LMFDB - Embedded newform 350.5.k.e.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,5,Mod(101,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("350.101");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	350.k (of order $6$, degree $2$, 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:	$36.1794870793$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			201.1
Character	$\chi$	$=$	350.201
Dual form			350.5.k.e.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 + 2.44949i) q^{2} +(10.8605 - 6.27030i) q^{3} +(-4.00000 - 6.92820i) q^{4} +35.4702i q^{6} +(37.0123 + 32.1106i) q^{7} +22.6274 q^{8} +(38.1334 - 66.0490i) q^{9} +O(q^{10})$	\(q+(-1.41421 + 2.44949i) q^{2} +(10.8605 - 6.27030i) q^{3} +(-4.00000 - 6.92820i) q^{4} +35.4702i q^{6} +(37.0123 + 32.1106i) q^{7} +22.6274 q^{8} +(38.1334 - 66.0490i) q^{9} +(3.60139 + 6.23778i) q^{11} +(-86.8839 - 50.1624i) q^{12} +292.752i q^{13} +(-130.998 + 45.2500i) q^{14} +(-32.0000 + 55.4256i) q^{16} +(106.471 - 61.4709i) q^{17} +(107.858 + 186.815i) q^{18} +(75.8198 + 43.7746i) q^{19} +(603.315 + 116.658i) q^{21} -20.3725 q^{22} +(-257.154 + 445.403i) q^{23} +(245.745 - 141.881i) q^{24} +(-717.094 - 414.014i) q^{26} +59.3570i q^{27} +(74.4194 - 384.871i) q^{28} -931.646 q^{29} +(-12.4789 + 7.20472i) q^{31} +(-90.5097 - 156.767i) q^{32} +(78.2256 + 45.1636i) q^{33} +347.732i q^{34} -610.135 q^{36} +(864.280 - 1496.98i) q^{37} +(-214.451 + 123.813i) q^{38} +(1835.65 + 3179.43i) q^{39} +2540.41i q^{41} +(-1138.97 + 1312.83i) q^{42} -410.931 q^{43} +(28.8111 - 49.9023i) q^{44} +(-727.340 - 1259.79i) q^{46} +(2631.70 + 1519.41i) q^{47} +802.599i q^{48} +(338.821 + 2376.97i) q^{49} +(770.882 - 1335.21i) q^{51} +(2028.25 - 1171.01i) q^{52} +(-994.156 - 1721.93i) q^{53} +(-145.394 - 83.9435i) q^{54} +(837.493 + 726.580i) q^{56} +1097.92 q^{57} +(1317.55 - 2282.06i) q^{58} +(3389.27 - 1956.80i) q^{59} +(4131.01 + 2385.04i) q^{61} -40.7560i q^{62} +(3532.28 - 1220.14i) q^{63} +512.000 q^{64} +(-221.255 + 127.742i) q^{66} +(-3824.99 - 6625.07i) q^{67} +(-851.766 - 491.767i) q^{68} +6449.73i q^{69} +1844.25 q^{71} +(862.860 - 1494.52i) q^{72} +(9178.65 - 5299.30i) q^{73} +(2444.55 + 4234.09i) q^{74} -700.394i q^{76} +(-67.0033 + 346.517i) q^{77} -10384.0 q^{78} +(-1890.26 + 3274.03i) q^{79} +(3460.99 + 5994.61i) q^{81} +(-6222.71 - 3592.68i) q^{82} +3661.83i q^{83} +(-1605.03 - 4646.52i) q^{84} +(581.144 - 1006.57i) q^{86} +(-10118.1 + 5841.71i) q^{87} +(81.4901 + 141.145i) q^{88} +(-129.635 - 74.8449i) q^{89} +(-9400.45 + 10835.4i) q^{91} +4114.46 q^{92} +(-90.3515 + 156.493i) q^{93} +(-7443.58 + 4297.55i) q^{94} +(-1965.96 - 1135.05i) q^{96} +12754.1i q^{97} +(-6301.54 - 2531.61i) q^{98} +549.333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 128 q^{4} + 516 q^{9}+O(q^{10}) $ 32 * q - 128 * q^4 + 516 * q^9	$ 32 q - 128 q^{4} + 516 q^{9} - 144 q^{11} - 96 q^{14} - 1024 q^{16} + 816 q^{19} + 1084 q^{21} - 768 q^{24} - 576 q^{26} - 912 q^{29} + 6468 q^{31} - 8256 q^{36} + 2424 q^{39} - 1152 q^{44} + 1664 q^{46} + 7712 q^{49} + 2708 q^{51} - 7776 q^{54} - 768 q^{56} - 3924 q^{59} + 41556 q^{61} + 16384 q^{64} - 15360 q^{66} - 53808 q^{71} + 6336 q^{74} + 24076 q^{79} + 17680 q^{81} + 19232 q^{84} + 6624 q^{86} + 41436 q^{89} + 12928 q^{91} - 62880 q^{94} + 6144 q^{96} - 101048 q^{99}+O(q^{100}) $ 32 * q - 128 * q^4 + 516 * q^9 - 144 * q^11 - 96 * q^14 - 1024 * q^16 + 816 * q^19 + 1084 * q^21 - 768 * q^24 - 576 * q^26 - 912 * q^29 + 6468 * q^31 - 8256 * q^36 + 2424 * q^39 - 1152 * q^44 + 1664 * q^46 + 7712 * q^49 + 2708 * q^51 - 7776 * q^54 - 768 * q^56 - 3924 * q^59 + 41556 * q^61 + 16384 * q^64 - 15360 * q^66 - 53808 * q^71 + 6336 * q^74 + 24076 * q^79 + 17680 * q^81 + 19232 * q^84 + 6624 * q^86 + 41436 * q^89 + 12928 * q^91 - 62880 * q^94 + 6144 * q^96 - 101048 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.41421	+	2.44949i	−0.353553	+	0.612372i
$2$	−1.41421	+	2.44949i	−0.353553	+	0.612372i
$3$	10.8605	−	6.27030i	1.20672	−	0.696700i	0.244679	−	0.969604i	$-0.421317\pi$
$3$	10.8605	−	6.27030i	1.20672	−	0.696700i	0.962041	+	0.272904i	$0.0879841\pi$
$4$	−4.00000	−	6.92820i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			35.4702i			0.985283i
$7$	37.0123	+	32.1106i	0.755353	+	0.655318i
$7$	37.0123	+	32.1106i	0.755353	+	0.655318i
$8$	22.6274			0.353553
$9$	38.1334	−	66.0490i	0.470783	−	0.815420i
$10$		0			0
$11$	3.60139	+	6.23778i	0.0297635	+	0.0515519i	0.880523	−	0.474003i	$-0.157191\pi$
$11$	3.60139	+	6.23778i	0.0297635	+	0.0515519i	−0.850760	+	0.525554i	$0.823858\pi$
$12$	−86.8839	−	50.1624i	−0.603360	−	0.348350i
$13$			292.752i			1.73226i	0.499816	+	0.866131i	$0.333401\pi$
$13$			292.752i			1.73226i	−0.499816	+	0.866131i	$0.666599\pi$
$14$	−130.998	+	45.2500i	−0.668356	+	0.230868i
$15$		0			0
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	106.471	−	61.4709i	0.368411	−	0.212702i	−0.304353	−	0.952559i	$-0.598440\pi$
$17$	106.471	−	61.4709i	0.368411	−	0.212702i	0.672764	+	0.739857i	$0.265107\pi$
$18$	107.858	+	186.815i	0.332894	+	0.576589i
$19$	75.8198	+	43.7746i	0.210027	+	0.121259i	0.601324	−	0.799005i	$-0.294640\pi$
$19$	75.8198	+	43.7746i	0.210027	+	0.121259i	−0.391297	+	0.920265i	$0.627973\pi$
$20$		0			0
$21$	603.315	+	116.658i	1.36806	+	0.264531i
$22$	−20.3725			−0.0420920
$23$	−257.154	+	445.403i	−0.486113	+	0.841972i	−0.999873	−	0.0159620i	$-0.994919\pi$
$23$	−257.154	+	445.403i	−0.486113	+	0.841972i	0.513760	+	0.857934i	$0.328252\pi$
$24$	245.745	−	141.881i	0.426640	−	0.246321i
$25$		0			0
$26$	−717.094	−	414.014i	−1.06079	−	0.612447i
$27$			59.3570i			0.0814225i
$28$	74.4194	−	384.871i	0.0949227	−	0.490907i
$29$	−931.646			−1.10778			−0.553892	−	0.832589i	$-0.686858\pi$
$29$	−931.646			−1.10778			−0.553892	+	0.832589i	$0.686858\pi$
$30$		0			0
$31$	−12.4789	+	7.20472i	−0.0129854	+	0.00749711i	−0.506479	−	0.862253i	$-0.669053\pi$
$31$	−12.4789	+	7.20472i	−0.0129854	+	0.00749711i	0.493493	+	0.869750i	$0.335720\pi$
$32$	−90.5097	−	156.767i	−0.0883883	−	0.153093i
$33$	78.2256	+	45.1636i	0.0718325	+	0.0414725i
$34$			347.732i			0.300806i
$35$		0			0
$36$	−610.135			−0.470783
$37$	864.280	−	1496.98i	0.631322	−	1.09348i	−0.355960	−	0.934501i	$-0.615846\pi$
$37$	864.280	−	1496.98i	0.631322	−	1.09348i	0.987282	−	0.158980i	$-0.0508207\pi$
$38$	−214.451	+	123.813i	−0.148512	+	0.0857433i
$39$	1835.65	+	3179.43i	1.20687	+	2.09036i
$40$		0			0
$41$			2540.41i			1.51125i	0.655005	+	0.755625i	$0.272667\pi$
$41$			2540.41i			1.51125i	−0.655005	+	0.755625i	$0.727333\pi$
$42$	−1138.97	+	1312.83i	−0.645674	+	0.744237i
$43$	−410.931			−0.222245			−0.111122	−	0.993807i	$-0.535445\pi$
$43$	−410.931			−0.222245			−0.111122	+	0.993807i	$0.535445\pi$
$44$	28.8111	−	49.9023i	0.0148818	−	0.0257760i
$45$		0			0
$46$	−727.340	−	1259.79i	−0.343734	−	0.595364i
$47$	2631.70	+	1519.41i	1.19136	+	0.687829i	0.958614	−	0.284709i	$-0.0918971\pi$
$47$	2631.70	+	1519.41i	1.19136	+	0.687829i	0.232741	+	0.972539i	$0.425230\pi$
$48$			802.599i			0.348350i
$49$	338.821	+	2376.97i	0.141117	+	0.989993i
$50$		0			0
$51$	770.882	−	1335.21i	0.296379	−	0.513344i
$52$	2028.25	−	1171.01i	0.750092	−	0.433066i
$53$	−994.156	−	1721.93i	−0.353918	−	0.613004i	0.633014	−	0.774140i	$-0.281818\pi$
$53$	−994.156	−	1721.93i	−0.353918	−	0.613004i	−0.986932	+	0.161136i	$0.948484\pi$
$54$	−145.394	−	83.9435i	−0.0498609	−	0.0287872i
$55$		0			0
$56$	837.493	+	726.580i	0.267058	+	0.231690i
$57$	1097.92			0.337926
$58$	1317.55	−	2282.06i	0.391661	−	0.678376i
$59$	3389.27	−	1956.80i	0.973649	−	0.562136i	0.0733020	−	0.997310i	$-0.476646\pi$
$59$	3389.27	−	1956.80i	0.973649	−	0.562136i	0.900347	+	0.435173i	$0.143313\pi$
$60$		0			0
$61$	4131.01	+	2385.04i	1.11019	+	0.640968i	0.938878	−	0.344250i	$-0.111867\pi$
$61$	4131.01	+	2385.04i	1.11019	+	0.640968i	0.171310	+	0.985217i	$0.445200\pi$
$62$		−	40.7560i		−	0.0106025i
$63$	3532.28	−	1220.14i	0.889966	−	0.307417i
$64$	512.000			0.125000
$65$		0			0
$66$	−221.255	+	127.742i	−0.0507933	+	0.0293255i
