LMFDB - Embedded newform 403.2.c.b.311.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(311,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("403.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			311.14
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.624841i q^{2} -2.78388 q^{3} +1.60957 q^{4} -0.619834i q^{5} +1.73948i q^{6} +2.35216i q^{7} -2.25541i q^{8} +4.74999 q^{9} +O(q^{10})$	\(q-0.624841i q^{2} -2.78388 q^{3} +1.60957 q^{4} -0.619834i q^{5} +1.73948i q^{6} +2.35216i q^{7} -2.25541i q^{8} +4.74999 q^{9} -0.387298 q^{10} +1.21518i q^{11} -4.48086 q^{12} +(-0.818917 + 3.51132i) q^{13} +1.46972 q^{14} +1.72554i q^{15} +1.80988 q^{16} +4.00546 q^{17} -2.96799i q^{18} -4.95017i q^{19} -0.997669i q^{20} -6.54812i q^{21} +0.759295 q^{22} +2.11759 q^{23} +6.27879i q^{24} +4.61581 q^{25} +(2.19402 + 0.511692i) q^{26} -4.87176 q^{27} +3.78597i q^{28} +10.4829 q^{29} +1.07819 q^{30} +1.00000i q^{31} -5.64170i q^{32} -3.38292i q^{33} -2.50277i q^{34} +1.45795 q^{35} +7.64546 q^{36} +10.5475i q^{37} -3.09307 q^{38} +(2.27977 - 9.77510i) q^{39} -1.39798 q^{40} -1.88041i q^{41} -4.09153 q^{42} -5.95396 q^{43} +1.95592i q^{44} -2.94420i q^{45} -1.32315i q^{46} -12.5015i q^{47} -5.03848 q^{48} +1.46736 q^{49} -2.88414i q^{50} -11.1507 q^{51} +(-1.31811 + 5.65173i) q^{52} -2.74137 q^{53} +3.04407i q^{54} +0.753211 q^{55} +5.30507 q^{56} +13.7807i q^{57} -6.55011i q^{58} +7.46822i q^{59} +2.77739i q^{60} -6.44716 q^{61} +0.624841 q^{62} +11.1727i q^{63} +0.0945869 q^{64} +(2.17644 + 0.507592i) q^{65} -2.11379 q^{66} +13.2892i q^{67} +6.44708 q^{68} -5.89511 q^{69} -0.910984i q^{70} +2.71975i q^{71} -10.7132i q^{72} -7.81310i q^{73} +6.59050 q^{74} -12.8498 q^{75} -7.96766i q^{76} -2.85830 q^{77} +(-6.10788 - 1.42449i) q^{78} +2.11825 q^{79} -1.12182i q^{80} -0.687580 q^{81} -1.17495 q^{82} +11.0061i q^{83} -10.5397i q^{84} -2.48272i q^{85} +3.72027i q^{86} -29.1830 q^{87} +2.74073 q^{88} -2.01694i q^{89} -1.83966 q^{90} +(-8.25917 - 1.92622i) q^{91} +3.40841 q^{92} -2.78388i q^{93} -7.81144 q^{94} -3.06828 q^{95} +15.7058i q^{96} +5.43723i q^{97} -0.916869i q^{98} +5.77210i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.624841i		−	0.441829i	−0.975293	−	0.220915i	$-0.929096\pi$
$2$		−	0.624841i		−	0.441829i	0.975293	−	0.220915i	$-0.0709042\pi$
$3$	−2.78388			−1.60727			−0.803637	−	0.595120i	$-0.797105\pi$
$3$	−2.78388			−1.60727			−0.803637	+	0.595120i	$0.797105\pi$
$4$	1.60957			0.804787
$5$		−	0.619834i		−	0.277198i	−0.990349	−	0.138599i	$-0.955740\pi$
$5$		−	0.619834i		−	0.277198i	0.990349	−	0.138599i	$-0.0442599\pi$
$6$			1.73948i			0.710140i
$7$			2.35216i			0.889031i	0.895771	+	0.444516i	$0.146624\pi$
$7$			2.35216i			0.889031i	−0.895771	+	0.444516i	$0.853376\pi$
$8$		−	2.25541i		−	0.797408i
$9$	4.74999			1.58333
$10$	−0.387298			−0.122474
$11$			1.21518i			0.366391i	0.983077	+	0.183196i	$0.0586441\pi$
$11$			1.21518i			0.366391i	−0.983077	+	0.183196i	$0.941356\pi$
$12$	−4.48086			−1.29351
$13$	−0.818917	+	3.51132i	−0.227127	+	0.973865i
$13$	−0.818917	+	3.51132i	−0.227127	+	0.973865i
$14$	1.46972			0.392800
$15$			1.72554i			0.445533i
$16$	1.80988			0.452469
$17$	4.00546			0.971466			0.485733	−	0.874107i	$-0.338553\pi$
$17$	4.00546			0.971466			0.485733	+	0.874107i	$0.338553\pi$
$18$		−	2.96799i		−	0.699561i
$19$		−	4.95017i		−	1.13565i	−0.823151	−	0.567823i	$-0.807786\pi$
$19$		−	4.95017i		−	1.13565i	0.823151	−	0.567823i	$-0.192214\pi$
$20$		−	0.997669i		−	0.223086i
$21$		−	6.54812i		−	1.42892i
$22$	0.759295			0.161882
$23$	2.11759			0.441547			0.220774	−	0.975325i	$-0.429142\pi$
$23$	2.11759			0.441547			0.220774	+	0.975325i	$0.429142\pi$
$24$			6.27879i			1.28165i
$25$	4.61581			0.923161
$26$	2.19402	+	0.511692i	0.430282	+	0.100351i
$27$	−4.87176			−0.937570
$28$			3.78597i			0.715481i
$29$	10.4829			1.94662			0.973309	−	0.229500i	$-0.0737092\pi$
$29$	10.4829			1.94662			0.973309	+	0.229500i	$0.0737092\pi$
$30$	1.07819			0.196850
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$		−	5.64170i		−	0.997322i
$33$		−	3.38292i		−	0.588891i
$34$		−	2.50277i		−	0.429222i
$35$	1.45795			0.246438
$36$	7.64546			1.27424
$37$			10.5475i			1.73400i	0.498310	+	0.866999i	$0.333954\pi$
$37$			10.5475i			1.73400i	−0.498310	+	0.866999i	$0.666046\pi$
$38$	−3.09307			−0.501761
$39$	2.27977	−	9.77510i	0.365055	−	1.56527i
$40$	−1.39798			−0.221040
$41$		−	1.88041i		−	0.293670i	−0.989161	−	0.146835i	$-0.953091\pi$
$41$		−	1.88041i		−	0.293670i	0.989161	−	0.146835i	$-0.0469086\pi$
$42$	−4.09153			−0.631337
$43$	−5.95396			−0.907970			−0.453985	−	0.891009i	$-0.649998\pi$
$43$	−5.95396			−0.907970			−0.453985	+	0.891009i	$0.649998\pi$
$44$			1.95592i			0.294867i
$45$		−	2.94420i		−	0.438896i
$46$		−	1.32315i		−	0.195089i
$47$		−	12.5015i		−	1.82353i	−0.410712	−	0.911765i	$-0.634720\pi$
$47$		−	12.5015i		−	1.82353i	0.410712	−	0.911765i	$-0.365280\pi$
$48$	−5.03848			−0.727242
$49$	1.46736			0.209623
$50$		−	2.88414i		−	0.407880i
$51$	−11.1507			−1.56141
$52$	−1.31811	+	5.65173i	−0.182789	+	0.783754i
$53$	−2.74137			−0.376557			−0.188278	−	0.982116i	$-0.560291\pi$
$53$	−2.74137			−0.376557			−0.188278	+	0.982116i	$0.560291\pi$
$54$			3.04407i			0.414246i
$55$	0.753211			0.101563
$56$	5.30507			0.708920
$57$			13.7807i			1.82529i
$58$		−	6.55011i		−	0.860072i
$59$			7.46822i			0.972280i	0.873881	+	0.486140i	$0.161595\pi$
$59$			7.46822i			0.972280i	−0.873881	+	0.486140i	$0.838405\pi$
$60$			2.77739i			0.358560i
$61$	−6.44716			−0.825474			−0.412737	−	0.910850i	$-0.635427\pi$
$61$	−6.44716			−0.825474			−0.412737	+	0.910850i	$0.635427\pi$
$62$	0.624841			0.0793549
$63$			11.1727i			1.40763i
$64$	0.0945869			0.0118234
$65$	2.17644	+	0.507592i	0.269954	+	0.0629591i
$66$	−2.11379			−0.260189
$67$			13.2892i			1.62353i	0.583985	+	0.811764i	$0.301493\pi$
$67$			13.2892i			1.62353i	−0.583985	+	0.811764i	$0.698507\pi$
$68$	6.44708			0.781823
$69$	−5.89511			−0.709688
$70$		−	0.910984i		−	0.108883i
$71$			2.71975i			0.322775i	0.986891	+	0.161388i	$0.0515969\pi$
$71$			2.71975i			0.322775i	−0.986891	+	0.161388i	$0.948403\pi$
$72$		−	10.7132i		−	1.26256i
$73$		−	7.81310i		−	0.914455i	−0.889350	−	0.457227i	$-0.848843\pi$
$73$		−	7.81310i		−	0.914455i	0.889350	−	0.457227i	$-0.151157\pi$
$74$	6.59050			0.766131
$75$	−12.8498			−1.48377
$76$		−	7.96766i		−	0.913953i
$77$	−2.85830			−0.325733
$78$	−6.10788	−	1.42449i	−0.691581	−	0.161292i
