LMFDB - Embedded newform 234.2.z.a.41.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.14
Character	$\chi$	$=$	234.41
Dual form			234.2.z.a.137.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(1.61301 + 0.631032i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.748082 + 0.200448i) q^{5} +(1.72137 + 0.192053i) q^{6} +(-0.456400 - 0.456400i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.20360 + 2.03572i) q^{9} +(-0.670712 + 0.387236i) q^{10} +(0.285599 + 1.06587i) q^{11} +(1.71242 - 0.260014i) q^{12} +(-1.23841 - 3.38620i) q^{13} +(-0.558973 - 0.322723i) q^{14} +(-1.33315 - 0.148740i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.49547 + 2.59023i) q^{17} +(2.65539 + 1.39602i) q^{18} +(-0.360069 - 1.34379i) q^{19} +(-0.547634 + 0.547634i) q^{20} +(-0.448174 - 1.02418i) q^{21} +(0.551734 + 0.955631i) q^{22} -5.29497 q^{23} +(1.58678 - 0.694362i) q^{24} +(-3.81068 + 2.20010i) q^{25} +(-2.07263 - 2.95029i) q^{26} +(2.26981 + 4.67418i) q^{27} +(-0.623453 - 0.167054i) q^{28} +(0.786294 + 0.453967i) q^{29} +(-1.32622 + 0.201374i) q^{30} +(-1.43905 - 5.37059i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.211925 + 1.89948i) q^{33} +(-0.774112 + 2.88903i) q^{34} +(0.432909 + 0.249940i) q^{35} +(2.92623 + 0.661189i) q^{36} +(1.88903 - 7.04995i) q^{37} +(-0.695599 - 1.20481i) q^{38} +(0.139227 - 6.24345i) q^{39} +(-0.387236 + 0.670712i) q^{40} +(0.717671 + 0.717671i) q^{41} +(-0.697980 - 0.873286i) q^{42} +6.49134i q^{43} +(0.780270 + 0.780270i) q^{44} +(-2.05653 - 1.08118i) q^{45} +(-5.11455 + 1.37044i) q^{46} +(2.99897 + 0.803570i) q^{47} +(1.35299 - 1.08139i) q^{48} -6.58340i q^{49} +(-3.11141 + 3.11141i) q^{50} +(-4.04673 + 3.23437i) q^{51} +(-2.76560 - 2.31333i) q^{52} +10.8935i q^{53} +(3.40224 + 3.92744i) q^{54} +(-0.427302 - 0.740109i) q^{55} -0.645446 q^{56} +(0.267184 - 2.39477i) q^{57} +(0.876997 + 0.234991i) q^{58} +(-9.75565 - 2.61402i) q^{59} +(-1.22891 + 0.537764i) q^{60} +10.8544 q^{61} +(-2.78002 - 4.81514i) q^{62} +(-0.0766175 - 1.93482i) q^{63} -1.00000i q^{64} +(1.60519 + 2.28492i) q^{65} +(0.286917 + 1.88960i) q^{66} +(0.762137 - 0.762137i) q^{67} +2.99094i q^{68} +(-8.54083 - 3.34130i) q^{69} +(0.482847 + 0.129378i) q^{70} +(-1.68422 + 0.451285i) q^{71} +(2.99765 - 0.118705i) q^{72} +(-2.70493 - 2.70493i) q^{73} -7.29864i q^{74} +(-7.53499 + 1.14411i) q^{75} +(-0.983725 - 0.983725i) q^{76} +(0.356115 - 0.616809i) q^{77} +(-1.48144 - 6.06674i) q^{78} +(3.01910 + 5.22924i) q^{79} +(-0.200448 + 0.748082i) q^{80} +(0.711670 + 8.97182i) q^{81} +(0.878964 + 0.507470i) q^{82} +(-2.95813 + 11.0399i) q^{83} +(-0.900220 - 0.662879i) q^{84} +(0.599528 - 2.23747i) q^{85} +(1.68008 + 6.27015i) q^{86} +(0.981831 + 1.22843i) q^{87} +(0.955631 + 0.551734i) q^{88} +(12.0109 + 3.21832i) q^{89} +(-2.26628 - 0.512072i) q^{90} +(-0.980247 + 2.11067i) q^{91} +(-4.58558 + 2.64748i) q^{92} +(1.06782 - 9.57090i) q^{93} +3.10476 q^{94} +(0.538722 + 0.933093i) q^{95} +(1.02701 - 1.39472i) q^{96} +(9.31815 - 9.31815i) q^{97} +(-1.70391 - 6.35908i) q^{98} +(-1.54047 + 2.93014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	1.61301	+	0.631032i	0.931271	+	0.364327i
$3$	1.61301	+	0.631032i	0.931271	+	0.364327i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.748082	+	0.200448i	−0.334552	+	0.0896431i	−0.422185	−	0.906510i	$-0.638737\pi$
$5$	−0.748082	+	0.200448i	−0.334552	+	0.0896431i	0.0876323	+	0.996153i	$0.472070\pi$
$6$	1.72137	+	0.192053i	0.702746	+	0.0784054i
$7$	−0.456400	−	0.456400i	−0.172503	−	0.172503i	0.615575	−	0.788078i	$-0.288924\pi$
$7$	−0.456400	−	0.456400i	−0.172503	−	0.172503i	−0.788078	+	0.615575i	$0.788924\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.20360	+	2.03572i	0.734532	+	0.678574i
$10$	−0.670712	+	0.387236i	−0.212098	+	0.122455i
$11$	0.285599	+	1.06587i	0.0861112	+	0.321371i	0.995522	−	0.0945270i	$-0.0301339\pi$
$11$	0.285599	+	1.06587i	0.0861112	+	0.321371i	−0.909411	+	0.415898i	$0.863467\pi$
$12$	1.71242	−	0.260014i	0.494334	−	0.0750597i
$13$	−1.23841	−	3.38620i	−0.343474	−	0.939162i
$13$	−1.23841	−	3.38620i	−0.343474	−	0.939162i
$14$	−0.558973	−	0.322723i	−0.149392	−	0.0862514i
$15$	−1.33315	−	0.148740i	−0.344218	−	0.0384044i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.49547	+	2.59023i	−0.362705	+	0.628223i	−0.988405	−	0.151840i	$-0.951480\pi$
$17$	−1.49547	+	2.59023i	−0.362705	+	0.628223i	0.625700	+	0.780064i	$0.284813\pi$
$18$	2.65539	+	1.39602i	0.625882	+	0.329046i
$19$	−0.360069	−	1.34379i	−0.0826054	−	0.308287i	0.912245	−	0.409646i	$-0.134348\pi$
$19$	−0.360069	−	1.34379i	−0.0826054	−	0.308287i	−0.994850	+	0.101358i	$0.967681\pi$
$20$	−0.547634	+	0.547634i	−0.122455	+	0.122455i
$21$	−0.448174	−	1.02418i	−0.0977995	−	0.223494i
$22$	0.551734	+	0.955631i	0.117630	+	0.203741i
$23$	−5.29497			−1.10408			−0.552039	−	0.833819i	$-0.686150\pi$
$23$	−5.29497			−1.10408			−0.552039	+	0.833819i	$0.686150\pi$
$24$	1.58678	−	0.694362i	0.323899	−	0.141736i
$25$	−3.81068	+	2.20010i	−0.762136	+	0.440019i
$26$	−2.07263	−	2.95029i	−0.406476	−	0.578599i
$27$	2.26981	+	4.67418i	0.436826	+	0.899546i
$28$	−0.623453	−	0.167054i	−0.117822	−	0.0315702i
$29$	0.786294	+	0.453967i	0.146011	+	0.0842996i	0.571226	−	0.820793i	$-0.306468\pi$
$29$	0.786294	+	0.453967i	0.146011	+	0.0842996i	−0.425215	+	0.905093i	$0.639801\pi$
$30$	−1.32622	+	0.201374i	−0.242134	+	0.0367656i
$31$	−1.43905	−	5.37059i	−0.258460	−	0.964587i	−0.966133	−	0.258046i	$-0.916921\pi$
$31$	−1.43905	−	5.37059i	−0.258460	−	0.964587i	0.707672	−	0.706541i	$-0.249745\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.211925	+	1.89948i	−0.0368913	+	0.330657i
$34$	−0.774112	+	2.88903i	−0.132759	+	0.495464i
$35$	0.432909	+	0.249940i	0.0731749	+	0.0422476i
$36$	2.92623	+	0.661189i	0.487705	+	0.110198i
$37$	1.88903	−	7.04995i	0.310554	−	1.15900i	−0.617504	−	0.786568i	$-0.711856\pi$
$37$	1.88903	−	7.04995i	0.310554	−	1.15900i	0.928058	−	0.372436i	$-0.121477\pi$
$38$	−0.695599	−	1.20481i	−0.112841	−	0.195446i
$39$	0.139227	−	6.24345i	0.0222942	−	0.999751i
$40$	−0.387236	+	0.670712i	−0.0612273	+	0.106049i
$41$	0.717671	+	0.717671i	0.112081	+	0.112081i	0.760923	−	0.648842i	$-0.224746\pi$
$41$	0.717671	+	0.717671i	0.112081	+	0.112081i	−0.648842	+	0.760923i	$0.724746\pi$
$42$	−0.697980	−	0.873286i	−0.107701	−	0.134751i
$43$			6.49134i			0.989920i	0.868916	+	0.494960i	$0.164817\pi$
$43$			6.49134i			0.989920i	−0.868916	+	0.494960i	$0.835183\pi$
$44$	0.780270	+	0.780270i	0.117630	+	0.117630i
$45$	−2.05653	−	1.08118i	−0.306569	−	0.161173i
$46$	−5.11455	+	1.37044i	−0.754099	+	0.202060i
$47$	2.99897	+	0.803570i	0.437444	+	0.117213i	0.470818	−	0.882230i	$-0.343959\pi$
$47$	2.99897	+	0.803570i	0.437444	+	0.117213i	−0.0333743	+	0.999443i	$0.510625\pi$
$48$	1.35299	−	1.08139i	0.195288	−	0.156085i
$49$		−	6.58340i		−	0.940486i
$50$	−3.11141	+	3.11141i	−0.440019	+	0.440019i
$51$	−4.04673	+	3.23437i	−0.566655	+	0.452903i
$52$	−2.76560	−	2.31333i	−0.383519	−	0.320801i
$53$			10.8935i			1.49634i	0.663507	+	0.748170i	$0.269067\pi$
$53$			10.8935i			1.49634i	−0.663507	+	0.748170i	$0.730933\pi$
$54$	3.40224	+	3.92744i	0.462986	+	0.534457i
$55$	−0.427302	−	0.740109i	−0.0576174	−	0.0997963i
$56$	−0.645446			−0.0862514
$57$	0.267184	−	2.39477i	0.0353894	−	0.317195i
$58$	0.876997	+	0.234991i	0.115155	+	0.0308558i
$59$	−9.75565	−	2.61402i	−1.27008	−	0.340316i	−0.440017	−	0.897989i	$-0.645028\pi$
$59$	−9.75565	−	2.61402i	−1.27008	−	0.340316i	−0.830061	+	0.557673i	$0.811694\pi$
$60$	−1.22891	+	0.537764i	−0.158652	+	0.0694250i
$61$	10.8544			1.38977			0.694884	−	0.719122i	$-0.255456\pi$
$61$	10.8544			1.38977			0.694884	+	0.719122i	$0.255456\pi$
$62$	−2.78002	−	4.81514i	−0.353063	−	0.611524i
$63$	−0.0766175	−	1.93482i	−0.00965290	−	0.243765i
$64$		−	1.00000i		−	0.125000i
$65$	1.60519	+	2.28492i	0.199100	+	0.283409i
$66$	0.286917	+	1.88960i	0.0353171	+	0.232594i
$67$	0.762137	−	0.762137i	0.0931098	−	0.0931098i	−0.659018	−	0.752127i	$-0.729028\pi$
$67$	0.762137	−	0.762137i	0.0931098	−	0.0931098i	0.752127	+	0.659018i	$0.229028\pi$
$68$			2.99094i			0.362705i
$69$	−8.54083	−	3.34130i	−1.02820	−	0.402245i
$70$	0.482847	+	0.129378i	0.0577112	+	0.0154637i
$71$	−1.68422	+	0.451285i	−0.199880	+	0.0535576i	−0.357370	−	0.933963i	$-0.616326\pi$
$71$	−1.68422	+	0.451285i	−0.199880	+	0.0535576i	0.157490	+	0.987521i	$0.449660\pi$
$72$	2.99765	−	0.118705i	0.353277	−	0.0139895i
$73$	−2.70493	−	2.70493i	−0.316588	−	0.316588i	0.530867	−	0.847455i	$-0.321866\pi$
$73$	−2.70493	−	2.70493i	−0.316588	−	0.316588i	−0.847455	+	0.530867i	$0.821866\pi$
$74$		−	7.29864i		−	0.848450i
$75$	−7.53499	+	1.14411i	−0.870066	+	0.132111i
$76$	−0.983725	−	0.983725i	−0.112841	−	0.112841i
$77$	0.356115	−	0.616809i	0.0405830	−	0.0702919i
$78$	−1.48144	−	6.06674i	−0.167740	−	0.686923i
$79$	3.01910	+	5.22924i	0.339675	+	0.588335i	0.984372	−	0.176104i	$-0.0563494\pi$
$79$	3.01910	+	5.22924i	0.339675	+	0.588335i	−0.644696	+	0.764439i	$0.723016\pi$
$80$	−0.200448	+	0.748082i	−0.0224108	+	0.0836381i
$81$	0.711670	+	8.97182i	0.0790745	+	0.996869i
