LMFDB - Embedded newform 1166.2.c.b.529.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1166,2,Mod(529,1166)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1166, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1166.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1166 = 2 \cdot 11 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1166.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,0,-22,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.31055687568$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			529.20
Character	$\chi$	$=$	1166.529
Dual form			1166.2.c.b.529.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +2.17721i q^{3} -1.00000 q^{4} -1.32192i q^{5} -2.17721 q^{6} -1.38716 q^{7} -1.00000i q^{8} -1.74022 q^{9} +1.32192 q^{10} -1.00000 q^{11} -2.17721i q^{12} -5.36704 q^{13} -1.38716i q^{14} +2.87809 q^{15} +1.00000 q^{16} -0.857557 q^{17} -1.74022i q^{18} +2.03182i q^{19} +1.32192i q^{20} -3.02013i q^{21} -1.00000i q^{22} -8.68202i q^{23} +2.17721 q^{24} +3.25253 q^{25} -5.36704i q^{26} +2.74279i q^{27} +1.38716 q^{28} -7.91739 q^{29} +2.87809i q^{30} -8.54119i q^{31} +1.00000i q^{32} -2.17721i q^{33} -0.857557i q^{34} +1.83371i q^{35} +1.74022 q^{36} +4.45516 q^{37} -2.03182 q^{38} -11.6852i q^{39} -1.32192 q^{40} -9.95008i q^{41} +3.02013 q^{42} -2.64324 q^{43} +1.00000 q^{44} +2.30044i q^{45} +8.68202 q^{46} +10.3663 q^{47} +2.17721i q^{48} -5.07579 q^{49} +3.25253i q^{50} -1.86708i q^{51} +5.36704 q^{52} +(-5.71903 + 4.50474i) q^{53} -2.74279 q^{54} +1.32192i q^{55} +1.38716i q^{56} -4.42369 q^{57} -7.91739i q^{58} -7.46518 q^{59} -2.87809 q^{60} +3.38583i q^{61} +8.54119 q^{62} +2.41397 q^{63} -1.00000 q^{64} +7.09480i q^{65} +2.17721 q^{66} -7.37868i q^{67} +0.857557 q^{68} +18.9025 q^{69} -1.83371 q^{70} -9.49215i q^{71} +1.74022i q^{72} +1.29767i q^{73} +4.45516i q^{74} +7.08142i q^{75} -2.03182i q^{76} +1.38716 q^{77} +11.6852 q^{78} -0.406000i q^{79} -1.32192i q^{80} -11.1923 q^{81} +9.95008 q^{82} +7.86709i q^{83} +3.02013i q^{84} +1.13362i q^{85} -2.64324i q^{86} -17.2378i q^{87} +1.00000i q^{88} +9.67232 q^{89} -2.30044 q^{90} +7.44493 q^{91} +8.68202i q^{92} +18.5959 q^{93} +10.3663i q^{94} +2.68590 q^{95} -2.17721 q^{96} -11.8009 q^{97} -5.07579i q^{98} +1.74022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{4} - 6 q^{6} - 24 q^{9} + 4 q^{10} - 22 q^{11} + 6 q^{13} + 30 q^{15} + 22 q^{16} + 18 q^{17} + 6 q^{24} - 30 q^{25} + 28 q^{29} + 24 q^{36} - 34 q^{37} - 18 q^{38} - 4 q^{40} + 4 q^{42} - 34 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) $ 22 * q - 22 * q^4 - 6 * q^6 - 24 * q^9 + 4 * q^10 - 22 * q^11 + 6 * q^13 + 30 * q^15 + 22 * q^16 + 18 * q^17 + 6 * q^24 - 30 * q^25 + 28 * q^29 + 24 * q^36 - 34 * q^37 - 18 * q^38 - 4 * q^40 + 4 * q^42 - 34 * q^43 + 22 * q^44 + 6 * q^46 + 8 * q^47 + 6 * q^49 - 6 * q^52 + 16 * q^53 + 12 * q^54 + 14 * q^57 - 60 * q^59 - 30 * q^60 - 8 * q^62 + 116 * q^63 - 22 * q^64 + 6 * q^66 - 18 * q^68 - 26 * q^69 - 32 * q^70 - 4 * q^78 + 62 * q^81 - 44 * q^82 - 34 * q^89 - 6 * q^90 + 12 * q^91 + 4 * q^93 - 6 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1166\mathbb{Z}\right)^\times$.

$n$	$849$	$903$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			2.17721i			1.25701i	0.777805	+	0.628505i	$0.216333\pi$
$3$			2.17721i			1.25701i	−0.777805	+	0.628505i	$0.783667\pi$
$4$	−1.00000			−0.500000
$5$		−	1.32192i		−	0.591180i	−0.955315	−	0.295590i	$-0.904484\pi$
$5$		−	1.32192i		−	0.591180i	0.955315	−	0.295590i	$-0.0955163\pi$
$6$	−2.17721			−0.888840
$7$	−1.38716			−0.524296			−0.262148	−	0.965028i	$-0.584431\pi$
$7$	−1.38716			−0.524296			−0.262148	+	0.965028i	$0.584431\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.74022			−0.580075
$10$	1.32192			0.418028
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	2.17721i		−	0.628505i
$13$	−5.36704			−1.48855			−0.744275	−	0.667873i	$-0.767205\pi$
$13$	−5.36704			−1.48855			−0.744275	+	0.667873i	$0.767205\pi$
$14$		−	1.38716i		−	0.370733i
$15$	2.87809			0.743120
$16$	1.00000			0.250000
$17$	−0.857557			−0.207988			−0.103994	−	0.994578i	$-0.533162\pi$
$17$	−0.857557			−0.207988			−0.103994	+	0.994578i	$0.533162\pi$
$18$		−	1.74022i		−	0.410175i
$19$			2.03182i			0.466132i	0.972461	+	0.233066i	$0.0748757\pi$
$19$			2.03182i			0.466132i	−0.972461	+	0.233066i	$0.925124\pi$
$20$			1.32192i			0.295590i
$21$		−	3.02013i		−	0.659046i
$22$		−	1.00000i		−	0.213201i
$23$		−	8.68202i		−	1.81033i	−0.425065	−	0.905163i	$-0.639749\pi$
$23$		−	8.68202i		−	1.81033i	0.425065	−	0.905163i	$-0.360251\pi$
$24$	2.17721			0.444420
$25$	3.25253			0.650506
$26$		−	5.36704i		−	1.05256i
$27$			2.74279i			0.527850i
$28$	1.38716			0.262148
$29$	−7.91739			−1.47022			−0.735111	−	0.677946i	$-0.762870\pi$
$29$	−7.91739			−1.47022			−0.735111	+	0.677946i	$0.762870\pi$
$30$			2.87809i			0.525465i
$31$		−	8.54119i		−	1.53404i	−0.641621	−	0.767022i	$-0.721738\pi$
$31$		−	8.54119i		−	1.53404i	0.641621	−	0.767022i	$-0.278262\pi$
$32$			1.00000i			0.176777i
$33$		−	2.17721i		−	0.379003i
$34$		−	0.857557i		−	0.147070i
$35$			1.83371i			0.309954i
$36$	1.74022			0.290037
$37$	4.45516			0.732424			0.366212	−	0.930531i	$-0.380654\pi$
$37$	4.45516			0.732424			0.366212	+	0.930531i	$0.380654\pi$
$38$	−2.03182			−0.329605
$39$		−	11.6852i		−	1.87112i
$40$	−1.32192			−0.209014
$41$		−	9.95008i		−	1.55394i	−0.629537	−	0.776971i	$-0.716755\pi$
$41$		−	9.95008i		−	1.55394i	0.629537	−	0.776971i	$-0.283245\pi$
$42$	3.02013			0.466016
$43$	−2.64324			−0.403090			−0.201545	−	0.979479i	$-0.564596\pi$
$43$	−2.64324			−0.403090			−0.201545	+	0.979479i	$0.564596\pi$
$44$	1.00000			0.150756
$45$			2.30044i			0.342929i
$46$	8.68202			1.28009
$47$	10.3663			1.51208			0.756041	−	0.654524i	$-0.227131\pi$
$47$	10.3663			1.51208			0.756041	+	0.654524i	$0.227131\pi$
$48$			2.17721i			0.314253i
$49$	−5.07579			−0.725113
$50$			3.25253i			0.459977i
$51$		−	1.86708i		−	0.261443i
$52$	5.36704			0.744275
$53$	−5.71903	+	4.50474i	−0.785569	+	0.618774i
$53$	−5.71903	+	4.50474i	−0.785569	+	0.618774i
$54$	−2.74279			−0.373246
$55$			1.32192i			0.178248i
$56$			1.38716i			0.185367i
$57$	−4.42369			−0.585932
$58$		−	7.91739i		−	1.03960i
$59$	−7.46518			−0.971883			−0.485942	−	0.873991i	$-0.661523\pi$
$59$	−7.46518			−0.971883			−0.485942	+	0.873991i	$0.661523\pi$
$60$	−2.87809			−0.371560
$61$			3.38583i			0.433511i	0.976226	+	0.216755i	$0.0695474\pi$
$61$			3.38583i			0.433511i	−0.976226	+	0.216755i	$0.930453\pi$