$79$	2.11825			0.238322			0.119161	−	0.992875i	$-0.461980\pi$
$79$	2.11825			0.238322			0.119161	+	0.992875i	$0.461980\pi$
$80$		−	1.12182i		−	0.125424i
$81$	−0.687580			−0.0763978
$82$	−1.17495			−0.129752
$83$			11.0061i			1.20808i	0.796955	+	0.604039i	$0.206443\pi$
$83$			11.0061i			1.20808i	−0.796955	+	0.604039i	$0.793557\pi$
$84$		−	10.5397i		−	1.14997i
$85$		−	2.48272i		−	0.269289i
$86$			3.72027i			0.401168i
$87$	−29.1830			−3.12875
$88$	2.74073			0.292163
$89$		−	2.01694i		−	0.213795i	−0.994270	−	0.106898i	$-0.965908\pi$
$89$		−	2.01694i		−	0.213795i	0.994270	−	0.106898i	$-0.0340917\pi$
$90$	−1.83966			−0.193917
$91$	−8.25917	−	1.92622i	−0.865797	−	0.201923i
$92$	3.40841			0.355352
$93$		−	2.78388i		−	0.288675i
$94$	−7.81144			−0.805689
$95$	−3.06828			−0.314799
$96$			15.7058i			1.60297i
$97$			5.43723i			0.552067i	0.961148	+	0.276034i	$0.0890201\pi$
$97$			5.43723i			0.552067i	−0.961148	+	0.276034i	$0.910980\pi$
$98$		−	0.916869i		−	0.0926178i
$99$			5.77210i			0.580118i
$100$	7.42948			0.742948
$101$	−12.4640			−1.24022			−0.620108	−	0.784516i	$-0.712911\pi$
$101$	−12.4640			−1.24022			−0.620108	+	0.784516i	$0.712911\pi$
$102$			6.96742i			0.689877i
$103$	−12.3489			−1.21678			−0.608388	−	0.793640i	$-0.708184\pi$
$103$	−12.3489			−1.21678			−0.608388	+	0.793640i	$0.708184\pi$
$104$	7.91947	+	1.84699i	0.776567	+	0.181112i
$105$	−4.05875			−0.396093
$106$			1.71292i			0.166374i
$107$	−2.92701			−0.282965			−0.141482	−	0.989941i	$-0.545187\pi$
$107$	−2.92701			−0.282965			−0.141482	+	0.989941i	$0.545187\pi$
$108$	−7.84145			−0.754544
$109$		−	9.65896i		−	0.925160i	−0.886577	−	0.462580i	$-0.846924\pi$
$109$		−	9.65896i		−	0.925160i	0.886577	−	0.462580i	$-0.153076\pi$
$110$		−	0.470637i		−	0.0448735i
$111$		−	29.3630i		−	2.78701i
$112$			4.25711i			0.402259i
$113$	11.8792			1.11750			0.558748	−	0.829337i	$-0.311282\pi$
$113$	11.8792			1.11750			0.558748	+	0.829337i	$0.311282\pi$
$114$	8.61072			0.806468
$115$		−	1.31255i		−	0.122396i
$116$	16.8729			1.56661
$117$	−3.88984	+	16.6787i	−0.359616	+	1.54195i
$118$	4.66645			0.429582
$119$			9.42146i			0.863664i
$120$	3.89181			0.355272
$121$	9.52333			0.865758
$122$			4.02845i			0.364718i
$123$			5.23482i			0.472008i
$124$			1.60957i			0.144544i
$125$		−	5.96020i		−	0.533097i
$126$	6.98116			0.621932
$127$	−8.62348			−0.765210			−0.382605	−	0.923912i	$-0.624973\pi$
$127$	−8.62348			−0.765210			−0.382605	+	0.923912i	$0.624973\pi$
$128$		−	11.3425i		−	1.00255i
$129$	16.5751			1.45936
$130$	0.317164	−	1.35993i	0.0278172	−	0.119273i
$131$	11.3070			0.987898			0.493949	−	0.869491i	$-0.335553\pi$
$131$	11.3070			0.987898			0.493949	+	0.869491i	$0.335553\pi$
$132$		−	5.44506i		−	0.473932i
$133$	11.6436			1.00962
$134$	8.30360			0.717322
$135$			3.01968i			0.259893i
$136$		−	9.03394i		−	0.774654i
$137$		−	6.79159i		−	0.580244i	−0.956990	−	0.290122i	$-0.906304\pi$
$137$		−	6.79159i		−	0.580244i	0.956990	−	0.290122i	$-0.0936960\pi$
$138$			3.68350i			0.313561i
$139$	4.80698			0.407723			0.203862	−	0.979000i	$-0.434651\pi$
$139$	4.80698			0.407723			0.203862	+	0.979000i	$0.434651\pi$
$140$	2.34667			0.198330
$141$			34.8027i			2.93091i
$142$	1.69941			0.142611
$143$	−4.26689	−	0.995132i	−0.356815	−	0.0832171i
$144$	8.59689			0.716408
$145$		−	6.49763i		−	0.539599i
$146$	−4.88195			−0.404033
$147$	−4.08497			−0.336922
$148$			16.9770i			1.39550i
$149$		−	10.3179i		−	0.845277i	−0.906298	−	0.422639i	$-0.861104\pi$
$149$		−	10.3179i		−	0.845277i	0.906298	−	0.422639i	$-0.138896\pi$
$150$			8.02911i			0.655574i
$151$		−	7.91075i		−	0.643768i	−0.946779	−	0.321884i	$-0.895684\pi$
$151$		−	7.91075i		−	0.643768i	0.946779	−	0.321884i	$-0.104316\pi$
$152$	−11.1646			−0.905573
$153$	19.0259			1.53815
$154$			1.78598i			0.143918i
$155$	0.619834			0.0497863
$156$	3.66945	−	15.7337i	0.293791	−	1.25971i
$157$	−4.63624			−0.370012			−0.185006	−	0.982737i	$-0.559230\pi$
$157$	−4.63624			−0.370012			−0.185006	+	0.982737i	$0.559230\pi$
$158$		−	1.32357i		−	0.105298i
$159$	7.63166			0.605230
$160$	−3.49692			−0.276456
$161$			4.98089i			0.392549i
$162$			0.429628i			0.0337548i
$163$		−	7.44256i		−	0.582946i	−0.956579	−	0.291473i	$-0.905855\pi$
$163$		−	7.44256i		−	0.582946i	0.956579	−	0.291473i	$-0.0941454\pi$
$164$		−	3.02665i		−	0.236342i
$165$	−2.09685			−0.163239
$166$	6.87707			0.533764
$167$			6.43784i			0.498175i	0.968481	+	0.249087i	$0.0801306\pi$
$167$			6.43784i			0.498175i	−0.968481	+	0.249087i	$0.919869\pi$
$168$	−14.7687			−1.13943
$169$	−11.6588	−	5.75096i	−0.896827	−	0.442381i
$170$	−1.55130			−0.118980
$171$		−	23.5132i		−	1.79810i
$172$	−9.58333			−0.730722
$173$	−10.0469			−0.763854			−0.381927	−	0.924192i	$-0.624739\pi$
$173$	−10.0469			−0.763854			−0.381927	+	0.924192i	$0.624739\pi$
$174$			18.2347i			1.38237i
$175$			10.8571i			0.820719i
$176$			2.19933i			0.165781i
$177$		−	20.7906i		−	1.56272i
$178$	−1.26027			−0.0944610
$179$	−19.8830			−1.48612			−0.743061	−	0.669223i	$-0.766627\pi$
$179$	−19.8830			−1.48612			−0.743061	+	0.669223i	$0.766627\pi$
$180$		−	4.73891i		−	0.353218i
$181$	6.79278			0.504903			0.252452	−	0.967609i	$-0.418763\pi$
$181$	6.79278			0.504903			0.252452	+	0.967609i	$0.418763\pi$
$182$	−1.20358	+	5.16067i	−0.0892153	+	0.382534i
$183$	17.9481			1.32676
$184$		−	4.77603i		−	0.352093i
$185$	6.53770			0.480661
$186$	−1.73948			−0.127545
$187$			4.86736i			0.355936i
$188$		−	20.1221i		−	1.46755i
$189$		−	11.4591i		−	0.833529i
$190$			1.91719i			0.139087i
$191$	10.4860			0.758738			0.379369	−	0.925245i	$-0.376141\pi$
$191$	10.4860			0.758738			0.379369	+	0.925245i	$0.376141\pi$
$192$	−0.263319			−0.0190034
$193$			12.9006i			0.928604i	0.885677	+	0.464302i	$0.153695\pi$
$193$			12.9006i			0.928604i	−0.885677	+	0.464302i	$0.846305\pi$
$194$	3.39740			0.243919
$195$	−6.05894	−	1.41308i	−0.433890	−	0.101192i
$196$	2.36183			0.168702
$197$		−	20.5640i		−	1.46513i	−0.680699	−	0.732563i	$-0.738324\pi$
$197$		−	20.5640i		−	1.46513i	0.680699	−	0.732563i	$-0.261676\pi$
$198$	3.60664			0.256313
$199$	−1.44890			−0.102710			−0.0513549	−	0.998680i	$-0.516354\pi$
$199$	−1.44890			−0.102710			−0.0513549	+	0.998680i	$0.516354\pi$
$200$		−	10.4105i		−	0.736136i
$201$		−	36.9954i		−	2.60945i
$202$			7.78803i			0.547964i
$203$			24.6573i			1.73060i
$204$	−17.9479			−1.25660
$205$	−1.16554			−0.0814048
$206$			7.71612i			0.537607i
$207$	10.0585			0.699115
$208$	−1.48214	+	6.35506i	−0.102768	+	0.440644i
