LMFDB - Embedded newform 1155.2.i.d.76.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.i (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.18
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.d.76.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23885i q^{2} -1.00000i q^{3} -3.01246 q^{4} -1.00000i q^{5} +2.23885 q^{6} +(0.322004 - 2.62608i) q^{7} -2.26674i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.23885i q^{2} -1.00000i q^{3} -3.01246 q^{4} -1.00000i q^{5} +2.23885 q^{6} +(0.322004 - 2.62608i) q^{7} -2.26674i q^{8} -1.00000 q^{9} +2.23885 q^{10} +(-2.55226 + 2.11802i) q^{11} +3.01246i q^{12} +0.842387 q^{13} +(5.87941 + 0.720920i) q^{14} -1.00000 q^{15} -0.950014 q^{16} -3.42003 q^{17} -2.23885i q^{18} +6.30984 q^{19} +3.01246i q^{20} +(-2.62608 - 0.322004i) q^{21} +(-4.74192 - 5.71412i) q^{22} -5.97493 q^{23} -2.26674 q^{24} -1.00000 q^{25} +1.88598i q^{26} +1.00000i q^{27} +(-0.970024 + 7.91096i) q^{28} -9.40952i q^{29} -2.23885i q^{30} -0.997372i q^{31} -6.66043i q^{32} +(2.11802 + 2.55226i) q^{33} -7.65694i q^{34} +(-2.62608 - 0.322004i) q^{35} +3.01246 q^{36} +1.41004 q^{37} +14.1268i q^{38} -0.842387i q^{39} -2.26674 q^{40} -10.3306 q^{41} +(0.720920 - 5.87941i) q^{42} -10.0756i q^{43} +(7.68856 - 6.38043i) q^{44} +1.00000i q^{45} -13.3770i q^{46} -8.10188i q^{47} +0.950014i q^{48} +(-6.79263 - 1.69122i) q^{49} -2.23885i q^{50} +3.42003i q^{51} -2.53766 q^{52} -3.80872 q^{53} -2.23885 q^{54} +(2.11802 + 2.55226i) q^{55} +(-5.95266 - 0.729901i) q^{56} -6.30984i q^{57} +21.0665 q^{58} -10.7490i q^{59} +3.01246 q^{60} -3.15296 q^{61} +2.23297 q^{62} +(-0.322004 + 2.62608i) q^{63} +13.0117 q^{64} -0.842387i q^{65} +(-5.71412 + 4.74192i) q^{66} -11.4139 q^{67} +10.3027 q^{68} +5.97493i q^{69} +(0.720920 - 5.87941i) q^{70} -4.24318 q^{71} +2.26674i q^{72} +15.6260 q^{73} +3.15688i q^{74} +1.00000i q^{75} -19.0081 q^{76} +(4.74025 + 7.38445i) q^{77} +1.88598 q^{78} +14.3009i q^{79} +0.950014i q^{80} +1.00000 q^{81} -23.1286i q^{82} -0.946456 q^{83} +(7.91096 + 0.970024i) q^{84} +3.42003i q^{85} +22.5578 q^{86} -9.40952 q^{87} +(4.80100 + 5.78531i) q^{88} +17.4593i q^{89} -2.23885 q^{90} +(0.271252 - 2.21218i) q^{91} +17.9992 q^{92} -0.997372 q^{93} +18.1389 q^{94} -6.30984i q^{95} -6.66043 q^{96} -17.6891i q^{97} +(3.78639 - 15.2077i) q^{98} +(2.55226 - 2.11802i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 36 * q^4 - 32 * q^9	$ 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) $ 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$1$	$-1$

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 $

$2$			2.23885i			1.58311i	0.611100	+	0.791554i	$0.290727\pi$
$2$			2.23885i			1.58311i	−0.611100	+	0.791554i	$0.709273\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−3.01246			−1.50623
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.23885			0.914007
$7$	0.322004	−	2.62608i	0.121706	−	0.992566i
$7$	0.322004	−	2.62608i	0.121706	−	0.992566i
$8$		−	2.26674i		−	0.801415i
$9$	−1.00000			−0.333333
$10$	2.23885			0.707987
$11$	−2.55226	+	2.11802i	−0.769534	+	0.638606i
$11$	−2.55226	+	2.11802i	−0.769534	+	0.638606i
$12$			3.01246i			0.869622i
$13$	0.842387			0.233636			0.116818	−	0.993153i	$-0.462731\pi$
$13$	0.842387			0.233636			0.116818	+	0.993153i	$0.462731\pi$
$14$	5.87941	+	0.720920i	1.57134	+	0.192674i
$15$	−1.00000			−0.258199
$16$	−0.950014			−0.237504
$17$	−3.42003			−0.829479			−0.414739	−	0.909940i	$-0.636127\pi$
$17$	−3.42003			−0.829479			−0.414739	+	0.909940i	$0.636127\pi$
$18$		−	2.23885i		−	0.527702i
$19$	6.30984			1.44758			0.723788	−	0.690022i	$-0.242399\pi$
$19$	6.30984			1.44758			0.723788	+	0.690022i	$0.242399\pi$
$20$			3.01246i			0.673606i
$21$	−2.62608	−	0.322004i	−0.573058	−	0.0702671i
$22$	−4.74192	−	5.71412i	−1.01098	−	1.21826i
$23$	−5.97493			−1.24586			−0.622929	−	0.782278i	$-0.714058\pi$
$23$	−5.97493			−1.24586			−0.622929	+	0.782278i	$0.714058\pi$
$24$	−2.26674			−0.462697
$25$	−1.00000			−0.200000
$26$			1.88598i			0.369871i
$27$			1.00000i			0.192450i
$28$	−0.970024	+	7.91096i	−0.183317	+	1.49503i
$29$		−	9.40952i		−	1.74730i	−0.486550	−	0.873652i	$-0.661745\pi$
$29$		−	9.40952i		−	1.74730i	0.486550	−	0.873652i	$-0.338255\pi$
$30$		−	2.23885i		−	0.408757i
$31$		−	0.997372i		−	0.179133i	−0.995981	−	0.0895666i	$-0.971452\pi$
$31$		−	0.997372i		−	0.179133i	0.995981	−	0.0895666i	$-0.0285482\pi$
$32$		−	6.66043i		−	1.17741i
$33$	2.11802	+	2.55226i	0.368699	+	0.444291i
$34$		−	7.65694i		−	1.31315i
$35$	−2.62608	−	0.322004i	−0.443889	−	0.0544286i
$36$	3.01246			0.502076
$37$	1.41004			0.231810			0.115905	−	0.993260i	$-0.463023\pi$
$37$	1.41004			0.231810			0.115905	+	0.993260i	$0.463023\pi$
$38$			14.1268i			2.29167i
$39$		−	0.842387i		−	0.134890i
$40$	−2.26674			−0.358403
$41$	−10.3306			−1.61337			−0.806683	−	0.590984i	$-0.798740\pi$
$41$	−10.3306			−1.61337			−0.806683	+	0.590984i	$0.798740\pi$
$42$	0.720920	−	5.87941i	0.111240	−	0.907213i
$43$		−	10.0756i		−	1.53652i	−0.640140	−	0.768258i	$-0.721124\pi$
$43$		−	10.0756i		−	1.53652i	0.640140	−	0.768258i	$-0.278876\pi$
$44$	7.68856	−	6.38043i	1.15909	−	0.961886i
$45$			1.00000i			0.149071i
$46$		−	13.3770i		−	1.97233i
$47$		−	8.10188i		−	1.18178i	−0.806752	−	0.590891i	$-0.798776\pi$
$47$		−	8.10188i		−	1.18178i	0.806752	−	0.590891i	$-0.201224\pi$
$48$			0.950014i			0.137123i
$49$	−6.79263	−	1.69122i	−0.970375	−	0.241603i
$50$		−	2.23885i		−	0.316621i
$51$			3.42003i			0.478900i
$52$	−2.53766			−0.351910
$53$	−3.80872			−0.523167			−0.261584	−	0.965181i	$-0.584245\pi$
$53$	−3.80872			−0.523167			−0.261584	+	0.965181i	$0.584245\pi$
$54$	−2.23885			−0.304669
$55$	2.11802	+	2.55226i	0.285593	+	0.344146i
$56$	−5.95266	−	0.729901i	−0.795457	−	0.0975371i
$57$		−	6.30984i		−	0.835759i
$58$	21.0665			2.76617
$59$		−	10.7490i		−	1.39940i	−0.714437	−	0.699700i	$-0.753317\pi$
$59$		−	10.7490i		−	1.39940i	0.714437	−	0.699700i	$-0.246683\pi$
$60$	3.01246			0.388907
$61$	−3.15296			−0.403695			−0.201848	−	0.979417i	$-0.564695\pi$
$61$	−3.15296			−0.403695			−0.201848	+	0.979417i	$0.564695\pi$
$62$	2.23297			0.283587
$63$	−0.322004	+	2.62608i	−0.0405687	+	0.330855i
$64$	13.0117			1.62646
$65$		−	0.842387i		−	0.104485i
$66$	−5.71412	+	4.74192i	−0.703360	+	0.583690i
$67$	−11.4139			−1.39442			−0.697212	−	0.716865i	$-0.745576\pi$
$67$	−11.4139			−1.39442			−0.697212	+	0.716865i	$0.745576\pi$
$68$	10.3027			1.24939
$69$			5.97493i			0.719297i
$70$	0.720920	−	5.87941i	0.0861664	−	0.702724i
$71$	−4.24318			−0.503573			−0.251786	−	0.967783i	$-0.581018\pi$
$71$	−4.24318			−0.503573			−0.251786	+	0.967783i	$0.581018\pi$
$72$			2.26674i			0.267138i
$73$	15.6260			1.82889			0.914445	−	0.404710i	$-0.132628\pi$
$73$	15.6260			1.82889			0.914445	+	0.404710i	$0.132628\pi$
$74$			3.15688i			0.366980i
$75$			1.00000i			0.115470i
$76$	−19.0081			−2.18038
