LMFDB - Embedded newform 961.2.c.i.439.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] 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("961.439"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,-3,16,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.1
Root			$-0.333129i$ of defining polynomial
Character	$\chi$	$=$	961.439
Dual form			961.2.c.i.521.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.69016 q^{2} +(0.709582 - 1.22903i) q^{3} +5.23694 q^{4} +(-0.304192 - 0.526876i) q^{5} +(-1.90889 + 3.30629i) q^{6} +(0.863440 - 1.49552i) q^{7} -8.70786 q^{8} +(0.492986 + 0.853878i) q^{9} +(0.818323 + 1.41738i) q^{10} +(-0.668696 - 1.15822i) q^{11} +(3.71604 - 6.43636i) q^{12} +(1.83533 + 3.17889i) q^{13} +(-2.32279 + 4.02318i) q^{14} -0.863396 q^{15} +12.9516 q^{16} +(-1.38141 + 2.39267i) q^{17} +(-1.32621 - 2.29706i) q^{18} +(1.28384 - 2.22367i) q^{19} +(-1.59303 - 2.75922i) q^{20} +(-1.22536 - 2.12239i) q^{21} +(1.79890 + 3.11578i) q^{22} +0.539261 q^{23} +(-6.17894 + 10.7022i) q^{24} +(2.31493 - 4.00958i) q^{25} +(-4.93733 - 8.55171i) q^{26} +5.65675 q^{27} +(4.52178 - 7.83195i) q^{28} +8.13087 q^{29} +2.32267 q^{30} -17.4262 q^{32} -1.89798 q^{33} +(3.71621 - 6.43666i) q^{34} -1.05061 q^{35} +(2.58174 + 4.47170i) q^{36} +(3.87249 - 6.70735i) q^{37} +(-3.45373 + 5.98203i) q^{38} +5.20928 q^{39} +(2.64886 + 4.58796i) q^{40} +(0.0520259 + 0.0901115i) q^{41} +(3.29642 + 5.70956i) q^{42} +(-1.50235 + 2.60215i) q^{43} +(-3.50192 - 6.06550i) q^{44} +(0.299925 - 0.519485i) q^{45} -1.45070 q^{46} -6.72498 q^{47} +(9.19025 - 15.9180i) q^{48} +(2.00894 + 3.47959i) q^{49} +(-6.22753 + 10.7864i) q^{50} +(1.96045 + 3.39559i) q^{51} +(9.61152 + 16.6476i) q^{52} +(1.39937 + 2.42378i) q^{53} -15.2175 q^{54} +(-0.406824 + 0.704640i) q^{55} +(-7.51871 + 13.0228i) q^{56} +(-1.82198 - 3.15576i) q^{57} -21.8733 q^{58} +(-0.233116 + 0.403769i) q^{59} -4.52155 q^{60} +5.11468 q^{61} +1.70266 q^{63} +20.9759 q^{64} +(1.11659 - 1.93398i) q^{65} +5.10586 q^{66} +(-4.14923 - 7.18668i) q^{67} +(-7.23436 + 12.5303i) q^{68} +(0.382650 - 0.662769i) q^{69} +2.82629 q^{70} +(-2.37935 - 4.12116i) q^{71} +(-4.29286 - 7.43545i) q^{72} +(3.75310 + 6.50055i) q^{73} +(-10.4176 + 18.0438i) q^{74} +(-3.28527 - 5.69026i) q^{75} +(6.72338 - 11.6452i) q^{76} -2.30951 q^{77} -14.0138 q^{78} +(-4.84948 + 8.39954i) q^{79} +(-3.93978 - 6.82390i) q^{80} +(2.53497 - 4.39070i) q^{81} +(-0.139958 - 0.242414i) q^{82} +(-8.34229 - 14.4493i) q^{83} +(-6.41715 - 11.1148i) q^{84} +1.68085 q^{85} +(4.04156 - 7.00019i) q^{86} +(5.76952 - 9.99310i) q^{87} +(5.82292 + 10.0856i) q^{88} +15.3163 q^{89} +(-0.806845 + 1.39750i) q^{90} +6.33879 q^{91} +2.82407 q^{92} +18.0912 q^{94} -1.56213 q^{95} +(-12.3653 + 21.4173i) q^{96} -1.27918 q^{97} +(-5.40437 - 9.36065i) q^{98} +(0.659316 - 1.14197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 3 q^{3} + 16 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} - 18 q^{11} - 8 q^{13} + 9 q^{14} + 36 q^{15} + 8 q^{16} - 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 3 * q^3 + 16 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 - 18 * q^11 - 8 * q^13 + 9 * q^14 + 36 * q^15 + 8 * q^16 - 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 + q^21 - 4 * q^22 + 44 * q^23 - 30 * q^24 - 13 * q^25 - 9 * q^26 + 36 * q^27 + 5 * q^28 + 24 * q^29 + 22 * q^30 - 42 * q^32 + 12 * q^33 + 7 * q^34 - 24 * q^35 + q^36 + 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 + 36 * q^46 - 36 * q^47 + q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 + q^52 - 6 * q^53 - 14 * q^54 - 28 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 4 * q^59 - 80 * q^60 + 60 * q^61 - 46 * q^63 + 18 * q^64 - 3 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 + 33 * q^76 - 48 * q^77 - 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 - 39 * q^83 - 8 * q^84 - 52 * q^85 + 16 * q^86 + 15 * q^87 + 17 * q^88 + 54 * q^89 - 8 * q^90 + 32 * q^91 + 64 * q^92 + 44 * q^94 - 12 * q^95 + 12 * q^96 + 68 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.69016			−1.90223			−0.951114	−	0.308841i	$-0.900059\pi$
$2$	−2.69016			−1.90223			−0.951114	+	0.308841i	$0.900059\pi$
$3$	0.709582	−	1.22903i	0.409677	−	0.709582i	−0.585176	−	0.810906i	$-0.698975\pi$
$3$	0.709582	−	1.22903i	0.409677	−	0.709582i	0.994853	+	0.101324i	$0.0323079\pi$
$4$	5.23694			2.61847
$5$	−0.304192	−	0.526876i	−0.136039	−	0.235626i	0.789955	−	0.613165i	$-0.210104\pi$
$5$	−0.304192	−	0.526876i	−0.136039	−	0.235626i	−0.925994	+	0.377539i	$0.876770\pi$
$6$	−1.90889	+	3.30629i	−0.779300	+	1.34979i
$7$	0.863440	−	1.49552i	0.326349	−	0.565254i	−0.655435	−	0.755252i	$-0.727515\pi$
$7$	0.863440	−	1.49552i	0.326349	−	0.565254i	0.981785	+	0.189998i	$0.0608480\pi$
$8$	−8.70786			−3.07869
$9$	0.492986	+	0.853878i	0.164329	+	0.284626i
$10$	0.818323	+	1.41738i	0.258777	+	0.448214i
$11$	−0.668696	−	1.15822i	−0.201619	−	0.349215i	0.747431	−	0.664340i	$-0.231287\pi$
$11$	−0.668696	−	1.15822i	−0.201619	−	0.349215i	−0.949050	+	0.315124i	$0.897954\pi$
$12$	3.71604	−	6.43636i	1.07273	−	1.85802i
$13$	1.83533	+	3.17889i	0.509030	+	0.881665i	0.999945	+	0.0104581i	$0.00332898\pi$
$13$	1.83533	+	3.17889i	0.509030	+	0.881665i	−0.490916	+	0.871207i	$0.663338\pi$
$14$	−2.32279	+	4.02318i	−0.620791	+	1.07524i
$15$	−0.863396			−0.222928
$16$	12.9516			3.23791
$17$	−1.38141	+	2.39267i	−0.335041	+	0.580308i	−0.983493	−	0.180948i	$-0.942084\pi$
$17$	−1.38141	+	2.39267i	−0.335041	+	0.580308i	0.648452	+	0.761256i	$0.275417\pi$
$18$	−1.32621	−	2.29706i	−0.312591	−	0.541423i
$19$	1.28384	−	2.22367i	0.294533	−	0.510146i	−0.680343	−	0.732894i	$-0.738169\pi$
$19$	1.28384	−	2.22367i	0.294533	−	0.510146i	0.974876	+	0.222748i	$0.0715026\pi$
$20$	−1.59303	−	2.75922i	−0.356213	−	0.616979i
$21$	−1.22536	−	2.12239i	−0.267396	−	0.463143i
$22$	1.79890	+	3.11578i	0.383526	+	0.664287i
$23$	0.539261			0.112444			0.0562218	−	0.998418i	$-0.482095\pi$
$23$	0.539261			0.112444			0.0562218	+	0.998418i	$0.482095\pi$
$24$	−6.17894	+	10.7022i	−1.26127	+	2.18459i
$25$	2.31493	−	4.00958i	0.462987	−	0.801917i
$26$	−4.93733	−	8.55171i	−0.968290	−	1.67713i
$27$	5.65675			1.08864
$28$	4.52178	−	7.83195i	0.854536	−	1.48010i
$29$	8.13087			1.50986			0.754932	−	0.655803i	$-0.227670\pi$
$29$	8.13087			1.50986			0.754932	+	0.655803i	$0.227670\pi$
$30$	2.32267			0.424060
$31$		0			0
$31$		0			0
$32$	−17.4262			−3.08054
$33$	−1.89798			−0.330396
$34$	3.71621	−	6.43666i	0.637324	−	1.10388i
$35$	−1.05061			−0.177585
$36$	2.58174	+	4.47170i	0.430290	+	0.745284i
$37$	3.87249	−	6.70735i	0.636633	−	1.10268i	−0.349533	−	0.936924i	$-0.613660\pi$
$37$	3.87249	−	6.70735i	0.636633	−	1.10268i	0.986167	−	0.165757i	$-0.0530068\pi$
$38$	−3.45373	+	5.98203i	−0.560268	+	0.970413i
$39$	5.20928			0.834152
$40$	2.64886	+	4.58796i	0.418822	+	0.725421i
$41$	0.0520259	+	0.0901115i	0.00812508	+	0.0140731i	0.870059	−	0.492947i	$-0.164080\pi$
$41$	0.0520259	+	0.0901115i	0.00812508	+	0.0140731i	−0.861934	+	0.507020i	$0.830747\pi$
$42$	3.29642	+	5.70956i	0.508648	+	0.881004i
$43$	−1.50235	+	2.60215i	−0.229106	+	0.396824i	−0.957544	−	0.288289i	$-0.906914\pi$
$43$	−1.50235	+	2.60215i	−0.229106	+	0.396824i	0.728437	+	0.685113i	$0.240247\pi$
$44$	−3.50192	−	6.06550i	−0.527934	−	0.914409i
$45$	0.299925	−	0.519485i	0.0447102	−	0.0774403i
$46$	−1.45070			−0.213893
$47$	−6.72498			−0.980939			−0.490470	−	0.871458i	$-0.663175\pi$
$47$	−6.72498			−0.980939			−0.490470	+	0.871458i	$0.663175\pi$
$48$	9.19025	−	15.9180i	1.32650	−	2.29756i
$49$	2.00894	+	3.47959i	0.286992	+	0.497085i
$50$	−6.22753	+	10.7864i	−0.880706	+	1.52543i
$51$	1.96045	+	3.39559i	0.274518	+	0.475478i
$52$	9.61152	+	16.6476i	1.33288	+	2.30861i
$53$	1.39937	+	2.42378i	0.192219	+	0.332932i	0.945985	−	0.324210i	$-0.105098\pi$
$53$	1.39937	+	2.42378i	0.192219	+	0.332932i	−0.753767	+	0.657142i	$0.771765\pi$
$54$	−15.2175			−2.07084
$55$	−0.406824	+	0.704640i	−0.0548561	+	0.0950136i
$56$	−7.51871	+	13.0228i	−1.00473	+	1.74024i
$57$	−1.82198	−	3.15576i	−0.241327	−	0.417990i
$58$	−21.8733			−2.87210
$59$	−0.233116	+	0.403769i	−0.0303492	+	0.0525663i	−0.880801	−	0.473487i	$-0.842995\pi$
$59$	−0.233116	+	0.403769i	−0.0303492	+	0.0525663i	0.850452	+	0.526053i	$0.176329\pi$
$60$	−4.52155			−0.583730
$61$	5.11468			0.654867			0.327434	−	0.944874i	$-0.393816\pi$
$61$	5.11468			0.654867			0.327434	+	0.944874i	$0.393816\pi$
$62$		0			0
$63$	1.70266			0.214514
$64$	20.9759			2.62198
$65$	1.11659	−	1.93398i	0.138496	−	0.239881i
$66$	5.10586			0.628488
$67$	−4.14923	−	7.18668i	−0.506910	−	0.877993i	−0.999968	−	0.00799701i	$-0.997454\pi$
$67$	−4.14923	−	7.18668i	−0.506910	−	0.877993i	0.493058	−	0.869996i	$-0.335879\pi$
