LMFDB - Embedded newform 63.6.i.a.5.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,6,Mod(5,63)] 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("63.5"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.i (of order $6$, degree $2$, 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:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	63.5
Dual form			63.6.i.a.38.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.279751i q^{2} +(-15.2895 - 3.03836i) q^{3} +31.9217 q^{4} +(9.68296 + 16.7714i) q^{5} +(-0.849983 + 4.27725i) q^{6} +(-129.532 + 5.33078i) q^{7} -17.8822i q^{8} +(224.537 + 92.9099i) q^{9} +(4.69181 - 2.70882i) q^{10} +(-62.4661 - 36.0648i) q^{11} +(-488.067 - 96.9897i) q^{12} +(613.086 + 353.966i) q^{13} +(1.49129 + 36.2367i) q^{14} +(-97.0900 - 285.846i) q^{15} +1016.49 q^{16} +(1184.72 + 2052.00i) q^{17} +(25.9916 - 62.8144i) q^{18} +(1583.71 + 914.355i) q^{19} +(309.097 + 535.371i) q^{20} +(1996.68 + 312.060i) q^{21} +(-10.0892 + 17.4749i) q^{22} +(-2838.25 + 1638.66i) q^{23} +(-54.3324 + 273.409i) q^{24} +(1374.98 - 2381.54i) q^{25} +(99.0222 - 171.511i) q^{26} +(-3150.76 - 2102.77i) q^{27} +(-4134.89 + 170.168i) q^{28} +(2515.93 - 1452.57i) q^{29} +(-79.9656 + 27.1610i) q^{30} +3701.23i q^{31} -856.594i q^{32} +(845.496 + 741.206i) q^{33} +(574.048 - 331.427i) q^{34} +(-1343.66 - 2120.81i) q^{35} +(7167.60 + 2965.84i) q^{36} +(2257.86 - 3910.73i) q^{37} +(255.792 - 443.044i) q^{38} +(-8298.30 - 7274.73i) q^{39} +(299.908 - 173.152i) q^{40} +(-6571.37 + 11382.0i) q^{41} +(87.2991 - 558.572i) q^{42} +(-3666.20 - 6350.05i) q^{43} +(-1994.03 - 1151.25i) q^{44} +(615.954 + 4665.43i) q^{45} +(458.418 + 794.003i) q^{46} +9969.70 q^{47} +(-15541.7 - 3088.47i) q^{48} +(16750.2 - 1381.01i) q^{49} +(-666.237 - 384.652i) q^{50} +(-11879.1 - 34973.6i) q^{51} +(19570.8 + 11299.2i) q^{52} +(-25517.8 + 14732.7i) q^{53} +(-588.251 + 881.427i) q^{54} -1396.86i q^{55} +(95.3258 + 2316.32i) q^{56} +(-21436.0 - 18791.9i) q^{57} +(-406.358 - 703.833i) q^{58} -40234.8 q^{59} +(-3099.28 - 9124.70i) q^{60} -36052.6i q^{61} +1035.42 q^{62} +(-29580.0 - 10837.9i) q^{63} +32288.1 q^{64} +13709.7i q^{65} +(207.353 - 236.528i) q^{66} +15494.8 q^{67} +(37818.3 + 65503.3i) q^{68} +(48374.2 - 16430.7i) q^{69} +(-593.300 + 375.890i) q^{70} +3103.20i q^{71} +(1661.43 - 4015.20i) q^{72} +(-35514.8 + 20504.5i) q^{73} +(-1094.03 - 631.639i) q^{74} +(-28258.7 + 32234.8i) q^{75} +(50554.8 + 29187.8i) q^{76} +(8283.62 + 4338.56i) q^{77} +(-2035.11 + 2321.46i) q^{78} +76810.2 q^{79} +(9842.66 + 17048.0i) q^{80} +(41784.5 + 41723.4i) q^{81} +(3184.11 + 1838.35i) q^{82} +(6020.56 + 10427.9i) q^{83} +(63737.4 + 9961.50i) q^{84} +(-22943.2 + 39738.8i) q^{85} +(-1776.43 + 1025.62i) q^{86} +(-42880.7 + 14564.8i) q^{87} +(-644.916 + 1117.03i) q^{88} +(70854.6 - 122724. i) q^{89} +(1305.16 - 172.314i) q^{90} +(-81301.3 - 42581.7i) q^{91} +(-90601.9 + 52309.0i) q^{92} +(11245.7 - 56590.0i) q^{93} -2789.03i q^{94} +35414.6i q^{95} +(-2602.64 + 13096.9i) q^{96} +(-71300.8 + 41165.5i) q^{97} +(-386.340 - 4685.87i) q^{98} +(-10675.2 - 13901.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9} - 6 q^{10} + 567 q^{11} - 1542 q^{12} + 543 q^{13} - 1638 q^{14} + 234 q^{15} + 16446 q^{16} - 801 q^{17} - 2022 q^{18} - 6 q^{19}+ \cdots - 144540 q^{99}+O(q^{100}) $ 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * q^96 - 104037 * q^97 - 646797 * q^98 - 144540 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	0.279751i		−	0.0494534i	−0.999694	−	0.0247267i	$-0.992128\pi$
$2$		−	0.279751i		−	0.0494534i	0.999694	−	0.0247267i	$-0.00787156\pi$
$3$	−15.2895	−	3.03836i	−0.980821	−	0.194911i
$3$	−15.2895	−	3.03836i	−0.980821	−	0.194911i
$4$	31.9217			0.997554
$5$	9.68296	+	16.7714i	0.173214	+	0.300015i	0.939542	−	0.342434i	$-0.111251\pi$
$5$	9.68296	+	16.7714i	0.173214	+	0.300015i	−0.766328	+	0.642450i	$0.777918\pi$
$6$	−0.849983	+	4.27725i	−0.00963901	+	0.0485050i
$7$	−129.532	+	5.33078i	−0.999154	+	0.0411193i
$7$	−129.532	+	5.33078i	−0.999154	+	0.0411193i
$8$		−	17.8822i		−	0.0987859i
$9$	224.537	+	92.9099i	0.924020	+	0.382345i
$10$	4.69181	−	2.70882i	0.0148368	−	0.00856603i
$11$	−62.4661	−	36.0648i	−0.155655	−	0.0898673i	0.420150	−	0.907455i	$-0.361978\pi$
$11$	−62.4661	−	36.0648i	−0.155655	−	0.0898673i	−0.575804	+	0.817588i	$0.695311\pi$
$12$	−488.067	−	96.9897i	−0.978422	−	0.194434i
$13$	613.086	+	353.966i	1.00615	+	0.580902i	0.910063	−	0.414471i	$-0.136033\pi$
$13$	613.086	+	353.966i	1.00615	+	0.580902i	0.0960889	+	0.995373i	$0.469367\pi$
$14$	1.49129	+	36.2367i	0.00203349	+	0.0494116i
$15$	−97.0900	−	285.846i	−0.111416	−	0.328023i
$16$	1016.49			0.992669
$17$	1184.72	+	2052.00i	0.994245	+	1.72208i	0.589897	+	0.807478i	$0.299168\pi$
$17$	1184.72	+	2052.00i	0.994245	+	1.72208i	0.404348	+	0.914605i	$0.367498\pi$
$18$	25.9916	−	62.8144i	0.0189083	−	0.0456959i
$19$	1583.71	+	914.355i	1.00645	+	0.581073i	0.910150	−	0.414279i	$-0.135966\pi$
$19$	1583.71	+	914.355i	1.00645	+	0.581073i	0.0962985	+	0.995352i	$0.469300\pi$
$20$	309.097	+	535.371i	0.172790	+	0.299282i
$21$	1996.68	+	312.060i	0.988006	+	0.154415i
$22$	−10.0892	+	17.4749i	−0.00444425	+	0.00769766i
$23$	−2838.25	+	1638.66i	−1.11875	+	0.645908i	−0.941080	−	0.338183i	$-0.890188\pi$
$23$	−2838.25	+	1638.66i	−1.11875	+	0.645908i	−0.177665	+	0.984091i	$0.556854\pi$
$24$	−54.3324	+	273.409i	−0.0192544	+	0.0968913i
$25$	1374.98	−	2381.54i	0.439994	−	0.762092i
$26$	99.0222	−	171.511i	0.0287276	−	0.0497576i
$27$	−3150.76	−	2102.77i	−0.831775	−	0.555113i
$28$	−4134.89	+	170.168i	−0.996711	+	0.0410187i
$29$	2515.93	−	1452.57i	0.555524	−	0.320732i	−0.195823	−	0.980639i	$-0.562738\pi$
$29$	2515.93	−	1452.57i	0.555524	−	0.320732i	0.751347	+	0.659907i	$0.229404\pi$
$30$	−79.9656	+	27.1610i	−0.0162218	+	0.00550989i
$31$			3701.23i			0.691739i	0.938283	+	0.345870i	$0.112416\pi$
$31$			3701.23i			0.691739i	−0.938283	+	0.345870i	$0.887584\pi$
$32$		−	856.594i		−	0.147877i
$33$	845.496	+	741.206i	0.135153	+	0.118483i
$34$	574.048	−	331.427i	0.0851629	−	0.0491688i
$35$	−1343.66	−	2120.81i	−0.185404	−	0.292639i
$36$	7167.60	+	2965.84i	0.921760	+	0.381410i
$37$	2257.86	−	3910.73i	0.271140	−	0.469628i	−0.698014	−	0.716084i	$-0.745933\pi$
$37$	2257.86	−	3910.73i	0.271140	−	0.469628i	0.969154	+	0.246456i	$0.0792662\pi$
$38$	255.792	−	443.044i	0.0287361	−	0.0497723i
$39$	−8298.30	−	7274.73i	−0.873630	−	0.765870i
$40$	299.908	−	173.152i	0.0296373	−	0.0171111i
$41$	−6571.37	+	11382.0i	−0.610515	+	1.05744i	0.380638	+	0.924724i	$0.375704\pi$
$41$	−6571.37	+	11382.0i	−0.610515	+	1.05744i	−0.991154	+	0.132720i	$0.957629\pi$
$42$	87.2991	−	558.572i	0.00763636	−	0.0488603i
$43$	−3666.20	−	6350.05i	−0.302375	−	0.523728i	0.674299	−	0.738459i	$-0.264446\pi$
$43$	−3666.20	−	6350.05i	−0.302375	−	0.523728i	−0.976673	+	0.214730i	$0.931113\pi$
$44$	−1994.03	−	1151.25i	−0.155274	−	0.0896475i
$45$	615.954	+	4665.43i	0.0453437	+	0.343448i
$46$	458.418	+	794.003i	0.0319424	+	0.0553258i
$47$	9969.70			0.658321			0.329160	−	0.944274i	$-0.393234\pi$
$47$	9969.70			0.658321			0.329160	+	0.944274i	$0.393234\pi$
$48$	−15541.7	−	3088.47i	−0.973631	−	0.193482i
$49$	16750.2	−	1381.01i	0.996618	−	0.0821690i
$50$	−666.237	−	384.652i	−0.0376880	−	0.0217592i
$51$	−11879.1	−	34973.6i	−0.639524	−	1.88284i
$52$	19570.8	+	11299.2i	1.00369	+	0.579481i
$53$	−25517.8	+	14732.7i	−1.24782	+	0.720431i	−0.970675	−	0.240396i	$-0.922723\pi$
$53$	−25517.8	+	14732.7i	−1.24782	+	0.720431i	−0.277148	+	0.960827i	$0.589389\pi$
$54$	−588.251	+	881.427i	−0.0274523	+	0.0411341i
$55$		−	1396.86i		−	0.0622651i
$56$	95.3258	+	2316.32i	0.00406201	+	0.0987024i
$57$	−21436.0	−	18791.9i	−0.873888	−	0.766096i
$58$	−406.358	−	703.833i	−0.0158613	−	0.0274726i
$59$	−40234.8			−1.50478			−0.752388	−	0.658721i	$-0.771098\pi$
$59$	−40234.8			−1.50478			−0.752388	+	0.658721i	$0.771098\pi$
$60$	−3099.28	−	9124.70i	−0.111143	−	0.327220i
$61$		−	36052.6i		−	1.24054i	−0.784388	−	0.620271i	$-0.787023\pi$
$61$		−	36052.6i		−	1.24054i	0.784388	−	0.620271i	$-0.212977\pi$
$62$	1035.42			0.0342089
$63$	−29580.0	−	10837.9i	−0.938960	−	0.344027i
$64$	32288.1			0.985356
$65$			13709.7i			0.402481i
$66$	207.353	−	236.528i	0.00585937	−	0.00668380i
$67$	15494.8			0.421695			0.210848	−	0.977519i	$-0.432378\pi$
$67$	15494.8			0.421695			0.210848	+	0.977519i	$0.432378\pi$
$68$	37818.3	+	65503.3i	0.991814	+	1.71787i
$69$	48374.2	−	16430.7i	1.22318	−	0.415465i
$70$	−593.300	+	375.890i	−0.0144720	+	0.00916886i
$71$			3103.20i			0.0730573i	0.999333	+	0.0365286i	$0.0116300\pi$
$71$			3103.20i			0.0730573i	−0.999333	+	0.0365286i	$0.988370\pi$
$72$	1661.43	−	4015.20i	0.0377703	−	0.0912801i
$73$	−35514.8	+	20504.5i	−0.780014	+	0.450341i	−0.836435	−	0.548066i	$-0.815364\pi$
$73$	−35514.8	+	20504.5i	−0.780014	+	0.450341i	0.0564210	+	0.998407i	$0.482031\pi$
$74$	−1094.03	−	631.639i	−0.0232247	−	0.0134088i
$75$	−28258.7	+	32234.8i	−0.580095	+	0.661716i
$76$	50554.8	+	29187.8i	1.00399	+	0.579652i
$77$	8283.62	+	4338.56i	0.159218	+	0.0833909i
$78$	−2035.11	+	2321.46i	−0.0378749	+	0.0432040i
