LMFDB - Embedded newform 234.2.t.a.103.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(25,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("234.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.t (of order $6$, degree $2$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.6
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.21476 - 1.23465i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.73536 + 1.57926i) q^{5} +(-0.434692 + 1.67662i) q^{6} +(1.36392 - 0.787458i) q^{7} +1.00000i q^{8} +(-0.0487053 - 2.99960i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.21476 - 1.23465i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.73536 + 1.57926i) q^{5} +(-0.434692 + 1.67662i) q^{6} +(1.36392 - 0.787458i) q^{7} +1.00000i q^{8} +(-0.0487053 - 2.99960i) q^{9} -3.15852 q^{10} +(-3.26194 + 1.88328i) q^{11} +(-0.461854 - 1.66934i) q^{12} +(-3.47351 + 0.966830i) q^{13} +(-0.787458 + 1.36392i) q^{14} +(5.27264 - 1.45878i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.06565 q^{17} +(1.54198 + 2.57338i) q^{18} -3.76656i q^{19} +(2.73536 - 1.57926i) q^{20} +(0.684603 - 2.64053i) q^{21} +(1.88328 - 3.26194i) q^{22} +(-1.84873 + 3.20209i) q^{23} +(1.23465 + 1.21476i) q^{24} +(2.48812 + 4.30955i) q^{25} +(2.52473 - 2.57405i) q^{26} +(-3.76262 - 3.58367i) q^{27} -1.57492i q^{28} +(0.109128 + 0.189015i) q^{29} +(-3.83685 + 3.89965i) q^{30} +(-2.65792 - 1.53455i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.63729 + 6.31508i) q^{33} +(-6.11904 + 3.53283i) q^{34} +4.97440 q^{35} +(-2.62209 - 1.45762i) q^{36} -0.292126i q^{37} +(1.88328 + 3.26194i) q^{38} +(-3.02579 + 5.46302i) q^{39} +(-1.57926 + 2.73536i) q^{40} +(6.39272 + 3.69084i) q^{41} +(0.727382 + 2.62907i) q^{42} +(-3.05835 - 5.29722i) q^{43} +3.76656i q^{44} +(4.60393 - 8.28191i) q^{45} -3.69746i q^{46} +(-6.17888 + 3.56738i) q^{47} +(-1.67662 - 0.434692i) q^{48} +(-2.25982 + 3.91412i) q^{49} +(-4.30955 - 2.48812i) q^{50} +(8.58309 - 8.72359i) q^{51} +(-0.899453 + 3.49156i) q^{52} -14.4175 q^{53} +(5.05036 + 1.22224i) q^{54} -11.8968 q^{55} +(0.787458 + 1.36392i) q^{56} +(-4.65037 - 4.57548i) q^{57} +(-0.189015 - 0.109128i) q^{58} +(-9.04745 - 5.22355i) q^{59} +(1.37298 - 5.29562i) q^{60} +(3.00007 + 5.19627i) q^{61} +3.06910 q^{62} +(-2.42849 - 4.05286i) q^{63} -1.00000 q^{64} +(-11.0282 - 2.84094i) q^{65} +(-1.73960 - 6.28766i) q^{66} +(6.33583 + 3.65799i) q^{67} +(3.53283 - 6.11904i) q^{68} +(1.70769 + 6.17231i) q^{69} +(-4.30796 + 2.48720i) q^{70} -0.772410i q^{71} +(2.99960 - 0.0487053i) q^{72} -13.5342i q^{73} +(0.146063 + 0.252988i) q^{74} +(8.34324 + 2.16313i) q^{75} +(-3.26194 - 1.88328i) q^{76} +(-2.96601 + 5.13728i) q^{77} +(-0.111100 - 6.24401i) q^{78} +(6.34033 + 10.9818i) q^{79} -3.15852i q^{80} +(-8.99526 + 0.292193i) q^{81} -7.38168 q^{82} +(0.314795 - 0.181747i) q^{83} +(-1.94447 - 1.91315i) q^{84} +(19.3271 + 11.1585i) q^{85} +(5.29722 + 3.05835i) q^{86} +(0.365931 + 0.0948738i) q^{87} +(-1.88328 - 3.26194i) q^{88} +7.06555i q^{89} +(0.153837 + 9.47431i) q^{90} +(-3.97624 + 4.05392i) q^{91} +(1.84873 + 3.20209i) q^{92} +(-5.12337 + 1.41748i) q^{93} +(3.56738 - 6.17888i) q^{94} +(5.94838 - 10.3029i) q^{95} +(1.66934 - 0.461854i) q^{96} +(0.535716 - 0.309296i) q^{97} -4.51964i q^{98} +(5.80797 + 9.69280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 - 16 * q^9	$ 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.21476	−	1.23465i	0.701343	−	0.712824i
$3$	1.21476	−	1.23465i	0.701343	−	0.712824i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.73536	+	1.57926i	1.22329	+	0.706266i	0.965618	−	0.259967i	$-0.0837115\pi$
$5$	2.73536	+	1.57926i	1.22329	+	0.706266i	0.257671	+	0.966233i	$0.417045\pi$
$6$	−0.434692	+	1.67662i	−0.177462	+	0.684476i
$7$	1.36392	−	0.787458i	0.515512	−	0.297631i	−0.219584	−	0.975594i	$-0.570470\pi$
$7$	1.36392	−	0.787458i	0.515512	−	0.297631i	0.735097	+	0.677962i	$0.237137\pi$
$8$			1.00000i			0.353553i
$9$	−0.0487053	−	2.99960i	−0.0162351	−	0.999868i
$10$	−3.15852			−0.998811
$11$	−3.26194	+	1.88328i	−0.983511	+	0.567830i	−0.903328	−	0.428950i	$-0.858884\pi$
$11$	−3.26194	+	1.88328i	−0.983511	+	0.567830i	−0.0801828	+	0.996780i	$0.525550\pi$
$12$	−0.461854	−	1.66934i	−0.133326	−	0.481896i
$13$	−3.47351	+	0.966830i	−0.963377	+	0.268150i
$13$	−3.47351	+	0.966830i	−0.963377	+	0.268150i
$14$	−0.787458	+	1.36392i	−0.210457	+	0.364522i
$15$	5.27264	−	1.45878i	1.36139	−	0.376654i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	7.06565			1.71367			0.856836	−	0.515588i	$-0.172427\pi$
$17$	7.06565			1.71367			0.856836	+	0.515588i	$0.172427\pi$
$18$	1.54198	+	2.57338i	0.363449	+	0.606552i
$19$		−	3.76656i		−	0.864108i	−0.901848	−	0.432054i	$-0.857789\pi$
$19$		−	3.76656i		−	0.864108i	0.901848	−	0.432054i	$-0.142211\pi$
$20$	2.73536	−	1.57926i	0.611644	−	0.353133i
$21$	0.684603	−	2.64053i	0.149393	−	0.576211i
$22$	1.88328	−	3.26194i	0.401517	−	0.695447i
$23$	−1.84873	+	3.20209i	−0.385487	+	0.667683i	−0.991837	−	0.127515i	$-0.959300\pi$
$23$	−1.84873	+	3.20209i	−0.385487	+	0.667683i	0.606350	+	0.795198i	$0.292633\pi$
$24$	1.23465	+	1.21476i	0.252021	+	0.247962i
$25$	2.48812	+	4.30955i	0.497624	+	0.861910i
$26$	2.52473	−	2.57405i	0.495140	−	0.504813i
$27$	−3.76262	−	3.58367i	−0.724116	−	0.689678i
$28$		−	1.57492i		−	0.297631i
$29$	0.109128	+	0.189015i	0.0202645	+	0.0350992i	0.875980	−	0.482348i	$-0.160216\pi$
$29$	0.109128	+	0.189015i	0.0202645	+	0.0350992i	−0.855715	+	0.517447i	$0.826882\pi$
$30$	−3.83685	+	3.89965i	−0.700510	+	0.711976i
$31$	−2.65792	−	1.53455i	−0.477376	−	0.275613i	0.241946	−	0.970290i	$-0.422214\pi$
$31$	−2.65792	−	1.53455i	−0.477376	−	0.275613i	−0.719322	+	0.694676i	$0.755548\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.63729	+	6.31508i	−0.285016	+	1.09931i
$34$	−6.11904	+	3.53283i	−1.04941	+	0.605875i
$35$	4.97440			0.840827
$36$	−2.62209	−	1.45762i	−0.437014	−	0.242937i
$37$		−	0.292126i		−	0.0480251i	−0.999712	−	0.0240126i	$-0.992356\pi$
$37$		−	0.292126i		−	0.0480251i	0.999712	−	0.0240126i	$-0.00764417\pi$
$38$	1.88328	+	3.26194i	0.305508	+	0.529156i
$39$	−3.02579	+	5.46302i	−0.484514	+	0.874783i
$40$	−1.57926	+	2.73536i	−0.249703	+	0.432498i
$41$	6.39272	+	3.69084i	0.998375	+	0.576412i	0.907767	−	0.419474i	$-0.137786\pi$
$41$	6.39272	+	3.69084i	0.998375	+	0.576412i	0.0906081	+	0.995887i	$0.471119\pi$
$42$	0.727382	+	2.62907i	0.112237	+	0.405674i
$43$	−3.05835	−	5.29722i	−0.466395	−	0.807819i	0.532869	−	0.846198i	$-0.321114\pi$
$43$	−3.05835	−	5.29722i	−0.466395	−	0.807819i	−0.999263	+	0.0383789i	$0.987781\pi$
$44$			3.76656i			0.567830i
$45$	4.60393	−	8.28191i	0.686313	−	1.23459i
$46$		−	3.69746i		−	0.545161i
$47$	−6.17888	+	3.56738i	−0.901282	+	0.520356i	−0.877616	−	0.479364i	$-0.840867\pi$
$47$	−6.17888	+	3.56738i	−0.901282	+	0.520356i	−0.0236662	+	0.999720i	$0.507534\pi$
$48$	−1.67662	−	0.434692i	−0.241999	−	0.0627423i
$49$	−2.25982	+	3.91412i	−0.322831	+	0.559160i
$50$	−4.30955	−	2.48812i	−0.609462	−	0.351873i
