LMFDB - Embedded newform 1110.2.u.e.401.9

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			401.9
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.e.191.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.44660 - 0.952541i) q^{6} +2.97676 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.75590 + 1.18533i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.44660 - 0.952541i) 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} +(0.952541 - 1.44660i) q^{15} -1.00000 q^{16} +(-2.64124 - 2.64124i) q^{17} +(1.11056 - 2.78687i) 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} +(-0.952541 + 1.44660i) 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} +(6.91433 + 4.55285i) q^{39} -1.00000i q^{40} +7.04761 q^{41} +(-4.30620 - 2.83549i) q^{42} +(-3.83120 + 3.83120i) q^{43} -2.43854i q^{44} +(2.78687 + 1.11056i) 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} +(3.55800 - 5.40347i) q^{51} +(-3.37975 - 3.37975i) q^{52} -0.00856748i q^{53} +(5.11578 + 0.910402i) q^{54} +(-1.72431 - 1.72431i) q^{55} +(2.10489 + 2.10489i) q^{56} +(10.6098 + 6.98623i) q^{57} +3.07883i q^{58} +(-3.57544 - 3.57544i) q^{59} +(-1.44660 - 0.952541i) 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} +(-3.52760 - 2.32281i) q^{66} +3.64813i q^{67} +(-2.64124 + 2.64124i) q^{68} +(6.15521 - 9.34779i) q^{69} +2.97676 q^{70} +9.63129i q^{71} +(-2.78687 - 1.11056i) 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} +(4.45385 + 2.93271i) 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} +(1.61849 - 2.45796i) q^{93} +(4.64528 + 4.64528i) q^{94} -7.33431 q^{95} +(1.44660 + 0.952541i) 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
$6$	−1.44660	−	0.952541i	−0.590574	−	0.388873i
$7$	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	$-0.380171\pi$
$11$	2.43854			0.735247			0.367624	+	0.929975i	$0.380171\pi$
$12$	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
$15$	0.952541	−	1.44660i	0.245945	−	0.373512i
$16$	−1.00000			−0.250000
$17$	−2.64124	−	2.64124i	−0.640594	−	0.640594i	0.310107	−	0.950702i	$-0.399635\pi$
$17$	−2.64124	−	2.64124i	−0.640594	−	0.640594i	−0.950702	+	0.310107i	$0.899635\pi$
$18$	1.11056	−	2.78687i	0.261762	−	0.656872i
$19$	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	0.0461806	−	0.998933i	$-0.485295\pi$
$23$	−4.56924	−	4.56924i	−0.952753	−	0.952753i	−0.998933	+	0.0461806i	$0.985295\pi$
$24$	−0.952541	+	1.44660i	−0.194437	+	0.295287i
$25$			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	−0.475465	−	0.879735i	$-0.657720\pi$
$29$	2.17706	−	2.17706i	0.404270	−	0.404270i	0.879735	+	0.475465i	$0.157720\pi$
$30$	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
$39$	6.91433	+	4.55285i	1.10718	+	0.729040i
$40$		−	1.00000i		−	0.158114i
$41$	7.04761			1.10065			0.550326	−	0.834950i	$-0.314504\pi$
$41$	7.04761			1.10065			0.550326	+	0.834950i	$0.314504\pi$
$42$	−4.30620	−	2.83549i	−0.664460	−	0.437525i
$43$	−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
$45$	2.78687	+	1.11056i	0.415442	+	0.165553i
$46$	6.46188			0.952753
$47$		−	6.56942i		−	0.958249i	−0.877747	−	0.479124i	$-0.840954\pi$
$47$		−	6.56942i		−	0.958249i	0.877747	−	0.479124i	$-0.159046\pi$
$48$	−0.349356	−	1.69645i	−0.0504252	−	0.244862i
$49$	1.86110			0.265871
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	3.55800	−	5.40347i	0.498220	−	0.756637i
$52$	−3.37975	−	3.37975i	−0.468688	−	0.468688i
$53$		−	0.00856748i		−	0.00117683i	−1.00000		0.000588417i	$-0.999813\pi$
$53$		−	0.00856748i		−	0.00117683i	1.00000		0.000588417i	$-0.000187299\pi$
$54$	5.11578	+	0.910402i	0.696169	+	0.123890i
$55$	−1.72431	−	1.72431i	−0.232506	−	0.232506i
$56$	2.10489	+	2.10489i	0.281277	+	0.281277i
$57$	10.6098	+	6.98623i	1.40531	+	0.925348i
$58$			3.07883i			0.404270i
$59$	−3.57544	−	3.57544i	−0.465483	−	0.465483i	0.434965	−	0.900447i	$-0.356761\pi$
$59$	−3.57544	−	3.57544i	−0.465483	−	0.465483i	−0.900447	+	0.434965i	$0.856761\pi$
$60$	−1.44660	−	0.952541i	−0.186756	−	0.122973i
$61$	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
$66$	−3.52760	−	2.32281i	−0.434218	−	0.285918i
$67$			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
$69$	6.15521	−	9.34779i	0.741000	−	1.12534i
$70$	2.97676			0.355791
$71$			9.63129i			1.14302i	0.820594	+	0.571512i	$0.193643\pi$
$71$			9.63129i			1.14302i	−0.820594	+	0.571512i	$0.806357\pi$
$72$	−2.78687	−	1.11056i	−0.328436	−	0.130881i
