LMFDB - Embedded newform 349.2.b.b.348.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(348,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("349.348");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			348.9
Character	$\chi$	$=$	349.348
Dual form			349.2.b.b.348.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.25654i q^{2} +0.849271 q^{3} +0.421101 q^{4} +3.08880 q^{5} -1.06714i q^{6} -1.10667i q^{7} -3.04222i q^{8} -2.27874 q^{9} +O(q^{10})$	\(q-1.25654i q^{2} +0.849271 q^{3} +0.421101 q^{4} +3.08880 q^{5} -1.06714i q^{6} -1.10667i q^{7} -3.04222i q^{8} -2.27874 q^{9} -3.88121i q^{10} +3.82134i q^{11} +0.357629 q^{12} +1.93980i q^{13} -1.39058 q^{14} +2.62323 q^{15} -2.98047 q^{16} -1.58811 q^{17} +2.86333i q^{18} +0.716027 q^{19} +1.30070 q^{20} -0.939863i q^{21} +4.80167 q^{22} +2.47752 q^{23} -2.58367i q^{24} +4.54068 q^{25} +2.43744 q^{26} -4.48308 q^{27} -0.466021i q^{28} -6.48565 q^{29} -3.29619i q^{30} -3.13454 q^{31} -2.33934i q^{32} +3.24535i q^{33} +1.99552i q^{34} -3.41828i q^{35} -0.959580 q^{36} -0.373131 q^{37} -0.899719i q^{38} +1.64741i q^{39} -9.39679i q^{40} -3.26884 q^{41} -1.18098 q^{42} -1.06957i q^{43} +1.60917i q^{44} -7.03857 q^{45} -3.11311i q^{46} -6.35089i q^{47} -2.53123 q^{48} +5.77528 q^{49} -5.70555i q^{50} -1.34873 q^{51} +0.816851i q^{52} +5.86436i q^{53} +5.63318i q^{54} +11.8033i q^{55} -3.36673 q^{56} +0.608101 q^{57} +8.14949i q^{58} -3.60809i q^{59} +1.10464 q^{60} +11.0907i q^{61} +3.93869i q^{62} +2.52181i q^{63} -8.90043 q^{64} +5.99164i q^{65} +4.07792 q^{66} +10.4701 q^{67} -0.668753 q^{68} +2.10409 q^{69} -4.29522 q^{70} -7.96314i q^{71} +6.93242i q^{72} +6.19683 q^{73} +0.468854i q^{74} +3.85626 q^{75} +0.301520 q^{76} +4.22896 q^{77} +2.07004 q^{78} +2.15658i q^{79} -9.20607 q^{80} +3.02887 q^{81} +4.10744i q^{82} -5.06407 q^{83} -0.395778i q^{84} -4.90534 q^{85} -1.34396 q^{86} -5.50807 q^{87} +11.6253 q^{88} -3.12440i q^{89} +8.84426i q^{90} +2.14672 q^{91} +1.04329 q^{92} -2.66208 q^{93} -7.98016 q^{94} +2.21166 q^{95} -1.98674i q^{96} +14.4538i q^{97} -7.25688i q^{98} -8.70784i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	1.25654i		−	0.888510i	−0.895900	−	0.444255i	$-0.853468\pi$
$2$		−	1.25654i		−	0.888510i	0.895900	−	0.444255i	$-0.146532\pi$
$3$	0.849271			0.490327			0.245163	−	0.969482i	$-0.421158\pi$
$3$	0.849271			0.490327			0.245163	+	0.969482i	$0.421158\pi$
$4$	0.421101			0.210551
$5$	3.08880			1.38135			0.690676	−	0.723164i	$-0.257313\pi$
$5$	3.08880			1.38135			0.690676	+	0.723164i	$0.257313\pi$
$6$		−	1.06714i		−	0.435660i
$7$		−	1.10667i		−	0.418282i	−0.977885	−	0.209141i	$-0.932933\pi$
$7$		−	1.10667i		−	0.418282i	0.977885	−	0.209141i	$-0.0670668\pi$
$8$		−	3.04222i		−	1.07559i
$9$	−2.27874			−0.759580
$10$		−	3.88121i		−	1.22735i
$11$			3.82134i			1.15218i	0.817387	+	0.576089i	$0.195422\pi$
$11$			3.82134i			1.15218i	−0.817387	+	0.576089i	$0.804578\pi$
$12$	0.357629			0.103239
$13$			1.93980i			0.538003i	0.963140	+	0.269002i	$0.0866937\pi$
$13$			1.93980i			0.538003i	−0.963140	+	0.269002i	$0.913306\pi$
$14$	−1.39058			−0.371648
$15$	2.62323			0.677314
$16$	−2.98047			−0.745118
$17$	−1.58811			−0.385172			−0.192586	−	0.981280i	$-0.561687\pi$
$17$	−1.58811			−0.385172			−0.192586	+	0.981280i	$0.561687\pi$
$18$			2.86333i			0.674894i
$19$	0.716027			0.164268			0.0821340	−	0.996621i	$-0.473826\pi$
$19$	0.716027			0.164268			0.0821340	+	0.996621i	$0.473826\pi$
$20$	1.30070			0.290845
$21$		−	0.939863i		−	0.205095i
$22$	4.80167			1.02372
$23$	2.47752			0.516599			0.258300	−	0.966065i	$-0.416838\pi$
$23$	2.47752			0.516599			0.258300	+	0.966065i	$0.416838\pi$
$24$		−	2.58367i		−	0.527388i
$25$	4.54068			0.908135
$26$	2.43744			0.478021
$27$	−4.48308			−0.862769
$28$		−	0.466021i		−	0.0880696i
$29$	−6.48565			−1.20435			−0.602177	−	0.798362i	$-0.705700\pi$
$29$	−6.48565			−1.20435			−0.602177	+	0.798362i	$0.705700\pi$
$30$		−	3.29619i		−	0.601800i
$31$	−3.13454			−0.562980			−0.281490	−	0.959564i	$-0.590829\pi$
$31$	−3.13454			−0.562980			−0.281490	+	0.959564i	$0.590829\pi$
$32$		−	2.33934i		−	0.413542i
$33$			3.24535i			0.564943i
$34$			1.99552i			0.342229i
$35$		−	3.41828i		−	0.577795i
$36$	−0.959580			−0.159930
$37$	−0.373131			−0.0613423			−0.0306711	−	0.999530i	$-0.509764\pi$
$37$	−0.373131			−0.0613423			−0.0306711	+	0.999530i	$0.509764\pi$
$38$		−	0.899719i		−	0.145954i
$39$			1.64741i			0.263797i
$40$		−	9.39679i		−	1.48576i
$41$	−3.26884			−0.510507			−0.255254	−	0.966874i	$-0.582159\pi$
$41$	−3.26884			−0.510507			−0.255254	+	0.966874i	$0.582159\pi$
$42$	−1.18098			−0.182229
$43$		−	1.06957i		−	0.163108i	−0.996669	−	0.0815542i	$-0.974012\pi$
$43$		−	1.06957i		−	0.163108i	0.996669	−	0.0815542i	$-0.0259884\pi$
$44$			1.60917i			0.242592i
$45$	−7.03857			−1.04925
$46$		−	3.11311i		−	0.459003i
$47$		−	6.35089i		−	0.926373i	−0.886261	−	0.463186i	$-0.846706\pi$
$47$		−	6.35089i		−	0.926373i	0.886261	−	0.463186i	$-0.153294\pi$
$48$	−2.53123			−0.365351
$49$	5.77528			0.825040
$50$		−	5.70555i		−	0.806887i
$51$	−1.34873			−0.188860
$52$			0.816851i			0.113277i
$53$			5.86436i			0.805532i	0.915303	+	0.402766i	$0.131951\pi$
$53$			5.86436i			0.805532i	−0.915303	+	0.402766i	$0.868049\pi$
$54$			5.63318i			0.766578i
$55$			11.8033i			1.59156i
$56$	−3.36673			−0.449898
$57$	0.608101			0.0805450
$58$			8.14949i			1.07008i
$59$		−	3.60809i		−	0.469733i	−0.972028	−	0.234867i	$-0.924535\pi$
$59$		−	3.60809i		−	0.469733i	0.972028	−	0.234867i	$-0.0754654\pi$
$60$	1.10464			0.142609
$61$			11.0907i			1.42002i	0.704192	+	0.710009i	$0.251309\pi$
$61$			11.0907i			1.42002i	−0.704192	+	0.710009i	$0.748691\pi$
$62$			3.93869i			0.500214i
$63$			2.52181i			0.317719i
$64$	−8.90043			−1.11255
$65$			5.99164i			0.743172i
$66$	4.07792			0.501957
$67$	10.4701			1.27912			0.639561	−	0.768741i	$-0.279116\pi$
$67$	10.4701			1.27912			0.639561	+	0.768741i	$0.279116\pi$
$68$	−0.668753			−0.0810982
$69$	2.10409			0.253302
$70$	−4.29522			−0.513377
$71$		−	7.96314i		−	0.945051i	−0.881317	−	0.472525i	$-0.843342\pi$
$71$		−	7.96314i		−	0.945051i	0.881317	−	0.472525i	$-0.156658\pi$
$72$			6.93242i			0.816993i
$73$	6.19683			0.725284			0.362642	−	0.931928i	$-0.381875\pi$