$51$	8.58309	−	8.72359i	1.20187	−	1.22155i
$52$	−0.899453	+	3.49156i	−0.124732	+	0.484192i
$53$	−14.4175			−1.98040			−0.990201	−	0.139649i	$-0.955403\pi$
$53$	−14.4175			−1.98040			−0.990201	+	0.139649i	$0.955403\pi$
$54$	5.05036	+	1.22224i	0.687267	+	0.166326i
$55$	−11.8968			−1.60416
$56$	0.787458	+	1.36392i	0.105229	+	0.182261i
$57$	−4.65037	−	4.57548i	−0.615957	−	0.606037i
$58$	−0.189015	−	0.109128i	−0.0248188	−	0.0143292i
$59$	−9.04745	−	5.22355i	−1.17788	−	0.680048i	−0.222355	−	0.974966i	$-0.571374\pi$
$59$	−9.04745	−	5.22355i	−1.17788	−	0.680048i	−0.955523	+	0.294918i	$0.904708\pi$
$60$	1.37298	−	5.29562i	0.177251	−	0.683662i
$61$	3.00007	+	5.19627i	0.384119	+	0.665314i	0.991647	−	0.128985i	$-0.0411718\pi$
$61$	3.00007	+	5.19627i	0.384119	+	0.665314i	−0.607527	+	0.794299i	$0.707838\pi$
$62$	3.06910			0.389776
$63$	−2.42849	−	4.05286i	−0.305961	−	0.510612i
$64$	−1.00000			−0.125000
$65$	−11.0282	−	2.84094i	−1.36787	−	0.352375i
$66$	−1.73960	−	6.28766i	−0.214130	−	0.773958i
$67$	6.33583	+	3.65799i	0.774045	+	0.446895i	0.834316	−	0.551287i	$-0.185863\pi$
$67$	6.33583	+	3.65799i	0.774045	+	0.446895i	−0.0602708	+	0.998182i	$0.519196\pi$
$68$	3.53283	−	6.11904i	0.428418	−	0.742042i
$69$	1.70769	+	6.17231i	0.205581	+	0.743059i
$70$	−4.30796	+	2.48720i	−0.514900	+	0.297277i
$71$		−	0.772410i		−	0.0916682i	−0.998949	−	0.0458341i	$-0.985405\pi$
$71$		−	0.772410i		−	0.0916682i	0.998949	−	0.0458341i	$-0.0145946\pi$
$72$	2.99960	−	0.0487053i	0.353507	−	0.00573997i
$73$		−	13.5342i		−	1.58406i	−0.610480	−	0.792032i	$-0.709024\pi$
$73$		−	13.5342i		−	1.58406i	0.610480	−	0.792032i	$-0.290976\pi$
$74$	0.146063	+	0.252988i	0.0169795	+	0.0294093i
$75$	8.34324	+	2.16313i	0.963395	+	0.249777i
$76$	−3.26194	−	1.88328i	−0.374170	−	0.216027i
$77$	−2.96601	+	5.13728i	−0.338008	+	0.585447i
$78$	−0.111100	−	6.24401i	−0.0125796	−	0.706995i
$79$	6.34033	+	10.9818i	0.713343	+	1.23555i	0.963595	+	0.267366i	$0.0861532\pi$
$79$	6.34033	+	10.9818i	0.713343	+	1.23555i	−0.250252	+	0.968181i	$0.580513\pi$
$80$		−	3.15852i		−	0.353133i
$81$	−8.99526	+	0.292193i	−0.999473	+	0.0324659i
$82$	−7.38168			−0.815170
$83$	0.314795	−	0.181747i	0.0345533	−	0.0199494i	−0.482624	−	0.875828i	$-0.660316\pi$
$83$	0.314795	−	0.181747i	0.0345533	−	0.0199494i	0.517177	+	0.855878i	$0.326983\pi$
$84$	−1.94447	−	1.91315i	−0.212159	−	0.208742i
$85$	19.3271	+	11.1585i	2.09632	+	1.21031i
$86$	5.29722	+	3.05835i	0.571214	+	0.329791i
$87$	0.365931	+	0.0948738i	0.0392319	+	0.0101715i
$88$	−1.88328	−	3.26194i	−0.200758	−	0.347724i
$89$			7.06555i			0.748947i	0.927238	+	0.374473i	$0.122176\pi$
$89$			7.06555i			0.748947i	−0.927238	+	0.374473i	$0.877824\pi$
$90$	0.153837	+	9.47431i	0.0162158	+	0.998680i
$91$	−3.97624	+	4.05392i	−0.416823	+	0.424966i
$92$	1.84873	+	3.20209i	0.192743	+	0.333841i
$93$	−5.12337	+	1.41748i	−0.531268	+	0.146986i
$94$	3.56738	−	6.17888i	0.367947	−	0.637303i
$95$	5.94838	−	10.3029i	0.610290	−	1.05705i
$96$	1.66934	−	0.461854i	0.170376	−	0.0471378i
$97$	0.535716	−	0.309296i	0.0543937	−	0.0314042i	−0.472557	−	0.881300i	$-0.656669\pi$
$97$	0.535716	−	0.309296i	0.0543937	−	0.0314042i	0.526950	+	0.849896i	$0.323335\pi$
$98$		−	4.51964i		−	0.456552i
$99$	5.80797	+	9.69280i	0.583723	+	0.974163i
$100$	4.97624			0.497624
$101$	−4.16781	−	7.21887i	−0.414713	−	0.718304i	0.580685	−	0.814128i	$-0.302785\pi$
$101$	−4.16781	−	7.21887i	−0.414713	−	0.718304i	−0.995398	+	0.0958241i	$0.969451\pi$
$102$	−3.07138	+	11.8464i	−0.304112	+	1.17297i
$103$	4.94838	−	8.57084i	0.487578	−	0.844510i	−0.512320	−	0.858795i	$-0.671214\pi$
$103$	4.94838	−	8.57084i	0.487578	−	0.844510i	0.999898	+	0.0142849i	$0.00454717\pi$
$104$	−0.966830	−	3.47351i	−0.0948055	−	0.340605i
$105$	6.04272	−	6.14163i	0.589709	−	0.599362i
$106$	12.4860	−	7.20877i	1.21274	−	0.700178i
$107$	0.115559			0.0111715			0.00558574	−	0.999984i	$-0.498222\pi$
$107$	0.115559			0.0111715			0.00558574	+	0.999984i	$0.498222\pi$
$108$	−4.98486	+	1.46669i	−0.479668	+	0.141132i
$109$			14.1301i			1.35342i	0.736251	+	0.676708i	$0.236594\pi$
$109$			14.1301i			1.35342i	−0.736251	+	0.676708i	$0.763406\pi$
$110$	10.3029	−	5.94838i	0.982342	−	0.567155i
$111$	−0.360672	−	0.354863i	−0.0342335	−	0.0336821i
$112$	−1.36392	−	0.787458i	−0.128878	−	0.0744078i
$113$	−9.70968	+	16.8177i	−0.913410	+	1.58207i	−0.104197	+	0.994557i	$0.533227\pi$
$113$	−9.70968	+	16.8177i	−0.913410	+	1.58207i	−0.809213	+	0.587516i	$0.800106\pi$
$114$	6.31508	+	1.63729i	0.591461	+	0.153346i
$115$	−10.1139	+	5.83925i	−0.943124	+	0.544513i
$116$	0.218255			0.0202645
$117$	3.06929	+	10.3721i	0.283756	+	0.958897i
$118$	10.4471			0.961733
$119$	9.63697	−	5.56391i	0.883420	−	0.510043i
$120$	1.45878	+	5.27264i	0.133167	+	0.481324i
$121$	1.59349	−	2.76001i	0.144863	−	0.250910i
$122$	−5.19627	−	3.00007i	−0.470448	−	0.271613i
$123$	12.3225	−	3.40926i	1.11108	−	0.307403i
$124$	−2.65792	+	1.53455i	−0.238688	+	0.137807i
$125$		−	0.0750557i		−	0.00671318i
$126$	4.12957	+	2.29563i	0.367891	+	0.204511i
$127$	5.42904			0.481750			0.240875	−	0.970556i	$-0.422566\pi$
$127$	5.42904			0.481750			0.240875	+	0.970556i	$0.422566\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−10.2554	−	2.65888i	−0.902935	−	0.234101i
$130$	10.9711	−	3.05375i	0.962232	−	0.267832i
$131$	6.34342	−	10.9871i	0.554227	−	0.959950i	−0.443736	−	0.896158i	$-0.646347\pi$
$131$	6.34342	−	10.9871i	0.554227	−	0.959950i	0.997963	−	0.0637922i	$-0.0203195\pi$
$132$	4.65037	+	4.57548i	0.404763	+	0.398244i
$133$	−2.96601	−	5.13728i	−0.257186	−	0.445459i
$134$	−7.31599			−0.632005
$135$	−4.63255	−	15.7448i	−0.398707	−	1.35509i
$136$			7.06565i			0.605875i
$137$	6.36997	−	3.67770i	0.544223	−	0.314207i	−0.202566	−	0.979269i	$-0.564928\pi$
$137$	6.36997	−	3.67770i	0.544223	−	0.314207i	0.746789	+	0.665061i	$0.231595\pi$
$138$	−4.56506	−	4.49154i	−0.388603	−	0.382345i
$139$	3.65559	−	6.33167i	0.310063	−	0.537046i	−0.668312	−	0.743881i	$-0.732983\pi$
$139$	3.65559	−	6.33167i	0.310063	−	0.537046i	0.978376	+	0.206835i	$0.0663164\pi$
$140$	2.48720	−	4.30796i	0.210207	−	0.364089i
$141$	−3.10142	+	11.9622i	−0.261187	+	1.00740i
$142$	0.386205	+	0.668927i	0.0324096	+	0.0561351i
$143$	9.50955	−	9.69532i	0.795228	−	0.810764i
$144$	−2.57338	+	1.54198i	−0.214448	+	0.128499i
$145$			0.689364i			0.0572485i
$146$	6.76712	+	11.7210i	0.560051	+	0.970037i
$147$	2.08741	+	7.54481i	0.172167	+	0.622285i
$148$	−0.252988	−	0.146063i	−0.0207955	−	0.0120063i
$149$	20.5800	+	11.8819i	1.68598	+	0.973401i	0.957544	+	0.288289i	$0.0930862\pi$
$149$	20.5800	+	11.8819i	1.68598	+	0.973401i	0.728437	+	0.685113i	$0.240247\pi$
$150$	−8.30702	+	2.29830i	−0.678266	+	0.187655i
$151$	−8.99711	+	5.19448i	−0.732174	+	0.422721i	−0.819217	−	0.573484i	$-0.805592\pi$
$151$	−8.99711	+	5.19448i	−0.732174	+	0.422721i	0.0870428	+	0.996205i	$0.472258\pi$
$152$	3.76656			0.305508
$153$	−0.344135	−	21.1942i	−0.0278216	−	1.71345i
$154$		−	5.93202i		−	0.478016i
$155$	−4.84690	−	8.39509i	−0.389313	−	0.674310i
