LMFDB - Embedded newform 287.2.c.b.204.9

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 113x^{8} + 290x^{6} + 258x^{4} + 49x^{2} + 1 $ x^12 + 18x^10 + 113x^8 + 290x^6 + 258x^4 + 49*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			204.9
Root			$1.12463i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.b.204.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.12463 q^{2} -2.12463i q^{3} -0.735213 q^{4} -4.04675 q^{5} -2.38941i q^{6} +1.00000i q^{7} -3.07610 q^{8} -1.51404 q^{9} +O(q^{10})$	\(q+1.12463 q^{2} -2.12463i q^{3} -0.735213 q^{4} -4.04675 q^{5} -2.38941i q^{6} +1.00000i q^{7} -3.07610 q^{8} -1.51404 q^{9} -4.55109 q^{10} -2.55109i q^{11} +1.56205i q^{12} +0.235444i q^{13} +1.12463i q^{14} +8.59784i q^{15} -1.98904 q^{16} -2.08991i q^{17} -1.70273 q^{18} -7.06513i q^{19} +2.97523 q^{20} +2.12463 q^{21} -2.86903i q^{22} -5.74724 q^{23} +6.53556i q^{24} +11.3762 q^{25} +0.264787i q^{26} -3.15711i q^{27} -0.735213i q^{28} +8.12695i q^{29} +9.66937i q^{30} -1.79750 q^{31} +3.91527 q^{32} -5.42012 q^{33} -2.35037i q^{34} -4.04675i q^{35} +1.11314 q^{36} +4.78653 q^{37} -7.94564i q^{38} +0.500231 q^{39} +12.4482 q^{40} +(-1.40323 - 6.24748i) q^{41} +2.38941 q^{42} +1.78197 q^{43} +1.87559i q^{44} +6.12695 q^{45} -6.46351 q^{46} -3.31611i q^{47} +4.22596i q^{48} -1.00000 q^{49} +12.7940 q^{50} -4.44027 q^{51} -0.173102i q^{52} -1.82512i q^{53} -3.55057i q^{54} +10.3236i q^{55} -3.07610i q^{56} -15.0108 q^{57} +9.13980i q^{58} -10.0468 q^{59} -6.32125i q^{60} +8.09961 q^{61} -2.02152 q^{62} -1.51404i q^{63} +8.38129 q^{64} -0.952785i q^{65} -6.09561 q^{66} -5.98807i q^{67} +1.53653i q^{68} +12.2108i q^{69} -4.55109i q^{70} +2.16905i q^{71} +4.65734 q^{72} -12.5787 q^{73} +5.38307 q^{74} -24.1702i q^{75} +5.19438i q^{76} +2.55109 q^{77} +0.562574 q^{78} -3.69206i q^{79} +8.04914 q^{80} -11.2498 q^{81} +(-1.57811 - 7.02608i) q^{82} +9.32078 q^{83} -1.56205 q^{84} +8.45734i q^{85} +2.00405 q^{86} +17.2668 q^{87} +7.84740i q^{88} +16.2066i q^{89} +6.89054 q^{90} -0.235444 q^{91} +4.22545 q^{92} +3.81901i q^{93} -3.72939i q^{94} +28.5908i q^{95} -8.31848i q^{96} +17.8408i q^{97} -1.12463 q^{98} +3.86246i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9	$ 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9 - 4 * q^10 + 28 * q^16 - 40 * q^18 + 2 * q^20 + 8 * q^21 + 16 * q^23 + 34 * q^25 - 6 * q^31 - 42 * q^32 + 18 * q^33 - 36 * q^36 - 10 * q^37 + 10 * q^39 + 38 * q^40 - 2 * q^41 + 32 * q^42 - 50 * q^43 + 6 * q^45 - 8 * q^46 - 12 * q^49 + 18 * q^50 - 2 * q^51 - 50 * q^57 - 70 * q^59 + 52 * q^61 + 68 * q^62 + 8 * q^64 + 92 * q^66 + 2 * q^72 - 64 * q^73 + 18 * q^74 - 20 * q^77 - 12 * q^78 - 32 * q^80 - 4 * q^81 - 56 * q^82 + 60 * q^83 - 20 * q^84 + 48 * q^86 - 20 * q^87 - 42 * q^90 + 14 * q^91 + 56 * 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 $

$2$	1.12463			0.795232			0.397616	−	0.917552i	$-0.369838\pi$
$2$	1.12463			0.795232			0.397616	+	0.917552i	$0.369838\pi$
$3$		−	2.12463i		−	1.22665i	−0.789829	−	0.613327i	$-0.789831\pi$
$3$		−	2.12463i		−	1.22665i	0.789829	−	0.613327i	$-0.210169\pi$
$4$	−0.735213			−0.367606
$5$	−4.04675			−1.80976			−0.904881	−	0.425664i	$-0.860041\pi$
$5$	−4.04675			−1.80976			−0.904881	+	0.425664i	$0.860041\pi$
$6$		−	2.38941i		−	0.975474i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−3.07610			−1.08756
$9$	−1.51404			−0.504681
$10$	−4.55109			−1.43918
$11$		−	2.55109i		−	0.769182i	−0.923087	−	0.384591i	$-0.874342\pi$
$11$		−	2.55109i		−	0.769182i	0.923087	−	0.384591i	$-0.125658\pi$
$12$			1.56205i			0.450926i
$13$			0.235444i			0.0653005i	0.999467	+	0.0326502i	$0.0103947\pi$
$13$			0.235444i			0.0653005i	−0.999467	+	0.0326502i	$0.989605\pi$
$14$			1.12463i			0.300569i
$15$			8.59784i			2.21995i
$16$	−1.98904			−0.497259
$17$		−	2.08991i		−	0.506877i	−0.967352	−	0.253438i	$-0.918438\pi$
$17$		−	2.08991i		−	0.506877i	0.967352	−	0.253438i	$-0.0815615\pi$
$18$	−1.70273			−0.401338
$19$		−	7.06513i		−	1.62085i	−0.585841	−	0.810426i	$-0.699236\pi$
$19$		−	7.06513i		−	1.62085i	0.585841	−	0.810426i	$-0.300764\pi$
$20$	2.97523			0.665281
$21$	2.12463			0.463632
$22$		−	2.86903i		−	0.611678i
$23$	−5.74724			−1.19838			−0.599192	−	0.800606i	$-0.704511\pi$
$23$	−5.74724			−1.19838			−0.599192	+	0.800606i	$0.704511\pi$
$24$			6.53556i			1.33407i
$25$	11.3762			2.27524
$26$			0.264787i			0.0519290i
$27$		−	3.15711i		−	0.607586i
$28$		−	0.735213i		−	0.138942i
$29$			8.12695i			1.50914i	0.656221	+	0.754569i	$0.272154\pi$
$29$			8.12695i			1.50914i	−0.656221	+	0.754569i	$0.727846\pi$
$30$			9.66937i			1.76538i
$31$	−1.79750			−0.322840			−0.161420	−	0.986886i	$-0.551607\pi$
$31$	−1.79750			−0.322840			−0.161420	+	0.986886i	$0.551607\pi$
$32$	3.91527			0.692128
$33$	−5.42012			−0.943521
$34$		−	2.35037i		−	0.403085i
$35$		−	4.04675i		−	0.684026i
$36$	1.11314			0.185524
$37$	4.78653			0.786901			0.393451	−	0.919346i	$-0.371281\pi$
$37$	4.78653			0.786901			0.393451	+	0.919346i	$0.371281\pi$
$38$		−	7.94564i		−	1.28895i
$39$	0.500231			0.0801011
$40$	12.4482			1.96823
$41$	−1.40323	−	6.24748i	−0.219147	−	0.975692i
$41$	−1.40323	−	6.24748i	−0.219147	−	0.975692i
$42$	2.38941			0.368695
$43$	1.78197			0.271747			0.135874	−	0.990726i	$-0.456616\pi$
$43$	1.78197			0.271747			0.135874	+	0.990726i	$0.456616\pi$
$44$			1.87559i			0.282756i
$45$	6.12695			0.913352
$46$	−6.46351			−0.952993
$47$		−	3.31611i		−	0.483704i	−0.970313	−	0.241852i	$-0.922245\pi$
$47$		−	3.31611i		−	0.483704i	0.970313	−	0.241852i	$-0.0777549\pi$
$48$			4.22596i			0.609965i
$49$	−1.00000			−0.142857
$50$	12.7940			1.80934
$51$	−4.44027			−0.621763
$52$		−	0.173102i		−	0.0240049i
$53$		−	1.82512i		−	0.250699i	−0.992113	−	0.125350i	$-0.959995\pi$
$53$		−	1.82512i		−	0.250699i	0.992113	−	0.125350i	$-0.0400053\pi$
$54$		−	3.55057i		−	0.483171i
$55$			10.3236i			1.39204i
$56$		−	3.07610i		−	0.411061i
$57$	−15.0108			−1.98823
$58$			9.13980i			1.20011i
$59$	−10.0468			−1.30798			−0.653988	−	0.756505i	$-0.726905\pi$
$59$	−10.0468			−1.30798			−0.653988	+	0.756505i	$0.726905\pi$
$60$		−	6.32125i		−	0.816069i
$61$	8.09961			1.03705			0.518525	−	0.855063i	$-0.326481\pi$
$61$	8.09961			1.03705			0.518525	+	0.855063i	$0.326481\pi$
$62$	−2.02152			−0.256733
$63$		−	1.51404i		−	0.190751i
$64$	8.38129			1.04766
$65$		−	0.952785i		−	0.118178i
$66$	−6.09561			−0.750318
$67$		−	5.98807i		−	0.731559i	−0.930702	−	0.365779i	$-0.880802\pi$