$77$	4.74025	+	7.38445i	0.540201	+	0.841536i
$78$	1.88598			0.213545
$79$			14.3009i			1.60898i	0.593969	+	0.804488i	$0.297560\pi$
$79$			14.3009i			1.60898i	−0.593969	+	0.804488i	$0.702440\pi$
$80$			0.950014i			0.106215i
$81$	1.00000			0.111111
$82$		−	23.1286i		−	2.55413i
$83$	−0.946456			−0.103887			−0.0519435	−	0.998650i	$-0.516542\pi$
$83$	−0.946456			−0.103887			−0.0519435	+	0.998650i	$0.516542\pi$
$84$	7.91096	+	0.970024i	0.863157	+	0.105838i
$85$			3.42003i			0.370954i
$86$	22.5578			2.43247
$87$	−9.40952			−1.00881
$88$	4.80100	+	5.78531i	0.511788	+	0.616716i
$89$			17.4593i			1.85068i	0.379142	+	0.925339i	$0.376219\pi$
$89$			17.4593i			1.85068i	−0.379142	+	0.925339i	$0.623781\pi$
$90$	−2.23885			−0.235996
$91$	0.271252	−	2.21218i	0.0284350	−	0.231899i
$92$	17.9992			1.87655
$93$	−0.997372			−0.103423
$94$	18.1389			1.87089
$95$		−	6.30984i		−	0.647376i
$96$	−6.66043			−0.679777
$97$		−	17.6891i		−	1.79605i	−0.439943	−	0.898026i	$-0.645001\pi$
$97$		−	17.6891i		−	1.79605i	0.439943	−	0.898026i	$-0.354999\pi$
$98$	3.78639	−	15.2077i	0.382483	−	1.53621i
$99$	2.55226	−	2.11802i	0.256511	−	0.212869i
$100$	3.01246			0.301246
$101$	0.702211			0.0698727			0.0349363	−	0.999390i	$-0.488877\pi$
$101$	0.702211			0.0698727			0.0349363	+	0.999390i	$0.488877\pi$
$102$	−7.65694			−0.758150
$103$			7.05904i			0.695548i	0.937578	+	0.347774i	$0.113062\pi$
$103$			7.05904i			0.695548i	−0.937578	+	0.347774i	$0.886938\pi$
$104$		−	1.90948i		−	0.187239i
$105$	−0.322004	+	2.62608i	−0.0314244	+	0.256279i
$106$		−	8.52715i		−	0.828230i
$107$			10.5977i			1.02451i	0.858832	+	0.512257i	$0.171190\pi$
$107$			10.5977i			1.02451i	−0.858832	+	0.512257i	$0.828810\pi$
$108$		−	3.01246i		−	0.289874i
$109$		−	8.56633i		−	0.820505i	−0.911972	−	0.410253i	$-0.865441\pi$
$109$		−	8.56633i		−	0.820505i	0.911972	−	0.410253i	$-0.134559\pi$
$110$	−5.71412	+	4.74192i	−0.544820	+	0.452125i
$111$		−	1.41004i		−	0.133835i
$112$	−0.305909	+	2.49482i	−0.0289056	+	0.235738i
$113$	−1.51910			−0.142905			−0.0714526	−	0.997444i	$-0.522763\pi$
$113$	−1.51910			−0.142905			−0.0714526	+	0.997444i	$0.522763\pi$
$114$	14.1268			1.32310
$115$			5.97493i			0.557165i
$116$			28.3458i			2.63184i
$117$	−0.842387			−0.0778787
$118$	24.0654			2.21540
$119$	−1.10126	+	8.98128i	−0.100953	+	0.823313i
$120$			2.26674i			0.206924i
$121$	2.02802	−	10.8114i	0.184365	−	0.982858i
$122$		−	7.05901i		−	0.639093i
$123$			10.3306i			0.931477i
$124$			3.00454i			0.269816i
$125$			1.00000i			0.0894427i
$126$	−5.87941	−	0.720920i	−0.523780	−	0.0642246i
$127$			4.72234i			0.419040i	0.977804	+	0.209520i	$0.0671901\pi$
$127$			4.72234i			0.419040i	−0.977804	+	0.209520i	$0.932810\pi$
$128$			15.8104i			1.39745i
$129$	−10.0756			−0.887108
$130$	1.88598			0.165411
$131$	9.88715			0.863844			0.431922	−	0.901911i	$-0.357836\pi$
$131$	9.88715			0.863844			0.431922	+	0.901911i	$0.357836\pi$
$132$	−6.38043	−	7.68856i	−0.555345	−	0.669203i
$133$	2.03180	−	16.5702i	0.176179	−	1.43682i
$134$		−	25.5539i		−	2.20752i
$135$	1.00000			0.0860663
$136$			7.75233i			0.664757i
$137$	−5.77144			−0.493087			−0.246544	−	0.969132i	$-0.579295\pi$
$137$	−5.77144			−0.493087			−0.246544	+	0.969132i	$0.579295\pi$
$138$	−13.3770			−1.13872
$139$	−9.94116			−0.843198			−0.421599	−	0.906782i	$-0.638531\pi$
$139$	−9.94116			−0.843198			−0.421599	+	0.906782i	$0.638531\pi$
$140$	7.91096	+	0.970024i	0.668599	+	0.0819820i
$141$	−8.10188			−0.682302
$142$		−	9.49985i		−	0.797210i
$143$	−2.14999	+	1.78419i	−0.179791	+	0.149201i
$144$	0.950014			0.0791678
$145$	−9.40952			−0.781419
$146$			34.9844i			2.89533i
$147$	−1.69122	+	6.79263i	−0.139489	+	0.560246i
$148$	−4.24770			−0.349159
$149$			12.3780i			1.01405i	0.861933	+	0.507023i	$0.169254\pi$
$149$			12.3780i			1.01405i	−0.861933	+	0.507023i	$0.830746\pi$
$150$	−2.23885			−0.182801
$151$			13.3219i			1.08412i	0.840340	+	0.542060i	$0.182356\pi$
$151$			13.3219i			1.08412i	−0.840340	+	0.542060i	$0.817644\pi$
$152$		−	14.3028i		−	1.16011i
$153$	3.42003			0.276493
$154$	−16.5327	+	10.6127i	−1.33224	+	0.855197i
$155$	−0.997372			−0.0801108
$156$			2.53766i			0.203175i
$157$		−	8.99722i		−	0.718056i	−0.933327	−	0.359028i	$-0.883108\pi$
$157$		−	8.99722i		−	0.718056i	0.933327	−	0.359028i	$-0.116892\pi$
$158$	−32.0176			−2.54718
$159$			3.80872i			0.302051i
$160$	−6.66043			−0.526553
$161$	−1.92395	+	15.6907i	−0.151629	+	1.23660i
$162$			2.23885i			0.175901i
$163$	−1.25085			−0.0979742			−0.0489871	−	0.998799i	$-0.515599\pi$
$163$	−1.25085			−0.0979742			−0.0489871	+	0.998799i	$0.515599\pi$
$164$	31.1204			2.43010
$165$	2.55226	−	2.11802i	0.198693	−	0.164887i
$166$		−	2.11897i		−	0.164464i
$167$	16.5043			1.27714			0.638572	−	0.769562i	$-0.279525\pi$
$167$	16.5043			1.27714			0.638572	+	0.769562i	$0.279525\pi$
$168$	−0.729901	+	5.95266i	−0.0563131	+	0.459257i
$169$	−12.2904			−0.945414
$170$	−7.65694			−0.587260
$171$	−6.30984			−0.482526
$172$			30.3524i			2.31435i
$173$	19.4351			1.47762			0.738811	−	0.673912i	$-0.235387\pi$
$173$	19.4351			1.47762			0.738811	+	0.673912i	$0.235387\pi$
$174$		−	21.0665i		−	1.59705i
$175$	−0.322004	+	2.62608i	−0.0243412	+	0.198513i
$176$	2.42468	−	2.01214i	0.182767	−	0.151671i
$177$	−10.7490			−0.807944
$178$	−39.0887			−2.92982
$179$	15.1145			1.12971			0.564856	−	0.825189i	$-0.308932\pi$
$179$	15.1145			1.12971			0.564856	+	0.825189i	$0.308932\pi$
$180$		−	3.01246i		−	0.224535i
$181$			10.4440i			0.776298i	0.921597	+	0.388149i	$0.126885\pi$
$181$			10.4440i			0.776298i	−0.921597	+	0.388149i	$0.873115\pi$
$182$	4.95274	+	0.607294i	0.367122	+	0.0450156i
$183$			3.15296i			0.233074i
$184$			13.5436i			0.998449i
$185$		−	1.41004i		−	0.103669i
$186$		−	2.23297i		−	0.163729i
$187$	8.72879	−	7.24368i	0.638312	−	0.529710i
$188$			24.4066i			1.78003i
$189$	2.62608	+	0.322004i	0.191019	+	0.0234224i
$190$	14.1268			1.02487
$191$	12.2395			0.885622			0.442811	−	0.896615i	$-0.353981\pi$
$191$	12.2395			0.885622			0.442811	+	0.896615i	$0.353981\pi$
$192$		−	13.0117i		−	0.939037i
$193$		−	6.70826i		−	0.482871i	−0.970417	−	0.241435i	$-0.922382\pi$
$193$		−	6.70826i		−	0.482871i	0.970417	−	0.241435i	$-0.0776182\pi$
$194$	39.6032			2.84334
$195$	−0.842387			−0.0603246
$196$	20.4625	+	5.09473i	1.46161	+	0.363909i
$197$		−	7.20052i		−	0.513015i	−0.966542	−	0.256508i	$-0.917428\pi$
$197$		−	7.20052i		−	0.513015i	0.966542	−	0.256508i	$-0.0825719\pi$
$198$	4.74192	+	5.71412i	0.336994	+	0.406085i
$199$			24.0485i			1.70475i	0.522927	+	0.852377i	$0.324840\pi$
$199$			24.0485i			1.70475i	−0.522927	+	0.852377i	$0.675160\pi$
$200$			2.26674i			0.160283i
$201$			11.4139i			0.805071i
$202$			1.57215i			0.110616i
$203$	−24.7102	−	3.02991i	−1.73432	−	0.212658i
$204$		−	10.3027i		−	0.721333i
$205$			10.3306i			0.721519i
$206$	−15.8042			−1.10113
$207$	5.97493			0.415286
$208$	−0.800280			−0.0554894