$73$		−	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	$0.373290\pi$
$83$			16.7962i			1.84362i	−0.387640	+	0.921811i	$0.626710\pi$
$84$	5.04993	−	1.03995i	0.550993	−	0.113468i
$85$			3.73527i			0.405147i
$86$		−	5.41814i		−	0.584253i
$87$	4.45385	+	2.93271i	0.477503	+	0.314420i
$88$	1.72431	+	1.72431i	0.183812	+	0.183812i
$89$	−1.72334	+	1.72334i	−0.182674	+	0.182674i	−0.792520	−	0.609846i	$-0.791231\pi$
$89$	−1.72334	+	1.72334i	−0.182674	+	0.182674i	0.609846	+	0.792520i	$0.291231\pi$
$90$	−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
$93$	1.61849	−	2.45796i	0.167829	−	0.254879i
$94$	4.64528	+	4.64528i	0.479124	+	0.479124i
$95$	−7.33431			−0.752484
$96$	1.44660	+	0.952541i	0.147643	+	0.0972183i
$97$	−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	$-0.503547\pi$
$101$	−0.223998			−0.0222886			−0.0111443	+	0.999938i	$0.503547\pi$
$102$	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
$105$	2.83549	−	4.30620i	0.276715	−	0.420242i
$106$	0.00605812	+	0.00605812i	0.000588417	+	0.000588417i
$107$			13.3421i			1.28983i	0.764256	+	0.644914i	$0.223107\pi$
$107$			13.3421i			1.28983i	−0.764256	+	0.644914i	$0.776893\pi$
$108$	−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
$111$	−3.61521	+	9.89597i	−0.343140	+	0.939284i
$112$	−2.97676			−0.281277
$113$	−1.62412	+	1.62412i	−0.152784	+	0.152784i	−0.779360	−	0.626576i	$-0.784456\pi$
$113$	−1.62412	+	1.62412i	−0.152784	+	0.152784i	0.626576	+	0.779360i	$0.284456\pi$
$114$	−12.4423	+	2.56228i	−1.16533	+	0.239980i
$115$			6.46188i			0.602574i
$116$	−2.17706	−	2.17706i	−0.202135	−	0.202135i
$117$	−5.30814	+	13.3204i	−0.490738	+	1.23147i
$118$	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
$126$	3.30587	−	8.29585i	0.294510	−	0.739053i
$127$	−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
$129$	−7.83791	−	5.16100i	−0.690090	−	0.454401i
$130$	3.37975	−	3.37975i	0.296424	−	0.296424i
$131$	5.37214	−	5.37214i	0.469366	−	0.469366i	−0.432343	−	0.901709i	$-0.642313\pi$
$131$	5.37214	−	5.37214i	0.469366	−	0.469366i	0.901709	+	0.432343i	$0.142313\pi$
$132$	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
$135$	−0.910402	+	5.11578i	−0.0783549	+	0.440296i
$136$		−	3.73527i		−	0.320297i
$137$			7.45566i			0.636980i	0.947926	+	0.318490i	$0.103176\pi$
$137$			7.45566i			0.636980i	−0.947926	+	0.318490i	$0.896824\pi$
$138$	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	$-0.861049\pi$
$149$		−	10.3217i		−	0.845589i	0.906226	−	0.422795i	$-0.138951\pi$
$150$	0.952541	−	1.44660i	0.0777746	−	0.118115i
$151$			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
$153$	10.4097	+	4.14825i	0.841577	+	0.335366i
$154$	−5.13285	+	5.13285i	−0.413617	+	0.413617i
$155$			1.69913i			0.136477i
$156$	4.55285	−	6.91433i	0.364520	−	0.553589i
$157$	−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
$162$	0.242774	+	8.99672i	0.0190742	+	0.706849i
$163$	−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
$165$	2.32281	−	3.52760i	0.180830	−	0.274624i
$166$	−11.8767	−	11.8767i	−0.921811	−	0.921811i
$167$	11.4214	+	11.4214i	0.883817	+	0.883817i	0.993920	−	0.110103i	$-0.0351182\pi$
$167$	11.4214	+	11.4214i	0.883817	+	0.883817i	−0.110103	+	0.993920i	$0.535118\pi$
$168$	−2.83549	+	4.30620i	−0.218762	+	0.332230i
$169$		−	9.84548i		−	0.757345i
$170$	−2.64124	−	2.64124i	−0.202574	−	0.202574i
$171$	−8.14519	+	20.4398i	−0.622878	+	1.56307i
$172$	3.83120	+	3.83120i	0.292127	+	0.292127i
$173$	18.3766			1.39715			0.698573	−	0.715539i	$-0.253819\pi$
$173$	18.3766			1.39715			0.698573	+	0.715539i	$0.253819\pi$
$174$	−5.22309	+	1.07561i	−0.395961	+	0.0815417i
$175$			2.97676i			0.225022i
$176$	−2.43854			−0.183812
$177$	4.81646	−	7.31466i	0.362027	−	0.549804i
$178$		−	2.43717i		−	0.182674i
$179$	14.5304	−	14.5304i	1.08606	−	1.08606i	0.0901264	−	0.995930i	$-0.471273\pi$
$179$	14.5304	−	14.5304i	1.08606	−	1.08606i	0.995930	−	0.0901264i	$-0.0287271\pi$
$180$	1.11056	−	2.78687i	0.0827763	−	0.207721i
$181$	−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
$183$	−11.1666	+	16.9585i	−0.825458	+	1.25361i
$184$		−	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	0.879042	−	0.476745i	$-0.158183\pi$
$191$	5.55986	+	5.55986i	0.402297	+	0.402297i	−0.476745	+	0.879042i	$0.658183\pi$
$192$	−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	$-0.987641\pi$