$68$	−7.23436	+	12.5303i	−0.877294	+	1.51952i
$69$	0.382650	−	0.662769i	0.0460656	−	0.0797880i
$70$	2.82629			0.337806
$71$	−2.37935	−	4.12116i	−0.282377	−	0.489092i	0.689592	−	0.724198i	$-0.257790\pi$
$71$	−2.37935	−	4.12116i	−0.282377	−	0.489092i	−0.971970	+	0.235106i	$0.924456\pi$
$72$	−4.29286	−	7.43545i	−0.505918	−	0.876276i
$73$	3.75310	+	6.50055i	0.439267	+	0.760832i	0.997633	−	0.0687624i	$-0.0219050\pi$
$73$	3.75310	+	6.50055i	0.439267	+	0.760832i	−0.558367	+	0.829594i	$0.688572\pi$
$74$	−10.4176	+	18.0438i	−1.21102	+	2.09755i
$75$	−3.28527	−	5.69026i	−0.379351	−	0.657054i
$76$	6.72338	−	11.6452i	0.771225	−	1.33580i
$77$	−2.30951			−0.263194
$78$	−14.0138			−1.58675
$79$	−4.84948	+	8.39954i	−0.545609	+	0.945022i	0.452959	+	0.891531i	$0.350368\pi$
$79$	−4.84948	+	8.39954i	−0.545609	+	0.945022i	−0.998568	+	0.0534912i	$0.982965\pi$
$80$	−3.93978	−	6.82390i	−0.440481	−	0.762935i
$81$	2.53497	−	4.39070i	0.281663	−	0.487855i
$82$	−0.139958	−	0.242414i	−0.0154558	−	0.0267702i
$83$	−8.34229	−	14.4493i	−0.915686	−	1.58601i	−0.805894	−	0.592059i	$-0.798315\pi$
$83$	−8.34229	−	14.4493i	−0.915686	−	1.58601i	−0.109791	−	0.993955i	$-0.535018\pi$
$84$	−6.41715	−	11.1148i	−0.700168	−	1.21273i
$85$	1.68085			0.182314
$86$	4.04156	−	7.00019i	0.435813	−	0.754850i
$87$	5.76952	−	9.99310i	0.618557	−	1.07137i
$88$	5.82292	+	10.0856i	0.620725	+	1.07513i
$89$	15.3163			1.62352			0.811761	−	0.583990i	$-0.198509\pi$
$89$	15.3163			1.62352			0.811761	+	0.583990i	$0.198509\pi$
$90$	−0.806845	+	1.39750i	−0.0850489	+	0.147309i
$91$	6.33879			0.664486
$92$	2.82407			0.294430
$93$		0			0
$94$	18.0912			1.86597
$95$	−1.56213			−0.160271
$96$	−12.3653	+	21.4173i	−1.26203	+	2.18590i
$97$	−1.27918			−0.129881			−0.0649404	−	0.997889i	$-0.520686\pi$
$97$	−1.27918			−0.129881			−0.0649404	+	0.997889i	$0.520686\pi$
$98$	−5.40437	−	9.36065i	−0.545924	−	0.945568i
$99$	0.659316	−	1.14197i	0.0662638	−	0.114772i
$100$	12.1232	−	20.9979i	1.21232	−	2.09979i
$101$	8.12024			0.807994			0.403997	−	0.914760i	$-0.367621\pi$
$101$	8.12024			0.807994			0.403997	+	0.914760i	$0.367621\pi$
$102$	−5.27391	−	9.13468i	−0.522195	−	0.904468i
$103$	−7.57625	−	13.1225i	−0.746511	−	1.29299i	−0.949486	−	0.313810i	$-0.898394\pi$
$103$	−7.57625	−	13.1225i	−0.746511	−	1.29299i	0.202975	−	0.979184i	$-0.434939\pi$
$104$	−15.9818	−	27.6813i	−1.56715	−	2.71438i
$105$	−0.745491	+	1.29123i	−0.0727524	+	0.126011i
$106$	−3.76453	−	6.52036i	−0.365643	−	0.633313i
$107$	6.18781	−	10.7176i	0.598198	−	1.03611i	−0.394889	−	0.918729i	$-0.629217\pi$
$107$	6.18781	−	10.7176i	0.598198	−	1.03611i	0.993087	−	0.117380i	$-0.0374496\pi$
$108$	29.6240			2.85057
$109$	7.20958			0.690553			0.345276	−	0.938501i	$-0.387785\pi$
$109$	7.20958			0.690553			0.345276	+	0.938501i	$0.387785\pi$
$110$	1.09442	−	1.89559i	0.104349	−	0.180737i
$111$	−5.49570	−	9.51883i	−0.521628	−	0.903487i
$112$	11.1830	−	19.3694i	1.05669	−	1.83024i
$113$	−8.33590	−	14.4382i	−0.784176	−	1.35823i	−0.929490	−	0.368846i	$-0.879753\pi$
$113$	−8.33590	−	14.4382i	−0.784176	−	1.35823i	0.145315	−	0.989385i	$-0.453580\pi$
$114$	4.90140	+	8.48948i	0.459059	+	0.795113i
$115$	−0.164039	−	0.284123i	−0.0152967	−	0.0264946i
$116$	42.5808			3.95353
$117$	−1.80959	+	3.13430i	−0.167296	+	0.289766i
$118$	0.627119	−	1.08620i	0.0577310	−	0.0999930i
$119$	2.38553	+	4.13185i	0.218681	+	0.378767i
$120$	7.51834			0.686327
$121$	4.60569	−	7.97729i	0.418699	−	0.725208i
$122$	−13.7593			−1.24571
$123$	0.147667			0.0133147
$124$		0			0
$125$	−5.85866			−0.524014
$126$	−4.58041			−0.408055
$127$	−6.45472	+	11.1799i	−0.572764	+	0.992056i	0.423517	+	0.905888i	$0.360795\pi$
$127$	−6.45472	+	11.1799i	−0.572764	+	0.992056i	−0.996281	+	0.0861675i	$0.972538\pi$
$128$	−21.5760			−1.90707
$129$	2.13208	+	3.69288i	0.187720	+	0.325140i
$130$	−3.00379	+	5.20272i	−0.263450	+	0.456309i
$131$	1.21889	−	2.11118i	0.106495	−	0.184455i	−0.807853	−	0.589384i	$-0.799370\pi$
$131$	1.21889	−	2.11118i	0.106495	−	0.184455i	0.914348	+	0.404929i	$0.132704\pi$
$132$	−9.93960			−0.865131
$133$	−2.21703	−	3.84002i	−0.192241	−	0.332972i
$134$	11.1621	+	19.3333i	0.964257	+	1.67014i
$135$	−1.72074	−	2.98040i	−0.148097	−	0.256512i
$136$	12.0291	−	20.8351i	1.03149	−	1.78659i
$137$	4.07191	+	7.05276i	0.347887	+	0.602558i	0.985874	−	0.167489i	$-0.0535660\pi$
$137$	4.07191	+	7.05276i	0.347887	+	0.602558i	−0.637987	+	0.770047i	$0.720233\pi$
$138$	−1.02939	+	1.78295i	−0.0876273	+	0.151775i
$139$	1.35336			0.114791			0.0573954	−	0.998352i	$-0.481720\pi$
$139$	1.35336			0.114791			0.0573954	+	0.998352i	$0.481720\pi$
$140$	−5.50195			−0.465000
$141$	−4.77193	+	8.26522i	−0.401869	+	0.696057i
$142$	6.40083	+	11.0866i	0.537146	+	0.930364i
$143$	2.45456	−	4.25142i	0.205261	−	0.355522i
$144$	6.38498	+	11.0591i	0.532082	+	0.921592i
$145$	−2.47334	−	4.28396i	−0.205400	−	0.355763i
$146$	−10.0964	−	17.4875i	−0.835585	−	1.44728i
$147$	5.70204			0.470297
$148$	20.2800	−	35.1260i	1.66700	−	2.88734i
$149$	4.50192	−	7.79756i	0.368812	−	0.638801i	−0.620568	−	0.784153i	$-0.713098\pi$
$149$	4.50192	−	7.79756i	0.368812	−	0.638801i	0.989380	+	0.145351i	$0.0464313\pi$
$150$	8.83789	+	15.3077i	0.721611	+	1.24987i
$151$	3.20841			0.261097			0.130548	−	0.991442i	$-0.458326\pi$
$151$	3.20841			0.261097			0.130548	+	0.991442i	$0.458326\pi$
$152$	−11.1795	+	19.3634i	−0.906777	+	1.57058i
$153$	−2.72407			−0.220228
$154$	6.21295			0.500654
$155$		0			0
$156$	27.2807			2.18420
$157$	−3.32677			−0.265505			−0.132753	−	0.991149i	$-0.542382\pi$
$157$	−3.32677			−0.265505			−0.132753	+	0.991149i	$0.542382\pi$
$158$	13.0458	−	22.5961i	1.03787	−	1.79765i
$159$	3.97188			0.314991
$160$	5.30090	+	9.18143i	0.419073	+	0.725856i
$161$	0.465619	−	0.806476i	0.0366959	−	0.0635592i
$162$	−6.81946	+	11.8117i	−0.535788	+	0.928011i
$163$	1.74035			0.136314			0.0681572	−	0.997675i	$-0.478288\pi$
$163$	1.74035			0.136314			0.0681572	+	0.997675i	$0.478288\pi$
$164$	0.272456	+	0.471908i	0.0212753	+	0.0368499i
$165$	0.577350	+	0.999999i	0.0449466	+	0.0778499i
$166$	22.4421	+	38.8708i	1.74184	+	3.01696i
$167$	−7.00824	+	12.1386i	−0.542314	+	0.939315i	0.456457	+	0.889745i	$0.349118\pi$
$167$	−7.00824	+	12.1386i	−0.542314	+	0.939315i	−0.998771	+	0.0495694i	$0.984215\pi$
$168$	10.6703	+	18.4815i	0.823231	+	1.42588i
$169$	−0.236891	+	0.410307i	−0.0182224	+	0.0315621i
$170$	−4.52176			−0.346803
$171$	2.53166			0.193601
$172$	−7.86772	+	13.6273i	−0.599908	+	1.03907i
$173$	0.00599044	+	0.0103757i	0.000455445	+	0.000788854i	0.866253	−	0.499606i	$-0.166522\pi$
$173$	0.00599044	+	0.0103757i	0.000455445	+	0.000788854i	−0.865798	+	0.500394i	$0.833188\pi$
$174$	−15.5209	+	26.8830i	−1.17664	+	2.03799i
$175$	−3.99761	−	6.92407i	−0.302191	−	0.523410i
$176$	−8.66071	−	15.0008i	−0.652825	−	1.13073i
$177$	0.330830	+	0.573015i	0.0248667	+	0.0430704i
$178$	−41.2032			−3.08831
$179$	−4.98900	+	8.64121i	−0.372896	+	0.645874i	−0.990010	−	0.141000i	$-0.954968\pi$
$179$	−4.98900	+	8.64121i	−0.372896	+	0.645874i	0.617114	+	0.786874i	$0.288302\pi$
$180$	1.57069	−	2.72051i	0.117072	−	0.202775i
$181$	−9.30158	−	16.1108i	−0.691381	−	1.19751i	−0.971385	−	0.237509i	$-0.923669\pi$
$181$	−9.30158	−	16.1108i	−0.691381	−	1.19751i	0.280004	−	0.959999i	$-0.409664\pi$
$182$	−17.0523			−1.26400
$183$	3.62928	−	6.28610i	0.268284	−	0.464682i
$184$	−4.69581			−0.346180
$185$	−4.71192			−0.346427
$186$		0			0
$187$	3.69497			0.270203
$188$	−35.2183			−2.56856
$189$	4.88426	−	8.45979i	0.355278	−	0.615359i
$190$	4.20238			0.304873
$191$	−0.599059	−	1.03760i	−0.0433464	−	0.0750782i	0.843538	−	0.537069i	$-0.180469\pi$
$191$	−0.599059	−	1.03760i	−0.0433464	−	0.0750782i	−0.886885	+	0.461991i	$0.847135\pi$
$192$	14.8841	−	25.7800i	1.07417	−	1.86051i
$193$	−6.36328	+	11.0215i	−0.458039	+	0.793347i	−0.998857	−	0.0477928i	$-0.984781\pi$
$193$	−6.36328	+	11.0215i	−0.458039	+	0.793347i	0.540818	+	0.841139i	$0.318115\pi$
$194$	3.44118			0.247063
$195$	−1.58462	−	2.74464i	−0.113477	−	0.196548i
$196$	10.5207	+	18.2224i	0.751480	+	1.30160i
$197$	−1.48430	−	2.57088i	−0.105752	−	0.183168i	0.808293	−	0.588780i	$-0.200392\pi$
$197$	−1.48430	−	2.57088i	−0.105752	−	0.183168i	−0.914045	+	0.405612i	$0.867058\pi$
$198$	−1.77366	+	3.07208i	−0.126049	+	0.218323i
$199$	−6.59203	−	11.4177i	−0.467296	−	0.809381i	0.532005	−	0.846741i	$-0.321439\pi$
$199$	−6.59203	−	11.4177i	−0.467296	−	0.809381i	−0.999302	+	0.0373598i	$0.988105\pi$
$200$	−20.1581	+	34.9149i	−1.42540	+	2.46886i
$201$	−11.7769			−0.830678
$202$	−21.8447			−1.53699
$203$	7.02051	−	12.1599i	0.492743	−	0.853457i
$204$	10.2667	+	17.7825i	0.718815	+	1.24502i
$205$	0.0316517	−	0.0548224i	0.00221065	−	0.00382896i
$206$	20.3813	+	35.3015i	1.42003	+	2.45957i