$67$		−	5.98807i		−	0.731559i	0.930702	−	0.365779i	$-0.119198\pi$
$68$			1.53653i			0.186331i
$69$			12.2108i			1.47000i
$70$		−	4.55109i		−	0.543959i
$71$			2.16905i			0.257419i	0.991682	+	0.128710i	$0.0410835\pi$
$71$			2.16905i			0.257419i	−0.991682	+	0.128710i	$0.958916\pi$
$72$	4.65734			0.548873
$73$	−12.5787			−1.47223			−0.736113	−	0.676858i	$-0.763341\pi$
$73$	−12.5787			−1.47223			−0.736113	+	0.676858i	$0.763341\pi$
$74$	5.38307			0.625769
$75$		−	24.1702i		−	2.79094i
$76$			5.19438i			0.595836i
$77$	2.55109			0.290724
$78$	0.562574			0.0636989
$79$		−	3.69206i		−	0.415389i	−0.978194	−	0.207695i	$-0.933404\pi$
$79$		−	3.69206i		−	0.415389i	0.978194	−	0.207695i	$-0.0665960\pi$
$80$	8.04914			0.899921
$81$	−11.2498			−1.24998
$82$	−1.57811	−	7.02608i	−0.174273	−	0.775901i
$83$	9.32078			1.02309			0.511544	−	0.859257i	$-0.329074\pi$
$83$	9.32078			1.02309			0.511544	+	0.859257i	$0.329074\pi$
$84$	−1.56205			−0.170434
$85$			8.45734i			0.917327i
$86$	2.00405			0.216102
$87$	17.2668			1.85119
$88$			7.84740i			0.836535i
$89$			16.2066i			1.71790i	0.512058	+	0.858951i	$0.328883\pi$
$89$			16.2066i			1.71790i	−0.512058	+	0.858951i	$0.671117\pi$
$90$	6.89054			0.726327
$91$	−0.235444			−0.0246813
$92$	4.22545			0.440534
$93$			3.81901i			0.396013i
$94$		−	3.72939i		−	0.384657i
$95$			28.5908i			2.93336i
$96$		−	8.31848i		−	0.849002i
$97$			17.8408i			1.81145i	0.423862	+	0.905727i	$0.360674\pi$
$97$			17.8408i			1.81145i	−0.423862	+	0.905727i	$0.639326\pi$
$98$	−1.12463			−0.113605
$99$			3.86246i			0.388192i
$100$	−8.36394			−0.836394
$101$		−	12.2801i		−	1.22192i	−0.791662	−	0.610959i	$-0.790784\pi$
$101$		−	12.2801i		−	1.22192i	0.791662	−	0.610959i	$-0.209216\pi$
$102$	−4.99365			−0.494445
$103$	−3.59273			−0.354002			−0.177001	−	0.984211i	$-0.556640\pi$
$103$	−3.59273			−0.354002			−0.177001	+	0.984211i	$0.556640\pi$
$104$		−	0.724249i		−	0.0710185i
$105$	−8.59784			−0.839064
$106$		−	2.05258i		−	0.199364i
$107$	9.71090			0.938788			0.469394	−	0.882989i	$-0.344472\pi$
$107$	9.71090			0.938788			0.469394	+	0.882989i	$0.344472\pi$
$108$			2.32115i			0.223352i
$109$		−	7.44280i		−	0.712891i	−0.934316	−	0.356446i	$-0.883988\pi$
$109$		−	7.44280i		−	0.712891i	0.934316	−	0.356446i	$-0.116012\pi$
$110$			11.6102i			1.10699i
$111$		−	10.1696i		−	0.965256i
$112$		−	1.98904i		−	0.187946i
$113$	−13.7506			−1.29354			−0.646772	−	0.762684i	$-0.723881\pi$
$113$	−13.7506			−1.29354			−0.646772	+	0.762684i	$0.723881\pi$
$114$	−16.8815			−1.58110
$115$	23.2577			2.16879
$116$		−	5.97504i		−	0.554769i
$117$		−	0.356472i		−	0.0329559i
$118$	−11.2989			−1.04014
$119$	2.08991			0.191581
$120$		−	26.4478i		−	2.41434i
$121$	4.49194			0.408358
$122$	9.10905			0.824694
$123$	−13.2736	+	2.98133i	−1.19684	+	0.268818i
$124$	1.32154			0.118678
$125$	−25.8029			−2.30789
$126$		−	1.70273i		−	0.151692i
$127$	−12.2677			−1.08858			−0.544292	−	0.838896i	$-0.683202\pi$
$127$	−12.2677			−1.08858			−0.544292	+	0.838896i	$0.683202\pi$
$128$	1.59529			0.141005
$129$		−	3.78601i		−	0.333340i
$130$		−	1.07153i		−	0.0939792i
$131$	10.6039			0.926471			0.463236	−	0.886235i	$-0.346688\pi$
$131$	10.6039			0.926471			0.463236	+	0.886235i	$0.346688\pi$
$132$	3.98494			0.346844
$133$	7.06513			0.612625
$134$		−	6.73435i		−	0.581759i
$135$			12.7760i			1.09959i
$136$			6.42875i			0.551261i
$137$		−	8.11113i		−	0.692981i	−0.938054	−	0.346490i	$-0.887373\pi$
$137$		−	8.11113i		−	0.692981i	0.938054	−	0.346490i	$-0.112627\pi$
$138$			13.7326i			1.16899i
$139$	7.45105			0.631989			0.315995	−	0.948761i	$-0.397662\pi$
$139$	7.45105			0.631989			0.315995	+	0.948761i	$0.397662\pi$
$140$			2.97523i			0.251452i
$141$	−7.04549			−0.593338
$142$			2.43938i			0.204708i
$143$	0.600639			0.0502280
$144$	3.01148			0.250957
$145$		−	32.8878i		−	2.73118i
$146$	−14.1464			−1.17076
$147$			2.12463i			0.175236i
$148$	−3.51912			−0.289270
$149$		−	21.9745i		−	1.80022i	−0.435660	−	0.900111i	$-0.643485\pi$
$149$		−	21.9745i		−	1.80022i	0.435660	−	0.900111i	$-0.356515\pi$
$150$		−	27.1825i		−	2.21944i
$151$		−	1.95207i		−	0.158858i	−0.996841	−	0.0794288i	$-0.974690\pi$
$151$		−	1.95207i		−	0.158858i	0.996841	−	0.0794288i	$-0.0253096\pi$
$152$			21.7330i			1.76278i
$153$			3.16421i			0.255811i
$154$	2.86903			0.231193
$155$	7.27403			0.584264
$156$	−0.367777			−0.0294457
$157$			9.79365i			0.781618i	0.920472	+	0.390809i	$0.127805\pi$
$157$			9.79365i			0.781618i	−0.920472	+	0.390809i	$0.872195\pi$
$158$		−	4.15219i		−	0.330331i
$159$	−3.87770			−0.307522
$160$	−15.8441			−1.25259
$161$		−	5.74724i		−	0.452946i
$162$	−12.6518			−0.994022
$163$	6.47019			0.506784			0.253392	−	0.967364i	$-0.418454\pi$
$163$	6.47019			0.506784			0.253392	+	0.967364i	$0.418454\pi$
$164$	1.03167	+	4.59323i	0.0805599	+	0.358671i
$165$	21.9339			1.70755
$166$	10.4824			0.813593
$167$		−	11.7728i		−	0.911009i	−0.890233	−	0.455504i	$-0.849459\pi$
$167$		−	11.7728i		−	0.911009i	0.890233	−	0.455504i	$-0.150541\pi$
$168$	−6.53556			−0.504229
$169$	12.9446			0.995736
$170$			9.51135i			0.729487i
$171$			10.6969i			0.818013i
$172$	−1.31012			−0.0998960
$173$	−19.0552			−1.44874			−0.724369	−	0.689412i	$-0.757869\pi$
$173$	−19.0552			−1.44874			−0.724369	+	0.689412i	$0.757869\pi$
$174$	19.4187			1.47213
$175$			11.3762i			0.859961i
$176$			5.07421i			0.382483i
$177$			21.3456i			1.60443i
$178$			18.2264i			1.36613i
$179$		−	26.6194i		−	1.98962i	−0.101729	−	0.994812i	$-0.532438\pi$
$179$		−	26.6194i		−	1.98962i	0.101729	−	0.994812i	$-0.467562\pi$
$180$	−4.50462			−0.335754
$181$		−	12.8808i		−	0.957420i	−0.877973	−	0.478710i	$-0.841105\pi$
$181$		−	12.8808i		−	0.957420i	0.877973	−	0.478710i	$-0.158895\pi$
$182$	−0.264787			−0.0196273
$183$		−	17.2087i		−	1.27210i
$184$	17.6791			1.30332
$185$	−19.3699			−1.42410
$186$			4.29497i			0.314922i
$187$	−5.33154			−0.389881
$188$			2.43805i			0.177813i
$189$	3.15711			0.229646
$190$			32.1540i			2.33270i
$191$			8.74421i			0.632709i	0.948641	+	0.316354i	$0.102459\pi$
$191$			8.74421i			0.632709i	−0.948641	+	0.316354i	$0.897541\pi$
$192$		−	17.8071i		−	1.28512i
$193$		−	12.3350i		−	0.887895i	−0.896053	−	0.443948i	$-0.853578\pi$
$193$		−	12.3350i		−	0.887895i	0.896053	−	0.443948i	$-0.146422\pi$
$194$			20.0642i			1.44053i
$195$	−2.02431			−0.144964
$196$	0.735213			0.0525152
$197$	2.49880			0.178032			0.0890161	−	0.996030i	$-0.471628\pi$
$197$	2.49880			0.178032			0.0890161	+	0.996030i	$0.471628\pi$