$209$	−16.1043	+	13.3643i	−1.11396	+	0.924431i
$210$	−5.87941	−	0.720920i	−0.405718	−	0.0497482i
$211$		−	6.53762i		−	0.450068i	−0.974351	−	0.225034i	$-0.927751\pi$
$211$		−	6.53762i		−	0.450068i	0.974351	−	0.225034i	$-0.0722493\pi$
$212$	11.4736			0.788010
$213$			4.24318i			0.290738i
$214$	−23.7266			−1.62192
$215$	−10.0756			−0.687151
$216$	2.26674			0.154232
$217$	−2.61918	−	0.321158i	−0.177802	−	0.0218016i
$218$	19.1787			1.29895
$219$		−	15.6260i		−	1.05591i
$220$	−6.38043	−	7.68856i	−0.430169	−	0.518363i
$221$	−2.88099			−0.193796
$222$	3.15688			0.211876
$223$		−	25.7539i		−	1.72461i	−0.506388	−	0.862305i	$-0.669020\pi$
$223$		−	25.7539i		−	1.72461i	0.506388	−	0.862305i	$-0.330980\pi$
$224$	−17.4908	−	2.14469i	−1.16866	−	0.143298i
$225$	1.00000			0.0666667
$226$		−	3.40105i		−	0.226234i
$227$	−7.83215			−0.519838			−0.259919	−	0.965630i	$-0.583696\pi$
$227$	−7.83215			−0.519838			−0.259919	+	0.965630i	$0.583696\pi$
$228$			19.0081i			1.25884i
$229$		−	12.8659i		−	0.850205i	−0.905145	−	0.425102i	$-0.860238\pi$
$229$		−	12.8659i		−	0.850205i	0.905145	−	0.425102i	$-0.139762\pi$
$230$	−13.3770			−0.882052
$231$	7.38445	−	4.74025i	0.485861	−	0.311885i
$232$	−21.3290			−1.40032
$233$		−	17.1634i		−	1.12441i	−0.826997	−	0.562206i	$-0.809953\pi$
$233$		−	17.1634i		−	1.12441i	0.826997	−	0.562206i	$-0.190047\pi$
$234$		−	1.88598i		−	0.123290i
$235$	−8.10188			−0.528509
$236$			32.3809i			2.10782i
$237$	14.3009			0.928943
$238$	−20.1078	−	2.46557i	−1.30339	−	0.159819i
$239$			10.3445i			0.669129i	0.942373	+	0.334564i	$0.108589\pi$
$239$			10.3445i			0.669129i	−0.942373	+	0.334564i	$0.891411\pi$
$240$	0.950014			0.0613231
$241$	8.03134			0.517344			0.258672	−	0.965965i	$-0.416715\pi$
$241$	8.03134			0.517344			0.258672	+	0.965965i	$0.416715\pi$
$242$	24.2052	+	4.54044i	1.55597	+	0.291870i
$243$		−	1.00000i		−	0.0641500i
$244$	9.49816			0.608057
$245$	−1.69122	+	6.79263i	−0.108048	+	0.433965i
$246$	−23.1286			−1.47463
$247$	5.31533			0.338206
$248$	−2.26079			−0.143560
$249$			0.946456i			0.0599792i
$250$	−2.23885			−0.141597
$251$			27.1281i			1.71231i	0.516717	+	0.856156i	$0.327154\pi$
$251$			27.1281i			1.71231i	−0.516717	+	0.856156i	$0.672846\pi$
$252$	0.970024	−	7.91096i	0.0611058	−	0.498344i
$253$	15.2495	−	12.6550i	0.958731	−	0.795613i
$254$	−10.5726			−0.663385
$255$	3.42003			0.214171
$256$	−9.37372			−0.585857
$257$		−	23.0643i		−	1.43871i	−0.694641	−	0.719356i	$-0.744437\pi$
$257$		−	23.0643i		−	1.43871i	0.694641	−	0.719356i	$-0.255563\pi$
$258$		−	22.5578i		−	1.40439i
$259$	0.454040	−	3.70289i	0.0282127	−	0.230087i
$260$			2.53766i			0.157379i
$261$			9.40952i			0.582435i
$262$			22.1359i			1.36756i
$263$		−	2.49039i		−	0.153564i	−0.997048	−	0.0767820i	$-0.975535\pi$
$263$		−	2.49039i		−	0.153564i	0.997048	−	0.0767820i	$-0.0244645\pi$
$264$	5.78531	−	4.80100i	0.356061	−	0.295481i
$265$			3.80872i			0.233968i
$266$	37.0981	+	4.54889i	2.27463	+	0.278910i
$267$	17.4593			1.06849
$268$	34.3837			2.10032
$269$		−	4.78537i		−	0.291769i	−0.989302	−	0.145885i	$-0.953397\pi$
$269$		−	4.78537i		−	0.291769i	0.989302	−	0.145885i	$-0.0466029\pi$
$270$			2.23885i			0.136252i
$271$	−12.9173			−0.784671			−0.392336	−	0.919822i	$-0.628333\pi$
$271$	−12.9173			−0.784671			−0.392336	+	0.919822i	$0.628333\pi$
$272$	3.24908			0.197004
$273$	−2.21218	−	0.271252i	−0.133887	−	0.0164169i
$274$		−	12.9214i		−	0.780610i
$275$	2.55226	−	2.11802i	0.153907	−	0.127721i
$276$		−	17.9992i		−	1.08343i
$277$		−	5.81500i		−	0.349389i	−0.984623	−	0.174695i	$-0.944106\pi$
$277$		−	5.81500i		−	0.349389i	0.984623	−	0.174695i	$-0.0558938\pi$
$278$		−	22.2568i		−	1.33487i
$279$			0.997372i			0.0597111i
$280$	−0.729901	+	5.95266i	−0.0436199	+	0.355739i
$281$			2.47572i			0.147689i	0.997270	+	0.0738446i	$0.0235269\pi$
$281$			2.47572i			0.147689i	−0.997270	+	0.0738446i	$0.976473\pi$
$282$		−	18.1389i		−	1.08016i
$283$	26.9187			1.60015			0.800075	−	0.599901i	$-0.204793\pi$
$283$	26.9187			1.60015			0.800075	+	0.599901i	$0.204793\pi$
$284$	12.7824			0.758496
$285$	−6.30984			−0.373763
$286$	−3.99454	−	4.81350i	−0.236202	−	0.284628i
$287$	−3.32649	+	27.1290i	−0.196357	+	1.60137i
$288$			6.66043i			0.392469i
$289$	−5.30340			−0.311965
$290$		−	21.0665i		−	1.23707i
$291$	−17.6891			−1.03695
$292$	−47.0728			−2.75473
$293$	5.92944			0.346402			0.173201	−	0.984887i	$-0.444589\pi$
$293$	5.92944			0.346402			0.173201	+	0.984887i	$0.444589\pi$
$294$	−15.2077	−	3.78639i	−0.886930	−	0.220827i
$295$	−10.7490			−0.625831
$296$		−	3.19621i		−	0.185776i
$297$	−2.11802	−	2.55226i	−0.122900	−	0.148097i
$298$	−27.7125			−1.60534
$299$	−5.03320			−0.291078
$300$		−	3.01246i		−	0.173924i
$301$	−26.4594	−	3.24439i	−1.52509	−	0.187003i
$302$	−29.8257			−1.71628
$303$		−	0.702211i		−	0.0403410i
$304$	−5.99444			−0.343805
$305$			3.15296i			0.180538i
$306$			7.65694i			0.437718i
$307$	7.12996			0.406928			0.203464	−	0.979082i	$-0.434780\pi$
$307$	7.12996			0.406928			0.203464	+	0.979082i	$0.434780\pi$
$308$	−14.2798	−	22.2453i	−0.813667	−	1.26755i
$309$	7.05904			0.401575
$310$		−	2.23297i		−	0.126824i
$311$		−	34.4437i		−	1.95312i	−0.215238	−	0.976562i	$-0.569053\pi$
$311$		−	34.4437i		−	1.95312i	0.215238	−	0.976562i	$-0.430947\pi$
$312$	−1.90948			−0.108103
$313$		−	6.36649i		−	0.359855i	−0.983680	−	0.179928i	$-0.942414\pi$
$313$		−	6.36649i		−	0.359855i	0.983680	−	0.179928i	$-0.0575864\pi$
$314$	20.1434			1.13676
$315$	2.62608	+	0.322004i	0.147963	+	0.0181429i
$316$		−	43.0808i		−	2.42349i
$317$	−16.9314			−0.950961			−0.475480	−	0.879726i	$-0.657726\pi$
$317$	−16.9314			−0.950961			−0.475480	+	0.879726i	$0.657726\pi$
$318$	−8.52715			−0.478179
$319$	19.9295	+	24.0155i	1.11584	+	1.34461i
$320$		−	13.0117i		−	0.727375i
$321$	10.5977			0.591503
$322$	−35.1291	−	4.30744i	−1.95767	−	0.240044i
$323$	−21.5798			−1.20073
$324$	−3.01246			−0.167359
$325$	−0.842387			−0.0467272
$326$		−	2.80047i		−	0.155104i
$327$	−8.56633			−0.473719
$328$			23.4168i			1.29298i
$329$	−21.2762	−	2.60884i	−1.17300	−	0.143830i
$330$	4.74192	+	5.71412i	0.261034	+	0.314552i
$331$	−22.2475			−1.22284			−0.611418	−	0.791308i	$-0.709400\pi$
$331$	−22.2475			−1.22284			−0.611418	+	0.791308i	$0.709400\pi$
$332$	2.85116			0.156478
$333$	−1.41004			−0.0772699
$334$			36.9508i			2.02186i
$335$			11.4139i			0.623605i
$336$	2.49482	+	0.305909i	0.136103	+	0.0166887i
$337$		−	15.7574i		−	0.858361i	−0.903219	−	0.429180i	$-0.858802\pi$
$337$		−	15.7574i		−	0.858361i	0.903219	−	0.429180i	$-0.141198\pi$
$338$		−	27.5163i		−	1.49669i
$339$			1.51910i			0.0825064i
$340$		−	10.3027i		−	0.558742i
$341$	2.11245	+	2.54555i	0.114396	+	0.137849i
$342$		−	14.1268i		−	0.763890i
$343$	−6.62854	+	17.2934i	−0.357907	+	0.933757i
$344$	−22.8388			−1.23139
$345$	5.97493			0.321679
$346$			43.5123i			2.33924i
$347$		−	12.6941i		−	0.681454i	−0.940162	−	0.340727i	$-0.889327\pi$
