LMFDB - Embedded newform 287.2.c.a.204.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(204,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("287.204");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.c (of order $2$, degree $1$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 60x^{6} + 118x^{4} + 96x^{2} + 25 $ x^10 + 13x^8 + 60x^6 + 118x^4 + 96x^2 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			204.7
Root			$-1.06459i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.a.204.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.86664 q^{2} -0.0645923i q^{3} +1.48436 q^{4} +1.44688 q^{5} -0.120571i q^{6} +1.00000i q^{7} -0.962521 q^{8} +2.99583 q^{9} +O(q^{10})$	\(q+1.86664 q^{2} -0.0645923i q^{3} +1.48436 q^{4} +1.44688 q^{5} -0.120571i q^{6} +1.00000i q^{7} -0.962521 q^{8} +2.99583 q^{9} +2.70081 q^{10} -3.66952i q^{11} -0.0958780i q^{12} +3.50286i q^{13} +1.86664i q^{14} -0.0934572i q^{15} -4.76540 q^{16} -3.58024i q^{17} +5.59214 q^{18} +4.69663i q^{19} +2.14768 q^{20} +0.0645923 q^{21} -6.84969i q^{22} -4.19378 q^{23} +0.0621714i q^{24} -2.90654 q^{25} +6.53858i q^{26} -0.387284i q^{27} +1.48436i q^{28} -6.35183i q^{29} -0.174451i q^{30} -6.39002 q^{31} -6.97026 q^{32} -0.237023 q^{33} -6.68302i q^{34} +1.44688i q^{35} +4.44688 q^{36} +4.85628 q^{37} +8.76694i q^{38} +0.226258 q^{39} -1.39265 q^{40} +(0.0637664 + 6.40281i) q^{41} +0.120571 q^{42} +0.370379 q^{43} -5.44688i q^{44} +4.33460 q^{45} -7.82829 q^{46} +3.74519i q^{47} +0.307808i q^{48} -1.00000 q^{49} -5.42548 q^{50} -0.231256 q^{51} +5.19949i q^{52} -4.45259i q^{53} -0.722921i q^{54} -5.30935i q^{55} -0.962521i q^{56} +0.303366 q^{57} -11.8566i q^{58} -5.66245 q^{59} -0.138724i q^{60} -5.22424 q^{61} -11.9279 q^{62} +2.99583i q^{63} -3.48018 q^{64} +5.06821i q^{65} -0.442437 q^{66} +10.5818i q^{67} -5.31435i q^{68} +0.270886i q^{69} +2.70081i q^{70} -8.10481i q^{71} -2.88355 q^{72} +14.6669 q^{73} +9.06494 q^{74} +0.187740i q^{75} +6.97148i q^{76} +3.66952 q^{77} +0.422342 q^{78} -15.8739i q^{79} -6.89495 q^{80} +8.96247 q^{81} +(0.119029 + 11.9518i) q^{82} +6.50071 q^{83} +0.0958780 q^{84} -5.18016i q^{85} +0.691366 q^{86} -0.410279 q^{87} +3.53199i q^{88} +17.3213i q^{89} +8.09115 q^{90} -3.50286 q^{91} -6.22506 q^{92} +0.412746i q^{93} +6.99094i q^{94} +6.79546i q^{95} +0.450225i q^{96} -6.01521i q^{97} -1.86664 q^{98} -10.9933i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9	$ 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9} + 8 q^{10} - 16 q^{16} + 20 q^{18} - 22 q^{20} - 12 q^{21} - 4 q^{23} - 4 q^{25} + 14 q^{31} + 18 q^{32} - 2 q^{33} + 20 q^{36} - 22 q^{37} - 46 q^{39} - 58 q^{40} - 4 q^{41} - 8 q^{42} + 18 q^{43} + 50 q^{45} + 8 q^{46} - 10 q^{49} - 22 q^{50} + 14 q^{51} + 62 q^{57} + 34 q^{59} - 28 q^{61} - 44 q^{62} + 8 q^{64} - 36 q^{66} - 20 q^{72} + 12 q^{74} + 12 q^{77} + 78 q^{78} - 4 q^{80} + 10 q^{81} + 74 q^{82} - 20 q^{83} - 6 q^{84} + 12 q^{86} - 8 q^{87} - 54 q^{90} - 14 q^{91} - 30 q^{92} - 4 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9 + 8 * q^10 - 16 * q^16 + 20 * q^18 - 22 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^25 + 14 * q^31 + 18 * q^32 - 2 * q^33 + 20 * q^36 - 22 * q^37 - 46 * q^39 - 58 * q^40 - 4 * q^41 - 8 * q^42 + 18 * q^43 + 50 * q^45 + 8 * q^46 - 10 * q^49 - 22 * q^50 + 14 * q^51 + 62 * q^57 + 34 * q^59 - 28 * q^61 - 44 * q^62 + 8 * q^64 - 36 * q^66 - 20 * q^72 + 12 * q^74 + 12 * q^77 + 78 * q^78 - 4 * q^80 + 10 * q^81 + 74 * q^82 - 20 * q^83 - 6 * q^84 + 12 * q^86 - 8 * q^87 - 54 * q^90 - 14 * q^91 - 30 * q^92 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.86664			1.31992			0.659958	−	0.751302i	$-0.270574\pi$
$2$	1.86664			1.31992			0.659958	+	0.751302i	$0.270574\pi$
$3$		−	0.0645923i		−	0.0372924i	−0.999826	−	0.0186462i	$-0.994064\pi$
$3$		−	0.0645923i		−	0.0372924i	0.999826	−	0.0186462i	$-0.00593561\pi$
$4$	1.48436			0.742179
$5$	1.44688			0.647064			0.323532	−	0.946217i	$-0.395130\pi$
$5$	1.44688			0.647064			0.323532	+	0.946217i	$0.395130\pi$
$6$		−	0.120571i		−	0.0492228i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−0.962521			−0.340303
$9$	2.99583			0.998609
$10$	2.70081			0.854070
$11$		−	3.66952i		−	1.10640i	−0.833048	−	0.553201i	$-0.813406\pi$
$11$		−	3.66952i		−	1.10640i	0.833048	−	0.553201i	$-0.186594\pi$
$12$		−	0.0958780i		−	0.0276776i
$13$			3.50286i			0.971518i	0.874093	+	0.485759i	$0.161457\pi$
$13$			3.50286i			0.971518i	−0.874093	+	0.485759i	$0.838543\pi$
$14$			1.86664i			0.498881i
$15$		−	0.0934572i		−	0.0241305i
$16$	−4.76540			−1.19135
$17$		−	3.58024i		−	0.868335i	−0.900832	−	0.434167i	$-0.857043\pi$
$17$		−	3.58024i		−	0.868335i	0.900832	−	0.434167i	$-0.142957\pi$
$18$	5.59214			1.31808
$19$			4.69663i			1.07748i	0.842472	+	0.538741i	$0.181100\pi$
$19$			4.69663i			1.07748i	−0.842472	+	0.538741i	$0.818900\pi$
$20$	2.14768			0.480237
$21$	0.0645923			0.0140952
$22$		−	6.84969i		−	1.46036i
$23$	−4.19378			−0.874463			−0.437231	−	0.899349i	$-0.644041\pi$
$23$	−4.19378			−0.874463			−0.437231	+	0.899349i	$0.644041\pi$
$24$			0.0621714i			0.0126907i
$25$	−2.90654			−0.581309
$26$			6.53858i			1.28232i
$27$		−	0.387284i		−	0.0745329i
$28$			1.48436i			0.280517i
$29$		−	6.35183i		−	1.17950i	−0.807584	−	0.589752i	$-0.799225\pi$
$29$		−	6.35183i		−	1.17950i	0.807584	−	0.589752i	$-0.200775\pi$
$30$		−	0.174451i		−	0.0318503i
$31$	−6.39002			−1.14768			−0.573841	−	0.818967i	$-0.694547\pi$
$31$	−6.39002			−1.14768			−0.573841	+	0.818967i	$0.694547\pi$
$32$	−6.97026			−1.23218
$33$	−0.237023			−0.0412604
$34$		−	6.68302i		−	1.14613i
$35$			1.44688i			0.244567i
$36$	4.44688			0.741146
$37$	4.85628			0.798367			0.399184	−	0.916871i	$-0.369294\pi$
$37$	4.85628			0.798367			0.399184	+	0.916871i	$0.369294\pi$
$38$			8.76694i			1.42219i
$39$	0.226258			0.0362302
$40$	−1.39265			−0.220198
$41$	0.0637664	+	6.40281i	0.00995864	+	0.999950i
$41$	0.0637664	+	6.40281i	0.00995864	+	0.999950i
$42$	0.120571			0.0186045
$43$	0.370379			0.0564823			0.0282412	−	0.999601i	$-0.491009\pi$
$43$	0.370379			0.0564823			0.0282412	+	0.999601i	$0.491009\pi$
$44$		−	5.44688i		−	0.821148i
$45$	4.33460			0.646164
$46$	−7.82829			−1.15422
$47$			3.74519i			0.546293i	0.961973	+	0.273146i	$0.0880643\pi$
$47$			3.74519i			0.546293i	−0.961973	+	0.273146i	$0.911936\pi$
$48$			0.307808i			0.0444282i
$49$	−1.00000			−0.142857
$50$	−5.42548			−0.767279
$51$	−0.231256			−0.0323823
$52$			5.19949i			0.721040i
$53$		−	4.45259i		−	0.611611i	−0.952094	−	0.305805i	$-0.901074\pi$
$53$		−	4.45259i		−	0.611611i	0.952094	−	0.305805i	$-0.0989257\pi$
$54$		−	0.722921i		−	0.0983771i
$55$		−	5.30935i		−	0.715913i
