$345$	−10.9623	−	2.25750i	−0.590189	−	0.121540i
$346$	−12.9942	+	12.9942i	−0.698573	+	0.698573i
$347$	24.0122	−	24.0122i	1.28904	−	1.28904i	0.353671	−	0.935370i	$-0.384933\pi$
$347$	24.0122	−	24.0122i	1.28904	−	1.28904i	0.935370	−	0.353671i	$-0.115067\pi$
$348$	−4.45385	+	2.93271i	−0.238752	+	0.157210i
$349$	18.2431			0.976531			0.488266	−	0.872695i	$-0.337630\pi$
$349$	18.2431			0.976531			0.488266	+	0.872695i	$0.337630\pi$
$350$	2.10489	+	2.10489i	0.112511	+	0.112511i
$351$	−4.35144	−	24.4519i	−0.232263	−	1.30514i
$352$	1.72431	−	1.72431i	0.0919059	−	0.0919059i
$353$	−22.0357	+	22.0357i	−1.17284	+	1.17284i	−0.191310	+	0.981530i	$0.561273\pi$
$353$	−22.0357	+	22.0357i	−1.17284	+	1.17284i	−0.981530	+	0.191310i	$0.938727\pi$
$354$	−1.76650	+	8.57800i	−0.0938882	+	0.455916i
$355$	6.81035	−	6.81035i	0.361456	−	0.361456i
$356$	−1.72334	−	1.72334i	−0.0913368	−	0.0913368i
$357$	−16.0848	+	10.5913i	−0.851299	+	0.560552i
$358$			20.5492i			1.08606i
$359$		−	2.38803i		−	0.126035i	−0.998012	−	0.0630177i	$-0.979928\pi$
$359$		−	2.38803i		−	0.126035i	0.998012	−	0.0630177i	$-0.0200725\pi$
$360$	−1.18533	+	2.75590i	−0.0624725	+	0.145249i
$361$		−	34.7921i		−	1.83116i
$362$	−1.62028	+	1.62028i	−0.0851599	+	0.0851599i
$363$	1.76548	−	8.57306i	0.0926636	−	0.449969i
$364$	−10.0607	−	10.0607i	−0.527325	−	0.527325i
$365$	4.06669	−	4.06669i	0.212860	−	0.212860i
$366$	−4.09548	+	19.8874i	−0.214074	+	1.03953i
$367$	−21.6442			−1.12982			−0.564909	−	0.825153i	$-0.691089\pi$
$367$	−21.6442			−1.12982			−0.564909	+	0.825153i	$0.691089\pi$
$368$	−4.56924	−	4.56924i	−0.238188	−	0.238188i
$369$	19.4225	+	8.35375i	1.01110	+	0.434879i
$370$	5.17502	+	3.19675i	0.269036	+	0.166191i
$371$			0.0255033i			0.00132407i
$372$	−1.61849	−	2.45796i	−0.0839146	−	0.127439i
$373$			6.01294i			0.311338i	0.987809	+	0.155669i	$0.0497533\pi$
$373$			6.01294i			0.311338i	−0.987809	+	0.155669i	$0.950247\pi$
$374$	−9.10862			−0.470995
$375$	−0.952541	−	1.44660i	−0.0491890	−	0.0747024i
$376$	4.64528	−	4.64528i	0.239562	−	0.239562i
$377$			14.7159i			0.757906i
$378$	−2.71005	−	15.2284i	−0.139390	−	0.783266i
$379$	−38.0594			−1.95498			−0.977491	−	0.210977i	$-0.932336\pi$
$379$	−38.0594			−1.95498			−0.977491	+	0.210977i	$0.932336\pi$
$380$		−	7.33431i		−	0.376242i
$381$	0.0928354	−	0.450803i	0.00475610	−	0.0230953i
$382$	−7.86283			−0.402297
$383$	−11.9705	−	11.9705i	−0.611662	−	0.611662i	0.331717	−	0.943379i	$-0.392372\pi$
$383$	−11.9705	−	11.9705i	−0.611662	−	0.611662i	−0.943379	+	0.331717i	$0.892372\pi$
$384$	−1.44660	+	0.952541i	−0.0738217	+	0.0486091i
$385$	−5.13285	−	5.13285i	−0.261594	−	0.261594i
$386$			9.81400i			0.499519i
$387$	15.0997	−	6.01717i	0.767559	−	0.305870i
$388$	4.30682	+	4.30682i	0.218646	+	0.218646i
$389$	19.1226	+	19.1226i	0.969555	+	0.969555i	0.999550	−	0.0299951i	$-0.00954917\pi$
$389$	19.1226	+	19.1226i	0.969555	+	0.969555i	−0.0299951	+	0.999550i	$0.509549\pi$
$390$	4.55285	+	6.91433i	0.230543	+	0.350121i
$391$			24.1369i			1.22066i
$392$	−1.31599	−	1.31599i	−0.0664678	−	0.0664678i
$393$	−7.23680	−	10.9904i	−0.365048	−	0.554391i
$394$	0.770518	+	0.770518i	0.0388182	+	0.0388182i
$395$	8.98011			0.451838
$396$	2.89048	−	6.72037i	0.145252	−	0.337711i
$397$			22.1145i			1.10990i	0.831885	+	0.554948i	$0.187262\pi$
$397$			22.1145i			1.10990i	−0.831885	+	0.554948i	$0.812738\pi$
$398$	−8.78688			−0.440447
$399$	20.7963	+	31.5830i	1.04112	+	1.58113i
$400$		−	1.00000i		−	0.0500000i
$401$	−14.1223	+	14.1223i	−0.705233	+	0.705233i	−0.965529	−	0.260296i	$-0.916180\pi$
$401$	−14.1223	+	14.1223i	−0.705233	+	0.705233i	0.260296	+	0.965529i	$0.416180\pi$
$402$	−5.27740	+	3.47499i	−0.263213	+	0.173317i
$403$	−8.12130			−0.404551
$404$		−	0.223998i		−	0.0111443i
$405$	−0.242774	+	8.99672i	−0.0120636	+	0.447051i
$406$			9.16494i			0.454848i
$407$	−12.6195	−	7.79540i	−0.625525	−	0.386404i
$408$	6.33672	+	1.30494i	0.313714	+	0.0646042i
$409$	5.85980	+	5.85980i	0.289749	+	0.289749i	0.836981	−	0.547232i	$-0.184319\pi$
$409$	5.85980	+	5.85980i	0.289749	+	0.289749i	−0.547232	+	0.836981i	$0.684319\pi$
$410$	−7.04761			−0.348057
$411$	12.6482	+	2.60468i	0.623889	+	0.128479i
$412$	−0.790994	+	0.790994i	−0.0389695	+	0.0389695i
$413$	10.6432	+	10.6432i	0.523719	+	0.523719i
$414$	−17.8083	−	7.65947i	−0.875230	−	0.376443i
$415$	11.8767	−	11.8767i	0.583004	−	0.583004i
$416$			4.77969i			0.234344i
$417$	31.1853	+	6.42209i	1.52715	+	0.314491i
$418$			17.8850i			0.874784i
$419$		−	2.86911i		−	0.140165i	−0.997541	−	0.0700825i	$-0.977674\pi$
$419$		−	2.86911i		−	0.140165i	0.997541	−	0.0700825i	$-0.0223262\pi$
$420$	2.83549	+	4.30620i	0.138358	+	0.210121i
$421$	16.1956	+	16.1956i	0.789327	+	0.789327i	0.981384	−	0.192057i	$-0.0615157\pi$
$421$	16.1956	+	16.1956i	0.789327	+	0.789327i	−0.192057	+	0.981384i	$0.561516\pi$
$422$	14.0343	−	14.0343i	0.683180	−	0.683180i
$423$	7.78695	−	18.1047i	0.378614	−	0.880280i
$424$	0.00605812	−	0.00605812i	0.000294208	−	0.000294208i
$425$	−2.64124	+	2.64124i	−0.128119	+	0.128119i
$426$	13.9327	−	9.17419i	0.675040	−	0.444491i
$427$	24.6755	+	24.6755i	1.19413	+	1.19413i
$428$	−13.3421			−0.644914
$429$	−11.1023	−	16.8609i	−0.536025	−	0.814050i
$430$	−3.83120	+	3.83120i	−0.184757	+	0.184757i