$198$			4.34383i			0.308702i
$199$		−	6.66958i		−	0.472794i	−0.971657	−	0.236397i	$-0.924033\pi$
$199$		−	6.66958i		−	0.472794i	0.971657	−	0.236397i	$-0.0759665\pi$
$200$	−34.9943			−2.47447
$201$	−12.7224			−0.897370
$202$		−	13.8106i		−	0.971708i
$203$	−8.12695			−0.570400
$204$	3.26455			0.228564
$205$	5.67851	+	25.2820i	0.396604	+	1.76577i
$206$	−4.04048			−0.281514
$207$	8.70157			0.604801
$208$		−	0.468307i		−	0.0324712i
$209$	−18.0238			−1.24673
$210$	−9.66937			−0.667250
$211$			10.6816i			0.735354i	0.929954	+	0.367677i	$0.119847\pi$
$211$			10.6816i			0.735354i	−0.929954	+	0.367677i	$0.880153\pi$
$212$			1.34185i			0.0921587i
$213$	4.60843			0.315765
$214$	10.9211			0.746554
$215$	−7.21118			−0.491798
$216$			9.71156i			0.660788i
$217$		−	1.79750i		−	0.122022i
$218$		−	8.37038i		−	0.566914i
$219$			26.7251i			1.80591i
$220$		−	7.59007i		−	0.511722i
$221$	0.492056			0.0330993
$222$		−	11.4370i		−	0.767602i
$223$	26.3355			1.76355			0.881777	−	0.471666i	$-0.156347\pi$
$223$	26.3355			1.76355			0.881777	+	0.471666i	$0.156347\pi$
$224$			3.91527i			0.261600i
$225$	−17.2241			−1.14827
$226$	−15.4643			−1.02867
$227$			8.99343i			0.596915i	0.954423	+	0.298458i	$0.0964721\pi$
$227$			8.99343i			0.596915i	−0.954423	+	0.298458i	$0.903528\pi$
$228$	11.0361			0.730885
$229$		−	12.1592i		−	0.803500i	−0.915749	−	0.401750i	$-0.868402\pi$
$229$		−	12.1592i		−	0.803500i	0.915749	−	0.401750i	$-0.131598\pi$
$230$	26.1562			1.72469
$231$		−	5.42012i		−	0.356617i
$232$		−	24.9993i		−	1.64128i
$233$		−	12.6908i		−	0.831400i	−0.909502	−	0.415700i	$-0.863537\pi$
$233$		−	12.6908i		−	0.831400i	0.909502	−	0.415700i	$-0.136463\pi$
$234$		−	0.400899i		−	0.0262076i
$235$			13.4195i			0.875390i
$236$	7.38650			0.480820
$237$	−7.84425			−0.509539
$238$	2.35037			0.152352
$239$		−	23.3829i		−	1.51252i	−0.654273	−	0.756258i	$-0.727025\pi$
$239$		−	23.3829i		−	1.51252i	0.654273	−	0.756258i	$-0.272975\pi$
$240$		−	17.1014i		−	1.10389i
$241$	5.84781			0.376690			0.188345	−	0.982103i	$-0.439688\pi$
$241$	5.84781			0.376690			0.188345	+	0.982103i	$0.439688\pi$
$242$	5.05176			0.324739
$243$			14.4303i			0.925705i
$244$	−5.95494			−0.381226
$245$	4.04675			0.258538
$246$	−14.9278	+	3.35289i	−0.951762	+	0.213772i
$247$	1.66344			0.105842
$248$	5.52928			0.351109
$249$		−	19.8032i		−	1.25498i
$250$	−29.0187			−1.83530
$251$	9.19552			0.580416			0.290208	−	0.956964i	$-0.406276\pi$
$251$	9.19552			0.580416			0.290208	+	0.956964i	$0.406276\pi$
$252$			1.11314i			0.0701214i
$253$			14.6617i			0.921776i
$254$	−13.7966			−0.865677
$255$	17.9687			1.12524
$256$	−14.9685			−0.935529
$257$			18.7225i			1.16788i	0.811798	+	0.583938i	$0.198489\pi$
$257$			18.7225i			1.16788i	−0.811798	+	0.583938i	$0.801511\pi$
$258$		−	4.25786i		−	0.265082i
$259$			4.78653i			0.297421i
$260$			0.700500i			0.0434431i
$261$		−	12.3046i		−	0.761633i
$262$	11.9255			0.736759
$263$			15.9577i			0.983991i	0.870598	+	0.491995i	$0.163732\pi$
$263$			15.9577i			0.983991i	−0.870598	+	0.491995i	$0.836268\pi$
$264$	16.6728			1.02614
$265$			7.38581i			0.453707i
$266$	7.94564			0.487179
$267$	34.4331			2.10727
$268$			4.40250i			0.268926i
$269$	−3.66520			−0.223471			−0.111736	−	0.993738i	$-0.535641\pi$
$269$	−3.66520			−0.223471			−0.111736	+	0.993738i	$0.535641\pi$
$270$			14.3683i			0.874426i
$271$	15.5169			0.942586			0.471293	−	0.881977i	$-0.343787\pi$
$271$	15.5169			0.942586			0.471293	+	0.881977i	$0.343787\pi$
$272$			4.15690i			0.252049i
$273$			0.500231i			0.0302754i
$274$		−	9.12200i		−	0.551080i
$275$		−	29.0217i		−	1.75008i
$276$		−	8.97751i		−	0.540382i
$277$	6.72085			0.403817			0.201908	−	0.979404i	$-0.435286\pi$
$277$	6.72085			0.403817			0.201908	+	0.979404i	$0.435286\pi$
$278$	8.37965			0.502578
$279$	2.72149			0.162931
$280$			12.4482i			0.743922i
$281$			22.9179i			1.36717i	0.729872	+	0.683584i	$0.239580\pi$
$281$			22.9179i			1.36717i	−0.729872	+	0.683584i	$0.760420\pi$
$282$	−7.92356			−0.471841
$283$	−8.44734			−0.502142			−0.251071	−	0.967969i	$-0.580783\pi$
$283$	−8.44734			−0.502142			−0.251071	+	0.967969i	$0.580783\pi$
$284$		−	1.59472i		−	0.0946290i
$285$	60.7449			3.59822
$286$	0.675495			0.0399429
$287$	6.24748	−	1.40323i	0.368777	−	0.0828298i
$288$	−5.92788			−0.349304
$289$	12.6323			0.743076
$290$		−	36.9865i		−	2.17192i
$291$	37.9049			2.22203
$292$	9.24803			0.541200
$293$		−	16.1936i		−	0.946040i	−0.881052	−	0.473020i	$-0.843164\pi$
$293$		−	16.1936i		−	0.946040i	0.881052	−	0.473020i	$-0.156836\pi$
$294$			2.38941i			0.139353i
$295$	40.6567			2.36713
$296$	−14.7238			−0.855806
$297$	−8.05406			−0.467344
$298$		−	24.7131i		−	1.43159i
$299$		−	1.35316i		−	0.0782550i
$300$			17.7702i			1.02597i
$301$			1.78197i			0.102711i
$302$		−	2.19536i		−	0.126329i
$303$	−26.0907			−1.49887
$304$			14.0528i			0.805983i
$305$	−32.7771			−1.87681
$306$			3.55855i			0.203429i
$307$	−2.45100			−0.139886			−0.0699429	−	0.997551i	$-0.522282\pi$
$307$	−2.45100			−0.139886			−0.0699429	+	0.997551i	$0.522282\pi$
$308$	−1.87559			−0.106872
$309$			7.63321i			0.434238i
$310$	8.18057			0.464625
$311$			15.5524i			0.881893i	0.897533	+	0.440947i	$0.145357\pi$
$311$			15.5524i			0.881893i	−0.897533	+	0.440947i	$0.854643\pi$
$312$	−1.53876			−0.0871151
$313$			15.4367i			0.872533i	0.899817	+	0.436267i	$0.143700\pi$
$313$			15.4367i			0.872533i	−0.899817	+	0.436267i	$0.856300\pi$
$314$			11.0142i			0.621568i
$315$			6.12695i			0.345215i
$316$			2.71445i			0.152700i
$317$		−	0.472512i		−	0.0265389i	−0.999912	−	0.0132695i	$-0.995776\pi$
$317$		−	0.472512i		−	0.0265389i	0.999912	−	0.0132695i	$-0.00422392\pi$
$318$	−4.36097			−0.244551
$319$	20.7326			1.16080
$320$	−33.9170			−1.89602
$321$		−	20.6320i		−	1.15157i
$322$		−	6.46351i		−	0.360197i
$323$	−14.7655			−0.821572
$324$	8.27100			0.459500
$325$			2.67846i			0.148574i
$326$	7.27655			0.403011
$327$	−15.8132			−0.874471
$328$	4.31646	+	19.2178i	0.238336	+	1.06113i
$329$	3.31611			0.182823
$330$	24.6674			1.35790
$331$		−	25.0870i		−	1.37890i	−0.724331	−	0.689452i	$-0.757851\pi$
$331$		−	25.0870i		−	1.37890i	0.724331	−	0.689452i	$-0.242149\pi$
$332$	−6.85276			−0.376094
$333$	−7.24701			−0.397134
$334$		−	13.2400i		−	0.724463i
$335$			24.2322i			1.32395i
$336$	−4.22596			−0.230545
$337$	17.1311			0.933190			0.466595	−	0.884471i	$-0.345481\pi$
$337$	17.1311			0.933190			0.466595	+	0.884471i	$0.345481\pi$
$338$	14.5578			0.791841
$339$			29.2148i			1.58673i
