LMFDB - Embedded newform 51.6.h.a.25.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,6,Mod(19,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.19"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	51.h (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$8.17957481046$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	51.25
Dual form			51.6.h.a.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.79991 + 5.79991i) q^{2} +(-3.44415 + 8.31492i) q^{3} -35.2780i q^{4} +(-42.7660 - 17.7142i) q^{5} +(-28.2500 - 68.2015i) q^{6} +(151.688 - 62.8311i) q^{7} +(19.0118 + 19.0118i) q^{8} +(-57.2756 - 57.2756i) q^{9} +(350.780 - 145.298i) q^{10} +(-221.368 - 534.431i) q^{11} +(293.333 + 121.503i) q^{12} +977.303i q^{13} +(-515.361 + 1244.19i) q^{14} +(294.585 - 294.585i) q^{15} +908.361 q^{16} +(1180.96 + 158.720i) q^{17} +664.387 q^{18} +(599.257 - 599.257i) q^{19} +(-624.922 + 1508.70i) q^{20} +1477.67i q^{21} +(4383.57 + 1815.73i) q^{22} +(248.486 + 599.899i) q^{23} +(-223.561 + 92.6022i) q^{24} +(-694.575 - 694.575i) q^{25} +(-5668.27 - 5668.27i) q^{26} +(673.508 - 278.976i) q^{27} +(-2216.55 - 5351.23i) q^{28} +(-411.249 - 170.345i) q^{29} +3417.13i q^{30} +(3533.87 - 8531.52i) q^{31} +(-5876.79 + 5876.79i) q^{32} +5206.17 q^{33} +(-7770.02 + 5928.90i) q^{34} -7600.08 q^{35} +(-2020.57 + 2020.57i) q^{36} +(4627.64 - 11172.1i) q^{37} +6951.28i q^{38} +(-8126.19 - 3365.98i) q^{39} +(-476.279 - 1149.84i) q^{40} +(13886.3 - 5751.90i) q^{41} +(-8570.36 - 8570.36i) q^{42} +(285.057 + 285.057i) q^{43} +(-18853.6 + 7809.43i) q^{44} +(1434.85 + 3464.04i) q^{45} +(-4920.56 - 2038.16i) q^{46} -4113.05i q^{47} +(-3128.53 + 7552.94i) q^{48} +(7177.08 - 7177.08i) q^{49} +8056.95 q^{50} +(-5387.15 + 9272.92i) q^{51} +34477.3 q^{52} +(11561.4 - 11561.4i) q^{53} +(-2288.25 + 5524.33i) q^{54} +26776.8i q^{55} +(4078.40 + 1689.33i) q^{56} +(2918.84 + 7046.70i) q^{57} +(3373.19 - 1397.22i) q^{58} +(13073.1 + 13073.1i) q^{59} +(-10392.4 - 10392.4i) q^{60} +(-36028.1 + 14923.3i) q^{61} +(28985.9 + 69978.2i) q^{62} +(-12286.7 - 5089.32i) q^{63} -39102.2i q^{64} +(17312.2 - 41795.3i) q^{65} +(-30195.3 + 30195.3i) q^{66} +17383.7 q^{67} +(5599.32 - 41661.8i) q^{68} -5843.93 q^{69} +(44079.8 - 44079.8i) q^{70} +(6730.66 - 16249.2i) q^{71} -2177.83i q^{72} +(21274.7 + 8812.28i) q^{73} +(37957.4 + 91637.2i) q^{74} +(8167.56 - 3383.11i) q^{75} +(-21140.6 - 21140.6i) q^{76} +(-67157.8 - 67157.8i) q^{77} +(66653.6 - 27608.8i) q^{78} +(-35385.1 - 85427.1i) q^{79} +(-38846.9 - 16090.9i) q^{80} +6561.00i q^{81} +(-47178.8 + 113900. i) q^{82} +(15888.6 - 15888.6i) q^{83} +52129.2 q^{84} +(-47693.3 - 27707.6i) q^{85} -3306.61 q^{86} +(2832.81 - 2832.81i) q^{87} +(5951.89 - 14369.1i) q^{88} +69495.8i q^{89} +(-28413.2 - 11769.1i) q^{90} +(61405.0 + 148245. i) q^{91} +(21163.2 - 8766.09i) q^{92} +(58767.7 + 58767.7i) q^{93} +(23855.3 + 23855.3i) q^{94} +(-36243.2 + 15012.4i) q^{95} +(-28624.5 - 69105.6i) q^{96} +(-97647.8 - 40447.1i) q^{97} +83252.9i q^{98} +(-17930.8 + 43288.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) $ 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−5.79991	+	5.79991i	−1.02529	+	1.02529i	−0.0256174	+	0.999672i	$0.508155\pi$
$2$	−5.79991	+	5.79991i	−1.02529	+	1.02529i	−0.999672	+	0.0256174i	$0.991845\pi$
$3$	−3.44415	+	8.31492i	−0.220942	+	0.533402i
$3$	−3.44415	+	8.31492i	−0.220942	+	0.533402i
$4$		−	35.2780i		−	1.10244i
$5$	−42.7660	−	17.7142i	−0.765021	−	0.316882i	−0.0341671	−	0.999416i	$-0.510878\pi$
$5$	−42.7660	−	17.7142i	−0.765021	−	0.316882i	−0.730854	+	0.682534i	$0.760878\pi$
$6$	−28.2500	−	68.2015i	−0.320362	−	0.773421i
$7$	151.688	−	62.8311i	1.17005	−	0.484652i	0.288843	−	0.957377i	$-0.406730\pi$
$7$	151.688	−	62.8311i	1.17005	−	0.484652i	0.881210	+	0.472725i	$0.156730\pi$
$8$	19.0118	+	19.0118i	0.105027	+	0.105027i
$9$	−57.2756	−	57.2756i	−0.235702	−	0.235702i
$10$	350.780	−	145.298i	1.10926	−	0.459472i
$11$	−221.368	−	534.431i	−0.551612	−	1.33171i	−0.916267	−	0.400568i	$-0.868813\pi$
$11$	−221.368	−	534.431i	−0.551612	−	1.33171i	0.364655	−	0.931143i	$-0.381187\pi$
$12$	293.333	+	121.503i	0.588042	+	0.243575i
$13$			977.303i			1.60388i	0.597407	+	0.801938i	$0.296198\pi$
$13$			977.303i			1.60388i	−0.597407	+	0.801938i	$0.703802\pi$
$14$	−515.361	+	1244.19i	−0.702734	+	1.69655i
$15$	294.585	−	294.585i	0.338051	−	0.338051i
$16$	908.361			0.887071
$17$	1180.96	+	158.720i	0.991089	+	0.133202i
$17$	1180.96	+	158.720i	0.991089	+	0.133202i
$18$	664.387			0.483326
$19$	599.257	−	599.257i	0.380828	−	0.380828i	−0.490572	−	0.871401i	$-0.663212\pi$
$19$	599.257	−	599.257i	0.380828	−	0.380828i	0.871401	+	0.490572i	$0.163212\pi$
$20$	−624.922	+	1508.70i	−0.349342	+	0.843386i
$21$			1477.67i			0.731189i
$22$	4383.57	+	1815.73i	1.93095	+	0.799826i
$23$	248.486	+	599.899i	0.0979451	+	0.236461i	0.965256	−	0.261307i	$-0.0841534\pi$
$23$	248.486	+	599.899i	0.0979451	+	0.236461i	−0.867311	+	0.497767i	$0.834153\pi$
$24$	−223.561	+	92.6022i	−0.0792262	+	0.0328166i
$25$	−694.575	−	694.575i	−0.222264	−	0.222264i
$26$	−5668.27	−	5668.27i	−1.64444	−	1.64444i
$27$	673.508	−	278.976i	0.177801	−	0.0736475i
$28$	−2216.55	−	5351.23i	−0.534297	−	1.28991i
$29$	−411.249	−	170.345i	−0.0908050	−	0.0376127i	0.336819	−	0.941570i	$-0.390649\pi$
$29$	−411.249	−	170.345i	−0.0908050	−	0.0376127i	−0.427624	+	0.903957i	$0.640649\pi$
$30$			3417.13i			0.693200i
$31$	3533.87	−	8531.52i	0.660460	−	1.59449i	−0.136625	−	0.990623i	$-0.543626\pi$
$31$	3533.87	−	8531.52i	0.660460	−	1.59449i	0.797085	−	0.603868i	$-0.206374\pi$
$32$	−5876.79	+	5876.79i	−1.01453	+	1.01453i
$33$	5206.17			0.832212
$34$	−7770.02	+	5928.90i	−1.15272	+	0.879582i
$35$	−7600.08			−1.04869
$36$	−2020.57	+	2020.57i	−0.259847	+	0.259847i
$37$	4627.64	−	11172.1i	0.555719	−	1.34162i	−0.357408	−	0.933949i	$-0.616339\pi$
$37$	4627.64	−	11172.1i	0.555719	−	1.34162i	0.913127	−	0.407676i	$-0.133661\pi$
$38$			6951.28i			0.780918i
$39$	−8126.19	−	3365.98i	−0.855511	−	0.354364i
$40$	−476.279	−	1149.84i	−0.0470665	−	0.113628i
$41$	13886.3	−	5751.90i	1.29011	−	0.534381i	0.371092	−	0.928596i	$-0.378983\pi$
$41$	13886.3	−	5751.90i	1.29011	−	0.534381i	0.919018	+	0.394215i	$0.128983\pi$
$42$	−8570.36	−	8570.36i	−0.749680	−	0.749680i
$43$	285.057	+	285.057i	0.0235104	+	0.0235104i	0.718764	−	0.695254i	$-0.244708\pi$
$43$	285.057	+	285.057i	0.0235104	+	0.0235104i	−0.695254	+	0.718764i	$0.744708\pi$
$44$	−18853.6	+	7809.43i	−1.46813	+	0.608117i
$45$	1434.85	+	3464.04i	0.105627	+	0.255007i
$46$	−4920.56	−	2038.16i	−0.342863	−	0.142018i
$47$		−	4113.05i		−	0.271594i	−0.990737	−	0.135797i	$-0.956641\pi$
$47$		−	4113.05i		−	0.271594i	0.990737	−	0.135797i	$-0.0433594\pi$
$48$	−3128.53	+	7552.94i	−0.195992	+	0.473165i
$49$	7177.08	−	7177.08i	0.427029	−	0.427029i
$50$	8056.95			0.455770
$51$	−5387.15	+	9272.92i	−0.290024	+	0.499219i
$52$	34477.3			1.76817
$53$	11561.4	−	11561.4i	0.565352	−	0.565352i	−0.365470	−	0.930823i	$-0.619092\pi$
$53$	11561.4	−	11561.4i	0.565352	−	0.565352i	0.930823	+	0.365470i	$0.119092\pi$
$54$	−2288.25	+	5524.33i	−0.106787	+	0.257807i
$55$			26776.8i			1.19358i
$56$	4078.40	+	1689.33i	0.173788	+	0.0719853i
$57$	2918.84	+	7046.70i	0.118993	+	0.287276i
$58$	3373.19	−	1397.22i	0.131665	−	0.0545376i
$59$	13073.1	+	13073.1i	0.488931	+	0.488931i	0.907969	−	0.419038i	$-0.137633\pi$
$59$	13073.1	+	13073.1i	0.488931	+	0.488931i	−0.419038	+	0.907969i	$0.637633\pi$
$60$	−10392.4	−	10392.4i	−0.372680	−	0.372680i
$61$	−36028.1	+	14923.3i	−1.23970	+	0.513500i	−0.903621	−	0.428334i	$-0.859101\pi$
$61$	−36028.1	+	14923.3i	−1.23970	+	0.513500i	−0.336078	+	0.941834i	$0.609101\pi$
$62$	28985.9	+	69978.2i	0.957652	+	2.31198i
$63$	−12286.7	−	5089.32i	−0.390018	−	0.161551i
$64$		−	39102.2i		−	1.19330i
$65$	17312.2	−	41795.3i	0.508240	−	1.22700i
$66$	−30195.3	+	30195.3i	−0.853258	+	0.853258i
$67$	17383.7			0.473101			0.236551	−	0.971619i	$-0.423983\pi$
$67$	17383.7			0.473101			0.236551	+	0.971619i	$0.423983\pi$
$68$	5599.32	−	41661.8i	0.146846	−	1.09261i
$69$	−5843.93			−0.147769
$70$	44079.8	−	44079.8i	1.07521	−	1.07521i
$71$	6730.66	−	16249.2i	0.158457	−	0.382549i	−0.824634	−	0.565667i	$-0.808619\pi$
$71$	6730.66	−	16249.2i	0.158457	−	0.382549i	0.983091	+	0.183118i	$0.0586189\pi$
$72$		−	2177.83i		−	0.0495100i
$73$	21274.7	+	8812.28i	0.467258	+	0.193545i	0.603875	−	0.797079i	$-0.293623\pi$
$73$	21274.7	+	8812.28i	0.467258	+	0.193545i	−0.136616	+	0.990624i	$0.543623\pi$
$74$	37957.4	+	91637.2i	0.805780	+	1.94533i
$75$	8167.56	−	3383.11i	0.167664	−	0.0694486i
$76$	−21140.6	−	21140.6i	−0.419839	−	0.419839i
$77$	−67157.8	−	67157.8i	−1.29083	−	1.29083i
$78$	66653.6	−	27608.8i	1.24047	−	0.513820i
$79$	−35385.1	−	85427.1i	−0.637900	−	1.54003i	−0.829473	−	0.558548i	$-0.811359\pi$
$79$	−35385.1	−	85427.1i	−0.637900	−	1.54003i	0.191573	−	0.981478i	$-0.438641\pi$
$80$	−38846.9	−	16090.9i	−0.678628	−	0.281097i