$56$		−	0.962521i		−	0.128622i
$57$	0.303366			0.0401818
$58$		−	11.8566i		−	1.55685i
$59$	−5.66245			−0.737188			−0.368594	−	0.929590i	$-0.620161\pi$
$59$	−5.66245			−0.737188			−0.368594	+	0.929590i	$0.620161\pi$
$60$		−	0.138724i		−	0.0179092i
$61$	−5.22424			−0.668895			−0.334447	−	0.942414i	$-0.608550\pi$
$61$	−5.22424			−0.668895			−0.334447	+	0.942414i	$0.608550\pi$
$62$	−11.9279			−1.51484
$63$			2.99583i			0.377439i
$64$	−3.48018			−0.435023
$65$			5.06821i			0.628634i
$66$	−0.442437			−0.0544602
$67$			10.5818i			1.29277i	0.763012	+	0.646385i	$0.223720\pi$
$67$			10.5818i			1.29277i	−0.763012	+	0.646385i	$0.776280\pi$
$68$		−	5.31435i		−	0.644459i
$69$			0.270886i			0.0326108i
$70$			2.70081i			0.322808i
$71$		−	8.10481i		−	0.961864i	−0.876758	−	0.480932i	$-0.840298\pi$
$71$		−	8.10481i		−	0.961864i	0.876758	−	0.480932i	$-0.159702\pi$
$72$	−2.88355			−0.339829
$73$	14.6669			1.71663			0.858315	−	0.513123i	$-0.171512\pi$
$73$	14.6669			1.71663			0.858315	+	0.513123i	$0.171512\pi$
$74$	9.06494			1.05378
$75$			0.187740i			0.0216784i
$76$			6.97148i			0.799684i
$77$	3.66952			0.418181
$78$	0.422342			0.0478208
$79$		−	15.8739i		−	1.78595i	−0.450103	−	0.892977i	$-0.648613\pi$
$79$		−	15.8739i		−	1.78595i	0.450103	−	0.892977i	$-0.351387\pi$
$80$	−6.89495			−0.770879
$81$	8.96247			0.995830
$82$	0.119029	+	11.9518i	0.0131446	+	1.31985i
$83$	6.50071			0.713545			0.356773	−	0.934191i	$-0.383877\pi$
$83$	6.50071			0.713545			0.356773	+	0.934191i	$0.383877\pi$
$84$	0.0958780			0.0104611
$85$		−	5.18016i		−	0.561868i
$86$	0.691366			0.0745519
$87$	−0.410279			−0.0439865
$88$			3.53199i			0.376512i
$89$			17.3213i			1.83605i	0.396523	+	0.918025i	$0.370217\pi$
$89$			17.3213i			1.83605i	−0.396523	+	0.918025i	$0.629783\pi$
$90$	8.09115			0.852882
$91$	−3.50286			−0.367199
$92$	−6.22506			−0.649008
$93$			0.412746i			0.0427998i
$94$			6.99094i			0.721060i
$95$			6.79546i			0.697199i
$96$			0.450225i			0.0459509i
$97$		−	6.01521i		−	0.610752i	−0.952232	−	0.305376i	$-0.901218\pi$
$97$		−	6.01521i		−	0.610752i	0.952232	−	0.305376i	$-0.0987821\pi$
$98$	−1.86664			−0.188559
$99$		−	10.9933i		−	1.10486i
$100$	−4.31435			−0.431435
$101$		−	16.8887i		−	1.68049i	−0.542208	−	0.840245i	$-0.682411\pi$
$101$		−	16.8887i		−	1.68049i	0.542208	−	0.840245i	$-0.317589\pi$
$102$	−0.431672			−0.0427419
$103$	11.2826			1.11171			0.555853	−	0.831281i	$-0.312392\pi$
$103$	11.2826			1.11171			0.555853	+	0.831281i	$0.312392\pi$
$104$		−	3.37157i		−	0.330610i
$105$	0.0934572			0.00912049
$106$		−	8.31140i		−	0.807275i
$107$	6.27270			0.606404			0.303202	−	0.952926i	$-0.401944\pi$
$107$	6.27270			0.606404			0.303202	+	0.952926i	$0.401944\pi$
$108$		−	0.574868i		−	0.0553167i
$109$			15.7743i			1.51091i	0.655203	+	0.755453i	$0.272583\pi$
$109$			15.7743i			1.51091i	−0.655203	+	0.755453i	$0.727417\pi$
$110$		−	9.91066i		−	0.944945i
$111$		−	0.313678i		−	0.0297730i
$112$		−	4.76540i		−	0.450288i
$113$	17.5907			1.65479			0.827397	−	0.561617i	$-0.189821\pi$
$113$	17.5907			1.65479			0.827397	+	0.561617i	$0.189821\pi$
$114$	0.566277			0.0530367
$115$	−6.06789			−0.565833
$116$		−	9.42838i		−	0.875403i
$117$			10.4940i			0.970167i
$118$	−10.5698			−0.973026
$119$	3.58024			0.328200
$120$			0.0899545i			0.00821169i
$121$	−2.46538			−0.224125
$122$	−9.75179			−0.882885
$123$	0.413572	−	0.00411882i	0.0372905	−	0.000371381i
$124$	−9.48507			−0.851785
$125$	−11.4398			−1.02321
$126$			5.59214i			0.498188i
$127$	−11.4945			−1.01997			−0.509987	−	0.860182i	$-0.670350\pi$
$127$	−11.4945			−1.01997			−0.509987	+	0.860182i	$0.670350\pi$
$128$	7.44425			0.657985
$129$		−	0.0239236i		−	0.00210636i
$130$			9.46054i			0.829744i
$131$	−2.33579			−0.204079			−0.102040	−	0.994780i	$-0.532537\pi$
$131$	−2.33579			−0.204079			−0.102040	+	0.994780i	$0.532537\pi$
$132$	−0.351826			−0.0306225
$133$	−4.69663			−0.407250
$134$			19.7524i			1.70635i
$135$		−	0.560353i		−	0.0482275i
$136$			3.44605i			0.295497i
$137$			9.60307i			0.820445i	0.911985	+	0.410223i	$0.134549\pi$
$137$			9.60307i			0.820445i	−0.911985	+	0.410223i	$0.865451\pi$
$138$			0.505647i			0.0430435i
$139$	5.23258			0.443822			0.221911	−	0.975067i	$-0.428771\pi$
$139$	5.23258			0.443822			0.221911	+	0.975067i	$0.428771\pi$
$140$			2.14768i			0.181512i
$141$	0.241911			0.0203725
$142$		−	15.1288i		−	1.26958i
$143$	12.8538			1.07489
$144$	−14.2763			−1.18969
$145$		−	9.19032i		−	0.763215i
$146$	27.3779			2.26581
$147$			0.0645923i			0.00532748i
$148$	7.20845			0.592531
$149$			2.08814i			0.171067i	0.996335	+	0.0855337i	$0.0272595\pi$
$149$			2.08814i			0.171067i	−0.996335	+	0.0855337i	$0.972740\pi$
$150$			0.350444i			0.0286136i
$151$			5.40446i			0.439809i	0.975521	+	0.219904i	$0.0705745\pi$
$151$			5.40446i			0.439809i	−0.975521	+	0.219904i	$0.929425\pi$
$152$		−	4.52061i		−	0.366670i
$153$		−	10.7258i		−	0.867127i
$154$	6.84969			0.551963
$155$	−9.24558			−0.742623
$156$	0.335847			0.0268893
$157$		−	4.48353i		−	0.357825i	−0.983865	−	0.178912i	$-0.942742\pi$
$157$		−	4.48353i		−	0.357825i	0.983865	−	0.178912i	$-0.0572579\pi$
$158$		−	29.6309i		−	2.35731i
$159$	−0.287603			−0.0228084
$160$	−10.0851			−0.797298
$161$		−	4.19378i		−	0.330516i
$162$	16.7297			1.31441
$163$	−11.9188			−0.933552			−0.466776	−	0.884376i	$-0.654585\pi$
$163$	−11.9188			−0.933552			−0.466776	+	0.884376i	$0.654585\pi$
$164$	0.0946521	+	9.50405i	0.00739109	+	0.742142i
$165$	−0.342943			−0.0266981
$166$	12.1345			0.941820
$167$		−	1.24691i		−	0.0964887i	−0.998836	−	0.0482443i	$-0.984637\pi$
$167$		−	1.24691i		−	0.0964887i	0.998836	−	0.0482443i	$-0.0153626\pi$
$168$	−0.0621714			−0.00479663
$169$	0.729994			0.0561534
$170$		−	9.66952i		−	0.741618i
$171$			14.0703i			1.07598i
$172$	0.549775			0.0419200
$173$	10.8966			0.828453			0.414227	−	0.910174i	$-0.364052\pi$
$173$	10.8966			0.828453			0.414227	+	0.910174i	$0.364052\pi$
$174$	−0.765844			−0.0580585
$175$		−	2.90654i		−	0.219714i
$176$			17.4867i			1.31811i
$177$			0.365750i			0.0274915i
$178$			32.3326i			2.42343i
$179$			3.91369i			0.292523i	0.989246	+	0.146262i	$0.0467241\pi$
$179$			3.91369i			0.292523i	−0.989246	+	0.146262i	$0.953276\pi$
$180$	6.43409			0.479569
$181$		−	16.6941i		−	1.24086i	−0.784261	−	0.620431i	$-0.786958\pi$
$181$		−	16.6941i		−	1.24086i	0.784261	−	0.620431i	$-0.213042\pi$
$182$	−6.53858			−0.484672
$183$			0.337445i			0.0249447i
$184$	4.03660			0.297582
$185$	7.02644			0.516594
$186$			0.770450i			0.0564921i
$187$	−13.1377			−0.960727
$188$			5.55920i			0.405447i
$189$	0.387284			0.0281708
$190$			12.6847i			0.920245i
$191$			18.8426i			1.36340i	0.731630	+	0.681702i	$0.238760\pi$
