LMFDB - Embedded newform 150.6.e.b.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(107,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("150.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.e (of order $4$, 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:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1126 x^{18} + 420245 x^{16} + 66878446 x^{14} + 5652274660 x^{12} + 280235806770 x^{10} + \cdots + 87\!\cdots\!24 $ x^20 + 1126x^18 + 420245x^16 + 66878446x^14 + 5652274660x^12 + 280235806770x^10 + 8434804524517x^8 + 152000977499746x^6 + 1527059794861601x^4 + 7117033734175912*x^2 + 8701432272235024
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{14}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.1
Root			$-5.20628i$ of defining polynomial
Character	$\chi$	$=$	150.143
Dual form			150.6.e.b.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82843 - 2.82843i) q^{2} +(-14.4107 + 5.94397i) q^{3} +16.0000i q^{4} +(57.5718 + 23.9476i) q^{6} +(-93.4247 + 93.4247i) q^{7} +(45.2548 - 45.2548i) q^{8} +(172.338 - 171.314i) q^{9} +O(q^{10})$	\(q+(-2.82843 - 2.82843i) q^{2} +(-14.4107 + 5.94397i) q^{3} +16.0000i q^{4} +(57.5718 + 23.9476i) q^{6} +(-93.4247 + 93.4247i) q^{7} +(45.2548 - 45.2548i) q^{8} +(172.338 - 171.314i) q^{9} +532.389i q^{11} +(-95.1035 - 230.572i) q^{12} +(228.745 + 228.745i) q^{13} +528.490 q^{14} -256.000 q^{16} +(1251.27 + 1251.27i) q^{17} +(-971.996 - 2.89756i) q^{18} -1775.34i q^{19} +(791.005 - 1901.63i) q^{21} +(1505.82 - 1505.82i) q^{22} +(-102.888 + 102.888i) q^{23} +(-383.162 + 921.149i) q^{24} -1293.98i q^{26} +(-1465.24 + 3493.13i) q^{27} +(-1494.80 - 1494.80i) q^{28} +1458.94 q^{29} -8197.54 q^{31} +(724.077 + 724.077i) q^{32} +(-3164.51 - 7672.12i) q^{33} -7078.26i q^{34} +(2741.02 + 2757.41i) q^{36} +(-3940.57 + 3940.57i) q^{37} +(-5021.41 + 5021.41i) q^{38} +(-4656.04 - 1936.73i) q^{39} +6504.96i q^{41} +(-7615.93 + 3141.33i) q^{42} +(-11726.4 - 11726.4i) q^{43} -8518.22 q^{44} +582.021 q^{46} +(-10710.1 - 10710.1i) q^{47} +(3689.15 - 1521.66i) q^{48} -649.348i q^{49} +(-25469.3 - 10594.2i) q^{51} +(-3659.92 + 3659.92i) q^{52} +(-6133.46 + 6133.46i) q^{53} +(14024.4 - 5735.76i) q^{54} +8455.84i q^{56} +(10552.6 + 25583.9i) q^{57} +(-4126.51 - 4126.51i) q^{58} -40936.2 q^{59} +35185.1 q^{61} +(23186.1 + 23186.1i) q^{62} +(-95.7082 + 32105.6i) q^{63} -4096.00i q^{64} +(-12749.4 + 30650.6i) q^{66} +(1217.35 - 1217.35i) q^{67} +(-20020.3 + 20020.3i) q^{68} +(871.126 - 2094.25i) q^{69} +7273.05i q^{71} +(46.3610 - 15551.9i) q^{72} +(-47807.2 - 47807.2i) q^{73} +22291.2 q^{74} +28405.4 q^{76} +(-49738.3 - 49738.3i) q^{77} +(7691.36 + 18647.2i) q^{78} -55381.1i q^{79} +(352.052 - 59048.0i) q^{81} +(18398.8 - 18398.8i) q^{82} +(40503.2 - 40503.2i) q^{83} +(30426.1 + 12656.1i) q^{84} +66334.8i q^{86} +(-21024.4 + 8671.91i) q^{87} +(24093.2 + 24093.2i) q^{88} -16115.1 q^{89} -42740.9 q^{91} +(-1646.20 - 1646.20i) q^{92} +(118133. - 48725.9i) q^{93} +60585.5i q^{94} +(-14738.4 - 6130.59i) q^{96} +(48244.0 - 48244.0i) q^{97} +(-1836.63 + 1836.63i) q^{98} +(91205.7 + 91751.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} + 80 q^{6} - 76 q^{7}+O(q^{10}) $ 20 * q + 4 * q^3 + 80 * q^6 - 76 * q^7	$ 20 q + 4 q^{3} + 80 q^{6} - 76 q^{7} - 64 q^{12} - 2640 q^{13} - 5120 q^{16} + 2272 q^{18} - 760 q^{21} + 464 q^{22} - 16556 q^{27} - 1216 q^{28} + 23960 q^{31} + 7684 q^{33} - 13120 q^{36} + 60696 q^{37} - 46864 q^{42} - 48024 q^{43} + 58880 q^{46} - 1024 q^{48} - 155240 q^{51} + 42240 q^{52} - 167744 q^{57} - 38000 q^{58} + 160680 q^{61} + 219364 q^{63} - 158560 q^{66} + 118736 q^{67} - 36352 q^{72} - 379100 q^{73} + 78080 q^{76} + 25440 q^{78} - 282260 q^{81} + 262976 q^{82} - 249380 q^{87} + 7424 q^{88} + 499200 q^{91} + 304072 q^{93} - 20480 q^{96} + 288228 q^{97}+O(q^{100}) $ 20 * q + 4 * q^3 + 80 * q^6 - 76 * q^7 - 64 * q^12 - 2640 * q^13 - 5120 * q^16 + 2272 * q^18 - 760 * q^21 + 464 * q^22 - 16556 * q^27 - 1216 * q^28 + 23960 * q^31 + 7684 * q^33 - 13120 * q^36 + 60696 * q^37 - 46864 * q^42 - 48024 * q^43 + 58880 * q^46 - 1024 * q^48 - 155240 * q^51 + 42240 * q^52 - 167744 * q^57 - 38000 * q^58 + 160680 * q^61 + 219364 * q^63 - 158560 * q^66 + 118736 * q^67 - 36352 * q^72 - 379100 * q^73 + 78080 * q^76 + 25440 * q^78 - 282260 * q^81 + 262976 * q^82 - 249380 * q^87 + 7424 * q^88 + 499200 * q^91 + 304072 * q^93 - 20480 * q^96 + 288228 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−2.82843	−	2.82843i	−0.500000	−	0.500000i
$2$	−2.82843	−	2.82843i	−0.500000	−	0.500000i
$3$	−14.4107	+	5.94397i	−0.924449	+	0.381306i
$3$	−14.4107	+	5.94397i	−0.924449	+	0.381306i
$4$			16.0000i			0.500000i
$5$		0			0
$5$		0			0
$6$	57.5718	+	23.9476i	0.652877	+	0.271571i
$7$	−93.4247	+	93.4247i	−0.720637	+	0.720637i	−0.968735	−	0.248098i	$-0.920195\pi$
$7$	−93.4247	+	93.4247i	−0.720637	+	0.720637i	0.248098	+	0.968735i	$0.420195\pi$
$8$	45.2548	−	45.2548i	0.250000	−	0.250000i
$9$	172.338	−	171.314i	0.709212	−	0.704996i
$10$		0			0
$11$			532.389i			1.32662i	0.748344	+	0.663311i	$0.230849\pi$
$11$			532.389i			1.32662i	−0.748344	+	0.663311i	$0.769151\pi$
$12$	−95.1035	−	230.572i	−0.190653	−	0.462224i
$13$	228.745	+	228.745i	0.375399	+	0.375399i	0.869439	−	0.494040i	$-0.164480\pi$