$156$	3.21822	+	5.35192i	0.257664	+	0.428497i
$157$	4.57412	−	7.92261i	0.365054	−	0.632293i	−0.623730	−	0.781640i	$-0.714384\pi$
$157$	4.57412	−	7.92261i	0.365054	−	0.632293i	0.988785	+	0.149347i	$0.0477170\pi$
$158$	−10.9818	−	6.34033i	−0.873663	−	0.504410i
$159$	−17.5139	+	17.8006i	−1.38894	+	1.41168i
$160$	1.57926	+	2.73536i	0.124851	+	0.216249i
$161$			5.82319i			0.458932i
$162$	7.64402	−	4.75067i	0.600571	−	0.373248i
$163$		−	13.5935i		−	1.06473i	−0.846516	−	0.532363i	$-0.821304\pi$
$163$		−	13.5935i		−	1.06473i	0.846516	−	0.532363i	$-0.178696\pi$
$164$	6.39272	−	3.69084i	0.499188	−	0.288206i
$165$	−14.4517	+	14.6883i	−1.12507	+	1.14348i
$166$	−0.181747	+	0.314795i	−0.0141063	+	0.0244329i
$167$	−6.20607	−	3.58308i	−0.480240	−	0.277267i	0.240276	−	0.970705i	$-0.422762\pi$
$167$	−6.20607	−	3.58308i	−0.480240	−	0.277267i	−0.720517	+	0.693438i	$0.756095\pi$
$168$	2.64053	+	0.684603i	0.203721	+	0.0528183i
$169$	11.1305	−	6.71658i	0.856191	−	0.516660i
$170$	−22.3170			−1.71164
$171$	−11.2982	+	0.183451i	−0.863994	+	0.0140289i
$172$	−6.11671			−0.466395
$173$	−1.50582	−	2.60815i	−0.114485	−	0.198294i	0.803089	−	0.595859i	$-0.203188\pi$
$173$	−1.50582	−	2.60815i	−0.114485	−	0.198294i	−0.917574	+	0.397566i	$0.869855\pi$
$174$	−0.364342	+	0.100802i	−0.0276207	+	0.00764180i
$175$	6.78718	+	3.91858i	0.513062	+	0.296217i
$176$	3.26194	+	1.88328i	0.245878	+	0.141958i
$177$	−17.4397	+	4.82503i	−1.31085	+	0.362672i
$178$	−3.53277	−	6.11894i	−0.264793	−	0.458634i
$179$	−19.2107			−1.43587			−0.717936	−	0.696109i	$-0.754913\pi$
$179$	−19.2107			−1.43587			−0.717936	+	0.696109i	$0.754913\pi$
$180$	−4.87038	−	8.12807i	−0.363017	−	0.605831i
$181$	9.14810			0.679973			0.339987	−	0.940430i	$-0.389577\pi$
$181$	9.14810			0.679973			0.339987	+	0.940430i	$0.389577\pi$
$182$	1.41656	−	5.49891i	0.105003	−	0.407607i
$183$	10.0599	+	2.60821i	0.743651	+	0.192804i
$184$	−3.20209	−	1.84873i	−0.236062	−	0.136290i
$185$	0.461342	−	0.799068i	0.0339185	−	0.0587486i
$186$	3.72823	−	3.78926i	0.273367	−	0.277842i
$187$	−23.0477	+	13.3066i	−1.68542	+	0.973076i
$188$			7.13476i			0.520356i
$189$	−7.95389	−	1.92493i	−0.578561	−	0.140018i
$190$			11.8968i			0.863081i
$191$	−0.131627	−	0.227985i	−0.00952420	−	0.0164964i	0.861224	−	0.508226i	$-0.169698\pi$
$191$	−0.131627	−	0.227985i	−0.00952420	−	0.0164964i	−0.870748	+	0.491729i	$0.836365\pi$
$192$	−1.21476	+	1.23465i	−0.0876679	+	0.0891030i
$193$	−10.1470	−	5.85837i	−0.730397	−	0.421695i	0.0881704	−	0.996105i	$-0.471898\pi$
$193$	−10.1470	−	5.85837i	−0.730397	−	0.421695i	−0.818567	+	0.574410i	$0.805231\pi$
$194$	−0.309296	+	0.535716i	−0.0222061	+	0.0384622i
$195$	−16.9041	+	10.1648i	−1.21053	+	0.727917i
$196$	2.25982	+	3.91412i	0.161416	+	0.279580i
$197$		−	20.5283i		−	1.46258i	−0.682066	−	0.731291i	$-0.738918\pi$
$197$		−	20.5283i		−	1.46258i	0.682066	−	0.731291i	$-0.261082\pi$
$198$	−9.87625	−	5.49022i	−0.701874	−	0.390173i
$199$	5.95247			0.421960			0.210980	−	0.977490i	$-0.432335\pi$
$199$	5.95247			0.421960			0.210980	+	0.977490i	$0.432335\pi$
$200$	−4.30955	+	2.48812i	−0.304731	+	0.175937i
$201$	12.2129	−	3.37892i	0.861428	−	0.238331i
$202$	7.21887	+	4.16781i	0.507918	+	0.293246i
$203$	0.297682	+	0.171867i	0.0208932	+	0.0120627i
$204$	−3.26330	−	11.7950i	−0.228477	−	0.825813i
$205$	11.6576	+	20.1915i	0.814201	+	1.41024i
$206$			9.89675i			0.689539i
$207$	9.69506	+	5.38950i	0.673853	+	0.374596i
$208$	2.57405	+	2.52473i	0.178478	+	0.175058i
$209$	7.09349	+	12.2863i	0.490667	+	0.849860i
$210$	−2.16233	+	8.34017i	−0.149215	+	0.575526i
$211$	8.69625	−	15.0623i	0.598674	−	1.03693i	−0.394343	−	0.918963i	$-0.629028\pi$
$211$	8.69625	−	15.0623i	0.598674	−	1.03693i	0.993017	−	0.117971i	$-0.0376389\pi$
$212$	−7.20877	+	12.4860i	−0.495101	+	0.857539i
$213$	−0.953653	−	0.938294i	−0.0653433	−	0.0642909i
$214$	−0.100077	+	0.0577794i	−0.00684111	+	0.00394972i
$215$		−	19.3197i		−	1.31759i
$216$	3.58367	−	3.76262i	0.243838	−	0.256014i
$217$	−4.83358			−0.328125
$218$	−7.06504	−	12.2370i	−0.478505	−	0.828795i
$219$	−16.7100	−	16.4409i	−1.12916	−	1.11097i
$220$	−5.94838	+	10.3029i	−0.401039	+	0.694621i
$221$	−24.5426	+	6.83129i	−1.65091	+	0.459522i
$222$	0.489783	+	0.126985i	0.0328721	+	0.00852264i
$223$	20.5643	−	11.8728i	1.37709	−	0.795062i	0.385280	−	0.922800i	$-0.374105\pi$
$223$	20.5643	−	11.8728i	1.37709	−	0.795062i	0.991808	+	0.127737i	$0.0407714\pi$
$224$	1.57492			0.105229
$225$	12.8058	−	7.67327i	0.853717	−	0.511551i
$226$		−	19.4194i		−	1.29176i
$227$	3.93292	−	2.27067i	0.261037	−	0.150710i	−0.363770	−	0.931489i	$-0.618511\pi$
$227$	3.93292	−	2.27067i	0.261037	−	0.150710i	0.624808	+	0.780779i	$0.285177\pi$
$228$	−6.28766	+	1.73960i	−0.416411	+	0.115208i
$229$	10.3673	+	5.98556i	0.685091	+	0.395537i	0.801770	−	0.597632i	$-0.203892\pi$
$229$	10.3673	+	5.98556i	0.685091	+	0.395537i	−0.116680	+	0.993170i	$0.537225\pi$
$230$	5.83925	−	10.1139i	0.385029	−	0.666889i
$231$	2.73973	+	9.90255i	0.180261	+	0.651540i
$232$	−0.189015	+	0.109128i	−0.0124094	+	0.00716458i
$233$	10.6895			0.700290			0.350145	−	0.936696i	$-0.386132\pi$
$233$	10.6895			0.700290			0.350145	+	0.936696i	$0.386132\pi$
$234$	−7.84411	−	7.44782i	−0.512785	−	0.486879i
$235$	−22.5353			−1.47004
$236$	−9.04745	+	5.22355i	−0.588939	+	0.340024i
$237$	21.2606	+	5.51218i	1.38103	+	0.358054i
$238$	−5.56391	+	9.63697i	−0.360655	+	0.624672i
$239$	20.8684	+	12.0484i	1.34987	+	0.779346i	0.988230	−	0.152974i	$-0.0488849\pi$
$239$	20.8684	+	12.0484i	1.34987	+	0.779346i	0.361636	+	0.932319i	$0.382218\pi$
$240$	−3.89965	−	3.83685i	−0.251722	−	0.247668i
$241$	9.63879	−	5.56496i	0.620889	−	0.358470i	−0.156326	−	0.987705i	$-0.549965\pi$
$241$	9.63879	−	5.56496i	0.620889	−	0.358470i	0.777215	+	0.629235i	$0.216632\pi$
$242$			3.18698i			0.204867i
$243$	−10.5663	+	11.4609i	−0.677831	+	0.735218i
$244$	6.00013			0.384119
$245$	−12.3628	+	7.13768i	−0.789832	+	0.456010i
$246$	−8.96698	+	9.11376i	−0.571714	+	0.581072i
$247$	3.64162	+	13.0832i	0.231711	+	0.832462i
$248$	1.53455	−	2.65792i	0.0974440	−	0.168778i
$249$	0.158008	−	0.609441i	0.0100134	−	0.0386218i
$250$	0.0375278	+	0.0650001i	0.00237347	+	0.00411097i
$251$	11.3356			0.715499			0.357749	−	0.933818i	$-0.383544\pi$
$251$	11.3356			0.715499			0.357749	+	0.933818i	$0.383544\pi$
$252$	−4.72413	+	0.0767067i	−0.297592	+	0.00483207i
$253$		−	13.9267i		−	0.875565i
$254$	−4.70169	+	2.71452i	−0.295010	+	0.170324i
$255$	37.2546	−	10.3072i	2.33297	−	0.645462i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.16026	+	7.20579i	−0.259510	+	0.449485i	−0.966111	−	0.258128i	$-0.916894\pi$
$257$	−4.16026	+	7.20579i	−0.259510	+	0.449485i	0.706601	+	0.707613i	$0.250228\pi$
$258$	10.2109	−	2.82503i	0.635700	−	0.175879i
$259$	−0.230037	−	0.398435i	−0.0142938	−	0.0247576i
$260$	−7.97440	+	8.13019i	−0.494551	+	0.504213i
$261$	0.561654	−	0.336546i	0.0347655	−	0.0208317i
$262$			12.6868i			0.783796i
$263$	7.19133	+	12.4557i	0.443436	+	0.768054i	0.997942	−	0.0641260i	$-0.0204259\pi$