$209$	6.01535			0.416090
$210$			2.53607i			0.175006i
$211$	−7.11123			−0.489557			−0.244779	−	0.969579i	$-0.578715\pi$
$211$	−7.11123			−0.489557			−0.244779	+	0.969579i	$0.578715\pi$
$212$	−4.41244			−0.303048
$213$		−	7.57146i		−	0.518788i
$214$			1.82892i			0.125022i
$215$			3.69046i			0.251688i
$216$			10.9878i			0.747625i
$217$	−2.35216			−0.159675
$218$	−6.03531			−0.408763
$219$			21.7507i			1.46978i
$220$	1.21235			0.0817365
$221$	−3.28014	+	14.0644i	−0.220646	+	0.946077i
$222$	−18.3472			−1.23138
$223$		−	8.70644i		−	0.583026i	−0.956567	−	0.291513i	$-0.905841\pi$
$223$		−	8.70644i		−	0.583026i	0.956567	−	0.291513i	$-0.0941587\pi$
$224$	13.2702			0.886650
$225$	21.9250			1.46167
$226$		−	7.42258i		−	0.493743i
$227$		−	0.260146i		−	0.0172665i	−0.999963	−	0.00863326i	$-0.997252\pi$
$227$		−	0.260146i		−	0.0172665i	0.999963	−	0.00863326i	$-0.00274809\pi$
$228$			22.1810i			1.46897i
$229$		−	1.38191i		−	0.0913190i	−0.998957	−	0.0456595i	$-0.985461\pi$
$229$		−	1.38191i		−	0.0913190i	0.998957	−	0.0456595i	$-0.0145389\pi$
$230$	−0.820136			−0.0540782
$231$	7.95715			0.523542
$232$		−	23.6431i		−	1.55225i
$233$	14.6663			0.960823			0.480412	−	0.877043i	$-0.340487\pi$
$233$	14.6663			0.960823			0.480412	+	0.877043i	$0.340487\pi$
$234$	10.4216	+	2.43053i	0.681278	+	0.158889i
$235$	−7.74885			−0.505479
$236$			12.0207i			0.782478i
$237$	−5.89696			−0.383048
$238$	5.88691			0.381592
$239$		−	27.1469i		−	1.75599i	−0.478670	−	0.877995i	$-0.658881\pi$
$239$		−	27.1469i		−	1.75599i	0.478670	−	0.877995i	$-0.341119\pi$
$240$			3.12302i			0.201590i
$241$			22.9384i			1.47759i	0.673929	+	0.738796i	$0.264605\pi$
$241$			22.9384i			1.47759i	−0.673929	+	0.738796i	$0.735395\pi$
$242$		−	5.95057i		−	0.382517i
$243$	16.5294			1.06036
$244$	−10.3772			−0.664331
$245$		−	0.909522i		−	0.0581072i
$246$	3.27093			0.208547
$247$	17.3816	+	4.05377i	1.10597	+	0.257935i
$248$	2.25541			0.143219
$249$		−	30.6397i		−	1.94171i
$250$	−3.72418			−0.235538
$251$	−5.40311			−0.341041			−0.170521	−	0.985354i	$-0.554545\pi$
$251$	−5.40311			−0.341041			−0.170521	+	0.985354i	$0.554545\pi$
$252$			17.9833i			1.13284i
$253$			2.57325i			0.161779i
$254$			5.38830i			0.338092i
$255$			6.91159i			0.432821i
$256$	−6.89809			−0.431130
$257$	−21.4190			−1.33608			−0.668042	−	0.744124i	$-0.732867\pi$
$257$	−21.4190			−1.33608			−0.668042	+	0.744124i	$0.732867\pi$
$258$		−	10.3568i		−	0.644786i
$259$	−24.8093			−1.54158
$260$	3.50314	+	0.817008i	0.217255	+	0.0506687i
$261$	49.7934			3.08214
$262$		−	7.06508i		−	0.436482i
$263$	6.53589			0.403020			0.201510	−	0.979486i	$-0.435415\pi$
$263$	6.53589			0.403020			0.201510	+	0.979486i	$0.435415\pi$
$264$	−7.62987			−0.469586
$265$			1.69920i			0.104381i
$266$		−	7.27537i		−	0.446082i
$267$			5.61492i			0.343628i
$268$			21.3899i			1.30659i
$269$	−18.8323			−1.14822			−0.574112	−	0.818777i	$-0.694653\pi$
$269$	−18.8323			−1.14822			−0.574112	+	0.818777i	$0.694653\pi$
$270$	1.88682			0.114828
$271$			18.1725i			1.10390i	0.833877	+	0.551950i	$0.186116\pi$
$271$			18.1725i			1.10390i	−0.833877	+	0.551950i	$0.813884\pi$
$272$	7.24938			0.439558
$273$	22.9925	+	5.36236i	1.39157	+	0.324545i
$274$	−4.24366			−0.256369
$275$			5.60904i			0.338238i
$276$	−9.48861			−0.571147
$277$	−31.5861			−1.89782			−0.948912	−	0.315541i	$-0.897814\pi$
$277$	−31.5861			−1.89782			−0.948912	+	0.315541i	$0.897814\pi$
$278$		−	3.00360i		−	0.180144i
$279$			4.74999i			0.284374i
$280$		−	3.28826i		−	0.196511i
$281$			27.0399i			1.61306i	0.591191	+	0.806531i	$0.298658\pi$
$281$			27.0399i			1.61306i	−0.591191	+	0.806531i	$0.701342\pi$
$282$	21.7461			1.29496
$283$	32.3052			1.92035			0.960173	−	0.279405i	$-0.0901371\pi$
$283$	32.3052			1.92035			0.960173	+	0.279405i	$0.0901371\pi$
$284$			4.37764i			0.259765i
$285$	8.54173			0.505968
$286$	−0.621799	+	2.66613i	−0.0367678	+	0.157651i
$287$	4.42301			0.261082
$288$		−	26.7980i		−	1.57909i
$289$	−0.956311			−0.0562536
$290$	−4.05998			−0.238410
$291$		−	15.1366i		−	0.887323i
$292$		−	12.5758i		−	0.735941i
$293$		−	18.6860i		−	1.09165i	−0.837899	−	0.545825i	$-0.816216\pi$
$293$		−	18.6860i		−	1.09165i	0.837899	−	0.545825i	$-0.183784\pi$
$294$			2.55245i			0.148862i
$295$	4.62906			0.269514
$296$	23.7889			1.38270
$297$		−	5.92007i		−	0.343517i
$298$	−6.44706			−0.373468
$299$	−1.73413	+	7.43553i	−0.100287	+	0.430008i
$300$	−20.6828			−1.19412
$301$		−	14.0046i		−	0.807213i
$302$	−4.94296			−0.284435
$303$	34.6983			1.99337
$304$		−	8.95919i		−	0.513845i
$305$			3.99617i			0.228820i
$306$		−	11.8881i		−	0.679600i
$307$		−	21.9423i		−	1.25231i	−0.779698	−	0.626156i	$-0.784627\pi$
$307$		−	21.9423i		−	1.25231i	0.779698	−	0.626156i	$-0.215373\pi$
$308$	−4.60064			−0.262146
$309$	34.3779			1.95569
$310$		−	0.387298i		−	0.0219970i
$311$	−17.9051			−1.01531			−0.507653	−	0.861562i	$-0.669487\pi$
$311$	−17.9051			−1.01531			−0.507653	+	0.861562i	$0.669487\pi$
$312$	−22.0468	−	5.14180i	−1.24816	−	0.291097i
$313$	−4.73057			−0.267388			−0.133694	−	0.991023i	$-0.542684\pi$
$313$	−4.73057			−0.267388			−0.133694	+	0.991023i	$0.542684\pi$
$314$			2.89691i			0.163482i
$315$	6.92523			0.390192
$316$	3.40948			0.191798
$317$		−	19.0145i		−	1.06796i	−0.845496	−	0.533981i	$-0.820695\pi$
$317$		−	19.0145i		−	1.06796i	0.845496	−	0.533981i	$-0.179305\pi$
$318$		−	4.76857i		−	0.267408i
$319$			12.7386i			0.713223i
$320$		−	0.0586282i		−	0.00327742i
$321$	8.14845			0.454802
$322$	3.11227			0.173440
$323$		−	19.8277i		−	1.10324i
$324$	−1.10671			−0.0614840
$325$	−3.77996	+	16.2076i	−0.209674	+	0.899035i
$326$	−4.65042			−0.257563
$327$			26.8894i			1.48699i
$328$	−4.24108			−0.234175
$329$	29.4055			1.62118
$330$			1.31020i			0.0721239i
$331$		−	24.5020i		−	1.34675i	−0.739301	−	0.673375i	$-0.764844\pi$
$331$		−	24.5020i		−	1.34675i	0.739301	−	0.673375i	$-0.235156\pi$
$332$			17.7152i			0.972245i
$333$			50.1005i			2.74549i
$334$	4.02262			0.220108
$335$	8.23707			0.450039
$336$		−	11.8513i		−	0.646541i
$337$	6.91654			0.376768			0.188384	−	0.982095i	$-0.439675\pi$
$337$	6.91654			0.376768			0.188384	+	0.982095i	$0.439675\pi$
$338$	−3.59343	+	7.28486i	−0.195457	+	0.396244i
$339$	−33.0701			−1.79612
$340$		−	3.99612i		−	0.216720i
$341$	−1.21518			−0.0658058
$342$	−14.6920			−0.794454
$343$			19.9166i			1.07539i
$344$			13.4286i			0.724022i
$345$			3.65399i			0.196724i
$346$			6.27773i			0.337493i
$347$	−17.8295			−0.957137			−0.478569	−	0.878050i	$-0.658844\pi$
