LMFDB - Embedded newform 354.5.b.a.119.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	354.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.6
Character	$\chi$	$=$	354.119
Dual form			354.5.b.a.119.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} +(-8.08417 + 3.95552i) q^{3} -8.00000 q^{4} +31.0925i q^{5} +(11.1879 + 22.8655i) q^{6} +88.3750 q^{7} +22.6274i q^{8} +(49.7077 - 63.9542i) q^{9} +O(q^{10})$	\(q-2.82843i q^{2} +(-8.08417 + 3.95552i) q^{3} -8.00000 q^{4} +31.0925i q^{5} +(11.1879 + 22.8655i) q^{6} +88.3750 q^{7} +22.6274i q^{8} +(49.7077 - 63.9542i) q^{9} +87.9429 q^{10} +16.8495i q^{11} +(64.6734 - 31.6442i) q^{12} +16.0766 q^{13} -249.962i q^{14} +(-122.987 - 251.357i) q^{15} +64.0000 q^{16} -41.7741i q^{17} +(-180.890 - 140.595i) q^{18} +311.693 q^{19} -248.740i q^{20} +(-714.439 + 349.569i) q^{21} +47.6575 q^{22} -140.640i q^{23} +(-89.5032 - 182.924i) q^{24} -341.743 q^{25} -45.4714i q^{26} +(-148.873 + 713.637i) q^{27} -707.000 q^{28} -752.455i q^{29} +(-710.945 + 347.860i) q^{30} -667.932 q^{31} -181.019i q^{32} +(-66.6484 - 136.214i) q^{33} -118.155 q^{34} +2747.80i q^{35} +(-397.662 + 511.634i) q^{36} +2484.23 q^{37} -881.600i q^{38} +(-129.966 + 63.5911i) q^{39} -703.543 q^{40} -914.629i q^{41} +(988.731 + 2020.74i) q^{42} -895.563 q^{43} -134.796i q^{44} +(1988.50 + 1545.54i) q^{45} -397.790 q^{46} +1248.42i q^{47} +(-517.387 + 253.153i) q^{48} +5409.14 q^{49} +966.596i q^{50} +(165.238 + 337.709i) q^{51} -128.612 q^{52} +3271.86i q^{53} +(2018.47 + 421.078i) q^{54} -523.892 q^{55} +1999.70i q^{56} +(-2519.78 + 1232.91i) q^{57} -2128.27 q^{58} -453.188i q^{59} +(983.896 + 2010.86i) q^{60} +6153.95 q^{61} +1889.20i q^{62} +(4392.92 - 5651.95i) q^{63} -512.000 q^{64} +499.860i q^{65} +(-385.271 + 188.510i) q^{66} +7173.67 q^{67} +334.193i q^{68} +(556.305 + 1136.96i) q^{69} +7771.95 q^{70} +1411.86i q^{71} +(1447.12 + 1124.76i) q^{72} -6306.01 q^{73} -7026.45i q^{74} +(2762.71 - 1351.77i) q^{75} -2493.54 q^{76} +1489.07i q^{77} +(179.863 + 367.598i) q^{78} +2757.77 q^{79} +1989.92i q^{80} +(-1619.29 - 6358.04i) q^{81} -2586.96 q^{82} -6133.03i q^{83} +(5715.51 - 2796.55i) q^{84} +1298.86 q^{85} +2533.03i q^{86} +(2976.35 + 6082.98i) q^{87} -381.260 q^{88} +9565.23i q^{89} +(4371.44 - 5624.32i) q^{90} +1420.77 q^{91} +1125.12i q^{92} +(5399.67 - 2642.02i) q^{93} +3531.06 q^{94} +9691.30i q^{95} +(716.026 + 1463.39i) q^{96} -10050.0 q^{97} -15299.4i q^{98} +(1077.59 + 837.549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−8.08417	+	3.95552i	−0.898241	+	0.439502i
$3$	−8.08417	+	3.95552i	−0.898241	+	0.439502i
$4$	−8.00000			−0.500000
$5$			31.0925i			1.24370i	0.783136	+	0.621850i	$0.213619\pi$
$5$			31.0925i			1.24370i	−0.783136	+	0.621850i	$0.786381\pi$
$6$	11.1879	+	22.8655i	0.310775	+	0.635153i
$7$	88.3750			1.80357			0.901786	−	0.432184i	$-0.142257\pi$
$7$	88.3750			1.80357			0.901786	+	0.432184i	$0.142257\pi$
$8$			22.6274i			0.353553i
$9$	49.7077	−	63.9542i	0.613675	−	0.789558i
$10$	87.9429			0.879429
$11$			16.8495i			0.139252i	0.997573	+	0.0696259i	$0.0221806\pi$
$11$			16.8495i			0.139252i	−0.997573	+	0.0696259i	$0.977819\pi$
$12$	64.6734	−	31.6442i	0.449121	−	0.219751i
$13$	16.0766			0.0951275			0.0475638	−	0.998868i	$-0.484854\pi$
$13$	16.0766			0.0951275			0.0475638	+	0.998868i	$0.484854\pi$
$14$		−	249.962i		−	1.27532i
$15$	−122.987	−	251.357i	−0.546609	−	1.11714i
$16$	64.0000			0.250000
$17$		−	41.7741i		−	0.144547i	−0.997385	−	0.0722735i	$-0.976975\pi$
$17$		−	41.7741i		−	0.144547i	0.997385	−	0.0722735i	$-0.0230255\pi$
$18$	−180.890	−	140.595i	−0.558302	−	0.433934i
$19$	311.693			0.863415			0.431707	−	0.902014i	$-0.357911\pi$
$19$	311.693			0.863415			0.431707	+	0.902014i	$0.357911\pi$
$20$		−	248.740i		−	0.621850i
$21$	−714.439	+	349.569i	−1.62004	+	0.792674i
$22$	47.6575			0.0984659
$23$		−	140.640i		−	0.265860i	−0.991125	−	0.132930i	$-0.957561\pi$
$23$		−	140.640i		−	0.265860i	0.991125	−	0.132930i	$-0.0424386\pi$
$24$	−89.5032	−	182.924i	−0.155388	−	0.317576i
$25$	−341.743			−0.546789
$26$		−	45.4714i		−	0.0672653i
$27$	−148.873	+	713.637i	−0.204216	+	0.978926i
$28$	−707.000			−0.901786
$29$		−	752.455i		−	0.894715i	−0.894355	−	0.447358i	$-0.852365\pi$
$29$		−	752.455i		−	0.894715i	0.894355	−	0.447358i	$-0.147635\pi$
$30$	−710.945	+	347.860i	−0.789939	+	0.386511i
$31$	−667.932			−0.695038			−0.347519	−	0.937673i	$-0.612976\pi$
$31$	−667.932			−0.695038			−0.347519	+	0.937673i	$0.612976\pi$
$32$		−	181.019i		−	0.176777i
$33$	−66.6484	−	136.214i	−0.0612015	−	0.125082i
$34$	−118.155			−0.102210
$35$			2747.80i			2.24310i
$36$	−397.662	+	511.634i	−0.306838	+	0.394779i
$37$	2484.23			1.81463			0.907314	−	0.420454i	$-0.138129\pi$
$37$	2484.23			1.81463			0.907314	+	0.420454i	$0.138129\pi$
$38$		−	881.600i		−	0.610526i
$39$	−129.966	+	63.5911i	−0.0854475	+	0.0418088i
$40$	−703.543			−0.439714
$41$		−	914.629i		−	0.544098i	−0.962283	−	0.272049i	$-0.912299\pi$
$41$		−	914.629i		−	0.544098i	0.962283	−	0.272049i	$-0.0877013\pi$
$42$	988.731	+	2020.74i	0.560505	+	1.14554i
$43$	−895.563			−0.484350			−0.242175	−	0.970233i	$-0.577861\pi$
$43$	−895.563			−0.484350			−0.242175	+	0.970233i	$0.577861\pi$
$44$		−	134.796i		−	0.0696259i
$45$	1988.50	+	1545.54i	0.981974	+	0.763228i
$46$	−397.790			−0.187992
$47$			1248.42i			0.565150i	0.959245	+	0.282575i	$0.0911887\pi$
$47$			1248.42i			0.565150i	−0.959245	+	0.282575i	$0.908811\pi$
$48$	−517.387	+	253.153i	−0.224560	+	0.109876i
$49$	5409.14			2.25287
$50$			966.596i			0.386639i
$51$	165.238	+	337.709i	0.0635288	+	0.129838i
$52$	−128.612			−0.0475638
$53$			3271.86i			1.16478i	0.812910	+	0.582389i	$0.197882\pi$
$53$			3271.86i			1.16478i	−0.812910	+	0.582389i	$0.802118\pi$
$54$	2018.47	+	421.078i	0.692205	+	0.144403i
$55$	−523.892			−0.173187
$56$			1999.70i			0.637659i
$57$	−2519.78	+	1232.91i	−0.775555	+	0.379473i
$58$	−2128.27			−0.632659
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	983.896	+	2010.86i	0.273304	+	0.558571i
$61$	6153.95			1.65384			0.826921	−	0.562318i	$-0.190090\pi$
$61$	6153.95			1.65384			0.826921	+	0.562318i	$0.190090\pi$
$62$			1889.20i			0.491466i
$63$	4392.92	−	5651.95i	1.10681	−	1.42402i
$64$	−512.000			−0.125000
$65$			499.860i			0.118310i
$66$	−385.271	+	188.510i	−0.0884462	+	0.0432760i
$67$	7173.67			1.59806			0.799028	−	0.601294i	$-0.205348\pi$
$67$	7173.67			1.59806			0.799028	+	0.601294i	$0.205348\pi$
$68$			334.193i			0.0722735i
$69$	556.305	+	1136.96i	0.116846	+	0.238807i
$70$	7771.95			1.58611
$71$			1411.86i			0.280076i	0.990146	+	0.140038i	$0.0447225\pi$
$71$			1411.86i			0.280076i	−0.990146	+	0.140038i	$0.955277\pi$
$72$	1447.12	+	1124.76i	0.279151	+	0.216967i
$73$	−6306.01			−1.18334			−0.591669	−	0.806181i	$-0.701531\pi$
$73$	−6306.01			−1.18334			−0.591669	+	0.806181i	$0.701531\pi$
$74$		−	7026.45i		−	1.28314i
$75$	2762.71	−	1351.77i	0.491149	−	0.240315i
$76$	−2493.54			−0.431707
$77$			1489.07i			0.251151i
$78$	179.863	+	367.598i	0.0295633	+	0.0604205i
$79$	2757.77			0.441880			0.220940	−	0.975287i	$-0.429088\pi$
$79$	2757.77			0.441880			0.220940	+	0.975287i	$0.429088\pi$