$263$	7.19133	+	12.4557i	0.443436	+	0.768054i	−0.554506	+	0.832180i	$0.687093\pi$
$264$	−6.31508	−	1.63729i	−0.388666	−	0.100768i
$265$	−39.4371	−	22.7690i	−2.42260	−	1.39869i
$266$	5.13728	+	2.96601i	0.314987	+	0.181858i
$267$	8.72346	+	8.58296i	0.533867	+	0.525269i
$268$	6.33583	−	3.65799i	0.387022	−	0.223447i
$269$	9.01366			0.549572			0.274786	−	0.961505i	$-0.411393\pi$
$269$	9.01366			0.549572			0.274786	+	0.961505i	$0.411393\pi$
$270$	11.8843	+	11.3191i	0.723255	+	0.688858i
$271$			19.9094i			1.20941i	0.796449	+	0.604705i	$0.206709\pi$
$271$			19.9094i			1.20941i	−0.796449	+	0.604705i	$0.793291\pi$
$272$	−3.53283	−	6.11904i	−0.214209	−	0.371021i
$273$	0.174973	+	9.83379i	0.0105898	+	0.595168i
$274$	−3.67770	+	6.36997i	−0.222178	+	0.384824i
$275$	−16.2322	−	9.37165i	−0.978837	−	0.565132i
$276$	6.19922	+	1.60725i	0.373149	+	0.0967454i
$277$	−6.69157	−	11.5901i	−0.402058	−	0.696384i	0.591916	−	0.805999i	$-0.298372\pi$
$277$	−6.69157	−	11.5901i	−0.402058	−	0.696384i	−0.993974	+	0.109615i	$0.965038\pi$
$278$			7.31119i			0.438496i
$279$	−4.47359	+	8.04745i	−0.267827	+	0.481788i
$280$			4.97440i			0.297277i
$281$	0.606470	−	0.350146i	0.0361790	−	0.0208879i	−0.481801	−	0.876280i	$-0.660017\pi$
$281$	0.606470	−	0.350146i	0.0361790	−	0.0208879i	0.517980	+	0.855392i	$0.326684\pi$
$282$	−3.29522	−	11.9103i	−0.196227	−	0.709249i
$283$	−9.71783	+	16.8318i	−0.577665	+	1.00055i	0.418081	+	0.908410i	$0.362703\pi$
$283$	−9.71783	+	16.8318i	−0.577665	+	1.00055i	−0.995746	+	0.0921358i	$0.970631\pi$
$284$	−0.668927	−	0.386205i	−0.0396935	−	0.0229170i
$285$	−5.49457	−	19.8597i	−0.325470	−	1.17639i
$286$	−3.38785	+	13.1512i	−0.200328	+	0.777645i
$287$	11.6255			0.686233
$288$	1.45762	−	2.62209i	0.0858912	−	0.154508i
$289$	32.9235			1.93668
$290$	−0.344682	−	0.597006i	−0.0202404	−	0.0350574i
$291$	0.268897	−	1.03714i	0.0157630	−	0.0607983i
$292$	−11.7210	−	6.76712i	−0.685919	−	0.396016i
$293$	−3.68719	−	2.12880i	−0.215408	−	0.124366i	0.388414	−	0.921485i	$-0.373023\pi$
$293$	−3.68719	−	2.12880i	−0.215408	−	0.124366i	−0.603822	+	0.797119i	$0.706356\pi$
$294$	−5.58016	−	5.49029i	−0.325441	−	0.320200i
$295$	−16.4987	−	28.5765i	−0.960589	−	1.66379i
$296$	0.292126			0.0169795
$297$	19.0225	+	4.60365i	1.10380	+	0.267131i
$298$	−23.7638			−1.37660
$299$	3.32569	−	12.9099i	0.192330	−	0.746599i
$300$	6.04495	−	6.14390i	0.349005	−	0.354718i
$301$	−8.34268	−	4.81665i	−0.480864	−	0.277627i
$302$	5.19448	−	8.99711i	0.298909	−	0.517725i
$303$	−13.9757	−	3.62343i	−0.802880	−	0.208160i
$304$	−3.26194	+	1.88328i	−0.187085	+	0.108014i
$305$			18.9515i			1.08516i
$306$	10.8951	+	18.1826i	0.622832	+	1.03943i
$307$		−	7.35088i		−	0.419537i	−0.977751	−	0.209768i	$-0.932729\pi$
$307$		−	7.35088i		−	0.419537i	0.977751	−	0.209768i	$-0.0672710\pi$
$308$	2.96601	+	5.13728i	0.169004	+	0.292724i
$309$	−4.57086	−	16.5210i	−0.260027	−	0.939848i
$310$	8.39509	+	4.84690i	0.476809	+	0.275286i
$311$	1.40756	−	2.43796i	0.0798152	−	0.138244i	−0.823355	−	0.567527i	$-0.807900\pi$
$311$	1.40756	−	2.43796i	0.0798152	−	0.138244i	0.903170	+	0.429283i	$0.141234\pi$
$312$	−5.46302	−	3.02579i	−0.309283	−	0.171302i
$313$	−13.5459	−	23.4621i	−0.765657	−	1.32616i	−0.939898	−	0.341454i	$-0.889081\pi$
$313$	−13.5459	−	23.4621i	−0.765657	−	1.32616i	0.174241	−	0.984703i	$-0.444253\pi$
$314$			9.14824i			0.516265i
$315$	−0.242280	−	14.9212i	−0.0136509	−	0.840717i
$316$	12.6807			0.713343
$317$	0.655352	−	0.378368i	0.0368083	−	0.0212513i	−0.481483	−	0.876455i	$-0.659902\pi$
$317$	0.655352	−	0.378368i	0.0368083	−	0.0212513i	0.518291	+	0.855204i	$0.326568\pi$
$318$	6.26719	−	24.1727i	0.351446	−	1.35554i
$319$	−0.711935	−	0.411036i	−0.0398607	−	0.0230136i
$320$	−2.73536	−	1.57926i	−0.152911	−	0.0882833i
$321$	0.140376	−	0.142674i	0.00783505	−	0.00796330i
$322$	−2.91160	−	5.04303i	−0.162257	−	0.281037i
$323$		−	26.6132i		−	1.48080i
$324$	−4.24458	+	7.93622i	−0.235810	+	0.440901i
$325$	−12.8091	−	12.5636i	−0.710521	−	0.696906i
$326$	6.79676	+	11.7723i	0.376438	+	0.652009i
$327$	17.4457	+	17.1647i	0.964747	+	0.949210i
$328$	−3.69084	+	6.39272i	−0.203792	+	0.352979i
$329$	−5.61832	+	9.73122i	−0.309748	+	0.536499i
$330$	5.17142	−	19.9463i	0.284677	−	1.09801i
$331$	−28.5504	+	16.4836i	−1.56927	+	0.906021i	−0.573020	+	0.819541i	$0.694228\pi$
$331$	−28.5504	+	16.4836i	−1.56927	+	0.906021i	−0.996254	+	0.0864792i	$0.972438\pi$
$332$		−	0.363495i		−	0.0199494i
$333$	−0.876261	+	0.0142281i	−0.0480188	+	0.000779693i
$334$	7.16615			0.392114
$335$	11.5538	+	20.0118i	0.631254	+	1.09336i
$336$	−2.62907	+	0.727382i	−0.143427	+	0.0396819i
$337$	−2.25348	+	3.90313i	−0.122755	+	0.212617i	−0.920853	−	0.389910i	$-0.872506\pi$
$337$	−2.25348	+	3.90313i	−0.122755	+	0.212617i	0.798098	+	0.602527i	$0.205839\pi$
$338$	−6.28099	+	11.3820i	−0.341641	+	0.619097i
$339$	8.96892	+	32.4175i	0.487125	+	1.76068i
$340$	19.3271	−	11.1585i	1.04816	−	0.605155i
$341$	11.5600			0.626007
$342$	9.69280	−	5.80797i	0.524126	−	0.314059i
$343$			18.1425i			0.979601i
$344$	5.29722	−	3.05835i	0.285607	−	0.164895i
$345$	−5.07654	+	19.5804i	−0.273312	+	1.05417i
$346$	2.60815	+	1.50582i	0.140215	+	0.0809532i
$347$	14.9859	−	25.9563i	0.804484	−	1.39341i	−0.112155	−	0.993691i	$-0.535775\pi$
$347$	14.9859	−	25.9563i	0.804484	−	1.39341i	0.916639	−	0.399716i	$-0.130891\pi$
$348$	0.265128	−	0.269468i	0.0142124	−	0.0144450i
$349$	15.0992	−	8.71753i	0.808242	−	0.466639i	−0.0381029	−	0.999274i	$-0.512131\pi$
$349$	15.0992	−	8.71753i	0.808242	−	0.466639i	0.846345	+	0.532635i	$0.178798\pi$
$350$	−7.83716			−0.418914
$351$	16.5343	+	8.81009i	0.882534	+	0.470248i
$352$	−3.76656			−0.200758
$353$	3.91310	−	2.25923i	0.208273	−	0.120247i	−0.392235	−	0.919865i	$-0.628298\pi$
$353$	3.91310	−	2.25923i	0.208273	−	0.120247i	0.600509	+	0.799618i	$0.294965\pi$
$354$	12.6907	−	12.8985i	0.674505	−	0.685546i
$355$	1.21984	−	2.11282i	0.0647421	−	0.112137i
$356$	6.11894	+	3.53277i	0.324303	+	0.187237i
$357$	4.83717	−	18.6571i	0.256010	−	0.987437i
$358$	16.6369	−	9.60533i	0.879288	−	0.507657i
$359$			30.5681i			1.61332i	0.591013	+	0.806662i	$0.298728\pi$
$359$			30.5681i			1.61332i	−0.591013	+	0.806662i	$0.701272\pi$
$360$	8.28191	+	4.60393i	0.436495	+	0.242648i
$361$	4.81302			0.253317
$362$	−7.92249	+	4.57405i	−0.416397	+	0.240407i
$363$	−1.47192	−	5.32015i	−0.0772558	−	0.279235i
$364$	1.52268	+	5.47048i	0.0798099	+	0.286731i
$365$	21.3741	−	37.0210i	1.11877	−	1.93777i
$366$	−10.0163	+	2.77119i	−0.523558	+	0.144852i
$367$	5.33420	+	9.23911i	0.278443	+	0.482278i	0.970998	−	0.239087i	$-0.0768483\pi$
$367$	5.33420	+	9.23911i	0.278443	+	0.482278i	−0.692555	+	0.721365i	$0.743515\pi$
$368$	3.69746			0.192743
$369$	10.7597	−	19.3554i	0.560128	−	1.00760i
$370$			0.922684i			0.0479681i
$371$	−19.6643	+	11.3532i	−1.02092	+	0.589430i
$372$	−1.33411	+	5.14570i	−0.0691705	+	0.266792i
$373$	−4.18223	+	7.24383i	−0.216548	+	0.375072i	−0.953750	−	0.300600i	$-0.902813\pi$
$373$	−4.18223	+	7.24383i	−0.216548	+	0.375072i	0.737203	+	0.675672i	$0.236146\pi$