$340$		−	6.21794i		−	0.337215i
$341$			4.58558i			0.248323i
$342$			12.0300i			0.650510i
$343$		−	1.00000i		−	0.0539949i
$344$	−5.48150			−0.295543
$345$		−	49.4139i		−	2.66036i
$346$	−21.4300			−1.15208
$347$			17.0399i			0.914752i	0.889273	+	0.457376i	$0.151211\pi$
$347$			17.0399i			0.914752i	−0.889273	+	0.457376i	$0.848789\pi$
$348$	−12.6947			−0.680509
$349$	−4.39069			−0.235028			−0.117514	−	0.993071i	$-0.537493\pi$
$349$	−4.39069			−0.235028			−0.117514	+	0.993071i	$0.537493\pi$
$350$			12.7940i			0.683868i
$351$	0.743323			0.0396756
$352$		−	9.98820i		−	0.532373i
$353$	−16.6488			−0.886124			−0.443062	−	0.896491i	$-0.646108\pi$
$353$	−16.6488			−0.886124			−0.443062	+	0.896491i	$0.646108\pi$
$354$			24.0059i			1.27590i
$355$		−	8.77762i		−	0.465868i
$356$		−	11.9153i		−	0.631512i
$357$		−	4.44027i		−	0.235004i
$358$		−	29.9369i		−	1.58221i
$359$	26.9628			1.42304			0.711521	−	0.702665i	$-0.248007\pi$
$359$	26.9628			1.42304			0.711521	+	0.702665i	$0.248007\pi$
$360$	−18.8471			−0.993329
$361$	−30.9161			−1.62716
$362$		−	14.4861i		−	0.761371i
$363$		−	9.54370i		−	0.500914i
$364$	0.173102			0.00907299
$365$	50.9029			2.66438
$366$		−	19.3533i		−	1.01161i
$367$	−37.2214			−1.94294			−0.971472	−	0.237156i	$-0.923785\pi$
$367$	−37.2214			−1.94294			−0.971472	+	0.237156i	$0.923785\pi$
$368$	11.4315			0.595907
$369$	2.12454	+	9.45894i	0.110599	+	0.492413i
$370$	−21.7839			−1.13249
$371$	1.82512			0.0947555
$372$		−	2.80779i		−	0.145577i
$373$	−9.47733			−0.490718			−0.245359	−	0.969432i	$-0.578906\pi$
$373$	−9.47733			−0.490718			−0.245359	+	0.969432i	$0.578906\pi$
$374$	−5.99600			−0.310046
$375$			54.8216i			2.83098i
$376$			10.2007i			0.526059i
$377$	−1.91344			−0.0985474
$378$	3.55057			0.182622
$379$	−35.6537			−1.83141			−0.915703	−	0.401856i	$-0.868365\pi$
$379$	−35.6537			−1.83141			−0.915703	+	0.401856i	$0.868365\pi$
$380$		−	21.0204i		−	1.07832i
$381$			26.0643i			1.33532i
$382$			9.83398i			0.503150i
$383$		−	2.61355i		−	0.133546i	−0.997768	−	0.0667732i	$-0.978730\pi$
$383$		−	2.61355i		−	0.133546i	0.997768	−	0.0667732i	$-0.0212704\pi$
$384$		−	3.38941i		−	0.172965i
$385$	−10.3236			−0.526141
$386$		−	13.8723i		−	0.706082i
$387$	−2.69797			−0.137146
$388$		−	13.1168i		−	0.665902i
$389$	1.37310			0.0696192			0.0348096	−	0.999394i	$-0.488918\pi$
$389$	1.37310			0.0696192			0.0348096	+	0.999394i	$0.488918\pi$
$390$	−2.27660			−0.115280
$391$			12.0112i			0.607433i
$392$	3.07610			0.155366
$393$		−	22.5294i		−	1.13646i
$394$	2.81022			0.141577
$395$			14.9409i			0.751756i
$396$		−	2.83973i		−	0.142702i
$397$			32.0530i			1.60870i	0.594159	+	0.804348i	$0.297485\pi$
$397$			32.0530i			1.60870i	−0.594159	+	0.804348i	$0.702515\pi$
$398$		−	7.50079i		−	0.375981i
$399$		−	15.0108i		−	0.751479i
$400$	−22.6277			−1.13138
$401$	18.3994			0.918824			0.459412	−	0.888223i	$-0.348060\pi$
$401$	18.3994			0.918824			0.459412	+	0.888223i	$0.348060\pi$
$402$	−14.3080			−0.713617
$403$		−	0.423210i		−	0.0210816i
$404$			9.02851i			0.449185i
$405$	45.5252			2.26216
$406$	−9.13980			−0.453600
$407$		−	12.2109i		−	0.605271i
$408$	13.6587			0.676207
$409$	16.9221			0.836742			0.418371	−	0.908276i	$-0.362601\pi$
$409$	16.9221			0.836742			0.418371	+	0.908276i	$0.362601\pi$
$410$	6.38620	+	28.4328i	0.315392	+	1.40420i
$411$	−17.2331			−0.850048
$412$	2.64142			0.130133
$413$		−	10.0468i		−	0.494368i
$414$	9.78603			0.480957
$415$	−37.7189			−1.85155
$416$			0.921827i			0.0451963i
$417$		−	15.8307i		−	0.775233i
$418$	−20.2700			−0.991440
$419$	37.2216			1.81839			0.909196	−	0.416369i	$-0.136697\pi$
$419$	37.2216			1.81839			0.909196	+	0.416369i	$0.136697\pi$
$420$	6.32125			0.308445
$421$			17.8034i			0.867682i	0.900989	+	0.433841i	$0.142842\pi$
$421$			17.8034i			0.867682i	−0.900989	+	0.433841i	$0.857158\pi$
$422$			12.0129i			0.584777i
$423$			5.02073i			0.244116i
$424$			5.61424i			0.272652i
$425$		−	23.7752i		−	1.15327i
$426$	5.18277			0.251106
$427$			8.09961i			0.391968i
$428$	−7.13958			−0.345105
$429$		−	1.27613i		−	0.0616124i
$430$	−8.10989			−0.391093
$431$	−21.9203			−1.05586			−0.527932	−	0.849287i	$-0.677032\pi$
$431$	−21.9203			−1.05586			−0.527932	+	0.849287i	$0.677032\pi$
$432$			6.27960i			0.302127i
$433$	−20.1275			−0.967264			−0.483632	−	0.875271i	$-0.660683\pi$
$433$	−20.1275			−0.967264			−0.483632	+	0.875271i	$0.660683\pi$
$434$		−	2.02152i		−	0.0970359i
$435$	−69.8743			−3.35021
$436$			5.47205i			0.262063i
$437$			40.6050i			1.94240i
$438$			30.0558i			1.43612i
$439$			0.0416296i			0.00198687i	1.00000		0.000993435i	$0.000316220\pi$
$439$			0.0416296i			0.00198687i	−1.00000		0.000993435i	$0.999684\pi$
$440$		−	31.7565i		−	1.51393i
$441$	1.51404			0.0720972
$442$	0.553380			0.0263216
$443$	−3.78579			−0.179868			−0.0899342	−	0.995948i	$-0.528666\pi$
$443$	−3.78579			−0.179868			−0.0899342	+	0.995948i	$0.528666\pi$
$444$			7.47682i			0.354834i
$445$		−	65.5843i		−	3.10899i
$446$	29.6176			1.40243
$447$	−46.6877			−2.20825
$448$			8.38129i			0.395979i
$449$	−9.32565			−0.440105			−0.220052	−	0.975488i	$-0.570623\pi$
$449$	−9.32565			−0.440105			−0.220052	+	0.975488i	$0.570623\pi$
$450$	−19.3707			−0.913141
$451$	−15.9379	+	3.57975i	−0.750485	+	0.168564i
$452$	10.1096			0.475515
$453$	−4.14743			−0.194863
$454$			10.1143i			0.474686i
$455$	0.952785			0.0446672
$456$	46.1746			2.16232
$457$			4.81304i			0.225144i	0.993644	+	0.112572i	$0.0359090\pi$
$457$			4.81304i			0.225144i	−0.993644	+	0.112572i	$0.964091\pi$
$458$		−	13.6745i		−	0.638969i
$459$	−6.59806			−0.307971
$460$	−17.0993			−0.797261
$461$	−32.7239			−1.52410			−0.762052	−	0.647516i	$-0.775808\pi$
$461$	−32.7239			−1.52410			−0.762052	+	0.647516i	$0.775808\pi$
$462$		−	6.09561i		−	0.283593i
$463$		−	23.0519i		−	1.07131i	−0.844436	−	0.535656i	$-0.820064\pi$
$463$		−	23.0519i		−	1.07131i	0.844436	−	0.535656i	$-0.179936\pi$
$464$		−	16.1648i		−	0.750432i
$465$		−	15.4546i		−	0.716690i
$466$		−	14.2724i		−	0.661156i
$467$	3.89481			0.180230			0.0901152	−	0.995931i	$-0.471276\pi$
$467$	3.89481			0.180230			0.0901152	+	0.995931i	$0.471276\pi$
$468$			0.262083i			0.0121148i
$469$	5.98807			0.276503
$470$			15.0919i			0.696138i
$471$	20.8079			0.958776
$472$	30.9048			1.42251
$473$		−	4.54595i		−	0.209023i
$474$	−8.82186			−0.405201
$475$		−	80.3744i		−	3.68783i
$476$	−1.53653			−0.0704266
$477$			2.76331i			0.126523i
$478$		−	26.2971i		−	1.20280i