$80$			1989.92i			0.310925i
$81$	−1619.29	−	6358.04i	−0.246805	−	0.969065i
$82$	−2586.96			−0.384735
$83$		−	6133.03i		−	0.890264i	−0.895465	−	0.445132i	$-0.853157\pi$
$83$		−	6133.03i		−	0.890264i	0.895465	−	0.445132i	$-0.146843\pi$
$84$	5715.51	−	2796.55i	0.810021	−	0.396337i
$85$	1298.86			0.179773
$86$			2533.03i			0.342487i
$87$	2976.35	+	6082.98i	0.393229	+	0.803670i
$88$	−381.260			−0.0492330
$89$			9565.23i			1.20758i	0.797144	+	0.603789i	$0.206343\pi$
$89$			9565.23i			1.20758i	−0.797144	+	0.603789i	$0.793657\pi$
$90$	4371.44	−	5624.32i	0.539684	−	0.694360i
$91$	1420.77			0.171569
$92$			1125.12i			0.132930i
$93$	5399.67	−	2642.02i	0.624312	−	0.305471i
$94$	3531.06			0.399622
$95$			9691.30i			1.07383i
$96$	716.026	+	1463.39i	0.0776938	+	0.158788i
$97$	−10050.0			−1.06812			−0.534061	−	0.845446i	$-0.679335\pi$
$97$	−10050.0			−1.06812			−0.534061	+	0.845446i	$0.679335\pi$
$98$		−	15299.4i		−	1.59302i
$99$	1077.59	+	837.549i	0.109947	+	0.0854554i
$100$	2733.95			0.273395
$101$			13958.5i			1.36835i	0.729320	+	0.684173i	$0.239837\pi$
$101$			13958.5i			1.36835i	−0.729320	+	0.684173i	$0.760163\pi$
$102$	955.185	−	467.365i	0.0918094	−	0.0449216i
$103$	−12789.4			−1.20553			−0.602763	−	0.797920i	$-0.705934\pi$
$103$	−12789.4			−1.20553			−0.602763	+	0.797920i	$0.705934\pi$
$104$			363.771i			0.0336327i
$105$	−10869.0	−	22213.7i	−0.985848	−	2.01485i
$106$	9254.22			0.823623
$107$			13346.3i			1.16571i	0.812575	+	0.582857i	$0.198065\pi$
$107$			13346.3i			1.16571i	−0.812575	+	0.582857i	$0.801935\pi$
$108$	1190.99	−	5709.10i	0.102108	−	0.489463i
$109$	−6019.43			−0.506643			−0.253322	−	0.967382i	$-0.581523\pi$
$109$	−6019.43			−0.506643			−0.253322	+	0.967382i	$0.581523\pi$
$110$			1481.79i			0.122462i
$111$	−20082.9	+	9826.40i	−1.62997	+	0.797533i
$112$	5656.00			0.450893
$113$			2254.69i			0.176575i	0.996095	+	0.0882876i	$0.0281395\pi$
$113$			2254.69i			0.176575i	−0.996095	+	0.0882876i	$0.971861\pi$
$114$	3487.19	+	7127.01i	0.268328	+	0.548400i
$115$	4372.85			0.330650
$116$			6019.64i			0.447358i
$117$	799.129	−	1028.16i	0.0583774	−	0.0751087i
$118$	−1281.81			−0.0920575
$119$		−	3691.79i		−	0.260701i
$120$	5687.56	−	2782.88i	0.394970	−	0.193255i
$121$	14357.1			0.980609
$122$		−	17406.0i		−	1.16944i
$123$	3617.83	+	7394.02i	0.239132	+	0.488731i
$124$	5343.45			0.347519
$125$			8807.15i			0.563658i
$126$	−15986.1	−	12425.0i	−1.00694	−	0.782631i
$127$	21776.7			1.35016			0.675079	−	0.737745i	$-0.264110\pi$
$127$	21776.7			1.35016			0.675079	+	0.737745i	$0.264110\pi$
$128$			1448.15i			0.0883883i
$129$	7239.88	−	3542.42i	0.435063	−	0.212873i
$130$	1413.82			0.0836579
$131$		−	14107.2i		−	0.822052i	−0.911624	−	0.411026i	$-0.865171\pi$
$131$		−	14107.2i		−	0.822052i	0.911624	−	0.411026i	$-0.134829\pi$
$132$	533.187	+	1089.71i	0.0306007	+	0.0625409i
$133$	27545.8			1.55723
$134$		−	20290.2i		−	1.13000i
$135$	−22188.8	−	4628.85i	−1.21749	−	0.253983i
$136$	945.240			0.0511051
$137$			22450.0i			1.19612i	0.801452	+	0.598060i	$0.204061\pi$
$137$			22450.0i			1.19612i	−0.801452	+	0.598060i	$0.795939\pi$
$138$	3215.81	−	1573.47i	0.168862	−	0.0826228i
$139$	−1130.00			−0.0584854			−0.0292427	−	0.999572i	$-0.509310\pi$
$139$	−1130.00			−0.0584854			−0.0292427	+	0.999572i	$0.509310\pi$
$140$		−	21982.4i		−	1.12155i
$141$	−4938.14	−	10092.4i	−0.248385	−	0.507642i
$142$	3993.36			0.198044
$143$			270.881i			0.0132467i
$144$	3181.29	−	4093.07i	0.153419	−	0.197390i
$145$	23395.7			1.11276
$146$			17836.1i			0.836747i
$147$	−43728.4	+	21396.0i	−2.02362	+	0.990141i
$148$	−19873.8			−0.907314
$149$			28215.3i			1.27090i	0.772142	+	0.635450i	$0.219186\pi$
$149$			28215.3i			1.27090i	−0.772142	+	0.635450i	$0.780814\pi$
$150$	−3823.39	−	7814.13i	−0.169929	−	0.347295i
$151$	10609.9			0.465328			0.232664	−	0.972557i	$-0.425256\pi$
$151$	10609.9			0.465328			0.232664	+	0.972557i	$0.425256\pi$
$152$			7052.80i			0.305263i
$153$	−2671.63	−	2076.49i	−0.114128	−	0.0887050i
$154$	4211.73			0.177590
$155$		−	20767.7i		−	0.864419i
$156$	1039.73	−	508.729i	0.0427237	−	0.0209044i
$157$	−14678.5			−0.595499			−0.297750	−	0.954644i	$-0.596236\pi$
$157$	−14678.5			−0.595499			−0.297750	+	0.954644i	$0.596236\pi$
$158$		−	7800.15i		−	0.312456i
$159$	−12941.9	−	26450.3i	−0.511923	−	1.04625i
$160$	5628.34			0.219857
$161$		−	12429.1i		−	0.479498i
$162$	−17983.2	+	4580.04i	−0.685233	+	0.174517i
$163$	15749.8			0.592789			0.296394	−	0.955066i	$-0.404216\pi$
$163$	15749.8			0.592789			0.296394	+	0.955066i	$0.404216\pi$
$164$			7317.03i			0.272049i
$165$	4235.23	−	2072.27i	0.155564	−	0.0761163i
$166$	−17346.8			−0.629512
$167$			48963.7i			1.75566i	0.478970	+	0.877831i	$0.341010\pi$
$167$			48963.7i			1.75566i	−0.478970	+	0.877831i	$0.658990\pi$
$168$	−7909.85	−	16165.9i	−0.280252	−	0.572771i
$169$	−28302.5			−0.990951
$170$		−	3673.73i		−	0.127119i
$171$	15493.5	−	19934.1i	0.529856	−	0.681716i
$172$	7164.50			0.242175
$173$		−	22865.5i		−	0.763993i	−0.924164	−	0.381996i	$-0.875237\pi$
$173$		−	22865.5i		−	0.763993i	0.924164	−	0.381996i	$-0.124763\pi$
$174$	17205.3	−	8418.40i	0.568281	−	0.278055i
$175$	−30201.6			−0.986174
$176$			1078.37i			0.0348130i
$177$	1792.59	+	3663.65i	0.0572183	+	0.116941i
$178$	27054.5			0.853887
$179$			7524.35i			0.234835i	0.993083	+	0.117417i	$0.0374616\pi$
$179$			7524.35i			0.234835i	−0.993083	+	0.117417i	$0.962538\pi$
$180$	−15908.0	−	12364.3i	−0.490987	−	0.381614i
$181$	−8021.29			−0.244843			−0.122421	−	0.992478i	$-0.539066\pi$
$181$	−8021.29			−0.244843			−0.122421	+	0.992478i	$0.539066\pi$
$182$		−	4018.53i		−	0.121318i
$183$	−49749.6	+	24342.1i	−1.48555	+	0.726868i
$184$	3182.32			0.0939958
$185$			77240.8i			2.25685i
$186$	−7472.75	−	15272.6i	−0.216000	−	0.441455i
$187$	703.871			0.0201284
$188$		−	9987.34i		−	0.282575i
$189$	−13156.7	+	63067.7i	−0.368318	+	1.76556i
$190$	27411.1			0.759311
$191$		−	53331.2i		−	1.46189i	−0.682437	−	0.730944i	$-0.739080\pi$
$191$		−	53331.2i		−	1.46189i	0.682437	−	0.730944i	$-0.260920\pi$
$192$	4139.10	−	2025.23i	0.112280	−	0.0549378i
$193$	−3392.39			−0.0910734			−0.0455367	−	0.998963i	$-0.514500\pi$
$193$	−3392.39			−0.0910734			−0.0455367	+	0.998963i	$0.514500\pi$
$194$			28425.6i			0.755277i
$195$	−1977.21	−	4040.96i	−0.0519976	−	0.106271i
$196$	−43273.1			−1.12643
$197$		−	27904.3i		−	0.719017i	−0.933142	−	0.359509i	$-0.882944\pi$
$197$		−	27904.3i		−	0.719017i	0.933142	−	0.359509i	$-0.117056\pi$
$198$	2368.95	−	3047.90i	0.0604261	−	0.0777446i
$199$	14557.3			0.367600			0.183800	−	0.982964i	$-0.441160\pi$
$199$	14557.3			0.367600			0.183800	+	0.982964i	$0.441160\pi$
$200$		−	7732.77i		−	0.193319i
$201$	−57993.2	+	28375.6i	−1.43544	+	0.702349i
$202$	39480.6			0.967567
$203$		−	66498.2i		−	1.61368i
$204$	−1321.91	−	2701.67i	−0.0317644	−	0.0649191i
$205$	28438.1			0.676695
$206$			36174.0i			0.852436i
$207$	−8994.53	−	6990.90i	−0.209912	−	0.163152i
$208$	1028.90			0.0237819
$209$			5251.86i			0.120232i
$210$	−62829.8	+	30742.1i	−1.42471	+	0.697100i
$211$	32906.9			0.739132			0.369566	−	0.929205i	$-0.379506\pi$
$211$	32906.9			0.739132			0.369566	+	0.929205i	$0.379506\pi$