$374$	13.3066	−	23.0477i	0.688068	−	1.19177i
$375$	−0.0926672	−	0.0911748i	−0.00478531	−	0.00470825i
$376$	−3.56738	−	6.17888i	−0.183973	−	0.318651i
$377$	−0.561801	−	0.551036i	−0.0289342	−	0.0283798i
$378$	7.85074	−	2.30991i	0.403798	−	0.118809i
$379$			26.5494i			1.36375i	0.731467	+	0.681877i	$0.238836\pi$
$379$			26.5494i			1.36375i	−0.731467	+	0.681877i	$0.761164\pi$
$380$	−5.94838	−	10.3029i	−0.305145	−	0.528527i
$381$	6.59500	−	6.70295i	0.337872	−	0.343403i
$382$	0.227985	+	0.131627i	0.0116647	+	0.00673463i
$383$	−2.83624	−	1.63751i	−0.144925	−	0.0836727i	0.425784	−	0.904825i	$-0.359998\pi$
$383$	−2.83624	−	1.63751i	−0.144925	−	0.0836727i	−0.570709	+	0.821152i	$0.693332\pi$
$384$	0.434692	−	1.67662i	0.0221828	−	0.0855595i
$385$	−16.2262	+	9.36819i	−0.826963	+	0.477447i
$386$	11.7167			0.596367
$387$	−15.7406	+	9.43185i	−0.800141	+	0.479448i
$388$		−	0.618592i		−	0.0314042i
$389$	−12.7599	−	22.1008i	−0.646951	−	1.12055i	−0.983847	−	0.179011i	$-0.942710\pi$
$389$	−12.7599	−	22.1008i	−0.646951	−	1.12055i	0.336896	−	0.941542i	$-0.390623\pi$
$390$	9.55701	−	17.2551i	0.483938	−	0.873743i
$391$	−13.0625	+	22.6249i	−0.660598	+	1.14419i
$392$	−3.91412	−	2.25982i	−0.197693	−	0.114138i
$393$	−5.85947	−	21.1786i	−0.295571	−	1.06832i
$394$	10.2642	+	17.7780i	0.517101	+	0.895645i
$395$			40.0521i			2.01524i
$396$	11.2982	−	0.183451i	0.567756	−	0.00921878i
$397$			4.70957i			0.236367i	0.992992	+	0.118183i	$0.0377071\pi$
$397$			4.70957i			0.236367i	−0.992992	+	0.118183i	$0.962293\pi$
$398$	−5.15499	+	2.97624i	−0.258396	+	0.149185i
$399$	−9.94572	−	2.57860i	−0.497909	−	0.129091i
$400$	2.48812	−	4.30955i	0.124406	−	0.215477i
$401$	12.5429	+	7.24166i	0.626364	+	0.361631i	0.779343	−	0.626598i	$-0.215553\pi$
$401$	12.5429	+	7.24166i	0.626364	+	0.361631i	−0.152979	+	0.988229i	$0.548887\pi$
$402$	−8.88718	+	9.03266i	−0.443252	+	0.450508i
$403$	10.7159	+	2.76051i	0.533799	+	0.137511i
$404$	−8.33563			−0.414713
$405$	−25.0667	−	13.4066i	−1.24557	−	0.666179i
$406$	−0.343734			−0.0170592
$407$	0.550154	+	0.952895i	0.0272701	+	0.0472333i
$408$	8.72359	+	8.58309i	0.431882	+	0.424926i
$409$	−14.2191	−	8.20943i	−0.703091	−	0.405930i	0.105406	−	0.994429i	$-0.466386\pi$
$409$	−14.2191	−	8.20943i	−0.703091	−	0.405930i	−0.808498	+	0.588499i	$0.799719\pi$
$410$	−20.1915	−	11.6576i	−0.997188	−	0.575727i
$411$	3.19733	−	12.3322i	0.157713	−	0.608302i
$412$	−4.94838	−	8.57084i	−0.243789	−	0.422255i
$413$	−16.4533			−0.809614
$414$	−11.0909	+	0.180086i	−0.545089	+	0.00885074i
$415$	1.14810			0.0563582
$416$	−3.49156	−	0.899453i	−0.171188	−	0.0440993i
$417$	−3.37670	−	12.2048i	−0.165358	−	0.597674i
$418$	−12.2863	−	7.09349i	−0.600942	−	0.346954i
$419$	−7.15411	+	12.3913i	−0.349501	+	0.605354i	−0.986161	−	0.165791i	$-0.946982\pi$
$419$	−7.15411	+	12.3913i	−0.349501	+	0.605354i	0.636660	+	0.771145i	$0.280316\pi$
$420$	−2.29745	−	8.30396i	−0.112104	−	0.405192i
$421$	20.8668	−	12.0475i	1.01699	−	0.587158i	0.103757	−	0.994603i	$-0.466913\pi$
$421$	20.8668	−	12.0475i	1.01699	−	0.587158i	0.913230	+	0.407445i	$0.133580\pi$
$422$			17.3925i			0.846653i
$423$	11.0017	+	18.3604i	0.534919	+	0.892715i
$424$		−	14.4175i		−	0.700178i
$425$	17.5802	+	30.4498i	0.852764	+	1.47703i
$426$	1.29504	+	0.335760i	0.0627447	+	0.0162676i
$427$	8.18369	+	4.72486i	0.396036	+	0.228652i
$428$	0.0577794	−	0.100077i	0.00279287	−	0.00483740i
$429$	−0.418463	−	23.5184i	−0.0202036	−	1.13548i
$430$	9.65986	+	16.7314i	0.465840	+	0.806859i
$431$			9.12376i			0.439476i	0.975559	+	0.219738i	$0.0705202\pi$
$431$			9.12376i			0.439476i	−0.975559	+	0.219738i	$0.929480\pi$
$432$	−1.22224	+	5.05036i	−0.0588052	+	0.242985i
$433$	0.372606			0.0179063			0.00895315	−	0.999960i	$-0.497150\pi$
$433$	0.372606			0.0179063			0.00895315	+	0.999960i	$0.497150\pi$
$434$	4.18600	−	2.41679i	0.200934	−	0.116010i
$435$	0.851121	+	0.837413i	0.0408081	+	0.0401509i
$436$	12.2370	+	7.06504i	0.586047	+	0.338354i
$437$	12.0609	+	6.96335i	0.576950	+	0.333102i
$438$	22.6917	+	5.88322i	1.08425	+	0.281111i
$439$	1.91160	+	3.31098i	0.0912355	+	0.158024i	0.908031	−	0.418902i	$-0.137585\pi$
$439$	1.91160	+	3.31098i	0.0912355	+	0.158024i	−0.816796	+	0.576927i	$0.804252\pi$
$440$		−	11.8968i		−	0.567155i
$441$	11.8509	+	6.58793i	0.564328	+	0.313711i
$442$	17.8389	−	18.1874i	0.848508	−	0.865085i
$443$	3.98203	+	6.89708i	0.189192	+	0.327690i	0.944981	−	0.327125i	$-0.106080\pi$
$443$	3.98203	+	6.89708i	0.189192	+	0.327690i	−0.755789	+	0.654815i	$0.772746\pi$
$444$	−0.487656	+	0.134919i	−0.0231431	+	0.00640299i
$445$	−11.1583	+	19.3268i	−0.528956	+	0.916178i
$446$	−11.8728	+	20.5643i	−0.562194	+	0.973749i
$447$	39.6697	−	10.9754i	1.87631	−	0.519118i
$448$	−1.36392	+	0.787458i	−0.0644391	+	0.0372039i
$449$		−	26.4088i		−	1.24631i	−0.782098	−	0.623155i	$-0.785851\pi$
$449$		−	26.4088i		−	1.24631i	0.782098	−	0.623155i	$-0.214149\pi$
$450$	−7.25347	+	13.0481i	−0.341932	+	0.615094i
$451$	−27.8035			−1.30922
$452$	9.70968	+	16.8177i	0.456705	+	0.791036i
$453$	−4.51600	+	17.4183i	−0.212180	+	0.818384i
$454$	−2.27067	+	3.93292i	−0.106568	+	0.184581i
$455$	−17.2786	+	4.80940i	−0.810034	+	0.225468i
$456$	4.57548	−	4.65037i	0.214266	−	0.217774i
$457$	7.46066	−	4.30742i	0.348995	−	0.201492i	−0.315248	−	0.949009i	$-0.602088\pi$
$457$	7.46066	−	4.30742i	0.348995	−	0.201492i	0.664243	+	0.747517i	$0.268754\pi$
$458$	−11.9711			−0.559374
$459$	−26.5854	−	25.3210i	−1.24090	−	1.18188i
$460$			11.6785i			0.544513i
$461$	−24.0754	+	13.8999i	−1.12130	+	0.647384i	−0.941733	−	0.336362i	$-0.890803\pi$
$461$	−24.0754	+	13.8999i	−1.12130	+	0.647384i	−0.179569	+	0.983745i	$0.557470\pi$
$462$	−7.32395	−	7.20599i	−0.340741	−	0.335253i
$463$	−31.4451	−	18.1548i	−1.46138	−	0.843727i	−0.462302	−	0.886723i	$-0.652976\pi$
$463$	−31.4451	−	18.1548i	−1.46138	−	0.843727i	−0.999075	+	0.0429960i	$0.986310\pi$
$464$	0.109128	−	0.189015i	0.00506613	−	0.00877479i
$465$	−16.2528	−	4.21382i	−0.753706	−	0.195411i
$466$	−9.25734	+	5.34473i	−0.428838	+	0.247590i
$467$	13.8295			0.639954			0.319977	−	0.947425i	$-0.396325\pi$
$467$	13.8295			0.639954			0.319977	+	0.947425i	$0.396325\pi$
$468$	10.5171	+	2.52795i	0.486153	+	0.116854i
$469$	11.5221			0.532040
$470$	19.5161	−	11.2676i	0.900211	−	0.519737i
$471$	−4.22515	−	15.2715i	−0.194685	−	0.703674i
$472$	5.22355	−	9.04745i	0.240433	−	0.416442i
$473$	19.9523	+	11.5195i	0.917408	+	0.529666i
$474$	−21.1683	+	5.85662i	−0.972293	+	0.269003i
$475$	16.2322	−	9.37165i	0.744783	−	0.430001i
$476$		−	11.1278i		−	0.510043i
$477$	0.702211	+	43.2469i	0.0321520	+	1.98014i
$478$	−24.0968			−1.10216
$479$	24.4509	−	14.1167i	1.11719	−	0.645010i	0.176508	−	0.984299i	$-0.443520\pi$
$479$	24.4509	−	14.1167i	1.11719	−	0.645010i	0.940682	+	0.339289i	$0.110187\pi$
$480$	5.29562	+	1.37298i	0.241711	+	0.0626677i
$481$	0.282436	+	1.01470i	0.0128780	+	0.0462663i
$482$	−5.56496	+	9.63879i	−0.253477	+	0.439035i
$483$	7.18958	+	7.07379i	0.327137	+	0.321869i