$81$			6561.00i			0.111111i
$82$	−47178.8	+	113900.i	−0.774841	+	1.87063i
$83$	15888.6	−	15888.6i	0.253157	−	0.253157i	−0.569107	−	0.822264i	$-0.692711\pi$
$83$	15888.6	−	15888.6i	0.253157	−	0.253157i	0.822264	+	0.569107i	$0.192711\pi$
$84$	52129.2			0.806089
$85$	−47693.3	−	27707.6i	−0.715994	−	0.415960i
$86$	−3306.61			−0.0482099
$87$	2832.81	−	2832.81i	0.0401254	−	0.0401254i
$88$	5951.89	−	14369.1i	0.0819310	−	0.197799i
$89$			69495.8i			0.930001i	0.885310	+	0.465001i	$0.153946\pi$
$89$			69495.8i			0.930001i	−0.885310	+	0.465001i	$0.846054\pi$
$90$	−28413.2	−	11769.1i	−0.369754	−	0.153157i
$91$	61405.0	+	148245.i	0.777321	+	1.87662i
$92$	21163.2	−	8766.09i	0.260683	−	0.107978i
$93$	58767.7	+	58767.7i	0.704581	+	0.704581i
$94$	23855.3	+	23855.3i	0.278462	+	0.278462i
$95$	−36243.2	+	15012.4i	−0.412019	+	0.170664i
$96$	−28624.5	−	69105.6i	−0.317000	−	0.765306i
$97$	−97647.8	−	40447.1i	−1.05374	−	0.436473i	−0.212514	−	0.977158i	$-0.568165\pi$
$97$	−97647.8	−	40447.1i	−1.05374	−	0.436473i	−0.841225	+	0.540685i	$0.818165\pi$
$98$			83252.9i			0.875657i
$99$	−17930.8	+	43288.9i	−0.183871	+	0.443903i
$100$	−24503.2	+	24503.2i	−0.245032	+	0.245032i
$101$	−128402.			−1.25247			−0.626235	−	0.779634i	$-0.715405\pi$
$101$	−128402.			−1.25247			−0.626235	+	0.779634i	$0.715405\pi$
$102$	−22537.1	−	85027.1i	−0.214486	−	0.809202i
$103$	137487.			1.27693			0.638466	−	0.769650i	$-0.279569\pi$
$103$	137487.			1.27693			0.638466	+	0.769650i	$0.279569\pi$
$104$	−18580.3	+	18580.3i	−0.168450	+	0.168450i
$105$	26175.8	−	63194.0i	0.231701	−	0.559375i
$106$			134110.i			1.15930i
$107$	−103879.	−	43028.2i	−0.877141	−	0.363324i	−0.101754	−	0.994810i	$-0.532445\pi$
$107$	−103879.	−	43028.2i	−0.877141	−	0.363324i	−0.775387	+	0.631486i	$0.782445\pi$
$108$	−9841.71	−	23760.0i	−0.0811916	−	0.196014i
$109$	−6463.56	+	2677.29i	−0.0521081	+	0.0215839i	−0.408585	−	0.912720i	$-0.633978\pi$
$109$	−6463.56	+	2677.29i	−0.0521081	+	0.0215839i	0.356477	+	0.934304i	$0.383978\pi$
$110$	−155303.	−	155303.i	−1.22377	−	1.22377i
$111$	76956.9	+	76956.9i	0.592843	+	0.592843i
$112$	137787.	−	57073.3i	1.03792	−	0.429920i
$113$	−84743.2	−	204588.i	−0.624322	−	1.50725i	−0.846581	−	0.532260i	$-0.821343\pi$
$113$	−84743.2	−	204588.i	−0.624322	−	1.50725i	0.222259	−	0.974988i	$-0.428657\pi$
$114$	−57799.3	−	23941.2i	−0.416543	−	0.172538i
$115$		−	30057.0i		−	0.211934i
$116$	−6009.42	+	14508.0i	−0.0414656	+	0.100107i
$117$	55975.7	−	55975.7i	0.378037	−	0.378037i
$118$	−151645.			−1.00259
$119$	189110.	−	50125.1i	1.22418	−	0.324480i
$120$	11201.2			0.0710086
$121$	−122732.	+	122732.i	−0.762069	+	0.762069i
$122$	122406.	−	295513.i	0.744564	−	1.79754i
$123$			135274.i			0.806215i
$124$	−300974.	−	124668.i	−1.75782	−	0.728114i
$125$	72757.3	+	175652.i	0.416487	+	1.00549i
$126$	100779.	−	41744.2i	0.565517	−	0.234245i
$127$	−117890.	−	117890.i	−0.648588	−	0.648588i	0.304064	−	0.952652i	$-0.401656\pi$
$127$	−117890.	−	117890.i	−0.648588	−	0.648588i	−0.952652	+	0.304064i	$0.901656\pi$
$128$	38731.9	+	38731.9i	0.208951	+	0.208951i
$129$	−3352.00	+	1388.44i	−0.0177349	+	0.00734605i
$130$	142000.	+	342818.i	0.736936	+	1.77912i
$131$	140825.	+	58331.6i	0.716971	+	0.296979i	0.711186	−	0.703004i	$-0.248158\pi$
$131$	140825.	+	58331.6i	0.716971	+	0.296979i	0.00578525	+	0.999983i	$0.498158\pi$
$132$		−	183663.i		−	0.917460i
$133$	53248.0	−	128552.i	0.261020	−	0.630158i
$134$	−100824.	+	100824.i	−0.485065	+	0.485065i
$135$	−33745.1			−0.159359
$136$	19434.6	+	25469.8i	0.0901009	+	0.118080i
$137$	314798.			1.43295			0.716474	−	0.697613i	$-0.245755\pi$
$137$	314798.			1.43295			0.716474	+	0.697613i	$0.245755\pi$
$138$	33894.3	−	33894.3i	0.151506	−	0.151506i
$139$	−55169.1	+	133190.i	−0.242192	+	0.584702i	−0.997500	−	0.0706674i	$-0.977487\pi$
$139$	−55169.1	+	133190.i	−0.242192	+	0.584702i	0.755308	+	0.655370i	$0.227487\pi$
$140$			268115.i			1.15612i
$141$	34199.7	+	14166.0i	0.144869	+	0.0600065i
$142$	55207.0	+	133281.i	0.229759	+	0.554688i
$143$	522301.	−	216344.i	2.13590	−	0.884718i
$144$	−52026.9	−	52026.9i	−0.209085	−	0.209085i
$145$	14569.9	+	14569.9i	0.0575490	+	0.0575490i
$146$	−174502.	+	72281.1i	−0.677514	+	0.280636i
$147$	34957.9	+	84395.8i	0.133429	+	0.322127i
$148$	−394129.	−	163254.i	−1.47906	−	0.612645i
$149$			176514.i			0.651348i	0.945482	+	0.325674i	$0.105591\pi$
$149$			176514.i			0.651348i	−0.945482	+	0.325674i	$0.894409\pi$
$150$	−27749.4	+	66992.9i	−0.100699	+	0.243109i
$151$	−170491.	+	170491.i	−0.608497	+	0.608497i	−0.942553	−	0.334056i	$-0.891583\pi$
$151$	−170491.	+	170491.i	−0.608497	+	0.608497i	0.334056	+	0.942553i	$0.391583\pi$
$152$	22785.9			0.0799941
$153$	−58549.4	−	76731.0i	−0.202206	−	0.264998i
$154$	779018.			2.64695
$155$	−302259.	+	302259.i	−1.01053	+	1.01053i
$156$	−118745.	+	286675.i	−0.390664	+	0.943146i
$157$		−	265398.i		−	0.859308i	−0.902994	−	0.429654i	$-0.858635\pi$
$157$		−	265398.i		−	0.859308i	0.902994	−	0.429654i	$-0.141365\pi$
$158$	700700.	+	290239.i	2.23300	+	0.924940i
$159$	56312.7	+	135951.i	0.176650	+	0.426471i
$160$	355429.	−	147224.i	1.09762	−	0.454651i
$161$	75384.7	+	75384.7i	0.229202	+	0.229202i
$162$	−38053.2	−	38053.2i	−0.113921	−	0.113921i
$163$	174825.	−	72415.0i	0.515389	−	0.213481i	−0.109801	−	0.993954i	$-0.535021\pi$
$163$	174825.	−	72415.0i	0.515389	−	0.213481i	0.625190	+	0.780472i	$0.285021\pi$
$164$	−202915.	−	489880.i	−0.589121	−	1.42226i
$165$	−222647.	−	92223.4i	−0.636659	−	0.263713i
$166$			184305.i			0.519118i
$167$	43137.8	−	104144.i	0.119693	−	0.288963i	−0.852666	−	0.522457i	$-0.825016\pi$
$167$	43137.8	−	104144.i	0.119693	−	0.288963i	0.972358	+	0.233493i	$0.0750157\pi$
$168$	−28093.2	+	28093.2i	−0.0767942	+	0.0767942i
$169$	−583828.			−1.57242
$170$	437318.	−	115915.i	1.16058	−	0.307622i
$171$	−68645.7			−0.179524
$172$	10056.2	−	10056.2i	0.0259187	−	0.0259187i
$173$	−112113.	+	270665.i	−0.284800	+	0.687569i	−0.999935	−	0.0114179i	$-0.996365\pi$
$173$	−112113.	+	270665.i	−0.284800	+	0.687569i	0.715134	+	0.698987i	$0.246365\pi$
$174$			32860.1i			0.0822802i
$175$	−149000.	−	61717.6i	−0.367781	−	0.152340i
$176$	−201082.	−	485456.i	−0.489319	−	1.18132i
$177$	−153727.	+	63675.8i	−0.368822	+	0.152771i
$178$	−403070.	−	403070.i	−0.953520	−	0.953520i
$179$	−290425.	−	290425.i	−0.677488	−	0.677488i	0.281943	−	0.959431i	$-0.409021\pi$
$179$	−290425.	−	290425.i	−0.677488	−	0.677488i	−0.959431	+	0.281943i	$0.909021\pi$
$180$	122204.	−	50618.7i	0.281129	−	0.116447i
$181$	294212.	+	710291.i	0.667520	+	1.61154i	0.785746	+	0.618549i	$0.212279\pi$
$181$	294212.	+	710291.i	0.667520	+	1.61154i	−0.118226	+	0.992987i	$0.537721\pi$
$182$	−1.21595e6	−	503663.i	−2.72106	−	1.12710i
$183$		−	350968.i		−	0.774712i
$184$	−6681.00	+	16129.4i	−0.0145478	+	0.0351215i
$185$	−395811.	+	395811.i	−0.850273	+	0.850273i
$186$	−681694.			−1.44480
$187$	−176602.	−	666277.i	−0.369311	−	1.39332i
$188$	−145100.			−0.299414
$189$	84634.6	−	84634.6i	0.172343	−	0.172343i
$190$	123137.	−	297278.i	0.247459	−	0.597419i
$191$			286522.i			0.568297i	0.958780	+	0.284148i	$0.0917108\pi$
$191$			286522.i			0.568297i	−0.958780	+	0.284148i	$0.908289\pi$
$192$	325131.	+	134674.i	0.636511	+	0.263651i
$193$	13689.4	+	33049.1i	0.0264539	+	0.0638655i	0.936554	−	0.350522i	$-0.113996\pi$
$193$	13689.4	+	33049.1i	0.0264539	+	0.0638655i	−0.910101	+	0.414388i	$0.863996\pi$
$194$	800938.	−	331759.i	1.52790	−	0.632877i
$195$	287899.	+	287899.i	0.542192	+	0.542192i
$196$	−253193.	−	253193.i	−0.470772	−	0.470772i
$197$	−99975.8	+	41411.3i	−0.183539	+	0.0760245i	−0.472561	−	0.881298i	$-0.656670\pi$
$197$	−99975.8	+	41411.3i	−0.183539	+	0.0760245i	0.289021	+	0.957323i	$0.406670\pi$
$198$	−147074.	−	355069.i	−0.266609	−	0.643650i
$199$	716684.	+	296860.i	1.28291	+	0.531397i	0.916864	−	0.399200i	$-0.130712\pi$
$199$	716684.	+	296860.i	1.28291	+	0.531397i	0.366043	+	0.930598i	$0.380712\pi$
$200$		−	26410.3i		−	0.0466873i
$201$	−59871.9	+	144544.i	−0.104528	+	0.252353i
$202$	744719.	−	744719.i	1.28414	−	1.28414i
$203$	−73084.4			−0.124476
$204$	327130.	+	190048.i	0.550357	+	0.319733i
$205$	−695752.			−1.15630
$206$	−797411.	+	797411.i	−1.30923	+	1.30923i
$207$	20127.4	−	48591.8i	0.0326484	−	0.0788202i
$208$			887744.i			1.42275i
$209$	−452918.	−	187605.i	−0.717223	−	0.297083i
$210$	214702.	+	518337.i	0.335961	+	0.811081i
$211$	189781.	−	78609.7i	0.293458	−	0.121554i	−0.231097	−	0.972931i	$-0.574232\pi$
$211$	189781.	−	78609.7i	0.293458	−	0.121554i	0.524555	+	0.851376i	$0.324232\pi$
$212$	−407861.	−	407861.i	−0.623265	−	0.623265i
$213$	111930.	+	111930.i	0.169043	+	0.169043i
$214$	852050.	−	352931.i	1.27183	−	0.526811i
$215$	−7141.16	−	17240.3i	−0.0105359	−	0.0254360i
$216$	18108.5	+	7500.77i	0.0264087	+	0.0109389i
$217$		−	1.51616e6i		−	2.18573i
$218$	21960.0	−	53016.1i	0.0312962	−	0.0755556i
$219$	−146547.	+	146547.i	−0.206474	+	0.206474i
$220$	944631.			1.31585