$79$	76810.2			1.38469			0.692343	−	0.721569i	$-0.256579\pi$
$79$	76810.2			1.38469			0.692343	+	0.721569i	$0.256579\pi$
$80$	9842.66	+	17048.0i	0.171944	+	0.297816i
$81$	41784.5	+	41723.4i	0.707624	+	0.706589i
$82$	3184.11	+	1838.35i	0.0522942	+	0.0301921i
$83$	6020.56	+	10427.9i	0.0959272	+	0.166151i	0.909995	−	0.414619i	$-0.136085\pi$
$83$	6020.56	+	10427.9i	0.0959272	+	0.166151i	−0.814068	+	0.580770i	$0.802752\pi$
$84$	63737.4	+	9961.50i	0.985590	+	0.154038i
$85$	−22943.2	+	39738.8i	−0.344434	+	0.596578i
$86$	−1776.43	+	1025.62i	−0.0259002	+	0.0149535i
$87$	−42880.7	+	14564.8i	−0.607384	+	0.206303i
$88$	−644.916	+	1117.03i	−0.00887762	+	0.0153765i
$89$	70854.6	−	122724.i	0.948185	−	1.64231i	0.198941	−	0.980011i	$-0.436250\pi$
$89$	70854.6	−	122724.i	0.948185	−	1.64231i	0.749244	−	0.662294i	$-0.230417\pi$
$90$	1305.16	−	172.314i	0.0169847	−	0.00224240i
$91$	−81301.3	−	42581.7i	−1.02919	−	0.539038i
$92$	−90601.9	+	52309.0i	−1.11601	+	0.644328i
$93$	11245.7	−	56590.0i	0.134827	−	0.678472i
$94$		−	2789.03i		−	0.0325562i
$95$			35414.6i			0.402600i
$96$	−2602.64	+	13096.9i	−0.0288228	+	0.145041i
$97$	−71300.8	+	41165.5i	−0.769422	+	0.444226i	−0.832669	−	0.553772i	$-0.813188\pi$
$97$	−71300.8	+	41165.5i	−0.769422	+	0.444226i	0.0632461	+	0.997998i	$0.479855\pi$
$98$	−386.340	−	4685.87i	−0.00406354	−	0.0492862i
$99$	−10675.2	−	13901.6i	−0.109468	−	0.142553i
$100$	43891.8	−	76022.8i	0.438918	−	0.760228i
$101$	9656.41	−	16725.4i	0.0941916	−	0.163145i	−0.815079	−	0.579349i	$-0.803307\pi$
$101$	9656.41	−	16725.4i	0.0941916	−	0.163145i	0.909271	+	0.416205i	$0.136640\pi$
$102$	−9783.89	+	3323.18i	−0.0931131	+	0.0316267i
$103$	57273.5	−	33066.9i	0.531938	−	0.307114i	−0.209867	−	0.977730i	$-0.567303\pi$
$103$	57273.5	−	33066.9i	0.531938	−	0.307114i	0.741805	+	0.670615i	$0.233970\pi$
$104$	6329.67	−	10963.3i	0.0573849	−	0.0993936i
$105$	14100.1	+	36508.7i	0.124810	+	0.323164i
$106$	4121.48	+	7138.62i	0.0356278	+	0.0617091i
$107$	842.154	+	486.218i	0.00711102	+	0.00410555i	0.503551	−	0.863965i	$-0.332026\pi$
$107$	842.154	+	486.218i	0.00711102	+	0.00410555i	−0.496440	+	0.868071i	$0.665360\pi$
$108$	−100578.	−	67124.0i	−0.829740	−	0.553756i
$109$	67228.6	+	116443.i	0.541986	+	0.938747i	0.998790	+	0.0491795i	$0.0156606\pi$
$109$	67228.6	+	116443.i	0.541986	+	0.938747i	−0.456804	+	0.889567i	$0.651006\pi$
$110$	−390.771			−0.00307922
$111$	−46403.7	+	52932.9i	−0.357475	+	0.407773i
$112$	−131669.	+	5418.70i	−0.991830	+	0.0408178i
$113$	27529.2	+	15894.0i	0.202814	+	0.117095i	0.597967	−	0.801521i	$-0.295975\pi$
$113$	27529.2	+	15894.0i	0.202814	+	0.117095i	−0.395154	+	0.918615i	$0.629309\pi$
$114$	−5257.05	+	5996.73i	−0.0378861	+	0.0432168i
$115$	−54965.3	−	31734.2i	−0.387565	−	0.223761i
$116$	80312.7	−	46368.6i	0.554166	−	0.319948i
$117$	104774.	+	136440.i	0.707599	+	0.921462i
$118$			11255.7i			0.0744163i
$119$	−164398.	−	259484.i	−1.06422	−	1.67974i
$120$	−5111.54	+	1736.18i	−0.0324040	+	0.0110063i
$121$	−77924.2	−	134969.i	−0.483848	−	0.838049i
$122$	−10085.7			−0.0613491
$123$	135055.	−	154058.i	0.804913	−	0.918167i
$124$			118150.i			0.690047i
$125$	113774.			0.651280
$126$	−3031.90	+	8275.03i	−0.0170133	+	0.0464348i
$127$	−36741.8			−0.202140			−0.101070	−	0.994879i	$-0.532227\pi$
$127$	−36741.8			−0.202140			−0.101070	+	0.994879i	$0.532227\pi$
$128$		−	36443.6i		−	0.196606i
$129$	36760.6	+	108228.i	0.194495	+	0.572620i
$130$	3835.31			0.0199041
$131$	107252.	+	185766.i	0.546043	+	0.945774i	0.998540	+	0.0540082i	$0.0171997\pi$
$131$	107252.	+	185766.i	0.546043	+	0.945774i	−0.452498	+	0.891766i	$0.649467\pi$
$132$	26989.7	+	23660.6i	0.134823	+	0.118193i
$133$	−210016.	−	109996.i	−1.02949	−	0.539197i
$134$		−	4334.68i		−	0.0208543i
$135$	4757.63	−	73203.5i	0.0224676	−	0.345699i
$136$	36694.1	−	21185.4i	0.170118	−	0.0982174i
$137$	−265122.	−	153068.i	−1.20683	−	0.696762i	−0.244762	−	0.969583i	$-0.578710\pi$
$137$	−265122.	−	153068.i	−1.20683	−	0.696762i	−0.962065	+	0.272821i	$0.912043\pi$
$138$	−4596.51	−	13532.7i	−0.0205461	−	0.0604906i
$139$	−236346.	−	136454.i	−1.03755	−	0.599032i	−0.118415	−	0.992964i	$-0.537781\pi$
$139$	−236346.	−	136454.i	−1.03755	−	0.599032i	−0.919140	+	0.393932i	$0.871115\pi$
$140$	−42891.9	−	67700.1i	−0.184950	−	0.291924i
$141$	−152432.	−	30291.5i	−0.645695	−	0.128314i
$142$	868.122			0.00361293
$143$	−25531.4	−	44221.7i	−0.104408	−	0.180840i
$144$	228240.	+	94442.2i	0.917246	+	0.379542i
$145$	48723.2	+	28130.4i	0.192449	+	0.111111i
$146$	5736.15	+	9935.30i	0.0222709	+	0.0385744i
$147$	−260297.	−	29778.0i	−0.993520	−	0.113659i
$148$	72074.9	−	124837.i	0.270476	−	0.468479i
$149$	245740.	−	141878.i	0.906798	−	0.523540i	0.0273982	−	0.999625i	$-0.491278\pi$
$149$	245740.	−	141878.i	0.906798	−	0.523540i	0.879399	+	0.476085i	$0.157944\pi$
$150$	9017.71	+	7905.40i	0.0327241	+	0.0286877i
$151$	−125763.	+	217829.i	−0.448861	+	0.777451i	−0.998312	−	0.0580754i	$-0.981504\pi$
$151$	−125763.	+	217829.i	−0.448861	+	0.777451i	0.549451	+	0.835526i	$0.314837\pi$
$152$	16350.6	−	28320.1i	0.0574019	−	0.0994229i
$153$	75362.6	+	570821.i	0.260272	+	1.97138i
$154$	1213.72	−	2317.35i	0.00412397	−	0.00787390i
$155$	−62074.8	+	35838.9i	−0.207532	+	0.119819i
$156$	−264896.	−	232222.i	−0.871494	−	0.763997i
$157$			249719.i			0.808541i	0.914640	+	0.404270i	$0.132475\pi$
$157$			249719.i			0.808541i	−0.914640	+	0.404270i	$0.867525\pi$
$158$		−	21487.7i		−	0.0684775i
$159$	434917.	−	147723.i	1.36431	−	0.463400i
$160$	14366.3	−	8294.36i	0.0443653	−	0.0256143i
$161$	358909.	−	227390.i	1.09124	−	0.691364i
$162$	11672.1	−	11689.3i	0.0349432	−	0.0349945i
$163$	27230.3	−	47164.3i	0.0802756	−	0.139041i	−0.823093	−	0.567907i	$-0.807753\pi$
$163$	27230.3	−	47164.3i	0.0802756	−	0.139041i	0.903368	+	0.428866i	$0.141087\pi$
$164$	−209770.	+	363332.i	−0.609022	+	1.05486i
$165$	−4244.15	+	21357.2i	−0.0121361	+	0.0610709i
$166$	2917.22	−	1684.26i	0.00821672	−	0.00474393i
$167$	15599.4	−	27019.0i	0.0432831	−	0.0749685i	−0.843572	−	0.537016i	$-0.819552\pi$
$167$	15599.4	−	27019.0i	0.0432831	−	0.0749685i	0.886855	+	0.462047i	$0.152885\pi$
$168$	5580.31	−	35704.9i	0.0152541	−	0.0976011i
$169$	64936.9	+	112474.i	0.174894	+	0.302925i
$170$	11117.0	+	6418.38i	0.0295028	+	0.0170335i
$171$	270648.	+	352449.i	0.707807	+	0.921734i
$172$	−117032.	−	202705.i	−0.301635	−	0.522447i
$173$	191874.			0.487416			0.243708	−	0.969849i	$-0.421636\pi$
$173$	191874.			0.487416			0.243708	+	0.969849i	$0.421636\pi$
$174$	4074.51	+	11995.9i	0.0102024	+	0.0300372i
$175$	−165409.	+	315815.i	−0.408285	+	0.779539i
$176$	−63496.3	−	36659.6i	−0.154514	−	0.0892085i
$177$	615169.	+	122248.i	1.47592	+	0.293297i
$178$	−34332.1	−	19821.6i	−0.0812176	−	0.0468910i
$179$	292453.	−	168848.i	0.682220	−	0.393880i	−0.118471	−	0.992957i	$-0.537799\pi$
$179$	292453.	−	168848.i	0.682220	−	0.393880i	0.800691	+	0.599078i	$0.204466\pi$
$180$	19662.3	+	148929.i	0.0452328	+	0.342608i
$181$			157471.i			0.357277i	0.983915	+	0.178638i	$0.0571692\pi$
$181$			157471.i			0.357277i	−0.983915	+	0.178638i	$0.942831\pi$
$182$	−11912.3	+	22744.1i	−0.0266573	+	0.0508968i
$183$	−109541.	+	551225.i	−0.241795	+	1.21675i
$184$	29302.9	+	50754.1i	0.0638066	+	0.110516i
$185$	87451.1			0.187861
$186$	−15831.1	−	3145.99i	−0.0335528	−	0.00666768i
$187$		−	170907.i		−	0.357401i
$188$	318250.			0.656711
$189$	419334.	+	255580.i	0.853897	+	0.520442i
$190$	9907.27			0.0199100
$191$		−	858285.i		−	1.70235i	−0.524885	−	0.851173i	$-0.675892\pi$
$191$		−	858285.i		−	1.70235i	0.524885	−	0.851173i	$-0.324108\pi$
$192$	−493669.	−	98102.9i	−0.966458	−	0.192056i
$193$	5366.50			0.0103705			0.00518523	−	0.999987i	$-0.498349\pi$
$193$	5366.50			0.0103705			0.00518523	+	0.999987i	$0.498349\pi$
$194$	11516.1	+	19946.4i	0.0219685	+	0.0380506i
$195$	41655.1	−	209615.i	0.0784479	−	0.394762i
$196$	534694.	−	44084.4i	0.994181	−	0.0819681i
$197$			523078.i			0.960286i	0.877190	+	0.480143i	$0.159415\pi$
$197$			523078.i			0.960286i	−0.877190	+	0.480143i	$0.840585\pi$
$198$	−3888.98	+	2986.38i	−0.00704973	+	0.00541355i
$199$	−578380.	+	333928.i	−1.03533	+	0.597751i	−0.918508	−	0.395402i	$-0.870605\pi$
$199$	−578380.	+	333928.i	−1.03533	+	0.597751i	−0.116826	+	0.993152i	$0.537272\pi$
$200$	−42587.0	−	24587.6i	−0.0752839	−	0.0434652i
$201$	−236907.	−	47078.7i	−0.413607	−	0.0821929i
$202$	−4678.94	−	2701.39i	−0.00806806	−	0.00465810i
$203$	−318150.	+	201566.i	−0.541866	+	0.343303i
$204$	−379201.	−	1.11642e6i	−0.637960	−	1.87824i
$205$	−254521.			−0.422999
$206$	−9250.49	−	16022.3i	−0.0151879	−	0.0263061i
$207$	−789540.	+	104239.i	−1.28070	+	0.169085i
$208$	623198.	+	359804.i	0.998775	+	0.576643i
$209$	−65952.0	−	114232.i	−0.104439	−	0.180894i
$210$	10213.3	−	3944.50i	0.0159816	−	0.00617226i
$211$	385602.	−	667882.i	0.596257	−	1.03275i	−0.397112	−	0.917770i	$-0.629987\pi$
$211$	385602.	−	667882.i	0.596257	−	1.03275i	0.993368	−	0.114976i	$-0.0366793\pi$
$212$	−814571.	+	470293.i	−1.24477	+	0.718669i
$213$	9428.62	−	47446.3i	0.0142397	−	0.0716561i
$214$	136.020	−	235.593i	0.000203033	−	0.000351664i
$215$	70999.4	−	122974.i	0.104751	−	0.181434i
$216$	−37602.0	+	56342.4i	−0.0548374	+	0.0821676i
