LMFDB - Embedded newform 1110.2.u.e.191.9

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			191.9
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.9

$q$-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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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	0.998151	−	0.0607761i	$-0.0193576\pi$
$13$	3.37975	+	3.37975i	0.937375	+	0.937375i	−0.0607761	+	0.998151i	$0.519358\pi$
$14$	−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	−0.950702	−	0.310107i	$-0.899635\pi$
$17$	−2.64124	+	2.64124i	−0.640594	+	0.640594i	0.310107	+	0.950702i	$0.399635\pi$
$18$	1.11056	+	2.78687i	0.261762	+	0.656872i
$19$	5.18614	+	5.18614i	1.18978	+	1.18978i	0.977128	+	0.212654i	$0.0682108\pi$
$19$	5.18614	+	5.18614i	1.18978	+	1.18978i	0.212654	+	0.977128i	$0.431789\pi$
$20$	−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	$-0.985295\pi$
$23$	−4.56924	+	4.56924i	−0.952753	+	0.952753i	0.0461806	+	0.998933i	$0.485295\pi$
$24$	−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	0.879735	−	0.475465i	$-0.157720\pi$
$29$	2.17706	+	2.17706i	0.404270	+	0.404270i	−0.475465	+	0.879735i	$0.657720\pi$
$30$	0.349356	−	1.69645i	0.0637834	−	0.309728i
$31$	−1.20146	+	1.20146i	−0.215789	+	0.215789i	−0.806721	−	0.590932i	$-0.798760\pi$
$31$	−1.20146	+	1.20146i	−0.215789	+	0.215789i	0.590932	+	0.806721i	$0.298760\pi$
$32$	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	0.351816	−	0.936069i	$-0.385564\pi$
$43$	−3.83120	−	3.83120i	−0.584253	−	0.584253i	−0.936069	+	0.351816i	$0.885564\pi$
$44$			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	$0.159046\pi$
$47$			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
$51$	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	$0.000187299\pi$
$53$			0.00856748i			0.00117683i	−1.00000		0.000588417i	$0.999813\pi$
$54$	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	−0.900447	−	0.434965i	$-0.856761\pi$
$59$	−3.57544	+	3.57544i	−0.465483	+	0.465483i	0.434965	+	0.900447i	$0.356761\pi$
$60$	−1.44660	+	0.952541i	−0.186756	+	0.122973i
$61$	8.28937	−	8.28937i	1.06135	−	1.06135i	0.0633543	−	0.997991i	$-0.479820\pi$
$61$	8.28937	−	8.28937i	1.06135	−	1.06135i	0.997991	−	0.0633543i	$-0.0201798\pi$
$62$	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	$-0.928466\pi$
$67$		−	3.64813i		−	0.445689i	0.974854	−	0.222845i	$-0.0715343\pi$
$68$	−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	$-0.806357\pi$
$71$		−	9.63129i		−	1.14302i	0.820594	−	0.571512i	$-0.193643\pi$
$72$	−2.78687	+	1.11056i	−0.328436	+	0.130881i
$73$			5.75117i			0.673123i	0.941661	+	0.336561i	$0.109264\pi$
$73$			5.75117i			0.673123i	−0.941661	+	0.336561i	$0.890736\pi$
$74$	−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	0.967456	−	0.253038i	$-0.0814296\pi$
$79$	6.34989	+	6.34989i	0.714419	+	0.714419i	−0.253038	+	0.967456i	$0.581430\pi$
$80$	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
$87$	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	0.609846	−	0.792520i	$-0.291231\pi$
$89$	−1.72334	−	1.72334i	−0.182674	−	0.182674i	−0.792520	+	0.609846i	$0.791231\pi$
$90$	−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	0.453808	−	0.891099i	$-0.350065\pi$
$97$	−4.30682	−	4.30682i	−0.437291	−	0.437291i	−0.891099	+	0.453808i	$0.850065\pi$
$98$	−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	−0.745002	−	0.667063i	$-0.767551\pi$
$103$	−0.790994	+	0.790994i	−0.0779389	+	0.0779389i	0.667063	+	0.745002i	$0.267551\pi$
$104$	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	$-0.776893\pi$