$62$	8.54119			1.08473
$63$	2.41397			0.304131
$64$	−1.00000			−0.125000
$65$			7.09480i			0.880001i
$66$	2.17721			0.267995
$67$		−	7.37868i		−	0.901450i	−0.892663	−	0.450725i	$-0.851166\pi$
$67$		−	7.37868i		−	0.901450i	0.892663	−	0.450725i	$-0.148834\pi$
$68$	0.857557			0.103994
$69$	18.9025			2.27560
$70$	−1.83371			−0.219170
$71$		−	9.49215i		−	1.12651i	−0.826283	−	0.563255i	$-0.809549\pi$
$71$		−	9.49215i		−	1.12651i	0.826283	−	0.563255i	$-0.190451\pi$
$72$			1.74022i			0.205087i
$73$			1.29767i			0.151881i	0.997112	+	0.0759403i	$0.0241958\pi$
$73$			1.29767i			0.151881i	−0.997112	+	0.0759403i	$0.975804\pi$
$74$			4.45516i			0.517902i
$75$			7.08142i			0.817692i
$76$		−	2.03182i		−	0.233066i
$77$	1.38716			0.158081
$78$	11.6852			1.32308
$79$		−	0.406000i		−	0.0456785i	−0.999739	−	0.0228393i	$-0.992729\pi$
$79$		−	0.406000i		−	0.0456785i	0.999739	−	0.0228393i	$-0.00727060\pi$
$80$		−	1.32192i		−	0.147795i
$81$	−11.1923			−1.24359
$82$	9.95008			1.09880
$83$			7.86709i			0.863526i	0.901987	+	0.431763i	$0.142108\pi$
$83$			7.86709i			0.863526i	−0.901987	+	0.431763i	$0.857892\pi$
$84$			3.02013i			0.329523i
$85$			1.13362i			0.122958i
$86$		−	2.64324i		−	0.285028i
$87$		−	17.2378i		−	1.84808i
$88$			1.00000i			0.106600i
$89$	9.67232			1.02526			0.512632	−	0.858608i	$-0.328670\pi$
$89$	9.67232			1.02526			0.512632	+	0.858608i	$0.328670\pi$
$90$	−2.30044			−0.242487
$91$	7.44493			0.780441
$92$			8.68202i			0.905163i
$93$	18.5959			1.92831
$94$			10.3663i			1.06920i
$95$	2.68590			0.275568
$96$	−2.17721			−0.222210
$97$	−11.8009			−1.19820			−0.599100	−	0.800675i	$-0.704475\pi$
$97$	−11.8009			−1.19820			−0.599100	+	0.800675i	$0.704475\pi$
$98$		−	5.07579i		−	0.512733i
$99$	1.74022			0.174899
$100$	−3.25253			−0.325253
$101$			15.2396i			1.51639i	0.652026	+	0.758196i	$0.273919\pi$
$101$			15.2396i			1.51639i	−0.652026	+	0.758196i	$0.726081\pi$
$102$	1.86708			0.184868
$103$		−	0.0304229i		−	0.00299766i	−0.999999	−	0.00149883i	$-0.999523\pi$
$103$		−	0.0304229i		−	0.00299766i	0.999999	−	0.00149883i	$-0.000477093\pi$
$104$			5.36704i			0.526282i
$105$	−3.99237			−0.389615
$106$	−4.50474	−	5.71903i	−0.437539	−	0.555481i
$107$	−10.0991			−0.976320			−0.488160	−	0.872754i	$-0.662332\pi$
$107$	−10.0991			−0.976320			−0.488160	+	0.872754i	$0.662332\pi$
$108$		−	2.74279i		−	0.263925i
$109$			8.35301i			0.800073i	0.916499	+	0.400037i	$0.131003\pi$
$109$			8.35301i			0.800073i	−0.916499	+	0.400037i	$0.868997\pi$
$110$	−1.32192			−0.126040
$111$			9.69981i			0.920665i
$112$	−1.38716			−0.131074
$113$	−13.6292			−1.28212			−0.641062	−	0.767489i	$-0.721506\pi$
$113$	−13.6292			−1.28212			−0.641062	+	0.767489i	$0.721506\pi$
$114$		−	4.42369i		−	0.414317i
$115$	−11.4769			−1.07023
$116$	7.91739			0.735111
$117$	9.33986			0.863470
$118$		−	7.46518i		−	0.687225i
$119$	1.18957			0.109047
$120$		−	2.87809i		−	0.262733i
$121$	1.00000			0.0909091
$122$	−3.38583			−0.306538
$123$	21.6634			1.95332
$124$			8.54119i			0.767022i
$125$		−	10.9092i		−	0.975747i
$126$			2.41397i			0.215053i
$127$			7.34805i			0.652034i	0.945364	+	0.326017i	$0.105707\pi$
$127$			7.34805i			0.652034i	−0.945364	+	0.326017i	$0.894293\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		−	5.75487i		−	0.506688i
$130$	−7.09480			−0.622255
$131$	6.24449			0.545584			0.272792	−	0.962073i	$-0.412053\pi$
$131$	6.24449			0.545584			0.272792	+	0.962073i	$0.412053\pi$
$132$			2.17721i			0.189501i
$133$		−	2.81845i		−	0.244391i
$134$	7.37868			0.637421
$135$	3.62575			0.312055
$136$			0.857557i			0.0735349i
$137$			11.7374i			1.00279i	0.865218	+	0.501396i	$0.167180\pi$
$137$			11.7374i			1.00279i	−0.865218	+	0.501396i	$0.832820\pi$
$138$			18.9025i			1.60909i
$139$		−	23.3030i		−	1.97653i	−0.152747	−	0.988265i	$-0.548812\pi$
$139$		−	23.3030i		−	1.97653i	0.152747	−	0.988265i	$-0.451188\pi$
$140$		−	1.83371i		−	0.154977i
$141$			22.5696i			1.90070i
$142$	9.49215			0.796563
$143$	5.36704			0.448815
$144$	−1.74022			−0.145019
$145$			10.4662i			0.869167i
$146$	−1.29767			−0.107396
$147$		−	11.0510i		−	0.911475i
$148$	−4.45516			−0.366212
$149$	14.1854			1.16211			0.581055	−	0.813864i	$-0.302640\pi$
$149$	14.1854			1.16211			0.581055	+	0.813864i	$0.302640\pi$
$150$	−7.08142			−0.578196
$151$			9.37198i			0.762681i	0.924435	+	0.381340i	$0.124537\pi$
$151$			9.37198i			0.762681i	−0.924435	+	0.381340i	$0.875463\pi$
$152$	2.03182			0.164802
$153$	1.49234			0.120649
$154$			1.38716i			0.111780i
$155$	−11.2908			−0.906896
$156$			11.6852i			0.935561i
$157$			15.3587i			1.22576i	0.790176	+	0.612880i	$0.209989\pi$
$157$			15.3587i			1.22576i	−0.790176	+	0.612880i	$0.790011\pi$
$158$	0.406000			0.0322996
$159$	−9.80775	−	12.4515i	−0.777805	−	0.987469i
$160$	1.32192			0.104507
$161$			12.0433i			0.949147i
$162$		−	11.1923i		−	0.879350i
$163$	−25.1400			−1.96912			−0.984559	−	0.175052i	$-0.943991\pi$
$163$	−25.1400			−1.96912			−0.984559	+	0.175052i	$0.943991\pi$
$164$			9.95008i			0.776971i
$165$	−2.87809			−0.224059
$166$	−7.86709			−0.610605
$167$		−	19.2301i		−	1.48807i	−0.668141	−	0.744035i	$-0.732910\pi$
$167$		−	19.2301i		−	1.48807i	0.668141	−	0.744035i	$-0.267090\pi$
$168$	−3.02013			−0.233008
$169$	15.8051			1.21578
$170$	−1.13362			−0.0869447
$171$		−	3.53582i		−	0.270391i
$172$	2.64324			0.201545
$173$		−	21.1747i		−	1.60988i	−0.593354	−	0.804942i	$-0.702196\pi$
$173$		−	21.1747i		−	1.60988i	0.593354	−	0.804942i	$-0.297804\pi$
$174$	17.2378			1.30679
$175$	−4.51177			−0.341058
$176$	−1.00000			−0.0753778
$177$		−	16.2532i		−	1.22167i
$178$			9.67232i			0.724971i
$179$		−	2.18176i		−	0.163072i	−0.996670	−	0.0815362i	$-0.974017\pi$
$179$		−	2.18176i		−	0.163072i	0.996670	−	0.0815362i	$-0.0259826\pi$
$180$		−	2.30044i		−	0.171464i
$181$		−	23.8870i		−	1.77551i	−0.460316	−	0.887755i	$-0.652264\pi$
$181$		−	23.8870i		−	1.77551i	0.460316	−	0.887755i	$-0.347736\pi$
$182$			7.44493i			0.551855i
$183$	−7.37164			−0.544927
$184$	−8.68202			−0.640047
$185$		−	5.88937i		−	0.432995i
$186$			18.5959i			1.36352i
$187$	0.857557			0.0627108
$188$	−10.3663			−0.756041
$189$		−	3.80468i		−	0.276750i
$190$			2.68590i			0.194856i
$191$		−	8.00564i		−	0.579268i	−0.957137	−	0.289634i	$-0.906466\pi$
$191$		−	8.00564i		−	0.579268i	0.957137	−	0.289634i	$-0.0935336\pi$
$192$		−	2.17721i		−	0.157126i
$193$			17.2592i			1.24235i	0.783674	+	0.621173i	$0.213344\pi$
$193$			17.2592i			1.24235i	−0.783674	+	0.621173i	$0.786656\pi$
$194$		−	11.8009i		−	0.847255i