$431$	−9.00474	+	9.00474i	−0.433743	+	0.433743i	−0.889900	−	0.456157i	$-0.849226\pi$
$431$	−9.00474	+	9.00474i	−0.433743	+	0.433743i	0.456157	+	0.889900i	$0.349226\pi$
$432$	−2.97365	+	4.26115i	−0.143070	+	0.205015i
$433$	22.2256			1.06809			0.534046	−	0.845455i	$-0.320671\pi$
$433$	22.2256			1.06809			0.534046	+	0.845455i	$0.320671\pi$
$434$	−5.05789			−0.242786
$435$	1.07561	−	5.22309i	0.0515715	−	0.250428i
$436$	8.23612	+	8.23612i	0.394438	+	0.394438i
$437$	47.3934			2.26714
$438$	8.31966	−	5.47822i	0.397529	−	0.261759i
$439$	25.2304	+	25.2304i	1.20418	+	1.20418i	0.972883	+	0.231298i	$0.0742971\pi$
$439$	25.2304	+	25.2304i	1.20418	+	1.20418i	0.231298	+	0.972883i	$0.425703\pi$
$440$			2.43854i			0.116253i
$441$	−5.12900	−	2.20602i	−0.244238	−	0.105048i
$442$	12.6243	−	12.6243i	0.600477	−	0.600477i
$443$	−26.9345			−1.27969			−0.639847	−	0.768502i	$-0.721002\pi$
$443$	−26.9345			−1.27969			−0.639847	+	0.768502i	$0.721002\pi$
$444$	7.66236	+	7.23106i	0.363640	+	0.343171i
$445$	2.43717			0.115533
$446$	−13.2252	+	13.2252i	−0.626232	+	0.626232i
$447$	−17.5103	−	3.60596i	−0.828210	−	0.170556i
$448$			2.97676i			0.140639i
$449$	−7.92152	−	7.92152i	−0.373840	−	0.373840i	0.495034	−	0.868874i	$-0.335156\pi$
$449$	−7.92152	−	7.92152i	−0.373840	−	0.373840i	−0.868874	+	0.495034i	$0.835156\pi$
$450$	−1.11056	−	2.78687i	−0.0523523	−	0.131374i
$451$	17.1859			0.809251
$452$	−1.62412	−	1.62412i	−0.0763921	−	0.0763921i
$453$	−37.0469	−	7.62919i	−1.74062	−	0.358451i
$454$	20.6776			0.970449
$455$	14.2280			0.667019
$456$	2.56228	−	12.4423i	0.119990	−	0.582664i
$457$	−20.7696	+	20.7696i	−0.971561	+	0.971561i	−0.999607	−	0.0280458i	$-0.991072\pi$
$457$	−20.7696	+	20.7696i	−0.971561	+	0.971561i	0.0280458	+	0.999607i	$0.491072\pi$
$458$	−4.52784	+	4.52784i	−0.211572	+	0.211572i
$459$	19.1088	−	3.40060i	0.891924	−	0.158726i
$460$	6.46188			0.301287
$461$	6.14385	+	6.14385i	0.286148	+	0.286148i	0.835555	−	0.549407i	$-0.185146\pi$
$461$	6.14385	+	6.14385i	0.286148	+	0.286148i	−0.549407	+	0.835555i	$0.685146\pi$
$462$	−6.91444	−	10.5008i	−0.321689	−	0.488543i
$463$	−22.3895	+	22.3895i	−1.04053	+	1.04053i	−0.0413850	+	0.999143i	$0.513177\pi$
$463$	−22.3895	+	22.3895i	−1.04053	+	1.04053i	−0.999143	+	0.0413850i	$0.986823\pi$
$464$	2.17706	−	2.17706i	0.101068	−	0.101068i
$465$	2.88249	+	0.593600i	0.133672	+	0.0275275i
$466$	−7.02008	+	7.02008i	−0.325199	+	0.325199i
$467$	−0.258047	−	0.258047i	−0.0119410	−	0.0119410i	0.701111	−	0.713052i	$-0.252688\pi$
$467$	−0.258047	−	0.258047i	−0.0119410	−	0.0119410i	−0.713052	+	0.701111i	$0.752688\pi$
$468$	5.30814	+	13.3204i	0.245369	+	0.615736i
$469$			10.8596i			0.501449i
$470$			6.56942i			0.303025i
$471$	2.22834	−	10.8207i	0.102676	−	0.498591i
$472$		−	5.05644i		−	0.232741i
$473$	9.34255	−	9.34255i	0.429571	−	0.429571i
$474$	15.2343	+	3.13725i	0.699735	+	0.144099i
$475$	5.18614	+	5.18614i	0.237956	+	0.237956i
$476$	7.86233	−	7.86233i	0.360369	−	0.360369i
$477$	0.0101553	−	0.0236111i	0.000464979	−	0.00108108i
$478$	−26.0212			−1.19018
$479$	−27.1667	−	27.1667i	−1.24128	−	1.24128i	−0.959472	−	0.281804i	$-0.909067\pi$
$479$	−27.1667	−	27.1667i	−1.24128	−	1.24128i	−0.281804	−	0.959472i	$-0.590933\pi$
$480$	0.349356	−	1.69645i	0.0159458	−	0.0774321i
$481$	28.2945	−	6.68606i	1.29012	−	0.304858i
$482$		−	25.8238i		−	1.17624i
$483$	−27.8261	+	18.3226i	−1.26613	+	0.833706i
$484$			5.05352i			0.229706i
$485$	−6.09076			−0.276567
$486$	−3.55492	+	15.1777i	−0.161254	+	0.688474i
$487$	23.3376	−	23.3376i	1.05753	−	1.05753i	0.0592882	−	0.998241i	$-0.481117\pi$
$487$	23.3376	−	23.3376i	1.05753	−	1.05753i	0.998241	−	0.0592882i	$-0.0188831\pi$
$488$		−	11.7229i		−	0.530673i
$489$	27.0102	−	17.7853i	1.22145	−	0.804281i
$490$	1.86110			0.0840758
$491$		−	0.227143i		−	0.0102508i	−0.999987	−	0.00512541i	$-0.998369\pi$
$491$		−	0.227143i		−	0.0102508i	0.999987	−	0.00512541i	$-0.00163148\pi$
$492$	−11.9559	−	2.46212i	−0.539015	−	0.111001i
$493$	−11.5003			−0.517947
$494$	−24.7882	−	24.7882i	−1.11527	−	1.11527i
$495$	2.70815	+	6.79590i	0.121722	+	0.305453i
$496$	1.20146	+	1.20146i	0.0539473	+	0.0539473i
$497$		−	28.6700i		−	1.28603i
$498$	24.2975	−	15.9991i	1.08880	−	0.716935i
$499$	−10.1088	−	10.1088i	−0.452530	−	0.452530i	0.443663	−	0.896194i	$-0.353679\pi$
$499$	−10.1088	−	10.1088i	−0.452530	−	0.452530i	−0.896194	+	0.443663i	$0.853679\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$	23.3661	−	15.3858i	1.04392	−	0.687385i
$502$		−	24.5160i		−	1.09420i
$503$	−9.08858	−	9.08858i	−0.405240	−	0.405240i	0.474835	−	0.880075i	$-0.342508\pi$
$503$	−9.08858	−	9.08858i	−0.405240	−	0.405240i	−0.880075	+	0.474835i	$0.842508\pi$
$504$	3.30587	+	8.29585i	0.147255	+	0.369526i
$505$	0.158390	+	0.158390i	0.00704828	+	0.00704828i
$506$	−15.7576			−0.700509
$507$	16.7024	+	3.43958i	0.741779	+	0.152757i
$508$			0.265733i			0.0117900i
$509$	13.3598			0.592163			0.296082	−	0.955163i	$-0.404320\pi$
$509$	13.3598			0.592163			0.296082	+	0.955163i	$0.404320\pi$
$510$	−5.40347	+	3.55800i	−0.239270	+	0.157551i
$511$		−	17.1198i		−	0.757337i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−6.67716	−	37.5207i	−0.294804	−	1.65658i
$514$	30.3521			1.33877
$515$		−	1.11863i		−	0.0492929i