$347$		−	12.6941i		−	0.681454i	0.940162	−	0.340727i	$-0.110673\pi$
$348$	28.3458			1.51949
$349$	21.6081			1.15665			0.578326	−	0.815805i	$-0.303706\pi$
$349$	21.6081			1.15665			0.578326	+	0.815805i	$0.303706\pi$
$350$	−5.87941	−	0.720920i	−0.314268	−	0.0385348i
$351$			0.842387i			0.0449633i
$352$	14.1069	+	16.9991i	0.751900	+	0.906056i
$353$		−	8.18411i		−	0.435596i	−0.975994	−	0.217798i	$-0.930113\pi$
$353$		−	8.18411i		−	0.435596i	0.975994	−	0.217798i	$-0.0698874\pi$
$354$		−	24.0654i		−	1.27906i
$355$			4.24318i			0.225205i
$356$		−	52.5953i		−	2.78754i
$357$	8.98128	+	1.10126i	0.475340	+	0.0582851i
$358$			33.8392i			1.78846i
$359$			13.4331i			0.708970i	0.935062	+	0.354485i	$0.115344\pi$
$359$			13.4331i			0.708970i	−0.935062	+	0.354485i	$0.884656\pi$
$360$	2.26674			0.119468
$361$	20.8141			1.09548
$362$	−23.3826			−1.22896
$363$	−10.8114	−	2.02802i	−0.567453	−	0.106443i
$364$	−0.817136	+	6.66410i	−0.0428296	+	0.349294i
$365$		−	15.6260i		−	0.817905i
$366$	−7.05901			−0.368980
$367$			19.2541i			1.00506i	0.864561	+	0.502529i	$0.167597\pi$
$367$			19.2541i			1.00506i	−0.864561	+	0.502529i	$0.832403\pi$
$368$	5.67627			0.295896
$369$	10.3306			0.537789
$370$	3.15688			0.164118
$371$	−1.22642	+	10.0020i	−0.0636727	+	0.519278i
$372$	3.00454			0.155778
$373$			29.4605i			1.52541i	0.646748	+	0.762704i	$0.276128\pi$
$373$			29.4605i			1.52541i	−0.646748	+	0.762704i	$0.723872\pi$
$374$	16.2175	+	19.5425i	0.838588	+	1.01052i
$375$	1.00000			0.0516398
$376$	−18.3649			−0.947097
$377$		−	7.92646i		−	0.408234i
$378$	−0.720920	+	5.87941i	−0.0370801	+	0.302404i
$379$	−32.0801			−1.64785			−0.823923	−	0.566701i	$-0.808219\pi$
$379$	−32.0801			−1.64785			−0.823923	+	0.566701i	$0.808219\pi$
$380$			19.0081i			0.975096i
$381$	4.72234			0.241933
$382$			27.4025i			1.40203i
$383$			1.37119i			0.0700644i	0.999386	+	0.0350322i	$0.0111534\pi$
$383$			1.37119i			0.0700644i	−0.999386	+	0.0350322i	$0.988847\pi$
$384$	15.8104			0.806820
$385$	7.38445	−	4.74025i	0.376346	−	0.241585i
$386$	15.0188			0.764436
$387$			10.0756i			0.512172i
$388$			53.2875i			2.70526i
$389$	4.19889			0.212892			0.106446	−	0.994318i	$-0.466053\pi$
$389$	4.19889			0.212892			0.106446	+	0.994318i	$0.466053\pi$
$390$		−	1.88598i		−	0.0955003i
$391$	20.4344			1.03341
$392$	−3.83356	+	15.3971i	−0.193624	+	0.777673i
$393$		−	9.88715i		−	0.498741i
$394$	16.1209			0.812159
$395$	14.3009			0.719556
$396$	−7.68856	+	6.38043i	−0.386365	+	0.320629i
$397$			4.12458i			0.207007i	0.994629	+	0.103503i	$0.0330052\pi$
$397$			4.12458i			0.207007i	−0.994629	+	0.103503i	$0.966995\pi$
$398$	−53.8411			−2.69881
$399$	−16.5702	−	2.03180i	−0.829546	−	0.101717i
$400$	0.950014			0.0475007
$401$	12.2122			0.609847			0.304923	−	0.952377i	$-0.401369\pi$
$401$	12.2122			0.609847			0.304923	+	0.952377i	$0.401369\pi$
$402$	−25.5539			−1.27451
$403$		−	0.840173i		−	0.0418520i
$404$	−2.11538			−0.105244
$405$		−	1.00000i		−	0.0496904i
$406$	6.78351	−	55.3225i	0.336660	−	2.74561i
$407$	−3.59879	+	2.98650i	−0.178386	+	0.148035i
$408$	7.75233			0.383797
$409$	1.39729			0.0690914			0.0345457	−	0.999403i	$-0.489002\pi$
$409$	1.39729			0.0690914			0.0345457	+	0.999403i	$0.489002\pi$
$410$	−23.1286			−1.14224
$411$			5.77144i			0.284684i
$412$		−	21.2651i		−	1.04765i
$413$	−28.2278	−	3.46122i	−1.38900	−	0.170316i
$414$			13.3770i			0.657443i
$415$			0.946456i			0.0464597i
$416$		−	5.61066i		−	0.275085i
$417$			9.94116i			0.486821i
$418$	−29.9208	−	36.0552i	−1.46347	−	1.76352i
$419$		−	13.6032i		−	0.664558i	−0.943181	−	0.332279i	$-0.892183\pi$
$419$		−	13.6032i		−	0.664558i	0.943181	−	0.332279i	$-0.107817\pi$
$420$	0.970024	−	7.91096i	0.0473323	−	0.386016i
$421$	19.9582			0.972703			0.486352	−	0.873763i	$-0.338327\pi$
$421$	19.9582			0.972703			0.486352	+	0.873763i	$0.338327\pi$
$422$	14.6368			0.712506
$423$			8.10188i			0.393927i
$424$			8.63338i			0.419274i
$425$	3.42003			0.165896
$426$	−9.49985			−0.460269
$427$	−1.01527	+	8.27994i	−0.0491322	+	0.400694i
$428$		−	31.9250i		−	1.54315i
$429$	1.78419	+	2.14999i	0.0861415	+	0.103802i
$430$		−	22.5578i		−	1.08783i
$431$			11.6976i			0.563454i	0.959495	+	0.281727i	$0.0909072\pi$
$431$			11.6976i			0.563454i	−0.959495	+	0.281727i	$0.909093\pi$
$432$		−	0.950014i		−	0.0457076i
$433$			22.6313i			1.08759i	0.839218	+	0.543796i	$0.183013\pi$
$433$			22.6313i			1.08759i	−0.839218	+	0.543796i	$0.816987\pi$
$434$	0.719025	−	5.86396i	0.0345143	−	0.281479i
$435$			9.40952i			0.451152i
$436$			25.8057i			1.23587i
$437$	−37.7009			−1.80348
$438$	34.9844			1.67162
$439$	−8.05202			−0.384302			−0.192151	−	0.981365i	$-0.561546\pi$
$439$	−8.05202			−0.384302			−0.192151	+	0.981365i	$0.561546\pi$
$440$	5.78531	−	4.80100i	0.275804	−	0.228879i
$441$	6.79263	+	1.69122i	0.323458	+	0.0805343i
$442$		−	6.45011i		−	0.306800i
$443$	−18.0248			−0.856384			−0.428192	−	0.903688i	$-0.640849\pi$
$443$	−18.0248			−0.856384			−0.428192	+	0.903688i	$0.640849\pi$
$444$			4.24770i			0.201587i
$445$	17.4593			0.827648
$446$	57.6592			2.73024
$447$	12.3780			0.585460
$448$	4.18982	−	34.1698i	0.197950	−	1.61437i
$449$	32.9988			1.55731			0.778655	−	0.627452i	$-0.215902\pi$
$449$	32.9988			1.55731			0.778655	+	0.627452i	$0.215902\pi$
$450$			2.23885i			0.105540i
$451$	26.3663	−	21.8803i	1.24154	−	1.03030i
$452$	4.57623			0.215248
$453$	13.3219			0.625917
$454$		−	17.5350i		−	0.822959i
$455$	−2.21218	−	0.271252i	−0.103709	−	0.0127165i
$456$	−14.3028			−0.669789
$457$		−	1.75226i		−	0.0819673i	−0.999160	−	0.0409836i	$-0.986951\pi$
$457$		−	1.75226i		−	0.0819673i	0.999160	−	0.0409836i	$-0.0130492\pi$
$458$	28.8049			1.34597
$459$		−	3.42003i		−	0.159633i
$460$		−	17.9992i		−	0.839218i
$461$	−29.6847			−1.38255			−0.691277	−	0.722589i	$-0.742952\pi$
$461$	−29.6847			−1.38255			−0.691277	+	0.722589i	$0.742952\pi$
$462$	10.6127	+	16.5327i	0.493748	+	0.769170i
$463$	19.0858			0.886994			0.443497	−	0.896276i	$-0.353738\pi$
$463$	19.0858			0.886994			0.443497	+	0.896276i	$0.353738\pi$
$464$			8.93918i			0.414991i
$465$			0.997372i			0.0462520i
$466$	38.4263			1.78007
$467$		−	7.19573i		−	0.332979i	−0.986043	−	0.166489i	$-0.946757\pi$
$467$		−	7.19573i		−	0.332979i	0.986043	−	0.166489i	$-0.0532431\pi$
$468$	2.53766			0.117303
$469$	−3.67531	+	29.9737i	−0.169710	+	1.38406i
$470$		−	18.1389i		−	0.836686i
$471$	−8.99722			−0.414570
$472$	−24.3652			−1.12150
$473$	21.3403	+	25.7155i	0.981228	+	1.18240i
$474$			32.0176i			1.47062i
$475$	−6.30984			−0.289515
$476$	3.31751	−	27.0557i	0.152058	−	1.24010i
$477$	3.80872			0.174389
$478$	−23.1598			−1.05930
$479$	−19.1149			−0.873382			−0.436691	−	0.899611i	$-0.643850\pi$
$479$	−19.1149			−0.873382			−0.436691	+	0.899611i	$0.643850\pi$
$480$			6.66043i			0.304005i
$481$	1.18780			0.0541592
$482$			17.9810i			0.819011i
$483$	15.6907	+	1.92395i	0.713950	+	0.0875429i
$484$	−6.10932	+	32.5690i	−0.277697	+	1.48041i