$13$	228.745	+	228.745i	0.375399	+	0.375399i	−0.494040	+	0.869439i	$0.664480\pi$
$14$	528.490			0.720637
$15$		0			0
$16$	−256.000			−0.250000
$17$	1251.27	+	1251.27i	1.05010	+	1.05010i	0.998677	+	0.0514194i	$0.0163745\pi$
$17$	1251.27	+	1251.27i	1.05010	+	1.05010i	0.0514194	+	0.998677i	$0.483625\pi$
$18$	−971.996	−	2.89756i	−0.707104	−	0.00210791i
$19$		−	1775.34i		−	1.12823i	−0.825697	−	0.564114i	$-0.809218\pi$
$19$		−	1775.34i		−	1.12823i	0.825697	−	0.564114i	$-0.190782\pi$
$20$		0			0
$21$	791.005	−	1901.63i	0.391409	−	0.940975i
$22$	1505.82	−	1505.82i	0.663311	−	0.663311i
$23$	−102.888	+	102.888i	−0.0405550	+	0.0405550i	−0.727093	−	0.686538i	$-0.759129\pi$
$23$	−102.888	+	102.888i	−0.0405550	+	0.0405550i	0.686538	+	0.727093i	$0.259129\pi$
$24$	−383.162	+	921.149i	−0.135786	+	0.326439i
$25$		0			0
$26$		−	1293.98i		−	0.375399i
$27$	−1465.24	+	3493.13i	−0.386811	+	0.922159i
$28$	−1494.80	−	1494.80i	−0.360319	−	0.360319i
$29$	1458.94			0.322139			0.161069	−	0.986943i	$-0.448506\pi$
$29$	1458.94			0.322139			0.161069	+	0.986943i	$0.448506\pi$
$30$		0			0
$31$	−8197.54			−1.53207			−0.766036	−	0.642798i	$-0.777774\pi$
$31$	−8197.54			−1.53207			−0.766036	+	0.642798i	$0.777774\pi$
$32$	724.077	+	724.077i	0.125000	+	0.125000i
$33$	−3164.51	−	7672.12i	−0.505849	−	1.22639i
$34$		−	7078.26i		−	1.05010i
$35$		0			0
$36$	2741.02	+	2757.41i	0.352498	+	0.354606i
$37$	−3940.57	+	3940.57i	−0.473210	+	0.473210i	−0.902952	−	0.429742i	$-0.858605\pi$
$37$	−3940.57	+	3940.57i	−0.473210	+	0.473210i	0.429742	+	0.902952i	$0.358605\pi$
$38$	−5021.41	+	5021.41i	−0.564114	+	0.564114i
$39$	−4656.04	−	1936.73i	−0.490179	−	0.203895i
$40$		0			0
$41$			6504.96i			0.604345i	0.953253	+	0.302173i	$0.0977119\pi$
$41$			6504.96i			0.604345i	−0.953253	+	0.302173i	$0.902288\pi$
$42$	−7615.93	+	3141.33i	−0.666192	+	0.274783i
$43$	−11726.4	−	11726.4i	−0.967153	−	0.967153i	0.0323242	−	0.999477i	$-0.489709\pi$
$43$	−11726.4	−	11726.4i	−0.967153	−	0.967153i	−0.999477	+	0.0323242i	$0.989709\pi$
$44$	−8518.22			−0.663311
$45$		0			0
$46$	582.021			0.0405550
$47$	−10710.1	−	10710.1i	−0.707211	−	0.707211i	0.258737	−	0.965948i	$-0.416694\pi$
$47$	−10710.1	−	10710.1i	−0.707211	−	0.707211i	−0.965948	+	0.258737i	$0.916694\pi$
$48$	3689.15	−	1521.66i	0.231112	−	0.0953265i
$49$		−	649.348i		−	0.0386356i
$50$		0			0
$51$	−25469.3	−	10594.2i	−1.37117	−	0.570353i
$52$	−3659.92	+	3659.92i	−0.187700	+	0.187700i
$53$	−6133.46	+	6133.46i	−0.299927	+	0.299927i	−0.840985	−	0.541058i	$-0.818024\pi$
$53$	−6133.46	+	6133.46i	−0.299927	+	0.299927i	0.541058	+	0.840985i	$0.318024\pi$
$54$	14024.4	−	5735.76i	0.654485	−	0.267674i
$55$		0			0
$56$			8455.84i			0.360319i
$57$	10552.6	+	25583.9i	0.430200	+	1.04299i
$58$	−4126.51	−	4126.51i	−0.161069	−	0.161069i
$59$	−40936.2			−1.53101			−0.765504	−	0.643432i	$-0.777510\pi$
$59$	−40936.2			−1.53101			−0.765504	+	0.643432i	$0.777510\pi$
$60$		0			0
$61$	35185.1			1.21070			0.605348	−	0.795961i	$-0.293034\pi$
$61$	35185.1			1.21070			0.605348	+	0.795961i	$0.293034\pi$
$62$	23186.1	+	23186.1i	0.766036	+	0.766036i
$63$	−95.7082	+	32105.6i	−0.00303807	+	1.01913i
$64$		−	4096.00i		−	0.125000i
$65$		0			0
$66$	−12749.4	+	30650.6i	−0.360273	+	0.866122i
$67$	1217.35	−	1217.35i	0.0331306	−	0.0331306i	−0.690347	−	0.723478i	$-0.742542\pi$
$67$	1217.35	−	1217.35i	0.0331306	−	0.0331306i	0.723478	+	0.690347i	$0.242542\pi$
$68$	−20020.3	+	20020.3i	−0.525048	+	0.525048i
$69$	871.126	−	2094.25i	0.0220271	−	0.0529548i
$70$		0			0
$71$			7273.05i			0.171226i	0.996328	+	0.0856132i	$0.0272849\pi$
$71$			7273.05i			0.171226i	−0.996328	+	0.0856132i	$0.972715\pi$
$72$	46.3610	−	15551.9i	0.00105395	−	0.353552i
$73$	−47807.2	−	47807.2i	−1.04999	−	1.04999i	−0.998683	−	0.0513096i	$-0.983660\pi$
$73$	−47807.2	−	47807.2i	−1.04999	−	1.04999i	−0.0513096	−	0.998683i	$-0.516340\pi$
$74$	22291.2			0.473210
$75$		0			0
$76$	28405.4			0.564114
$77$	−49738.3	−	49738.3i	−0.956013	−	0.956013i
$78$	7691.36	+	18647.2i	0.143142	+	0.347037i
$79$		−	55381.1i		−	0.998375i	−0.866494	−	0.499187i	$-0.833632\pi$
$79$		−	55381.1i		−	0.998375i	0.866494	−	0.499187i	$-0.166368\pi$
$80$		0			0
$81$	352.052	−	59048.0i	0.00596203	−	0.999982i
$82$	18398.8	−	18398.8i	0.302173	−	0.302173i
$83$	40503.2	−	40503.2i	0.645349	−	0.645349i	−0.306517	−	0.951865i	$-0.599164\pi$
$83$	40503.2	−	40503.2i	0.645349	−	0.645349i	0.951865	+	0.306517i	$0.0991635\pi$
$84$	30426.1	+	12656.1i	0.470488	+	0.195704i
$85$		0			0
$86$			66334.8i			0.967153i
$87$	−21024.4	+	8671.91i	−0.297801	+	0.122834i
$88$	24093.2	+	24093.2i	0.331656	+	0.331656i
$89$	−16115.1			−0.215654			−0.107827	−	0.994170i	$-0.534389\pi$
$89$	−16115.1			−0.215654			−0.107827	+	0.994170i	$0.534389\pi$
$90$		0			0
$91$	−42740.9			−0.541053
$92$	−1646.20	−	1646.20i	−0.0202775	−	0.0202775i
$93$	118133.	−	48725.9i	1.41632	−	0.584188i
$94$			60585.5i			0.707211i
$95$		0			0
$96$	−14738.4	−	6130.59i	−0.163219	−	0.0678929i
$97$	48244.0	−	48244.0i	0.520611	−	0.520611i	−0.397145	−	0.917756i	$-0.629999\pi$
$97$	48244.0	−	48244.0i	0.520611	−	0.520611i	0.917756	+	0.397145i	$0.129999\pi$
$98$	−1836.63	+	1836.63i	−0.0193178	+	0.0193178i
$99$	91205.7	+	91751.1i	0.935263	+	0.940856i
$100$		0			0
$101$		−	167879.i		−	1.63755i	−0.574116	−	0.818774i	$-0.694654\pi$
$101$		−	167879.i		−	1.63755i	0.574116	−	0.818774i	$-0.305346\pi$