$516$	−7.83791	+	5.16100i	−0.345045	+	0.227200i
$517$		−	16.0198i		−	0.704550i
$518$	17.6216	−	4.16403i	0.774250	−	0.182957i
$519$	6.41997	−	31.1750i	0.281805	−	1.36843i
$520$	−3.37975	−	3.37975i	−0.148212	−	0.148212i
$521$	−18.0686			−0.791601			−0.395801	−	0.918337i	$-0.629533\pi$
$521$	−18.0686			−0.791601			−0.395801	+	0.918337i	$0.629533\pi$
$522$	3.64944	−	8.48495i	0.159731	−	0.371376i
$523$	19.5508	−	19.5508i	0.854895	−	0.854895i	−0.135836	−	0.990731i	$-0.543372\pi$
$523$	19.5508	−	19.5508i	0.854895	−	0.854895i	0.990731	+	0.135836i	$0.0433721\pi$
$524$	5.37214	+	5.37214i	0.234683	+	0.234683i
$525$	−5.04993	−	1.03995i	−0.220397	−	0.0453871i
$526$	5.49364	−	5.49364i	0.239534	−	0.239534i
$527$		−	6.34670i		−	0.276467i
$528$	−0.851919	+	4.13687i	−0.0370750	+	0.180034i
$529$			18.7559i			0.815475i
$530$			0.00856748i			0.000372147i
$531$	−5.61548	−	14.0916i	−0.243691	−	0.611525i
$532$	−15.4379	−	15.4379i	−0.669317	−	0.669317i
$533$	−23.8192	+	23.8192i	−1.03172	+	1.03172i
$534$	4.13454	+	0.851439i	0.178919	+	0.0368454i
$535$	9.43427	−	9.43427i	0.407879	−	0.407879i
$536$	2.57961	−	2.57961i	0.111422	−	0.111422i
$537$	−19.5739	−	29.7265i	−0.844677	−	1.28279i
$538$	18.0942	+	18.0942i	0.780097	+	0.780097i
$539$	−4.53836			−0.195481
$540$	−0.910402	−	5.11578i	−0.0391774	−	0.220148i
$541$	11.4750	−	11.4750i	0.493349	−	0.493349i	−0.416011	−	0.909360i	$-0.636572\pi$
$541$	11.4750	−	11.4750i	0.493349	−	0.493349i	0.909360	+	0.416011i	$0.136572\pi$
$542$	−5.19506	+	5.19506i	−0.223147	+	0.223147i
$543$	0.800521	−	3.88728i	0.0343536	−	0.166819i
$544$	−3.73527			−0.160149
$545$	−11.6476			−0.498930
$546$	24.1371	+	4.97064i	1.03297	+	0.212724i
$547$	16.5717	+	16.5717i	0.708555	+	0.708555i	0.966231	−	0.257676i	$-0.0829567\pi$
$547$	16.5717	+	16.5717i	0.708555	+	0.708555i	−0.257676	+	0.966231i	$0.582957\pi$
$548$	−7.45566			−0.318490
$549$	−13.0190	−	32.6703i	−0.555639	−	1.39434i
$550$	−1.72431	−	1.72431i	−0.0735247	−	0.0735247i
$551$			22.5811i			0.961987i
$552$	10.9623	+	2.25750i	0.466585	+	0.0960855i
$553$	18.9021	−	18.9021i	0.803799	−	0.803799i
$554$	5.14981			0.218795
$555$	−10.5312	+	0.304982i	−0.447026	+	0.0129458i
$556$	−18.3826			−0.779598
$557$	15.3019	−	15.3019i	0.648361	−	0.648361i	−0.304236	−	0.952597i	$-0.598401\pi$
$557$	15.3019	−	15.3019i	0.648361	−	0.648361i	0.952597	+	0.304236i	$0.0984011\pi$
$558$	4.68262	+	2.01403i	0.198231	+	0.0852606i
$559$			25.8971i			1.09533i
$560$	−2.10489	−	2.10489i	−0.0889477	−	0.0889477i
$561$	13.1766	−	8.67633i	0.556315	−	0.366315i
$562$	−23.4457			−0.988999
$563$	19.7443	+	19.7443i	0.832124	+	0.832124i	0.987807	−	0.155683i	$-0.0497579\pi$
$563$	19.7443	+	19.7443i	0.832124	+	0.832124i	−0.155683	+	0.987807i	$0.549758\pi$
$564$	−2.29507	+	11.1447i	−0.0966398	+	0.469277i
$565$	2.29685			0.0966292
$566$	−6.85802			−0.288264
$567$	18.4261	+	19.4481i	0.773822	+	0.816743i
$568$	−6.81035	+	6.81035i	−0.285756	+	0.285756i
$569$	−9.21438	+	9.21438i	−0.386287	+	0.386287i	−0.873361	−	0.487074i	$-0.838064\pi$
$569$	−9.21438	+	9.21438i	−0.386287	+	0.386287i	0.487074	+	0.873361i	$0.338064\pi$
$570$	6.98623	+	10.6098i	0.292621	+	0.444397i
$571$	−20.1810			−0.844548			−0.422274	−	0.906468i	$-0.638768\pi$
$571$	−20.1810			−0.844548			−0.422274	+	0.906468i	$0.638768\pi$
$572$	8.24167	+	8.24167i	0.344601	+	0.344601i
$573$	11.3744	−	7.48967i	0.475173	−	0.312885i
$574$	−14.8344	+	14.8344i	−0.619177	+	0.619177i
$575$	−4.56924	+	4.56924i	−0.190551	+	0.190551i
$576$	1.18533	−	2.75590i	0.0493888	−	0.114829i
$577$	−10.8935	+	10.8935i	−0.453502	+	0.453502i	−0.896515	−	0.443013i	$-0.853909\pi$
$577$	−10.8935	+	10.8935i	−0.453502	+	0.453502i	0.443013	+	0.896515i	$0.353909\pi$
$578$	−2.15506	−	2.15506i	−0.0896389	−	0.0896389i
$579$	−9.34824	−	14.1970i	−0.388499	−	0.590006i
$580$			3.07883i			0.127842i
$581$		−	49.9982i		−	2.07428i
$582$	−10.3327	−	2.12784i	−0.428304	−	0.0882020i
$583$		−	0.0208921i		−	0.000865264i
$584$	−4.06669	+	4.06669i	−0.168281	+	0.168281i
$585$	−13.1724	−	5.66552i	−0.544610	−	0.234241i
$586$	−11.9304	−	11.9304i	−0.492840	−	0.492840i
$587$	3.91169	−	3.91169i	0.161453	−	0.161453i	−0.621757	−	0.783210i	$-0.713581\pi$
$587$	3.91169	−	3.91169i	0.161453	−	0.161453i	0.783210	+	0.621757i	$0.213581\pi$
$588$	3.15726	+	0.650186i	0.130203	+	0.0268132i
$589$	−12.4619			−0.513484
$590$	3.57544	+	3.57544i	0.147199	+	0.147199i
$591$	−1.84859	−	0.380685i	−0.0760407	−	0.0156593i
$592$	−5.17502	−	3.19675i	−0.212692	−	0.131386i
$593$			21.6725i			0.889983i	0.895535	+	0.444991i	$0.146793\pi$
$593$			21.6725i			0.889983i	−0.895535	+	0.444991i	$0.853207\pi$
$594$	2.22005	+	12.4750i	0.0910898	+	0.511856i
$595$			11.1190i			0.455835i
$596$	10.3217			0.422795
$597$	12.7112	−	8.36987i	0.520233	−	0.342556i
$598$	21.8396	−	21.8396i	0.893087	−	0.893087i
$599$			14.8293i			0.605907i	0.953005	+	0.302954i	$0.0979727\pi$
$599$			14.8293i			0.605907i	−0.953005	+	0.302954i	$0.902027\pi$
$600$	0.952541	+	1.44660i	0.0388873	+	0.0590574i
$601$	−19.8353			−0.809097			−0.404549	−	0.914517i	$-0.632571\pi$
$601$	−19.8353			−0.809097			−0.404549	+	0.914517i	$0.632571\pi$
$602$			16.1285i			0.657349i
$603$	4.32424	−	10.0539i	0.176097	−	0.409425i
$604$	21.8379			0.888570
$605$	−3.57338	−	3.57338i	−0.145279	−	0.145279i