$485$	−17.6891			−0.803219
$486$	2.23885			0.101556
$487$	14.7143			0.666768			0.333384	−	0.942791i	$-0.391810\pi$
$487$	14.7143			0.666768			0.333384	+	0.942791i	$0.391810\pi$
$488$			7.14695i			0.323527i
$489$			1.25085i			0.0565655i
$490$	−15.2077	−	3.78639i	−0.687013	−	0.171052i
$491$			19.2562i			0.869022i	0.900667	+	0.434511i	$0.143079\pi$
$491$			19.2562i			0.869022i	−0.900667	+	0.434511i	$0.856921\pi$
$492$		−	31.1204i		−	1.40302i
$493$			32.1809i			1.44935i
$494$			11.9002i			0.535417i
$495$	−2.11802	−	2.55226i	−0.0951977	−	0.114715i
$496$			0.947517i			0.0425448i
$497$	−1.36632	+	11.1429i	−0.0612879	+	0.499830i
$498$	−2.11897			−0.0949535
$499$	−10.7689			−0.482081			−0.241040	−	0.970515i	$-0.577489\pi$
$499$	−10.7689			−0.482081			−0.241040	+	0.970515i	$0.577489\pi$
$500$		−	3.01246i		−	0.134721i
$501$		−	16.5043i		−	0.737360i
$502$	−60.7359			−2.71077
$503$	−8.00112			−0.356752			−0.178376	−	0.983962i	$-0.557084\pi$
$503$	−8.00112			−0.356752			−0.178376	+	0.983962i	$0.557084\pi$
$504$	5.95266	+	0.729901i	0.265152	+	0.0325124i
$505$		−	0.702211i		−	0.0312480i
$506$	28.3327	+	34.1415i	1.25954	+	1.51777i
$507$			12.2904i			0.545835i
$508$		−	14.2258i		−	0.631169i
$509$			7.68605i			0.340678i	0.985385	+	0.170339i	$0.0544863\pi$
$509$			7.68605i			0.340678i	−0.985385	+	0.170339i	$0.945514\pi$
$510$			7.65694i			0.339055i
$511$	5.03165	−	41.0353i	0.222587	−	1.81529i
$512$			10.6344i			0.469977i
$513$			6.30984i			0.278586i
$514$	51.6376			2.27764
$515$	7.05904			0.311059
$516$	30.3524			1.33619
$517$	17.1599	+	20.6781i	0.754692	+	0.909421i
$518$	8.29023	+	1.01653i	0.364252	+	0.0446637i
$519$		−	19.4351i		−	0.853106i
$520$	−1.90948			−0.0837360
$521$		−	41.8300i		−	1.83261i	−0.400486	−	0.916303i	$-0.631159\pi$
$521$		−	41.8300i		−	1.83261i	0.400486	−	0.916303i	$-0.368841\pi$
$522$	−21.0665			−0.922057
$523$	8.26292			0.361312			0.180656	−	0.983546i	$-0.442178\pi$
$523$	8.26292			0.361312			0.180656	+	0.983546i	$0.442178\pi$
$524$	−29.7846			−1.30115
$525$	2.62608	+	0.322004i	0.114612	+	0.0140534i
$526$	5.57561			0.243108
$527$			3.41104i			0.148587i
$528$	−2.01214	−	2.42468i	−0.0875674	−	0.105521i
$529$	12.6998			0.552164
$530$	−8.52715			−0.370396
$531$			10.7490i			0.466467i
$532$	−6.12070	+	49.9169i	−0.265366	+	2.16417i
$533$	−8.70235			−0.376941
$534$			39.0887i			1.69153i
$535$	10.5977			0.458177
$536$			25.8723i			1.11751i
$537$		−	15.1145i		−	0.652240i
$538$	10.7137			0.461902
$539$	20.9186	−	10.0705i	0.901026	−	0.433766i
$540$	−3.01246			−0.129636
$541$		−	22.0864i		−	0.949569i	−0.880102	−	0.474784i	$-0.842526\pi$
$541$		−	22.0864i		−	0.949569i	0.880102	−	0.474784i	$-0.157474\pi$
$542$		−	28.9200i		−	1.24222i
$543$	10.4440			0.448196
$544$			22.7789i			0.976635i
$545$	−8.56633			−0.366941
$546$	0.607294	−	4.95274i	0.0259898	−	0.211958i
$547$			5.38070i			0.230062i	0.993362	+	0.115031i	$0.0366967\pi$
$547$			5.38070i			0.230062i	−0.993362	+	0.115031i	$0.963303\pi$
$548$	17.3862			0.742702
$549$	3.15296			0.134565
$550$	4.74192	+	5.71412i	0.202196	+	0.243651i
$551$		−	59.3726i		−	2.52936i
$552$	13.5436			0.576455
$553$	37.5553	+	4.60495i	1.59702	+	0.195822i
$554$	13.0189			0.553121
$555$	−1.41004			−0.0598530
$556$	29.9473			1.27005
$557$		−	8.75524i		−	0.370971i	−0.982647	−	0.185486i	$-0.940614\pi$
$557$		−	8.75524i		−	0.370971i	0.982647	−	0.185486i	$-0.0593858\pi$
$558$	−2.23297			−0.0945291
$559$		−	8.48757i		−	0.358986i
$560$	2.49482	+	0.305909i	0.105425	+	0.0129270i
$561$	−7.24368	−	8.72879i	−0.305828	−	0.368530i
$562$	−5.54277			−0.233808
$563$	16.7749			0.706977			0.353488	−	0.935439i	$-0.384995\pi$
$563$	16.7749			0.706977			0.353488	+	0.935439i	$0.384995\pi$
$564$	24.4066			1.02770
$565$			1.51910i			0.0639092i
$566$			60.2669i			2.53321i
$567$	0.322004	−	2.62608i	0.0135229	−	0.110285i
$568$			9.61820i			0.403571i
$569$		−	11.1514i		−	0.467491i	−0.972298	−	0.233745i	$-0.924902\pi$
$569$		−	11.1514i		−	0.467491i	0.972298	−	0.233745i	$-0.0750982\pi$
$570$		−	14.1268i		−	0.591706i
$571$			11.1466i			0.466469i	0.972420	+	0.233235i	$0.0749310\pi$
$571$			11.1466i			0.466469i	−0.972420	+	0.233235i	$0.925069\pi$
$572$	6.47675	−	5.37479i	0.270806	−	0.224731i
$573$		−	12.2395i		−	0.511314i
$574$	−60.7378	−	7.44752i	−2.53515	−	0.310854i
$575$	5.97493			0.249172
$576$	−13.0117			−0.542153
$577$		−	18.4249i		−	0.767038i	−0.923533	−	0.383519i	$-0.874712\pi$
$577$		−	18.4249i		−	0.767038i	0.923533	−	0.383519i	$-0.125288\pi$
$578$		−	11.8735i		−	0.493873i
$579$	−6.70826			−0.278786
$580$	28.3458			1.17700
$581$	−0.304763	+	2.48547i	−0.0126437	+	0.103115i
$582$		−	39.6032i		−	1.64160i
$583$	9.72082	−	8.06692i	0.402595	−	0.334098i
$584$		−	35.4202i		−	1.46570i
$585$			0.842387i			0.0348284i
$586$			13.2751i			0.548391i
$587$			14.8917i			0.614645i	0.951605	+	0.307323i	$0.0994331\pi$
$587$			14.8917i			0.614645i	−0.951605	+	0.307323i	$0.900567\pi$
$588$	5.09473	−	20.4625i	0.210103	−	0.843859i
$589$		−	6.29326i		−	0.259309i
$590$		−	24.0654i		−	0.990757i
$591$	−7.20052			−0.296190
$592$	−1.33956			−0.0550557
$593$	15.1514			0.622195			0.311098	−	0.950378i	$-0.399303\pi$
$593$	15.1514			0.622195			0.311098	+	0.950378i	$0.399303\pi$
$594$	5.71412	−	4.74192i	0.234453	−	0.194563i
$595$	8.98128	+	1.10126i	0.368197	+	0.0451474i
$596$		−	37.2882i		−	1.52739i
$597$	24.0485			0.984241
$598$		−	11.2686i		−	0.460807i
$599$	38.6892			1.58080			0.790398	−	0.612593i	$-0.209874\pi$
$599$	38.6892			1.58080			0.790398	+	0.612593i	$0.209874\pi$
$600$	2.26674			0.0925394
$601$	−40.7993			−1.66424			−0.832118	−	0.554598i	$-0.812872\pi$
$601$	−40.7993			−1.66424			−0.832118	+	0.554598i	$0.812872\pi$
$602$	7.26371	−	59.2387i	0.296047	−	2.41439i
$603$	11.4139			0.464808
$604$		−	40.1316i		−	1.63293i
$605$	−10.8114	−	2.02802i	−0.439547	−	0.0824507i
$606$	1.57215			0.0638641
$607$	−8.74411			−0.354912			−0.177456	−	0.984129i	$-0.556787\pi$
$607$	−8.74411			−0.354912			−0.177456	+	0.984129i	$0.556787\pi$
$608$		−	42.0262i		−	1.70439i
$609$	−3.02991	+	24.7102i	−0.122778	+	1.00131i
$610$	−7.05901			−0.285811
$611$		−	6.82492i		−	0.276107i
$612$	−10.3027			−0.416462
$613$		−	20.0772i		−	0.810911i	−0.914115	−	0.405455i	$-0.867113\pi$
$613$		−	20.0772i		−	0.810911i	0.914115	−	0.405455i	$-0.132887\pi$
$614$			15.9629i			0.644211i
$615$	10.3306			0.416569
$616$	16.7386	−	10.7449i	0.674419	−	0.432925i
$617$	−2.92259			−0.117659			−0.0588296	−	0.998268i	$-0.518737\pi$
$617$	−2.92259			−0.117659			−0.0588296	+	0.998268i	$0.518737\pi$
$618$			15.8042i			0.635736i
$619$			33.9078i			1.36287i	0.731880	+	0.681434i	$0.238643\pi$
$619$			33.9078i			1.36287i	−0.731880	+	0.681434i	$0.761357\pi$
$620$	3.00454			0.120665
$621$		−	5.97493i		−	0.239766i
$622$	77.1144			3.09200
$623$	45.8494	+	5.62195i	1.83692	+	0.225239i
$624$			0.800280i			0.0320368i
$625$	1.00000			0.0400000