$212$		−	26174.9i		−	0.582389i
$213$	−5584.66	−	11413.8i	−0.123094	−	0.251576i
$214$	37748.9			0.824284
$215$		−	27845.3i		−	0.602386i
$216$	−16147.8	−	3368.62i	−0.346103	−	0.0722013i
$217$	−59028.4			−1.25355
$218$			17025.5i			0.358251i
$219$	50978.9	−	24943.6i	1.06292	−	0.520080i
$220$	4191.14			0.0865937
$221$		−	671.584i		−	0.0137504i
$222$	27793.3	+	56803.0i	0.563941	+	1.15257i
$223$	−35496.2			−0.713793			−0.356897	−	0.934144i	$-0.616165\pi$
$223$	−35496.2			−0.713793			−0.356897	+	0.934144i	$0.616165\pi$
$224$		−	15997.6i		−	0.318829i
$225$	−16987.3	+	21855.9i	−0.335551	+	0.431722i
$226$	6377.22			0.124858
$227$			34685.1i			0.673117i	0.941663	+	0.336559i	$0.109263\pi$
$227$			34685.1i			0.673117i	−0.941663	+	0.336559i	$0.890737\pi$
$228$	20158.2	−	9863.25i	0.387777	−	0.189736i
$229$	−67638.3			−1.28980			−0.644899	−	0.764268i	$-0.723101\pi$
$229$	−67638.3			−1.28980			−0.644899	+	0.764268i	$0.723101\pi$
$230$		−	12368.3i		−	0.233805i
$231$	−5890.05	−	12037.9i	−0.110381	−	0.225594i
$232$	17026.1			0.316330
$233$			85668.4i			1.57801i	0.614388	+	0.789004i	$0.289403\pi$
$233$			85668.4i			1.57801i	−0.614388	+	0.789004i	$0.710597\pi$
$234$	−2908.09	−	2260.28i	−0.0531099	−	0.0412791i
$235$	−38816.4			−0.702878
$236$			3625.50i			0.0650945i
$237$	−22294.3	+	10908.4i	−0.396915	+	0.194207i
$238$	−10441.9			−0.184343
$239$			9637.06i			0.168713i	0.996436	+	0.0843566i	$0.0268835\pi$
$239$			9637.06i			0.168713i	−0.996436	+	0.0843566i	$0.973117\pi$
$240$	−7871.17	−	16086.9i	−0.136652	−	0.279286i
$241$	−45035.7			−0.775394			−0.387697	−	0.921787i	$-0.626729\pi$
$241$	−45035.7			−0.775394			−0.387697	+	0.921787i	$0.626729\pi$
$242$		−	40608.0i		−	0.693395i
$243$	38239.9	+	44994.3i	0.647597	+	0.761983i
$244$	−49231.6			−0.826921
$245$			168184.i			2.80189i
$246$	20913.4	−	10232.8i	0.345585	−	0.169092i
$247$	5010.94			0.0821345
$248$		−	15113.6i		−	0.245733i
$249$	24259.3	+	49580.5i	0.391273	+	0.799672i
$250$	24910.4			0.398566
$251$		−	60743.6i		−	0.964169i	−0.876125	−	0.482085i	$-0.839880\pi$
$251$		−	60743.6i		−	0.964169i	0.876125	−	0.482085i	$-0.160120\pi$
$252$	−35143.3	+	45215.6i	−0.553404	+	0.712012i
$253$	2369.71			0.0370215
$254$		−	61593.8i		−	0.954706i
$255$	−10500.2	+	5137.67i	−0.161480	+	0.0790107i
$256$	4096.00			0.0625000
$257$		−	31736.9i		−	0.480505i	−0.970710	−	0.240253i	$-0.922770\pi$
$257$		−	31736.9i		−	0.480505i	0.970710	−	0.240253i	$-0.0772303\pi$
$258$	−10019.5	−	20477.5i	−0.150524	−	0.307636i
$259$	219543.			3.27281
$260$		−	3998.88i		−	0.0591551i
$261$	−48122.7	−	37402.8i	−0.706430	−	0.549065i
$262$	−39901.3			−0.581278
$263$		−	125019.i		−	1.80745i	−0.428117	−	0.903723i	$-0.640823\pi$
$263$		−	125019.i		−	1.80745i	0.428117	−	0.903723i	$-0.359177\pi$
$264$	3082.17	−	1508.08i	0.0442231	−	0.0216380i
$265$	−101730.			−1.44863
$266$		−	77911.4i		−	1.10113i
$267$	−37835.4	−	77326.9i	−0.530733	−	1.08470i
$268$	−57389.4			−0.799028
$269$		−	98278.0i		−	1.35816i	−0.734063	−	0.679081i	$-0.762378\pi$
$269$		−	98278.0i		−	1.35816i	0.734063	−	0.679081i	$-0.237622\pi$
$270$	−13092.4	+	62759.3i	−0.179593	+	0.860895i
$271$	20614.5			0.280695			0.140348	−	0.990102i	$-0.455178\pi$
$271$	20614.5			0.280695			0.140348	+	0.990102i	$0.455178\pi$
$272$		−	2673.54i		−	0.0361368i
$273$	−11485.7	+	5619.87i	−0.154111	+	0.0754051i
$274$	63498.1			0.845784
$275$		−	5758.20i		−	0.0761414i
$276$	−4450.44	−	9095.67i	−0.0584231	−	0.119403i
$277$	17695.8			0.230628			0.115314	−	0.993329i	$-0.463213\pi$
$277$	17695.8			0.230628			0.115314	+	0.993329i	$0.463213\pi$
$278$			3196.11i			0.0413555i
$279$	−33201.3	+	42717.0i	−0.426528	+	0.548773i
$280$	−62175.6			−0.793056
$281$		−	46444.8i		−	0.588199i	−0.955775	−	0.294099i	$-0.904980\pi$
$281$		−	46444.8i		−	0.588199i	0.955775	−	0.294099i	$-0.0950197\pi$
$282$	−28545.7	+	13967.2i	−0.358957	+	0.175635i
$283$	−82108.7			−1.02522			−0.512609	−	0.858622i	$-0.671321\pi$
$283$	−82108.7			−1.02522			−0.512609	+	0.858622i	$0.671321\pi$
$284$		−	11294.9i		−	0.140038i
$285$	−38334.1	−	78346.2i	−0.471950	−	0.964557i
$286$	766.168			0.00936682
$287$		−	80830.3i		−	0.981319i
$288$	−11577.0	−	8998.06i	−0.139576	−	0.108484i
$289$	81775.9			0.979106
$290$		−	66173.1i		−	0.786838i
$291$	81245.7	−	39752.9i	0.959432	−	0.469442i
$292$	50448.1			0.591669
$293$		−	162979.i		−	1.89844i	−0.314613	−	0.949220i	$-0.601875\pi$
$293$		−	162979.i		−	1.89844i	0.314613	−	0.949220i	$-0.398125\pi$
$294$	60516.9	+	123683.i	0.700135	+	1.43092i
$295$	14090.7			0.161916
$296$			56211.6i			0.641568i
$297$	−12024.4	−	2508.44i	−0.136317	−	0.0284374i
$298$	79804.8			0.898662
$299$		−	2261.01i		−	0.0252906i
$300$	−22101.7	+	10814.2i	−0.245574	+	0.120158i
$301$	−79145.3			−0.873559
$302$		−	30009.5i		−	0.329037i
$303$	−55213.1	−	112843.i	−0.601391	−	1.22911i
$304$	19948.3			0.215854
$305$			191342.i			2.05688i
$306$	−5873.21	+	7556.51i	−0.0627239	+	0.0807009i
$307$	−8097.67			−0.0859179			−0.0429589	−	0.999077i	$-0.513678\pi$
$307$	−8097.67			−0.0859179			−0.0429589	+	0.999077i	$0.513678\pi$
$308$		−	11912.6i		−	0.125575i
$309$	103392.	−	50588.8i	1.08285	−	0.529832i
$310$	−58739.8			−0.611236
$311$		−	146539.i		−	1.51506i	−0.652798	−	0.757532i	$-0.726405\pi$
$311$		−	146539.i		−	1.51506i	0.652798	−	0.757532i	$-0.273595\pi$
$312$	−1438.90	−	2940.79i	−0.0147816	−	0.0302103i
$313$	17525.6			0.178890			0.0894448	−	0.995992i	$-0.471491\pi$
$313$	17525.6			0.178890			0.0894448	+	0.995992i	$0.471491\pi$
$314$			41517.0i			0.421082i
$315$	175733.	+	136587.i	1.77106	+	1.37654i
$316$	−22062.2			−0.220940
$317$			28410.7i			0.282725i	0.989958	+	0.141362i	$0.0451483\pi$
$317$			28410.7i			0.282725i	−0.989958	+	0.141362i	$0.954852\pi$
$318$	−74812.7	+	36605.3i	−0.739812	+	0.361984i
$319$	12678.5			0.124591
$320$		−	15919.4i		−	0.155462i
$321$	−52791.4	−	107893.i	−0.512334	−	1.04709i
$322$	−35154.7			−0.339056
$323$		−	13020.7i		−	0.124804i
$324$	12954.3	+	50864.3i	0.123402	+	0.484533i
$325$	−5494.06			−0.0520147
$326$		−	44547.2i		−	0.419165i
$327$	48662.1	−	23810.0i	0.455088	−	0.222671i
$328$	20695.7			0.192368
$329$			110329.i			1.01929i
$330$	−5861.25	−	11979.1i	−0.0538223	−	0.110000i
$331$	204830.			1.86956			0.934778	−	0.355233i	$-0.115598\pi$
$331$	204830.			1.86956			0.934778	+	0.355233i	$0.115598\pi$
$332$			49064.3i			0.445132i
$333$	123485.	−	158877.i	1.11359	−	1.43275i
$334$	138490.			1.24144
$335$			223047.i			1.98750i
$336$	−45724.1	+	22372.4i	−0.405011	+	0.198168i
$337$	−77376.8			−0.681319			−0.340660	−	0.940187i	$-0.610650\pi$
$337$	−77376.8			−0.681319			−0.340660	+	0.940187i	$0.610650\pi$
$338$			80051.7i			0.700708i
$339$	−8918.47	−	18227.3i	−0.0776052	−	0.158607i
$340$	−10390.9			−0.0898866
$341$		−	11254.3i		−	0.0967853i
$342$	−56382.0	−	43822.3i	−0.482046	−	0.374665i
$343$	265844.			2.25964
$344$		−	20264.3i		−	0.171243i
$345$	−35350.9	+	17296.9i	−0.297004	+	0.145322i
$346$	−64673.5			−0.540224
$347$		−	50147.0i		−	0.416473i	−0.978079	−	0.208236i	$-0.933228\pi$
$347$		−	50147.0i		−	0.416473i	0.978079	−	0.208236i	$-0.0667723\pi$
$348$	−23810.8	−	48663.8i	−0.196615	−	0.401835i