$195$	−15.4468			−1.10617
$196$	5.07579			0.362557
$197$	−25.5123			−1.81768			−0.908839	−	0.417147i	$-0.863030\pi$
$197$	−25.5123			−1.81768			−0.908839	+	0.417147i	$0.863030\pi$
$198$			1.74022i			0.123672i
$199$	−19.7608			−1.40081			−0.700405	−	0.713746i	$-0.746997\pi$
$199$	−19.7608			−1.40081			−0.700405	+	0.713746i	$0.746997\pi$
$200$		−	3.25253i		−	0.229989i
$201$	16.0649			1.13313
$202$	−15.2396			−1.07225
$203$	10.9827			0.770832
$204$			1.86708i			0.130722i
$205$	−13.1532			−0.918659
$206$	0.0304229			0.00211967
$207$			15.1087i			1.05012i
$208$	−5.36704			−0.372137
$209$		−	2.03182i		−	0.140544i
$210$		−	3.99237i		−	0.275499i
$211$	−16.2588			−1.11930			−0.559650	−	0.828729i	$-0.689064\pi$
$211$	−16.2588			−1.11930			−0.559650	+	0.828729i	$0.689064\pi$
$212$	5.71903	−	4.50474i	0.392785	−	0.309387i
$213$	20.6664			1.41604
$214$		−	10.0991i		−	0.690363i
$215$			3.49415i			0.238299i
$216$	2.74279			0.186623
$217$			11.8480i			0.804293i
$218$	−8.35301			−0.565737
$219$	−2.82529			−0.190916
$220$		−	1.32192i		−	0.0891238i
$221$	4.60254			0.309601
$222$	−9.69981			−0.651008
$223$	22.5545			1.51036			0.755180	−	0.655517i	$-0.227549\pi$
$223$	22.5545			1.51036			0.755180	+	0.655517i	$0.227549\pi$
$224$		−	1.38716i		−	0.0926834i
$225$	−5.66013			−0.377342
$226$		−	13.6292i		−	0.906599i
$227$	6.26650			0.415923			0.207961	−	0.978137i	$-0.433317\pi$
$227$	6.26650			0.415923			0.207961	+	0.978137i	$0.433317\pi$
$228$	4.42369			0.292966
$229$	−29.4801			−1.94810			−0.974049	−	0.226338i	$-0.927325\pi$
$229$	−29.4801			−1.94810			−0.974049	+	0.226338i	$0.927325\pi$
$230$		−	11.4769i		−	0.756766i
$231$			3.02013i			0.198710i
$232$			7.91739i			0.519802i
$233$			22.9356i			1.50256i	0.659984	+	0.751279i	$0.270563\pi$
$233$			22.9356i			1.50256i	−0.659984	+	0.751279i	$0.729437\pi$
$234$			9.33986i			0.610566i
$235$		−	13.7034i		−	0.893913i
$236$	7.46518			0.485942
$237$	0.883945			0.0574184
$238$			1.18957i			0.0771081i
$239$		−	4.86965i		−	0.314992i	−0.987520	−	0.157496i	$-0.949658\pi$
$239$		−	4.86965i		−	0.314992i	0.987520	−	0.157496i	$-0.0503421\pi$
$240$	2.87809			0.185780
$241$	−4.42829			−0.285251			−0.142626	−	0.989777i	$-0.545554\pi$
$241$	−4.42829			−0.285251			−0.142626	+	0.989777i	$0.545554\pi$
$242$			1.00000i			0.0642824i
$243$		−	16.1396i		−	1.03535i
$244$		−	3.38583i		−	0.216755i
$245$			6.70979i			0.428673i
$246$			21.6634i			1.38121i
$247$		−	10.9049i		−	0.693860i
$248$	−8.54119			−0.542366
$249$	−17.1283			−1.08546
$250$	10.9092			0.689957
$251$			3.07178i			0.193889i	0.995290	+	0.0969445i	$0.0309069\pi$
$251$			3.07178i			0.193889i	−0.995290	+	0.0969445i	$0.969093\pi$
$252$	−2.41397			−0.152066
$253$			8.68202i			0.545834i
$254$	−7.34805			−0.461058
$255$	−2.46813			−0.154560
$256$	1.00000			0.0625000
$257$		−	22.7556i		−	1.41945i	−0.704478	−	0.709726i	$-0.748819\pi$
$257$		−	22.7556i		−	1.41945i	0.704478	−	0.709726i	$-0.251181\pi$
$258$	5.75487			0.358283
$259$	−6.18001			−0.384007
$260$		−	7.09480i		−	0.440001i
$261$	13.7780			0.852839
$262$			6.24449i			0.385786i
$263$		−	14.4071i		−	0.888382i	−0.895932	−	0.444191i	$-0.853491\pi$
$263$		−	14.4071i		−	0.888382i	0.895932	−	0.444191i	$-0.146509\pi$
$264$	−2.17721			−0.133998
$265$	5.95490	+	7.56010i	0.365807	+	0.464413i
$266$	2.81845			0.172811
$267$			21.0586i			1.28877i
$268$			7.37868i			0.450725i
$269$	−11.1298			−0.678599			−0.339299	−	0.940678i	$-0.610190\pi$
$269$	−11.1298			−0.678599			−0.339299	+	0.940678i	$0.610190\pi$
$270$			3.62575i			0.220656i
$271$	−9.31734			−0.565988			−0.282994	−	0.959122i	$-0.591328\pi$
$271$	−9.31734			−0.565988			−0.282994	+	0.959122i	$0.591328\pi$
$272$	−0.857557			−0.0519970
$273$			16.2092i			0.981022i
$274$	−11.7374			−0.709081
$275$	−3.25253			−0.196135
$276$	−18.9025			−1.13780
$277$		−	9.82156i		−	0.590120i	−0.955479	−	0.295060i	$-0.904660\pi$
$277$		−	9.82156i		−	0.590120i	0.955479	−	0.295060i	$-0.0953397\pi$
$278$	23.3030			1.39762
$279$			14.8636i			0.889860i
$280$	1.83371			0.109585
$281$	−18.2965			−1.09148			−0.545739	−	0.837955i	$-0.683751\pi$
$281$	−18.2965			−1.09148			−0.545739	+	0.837955i	$0.683751\pi$
$282$	−22.5696			−1.34400
$283$			16.4603i			0.978464i	0.872154	+	0.489232i	$0.162723\pi$
$283$			16.4603i			0.978464i	−0.872154	+	0.489232i	$0.837277\pi$
$284$			9.49215i			0.563255i
$285$			5.84776i			0.346392i
$286$			5.36704i			0.317360i
$287$			13.8023i			0.814726i
$288$		−	1.74022i		−	0.102544i
$289$	−16.2646			−0.956741
$290$	−10.4662			−0.614594
$291$		−	25.6930i		−	1.50615i
$292$		−	1.29767i		−	0.0759403i
$293$	27.4941			1.60622			0.803110	−	0.595831i	$-0.203177\pi$
$293$	27.4941			1.60622			0.803110	+	0.595831i	$0.203177\pi$
$294$	11.0510			0.644510
$295$			9.86836i			0.574558i
$296$		−	4.45516i		−	0.258951i
$297$		−	2.74279i		−	0.159153i
$298$			14.1854i			0.821737i
$299$			46.5968i			2.69476i
$300$		−	7.08142i		−	0.408846i
$301$	3.66659			0.211339
$302$	−9.37198			−0.539297
$303$	−33.1796			−1.90612
$304$			2.03182i			0.116533i
$305$	4.47579			0.256283
$306$			1.49234i			0.0853115i
$307$	15.4752			0.883217			0.441608	−	0.897208i	$-0.354408\pi$
$307$	15.4752			0.883217			0.441608	+	0.897208i	$0.354408\pi$
$308$	−1.38716			−0.0790406
$309$	0.0662370			0.00376809
$310$		−	11.2908i		−	0.641273i
$311$	19.7022			1.11721			0.558605	−	0.829434i	$-0.311337\pi$
$311$	19.7022			1.11721			0.558605	+	0.829434i	$0.311337\pi$
$312$	−11.6852			−0.661542
$313$			23.5089i			1.32880i	0.747375	+	0.664402i	$0.231314\pi$
$313$			23.5089i			1.32880i	−0.747375	+	0.664402i	$0.768686\pi$
$314$	−15.3587			−0.866744
$315$		−	3.19107i		−	0.179796i
$316$			0.406000i			0.0228393i
$317$	21.8608			1.22782			0.613912	−	0.789374i	$-0.289595\pi$
$317$	21.8608			1.22782			0.613912	+	0.789374i	$0.289595\pi$
$318$	12.4515	−	9.80775i	0.698246	−	0.549991i
$319$	7.91739			0.443289
$320$			1.32192i			0.0738975i
$321$		−	21.9879i		−	1.22724i
$322$	−12.0433			−0.671148
$323$		−	1.74240i		−	0.0969498i
$324$	11.1923			0.621794
$325$	−17.4565			−0.968310
$326$		−	25.1400i		−	1.39238i
$327$	−18.1862			−1.00570
$328$	−9.95008			−0.549401
$329$	−14.3797			−0.792779
$330$		−	2.87809i		−	0.158434i
$331$	−1.48738			−0.0817540			−0.0408770	−	0.999164i	$-0.513015\pi$
$331$	−1.48738			−0.0817540			−0.0408770	+	0.999164i	$0.513015\pi$
$332$		−	7.86709i		−	0.431763i
$333$	−7.75299			−0.424861
$334$	19.2301			1.05222
$335$	−9.75402			−0.532919
$336$		−	3.02013i		−	0.164761i
$337$			3.10448i			0.169112i	0.996419	+	0.0845559i	$0.0269471\pi$