$626$	14.2536			0.569690
$627$	13.3643	+	16.1043i	0.533720	+	0.643145i
$628$			27.1037i			1.08156i
$629$	−4.82239			−0.192281
$630$	−0.720920	+	5.87941i	−0.0287221	+	0.234241i
$631$	3.05134			0.121472			0.0607360	−	0.998154i	$-0.480655\pi$
$631$	3.05134			0.121472			0.0607360	+	0.998154i	$0.480655\pi$
$632$	32.4164			1.28946
$633$	−6.53762			−0.259847
$634$		−	37.9068i		−	1.50547i
$635$	4.72234			0.187400
$636$		−	11.4736i		−	0.454958i
$637$	−5.72202	−	1.42466i	−0.226715	−	0.0564472i
$638$	−53.7672	+	44.6192i	−2.12866	+	1.76649i
$639$	4.24318			0.167858
$640$	15.8104			0.624960
$641$	42.3257			1.67176			0.835882	−	0.548910i	$-0.184957\pi$
$641$	42.3257			1.67176			0.835882	+	0.548910i	$0.184957\pi$
$642$			23.7266i			0.936413i
$643$		−	22.3867i		−	0.882847i	−0.897299	−	0.441423i	$-0.854474\pi$
$643$		−	22.3867i		−	0.882847i	0.897299	−	0.441423i	$-0.145526\pi$
$644$	5.79582	−	47.2675i	0.228387	−	1.86260i
$645$			10.0756i			0.396727i
$646$		−	48.3141i		−	1.90089i
$647$		−	7.10723i		−	0.279414i	−0.990193	−	0.139707i	$-0.955384\pi$
$647$		−	7.10723i		−	0.279414i	0.990193	−	0.139707i	$-0.0446161\pi$
$648$		−	2.26674i		−	0.0890461i
$649$	22.7665	+	27.4342i	0.893665	+	1.07689i
$650$		−	1.88598i		−	0.0739742i
$651$	−0.321158	+	2.61918i	−0.0125872	+	0.102654i
$652$	3.76814			0.147572
$653$	22.3253			0.873655			0.436827	−	0.899545i	$-0.356102\pi$
$653$	22.3253			0.873655			0.436827	+	0.899545i	$0.356102\pi$
$654$		−	19.1787i		−	0.749948i
$655$		−	9.88715i		−	0.386323i
$656$	9.81420			0.383180
$657$	−15.6260			−0.609630
$658$	5.84081	−	47.6343i	0.227698	−	1.85698i
$659$			39.4137i			1.53534i	0.640846	+	0.767670i	$0.278584\pi$
$659$			39.4137i			1.53534i	−0.640846	+	0.767670i	$0.721416\pi$
$660$	−7.68856	+	6.38043i	−0.299277	+	0.248358i
$661$		−	35.0721i		−	1.36414i	−0.731285	−	0.682072i	$-0.761079\pi$
$661$		−	35.0721i		−	1.36414i	0.731285	−	0.682072i	$-0.238921\pi$
$662$		−	49.8090i		−	1.93588i
$663$			2.88099i			0.111888i
$664$			2.14537i			0.0832566i
$665$	−16.5702	−	2.03180i	−0.642564	−	0.0787896i
$666$		−	3.15688i		−	0.122327i
$667$			56.2212i			2.17690i
$668$	−49.7186			−1.92367
$669$	−25.7539			−0.995705
$670$	−25.5539			−0.987234
$671$	8.04716	−	6.67802i	0.310657	−	0.257802i
$672$	−2.14469	+	17.4908i	−0.0827330	+	0.674724i
$673$		−	19.1635i		−	0.738697i	−0.929291	−	0.369349i	$-0.879581\pi$
$673$		−	19.1635i		−	0.738697i	0.929291	−	0.369349i	$-0.120419\pi$
$674$	35.2785			1.35888
$675$		−	1.00000i		−	0.0384900i
$676$	37.0243			1.42401
$677$	−36.5750			−1.40569			−0.702846	−	0.711342i	$-0.748088\pi$
$677$	−36.5750			−1.40569			−0.702846	+	0.711342i	$0.748088\pi$
$678$	−3.40105			−0.130616
$679$	−46.4529	−	5.69595i	−1.78270	−	0.218590i
$680$	7.75233			0.297288
$681$			7.83215i			0.300129i
$682$	−5.69910	+	4.72946i	−0.218230	+	0.181100i
$683$	20.6810			0.791337			0.395668	−	0.918393i	$-0.370513\pi$
$683$	20.6810			0.791337			0.395668	+	0.918393i	$0.370513\pi$
$684$	19.0081			0.726794
$685$			5.77144i			0.220515i
$686$	−38.7174	−	14.8403i	−1.47824	−	0.566606i
$687$	−12.8659			−0.490866
$688$			9.57197i			0.364928i
$689$	−3.20841			−0.122231
$690$			13.3770i			0.509253i
$691$			11.4257i			0.434655i	0.976099	+	0.217327i	$0.0697339\pi$
$691$			11.4257i			0.434655i	−0.976099	+	0.217327i	$0.930266\pi$
$692$	−58.5474			−2.22564
$693$	−4.74025	−	7.38445i	−0.180067	−	0.280512i
$694$	28.4202			1.07881
$695$			9.94116i			0.377090i
$696$			21.3290i			0.808473i
$697$	35.3309			1.33825
$698$			48.3772i			1.83111i
$699$	−17.1634			−0.649180
$700$	0.970024	−	7.91096i	0.0366635	−	0.299006i
$701$		−	7.53673i		−	0.284658i	−0.989819	−	0.142329i	$-0.954541\pi$
$701$		−	7.53673i		−	0.284658i	0.989819	−	0.142329i	$-0.0454592\pi$
$702$	−1.88598			−0.0711817
$703$	8.89715			0.335563
$704$	−33.2091	+	27.5589i	−1.25162	+	1.03867i
$705$			8.10188i			0.305135i
$706$	18.3230			0.689595
$707$	0.226115	−	1.84407i	0.00850393	−	0.0693532i
$708$	32.3809			1.21695
$709$	10.9203			0.410121			0.205061	−	0.978749i	$-0.434261\pi$
$709$	10.9203			0.410121			0.205061	+	0.978749i	$0.434261\pi$
$710$	−9.49985			−0.356523
$711$		−	14.3009i		−	0.536325i
$712$	39.5756			1.48316
$713$			5.95923i			0.223175i
$714$	−2.46557	+	20.1078i	−0.0922715	+	0.752514i
$715$	1.78419	+	2.14999i	0.0667249	+	0.0804050i
$716$	−45.5319			−1.70161
$717$	10.3445			0.386322
$718$	−30.0746			−1.12238
$719$			13.1791i			0.491496i	0.969334	+	0.245748i	$0.0790336\pi$
$719$			13.1791i			0.491496i	−0.969334	+	0.245748i	$0.920966\pi$
$720$		−	0.950014i		−	0.0354049i
$721$	18.5376	+	2.27304i	0.690378	+	0.0846525i
$722$			46.5997i			1.73426i
$723$		−	8.03134i		−	0.298689i
$724$		−	31.4622i		−	1.16928i
$725$			9.40952i			0.349461i
$726$	4.54044	−	24.2052i	0.168511	−	0.898339i
$727$			32.0278i			1.18784i	0.804522	+	0.593922i	$0.202421\pi$
$727$			32.0278i			1.18784i	−0.804522	+	0.593922i	$0.797579\pi$
$728$	−5.01444	−	0.614859i	−0.185848	−	0.0227882i
$729$	−1.00000			−0.0370370
$730$	34.9844			1.29483
$731$			34.4589i			1.27451i
$732$		−	9.49816i		−	0.351062i
$733$	48.4494			1.78952			0.894759	−	0.446549i	$-0.147347\pi$
$733$	48.4494			1.78952			0.894759	+	0.446549i	$0.147347\pi$
$734$	−43.1071			−1.59111
$735$	6.79263	+	1.69122i	0.250550	+	0.0623816i
$736$			39.7956i			1.46688i
$737$	29.1311	−	24.1747i	1.07306	−	0.890487i
$738$			23.1286i			0.851377i
$739$		−	29.2845i		−	1.07725i	−0.842546	−	0.538624i	$-0.818944\pi$
$739$		−	29.2845i		−	1.07725i	0.842546	−	0.538624i	$-0.181056\pi$
$740$			4.24770i			0.156149i
$741$		−	5.31533i		−	0.195263i
$742$	−22.3930	−	2.74578i	−0.822073	−	0.100801i
$743$			18.2116i			0.668118i	0.942552	+	0.334059i	$0.108419\pi$
$743$			18.2116i			0.668118i	−0.942552	+	0.334059i	$0.891581\pi$
$744$			2.26079i			0.0828844i
$745$	12.3780			0.453495
$746$	−65.9577			−2.41488
$747$	0.946456			0.0346290
$748$	−26.2951	+	21.8213i	−0.961444	+	0.797865i
$749$	27.8303	+	3.41249i	1.01690	+	0.124690i
$750$			2.23885i			0.0817513i
$751$	−31.6089			−1.15343			−0.576713	−	0.816947i	$-0.695665\pi$
$751$	−31.6089			−1.15343			−0.576713	+	0.816947i	$0.695665\pi$
$752$			7.69690i			0.280677i
$753$	27.1281			0.988604
$754$	17.7462			0.646278
$755$	13.3219			0.484833
$756$	−7.91096	−	0.970024i	−0.287719	−	0.0352794i
$757$	−31.2329			−1.13518			−0.567589	−	0.823312i	$-0.692124\pi$
$757$	−31.2329			−1.13518			−0.567589	+	0.823312i	$0.692124\pi$
$758$		−	71.8227i		−	2.60872i
$759$	−12.6550	−	15.2495i	−0.459347	−	0.553524i
$760$	−14.3028			−0.518817
$761$	−47.1414			−1.70887			−0.854437	−	0.519556i	$-0.826097\pi$
$761$	−47.1414			−1.70887			−0.854437	+	0.519556i	$0.826097\pi$
$762$			10.5726i			0.383005i
$763$	−22.4959	−	2.75839i	−0.814406	−	0.0998605i
$764$	−36.8711			−1.33395
$765$		−	3.42003i		−	0.123651i
$766$	−3.06989			−0.110920
$767$		−	9.05481i		−	0.326950i
$768$			9.37372i			0.338245i
$769$	−3.27088			−0.117951			−0.0589756	−	0.998259i	$-0.518783\pi$