$102$	42073.0	+	102003.i	0.400408	+	0.970761i
$103$	71223.9	+	71223.9i	0.661504	+	0.661504i	0.955735	−	0.294230i	$-0.0950632\pi$
$103$	71223.9	+	71223.9i	0.661504	+	0.661504i	−0.294230	+	0.955735i	$0.595063\pi$
$104$	20703.6			0.187700
$105$		0			0
$106$	34696.1			0.299927
$107$	16177.5	+	16177.5i	0.136600	+	0.136600i	0.772101	−	0.635500i	$-0.219206\pi$
$107$	16177.5	+	16177.5i	0.136600	+	0.136600i	−0.635500	+	0.772101i	$0.719206\pi$
$108$	−55890.1	−	23443.8i	−0.461080	−	0.193405i
$109$			174317.i			1.40531i	0.711529	+	0.702657i	$0.248003\pi$
$109$			174317.i			1.40531i	−0.711529	+	0.702657i	$0.751997\pi$
$110$		0			0
$111$	33363.8	−	80209.0i	0.257021	−	0.617897i
$112$	23916.7	−	23916.7i	0.180159	−	0.180159i
$113$	6071.04	−	6071.04i	0.0447267	−	0.0447267i	−0.684390	−	0.729116i	$-0.739931\pi$
$113$	6071.04	−	6071.04i	0.0447267	−	0.0447267i	0.729116	+	0.684390i	$0.239931\pi$
$114$	42515.1	−	102209.i	0.306395	−	0.736595i
$115$		0			0
$116$			23343.1i			0.161069i
$117$	78608.8	+	234.336i	0.530892	+	0.00158261i
$118$	115785.	+	115785.i	0.765504	+	0.765504i
$119$	−233799.			−1.51348
$120$		0			0
$121$	−122387.			−0.759927
$122$	−99518.6	−	99518.6i	−0.605348	−	0.605348i
$123$	−38665.3	−	93741.2i	−0.230440	−	0.558686i
$124$		−	131161.i		−	0.766036i
$125$		0			0
$126$	91079.1	−	90537.7i	0.511084	−	0.508046i
$127$	59728.9	−	59728.9i	0.328606	−	0.328606i	−0.523451	−	0.852056i	$-0.675356\pi$
$127$	59728.9	−	59728.9i	0.328606	−	0.328606i	0.852056	+	0.523451i	$0.175356\pi$
$128$	−11585.2	+	11585.2i	−0.0625000	+	0.0625000i
$129$	238688.	+	99285.0i	1.26287	+	0.525302i
$130$		0			0
$131$			277065.i			1.41060i	0.708910	+	0.705299i	$0.249187\pi$
$131$			277065.i			1.41060i	−0.708910	+	0.705299i	$0.750813\pi$
$132$	122754.	−	50632.1i	0.613197	−	0.252925i
$133$	165860.	+	165860.i	0.813043	+	0.813043i
$134$	−6886.38			−0.0331306
$135$		0			0
$136$	113252.			0.525048
$137$	−177207.	−	177207.i	−0.806640	−	0.806640i	0.177484	−	0.984124i	$-0.443204\pi$
$137$	−177207.	−	177207.i	−0.806640	−	0.806640i	−0.984124	+	0.177484i	$0.943204\pi$
$138$	−8387.35	+	3459.52i	−0.0374910	+	0.0154638i
$139$		−	41386.0i		−	0.181684i	−0.995865	−	0.0908420i	$-0.971044\pi$
$139$		−	41386.0i		−	0.181684i	0.995865	−	0.0908420i	$-0.0289558\pi$
$140$		0			0
$141$	218001.	+	90679.9i	0.923444	+	0.384117i
$142$	20571.3	−	20571.3i	0.0856132	−	0.0856132i
$143$	−121781.	+	121781.i	−0.498013	+	0.498013i
$144$	−44118.6	+	43856.4i	−0.177303	+	0.176249i
$145$		0			0
$146$			270438.i			1.04999i
$147$	3859.70	+	9357.58i	0.0147320	+	0.0357166i
$148$	−63049.0	−	63049.0i	−0.236605	−	0.236605i
$149$	−50199.3			−0.185239			−0.0926194	−	0.995702i	$-0.529524\pi$
$149$	−50199.3			−0.185239			−0.0926194	+	0.995702i	$0.529524\pi$
$150$		0			0
$151$	198295.			0.707733			0.353867	−	0.935296i	$-0.384867\pi$
$151$	198295.			0.707733			0.353867	+	0.935296i	$0.384867\pi$
$152$	−80342.6	−	80342.6i	−0.282057	−	0.282057i
$153$	430002.	+	1281.86i	1.48505	+	0.00442701i
$154$			281362.i			0.956013i
$155$		0			0
$156$	30987.7	−	74496.6i	0.101948	−	0.245090i
$157$	−314306.	+	314306.i	−1.01766	+	1.01766i	−0.0178196	+	0.999841i	$0.505672\pi$
$157$	−314306.	+	314306.i	−1.01766	+	1.01766i	−0.999841	+	0.0178196i	$0.994328\pi$
$158$	−156641.	+	156641.i	−0.499187	+	0.499187i
$159$	51930.6	−	124845.i	0.162903	−	0.391632i
$160$		0			0
$161$		−	19224.5i		−	0.0584508i
$162$	−168009.	+	166017.i	−0.502972	+	0.497010i
$163$	−342470.	−	342470.i	−1.00961	−	1.00961i	−0.999953	−	0.00965779i	$-0.996926\pi$
$163$	−342470.	−	342470.i	−1.00961	−	1.00961i	−0.00965779	−	0.999953i	$-0.503074\pi$
$164$	−104079.			−0.302173
$165$		0			0
$166$	−229121.			−0.645349
$167$	88908.4	+	88908.4i	0.246690	+	0.246690i	0.819611	−	0.572921i	$-0.194190\pi$
$167$	88908.4	+	88908.4i	0.246690	+	0.246690i	−0.572921	+	0.819611i	$0.694190\pi$
$168$	−50261.3	−	121855.i	−0.137392	−	0.333096i
$169$		−	266644.i		−	0.718151i
$170$		0			0
$171$	−304140.	−	305959.i	−0.795396	−	0.800153i
$172$	187623.	−	187623.i	0.483577	−	0.483577i
$173$	−100832.	+	100832.i	−0.256144	+	0.256144i	−0.823484	−	0.567340i	$-0.807973\pi$
$173$	−100832.	+	100832.i	−0.256144	+	0.256144i	0.567340	+	0.823484i	$0.307973\pi$
$174$	83994.0	+	34938.2i	0.210317	+	0.0874838i
$175$		0			0
$176$		−	136292.i		−	0.331656i
$177$	589920.	−	243323.i	1.41534	−	0.583782i
$178$	45580.3	+	45580.3i	0.107827	+	0.107827i
$179$	−551834.			−1.28729			−0.643645	−	0.765324i	$-0.722579\pi$
$179$	−551834.			−1.28729			−0.643645	+	0.765324i	$0.722579\pi$
$180$		0			0
$181$	−437959.			−0.993658			−0.496829	−	0.867848i	$-0.665502\pi$
$181$	−437959.			−0.993658			−0.496829	+	0.867848i	$0.665502\pi$
$182$	120889.	+	120889.i	0.270527	+	0.270527i
$183$	−507044.	+	209140.i	−1.11923	+	0.461645i
$184$			9312.34i			0.0202775i
$185$		0			0
$186$	−471947.	−	196311.i	−1.00026	−	0.416067i
$187$	−666163.	+	666163.i	−1.39308	+	1.39308i
$188$	171362.	−	171362.i	0.353606	−	0.353606i
$189$	−189456.	−	463234.i	−0.385792	−	0.943292i
$190$		0			0
$191$			269362.i			0.534260i	0.963661	+	0.267130i	$0.0860753\pi$
$191$			269362.i			0.534260i	−0.963661	+	0.267130i	$0.913925\pi$
$192$	24346.5	+	59026.4i	0.0476632	+	0.115556i
$193$	−383856.	−	383856.i	−0.741779	−	0.741779i	0.231141	−	0.972920i	$-0.425754\pi$