$197$		−	1.08968i		−	0.0776363i	0.999246	−	0.0388182i	$-0.0123593\pi$
$198$	2.70815	−	6.79590i	0.192459	−	0.482964i
$199$	−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
$204$	−5.40347	−	3.55800i	−0.378318	−	0.249110i
$205$	−4.98341	−	4.98341i	−0.348057	−	0.348057i
$206$	1.11863			0.0779389
$207$	18.0084	+	7.17631i	1.25167	+	0.498788i
$208$	−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
$216$	0.910402	−	5.11578i	0.0619450	−	0.348084i
$217$	−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
$222$	−4.44117	−	9.55385i	−0.298072	−	0.641212i
$223$	−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	0.0291269	−	0.999576i	$-0.490727\pi$
$227$	−14.6213	−	14.6213i	−0.970449	−	0.970449i	−0.999576	+	0.0291269i	$0.990727\pi$
$228$	6.98623	−	10.6098i	0.462674	−	0.702654i
$229$	−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	$-0.394569\pi$
$233$	9.92789			0.650398			0.325199	+	0.945646i	$0.394569\pi$
$234$	−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
$237$	12.9907	+	8.55392i	0.843834	+	0.555637i
$238$	11.1190			0.720739
$239$	18.3998	+	18.3998i	1.19018	+	1.19018i	0.977016	+	0.213168i	$0.0683782\pi$
$239$	18.3998	+	18.3998i	1.19018	+	1.19018i	0.213168	+	0.977016i	$0.431622\pi$
$240$	−0.952541	+	1.44660i	−0.0614863	+	0.0933779i
$241$	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
$246$	−10.1951	−	6.71314i	−0.650016	−	0.428014i
$247$		−	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	$0.531606\pi$
$251$	−17.3355	+	17.3355i	−1.09420	+	1.09420i	−0.995075	+	0.0991297i	$0.968394\pi$
$252$	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	$-0.854437\pi$
$257$	−21.4622	−	21.4622i	−1.33877	−	1.33877i	−0.441526	−	0.897248i	$-0.645563\pi$
$258$	9.19162	−	1.89286i	0.572245	−	0.117844i
$259$	15.4048	+	9.51595i	0.957206	+	0.591293i
$260$			4.77969i			0.296424i
$261$	−3.41923	+	8.58031i	−0.211645	+	0.531108i
$262$			7.59736i			0.469366i
$263$	−7.76918			−0.479068			−0.239534	−	0.970888i	$-0.576995\pi$
$263$	−7.76918			−0.479068			−0.239534	+	0.970888i	$0.576995\pi$
$264$	−2.32281	+	3.52760i	−0.142959	+	0.217109i
$265$	−0.00605812	+	0.00605812i	−0.000372147	+	0.000372147i
$266$			21.8325i			1.33863i
$267$	−3.52562	−	2.32150i	−0.215764	−	0.142074i
$268$	3.64813			0.222845
$269$		−	25.5891i		−	1.56019i	−0.625659	−	0.780097i	$-0.715170\pi$
$269$		−	25.5891i		−	1.56019i	0.625659	−	0.780097i	$-0.284830\pi$
$270$	−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
$273$	20.5823	+	13.5528i	1.24570	+	0.820250i
$274$	−5.27195	−	5.27195i	−0.318490	−	0.318490i
$275$			2.43854i			0.147049i
$276$	−9.34779	−	6.15521i	−0.562671	−	0.370500i
$277$	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
$279$	4.73525	+	1.88698i	0.283492	+	0.112971i
$280$		−	2.97676i		−	0.177895i
$281$	16.5786	+	16.5786i	0.988999	+	0.988999i	0.999940	−	0.0109410i	$-0.00348270\pi$
$281$	16.5786	+	16.5786i	0.988999	+	0.988999i	−0.0109410	+	0.999940i	$0.503483\pi$
$282$	−6.25765	+	9.50336i	−0.372637	+	0.565917i
$283$	−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
$288$	−1.11056	+	2.78687i	−0.0654404	+	0.164218i
$289$		−	3.04772i		−	0.179278i
$290$	2.17706	−	2.17706i	0.127842	−	0.127842i
$291$	−8.81093	−	5.80170i	−0.516506	−	0.340102i
$292$	−5.75117			−0.336561
$293$			16.8721i			0.985681i	0.870120	+	0.492840i	$0.164041\pi$
$293$			16.8721i			0.985681i	−0.870120	+	0.492840i	$0.835959\pi$
$294$	−2.69227	−	1.77277i	−0.157017	−	0.103390i
$295$			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
$309$	1.06554	−	1.61822i	0.0606167	−	0.0920574i
$310$	−1.20146	−	1.20146i	−0.0682385	−	0.0682385i
$311$	−2.69292	+	2.69292i	−0.152702	+	0.152702i	−0.779323	−	0.626622i	$-0.784437\pi$
$311$	−2.69292	+	2.69292i	−0.152702	+	0.152702i	0.626622	+	0.779323i	$0.284437\pi$
$312$	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
$315$	8.29585	+	3.30587i	0.467418	+	0.186265i
$316$	−6.34989	−	6.34989i	−0.357209	−	0.357209i
$317$	−12.5140			−0.702854			−0.351427	−	0.936215i	$-0.614303\pi$
$317$	−12.5140			−0.702854			−0.351427	+	0.936215i	$0.614303\pi$
$318$	−0.00816087	+	0.0123938i	−0.000457639	+	0.000695007i
$319$	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
$327$	−16.8495	−	11.0948i	−0.931780	−	0.613546i
$328$	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
$333$	−18.0510	−	2.67581i	−0.989191	−	0.146634i
$334$	−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
$339$	−3.32263	−	2.18784i	−0.180461	−	0.118827i
