LMFDB - Embedded newform 690.3.k.b.277.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.23
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.24543 + 3.80358i) q^{5} -2.44949 q^{6} +(-6.75617 - 6.75617i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.24543 + 3.80358i) q^{5} -2.44949 q^{6} +(-6.75617 - 6.75617i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(0.558148 - 7.04900i) q^{10} +21.5756 q^{11} +(2.44949 + 2.44949i) q^{12} +(-1.08406 + 1.08406i) q^{13} +13.5123i q^{14} +(8.63323 + 0.683589i) q^{15} -4.00000 q^{16} +(4.33966 + 4.33966i) q^{17} +(-3.00000 + 3.00000i) q^{18} +1.61010i q^{19} +(-7.60715 + 6.49086i) q^{20} -16.5492 q^{21} +(-21.5756 - 21.5756i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-3.93439 + 24.6885i) q^{25} +2.16811 q^{26} +(-3.67423 - 3.67423i) q^{27} +(13.5123 - 13.5123i) q^{28} -10.6578i q^{29} +(-7.94964 - 9.31682i) q^{30} +21.7512 q^{31} +(4.00000 + 4.00000i) q^{32} +(26.4246 - 26.4246i) q^{33} -8.67933i q^{34} +(3.77094 - 47.6243i) q^{35} +6.00000 q^{36} +(-18.5343 - 18.5343i) q^{37} +(1.61010 - 1.61010i) q^{38} +2.65538i q^{39} +(14.0980 + 1.11630i) q^{40} +55.4586 q^{41} +(16.5492 + 16.5492i) q^{42} +(45.1244 - 45.1244i) q^{43} +43.1512i q^{44} +(11.4107 - 9.73629i) q^{45} +6.78233 q^{46} +(-40.0209 - 40.0209i) q^{47} +(-4.89898 + 4.89898i) q^{48} +42.2916i q^{49} +(28.6229 - 20.7541i) q^{50} +10.6300 q^{51} +(-2.16811 - 2.16811i) q^{52} +(-22.8485 + 22.8485i) q^{53} +7.34847i q^{54} +(70.0220 + 82.0644i) q^{55} -27.0247 q^{56} +(1.97196 + 1.97196i) q^{57} +(-10.6578 + 10.6578i) q^{58} -45.0275i q^{59} +(-1.36718 + 17.2665i) q^{60} +106.893 q^{61} +(-21.7512 - 21.7512i) q^{62} +(-20.2685 + 20.2685i) q^{63} -8.00000i q^{64} +(-7.64152 - 0.605064i) q^{65} -52.8492 q^{66} +(62.2296 + 62.2296i) q^{67} +(-8.67933 + 8.67933i) q^{68} +8.30662i q^{69} +(-51.3952 + 43.8533i) q^{70} +95.7602 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-18.3047 + 18.3047i) q^{73} +37.0687i q^{74} +(25.4185 + 35.0557i) q^{75} -3.22020 q^{76} +(-145.768 - 145.768i) q^{77} +(2.65538 - 2.65538i) q^{78} -74.1858i q^{79} +(-12.9817 - 15.2143i) q^{80} -9.00000 q^{81} +(-55.4586 - 55.4586i) q^{82} +(29.2294 - 29.2294i) q^{83} -33.0983i q^{84} +(-2.42217 + 30.5903i) q^{85} -90.2487 q^{86} +(-13.0530 - 13.0530i) q^{87} +(43.1512 - 43.1512i) q^{88} -148.863i q^{89} +(-21.1470 - 1.67444i) q^{90} +14.6481 q^{91} +(-6.78233 - 6.78233i) q^{92} +(26.6397 - 26.6397i) q^{93} +80.0419i q^{94} +(-6.12413 + 5.22546i) q^{95} +9.79796 q^{96} +(-47.9480 - 47.9480i) q^{97} +(42.2916 - 42.2916i) q^{98} -64.7268i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$	3.24543	+	3.80358i	0.649086	+	0.760715i
$5$	3.24543	+	3.80358i	0.649086	+	0.760715i
$6$	−2.44949			−0.408248
$7$	−6.75617	−	6.75617i	−0.965167	−	0.965167i	0.0342467	−	0.999413i	$-0.489097\pi$
$7$	−6.75617	−	6.75617i	−0.965167	−	0.965167i	−0.999413	+	0.0342467i	$0.989097\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	0.558148	−	7.04900i	0.0558148	−	0.704900i
$11$	21.5756			1.96142			0.980708	−	0.195477i	$-0.0626254\pi$
$11$	21.5756			1.96142			0.980708	+	0.195477i	$0.0626254\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−1.08406	+	1.08406i	−0.0833889	+	0.0833889i	−0.747571	−	0.664182i	$-0.768780\pi$
$13$	−1.08406	+	1.08406i	−0.0833889	+	0.0833889i	0.664182	+	0.747571i	$0.268780\pi$
$14$			13.5123i			0.965167i
$15$	8.63323	+	0.683589i	0.575549	+	0.0455726i
$16$	−4.00000			−0.250000
$17$	4.33966	+	4.33966i	0.255274	+	0.255274i	0.823129	−	0.567855i	$-0.192226\pi$
$17$	4.33966	+	4.33966i	0.255274	+	0.255274i	−0.567855	+	0.823129i	$0.692226\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			1.61010i			0.0847420i	0.999102	+	0.0423710i	$0.0134911\pi$
$19$			1.61010i			0.0847420i	−0.999102	+	0.0423710i	$0.986509\pi$
$20$	−7.60715	+	6.49086i	−0.380358	+	0.324543i
$21$	−16.5492			−0.788055
$22$	−21.5756	−	21.5756i	−0.980708	−	0.980708i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−3.93439	+	24.6885i	−0.157376	+	0.987539i
$26$	2.16811			0.0833889
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	13.5123	−	13.5123i	0.482583	−	0.482583i
$29$		−	10.6578i		−	0.367509i	−0.982972	−	0.183754i	$-0.941175\pi$
$29$		−	10.6578i		−	0.367509i	0.982972	−	0.183754i	$-0.0588251\pi$
$30$	−7.94964	−	9.31682i	−0.264988	−	0.310561i
$31$	21.7512			0.701653			0.350826	−	0.936441i	$-0.385901\pi$
$31$	21.7512			0.701653			0.350826	+	0.936441i	$0.385901\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	26.4246	−	26.4246i	0.800745	−	0.800745i
$34$		−	8.67933i		−	0.255274i
$35$	3.77094	−	47.6243i	0.107741	−	1.36069i
$36$	6.00000			0.166667
$37$	−18.5343	−	18.5343i	−0.500928	−	0.500928i	0.410798	−	0.911726i	$-0.365250\pi$
$37$	−18.5343	−	18.5343i	−0.500928	−	0.500928i	−0.911726	+	0.410798i	$0.865250\pi$
$38$	1.61010	−	1.61010i	0.0423710	−	0.0423710i
$39$			2.65538i			0.0680868i
$40$	14.0980	+	1.11630i	0.352450	+	0.0279074i
$41$	55.4586			1.35265			0.676325	−	0.736604i	$-0.263572\pi$
$41$	55.4586			1.35265			0.676325	+	0.736604i	$0.263572\pi$
$42$	16.5492	+	16.5492i	0.394028	+	0.394028i
$43$	45.1244	−	45.1244i	1.04940	−	1.04940i	0.0506893	−	0.998714i	$-0.483858\pi$
$43$	45.1244	−	45.1244i	1.04940	−	1.04940i	0.998714	−	0.0506893i	$-0.0161418\pi$
$44$			43.1512i			0.980708i
$45$	11.4107	−	9.73629i	0.253572	−	0.216362i
$46$	6.78233			0.147442
$47$	−40.0209	−	40.0209i	−0.851509	−	0.851509i	0.138810	−	0.990319i	$-0.455672\pi$
$47$	−40.0209	−	40.0209i	−0.851509	−	0.851509i	−0.990319	+	0.138810i	$0.955672\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			42.2916i			0.863094i
$50$	28.6229	−	20.7541i	0.572457	−	0.415082i
$51$	10.6300			0.208431
$52$	−2.16811	−	2.16811i	−0.0416945	−	0.0416945i
$53$	−22.8485	+	22.8485i	−0.431105	+	0.431105i	−0.889004	−	0.457899i	$-0.848602\pi$
$53$	−22.8485	+	22.8485i	−0.431105	+	0.431105i	0.457899	+	0.889004i	$0.348602\pi$
$54$			7.34847i			0.136083i
$55$	70.0220	+	82.0644i	1.27313	+	1.49208i
$56$	−27.0247			−0.482583
$57$	1.97196	+	1.97196i	0.0345958	+	0.0345958i
$58$	−10.6578	+	10.6578i	−0.183754	+	0.183754i
$59$		−	45.0275i		−	0.763178i	−0.924332	−	0.381589i	$-0.875377\pi$
$59$		−	45.0275i		−	0.763178i	0.924332	−	0.381589i	$-0.124623\pi$
$60$	−1.36718	+	17.2665i	−0.0227863	+	0.287774i
$61$	106.893			1.75235			0.876174	−	0.481995i	$-0.160088\pi$
$61$	106.893			1.75235			0.876174	+	0.481995i	$0.160088\pi$
$62$	−21.7512	−	21.7512i	−0.350826	−	0.350826i
$63$	−20.2685	+	20.2685i	−0.321722	+	0.321722i
$64$		−	8.00000i		−	0.125000i
$65$	−7.64152	−	0.605064i	−0.117562	−	0.00930867i
$66$	−52.8492			−0.800745
$67$	62.2296	+	62.2296i	0.928800	+	0.928800i	0.997629	−	0.0688280i	$-0.0219260\pi$
$67$	62.2296	+	62.2296i	0.928800	+	0.928800i	−0.0688280	+	0.997629i	$0.521926\pi$
$68$	−8.67933	+	8.67933i	−0.127637	+	0.127637i
$69$			8.30662i			0.120386i
$70$	−51.3952	+	43.8533i	−0.734217	+	0.626476i
$71$	95.7602			1.34874			0.674368	−	0.738396i	$-0.264416\pi$
$71$	95.7602			1.34874			0.674368	+	0.738396i	$0.264416\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−18.3047	+	18.3047i	−0.250749	+	0.250749i	−0.821278	−	0.570529i	$-0.806738\pi$
$73$	−18.3047	+	18.3047i	−0.250749	+	0.250749i	0.570529	+	0.821278i	$0.306738\pi$
$74$			37.0687i			0.500928i
$75$	25.4185	+	35.0557i	0.338913	+	0.467409i
$76$	−3.22020			−0.0423710
$77$	−145.768	−	145.768i	−1.89309	−	1.89309i
$78$	2.65538	−	2.65538i	0.0340434	−	0.0340434i
$79$		−	74.1858i		−	0.939061i	−0.882916	−	0.469530i	$-0.844423\pi$
$79$		−	74.1858i		−	0.939061i	0.882916	−	0.469530i	$-0.155577\pi$
$80$	−12.9817	−	15.2143i	−0.162271	−	0.190179i
$81$	−9.00000			−0.111111
$82$	−55.4586	−	55.4586i	−0.676325	−	0.676325i
$83$	29.2294	−	29.2294i	0.352162	−	0.352162i	−0.508751	−	0.860913i	$-0.669893\pi$
$83$	29.2294	−	29.2294i	0.352162	−	0.352162i	0.860913	+	0.508751i	$0.169893\pi$
$84$		−	33.0983i		−	0.394028i
$85$	−2.42217	+	30.5903i	−0.0284962	+	0.359886i
$86$	−90.2487			−1.04940