$337$			3.10448i			0.169112i	−0.996419	+	0.0845559i	$0.973053\pi$
$338$			15.8051i			0.859686i
$339$		−	29.6735i		−	1.61164i
$340$		−	1.13362i		−	0.0614792i
$341$			8.54119i			0.462532i
$342$	3.53582			0.191195
$343$	16.7510			0.904471
$344$			2.64324i			0.142514i
$345$		−	24.9876i		−	1.34529i
$346$	21.1747			1.13836
$347$	32.3640			1.73739			0.868696	−	0.495345i	$-0.164958\pi$
$347$	32.3640			1.73739			0.868696	+	0.495345i	$0.164958\pi$
$348$			17.2378i			0.924042i
$349$		−	23.2104i		−	1.24242i	−0.783643	−	0.621212i	$-0.786641\pi$
$349$		−	23.2104i		−	1.24242i	0.783643	−	0.621212i	$-0.213359\pi$
$350$		−	4.51177i		−	0.241164i
$351$		−	14.7207i		−	0.785731i
$352$		−	1.00000i		−	0.0533002i
$353$			18.1113i			0.963969i	0.876180	+	0.481985i	$0.160084\pi$
$353$			18.1113i			0.963969i	−0.876180	+	0.481985i	$0.839916\pi$
$354$	16.2532			0.863849
$355$	−12.5479			−0.665971
$356$	−9.67232			−0.512632
$357$			2.58993i			0.137074i
$358$	2.18176			0.115310
$359$			3.84394i			0.202875i	0.994842	+	0.101438i	$0.0323442\pi$
$359$			3.84394i			0.202875i	−0.994842	+	0.101438i	$0.967656\pi$
$360$	2.30044			0.121244
$361$	14.8717			0.782721
$362$	23.8870			1.25548
$363$			2.17721i			0.114274i
$364$	−7.44493			−0.390221
$365$	1.71541			0.0897888
$366$		−	7.37164i		−	0.385322i
$367$	−2.80336			−0.146334			−0.0731671	−	0.997320i	$-0.523311\pi$
$367$	−2.80336			−0.146334			−0.0731671	+	0.997320i	$0.523311\pi$
$368$		−	8.68202i		−	0.452581i
$369$			17.3154i			0.901402i
$370$	5.88937			0.306174
$371$	7.93320	−	6.24878i	0.411871	−	0.324421i
$372$	−18.5959			−0.964154
$373$			25.1263i			1.30099i	0.759509	+	0.650497i	$0.225439\pi$
$373$			25.1263i			1.30099i	−0.759509	+	0.650497i	$0.774561\pi$
$374$			0.857557i			0.0443432i
$375$	23.7515			1.22652
$376$		−	10.3663i		−	0.534602i
$377$	42.4930			2.18850
$378$	3.80468			0.195692
$379$			1.02127i			0.0524592i	0.999656	+	0.0262296i	$0.00835010\pi$
$379$			1.02127i			0.0524592i	−0.999656	+	0.0262296i	$0.991650\pi$
$380$	−2.68590			−0.137784
$381$	−15.9982			−0.819614
$382$	8.00564			0.409604
$383$			32.8031i			1.67616i	0.545548	+	0.838080i	$0.316322\pi$
$383$			32.8031i			1.67616i	−0.545548	+	0.838080i	$0.683678\pi$
$384$	2.17721			0.111105
$385$		−	1.83371i		−	0.0934545i
$386$	−17.2592			−0.878471
$387$	4.59983			0.233822
$388$	11.8009			0.599100
$389$			25.2737i			1.28143i	0.767780	+	0.640713i	$0.221361\pi$
$389$			25.2737i			1.28143i	−0.767780	+	0.640713i	$0.778639\pi$
$390$		−	15.4468i		−	0.782181i
$391$			7.44532i			0.376526i
$392$			5.07579i			0.256366i
$393$			13.5955i			0.685804i
$394$		−	25.5123i		−	1.28529i
$395$	−0.536699			−0.0270043
$396$	−1.74022			−0.0874496
$397$		−	4.72481i		−	0.237131i	−0.992946	−	0.118566i	$-0.962170\pi$
$397$		−	4.72481i		−	0.237131i	0.992946	−	0.118566i	$-0.0378296\pi$
$398$		−	19.7608i		−	0.990522i
$399$	6.13636			0.307202
$400$	3.25253			0.162626
$401$			6.37140i			0.318172i	0.987265	+	0.159086i	$0.0508548\pi$
$401$			6.37140i			0.318172i	−0.987265	+	0.159086i	$0.949145\pi$
$402$			16.0649i			0.801245i
$403$			45.8409i			2.28350i
$404$		−	15.2396i		−	0.758196i
$405$			14.7953i			0.735185i
$406$			10.9827i			0.545061i
$407$	−4.45516			−0.220834
$408$	−1.86708			−0.0924341
$409$	−13.3300			−0.659128			−0.329564	−	0.944133i	$-0.606902\pi$
$409$	−13.3300			−0.659128			−0.329564	+	0.944133i	$0.606902\pi$
$410$		−	13.1532i		−	0.649590i
$411$	−25.5547			−1.26052
$412$			0.0304229i			0.00149883i
$413$	10.3554			0.509555
$414$	−15.1087			−0.742550
$415$	10.3997			0.510499
$416$		−	5.36704i		−	0.263141i
$417$	50.7353			2.48452
$418$	2.03182			0.0993796
$419$		−	13.8325i		−	0.675764i	−0.941189	−	0.337882i	$-0.890290\pi$
$419$		−	13.8325i		−	0.675764i	0.941189	−	0.337882i	$-0.109710\pi$
$420$	3.99237			0.194807
$421$		−	16.2907i		−	0.793961i	−0.917827	−	0.396981i	$-0.870058\pi$
$421$		−	16.2907i		−	0.793961i	0.917827	−	0.396981i	$-0.129942\pi$
$422$		−	16.2588i		−	0.791464i
$423$	−18.0397			−0.877121
$424$	4.50474	+	5.71903i	0.218770	+	0.277741i
$425$	−2.78923			−0.135297
$426$			20.6664i			1.00129i
$427$		−	4.69667i		−	0.227288i
$428$	10.0991			0.488160
$429$			11.6852i			0.564165i
$430$	−3.49415			−0.168503
$431$	−14.1599			−0.682060			−0.341030	−	0.940052i	$-0.610776\pi$
$431$	−14.1599			−0.682060			−0.341030	+	0.940052i	$0.610776\pi$
$432$			2.74279i			0.131963i
$433$	−12.9011			−0.619985			−0.309993	−	0.950739i	$-0.600327\pi$
$433$	−12.9011			−0.619985			−0.309993	+	0.950739i	$0.600327\pi$
$434$	−11.8480			−0.568721
$435$	−22.7870			−1.09255
$436$		−	8.35301i		−	0.400037i
$437$	17.6403			0.843850
$438$		−	2.82529i		−	0.134998i
$439$	−29.1606			−1.39176			−0.695880	−	0.718158i	$-0.744986\pi$
$439$	−29.1606			−1.39176			−0.695880	+	0.718158i	$0.744986\pi$
$440$	1.32192			0.0630200
$441$	8.83302			0.420620
$442$			4.60254i			0.218921i
$443$		−	5.38596i		−	0.255895i	−0.991781	−	0.127947i	$-0.959161\pi$
$443$		−	5.38596i		−	0.255895i	0.991781	−	0.127947i	$-0.0408388\pi$
$444$		−	9.69981i		−	0.460333i
$445$		−	12.7860i		−	0.606116i
$446$			22.5545i			1.06799i
$447$			30.8845i			1.46079i
$448$	1.38716			0.0655370
$449$	13.2476			0.625195			0.312597	−	0.949886i	$-0.398801\pi$
$449$	13.2476			0.625195			0.312597	+	0.949886i	$0.398801\pi$
$450$		−	5.66013i		−	0.266821i
$451$			9.95008i			0.468531i
$452$	13.6292			0.641062
$453$	−20.4047			−0.958698
$454$			6.26650i			0.294102i
$455$		−	9.84160i		−	0.461381i
$456$			4.42369i			0.207158i
$457$		−	15.7262i		−	0.735640i	−0.929897	−	0.367820i	$-0.880104\pi$
$457$		−	15.7262i		−	0.735640i	0.929897	−	0.367820i	$-0.119896\pi$
$458$		−	29.4801i		−	1.37751i
$459$		−	2.35210i		−	0.109787i
$460$	11.4769			0.535114
$461$	17.3885			0.809862			0.404931	−	0.914347i	$-0.367296\pi$
$461$	17.3885			0.809862			0.404931	+	0.914347i	$0.367296\pi$
$462$	−3.02013			−0.140509
$463$		−	6.43743i		−	0.299173i	−0.988749	−	0.149586i	$-0.952206\pi$
$463$		−	6.43743i		−	0.299173i	0.988749	−	0.149586i	$-0.0477942\pi$
$464$	−7.91739			−0.367556
$465$		−	24.5823i		−	1.13998i
$466$	−22.9356			−1.06247
$467$	35.2319			1.63034			0.815168	−	0.579225i	$-0.196645\pi$
$467$	35.2319			1.63034			0.815168	+	0.579225i	$0.196645\pi$
$468$	−9.33986			−0.431735
$469$			10.2354i			0.472627i
$470$	13.7034			0.632092
$471$	−33.4391			−1.54079
$472$			7.46518i			0.343613i
$473$	2.64324			0.121536
$474$			0.883945i			0.0406009i
$475$			6.60855i			0.303221i
$476$	−1.18957			−0.0545237
$477$	9.95240	−	7.83926i	0.455689	−	0.358935i