$67$	−3824.99	−	6625.07i	−0.852080	−	1.47585i	−0.879328	−	0.476217i	$-0.842008\pi$
$67$	−3824.99	−	6625.07i	−0.852080	−	1.47585i	0.0272481	−	0.999629i	$-0.491326\pi$
$68$	−851.766	−	491.767i	−0.184205	−	0.106351i
$69$			6449.73i			1.35470i
$70$		0			0
$71$	1844.25			0.365849			0.182925	−	0.983127i	$-0.441444\pi$
$71$	1844.25			0.365849			0.182925	+	0.983127i	$0.441444\pi$
$72$	862.860	−	1494.52i	0.166447	−	0.288294i
$73$	9178.65	−	5299.30i	1.72240	−	0.994426i	0.808479	−	0.588525i	$-0.200291\pi$
$73$	9178.65	−	5299.30i	1.72240	−	0.994426i	0.913917	−	0.405901i	$-0.133042\pi$
$74$	2444.55	+	4234.09i	0.446412	+	0.773208i
$75$		0			0
$76$		−	700.394i		−	0.121259i
$77$	−67.0033	+	346.517i	−0.0113009	+	0.0584445i
$78$	−10384.0			−1.70677
$79$	−1890.26	+	3274.03i	−0.302878	+	0.524600i	−0.976787	−	0.214215i	$-0.931281\pi$
$79$	−1890.26	+	3274.03i	−0.302878	+	0.524600i	0.673909	+	0.738815i	$0.264614\pi$
$80$		0			0
$81$	3460.99	+	5994.61i	0.527510	+	0.913674i
$82$	−6222.71	−	3592.68i	−0.925447	−	0.534307i
$83$			3661.83i			0.531547i	0.964035	+	0.265774i	$0.0856273\pi$
$83$			3661.83i			0.531547i	−0.964035	+	0.265774i	$0.914373\pi$
$84$	−1605.03	−	4646.52i	−0.227470	−	0.658520i
$85$		0			0
$86$	581.144	−	1006.57i	0.0785754	−	0.136097i
$87$	−10118.1	+	5841.71i	−1.33679	+	0.771794i
$88$	81.4901	+	141.145i	0.0105230	+	0.0182264i
$89$	−129.635	−	74.8449i	−0.0163660	−	0.00944892i	0.491795	−	0.870711i	$-0.336341\pi$
$89$	−129.635	−	74.8449i	−0.0163660	−	0.00944892i	−0.508161	+	0.861262i	$0.669674\pi$
$90$		0			0
$91$	−9400.45	+	10835.4i	−1.13518	+	1.30847i
$92$	4114.46			0.486113
$93$	−90.3515	+	156.493i	−0.0104465	+	0.0180938i
$94$	−7443.58	+	4297.55i	−0.842415	+	0.486369i
$95$		0			0
$96$	−1965.96	−	1135.05i	−0.213320	−	0.123160i
$97$			12754.1i			1.35552i	0.735284	+	0.677759i	$0.237049\pi$
$97$			12754.1i			1.35552i	−0.735284	+	0.677759i	$0.762951\pi$
$98$	−6301.54	−	2531.61i	−0.656137	−	0.263599i
$99$	549.333			0.0560486
$100$		0			0
$101$	−9960.79	+	5750.87i	−0.976453	+	0.563755i	−0.901197	−	0.433409i	$-0.857311\pi$
$101$	−9960.79	+	5750.87i	−0.976453	+	0.563755i	−0.0752554	+	0.997164i	$0.523977\pi$
$102$	2180.38	+	3776.54i	0.209572	+	0.362989i
$103$	6558.51	+	3786.56i	0.618203	+	0.356919i	0.776169	−	0.630525i	$-0.217160\pi$
$103$	6558.51	+	3786.56i	0.618203	+	0.356919i	−0.157966	+	0.987445i	$0.550494\pi$
$104$			6624.23i			0.612447i
$105$		0			0
$106$	5623.80			0.500516
$107$	3159.97	−	5473.23i	0.276004	−	0.478053i	−0.694384	−	0.719605i	$-0.744323\pi$
$107$	3159.97	−	5473.23i	0.276004	−	0.478053i	0.970388	+	0.241552i	$0.0776563\pi$
$108$	411.238	−	237.428i	0.0352570	−	0.0203556i
$109$	9805.80	+	16984.1i	0.825335	+	1.42952i	0.901663	+	0.432439i	$0.142347\pi$
$109$	9805.80	+	16984.1i	0.825335	+	1.42952i	−0.0763284	+	0.997083i	$0.524320\pi$
$110$		0			0
$111$		−	21677.2i		−	1.75937i
$112$	−2964.14	+	1023.89i	−0.236300	+	0.0816240i
$113$	−15860.1			−1.24208			−0.621039	−	0.783780i	$-0.713289\pi$
$113$	−15860.1			−1.24208			−0.621039	+	0.783780i	$0.713289\pi$
$114$	−1552.69	+	2689.34i	−0.119475	+	0.206936i
$115$		0			0
$116$	3726.59	+	6454.64i	0.276946	+	0.479685i
$117$	19336.0	+	11163.6i	1.41252	+	0.815520i
$118$			11069.3i			0.794981i
$119$	5914.59	+	1143.66i	0.417668	+	0.0807611i
$120$		0			0
$121$	7294.56	−	12634.5i	0.498228	−	0.862957i
$122$	−11684.3	+	6745.91i	−0.785022	+	0.453232i
$123$	15929.1	+	27590.1i	1.05289	+	1.82366i
$124$	99.8315	+	57.6378i	0.00649268	+	0.00374855i
$125$		0			0
$126$	−2006.67	+	10377.8i	−0.126397	+	0.653679i
$127$	−3905.57			−0.242146			−0.121073	−	0.992644i	$-0.538633\pi$
$127$	−3905.57			−0.242146			−0.121073	+	0.992644i	$0.538633\pi$
$128$	−724.077	+	1254.14i	−0.0441942	+	0.0765466i
$129$	−4462.91	+	2576.66i	−0.268187	+	0.154838i
$130$		0			0
$131$	−28422.1	−	16409.5i	−1.65620	−	0.956208i	−0.974444	−	0.224629i	$-0.927883\pi$
$131$	−28422.1	−	16409.5i	−1.65620	−	0.956208i	−0.681756	−	0.731579i	$-0.738784\pi$
$132$		−	722.617i		−	0.0414725i
$133$	1400.64	+	4054.82i	0.0791813	+	0.229228i
$134$	21637.4			1.20502
$135$		0			0
$136$	2409.16	−	1390.93i	0.130253	−	0.0752015i
$137$	−7241.86	−	12543.3i	−0.385842	−	0.668297i	0.606044	−	0.795431i	$-0.292756\pi$
$137$	−7241.86	−	12543.3i	−0.385842	−	0.668297i	−0.991886	+	0.127134i	$0.959422\pi$
$138$	−15798.5	−	9121.29i	−0.829581	−	0.478959i
$139$		−	20012.6i		−	1.03580i	−0.855442	−	0.517899i	$-0.826714\pi$
$139$		−	20012.6i		−	1.03580i	0.855442	−	0.517899i	$-0.173286\pi$
$140$		0			0
$141$	38108.8			1.91684
$142$	−2608.16	+	4517.46i	−0.129347	+	0.224036i
$143$	−1826.13	+	1054.31i	−0.0893015	+	0.0515582i
$144$	2440.54	+	4227.14i	0.117696	+	0.203855i
$145$		0			0
$146$			29977.3i			1.40633i
$147$	18584.1	+	23690.6i	0.860017	+	1.09633i
$148$	−13828.5			−0.631322
$149$	9030.06	−	15640.5i	0.406741	−	0.704496i	−0.587781	−	0.809020i	$-0.699998\pi$
$149$	9030.06	−	15640.5i	0.406741	−	0.704496i	0.994522	+	0.104524i	$0.0333318\pi$
$150$		0			0
$151$	8980.40	+	15554.5i	0.393860	+	0.682186i	0.992955	−	0.118492i	$-0.0378061\pi$
$151$	8980.40	+	15554.5i	0.393860	+	0.682186i	−0.599095	+	0.800678i	$0.704473\pi$
$152$	1715.61	+	990.506i	0.0742558	+	0.0428716i
$153$		−	9376.38i		−	0.400546i
$154$	−754.034	−	654.173i	−0.0317943	−	0.0275836i
$155$		0			0
$156$	14685.2	−	25435.5i	0.603434	−	1.04518i
$157$	−12733.6	+	7351.76i	−0.516598	+	0.298258i	−0.735542	−	0.677480i	$-0.763072\pi$
$157$	−12733.6	+	7351.76i	−0.516598	+	0.298258i	0.218944	+	0.975737i	$0.429739\pi$
$158$	−5346.47	−	9260.35i	−0.214167	−	0.370948i
$159$	−21594.0	−	12467.3i	−0.854160	−	0.493150i
$160$		0			0
$161$	−23820.0	+	8228.05i	−0.918946	+	0.317428i
$162$	−19578.3			−0.746012
$163$	7041.92	−	12197.0i	0.265043	−	0.459067i	−0.702532	−	0.711652i	$-0.747947\pi$
$163$	7041.92	−	12197.0i	0.265043	−	0.459067i	0.967575	+	0.252585i	$0.0812806\pi$
$164$	17600.5	−	10161.6i	0.654390	−	0.377812i
$165$		0			0
$166$	−8969.61	−	5178.61i	−0.325505	−	0.187930i
$167$		−	43007.4i		−	1.54209i	−0.636781	−	0.771045i	$-0.719734\pi$
$167$		−	43007.4i		−	1.54209i	0.636781	−	0.771045i	$-0.280266\pi$
$168$	13651.5	+	2639.67i	0.483682	+	0.0935258i
$169$	−57143.0			−2.00073
$170$		0			0
$171$	5782.54	−	3338.55i	0.197754	−	0.114174i
$172$	1643.72	+	2847.01i	0.0555612	+	0.0962348i
$173$	19743.2	+	11398.8i	0.659670	+	0.380860i	0.792151	−	0.610325i	$-0.208961\pi$
$173$	19743.2	+	11398.8i	0.659670	+	0.380860i	−0.132482	+	0.991185i	$0.542295\pi$
$174$		−	33045.7i		−	1.09148i
$175$		0			0
$176$	−460.977			−0.0148818
$177$	24539.4	−	42503.5i	0.783281	−	1.35668i
$178$	366.663	−	211.693i	0.0115725	−	0.00668139i
$179$	−6165.35	−	10678.7i	−0.192421	−	0.333283i	0.753631	−	0.657298i	$-0.228301\pi$
$179$	−6165.35	−	10678.7i	−0.192421	−	0.333283i	−0.946052	+	0.324015i	$0.894967\pi$
$180$		0			0
$181$			35555.8i			1.08531i	0.839956	+	0.542655i	$0.182581\pi$
$181$			35555.8i			1.08531i	−0.839956	+	0.542655i	$0.817419\pi$
$182$	−13247.1	−	38349.9i	−0.399923	−	1.15777i
$183$	59819.7			1.78625
$184$	−5818.72	+	10078.3i	−0.171867	+	0.297682i
$185$		0			0
$186$	−255.553	−	442.630i	−0.00738677	−	0.0127943i
$187$	766.884	+	442.761i	0.0219304	+	0.0126615i
$188$		−	24310.6i		−	0.687829i
$189$	−1905.99	+	2196.94i	−0.0533577	+	0.0615028i
$190$		0			0
$191$	26972.8	−	46718.3i	0.739366	−	1.28062i	−0.213416	−	0.976961i	$-0.568459\pi$
$191$	26972.8	−	46718.3i	0.739366	−	1.28062i	0.952781	−	0.303657i	$-0.0982078\pi$
$192$	5560.57	−	3210.40i	0.150840	−	0.0870875i
$193$	−1207.54	−	2091.52i	−0.0324181	−	0.0561497i	0.849361	−	0.527812i	$-0.176987\pi$
$193$	−1207.54	−	2091.52i	−0.0324181	−	0.0561497i	−0.881779	+	0.471662i	$0.843654\pi$
$194$	−31241.0	−	18037.0i	−0.830082	−	0.479248i
$195$		0			0
$196$	15112.9	−	11855.3i	0.393400	−	0.308604i
$197$	26051.4			0.671272			0.335636	−	0.941992i	$-0.391049\pi$
$197$	26051.4			0.671272			0.335636	+	0.941992i	$0.391049\pi$
$198$	−776.874	+	1345.58i	−0.0198162	+	0.0343226i
$199$	−1143.89	+	660.427i	−0.0288854	+	0.0166770i	−0.514373	−	0.857566i	$-0.671975\pi$