$349$	139564.			1.14584			0.572918	−	0.819613i	$-0.305811\pi$
$349$	139564.			1.14584			0.572918	+	0.819613i	$0.305811\pi$
$350$			85422.9i			0.697330i
$351$	−2393.37	+	11472.8i	−0.0194266	+	0.0931228i
$352$	3050.08			0.0246165
$353$			186639.i			1.49780i	0.662683	+	0.748900i	$0.269418\pi$
$353$			186639.i			1.49780i	−0.662683	+	0.748900i	$0.730582\pi$
$354$	10362.4	−	5070.22i	0.0826898	−	0.0404595i
$355$	−43898.4			−0.348331
$356$		−	76521.8i		−	0.603789i
$357$	14602.9	+	29845.0i	0.114579	+	0.234172i
$358$	21282.1			0.166053
$359$			41075.6i			0.318709i	0.987221	+	0.159355i	$0.0509413\pi$
$359$			41075.6i			0.318709i	−0.987221	+	0.159355i	$0.949059\pi$
$360$	−34971.5	+	44994.5i	−0.269842	+	0.347180i
$361$	−33168.7			−0.254515
$362$			22687.6i			0.173130i
$363$	−116065.	+	56789.8i	−0.880824	+	0.430980i
$364$	−11366.1			−0.0857846
$365$		−	196070.i		−	1.47172i
$366$	68849.8	+	140713.i	0.513973	+	1.05044i
$367$	221492.			1.64447			0.822237	−	0.569146i	$-0.192726\pi$
$367$	221492.			1.64447			0.822237	+	0.569146i	$0.192726\pi$
$368$		−	9000.97i		−	0.0664651i
$369$	−58494.4	−	45464.1i	−0.429597	−	0.333900i
$370$	218470.			1.59584
$371$			289151.i			2.10076i
$372$	−43197.4	+	21136.1i	−0.312156	+	0.152735i
$373$	136027.			0.977702			0.488851	−	0.872367i	$-0.337416\pi$
$373$	136027.			0.977702			0.488851	+	0.872367i	$0.337416\pi$
$374$		−	1990.85i		−	0.0142330i
$375$	−34836.9	−	71198.6i	−0.247729	−	0.506301i
$376$	−28248.5			−0.199811
$377$		−	12096.9i		−	0.0851120i
$378$	178382.	+	37212.7i	1.24844	+	0.260440i
$379$	71354.5			0.496756			0.248378	−	0.968663i	$-0.420103\pi$
$379$	71354.5			0.496756			0.248378	+	0.968663i	$0.420103\pi$
$380$		−	77530.4i		−	0.536914i
$381$	−176047.	+	86138.2i	−1.21277	+	0.593398i
$382$	−150843.			−1.03371
$383$		−	20424.4i		−	0.139236i	−0.997574	−	0.0696180i	$-0.977822\pi$
$383$		−	20424.4i		−	0.139236i	0.997574	−	0.0696180i	$-0.0221780\pi$
$384$	−5728.21	−	11707.1i	−0.0388469	−	0.0793941i
$385$	−46299.0			−0.312356
$386$			9595.13i			0.0643986i
$387$	−44516.4	+	57275.0i	−0.297233	+	0.382422i
$388$	80399.7			0.534061
$389$			166800.i			1.10229i	0.834410	+	0.551145i	$0.185809\pi$
$389$			166800.i			1.10229i	−0.834410	+	0.551145i	$0.814191\pi$
$390$	−11429.6	+	5592.39i	−0.0751450	+	0.0367678i
$391$	−5875.11			−0.0384293
$392$			122395.i			0.796509i
$393$	55801.4	+	114045.i	0.361294	+	0.738401i
$394$	−78925.4			−0.508422
$395$			85746.0i			0.549566i
$396$	−8620.76	−	6700.39i	−0.0549737	−	0.0427277i
$397$	−6523.93			−0.0413931			−0.0206966	−	0.999786i	$-0.506588\pi$
$397$	−6523.93			−0.0413931			−0.0206966	+	0.999786i	$0.506588\pi$
$398$		−	41174.4i		−	0.259933i
$399$	−222685.	+	108958.i	−1.39877	+	0.684406i
$400$	−21871.6			−0.136697
$401$			236260.i			1.46927i	0.678463	+	0.734635i	$0.262646\pi$
$401$			236260.i			1.46927i	−0.678463	+	0.734635i	$0.737354\pi$
$402$	80258.4	+	164030.i	0.496636	+	1.01501i
$403$	−10738.0			−0.0661173
$404$		−	111668.i		−	0.684173i
$405$	197687.	−	50347.7i	1.20523	−	0.306951i
$406$	−188085.			−1.14105
$407$			41857.9i			0.252690i
$408$	−7641.48	+	3738.92i	−0.0459047	+	0.0224608i
$409$	−301912.			−1.80482			−0.902409	−	0.430880i	$-0.858203\pi$
$409$	−301912.			−1.80482			−0.902409	+	0.430880i	$0.858203\pi$
$410$		−	80435.1i		−	0.478495i
$411$	−88801.3	−	181489.i	−0.525697	−	1.07440i
$412$	102315.			0.602763
$413$		−	40050.4i		−	0.234805i
$414$	−19773.2	+	25440.4i	−0.115366	+	0.148430i
$415$	190691.			1.10722
$416$		−	2910.17i		−	0.0168163i
$417$	9135.09	−	4469.73i	0.0525340	−	0.0257045i
$418$	14854.5			0.0850169
$419$		−	89246.6i		−	0.508351i	−0.967158	−	0.254175i	$-0.918196\pi$
$419$		−	89246.6i		−	0.508351i	0.967158	−	0.254175i	$-0.0818041\pi$
$420$	86951.8	+	177709.i	0.492924	+	1.00742i
$421$	137951.			0.778323			0.389162	−	0.921169i	$-0.372765\pi$
$421$	137951.			0.778323			0.389162	+	0.921169i	$0.372765\pi$
$422$		−	93074.7i		−	0.522645i
$423$	79841.6	+	62056.0i	0.446219	+	0.346819i
$424$	−74033.8			−0.411811
$425$			14276.0i			0.0790368i
$426$	−32283.0	+	15795.8i	−0.177891	+	0.0870408i
$427$	543855.			2.98282
$428$		−	106770.i		−	0.582857i
$429$	−1071.48	−	2189.85i	−0.00582195	−	0.0118987i
$430$	−78758.3			−0.425951
$431$		−	286759.i		−	1.54370i	−0.635804	−	0.771850i	$-0.719331\pi$
$431$		−	286759.i		−	1.54370i	0.635804	−	0.771850i	$-0.280669\pi$
$432$	−9527.90	+	45672.8i	−0.0510540	+	0.244731i
$433$	−224633.			−1.19811			−0.599055	−	0.800708i	$-0.704457\pi$
$433$	−224633.			−1.19811			−0.599055	+	0.800708i	$0.704457\pi$
$434$			166958.i			0.886394i
$435$	−189135.	+	92542.3i	−0.999525	+	0.489059i
$436$	48155.4			0.253322
$437$		−	43836.5i		−	0.229548i
$438$	−70551.0	−	144190.i	−0.367752	−	0.751601i
$439$	−264099.			−1.37037			−0.685184	−	0.728370i	$-0.740278\pi$
$439$	−264099.			−1.37037			−0.685184	+	0.728370i	$0.740278\pi$
$440$		−	11854.3i		−	0.0612310i
$441$	268876.	−	345937.i	1.38253	−	1.77877i
$442$	−1899.53			−0.00972300
$443$			53923.4i			0.274770i	0.990518	+	0.137385i	$0.0438698\pi$
$443$			53923.4i			0.274770i	−0.990518	+	0.137385i	$0.956130\pi$
$444$	160663.	−	78611.2i	0.814987	−	0.398767i
$445$	−297407.			−1.50186
$446$			100398.i			0.504728i
$447$	−111606.	−	228097.i	−0.558564	−	1.14158i
$448$	−45248.0			−0.225446
$449$			9955.62i			0.0493828i	0.999695	+	0.0246914i	$0.00786032\pi$
$449$			9955.62i			0.0493828i	−0.999695	+	0.0246914i	$0.992140\pi$
$450$	61817.9	+	48047.3i	0.305274	+	0.237271i
$451$	15411.0			0.0757666
$452$		−	18037.5i		−	0.0882876i
$453$	−85772.7	+	41967.9i	−0.417977	+	0.204513i
$454$	98104.1			0.475966
$455$			44175.1i			0.213381i
$456$	−27897.5	−	57016.1i	−0.134164	−	0.274200i
$457$	197672.			0.946485			0.473242	−	0.880932i	$-0.343083\pi$
$457$	197672.			0.946485			0.473242	+	0.880932i	$0.343083\pi$
$458$			191310.i			0.912025i
$459$	29811.5	+	6219.05i	0.141501	+	0.0295188i
$460$	−34982.8			−0.165325
$461$			189643.i			0.892350i	0.894946	+	0.446175i	$0.147214\pi$
$461$			189643.i			0.892350i	−0.894946	+	0.446175i	$0.852786\pi$
$462$	−34048.4	+	16659.6i	−0.159519	+	0.0780513i
$463$	−61766.1			−0.288130			−0.144065	−	0.989568i	$-0.546017\pi$
$463$	−61766.1			−0.288130			−0.144065	+	0.989568i	$0.546017\pi$
$464$		−	48157.1i		−	0.223679i
$465$	82146.9	+	167889.i	0.379914	+	0.776457i
$466$	242307.			1.11582
$467$		−	7799.27i		−	0.0357618i	−0.999840	−	0.0178809i	$-0.994308\pi$
$467$		−	7799.27i		−	0.0357618i	0.999840	−	0.0178809i	$-0.00569198\pi$
$468$	−6393.03	+	8225.31i	−0.0291887	+	0.0375544i
$469$	633973.			2.88221
$470$			109789.i			0.497009i
$471$	118663.	−	58061.0i	0.534902	−	0.261723i
$472$	10254.5			0.0460287
$473$		−	15089.8i		−	0.0674466i
$474$	30853.7	+	63057.8i	0.137325	+	0.280661i
$475$	−106519.			−0.472106
$476$			29534.3i			0.130350i
$477$	209249.	+	162637.i	0.919660	+	0.714796i
$478$	27257.7			0.119298
$479$			352736.i			1.53737i	0.639626	+	0.768687i	$0.279089\pi$
$479$			352736.i			1.53737i	−0.639626	+	0.768687i	$0.720911\pi$
$480$	−45500.5	+	22263.0i	−0.197485	+	0.0966277i
$481$	39937.8			0.172621
$482$			127380.i			0.548286i
$483$	49163.4	+	100479.i	0.210740	+	0.430705i
$484$	−114857.			−0.490304
$485$		−	312479.i		−	1.32842i