$73$	6.19683			0.725284			0.362642	+	0.931928i	$0.381875\pi$
$74$			0.468854i			0.0545032i
$75$	3.85626			0.445283
$76$	0.301520			0.0345867
$77$	4.22896			0.481935
$78$	2.07004			0.234386
$79$			2.15658i			0.242635i	0.992614	+	0.121317i	$0.0387118\pi$
$79$			2.15658i			0.242635i	−0.992614	+	0.121317i	$0.961288\pi$
$80$	−9.20607			−1.02927
$81$	3.02887			0.336541
$82$			4.10744i			0.453591i
$83$	−5.06407			−0.555854			−0.277927	−	0.960602i	$-0.589647\pi$
$83$	−5.06407			−0.555854			−0.277927	+	0.960602i	$0.589647\pi$
$84$		−	0.395778i		−	0.0431829i
$85$	−4.90534			−0.532058
$86$	−1.34396			−0.144923
$87$	−5.50807			−0.590527
$88$	11.6253			1.23927
$89$		−	3.12440i		−	0.331185i	−0.986194	−	0.165593i	$-0.947046\pi$
$89$		−	3.12440i		−	0.331185i	0.986194	−	0.165593i	$-0.0529537\pi$
$90$			8.84426i			0.932267i
$91$	2.14672			0.225037
$92$	1.04329			0.108770
$93$	−2.66208			−0.276044
$94$	−7.98016			−0.823091
$95$	2.21166			0.226912
$96$		−	1.98674i		−	0.202770i
$97$			14.4538i			1.46756i	0.679387	+	0.733780i	$0.262246\pi$
$97$			14.4538i			1.46756i	−0.679387	+	0.733780i	$0.737754\pi$
$98$		−	7.25688i		−	0.733056i
$99$		−	8.70784i		−	0.875170i
$100$	1.91208			0.191208
$101$			3.71151i			0.369309i	0.982804	+	0.184654i	$0.0591166\pi$
$101$			3.71151i			0.369309i	−0.982804	+	0.184654i	$0.940883\pi$
$102$			1.69474i			0.167804i
$103$			7.48244i			0.737266i	0.929575	+	0.368633i	$0.120174\pi$
$103$			7.48244i			0.737266i	−0.929575	+	0.368633i	$0.879826\pi$
$104$	5.90128			0.578669
$105$		−	2.90305i		−	0.283308i
$106$	7.36882			0.715723
$107$		−	18.8641i		−	1.82367i	−0.410562	−	0.911833i	$-0.634668\pi$
$107$		−	18.8641i		−	1.82367i	0.410562	−	0.911833i	$-0.365332\pi$
$108$	−1.88783			−0.181657
$109$	−15.1718			−1.45319			−0.726595	−	0.687066i	$-0.758898\pi$
$109$	−15.1718			−1.45319			−0.726595	+	0.687066i	$0.758898\pi$
$110$	14.8314			1.41412
$111$	−0.316889			−0.0300778
$112$			3.29840i			0.311670i
$113$			18.1957i			1.71171i	0.517219	+	0.855853i	$0.326967\pi$
$113$			18.1957i			1.71171i	−0.517219	+	0.855853i	$0.673033\pi$
$114$		−	0.764105i		−	0.0715650i
$115$	7.65257			0.713605
$116$	−2.73112			−0.253578
$117$		−	4.42029i		−	0.408656i
$118$	−4.53372			−0.417363
$119$			1.75751i			0.161111i
$120$		−	7.98042i		−	0.728509i
$121$	−3.60264			−0.327512
$122$	13.9359			1.26170
$123$	−2.77613			−0.250315
$124$	−1.31996			−0.118536
$125$	−1.41876			−0.126898
$126$	3.16877			0.282296
$127$			3.35986i			0.298139i	0.988827	+	0.149070i	$0.0476278\pi$
$127$			3.35986i			0.298139i	−0.988827	+	0.149070i	$0.952372\pi$
$128$			6.50508i			0.574973i
$129$		−	0.908357i		−	0.0799764i
$130$	7.52876			0.660316
$131$		−	0.560030i		−	0.0489301i	−0.999701	−	0.0244650i	$-0.992212\pi$
$131$		−	0.560030i		−	0.0489301i	0.999701	−	0.0244650i	$-0.00778824\pi$
$132$			1.36662i			0.118949i
$133$		−	0.792407i		−	0.0687104i
$134$		−	13.1561i		−	1.13651i
$135$	−13.8473			−1.19179
$136$			4.83136i			0.414286i
$137$			0.584495i			0.0499368i	0.999688	+	0.0249684i	$0.00794852\pi$
$137$			0.584495i			0.0499368i	−0.999688	+	0.0249684i	$0.992051\pi$
$138$		−	2.64387i		−	0.225062i
$139$	−5.93419			−0.503331			−0.251666	−	0.967814i	$-0.580978\pi$
$139$	−5.93419			−0.503331			−0.251666	+	0.967814i	$0.580978\pi$
$140$		−	1.43944i		−	0.121655i
$141$		−	5.39363i		−	0.454225i
$142$	−10.0060			−0.839687
$143$	−7.41263			−0.619875
$144$	6.79172			0.565976
$145$	−20.0329			−1.66364
$146$		−	7.78658i		−	0.644422i
$147$	4.90478			0.404539
$148$	−0.157126			−0.0129157
$149$		−	4.99335i		−	0.409071i	−0.978859	−	0.204535i	$-0.934432\pi$
$149$		−	4.99335i		−	0.409071i	0.978859	−	0.204535i	$-0.0655684\pi$
$150$		−	4.84556i		−	0.395638i
$151$	8.41203			0.684561			0.342281	−	0.939598i	$-0.388801\pi$
$151$	8.41203			0.684561			0.342281	+	0.939598i	$0.388801\pi$
$152$		−	2.17831i		−	0.176684i
$153$	3.61888			0.292569
$154$		−	5.31387i		−	0.428204i
$155$	−9.68197			−0.777675
$156$			0.693728i			0.0555427i
$157$	11.2946			0.901411			0.450705	−	0.892673i	$-0.351173\pi$
$157$	11.2946			0.901411			0.450705	+	0.892673i	$0.351173\pi$
$158$	2.70984			0.215583
$159$			4.98043i			0.394974i
$160$		−	7.22576i		−	0.571247i
$161$		−	2.74180i		−	0.216084i
$162$		−	3.80590i		−	0.299020i
$163$			4.19762i			0.328783i	0.986395	+	0.164392i	$0.0525661\pi$
$163$			4.19762i			0.328783i	−0.986395	+	0.164392i	$0.947434\pi$
$164$	−1.37651			−0.107488
$165$			10.0242i			0.780386i
$166$			6.36322i			0.493881i
$167$		−	12.5812i		−	0.973559i	−0.873525	−	0.486779i	$-0.838172\pi$
$167$		−	12.5812i		−	0.973559i	0.873525	−	0.486779i	$-0.161828\pi$
$168$	−2.85927			−0.220597
$169$	9.23718			0.710553
$170$			6.16376i			0.472739i
$171$	−1.63164			−0.124775
$172$		−	0.450399i		−	0.0343426i
$173$		−	7.41856i		−	0.564023i	−0.959411	−	0.282011i	$-0.908998\pi$
$173$		−	7.41856i		−	0.564023i	0.959411	−	0.282011i	$-0.0910016\pi$
$174$			6.92113i			0.524689i
$175$		−	5.02503i		−	0.379857i
$176$		−	11.3894i		−	0.858508i
$177$		−	3.06425i		−	0.230323i
$178$	−3.92594			−0.294261
$179$		−	17.5661i		−	1.31295i	−0.754348	−	0.656474i	$-0.772047\pi$
$179$		−	17.5661i		−	1.31295i	0.754348	−	0.656474i	$-0.227953\pi$
$180$	−2.96395			−0.220920
$181$	−12.5761			−0.934777			−0.467389	−	0.884052i	$-0.654805\pi$
$181$	−12.5761			−0.934777			−0.467389	+	0.884052i	$0.654805\pi$
$182$		−	2.69744i		−	0.199948i
$183$			9.41901i			0.696273i
$184$		−	7.53716i		−	0.555647i
$185$	−1.15253			−0.0847353
$186$			3.34501i			0.245268i
$187$		−	6.06869i		−	0.443786i
$188$		−	2.67437i		−	0.195048i
$189$			4.96129i			0.360881i
$190$		−	2.77905i		−	0.201613i
$191$	27.3642			1.98000			0.990002	−	0.141050i	$-0.0450478\pi$
$191$	27.3642			1.98000			0.990002	+	0.141050i	$0.0450478\pi$
$192$	−7.55887			−0.545515
$193$		−	7.25173i		−	0.521991i	−0.965340	−	0.260995i	$-0.915949\pi$
$193$		−	7.25173i		−	0.521991i	0.965340	−	0.260995i	$-0.0840507\pi$
$194$	18.1618			1.30394
$195$			5.08853i			0.364397i
$196$	2.43198			0.173713
$197$		−	25.3180i		−	1.80384i	−0.431907	−	0.901918i	$-0.642159\pi$
$197$		−	25.3180i		−	1.80384i	0.431907	−	0.901918i	$-0.357841\pi$
$198$	−10.9418			−0.777597
$199$			13.4793i			0.955526i	0.878489	+	0.477763i	$0.158552\pi$
$199$			13.4793i			0.955526i	−0.878489	+	0.477763i	$0.841448\pi$
