LMFDB - Embedded newform 99.5.k.c.28.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,5,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, 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:	$10.2336263453$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			28.7
Character	$\chi$	$=$	99.28
Dual form			99.5.k.c.46.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.49285 - 1.45982i) q^{2} +(5.11038 - 3.71291i) q^{4} +(-5.35863 + 16.4922i) q^{5} +(48.2339 + 66.3883i) q^{7} +(-26.8877 + 37.0078i) q^{8} +O(q^{10})$	\(q+(4.49285 - 1.45982i) q^{2} +(5.11038 - 3.71291i) q^{4} +(-5.35863 + 16.4922i) q^{5} +(48.2339 + 66.3883i) q^{7} +(-26.8877 + 37.0078i) q^{8} +81.9194i q^{10} +(-120.968 - 2.78945i) q^{11} +(162.182 - 52.6960i) q^{13} +(313.623 + 227.860i) q^{14} +(-98.0099 + 301.644i) q^{16} +(314.317 + 102.128i) q^{17} +(159.158 - 219.062i) q^{19} +(33.8493 + 104.177i) q^{20} +(-547.563 + 164.058i) q^{22} -414.069 q^{23} +(262.359 + 190.615i) q^{25} +(651.732 - 473.511i) q^{26} +(492.987 + 160.181i) q^{28} +(-631.311 - 868.925i) q^{29} +(167.845 + 516.573i) q^{31} +766.410i q^{32} +1561.27 q^{34} +(-1353.35 + 439.731i) q^{35} +(-508.083 + 369.144i) q^{37} +(395.283 - 1216.55i) q^{38} +(-466.257 - 641.748i) q^{40} +(144.517 - 198.911i) q^{41} -3521.17i q^{43} +(-628.549 + 434.888i) q^{44} +(-1860.35 + 604.465i) q^{46} +(1909.71 + 1387.48i) q^{47} +(-1338.94 + 4120.85i) q^{49} +(1457.00 + 473.410i) q^{50} +(633.155 - 871.463i) q^{52} +(-316.208 - 973.189i) q^{53} +(694.225 - 1980.07i) q^{55} -3753.79 q^{56} +(-4104.86 - 2982.35i) q^{58} +(1755.04 - 1275.11i) q^{59} +(3673.05 + 1193.45i) q^{61} +(1508.20 + 2075.86i) q^{62} +(-449.342 - 1382.93i) q^{64} +2957.10i q^{65} -70.0820 q^{67} +(1985.47 - 645.118i) q^{68} +(-5438.49 + 3951.29i) q^{70} +(141.635 - 435.908i) q^{71} +(-3913.19 - 5386.05i) q^{73} +(-1743.86 + 2400.22i) q^{74} -1710.43i q^{76} +(-5649.57 - 8165.39i) q^{77} +(7783.85 - 2529.13i) q^{79} +(-4449.55 - 3232.79i) q^{80} +(358.921 - 1104.64i) q^{82} +(-301.994 - 98.1237i) q^{83} +(-3368.61 + 4636.49i) q^{85} +(-5140.26 - 15820.1i) q^{86} +(3355.78 - 4401.75i) q^{88} +5300.49 q^{89} +(11321.1 + 8225.23i) q^{91} +(-2116.05 + 1537.40i) q^{92} +(10605.5 + 3445.93i) q^{94} +(2759.94 + 3798.73i) q^{95} +(-1625.00 - 5001.22i) q^{97} +20469.0i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8}+O(q^{10}) $ 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8	$ 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8} + 246 q^{11} - 510 q^{13} + 1290 q^{14} - 232 q^{16} - 2490 q^{17} + 582 q^{20} - 510 q^{22} + 2196 q^{23} - 370 q^{25} + 5226 q^{26} + 4310 q^{28} - 960 q^{29} + 1658 q^{31} - 2320 q^{34} - 1920 q^{35} + 1374 q^{37} - 12054 q^{38} + 11070 q^{40} - 9360 q^{41} + 4350 q^{44} - 12950 q^{46} + 3450 q^{47} - 11838 q^{49} + 11550 q^{50} - 19250 q^{52} + 2790 q^{53} + 12356 q^{55} + 5604 q^{56} + 9486 q^{58} - 2682 q^{59} - 17190 q^{61} + 39360 q^{62} + 16248 q^{64} + 2796 q^{67} - 68160 q^{68} + 18188 q^{70} - 132 q^{71} - 21790 q^{73} + 2130 q^{74} - 4542 q^{77} + 12270 q^{79} - 32346 q^{80} + 29442 q^{82} - 35430 q^{83} - 11990 q^{85} + 49416 q^{86} + 1176 q^{88} + 38748 q^{89} - 51858 q^{91} + 25590 q^{92} - 34510 q^{94} + 71670 q^{95} + 30306 q^{97}+O(q^{100}) $ 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8 + 246 * q^11 - 510 * q^13 + 1290 * q^14 - 232 * q^16 - 2490 * q^17 + 582 * q^20 - 510 * q^22 + 2196 * q^23 - 370 * q^25 + 5226 * q^26 + 4310 * q^28 - 960 * q^29 + 1658 * q^31 - 2320 * q^34 - 1920 * q^35 + 1374 * q^37 - 12054 * q^38 + 11070 * q^40 - 9360 * q^41 + 4350 * q^44 - 12950 * q^46 + 3450 * q^47 - 11838 * q^49 + 11550 * q^50 - 19250 * q^52 + 2790 * q^53 + 12356 * q^55 + 5604 * q^56 + 9486 * q^58 - 2682 * q^59 - 17190 * q^61 + 39360 * q^62 + 16248 * q^64 + 2796 * q^67 - 68160 * q^68 + 18188 * q^70 - 132 * q^71 - 21790 * q^73 + 2130 * q^74 - 4542 * q^77 + 12270 * q^79 - 32346 * q^80 + 29442 * q^82 - 35430 * q^83 - 11990 * q^85 + 49416 * q^86 + 1176 * q^88 + 38748 * q^89 - 51858 * q^91 + 25590 * q^92 - 34510 * q^94 + 71670 * q^95 + 30306 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	4.49285	−	1.45982i	1.12321	−	0.364954i	0.312220	−	0.950010i	$-0.398927\pi$
$2$	4.49285	−	1.45982i	1.12321	−	0.364954i	0.810993	+	0.585056i	$0.198927\pi$
$3$		0			0
$3$		0			0
$4$	5.11038	−	3.71291i	0.319399	−	0.232057i
$5$	−5.35863	+	16.4922i	−0.214345	+	0.659686i	0.784854	+	0.619680i	$0.212738\pi$
$5$	−5.35863	+	16.4922i	−0.214345	+	0.659686i	−0.999199	+	0.0400059i	$0.987262\pi$
$6$		0			0
$7$	48.2339	+	66.3883i	0.984366	+	1.35486i	0.934444	+	0.356110i	$0.115897\pi$
$7$	48.2339	+	66.3883i	0.984366	+	1.35486i	0.0499215	+	0.998753i	$0.484103\pi$
$8$	−26.8877	+	37.0078i	−0.420121	+	0.578247i
$9$		0			0
$10$			81.9194i			0.819194i
$11$	−120.968	−	2.78945i	−0.999734	−	0.0230533i
$11$	−120.968	−	2.78945i	−0.999734	−	0.0230533i
$12$		0			0
$13$	162.182	−	52.6960i	0.959655	−	0.311811i	0.213022	−	0.977047i	$-0.431669\pi$
$13$	162.182	−	52.6960i	0.959655	−	0.311811i	0.746633	+	0.665237i	$0.231669\pi$
$14$	313.623	+	227.860i	1.60011	+	1.16255i
$15$		0			0
$16$	−98.0099	+	301.644i	−0.382851	+	1.17830i
$17$	314.317	+	102.128i	1.08760	+	0.353383i	0.797319	−	0.603558i	$-0.206251\pi$
$17$	314.317	+	102.128i	1.08760	+	0.353383i	0.290282	+	0.956941i	$0.406251\pi$
$18$		0			0
$19$	159.158	−	219.062i	0.440881	−	0.606820i	−0.529527	−	0.848293i	$-0.677631\pi$
$19$	159.158	−	219.062i	0.440881	−	0.606820i	0.970408	+	0.241473i	$0.0776305\pi$
$20$	33.8493	+	104.177i	0.0846231	+	0.260443i
$21$		0			0
$22$	−547.563	+	164.058i	−1.13133	+	0.338963i
$23$	−414.069			−0.782739			−0.391370	−	0.920234i	$-0.627999\pi$
$23$	−414.069			−0.782739			−0.391370	+	0.920234i	$0.627999\pi$
$24$		0			0
$25$	262.359	+	190.615i	0.419775	+	0.304984i
$26$	651.732	−	473.511i	0.964100	−	0.700460i
$27$		0			0
$28$	492.987	+	160.181i	0.628811	+	0.204313i
$29$	−631.311	−	868.925i	−0.750667	−	1.03321i	−0.997933	−	0.0642574i	$-0.979532\pi$
$29$	−631.311	−	868.925i	−0.750667	−	1.03321i	0.247266	−	0.968948i	$-0.420468\pi$
$30$		0			0
$31$	167.845	+	516.573i	0.174656	+	0.537537i	0.999618	−	0.0276521i	$-0.00880307\pi$
$31$	167.845	+	516.573i	0.174656	+	0.537537i	−0.824961	+	0.565189i	$0.808803\pi$
$32$			766.410i			0.748447i
$33$		0			0
$34$	1561.27			1.35058
$35$	−1353.35	+	439.731i	−1.10478	+	0.358964i
$36$		0			0
$37$	−508.083	+	369.144i	−0.371134	+	0.269645i	−0.757681	−	0.652625i	$-0.773668\pi$
$37$	−508.083	+	369.144i	−0.371134	+	0.269645i	0.386547	+	0.922270i	$0.373668\pi$
$38$	395.283	−	1216.55i	0.273741	−	0.842489i
$39$		0			0
$40$	−466.257	−	641.748i	−0.291411	−	0.401092i
$41$	144.517	−	198.911i	0.0859709	−	0.118329i	−0.763865	−	0.645376i	$-0.776701\pi$
$41$	144.517	−	198.911i	0.0859709	−	0.118329i	0.849836	+	0.527047i	$0.176701\pi$
$42$		0			0
$43$		−	3521.17i		−	1.90436i	−0.305533	−	0.952181i	$-0.598835\pi$
$43$		−	3521.17i		−	1.90436i	0.305533	−	0.952181i	$-0.401165\pi$
$44$	−628.549	+	434.888i	−0.324664	+	0.224632i
$45$		0			0
$46$	−1860.35	+	604.465i	−0.879183	+	0.285664i
$47$	1909.71	+	1387.48i	0.864511	+	0.628104i	0.929109	−	0.369807i	$-0.120576\pi$
$47$	1909.71	+	1387.48i	0.864511	+	0.628104i	−0.0645972	+	0.997911i	$0.520576\pi$
$48$		0			0
$49$	−1338.94	+	4120.85i	−0.557661	+	1.71630i
$50$	1457.00	+	473.410i	0.582802	+	0.189364i
$51$		0			0
$52$	633.155	−	871.463i	0.234155	−	0.322287i
$53$	−316.208	−	973.189i	−0.112570	−	0.346454i	0.878863	−	0.477075i	$-0.158303\pi$
$53$	−316.208	−	973.189i	−0.112570	−	0.346454i	−0.991432	+	0.130621i	$0.958303\pi$
$54$		0			0
$55$	694.225	−	1980.07i	0.229496	−	0.654569i
$56$	−3753.79			−1.19700
$57$		0			0
$58$	−4104.86	−	2982.35i	−1.22023	−	0.886550i