$107$		−	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	0.192433	−	0.981310i	$-0.438362\pi$
$109$	−8.23612	−	8.23612i	−0.788877	−	0.788877i	−0.981310	+	0.192433i	$0.938362\pi$
$110$	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	0.626576	−	0.779360i	$-0.284456\pi$
$113$	−1.62412	−	1.62412i	−0.152784	−	0.152784i	−0.779360	+	0.626576i	$0.784456\pi$
$114$	−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	0.901709	−	0.432343i	$-0.142313\pi$
$131$	5.37214	+	5.37214i	0.469366	+	0.469366i	−0.432343	+	0.901709i	$0.642313\pi$
$132$	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	$-0.896824\pi$
$137$		−	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	$0.284576\pi$
$139$			18.3826i			1.55920i	−0.626281	+	0.779598i	$0.715424\pi$
$140$	−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	$0.861049\pi$
$150$	0.952541	+	1.44660i	0.0777746	+	0.118115i
$151$		−	21.8379i		−	1.77714i	−0.458741	−	0.888570i	$-0.651699\pi$
$151$		−	21.8379i		−	1.77714i	0.458741	−	0.888570i	$-0.348301\pi$
$152$	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	−0.0347202	+	0.999397i	$0.511054\pi$
$163$	−13.2027	+	13.2027i	−1.03412	+	1.03412i	−0.999397	+	0.0347202i	$0.988946\pi$
$164$			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	−0.110103	−	0.993920i	$-0.535118\pi$
$167$	11.4214	−	11.4214i	0.883817	−	0.883817i	0.993920	+	0.110103i	$0.0351182\pi$
$168$	−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	0.995930	+	0.0901264i	$0.0287271\pi$
$179$	14.5304	+	14.5304i	1.08606	+	1.08606i	0.0901264	+	0.995930i	$0.471273\pi$
$180$	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	−0.476745	−	0.879042i	$-0.658183\pi$
$191$	5.55986	−	5.55986i	0.402297	−	0.402297i	0.879042	+	0.476745i	$0.158183\pi$
$192$	−1.69645	−	0.349356i	−0.122431	−	0.0252126i
$193$	−6.93955	−	6.93955i	−0.499519	−	0.499519i	0.411769	−	0.911288i	$-0.364911\pi$
$193$	−6.93955	−	6.93955i	−0.499519	−	0.499519i	−0.911288	+	0.411769i	$0.864911\pi$
$194$			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	$0.987641\pi$
$198$	2.70815	+	6.79590i	0.192459	+	0.482964i
$199$	−6.21327	+	6.21327i	−0.440447	+	0.440447i	−0.892162	−	0.451715i	$-0.850812\pi$
$199$	−6.21327	+	6.21327i	−0.440447	+	0.440447i	0.451715	+	0.892162i	$0.350812\pi$
$200$	−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	−0.999576	−	0.0291269i	$-0.990727\pi$
$227$	−14.6213	+	14.6213i	−0.970449	+	0.970449i	0.0291269	+	0.999576i	$0.490727\pi$
$228$	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	0.213168	−	0.977016i	$-0.431622\pi$
$239$	18.3998	−	18.3998i	1.19018	−	1.19018i	0.977016	−	0.213168i	$-0.0683782\pi$
$240$	−0.952541	−	1.44660i	−0.0614863	−	0.0933779i
$241$	18.2602	+	18.2602i	1.17624	+	1.17624i	0.980694	+	0.195550i	$0.0626492\pi$
$241$	18.2602	+	18.2602i	1.17624	+	1.17624i	0.195550	+	0.980694i	$0.437351\pi$
$242$	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	−0.995075	−	0.0991297i	$-0.968394\pi$
$251$	−17.3355	−	17.3355i	−1.09420	−	1.09420i	−0.0991297	−	0.995075i	$-0.531606\pi$
$252$	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	−0.441526	+	0.897248i	$0.645563\pi$
$257$	−21.4622	+	21.4622i	−1.33877	+	1.33877i	−0.897248	+	0.441526i	$0.854437\pi$
$258$	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	$0.284830\pi$
$269$			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
$273$	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	−0.589196	−	0.807990i	$-0.700555\pi$
$277$	3.64147	−	3.64147i	0.218795	−	0.218795i	0.807990	+	0.589196i	$0.200555\pi$
$278$	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	−0.0109410	−	0.999940i	$-0.503483\pi$