$484$	−1.59349	−	2.76001i	−0.0724314	−	0.125455i
$485$	1.95383			0.0887190
$486$	3.42027	−	15.2086i	0.155146	−	0.689877i
$487$		−	15.5579i		−	0.704995i	−0.935813	−	0.352498i	$-0.885332\pi$
$487$		−	15.5579i		−	0.704995i	0.935813	−	0.352498i	$-0.114668\pi$
$488$	−5.19627	+	3.00007i	−0.235224	+	0.135807i
$489$	−16.7832	−	16.5129i	−0.758962	−	0.746739i
$490$	7.13768	−	12.3628i	0.322448	−	0.558495i
$491$	−7.48935	+	12.9719i	−0.337990	+	0.585416i	−0.984055	−	0.177867i	$-0.943080\pi$
$491$	−7.48935	+	12.9719i	−0.337990	+	0.585416i	0.646065	+	0.763283i	$0.276414\pi$
$492$	3.20875	−	12.3762i	0.144662	−	0.557964i
$493$	0.771059	+	1.33551i	0.0347267	+	0.0601485i
$494$	−9.69532	−	9.50955i	−0.436213	−	0.427855i
$495$	0.579435	+	35.6855i	0.0260436	+	1.60395i
$496$			3.06910i			0.137807i
$497$	−0.608241	−	1.05350i	−0.0272833	−	0.0472561i
$498$	0.167882	+	0.606795i	0.00752295	+	0.0271912i
$499$	−29.5341	−	17.0515i	−1.32213	−	0.763330i	−0.338059	−	0.941125i	$-0.609770\pi$
$499$	−29.5341	−	17.0515i	−1.32213	−	0.763330i	−0.984068	+	0.177795i	$0.943104\pi$
$500$	−0.0650001	−	0.0375278i	−0.00290689	−	0.00167830i
$501$	−11.9627	+	3.30972i	−0.534456	+	0.147867i
$502$	−9.81694	+	5.66781i	−0.438152	+	0.252967i
$503$	−22.7259			−1.01330			−0.506648	−	0.862153i	$-0.669116\pi$
$503$	−22.7259			−1.01330			−0.506648	+	0.862153i	$0.669116\pi$
$504$	4.05286	−	2.42849i	0.180529	−	0.108174i
$505$		−	26.3282i		−	1.17159i
$506$	6.96335	+	12.0609i	0.309559	+	0.536172i
$507$	5.22828	−	21.9013i	0.232196	−	0.972669i
$508$	2.71452	−	4.70169i	0.120437	−	0.208604i
$509$	−5.48563	−	3.16713i	−0.243146	−	0.140380i	0.373476	−	0.927640i	$-0.378166\pi$
$509$	−5.48563	−	3.16713i	−0.243146	−	0.140380i	−0.616622	+	0.787259i	$0.711499\pi$
$510$	−27.1098	+	27.5536i	−1.20044	+	1.22009i
$511$	−10.6576	−	18.4596i	−0.471467	−	0.816604i
$512$		−	1.00000i		−	0.0441942i
$513$	−13.4981	+	14.1721i	−0.595957	+	0.625715i
$514$		−	8.32053i		−	0.367003i
$515$	27.0711	−	15.6295i	1.19290	−	0.688720i
$516$	−7.43034	+	7.55197i	−0.327103	+	0.332457i
$517$	13.4367	−	23.2731i	0.590947	−	1.02355i
$518$	0.398435	+	0.230037i	0.0175062	+	0.0101072i
$519$	−5.04935	−	1.30913i	−0.221642	−	0.0574645i
$520$	2.84094	−	11.0282i	0.124583	−	0.483616i
$521$	19.5169			0.855052			0.427526	−	0.904003i	$-0.359385\pi$
$521$	19.5169			0.855052			0.427526	+	0.904003i	$0.359385\pi$
$522$	−0.318134	+	0.572285i	−0.0139243	+	0.0250482i
$523$	4.76549			0.208380			0.104190	−	0.994557i	$-0.466775\pi$
$523$	4.76549			0.208380			0.104190	+	0.994557i	$0.466775\pi$
$524$	−6.34342	−	10.9871i	−0.277114	−	0.479975i
$525$	13.0829	−	3.61963i	0.570983	−	0.157973i
$526$	−12.4557	−	7.19133i	−0.543096	−	0.313557i
$527$	−18.7799	−	10.8426i	−0.818067	−	0.472311i
$528$	6.28766	−	1.73960i	0.273635	−	0.0757065i
$529$	4.66439	+	8.07897i	0.202800	+	0.351259i
$530$	45.5381			1.97805
$531$	−15.2279	+	27.3932i	−0.660835	+	1.18876i
$532$	−5.93202			−0.257186
$533$	−25.7736	−	6.63948i	−1.11638	−	0.287588i
$534$	−11.8462	−	3.07133i	−0.512636	−	0.132910i
$535$	0.316094	+	0.182497i	0.0136660	+	0.00789004i
$536$	−3.65799	+	6.33583i	−0.158001	+	0.273666i
$537$	−23.3364	+	23.7184i	−1.00704	+	1.02352i
$538$	−7.80606	+	4.50683i	−0.336543	+	0.194303i
$539$		−	17.0235i		−	0.733254i
$540$	−15.9516	−	3.86048i	−0.686450	−	0.166128i
$541$			25.2325i			1.08483i	0.840111	+	0.542414i	$0.182490\pi$
$541$			25.2325i			1.08483i	−0.840111	+	0.542414i	$0.817510\pi$
$542$	−9.95470	−	17.2420i	−0.427591	−	0.740609i
$543$	11.1128	−	11.2947i	0.476895	−	0.484701i
$544$	6.11904	+	3.53283i	0.262352	+	0.151469i
$545$	−22.3151	+	38.6508i	−0.955872	+	1.65562i
$546$	−5.06843	−	8.42883i	−0.216909	−	0.360721i
$547$	−14.3916	−	24.9271i	−0.615343	−	1.06580i	−0.990324	−	0.138772i	$-0.955684\pi$
$547$	−14.3916	−	24.9271i	−0.615343	−	1.06580i	0.374982	−	0.927032i	$-0.377649\pi$
$548$		−	7.35541i		−	0.314207i
$549$	15.4406	−	9.25210i	0.658990	−	0.394870i
$550$	18.7433			0.799217
$551$	0.711935	−	0.411036i	0.0303295	−	0.0175107i
$552$	−6.17231	+	1.70769i	−0.262711	+	0.0726840i
$553$	17.2954	+	9.98549i	0.735475	+	0.424626i
$554$	11.5901	+	6.69157i	0.492418	+	0.284298i
$555$	−0.426146	−	1.54027i	−0.0180889	−	0.0653809i
$556$	−3.65559	−	6.33167i	−0.155032	−	0.268523i
$557$		−	11.4847i		−	0.486624i	−0.969948	−	0.243312i	$-0.921766\pi$
$557$		−	11.4847i		−	0.486624i	0.969948	−	0.243312i	$-0.0782339\pi$
$558$	−0.149481	−	9.20609i	−0.00632805	−	0.389725i
$559$	15.7447	+	15.4430i	0.665931	+	0.653170i
$560$	−2.48720	−	4.30796i	−0.105103	−	0.182044i
$561$	−11.5685	+	44.6202i	−0.488424	+	1.88386i
$562$	−0.350146	+	0.606470i	−0.0147700	+	0.0255824i
$563$	−7.42388	+	12.8585i	−0.312879	+	0.541923i	−0.978984	−	0.203935i	$-0.934627\pi$
$563$	−7.42388	+	12.8585i	−0.312879	+	0.541923i	0.666105	+	0.745858i	$0.267960\pi$
$564$	8.80890	+	8.66703i	0.370922	+	0.364948i
$565$	−53.1189	+	30.6682i	−2.23473	+	1.29022i
$566$		−	19.4357i		−	0.816942i
$567$	−12.0387	+	7.48192i	−0.505578	+	0.314211i
$568$	0.772410			0.0324096
$569$	−13.8881	−	24.0549i	−0.582220	−	1.00843i	−0.995216	−	0.0977019i	$-0.968851\pi$
$569$	−13.8881	−	24.0549i	−0.582220	−	1.00843i	0.412996	−	0.910733i	$-0.364483\pi$
$570$	14.6883	+	14.4517i	0.615225	+	0.605316i
$571$	9.56039	−	16.5591i	0.400090	−	0.692976i	−0.593646	−	0.804726i	$-0.702312\pi$
$571$	9.56039	−	16.5591i	0.400090	−	0.692976i	0.993736	+	0.111750i	$0.0356455\pi$
$572$	−3.64162	−	13.0832i	−0.152264	−	0.547035i
$573$	−0.441376	−	0.114434i	−0.0184388	−	0.00478057i
$574$	−10.0680	+	5.81276i	−0.420230	+	0.242620i
$575$	−18.3994			−0.767310
$576$	0.0487053	+	2.99960i	0.00202939	+	0.124984i
$577$			26.8961i			1.11970i	0.828595	+	0.559849i	$0.189141\pi$
$577$			26.8961i			1.11970i	−0.828595	+	0.559849i	$0.810859\pi$
$578$	−28.5126	+	16.4617i	−1.18597	+	0.684718i
$579$	−19.5592	+	5.41143i	−0.812853	+	0.224891i
$580$	0.597006	+	0.344682i	0.0247893	+	0.0143121i
$581$	0.286237	−	0.495777i	0.0118751	−	0.0205683i
$582$	0.285699	+	1.03264i	0.0118426	+	0.0428042i
$583$	47.0291	−	27.1523i	1.94775	−	1.12453i
$584$	13.5342			0.560051
$585$	−7.98457	+	33.2185i	−0.330121	+	1.37341i
$586$	4.25760			0.175880
$587$	−33.7791	+	19.5024i	−1.39421	+	0.804949i	−0.993778	−	0.111376i	$-0.964474\pi$
$587$	−33.7791	+	19.5024i	−1.39421	+	0.804949i	−0.400434	+	0.916325i	$0.631141\pi$
$588$	7.57770	+	1.96465i	0.312499	+	0.0810207i
$589$	−5.77998	+	10.0112i	−0.238160	+	0.412505i
$590$	28.5765	+	16.4987i	1.17648	+	0.679239i
$591$	−25.3452	−	24.9370i	−1.04256	−	1.02577i
$592$	−0.252988	+	0.146063i	−0.0103977	+	0.00600314i
$593$		−	24.2756i		−	0.996881i	−0.866924	−	0.498441i	$-0.833906\pi$
$593$		−	24.2756i		−	0.996881i	0.866924	−	0.498441i	$-0.166094\pi$
$594$	−18.7758	+	5.52436i	−0.770380	+	0.226667i
$595$	35.1474			1.44090
$596$	20.5800	−	11.8819i	0.842990	−	0.486701i
$597$	7.23084	−	7.34920i	0.295939	−	0.300783i
$598$	3.57482	+	12.8431i	0.146185	+	0.525195i
$599$	9.53752	−	16.5195i	0.389692	−	0.674967i	−0.602716	−	0.797956i	$-0.705915\pi$