$340$	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	$0.615067\pi$
$347$	−24.0122	+	24.0122i	−1.28904	+	1.28904i	−0.935370	+	0.353671i	$0.884933\pi$
$348$	2.93271	−	4.45385i	0.157210	−	0.238752i
$349$	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
$351$	−24.4519	−	4.35144i	−1.30514	−	0.232263i
$352$	1.72431	−	1.72431i	0.0919059	−	0.0919059i
$353$	22.0357	−	22.0357i	1.17284	−	1.17284i	0.191310	−	0.981530i	$-0.438727\pi$
$353$	22.0357	−	22.0357i	1.17284	−	1.17284i	0.981530	−	0.191310i	$-0.0612735\pi$
$354$	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
$357$	10.5913	−	16.0848i	0.560552	−	0.851299i
$358$			20.5492i			1.08606i
$359$			2.38803i			0.126035i	0.998012	+	0.0630177i	$0.0200725\pi$
$359$			2.38803i			0.126035i	−0.998012	+	0.0630177i	$0.979928\pi$
$360$	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
$372$	−2.45796	−	1.61849i	−0.127439	−	0.0839146i
$373$			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
$375$	1.44660	+	0.952541i	0.0747024	+	0.0491890i
$376$	4.64528	−	4.64528i	0.239562	−	0.239562i
$377$		−	14.7159i		−	0.757906i
$378$	15.2284	+	2.71005i	0.783266	+	0.139390i
$379$	−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	0.943379	−	0.331717i	$-0.107628\pi$
$383$	11.9705	+	11.9705i	0.611662	+	0.611662i	−0.331717	+	0.943379i	$0.607628\pi$
$384$	0.952541	−	1.44660i	0.0486091	−	0.0738217i
$385$	−5.13285	−	5.13285i	−0.261594	−	0.261594i
$386$		−	9.81400i		−	0.499519i
$387$	6.01717	−	15.0997i	0.305870	−	0.767559i
$388$	4.30682	+	4.30682i	0.218646	+	0.218646i
$389$	−19.1226	−	19.1226i	−0.969555	−	0.969555i	0.0299951	−	0.999550i	$-0.490451\pi$
$389$	−19.1226	−	19.1226i	−0.969555	−	0.969555i	−0.999550	+	0.0299951i	$0.990451\pi$
$390$	6.91433	+	4.55285i	0.350121	+	0.230543i
$391$			24.1369i			1.22066i
$392$	1.31599	+	1.31599i	0.0664678	+	0.0664678i
$393$	10.9904	+	7.23680i	0.554391	+	0.365048i
$394$	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
$399$	31.5830	+	20.7963i	1.58113	+	1.04112i
$400$		−	1.00000i		−	0.0500000i
$401$	14.1223	−	14.1223i	0.705233	−	0.705233i	−0.260296	−	0.965529i	$-0.583820\pi$
$401$	14.1223	−	14.1223i	0.705233	−	0.705233i	0.965529	+	0.260296i	$0.0838202\pi$
$402$	3.47499	−	5.27740i	0.173317	−	0.263213i
$403$	−8.12130			−0.404551
$404$			0.223998i			0.0111443i
$405$	−8.99672	+	0.242774i	−0.447051	+	0.0120636i
$406$			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	$0.0223262\pi$
$419$			2.86911i			0.140165i	−0.997541	+	0.0700825i	$0.977674\pi$
$420$	−4.30620	−	2.83549i	−0.210121	−	0.138358i
$421$	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
$426$	9.17419	−	13.9327i	0.444491	−	0.675040i
$427$	24.6755	+	24.6755i	1.19413	+	1.19413i
$428$	13.3421			0.644914
$429$	16.8609	+	11.1023i	0.814050	+	0.536025i
$430$	−3.83120	+	3.83120i	−0.184757	+	0.184757i
$431$	9.00474	−	9.00474i	0.433743	−	0.433743i	−0.456157	−	0.889900i	$-0.650774\pi$
$431$	9.00474	−	9.00474i	0.433743	−	0.433743i	0.889900	+	0.456157i	$0.150774\pi$
$432$	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
$438$	−5.47822	+	8.31966i	−0.261759	+	0.397529i
$439$	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	$-0.278998\pi$
$443$	26.9345			1.27969			0.639847	+	0.768502i	$0.278998\pi$
$444$	9.89597	+	3.61521i	0.469642	+	0.171570i
$445$	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	0.868874	−	0.495034i	$-0.164844\pi$
$449$	7.92152	+	7.92152i	0.373840	+	0.373840i	−0.495034	+	0.868874i	$0.664844\pi$
$450$	2.78687	+	1.11056i	0.131374	+	0.0523523i
$451$	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
$459$	−3.40060	+	19.1088i	−0.158726	+	0.891924i
$460$	6.46188			0.301287
$461$	−6.14385	−	6.14385i	−0.286148	−	0.286148i	0.549407	−	0.835555i	$-0.314854\pi$
$461$	−6.14385	−	6.14385i	−0.286148	−	0.286148i	−0.835555	+	0.549407i	$0.814854\pi$
$462$	−10.5008	−	6.91444i	−0.488543	−	0.321689i
$463$	−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	0.713052	−	0.701111i	$-0.247312\pi$
$467$	0.258047	+	0.258047i	0.0119410	+	0.0119410i	−0.701111	+	0.713052i	$0.747312\pi$
$468$	13.3204	+	5.30814i	0.615736	+	0.245369i
$469$			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	$0.0909329\pi$
$479$	27.1667	+	27.1667i	1.24128	+	1.24128i	0.281804	+	0.959472i	$0.409067\pi$
$480$	−0.349356	−	1.69645i	−0.0159458	−	0.0774321i
$481$	28.2945	−	6.68606i	1.29012	−	0.304858i
$482$			25.8238i			1.17624i