$606$	0.213367	+	0.324036i	0.00866744	+	0.0131631i
$607$	12.9523	+	12.9523i	0.525718	+	0.525718i	0.919293	−	0.393575i	$-0.128762\pi$
$607$	12.9523	+	12.9523i	0.525718	+	0.525718i	−0.393575	+	0.919293i	$0.628762\pi$
$608$			7.33431i			0.297445i
$609$	−8.72998	−	13.2580i	−0.353757	−	0.537243i
$610$	8.28937	+	8.28937i	0.335627	+	0.335627i
$611$	22.2030	+	22.2030i	0.898239	+	0.898239i
$612$	−10.4097	+	4.14825i	−0.420789	+	0.167683i
$613$			1.24321i			0.0502128i	0.999685	+	0.0251064i	$0.00799245\pi$
$613$			1.24321i			0.0502128i	−0.999685	+	0.0251064i	$0.992008\pi$
$614$	1.83554	+	1.83554i	0.0740763	+	0.0740763i
$615$	10.1951	−	6.71314i	0.411106	−	0.270700i
$616$	5.13285	+	5.13285i	0.206808	+	0.206808i
$617$	−4.87072			−0.196088			−0.0980438	−	0.995182i	$-0.531259\pi$
$617$	−4.87072			−0.196088			−0.0980438	+	0.995182i	$0.531259\pi$
$618$	0.390801	−	1.89771i	0.0157203	−	0.0763371i
$619$			29.3840i			1.18104i	0.807023	+	0.590521i	$0.201078\pi$
$619$			29.3840i			1.18104i	−0.807023	+	0.590521i	$0.798922\pi$
$620$	−1.69913			−0.0682385
$621$	33.0575	−	5.88291i	1.32655	−	0.236073i
$622$		−	3.80837i		−	0.152702i
$623$	5.12996	−	5.12996i	0.205528	−	0.205528i
$624$	−4.55285	−	6.91433i	−0.182260	−	0.276795i
$625$	−1.00000			−0.0400000
$626$			10.8341i			0.433017i
$627$	−17.0362	−	25.8725i	−0.680360	−	1.03325i
$628$			6.37842i			0.254527i
$629$	5.22507	+	22.1118i	0.208337	+	0.881656i
$630$	−8.20365	−	3.52845i	−0.326841	−	0.140577i
$631$	23.3422	+	23.3422i	0.929237	+	0.929237i	0.997657	−	0.0684200i	$-0.0217958\pi$
$631$	23.3422	+	23.3422i	0.929237	+	0.929237i	−0.0684200	+	0.997657i	$0.521796\pi$
$632$	−8.98011			−0.357209
$633$	−6.93385	+	33.6704i	−0.275596	+	1.33828i
$634$	8.84871	−	8.84871i	0.351427	−	0.351427i
$635$	−0.187902	−	0.187902i	−0.00745664	−	0.00745664i
$636$	−0.00299310	+	0.0145343i	−0.000118684	+	0.000576323i
$637$	6.29005	−	6.29005i	0.249221	−	0.249221i
$638$		−	7.50785i		−	0.297239i
$639$	−11.4163	+	26.5429i	−0.451621	+	1.05002i
$640$			1.00000i			0.0395285i
$641$		−	47.2866i		−	1.86771i	−0.357653	−	0.933854i	$-0.616423\pi$
$641$		−	47.2866i		−	1.86771i	0.357653	−	0.933854i	$-0.383577\pi$
$642$	19.3007	−	12.7089i	0.761738	−	0.501579i
$643$	7.59274	+	7.59274i	0.299428	+	0.299428i	0.840790	−	0.541362i	$-0.182091\pi$
$643$	7.59274	+	7.59274i	0.299428	+	0.299428i	−0.541362	+	0.840790i	$0.682091\pi$
$644$	13.6015	−	13.6015i	0.535975	−	0.535975i
$645$	1.89286	−	9.19162i	0.0745313	−	0.361920i
$646$	19.3717	−	19.3717i	0.762167	−	0.762167i
$647$	15.2305	−	15.2305i	0.598773	−	0.598773i	−0.341213	−	0.939986i	$-0.610838\pi$
$647$	15.2305	−	15.2305i	0.598773	−	0.598773i	0.939986	+	0.341213i	$0.110838\pi$
$648$	0.242774	−	8.99672i	0.00953708	−	0.353425i
$649$	−8.71885	−	8.71885i	−0.342245	−	0.342245i
$650$	4.77969			0.187475
$651$	7.31677	−	4.81785i	0.286767	−	0.188826i
$652$	−13.2027	+	13.2027i	−0.517059	+	0.517059i
$653$	23.9793	−	23.9793i	0.938382	−	0.938382i	−0.0598267	−	0.998209i	$-0.519055\pi$
$653$	23.9793	−	23.9793i	0.938382	−	0.938382i	0.998209	+	0.0598267i	$0.0190548\pi$
$654$	−19.7596	−	4.06917i	−0.772663	−	0.159117i
$655$	−7.59736			−0.296853
$656$	7.04761			0.275163
$657$	−6.81704	+	15.8496i	−0.265958	+	0.618353i
$658$	13.8279	+	13.8279i	0.539067	+	0.539067i
$659$	40.4873			1.57716			0.788581	−	0.614931i	$-0.210816\pi$
$659$	40.4873			1.57716			0.788581	+	0.614931i	$0.210816\pi$
$660$	−2.32281	−	3.52760i	−0.0904152	−	0.137312i
$661$	−0.591033	−	0.591033i	−0.0229885	−	0.0229885i	0.695519	−	0.718508i	$-0.255174\pi$
$661$	−0.591033	−	0.591033i	−0.0229885	−	0.0229885i	−0.718508	+	0.695519i	$0.755174\pi$
$662$			7.99386i			0.310690i
$663$	−6.23722	+	30.2876i	−0.242233	+	1.17627i
$664$	−11.8767	+	11.8767i	−0.460905	+	0.460905i
$665$	21.8325			0.846627
$666$	−17.9723	−	3.16176i	−0.696412	−	0.122516i
$667$	−19.8950			−0.770339
$668$	−11.4214	+	11.4214i	−0.441908	+	0.441908i
$669$	6.53410	−	31.7292i	0.252623	−	1.22672i
$670$			3.64813i			0.140939i
$671$	−20.2140	−	20.2140i	−0.780351	−	0.780351i
$672$	−2.83549	−	4.30620i	−0.109381	−	0.166115i
$673$	−27.2271			−1.04953			−0.524765	−	0.851247i	$-0.675847\pi$
$673$	−27.2271			−1.04953			−0.524765	+	0.851247i	$0.675847\pi$
$674$	−4.91634	−	4.91634i	−0.189370	−	0.189370i
$675$	4.26115	+	2.97365i	0.164012	+	0.114456i
$676$	−9.84548			−0.378672
$677$	7.44693			0.286209			0.143104	−	0.989708i	$-0.454292\pi$
$677$	7.44693			0.286209			0.143104	+	0.989708i	$0.454292\pi$
$678$	3.89650	+	0.802418i	0.149644	+	0.0308167i
$679$	−12.8204	+	12.8204i	−0.492001	+	0.492001i
$680$	2.64124	−	2.64124i	0.101287	−	0.101287i
$681$	−29.9123	+	19.6963i	−1.14624	+	0.754763i
$682$	4.14339			0.158658
$683$	−16.2355	−	16.2355i	−0.621235	−	0.621235i	0.324612	−	0.945847i	$-0.394766\pi$
$683$	−16.2355	−	16.2355i	−0.621235	−	0.621235i	−0.945847	+	0.324612i	$0.894766\pi$
$684$	8.14519	+	20.4398i	0.311439	+	0.781534i
$685$	5.27195	−	5.27195i	0.201431	−	0.201431i
$686$	−10.8168	+	10.8168i	−0.412988	+	0.412988i
$687$	2.23704	−	10.8630i	0.0853486	−	0.414448i
$688$	3.83120	−	3.83120i	0.146063	−	0.146063i
$689$	0.0289560	+	0.0289560i	0.00110313	+	0.00110313i
$690$	−9.34779	+	6.15521i	−0.355864	+	0.234325i
$691$		−	6.50183i		−	0.247341i	−0.992323	−	0.123671i	$-0.960533\pi$