$200$		−	13.8137i		−	0.976777i
$201$	8.89191			0.627187
$202$	4.66366			0.328134
$203$			7.17748i			0.503760i
$204$	−0.567952			−0.0397646
$205$	−10.0968			−0.705191
$206$	9.40200			0.655068
$207$	−5.64563			−0.392398
$208$		−	5.78151i		−	0.400876i
$209$			2.73618i			0.189266i
$210$	−3.64780			−0.251722
$211$		−	23.7766i		−	1.63685i	−0.574615	−	0.818424i	$-0.694848\pi$
$211$		−	23.7766i		−	1.63685i	0.574615	−	0.818424i	$-0.305152\pi$
$212$			2.46949i			0.169605i
$213$		−	6.76286i		−	0.463384i
$214$	−23.7036			−1.62034
$215$		−	3.30369i		−	0.225310i
$216$			13.6385i			0.927982i
$217$			3.46891i			0.235485i
$218$			19.0639i			1.29117i
$219$	5.26279			0.355626
$220$			4.97041i			0.335105i
$221$		−	3.08060i		−	0.207224i
$222$			0.398184i			0.0267244i
$223$	15.8239			1.05964			0.529822	−	0.848109i	$-0.322259\pi$
$223$	15.8239			1.05964			0.529822	+	0.848109i	$0.322259\pi$
$224$	−2.58888			−0.172977
$225$	−10.3470			−0.689801
$226$	22.8637			1.52087
$227$	−10.5591			−0.700831			−0.350415	−	0.936594i	$-0.613960\pi$
$227$	−10.5591			−0.700831			−0.350415	+	0.936594i	$0.613960\pi$
$228$	0.256072			0.0169588
$229$		−	22.3594i		−	1.47755i	−0.673951	−	0.738776i	$-0.735404\pi$
$229$		−	22.3594i		−	1.47755i	0.673951	−	0.738776i	$-0.264596\pi$
$230$		−	9.61577i		−	0.634045i
$231$	3.59154			0.236306
$232$			19.7307i			1.29539i
$233$	23.2210			1.52126			0.760628	−	0.649188i	$-0.224891\pi$
$233$	23.2210			1.52126			0.760628	+	0.649188i	$0.224891\pi$
$234$	−5.55429			−0.363095
$235$		−	19.6166i		−	1.27965i
$236$		−	1.51937i		−	0.0989027i
$237$			1.83152i			0.118970i
$238$	2.20838			0.143148
$239$	−14.7245			−0.952449			−0.476224	−	0.879324i	$-0.657995\pi$
$239$	−14.7245			−0.952449			−0.476224	+	0.879324i	$0.657995\pi$
$240$	−7.81845			−0.504679
$241$	7.56794			0.487494			0.243747	−	0.969839i	$-0.421623\pi$
$241$	7.56794			0.487494			0.243747	+	0.969839i	$0.421623\pi$
$242$			4.52686i			0.290998i
$243$	16.0216			1.02778
$244$			4.67031i			0.298986i
$245$	17.8387			1.13967
$246$			3.48833i			0.222408i
$247$			1.38895i			0.0883767i
$248$			9.53596i			0.605534i
$249$	−4.30077			−0.272550
$250$			1.78273i			0.112750i
$251$			10.8870i			0.687181i	0.939120	+	0.343590i	$0.111643\pi$
$251$			10.8870i			0.687181i	−0.939120	+	0.343590i	$0.888357\pi$
$252$			1.06194i			0.0668959i
$253$			9.46745i			0.595214i
$254$	4.22180			0.264899
$255$	−4.16596			−0.260882
$256$	−9.62695			−0.601685
$257$	−13.4022			−0.836004			−0.418002	−	0.908446i	$-0.637269\pi$
$257$	−13.4022			−0.836004			−0.418002	+	0.908446i	$0.637269\pi$
$258$	−1.14139			−0.0710598
$259$			0.412933i			0.0256584i
$260$			2.52309i			0.156475i
$261$	14.7791			0.914804
$262$	−0.703701			−0.0434748
$263$	−27.4217			−1.69089			−0.845446	−	0.534061i	$-0.820665\pi$
$263$	−27.4217			−1.69089			−0.845446	+	0.534061i	$0.820665\pi$
$264$	9.87306			0.607645
$265$			18.1138i			1.11272i
$266$	−0.995693			−0.0610498
$267$		−	2.65346i		−	0.162389i
$268$	4.40895			0.269320
$269$	16.8794			1.02916			0.514578	−	0.857443i	$-0.327949\pi$
$269$	16.8794			1.02916			0.514578	+	0.857443i	$0.327949\pi$
$270$			17.3998i			1.05892i
$271$	16.5924			1.00792			0.503960	−	0.863727i	$-0.331876\pi$
$271$	16.5924			1.00792			0.503960	+	0.863727i	$0.331876\pi$
$272$	4.73330			0.286999
$273$	1.82314			0.110342
$274$	0.734443			0.0443693
$275$			17.3515i			1.04633i
$276$	0.886034			0.0533330
$277$			11.8911i			0.714468i	0.934015	+	0.357234i	$0.116280\pi$
$277$			11.8911i			0.714468i	−0.934015	+	0.357234i	$0.883720\pi$
$278$			7.45656i			0.447214i
$279$	7.14280			0.427629
$280$	−10.3992			−0.621468
$281$	−26.9349			−1.60680			−0.803401	−	0.595439i	$-0.796978\pi$
$281$	−26.9349			−1.60680			−0.803401	+	0.595439i	$0.796978\pi$
$282$	−6.77732			−0.403584
$283$	3.18009			0.189037			0.0945183	−	0.995523i	$-0.469869\pi$
$283$	3.18009			0.189037			0.0945183	+	0.995523i	$0.469869\pi$
$284$		−	3.35329i		−	0.198981i
$285$	1.87830			0.111261
$286$			9.31428i			0.550765i
$287$			3.61753i			0.213536i
$288$			5.33076i			0.314118i
$289$	−14.4779			−0.851642
$290$			25.1721i			1.47816i
$291$			12.2752i			0.719584i
$292$	2.60949			0.152709
$293$	−12.7553			−0.745173			−0.372586	−	0.927998i	$-0.621529\pi$
$293$	−12.7553			−0.745173			−0.372586	+	0.927998i	$0.621529\pi$
$294$		−	6.16306i		−	0.359437i
$295$		−	11.1447i		−	0.648868i
$296$			1.13514i			0.0659789i
$297$		−	17.1314i		−	0.994063i
$298$	−6.27435			−0.363463
$299$			4.80589i			0.277932i
$300$	1.62388			0.0937546
$301$	−1.18366			−0.0682253
$302$		−	10.5701i		−	0.608239i
$303$			3.15207i			0.181082i
$304$	−2.13410			−0.122399
$305$			34.2569i			1.96155i
$306$		−	4.54727i		−	0.259950i
$307$	23.9235			1.36539			0.682693	−	0.730706i	$-0.260809\pi$
$307$	23.9235			1.36539			0.682693	+	0.730706i	$0.260809\pi$
$308$	1.78082			0.101472
$309$			6.35462i			0.361501i
$310$			12.1658i			0.690971i
$311$		−	28.5986i		−	1.62168i	−0.585268	−	0.810840i	$-0.699011\pi$
$311$		−	28.5986i		−	1.62168i	0.585268	−	0.810840i	$-0.300989\pi$
$312$	5.01179			0.283737
$313$	6.25597			0.353609			0.176804	−	0.984246i	$-0.443424\pi$
$313$	6.25597			0.353609			0.176804	+	0.984246i	$0.443424\pi$
$314$		−	14.1922i		−	0.800912i
$315$			7.78938i			0.438882i
$316$			0.908140i			0.0510869i
$317$			14.5533i			0.817396i	0.912670	+	0.408698i	$0.134017\pi$
$317$			14.5533i			0.817396i	−0.912670	+	0.408698i	$0.865983\pi$
$318$	6.25812			0.350938
$319$		−	24.7839i		−	1.38763i
$320$	−27.4916			−1.53683
$321$		−	16.0208i		−	0.894192i
$322$	−3.44519			−0.191993
$323$	−1.13713			−0.0632714
$324$	1.27546			0.0708590
$325$			8.80799i			0.488580i
$326$	5.27449			0.292127
$327$	−12.8849			−0.712538
$328$			9.94452i			0.549095i
$329$	−7.02835			−0.387485
$330$	12.5959			0.693380
$331$		−	5.53734i		−	0.304360i	−0.988353	−	0.152180i	$-0.951371\pi$
$331$		−	5.53734i		−	0.304360i	0.988353	−	0.152180i	$-0.0486293\pi$
$332$	−2.13249			−0.117035
$333$	0.850267			0.0465944
$334$	−15.8088			−0.865016
$335$	32.3399			1.76692
$336$			2.80123i			0.152820i
$337$	−16.8706			−0.919002			−0.459501	−	0.888177i	$-0.651972\pi$
$337$	−16.8706			−0.919002			−0.459501	+	0.888177i	$0.651972\pi$
$338$		−	11.6069i		−	0.631333i
$339$			15.4531i			0.839295i
$340$	−2.06564			−0.112025