$478$	4.86965			0.222733
$479$			10.9387i			0.499804i	0.968271	+	0.249902i	$0.0803983\pi$
$479$			10.9387i			0.499804i	−0.968271	+	0.249902i	$0.919602\pi$
$480$			2.87809i			0.131366i
$481$	−23.9111			−1.09025
$482$		−	4.42829i		−	0.201703i
$483$	−26.2208			−1.19309
$484$	−1.00000			−0.0454545
$485$			15.5998i			0.708352i
$486$	16.1396			0.732105
$487$	2.25381			0.102130			0.0510649	−	0.998695i	$-0.483738\pi$
$487$	2.25381			0.102130			0.0510649	+	0.998695i	$0.483738\pi$
$488$	3.38583			0.153269
$489$		−	54.7350i		−	2.47520i
$490$	−6.70979			−0.303117
$491$			16.8369i			0.759837i	0.925020	+	0.379919i	$0.124048\pi$
$491$			16.8369i			0.759837i	−0.925020	+	0.379919i	$0.875952\pi$
$492$	−21.6634			−0.976660
$493$	6.78961			0.305789
$494$	10.9049			0.490633
$495$		−	2.30044i		−	0.103397i
$496$		−	8.54119i		−	0.383511i
$497$			13.1671i			0.590625i
$498$		−	17.1283i		−	0.767537i
$499$		−	5.92817i		−	0.265381i	−0.991158	−	0.132691i	$-0.957638\pi$
$499$		−	5.92817i		−	0.265381i	0.991158	−	0.132691i	$-0.0423617\pi$
$500$			10.9092i			0.487873i
$501$	41.8679			1.87052
$502$	−3.07178			−0.137100
$503$		−	19.2911i		−	0.860148i	−0.902794	−	0.430074i	$-0.858487\pi$
$503$		−	19.2911i		−	0.860148i	0.902794	−	0.430074i	$-0.141513\pi$
$504$		−	2.41397i		−	0.107527i
$505$	20.1455			0.896461
$506$	−8.68202			−0.385963
$507$			34.4110i			1.52825i
$508$		−	7.34805i		−	0.326017i
$509$		−	15.6545i		−	0.693872i	−0.937889	−	0.346936i	$-0.887222\pi$
$509$		−	15.6545i		−	0.693872i	0.937889	−	0.346936i	$-0.112778\pi$
$510$		−	2.46813i		−	0.109290i
$511$		−	1.80007i		−	0.0796304i
$512$			1.00000i			0.0441942i
$513$	−5.57286			−0.246048
$514$	22.7556			1.00370
$515$	−0.0402167			−0.00177216
$516$			5.75487i			0.253344i
$517$	−10.3663			−0.455910
$518$		−	6.18001i		−	0.271534i
$519$	46.1017			2.02364
$520$	7.09480			0.311127
$521$	42.9854			1.88323			0.941613	−	0.336697i	$-0.109310\pi$
$521$	42.9854			1.88323			0.941613	+	0.336697i	$0.109310\pi$
$522$			13.7780i			0.603048i
$523$	−19.9585			−0.872726			−0.436363	−	0.899771i	$-0.643734\pi$
$523$	−19.9585			−0.872726			−0.436363	+	0.899771i	$0.643734\pi$
$524$	−6.24449			−0.272792
$525$		−	9.82305i		−	0.428713i
$526$	14.4071			0.628181
$527$			7.32456i			0.319063i
$528$		−	2.17721i		−	0.0947507i
$529$	−52.3774			−2.27728
$530$	−7.56010	+	5.95490i	−0.328390	+	0.258664i
$531$	12.9911			0.563765
$532$			2.81845i			0.122196i
$533$			53.4025i			2.31312i
$534$	−21.0586			−0.911296
$535$			13.3502i			0.577181i
$536$	−7.37868			−0.318711
$537$	4.75014			0.204984
$538$		−	11.1298i		−	0.479842i
$539$	5.07579			0.218630
$540$	−3.62575			−0.156027
$541$	−17.9390			−0.771256			−0.385628	−	0.922654i	$-0.626015\pi$
$541$	−17.9390			−0.771256			−0.385628	+	0.922654i	$0.626015\pi$
$542$		−	9.31734i		−	0.400214i
$543$	52.0070			2.23183
$544$		−	0.857557i		−	0.0367674i
$545$	11.0420			0.472988
$546$	−16.2092			−0.693688
$547$	−8.91465			−0.381163			−0.190581	−	0.981671i	$-0.561037\pi$
$547$	−8.91465			−0.381163			−0.190581	+	0.981671i	$0.561037\pi$
$548$		−	11.7374i		−	0.501396i
$549$		−	5.89210i		−	0.251469i
$550$		−	3.25253i		−	0.138688i
$551$		−	16.0867i		−	0.685317i
$552$		−	18.9025i		−	0.804545i
$553$			0.563186i			0.0239491i
$554$	9.82156			0.417278
$555$	12.8224			0.544279
$556$			23.3030i			0.988265i
$557$		−	27.4937i		−	1.16495i	−0.812850	−	0.582474i	$-0.802085\pi$
$557$		−	27.4937i		−	1.16495i	0.812850	−	0.582474i	$-0.197915\pi$
$558$	−14.8636			−0.629226
$559$	14.1864			0.600019
$560$			1.83371i			0.0774884i
$561$			1.86708i			0.0788281i
$562$		−	18.2965i		−	0.771791i
$563$		−	12.4778i		−	0.525879i	−0.964812	−	0.262939i	$-0.915308\pi$
$563$		−	12.4778i		−	0.525879i	0.964812	−	0.262939i	$-0.0846919\pi$
$564$		−	22.5696i		−	0.950351i
$565$			18.0167i			0.757967i
$566$	−16.4603			−0.691878
$567$	15.5255			0.652009
$568$	−9.49215			−0.398282
$569$		−	46.3059i		−	1.94124i	−0.240610	−	0.970622i	$-0.577347\pi$
$569$		−	46.3059i		−	1.94124i	0.240610	−	0.970622i	$-0.422653\pi$
$570$	−5.84776			−0.244936
$571$		−	14.0526i		−	0.588084i	−0.955792	−	0.294042i	$-0.904999\pi$
$571$		−	14.0526i		−	0.588084i	0.955792	−	0.294042i	$-0.0950006\pi$
$572$	−5.36704			−0.224407
$573$	17.4299			0.728146
$574$	−13.8023			−0.576098
$575$		−	28.2385i		−	1.17763i
$576$	1.74022			0.0725094
$577$	−9.12750			−0.379983			−0.189991	−	0.981786i	$-0.560846\pi$
$577$	−9.12750			−0.379983			−0.189991	+	0.981786i	$0.560846\pi$
$578$		−	16.2646i		−	0.676518i
$579$	−37.5769			−1.56164
$580$		−	10.4662i		−	0.434583i
$581$		−	10.9129i		−	0.452743i
$582$	25.6930			1.06501
$583$	5.71903	−	4.50474i	0.236858	−	0.186567i
$584$	1.29767			0.0536979
$585$		−	12.3465i		−	0.510467i
$586$			27.4941i			1.13577i
$587$	−23.4334			−0.967199			−0.483599	−	0.875289i	$-0.660671\pi$
$587$	−23.4334			−0.967199			−0.483599	+	0.875289i	$0.660671\pi$
$588$			11.0510i			0.455737i
$589$	17.3542			0.715066
$590$	−9.86836			−0.406274
$591$		−	55.5456i		−	2.28484i
$592$	4.45516			0.183106
$593$	35.7696			1.46888			0.734441	−	0.678672i	$-0.237444\pi$
$593$	35.7696			1.46888			0.734441	+	0.678672i	$0.237444\pi$
$594$	2.74279			0.112538
$595$		−	1.57251i		−	0.0644667i
$596$	−14.1854			−0.581055
$597$		−	43.0234i		−	1.76083i
$598$	−46.5968			−1.90548
$599$	37.6923			1.54007			0.770033	−	0.638004i	$-0.220240\pi$
$599$	37.6923			1.54007			0.770033	+	0.638004i	$0.220240\pi$
$600$	7.08142			0.289098
$601$			23.4346i			0.955918i	0.878382	+	0.477959i	$0.158623\pi$
$601$			23.4346i			0.955918i	−0.878382	+	0.477959i	$0.841377\pi$
$602$			3.66659i			0.149439i
$603$			12.8406i			0.522908i
$604$		−	9.37198i		−	0.381340i
$605$		−	1.32192i		−	0.0537437i
$606$		−	33.1796i		−	1.34783i
$607$	−15.7219			−0.638132			−0.319066	−	0.947732i	$-0.603369\pi$
$607$	−15.7219			−0.638132			−0.319066	+	0.947732i	$0.603369\pi$
$608$	−2.03182			−0.0824012
$609$			23.9115i			0.968944i
$610$			4.47579i			0.181219i
$611$	−55.6364			−2.25081
$612$	−1.49234			−0.0603243
$613$			34.2775i			1.38446i	0.721678	+	0.692228i	$0.243371\pi$
$613$			34.2775i			1.38446i	−0.721678	+	0.692228i	$0.756629\pi$
$614$			15.4752i			0.624529i
$615$		−	28.6372i		−	1.15476i
$616$		−	1.38716i		−	0.0558902i
$617$			28.5966i			1.15125i	0.817712	+	0.575627i	$0.195242\pi$
$617$			28.5966i			1.15125i	−0.817712	+	0.575627i	$0.804758\pi$
$618$			0.0662370i			0.00266444i
$619$	−10.3771			−0.417091			−0.208546	−	0.978013i	$-0.566873\pi$
$619$	−10.3771			−0.417091			−0.208546	+	0.978013i	$0.566873\pi$
$620$	11.2908			0.453448