$483$	18.3226	−	27.8261i	0.833706	−	1.26613i
$484$			5.05352i			0.229706i
$485$	6.09076			0.276567
$486$	−15.1777	+	3.55492i	−0.688474	+	0.161254i
$487$	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
$489$	17.7853	−	27.0102i	0.804281	−	1.22145i
$490$	1.86110			0.0840758
$491$			0.227143i			0.0102508i	0.999987	+	0.00512541i	$0.00163148\pi$
$491$			0.227143i			0.0102508i	−0.999987	+	0.00512541i	$0.998369\pi$
$492$	11.9559	−	2.46212i	0.539015	−	0.111001i
$493$	−11.5003			−0.517947
$494$	24.7882	+	24.7882i	1.11527	+	1.11527i
$495$	6.79590	+	2.70815i	0.305453	+	0.121722i
$496$	1.20146	+	1.20146i	0.0539473	+	0.0539473i
$497$			28.6700i			1.28603i
$498$	15.9991	−	24.2975i	0.716935	−	1.08880i
$499$	−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
$501$	−15.3858	+	23.3661i	−0.687385	+	1.04392i
$502$		−	24.5160i		−	1.09420i
$503$	9.08858	+	9.08858i	0.405240	+	0.405240i	0.880075	−	0.474835i	$-0.157492\pi$
$503$	9.08858	+	9.08858i	0.405240	+	0.405240i	−0.474835	+	0.880075i	$0.657492\pi$
$504$	−8.29585	−	3.30587i	−0.369526	−	0.147255i
$505$	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	$-0.595680\pi$
$509$	−13.3598			−0.592163			−0.296082	+	0.955163i	$0.595680\pi$
$510$	3.55800	−	5.40347i	0.157551	−	0.239270i
$511$		−	17.1198i		−	0.757337i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−37.5207	−	6.67716i	−1.65658	−	0.294804i
$514$	30.3521			1.33877
$515$			1.11863i			0.0492929i
$516$	−5.16100	+	7.83791i	−0.227200	+	0.345045i
$517$		−	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	$-0.370467\pi$
$521$	18.0686			0.791601			0.395801	+	0.918337i	$0.370467\pi$
$522$	−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
$531$	14.0916	+	5.61548i	0.611525	+	0.243691i
$532$	−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
$537$	29.7265	+	19.5739i	1.28279	+	0.844677i
$538$	18.0942	+	18.0942i	0.780097	+	0.780097i
$539$	4.53836			0.195481
$540$	5.11578	+	0.910402i	0.220148	+	0.0391774i
$541$	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
$549$	−32.6703	−	13.0190i	−1.39434	−	0.555639i
$550$	−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
$555$	9.55385	−	4.44117i	0.405538	−	0.188517i
$556$	−18.3826			−0.779598
$557$	−15.3019	+	15.3019i	−0.648361	+	0.648361i	−0.952597	−	0.304236i	$-0.901599\pi$
$557$	−15.3019	+	15.3019i	−0.648361	+	0.648361i	0.304236	+	0.952597i	$0.401599\pi$
$558$	−4.68262	+	2.01403i	−0.198231	+	0.0852606i
$559$			25.8971i			1.09533i
$560$	2.10489	+	2.10489i	0.0889477	+	0.0889477i
$561$	8.67633	−	13.1766i	0.366315	−	0.556315i
$562$	−23.4457			−0.988999
$563$	−19.7443	−	19.7443i	−0.832124	−	0.832124i	0.155683	−	0.987807i	$-0.450242\pi$
$563$	−19.7443	−	19.7443i	−0.832124	−	0.832124i	−0.987807	+	0.155683i	$0.950242\pi$
$564$	−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	−0.487074	−	0.873361i	$-0.661936\pi$
$569$	9.21438	−	9.21438i	0.386287	−	0.386287i	0.873361	+	0.487074i	$0.161936\pi$
$570$	10.6098	+	6.98623i	0.444397	+	0.292621i
$571$	−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
$573$	−7.48967	+	11.3744i	−0.312885	+	0.475173i
$574$	−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
$579$	−14.1970	−	9.34824i	−0.590006	−	0.388499i
$580$			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	−0.783210	−	0.621757i	$-0.786419\pi$
$587$	−3.91169	+	3.91169i	−0.161453	+	0.161453i	0.621757	+	0.783210i	$0.286419\pi$
$588$	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	$-0.853207\pi$
$593$		−	21.6725i		−	0.889983i	0.895535	−	0.444991i	$-0.146793\pi$
$594$	12.4750	+	2.22005i	0.511856	+	0.0910898i
$595$			11.1190i			0.455835i
$596$	−10.3217			−0.422795
$597$	8.36987	−	12.7112i	0.342556	−	0.520233i
$598$	21.8396	−	21.8396i	0.893087	−	0.893087i
$599$		−	14.8293i		−	0.605907i	−0.953005	−	0.302954i	$-0.902027\pi$
$599$		−	14.8293i		−	0.605907i	0.953005	−	0.302954i	$-0.0979727\pi$
$600$	−1.44660	−	0.952541i	−0.0590574	−	0.0388873i
$601$	−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
$606$	0.324036	+	0.213367i	0.0131631	+	0.00866744i
$607$	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
$609$	13.2580	+	8.72998i	0.537243	+	0.353757i
$610$	8.28937	+	8.28937i	0.335627	+	0.335627i
$611$	−22.2030	−	22.2030i	−0.898239	−	0.898239i
$612$	4.14825	−	10.4097i	0.167683	−	0.420789i
$613$			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
$615$	6.71314	−	10.1951i	0.270700	−	0.411106i