$599$	9.53752	−	16.5195i	0.389692	−	0.674967i	0.992408	+	0.122989i	$0.0392480\pi$
$600$	−2.16313	+	8.34324i	−0.0883093	+	0.340611i
$601$	7.43342	+	12.8751i	0.303216	+	0.525185i	0.976862	−	0.213869i	$-0.0686064\pi$
$601$	7.43342	+	12.8751i	0.303216	+	0.525185i	−0.673647	+	0.739053i	$0.735273\pi$
$602$	9.63330			0.392624
$603$	10.6639	−	19.1831i	0.434269	−	0.781198i
$604$			10.3890i			0.422721i
$605$	8.71753	−	5.03307i	0.354418	−	0.204623i
$606$	13.9150	−	3.84985i	0.565258	−	0.156389i
$607$	−18.3898	+	31.8521i	−0.746419	+	1.29284i	0.203110	+	0.979156i	$0.434895\pi$
$607$	−18.3898	+	31.8521i	−0.746419	+	1.29284i	−0.949529	+	0.313680i	$0.898438\pi$
$608$	1.88328	−	3.26194i	0.0763771	−	0.132289i
$609$	0.573808	−	0.158755i	0.0232519	−	0.00643308i
$610$	−9.47577	−	16.4125i	−0.383663	−	0.664523i
$611$	18.0133	−	18.3652i	0.728741	−	0.742978i
$612$	−18.5268	−	10.2991i	−0.748900	−	0.416315i
$613$			9.13501i			0.368959i	0.982836	+	0.184480i	$0.0590600\pi$
$613$			9.13501i			0.368959i	−0.982836	+	0.184480i	$0.940940\pi$
$614$	3.67544	+	6.36605i	0.148329	+	0.256913i
$615$	39.0906	+	10.1349i	1.57628	+	0.408679i
$616$	−5.13728	−	2.96601i	−0.206987	−	0.119504i
$617$	12.3504	+	7.13051i	0.497209	+	0.287063i	0.727560	−	0.686044i	$-0.240654\pi$
$617$	12.3504	+	7.13051i	0.497209	+	0.287063i	−0.230352	+	0.973107i	$0.573988\pi$
$618$	12.2190	+	12.0222i	0.491520	+	0.483604i
$619$	−5.16609	+	2.98264i	−0.207643	+	0.119883i	−0.600215	−	0.799838i	$-0.704918\pi$
$619$	−5.16609	+	2.98264i	−0.207643	+	0.119883i	0.392573	+	0.919721i	$0.371585\pi$
$620$	−9.69381			−0.389313
$621$	18.4313	−	5.42301i	0.739624	−	0.217618i
$622$			2.81511i			0.112876i
$623$	5.56382	+	9.63683i	0.222910	+	0.386091i
$624$	6.24401	−	0.111100i	0.249960	−	0.00444754i
$625$	12.5591	−	21.7530i	0.502365	−	0.870122i
$626$	23.4621	+	13.5459i	0.937735	+	0.541401i
$627$	23.7861	+	6.16696i	0.949926	+	0.246285i
$628$	−4.57412	−	7.92261i	−0.182527	−	0.316146i
$629$		−	2.06406i		−	0.0822994i
$630$	7.67044	+	12.8010i	0.305598	+	0.510005i
$631$		−	3.19802i		−	0.127311i	−0.997972	−	0.0636557i	$-0.979724\pi$
$631$		−	3.19802i		−	0.127311i	0.997972	−	0.0636557i	$-0.0202759\pi$
$632$	−10.9818	+	6.34033i	−0.436832	+	0.252205i
$633$	−8.03280	−	29.0340i	−0.319275	−	1.15400i
$634$	−0.378368	+	0.655352i	−0.0150269	+	0.0260274i
$635$	14.8504	+	8.57387i	0.589319	+	0.340243i
$636$	6.65881	+	24.0678i	0.264039	+	0.954349i
$637$	4.06520	−	15.7806i	0.161069	−	0.625249i
$638$	0.822072			0.0325462
$639$	−2.31692	+	0.0376204i	−0.0916561	+	0.00148824i
$640$	3.15852			0.124851
$641$	−15.4801	−	26.8123i	−0.611426	−	1.05902i	−0.991000	−	0.133860i	$-0.957263\pi$
$641$	−15.4801	−	26.8123i	−0.611426	−	1.05902i	0.379574	−	0.925161i	$-0.376071\pi$
$642$	−0.0502324	+	0.193748i	−0.00198252	+	0.00764661i
$643$	25.5058	+	14.7258i	1.00585	+	0.580729i	0.909975	−	0.414664i	$-0.136101\pi$
$643$	25.5058	+	14.7258i	1.00585	+	0.580729i	0.0958776	+	0.995393i	$0.469434\pi$
$644$	5.04303	+	2.91160i	0.198723	+	0.114733i
$645$	−23.8530	−	23.4689i	−0.939213	−	0.924086i
$646$	13.3066	+	23.0477i	0.523542	+	0.906801i
$647$	−27.8656			−1.09551			−0.547756	−	0.836638i	$-0.684518\pi$
$647$	−27.8656			−1.09551			−0.547756	+	0.836638i	$0.684518\pi$
$648$	−0.292193	−	8.99526i	−0.0114784	−	0.353367i
$649$	39.3496			1.54461
$650$	17.3748	+	4.47589i	0.681497	+	0.175559i
$651$	−5.87165	+	5.96776i	−0.230128	+	0.233895i
$652$	−11.7723	−	6.79676i	−0.461040	−	0.266182i
$653$	−9.48617	+	16.4305i	−0.371223	+	0.642976i	−0.989754	−	0.142784i	$-0.954395\pi$
$653$	−9.48617	+	16.4305i	−0.371223	+	0.642976i	0.618531	+	0.785760i	$0.287728\pi$
$654$	−23.6907	−	6.14223i	−0.926381	−	0.240180i
$655$	34.7030	−	20.0358i	1.35596	−	0.782864i
$656$		−	7.38168i		−	0.288206i
$657$	−40.5974	+	0.659189i	−1.58385	+	0.0257174i
$658$		−	11.2366i		−	0.438050i
$659$	−9.05886	−	15.6904i	−0.352883	−	0.611211i	0.633870	−	0.773439i	$-0.281465\pi$
$659$	−9.05886	−	15.6904i	−0.352883	−	0.611211i	−0.986753	+	0.162228i	$0.948132\pi$
$660$	5.49457	+	19.8597i	0.213876	+	0.773038i
$661$	20.5705	+	11.8764i	0.800101	+	0.461939i	0.843507	−	0.537119i	$-0.180487\pi$
$661$	20.5705	+	11.8764i	0.800101	+	0.461939i	−0.0434052	+	0.999058i	$0.513821\pi$
$662$	16.4836	−	28.5504i	0.640653	−	1.10964i
$663$	−21.3792	+	38.5998i	−0.830299	+	1.49909i
$664$	0.181747	+	0.314795i	0.00705316	+	0.0122164i
$665$		−	18.7364i		−	0.726566i
$666$	0.751750	−	0.450452i	0.0291297	−	0.0174547i
$667$	−0.806991			−0.0312468
$668$	−6.20607	+	3.58308i	−0.240120	+	0.138633i
$669$	10.3220	−	39.8123i	0.399073	−	1.53923i
$670$	−20.0118	−	11.5538i	−0.773125	−	0.446364i
$671$	−19.5721	−	11.2999i	−0.755571	−	0.436229i
$672$	1.91315	−	1.94447i	0.0738013	−	0.0750094i
$673$	−12.1157	−	20.9850i	−0.467026	−	0.808913i	0.532264	−	0.846578i	$-0.321341\pi$
$673$	−12.1157	−	20.9850i	−0.467026	−	0.808913i	−0.999290	+	0.0376653i	$0.988008\pi$
$674$		−	4.50695i		−	0.173601i
$675$	6.08217	−	25.1318i	0.234103	−	0.967323i
$676$	−0.251488	−	12.9976i	−0.00967261	−	0.499906i
$677$	−9.77002	−	16.9222i	−0.375492	−	0.650372i	0.614908	−	0.788599i	$-0.289193\pi$
$677$	−9.77002	−	16.9222i	−0.375492	−	0.650372i	−0.990401	+	0.138227i	$0.955860\pi$
$678$	−23.9761	−	23.5899i	−0.920795	−	0.905965i
$679$	0.487115	−	0.843708i	0.0186938	−	0.0323785i
$680$	−11.1585	+	19.3271i	−0.427909	+	0.741160i
$681$	1.97408	−	7.61409i	0.0756471	−	0.291773i
$682$	−10.0112	+	5.77998i	−0.383349	+	0.221327i
$683$			40.5718i			1.55244i	0.630465	+	0.776218i	$0.282864\pi$
$683$			40.5718i			1.55244i	−0.630465	+	0.776218i	$0.717136\pi$
$684$	−5.49022	+	9.87625i	−0.209924	+	0.377628i
$685$	23.2322			0.887656
$686$	−9.07123	−	15.7118i	−0.346341	−	0.599881i
$687$	19.9839	−	5.52892i	0.762432	−	0.210941i
$688$	−3.05835	+	5.29722i	−0.116599	+	0.201955i
$689$	50.0794	−	13.9393i	1.90787	−	0.531046i
$690$	−5.39376	−	19.4954i	−0.205337	−	0.742176i
$691$	25.6366	−	14.8013i	0.975264	−	0.563069i	0.0744270	−	0.997226i	$-0.476287\pi$
$691$	25.6366	−	14.8013i	0.975264	−	0.563069i	0.900837	+	0.434158i	$0.142954\pi$
$692$	−3.01163			−0.114485
$693$	15.5543	+	8.64664i	0.590858	+	0.328459i
$694$			29.9717i			1.13771i
$695$	19.9987	−	11.5463i	0.758594	−	0.437975i
$696$	−0.0948738	+	0.365931i	−0.00359618	+	0.0138706i
$697$	45.1688	+	26.0782i	1.71089	+	0.987782i
$698$	−8.71753	+	15.0992i	−0.329964	+	0.571514i
$699$	12.9851	−	13.1977i	0.491143	−	0.499183i
$700$	6.78718	−	3.91858i	0.256531	−	0.148108i
$701$	−14.6213			−0.552238			−0.276119	−	0.961123i	$-0.589048\pi$
$701$	−14.6213			−0.552238			−0.276119	+	0.961123i	$0.589048\pi$
$702$	−18.7241	+	0.637371i	−0.706697	+	0.0240560i
$703$	−1.10031			−0.0414989
$704$	3.26194	−	1.88328i	0.122939	−	0.0709788i
$705$	−27.3750	+	27.8231i	−1.03100	+	1.04788i
$706$	−2.25923	+	3.91310i	−0.0850272	+	0.147271i
$707$	−11.3691	−	6.56396i	−0.427579	−	0.246863i
$708$	−4.54126	+	17.5158i	−0.170671	+	0.658283i
$709$	−5.54229	+	3.19984i	−0.208145	+	0.120173i	−0.600449	−	0.799663i	$-0.705011\pi$
$709$	−5.54229	+	3.19984i	−0.208145	+	0.120173i	0.392304	+	0.919836i	$0.371678\pi$