$191$			18.8426i			1.36340i	−0.731630	+	0.681702i	$0.761240\pi$
$192$			0.224793i			0.0162230i
$193$		−	1.30404i		−	0.0938665i	−0.998898	−	0.0469333i	$-0.985055\pi$
$193$		−	1.30404i		−	0.0938665i	0.998898	−	0.0469333i	$-0.0149448\pi$
$194$		−	11.2282i		−	0.806141i
$195$	0.327367			0.0234432
$196$	−1.48436			−0.106026
$197$	−2.02020			−0.143934			−0.0719668	−	0.997407i	$-0.522928\pi$
$197$	−2.02020			−0.143934			−0.0719668	+	0.997407i	$0.522928\pi$
$198$		−	20.5205i		−	1.45833i
$199$		−	6.66333i		−	0.472351i	−0.971710	−	0.236175i	$-0.924106\pi$
$199$		−	6.66333i		−	0.472351i	0.971710	−	0.236175i	$-0.0758940\pi$
$200$	2.79761			0.197821
$201$	0.683501			0.0482104
$202$		−	31.5252i		−	2.21810i
$203$	6.35183			0.445811
$204$	−0.343266			−0.0240334
$205$	0.0922622	+	9.26408i	0.00644387	+	0.647032i
$206$	21.0606			1.46736
$207$	−12.5638			−0.873247
$208$		−	16.6925i		−	1.15742i
$209$	17.2344			1.19213
$210$	0.174451			0.0120383
$211$			16.4414i			1.13187i	0.824449	+	0.565936i	$0.191485\pi$
$211$			16.4414i			1.13187i	−0.824449	+	0.565936i	$0.808515\pi$
$212$		−	6.60924i		−	0.453924i
$213$	−0.523508			−0.0358702
$214$	11.7089			0.800403
$215$	0.535894			0.0365477
$216$			0.372769i			0.0253637i
$217$		−	6.39002i		−	0.433783i
$218$			29.4450i			1.99427i
$219$		−	0.947368i		−	0.0640172i
$220$		−	7.88097i		−	0.531335i
$221$	12.5411			0.843602
$222$		−	0.585525i		−	0.0392979i
$223$	3.84278			0.257331			0.128666	−	0.991688i	$-0.458931\pi$
$223$	3.84278			0.257331			0.128666	+	0.991688i	$0.458931\pi$
$224$		−	6.97026i		−	0.465720i
$225$	−8.70750			−0.580500
$226$	32.8356			2.18419
$227$		−	6.79793i		−	0.451194i	−0.974221	−	0.225597i	$-0.927567\pi$
$227$		−	6.79793i		−	0.451194i	0.974221	−	0.225597i	$-0.0724333\pi$
$228$	0.450304			0.0298221
$229$			4.69575i			0.310304i	0.987891	+	0.155152i	$0.0495868\pi$
$229$			4.69575i			0.310304i	−0.987891	+	0.155152i	$0.950413\pi$
$230$	−11.3266			−0.746852
$231$		−	0.237023i		−	0.0155949i
$232$			6.11377i			0.401389i
$233$		−	2.09654i		−	0.137349i	−0.997639	−	0.0686745i	$-0.978123\pi$
$233$		−	2.09654i		−	0.137349i	0.997639	−	0.0686745i	$-0.0218770\pi$
$234$			19.5885i			1.28054i
$235$			5.41884i			0.353486i
$236$	−8.40510			−0.547125
$237$	−1.02533			−0.0666024
$238$	6.68302			0.433196
$239$		−	22.0865i		−	1.42866i	−0.699809	−	0.714330i	$-0.746732\pi$
$239$		−	22.0865i		−	1.42866i	0.699809	−	0.714330i	$-0.253268\pi$
$240$			0.445361i			0.0287479i
$241$	−25.0114			−1.61113			−0.805563	−	0.592510i	$-0.798137\pi$
$241$	−25.0114			−1.61113			−0.805563	+	0.592510i	$0.798137\pi$
$242$	−4.60198			−0.295827
$243$		−	1.74076i		−	0.111670i
$244$	−7.75463			−0.496440
$245$	−1.44688			−0.0924377
$246$	0.771991	−	0.00768836i	0.0492204	−	0.000490192i
$247$	−16.4516			−1.04679
$248$	6.15053			0.390559
$249$		−	0.419895i		−	0.0266098i
$250$	−21.3540			−1.35055
$251$	−11.2481			−0.709971			−0.354985	−	0.934872i	$-0.615514\pi$
$251$	−11.2481			−0.709971			−0.354985	+	0.934872i	$0.615514\pi$
$252$			4.44688i			0.280127i
$253$			15.3891i			0.967507i
$254$	−21.4562			−1.34628
$255$	−0.334599			−0.0209534
$256$	20.8561			1.30351
$257$		−	13.3644i		−	0.833649i	−0.908987	−	0.416824i	$-0.863143\pi$
$257$		−	13.3644i		−	0.833649i	0.908987	−	0.416824i	$-0.136857\pi$
$258$		−	0.0446569i		−	0.00278022i
$259$			4.85628i			0.301754i
$260$			7.52303i			0.466559i
$261$		−	19.0290i		−	1.17786i
$262$	−4.36009			−0.269367
$263$		−	6.67762i		−	0.411760i	−0.978577	−	0.205880i	$-0.933994\pi$
$263$		−	6.67762i		−	0.411760i	0.978577	−	0.205880i	$-0.0660056\pi$
$264$	0.228139			0.0140410
$265$		−	6.44236i		−	0.395751i
$266$	−8.76694			−0.537536
$267$	1.11882			0.0684706
$268$			15.7071i			0.959466i
$269$	−8.76154			−0.534201			−0.267100	−	0.963669i	$-0.586066\pi$
$269$	−8.76154			−0.534201			−0.267100	+	0.963669i	$0.586066\pi$
$270$		−	1.04598i		−	0.0636563i
$271$	−14.1378			−0.858808			−0.429404	−	0.903112i	$-0.641276\pi$
$271$	−14.1378			−0.858808			−0.429404	+	0.903112i	$0.641276\pi$
$272$			17.0612i			1.03449i
$273$			0.226258i			0.0136937i
$274$			17.9255i			1.08292i
$275$			10.6656i			0.643161i
$276$			0.402091i			0.0242030i
$277$	−12.8517			−0.772184			−0.386092	−	0.922460i	$-0.626175\pi$
$277$	−12.8517			−0.772184			−0.386092	+	0.922460i	$0.626175\pi$
$278$	9.76736			0.585807
$279$	−19.1434			−1.14609
$280$		−	1.39265i		−	0.0832268i
$281$		−	16.8686i		−	1.00630i	−0.864199	−	0.503149i	$-0.832175\pi$
$281$		−	16.8686i		−	1.00630i	0.864199	−	0.503149i	$-0.167825\pi$
$282$	0.451561			0.0268901
$283$	−31.2170			−1.85566			−0.927828	−	0.373007i	$-0.878327\pi$
$283$	−31.2170			−1.85566			−0.927828	+	0.373007i	$0.878327\pi$
$284$		−	12.0304i		−	0.713875i
$285$	0.438934			0.0260002
$286$	23.9935			1.41876
$287$	−6.40281	+	0.0637664i	−0.377946	+	0.00376401i
$288$	−20.8817			−1.23047
$289$	4.18192			0.245995
$290$		−	17.1550i		−	1.00738i
$291$	−0.388536			−0.0227764
$292$	21.7709			1.27405
$293$			25.9615i			1.51669i	0.651856	+	0.758343i	$0.273991\pi$
$293$			25.9615i			1.51669i	−0.651856	+	0.758343i	$0.726009\pi$
$294$			0.120571i			0.00703183i
$295$	−8.19287			−0.477008
$296$	−4.67427			−0.271686
$297$	−1.42115			−0.0824633
$298$			3.89782i			0.225795i
$299$		−	14.6902i		−	0.849556i
$300$			0.278674i			0.0160892i
$301$			0.370379i			0.0213483i
$302$			10.0882i			0.580510i
$303$	−1.09088			−0.0626694
$304$		−	22.3813i		−	1.28366i
$305$	−7.55884			−0.432818
$306$		−	20.0212i		−	1.14453i
$307$	−13.6805			−0.780787			−0.390393	−	0.920648i	$-0.627661\pi$
$307$	−13.6805			−0.780787			−0.390393	+	0.920648i	$0.627661\pi$
$308$	5.44688			0.310365
$309$		−	0.728768i		−	0.0414581i
$310$	−17.2582			−0.980200
$311$			13.4129i			0.760576i	0.924868	+	0.380288i	$0.124175\pi$
$311$			13.4129i			0.760576i	−0.924868	+	0.380288i	$0.875825\pi$
$312$	−0.217778			−0.0123292
$313$			4.79493i			0.271026i	0.990776	+	0.135513i	$0.0432682\pi$
$313$			4.79493i			0.271026i	−0.990776	+	0.135513i	$0.956732\pi$
$314$		−	8.36915i		−	0.472299i
$315$			4.33460i			0.244227i
$316$		−	23.5625i		−	1.32550i
$317$			30.1047i			1.69085i	0.534095	+	0.845424i	$0.320652\pi$
$317$			30.1047i			1.69085i	−0.534095	+	0.845424i	$0.679348\pi$
$318$	−0.536852			−0.0301052
$319$	−23.3082			−1.30501
$320$	−5.03540			−0.281488
$321$		−	0.405168i		−	0.0226143i
$322$		−	7.82829i		−	0.436253i
$323$	16.8151			0.935615
$324$	13.3035			0.739084
$325$		−	10.1812i		−	0.564752i
$326$	−22.2481			−1.23221
$327$	1.01890			0.0563453
$328$	−0.0613765	−	6.16284i	−0.00338895	−	0.340286i
$329$	−3.74519			−0.206479
$330$	−0.640152			−0.0352392
$331$		−	9.22719i		−	0.507172i	−0.967313	−	0.253586i	$-0.918390\pi$
$331$		−	9.22719i		−	0.507172i	0.967313	−	0.253586i	$-0.0816101\pi$