$341$		−	11.9782i		−	0.648653i
$342$			2.05022i			0.110863i
$343$		−	14.1380i		−	0.763382i
$344$	−3.25387			−0.175437
$345$	6.49910			0.349900
$346$	−9.32174			−0.501140
$347$			10.9559i			0.588146i	0.955783	+	0.294073i	$0.0950108\pi$
$347$			10.9559i			0.588146i	−0.955783	+	0.294073i	$0.904989\pi$
$348$	−2.31946			−0.124336
$349$	−6.58356	−	17.4830i	−0.352410	−	0.935846i
$349$	−6.58356	−	17.4830i	−0.352410	−	0.935846i
$350$	−6.31417			−0.337506
$351$		−	8.69627i		−	0.464172i
$352$	8.93943			0.476473
$353$	10.7831			0.573929			0.286965	−	0.957941i	$-0.407354\pi$
$353$	10.7831			0.573929			0.286965	+	0.957941i	$0.407354\pi$
$354$	−3.85036			−0.204644
$355$		−	24.5965i		−	1.30545i
$356$		−	1.31569i		−	0.0697313i
$357$			1.49260i			0.0789968i
$358$	−22.0725			−1.16657
$359$			2.40990i			0.127190i	0.997976	+	0.0635948i	$0.0202565\pi$
$359$			2.40990i			0.127190i	−0.997976	+	0.0635948i	$0.979743\pi$
$360$			21.4128i			1.12856i
$361$	−18.4873			−0.973016
$362$			15.8025i			0.830558i
$363$	−3.05961			−0.160588
$364$	0.903986			0.0473817
$365$	19.1408			1.00187
$366$	11.8354			0.618645
$367$		−	29.9101i		−	1.56129i	−0.624973	−	0.780646i	$-0.714890\pi$
$367$		−	29.9101i		−	1.56129i	0.624973	−	0.780646i	$-0.285110\pi$
$368$	−7.38418			−0.384927
$369$	7.44884			0.387771
$370$			1.44820i			0.0752882i
$371$	6.48992			0.336940
$372$	−1.12100			−0.0581213
$373$			30.5754i			1.58313i	0.611082	+	0.791567i	$0.290734\pi$
$373$			30.5754i			1.58313i	−0.611082	+	0.791567i	$0.709266\pi$
$374$	−7.62556			−0.394309
$375$	−1.20491			−0.0622213
$376$	−19.3208			−0.996393
$377$		−	12.5808i		−	0.647947i
$378$	6.23407			0.320646
$379$			30.4682i			1.56505i	0.622621	+	0.782523i	$0.286068\pi$
$379$			30.4682i			1.56505i	−0.622621	+	0.782523i	$0.713932\pi$
$380$	0.931335			0.0477765
$381$			2.85343i			0.146186i
$382$		−	34.3843i		−	1.75925i
$383$			19.8647i			1.01504i	0.861640	+	0.507519i	$0.169437\pi$
$383$			19.8647i			1.01504i	−0.861640	+	0.507519i	$0.830563\pi$
$384$			5.52457i			0.281925i
$385$	13.0624			0.665723
$386$	−9.11210			−0.463794
$387$			2.43728i			0.123894i
$388$			6.08651i			0.308996i
$389$			10.9907i			0.557248i	0.960400	+	0.278624i	$0.0898784\pi$
$389$			10.9907i			0.557248i	−0.960400	+	0.278624i	$0.910122\pi$
$390$	6.39395			0.323770
$391$	−3.93457			−0.198980
$392$		−	17.5697i		−	0.887401i
$393$		−	0.475617i		−	0.0239917i
$394$	−31.8132			−1.60273
$395$			6.66125i			0.335164i
$396$		−	3.66688i		−	0.184268i
$397$	−8.11118			−0.407088			−0.203544	−	0.979066i	$-0.565246\pi$
$397$	−8.11118			−0.407088			−0.203544	+	0.979066i	$0.565246\pi$
$398$	16.9374			0.848994
$399$		−	0.672968i		−	0.0336905i
$400$	−13.5334			−0.676668
$401$			20.6819i			1.03280i	0.856346	+	0.516402i	$0.172729\pi$
$401$			20.6819i			1.03280i	−0.856346	+	0.516402i	$0.827271\pi$
$402$		−	11.1731i		−	0.557262i
$403$		−	6.08038i		−	0.302885i
$404$			1.56292i			0.0777582i
$405$	9.35557			0.464882
$406$	9.01881			0.447596
$407$		−	1.42586i		−	0.0706772i
$408$			4.10313i			0.203135i
$409$	1.10949			0.0548608			0.0274304	−	0.999624i	$-0.491268\pi$
$409$	1.10949			0.0548608			0.0274304	+	0.999624i	$0.491268\pi$
$410$			12.6870i			0.626569i
$411$			0.496395i			0.0244854i
$412$			3.15086i			0.155232i
$413$	−3.99297			−0.196481
$414$			7.09397i			0.348650i
$415$	−15.6419			−0.767830
$416$	4.53786			0.222487
$417$	−5.03973			−0.246797
$418$	3.43813			0.168164
$419$	−34.7833			−1.69927			−0.849637	−	0.527368i	$-0.823179\pi$
$419$	−34.7833			−1.69927			−0.849637	+	0.527368i	$0.823179\pi$
$420$		−	1.22248i		−	0.0596508i
$421$		−	35.5873i		−	1.73442i	−0.497942	−	0.867210i	$-0.665911\pi$
$421$		−	35.5873i		−	1.73442i	0.497942	−	0.867210i	$-0.334089\pi$
$422$	−29.8763			−1.45436
$423$			14.4720i			0.703654i
$424$	17.8407			0.866419
$425$	−7.21107			−0.349788
$426$	−8.49782			−0.411721
$427$	12.2738			0.593968
$428$		−	7.94371i		−	0.383974i
$429$	−6.29533			−0.303941
$430$	−4.15123			−0.200190
$431$		−	20.9242i		−	1.00788i	−0.863738	−	0.503941i	$-0.831883\pi$
$431$		−	20.9242i		−	1.00788i	0.863738	−	0.503941i	$-0.168117\pi$
$432$	13.3617			0.642864
$433$			35.9925i			1.72969i	0.502038	+	0.864846i	$0.332584\pi$
$433$			35.9925i			1.72969i	−0.502038	+	0.864846i	$0.667416\pi$
$434$	4.35883			0.209230
$435$	−17.0133			−0.815727
$436$	−6.38884			−0.305970
$437$	1.77397			0.0848607
$438$		−	6.61292i		−	0.315977i
$439$		−	10.7574i		−	0.513420i	−0.966488	−	0.256710i	$-0.917361\pi$
$439$		−	10.7574i		−	0.513420i	0.966488	−	0.256710i	$-0.0826386\pi$
$440$	35.9083			1.71186
$441$	−13.1604			−0.626684
$442$	−3.87091			−0.184120
$443$	4.16673			0.197967			0.0989837	−	0.995089i	$-0.468441\pi$
$443$	4.16673			0.197967			0.0989837	+	0.995089i	$0.468441\pi$
$444$	−0.133442			−0.00633289
$445$		−	9.65063i		−	0.457484i
$446$		−	19.8834i		−	0.941504i
$447$		−	4.24070i		−	0.200578i
$448$			9.84984i			0.465361i
$449$	28.5685			1.34823			0.674116	−	0.738625i	$-0.264525\pi$
$449$	28.5685			1.34823			0.674116	+	0.738625i	$0.264525\pi$
$450$			13.0015i			0.612895i
$451$		−	12.4914i		−	0.588195i
$452$			7.66223i			0.360401i
$453$	7.14409			0.335659
$454$			13.2679i			0.622695i
$455$	6.63078			0.310856
$456$		−	1.84998i		−	0.0866330i
$457$	22.5438			1.05456			0.527278	−	0.849693i	$-0.323213\pi$
$457$	22.5438			1.05456			0.527278	+	0.849693i	$0.323213\pi$
$458$	−28.0956			−1.31282
$459$	7.11960			0.332314
$460$	3.22251			0.150250
$461$			35.7235i			1.66381i	0.554920	+	0.831904i	$0.312749\pi$
$461$			35.7235i			1.66381i	−0.554920	+	0.831904i	$0.687251\pi$
$462$		−	4.51292i		−	0.209960i
$463$			32.5994i			1.51502i	0.652822	+	0.757511i	$0.273585\pi$
$463$			32.5994i			1.51502i	−0.652822	+	0.757511i	$0.726415\pi$
$464$	19.3303			0.897386
$465$	−8.22261			−0.381315
$466$		−	29.1781i		−	1.35165i
$467$	22.2967			1.03177			0.515884	−	0.856658i	$-0.327463\pi$
$467$	22.2967			1.03177			0.515884	+	0.856658i	$0.327463\pi$
$468$		−	1.86139i		−	0.0860429i
$469$		−	11.5869i		−	0.535034i
$470$	−24.6491			−1.13698
$471$	9.59221			0.441986
$472$	−10.9766			−0.505239
$473$	4.08720			0.187930
$474$	2.30139			0.105706
$475$	3.25125			0.149178
$476$			0.740090i			0.0339219i
$477$		−	13.3634i		−	0.611866i
$478$			18.5020i			0.846260i