$82$	0.878964	+	0.507470i	0.0970653	+	0.0560407i
$83$	−2.95813	+	11.0399i	−0.324697	+	1.21179i	0.589919	+	0.807462i	$0.299160\pi$
$83$	−2.95813	+	11.0399i	−0.324697	+	1.21179i	−0.914616	+	0.404323i	$0.867507\pi$
$84$	−0.900220	−	0.662879i	−0.0982220	−	0.0723260i
$85$	0.599528	−	2.23747i	0.0650279	−	0.242688i
$86$	1.68008	+	6.27015i	0.181168	+	0.676128i
$87$	0.981831	+	1.22843i	0.105263	+	0.131702i
$88$	0.955631	+	0.551734i	0.101871	+	0.0588150i
$89$	12.0109	+	3.21832i	1.27316	+	0.341141i	0.831239	−	0.555915i	$-0.187632\pi$
$89$	12.0109	+	3.21832i	1.27316	+	0.341141i	0.441916	+	0.897056i	$0.354299\pi$
$90$	−2.26628	−	0.512072i	−0.238887	−	0.0539771i
$91$	−0.980247	+	2.11067i	−0.102758	+	0.221258i
$92$	−4.58558	+	2.64748i	−0.478079	+	0.276019i
$93$	1.06782	−	9.57090i	0.110728	−	0.992456i
$94$	3.10476			0.320231
$95$	0.538722	+	0.933093i	0.0552717	+	0.0957333i
$96$	1.02701	−	1.39472i	0.104819	−	0.142348i
$97$	9.31815	−	9.31815i	0.946114	−	0.946114i	−0.0525063	−	0.998621i	$-0.516721\pi$
$97$	9.31815	−	9.31815i	0.946114	−	0.946114i	0.998621	+	0.0525063i	$0.0167210\pi$
$98$	−1.70391	−	6.35908i	−0.172121	−	0.642364i
$99$	−1.54047	+	2.93014i	−0.154823	+	0.294490i
$100$	−2.20010	+	3.81068i	−0.220010	+	0.381068i
$101$	5.86656	−	10.1612i	0.583745	−	1.01108i	−0.411286	−	0.911506i	$-0.634920\pi$
$101$	5.86656	−	10.1612i	0.583745	−	1.01108i	0.995031	−	0.0995694i	$-0.0317465\pi$
$102$	−3.07172	+	4.17154i	−0.304146	+	0.413044i
$103$	4.05306	+	2.34003i	0.399360	+	0.230570i	0.686208	−	0.727406i	$-0.259274\pi$
$103$	4.05306	+	2.34003i	0.399360	+	0.230570i	−0.286848	+	0.957976i	$0.592607\pi$
$104$	−3.27009	−	1.51871i	−0.320659	−	0.148922i
$105$	0.540565	+	0.676335i	0.0527538	+	0.0660035i
$106$	2.81945	+	10.5223i	0.273849	+	1.02202i
$107$	−2.78643	+	1.60874i	−0.269374	+	0.155523i	−0.628603	−	0.777726i	$-0.716373\pi$
$107$	−2.78643	+	1.60874i	−0.269374	+	0.155523i	0.359229	+	0.933249i	$0.383040\pi$
$108$	4.30281	+	2.91305i	0.414038	+	0.280308i
$109$	−3.63346	+	3.63346i	−0.348023	+	0.348023i	−0.859373	−	0.511350i	$-0.829146\pi$
$109$	−3.63346	+	3.63346i	−0.348023	+	0.348023i	0.511350	+	0.859373i	$0.329146\pi$
$110$	−0.604297	−	0.604297i	−0.0576174	−	0.0576174i
$111$	7.49576	−	10.1796i	0.711466	−	0.966204i
$112$	−0.623453	+	0.167054i	−0.0589108	+	0.0157851i
$113$	9.36902	−	5.40921i	0.881363	−	0.508855i	0.0102556	−	0.999947i	$-0.496735\pi$
$113$	9.36902	−	5.40921i	0.881363	−	0.508855i	0.871108	+	0.491092i	$0.163402\pi$
$114$	−0.361731	−	2.38232i	−0.0338792	−	0.223125i
$115$	3.96107	−	1.06137i	0.369372	−	0.0989729i
$116$	0.907934			0.0842996
$117$	4.16439	−	9.98288i	0.384998	−	0.922917i
$118$	−10.0998			−0.929761
$119$	1.86471	−	0.499648i	0.170938	−	0.0458027i
$120$	−1.04786	+	0.837506i	−0.0956557	+	0.0764535i
$121$	8.47177	−	4.89118i	0.770161	−	0.444653i
$122$	10.4846	−	2.80934i	0.949229	−	0.254345i
$123$	0.704736	+	1.61048i	0.0635439	+	0.145212i
$124$	−3.93155	−	3.93155i	−0.353063	−	0.353063i
$125$	5.14787	−	5.14787i	0.460439	−	0.460439i
$126$	−0.574776	−	1.84907i	−0.0512051	−	0.164728i
$127$	−5.39157	+	3.11283i	−0.478425	+	0.276219i	−0.719760	−	0.694223i	$-0.755748\pi$
$127$	−5.39157	+	3.11283i	−0.478425	+	0.276219i	0.241335	+	0.970442i	$0.422415\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−4.09625	+	10.4706i	−0.360654	+	0.921884i
$130$	2.14188	+	1.79160i	0.187855	+	0.157134i
$131$	4.68122	+	2.70270i	0.409000	+	0.236136i	0.690360	−	0.723466i	$-0.257452\pi$
$131$	4.68122	+	2.70270i	0.409000	+	0.236136i	−0.281360	+	0.959602i	$0.590785\pi$
$132$	0.766207	+	1.75096i	0.0666897	+	0.152401i
$133$	−0.448972	+	0.777642i	−0.0389308	+	0.0674301i
$134$	0.538912	−	0.933423i	0.0465549	−	0.0806355i
$135$	−2.63494	−	3.04169i	−0.226779	−	0.261787i
$136$	0.774112	+	2.88903i	0.0663796	+	0.247732i
$137$	5.01444	−	5.01444i	0.428413	−	0.428413i	−0.459675	−	0.888087i	$-0.652034\pi$
$137$	5.01444	−	5.01444i	0.428413	−	0.428413i	0.888087	+	0.459675i	$0.152034\pi$
$138$	−9.11460	−	1.01692i	−0.775886	−	0.0865656i
$139$	10.3141	+	17.8645i	0.874828	+	1.51525i	0.856945	+	0.515407i	$0.172359\pi$
$139$	10.3141	+	17.8645i	0.874828	+	1.51525i	0.0178829	+	0.999840i	$0.494307\pi$
$140$	0.499880			0.0422476
$141$	4.33028	+	3.18861i	0.364675	+	0.268529i
$142$	−1.51003	+	0.871815i	−0.126719	+	0.0731611i
$143$	3.25555	−	2.28708i	0.272243	−	0.191255i
$144$	2.86479	−	0.890509i	0.238732	−	0.0742091i
$145$	−0.679209	−	0.181994i	−0.0564053	−	0.0151137i
$146$	−3.31285	−	1.91267i	−0.274173	−	0.158294i
$147$	4.15434	−	10.6191i	0.342644	−	0.875847i
$148$	−1.88903	−	7.04995i	−0.155277	−	0.579502i
$149$	4.22688	−	15.7749i	0.346280	−	1.29233i	−0.544831	−	0.838546i	$-0.683406\pi$
$149$	4.22688	−	15.7749i	0.346280	−	1.29233i	0.891110	−	0.453787i	$-0.149927\pi$
$150$	−6.98213	+	3.05533i	−0.570088	+	0.249467i
$151$	−4.19291	+	15.6482i	−0.341214	+	1.27343i	0.555759	+	0.831344i	$0.312428\pi$
$151$	−4.19291	+	15.6482i	−0.341214	+	1.27343i	−0.896973	+	0.442086i	$0.854239\pi$
$152$	−1.20481	−	0.695599i	−0.0977232	−	0.0564205i
$153$	−8.56840	+	2.66346i	−0.692714	+	0.215328i
$154$	0.184339	−	0.687961i	0.0148544	−	0.0554375i
$155$	2.15305	+	3.72919i	0.172937	+	0.299536i
$156$	−3.00115	−	5.47660i	−0.240284	−	0.438479i
$157$	7.67271	−	13.2895i	0.612349	−	1.06062i	−0.378494	−	0.925604i	$-0.623558\pi$
$157$	7.67271	−	13.2895i	0.612349	−	1.06062i	0.990843	−	0.135016i	$-0.0431087\pi$
$158$	4.26965	+	4.26965i	0.339675	+	0.339675i
$159$	−6.87416	+	17.5713i	−0.545157	+	1.39350i
$160$			0.774471i			0.0612273i
$161$	2.41662	+	2.41662i	0.190456	+	0.190456i
$162$	3.00950	+	8.48192i	0.236449	+	0.666402i
$163$	−19.4221	+	5.20413i	−1.52125	+	0.407619i	−0.920155	−	0.391555i	$-0.871937\pi$
$163$	−19.4221	+	5.20413i	−1.52125	+	0.407619i	−0.601100	+	0.799174i	$0.705271\pi$
$164$	0.980356	+	0.262686i	0.0765530	+	0.0205123i
$165$	−0.222209	−	1.46344i	−0.0172990	−	0.113929i
$166$			11.4293i			0.887089i
$167$	6.90323	−	6.90323i	0.534188	−	0.534188i	−0.387628	−	0.921816i	$-0.626705\pi$
$167$	6.90323	−	6.90323i	0.534188	−	0.534188i	0.921816	+	0.387628i	$0.126705\pi$
$168$	−1.04111	−	0.407298i	−0.0803234	−	0.0314237i
$169$	−9.93266	+	8.38703i	−0.764051	+	0.645156i
$170$		−	2.31640i		−	0.177660i
$171$	1.94215	−	3.69418i	0.148520	−	0.282501i
$172$	3.24567	+	5.62166i	0.247480	+	0.428648i
$173$	−7.16824			−0.544991			−0.272495	−	0.962157i	$-0.587849\pi$
$173$	−7.16824			−0.544991			−0.272495	+	0.962157i	$0.587849\pi$
$174$	1.26632	+	0.932456i	0.0959993	+	0.0706893i
$175$	2.74332	+	0.735069i	0.207375	+	0.0555660i
$176$	1.06587	+	0.285599i	0.0803428	+	0.0215278i
$177$	−14.0864	−	10.3726i	−1.05880	−	0.779650i
$178$	12.4346			0.932014
$179$	−5.59035	−	9.68278i	−0.417843	−	0.723725i	0.577879	−	0.816122i	$-0.303880\pi$
$179$	−5.59035	−	9.68278i	−0.417843	−	0.723725i	−0.995722	+	0.0923973i	$0.970547\pi$
$180$	−2.32159	+	0.0919334i	−0.173041	+	0.00685231i
$181$			8.76194i			0.651270i	0.945496	+	0.325635i	$0.105578\pi$
$181$			8.76194i			0.651270i	−0.945496	+	0.325635i	$0.894422\pi$
$182$	−0.400564	+	2.29246i	−0.0296918	+	0.169928i
$183$	17.5083	+	6.84950i	1.29425	+	0.506330i
$184$	−3.74411	+	3.74411i	−0.276019	+	0.276019i
$185$			5.65259i			0.415587i
$186$	−1.44569	−	9.52115i	−0.106003	−	0.698125i
$187$	−3.18795	−	0.854208i	−0.233126	−	0.0624659i
$188$	2.99897	−	0.803570i	0.218722	−	0.0586064i
$189$	1.09735	−	3.16923i	0.0798206	−	0.230528i
$190$	0.761867	+	0.761867i	0.0552717	+	0.0552717i
$191$		−	24.3114i		−	1.75911i	−0.475798	−	0.879555i	$-0.657841\pi$
$191$		−	24.3114i		−	1.75911i	0.475798	−	0.879555i	$-0.342159\pi$
$192$	0.631032	−	1.61301i	0.0455408	−	0.116409i
$193$	6.98571	+	6.98571i	0.502842	+	0.502842i	0.912320	−	0.409478i	$-0.134289\pi$
$193$	6.98571	+	6.98571i	0.502842	+	0.502842i	−0.409478	+	0.912320i	$0.634289\pi$
$194$	6.58892	−	11.4124i	0.473057	−	0.819359i
$195$	1.14733	+	4.69852i	0.0821622	+	0.336468i
$196$	−3.29170	−	5.70139i	−0.235121	−	0.407242i
$197$	−7.01655	+	26.1861i	−0.499908	+	1.86568i	0.000684309		1.00000i	$0.499782\pi$
$197$	−7.01655	+	26.1861i	−0.499908	+	1.86568i	−0.500593	+	0.865683i	$0.666884\pi$
$198$	−0.729601	+	3.22900i	−0.0518505	+	0.229475i
$199$	5.45399	+	3.14886i	0.386623	+	0.223217i	0.680696	−	0.732566i	$-0.261677\pi$
$199$	5.45399	+	3.14886i	0.386623	+	0.223217i	−0.294073	+	0.955783i	$0.595011\pi$
$200$	−1.13885	+	4.25026i	−0.0805291	+	0.300539i
$201$	1.71027	−	0.748400i	0.120633	−	0.0527881i
$202$	3.03676	−	11.3333i	0.213665	−	0.797410i
$203$	−0.151674	−	0.566055i	−0.0106454	−	0.0397292i
$204$	−1.88738	+	4.82441i	−0.132143	+	0.337777i
$205$	−0.680732	−	0.393021i	−0.0475444	−	0.0274498i
$206$	4.52060	+	1.21129i	0.314965	+	0.0843946i
$207$	−11.6680	−	10.7791i	−0.810980	−	0.749198i
$208$	−3.55174	−	0.620600i	−0.246269	−	0.0430309i
$209$	1.32947	−	0.767571i	0.0919615	−	0.0530940i
$210$	0.697194	+	0.513381i	0.0481110	+	0.0354266i
$211$	−21.9038			−1.50792			−0.753960	−	0.656921i	$-0.771859\pi$
$211$	−21.9038			−1.50792			−0.753960	+	0.656921i	$0.771859\pi$
$212$	5.44676	+	9.43406i	0.374085	+	0.647934i
$213$	−3.00143	−	0.334870i	−0.205655	−	0.0229449i
$214$	−2.27511	+	2.27511i	−0.155523	+	0.155523i