$332$	9.64937			0.529578
$333$	14.5486			0.797257
$334$		−	2.32753i		−	0.127357i
$335$			15.3105i			0.836504i
$336$	−0.307808			−0.0167923
$337$	−17.0199			−0.927132			−0.463566	−	0.886062i	$-0.653430\pi$
$337$	−17.0199			−0.927132			−0.463566	+	0.886062i	$0.653430\pi$
$338$	1.36264			0.0741177
$339$		−	1.13622i		−	0.0617112i
$340$		−	7.68921i		−	0.417006i
$341$			23.4483i			1.26980i
$342$			26.2642i			1.42021i
$343$		−	1.00000i		−	0.0539949i
$344$	−0.356498			−0.0192211
$345$			0.391939i			0.0211013i
$346$	20.3401			1.09349
$347$		−	33.2399i		−	1.78441i	−0.451627	−	0.892207i	$-0.649156\pi$
$347$		−	33.2399i		−	1.78441i	0.451627	−	0.892207i	$-0.350844\pi$
$348$	−0.609000			−0.0326459
$349$	−35.1497			−1.88152			−0.940760	−	0.339072i	$-0.889887\pi$
$349$	−35.1497			−1.88152			−0.940760	+	0.339072i	$0.889887\pi$
$350$		−	5.42548i		−	0.290004i
$351$	1.35660			0.0724100
$352$			25.5775i			1.36329i
$353$	28.2311			1.50259			0.751296	−	0.659965i	$-0.229429\pi$
$353$	28.2311			1.50259			0.751296	+	0.659965i	$0.229429\pi$
$354$			0.682726i			0.0362865i
$355$		−	11.7267i		−	0.622387i
$356$			25.7109i			1.36268i
$357$		−	0.231256i		−	0.0122393i
$358$			7.30547i			0.386106i
$359$	6.36389			0.335873			0.167937	−	0.985798i	$-0.446290\pi$
$359$	6.36389			0.335873			0.167937	+	0.985798i	$0.446290\pi$
$360$	−4.17214			−0.219891
$361$	−3.05837			−0.160967
$362$		−	31.1619i		−	1.63783i
$363$			0.159244i			0.00835816i
$364$	−5.19949			−0.272527
$365$	21.2212			1.11077
$366$			0.629890i			0.0329249i
$367$	6.35326			0.331637			0.165819	−	0.986156i	$-0.446973\pi$
$367$	6.35326			0.331637			0.165819	+	0.986156i	$0.446973\pi$
$368$	19.9850			1.04179
$369$	0.191033	+	19.1817i	0.00994479	+	0.998560i
$370$	13.1159			0.681861
$371$	4.45259			0.231167
$372$			0.612662i			0.0317651i
$373$	−5.49171			−0.284350			−0.142175	−	0.989842i	$-0.545410\pi$
$373$	−5.49171			−0.284350			−0.142175	+	0.989842i	$0.545410\pi$
$374$	−24.5235			−1.26808
$375$			0.738923i			0.0381578i
$376$		−	3.60483i		−	0.185905i
$377$	22.2495			1.14591
$378$	0.722921			0.0371831
$379$	7.01031			0.360095			0.180048	−	0.983658i	$-0.442375\pi$
$379$	7.01031			0.360095			0.180048	+	0.983658i	$0.442375\pi$
$380$			10.0869i			0.517446i
$381$			0.742457i			0.0380372i
$382$			35.1724i			1.79958i
$383$			3.16552i			0.161751i	0.996724	+	0.0808753i	$0.0257716\pi$
$383$			3.16552i			0.161751i	−0.996724	+	0.0808753i	$0.974228\pi$
$384$		−	0.480841i		−	0.0245378i
$385$	5.30935			0.270590
$386$		−	2.43417i		−	0.123896i
$387$	1.10959			0.0564038
$388$		−	8.92872i		−	0.453287i
$389$	4.68467			0.237522			0.118761	−	0.992923i	$-0.462108\pi$
$389$	4.68467			0.237522			0.118761	+	0.992923i	$0.462108\pi$
$390$	0.611078			0.0309431
$391$			15.0147i			0.759326i
$392$	0.962521			0.0486147
$393$			0.150874i			0.00761060i
$394$	−3.77100			−0.189980
$395$		−	22.9676i		−	1.15563i
$396$		−	16.3179i		−	0.820006i
$397$			5.87659i			0.294937i	0.989067	+	0.147469i	$0.0471126\pi$
$397$			5.87659i			0.294937i	−0.989067	+	0.147469i	$0.952887\pi$
$398$		−	12.4381i		−	0.623463i
$399$			0.303366i			0.0151873i
$400$	13.8508			0.692542
$401$	−0.315726			−0.0157666			−0.00788331	−	0.999969i	$-0.502509\pi$
$401$	−0.315726			−0.0157666			−0.00788331	+	0.999969i	$0.502509\pi$
$402$	1.27585			0.0636337
$403$		−	22.3833i		−	1.11499i
$404$		−	25.0689i		−	1.24722i
$405$	12.9676			0.644365
$406$	11.8566			0.588433
$407$		−	17.8202i		−	0.883315i
$408$	0.222588			0.0110198
$409$	19.0784			0.943364			0.471682	−	0.881769i	$-0.343647\pi$
$409$	19.0784			0.943364			0.471682	+	0.881769i	$0.343647\pi$
$410$	0.172221	+	17.2927i	0.00850537	+	0.854027i
$411$	0.620284			0.0305964
$412$	16.7474			0.825084
$413$		−	5.66245i		−	0.278631i
$414$	−23.4522			−1.15261
$415$	9.40573			0.461709
$416$		−	24.4158i		−	1.19708i
$417$		−	0.337984i		−	0.0165512i
$418$	32.1705			1.57351
$419$	13.1302			0.641453			0.320727	−	0.947172i	$-0.396073\pi$
$419$	13.1302			0.641453			0.320727	+	0.947172i	$0.396073\pi$
$420$	0.138724			0.00676903
$421$		−	22.9414i		−	1.11809i	−0.829136	−	0.559047i	$-0.811167\pi$
$421$		−	22.9414i		−	1.11809i	0.829136	−	0.559047i	$-0.188833\pi$
$422$			30.6902i			1.49398i
$423$			11.2200i			0.545533i
$424$			4.28571i			0.208133i
$425$			10.4061i			0.504770i
$426$	−0.977203			−0.0473456
$427$		−	5.22424i		−	0.252819i
$428$	9.31092			0.450060
$429$		−	0.830256i		−	0.0400852i
$430$	1.00032			0.0482399
$431$	−3.18713			−0.153519			−0.0767593	−	0.997050i	$-0.524457\pi$
$431$	−3.18713			−0.153519			−0.0767593	+	0.997050i	$0.524457\pi$
$432$			1.84556i			0.0887947i
$433$	30.2234			1.45244			0.726222	−	0.687460i	$-0.241274\pi$
$433$	30.2234			1.45244			0.726222	+	0.687460i	$0.241274\pi$
$434$		−	11.9279i		−	0.572557i
$435$	−0.593624			−0.0284621
$436$			23.4147i			1.12136i
$437$		−	19.6966i		−	0.942218i
$438$		−	1.76840i		−	0.0844973i
$439$			30.2194i			1.44229i	0.692782	+	0.721147i	$0.256385\pi$
$439$			30.2194i			1.44229i	−0.692782	+	0.721147i	$0.743615\pi$
$440$			5.11036i			0.243627i
$441$	−2.99583			−0.142658
$442$	23.4097			1.11348
$443$	40.2402			1.91187			0.955934	−	0.293582i	$-0.0948473\pi$
$443$	40.2402			1.91187			0.955934	+	0.293582i	$0.0948473\pi$
$444$		−	0.465610i		−	0.0220969i
$445$			25.0618i			1.18804i
$446$	7.17309			0.339656
$447$	0.134878			0.00637951
$448$		−	3.48018i		−	0.164423i
$449$	14.4564			0.682238			0.341119	−	0.940020i	$-0.389194\pi$
$449$	14.4564			0.682238			0.341119	+	0.940020i	$0.389194\pi$
$450$	−16.2538			−0.766211
$451$	23.4952	−	0.233992i	1.10635	−	0.0110183i
$452$	26.1109			1.22815
$453$	0.349086			0.0164015
$454$		−	12.6893i		−	0.595538i
$455$	−5.06821			−0.237601
$456$	−0.291996			−0.0136740
$457$			22.9392i			1.07305i	0.843885	+	0.536525i	$0.180263\pi$
$457$			22.9392i			1.07305i	−0.843885	+	0.536525i	$0.819737\pi$
$458$			8.76530i			0.409576i
$459$	−1.38657			−0.0647195
$460$	−9.00691			−0.419949
$461$	−13.0678			−0.608629			−0.304315	−	0.952572i	$-0.598427\pi$
$461$	−13.0678			−0.608629			−0.304315	+	0.952572i	$0.598427\pi$
$462$		−	0.442437i		−	0.0205840i
$463$		−	26.0405i		−	1.21020i	−0.796148	−	0.605101i	$-0.793133\pi$
$463$		−	26.0405i		−	1.21020i	0.796148	−	0.605101i	$-0.206867\pi$
$464$			30.2690i			1.40520i
$465$			0.597193i			0.0276942i
$466$		−	3.91349i		−	0.181289i
$467$	−33.7711			−1.56274			−0.781369	−	0.624069i	$-0.785478\pi$
$467$	−33.7711			−1.56274			−0.781369	+	0.624069i	$0.785478\pi$
$468$			15.5768i			0.720037i
$469$	−10.5818			−0.488621
$470$			10.1150i			0.466572i
$471$	−0.289602			−0.0133441
$472$	5.45023			0.250867
$473$		−	1.35911i		−	0.0624922i
$474$	−1.91393			−0.0879096
$475$		−	13.6510i		−	0.626349i