$217$	−19730.5	−	479429.i	−0.0284438	−	0.691154i
$218$	32575.1	−	18807.3i	0.0464242	−	0.0268031i
$219$	605303.	−	205596.i	0.852831	−	0.289671i
$220$		−	44590.0i		−	0.0621128i
$221$			1.67740e6i			2.31024i
$222$	14808.0	+	12981.5i	0.0201658	+	0.0176784i
$223$	471993.	−	272505.i	0.635584	−	0.366955i	−0.147327	−	0.989088i	$-0.547067\pi$
$223$	471993.	−	272505.i	0.635584	−	0.366955i	0.782912	+	0.622133i	$0.213734\pi$
$224$	4566.31	+	110956.i	0.00608059	+	0.147752i
$225$	530002.	−	406993.i	0.697945	−	0.535958i
$226$	4446.36	−	7701.31i	0.00579073	−	0.0100298i
$227$	65954.1	−	114236.i	0.0849527	−	0.147142i	−0.820418	−	0.571764i	$-0.806259\pi$
$227$	65954.1	−	114236.i	0.0849527	−	0.147142i	0.905371	+	0.424621i	$0.139593\pi$
$228$	−684273.	−	599870.i	−0.871751	−	0.764223i
$229$	313632.	−	181075.i	0.395213	−	0.228176i	−0.289203	−	0.957268i	$-0.593390\pi$
$229$	313632.	−	181075.i	0.395213	−	0.228176i	0.684416	+	0.729091i	$0.260057\pi$
$230$	−8877.68	+	15376.6i	−0.0110657	+	0.0191664i
$231$	−113470.	−	91502.9i	−0.139911	−	0.112825i
$232$	−25975.1	−	44990.2i	−0.0316838	−	0.0548780i
$233$	−708649.	−	409139.i	−0.855148	−	0.493720i	0.00723637	−	0.999974i	$-0.497697\pi$
$233$	−708649.	−	409139.i	−0.855148	−	0.493720i	−0.862385	+	0.506254i	$0.831030\pi$
$234$	38169.2	−	29310.5i	0.0455694	−	0.0349932i
$235$	96536.2	+	167206.i	0.114030	+	0.197506i
$236$	−1.28436e6			−1.50109
$237$	−1.17439e6	−	233377.i	−1.35813	−	0.269890i
$238$	−72590.9	+	45990.5i	−0.0830691	+	0.0526291i
$239$	205734.	+	118781.i	0.232977	+	0.134509i	0.611944	−	0.790901i	$-0.290388\pi$
$239$	205734.	+	118781.i	0.232977	+	0.134509i	−0.378968	+	0.925410i	$0.623721\pi$
$240$	−98691.3	−	290560.i	−0.110599	−	0.325618i
$241$	−108137.	−	62433.0i	−0.119931	−	0.0692423i	0.438834	−	0.898568i	$-0.355391\pi$
$241$	−108137.	−	62433.0i	−0.119931	−	0.0692423i	−0.558766	+	0.829326i	$0.688725\pi$
$242$	−37757.6	+	21799.4i	−0.0414444	+	0.0239279i
$243$	−512093.	−	764885.i	−0.556331	−	0.830961i
$244$		−	1.15086e6i		−	1.23751i
$245$	185353.	+	267551.i	0.197280	+	0.284768i
$246$	−43097.9	−	37781.9i	−0.0454065	−	0.0398057i
$247$	647301.	+	1.12116e6i	0.675093	+	1.16930i
$248$	66186.1			0.0683341
$249$	−60367.5	−	177730.i	−0.0617028	−	0.181661i
$250$		−	31828.4i		−	0.0322080i
$251$	146234.			0.146509			0.0732543	−	0.997313i	$-0.476662\pi$
$251$	146234.			0.146509			0.0732543	+	0.997313i	$0.476662\pi$
$252$	−944246.	−	345963.i	−0.936664	−	0.343185i
$253$	236392.			0.232184
$254$			10278.6i			0.00999649i
$255$	471530.	−	537876.i	0.454108	−	0.518002i
$256$	1.02303e6			0.975633
$257$	354325.	+	613708.i	0.334633	+	0.579601i	0.983414	−	0.181374i	$-0.0580544\pi$
$257$	354325.	+	613708.i	0.334633	+	0.579601i	−0.648781	+	0.760975i	$0.724721\pi$
$258$	30276.9	−	10283.8i	0.0283180	−	0.00961845i
$259$	−271618.	+	518602.i	−0.251600	+	0.480379i
$260$			437639.i			0.401497i
$261$	699876.	−	92401.2i	0.635945	−	0.0839607i
$262$	51968.1	−	30003.8i	0.0467718	−	0.0270037i
$263$	−172879.	−	99811.7i	−0.154118	−	0.0889800i	0.420958	−	0.907080i	$-0.361694\pi$
$263$	−172879.	−	99811.7i	−0.154118	−	0.0889800i	−0.575076	+	0.818100i	$0.695027\pi$
$264$	13254.4	−	15119.3i	0.0117044	−	0.0133512i
$265$	−494175.	−	285312.i	−0.432281	−	0.249577i
$266$	−30771.5	+	58752.0i	−0.0266652	+	0.0509118i
$267$	−1.45621e6	+	1.66110e6i	−1.25010	+	1.42600i
$268$	494620.			0.420664
$269$	−845922.	−	1.46518e6i	−0.712771	−	1.23455i	−0.963813	−	0.266579i	$-0.914107\pi$
$269$	−845922.	−	1.46518e6i	−0.712771	−	1.23455i	0.251043	−	0.967976i	$-0.419227\pi$
$270$	−20478.8	−	1330.95i	−0.0170960	−	0.00111110i
$271$	−155172.	−	89588.8i	−0.128349	−	0.0741021i	0.434451	−	0.900695i	$-0.356942\pi$
$271$	−155172.	−	89588.8i	−0.128349	−	0.0741021i	−0.562800	+	0.826593i	$0.690276\pi$
$272$	1.20426e6	+	2.08584e6i	0.986957	+	1.70946i
$273$	1.11368e6	+	898075.i	0.904384	+	0.729300i
$274$	−42821.0	+	74168.2i	−0.0344573	+	0.0596817i
$275$	−171779.	+	99176.8i	−0.136974	+	0.0790821i
$276$	1.54419e6	−	524497.i	1.22019	−	0.414448i
$277$	860819.	−	1.49098e6i	0.674081	−	1.16754i	−0.302655	−	0.953100i	$-0.597873\pi$
$277$	860819.	−	1.49098e6i	0.674081	−	1.16754i	0.976737	−	0.214443i	$-0.0687936\pi$
$278$	−38173.2	+	66118.0i	−0.0296242	+	0.0513106i
$279$	−343881.	+	831063.i	−0.264483	+	0.639180i
$280$	−37924.7	+	24027.5i	−0.0289086	+	0.0183153i
$281$	787370.	−	454588.i	0.594857	−	0.343441i	−0.172158	−	0.985069i	$-0.555074\pi$
$281$	787370.	−	454588.i	0.594857	−	0.343441i	0.767016	+	0.641628i	$0.221741\pi$
$282$	−8474.08	+	42642.9i	−0.00634556	+	0.0319318i
$283$		−	276609.i		−	0.205305i	−0.994717	−	0.102653i	$-0.967267\pi$
$283$		−	276609.i		−	0.205305i	0.994717	−	0.102653i	$-0.0327330\pi$
$284$			99059.5i			0.0728786i
$285$	107602.	−	541472.i	0.0784711	−	0.394879i
$286$	−12371.1	+	7142.43i	−0.00894317	+	0.00516334i
$287$	790530.	−	1.50936e6i	0.566518	−	1.08165i
$288$	79586.0	−	192337.i	0.0565400	−	0.136641i
$289$	−2.09720e6	+	3.63245e6i	−1.47705	+	2.55832i
$290$	7869.49	−	13630.4i	0.00549480	−	0.00951727i
$291$	1.21523e6	−	412762.i	0.841250	−	0.285738i
$292$	−1.13370e6	+	654539.i	−0.778107	+	0.449240i
$293$	565429.	−	979352.i	0.384777	−	0.666453i	−0.606961	−	0.794731i	$-0.707612\pi$
$293$	565429.	−	979352.i	0.384777	−	0.666453i	0.991738	+	0.128278i	$0.0409450\pi$
$294$	−8330.42	+	72818.4i	−0.00562081	+	0.0491330i
$295$	−389592.	−	674792.i	−0.260648	−	0.451456i
$296$	−69932.3	−	40375.4i	−0.0463926	−	0.0267848i
$297$	120980.	+	244983.i	0.0795831	+	0.161155i
$298$	−39690.5	−	68746.0i	−0.0258908	−	0.0448443i
$299$	−2.32012e6			−1.50084
$300$	−902067.	+	1.02899e6i	−0.578676	+	0.660098i
$301$	508742.	+	802992.i	0.323654	+	0.510852i
$302$	60937.8	+	35182.4i	0.0384476	+	0.0221977i
$303$	−198459.	+	226383.i	−0.124184	+	0.141657i
$304$	1.60983e6	+	929436.i	0.999070	+	0.576813i
$305$	604651.	−	349095.i	0.372182	−	0.214879i
$306$	159688.	−	21082.8i	0.0974917	−	0.0128713i
$307$		−	2.56004e6i		−	1.55025i	−0.631810	−	0.775123i	$-0.717688\pi$
$307$		−	2.56004e6i		−	1.55025i	0.631810	−	0.775123i	$-0.282312\pi$
$308$	264427.	+	138494.i	0.158829	+	0.0831869i
$309$	−976152.	+	331558.i	−0.581596	+	0.197544i
$310$	10026.0	+	17365.5i	0.00592545	+	0.0102632i
$311$	843325.			0.494418			0.247209	−	0.968962i	$-0.420487\pi$
$311$	843325.			0.494418			0.247209	+	0.968962i	$0.420487\pi$
$312$	−130088.	+	148392.i	−0.0756572	+	0.0863024i
$313$		−	4946.03i		−	0.00285362i	−0.999999	−	0.00142681i	$-0.999546\pi$
$313$		−	4946.03i		−	0.00285362i	0.999999	−	0.00142681i	$-0.000454167\pi$
$314$	69859.0			0.0399851
$315$	−104656.	−	601040.i	−0.0594277	−	0.341293i
$316$	2.45192e6			1.38130
$317$			1.21770e6i			0.680601i	0.940317	+	0.340301i	$0.110529\pi$
$317$			1.21770e6i			0.680601i	−0.940317	+	0.340301i	$0.889471\pi$
$318$	−41325.7	−	121668.i	−0.0229167	−	0.0674698i
$319$	−209547.			−0.115293
$320$	312645.	+	541516.i	0.170677	+	0.295622i
$321$	−11398.8	−	9992.78i	−0.00617442	−	0.00541282i
$322$	−63612.5	−	100405.i	−0.0341903	−	0.0539656i
$323$			4.33302e6i			2.31092i
$324$	1.33383e6	+	1.33188e6i	0.705894	+	0.704861i
$325$	1.68596e6	−	973392.i	0.885401	−	0.511186i
$326$	−13194.2	−	7617.70i	−0.00687607	−	0.00396990i
$327$	−674094.	−	1.98462e6i	−0.348619	−	1.02638i
$328$	203534.	+	117510.i	0.104461	+	0.0603103i
$329$	−1.29140e6	+	53146.3i	−0.657764	+	0.0270697i
$330$	5974.69	+	1187.30i	0.00302017	+	0.000600174i
$331$	−527489.			−0.264633			−0.132316	−	0.991208i	$-0.542241\pi$
$331$	−527489.			−0.264633			−0.132316	+	0.991208i	$0.542241\pi$
$332$	192187.	+	332877.i	0.0956926	+	0.165744i
$333$	870318.	−	668325.i	0.430098	−	0.330276i
$334$	−7558.60	−	4363.96i	−0.00370745	−	0.00214050i
$335$	150035.	+	259869.i	0.0730435	+	0.126515i
$336$	2.02961e6	+	317207.i	0.980763	+	0.153283i
$337$	682414.	−	1.18198e6i	0.327321	−	0.566936i	−0.654659	−	0.755925i	$-0.727188\pi$
$337$	682414.	−	1.18198e6i	0.327321	−	0.566936i	0.981979	+	0.188989i	$0.0605210\pi$
$338$	31464.7	−	18166.1i	0.0149807	−	0.00864910i
$339$	−372616.	−	326654.i	−0.176101	−	0.154379i
$340$	−732387.	+	1.26853e6i	−0.343592	+	0.595119i
$341$	133484.	−	231201.i	0.0621647	−	0.107672i
$342$	98597.8	−	75714.1i	0.0455829	−	0.0350035i
$343$	−2.16232e6	+	268177.i	−0.992397	+	0.123080i
$344$	−113553.	+	65559.6i	−0.0517370	+	0.0298704i
$345$	743971.	+	652204.i	0.336518	+	0.295010i
$346$		−	53676.8i		−	0.0241044i
$347$		−	2.15087e6i		−	0.958937i	−0.877559	−	0.479469i	$-0.840829\pi$
$347$		−	2.15087e6i		−	0.958937i	0.877559	−	0.479469i	$-0.159171\pi$
$348$	−1.36882e6	+	464933.i	−0.605898	+	0.205799i
$349$	−2.96896e6	+	1.71413e6i	−1.30479	+	0.753322i	−0.981222	−	0.192882i	$-0.938216\pi$
$349$	−2.96896e6	+	1.71413e6i	−1.30479	+	0.753322i	−0.323570	+	0.946204i	$0.604883\pi$
$350$	88349.6	+	46273.3i	0.0385509	+	0.0201911i
$351$	−1.18738e6	−	2.40444e6i	−0.514425	−	1.04171i
$352$	−30892.9	+	53508.0i	−0.0132893	+	0.0230177i
$353$	1.83294e6	−	3.17475e6i	0.782910	−	1.35604i	−0.147330	−	0.989087i	$-0.547068\pi$
$353$	1.83294e6	−	3.17475e6i	0.782910	−	1.35604i	0.930240	−	0.366952i	$-0.119599\pi$
$354$	34198.9	−	172094.i	0.0145045	−	0.0729891i
$355$	−52044.9	+	30048.1i	−0.0219183	+	0.0126545i