$486$	127263.	−	108159.i	0.538803	−	0.457920i
$487$	−175334.			−0.739281			−0.369640	−	0.929175i	$-0.620519\pi$
$487$	−175334.			−0.739281			−0.369640	+	0.929175i	$0.620519\pi$
$488$			139248.i			0.584722i
$489$	−127324.	+	62298.7i	−0.532468	+	0.260532i
$490$	475695.			1.98124
$491$		−	208129.i		−	0.863317i	−0.902037	−	0.431659i	$-0.857929\pi$
$491$		−	208129.i		−	0.863317i	0.902037	−	0.431659i	$-0.142071\pi$
$492$	−28942.7	−	59152.1i	−0.119566	−	0.244366i
$493$	−31433.1			−0.129328
$494$		−	14173.1i		−	0.0580779i
$495$	−26041.5	+	33505.1i	−0.106281	+	0.136742i
$496$	−42747.6			−0.173759
$497$			124774.i			0.505138i
$498$	140235.	−	68615.8i	0.565454	−	0.276672i
$499$	−161119.			−0.647063			−0.323532	−	0.946217i	$-0.604870\pi$
$499$	−161119.			−0.647063			−0.323532	+	0.946217i	$0.604870\pi$
$500$		−	70457.2i		−	0.281829i
$501$	−193677.	−	395831.i	−0.771618	−	1.57701i
$502$	−171809.			−0.681771
$503$		−	305782.i		−	1.20858i	−0.796764	−	0.604291i	$-0.793456\pi$
$503$		−	305782.i		−	1.20858i	0.796764	−	0.604291i	$-0.206544\pi$
$504$	127889.	+	99400.4i	0.503469	+	0.391315i
$505$	−434005.			−1.70181
$506$		−	6702.56i		−	0.0261782i
$507$	228803.	−	111951.i	0.890113	−	0.435525i
$508$	−174214.			−0.675079
$509$		−	228190.i		−	0.880768i	−0.897810	−	0.440384i	$-0.854842\pi$
$509$		−	228190.i		−	0.880768i	0.897810	−	0.440384i	$-0.145158\pi$
$510$	14531.5	+	29699.1i	0.0558690	+	0.114183i
$511$	−557294.			−2.13424
$512$		−	11585.2i		−	0.0441942i
$513$	−46402.8	+	222435.i	−0.176323	+	0.845219i
$514$	−89765.5			−0.339769
$515$		−	397655.i		−	1.49931i
$516$	−57919.1	+	28339.3i	−0.217531	+	0.106436i
$517$	−21035.2			−0.0786982
$518$		−	620962.i		−	2.31423i
$519$	90445.1	+	184849.i	0.335777	+	0.686250i
$520$	−11310.5			−0.0418289
$521$			451377.i			1.66289i	0.555605	+	0.831446i	$0.312487\pi$
$521$			451377.i			1.66289i	−0.555605	+	0.831446i	$0.687513\pi$
$522$	−105791.	+	136112.i	−0.388247	+	0.499521i
$523$	−14447.7			−0.0528197			−0.0264098	−	0.999651i	$-0.508407\pi$
$523$	−14447.7			−0.0528197			−0.0264098	+	0.999651i	$0.508407\pi$
$524$			112858.i			0.411026i
$525$	244155.	−	119463.i	0.885822	−	0.433426i
$526$	−353608.			−1.27806
$527$			27902.2i			0.100466i
$528$	−4265.50	−	8717.70i	−0.0153004	−	0.0312704i
$529$	260061.			0.929318
$530$			287737.i			1.02434i
$531$	−28983.3	−	22526.9i	−0.102792	−	0.0798937i
$532$	−220367.			−0.778615
$533$		−	14704.1i		−	0.0517587i
$534$	−218714.	+	107015.i	−0.766996	+	0.375285i
$535$	−414968.			−1.44980
$536$			162322.i			0.564998i
$537$	−29762.7	−	60828.1i	−0.103211	−	0.210938i
$538$	−277972.			−0.960366
$539$			91141.1i			0.313716i
$540$	177510.	+	37030.8i	0.608745	+	0.126992i
$541$	−498157.			−1.70205			−0.851024	−	0.525126i	$-0.824018\pi$
$541$	−498157.			−1.70205			−0.851024	+	0.525126i	$0.824018\pi$
$542$		−	58306.7i		−	0.198481i
$543$	64845.5	−	31728.4i	0.219928	−	0.107609i
$544$	−7561.92			−0.0255526
$545$		−	187159.i		−	0.630112i
$546$	15895.4	+	32486.5i	0.0533194	+	0.108973i
$547$	−1715.74			−0.00573426			−0.00286713	−	0.999996i	$-0.500913\pi$
$547$	−1715.74			−0.00573426			−0.00286713	+	0.999996i	$0.500913\pi$
$548$		−	179600.i		−	0.598060i
$549$	305899.	−	393571.i	1.01492	−	1.30581i
$550$	−16286.6			−0.0538401
$551$		−	234535.i		−	0.772510i
$552$	−25726.4	+	12587.7i	−0.0844309	+	0.0413114i
$553$	243718.			0.796961
$554$		−	50051.3i		−	0.163078i
$555$	−305527.	−	624428.i	−0.991892	−	2.02720i
$556$	9039.98			0.0292427
$557$		−	487736.i		−	1.57208i	−0.618177	−	0.786039i	$-0.712129\pi$
$557$		−	487736.i		−	1.57208i	0.618177	−	0.786039i	$-0.287871\pi$
$558$	120822.	+	93907.6i	0.388041	+	0.301601i
$559$	−14397.6			−0.0460750
$560$			175859.i			0.560775i
$561$	−5690.22	+	2784.18i	−0.0180802	+	0.00884650i
$562$	−131366.			−0.415919
$563$			81667.0i			0.257650i	0.991667	+	0.128825i	$0.0411205\pi$
$563$			81667.0i			0.257650i	−0.991667	+	0.128825i	$0.958880\pi$
$564$	39505.1	+	80739.4i	0.124192	+	0.253821i
$565$	−70103.9			−0.219607
$566$			232239.i			0.724939i
$567$	−143104.	−	561891.i	−0.445130	−	1.74778i
$568$	−31946.9			−0.0990220
$569$			281412.i			0.869195i	0.900625	+	0.434598i	$0.143109\pi$
$569$			281412.i			0.869195i	−0.900625	+	0.434598i	$0.856891\pi$
$570$	−221596.	+	108425.i	−0.682045	+	0.333719i
$571$	235739.			0.723034			0.361517	−	0.932365i	$-0.382259\pi$
$571$	235739.			0.723034			0.361517	+	0.932365i	$0.382259\pi$
$572$		−	2167.05i		−	0.00662334i
$573$	210952.	+	431138.i	0.642503	+	1.31313i
$574$	−228623.			−0.693898
$575$			48062.8i			0.145370i
$576$	−25450.3	+	32744.6i	−0.0767094	+	0.0986948i
$577$	479542.			1.44037			0.720186	−	0.693781i	$-0.244056\pi$
$577$	479542.			1.44037			0.720186	+	0.693781i	$0.244056\pi$
$578$		−	231297.i		−	0.692333i
$579$	27424.7	−	13418.7i	0.0818059	−	0.0400270i
$580$	−187166.			−0.556379
$581$		−	542007.i		−	1.60566i
$582$	−112438.	−	229797.i	−0.331946	−	0.678421i
$583$	−55129.1			−0.162197
$584$		−	142689.i		−	0.418373i
$585$	31968.2	+	24846.9i	0.0934127	+	0.0726040i
$586$	−460975.			−1.34240
$587$		−	395632.i		−	1.14819i	−0.818788	−	0.574096i	$-0.805353\pi$
$587$		−	395632.i		−	1.14819i	0.818788	−	0.574096i	$-0.194647\pi$
$588$	349827.	−	171168.i	1.01181	−	0.495070i
$589$	−208189.			−0.600106
$590$		−	39854.6i		−	0.114492i
$591$	110376.	+	225584.i	0.316010	+	0.645851i
$592$	158990.			0.453657
$593$		−	130948.i		−	0.372384i	−0.982513	−	0.186192i	$-0.940385\pi$
$593$		−	130948.i		−	0.372384i	0.982513	−	0.186192i	$-0.0596146\pi$
$594$	−7094.94	+	34010.2i	−0.0201083	+	0.0963908i
$595$	114787.			0.324234
$596$		−	225722.i		−	0.635450i
$597$	−117684.	+	57581.8i	−0.330194	+	0.161561i
$598$	−6395.10			−0.0178832
$599$			33862.4i			0.0943767i	0.998886	+	0.0471883i	$0.0150261\pi$
$599$			33862.4i			0.0943767i	−0.998886	+	0.0471883i	$0.984974\pi$
$600$	30587.1	+	62513.1i	0.0849643	+	0.173647i
$601$	245054.			0.678441			0.339221	−	0.940707i	$-0.389837\pi$
$601$	245054.			0.678441			0.339221	+	0.940707i	$0.389837\pi$
$602$			223857.i			0.617700i
$603$	356587.	−	458787.i	0.980688	−	1.26176i
$604$	−84879.6			−0.232664
$605$			446398.i			1.21958i
$606$	−319168.	+	156166.i	−0.869109	+	0.425248i
$607$	−438939.			−1.19132			−0.595658	−	0.803238i	$-0.703109\pi$
$607$	−438939.			−1.19132			−0.595658	+	0.803238i	$0.703109\pi$
$608$		−	56422.4i		−	0.152632i
$609$	263035.	+	537583.i	0.709217	+	1.44948i
$610$	541196.			1.45444
$611$			20070.2i			0.0537614i
$612$	21373.0	+	16612.0i	0.0570642	+	0.0443525i
$613$	−187738.			−0.499610			−0.249805	−	0.968296i	$-0.580367\pi$
$613$	−187738.			−0.499610			−0.249805	+	0.968296i	$0.580367\pi$
$614$			22903.7i			0.0607531i
$615$	−229898.	+	112487.i	−0.607835	+	0.297409i
$616$	−33693.8			−0.0887951
$617$		−	219503.i		−	0.576594i	−0.957541	−	0.288297i	$-0.906911\pi$
$617$		−	219503.i		−	0.576594i	0.957541	−	0.288297i	$-0.0930890\pi$
$618$	−143087.	−	292437.i	−0.374647	−	0.765693i
$619$	−349288.			−0.911597			−0.455799	−	0.890083i	$-0.650646\pi$
$619$	−349288.			−0.911597			−0.455799	+	0.890083i	$0.650646\pi$
$620$			166141.i			0.432209i
$621$	100366.	+	20937.6i	0.260258	+	0.0542929i
$622$	−414474.			−1.07131