$87$	−13.0530	−	13.0530i	−0.150035	−	0.150035i
$88$	43.1512	−	43.1512i	0.490354	−	0.490354i
$89$		−	148.863i		−	1.67261i	−0.548261	−	0.836307i	$-0.684710\pi$
$89$		−	148.863i		−	1.67261i	0.548261	−	0.836307i	$-0.315290\pi$
$90$	−21.1470	−	1.67444i	−0.234967	−	0.0186049i
$91$	14.6481			0.160968
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	26.6397	−	26.6397i	0.286449	−	0.286449i
$94$			80.0419i			0.851509i
$95$	−6.12413	+	5.22546i	−0.0644645	+	0.0550048i
$96$	9.79796			0.102062
$97$	−47.9480	−	47.9480i	−0.494309	−	0.494309i	0.415352	−	0.909661i	$-0.363659\pi$
$97$	−47.9480	−	47.9480i	−0.494309	−	0.494309i	−0.909661	+	0.415352i	$0.863659\pi$
$98$	42.2916	−	42.2916i	0.431547	−	0.431547i
$99$		−	64.7268i		−	0.653806i
$100$	−49.3769	−	7.86878i	−0.493769	−	0.0786878i
$101$	−148.987			−1.47512			−0.737558	−	0.675284i	$-0.764021\pi$
$101$	−148.987			−1.47512			−0.737558	+	0.675284i	$0.764021\pi$
$102$	−10.6300	−	10.6300i	−0.104215	−	0.104215i
$103$	10.6269	−	10.6269i	0.103174	−	0.103174i	−0.653636	−	0.756809i	$-0.726757\pi$
$103$	10.6269	−	10.6269i	0.103174	−	0.103174i	0.756809	+	0.653636i	$0.226757\pi$
$104$			4.33622i			0.0416945i
$105$	−53.7091	−	62.9460i	−0.511515	−	0.599486i
$106$	45.6971			0.431105
$107$	65.2102	+	65.2102i	0.609442	+	0.609442i	0.942800	−	0.333359i	$-0.108182\pi$
$107$	65.2102	+	65.2102i	0.609442	+	0.609442i	−0.333359	+	0.942800i	$0.608182\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	64.0878i		−	0.587962i	−0.955811	−	0.293981i	$-0.905020\pi$
$109$		−	64.0878i		−	0.587962i	0.955811	−	0.293981i	$-0.0949802\pi$
$110$	12.0424	−	152.086i	0.109476	−	1.38260i
$111$	−45.3997			−0.409006
$112$	27.0247	+	27.0247i	0.241292	+	0.241292i
$113$	−25.5020	+	25.5020i	−0.225682	+	0.225682i	−0.810886	−	0.585204i	$-0.801014\pi$
$113$	−25.5020	+	25.5020i	−0.225682	+	0.225682i	0.585204	+	0.810886i	$0.301014\pi$
$114$		−	3.94392i		−	0.0345958i
$115$	−23.9043	−	1.89277i	−0.207864	−	0.0164589i
$116$	21.3155			0.183754
$117$	3.25217	+	3.25217i	0.0277963	+	0.0277963i
$118$	−45.0275	+	45.0275i	−0.381589	+	0.381589i
$119$		−	58.6390i		−	0.492764i
$120$	18.6336	−	15.8993i	0.155280	−	0.132494i
$121$	344.506			2.84716
$122$	−106.893	−	106.893i	−0.876174	−	0.876174i
$123$	67.9227	−	67.9227i	0.552217	−	0.552217i
$124$			43.5025i			0.350826i
$125$	−106.673	+	65.1599i	−0.853386	+	0.521279i
$126$	40.5370			0.321722
$127$	45.7519	+	45.7519i	0.360251	+	0.360251i	0.863905	−	0.503654i	$-0.168011\pi$
$127$	45.7519	+	45.7519i	0.360251	+	0.360251i	−0.503654	+	0.863905i	$0.668011\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	110.532i		−	0.856835i
$130$	7.03645	+	8.24658i	0.0541266	+	0.0634352i
$131$	72.3213			0.552071			0.276035	−	0.961147i	$-0.410979\pi$
$131$	72.3213			0.552071			0.276035	+	0.961147i	$0.410979\pi$
$132$	52.8492	+	52.8492i	0.400373	+	0.400373i
$133$	10.8781	−	10.8781i	0.0817902	−	0.0817902i
$134$		−	124.459i		−	0.928800i
$135$	2.05077	−	25.8997i	0.0151909	−	0.191850i
$136$	17.3587			0.127637
$137$	−176.166	−	176.166i	−1.28588	−	1.28588i	−0.937264	−	0.348621i	$-0.886650\pi$
$137$	−176.166	−	176.166i	−1.28588	−	1.28588i	−0.348621	−	0.937264i	$-0.613350\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$			113.493i			0.816494i	0.912871	+	0.408247i	$0.133860\pi$
$139$			113.493i			0.816494i	−0.912871	+	0.408247i	$0.866140\pi$
$140$	95.2485	+	7.54188i	0.680346	+	0.0538706i
$141$	−98.0309			−0.695254
$142$	−95.7602	−	95.7602i	−0.674368	−	0.674368i
$143$	−23.3891	+	23.3891i	−0.163560	+	0.163560i
$144$			12.0000i			0.0833333i
$145$	40.5376	−	34.5890i	0.279570	−	0.238545i
$146$	36.6093			0.250749
$147$	51.7964	+	51.7964i	0.352356	+	0.352356i
$148$	37.0687	−	37.0687i	0.250464	−	0.250464i
$149$			221.934i			1.48949i	0.667349	+	0.744745i	$0.267429\pi$
$149$			221.934i			1.48949i	−0.667349	+	0.744745i	$0.732571\pi$
$150$	9.63725	−	60.4742i	0.0642483	−	0.403161i
$151$	−180.400			−1.19470			−0.597350	−	0.801981i	$-0.703780\pi$
$151$	−180.400			−1.19470			−0.597350	+	0.801981i	$0.703780\pi$
$152$	3.22020	+	3.22020i	0.0211855	+	0.0211855i
$153$	13.0190	−	13.0190i	0.0850914	−	0.0850914i
$154$			291.536i			1.89309i
$155$	70.5921	+	82.7325i	0.455433	+	0.533758i
$156$	−5.31077			−0.0340434
$157$	12.4596	+	12.4596i	0.0793604	+	0.0793604i	0.745673	−	0.666312i	$-0.232128\pi$
$157$	12.4596	+	12.4596i	0.0793604	+	0.0793604i	−0.666312	+	0.745673i	$0.732128\pi$
$158$	−74.1858	+	74.1858i	−0.469530	+	0.469530i
$159$			55.9673i			0.351995i
$160$	−2.23259	+	28.1960i	−0.0139537	+	0.176225i
$161$	45.8226			0.284612
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−117.984	+	117.984i	−0.723827	+	0.723827i	−0.969382	−	0.245556i	$-0.921030\pi$
$163$	−117.984	+	117.984i	−0.723827	+	0.723827i	0.245556	+	0.969382i	$0.421030\pi$
$164$			110.917i			0.676325i
$165$	186.267	+	14.7488i	1.12889	+	0.0893869i
$166$	−58.4589			−0.352162
$167$	158.202	+	158.202i	0.947318	+	0.947318i	0.998680	−	0.0513618i	$-0.0163562\pi$
$167$	158.202	+	158.202i	0.947318	+	0.947318i	−0.0513618	+	0.998680i	$0.516356\pi$
$168$	−33.0983	+	33.0983i	−0.197014	+	0.197014i
$169$			166.650i			0.986093i
$170$	33.0125	−	28.1681i	0.194191	−	0.165695i
$171$	4.83029			0.0282473
$172$	90.2487	+	90.2487i	0.524702	+	0.524702i
$173$	−45.6033	+	45.6033i	−0.263603	+	0.263603i	−0.826516	−	0.562913i	$-0.809681\pi$
$173$	−45.6033	+	45.6033i	−0.263603	+	0.263603i	0.562913	+	0.826516i	$0.309681\pi$
$174$			26.1061i			0.150035i
$175$	193.381	−	140.218i	1.10503	−	0.801246i
$176$	−86.3023			−0.490354
$177$	−55.1472	−	55.1472i	−0.311566	−	0.311566i
$178$	−148.863	+	148.863i	−0.836307	+	0.836307i
$179$			111.478i			0.622781i	0.950282	+	0.311391i	$0.100795\pi$
$179$			111.478i			0.622781i	−0.950282	+	0.311391i	$0.899205\pi$
$180$	19.4726	+	22.8215i	0.108181	+	0.126786i
$181$	−247.255			−1.36605			−0.683025	−	0.730395i	$-0.739336\pi$
$181$	−247.255			−1.36605			−0.683025	+	0.730395i	$0.739336\pi$
$182$	−14.6481	−	14.6481i	−0.0804842	−	0.0804842i
$183$	130.917	−	130.917i	0.715393	−	0.715393i
$184$			13.5647i			0.0737210i
$185$	10.3449	−	130.649i	0.0559184	−	0.706209i
$186$	−53.2794			−0.286449
$187$	93.6308	+	93.6308i	0.500699	+	0.500699i
$188$	80.0419	−	80.0419i	0.425755	−	0.425755i
$189$			49.6475i			0.262685i
$190$	11.3496	+	0.898673i	0.0597347	+	0.00472986i
$191$	−113.944			−0.596567			−0.298283	−	0.954477i	$-0.596414\pi$
$191$	−113.944			−0.596567			−0.298283	+	0.954477i	$0.596414\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−39.6216	+	39.6216i	−0.205293	+	0.205293i	−0.802263	−	0.596970i	$-0.796371\pi$
$193$	−39.6216	+	39.6216i	−0.205293	+	0.205293i	0.596970	+	0.802263i	$0.296371\pi$
$194$			95.8960i			0.494309i
$195$	−10.1000	+	8.61786i	−0.0517946	+	0.0441941i
$196$	−84.5832			−0.431547
$197$	−167.861	−	167.861i	−0.852085	−	0.852085i	0.138304	−	0.990390i	$-0.455835\pi$
$197$	−167.861	−	167.861i	−0.852085	−	0.852085i	−0.990390	+	0.138304i	$0.955835\pi$
$198$	−64.7268	+	64.7268i	−0.326903	+	0.326903i
$199$			177.527i			0.892094i	0.895009	+	0.446047i	$0.147169\pi$
$199$			177.527i			0.892094i	−0.895009	+	0.446047i	$0.852831\pi$
$200$	41.5082	+	57.2457i	0.207541	+	0.286229i
$201$	152.431			0.758362
$202$	148.987	+	148.987i	0.737558	+	0.737558i
$203$	−72.0056	+	72.0056i	−0.354707	+	0.354707i
$204$			21.2599i			0.104215i
$205$	179.987	+	210.941i	0.877985	+	1.02898i
$206$	−21.2538			−0.103174
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	4.33622	−	4.33622i	0.0208472	−	0.0208472i
$209$			34.7388i			0.166214i
$210$	−9.23688	+	116.655i	−0.0439852	+	0.555501i
$211$	−236.548			−1.12108			−0.560541	−	0.828127i	$-0.689407\pi$
$211$	−236.548			−1.12108			−0.560541	+	0.828127i	$0.689407\pi$
$212$	−45.6971	−	45.6971i	−0.215552	−	0.215552i
$213$	117.282	−	117.282i	0.550619	−	0.550619i
$214$		−	130.420i		−	0.609442i
$215$	318.082	+	25.1861i	1.47945	+	0.117145i
$216$	−14.6969			−0.0680414
$217$	−146.955	−	146.955i	−0.677212	−	0.677212i
$218$	−64.0878	+	64.0878i	−0.293981	+	0.293981i
$219$			44.8371i			0.204736i