$356$	2.26180e6	−	3.91756e6i	0.945867	−	1.63829i
$357$	1.72516e6	+	4.46688e6i	0.716404	+	1.85496i
$358$	−47235.4	−	81814.1i	−0.0194787	−	0.0337381i
$359$	−3.39881e6	−	1.96230e6i	−1.39184	−	0.803581i	−0.398324	−	0.917245i	$-0.630408\pi$
$359$	−3.39881e6	−	1.96230e6i	−1.39184	−	0.803581i	−0.993519	+	0.113664i	$0.963741\pi$
$360$	83428.0	−	11014.6i	0.0339278	−	0.00447932i
$361$	434041.	+	751781.i	0.175292	+	0.303615i
$362$	44052.7			0.0176686
$363$	781337.	+	2.30036e6i	0.311223	+	0.916283i
$364$	−2.59528e6	−	1.35928e6i	−1.02667	−	0.537720i
$365$	−687777.	−	397088.i	−0.270219	−	0.156011i
$366$	154206.	+	30644.1i	0.0601724	+	0.0119576i
$367$	−2.40059e6	−	1.38598e6i	−0.930364	−	0.537146i	−0.0434373	−	0.999056i	$-0.513831\pi$
$367$	−2.40059e6	−	1.38598e6i	−0.930364	−	0.537146i	−0.886927	+	0.461910i	$0.847164\pi$
$368$	−2.88506e6	+	1.66569e6i	−1.11054	+	0.641173i
$369$	−2.53301e6	+	1.94512e6i	−0.968437	+	0.743671i
$370$		−	24464.5i		−	0.00929035i
$371$	3.22683e6	−	2.04439e6i	1.21714	−	0.771131i
$372$	358981.	−	1.80645e6i	0.134498	−	0.676813i
$373$	168844.	+	292446.i	0.0628367	+	0.108836i	0.895732	−	0.444594i	$-0.146652\pi$
$373$	168844.	+	292446.i	0.0628367	+	0.108836i	−0.832896	+	0.553430i	$0.813319\pi$
$374$	−47811.3			−0.0176747
$375$	−1.73955e6	−	345686.i	−0.638789	−	0.126942i
$376$		−	178280.i		−	0.0650328i
$377$	2.05664e6			0.745255
$378$	71498.7	−	117309.i	0.0257376	−	0.0422281i
$379$	2.60960e6			0.933201			0.466601	−	0.884468i	$-0.345479\pi$
$379$	2.60960e6			0.933201			0.466601	+	0.884468i	$0.345479\pi$
$380$			1.13050e6i			0.401615i
$381$	561763.	+	111635.i	0.198263	+	0.0393992i
$382$	−240106.			−0.0841869
$383$	−1.92385e6	−	3.33220e6i	−0.670153	−	1.16074i	−0.977860	−	0.209258i	$-0.932895\pi$
$383$	−1.92385e6	−	3.33220e6i	−0.670153	−	1.16074i	0.307707	−	0.951481i	$-0.400438\pi$
$384$	−110729.	+	557205.i	−0.0383206	+	0.192835i
$385$	7446.32	+	180938.i	0.00256030	+	0.0622124i
$386$		−	1501.28i		−	0.000512855i
$387$	−233215.	−	1.76645e6i	−0.0791552	−	0.599547i
$388$	−2.27604e6	+	1.31407e6i	−0.767541	+	0.443140i
$389$	−2.71888e6	−	1.56975e6i	−0.910996	−	0.525964i	−0.0302446	−	0.999543i	$-0.509629\pi$
$389$	−2.71888e6	−	1.56975e6i	−0.910996	−	0.525964i	−0.880752	+	0.473579i	$0.842962\pi$
$390$	−58639.9	−	11653.0i	−0.0195223	−	0.00387952i
$391$	−6.72507e6	−	3.88272e6i	−2.22461	−	1.28438i
$392$	−24695.5	−	299529.i	−0.00811714	−	0.0984519i
$393$	−1.07540e6	−	3.16613e6i	−0.351229	−	1.03406i
$394$	146331.			0.0474895
$395$	743750.	+	1.28821e6i	0.239847	+	0.415427i
$396$	−340769.	−	443763.i	−0.109200	−	0.142204i
$397$	−1.85309e6	−	1.06988e6i	−0.590092	−	0.340690i	0.175042	−	0.984561i	$-0.443994\pi$
$397$	−1.85309e6	−	1.06988e6i	−0.590092	−	0.340690i	−0.765134	+	0.643871i	$0.777327\pi$
$398$	93416.6	+	161802.i	0.0295608	+	0.0512008i
$399$	2.87682e6	+	2.31988e6i	0.904650	+	0.729515i
$400$	1.39766e6	−	2.42082e6i	0.436768	−	0.756505i
$401$	−783884.	+	452576.i	−0.243439	+	0.140550i	−0.616756	−	0.787154i	$-0.711554\pi$
$401$	−783884.	+	452576.i	−0.243439	+	0.140550i	0.373317	+	0.927704i	$0.378220\pi$
$402$	−13170.3	+	66275.0i	−0.00406472	+	0.0204543i
$403$	−1.31011e6	+	2.26918e6i	−0.401832	+	0.695994i
$404$	308249.	−	533904.i	0.0939613	−	0.162746i
$405$	−295160.	+	1.10479e6i	−0.0894171	+	0.334689i
$406$	56388.4	+	89002.8i	0.0169775	+	0.0267971i
$407$	−282079.	+	162859.i	−0.0844083	+	0.0487332i
$408$	−625403.	+	212423.i	−0.185999	+	0.0631760i
$409$			1.76491e6i			0.521692i	0.965380	+	0.260846i	$0.0840014\pi$
$409$			1.76491e6i			0.521692i	−0.965380	+	0.260846i	$0.915999\pi$
$410$			71202.6i			0.0209188i
$411$	3.58851e6	+	3.14587e6i	1.04787	+	0.918622i
$412$	1.82827e6	−	1.05555e6i	0.530637	−	0.306363i
$413$	5.21170e6	−	214483.i	1.50350	−	0.0618753i
$414$	29161.0	+	220874.i	0.00836182	+	0.0633351i
$415$	−116594.	+	201946.i	−0.0332318	+	0.0575593i
$416$	303205.	−	525166.i	0.0859019	−	0.148786i
$417$	3.19901e6	+	2.80442e6i	0.900898	+	0.789774i
$418$	−31956.6	+	18450.1i	−0.00894581	+	0.00516487i
$419$	2.40982e6	−	4.17393e6i	0.670579	−	1.16148i	−0.307162	−	0.951657i	$-0.599379\pi$
$419$	2.40982e6	−	4.17393e6i	0.670579	−	1.16148i	0.977740	−	0.209819i	$-0.0672875\pi$
$420$	450098.	+	1.16542e6i	0.124504	+	0.322374i
$421$	2.26419e6	+	3.92170e6i	0.622599	+	1.07837i	0.989000	+	0.147916i	$0.0472566\pi$
$421$	2.26419e6	+	3.92170e6i	0.622599	+	1.07837i	−0.366401	+	0.930457i	$0.619410\pi$
$422$	−186841.	−	107873.i	−0.0510729	−	0.0294869i
$423$	2.23856e6	+	926284.i	0.608301	+	0.251706i
$424$	263452.	+	456313.i	0.0711684	+	0.123267i
$425$	6.51587e6			1.74985
$426$	−13273.1	−	2637.67i	−0.00354364	−	0.000704200i
$427$	192188.	+	4.66997e6i	0.0510102	+	1.23949i
$428$	26883.0	+	15520.9i	0.00709363	+	0.00409551i
$429$	256001.	+	753700.i	0.0671580	+	0.197722i
$430$	−34402.2	−	19862.1i	−0.00897254	−	0.00518030i
$431$	−3.41505e6	+	1.97168e6i	−0.885531	+	0.511261i	−0.872478	−	0.488654i	$-0.837488\pi$
$431$	−3.41505e6	+	1.97168e6i	−0.885531	+	0.511261i	−0.0130526	+	0.999915i	$0.504155\pi$
$432$	−3.20272e6	−	2.13745e6i	−0.825677	−	0.551044i
$433$		−	3.11726e6i		−	0.799012i	−0.916731	−	0.399506i	$-0.869182\pi$
$433$		−	3.11726e6i		−	0.799012i	0.916731	−	0.399506i	$-0.130818\pi$
$434$	−134121.	+	5519.61i	−0.0341799	+	0.00140664i
$435$	−659483.	−	578137.i	−0.167101	−	0.146490i
$436$	2.14605e6	+	3.71707e6i	0.540660	+	0.936451i
$437$	−5.99329e6			−1.50128
$438$	−57515.8	−	169334.i	−0.0143252	−	0.0421754i
$439$		−	2.07832e6i		−	0.514697i	−0.966319	−	0.257349i	$-0.917151\pi$
$439$		−	2.07832e6i		−	0.514697i	0.966319	−	0.257349i	$-0.0828488\pi$
$440$	−24978.8			−0.00615091
$441$	3.88934e6	+	1.24617e6i	0.952312	+	0.305126i
$442$	469254.			0.114249
$443$			1.10755e6i			0.268136i	0.990972	+	0.134068i	$0.0428041\pi$
$443$			1.10755e6i			0.268136i	−0.990972	+	0.134068i	$0.957196\pi$
$444$	−1.48129e6	+	1.68971e6i	−0.356601	+	0.406775i
$445$	2.74433e6			0.656956
$446$	−76233.5	−	132040.i	−0.0181472	−	0.0314318i
$447$	−4.18832e6	+	1.42260e6i	−0.991450	+	0.336754i
$448$	−4.18235e6	+	172121.i	−0.984523	+	0.0405171i
$449$			6.61964e6i			1.54960i	0.632208	+	0.774798i	$0.282149\pi$
$449$			6.61964e6i			1.54960i	−0.632208	+	0.774798i	$0.717851\pi$
$450$	−113857.	−	148268.i	−0.0265050	−	0.0345158i
$451$	820976.	−	473991.i	0.190059	−	0.109731i
$452$	878780.	+	507364.i	0.202318	+	0.116808i
$453$	2.58470e6	−	2.94837e6i	0.591786	−	0.675052i
$454$	−31957.6	−	18450.7i	−0.00727669	−	0.00420120i
$455$	−73083.6	−	1.77585e6i	−0.0165497	−	0.402141i
$456$	−336040.	+	383321.i	−0.0756795	+	0.0863279i
$457$	263119.			0.0589335			0.0294667	−	0.999566i	$-0.490619\pi$
$457$	263119.			0.0589335			0.0294667	+	0.999566i	$0.490619\pi$
$458$	−50656.0	−	87738.7i	−0.0112841	−	0.0195446i
$459$	582102.	−	8.95653e6i	0.128964	−	1.98430i
$460$	−1.75459e6	−	1.01301e6i	−0.386617	−	0.223213i
$461$	3.29679e6	+	5.71021e6i	0.722503	+	1.25141i	0.959994	+	0.280022i	$0.0903417\pi$
$461$	3.29679e6	+	5.71021e6i	0.722503	+	1.25141i	−0.237491	+	0.971390i	$0.576325\pi$
$462$	−25598.0	+	31743.4i	−0.00557958	+	0.00691908i
$463$	2.67059e6	−	4.62560e6i	0.578968	−	1.00280i	−0.416630	−	0.909076i	$-0.636789\pi$
$463$	2.67059e6	−	4.62560e6i	0.578968	−	1.00280i	0.995598	−	0.0937260i	$-0.0298778\pi$
$464$	2.55742e6	−	1.47653e6i	0.551452	−	0.318381i
$465$	1.05798e6	−	359353.i	0.226906	−	0.0770706i
$466$	−114457.	+	198245.i	−0.0244162	+	0.0422900i
$467$	−3.80793e6	+	6.59553e6i	−0.807973	+	1.39945i	0.106293	+	0.994335i	$0.466102\pi$
$467$	−3.80793e6	+	6.59553e6i	−0.807973	+	1.39945i	−0.914266	+	0.405115i	$0.867232\pi$
$468$	3.34455e6	+	4.35540e6i	0.705868	+	0.919208i
$469$	−2.00707e6	+	82599.2i	−0.421338	+	0.0173398i
$470$	46775.9	−	27006.1i	0.00976737	−	0.00563919i
$471$	758735.	−	3.81807e6i	0.157593	−	0.793034i
$472$			719485.i			0.148651i
$473$			528883.i			0.108694i
$474$	−65287.4	+	328536.i	−0.0133470	+	0.0671641i
$475$	4.35514e6	−	2.51444e6i	0.885662	−	0.511337i
$476$	−5.24787e6	−	8.28318e6i	−1.06161	−	1.67564i
$477$	−7.09849e6	+	937178.i	−1.42847	+	0.188593i
$478$	33229.0	−	57554.4i	0.00665194	−	0.0115215i
$479$	−2.15731e6	+	3.73657e6i	−0.429610	+	0.744106i	−0.996839	−	0.0794543i	$-0.974682\pi$
$479$	−2.15731e6	+	3.73657e6i	−0.429610	+	0.744106i	0.567229	+	0.823560i	$0.308016\pi$
$480$	−244854.	+	83166.7i	−0.0485069	+	0.0164758i
$481$	2.76853e6	−	1.59841e6i	0.545615	−	0.315011i
$482$	−17465.7	+	30251.4i	−0.00342427	+	0.00593101i
$483$	−6.17843e6	+	2.38618e6i	−1.20507	+	0.465410i
$484$	−2.48747e6	−	4.30843e6i	−0.482664	−	0.835999i
$485$	−1.38080e6	−	797208.i	−0.266549	−	0.153892i
$486$	−213977.	+	143259.i	−0.0410939	+	0.0275125i
$487$	2.47333e6	+	4.28394e6i	0.472564	+	0.818504i	0.999507	−	0.0313962i	$-0.00999536\pi$
$487$	2.47333e6	+	4.28394e6i	0.472564	+	0.818504i	−0.526943	+	0.849900i	$0.676662\pi$
$488$	−644698.			−0.122548
$489$	−559639.	+	638382.i	−0.105837	+	0.120728i
$490$	74847.6	−	51852.6i	0.0140828	−	0.00975618i
$491$	3.98921e6	+	2.30317e6i	0.746764	+	0.431144i	0.824523	−	0.565828i	$-0.191443\pi$
$491$	3.98921e6	+	2.30317e6i	0.746764	+	0.431144i	−0.0777595	+	0.996972i	$0.524777\pi$
$492$	4.31120e6	−	4.91780e6i	0.802945	−	0.915921i