$621$	23.8130			0.955581
$622$			19.7022i			0.789987i
$623$	−13.4170			−0.537542
$624$		−	11.6852i		−	0.467781i
$625$	1.84159			0.0736636
$626$	−23.5089			−0.939606
$627$	4.42369			0.176665
$628$		−	15.3587i		−	0.612880i
$629$	−3.82056			−0.152336
$630$	3.19107			0.127135
$631$		−	17.5509i		−	0.698689i	−0.936994	−	0.349345i	$-0.886404\pi$
$631$		−	17.5509i		−	0.698689i	0.936994	−	0.349345i	$-0.113596\pi$
$632$	−0.406000			−0.0161498
$633$		−	35.3987i		−	1.40697i
$634$			21.8608i			0.868203i
$635$	9.71354			0.385470
$636$	9.80775	+	12.4515i	0.388902	+	0.493734i
$637$	27.2420			1.07937
$638$			7.91739i			0.313452i
$639$			16.5185i			0.653460i
$640$	−1.32192			−0.0522535
$641$			3.16719i			0.125097i	0.998042	+	0.0625483i	$0.0199227\pi$
$641$			3.16719i			0.125097i	−0.998042	+	0.0625483i	$0.980077\pi$
$642$	21.9879			0.867793
$643$	−32.8923			−1.29715			−0.648573	−	0.761152i	$-0.724634\pi$
$643$	−32.8923			−1.29715			−0.648573	+	0.761152i	$0.724634\pi$
$644$		−	12.0433i		−	0.474574i
$645$	−7.60748			−0.299544
$646$	1.74240			0.0685539
$647$	34.0414			1.33831			0.669153	−	0.743125i	$-0.266657\pi$
$647$	34.0414			1.33831			0.669153	+	0.743125i	$0.266657\pi$
$648$			11.1923i			0.439675i
$649$	7.46518			0.293034
$650$		−	17.4565i		−	0.684699i
$651$	−25.7955			−1.01101
$652$	25.1400			0.984559
$653$	17.7473			0.694507			0.347254	−	0.937771i	$-0.387114\pi$
$653$	17.7473			0.694507			0.347254	+	0.937771i	$0.387114\pi$
$654$		−	18.1862i		−	0.711138i
$655$		−	8.25472i		−	0.322538i
$656$		−	9.95008i		−	0.388485i
$657$		−	2.25823i		−	0.0881021i
$658$		−	14.3797i		−	0.560579i
$659$			8.96710i			0.349309i	0.984630	+	0.174654i	$0.0558808\pi$
$659$			8.96710i			0.349309i	−0.984630	+	0.174654i	$0.944119\pi$
$660$	2.87809			0.112030
$661$	48.5318			1.88767			0.943834	−	0.330420i	$-0.107190\pi$
$661$	48.5318			1.88767			0.943834	+	0.330420i	$0.107190\pi$
$662$		−	1.48738i		−	0.0578088i
$663$			10.0207i			0.389171i
$664$	7.86709			0.305302
$665$	−3.72577			−0.144479
$666$		−	7.75299i		−	0.300422i
$667$			68.7389i			2.66158i
$668$			19.2301i			0.744035i
$669$			49.1058i			1.89854i
$670$		−	9.75402i		−	0.376831i
$671$		−	3.38583i		−	0.130708i
$672$	3.02013			0.116504
$673$	25.2982			0.975176			0.487588	−	0.873074i	$-0.337877\pi$
$673$	25.2982			0.975176			0.487588	+	0.873074i	$0.337877\pi$
$674$	−3.10448			−0.119580
$675$			8.92100i			0.343370i
$676$	−15.8051			−0.607890
$677$		−	48.0672i		−	1.84737i	−0.383148	−	0.923687i	$-0.625160\pi$
$677$		−	48.0672i		−	1.84737i	0.383148	−	0.923687i	$-0.374840\pi$
$678$	29.6735			1.13960
$679$	16.3697			0.628211
$680$	1.13362			0.0434724
$681$			13.6435i			0.522819i
$682$	−8.54119			−0.327059
$683$	−17.8134			−0.681613			−0.340806	−	0.940134i	$-0.610700\pi$
$683$	−17.8134			−0.681613			−0.340806	+	0.940134i	$0.610700\pi$
$684$			3.53582i			0.135196i
$685$	15.5159			0.592831
$686$			16.7510i			0.639557i
$687$		−	64.1842i		−	2.44878i
$688$	−2.64324			−0.100772
$689$	30.6943	−	24.1771i	1.16936	−	0.921075i
$690$	24.9876			0.951263
$691$			13.4038i			0.509905i	0.966954	+	0.254952i	$0.0820598\pi$
$691$			13.4038i			0.509905i	−0.966954	+	0.254952i	$0.917940\pi$
$692$			21.1747i			0.804942i
$693$	−2.41397			−0.0916990
$694$			32.3640i			1.22852i
$695$	−30.8046			−1.16849
$696$	−17.2378			−0.653397
$697$			8.53276i			0.323201i
$698$	23.2104			0.878526
$699$	−49.9354			−1.88873
$700$	4.51177			0.170529
$701$		−	2.47305i		−	0.0934059i	−0.998909	−	0.0467030i	$-0.985129\pi$
$701$		−	2.47305i		−	0.0934059i	0.998909	−	0.0467030i	$-0.0148714\pi$
$702$	14.7207			0.555596
$703$			9.05209i			0.341406i
$704$	1.00000			0.0376889
$705$	29.8352			1.12366
$706$	−18.1113			−0.681629
$707$		−	21.1397i		−	0.795039i
$708$			16.2532i			0.610834i
$709$		−	10.7117i		−	0.402285i	−0.979562	−	0.201143i	$-0.935535\pi$
$709$		−	10.7117i		−	0.402285i	0.979562	−	0.201143i	$-0.0644655\pi$
$710$		−	12.5479i		−	0.470912i
$711$			0.706531i			0.0264970i
$712$		−	9.67232i		−	0.362486i
$713$	−74.1548			−2.77712
$714$	−2.58993			−0.0969257
$715$		−	7.09480i		−	0.265330i
$716$			2.18176i			0.0815362i
$717$	10.6022			0.395948
$718$	−3.84394			−0.143454
$719$		−	31.5401i		−	1.17625i	−0.808771	−	0.588124i	$-0.799867\pi$
$719$		−	31.5401i		−	1.17625i	0.808771	−	0.588124i	$-0.200133\pi$
$720$			2.30044i			0.0857322i
$721$			0.0422014i			0.00157166i
$722$			14.8717i			0.553468i
$723$		−	9.64130i		−	0.358564i
$724$			23.8870i			0.887755i
$725$	−25.7515			−0.956388
$726$	−2.17721			−0.0808037
$727$	33.5464			1.24417			0.622084	−	0.782950i	$-0.286286\pi$
$727$	33.5464			1.24417			0.622084	+	0.782950i	$0.286286\pi$
$728$		−	7.44493i		−	0.275928i
$729$	1.56225			0.0578610
$730$			1.71541i			0.0634903i
$731$	2.26673			0.0838379
$732$	7.37164			0.272464
$733$	35.5610			1.31348			0.656738	−	0.754119i	$-0.271936\pi$
$733$	35.5610			1.31348			0.656738	+	0.754119i	$0.271936\pi$
$734$		−	2.80336i		−	0.103474i
$735$	−14.6086			−0.538846
$736$	8.68202			0.320023
$737$			7.37868i			0.271797i
$738$	−17.3154			−0.637388
$739$		−	5.51947i		−	0.203037i	−0.994834	−	0.101518i	$-0.967630\pi$
$739$		−	5.51947i		−	0.203037i	0.994834	−	0.101518i	$-0.0323701\pi$
$740$			5.88937i			0.216497i
$741$	23.7421			0.872189
$742$	6.24878	+	7.93320i	0.229400	+	0.291237i
$743$	−22.6572			−0.831212			−0.415606	−	0.909545i	$-0.636431\pi$
$743$	−22.6572			−0.831212			−0.415606	+	0.909545i	$0.636431\pi$
$744$		−	18.5959i		−	0.681760i
$745$		−	18.7519i		−	0.687017i
$746$	−25.1263			−0.919941
$747$		−	13.6905i		−	0.500910i
$748$	−0.857557			−0.0313554
$749$	14.0091			0.511881
$750$			23.7515i			0.867283i
$751$	24.0657			0.878171			0.439086	−	0.898445i	$-0.355303\pi$
$751$	24.0657			0.878171			0.439086	+	0.898445i	$0.355303\pi$
$752$	10.3663			0.378021
$753$	−6.68790			−0.243721
$754$			42.4930i			1.54750i
$755$	12.3890			0.450882
$756$			3.80468i			0.138375i
$757$	0.558282			0.0202911			0.0101456	−	0.999949i	$-0.496771\pi$
$757$	0.558282			0.0202911			0.0101456	+	0.999949i	$0.496771\pi$
$758$	−1.02127			−0.0370943
$759$	−18.9025			−0.686119
$760$		−	2.68590i		−	0.0974279i
$761$		−	8.80954i		−	0.319345i	−0.987170	−	0.159673i	$-0.948956\pi$
$761$		−	8.80954i		−	0.319345i	0.987170	−	0.159673i	$-0.0510439\pi$
$762$		−	15.9982i		−	0.579555i
$763$		−	11.5869i		−	0.419475i
$764$			8.00564i			0.289634i
$765$		−	1.97275i		−	0.0713251i
$766$	−32.8031			−1.18522
$767$	40.0659			1.44670
$768$			2.17721i			0.0785631i
$769$			15.5824i			0.561915i	0.959720	+	0.280957i	$0.0906520\pi$