$479$			20.2308i			0.924370i	0.886784	+	0.462185i	$0.152934\pi$
$479$			20.2308i			0.924370i	−0.886784	+	0.462185i	$0.847066\pi$
$480$			33.6628i			1.53649i
$481$			1.12696i			0.0513850i
$482$	6.57661			0.299556
$483$	−12.2108			−0.555609
$484$	−3.30253			−0.150115
$485$		−	72.1971i		−	3.27830i
$486$			16.2287i			0.736150i
$487$	15.4301			0.699205			0.349602	−	0.936898i	$-0.386317\pi$
$487$	15.4301			0.699205			0.349602	+	0.936898i	$0.386317\pi$
$488$	−24.9152			−1.12786
$489$		−	13.7467i		−	0.621649i
$490$	4.55109			0.205597
$491$	9.80540			0.442512			0.221256	−	0.975216i	$-0.428984\pi$
$491$	9.80540			0.442512			0.221256	+	0.975216i	$0.428984\pi$
$492$	9.75889	−	2.19191i	0.439965	−	0.0988191i
$493$	16.9846			0.764947
$494$	1.87076			0.0841693
$495$		−	15.6304i		−	0.702535i
$496$	3.57529			0.160535
$497$	−2.16905			−0.0972954
$498$		−	22.2712i		−	0.997997i
$499$			1.52411i			0.0682287i	0.999418	+	0.0341143i	$0.0108610\pi$
$499$			1.52411i			0.0682287i	−0.999418	+	0.0341143i	$0.989139\pi$
$500$	18.9707			0.848394
$501$	−25.0129			−1.11749
$502$	10.3415			0.461565
$503$			15.8474i			0.706602i	0.935510	+	0.353301i	$0.114941\pi$
$503$			15.8474i			0.706602i	−0.935510	+	0.353301i	$0.885059\pi$
$504$			4.65734i			0.207454i
$505$			49.6946i			2.21138i
$506$			16.4890i			0.733025i
$507$		−	27.5024i		−	1.22142i
$508$	9.01939			0.400171
$509$		−	23.6031i		−	1.04619i	−0.852274	−	0.523096i	$-0.824777\pi$
$509$		−	23.6031i		−	1.04619i	0.852274	−	0.523096i	$-0.175223\pi$
$510$	20.2081			0.894829
$511$		−	12.5787i		−	0.556449i
$512$	−20.0245			−0.884968
$513$	−22.3054			−0.984806
$514$			21.0558i			0.928732i
$515$	14.5389			0.640659
$516$			2.78353i			0.122538i
$517$	−8.45969			−0.372057
$518$			5.38307i			0.236518i
$519$			40.4852i			1.77710i
$520$			2.93086i			0.128527i
$521$			22.2811i			0.976152i	0.872801	+	0.488076i	$0.162301\pi$
$521$			22.2811i			0.976152i	−0.872801	+	0.488076i	$0.837699\pi$
$522$		−	13.8380i		−	0.605674i
$523$	4.14305			0.181163			0.0905815	−	0.995889i	$-0.471127\pi$
$523$	4.14305			0.181163			0.0905815	+	0.995889i	$0.471127\pi$
$524$	−7.79616			−0.340577
$525$	24.1702			1.05487
$526$			17.9464i			0.782501i
$527$			3.75660i			0.163640i
$528$	10.7808			0.469174
$529$	10.0308			0.436123
$530$			8.30628i			0.360802i
$531$	15.2112			0.660110
$532$	−5.19438			−0.225205
$533$	1.47093	−	0.330381i	0.0637131	−	0.0143104i
$534$	38.7244			1.67577
$535$	−39.2976			−1.69898
$536$			18.4199i			0.795617i
$537$	−56.5562			−2.44058
$538$	−4.12199			−0.177711
$539$			2.55109i			0.109883i
$540$		−	9.39310i		−	0.404215i
$541$	−18.4483			−0.793155			−0.396578	−	0.918001i	$-0.629802\pi$
$541$	−18.4483			−0.793155			−0.396578	+	0.918001i	$0.629802\pi$
$542$	17.4508			0.749575
$543$	−27.3668			−1.17442
$544$		−	8.18254i		−	0.350824i
$545$			30.1192i			1.29016i
$546$			0.562574i			0.0240759i
$547$			25.0193i			1.06975i	0.844931	+	0.534875i	$0.179641\pi$
$547$			25.0193i			1.06975i	−0.844931	+	0.534875i	$0.820359\pi$
$548$			5.96341i			0.254744i
$549$	−12.2632			−0.523379
$550$		−	32.6386i		−	1.39172i
$551$	57.4180			2.44609
$552$		−	37.5615i		−	1.59872i
$553$	3.69206			0.157002
$554$	7.55845			0.321128
$555$			41.1539i			1.74688i
$556$	−5.47811			−0.232323
$557$			20.2281i			0.857092i	0.903520	+	0.428546i	$0.140974\pi$
$557$			20.2281i			0.857092i	−0.903520	+	0.428546i	$0.859026\pi$
$558$	3.06066			0.129568
$559$			0.419554i			0.0177452i
$560$			8.04914i			0.340138i
$561$			11.3275i			0.478249i
$562$			25.7741i			1.08722i
$563$		−	17.2330i		−	0.726286i	−0.931733	−	0.363143i	$-0.881704\pi$
$563$		−	17.2330i		−	0.726286i	0.931733	−	0.363143i	$-0.118296\pi$
$564$	5.17994			0.218115
$565$	55.6451			2.34101
$566$	−9.50011			−0.399319
$567$		−	11.2498i		−	0.472447i
$568$		−	6.67222i		−	0.279960i
$569$	21.4579			0.899563			0.449781	−	0.893139i	$-0.351502\pi$
$569$	21.4579			0.899563			0.449781	+	0.893139i	$0.351502\pi$
$570$	68.3154			2.86142
$571$			15.6803i			0.656200i	0.944643	+	0.328100i	$0.106408\pi$
$571$			15.6803i			0.656200i	−0.944643	+	0.328100i	$0.893592\pi$
$572$	−0.441598			−0.0184641
$573$	18.5782			0.776115
$574$	7.02608	−	1.57811i	0.293263	−	0.0658689i
$575$	−65.3819			−2.72661
$576$	−12.6896			−0.528734
$577$		−	22.4227i		−	0.933471i	−0.884397	−	0.466735i	$-0.845430\pi$
$577$		−	22.4227i		−	0.933471i	0.884397	−	0.466735i	$-0.154570\pi$
$578$	14.2066			0.590918
$579$	−26.2074			−1.08914
$580$			24.1795i			1.00400i
$581$			9.32078i			0.386691i
$582$	42.6289			1.76703
$583$	−4.65604			−0.192834
$584$	38.6933			1.60114
$585$			1.44256i			0.0596423i
$586$		−	18.2118i		−	0.752321i
$587$		−	44.3924i		−	1.83227i	−0.400868	−	0.916136i	$-0.631291\pi$
$587$		−	44.3924i		−	1.83227i	0.400868	−	0.916136i	$-0.368709\pi$
$588$		−	1.56205i		−	0.0644180i
$589$			12.6996i			0.523276i
$590$	45.7237			1.88241
$591$		−	5.30902i		−	0.218384i
$592$	−9.52059			−0.391294
$593$		−	5.46737i		−	0.224518i	−0.993679	−	0.112259i	$-0.964191\pi$
$593$		−	5.46737i		−	0.224518i	0.993679	−	0.112259i	$-0.0358087\pi$
$594$	−9.05782			−0.371647
$595$	−8.45734			−0.346717
$596$			16.1559i			0.661773i
$597$	−14.1704			−0.579954
$598$		−	1.52180i		−	0.0622309i
$599$	37.2219			1.52084			0.760422	−	0.649429i	$-0.224992\pi$
$599$	37.2219			1.52084			0.760422	+	0.649429i	$0.224992\pi$
$600$			74.3499i			3.03532i
$601$		−	2.64469i		−	0.107879i	−0.998544	−	0.0539395i	$-0.982822\pi$
$601$		−	2.64469i		−	0.107879i	0.998544	−	0.0539395i	$-0.0171778\pi$
$602$			2.00405i			0.0816789i
$603$			9.06619i			0.369204i
$604$			1.43519i			0.0583970i
$605$	−18.1778			−0.739032
$606$	−29.3423			−1.19195
$607$	−4.36558			−0.177194			−0.0885968	−	0.996068i	$-0.528238\pi$
$607$	−4.36558			−0.177194			−0.0885968	+	0.996068i	$0.528238\pi$
$608$		−	27.6619i		−	1.12184i
$609$			17.2668i			0.699684i
$610$	−36.8621			−1.49250
$611$	0.780758			0.0315861
$612$		−	2.32637i		−	0.0940378i
$613$	−23.4501			−0.947139			−0.473570	−	0.880756i	$-0.657035\pi$
$613$	−23.4501			−0.947139			−0.473570	+	0.880756i	$0.657035\pi$
$614$	−2.75646			−0.111242
$615$	53.7148	−	12.0647i	2.16599	−	0.486496i
$616$	−7.84740			−0.316181
$617$	3.43169			0.138155			0.0690773	−	0.997611i	$-0.477994\pi$
$617$	3.43169			0.138155			0.0690773	+	0.997611i	$0.477994\pi$
$618$			8.58451i			0.345320i
$619$	33.4774			1.34557			0.672785	−	0.739838i	$-0.265098\pi$
$619$	33.4774			1.34557			0.672785	+	0.739838i	$0.265098\pi$
$620$	−5.34796			−0.214779