$710$			2.43967i			0.0915592i
$711$	32.6322	−	19.5534i	1.22380	−	0.733308i
$712$	−7.06555			−0.264793
$713$	9.82755	−	5.67394i	0.368045	−	0.212491i
$714$	5.13943	+	18.5761i	0.192338	+	0.695193i
$715$	41.3234	−	11.5021i	1.54541	−	0.430155i
$716$	−9.60533	+	16.6369i	−0.358968	+	0.621751i
$717$	40.2257	−	11.1292i	1.50226	−	0.415628i
$718$	−15.2841	−	26.4728i	−0.570396	−	0.987955i
$719$	13.5954			0.507022			0.253511	−	0.967332i	$-0.418415\pi$
$719$	13.5954			0.507022			0.253511	+	0.967332i	$0.418415\pi$
$720$	−9.47431	+	0.153837i	−0.353087	+	0.00573315i
$721$		−	15.5866i		−	0.580474i
$722$	−4.16820	+	2.40651i	−0.155124	+	0.0895610i
$723$	4.83808	−	18.6606i	0.179930	−	0.693995i
$724$	4.57405	−	7.92249i	0.169993	−	0.294437i
$725$	−0.543045	+	0.940582i	−0.0201682	+	0.0349323i
$726$	3.93480	+	3.87142i	0.146034	+	0.143682i
$727$	11.1176	+	19.2562i	0.412329	+	0.714174i	0.995144	−	0.0984307i	$-0.0313823\pi$
$727$	11.1176	+	19.2562i	0.412329	+	0.714174i	−0.582815	+	0.812605i	$0.698049\pi$
$728$	−4.05392	−	3.97624i	−0.150248	−	0.147369i
$729$	1.31458	+	26.9680i	0.0486882	+	0.998814i
$730$			42.7481i			1.58218i
$731$	−21.6093	−	37.4284i	−0.799248	−	1.38434i
$732$	7.28874	−	7.40805i	0.269399	−	0.273809i
$733$	−14.7765	−	8.53119i	−0.545781	−	0.315107i	0.201638	−	0.979460i	$-0.435374\pi$
$733$	−14.7765	−	8.53119i	−0.545781	−	0.315107i	−0.747419	+	0.664354i	$0.768707\pi$
$734$	−9.23911	−	5.33420i	−0.341022	−	0.196889i
$735$	−6.20538	+	23.9343i	−0.228889	+	0.882830i
$736$	−3.20209	+	1.84873i	−0.118031	+	0.0681451i
$737$	−27.5561			−1.01504
$738$	0.359527	+	22.1421i	0.0132344	+	0.815063i
$739$			47.4169i			1.74426i	0.489274	+	0.872130i	$0.337262\pi$
$739$			47.4169i			1.74426i	−0.489274	+	0.872130i	$0.662738\pi$
$740$	−0.461342	−	0.799068i	−0.0169593	−	0.0293743i
$741$	20.5768	+	11.3968i	0.755908	+	0.418673i
$742$	11.3532	−	19.6643i	0.416790	−	0.721901i
$743$	−22.7717	−	13.1472i	−0.835411	−	0.482325i	0.0202905	−	0.999794i	$-0.493541\pi$
$743$	−22.7717	−	13.1472i	−0.835411	−	0.482325i	−0.855702	+	0.517469i	$0.826874\pi$
$744$	−1.41748	−	5.12337i	−0.0519672	−	0.187832i
$745$	37.5291	+	65.0024i	1.37496	+	2.38150i
$746$		−	8.36446i		−	0.306245i
$747$	−0.560502	−	0.935410i	−0.0205077	−	0.0342249i
$748$			26.6132i			0.973076i
$749$	0.157613	−	0.0909977i	0.00575904	−	0.00332498i
$750$	0.125840	+	0.0326261i	0.00459501	+	0.00119134i
$751$	−16.9255	+	29.3158i	−0.617620	+	1.06975i	0.372299	+	0.928113i	$0.378570\pi$
$751$	−16.9255	+	29.3158i	−0.617620	+	1.06975i	−0.989919	+	0.141636i	$0.954764\pi$
$752$	6.17888	+	3.56738i	0.225321	+	0.130089i
$753$	13.7701	−	13.9955i	0.501810	−	0.510024i
$754$	0.762052	+	0.196311i	0.0277523	+	0.00714921i
$755$	−32.8137			−1.19421
$756$	−5.64398	+	5.92581i	−0.205270	+	0.215520i
$757$	−35.4490			−1.28841			−0.644207	−	0.764851i	$-0.722813\pi$
$757$	−35.4490			−1.28841			−0.644207	+	0.764851i	$0.722813\pi$
$758$	−13.2747	−	22.9925i	−0.482160	−	0.835125i
$759$	−17.1946	−	16.9176i	−0.624123	−	0.614071i
$760$	10.3029	+	5.94838i	0.373725	+	0.215770i
$761$	−23.7086	−	13.6882i	−0.859436	−	0.496196i	0.00438738	−	0.999990i	$-0.498603\pi$
$761$	−23.7086	−	13.6882i	−0.859436	−	0.496196i	−0.863823	+	0.503795i	$0.831937\pi$
$762$	−2.35996	+	9.10242i	−0.0854923	+	0.329746i
$763$	11.1269	+	19.2723i	0.402819	+	0.697703i
$764$	−0.263254			−0.00952420
$765$	32.5298	−	58.5171i	1.17612	−	2.11569i
$766$	3.27501			0.118331
$767$	36.4766	+	9.39667i	1.31710	+	0.339294i
$768$	0.461854	+	1.66934i	0.0166657	+	0.0602371i
$769$	12.8943	+	7.44450i	0.464979	+	0.268456i	0.714135	−	0.700008i	$-0.246820\pi$
$769$	12.8943	+	7.44450i	0.464979	+	0.268456i	−0.249157	+	0.968463i	$0.580153\pi$
$770$	9.36819	−	16.2262i	0.337606	−	0.584751i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.21476 - 1.23465i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.73536 + 1.57926i) q^{5} +(-0.434692 + 1.67662i) q^{6} +(1.36392 - 0.787458i) q^{7} +1.00000i q^{8} +(-0.0487053 - 2.99960i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.21476 - 1.23465i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.73536 + 1.57926i) q^{5} +(-0.434692 + 1.67662i) q^{6} +(1.36392 - 0.787458i) q^{7} +1.00000i q^{8} +(-0.0487053 - 2.99960i) q^{9} -3.15852 q^{10} +(-3.26194 + 1.88328i) q^{11} +(-0.461854 - 1.66934i) q^{12} +(-3.47351 + 0.966830i) q^{13} +(-0.787458 + 1.36392i) q^{14} +(5.27264 - 1.45878i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.06565 q^{17} +(1.54198 + 2.57338i) q^{18} -3.76656i q^{19} +(2.73536 - 1.57926i) q^{20} +(0.684603 - 2.64053i) q^{21} +(1.88328 - 3.26194i) q^{22} +(-1.84873 + 3.20209i) q^{23} +(1.23465 + 1.21476i) q^{24} +(2.48812 + 4.30955i) q^{25} +(2.52473 - 2.57405i) q^{26} +(-3.76262 - 3.58367i) q^{27} -1.57492i q^{28} +(0.109128 + 0.189015i) q^{29} +(-3.83685 + 3.89965i) q^{30} +(-2.65792 - 1.53455i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.63729 + 6.31508i) q^{33} +(-6.11904 + 3.53283i) q^{34} +4.97440 q^{35} +(-2.62209 - 1.45762i) q^{36} -0.292126i q^{37} +(1.88328 + 3.26194i) q^{38} +(-3.02579 + 5.46302i) q^{39} +(-1.57926 + 2.73536i) q^{40} +(6.39272 + 3.69084i) q^{41} +(0.727382 + 2.62907i) q^{42} +(-3.05835 - 5.29722i) q^{43} +3.76656i q^{44} +(4.60393 - 8.28191i) q^{45} -3.69746i q^{46} +(-6.17888 + 3.56738i) q^{47} +(-1.67662 - 0.434692i) q^{48} +(-2.25982 + 3.91412i) q^{49} +(-4.30955 - 2.48812i) q^{50} +(8.58309 - 8.72359i) q^{51} +(-0.899453 + 3.49156i) q^{52} -14.4175 q^{53} +(5.05036 + 1.22224i) q^{54} -11.8968 q^{55} +(0.787458 + 1.36392i) q^{56} +(-4.65037 - 4.57548i) q^{57} +(-0.189015 - 0.109128i) q^{58} +(-9.04745 - 5.22355i) q^{59} +(1.37298 - 5.29562i) q^{60} +(3.00007 + 5.19627i) q^{61} +3.06910 q^{62} +(-2.42849 - 4.05286i) q^{63} -1.00000 q^{64} +(-11.0282 - 2.84094i) q^{65} +(-1.73960 - 6.28766i) q^{66} +(6.33583 + 3.65799i) q^{67} +(3.53283 - 6.11904i) q^{68} +(1.70769 + 6.17231i) q^{69} +(-4.30796 + 2.48720i) q^{70} -0.772410i q^{71} +(2.99960 - 0.0487053i) q^{72} -13.5342i q^{73} +(0.146063 + 0.252988i) q^{74} +(8.34324 + 2.16313i) q^{75} +(-3.26194 - 1.88328i) q^{76} +(-2.96601 + 5.13728i) q^{77} +(-0.111100 - 6.24401i) q^{78} +(6.34033 + 10.9818i) q^{79} -3.15852i q^{80} +(-8.99526 + 0.292193i) q^{81} -7.38168 q^{82} +(0.314795 - 0.181747i) q^{83} +(-1.94447 - 1.91315i) q^{84} +(19.3271 + 11.1585i) q^{85} +(5.29722 + 3.05835i) q^{86} +(0.365931 + 0.0948738i) q^{87} +(-1.88328 - 3.26194i) q^{88} +7.06555i q^{89} +(0.153837 + 9.47431i) q^{90} +(-3.97624 + 4.05392i) q^{91} +(1.84873 + 3.20209i) q^{92} +(-5.12337 + 1.41748i) q^{93} +(3.56738 - 6.17888i) q^{94} +(5.94838 - 10.3029i) q^{95} +(1.66934 - 0.461854i) q^{96} +(0.535716 - 0.309296i) q^{97} -4.51964i q^{98} +(5.80797 + 9.69280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 - 16 * q^9	\( 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Introduction

L-functions

Modular forms

Varieties

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