$193$	−383856.	−	383856.i	−0.741779	−	0.741779i	−0.972920	+	0.231141i	$0.925754\pi$
$194$	−272909.			−0.520611
$195$		0			0
$196$	10389.6			0.0193178
$197$	168090.	+	168090.i	0.308587	+	0.308587i	0.844361	−	0.535774i	$-0.179980\pi$
$197$	168090.	+	168090.i	0.308587	+	0.308587i	−0.535774	+	0.844361i	$0.679980\pi$
$198$	1542.63	−	517480.i	0.00279640	−	0.938060i
$199$			174867.i			0.313023i	0.987676	+	0.156511i	$0.0500248\pi$
$199$			174867.i			0.313023i	−0.987676	+	0.156511i	$0.949975\pi$
$200$		0			0
$201$	−10307.0	+	24778.8i	−0.0179946	+	0.0432604i
$202$	−474835.	+	474835.i	−0.818774	+	0.818774i
$203$	−136301.	+	136301.i	−0.232145	+	0.232145i
$204$	169507.	−	407508.i	0.285176	−	0.685584i
$205$		0			0
$206$		−	402903.i		−	0.661504i
$207$	−105.403	+	35357.6i	−0.000170972	+	0.0573531i
$208$	−58558.7	−	58558.7i	−0.0938498	−	0.0938498i
$209$	945170.			1.49673
$210$		0			0
$211$	406098.			0.627950			0.313975	−	0.949431i	$-0.398339\pi$
$211$	406098.			0.627950			0.313975	+	0.949431i	$0.398339\pi$
$212$	−98135.4	−	98135.4i	−0.149964	−	0.149964i
$213$	−43230.8	−	104810.i	−0.0652896	−	0.158290i
$214$		−	91513.8i		−	0.136600i
$215$		0			0
$216$	91772.1	+	224390.i	0.133837	+	0.327242i
$217$	765853.	−	765853.i	1.10407	−	1.10407i
$218$	493043.	−	493043.i	0.702657	−	0.702657i
$219$	973101.	+	404772.i	1.37103	+	0.570296i
$220$		0			0
$221$			572444.i			0.788411i
$222$	−321233.	+	132498.i	−0.437459	+	0.180438i
$223$	−211557.	−	211557.i	−0.284882	−	0.284882i	0.550171	−	0.835052i	$-0.314563\pi$
$223$	−211557.	−	211557.i	−0.284882	−	0.284882i	−0.835052	+	0.550171i	$0.814563\pi$
$224$	−135293.			−0.180159
$225$		0			0
$226$	−34343.0			−0.0447267
$227$	−683506.	−	683506.i	−0.880395	−	0.880395i	0.113179	−	0.993575i	$-0.463897\pi$
$227$	−683506.	−	683506.i	−0.880395	−	0.880395i	−0.993575	+	0.113179i	$0.963897\pi$
$228$	−409343.	+	168841.i	−0.521495	+	0.215100i
$229$		−	1.31462e6i		−	1.65658i	−0.560301	−	0.828289i	$-0.689315\pi$
$229$		−	1.31462e6i		−	1.65658i	0.560301	−	0.828289i	$-0.310685\pi$
$230$		0			0
$231$	1.01241e6	+	421122.i	1.24832	+	0.519252i
$232$	66024.2	−	66024.2i	0.0805347	−	0.0805347i
$233$	−446598.	+	446598.i	−0.538923	+	0.538923i	−0.923213	−	0.384289i	$-0.874447\pi$
$233$	−446598.	+	446598.i	−0.538923	+	0.538923i	0.384289	+	0.923213i	$0.374447\pi$
$234$	−221676.	−	223002.i	−0.264655	−	0.266237i
$235$		0			0
$236$		−	654979.i		−	0.765504i
$237$	329184.	+	798082.i	0.380686	+	0.922946i
$238$	661284.	+	661284.i	0.756739	+	0.756739i
$239$	−784272.			−0.888120			−0.444060	−	0.895997i	$-0.646462\pi$
$239$	−784272.			−0.888120			−0.444060	+	0.895997i	$0.646462\pi$
$240$		0			0
$241$	−776997.			−0.861741			−0.430870	−	0.902414i	$-0.641793\pi$
$241$	−776997.			−0.861741			−0.430870	+	0.902414i	$0.641793\pi$
$242$	346163.	+	346163.i	0.379964	+	0.379964i
$243$	345906.	+	853017.i	0.375788	+	0.926706i
$244$			562962.i			0.605348i
$245$		0			0
$246$	−155778.	+	374502.i	−0.164123	+	0.394563i
$247$	406100.	−	406100.i	0.423536	−	0.423536i
$248$	−370978.	+	370978.i	−0.383018	+	0.383018i
$249$	−342931.	+	824431.i	−0.350517	+	0.842667i
$250$		0			0
$251$			484741.i			0.485653i	0.970070	+	0.242826i	$0.0780745\pi$
$251$			484741.i			0.485653i	−0.970070	+	0.242826i	$0.921925\pi$
$252$	−513690.	−	1531.33i	−0.509565	−	0.00151903i
$253$	−54776.3	−	54776.3i	−0.0538011	−	0.0538011i
$254$	−337877.			−0.328606
$255$		0			0
$256$	65536.0			0.0625000
$257$	897578.	+	897578.i	0.847694	+	0.847694i	0.989845	−	0.142151i	$-0.0454017\pi$
$257$	897578.	+	897578.i	0.847694	+	0.847694i	−0.142151	+	0.989845i	$0.545402\pi$
$258$	−394292.	−	955933.i	−0.368781	−	0.894084i
$259$		−	736292.i		−	0.682026i
$260$		0			0
$261$	251432.	−	249937.i	0.228465	−	0.227107i
$262$	783658.	−	783658.i	0.705299	−	0.705299i
$263$	208597.	−	208597.i	0.185960	−	0.185960i	−0.607987	−	0.793947i	$-0.708023\pi$
$263$	208597.	−	208597.i	0.185960	−	0.185960i	0.793947	+	0.607987i	$0.208023\pi$
$264$	−490409.	−	203991.i	−0.433061	−	0.180136i
$265$		0			0
$266$		−	938248.i		−	0.813043i
$267$	232230.	−	95787.4i	0.199361	−	0.0822300i
$268$	19477.6	+	19477.6i	0.0165653	+	0.0165653i
$269$	1.94547e6			1.63925			0.819624	−	0.572902i	$-0.194183\pi$
$269$	1.94547e6			1.63925			0.819624	+	0.572902i	$0.194183\pi$
$270$		0			0
$271$	−360386.			−0.298088			−0.149044	−	0.988831i	$-0.547620\pi$
$271$	−360386.			−0.298088			−0.149044	+	0.988831i	$0.547620\pi$
$272$	−320326.	−	320326.i	−0.262524	−	0.262524i
$273$	615927.	−	254050.i	0.500176	−	0.206307i
$274$			1.00243e6i			0.806640i
$275$		0			0
$276$	33508.0	+	13938.0i	0.0264774	+	0.0110136i
$277$	−1.25671e6	+	1.25671e6i	−0.984093	+	0.984093i	−0.999875	−	0.0157822i	$-0.994976\pi$
$277$	−1.25671e6	+	1.25671e6i	−0.984093	+	0.984093i	0.0157822	+	0.999875i	$0.494976\pi$
$278$	−117057.	+	117057.i	−0.0908420	+	0.0908420i
$279$	−1.41275e6	+	1.40435e6i	−1.08656	+	1.08010i
$280$		0			0
$281$		−	597622.i		−	0.451503i	−0.974185	−	0.225752i	$-0.927516\pi$
$281$		−	597622.i		−	0.451503i	0.974185	−	0.225752i	$-0.0724837\pi$
$282$	−360119.	−	873082.i	−0.269664	−	0.653781i
$283$	1.71075e6	+	1.71075e6i	1.26976	+	1.26976i	0.946214	+	0.323542i	$0.104874\pi$
$283$	1.71075e6	+	1.71075e6i	1.26976	+	1.26976i	0.323542	+	0.946214i	$0.395126\pi$
$284$	−116369.			−0.0856132
$285$		0			0
$286$	688899.			0.498013