$207$	0.265848	+	0.460463i	0.0184777	+	0.0320044i
$208$	23.7706	+	41.1718i	1.64819	+	2.85475i
$209$	−3.43399			−0.237534
$210$	2.00549	−	3.47360i	0.138392	−	0.239701i
$211$	−9.16614	+	15.8762i	−0.631023	+	1.09296i	0.356320	+	0.934364i	$0.384031\pi$
$211$	−9.16614	+	15.8762i	−0.631023	+	1.09296i	−0.987343	+	0.158600i	$0.949302\pi$
$212$	7.32843	+	12.6932i	0.503318	+	0.871773i
$213$	−6.75339			−0.462735
$214$	−16.6462	+	28.8320i	−1.13791	+	1.97091i
$215$	1.82801			0.124669
$216$	−49.2582			−3.35160
$217$		0			0
$218$	−19.3949			−1.31359
$219$	10.6525			0.719830
$220$	−2.13051	+	3.69015i	−0.143639	+	0.248790i
$221$	−10.1414			−0.682183
$222$	14.7843	+	25.6071i	0.992256	+	1.71864i
$223$	4.69801	−	8.13718i	0.314602	−	0.544906i	−0.664751	−	0.747065i	$-0.731462\pi$
$223$	4.69801	−	8.13718i	0.314602	−	0.544906i	0.979353	+	0.202159i	$0.0647957\pi$
$224$	−15.0465	+	26.0612i	−1.00533	+	1.74129i
$225$	4.56493			0.304328
$226$	22.4249	+	38.8410i	1.49168	+	2.58367i
$227$	−4.22971	−	7.32607i	−0.280736	−	0.486249i	0.690830	−	0.723017i	$-0.257245\pi$
$227$	−4.22971	−	7.32607i	−0.280736	−	0.486249i	−0.971566	+	0.236768i	$0.923912\pi$
$228$	−9.54158	−	16.5265i	−0.631907	−	1.09449i
$229$	11.4217	−	19.7830i	0.754768	−	1.30730i	−0.190721	−	0.981644i	$-0.561083\pi$
$229$	11.4217	−	19.7830i	0.754768	−	1.30730i	0.945489	−	0.325653i	$-0.105584\pi$
$230$	0.441290	+	0.764336i	0.0290978	+	0.0503988i
$231$	−1.63879	+	2.83847i	−0.107824	+	0.186758i
$232$	−70.8025			−4.64841
$233$	16.2535			1.06480			0.532400	−	0.846493i	$-0.321290\pi$
$233$	16.2535			1.06480			0.532400	+	0.846493i	$0.321290\pi$
$234$	4.86807	−	8.43175i	0.318236	−	0.551201i
$235$	2.04568	+	3.54323i	0.133446	+	0.231135i
$236$	−1.22082	+	2.11451i	−0.0794683	+	0.137643i
$237$	6.88221	+	11.9203i	0.447047	+	0.774309i
$238$	−6.41744	−	11.1153i	−0.415981	−	0.720500i
$239$	9.13650	+	15.8249i	0.590991	+	1.02363i	0.994099	+	0.108474i	$0.0345964\pi$
$239$	9.13650	+	15.8249i	0.590991	+	1.02363i	−0.403108	+	0.915152i	$0.632070\pi$
$240$	−11.1824			−0.721820
$241$	−9.08577	+	15.7370i	−0.585266	+	1.01371i	0.409576	+	0.912276i	$0.365677\pi$
$241$	−9.08577	+	15.7370i	−0.585266	+	1.01371i	−0.994842	+	0.101435i	$0.967657\pi$
$242$	−12.3900	+	21.4602i	−0.796461	+	1.37951i
$243$	4.88759	+	8.46555i	0.313539	+	0.543065i
$244$	26.7852			1.71475
$245$	1.22221	−	2.11693i	0.0780841	−	0.135246i
$246$	−0.397246			−0.0253275
$247$	9.42508			0.599704
$248$		0			0
$249$	−23.6782			−1.50054
$250$	15.7607			0.996794
$251$	−11.4651	+	19.8581i	−0.723671	+	1.25344i	0.235848	+	0.971790i	$0.424213\pi$
$251$	−11.4651	+	19.8581i	−0.723671	+	1.25344i	−0.959519	+	0.281645i	$0.909120\pi$
$252$	8.91670			0.561699
$253$	−0.360602	−	0.624580i	−0.0226708	−	0.0392670i
$254$	17.3642	−	30.0757i	1.08953	−	1.88712i
$255$	1.19270	−	2.06582i	0.0746900	−	0.129367i
$256$	16.0910			1.00569
$257$	−0.0530965	−	0.0919659i	−0.00331207	−	0.00573667i	0.864365	−	0.502866i	$-0.167721\pi$
$257$	−0.0530965	−	0.0919659i	−0.00331207	−	0.00573667i	−0.867677	+	0.497129i	$0.834388\pi$
$258$	−5.73564	−	9.93441i	−0.357085	−	0.618490i
$259$	−6.68732	−	11.5828i	−0.415530	−	0.719719i
$260$	5.84749	−	10.1282i	0.362646	−	0.628121i
$261$	4.00841	+	6.94277i	0.248114	+	0.429746i
$262$	−3.27901	+	5.67941i	−0.202578	+	0.350875i
$263$	7.29731			0.449971			0.224986	−	0.974362i	$-0.427766\pi$
$263$	7.29731			0.449971			0.224986	+	0.974362i	$0.427766\pi$
$264$	16.5273			1.01719
$265$	0.851356	−	1.47459i	0.0522984	−	0.0905834i
$266$	5.96417	+	10.3302i	0.365687	+	0.633388i
$267$	10.8682	−	18.8242i	0.665120	−	1.15202i
$268$	−21.7293	−	37.6362i	−1.32733	−	2.29900i
$269$	8.10968	+	14.0464i	0.494456	+	0.856423i	0.999980	−	0.00638992i	$-0.00203399\pi$
$269$	8.10968	+	14.0464i	0.494456	+	0.856423i	−0.505524	+	0.862813i	$0.668701\pi$
$270$	4.62905	+	8.01775i	0.281715	+	0.487945i
$271$	5.14564			0.312575			0.156288	−	0.987712i	$-0.450047\pi$
$271$	5.14564			0.312575			0.156288	+	0.987712i	$0.450047\pi$
$272$	−17.8915	+	30.9890i	−1.08483	+	1.87898i
$273$	4.49790	−	7.79058i	0.272225	−	0.471508i
$274$	−10.9541	−	18.9730i	−0.661760	−	1.14620i
$275$	−6.19195			−0.373389
$276$	2.00391	−	3.47088i	0.120621	−	0.208922i
$277$	16.9228			1.01679			0.508397	−	0.861123i	$-0.330238\pi$
$277$	16.9228			1.01679			0.508397	+	0.861123i	$0.330238\pi$
$278$	−3.64076			−0.218358
$279$		0			0
$280$	9.14853			0.546729
$281$	1.90667			0.113742			0.0568711	−	0.998382i	$-0.481888\pi$
$281$	1.90667			0.113742			0.0568711	+	0.998382i	$0.481888\pi$
$282$	12.8372	−	22.2347i	0.764445	−	1.32406i
$283$	−15.3098			−0.910074			−0.455037	−	0.890473i	$-0.650374\pi$
$283$	−15.3098			−0.910074			−0.455037	+	0.890473i	$0.650374\pi$
$284$	−12.4605	−	21.5823i	−0.739396	−	1.28067i
$285$	−1.10846	+	1.91991i	−0.0656596	+	0.113726i
$286$	−6.60315	+	11.4370i	−0.390452	+	0.676283i
$287$	0.179685			0.0106065
$288$	−8.59087	−	14.8798i	−0.506222	−	0.876802i
$289$	4.68341	+	8.11191i	0.275495	+	0.477171i
$290$	6.65368	+	11.5245i	0.390718	+	0.676743i
$291$	−0.907681	+	1.57215i	−0.0532092	+	0.0921610i
$292$	19.6547	+	34.0430i	1.15021	+	1.99221i
$293$	−13.3968	+	23.2040i	−0.782651	+	1.35559i	0.147741	+	0.989026i	$0.452800\pi$
$293$	−13.3968	+	23.2040i	−0.782651	+	1.35559i	−0.930392	+	0.366566i	$0.880533\pi$
$294$	−15.3394			−0.894611
$295$	0.283648			0.0165146
$296$	−33.7211	+	58.4067i	−1.96000	+	3.39482i
$297$	−3.78265	−	6.55174i	−0.219491	−	0.380170i
$298$	−12.1109	+	20.9767i	−0.701564	+	1.21514i
$299$	0.989723	+	1.71425i	0.0572371	+	0.0991376i
$300$	−17.2048	−	29.7995i	−0.993317	−	1.72048i
$301$	2.59438	+	4.49360i	0.149538	+	0.259007i
$302$	−8.63112			−0.496665
$303$	5.76198	−	9.98004i	0.331017	−	0.573338i
$304$	16.6278	−	28.8002i	0.953670	−	1.65181i
$305$	−1.55584	−	2.69480i	−0.0890873	−	0.154304i
$306$	7.32816			0.418923
$307$	−4.47563	+	7.75202i	−0.255438	+	0.442431i	−0.965014	−	0.262197i	$-0.915553\pi$
$307$	−4.47563	+	7.75202i	−0.255438	+	0.442431i	0.709577	+	0.704628i	$0.248886\pi$
$308$	−12.0948			−0.689164
$309$	−21.5039			−1.22331
$310$		0			0
$311$	20.6556			1.17127			0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556			1.17127			0.585637	+	0.810574i	$0.300844\pi$
$312$	−45.3617			−2.56810
$313$	0.225660	−	0.390855i	0.0127551	−	0.0220924i	−0.859577	−	0.511006i	$-0.829273\pi$
$313$	0.225660	−	0.390855i	0.0127551	−	0.0220924i	0.872332	+	0.488913i	$0.162606\pi$
$314$	8.94953			0.505051
$315$	−0.517934	−	0.897088i	−0.0291823	−	0.0505452i
$316$	−25.3964	+	43.9879i	−1.42866	+	2.47451i
$317$	2.79042	−	4.83315i	0.156726	−	0.271457i	−0.776960	−	0.629550i	$-0.783239\pi$
$317$	2.79042	−	4.83315i	0.156726	−	0.271457i	0.933686	+	0.358093i	$0.116573\pi$
$318$	−10.6850			−0.599184
$319$	−5.43708	−	9.41730i	−0.304418	−	0.527268i
$320$	−6.38069	−	11.0517i	−0.356691	−	0.617808i
$321$	−8.78151	−	15.2100i	−0.490136	−	0.848941i
$322$	−1.25259	+	2.16955i	−0.0698040	+	0.120904i
$323$	3.54701	+	6.14361i	0.197361	+	0.341840i
$324$	13.2755	−	22.9938i	0.737526	−	1.27743i
$325$	16.9947			0.942696
$326$	−4.68180			−0.259301
$327$	5.11579	−	8.86081i	0.282904	−	0.490004i
$328$	−0.453035	−	0.784679i	−0.0250147	−	0.0433267i
$329$	−5.80661	+	10.0574i	−0.320129	+	0.554480i
$330$	−1.55316	−	2.69015i	−0.0854987	−	0.148088i
$331$	12.1027	+	20.9625i	0.665226	+	1.15221i	0.979224	+	0.202782i	$0.0649982\pi$
$331$	12.1027	+	20.9625i	0.665226	+	1.15221i	−0.313998	+	0.949424i	$0.601668\pi$
$332$	−43.6881	−	75.6699i	−2.39769	−	4.15293i
$333$	7.63634			0.418469
$334$	18.8532	−	32.6548i	1.03160	−	1.78679i
$335$	−2.52433	+	4.37226i	−0.137919	+	0.238882i
$336$	−15.8704	−	27.4884i	−0.865804	−	1.49962i
$337$	−11.0360			−0.601168			−0.300584	−	0.953755i	$-0.597182\pi$
$337$	−11.0360			−0.601168			−0.300584	+	0.953755i	$0.597182\pi$
$338$	0.637273	−	1.10379i	0.0346631	−	0.0600382i
$339$	−23.6600			−1.28504
$340$	8.80253			0.477384
$341$		0			0
$342$	−6.81056			−0.368273
$343$	19.0266			1.02734
$344$	13.0823	−	22.6592i	0.705349	−	1.22170i
$345$	−0.465596			−0.0250668
$346$	−0.0161152	−	0.0279124i	−0.000866360	−	0.00150058i
$347$	−9.28369	+	16.0798i	−0.498375	+	0.863210i	−0.999998	−	0.00187589i	$-0.999403\pi$
$347$	−9.28369	+	16.0798i	−0.498375	+	0.863210i	0.501624	+	0.865086i	$0.332736\pi$
$348$	30.2146	−	52.3332i	1.61967	−	2.80536i
$349$	−32.1746			−1.72227			−0.861134	−	0.508378i	$-0.830245\pi$
$349$	−32.1746			−1.72227			−0.861134	+	0.508378i	$0.830245\pi$
$350$	10.7542	+	18.6268i	0.574836	+	0.995645i
$351$	10.3820	+	17.9822i	0.554151	+	0.959818i
$352$	11.6528	+	20.1833i	0.621097	+	1.07577i
$353$	16.1067	−	27.8976i	0.857273	−	1.48484i	−0.0172478	−	0.999851i	$-0.505490\pi$
$353$	16.1067	−	27.8976i	0.857273	−	1.48484i	0.874520	−	0.484989i	$-0.161176\pi$
$354$	−0.889985	−	1.54150i	−0.0473022	−	0.0819298i