$215$	−1.30118	−	4.85605i	−0.0887394	−	0.331180i
$216$	4.91014	+	1.70014i	0.334093	+	0.115680i
$217$	−1.79436	+	3.10792i	−0.121809	+	0.210979i
$218$	−2.56925	+	4.45007i	−0.174011	+	0.301396i
$219$	−2.65618	−	6.06997i	−0.179488	−	0.410171i
$220$	−0.740109	−	0.427302i	−0.0498982	−	0.0288087i
$221$	10.6230	+	1.85618i	0.714583	+	0.124860i
$222$	4.60568	−	11.7728i	0.309113	−	0.790137i
$223$	−1.22894	−	4.58647i	−0.0822959	−	0.307132i	0.912493	−	0.409093i	$-0.134155\pi$
$223$	−1.22894	−	4.58647i	−0.0822959	−	0.307132i	−0.994788	+	0.101961i	$0.967488\pi$
$224$	−0.558973	+	0.322723i	−0.0373480	+	0.0215629i
$225$	−12.8760	−	2.90936i	−0.858399	−	0.193957i
$226$	7.64977	−	7.64977i	0.508855	−	0.508855i
$227$	−6.54115	−	6.54115i	−0.434151	−	0.434151i	0.455887	−	0.890038i	$-0.349322\pi$
$227$	−6.54115	−	6.54115i	−0.434151	−	0.434151i	−0.890038	+	0.455887i	$0.849322\pi$
$228$	−0.965995	−	2.20752i	−0.0639746	−	0.146197i
$229$	−18.4626	+	4.94704i	−1.22004	+	0.326910i	−0.810695	−	0.585469i	$-0.800911\pi$
$229$	−18.4626	+	4.94704i	−1.22004	+	0.326910i	−0.409348	+	0.912378i	$0.634244\pi$
$230$	3.55140	−	2.05040i	0.234172	−	0.135199i
$231$	0.963643	−	0.770198i	0.0634030	−	0.0506753i
$232$	0.876997	−	0.234991i	0.0575777	−	0.0154279i
$233$	−23.5311			−1.54157			−0.770786	−	0.637094i	$-0.780136\pi$
$233$	−23.5311			−1.54157			−0.770786	+	0.637094i	$0.780136\pi$
$234$	1.43873	−	10.7205i	0.0940530	−	0.700824i
$235$	−2.40455			−0.156855
$236$	−9.75565	+	2.61402i	−0.635039	+	0.170158i
$237$	1.57002	+	10.3400i	0.101984	+	0.671652i
$238$	1.67185	−	0.965246i	0.108370	−	0.0625676i
$239$	−22.8065	+	6.11098i	−1.47523	+	0.395287i	−0.904721	−	0.426005i	$-0.859921\pi$
$239$	−22.8065	+	6.11098i	−1.47523	+	0.395287i	−0.570509	+	0.821291i	$0.693254\pi$
$240$	−0.795388	+	1.08017i	−0.0513421	+	0.0697249i
$241$	−7.79438	−	7.79438i	−0.502080	−	0.502080i	0.410004	−	0.912084i	$-0.365527\pi$
$241$	−7.79438	−	7.79438i	−0.502080	−	0.502080i	−0.912084	+	0.410004i	$0.865527\pi$
$242$	6.91717	−	6.91717i	0.444653	−	0.444653i
$243$	−4.51358	+	14.9207i	−0.289546	+	0.957164i
$244$	9.40022	−	5.42722i	0.601787	−	0.347442i
$245$	1.31963	+	4.92492i	0.0843080	+	0.314642i
$246$	1.09755	+	1.37321i	0.0699770	+	0.0875525i
$247$	−4.10444	+	2.88344i	−0.261159	+	0.183469i
$248$	−4.81514	−	2.78002i	−0.305762	−	0.176532i
$249$	−11.7380	+	15.9408i	−0.743867	+	1.01021i
$250$	3.64009	−	6.30482i	0.230220	−	0.398752i
$251$	4.48555	−	7.76920i	0.283125	−	0.490387i	−0.689027	−	0.724735i	$-0.741962\pi$
$251$	4.48555	−	7.76920i	0.283125	−	0.490387i	0.972153	+	0.234348i	$0.0752954\pi$
$252$	−1.03376	−	1.63730i	−0.0651210	−	0.103140i
$253$	−1.51224	−	5.64374i	−0.0950734	−	0.354819i
$254$	−4.40220	+	4.40220i	−0.276219	+	0.276219i
$255$	2.37896	−	3.23074i	0.148976	−	0.202317i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.0952			0.879235			0.439617	−	0.898185i	$-0.355114\pi$
$257$	14.0952			0.879235			0.439617	+	0.898185i	$0.355114\pi$
$258$	−1.24668	+	11.1740i	−0.0776150	+	0.695663i
$259$	−4.07974	+	2.35544i	−0.253503	+	0.146360i
$260$	2.53259	+	1.17620i	0.157065	+	0.0729448i
$261$	0.808524	+	2.60104i	0.0500464	+	0.161000i
$262$	5.22122	+	1.39902i	0.322568	+	0.0864319i
$263$	−16.6786	−	9.62939i	−1.02845	−	0.593774i	−0.111907	−	0.993719i	$-0.535696\pi$
$263$	−16.6786	−	9.62939i	−1.02845	−	0.593774i	−0.916539	+	0.399945i	$0.869029\pi$
$264$	1.19328	+	1.49299i	0.0734413	+	0.0918870i
$265$	−2.18358	−	8.14924i	−0.134136	−	0.500604i
$266$	−0.232405	+	0.867347i	−0.0142497	+	0.0531805i
$267$	17.3429	+	12.7705i	1.06137	+	0.781539i
$268$	0.278961	−	1.04110i	0.0170403	−	0.0635952i
$269$	−20.4816	−	11.8251i	−1.24879	−	0.720987i	−0.277918	−	0.960605i	$-0.589644\pi$
$269$	−20.4816	−	11.8251i	−1.24879	−	0.720987i	−0.970867	+	0.239618i	$0.922978\pi$
$270$	−3.33240	−	2.25607i	−0.202803	−	0.137300i
$271$	6.89336	−	25.7264i	0.418742	−	1.56276i	−0.358480	−	0.933537i	$-0.616705\pi$
$271$	6.89336	−	25.7264i	0.418742	−	1.56276i	0.777221	−	0.629227i	$-0.216629\pi$
$272$	1.49547	+	2.59023i	0.0906762	+	0.157056i
$273$	−2.91305	+	2.78596i	−0.176306	+	0.168614i
$274$	3.54575	−	6.14141i	0.214206	−	0.371016i
$275$	−3.43334	−	3.43334i	−0.207038	−	0.207038i
$276$	−9.06723	+	1.37677i	−0.545783	+	0.0828717i
$277$			10.9761i			0.659493i	0.944070	+	0.329746i	$0.106963\pi$
$277$			10.9761i			0.659493i	−0.944070	+	0.329746i	$0.893037\pi$
$278$	14.5863	+	14.5863i	0.874828	+	0.874828i
$279$	7.76196	−	14.7641i	0.464696	−	0.883905i
$280$	0.482847	−	0.129378i	0.0288556	−	0.00773184i
$281$	30.2719	+	8.11132i	1.80587	+	0.483881i	0.994869	−	0.101167i	$-0.0322576\pi$
$281$	30.2719	+	8.11132i	1.80587	+	0.483881i	0.810999	+	0.585048i	$0.198924\pi$
$282$	5.00800	+	1.95920i	0.298222	+	0.116669i
$283$			24.7434i			1.47084i	0.677611	+	0.735420i	$0.263015\pi$
$283$			24.7434i			1.47084i	−0.677611	+	0.735420i	$0.736985\pi$
$284$	−1.23293	+	1.23293i	−0.0731611	+	0.0731611i
$285$	0.280151	+	1.84504i	0.0165947	+	0.109291i
$286$	2.55268	−	3.05175i	0.150943	−	0.180454i
$287$		−	0.655089i		−	0.0386687i
$288$	2.53669	−	1.60163i	0.149476	−	0.0943768i
$289$	4.02714	+	6.97521i	0.236890	+	0.410306i
$290$	−0.703169			−0.0412915
$291$	20.9103	−	9.15020i	1.22578	−	0.536394i
$292$	−3.69500	−	0.990073i	−0.216234	−	0.0579396i
$293$	−21.5007	−	5.76109i	−1.25608	−	0.336566i	−0.431399	−	0.902161i	$-0.641980\pi$
$293$	−21.5007	−	5.76109i	−1.25608	−	0.336566i	−0.824683	+	0.565595i	$0.808647\pi$
$294$	1.26436	−	11.3325i	0.0737391	−	0.660923i
$295$	7.82200			0.455415
$296$	−3.64932	−	6.32081i	−0.212112	−	0.367390i
$297$	−4.33380	+	3.75426i	−0.251473	+	0.217844i
$298$		−	16.3314i		−	0.946053i
$299$	6.55736	+	17.9298i	0.379222	+	1.03691i
$300$	−5.95344	+	4.75833i	−0.343722	+	0.274722i
$301$	2.96264	−	2.96264i	0.170764	−	0.170764i
$302$			16.2002i			0.932215i
$303$	15.8749	−	12.6881i	0.911987	−	0.728912i
$304$	−1.34379	−	0.360069i	−0.0770719	−	0.0206513i
$305$	−8.12001	+	2.17575i	−0.464950	+	0.124583i
$306$	−7.58709	+	4.79037i	−0.433725	+	0.273847i
$307$	4.37539	+	4.37539i	0.249716	+	0.249716i	0.820854	−	0.571138i	$-0.193498\pi$
$307$	4.37539	+	4.37539i	0.249716	+	0.249716i	−0.571138	+	0.820854i	$0.693498\pi$
$308$		−	0.712230i		−	0.0405830i
$309$	5.06098	+	6.33211i	0.287909	+	0.360221i
$310$	3.04487	+	3.04487i	0.172937	+	0.172937i
$311$	−6.01736	+	10.4224i	−0.341213	+	0.590999i	−0.984658	−	0.174494i	$-0.944171\pi$
$311$	−6.01736	+	10.4224i	−0.341213	+	0.590999i	0.643445	+	0.765492i	$0.277505\pi$
$312$	−4.31633	−	4.51323i	−0.244364	−	0.255511i
$313$	−12.1822	−	21.1002i	−0.688578	−	1.19265i	−0.972298	−	0.233745i	$-0.924902\pi$
$313$	−12.1822	−	21.1002i	−0.688578	−	1.19265i	0.283719	−	0.958907i	$-0.408432\pi$
$314$	3.97169	−	14.8225i	0.224135	−	0.836485i
$315$	0.445148	+	1.43205i	0.0250812	+	0.0806868i
$316$	5.22924	+	3.01910i	0.294168	+	0.169838i
$317$	−4.54488	+	16.9617i	−0.255266	+	0.952665i	0.712677	+	0.701493i	$0.247483\pi$
$317$	−4.54488	+	16.9617i	−0.255266	+	0.952665i	−0.967942	+	0.251172i	$0.919184\pi$
$318$	−2.09213	+	18.7518i	−0.117321	+	1.05155i
$319$	−0.259305	+	0.967738i	−0.0145183	+	0.0541829i
$320$	0.200448	+	0.748082i	0.0112054	+	0.0418191i
$321$	−5.50970	+	0.836593i	−0.307521	+	0.0466941i
$322$	2.95974	+	1.70881i	0.164940	+	0.0952282i
$323$	4.01921	+	1.07694i	0.223635	+	0.0599227i
$324$	5.10223	+	7.41399i	0.283457	+	0.411888i
$325$	12.1692	+	10.1791i	0.675024	+	0.564634i
$326$	−17.4134	+	10.0536i	−0.964437	+	0.556818i
$327$	−8.15364	+	3.56798i	−0.450897	+	0.197309i
$328$	1.01494			0.0560407
$329$	−1.00198	−	1.73548i	−0.0552408	−	0.0956799i
$330$	−0.593405	−	1.35607i	−0.0326659	−	0.0746490i
$331$	22.0364	−	22.0364i	1.21123	−	1.21123i	0.240607	−	0.970623i	$-0.422653\pi$
$331$	22.0364	−	22.0364i	1.21123	−	1.21123i	0.970623	−	0.240607i	$-0.0773465\pi$
$332$	2.95813	+	11.0399i	0.162348	+	0.605893i
$333$	18.5144	−	11.6897i	1.01458	−	0.640592i
$334$	4.88132	−	8.45470i	0.267094	−	0.462620i
$335$	−0.417372	+	0.722910i	−0.0228035	+	0.0394968i
$336$	−1.11105	−	0.123960i	−0.0606129	−	0.00676257i
$337$	2.67699	+	1.54556i	0.145825	+	0.0841921i	0.571137	−	0.820855i	$-0.306502\pi$
$337$	2.67699	+	1.54556i	0.145825	+	0.0841921i	−0.425312	+	0.905047i	$0.639836\pi$
$338$	−7.42349	+	10.6720i	−0.403785	+	0.580481i
$339$	18.5257	−	2.81294i	1.00618	−	0.152778i
$340$	−0.599528	−	2.23747i	−0.0325140	−	0.121344i
$341$	5.31336	−	3.06767i	0.287734	−	0.166123i
$342$	0.919845	−	4.07097i	0.0497395	−	0.220133i
$343$	−6.19946	+	6.19946i	−0.334739	+	0.334739i
$344$	4.59007	+	4.59007i	0.247480	+	0.247480i
$345$	7.05900	+	0.787572i	0.380044	+	0.0424014i
$346$	−6.92398	+	1.85528i	−0.372236	+	0.0997403i
$347$	−16.8787	+	9.74492i	−0.906096	+	0.523135i	−0.879173	−	0.476503i	$-0.841904\pi$
$347$	−16.8787	+	9.74492i	−0.906096	+	0.523135i	−0.0269231	+	0.999638i	$0.508571\pi$
$348$	1.46451	+	0.572936i	0.0785058	+	0.0307126i
$349$	−21.1940	+	5.67891i	−1.13449	+	0.303985i	−0.776733	−	0.629830i	$-0.783125\pi$
$349$	−21.1940	+	5.67891i	−1.13449	+	0.303985i	−0.357755	+	0.933815i	$0.616458\pi$
$350$	2.84009			0.151809
$351$	13.0167	−	13.4746i	0.694781	−	0.719221i