$623$			845327.i			2.17795i
$624$	−8317.80	+	4069.83i	−0.0213619	+	0.0104522i
$625$	−487426.			−1.24781
$626$		−	49570.0i		−	0.126494i
$627$	−20773.8	−	42456.9i	−0.0528423	−	0.107997i
$628$	117428.			0.297750
$629$		−	103776.i		−	0.262299i
$630$	386326.	−	497049.i	0.973358	−	1.25233i
$631$	−771864.			−1.93857			−0.969287	−	0.245933i	$-0.920906\pi$
$631$	−771864.			−1.93857			−0.969287	+	0.245933i	$0.920906\pi$
$632$			62401.2i			0.156228i
$633$	−266025.	+	130164.i	−0.663919	+	0.324850i
$634$	80357.7			0.199917
$635$			677092.i			1.67919i
$636$	103535.	+	211602.i	0.255961	+	0.523126i
$637$	86960.3			0.214310
$638$		−	35860.1i		−	0.0880989i
$639$	90294.7	+	70180.6i	0.221137	+	0.171876i
$640$	−45026.7			−0.109929
$641$		−	539132.i		−	1.31214i	−0.754702	−	0.656068i	$-0.772219\pi$
$641$		−	539132.i		−	1.31214i	0.754702	−	0.656068i	$-0.227781\pi$
$642$	−305169.	+	149317.i	−0.740406	+	0.362275i
$643$	597771.			1.44582			0.722908	−	0.690944i	$-0.242805\pi$
$643$	597771.			1.44582			0.722908	+	0.690944i	$0.242805\pi$
$644$			99432.5i			0.239749i
$645$	110143.	+	225106.i	0.264750	+	0.541088i
$646$	−36828.0			−0.0882498
$647$		−	663141.i		−	1.58415i	−0.610421	−	0.792077i	$-0.709000\pi$
$647$		−	663141.i		−	1.58415i	0.610421	−	0.792077i	$-0.291000\pi$
$648$	143866.	−	36640.3i	0.342616	−	0.0872587i
$649$	7635.97			0.0181290
$650$			15539.5i			0.0367800i
$651$	477196.	−	233488.i	1.12599	−	0.550938i
$652$	−125998.			−0.296394
$653$			582682.i			1.36649i	0.730190	+	0.683244i	$0.239431\pi$
$653$			582682.i			1.36649i	−0.730190	+	0.683244i	$0.760569\pi$
$654$	−67344.8	−	137637.i	−0.157452	−	0.321796i
$655$	438629.			1.02239
$656$		−	58536.2i		−	0.136025i
$657$	−313457.	+	403296.i	−0.726186	+	0.934315i
$658$	312057.			0.720746
$659$			59310.4i			0.136571i	0.997666	+	0.0682857i	$0.0217529\pi$
$659$			59310.4i			0.136571i	−0.997666	+	0.0682857i	$0.978247\pi$
$660$	−33881.9	+	16578.1i	−0.0777821	+	0.0380581i
$661$	424035.			0.970506			0.485253	−	0.874374i	$-0.338727\pi$
$661$	424035.			0.970506			0.485253	+	0.874374i	$0.338727\pi$
$662$		−	579348.i		−	1.32198i
$663$	2656.46	+	5429.20i	0.00604333	+	0.0123512i
$664$	138775.			0.314756
$665$			856469.i			1.93673i
$666$	−449371.	−	349269.i	−1.01311	−	0.787429i
$667$	−105825.			−0.237869
$668$		−	391709.i		−	0.877831i
$669$	286958.	−	140406.i	0.641159	−	0.313714i
$670$	630874.			1.40538
$671$			103691.i			0.230301i
$672$	63278.8	+	129327.i	0.140126	+	0.286386i
$673$	498942.			1.10159			0.550795	−	0.834641i	$-0.314325\pi$
$673$	498942.			1.10159			0.550795	+	0.834641i	$0.314325\pi$
$674$			218855.i			0.481766i
$675$	50876.5	−	243881.i	0.111663	−	0.535266i
$676$	226420.			0.495475
$677$			679235.i			1.48198i	0.671515	+	0.740991i	$0.265644\pi$
$677$			679235.i			1.48198i	−0.671515	+	0.740991i	$0.734356\pi$
$678$	−51554.6	+	25225.2i	−0.112152	+	0.0548752i
$679$	−888166.			−1.92644
$680$			29389.9i			0.0635594i
$681$	−137197.	−	280400.i	−0.295837	−	0.604622i
$682$	−31831.9			−0.0684375
$683$			558191.i			1.19658i	0.801280	+	0.598289i	$0.204153\pi$
$683$			558191.i			1.19658i	−0.801280	+	0.598289i	$0.795847\pi$
$684$	−123948.	+	159473.i	−0.264928	+	0.340858i
$685$	−698025.			−1.48761
$686$		−	751921.i		−	1.59780i
$687$	546800.	−	267545.i	1.15855	−	0.566869i
$688$	−57316.0			−0.121087
$689$			52600.3i			0.110802i
$690$	48923.0	+	99987.4i	0.102758	+	0.210014i
$691$	428290.			0.896978			0.448489	−	0.893788i	$-0.351962\pi$
$691$	428290.			0.896978			0.448489	+	0.893788i	$0.351962\pi$
$692$			182924.i			0.381996i
$693$	95232.4	+	74018.3i	0.198298	+	0.154125i
$694$	−141837.			−0.294491
$695$		−	35134.4i		−	0.0727383i
$696$	−137642.	+	67347.2i	−0.284140	+	0.139028i
$697$	−38207.8			−0.0786478
$698$		−	394746.i		−	0.810228i
$699$	−338863.	−	692559.i	−0.693538	−	1.41743i
$700$	241613.			0.493087
$701$			93635.8i			0.190549i	0.995451	+	0.0952743i	$0.0303728\pi$
$701$			93635.8i			0.190549i	−0.995451	+	0.0952743i	$0.969627\pi$
$702$	32450.0	+	6769.48i	0.0658478	+	0.0137367i
$703$	774315.			1.56678
$704$		−	8626.93i		−	0.0174065i
$705$	313799.	−	153539.i	0.631354	−	0.308916i
$706$	527896.			1.05911
$707$			1.23358e6i			2.46791i
$708$	−14340.7	−	29309.2i	−0.0286092	−	0.0584705i
$709$	−893557.			−1.77758			−0.888791	−	0.458312i	$-0.848454\pi$
$709$	−893557.			−1.77758			−0.888791	+	0.458312i	$0.848454\pi$
$710$			124163.i			0.246307i
$711$	137082.	−	176371.i	0.271171	−	0.348890i
$712$	−216436.			−0.426943
$713$			93938.0i			0.184783i
$714$	84414.5	−	41303.3i	0.165585	−	0.0810193i
$715$	−8422.38			−0.0164749
$716$		−	60194.8i		−	0.117417i
$717$	−38119.6	−	77907.7i	−0.0741498	−	0.151545i
$718$	116179.			0.225362
$719$		−	305009.i		−	0.590004i	−0.955497	−	0.295002i	$-0.904680\pi$
$719$		−	305009.i		−	0.590004i	0.955497	−	0.295002i	$-0.0953203\pi$
$720$	127264.	+	98914.4i	0.245493	+	0.190807i
$721$	−1.13027e6			−2.17425
$722$			93815.2i			0.179970i
$723$	364076.	−	178140.i	0.696491	−	0.340787i
$724$	64170.3			0.122421
$725$			257147.i			0.489221i
$726$	160626.	+	328282.i	0.304749	+	0.622836i
$727$	207110.			0.391861			0.195930	−	0.980618i	$-0.437227\pi$
$727$	207110.			0.391861			0.195930	+	0.980618i	$0.437227\pi$
$728$			32148.2i			0.0606589i
$729$	−487114.	−	212483.i	−0.916592	−	0.399825i
$730$	−554569.			−1.04066
$731$			37411.3i			0.0700113i
$732$	397997.	−	194737.i	0.742775	−	0.363434i
$733$	−271184.			−0.504726			−0.252363	−	0.967633i	$-0.581208\pi$
$733$	−271184.			−0.504726			−0.252363	+	0.967633i	$0.581208\pi$
$734$		−	626475.i		−	1.16282i
$735$	−665254.	−	1.35963e6i	−1.23144	−	2.51678i
$736$	−25458.6			−0.0469979
$737$			120873.i			0.222532i
$738$	−128592.	+	165447.i	−0.236103	+	0.303771i
$739$	−285941.			−0.523585			−0.261792	−	0.965124i	$-0.584314\pi$
$739$	−285941.			−0.523585			−0.261792	+	0.965124i	$0.584314\pi$
$740$		−	617926.i		−	1.12843i
$741$	−40509.3	+	19820.9i	−0.0737766	+	0.0360983i
$742$	817842.			1.48546
$743$		−	799887.i		−	1.44894i	−0.689305	−	0.724471i	$-0.742084\pi$
$743$		−	799887.i		−	1.44894i	0.689305	−	0.724471i	$-0.257916\pi$
$744$	59782.0	+	122181.i	0.108000	+	0.220728i
$745$	−877283.			−1.58062
$746$		−	384742.i		−	0.691340i
$747$	−392233.	−	304859.i	−0.702916	−	0.546333i
$748$	−5630.97			−0.0100642
$749$			1.17947e6i			2.10245i
$750$	−201380.	+	98533.6i	−0.358009	+	0.175171i
$751$	−245758.			−0.435741			−0.217870	−	0.975978i	$-0.569911\pi$
$751$	−245758.			−0.435741			−0.217870	+	0.975978i	$0.569911\pi$
$752$			79898.7i			0.141288i
$753$	240273.	+	491062.i	0.423755	+	0.866057i
$754$	−34215.2			−0.0601833
$755$			329890.i			0.578729i
$756$	105254.	−	504541.i	0.184159	−	0.882781i
$757$	704066.			1.22863			0.614316	−	0.789060i	$-0.289432\pi$
$757$	704066.			1.22863			0.614316	+	0.789060i	$0.289432\pi$
$758$		−	201821.i		−	0.351259i
$759$	−19157.2	+	9373.44i	−0.0332543	+	0.0162710i
$760$	−219289.			−0.379656
$761$		−	749283.i		−	1.29383i	−0.762563	−	0.646914i	$-0.776059\pi$
$761$		−	749283.i		−	1.29383i	0.762563	−	0.646914i	$-0.223941\pi$
$762$	243636.	+	497935.i	0.419595	+	0.857556i
$763$	−531967.			−0.913767
$764$			426649.i			0.730944i
$765$	64563.4	−	83067.7i	0.110322	−	0.141941i