$199$	−1143.89	+	660.427i	−0.0288854	+	0.0166770i	0.485488	+	0.874243i	$0.338642\pi$
$200$		0			0
$201$	−83082.4	−	47967.6i	−2.05644	−	1.18729i
$202$		−	32531.8i		−	0.797270i
$203$	−34482.4	−	29915.7i	−0.836768	−	0.725951i
$204$	−12334.1			−0.296379
$205$		0			0
$206$	−18550.3	+	10710.0i	−0.437135	+	0.252380i
$207$	19612.3	+	33969.5i	0.457707	+	0.792772i
$208$	−16226.0	−	9368.08i	−0.375046	−	0.216533i
$209$			630.597i			0.0144364i
$210$		0			0
$211$	−5370.71			−0.120633			−0.0603166	−	0.998179i	$-0.519211\pi$
$211$	−5370.71			−0.120633			−0.0603166	+	0.998179i	$0.519211\pi$
$212$	−7953.25	+	13775.4i	−0.176959	+	0.306502i
$213$	20029.4	−	11564.0i	0.441478	−	0.254887i
$214$	8937.75	+	15480.6i	0.195164	+	0.338035i
$215$		0			0
$216$			1343.10i			0.0287872i
$217$	−693.222	−	134.043i	−0.0147215	−	0.00284658i
$218$	−55470.0			−1.16720
$219$	66456.4	−	115106.i	1.38563	−	2.39999i
$220$		0			0
$221$	17995.8	+	31169.6i	0.368456	+	0.638184i
$222$	53098.0	+	30656.2i	1.07739	+	0.622031i
$223$		−	63898.3i		−	1.28493i	−0.766315	−	0.642465i	$-0.777912\pi$
$223$		−	63898.3i		−	1.28493i	0.766315	−	0.642465i	$-0.222088\pi$
$224$	1683.92	−	8708.64i	0.0335603	−	0.173562i
$225$		0			0
$226$	22429.6	−	38849.1i	0.439141	−	0.760614i
$227$	21383.7	−	12345.9i	0.414984	−	0.239591i	−0.277945	−	0.960597i	$-0.589653\pi$
$227$	21383.7	−	12345.9i	0.414984	−	0.239591i	0.692929	+	0.721006i	$0.256320\pi$
$228$	−4391.68	−	7606.61i	−0.0844814	−	0.146326i
$229$	−29099.2	−	16800.4i	−0.554894	−	0.320368i	0.196199	−	0.980564i	$-0.437140\pi$
$229$	−29099.2	−	16800.4i	−0.554894	−	0.320368i	−0.751094	+	0.660196i	$0.770473\pi$
$230$		0			0
$231$	1445.08	+	4183.48i	0.0270812	+	0.0783995i
$232$	−21080.8			−0.391661
$233$	12902.8	−	22348.3i	0.237669	−	0.411655i	−0.722376	−	0.691500i	$-0.756950\pi$
$233$	12902.8	−	22348.3i	0.237669	−	0.411655i	0.960045	+	0.279846i	$0.0902834\pi$
$234$	−54690.5	+	31575.6i	−0.998803	+	0.576659i
$235$		0			0
$236$	−27114.2	−	15654.4i	−0.486824	−	0.281068i
$237$			47410.1i			0.844061i
$238$	−11165.9	+	12870.4i	−0.197124	+	0.227215i
$239$	31292.6			0.547830			0.273915	−	0.961754i	$-0.411681\pi$
$239$	31292.6			0.547830			0.273915	+	0.961754i	$0.411681\pi$
$240$		0			0
$241$	31606.1	−	18247.8i	0.544172	−	0.314178i	−0.202596	−	0.979262i	$-0.564938\pi$
$241$	31606.1	−	18247.8i	0.544172	−	0.314178i	0.746768	+	0.665084i	$0.231604\pi$
$242$	20632.1	+	35735.9i	0.352301	+	0.610203i
$243$	71012.3	+	40999.0i	1.20260	+	0.694321i
$244$		−	38160.6i		−	0.640968i
$245$		0			0
$246$	−90108.8			−1.48901
$247$	−12815.1	+	22196.4i	−0.210053	+	0.363822i
$248$	−282.366	+	163.024i	−0.00459102	+	0.00265063i
$249$	22960.8	+	39769.2i	0.370329	+	0.641429i
$250$		0			0
$251$		−	69357.1i		−	1.10089i	−0.834872	−	0.550444i	$-0.814458\pi$
$251$		−	69357.1i		−	1.10089i	0.834872	−	0.550444i	$-0.185542\pi$
$252$	−22582.5	−	19591.8i	−0.355607	−	0.308512i
$253$	−3704.44			−0.0578737
$254$	5523.31	−	9566.65i	0.0856114	−	0.148283i
$255$		0			0
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−95337.8	−	55043.3i	−1.44344	−	0.833371i	−0.445363	−	0.895350i	$-0.646925\pi$
$257$	−95337.8	−	55043.3i	−1.44344	−	0.833371i	−0.998077	+	0.0619795i	$0.980259\pi$
$258$		−	14575.8i		−	0.218974i
$259$	80057.8	−	27654.0i	1.19345	−	0.412248i
$260$		0			0
$261$	−35526.8	+	61534.3i	−0.521526	+	0.903309i
$262$	80389.7	−	46413.0i	1.17111	−	0.676141i
$263$	284.690	+	493.097i	0.00411586	+	0.00712888i	0.868076	−	0.496431i	$-0.165357\pi$
$263$	284.690	+	493.097i	0.00411586	+	0.00712888i	−0.863960	+	0.503560i	$0.832023\pi$
$264$	1770.04	+	1021.93i	0.0253966	+	0.0146627i
$265$		0			0
$266$	−11913.0	−	2303.53i	−0.168368	−	0.0325559i
$267$	−1877.20			−0.0263323
$268$	−30599.9	+	53000.6i	−0.426040	+	0.737923i
$269$	−49537.8	+	28600.7i	−0.684593	+	0.395250i	−0.801583	−	0.597883i	$-0.796009\pi$
$269$	−49537.8	+	28600.7i	−0.684593	+	0.395250i	0.116990	+	0.993133i	$0.462675\pi$
$270$		0			0
$271$	72714.2	+	41981.6i	0.990104	+	0.571637i	0.905305	−	0.424761i	$-0.139642\pi$
$271$	72714.2	+	41981.6i	0.990104	+	0.571637i	0.0847985	+	0.996398i	$0.472975\pi$
$272$			7868.28i			0.106351i
$273$	−34151.9	+	176622.i	−0.458237	+	2.36984i
$274$	40966.2			0.545663
$275$		0			0
$276$	44685.0	−	25798.9i	0.586602	−	0.338675i
$277$	−29181.1	−	50543.2i	−0.380314	−	0.658723i	0.610793	−	0.791790i	$-0.290851\pi$
$277$	−29181.1	−	50543.2i	−0.380314	−	0.658723i	−0.991107	+	0.133067i	$0.957517\pi$
$278$	49020.7	+	28302.1i	0.634294	+	0.366210i
$279$			1098.96i			0.0141180i
$280$		0			0
$281$	29284.0			0.370867			0.185434	−	0.982657i	$-0.440631\pi$
$281$	29284.0			0.370867			0.185434	+	0.982657i	$0.440631\pi$
$282$	−53893.9	+	93347.0i	−0.677707	+	1.17382i
$283$	−111333.	+	64277.9i	−1.39011	+	0.802581i	−0.993327	−	0.115332i	$-0.963207\pi$
$283$	−111333.	+	64277.9i	−1.39011	+	0.802581i	−0.396783	+	0.917912i	$0.629874\pi$
$284$	−7376.98	−	12777.3i	−0.0914623	−	0.158417i
$285$		0			0
$286$		−	5964.10i		−	0.0729144i
$287$	−81574.0	+	94026.4i	−0.990349	+	1.14153i
$288$	−13805.8			−0.166447
$289$	−34203.2	+	59241.6i	−0.409516	+	0.709302i
$290$		0			0
$291$	79971.9	+	138515.i	0.944390	+	1.63573i
$292$	−73429.2	−	42394.4i	−0.861198	−	0.497213i
$293$		−	127398.i		−	1.48398i	−0.670411	−	0.741990i	$-0.733882\pi$
$293$		−	127398.i		−	1.48398i	0.670411	−	0.741990i	$-0.266118\pi$
$294$	−84311.7	+	12018.1i	−0.975423	+	0.139040i
$295$		0			0
$296$	19556.4	−	33872.7i	0.223206	−	0.386604i
$297$	−370.256	+	213.768i	−0.00419749	+	0.00242342i
$298$	25540.9	+	44238.1i	0.287609	+	0.498154i
$299$	−130393.	−	75282.4i	−1.45852	−	0.842075i
$300$		0			0
$301$	−15209.5	−	13195.2i	−0.167873	−	0.145641i
$302$	−50800.8			−0.557002
$303$	−72119.4	+	124914.i	−0.785537	+	1.36059i
$304$	−4852.47	+	2801.57i	−0.0525068	+	0.0303148i
$305$		0			0
$306$	22967.3	+	13260.2i	0.245283	+	0.141614i
$307$			63793.8i			0.676865i	0.940991	+	0.338432i	$0.109897\pi$
$307$			63793.8i			0.676865i	−0.940991	+	0.338432i	$0.890103\pi$
$308$	2668.76	−	921.857i	0.0281324	−	0.00971767i
$309$	94971.5			0.994664
$310$		0			0
$311$	−17599.8	+	10161.2i	−0.181964	+	0.105057i	−0.588215	−	0.808704i	$-0.700169\pi$
$311$	−17599.8	+	10161.2i	−0.181964	+	0.105057i	0.406251	+	0.913762i	$0.366836\pi$
$312$	41535.9	+	71942.4i	0.426692	+	0.739053i
$313$	84037.5	+	48519.0i	0.857796	+	0.495249i	0.863274	−	0.504736i	$-0.168410\pi$
$313$	84037.5	+	48519.0i	0.857796	+	0.495249i	−0.00547733	+	0.999985i	$0.501743\pi$
$314$		−	41587.8i		−	0.421800i
$315$		0			0
$316$	30244.2			0.302878
$317$	10673.4	−	18486.9i	0.106215	−	0.183969i	−0.808019	−	0.589156i	$-0.799460\pi$
$317$	10673.4	−	18486.9i	0.106215	−	0.183969i	0.914234	+	0.405187i	$0.132794\pi$
$318$	61077.1	−	35262.9i	0.603983	−	0.348710i
$319$	−3355.22	−	5811.41i	−0.0329716	−	0.0571084i
$320$		0			0
$321$		−	79255.9i		−	0.769169i
$322$	13532.1	−	69983.1i	0.130513	−	0.674965i
$323$	10763.5			0.103168
$324$	27687.9	−	47956.9i	0.263755	−	0.456837i
$325$		0			0
$326$	19917.6	+	34498.2i	0.187414	+	0.324610i
$327$	212992.	+	122971.i	1.99190	+	1.15002i
$328$			57482.9i			0.534307i
$329$	48616.1	+	140743.i	0.449147	+	1.30027i
$330$		0			0
$331$	−29010.4	+	50247.5i	−0.264788	+	0.458626i	−0.967508	−	0.252841i	$-0.918635\pi$
$331$	−29010.4	+	50247.5i	−0.264788	+	0.458626i	0.702720	+	0.711466i	$0.251969\pi$
$332$	25369.9	−	14647.3i	0.230167	−	0.132887i
$333$	−65915.9	−	114170.i	−0.594431	−	1.02958i
$334$	105346.	+	60821.6i	0.944334	+	0.545211i
$335$		0			0
$336$	−25771.9	+	29706.0i	−0.228280	+	0.263127i
$337$	−98548.0			−0.867737			−0.433869	−	0.900976i	$-0.642852\pi$
$337$	−98548.0			−0.867737			−0.433869	+	0.900976i	$0.642852\pi$
$338$	80812.4	−	139971.i	0.707367	−	1.22519i
$339$	−172248.	+	99447.6i	−1.49884	+	0.865356i
$340$		0			0
$341$	−89.8830	−	51.8940i	−0.000772981	−	0.000446281i
$342$			18885.7i			0.161466i
$343$	−63785.4	+	98857.0i	−0.542167	+	0.840271i
$344$	−9298.30			−0.0785754
$345$		0			0
$346$	−55842.3	+	32240.6i	−0.466457	+	0.269309i