$220$	−164.129	+	140.044i	−0.746040	+	0.636564i
$221$	−9.40887			−0.0425741
$222$	45.3997	+	45.3997i	0.204503	+	0.204503i
$223$	274.188	−	274.188i	1.22954	−	1.22954i	0.265405	−	0.964137i	$-0.414494\pi$
$223$	274.188	−	274.188i	1.22954	−	1.22954i	0.964137	−	0.265405i	$-0.0855055\pi$
$224$		−	54.0493i		−	0.241292i
$225$	74.0654	+	11.8032i	0.329180	+	0.0524585i
$226$	51.0041			0.225682
$227$	−61.8993	−	61.8993i	−0.272684	−	0.272684i	0.557496	−	0.830180i	$-0.311762\pi$
$227$	−61.8993	−	61.8993i	−0.272684	−	0.272684i	−0.830180	+	0.557496i	$0.811762\pi$
$228$	−3.94392	+	3.94392i	−0.0172979	+	0.0172979i
$229$			421.368i			1.84003i	0.391878	+	0.920017i	$0.371826\pi$
$229$			421.368i			1.84003i	−0.391878	+	0.920017i	$0.628174\pi$
$230$	22.0116	+	25.7971i	0.0957025	+	0.112161i
$231$	−357.058			−1.54570
$232$	−21.3155	−	21.3155i	−0.0918772	−	0.0918772i
$233$	225.024	−	225.024i	0.965768	−	0.965768i	−0.0336653	−	0.999433i	$-0.510718\pi$
$233$	225.024	−	225.024i	0.965768	−	0.965768i	0.999433	+	0.0336653i	$0.0107180\pi$
$234$		−	6.50434i		−	0.0277963i
$235$	22.3376	−	282.108i	0.0950536	−	1.20046i
$236$	90.0550			0.381589
$237$	−90.8587	−	90.8587i	−0.383370	−	0.383370i
$238$	−58.6390	+	58.6390i	−0.246382	+	0.246382i
$239$			222.316i			0.930193i	0.885260	+	0.465096i	$0.153980\pi$
$239$			222.316i			0.930193i	−0.885260	+	0.465096i	$0.846020\pi$
$240$	−34.5329	−	2.73436i	−0.143887	−	0.0113932i
$241$	37.5718			0.155900			0.0779498	−	0.996957i	$-0.475163\pi$
$241$	37.5718			0.155900			0.0779498	+	0.996957i	$0.475163\pi$
$242$	−344.506	−	344.506i	−1.42358	−	1.42358i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			213.787i			0.876174i
$245$	−160.859	+	137.254i	−0.656568	+	0.560222i
$246$	−135.845			−0.552217
$247$	−1.74544	−	1.74544i	−0.00706654	−	0.00706654i
$248$	43.5025	−	43.5025i	0.175413	−	0.175413i
$249$		−	71.5972i		−	0.287539i
$250$	171.833	+	41.5134i	0.687333	+	0.166053i
$251$	117.012			0.466183			0.233091	−	0.972455i	$-0.425116\pi$
$251$	117.012			0.466183			0.233091	+	0.972455i	$0.425116\pi$
$252$	−40.5370	−	40.5370i	−0.160861	−	0.160861i
$253$	−73.1664	+	73.1664i	−0.289195	+	0.289195i
$254$		−	91.5037i		−	0.360251i
$255$	34.4988	+	40.4319i	0.135289	+	0.158556i
$256$	16.0000			0.0625000
$257$	255.718	+	255.718i	0.995013	+	0.995013i	0.999988	−	0.00497439i	$-0.00158340\pi$
$257$	255.718	+	255.718i	0.995013	+	0.995013i	−0.00497439	+	0.999988i	$0.501583\pi$
$258$	−110.532	+	110.532i	−0.428417	+	0.428417i
$259$			250.442i			0.966958i
$260$	1.21013	−	15.2830i	0.00465434	−	0.0587809i
$261$	−31.9733			−0.122503
$262$	−72.3213	−	72.3213i	−0.276035	−	0.276035i
$263$	97.8083	−	97.8083i	0.371895	−	0.371895i	−0.496272	−	0.868167i	$-0.665298\pi$
$263$	97.8083	−	97.8083i	0.371895	−	0.371895i	0.868167	+	0.496272i	$0.165298\pi$
$264$		−	105.698i		−	0.400373i
$265$	−161.060	−	12.7529i	−0.607772	−	0.0481241i
$266$	−21.7562			−0.0817902
$267$	−182.319	−	182.319i	−0.682842	−	0.682842i
$268$	−124.459	+	124.459i	−0.464400	+	0.464400i
$269$			247.337i			0.919469i	0.888057	+	0.459734i	$0.152055\pi$
$269$			247.337i			0.919469i	−0.888057	+	0.459734i	$0.847945\pi$
$270$	−27.9505	+	23.8489i	−0.103520	+	0.0883294i
$271$	−174.097			−0.642424			−0.321212	−	0.947007i	$-0.604090\pi$
$271$	−174.097			−0.642424			−0.321212	+	0.947007i	$0.604090\pi$
$272$	−17.3587	−	17.3587i	−0.0638186	−	0.0638186i
$273$	17.9402	−	17.9402i	0.0657151	−	0.0657151i
$274$			352.332i			1.28588i
$275$	−84.8867	+	532.668i	−0.308679	+	1.93698i
$276$	−16.6132			−0.0601929
$277$	66.2186	+	66.2186i	0.239056	+	0.239056i	0.816459	−	0.577403i	$-0.195934\pi$
$277$	66.2186	+	66.2186i	0.239056	+	0.239056i	−0.577403	+	0.816459i	$0.695934\pi$
$278$	113.493	−	113.493i	0.408247	−	0.408247i
$279$		−	65.2537i		−	0.233884i
$280$	−87.7066	−	102.790i	−0.313238	−	0.367109i
$281$	90.6244			0.322507			0.161253	−	0.986913i	$-0.448446\pi$
$281$	90.6244			0.322507			0.161253	+	0.986913i	$0.448446\pi$
$282$	98.0309	+	98.0309i	0.347627	+	0.347627i
$283$	−351.544	+	351.544i	−1.24221	+	1.24221i	−0.283121	+	0.959084i	$0.591370\pi$
$283$	−351.544	+	351.544i	−1.24221	+	1.24221i	−0.959084	+	0.283121i	$0.908630\pi$
$284$			191.520i			0.674368i
$285$	−1.10065	+	13.9004i	−0.00386191	+	0.0487732i
$286$	46.7783			0.163560
$287$	−374.688	−	374.688i	−1.30553	−	1.30553i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	251.335i		−	0.869670i
$290$	−75.1266	−	5.94860i	−0.259057	−	0.0205124i
$291$	−117.448			−0.403602
$292$	−36.6093	−	36.6093i	−0.125374	−	0.125374i
$293$	40.2972	−	40.2972i	0.137533	−	0.137533i	−0.634988	−	0.772522i	$-0.718995\pi$
$293$	40.2972	−	40.2972i	0.137533	−	0.137533i	0.772522	+	0.634988i	$0.218995\pi$
$294$		−	103.593i		−	0.352356i
$295$	171.266	−	146.134i	0.580561	−	0.495368i
$296$	−74.1374			−0.250464
$297$	−79.2738	−	79.2738i	−0.266915	−	0.266915i
$298$	221.934	−	221.934i	0.744745	−	0.744745i
$299$		−	7.35242i		−	0.0245900i
$300$	−70.1114	+	50.8369i	−0.233705	+	0.169456i
$301$	−609.735			−2.02570
$302$	180.400	+	180.400i	0.597350	+	0.597350i
$303$	−182.471	+	182.471i	−0.602213	+	0.602213i
$304$		−	6.44039i		−	0.0211855i
$305$	346.914	+	406.577i	1.13742	+	1.33304i
$306$	−26.0380			−0.0850914
$307$	230.119	+	230.119i	0.749575	+	0.749575i	0.974399	−	0.224825i	$-0.0721809\pi$
$307$	230.119	+	230.119i	0.749575	+	0.749575i	−0.224825	+	0.974399i	$0.572181\pi$
$308$	291.536	−	291.536i	0.946547	−	0.946547i
$309$		−	26.0304i		−	0.0842409i
$310$	12.1404	−	153.325i	0.0391626	−	0.494595i
$311$	−350.808			−1.12800			−0.564000	−	0.825775i	$-0.690738\pi$
$311$	−350.808			−1.12800			−0.564000	+	0.825775i	$0.690738\pi$
$312$	5.31077	+	5.31077i	0.0170217	+	0.0170217i
$313$	299.963	−	299.963i	0.958348	−	0.958348i	−0.0408185	−	0.999167i	$-0.512997\pi$
$313$	299.963	−	299.963i	0.958348	−	0.958348i	0.999167	+	0.0408185i	$0.0129965\pi$
$314$		−	24.9192i		−	0.0793604i
$315$	−142.873	−	11.3128i	−0.453564	−	0.0359137i
$316$	148.372			0.469530
$317$	−270.830	−	270.830i	−0.854353	−	0.854353i	0.136313	−	0.990666i	$-0.456475\pi$
$317$	−270.830	−	270.830i	−0.854353	−	0.854353i	−0.990666	+	0.136313i	$0.956475\pi$
$318$	55.9673	−	55.9673i	0.175998	−	0.175998i
$319$		−	229.947i		−	0.720838i
$320$	30.4286	−	25.9634i	0.0950894	−	0.0811357i
$321$	159.732			0.497607
$322$	−45.8226	−	45.8226i	−0.142306	−	0.142306i
$323$	−6.98728	+	6.98728i	−0.0216325	+	0.0216325i
$324$		−	18.0000i		−	0.0555556i
$325$	−22.4986	−	31.0288i	−0.0692264	−	0.0954732i
$326$	235.967			0.723827
$327$	−78.4912	−	78.4912i	−0.240034	−	0.240034i
$328$	110.917	−	110.917i	0.338162	−	0.338162i
$329$			540.776i			1.64370i
$330$	−171.518	−	201.016i	−0.519752	−	0.609139i
$331$	−331.091			−1.00028			−0.500138	−	0.865946i	$-0.666717\pi$
$331$	−331.091			−1.00028			−0.500138	+	0.865946i	$0.666717\pi$
$332$	58.4589	+	58.4589i	0.176081	+	0.176081i
$333$	−55.6030	+	55.6030i	−0.166976	+	0.166976i
$334$		−	316.404i		−	0.947318i
$335$	−34.7334	+	438.657i	−0.103682	+	1.30942i
$336$	66.1966			0.197014
$337$	353.159	+	353.159i	1.04795	+	1.04795i	0.998791	+	0.0491601i	$0.0156545\pi$
$337$	353.159	+	353.159i	1.04795	+	1.04795i	0.0491601	+	0.998791i	$0.484346\pi$
$338$	166.650	−	166.650i	0.493046	−	0.493046i
$339$			62.4670i			0.184268i
$340$	−61.1806	−	4.84435i	−0.179943	−	0.0142481i
$341$	469.296			1.37623
$342$	−4.83029	−	4.83029i	−0.0141237	−	0.0141237i
$343$	−45.3232	+	45.3232i	−0.132138	+	0.132138i
$344$		−	180.497i		−	0.524702i
$345$	−31.5949	+	26.9586i	−0.0915794	+	0.0781407i
$346$	91.2066			0.263603
$347$	−60.6618	−	60.6618i	−0.174818	−	0.174818i	0.614274	−	0.789092i	$-0.289449\pi$
$347$	−60.6618	−	60.6618i	−0.174818	−	0.174818i	−0.789092	+	0.614274i	$0.789449\pi$
$348$	26.1061	−	26.1061i	0.0750174	−	0.0750174i
$349$			185.071i			0.530288i	0.964209	+	0.265144i	$0.0854195\pi$
$349$			185.071i			0.530288i	−0.964209	+	0.265144i	$0.914580\pi$
$350$	−333.599	−	53.1628i	−0.953140	−	0.151894i
$351$	7.96615			0.0226956
$352$	86.3023	+	86.3023i	0.245177	+	0.245177i