$479$	23.1613			1.05827			0.529134	−	0.848538i	$-0.322517\pi$
$479$	23.1613			1.05827			0.529134	+	0.848538i	$0.322517\pi$
$480$		−	6.13663i		−	0.280098i
$481$		−	0.723798i		−	0.0330023i
$482$		−	9.50944i		−	0.433143i
$483$		−	2.32853i		−	0.105952i
$484$	−1.51707			−0.0689579
$485$			44.6449i			2.02722i
$486$		−	20.1318i		−	0.913196i
$487$		−	19.5644i		−	0.886550i	−0.896386	−	0.443275i	$-0.853817\pi$
$487$		−	19.5644i		−	0.886550i	0.896386	−	0.443275i	$-0.146183\pi$
$488$	33.7403			1.52735
$489$			3.56492i			0.161211i
$490$		−	22.4151i		−	1.01261i
$491$	−7.43055			−0.335336			−0.167668	−	0.985844i	$-0.553624\pi$
$491$	−7.43055			−0.335336			−0.167668	+	0.985844i	$0.553624\pi$
$492$	−1.16903			−0.0527041
$493$	10.2999			0.463884
$494$	1.74527			0.0785235
$495$		−	26.8968i		−	1.20892i
$496$	9.34241			0.419487
$497$	−8.81257			−0.395298
$498$			5.40409i			0.242163i
$499$		−	24.0068i		−	1.07469i	−0.843362	−	0.537346i	$-0.819427\pi$
$499$		−	24.0068i		−	1.07469i	0.843362	−	0.537346i	$-0.180573\pi$
$500$	−0.597441			−0.0267184
$501$		−	10.6848i		−	0.477362i
$502$	13.6800			0.610567
$503$		−	33.1054i		−	1.47609i	−0.674749	−	0.738047i	$-0.735748\pi$
$503$		−	33.1054i		−	1.47609i	0.674749	−	0.738047i	$-0.264252\pi$
$504$	7.67190			0.341734
$505$			11.4641i			0.510146i
$506$	11.8963			0.528853
$507$	7.84487			0.348403
$508$			1.41484i			0.0627734i
$509$		−	22.0021i		−	0.975225i	−0.873060	−	0.487613i	$-0.837868\pi$
$509$		−	22.0021i		−	0.975225i	0.873060	−	0.487613i	$-0.162132\pi$
$510$			5.23470i			0.231797i
$511$		−	6.85785i		−	0.303374i
$512$			25.1068i			1.10958i
$513$	−3.21001			−0.141725
$514$			16.8404i			0.742797i
$515$			23.1117i			1.01843i
$516$		−	0.382510i		−	0.0168391i
$517$	24.2689			1.06735
$518$	0.518867			0.0227977
$519$		−	6.30037i		−	0.276556i
$520$	18.2279			0.799345
$521$		−	32.3127i		−	1.41565i	−0.706390	−	0.707823i	$-0.749677\pi$
$521$		−	32.3127i		−	1.41565i	0.706390	−	0.707823i	$-0.250323\pi$
$522$		−	18.5706i		−	0.812812i
$523$			9.64321i			0.421668i	0.977522	+	0.210834i	$0.0676179\pi$
$523$			9.64321i			0.421668i	−0.977522	+	0.210834i	$0.932382\pi$
$524$		−	0.235829i		−	0.0103023i
$525$		−	4.26761i		−	0.186254i
$526$			34.4565i			1.50237i
$527$	4.97798			0.216844
$528$		−	9.67268i		−	0.420949i
$529$	−16.8619			−0.733125
$530$	22.7608			0.988666
$531$			8.22190i			0.356800i
$532$		−	0.333683i		−	0.0144670i
$533$		−	6.34089i		−	0.274655i
$534$	−3.33418			−0.144284
$535$		−	58.2675i		−	2.51912i
$536$		−	31.8522i		−	1.37580i
$537$		−	14.9183i		−	0.643774i
$538$		−	21.2097i		−	0.914415i
$539$			22.0693i			0.950592i
$540$	−5.83113			−0.250932
$541$	−10.5474			−0.453468			−0.226734	−	0.973957i	$-0.572805\pi$
$541$	−10.5474			−0.453468			−0.226734	+	0.973957i	$0.572805\pi$
$542$		−	20.8491i		−	0.895546i
$543$	−10.6805			−0.458346
$544$			3.71512i			0.159285i
$545$	−46.8625			−2.00737
$546$		−	2.29086i		−	0.0980397i
$547$	−14.2828			−0.610690			−0.305345	−	0.952242i	$-0.598772\pi$
$547$	−14.2828			−0.610690			−0.305345	+	0.952242i	$0.598772\pi$
$548$			0.246132i			0.0105142i
$549$		−	25.2728i		−	1.07862i
$550$	21.8029			0.929677
$551$	−4.64390			−0.197837
$552$		−	6.40109i		−	0.272448i
$553$	2.38663			0.101490
$554$	14.9417			0.634812
$555$	−0.978806			−0.0415480
$556$	−2.49889			−0.105977
$557$			16.0622i			0.680579i	0.940321	+	0.340289i	$0.110525\pi$
$557$			16.0622i			0.680579i	−0.940321	+	0.340289i	$0.889475\pi$
$558$		−	8.97524i		−	0.379952i
$559$	2.07476			0.0877528
$560$			10.1881i			0.430526i
$561$		−	5.15396i		−	0.217600i
$562$			33.8448i			1.42766i
$563$	−26.8919			−1.13336			−0.566679	−	0.823939i	$-0.691772\pi$
$563$	−26.8919			−1.13336			−0.566679	+	0.823939i	$0.691772\pi$
$564$		−	2.27126i		−	0.0956374i
$565$			56.2028i			2.36447i
$566$		−	3.99591i		−	0.167961i
$567$		−	3.35196i		−	0.140769i
$568$	−24.2256			−1.01648
$569$			38.6086i			1.61856i	0.587426	+	0.809278i	$0.300141\pi$
$569$			38.6086i			1.61856i	−0.587426	+	0.809278i	$0.699859\pi$
$570$		−	2.36017i		−	0.0988565i
$571$		−	31.0616i		−	1.29989i	−0.759982	−	0.649944i	$-0.774792\pi$
$571$		−	31.0616i		−	1.29989i	0.759982	−	0.649944i	$-0.225208\pi$
$572$	−3.12147			−0.130515
$573$	23.2396			0.970849
$574$	4.54558			0.189729
$575$	11.2496			0.469142
$576$	20.2818			0.845073
$577$	40.0447			1.66708			0.833542	−	0.552457i	$-0.186310\pi$
$577$	40.0447			1.66708			0.833542	+	0.552457i	$0.186310\pi$
$578$			18.1921i			0.756693i
$579$		−	6.15868i		−	0.255946i
$580$	−8.43587			−0.350280
$581$			5.60426i			0.232504i
$582$	15.4243			0.639357
$583$	−22.4097			−0.928116
$584$		−	18.8521i		−	0.780106i
$585$		−	13.6534i		−	0.564498i
$586$			16.0276i			0.662093i
$587$	−0.789682			−0.0325937			−0.0162968	−	0.999867i	$-0.505188\pi$
$587$	−0.789682			−0.0325937			−0.0162968	+	0.999867i	$0.505188\pi$
$588$	2.06541			0.0851760
$589$	−2.24442			−0.0924796
$590$	−14.0037			−0.576525
$591$		−	21.5019i		−	0.884469i
$592$	1.11210			0.0457072
$593$			20.6423i			0.847679i	0.905737	+	0.423839i	$0.139318\pi$
$593$			20.6423i			0.847679i	−0.905737	+	0.423839i	$0.860682\pi$
$594$	−21.5263			−0.883234
$595$			5.42859i			0.222551i
$596$		−	2.10270i		−	0.0861301i
$597$			11.4476i			0.468520i
$598$	6.03881			0.246945
$599$			4.21442i			0.172196i	0.996287	+	0.0860982i	$0.0274399\pi$
$599$			4.21442i			0.172196i	−0.996287	+	0.0860982i	$0.972560\pi$
$600$		−	11.7316i		−	0.478940i
$601$		−	13.7135i		−	0.559386i	−0.960089	−	0.279693i	$-0.909767\pi$
$601$		−	13.7135i		−	0.559386i	0.960089	−	0.279693i	$-0.0902327\pi$
$602$			1.48733i			0.0606188i
$603$	−23.8585			−0.971594
$604$	3.54232			0.144135
$605$	−11.1278			−0.452410
$606$	3.96071			0.160893
$607$	38.0111			1.54282			0.771412	−	0.636336i	$-0.219551\pi$
$607$	38.0111			1.54282			0.771412	+	0.636336i	$0.219551\pi$
$608$		−	1.67503i		−	0.0679316i
$609$			6.09562i			0.247007i
$610$	43.0453			1.74285
$611$	12.3194			0.498391
$612$	1.52391			0.0616006
$613$	15.8154			0.638780			0.319390	−	0.947623i	$-0.396522\pi$
$613$	15.8154			0.638780			0.319390	+	0.947623i	$0.396522\pi$
$614$		−	30.0609i		−	1.21316i
$615$	−8.57491			−0.345774
$616$		−	12.8654i		−	0.518363i
$617$	−0.797487			−0.0321056			−0.0160528	−	0.999871i	$-0.505110\pi$
$617$	−0.797487			−0.0321056			−0.0160528	+	0.999871i	$0.505110\pi$