$347$	−22955.5	−	39760.1i	−0.190646	−	0.330209i	0.754818	−	0.655934i	$-0.227725\pi$
$347$	−22955.5	−	39760.1i	−0.190646	−	0.330209i	−0.945465	+	0.325725i	$0.894392\pi$
$348$	80945.0	+	46733.6i	0.668393	+	0.385897i
$349$		−	14058.4i		−	0.115421i	−0.998333	−	0.0577104i	$-0.981620\pi$
$349$		−	14058.4i		−	0.115421i	0.998333	−	0.0577104i	$-0.0183800\pi$
$350$		0			0
$351$	−17376.9			−0.141045
$352$	651.921	−	1129.16i	0.00526150	−	0.00911318i
$353$	11625.3	−	6711.88i	0.0932944	−	0.0538635i	−0.452627	−	0.891700i	$-0.649513\pi$
$353$	11625.3	−	6711.88i	0.0932944	−	0.0538635i	0.545921	+	0.837836i	$0.316180\pi$
$354$	69407.9	+	120218.i	0.553863	+	0.959320i
$355$		0			0
$356$			1197.52i			0.00944892i
$357$	71406.4	−	24665.6i	0.560274	−	0.193533i
$358$	34876.5			0.272124
$359$	−48550.5	+	84091.9i	−0.376708	+	0.652477i	−0.990581	−	0.136927i	$-0.956277\pi$
$359$	−48550.5	+	84091.9i	−0.376708	+	0.652477i	0.613873	+	0.789405i	$0.289611\pi$
$360$		0			0
$361$	−61328.1	−	106223.i	−0.470592	−	0.815090i
$362$	−87093.7	−	50283.6i	−0.664614	−	0.383715i
$363$		−	182956.i		−	1.38846i
$364$	112672.	+	21786.5i	0.850380	+	0.164431i
$365$		0			0
$366$	−84597.8	+	146528.i	−0.631534	+	1.09385i
$367$	−10108.4	+	5836.08i	−0.0750499	+	0.0433301i	−0.537055	−	0.843547i	$-0.680463\pi$
$367$	−10108.4	+	5836.08i	−0.0750499	+	0.0433301i	0.462005	+	0.886877i	$0.347130\pi$
$368$	−16457.8	−	28505.8i	−0.121528	−	0.210493i
$369$	167792.	+	96874.5i	1.23230	+	0.711470i
$370$		0			0
$371$	18496.1	−	95655.5i	0.134379	−	0.694963i
$372$	1445.62			0.0104465
$373$	98875.9	−	171258.i	0.710678	−	1.23093i	−0.253925	−	0.967224i	$-0.581722\pi$
$373$	98875.9	−	171258.i	0.710678	−	1.23093i	0.964603	−	0.263707i	$-0.0849451\pi$
$374$	−2169.08	+	1252.32i	−0.0155071	+	0.00895305i
$375$		0			0
$376$	59548.7	+	34380.4i	0.421208	+	0.243184i
$377$		−	272742.i		−	1.91897i
$378$	−2685.91	−	7775.64i	−0.0187978	−	0.0544193i
$379$	8503.45			0.0591993			0.0295997	−	0.999562i	$-0.490577\pi$
$379$	8503.45			0.0591993			0.0295997	+	0.999562i	$0.490577\pi$
$380$		0			0
$381$	−42416.4	+	24489.1i	−0.292202	+	0.168703i
$382$	76290.6	+	132139.i	0.522810	+	0.905534i
$383$	−199342.	−	115090.i	−1.35894	−	0.784584i	−0.369459	−	0.929247i	$-0.620457\pi$
$383$	−199342.	−	115090.i	−1.35894	−	0.784584i	−0.989481	+	0.144663i	$0.953790\pi$
$384$			18160.7i			0.123160i
$385$		0			0
$386$	6830.88			0.0458461
$387$	−15670.2	+	27141.6i	−0.104629	+	0.181223i
$388$	88362.8	−	51016.3i	0.586956	−	0.338879i
$389$	40004.1	+	69289.1i	0.264366	+	0.457895i	0.967397	−	0.253264i	$-0.0815041\pi$
$389$	40004.1	+	69289.1i	0.264366	+	0.457895i	−0.703032	+	0.711159i	$0.748171\pi$
$390$		0			0
$391$			63229.9i			0.413589i
$392$	7666.65	+	53784.8i	0.0498923	+	0.350015i
$393$	−411570.			−2.66476
$394$	−36842.3	+	63812.7i	−0.237331	+	0.411069i
$395$		0			0
$396$	−2197.33	−	3805.89i	−0.0140122	−	0.0242698i
$397$	−41319.0	−	23855.6i	−0.262162	−	0.151359i	0.363159	−	0.931727i	$-0.381698\pi$
$397$	−41319.0	−	23855.6i	−0.262162	−	0.151359i	−0.625320	+	0.780368i	$0.715032\pi$
$398$		−	3735.94i		−	0.0235849i
$399$	40636.6	+	35254.9i	0.255253	+	0.221449i
$400$		0			0
$401$	−27054.9	+	46860.4i	−0.168251	+	0.291419i	−0.937805	−	0.347163i	$-0.887145\pi$
$401$	−27054.9	+	46860.4i	−0.168251	+	0.291419i	0.769554	+	0.638582i	$0.220478\pi$
$402$	234993.	−	135673.i	1.45413	−	0.839540i
$403$	−2109.20	−	3653.24i	−0.0129870	−	0.0224941i
$404$	79686.4	+	46006.9i	0.488226	+	0.281878i
$405$		0			0
$406$	122044.	−	42157.0i	0.740394	−	0.255751i
$407$	12450.4			0.0751615
$408$	17443.1	−	30212.3i	0.104786	−	0.181494i
$409$	157861.	−	91141.0i	0.943687	−	0.544838i	0.0525726	−	0.998617i	$-0.483258\pi$
$409$	157861.	−	91141.0i	0.943687	−	0.544838i	0.891114	+	0.453779i	$0.149925\pi$
$410$		0			0
$411$	−157300.	−	90817.3i	−0.931206	−	0.537632i
$412$		−	60584.9i		−	0.356919i
$413$	188279.	+	36405.9i	1.10383	+	0.213438i
$414$	−110944.			−0.647296
$415$		0			0
$416$	45894.0	−	26496.9i	0.265198	−	0.153112i
$417$	−125485.	−	217347.i	−0.721640	−	1.24992i
$418$	−1544.64	−	891.799i	−0.00884046	−	0.00510404i
$419$			50823.7i			0.289493i	0.989469	+	0.144746i	$0.0462366\pi$
$419$			50823.7i			0.289493i	−0.989469	+	0.144746i	$0.953763\pi$
$420$		0			0
$421$	10731.4			0.0605471			0.0302735	−	0.999542i	$-0.490362\pi$
$421$	10731.4			0.0605471			0.0302735	+	0.999542i	$0.490362\pi$
$422$	7595.33	−	13155.5i	0.0426503	−	0.0738725i
$423$	200712.	−	115881.i	1.12174	−	0.647636i
$424$	−22495.2	−	38962.8i	−0.125129	−	0.216730i
$425$		0			0
$426$			65415.7i			0.360465i
$427$	76313.2	+	220925.i	0.418547	+	1.21168i
$428$	−50559.6			−0.276004
$429$	−13221.7	+	22900.7i	−0.0718413	+	0.124433i
$430$		0			0
$431$	−41981.9	−	72714.7i	−0.225999	−	0.391442i	0.730619	−	0.682785i	$-0.239231\pi$
$431$	−41981.9	−	72714.7i	−0.225999	−	0.391442i	−0.956619	+	0.291343i	$0.905898\pi$
$432$	−3289.90	−	1899.42i	−0.0176285	−	0.0101778i
$433$			7149.73i			0.0381342i	0.999818	+	0.0190671i	$0.00606961\pi$
$433$			7149.73i			0.0381342i	−0.999818	+	0.0190671i	$0.993930\pi$
$434$	1308.70	−	1508.48i	0.00694801	−	0.00800864i
$435$		0			0
$436$	78446.4	−	135873.i	0.412667	−	0.714761i
$437$	−38994.7	+	22513.6i	−0.204194	+	0.117891i
$438$	187967.	+	325568.i	0.979791	+	1.69705i
$439$	219582.	+	126775.i	1.13938	+	0.657819i	0.946276	−	0.323361i	$-0.104813\pi$
$439$	219582.	+	126775.i	1.13938	+	0.657819i	0.193099	+	0.981179i	$0.438146\pi$
$440$		0			0
$441$	169917.	+	68263.3i	0.873695	+	0.351002i
$442$	−101799.			−0.521075
$443$	35703.2	−	61839.7i	0.181928	−	0.315108i	−0.760609	−	0.649210i	$-0.775100\pi$
$443$	35703.2	−	61839.7i	0.181928	−	0.315108i	0.942537	+	0.334102i	$0.108433\pi$
$444$	−150184.	+	86708.7i	−0.761829	+	0.439842i
$445$		0			0
$446$	156518.	+	90365.8i	0.786855	+	0.454291i
$447$		−	226485.i		−	1.13351i
$448$	18950.3	+	16440.6i	0.0944191	+	0.0819147i
$449$	−315051.			−1.56275			−0.781373	−	0.624064i	$-0.785480\pi$
$449$	−315051.			−1.56275			−0.781373	+	0.624064i	$0.785480\pi$
$450$		0			0
$451$	−15846.5	+	9149.00i	−0.0779078	+	0.0449801i
$452$	63440.4	+	109882.i	0.310520	+	0.537836i
$453$	195063.	+	112620.i	0.950558	+	0.548805i
$454$			69838.9i			0.338833i
$455$		0			0
$456$	24843.1			0.119475
$457$	34703.6	−	60108.5i	0.166166	−	0.287808i	−0.770903	−	0.636953i	$-0.780195\pi$
$457$	34703.6	−	60108.5i	0.166166	−	0.287808i	0.937069	+	0.349145i	$0.113528\pi$
$458$	82305.0	−	47518.8i	0.392370	−	0.226535i
$459$	3648.73	+	6319.79i	0.0173187	+	0.0299969i
$460$		0			0
$461$			166851.i			0.785104i	0.919730	+	0.392552i	$0.128408\pi$
$461$			166851.i			0.785104i	−0.919730	+	0.392552i	$0.871592\pi$
$462$	−12291.0	−	2376.62i	−0.0575844	−	0.0111346i
$463$	−166871.			−0.778429			−0.389214	−	0.921147i	$-0.627253\pi$
$463$	−166871.			−0.778429			−0.389214	+	0.921147i	$0.627253\pi$
$464$	29812.7	−	51637.1i	0.138473	−	0.239842i
$465$		0			0
$466$	36494.6	+	63210.6i	0.168057	+	0.291084i
$467$	158090.	+	91273.3i	0.724888	+	0.418514i	0.816549	−	0.577276i	$-0.195884\pi$
$467$	158090.	+	91273.3i	0.724888	+	0.418514i	−0.0916612	+	0.995790i	$0.529218\pi$
$468$		−	178618.i		−	0.815520i
$469$	71163.3	−	368032.i	0.323527	−	1.67317i
$470$		0			0
$471$	−92195.5	+	159687.i	−0.415593	+	0.719828i
$472$	76690.4	−	44277.2i	0.344237	−	0.198745i
$473$	−1479.92	−	2563.30i	−0.00661479	−	0.0114571i
$474$	−116130.	−	67047.9i	−0.516880	−	0.298421i
$475$		0			0
$476$	−15734.9	−	45552.1i	−0.0694464	−	0.201046i
$477$	−151642.			−0.666474
$478$	−44254.4	+	76650.9i	−0.193687	+	0.335476i
$479$	−62412.7	+	36034.0i	−0.272021	+	0.157051i	−0.629806	−	0.776753i	$-0.716865\pi$
$479$	−62412.7	+	36034.0i	−0.272021	+	0.157051i	0.357785	+	0.933804i	$0.383532\pi$
$480$		0			0
$481$	438243.	+	253020.i	1.89420	+	1.09362i
$482$			103225.i			0.444315i
$483$	−207104.	+	238719.i	−0.887759	+	1.02328i
$484$	−116713.			−0.498228
$485$		0			0
$486$	−200853.	+	115963.i	−0.850367	+	0.490959i
$487$	42755.5	+	74054.8i	0.180275	+	0.312245i	0.941974	−	0.335686i	$-0.108968\pi$