$353$	−383.652	+	383.652i	−1.08683	+	1.08683i	−0.0909792	+	0.995853i	$0.529000\pi$
$353$	−383.652	+	383.652i	−1.08683	+	1.08683i	−0.995853	+	0.0909792i	$0.971000\pi$
$354$			110.294i			0.311566i
$355$	310.783	+	364.231i	0.875445	+	1.02600i
$356$	297.725			0.836307
$357$	−71.8178	−	71.8178i	−0.201170	−	0.201170i
$358$	111.478	−	111.478i	0.311391	−	0.311391i
$359$		−	7.62023i		−	0.0212263i	−0.999944	−	0.0106131i	$-0.996622\pi$
$359$		−	7.62023i		−	0.0212263i	0.999944	−	0.0106131i	$-0.00337833\pi$
$360$	3.34889	−	42.2940i	0.00930247	−	0.117483i
$361$	358.408			0.992819
$362$	247.255	+	247.255i	0.683025	+	0.683025i
$363$	421.932	−	421.932i	1.16235	−	1.16235i
$364$			29.2963i			0.0804842i
$365$	−129.030	−	10.2167i	−0.353506	−	0.0279910i
$366$	−261.834			−0.715393
$367$	2.44002	+	2.44002i	0.00664855	+	0.00664855i	0.710423	−	0.703775i	$-0.248504\pi$
$367$	2.44002	+	2.44002i	0.00664855	+	0.00664855i	−0.703775	+	0.710423i	$0.748504\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$		−	166.376i		−	0.450883i
$370$	−140.994	+	120.304i	−0.381064	+	0.325145i
$371$	308.737			0.832176
$372$	53.2794	+	53.2794i	0.143224	+	0.143224i
$373$	−355.285	+	355.285i	−0.952507	+	0.952507i	−0.998922	−	0.0464155i	$-0.985220\pi$
$373$	−355.285	+	355.285i	−0.952507	+	0.952507i	0.0464155	+	0.998922i	$0.485220\pi$
$374$		−	187.262i		−	0.500699i
$375$	−50.8433	+	210.452i	−0.135582	+	0.561205i
$376$	−160.084			−0.425755
$377$	11.5536	+	11.5536i	0.0306462	+	0.0306462i
$378$	49.6475	−	49.6475i	0.131343	−	0.131343i
$379$			175.743i			0.463703i	0.972751	+	0.231851i	$0.0744783\pi$
$379$			175.743i			0.463703i	−0.972751	+	0.231851i	$0.925522\pi$
$380$	−10.4509	−	12.2483i	−0.0275024	−	0.0322323i
$381$	112.069			0.294144
$382$	113.944	+	113.944i	0.298283	+	0.298283i
$383$	154.583	−	154.583i	0.403610	−	0.403610i	−0.475893	−	0.879503i	$-0.657875\pi$
$383$	154.583	−	154.583i	0.403610	−	0.403610i	0.879503	+	0.475893i	$0.157875\pi$
$384$			19.5959i			0.0510310i
$385$	81.3603	−	1027.52i	0.211325	−	2.66889i
$386$	79.2432			0.205293
$387$	−135.373	−	135.373i	−0.349801	−	0.349801i
$388$	95.8960	−	95.8960i	0.247155	−	0.247155i
$389$		−	744.952i		−	1.91504i	−0.288362	−	0.957522i	$-0.593111\pi$
$389$		−	744.952i		−	1.91504i	0.288362	−	0.957522i	$-0.406889\pi$
$390$	18.7178	+	1.48210i	0.0479944	+	0.00380025i
$391$	−29.4330			−0.0752763
$392$	84.5832	+	84.5832i	0.215773	+	0.215773i
$393$	88.5751	−	88.5751i	0.225382	−	0.225382i
$394$			335.722i			0.852085i
$395$	282.171	−	240.765i	0.714358	−	0.609531i
$396$	129.454			0.326903
$397$	−71.7915	−	71.7915i	−0.180835	−	0.180835i	0.610885	−	0.791720i	$-0.290814\pi$
$397$	−71.7915	−	71.7915i	−0.180835	−	0.180835i	−0.791720	+	0.610885i	$0.790814\pi$
$398$	177.527	−	177.527i	0.446047	−	0.446047i
$399$		−	26.6458i		−	0.0667814i
$400$	15.7376	−	98.7539i	0.0393439	−	0.246885i
$401$	−460.952			−1.14951			−0.574754	−	0.818327i	$-0.694902\pi$
$401$	−460.952			−1.14951			−0.574754	+	0.818327i	$0.694902\pi$
$402$	−152.431	−	152.431i	−0.379181	−	0.379181i
$403$	−23.5796	+	23.5796i	−0.0585101	+	0.0585101i
$404$		−	297.973i		−	0.737558i
$405$	−29.2089	−	34.2322i	−0.0721206	−	0.0845239i
$406$	144.011			0.354707
$407$	−399.889	−	399.889i	−0.982529	−	0.982529i
$408$	21.2599	−	21.2599i	0.0521076	−	0.0521076i
$409$		−	24.4609i		−	0.0598066i	−0.999553	−	0.0299033i	$-0.990480\pi$
$409$		−	24.4609i		−	0.0598066i	0.999553	−	0.0299033i	$-0.00951993\pi$
$410$	30.9541	−	390.928i	0.0754979	−	0.953483i
$411$	−431.517			−1.04992
$412$	21.2538	+	21.2538i	0.0515868	+	0.0515868i
$413$	−304.213	+	304.213i	−0.736594	+	0.736594i
$414$		−	20.3470i		−	0.0491473i
$415$	206.039	+	16.3144i	0.496478	+	0.0393117i
$416$	−8.67245			−0.0208472
$417$	139.000	+	139.000i	0.333332	+	0.333332i
$418$	34.7388	−	34.7388i	0.0831072	−	0.0831072i
$419$			671.275i			1.60209i	0.598605	+	0.801045i	$0.295722\pi$
$419$			671.275i			1.60209i	−0.598605	+	0.801045i	$0.704278\pi$
$420$	125.892	−	107.418i	0.299743	−	0.255758i
$421$	386.936			0.919089			0.459544	−	0.888155i	$-0.348013\pi$
$421$	386.936			0.919089			0.459544	+	0.888155i	$0.348013\pi$
$422$	236.548	+	236.548i	0.560541	+	0.560541i
$423$	−120.063	+	120.063i	−0.283836	+	0.283836i
$424$			91.3942i			0.215552i
$425$	−124.214	+	90.0657i	−0.292267	+	0.211919i
$426$	−234.564			−0.550619
$427$	−722.189	−	722.189i	−1.69131	−	1.69131i
$428$	−130.420	+	130.420i	−0.304721	+	0.304721i
$429$			57.2915i			0.133547i
$430$	−292.896	−	343.268i	−0.681153	−	0.798298i
$431$	−238.331			−0.552973			−0.276487	−	0.961018i	$-0.589170\pi$
$431$	−238.331			−0.552973			−0.276487	+	0.961018i	$0.589170\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−178.331	+	178.331i	−0.411851	+	0.411851i	−0.882383	−	0.470532i	$-0.844062\pi$
$433$	−178.331	+	178.331i	−0.411851	+	0.411851i	0.470532	+	0.882383i	$0.344062\pi$
$434$			293.910i			0.677212i
$435$	7.28552	−	92.0109i	0.0167483	−	0.211519i
$436$	128.176			0.293981
$437$	−5.46011	−	5.46011i	−0.0124945	−	0.0124945i
$438$	44.8371	−	44.8371i	0.102368	−	0.102368i
$439$		−	739.579i		−	1.68469i	−0.538938	−	0.842345i	$-0.681174\pi$
$439$		−	739.579i		−	1.68469i	0.538938	−	0.842345i	$-0.318826\pi$
$440$	304.173	+	24.0847i	0.691302	+	0.0547381i
$441$	126.875			0.287698
$442$	9.40887	+	9.40887i	0.0212870	+	0.0212870i
$443$	180.225	−	180.225i	0.406828	−	0.406828i	−0.473803	−	0.880631i	$-0.657119\pi$
$443$	180.225	−	180.225i	0.406828	−	0.406828i	0.880631	+	0.473803i	$0.157119\pi$
$444$		−	90.7993i		−	0.204503i
$445$	566.211	−	483.123i	1.27238	−	1.08567i
$446$	−548.376			−1.22954
$447$	271.812	+	271.812i	0.608082	+	0.608082i
$448$	−54.0493	+	54.0493i	−0.120646	+	0.120646i
$449$		−	798.750i		−	1.77895i	−0.456981	−	0.889476i	$-0.651069\pi$
$449$		−	798.750i		−	1.77895i	0.456981	−	0.889476i	$-0.348931\pi$
$450$	−62.2622	−	85.8686i	−0.138361	−	0.190819i
$451$	1196.55			2.65311
$452$	−51.0041	−	51.0041i	−0.112841	−	0.112841i
$453$	−220.944	+	220.944i	−0.487734	+	0.487734i
$454$			123.799i			0.272684i
$455$	47.5394	+	55.7153i	0.104482	+	0.122451i
$456$	7.88784			0.0172979
$457$	−217.052	−	217.052i	−0.474950	−	0.474950i	0.428562	−	0.903512i	$-0.359020\pi$
$457$	−217.052	−	217.052i	−0.474950	−	0.474950i	−0.903512	+	0.428562i	$0.859020\pi$
$458$	421.368	−	421.368i	0.920017	−	0.920017i
$459$		−	31.8899i		−	0.0694769i
$460$	3.78554	−	47.8087i	0.00822945	−	0.103932i
$461$	−297.784			−0.645952			−0.322976	−	0.946407i	$-0.604683\pi$
$461$	−297.784			−0.645952			−0.322976	+	0.946407i	$0.604683\pi$
$462$	357.058	+	357.058i	0.772852	+	0.772852i
$463$	126.175	−	126.175i	0.272517	−	0.272517i	−0.557596	−	0.830113i	$-0.688276\pi$
$463$	126.175	−	126.175i	0.272517	−	0.272517i	0.830113	+	0.557596i	$0.188276\pi$
$464$			42.6310i			0.0918772i
$465$	187.783	+	14.8689i	0.403835	+	0.0319761i
$466$	−450.048			−0.965768
$467$	372.155	+	372.155i	0.796905	+	0.796905i	0.982606	−	0.185701i	$-0.0594556\pi$
$467$	372.155	+	372.155i	0.796905	+	0.796905i	−0.185701	+	0.982606i	$0.559456\pi$
$468$	−6.50434	+	6.50434i	−0.0138982	+	0.0138982i
$469$		−	840.868i		−	1.79289i
$470$	−304.445	+	259.770i	−0.647756	+	0.552702i
$471$	30.5196			0.0647975
$472$	−90.0550	−	90.0550i	−0.190794	−	0.190794i
$473$	973.584	−	973.584i	2.05832	−	2.05832i
$474$			181.717i			0.383370i
$475$	−39.7509	−	6.33475i	−0.0836860	−	0.0133363i
$476$	117.278			0.246382
$477$	68.5456	+	68.5456i	0.143702	+	0.143702i
$478$	222.316	−	222.316i	0.465096	−	0.465096i
$479$			149.254i			0.311594i	0.987789	+	0.155797i	$0.0497946\pi$
$479$			149.254i			0.311594i	−0.987789	+	0.155797i	$0.950205\pi$
$480$	31.7986	+	37.2673i	0.0662470	+	0.0776402i
$481$	40.1845			0.0835437
$482$	−37.5718	−	37.5718i	−0.0779498	−	0.0779498i
$483$	56.1209	−	56.1209i	0.116192	−	0.116192i
$484$			689.012i			1.42358i
$485$	26.7621	−	337.986i	0.0551796	−	0.696878i
$486$	22.0454			0.0453609
$487$	−63.4861	−	63.4861i	−0.130362	−	0.130362i	0.638915	−	0.769277i	$-0.279383\pi$
$487$	−63.4861	−	63.4861i	−0.130362	−	0.130362i	−0.769277	+	0.638915i	$0.779383\pi$
$488$	213.787	−	213.787i	0.438087	−	0.438087i