$618$	7.98484			0.321197
$619$			12.4508i			0.500439i	0.968189	+	0.250220i	$0.0805028\pi$
$619$			12.4508i			0.500439i	−0.968189	+	0.250220i	$0.919497\pi$
$620$	−4.07709			−0.163740
$621$	−11.1069			−0.445706
$622$	−35.9354			−1.44088
$623$	−3.45768			−0.138529
$624$		−	4.91007i		−	0.196560i
$625$	−27.0856			−1.08343
$626$		−	7.86090i		−	0.314185i
$627$			2.32376i			0.0928021i
$628$	4.75619			0.189793
$629$	0.592570			0.0236273
$630$	9.78768			0.389951
$631$	29.9406			1.19192			0.595959	−	0.803015i	$-0.296772\pi$
$631$	29.9406			1.19192			0.595959	+	0.803015i	$0.296772\pi$
$632$	6.56079			0.260974
$633$		−	20.1928i		−	0.802590i
$634$	18.2869			0.726264
$635$			10.3779i			0.411835i
$636$			2.09727i			0.0831620i
$637$			11.2029i			0.443874i
$638$	−31.1420			−1.23292
$639$			18.1459i			0.717841i
$640$			20.0929i			0.794240i
$641$	−25.6518			−1.01318			−0.506592	−	0.862186i	$-0.669095\pi$
$641$	−25.6518			−1.01318			−0.506592	+	0.862186i	$0.669095\pi$
$642$	−20.1308			−0.794498
$643$			15.1570i			0.597732i	0.954295	+	0.298866i	$0.0966083\pi$
$643$			15.1570i			0.597732i	−0.954295	+	0.298866i	$0.903392\pi$
$644$		−	1.15458i		−	0.0454967i
$645$		−	2.80573i		−	0.110476i
$646$			1.42885i			0.0562173i
$647$	31.3344			1.23188			0.615941	−	0.787792i	$-0.288776\pi$
$647$	31.3344			1.23188			0.615941	+	0.787792i	$0.288776\pi$
$648$		−	9.21448i		−	0.361979i
$649$	13.7877			0.541216
$650$	11.0676			0.434108
$651$			2.94604i			0.115464i
$652$			1.76762i			0.0692255i
$653$	1.31205			0.0513443			0.0256721	−	0.999670i	$-0.491827\pi$
$653$	1.31205			0.0513443			0.0256721	+	0.999670i	$0.491827\pi$
$654$			16.1905i			0.633097i
$655$		−	1.72982i		−	0.0675897i
$656$	9.74269			0.380388
$657$	−14.1210			−0.550911
$658$			8.83141i			0.344284i
$659$			22.8446i			0.889899i	0.895556	+	0.444949i	$0.146778\pi$
$659$			22.8446i			0.889899i	−0.895556	+	0.444949i	$0.853222\pi$
$660$			4.22122i			0.164311i
$661$	−5.69457			−0.221493			−0.110747	−	0.993849i	$-0.535324\pi$
$661$	−5.69457			−0.221493			−0.110747	+	0.993849i	$0.535324\pi$
$662$	−6.95790			−0.270426
$663$		−	2.61627i		−	0.101607i
$664$			15.4060i			0.597868i
$665$		−	2.44758i		−	0.0949133i
$666$		−	1.06840i		−	0.0413995i
$667$	−16.0683			−0.622169
$668$		−	5.29794i		−	0.204983i
$669$	13.4387			0.519572
$670$		−	40.6364i		−	1.56992i
$671$	−42.3813			−1.63611
$672$	−2.19866			−0.0848153
$673$	−20.3466			−0.784303			−0.392151	−	0.919901i	$-0.628269\pi$
$673$	−20.3466			−0.784303			−0.392151	+	0.919901i	$0.628269\pi$
$674$			21.1987i			0.816542i
$675$	−20.3562			−0.783511
$676$	3.88979			0.149607
$677$			8.95977i			0.344352i	0.985066	+	0.172176i	$0.0550798\pi$
$677$			8.95977i			0.344352i	−0.985066	+	0.172176i	$0.944920\pi$
$678$	19.4174			0.745722
$679$	15.9956			0.613854
$680$			14.9231i			0.572275i
$681$	−8.96752			−0.343636
$682$	−15.0511			−0.576335
$683$	−41.6172			−1.59244			−0.796219	−	0.605009i	$-0.793169\pi$
$683$	−41.6172			−1.59244			−0.796219	+	0.605009i	$0.793169\pi$
$684$	−0.687086			−0.0262714
$685$			1.80539i			0.0689803i
$686$	−17.7650			−0.678272
$687$		−	18.9892i		−	0.724484i
$688$			3.18783i			0.121535i
$689$	−11.3757			−0.433379
$690$		−	8.16640i		−	0.310889i
$691$			39.5724i			1.50541i	0.658361	+	0.752703i	$0.271250\pi$
$691$			39.5724i			1.50541i	−0.658361	+	0.752703i	$0.728750\pi$
$692$		−	3.12397i		−	0.118755i
$693$	−9.63671			−0.366068
$694$	13.7666			0.522573
$695$	−18.3295			−0.695278
$696$			16.7567i			0.635163i
$697$	5.19126			0.196633
$698$	−21.9682	+	8.27253i	−0.831508	+	0.313120i
$699$	19.7209			0.745912
$700$		−	2.11605i		−	0.0799791i
$701$	−20.4903			−0.773908			−0.386954	−	0.922099i	$-0.626473\pi$
$701$	−20.4903			−0.773908			−0.386954	+	0.922099i	$0.626473\pi$
$702$	−10.9272			−0.412422
$703$	−0.267172			−0.0100766
$704$		−	34.0116i		−	1.28186i
$705$		−	16.6598i		−	0.627445i
$706$		−	13.5495i		−	0.509942i
$707$	4.10742			0.154475
$708$		−	1.29036i		−	0.0484946i
$709$			26.2962i			0.987575i	0.869583	+	0.493787i	$0.164388\pi$
$709$			26.2962i			0.987575i	−0.869583	+	0.493787i	$0.835612\pi$
$710$	−30.9066			−1.15990
$711$		−	4.91429i		−	0.184300i
$712$	−9.50509			−0.356218
$713$	−7.76590			−0.290835
$714$	1.87552			0.0701894
$715$	−22.8961			−0.856266
$716$		−	7.39709i		−	0.276442i
$717$	−12.5051			−0.467011
$718$	3.02814			0.113009
$719$		−	5.03488i		−	0.187769i	−0.995583	−	0.0938846i	$-0.970072\pi$
$719$		−	5.03488i		−	0.187769i	0.995583	−	0.0938846i	$-0.0299285\pi$
$720$	20.9782			0.781813
$721$	8.28059			0.308385
$722$			23.2301i			0.864534i
$723$	6.42723			0.239031
$724$	−5.29583			−0.196818
$725$	−29.4492			−1.09372
$726$			3.84453i			0.142684i
$727$	0.812083			0.0301185			0.0150592	−	0.999887i	$-0.495206\pi$
$727$	0.812083			0.0301185			0.0150592	+	0.999887i	$0.495206\pi$
$728$		−	6.53078i		−	0.242047i
$729$	4.52004			0.167409
$730$		−	24.0512i		−	0.890174i
$731$			1.69859i			0.0628248i
$732$			3.96636i			0.146601i
$733$		−	16.6815i		−	0.616146i	−0.951363	−	0.308073i	$-0.900316\pi$
$733$		−	16.6815i		−	0.616146i	0.951363	−	0.308073i	$-0.0996841\pi$
$734$	−37.5833			−1.38722
$735$	15.1499			0.558811
$736$		−	5.79578i		−	0.213635i
$737$			40.0096i			1.47377i
$738$		−	9.35978i		−	0.344538i
$739$	14.4267			0.530696			0.265348	−	0.964153i	$-0.414513\pi$
$739$	14.4267			0.530696			0.265348	+	0.964153i	$0.414513\pi$
$740$	−0.485330			−0.0178411
$741$			1.17959i			0.0433334i
$742$		−	8.15486i		−	0.299374i
$743$	−7.53896			−0.276578			−0.138289	−	0.990392i	$-0.544160\pi$
$743$	−7.53896			−0.276578			−0.138289	+	0.990392i	$0.544160\pi$
$744$			8.09861i			0.296909i
$745$		−	15.4234i		−	0.565071i
$746$	38.4193			1.40663
$747$	11.5397			0.422215
$748$		−	2.55553i		−	0.0934395i
$749$	−20.8764			−0.762807
$750$			1.51402i			0.0552842i
$751$			20.4414i			0.745919i	0.927848	+	0.372959i	$0.121657\pi$
$751$			20.4414i			0.745919i	−0.927848	+	0.372959i	$0.878343\pi$
$752$			18.9286i			0.690257i
$753$			9.24601i			0.336943i
$754$	−15.8084			−0.575707
$755$	25.9831			0.945621
$756$			2.08921i			0.0759837i
$757$			5.88101i			0.213749i	0.994273	+	0.106875i	$0.0340843\pi$
$757$			5.88101i			0.213749i	−0.994273	+	0.106875i	$0.965916\pi$
$758$	38.2846			1.39056
$759$			8.04043i			0.291849i