$691$		−	6.50183i		−	0.247341i	0.992323	−	0.123671i	$-0.0394666\pi$
$692$			18.3766i			0.698573i
$693$	20.0049	+	8.60426i	0.759925	+	0.326849i
$694$		−	33.9583i		−	1.28904i
$695$	12.9985	−	12.9985i	0.493061	−	0.493061i
$696$	−1.07561	+	5.22309i	−0.0407708	+	0.197981i
$697$	−18.6144	−	18.6144i	−0.705071	−	0.705071i
$698$	12.8998	−	12.8998i	0.488266	−	0.488266i
$699$	3.46837	−	16.8422i	0.131186	−	0.637030i
$700$	2.97676			0.112511
$701$	34.0802	+	34.0802i	1.28719	+	1.28719i	0.936486	+	0.350705i	$0.114058\pi$
$701$	34.0802	+	34.0802i	1.28719	+	1.28719i	0.350705	+	0.936486i	$0.385942\pi$
$702$	−20.3670	−	14.2131i	−0.768703	−	0.536440i
$703$	43.4171	−	10.2596i	1.63751	−	0.386947i
$704$		−	2.43854i		−	0.0919059i
$705$	−6.25765	−	9.50336i	−0.235677	−	0.357917i
$706$			31.1631i			1.17284i
$707$	0.666787			0.0250771
$708$	4.81646	+	7.31466i	0.181014	+	0.274902i
$709$	1.56111	−	1.56111i	0.0586286	−	0.0586286i	−0.677185	−	0.735813i	$-0.736800\pi$
$709$	1.56111	−	1.56111i	0.0586286	−	0.0586286i	0.735813	+	0.677185i	$0.236800\pi$
$710$		−	9.63129i		−	0.361456i
$711$	−25.0264	+	9.97295i	−0.938564	+	0.374015i
$712$	−2.43717			−0.0913368
$713$		−	10.9795i		−	0.411187i
$714$	−3.88449	+	18.8629i	−0.145374	+	0.705925i
$715$	−11.6555			−0.435890
$716$	14.5304	+	14.5304i	0.543028	+	0.543028i
$717$	37.6424	−	24.7863i	1.40578	−	0.925661i
$718$	−1.68859	−	1.68859i	−0.0630177	−	0.0630177i
$719$		−	12.6157i		−	0.470487i	−0.971936	−	0.235243i	$-0.924411\pi$
$719$		−	12.6157i		−	0.470487i	0.971936	−	0.235243i	$-0.0755887\pi$
$720$	1.11056	+	2.78687i	0.0413881	+	0.103861i
$721$	−2.35460	−	2.35460i	−0.0876898	−	0.0876898i
$722$	−24.6017	−	24.6017i	−0.915580	−	0.915580i
$723$	24.5983	+	37.3569i	0.914819	+	1.38932i
$724$			2.29142i			0.0851599i
$725$	−2.17706	−	2.17706i	−0.0808541	−	0.0808541i
$726$	−4.81369	−	7.31045i	−0.178653	−	0.271316i
$727$	−29.4763	−	29.4763i	−1.09322	−	1.09322i	−0.995183	−	0.0980326i	$-0.968745\pi$
$727$	−29.4763	−	29.4763i	−1.09322	−	1.09322i	−0.0980326	−	0.995183i	$-0.531255\pi$
$728$	−14.2280			−0.527325
$729$	−9.31482	−	25.3423i	−0.344993	−	0.938605i
$730$		−	5.75117i		−	0.212860i
$731$	−20.2382			−0.748539
$732$	11.1666	+	16.9585i	0.412729	+	0.626803i
$733$			33.6287i			1.24210i	0.783769	+	0.621052i	$0.213294\pi$
$733$			33.6287i			1.24210i	−0.783769	+	0.621052i	$0.786706\pi$
$734$	−15.3048	+	15.3048i	−0.564909	+	0.564909i
$735$	−2.69227	+	1.77277i	−0.0993060	+	0.0653897i
$736$	−6.46188			−0.238188
$737$		−	8.89610i		−	0.327692i
$738$	19.6408	−	7.82679i	0.722987	−	0.288108i
$739$		−	7.04612i		−	0.259196i	−0.991567	−	0.129598i	$-0.958631\pi$
$739$		−	7.04612i		−	0.259196i	0.991567	−	0.129598i	$-0.0413687\pi$
$740$	5.91973	−	1.39885i	0.217614	−	0.0514226i
$741$	59.4704	+	12.2469i	2.18470	+	0.449902i
$742$	0.0180336	+	0.0180336i	0.000662033	+	0.000662033i
$743$	12.5185			0.459260			0.229630	−	0.973278i	$-0.426248\pi$
$743$	12.5185			0.459260			0.229630	+	0.973278i	$0.426248\pi$
$744$	−2.88249	−	0.593600i	−0.105677	−	0.0217624i
$745$	−7.29857	+	7.29857i	−0.267399	+	0.267399i
$746$	4.25179	+	4.25179i	0.155669	+	0.155669i
$747$	−19.9091	+	46.2886i	−0.728434	+	1.69361i
$748$	−6.44076	+	6.44076i	−0.235498	+	0.235498i
$749$		−	39.7162i		−	1.45120i
$750$	−1.69645	−	0.349356i	−0.0619457	−	0.0127567i
$751$			13.2399i			0.483131i	0.970385	+	0.241566i	$0.0776609\pi$
$751$			13.2399i			0.483131i	−0.970385	+	0.241566i	$0.922339\pi$
$752$		−	6.56942i		−	0.239562i
$753$	23.3525	+	35.4650i	0.851013	+	1.29242i
$754$	10.4057	+	10.4057i	0.378953	+	0.378953i
$755$	−15.4417	+	15.4417i	−0.561981	+	0.561981i
$756$	−12.6844	−	8.85184i	−0.461328	−	0.321938i
$757$	30.6772	−	30.6772i	1.11498	−	1.11498i	0.122516	−	0.992466i	$-0.460904\pi$
$757$	30.6772	−	30.6772i	1.11498	−	1.11498i	0.992466	−	0.122516i	$-0.0390964\pi$
$758$	−26.9121	+	26.9121i	−0.977491	+	0.977491i
$759$	22.7950	−	15.0097i	0.827405	−	0.544818i
$760$	−5.18614	−	5.18614i	−0.188121	−	0.188121i
$761$	−22.0349			−0.798766			−0.399383	−	0.916784i	$-0.630776\pi$
$761$	−22.0349			−0.798766			−0.399383	+	0.916784i	$0.630776\pi$
$762$	−0.253121	−	0.384411i	−0.00916962	−	0.0139257i
$763$	−24.5169	+	24.5169i	−0.887573	+	0.887573i
$764$	−5.55986	+	5.55986i	−0.201149	+	0.201149i
$765$	4.42754	−	10.2940i	0.160078	−	0.372182i
$766$	−16.9288			−0.611662
$767$	24.1682			0.872664
$768$	−0.349356	+	1.69645i	−0.0126063	+	0.0612154i
$769$	21.8399	+	21.8399i	0.787567	+	0.787567i	0.981095	−	0.193528i	$-0.0619929\pi$
$769$	21.8399	+	21.8399i	0.787567	+	0.787567i	−0.193528	+	0.981095i	$0.561993\pi$
$770$	−7.25895			−0.261594
$771$	−43.9075	+	28.9116i	−1.58129	+	1.04123i
$772$	6.93955	+	6.93955i	0.249760	+	0.249760i
$773$			11.9686i			0.430481i	0.976561	+	0.215240i	$0.0690535\pi$
$773$			11.9686i			0.430481i	−0.976561	+	0.215240i	$0.930947\pi$
$774$	6.42229	−	14.9319i	0.230845	−	0.536715i
$775$	1.20146	−	1.20146i	0.0431578	−	0.0431578i
$776$	6.09076			0.218646
$777$	−21.5251	+	22.8090i	−0.772209	+	0.818269i
$778$	27.0435			0.969555
$779$	−36.5499	+	36.5499i	−1.30954	+	1.30954i
$780$	8.10852	+	1.66982i	0.290332	+	0.0597890i
$781$			23.4863i			0.840405i
$782$	17.0674	+	17.0674i	0.610328	+	0.610328i
$783$	2.80297	+	15.7506i	0.100170	+	0.562881i