$221$	−155118.	+	1.15416e6i	−0.213639	+	1.58958i
$222$	−892686.			−1.21567
$223$	−666745.	+	666745.i	−0.897837	+	0.897837i	−0.995245	−	0.0974075i	$-0.968945\pi$
$223$	−666745.	+	666745.i	−0.897837	+	0.897837i	0.0974075	+	0.995245i	$0.468945\pi$
$224$	−522192.	+	1.26068e6i	−0.695360	+	1.67875i
$225$			79564.5i			0.104776i
$226$	1.67810e6	+	695091.i	2.18548	+	0.905254i
$227$	491739.	+	1.18716e6i	0.633389	+	1.52914i	0.835336	+	0.549740i	$0.185273\pi$
$227$	491739.	+	1.18716e6i	0.633389	+	1.52914i	−0.201947	+	0.979396i	$0.564727\pi$
$228$	248593.	−	102971.i	0.316703	−	0.131183i
$229$	−920190.	−	920190.i	−1.15955	−	1.15955i	−0.984573	−	0.174975i	$-0.944016\pi$
$229$	−920190.	−	920190.i	−1.15955	−	1.15955i	−0.174975	−	0.984573i	$-0.555984\pi$
$230$	174328.	+	174328.i	0.217294	+	0.217294i
$231$	789713.	−	327110.i	0.973731	−	0.403333i
$232$	−4580.03	−	11057.2i	−0.00558661	−	0.0134873i
$233$	−352193.	−	145883.i	−0.425002	−	0.176042i	0.159922	−	0.987130i	$-0.448876\pi$
$233$	−352193.	−	145883.i	−0.425002	−	0.176042i	−0.584924	+	0.811088i	$0.698876\pi$
$234$			649308.i			0.775195i
$235$	−72859.6	+	175899.i	−0.0860631	+	0.207775i
$236$	461191.	−	461191.i	0.539015	−	0.539015i
$237$	832191.			0.962392
$238$	−806098.	+	1.38754e6i	−0.922456	+	1.58783i
$239$	849666.			0.962174			0.481087	−	0.876673i	$-0.340242\pi$
$239$	849666.			0.962174			0.481087	+	0.876673i	$0.340242\pi$
$240$	267589.	−	267589.i	0.299875	−	0.299875i
$241$	641510.	−	1.54874e6i	0.711477	−	1.71766i	0.0151986	−	0.999884i	$-0.495162\pi$
$241$	641510.	−	1.54874e6i	0.711477	−	1.71766i	0.696278	−	0.717772i	$-0.254838\pi$
$242$		−	1.42367e6i		−	1.56268i
$243$	−54554.2	−	22597.1i	−0.0592669	−	0.0245492i
$244$	526464.	+	1.27100e6i	0.566101	+	1.36669i
$245$	−434071.	+	179798.i	−0.462004	+	0.191368i
$246$	−784576.	−	784576.i	−0.826604	−	0.826604i
$247$	585656.	+	585656.i	0.610801	+	0.610801i
$248$	229385.	−	95014.4i	0.236830	−	0.0980980i
$249$	77389.5	+	186835.i	0.0791013	+	0.190967i
$250$	−1.44075e6	−	596778.i	−1.45794	−	0.603897i
$251$		−	1.25139e6i		−	1.25375i	−0.779122	−	0.626873i	$-0.784335\pi$
$251$		−	1.25139e6i		−	1.25375i	0.779122	−	0.626873i	$-0.215665\pi$
$252$	−179541.	+	433450.i	−0.178099	+	0.429969i
$253$	265598.	−	265598.i	0.260869	−	0.260869i
$254$	1.36751e6			1.32998
$255$	394649.	−	301136.i	0.380068	−	0.290010i
$256$	801986.			0.764834
$257$	975965.	−	975965.i	0.921725	−	0.921725i	−0.0754262	−	0.997151i	$-0.524032\pi$
$257$	975965.	−	975965.i	0.921725	−	0.921725i	0.997151	+	0.0754262i	$0.0240317\pi$
$258$	11388.5	−	27494.2i	0.0106516	−	0.0257153i
$259$		−	1.98543e6i		−	1.83910i
$260$	−1.47445e6	−	610738.i	−1.35269	−	0.560302i
$261$	13797.9	+	33311.2i	0.0125376	+	0.0302683i
$262$	−1.15509e6	+	478454.i	−1.03959	+	0.430613i
$263$	1.13025e6	+	1.13025e6i	1.00759	+	1.00759i	0.999971	+	0.00761996i	$0.00242553\pi$
$263$	1.13025e6	+	1.13025e6i	1.00759	+	1.00759i	0.00761996	+	0.999971i	$0.497574\pi$
$264$	98978.9	+	98978.9i	0.0874043	+	0.0874043i
$265$	−699234.	+	289632.i	−0.611656	+	0.253356i
$266$	436756.	+	1.05442e6i	0.378473	+	0.913715i
$267$	−577852.	−	239354.i	−0.496065	−	0.205477i
$268$		−	613260.i		−	0.521564i
$269$	187631.	−	452981.i	0.158097	−	0.381680i	−0.824906	−	0.565270i	$-0.808772\pi$
$269$	187631.	−	452981.i	0.158097	−	0.381680i	0.983003	+	0.183590i	$0.0587720\pi$
$270$	195718.	−	195718.i	0.163389	−	0.163389i
$271$	−470605.			−0.389254			−0.194627	−	0.980877i	$-0.562350\pi$
$271$	−470605.			−0.389254			−0.194627	+	0.980877i	$0.562350\pi$
$272$	1.07274e6	+	144175.i	0.879166	+	0.118159i
$273$	−1.44413e6			−1.17274
$274$	−1.82580e6	+	1.82580e6i	−1.46919	+	1.46919i
$275$	−217445.	+	524960.i	−0.173388	+	0.418595i
$276$			206162.i			0.162906i
$277$	641688.	+	265796.i	0.502487	+	0.208137i	0.619505	−	0.784993i	$-0.287333\pi$
$277$	641688.	+	265796.i	0.502487	+	0.208137i	−0.117018	+	0.993130i	$0.537333\pi$
$278$	−452514.	−	1.09247e6i	−0.351172	−	0.847805i
$279$	−691053.	+	286243.i	−0.531497	+	0.220153i
$280$	−144491.	−	144491.i	−0.110140	−	0.110140i
$281$	−1.33636e6	−	1.33636e6i	−1.00962	−	1.00962i	−0.999953	−	0.00966814i	$-0.996922\pi$
$281$	−1.33636e6	−	1.33636e6i	−1.00962	−	1.00962i	−0.00966814	−	0.999953i	$-0.503078\pi$
$282$	−280516.	+	116194.i	−0.210056	+	0.0870081i
$283$	764031.	+	1.84453e6i	0.567081	+	1.36905i	0.904005	+	0.427522i	$0.140613\pi$
$283$	764031.	+	1.84453e6i	0.567081	+	1.36905i	−0.336924	+	0.941532i	$0.609387\pi$
$284$	−573240.	−	237444.i	−0.421736	−	0.174689i
$285$		−	353064.i		−	0.257479i
$286$	−1.77452e6	+	4.28408e6i	−1.28282	+	3.09701i
$287$	1.74498e6	−	1.74498e6i	1.25051	−	1.25051i
$288$	673194.			0.478254
$289$	1.36947e6	+	374884.i	0.964515	+	0.264030i
$290$	−169009.			−0.118009
$291$	672628.	−	672628.i	0.465631	−	0.465631i
$292$	310879.	−	750529.i	0.213371	−	0.515122i
$293$			1.99105e6i			1.35492i	0.735560	+	0.677459i	$0.236919\pi$
$293$			1.99105e6i			1.35492i	−0.735560	+	0.677459i	$0.763081\pi$
$294$	−692240.	−	286735.i	−0.467077	−	0.193470i
$295$	−327503.	−	790662.i	−0.219109	−	0.528976i
$296$	300382.	−	124422.i	0.199271	−	0.0825409i
$297$	−298187.	−	298187.i	−0.196154	−	0.196154i
$298$	−1.02376e6	−	1.02376e6i	−0.667820	−	0.667820i
$299$	−586283.	+	242846.i	−0.379253	+	0.157092i
$300$	−119349.	−	288135.i	−0.0765626	−	0.184839i
$301$	61150.0	+	25329.2i	0.0389028	+	0.0161141i
$302$		−	1.97766e6i		−	1.24777i
$303$	442235.	−	1.06765e6i	0.276724	−	0.668070i
$304$	544342.	−	544342.i	0.337822	−	0.337822i
$305$	1.80513e6			1.11111
$306$	784615.	+	105452.i	0.479019	+	0.0643799i
$307$	−802799.			−0.486140			−0.243070	−	0.970009i	$-0.578154\pi$
$307$	−802799.			−0.486140			−0.243070	+	0.970009i	$0.578154\pi$
$308$	−2.36919e6	+	2.36919e6i	−1.42306	+	1.42306i
$309$	−473525.	+	1.14319e6i	−0.282129	+	0.681119i
$310$		−	3.50615e6i		−	2.07217i
$311$	2.62609e6	+	1.08776e6i	1.53960	+	0.637723i	0.981398	−	0.191982i	$-0.0614914\pi$
$311$	2.62609e6	+	1.08776e6i	1.53960	+	0.637723i	0.558202	+	0.829705i	$0.311491\pi$
$312$	−90500.4	−	218487.i	−0.0526337	−	0.127069i
$313$	−992488.	+	411102.i	−0.572617	+	0.237186i	−0.650153	−	0.759804i	$-0.725295\pi$
$313$	−992488.	+	411102.i	−0.572617	+	0.237186i	0.0775351	+	0.996990i	$0.475295\pi$
$314$	1.53929e6	+	1.53929e6i	0.881039	+	0.881039i
$315$	435299.	+	435299.i	0.247179	+	0.247179i
$316$	−3.01369e6	+	1.24831e6i	−1.69778	+	0.703243i
$317$	−770696.	−	1.86062e6i	−0.430759	−	1.03995i	−0.979043	−	0.203653i	$-0.934719\pi$
$317$	−770696.	−	1.86062e6i	−0.430759	−	1.03995i	0.548284	−	0.836292i	$-0.315281\pi$
$318$	−1.11511e6	−	461894.i	−0.618373	−	0.256138i
$319$			257493.i			0.141674i
$320$	−692666.	+	1.67224e6i	−0.378137	+	0.912902i
$321$	715552.	−	715552.i	0.387595	−	0.387595i
$322$	−874449.			−0.469997
$323$	802812.	−	612584.i	0.428162	−	0.326708i
$324$	231459.			0.122493
$325$	678811.	−	678811.i	0.356484	−	0.356484i
$326$	−593971.	+	1.43397e6i	−0.309543	+	0.747303i
$327$		−	62965.0i		−	0.0325634i
$328$	373358.	+	154650.i	0.191620	+	0.0793716i
$329$	−258428.	−	623899.i	−0.131628	−	0.317779i
$330$	1.82622e6	−	756445.i	0.923142	−	0.382378i
$331$	−183361.	−	183361.i	−0.0919895	−	0.0919895i	0.659615	−	0.751604i	$-0.270720\pi$
$331$	−183361.	−	183361.i	−0.0919895	−	0.0919895i	−0.751604	+	0.659615i	$0.770720\pi$
$332$	−560516.	−	560516.i	−0.279089	−	0.279089i
$333$	−904941.	+	374839.i	−0.447208	+	0.185240i
$334$	353830.	+	854221.i	0.173551	+	0.418990i
$335$	−743429.	−	307938.i	−0.361932	−	0.149917i
$336$			1.34226e6i			0.648616i
$337$	−915671.	+	2.21063e6i	−0.439203	+	1.06033i	0.537022	+	0.843568i	$0.319549\pi$
$337$	−915671.	+	2.21063e6i	−0.439203	+	1.06033i	−0.976225	+	0.216761i	$0.930451\pi$
$338$	3.38615e6	−	3.38615e6i	1.61218	−	1.61218i
$339$	1.99300e6			0.941908
$340$	−977468.	+	1.68252e6i	−0.458570	+	0.789338i
$341$	−5.34179e6			−2.48772
$342$	398139.	−	398139.i	0.184064	−	0.184064i
$343$	−418272.	+	1.00980e6i	−0.191965	+	0.463446i
$344$			10838.9i			0.00493843i
$345$	249922.	+	103521.i	0.113046	+	0.0468253i
$346$	−919586.	−	2.22008e6i	−0.412954	−	0.996960i
$347$	−477089.	+	197617.i	−0.212704	+	0.0881048i	−0.486491	−	0.873685i	$-0.661723\pi$
$347$	−477089.	+	197617.i	−0.212704	+	0.0881048i	0.273788	+	0.961790i	$0.411723\pi$
$348$	−99935.7	−	99935.7i	−0.0442356	−	0.0442356i
$349$	−2.58729e6	−	2.58729e6i	−1.13706	−	1.13706i	−0.988975	−	0.148081i	$-0.952690\pi$
$349$	−2.58729e6	−	2.58729e6i	−1.13706	−	1.13706i	−0.148081	−	0.988975i	$-0.547310\pi$
$350$	1.22214e6	−	506227.i	0.533275	−	0.220890i
$351$	272644.	+	658222.i	0.118121	+	0.285170i
$352$	4.44167e6	+	1.83980e6i	1.91069	+	0.791433i
$353$		−	1.30694e6i		−	0.558237i	−0.960257	−	0.279119i	$-0.909958\pi$
$353$		−	1.30694e6i		−	0.558237i	0.960257	−	0.279119i	$-0.0900423\pi$
$354$	522289.	−	1.26092e6i	0.221515	−	0.534784i
$355$	−575686.	+	575686.i	−0.242446	+	0.242446i
$356$	2.45167e6			1.02527
$357$	−234536.	+	1.74507e6i	−0.0973956	+	0.724673i
$358$	3.36888e6			1.38924