$760$		−	6.72836i		−	0.244063i
$761$			23.7487i			0.860890i	0.902617	+	0.430445i	$0.141643\pi$
$761$			23.7487i			0.860890i	−0.902617	+	0.430445i	$0.858357\pi$
$762$	3.58545			0.129887
$763$			16.7901i			0.607844i
$764$	11.5231			0.416891
$765$	11.1780			0.404141
$766$	24.9608			0.901871
$767$	6.99897			0.252718
$768$	−8.17589			−0.295022
$769$		−	2.49509i		−	0.0899751i	−0.998988	−	0.0449876i	$-0.985675\pi$
$769$		−	2.49509i		−	0.0899751i	0.998988	−	0.0449876i	$-0.0143248\pi$
$770$		−	16.4135i		−	0.591501i
$771$	−11.3821			−0.409915
$772$		−	3.05371i		−	0.109905i
$773$	−47.0372			−1.69181			−0.845905	−	0.533334i	$-0.820939\pi$
$773$	−47.0372			−1.69181			−0.845905	+	0.533334i	$0.820939\pi$
$774$	3.06254			0.110081
$775$	−14.2329			−0.511262
$776$	43.9716			1.57849
$777$			0.350692i			0.0125810i
$778$	13.8102			0.495121
$779$	−2.34058			−0.0838600
$780$			2.14279i			0.0767241i
$781$	30.4299			1.08887
$782$			4.94395i			0.176795i
$783$	29.0757			1.03908
$784$	−17.2131			−0.614752
$785$	34.8869			1.24517
$786$	−0.597633			−0.0213169
$787$			12.2068i			0.435124i	0.976047	+	0.217562i	$0.0698104\pi$
$787$			12.2068i			0.435124i	−0.976047	+	0.217562i	$0.930190\pi$
$788$		−	10.6615i		−	0.379799i
$789$	−23.2884			−0.829089
$790$	8.37014			0.297796
$791$	20.1366			0.715976
$792$	−26.4911			−0.941321
$793$	−21.5137			−0.763974
$794$			10.1920i			0.361702i
$795$			15.3836i			0.545598i
$796$			5.67617i			0.201187i
$797$			28.9168i			1.02429i	0.858900	+	0.512144i	$0.171148\pi$
$797$			28.9168i			1.02429i	−0.858900	+	0.512144i	$0.828852\pi$
$798$	−0.845612			−0.0299344
$799$			10.0859i			0.356813i
$800$		−	10.6222i		−	0.375552i
$801$			7.11969i			0.251562i
$802$	25.9877			0.917656
$803$			23.6802i			0.835656i
$804$	3.74440			0.132055
$805$		−	8.46887i		−	0.298488i
$806$	−7.64025			−0.269116
$807$	14.3352			0.504623
$808$	11.2912			0.397223
$809$	35.0893			1.23367			0.616837	−	0.787091i	$-0.288414\pi$
$809$	35.0893			1.23367			0.616837	+	0.787091i	$0.288414\pi$
$810$		−	11.7557i		−	0.413052i
$811$			32.3316i			1.13532i	0.823264	+	0.567659i	$0.192151\pi$
$811$			32.3316i			1.13532i	−0.823264	+	0.567659i	$0.807849\pi$
$812$			3.02245i			0.106067i
$813$	14.0915			0.494210
$814$	−1.79165			−0.0627974
$815$			12.9656i			0.454166i
$816$	4.01985			0.140723
$817$		−	0.765844i		−	0.0267935i
$818$		−	1.39412i		−	0.0487443i
$819$	−4.89181			−0.170934
$820$	−4.25177			−0.148478
$821$	−29.2971			−1.02248			−0.511238	−	0.859439i	$-0.670813\pi$
$821$	−29.2971			−1.02248			−0.511238	+	0.859439i	$0.670813\pi$
$822$	0.623741			0.0217555
$823$	−37.7408			−1.31556			−0.657782	−	0.753209i	$-0.728505\pi$
$823$	−37.7408			−1.31556			−0.657782	+	0.753209i	$0.728505\pi$
$824$	22.7632			0.792993
$825$			14.7361i			0.513045i
$826$			5.01733i			0.174575i
$827$			42.6527i			1.48318i	0.670853	+	0.741591i	$0.265928\pi$
$827$			42.6527i			1.48318i	−0.670853	+	0.741591i	$0.734072\pi$
$828$	−2.37738			−0.0826197
$829$		−	38.1041i		−	1.32341i	−0.749764	−	0.661705i	$-0.769833\pi$
$829$		−	38.1041i		−	1.32341i	0.749764	−	0.661705i	$-0.230167\pi$
$830$			19.6547i			0.682224i
$831$			10.0988i			0.350323i
$832$		−	17.2650i		−	0.598557i
$833$	−9.17175			−0.317782
$834$			6.33263i			0.219281i
$835$		−	38.8606i		−	1.34483i
$836$			1.15221i			0.0398500i
$837$	14.0524			0.485722
$838$			43.7067i			1.50982i
$839$		−	13.0193i		−	0.449478i	−0.974419	−	0.224739i	$-0.927847\pi$
$839$		−	13.0193i		−	0.449478i	0.974419	−	0.224739i	$-0.0721529\pi$
$840$	−8.83170			−0.304723
$841$	13.0637			0.450471
$842$	−44.7170			−1.54105
$843$	−22.8750			−0.787858
$844$		−	10.0124i		−	0.344639i
$845$	28.5318			0.981524
$846$	18.1847			0.625203
$847$			3.98693i			0.136993i
$848$		−	17.4786i		−	0.600216i
$849$	2.70076			0.0926897
$850$			9.06102i			0.310790i
$851$	−0.924439			−0.0316894
$852$		−	2.84785i		−	0.0975657i
$853$	18.1303			0.620768			0.310384	−	0.950611i	$-0.399542\pi$
$853$	18.1303			0.620768			0.310384	+	0.950611i	$0.399542\pi$
$854$		−	15.4225i		−	0.527747i
$855$	−5.03981			−0.172358
$856$	−57.3888			−1.96151
$857$		−	32.8604i		−	1.12249i	−0.827650	−	0.561245i	$-0.810323\pi$
$857$		−	32.8604i		−	1.12249i	0.827650	−	0.561245i	$-0.189677\pi$
$858$			7.91034i			0.270055i
$859$			32.1826i			1.09805i	0.835804	+	0.549027i	$0.185002\pi$
$859$			32.1826i			1.09805i	−0.835804	+	0.549027i	$0.814998\pi$
$860$		−	1.39119i		−	0.0474392i
$861$			3.07226i			0.104702i
$862$	−26.2921			−0.895512
$863$			41.1371i			1.40032i	0.713984	+	0.700162i	$0.246889\pi$
$863$			41.1371i			1.40032i	−0.713984	+	0.700162i	$0.753111\pi$
$864$			10.4875i			0.356791i
$865$		−	22.9144i		−	0.779115i
$866$	45.2262			1.53685
$867$	−12.2957			−0.417583
$868$			1.46076i			0.0495815i
$869$	−8.24104			−0.279558
$870$			21.3780i			0.724781i
$871$			20.3098i			0.688171i
$872$			46.1558i			1.56303i
$873$		−	32.9364i		−	1.11473i
$874$		−	2.22907i		−	0.0753995i
$875$			1.57010i			0.0530790i
$876$	2.21617			0.0748773
$877$		−	45.9827i		−	1.55273i	−0.630286	−	0.776363i	$-0.717062\pi$
$877$		−	45.9827i		−	1.55273i	0.630286	−	0.776363i	$-0.282938\pi$
$878$	−13.5171			−0.456179
$879$	−10.8327			−0.365378
$880$		−	35.1795i		−	1.18590i
$881$			31.6621i			1.06672i	0.845887	+	0.533361i	$0.179071\pi$
$881$			31.6621i			1.06672i	−0.845887	+	0.533361i	$0.820929\pi$
$882$			16.5365i			0.556814i
$883$	−45.7465			−1.53949			−0.769746	−	0.638350i	$-0.779617\pi$
$883$	−45.7465			−1.53949			−0.769746	+	0.638350i	$0.779617\pi$
$884$		−	1.29725i		−	0.0436311i
$885$		−	9.46484i		−	0.318157i
$886$		−	5.23568i		−	0.175896i
$887$			32.2386i			1.08247i	0.840872	+	0.541234i	$0.182043\pi$
$887$			32.2386i			1.08247i	−0.840872	+	0.541234i	$0.817957\pi$
$888$			0.964044i			0.0323512i
$889$	3.71825			0.124706
$890$	−12.1264			−0.406479
$891$			11.5743i			0.387755i
$892$	6.66345			0.223109
$893$		−	4.54741i		−	0.152173i
$894$	−5.32862			−0.178216
$895$		−	54.2580i		−	1.81364i
$896$	7.19898			0.240501
$897$			4.08150i			0.136277i
$898$		−	35.8976i		−	1.19792i
$899$	20.3295			0.678028
$900$	−4.35714			−0.145238
$901$		−	9.31323i		−	0.310269i
$902$	−15.6959			−0.522617
$903$	−1.00525			−0.0334527
$904$	55.3552			1.84109
$905$	−38.8452			−1.29126
$906$		−	8.97685i		−	0.298236i