$347$	−17.8295			−0.957137			−0.478569	+	0.878050i	$0.658844\pi$
$348$	−46.9722			−2.51797
$349$			7.98868i			0.427624i	0.976875	+	0.213812i	$0.0685880\pi$
$349$			7.98868i			0.427624i	−0.976875	+	0.213812i	$0.931412\pi$
$350$	6.78395			0.362618
$351$	3.98956	−	17.1063i	0.212947	−	0.913067i
$352$	6.85569			0.365410
$353$		−	4.94127i		−	0.262997i	−0.991316	−	0.131499i	$-0.958021\pi$
$353$		−	4.94127i		−	0.262997i	0.991316	−	0.131499i	$-0.0419789\pi$
$354$	−12.9908			−0.690455
$355$	1.68579			0.0894727
$356$		−	3.24642i		−	0.172060i
$357$		−	26.2282i		−	1.38814i
$358$			12.4237i			0.656612i
$359$			9.47701i			0.500178i	0.968223	+	0.250089i	$0.0804598\pi$
$359$			9.47701i			0.500178i	−0.968223	+	0.250089i	$0.919540\pi$
$360$	−6.64038			−0.349979
$361$	−5.50414			−0.289691
$362$		−	4.24441i		−	0.223081i
$363$	−26.5118			−1.39151
$364$	−13.2938	−	3.10039i	−0.696782	−	0.162505i
$365$	−4.84283			−0.253485
$366$		−	11.2147i		−	0.586202i
$367$	−11.4595			−0.598183			−0.299091	−	0.954225i	$-0.596684\pi$
$367$	−11.4595			−0.598183			−0.299091	+	0.954225i	$0.596684\pi$
$368$	3.83257			0.199787
$369$		−	8.93190i		−	0.464976i
$370$		−	4.08502i		−	0.212370i
$371$		−	6.44814i		−	0.334771i
$372$		−	4.48086i		−	0.232322i
$373$	34.3146			1.77674			0.888372	−	0.459124i	$-0.151836\pi$
$373$	34.3146			1.77674			0.888372	+	0.459124i	$0.151836\pi$
$374$	3.04132			0.157263
$375$			16.5925i			0.856833i
$376$	−28.1960			−1.45410
$377$	−8.58458	+	36.8087i	−0.442129	+	1.89574i
$378$	−7.16013			−0.368277
$379$			29.0334i			1.49135i	0.666311	+	0.745674i	$0.267872\pi$
$379$			29.0334i			1.49135i	−0.666311	+	0.745674i	$0.732128\pi$
$380$	−4.93863			−0.253346
$381$	24.0067			1.22990
$382$		−	6.55206i		−	0.335233i
$383$		−	19.8755i		−	1.01559i	−0.861478	−	0.507794i	$-0.830461\pi$
$383$		−	19.8755i		−	1.01559i	0.861478	−	0.507794i	$-0.169539\pi$
$384$			31.5762i			1.61137i
$385$			1.77167i			0.0902926i
$386$	8.06081			0.410284
$387$	−28.2812			−1.43762
$388$			8.75163i			0.444297i
$389$	−25.2071			−1.27805			−0.639024	−	0.769187i	$-0.720662\pi$
$389$	−25.2071			−1.27805			−0.639024	+	0.769187i	$0.720662\pi$
$390$	−0.882948	+	3.78587i	−0.0447098	+	0.191705i
$391$	8.48190			0.428948
$392$		−	3.30951i		−	0.167155i
$393$	−31.4774			−1.58782
$394$	−12.8492			−0.647335
$395$		−	1.31296i		−	0.0660624i
$396$			9.29062i			0.466871i
$397$		−	7.74047i		−	0.388483i	−0.980954	−	0.194241i	$-0.937775\pi$
$397$		−	7.74047i		−	0.388483i	0.980954	−	0.194241i	$-0.0622245\pi$
$398$			0.905332i			0.0453802i
$399$	−32.4143			−1.62274
$400$	8.35404			0.417702
$401$		−	7.36568i		−	0.367825i	−0.982943	−	0.183912i	$-0.941124\pi$
$401$		−	7.36568i		−	0.367825i	0.982943	−	0.183912i	$-0.0588762\pi$
$402$	−23.1162			−1.15293
$403$	−3.51132	−	0.818917i	−0.174911	−	0.0407931i
$404$	−20.0618			−0.998110
$405$			0.426186i			0.0211773i
$406$	15.4069			0.764631
$407$	−12.8171			−0.635321
$408$			25.1494i			1.24508i
$409$			8.29760i			0.410290i	0.978732	+	0.205145i	$0.0657666\pi$
$409$			8.29760i			0.410290i	−0.978732	+	0.205145i	$0.934233\pi$
$410$			0.728277i			0.0359670i
$411$			18.9070i			0.932612i
$412$	−19.8765			−0.979246
$413$	−17.5664			−0.864387
$414$		−	6.28497i		−	0.308889i
$415$	6.82196			0.334877
$416$	19.8098	+	4.62008i	0.971257	+	0.226518i
$417$	−13.3821			−0.655323
$418$		−	3.75864i		−	0.183841i
$419$	6.23536			0.304617			0.152309	−	0.988333i	$-0.451329\pi$
$419$	6.23536			0.304617			0.152309	+	0.988333i	$0.451329\pi$
$420$	−6.53285			−0.318771
$421$		−	10.9675i		−	0.534525i	−0.963624	−	0.267262i	$-0.913881\pi$
$421$		−	10.9675i		−	0.534525i	0.963624	−	0.267262i	$-0.0861190\pi$
$422$			4.44339i			0.216301i
$423$		−	59.3819i		−	2.88725i
$424$			6.18292i			0.300269i
$425$	18.4884			0.896820
$426$	−4.73096			−0.229216
$427$		−	15.1647i		−	0.733872i
$428$	−4.71124			−0.227726
$429$	11.8785	+	2.77033i	0.573500	+	0.133753i
$430$	2.30595			0.111203
$431$		−	7.82125i		−	0.376736i	−0.982098	−	0.188368i	$-0.939680\pi$
$431$		−	7.82125i		−	0.376736i	0.982098	−	0.188368i	$-0.0603198\pi$
$432$	−8.81728			−0.424221
$433$	−33.6131			−1.61534			−0.807671	−	0.589633i	$-0.799272\pi$
$433$	−33.6131			−1.61534			−0.807671	+	0.589633i	$0.799272\pi$
$434$			1.46972i			0.0705489i
$435$			18.0886i			0.867283i
$436$		−	15.5468i		−	0.744557i
$437$		−	10.4824i		−	0.501441i
$438$	13.5908			0.649391
$439$	17.3442			0.827793			0.413896	−	0.910324i	$-0.364168\pi$
$439$	17.3442			0.827793			0.413896	+	0.910324i	$0.364168\pi$
$440$		−	1.69880i		−	0.0809870i
$441$	6.96996			0.331903
$442$	8.78804	+	2.04956i	0.418004	+	0.0974877i
$443$	−10.2049			−0.484849			−0.242425	−	0.970170i	$-0.577943\pi$
$443$	−10.2049			−0.484849			−0.242425	+	0.970170i	$0.577943\pi$
$444$		−	47.2619i		−	2.24295i
$445$	−1.25017			−0.0592637
$446$	−5.44014			−0.257598
$447$			28.7239i			1.35859i
$448$			0.222483i			0.0105113i
$449$			3.32509i			0.156921i	0.996917	+	0.0784604i	$0.0250004\pi$
$449$			3.32509i			0.156921i	−0.996917	+	0.0784604i	$0.975000\pi$
$450$		−	13.6996i		−	0.645808i
$451$	2.28503			0.107598
$452$	19.1204			0.899347
$453$			22.0226i			1.03471i
$454$	−0.162550			−0.00762885
$455$	−1.19394	+	5.11932i	−0.0559726	+	0.239997i
$456$	31.0810			1.45550
$457$		−	29.0747i		−	1.36006i	−0.733185	−	0.680029i	$-0.761967\pi$
$457$		−	29.0747i		−	1.36006i	0.733185	−	0.680029i	$-0.238033\pi$
$458$	−0.863472			−0.0403474
$459$	−19.5136			−0.910817
$460$		−	2.11265i		−	0.0985028i
$461$			28.7557i			1.33929i	0.742684	+	0.669643i	$0.233553\pi$
$461$			28.7557i			1.33929i	−0.742684	+	0.669643i	$0.766447\pi$
$462$		−	4.97195i		−	0.231316i
$463$		−	34.6020i		−	1.60809i	−0.594568	−	0.804045i	$-0.702677\pi$
$463$		−	34.6020i		−	1.60809i	0.594568	−	0.804045i	$-0.297323\pi$
$464$	18.9727			0.880784
$465$	−1.72554			−0.0800202
$466$		−	9.16412i		−	0.424520i
$467$	33.1318			1.53316			0.766578	−	0.642152i	$-0.221958\pi$
$467$	33.1318			1.53316			0.766578	+	0.642152i	$0.221958\pi$
$468$	−6.26099	+	26.8457i	−0.289414	+	1.24094i
$469$	−31.2582			−1.44337
$470$			4.84180i			0.223335i
$471$	12.9067			0.594711
$472$	16.8439			0.775303
$473$		−	7.23514i		−	0.332672i
$474$			3.68466i			0.169242i
$475$		−	22.8490i		−	1.04838i
$476$			15.1645i			0.695065i
$477$	−13.0215			−0.596213
$478$	−16.9625			−0.775847
$479$		−	28.5444i		−	1.30423i	−0.758122	−	0.652113i	$-0.773883\pi$
$479$		−	28.5444i		−	1.30423i	0.758122	−	0.652113i	$-0.226117\pi$