$59$	1755.04	−	1275.11i	0.504176	−	0.366305i	−0.306434	−	0.951892i	$-0.599136\pi$
$59$	1755.04	−	1275.11i	0.504176	−	0.366305i	0.810610	+	0.585587i	$0.199136\pi$
$60$		0			0
$61$	3673.05	+	1193.45i	0.987114	+	0.320733i	0.757705	−	0.652597i	$-0.226321\pi$
$61$	3673.05	+	1193.45i	0.987114	+	0.320733i	0.229409	+	0.973330i	$0.426321\pi$
$62$	1508.20	+	2075.86i	0.392353	+	0.540027i
$63$		0			0
$64$	−449.342	−	1382.93i	−0.109703	−	0.337630i
$65$			2957.10i			0.699906i
$66$		0			0
$67$	−70.0820			−0.0156119			−0.00780597	−	0.999970i	$-0.502485\pi$
$67$	−70.0820			−0.0156119			−0.00780597	+	0.999970i	$0.502485\pi$
$68$	1985.47	−	645.118i	0.429383	−	0.139515i
$69$		0			0
$70$	−5438.49	+	3951.29i	−1.10990	+	0.806386i
$71$	141.635	−	435.908i	0.0280966	−	0.0864725i	−0.936025	−	0.351934i	$-0.885524\pi$
$71$	141.635	−	435.908i	0.0280966	−	0.0864725i	0.964122	+	0.265461i	$0.0855242\pi$
$72$		0			0
$73$	−3913.19	−	5386.05i	−0.734320	−	1.01071i	−0.998925	−	0.0463485i	$-0.985242\pi$
$73$	−3913.19	−	5386.05i	−0.734320	−	1.01071i	0.264605	−	0.964357i	$-0.414758\pi$
$74$	−1743.86	+	2400.22i	−0.318455	+	0.438315i
$75$		0			0
$76$		−	1710.43i		−	0.296127i
$77$	−5649.57	−	8165.39i	−0.952870	−	1.37720i
$78$		0			0
$79$	7783.85	−	2529.13i	1.24721	−	0.405244i	0.390291	−	0.920692i	$-0.372374\pi$
$79$	7783.85	−	2529.13i	1.24721	−	0.405244i	0.856921	+	0.515448i	$0.172374\pi$
$80$	−4449.55	−	3232.79i	−0.695243	−	0.505123i
$81$		0			0
$82$	358.921	−	1104.64i	0.0533791	−	0.164284i
$83$	−301.994	−	98.1237i	−0.0438371	−	0.0142435i	0.287016	−	0.957926i	$-0.407337\pi$
$83$	−301.994	−	98.1237i	−0.0438371	−	0.0142435i	−0.330853	+	0.943682i	$0.607337\pi$
$84$		0			0
$85$	−3368.61	+	4636.49i	−0.466244	+	0.641729i
$86$	−5140.26	−	15820.1i	−0.695005	−	2.13900i
$87$		0			0
$88$	3355.78	−	4401.75i	0.433340	−	0.568408i
$89$	5300.49			0.669169			0.334585	−	0.942366i	$-0.391404\pi$
$89$	5300.49			0.669169			0.334585	+	0.942366i	$0.391404\pi$
$90$		0			0
$91$	11321.1	+	8225.23i	1.36711	+	0.993265i
$92$	−2116.05	+	1537.40i	−0.250006	+	0.181640i
$93$		0			0
$94$	10605.5	+	3445.93i	1.20026	+	0.389988i
$95$	2759.94	+	3798.73i	0.305810	+	0.420912i
$96$		0			0
$97$	−1625.00	−	5001.22i	−0.172707	−	0.531536i	0.826815	−	0.562474i	$-0.190150\pi$
$97$	−1625.00	−	5001.22i	−0.172707	−	0.531536i	−0.999521	+	0.0309382i	$0.990150\pi$
$98$			20469.0i			2.13130i
$99$		0			0
$100$	2048.49			0.204849
$101$	19321.0	−	6277.78i	1.89403	−	0.615408i	0.918560	−	0.395282i	$-0.129353\pi$
$101$	19321.0	−	6277.78i	1.89403	−	0.615408i	0.975472	−	0.220126i	$-0.0706468\pi$
$102$		0			0
$103$	−15948.6	+	11587.3i	−1.50330	+	1.09221i	−0.534263	+	0.845319i	$0.679411\pi$
$103$	−15948.6	+	11587.3i	−1.50330	+	1.09221i	−0.969042	+	0.246896i	$0.920589\pi$
$104$	−2410.53	+	7418.86i	−0.222867	+	0.685916i
$105$		0			0
$106$	−2841.35	−	3910.79i	−0.252880	−	0.348059i
$107$	−5430.59	+	7474.57i	−0.474329	+	0.652858i	−0.977403	−	0.211386i	$-0.932202\pi$
$107$	−5430.59	+	7474.57i	−0.474329	+	0.652858i	0.503074	+	0.864244i	$0.332202\pi$
$108$		0			0
$109$			14033.0i			1.18113i	0.806990	+	0.590566i	$0.201095\pi$
$109$			14033.0i			1.18113i	−0.806990	+	0.590566i	$0.798905\pi$
$110$	228.510	−	9909.61i	0.0188852	−	0.818976i
$111$		0			0
$112$	−24753.0	+	8042.74i	−1.97329	+	0.641162i
$113$	12820.2	+	9314.41i	1.00401	+	0.729455i	0.962944	−	0.269702i	$-0.0869251\pi$
$113$	12820.2	+	9314.41i	1.00401	+	0.729455i	0.0410645	+	0.999156i	$0.486925\pi$
$114$		0			0
$115$	2218.84	−	6828.89i	0.167776	−	0.516362i
$116$	−6452.48	−	2096.54i	−0.479525	−	0.155807i
$117$		0			0
$118$	6023.70	−	8290.91i	0.432612	−	0.595440i
$119$	8380.64	+	25793.0i	0.591811	+	1.82141i
$120$		0			0
$121$	14625.4	+	674.868i	0.998937	+	0.0460944i
$122$	18244.7			1.22579
$123$		0			0
$124$	2775.74	+	2016.69i	0.180524	+	0.131159i
$125$	−13317.7	+	9675.88i	−0.852333	+	0.619256i
$126$		0			0
$127$	21607.0	+	7020.53i	1.33963	+	0.435274i	0.889193	−	0.457532i	$-0.151267\pi$
$127$	21607.0	+	7020.53i	1.33963	+	0.435274i	0.450441	+	0.892806i	$0.351267\pi$
$128$	−11245.4	−	15478.0i	−0.686365	−	0.944700i
$129$		0			0
$130$	4316.83	+	13285.8i	0.255434	+	0.786144i
$131$		−	10558.8i		−	0.615277i	−0.951503	−	0.307638i	$-0.900461\pi$
$131$		−	10558.8i		−	0.615277i	0.951503	−	0.307638i	$-0.0995387\pi$
$132$		0			0
$133$	22220.0			1.25615
$134$	−314.868	+	102.307i	−0.0175355	+	0.00569764i
$135$		0			0
$136$	−12230.8	+	8886.18i	−0.661266	+	0.480438i
$137$	6006.33	−	18485.6i	0.320014	−	0.984900i	−0.653628	−	0.756816i	$-0.726754\pi$
$137$	6006.33	−	18485.6i	0.320014	−	0.984900i	0.973641	−	0.228084i	$-0.0732462\pi$
$138$		0			0
$139$	−12414.0	−	17086.4i	−0.642513	−	0.884343i	0.356234	−	0.934397i	$-0.384061\pi$
$139$	−12414.0	−	17086.4i	−0.642513	−	0.884343i	−0.998747	+	0.0500539i	$0.984061\pi$
$140$	−5283.47	+	7272.07i	−0.269565	+	0.371024i
$141$		0			0
$142$		−	2165.23i		−	0.107381i
$143$	−19765.8	+	5922.13i	−0.966588	+	0.289605i
$144$		0			0
$145$	17713.4	−	5755.44i	0.842493	−	0.273743i
$146$	−25444.0	−	18486.2i	−1.19366	−	0.867244i
$147$		0			0
$148$	−1225.90	+	3772.93i	−0.0559669	+	0.172248i
$149$	17529.0	+	5695.52i	0.789559	+	0.256543i	0.675916	−	0.736978i	$-0.263748\pi$
$149$	17529.0	+	5695.52i	0.789559	+	0.256543i	0.113643	+	0.993522i	$0.463748\pi$
$150$		0			0
$151$	−3572.99	+	4917.80i	−0.156703	+	0.215683i	−0.880149	−	0.474698i	$-0.842557\pi$
$151$	−3572.99	+	4917.80i	−0.156703	+	0.215683i	0.723446	+	0.690381i	$0.242557\pi$
$152$	3827.61	+	11780.2i	0.165669	+	0.509876i
$153$		0			0
$154$	−37302.6	−	28438.6i	−1.57289	−	1.19913i
$155$	−9418.82			−0.392043
$156$		0			0
$157$	−18583.7	−	13501.9i	−0.753934	−	0.547765i	0.143110	−	0.989707i	$-0.454290\pi$
$157$	−18583.7	−	13501.9i	−0.753934	−	0.547765i	−0.897044	+	0.441942i	$0.854290\pi$
$158$	31279.6	−	22726.0i	1.25299	−	0.910350i
$159$		0			0
$160$	−12639.7	−	4106.90i	−0.493740	−	0.160426i
$161$	−19972.2	−	27489.3i	−0.770502	−	1.06050i
$162$		0			0
$163$	−7806.21	−	24025.0i	−0.293809	−	0.904251i	−0.983619	−	0.180260i	$-0.942306\pi$
$163$	−7806.21	−	24025.0i	−0.293809	−	0.904251i	0.689810	−	0.723990i	$-0.257694\pi$
$164$		−	1553.09i		−	0.0577442i
$165$		0			0
$166$	−1500.06			−0.0544366
$167$	−37901.6	+	12315.0i	−1.35901	+	0.441571i	−0.895714	−	0.444631i	$-0.853335\pi$
$167$	−37901.6	+	12315.0i	−1.35901	+	0.441571i	−0.463301	+	0.886201i	$0.653335\pi$
$168$		0			0
$169$	419.690	−	304.923i	0.0146945	−	0.0106762i
$170$	−8366.24	+	25748.6i	−0.289489	+	0.890956i
$171$		0			0
$172$	−13073.8	−	17994.5i	−0.441920	−	0.608251i
$173$	17186.0	−	23654.5i	0.574225	−	0.790353i	−0.418822	−	0.908068i	$-0.637557\pi$
$173$	17186.0	−	23654.5i	0.574225	−	0.790353i	0.993047	+	0.117715i	$0.0375569\pi$
$174$		0			0
$175$			26611.7i			0.868954i
$176$	12697.5	−	36215.8i	0.409913	−	1.16916i
$177$		0			0
$178$	23814.3	−	7737.74i	0.751619	−	0.244216i
$179$	−10229.4	−	7432.10i	−0.319260	−	0.231956i	0.416600	−	0.909090i	$-0.363222\pi$
$179$	−10229.4	−	7432.10i	−0.319260	−	0.231956i	−0.735860	+	0.677134i	$0.763222\pi$
$180$		0			0
$181$	1153.66	−	3550.60i	0.0352144	−	0.108379i	−0.931904	−	0.362704i	$-0.881853\pi$
$181$	1153.66	−	3550.60i	0.0352144	−	0.108379i	0.967119	+	0.254326i	$0.0818535\pi$
$182$	62871.1	+	20428.1i	1.89805	+	0.616715i
$183$		0			0
$184$	11133.4	−	15323.8i	0.328845	−	0.452617i
$185$	−3365.35	−	10357.5i	−0.0983302	−	0.302629i
$186$		0			0
$187$	−37737.3	−	13230.9i	−1.07917	−	0.378362i
$188$	14910.9			0.421880
$189$		0			0
$190$	17945.4	+	13038.1i	0.497103	+	0.361167i
$191$	−20245.9	+	14709.5i	−0.554972	+	0.403211i	−0.829615	−	0.558335i	$-0.811440\pi$
$191$	−20245.9	+	14709.5i	−0.554972	+	0.403211i	0.274643	+	0.961546i	$0.411440\pi$
$192$		0			0