$621$			18.1447i			0.728120i
$622$			17.4906i			0.701310i
$623$	−16.2066			−0.649306
$624$	−0.994978			−0.0398310
$625$	47.5371			1.90148
$626$			17.3605i			0.693866i
$627$			38.2938i			1.52931i
$628$		−	7.20042i		−	0.287328i
$629$		−	10.0034i		−	0.398862i
$630$			6.89054i			0.274526i
$631$	8.36357			0.332949			0.166474	−	0.986046i	$-0.446762\pi$
$631$	8.36357			0.332949			0.166474	+	0.986046i	$0.446762\pi$
$632$			11.3571i			0.451762i
$633$	22.6945			0.902025
$634$		−	0.531400i		−	0.0211046i
$635$	49.6444			1.97008
$636$	2.85093			0.113047
$637$		−	0.235444i		−	0.00932864i
$638$	23.3164			0.923107
$639$		−	3.28404i		−	0.129915i
$640$	−6.45576			−0.255186
$641$			9.99103i			0.394622i	0.980341	+	0.197311i	$0.0632209\pi$
$641$			9.99103i			0.394622i	−0.980341	+	0.197311i	$0.936779\pi$
$642$		−	23.2034i		−	0.915764i
$643$		−	36.1454i		−	1.42544i	−0.701450	−	0.712719i	$-0.747464\pi$
$643$		−	36.1454i		−	1.42544i	0.701450	−	0.712719i	$-0.252536\pi$
$644$			4.22545i			0.166506i
$645$			15.3211i			0.603266i
$646$	−16.6056			−0.653340
$647$	29.0169			1.14077			0.570386	−	0.821377i	$-0.306793\pi$
$647$	29.0169			1.14077			0.570386	+	0.821377i	$0.306793\pi$
$648$	34.6055			1.35943
$649$			25.6302i			1.00607i
$650$			3.01227i			0.118151i
$651$	−3.81901			−0.149679
$652$	−4.75696			−0.186297
$653$			27.8090i			1.08825i	0.839004	+	0.544125i	$0.183138\pi$
$653$			27.8090i			1.08825i	−0.839004	+	0.544125i	$0.816862\pi$
$654$	−17.7839			−0.695407
$655$	−42.9116			−1.67669
$656$	2.79107	+	12.4265i	0.108973	+	0.485172i
$657$	19.0447			0.743004
$658$	3.72939			0.145387
$659$		−	40.0208i		−	1.55899i	−0.626409	−	0.779494i	$-0.715476\pi$
$659$		−	40.0208i		−	1.55899i	0.626409	−	0.779494i	$-0.284524\pi$
$660$	−16.1261			−0.627706
$661$	15.4005			0.599008			0.299504	−	0.954095i	$-0.403179\pi$
$661$	15.4005			0.599008			0.299504	+	0.954095i	$0.403179\pi$
$662$		−	28.2135i		−	1.09655i
$663$		−	1.04544i		−	0.0406014i
$664$	−28.6716			−1.11267
$665$	−28.5908			−1.10871
$666$	−8.15019			−0.315813
$667$		−	46.7076i		−	1.80853i
$668$			8.65554i			0.334893i
$669$		−	55.9531i		−	2.16327i
$670$			27.2522i			1.05285i
$671$		−	20.6628i		−	0.797680i
$672$	8.31848			0.320892
$673$		−	32.3269i		−	1.24611i	−0.782177	−	0.623056i	$-0.785891\pi$
$673$		−	32.3269i		−	1.24611i	0.782177	−	0.623056i	$-0.214109\pi$
$674$	19.2661			0.742102
$675$		−	35.9159i		−	1.38240i
$676$	−9.51701			−0.366039
$677$	−46.8769			−1.80162			−0.900812	−	0.434210i	$-0.857028\pi$
$677$	−46.8769			−1.80162			−0.900812	+	0.434210i	$0.857028\pi$
$678$			32.8558i			1.26182i
$679$	−17.8408			−0.684665
$680$		−	26.0156i		−	0.997652i
$681$	19.1077			0.732208
$682$			5.15707i			0.197474i
$683$		−	3.22279i		−	0.123317i	−0.998097	−	0.0616584i	$-0.980361\pi$
$683$		−	3.22279i		−	0.123317i	0.998097	−	0.0616584i	$-0.0196389\pi$
$684$		−	7.86450i		−	0.300707i
$685$			32.8237i			1.25413i
$686$		−	1.12463i		−	0.0429385i
$687$	−25.8337			−0.985617
$688$	−3.54439			−0.135129
$689$	0.429714			0.0163708
$690$		−	55.5722i		−	2.11560i
$691$		−	28.1393i		−	1.07047i	−0.844703	−	0.535235i	$-0.820223\pi$
$691$		−	28.1393i		−	1.07047i	0.844703	−	0.535235i	$-0.179777\pi$
$692$	14.0096			0.532566
$693$	−3.86246			−0.146723
$694$			19.1636i			0.727440i
$695$	−30.1525			−1.14375
$696$	−53.1142			−2.01329
$697$	−13.0566	+	2.93261i	−0.494556	+	0.111081i
$698$	−4.93789			−0.186902
$699$	−26.9632			−1.01984
$700$		−	8.36394i		−	0.316127i
$701$	52.2820			1.97466			0.987332	−	0.158670i	$-0.0507207\pi$
$701$	52.2820			1.97466			0.987332	+	0.158670i	$0.0507207\pi$
$702$	0.835961			0.0315513
$703$		−	33.8175i		−	1.27545i
$704$		−	21.3814i		−	0.805843i
$705$	28.5114			1.07380
$706$	−18.7237			−0.704674
$707$	12.2801			0.461842
$708$		−	15.6936i		−	0.589800i
$709$			6.75040i			0.253517i	0.991934	+	0.126758i	$0.0404572\pi$
$709$			6.75040i			0.253517i	−0.991934	+	0.126758i	$0.959543\pi$
$710$		−	9.87156i		−	0.370473i
$711$			5.58993i			0.209639i
$712$		−	49.8532i		−	1.86833i
$713$	10.3307			0.386886
$714$		−	4.99365i		−	0.186883i
$715$	−2.43064			−0.0909007
$716$			19.5709i			0.731399i
$717$	−49.6800			−1.85534
$718$	30.3231			1.13165
$719$		−	0.580649i		−	0.0216545i	−0.999941	−	0.0108273i	$-0.996554\pi$
$719$		−	0.580649i		−	0.0216545i	0.999941	−	0.0108273i	$-0.00344650\pi$
$720$	−12.1867			−0.454173
$721$		−	3.59273i		−	0.133800i
$722$	−34.7691			−1.29397
$723$		−	12.4244i		−	0.462069i
$724$			9.47011i			0.351954i
$725$			92.4539i			3.43365i
$726$		−	10.7331i		−	0.398343i
$727$			28.9350i			1.07314i	0.843856	+	0.536569i	$0.180280\pi$
$727$			28.9350i			1.07314i	−0.843856	+	0.536569i	$0.819720\pi$
$728$	0.724249			0.0268425
$729$	−3.09036			−0.114458
$730$	57.2468			2.11880
$731$		−	3.72414i		−	0.137742i
$732$			12.6520i			0.467632i
$733$	−11.8458			−0.437534			−0.218767	−	0.975777i	$-0.570203\pi$
$733$	−11.8458			−0.437534			−0.218767	+	0.975777i	$0.570203\pi$
$734$	−41.8603			−1.54509
$735$		−	8.59784i		−	0.317136i
$736$	−22.5020			−0.829435
$737$	−15.2761			−0.562702
$738$	2.38932	+	10.6378i	0.0879520	+	0.391582i
$739$	−23.2609			−0.855668			−0.427834	−	0.903857i	$-0.640723\pi$
$739$	−23.2609			−0.855668			−0.427834	+	0.903857i	$0.640723\pi$
$740$	14.2410			0.523510
$741$		−	3.53420i		−	0.129832i
$742$	2.05258			0.0753526
$743$	34.0489			1.24913			0.624567	−	0.780971i	$-0.285275\pi$
$743$	34.0489			1.24913			0.624567	+	0.780971i	$0.285275\pi$
$744$		−	11.7477i		−	0.430690i
$745$			88.9254i			3.25798i
$746$	−10.6585			−0.390234
$747$	−14.1121			−0.516333
$748$	3.91982			0.143323
$749$			9.71090i			0.354829i
$750$			61.6539i			2.25128i
$751$		−	25.2472i		−	0.921284i	−0.887586	−	0.460642i	$-0.847619\pi$
$751$		−	25.2472i		−	0.921284i	0.887586	−	0.460642i	$-0.152381\pi$
$752$			6.59586i			0.240526i
$753$		−	19.5370i		−	0.711970i
$754$	−2.15191			−0.0783680
$755$			7.89956i			0.287494i
$756$	−2.32115			−0.0844193
$757$			15.4127i			0.560184i	0.959973	+	0.280092i	$0.0903650\pi$
$757$			15.4127i			0.560184i	−0.959973	+	0.280092i	$0.909635\pi$
$758$	−40.0971			−1.45639
$759$	31.1507			1.13070
$760$		−	87.9482i		−	3.19022i
$761$	33.9154			1.22943			0.614716	−	0.788748i	$-0.289270\pi$
$761$	33.9154			1.22943			0.614716	+	0.788748i	$0.289270\pi$
$762$			29.3127i			1.06189i
$763$	7.44280			0.269448
$764$		−	6.42885i		−	0.232588i
$765$		−	12.8048i		−	0.462957i
$766$		−	2.93928i		−	0.106200i
$767$		−	2.36545i		−	0.0854114i
$768$			31.8024i			1.14757i