$489$			289.000i			0.591002i
$490$	298.114	+	23.6050i	0.608395	+	0.0481734i
$491$	−574.263			−1.16958			−0.584789	−	0.811186i	$-0.698823\pi$
$491$	−574.263			−1.16958			−0.584789	+	0.811186i	$0.698823\pi$
$492$	135.845	+	135.845i	0.276108	+	0.276108i
$493$	46.2511	−	46.2511i	0.0938155	−	0.0938155i
$494$			3.49087i			0.00706654i
$495$	246.193	−	210.066i	0.497360	−	0.424376i
$496$	−87.0049			−0.175413
$497$	−646.972	−	646.972i	−1.30175	−	1.30175i
$498$	−71.5972	+	71.5972i	−0.143770	+	0.143770i
$499$			138.028i			0.276609i	0.990390	+	0.138305i	$0.0441653\pi$
$499$			138.028i			0.276609i	−0.990390	+	0.138305i	$0.955835\pi$
$500$	−130.320	−	213.347i	−0.260640	−	0.426693i
$501$	387.515			0.773482
$502$	−117.012	−	117.012i	−0.233091	−	0.233091i
$503$	−148.954	+	148.954i	−0.296131	+	0.296131i	−0.839496	−	0.543365i	$-0.817150\pi$
$503$	−148.954	+	148.954i	−0.296131	+	0.296131i	0.543365	+	0.839496i	$0.317150\pi$
$504$			81.0740i			0.160861i
$505$	−483.526	−	566.682i	−0.957476	−	1.12214i
$506$	146.333			0.289195
$507$	204.103	+	204.103i	0.402571	+	0.402571i
$508$	−91.5037	+	91.5037i	−0.180125	+	0.180125i
$509$		−	584.754i		−	1.14883i	−0.818564	−	0.574415i	$-0.805230\pi$
$509$		−	584.754i		−	1.14883i	0.818564	−	0.574415i	$-0.194770\pi$
$510$	5.93309	−	74.9306i	0.0116335	−	0.146923i
$511$	247.339			0.484029
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	5.91588	−	5.91588i	0.0115319	−	0.0115319i
$514$		−	511.437i		−	0.995013i
$515$	74.9090	+	5.93138i	0.145454	+	0.0115172i
$516$	221.063			0.428417
$517$	−863.475	−	863.475i	−1.67016	−	1.67016i
$518$	250.442	−	250.442i	0.483479	−	0.483479i
$519$			111.705i			0.215231i
$520$	−16.4932	+	14.0729i	−0.0317176	+	0.0270633i
$521$	−655.891			−1.25891			−0.629454	−	0.777038i	$-0.716721\pi$
$521$	−655.891			−1.25891			−0.629454	+	0.777038i	$0.716721\pi$
$522$	31.9733	+	31.9733i	0.0612515	+	0.0612515i
$523$	−133.671	+	133.671i	−0.255584	+	0.255584i	−0.823255	−	0.567671i	$-0.807845\pi$
$523$	−133.671	+	133.671i	−0.255584	+	0.255584i	0.567671	+	0.823255i	$0.307845\pi$
$524$			144.643i			0.276035i
$525$	65.1108	−	408.573i	0.124021	−	0.778235i
$526$	−195.617			−0.371895
$527$	94.3930	+	94.3930i	0.179114	+	0.179114i
$528$	−105.698	+	105.698i	−0.200186	+	0.200186i
$529$		−	23.0000i		−	0.0434783i
$530$	148.307	+	173.812i	0.279824	+	0.327948i
$531$	−135.083			−0.254393
$532$	21.7562	+	21.7562i	0.0408951	+	0.0408951i
$533$	−60.1203	+	60.1203i	−0.112796	+	0.112796i
$534$			364.638i			0.682842i
$535$	−36.3970	+	459.667i	−0.0680317	+	0.859191i
$536$	248.919			0.464400
$537$	136.532	+	136.532i	0.254249	+	0.254249i
$538$	247.337	−	247.337i	0.459734	−	0.459734i
$539$			912.466i			1.69289i
$540$	51.7994	+	4.10153i	0.0959248	+	0.00759543i
$541$	−121.373			−0.224349			−0.112174	−	0.993689i	$-0.535782\pi$
$541$	−121.373			−0.224349			−0.112174	+	0.993689i	$0.535782\pi$
$542$	174.097	+	174.097i	0.321212	+	0.321212i
$543$	−302.824	+	302.824i	−0.557688	+	0.557688i
$544$			34.7173i			0.0638186i
$545$	243.763	−	207.992i	0.447272	−	0.381638i
$546$	−35.8804			−0.0657151
$547$	529.758	+	529.758i	0.968480	+	0.968480i	0.999518	−	0.0310385i	$-0.00988143\pi$
$547$	529.758	+	529.758i	0.968480	+	0.968480i	−0.0310385	+	0.999518i	$0.509881\pi$
$548$	352.332	−	352.332i	0.642942	−	0.642942i
$549$		−	320.680i		−	0.584116i
$550$	617.555	−	447.781i	1.12283	−	0.814148i
$551$	17.1600			0.0311434
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	−501.212	+	501.212i	−0.906350	+	0.906350i
$554$		−	132.437i		−	0.239056i
$555$	−147.341	−	172.681i	−0.265480	−	0.311137i
$556$	−226.985			−0.408247
$557$	360.364	+	360.364i	0.646973	+	0.646973i	0.952260	−	0.305288i	$-0.0987526\pi$
$557$	360.364	+	360.364i	0.646973	+	0.646973i	−0.305288	+	0.952260i	$0.598753\pi$
$558$	−65.2537	+	65.2537i	−0.116942	+	0.116942i
$559$			97.8347i			0.175017i
$560$	−15.0838	+	190.497i	−0.0269353	+	0.340173i
$561$	229.348			0.408819
$562$	−90.6244	−	90.6244i	−0.161253	−	0.161253i
$563$	190.104	−	190.104i	0.337662	−	0.337662i	−0.517825	−	0.855487i	$-0.673258\pi$
$563$	190.104	−	190.104i	0.337662	−	0.337662i	0.855487	+	0.517825i	$0.173258\pi$
$564$		−	196.062i		−	0.347627i
$565$	−179.764	−	14.2339i	−0.318166	−	0.0251928i
$566$	703.088			1.24221
$567$	60.8055	+	60.8055i	0.107241	+	0.107241i
$568$	191.520	−	191.520i	0.337184	−	0.337184i
$569$			547.652i			0.962481i	0.876589	+	0.481241i	$0.159814\pi$
$569$			547.652i			0.962481i	−0.876589	+	0.481241i	$0.840186\pi$
$570$	15.0010	−	12.7997i	0.0263175	−	0.0224556i
$571$	−827.747			−1.44964			−0.724822	−	0.688936i	$-0.758078\pi$
$571$	−827.747			−1.44964			−0.724822	+	0.688936i	$0.758078\pi$
$572$	−46.7783	−	46.7783i	−0.0817802	−	0.0817802i
$573$	−139.553	+	139.553i	−0.243547	+	0.243547i
$574$			749.376i			1.30553i
$575$	−70.3805	−	97.0648i	−0.122401	−	0.168808i
$576$	−24.0000			−0.0416667
$577$	14.5416	+	14.5416i	0.0252021	+	0.0252021i	0.719596	−	0.694393i	$-0.244327\pi$
$577$	14.5416	+	14.5416i	0.0252021	+	0.0252021i	−0.694393	+	0.719596i	$0.744327\pi$
$578$	−251.335	+	251.335i	−0.434835	+	0.434835i
$579$			97.0527i			0.167621i
$580$	69.1779	+	81.0752i	0.119272	+	0.139785i
$581$	−394.958			−0.679790
$582$	117.448	+	117.448i	0.201801	+	0.201801i
$583$	−492.971	+	492.971i	−0.845576	+	0.845576i
$584$			73.2187i			0.125374i
$585$	−1.81519	+	22.9245i	−0.00310289	+	0.0391873i
$586$	−80.5945			−0.137533
$587$	86.3579	+	86.3579i	0.147117	+	0.147117i	0.776829	−	0.629712i	$-0.216827\pi$
$587$	86.3579	+	86.3579i	0.147117	+	0.147117i	−0.629712	+	0.776829i	$0.716827\pi$
$588$	−103.593	+	103.593i	−0.176178	+	0.176178i
$589$			35.0216i			0.0594595i
$590$	−317.399	−	25.1320i	−0.537965	−	0.0425966i
$591$	−411.173			−0.695725
$592$	74.1374	+	74.1374i	0.125232	+	0.125232i
$593$	−464.807	+	464.807i	−0.783823	+	0.783823i	−0.980474	−	0.196651i	$-0.936993\pi$
$593$	−464.807	+	464.807i	−0.783823	+	0.783823i	0.196651	+	0.980474i	$0.436993\pi$
$594$			158.548i			0.266915i
$595$	223.038	−	190.309i	0.374853	−	0.319846i
$596$	−443.868			−0.744745
$597$	217.425	+	217.425i	0.364196	+	0.364196i
$598$	−7.35242	+	7.35242i	−0.0122950	+	0.0122950i
$599$			573.997i			0.958259i	0.877744	+	0.479130i	$0.159048\pi$
$599$			573.997i			0.958259i	−0.877744	+	0.479130i	$0.840952\pi$
$600$	120.948	+	19.2745i	0.201581	+	0.0321242i
$601$	−141.986			−0.236250			−0.118125	−	0.992999i	$-0.537688\pi$
$601$	−141.986			−0.236250			−0.118125	+	0.992999i	$0.537688\pi$
$602$	609.735	+	609.735i	1.01285	+	1.01285i
$603$	186.689	−	186.689i	0.309600	−	0.309600i
$604$		−	360.799i		−	0.597350i
$605$	1118.07	+	1310.35i	1.84805	+	2.16587i
$606$	364.941			0.602213
$607$	369.871	+	369.871i	0.609342	+	0.609342i	0.942774	−	0.333432i	$-0.108207\pi$
$607$	369.871	+	369.871i	0.609342	+	0.609342i	−0.333432	+	0.942774i	$0.608207\pi$
$608$	−6.44039	+	6.44039i	−0.0105928	+	0.0105928i
$609$			176.377i			0.289617i
$610$	59.6623	−	753.491i	0.0978070	−	1.23523i
$611$	86.7698			0.142013
$612$	26.0380	+	26.0380i	0.0425457	+	0.0425457i
$613$	−196.795	+	196.795i	−0.321036	+	0.321036i	−0.849164	−	0.528129i	$-0.822894\pi$
$613$	−196.795	+	196.795i	−0.321036	+	0.321036i	0.528129	+	0.849164i	$0.322894\pi$
$614$		−	460.239i		−	0.749575i
$615$	478.787	+	37.9109i	0.778516	+	0.0616438i
$616$	−583.073			−0.946547
$617$	−323.009	−	323.009i	−0.523516	−	0.523516i	0.395116	−	0.918631i	$-0.370705\pi$
$617$	−323.009	−	323.009i	−0.523516	−	0.523516i	−0.918631	+	0.395116i	$0.870705\pi$
$618$	−26.0304	+	26.0304i	−0.0421205	+	0.0421205i
$619$		−	326.754i		−	0.527874i	−0.964540	−	0.263937i	$-0.914979\pi$
$619$		−	326.754i		−	0.527874i	0.964540	−	0.263937i	$-0.0850211\pi$
$620$	−165.465	+	141.184i	−0.266879	+	0.227716i
$621$	24.9199			0.0401286
$622$	350.808	+	350.808i	0.564000	+	0.564000i
$623$	−1005.74	+	1005.74i	−1.61435	+	1.61435i
$624$		−	10.6215i		−	0.0170217i
$625$	−594.041	−	194.268i	−0.950466	−	0.310829i
$626$	−599.926			−0.958348
$627$	42.5462	+	42.5462i	0.0678567	+	0.0678567i