$352$	1.10347			0.0588150
$353$	9.47129	−	2.53782i	0.504106	−	0.135075i	0.00220088	−	0.999998i	$-0.499299\pi$
$353$	9.47129	−	2.53782i	0.504106	−	0.135075i	0.501905	+	0.864923i	$0.332633\pi$
$354$	−16.2911	−	6.37330i	−0.865860	−	0.338737i
$355$	1.16947	−	0.675196i	0.0620692	−	0.0358357i
$356$	12.0109	−	3.21832i	0.636578	−	0.170570i
$357$	3.32309	+	0.370757i	0.175877	+	0.0196225i
$358$	−7.90596	−	7.90596i	−0.417843	−	0.417843i
$359$	21.8739	−	21.8739i	1.15446	−	1.15446i	0.168810	−	0.985649i	$-0.446008\pi$
$359$	21.8739	−	21.8739i	1.15446	−	1.15446i	0.985649	−	0.168810i	$-0.0539923\pi$
$360$	−2.21869	+	0.689674i	−0.116935	+	0.0363490i
$361$	14.7783	−	8.53228i	0.777808	−	0.449068i
$362$	2.26776	+	8.46338i	0.119191	+	0.444826i
$363$	16.7515	−	2.54355i	0.879228	−	0.133502i
$364$	0.206416	+	2.31802i	0.0108192	+	0.121497i
$365$	2.56571	+	1.48131i	0.134295	+	0.0775354i
$366$	18.6845	+	2.08463i	0.976655	+	0.108965i
$367$	10.9588	−	18.9812i	0.572045	−	0.990811i	−0.424311	−	0.905516i	$-0.639484\pi$
$367$	10.9588	−	18.9812i	0.572045	−	0.990811i	0.996356	−	0.0852940i	$-0.0271830\pi$
$368$	−2.64748	+	4.58558i	−0.138010	+	0.239040i
$369$	0.120478	+	3.04243i	0.00627184	+	0.158383i
$370$	1.46300	+	5.45998i	0.0760576	+	0.283851i
$371$	4.97180	−	4.97180i	0.258123	−	0.258123i
$372$	−3.86069	−	8.82255i	−0.200167	−	0.457428i
$373$	−0.731744	−	1.26742i	−0.0378883	−	0.0656244i	0.846459	−	0.532453i	$-0.178730\pi$
$373$	−0.731744	−	1.26742i	−0.0378883	−	0.0656244i	−0.884348	+	0.466829i	$0.845396\pi$
$374$	−3.30041			−0.170660
$375$	11.5520	−	5.05508i	0.596544	−	0.261043i
$376$	2.68880	−	1.55238i	0.138664	−	0.0800578i
$377$	0.563464	−	3.22475i	0.0290199	−	0.166083i
$378$	0.239702	−	3.34526i	0.0123289	−	0.172062i
$379$	16.3714	+	4.38670i	0.840942	+	0.225330i	0.653481	−	0.756943i	$-0.273308\pi$
$379$	16.3714	+	4.38670i	0.840942	+	0.225330i	0.187460	+	0.982272i	$0.439974\pi$
$380$	0.933093	+	0.538722i	0.0478667	+	0.0276358i
$381$	−10.6609	+	1.61876i	−0.546177	+	0.0829315i
$382$	−6.29225	−	23.4830i	−0.321939	−	1.20149i
$383$	−2.34343	+	8.74581i	−0.119744	+	0.446890i	−0.999598	−	0.0283538i	$-0.990974\pi$
$383$	−2.34343	+	8.74581i	−0.119744	+	0.446890i	0.879854	+	0.475244i	$0.157640\pi$
$384$	0.192053	−	1.72137i	0.00980067	−	0.0878433i
$385$	−0.142765	+	0.532806i	−0.00727598	+	0.0271543i
$386$	8.55571	+	4.93964i	0.435474	+	0.251421i
$387$	−13.2146	+	14.3043i	−0.671734	+	0.727128i
$388$	3.41068	−	12.7288i	0.173151	−	0.646208i
$389$	10.8255	+	18.7504i	0.548876	+	0.950681i	0.998352	+	0.0573883i	$0.0182773\pi$
$389$	10.8255	+	18.7504i	0.548876	+	0.950681i	−0.449476	+	0.893292i	$0.648389\pi$
$390$	2.32430	+	4.24147i	0.117696	+	0.214775i
$391$	7.91847	−	13.7152i	0.400454	−	0.693607i
$392$	−4.65517	−	4.65517i	−0.235121	−	0.235121i
$393$	5.84536	+	7.31349i	0.294859	+	0.368917i
$394$			27.1099i			1.36577i
$395$	−3.30673	−	3.30673i	−0.166379	−	0.166379i
$396$	0.130987	+	3.30781i	0.00658234	+	0.166224i
$397$	11.6065	−	3.10995i	0.582514	−	0.156084i	0.0444843	−	0.999010i	$-0.485836\pi$
$397$	11.6065	−	3.10995i	0.582514	−	0.156084i	0.538030	+	0.842926i	$0.319169\pi$
$398$	6.08314	+	1.62997i	0.304920	+	0.0817031i
$399$	−1.21491	+	0.971028i	−0.0608217	+	0.0486122i
$400$			4.40019i			0.220010i
$401$	−11.2322	+	11.2322i	−0.560911	+	0.560911i	−0.929566	−	0.368655i	$-0.879818\pi$
$401$	−11.2322	+	11.2322i	−0.560911	+	0.560911i	0.368655	+	0.929566i	$0.379818\pi$
$402$	1.45829	−	1.16555i	0.0727329	−	0.0581323i
$403$	−16.4038	+	11.5239i	−0.817129	+	0.574047i
$404$		−	11.7331i		−	0.583745i
$405$	−2.33077	−	6.56900i	−0.115817	−	0.326416i
$406$	−0.293011	−	0.507511i	−0.0145419	−	0.0251873i
$407$	8.05382			0.399213
$408$	−0.574419	+	5.14852i	−0.0284380	+	0.254890i
$409$	17.7677	+	4.76083i	0.878554	+	0.235408i	0.669783	−	0.742557i	$-0.266387\pi$
$409$	17.7677	+	4.76083i	0.878554	+	0.235408i	0.208771	+	0.977965i	$0.433054\pi$
$410$	−0.759258	−	0.203443i	−0.0374971	−	0.0100473i
$411$	11.2526	−	4.92406i	0.555050	−	0.242886i
$412$	4.68007			0.230570
$413$	3.25944	+	5.64551i	0.160386	+	0.277797i
$414$	−14.0602	−	7.39190i	−0.691022	−	0.363292i
$415$		−	8.85170i		−	0.434513i
$416$	−3.59134	+	0.319804i	−0.176080	+	0.0156797i
$417$	5.36361	+	35.3241i	0.262657	+	1.72983i
$418$	1.08551	−	1.08551i	0.0530940	−	0.0530940i
$419$		−	29.1614i		−	1.42463i	−0.701861	−	0.712314i	$-0.747647\pi$
$419$		−	29.1614i		−	1.42463i	0.701861	−	0.712314i	$-0.252353\pi$
$420$	0.806311	+	0.315440i	0.0393439	+	0.0153919i
$421$	−0.816008	−	0.218649i	−0.0397698	−	0.0106563i	0.238879	−	0.971049i	$-0.423220\pi$
$421$	−0.816008	−	0.218649i	−0.0397698	−	0.0106563i	−0.278649	+	0.960393i	$0.589887\pi$
$422$	−21.1574	+	5.66912i	−1.02993	+	0.275968i
$423$	4.97266	+	7.87581i	0.241779	+	0.382935i
$424$	7.70288	+	7.70288i	0.374085	+	0.374085i
$425$		−	13.1607i		−	0.638389i
$426$	−2.98583	+	0.453369i	−0.144664	+	0.0219658i
$427$	−4.95396	−	4.95396i	−0.239739	−	0.239739i
$428$	−1.60874	+	2.78643i	−0.0777616	+	0.134687i
$429$	6.69445	−	1.63472i	0.323211	−	0.0789251i
$430$	−2.51368	−	4.35382i	−0.121220	−	0.209960i
$431$	−2.61175	+	9.74717i	−0.125803	+	0.469505i	−0.999867	−	0.0163068i	$-0.994809\pi$
$431$	−2.61175	+	9.74717i	−0.125803	+	0.469505i	0.874064	+	0.485811i	$0.161476\pi$
$432$	5.18286	+	0.371373i	0.249361	+	0.0178677i
$433$	−19.4083	−	11.2054i	−0.932703	−	0.538496i	−0.0450375	−	0.998985i	$-0.514341\pi$
$433$	−19.4083	−	11.2054i	−0.932703	−	0.538496i	−0.887665	+	0.460489i	$0.847674\pi$
$434$	−0.928827	+	3.46643i	−0.0445851	+	0.166394i
$435$	−0.980727	−	0.722160i	−0.0470222	−	0.0346249i
$436$	−1.32994	+	4.96340i	−0.0636926	+	0.237704i
$437$	1.90655	+	7.11535i	0.0912027	+	0.340373i
$438$	−4.13670	−	5.17568i	−0.197659	−	0.247303i
$439$	5.84221	+	3.37300i	0.278834	+	0.160985i	0.632895	−	0.774237i	$-0.281866\pi$
$439$	5.84221	+	3.37300i	0.278834	+	0.160985i	−0.354062	+	0.935222i	$0.615200\pi$
$440$	−0.825485	−	0.221188i	−0.0393534	−	0.0105447i
$441$	13.4020	−	14.5072i	0.638189	−	0.690817i
$442$	10.7415	−	0.956514i	0.510920	−	0.0454968i
$443$	−33.6394	+	19.4217i	−1.59825	+	0.922753i	−0.606431	+	0.795136i	$0.707400\pi$
$443$	−33.6394	+	19.4217i	−1.59825	+	0.922753i	−0.991824	+	0.127617i	$0.959267\pi$
$444$	1.40173	−	12.5637i	0.0665230	−	0.596245i
$445$	−9.63026			−0.456518
$446$	−2.37413	−	4.11211i	−0.112418	−	0.194714i
$447$	16.7725	−	22.7778i	0.793312	−	1.07735i
$448$	−0.456400	+	0.456400i	−0.0215629	+	0.0215629i
$449$	3.83851	+	14.3255i	0.181151	+	0.676063i	0.995422	+	0.0955787i	$0.0304702\pi$
$449$	3.83851	+	14.3255i	0.181151	+	0.676063i	−0.814271	+	0.580485i	$0.802863\pi$
$450$	−13.1902	+	0.522324i	−0.621794	+	0.0246226i
$451$	−0.559977	+	0.969908i	−0.0263683	+	0.0456712i
$452$	5.40921	−	9.36902i	0.254428	−	0.440682i
$453$	−16.6377	+	22.5948i	−0.781707	+	1.06159i
$454$	−8.01124	−	4.62529i	−0.375986	−	0.217076i
$455$	0.310226	−	1.77544i	0.0145436	−	0.0832341i
$456$	−1.50443	−	1.88228i	−0.0704513	−	0.0881460i
$457$	−9.22269	−	34.4195i	−0.431419	−	1.61008i	−0.749493	−	0.662012i	$-0.769703\pi$
$457$	−9.22269	−	34.4195i	−0.431419	−	1.61008i	0.318074	−	0.948066i	$-0.396964\pi$
$458$	−16.5531	+	9.55695i	−0.773477	+	0.446567i
$459$	−15.5016	−	1.11076i	−0.723554	−	0.0518456i
$460$	2.89970	−	2.89970i	0.135199	−	0.135199i
$461$	−8.01748	−	8.01748i	−0.373411	−	0.373411i	0.495307	−	0.868718i	$-0.335056\pi$
$461$	−8.01748	−	8.01748i	−0.373411	−	0.373411i	−0.868718	+	0.495307i	$0.835056\pi$
$462$	0.731465	−	0.993363i	0.0340309	−	0.0462155i
$463$	−37.3633	+	10.0115i	−1.73642	+	0.465273i	−0.981646	−	0.190711i	$-0.938921\pi$
$463$	−37.3633	+	10.0115i	−1.73642	+	0.465273i	−0.754775	+	0.655984i	$0.772254\pi$
$464$	0.786294	−	0.453967i	0.0365028	−	0.0210749i
$465$	1.11965	+	7.37386i	0.0519224	+	0.341955i
$466$	−22.7293	+	6.09029i	−1.05291	+	0.282127i
$467$	1.10308			0.0510444			0.0255222	−	0.999674i	$-0.491875\pi$
$467$	1.10308			0.0510444			0.0255222	+	0.999674i	$0.491875\pi$
$468$	−1.38497	−	10.7276i	−0.0640202	−	0.495884i
$469$	−0.695678			−0.0321234
$470$	−2.32261	+	0.622342i	−0.107134	+	0.0287065i
$471$	20.7623	−	16.5944i	0.956675	−	0.764630i
$472$	−8.74668	+	5.04990i	−0.402598	+	0.232440i
$473$	−6.91891	+	1.85392i	−0.318132	+	0.0852432i
$474$	4.19270	+	9.58128i	0.192577	+	0.440083i
$475$	4.32858	+	4.32858i	0.198609	+	0.198609i
$476$	1.36506	−	1.36506i	0.0625676	−	0.0625676i
$477$	−22.1762	+	24.0049i	−1.01538	+	1.09911i
$478$	−20.4478	+	11.8055i	−0.935258	+	0.539972i
$479$	−9.02947	−	33.6984i	−0.412567	−	1.53972i	−0.789660	−	0.613545i	$-0.789743\pi$
$479$	−9.02947	−	33.6984i	−0.412567	−	1.53972i	0.377093	−	0.926176i	$-0.376924\pi$
$480$	−0.488717	+	1.24923i	−0.0223068	+	0.0570193i
$481$	−26.2119	+	2.33413i	−1.19516	+	0.106427i
$482$	−9.54613	−	5.51146i	−0.434814	−	0.251040i
$483$	2.37307	+	5.42300i	0.107978	+	0.246755i
$484$	4.89118	−	8.47177i	0.222326	−	0.385080i
$485$	−5.10293	+	8.83854i	−0.231712	+	0.401337i
$486$	−0.498018	+	15.5805i	−0.0225905	+	0.706746i
$487$	2.86697	+	10.6997i	0.129915	+	0.484849i	0.999967	−	0.00811050i	$-0.00258168\pi$
$487$	2.86697	+	10.6997i	0.129915	+	0.484849i	−0.870052	+	0.492960i	$0.835915\pi$