$476$	5.31435			0.243583
$477$		−	13.3392i		−	0.610760i
$478$		−	41.2277i		−	1.88571i
$479$		−	15.0034i		−	0.685524i	−0.939422	−	0.342762i	$-0.888638\pi$
$479$		−	15.0034i		−	0.685524i	0.939422	−	0.342762i	$-0.111362\pi$
$480$			0.651420i			0.0297331i
$481$			17.0108i			0.775628i
$482$	−46.6874			−2.12655
$483$	−0.270886			−0.0123257
$484$	−3.65950			−0.166341
$485$		−	8.70327i		−	0.395195i
$486$		−	3.24938i		−	0.147395i
$487$	43.6766			1.97918			0.989588	−	0.143932i	$-0.0459745\pi$
$487$	43.6766			1.97918			0.989588	+	0.143932i	$0.0459745\pi$
$488$	5.02844			0.227627
$489$			0.769862i			0.0348144i
$490$	−2.70081			−0.122010
$491$	−32.9897			−1.48881			−0.744403	−	0.667730i	$-0.767266\pi$
$491$	−32.9897			−1.48881			−0.744403	+	0.667730i	$0.767266\pi$
$492$	0.613888	−	0.00611380i	0.0276762	−	0.000275631i
$493$	−22.7410			−1.02420
$494$	−30.7093			−1.38168
$495$		−	15.9059i		−	0.714917i
$496$	30.4510			1.36729
$497$	8.10481			0.363550
$498$		−	0.783795i		−	0.0351227i
$499$			33.8556i			1.51558i	0.652497	+	0.757791i	$0.273722\pi$
$499$			33.8556i			1.51558i	−0.652497	+	0.757791i	$0.726278\pi$
$500$	−16.9808			−0.759403
$501$	−0.0805407			−0.00359829
$502$	−20.9961			−0.937102
$503$			29.3143i			1.30706i	0.756901	+	0.653530i	$0.226713\pi$
$503$			29.3143i			1.30706i	−0.756901	+	0.653530i	$0.773287\pi$
$504$		−	2.88355i		−	0.128443i
$505$		−	24.4359i		−	1.08738i
$506$			28.7261i			1.27703i
$507$		−	0.0471520i		−	0.00209409i
$508$	−17.0620			−0.757002
$509$		−	4.56702i		−	0.202430i	−0.994865	−	0.101215i	$-0.967727\pi$
$509$		−	4.56702i		−	0.202430i	0.994865	−	0.101215i	$-0.0322730\pi$
$510$	−0.624576			−0.0276567
$511$			14.6669i			0.648825i
$512$	24.0425			1.06254
$513$	1.81893			0.0803078
$514$		−	24.9466i		−	1.10035i
$515$	16.3245			0.719345
$516$		−	0.0355112i		−	0.00156330i
$517$	13.7431			0.604419
$518$			9.06494i			0.398291i
$519$		−	0.703836i		−	0.0308950i
$520$		−	4.87826i		−	0.213926i
$521$		−	7.67776i		−	0.336369i	−0.985756	−	0.168184i	$-0.946210\pi$
$521$		−	7.67776i		−	0.336369i	0.985756	−	0.168184i	$-0.0537904\pi$
$522$		−	35.5203i		−	1.55468i
$523$	12.9188			0.564898			0.282449	−	0.959282i	$-0.408853\pi$
$523$	12.9188			0.564898			0.282449	+	0.959282i	$0.408853\pi$
$524$	−3.46715			−0.151463
$525$	−0.187740			−0.00819366
$526$		−	12.4647i		−	0.543489i
$527$			22.8778i			0.996572i
$528$	1.12951			0.0491555
$529$	−5.41224			−0.235315
$530$		−	12.0256i		−	0.522358i
$531$	−16.9637			−0.736163
$532$	−6.97148			−0.302252
$533$	−22.4281	+	0.223365i	−0.971470	+	0.00967499i
$534$	2.08844			0.0903755
$535$	9.07583			0.392382
$536$		−	10.1852i		−	0.439933i
$537$	0.252794			0.0109089
$538$	−16.3547			−0.705100
$539$			3.66952i			0.158057i
$540$		−	0.831764i		−	0.0357934i
$541$	19.0299			0.818157			0.409079	−	0.912499i	$-0.365850\pi$
$541$	19.0299			0.818157			0.409079	+	0.912499i	$0.365850\pi$
$542$	−26.3902			−1.13355
$543$	−1.07831			−0.0462747
$544$			24.9552i			1.06994i
$545$			22.8235i			0.977653i
$546$			0.422342i			0.0180746i
$547$			8.94019i			0.382255i	0.981565	+	0.191127i	$0.0612144\pi$
$547$			8.94019i			0.382255i	−0.981565	+	0.191127i	$0.938786\pi$
$548$			14.2544i			0.608917i
$549$	−15.6509			−0.667965
$550$			19.9089i			0.848918i
$551$	29.8322			1.27089
$552$		−	0.260733i		−	0.0110975i
$553$	15.8739			0.675027
$554$	−23.9896			−1.01922
$555$		−	0.453854i		−	0.0192650i
$556$	7.76702			0.329395
$557$		−	38.8166i		−	1.64471i	−0.568974	−	0.822355i	$-0.692660\pi$
$557$		−	38.8166i		−	1.64471i	0.568974	−	0.822355i	$-0.307340\pi$
$558$	−35.7339			−1.51274
$559$			1.29739i			0.0548736i
$560$		−	6.89495i		−	0.291365i
$561$			0.848597i			0.0358278i
$562$		−	31.4877i		−	1.32823i
$563$			13.9821i			0.589273i	0.955609	+	0.294637i	$0.0951986\pi$
$563$			13.9821i			0.589273i	−0.955609	+	0.294637i	$0.904801\pi$
$564$	0.359082			0.0151201
$565$	25.4516			1.07076
$566$	−58.2710			−2.44931
$567$			8.96247i			0.376388i
$568$			7.80105i			0.327325i
$569$	−36.5795			−1.53349			−0.766747	−	0.641950i	$-0.778126\pi$
$569$	−36.5795			−1.53349			−0.766747	+	0.641950i	$0.778126\pi$
$570$	0.819333			0.0343181
$571$		−	11.1022i		−	0.464613i	−0.972643	−	0.232306i	$-0.925373\pi$
$571$		−	11.1022i		−	0.464613i	0.972643	−	0.232306i	$-0.0746272\pi$
$572$	19.0796			0.797760
$573$	1.21709			0.0508446
$574$	−11.9518	+	0.119029i	−0.498857	+	0.00496818i
$575$	12.1894			0.508333
$576$	−10.4260			−0.434418
$577$		−	41.0118i		−	1.70734i	−0.520810	−	0.853672i	$-0.674370\pi$
$577$		−	41.0118i		−	1.70734i	0.520810	−	0.853672i	$-0.325630\pi$
$578$	7.80615			0.324693
$579$	−0.0842306			−0.00350051
$580$		−	13.6417i		−	0.566441i
$581$			6.50071i			0.269695i
$582$	−0.725258			−0.0300629
$583$	−16.3389			−0.676687
$584$	−14.1172			−0.584174
$585$			15.1835i			0.627760i
$586$			48.4608i			2.00190i
$587$			40.3049i			1.66356i	0.555103	+	0.831781i	$0.312679\pi$
$587$			40.3049i			1.66356i	−0.555103	+	0.831781i	$0.687321\pi$
$588$			0.0958780i			0.00395394i
$589$		−	30.0116i		−	1.23661i
$590$	−15.2932			−0.629610
$591$			0.130490i			0.00536763i
$592$	−23.1421			−0.951134
$593$		−	28.4907i		−	1.16997i	−0.811043	−	0.584986i	$-0.801100\pi$
$593$		−	28.4907i		−	1.16997i	0.811043	−	0.584986i	$-0.198900\pi$
$594$	−2.65277			−0.108845
$595$	5.18016			0.212366
$596$			3.09955i			0.126963i
$597$	−0.430399			−0.0176151
$598$		−	27.4214i		−	1.12134i
$599$	−20.3928			−0.833226			−0.416613	−	0.909084i	$-0.636783\pi$
$599$	−20.3928			−0.833226			−0.416613	+	0.909084i	$0.636783\pi$
$600$		−	0.180704i		−	0.00737721i
$601$			1.71109i			0.0697967i	0.999391	+	0.0348983i	$0.0111107\pi$
$601$			1.71109i			0.0697967i	−0.999391	+	0.0348983i	$0.988889\pi$
$602$			0.691366i			0.0281780i
$603$			31.7012i			1.29097i
$604$			8.02215i			0.326417i
$605$	−3.56710			−0.145023
$606$	−2.03628			−0.0827184
$607$	22.1375			0.898534			0.449267	−	0.893398i	$-0.351685\pi$
$607$	22.1375			0.898534			0.449267	+	0.893398i	$0.351685\pi$
$608$		−	32.7367i		−	1.32765i
$609$		−	0.410279i		−	0.0166253i
$610$	−14.1096			−0.571283
$611$	−13.1189			−0.530733
$612$		−	15.9209i		−	0.643563i
$613$	−1.87188			−0.0756044			−0.0378022	−	0.999285i	$-0.512036\pi$
$613$	−1.87188			−0.0756044			−0.0378022	+	0.999285i	$0.512036\pi$
$614$	−25.5366			−1.03057
$615$	0.598388	−	0.00595943i	0.0241293	−	0.000240307i
$616$	−3.53199			−0.142308
$617$	12.9868			0.522828			0.261414	−	0.965227i	$-0.415811\pi$
$617$	12.9868			0.522828			0.261414	+	0.965227i	$0.415811\pi$
$618$		−	1.36035i		−	0.0547213i
$619$	33.7456			1.35635			0.678176	−	0.734900i	$-0.262771\pi$
$619$	33.7456			1.35635			0.678176	+	0.734900i	$0.262771\pi$
$620$	−13.7237			−0.551159