$281$	16.5786	−	16.5786i	0.988999	−	0.988999i	0.999940	+	0.0109410i	$0.00348270\pi$
$282$	−6.25765	−	9.50336i	−0.372637	−	0.565917i
$283$	−4.84935	+	4.84935i	−0.288264	+	0.288264i	−0.836393	−	0.548130i	$-0.815340\pi$
$283$	−4.84935	+	4.84935i	−0.288264	+	0.288264i	0.548130	+	0.836393i	$0.315340\pi$
$284$	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	$-0.835959\pi$
$293$		−	16.8721i		−	0.985681i	0.870120	−	0.492840i	$-0.164041\pi$
$294$	−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	$-0.976399\pi$
$307$		−	2.59584i		−	0.148153i	0.997253	−	0.0740763i	$-0.0236008\pi$
$308$			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	0.626622	−	0.779323i	$-0.284437\pi$
$311$	−2.69292	−	2.69292i	−0.152702	−	0.152702i	−0.779323	+	0.626622i	$0.784437\pi$
$312$	1.66982	−	8.10852i	0.0945347	−	0.459055i
$313$	−7.66085	−	7.66085i	−0.433017	−	0.433017i	0.456636	−	0.889653i	$-0.349054\pi$
$313$	−7.66085	−	7.66085i	−0.433017	−	0.433017i	−0.889653	+	0.456636i	$0.849054\pi$
$314$	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	0.534487	−	0.845177i	$-0.320505\pi$
$331$	−5.65251	−	5.65251i	−0.310690	−	0.310690i	−0.845177	+	0.534487i	$0.820505\pi$
$332$	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	$0.0606446\pi$
$337$			6.95275i			0.378740i	−0.981906	+	0.189370i	$0.939355\pi$
$338$	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	−0.935370	−	0.353671i	$-0.884933\pi$
$347$	−24.0122	−	24.0122i	−1.28904	−	1.28904i	−0.353671	−	0.935370i	$-0.615067\pi$
$348$	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	0.981530	+	0.191310i	$0.0612735\pi$
$353$	22.0357	+	22.0357i	1.17284	+	1.17284i	0.191310	+	0.981530i	$0.438727\pi$
$354$	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	$-0.979928\pi$
$359$		−	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
$372$	−2.45796	+	1.61849i	−0.127439	+	0.0839146i
$373$		−	6.01294i		−	0.311338i	−0.987809	−	0.155669i	$-0.950247\pi$
$373$		−	6.01294i		−	0.311338i	0.987809	−	0.155669i	$-0.0497533\pi$
$374$	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	−0.331717	−	0.943379i	$-0.607628\pi$
$383$	11.9705	−	11.9705i	0.611662	−	0.611662i	0.943379	+	0.331717i	$0.107628\pi$
$384$	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	−0.999550	−	0.0299951i	$-0.990451\pi$
$389$	−19.1226	+	19.1226i	−0.969555	+	0.969555i	0.0299951	+	0.999550i	$0.490451\pi$
$390$	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	$-0.812738\pi$
$397$		−	22.1145i		−	1.10990i	0.831885	−	0.554948i	$-0.187262\pi$
$398$	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	0.965529	−	0.260296i	$-0.0838202\pi$
$401$	14.1223	+	14.1223i	0.705233	+	0.705233i	−0.260296	+	0.965529i	$0.583820\pi$
$402$	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	−0.547232	−	0.836981i	$-0.684319\pi$
$409$	5.85980	−	5.85980i	0.289749	−	0.289749i	0.836981	+	0.547232i	$0.184319\pi$
$410$	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	$-0.0223262\pi$
$420$	−4.30620	+	2.83549i	−0.210121	+	0.138358i
$421$	16.1956	−	16.1956i	0.789327	−	0.789327i	−0.192057	−	0.981384i	$-0.561516\pi$
$421$	16.1956	−	16.1956i	0.789327	−	0.789327i	0.981384	+	0.192057i	$0.0615157\pi$
$422$	−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	0.889900	−	0.456157i	$-0.150774\pi$
$431$	9.00474	+	9.00474i	0.433743	+	0.433743i	−0.456157	+	0.889900i	$0.650774\pi$
$432$	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	0.231298	−	0.972883i	$-0.425703\pi$
$439$	25.2304	−	25.2304i	1.20418	−	1.20418i	0.972883	−	0.231298i	$-0.0742971\pi$