$480$	9.73500			0.444340
$481$	−37.0356	−	8.63752i	−1.68868	−	0.393837i
$482$	14.3328			0.652843
$483$		−	13.8662i		−	0.630934i
$484$	15.3285			0.696750
$485$	3.37018			0.153032
$486$		−	10.3282i		−	0.468499i
$487$			22.2944i			1.01026i	0.863044	+	0.505129i	$0.168555\pi$
$487$			22.2944i			1.01026i	−0.863044	+	0.505129i	$0.831445\pi$
$488$			14.5410i			0.658239i
$489$			20.7192i			0.936955i
$490$	−0.568307			−0.0256735
$491$	−2.28882			−0.103293			−0.0516465	−	0.998665i	$-0.516447\pi$
$491$	−2.28882			−0.103293			−0.0516465	+	0.998665i	$0.516447\pi$
$492$			8.42584i			0.379866i
$493$	41.9886			1.89107
$494$	2.53296	−	10.8607i	0.113963	−	0.488648i
$495$	3.57774			0.160808
$496$			1.80988i			0.0812659i
$497$	−6.39728			−0.286957
$498$	−19.1449			−0.857905
$499$		−	10.7617i		−	0.481758i	−0.970555	−	0.240879i	$-0.922564\pi$
$499$		−	10.7617i		−	0.481758i	0.970555	−	0.240879i	$-0.0774358\pi$
$500$		−	9.59339i		−	0.429029i
$501$		−	17.9222i		−	0.800703i
$502$			3.37608i			0.150682i
$503$	15.7196			0.700901			0.350451	−	0.936581i	$-0.386028\pi$
$503$	15.7196			0.700901			0.350451	+	0.936581i	$0.386028\pi$
$504$	25.1990			1.12245
$505$			7.72562i			0.343786i
$506$	1.60787			0.0714787
$507$	32.4566	+	16.0100i	1.44145	+	0.711028i
$508$	−13.8801			−0.615831
$509$			9.05022i			0.401144i	0.979679	+	0.200572i	$0.0642800\pi$
$509$			9.05022i			0.401144i	−0.979679	+	0.200572i	$0.935720\pi$
$510$	4.31864			0.191233
$511$	18.3776			0.812979
$512$		−	18.3748i		−	0.812059i
$513$			24.1160i			1.06475i
$514$			13.3835i			0.590321i
$515$			7.65429i			0.337288i
$516$	26.6788			1.17447
$517$	15.1916			0.668125
$518$			15.5019i			0.681114i
$519$	27.9694			1.22772
$520$	1.14483	−	4.90875i	0.0502041	−	0.215263i
$521$	−14.5767			−0.638615			−0.319308	−	0.947651i	$-0.603450\pi$
$521$	−14.5767			−0.638615			−0.319308	+	0.947651i	$0.603450\pi$
$522$		−	31.1130i		−	1.36178i
$523$	21.1296			0.923935			0.461967	−	0.886897i	$-0.347144\pi$
$523$	21.1296			0.923935			0.461967	+	0.886897i	$0.347144\pi$
$524$	18.1995			0.795048
$525$		−	30.2248i		−	1.31912i
$526$		−	4.08389i		−	0.178066i
$527$			4.00546i			0.174480i
$528$		−	6.12267i		−	0.266455i
$529$	−18.5158			−0.805036
$530$	1.06173			0.0461185
$531$			35.4740i			1.53944i
$532$	18.7412			0.812533
$533$	6.60271	+	1.53990i	0.285995	+	0.0667003i
$534$	3.50843			0.151825
$535$			1.81426i			0.0784373i
$536$	29.9725			1.29461
$537$	55.3518			2.38861
$538$			11.7672i			0.507319i
$539$			1.78311i			0.0768042i
$540$			4.86040i			0.209158i
$541$			16.1842i			0.695811i	0.937530	+	0.347906i	$0.113107\pi$
$541$			16.1842i			0.695811i	−0.937530	+	0.347906i	$0.886893\pi$
$542$	11.3549			0.487736
$543$	−18.9103			−0.811518
$544$		−	22.5976i		−	0.968864i
$545$	−5.98695			−0.256453
$546$	3.35062	−	14.3667i	0.143393	−	0.614837i
$547$	−21.4532			−0.917274			−0.458637	−	0.888624i	$-0.651662\pi$
$547$	−21.4532			−0.917274			−0.458637	+	0.888624i	$0.651662\pi$
$548$		−	10.9316i		−	0.466973i
$549$	−30.6239			−1.30700
$550$	3.50476			0.149443
$551$		−	51.8919i		−	2.21067i
$552$			13.2959i			0.565910i
$553$			4.98246i			0.211876i
$554$			19.7363i			0.838514i
$555$	−18.2002			−0.772554
$556$	7.73720			0.328130
$557$			24.1842i			1.02472i	0.858772	+	0.512359i	$0.171228\pi$
$557$			24.1842i			1.02472i	−0.858772	+	0.512359i	$0.828772\pi$
$558$	2.96799			0.125645
$559$	4.87579	−	20.9063i	0.206224	−	0.884240i
$560$	2.63870			0.111506
$561$		−	13.5501i		−	0.572087i
$562$	16.8956			0.712698
$563$	−29.9506			−1.26227			−0.631133	−	0.775675i	$-0.717410\pi$
$563$	−29.9506			−1.26227			−0.631133	+	0.775675i	$0.717410\pi$
$564$			56.0174i			2.35876i
$565$		−	7.36311i		−	0.309768i
$566$		−	20.1856i		−	0.848465i
$567$		−	1.61730i		−	0.0679200i
$568$	6.13415			0.257383
$569$	7.78865			0.326517			0.163259	−	0.986583i	$-0.447800\pi$
$569$	7.78865			0.326517			0.163259	+	0.986583i	$0.447800\pi$
$570$		−	5.33722i		−	0.223551i
$571$	20.2796			0.848676			0.424338	−	0.905504i	$-0.360507\pi$
$571$	20.2796			0.848676			0.424338	+	0.905504i	$0.360507\pi$
$572$	−6.86788	−	1.60174i	−0.287160	−	0.0669721i
$573$	−29.1917			−1.21950
$574$		−	2.76367i		−	0.115354i
$575$	9.77437			0.407619
$576$	0.449287			0.0187203
$577$		−	16.5988i		−	0.691016i	−0.938416	−	0.345508i	$-0.887707\pi$
$577$		−	16.5988i		−	0.691016i	0.938416	−	0.345508i	$-0.112293\pi$
$578$			0.597542i			0.0248545i
$579$		−	35.9137i		−	1.49252i
$580$		−	10.4584i		−	0.434262i
$581$	−25.8881			−1.07402
$582$	−9.45797			−0.392045
$583$		−	3.33127i		−	0.137967i
$584$	−17.6217			−0.729193
$585$	10.3380	+	2.41106i	0.427426	+	0.0996850i
$586$	−11.6758			−0.482323
$587$			12.9010i			0.532482i	0.963907	+	0.266241i	$0.0857816\pi$
$587$			12.9010i			0.532482i	−0.963907	+	0.266241i	$0.914218\pi$
$588$	−6.57505			−0.271151
$589$	4.95017			0.203968
$590$		−	2.89243i		−	0.119079i
$591$			57.2478i			2.35486i
$592$			19.0897i			0.784580i
$593$			44.5857i			1.83091i	0.402415	+	0.915457i	$0.368171\pi$
$593$			44.5857i			1.83091i	−0.402415	+	0.915457i	$0.631829\pi$
$594$	−3.69910			−0.151776
$595$	5.83974			0.239406
$596$		−	16.6075i		−	0.680268i
$597$	4.03356			0.165083
$598$	4.64602	+	1.08355i	0.189990	+	0.0443098i
$599$	−7.39164			−0.302014			−0.151007	−	0.988533i	$-0.548252\pi$
$599$	−7.39164			−0.302014			−0.151007	+	0.988533i	$0.548252\pi$
$600$			28.9817i			1.18317i
$601$	20.6091			0.840662			0.420331	−	0.907371i	$-0.361914\pi$
$601$	20.6091			0.840662			0.420331	+	0.907371i	$0.361914\pi$
$602$	−8.75066			−0.356650
$603$			63.1233i			2.57058i
$604$		−	12.7329i		−	0.518096i
$605$		−	5.90289i		−	0.239986i
$606$		−	21.6809i		−	0.880728i
$607$	32.5879			1.32270			0.661350	−	0.750077i	$-0.269984\pi$
$607$	32.5879			1.32270			0.661350	+	0.750077i	$0.269984\pi$
$608$	−27.9274			−1.13260
$609$		−	68.6430i		−	2.78155i
$610$	2.49697			0.101099
$611$	43.8968	+	10.2377i	1.77587	+	0.414172i
$612$	30.6236			1.23788
$613$			2.62416i			0.105989i	0.998595	+	0.0529943i	$0.0168765\pi$
$613$			2.62416i			0.105989i	−0.998595	+	0.0529943i	$0.983123\pi$
$614$	−13.7104			−0.553308
$615$	3.24472			0.130840
$616$			6.44663i			0.259742i
$617$			2.69130i			0.108348i	0.998532	+	0.0541738i	$0.0172525\pi$
$617$			2.69130i			0.108348i	−0.998532	+	0.0541738i	$0.982748\pi$
$618$		−	21.4807i		−	0.864082i
$619$		−	27.2021i		−	1.09334i	−0.837347	−	0.546672i	$-0.815895\pi$
$619$		−	27.2021i		−	1.09334i	0.837347	−	0.546672i	$-0.184105\pi$
$620$	0.997669			0.0400673