$287$	−607724.	−	607724.i	−0.435513	−	0.435513i
$288$	248831.	+	741.775i	0.176776	+	0.000526976i
$289$			1.71150e6i			1.20541i
$290$		0			0
$291$	−408470.	+	981991.i	−0.282766	+	0.679791i
$292$	764915.	−	764915.i	0.524996	−	0.524996i
$293$	795750.	−	795750.i	0.541511	−	0.541511i	−0.382461	−	0.923972i	$-0.624923\pi$
$293$	795750.	−	795750.i	0.541511	−	0.541511i	0.923972	+	0.382461i	$0.124923\pi$
$294$	15550.3	−	37384.1i	0.0104923	−	0.0252243i
$295$		0			0
$296$			356659.i			0.236605i
$297$	−1.85971e6	−	780076.i	−1.22336	−	0.513152i
$298$	141985.	+	141985.i	0.0926194	+	0.0926194i
$299$	−47070.1			−0.0304486
$300$		0			0
$301$	2.19108e6			1.39393
$302$	−560863.	−	560863.i	−0.353867	−	0.353867i
$303$	997870.	+	2.41926e6i	0.624407	+	1.51383i
$304$			454486.i			0.282057i
$305$		0			0
$306$	−1.21260e6	−	1.21986e6i	−0.740314	−	0.744741i
$307$	921850.	−	921850.i	0.558232	−	0.558232i	−0.370572	−	0.928804i	$-0.620838\pi$
$307$	921850.	−	921850.i	0.558232	−	0.558232i	0.928804	+	0.370572i	$0.120838\pi$
$308$	795813.	−	795813.i	0.478007	−	0.478007i
$309$	−1.44974e6	−	603036.i	−0.863763	−	0.359291i
$310$		0			0
$311$			317349.i			0.186053i	0.995664	+	0.0930263i	$0.0296541\pi$
$311$			317349.i			0.186053i	−0.995664	+	0.0930263i	$0.970346\pi$
$312$	−298355.	+	123062.i	−0.173519	+	0.0715710i
$313$	−1.85447e6	−	1.85447e6i	−1.06994	−	1.06994i	−0.997363	−	0.0725788i	$-0.976877\pi$
$313$	−1.85447e6	−	1.85447e6i	−1.06994	−	1.06994i	−0.0725788	−	0.997363i	$-0.523123\pi$
$314$	1.77798e6			1.01766
$315$		0			0
$316$	886097.			0.499187
$317$	1.31175e6	+	1.31175e6i	0.733164	+	0.733164i	0.971245	−	0.238081i	$-0.0765184\pi$
$317$	1.31175e6	+	1.31175e6i	0.733164	+	0.733164i	−0.238081	+	0.971245i	$0.576518\pi$
$318$	−499996.	+	206233.i	−0.277268	+	0.114364i
$319$			776725.i			0.427357i
$320$		0			0
$321$	−329288.	−	136971.i	−0.178367	−	0.0741936i
$322$	−54375.1	+	54375.1i	−0.0292254	+	0.0292254i
$323$	2.22143e6	−	2.22143e6i	1.18475	−	1.18475i
$324$	944767.	+	5632.83i	0.499991	+	0.00298102i
$325$		0			0
$326$			1.93731e6i			1.00961i
$327$	−1.03613e6	−	2.51203e6i	−0.535854	−	1.29914i
$328$	294381.	+	294381.i	0.151086	+	0.151086i
$329$	2.00118e6			1.01929
$330$		0			0
$331$	−24698.1			−0.0123906			−0.00619531	−	0.999981i	$-0.501972\pi$
$331$	−24698.1			−0.0123906			−0.00619531	+	0.999981i	$0.501972\pi$
$332$	648052.	+	648052.i	0.322674	+	0.322674i
$333$	−4036.88	+	1.35418e6i	−0.00199497	+	0.669217i
$334$		−	502942.i		−	0.246690i
$335$		0			0
$336$	−202497.	+	486818.i	−0.0978522	+	0.235244i
$337$	891959.	−	891959.i	0.427829	−	0.427829i	−0.460059	−	0.887888i	$-0.652172\pi$
$337$	891959.	−	891959.i	0.427829	−	0.427829i	0.887888	+	0.460059i	$0.152172\pi$
$338$	−754184.	+	754184.i	−0.359076	+	0.359076i
$339$	−51402.1	+	123574.i	−0.0242930	+	0.0584022i
$340$		0			0
$341$		−	4.36428e6i		−	2.03248i
$342$	−5144.15	+	1.72562e6i	−0.00237820	+	0.797774i
$343$	−1.50952e6	−	1.50952e6i	−0.692795	−	0.692795i
$344$	−1.06136e6			−0.483577
$345$		0			0
$346$	570392.			0.256144
$347$	1.17421e6	+	1.17421e6i	0.523507	+	0.523507i	0.918629	−	0.395122i	$-0.129298\pi$
$347$	1.17421e6	+	1.17421e6i	0.523507	+	0.523507i	−0.395122	+	0.918629i	$0.629298\pi$
$348$	−138751.	−	336391.i	−0.0614168	−	0.148901i
$349$		−	2.93759e6i		−	1.29100i	−0.763758	−	0.645502i	$-0.776648\pi$
$349$		−	2.93759e6i		−	1.29100i	0.763758	−	0.645502i	$-0.223352\pi$
$350$		0			0
$351$	−1.13420e6	+	463871.i	−0.491386	+	0.200969i
$352$	−385491.	+	385491.i	−0.165828	+	0.165828i
$353$	−2.12837e6	+	2.12837e6i	−0.909097	+	0.909097i	−0.996199	−	0.0871019i	$-0.972239\pi$
$353$	−2.12837e6	+	2.12837e6i	−0.909097	+	0.909097i	0.0871019	+	0.996199i	$0.472239\pi$
$354$	−2.35677e6	−	980324.i	−0.999560	−	0.415778i
$355$		0			0
$356$		−	257841.i		−	0.107827i
$357$	3.36922e6	−	1.38970e6i	1.39913	−	0.577098i
$358$	1.56082e6	+	1.56082e6i	0.643645	+	0.643645i
$359$	−11800.2			−0.00483230			−0.00241615	−	0.999997i	$-0.500769\pi$
$359$	−11800.2			−0.00483230			−0.00241615	+	0.999997i	$0.500769\pi$
$360$		0			0
$361$	−675725.			−0.272899
$362$	1.23873e6	+	1.23873e6i	0.496829	+	0.496829i
$363$	1.76369e6	−	727465.i	0.702514	−	0.289765i
$364$		−	683854.i		−	0.270527i
$365$		0			0
$366$	2.02567e6	+	842600.i	0.790435	+	0.328790i
$367$	−644485.	+	644485.i	−0.249774	+	0.249774i	−0.820878	−	0.571104i	$-0.806515\pi$
$367$	−644485.	+	644485.i	−0.249774	+	0.249774i	0.571104	+	0.820878i	$0.306515\pi$
$368$	26339.3	−	26339.3i	0.0101387	−	0.0101387i
$369$	1.11439e6	+	1.12105e6i	0.426061	+	0.428608i
$370$		0			0
$371$		−	1.14603e6i		−	0.432278i
$372$	779615.	+	1.89012e6i	0.292094	+	0.708161i
$373$	−94546.2	−	94546.2i	−0.0351862	−	0.0351862i	0.689295	−	0.724481i	$-0.257920\pi$
$373$	−94546.2	−	94546.2i	−0.0351862	−	0.0351862i	−0.724481	+	0.689295i	$0.757920\pi$
$374$	3.76839e6			1.39308
$375$		0			0
$376$	−969368.			−0.353606
$377$	333726.	+	333726.i	0.120931	+	0.120931i
$378$	−774363.	+	1.84609e6i	−0.278750	+	0.664542i
$379$			2.59501e6i			0.927985i	0.885839	+	0.463992i	$0.153584\pi$
$379$			2.59501e6i			0.927985i	−0.885839	+	0.463992i	$0.846416\pi$
$380$		0			0
$381$	−505710.	+	1.21576e6i	−0.178480	+	0.429078i
$382$	761870.	−	761870.i	0.267130	−	0.267130i
$383$	−842011.	+	842011.i	−0.293306	+	0.293306i	−0.838385	−	0.545079i	$-0.816500\pi$