$628$	−24.9192	+	24.9192i	−0.0396802	+	0.0396802i
$629$		−	160.866i		−	0.255748i
$630$	131.560	+	154.186i	0.208825	+	0.244739i
$631$	818.531			1.29720			0.648598	−	0.761131i	$-0.275356\pi$
$631$	818.531			1.29720			0.648598	+	0.761131i	$0.275356\pi$
$632$	−148.372	−	148.372i	−0.234765	−	0.234765i
$633$	−289.711	+	289.711i	−0.457680	+	0.457680i
$634$			541.660i			0.854353i
$635$	−25.5363	+	322.505i	−0.0402147	+	0.507882i
$636$	−111.935			−0.175998
$637$	−45.8464	−	45.8464i	−0.0719724	−	0.0719724i
$638$	−229.947	+	229.947i	−0.360419	+	0.360419i
$639$		−	287.281i		−	0.449579i
$640$	−56.3920	−	4.46519i	−0.0881126	−	0.00697685i
$641$	−1117.35			−1.74314			−0.871570	−	0.490271i	$-0.836898\pi$
$641$	−1117.35			−1.74314			−0.871570	+	0.490271i	$0.836898\pi$
$642$	−159.732	−	159.732i	−0.248803	−	0.248803i
$643$	−374.672	+	374.672i	−0.582694	+	0.582694i	−0.935643	−	0.352949i	$-0.885179\pi$
$643$	−374.672	+	374.672i	−0.582694	+	0.582694i	0.352949	+	0.935643i	$0.385179\pi$
$644$			91.6451i			0.142306i
$645$	420.416	−	358.723i	0.651807	−	0.556159i
$646$	13.9746			0.0216325
$647$	−706.633	−	706.633i	−1.09217	−	1.09217i	−0.995297	−	0.0968710i	$-0.969117\pi$
$647$	−706.633	−	706.633i	−1.09217	−	1.09217i	−0.0968710	−	0.995297i	$-0.530883\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	971.495i		−	1.49691i
$650$	−8.53020	+	53.5274i	−0.0131234	+	0.0823498i
$651$	−359.965			−0.552941
$652$	−235.967	−	235.967i	−0.361913	−	0.361913i
$653$	845.591	−	845.591i	1.29493	−	1.29493i	0.363236	−	0.931697i	$-0.381672\pi$
$653$	845.591	−	845.591i	1.29493	−	1.29493i	0.931697	−	0.363236i	$-0.118328\pi$
$654$			156.982i			0.240034i
$655$	234.714	+	275.080i	0.358341	+	0.419969i
$656$	−221.835			−0.338162
$657$	54.9140	+	54.9140i	0.0835829	+	0.0835829i
$658$	540.776	−	540.776i	0.821848	−	0.821848i
$659$			1313.34i			1.99293i	0.0840117	+	0.996465i	$0.473227\pi$
$659$			1313.34i			1.99293i	−0.0840117	+	0.996465i	$0.526773\pi$
$660$	−29.4977	+	372.534i	−0.0446934	+	0.564446i
$661$	−706.286			−1.06851			−0.534255	−	0.845323i	$-0.679408\pi$
$661$	−706.286			−1.06851			−0.534255	+	0.845323i	$0.679408\pi$
$662$	331.091	+	331.091i	0.500138	+	0.500138i
$663$	−11.5235	+	11.5235i	−0.0173808	+	0.0173808i
$664$		−	116.918i		−	0.176081i
$665$	76.6797	+	6.07159i	0.115308	+	0.00913021i
$666$	111.206			0.166976
$667$	36.1422	+	36.1422i	0.0541862	+	0.0541862i
$668$	−316.404	+	316.404i	−0.473659	+	0.473659i
$669$		−	671.620i		−	1.00392i
$670$	473.390	−	403.924i	0.706553	−	0.602871i
$671$	2306.28			3.43709
$672$	−66.1966	−	66.1966i	−0.0985069	−	0.0985069i
$673$	99.1229	−	99.1229i	0.147285	−	0.147285i	−0.629619	−	0.776904i	$-0.716789\pi$
$673$	99.1229	−	99.1229i	0.147285	−	0.147285i	0.776904	+	0.629619i	$0.216789\pi$
$674$		−	706.319i		−	1.04795i
$675$	105.167	−	76.2554i	0.155803	−	0.112971i
$676$	−333.299			−0.493046
$677$	−616.977	−	616.977i	−0.911339	−	0.911339i	0.0850382	−	0.996378i	$-0.472899\pi$
$677$	−616.977	−	616.977i	−0.911339	−	0.911339i	−0.996378	+	0.0850382i	$0.972899\pi$
$678$	62.4670	−	62.4670i	0.0921342	−	0.0921342i
$679$			647.890i			0.954182i
$680$	56.3363	+	66.0250i	0.0828474	+	0.0970955i
$681$	−151.622			−0.222646
$682$	−469.296	−	469.296i	−0.688117	−	0.688117i
$683$	229.053	−	229.053i	0.335363	−	0.335363i	−0.519256	−	0.854619i	$-0.673791\pi$
$683$	229.053	−	229.053i	0.335363	−	0.335363i	0.854619	+	0.519256i	$0.173791\pi$
$684$			9.66059i			0.0141237i
$685$	98.3268	−	1241.80i	0.143543	−	1.81284i
$686$	90.6463			0.132138
$687$	516.068	+	516.068i	0.751191	+	0.751191i
$688$	−180.497	+	180.497i	−0.262351	+	0.262351i
$689$		−	49.5382i		−	0.0718987i
$690$	58.5534	+	4.63633i	0.0848600	+	0.00671931i
$691$	609.437			0.881964			0.440982	−	0.897516i	$-0.354630\pi$
$691$	609.437			0.881964			0.440982	+	0.897516i	$0.354630\pi$
$692$	−91.2066	−	91.2066i	−0.131801	−	0.131801i
$693$	−437.305	+	437.305i	−0.631031	+	0.631031i
$694$			121.324i			0.174818i
$695$	−431.678	+	368.332i	−0.621120	+	0.529975i
$696$	−52.2121			−0.0750174
$697$	240.672	+	240.672i	0.345297	+	0.345297i
$698$	185.071	−	185.071i	0.265144	−	0.265144i
$699$		−	551.194i		−	0.788546i
$700$	280.436	+	386.762i	0.400623	+	0.552517i
$701$	−827.352			−1.18025			−0.590123	−	0.807313i	$-0.700921\pi$
$701$	−827.352			−1.18025			−0.590123	+	0.807313i	$0.700921\pi$
$702$	−7.96615	−	7.96615i	−0.0113478	−	0.0113478i
$703$	29.8421	−	29.8421i	0.0424497	−	0.0424497i
$704$		−	172.605i		−	0.245177i
$705$	−318.152	−	372.868i	−0.451280	−	0.528891i
$706$	767.303			1.08683
$707$	1006.58	+	1006.58i	1.42373	+	1.42373i
$708$	110.294	−	110.294i	0.155783	−	0.155783i
$709$		−	339.906i		−	0.479416i	−0.970845	−	0.239708i	$-0.922948\pi$
$709$		−	339.906i		−	0.479416i	0.970845	−	0.239708i	$-0.0770518\pi$
$710$	53.4484	−	675.014i	0.0752794	−	0.950724i
$711$	−222.557			−0.313020
$712$	−297.725	−	297.725i	−0.418154	−	0.418154i
$713$	−73.7620	+	73.7620i	−0.103453	+	0.103453i
$714$			143.636i			0.201170i
$715$	−164.870	−	13.0546i	−0.230588	−	0.0182582i
$716$	−222.956			−0.311391
$717$	272.280	+	272.280i	0.379750	+	0.379750i
$718$	−7.62023	+	7.62023i	−0.0106131	+	0.0106131i
$719$		−	114.840i		−	0.159722i	−0.996806	−	0.0798610i	$-0.974552\pi$
$719$		−	114.840i		−	0.159722i	0.996806	−	0.0798610i	$-0.0254476\pi$
$720$	−45.6429	+	38.9451i	−0.0633929	+	0.0540905i
$721$	−143.594			−0.199160
$722$	−358.408	−	358.408i	−0.496409	−	0.496409i
$723$	46.0159	−	46.0159i	0.0636457	−	0.0636457i
$724$		−	494.510i		−	0.683025i
$725$	263.124	+	41.9317i	0.362929	+	0.0578369i
$726$	−843.863			−1.16235
$727$	−48.1716	−	48.1716i	−0.0662609	−	0.0662609i	0.673200	−	0.739461i	$-0.264919\pi$
$727$	−48.1716	−	48.1716i	−0.0662609	−	0.0662609i	−0.739461	+	0.673200i	$0.764919\pi$
$728$	29.2963	−	29.2963i	0.0402421	−	0.0402421i
$729$			27.0000i			0.0370370i
$730$	118.813	+	139.246i	0.162757	+	0.190748i
$731$	391.649			0.535772
$732$	261.834	+	261.834i	0.357697	+	0.357697i
$733$	−171.334	+	171.334i	−0.233743	+	0.233743i	−0.814253	−	0.580510i	$-0.802853\pi$
$733$	−171.334	+	171.334i	−0.233743	+	0.233743i	0.580510	+	0.814253i	$0.302853\pi$
$734$		−	4.88004i		−	0.00664855i
$735$	−28.9101	+	365.113i	−0.0393334	+	0.496753i
$736$	−27.1293			−0.0368605
$737$	1342.64	+	1342.64i	1.82176	+	1.82176i
$738$	−166.376	+	166.376i	−0.225442	+	0.225442i
$739$		−	285.604i		−	0.386474i	−0.981152	−	0.193237i	$-0.938101\pi$
$739$		−	285.604i		−	0.386474i	0.981152	−	0.193237i	$-0.0618986\pi$
$740$	261.297	+	20.6898i	0.353104	+	0.0279592i
$741$	−4.27543			−0.00576981
$742$	−308.737	−	308.737i	−0.416088	−	0.416088i
$743$	38.7694	−	38.7694i	0.0521796	−	0.0521796i	−0.680536	−	0.732715i	$-0.738253\pi$
$743$	38.7694	−	38.7694i	0.0521796	−	0.0521796i	0.732715	+	0.680536i	$0.238253\pi$
$744$		−	106.559i		−	0.143224i
$745$	−844.143	+	720.271i	−1.13308	+	0.966806i
$746$	710.570			0.952507
$747$	−87.6883	−	87.6883i	−0.117387	−	0.117387i
$748$	−187.262	+	187.262i	−0.250350	+	0.250350i
$749$		−	881.143i		−	1.17643i
$750$	261.295	−	159.609i	0.348393	−	0.212811i
$751$	−98.0276			−0.130529			−0.0652647	−	0.997868i	$-0.520789\pi$
$751$	−98.0276			−0.130529			−0.0652647	+	0.997868i	$0.520789\pi$
$752$	160.084	+	160.084i	0.212877	+	0.212877i
$753$	143.310	−	143.310i	0.190318	−	0.190318i
$754$		−	23.1072i		−	0.0306462i
$755$	−585.474	−	686.164i	−0.775462	−	0.908826i
$756$	−99.2950			−0.131343
$757$	371.185	+	371.185i	0.490336	+	0.490336i	0.908412	−	0.418076i	$-0.137295\pi$
$757$	371.185	+	371.185i	0.490336	+	0.490336i	−0.418076	+	0.908412i	$0.637295\pi$
$758$	175.743	−	175.743i	0.231851	−	0.231851i
$759$			179.220i			0.236127i
$760$	−1.79735	+	22.6992i	−0.00236493	+	0.0298673i
$761$	15.1023			0.0198453			0.00992264	−	0.999951i	$-0.496841\pi$
$761$	15.1023			0.0198453			0.00992264	+	0.999951i	$0.496841\pi$
$762$	−112.069	−	112.069i	−0.147072	−	0.147072i
$763$	−432.988	+	432.988i	−0.567481	+	0.567481i
$764$		−	227.888i		−	0.298283i
$765$	91.7709	+	7.26652i	0.119962	+	0.00949872i
$766$	−309.165			−0.403610