$359$	−2.65010e6	+	2.65010e6i	−1.08524	+	1.08524i	−0.0892297	+	0.996011i	$0.528441\pi$
$359$	−2.65010e6	+	2.65010e6i	−1.08524	+	1.08524i	−0.996011	+	0.0892297i	$0.971559\pi$
$360$	−38578.6	+	93137.0i	−0.0156888	+	0.0378762i
$361$			1.75788e6i			0.709940i
$362$	−5.82603e6	−	2.41322e6i	−2.33669	−	0.967889i
$363$	−597799.	−	1.44321e6i	−0.238116	−	0.574863i
$364$	5.22978e6	−	2.16624e6i	2.06885	−	0.856947i
$365$	−753732.	−	753732.i	−0.296131	−	0.296131i
$366$	2.03559e6	+	2.03559e6i	0.794304	+	0.794304i
$367$	739539.	−	306327.i	0.286613	−	0.118719i	−0.234745	−	0.972057i	$-0.575426\pi$
$367$	739539.	−	306327.i	0.286613	−	0.118719i	0.521358	+	0.853338i	$0.325426\pi$
$368$	225715.	+	544925.i	0.0868843	+	0.209757i
$369$	−1.12479e6	−	465904.i	−0.430037	−	0.178127i
$370$		−	4.59134e6i		−	1.74355i
$371$	1.02730e6	−	2.48013e6i	0.387493	−	0.935491i
$372$	2.07320e6	−	2.07320e6i	0.776756	−	0.776756i
$373$	1.63210e6			0.607399			0.303699	−	0.952768i	$-0.401778\pi$
$373$	1.63210e6			0.607399			0.303699	+	0.952768i	$0.401778\pi$
$374$	4.88862e6	+	2.84007e6i	1.80721	+	1.04990i
$375$	−1.71112e6			−0.628350
$376$	78196.6	−	78196.6i	0.0285245	−	0.0285245i
$377$	166479.	−	401915.i	0.0603261	−	0.145640i
$378$			981746.i			0.353402i
$379$	1.11710e6	+	462719.i	0.399480	+	0.165470i	0.573373	−	0.819294i	$-0.305635\pi$
$379$	1.11710e6	+	462719.i	0.399480	+	0.165470i	−0.173893	+	0.984765i	$0.555635\pi$
$380$	529607.	+	1.27859e6i	0.188146	+	0.454225i
$381$	1.38628e6	−	574216.i	0.489258	−	0.202657i
$382$	−1.66180e6	−	1.66180e6i	−0.582668	−	0.582668i
$383$	1.46148e6	+	1.46148e6i	0.509090	+	0.509090i	0.914247	−	0.405157i	$-0.132783\pi$
$383$	1.46148e6	+	1.46148e6i	0.509090	+	0.509090i	−0.405157	+	0.914247i	$0.632783\pi$
$384$	−455452.	+	188654.i	−0.157621	+	0.0652888i
$385$	1.68242e6	+	4.06172e6i	0.578472	+	1.39655i
$386$	−271079.	−	112285.i	−0.0926035	−	0.0383576i
$387$		−	32653.6i		−	0.0110829i
$388$	−1.42689e6	+	3.44482e6i	−0.481184	+	1.16168i
$389$	−569258.	+	569258.i	−0.190737	+	0.190737i	−0.796015	−	0.605277i	$-0.793062\pi$
$389$	−569258.	+	569258.i	−0.190737	+	0.190737i	0.605277	+	0.796015i	$0.293062\pi$
$390$	−3.33957e6			−1.11181
$391$	198236.	+	747896.i	0.0655754	+	0.247400i
$392$	272899.			0.0896988
$393$	−970045.	+	970045.i	−0.316819	+	0.316819i
$394$	339669.	−	820033.i	0.110234	−	0.266128i
$395$			4.28019e6i			1.38029i
$396$	1.52714e6	+	632564.i	0.489375	+	0.202706i
$397$	−1.20439e6	−	2.90765e6i	−0.383522	−	0.925903i	−0.991279	−	0.131780i	$-0.957931\pi$
$397$	−1.20439e6	−	2.90765e6i	−0.383522	−	0.925903i	0.607757	−	0.794123i	$-0.292069\pi$
$398$	−5.87847e6	+	2.43494e6i	−1.86019	+	0.770515i
$399$	885505.	+	885505.i	0.278457	+	0.278457i
$400$	−630925.	−	630925.i	−0.197164	−	0.197164i
$401$	2.69449e6	−	1.11609e6i	0.836787	−	0.346609i	0.0772013	−	0.997016i	$-0.475402\pi$
$401$	2.69449e6	−	1.11609e6i	0.836787	−	0.346609i	0.759586	+	0.650407i	$0.225402\pi$
$402$	−491088.	−	1.18559e6i	−0.151563	−	0.365906i
$403$	8.33788e6	+	3.45366e6i	2.55737	+	1.05930i
$404$			4.52975e6i			1.38077i
$405$	116223.	−	280587.i	0.0352091	−	0.0850023i
$406$	423883.	−	423883.i	0.127624	−	0.127624i
$407$	−6.99514e6			−2.09320
$408$	−278715.	+	73875.7i	−0.0828914	+	0.0219711i
$409$	2.05142e6			0.606382			0.303191	−	0.952930i	$-0.401948\pi$
$409$	2.05142e6			0.606382			0.303191	+	0.952930i	$0.401948\pi$
$410$	4.03530e6	−	4.03530e6i	1.18554	−	1.18554i
$411$	−1.08421e6	+	2.61752e6i	−0.316599	+	0.764338i
$412$		−	4.85025e6i		−	1.40774i
$413$	2.80442e6	+	1.16163e6i	0.809036	+	0.335114i
$414$	165091.	+	398565.i	0.0473394	+	0.114288i
$415$	−960944.	+	398036.i	−0.273891	+	0.113449i
$416$	−5.74340e6	−	5.74340e6i	−1.62718	−	1.62718i
$417$	−917453.	−	917453.i	−0.258371	−	0.258371i
$418$	3.71498e6	−	1.53879e6i	1.03996	−	0.430764i
$419$	−1.42637e6	−	3.44356e6i	−0.396915	−	0.958238i	−0.988393	−	0.151917i	$-0.951455\pi$
$419$	−1.42637e6	−	3.44356e6i	−0.396915	−	0.958238i	0.591478	−	0.806321i	$-0.298545\pi$
$420$	−2.22936e6	−	923429.i	−0.616675	−	0.255435i
$421$			2.49273e6i			0.685442i	0.939437	+	0.342721i	$0.111349\pi$
$421$			2.49273e6i			0.685442i	−0.939437	+	0.342721i	$0.888651\pi$
$422$	−644782.	+	1.55664e6i	−0.176251	+	0.425507i
$423$	−235578.	+	235578.i	−0.0640152	+	0.0640152i
$424$	439605.			0.118754
$425$	−710022.	−	930509.i	−0.190678	−	0.249890i
$426$	−1.29836e6			−0.346635
$427$	−4.52737e6	+	4.52737e6i	−1.20164	+	1.20164i
$428$	−1.51795e6	+	3.66465e6i	−0.400541	+	0.966992i
$429$			5.08801e6i			1.33476i
$430$	141410.	+	58574.0i	0.0368816	+	0.0152769i
$431$	249000.	+	601139.i	0.0645663	+	0.155877i	0.952869	−	0.303381i	$-0.0981155\pi$
$431$	249000.	+	601139.i	0.0645663	+	0.155877i	−0.888303	+	0.459258i	$0.848115\pi$
$432$	611788.	−	253411.i	0.157722	−	0.0653305i
$433$	−2.70944e6	−	2.70944e6i	−0.694479	−	0.694479i	0.268735	−	0.963214i	$-0.413394\pi$
$433$	−2.70944e6	−	2.70944e6i	−0.694479	−	0.694479i	−0.963214	+	0.268735i	$0.913394\pi$
$434$	8.79361e6	+	8.79361e6i	2.24101	+	2.24101i
$435$	−171329.	+	70966.7i	−0.0434117	+	0.0179817i
$436$	94449.5	+	228021.i	0.0237949	+	0.0574459i
$437$	508401.	+	210587.i	0.127351	+	0.0527506i
$438$		−	1.69992e6i		−	0.423392i
$439$	−694269.	+	1.67611e6i	−0.171936	+	0.415090i	−0.986234	−	0.165358i	$-0.947122\pi$
$439$	−694269.	+	1.67611e6i	−0.171936	+	0.415090i	0.814298	+	0.580447i	$0.197122\pi$
$440$	−509076.	+	509076.i	−0.125358	+	0.125358i
$441$	−822144.			−0.201303
$442$	−5.79433e6	−	7.59367e6i	−1.41074	−	1.84883i
$443$	3.84934e6			0.931917			0.465959	−	0.884807i	$-0.345710\pi$
$443$	3.84934e6			0.931917			0.465959	+	0.884807i	$0.345710\pi$
$444$	2.71488e6	−	2.71488e6i	0.653572	−	0.653572i
$445$	1.23107e6	−	2.97206e6i	0.294701	−	0.711470i
$446$		−	7.73412e6i		−	1.84109i
$447$	−1.46770e6	−	607940.i	−0.347430	−	0.143910i
$448$	−2.45683e6	−	5.93132e6i	−0.578337	−	1.39623i
$449$	−3.44732e6	+	1.42793e6i	−0.806985	+	0.334264i	−0.747750	−	0.663980i	$-0.768866\pi$
$449$	−3.44732e6	+	1.42793e6i	−0.806985	+	0.334264i	−0.0592347	+	0.998244i	$0.518866\pi$
$450$	−461467.	−	461467.i	−0.107426	−	0.107426i
$451$	−6.14798e6	−	6.14798e6i	−1.42328	−	1.42328i
$452$	−7.21745e6	+	2.98957e6i	−1.66164	+	0.688275i
$453$	−830421.	−	2.00481e6i	−0.190131	−	0.459017i
$454$	−9.73749e6	−	4.03340e6i	−2.21721	−	0.918400i
$455$		−	7.42758e6i		−	1.68197i
$456$	−78478.2	+	189463.i	−0.0176741	+	0.0426690i
$457$	−2.34110e6	+	2.34110e6i	−0.524359	+	0.524359i	−0.918885	−	0.394525i	$-0.870909\pi$
$457$	−2.34110e6	+	2.34110e6i	−0.524359	+	0.524359i	0.394525	+	0.918885i	$0.370909\pi$
$458$	1.06740e7			2.37774
$459$	839665.	−	222560.i	0.186026	−	0.0493078i
$460$	−1.06035e6			−0.233644
$461$	4.27435e6	−	4.27435e6i	0.936737	−	0.936737i	−0.0613776	−	0.998115i	$-0.519549\pi$
$461$	4.27435e6	−	4.27435e6i	0.936737	−	0.936737i	0.998115	+	0.0613776i	$0.0195494\pi$
$462$	−2.68306e6	+	6.47747e6i	−0.584824	+	1.41189i
$463$		−	2.62955e6i		−	0.570070i	−0.958517	−	0.285035i	$-0.907995\pi$
$463$		−	2.62955e6i		−	0.570070i	0.958517	−	0.285035i	$-0.0920052\pi$
$464$	−373562.	−	154735.i	−0.0805505	−	0.0333651i
$465$	−1.47223e6	−	3.55428e6i	−0.315750	−	0.762288i
$466$	2.88880e6	−	1.19658e6i	0.616244	−	0.255256i
$467$	−1.26730e6	−	1.26730e6i	−0.268898	−	0.268898i	0.559758	−	0.828656i	$-0.310894\pi$
$467$	−1.26730e6	−	1.26730e6i	−0.268898	−	0.268898i	−0.828656	+	0.559758i	$0.810894\pi$
$468$	−1.97471e6	−	1.97471e6i	−0.416762	−	0.416762i
$469$	2.63689e6	−	1.09223e6i	0.553553	−	0.229289i
$470$	−597617.	−	1.44278e6i	−0.124790	−	0.301269i
$471$	2.20676e6	+	914072.i	0.458357	+	0.189858i
$472$			497086.i			0.102701i
$473$	89240.5	−	215446.i	0.0183404	−	0.0442777i
$474$	−4.82663e6	+	4.82663e6i	−0.986730	+	0.986730i
$475$	−832459.			−0.169289
$476$	−1.76831e6	−	6.67140e6i	−0.357718	−	1.34958i
$477$	−1.32437e6			−0.266510
$478$	−4.92799e6	+	4.92799e6i	−0.986506	+	0.986506i
$479$	−337351.	+	814438.i	−0.0671805	+	0.162188i	−0.953904	−	0.300112i	$-0.902976\pi$
$479$	−337351.	+	814438.i	−0.0671805	+	0.162188i	0.886723	+	0.462300i	$0.152976\pi$
$480$			3.46243e6i			0.685926i
$481$	1.09185e7	+	4.52261e6i	2.15180	+	0.891305i
$482$	5.26186e6	+	1.27033e7i	1.03163	+	2.49056i
$483$	−886453.	+	367181.i	−0.172897	+	0.0716164i
$484$	4.32973e6	+	4.32973e6i	0.840133	+	0.840133i
$485$	3.45951e6	+	3.45951e6i	0.667822	+	0.667822i
$486$	447470.	−	185348.i	0.0859357	−	0.0355957i
$487$	1.87824e6	+	4.53448e6i	0.358863	+	0.866373i	0.995460	+	0.0951763i	$0.0303415\pi$
$487$	1.87824e6	+	4.53448e6i	0.358863	+	0.866373i	−0.636597	+	0.771197i	$0.719659\pi$
$488$	−968679.	−	401240.i	−0.184132	−	0.0762701i
$489$			1.70307e6i			0.322077i
$490$	1.47476e6	−	3.56039e6i	0.277480	−	0.669896i
$491$	−3.22861e6	+	3.22861e6i	−0.604382	+	0.604382i	−0.941472	−	0.337090i	$-0.890557\pi$
$491$	−3.22861e6	+	3.22861e6i	−0.604382	+	0.604382i	0.337090	+	0.941472i	$0.390557\pi$
$492$	4.77218e6			0.888801
$493$	−458631.	−	266444.i	−0.0849858	−	0.0493729i