$355$	−1.44756	+	2.50725i	−0.0768285	+	0.133071i
$356$	80.2104			4.25114
$357$	6.77091			0.358355
$358$	13.4212	−	23.2462i	0.709332	−	1.22860i
$359$	−10.5811	−	18.3271i	−0.558451	−	0.967265i	−0.997626	−	0.0688636i	$-0.978063\pi$
$359$	−10.5811	−	18.3271i	−0.558451	−	0.967265i	0.439175	−	0.898401i	$-0.355271\pi$
$360$	−2.61171	+	4.52361i	−0.137649	+	0.238415i
$361$	6.20352	+	10.7448i	0.326501	+	0.565516i
$362$	25.0227	+	43.3406i	1.31516	+	2.27793i
$363$	−6.53623	−	11.3211i	−0.343063	−	0.594203i
$364$	33.1959			1.73994
$365$	2.28332	−	3.95483i	0.119515	−	0.207005i
$366$	−9.76334	+	16.9106i	−0.510338	+	0.883931i
$367$	6.49822	+	11.2552i	0.339204	+	0.587519i	0.984283	−	0.176597i	$-0.0565089\pi$
$367$	6.49822	+	11.2552i	0.339204	+	0.587519i	−0.645079	+	0.764116i	$0.723176\pi$
$368$	6.98431			0.364082
$369$	−0.0512962	+	0.0888475i	−0.00267037	+	0.00462522i
$370$	12.6758			0.658983
$371$	4.83309			0.250922
$372$		0			0
$373$	−4.42592			−0.229166			−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592			−0.229166			−0.114583	+	0.993414i	$0.536553\pi$
$374$	−9.94005			−0.513988
$375$	−4.15720	+	7.20048i	−0.214677	+	0.371831i
$376$	58.5602			3.02001
$377$	14.9228	+	25.8471i	0.768566	+	1.33119i
$378$	−13.1394	+	22.7581i	−0.675819	+	1.17055i
$379$	7.47787	−	12.9520i	0.384112	−	0.665302i	−0.607533	−	0.794294i	$-0.707841\pi$
$379$	7.47787	−	12.9520i	0.384112	−	0.665302i	0.991646	+	0.128992i	$0.0411742\pi$
$380$	−8.18079			−0.419666
$381$	9.16030	+	15.8661i	0.469297	+	0.812846i
$382$	1.61156	+	2.79131i	0.0824547	+	0.142816i
$383$	−5.82517	−	10.0895i	−0.297652	−	0.515549i	0.677946	−	0.735112i	$-0.262870\pi$
$383$	−5.82517	−	10.0895i	−0.297652	−	0.515549i	−0.975598	+	0.219563i	$0.929537\pi$
$384$	−15.3099	+	26.5176i	−0.781282	+	1.35322i
$385$	0.702536	+	1.21683i	0.0358045	+	0.0620153i
$386$	17.1182	−	29.6496i	0.871294	−	1.50913i
$387$	−2.96256			−0.150595
$388$	−6.69897			−0.340089
$389$	7.20097	−	12.4724i	0.365103	−	0.632378i	−0.623689	−	0.781672i	$-0.714367\pi$
$389$	7.20097	−	12.4724i	0.365103	−	0.632378i	0.988793	+	0.149295i	$0.0477003\pi$
$390$	4.26287	+	7.38351i	0.215859	+	0.373879i
$391$	−0.744940	+	1.29027i	−0.0376732	+	0.0652520i
$392$	−17.4936	−	30.2998i	−0.883561	−	1.53037i
$393$	−1.72981	−	2.99612i	−0.0872573	−	0.151134i
$394$	3.99299	+	6.91607i	0.201164	+	0.348426i
$395$	5.90069			0.296896
$396$	3.45280	−	5.98042i	0.173510	−	0.300527i
$397$	−7.89506	+	13.6746i	−0.396242	+	0.686311i	−0.993259	−	0.115918i	$-0.963019\pi$
$397$	−7.89506	+	13.6746i	−0.396242	+	0.686311i	0.597017	+	0.802229i	$0.296352\pi$
$398$	17.7336	+	30.7155i	0.888904	+	1.53963i
$399$	−6.29267			−0.315028
$400$	29.9822	−	51.9307i	1.49911	−	2.59653i
$401$	−31.0232			−1.54923			−0.774613	−	0.632436i	$-0.782055\pi$
$401$	−31.0232			−1.54923			−0.774613	+	0.632436i	$0.782055\pi$
$402$	31.6817			1.58014
$403$		0			0
$404$	42.5252			2.11571
$405$	−3.08447			−0.153268
$406$	−18.8863	+	32.7120i	−0.937310	+	1.62347i
$407$	−10.3581			−0.513431
$408$	−17.0713	−	29.5684i	−0.845156	−	1.46385i
$409$	3.29291	−	5.70349i	0.162824	−	0.282019i	−0.773056	−	0.634337i	$-0.781273\pi$
$409$	3.29291	−	5.70349i	0.162824	−	0.282019i	0.935880	+	0.352318i	$0.114606\pi$
$410$	−0.0851481	+	0.147481i	−0.00420516	+	0.00728356i
$411$	11.5574			0.570086
$412$	−39.6764	−	68.7215i	−1.95471	−	3.38566i
$413$	0.402564	+	0.697261i	0.0198089	+	0.0343100i
$414$	−0.715173	−	1.23872i	−0.0351488	−	0.0608796i
$415$	−5.07532	+	8.79070i	−0.249137	+	0.431519i
$416$	−31.9828	−	55.3959i	−1.56809	−	2.71601i
$417$	0.960322	−	1.66333i	0.0470272	−	0.0814535i
$418$	9.23797			0.451844
$419$	−14.6720			−0.716773			−0.358387	−	0.933573i	$-0.616673\pi$
$419$	−14.6720			−0.716773			−0.358387	+	0.933573i	$0.616673\pi$
$420$	−3.90409	+	6.76208i	−0.190500	+	0.329956i
$421$	13.3579	+	23.1366i	0.651026	+	1.12761i	0.982874	+	0.184277i	$0.0589944\pi$
$421$	13.3579	+	23.1366i	0.651026	+	1.12761i	−0.331848	+	0.943333i	$0.607672\pi$
$422$	24.6583	−	42.7095i	1.20035	−	2.07907i
$423$	−3.31532	−	5.74231i	−0.161197	−	0.279201i
$424$	−12.1855	−	21.1060i	−0.591782	−	1.02500i
$425$	6.39575	+	11.0778i	0.310239	+	0.537350i
$426$	18.1677			0.880226
$427$	4.41621	−	7.64911i	0.213716	−	0.370166i
$428$	32.4052	−	56.1274i	1.56636	−	2.71302i
$429$	−3.48342	−	6.03347i	−0.168181	−	0.291299i
$430$	−4.91764			−0.237150
$431$	−1.99400	+	3.45372i	−0.0960478	+	0.166360i	−0.910045	−	0.414509i	$-0.863954\pi$
$431$	−1.99400	+	3.45372i	−0.0960478	+	0.166360i	0.813998	+	0.580868i	$0.197287\pi$
$432$	73.2642			3.52492
$433$	−18.0766			−0.868704			−0.434352	−	0.900743i	$-0.643023\pi$
$433$	−18.0766			−0.868704			−0.434352	+	0.900743i	$0.643023\pi$
$434$		0			0
$435$	−7.02016			−0.336591
$436$	37.7561			1.80819
$437$	0.692324	−	1.19914i	0.0331183	−	0.0573626i
$438$	−28.6569			−1.36928
$439$	−11.4543	−	19.8394i	−0.546684	−	0.946884i	−0.998499	−	0.0547723i	$-0.982557\pi$
$439$	−11.4543	−	19.8394i	−0.546684	−	0.946884i	0.451815	−	0.892112i	$-0.350777\pi$
$440$	3.54257	−	6.13591i	0.168885	−	0.292518i
$441$	−1.98076	+	3.43079i	−0.0943221	+	0.163371i
$442$	27.2819			1.29767
$443$	10.7457	+	18.6120i	0.510542	+	0.884284i	0.999925	+	0.0122154i	$0.00388839\pi$
$443$	10.7457	+	18.6120i	0.510542	+	0.884284i	−0.489384	+	0.872069i	$0.662778\pi$
$444$	−28.7806	−	49.8495i	−1.36587	−	2.36575i
$445$	−4.65909	−	8.06977i	−0.220862	−	0.382544i
$446$	−12.6384	+	21.8903i	−0.598444	+	1.03654i
$447$	−6.38897	−	11.0660i	−0.302188	−	0.523405i
$448$	18.1114	−	31.3699i	0.855683	−	1.48209i
$449$	−18.7996			−0.887209			−0.443604	−	0.896223i	$-0.646300\pi$
$449$	−18.7996			−0.887209			−0.443604	+	0.896223i	$0.646300\pi$
$450$	−12.2804			−0.578902
$451$	0.0695791	−	0.120515i	0.00327635	−	0.00567481i
$452$	−43.6546	−	75.6120i	−2.05334	−	3.55649i
$453$	2.27663	−	3.94324i	0.106965	−	0.185269i
$454$	11.3786	+	19.7083i	0.534023	+	0.924955i
$455$	−1.92821	−	3.33976i	−0.0903959	−	0.156570i
$456$	15.8655	+	27.4799i	0.742972	+	1.28686i
$457$	−4.10599			−0.192070			−0.0960351	−	0.995378i	$-0.530616\pi$
$457$	−4.10599			−0.192070			−0.0960351	+	0.995378i	$0.530616\pi$
$458$	−30.7262	+	53.2193i	−1.43574	+	2.48678i
$459$	−7.81429	+	13.5347i	−0.364740	+	0.631748i
$460$	−0.859060	−	1.48794i	−0.0400539	−	0.0693754i
$461$	22.8750			1.06540			0.532698	−	0.846305i	$-0.321178\pi$
$461$	22.8750			1.06540			0.532698	+	0.846305i	$0.321178\pi$
$462$	4.40860	−	7.63592i	0.205107	−	0.355255i
$463$	16.5670			0.769932			0.384966	−	0.922931i	$-0.374213\pi$
$463$	16.5670			0.769932			0.384966	+	0.922931i	$0.374213\pi$
$464$	105.308			4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	38.1462			1.76520			0.882599	−	0.470127i	$-0.155792\pi$
$467$	38.1462			1.76520			0.882599	+	0.470127i	$0.155792\pi$
$468$	−9.47670	+	16.4141i	−0.438061	+	0.758743i
$469$	−14.3305			−0.661719
$470$	−5.50321	−	9.53184i	−0.253844	−	0.439671i
$471$	−2.36062	+	4.08871i	−0.108771	+	0.188398i
$472$	2.02994	−	3.51597i	0.0934358	−	0.161836i
$473$	4.01847			0.184769
$474$	−18.5142	−	32.0675i	−0.850386	−	1.47291i
$475$	−5.94401	−	10.2953i	−0.272730	−	0.472382i
$476$	12.4929	+	21.6383i	0.572609	+	0.991788i
$477$	−1.37974	+	2.38979i	−0.0631741	+	0.109421i
$478$	−24.5786	−	42.5714i	−1.12420	−	1.94717i
$479$	16.8424	−	29.1719i	0.769548	−	1.33290i	−0.168260	−	0.985743i	$-0.553815\pi$
$479$	16.8424	−	29.1719i	0.769548	−	1.33290i	0.937808	−	0.347154i	$-0.112852\pi$
$480$	15.0457			0.686739
$481$	28.4292			1.29626
$482$	24.4421	−	42.3350i	1.11331	−	1.92831i
$483$	−0.660790	−	1.14452i	−0.0300670	−	0.0520775i
$484$	24.1197	−	41.7766i	1.09635	−	1.89893i
$485$	0.389115	+	0.673967i	0.0176688	+	0.0306033i
$486$	−13.1484	−	22.7736i	−0.596422	−	1.03303i
$487$	−10.3383	−	17.9065i	−0.468475	−	0.811422i	0.530876	−	0.847449i	$-0.321863\pi$
$487$	−10.3383	−	17.9065i	−0.468475	−	0.811422i	−0.999351	+	0.0360274i	$0.988530\pi$
$488$	−44.5379			−2.01614
$489$	1.23492	−	2.13894i	0.0558449	−	0.0967263i
$490$	−3.28793	+	5.69487i	−0.148534	+	0.257268i
$491$	12.3664	+	21.4192i	0.558087	+	0.966634i	0.997656	+	0.0684258i	$0.0217976\pi$
$491$	12.3664	+	21.4192i	0.558087	+	0.966634i	−0.439570	+	0.898209i	$0.644869\pi$
$492$	0.773321			0.0348640
$493$	−11.2321	+	19.4545i	−0.505867	+	0.876186i
$494$	−25.3549			−1.14077
$495$	−0.802235			−0.0360578
$496$		0			0
$497$	−8.21771			−0.368615
$498$	63.6980			2.85437
$499$	−12.2801	+	21.2697i	−0.549732	+	0.952164i	0.448560	+	0.893753i	$0.351937\pi$
$499$	−12.2801	+	21.2697i	−0.549732	+	0.952164i	−0.998293	+	0.0584115i	$0.981396\pi$
$500$	−30.6814			−1.37211
$501$	9.94584	+	17.2267i	0.444347	+	0.769632i
$502$	30.8429	−	53.4215i	1.37659	−	2.38432i
$503$	−7.36956	+	12.7645i	−0.328593	+	0.569139i	−0.982233	−	0.187666i	$-0.939908\pi$