$493$	5.96134e6	+	3.44178e6i	1.10465	+	0.637773i
$494$	313645.	−	181083.i	0.0578257	−	0.0333857i
$495$	129782.	−	313645.i	0.0238068	−	0.0575342i
$496$			3.76228e6i			0.686668i
$497$	−16542.5	−	401964.i	−0.00300406	−	0.0729955i
$498$	−49720.1	+	16887.9i	−0.00898378	+	0.00305142i
$499$	2.71548e6	+	4.70335e6i	0.488198	+	0.845583i	0.999908	−	0.0135752i	$-0.00432124\pi$
$499$	2.71548e6	+	4.70335e6i	0.488198	+	0.845583i	−0.511710	+	0.859158i	$0.670988\pi$
$500$	3.63186e6			0.649687
$501$	−320601.	+	365710.i	−0.0570651	+	0.0650943i
$502$		−	40909.0i		−	0.00724536i
$503$	−1.80508e6			−0.318109			−0.159055	−	0.987270i	$-0.550845\pi$
$503$	−1.80508e6			−0.318109			−0.159055	+	0.987270i	$0.550845\pi$
$504$	−193804.	+	528955.i	−0.0339850	+	0.0927560i
$505$	374010.			0.0652612
$506$		−	66131.0i		−	0.0114823i
$507$	−651115.	−	1.91697e6i	−0.112496	−	0.331204i
$508$	−1.17286e6			−0.201645
$509$	2.83525e6	+	4.91079e6i	0.485061	+	0.840150i	0.999853	−	0.0171650i	$-0.00546406\pi$
$509$	2.83525e6	+	4.91079e6i	0.485061	+	0.840150i	−0.514792	+	0.857315i	$0.672131\pi$
$510$	−150471.	−	131911.i	−0.0256170	−	0.0224572i
$511$	4.49101e6	−	2.84531e6i	0.760837	−	0.482034i
$512$		−	1.45239e6i		−	0.244854i
$513$	−3.06721e6	−	6.21108e6i	−0.514577	−	1.04201i
$514$	171685.	−	99122.6i	0.0286633	−	0.0165487i
$515$	1.10915e6	+	640370.i	0.184278	+	0.106393i
$516$	1.17346e6	+	3.45483e6i	0.194019	+	0.571219i
$517$	−622768.	−	359555.i	−0.102471	−	0.0591615i
$518$	145079.	+	75985.5i	0.0237564	+	0.0124425i
$519$	−2.93365e6	−	582980.i	−0.478068	−	0.0950026i
$520$	245160.			0.0397595
$521$	−1.67173e6	−	2.89552e6i	−0.269818	−	0.467339i	0.698996	−	0.715125i	$-0.253630\pi$
$521$	−1.67173e6	−	2.89552e6i	−0.269818	−	0.467339i	−0.968815	+	0.247786i	$0.920297\pi$
$522$	−25849.3	−	195791.i	−0.00415215	−	0.0314497i
$523$	7.88532e6	+	4.55259e6i	1.26056	+	0.727787i	0.973184	−	0.230029i	$-0.0738821\pi$
$523$	7.88532e6	+	4.55259e6i	1.26056	+	0.727787i	0.287381	+	0.957816i	$0.407215\pi$
$524$	3.42367e6	+	5.92996e6i	0.544707	+	0.943461i
$525$	3.48858e6	−	4.32608e6i	0.552395	−	0.685009i
$526$	−27922.4	+	48363.1i	−0.00440037	+	0.00762166i
$527$	−7.59492e6	+	4.38493e6i	−1.19123	+	0.687758i
$528$	859441.	+	753431.i	0.134163	+	0.117614i
$529$	2.15227e6	−	3.72785e6i	0.334394	−	0.579187i
$530$	−79816.3	+	138246.i	−0.0123425	+	0.0213778i
$531$	−9.03419e6	−	3.73821e6i	−1.39044	−	0.575343i
$532$	−6.70406e6	−	3.51126e6i	−1.02697	−	0.537879i
$533$	−8.05764e6	+	4.65208e6i	−1.22854	+	0.709299i
$534$	464695.	+	407376.i	0.0705204	+	0.0618219i
$535$			18832.1i			0.00284455i
$536$		−	277080.i		−	0.0416575i
$537$	−4.98448e6	+	1.69302e6i	−0.745907	+	0.253354i
$538$	−409885.	+	236647.i	−0.0610530	+	0.0352490i
$539$	−1.09612e6	−	517825.i	−0.162513	−	0.0767734i
$540$	151872.	−	2.33678e6i	0.0224126	−	0.344853i
$541$	4.29430e6	−	7.43795e6i	0.630812	−	1.09260i	−0.356574	−	0.934267i	$-0.616055\pi$
$541$	4.29430e6	−	7.43795e6i	0.630812	−	1.09260i	0.987386	−	0.158331i	$-0.0506113\pi$
$542$	−25062.5	+	43409.6i	−0.00366460	+	0.00634728i
$543$	478454.	−	2.40765e6i	0.0696371	−	0.350425i
$544$	1.75773e6	−	1.01482e6i	0.254656	−	0.147026i
$545$	−1.30194e6	+	2.25503e6i	−0.187759	+	0.325208i
$546$	251237.	−	311552.i	0.0360664	−	0.0447249i
$547$	1.57975e6	+	2.73621e6i	0.225746	+	0.391004i	0.956543	−	0.291591i	$-0.0941846\pi$
$547$	1.57975e6	+	2.73621e6i	0.225746	+	0.391004i	−0.730797	+	0.682595i	$0.760851\pi$
$548$	−8.46317e6	−	4.88621e6i	−1.20388	−	0.695058i
$549$	3.34964e6	−	8.09512e6i	0.474315	−	1.14629i
$550$	27744.8	+	48055.4i	0.00391088	+	0.00677385i
$551$	5.31266e6			0.745475
$552$	−293817.	−	865036.i	−0.0410420	−	0.120833i
$553$	−9.94939e6	+	409458.i	−1.38351	+	0.0569373i
$554$	−417103.	−	240815.i	−0.0577390	−	0.0333356i
$555$	−1.33708e6	−	265708.i	−0.184258	−	0.0366161i
$556$	−7.54457e6	−	4.35586e6i	−1.03502	−	0.597567i
$557$	5.27081e6	−	3.04310e6i	0.719845	−	0.415603i	−0.0948504	−	0.995492i	$-0.530237\pi$
$557$	5.27081e6	−	3.04310e6i	0.719845	−	0.415603i	0.814696	+	0.579889i	$0.196904\pi$
$558$	232491.	+	96201.0i	0.0316097	+	0.0130796i
$559$		−	5.19084e6i		−	0.702600i
$560$	−1.36582e6	−	2.15579e6i	−0.184045	−	0.290494i
$561$	−519276.	+	2.61308e6i	−0.0696612	+	0.350546i
$562$	−127171.	−	220267.i	−0.0169843	−	0.0294177i
$563$	−5.20670e6			−0.692295			−0.346148	−	0.938180i	$-0.612510\pi$
$563$	−5.20670e6			−0.692295			−0.346148	+	0.938180i	$0.612510\pi$
$564$	−4.86588e6	−	966958.i	−0.644116	−	0.128000i
$565$			615603.i			0.0811297i
$566$	−77381.5			−0.0101530
$567$	−5.63486e6	−	5.18177e6i	−0.736080	−	0.676894i
$568$	55491.9			0.00721703
$569$		−	1.29199e7i		−	1.67294i	−0.548014	−	0.836469i	$-0.684616\pi$
$569$		−	1.29199e7i		−	1.67294i	0.548014	−	0.836469i	$-0.315384\pi$
$570$	−151477.	−	30101.8i	−0.0195281	−	0.00388066i
$571$	9.86054e6			1.26564			0.632821	−	0.774298i	$-0.281897\pi$
$571$	9.86054e6			1.26564			0.632821	+	0.774298i	$0.281897\pi$
$572$	−815007.	−	1.41163e6i	−0.104153	−	0.180398i
$573$	−2.60778e6	+	1.31227e7i	−0.331806	+	1.66970i
$574$	−422245.	−	221151.i	−0.0534915	−	0.0280162i
$575$			9.01253e6i			1.13678i
$576$	7.24988e6	+	2.99989e6i	0.910488	+	0.376746i
$577$	−1.03004e7	+	5.94694e6i	−1.28800	+	0.743625i	−0.978297	−	0.207209i	$-0.933562\pi$
$577$	−1.03004e7	+	5.94694e6i	−1.28800	+	0.743625i	−0.309700	+	0.950834i	$0.600229\pi$
$578$	1.01618e6	+	586693.i	0.126518	+	0.0730451i
$579$	−82051.0	−	16305.4i	−0.0101716	−	0.00202131i
$580$	1.55533e6	+	897970.i	0.191978	+	0.110839i
$581$	−835445.	−	1.31866e6i	−0.102678	−	0.162066i
$582$	−115471.	−	339961.i	−0.0141307	−	0.0416027i
$583$	2.12533e6			0.258973
$584$	366665.	+	635082.i	0.0444874	+	0.0770544i
$585$	−1.27377e6	+	3.07834e6i	−0.153887	+	0.371901i
$586$	−273974.	−	158179.i	−0.0329584	−	0.0190285i
$587$	−1.67394e6	−	2.89935e6i	−0.200514	−	0.347300i	0.748180	−	0.663495i	$-0.230928\pi$
$587$	−1.67394e6	−	2.89935e6i	−0.200514	−	0.347300i	−0.948694	+	0.316195i	$0.897594\pi$
$588$	−8.30915e6	−	950565.i	−0.991090	−	0.113381i
$589$	−3.38424e6	+	5.86168e6i	−0.401951	+	0.696200i
$590$	−188774.	+	108989.i	−0.0223260	+	0.0128899i
$591$	1.58930e6	−	7.99759e6i	0.187170	−	0.941869i
$592$	2.29510e6	−	3.97523e6i	0.269152	−	0.466185i
$593$	3.94538e6	−	6.83360e6i	0.460736	−	0.798018i	−0.538262	−	0.842778i	$-0.680919\pi$
$593$	3.94538e6	−	6.83360e6i	0.460736	−	0.798018i	0.998998	+	0.0447596i	$0.0142522\pi$
$594$	68534.2	−	33844.1i	0.00796969	−	0.00393566i
$595$	2.76004e6	−	5.26975e6i	0.319612	−	0.610236i
$596$	7.84445e6	−	4.52900e6i	0.904580	−	0.522259i
$597$	9.85773e6	−	3.34826e6i	1.13199	−	0.384489i
$598$			649057.i			0.0742215i
$599$			1.73163e7i			1.97192i	0.166988	+	0.985959i	$0.446596\pi$
$599$			1.73163e7i			1.97192i	−0.166988	+	0.985959i	$0.553404\pi$
$600$	576428.	+	505327.i	0.0653682	+	0.0573052i
$601$	−3.86528e6	+	2.23162e6i	−0.436511	+	0.252020i	−0.702116	−	0.712062i	$-0.747761\pi$
$601$	−3.86528e6	+	2.23162e6i	−0.436511	+	0.252020i	0.265606	+	0.964082i	$0.414428\pi$
$602$	224638.	−	142321.i	0.0252634	−	0.0160058i
$603$	3.47915e6	+	1.43962e6i	0.389654	+	0.161233i
$604$	−4.01459e6	+	6.95347e6i	−0.447764	+	0.775549i
$605$	1.50907e6	−	2.61379e6i	0.167618	−	0.290324i
$606$	63330.9	+	55519.2i	0.00700541	+	0.00614131i
$607$	3.56422e6	−	2.05781e6i	0.392639	−	0.226690i	−0.290664	−	0.956825i	$-0.593876\pi$
$607$	3.56422e6	−	2.05781e6i	0.392639	−	0.226690i	0.683303	+	0.730135i	$0.260543\pi$
$608$	783231.	−	1.35660e6i	0.0859273	−	0.148830i
$609$	5.47678e6	−	2.11519e6i	0.598387	−	0.231104i
$610$	−97659.7	−	169152.i	−0.0106265	−	0.0184057i
$611$	6.11229e6	+	3.52893e6i	0.662370	+	0.382420i
$612$	2.40571e6	+	1.82216e7i	0.259636	+	1.96656i
$613$	−476125.	−	824673.i	−0.0511765	−	0.0886402i	0.839302	−	0.543665i	$-0.182964\pi$
$613$	−476125.	−	824673.i	−0.0511765	−	0.0886402i	−0.890479	+	0.455025i	$0.849630\pi$
$614$	−716173.			−0.0766650
$615$	3.89150e6	+	773327.i	0.414886	+	0.0824471i
$616$	77582.8	−	148129.i	0.00823785	−	0.0157285i
$617$	−5.99419e6	−	3.46075e6i	−0.633895	−	0.365980i	0.148364	−	0.988933i	$-0.452599\pi$
$617$	−5.99419e6	−	3.46075e6i	−0.633895	−	0.365980i	−0.782259	+	0.622953i	$0.785933\pi$
$618$	92753.7	+	273079.i	0.00976922	+	0.0287619i
$619$	−731703.	−	422449.i	−0.0767552	−	0.0443147i	0.461131	−	0.887332i	$-0.347444\pi$
$619$	−731703.	−	422449.i	−0.0767552	−	0.0443147i	−0.537886	+	0.843017i	$0.680777\pi$
$620$	−1.98153e6	+	1.14404e6i	−0.207025	+	0.119526i
$621$	1.23884e7	+	805143.i	1.28910	+	0.0837807i
$622$		−	235921.i		−	0.0244507i
$623$	−8.52374e6	+	1.62744e7i	−0.879853	+	1.67991i
$624$	−8.43517e6	−	7.39471e6i	−0.867226	−	0.760256i
$625$	−3.19515e6	−	5.53416e6i	−0.327183	−	0.566698i
$626$	−1383.65			−0.000141121
$627$	661294.	+	1.94694e6i	0.0671778	+	0.197781i
$628$			7.97145e6i			0.806563i
$629$	1.06997e7			1.07832
$630$	−168141.	+	29277.7i	−0.0168781	+	0.00293890i
$631$	8.93454e6			0.893303			0.446652	−	0.894708i	$-0.352616\pi$
$631$	8.93454e6			0.893303			0.446652	+	0.894708i	$0.352616\pi$
$632$		−	1.37353e6i		−	0.136787i
$633$	−7.92492e6	+	9.03998e6i	−0.786115	+	0.896723i
$634$	340653.			0.0336581
$635$	−355769.	−	616211.i	−0.0350134	−	0.0606450i