$907$			8.65627i			0.287427i	0.989619	+	0.143713i	$0.0459043\pi$
$907$			8.65627i			0.287427i	−0.989619	+	0.143713i	$0.954096\pi$
$908$	−4.44644			−0.147560
$909$		−	8.45755i		−	0.280519i
$910$		−	8.33185i		−	0.276198i
$911$		−	47.1444i		−	1.56196i	−0.624555	−	0.780981i	$-0.714719\pi$
$911$		−	47.1444i		−	1.56196i	0.624555	−	0.780981i	$-0.285281\pi$
$912$	−1.81243			−0.0600155
$913$		−	19.3515i		−	0.640442i
$914$		−	28.3273i		−	0.936983i
$915$			29.0934i			0.961798i
$916$		−	9.41559i		−	0.311100i
$917$	−0.619769			−0.0204666
$918$		−	8.94608i		−	0.295265i
$919$			41.5162i			1.36949i	0.728781	+	0.684746i	$0.240087\pi$
$919$			41.5162i			1.36949i	−0.728781	+	0.684746i	$0.759913\pi$
$920$		−	23.2808i		−	0.767544i
$921$	20.3175			0.669485
$922$	44.8880			1.47831
$923$	15.4469			0.508440
$924$	1.51240			0.0497543
$925$	−1.69426			−0.0557071
$926$	40.9625			1.34611
$927$		−	17.0505i		−	0.560013i
$928$			15.1722i			0.498051i
$929$	57.5751			1.88898			0.944489	−	0.328544i	$-0.106558\pi$
$929$	57.5751			1.88898			0.944489	+	0.328544i	$0.106558\pi$
$930$			10.3321i			0.338802i
$931$	4.13526			0.135528
$932$	9.77838			0.320301
$933$		−	24.2880i		−	0.795153i
$934$		−	28.0168i		−	0.916737i
$935$		−	18.7450i		−	0.613026i
$936$	−13.4475			−0.439545
$937$	38.4664			1.25664			0.628320	−	0.777955i	$-0.283743\pi$
$937$	38.4664			1.25664			0.628320	+	0.777955i	$0.283743\pi$
$938$	−14.5594			−0.475382
$939$	5.31302			0.173384
$940$		−	8.26059i		−	0.269431i
$941$	9.33716			0.304383			0.152191	−	0.988351i	$-0.451367\pi$
$941$	9.33716			0.304383			0.152191	+	0.988351i	$0.451367\pi$
$942$		−	12.0530i		−	0.392709i
$943$	−8.09863			−0.263728
$944$			10.7538i			0.350007i
$945$			15.3244i			0.498504i
$946$		−	5.13574i		−	0.166977i
$947$	−36.6073			−1.18958			−0.594789	−	0.803882i	$-0.702764\pi$
$947$	−36.6073			−1.18958			−0.594789	+	0.803882i	$0.702764\pi$
$948$			0.771257i			0.0250493i
$949$			12.0206i			0.390205i
$950$		−	4.08533i		−	0.132546i
$951$			12.3597i			0.400791i
$952$	5.34672			0.173288
$953$	40.5875			1.31476			0.657379	−	0.753560i	$-0.271665\pi$
$953$	40.5875			1.31476			0.657379	+	0.753560i	$0.271665\pi$
$954$	−16.7916			−0.543649
$955$	84.5225			2.73509
$956$	−6.20051			−0.200539
$957$		−	21.0482i		−	0.680392i
$958$		−	29.1032i		−	0.940281i
$959$	0.646844			0.0208877
$960$	−23.3478			−0.753548
$961$	−21.1746			−0.683053
$962$	−0.909483			−0.0293229
$963$			42.9865i			1.38522i
$964$	3.18687			0.102642
$965$		−	22.3991i		−	0.721053i
$966$	−2.92590			−0.0941392
$967$	24.6725			0.793414			0.396707	−	0.917945i	$-0.370153\pi$
$967$	24.6725			0.793414			0.396707	+	0.917945i	$0.370153\pi$
$968$			10.9600i			0.352268i
$969$	−0.965729			−0.0310237
$970$	56.0982			1.80120
$971$	−41.4458			−1.33006			−0.665029	−	0.746817i	$-0.731581\pi$
$971$	−41.4458			−1.33006			−0.665029	+	0.746817i	$0.731581\pi$
$972$	6.74670			0.216401
$973$			6.56719i			0.210534i
$974$	−24.5836			−0.787708
$975$			7.48037i			0.239564i
$976$		−	33.0555i		−	1.05808i
$977$	−16.1801			−0.517648			−0.258824	−	0.965924i	$-0.583335\pi$
$977$	−16.1801			−0.517648			−0.258824	+	0.965924i	$0.583335\pi$
$978$	4.47947			0.143238
$979$	11.9394			0.381584
$980$	7.51189			0.239959
$981$	34.5725			1.10381
$982$			9.33680i			0.297949i
$983$	37.7743			1.20481			0.602407	−	0.798189i	$-0.294208\pi$
$983$	37.7743			1.20481			0.602407	+	0.798189i	$0.294208\pi$
$984$			8.44559i			0.269236i
$985$		−	78.2023i		−	2.49173i
$986$		−	12.9423i		−	0.412165i
$987$	−5.96897			−0.189994
$988$			0.584888i			0.0186078i
$989$		−	2.64989i		−	0.0842616i
$990$	−33.7969			−1.07414
$991$	−29.9693			−0.952006			−0.476003	−	0.879444i	$-0.657915\pi$
$991$	−29.9693			−0.952006			−0.476003	+	0.879444i	$0.657915\pi$
$992$			7.33277i			0.232816i
$993$		−	4.70270i		−	0.149236i
$994$			11.0734i			0.351226i
$995$			41.6350i			1.31992i
$996$	−1.81106			−0.0573856
$997$		−	35.5205i		−	1.12495i	−0.826815	−	0.562473i	$-0.809850\pi$
$997$		−	35.5205i		−	1.12495i	0.826815	−	0.562473i	$-0.190150\pi$
$998$	−30.1655			−0.954874
$999$	1.67277			0.0529242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.b.b.348.9	✓	26
349.348	even	2	inner	349.2.b.b.348.18	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.b.b.348.9	✓	26	1.1	even	1	trivial
349.2.b.b.348.18	yes	26	349.348	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.25654i q^{2} +0.849271 q^{3} +0.421101 q^{4} +3.08880 q^{5} -1.06714i q^{6} -1.10667i q^{7} -3.04222i q^{8} -2.27874 q^{9} +O(q^{10})\)	\(q-1.25654i q^{2} +0.849271 q^{3} +0.421101 q^{4} +3.08880 q^{5} -1.06714i q^{6} -1.10667i q^{7} -3.04222i q^{8} -2.27874 q^{9} -3.88121i q^{10} +3.82134i q^{11} +0.357629 q^{12} +1.93980i q^{13} -1.39058 q^{14} +2.62323 q^{15} -2.98047 q^{16} -1.58811 q^{17} +2.86333i q^{18} +0.716027 q^{19} +1.30070 q^{20} -0.939863i q^{21} +4.80167 q^{22} +2.47752 q^{23} -2.58367i q^{24} +4.54068 q^{25} +2.43744 q^{26} -4.48308 q^{27} -0.466021i q^{28} -6.48565 q^{29} -3.29619i q^{30} -3.13454 q^{31} -2.33934i q^{32} +3.24535i q^{33} +1.99552i q^{34} -3.41828i q^{35} -0.959580 q^{36} -0.373131 q^{37} -0.899719i q^{38} +1.64741i q^{39} -9.39679i q^{40} -3.26884 q^{41} -1.18098 q^{42} -1.06957i q^{43} +1.60917i q^{44} -7.03857 q^{45} -3.11311i q^{46} -6.35089i q^{47} -2.53123 q^{48} +5.77528 q^{49} -5.70555i q^{50} -1.34873 q^{51} +0.816851i q^{52} +5.86436i q^{53} +5.63318i q^{54} +11.8033i q^{55} -3.36673 q^{56} +0.608101 q^{57} +8.14949i q^{58} -3.60809i q^{59} +1.10464 q^{60} +11.0907i q^{61} +3.93869i q^{62} +2.52181i q^{63} -8.90043 q^{64} +5.99164i q^{65} +4.07792 q^{66} +10.4701 q^{67} -0.668753 q^{68} +2.10409 q^{69} -4.29522 q^{70} -7.96314i q^{71} +6.93242i q^{72} +6.19683 q^{73} +0.468854i q^{74} +3.85626 q^{75} +0.301520 q^{76} +4.22896 q^{77} +2.07004 q^{78} +2.15658i q^{79} -9.20607 q^{80} +3.02887 q^{81} +4.10744i q^{82} -5.06407 q^{83} -0.395778i q^{84} -4.90534 q^{85} -1.34396 q^{86} -5.50807 q^{87} +11.6253 q^{88} -3.12440i q^{89} +8.84426i q^{90} +2.14672 q^{91} +1.04329 q^{92} -2.66208 q^{93} -7.98016 q^{94} +2.21166 q^{95} -1.98674i q^{96} +14.4538i q^{97} -7.25688i q^{98} -8.70784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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