$769$	1.27109			0.0458366			0.0229183	−	0.999737i	$-0.492704\pi$
$769$	1.27109			0.0458366			0.0229183	+	0.999737i	$0.492704\pi$
$770$	−11.6102			−0.418404
$771$	39.7783			1.43258
$772$			9.06888i			0.326396i
$773$		−	11.2160i		−	0.403410i	−0.979446	−	0.201705i	$-0.935352\pi$
$773$		−	11.2160i		−	0.403410i	0.979446	−	0.201705i	$-0.0646482\pi$
$774$	−3.03421			−0.109063
$775$	−20.4487			−0.734539
$776$		−	54.8799i		−	1.97007i
$777$	10.1696			0.364832
$778$	1.54423			0.0553634
$779$	−44.1392	+	9.91397i	−1.58145	+	0.355205i
$780$	1.48830			0.0532897
$781$	5.53345			0.198002
$782$			13.5081i			0.483050i
$783$	25.6577			0.916930
$784$	1.98904			0.0710370
$785$		−	39.6325i		−	1.41454i
$786$		−	25.3372i		−	0.903749i
$787$	−41.8511			−1.49183			−0.745915	−	0.666041i	$-0.767988\pi$
$787$	−41.8511			−1.49183			−0.745915	+	0.666041i	$0.767988\pi$
$788$	−1.83715			−0.0654458
$789$	33.9041			1.20702
$790$			16.8029i			0.597820i
$791$		−	13.7506i		−	0.488913i
$792$		−	11.8813i		−	0.422183i
$793$			1.90701i			0.0677198i
$794$			36.0477i			1.27929i
$795$	15.6921			0.556541
$796$			4.90356i			0.173802i
$797$	9.08035			0.321642			0.160821	−	0.986984i	$-0.448586\pi$
$797$	9.08035			0.321642			0.160821	+	0.986984i	$0.448586\pi$
$798$		−	16.8815i		−	0.597600i
$799$	−6.93036			−0.245178
$800$	44.5409			1.57476
$801$		−	24.5375i		−	0.866992i
$802$	20.6925			0.730678
$803$			32.0894i			1.13241i
$804$	9.35368			0.329879
$805$			23.2577i			0.819726i
$806$		−	0.475954i		−	0.0167648i
$807$			7.78719i			0.274122i
$808$			37.7749i			1.32891i
$809$			36.8884i			1.29693i	0.761246	+	0.648463i	$0.224588\pi$
$809$			36.8884i			1.29693i	−0.761246	+	0.648463i	$0.775412\pi$
$810$	51.1989			1.79894
$811$	−1.93107			−0.0678091			−0.0339045	−	0.999425i	$-0.510794\pi$
$811$	−1.93107			−0.0678091			−0.0339045	+	0.999425i	$0.510794\pi$
$812$	5.97504			0.209683
$813$		−	32.9677i		−	1.15623i
$814$		−	13.7327i		−	0.481330i
$815$	−26.1832			−0.917159
$816$	8.83186			0.309177
$817$		−	12.5898i		−	0.440462i
$818$	19.0310			0.665403
$819$	0.356472			0.0124562
$820$	−4.17491	−	18.5876i	−0.145794	−	0.649109i
$821$	−18.3311			−0.639761			−0.319880	−	0.947458i	$-0.603643\pi$
$821$	−18.3311			−0.639761			−0.319880	+	0.947458i	$0.603643\pi$
$822$	−19.3809			−0.675985
$823$			14.7997i			0.515885i	0.966160	+	0.257943i	$0.0830445\pi$
$823$			14.7997i			0.515885i	−0.966160	+	0.257943i	$0.916955\pi$
$824$	11.0516			0.385000
$825$	−61.6604			−2.14674
$826$		−	11.2989i		−	0.393137i
$827$			46.1075i			1.60331i	0.597785	+	0.801657i	$0.296048\pi$
$827$			46.1075i			1.60331i	−0.597785	+	0.801657i	$0.703952\pi$
$828$	−6.39751			−0.222329
$829$	38.5967			1.34052			0.670259	−	0.742127i	$-0.266183\pi$
$829$	38.5967			1.34052			0.670259	+	0.742127i	$0.266183\pi$
$830$	−42.4197			−1.47241
$831$		−	14.2793i		−	0.495344i
$832$			1.97333i			0.0684128i
$833$			2.08991i			0.0724110i
$834$		−	17.8036i		−	0.616490i
$835$			47.6417i			1.64871i
$836$	13.2513			0.458306
$837$			5.67489i			0.196153i
$838$	41.8604			1.44604
$839$			30.1541i			1.04104i	0.853851	+	0.520518i	$0.174261\pi$
$839$			30.1541i			1.04104i	−0.853851	+	0.520518i	$0.825739\pi$
$840$	26.4478			0.912535
$841$	−37.0474			−1.27750
$842$			20.0221i			0.690009i
$843$	48.6920			1.67704
$844$		−	7.85327i		−	0.270321i
$845$	−52.3835			−1.80205
$846$			5.64645i			0.194129i
$847$			4.49194i			0.154345i
$848$			3.63023i			0.124663i
$849$			17.9475i			0.615955i
$850$		−	26.7383i		−	0.917115i
$851$	−27.5094			−0.943009
$852$	−3.38818			−0.116077
$853$	−53.0601			−1.81674			−0.908372	−	0.418162i	$-0.862674\pi$
$853$	−53.0601			−1.81674			−0.908372	+	0.418162i	$0.862674\pi$
$854$			9.10905i			0.311705i
$855$		−	43.2877i		−	1.48041i
$856$	−29.8717			−1.02099
$857$	14.5980			0.498657			0.249329	−	0.968419i	$-0.419790\pi$
$857$	14.5980			0.498657			0.249329	+	0.968419i	$0.419790\pi$
$858$		−	1.43518i		−	0.0489961i
$859$	−26.3824			−0.900156			−0.450078	−	0.892989i	$-0.648604\pi$
$859$	−26.3824			−0.900156			−0.450078	+	0.892989i	$0.648604\pi$
$860$	5.30175			0.180788
$861$	−2.98133	−	13.2736i	−0.101603	−	0.452362i
$862$	−24.6522			−0.839657
$863$	2.86153			0.0974077			0.0487039	−	0.998813i	$-0.484491\pi$
$863$	2.86153			0.0974077			0.0487039	+	0.998813i	$0.484491\pi$
$864$		−	12.3609i		−	0.420527i
$865$	77.1116			2.62187
$866$	−22.6359			−0.769199
$867$		−	26.8389i		−	0.911497i
$868$			1.32154i			0.0448561i
$869$	−9.41877			−0.319510
$870$	−78.5825			−2.66420
$871$	1.40986			0.0477711
$872$			22.8948i			0.775315i
$873$		−	27.0116i		−	0.914206i
$874$			45.6655i			1.54466i
$875$		−	25.8029i		−	0.872299i
$876$		−	19.6486i		−	0.663865i
$877$	−28.8000			−0.972507			−0.486253	−	0.873818i	$-0.661637\pi$
$877$	−28.8000			−0.972507			−0.486253	+	0.873818i	$0.661637\pi$
$878$			0.0468177i			0.00158002i
$879$	−34.4054			−1.16046
$880$		−	20.5341i		−	0.692203i
$881$	36.1942			1.21941			0.609706	−	0.792627i	$-0.291287\pi$
$881$	36.1942			1.21941			0.609706	+	0.792627i	$0.291287\pi$
$882$	1.70273			0.0573340
$883$			22.3364i			0.751680i	0.926684	+	0.375840i	$0.122646\pi$
$883$			22.3364i			0.751680i	−0.926684	+	0.375840i	$0.877354\pi$
$884$	−0.361766			−0.0121675
$885$		−	86.3804i		−	2.90365i
$886$	−4.25761			−0.143037
$887$		−	55.0841i		−	1.84954i	−0.380522	−	0.924772i	$-0.624256\pi$
$887$		−	55.0841i		−	1.84954i	0.380522	−	0.924772i	$-0.375744\pi$
$888$			31.2827i			1.04978i
$889$		−	12.2677i		−	0.411446i
$890$		−	73.7579i		−	2.47237i
$891$			28.6993i			0.961461i
$892$	−19.3622			−0.648294
$893$	−23.4287			−0.784013
$894$	−52.5062			−1.75607
$895$			107.722i			3.60075i
$896$			1.59529i			0.0532950i
$897$	−2.87495			−0.0959918
$898$	−10.4879			−0.349985
$899$		−	14.6082i		−	0.487210i
$900$	12.6634			0.422112
$901$	−3.81433			−0.127074
$902$	−17.9242	+	4.02589i	−0.596810	+	0.134047i
$903$	3.78601			0.125991
$904$	42.2980			1.40681
$905$			52.1253i			1.73270i
$906$	−4.66431			−0.154961
$907$	−5.99003			−0.198896			−0.0994478	−	0.995043i	$-0.531708\pi$
$907$	−5.99003			−0.198896			−0.0994478	+	0.995043i	$0.531708\pi$
$908$		−	6.61209i		−	0.219430i
$909$			18.5926i			0.616679i
$910$	1.07153			0.0355208
$911$	−8.59198			−0.284665			−0.142332	−	0.989819i	$-0.545460\pi$
$911$	−8.59198			−0.284665			−0.142332	+	0.989819i	$0.545460\pi$
$912$	29.8570			0.988663
$913$		−	23.7782i		−	0.786942i
$914$			5.41288i			0.179042i
$915$			69.6392i			2.30220i
$916$			8.93958i			0.295372i
$917$			10.6039i			0.350173i