$766$	−57768.9			−0.0984547
$767$		−	7285.69i		−	0.0123846i
$768$	−33112.8	+	16201.8i	−0.0561401	+	0.0274689i
$769$	−686439.			−1.16078			−0.580389	−	0.814339i	$-0.697100\pi$
$769$	−686439.			−1.16078			−0.580389	+	0.814339i	$0.697100\pi$
$770$			130953.i			0.220869i
$771$	125536.	+	256567.i	0.211183	+	0.431610i
$772$	27139.1			0.0455367
$773$			1.07379e6i			1.79705i	0.438922	+	0.898525i	$0.355360\pi$
$773$			1.07379e6i			1.79705i	−0.438922	+	0.898525i	$0.644640\pi$
$774$	161998.	+	125911.i	0.270413	+	0.210176i
$775$	228261.			0.380039
$776$		−	227405.i		−	0.377638i
$777$	−1.77483e6	+	868408.i	−2.93977	+	1.43841i
$778$	471780.			0.779436
$779$		−	285083.i		−	0.469782i
$780$	15817.7	+	32327.7i	0.0259988	+	0.0531355i
$781$	−23789.2			−0.0390011
$782$			16617.3i			0.0271736i
$783$	536980.	+	112021.i	0.875860	+	0.182715i
$784$	346185.			0.563217
$785$		−	456390.i		−	0.740622i
$786$	322569.	−	157830.i	0.522128	−	0.255473i
$787$	−116339.			−0.187835			−0.0939177	−	0.995580i	$-0.529939\pi$
$787$	−116339.			−0.187835			−0.0939177	+	0.995580i	$0.529939\pi$
$788$			223235.i			0.359509i
$789$	494516.	+	1.01068e6i	0.794377	+	1.62352i
$790$	242526.			0.388602
$791$			199258.i			0.318466i
$792$	−18951.6	+	24383.2i	−0.0302131	+	0.0388723i
$793$	98934.3			0.157326
$794$			18452.5i			0.0292694i
$795$	822406.	−	402397.i	1.30122	−	0.636678i
$796$	−116459.			−0.183800
$797$			650444.i			1.02398i	0.858990	+	0.511992i	$0.171092\pi$
$797$			650444.i			1.02398i	−0.858990	+	0.511992i	$0.828908\pi$
$798$	308180.	+	629849.i	0.483948	+	0.989078i
$799$	52151.5			0.0816908
$800$			61862.2i			0.0966596i
$801$	611737.	+	475465.i	0.953453	+	0.741061i
$802$	668244.			1.03893
$803$		−	106253.i		−	0.164782i
$804$	463946.	−	227005.i	0.717720	−	0.351175i
$805$	386451.			0.596352
$806$			30371.8i			0.0467520i
$807$	388741.	+	794496.i	0.596915	+	1.21996i
$808$	−315845.			−0.483783
$809$			303984.i			0.464466i	0.972660	+	0.232233i	$0.0746032\pi$
$809$			303984.i			0.464466i	−0.972660	+	0.232233i	$0.925397\pi$
$810$	−142405.	−	559144.i	−0.217047	−	0.852224i
$811$	−953059.			−1.44903			−0.724516	−	0.689258i	$-0.757937\pi$
$811$	−953059.			−1.44903			−0.724516	+	0.689258i	$0.757937\pi$
$812$			531986.i			0.806841i
$813$	−166651.	+	81541.2i	−0.252132	+	0.123366i
$814$	118392.			0.178679
$815$			489701.i			0.737252i
$816$	10575.3	+	21613.4i	0.0158822	+	0.0324595i
$817$	−279140.			−0.418195
$818$			853936.i			1.27620i
$819$	70623.0	−	90863.9i	0.105288	−	0.135464i
$820$	−227505.			−0.338347
$821$		−	574332.i		−	0.852073i	−0.904706	−	0.426037i	$-0.859909\pi$
$821$		−	574332.i		−	0.852073i	0.904706	−	0.426037i	$-0.140091\pi$
$822$	−513330.	+	251168.i	−0.759718	+	0.371724i
$823$	806299.			1.19041			0.595205	−	0.803574i	$-0.297071\pi$
$823$	806299.			1.19041			0.595205	+	0.803574i	$0.297071\pi$
$824$		−	289392.i		−	0.426218i
$825$	22776.7	+	46550.2i	0.0334643	+	0.0683934i
$826$	−113280.			−0.166032
$827$		−	80581.9i		−	0.117822i	−0.998263	−	0.0589110i	$-0.981237\pi$
$827$		−	80581.9i		−	0.117822i	0.998263	−	0.0589110i	$-0.0187628\pi$
$828$	71956.2	+	55927.2i	0.104956	+	0.0815760i
$829$	−1.05845e6			−1.54015			−0.770074	−	0.637954i	$-0.779781\pi$
$829$	−1.05845e6			−1.54015			−0.770074	+	0.637954i	$0.779781\pi$
$830$		−	539356.i		−	0.782924i
$831$	−143056.	+	69996.2i	−0.207159	+	0.101361i
$832$	−8231.20			−0.0118909
$833$		−	225962.i		−	0.325645i
$834$	−12642.3	−	25837.9i	−0.0181758	−	0.0371472i
$835$	−1.52240e6			−2.18352
$836$		−	42014.8i		−	0.0601160i
$837$	99437.3	−	476661.i	0.141938	−	0.680391i
$838$	−252427.			−0.359458
$839$		−	781619.i		−	1.11038i	−0.831724	−	0.555190i	$-0.812646\pi$
$839$		−	781619.i		−	1.11038i	0.831724	−	0.555190i	$-0.187354\pi$
$840$	502638.	−	245937.i	0.712356	−	0.348550i
$841$	141092.			0.199485
$842$		−	390184.i		−	0.550358i
$843$	183713.	+	375467.i	0.258515	+	0.528344i
$844$	−263255.			−0.369566
$845$		−	879997.i		−	1.23245i
$846$	175521.	−	225826.i	0.245238	−	0.315525i
$847$	1.26881e6			1.76860
$848$			209399.i			0.291195i
$849$	663781.	−	324783.i	0.920894	−	0.450586i
$850$	40378.7			0.0558875
$851$		−	349382.i		−	0.482438i
$852$	44677.3	+	91310.1i	0.0615471	+	0.125788i
$853$	311794.			0.428518			0.214259	−	0.976777i	$-0.431266\pi$
$853$	311794.			0.428518			0.214259	+	0.976777i	$0.431266\pi$
$854$		−	1.53825e6i		−	2.10917i
$855$	619800.	+	481732.i	0.847850	+	0.658982i
$856$	−301991.			−0.412142
$857$			416924.i			0.567669i	0.958873	+	0.283835i	$0.0916067\pi$
$857$			416924.i			0.567669i	−0.958873	+	0.283835i	$0.908393\pi$
$858$	−6193.84	+	3030.59i	−0.00841367	+	0.00411674i
$859$	−199244.			−0.270022			−0.135011	−	0.990844i	$-0.543107\pi$
$859$	−199244.			−0.270022			−0.135011	+	0.990844i	$0.543107\pi$
$860$			222762.i			0.301193i
$861$	319726.	+	653446.i	0.431292	+	0.881462i
$862$	−811078.			−1.09156
$863$		−	1.10761e6i		−	1.48718i	−0.668635	−	0.743591i	$-0.733121\pi$
$863$		−	1.10761e6i		−	1.48718i	0.668635	−	0.743591i	$-0.266879\pi$
$864$	129182.	+	26949.0i	0.173051	+	0.0361006i
$865$	710947.			0.950178
$866$			635357.i			0.847192i
$867$	−661091.	+	323466.i	−0.879474	+	0.430319i
$868$	472227.			0.626775
$869$			46467.0i			0.0615325i
$870$	261749.	+	534955.i	0.345817	+	0.706771i
$871$	115328.			0.152019
$872$		−	136204.i		−	0.179125i
$873$	−499561.	+	642738.i	−0.655481	+	0.843345i
$874$	−123988.			−0.162315
$875$			778332.i			1.01660i
$876$	−407831.	+	199548.i	−0.531462	+	0.260040i
$877$	990782.			1.28819			0.644093	−	0.764947i	$-0.277235\pi$
$877$	990782.			1.28819			0.644093	+	0.764947i	$0.277235\pi$
$878$			746984.i			0.968996i
$879$	644668.	+	1.31755e6i	0.834369	+	1.70526i
$880$	−33529.1			−0.0432969
$881$		−	773851.i		−	0.997024i	−0.866883	−	0.498512i	$-0.833880\pi$
$881$		−	773851.i		−	0.997024i	0.866883	−	0.498512i	$-0.166120\pi$
$882$	−978458.	−	760496.i	−1.25778	−	0.977596i
$883$	195516.			0.250762			0.125381	−	0.992109i	$-0.459985\pi$
$883$	195516.			0.250762			0.125381	+	0.992109i	$0.459985\pi$
$884$			5372.67i			0.00687520i
$885$	−113912.	+	55736.2i	−0.145440	+	0.0711624i
$886$	152518.			0.194292
$887$			43719.6i			0.0555685i	0.999614	+	0.0277842i	$0.00884514\pi$
$887$			43719.6i			0.0555685i	−0.999614	+	0.0277842i	$0.991155\pi$
$888$	−222346.	−	454424.i	−0.281971	−	0.576283i
$889$	1.92452e6			2.43511
$890$			841193.i			1.06198i
$891$	107130.	−	27284.1i	0.134944	−	0.0343680i
$892$	283970.			0.356897
$893$			389122.i			0.487959i
$894$	−645156.	+	315670.i	−0.807216	+	0.394964i
$895$	−233951.			−0.292064
$896$			127981.i			0.159415i
$897$	8943.47	+	18278.4i	0.0111153	+	0.0227171i
$898$	28158.8			0.0349189
$899$			502589.i			0.621861i
$900$	135898.	−	174847.i	0.167776	−	0.215861i
$901$	136679.			0.168365
$902$		−	43588.9i		−	0.0535751i
$903$	639824.	−	313061.i	0.784667	−	0.383931i
$904$	−51017.8			−0.0624288
$905$		−	249402.i		−	0.304511i
$906$	118703.	+	242602.i	0.144612	+	0.295554i
$907$	1.44634e6			1.75815			0.879077	−	0.476680i	$-0.158160\pi$
$907$	1.44634e6			1.75815			0.879077	+	0.476680i	$0.158160\pi$
$908$		−	277480.i		−	0.336559i
$909$	892705.	+	693845.i	1.08039	+	0.839720i
$910$	124946.			0.150883