$636$	1.38833e7	−	4.71558e6i	1.36097	−	0.462266i
$637$	1.07581e7	+	5.08230e6i	1.05048	+	0.496263i
$638$			58620.9i			0.00570165i
$639$	−288318.	+	696782.i	−0.0279331	+	0.0675064i
$640$	611210.	−	352882.i	0.0589848	−	0.0340549i
$641$	−7.30582e6	−	4.21802e6i	−0.702302	−	0.405474i	0.105902	−	0.994377i	$-0.466227\pi$
$641$	−7.30582e6	−	4.21802e6i	−0.702302	−	0.405474i	−0.808204	+	0.588902i	$0.799560\pi$
$642$	−2795.49	+	3188.82i	−0.000267683	+	0.000305346i
$643$	2.10685e6	+	1.21639e6i	0.200958	+	0.116023i	0.597102	−	0.802165i	$-0.296319\pi$
$643$	2.10685e6	+	1.21639e6i	0.200958	+	0.116023i	−0.396144	+	0.918188i	$0.629652\pi$
$644$	1.14570e7	−	7.25868e6i	1.08857	−	0.689673i
$645$	−1.45918e6	+	1.66450e6i	−0.138105	+	0.157537i
$646$	1.21217e6			0.114283
$647$	4.88949e6	+	8.46885e6i	0.459201	+	0.795360i	0.998919	−	0.0464862i	$-0.0148023\pi$
$647$	4.88949e6	+	8.46885e6i	0.459201	+	0.795360i	−0.539718	+	0.841846i	$0.681469\pi$
$648$	746104.	−	747197.i	0.0698010	−	0.0699033i
$649$	2.51331e6	+	1.45106e6i	0.234225	+	0.135230i
$650$	−272307.	−	471650.i	−0.0252799	−	0.0437861i
$651$	−1.15501e6	+	7.39017e6i	−0.106815	+	0.683442i
$652$	869239.	−	1.50557e6i	0.0800793	−	0.138701i
$653$	1.48721e7	−	8.58641e6i	1.36486	−	0.788004i	0.374597	−	0.927188i	$-0.377781\pi$
$653$	1.48721e7	−	8.58641e6i	1.36486	−	0.788004i	0.990267	+	0.139184i	$0.0444478\pi$
$654$	−555200.	+	188578.i	−0.0507581	+	0.0172404i
$655$	−2.07703e6	+	3.59752e6i	−0.189164	+	0.327642i
$656$	−6.67976e6	+	1.15697e7i	−0.606040	+	1.04969i
$657$	−9.87945e6	+	1.30434e6i	−0.892934	+	0.117890i
$658$	14867.7	+	361269.i	0.00133869	+	0.0325287i
$659$	−2.60676e6	+	1.50501e6i	−0.233823	+	0.134998i	−0.612335	−	0.790599i	$-0.709769\pi$
$659$	−2.60676e6	+	1.50501e6i	−0.233823	+	0.134998i	0.378511	+	0.925597i	$0.376436\pi$
$660$	−135481.	+	681759.i	−0.0121065	+	0.0609216i
$661$			3.92450e6i			0.349366i	0.984625	+	0.174683i	$0.0558901\pi$
$661$			3.92450e6i			0.349366i	−0.984625	+	0.174683i	$0.944110\pi$
$662$			147566.i			0.0130870i
$663$	5.09655e6	−	2.56466e7i	0.450290	−	2.26593i
$664$	186474.	−	107661.i	0.0164134	−	0.00947625i
$665$	−188788.	−	4.58733e6i	−0.0165546	−	0.402259i
$666$	−186965.	−	243472.i	−0.0163333	−	0.0212698i
$667$	−4.76055e6	+	8.24552e6i	−0.414327	+	0.717635i
$668$	497961.	−	862495.i	0.0431772	−	0.0747851i
$669$	−8.04449e6	+	2.73238e6i	−0.694918	+	0.236035i
$670$	72698.5	−	41972.5i	0.00625660	−	0.00361225i
$671$	−1.30023e6	+	2.25206e6i	−0.111484	+	0.193096i
$672$	267309.	−	1.71034e6i	0.0228344	−	0.146103i
$673$	−8.25744e6	−	1.43023e7i	−0.702761	−	1.21722i	−0.967494	−	0.252896i	$-0.918617\pi$
$673$	−8.25744e6	−	1.43023e7i	−0.702761	−	1.21722i	0.264733	−	0.964322i	$-0.414716\pi$
$674$	−330659.	−	190906.i	−0.0280369	−	0.0161871i
$675$	−9.34005e6	+	4.61238e6i	−0.789023	+	0.389642i
$676$	2.07290e6	+	3.59036e6i	0.174466	+	0.302184i
$677$	−8.28200e6			−0.694486			−0.347243	−	0.937775i	$-0.612882\pi$
$677$	−8.28200e6			−0.694486			−0.347243	+	0.937775i	$0.612882\pi$
$678$	−91381.8	+	104240.i	−0.00763459	+	0.00870880i
$679$	9.01630e6	−	5.71235e6i	0.750505	−	0.475489i
$680$	710615.	+	410274.i	0.0589335	+	0.0340253i
$681$	−1.35549e6	+	1.54622e6i	−0.112003	+	0.127762i
$682$	−64678.8	−	37342.3i	−0.00532477	−	0.00307426i
$683$	1.61719e7	−	9.33687e6i	1.32651	−	0.765860i	0.341751	−	0.939791i	$-0.388980\pi$
$683$	1.61719e7	−	9.33687e6i	1.32651	−	0.765860i	0.984758	+	0.173930i	$0.0556468\pi$
$684$	8.63957e6	+	1.12508e7i	0.706076	+	0.919479i
$685$		−	5.92862e6i		−	0.482755i
$686$	75022.8	+	604912.i	0.00608672	+	0.0490774i
$687$	−5.34544e6	+	1.81562e6i	−0.432107	+	0.146769i
$688$	−3.72667e6	−	6.45478e6i	−0.300158	−	0.519889i
$689$	−2.08595e7			−1.67400
$690$	182455.	−	208127.i	0.0145892	−	0.0166420i
$691$			6.99202e6i			0.557067i	0.960426	+	0.278534i	$0.0898484\pi$
$691$			6.99202e6i			0.557067i	−0.960426	+	0.278534i	$0.910152\pi$
$692$	6.12494e6			0.486224
$693$	1.45688e6	+	1.74380e6i	0.115237	+	0.137931i
$694$	−601707.			−0.0474227
$695$		−	5.28513e6i		−	0.415043i
$696$	260450.	+	766799.i	0.0203798	+	0.0600010i
$697$	−3.11410e7			−2.42801
$698$	479530.	+	830570.i	0.0372544	+	0.0645264i
$699$	9.59177e6	+	8.40865e6i	0.742516	+	0.650929i
$700$	−5.28014e6	+	1.00814e7i	−0.407287	+	0.777633i
$701$		−	1.38957e7i		−	1.06803i	−0.845474	−	0.534016i	$-0.820682\pi$
$701$		−	1.38957e7i		−	1.06803i	0.845474	−	0.534016i	$-0.179318\pi$
$702$	−672644.	+	332171.i	−0.0515160	+	0.0254401i
$703$	7.15159e6	−	4.12897e6i	0.545776	−	0.315104i
$704$	−2.01691e6	−	1.16447e6i	−0.153375	−	0.0885513i
$705$	−967958.	−	2.84980e6i	−0.0733472	−	0.215944i
$706$	−888138.	−	512767.i	−0.0670608	−	0.0387176i
$707$	−1.16166e6	+	2.21795e6i	−0.0874036	+	0.166880i
$708$	1.96373e7	+	3.90236e6i	1.47231	+	0.292580i
$709$	−1.52967e7			−1.14283			−0.571415	−	0.820661i	$-0.693605\pi$
$709$	−1.52967e7			−1.14283			−0.571415	+	0.820661i	$0.693605\pi$
$710$	8405.99	+	14559.6i	0.000625811	+	0.00108394i
$711$	1.72467e7	+	7.13643e6i	1.27948	+	0.529428i
$712$	−2.19457e6	−	1.26703e6i	−0.162237	−	0.0936674i
$713$	−6.06508e6	−	1.05050e7i	−0.446800	−	0.773880i
$714$	1.24961e6	−	482614.i	0.0917339	−	0.0354287i
$715$	494439.	−	856393.i	0.0361699	−	0.0626481i
$716$	9.33562e6	−	5.38993e6i	0.680551	−	0.392916i
$717$	−2.78468e6	−	2.44119e6i	−0.202291	−	0.177339i
$718$	−548956.	+	950819.i	−0.0397398	+	0.0688314i
$719$	2.77154e6	−	4.80045e6i	0.199940	−	0.346306i	−0.748569	−	0.663057i	$-0.769259\pi$
$719$	2.77154e6	−	4.80045e6i	0.199940	−	0.346306i	0.948509	+	0.316751i	$0.102592\pi$
$720$	626113.	+	4.74238e6i	0.0450113	+	0.340930i
$721$	−7.24249e6	+	4.58854e6i	−0.518860	+	0.328728i
$722$	210311.	−	121423.i	0.0150148	−	0.00866880i
$723$	1.46367e6	+	1.28313e6i	0.104135	+	0.0912902i
$724$			5.02676e6i			0.356403i
$725$		−	7.98903e6i		−	0.564480i
$726$	643528.	−	218580.i	0.0453133	−	0.0153911i
$727$	−1.07848e7	+	6.22661e6i	−0.756791	+	0.436933i	−0.828142	−	0.560518i	$-0.810602\pi$
$727$	−1.07848e7	+	6.22661e6i	−0.756791	+	0.436933i	0.0713514	+	0.997451i	$0.477269\pi$
$728$	−761453.	+	1.45384e6i	−0.0532494	+	0.101669i
$729$	5.50565e6	+	1.32506e7i	0.383698	+	0.923459i
$730$	−111086.	+	192406.i	−0.00771527	+	0.0133632i
$731$	8.68685e6	−	1.50461e7i	0.601269	−	1.04143i
$732$	−3.49673e6	+	1.75961e7i	−0.241204	+	1.21377i
$733$	−1703.94	+	983.770i	−0.000117137	+	6.76291e-5i	−0.500059	−	0.865992i	$-0.666688\pi$
$733$	−1703.94	+	983.770i	−0.000117137	+	6.76291e-5i	0.499941	+	0.866059i	$0.333355\pi$
$734$	−387729.	+	671567.i	−0.0265637	+	0.0460097i
$735$	−2.02103e6	−	4.65388e6i	−0.137992	−	0.317759i
$736$	1.40367e6	+	2.43123e6i	0.0955148	+	0.165436i
$737$	−967898.	−	558816.i	−0.0656388	−	0.0378966i
$738$	544150.	+	708612.i	0.0367771	+	0.0478925i
$739$	−6.79948e6	−	1.17771e7i	−0.457999	−	0.793278i	0.540856	−	0.841115i	$-0.318100\pi$
$739$	−6.79948e6	−	1.17771e7i	−0.457999	−	0.793278i	−0.998855	+	0.0478371i	$0.984767\pi$
$740$	2.79159e6			0.187401
$741$	−6.49041e6	−	1.91087e7i	−0.434237	−	1.27845i
$742$	−571919.	−	902710.i	−0.0381351	−	0.0601919i
$743$	2.29552e7	+	1.32532e7i	1.52549	+	0.880740i	0.999543	+	0.0302206i	$0.00962097\pi$
$743$	2.29552e7	+	1.32532e7i	1.52549	+	0.880740i	0.525943	+	0.850520i	$0.323712\pi$
$744$	−1.01195e6	−	201097.i	−0.0670235	−	0.0133190i
$745$	4.75898e6	+	2.74760e6i	0.314140	+	0.181369i
$746$	81812.2	−	47234.3i	0.00538234	−	0.00310749i
$747$	382981.	+	2.90082e6i	0.0251117	+	0.190204i
$748$		−	5.45564e6i		−	0.356527i
$749$	−111678.	−	58491.5i	−0.00727382	−	0.00380968i
$750$	−96706.0	+	486639.i	−0.00627769	+	0.0315903i
$751$	−1.45049e6	−	2.51231e6i	−0.0938455	−	0.162545i	0.815281	−	0.579066i	$-0.196583\pi$
$751$	−1.45049e6	−	2.51231e6i	−0.0938455	−	0.162545i	−0.909126	+	0.416521i	$0.863249\pi$
$752$	1.01341e7			0.653495
$753$	−2.23584e6	−	444310.i	−0.143699	−	0.0285561i
$754$		−	575347.i		−	0.0368554i
$755$	−4.87105e6			−0.310996
$756$	1.33859e7	+	8.15856e6i	0.851809	+	0.519169i
$757$	−1.92774e7			−1.22267			−0.611334	−	0.791373i	$-0.709367\pi$
$757$	−1.92774e7			−1.22267			−0.611334	+	0.791373i	$0.709367\pi$
$758$		−	730037.i		−	0.0461500i
$759$	−3.61432e6	−	718245.i	−0.227731	−	0.0452552i
$760$	633290.			0.0397712
$761$	−1.20968e7	−	2.09522e7i	−0.757195	−	1.31150i	−0.944275	−	0.329156i	$-0.893236\pi$
$761$	−1.20968e7	−	2.09522e7i	−0.757195	−	1.31150i	0.187080	−	0.982345i	$-0.440098\pi$
$762$	31229.9	−	157154.i	0.00194842	−	0.00980477i
$763$	−9.32900e6	−	1.47248e7i	−0.580128	−	0.915667i
$764$		−	2.73979e7i		−	1.69818i
$765$	−8.84371e6	+	6.79117e6i	−0.546363	+	0.419557i
$766$	−932187.	+	538198.i	−0.0574025	+	0.0331414i
$767$	−2.46674e7	−	1.42417e7i	−1.51403	−	0.874127i
$768$	−1.56415e7	−	3.10832e6i	−0.956922	−	0.190161i
$769$	−9.57465e6	−	5.52793e6i	−0.583858	−	0.337091i	0.178807	−	0.983884i	$-0.442776\pi$
$769$	−9.57465e6	−	5.52793e6i	−0.583858	−	0.337091i	−0.762665	+	0.646794i	$0.776110\pi$
$770$	50617.5	−	2083.12i	0.00307662	−	0.000126615i
$771$	−3.55278e6	−	1.04598e7i	−0.215244	−	0.633708i
$772$	171308.			0.0103451
$773$	1.27944e7	+	2.21606e7i	0.770145	+	1.33393i	0.937483	+	0.348031i	$0.113150\pi$
$773$	1.27944e7	+	2.21606e7i	0.770145	+	1.33393i	−0.167337	+	0.985900i	$0.553517\pi$