$769$	−3.27088			−0.117951			−0.0589756	+	0.998259i	$0.518783\pi$
$770$	10.6127	+	16.5327i	0.382456	+	0.595796i
$771$	−23.0643			−0.830641
$772$			20.2083i			0.727314i
$773$			0.757839i			0.0272576i	0.999907	+	0.0136288i	$0.00433831\pi$
$773$			0.757839i			0.0272576i	−0.999907	+	0.0136288i	$0.995662\pi$
$774$	−22.5578			−0.810823
$775$			0.997372i			0.0358266i
$776$	−40.0965			−1.43938
$777$	−3.70289	−	0.454040i	−0.132841	−	0.0162886i
$778$			9.40068i			0.337031i
$779$	−65.1843			−2.33547
$780$	2.53766			0.0908627
$781$	10.8297	−	8.98712i	0.387517	−	0.321585i
$782$			45.7497i			1.63600i
$783$	9.40952			0.336269
$784$	6.45309	+	1.60668i	0.230468	+	0.0573815i
$785$	−8.99722			−0.321124
$786$	22.1359			0.789560
$787$	−31.1745			−1.11125			−0.555626	−	0.831433i	$-0.687521\pi$
$787$	−31.1745			−1.11125			−0.555626	+	0.831433i	$0.687521\pi$
$788$			21.6912i			0.772719i
$789$	−2.49039			−0.0886602
$790$			32.0176i			1.13913i
$791$	−0.489158	+	3.98929i	−0.0173924	+	0.141843i
$792$	−4.80100	−	5.78531i	−0.170596	−	0.205572i
$793$	−2.65601			−0.0943178
$794$	−9.23431			−0.327714
$795$	3.80872			0.135081
$796$		−	72.4452i		−	2.56775i
$797$		−	15.7552i		−	0.558079i	−0.960280	−	0.279040i	$-0.909984\pi$
$797$		−	15.7552i		−	0.558079i	0.960280	−	0.279040i	$-0.0900161\pi$
$798$	4.54889	−	37.0981i	0.161029	−	1.31326i
$799$			27.7087i			0.980263i
$800$			6.66043i			0.235482i
$801$		−	17.4593i		−	0.616892i
$802$			27.3412i			0.965453i
$803$	−39.8817	+	33.0962i	−1.40739	+	1.16794i
$804$		−	34.3837i		−	1.21262i
$805$	15.6907	+	1.92395i	0.553023	+	0.0678104i
$806$	1.88102			0.0662562
$807$	−4.78537			−0.168453
$808$		−	1.59173i		−	0.0559970i
$809$		−	30.3467i		−	1.06693i	−0.845821	−	0.533467i	$-0.820889\pi$
$809$		−	30.3467i		−	1.06693i	0.845821	−	0.533467i	$-0.179111\pi$
$810$	2.23885			0.0786652
$811$	18.4970			0.649516			0.324758	−	0.945797i	$-0.394717\pi$
$811$	18.4970			0.649516			0.324758	+	0.945797i	$0.394717\pi$
$812$	74.4384	+	9.12746i	2.61228	+	0.320311i
$813$			12.9173i			0.453030i
$814$	−6.68632	−	8.05717i	−0.234355	−	0.282404i
$815$			1.25085i			0.0438154i
$816$		−	3.24908i		−	0.113740i
$817$		−	63.5755i		−	2.22423i
$818$			3.12832i			0.109379i
$819$	−0.271252	+	2.21218i	−0.00947832	+	0.0772998i
$820$		−	31.1204i		−	1.08677i
$821$			43.9533i			1.53398i	0.641659	+	0.766990i	$0.278246\pi$
$821$			43.9533i			1.53398i	−0.641659	+	0.766990i	$0.721754\pi$
$822$	−12.9214			−0.450685
$823$	−37.6212			−1.31139			−0.655697	−	0.755024i	$-0.727625\pi$
$823$	−37.6212			−1.31139			−0.655697	+	0.755024i	$0.727625\pi$
$824$	16.0010			0.557422
$825$	−2.11802	−	2.55226i	−0.0737398	−	0.0888581i
$826$	7.74916	−	63.1978i	0.269628	−	2.19893i
$827$		−	43.1499i		−	1.50047i	−0.661171	−	0.750235i	$-0.729940\pi$
$827$		−	43.1499i		−	1.50047i	0.661171	−	0.750235i	$-0.270060\pi$
$828$	−17.9992			−0.625516
$829$		−	5.19313i		−	0.180365i	−0.995925	−	0.0901825i	$-0.971255\pi$
$829$		−	5.19313i		−	0.180365i	0.995925	−	0.0901825i	$-0.0287450\pi$
$830$	−2.11897			−0.0735507
$831$	−5.81500			−0.201720
$832$	10.9609			0.380000
$833$	23.2310	+	5.78402i	0.804906	+	0.200404i
$834$	−22.2568			−0.770689
$835$		−	16.5043i		−	0.571156i
$836$	48.5136	−	40.2595i	1.67788	−	1.39240i
$837$	0.997372			0.0344742
$838$	30.4554			1.05207
$839$		−	13.4423i		−	0.464080i	−0.972706	−	0.232040i	$-0.925460\pi$
$839$		−	13.4423i		−	0.464080i	0.972706	−	0.232040i	$-0.0745401\pi$
$840$	5.95266	+	0.729901i	0.205386	+	0.0251840i
$841$	−59.5392			−2.05307
$842$			44.6835i			1.53989i
$843$	2.47572			0.0852683
$844$			19.6943i			0.677905i
$845$			12.2904i			0.422802i
$846$	−18.1389			−0.623629
$847$	−27.7387	−	8.80708i	−0.953113	−	0.302615i
$848$	3.61833			0.124254
$849$		−	26.9187i		−	0.923847i
$850$			7.65694i			0.262631i
$851$	−8.42491			−0.288802
$852$		−	12.7824i		−	0.437918i
$853$	−4.82906			−0.165344			−0.0826719	−	0.996577i	$-0.526345\pi$
$853$	−4.82906			−0.165344			−0.0826719	+	0.996577i	$0.526345\pi$
$854$	−18.5376	−	2.27303i	−0.634342	−	0.0777815i
$855$			6.30984i			0.215792i
$856$	24.0222			0.821060
$857$	5.94945			0.203229			0.101615	−	0.994824i	$-0.467599\pi$
$857$	5.94945			0.203229			0.101615	+	0.994824i	$0.467599\pi$
$858$	−4.81350	+	3.99454i	−0.164330	+	0.136371i
$859$			19.8001i			0.675570i	0.941223	+	0.337785i	$0.109678\pi$
$859$			19.8001i			0.675570i	−0.941223	+	0.337785i	$0.890322\pi$
$860$	30.3524			1.03501
$861$	27.1290	+	3.32649i	0.924553	+	0.113367i
$862$	−26.1892			−0.892007
$863$	9.47598			0.322566			0.161283	−	0.986908i	$-0.448437\pi$
$863$	9.47598			0.322566			0.161283	+	0.986908i	$0.448437\pi$
$864$	6.66043			0.226592
$865$		−	19.4351i		−	0.660813i
$866$	−50.6681			−1.72177
$867$			5.30340i			0.180113i
$868$	7.89017	+	0.967474i	0.267810	+	0.0328382i
$869$	−30.2895	−	36.4995i	−1.02750	−	1.23816i
$870$	−21.0665			−0.714222
$871$	−9.61488			−0.325788
$872$	−19.4177			−0.657565
$873$			17.6891i			0.598684i
$874$		−	84.4066i		−	2.85510i
$875$	2.62608	+	0.322004i	0.0887778	+	0.0108857i
$876$			47.0728i			1.59044i
$877$		−	35.3287i		−	1.19297i	−0.802626	−	0.596483i	$-0.796564\pi$
$877$		−	35.3287i		−	1.19297i	0.802626	−	0.596483i	$-0.203436\pi$
$878$		−	18.0273i		−	0.608391i
$879$		−	5.92944i		−	0.199995i
$880$	−2.01214	−	2.42468i	−0.0678294	−	0.0817359i
$881$		−	26.0042i		−	0.876105i	−0.898949	−	0.438052i	$-0.855668\pi$
$881$		−	26.0042i		−	0.876105i	0.898949	−	0.438052i	$-0.144332\pi$
$882$	−3.78639	+	15.2077i	−0.127494	+	0.512069i
$883$	−9.50807			−0.319972			−0.159986	−	0.987119i	$-0.551145\pi$
$883$	−9.50807			−0.319972			−0.159986	+	0.987119i	$0.551145\pi$
$884$	8.67886			0.291902
$885$			10.7490i			0.361323i
$886$		−	40.3548i		−	1.35575i
$887$	−15.5638			−0.522582			−0.261291	−	0.965260i	$-0.584148\pi$
$887$	−15.5638			−0.522582			−0.261291	+	0.965260i	$0.584148\pi$
$888$	−3.19621			−0.107258
$889$	12.4012	+	1.52061i	0.415925	+	0.0509997i
$890$			39.0887i			1.31026i
$891$	−2.55226	+	2.11802i	−0.0855038	+	0.0709562i
$892$			77.5826i			2.59766i
$893$		−	51.1216i		−	1.71072i
$894$			27.7125i			0.926846i
$895$		−	15.1145i		−	0.505223i
$896$	41.5193	+	5.09101i	1.38706	+	0.170079i
$897$			5.03320i			0.168054i
$898$			73.8795i			2.46539i
$899$	−9.38479			−0.313000
$900$	−3.01246			−0.100415
$901$	13.0259			0.433956
$902$	48.9868	+	59.0302i	1.63108	+	1.96549i
$903$	−3.24439	+	26.4594i	−0.107967	+	0.880514i
$904$			3.44342i			0.114526i
$905$	10.4440			0.347171
$906$			29.8257i			0.990894i
$907$	4.27141			0.141830			0.0709149	−	0.997482i	$-0.477408\pi$
$907$	4.27141			0.141830			0.0709149	+	0.997482i	$0.477408\pi$
$908$	23.5940			0.782995
$909$	−0.702211			−0.0232909
$910$	0.607294	−	4.95274i	0.0201316	−	0.164182i
$911$	−41.7023			−1.38166			−0.690829	−	0.723018i	$-0.742754\pi$
$911$	−41.7023			−1.38166			−0.690829	+	0.723018i	$0.742754\pi$
$912$			5.99444i			0.198496i