$767$	48.8123	+	48.8123i	0.0636406	+	0.0636406i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	69.2758i		−	0.0900855i	−0.998985	−	0.0450428i	$-0.985658\pi$
$769$		−	69.2758i		−	0.0900855i	0.998985	−	0.0450428i	$-0.0143424\pi$
$770$	−1108.88	+	946.161i	−1.44011	+	1.22878i
$771$	626.380			0.812425
$772$	−79.2432	−	79.2432i	−0.102647	−	0.102647i
$773$	−741.092	+	741.092i	−0.958722	+	0.958722i	−0.999181	−	0.0404588i	$-0.987118\pi$
$773$	−741.092	+	741.092i	−0.958722	+	0.958722i	0.0404588	+	0.999181i	$0.487118\pi$
$774$			270.746i			0.349801i
$775$	−85.5778	+	537.005i	−0.110423	+	0.692909i
$776$	−191.792			−0.247155
$777$	306.728	+	306.728i	0.394759	+	0.394759i
$778$	−744.952	+	744.952i	−0.957522	+	0.957522i
$779$			89.2938i			0.114626i
$780$	−17.2357	−	20.1999i	−0.0220971	−	0.0258973i
$781$	2066.08			2.64543
$782$	29.4330	+	29.4330i	0.0376381	+	0.0376381i
$783$	−39.1591	+	39.1591i	−0.0500116	+	0.0500116i
$784$		−	169.166i		−	0.215773i
$785$	−6.95429	+	87.8277i	−0.00885897	+	0.111882i
$786$	−177.150			−0.225382
$787$	−249.487	−	249.487i	−0.317010	−	0.317010i	0.530608	−	0.847618i	$-0.321964\pi$
$787$	−249.487	−	249.487i	−0.317010	−	0.317010i	−0.847618	+	0.530608i	$0.821964\pi$
$788$	335.722	−	335.722i	0.426043	−	0.426043i
$789$		−	239.580i		−	0.303651i
$790$	−522.936	−	41.4067i	−0.661944	−	0.0524135i
$791$	344.592			0.435641
$792$	−129.454	−	129.454i	−0.163451	−	0.163451i
$793$	−115.878	+	115.878i	−0.146126	+	0.146126i
$794$			143.583i			0.180835i
$795$	−212.876	+	181.638i	−0.267768	+	0.228475i
$796$	−355.054			−0.446047
$797$	−708.670	−	708.670i	−0.889172	−	0.889172i	0.105271	−	0.994444i	$-0.466429\pi$
$797$	−708.670	−	708.670i	−0.889172	−	0.889172i	−0.994444	+	0.105271i	$0.966429\pi$
$798$	−26.6458	+	26.6458i	−0.0333907	+	0.0333907i
$799$		−	347.355i		−	0.434737i
$800$	−114.491	+	83.0163i	−0.143114	+	0.103770i
$801$	−446.588			−0.557538
$802$	460.952	+	460.952i	0.574754	+	0.574754i
$803$	−394.934	+	394.934i	−0.491823	+	0.491823i
$804$			304.862i			0.379181i
$805$	148.714	+	174.290i	0.184738	+	0.216509i
$806$	47.1591			0.0585101
$807$	302.925	+	302.925i	0.375371	+	0.375371i
$808$	−297.973	+	297.973i	−0.368779	+	0.368779i
$809$			48.4853i			0.0599324i	0.999551	+	0.0299662i	$0.00953997\pi$
$809$			48.4853i			0.0599324i	−0.999551	+	0.0299662i	$0.990460\pi$
$810$	−5.02333	+	63.4410i	−0.00620165	+	0.0783223i
$811$	823.080			1.01490			0.507448	−	0.861682i	$-0.330589\pi$
$811$	823.080			1.01490			0.507448	+	0.861682i	$0.330589\pi$
$812$	−144.011	−	144.011i	−0.177354	−	0.177354i
$813$	−213.224	+	213.224i	−0.262269	+	0.262269i
$814$			799.778i			0.982529i
$815$	−831.668	−	65.8524i	−1.02045	−	0.0808005i
$816$	−42.5198			−0.0521076
$817$	72.6547	+	72.6547i	0.0889286	+	0.0889286i
$818$	−24.4609	+	24.4609i	−0.0299033	+	0.0299033i
$819$		−	43.9444i		−	0.0536561i
$820$	−421.882	+	359.974i	−0.514491	+	0.438993i
$821$	1372.41			1.67164			0.835818	−	0.549007i	$-0.184994\pi$
$821$	1372.41			1.67164			0.835818	+	0.549007i	$0.184994\pi$
$822$	431.517	+	431.517i	0.524960	+	0.524960i
$823$	719.853	−	719.853i	0.874669	−	0.874669i	−0.118308	−	0.992977i	$-0.537747\pi$
$823$	719.853	−	719.853i	0.874669	−	0.874669i	0.992977	+	0.118308i	$0.0377469\pi$
$824$		−	42.5075i		−	0.0515868i
$825$	548.418	+	756.347i	0.664749	+	0.916784i
$826$	608.427			0.736594
$827$	−299.280	−	299.280i	−0.361886	−	0.361886i	0.502621	−	0.864507i	$-0.332369\pi$
$827$	−299.280	−	299.280i	−0.361886	−	0.361886i	−0.864507	+	0.502621i	$0.832369\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$			1071.91i			1.29302i	0.762905	+	0.646510i	$0.223772\pi$
$829$			1071.91i			1.29302i	−0.762905	+	0.646510i	$0.776228\pi$
$830$	−189.724	−	222.353i	−0.228583	−	0.267895i
$831$	162.202			0.195189
$832$	8.67245	+	8.67245i	0.0104236	+	0.0104236i
$833$	−183.531	+	183.531i	−0.220326	+	0.220326i
$834$		−	277.999i		−	0.333332i
$835$	−88.3002	+	1115.17i	−0.105749	+	1.33553i
$836$	−69.4776			−0.0831072
$837$	−79.9191	−	79.9191i	−0.0954828	−	0.0954828i
$838$	671.275	−	671.275i	0.801045	−	0.801045i
$839$			383.200i			0.456734i	0.973575	+	0.228367i	$0.0733387\pi$
$839$			383.200i			0.456734i	−0.973575	+	0.228367i	$0.926661\pi$
$840$	−233.310	−	18.4738i	−0.277750	−	0.0219926i
$841$	727.412			0.864937
$842$	−386.936	−	386.936i	−0.459544	−	0.459544i
$843$	110.992	−	110.992i	0.131663	−	0.131663i
$844$		−	473.097i		−	0.560541i
$845$	−633.865	+	540.849i	−0.750136	+	0.640059i
$846$	240.126			0.283836
$847$	−2327.54	−	2327.54i	−2.74798	−	2.74798i
$848$	91.3942	−	91.3942i	0.107776	−	0.107776i
$849$			861.104i			1.01426i
$850$	214.279	+	34.1478i	0.252093	+	0.0401739i
$851$	125.706			0.147716
$852$	234.564	+	234.564i	0.275310	+	0.275310i
$853$	−651.300	+	651.300i	−0.763540	+	0.763540i	−0.976960	−	0.213420i	$-0.931540\pi$
$853$	−651.300	+	651.300i	−0.763540	+	0.763540i	0.213420	+	0.976960i	$0.431540\pi$
$854$			1444.38i			1.69131i
$855$	15.6764	+	18.3724i	0.0183349	+	0.0214882i
$856$	260.841			0.304721
$857$	−205.089	−	205.089i	−0.239311	−	0.239311i	0.577254	−	0.816565i	$-0.304124\pi$
$857$	−205.089	−	205.089i	−0.239311	−	0.239311i	−0.816565	+	0.577254i	$0.804124\pi$
$858$	57.2915	−	57.2915i	0.0667733	−	0.0667733i
$859$		−	1544.42i		−	1.79793i	−0.438021	−	0.898965i	$-0.644320\pi$
$859$		−	1544.42i		−	1.79793i	0.438021	−	0.898965i	$-0.355680\pi$
$860$	−50.3722	+	636.164i	−0.0585723	+	0.739725i
$861$	−917.794			−1.06596
$862$	238.331	+	238.331i	0.276487	+	0.276487i
$863$	284.031	−	284.031i	0.329121	−	0.329121i	−0.523131	−	0.852252i	$-0.675236\pi$
$863$	284.031	−	284.031i	0.329121	−	0.329121i	0.852252	+	0.523131i	$0.175236\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−321.458	−	25.4534i	−0.371628	−	0.0294259i
$866$	356.663			0.411851
$867$	−307.821	−	307.821i	−0.355041	−	0.355041i
$868$	293.910	−	293.910i	0.338606	−	0.338606i
$869$		−	1600.60i		−	1.84189i
$870$	−99.2964	+	84.7253i	−0.114134	+	0.0973854i
$871$	−134.921			−0.154903
$872$	−128.176	−	128.176i	−0.146990	−	0.146990i
$873$	−143.844	+	143.844i	−0.164770	+	0.164770i
$874$			10.9202i			0.0124945i
$875$	1160.93	+	280.471i	1.32678	+	0.320538i
$876$	−89.6742			−0.102368
$877$	1226.80	+	1226.80i	1.39885	+	1.39885i	0.803357	+	0.595498i	$0.203045\pi$
$877$	1226.80	+	1226.80i	1.39885	+	1.39885i	0.595498	+	0.803357i	$0.296955\pi$
$878$	−739.579	+	739.579i	−0.842345	+	0.842345i
$879$		−	98.7076i		−	0.112295i
$880$	−280.088	−	328.258i	−0.318282	−	0.373020i
$881$	1011.62			1.14827			0.574133	−	0.818762i	$-0.305339\pi$
$881$	1011.62			1.14827			0.574133	+	0.818762i	$0.305339\pi$
$882$	−126.875	−	126.875i	−0.143849	−	0.143849i
$883$	577.715	−	577.715i	0.654264	−	0.654264i	−0.299753	−	0.954017i	$-0.596904\pi$
$883$	577.715	−	577.715i	0.654264	−	0.654264i	0.954017	+	0.299753i	$0.0969042\pi$
$884$		−	18.8177i		−	0.0212870i
$885$	30.7803	−	388.733i	0.0347800	−	0.439246i
$886$	−360.450			−0.406828
$887$	−403.325	−	403.325i	−0.454707	−	0.454707i	0.442206	−	0.896913i	$-0.354196\pi$
$887$	−403.325	−	403.325i	−0.454707	−	0.454707i	−0.896913	+	0.442206i	$0.854196\pi$
$888$	−90.7993	+	90.7993i	−0.102252	+	0.102252i
$889$		−	618.214i		−	0.695404i
$890$	−1049.33	−	83.0874i	−1.17903	−	0.0933567i
$891$	−194.180			−0.217935
$892$	548.376	+	548.376i	0.614771	+	0.614771i
$893$	64.4376	−	64.4376i	0.0721586	−	0.0721586i
$894$		−	543.625i		−	0.608082i
$895$	−424.015	+	361.793i	−0.473759	+	0.404238i
$896$	108.099			0.120646
$897$	−9.00484	−	9.00484i	−0.0100388	−	0.0100388i
$898$	−798.750	+	798.750i	−0.889476	+	0.889476i
$899$		−	231.819i		−	0.257863i
$900$	−23.6063	+	148.131i	−0.0262293	+	0.164590i
$901$	−198.310			−0.220100
$902$	−1196.55	−	1196.55i	−1.32655	−	1.32655i
$903$	−746.770	+	746.770i	−0.826988	+	0.826988i
$904$			102.008i			0.112841i
$905$	−802.448	−	940.453i	−0.886683	−	1.03918i
$906$	441.887			0.487734
$907$	633.280	+	633.280i	0.698214	+	0.698214i	0.964025	−	0.265811i	$-0.0856398\pi$
$907$	633.280	+	633.280i	0.698214	+	0.698214i	−0.265811	+	0.964025i	$0.585640\pi$
$908$	123.799	−	123.799i	0.136342	−	0.136342i