$494$	−6.79350e6			−1.25250
$495$	1.53366e6	−	1.53366e6i	0.281330	−	0.281330i
$496$	3.21003e6	−	7.74969e6i	0.585875	−	1.41443i
$497$		−	2.88771e6i		−	0.524399i
$498$	−1.53248e6	−	634773.i	−0.276899	−	0.114695i
$499$	2.70817e6	+	6.53809e6i	0.486882	+	1.17544i	0.956280	+	0.292451i	$0.0944709\pi$
$499$	2.70817e6	+	6.53809e6i	0.486882	+	1.17544i	−0.469398	+	0.882987i	$0.655529\pi$
$500$	6.19663e6	−	2.56673e6i	1.10849	−	0.459150i
$501$	717375.	+	717375.i	0.127688	+	0.127688i
$502$	7.25797e6	+	7.25797e6i	1.28545	+	1.28545i
$503$	3.16748e6	−	1.31202e6i	0.558206	−	0.231217i	−0.0857001	−	0.996321i	$-0.527313\pi$
$503$	3.16748e6	−	1.31202e6i	0.558206	−	0.231217i	0.643906	+	0.765104i	$0.277313\pi$
$504$	−136835.	−	330350.i	−0.0239951	−	0.0579293i
$505$	5.49122e6	+	2.27454e6i	0.958166	+	0.396885i
$506$			3.08088e6i			0.534933i
$507$	2.01079e6	−	4.85448e6i	0.347414	−	0.838732i
$508$	−4.15893e6	+	4.15893e6i	−0.715026	+	0.715026i
$509$	−6.79451e6			−1.16242			−0.581211	−	0.813753i	$-0.697421\pi$
$509$	−6.79451e6			−1.16242			−0.581211	+	0.813753i	$0.697421\pi$
$510$	−542368.	+	4.03549e6i	−0.0923355	+	0.687023i
$511$	3.78080e6			0.640519
$512$	−5.89087e6	+	5.89087e6i	−0.993127	+	0.993127i
$513$	236426.	−	570783.i	0.0396645	−	0.0957586i
$514$			1.13210e7i			1.89007i
$515$	−5.87976e6	−	2.43547e6i	−0.976880	−	0.404637i
$516$	48981.5	+	118252.i	0.00809856	+	0.0195516i
$517$	−2.19814e6	+	910500.i	−0.361684	+	0.149814i
$518$	1.15153e7	+	1.15153e7i	1.88561	+	1.88561i
$519$	−1.86442e6	−	1.86442e6i	−0.303826	−	0.303826i
$520$	1.12374e6	−	465469.i	0.182246	−	0.0754888i
$521$	−482071.	−	1.16382e6i	−0.0778067	−	0.187842i	0.880190	−	0.474622i	$-0.157415\pi$
$521$	−482071.	−	1.16382e6i	−0.0778067	−	0.187842i	−0.957997	+	0.286780i	$0.907415\pi$
$522$	−273229.	−	113175.i	−0.0438884	−	0.0181792i
$523$		−	4.73404e6i		−	0.756794i	−0.925643	−	0.378397i	$-0.876475\pi$
$523$		−	4.73404e6i		−	0.756794i	0.925643	−	0.378397i	$-0.123525\pi$
$524$	2.05782e6	−	4.96802e6i	0.327400	−	0.790415i
$525$	1.02635e6	−	1.02635e6i	0.162517	−	0.162517i
$526$	−1.31107e7			−2.06614
$527$	5.52748e6	−	9.51448e6i	0.866963	−	1.49231i
$528$	4.72908e6			0.738231
$529$	4.25305e6	−	4.25305e6i	0.660786	−	0.660786i
$530$	2.37565e6	−	5.73533e6i	0.367361	−	0.886888i
$531$		−	1.49754e6i		−	0.230484i
$532$	−4.53505e6	−	1.87848e6i	−0.694709	−	0.287758i
$533$	5.62134e6	+	1.35711e7i	0.857082	+	2.06918i
$534$	4.73972e6	−	1.96326e6i	0.719283	−	0.297937i
$535$	3.68028e6	+	3.68028e6i	0.555900	+	0.555900i
$536$	330495.	+	330495.i	0.0496882	+	0.0496882i
$537$	3.41513e6	−	1.41459e6i	0.511060	−	0.211688i
$538$	1.53901e6	+	3.71549e6i	0.229237	+	0.553427i
$539$	−5.42443e6	−	2.24687e6i	−0.804234	−	0.333125i
$540$			1.19046e6i			0.175683i
$541$	2.30681e6	−	5.56914e6i	0.338859	−	0.818078i	−0.658967	−	0.752172i	$-0.729006\pi$
$541$	2.30681e6	−	5.56914e6i	0.338859	−	0.818078i	0.997826	−	0.0659059i	$-0.0209937\pi$
$542$	2.72947e6	−	2.72947e6i	0.399098	−	0.399098i
$543$	−6.91932e6			−1.00708
$544$	−7.87301e6	+	6.00748e6i	−1.14063	+	0.870353i
$545$	323847.			0.0467034
$546$	8.37584e6	−	8.37584e6i	1.20239	−	1.20239i
$547$	672154.	−	1.62272e6i	0.0960506	−	0.231887i	−0.868550	−	0.495601i	$-0.834948\pi$
$547$	672154.	−	1.62272e6i	0.0960506	−	0.231887i	0.964601	+	0.263715i	$0.0849477\pi$
$548$		−	1.11054e7i		−	1.57973i
$549$	2.91827e6	+	1.20879e6i	0.413233	+	0.171167i
$550$	−1.78356e6	−	4.30588e6i	−0.251408	−	0.606954i
$551$	−348524.	+	144364.i	−0.0489051	+	0.0202572i
$552$	−111104.	−	111104.i	−0.0155196	−	0.0155196i
$553$	−1.07350e7	−	1.07350e7i	−1.49275	−	1.49275i
$554$	−5.26333e6	+	2.18014e6i	−0.728595	+	0.301794i
$555$	−1.92790e6	−	4.65437e6i	−0.265676	−	0.641399i
$556$	4.69867e6	+	1.94625e6i	0.644597	+	0.267001i
$557$			1.22372e7i			1.67126i	0.549294	+	0.835629i	$0.314897\pi$
$557$			1.22372e7i			1.67126i	−0.549294	+	0.835629i	$0.685103\pi$
$558$	2.34786e6	−	5.66823e6i	0.319217	−	0.770659i
$559$	−278587.	+	278587.i	−0.0377078	+	0.0377078i
$560$	−6.90361e6			−0.930264
$561$	6.14828e6	+	826325.i	0.824796	+	0.110852i
$562$	1.55016e7			2.07031
$563$	2.66586e6	−	2.66586e6i	0.354460	−	0.354460i	−0.507306	−	0.861766i	$-0.669359\pi$
$563$	2.66586e6	−	2.66586e6i	0.354460	−	0.354460i	0.861766	+	0.507306i	$0.169359\pi$
$564$	499746.	−	1.20649e6i	0.0661533	−	0.159708i
$565$			1.02506e7i			1.35091i
$566$	−1.51294e7	−	6.26682e6i	−1.98510	−	0.822255i
$567$	412235.	+	995223.i	0.0538502	+	0.130006i
$568$	436890.	−	180966.i	0.0568200	−	0.0235356i
$569$	2.36259e6	+	2.36259e6i	0.305919	+	0.305919i	0.843324	−	0.537405i	$-0.180595\pi$
$569$	2.36259e6	+	2.36259e6i	0.305919	+	0.305919i	−0.537405	+	0.843324i	$0.680595\pi$
$570$	2.04774e6	+	2.04774e6i	0.263990	+	0.263990i
$571$	−5.02118e6	+	2.07984e6i	−0.644490	+	0.266956i	−0.680895	−	0.732381i	$-0.738409\pi$
$571$	−5.02118e6	+	2.07984e6i	−0.644490	+	0.266956i	0.0364058	+	0.999337i	$0.488409\pi$
$572$	−7.63218e6	−	1.84257e7i	−0.975345	−	2.35469i
$573$	−2.38241e6	−	986826.i	−0.303131	−	0.125561i
$574$			2.02415e7i			2.56427i
$575$	244083.	−	589268.i	0.0307870	−	0.0743264i
$576$	−2.23960e6	+	2.23960e6i	−0.281264	+	0.281264i
$577$	7.66081e6			0.957933			0.478967	−	0.877833i	$-0.341011\pi$
$577$	7.66081e6			0.957933			0.478967	+	0.877833i	$0.341011\pi$
$578$	−1.01171e7	+	5.76853e6i	−1.25961	+	0.718200i
$579$	−321949.			−0.0399108
$580$	513997.	−	513997.i	0.0634441	−	0.0634441i
$581$	1.41180e6	−	3.40840e6i	0.173514	−	0.418900i
$582$			7.80236e6i			0.954814i
$583$	−8.73807e6	−	3.61943e6i	−1.06474	−	0.441030i
$584$	236934.	+	572009.i	0.0287472	+	0.0694018i
$585$	−3.38542e6	+	1.40229e6i	−0.409000	+	0.169413i
$586$	−1.15479e7	−	1.15479e7i	−1.38918	−	1.38918i
$587$	−8.19751e6	−	8.19751e6i	−0.981944	−	0.981944i	0.0178958	−	0.999840i	$-0.494303\pi$
$587$	−8.19751e6	−	8.19751e6i	−0.981944	−	0.981944i	−0.999840	+	0.0178958i	$0.994303\pi$
$588$	2.97731e6	−	1.23324e6i	0.355125	−	0.147097i
$589$	−2.99487e6	−	7.23027e6i	−0.355705	−	0.858749i
$590$	6.48525e6	+	2.68628e6i	0.767003	+	0.317703i
$591$		−	973917.i		−	0.114697i
$592$	4.20357e6	−	1.01483e7i	0.492962	−	1.19012i
$593$	−7.86197e6	+	7.86197e6i	−0.918110	+	0.918110i	−0.996892	−	0.0787818i	$-0.974897\pi$
$593$	−7.86197e6	+	7.86197e6i	−0.918110	+	0.918110i	0.0787818	+	0.996892i	$0.474897\pi$
$594$	3.45892e6			0.402230
$595$	−8.97538e6	−	1.20629e6i	−1.03935	−	0.139688i
$596$	6.22704e6			0.718069
$597$	−4.93674e6	+	4.93674e6i	−0.566897	+	0.566897i
$598$	1.99190e6	−	4.80888e6i	0.227780	−	0.549909i
$599$		−	706707.i		−	0.0804771i	−0.999190	−	0.0402385i	$-0.987188\pi$
$599$		−	706707.i		−	0.0804771i	0.999190	−	0.0402385i	$-0.0128118\pi$
$600$	219599.	+	90961.1i	0.0249031	+	0.0103152i
$601$	1.22520e6	+	2.95790e6i	0.138364	+	0.334039i	0.977839	−	0.209358i	$-0.0671375\pi$
$601$	1.22520e6	+	2.95790e6i	0.138364	+	0.334039i	−0.839475	+	0.543398i	$0.817138\pi$
$602$	−501572.	+	207758.i	−0.0564082	+	0.0233650i
$603$	−995660.	−	995660.i	−0.111511	−	0.111511i
$604$	6.01457e6	+	6.01457e6i	0.670829	+	0.670829i
$605$	7.42286e6	−	3.07465e6i	0.824485	−	0.341513i
$606$	3.62735e6	+	8.75720e6i	0.401243	+	0.968687i
$607$	−4.44637e6	−	1.84175e6i	−0.489817	−	0.202889i	0.124084	−	0.992272i	$-0.460401\pi$
$607$	−4.44637e6	−	1.84175e6i	−0.489817	−	0.202889i	−0.613901	+	0.789383i	$0.710401\pi$
$608$			7.04342e6i			0.772724i
$609$	251714.	−	607691.i	0.0275020	−	0.0663956i
$610$	−1.04696e7	+	1.04696e7i	−1.13921	+	1.13921i
$611$	4.01970e6			0.435602
$612$	−2.70691e6	+	2.06550e6i	−0.292143	+	0.222919i
$613$	7.61563e6			0.818568			0.409284	−	0.912407i	$-0.365779\pi$
$613$	7.61563e6			0.818568			0.409284	+	0.912407i	$0.365779\pi$
$614$	4.65617e6	−	4.65617e6i	0.498434	−	0.498434i
$615$	2.39627e6	−	5.78512e6i	0.255475	−	0.616771i
$616$		−	2.55358e6i		−	0.271143i
$617$	3.53661e6	+	1.46491e6i	0.374002	+	0.154917i	0.561763	−	0.827298i	$-0.310123\pi$
$617$	3.53661e6	+	1.46491e6i	0.374002	+	0.154917i	−0.187761	+	0.982215i	$0.560123\pi$
$618$	−3.88400e6	−	9.37681e6i	−0.409080	−	0.987607i
$619$	−1.12525e7	+	4.66095e6i	−1.18038	+	0.488931i	−0.884612	−	0.466327i	$-0.845577\pi$
$619$	−1.12525e7	+	4.66095e6i	−1.18038	+	0.488931i	−0.295772	+	0.955258i	$0.595577\pi$
$620$	1.06631e7	+	1.06631e7i	1.11405	+	1.11405i
$621$	334715.	+	334715.i	0.0348294	+	0.0348294i
$622$	−2.15400e7	+	8.92215e6i	−2.23239	+	0.924685i
$623$	4.36650e6	+	1.05417e7i	0.450727	+	1.08815i
$624$	−7.38151e6	−	3.05752e6i	−0.758899	−	0.314346i
$625$		−	5.73114e6i		−	0.586868i
$626$	3.37199e6	−	8.14070e6i	0.343914	−	0.830283i
$627$	3.11984e6	−	3.11984e6i	0.316930	−	0.316930i
$628$	−9.36271e6			−0.947332
$629$	7.23830e6	−	1.24593e7i	0.729474	−	1.25565i
$630$	−5.04940e6			−0.506860
$631$	7.27189e6	−	7.27189e6i	0.727066	−	0.727066i	−0.242968	−	0.970034i	$-0.578121\pi$
$631$	7.27189e6	−	7.27189e6i	0.727066	−	0.727066i	0.970034	+	0.242968i	$0.0781211\pi$
$632$	951391.	−	2.29686e6i	0.0947472	−	0.228740i
$633$			1.84875e6i			0.183388i