$616$	5.13285	+	5.13285i	0.206808	+	0.206808i
$617$	4.87072			0.196088			0.0980438	−	0.995182i	$-0.468741\pi$
$617$	4.87072			0.196088			0.0980438	+	0.995182i	$0.468741\pi$
$618$	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
$621$	−5.88291	+	33.0575i	−0.236073	+	1.32655i
$622$		−	3.80837i		−	0.152702i
$623$	−5.12996	+	5.12996i	−0.205528	+	0.205528i
$624$	−6.91433	−	4.55285i	−0.276795	−	0.182260i
$625$	−1.00000			−0.0400000
$626$		−	10.8341i		−	0.433017i
$627$	25.8725	+	17.0362i	1.03325	+	0.680360i
$628$			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	$0.383577\pi$
$641$			47.2866i			1.86771i	−0.357653	+	0.933854i	$0.616423\pi$
$642$	12.7089	−	19.3007i	0.501579	−	0.761738i
$643$	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	−0.939986	−	0.341213i	$-0.889162\pi$
$647$	−15.2305	+	15.2305i	−0.598773	+	0.598773i	0.341213	+	0.939986i	$0.389162\pi$
$648$	8.99672	−	0.242774i	0.353425	−	0.00953708i
$649$	−8.71885	−	8.71885i	−0.342245	−	0.342245i
$650$	−4.77969			−0.187475
$651$	4.81785	−	7.31677i	0.188826	−	0.286767i
$652$	−13.2027	+	13.2027i	−0.517059	+	0.517059i
$653$	−23.9793	+	23.9793i	−0.938382	+	0.938382i	−0.998209	−	0.0598267i	$-0.980945\pi$
$653$	−23.9793	+	23.9793i	−0.938382	+	0.938382i	0.0598267	+	0.998209i	$0.480945\pi$
$654$	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	$-0.789184\pi$
$659$	−40.4873			−1.57716			−0.788581	+	0.614931i	$0.789184\pi$
$660$	−3.52760	−	2.32281i	−0.137312	−	0.0904152i
$661$	−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
$666$	14.6561	−	10.8719i	0.567912	−	0.421279i
$667$	−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
$672$	4.30620	+	2.83549i	0.166115	+	0.109381i
$673$	−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	$-0.545708\pi$
$677$	−7.44693			−0.286209			−0.143104	+	0.989708i	$0.545708\pi$
$678$	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
$681$	19.6963	−	29.9123i	0.754763	−	1.14624i
$682$	4.14339			0.158658
$683$	16.2355	+	16.2355i	0.621235	+	0.621235i	0.945847	−	0.324612i	$-0.105234\pi$
$683$	16.2355	+	16.2355i	0.621235	+	0.621235i	−0.324612	+	0.945847i	$0.605234\pi$
$684$	20.4398	+	8.14519i	0.781534	+	0.311439i
$685$	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
$690$	6.15521	−	9.34779i	0.234325	−	0.355864i
$691$		−	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	$-0.885942\pi$
$701$	−34.0802	−	34.0802i	−1.28719	−	1.28719i	−0.350705	−	0.936486i	$-0.614058\pi$
$702$	20.3670	−	14.2131i	0.768703	−	0.536440i
$703$	43.4171	−	10.2596i	1.63751	−	0.386947i
$704$			2.43854i			0.0919059i
$705$	−9.50336	−	6.25765i	−0.357917	−	0.235677i
$706$			31.1631i			1.17284i
$707$	−0.666787			−0.0250771
$708$	−7.31466	−	4.81646i	−0.274902	−	0.181014i
$709$	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
$711$	−9.97295	+	25.0264i	−0.374015	+	0.938564i
$712$	−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
$717$	−24.7863	+	37.6424i	−0.925661	+	1.40578i
$718$	−1.68859	−	1.68859i	−0.0630177	−	0.0630177i
$719$			12.6157i			0.470487i	0.971936	+	0.235243i	$0.0755887\pi$
$719$			12.6157i			0.470487i	−0.971936	+	0.235243i	$0.924411\pi$
$720$	−2.78687	−	1.11056i	−0.103861	−	0.0413881i
$721$	−2.35460	−	2.35460i	−0.0876898	−	0.0876898i
$722$	24.6017	+	24.6017i	0.915580	+	0.915580i
$723$	37.3569	+	24.5983i	1.38932	+	0.914819i
$724$			2.29142i			0.0851599i
$725$	2.17706	+	2.17706i	0.0808541	+	0.0808541i
$726$	7.31045	+	4.81369i	0.271316	+	0.178653i
$727$	−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
$732$	16.9585	+	11.1666i	0.626803	+	0.412729i
$733$			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
$735$	1.77277	−	2.69227i	0.0653897	−	0.0993060i
$736$	−6.46188			−0.238188
$737$			8.89610i			0.327692i
$738$	7.82679	−	19.6408i	0.288108	−	0.722987i
$739$		−	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	$-0.573752\pi$
$743$	−12.5185			−0.459260			−0.229630	+	0.973278i	$0.573752\pi$
$744$	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
$753$	−35.4650	−	23.3525i	−1.29242	−	0.851013i
$754$	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
$759$	15.0097	−	22.7950i	0.544818	−	0.827405i
$760$	−5.18614	−	5.18614i	−0.188121	−	0.188121i
$761$	22.0349			0.798766			0.399383	−	0.916784i	$-0.369224\pi$
$761$	22.0349			0.798766			0.399383	+	0.916784i	$0.369224\pi$
$762$	0.384411	+	0.253121i	0.0139257	+	0.00916962i