$488$	7.67525	−	7.67525i	0.347442	−	0.347442i
$489$	−34.6120	−	3.86165i	−1.56521	−	0.174630i
$490$	2.54933	+	4.41556i	0.115167	+	0.199475i
$491$	20.5551			0.927639			0.463820	−	0.885930i	$-0.346479\pi$
$491$	20.5551			0.927639			0.463820	+	0.885930i	$0.346479\pi$
$492$	1.41556	+	1.04235i	0.0638184	+	0.0469928i
$493$	−2.35176	+	1.35779i	−0.105918	+	0.0611517i
$494$	−3.21829	+	3.84749i	−0.144798	+	0.173107i
$495$	0.565055	−	2.50077i	0.0253973	−	0.112401i
$496$	−5.37059	−	1.43905i	−0.241147	−	0.0646151i
$497$	0.974642	+	0.562710i	0.0437187	+	0.0252410i
$498$	−7.21228	+	18.4356i	−0.323190	+	0.826120i
$499$	2.82433	+	10.5406i	0.126434	+	0.471860i	0.999887	−	0.0150499i	$-0.00479072\pi$
$499$	2.82433	+	10.5406i	0.126434	+	0.471860i	−0.873452	+	0.486910i	$0.838124\pi$
$500$	1.88425	−	7.03212i	0.0842662	−	0.314486i
$501$	15.4911	−	6.77881i	0.692093	−	0.302855i
$502$	2.32189	−	8.66542i	0.103631	−	0.386756i
$503$	−15.4715	−	8.93246i	−0.689839	−	0.398279i	0.113713	−	0.993514i	$-0.463726\pi$
$503$	−15.4715	−	8.93246i	−0.689839	−	0.398279i	−0.803552	+	0.595235i	$0.797059\pi$
$504$	−1.42230	−	1.31395i	−0.0633544	−	0.0585280i
$505$	−2.35188	+	8.77734i	−0.104657	+	0.390587i
$506$	−2.92141	−	5.06004i	−0.129873	−	0.224946i
$507$	−21.3140	+	7.26052i	−0.946586	+	0.322451i
$508$	−3.11283	+	5.39157i	−0.138109	+	0.239212i
$509$	−18.7620	−	18.7620i	−0.831610	−	0.831610i	0.156127	−	0.987737i	$-0.450099\pi$
$509$	−18.7620	−	18.7620i	−0.831610	−	0.831610i	−0.987737	+	0.156127i	$0.950099\pi$
$510$	1.46172	−	3.73637i	0.0647262	−	0.165449i
$511$			2.46906i			0.109225i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	5.46385	−	4.73319i	0.241235	−	0.208975i
$514$	13.6149	−	3.64811i	0.600528	−	0.160911i
$515$	−3.50107	−	0.938110i	−0.154276	−	0.0413381i
$516$	1.68784	+	11.1159i	0.0743031	+	0.489351i
$517$			3.42600i			0.150675i
$518$	−3.33110	+	3.33110i	−0.146360	+	0.146360i
$519$	−11.5624	−	4.52339i	−0.507534	−	0.198555i
$520$	2.75072	+	0.480637i	0.120627	+	0.0210773i
$521$			19.1202i			0.837669i	0.908063	+	0.418835i	$0.137561\pi$
$521$			19.1202i			0.837669i	−0.908063	+	0.418835i	$0.862439\pi$
$522$	1.45417	+	2.30315i	0.0636474	+	0.100806i
$523$	0.547702	+	0.948647i	0.0239493	+	0.0414815i	0.877752	−	0.479116i	$-0.159043\pi$
$523$	0.547702	+	0.948647i	0.0239493	+	0.0414815i	−0.853802	+	0.520597i	$0.825709\pi$
$524$	5.40541			0.236136
$525$	3.96114	+	2.91679i	0.172878	+	0.127299i
$526$	−18.6026	−	4.98454i	−0.811110	−	0.217336i
$527$	16.0631	+	4.30410i	0.699721	+	0.187490i
$528$	1.53903	+	1.13327i	0.0669778	+	0.0493193i
$529$	5.03669			0.218986
$530$	−4.21836	−	7.30641i	−0.183234	−	0.317370i
$531$	−16.1761	−	25.6200i	−0.701983	−	1.11181i
$532$			0.897944i			0.0389308i
$533$	1.54140	−	3.31895i	0.0667655	−	0.143760i
$534$	20.0572	+	7.84665i	0.867958	+	0.339558i
$535$	1.76201	−	1.76201i	0.0761781	−	0.0761781i
$536$		−	1.07782i		−	0.0465549i
$537$	−2.90714	−	19.1461i	−0.125453	−	0.826215i
$538$	−22.8443	−	6.12110i	−0.984886	−	0.263899i
$539$	7.01704	−	1.88021i	0.302245	−	0.0809863i
$540$	−3.80277	−	1.31671i	−0.163645	−	0.0566623i
$541$	5.70214	+	5.70214i	0.245154	+	0.245154i	0.818978	−	0.573824i	$-0.194541\pi$
$541$	5.70214	+	5.70214i	0.245154	+	0.245154i	−0.573824	+	0.818978i	$0.694541\pi$
$542$		−	26.6339i		−	1.14402i
$543$	−5.52907	+	14.1331i	−0.237275	+	0.606509i
$544$	2.11491	+	2.11491i	0.0906762	+	0.0906762i
$545$	1.98981	−	3.44645i	0.0852340	−	0.147630i
$546$	−2.09273	+	3.44499i	−0.0895605	+	0.147432i
$547$	3.73629	+	6.47145i	0.159752	+	0.276699i	0.934779	−	0.355229i	$-0.115597\pi$
$547$	3.73629	+	6.47145i	0.159752	+	0.276699i	−0.775027	+	0.631928i	$0.782264\pi$
$548$	1.83541	−	6.84985i	0.0784049	−	0.292611i
$549$	23.9188	+	22.0966i	1.02083	+	0.943061i
$550$	−4.20496	−	2.42774i	−0.179300	−	0.103519i
$551$	0.326919	−	1.22008i	0.0139272	−	0.0519770i
$552$	−8.40193	+	3.67663i	−0.357610	+	0.156488i
$553$	1.00870	−	3.76454i	0.0428945	−	0.160084i
$554$	2.84084	+	10.6021i	0.120696	+	0.450442i
$555$	−3.56697	+	9.11768i	−0.151409	+	0.387024i
$556$	17.8645	+	10.3141i	0.757624	+	0.437414i
$557$	−10.2462	−	2.74546i	−0.434145	−	0.116329i	0.0351263	−	0.999383i	$-0.488817\pi$
$557$	−10.2462	−	2.74546i	−0.434145	−	0.116329i	−0.469271	+	0.883054i	$0.655483\pi$
$558$	3.67624	−	16.2700i	0.155628	−	0.688763i
$559$	21.9810	−	8.03897i	0.929695	−	0.340012i
$560$	0.432909	−	0.249940i	0.0182937	−	0.0105619i
$561$	−4.60316	−	3.38954i	−0.194345	−	0.143107i
$562$	31.3397			1.32199
$563$	8.65071	+	14.9835i	0.364584	+	0.631478i	0.988709	−	0.149846i	$-0.0478779\pi$
$563$	8.65071	+	14.9835i	0.364584	+	0.631478i	−0.624125	+	0.781324i	$0.714545\pi$
$564$	5.34444	+	0.596278i	0.225041	+	0.0251079i
$565$	−5.92453	+	5.92453i	−0.249247	+	0.249247i
$566$	6.40405	+	23.9003i	0.269182	+	1.00460i
$567$	3.76993	−	4.41954i	0.158322	−	0.185603i
$568$	−0.871815	+	1.51003i	−0.0365805	+	0.0633594i
$569$	16.3511	−	28.3209i	0.685474	−	1.18728i	−0.287814	−	0.957686i	$-0.592929\pi$
$569$	16.3511	−	28.3209i	0.685474	−	1.18728i	0.973288	−	0.229589i	$-0.0737381\pi$
$570$	0.748136	+	1.70966i	0.0313360	+	0.0716099i
$571$	22.1007	+	12.7598i	0.924883	+	0.533982i	0.885190	−	0.465230i	$-0.154028\pi$
$571$	22.1007	+	12.7598i	0.924883	+	0.533982i	0.0396937	+	0.999212i	$0.487362\pi$
$572$	1.67585	−	3.60844i	0.0700708	−	0.150877i
$573$	15.3413	−	39.2145i	0.640891	−	1.63821i
$574$	−0.169550	−	0.632768i	−0.00707686	−	0.0264112i
$575$	20.1774	−	11.6494i	0.841457	−	0.485815i
$576$	2.03572	−	2.20360i	0.0848218	−	0.0918165i
$577$	−15.1912	+	15.1912i	−0.632416	+	0.632416i	−0.948673	−	0.316257i	$-0.897574\pi$
$577$	−15.1912	+	15.1912i	−0.632416	+	0.632416i	0.316257	+	0.948673i	$0.397574\pi$
$578$	5.69523	+	5.69523i	0.236890	+	0.236890i
$579$	6.85980	+	15.6762i	0.285084	+	0.651482i
$580$	−0.679209	+	0.181994i	−0.0282026	+	0.00755687i
$581$	6.38869	−	3.68851i	0.265048	−	0.153025i
$582$	17.8296	−	14.2504i	0.739059	−	0.590698i
$583$	−11.6111	+	3.11117i	−0.480881	+	0.128852i
$584$	−3.82535			−0.158294
$585$	−1.11426	+	8.30275i	−0.0460689	+	0.343277i
$586$	−22.2591			−0.919516
$587$	16.7240	−	4.48118i	0.690273	−	0.184958i	0.103403	−	0.994639i	$-0.467027\pi$
$587$	16.7240	−	4.48118i	0.690273	−	0.184958i	0.586870	+	0.809681i	$0.300360\pi$
$588$	−1.71178	−	11.2736i	−0.0705925	−	0.464914i
$589$	−6.69882	+	3.86756i	−0.276020	+	0.159360i
$590$	7.55547	−	2.02448i	0.311054	−	0.0833466i
$591$	−27.8420	+	37.8108i	−1.14527	+	1.55533i
$592$	−5.16092	−	5.16092i	−0.212112	−	0.212112i
$593$	4.90812	−	4.90812i	0.201552	−	0.201552i	−0.599112	−	0.800665i	$-0.704480\pi$
$593$	4.90812	−	4.90812i	0.201552	−	0.201552i	0.800665	+	0.599112i	$0.204480\pi$
$594$	−3.21446	+	4.74801i	−0.131891	+	0.194813i
$595$	−1.29480	+	0.747555i	−0.0530818	+	0.0306468i
$596$	−4.22688	−	15.7749i	−0.173140	−	0.646167i
$597$	6.81030	+	8.52079i	0.278727	+	0.348733i
$598$	10.9745	+	15.6217i	0.448781	+	0.638818i
$599$	3.18471	+	1.83869i	0.130124	+	0.0751269i	0.563649	−	0.826015i	$-0.309397\pi$
$599$	3.18471	+	1.83869i	0.130124	+	0.0751269i	−0.433525	+	0.901141i	$0.642730\pi$
$600$	−4.51903	+	6.13706i	−0.184489	+	0.250544i
$601$	19.8617	−	34.4016i	0.810178	−	1.40327i	−0.102562	−	0.994727i	$-0.532704\pi$
$601$	19.8617	−	34.4016i	0.810178	−	1.40327i	0.912740	−	0.408542i	$-0.133963\pi$
$602$	2.09491	−	3.62848i	0.0853820	−	0.147886i
$603$	3.23094	−	0.127943i	0.131574	−	0.00521023i
$604$	4.19291	+	15.6482i	0.170607	+	0.636715i
$605$	−5.35715	+	5.35715i	−0.217799	+	0.217799i
$606$	12.0500	−	16.3645i	0.489498	−	0.664761i
$607$	0.591299	+	1.02416i	0.0240001	+	0.0415694i	0.877776	−	0.479071i	$-0.159026\pi$
$607$	0.591299	+	1.02416i	0.0240001	+	0.0415694i	−0.853776	+	0.520641i	$0.825693\pi$
$608$	−1.39120			−0.0564205
$609$	0.112548	−	1.00876i	0.00456066	−	0.0408771i
$610$	−7.28020	+	4.20323i	−0.294767	+	0.170184i
$611$	−0.992914	−	11.1502i	−0.0401690	−	0.451090i
$612$	−6.08872	+	6.59082i	−0.246122	+	0.266418i
$613$	27.5469	+	7.38116i	1.11261	+	0.298122i	0.767888	−	0.640584i	$-0.221308\pi$
$613$	27.5469	+	7.38116i	1.11261	+	0.298122i	0.344719	+	0.938706i	$0.387974\pi$
$614$	5.35873	+	3.09386i	0.216261	+	0.124858i
$615$	−0.850018	−	1.06351i	−0.0342760	−	0.0428849i
$616$	−0.184339	−	0.687961i	−0.00742721	−	0.0277187i
$617$	−2.04963	+	7.64931i	−0.0825148	+	0.307950i	−0.994832	−	0.101535i	$-0.967625\pi$
$617$	−2.04963	+	7.64931i	−0.0825148	+	0.307950i	0.912317	+	0.409484i	$0.134291\pi$
$618$	6.52740	+	4.80647i	0.262571	+	0.193344i
$619$	−6.21758	+	23.2043i	−0.249906	+	0.932660i	0.720948	+	0.692989i	$0.243706\pi$
$619$	−6.21758	+	23.2043i	−0.249906	+	0.932660i	−0.970854	+	0.239672i	$0.922960\pi$
$620$	3.72919	+	2.15305i	0.149768	+	0.0864685i
$621$	−12.0186	−	24.7496i	−0.482289	−	0.993168i
$622$	−3.11482	+	11.6247i	−0.124893	+	0.466106i
$623$	−4.01294	−	6.95062i	−0.160775	−	0.278471i
$624$	−5.33737	−	3.24230i	−0.213666	−	0.129796i
$625$	8.18134	−	14.1705i	0.327254	−	0.566820i
$626$	−17.2282	−	17.2282i	−0.688578	−	0.688578i
$627$	2.62881	−	0.399159i	0.104985	−	0.0159409i
$628$		−	15.3454i		−	0.612349i