$621$	−10.3164			−0.413982
$622$			11.1878i			0.448592i
$623$	4.74416			0.190071
$624$	4.12609	−	17.6917i	0.165176	−	0.708235i
$625$	19.3847			0.775388
$626$			2.95585i			0.118140i
$627$	−16.7460			−0.668771
$628$	−7.46237			−0.297781
$629$			42.2475i			1.68452i
$630$		−	4.32716i		−	0.172398i
$631$			26.9529i			1.07298i	0.843907	+	0.536490i	$0.180250\pi$
$631$			26.9529i			1.07298i	−0.843907	+	0.536490i	$0.819750\pi$
$632$		−	4.77752i		−	0.190040i
$633$	19.7968			0.786853
$634$	−11.8811			−0.471857
$635$			5.34512i			0.212115i
$636$	12.2837			0.487081
$637$	−1.20165	+	5.15239i	−0.0476111	+	0.204145i
$638$	7.95958			0.315123
$639$			12.9188i			0.511059i
$640$	−7.03047			−0.277904
$641$	−11.3030			−0.446441			−0.223220	−	0.974768i	$-0.571657\pi$
$641$	−11.3030			−0.446441			−0.223220	+	0.974768i	$0.571657\pi$
$642$		−	5.09148i		−	0.200945i
$643$		−	13.9895i		−	0.551693i	−0.961202	−	0.275847i	$-0.911042\pi$
$643$		−	13.9895i		−	0.551693i	0.961202	−	0.275847i	$-0.0889582\pi$
$644$			8.01712i			0.315919i
$645$		−	10.2738i		−	0.404531i
$646$	−12.3891			−0.487444
$647$	−22.5333			−0.885877			−0.442938	−	0.896552i	$-0.646064\pi$
$647$	−22.5333			−0.885877			−0.442938	+	0.896552i	$0.646064\pi$
$648$			1.55077i			0.0609202i
$649$	−9.07525			−0.356235
$650$	10.1272	+	2.36187i	0.397220	+	0.0926403i
$651$	6.54812			0.256641
$652$		−	11.9794i		−	0.469148i
$653$	−10.7751			−0.421663			−0.210831	−	0.977522i	$-0.567617\pi$
$653$	−10.7751			−0.421663			−0.210831	+	0.977522i	$0.567617\pi$
$654$	16.8016			0.656994
$655$		−	7.00847i		−	0.273844i
$656$		−	3.40330i		−	0.132877i
$657$		−	37.1121i		−	1.44788i
$658$		−	18.3737i		−	0.716282i
$659$	−39.5160			−1.53932			−0.769662	−	0.638452i	$-0.779575\pi$
$659$	−39.5160			−1.53932			−0.769662	+	0.638452i	$0.779575\pi$
$660$	−3.37503			−0.131373
$661$			40.9839i			1.59409i	0.603921	+	0.797044i	$0.293604\pi$
$661$			40.9839i			1.59409i	−0.603921	+	0.797044i	$0.706396\pi$
$662$	−15.3098			−0.595033
$663$	9.13150	−	39.1537i	0.354638	−	1.52060i
$664$	24.8233			0.963330
$665$		−	7.21707i		−	0.279866i
$666$	31.3048			1.21304
$667$	22.1984			0.859524
$668$			10.3622i			0.400925i
$669$			24.2377i			0.937083i
$670$		−	5.14686i		−	0.198840i
$671$		−	7.83446i		−	0.302446i
$672$	−36.9425			−1.42509
$673$	−16.4585			−0.634430			−0.317215	−	0.948354i	$-0.602748\pi$
$673$	−16.4585			−0.634430			−0.317215	+	0.948354i	$0.602748\pi$
$674$		−	4.32174i		−	0.166467i
$675$	−22.4871			−0.865528
$676$	−18.7656	−	9.25659i	−0.721755	−	0.356023i
$677$	31.8404			1.22372			0.611862	−	0.790964i	$-0.290421\pi$
$677$	31.8404			1.22372			0.611862	+	0.790964i	$0.290421\pi$
$678$			20.6636i			0.793580i
$679$	−12.7892			−0.490805
$680$	−5.59955			−0.214733
$681$			0.724216i			0.0277520i
$682$			0.759295i			0.0290749i
$683$		−	3.58966i		−	0.137354i	−0.997639	−	0.0686772i	$-0.978122\pi$
$683$		−	3.58966i		−	0.137354i	0.997639	−	0.0686772i	$-0.0218779\pi$
$684$		−	37.8463i		−	1.44709i
$685$	−4.20966			−0.160843
$686$	12.4447			0.475140
$687$			3.84706i			0.146775i
$688$	−10.7759			−0.410828
$689$	2.24496	−	9.62584i	0.0855260	−	0.366715i
$690$	2.28316			0.0869185
$691$			30.1287i			1.14615i	0.819503	+	0.573075i	$0.194250\pi$
$691$			30.1287i			1.14615i	−0.819503	+	0.573075i	$0.805750\pi$
$692$	−16.1713			−0.614740
$693$	−13.5769			−0.515743
$694$			11.1406i			0.422891i
$695$		−	2.97953i		−	0.113020i
$696$			65.8196i			2.49489i
$697$		−	7.53188i		−	0.285290i
$698$	4.99165			0.188937
$699$	−40.8293			−1.54431
$700$			17.4753i			0.660504i
$701$	−11.0470			−0.417238			−0.208619	−	0.977997i	$-0.566897\pi$
$701$	−11.0470			−0.417238			−0.208619	+	0.977997i	$0.566897\pi$
$702$	−10.6887	−	2.49284i	−0.403419	−	0.0940862i
$703$	52.2118			1.96921
$704$			0.114940i			0.00433197i
$705$	21.5719			0.812444
$706$	−3.08751			−0.116200
$707$		−	29.3173i		−	1.10259i
$708$		−	33.4641i		−	1.25766i
$709$			41.5907i			1.56197i	0.624549	+	0.780986i	$0.285283\pi$
$709$			41.5907i			1.56197i	−0.624549	+	0.780986i	$0.714717\pi$
$710$		−	1.05335i		−	0.0395316i
$711$	10.0617			0.377342
$712$	−4.54903			−0.170482
$713$			2.11759i			0.0793043i
$714$	−16.3885			−0.613323
$715$	−0.616817	+	2.64477i	−0.0230676	+	0.0989086i
$716$	−32.0031			−1.19601
$717$			75.5738i			2.82236i
$718$	5.92163			0.220993
$719$	−38.3515			−1.43027			−0.715134	−	0.698987i	$-0.753635\pi$
$719$	−38.3515			−1.43027			−0.715134	+	0.698987i	$0.753635\pi$
$720$		−	5.32865i		−	0.198587i
$721$		−	29.0466i		−	1.08175i
$722$			3.43921i			0.127994i
$723$		−	63.8578i		−	2.37490i
$724$	10.9335			0.406340
$725$	48.3868			1.79704
$726$			16.5657i			0.614810i
$727$	49.9648			1.85309			0.926546	−	0.376182i	$-0.122763\pi$
$727$	49.9648			1.85309			0.926546	+	0.376182i	$0.122763\pi$
$728$	−4.34441	+	18.6278i	−0.161015	+	0.690393i
$729$	−43.9531			−1.62789
$730$			3.02600i			0.111997i
$731$	−23.8483			−0.882062
$732$	28.8888			1.06776
$733$		−	32.9576i		−	1.21732i	−0.793433	−	0.608658i	$-0.791708\pi$
$733$		−	32.9576i		−	1.21732i	0.793433	−	0.608658i	$-0.208292\pi$
$734$			7.16038i			0.264294i
$735$			2.53200i			0.0933943i
$736$		−	11.9468i		−	0.440365i
$737$	−16.1487			−0.594846
$738$	−5.58102			−0.205440
$739$			19.5295i			0.718406i	0.933259	+	0.359203i	$0.116951\pi$
$739$			19.5295i			0.718406i	−0.933259	+	0.359203i	$0.883049\pi$
$740$	10.5229			0.386830
$741$	−48.3883	−	11.2852i	−1.77759	−	0.414573i
$742$	−4.02906			−0.147911
$743$		−	19.0224i		−	0.697864i	−0.937148	−	0.348932i	$-0.886544\pi$
$743$		−	19.0224i		−	0.697864i	0.937148	−	0.348932i	$-0.113456\pi$
$744$	−6.27879			−0.230192
$745$	−6.39540			−0.234309
$746$		−	21.4412i		−	0.785018i
$747$			52.2789i			1.91278i
$748$			7.83437i			0.286453i
$749$		−	6.88478i		−	0.251565i
$750$	10.3677			0.378574
$751$	−26.8083			−0.978248			−0.489124	−	0.872214i	$-0.662683\pi$
$751$	−26.8083			−0.978248			−0.489124	+	0.872214i	$0.662683\pi$
$752$		−	22.6262i		−	0.825091i
$753$	15.0416			0.548146
$754$	22.9996	+	5.36400i	0.837594	+	0.195345i
$755$	−4.90335			−0.178451
$756$		−	18.4443i		−	0.670813i
$757$	−17.2202			−0.625880			−0.312940	−	0.949773i	$-0.601314\pi$
$757$	−17.2202			−0.625880			−0.312940	+	0.949773i	$0.601314\pi$
$758$	18.1413			0.658921
$759$		−	7.16363i		−	0.260023i
$760$			6.92023i			0.251023i
$761$		−	43.3306i		−	1.57073i	−0.619032	−	0.785366i	$-0.712475\pi$
$761$		−	43.3306i		−	1.57073i	0.619032	−	0.785366i	$-0.287525\pi$
$762$		−	15.0004i		−	0.543406i
$763$	22.7194			0.822496