$769$			15.5824i			0.561915i	−0.959720	+	0.280957i	$0.909348\pi$
$770$	1.83371			0.0660823
$771$	49.5435			1.78427
$772$		−	17.2592i		−	0.621173i
$773$			20.8995i			0.751701i	0.926680	+	0.375851i	$0.122649\pi$
$773$			20.8995i			0.751701i	−0.926680	+	0.375851i	$0.877351\pi$
$774$			4.59983i			0.165337i
$775$		−	27.7805i		−	0.997904i
$776$			11.8009i			0.423627i
$777$		−	13.4552i		−	0.482701i
$778$	−25.2737			−0.906105
$779$	20.2168			0.724341
$780$	15.4468			0.553085
$781$			9.49215i			0.339656i
$782$	−7.44532			−0.266244
$783$		−	21.7157i		−	0.776057i
$784$	−5.07579			−0.181278
$785$	20.3030			0.724645
$786$	−13.5955			−0.484937
$787$		−	0.300152i		−	0.0106993i	−0.999986	−	0.00534963i	$-0.998297\pi$
$787$		−	0.300152i		−	0.0106993i	0.999986	−	0.00534963i	$-0.00170285\pi$
$788$	25.5123			0.908839
$789$	31.3673			1.11670
$790$		−	0.536699i		−	0.0190949i
$791$	18.9058			0.672213
$792$		−	1.74022i		−	0.0618362i
$793$		−	18.1719i		−	0.645302i
$794$	4.72481			0.167677
$795$	−16.4599	+	12.9650i	−0.583772	+	0.459823i
$796$	19.7608			0.700405
$797$		−	1.25688i		−	0.0445210i	−0.999752	−	0.0222605i	$-0.992914\pi$
$797$		−	1.25688i		−	0.0445210i	0.999752	−	0.0222605i	$-0.00708633\pi$
$798$			6.13636i			0.217225i
$799$	−8.88970			−0.314495
$800$			3.25253i			0.114994i
$801$	−16.8320			−0.594730
$802$	−6.37140			−0.224982
$803$		−	1.29767i		−	0.0457937i
$804$	−16.0649			−0.566566
$805$	15.9203			0.561117
$806$	−45.8409			−1.61468
$807$		−	24.2320i		−	0.853006i
$808$	15.2396			0.536126
$809$			33.2912i			1.17046i	0.810869	+	0.585228i	$0.198995\pi$
$809$			33.2912i			1.17046i	−0.810869	+	0.585228i	$0.801005\pi$
$810$	−14.7953			−0.519854
$811$	26.5517			0.932357			0.466178	−	0.884691i	$-0.345630\pi$
$811$	26.5517			0.932357			0.466178	+	0.884691i	$0.345630\pi$
$812$	−10.9827			−0.385416
$813$		−	20.2858i		−	0.711453i
$814$		−	4.45516i		−	0.156153i
$815$			33.2331i			1.16410i
$816$		−	1.86708i		−	0.0653608i
$817$		−	5.37058i		−	0.187893i
$818$		−	13.3300i		−	0.466074i
$819$	−12.9559			−0.452714
$820$	13.1532			0.459330
$821$		−	13.1442i		−	0.458736i	−0.973340	−	0.229368i	$-0.926334\pi$
$821$		−	13.1442i		−	0.458736i	0.973340	−	0.229368i	$-0.0736659\pi$
$822$		−	25.5547i		−	0.891322i
$823$	−24.1254			−0.840958			−0.420479	−	0.907302i	$-0.638138\pi$
$823$	−24.1254			−0.840958			−0.420479	+	0.907302i	$0.638138\pi$
$824$	−0.0304229			−0.00105983
$825$		−	7.08142i		−	0.246544i
$826$			10.3554i			0.360310i
$827$		−	8.74547i		−	0.304110i	−0.988372	−	0.152055i	$-0.951411\pi$
$827$		−	8.74547i		−	0.304110i	0.988372	−	0.152055i	$-0.0485890\pi$
$828$		−	15.1087i		−	0.525062i
$829$			12.8669i			0.446885i	0.974717	+	0.223443i	$0.0717295\pi$
$829$			12.8669i			0.446885i	−0.974717	+	0.223443i	$0.928271\pi$
$830$			10.3997i			0.360978i
$831$	21.3836			0.741787
$832$	5.36704			0.186069
$833$	4.35278			0.150815
$834$			50.7353i			1.75682i
$835$	−25.4206			−0.879718
$836$			2.03182i			0.0702720i
$837$	23.4267			0.809745
$838$	13.8325			0.477837
$839$	−20.5550			−0.709637			−0.354819	−	0.934935i	$-0.615457\pi$
$839$	−20.5550			−0.709637			−0.354819	+	0.934935i	$0.615457\pi$
$840$			3.99237i			0.137750i
$841$	33.6851			1.16155
$842$	16.2907			0.561415
$843$		−	39.8352i		−	1.37200i
$844$	16.2588			0.559650
$845$		−	20.8931i		−	0.718745i
$846$		−	18.0397i		−	0.620218i
$847$	−1.38716			−0.0476633
$848$	−5.71903	+	4.50474i	−0.196392	+	0.154693i
$849$	−35.8375			−1.22994
$850$		−	2.78923i		−	0.0956697i
$851$		−	38.6798i		−	1.32593i
$852$	−20.6664			−0.708018
$853$		−	4.60833i		−	0.157786i	−0.996883	−	0.0788931i	$-0.974861\pi$
$853$		−	4.60833i		−	0.157786i	0.996883	−	0.0788931i	$-0.0251386\pi$
$854$	4.69667			0.160717
$855$	−4.67407			−0.159850
$856$			10.0991i			0.345181i
$857$	−28.1484			−0.961532			−0.480766	−	0.876849i	$-0.659641\pi$
$857$	−28.1484			−0.961532			−0.480766	+	0.876849i	$0.659641\pi$
$858$	−11.6852			−0.398925
$859$	−24.0926			−0.822029			−0.411014	−	0.911629i	$-0.634825\pi$
$859$	−24.0926			−0.822029			−0.411014	+	0.911629i	$0.634825\pi$
$860$		−	3.49415i		−	0.119149i
$861$	−30.0505			−1.02412
$862$		−	14.1599i		−	0.482289i
$863$	29.5278			1.00514			0.502569	−	0.864537i	$-0.332388\pi$
$863$	29.5278			1.00514			0.502569	+	0.864537i	$0.332388\pi$
$864$	−2.74279			−0.0933116
$865$	−27.9913			−0.951732
$866$		−	12.9011i		−	0.438396i
$867$		−	35.4114i		−	1.20263i
$868$		−	11.8480i		−	0.402147i
$869$			0.406000i			0.0137726i
$870$		−	22.7870i		−	0.772550i
$871$			39.6017i			1.34185i
$872$	8.35301			0.282869
$873$	20.5362			0.695045
$874$			17.6403i			0.596692i
$875$			15.1327i			0.511580i
$876$	2.82529			0.0954578
$877$	−12.1910			−0.411662			−0.205831	−	0.978588i	$-0.565990\pi$
$877$	−12.1910			−0.411662			−0.205831	+	0.978588i	$0.565990\pi$
$878$		−	29.1606i		−	0.984124i
$879$			59.8602i			2.01903i
$880$			1.32192i			0.0445619i
$881$			17.6044i			0.593107i	0.955016	+	0.296554i	$0.0958374\pi$
$881$			17.6044i			0.593107i	−0.955016	+	0.296554i	$0.904163\pi$
$882$			8.83302i			0.297423i
$883$			34.1210i			1.14826i	0.818763	+	0.574132i	$0.194660\pi$
$883$			34.1210i			1.14826i	−0.818763	+	0.574132i	$0.805340\pi$
$884$	−4.60254			−0.154800
$885$	−21.4855			−0.722226
$886$	5.38596			0.180945
$887$			29.7967i			1.00048i	0.865888	+	0.500238i	$0.166754\pi$
$887$			29.7967i			1.00048i	−0.865888	+	0.500238i	$0.833246\pi$
$888$	9.69981			0.325504
$889$		−	10.1929i		−	0.341859i
$890$	12.7860			0.428589
$891$	11.1923			0.374956
$892$	−22.5545			−0.755180
$893$			21.0625i			0.704829i
$894$	−30.8845			−1.03293
$895$	−2.88411			−0.0964052
$896$			1.38716i			0.0463417i
$897$	−101.451			−3.38734
$898$			13.2476i			0.442080i
$899$			67.6240i			2.25539i
$900$	5.66013			0.188671
$901$	4.90439	−	3.86307i	0.163389	−	0.128698i
$902$	−9.95008			−0.331301
$903$			7.98291i			0.265655i
$904$			13.6292i			0.453299i
$905$	−31.5768			−1.04965
$906$		−	20.4047i		−	0.677902i
$907$	41.2563			1.36989			0.684947	−	0.728593i	$-0.259825\pi$
$907$	41.2563			1.36989			0.684947	+	0.728593i	$0.259825\pi$
$908$	−6.26650			−0.207961
$909$		−	26.5202i		−	0.879621i
$910$	9.84160			0.326246
$911$	5.80609			0.192364			0.0961821	−	0.995364i	$-0.469337\pi$
$911$	5.80609			0.192364			0.0961821	+	0.995364i	$0.469337\pi$
$912$	−4.42369			−0.146483
$913$		−	7.86709i		−	0.260363i
$914$	15.7262			0.520176
$915$			9.74471i			0.322150i
$916$	29.4801			0.974049
$917$	−8.66209			−0.286048
$918$	2.35210			0.0776308
$919$			26.2207i			0.864942i	0.901648	+	0.432471i	$0.142358\pi$