$621$			1.62418i			0.0651762i
$622$			25.0371i			1.00390i
$623$	−17.3213			−0.693961
$624$	−1.07821			−0.0431628
$625$	−2.01929			−0.0807718
$626$			8.95043i			0.357731i
$627$		−	1.11321i		−	0.0444573i
$628$		−	6.65516i		−	0.265570i
$629$		−	17.3866i		−	0.693250i
$630$			8.09115i			0.322359i
$631$	24.8794			0.990435			0.495217	−	0.868769i	$-0.335088\pi$
$631$	24.8794			0.990435			0.495217	+	0.868769i	$0.335088\pi$
$632$			15.2790i			0.607765i
$633$	1.06199			0.0422102
$634$			56.1947i			2.23178i
$635$	−16.6312			−0.659988
$636$	−0.426906			−0.0169279
$637$		−	3.50286i		−	0.138788i
$638$	−43.5080			−1.72250
$639$		−	24.2806i		−	0.960526i
$640$	10.7709			0.425758
$641$		−	9.84655i		−	0.388915i	−0.980911	−	0.194458i	$-0.937705\pi$
$641$		−	9.84655i		−	0.388915i	0.980911	−	0.194458i	$-0.0622947\pi$
$642$		−	0.756304i		−	0.0298489i
$643$		−	30.6949i		−	1.21049i	−0.796040	−	0.605244i	$-0.793076\pi$
$643$		−	30.6949i		−	1.21049i	0.796040	−	0.605244i	$-0.206924\pi$
$644$		−	6.22506i		−	0.245302i
$645$		−	0.0346146i		−	0.00136295i
$646$	31.3877			1.23493
$647$	−9.47031			−0.372316			−0.186158	−	0.982520i	$-0.559604\pi$
$647$	−9.47031			−0.372316			−0.186158	+	0.982520i	$0.559604\pi$
$648$	−8.62657			−0.338884
$649$			20.7785i			0.815626i
$650$		−	19.0047i		−	0.745425i
$651$	−0.412746			−0.0161768
$652$	−17.6918			−0.692862
$653$			6.09949i			0.238692i	0.992853	+	0.119346i	$0.0380797\pi$
$653$			6.09949i			0.238692i	−0.992853	+	0.119346i	$0.961920\pi$
$654$	1.90192			0.0743711
$655$	−3.37961			−0.132052
$656$	−0.303872	−	30.5119i	−0.0118642	−	1.19129i
$657$	43.9395			1.71424
$658$	−6.99094			−0.272535
$659$		−	10.8935i		−	0.424351i	−0.977232	−	0.212176i	$-0.931945\pi$
$659$		−	10.8935i		−	0.424351i	0.977232	−	0.212176i	$-0.0680549\pi$
$660$	−0.509050			−0.0198147
$661$	−37.0697			−1.44184			−0.720922	−	0.693017i	$-0.756281\pi$
$661$	−37.0697			−1.44184			−0.720922	+	0.693017i	$0.756281\pi$
$662$		−	17.2239i		−	0.669425i
$663$		−	0.810055i		−	0.0314599i
$664$	−6.25707			−0.242821
$665$	−6.79546			−0.263517
$666$	27.1570			1.05231
$667$			26.6381i			1.03143i
$668$		−	1.85086i		−	0.0716118i
$669$		−	0.248214i		−	0.00959650i
$670$			28.5793i			1.10412i
$671$			19.1704i			0.740067i
$672$	−0.450225			−0.0173678
$673$			34.3811i			1.32529i	0.748932	+	0.662647i	$0.230567\pi$
$673$			34.3811i			1.32529i	−0.748932	+	0.662647i	$0.769433\pi$
$674$	−31.7701			−1.22374
$675$			1.12566i			0.0433266i
$676$	1.08357			0.0416758
$677$	−3.23780			−0.124439			−0.0622194	−	0.998062i	$-0.519818\pi$
$677$	−3.23780			−0.124439			−0.0622194	+	0.998062i	$0.519818\pi$
$678$		−	2.12092i		−	0.0814536i
$679$	6.01521			0.230842
$680$			4.98602i			0.191205i
$681$	−0.439093			−0.0168261
$682$			43.7696i			1.67603i
$683$		−	32.6272i		−	1.24845i	−0.781246	−	0.624223i	$-0.785416\pi$
$683$		−	32.6272i		−	1.24845i	0.781246	−	0.624223i	$-0.214584\pi$
$684$			20.8854i			0.798572i
$685$			13.8945i			0.530880i
$686$		−	1.86664i		−	0.0712688i
$687$	0.303309			0.0115720
$688$	−1.76501			−0.0672902
$689$	15.5968			0.594191
$690$			0.731609i			0.0278519i
$691$		−	25.3454i		−	0.964183i	−0.876121	−	0.482092i	$-0.839877\pi$
$691$		−	25.3454i		−	0.964183i	0.876121	−	0.482092i	$-0.160123\pi$
$692$	16.1745			0.614860
$693$	10.9933			0.417599
$694$		−	62.0471i		−	2.35528i
$695$	7.57091			0.287181
$696$	0.394902			0.0149687
$697$	22.9236	−	0.228299i	0.868292	−	0.00864743i
$698$	−65.6120			−2.48345
$699$	−0.135420			−0.00512207
$700$		−	4.31435i		−	0.163067i
$701$	−33.2989			−1.25768			−0.628841	−	0.777534i	$-0.716470\pi$
$701$	−33.2989			−1.25768			−0.628841	+	0.777534i	$0.716470\pi$
$702$	2.53229			0.0955751
$703$			22.8082i			0.860226i
$704$			12.7706i			0.481310i
$705$	0.350015			0.0131823
$706$	52.6975			1.98330
$707$	16.8887			0.635165
$708$			0.542904i			0.0204036i
$709$			0.738894i			0.0277497i	0.999904	+	0.0138749i	$0.00441665\pi$
$709$			0.738894i			0.0277497i	−0.999904	+	0.0138749i	$0.995583\pi$
$710$		−	21.8895i		−	0.821499i
$711$		−	47.5555i		−	1.78347i
$712$		−	16.6721i		−	0.624813i
$713$	26.7983			1.00361
$714$		−	0.431672i		−	0.0161549i
$715$	18.5979			0.695522
$716$			5.80932i			0.217104i
$717$	−1.42662			−0.0532781
$718$	11.8791			0.443325
$719$			5.81098i			0.216713i	0.994112	+	0.108356i	$0.0345588\pi$
$719$			5.81098i			0.216713i	−0.994112	+	0.108356i	$0.965441\pi$
$720$	−20.6561			−0.769807
$721$			11.2826i			0.420185i
$722$	−5.70888			−0.212463
$723$			1.61554i			0.0600827i
$724$		−	24.7800i		−	0.920942i
$725$			18.4619i			0.685656i
$726$			0.297252i			0.0110321i
$727$			33.1205i			1.22837i	0.789161	+	0.614186i	$0.210515\pi$
$727$			33.1205i			1.22837i	−0.789161	+	0.614186i	$0.789485\pi$
$728$	3.37157			0.124959
$729$	26.7750			0.991665
$730$	39.6124			1.46612
$731$		−	1.32605i		−	0.0490456i
$732$			0.500889i			0.0185134i
$733$	−29.9061			−1.10461			−0.552304	−	0.833643i	$-0.686251\pi$
$733$	−29.9061			−1.10461			−0.552304	+	0.833643i	$0.686251\pi$
$734$	11.8593			0.437733
$735$			0.0934572i			0.00344722i
$736$	29.2317			1.07749
$737$	38.8300			1.43032
$738$	0.356591	+	35.8054i	0.0131263	+	1.31802i
$739$	35.7502			1.31509			0.657546	−	0.753414i	$-0.271594\pi$
$739$	35.7502			1.31509			0.657546	+	0.753414i	$0.271594\pi$
$740$	10.4298			0.383405
$741$			1.06265i			0.0390374i
$742$	8.31140			0.305121
$743$	11.3276			0.415571			0.207785	−	0.978174i	$-0.433374\pi$
$743$	11.3276			0.415571			0.207785	+	0.978174i	$0.433374\pi$
$744$		−	0.397277i		−	0.0145649i
$745$			3.02129i			0.110691i
$746$	−10.2511			−0.375318
$747$	19.4750			0.712553
$748$	−19.5011			−0.713031
$749$			6.27270i			0.229199i
$750$			1.37931i			0.0503651i
$751$		−	34.0798i		−	1.24359i	−0.783181	−	0.621794i	$-0.786404\pi$
$751$		−	34.0798i		−	1.24359i	0.783181	−	0.621794i	$-0.213596\pi$
$752$		−	17.8473i		−	0.650825i
$753$			0.726537i			0.0264765i
$754$	41.5320			1.51250
$755$			7.81959i			0.284584i
$756$	0.574868			0.0209077
$757$		−	10.5264i		−	0.382589i	−0.981533	−	0.191294i	$-0.938731\pi$
$757$		−	10.5264i		−	0.382589i	0.981533	−	0.191294i	$-0.0612685\pi$
$758$	13.0857			0.475296
$759$	0.994020			0.0360806
$760$		−	6.54077i		−	0.237259i
$761$	−5.96969			−0.216401			−0.108201	−	0.994129i	$-0.534509\pi$
$761$	−5.96969			−0.216401			−0.108201	+	0.994129i	$0.534509\pi$
$762$			1.38590i			0.0502059i
$763$	−15.7743			−0.571069
$764$			27.9692i			1.01189i
$765$		−	15.5189i		−	0.561086i
$766$			5.90890i			0.213497i
$767$		−	19.8347i		−	0.716191i
$768$		−	1.34714i		−	0.0486109i
$769$	−46.8066			−1.68789			−0.843945	−	0.536430i	$-0.819773\pi$
$769$	−46.8066			−1.68789			−0.843945	+	0.536430i	$0.819773\pi$
$770$	9.91066			0.357155
$771$	−0.863237			−0.0310887