$763$	−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
$771$	28.9116	−	43.9075i	1.04123	−	1.58129i
$772$	6.93955	+	6.93955i	0.249760	+	0.249760i
$773$		−	11.9686i		−	0.430481i	−0.976561	−	0.215240i	$-0.930947\pi$
$773$		−	11.9686i		−	0.430481i	0.976561	−	0.215240i	$-0.0690535\pi$
$774$	6.42229	+	14.9319i	0.230845	+	0.536715i
$775$	1.20146	−	1.20146i	0.0431578	−	0.0431578i
$776$	−6.09076			−0.218646
$777$	−10.7616	+	29.4579i	−0.386071	+	1.05680i
$778$	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
$783$	−15.7506	−	2.80297i	−0.562881	−	0.100170i
$784$	−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
$792$	−6.79590	−	2.70815i	−0.241482	−	0.0962297i
$793$	56.0321			1.98976
$794$	−15.6373	−	15.6373i	−0.554948	−	0.554948i
$795$	−0.0123938	−	0.00816087i	−0.000439561	−	0.000289436i
$796$	−6.21327	+	6.21327i	−0.220223	+	0.220223i
$797$	−29.0941	+	29.0941i	−1.03057	+	1.03057i	−0.0310478	+	0.999518i	$0.509884\pi$
$797$	−29.0941	+	29.0941i	−1.03057	+	1.03057i	−0.999518	+	0.0310478i	$0.990116\pi$
$798$	−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
$801$	2.70662	−	6.79208i	0.0956338	−	0.239986i
$802$			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	−0.438789	−	0.898590i	$-0.644592\pi$
$809$	13.0781	−	13.0781i	0.459801	−	0.459801i	0.898590	+	0.438789i	$0.144592\pi$
$810$	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
$816$	−3.55800	+	5.40347i	−0.124555	+	0.189159i
$817$			39.7383i			1.39027i
$818$	−8.28701			−0.289749
$819$	−15.8011	+	39.6516i	−0.552133	+	1.38554i
$820$	−4.98341	+	4.98341i	−0.174028	+	0.174028i
$821$		−	54.7891i		−	1.91215i	−0.293117	−	0.956076i	$-0.594693\pi$
$821$		−	54.7891i		−	1.91215i	0.293117	−	0.956076i	$-0.405307\pi$
$822$	7.10182	−	10.7854i	0.247705	−	0.376184i
$823$	−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	$0.0449629\pi$
$827$	32.5198	+	32.5198i	1.13083	+	1.13083i	0.140786	+	0.990040i	$0.455037\pi$
$828$	7.17631	−	18.0084i	0.249394	−	0.625837i
$829$	−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
$831$	−4.90541	+	7.44975i	−0.170167	+	0.258429i
$832$	3.37975	+	3.37975i	0.117172	+	0.117172i
$833$	−4.91560	−	4.91560i	−0.170316	−	0.170316i
$834$	−17.5102	+	26.5924i	−0.606329	+	0.920820i
$835$		−	16.1523i		−	0.558975i
$836$	−12.6466	−	12.6466i	−0.437392	−	0.437392i
$837$	−1.54689	+	8.69235i	−0.0534682	+	0.300451i
$838$	−2.02876	−	2.02876i	−0.0700825	−	0.0700825i
$839$	−42.0148			−1.45051			−0.725256	−	0.688480i	$-0.758278\pi$
$839$	−42.0148			−1.45051			−0.725256	+	0.688480i	$0.758278\pi$
$840$	5.04993	−	1.03995i	0.174239	−	0.0358816i
$841$			19.5208i			0.673131i
$842$	−22.9041			−0.789327
$843$	−22.3330	+	33.9167i	−0.769191	+	1.16815i
$844$		−	19.8475i		−	0.683180i
$845$	−6.96181	+	6.96181i	−0.239493	+	0.239493i
$846$	−18.3081	−	7.29574i	−0.629447	−	0.250833i
$847$	−15.0431			−0.516888
$848$			0.00856748i			0.000294208i
$849$	6.53254	−	9.92084i	0.224196	−	0.340482i
$850$			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	0.464037	−	0.885816i	$-0.346401\pi$
$857$	−12.3474	−	12.3474i	−0.421779	−	0.421779i	−0.885816	+	0.464037i	$0.846401\pi$
$858$	−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	$0.159077\pi$
$863$			28.1554i			0.958420i	−0.877700	+	0.479210i	$0.840923\pi$
$864$	−5.11578	−	0.910402i	−0.174042	−	0.0309725i
$865$	−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
$870$	4.45385	+	2.93271i	0.151000	+	0.0994283i
$871$	12.3298	+	12.3298i	0.417778	+	0.417778i
$872$	−11.6476			−0.394438
$873$	6.76416	−	16.9742i	0.228932	−	0.574489i
$874$	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	$-0.0707164\pi$
$881$	57.9043			1.95085			0.975423	+	0.220339i	$0.0707164\pi$
$882$	2.06686	−	5.18664i	0.0695948	−	0.174643i
$883$	−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	$-0.623683\pi$
$887$	−22.5666			−0.757714			−0.378857	+	0.925455i	$0.623683\pi$
$888$	−9.55385	+	4.44117i	−0.320606	+	0.149036i
$889$	−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
$894$	−9.83187	+	14.9315i	−0.328827	+	0.499383i
$895$	−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
$903$	−23.3316	−	15.3631i	−0.776426	−	0.511251i
$904$	−2.29685			−0.0763921
$905$	1.62028	+	1.62028i	0.0538598	+	0.0538598i
$906$	20.8015	−	31.5908i	0.691082	−	1.04953i
$907$	−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	0.359155	−	0.933278i	$-0.383065\pi$
$911$	−17.3286	−	17.3286i	−0.574123	−	0.574123i	−0.933278	+	0.359155i	$0.883065\pi$