$764$	16.8779			0.610622
$765$		−	11.7929i		−	0.426373i
$766$	−12.4190			−0.448716
$767$	−26.2233	−	6.11585i	−0.946870	−	0.220831i
$768$	19.2034			0.692945
$769$			29.5903i			1.06705i	0.845783	+	0.533527i	$0.179134\pi$
$769$			29.5903i			1.06705i	−0.845783	+	0.533527i	$0.820866\pi$
$770$	1.10701			0.0398939
$771$	59.6280			2.14745
$772$			20.7644i			0.747328i
$773$		−	47.4918i		−	1.70816i	−0.520142	−	0.854080i	$-0.674121\pi$
$773$		−	47.4918i		−	1.70816i	0.520142	−	0.854080i	$-0.325879\pi$
$774$			17.6713i			0.635180i
$775$			4.61581i			0.165805i
$776$	12.2632			0.440223
$777$	69.0662			2.47774
$778$			15.7504i			0.564679i
$779$	−9.30832			−0.333505
$780$	−9.75231	−	2.27445i	−0.349189	−	0.0814384i
$781$	−3.30499			−0.118262
$782$		−	5.29984i		−	0.189522i
$783$	−51.0699			−1.82509
$784$	2.65575			0.0948481
$785$			2.87370i			0.102567i
$786$			19.6683i			0.701546i
$787$			37.6005i			1.34031i	0.742220	+	0.670157i	$0.233773\pi$
$787$			37.6005i			1.34031i	−0.742220	+	0.670157i	$0.766227\pi$
$788$		−	33.0993i		−	1.17911i
$789$	−18.1951			−0.647764
$790$	−0.820393			−0.0291883
$791$			27.9416i			0.993490i
$792$	13.0184			0.462590
$793$	5.27968	−	22.6380i	0.187487	−	0.803900i
$794$	−4.83656			−0.171643
$795$		−	4.73036i		−	0.167769i
$796$	−2.33211			−0.0826595
$797$	−22.2917			−0.789611			−0.394806	−	0.918765i	$-0.629188\pi$
$797$	−22.2917			−0.789611			−0.394806	+	0.918765i	$0.629188\pi$
$798$			20.2538i			0.716975i
$799$		−	50.0742i		−	1.77150i
$800$		−	26.0410i		−	0.920689i
$801$		−	9.58045i		−	0.338508i
$802$	−4.60238			−0.162516
$803$	9.49434			0.335048
$804$		−	59.5468i		−	2.10006i
$805$	3.08733			0.108814
$806$	−0.511692	+	2.19402i	−0.0180236	+	0.0772809i
$807$	52.4268			1.84551
$808$			28.1115i			0.988958i
$809$	16.2551			0.571498			0.285749	−	0.958305i	$-0.407758\pi$
$809$	16.2551			0.571498			0.285749	+	0.958305i	$0.407758\pi$
$810$	0.266298			0.00935676
$811$		−	28.5796i		−	1.00356i	−0.864994	−	0.501782i	$-0.832678\pi$
$811$		−	28.5796i		−	1.00356i	0.864994	−	0.501782i	$-0.167322\pi$
$812$			39.6878i			1.39277i
$813$		−	50.5901i		−	1.77427i
$814$			8.00866i			0.280703i
$815$	−4.61315			−0.161592
$816$	−20.1814			−0.706491
$817$			29.4731i			1.03113i
$818$	5.18468			0.181278
$819$	−39.2310	−	9.14952i	−1.37084	−	0.319710i
$820$	−1.87602			−0.0655135
$821$			15.3714i			0.536464i	0.963354	+	0.268232i	$0.0864394\pi$
$821$			15.3714i			0.536464i	−0.963354	+	0.268232i	$0.913561\pi$
$822$	11.8138			0.412055
$823$	47.1895			1.64492			0.822462	−	0.568820i	$-0.192600\pi$
$823$	47.1895			1.64492			0.822462	+	0.568820i	$0.192600\pi$
$824$			27.8519i			0.970267i
$825$		−	15.6149i		−	0.543641i
$826$			10.9762i			0.381912i
$827$		−	10.7778i		−	0.374781i	−0.982286	−	0.187390i	$-0.939997\pi$
$827$		−	10.7778i		−	0.374781i	0.982286	−	0.187390i	$-0.0600029\pi$
$828$	16.1899			0.562639
$829$	−30.4045			−1.05599			−0.527997	−	0.849246i	$-0.677057\pi$
$829$	−30.4045			−1.05599			−0.527997	+	0.849246i	$0.677057\pi$
$830$		−	4.26264i		−	0.147958i
$831$	87.9319			3.05032
$832$	−0.0774588	+	0.332125i	−0.00268540	+	0.0115144i
$833$	5.87746			0.203642
$834$			8.36166i			0.289541i
$835$	3.99039			0.138093
$836$	9.68215			0.334864
$837$		−	4.87176i		−	0.168393i
$838$		−	3.89611i		−	0.134589i
$839$			41.7161i			1.44020i	0.693871	+	0.720099i	$0.255904\pi$
$839$			41.7161i			1.44020i	−0.693871	+	0.720099i	$0.744096\pi$
$840$			9.15413i			0.315848i
$841$	80.8902			2.78932
$842$	−6.85296			−0.236169
$843$		−	75.2757i		−	2.59263i
$844$	−11.4461			−0.393989
$845$	−3.56464	+	7.22649i	−0.122627	+	0.248599i
$846$	−37.1043			−1.27567
$847$			22.4004i			0.769686i
$848$	−4.96155			−0.170380
$849$	−89.9339			−3.08652
$850$		−	11.5523i		−	0.396241i
$851$			22.3352i			0.765642i
$852$		−	12.1868i		−	0.417514i
$853$		−	36.5309i		−	1.25080i	−0.780306	−	0.625398i	$-0.784937\pi$
$853$		−	36.5309i		−	1.25080i	0.780306	−	0.625398i	$-0.215063\pi$
$854$	−9.47553			−0.324246
$855$	−14.5743			−0.498430
$856$			6.60161i			0.225638i
$857$	−37.5045			−1.28113			−0.640565	−	0.767904i	$-0.721300\pi$
$857$	−37.5045			−1.28113			−0.640565	+	0.767904i	$0.721300\pi$
$858$	1.73101	−	7.42218i	0.0590959	−	0.253389i
$859$	56.8532			1.93981			0.969903	−	0.243492i	$-0.0782931\pi$
$859$	56.8532			1.93981			0.969903	+	0.243492i	$0.0782931\pi$
$860$			5.94008i			0.202555i
$861$	−12.3131			−0.419630
$862$	−4.88704			−0.166453
$863$		−	15.5581i		−	0.529602i	−0.964303	−	0.264801i	$-0.914694\pi$
$863$		−	15.5581i		−	0.529602i	0.964303	−	0.264801i	$-0.0853063\pi$
$864$			27.4850i			0.935059i
$865$			6.22743i			0.211739i
$866$			21.0028i			0.713705i
$867$	2.66226			0.0904150
$868$	−3.78597			−0.128504
$869$			2.57406i			0.0873190i
$870$	11.3025			0.383191
$871$	−46.6625	−	10.8827i	−1.58110	−	0.368746i
$872$	−21.7849			−0.737730
$873$			25.8268i			0.874104i
$874$	−6.54983			−0.221551
$875$	14.0193			0.473940
$876$			35.0094i			1.18286i
$877$			3.07559i			0.103855i	0.998651	+	0.0519277i	$0.0165365\pi$
$877$			3.07559i			0.103855i	−0.998651	+	0.0519277i	$0.983463\pi$
$878$		−	10.8374i		−	0.365743i
$879$			52.0197i			1.75458i
$880$	1.36322			0.0459541
$881$	−33.1770			−1.11776			−0.558880	−	0.829248i	$-0.688769\pi$
$881$	−33.1770			−1.11776			−0.558880	+	0.829248i	$0.688769\pi$
$882$		−	4.35512i		−	0.146644i
$883$	−34.0077			−1.14445			−0.572225	−	0.820097i	$-0.693919\pi$
$883$	−34.0077			−1.14445			−0.572225	+	0.820097i	$0.693919\pi$
$884$	−5.27962	+	22.6378i	−0.177573	+	0.761391i
$885$	−12.8867			−0.433183
$886$			6.37643i			0.214220i
$887$	−49.0181			−1.64587			−0.822934	−	0.568137i	$-0.807664\pi$
$887$	−49.0181			−1.64587			−0.822934	+	0.568137i	$0.807664\pi$
$888$	−66.2255			−2.22238
$889$		−	20.2838i		−	0.680295i
$890$			0.781156i			0.0261844i
$891$		−	0.835535i		−	0.0279915i
$892$		−	14.0137i		−	0.469212i
$893$	−61.8845			−2.07088
$894$	17.9478			0.600265
$895$			12.3241i			0.411950i
$896$	26.6793			0.891294
$897$	4.82760	−	20.6996i	0.161189	−	0.691140i
$898$	2.07765			0.0693322
$899$			10.4829i			0.349623i
$900$	35.2899			1.17633
$901$	−10.9805			−0.365812
$902$		−	1.42778i		−	0.0475400i
$903$			38.9872i			1.29741i
$904$		−	26.7924i		−	0.891100i
$905$		−	4.21040i		−	0.139958i
$906$	13.7606			0.457166
$907$	27.1941			0.902965			0.451483	−	0.892280i	$-0.350895\pi$
$907$	27.1941			0.902965			0.451483	+	0.892280i	$0.350895\pi$
$908$		−	0.418725i		−	0.0138959i
$909$	−59.2039			−1.96367