$772$		−	1.93565i		−	0.0696657i
$773$			18.2524i			0.656492i	0.944592	+	0.328246i	$0.106457\pi$
$773$			18.2524i			0.656492i	−0.944592	+	0.328246i	$0.893543\pi$
$774$	2.07121			0.0744483
$775$	18.5729			0.667157
$776$			5.78976i			0.207840i
$777$	0.313678			0.0112531
$778$	8.74461			0.313510
$779$	−30.0716	+	0.299487i	−1.07743	+	0.0107303i
$780$	0.485930			0.0173991
$781$	−29.7408			−1.06421
$782$			28.0271i			1.00225i
$783$	−2.45996			−0.0879119
$784$	4.76540			0.170193
$785$		−	6.48712i		−	0.231535i
$786$			0.281628i			0.0100454i
$787$	41.2647			1.47093			0.735464	−	0.677564i	$-0.236964\pi$
$787$	41.2647			1.47093			0.735464	+	0.677564i	$0.236964\pi$
$788$	−2.99871			−0.106824
$789$	−0.431323			−0.0153555
$790$		−	42.8723i		−	1.52533i
$791$			17.5907i			0.625454i
$792$			10.5812i			0.375988i
$793$		−	18.2998i		−	0.649843i
$794$			10.9695i			0.389293i
$795$	−0.416127			−0.0147585
$796$		−	9.89076i		−	0.350569i
$797$	−17.4622			−0.618542			−0.309271	−	0.950974i	$-0.600085\pi$
$797$	−17.4622			−0.618542			−0.309271	+	0.950974i	$0.600085\pi$
$798$			0.566277i			0.0200460i
$799$	13.4087			0.474365
$800$	20.2593			0.716276
$801$			51.8915i			1.83350i
$802$	−0.589349			−0.0208106
$803$		−	53.8204i		−	1.89928i
$804$	1.01456			0.0357808
$805$		−	6.06789i		−	0.213865i
$806$		−	41.7817i		−	1.47170i
$807$			0.565928i			0.0199216i
$808$			16.2557i			0.571875i
$809$			43.6546i			1.53482i	0.641159	+	0.767408i	$0.278454\pi$
$809$			43.6546i			1.53482i	−0.641159	+	0.767408i	$0.721546\pi$
$810$	24.2059			0.850508
$811$	−13.7049			−0.481243			−0.240622	−	0.970619i	$-0.577351\pi$
$811$	−13.7049			−0.481243			−0.240622	+	0.970619i	$0.577351\pi$
$812$	9.42838			0.330871
$813$			0.913190i			0.0320270i
$814$		−	33.2640i		−	1.16590i
$815$	−17.2450			−0.604068
$816$	1.10202			0.0385786
$817$			1.73954i			0.0608587i
$818$	35.6125			1.24516
$819$	−10.4940			−0.366689
$820$	0.136950	+	13.7512i	0.00478251	+	0.480213i
$821$	−44.5615			−1.55521			−0.777604	−	0.628754i	$-0.783565\pi$
$821$	−44.5615			−1.55521			−0.777604	+	0.628754i	$0.783565\pi$
$822$	1.15785			0.0403846
$823$		−	18.1140i		−	0.631413i	−0.948857	−	0.315707i	$-0.897758\pi$
$823$		−	18.1140i		−	0.631413i	0.948857	−	0.315707i	$-0.102242\pi$
$824$	−10.8597			−0.378316
$825$	0.688917			0.0239850
$826$		−	10.5698i		−	0.367769i
$827$			39.2469i			1.36475i	0.731002	+	0.682375i	$0.239053\pi$
$827$			39.2469i			1.36475i	−0.731002	+	0.682375i	$0.760947\pi$
$828$	−18.6492			−0.648105
$829$	28.4642			0.988602			0.494301	−	0.869291i	$-0.335424\pi$
$829$	28.4642			0.988602			0.494301	+	0.869291i	$0.335424\pi$
$830$	17.5571			0.609417
$831$			0.830121i			0.0287966i
$832$		−	12.1906i		−	0.422633i
$833$			3.58024i			0.124048i
$834$		−	0.630896i		−	0.0218461i
$835$		−	1.80413i		−	0.0624343i
$836$	25.5820			0.884772
$837$			2.47475i			0.0855400i
$838$	24.5094			0.846664
$839$		−	9.91141i		−	0.342180i	−0.985255	−	0.171090i	$-0.945271\pi$
$839$		−	9.91141i		−	0.342180i	0.985255	−	0.171090i	$-0.0547289\pi$
$840$	−0.0899545			−0.00310373
$841$	−11.3457			−0.391231
$842$		−	42.8234i		−	1.47579i
$843$	−1.08958			−0.0375273
$844$			24.4049i			0.840052i
$845$	1.05621			0.0363348
$846$			20.9437i			0.720058i
$847$		−	2.46538i		−	0.0847114i
$848$			21.2184i			0.728642i
$849$			2.01638i			0.0692018i
$850$			19.4245i			0.666254i
$851$	−20.3661			−0.698143
$852$	−0.777073			−0.0266221
$853$	−41.1732			−1.40974			−0.704871	−	0.709335i	$-0.748995\pi$
$853$	−41.1732			−1.40974			−0.704871	+	0.709335i	$0.748995\pi$
$854$		−	9.75179i		−	0.333699i
$855$			20.3580i			0.696230i
$856$	−6.03760			−0.206361
$857$	−8.95032			−0.305737			−0.152869	−	0.988247i	$-0.548851\pi$
$857$	−8.95032			−0.305737			−0.152869	+	0.988247i	$0.548851\pi$
$858$		−	1.54979i		−	0.0529091i
$859$	−44.6858			−1.52466			−0.762330	−	0.647188i	$-0.775945\pi$
$859$	−44.6858			−1.52466			−0.762330	+	0.647188i	$0.775945\pi$
$860$	0.795458			0.0271249
$861$	0.00411882	+	0.413572i	0.000140369	+	0.0140945i
$862$	−5.94924			−0.202632
$863$	28.6191			0.974207			0.487103	−	0.873344i	$-0.338054\pi$
$863$	28.6191			0.974207			0.487103	+	0.873344i	$0.338054\pi$
$864$			2.69947i			0.0918378i
$865$	15.7661			0.536062
$866$	56.4163			1.91711
$867$		−	0.270120i		−	0.00917374i
$868$		−	9.48507i		−	0.321944i
$869$	−58.2496			−1.97598
$870$	−1.10808			−0.0375676
$871$	−37.0664			−1.25595
$872$		−	15.1831i		−	0.514166i
$873$		−	18.0205i		−	0.609902i
$874$		−	36.7666i		−	1.24365i
$875$		−	11.4398i		−	0.386736i
$876$		−	1.40623i		−	0.0475122i
$877$	−18.2459			−0.616120			−0.308060	−	0.951367i	$-0.599680\pi$
$877$	−18.2459			−0.616120			−0.308060	+	0.951367i	$0.599680\pi$
$878$			56.4088i			1.90371i
$879$	1.67691			0.0565608
$880$			25.3012i			0.852902i
$881$	−39.7209			−1.33823			−0.669116	−	0.743158i	$-0.733327\pi$
$881$	−39.7209			−1.33823			−0.669116	+	0.743158i	$0.733327\pi$
$882$	−5.59214			−0.188297
$883$			53.6218i			1.80452i	0.431194	+	0.902259i	$0.358092\pi$
$883$			53.6218i			1.80452i	−0.431194	+	0.902259i	$0.641908\pi$
$884$	18.6154			0.626104
$885$			0.529196i			0.0177887i
$886$	75.1140			2.52351
$887$		−	42.3401i		−	1.42164i	−0.703374	−	0.710820i	$-0.748324\pi$
$887$		−	42.3401i		−	1.42164i	0.703374	−	0.710820i	$-0.251676\pi$
$888$			0.301922i			0.0101318i
$889$		−	11.4945i		−	0.385514i
$890$			46.7814i			1.56811i
$891$		−	32.8880i		−	1.10179i
$892$	5.70405			0.190986
$893$	−17.5898			−0.588620
$894$	0.251769			0.00842042
$895$			5.66264i			0.189281i
$896$			7.44425i			0.248695i
$897$	−0.948873			−0.0316820
$898$	26.9849			0.900497
$899$			40.5883i			1.35370i
$900$	−12.9250			−0.430835
$901$	−15.9413			−0.531083
$902$	43.8572	−	0.436780i	1.46029	−	0.0145432i
$903$	0.0239236			0.000796129
$904$	−16.9314			−0.563131
$905$		−	24.1543i		−	0.802917i
$906$	0.651620			0.0216486
$907$	−17.1650			−0.569954			−0.284977	−	0.958534i	$-0.591986\pi$
$907$	−17.1650			−0.569954			−0.284977	+	0.958534i	$0.591986\pi$
$908$		−	10.0905i		−	0.334867i
$909$		−	50.5957i		−	1.67815i
$910$	−9.46054			−0.313614
$911$	−7.34926			−0.243492			−0.121746	−	0.992561i	$-0.538849\pi$
$911$	−7.34926			−0.243492			−0.121746	+	0.992561i	$0.538849\pi$
$912$	−1.44566			−0.0478706
$913$		−	23.8545i		−	0.789468i
$914$			42.8193i			1.41634i
$915$			0.488242i			0.0161408i
$916$			6.97018i			0.230301i
$917$		−	2.33579i		−	0.0771347i
$918$	−2.58823			−0.0854243
$919$		−	45.8739i		−	1.51324i	−0.653855	−	0.756619i	$-0.726850\pi$
$919$		−	45.8739i		−	1.51324i	0.653855	−	0.756619i	$-0.273150\pi$
$920$	5.84047			0.192555
$921$			0.883654i			0.0291174i
$922$	−24.3930			−0.803340
$923$	28.3900			0.934468
$924$		−	0.351826i		−	0.0115742i