$629$	15.4360	+	15.4360i	0.615474	+	0.615474i
$630$	0.800621	+	1.26804i	0.0318975	+	0.0505199i
$631$	−1.75718	+	0.470835i	−0.0699522	+	0.0187436i	−0.293625	−	0.955921i	$-0.594862\pi$
$631$	−1.75718	+	0.470835i	−0.0699522	+	0.0187436i	0.223673	+	0.974664i	$0.428195\pi$
$632$	5.83246	+	1.56280i	0.232003	+	0.0621649i
$633$	−35.3310	−	13.8220i	−1.40428	−	0.549375i
$634$			17.5601i			0.697399i
$635$	3.40938	−	3.40938i	0.135297	−	0.135297i
$636$	2.83247	+	18.6543i	0.112315	+	0.739692i
$637$	−22.2927	+	8.15297i	−0.883268	+	0.323033i
$638$			1.00188i			0.0396647i
$639$	−4.63002	−	2.43415i	−0.183161	−	0.0962935i
$640$	0.387236	+	0.670712i	0.0153068	+	0.0265122i
$641$	10.0435			0.396692			0.198346	−	0.980132i	$-0.436443\pi$
$641$	10.0435			0.396692			0.198346	+	0.980132i	$0.436443\pi$
$642$	−5.10544	+	2.23410i	−0.201495	+	0.0881730i
$643$	0.461597	+	0.123684i	0.0182036	+	0.00487764i	0.267909	−	0.963444i	$-0.413667\pi$
$643$	0.461597	+	0.123684i	0.0182036	+	0.00487764i	−0.249706	+	0.968322i	$0.580334\pi$
$644$	3.30117	+	0.884545i	0.130084	+	0.0348559i
$645$	0.965520	−	8.65394i	0.0380173	−	0.340749i
$646$	4.16099			0.163712
$647$	13.4402	+	23.2791i	0.528389	+	0.915197i	0.999452	+	0.0330972i	$0.0105371\pi$
$647$	13.4402	+	23.2791i	0.528389	+	0.915197i	−0.471063	+	0.882100i	$0.656130\pi$
$648$	6.84726	+	5.84081i	0.268986	+	0.229449i
$649$		−	11.1448i		−	0.437472i
$650$	14.3890	+	6.68263i	0.564385	+	0.262114i
$651$	−4.85551	+	3.88080i	−0.190302	+	0.152101i
$652$	−14.2180	+	14.2180i	−0.556818	+	0.556818i
$653$		−	32.7229i		−	1.28054i	−0.768148	−	0.640272i	$-0.778822\pi$
$653$		−	32.7229i		−	1.28054i	0.768148	−	0.640272i	$-0.221178\pi$
$654$	−6.95235	+	5.55672i	−0.271859	+	0.217285i
$655$	−4.04369	−	1.08350i	−0.158000	−	0.0423360i
$656$	0.980356	−	0.262686i	0.0382765	−	0.0102562i
$657$	−0.454087	−	11.4671i	−0.0177156	−	0.447373i
$658$	−1.41701	−	1.41701i	−0.0552408	−	0.0552408i
$659$			17.0035i			0.662361i	0.943567	+	0.331180i	$0.107447\pi$
$659$			17.0035i			0.662361i	−0.943567	+	0.331180i	$0.892553\pi$
$660$	−0.924161	−	1.15628i	−0.0359729	−	0.0450080i
$661$	31.5432	+	31.5432i	1.22689	+	1.22689i	0.965135	+	0.261754i	$0.0843011\pi$
$661$	31.5432	+	31.5432i	1.22689	+	1.22689i	0.261754	+	0.965135i	$0.415699\pi$
$662$	15.5821	−	26.9890i	0.605615	−	1.04896i
$663$	15.9638	+	9.69752i	0.619981	+	0.376620i
$664$	5.71467	+	9.89810i	0.221772	+	0.384121i
$665$	0.179991	−	0.671736i	0.00697975	−	0.0260488i
$666$	14.8580	−	16.0833i	0.575736	−	0.623214i
$667$	−4.16340	−	2.40374i	−0.161208	−	0.0930732i
$668$	2.52676	−	9.42999i	0.0977632	−	0.364857i
$669$	0.911918	−	8.17351i	0.0352568	−	0.316006i
$670$	−0.216048	+	0.806301i	−0.00834665	+	0.0311501i
$671$	3.10001	+	11.5694i	0.119675	+	0.446632i
$672$	−1.10528	+	0.167825i	−0.0426370	+	0.00647400i
$673$	4.42806	+	2.55654i	0.170689	+	0.0985475i	0.582911	−	0.812536i	$-0.301914\pi$
$673$	4.42806	+	2.55654i	0.170689	+	0.0985475i	−0.412222	+	0.911084i	$0.635247\pi$
$674$	2.98580	+	0.800042i	0.115009	+	0.0308165i
$675$	−18.9332	−	12.8180i	−0.728738	−	0.493365i
$676$	−4.40842	+	12.2297i	−0.169555	+	0.470373i
$677$	−10.2029	+	5.89065i	−0.392130	+	0.226396i	−0.683083	−	0.730341i	$-0.739361\pi$
$677$	−10.2029	+	5.89065i	−0.392130	+	0.226396i	0.290953	+	0.956737i	$0.406028\pi$
$678$	17.1664	−	7.51190i	0.659272	−	0.288493i
$679$	−8.50559			−0.326415
$680$	−1.15820	−	2.00606i	−0.0444149	−	0.0769289i
$681$	−6.42325	−	14.6786i	−0.246140	−	0.562485i
$682$	4.33834	−	4.33834i	0.166123	−	0.166123i
$683$	11.2235	+	41.8867i	0.429456	+	1.60275i	0.753996	+	0.656879i	$0.228124\pi$
$683$	11.2235	+	41.8867i	0.429456	+	1.60275i	−0.324540	+	0.945872i	$0.605210\pi$
$684$	−0.165142	−	4.17033i	−0.00631435	−	0.159456i
$685$	−2.74608	+	4.75635i	−0.104922	+	0.181731i
$686$	−4.38368	+	7.59275i	−0.167370	+	0.289893i
$687$	−32.9021	−	3.67088i	−1.25529	−	0.140053i
$688$	5.62166	+	3.24567i	0.214324	+	0.123740i
$689$	36.8876	−	13.4907i	1.40531	−	0.513954i
$690$	7.02231	−	1.06627i	0.267335	−	0.0405921i
$691$	−10.5005	−	39.1885i	−0.399459	−	1.49080i	−0.814051	−	0.580793i	$-0.802742\pi$
$691$	−10.5005	−	39.1885i	−0.399459	−	1.49080i	0.414592	−	0.910007i	$-0.363924\pi$
$692$	−6.20787	+	3.58412i	−0.235988	+	0.136248i
$693$	2.04038	−	0.634247i	0.0775078	−	0.0240930i
$694$	−13.7814	+	13.7814i	−0.523135	+	0.523135i
$695$	−11.2967	−	11.2967i	−0.428507	−	0.428507i
$696$	1.56289	+	0.174372i	0.0592412	+	0.00660954i
$697$	−2.93219	+	0.785677i	−0.111065	+	0.0297596i
$698$	−19.0020	+	10.9708i	−0.719237	+	0.415252i
$699$	−37.9559	−	14.8489i	−1.43562	−	0.561636i
$700$	2.74332	−	0.735069i	0.103688	−	0.0277830i
$701$	4.00390			0.151225			0.0756127	−	0.997137i	$-0.475909\pi$
$701$	4.00390			0.151225			0.0756127	+	0.997137i	$0.475909\pi$
$702$	9.08570	−	16.3844i	0.342918	−	0.618391i
$703$	−10.1539			−0.382960
$704$	1.06587	−	0.285599i	0.0401714	−	0.0107639i
$705$	−3.87855	−	1.51735i	−0.146075	−	0.0571466i
$706$	8.49172	−	4.90270i	0.319590	−	0.184515i
$707$	−7.31506	+	1.96006i	−0.275111	+	0.0737158i
$708$	−17.3855	−	1.93970i	−0.653387	−	0.0728983i
$709$	36.5550	+	36.5550i	1.37285	+	1.37285i	0.856187	+	0.516665i	$0.172827\pi$
$709$	36.5550	+	36.5550i	1.37285	+	1.37285i	0.516665	+	0.856187i	$0.327173\pi$
$710$	0.954871	−	0.954871i	0.0358357	−	0.0358357i
$711$	−3.99239	+	17.6692i	−0.149726	+	0.662646i
$712$	10.7687	−	6.21731i	0.403574	−	0.233004i
$713$	7.61970	+	28.4371i	0.285360	+	1.06498i
$714$	3.30582	−	0.501956i	0.123717	−	0.0187852i
$715$	−1.97698	+	2.36349i	−0.0739348	+	0.0883896i
$716$	−9.68278	−	5.59035i	−0.361862	−	0.208921i
$717$	−40.6433	−	4.53457i	−1.51785	−	0.169347i
$718$	15.4672	−	26.7899i	0.577229	−	0.999790i
$719$	19.0888	−	33.0627i	0.711891	−	1.23303i	−0.252256	−	0.967661i	$-0.581172\pi$
$719$	19.0888	−	33.0627i	0.711891	−	1.23303i	0.964147	−	0.265370i	$-0.0854942\pi$
$720$	−1.96459	+	1.24041i	−0.0732161	+	0.0462275i
$721$	−0.781823	−	2.91780i	−0.0291166	−	0.108665i
$722$	12.0665	−	12.0665i	0.449068	−	0.449068i
$723$	−7.65390	−	17.4909i	−0.284652	−	0.650494i
$724$	4.38097	+	7.58806i	0.162817	+	0.282008i
$725$	−3.99509			−0.148374
$726$	15.5224	−	6.79250i	0.576091	−	0.252093i
$727$	19.7831	−	11.4218i	0.733715	−	0.423611i	−0.0860647	−	0.996290i	$-0.527429\pi$
$727$	19.7831	−	11.4218i	0.733715	−	0.423611i	0.819780	+	0.572679i	$0.194096\pi$
$728$	0.799330	+	2.18561i	0.0296251	+	0.0810041i
$729$	−16.6959	+	21.2190i	−0.618366	+	0.785890i
$730$	2.86167	+	0.766783i	0.105915	+	0.0283799i
$731$	−16.8141	−	9.70760i	−0.621891	−	0.359049i
$732$	18.5874	−	2.82231i	0.687010	−	0.104316i
$733$	5.31510	+	19.8362i	0.196318	+	0.732668i	0.991922	+	0.126851i	$0.0404870\pi$
$733$	5.31510	+	19.8362i	0.196318	+	0.732668i	−0.795604	+	0.605817i	$0.792846\pi$
$734$	5.67269	−	21.1708i	0.209383	−	0.781428i
$735$	−0.979213	+	8.77667i	−0.0361188	+	0.323732i
$736$	−1.37044	+	5.11455i	−0.0505150	+	0.188525i
$737$	1.03000	+	0.594672i	0.0379406	+	0.0219050i
$738$	0.903813	+	2.90758i	0.0332698	+	0.107030i
$739$	2.52195	−	9.41204i	0.0927713	−	0.346227i	−0.903901	−	0.427742i	$-0.859309\pi$
$739$	2.52195	−	9.41204i	0.0927713	−	0.346227i	0.996672	+	0.0815148i	$0.0259758\pi$
$740$	2.82630	+	4.89529i	0.103897	+	0.179954i
$741$	−8.44004	+	2.06098i	−0.310052	+	0.0757118i
$742$	3.51559	−	6.08918i	0.129061	−	0.223541i
$743$	24.5627	+	24.5627i	0.901120	+	0.901120i	0.995533	−	0.0944135i	$-0.0300976\pi$
$743$	24.5627	+	24.5627i	0.901120	+	0.901120i	−0.0944135	+	0.995533i	$0.530098\pi$
$744$	−6.01258	−	7.52271i	−0.220432	−	0.275796i
$745$			12.6482i			0.463395i
$746$	−1.03484	−	1.03484i	−0.0378883	−	0.0378883i
$747$	−28.9927	+	18.3055i	−1.06079	+	0.669764i
$748$	−3.18795	+	0.854208i	−0.116563	+	0.0312329i
$749$	2.00595	+	0.537494i	0.0732959	+	0.0196396i
$750$	9.85005	−	7.87272i	0.359673	−	0.287471i
$751$		−	20.5860i		−	0.751193i	−0.926783	−	0.375596i	$-0.877438\pi$
$751$		−	20.5860i		−	0.751193i	0.926783	−	0.375596i	$-0.122562\pi$
$752$	2.19540	−	2.19540i	0.0800578	−	0.0800578i
$753$	12.1378	−	9.70126i	0.442328	−	0.353534i
$754$	−0.290361	−	3.26070i	−0.0105743	−	0.118748i
$755$		−	12.5466i		−	0.456616i
$756$	−0.634283	−	3.29331i	−0.0230687	−	0.119777i
$757$	7.26256	+	12.5791i	0.263962	+	0.457196i	0.967291	−	0.253668i	$-0.0816372\pi$
$757$	7.26256	+	12.5791i	0.263962	+	0.457196i	−0.703329	+	0.710865i	$0.748304\pi$
$758$	16.9489			0.615612
$759$	1.12213	−	10.0577i	0.0407309	−	0.365070i
$760$	1.04073	+	0.278863i	0.0377512	+	0.0101154i
$761$	−7.39827	−	1.98236i	−0.268187	−	0.0718605i	0.122219	−	0.992503i	$-0.460999\pi$
$761$	−7.39827	−	1.98236i	−0.268187	−	0.0718605i	−0.390406	+	0.920643i	$0.627666\pi$
$762$	−9.87872	+	4.32286i	−0.357868	+	0.156601i
$763$	3.31662			0.120070
$764$	−12.1557	−	21.0543i	−0.439777	−	0.761717i
$765$	5.87598	−	3.71000i	0.212447	−	0.134136i
$766$			9.05433i			0.327146i
$767$	3.22995	+	36.2718i	0.116627	+	1.30970i
$768$	−0.260014	−	1.71242i	−0.00938246	−	0.0617917i
$769$	−6.40514	+	6.40514i	−0.230975	+	0.230975i	−0.813100	−	0.582125i	$-0.802222\pi$
$769$	−6.40514	+	6.40514i	−0.230975	+	0.230975i	0.582125	+	0.813100i	$0.302222\pi$
$770$			0.551601i			0.0198783i