$784$	−1.86110			−0.0664678
$785$	−4.51022	−	4.51022i	−0.160977	−	0.160977i
$786$	−12.8886	−	2.65418i	−0.459720	−	0.0946716i
$787$	32.4401			1.15636			0.578182	−	0.815908i	$-0.303762\pi$
$787$	32.4401			1.15636			0.578182	+	0.815908i	$0.303762\pi$
$788$	1.08968			0.0388182
$789$	−2.71421	+	13.1800i	−0.0966284	+	0.469222i
$790$	6.34989	−	6.34989i	0.225919	−	0.225919i
$791$	4.83461	−	4.83461i	0.171899	−	0.171899i
$792$	−2.70815	−	6.79590i	−0.0962297	−	0.241482i
$793$	56.0321			1.98976
$794$	15.6373	+	15.6373i	0.554948	+	0.554948i
$795$	−0.00816087	−	0.0123938i	−0.000289436	−	0.000439561i
$796$	−6.21327	+	6.21327i	−0.220223	+	0.220223i
$797$	29.0941	−	29.0941i	1.03057	−	1.03057i	0.0310478	−	0.999518i	$-0.490116\pi$
$797$	29.0941	−	29.0941i	1.03057	−	1.03057i	0.999518	−	0.0310478i	$-0.00988441\pi$
$798$	37.0377	+	7.62730i	1.31112	+	0.270004i
$799$	−17.3514	+	17.3514i	−0.613849	+	0.613849i
$800$	−0.707107	−	0.707107i	−0.0250000	−	0.0250000i
$801$	−6.79208	+	2.70662i	−0.239986	+	0.0956338i
$802$			19.9719i			0.705233i
$803$			14.0244i			0.494912i
$804$	−1.27449	+	6.18887i	−0.0449480	+	0.218265i
$805$			19.2355i			0.677961i
$806$	−5.74263	+	5.74263i	−0.202275	+	0.202275i
$807$	−43.4107	−	8.93970i	−1.52813	−	0.314692i
$808$	−0.158390	−	0.158390i	−0.00557215	−	0.00557215i
$809$	−13.0781	+	13.0781i	−0.459801	+	0.459801i	−0.898590	−	0.438789i	$-0.855408\pi$
$809$	−13.0781	+	13.0781i	−0.459801	+	0.459801i	0.438789	+	0.898590i	$0.355408\pi$
$810$	6.18998	+	6.53331i	0.217494	+	0.229557i
$811$	46.3338			1.62700			0.813500	−	0.581564i	$-0.197559\pi$
$811$	46.3338			1.62700			0.813500	+	0.581564i	$0.197559\pi$
$812$	6.48059	+	6.48059i	0.227424	+	0.227424i
$813$	2.56669	−	12.4637i	0.0900179	−	0.437122i
$814$	−14.4355	+	3.41114i	−0.505964	+	0.119560i
$815$		−	18.6715i		−	0.654033i
$816$	5.40347	−	3.55800i	0.189159	−	0.124555i
$817$			39.7383i			1.39027i
$818$	8.28701			0.289749
$819$	−39.6516	+	15.8011i	−1.38554	+	0.552133i
$820$	−4.98341	+	4.98341i	−0.174028	+	0.174028i
$821$			54.7891i			1.91215i	0.293117	+	0.956076i	$0.405307\pi$
$821$			54.7891i			1.91215i	−0.293117	+	0.956076i	$0.594693\pi$
$822$	10.7854	−	7.10182i	0.376184	−	0.247705i
$823$	−27.8941			−0.972328			−0.486164	−	0.873868i	$-0.661604\pi$
$823$	−27.8941			−0.972328			−0.486164	+	0.873868i	$0.661604\pi$
$824$			1.11863i			0.0389695i
$825$	4.13687	+	0.851919i	0.144027	+	0.0296600i
$826$	15.0518			0.523719
$827$	−32.5198	−	32.5198i	−1.13083	−	1.13083i	−0.990040	−	0.140786i	$-0.955037\pi$
$827$	−32.5198	−	32.5198i	−1.13083	−	1.13083i	−0.140786	−	0.990040i	$-0.544963\pi$
$828$	−18.0084	+	7.17631i	−0.625837	+	0.249394i
$829$	−18.3804	−	18.3804i	−0.638377	−	0.638377i	0.311778	−	0.950155i	$-0.399076\pi$
$829$	−18.3804	−	18.3804i	−0.638377	−	0.638377i	−0.950155	+	0.311778i	$0.899076\pi$
$830$		−	16.7962i		−	0.583004i
$831$	−7.44975	+	4.90541i	−0.258429	+	0.170167i
$832$	3.37975	+	3.37975i	0.117172	+	0.117172i
$833$	4.91560	+	4.91560i	0.170316	+	0.170316i
$834$	26.5924	−	17.5102i	0.920820	−	0.606329i
$835$		−	16.1523i		−	0.558975i
$836$	12.6466	+	12.6466i	0.437392	+	0.437392i
$837$	−8.69235	+	1.54689i	−0.300451	+	0.0534682i
$838$	−2.02876	−	2.02876i	−0.0700825	−	0.0700825i
$839$	42.0148			1.45051			0.725256	−	0.688480i	$-0.241722\pi$
$839$	42.0148			1.45051			0.725256	+	0.688480i	$0.241722\pi$
$840$	5.04993	+	1.03995i	0.174239	+	0.0358816i
$841$			19.5208i			0.673131i
$842$	22.9041			0.789327
$843$	33.9167	−	22.3330i	1.16815	−	0.769191i
$844$		−	19.8475i		−	0.683180i
$845$	6.96181	−	6.96181i	0.239493	−	0.239493i
$846$	−7.29574	−	18.3081i	−0.250833	−	0.629447i
$847$	−15.0431			−0.516888
$848$		−	0.00856748i		−	0.000294208i
$849$	9.92084	−	6.53254i	0.340482	−	0.224196i
$850$			3.73527i			0.128119i
$851$	9.03918	+	38.2526i	0.309859	+	1.31128i
$852$	3.36475	−	16.3390i	0.115274	−	0.559765i
$853$	−15.0572	−	15.0572i	−0.515548	−	0.515548i	0.400673	−	0.916221i	$-0.368776\pi$
$853$	−15.0572	−	15.0572i	−0.515548	−	0.515548i	−0.916221	+	0.400673i	$0.868776\pi$
$854$	34.8964			1.19413
$855$	−20.2126	−	8.69359i	−0.691257	−	0.297314i
$856$	−9.43427	+	9.43427i	−0.322457	+	0.322457i
$857$	12.3474	+	12.3474i	0.421779	+	0.421779i	0.885816	−	0.464037i	$-0.153599\pi$
$857$	12.3474	+	12.3474i	0.421779	+	0.421779i	−0.464037	+	0.885816i	$0.653599\pi$
$858$	−19.7730	−	4.07191i	−0.675038	−	0.139013i
$859$	−39.7979	+	39.7979i	−1.35789	+	1.35789i	−0.481371	+	0.876517i	$0.659861\pi$
$859$	−39.7979	+	39.7979i	−1.35789	+	1.35789i	−0.876517	+	0.481371i	$0.840139\pi$
$860$			5.41814i			0.184757i
$861$	7.32915	−	35.5899i	0.249777	−	1.21290i
$862$			12.7346i			0.433743i
$863$		−	28.1554i		−	0.958420i	−0.877700	−	0.479210i	$-0.840923\pi$
$863$		−	28.1554i		−	0.958420i	0.877700	−	0.479210i	$-0.159077\pi$
$864$	0.910402	+	5.11578i	0.0309725	+	0.174042i
$865$	−12.9942	−	12.9942i	−0.441816	−	0.441816i
$866$	15.7158	−	15.7158i	0.534046	−	0.534046i
$867$	5.17031	+	1.06474i	0.175593	+	0.0361605i
$868$	−3.57647	+	3.57647i	−0.121393	+	0.121393i
$869$	−15.4845	+	15.4845i	−0.525275	+	0.525275i
$870$	−2.93271	−	4.45385i	−0.0994283	−	0.151000i
$871$	12.3298	+	12.3298i	0.417778	+	0.417778i
$872$	11.6476			0.394438
$873$	16.9742	−	6.76416i	0.574489	−	0.228932i