$193$	−25108.9	−	8158.38i	−0.674083	−	0.219023i	−0.0480800	−	0.998843i	$-0.515310\pi$
$193$	−25108.9	−	8158.38i	−0.674083	−	0.219023i	−0.626003	+	0.779821i	$0.715310\pi$
$194$	−14601.7	−	20097.6i	−0.387973	−	0.533998i
$195$		0			0
$196$	8457.82	+	26030.5i	0.220164	+	0.677595i
$197$			40491.4i			1.04335i	0.853144	+	0.521676i	$0.174693\pi$
$197$			40491.4i			1.04335i	−0.853144	+	0.521676i	$0.825307\pi$
$198$		0			0
$199$	−57554.9			−1.45337			−0.726685	−	0.686971i	$-0.758940\pi$
$199$	−57554.9			−1.45337			−0.726685	+	0.686971i	$0.758940\pi$
$200$	−14108.5	+	4584.13i	−0.352712	+	0.114603i
$201$		0			0
$202$	77642.0	−	56410.2i	1.90280	−	1.38247i
$203$	27235.9	−	83823.4i	0.660920	−	2.03410i
$204$		0			0
$205$	2506.05	+	3449.29i	0.0596324	+	0.0820770i
$206$	−54739.2	+	75342.0i	−1.28992	+	1.77543i
$207$		0			0
$208$			54085.8i			1.25013i
$209$	−19864.1	+	26055.5i	−0.454753	+	0.596495i
$210$		0			0
$211$	34322.9	−	11152.2i	0.770936	−	0.250492i	0.102971	−	0.994684i	$-0.467165\pi$
$211$	34322.9	−	11152.2i	0.770936	−	0.250492i	0.667966	+	0.744192i	$0.267165\pi$
$212$	−5229.31	−	3799.32i	−0.116352	−	0.0845344i
$213$		0			0
$214$	−13487.4	+	41509.8i	−0.294509	+	0.906407i
$215$	58071.6	+	18868.6i	1.25628	+	0.408191i
$216$		0			0
$217$	−26198.6	+	36059.3i	−0.556364	+	0.765769i
$218$	20485.6	+	63048.3i	0.431059	+	1.32666i
$219$		0			0
$220$	−3804.07	−	12696.5i	−0.0785966	−	0.262325i
$221$	56358.1			1.15391
$222$		0			0
$223$	−4302.42	−	3125.89i	−0.0865173	−	0.0628585i	0.543686	−	0.839289i	$-0.317028\pi$
$223$	−4302.42	−	3125.89i	−0.0865173	−	0.0628585i	−0.630203	+	0.776430i	$0.717028\pi$
$224$	−50880.6	+	36966.9i	−1.01404	+	0.736745i
$225$		0			0
$226$	71196.5	+	23133.1i	1.39393	+	0.452916i
$227$	−11067.5	−	15233.2i	−0.214783	−	0.295623i	0.688008	−	0.725703i	$-0.258485\pi$
$227$	−11067.5	−	15233.2i	−0.214783	−	0.295623i	−0.902791	+	0.430080i	$0.858485\pi$
$228$		0			0
$229$	3780.70	+	11635.8i	0.0720943	+	0.221883i	0.980611	−	0.195966i	$-0.0627841\pi$
$229$	3780.70	+	11635.8i	0.0720943	+	0.221883i	−0.908516	+	0.417849i	$0.862784\pi$
$230$		−	33920.3i		−	0.641215i
$231$		0			0
$232$	49131.5			0.912819
$233$	−32841.0	+	10670.7i	−0.604929	+	0.196553i	−0.595437	−	0.803402i	$-0.703021\pi$
$233$	−32841.0	+	10670.7i	−0.604929	+	0.196553i	−0.00949141	+	0.999955i	$0.503021\pi$
$234$		0			0
$235$	−33116.0	+	24060.2i	−0.599655	+	0.435675i
$236$	4234.54	−	13032.6i	0.0760296	−	0.233995i
$237$		0			0
$238$	75306.0	+	103650.i	1.32946	+	1.82985i
$239$	−36410.9	+	50115.3i	−0.637434	+	0.877353i	−0.998476	−	0.0551967i	$-0.982421\pi$
$239$	−36410.9	+	50115.3i	−0.637434	+	0.877353i	0.361041	+	0.932550i	$0.382421\pi$
$240$		0			0
$241$		−	10177.0i		−	0.175221i	−0.996155	−	0.0876107i	$-0.972077\pi$
$241$		−	10177.0i		−	0.175221i	0.996155	−	0.0876107i	$-0.0279232\pi$
$242$	66695.1	−	18318.4i	1.13884	−	0.312792i
$243$		0			0
$244$	23201.8	−	7538.74i	0.389711	−	0.126625i
$245$	−60786.7	−	44164.2i	−1.01269	−	0.735763i
$246$		0			0
$247$	14268.8	−	43914.8i	0.233880	−	0.719809i
$248$	−23630.2	−	7677.92i	−0.384206	−	0.124836i
$249$		0			0
$250$	−45709.5	+	62913.7i	−0.731352	+	1.00662i
$251$	−1440.97	−	4434.86i	−0.0228722	−	0.0703934i	0.938969	−	0.344002i	$-0.111783\pi$
$251$	−1440.97	−	4434.86i	−0.0228722	−	0.0703934i	−0.961841	+	0.273609i	$0.911783\pi$
$252$		0			0
$253$	50089.0	+	1155.03i	0.782531	+	0.0180447i
$254$	107326.			1.66355
$255$		0			0
$256$	−54296.6	−	39448.8i	−0.828501	−	0.601941i
$257$	42005.6	−	30518.8i	0.635976	−	0.462064i	−0.222489	−	0.974935i	$-0.571418\pi$
$257$	42005.6	−	30518.8i	0.635976	−	0.462064i	0.858465	+	0.512872i	$0.171418\pi$
$258$		0			0
$259$	−49013.6	−	15925.5i	−0.730663	−	0.237407i
$260$	10979.5	+	15111.9i	0.162418	+	0.223549i
$261$		0			0
$262$	−15413.9	−	47439.0i	−0.224548	−	0.691087i
$263$		−	69680.9i		−	1.00740i	−0.863879	−	0.503700i	$-0.831972\pi$
$263$		−	69680.9i		−	1.00740i	0.863879	−	0.503700i	$-0.168028\pi$
$264$		0			0
$265$	17744.4			0.252680
$266$	99831.0	−	32437.1i	1.41092	−	0.458436i
$267$		0			0
$268$	−358.146	+	260.208i	−0.00498644	+	0.00362286i
$269$	−17296.4	+	53232.7i	−0.239029	+	0.735655i	0.757533	+	0.652797i	$0.226405\pi$
$269$	−17296.4	+	53232.7i	−0.239029	+	0.735655i	−0.996561	+	0.0828575i	$0.973595\pi$
$270$		0			0
$271$	−49683.9	−	68384.0i	−0.676514	−	0.931142i	0.323371	−	0.946272i	$-0.395184\pi$
$271$	−49683.9	−	68384.0i	−0.676514	−	0.931142i	−0.999886	+	0.0151300i	$0.995184\pi$
$272$	−61612.3	+	84802.1i	−0.832779	+	1.14622i
$273$		0			0
$274$		−	91821.2i		−	1.22304i
$275$	−31205.3	−	23790.2i	−0.412633	−	0.314581i
$276$		0			0
$277$	−61673.2	+	20038.9i	−0.803780	+	0.261164i	−0.681961	−	0.731388i	$-0.738873\pi$
$277$	−61673.2	+	20038.9i	−0.803780	+	0.261164i	−0.121819	+	0.992552i	$0.538873\pi$
$278$	−80717.2	−	58644.5i	−1.04442	−	0.758818i
$279$		0			0
$280$	20115.1	−	61908.0i	0.256571	−	0.789643i
$281$	2764.86	+	898.357i	0.0350155	+	0.0113772i	0.326472	−	0.945207i	$-0.394140\pi$
$281$	2764.86	+	898.357i	0.0350155	+	0.0113772i	−0.291457	+	0.956584i	$0.594140\pi$
$282$		0			0
$283$	−82823.4	+	113997.i	−1.03414	+	1.42337i	−0.132350	+	0.991203i	$0.542252\pi$
$283$	−82823.4	+	113997.i	−1.03414	+	1.42337i	−0.901792	+	0.432171i	$0.857748\pi$
$284$	−894.678	−	2753.54i	−0.0110925	−	0.0341392i
$285$		0			0
$286$	−80159.4	+	55461.6i	−0.979992	+	0.678048i
$287$	20176.0			0.244946
$288$		0			0
$289$	20795.0	+	15108.4i	0.248979	+	0.180894i
$290$	71181.9	−	51716.6i	0.846395	−	0.614942i
$291$		0			0
$292$	−39995.8	−	12995.4i	−0.469082	−	0.152414i
$293$	39565.1	+	54456.7i	0.460868	+	0.634331i	0.974689	−	0.223567i	$-0.0717701\pi$
$293$	39565.1	+	54456.7i	0.460868	+	0.634331i	−0.513820	+	0.857898i	$0.671770\pi$
$294$		0			0
$295$	11624.7	+	35777.2i	0.133579	+	0.411114i
$296$		−	28728.5i		−	0.327891i
$297$		0			0
$298$	87069.6			0.980470
$299$	−67154.4	+	21819.8i	−0.751160	+	0.244067i
$300$		0			0
$301$	233764.	−	169840.i	2.58015	−	1.87459i
$302$	−8873.83	+	27310.8i	−0.0972965	+	0.299448i
$303$		0			0
$304$	50479.6	+	69479.2i	0.546221	+	0.751809i
$305$	−39365.0	+	54181.3i	−0.423166	+	0.582438i
$306$		0			0
$307$			85320.9i			0.905272i	0.891696	+	0.452636i	$0.149516\pi$
$307$			85320.9i			0.905272i	−0.891696	+	0.452636i	$0.850484\pi$
$308$	−59188.8	−	20752.0i	−0.623933	−	0.218755i
$309$		0			0
$310$	−42317.4	+	13749.8i	−0.440347	+	0.143078i
$311$	−24896.9	−	18088.7i	−0.257410	−	0.187019i	0.451594	−	0.892223i	$-0.350855\pi$
$311$	−24896.9	−	18088.7i	−0.257410	−	0.187019i	−0.709004	+	0.705204i	$0.750855\pi$
$312$		0			0
$313$	35139.2	−	108147.i	0.358677	−	1.10389i	−0.595170	−	0.803600i	$-0.702915\pi$
$313$	35139.2	−	108147.i	0.358677	−	1.10389i	0.953847	−	0.300294i	$-0.0970849\pi$
$314$	−103204.	−	33533.1i	−1.04674	−	0.340106i
$315$		0			0
$316$	30388.0	−	41825.5i	0.304318	−	0.418858i
$317$	−15305.0	−	47104.0i	−0.152306	−	0.468748i	0.845572	−	0.533861i	$-0.179259\pi$
$317$	−15305.0	−	47104.0i	−0.152306	−	0.468748i	−0.997878	+	0.0651126i	$0.979259\pi$
$318$		0			0
$319$	73944.5	+	106873.i	0.726649	+	1.05024i
$320$	25215.4			0.246244
$321$		0			0
$322$	−129861.	−	94349.8i	−1.25247	−	0.909975i
$323$	72398.3	−	52600.4i	0.693942	−	0.504178i
$324$		0			0
$325$	52594.5	+	17089.0i	0.497937	+	0.161789i
$326$	−70144.3	−	96545.3i	−0.660020	−	0.908439i
$327$		0			0
$328$	3475.51	+	10696.5i	0.0323051	+	0.0994248i
$329$			193706.i			1.78958i
$330$		0			0
$331$	−148612.			−1.35644			−0.678218	−	0.734861i	$-0.737247\pi$
$331$	−148612.			−1.35644			−0.678218	+	0.734861i	$0.737247\pi$
$332$	−1907.63	+	619.826i	−0.0173068	+	0.00562333i
$333$		0			0
$334$	−152308.	+	110659.i	−1.36531	+	0.991956i
$335$	375.543	−	1155.80i	0.00334634	−	0.0102990i
$336$		0			0
$337$	−64895.3	−	89320.7i	−0.571417	−	0.786489i	0.421304	−	0.906919i	$-0.361572\pi$