$383$	−842011.	+	842011.i	−0.293306	+	0.293306i	0.545079	+	0.838385i	$0.316500\pi$
$384$	98089.4	−	235814.i	0.0339464	−	0.0816097i
$385$		0			0
$386$			2.17142e6i			0.741779i
$387$	−4.02982e6	−	12013.1i	−1.36776	−	0.00407734i
$388$	771903.	+	771903.i	0.260306	+	0.260306i
$389$	413943.			0.138697			0.0693484	−	0.997593i	$-0.477908\pi$
$389$	413943.			0.138697			0.0693484	+	0.997593i	$0.477908\pi$
$390$		0			0
$391$	−257481.			−0.0851733
$392$	−29386.1	−	29386.1i	−0.00965889	−	0.00965889i
$393$	−1.64687e6	−	3.99271e6i	−0.537870	−	1.30403i
$394$		−	950863.i		−	0.308587i
$395$		0			0
$396$	−1.46802e6	+	1.45929e6i	−0.470428	+	0.467632i
$397$	−2.20049e6	+	2.20049e6i	−0.700719	+	0.700719i	−0.964565	−	0.263846i	$-0.915009\pi$
$397$	−2.20049e6	+	2.20049e6i	−0.700719	+	0.700719i	0.263846	+	0.964565i	$0.415009\pi$
$398$	494599.	−	494599.i	0.156511	−	0.156511i
$399$	−3.37604e6	−	1.40430e6i	−1.06164	−	0.441599i
$400$		0			0
$401$		−	2.50202e6i		−	0.777017i	−0.921445	−	0.388509i	$-0.872990\pi$
$401$		−	2.50202e6i		−	0.777017i	0.921445	−	0.388509i	$-0.127010\pi$
$402$	99237.8	−	40932.5i	0.0306275	−	0.0126329i
$403$	−1.87515e6	−	1.87515e6i	−0.575139	−	0.575139i
$404$	2.68607e6			0.818774
$405$		0			0
$406$	771037.			0.232145
$407$	−2.09791e6	−	2.09791e6i	−0.627772	−	0.627772i
$408$	−1.63205e6	+	673168.i	−0.485380	+	0.200204i
$409$		−	3.10580e6i		−	0.918047i	−0.888424	−	0.459024i	$-0.848199\pi$
$409$		−	3.10580e6i		−	0.918047i	0.888424	−	0.459024i	$-0.151801\pi$
$410$		0			0
$411$	3.60700e6	+	1.50037e6i	1.05327	+	0.438121i
$412$	−1.13958e6	+	1.13958e6i	−0.330752	+	0.330752i
$413$	3.82445e6	−	3.82445e6i	1.10330	−	1.10330i
$414$	100305.	−	99708.3i	0.0287620	−	0.0285911i
$415$		0			0
$416$			331258.i			0.0938498i
$417$	245997.	+	596403.i	0.0692772	+	0.167958i
$418$	−2.67335e6	−	2.67335e6i	−0.748367	−	0.748367i
$419$	−4.56125e6			−1.26925			−0.634627	−	0.772818i	$-0.718846\pi$
$419$	−4.56125e6			−1.26925			−0.634627	+	0.772818i	$0.718846\pi$
$420$		0			0
$421$	−5.70191e6			−1.56789			−0.783945	−	0.620831i	$-0.786795\pi$
$421$	−5.70191e6			−1.56789			−0.783945	+	0.620831i	$0.786795\pi$
$422$	−1.14862e6	−	1.14862e6i	−0.313975	−	0.313975i
$423$	−3.68055e6	−	10971.9i	−1.00014	−	0.00298147i
$424$			555138.i			0.149964i
$425$		0			0
$426$	−174172.	+	418723.i	−0.0465002	+	0.111790i
$427$	−3.28716e6	+	3.28716e6i	−0.872472	+	0.872472i
$428$	−258840.	+	258840.i	−0.0683002	+	0.0683002i
$429$	1.03109e6	−	2.47882e6i	0.270492	−	0.650283i
$430$		0			0
$431$			71392.2i			0.0185122i	0.999957	+	0.00925610i	$0.00294635\pi$
$431$			71392.2i			0.0185122i	−0.999957	+	0.00925610i	$0.997054\pi$
$432$	375101.	−	894242.i	0.0967027	−	0.230540i
$433$	1.89395e6	+	1.89395e6i	0.485454	+	0.485454i	0.906868	−	0.421414i	$-0.138466\pi$
$433$	1.89395e6	+	1.89395e6i	0.485454	+	0.485454i	−0.421414	+	0.906868i	$0.638466\pi$
$434$	−4.33232e6			−1.10407
$435$		0			0
$436$	−2.78907e6			−0.702657
$437$	182660.	+	182660.i	0.0457553	+	0.0457553i
$438$	−1.60748e6	−	3.89721e6i	−0.400368	−	0.970664i
$439$		−	1.96731e6i		−	0.487205i	−0.969875	−	0.243602i	$-0.921671\pi$
$439$		−	1.96731e6i		−	0.487205i	0.969875	−	0.243602i	$-0.0783292\pi$
$440$		0			0
$441$	−111242.	−	111908.i	−0.0272379	−	0.0274008i
$442$	1.61912e6	−	1.61912e6i	0.394205	−	0.394205i
$443$	−4.24624e6	+	4.24624e6i	−1.02801	+	1.02801i	−0.0284090	+	0.999596i	$0.509044\pi$
$443$	−4.24624e6	+	4.24624e6i	−1.02801	+	1.02801i	−0.999596	+	0.0284090i	$0.990956\pi$
$444$	1.28334e6	+	533821.i	0.308948	+	0.128510i
$445$		0			0
$446$			1.19674e6i			0.284882i
$447$	723409.	−	298383.i	0.171244	−	0.0706327i
$448$	382668.	+	382668.i	0.0900796	+	0.0900796i
$449$	−4.02040e6			−0.941139			−0.470570	−	0.882363i	$-0.655952\pi$
$449$	−4.02040e6			−0.941139			−0.470570	+	0.882363i	$0.655952\pi$
$450$		0			0
$451$	−3.46317e6			−0.801738
$452$	97136.7	+	97136.7i	0.0223634	+	0.0223634i
$453$	−2.85758e6	+	1.17866e6i	−0.654263	+	0.269863i
$454$			3.86649e6i			0.880395i
$455$		0			0
$456$	1.63535e6	+	680242.i	0.368297	+	0.153197i
$457$	568745.	−	568745.i	0.127388	−	0.127388i	−0.640539	−	0.767926i	$-0.721289\pi$
$457$	568745.	−	568745.i	0.127388	−	0.127388i	0.767926	+	0.640539i	$0.221289\pi$
$458$	−3.71831e6	+	3.71831e6i	−0.828289	+	0.828289i
$459$	−6.20427e6	+	2.53745e6i	−1.37454	+	0.562167i
$460$		0			0
$461$			875548.i			0.191879i	0.995387	+	0.0959395i	$0.0305855\pi$
$461$			875548.i			0.191879i	−0.995387	+	0.0959395i	$0.969414\pi$
$462$	−1.67241e6	−	4.05464e6i	−0.364534	−	0.883786i
$463$	−1.20171e6	−	1.20171e6i	−0.260523	−	0.260523i	0.564743	−	0.825267i	$-0.308975\pi$
$463$	−1.20171e6	−	1.20171e6i	−0.260523	−	0.260523i	−0.825267	+	0.564743i	$0.808975\pi$
$464$	−373489.			−0.0805347
$465$		0			0
$466$	2.52634e6			0.538923
$467$	3.16627e6	+	3.16627e6i	0.671824	+	0.671824i	0.958136	−	0.286312i	$-0.0924295\pi$
$467$	3.16627e6	+	3.16627e6i	0.671824	+	0.671824i	−0.286312	+	0.958136i	$0.592430\pi$
$468$	−3749.38	+	1.25774e6i	−0.000791306	+	0.265446i
$469$			227461.i			0.0477503i
$470$		0			0
$471$	2.66115e6	−	6.39760e6i	0.552735	−	1.32882i
$472$	−1.85256e6	+	1.85256e6i	−0.382752	+	0.382752i
$473$	6.24303e6	−	6.24303e6i	1.28305	−	1.28305i
$474$	1.32624e6	−	3.18839e6i	0.271130	−	0.651816i
$475$		0			0
$476$		−	3.74079e6i		−	0.756739i
$477$	−6283.38	+	2.10778e6i	−0.00126444	+	0.424160i