$440$			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	−0.495034	−	0.868874i	$-0.664844\pi$
$449$	7.92152	−	7.92152i	0.373840	−	0.373840i	0.868874	+	0.495034i	$0.164844\pi$
$450$	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	0.0280458	−	0.999607i	$-0.491072\pi$
$457$	−20.7696	−	20.7696i	−0.971561	−	0.971561i	−0.999607	+	0.0280458i	$0.991072\pi$
$458$	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	−0.835555	−	0.549407i	$-0.814854\pi$
$461$	−6.14385	+	6.14385i	−0.286148	+	0.286148i	0.549407	+	0.835555i	$0.314854\pi$
$462$	−10.5008	+	6.91444i	−0.488543	+	0.321689i
$463$	−22.3895	−	22.3895i	−1.04053	−	1.04053i	−0.999143	−	0.0413850i	$-0.986823\pi$
$463$	−22.3895	−	22.3895i	−1.04053	−	1.04053i	−0.0413850	−	0.999143i	$-0.513177\pi$
$464$	−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	$-0.747312\pi$
$467$	0.258047	−	0.258047i	0.0119410	−	0.0119410i	0.713052	+	0.701111i	$0.247312\pi$
$468$	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	0.281804	−	0.959472i	$-0.409067\pi$
$479$	27.1667	−	27.1667i	1.24128	−	1.24128i	0.959472	−	0.281804i	$-0.0909329\pi$
$480$	−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	0.998241	+	0.0592882i	$0.0188831\pi$
$487$	23.3376	+	23.3376i	1.05753	+	1.05753i	0.0592882	+	0.998241i	$0.481117\pi$
$488$		−	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	$-0.998369\pi$
$491$		−	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
$495$	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	−0.896194	−	0.443663i	$-0.853679\pi$
$499$	−10.1088	+	10.1088i	−0.452530	+	0.452530i	0.443663	+	0.896194i	$0.353679\pi$
$500$	−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	−0.474835	−	0.880075i	$-0.657492\pi$
$503$	9.08858	−	9.08858i	0.405240	−	0.405240i	0.880075	+	0.474835i	$0.157492\pi$
$504$	−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	0.990731	−	0.135836i	$-0.0433721\pi$
$523$	19.5508	+	19.5508i	0.854895	+	0.854895i	−0.135836	+	0.990731i	$0.543372\pi$
$524$	−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	0.909360	−	0.416011i	$-0.136572\pi$
$541$	11.4750	+	11.4750i	0.493349	+	0.493349i	−0.416011	+	0.909360i	$0.636572\pi$
$542$	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	−0.257676	−	0.966231i	$-0.582957\pi$
$547$	16.5717	−	16.5717i	0.708555	−	0.708555i	0.966231	+	0.257676i	$0.0829567\pi$
$548$	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	0.304236	−	0.952597i	$-0.401599\pi$
$557$	−15.3019	−	15.3019i	−0.648361	−	0.648361i	−0.952597	+	0.304236i	$0.901599\pi$
$558$	−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	−0.987807	−	0.155683i	$-0.950242\pi$
$563$	−19.7443	+	19.7443i	−0.832124	+	0.832124i	0.155683	+	0.987807i	$0.450242\pi$
$564$	−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	$-0.161936\pi$
$569$	9.21438	+	9.21438i	0.386287	+	0.386287i	−0.487074	+	0.873361i	$0.661936\pi$
$570$	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	0.443013	−	0.896515i	$-0.353909\pi$
$577$	−10.8935	−	10.8935i	−0.453502	−	0.453502i	−0.896515	+	0.443013i	$0.853909\pi$
$578$	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	0.621757	−	0.783210i	$-0.286419\pi$
$587$	−3.91169	−	3.91169i	−0.161453	−	0.161453i	−0.783210	+	0.621757i	$0.786419\pi$
$588$	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	$0.853207\pi$
$594$	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	$0.0979727\pi$
$599$			14.8293i			0.605907i	−0.953005	+	0.302954i	$0.902027\pi$
$600$	−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	−0.393575	−	0.919293i	$-0.628762\pi$
$607$	12.9523	−	12.9523i	0.525718	−	0.525718i	0.919293	+	0.393575i	$0.128762\pi$