$913$	2.41560	−	2.00461i	0.0799446	−	0.0663429i
$914$	3.92305			0.129763
$915$	3.15296			0.104234
$916$			38.7581i			1.28060i
$917$	3.18370	−	25.9645i	0.105135	−	0.857423i
$918$	7.65694			0.252717
$919$		−	28.0644i		−	0.925758i	−0.886421	−	0.462879i	$-0.846816\pi$
$919$		−	28.0644i		−	0.925758i	0.886421	−	0.462879i	$-0.153184\pi$
$920$	13.5436			0.446520
$921$		−	7.12996i		−	0.234940i
$922$		−	66.4597i		−	2.18873i
$923$	−3.57440			−0.117653
$924$	−22.2453	+	14.2798i	−0.731818	+	0.469771i
$925$	−1.41004			−0.0463620
$926$			42.7304i			1.40421i
$927$		−	7.05904i		−	0.231849i
$928$	−62.6714			−2.05729
$929$			2.91014i			0.0954785i	0.998860	+	0.0477392i	$0.0152017\pi$
$929$			2.91014i			0.0954785i	−0.998860	+	0.0477392i	$0.984798\pi$
$930$	−2.23297			−0.0732219
$931$	−42.8604	−	10.6713i	−1.40469	−	0.349739i
$932$			51.7040i			1.69362i
$933$	−34.4437			−1.12764
$934$	16.1102			0.527141
$935$	−7.24368	−	8.72879i	−0.236894	−	0.285462i
$936$			1.90948i			0.0624131i
$937$	−25.5190			−0.833669			−0.416835	−	0.908982i	$-0.636861\pi$
$937$	−25.5190			−0.833669			−0.416835	+	0.908982i	$0.636861\pi$
$938$	−67.1067	−	8.22847i	−2.19111	−	0.268669i
$939$	−6.36649			−0.207763
$940$	24.4066			0.796055
$941$	28.3781			0.925099			0.462550	−	0.886593i	$-0.346935\pi$
$941$	28.3781			0.925099			0.462550	+	0.886593i	$0.346935\pi$
$942$		−	20.1434i		−	0.656309i
$943$	61.7245			2.01003
$944$			10.2117i			0.332362i
$945$	0.322004	−	2.62608i	0.0104748	−	0.0854265i
$946$	−57.5733	+	47.7778i	−1.87187	+	1.55339i
$947$	−37.1288			−1.20652			−0.603262	−	0.797543i	$-0.706133\pi$
$947$	−37.1288			−1.20652			−0.603262	+	0.797543i	$0.706133\pi$
$948$	−43.0808			−1.39920
$949$	13.1632			0.427295
$950$		−	14.1268i		−	0.458334i
$951$			16.9314i			0.549038i
$952$	20.3583	+	2.49628i	0.659815	+	0.0809050i
$953$		−	4.50804i		−	0.146030i	−0.997331	−	0.0730148i	$-0.976738\pi$
$953$		−	4.50804i		−	0.146030i	0.997331	−	0.0730148i	$-0.0232620\pi$
$954$			8.52715i			0.276077i
$955$		−	12.2395i		−	0.396062i
$956$		−	31.1623i		−	1.00786i
$957$	24.0155	−	19.9295i	0.776311	−	0.644230i
$958$		−	42.7954i		−	1.38266i
$959$	−1.85843	+	15.1563i	−0.0600117	+	0.489422i
$960$	−13.0117			−0.419950
$961$	30.0052			0.967911
$962$			2.65932i			0.0857398i
$963$		−	10.5977i		−	0.341505i
$964$	−24.1941			−0.779239
$965$	−6.70826			−0.215946
$966$	−4.30744	+	35.1291i	−0.138590	+	1.13026i
$967$		−	2.23412i		−	0.0718443i	−0.999355	−	0.0359222i	$-0.988563\pi$
$967$		−	2.23412i		−	0.0718443i	0.999355	−	0.0359222i	$-0.0114368\pi$
$968$	−24.5067	−	4.59700i	−0.787677	−	0.147753i
$969$			21.5798i			0.693244i
$970$		−	39.6032i		−	1.27158i
$971$			38.0083i			1.21974i	0.792500	+	0.609872i	$0.208779\pi$
$971$			38.0083i			1.21974i	−0.792500	+	0.609872i	$0.791221\pi$
$972$			3.01246i			0.0966246i
$973$	−3.20109	+	26.1063i	−0.102622	+	0.836930i
$974$			32.9431i			1.05556i
$975$			0.842387i			0.0269780i
$976$	2.99536			0.0958790
$977$	−6.02399			−0.192725			−0.0963623	−	0.995346i	$-0.530721\pi$
$977$	−6.02399			−0.192725			−0.0963623	+	0.995346i	$0.530721\pi$
$978$	−2.80047			−0.0895492
$979$	−36.9790	−	44.5605i	−1.18185	−	1.42416i
$980$	5.09473	−	20.4625i	0.162745	−	0.653651i
$981$			8.56633i			0.273502i
$982$	−43.1119			−1.37576
$983$		−	11.4819i		−	0.366214i	−0.983093	−	0.183107i	$-0.941384\pi$
$983$		−	11.4819i		−	0.366214i	0.983093	−	0.183107i	$-0.0586155\pi$
$984$	23.4168			0.746500
$985$	−7.20052			−0.229427
$986$	−72.0482			−2.29448
$987$	−2.60884	+	21.2762i	−0.0830403	+	0.677230i
$988$	−16.0122			−0.509416
$989$			60.2011i			1.91428i
$990$	5.71412	−	4.74192i	0.181607	−	0.150708i
$991$	42.8247			1.36037			0.680185	−	0.733040i	$-0.261899\pi$
$991$	42.8247			1.36037			0.680185	+	0.733040i	$0.261899\pi$
$992$	−6.64292			−0.210913
$993$			22.2475i			0.706004i
$994$	−24.9474	−	3.05899i	−0.791284	−	0.0970254i
$995$	24.0485			0.762390
$996$		−	2.85116i		−	0.0903424i
$997$	−19.3516			−0.612873			−0.306436	−	0.951891i	$-0.599137\pi$
$997$	−19.3516			−0.612873			−0.306436	+	0.951891i	$0.599137\pi$
$998$		−	24.1099i		−	0.763185i
$999$			1.41004i			0.0446118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.d.76.18	yes	32
7.6	odd	2	inner	1155.2.i.d.76.16	yes	32
11.10	odd	2	inner	1155.2.i.d.76.15	✓	32
77.76	even	2	inner	1155.2.i.d.76.17	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.d.76.15	✓	32	11.10	odd	2	inner
1155.2.i.d.76.16	yes	32	7.6	odd	2	inner
1155.2.i.d.76.17	yes	32	77.76	even	2	inner
1155.2.i.d.76.18	yes	32	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.23885i q^{2} -1.00000i q^{3} -3.01246 q^{4} -1.00000i q^{5} +2.23885 q^{6} +(0.322004 - 2.62608i) q^{7} -2.26674i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.23885i q^{2} -1.00000i q^{3} -3.01246 q^{4} -1.00000i q^{5} +2.23885 q^{6} +(0.322004 - 2.62608i) q^{7} -2.26674i q^{8} -1.00000 q^{9} +2.23885 q^{10} +(-2.55226 + 2.11802i) q^{11} +3.01246i q^{12} +0.842387 q^{13} +(5.87941 + 0.720920i) q^{14} -1.00000 q^{15} -0.950014 q^{16} -3.42003 q^{17} -2.23885i q^{18} +6.30984 q^{19} +3.01246i q^{20} +(-2.62608 - 0.322004i) q^{21} +(-4.74192 - 5.71412i) q^{22} -5.97493 q^{23} -2.26674 q^{24} -1.00000 q^{25} +1.88598i q^{26} +1.00000i q^{27} +(-0.970024 + 7.91096i) q^{28} -9.40952i q^{29} -2.23885i q^{30} -0.997372i q^{31} -6.66043i q^{32} +(2.11802 + 2.55226i) q^{33} -7.65694i q^{34} +(-2.62608 - 0.322004i) q^{35} +3.01246 q^{36} +1.41004 q^{37} +14.1268i q^{38} -0.842387i q^{39} -2.26674 q^{40} -10.3306 q^{41} +(0.720920 - 5.87941i) q^{42} -10.0756i q^{43} +(7.68856 - 6.38043i) q^{44} +1.00000i q^{45} -13.3770i q^{46} -8.10188i q^{47} +0.950014i q^{48} +(-6.79263 - 1.69122i) q^{49} -2.23885i q^{50} +3.42003i q^{51} -2.53766 q^{52} -3.80872 q^{53} -2.23885 q^{54} +(2.11802 + 2.55226i) q^{55} +(-5.95266 - 0.729901i) q^{56} -6.30984i q^{57} +21.0665 q^{58} -10.7490i q^{59} +3.01246 q^{60} -3.15296 q^{61} +2.23297 q^{62} +(-0.322004 + 2.62608i) q^{63} +13.0117 q^{64} -0.842387i q^{65} +(-5.71412 + 4.74192i) q^{66} -11.4139 q^{67} +10.3027 q^{68} +5.97493i q^{69} +(0.720920 - 5.87941i) q^{70} -4.24318 q^{71} +2.26674i q^{72} +15.6260 q^{73} +3.15688i q^{74} +1.00000i q^{75} -19.0081 q^{76} +(4.74025 + 7.38445i) q^{77} +1.88598 q^{78} +14.3009i q^{79} +0.950014i q^{80} +1.00000 q^{81} -23.1286i q^{82} -0.946456 q^{83} +(7.91096 + 0.970024i) q^{84} +3.42003i q^{85} +22.5578 q^{86} -9.40952 q^{87} +(4.80100 + 5.78531i) q^{88} +17.4593i q^{89} -2.23885 q^{90} +(0.271252 - 2.21218i) q^{91} +17.9992 q^{92} -0.997372 q^{93} +18.1389 q^{94} -6.30984i q^{95} -6.66043 q^{96} -17.6891i q^{97} +(3.78639 - 15.2077i) q^{98} +(2.55226 - 2.11802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 36 * q^4 - 32 * q^9	\( 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) \) 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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