$337$	−64895.3	−	89320.7i	−0.571417	−	0.786489i	−0.992722	+	0.120431i	$0.961572\pi$
$338$	1440.47	−	1982.64i	0.0126088	−	0.0173545i
$339$		0			0
$340$			36201.6i			0.313163i
$341$	−18862.9	−	62957.0i	−0.162218	−	0.541421i
$342$		0			0
$343$	−150775.	+	48989.6i	−1.28156	+	0.416405i
$344$	130311.	+	94676.2i	1.10119	+	0.800063i
$345$		0			0
$346$	42682.9	−	131364.i	0.356535	−	1.09730i
$347$	−39953.7	−	12981.7i	−0.331816	−	0.107814i	0.138371	−	0.990381i	$-0.455813\pi$
$347$	−39953.7	−	12981.7i	−0.331816	−	0.107814i	−0.470187	+	0.882567i	$0.655813\pi$
$348$		0			0
$349$	55141.4	−	75895.7i	0.452717	−	0.623112i	−0.520261	−	0.854007i	$-0.674165\pi$
$349$	55141.4	−	75895.7i	0.452717	−	0.623112i	0.972979	+	0.230895i	$0.0741654\pi$
$350$	38848.2	+	119562.i	0.317128	+	0.976020i
$351$		0			0
$352$	2137.86	−	92710.9i	0.0172542	−	0.748248i
$353$	43599.5			0.349891			0.174945	−	0.984578i	$-0.444025\pi$
$353$	43599.5			0.349891			0.174945	+	0.984578i	$0.444025\pi$
$354$		0			0
$355$	6430.09	+	4671.74i	0.0510224	+	0.0370699i
$356$	27087.5	−	19680.2i	0.213732	−	0.155285i
$357$		0			0
$358$	−56808.7	−	18458.3i	−0.443250	−	0.144021i
$359$	115604.	+	159115.i	0.896979	+	1.23459i	0.971422	+	0.237361i	$0.0762823\pi$
$359$	115604.	+	159115.i	0.896979	+	1.23459i	−0.0744425	+	0.997225i	$0.523718\pi$
$360$		0			0
$361$	17614.5	+	54211.7i	0.135162	+	0.415986i
$362$		−	17636.5i		−	0.134584i
$363$		0			0
$364$	88394.5			0.667148
$365$	109797.	−	35675.2i	0.824146	−	0.267781i
$366$		0			0
$367$	152894.	−	111084.i	1.13516	−	0.824745i	0.148726	−	0.988878i	$-0.452483\pi$
$367$	152894.	−	111084.i	1.13516	−	0.824745i	0.986438	+	0.164134i	$0.0524829\pi$
$368$	40582.9	−	124901.i	0.299673	−	0.922298i
$369$		0			0
$370$	−30240.0	−	41621.8i	−0.220891	−	0.304031i
$371$	49356.4	−	67933.2i	0.358588	−	0.493554i
$372$		0			0
$373$		−	37487.8i		−	0.269447i	−0.990883	−	0.134723i	$-0.956985\pi$
$373$		−	37487.8i		−	0.269447i	0.990883	−	0.134723i	$-0.0430146\pi$
$374$	−188863.	−	4355.08i	−1.35022	−	0.0311353i
$375$		0			0
$376$	−102695.	+	33367.7i	−0.726399	+	0.236021i
$377$	−148176.	−	107656.i	−1.04255	−	0.757454i
$378$		0			0
$379$	−57580.9	+	177216.i	−0.400867	+	1.23374i	0.523430	+	0.852069i	$0.324652\pi$
$379$	−57580.9	+	177216.i	−0.400867	+	1.23374i	−0.924297	+	0.381673i	$0.875348\pi$
$380$	28208.7	+	9165.55i	0.195351	+	0.0634734i
$381$		0			0
$382$	−69488.8	+	95643.1i	−0.476199	+	0.655431i
$383$	37098.2	+	114176.i	0.252904	+	0.778357i	0.994235	+	0.107218i	$0.0341944\pi$
$383$	37098.2	+	114176.i	0.252904	+	0.778357i	−0.741332	+	0.671139i	$0.765806\pi$
$384$		0			0
$385$	164939.	−	49418.2i	1.11276	−	0.333400i
$386$	−124720.			−0.837072
$387$		0			0
$388$	−26873.4	−	19524.7i	−0.178509	−	0.129694i
$389$	102265.	−	74299.7i	0.675813	−	0.491007i	−0.196153	−	0.980573i	$-0.562845\pi$
$389$	102265.	−	74299.7i	0.675813	−	0.491007i	0.871966	+	0.489566i	$0.162845\pi$
$390$		0			0
$391$	−130149.	−	42287.9i	−0.851308	−	0.276607i
$392$	−116502.	−	160352.i	−0.758163	−	1.04352i
$393$		0			0
$394$	59110.0	+	181922.i	0.380775	+	1.17191i
$395$			141925.i			0.909630i
$396$		0			0
$397$	180759.			1.14688			0.573441	−	0.819247i	$-0.305608\pi$
$397$	180759.			1.14688			0.573441	+	0.819247i	$0.305608\pi$
$398$	−258586.	+	84019.5i	−1.63244	+	0.530413i
$399$		0			0
$400$	−83211.7	+	60456.8i	−0.520073	+	0.377855i
$401$	81129.4	−	249691.i	0.504533	−	1.55279i	−0.297022	−	0.954871i	$-0.595993\pi$
$401$	81129.4	−	249691.i	0.504533	−	1.55279i	0.801555	−	0.597922i	$-0.204007\pi$
$402$		0			0
$403$	54442.7	+	74934.0i	0.335220	+	0.461391i
$404$	75428.9	−	103819.i	0.462142	−	0.636084i
$405$		0			0
$406$		−	416365.i		−	2.52594i
$407$	62491.4	−	43237.2i	0.377252	−	0.261017i
$408$		0			0
$409$	3387.90	−	1100.80i	0.0202528	−	0.00658053i	−0.298873	−	0.954293i	$-0.596611\pi$
$409$	3387.90	−	1100.80i	0.0202528	−	0.00658053i	0.319126	+	0.947712i	$0.396611\pi$
$410$	16294.6	+	11838.8i	0.0969343	+	0.0704269i
$411$		0			0
$412$	−38480.6	+	118431.i	−0.226698	+	0.697704i
$413$	169305.	+	55010.4i	0.992587	+	0.322511i
$414$		0			0
$415$	3236.54	−	4454.72i	0.0187925	−	0.0258657i
$416$	40386.7	+	124298.i	0.233374	+	0.718251i
$417$		0			0
$418$	−51210.0	+	146061.i	−0.293091	+	0.835955i
$419$	−287386.			−1.63696			−0.818480	−	0.574536i	$-0.805183\pi$
$419$	−287386.			−1.63696			−0.818480	+	0.574536i	$0.805183\pi$
$420$		0			0
$421$	53082.6	+	38566.8i	0.299494	+	0.217595i	0.727375	−	0.686240i	$-0.240740\pi$
$421$	53082.6	+	38566.8i	0.299494	+	0.217595i	−0.427881	+	0.903835i	$0.640740\pi$
$422$	137927.	−	100210.i	0.774507	−	0.562713i
$423$		0			0
$424$	44517.7	+	14464.7i	0.247629	+	0.0804595i
$425$	62996.8	+	86707.7i	0.348771	+	0.480043i
$426$		0			0
$427$	97934.7	+	301412.i	0.537132	+	1.65312i
$428$			58361.2i			0.318593i
$429$		0			0
$430$	288452.			1.56004
$431$	12608.7	−	4096.81i	0.0678758	−	0.0220542i	−0.274882	−	0.961478i	$-0.588639\pi$
$431$	12608.7	−	4096.81i	0.0678758	−	0.0220542i	0.342758	+	0.939424i	$0.388639\pi$
$432$		0			0
$433$	−99830.2	+	72530.9i	−0.532459	+	0.386854i	−0.821277	−	0.570530i	$-0.806738\pi$
$433$	−99830.2	+	72530.9i	−0.532459	+	0.386854i	0.288818	+	0.957384i	$0.406738\pi$
$434$	−65066.5	+	200254.i	−0.345444	+	1.06317i
$435$		0			0
$436$	52103.3	+	71714.1i	0.274090	+	0.377252i
$437$	−65902.4	+	90706.8i	−0.345095	+	0.474982i
$438$		0			0
$439$		−	141451.i		−	0.733969i	−0.930227	−	0.366984i	$-0.880390\pi$
$439$		−	141451.i		−	0.733969i	0.930227	−	0.366984i	$-0.119610\pi$
$440$	54612.0	+	78931.4i	0.282087	+	0.407704i
$441$		0			0
$442$	253209.	−	82272.5i	1.29609	−	0.421124i
$443$	135201.	+	98229.4i	0.688927	+	0.500535i	0.876307	−	0.481753i	$-0.160000\pi$
$443$	135201.	+	98229.4i	0.688927	+	0.500535i	−0.187380	+	0.982287i	$0.560000\pi$
$444$		0			0
$445$	−28403.3	+	87416.5i	−0.143433	+	0.441442i
$446$	−23893.4	−	7763.42i	−0.120118	−	0.0390286i
$447$		0			0
$448$	70136.9	−	96535.2i	0.349455	−	0.480983i
$449$	−113077.	−	348015.i	−0.560894	−	1.72625i	−0.679847	−	0.733354i	$-0.737954\pi$
$449$	−113077.	−	348015.i	−0.560894	−	1.72625i	0.118953	−	0.992900i	$-0.462046\pi$
$450$		0			0
$451$	−18036.8	+	23658.7i	−0.0886759	+	0.116315i
$452$	100100.			0.489954
$453$		0			0
$454$	−71962.4	−	52283.7i	−0.349135	−	0.253662i
$455$	−196317.	+	142633.i	−0.948277	+	0.688963i
$456$		0			0
$457$	245995.	+	79928.6i	1.17786	+	0.382710i	0.831571	−	0.555418i	$-0.187442\pi$
$457$	245995.	+	79928.6i	1.17786	+	0.382710i	0.346289	+	0.938128i	$0.387442\pi$
$458$	33972.2	+	46758.8i	0.161954	+	0.222911i
$459$		0			0
$460$	−14015.9	−	43136.6i	−0.0662379	−	0.203859i
$461$			41493.9i			0.195246i	0.995223	+	0.0976231i	$0.0311240\pi$
$461$			41493.9i			0.195246i	−0.995223	+	0.0976231i	$0.968876\pi$
$462$		0			0
$463$	−300615.			−1.40232			−0.701161	−	0.713003i	$-0.747335\pi$
$463$	−300615.			−1.40232			−0.701161	+	0.713003i	$0.747335\pi$
$464$	323981.	−	105268.i	1.50481	−	0.488944i
$465$		0			0
$466$	−131972.	+	95883.6i	−0.607731	+	0.441542i
$467$	59962.3	−	184545.i	0.274944	−	0.846191i	−0.714290	−	0.699850i	$-0.753250\pi$
$467$	59962.3	−	184545.i	0.274944	−	0.846191i	0.989234	−	0.146341i	$-0.0467498\pi$
$468$		0			0
$469$	−3380.33	−	4652.62i	−0.0153679	−	0.0211520i
$470$	−113662.	+	156442.i	−0.514539	+	0.708203i
$471$		0			0
$472$			99234.8i			0.445431i
$473$	−9822.13	+	425948.i	−0.0439019	+	1.90386i
$474$		0			0
$475$	83513.1	−	27135.1i	0.370141	−	0.120266i
$476$	138595.	+	100695.i	0.611694	+	0.444422i
$477$		0			0
$478$	−90429.6	+	278314.i	−0.395781	+	1.21809i
$479$	−186339.	−	60545.2i	−0.812143	−	0.263881i	−0.126638	−	0.991949i	$-0.540419\pi$
$479$	−186339.	−	60545.2i	−0.812143	−	0.263881i	−0.685505	+	0.728068i	$0.740419\pi$
$480$		0			0
$481$	−62949.3	+	86642.3i	−0.272083	+	0.374490i