$503$	−7.36956	+	12.7645i	−0.328593	+	0.569139i	0.653640	+	0.756805i	$0.273241\pi$
$504$	−14.8265			−0.660425
$505$	−2.47011	−	4.27836i	−0.109918	−	0.190384i
$506$	0.970074	+	1.68022i	0.0431251	+	0.0746948i
$507$	0.336187	+	0.582293i	0.0149306	+	0.0258605i
$508$	−33.8029	+	58.5484i	−1.49976	+	2.59767i
$509$	7.75315	+	13.4288i	0.343652	+	0.595223i	0.985108	−	0.171937i	$-0.0550025\pi$
$509$	7.75315	+	13.4288i	0.343652	+	0.595223i	−0.641456	+	0.767160i	$0.721669\pi$
$510$	−3.20856	+	5.55739i	−0.142077	+	0.246085i
$511$	12.9623			0.573418
$512$	−0.135395			−0.00598366
$513$	7.26235	−	12.5788i	0.320641	−	0.555366i
$514$	0.142838	+	0.247402i	0.00630031	+	0.0109125i
$515$	−4.60927	+	7.98349i	−0.203109	+	0.351795i
$516$	11.1656	+	19.3394i	0.491538	+	0.851368i
$517$	4.49697	+	7.78898i	0.197776	+	0.342559i
$518$	17.9899	+	31.1595i	0.790432	+	1.36907i
$519$	0.0170028			0.000746342
$520$	−9.72308	+	16.8409i	−0.426385	+	0.738521i
$521$	−14.7073	+	25.4738i	−0.644337	+	1.11603i	0.340117	+	0.940383i	$0.389533\pi$
$521$	−14.7073	+	25.4738i	−0.644337	+	1.11603i	−0.984454	+	0.175642i	$0.943800\pi$
$522$	−10.7832	−	18.6771i	−0.471970	−	0.817475i
$523$	−45.0260			−1.96885			−0.984424	−	0.175810i	$-0.943746\pi$
$523$	−45.0260			−1.96885			−0.984424	+	0.175810i	$0.943746\pi$
$524$	6.38326	−	11.0561i	0.278854	−	0.482989i
$525$	−11.3465			−0.495203
$526$	−19.6309			−0.855947
$527$		0			0
$528$	−24.5819			−1.06979
$529$	−22.7092			−0.987356
$530$	−2.29028	+	3.96688i	−0.0994834	+	0.172310i
$531$	−0.459693			−0.0199490
$532$	−11.6105	−	20.1099i	−0.503378	−	0.871876i
$533$	−0.190970	+	0.330769i	−0.00827182	+	0.0143272i
$534$	−29.2370	+	50.6400i	−1.26521	+	2.19141i
$535$	−7.52912			−0.325512
$536$	36.1310	+	62.5807i	1.56062	+	2.70307i
$537$	7.08021	+	12.2633i	0.305534	+	0.529200i
$538$	−21.8163	−	37.7869i	−0.940568	−	1.62911i
$539$	2.68675	−	4.65358i	0.115726	−	0.200444i
$540$	−9.01139	−	15.6082i	−0.387789	−	0.671670i
$541$	−18.8894	+	32.7173i	−0.812117	+	1.40663i	0.0992628	+	0.995061i	$0.468352\pi$
$541$	−18.8894	+	32.7173i	−0.812117	+	1.40663i	−0.911380	+	0.411567i	$0.864982\pi$
$542$	−13.8426			−0.594589
$543$	−26.4009			−1.13297
$544$	24.0727	−	41.6951i	1.03211	−	1.78766i
$545$	−2.19310	−	3.79855i	−0.0939419	−	0.162712i
$546$	−12.1000	+	20.9579i	−0.517834	+	0.896914i
$547$	9.10438	+	15.7692i	0.389275	+	0.674244i	0.992352	−	0.123439i	$-0.0393922\pi$
$547$	9.10438	+	15.7692i	0.389275	+	0.674244i	−0.603077	+	0.797683i	$0.706059\pi$
$548$	21.3243	+	36.9349i	0.910931	+	1.57778i
$549$	2.52147	+	4.36731i	0.107614	+	0.186392i
$550$	16.6573			0.710270
$551$	10.4387	−	18.0804i	0.444705	−	0.770251i
$552$	−3.33206	+	5.77130i	−0.141822	+	0.245643i
$553$	8.37446	+	14.5050i	0.356118	+	0.616815i
$554$	−45.5250			−1.93417
$555$	−3.34349	+	5.79110i	−0.141923	+	0.245818i
$556$	7.08748			0.300576
$557$	9.19760			0.389715			0.194857	−	0.980832i	$-0.437576\pi$
$557$	9.19760			0.389715			0.194857	+	0.980832i	$0.437576\pi$
$558$		0			0
$559$	−11.0293			−0.466488
$560$	−13.6071			−0.575003
$561$	2.62189	−	4.54124i	0.110696	−	0.191731i
$562$	−5.12923			−0.216364
$563$	18.0809	+	31.3170i	0.762019	+	1.31986i	0.941808	+	0.336150i	$0.109125\pi$
$563$	18.0809	+	31.3170i	0.762019	+	1.31986i	−0.179790	+	0.983705i	$0.557542\pi$
$564$	−24.9903	+	43.2844i	−1.05228	+	1.82260i
$565$	−5.07143	+	8.78397i	−0.213356	+	0.369544i
$566$	41.1858			1.73117
$567$	−4.37759	−	7.58220i	−0.183841	−	0.318422i
$568$	20.7191	+	35.8865i	0.869354	+	1.50576i
$569$	20.7499	+	35.9399i	0.869880	+	1.50668i	0.862118	+	0.506707i	$0.169137\pi$
$569$	20.7499	+	35.9399i	0.869880	+	1.50668i	0.00776221	+	0.999970i	$0.497529\pi$
$570$	2.98193	−	5.16486i	0.124899	−	0.216332i
$571$	−16.1966	−	28.0533i	−0.677805	−	1.17399i	−0.975641	−	0.219375i	$-0.929598\pi$
$571$	−16.1966	−	28.0533i	−0.677805	−	1.17399i	0.297835	−	0.954617i	$-0.403735\pi$
$572$	12.8544	−	22.2644i	0.537468	−	0.930923i
$573$	−1.70033			−0.0710322
$574$	−0.483381			−0.0201759
$575$	1.24835	−	2.16221i	0.0520599	−	0.0901704i
$576$	10.3408	+	17.9108i	0.430867	+	0.746284i
$577$	−20.4913	+	35.4919i	−0.853063	+	1.47755i	0.0253683	+	0.999678i	$0.491924\pi$
$577$	−20.4913	+	35.4919i	−0.853063	+	1.47755i	−0.878431	+	0.477869i	$0.841409\pi$
$578$	−12.5991	−	21.8223i	−0.524054	−	0.907688i
$579$	9.03054	+	15.6413i	0.375296	+	0.650032i
$580$	−12.9527	−	22.4348i	−0.537833	−	0.931555i
$581$	−28.8123			−1.19533
$582$	2.44180	−	4.22933i	0.101216	−	0.175311i
$583$	1.87151	−	3.24155i	0.0775100	−	0.134251i
$584$	−32.6814	−	56.6059i	−1.35237	−	2.34237i
$585$	2.20185			0.0910352
$586$	36.0396	−	62.4224i	1.48878	−	2.57864i
$587$	−25.5314			−1.05379			−0.526897	−	0.849929i	$-0.676644\pi$
$587$	−25.5314			−1.05379			−0.526897	+	0.849929i	$0.676644\pi$
$588$	29.8612			1.23146
$589$		0			0
$590$	−0.763058			−0.0314146
$591$	−4.21292			−0.173297
$592$	50.1550	−	86.8711i	2.06136	−	3.57038i
$593$	44.5318			1.82870			0.914350	−	0.404925i	$-0.132702\pi$
$593$	44.5318			1.82870			0.914350	+	0.404925i	$0.132702\pi$
$594$	10.1759	+	17.6252i	0.417523	+	0.723170i
$595$	1.45132	−	2.51375i	0.0594982	−	0.103054i
$596$	23.5763	−	40.8353i	0.965723	−	1.67268i
$597$	−18.7103			−0.765763
$598$	−2.66251	−	4.61160i	−0.108878	−	0.188582i
$599$	−9.48998	−	16.4371i	−0.387750	−	0.671603i	0.604397	−	0.796684i	$-0.293414\pi$
$599$	−9.48998	−	16.4371i	−0.387750	−	0.671603i	−0.992147	+	0.125081i	$0.960081\pi$
$600$	28.6077	+	49.5500i	1.16790	+	2.02287i
$601$	−6.41990	+	11.1196i	−0.261873	+	0.453578i	−0.966740	−	0.255762i	$-0.917674\pi$
$601$	−6.41990	+	11.1196i	−0.261873	+	0.453578i	0.704866	+	0.709340i	$0.251007\pi$
$602$	−6.97928	−	12.0885i	−0.284454	−	0.492689i
$603$	4.09103	−	7.08588i	0.166600	−	0.288559i
$604$	16.8022			0.683673
$605$	−5.60405			−0.227837
$606$	−15.5006	+	26.8478i	−0.629669	+	1.09062i
$607$	19.0696	+	33.0296i	0.774013	+	1.34063i	0.935348	+	0.353730i	$0.115087\pi$
$607$	19.0696	+	33.0296i	0.774013	+	1.34063i	−0.161335	+	0.986900i	$0.551580\pi$
$608$	−22.3724	+	38.7501i	−0.907321	+	1.57153i
$609$	−9.96326	−	17.2569i	−0.403732	−	0.699284i
$610$	4.18546	+	7.24943i	0.169464	+	0.293521i
$611$	−12.3426	−	21.3780i	−0.499327	−	0.864860i
$612$	−14.2658			−0.576659
$613$	−9.27119	+	16.0582i	−0.374460	+	0.648583i	−0.990246	−	0.139330i	$-0.955505\pi$
$613$	−9.27119	+	16.0582i	−0.374460	+	0.648583i	0.615786	+	0.787913i	$0.288838\pi$
$614$	12.0401	−	20.8541i	0.485901	−	0.841605i
$615$	−0.0449190	−	0.0778020i	−0.00181131	−	0.00313728i
$616$	20.1109			0.810293
$617$	−4.06777	+	7.04559i	−0.163762	+	0.283645i	−0.936215	−	0.351428i	$-0.885696\pi$
$617$	−4.06777	+	7.04559i	−0.163762	+	0.283645i	0.772453	+	0.635072i	$0.219030\pi$
$618$	57.8488			2.32702
$619$	5.36063			0.215462			0.107731	−	0.994180i	$-0.465641\pi$
$619$	5.36063			0.215462			0.107731	+	0.994180i	$0.465641\pi$
$620$		0			0
$621$	3.05046			0.122411
$622$	−55.5669			−2.22803
$623$	13.2247	−	22.9058i	0.529835	−	0.917702i
$624$	67.4686			2.70091
$625$	−9.79252	−	16.9611i	−0.391701	−	0.678446i
$626$	−0.607062	+	1.05146i	−0.0242631	+	0.0420249i
$627$	−2.43670	+	4.22049i	−0.0973124	+	0.168550i
$628$	−17.4221			−0.695217
$629$	10.6990	+	18.5312i	0.426597	+	0.738887i
$630$	1.39332	+	2.41331i	0.0555113	+	0.0961484i
$631$	14.5235	+	25.1555i	0.578172	+	1.00142i	0.995689	+	0.0927538i	$0.0295670\pi$
$631$	14.5235	+	25.1555i	0.578172	+	1.00142i	−0.417517	+	0.908669i	$0.637100\pi$
$632$	42.2286	−	73.1421i	1.67976	−	2.90944i
$633$	13.0083	+	22.5310i	0.517032	+	0.895525i
$634$	−7.50667	+	13.0019i	−0.298128	+	0.516373i
$635$	7.85389			0.311672
$636$	20.8005			0.824793
$637$	−7.37416	+	12.7724i	−0.292175	+	0.506062i
$638$	14.6266	+	25.3340i	0.579072	+	1.00298i
$639$	2.34598	−	4.06335i	0.0928055	−	0.160744i
$640$	6.56324	+	11.3679i	0.259435	+	0.449354i
$641$	−13.8028	−	23.9071i	−0.545177	−	0.944274i	−0.998596	−	0.0529762i	$-0.983129\pi$
$641$	−13.8028	−	23.9071i	−0.545177	−	0.944274i	0.453419	−	0.891297i	$-0.350204\pi$
$642$	23.6236	+	40.9173i	0.932351	+	1.61488i
$643$	4.22904			0.166777			0.0833885	−	0.996517i	$-0.473426\pi$
$643$	4.22904			0.166777			0.0833885	+	0.996517i	$0.473426\pi$
$644$	2.43842	−	4.22346i	0.0960871	−	0.166428i
$645$	1.29713	−	2.24669i	0.0510742	−	0.0884632i
$646$	−9.54202	−	16.5273i	−0.375426	−	0.650257i
$647$	26.2809			1.03321			0.516604	−	0.856225i	$-0.327196\pi$
$647$	26.2809			1.03321			0.516604	+	0.856225i	$0.327196\pi$
$648$	−22.0742	+	38.2336i	−0.867155	+	1.50196i
$649$	0.623536			0.0244759
$650$	−45.7184			−1.79322
$651$		0			0
$652$	9.11408			0.356935
$653$	−13.3517			−0.522494			−0.261247	−	0.965272i	$-0.584134\pi$
$653$	−13.3517			−0.522494			−0.261247	+	0.965272i	$0.584134\pi$
$654$	−13.7623	+	23.8370i	−0.538147	+	0.932099i