$918$	−7.42036			−0.244908
$919$		−	26.5734i		−	0.876575i	−0.898835	−	0.438287i	$-0.855585\pi$
$919$		−	26.5734i		−	0.876575i	0.898835	−	0.438287i	$-0.144415\pi$
$920$	−71.5429			−2.35870
$921$			5.20745i			0.171591i
$922$	−36.8022			−1.21202
$923$	−0.510691			−0.0168096
$924$			3.98494i			0.131095i
$925$	54.4526			1.79039
$926$		−	25.9248i		−	0.851942i
$927$	5.43954			0.178658
$928$			31.8192i			1.04452i
$929$		−	29.8795i		−	0.980314i	−0.871634	−	0.490157i	$-0.836939\pi$
$929$		−	29.8795i		−	0.980314i	0.871634	−	0.490157i	$-0.163061\pi$
$930$		−	17.3807i		−	0.569935i
$931$			7.06513i			0.231550i
$932$			9.33042i			0.305628i
$933$	33.0430			1.08178
$934$	4.38021			0.143325
$935$	21.5754			0.705592
$936$			1.09654i			0.0358416i
$937$			27.6323i			0.902708i	0.892345	+	0.451354i	$0.149059\pi$
$937$			27.6323i			0.902708i	−0.892345	+	0.451354i	$0.850941\pi$
$938$	6.73435			0.219884
$939$	32.7972			1.07030
$940$		−	9.86617i		−	0.321799i
$941$	−4.27125			−0.139239			−0.0696194	−	0.997574i	$-0.522178\pi$
$941$	−4.27125			−0.139239			−0.0696194	+	0.997574i	$0.522178\pi$
$942$	23.4011			0.762449
$943$	8.06468	+	35.9058i	0.262622	+	1.16925i
$944$	19.9834			0.650403
$945$	−12.7760			−0.415604
$946$		−	5.11251i		−	0.166222i
$947$	22.0982			0.718095			0.359047	−	0.933319i	$-0.383102\pi$
$947$	22.0982			0.718095			0.359047	+	0.933319i	$0.383102\pi$
$948$	5.76719			0.187310
$949$		−	2.96158i		−	0.0961371i
$950$		−	90.3913i		−	2.93268i
$951$	−1.00391			−0.0325541
$952$	−6.42875			−0.208357
$953$	16.1785			0.524071			0.262036	−	0.965058i	$-0.415606\pi$
$953$	16.1785			0.524071			0.262036	+	0.965058i	$0.415606\pi$
$954$			3.10769i			0.100615i
$955$		−	35.3856i		−	1.14505i
$956$			17.1914i			0.556011i
$957$		−	44.0490i		−	1.42390i
$958$			22.7521i			0.735088i
$959$	8.11113			0.261922
$960$			72.0610i			2.32576i
$961$	−27.7690			−0.895774
$962$			1.26741i			0.0408630i
$963$	−14.7027			−0.473788
$964$	−4.29938			−0.138474
$965$			49.9168i			1.60688i
$966$	−13.7326			−0.441838
$967$		−	23.5486i		−	0.757272i	−0.925546	−	0.378636i	$-0.876393\pi$
$967$		−	23.5486i		−	0.757272i	0.925546	−	0.378636i	$-0.123607\pi$
$968$	−13.8176			−0.444116
$969$			31.3711i			1.00779i
$970$		−	81.1949i		−	2.60701i
$971$			38.7182i			1.24253i	0.783602	+	0.621263i	$0.213380\pi$
$971$			38.7182i			1.24253i	−0.783602	+	0.621263i	$0.786620\pi$
$972$		−	10.6094i		−	0.340295i
$973$			7.45105i			0.238870i
$974$	17.3531			0.556030
$975$	5.69074			0.182249
$976$	−16.1104			−0.515682
$977$		−	38.3632i		−	1.22735i	−0.789560	−	0.613674i	$-0.789691\pi$
$977$		−	38.3632i		−	1.22735i	0.789560	−	0.613674i	$-0.210309\pi$
$978$		−	15.4600i		−	0.494355i
$979$	41.3446			1.32138
$980$	−2.97523			−0.0950401
$981$			11.2687i			0.359783i
$982$	11.0274			0.351899
$983$	−14.0040			−0.446657			−0.223328	−	0.974743i	$-0.571692\pi$
$983$	−14.0040			−0.446657			−0.223328	+	0.974743i	$0.571692\pi$
$984$	40.8307	−	9.17086i	1.30164	−	0.292356i
$985$	−10.1120			−0.322196
$986$	19.1013			0.608310
$987$		−	7.04549i		−	0.224261i
$988$	−1.22299			−0.0389084
$989$	−10.2414			−0.325657
$990$		−	17.5784i		−	0.558678i
$991$		−	8.47251i		−	0.269138i	−0.990904	−	0.134569i	$-0.957035\pi$
$991$		−	8.47251i		−	0.269138i	0.990904	−	0.134569i	$-0.0429650\pi$
$992$	−7.03768			−0.223447
$993$	−53.3005			−1.69144
$994$	−2.43938			−0.0773724
$995$			26.9901i			0.855644i
$996$			14.5596i			0.461337i
$997$		−	5.40286i		−	0.171110i	−0.996333	−	0.0855552i	$-0.972734\pi$
$997$		−	5.40286i		−	0.171110i	0.996333	−	0.0855552i	$-0.0272664\pi$
$998$			1.71406i			0.0542576i
$999$		−	15.1116i		−	0.478110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.b.204.9	✓	12
41.40	even	2	inner	287.2.c.b.204.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.b.204.9	✓	12	1.1	even	1	trivial
287.2.c.b.204.10	yes	12	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)

\(f(q)\)	\(=\)	\(q+1.12463 q^{2} -2.12463i q^{3} -0.735213 q^{4} -4.04675 q^{5} -2.38941i q^{6} +1.00000i q^{7} -3.07610 q^{8} -1.51404 q^{9} +O(q^{10})\)	\(q+1.12463 q^{2} -2.12463i q^{3} -0.735213 q^{4} -4.04675 q^{5} -2.38941i q^{6} +1.00000i q^{7} -3.07610 q^{8} -1.51404 q^{9} -4.55109 q^{10} -2.55109i q^{11} +1.56205i q^{12} +0.235444i q^{13} +1.12463i q^{14} +8.59784i q^{15} -1.98904 q^{16} -2.08991i q^{17} -1.70273 q^{18} -7.06513i q^{19} +2.97523 q^{20} +2.12463 q^{21} -2.86903i q^{22} -5.74724 q^{23} +6.53556i q^{24} +11.3762 q^{25} +0.264787i q^{26} -3.15711i q^{27} -0.735213i q^{28} +8.12695i q^{29} +9.66937i q^{30} -1.79750 q^{31} +3.91527 q^{32} -5.42012 q^{33} -2.35037i q^{34} -4.04675i q^{35} +1.11314 q^{36} +4.78653 q^{37} -7.94564i q^{38} +0.500231 q^{39} +12.4482 q^{40} +(-1.40323 - 6.24748i) q^{41} +2.38941 q^{42} +1.78197 q^{43} +1.87559i q^{44} +6.12695 q^{45} -6.46351 q^{46} -3.31611i q^{47} +4.22596i q^{48} -1.00000 q^{49} +12.7940 q^{50} -4.44027 q^{51} -0.173102i q^{52} -1.82512i q^{53} -3.55057i q^{54} +10.3236i q^{55} -3.07610i q^{56} -15.0108 q^{57} +9.13980i q^{58} -10.0468 q^{59} -6.32125i q^{60} +8.09961 q^{61} -2.02152 q^{62} -1.51404i q^{63} +8.38129 q^{64} -0.952785i q^{65} -6.09561 q^{66} -5.98807i q^{67} +1.53653i q^{68} +12.2108i q^{69} -4.55109i q^{70} +2.16905i q^{71} +4.65734 q^{72} -12.5787 q^{73} +5.38307 q^{74} -24.1702i q^{75} +5.19438i q^{76} +2.55109 q^{77} +0.562574 q^{78} -3.69206i q^{79} +8.04914 q^{80} -11.2498 q^{81} +(-1.57811 - 7.02608i) q^{82} +9.32078 q^{83} -1.56205 q^{84} +8.45734i q^{85} +2.00405 q^{86} +17.2668 q^{87} +7.84740i q^{88} +16.2066i q^{89} +6.89054 q^{90} -0.235444 q^{91} +4.22545 q^{92} +3.81901i q^{93} -3.72939i q^{94} +28.5908i q^{95} -8.31848i q^{96} +17.8408i q^{97} -1.12463 q^{98} +3.86246i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9	\( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9 - 4 * q^10 + 28 * q^16 - 40 * q^18 + 2 * q^20 + 8 * q^21 + 16 * q^23 + 34 * q^25 - 6 * q^31 - 42 * q^32 + 18 * q^33 - 36 * q^36 - 10 * q^37 + 10 * q^39 + 38 * q^40 - 2 * q^41 + 32 * q^42 - 50 * q^43 + 6 * q^45 - 8 * q^46 - 12 * q^49 + 18 * q^50 - 2 * q^51 - 50 * q^57 - 70 * q^59 + 52 * q^61 + 68 * q^62 + 8 * q^64 + 92 * q^66 + 2 * q^72 - 64 * q^73 + 18 * q^74 - 20 * q^77 - 12 * q^78 - 32 * q^80 - 4 * q^81 - 56 * q^82 + 60 * q^83 - 20 * q^84 + 48 * q^86 - 20 * q^87 - 42 * q^90 + 14 * q^91 + 56 * q^92 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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