$874$	33.5122	−	33.5122i	1.13357	−	1.13357i
$875$	−2.10489	+	2.10489i	−0.0711582	+	0.0711582i
$876$	2.00920	−	9.75658i	0.0678847	−	0.329644i
$877$	−34.9015			−1.17854			−0.589270	−	0.807936i	$-0.700585\pi$
$877$	−34.9015			−1.17854			−0.589270	+	0.807936i	$0.700585\pi$
$878$	35.6812			1.20418
$879$	28.6228	+	5.89438i	0.965422	+	0.198813i
$880$	1.72431	+	1.72431i	0.0581264	+	0.0581264i
$881$	−57.9043			−1.95085			−0.975423	−	0.220339i	$-0.929284\pi$
$881$	−57.9043			−1.95085			−0.975423	+	0.220339i	$0.929284\pi$
$882$	−5.18664	+	2.06686i	−0.174643	+	0.0695948i
$883$	−26.6333	−	26.6333i	−0.896282	−	0.896282i	0.0988230	−	0.995105i	$-0.468492\pi$
$883$	−26.6333	−	26.6333i	−0.896282	−	0.896282i	−0.995105	+	0.0988230i	$0.968492\pi$
$884$		−	17.8535i		−	0.600477i
$885$	−8.57800	−	1.76650i	−0.288346	−	0.0593801i
$886$	−19.0455	+	19.0455i	−0.639847	+	0.639847i
$887$	22.5666			0.757714			0.378857	−	0.925455i	$-0.376317\pi$
$887$	22.5666			0.757714			0.378857	+	0.925455i	$0.376317\pi$
$888$	10.5312	−	0.304982i	0.353405	−	0.0102345i
$889$	−0.791023			−0.0265301
$890$	1.72334	−	1.72334i	0.0577664	−	0.0577664i
$891$	−15.0945	−	15.9317i	−0.505685	−	0.533733i
$892$			18.7033i			0.626232i
$893$	34.0699	+	34.0699i	1.14011	+	1.14011i
$894$	−14.9315	+	9.83187i	−0.499383	+	0.328827i
$895$	−20.5492			−0.686883
$896$	2.10489	+	2.10489i	0.0703193	+	0.0703193i
$897$	−10.7901	+	52.3963i	−0.360273	+	1.74946i
$898$	−11.2027			−0.373840
$899$	5.23132			0.174474
$900$	−2.75590	−	1.18533i	−0.0918634	−	0.0395111i
$901$	−0.0226287	+	0.0226287i	−0.000753873	+	0.000753873i
$902$	12.1522	−	12.1522i	0.404626	−	0.404626i
$903$	−15.3631	−	23.3316i	−0.511251	−	0.776426i
$904$	−2.29685			−0.0763921
$905$	−1.62028	−	1.62028i	−0.0538598	−	0.0538598i
$906$	−31.5908	+	20.8015i	−1.04953	+	0.691082i
$907$	−4.06839	+	4.06839i	−0.135089	+	0.135089i	−0.771418	−	0.636329i	$-0.780452\pi$
$907$	−4.06839	+	4.06839i	−0.135089	+	0.135089i	0.636329	+	0.771418i	$0.280452\pi$
$908$	14.6213	−	14.6213i	0.485224	−	0.485224i
$909$	−0.617316	−	0.265512i	−0.0204751	−	0.00880646i
$910$	10.0607	−	10.0607i	0.333510	−	0.333510i
$911$	17.3286	+	17.3286i	0.574123	+	0.574123i	0.933278	−	0.359155i	$-0.116935\pi$
$911$	17.3286	+	17.3286i	0.574123	+	0.574123i	−0.359155	+	0.933278i	$0.616935\pi$
$912$	−6.98623	−	10.6098i	−0.231337	−	0.351327i
$913$			40.9582i			1.35552i
$914$			29.3726i			0.971561i
$915$	−19.8874	−	4.09548i	−0.657458	−	0.135392i
$916$			6.40334i			0.211572i
$917$	−15.9916	+	15.9916i	−0.528089	+	0.528089i
$918$	11.1074	−	15.9166i	0.366599	−	0.525325i
$919$	8.73885	+	8.73885i	0.288268	+	0.288268i	0.836395	−	0.548127i	$-0.184659\pi$
$919$	8.73885	+	8.73885i	0.288268	+	0.288268i	−0.548127	+	0.836395i	$0.684659\pi$
$920$	4.56924	−	4.56924i	0.150643	−	0.150643i
$921$	−4.40372	−	0.906873i	−0.145108	−	0.0298825i
$922$	8.68872			0.286148
$923$	−32.5514	−	32.5514i	−1.07144	−	1.07144i
$924$	−12.3145	−	2.53596i	−0.405116	−	0.0834269i
$925$	−3.19675	+	5.17502i	−0.105108	+	0.170153i
$926$			31.6635i			1.04053i
$927$	1.24231	+	3.11749i	0.0408028	+	0.102392i
$928$		−	3.07883i		−	0.101068i
$929$	−35.2211			−1.15557			−0.577783	−	0.816190i	$-0.696082\pi$
$929$	−35.2211			−1.15557			−0.577783	+	0.816190i	$0.696082\pi$
$930$	2.45796	−	1.61849i	0.0805998	−	0.0530723i
$931$	9.65191	−	9.65191i	0.316329	−	0.316329i
$932$			9.92789i			0.325199i
$933$	3.62763	+	5.50920i	0.118763	+	0.180363i
$934$	−0.364934			−0.0119410
$935$		−	9.10862i		−	0.297884i
$936$	13.1724	+	5.66552i	0.430552	+	0.185183i
$937$	26.4210			0.863137			0.431568	−	0.902080i	$-0.357960\pi$
$937$	26.4210			0.863137			0.431568	+	0.902080i	$0.357960\pi$
$938$	7.67889	+	7.67889i	0.250725	+	0.250725i
$939$	−10.3199	−	15.6726i	−0.336777	−	0.511457i
$940$	4.64528	+	4.64528i	0.151512	+	0.151512i
$941$		−	1.57027i		−	0.0511894i	−0.999672	−	0.0255947i	$-0.991852\pi$
$941$		−	1.57027i		−	0.0511894i	0.999672	−	0.0255947i	$-0.00814794\pi$
$942$	−6.07571	−	9.22705i	−0.197957	−	0.300634i
$943$	−32.2022	−	32.2022i	−1.04865	−	1.04865i
$944$	−3.57544	−	3.57544i	−0.116371	−	0.116371i
$945$	15.2284	−	2.71005i	0.495381	−	0.0881578i
$946$		−	13.2124i		−	0.429571i
$947$	24.0788	+	24.0788i	0.782456	+	0.782456i	0.980245	−	0.197788i	$-0.0633759\pi$
$947$	24.0788	+	24.0788i	0.782456	+	0.782456i	−0.197788	+	0.980245i	$0.563376\pi$
$948$	12.9907	−	8.55392i	0.421917	−	0.277818i
$949$	−19.4375	−	19.4375i	−0.630969	−	0.630969i
$950$	7.33431			0.237956
$951$	−4.37183	+	21.2293i	−0.141766	+	0.688408i
$952$		−	11.1190i		−	0.360369i
$953$	−30.7757			−0.996922			−0.498461	−	0.866912i	$-0.666101\pi$
$953$	−30.7757			−0.996922			−0.498461	+	0.866912i	$0.666101\pi$
$954$	−0.00951470	−	0.0238765i	−0.000308050	−	0.000773029i
$955$		−	7.86283i		−	0.254435i
$956$	−18.3998	+	18.3998i	−0.595092	+	0.595092i
$957$	7.15154	+	10.8609i	0.231176	+	0.351083i
$958$	−38.4195			−1.24128
$959$		−	22.1937i		−	0.716673i
$960$	−0.952541	−	1.44660i	−0.0307431	−	0.0466890i
$961$		−	28.1130i		−	0.906870i
$962$	15.2795	−	24.7350i	0.492630	−	0.797488i
$963$	−15.8148	+	36.7694i	−0.509624	+	1.18488i
$964$	−18.2602	−	18.2602i	−0.588122	−	0.588122i
$965$	−9.81400			−0.315924
$966$	−6.72003	+	32.6321i	−0.216213	+	1.04992i
$967$	−7.03355	+	7.03355i	−0.226184	+	0.226184i	−0.811096	−	0.584913i	$-0.801129\pi$