$655$	−1.48311			−0.0579498
$656$	0.673821	+	1.16709i	0.0263083	+	0.0455673i
$657$	−3.70045	+	6.40937i	−0.144368	+	0.250053i
$658$	15.6207	−	27.0558i	0.608958	−	1.05475i
$659$	−15.4158			−0.600515			−0.300258	−	0.953858i	$-0.597073\pi$
$659$	−15.4158			−0.600515			−0.300258	+	0.953858i	$0.597073\pi$
$660$	3.02355	+	5.23693i	0.117691	+	0.203847i
$661$	2.36153	+	4.09029i	0.0918530	+	0.159094i	0.908291	−	0.418339i	$-0.137388\pi$
$661$	2.36153	+	4.09029i	0.0918530	+	0.159094i	−0.816438	+	0.577433i	$0.804054\pi$
$662$	−32.5582	−	56.3925i	−1.26541	−	2.19176i
$663$	−7.19615	+	12.4641i	−0.279475	+	0.484065i
$664$	72.6436	+	125.822i	2.81912	+	4.88285i
$665$	−1.34881	+	2.33620i	−0.0523045	+	0.0905941i
$666$	−20.5429			−0.796023
$667$	4.38466			0.169775
$668$	−36.7017	+	63.5692i	−1.42003	+	2.45957i
$669$	−6.66724	−	11.5480i	−0.257770	−	0.446472i
$670$	6.79083	−	11.7621i	0.262353	−	0.454408i
$671$	−3.42017	−	5.92390i	−0.132034	−	0.228690i
$672$	21.3534	+	36.9852i	0.823725	+	1.42673i
$673$	−15.5365	−	26.9100i	−0.598888	−	1.03730i	−0.992986	−	0.118236i	$-0.962276\pi$
$673$	−15.5365	−	26.9100i	−0.598888	−	1.03730i	0.394097	−	0.919069i	$-0.371057\pi$
$674$	29.6885			1.14356
$675$	13.0950	−	22.6812i	0.504027	−	0.873000i
$676$	−1.24058	+	2.14875i	−0.0477147	+	0.0826443i
$677$	−4.51998	−	7.82883i	−0.173717	−	0.300886i	0.766000	−	0.642841i	$-0.222244\pi$
$677$	−4.51998	−	7.82883i	−0.173717	−	0.300886i	−0.939716	+	0.341955i	$0.888911\pi$
$678$	63.6491			2.44443
$679$	−1.10449	+	1.91304i	−0.0423865	+	0.0734156i
$680$	−14.6367			−0.561290
$681$	−12.0053			−0.460044
$682$		0			0
$683$	7.13535			0.273027			0.136513	−	0.990638i	$-0.456410\pi$
$683$	7.13535			0.273027			0.136513	+	0.990638i	$0.456410\pi$
$684$	13.2581			0.506938
$685$	2.47729	−	4.29078i	0.0946522	−	0.163942i
$686$	−51.1844			−1.95423
$687$	−16.2093	−	28.0753i	−0.618423	−	1.07114i
$688$	−19.4579	+	33.7021i	−0.741826	+	1.28488i
$689$	−5.13663	+	8.89690i	−0.195690	+	0.338945i
$690$	1.25252			0.0476828
$691$	−18.2377	−	31.5886i	−0.693795	−	1.20169i	−0.970585	−	0.240758i	$-0.922604\pi$
$691$	−18.2377	−	31.5886i	−0.693795	−	1.20169i	0.276790	−	0.960930i	$-0.410729\pi$
$692$	0.0313716	+	0.0543371i	0.00119257	+	0.00206559i
$693$	−1.13856	−	1.97204i	−0.0432503	−	0.0749117i
$694$	24.9746	−	43.2572i	0.948022	−	1.64202i
$695$	−0.411682	−	0.713054i	−0.0156160	−	0.0270477i
$696$	−50.2402	+	87.0185i	−1.90435	+	3.29843i
$697$	−0.287476			−0.0108889
$698$	86.5547			3.27615
$699$	11.5332	−	19.9760i	0.436225	−	0.755564i
$700$	−20.9352	−	36.2609i	−0.791278	−	1.37053i
$701$	0.807220	−	1.39815i	0.0304883	−	0.0528073i	−0.850379	−	0.526171i	$-0.823627\pi$
$701$	0.807220	−	1.39815i	0.0304883	−	0.0528073i	0.880867	+	0.473364i	$0.156960\pi$
$702$	−27.9292	−	48.3749i	−1.05412	−	1.82579i
$703$	−9.94330	−	17.2223i	−0.375019	−	0.649551i
$704$	−14.0265	−	24.2946i	−0.528643	−	0.915637i
$705$	5.80632			0.218679
$706$	−43.3295	+	75.0489i	−1.63073	+	2.82450i
$707$	7.01134	−	12.1440i	0.263688	−	0.456722i
$708$	1.73254	+	3.00084i	0.0651127	+	0.112779i
$709$	−11.4880			−0.431439			−0.215720	−	0.976455i	$-0.569210\pi$
$709$	−11.4880			−0.431439			−0.215720	+	0.976455i	$0.569210\pi$
$710$	3.89416	−	6.74489i	0.146145	−	0.253131i
$711$	−9.56291			−0.358637
$712$	−133.372			−4.99833
$713$		0			0
$714$	−18.2148			−0.681672
$715$	−2.98663			−0.111694
$716$	−26.1271	+	45.2534i	−0.976415	+	1.69120i
$717$	25.9324			0.968462
$718$	28.4649	+	49.3026i	1.06230	+	1.83996i
$719$	−7.08549	+	12.2724i	−0.264244	+	0.457685i	−0.967365	−	0.253386i	$-0.918456\pi$
$719$	−7.08549	+	12.2724i	−0.264244	+	0.457685i	0.703121	+	0.711070i	$0.251789\pi$
$720$	3.88452	−	6.72818i	0.144767	−	0.250745i
$721$	−26.1666			−0.974493
$722$	−16.6884	−	28.9052i	−0.621079	−	1.07574i
$723$	12.8942	+	22.3334i	0.479541	+	0.830589i
$724$	−48.7118	−	84.3713i	−1.81036	−	3.13564i
$725$	18.8224	−	32.6014i	0.699047	−	1.21079i
$726$	17.5835	+	30.4555i	0.652584	+	1.13031i
$727$	13.4739	−	23.3374i	0.499718	−	0.865537i	−0.500282	−	0.865863i	$-0.666770\pi$
$727$	13.4739	−	23.3374i	0.499718	−	0.865537i	1.00000		0.000325630i	$0.000103651\pi$
$728$	−55.1974			−2.04575
$729$	29.0824			1.07713
$730$	−6.14249	+	10.6391i	−0.227344	+	0.393771i
$731$	−4.15073	−	7.18927i	−0.153520	−	0.265905i
$732$	19.0063	−	32.9199i	0.702494	−	1.21676i
$733$	14.2118	+	24.6155i	0.524924	+	0.909194i	0.999579	+	0.0290225i	$0.00923944\pi$
$733$	14.2118	+	24.6155i	0.524924	+	0.909194i	−0.474655	+	0.880172i	$0.657427\pi$
$734$	−17.4812	−	30.2784i	−0.645243	−	1.11759i
$735$	−1.73452	−	3.00427i	−0.0639786	−	0.110814i
$736$	−9.39725			−0.346387
$737$	−5.54915	+	9.61142i	−0.204406	+	0.354041i
$738$	0.137995	−	0.239014i	0.00507965	−	0.00879822i
$739$	−0.348653	−	0.603885i	−0.0128254	−	0.0222143i	0.859541	−	0.511066i	$-0.170749\pi$
$739$	−0.348653	−	0.603885i	−0.0128254	−	0.0222143i	−0.872367	+	0.488852i	$0.837416\pi$
$740$	−24.6760			−0.907108
$741$	6.68787	−	11.5837i	0.245685	−	0.425539i
$742$	−13.0018			−0.477310
$743$	18.1815			0.667015			0.333508	−	0.942747i	$-0.391768\pi$
$743$	18.1815			0.667015			0.333508	+	0.942747i	$0.391768\pi$
$744$		0			0
$745$	−5.47779			−0.200691
$746$	11.9064			0.435925
$747$	8.22528	−	14.2466i	0.300947	−	0.521256i
$748$	19.3503			0.707519
$749$	−10.6856	−	18.5080i	−0.390443	−	0.676267i
$750$	11.1835	−	19.3704i	0.408364	−	0.707307i
$751$	18.5330	−	32.1001i	0.676279	−	1.17135i	−0.299815	−	0.953997i	$-0.596925\pi$
$751$	18.5330	−	32.1001i	0.676279	−	1.17135i	0.976093	−	0.217352i	$-0.0697418\pi$
$752$	−87.0995			−3.17619
$753$	16.2709	+	28.1820i	0.592943	+	1.02701i
$754$	−40.1448	−	69.5328i	−1.46199	−	2.53223i
$755$	−0.975972	−	1.69043i	−0.0355192	−	0.0615211i
$756$	25.5786	−	44.3034i	0.930284	−	1.61130i
$757$	3.20100	+	5.54430i	0.116342	+	0.201511i	0.918316	−	0.395849i	$-0.129550\pi$
$757$	3.20100	+	5.54430i	0.116342	+	0.201511i	−0.801973	+	0.597360i	$0.796216\pi$
$758$	−20.1166	+	34.8430i	−0.730669	+	1.26556i
$759$	−1.02351			−0.0371509
$760$	13.6028			0.493427
$761$	−10.6694	+	18.4800i	−0.386766	+	0.669898i	−0.992012	−	0.126140i	$-0.959741\pi$
$761$	−10.6694	+	18.4800i	−0.386766	+	0.669898i	0.605246	+	0.796038i	$0.293075\pi$
$762$	−24.6426	−	42.6823i	−0.892709	−	1.54622i
$763$	6.22504	−	10.7821i	0.225361	−	0.390338i
$764$	−3.13724	−	5.43385i	−0.113501	−	0.196590i
$765$	0.828638	+	1.43524i	0.0299595	+	0.0518914i
$766$	15.6706	+	27.1423i	0.566203	+	0.980692i
$767$	−1.71138			−0.0617945
$768$	11.4179	−	19.7764i	0.412008	−	0.713619i
$769$	6.12828	−	10.6145i	0.220991	−	0.382768i	−0.734118	−	0.679022i	$-0.762404\pi$
$769$	6.12828	−	10.6145i	0.220991	−	0.382768i	0.955109	+	0.296254i	$0.0957374\pi$
$770$	−1.88993	−	3.27346i	−0.0681084	−	0.117967i
$771$	−0.150705			−0.00542752
$772$	−33.3241	+	57.7190i	−1.19936	+	2.07735i
$773$	34.7035			1.24820			0.624098	−	0.781346i	$-0.285466\pi$
$773$	34.7035			1.24820			0.624098	+	0.781346i	$0.285466\pi$
$774$	7.96974			0.286466
$775$		0			0
$776$	11.1389			0.399863
$777$	−18.9808			−0.680933
$778$	−19.3717	+	33.5528i	−0.694510	+	1.20293i
$779$	0.267172			0.00957242
$780$	−8.29855	−	14.3735i	−0.297136	−	0.514654i
$781$	−3.18213	+	5.51161i	−0.113866	+	0.197221i
$782$	2.00400	−	3.47104i	0.0716630	−	0.124124i
$783$	45.9943			1.64370
$784$	26.0191	+	45.0664i	0.929254	+	1.60952i
$785$	1.01198	+	1.75279i	0.0361190	+	0.0625599i
$786$	4.65345	+	8.06002i	0.165983	+	0.287491i
$787$	−10.0591	+	17.4229i	−0.358568	+	0.621058i	−0.987722	−	0.156223i	$-0.950068\pi$
$787$	−10.0591	+	17.4229i	−0.358568	+	0.621058i	0.629154	+	0.777281i	$0.283402\pi$
$788$	−7.77317	−	13.4635i	−0.276908	−	0.479618i
$789$	5.17804	−	8.96863i	0.184343	−	0.319292i
$790$	−15.8738			−0.564763
$791$	−28.7902			−1.02366
$792$	−5.74124	+	9.94411i	−0.204006	+	0.353349i
$793$	9.38713	+	16.2590i	0.333347	+	0.577374i
$794$	21.2389	−	36.7869i	0.753742	−	1.30552i
$795$	−1.20821	−	2.09269i	−0.0428509	−	0.0742200i
$796$	−34.5220	−	59.7939i	−1.22360	−	2.11934i
$797$	13.1010	+	22.6916i	0.464060	+	0.803776i	0.999159	−	0.0410138i	$-0.0130588\pi$
$797$	13.1010	+	22.6916i	0.464060	+	0.803776i	−0.535098	+	0.844790i	$0.679725\pi$
$798$	16.9283			0.599254
$799$	9.28995	−	16.0907i	0.328655	−	0.569247i
$800$	−40.3405	+	69.8717i	−1.42625	+	2.47034i
$801$	7.55072	+	13.0782i	0.266791	+	0.462096i
$802$	83.4573			2.94698
$803$	5.01936	−	8.69379i	0.177129	−	0.306797i
$804$	−61.6748			−2.17510
$805$	−0.566550			−0.0199683
$806$		0			0
$807$	23.0179			0.810270
$808$	−70.7099			−2.48757
$809$	18.2251	−	31.5668i	0.640759	−	1.10983i	−0.344504	−	0.938785i	$-0.611953\pi$
$809$	18.2251	−	31.5668i	0.640759	−	1.10983i	0.985264	−	0.171043i	$-0.0547138\pi$
$810$	8.29770			0.291551