$482$	−14856.6	−	45723.9i	−0.0639478	−	0.196811i
$483$		0			0
$484$	77247.3	−	50854.1i	0.329756	−	0.217088i
$485$	91188.7			0.387666
$486$		0			0
$487$	−75098.9	−	54562.5i	−0.316647	−	0.230058i	0.418096	−	0.908403i	$-0.362697\pi$
$487$	−75098.9	−	54562.5i	−0.316647	−	0.230058i	−0.734743	+	0.678345i	$0.762697\pi$
$488$	−142927.	+	103842.i	−0.600170	+	0.436049i
$489$		0			0
$490$	−337577.	−	109686.i	−1.40599	−	0.456833i
$491$	73669.6	+	101398.i	0.305580	+	0.420595i	0.933997	−	0.357282i	$-0.116296\pi$
$491$	73669.6	+	101398.i	0.305580	+	0.420595i	−0.628416	+	0.777877i	$0.716296\pi$
$492$		0			0
$493$	−109690.	−	337592.i	−0.451310	−	1.38899i
$494$		−	218133.i		−	0.893855i
$495$		0			0
$496$	−172271.			−0.700245
$497$	35770.8	−	11622.6i	0.144816	−	0.0470535i
$498$		0			0
$499$	−64009.3	+	46505.5i	−0.257065	+	0.186768i	−0.708852	−	0.705357i	$-0.750787\pi$
$499$	−64009.3	+	46505.5i	−0.257065	+	0.186768i	0.451787	+	0.892126i	$0.350787\pi$
$500$	−32132.9	+	98894.9i	−0.128532	+	0.395580i
$501$		0			0
$502$	−12948.1	−	17821.6i	−0.0513807	−	0.0707195i
$503$	83399.6	−	114790.i	0.329631	−	0.453698i	−0.611746	−	0.791054i	$-0.709533\pi$
$503$	83399.6	−	114790.i	0.329631	−	0.453698i	0.941377	+	0.337356i	$0.109533\pi$
$504$		0			0
$505$			352285.i			1.38138i
$506$	226729.	−	67931.4i	0.885535	−	0.265320i
$507$		0			0
$508$	136486.	−	44347.1i	0.528886	−	0.171845i
$509$	207925.	+	151067.i	0.802549	+	0.583086i	0.911661	−	0.410943i	$-0.134801\pi$
$509$	207925.	+	151067.i	0.802549	+	0.583086i	−0.109112	+	0.994030i	$0.534801\pi$
$510$		0			0
$511$	168822.	−	519580.i	0.646528	−	1.98981i
$512$	−10407.7	−	3381.66i	−0.0397021	−	0.0129000i
$513$		0			0
$514$	144173.	−	198437.i	0.545704	−	0.751098i
$515$	−105637.	−	325118.i	−0.398293	−	1.22582i
$516$		0			0
$517$	−227143.	−	173168.i	−0.849802	−	0.647867i
$518$	−243459.			−0.907333
$519$		0			0
$520$	−109436.	−	79509.8i	−0.404718	−	0.294045i
$521$	14205.5	−	10320.9i	0.0523336	−	0.0380226i	−0.561311	−	0.827605i	$-0.689703\pi$
$521$	14205.5	−	10320.9i	0.0523336	−	0.0380226i	0.613645	+	0.789582i	$0.289703\pi$
$522$		0			0
$523$	415631.	+	135047.i	1.51951	+	0.493720i	0.945638	−	0.325221i	$-0.105439\pi$
$523$	415631.	+	135047.i	1.51951	+	0.493720i	0.573877	+	0.818942i	$0.305439\pi$
$524$	−39203.7	−	53959.3i	−0.142779	−	0.196519i
$525$		0			0
$526$	−101721.	−	313066.i	−0.367655	−	1.13152i
$527$			179509.i			0.646347i
$528$		0			0
$529$	−108388.			−0.387319
$530$	79723.1	−	25903.6i	0.283813	−	0.0922164i
$531$		0			0
$532$	113553.	−	82500.7i	0.401212	−	0.291497i
$533$	12956.2	−	39875.2i	0.0456062	−	0.140361i
$534$		0			0
$535$	−94171.3	−	129616.i	−0.329011	−	0.452845i
$536$	1884.35	−	2593.58i	0.00655890	−	0.00902756i
$537$		0			0
$538$			264416.i			0.913531i
$539$	173464.	−	494755.i	0.597080	−	1.70299i
$540$		0			0
$541$	−110980.	+	36059.5i	−0.379184	+	0.123204i	−0.492406	−	0.870365i	$-0.663883\pi$
$541$	−110980.	+	36059.5i	−0.379184	+	0.123204i	0.113223	+	0.993570i	$0.463883\pi$
$542$	−323050.	−	234710.i	−1.09969	−	0.798974i
$543$		0			0
$544$	−78271.6	+	240895.i	−0.264488	+	0.814012i
$545$	−231435.	−	75197.7i	−0.779176	−	0.253170i
$546$		0			0
$547$	44528.7	−	61288.6i	0.148822	−	0.204835i	−0.728097	−	0.685474i	$-0.759595\pi$
$547$	44528.7	−	61288.6i	0.148822	−	0.204835i	0.876919	+	0.480639i	$0.159595\pi$
$548$	−37940.7	−	116769.i	−0.126341	−	0.388837i
$549$		0			0
$550$	−174930.	−	61331.6i	−0.578282	−	0.202749i
$551$	−290827.			−0.957924
$552$		0			0
$553$	543350.	+	394767.i	1.77676	+	1.29089i
$554$	−247836.	+	180063.i	−0.807503	+	0.586686i
$555$		0			0
$556$	−126880.	−	41226.0i	−0.410436	−	0.133359i
$557$	−276701.	−	380846.i	−0.891866	−	1.22755i	−0.972991	−	0.230845i	$-0.925851\pi$
$557$	−276701.	−	380846.i	−0.891866	−	1.22755i	0.0811244	−	0.996704i	$-0.474149\pi$
$558$		0			0
$559$	−185551.	−	571069.i	−0.593801	−	1.82753i
$560$		−	451328.i		−	1.43918i
$561$		0			0
$562$	13733.5			0.0434820
$563$	−54157.2	+	17596.8i	−0.170860	+	0.0555157i	−0.393198	−	0.919454i	$-0.628631\pi$
$563$	−54157.2	+	17596.8i	−0.170860	+	0.0555157i	0.222338	+	0.974970i	$0.428631\pi$
$564$		0			0
$565$	−222313.	+	161520.i	−0.696415	+	0.505975i
$566$	−205699.	+	633077.i	−0.642095	+	1.97617i
$567$		0			0
$568$	12323.7	+	16962.2i	0.0381985	+	0.0525757i
$569$	238454.	−	328204.i	0.736513	−	1.01372i	−0.262299	−	0.964987i	$-0.584481\pi$
$569$	238454.	−	328204.i	0.736513	−	1.01372i	0.998812	−	0.0487362i	$-0.0155194\pi$
$570$		0			0
$571$		−	196880.i		−	0.603851i	−0.953331	−	0.301926i	$-0.902371\pi$
$571$		−	196880.i		−	0.603851i	0.953331	−	0.301926i	$-0.0976294\pi$
$572$	−79022.3	+	103653.i	−0.241522	+	0.316803i
$573$		0			0
$574$	90647.6	−	29453.2i	0.275127	−	0.0893941i
$575$	−108635.	−	78927.9i	−0.328574	−	0.238723i
$576$		0			0
$577$	78288.3	−	240947.i	0.235150	−	0.723718i	−0.761951	−	0.647634i	$-0.775759\pi$
$577$	78288.3	−	240947.i	0.235150	−	0.723718i	0.997101	−	0.0760833i	$-0.0242415\pi$
$578$	115484.	+	37523.2i	0.345675	+	0.112317i
$579$		0			0
$580$	69152.9	−	95180.8i	0.205567	−	0.282939i
$581$	−8052.08	−	24781.7i	−0.0238537	−	0.0734141i
$582$		0			0
$583$	35536.4	+	118607.i	0.104553	+	0.348957i
$584$	304543.			0.892941
$585$		0			0
$586$	257257.	+	186908.i	0.749155	+	0.544293i
$587$	−487020.	+	353841.i	−1.41342	+	1.02691i	−0.420605	+	0.907244i	$0.638182\pi$
$587$	−487020.	+	353841.i	−1.41342	+	1.02691i	−0.992814	+	0.119665i	$0.961818\pi$
$588$		0			0
$589$	139875.	+	45448.3i	0.403191	+	0.131005i
$590$	104456.	+	143772.i	0.300075	+	0.413018i
$591$		0			0
$592$	−61552.7	−	189440.i	−0.175632	−	0.540539i
$593$			165959.i			0.471945i	0.971760	+	0.235973i	$0.0758276\pi$
$593$			165959.i			0.471945i	−0.971760	+	0.235973i	$0.924172\pi$
$594$		0			0
$595$	−470290.			−1.32841
$596$	110727.	−	35977.3i	0.311717	−	0.101283i
$597$		0			0
$598$	−269862.	+	196066.i	−0.754639	+	0.548277i
$599$	−130232.	+	400814.i	−0.362965	+	1.11709i	0.588280	+	0.808657i	$0.299805\pi$
$599$	−130232.	+	400814.i	−0.362965	+	1.11709i	−0.951245	+	0.308435i	$0.900195\pi$
$600$		0			0
$601$	−118770.	−	163473.i	−0.328819	−	0.452581i	0.612315	−	0.790614i	$-0.290238\pi$
$601$	−118770.	−	163473.i	−0.328819	−	0.452581i	−0.941134	+	0.338033i	$0.890238\pi$
$602$	802333.	−	1.10432e6i	2.21392	−	3.04720i
$603$		0			0
$604$			38398.0i			0.105253i
$605$	−89502.3	+	237589.i	−0.244525	+	0.649105i
$606$		0			0
$607$	−69760.5	+	22666.5i	−0.189335	+	0.0615188i	−0.402150	−	0.915574i	$-0.631737\pi$
$607$	−69760.5	+	22666.5i	−0.189335	+	0.0615188i	0.212815	+	0.977093i	$0.431737\pi$
$608$	167891.	+	121980.i	0.454173	+	0.329976i
$609$		0			0
$610$	−97766.4	+	300894.i	−0.262742	+	0.808638i
$611$	382834.	+	124390.i	1.02548	+	0.333199i
$612$		0			0
$613$	38611.7	−	53144.4i	0.102754	−	0.141428i	−0.754544	−	0.656250i	$-0.772142\pi$
$613$	38611.7	−	53144.4i	0.102754	−	0.141428i	0.857297	+	0.514821i	$0.172142\pi$
$614$	124553.	+	383334.i	0.330382	+	1.01681i
$615$		0			0
$616$	454087.	+	10471.0i	1.19668	+	0.0275948i
$617$	300650.			0.789752			0.394876	−	0.918734i	$-0.370787\pi$
$617$	300650.			0.789752			0.394876	+	0.918734i	$0.370787\pi$
$618$		0			0
$619$	306255.	+	222508.i	0.799286	+	0.580715i	0.910705	−	0.413058i	$-0.135539\pi$
$619$	306255.	+	222508.i	0.799286	+	0.580715i	−0.111418	+	0.993774i	$0.535539\pi$
$620$	−48133.8	+	34971.2i	−0.125218	+	0.0909762i
$621$		0			0
$622$	−138264.	−	44924.8i	−0.357380	−	0.116120i
$623$	255663.	+	351890.i	0.658707	+	0.906632i
$624$		0			0
$625$	−25578.8	−	78723.3i	−0.0654816	−	0.201532i
$626$		−	537187.i		−	1.37081i
$627$		0			0
$628$	−145101.			−0.367918
$629$	−197399.	+	64138.7i	−0.498934	+	0.162113i
$630$		0			0
$631$	185813.	−	135001.i	0.466678	−	0.339061i	−0.329467	−	0.944167i	$-0.606869\pi$