$925$	−14.1150			−0.464098
$926$		−	48.6083i		−	1.59737i
$927$	33.8007			1.11016
$928$			44.2739i			1.45336i
$929$			24.2793i			0.796578i	0.917260	+	0.398289i	$0.130396\pi$
$929$			24.2793i			0.796578i	−0.917260	+	0.398289i	$0.869604\pi$
$930$			1.11475i			0.0365540i
$931$		−	4.69663i		−	0.153926i
$932$		−	3.11201i		−	0.101937i
$933$	0.866370			0.0283637
$934$	−63.0385			−2.06268
$935$	−19.0087			−0.621652
$936$		−	10.1007i		−	0.330150i
$937$		−	43.8867i		−	1.43372i	−0.697219	−	0.716858i	$-0.745580\pi$
$937$		−	43.8867i		−	1.43372i	0.697219	−	0.716858i	$-0.254420\pi$
$938$	−19.7524			−0.644939
$939$	0.309716			0.0101072
$940$			8.04349i			0.262350i
$941$	−44.4530			−1.44913			−0.724564	−	0.689208i	$-0.757959\pi$
$941$	−44.4530			−1.44913			−0.724564	+	0.689208i	$0.757959\pi$
$942$	−0.540583			−0.0176131
$943$	−0.267422	−	26.8519i	−0.00870846	−	0.874420i
$944$	26.9838			0.878249
$945$	0.560353			0.0182283
$946$		−	2.53698i		−	0.0824844i
$947$	2.06266			0.0670274			0.0335137	−	0.999438i	$-0.489330\pi$
$947$	2.06266			0.0670274			0.0335137	+	0.999438i	$0.489330\pi$
$948$	−1.52196			−0.0494309
$949$			51.3760i			1.66774i
$950$		−	25.4815i		−	0.826729i
$951$	1.94453			0.0630557
$952$	−3.44605			−0.111687
$953$	49.6232			1.60745			0.803726	−	0.594999i	$-0.202848\pi$
$953$	49.6232			1.60745			0.803726	+	0.594999i	$0.202848\pi$
$954$		−	24.8995i		−	0.806152i
$955$			27.2630i			0.882209i
$956$		−	32.7843i		−	1.06032i
$957$			1.50553i			0.0486668i
$958$		−	28.0061i		−	0.904835i
$959$	−9.60307			−0.310099
$960$			0.325248i			0.0104973i
$961$	9.83237			0.317173
$962$			31.7532i			1.02376i
$963$	18.7919			0.605561
$964$	−37.1259			−1.19574
$965$		−	1.88678i		−	0.0607376i
$966$	−0.505647			−0.0162689
$967$		−	13.8889i		−	0.446638i	−0.974745	−	0.223319i	$-0.928311\pi$
$967$		−	13.8889i		−	0.446638i	0.974745	−	0.223319i	$-0.0716892\pi$
$968$	2.37298			0.0762704
$969$		−	1.08612i		−	0.0348913i
$970$		−	16.2459i		−	0.521625i
$971$			43.2366i			1.38753i	0.720202	+	0.693764i	$0.244049\pi$
$971$			43.2366i			1.38753i	−0.720202	+	0.693764i	$0.755951\pi$
$972$		−	2.58391i		−	0.0828789i
$973$			5.23258i			0.167749i
$974$	81.5286			2.61235
$975$	−0.657627			−0.0210609
$976$	24.8956			0.796888
$977$			6.38552i			0.204291i	0.994769	+	0.102145i	$0.0325707\pi$
$977$			6.38552i			0.204291i	−0.994769	+	0.102145i	$0.967429\pi$
$978$			1.43706i			0.0459521i
$979$	63.5607			2.03141
$980$	−2.14768			−0.0686053
$981$			47.2572i			1.50881i
$982$	−61.5801			−1.96510
$983$	18.0849			0.576820			0.288410	−	0.957507i	$-0.406873\pi$
$983$	18.0849			0.576820			0.288410	+	0.957507i	$0.406873\pi$
$984$	−0.398072	+	0.00396445i	−0.0126901	+	0.000126382i
$985$	−2.92299			−0.0931342
$986$	−42.4494			−1.35186
$987$			0.241911i			0.00770010i
$988$	−24.4201			−0.776907
$989$	−1.55329			−0.0493917
$990$		−	29.6906i		−	0.943630i
$991$			21.2424i			0.674786i	0.941364	+	0.337393i	$0.109545\pi$
$991$			21.2424i			0.674786i	−0.941364	+	0.337393i	$0.890455\pi$
$992$	44.5401			1.41415
$993$	−0.596005			−0.0189137
$994$	15.1288			0.479856
$995$		−	9.64102i		−	0.305641i
$996$		−	0.623275i		−	0.0197492i
$997$			19.1407i			0.606191i	0.952960	+	0.303096i	$0.0980202\pi$
$997$			19.1407i			0.606191i	−0.952960	+	0.303096i	$0.901980\pi$
$998$			63.1963i			2.00044i
$999$		−	1.88076i		−	0.0595046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.a.204.7	✓	10
41.40	even	2	inner	287.2.c.a.204.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.a.204.7	✓	10	1.1	even	1	trivial
287.2.c.a.204.8	yes	10	41.40	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.86664 q^{2} -0.0645923i q^{3} +1.48436 q^{4} +1.44688 q^{5} -0.120571i q^{6} +1.00000i q^{7} -0.962521 q^{8} +2.99583 q^{9} +O(q^{10})\)	\(q+1.86664 q^{2} -0.0645923i q^{3} +1.48436 q^{4} +1.44688 q^{5} -0.120571i q^{6} +1.00000i q^{7} -0.962521 q^{8} +2.99583 q^{9} +2.70081 q^{10} -3.66952i q^{11} -0.0958780i q^{12} +3.50286i q^{13} +1.86664i q^{14} -0.0934572i q^{15} -4.76540 q^{16} -3.58024i q^{17} +5.59214 q^{18} +4.69663i q^{19} +2.14768 q^{20} +0.0645923 q^{21} -6.84969i q^{22} -4.19378 q^{23} +0.0621714i q^{24} -2.90654 q^{25} +6.53858i q^{26} -0.387284i q^{27} +1.48436i q^{28} -6.35183i q^{29} -0.174451i q^{30} -6.39002 q^{31} -6.97026 q^{32} -0.237023 q^{33} -6.68302i q^{34} +1.44688i q^{35} +4.44688 q^{36} +4.85628 q^{37} +8.76694i q^{38} +0.226258 q^{39} -1.39265 q^{40} +(0.0637664 + 6.40281i) q^{41} +0.120571 q^{42} +0.370379 q^{43} -5.44688i q^{44} +4.33460 q^{45} -7.82829 q^{46} +3.74519i q^{47} +0.307808i q^{48} -1.00000 q^{49} -5.42548 q^{50} -0.231256 q^{51} +5.19949i q^{52} -4.45259i q^{53} -0.722921i q^{54} -5.30935i q^{55} -0.962521i q^{56} +0.303366 q^{57} -11.8566i q^{58} -5.66245 q^{59} -0.138724i q^{60} -5.22424 q^{61} -11.9279 q^{62} +2.99583i q^{63} -3.48018 q^{64} +5.06821i q^{65} -0.442437 q^{66} +10.5818i q^{67} -5.31435i q^{68} +0.270886i q^{69} +2.70081i q^{70} -8.10481i q^{71} -2.88355 q^{72} +14.6669 q^{73} +9.06494 q^{74} +0.187740i q^{75} +6.97148i q^{76} +3.66952 q^{77} +0.422342 q^{78} -15.8739i q^{79} -6.89495 q^{80} +8.96247 q^{81} +(0.119029 + 11.9518i) q^{82} +6.50071 q^{83} +0.0958780 q^{84} -5.18016i q^{85} +0.691366 q^{86} -0.410279 q^{87} +3.53199i q^{88} +17.3213i q^{89} +8.09115 q^{90} -3.50286 q^{91} -6.22506 q^{92} +0.412746i q^{93} +6.99094i q^{94} +6.79546i q^{95} +0.450225i q^{96} -6.01521i q^{97} -1.86664 q^{98} -10.9933i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9} + 8 q^{10} - 16 q^{16} + 20 q^{18} - 22 q^{20} - 12 q^{21} - 4 q^{23} - 4 q^{25} + 14 q^{31} + 18 q^{32} - 2 q^{33} + 20 q^{36} - 22 q^{37} - 46 q^{39} - 58 q^{40} - 4 q^{41} - 8 q^{42} + 18 q^{43} + 50 q^{45} + 8 q^{46} - 10 q^{49} - 22 q^{50} + 14 q^{51} + 62 q^{57} + 34 q^{59} - 28 q^{61} - 44 q^{62} + 8 q^{64} - 36 q^{66} - 20 q^{72} + 12 q^{74} + 12 q^{77} + 78 q^{78} - 4 q^{80} + 10 q^{81} + 74 q^{82} - 20 q^{83} - 6 q^{84} + 12 q^{86} - 8 q^{87} - 54 q^{90} - 14 q^{91} - 30 q^{92} - 4 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9 + 8 * q^10 - 16 * q^16 + 20 * q^18 - 22 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^25 + 14 * q^31 + 18 * q^32 - 2 * q^33 + 20 * q^36 - 22 * q^37 - 46 * q^39 - 58 * q^40 - 4 * q^41 - 8 * q^42 + 18 * q^43 + 50 * q^45 + 8 * q^46 - 10 * q^49 - 22 * q^50 + 14 * q^51 + 62 * q^57 + 34 * q^59 - 28 * q^61 - 44 * q^62 + 8 * q^64 - 36 * q^66 - 20 * q^72 + 12 * q^74 + 12 * q^77 + 78 * q^78 - 4 * q^80 + 10 * q^81 + 74 * q^82 - 20 * q^83 - 6 * q^84 + 12 * q^86 - 8 * q^87 - 54 * q^90 - 14 * q^91 - 30 * q^92 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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