$912$	−10.6098	−	6.98623i	−0.351327	−	0.231337i
$913$			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
$927$	3.11749	+	1.24231i	0.102392	+	0.0408028i
$928$		−	3.07883i		−	0.101068i
$929$	35.2211			1.15557			0.577783	−	0.816190i	$-0.303918\pi$
$929$	35.2211			1.15557			0.577783	+	0.816190i	$0.303918\pi$
$930$	1.61849	−	2.45796i	0.0530723	−	0.0805998i
$931$	9.65191	−	9.65191i	0.316329	−	0.316329i
$932$		−	9.92789i		−	0.325199i
$933$	−5.50920	−	3.62763i	−0.180363	−	0.118763i
$934$	−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
$939$	−15.6726	−	10.3199i	−0.511457	−	0.336777i
$940$	4.64528	+	4.64528i	0.151512	+	0.151512i
$941$			1.57027i			0.0511894i	0.999672	+	0.0255947i	$0.00814794\pi$
$941$			1.57027i			0.0511894i	−0.999672	+	0.0255947i	$0.991852\pi$
$942$	9.22705	+	6.07571i	0.300634	+	0.197957i
$943$	−32.2022	−	32.2022i	−1.04865	−	1.04865i
$944$	3.57544	+	3.57544i	0.116371	+	0.116371i
$945$	−2.71005	+	15.2284i	−0.0881578	+	0.495381i
$946$		−	13.2124i		−	0.429571i
$947$	−24.0788	−	24.0788i	−0.782456	−	0.782456i	0.197788	−	0.980245i	$-0.436624\pi$
$947$	−24.0788	−	24.0788i	−0.782456	−	0.782456i	−0.980245	+	0.197788i	$0.936624\pi$
$948$	8.55392	−	12.9907i	0.277818	−	0.421917i
$949$	−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	$-0.333899\pi$
$953$	30.7757			0.996922			0.498461	+	0.866912i	$0.333899\pi$
$954$	−0.0238765	−	0.00951470i	−0.000773029	−	0.000308050i
$955$		−	7.86283i		−	0.254435i
$956$	18.3998	−	18.3998i	0.595092	−	0.595092i
$957$	10.8609	+	7.15154i	0.351083	+	0.231176i
$958$	−38.4195			−1.24128
$959$			22.1937i			0.716673i
$960$	1.44660	+	0.952541i	0.0466890	+	0.0307431i
$961$		−	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	$0.198925\pi$
$971$			36.4612i			1.17010i	−0.810998	+	0.585048i	$0.801075\pi$
$972$	8.21855	−	13.2460i	0.263610	−	0.424864i
$973$		−	54.7207i		−	1.75427i
$974$			33.0044i			1.05753i
$975$	−4.55285	+	6.91433i	−0.145808	+	0.221436i
$976$	−8.28937	−	8.28937i	−0.265336	−	0.265336i
$977$	35.3768	−	35.3768i	1.13180	−	1.13180i	0.141926	−	0.989877i	$-0.454671\pi$
$977$	35.3768	−	35.3768i	1.13180	−	1.13180i	0.989877	−	0.141926i	$-0.0453295\pi$
$978$	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
$981$	12.9354	−	32.4604i	0.412995	−	1.03638i
$982$	−0.160614	−	0.160614i	−0.00512541	−	0.00512541i
$983$	3.36934			0.107465			0.0537326	−	0.998555i	$-0.482888\pi$
$983$	3.36934			0.107465			0.0537326	+	0.998555i	$0.482888\pi$
$984$	−6.71314	+	10.1951i	−0.214007	+	0.325008i
$985$	−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
$993$	−11.5640	−	7.61448i	−0.366971	−	0.241638i
$994$	−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
$999$	−1.76685	−	31.5575i	−0.0559007	−	0.998436i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.44660 - 0.952541i) q^{6} +2.97676 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.75590 + 1.18533i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.349356 + 1.69645i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.44660 - 0.952541i) 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} +(0.952541 - 1.44660i) q^{15} -1.00000 q^{16} +(-2.64124 - 2.64124i) q^{17} +(1.11056 - 2.78687i) 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} +(-0.952541 + 1.44660i) 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} +(6.91433 + 4.55285i) q^{39} -1.00000i q^{40} +7.04761 q^{41} +(-4.30620 - 2.83549i) q^{42} +(-3.83120 + 3.83120i) q^{43} -2.43854i q^{44} +(2.78687 + 1.11056i) 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} +(3.55800 - 5.40347i) q^{51} +(-3.37975 - 3.37975i) q^{52} -0.00856748i q^{53} +(5.11578 + 0.910402i) q^{54} +(-1.72431 - 1.72431i) q^{55} +(2.10489 + 2.10489i) q^{56} +(10.6098 + 6.98623i) q^{57} +3.07883i q^{58} +(-3.57544 - 3.57544i) q^{59} +(-1.44660 - 0.952541i) 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} +(-3.52760 - 2.32281i) q^{66} +3.64813i q^{67} +(-2.64124 + 2.64124i) q^{68} +(6.15521 - 9.34779i) q^{69} +2.97676 q^{70} +9.63129i q^{71} +(-2.78687 - 1.11056i) 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} +(4.45385 + 2.93271i) 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} +(1.61849 - 2.45796i) q^{93} +(4.64528 + 4.64528i) q^{94} -7.33431 q^{95} +(1.44660 + 0.952541i) 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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