$631$	185813.	−	135001.i	0.466678	−	0.339061i	0.796145	+	0.605106i	$0.206869\pi$
$632$	−115693.	+	356065.i	−0.289649	+	0.891447i
$633$		0			0
$634$	−137526.	−	189289.i	−0.342143	−	0.470920i
$635$	−231567.	+	318725.i	−0.574288	+	0.790439i
$636$		0			0
$637$			738883.i			1.82094i
$638$	488237.	+	372219.i	1.19947	+	0.914445i
$639$		0			0
$640$	315525.	−	102520.i	0.770324	−	0.250294i
$641$	449939.	+	326900.i	1.09506	+	0.795607i	0.980246	−	0.197780i	$-0.0633731\pi$
$641$	449939.	+	326900.i	1.09506	+	0.795607i	0.114813	+	0.993387i	$0.463373\pi$
$642$		0			0
$643$	−185375.	+	570525.i	−0.448362	+	1.37992i	0.430392	+	0.902642i	$0.358375\pi$
$643$	−185375.	+	570525.i	−0.448362	+	1.37992i	−0.878754	+	0.477275i	$0.841625\pi$
$644$	−204131.	−	66326.1i	−0.492195	−	0.159924i
$645$		0			0
$646$	248488.	−	342014.i	0.595443	−	0.819557i
$647$	114731.	+	353106.i	0.274077	+	0.843522i	0.989462	+	0.144792i	$0.0462513\pi$
$647$	114731.	+	353106.i	0.274077	+	0.843522i	−0.715385	+	0.698730i	$0.753749\pi$
$648$		0			0
$649$	−215860.	+	149352.i	−0.512487	+	0.354585i
$650$	261246.			0.618334
$651$		0			0
$652$	−129096.	−	93793.4i	−0.303680	−	0.220636i
$653$	342910.	−	249139.i	0.804182	−	0.584272i	−0.107956	−	0.994156i	$-0.534431\pi$
$653$	342910.	−	249139.i	0.804182	−	0.584272i	0.912138	+	0.409883i	$0.134431\pi$
$654$		0			0
$655$	174137.	+	56580.5i	0.405890	+	0.131881i
$656$	45836.0	+	63087.9i	0.106512	+	0.146601i
$657$		0			0
$658$	282775.	+	870291.i	0.653114	+	2.01008i
$659$		−	620818.i		−	1.42953i	−0.699364	−	0.714765i	$-0.746534\pi$
$659$		−	620818.i		−	1.42953i	0.699364	−	0.714765i	$-0.253466\pi$
$660$		0			0
$661$	69379.3			0.158791			0.0793957	−	0.996843i	$-0.474701\pi$
$661$	69379.3			0.158791			0.0793957	+	0.996843i	$0.474701\pi$
$662$	−667694.	+	216947.i	−1.52357	+	0.495037i
$663$		0			0
$664$	11751.3	−	8537.80i	0.0266532	−	0.0193647i
$665$	−119068.	+	366455.i	−0.269249	+	0.828662i
$666$		0			0
$667$	261406.	+	359795.i	0.587577	+	0.808730i
$668$	−147967.	+	203659.i	−0.331598	+	0.456406i
$669$		0			0
$670$		−	5741.08i		−	0.0127892i
$671$	−440992.	−	154614.i	−0.979457	−	0.343404i
$672$		0			0
$673$	−576094.	+	187184.i	−1.27193	+	0.413275i	−0.865731	−	0.500509i	$-0.833146\pi$
$673$	−576094.	+	187184.i	−1.27193	+	0.413275i	−0.406199	+	0.913785i	$0.633146\pi$
$674$	−421957.	−	306570.i	−0.928856	−	0.674853i
$675$		0			0
$676$	1012.63	−	3116.54i	0.00221593	−	0.00681993i
$677$	3154.20	+	1024.86i	0.00688196	+	0.00223608i	0.312456	−	0.949932i	$-0.398848\pi$
$677$	3154.20	+	1024.86i	0.00688196	+	0.00223608i	−0.305574	+	0.952168i	$0.598848\pi$
$678$		0			0
$679$	253643.	−	349109.i	0.550152	−	0.757220i
$680$	−81012.1	−	249330.i	−0.175199	−	0.539208i
$681$		0			0
$682$	−176654.	−	255320.i	−0.379799	−	0.548929i
$683$	−780979.			−1.67416			−0.837082	−	0.547078i	$-0.815740\pi$
$683$	−780979.			−1.67416			−0.837082	+	0.547078i	$0.815740\pi$
$684$		0			0
$685$	272682.	+	198115.i	0.581132	+	0.422217i
$686$	−605892.	+	440206.i	−1.28750	+	0.935423i
$687$		0			0
$688$	1.06214e6	+	345109.i	2.24390	+	0.729088i
$689$	−102566.	−	141171.i	−0.216056	−	0.297376i
$690$		0			0
$691$	−77230.0	−	237690.i	−0.161745	−	0.497799i	0.837037	−	0.547146i	$-0.184286\pi$
$691$	−77230.0	−	237690.i	−0.161745	−	0.497799i	−0.998782	+	0.0493473i	$0.984286\pi$
$692$		−	184694.i		−	0.385691i
$693$		0			0
$694$	−198457.			−0.412047
$695$	348313.	−	113174.i	0.721108	−	0.234302i
$696$		0			0
$697$	65738.4	−	47761.8i	0.135317	−	0.0983139i
$698$	136949.	−	421484.i	0.281091	−	0.865108i
$699$		0			0
$700$	98806.9	+	135996.i	0.201647	+	0.277543i
$701$	166024.	−	228512.i	0.337858	−	0.465022i	−0.605956	−	0.795498i	$-0.707209\pi$
$701$	166024.	−	228512.i	0.337858	−	0.465022i	0.943814	+	0.330476i	$0.107209\pi$
$702$		0			0
$703$			170054.i			0.344093i
$704$	50498.3	+	168544.i	0.101890	+	0.340069i
$705$		0			0
$706$	195886.	−	63647.3i	0.393002	−	0.127694i
$707$	1.34870e6	+	979887.i	2.69821	+	1.96037i
$708$		0			0
$709$	220763.	−	679440.i	0.439172	−	1.35163i	−0.449578	−	0.893241i	$-0.648426\pi$
$709$	220763.	−	679440.i	0.439172	−	1.35163i	0.888750	−	0.458392i	$-0.151574\pi$
$710$	35709.3	+	11602.7i	0.0708378	+	0.0230166i
$711$		0			0
$712$	−142518.	+	196159.i	−0.281132	+	0.386945i
$713$	−69499.4	−	213897.i	−0.136710	−	0.420752i
$714$		0			0
$715$	8248.70	−	357714.i	0.0161352	−	0.699720i
$716$	−79870.9			−0.155798
$717$		0			0
$718$	751668.	+	546119.i	1.45807	+	1.05935i
$719$	570512.	−	414501.i	1.10359	−	0.801804i	0.121946	−	0.992537i	$-0.461086\pi$
$719$	570512.	−	414501.i	1.10359	−	0.801804i	0.981642	+	0.190733i	$0.0610864\pi$
$720$		0			0
$721$	−1.53852e6	−	499896.i	−2.95960	−	0.961633i
$722$	158278.	+	217851.i	0.303631	+	0.417913i
$723$		0			0
$724$	−7287.42	−	22428.4i	−0.0139026	−	0.0427879i
$725$		−	348308.i		−	0.662655i
$726$		0			0
$727$	−348406.			−0.659200			−0.329600	−	0.944121i	$-0.606914\pi$
$727$	−348406.			−0.659200			−0.329600	+	0.944121i	$0.606914\pi$
$728$	−608795.	+	197810.i	−1.14870	+	0.373237i
$729$		0			0
$730$	441222.	−	320567.i	0.827964	−	0.601551i
$731$	359609.	−	1.10676e6i	0.672969	−	2.07119i
$732$		0			0
$733$	−298338.	−	410627.i	−0.555265	−	0.764257i	0.435450	−	0.900213i	$-0.356589\pi$
$733$	−298338.	−	410627.i	−0.555265	−	0.764257i	−0.990715	+	0.135956i	$0.956589\pi$
$734$	524768.	−	722281.i	0.974037	−	1.34065i
$735$		0			0
$736$		−	317347.i		−	0.585839i
$737$	8477.67	+	195.490i	0.0156078	+	0.000359907i
$738$		0			0
$739$	678298.	−	220392.i	1.24203	−	0.403559i	0.386970	−	0.922092i	$-0.373522\pi$
$739$	678298.	−	220392.i	1.24203	−	0.403559i	0.855058	+	0.518533i	$0.173522\pi$
$740$	−55654.6	−	40435.4i	−0.101634	−	0.0738412i
$741$		0			0
$742$	122581.	−	377265.i	0.222646	−	0.685234i
$743$	−887900.	−	288496.i	−1.60837	−	0.522592i	−0.639213	−	0.769030i	$-0.720740\pi$
$743$	−887900.	−	288496.i	−1.60837	−	0.522592i	−0.969159	+	0.246438i	$0.920740\pi$
$744$		0			0
$745$	−187863.	+	258571.i	−0.338476	+	0.465873i
$746$	−54725.4	−	168427.i	−0.0983356	−	0.302646i
$747$		0			0
$748$	−241977.	+	72500.2i	−0.432486	+	0.129579i
$749$	−758163.			−1.35145
$750$		0			0
$751$	−96880.7	−	70387.9i	−0.171774	−	0.124801i	0.498577	−	0.866846i	$-0.333856\pi$
$751$	−96880.7	−	70387.9i	−0.171774	−	0.124801i	−0.670351	+	0.742045i	$0.733856\pi$
$752$	−605695.	+	440063.i	−1.07107	+	0.778179i
$753$		0			0
$754$	−822891.	−	267374.i	−1.44744	−	0.470301i
$755$	−61958.8	−	85278.9i	−0.108695	−	0.149606i
$756$		0			0
$757$	−73308.6	−	225621.i	−0.127927	−	0.393720i	0.866496	−	0.499185i	$-0.166367\pi$
$757$	−73308.6	−	225621.i	−0.127927	−	0.393720i	−0.994423	+	0.105465i	$0.966367\pi$
$758$			880262.i			1.53205i
$759$		0			0
$760$	−214791.			−0.371868
$761$	−52489.3	+	17054.8i	−0.0906362	+	0.0294495i	−0.353984	−	0.935251i	$-0.615173\pi$
$761$	−52489.3	+	17054.8i	−0.0906362	+	0.0294495i	0.263348	+	0.964701i	$0.415173\pi$
$762$		0			0
$763$	−931628.	+	676868.i	−1.60027	+	1.16267i
$764$	−48849.3	+	150343.i	−0.0836897	+	0.257570i
$765$		0			0
$766$	333353.	+	458821.i	0.568129	+	0.781963i
$767$	217442.	−	299283.i	0.369617	−	0.508734i
$768$		0			0
$769$		−	73815.8i		−	0.124824i	−0.998050	−	0.0624118i	$-0.980121\pi$
$769$		−	73815.8i		−	0.124824i	0.998050	−	0.0624118i	$-0.0198792\pi$
$770$	668904.	−	462809.i	1.12819	−	0.780585i
$771$		0			0
$772$	−158608.	+	51534.7i	−0.266127	+	0.0864699i
$773$	−299959.	−	217933.i	−0.502000	−	0.364724i	0.307781	−	0.951457i	$-0.400414\pi$
$773$	−299959.	−	217933.i	−0.502000	−	0.364724i	−0.809780	+	0.586733i	$0.800414\pi$
$774$		0			0
$775$	−54431.1	+	167522.i	−0.0906241	+	0.278912i
$776$	228777.	+	74334.1i	0.379917	+	0.123442i
$777$		0			0
$778$	350997.	−	483105.i	0.579887	−	0.798146i
$779$	−20572.8	−	63316.4i	−0.0339014	−	0.104338i