$634$	1.52614e7	+	6.32149e6i	1.50790	+	0.624592i
$635$	2.95335e6	+	7.13003e6i	0.290657	+	0.701709i
$636$	4.79607e6	−	1.98660e6i	0.470156	−	0.194745i
$637$	7.01418e6	+	7.01418e6i	0.684902	+	0.684902i
$638$	−1.49344e6	−	1.49344e6i	−0.145256	−	0.145256i
$639$	−1.31619e6	+	545183.i	−0.127516	+	0.0528190i
$640$	−970302.	−	2.34252e6i	−0.0936390	−	0.226065i
$641$	−9.11210e6	−	3.77436e6i	−0.875938	−	0.362825i	−0.101018	−	0.994885i	$-0.532210\pi$
$641$	−9.11210e6	−	3.77436e6i	−0.875938	−	0.362825i	−0.774920	+	0.632059i	$0.782210\pi$
$642$			8.30027e6i			0.794794i
$643$	−5.48671e6	+	1.32461e7i	−0.523341	+	1.26346i	0.412475	+	0.910969i	$0.364664\pi$
$643$	−5.48671e6	+	1.32461e7i	−0.523341	+	1.26346i	−0.935816	+	0.352488i	$0.885336\pi$
$644$	2.65942e6	−	2.65942e6i	0.252680	−	0.252680i
$645$	167947.			0.0158954
$646$	−1.10331e6	+	8.20917e6i	−0.104020	+	0.773959i
$647$	27423.2			0.00257548			0.00128774	−	0.999999i	$-0.499590\pi$
$647$	27423.2			0.00257548			0.00128774	+	0.999999i	$0.499590\pi$
$648$	−124737.	+	124737.i	−0.0116696	+	0.0116696i
$649$	4.09268e6	−	9.88061e6i	0.381414	−	0.920814i
$650$			7.87408e6i			0.730999i
$651$	1.26068e7	+	5.22190e6i	1.16587	+	0.482921i
$652$	−2.55465e6	−	6.16748e6i	−0.235349	−	0.568184i
$653$	−1.88150e7	+	7.79344e6i	−1.72672	+	0.715231i	−0.727132	+	0.686497i	$0.759147\pi$
$653$	−1.88150e7	+	7.79344e6i	−1.72672	+	0.715231i	−0.999587	+	0.0287334i	$0.990853\pi$
$654$	365191.	+	365191.i	0.0333869	+	0.0333869i
$655$	−4.98922e6	−	4.98922e6i	−0.454390	−	0.454390i
$656$	1.26138e7	−	5.22479e6i	1.14442	−	0.474034i
$657$	−713795.	−	1.72325e6i	−0.0645149	−	0.155753i
$658$	5.11742e6	+	2.11970e6i	0.460772	+	0.190858i
$659$		−	1.78600e6i		−	0.160202i	−0.996787	−	0.0801012i	$-0.974476\pi$
$659$		−	1.78600e6i		−	0.160202i	0.996787	−	0.0801012i	$-0.0255243\pi$
$660$	−3.25345e6	+	7.85453e6i	−0.290727	+	0.701876i
$661$	−3.82643e6	+	3.82643e6i	−0.340635	+	0.340635i	−0.856606	−	0.515971i	$-0.827431\pi$
$661$	−3.82643e6	+	3.82643e6i	−0.340635	+	0.340635i	0.515971	+	0.856606i	$0.327431\pi$
$662$	2.12696e6			0.188632
$663$	−9.06245e6	−	5.26488e6i	−0.800686	−	0.465162i
$664$	604141.			0.0531763
$665$	−4.55440e6	+	4.55440e6i	−0.399372	+	0.399372i
$666$	3.07455e6	−	7.42261e6i	0.268593	−	0.648442i
$667$		−	289036.i		−	0.0251558i
$668$	−3.67398e6	−	1.52181e6i	−0.318563	−	0.131953i
$669$	−3.24756e6	−	7.84030e6i	−0.280538	−	0.677278i
$670$	6.09783e6	−	2.52581e6i	0.524794	−	0.217377i
$671$	1.59510e7	+	1.59510e7i	1.36767	+	1.36767i
$672$	−8.68396e6	−	8.68396e6i	−0.741813	−	0.741813i
$673$	1.48858e7	−	6.16590e6i	1.26688	−	0.524758i	0.354864	−	0.934918i	$-0.384527\pi$
$673$	1.48858e7	−	6.16590e6i	1.26688	−	0.524758i	0.912014	+	0.410160i	$0.134527\pi$
$674$	−7.51062e6	−	1.81322e7i	−0.636834	−	1.53745i
$675$	−661572.	−	274032.i	−0.0558879	−	0.0231495i
$676$			2.05963e7i			1.73349i
$677$	1.87992e6	−	4.53852e6i	0.157640	−	0.380577i	−0.825250	−	0.564767i	$-0.808966\pi$
$677$	1.87992e6	−	4.53852e6i	0.157640	−	0.380577i	0.982891	+	0.184190i	$0.0589661\pi$
$678$	−1.15592e7	+	1.15592e7i	−0.965728	+	0.965728i
$679$	−1.73533e7			−1.44447
$680$	−379963.	−	1.43351e6i	−0.0315115	−	0.118885i
$681$	−1.15648e7			−0.955587
$682$	3.09819e7	−	3.09819e7i	2.55063	−	2.55063i
$683$	5.06707e6	−	1.22330e7i	0.415628	−	1.00341i	−0.567971	−	0.823048i	$-0.692272\pi$
$683$	5.06707e6	−	1.22330e7i	0.415628	−	1.00341i	0.983599	−	0.180367i	$-0.0577284\pi$
$684$			2.42168e6i			0.197914i
$685$	−1.34626e7	−	5.57641e6i	−1.09624	−	0.454076i
$686$	−3.43080e6	−	8.28267e6i	−0.278346	−	0.671986i
$687$	1.08206e7	−	4.48203e6i	0.874699	−	0.362312i
$688$	258934.	+	258934.i	0.0208554	+	0.0208554i
$689$	1.12990e7	+	1.12990e7i	0.906755	+	0.906755i
$690$	−2.04993e6	+	849111.i	−0.163914	+	0.0678956i
$691$	4.62218e6	+	1.11589e7i	0.368258	+	0.889053i	0.994036	+	0.109052i	$0.0347815\pi$
$691$	4.62218e6	+	1.11589e7i	0.368258	+	0.889053i	−0.625778	+	0.780001i	$0.715218\pi$
$692$	9.54850e6	+	3.95512e6i	0.758001	+	0.313974i
$693$			7.69301e6i			0.608504i
$694$	1.62091e6	−	3.91323e6i	0.127750	−	0.308416i
$695$	4.71872e6	−	4.71872e6i	0.370563	−	0.370563i
$696$	107714.			0.00842845
$697$	1.73121e7	−	4.58872e6i	1.34980	−	0.357774i
$698$	3.00121e7			2.33162
$699$	2.42601e6	−	2.42601e6i	0.187802	−	0.187802i
$700$	−2.17727e6	+	5.25640e6i	−0.167945	+	0.405455i
$701$			1.53213e7i			1.17761i	0.808277	+	0.588803i	$0.200400\pi$
$701$			1.53213e7i			1.17761i	−0.808277	+	0.588803i	$0.799600\pi$
$702$	−5.39894e6	−	2.23631e6i	−0.413491	−	0.171273i
$703$	−3.92182e6	−	9.46811e6i	−0.299295	−	0.722562i
$704$	−2.08974e7	+	8.65599e6i	−1.58914	+	0.658241i
$705$	−1.21164e6	−	1.21164e6i	−0.0918125	−	0.0918125i
$706$	7.58013e6	+	7.58013e6i	0.572355	+	0.572355i
$707$	−1.94770e7	+	8.06762e6i	−1.46546	+	0.607012i
$708$	2.24635e6	+	5.42317e6i	0.168420	+	0.406603i
$709$	1.23512e6	+	511602.i	0.0922768	+	0.0382223i	0.428344	−	0.903616i	$-0.359097\pi$
$709$	1.23512e6	+	511602.i	0.0922768	+	0.0382223i	−0.336068	+	0.941838i	$0.609097\pi$
$710$		−	6.67786e6i		−	0.497154i
$711$	−2.86619e6	+	6.91960e6i	−0.212633	+	0.513342i
$712$	−1.32124e6	+	1.32124e6i	−0.0976748	+	0.0976748i
$713$	5.99617e6			0.441723
$714$	−8.76096e6	−	1.14815e7i	−0.643141	−	0.842858i
$715$	−2.61691e7			−1.91436
$716$	−1.02456e7	+	1.02456e7i	−0.746888	+	0.746888i
$717$	−2.92638e6	+	7.06490e6i	−0.212585	+	0.513225i
$718$		−	3.07407e7i		−	2.22537i
$719$	−3.33582e6	−	1.38174e6i	−0.240647	−	0.0996792i	0.259101	−	0.965850i	$-0.416574\pi$
$719$	−3.33582e6	−	1.38174e6i	−0.240647	−	0.0996792i	−0.499748	+	0.866171i	$0.666574\pi$
$720$	1.30336e6	+	3.14660e6i	0.0936989	+	0.226209i
$721$	2.08551e7	−	8.63845e6i	1.49408	−	0.618868i
$722$	−1.01956e7	−	1.01956e7i	−0.727893	−	0.727893i
$723$	1.06682e7	+	1.06682e7i	0.759006	+	0.759006i
$724$	2.50576e7	−	1.03792e7i	1.77662	−	0.735898i
$725$	167326.	+	403961.i	0.0118228	+	0.0285427i
$726$	1.18377e7	+	4.90333e6i	0.833538	+	0.345263i
$727$		−	9.15656e6i		−	0.642535i	−0.946989	−	0.321267i	$-0.895891\pi$
$727$		−	9.15656e6i		−	0.642535i	0.946989	−	0.321267i	$-0.104109\pi$
$728$	−1.65098e6	+	3.98583e6i	−0.115455	+	0.278734i
$729$	375786.	−	375786.i	0.0261891	−	0.0261891i
$730$	8.74315e6			0.607241
$731$	291396.	+	381885.i	0.0201693	+	0.0264325i
$732$	−1.23814e7			−0.854070
$733$	7.18981e6	−	7.18981e6i	0.494262	−	0.494262i	−0.415384	−	0.909646i	$-0.636353\pi$
$733$	7.18981e6	−	7.18981e6i	0.494262	−	0.494262i	0.909646	+	0.415384i	$0.136353\pi$
$734$	−2.51259e6	+	6.06593e6i	−0.172140	+	0.415583i
$735$		−	4.22852e6i		−	0.288715i
$736$	−4.98578e6	−	2.06518e6i	−0.339265	−	0.140528i
$737$	−3.84819e6	−	9.29036e6i	−0.260968	−	0.630034i
$738$	9.22589e6	−	3.82149e6i	0.623544	−	0.258280i
$739$	6.55620e6	+	6.55620e6i	0.441612	+	0.441612i	0.892554	−	0.450941i	$-0.148912\pi$
$739$	6.55620e6	+	6.55620e6i	0.441612	+	0.441612i	−0.450941	+	0.892554i	$0.648912\pi$
$740$	1.39634e7	+	1.39634e7i	0.937372	+	0.937372i
$741$	−6.88677e6	+	2.85259e6i	−0.460755	+	0.190851i
$742$	8.42627e6	+	2.03428e7i	0.561857	+	1.35644i
$743$	1.90422e7	+	7.88753e6i	1.26545	+	0.524166i	0.911578	−	0.411128i	$-0.134865\pi$
$743$	1.90422e7	+	7.88753e6i	1.26545	+	0.524166i	0.353872	+	0.935294i	$0.384865\pi$
$744$			2.23456e6i			0.147999i
$745$	3.12681e6	−	7.54878e6i	0.206400	−	0.498294i
$746$	−9.46602e6	+	9.46602e6i	−0.622760	+	0.622760i
$747$	−1.82006e6			−0.119339
$748$	−2.35049e7	+	6.23016e6i	−1.53605	+	0.407142i
$749$	−1.84607e7			−1.20239
$750$	9.92432e6	−	9.92432e6i	0.644240	−	0.644240i
$751$	−9.35981e6	+	2.25966e7i	−0.605574	+	1.46198i	0.262194	+	0.965015i	$0.415554\pi$
$751$	−9.35981e6	+	2.25966e7i	−0.605574	+	1.46198i	−0.867768	+	0.496970i	$0.834446\pi$
$752$		−	3.73613e6i		−	0.240923i
$753$	1.04052e7	+	4.30999e6i	0.668751	+	0.277006i
$754$	1.36551e6	+	3.29663e6i	0.0874715	+	0.211175i
$755$	1.03113e7	−	4.27109e6i	0.658335	−	0.272691i
$756$	−2.98573e6	−	2.98573e6i	−0.189997	−	0.189997i
$757$	1.97272e7	+	1.97272e7i	1.25120	+	1.25120i	0.955184	+	0.296012i	$0.0956569\pi$
$757$	1.97272e7	+	1.97272e7i	1.25120	+	1.25120i	0.296012	+	0.955184i	$0.404343\pi$
$758$	−9.16283e6	+	3.79537e6i	−0.579238	+	0.239928i
$759$	1.29366e6	+	3.12318e6i	0.0815111	+	0.196785i
$760$	−974463.	−	403636.i	−0.0611972	−	0.0253487i
$761$		−	1.82939e7i		−	1.14510i	−0.819869	−	0.572551i	$-0.805954\pi$
$761$		−	1.82939e7i		−	1.14510i	0.819869	−	0.572551i	$-0.194046\pi$
$762$	−4.70990e6	+	1.13707e7i	−0.293849	+	0.709414i
$763$	−812225.	+	812225.i	−0.0505086	+	0.0505086i
$764$	1.01079e7			0.626511
$765$	1.14469e6	+	4.31863e6i	0.0707187	+	0.266804i
$766$	−1.69529e7			−1.04393
$767$	−1.27763e7	+	1.27763e7i	−0.784184	+	0.784184i
$768$	−2.76216e6	+	6.66845e6i	−0.168984	+	0.407964i
$769$			5.21104e6i			0.317767i	0.987297	+	0.158884i	$0.0507894\pi$
$769$			5.21104e6i			0.317767i	−0.987297	+	0.158884i	$0.949211\pi$
$770$	−3.33155e7	−	1.37997e7i	−2.02497	−	0.838771i
$771$	4.75370e6	+	1.14764e7i	0.288002	+	0.695298i