$811$	9.55322	+	16.5467i	0.335459	+	0.581032i	0.983573	−	0.180511i	$-0.0577753\pi$
$811$	9.55322	+	16.5467i	0.335459	+	0.581032i	−0.648114	+	0.761543i	$0.724442\pi$
$812$	36.7660	−	63.6805i	1.29023	−	2.23475i
$813$	3.65125	−	6.32416i	0.128055	−	0.221798i
$814$	27.8648			0.976662
$815$	−0.529399	−	0.916946i	−0.0185440	−	0.0321192i
$816$	25.3910	+	43.9785i	0.888863	+	1.53956i
$817$	3.85755	+	6.68148i	0.134959	+	0.233755i
$818$	−8.85844	+	15.3433i	−0.309728	+	0.536465i
$819$	3.12494	+	5.41255i	0.109194	+	0.189130i
$820$	0.165758	−	0.287101i	0.00578852	−	0.0100260i
$821$	−39.4598			−1.37716			−0.688578	−	0.725162i	$-0.741765\pi$
$821$	−39.4598			−1.37716			−0.688578	+	0.725162i	$0.741765\pi$
$822$	−31.0913			−1.08443
$823$	−15.7940	+	27.3560i	−0.550544	+	0.953570i	0.447691	+	0.894188i	$0.352246\pi$
$823$	−15.7940	+	27.3560i	−0.550544	+	0.953570i	−0.998235	+	0.0593819i	$0.981087\pi$
$824$	65.9730	+	114.269i	2.29828	+	3.98073i
$825$	−4.39370	+	7.61011i	−0.152969	+	0.264950i
$826$	−1.08296	−	1.87574i	−0.0376810	−	0.0652653i
$827$	9.91492	+	17.1731i	0.344776	+	0.597169i	0.985313	−	0.170758i	$-0.0546217\pi$
$827$	9.91492	+	17.1731i	0.344776	+	0.597169i	−0.640537	+	0.767927i	$0.721288\pi$
$828$	1.39223	+	2.41141i	0.0483833	+	0.0838024i
$829$	−8.99987			−0.312578			−0.156289	−	0.987711i	$-0.549953\pi$
$829$	−8.99987			−0.312578			−0.156289	+	0.987711i	$0.549953\pi$
$830$	13.6534	−	23.6484i	0.473916	−	0.820847i
$831$	12.0081	−	20.7987i	0.416558	−	0.721499i
$832$	38.4977	+	66.6800i	1.33467	+	2.31171i
$833$	−11.1007			−0.384617
$834$	−2.58342	+	4.47461i	−0.0894564	+	0.154943i
$835$	8.52740			0.295103
$836$	−17.9836			−0.621976
$837$		0			0
$838$	39.4699			1.36347
$839$	−31.8452			−1.09942			−0.549709	−	0.835356i	$-0.685261\pi$
$839$	−31.8452			−1.09942			−0.549709	+	0.835356i	$0.685261\pi$
$840$	6.49163	−	11.2438i	0.223983	−	0.387949i
$841$	37.1110			1.27969
$842$	−35.9349	−	62.2411i	−1.23840	−	2.14497i
$843$	1.35294	−	2.34336i	0.0465976	−	0.0807095i
$844$	−48.0025	+	83.1428i	−1.65231	+	2.86189i
$845$	0.288241			0.00991579
$846$	8.91874	+	15.4477i	0.306633	+	0.531103i
$847$	−7.95347	−	13.7758i	−0.273284	−	0.473343i
$848$	18.1242	+	31.3920i	0.622386	+	1.07800i
$849$	−10.8636	+	18.8163i	−0.372837	+	0.645772i
$850$	−17.2056	−	29.8009i	−0.590146	−	1.02216i
$851$	2.08828	−	3.61701i	0.0715853	−	0.123989i
$852$	−35.3671			−1.21166
$853$	−49.0917			−1.68087			−0.840434	−	0.541914i	$-0.817700\pi$
$853$	−49.0917			−1.68087			−0.840434	+	0.541914i	$0.817700\pi$
$854$	−11.8803	+	20.5773i	−0.406536	+	0.704140i
$855$	−0.770110	−	1.33387i	−0.0263372	−	0.0456174i
$856$	−53.8826	+	93.3274i	−1.84167	+	3.18986i
$857$	−9.62023	−	16.6627i	−0.328621	−	0.569188i	0.653618	−	0.756825i	$-0.273251\pi$
$857$	−9.62023	−	16.6627i	−0.328621	−	0.569188i	−0.982238	+	0.187637i	$0.939917\pi$
$858$	9.37095	+	16.2310i	0.319919	+	0.554116i
$859$	2.32107	+	4.02022i	0.0791940	+	0.137168i	0.902902	−	0.429846i	$-0.141432\pi$
$859$	2.32107	+	4.02022i	0.0791940	+	0.137168i	−0.823708	+	0.567014i	$0.808099\pi$
$860$	9.57319			0.326443
$861$	0.127501	−	0.220839i	0.00434523	−	0.00752616i
$862$	5.36418	−	9.29104i	0.182705	−	0.316454i
$863$	−19.2652	−	33.3683i	−0.655795	−	1.13587i	−0.981694	−	0.190466i	$-0.939000\pi$
$863$	−19.2652	−	33.3683i	−0.655795	−	1.13587i	0.325899	−	0.945405i	$-0.394333\pi$
$864$	−98.5755			−3.35361
$865$	0.00364449	−	0.00631244i	0.000123916	−	0.000214629i
$866$	48.6287			1.65247
$867$	13.2931			0.451456
$868$		0			0
$869$	12.9713			0.440022
$870$	18.8853			0.640273
$871$	15.2304	−	26.3799i	0.516064	−	0.893849i
$872$	−62.7800			−2.12600
$873$	−0.630617	−	1.09226i	−0.0213431	−	0.0369674i
$874$	−1.86246	+	3.22587i	−0.0629986	+	0.109117i
$875$	−5.05859	+	8.76174i	−0.171012	+	0.296201i
$876$	55.7866			1.88485
$877$	4.62917	+	8.01796i	0.156316	+	0.270747i	0.933537	−	0.358480i	$-0.116705\pi$
$877$	4.62917	+	8.01796i	0.156316	+	0.270747i	−0.777221	+	0.629227i	$0.783372\pi$
$878$	30.8138	+	53.3711i	1.03992	+	1.80119i
$879$	19.0123	+	32.9303i	0.641269	+	1.11071i
$880$	−5.26903	+	9.12623i	−0.177619	+	0.307645i
$881$	−8.93954	−	15.4837i	−0.301181	−	0.521660i	0.675223	−	0.737614i	$-0.264047\pi$
$881$	−8.93954	−	15.4837i	−0.301181	−	0.521660i	−0.976404	+	0.215953i	$0.930714\pi$
$882$	5.32857	−	9.22935i	0.179422	−	0.310768i
$883$	48.3156			1.62595			0.812975	−	0.582299i	$-0.197847\pi$
$883$	48.3156			1.62595			0.812975	+	0.582299i	$0.197847\pi$
$884$	−53.1098			−1.78628
$885$	0.201272	−	0.348613i	0.00676568	−	0.0117185i
$886$	−28.9075	−	50.0692i	−0.971166	−	1.68211i
$887$	−11.7561	+	20.3622i	−0.394732	+	0.683695i	−0.993067	−	0.117551i	$-0.962496\pi$
$887$	−11.7561	+	20.3622i	−0.394732	+	0.683695i	0.598335	+	0.801246i	$0.295829\pi$
$888$	47.8558	+	82.8886i	1.60593	+	2.78156i
$889$	11.1465	+	19.3063i	0.373842	+	0.647514i
$890$	12.5337	+	21.7089i	0.420129	+	0.727686i
$891$	−6.78050			−0.227155
$892$	24.6032	−	42.6139i	0.823775	−	1.42682i
$893$	−8.63379	+	14.9542i	−0.288919	+	0.500422i
$894$	17.1873	+	29.7693i	0.574830	+	0.995635i
$895$	6.07046			0.202913
$896$	−18.6296	+	32.2673i	−0.622370	+	1.07798i
$897$	2.80916			0.0937951
$898$	50.5739			1.68767
$899$		0			0
$900$	23.9062			0.796874
$901$	−7.73243			−0.257605
$902$	−0.187179	+	0.324203i	−0.00623236	+	0.0107948i
$903$	7.36370			0.245049
$904$	72.5879	+	125.726i	2.41424	+	4.18158i
$905$	−5.65893	+	9.80156i	−0.188109	+	0.325815i
$906$	−6.12449	+	10.6079i	−0.203472	+	0.352425i
$907$	−12.5821			−0.417783			−0.208892	−	0.977939i	$-0.566986\pi$
$907$	−12.5821			−0.417783			−0.208892	+	0.977939i	$0.566986\pi$
$908$	−22.1507	−	38.3662i	−0.735098	−	1.27323i
$909$	4.00317	+	6.93369i	0.132777	+	0.229976i
$910$	5.18718	+	8.98447i	0.171953	+	0.297832i
$911$	−23.6422	+	40.9496i	−0.783302	+	1.35672i	0.146706	+	0.989180i	$0.453133\pi$
$911$	−23.6422	+	40.9496i	−0.783302	+	1.35672i	−0.930008	+	0.367539i	$0.880200\pi$
$912$	−23.5976	−	40.8722i	−0.781394	−	1.35341i
$913$	−11.1569	+	19.3244i	−0.369240	+	0.639543i
$914$	11.0458			0.365361
$915$	−4.41599			−0.145988
$916$	59.8148	−	103.602i	1.97634	−	3.42312i
$917$	−2.10488	−	3.64576i	−0.0695092	−	0.120394i
$918$	21.0217	−	36.4106i	0.693818	−	1.20173i
$919$	11.5659	+	20.0328i	0.381525	+	0.660821i	0.991280	−	0.131769i	$-0.0420657\pi$
$919$	11.5659	+	20.0328i	0.381525	+	0.660821i	−0.609755	+	0.792590i	$0.708732\pi$
$920$	1.42843	+	2.47411i	0.0470938	+	0.0815689i
$921$	6.35165	+	11.0014i	0.209294	+	0.362508i
$922$	−61.5374			−2.02663
$923$	8.73381	−	15.1274i	0.287477	−	0.497925i
$924$	−8.58224	+	14.8649i	−0.282335	+	0.489019i
$925$	−17.9291	−	31.0541i	−0.589506	−	1.02105i
$926$	−44.5677			−1.46459
$927$	7.46998	−	12.9384i	0.245346	−	0.424952i
$928$	−141.690			−4.65120
$929$	−1.68694			−0.0553468			−0.0276734	−	0.999617i	$-0.508810\pi$
$929$	−1.68694			−0.0553468			−0.0276734	+	0.999617i	$0.508810\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	85.1184			2.78815
$933$	14.6569	−	25.3864i	0.479844	−	0.831115i
$934$	−102.619			−3.35781
$935$	−1.12398	−	1.94679i	−0.0367581	−	0.0636669i
$936$	15.7576	−	27.2930i	0.515055	−	0.892101i
$937$	−9.86333	+	17.0838i	−0.322221	+	0.558103i	−0.980946	−	0.194281i	$-0.937763\pi$
$937$	−9.86333	+	17.0838i	−0.322221	+	0.558103i	0.658725	+	0.752384i	$0.271096\pi$
$938$	38.5511			1.25874
$939$	−0.320249	−	0.554688i	−0.0104509	−	0.0181016i
$940$	10.7131	+	18.5557i	0.349423	+	0.605219i
$941$	−4.41163	−	7.64117i	−0.143815	−	0.249095i	0.785115	−	0.619350i	$-0.212604\pi$
$941$	−4.41163	−	7.64117i	−0.143815	−	0.249095i	−0.928930	+	0.370255i	$0.879270\pi$
$942$	6.35043	−	10.9993i	0.206908	−	0.358375i
$943$	0.0280555	+	0.0485936i	0.000913614	+	0.00158243i
$944$	−3.01924	+	5.22947i	−0.0982678	+	0.170205i
$945$	−5.94301			−0.193326
$946$	−10.8103			−0.351473
$947$	7.78059	−	13.4764i	0.252835	−	0.437923i	−0.711470	−	0.702716i	$-0.751970\pi$
$947$	7.78059	−	13.4764i	0.252835	−	0.437923i	0.964305	+	0.264793i	$0.0853036\pi$
$948$	36.0417	+	62.4260i	1.17058	+	2.02750i
$949$	−13.7764	+	23.8613i	−0.447199	+	0.774572i
$950$	15.9903	+	27.6960i	0.518794	+	0.898577i
$951$	−3.96007	−	6.85904i	−0.128414	−	0.222420i
$952$	−20.7728	−	35.9796i	−0.673252	−	1.16611i
$953$	−9.65172			−0.312650			−0.156325	−	0.987706i	$-0.549965\pi$
$953$	−9.65172			−0.312650			−0.156325	+	0.987706i	$0.549965\pi$
$954$	3.71172	−	6.42890i	0.120172	−	0.208143i
$955$	−0.364458	+	0.631260i	−0.0117936	+	0.0204271i
$956$	47.8473	+	82.8739i	1.54749	+	2.68033i
$957$	−15.4322			−0.498853
$958$	−45.3086	+	78.4768i	−1.46386	+	2.53547i
$959$	14.0634			0.454131
$960$	−18.1105			−0.584514
$961$		0			0
$962$	−76.4790			−2.46578
$963$	12.2020			0.393205
$964$	−47.5816	+	82.4138i	−1.53250	+	2.65437i
$965$	7.74263			0.249244
$966$	1.77763	+	3.07894i	0.0571942	+	0.0990633i