$780$		0			0
$781$	−18349.2	+	52335.8i	−0.0300826	+	0.0858018i
$782$	−646472.			−1.05715
$783$		0			0
$784$	−1.11180e6	−	807768.i	−1.80881	−	1.31418i
$785$	322258.	−	234134.i	0.522955	−	0.379949i
$786$		0			0
$787$	−155067.	−	50384.2i	−0.250362	−	0.0813477i	0.181147	−	0.983456i	$-0.442019\pi$
$787$	−155067.	−	50384.2i	−0.250362	−	0.0813477i	−0.431510	+	0.902108i	$0.642019\pi$
$788$	150341.	+	206927.i	0.242117	+	0.333245i
$789$		0			0
$790$	207184.	+	637648.i	0.331973	+	1.02171i
$791$			1.30038e6i			2.07834i
$792$		0			0
$793$	658591.			1.04730
$794$	812122.	−	263875.i	1.28819	−	0.418559i
$795$		0			0
$796$	−294127.	+	213696.i	−0.464205	+	0.337264i
$797$	−135208.	+	416127.i	−0.212856	+	0.655103i	0.786443	+	0.617663i	$0.211920\pi$
$797$	−135208.	+	416127.i	−0.212856	+	0.655103i	−0.999299	+	0.0374401i	$0.988080\pi$
$798$		0			0
$799$	458552.	+	631143.i	0.718282	+	0.988630i
$800$	−146089.	+	201075.i	−0.228265	+	0.314179i
$801$		0			0
$802$		−	1.24026e6i		−	1.92825i
$803$	458346.	+	662454.i	0.710825	+	1.02737i
$804$		0			0
$805$	560382.	−	182079.i	0.864753	−	0.280975i
$806$	353993.	+	257191.i	0.544910	+	0.395900i
$807$		0			0
$808$	−287172.	+	883823.i	−0.439864	+	1.35376i
$809$	−58101.5	−	18878.3i	−0.0887750	−	0.0288447i	0.264293	−	0.964442i	$-0.414861\pi$
$809$	−58101.5	−	18878.3i	−0.0887750	−	0.0288447i	−0.353068	+	0.935598i	$0.614861\pi$
$810$		0			0
$811$	−121253.	+	166891.i	−0.184354	+	0.253741i	−0.891184	−	0.453642i	$-0.850124\pi$
$811$	−121253.	+	166891.i	−0.184354	+	0.253741i	0.706830	+	0.707383i	$0.250124\pi$
$812$	−172043.	−	529494.i	−0.260930	−	0.803061i
$813$		0			0
$814$	217646.	−	285484.i	0.328475	−	0.430857i
$815$	438055.			0.659498
$816$		0			0
$817$	−771354.	−	560422.i	−1.15561	−	0.839597i
$818$	13614.4	−	9891.44i	0.0203466	−	0.0147827i
$819$		0			0
$820$	25613.8	+	8322.42i	0.0380931	+	0.0123772i
$821$	−784252.	−	1.07943e6i	−1.16351	−	1.60143i	−0.697351	−	0.716730i	$-0.745638\pi$
$821$	−784252.	−	1.07943e6i	−1.16351	−	1.60143i	−0.466158	−	0.884702i	$-0.654362\pi$
$822$		0			0
$823$	−234287.	−	721062.i	−0.345899	−	1.06457i	−0.961101	−	0.276197i	$-0.910926\pi$
$823$	−234287.	−	721062.i	−0.345899	−	1.06457i	0.615202	−	0.788369i	$-0.289074\pi$
$824$		−	901777.i		−	1.32814i
$825$		0			0
$826$	840965.			1.23259
$827$	278305.	−	90426.7i	0.406920	−	0.132216i	−0.0984027	−	0.995147i	$-0.531373\pi$
$827$	278305.	−	90426.7i	0.406920	−	0.132216i	0.505323	+	0.862930i	$0.331373\pi$
$828$		0			0
$829$	413737.	−	300598.i	0.602027	−	0.437398i	−0.244571	−	0.969631i	$-0.578647\pi$
$829$	413737.	−	300598.i	0.602027	−	0.437398i	0.846598	+	0.532233i	$0.178647\pi$
$830$	8038.24	−	24739.2i	0.0116682	−	0.0359111i
$831$		0			0
$832$	−145750.	−	200608.i	−0.210553	−	0.289802i
$833$	−841705.	+	1.15851e6i	−1.21303	+	1.66959i
$834$		0			0
$835$		−	691070.i		−	0.991172i
$836$	−4771.16	+	206907.i	−0.00682672	+	0.296048i
$837$		0			0
$838$	−1.29118e6	+	419531.i	−1.83865	+	0.597415i
$839$	−507397.	−	368646.i	−0.720816	−	0.523703i	0.165829	−	0.986155i	$-0.446970\pi$
$839$	−507397.	−	368646.i	−0.720816	−	0.523703i	−0.886645	+	0.462451i	$0.846970\pi$
$840$		0			0
$841$	−137916.	+	424461.i	−0.194994	+	0.600130i
$842$	294793.	+	95784.0i	0.415808	+	0.135104i
$843$		0			0
$844$	133996.	−	184430.i	0.188108	−	0.258908i
$845$	2779.87	+	8555.56i	0.00389324	+	0.0119822i
$846$		0			0
$847$	660639.	+	1.00351e6i	0.920868	+	1.39880i
$848$	324548.			0.451322
$849$		0			0
$850$	409613.	+	297601.i	0.566938	+	0.411905i
$851$	210381.	−	152851.i	0.290501	−	0.211062i
$852$		0			0
$853$	−23954.7	−	7783.35i	−0.0329225	−	0.0106972i	0.292509	−	0.956263i	$-0.405510\pi$
$853$	−23954.7	−	7783.35i	−0.0329225	−	0.0106972i	−0.325432	+	0.945565i	$0.605510\pi$
$854$	880012.	+	1.21123e6i	1.20663	+	1.66078i
$855$		0			0
$856$	−130601.	−	401949.i	−0.178237	−	0.548559i
$857$			287947.i			0.392058i	0.980598	+	0.196029i	$0.0628047\pi$
$857$			287947.i			0.392058i	−0.980598	+	0.196029i	$0.937195\pi$
$858$		0			0
$859$	633150.			0.858065			0.429032	−	0.903289i	$-0.358855\pi$
$859$	633150.			0.858065			0.429032	+	0.903289i	$0.358855\pi$
$860$	366826.	−	119189.i	0.495978	−	0.161153i
$861$		0			0
$862$	50668.3	−	36812.7i	0.0681902	−	0.0495431i
$863$	−41338.2	+	127226.i	−0.0555047	+	0.170826i	−0.974966	−	0.222355i	$-0.928625\pi$
$863$	−41338.2	+	127226.i	−0.0555047	+	0.170826i	0.919461	+	0.393181i	$0.128625\pi$
$864$		0			0
$865$	298020.	+	410190.i	0.398303	+	0.548217i
$866$	−342641.	+	471604.i	−0.456881	+	0.628843i
$867$		0			0
$868$			281550.i			0.373694i
$869$	−948650.	+	284230.i	−1.25622	+	0.376384i
$870$		0			0
$871$	−11366.0	+	3693.04i	−0.0149821	+	0.00486797i
$872$	−519331.	−	377316.i	−0.682985	−	0.496218i
$873$		0			0
$874$	−163674.	+	503738.i	−0.214268	+	0.659450i
$875$	−1.28473e6	−	417434.i	−1.67801	−	0.545220i
$876$		0			0
$877$	139204.	−	191598.i	0.180989	−	0.249110i	−0.708877	−	0.705332i	$-0.750798\pi$
$877$	139204.	−	191598.i	0.180989	−	0.249110i	0.889866	+	0.456222i	$0.150798\pi$
$878$	−206493.	−	635519.i	−0.267865	−	0.824403i
$879$		0			0
$880$	529235.	+	403475.i	0.683413	+	0.521017i
$881$	−772779.			−0.995642			−0.497821	−	0.867280i	$-0.665866\pi$
$881$	−772779.			−0.995642			−0.497821	+	0.867280i	$0.665866\pi$
$882$		0			0
$883$	−739177.	−	537044.i	−0.948041	−	0.688792i	0.00230173	−	0.999997i	$-0.499267\pi$
$883$	−739177.	−	537044.i	−0.948041	−	0.688792i	−0.950343	+	0.311205i	$0.899267\pi$
$884$	288012.	−	209253.i	0.368558	−	0.267773i
$885$		0			0
$886$	750836.	+	243961.i	0.956483	+	0.310780i
$887$	216552.	+	298058.i	0.275242	+	0.378838i	0.924151	−	0.382028i	$-0.124774\pi$
$887$	216552.	+	298058.i	0.275242	+	0.378838i	−0.648909	+	0.760866i	$0.724774\pi$
$888$		0			0
$889$	576108.	+	1.77308e6i	0.728954	+	2.24349i
$890$			434213.i			0.548179i
$891$		0			0
$892$	−33593.1			−0.0422203
$893$	607890.	−	197515.i	0.762293	−	0.247684i
$894$		0			0
$895$	177387.	−	128879.i	0.221450	−	0.160893i
$896$	485146.	−	1.49313e6i	0.604305	−	1.85986i
$897$		0			0
$898$	−1.01607e6	−	1.39851e6i	−1.26001	−	1.73425i
$899$	342901.	−	471963.i	0.424277	−	0.583968i
$900$		0			0
$901$		−	338183.i		−	0.416584i
$902$	−46499.2	+	132625.i	−0.0571522	+	0.163010i
$903$		0			0
$904$	−689411.	+	224003.i	−0.843610	+	0.274105i
$905$	52375.0	+	38052.7i	0.0639480	+	0.0464610i
$906$		0			0
$907$	375369.	−	1.15527e6i	0.456293	−	1.40433i	−0.413317	−	0.910587i	$-0.635630\pi$
$907$	375369.	−	1.15527e6i	0.456293	−	1.40433i	0.869610	−	0.493739i	$-0.164370\pi$
$908$	−113119.	−	36754.5i	−0.137203	−	0.0445799i
$909$		0			0
$910$	−673806.	+	927414.i	−0.813677	+	1.11993i
$911$	−128438.	−	395293.i	−0.154760	−	0.476302i	0.843377	−	0.537323i	$-0.180564\pi$
$911$	−128438.	−	395293.i	−0.154760	−	0.476302i	−0.998136	+	0.0610211i	$0.980564\pi$
$912$		0			0
$913$	36257.8	+	12712.2i	0.0434971	+	0.0152503i
$914$	1.22190e6			1.46266
$915$		0			0
$916$	62523.4	+	45425.9i	0.0745164	+	0.0541393i
$917$	700978.	−	509291.i	0.833616	−	0.605657i
$918$		0			0
$919$	1.28887e6	+	418780.i	1.52608	+	0.495855i	0.947497	−	0.319766i	$-0.103604\pi$
$919$	1.28887e6	+	418780.i	1.52608	+	0.495855i	0.578587	+	0.815621i	$0.303604\pi$
$920$	193063.	+	265728.i	0.228099	+	0.313951i
$921$		0			0
$922$	60573.5	+	186426.i	0.0712559	+	0.219303i
$923$		−	78159.9i		−	0.0917446i
$924$		0			0
$925$	−203665.			−0.238030
$926$	−1.35062e6	+	438842.i	−1.57511	+	0.511783i
$927$		0			0
$928$	665953.	−	483843.i	0.773299	−	0.561835i
$929$	−375570.	+	1.15589e6i	−0.435171	+	1.33932i	0.457741	+	0.889085i	$0.348659\pi$
$929$	−375570.	+	1.15589e6i	−0.435171	+	1.33932i	−0.892912	+	0.450232i	$0.851341\pi$
$930$		0			0
$931$	689618.	+	949177.i	0.795626	+	1.09509i
$932$	−128211.	+	176467.i	−0.147602	+	0.203157i
$933$		0			0