$608$			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	$-0.992008\pi$
$613$		−	1.24321i		−	0.0502128i	0.999685	−	0.0251064i	$-0.00799245\pi$
$614$	−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	$-0.798922\pi$
$619$		−	29.3840i		−	1.18104i	0.807023	−	0.590521i	$-0.201078\pi$
$620$	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	−0.0684200	−	0.997657i	$-0.521796\pi$
$631$	23.3422	−	23.3422i	0.929237	−	0.929237i	0.997657	+	0.0684200i	$0.0217958\pi$
$632$	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	$-0.383577\pi$
$642$	12.7089	+	19.3007i	0.501579	+	0.761738i
$643$	7.59274	−	7.59274i	0.299428	−	0.299428i	−0.541362	−	0.840790i	$-0.682091\pi$
$643$	7.59274	−	7.59274i	0.299428	−	0.299428i	0.840790	+	0.541362i	$0.182091\pi$
$644$	−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	$-0.389162\pi$
$647$	−15.2305	−	15.2305i	−0.598773	−	0.598773i	−0.939986	+	0.341213i	$0.889162\pi$
$648$	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	0.0598267	−	0.998209i	$-0.480945\pi$
$653$	−23.9793	−	23.9793i	−0.938382	−	0.938382i	−0.998209	+	0.0598267i	$0.980945\pi$
$654$	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	−0.718508	−	0.695519i	$-0.755174\pi$
$661$	−0.591033	+	0.591033i	−0.0229885	+	0.0229885i	0.695519	+	0.718508i	$0.255174\pi$
$662$			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	−0.324612	−	0.945847i	$-0.605234\pi$
$683$	16.2355	−	16.2355i	0.621235	−	0.621235i	0.945847	+	0.324612i	$0.105234\pi$
$684$	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	$0.0394666\pi$
$691$			6.50183i			0.247341i	−0.992323	+	0.123671i	$0.960533\pi$
$692$			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	−0.350705	+	0.936486i	$0.614058\pi$
$701$	−34.0802	+	34.0802i	−1.28719	+	1.28719i	−0.936486	+	0.350705i	$0.885942\pi$
$702$	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	0.735813	−	0.677185i	$-0.236800\pi$
$709$	1.56111	+	1.56111i	0.0586286	+	0.0586286i	−0.677185	+	0.735813i	$0.736800\pi$
$710$		−	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	$-0.924411\pi$
$719$		−	12.6157i		−	0.470487i	0.971936	−	0.235243i	$-0.0755887\pi$
$720$	−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	−0.0980326	+	0.995183i	$0.531255\pi$
$727$	−29.4763	+	29.4763i	−1.09322	+	1.09322i	−0.995183	+	0.0980326i	$0.968745\pi$
$728$	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	$-0.786706\pi$
$733$		−	33.6287i		−	1.24210i	0.783769	−	0.621052i	$-0.213294\pi$
$734$	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	$0.0413687\pi$
$739$			7.04612i			0.259196i	−0.991567	+	0.129598i	$0.958631\pi$
$740$	−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	$-0.922339\pi$
$751$		−	13.2399i		−	0.483131i	0.970385	−	0.241566i	$-0.0776609\pi$
$752$		−	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	0.992466	+	0.122516i	$0.0390964\pi$
$757$	30.6772	+	30.6772i	1.11498	+	1.11498i	0.122516	+	0.992466i	$0.460904\pi$
$758$	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	−0.193528	−	0.981095i	$-0.561993\pi$
$769$	21.8399	−	21.8399i	0.787567	−	0.787567i	0.981095	+	0.193528i	$0.0619929\pi$
$770$	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	$0.0690535\pi$
$773$			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
$777$	−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	−0.999518	−	0.0310478i	$-0.990116\pi$
$797$	−29.0941	−	29.0941i	−1.03057	−	1.03057i	−0.0310478	−	0.999518i	$-0.509884\pi$
$798$	−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	0.898590	−	0.438789i	$-0.144592\pi$
$809$	13.0781	+	13.0781i	0.459801	+	0.459801i	−0.438789	+	0.898590i	$0.644592\pi$