$774$	−494165.	+	65242.1i	−0.0296496	+	0.00391450i
$775$	8.81462e6	+	5.08913e6i	0.527169	+	0.304361i
$776$	736128.	+	1.27501e6i	0.0438833	+	0.0760081i
$777$	5.72860e6	−	7.10388e6i	0.340405	−	0.422127i
$778$	−439138.	+	760610.i	−0.0260107	+	0.0450519i
$779$	−2.08143e7	+	1.20171e7i	−1.22890	+	0.709508i
$780$	1.32970e6	−	6.69127e6i	0.0782561	−	0.393797i
$781$	111916.	−	193845.i	0.00656546	−	0.0113717i
$782$	−1.08619e6	+	1.88134e6i	−0.0635171	+	0.110015i
$783$	−1.09815e7	−	713707.i	−0.640114	−	0.0416022i
$784$	1.70264e7	−	1.40379e6i	0.989312	−	0.0815666i
$785$	−4.18812e6	+	2.41801e6i	−0.242575	+	0.140051i
$786$	−885728.	+	300845.i	−0.0511380	+	0.0173695i
$787$		−	1.82508e7i		−	1.05038i	−0.850986	−	0.525188i	$-0.823995\pi$
$787$		−	1.82508e7i		−	1.05038i	0.850986	−	0.525188i	$-0.176005\pi$
$788$			1.66976e7i			0.957938i
$789$	2.33997e6	+	2.05134e6i	0.133819	+	0.117313i
$790$	360379.	−	208065.i	0.0205443	−	0.0118613i
$791$	−3.65064e6	−	1.91203e6i	−0.207457	−	0.108656i
$792$	−248590.	+	190895.i	−0.0140822	+	0.0108139i
$793$	1.27614e7	−	2.21033e7i	0.720633	−	1.24817i
$794$	−299300.	+	518403.i	−0.0168483	+	0.0291821i
$795$	6.68880e6	+	5.86375e6i	0.375345	+	0.329047i
$796$	−1.84629e7	+	1.06596e7i	−1.03280	+	0.596289i
$797$	−7.67571e6	+	1.32947e7i	−0.428028	+	0.741367i	−0.996698	−	0.0811991i	$-0.974125\pi$
$797$	−7.67571e6	+	1.32947e7i	−0.428028	+	0.741367i	0.568669	+	0.822566i	$0.307458\pi$
$798$	648990.	−	804794.i	0.0360770	−	0.0447381i
$799$	1.18113e7	+	2.04578e7i	0.654532	+	1.13368i
$800$	−2.04001e6	−	1.17780e6i	−0.112696	−	0.0650649i
$801$	2.73117e7	−	2.09729e7i	1.50407	−	1.15499i
$802$	126608.	+	219292.i	0.00695067	+	0.0120389i
$803$	2.95796e6			0.161884
$804$	−7.56249e6	−	1.50283e6i	−0.412596	−	0.0819919i
$805$	7.28894e6	+	3.81760e6i	0.396438	+	0.207635i
$806$	634804.	+	366504.i	0.0344193	+	0.0198720i
$807$	8.48197e6	+	2.49721e7i	0.458472	+	1.34980i
$808$	−299086.	−	172677.i	−0.0161164	−	0.00930481i
$809$	1.79242e7	−	1.03486e7i	0.962874	−	0.555916i	0.0658176	−	0.997832i	$-0.479034\pi$
$809$	1.79242e7	−	1.03486e7i	0.962874	−	0.555916i	0.897056	+	0.441916i	$0.145701\pi$
$810$	309066.	+	82571.3i	0.0165515	+	0.00442198i
$811$			3.62129e7i			1.93336i	0.255996	+	0.966678i	$0.417596\pi$
$811$			3.62129e7i			1.93336i	−0.255996	+	0.966678i	$0.582404\pi$
$812$	−1.01559e7	+	6.43435e6i	−0.540541	+	0.342464i
$813$	2.10030e6	+	1.84124e6i	0.111444	+	0.0976974i
$814$	45559.8	+	78911.9i	0.00241002	+	0.00417428i
$815$	1.05468e6			0.0556194
$816$	−1.20750e7	−	3.55504e7i	−0.634836	−	1.86904i
$817$		−	1.34088e7i		−	0.702807i
$818$	493735.			0.0257994
$819$	−1.42989e7	−	1.71149e7i	−0.744890	−	0.891586i
$820$	−8.12476e6			−0.421965
$821$			2.24406e7i			1.16192i	0.813931	+	0.580961i	$0.197323\pi$
$821$			2.24406e7i			1.16192i	−0.813931	+	0.580961i	$0.802677\pi$
$822$	880061.	−	1.00389e6i	0.0454290	−	0.0518210i
$823$	3.15266e7			1.62247			0.811237	−	0.584717i	$-0.198795\pi$
$823$	3.15266e7			1.62247			0.811237	+	0.584717i	$0.198795\pi$
$824$	−591307.	−	1.02417e6i	−0.0303386	−	0.0525480i
$825$	2.92775e6	−	994435.i	0.149761	−	0.0508677i
$826$	−60001.7	−	1.45798e6i	−0.00305994	−	0.0743534i
$827$		−	6.20984e6i		−	0.315730i	−0.987461	−	0.157865i	$-0.949539\pi$
$827$		−	6.20984e6i		−	0.315730i	0.987461	−	0.157865i	$-0.0504612\pi$
$828$	−2.52035e7	+	3.32749e6i	−1.27757	+	0.168671i
$829$	4.23154e6	−	2.44308e6i	0.213851	−	0.123467i	−0.389249	−	0.921133i	$-0.627265\pi$
$829$	4.23154e6	−	2.44308e6i	0.213851	−	0.123467i	0.603100	+	0.797666i	$0.293932\pi$
$830$	56494.6	+	32617.2i	0.00284650	+	0.00164343i
$831$	−1.76916e7	+	2.01809e7i	−0.888720	+	1.01377i
$832$	1.97954e7	+	1.14289e7i	0.991417	+	0.572395i
$833$	2.26781e7	+	3.27352e7i	1.13239	+	1.63456i
$834$	784539.	−	894926.i	0.0390570	−	0.0445525i
$835$	604195.			0.0299889
$836$	−2.10530e6	−	3.64649e6i	−0.104184	−	0.180451i
$837$	7.78283e6	−	1.16617e7i	0.383994	−	0.575371i
$838$	−1.16766e6	−	674150.i	−0.0574390	−	0.0331624i
$839$	−6.67668e6	−	1.15643e7i	−0.327458	−	0.567174i	0.654549	−	0.756020i	$-0.272859\pi$
$839$	−6.67668e6	−	1.15643e7i	−0.327458	−	0.567174i	−0.982007	+	0.188846i	$0.939525\pi$
$840$	652854.	−	252140.i	0.0319240	−	0.0123294i
$841$	−6.03565e6	+	1.04541e7i	−0.294262	+	0.509677i
$842$	1.09710e6	−	633410.i	0.0533293	−	0.0307897i
$843$	−1.34197e7	+	4.55811e6i	−0.650389	+	0.220910i
$844$	1.23091e7	−	2.13200e7i	0.594798	−	1.03022i
$845$	−1.25756e6	+	2.17816e6i	−0.0605881	+	0.104942i
$846$	259129.	−	626240.i	0.0124477	−	0.0300826i
$847$	1.08132e7	+	1.70674e7i	0.517898	+	0.817445i
$848$	−2.59386e7	+	1.49757e7i	−1.23868	+	0.715149i
$849$	−840436.	+	4.22920e6i	−0.0400162	+	0.201368i
$850$		−	1.82282e6i		−	0.0865360i
$851$			1.47995e7i			0.700525i
$852$	300978.	−	1.51457e6i	0.0142048	−	0.0714809i
$853$	2.37514e7	−	1.37129e7i	1.11768	−	0.645291i	0.176869	−	0.984234i	$-0.443403\pi$
$853$	2.37514e7	−	1.37129e7i	1.11768	−	0.645291i	0.940807	+	0.338944i	$0.110070\pi$
$854$	1.30643e6	−	53764.8i	0.0612972	−	0.00252263i
$855$	−3.29037e6	+	7.95189e6i	−0.153932	+	0.372010i
$856$	8694.62	−	15059.5i	0.000405570	−	0.000702469i
$857$	1.86706e7	−	3.23384e7i	0.868372	−	1.50406i	0.00471294	−	0.999989i	$-0.498500\pi$
$857$	1.86706e7	−	3.23384e7i	0.868372	−	1.50406i	0.863659	−	0.504076i	$-0.168167\pi$
$858$	210848.	−	71616.4i	0.00977804	−	0.00332119i
$859$	1.79809e6	−	1.03813e6i	0.0831438	−	0.0480031i	−0.457852	−	0.889029i	$-0.651381\pi$
$859$	1.79809e6	−	1.03813e6i	0.0831438	−	0.0480031i	0.540995	+	0.841026i	$0.318048\pi$
$860$	2.26642e6	−	3.92556e6i	0.104495	−	0.180990i
$861$	−1.66728e7	+	2.06754e7i	−0.766478	+	0.950488i
$862$	551579.	+	955362.i	0.0252836	+	0.0437925i
$863$	2.73518e7	+	1.57916e7i	1.25014	+	0.721770i	0.971138	−	0.238520i	$-0.0766621\pi$
$863$	2.73518e7	+	1.57916e7i	1.25014	+	0.721770i	0.279005	+	0.960290i	$0.409995\pi$
$864$	−1.80122e6	+	2.69892e6i	−0.0820884	+	0.123000i
$865$	1.85790e6	+	3.21798e6i	0.0844273	+	0.146232i
$866$	−872056.			−0.0395139
$867$	4.31017e7	−	4.91663e7i	1.94736	−	2.22136i
$868$	−629831.	−	1.53042e7i	−0.0283743	−	0.689464i
$869$	−4.79803e6	−	2.77014e6i	−0.215533	−	0.124438i
$870$	−161734.	+	184491.i	−0.00724443	+	0.00826374i
$871$	9.49964e6	+	5.48462e6i	0.424289	+	0.244963i
$872$	2.08226e6	−	1.20219e6i	0.0927350	−	0.0535406i
$873$	−1.98343e7	+	2.61863e6i	−0.880809	+	0.116289i
$874$			1.67663e6i			0.0742434i
$875$	−1.47374e7	+	606504.i	−0.650729	+	0.0267802i
$876$	1.93223e7	−	6.56300e6i	0.850745	−	0.288963i
$877$	1.96521e7	+	3.40384e7i	0.862800	+	1.49441i	0.869216	+	0.494433i	$0.164624\pi$
$877$	1.96521e7	+	3.40384e7i	0.862800	+	1.49441i	−0.00641613	+	0.999979i	$0.502042\pi$
$878$	−581413.			−0.0254535
$879$	−1.16207e7	+	1.32558e7i	−0.507296	+	0.578674i
$880$		−	1.41989e6i		−	0.0618086i
$881$	−3.35035e7			−1.45429			−0.727143	−	0.686486i	$-0.759152\pi$
$881$	−3.35035e7			−1.45429			−0.727143	+	0.686486i	$0.759152\pi$
$882$	348616.	−	1.08805e6i	0.0150895	−	0.0470951i
$883$	5.83836e6			0.251993			0.125997	−	0.992031i	$-0.459787\pi$
$883$	5.83836e6			0.251993			0.125997	+	0.992031i	$0.459787\pi$
$884$			5.35456e7i			2.30459i
$885$	3.90639e6	+	1.15009e7i	0.167656	+	0.493600i
$886$	309839.			0.0132603
$887$	8.56351e6	+	1.48324e7i	0.365462	+	0.632999i	0.988850	−	0.148913i	$-0.0475776\pi$
$887$	8.56351e6	+	1.48324e7i	0.365462	+	0.632999i	−0.623388	+	0.781913i	$0.714244\pi$
$888$	946554.	+	829799.i	0.0402822	+	0.0353135i
$889$	4.75925e6	−	195862.i	0.201969	−	0.00831183i
$890$		−	767728.i		−	0.0324887i
$891$	−1.10537e6	−	4.11324e6i	−0.0466459	−	0.173576i
$892$	1.50668e7	−	8.69884e6i	0.634030	−	0.366057i
$893$	1.57891e7	+	9.11585e6i	0.662566	+	0.382533i
$894$	397973.	+	1.17169e6i	0.0166537	+	0.0490306i
$895$	5.66363e6	+	3.26990e6i	0.236340	+	0.136451i
$896$	194273.	+	4.72062e6i	0.00808430	+	0.196440i
$897$	3.54735e7	+	7.04937e6i	1.47205	+	0.292529i
$898$	1.85185e6			0.0766329
$899$	5.37630e6	+	9.31203e6i	0.221863	+	0.384278i
$900$	1.69186e7	−	1.29919e7i	0.696238	−	0.534647i
$901$	−6.04628e7	−	3.49082e7i	−2.48128	−	1.43257i
$902$	−132599.	−	229669.i	−0.00542656	−	0.00939908i
$903$	−5.33863e6	−	1.38231e7i	−0.217876	−	0.564138i
$904$	284219.	−	492281.i	0.0115673	−	0.0200351i
$905$	−2.64101e6	+	1.52479e6i	−0.107189	+	0.0618853i
$906$	−824810.	−	723072.i	−0.0333836	−	0.0292659i
$907$	−1.72751e7	+	2.99213e7i	−0.697271	+	1.20771i	0.272138	+	0.962258i	$0.412269\pi$
$907$	−1.72751e7	+	2.99213e7i	−0.697271	+	1.20771i	−0.969409	+	0.245451i	$0.921064\pi$
$908$	2.10537e6	−	3.64661e6i	0.0847449	−	0.146783i
$909$	3.72217e6	−	2.85829e6i	0.149412	−	0.114735i
$910$	−496796.	+	20445.2i	−0.0198872	+	0.000818441i
$911$	2.10411e7	−	1.21481e7i	0.839986	−	0.484966i	−0.0172732	−	0.999851i	$-0.505498\pi$
$911$	2.10411e7	−	1.21481e7i	0.839986	−	0.484966i	0.857260	+	0.514884i	$0.172165\pi$
$912$	−2.17895e7	−	1.91018e7i	−0.867482	−	0.760480i
$913$		−	868521.i		−	0.0344829i
$914$		−	73607.8i		−	0.00291446i
$915$	−1.03055e7	+	3.50034e6i	−0.406926	+	0.138216i
$916$	1.00117e7	−	5.78024e6i	0.394246	−	0.227618i
$917$	−1.48828e7	−	2.34909e7i	−0.584470	−	0.922521i
$918$	−2.50560e6	−	162843.i	−0.0981307	−	0.00637769i