$934$		−	916667.i		−	1.05079i
$935$	420427.	−	551470.i	0.480914	−	0.630810i
$936$		0			0
$937$	−401921.	+	130592.i	−0.457785	+	0.148744i	−0.528827	−	0.848730i	$-0.677368\pi$
$937$	−401921.	+	130592.i	−0.457785	+	0.148744i	0.0710412	+	0.997473i	$0.477368\pi$
$938$	−21979.3	−	15968.9i	−0.0249809	−	0.0181497i
$939$		0			0
$940$	−79902.0	+	245913.i	−0.0904278	+	0.278308i
$941$	984983.	+	320041.i	1.11237	+	0.361431i	0.806851	−	0.590754i	$-0.201170\pi$
$941$	984983.	+	320041.i	1.11237	+	0.361431i	0.305520	+	0.952186i	$0.401170\pi$
$942$		0			0
$943$	−59840.1	+	82362.8i	−0.0672928	+	0.0926206i
$944$	212617.	+	654369.i	0.238591	+	0.734309i
$945$		0			0
$946$	577676.	+	1.92806e6i	0.645509	+	2.15446i
$947$	−181714.			−0.202623			−0.101312	−	0.994855i	$-0.532304\pi$
$947$	−181714.			−0.202623			−0.101312	+	0.994855i	$0.532304\pi$
$948$		0			0
$949$	−918472.	−	667309.i	−1.01984	−	0.740959i
$950$	335600.	−	243828.i	0.371856	−	0.270169i
$951$		0			0
$952$	−1.17988e6	−	383365.i	−1.30186	−	0.422999i
$953$	715209.	+	984401.i	0.787494	+	1.08389i	0.994416	+	0.105535i	$0.0336556\pi$
$953$	715209.	+	984401.i	0.787494	+	1.08389i	−0.206921	+	0.978358i	$0.566344\pi$
$954$		0			0
$955$	−134102.	−	412722.i	−0.147037	−	0.452534i
$956$			391299.i			0.428147i
$957$		0			0
$958$	−925578.			−1.00851
$959$	1.51694e6	−	492882.i	1.64942	−	0.535928i
$960$		0			0
$961$	508468.	−	369424.i	0.550576	−	0.400017i
$962$	−156340.	+	481165.i	−0.168935	+	0.519929i
$963$		0			0
$964$	−37786.4	−	52008.5i	−0.0406613	−	0.0559655i
$965$	269099.	−	370382.i	0.288973	−	0.397737i
$966$		0			0
$967$			1.10152e6i			1.17798i	0.808140	+	0.588990i	$0.200474\pi$
$967$			1.10152e6i			1.17798i	−0.808140	+	0.588990i	$0.799526\pi$
$968$	−418220.	+	523110.i	−0.446328	+	0.558267i
$969$		0			0
$970$	409697.	−	133119.i	0.435431	−	0.141480i
$971$	−985107.	−	715722.i	−1.04483	−	0.759112i	−0.0736061	−	0.997287i	$-0.523451\pi$
$971$	−985107.	−	715722.i	−1.04483	−	0.759112i	−0.971222	+	0.238175i	$0.923451\pi$
$972$		0			0
$973$	535561.	−	1.64829e6i	0.565696	−	1.74103i
$974$	−417059.	−	135511.i	−0.439622	−	0.142842i
$975$		0			0
$976$	−719991.	+	990982.i	−0.755835	+	1.04032i
$977$	222343.	+	684302.i	0.232935	+	0.716900i	0.997389	+	0.0722216i	$0.0230089\pi$
$977$	222343.	+	684302.i	0.232935	+	0.716900i	−0.764454	+	0.644679i	$0.776991\pi$
$978$		0			0
$979$	−641189.	−	14785.5i	−0.668991	−	0.0154266i
$980$	−474621.			−0.494191
$981$		0			0
$982$	479008.	+	348020.i	0.496730	+	0.360895i
$983$	1.43944e6	−	1.04582e6i	1.48966	−	1.08230i	0.515378	−	0.856963i	$-0.327651\pi$
$983$	1.43944e6	−	1.04582e6i	1.48966	−	1.08230i	0.974281	−	0.225338i	$-0.0723486\pi$
$984$		0			0
$985$	−667791.	−	216978.i	−0.688285	−	0.223637i
$986$	−985645.	−	1.35662e6i	−1.01383	−	1.39542i
$987$		0			0
$988$	−90132.9	−	277400.i	−0.0923356	−	0.284180i
$989$			1.45801e6i			1.49062i
$990$		0			0
$991$	51647.2			0.0525895			0.0262948	−	0.999654i	$-0.491629\pi$
$991$	51647.2			0.0525895			0.0262948	+	0.999654i	$0.491629\pi$
$992$	−395907.	+	128638.i	−0.402318	+	0.130721i
$993$		0			0
$994$	143746.	−	104438.i	0.145487	−	0.105702i
$995$	308415.	−	949204.i	0.311522	−	0.958768i
$996$		0			0
$997$	456212.	+	627922.i	0.458962	+	0.631707i	0.974293	−	0.225284i	$-0.0723311\pi$
$997$	456212.	+	627922.i	0.458962	+	0.631707i	−0.515331	+	0.856991i	$0.672331\pi$
$998$	−219695.	+	302384.i	−0.220576	+	0.303597i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.5.k.c.28.7		32
3.2	odd	2		33.5.g.a.28.2	yes	32
11.2	odd	10	inner	99.5.k.c.46.7		32
33.2	even	10		33.5.g.a.13.2	✓	32
33.8	even	10		363.5.c.e.241.7		32
33.14	odd	10		363.5.c.e.241.26		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.g.a.13.2	✓	32	33.2	even	10
33.5.g.a.28.2	yes	32	3.2	odd	2
99.5.k.c.28.7		32	1.1	even	1	trivial
99.5.k.c.46.7		32	11.2	odd	10	inner
363.5.c.e.241.7		32	33.8	even	10
363.5.c.e.241.26		32	33.14	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.49285 - 1.45982i) q^{2} +(5.11038 - 3.71291i) q^{4} +(-5.35863 + 16.4922i) q^{5} +(48.2339 + 66.3883i) q^{7} +(-26.8877 + 37.0078i) q^{8} +O(q^{10})\)	\(q+(4.49285 - 1.45982i) q^{2} +(5.11038 - 3.71291i) q^{4} +(-5.35863 + 16.4922i) q^{5} +(48.2339 + 66.3883i) q^{7} +(-26.8877 + 37.0078i) q^{8} +81.9194i q^{10} +(-120.968 - 2.78945i) q^{11} +(162.182 - 52.6960i) q^{13} +(313.623 + 227.860i) q^{14} +(-98.0099 + 301.644i) q^{16} +(314.317 + 102.128i) q^{17} +(159.158 - 219.062i) q^{19} +(33.8493 + 104.177i) q^{20} +(-547.563 + 164.058i) q^{22} -414.069 q^{23} +(262.359 + 190.615i) q^{25} +(651.732 - 473.511i) q^{26} +(492.987 + 160.181i) q^{28} +(-631.311 - 868.925i) q^{29} +(167.845 + 516.573i) q^{31} +766.410i q^{32} +1561.27 q^{34} +(-1353.35 + 439.731i) q^{35} +(-508.083 + 369.144i) q^{37} +(395.283 - 1216.55i) q^{38} +(-466.257 - 641.748i) q^{40} +(144.517 - 198.911i) q^{41} -3521.17i q^{43} +(-628.549 + 434.888i) q^{44} +(-1860.35 + 604.465i) q^{46} +(1909.71 + 1387.48i) q^{47} +(-1338.94 + 4120.85i) q^{49} +(1457.00 + 473.410i) q^{50} +(633.155 - 871.463i) q^{52} +(-316.208 - 973.189i) q^{53} +(694.225 - 1980.07i) q^{55} -3753.79 q^{56} +(-4104.86 - 2982.35i) q^{58} +(1755.04 - 1275.11i) q^{59} +(3673.05 + 1193.45i) q^{61} +(1508.20 + 2075.86i) q^{62} +(-449.342 - 1382.93i) q^{64} +2957.10i q^{65} -70.0820 q^{67} +(1985.47 - 645.118i) q^{68} +(-5438.49 + 3951.29i) q^{70} +(141.635 - 435.908i) q^{71} +(-3913.19 - 5386.05i) q^{73} +(-1743.86 + 2400.22i) q^{74} -1710.43i q^{76} +(-5649.57 - 8165.39i) q^{77} +(7783.85 - 2529.13i) q^{79} +(-4449.55 - 3232.79i) q^{80} +(358.921 - 1104.64i) q^{82} +(-301.994 - 98.1237i) q^{83} +(-3368.61 + 4636.49i) q^{85} +(-5140.26 - 15820.1i) q^{86} +(3355.78 - 4401.75i) q^{88} +5300.49 q^{89} +(11321.1 + 8225.23i) q^{91} +(-2116.05 + 1537.40i) q^{92} +(10605.5 + 3445.93i) q^{94} +(2759.94 + 3798.73i) q^{95} +(-1625.00 - 5001.22i) q^{97} +20469.0i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8}+O(q^{10}) \) 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8	\( 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8} + 246 q^{11} - 510 q^{13} + 1290 q^{14} - 232 q^{16} - 2490 q^{17} + 582 q^{20} - 510 q^{22} + 2196 q^{23} - 370 q^{25} + 5226 q^{26} + 4310 q^{28} - 960 q^{29} + 1658 q^{31} - 2320 q^{34} - 1920 q^{35} + 1374 q^{37} - 12054 q^{38} + 11070 q^{40} - 9360 q^{41} + 4350 q^{44} - 12950 q^{46} + 3450 q^{47} - 11838 q^{49} + 11550 q^{50} - 19250 q^{52} + 2790 q^{53} + 12356 q^{55} + 5604 q^{56} + 9486 q^{58} - 2682 q^{59} - 17190 q^{61} + 39360 q^{62} + 16248 q^{64} + 2796 q^{67} - 68160 q^{68} + 18188 q^{70} - 132 q^{71} - 21790 q^{73} + 2130 q^{74} - 4542 q^{77} + 12270 q^{79} - 32346 q^{80} + 29442 q^{82} - 35430 q^{83} - 11990 q^{85} + 49416 q^{86} + 1176 q^{88} + 38748 q^{89} - 51858 q^{91} + 25590 q^{92} - 34510 q^{94} + 71670 q^{95} + 30306 q^{97}+O(q^{100}) \) 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8 + 246 * q^11 - 510 * q^13 + 1290 * q^14 - 232 * q^16 - 2490 * q^17 + 582 * q^20 - 510 * q^22 + 2196 * q^23 - 370 * q^25 + 5226 * q^26 + 4310 * q^28 - 960 * q^29 + 1658 * q^31 - 2320 * q^34 - 1920 * q^35 + 1374 * q^37 - 12054 * q^38 + 11070 * q^40 - 9360 * q^41 + 4350 * q^44 - 12950 * q^46 + 3450 * q^47 - 11838 * q^49 + 11550 * q^50 - 19250 * q^52 + 2790 * q^53 + 12356 * q^55 + 5604 * q^56 + 9486 * q^58 - 2682 * q^59 - 17190 * q^61 + 39360 * q^62 + 16248 * q^64 + 2796 * q^67 - 68160 * q^68 + 18188 * q^70 - 132 * q^71 - 21790 * q^73 + 2130 * q^74 - 4542 * q^77 + 12270 * q^79 - 32346 * q^80 + 29442 * q^82 - 35430 * q^83 - 11990 * q^85 + 49416 * q^86 + 1176 * q^88 + 38748 * q^89 - 51858 * q^91 + 25590 * q^92 - 34510 * q^94 + 71670 * q^95 + 30306 * q^97

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