$810$	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	$0.405307\pi$
$821$			54.7891i			1.91215i	−0.293117	+	0.956076i	$0.594693\pi$
$822$	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	0.140786	−	0.990040i	$-0.455037\pi$
$827$	32.5198	−	32.5198i	1.13083	−	1.13083i	0.990040	−	0.140786i	$-0.0449629\pi$
$828$	7.17631	+	18.0084i	0.249394	+	0.625837i
$829$	−18.3804	+	18.3804i	−0.638377	+	0.638377i	−0.950155	−	0.311778i	$-0.899076\pi$
$829$	−18.3804	+	18.3804i	−0.638377	+	0.638377i	0.311778	+	0.950155i	$0.399076\pi$
$830$		−	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	−0.916221	−	0.400673i	$-0.868776\pi$
$853$	−15.0572	+	15.0572i	−0.515548	+	0.515548i	0.400673	+	0.916221i	$0.368776\pi$
$854$	−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	$-0.846401\pi$
$857$	−12.3474	+	12.3474i	−0.421779	+	0.421779i	0.464037	+	0.885816i	$0.346401\pi$
$858$	−19.7730	−	4.07191i	−0.675038	−	0.139013i
$859$	−39.7979	−	39.7979i	−1.35789	−	1.35789i	−0.876517	−	0.481371i	$-0.840139\pi$
$859$	−39.7979	−	39.7979i	−1.35789	−	1.35789i	−0.481371	−	0.876517i	$-0.659861\pi$
$860$			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	$-0.159077\pi$
$864$	−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	−0.995105	−	0.0988230i	$-0.968492\pi$
$883$	−26.6333	+	26.6333i	−0.896282	+	0.896282i	0.0988230	+	0.995105i	$0.468492\pi$
$884$		−	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	0.636329	−	0.771418i	$-0.280452\pi$
$907$	−4.06839	−	4.06839i	−0.135089	−	0.135089i	−0.771418	+	0.636329i	$0.780452\pi$
$908$	−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	$-0.883065\pi$
$911$	−17.3286	+	17.3286i	−0.574123	+	0.574123i	0.359155	+	0.933278i	$0.383065\pi$
$912$	−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	−0.548127	−	0.836395i	$-0.684659\pi$
$919$	8.73885	−	8.73885i	0.288268	−	0.288268i	0.836395	+	0.548127i	$0.184659\pi$
$920$	−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	$-0.991852\pi$
$941$		−	1.57027i		−	0.0511894i	0.999672	−	0.0255947i	$-0.00814794\pi$
$942$	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	−0.980245	−	0.197788i	$-0.936624\pi$
$947$	−24.0788	+	24.0788i	−0.782456	+	0.782456i	0.197788	+	0.980245i	$0.436624\pi$
$948$	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	0.584913	−	0.811096i	$-0.301129\pi$
$967$	−7.03355	−	7.03355i	−0.226184	−	0.226184i	−0.811096	+	0.584913i	$0.801129\pi$
$968$	−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
$975$	−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	0.989877	+	0.141926i	$0.0453295\pi$
$977$	35.3768	+	35.3768i	1.13180	+	1.13180i	0.141926	+	0.989877i	$0.454671\pi$
$978$	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	−0.914238	−	0.405177i	$-0.867210\pi$
$991$	−16.0253	+	16.0253i	−0.509061	+	0.509061i	0.405177	+	0.914238i	$0.367210\pi$
$992$	−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	0.932782	−	0.360442i	$-0.117374\pi$
$997$	18.0718	+	18.0718i	0.572340	+	0.572340i	−0.360442	+	0.932782i	$0.617374\pi$
$998$	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.191.9	✓	40
3.2	odd	2	inner	1110.2.u.e.191.18	yes	40
37.31	odd	4	inner	1110.2.u.e.401.18	yes	40
111.68	even	4	inner	1110.2.u.e.401.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.9	✓	40	1.1	even	1	trivial
1110.2.u.e.191.18	yes	40	3.2	odd	2	inner
1110.2.u.e.401.9	yes	40	111.68	even	4	inner
1110.2.u.e.401.18	yes	40	37.31	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.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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