$919$			26.2207i			0.864942i	−0.901648	+	0.432471i	$0.857642\pi$
$920$			11.4769i			0.378383i
$921$			33.6927i			1.11021i
$922$			17.3885i			0.572659i
$923$			50.9447i			1.67687i
$924$		−	3.02013i		−	0.0993549i
$925$	14.4905			0.476446
$926$	6.43743			0.211547
$927$			0.0529428i			0.00173887i
$928$		−	7.91739i		−	0.259901i
$929$	−33.7900			−1.10861			−0.554307	−	0.832312i	$-0.687017\pi$
$929$	−33.7900			−1.10861			−0.554307	+	0.832312i	$0.687017\pi$
$930$	24.5823			0.806086
$931$		−	10.3131i		−	0.337998i
$932$		−	22.9356i		−	0.751279i
$933$			42.8958i			1.40435i
$934$			35.2319i			1.15282i
$935$		−	1.13362i		−	0.0370734i
$936$		−	9.33986i		−	0.305283i
$937$	−11.8886			−0.388383			−0.194192	−	0.980964i	$-0.562208\pi$
$937$	−11.8886			−0.388383			−0.194192	+	0.980964i	$0.562208\pi$
$938$	−10.2354			−0.334198
$939$	−51.1838			−1.67032
$940$			13.7034i			0.446957i
$941$	−60.5445			−1.97369			−0.986847	−	0.161655i	$-0.948317\pi$
$941$	−60.5445			−1.97369			−0.986847	+	0.161655i	$0.948317\pi$
$942$		−	33.4391i		−	1.08951i
$943$	−86.3867			−2.81314
$944$	−7.46518			−0.242971
$945$	−5.02948			−0.163609
$946$			2.64324i			0.0859391i
$947$	44.7497			1.45417			0.727085	−	0.686547i	$-0.240875\pi$
$947$	44.7497			1.45417			0.727085	+	0.686547i	$0.240875\pi$
$948$	−0.883945			−0.0287092
$949$		−	6.96464i		−	0.226082i
$950$	−6.60855			−0.214410
$951$			47.5954i			1.54339i
$952$		−	1.18957i		−	0.0385541i
$953$	12.8891			0.417519			0.208760	−	0.977967i	$-0.433057\pi$
$953$	12.8891			0.417519			0.208760	+	0.977967i	$0.433057\pi$
$954$	7.83926	+	9.95240i	0.253805	+	0.322221i
$955$	−10.5828			−0.342452
$956$			4.86965i			0.157496i
$957$			17.2378i			0.557219i
$958$	−10.9387			−0.353414
$959$		−	16.2816i		−	0.525760i
$960$	−2.87809			−0.0928900
$961$	−41.9520			−1.35329
$962$		−	23.9111i		−	0.770923i
$963$	17.5748			0.566339
$964$	4.42829			0.142626
$965$	22.8153			0.734450
$966$		−	26.2208i		−	0.843640i
$967$	−21.0364			−0.676485			−0.338243	−	0.941059i	$-0.609832\pi$
$967$	−21.0364			−0.676485			−0.338243	+	0.941059i	$0.609832\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	3.79357			0.121867
$970$	−15.5998			−0.500880
$971$	30.0578			0.964599			0.482300	−	0.876006i	$-0.339802\pi$
$971$	30.0578			0.964599			0.482300	+	0.876006i	$0.339802\pi$
$972$			16.1396i			0.517676i
$973$			32.3249i			1.03629i
$974$			2.25381i			0.0722167i
$975$		−	38.0063i		−	1.21718i
$976$			3.38583i			0.108378i
$977$		−	4.89770i		−	0.156691i	−0.996926	−	0.0783457i	$-0.975036\pi$
$977$		−	4.89770i		−	0.156691i	0.996926	−	0.0783457i	$-0.0249638\pi$
$978$	54.7350			1.75023
$979$	−9.67232			−0.309129
$980$		−	6.70979i		−	0.214336i
$981$		−	14.5361i		−	0.464102i
$982$	−16.8369			−0.537286
$983$	36.0306			1.14920			0.574599	−	0.818435i	$-0.305158\pi$
$983$	36.0306			1.14920			0.574599	+	0.818435i	$0.305158\pi$
$984$		−	21.6634i		−	0.690603i
$985$			33.7252i			1.07458i
$986$			6.78961i			0.216225i
$987$		−	31.3076i		−	0.996532i
$988$			10.9049i			0.346930i
$989$			22.9486i			0.729724i
$990$	2.30044			0.0731127
$991$	−16.0058			−0.508441			−0.254220	−	0.967146i	$-0.581819\pi$
$991$	−16.0058			−0.508441			−0.254220	+	0.967146i	$0.581819\pi$
$992$	8.54119			0.271183
$993$		−	3.23834i		−	0.102766i
$994$	−13.1671			−0.417635
$995$			26.1222i			0.828131i
$996$	17.1283			0.542730
$997$	6.41561			0.203184			0.101592	−	0.994826i	$-0.467606\pi$
$997$	6.41561			0.203184			0.101592	+	0.994826i	$0.467606\pi$
$998$	5.92817			0.187653
$999$			12.2196i			0.386610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1166.2.c.b.529.20	yes	22
53.52	even	2	inner	1166.2.c.b.529.3	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1166.2.c.b.529.3	✓	22	53.52	even	2	inner
1166.2.c.b.529.20	yes	22	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1166 = 2 \cdot 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1166.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.17721i q^{3} -1.00000 q^{4} -1.32192i q^{5} -2.17721 q^{6} -1.38716 q^{7} -1.00000i q^{8} -1.74022 q^{9} +1.32192 q^{10} -1.00000 q^{11} -2.17721i q^{12} -5.36704 q^{13} -1.38716i q^{14} +2.87809 q^{15} +1.00000 q^{16} -0.857557 q^{17} -1.74022i q^{18} +2.03182i q^{19} +1.32192i q^{20} -3.02013i q^{21} -1.00000i q^{22} -8.68202i q^{23} +2.17721 q^{24} +3.25253 q^{25} -5.36704i q^{26} +2.74279i q^{27} +1.38716 q^{28} -7.91739 q^{29} +2.87809i q^{30} -8.54119i q^{31} +1.00000i q^{32} -2.17721i q^{33} -0.857557i q^{34} +1.83371i q^{35} +1.74022 q^{36} +4.45516 q^{37} -2.03182 q^{38} -11.6852i q^{39} -1.32192 q^{40} -9.95008i q^{41} +3.02013 q^{42} -2.64324 q^{43} +1.00000 q^{44} +2.30044i q^{45} +8.68202 q^{46} +10.3663 q^{47} +2.17721i q^{48} -5.07579 q^{49} +3.25253i q^{50} -1.86708i q^{51} +5.36704 q^{52} +(-5.71903 + 4.50474i) q^{53} -2.74279 q^{54} +1.32192i q^{55} +1.38716i q^{56} -4.42369 q^{57} -7.91739i q^{58} -7.46518 q^{59} -2.87809 q^{60} +3.38583i q^{61} +8.54119 q^{62} +2.41397 q^{63} -1.00000 q^{64} +7.09480i q^{65} +2.17721 q^{66} -7.37868i q^{67} +0.857557 q^{68} +18.9025 q^{69} -1.83371 q^{70} -9.49215i q^{71} +1.74022i q^{72} +1.29767i q^{73} +4.45516i q^{74} +7.08142i q^{75} -2.03182i q^{76} +1.38716 q^{77} +11.6852 q^{78} -0.406000i q^{79} -1.32192i q^{80} -11.1923 q^{81} +9.95008 q^{82} +7.86709i q^{83} +3.02013i q^{84} +1.13362i q^{85} -2.64324i q^{86} -17.2378i q^{87} +1.00000i q^{88} +9.67232 q^{89} -2.30044 q^{90} +7.44493 q^{91} +8.68202i q^{92} +18.5959 q^{93} +10.3663i q^{94} +2.68590 q^{95} -2.17721 q^{96} -11.8009 q^{97} -5.07579i q^{98} +1.74022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{4} - 6 q^{6} - 24 q^{9} + 4 q^{10} - 22 q^{11} + 6 q^{13} + 30 q^{15} + 22 q^{16} + 18 q^{17} + 6 q^{24} - 30 q^{25} + 28 q^{29} + 24 q^{36} - 34 q^{37} - 18 q^{38} - 4 q^{40} + 4 q^{42} - 34 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) 22 * q - 22 * q^4 - 6 * q^6 - 24 * q^9 + 4 * q^10 - 22 * q^11 + 6 * q^13 + 30 * q^15 + 22 * q^16 + 18 * q^17 + 6 * q^24 - 30 * q^25 + 28 * q^29 + 24 * q^36 - 34 * q^37 - 18 * q^38 - 4 * q^40 + 4 * q^42 - 34 * q^43 + 22 * q^44 + 6 * q^46 + 8 * q^47 + 6 * q^49 - 6 * q^52 + 16 * q^53 + 12 * q^54 + 14 * q^57 - 60 * q^59 - 30 * q^60 - 8 * q^62 + 116 * q^63 - 22 * q^64 + 6 * q^66 - 18 * q^68 - 26 * q^69 - 32 * q^70 - 4 * q^78 + 62 * q^81 - 44 * q^82 - 34 * q^89 - 6 * q^90 + 12 * q^91 + 4 * q^93 - 6 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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