$478$	2.21826e6	+	2.21826e6i	0.444060	+	0.444060i
$479$	3.32590e6			0.662325			0.331162	−	0.943574i	$-0.392559\pi$
$479$	3.32590e6			0.662325			0.331162	+	0.943574i	$0.392559\pi$
$480$		0			0
$481$	−1.80277e6			−0.355285
$482$	2.19768e6	+	2.19768e6i	0.430870	+	0.430870i
$483$	114270.	+	277039.i	0.0222876	+	0.0540348i
$484$		−	1.95819e6i		−	0.379964i
$485$		0			0
$486$	1.43433e6	−	3.39107e6i	0.275459	−	0.651247i
$487$	−1.04959e6	+	1.04959e6i	−0.200538	+	0.200538i	−0.800231	−	0.599692i	$-0.795290\pi$
$487$	−1.04959e6	+	1.04959e6i	−0.200538	+	0.200538i	0.599692	+	0.800231i	$0.295290\pi$
$488$	1.59230e6	−	1.59230e6i	0.302674	−	0.302674i
$489$	6.97089e6	+	2.89962e6i	1.31830	+	0.548363i
$490$		0			0
$491$			7.57152e6i			1.41736i	0.705532	+	0.708678i	$0.250708\pi$
$491$			7.57152e6i			1.41736i	−0.705532	+	0.708678i	$0.749292\pi$
$492$	1.49986e6	−	618645.i	0.279343	−	0.115220i
$493$	1.82553e6	+	1.82553e6i	0.338277	+	0.338277i
$494$	−2.29725e6			−0.423536
$495$		0			0
$496$	2.09857e6			0.383018
$497$	−679482.	−	679482.i	−0.123392	−	0.123392i
$498$	3.30180e6	−	1.36189e6i	0.596592	−	0.246075i
$499$			3.56269e6i			0.640511i	0.947331	+	0.320256i	$0.103769\pi$
$499$			3.56269e6i			0.640511i	−0.947331	+	0.320256i	$0.896231\pi$
$500$		0			0
$501$	−1.80970e6	−	752766.i	−0.322117	−	0.133988i
$502$	1.37106e6	−	1.37106e6i	0.242826	−	0.242826i
$503$	−2.41414e6	+	2.41414e6i	−0.425443	+	0.425443i	−0.887073	−	0.461630i	$-0.847265\pi$
$503$	−2.41414e6	+	2.41414e6i	−0.425443	+	0.425443i	0.461630	+	0.887073i	$0.347265\pi$
$504$	1.44860e6	+	1.45727e6i	0.254023	+	0.255542i
$505$		0			0
$506$			309862.i			0.0538011i
$507$	1.58493e6	+	3.84254e6i	0.273835	+	0.663894i
$508$	955662.	+	955662.i	0.164303	+	0.164303i
$509$	8.05132e6			1.37744			0.688720	−	0.725028i	$-0.258173\pi$
$509$	8.05132e6			1.37744			0.688720	+	0.725028i	$0.258173\pi$
$510$		0			0
$511$	8.93275e6			1.51333
$512$	−185364.	−	185364.i	−0.0312500	−	0.0312500i
$513$	6.20149e6	+	2.60129e6i	1.04041	+	0.436411i
$514$		−	5.07747e6i		−	0.847694i
$515$		0			0
$516$	−1.58856e6	+	3.81901e6i	−0.262651	+	0.631433i
$517$	5.70194e6	−	5.70194e6i	0.938202	−	0.938202i
$518$	−2.08255e6	+	2.08255e6i	−0.341013	+	0.341013i
$519$	853721.	−	2.05241e6i	0.139123	−	0.334461i
$520$		0			0
$521$			4.61375e6i			0.744663i	0.928100	+	0.372332i	$0.121442\pi$
$521$			4.61375e6i			0.744663i	−0.928100	+	0.372332i	$0.878558\pi$
$522$	−1.41809e6	−	4227.37i	−0.227786	−	0.000679039i
$523$	1.14601e6	+	1.14601e6i	0.183203	+	0.183203i	0.792750	−	0.609547i	$-0.208649\pi$
$523$	1.14601e6	+	1.14601e6i	0.183203	+	0.183203i	−0.609547	+	0.792750i	$0.708649\pi$
$524$	−4.43304e6			−0.705299
$525$		0			0
$526$	−1.18000e6			−0.185960
$527$	−1.02573e7	−	1.02573e7i	−1.60882	−	1.60882i
$528$	810113.	+	1.96406e6i	0.126462	+	0.306599i
$529$			6.41517e6i			0.996711i
$530$		0			0
$531$	−7.05488e6	+	7.01294e6i	−1.08581	+	1.07935i
$532$	−2.65377e6	+	2.65377e6i	−0.406522	+	0.406522i
$533$	−1.48798e6	+	1.48798e6i	−0.226871	+	0.226871i
$534$	−927773.	−	385917.i	−0.140795	−	0.0585654i
$535$		0			0
$536$		−	110182.i		−	0.0165653i
$537$	7.95234e6	−	3.28009e6i	1.19003	−	0.490851i
$538$	−5.50263e6	−	5.50263e6i	−0.819624	−	0.819624i
$539$	345706.			0.0512548
$540$		0			0
$541$	6.98911e6			1.02667			0.513333	−	0.858190i	$-0.328411\pi$
$541$	6.98911e6			1.02667			0.513333	+	0.858190i	$0.328411\pi$
$542$	1.01933e6	+	1.01933e6i	0.149044	+	0.149044i
$543$	6.31131e6	−	2.60322e6i	0.918586	−	0.378888i
$544$			1.81203e6i			0.262524i
$545$		0			0
$546$	−2.46067e6	−	1.02354e6i	−0.353241	−	0.146935i
$547$	2.25933e6	−	2.25933e6i	0.322858	−	0.322858i	−0.527004	−	0.849863i	$-0.676685\pi$
$547$	2.25933e6	−	2.25933e6i	0.322858	−	0.322858i	0.849863	+	0.527004i	$0.176685\pi$
$548$	2.83531e6	−	2.83531e6i	0.403320	−	0.403320i
$549$	6.06375e6	−	6.02771e6i	0.858639	−	0.853535i
$550$		0			0
$551$		−	2.59012e6i		−	0.363446i
$552$	−55352.3	−	134198.i	−0.00773192	−	0.0187455i
$553$	5.17396e6	+	5.17396e6i	0.719466	+	0.719466i
$554$	7.10904e6			0.984093
$555$		0			0
$556$	662177.			0.0908420
$557$	−785528.	−	785528.i	−0.107281	−	0.107281i	0.651429	−	0.758710i	$-0.274170\pi$
$557$	−785528.	−	785528.i	−0.107281	−	0.107281i	−0.758710	+	0.651429i	$0.774170\pi$
$558$	7.96797e6	+	23752.9i	1.08333	+	0.00322946i
$559$		−	5.36473e6i		−	0.726137i
$560$		0			0
$561$	5.64024e6	−	1.35596e7i	0.756643	−	1.81902i
$562$	−1.69033e6	+	1.69033e6i	−0.225752	+	0.225752i
$563$	−6.23549e6	+	6.23549e6i	−0.829086	+	0.829086i	−0.987390	−	0.158304i	$-0.949397\pi$
$563$	−6.23549e6	+	6.23549e6i	−0.829086	+	0.829086i	0.158304	+	0.987390i	$0.449397\pi$
$564$	−1.45088e6	+	3.48802e6i	−0.192058	+	0.461722i
$565$		0			0
$566$		−	9.67746e6i		−	1.26976i
$567$	5.48365e6	+	5.54943e6i	0.716328	+	0.724921i
$568$	329141.	+	329141.i	0.0428066	+	0.0428066i
$569$	−4.00344e6			−0.518385			−0.259192	−	0.965826i	$-0.583456\pi$
$569$	−4.00344e6			−0.518385			−0.259192	+	0.965826i	$0.583456\pi$
$570$		0			0
$571$	4.46162e6			0.572668			0.286334	−	0.958130i	$-0.407563\pi$
$571$	4.46162e6			0.572668			0.286334	+	0.958130i	$0.407563\pi$
$572$	−1.94850e6	−	1.94850e6i	−0.249006	−	0.249006i
$573$	−1.60108e6	−	3.88170e6i	−0.203716	−	0.493896i
$574$			3.43781e6i			0.435513i
$575$		0			0
$576$	−701702.	−	705898.i	−0.0881245	−	0.0886514i