$967$	14.1988	−	24.5930i	0.456602	−	0.790858i	−0.542177	−	0.840264i	$-0.682400\pi$
$967$	14.1988	−	24.5930i	0.456602	−	0.790858i	0.998779	+	0.0494066i	$0.0157330\pi$
$968$	−40.1057	+	69.4652i	−1.28905	+	2.23269i
$969$	10.0676			0.323418
$970$	−1.04678	−	1.81308i	−0.0336101	−	0.0582144i
$971$	11.0635	+	19.1626i	0.355046	+	0.614957i	0.987126	−	0.159946i	$-0.0511319\pi$
$971$	11.0635	+	19.1626i	0.355046	+	0.614957i	−0.632080	+	0.774903i	$0.717799\pi$
$972$	25.5960	+	44.3335i	0.820992	+	1.42200i
$973$	1.16855	−	2.02398i	0.0374619	−	0.0648859i
$974$	27.8117	+	48.1713i	0.891145	+	1.54351i
$975$	12.0591	−	20.8870i	0.386201	−	0.668920i
$976$	66.2434			2.12040
$977$	−19.9123			−0.637051			−0.318525	−	0.947914i	$-0.603188\pi$
$977$	−19.9123			−0.637051			−0.318525	+	0.947914i	$0.603188\pi$
$978$	−3.32212	+	5.75408i	−0.106230	+	0.183995i
$979$	−10.2419	−	17.7396i	−0.327334	−	0.566959i
$980$	6.40063	−	11.0862i	0.204461	−	0.354136i
$981$	3.55423	+	6.15610i	0.113478	+	0.196549i
$982$	−33.2675	−	57.6209i	−1.06161	−	1.83876i
$983$	−12.4652	−	21.5903i	−0.397578	−	0.688625i	0.595849	−	0.803097i	$-0.296816\pi$
$983$	−12.4652	−	21.5903i	−0.397578	−	0.688625i	−0.993427	+	0.114472i	$0.963482\pi$
$984$	−1.28586			−0.0409918
$985$	−0.903023	+	1.56408i	−0.0287727	+	0.0498358i
$986$	30.2160	−	52.3356i	0.962273	−	1.66671i
$987$	8.24054	+	14.2730i	0.262299	+	0.454316i
$988$	49.3586			1.57031
$989$	−0.810159	+	1.40324i	−0.0257616	+	0.0446203i
$990$	2.15814			0.0685901
$991$	42.0512			1.33580			0.667900	−	0.744251i	$-0.267193\pi$
$991$	42.0512			1.33580			0.667900	+	0.744251i	$0.267193\pi$
$992$		0			0
$993$	34.3515			1.09011
$994$	22.1069			0.701189
$995$	−4.01048	+	6.94636i	−0.127141	+	0.220214i
$996$	−124.001			−3.92912
$997$	−7.23233	−	12.5268i	−0.229050	−	0.396727i	0.728477	−	0.685071i	$-0.240229\pi$
$997$	−7.23233	−	12.5268i	−0.229050	−	0.396727i	−0.957527	+	0.288344i	$0.906895\pi$
$998$	33.0353	−	57.2189i	1.04572	−	1.81123i
$999$	21.9057	−	37.9418i	0.693066	−	1.20042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.i.439.1		16
31.2	even	5		961.2.g.l.547.1		16
31.3	odd	30		31.2.g.a.14.1	✓	16
31.4	even	5		961.2.g.m.235.2		16
31.5	even	3		961.2.a.j.1.1		8
31.6	odd	6		961.2.c.j.521.1		16
31.7	even	15		961.2.g.n.338.2		16
31.8	even	5		961.2.g.n.816.2		16
31.9	even	15		961.2.d.q.374.4		16
31.10	even	15		961.2.d.n.531.1		16
31.11	odd	30		961.2.d.p.388.4		16
31.12	odd	30		961.2.g.k.844.1		16
31.13	odd	30		961.2.d.o.628.1		16
31.14	even	15		961.2.g.m.732.2		16
31.15	odd	10		961.2.g.k.846.1		16
31.16	even	5		961.2.g.j.846.1		16
31.17	odd	30		961.2.g.s.732.2		16
31.18	even	15		961.2.d.n.628.1		16
31.19	even	15		961.2.g.j.844.1		16
31.20	even	15		961.2.d.q.388.4		16
31.21	odd	30		961.2.d.o.531.1		16
31.22	odd	30		961.2.d.p.374.4		16
31.23	odd	10		961.2.g.t.816.2		16
31.24	odd	30		961.2.g.t.338.2		16
31.25	even	3	inner	961.2.c.i.521.1		16
31.26	odd	6		961.2.a.i.1.1		8
31.27	odd	10		961.2.g.s.235.2		16
31.28	even	15		961.2.g.l.448.1		16
31.29	odd	10		31.2.g.a.20.1	yes	16
31.30	odd	2		961.2.c.j.439.1		16
93.5	odd	6		8649.2.a.be.1.8		8
93.26	even	6		8649.2.a.bf.1.8		8
93.29	even	10		279.2.y.c.82.2		16
93.65	even	30		279.2.y.c.262.2		16
124.3	even	30		496.2.bg.c.417.1		16
124.91	even	10		496.2.bg.c.113.1		16
155.3	even	60		775.2.ck.a.324.4		32
155.29	odd	10		775.2.bl.a.51.2		16
155.34	odd	30		775.2.bl.a.76.2		16
155.122	even	20		775.2.ck.a.299.4		32
155.127	even	60		775.2.ck.a.324.1		32
155.153	even	20		775.2.ck.a.299.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.3	odd	30
31.2.g.a.20.1	yes	16	31.29	odd	10
279.2.y.c.82.2		16	93.29	even	10
279.2.y.c.262.2		16	93.65	even	30
496.2.bg.c.113.1		16	124.91	even	10
496.2.bg.c.417.1		16	124.3	even	30
775.2.bl.a.51.2		16	155.29	odd	10
775.2.bl.a.76.2		16	155.34	odd	30
775.2.ck.a.299.1		32	155.153	even	20
775.2.ck.a.299.4		32	155.122	even	20
775.2.ck.a.324.1		32	155.127	even	60
775.2.ck.a.324.4		32	155.3	even	60
961.2.a.i.1.1		8	31.26	odd	6
961.2.a.j.1.1		8	31.5	even	3
961.2.c.i.439.1		16	1.1	even	1	trivial
961.2.c.i.521.1		16	31.25	even	3	inner
961.2.c.j.439.1		16	31.30	odd	2
961.2.c.j.521.1		16	31.6	odd	6
961.2.d.n.531.1		16	31.10	even	15
961.2.d.n.628.1		16	31.18	even	15
961.2.d.o.531.1		16	31.21	odd	30
961.2.d.o.628.1		16	31.13	odd	30
961.2.d.p.374.4		16	31.22	odd	30
961.2.d.p.388.4		16	31.11	odd	30
961.2.d.q.374.4		16	31.9	even	15
961.2.d.q.388.4		16	31.20	even	15
961.2.g.j.844.1		16	31.19	even	15
961.2.g.j.846.1		16	31.16	even	5
961.2.g.k.844.1		16	31.12	odd	30
961.2.g.k.846.1		16	31.15	odd	10
961.2.g.l.448.1		16	31.28	even	15
961.2.g.l.547.1		16	31.2	even	5
961.2.g.m.235.2		16	31.4	even	5
961.2.g.m.732.2		16	31.14	even	15
961.2.g.n.338.2		16	31.7	even	15
961.2.g.n.816.2		16	31.8	even	5
961.2.g.s.235.2		16	31.27	odd	10
961.2.g.s.732.2		16	31.17	odd	30
961.2.g.t.338.2		16	31.24	odd	30
961.2.g.t.816.2		16	31.23	odd	10
8649.2.a.be.1.8		8	93.5	odd	6
8649.2.a.bf.1.8		8	93.26	even	6

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.69016 q^{2} +(0.709582 - 1.22903i) q^{3} +5.23694 q^{4} +(-0.304192 - 0.526876i) q^{5} +(-1.90889 + 3.30629i) q^{6} +(0.863440 - 1.49552i) q^{7} -8.70786 q^{8} +(0.492986 + 0.853878i) q^{9} +(0.818323 + 1.41738i) q^{10} +(-0.668696 - 1.15822i) q^{11} +(3.71604 - 6.43636i) q^{12} +(1.83533 + 3.17889i) q^{13} +(-2.32279 + 4.02318i) q^{14} -0.863396 q^{15} +12.9516 q^{16} +(-1.38141 + 2.39267i) q^{17} +(-1.32621 - 2.29706i) q^{18} +(1.28384 - 2.22367i) q^{19} +(-1.59303 - 2.75922i) q^{20} +(-1.22536 - 2.12239i) q^{21} +(1.79890 + 3.11578i) q^{22} +0.539261 q^{23} +(-6.17894 + 10.7022i) q^{24} +(2.31493 - 4.00958i) q^{25} +(-4.93733 - 8.55171i) q^{26} +5.65675 q^{27} +(4.52178 - 7.83195i) q^{28} +8.13087 q^{29} +2.32267 q^{30} -17.4262 q^{32} -1.89798 q^{33} +(3.71621 - 6.43666i) q^{34} -1.05061 q^{35} +(2.58174 + 4.47170i) q^{36} +(3.87249 - 6.70735i) q^{37} +(-3.45373 + 5.98203i) q^{38} +5.20928 q^{39} +(2.64886 + 4.58796i) q^{40} +(0.0520259 + 0.0901115i) q^{41} +(3.29642 + 5.70956i) q^{42} +(-1.50235 + 2.60215i) q^{43} +(-3.50192 - 6.06550i) q^{44} +(0.299925 - 0.519485i) q^{45} -1.45070 q^{46} -6.72498 q^{47} +(9.19025 - 15.9180i) q^{48} +(2.00894 + 3.47959i) q^{49} +(-6.22753 + 10.7864i) q^{50} +(1.96045 + 3.39559i) q^{51} +(9.61152 + 16.6476i) q^{52} +(1.39937 + 2.42378i) q^{53} -15.2175 q^{54} +(-0.406824 + 0.704640i) q^{55} +(-7.51871 + 13.0228i) q^{56} +(-1.82198 - 3.15576i) q^{57} -21.8733 q^{58} +(-0.233116 + 0.403769i) q^{59} -4.52155 q^{60} +5.11468 q^{61} +1.70266 q^{63} +20.9759 q^{64} +(1.11659 - 1.93398i) q^{65} +5.10586 q^{66} +(-4.14923 - 7.18668i) q^{67} +(-7.23436 + 12.5303i) q^{68} +(0.382650 - 0.662769i) q^{69} +2.82629 q^{70} +(-2.37935 - 4.12116i) q^{71} +(-4.29286 - 7.43545i) q^{72} +(3.75310 + 6.50055i) q^{73} +(-10.4176 + 18.0438i) q^{74} +(-3.28527 - 5.69026i) q^{75} +(6.72338 - 11.6452i) q^{76} -2.30951 q^{77} -14.0138 q^{78} +(-4.84948 + 8.39954i) q^{79} +(-3.93978 - 6.82390i) q^{80} +(2.53497 - 4.39070i) q^{81} +(-0.139958 - 0.242414i) q^{82} +(-8.34229 - 14.4493i) q^{83} +(-6.41715 - 11.1148i) q^{84} +1.68085 q^{85} +(4.04156 - 7.00019i) q^{86} +(5.76952 - 9.99310i) q^{87} +(5.82292 + 10.0856i) q^{88} +15.3163 q^{89} +(-0.806845 + 1.39750i) q^{90} +6.33879 q^{91} +2.82407 q^{92} +18.0912 q^{94} -1.56213 q^{95} +(-12.3653 + 21.4173i) q^{96} -1.27918 q^{97} +(-5.40437 - 9.36065i) q^{98} +(0.659316 - 1.14197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 16 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} - 18 q^{11} - 8 q^{13} + 9 q^{14} + 36 q^{15} + 8 q^{16} - 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 3 * q^3 + 16 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 - 18 * q^11 - 8 * q^13 + 9 * q^14 + 36 * q^15 + 8 * q^16 - 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 + q^21 - 4 * q^22 + 44 * q^23 - 30 * q^24 - 13 * q^25 - 9 * q^26 + 36 * q^27 + 5 * q^28 + 24 * q^29 + 22 * q^30 - 42 * q^32 + 12 * q^33 + 7 * q^34 - 24 * q^35 + q^36 + 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 + 36 * q^46 - 36 * q^47 + q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 + q^52 - 6 * q^53 - 14 * q^54 - 28 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 4 * q^59 - 80 * q^60 + 60 * q^61 - 46 * q^63 + 18 * q^64 - 3 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 + 33 * q^76 - 48 * q^77 - 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 - 39 * q^83 - 8 * q^84 - 52 * q^85 + 16 * q^86 + 15 * q^87 + 17 * q^88 + 54 * q^89 - 8 * q^90 + 32 * q^91 + 64 * q^92 + 44 * q^94 - 12 * q^95 + 12 * q^96 + 68 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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