$772$	1.16590e6	−	482933.i	0.0704076	−	0.0291638i
$773$	1.11858e7	+	1.11858e7i	0.673312	+	0.673312i	0.958478	−	0.285166i	$-0.0920487\pi$
$773$	1.11858e7	+	1.11858e7i	0.673312	+	0.673312i	−0.285166	+	0.958478i	$0.592049\pi$
$774$	189388.	+	189388.i	0.0113632	+	0.0113632i
$775$	−8.38032e6	+	3.47124e6i	−0.501195	+	0.207602i
$776$	−1.08749e6	−	2.62544e6i	−0.0648293	−	0.156512i
$777$	1.65087e7	+	6.83813e6i	0.980981	+	0.406335i
$778$		−	6.60330e6i		−	0.391122i
$779$	4.87460e6	−	1.17683e7i	0.287803	−	0.694818i
$780$	1.01565e7	−	1.01565e7i	0.597732	−	0.597732i
$781$	−1.01741e7			−0.596852
$782$	−5.48748e6	−	3.18798e6i	−0.320890	−	0.186423i
$783$	−324502.			−0.0189153
$784$	6.51938e6	−	6.51938e6i	0.378805	−	0.378805i
$785$	−4.70133e6	+	1.13500e7i	−0.272299	+	0.657389i
$786$		−	1.12524e7i		−	0.649661i
$787$	6.90339e6	+	2.85948e6i	0.397306	+	0.164570i	0.572385	−	0.819985i	$-0.306018\pi$
$787$	6.90339e6	+	2.85948e6i	0.397306	+	0.164570i	−0.175079	+	0.984554i	$0.556018\pi$
$788$	1.46091e6	+	3.52694e6i	0.0838122	+	0.202340i
$789$	−1.32907e7	+	5.50517e6i	−0.760071	+	0.314832i
$790$	−2.48247e7	−	2.48247e7i	−1.41520	−	1.41520i
$791$	−2.57090e7	−	2.57090e7i	−1.46098	−	1.46098i
$792$	−1.16390e6	+	482103.i	−0.0659329	+	0.0273103i
$793$	−1.45846e7	−	3.52103e7i	−0.823591	−	1.98832i
$794$	2.38494e7	+	9.87876e6i	1.34254	+	0.556098i
$795$		−	6.81160e6i		−	0.382236i
$796$	1.04726e7	−	2.52832e7i	0.585832	−	1.41432i
$797$	−3.73890e6	+	3.73890e6i	−0.208496	+	0.208496i	−0.803628	−	0.595132i	$-0.797100\pi$
$797$	−3.73890e6	+	3.73890e6i	−0.208496	+	0.208496i	0.595132	+	0.803628i	$0.297100\pi$
$798$	−1.02717e7			−0.570999
$799$	652824.	−	4.85735e6i	0.0361767	−	0.269173i
$800$	8.16375e6			0.450988
$801$	3.98042e6	−	3.98042e6i	0.219203	−	0.219203i
$802$	−9.15454e6	+	2.21010e7i	−0.502575	+	1.21332i
$803$		−	1.33206e7i		−	0.729014i
$804$	5.09920e6	+	2.11216e6i	0.278203	+	0.115236i
$805$	−1.88852e6	−	4.55928e6i	−0.102714	−	0.247974i
$806$	−6.83899e7	+	2.83280e7i	−3.70812	+	1.53596i
$807$	3.12027e6	+	3.12027e6i	0.168658	+	0.168658i
$808$	−2.44115e6	−	2.44115e6i	−0.131543	−	0.131543i
$809$	62795.9	−	26010.9i	0.00337334	−	0.00139728i	−0.380996	−	0.924577i	$-0.624419\pi$
$809$	62795.9	−	26010.9i	0.00337334	−	0.00139728i	0.384369	+	0.923179i	$0.374419\pi$
$810$	953299.	+	2.30147e6i	0.0510524	+	0.123251i
$811$	1.92977e7	+	7.99339e6i	1.03028	+	0.426755i	0.832813	−	0.553555i	$-0.186729\pi$
$811$	1.92977e7	+	7.99339e6i	1.03028	+	0.426755i	0.197465	+	0.980310i	$0.436729\pi$
$812$			2.57827e6i			0.137227i
$813$	1.62083e6	−	3.91304e6i	0.0860028	−	0.207629i
$814$	4.05712e7	−	4.05712e7i	2.14613	−	2.14613i
$815$	−8.75935e6			−0.461932
$816$	−4.89347e6	+	8.42316e6i	−0.257272	+	0.442843i
$817$	341645.			0.0179069
$818$	−1.18980e7	+	1.18980e7i	−0.621717	+	0.621717i
$819$	4.97381e6	−	1.20078e7i	0.259107	−	0.625540i
$820$			2.45447e7i			1.27474i
$821$	1.12955e7	+	4.67875e6i	0.584854	+	0.242254i	0.655435	−	0.755252i	$-0.272485\pi$
$821$	1.12955e7	+	4.67875e6i	0.584854	+	0.242254i	−0.0705810	+	0.997506i	$0.522485\pi$
$822$	−8.89305e6	−	2.14697e7i	−0.459062	−	1.10827i
$823$	−1.83027e7	+	7.58121e6i	−0.941922	+	0.390157i	−0.800189	−	0.599748i	$-0.795267\pi$
$823$	−1.83027e7	+	7.58121e6i	−0.941922	+	0.390157i	−0.141733	+	0.989905i	$0.545267\pi$
$824$	2.61388e6	+	2.61388e6i	0.134112	+	0.134112i
$825$	−3.61608e6	−	3.61608e6i	−0.184971	−	0.184971i
$826$	−2.30027e7	+	9.52804e6i	−1.17308	+	0.485907i
$827$	−2.83174e6	−	6.83643e6i	−0.143976	−	0.347589i	0.835398	−	0.549646i	$-0.185237\pi$
$827$	−2.83174e6	−	6.83643e6i	−0.143976	−	0.347589i	−0.979374	+	0.202057i	$0.935237\pi$
$828$	−1.71422e6	−	710053.i	−0.0868942	−	0.0359928i
$829$			6.35936e6i			0.321386i	0.987004	+	0.160693i	$0.0513729\pi$
$829$			6.35936e6i			0.321386i	−0.987004	+	0.160693i	$0.948627\pi$
$830$	3.26482e6	−	7.88196e6i	0.164499	−	0.397136i
$831$	−4.42014e6	+	4.42014e6i	−0.222041	+	0.222041i
$832$	3.82147e7			1.91391
$833$	9.61499e6	−	7.33669e6i	0.480105	−	0.366343i
$834$	1.06423e7			0.529810
$835$	−3.68966e6	+	3.68966e6i	−0.183135	+	0.183135i
$836$	−6.61831e6	+	1.59780e7i	−0.327515	+	0.790692i
$837$		−	6.73191e6i		−	0.332143i
$838$	2.82452e7	+	1.16995e7i	1.38942	+	0.575518i
$839$	−1.31242e7	−	3.16846e7i	−0.643677	−	1.55397i	−0.821683	−	0.569944i	$-0.806965\pi$
$839$	−1.31242e7	−	3.16846e7i	−0.643677	−	1.55397i	0.178007	−	0.984029i	$-0.443035\pi$
$840$	1.69908e6	−	703784.i	0.0830839	−	0.0344145i
$841$	−1.43635e7	−	1.43635e7i	−0.700276	−	0.700276i
$842$	−1.44576e7	−	1.44576e7i	−0.702776	−	0.702776i
$843$	1.57144e7	−	6.50911e6i	0.761602	−	0.315466i
$844$	−2.77319e6	−	6.69507e6i	−0.134006	−	0.323519i
$845$	2.49680e7	+	1.03421e7i	1.20293	+	0.498271i
$846$		−	2.73266e6i		−	0.131268i
$847$	−1.09056e7	+	2.63283e7i	−0.522323	+	1.26100i
$848$	1.05019e7	−	1.05019e7i	0.501508	−	0.501508i
$849$	−1.79686e7			−0.855548
$850$	9.51493e6	+	1.27880e6i	0.451709	+	0.0607094i
$851$	7.85205e6			0.371671
$852$	3.94865e6	−	3.94865e6i	0.186359	−	0.186359i
$853$	−9.45870e6	+	2.28353e7i	−0.445101	+	1.07457i	0.529033	+	0.848601i	$0.322555\pi$
$853$	−9.45870e6	+	2.28353e7i	−0.445101	+	1.07457i	−0.974135	+	0.225969i	$0.927445\pi$
$854$		−	5.25166e7i		−	2.46407i
$855$	2.93570e6	+	1.21601e6i	0.137340	+	0.0568880i
$856$	−1.15689e6	−	2.79298e6i	−0.0539644	−	0.130282i
$857$	8.63980e6	−	3.57872e6i	0.401839	−	0.166447i	−0.172605	−	0.984991i	$-0.555218\pi$
$857$	8.63980e6	−	3.57872e6i	0.401839	−	0.166447i	0.574444	+	0.818544i	$0.305218\pi$
$858$	−2.95100e7	−	2.95100e7i	−1.36852	−	1.36852i
$859$	−1.54838e6	−	1.54838e6i	−0.0715971	−	0.0715971i	0.670401	−	0.741999i	$-0.266122\pi$
$859$	−1.54838e6	−	1.54838e6i	−0.0715971	−	0.0715971i	−0.741999	+	0.670401i	$0.766122\pi$
$860$	−608202.	+	251926.i	−0.0280415	+	0.0116152i
$861$	8.49941e6	+	2.05194e7i	0.390734	+	0.943314i
$862$	−4.93073e6	−	2.04237e6i	−0.226018	−	0.0936197i
$863$			1.20127e7i			0.549053i	0.961580	+	0.274526i	$0.0885211\pi$
$863$			1.20127e7i			0.549053i	−0.961580	+	0.274526i	$0.911479\pi$
$864$	−2.31858e6	+	5.59755e6i	−0.105667	+	0.255102i
$865$	9.58924e6	−	9.58924e6i	0.435757	−	0.435757i
$866$	3.14290e7			1.42408
$867$	−7.83380e6	+	1.00959e7i	−0.353936	+	0.456139i
$868$	−5.34871e7			−2.40963
$869$	−3.78217e7	+	3.78217e7i	−1.69899	+	1.69899i
$870$	582091.	−	1.40529e6i	0.0260731	−	0.0629461i
$871$			1.69891e7i			0.758796i
$872$	−173784.	−	71983.8i	−0.00773962	−	0.00320585i
$873$	3.27621e6	+	7.90948e6i	0.145491	+	0.351247i
$874$	−4.17006e6	+	1.72730e6i	−0.184656	+	0.0764872i
$875$	2.20728e7	+	2.20728e7i	0.974624	+	0.974624i
$876$	5.16987e6	+	5.16987e6i	0.227625	+	0.227625i
$877$	−1.47080e6	+	609226.i	−0.0645736	+	0.0267473i	−0.414736	−	0.909942i	$-0.636126\pi$
$877$	−1.47080e6	+	609226.i	−0.0645736	+	0.0267473i	0.350163	+	0.936689i	$0.386126\pi$
$878$	−5.69461e6	−	1.37480e7i	−0.249303	−	0.601871i
$879$	−1.65554e7	−	6.85748e6i	−0.722716	−	0.299359i
$880$			2.43230e7i			1.05879i
$881$	−7.97692e6	+	1.92580e7i	−0.346255	+	0.835933i	0.650801	+	0.759248i	$0.274433\pi$
$881$	−7.97692e6	+	1.92580e7i	−0.346255	+	0.835933i	−0.997055	+	0.0766841i	$0.975567\pi$
$882$	4.76836e6	−	4.76836e6i	0.206394	−	0.206394i
$883$	2.21150e7			0.954520			0.477260	−	0.878762i	$-0.341630\pi$
$883$	2.21150e7			0.954520			0.477260	+	0.878762i	$0.341630\pi$
$884$	4.07162e7	+	5.47224e6i	1.75241	+	0.235523i
$885$	7.70225e6			0.330567
$886$	−2.23259e7	+	2.23259e7i	−0.955485	+	0.955485i
$887$	1.04312e7	−	2.51832e7i	0.445170	−	1.07474i	−0.528939	−	0.848660i	$-0.677410\pi$
$887$	1.04312e7	−	2.51832e7i	0.445170	−	1.07474i	0.974109	−	0.226077i	$-0.0725900\pi$
$888$			2.92618e6i			0.124529i
$889$	−2.52897e7	−	1.04753e7i	−1.07322	−	0.444543i
$890$	1.00976e7	+	2.43777e7i	0.427310	+	1.03162i
$891$	3.50640e6	−	1.45240e6i	0.147968	−	0.0612903i
$892$	2.35214e7	+	2.35214e7i	0.989808	+	0.989808i
$893$	−2.46477e6	−	2.46477e6i	−0.103430	−	0.103430i
$894$	1.20385e7	−	4.98651e6i	0.503766	−	0.208667i
$895$	7.27565e6	+	1.75650e7i	0.303609	+	0.732977i
$896$	8.30873e6	+	3.44159e6i	0.345752	+	0.143215i
$897$		−	5.71130e6i		−	0.237003i
$898$	1.17123e7	−	2.82760e7i	0.484676	−	1.17011i
$899$	−2.90660e6	+	2.90660e6i	−0.119946	+	0.119946i
$900$	2.80687e6			0.115509
$901$	1.54885e7	−	1.18185e7i	0.635621	−	0.485009i
$902$	7.13155e7			2.91855
$903$	−421220.	+	421220.i	−0.0171905	+	0.0171905i
$904$	2.27847e6	−	5.50072e6i	0.0927306	−	0.223871i
$905$		−	3.55880e7i		−	1.44438i
$906$	1.64441e7	+	6.81137e6i	0.665564	+	0.275686i
$907$	−1.81170e7	−	4.37383e7i	−0.731253	−	1.76540i	−0.638378	−	0.769723i	$-0.720394\pi$
$907$	−1.81170e7	−	4.37383e7i	−0.731253	−	1.76540i	−0.0928754	−	0.995678i	$-0.529606\pi$
$908$	4.18807e7	−	1.73476e7i	1.68577	−	0.698271i
$909$	7.35429e6	+	7.35429e6i	0.295210	+	0.295210i
$910$	4.30793e7	+	4.30793e7i	1.72451	+	1.72451i
$911$	−2.52943e6	+	1.04772e6i	−0.100978	+	0.0418264i	−0.432601	−	0.901586i	$-0.642404\pi$