$487$	42755.5	+	74054.8i	0.180275	+	0.312245i	−0.761699	+	0.647931i	$0.775635\pi$
$488$	93474.1	+	53967.3i	0.392511	+	0.226616i
$489$		−	176620.i		−	0.738621i
$490$		0			0
$491$	−360859.			−1.49684			−0.748418	−	0.663227i	$-0.769186\pi$
$491$	−360859.			−1.49684			−0.748418	+	0.663227i	$0.769186\pi$
$492$	127433.	−	220721.i	0.526444	−	0.911828i
$493$	−99193.1	+	57269.1i	−0.408120	+	0.235628i
$494$	−36246.6	−	62781.0i	−0.148530	−	0.257261i
$495$		0			0
$496$		−	922.204i		−	0.00374855i
$497$	68259.8	+	59219.8i	0.276345	+	0.239747i
$498$	−129886.			−0.523724
$499$	−193248.	+	334716.i	−0.776094	+	1.34423i	0.158083	+	0.987426i	$0.449469\pi$
$499$	−193248.	+	334716.i	−0.776094	+	1.34423i	−0.934177	+	0.356809i	$0.883865\pi$
$500$		0			0
$501$	−269669.	−	467081.i	−1.07437	−	1.86087i
$502$	169889.	+	98085.7i	0.674154	+	0.389223i
$503$			125251.i			0.495044i	0.968882	+	0.247522i	$0.0796163\pi$
$503$			125251.i			0.495044i	−0.968882	+	0.247522i	$0.920384\pi$
$504$	79926.3	−	27608.6i	0.314651	−	0.108688i
$505$		0			0
$506$	5238.87	−	9073.99i	0.0204615	−	0.0354403i
$507$	−620600.	+	358304.i	−2.41433	+	1.39391i
$508$	15622.3	+	27058.6i	0.0605364	+	0.104852i
$509$	−299969.	−	173187.i	−1.15782	−	0.668468i	−0.207040	−	0.978333i	$-0.566383\pi$
$509$	−299969.	−	173187.i	−1.15782	−	0.668468i	−0.950781	+	0.309865i	$0.899716\pi$
$510$		0			0
$511$	509886.	+	98592.6i	1.95268	+	0.377574i
$512$	11585.2			0.0441942
$513$	−2598.33	+	4500.44i	−0.00987324	+	0.0171010i
$514$	269656.	−	155686.i	1.02067	−	0.589282i
$515$		0			0
$516$	35703.2	+	20613.3i	0.134094	+	0.0774190i
$517$			21888.0i			0.0818889i
$518$	−45480.5	+	235209.i	−0.169499	+	0.876587i
$519$	285895.			1.06138
$520$		0			0
$521$	18587.3	−	10731.4i	0.0684764	−	0.0395349i	−0.465371	−	0.885116i	$-0.654079\pi$
$521$	18587.3	−	10731.4i	0.0684764	−	0.0395349i	0.533847	+	0.845581i	$0.320746\pi$
$522$	−100485.	−	174045.i	−0.368774	−	0.638736i
$523$	307327.	+	177435.i	1.12356	+	0.648689i	0.942308	−	0.334747i	$-0.108651\pi$
$523$	307327.	+	177435.i	1.12356	+	0.648689i	0.181254	+	0.983436i	$0.441984\pi$
$524$			262552.i			0.956208i
$525$		0			0
$526$	−1610.45			−0.00582070
$527$	−885.761	+	1534.18i	−0.00318930	+	0.00552403i
$528$	−5006.44	+	2890.47i	−0.0179581	+	0.0103681i
$529$	7664.46	+	13275.2i	0.0273886	+	0.0474385i
$530$		0			0
$531$		−	298477.i		−	1.05858i
$532$	22490.0	−	25923.2i	0.0794634	−	0.0915936i
$533$	−743711.			−2.61788
$534$	2654.76	−	4598.18i	0.00930986	−	0.0161251i
$535$		0			0
$536$	−86549.6	−	149908.i	−0.301256	−	0.521790i
$537$	−133917.	−	77317.3i	−0.464396	−	0.268119i
$538$		−	161790.i		−	0.558968i
$539$	−13606.8	+	10673.9i	−0.0468359	+	0.0367405i
$540$		0			0
$541$	−27795.2	+	48142.6i	−0.0949675	+	0.164488i	−0.909595	−	0.415496i	$-0.863608\pi$
$541$	−27795.2	+	48142.6i	−0.0949675	+	0.164488i	0.814628	+	0.579984i	$0.196941\pi$
$542$	−205667.	+	118742.i	−0.700109	+	0.404208i
$543$	222946.	+	386154.i	0.756136	+	1.30967i
$544$	−19273.3	−	11127.4i	−0.0651264	−	0.0376008i
$545$		0			0
$546$	−384335.	−	333436.i	−1.28921	−	1.11848i
$547$	486947.			1.62745			0.813725	−	0.581251i	$-0.197436\pi$
$547$	486947.			1.62745			0.813725	+	0.581251i	$0.197436\pi$
$548$	−57934.9	+	100346.i	−0.192921	+	0.334149i
$549$	315059.	−	181899.i	1.04532	−	0.603513i
$550$		0			0
$551$	−70637.3	−	40782.4i	−0.232665	−	0.134329i
$552$			145941.i			0.478959i
$553$	−175094.	+	60482.0i	−0.572560	+	0.197777i
$554$	165073.			0.537845
$555$		0			0
$556$	−138652.	+	80050.5i	−0.448513	+	0.258949i
$557$	−65455.7	−	113373.i	−0.210978	−	0.365424i	0.741043	−	0.671458i	$-0.234331\pi$
$557$	−65455.7	−	113373.i	−0.210978	−	0.365424i	−0.952021	+	0.306033i	$0.900998\pi$
$558$	−2691.90	−	1554.17i	−0.00864549	−	0.00499148i
$559$		−	120301.i		−	0.384986i
$560$		0			0
$561$	11105.0			0.0352852
$562$	−41413.9	+	71730.9i	−0.131121	+	0.227109i
$563$	426503.	−	246241.i	1.34557	−	0.776863i	0.357948	−	0.933742i	$-0.383477\pi$
$563$	426503.	−	246241.i	1.34557	−	0.776863i	0.987618	+	0.156879i	$0.0501432\pi$
$564$	−152435.	−	264025.i	−0.479211	−	0.830018i
$565$		0			0
$566$		−	363611.i		−	1.13502i
$567$	−64391.3	+	333009.i	−0.200291	+	1.03583i
$568$	41730.5			0.129347
$569$	43040.5	−	74548.3i	0.132939	−	0.230257i	−0.791869	−	0.610691i	$-0.790892\pi$
$569$	43040.5	−	74548.3i	0.132939	−	0.230257i	0.924808	+	0.380434i	$0.124225\pi$
$570$		0			0
$571$	−13812.5	−	23923.9i	−0.0423642	−	0.0733769i	0.844066	−	0.536240i	$-0.180156\pi$
$571$	−13812.5	−	23923.9i	−0.0423642	−	0.0733769i	−0.886430	+	0.462863i	$0.846822\pi$
$572$	14609.0	+	8434.52i	0.0446508	+	0.0257791i
$573$		−	676510.i		−	2.06047i
$574$	−114954.	−	332788.i	−0.348898	−	1.01005i
$575$		0			0
$576$	19524.3	−	33817.1i	0.0588478	−	0.101927i
$577$	261070.	−	150729.i	0.784162	−	0.452736i	−0.0537410	−	0.998555i	$-0.517115\pi$
$577$	261070.	−	150729.i	0.784162	−	0.452736i	0.837903	+	0.545819i	$0.183781\pi$
$578$	−96741.1	−	167561.i	−0.289571	−	0.501552i
$579$	−26228.9	−	15143.3i	−0.0782391	−	0.0451713i
$580$		0			0
$581$	−117583.	+	135533.i	−0.348332	+	0.401506i
$582$	−452389.			−1.33557
$583$	7160.68	−	12402.7i	0.0210677	−	0.0364903i
$584$	207689.	−	119909.i	0.608959	−	0.351583i
$585$		0			0
$586$	312061.	+	180168.i	0.908749	+	0.524666i
$587$			155451.i			0.451147i	0.974226	+	0.225574i	$0.0724256\pi$
$587$			155451.i			0.451147i	−0.974226	+	0.225574i	$0.927574\pi$
$588$	89796.6	−	223517.i	0.259720	−	0.646480i
$589$	−1261.53			−0.00363638
$590$		0			0
$591$	282931.	−	163350.i	0.810038	−	0.467676i
$592$	55313.9	+	95806.5i	0.157830	+	0.273370i
$593$	78574.0	+	45364.7i	0.223445	+	0.129006i	0.607544	−	0.794286i	$-0.292155\pi$
$593$	78574.0	+	45364.7i	0.223445	+	0.129006i	−0.384100	+	0.923292i	$0.625488\pi$
$594$		−	1209.25i		−	0.00342724i
$595$		0			0
$596$	−144481.			−0.406741
$597$	−8282.15	+	14345.1i	−0.0232378	+	0.0402490i
$598$	368807.	−	212931.i	1.03133	−	0.595437i
$599$	−66299.8	−	114835.i	−0.184782	−	0.320051i	0.758721	−	0.651415i	$-0.225824\pi$
$599$	−66299.8	−	114835.i	−0.184782	−	0.320051i	−0.943503	+	0.331364i	$0.892491\pi$
$600$		0			0
$601$		−	247185.i		−	0.684343i	−0.939638	−	0.342171i	$-0.888838\pi$
$601$		−	247185.i		−	0.684343i	0.939638	−	0.342171i	$-0.111162\pi$
$602$	53831.0	−	18594.6i	0.148539	−	0.0513091i
$603$	−583439.			−1.60458
$604$	71843.2	−	124436.i	0.196930	−	0.341093i
$605$		0			0
$606$	−203984.	−	353311.i	−0.555459	−	0.962082i
$607$	−83960.0	−	48474.3i	−0.227874	−	0.131563i	0.381717	−	0.924279i	$-0.375333\pi$
$607$	−83960.0	−	48474.3i	−0.227874	−	0.131563i	−0.609591	+	0.792716i	$0.708666\pi$
$608$		−	15848.1i		−	0.0428716i
$609$	−562076.	−	108684.i	−1.51552	−	0.293043i
$610$		0			0
$611$	−444812.	+	770438.i	−1.19150	+	2.06374i
$612$	−64961.5	+	37505.5i	−0.173441	+	0.100136i
$613$	−110055.	−	190621.i	−0.292880	−	0.507284i	0.681609	−	0.731716i	$-0.261280\pi$
$613$	−110055.	−	190621.i	−0.292880	−	0.507284i	−0.974490	+	0.224433i	$0.927947\pi$
$614$	−156262.	−	90218.1i	−0.414493	−	0.239308i
$615$		0			0
$616$	−1516.11	+	7840.79i	−0.00399549	+	0.0206632i
$617$	219063.			0.575438			0.287719	−	0.957715i	$-0.407103\pi$
$617$	219063.			0.575438			0.287719	+	0.957715i	$0.407103\pi$
$618$	−134310.	+	232632.i	−0.351667	+	0.609105i
$619$	15226.7	−	8791.15i	0.0397398	−	0.0229438i	−0.479999	−	0.877269i	$-0.659363\pi$
$619$	15226.7	−	8791.15i	0.0397398	−	0.0229438i	0.519738	+	0.854326i	$0.326029\pi$
$620$		0			0
$621$	−26437.8	−	15263.9i	−0.0685555	−	0.0395805i
$622$		−	57480.6i		−	0.148573i
$623$	−2394.78	−	6932.84i	−0.00617007	−	0.0178622i
$624$	−234963.			−0.603434
$625$		0			0
$626$	−237694.	+	137233.i	−0.606554	+	0.350194i
$627$	3954.03	+	6848.59i	0.0100579	+	0.0174207i
$628$	101869.	+	58814.1i	0.258299	+	0.149129i
$629$		−	212512.i		−	0.537134i
$630$		0			0
$631$	541622.			1.36031			0.680154	−	0.733069i	$-0.261913\pi$
$631$	541622.			1.36031			0.680154	+	0.733069i	$0.261913\pi$
$632$	−42771.7	+	74082.8i	−0.107084	+	0.185474i
$633$	−58328.5	+	33676.0i	−0.145571	+	0.0840452i
$634$	30189.0	+	52288.8i	0.0751052	+	0.130086i