$909$			446.960i			0.491705i
$910$	8.17582	−	103.255i	0.00898442	−	0.113467i
$911$	−8.24514			−0.00905065			−0.00452533	−	0.999990i	$-0.501440\pi$
$911$	−8.24514			−0.00905065			−0.00452533	+	0.999990i	$0.501440\pi$
$912$	−7.88784	−	7.88784i	−0.00864895	−	0.00864895i
$913$	630.642	−	630.642i	0.690736	−	0.690736i
$914$			434.104i			0.474950i
$915$	922.834	+	73.0711i	1.00856	+	0.0798591i
$916$	−842.736			−0.920017
$917$	−488.615	−	488.615i	−0.532840	−	0.532840i
$918$	−31.8899	+	31.8899i	−0.0347384	+	0.0347384i
$919$		−	297.033i		−	0.323213i	−0.986855	−	0.161607i	$-0.948332\pi$
$919$		−	297.033i		−	0.323213i	0.986855	−	0.161607i	$-0.0516676\pi$
$920$	−51.5942	+	44.0231i	−0.0560807	+	0.0478512i
$921$	563.675			0.612025
$922$	297.784	+	297.784i	0.322976	+	0.322976i
$923$	−103.809	+	103.809i	−0.112470	+	0.112470i
$924$		−	714.116i		−	0.772852i
$925$	530.506	−	384.663i	0.573520	−	0.415852i
$926$	−252.351			−0.272517
$927$	−31.8807	−	31.8807i	−0.0343912	−	0.0343912i
$928$	42.6310	−	42.6310i	0.0459386	−	0.0459386i
$929$		−	642.952i		−	0.692091i	−0.938218	−	0.346045i	$-0.887524\pi$
$929$		−	642.952i		−	0.692091i	0.938218	−	0.346045i	$-0.112476\pi$
$930$	−172.915	−	202.652i	−0.185930	−	0.217906i
$931$	−68.0936			−0.0731403
$932$	450.048	+	450.048i	0.482884	+	0.482884i
$933$	−429.650	+	429.650i	−0.460504	+	0.460504i
$934$		−	744.310i		−	0.796905i
$935$	−52.2598	+	660.004i	−0.0558929	+	0.705886i
$936$	13.0087			0.0138982
$937$	1255.14	+	1255.14i	1.33953	+	1.33953i	0.896511	+	0.443021i	$0.146093\pi$
$937$	1255.14	+	1255.14i	1.33953	+	1.33953i	0.443021	+	0.896511i	$0.353907\pi$
$938$	−840.868	+	840.868i	−0.896447	+	0.896447i
$939$		−	734.756i		−	0.782488i
$940$	564.215	+	44.6752i	0.600229	+	0.0475268i
$941$	898.683			0.955030			0.477515	−	0.878624i	$-0.341538\pi$
$941$	898.683			0.955030			0.477515	+	0.878624i	$0.341538\pi$
$942$	−30.5196	−	30.5196i	−0.0323987	−	0.0323987i
$943$	−188.069	+	188.069i	−0.199437	+	0.199437i
$944$			180.110i			0.190794i
$945$	−188.838	+	161.127i	−0.199829	+	0.170505i
$946$	−1947.17			−2.05832
$947$	−908.004	−	908.004i	−0.958822	−	0.958822i	0.0403634	−	0.999185i	$-0.487148\pi$
$947$	−908.004	−	908.004i	−0.958822	−	0.958822i	−0.999185	+	0.0403634i	$0.987148\pi$
$948$	181.717	−	181.717i	0.191685	−	0.191685i
$949$		−	39.6866i		−	0.0418193i
$950$	33.4161	+	46.0856i	0.0351749	+	0.0485112i
$951$	−663.395			−0.697576
$952$	−117.278	−	117.278i	−0.123191	−	0.123191i
$953$	−550.047	+	550.047i	−0.577174	+	0.577174i	−0.934124	−	0.356949i	$-0.883817\pi$
$953$	−550.047	+	550.047i	−0.577174	+	0.577174i	0.356949	+	0.934124i	$0.383817\pi$
$954$		−	137.091i		−	0.143702i
$955$	−369.798	−	433.396i	−0.387223	−	0.453817i
$956$	−444.632			−0.465096
$957$	−281.627	−	281.627i	−0.294281	−	0.294281i
$958$	149.254	−	149.254i	0.155797	−	0.155797i
$959$			2380.42i			2.48219i
$960$	5.46871	−	69.0659i	0.00569658	−	0.0719436i
$961$	−487.884			−0.507683
$962$	−40.1845	−	40.1845i	−0.0417718	−	0.0417718i
$963$	195.631	−	195.631i	0.203147	−	0.203147i
$964$			75.1436i			0.0779498i
$965$	−279.293	−	22.1147i	−0.289423	−	0.0229168i
$966$	−112.242			−0.116192
$967$	−764.523	−	764.523i	−0.790614	−	0.790614i	0.190980	−	0.981594i	$-0.438833\pi$
$967$	−764.523	−	764.523i	−0.790614	−	0.790614i	−0.981594	+	0.190980i	$0.938833\pi$
$968$	689.012	−	689.012i	0.711789	−	0.711789i
$969$			17.1153i			0.0176628i
$970$	−364.748	+	311.224i	−0.376029	+	0.320849i
$971$	1638.75			1.68769			0.843846	−	0.536585i	$-0.180286\pi$
$971$	1638.75			1.68769			0.843846	+	0.536585i	$0.180286\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	766.775	−	766.775i	0.788053	−	0.788053i
$974$			126.972i			0.130362i
$975$	−65.5574	−	10.4473i	−0.0672383	−	0.0107152i
$976$	−427.573			−0.438087
$977$	−30.1707	−	30.1707i	−0.0308810	−	0.0308810i	0.691498	−	0.722379i	$-0.256951\pi$
$977$	−30.1707	−	30.1707i	−0.0308810	−	0.0308810i	−0.722379	+	0.691498i	$0.756951\pi$
$978$	289.000	−	289.000i	0.295501	−	0.295501i
$979$		−	3211.80i		−	3.28069i
$980$	−274.509	−	321.719i	−0.280111	−	0.328284i
$981$	−192.264			−0.195987
$982$	574.263	+	574.263i	0.584789	+	0.584789i
$983$	−451.884	+	451.884i	−0.459699	+	0.459699i	−0.898557	−	0.438858i	$-0.855383\pi$
$983$	−451.884	+	451.884i	−0.459699	+	0.459699i	0.438858	+	0.898557i	$0.355383\pi$
$984$		−	271.691i		−	0.276108i
$985$	93.6912	−	1183.25i	0.0951180	−	1.20127i
$986$	−92.5021			−0.0938155
$987$	662.313	+	662.313i	0.671036	+	0.671036i
$988$	3.49087	−	3.49087i	0.00353327	−	0.00353327i
$989$			306.048i			0.309452i
$990$	−456.259	−	36.1271i	−0.460868	−	0.0364920i
$991$	−542.646			−0.547575			−0.273787	−	0.961790i	$-0.588276\pi$
$991$	−542.646			−0.547575			−0.273787	+	0.961790i	$0.588276\pi$
$992$	87.0049	+	87.0049i	0.0877066	+	0.0877066i
$993$	−405.502	+	405.502i	−0.408361	+	0.408361i
$994$			1293.94i			1.30175i
$995$	−675.237	+	576.150i	−0.678630	+	0.579046i
$996$	143.194			0.143770
$997$	−456.492	−	456.492i	−0.457865	−	0.457865i	0.440089	−	0.897954i	$-0.354947\pi$
$997$	−456.492	−	456.492i	−0.457865	−	0.457865i	−0.897954	+	0.440089i	$0.854947\pi$
$998$	138.028	−	138.028i	0.138305	−	0.138305i
$999$			136.199i			0.136335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.23	✓	48
5.3	odd	4	inner	690.3.k.b.553.23	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.23	✓	48	1.1	even	1	trivial
690.3.k.b.553.23	yes	48	5.3	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.24543 + 3.80358i) q^{5} -2.44949 q^{6} +(-6.75617 - 6.75617i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.24543 + 3.80358i) q^{5} -2.44949 q^{6} +(-6.75617 - 6.75617i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(0.558148 - 7.04900i) q^{10} +21.5756 q^{11} +(2.44949 + 2.44949i) q^{12} +(-1.08406 + 1.08406i) q^{13} +13.5123i q^{14} +(8.63323 + 0.683589i) q^{15} -4.00000 q^{16} +(4.33966 + 4.33966i) q^{17} +(-3.00000 + 3.00000i) q^{18} +1.61010i q^{19} +(-7.60715 + 6.49086i) q^{20} -16.5492 q^{21} +(-21.5756 - 21.5756i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-3.93439 + 24.6885i) q^{25} +2.16811 q^{26} +(-3.67423 - 3.67423i) q^{27} +(13.5123 - 13.5123i) q^{28} -10.6578i q^{29} +(-7.94964 - 9.31682i) q^{30} +21.7512 q^{31} +(4.00000 + 4.00000i) q^{32} +(26.4246 - 26.4246i) q^{33} -8.67933i q^{34} +(3.77094 - 47.6243i) q^{35} +6.00000 q^{36} +(-18.5343 - 18.5343i) q^{37} +(1.61010 - 1.61010i) q^{38} +2.65538i q^{39} +(14.0980 + 1.11630i) q^{40} +55.4586 q^{41} +(16.5492 + 16.5492i) q^{42} +(45.1244 - 45.1244i) q^{43} +43.1512i q^{44} +(11.4107 - 9.73629i) q^{45} +6.78233 q^{46} +(-40.0209 - 40.0209i) q^{47} +(-4.89898 + 4.89898i) q^{48} +42.2916i q^{49} +(28.6229 - 20.7541i) q^{50} +10.6300 q^{51} +(-2.16811 - 2.16811i) q^{52} +(-22.8485 + 22.8485i) q^{53} +7.34847i q^{54} +(70.0220 + 82.0644i) q^{55} -27.0247 q^{56} +(1.97196 + 1.97196i) q^{57} +(-10.6578 + 10.6578i) q^{58} -45.0275i q^{59} +(-1.36718 + 17.2665i) q^{60} +106.893 q^{61} +(-21.7512 - 21.7512i) q^{62} +(-20.2685 + 20.2685i) q^{63} -8.00000i q^{64} +(-7.64152 - 0.605064i) q^{65} -52.8492 q^{66} +(62.2296 + 62.2296i) q^{67} +(-8.67933 + 8.67933i) q^{68} +8.30662i q^{69} +(-51.3952 + 43.8533i) q^{70} +95.7602 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-18.3047 + 18.3047i) q^{73} +37.0687i q^{74} +(25.4185 + 35.0557i) q^{75} -3.22020 q^{76} +(-145.768 - 145.768i) q^{77} +(2.65538 - 2.65538i) q^{78} -74.1858i q^{79} +(-12.9817 - 15.2143i) q^{80} -9.00000 q^{81} +(-55.4586 - 55.4586i) q^{82} +(29.2294 - 29.2294i) q^{83} -33.0983i q^{84} +(-2.42217 + 30.5903i) q^{85} -90.2487 q^{86} +(-13.0530 - 13.0530i) q^{87} +(43.1512 - 43.1512i) q^{88} -148.863i q^{89} +(-21.1470 - 1.67444i) q^{90} +14.6481 q^{91} +(-6.78233 - 6.78233i) q^{92} +(26.6397 - 26.6397i) q^{93} +80.0419i q^{94} +(-6.12413 + 5.22546i) q^{95} +9.79796 q^{96} +(-47.9480 - 47.9480i) q^{97} +(42.2916 - 42.2916i) q^{98} -64.7268i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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