$910$	3.19876	+	0.746020i	0.106038	+	0.0247303i
$911$	−51.0536			−1.69148			−0.845741	−	0.533594i	$-0.820841\pi$
$911$	−51.0536			−1.69148			−0.845741	+	0.533594i	$0.820841\pi$
$912$			24.9413i			0.825889i
$913$	−13.3744			−0.442629
$914$	−18.1671			−0.600913
$915$		−	11.1248i		−	0.367776i
$916$		−	2.22428i		−	0.0734923i
$917$			26.5958i			0.878272i
$918$			12.1929i			0.402426i
$919$	−16.1289			−0.532045			−0.266022	−	0.963967i	$-0.585710\pi$
$919$	−16.1289			−0.532045			−0.266022	+	0.963967i	$0.585710\pi$
$920$	−2.96034			−0.0975996
$921$			61.0846i			2.01281i
$922$	17.9677			0.591735
$923$	−9.54992	−	2.22725i	−0.314339	−	0.0733108i
$924$	12.8076			0.421340
$925$			48.6852i			1.60076i
$926$	−21.6207			−0.710501
$927$	−58.6573			−1.92656
$928$		−	59.1411i		−	1.94140i
$929$		−	1.10502i		−	0.0362546i	−0.999836	−	0.0181273i	$-0.994230\pi$
$929$		−	1.10502i		−	0.0362546i	0.999836	−	0.0181273i	$-0.00577042\pi$
$930$			1.07819i			0.0353552i
$931$		−	7.26370i		−	0.238058i
$932$	23.6065			0.773258
$933$	49.8457			1.63188
$934$		−	20.7021i		−	0.677393i
$935$	3.01695			0.0986649
$936$	37.6174	+	8.77319i	1.22956	+	0.286761i
$937$	7.77910			0.254132			0.127066	−	0.991894i	$-0.459444\pi$
$937$	7.77910			0.254132			0.127066	+	0.991894i	$0.459444\pi$
$938$			19.5314i			0.637722i
$939$	13.1693			0.429765
$940$	−12.4723			−0.406803
$941$		−	57.1242i		−	1.86219i	−0.364771	−	0.931097i	$-0.618853\pi$
$941$		−	57.1242i		−	1.86219i	0.364771	−	0.931097i	$-0.381147\pi$
$942$		−	8.06465i		−	0.262761i
$943$		−	3.98192i		−	0.129669i
$944$			13.5166i			0.439927i
$945$	−7.10276			−0.231053
$946$	−4.52081			−0.146984
$947$		−	17.7962i		−	0.578299i	−0.957284	−	0.289150i	$-0.906627\pi$
$947$		−	17.7962i		−	0.578299i	0.957284	−	0.289150i	$-0.0933725\pi$
$948$	−9.49159			−0.308272
$949$	27.4343	+	6.39828i	0.890556	+	0.207697i
$950$	−14.2770			−0.463207
$951$			52.9342i			1.71651i
$952$	21.2492			0.688692
$953$	36.4920			1.18209			0.591045	−	0.806638i	$-0.298715\pi$
$953$	36.4920			1.18209			0.591045	+	0.806638i	$0.298715\pi$
$954$			8.13636i			0.263424i
$955$		−	6.49956i		−	0.210321i
$956$		−	43.6950i		−	1.41320i
$957$		−	35.4627i		−	1.14634i
$958$	−17.8357			−0.576245
$959$	15.9749			0.515855
$960$			0.163214i			0.00526770i
$961$	−1.00000			−0.0322581
$962$	−5.39707	+	23.1414i	−0.174009	+	0.746108i
$963$	−13.9033			−0.448026
$964$			36.9211i			1.18915i
$965$	7.99622			0.257407
$966$	−8.66417			−0.278765
$967$		−	0.254947i		−	0.00819854i	−0.999992	−	0.00409927i	$-0.998695\pi$
$967$		−	0.254947i		−	0.00819854i	0.999992	−	0.00409927i	$-0.00130484\pi$
$968$		−	21.4790i		−	0.690362i
$969$			55.1979i			1.77321i
$970$		−	2.10583i		−	0.0676140i
$971$	−33.0115			−1.05939			−0.529695	−	0.848188i	$-0.677694\pi$
$971$	−33.0115			−1.05939			−0.529695	+	0.848188i	$0.677694\pi$
$972$	26.6053			0.853366
$973$			11.3068i			0.362479i
$974$	13.9305			0.446361
$975$	10.5230	−	45.1199i	0.337004	−	1.44499i
$976$	−11.6686			−0.373501
$977$			20.0922i			0.642806i	0.946943	+	0.321403i	$0.104154\pi$
$977$			20.0922i			0.642806i	−0.946943	+	0.321403i	$0.895846\pi$
$978$	12.9462			0.413974
$979$	2.45095			0.0783327
$980$		−	1.46394i		−	0.0467640i
$981$		−	45.8799i		−	1.46483i
$982$			1.43015i			0.0456378i
$983$			38.2966i			1.22147i	0.791835	+	0.610736i	$0.209126\pi$
$983$			38.2966i			1.22147i	−0.791835	+	0.610736i	$0.790874\pi$
$984$	11.8067			0.376383
$985$	−12.7463			−0.406130
$986$		−	26.2362i		−	0.835531i
$987$	−81.8613			−2.60567
$988$	27.9770	+	6.52485i	0.890067	+	0.207583i
$989$	−12.6080			−0.400912
$990$		−	2.23552i		−	0.0710495i
$991$	−53.4115			−1.69667			−0.848337	−	0.529457i	$-0.822396\pi$
$991$	−53.4115			−1.69667			−0.848337	+	0.529457i	$0.822396\pi$
$992$	5.64170			0.179124
$993$			68.2105i			2.16460i
$994$			3.99728i			0.126786i
$995$			0.898077i			0.0284710i
$996$		−	49.3169i		−	1.56266i
$997$	−7.78304			−0.246491			−0.123246	−	0.992376i	$-0.539330\pi$
$997$	−7.78304			−0.246491			−0.123246	+	0.992376i	$0.539330\pi$
$998$	−6.72433			−0.212855
$999$		−	51.3848i		−	1.62574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.14	✓	32
13.5	odd	4		5239.2.a.k.1.8		16
13.8	odd	4		5239.2.a.l.1.9		16
13.12	even	2	inner	403.2.c.b.311.19	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.14	✓	32	1.1	even	1	trivial
403.2.c.b.311.19	yes	32	13.12	even	2	inner
5239.2.a.k.1.8		16	13.5	odd	4
5239.2.a.l.1.9		16	13.8	odd	4

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.624841i q^{2} -2.78388 q^{3} +1.60957 q^{4} -0.619834i q^{5} +1.73948i q^{6} +2.35216i q^{7} -2.25541i q^{8} +4.74999 q^{9} +O(q^{10})\)	\(q-0.624841i q^{2} -2.78388 q^{3} +1.60957 q^{4} -0.619834i q^{5} +1.73948i q^{6} +2.35216i q^{7} -2.25541i q^{8} +4.74999 q^{9} -0.387298 q^{10} +1.21518i q^{11} -4.48086 q^{12} +(-0.818917 + 3.51132i) q^{13} +1.46972 q^{14} +1.72554i q^{15} +1.80988 q^{16} +4.00546 q^{17} -2.96799i q^{18} -4.95017i q^{19} -0.997669i q^{20} -6.54812i q^{21} +0.759295 q^{22} +2.11759 q^{23} +6.27879i q^{24} +4.61581 q^{25} +(2.19402 + 0.511692i) q^{26} -4.87176 q^{27} +3.78597i q^{28} +10.4829 q^{29} +1.07819 q^{30} +1.00000i q^{31} -5.64170i q^{32} -3.38292i q^{33} -2.50277i q^{34} +1.45795 q^{35} +7.64546 q^{36} +10.5475i q^{37} -3.09307 q^{38} +(2.27977 - 9.77510i) q^{39} -1.39798 q^{40} -1.88041i q^{41} -4.09153 q^{42} -5.95396 q^{43} +1.95592i q^{44} -2.94420i q^{45} -1.32315i q^{46} -12.5015i q^{47} -5.03848 q^{48} +1.46736 q^{49} -2.88414i q^{50} -11.1507 q^{51} +(-1.31811 + 5.65173i) q^{52} -2.74137 q^{53} +3.04407i q^{54} +0.753211 q^{55} +5.30507 q^{56} +13.7807i q^{57} -6.55011i q^{58} +7.46822i q^{59} +2.77739i q^{60} -6.44716 q^{61} +0.624841 q^{62} +11.1727i q^{63} +0.0945869 q^{64} +(2.17644 + 0.507592i) q^{65} -2.11379 q^{66} +13.2892i q^{67} +6.44708 q^{68} -5.89511 q^{69} -0.910984i q^{70} +2.71975i q^{71} -10.7132i q^{72} -7.81310i q^{73} +6.59050 q^{74} -12.8498 q^{75} -7.96766i q^{76} -2.85830 q^{77} +(-6.10788 - 1.42449i) q^{78} +2.11825 q^{79} -1.12182i q^{80} -0.687580 q^{81} -1.17495 q^{82} +11.0061i q^{83} -10.5397i q^{84} -2.48272i q^{85} +3.72027i q^{86} -29.1830 q^{87} +2.74073 q^{88} -2.01694i q^{89} -1.83966 q^{90} +(-8.25917 - 1.92622i) q^{91} +3.40841 q^{92} -2.78388i q^{93} -7.81144 q^{94} -3.06828 q^{95} +15.7058i q^{96} +5.43723i q^{97} -0.916869i q^{98} +5.77210i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

Varieties

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