$911$	−2.52943e6	+	1.04772e6i	−0.100978	+	0.0418264i	0.331623	+	0.943412i	$0.392404\pi$
$912$	2.65136e6	+	6.40095e6i	0.105556	+	0.254834i
$913$	−1.20086e7	−	4.97411e6i	−0.476776	−	0.197487i
$914$		−	2.71563e7i		−	1.07524i
$915$	−6.21714e6	+	1.50095e7i	−0.245492	+	0.592671i
$916$	−3.24624e7	+	3.24624e7i	−1.27833	+	1.27833i
$917$	2.50265e7			0.982825
$918$	−3.57915e6	+	6.16081e6i	−0.140176	+	0.241286i
$919$	−4.54836e7			−1.77651			−0.888253	−	0.459355i	$-0.848080\pi$
$919$	−4.54836e7			−1.77651			−0.888253	+	0.459355i	$0.848080\pi$
$920$	571439.	−	571439.i	0.0222587	−	0.0222587i
$921$	2.76496e6	−	6.67521e6i	0.107409	−	0.259308i
$922$			4.95817e7i			1.92085i
$923$	1.58804e7	+	6.57789e6i	0.613562	+	0.254146i
$924$	−1.15398e7	−	2.78594e7i	−0.444649	−	1.07348i
$925$	−1.09741e7	+	4.54563e6i	−0.421711	+	0.174679i
$926$	1.52511e7	+	1.52511e7i	0.584487	+	0.584487i
$927$	−7.87465e6	−	7.87465e6i	−0.300976	−	0.300976i
$928$	3.41791e6	−	1.41574e6i	0.130284	−	0.0539653i
$929$	−5.49848e6	−	1.32745e7i	−0.209027	−	0.504637i	0.784243	−	0.620454i	$-0.213051\pi$
$929$	−5.49848e6	−	1.32745e7i	−0.209027	−	0.504637i	−0.993271	+	0.115817i	$0.963051\pi$
$930$	2.91533e7	+	1.20757e7i	1.10530	+	0.457831i
$931$		−	8.60183e6i		−	0.325250i
$932$	−5.14646e6	+	1.24246e7i	−0.194075	+	0.468538i
$933$	−1.80893e7	+	1.80893e7i	−0.680326	+	0.680326i
$934$	1.47004e7			0.551396
$935$	−4.25002e6	+	3.16223e7i	−0.158987	+	1.18295i
$936$	2.12840e6			0.0794079
$937$	1.08333e7	−	1.08333e7i	0.403097	−	0.403097i	−0.476226	−	0.879323i	$-0.657995\pi$
$937$	1.08333e7	−	1.08333e7i	0.403097	−	0.403097i	0.879323	+	0.476226i	$0.157995\pi$
$938$	−8.95885e6	+	2.16286e7i	−0.332464	+	0.802640i
$939$		−	9.66835e6i		−	0.357840i
$940$	6.20534e6	+	2.57034e6i	0.229058	+	0.0948791i
$941$	−7.67270e6	−	1.85235e7i	−0.282471	−	0.681946i	0.717421	−	0.696640i	$-0.245323\pi$
$941$	−7.67270e6	−	1.85235e7i	−0.282471	−	0.681946i	−0.999892	+	0.0146942i	$0.995323\pi$
$942$	−1.81006e7	+	7.49750e6i	−0.664607	+	0.275289i
$943$	6.90111e6	+	6.90111e6i	0.252720	+	0.252720i
$944$	1.18751e7	+	1.18751e7i	0.433716	+	0.433716i
$945$	−5.11871e6	+	2.12024e6i	−0.186458	+	0.0772335i
$946$	731979.	+	1.76715e6i	0.0265932	+	0.0642017i
$947$	2.26418e7	+	9.37855e6i	0.820420	+	0.339829i	0.753103	−	0.657902i	$-0.228556\pi$
$947$	2.26418e7	+	9.37855e6i	0.820420	+	0.339829i	0.0673170	+	0.997732i	$0.478556\pi$
$948$		−	2.93580e7i		−	1.06098i
$949$	−8.61227e6	+	2.07919e7i	−0.310422	+	0.749425i
$950$	4.82819e6	−	4.82819e6i	0.173570	−	0.173570i
$951$	1.81253e7			0.649882
$952$	4.54829e6	+	2.64235e6i	0.162651	+	0.0944927i
$953$	−2.86712e6			−0.102262			−0.0511309	−	0.998692i	$-0.516283\pi$
$953$	−2.86712e6			−0.102262			−0.0511309	+	0.998692i	$0.516283\pi$
$954$	7.68122e6	−	7.68122e6i	0.273250	−	0.273250i
$955$	5.07553e6	−	1.22534e7i	0.180083	−	0.434759i
$956$		−	2.99745e7i		−	1.06073i
$957$	−2.14103e6	−	886845.i	−0.0755690	−	0.0313017i
$958$	−2.76706e6	−	6.68028e6i	−0.0974103	−	0.235169i
$959$	4.77510e7	−	1.97791e7i	1.67663	−	0.694481i
$960$	−1.15189e7	−	1.15189e7i	−0.403398	−	0.403398i
$961$	−4.00547e7	−	4.00547e7i	−1.39909	−	1.39909i
$962$	−8.95573e7	+	3.70958e7i	−3.12006	+	1.29237i
$963$	3.48528e6	+	8.41422e6i	0.121108	+	0.292380i
$964$	−5.46364e7	−	2.26312e7i	−1.89361	−	0.784357i
$965$		−	1.65587e6i		−	0.0572412i
$966$	3.01173e6	−	7.27097e6i	0.103842	−	0.250697i
$967$	−8.41422e6	+	8.41422e6i	−0.289366	+	0.289366i	−0.836830	−	0.547463i	$-0.815594\pi$
$967$	−8.41422e6	+	8.41422e6i	−0.289366	+	0.289366i	0.547463	+	0.836830i	$0.315594\pi$
$968$	−4.66672e6			−0.160075
$969$	2.32858e6	+	8.78515e6i	0.0796675	+	0.300566i
$970$	−4.01298e7			−1.36942
$971$	−4.17791e6	+	4.17791e6i	−0.142204	+	0.142204i	−0.774625	−	0.632421i	$-0.782061\pi$
$971$	−4.17791e6	+	4.17791e6i	−0.142204	+	0.142204i	0.632421	+	0.774625i	$0.282061\pi$
$972$	−797178.	+	1.92456e6i	−0.0270639	+	0.0653380i
$973$			2.36696e7i			0.801511i
$974$	−3.71932e7	−	1.54059e7i	−1.25622	−	0.520344i
$975$	3.30633e6	+	7.98218e6i	0.111387	+	0.268912i
$976$	−3.27265e7	+	1.35557e7i	−1.09970	+	0.455511i
$977$	−2.26618e7	−	2.26618e7i	−0.759552	−	0.759552i	0.216689	−	0.976241i	$-0.430474\pi$
$977$	−2.26618e7	−	2.26618e7i	−0.759552	−	0.759552i	−0.976241	+	0.216689i	$0.930474\pi$
$978$	−9.87763e6	−	9.87763e6i	−0.330222	−	0.330222i
$979$	3.71407e7	−	1.53842e7i	1.23849	−	0.513000i
$980$	6.34291e6	+	1.53131e7i	0.210971	+	0.509330i
$981$	523548.	+	216861.i	0.0173694	+	0.00719463i
$982$		−	3.74513e7i		−	1.23933i
$983$	5.35600e6	−	1.29305e7i	0.176790	−	0.426808i	−0.810500	−	0.585738i	$-0.800805\pi$
$983$	5.35600e6	−	1.29305e7i	0.176790	−	0.426808i	0.987290	+	0.158931i	$0.0508046\pi$
$984$	−2.57180e6	+	2.57180e6i	−0.0846740	+	0.0846740i
$985$	5.00913e6			0.164502
$986$	4.20537e6	−	1.11467e6i	0.137757	−	0.0365135i
$987$	6.07773e6			0.198586
$988$	2.06607e7	−	2.06607e7i	0.673369	−	0.673369i
$989$	−100173.	+	241838.i	−0.00325655	+	0.00786201i
$990$			1.77902e7i			0.576889i
$991$	6.18296e6	+	2.56107e6i	0.199992	+	0.0828394i	0.480431	−	0.877032i	$-0.340480\pi$
$991$	6.18296e6	+	2.56107e6i	0.199992	+	0.0828394i	−0.280439	+	0.959872i	$0.590480\pi$
$992$	2.93701e7	+	7.09057e7i	0.947603	+	2.28772i
$993$	2.15616e6	−	893111.i	0.0693917	−	0.0287430i
$994$	1.67484e7	+	1.67484e7i	0.537661	+	0.537661i
$995$	−2.53910e7	−	2.53910e7i	−0.813060	−	0.813060i
$996$	6.59115e6	−	2.73014e6i	0.210529	−	0.0872041i
$997$	−9.46382e6	−	2.28477e7i	−0.301529	−	0.727954i	−0.999925	−	0.0122433i	$-0.996103\pi$
$997$	−9.46382e6	−	2.28477e7i	−0.301529	−	0.727954i	0.698396	−	0.715711i	$-0.253897\pi$
$998$	−5.36275e7	−	2.22132e7i	−1.70436	−	0.705969i
$999$		−	8.81551e6i		−	0.279469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.h.a.25.2	✓	56
17.7	odd	16		867.6.a.u.1.25		28
17.10	odd	16		867.6.a.t.1.25		28
17.15	even	8	inner	51.6.h.a.49.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.h.a.25.2	✓	56	1.1	even	1	trivial
51.6.h.a.49.2	yes	56	17.15	even	8	inner
867.6.a.t.1.25		28	17.10	odd	16
867.6.a.u.1.25		28	17.7	odd	16

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	51.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.79991 + 5.79991i) q^{2} +(-3.44415 + 8.31492i) q^{3} -35.2780i q^{4} +(-42.7660 - 17.7142i) q^{5} +(-28.2500 - 68.2015i) q^{6} +(151.688 - 62.8311i) q^{7} +(19.0118 + 19.0118i) q^{8} +(-57.2756 - 57.2756i) q^{9} +(350.780 - 145.298i) q^{10} +(-221.368 - 534.431i) q^{11} +(293.333 + 121.503i) q^{12} +977.303i q^{13} +(-515.361 + 1244.19i) q^{14} +(294.585 - 294.585i) q^{15} +908.361 q^{16} +(1180.96 + 158.720i) q^{17} +664.387 q^{18} +(599.257 - 599.257i) q^{19} +(-624.922 + 1508.70i) q^{20} +1477.67i q^{21} +(4383.57 + 1815.73i) q^{22} +(248.486 + 599.899i) q^{23} +(-223.561 + 92.6022i) q^{24} +(-694.575 - 694.575i) q^{25} +(-5668.27 - 5668.27i) q^{26} +(673.508 - 278.976i) q^{27} +(-2216.55 - 5351.23i) q^{28} +(-411.249 - 170.345i) q^{29} +3417.13i q^{30} +(3533.87 - 8531.52i) q^{31} +(-5876.79 + 5876.79i) q^{32} +5206.17 q^{33} +(-7770.02 + 5928.90i) q^{34} -7600.08 q^{35} +(-2020.57 + 2020.57i) q^{36} +(4627.64 - 11172.1i) q^{37} +6951.28i q^{38} +(-8126.19 - 3365.98i) q^{39} +(-476.279 - 1149.84i) q^{40} +(13886.3 - 5751.90i) q^{41} +(-8570.36 - 8570.36i) q^{42} +(285.057 + 285.057i) q^{43} +(-18853.6 + 7809.43i) q^{44} +(1434.85 + 3464.04i) q^{45} +(-4920.56 - 2038.16i) q^{46} -4113.05i q^{47} +(-3128.53 + 7552.94i) q^{48} +(7177.08 - 7177.08i) q^{49} +8056.95 q^{50} +(-5387.15 + 9272.92i) q^{51} +34477.3 q^{52} +(11561.4 - 11561.4i) q^{53} +(-2288.25 + 5524.33i) q^{54} +26776.8i q^{55} +(4078.40 + 1689.33i) q^{56} +(2918.84 + 7046.70i) q^{57} +(3373.19 - 1397.22i) q^{58} +(13073.1 + 13073.1i) q^{59} +(-10392.4 - 10392.4i) q^{60} +(-36028.1 + 14923.3i) q^{61} +(28985.9 + 69978.2i) q^{62} +(-12286.7 - 5089.32i) q^{63} -39102.2i q^{64} +(17312.2 - 41795.3i) q^{65} +(-30195.3 + 30195.3i) q^{66} +17383.7 q^{67} +(5599.32 - 41661.8i) q^{68} -5843.93 q^{69} +(44079.8 - 44079.8i) q^{70} +(6730.66 - 16249.2i) q^{71} -2177.83i q^{72} +(21274.7 + 8812.28i) q^{73} +(37957.4 + 91637.2i) q^{74} +(8167.56 - 3383.11i) q^{75} +(-21140.6 - 21140.6i) q^{76} +(-67157.8 - 67157.8i) q^{77} +(66653.6 - 27608.8i) q^{78} +(-35385.1 - 85427.1i) q^{79} +(-38846.9 - 16090.9i) q^{80} +6561.00i q^{81} +(-47178.8 + 113900. i) q^{82} +(15888.6 - 15888.6i) q^{83} +52129.2 q^{84} +(-47693.3 - 27707.6i) q^{85} -3306.61 q^{86} +(2832.81 - 2832.81i) q^{87} +(5951.89 - 14369.1i) q^{88} +69495.8i q^{89} +(-28413.2 - 11769.1i) q^{90} +(61405.0 + 148245. i) q^{91} +(21163.2 - 8766.09i) q^{92} +(58767.7 + 58767.7i) q^{93} +(23855.3 + 23855.3i) q^{94} +(-36243.2 + 15012.4i) q^{95} +(-28624.5 - 69105.6i) q^{96} +(-97647.8 - 40447.1i) q^{97} +83252.9i q^{98} +(-17930.8 + 43288.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) \) 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

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