$771$	22.7357	+	8.89453i	0.818806	+	0.320329i
$772$	9.54266	+	2.55695i	0.343448	+	0.0920266i
$773$	−41.5613	+	11.1363i	−1.49486	+	0.400545i	−0.911373	−	0.411580i	$-0.864977\pi$
$773$	−41.5613	+	11.1363i	−1.49486	+	0.400545i	−0.583482	+	0.812126i	$0.698310\pi$
$774$	−9.06206	+	17.2371i	−0.325729	+	0.619573i
$775$	17.2996	+	17.2996i	0.621419	+	0.621419i
$776$		−	13.1778i		−	0.473057i
$777$	−8.06702	+	1.22490i	−0.289403	+	0.0439429i
$778$	15.3096	+	15.3096i	0.548876	+	0.548876i
$779$	0.705991	−	1.22281i	0.0252948	−	0.0438118i
$780$	3.34288	+	3.49537i	0.119694	+	0.125154i
$781$	−0.962020	−	1.66627i	−0.0344238	−	0.0596237i
$782$	4.09890	−	15.2973i	0.146576	−	0.547030i
$783$	−0.337183	+	4.70570i	−0.0120499	+	0.168168i
$784$	−5.70139	−	3.29170i	−0.203621	−	0.117561i
$785$	−3.07596	+	11.4796i	−0.109786	+	0.409726i
$786$	7.53905	+	5.55140i	0.268909	+	0.198012i
$787$	−4.27480	+	15.9538i	−0.152380	+	0.568690i	0.846935	+	0.531696i	$0.178445\pi$
$787$	−4.27480	+	15.9538i	−0.152380	+	0.568690i	−0.999315	+	0.0369945i	$0.988222\pi$
$788$	7.01655	+	26.1861i	0.249954	+	0.932841i
$789$	−20.8263	−	26.0570i	−0.741435	−	0.927655i
$790$	−4.04989	−	2.33821i	−0.144089	−	0.0831897i
$791$	−6.74478	−	1.80726i	−0.239817	−	0.0642587i
$792$	0.982648	+	3.16120i	0.0349169	+	0.112328i
$793$	−13.4423	−	36.7553i	−0.477350	−	1.30522i
$794$	10.4061	−	6.00797i	0.369299	−	0.213215i
$795$	1.62030	−	14.5227i	0.0574661	−	0.515068i
$796$	6.29773			0.223217
$797$	0.633307	+	1.09692i	0.0224329	+	0.0388549i	0.877024	−	0.480447i	$-0.159525\pi$
$797$	0.633307	+	1.09692i	0.0224329	+	0.0388549i	−0.854591	+	0.519302i	$0.826192\pi$
$798$	−0.922195	+	1.25238i	−0.0326454	+	0.0443339i
$799$	−6.56630	+	6.56630i	−0.232299	+	0.232299i
$800$	1.13885	+	4.25026i	0.0402646	+	0.150269i
$801$	19.9156	+	31.5428i	0.703684	+	1.11451i
$802$	−7.94238	+	13.7566i	−0.280455	+	0.485763i
$803$	2.11057	−	3.65562i	0.0744806	−	0.129004i
$804$	1.10693	−	1.50327i	0.0390386	−	0.0530161i
$805$	−2.29224	−	1.32342i	−0.0807908	−	0.0466446i
$806$	−12.8622	+	15.3768i	−0.453052	+	0.541626i
$807$	−25.5750	−	31.9985i	−0.900283	−	1.12640i
$808$	−3.03676	−	11.3333i	−0.106833	−	0.398705i
$809$	20.7340	−	11.9708i	0.728968	−	0.420870i	−0.0890764	−	0.996025i	$-0.528392\pi$
$809$	20.7340	−	11.9708i	0.728968	−	0.420870i	0.818045	+	0.575155i	$0.195058\pi$
$810$	−3.95153	−	5.74192i	−0.138843	−	0.201751i
$811$	−3.24886	+	3.24886i	−0.114083	+	0.114083i	−0.761844	−	0.647761i	$-0.775706\pi$
$811$	−3.24886	+	3.24886i	−0.114083	+	0.114083i	0.647761	+	0.761844i	$0.275706\pi$
$812$	−0.414381	−	0.414381i	−0.0145419	−	0.0145419i
$813$	27.3532	−	37.1469i	0.959319	−	1.30280i
$814$	7.77939	−	2.08448i	0.272668	−	0.0730610i
$815$	13.4862	−	7.78623i	0.472399	−	0.272740i
$816$	0.777687	+	5.12176i	0.0272245	+	0.179297i
$817$	8.72302	−	2.33733i	0.305180	−	0.0817727i
$818$	18.3944			0.643146
$819$	−6.45681	+	2.65555i	−0.225619	+	0.0927926i
$820$	−0.786042			−0.0274498
$821$	−20.7649	+	5.56395i	−0.724701	+	0.194183i	−0.602268	−	0.798294i	$-0.705736\pi$
$821$	−20.7649	+	5.56395i	−0.724701	+	0.194183i	−0.122433	+	0.992477i	$0.539070\pi$
$822$	9.59475	−	7.66867i	0.334655	−	0.267476i
$823$	13.4056	−	7.73975i	0.467291	−	0.269791i	−0.247814	−	0.968808i	$-0.579712\pi$
$823$	13.4056	−	7.73975i	0.467291	−	0.269791i	0.715105	+	0.699017i	$0.246379\pi$
$824$	4.52060	−	1.21129i	0.157482	−	0.0421973i
$825$	−3.37146	−	7.70455i	−0.117379	−	0.268238i
$826$	4.60954	+	4.60954i	0.160386	+	0.160386i
$827$	−7.79726	+	7.79726i	−0.271137	+	0.271137i	−0.829558	−	0.558421i	$-0.811408\pi$
$827$	−7.79726	+	7.79726i	−0.271137	+	0.271137i	0.558421	+	0.829558i	$0.311408\pi$
$828$	−15.4943	−	3.50098i	−0.538464	−	0.121667i
$829$	33.4066	−	19.2873i	1.16026	−	0.669875i	0.208892	−	0.977939i	$-0.433014\pi$
$829$	33.4066	−	19.2873i	1.16026	−	0.669875i	0.951366	+	0.308063i	$0.0996809\pi$
$830$	−2.29099	−	8.55008i	−0.0795213	−	0.296778i
$831$	−6.92631	+	17.7046i	−0.240271	+	0.614167i
$832$	−3.38620	+	1.23841i	−0.117395	+	0.0429343i
$833$	17.0525	+	9.84528i	0.590835	+	0.341119i
$834$	14.3234	+	32.7323i	0.495979	+	1.13343i
$835$	−3.78044	+	6.54792i	−0.130828	+	0.226600i
$836$	0.767571	−	1.32947i	0.0265470	−	0.0459808i
$837$	21.8367	−	18.9166i	0.754788	−	0.653853i
$838$	−7.54753	−	28.1678i	−0.260725	−	0.973039i
$839$	−20.2107	+	20.2107i	−0.697750	+	0.697750i	−0.963925	−	0.266175i	$-0.914240\pi$
$839$	−20.2107	+	20.2107i	−0.697750	+	0.697750i	0.266175	+	0.963925i	$0.414240\pi$
$840$	0.860478	+	0.0960035i	0.0296893	+	0.00331244i
$841$	−14.0878	−	24.4008i	−0.485787	−	0.841408i
$842$	−0.844793			−0.0291135
$843$	43.7103	+	32.1862i	1.50546	+	1.10855i
$844$	−18.9692	+	10.9519i	−0.652948	+	0.376980i
$845$	5.74928	−	8.26517i	0.197781	−	0.284330i
$846$	6.84163	+	6.32042i	0.235220	+	0.217301i
$847$	−6.09884	−	1.63418i	−0.209559	−	0.0561511i
$848$	9.43406	+	5.44676i	0.323967	+	0.187042i
$849$	−15.6139	+	39.9113i	−0.535866	+	1.36975i
$850$	−3.40624	−	12.7123i	−0.116833	−	0.436028i
$851$	−10.0023	+	37.3292i	−0.342876	+	1.27963i
$852$	−2.76675	+	1.21071i	−0.0947874	+	0.0414783i
$853$	−0.211290	+	0.788547i	−0.00723445	+	0.0269993i	−0.969449	−	0.245294i	$-0.921115\pi$
$853$	−0.211290	+	0.788547i	−0.00723445	+	0.0269993i	0.962214	+	0.272293i	$0.0877821\pi$
$854$	−6.06734	−	3.50298i	−0.207620	−	0.119869i
$855$	−0.712394	+	3.15285i	−0.0243633	+	0.107825i
$856$	−0.832747	+	3.10785i	−0.0284627	+	0.106224i
$857$	−10.3366	−	17.9034i	−0.353090	−	0.611570i	0.633699	−	0.773580i	$-0.281536\pi$
$857$	−10.3366	−	17.9034i	−0.353090	−	0.611570i	−0.986789	+	0.162010i	$0.948202\pi$
$858$	6.04325	−	3.31167i	0.206313	−	0.113059i
$859$	27.1813	−	47.0794i	0.927414	−	1.60633i	0.139782	−	0.990182i	$-0.455360\pi$
$859$	27.1813	−	47.0794i	0.927414	−	1.60633i	0.787632	−	0.616146i	$-0.211307\pi$
$860$	−3.55488	−	3.55488i	−0.121220	−	0.121220i
$861$	0.413383	−	1.05666i	0.0140880	−	0.0360110i
$862$			10.0910i			0.343701i
$863$	−10.7382	−	10.7382i	−0.365532	−	0.365532i	0.500312	−	0.865845i	$-0.333218\pi$
$863$	−10.7382	−	10.7382i	−0.365532	−	0.365532i	−0.865845	+	0.500312i	$0.833218\pi$
$864$	5.10238	−	0.982705i	0.173587	−	0.0334323i
$865$	5.36243	−	1.43686i	0.182328	−	0.0488546i
$866$	−21.6471	−	5.80033i	−0.735600	−	0.197103i
$867$	2.09423	+	13.7923i	0.0711237	+	0.468412i
$868$			3.58871i			0.121809i
$869$	−4.71143	+	4.71143i	−0.159824	+	0.159824i
$870$	−1.13422	−	0.443723i	−0.0384536	−	0.0150436i
$871$	−3.52459	−	1.63690i	−0.119426	−	0.0554644i
$872$			5.13849i			0.174011i
$873$	39.5026	−	1.56427i	1.33696	−	0.0529426i
$874$	3.68317	+	6.37945i	0.124585	+	0.215788i
$875$	−4.69897			−0.158854
$876$	−5.33530	−	3.92866i	−0.180263	−	0.132737i
$877$	−12.4060	−	3.32418i	−0.418921	−	0.112250i	0.0432000	−	0.999066i	$-0.486245\pi$
$877$	−12.4060	−	3.32418i	−0.418921	−	0.112250i	−0.462121	+	0.886817i	$0.652911\pi$
$878$	6.51614	+	1.74599i	0.219909	+	0.0589245i
$879$	−31.0453	−	22.8603i	−1.04713	−	0.771059i
$880$	−0.854605			−0.0288087
$881$	0.639646	+	1.10790i	0.0215502	+	0.0373261i	0.876599	−	0.481221i	$-0.159806\pi$
$881$	0.639646	+	1.10790i	0.0215502	+	0.0373261i	−0.855049	+	0.518547i	$0.826473\pi$
$882$	9.19058	−	17.4815i	0.309463	−	0.588633i
$883$		−	31.9358i		−	1.07473i	−0.843351	−	0.537363i	$-0.819420\pi$
$883$		−	31.9358i		−	1.07473i	0.843351	−	0.537363i	$-0.180580\pi$
$884$	10.1279	−	3.70402i	0.340639	−	0.124580i
$885$	12.6170	+	4.93594i	0.424114	+	0.165920i
$886$	−27.4664	+	27.4664i	−0.922753	+	0.922753i
$887$			9.03673i			0.303424i	0.988425	+	0.151712i	$0.0484786\pi$
$887$			9.03673i			0.303424i	−0.988425	+	0.151712i	$0.951521\pi$
$888$	−1.89775	−	12.4984i	−0.0636844	−	0.419418i
$889$	3.88140	+	1.04002i	0.130178	+	0.0348811i
$890$	−9.30212	+	2.49249i	−0.311808	+	0.0835486i
$891$	−9.35952	+	3.32089i	−0.313556	+	0.111254i
$892$	−3.35753	−	3.35753i	−0.112418	−	0.112418i
$893$		−	4.31933i		−	0.144541i
$894$	10.3057	−	26.3427i	0.344673	−	0.881032i
$895$	6.12294	+	6.12294i	0.204667	+	0.204667i
$896$	−0.322723	+	0.558973i	−0.0107814	+	0.0186740i
$897$	−0.737204	+	33.0588i	−0.0246145	+	1.10380i
$898$	7.41544	+	12.8439i	0.247456	+	0.428607i
$899$	1.30656	−	4.87615i	0.0435762	−	0.162629i
$900$	−12.6056	+	3.91841i	−0.420187	+	0.130614i
$901$	−28.2167	−	16.2909i	−0.940035	−	0.542730i
$902$	−0.289865	+	1.08179i	−0.00965146	+	0.0360197i
$903$	6.64830	−	2.90925i	0.221241	−	0.0968137i
$904$	2.80001	−	10.4498i	0.0931270	−	0.347555i
$905$	−1.75631	−	6.55465i	−0.0583818	−	0.217884i
$906$	−10.2228	+	26.1310i	−0.339631	+	0.868145i
$907$	−11.3030	−	6.52581i	−0.375311	−	0.216686i	0.300465	−	0.953793i	$-0.402858\pi$
$907$	−11.3030	−	6.52581i	−0.375311	−	0.216686i	−0.675776	+	0.737107i	$0.736191\pi$
$908$	−8.93537	−	2.39423i	−0.296531	−	0.0794552i
$909$	33.6129	−	10.4485i	1.11487	−	0.346553i
$910$	−0.159864	−	1.79524i	−0.00529942	−	0.0595116i
$911$	−16.8868	+	9.74959i	−0.559484	+	0.323018i	−0.752938	−	0.658091i	$-0.771364\pi$
$911$	−16.8868	+	9.74959i	−0.559484	+	0.323018i	0.193454	+	0.981109i	$0.438031\pi$
$912$	−1.94034	−	1.42877i	−0.0642510	−	0.0473113i
$913$	−12.6119			−0.417393
$914$	−17.8169	−	30.8597i	−0.589330	−	1.02075i