$919$	786044.	−	1.36147e6i	0.0307014	−	0.0531764i	−0.850266	−	0.526352i	$-0.823559\pi$
$919$	786044.	−	1.36147e6i	0.0307014	−	0.0531764i	0.880968	+	0.473176i	$0.156893\pi$
$920$	−567477.	+	982899.i	−0.0221044	+	0.0382859i
$921$	−7.77832e6	+	3.91417e7i	−0.302160	+	1.52051i
$922$	1.59744e6	−	922281.i	0.0618866	−	0.0357302i
$923$	−1.09843e6	+	1.90253e6i	−0.0424391	+	0.0735067i
$924$	−3.62216e6	−	2.92093e6i	−0.139569	−	0.112549i
$925$	−6.20903e6	−	1.07544e7i	−0.238600	−	0.413266i
$926$	−1.29401e6	−	747100.i	−0.0495920	−	0.0286320i
$927$	1.59323e7	−	2.10346e6i	0.608945	−	0.0803959i
$928$	−1.24426e6	−	2.15513e6i	−0.0474288	−	0.0821491i
$929$	2.44473e7			0.929377			0.464689	−	0.885474i	$-0.346166\pi$
$929$	2.44473e7			0.929377			0.464689	+	0.885474i	$0.346166\pi$
$930$	−100529.	−	295972.i	−0.00381140	−	0.0112213i
$931$	2.77901e7	+	1.31285e7i	1.05079	+	0.496409i
$932$	−2.26213e7	−	1.30604e7i	−0.853057	−	0.492513i
$933$	−1.28940e7	−	2.56232e6i	−0.484935	−	0.0963673i
$934$	1.84510e6	+	1.06527e6i	0.0692076	+	0.0399570i
$935$	2.86634e6	−	1.65488e6i	0.107226	−	0.0619068i
$936$	2.43984e6	−	1.87358e6i	0.0910274	−	0.0699008i
$937$			1.45346e7i			0.540820i	0.962745	+	0.270410i	$0.0871592\pi$
$937$			1.45346e7i			0.540820i	−0.962745	+	0.270410i	$0.912841\pi$
$938$	23107.2	+	561480.i	0.000857512	+	0.0208366i
$939$	−15027.8	+	75622.2i	−0.000556200	+	0.00279889i
$940$	3.08160e6	+	5.33749e6i	0.113751	+	0.197023i
$941$	−4.09043e7			−1.50590			−0.752948	−	0.658080i	$-0.771369\pi$
$941$	−4.09043e7			−1.50590			−0.752948	+	0.658080i	$0.771369\pi$
$942$	−1.06811e6	−	212257.i	−0.0392182	−	0.00779353i
$943$		−	4.30731e7i		−	1.57735i
$944$	−4.08984e7			−1.49374
$945$	−226035.	+	9.50757e6i	−0.00823371	+	0.346330i
$946$	147956.			0.00537531
$947$		−	3.44912e6i		−	0.124978i	−0.998046	−	0.0624890i	$-0.980096\pi$
$947$		−	3.44912e6i		−	0.124978i	0.998046	−	0.0624890i	$-0.0199038\pi$
$948$	−3.74885e7	−	7.44980e6i	−1.35481	−	0.269230i
$949$	−2.90315e7			−1.04642
$950$	−703417.	−	1.21835e6i	−0.0252874	−	0.0437990i
$951$	3.69981e6	−	1.86180e7i	0.132657	−	0.667548i
$952$	−4.64013e6	+	2.93979e6i	−0.165935	+	0.105129i
$953$		−	1.59081e7i		−	0.567395i	−0.958914	−	0.283698i	$-0.908439\pi$
$953$		−	1.59081e7i		−	0.567395i	0.958914	−	0.283698i	$-0.0915612\pi$
$954$	262176.	+	1.98581e6i	0.00932659	+	0.0706426i
$955$	1.43946e7	−	8.31073e6i	0.510730	−	0.294870i
$956$	6.56740e6	+	3.79169e6i	0.232407	+	0.134180i
$957$	3.20386e6	+	636678.i	0.113082	+	0.0224719i
$958$	1.04531e6	+	603510.i	0.0367986	+	0.0212457i
$959$	3.51578e7	+	1.84140e7i	1.23446	+	0.646549i
$960$	−3.13486e6	−	9.22944e6i	−0.109784	−	0.323219i
$961$	1.49300e7			0.521497
$962$	−447157.	−	774498.i	−0.0155784	−	0.0269825i
$963$	143920.	+	187418.i	0.00500098	+	0.00651247i
$964$	−3.45192e6	−	1.99297e6i	−0.119638	−	0.0690729i
$965$	51963.6	+	90003.6i	0.00179631	+	0.00311130i
$966$	667536.	+	1.72842e6i	0.0230161	+	0.0595946i
$967$	−7.88840e6	+	1.36631e7i	−0.271283	+	0.469876i	−0.969191	−	0.246312i	$-0.920781\pi$
$967$	−7.88840e6	+	1.36631e7i	−0.271283	+	0.469876i	0.697908	+	0.716188i	$0.254115\pi$
$968$	−2.41353e6	+	1.39345e6i	−0.0827874	+	0.0477973i
$969$	1.31653e7	−	6.62497e7i	0.450423	−	2.26660i
$970$	−223020.	+	386281.i	−0.00761051	+	0.0131818i
$971$	−1.08411e7	+	1.87774e7i	−0.369001	+	0.639128i	−0.989410	−	0.145151i	$-0.953633\pi$
$971$	−1.08411e7	+	1.87774e7i	−0.369001	+	0.639128i	0.620409	+	0.784278i	$0.286967\pi$
$972$	−1.63469e7	−	2.44165e7i	−0.554971	−	0.828928i
$973$	3.13418e7	+	1.64153e7i	1.06131	+	0.555862i
$974$	1.19844e6	−	691917.i	0.0404778	−	0.0233699i
$975$	−2.87350e7	+	9.76010e6i	−0.968055	+	0.328808i
$976$		−	3.66472e7i		−	1.23145i
$977$		−	1.86371e7i		−	0.624657i	−0.949974	−	0.312329i	$-0.898891\pi$
$977$		−	1.86371e7i		−	0.624657i	0.949974	−	0.312329i	$-0.101109\pi$
$978$	178588.	+	156560.i	0.00597042	+	0.00523398i
$979$	−8.85202e6	+	5.11072e6i	−0.295179	+	0.170422i
$980$	5.91678e6	+	8.54069e6i	0.196798	+	0.284072i
$981$	4.27656e6	+	3.23920e7i	0.141880	+	1.07465i
$982$	644314.	−	1.11599e6i	0.0213216	−	0.0369300i
$983$	−4.28569e6	+	7.42304e6i	−0.141461	+	0.245018i	−0.928047	−	0.372463i	$-0.878513\pi$
$983$	−4.28569e6	+	7.42304e6i	−0.141461	+	0.245018i	0.786586	+	0.617481i	$0.211847\pi$
$984$	−2.75489e6	−	2.41508e6i	−0.0907020	−	0.0795141i
$985$	−8.77273e6	+	5.06494e6i	−0.288101	+	0.166335i
$986$	962841.	−	1.66769e6i	0.0315400	−	0.0546290i
$987$	1.99063e7	+	3.11115e6i	0.650425	+	0.101655i
$988$	2.06630e7	+	3.57893e7i	0.673442	+	1.16644i
$989$	2.08112e7	+	1.20154e7i	0.676560	+	0.390612i
$990$	−87742.6	−	36306.5i	−0.00284526	−	0.00117733i
$991$	−1.09342e7	−	1.89386e7i	−0.353674	−	0.612581i	0.633216	−	0.773975i	$-0.281734\pi$
$991$	−1.09342e7	−	1.89386e7i	−0.353674	−	0.612581i	−0.986890	+	0.161394i	$0.948401\pi$
$992$	3.17045e6			0.102292
$993$	8.06504e6	+	1.60270e6i	0.259557	+	0.0515797i
$994$	−112450.	+	4627.77i	−0.00360988	+	0.000148561i
$995$	−1.12009e7	−	6.46682e6i	−0.358669	−	0.207078i
$996$	−1.92704e6	−	5.67345e6i	−0.0615519	−	0.181217i
$997$	−1.74967e7	−	1.01017e7i	−0.557466	−	0.321853i	0.194662	−	0.980870i	$-0.437639\pi$
$997$	−1.74967e7	−	1.01017e7i	−0.557466	−	0.321853i	−0.752128	+	0.659017i	$0.770972\pi$
$998$	1.31577e6	−	759658.i	0.0418170	−	0.0241430i
$999$	−1.53373e7	+	7.57401e6i	−0.486224	+	0.240111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.i.a.5.18	✓	76
3.2	odd	2		189.6.i.a.152.21		76
7.3	odd	6		63.6.s.a.59.21	yes	76
9.2	odd	6		63.6.s.a.47.21	yes	76
9.7	even	3		189.6.s.a.89.18		76
21.17	even	6		189.6.s.a.17.18		76
63.38	even	6	inner	63.6.i.a.38.21	yes	76
63.52	odd	6		189.6.i.a.143.18		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.i.a.5.18	✓	76	1.1	even	1	trivial
63.6.i.a.38.21	yes	76	63.38	even	6	inner
63.6.s.a.47.21	yes	76	9.2	odd	6
63.6.s.a.59.21	yes	76	7.3	odd	6
189.6.i.a.143.18		76	63.52	odd	6
189.6.i.a.152.21		76	3.2	odd	2
189.6.s.a.17.18		76	21.17	even	6
189.6.s.a.89.18		76	9.7	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.279751i q^{2} +(-15.2895 - 3.03836i) q^{3} +31.9217 q^{4} +(9.68296 + 16.7714i) q^{5} +(-0.849983 + 4.27725i) q^{6} +(-129.532 + 5.33078i) q^{7} -17.8822i q^{8} +(224.537 + 92.9099i) q^{9} +(4.69181 - 2.70882i) q^{10} +(-62.4661 - 36.0648i) q^{11} +(-488.067 - 96.9897i) q^{12} +(613.086 + 353.966i) q^{13} +(1.49129 + 36.2367i) q^{14} +(-97.0900 - 285.846i) q^{15} +1016.49 q^{16} +(1184.72 + 2052.00i) q^{17} +(25.9916 - 62.8144i) q^{18} +(1583.71 + 914.355i) q^{19} +(309.097 + 535.371i) q^{20} +(1996.68 + 312.060i) q^{21} +(-10.0892 + 17.4749i) q^{22} +(-2838.25 + 1638.66i) q^{23} +(-54.3324 + 273.409i) q^{24} +(1374.98 - 2381.54i) q^{25} +(99.0222 - 171.511i) q^{26} +(-3150.76 - 2102.77i) q^{27} +(-4134.89 + 170.168i) q^{28} +(2515.93 - 1452.57i) q^{29} +(-79.9656 + 27.1610i) q^{30} +3701.23i q^{31} -856.594i q^{32} +(845.496 + 741.206i) q^{33} +(574.048 - 331.427i) q^{34} +(-1343.66 - 2120.81i) q^{35} +(7167.60 + 2965.84i) q^{36} +(2257.86 - 3910.73i) q^{37} +(255.792 - 443.044i) q^{38} +(-8298.30 - 7274.73i) q^{39} +(299.908 - 173.152i) q^{40} +(-6571.37 + 11382.0i) q^{41} +(87.2991 - 558.572i) q^{42} +(-3666.20 - 6350.05i) q^{43} +(-1994.03 - 1151.25i) q^{44} +(615.954 + 4665.43i) q^{45} +(458.418 + 794.003i) q^{46} +9969.70 q^{47} +(-15541.7 - 3088.47i) q^{48} +(16750.2 - 1381.01i) q^{49} +(-666.237 - 384.652i) q^{50} +(-11879.1 - 34973.6i) q^{51} +(19570.8 + 11299.2i) q^{52} +(-25517.8 + 14732.7i) q^{53} +(-588.251 + 881.427i) q^{54} -1396.86i q^{55} +(95.3258 + 2316.32i) q^{56} +(-21436.0 - 18791.9i) q^{57} +(-406.358 - 703.833i) q^{58} -40234.8 q^{59} +(-3099.28 - 9124.70i) q^{60} -36052.6i q^{61} +1035.42 q^{62} +(-29580.0 - 10837.9i) q^{63} +32288.1 q^{64} +13709.7i q^{65} +(207.353 - 236.528i) q^{66} +15494.8 q^{67} +(37818.3 + 65503.3i) q^{68} +(48374.2 - 16430.7i) q^{69} +(-593.300 + 375.890i) q^{70} +3103.20i q^{71} +(1661.43 - 4015.20i) q^{72} +(-35514.8 + 20504.5i) q^{73} +(-1094.03 - 631.639i) q^{74} +(-28258.7 + 32234.8i) q^{75} +(50554.8 + 29187.8i) q^{76} +(8283.62 + 4338.56i) q^{77} +(-2035.11 + 2321.46i) q^{78} +76810.2 q^{79} +(9842.66 + 17048.0i) q^{80} +(41784.5 + 41723.4i) q^{81} +(3184.11 + 1838.35i) q^{82} +(6020.56 + 10427.9i) q^{83} +(63737.4 + 9961.50i) q^{84} +(-22943.2 + 39738.8i) q^{85} +(-1776.43 + 1025.62i) q^{86} +(-42880.7 + 14564.8i) q^{87} +(-644.916 + 1117.03i) q^{88} +(70854.6 - 122724. i) q^{89} +(1305.16 - 172.314i) q^{90} +(-81301.3 - 42581.7i) q^{91} +(-90601.9 + 52309.0i) q^{92} +(11245.7 - 56590.0i) q^{93} -2789.03i q^{94} +35414.6i q^{95} +(-2602.64 + 13096.9i) q^{96} +(-71300.8 + 41165.5i) q^{97} +(-386.340 - 4685.87i) q^{98} +(-10675.2 - 13901.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9} - 6 q^{10} + 567 q^{11} - 1542 q^{12} + 543 q^{13} - 1638 q^{14} + 234 q^{15} + 16446 q^{16} - 801 q^{17} - 2022 q^{18} - 6 q^{19}+ \cdots - 144540 q^{99}+O(q^{100}) \) 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * q^96 - 104037 * q^97 - 646797 * q^98 - 144540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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