$635$		0			0
$636$			199477.i			0.493150i
$637$	−695865.	+	99190.7i	−1.71493	+	0.244451i
$638$	18980.0			0.0466288
$639$	70327.3	−	121811.i	0.172235	−	0.298321i
$640$		0			0
$641$	−190385.	−	329757.i	−0.463358	−	0.802560i	0.535768	−	0.844366i	$-0.320022\pi$
$641$	−190385.	−	329757.i	−0.463358	−	0.802560i	−0.999126	+	0.0418055i	$0.986689\pi$
$642$	194137.	+	112085.i	0.471018	+	0.271942i
$643$		−	209750.i		−	0.507319i	−0.967294	−	0.253659i	$-0.918366\pi$
$643$		−	209750.i		−	0.507319i	0.967294	−	0.253659i	$-0.0816342\pi$
$644$	152286.	+	132118.i	0.367187	+	0.318558i
$645$		0			0
$646$	−15221.8	+	26365.0i	−0.0364755	+	0.0631775i
$647$	367702.	−	212293.i	0.878391	−	0.507139i	0.00826322	−	0.999966i	$-0.497370\pi$
$647$	367702.	−	212293.i	0.878391	−	0.507139i	0.870127	+	0.492827i	$0.164036\pi$
$648$	78313.3	+	135643.i	0.186503	+	0.323033i
$649$	24412.1	+	14094.4i	0.0579584	+	0.0334623i
$650$		0			0
$651$	−8369.21	+	2890.94i	−0.0197480	+	0.00682146i
$652$	−112671.			−0.265043
$653$	178107.	−	308491.i	0.417691	−	0.723463i	−0.578016	−	0.816026i	$-0.696173\pi$
$653$	178107.	−	308491.i	0.417691	−	0.723463i	0.995707	+	0.0925633i	$0.0295060\pi$
$654$	−602431.	+	347814.i	−1.40848	+	0.813188i
$655$		0			0
$656$	−140804.	−	81293.1i	−0.327195	−	0.188906i
$657$		−	808321.i		−	1.87263i
$658$	−413501.	−	79955.4i	−0.955047	−	0.184670i
$659$	−252669.			−0.581810			−0.290905	−	0.956752i	$-0.593956\pi$
$659$	−252669.			−0.581810			−0.290905	+	0.956752i	$0.593956\pi$
$660$		0			0
$661$	245541.	−	141763.i	0.561980	−	0.324459i	−0.191960	−	0.981403i	$-0.561484\pi$
$661$	245541.	−	141763.i	0.561980	−	0.324459i	0.753940	+	0.656943i	$0.228151\pi$
$662$	−82053.8	−	142121.i	−0.187233	−	0.324297i
$663$	390885.	+	225678.i	0.889247	+	0.513407i
$664$			82857.7i			0.187930i
$665$		0			0
$666$	372876.			0.840652
$667$	239576.	−	414958.i	0.538508	−	0.932723i
$668$	−297964.	+	172029.i	−0.667745	+	0.385523i
$669$	−400662.	−	693966.i	−0.895211	−	1.55055i
$670$		0			0
$671$			34357.8i			0.0763098i
$672$	−36317.6	−	105139.i	−0.0804227	−	0.232822i
$673$	859774.			1.89825			0.949126	−	0.314896i	$-0.101970\pi$
$673$	859774.			1.89825			0.949126	+	0.314896i	$0.101970\pi$
$674$	139368.	−	241392.i	0.306791	−	0.531378i
$675$		0			0
$676$	228572.	+	395898.i	0.500184	+	0.866344i
$677$	667136.	+	385171.i	1.45558	+	0.840382i	0.998789	−	0.0491904i	$-0.0156641\pi$
$677$	667136.	+	385171.i	1.45558	+	0.840382i	0.456795	+	0.889572i	$0.348997\pi$
$678$		−	562561.i		−	1.22380i
$679$	−409540.	+	472057.i	−0.888295	+	1.02389i
$680$		0			0
$681$	154825.	−	268165.i	0.333847	−	0.578239i
$682$	254.227	−	146.778i	0.000546580	−	0.000315568i
$683$	451216.	+	781529.i	0.967260	+	1.67534i	0.703417	+	0.710777i	$0.251657\pi$
$683$	451216.	+	781529.i	0.967260	+	1.67534i	0.263842	+	0.964566i	$0.415010\pi$
$684$	−46260.3	−	26708.4i	−0.0988772	−	0.0570868i
$685$		0			0
$686$	−151943.	−	296047.i	−0.322873	−	0.629089i
$687$	−421375.			−0.892803
$688$	13149.8	−	22776.1i	0.0277806	−	0.0481174i
$689$	504099.	−	291042.i	1.06188	−	0.613079i
$690$		0			0
$691$	−199508.	−	115186.i	−0.417835	−	0.241237i	0.276316	−	0.961067i	$-0.410887\pi$
$691$	−199508.	−	115186.i	−0.417835	−	0.241237i	−0.694151	+	0.719830i	$0.744220\pi$
$692$		−	182380.i		−	0.380860i
$693$	20332.1	+	17639.4i	0.0423365	+	0.0367297i
$694$	129856.			0.269614
$695$		0			0
$696$	−228947.	+	132183.i	−0.472625	+	0.272870i
$697$	156161.	+	270479.i	0.321446	+	0.556761i
$698$	34435.8	+	19881.5i	0.0706805	+	0.0408074i
$699$		−	323618.i		−	0.662336i
$700$		0			0
$701$	236661.			0.481604			0.240802	−	0.970574i	$-0.422590\pi$
$701$	236661.			0.481604			0.240802	+	0.970574i	$0.422590\pi$
$702$	24574.7	−	42564.6i	0.0498670	−	0.0863722i
$703$	131059.	−	75667.0i	0.265190	−	0.153107i
$704$	1843.91	+	3193.75i	0.00372044	+	0.00644399i
$705$		0			0
$706$			37968.1i			0.0761746i
$707$	−553336.	−	106994.i	−1.10701	−	0.214053i
$708$	−392631.			−0.783281
$709$	−31409.8	+	54403.4i	−0.0624845	+	0.108226i	−0.895575	−	0.444910i	$-0.853236\pi$
$709$	−31409.8	+	54403.4i	−0.0624845	+	0.108226i	0.833091	+	0.553136i	$0.186569\pi$
$710$		0			0
$711$	144164.	+	249700.i	0.285180	+	0.493945i
$712$	−2933.31	−	1693.55i	−0.00578626	−	0.00334070i
$713$		−	7410.88i		−	0.0145778i
$714$	−40565.7	+	209792.i	−0.0795725	+	0.411521i
$715$		0			0
$716$	−49322.8	+	85429.7i	−0.0962104	+	0.166641i
$717$	339853.	−	196214.i	0.661078	−	0.381674i
$718$	−137322.	−	237848.i	−0.266373	−	0.461371i
$719$	444505.	+	256635.i	0.859843	+	0.496431i	0.863960	−	0.503561i	$-0.167977\pi$
$719$	444505.	+	256635.i	0.859843	+	0.496431i	−0.00411680	+	0.999992i	$0.501310\pi$
$720$		0			0
$721$	121157.	+	350747.i	0.233066	+	0.674720i
$722$	346924.			0.665518
$723$	228838.	−	396359.i	0.437776	−	0.758250i
$724$	246338.	−	142223.i	0.469953	−	0.271328i
$725$		0			0
$726$	448150.	+	258739.i	0.850257	+	0.490896i
$727$			724922.i			1.37158i	0.727797	+	0.685792i	$0.240544\pi$
$727$			724922.i			1.37158i	−0.727797	+	0.685792i	$0.759456\pi$
$728$	−212708.	+	245178.i	−0.401348	+	0.462614i
$729$	467624.			0.879916
$730$		0			0
$731$	−43752.1	+	25260.3i	−0.0818774	+	0.0472719i
$732$	−239279.	−	414443.i	−0.446562	−	0.773469i
$733$	286981.	+	165689.i	0.534128	+	0.308379i	0.742696	−	0.669629i	$-0.233547\pi$
$733$	286981.	+	165689.i	0.534128	+	0.308379i	−0.208568	+	0.978008i	$0.566880\pi$
$734$		−	33013.9i		−	0.0612780i
$735$		0			0
$736$	93099.6			0.171867
$737$	27550.5	−	47718.9i	0.0507218	−	0.0878527i
$738$	−474586.	+	274002.i	−0.871369	+	0.503085i
$739$	132295.	+	229141.i	0.242244	+	0.419580i	0.961353	−	0.275318i	$-0.0887831\pi$
$739$	132295.	+	229141.i	0.242244	+	0.419580i	−0.719109	+	0.694897i	$0.755450\pi$
$740$		0			0
$741$			321419.i			0.585376i
$742$	208150.	+	180583.i	0.378066	+	0.327997i
$743$	−105627.			−0.191337			−0.0956683	−	0.995413i	$-0.530499\pi$
$743$	−105627.			−0.191337			−0.0956683	+	0.995413i	$0.530499\pi$
$744$	−2044.42	+	3541.04i	−0.00369339	+	0.00639713i
$745$		0			0
$746$	279663.	+	484391.i	0.502525	+	0.870399i
$747$	241860.	+	139638.i	0.433434	+	0.250243i
$748$		−	7084.18i		−	0.0126615i
$749$	292707.	−	101108.i	0.521758	−	0.180229i
$750$		0			0
$751$	477793.	−	827562.i	0.847149	−	1.46731i	−0.0365919	−	0.999330i	$-0.511650\pi$
$751$	477793.	−	827562.i	0.847149	−	1.46731i	0.883741	−	0.467976i	$-0.155017\pi$
$752$	−168429.	+	97242.6i	−0.297839	+	0.171957i
$753$	−434890.	−	753251.i	−0.766989	−	1.32846i
$754$	668078.	+	385715.i	1.17513	+	0.678459i
$755$		0			0
$756$	22844.8	+	4417.32i	0.0399709	+	0.00772885i
$757$	−1.03602e6			−1.80791			−0.903957	−	0.427624i	$-0.859351\pi$
$757$	−1.03602e6			−1.80791			−0.903957	+	0.427624i	$0.859351\pi$
$758$	−12025.7	+	20829.1i	−0.0209301	+	0.0362520i
$759$	−40232.0	+	23228.0i	−0.0698374	+	0.0403206i
$760$		0			0
$761$	−950676.	−	548873.i	−1.64158	−	0.947769i	−0.980271	−	0.197660i	$-0.936666\pi$
$761$	−950676.	−	548873.i	−1.64158	−	0.947769i	−0.661314	−	0.750109i	$-0.730001\pi$
$762$		−	138531.i		−	0.238582i
$763$	−182436.	+	943492.i	−0.313372	+	1.62065i
$764$	−431565.			−0.739366
$765$		0			0
$766$	563823.	−	325523.i	0.960916	−	0.554785i
$767$	572857.	+	992217.i	0.973768	+	1.68662i
$768$	−44484.5	−	25683.2i	−0.0754200	−	0.0435438i
$769$			610743.i			1.03278i	0.856355	+	0.516388i	$0.172724\pi$
$769$			610743.i			1.03278i	−0.856355	+	0.516388i	$0.827276\pi$
$770$		0			0
$771$	−1.38055e6			−2.32244
$772$	−9660.32	+	16732.2i	−0.0162090	+	0.0280749i
$773$	95995.4	−	55423.0i	0.160654	−	0.0927536i	−0.417518	−	0.908669i	$-0.637100\pi$
$773$	95995.4	−	55423.0i	0.160654	−	0.0927536i	0.578172	+	0.815915i	$0.303766\pi$
$774$	−44322.0	−	76767.9i	−0.0739839	−	0.128144i
$775$		0			0
$776$			288592.i			0.479248i
$777$	696067.	−	802323.i	1.15295	−	1.32894i
$778$	−226297.			−0.373870
$779$	−111205.	+	192613.i	−0.183253	+	0.317404i
$780$		0			0
$781$	6641.84	+	11504.0i	0.0108890	+	0.0188602i
$782$	−154881.	−	89420.6i	−0.253270	−	0.146226i
$783$		−	55299.8i		−	0.0901986i
$784$	−142587.	−	57283.8i	−0.231979	−	0.0931965i