$915$	−14.4706	−	1.61449i	−0.478384	−	0.0533732i
$916$	−13.5156	+	13.5156i	−0.446567	+	0.446567i
$917$	−0.902994	−	3.37002i	−0.0298195	−	0.111288i
$918$	−15.2609	+	2.93921i	−0.503685	+	0.0970084i
$919$	−12.0734	+	20.9117i	−0.398263	+	0.689812i	−0.993512	−	0.113729i	$-0.963720\pi$
$919$	−12.0734	+	20.9117i	−0.398263	+	0.689812i	0.595248	+	0.803542i	$0.297054\pi$
$920$	2.05040	−	3.55140i	0.0675997	−	0.117086i
$921$	4.29653	+	9.81855i	0.141575	+	0.323532i
$922$	−9.81937	−	5.66921i	−0.323384	−	0.186706i
$923$	3.61390	+	5.14421i	0.118953	+	0.169324i
$924$	0.449440	−	1.14883i	0.0147855	−	0.0377938i
$925$	8.31209	+	31.0211i	0.273300	+	1.01997i
$926$	−33.4990	+	19.3407i	−1.10085	+	0.635574i
$927$	4.16764	+	13.4074i	0.136883	+	0.440356i
$928$	0.642006	−	0.642006i	0.0210749	−	0.0210749i
$929$	20.0059	+	20.0059i	0.656371	+	0.656371i	0.954519	−	0.298149i	$-0.0963691\pi$
$929$	20.0059	+	20.0059i	0.656371	+	0.656371i	−0.298149	+	0.954519i	$0.596369\pi$
$930$	2.98999	+	6.83282i	0.0980457	+	0.224057i
$931$	−8.84673	+	2.37047i	−0.289940	+	0.0776892i
$932$	−20.3785	+	11.7655i	−0.667521	+	0.385393i
$933$	−16.2829	+	13.0142i	−0.533079	+	0.426067i
$934$	1.06549	−	0.285498i	0.0348640	−	0.00934177i
$935$	2.55607			0.0835925
$936$	−4.11429	−	10.0036i	−0.134480	−	0.326979i
$937$	−43.5445			−1.42254			−0.711269	−	0.702920i	$-0.751879\pi$
$937$	−43.5445			−1.42254			−0.711269	+	0.702920i	$0.751879\pi$
$938$	−0.671973	+	0.180055i	−0.0219407	+	0.00587899i
$939$	−6.33509	−	41.7221i	−0.206738	−	1.36155i
$940$	−2.08240	+	1.20227i	−0.0679203	+	0.0392138i
$941$	−33.2309	+	8.90420i	−1.08330	+	0.290269i	−0.755946	−	0.654634i	$-0.772823\pi$
$941$	−33.2309	+	8.90420i	−1.08330	+	0.290269i	−0.327351	+	0.944903i	$0.606156\pi$
$942$	15.7599	−	21.4026i	0.513485	−	0.697335i
$943$	−3.80004	−	3.80004i	−0.123746	−	0.123746i
$944$	−7.14163	+	7.14163i	−0.232440	+	0.232440i
$945$	−0.185642	+	2.59081i	−0.00603894	+	0.0842790i
$946$	−6.20333	+	3.58149i	−0.201688	+	0.116444i
$947$	−1.97729	−	7.37935i	−0.0642534	−	0.239797i	0.926329	−	0.376716i	$-0.122947\pi$
$947$	−1.97729	−	7.37935i	−0.0642534	−	0.239797i	−0.990582	+	0.136919i	$0.956280\pi$
$948$	6.52966	+	8.16966i	0.212073	+	0.265338i
$949$	−5.80960	+	12.5092i	−0.188588	+	0.406067i
$950$	5.30141	+	3.06077i	0.172000	+	0.0993045i
$951$	−18.0343	+	24.4914i	−0.584803	+	0.794189i
$952$	0.965246	−	1.67185i	0.0312838	−	0.0541851i
$953$	13.1233	−	22.7302i	0.425104	−	0.736302i	−0.571326	−	0.820723i	$-0.693571\pi$
$953$	13.1233	−	22.7302i	0.425104	−	0.736302i	0.996430	+	0.0844210i	$0.0269041\pi$
$954$	−15.2076	+	28.9266i	−0.492365	+	0.936533i
$955$	4.87317	+	18.1869i	0.157692	+	0.588514i
$956$	−16.6955	+	16.6955i	−0.539972	+	0.539972i
$957$	−1.02894	+	1.39734i	−0.0332607	+	0.0451696i
$958$	−17.4436	−	30.2132i	−0.563577	−	0.976144i
$959$	−4.57718			−0.147805
$960$	−0.148740	+	1.33315i	−0.00480055	+	0.0430273i
$961$	0.0743685	−	0.0429367i	0.00239898	−	0.00138505i
$962$	−24.7146	+	9.03874i	−0.796832	+	0.291421i
$963$	−9.41511	−	2.12737i	−0.303398	−	0.0685535i
$964$	−10.6473	−	2.85294i	−0.342927	−	0.0918871i
$965$	−6.62616	−	3.82561i	−0.213304	−	0.123151i
$966$	3.69578	+	4.62402i	0.118910	+	0.148775i
$967$	−12.5015	−	46.6561i	−0.402020	−	1.50036i	−0.809486	−	0.587139i	$-0.800254\pi$
$967$	−12.5015	−	46.6561i	−0.402020	−	1.50036i	0.407466	−	0.913220i	$-0.366413\pi$
$968$	2.53186	−	9.44903i	0.0813771	−	0.303703i
$969$	5.80343	+	4.27337i	0.186433	+	0.137280i
$970$	−2.64147	+	9.85811i	−0.0848126	+	0.316525i
$971$	7.17740	+	4.14388i	0.230334	+	0.132983i	0.610726	−	0.791842i	$-0.290878\pi$
$971$	7.17740	+	4.14388i	0.230334	+	0.132983i	−0.380392	+	0.924825i	$0.624211\pi$
$972$	3.55148	+	15.1785i	0.113914	+	0.486851i
$973$	3.44601	−	12.8607i	0.110474	−	0.412295i
$974$	5.53857	+	9.59308i	0.177467	+	0.307382i
$975$	13.2056	+	24.0981i	0.422919	+	0.771756i
$976$	5.42722	−	9.40022i	0.173721	−	0.300894i
$977$	−1.44990	−	1.44990i	−0.0463865	−	0.0463865i	0.683533	−	0.729920i	$-0.260443\pi$
$977$	−1.44990	−	1.44990i	−0.0463865	−	0.0463865i	−0.729920	+	0.683533i	$0.760443\pi$
$978$	−34.4321	+	5.22817i	−1.10102	+	0.167178i
$979$			13.7212i			0.438532i
$980$	3.60529	+	3.60529i	0.115167	+	0.115167i
$981$	−15.4034	+	0.609963i	−0.491793	+	0.0194746i
$982$	19.8547	−	5.32006i	0.633589	−	0.169770i
$983$	−53.2967	−	14.2808i	−1.69990	−	0.455487i	−0.726987	−	0.686651i	$-0.759080\pi$
$983$	−53.2967	−	14.2808i	−1.69990	−	0.455487i	−0.972915	+	0.231163i	$0.925747\pi$
$984$	1.63711	+	0.640460i	0.0521891	+	0.0204171i
$985$		−	20.9958i		−	0.668982i
$986$	−1.92020	+	1.92020i	−0.0611517	+	0.0611517i
$987$	−0.521057	−	3.43162i	−0.0165854	−	0.109230i
$988$	−2.11283	+	4.54935i	−0.0672180	+	0.144734i
$989$		−	34.3714i		−	1.09295i
$990$	−0.101446	−	2.56181i	−0.00322415	−	0.0814195i
$991$	1.47601	+	2.55653i	0.0468871	+	0.0812108i	0.888516	−	0.458845i	$-0.151737\pi$
$991$	1.47601	+	2.55653i	0.0468871	+	0.0812108i	−0.841629	+	0.540056i	$0.818403\pi$
$992$	−5.56005			−0.176532
$993$	49.4506	−	21.6392i	1.56927	−	0.686700i
$994$	1.08707	+	0.291280i	0.0344798	+	0.00923884i
$995$	−4.71122	−	1.26237i	−0.149356	−	0.0400197i
$996$	−2.19504	+	19.6741i	−0.0695525	+	0.623398i
$997$	60.1259			1.90421			0.952104	−	0.305775i	$-0.0989155\pi$
$997$	60.1259			1.90421			0.952104	+	0.305775i	$0.0989155\pi$
$998$	5.45619	+	9.45040i	0.172713	+	0.299147i
$999$	37.2405	−	7.17241i	1.17824	−	0.226925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.41.14	yes	56
3.2	odd	2		702.2.bc.a.665.5		56
9.2	odd	6		234.2.y.a.119.11	yes	56
9.7	even	3		702.2.bb.a.197.5		56
13.7	odd	12		234.2.y.a.59.11	✓	56
39.20	even	12		702.2.bb.a.449.5		56
117.7	odd	12		702.2.bc.a.683.5		56
117.20	even	12	inner	234.2.z.a.137.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.11	✓	56	13.7	odd	12
234.2.y.a.119.11	yes	56	9.2	odd	6
234.2.z.a.41.14	yes	56	1.1	even	1	trivial
234.2.z.a.137.14	yes	56	117.20	even	12	inner
702.2.bb.a.197.5		56	9.7	even	3
702.2.bb.a.449.5		56	39.20	even	12
702.2.bc.a.665.5		56	3.2	odd	2
702.2.bc.a.683.5		56	117.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.61301 + 0.631032i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.748082 + 0.200448i) q^{5} +(1.72137 + 0.192053i) q^{6} +(-0.456400 - 0.456400i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.20360 + 2.03572i) q^{9} +(-0.670712 + 0.387236i) q^{10} +(0.285599 + 1.06587i) q^{11} +(1.71242 - 0.260014i) q^{12} +(-1.23841 - 3.38620i) q^{13} +(-0.558973 - 0.322723i) q^{14} +(-1.33315 - 0.148740i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.49547 + 2.59023i) q^{17} +(2.65539 + 1.39602i) q^{18} +(-0.360069 - 1.34379i) q^{19} +(-0.547634 + 0.547634i) q^{20} +(-0.448174 - 1.02418i) q^{21} +(0.551734 + 0.955631i) q^{22} -5.29497 q^{23} +(1.58678 - 0.694362i) q^{24} +(-3.81068 + 2.20010i) q^{25} +(-2.07263 - 2.95029i) q^{26} +(2.26981 + 4.67418i) q^{27} +(-0.623453 - 0.167054i) q^{28} +(0.786294 + 0.453967i) q^{29} +(-1.32622 + 0.201374i) q^{30} +(-1.43905 - 5.37059i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.211925 + 1.89948i) q^{33} +(-0.774112 + 2.88903i) q^{34} +(0.432909 + 0.249940i) q^{35} +(2.92623 + 0.661189i) q^{36} +(1.88903 - 7.04995i) q^{37} +(-0.695599 - 1.20481i) q^{38} +(0.139227 - 6.24345i) q^{39} +(-0.387236 + 0.670712i) q^{40} +(0.717671 + 0.717671i) q^{41} +(-0.697980 - 0.873286i) q^{42} +6.49134i q^{43} +(0.780270 + 0.780270i) q^{44} +(-2.05653 - 1.08118i) q^{45} +(-5.11455 + 1.37044i) q^{46} +(2.99897 + 0.803570i) q^{47} +(1.35299 - 1.08139i) q^{48} -6.58340i q^{49} +(-3.11141 + 3.11141i) q^{50} +(-4.04673 + 3.23437i) q^{51} +(-2.76560 - 2.31333i) q^{52} +10.8935i q^{53} +(3.40224 + 3.92744i) q^{54} +(-0.427302 - 0.740109i) q^{55} -0.645446 q^{56} +(0.267184 - 2.39477i) q^{57} +(0.876997 + 0.234991i) q^{58} +(-9.75565 - 2.61402i) q^{59} +(-1.22891 + 0.537764i) q^{60} +10.8544 q^{61} +(-2.78002 - 4.81514i) q^{62} +(-0.0766175 - 1.93482i) q^{63} -1.00000i q^{64} +(1.60519 + 2.28492i) q^{65} +(0.286917 + 1.88960i) q^{66} +(0.762137 - 0.762137i) q^{67} +2.99094i q^{68} +(-8.54083 - 3.34130i) q^{69} +(0.482847 + 0.129378i) q^{70} +(-1.68422 + 0.451285i) q^{71} +(2.99765 - 0.118705i) q^{72} +(-2.70493 - 2.70493i) q^{73} -7.29864i q^{74} +(-7.53499 + 1.14411i) q^{75} +(-0.983725 - 0.983725i) q^{76} +(0.356115 - 0.616809i) q^{77} +(-1.48144 - 6.06674i) q^{78} +(3.01910 + 5.22924i) q^{79} +(-0.200448 + 0.748082i) q^{80} +(0.711670 + 8.97182i) q^{81} +(0.878964 + 0.507470i) q^{82} +(-2.95813 + 11.0399i) q^{83} +(-0.900220 - 0.662879i) q^{84} +(0.599528 - 2.23747i) q^{85} +(1.68008 + 6.27015i) q^{86} +(0.981831 + 1.22843i) q^{87} +(0.955631 + 0.551734i) q^{88} +(12.0109 + 3.21832i) q^{89} +(-2.26628 - 0.512072i) q^{90} +(-0.980247 + 2.11067i) q^{91} +(-4.58558 + 2.64748i) q^{92} +(1.06782 - 9.57090i) q^{93} +3.10476 q^{94} +(0.538722 + 0.933093i) q^{95} +(1.02701 - 1.39472i) q^{96} +(9.31815 - 9.31815i) q^{97} +(-1.70391 - 6.35908i) q^{98} +(-1.54047 + 2.93014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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