$911$			166150.i			0.200200i	0.994977	+	0.100100i	$0.0319163\pi$
$911$			166150.i			0.200200i	−0.994977	+	0.100100i	$0.968084\pi$
$912$	−161266.	+	78906.0i	−0.193889	+	0.0948682i
$913$	103338.			0.123971
$914$		−	559102.i		−	0.669266i
$915$	−756856.	−	1.54684e6i	−0.904005	−	1.84758i
$916$	541106.			0.644899
$917$		−	1.24673e6i		−	1.48263i
$918$	17590.1	−	84319.8i	0.0208730	−	0.100056i
$919$	−690994.			−0.818170			−0.409085	−	0.912496i	$-0.634152\pi$
$919$	−690994.			−0.818170			−0.409085	+	0.912496i	$0.634152\pi$
$920$			98946.4i			0.116903i
$921$	65463.0	−	32030.5i	0.0771750	−	0.0377611i
$922$	536392.			0.630987
$923$			22697.9i			0.0266430i
$924$	47120.4	+	96303.3i	0.0551906	+	0.112797i
$925$	−848968.			−0.992219
$926$			174701.i			0.203739i
$927$	−635733.	+	817938.i	−0.739802	+	0.951833i
$928$	−136209.			−0.158165
$929$		−	102734.i		−	0.119037i	−0.998227	−	0.0595184i	$-0.981044\pi$
$929$		−	102734.i		−	0.119037i	0.998227	−	0.0595184i	$-0.0189565\pi$
$930$	474863.	−	232347.i	0.549038	−	0.268640i
$931$	1.68599e6			1.94516
$932$		−	685348.i		−	0.789004i
$933$	579636.	+	1.18464e6i	0.665874	+	1.36089i
$934$	−22059.7			−0.0252874
$935$			21885.1i			0.0250337i
$936$	23264.7	+	18082.2i	0.0265550	+	0.0206395i
$937$	185744.			0.211561			0.105781	−	0.994389i	$-0.466266\pi$
$937$	185744.			0.211561			0.105781	+	0.994389i	$0.466266\pi$
$938$		−	1.79315e6i		−	2.03803i
$939$	−141680.	+	69323.0i	−0.160686	+	0.0786224i
$940$	310531.			0.351439
$941$		−	147619.i		−	0.166711i	−0.996520	−	0.0833553i	$-0.973436\pi$
$941$		−	147619.i		−	0.166711i	0.996520	−	0.0833553i	$-0.0265636\pi$
$942$	−164221.	−	335630.i	−0.185066	−	0.378233i
$943$	−128633.			−0.144654
$944$		−	29004.0i		−	0.0325472i
$945$	−1.96093e6	−	409074.i	−2.19583	−	0.458077i
$946$	−42680.3			−0.0476919
$947$		−	1.10308e6i		−	1.23000i	−0.788526	−	0.615001i	$-0.789156\pi$
$947$		−	1.10308e6i		−	1.23000i	0.788526	−	0.615001i	$-0.210844\pi$
$948$	178354.	−	87267.3i	0.198457	−	0.0971035i
$949$	−101379.			−0.112568
$950$			301281.i			0.333829i
$951$	−112379.	−	229677.i	−0.124258	−	0.253955i
$952$	83535.6			0.0921717
$953$		−	535209.i		−	0.589302i	−0.955605	−	0.294651i	$-0.904797\pi$
$953$		−	535209.i		−	0.589302i	0.955605	−	0.294651i	$-0.0952033\pi$
$954$	460006.	−	591847.i	0.505437	−	0.650298i
$955$	1.65820e6			1.81815
$956$		−	77096.5i		−	0.0843566i
$957$	−102495.	+	50150.0i	−0.111913	+	0.0547579i
$958$	997689.			1.08709
$959$			1.98402e6i			2.15729i
$960$	62969.4	+	128695.i	0.0683261	+	0.139643i
$961$	−477388.			−0.516922
$962$		−	112961.i		−	0.122062i
$963$	853549.	+	663412.i	0.920399	+	0.715370i
$964$	360285.			0.387697
$965$		−	105478.i		−	0.113268i
$966$	284197.	−	139055.i	0.304554	−	0.149016i
$967$	1.01785e6			1.08851			0.544254	−	0.838921i	$-0.316813\pi$
$967$	1.01785e6			1.08851			0.544254	+	0.838921i	$0.316813\pi$
$968$			324864.i			0.346698i
$969$	51503.6	+	105261.i	0.0548517	+	0.112104i
$970$	−883823.			−0.939338
$971$			71934.6i			0.0762956i	0.999272	+	0.0381478i	$0.0121458\pi$
$971$			71934.6i			0.0762956i	−0.999272	+	0.0381478i	$0.987854\pi$
$972$	−305920.	−	359955.i	−0.323798	−	0.380992i
$973$	−99863.5			−0.105483
$974$			495921.i			0.522750i
$975$	44414.9	−	21731.9i	0.0467218	−	0.0228606i
$976$	393853.			0.413461
$977$		−	1.35336e6i		−	1.41783i	−0.705294	−	0.708915i	$-0.749185\pi$
$977$		−	1.35336e6i		−	1.41783i	0.705294	−	0.708915i	$-0.250815\pi$
$978$	176207.	+	360127.i	0.184224	+	0.376511i
$979$	−161169.			−0.168157
$980$		−	1.34547e6i		−	1.40095i
$981$	−299212.	+	384968.i	−0.310915	+	0.400025i
$982$	−588679.			−0.610457
$983$		−	815808.i		−	0.844269i	−0.906533	−	0.422135i	$-0.861281\pi$
$983$		−	815808.i		−	0.844269i	0.906533	−	0.422135i	$-0.138719\pi$
$984$	−167308.	+	81862.2i	−0.172793	+	0.0845460i
$985$	867616.			0.894242
$986$			88906.4i			0.0914490i
$987$	−436408.	−	891918.i	−0.447980	−	0.915568i
$988$	−40087.5			−0.0410672
$989$			125952.i			0.128769i
$990$	94766.8	+	73656.4i	0.0966909	+	0.0751519i
$991$	−425971.			−0.433743			−0.216872	−	0.976200i	$-0.569585\pi$
$991$	−425971.			−0.433743			−0.216872	+	0.976200i	$0.569585\pi$
$992$			120909.i			0.122867i
$993$	−1.65588e6	+	810211.i	−1.67931	+	0.821674i
$994$	352913.			0.357186
$995$			452624.i			0.457184i
$996$	−194075.	−	396644.i	−0.195637	−	0.399836i
$997$	1.77761e6			1.78832			0.894162	−	0.447744i	$-0.147772\pi$
$997$	1.77761e6			1.78832			0.894162	+	0.447744i	$0.147772\pi$
$998$			455714.i			0.457543i
$999$	−369835.	+	1.77283e6i	−0.370576	+	1.77639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.b.a.119.6	✓	76
3.2	odd	2	inner	354.5.b.a.119.44	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.b.a.119.6	✓	76	1.1	even	1	trivial
354.5.b.a.119.44	yes	76	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} +(-8.08417 + 3.95552i) q^{3} -8.00000 q^{4} +31.0925i q^{5} +(11.1879 + 22.8655i) q^{6} +88.3750 q^{7} +22.6274i q^{8} +(49.7077 - 63.9542i) q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} +(-8.08417 + 3.95552i) q^{3} -8.00000 q^{4} +31.0925i q^{5} +(11.1879 + 22.8655i) q^{6} +88.3750 q^{7} +22.6274i q^{8} +(49.7077 - 63.9542i) q^{9} +87.9429 q^{10} +16.8495i q^{11} +(64.6734 - 31.6442i) q^{12} +16.0766 q^{13} -249.962i q^{14} +(-122.987 - 251.357i) q^{15} +64.0000 q^{16} -41.7741i q^{17} +(-180.890 - 140.595i) q^{18} +311.693 q^{19} -248.740i q^{20} +(-714.439 + 349.569i) q^{21} +47.6575 q^{22} -140.640i q^{23} +(-89.5032 - 182.924i) q^{24} -341.743 q^{25} -45.4714i q^{26} +(-148.873 + 713.637i) q^{27} -707.000 q^{28} -752.455i q^{29} +(-710.945 + 347.860i) q^{30} -667.932 q^{31} -181.019i q^{32} +(-66.6484 - 136.214i) q^{33} -118.155 q^{34} +2747.80i q^{35} +(-397.662 + 511.634i) q^{36} +2484.23 q^{37} -881.600i q^{38} +(-129.966 + 63.5911i) q^{39} -703.543 q^{40} -914.629i q^{41} +(988.731 + 2020.74i) q^{42} -895.563 q^{43} -134.796i q^{44} +(1988.50 + 1545.54i) q^{45} -397.790 q^{46} +1248.42i q^{47} +(-517.387 + 253.153i) q^{48} +5409.14 q^{49} +966.596i q^{50} +(165.238 + 337.709i) q^{51} -128.612 q^{52} +3271.86i q^{53} +(2018.47 + 421.078i) q^{54} -523.892 q^{55} +1999.70i q^{56} +(-2519.78 + 1232.91i) q^{57} -2128.27 q^{58} -453.188i q^{59} +(983.896 + 2010.86i) q^{60} +6153.95 q^{61} +1889.20i q^{62} +(4392.92 - 5651.95i) q^{63} -512.000 q^{64} +499.860i q^{65} +(-385.271 + 188.510i) q^{66} +7173.67 q^{67} +334.193i q^{68} +(556.305 + 1136.96i) q^{69} +7771.95 q^{70} +1411.86i q^{71} +(1447.12 + 1124.76i) q^{72} -6306.01 q^{73} -7026.45i q^{74} +(2762.71 - 1351.77i) q^{75} -2493.54 q^{76} +1489.07i q^{77} +(179.863 + 367.598i) q^{78} +2757.77 q^{79} +1989.92i q^{80} +(-1619.29 - 6358.04i) q^{81} -2586.96 q^{82} -6133.03i q^{83} +(5715.51 - 2796.55i) q^{84} +1298.86 q^{85} +2533.03i q^{86} +(2976.35 + 6082.98i) q^{87} -381.260 q^{88} +9565.23i q^{89} +(4371.44 - 5624.32i) q^{90} +1420.77 q^{91} +1125.12i q^{92} +(5399.67 - 2642.02i) q^{93} +3531.06 q^{94} +9691.30i q^{95} +(716.026 + 1463.39i) q^{96} -10050.0 q^{97} -15299.4i q^{98} +(1077.59 + 837.549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

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