$967$	−7.03355	+	7.03355i	−0.226184	+	0.226184i	0.584913	+	0.811096i	$0.301129\pi$
$968$	3.57338	+	3.57338i	0.114853	+	0.114853i
$969$	−9.57084	+	46.4754i	−0.307460	+	1.49301i
$970$	−4.30682	+	4.30682i	−0.138284	+	0.138284i
$971$		−	36.4612i		−	1.17010i	−0.810998	−	0.585048i	$-0.801075\pi$
$971$		−	36.4612i		−	1.17010i	0.810998	−	0.585048i	$-0.198925\pi$
$972$	8.21855	+	13.2460i	0.263610	+	0.424864i
$973$		−	54.7207i		−	1.75427i
$974$		−	33.0044i		−	1.05753i
$975$	−6.91433	+	4.55285i	−0.221436	+	0.145808i
$976$	−8.28937	−	8.28937i	−0.265336	−	0.265336i
$977$	−35.3768	+	35.3768i	−1.13180	+	1.13180i	−0.141926	+	0.989877i	$0.545329\pi$
$977$	−35.3768	+	35.3768i	−1.13180	+	1.13180i	−0.989877	+	0.141926i	$0.954671\pi$
$978$	6.52299	−	31.6753i	0.208582	−	1.01286i
$979$	−4.20243	+	4.20243i	−0.134310	+	0.134310i
$980$	1.31599	−	1.31599i	0.0420379	−	0.0420379i
$981$	32.4604	−	12.9354i	1.03638	−	0.412995i
$982$	−0.160614	−	0.160614i	−0.00512541	−	0.00512541i
$983$	−3.36934			−0.107465			−0.0537326	−	0.998555i	$-0.517112\pi$
$983$	−3.36934			−0.107465			−0.0537326	+	0.998555i	$0.517112\pi$
$984$	−10.1951	+	6.71314i	−0.325008	+	0.214007i
$985$	−0.770518	+	0.770518i	−0.0245508	+	0.0245508i
$986$	−8.13193	+	8.13193i	−0.258973	+	0.258973i
$987$	−33.1751	−	6.83187i	−1.05598	−	0.217461i
$988$	−35.0557			−1.11527
$989$	−35.0114			−1.11330
$990$	6.72037	+	2.89048i	0.213588	+	0.0918654i
$991$	−16.0253	−	16.0253i	−0.509061	−	0.509061i	0.405177	−	0.914238i	$-0.367210\pi$
$991$	−16.0253	−	16.0253i	−0.509061	−	0.509061i	−0.914238	+	0.405177i	$0.867210\pi$
$992$	1.69913			0.0539473
$993$	−7.61448	−	11.5640i	−0.241638	−	0.366971i
$994$	−20.2728	−	20.2728i	−0.643013	−	0.643013i
$995$		−	8.78688i		−	0.278563i
$996$	5.86785	−	28.4939i	0.185930	−	0.902865i
$997$	18.0718	−	18.0718i	0.572340	−	0.572340i	−0.360442	−	0.932782i	$-0.617374\pi$
$997$	18.0718	−	18.0718i	0.572340	−	0.572340i	0.932782	+	0.360442i	$0.117374\pi$
$998$	−14.2959			−0.452530
$999$	29.0105	−	12.5455i	0.917852	−	0.396923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.401.18	yes	40
3.2	odd	2	inner	1110.2.u.e.401.9	yes	40
37.6	odd	4	inner	1110.2.u.e.191.9	✓	40
111.80	even	4	inner	1110.2.u.e.191.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.9	✓	40	37.6	odd	4	inner
1110.2.u.e.191.18	yes	40	111.80	even	4	inner
1110.2.u.e.401.9	yes	40	3.2	odd	2	inner
1110.2.u.e.401.18	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(0.952541 + 1.44660i) q^{6} +2.97676 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.75590 - 1.18533i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(0.952541 + 1.44660i) q^{6} +2.97676 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.75590 - 1.18533i) q^{9} +1.00000 q^{10} -2.43854 q^{11} +(1.69645 + 0.349356i) q^{12} +(3.37975 - 3.37975i) q^{13} +(2.10489 - 2.10489i) q^{14} +(-1.44660 + 0.952541i) q^{15} -1.00000 q^{16} +(2.64124 + 2.64124i) q^{17} +(-2.78687 + 1.11056i) q^{18} +(5.18614 - 5.18614i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-1.03995 + 5.04993i) q^{21} +(-1.72431 + 1.72431i) q^{22} +(4.56924 + 4.56924i) q^{23} +(1.44660 - 0.952541i) q^{24} +1.00000i q^{25} -4.77969i q^{26} +(2.97365 - 4.26115i) q^{27} -2.97676i q^{28} +(-2.17706 + 2.17706i) q^{29} +(-0.349356 + 1.69645i) q^{30} +(-1.20146 - 1.20146i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.851919 - 4.13687i) q^{33} +3.73527 q^{34} +(2.10489 + 2.10489i) q^{35} +(-1.18533 + 2.75590i) q^{36} +(5.17502 + 3.19675i) q^{37} -7.33431i q^{38} +(4.55285 + 6.91433i) q^{39} -1.00000i q^{40} -7.04761 q^{41} +(2.83549 + 4.30620i) q^{42} +(-3.83120 + 3.83120i) q^{43} +2.43854i q^{44} +(-1.11056 - 2.78687i) q^{45} +6.46188 q^{46} +6.56942i q^{47} +(0.349356 - 1.69645i) q^{48} +1.86110 q^{49} +(0.707107 + 0.707107i) q^{50} +(-5.40347 + 3.55800i) q^{51} +(-3.37975 - 3.37975i) q^{52} +0.00856748i q^{53} +(-0.910402 - 5.11578i) q^{54} +(-1.72431 - 1.72431i) q^{55} +(-2.10489 - 2.10489i) q^{56} +(6.98623 + 10.6098i) q^{57} +3.07883i q^{58} +(3.57544 + 3.57544i) q^{59} +(0.952541 + 1.44660i) q^{60} +(8.28937 + 8.28937i) q^{61} -1.69913 q^{62} +(-8.20365 - 3.52845i) q^{63} +1.00000i q^{64} +4.77969 q^{65} +(-2.32281 - 3.52760i) q^{66} +3.64813i q^{67} +(2.64124 - 2.64124i) q^{68} +(-9.34779 + 6.15521i) q^{69} +2.97676 q^{70} -9.63129i q^{71} +(1.11056 + 2.78687i) q^{72} -5.75117i q^{73} +(5.91973 - 1.39885i) q^{74} +(-1.69645 - 0.349356i) q^{75} +(-5.18614 - 5.18614i) q^{76} -7.25895 q^{77} +(8.10852 + 1.66982i) q^{78} +(6.34989 - 6.34989i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(6.18998 + 6.53331i) q^{81} +(-4.98341 + 4.98341i) q^{82} -16.7962i q^{83} +(5.04993 + 1.03995i) q^{84} +3.73527i q^{85} +5.41814i q^{86} +(-2.93271 - 4.45385i) q^{87} +(1.72431 + 1.72431i) q^{88} +(1.72334 - 1.72334i) q^{89} +(-2.75590 - 1.18533i) q^{90} +(10.0607 - 10.0607i) q^{91} +(4.56924 - 4.56924i) q^{92} +(2.45796 - 1.61849i) q^{93} +(4.64528 + 4.64528i) q^{94} +7.33431 q^{95} +(-0.952541 - 1.44660i) q^{96} +(-4.30682 + 4.30682i) q^{97} +(1.31599 - 1.31599i) q^{98} +(6.72037 + 2.89048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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