$785$		0			0
$786$	582048.	−	1.00814e6i	0.942136	−	1.63183i
$787$	23833.1	−	13760.1i	0.0384797	−	0.0222163i	−0.480637	−	0.876920i	$-0.659594\pi$
$787$	23833.1	−	13760.1i	0.0384797	−	0.0222163i	0.519116	+	0.854704i	$0.326261\pi$
$788$	−104206.	−	180489.i	−0.167818	−	0.290669i
$789$	6183.74	+	3570.18i	0.00993338	+	0.00573504i
$790$		0			0
$791$	−587019.	−	509277.i	−0.938207	−	0.813956i
$792$	12430.0			0.0198162
$793$	−698226.	+	1.20936e6i	−1.11032	+	1.92314i
$794$	116868.	−	67473.7i	0.185376	−	0.107027i
$795$		0			0
$796$	9151.14	+	5283.41i	0.0144427	+	0.00833851i
$797$		−	793651.i		−	1.24943i	−0.780852	−	0.624717i	$-0.785214\pi$
$797$		−	793651.i		−	1.24943i	0.780852	−	0.624717i	$-0.214786\pi$
$798$	−143825.	+	49680.9i	−0.225855	+	0.0780160i
$799$	373599.			0.585211
$800$		0			0
$801$	−9886.86	+	5708.18i	−0.0154097	+	0.00889678i
$802$	−76522.8	−	132541.i	−0.118971	−	0.206064i
$803$	66111.7	+	38169.6i	0.102529	+	0.0591952i
$804$			767482.i			1.18729i
$805$		0			0
$806$	11931.4			0.0183663
$807$	−358670.	+	621235.i	−0.550742	+	0.953912i
$808$	−225387.	+	130127.i	−0.345228	+	0.199318i
$809$	67222.0	+	116432.i	0.102710	+	0.177900i	0.912800	−	0.408406i	$-0.133915\pi$
$809$	67222.0	+	116432.i	0.102710	+	0.177900i	−0.810090	+	0.586305i	$0.800582\pi$
$810$		0			0
$811$			1.12692e6i			1.71337i	0.515838	+	0.856686i	$0.327481\pi$
$811$			1.12692e6i			1.71337i	−0.515838	+	0.856686i	$0.672519\pi$
$812$	−69332.6	+	358564.i	−0.105154	+	0.543819i
$813$	1.05295e6			1.59304
$814$	−17607.6	+	30497.2i	−0.0265736	+	0.0460268i
$815$		0			0
$816$	49336.5	+	85453.3i	0.0740948	+	0.128336i
$817$	−31156.7	−	17988.3i	−0.0466775	−	0.0269492i
$818$			515571.i			0.770517i
$819$	357199.	+	1.03408e6i	0.532528	+	1.54166i
$820$		0			0
$821$	−178657.	+	309443.i	−0.265054	+	0.459087i	−0.967578	−	0.252574i	$-0.918723\pi$
$821$	−178657.	+	309443.i	−0.265054	+	0.459087i	0.702524	+	0.711660i	$0.252056\pi$
$822$	444912.	−	256870.i	0.658462	−	0.380163i
$823$	286488.	+	496211.i	0.422967	+	0.732600i	0.996228	−	0.0867728i	$-0.0276554\pi$
$823$	286488.	+	496211.i	0.422967	+	0.732600i	−0.573262	+	0.819372i	$0.694322\pi$
$824$	148402.	+	85680.0i	0.218568	+	0.126190i
$825$		0			0
$826$	−355442.	+	409701.i	−0.520965	+	0.600491i
$827$	985411.			1.44081			0.720405	−	0.693554i	$-0.243956\pi$
$827$	985411.			1.44081			0.720405	+	0.693554i	$0.243956\pi$
$828$	156898.	−	271756.i	0.228854	−	0.396386i
$829$	−98948.8	+	57128.1i	−0.143980	+	0.0831267i	−0.570259	−	0.821465i	$-0.693157\pi$
$829$	−98948.8	+	57128.1i	−0.143980	+	0.0831267i	0.426280	+	0.904591i	$0.359824\pi$
$830$		0			0
$831$	−633842.	−	365949.i	−0.917865	−	0.529930i
$832$			149889.i			0.216533i
$833$	182189.	+	232250.i	0.262562	+	0.334708i
$834$	709852.			1.02055
$835$		0			0
$836$	4368.90	−	2522.39i	0.00625115	−	0.00360910i
$837$	−427.651	−	740.713i	−0.000610433	−	0.00105730i
$838$	−124492.	−	71875.5i	−0.177277	−	0.102351i
$839$			808131.i			1.14804i	0.818841	+	0.574021i	$0.194617\pi$
$839$			808131.i			1.14804i	−0.818841	+	0.574021i	$0.805383\pi$
$840$		0			0
$841$	160684.			0.227185
$842$	−15176.5	+	26286.5i	−0.0214066	+	0.0370773i
$843$	318039.	−	183620.i	0.447533	−	0.258383i
$844$	21482.8	+	37209.4i	0.0301583	+	0.0522357i
$845$		0			0
$846$			655522.i			0.915896i
$847$	675691.	−	233401.i	0.941849	−	0.325339i
$848$	127252.			0.176959
$849$	−806083.	+	1.39618e6i	−1.11832	+	1.93698i
$850$		0			0
$851$	444505.	+	769906.i	0.613787	+	1.06311i
$852$	−160235.	−	92511.8i	−0.220739	−	0.127444i
$853$		−	1.24179e6i		−	1.70668i	−0.521358	−	0.853338i	$-0.674574\pi$
$853$		−	1.24179e6i		−	1.70668i	0.521358	−	0.853338i	$-0.325426\pi$
$854$	−649077.	−	125507.i	−0.889980	−	0.172088i
$855$		0			0
$856$	71502.0	−	123845.i	0.0975822	−	0.169017i
$857$	36679.3	−	21176.8i	0.0499413	−	0.0288336i	−0.474821	−	0.880082i	$-0.657487\pi$
$857$	36679.3	−	21176.8i	0.0499413	−	0.0288336i	0.524763	+	0.851249i	$0.324154\pi$
$858$	−37396.7	−	64773.1i	−0.0507995	−	0.0879873i
$859$	−756574.	−	436808.i	−1.02533	−	0.591976i	−0.109689	−	0.993966i	$-0.534985\pi$
$859$	−756574.	−	436808.i	−1.02533	−	0.591976i	−0.915644	+	0.401990i	$0.868319\pi$
$860$		0			0
$861$	−296359.	+	1.53267e6i	−0.399772	+	2.06748i
$862$	237485.			0.319611
$863$	591510.	−	1.02453e6i	0.794219	−	1.37563i	−0.129114	−	0.991630i	$-0.541213\pi$
$863$	591510.	−	1.02453e6i	0.794219	−	1.37563i	0.923334	−	0.383999i	$-0.125453\pi$
$864$	9305.24	−	5372.39i	0.0124652	−	0.00719680i
$865$		0			0
$866$	−17513.2	−	10111.3i	−0.0233523	−	0.0134825i
$867$			857857.i			1.14124i
$868$	1844.21	+	5338.95i	0.00244778	+	0.00708625i
$869$	−27230.3			−0.0360589
$870$		0			0
$871$	1.93951e6	−	1.11977e6i	2.55655	−	1.47603i
$872$	221880.	+	384307.i	0.291800	+	0.505412i
$873$	842393.	+	486356.i	1.10532	+	0.638154i
$874$		−	127356.i		−	0.166724i
$875$		0			0
$876$	−1.06330e6			−1.38563
$877$	−8855.27	+	15337.8i	−0.0115134	+	0.0199418i	−0.871725	−	0.489996i	$-0.836998\pi$
$877$	−8855.27	+	15337.8i	−0.0115134	+	0.0199418i	0.860211	+	0.509938i	$0.170332\pi$
$878$	−621070.	+	358575.i	−0.805660	+	0.465148i
$879$	−798826.	−	1.38361e6i	−1.03389	−	1.79075i
$880$		0			0
$881$		−	761550.i		−	0.981175i	−0.871392	−	0.490588i	$-0.836782\pi$
$881$		−	761550.i		−	0.981175i	0.871392	−	0.490588i	$-0.163218\pi$
$882$	−407509.	+	319671.i	−0.523842	+	0.410929i
$883$	−1.12110e6			−1.43789			−0.718943	−	0.695069i	$-0.755374\pi$
$883$	−1.12110e6			−1.43789			−0.718943	+	0.695069i	$0.755374\pi$
$884$	143966.	−	249357.i	0.184228	−	0.319092i
$885$		0			0
$886$	100984.	+	174909.i	0.128642	+	0.222815i
$887$	−428407.	−	247341.i	−0.544514	−	0.314376i	0.202392	−	0.979305i	$-0.435128\pi$
$887$	−428407.	−	247341.i	−0.544514	−	0.314376i	−0.746907	+	0.664929i	$0.768462\pi$
$888$		−	490499.i		−	0.622031i
$889$	−144554.	−	125410.i	−0.182906	−	0.158682i
$890$		0			0
$891$	−24928.7	+	43177.8i	−0.0314011	+	0.0543883i
$892$	−442700.	+	255593.i	−0.556391	+	0.321232i
$893$	133024.	+	230404.i	0.166811	+	0.288926i
$894$	554772.	+	320298.i	0.694128	+	0.400755i
$895$		0			0
$896$	−67070.9	+	23168.0i	−0.0835445	+	0.0288584i
$897$	−1.88817e6			−2.34670
$898$	445550.	−	771715.i	0.552514	−	0.956983i
$899$	11626.0	−	6712.25i	0.0143850	−	0.00830517i
$900$		0			0
$901$	−211697.	−	122223.i	−0.260775	−	0.150558i
$902$		−	51754.5i		−	0.0636115i
$903$	−247920.	−	47938.4i	−0.304044	−	0.0587906i
$904$	−358873.			−0.439141
$905$		0			0
$906$	−551722.	+	318537.i	−0.672146	+	0.388064i
$907$	−62482.2	−	108222.i	−0.0759525	−	0.131554i	0.825548	−	0.564332i	$-0.190866\pi$
$907$	−62482.2	−	108222.i	−0.0759525	−	0.131554i	−0.901500	+	0.432779i	$0.857533\pi$
$908$	−171070.	−	98767.2i	−0.207492	−	0.119796i
$909$			877201.i			1.06163i
$910$		0			0
$911$	1.43305e6			1.72673			0.863366	−	0.504578i	$-0.168352\pi$
$911$	1.43305e6			1.72673			0.863366	+	0.504578i	$0.168352\pi$
$912$	−35133.4	+	60852.9i	−0.0422407	+	0.0731630i
$913$	−22841.7	+	13187.7i	−0.0274023	+	0.0158207i
$914$	98156.7	+	170012.i	0.117497	+	0.203511i
$915$		0			0
$916$			268807.i			0.320368i
$917$	−525048.	−	1.52000e6i	−0.624396	−	1.80761i
$918$	−20640.3			−0.0244924
$919$	721700.	−	1.25002e6i	0.854527	−	1.48008i	−0.0225570	−	0.999746i	$-0.507181\pi$
$919$	721700.	−	1.25002e6i	0.854527	−	1.48008i	0.877084	−	0.480338i	$-0.159486\pi$
$920$		0			0
$921$	400006.	+	692832.i	0.471572	+	0.816786i
$922$	−408700.	−	235963.i	−0.480776	−	0.277576i
$923$			539907.i			0.633747i
$924$	23203.7	−	26745.7i	0.0271777	−	0.0313264i
$925$		0			0
$926$	235991.	−	408749.i	0.275216	−	0.476688i
$927$	500197.	−	288789.i	0.582078	−	0.336063i
$928$	84323.0	+	146052.i	0.0979152	+	0.169594i
$929$	−457017.	−	263859.i	−0.529542	−	0.305731i	0.211288	−	0.977424i	$-0.432234\pi$
$929$	−457017.	−	263859.i	−0.529542	−	0.305731i	−0.740830	+	0.671693i	$0.765568\pi$
$930$		0			0
$931$	−78361.7	+	195053.i	−0.0904075	+	0.225037i
$932$	−206445.			−0.237669
$933$	−127428.	+	220712.i	−0.146387	+	0.253549i
$934$	−447146.	+	258160.i	−0.512573	+	0.295934i
$935$		0			0
$936$	437524.	+	252605.i	0.499402	+	0.288330i
$937$			37174.4i			0.0423413i	0.999776	+	0.0211707i	$0.00673934\pi$
$937$			37174.4i			0.0423413i	−0.999776	+	0.0211707i	$0.993261\pi$
$938$	800850.	+	694789.i	0.910218	+	0.789673i
$939$	1.21692e6			1.38016
$940$		0			0
$941$	672093.	−	388033.i	0.759014	−	0.438217i	−0.0699274	−	0.997552i	$-0.522277\pi$
$941$	672093.	−	388033.i	0.759014	−	0.438217i	0.828942	+	0.559335i	$0.188943\pi$
$942$	−260768.	−	451664.i	−0.293868	−	0.508995i
$943$	−1.13151e6	−	653276.i	−1.27243	−	0.734638i
$944$			250470.i			0.281068i
$945$		0			0
$946$	8371.69			0.00935472
$947$	−124041.	+	214846.i	−0.138314	+	0.239567i	−0.926858	−	0.375411i	$-0.877502\pi$
$947$	−124041.	+	214846.i	−0.138314	+	0.239567i	0.788545	+	0.614978i	$0.210835\pi$
$948$	328467.	−	189640.i	0.365489	−	0.211015i
$949$	1.55138e6	+	2.68707e6i	1.72261	+	2.98364i
$950$		0			0
$951$		−	267702.i		−	0.295999i
$952$	133832.	+	25878.0i	0.147668	+	0.0285533i
$953$	−899097.			−0.989968			−0.494984	−	0.868902i	$-0.664826\pi$
$953$	−899097.			−0.989968			−0.494984	+	0.868902i	$0.664826\pi$
$954$	214454.	−	371446.i	0.235634	−	0.408130i
$955$		0			0
$956$	−125170.	−	216802.i	−0.136958	−	0.237217i
$957$	−72878.6	−	42076.5i	−0.0795749	−	0.0459426i
$958$		−	203839.i		−	0.222104i
$959$	134734.	−	696796.i	0.146501	−	0.757650i
$960$		0			0
$961$	−461657.	+	799613.i	−0.499888	+	0.865831i
$962$	−1.23954e6	+	715649.i	−1.33940	+	0.773303i
$963$	−241001.	−	417426.i	−0.259876	−	0.450119i
$964$	−252848.	−	145982.i	−0.272086	−	0.157089i
$965$		0			0
$966$	−291850.	−	844900.i	−0.312756	−	0.905422i
$967$	−603847.			−0.645764			−0.322882	−	0.946439i	$-0.604652\pi$
$967$	−603847.			−0.645764			−0.322882	+	0.946439i	$0.604652\pi$
$968$	165057.	−	285887.i	0.176150	−	0.305101i
$969$	116896.	−	67490.1i	0.124495	−	0.0718775i
$970$		0			0
$971$	−1.02176e6	−	589916.i	−1.08371	−	0.625679i	−0.151814	−	0.988409i	$-0.548511\pi$
$971$	−1.02176e6	−	589916.i	−1.08371	−	0.625679i	−0.931894	+	0.362730i	$0.881845\pi$
$972$		−	655984.i		−	0.694321i
$973$	642617.	−	740714.i	0.678776	−	0.782393i
$974$	−241862.			−0.254947
$975$		0			0
$976$	−264385.	+	152643.i	−0.277547	+	0.160242i
$977$	665749.	+	1.15311e6i	0.697463	+	1.20804i	0.969343	+	0.245710i	$0.0790212\pi$
$977$	665749.	+	1.15311e6i	0.697463	+	1.20804i	−0.271880	+	0.962331i	$0.587645\pi$
$978$	432629.	+	249778.i	0.452311	+	0.261142i
$979$		−	1078.18i		−	0.00112493i
$980$		0			0
$981$	1.49571e6			1.55421
$982$	510331.	−	883920.i	0.529211	−	0.916621i
$983$	393944.	−	227444.i	0.407687	−	0.235378i	−0.282108	−	0.959383i	$-0.591034\pi$
$983$	393944.	−	227444.i	0.407687	−	0.235378i	0.689796	+	0.724004i	$0.257700\pi$
$984$	360435.	+	624292.i	0.372252	+	0.644760i
$985$		0			0
$986$		−	323963.i		−	0.333228i
$987$	1.41049e6	+	1.22369e6i	1.44789	+	1.25614i
$988$	205042.			0.210053
$989$	105672.	−	183030.i	0.108036	−	0.187124i
$990$		0			0
$991$	632867.	+	1.09616e6i	0.644415	+	1.11616i	0.984436	+	0.175741i	$0.0562323\pi$
$991$	632867.	+	1.09616e6i	0.644415	+	1.11616i	−0.340022	+	0.940418i	$0.610434\pi$
$992$	2258.93	+	1304.19i	0.00229551	+	0.00132531i
$993$			727616.i			0.737911i
$994$	−241592.	+	83452.2i	−0.244518	+	0.0844627i
$995$		0			0
$996$	183686.	−	318154.i	0.185164	−	0.320714i
$997$	1.24903e6	−	721126.i	1.25655	−	0.725472i	0.284151	−	0.958779i	$-0.408288\pi$
$997$	1.24903e6	−	721126.i	1.25655	−	0.725472i	0.972403	+	0.233307i	$0.0749548\pi$
$998$	−546589.	−	946719.i	−0.548781	−	0.950517i
$999$	88856.1	+	51301.1i	0.0890341	+	0.0514038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.5.k.e.201.1		32
5.2	odd	4		70.5.h.a.19.2	✓	32
5.3	odd	4		70.5.h.a.19.15	yes	32
5.4	even	2	inner	350.5.k.e.201.16		32
7.3	odd	6	inner	350.5.k.e.101.1		32
35.2	odd	12		490.5.d.a.489.20		32
35.3	even	12		70.5.h.a.59.2	yes	32
35.12	even	12		490.5.d.a.489.18		32
35.17	even	12		70.5.h.a.59.15	yes	32
35.23	odd	12		490.5.d.a.489.17		32
35.24	odd	6	inner	350.5.k.e.101.16		32
35.33	even	12		490.5.d.a.489.19		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.5.h.a.19.2	✓	32	5.2	odd	4
70.5.h.a.19.15	yes	32	5.3	odd	4
70.5.h.a.59.2	yes	32	35.3	even	12
70.5.h.a.59.15	yes	32	35.17	even	12
350.5.k.e.101.1		32	7.3	odd	6	inner
350.5.k.e.101.16		32	35.24	odd	6	inner
350.5.k.e.201.1		32	1.1	even	1	trivial
350.5.k.e.201.16		32	5.4	even	2	inner
490.5.d.a.489.17		32	35.23	odd	12
490.5.d.a.489.18		32	35.12	even	12
490.5.d.a.489.19		32	35.33	even	12
490.5.d.a.489.20		32	35.2	odd	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	350.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 2.44949i) q^{2} +(10.8605 - 6.27030i) q^{3} +(-4.00000 - 6.92820i) q^{4} +35.4702i q^{6} +(37.0123 + 32.1106i) q^{7} +22.6274 q^{8} +(38.1334 - 66.0490i) q^{9} +O(q^{10})\)	\(q+(-1.41421 + 2.44949i) q^{2} +(10.8605 - 6.27030i) q^{3} +(-4.00000 - 6.92820i) q^{4} +35.4702i q^{6} +(37.0123 + 32.1106i) q^{7} +22.6274 q^{8} +(38.1334 - 66.0490i) q^{9} +(3.60139 + 6.23778i) q^{11} +(-86.8839 - 50.1624i) q^{12} +292.752i q^{13} +(-130.998 + 45.2500i) q^{14} +(-32.0000 + 55.4256i) q^{16} +(106.471 - 61.4709i) q^{17} +(107.858 + 186.815i) q^{18} +(75.8198 + 43.7746i) q^{19} +(603.315 + 116.658i) q^{21} -20.3725 q^{22} +(-257.154 + 445.403i) q^{23} +(245.745 - 141.881i) q^{24} +(-717.094 - 414.014i) q^{26} +59.3570i q^{27} +(74.4194 - 384.871i) q^{28} -931.646 q^{29} +(-12.4789 + 7.20472i) q^{31} +(-90.5097 - 156.767i) q^{32} +(78.2256 + 45.1636i) q^{33} +347.732i q^{34} -610.135 q^{36} +(864.280 - 1496.98i) q^{37} +(-214.451 + 123.813i) q^{38} +(1835.65 + 3179.43i) q^{39} +2540.41i q^{41} +(-1138.97 + 1312.83i) q^{42} -410.931 q^{43} +(28.8111 - 49.9023i) q^{44} +(-727.340 - 1259.79i) q^{46} +(2631.70 + 1519.41i) q^{47} +802.599i q^{48} +(338.821 + 2376.97i) q^{49} +(770.882 - 1335.21i) q^{51} +(2028.25 - 1171.01i) q^{52} +(-994.156 - 1721.93i) q^{53} +(-145.394 - 83.9435i) q^{54} +(837.493 + 726.580i) q^{56} +1097.92 q^{57} +(1317.55 - 2282.06i) q^{58} +(3389.27 - 1956.80i) q^{59} +(4131.01 + 2385.04i) q^{61} -40.7560i q^{62} +(3532.28 - 1220.14i) q^{63} +512.000 q^{64} +(-221.255 + 127.742i) q^{66} +(-3824.99 - 6625.07i) q^{67} +(-851.766 - 491.767i) q^{68} +6449.73i q^{69} +1844.25 q^{71} +(862.860 - 1494.52i) q^{72} +(9178.65 - 5299.30i) q^{73} +(2444.55 + 4234.09i) q^{74} -700.394i q^{76} +(-67.0033 + 346.517i) q^{77} -10384.0 q^{78} +(-1890.26 + 3274.03i) q^{79} +(3460.99 + 5994.61i) q^{81} +(-6222.71 - 3592.68i) q^{82} +3661.83i q^{83} +(-1605.03 - 4646.52i) q^{84} +(581.144 - 1006.57i) q^{86} +(-10118.1 + 5841.71i) q^{87} +(81.4901 + 141.145i) q^{88} +(-129.635 - 74.8449i) q^{89} +(-9400.45 + 10835.4i) q^{91} +4114.46 q^{92} +(-90.3515 + 156.493i) q^{93} +(-7443.58 + 4297.55i) q^{94} +(-1965.96 - 1135.05i) q^{96} +12754.1i q^{97} +(-6301.54 - 2531.61i) q^{98} +549.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 128 q^{4} + 516 q^{9}+O(q^{10}) \) 32 * q - 128 * q^4 + 516 * q^9	\( 32 q - 128 q^{4} + 516 q^{9} - 144 q^{11} - 96 q^{14} - 1024 q^{16} + 816 q^{19} + 1084 q^{21} - 768 q^{24} - 576 q^{26} - 912 q^{29} + 6468 q^{31} - 8256 q^{36} + 2424 q^{39} - 1152 q^{44} + 1664 q^{46} + 7712 q^{49} + 2708 q^{51} - 7776 q^{54} - 768 q^{56} - 3924 q^{59} + 41556 q^{61} + 16384 q^{64} - 15360 q^{66} - 53808 q^{71} + 6336 q^{74} + 24076 q^{79} + 17680 q^{81} + 19232 q^{84} + 6624 q^{86} + 41436 q^{89} + 12928 q^{91} - 62880 q^{94} + 6144 q^{96} - 101048 q^{99}+O(q^{100}) \) 32 * q - 128 * q^4 + 516 * q^9 - 144 * q^11 - 96 * q^14 - 1024 * q^16 + 816 * q^19 + 1084 * q^21 - 768 * q^24 - 576 * q^26 - 912 * q^29 + 6468 * q^31 - 8256 * q^36 + 2424 * q^39 - 1152 * q^44 + 1664 * q^46 + 7712 * q^49 + 2708 * q^51 - 7776 * q^54 - 768 * q^56 - 3924 * q^59 + 41556 * q^61 + 16384 * q^64 - 15360 * q^66 - 53808 * q^71 + 6336 * q^74 + 24076 * q^79 + 17680 * q^81 + 19232 * q^84 + 6624 * q^86 + 41436 * q^89 + 12928 * q^91 - 62880 * q^94 + 6144 * q^96 - 101048 * q^99

Introduction

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