$577$	−2.95667e6	+	2.95667e6i	−0.369712	+	0.369712i	−0.867372	−	0.497660i	$-0.834193\pi$
$577$	−2.95667e6	+	2.95667e6i	−0.369712	+	0.369712i	0.497660	+	0.867372i	$0.334193\pi$
$578$	4.84086e6	−	4.84086e6i	0.602703	−	0.602703i
$579$	7.81327e6	+	3.25001e6i	0.968582	+	0.402892i
$580$		0			0
$581$			7.56800e6i			0.930124i
$582$	3.93282e6	−	1.62216e6i	0.481279	−	0.198512i
$583$	−3.26539e6	−	3.26539e6i	−0.397890	−	0.397890i
$584$	−4.32701e6			−0.524996
$585$		0			0
$586$	−4.50144e6			−0.541511
$587$	4.30683e6	+	4.30683e6i	0.515896	+	0.515896i	0.916327	−	0.400431i	$-0.131139\pi$
$587$	4.30683e6	+	4.30683e6i	0.515896	+	0.515896i	−0.400431	+	0.916327i	$0.631139\pi$
$588$	−149721.	+	61755.3i	−0.0178583	+	0.00736598i
$589$			1.45534e7i			1.72853i
$590$		0			0
$591$	−3.42143e6	−	1.42318e6i	−0.402939	−	0.167607i
$592$	1.00878e6	−	1.00878e6i	0.118303	−	0.118303i
$593$	−95880.2	+	95880.2i	−0.0111968	+	0.0111968i	−0.712683	−	0.701486i	$-0.752520\pi$
$593$	−95880.2	+	95880.2i	−0.0111968	+	0.0111968i	0.701486	+	0.712683i	$0.252520\pi$
$594$	3.05365e6	+	7.46643e6i	0.355103	+	0.868254i
$595$		0			0
$596$		−	803189.i		−	0.0926194i
$597$	−1.03941e6	−	2.51996e6i	−0.119357	−	0.289373i
$598$	133134.	+	133134.i	0.0152243	+	0.0152243i
$599$	−1.16068e7			−1.32173			−0.660866	−	0.750504i	$-0.729811\pi$
$599$	−1.16068e7			−1.32173			−0.660866	+	0.750504i	$0.729811\pi$
$600$		0			0
$601$	−4.95581e6			−0.559666			−0.279833	−	0.960049i	$-0.590279\pi$
$601$	−4.95581e6			−0.559666			−0.279833	+	0.960049i	$0.590279\pi$
$602$	−6.19731e6	−	6.19731e6i	−0.696966	−	0.696966i
$603$	1247.11	−	418346.i	0.000139672	−	0.0468535i
$604$			3.17272e6i			0.353867i
$605$		0			0
$606$	4.02031e6	−	9.66512e6i	0.444711	−	1.06912i
$607$	1.18261e7	−	1.18261e7i	1.30278	−	1.30278i	0.376265	−	0.926512i	$-0.377208\pi$
$607$	1.18261e7	−	1.18261e7i	1.30278	−	1.30278i	0.926512	−	0.376265i	$-0.122792\pi$
$608$	1.28548e6	−	1.28548e6i	0.141029	−	0.141029i
$609$	1.15403e6	−	2.77437e6i	0.126088	−	0.303125i
$610$		0			0
$611$		−	4.89977e6i		−	0.530973i
$612$	−20509.7	+	6.88004e6i	−0.00221350	+	0.742527i
$613$	6.36666e6	+	6.36666e6i	0.684322	+	0.684322i	0.960971	−	0.276649i	$-0.0892239\pi$
$613$	6.36666e6	+	6.36666e6i	0.684322	+	0.684322i	−0.276649	+	0.960971i	$0.589224\pi$
$614$	−5.21477e6			−0.558232
$615$		0			0
$616$	−4.50180e6			−0.478007
$617$	3.85761e6	+	3.85761e6i	0.407948	+	0.407948i	0.881022	−	0.473074i	$-0.156856\pi$
$617$	3.85761e6	+	3.85761e6i	0.407948	+	0.407948i	−0.473074	+	0.881022i	$0.656856\pi$
$618$	2.39485e6	+	5.80613e6i	0.252236	+	0.611527i
$619$		−	4.73303e6i		−	0.496493i	−0.968697	−	0.248246i	$-0.920146\pi$
$619$		−	4.73303e6i		−	0.496493i	0.968697	−	0.248246i	$-0.0798543\pi$
$620$		0			0
$621$	−208646.	−	510156.i	−0.0217110	−	0.0530852i
$622$	897598.	−	897598.i	0.0930263	−	0.0930263i
$623$	1.50554e6	−	1.50554e6i	0.155408	−	0.155408i
$624$	1.19195e6	+	495803.i	0.122545	+	0.0509738i
$625$		0			0
$626$			1.04905e7i			1.06994i
$627$	−1.36206e7	+	5.61807e6i	−1.38365	+	0.570713i
$628$	−5.02889e6	−	5.02889e6i	−0.508830	−	0.508830i
$629$	−9.86143e6			−0.993833
$630$		0			0
$631$	8.03410e6			0.803274			0.401637	−	0.915799i	$-0.368441\pi$
$631$	8.03410e6			0.803274			0.401637	+	0.915799i	$0.368441\pi$
$632$	−2.50626e6	−	2.50626e6i	−0.249594	−	0.249594i
$633$	−5.85218e6	+	2.41384e6i	−0.580508	+	0.239441i
$634$		−	7.42035e6i		−	0.733164i
$635$		0			0
$636$	1.99752e6	+	830889.i	0.195816	+	0.0814517i
$637$	148535.	−	148535.i	0.0145038	−	0.0145038i
$638$	2.19691e6	−	2.19691e6i	0.213678	−	0.213678i
$639$	1.24597e6	+	1.25343e6i	0.120714	+	0.121436i
$640$		0			0
$641$		−	531745.i		−	0.0511161i	−0.999673	−	0.0255581i	$-0.991864\pi$
$641$		−	531745.i		−	0.0511161i	0.999673	−	0.0255581i	$-0.00813627\pi$
$642$	543955.	+	1.31878e6i	0.0520866	+	0.126280i
$643$	1.00535e7	+	1.00535e7i	0.958938	+	0.958938i	0.999190	−	0.0402512i	$-0.0128158\pi$
$643$	1.00535e7	+	1.00535e7i	0.958938	+	0.958938i	−0.0402512	+	0.999190i	$0.512816\pi$
$644$	307592.			0.0292254
$645$		0			0
$646$	−1.25663e7			−1.18475
$647$	−6.49787e6	−	6.49787e6i	−0.610254	−	0.610254i	0.332758	−	0.943012i	$-0.392021\pi$
$647$	−6.49787e6	−	6.49787e6i	−0.610254	−	0.610254i	−0.943012	+	0.332758i	$0.892021\pi$
$648$	−2.65627e6	−	2.68814e6i	−0.248505	−	0.251486i
$649$		−	2.17940e7i		−	2.03107i
$650$		0			0
$651$	−6.48429e6	+	1.55887e7i	−0.599667	+	1.44164i
$652$	5.47953e6	−	5.47953e6i	0.504806	−	0.504806i
$653$	−7.51256e6	+	7.51256e6i	−0.689453	+	0.689453i	−0.962111	−	0.272658i	$-0.912097\pi$
$653$	−7.51256e6	+	7.51256e6i	−0.689453	+	0.689453i	0.272658	+	0.962111i	$0.412097\pi$
$654$	−4.17447e6	+	1.00357e7i	−0.381643	+	0.917498i
$655$		0			0
$656$		−	1.66527e6i		−	0.151086i
$657$	−1.64291e7	−	48975.7i	−1.48491	−	0.00442657i
$658$	−5.66018e6	−	5.66018e6i	−0.509643	−	0.509643i
$659$	8.99099e6			0.806481			0.403240	−	0.915094i	$-0.367884\pi$
$659$	8.99099e6			0.806481			0.403240	+	0.915094i	$0.367884\pi$
$660$		0			0
$661$	1.00555e7			0.895155			0.447578	−	0.894245i	$-0.352287\pi$
$661$	1.00555e7			0.895155			0.447578	+	0.894245i	$0.352287\pi$
$662$	69856.7	+	69856.7i	0.00619531	+	0.00619531i
$663$	−3.40259e6	−	8.24934e6i	−0.300626	−	0.728845i
$664$		−	3.66593e6i		−	0.322674i
$665$		0			0
$666$	3.84163e6	−	3.81879e6i	0.335606	−	0.333611i
$667$	−150107.	+	150107.i	−0.0130643	+	0.0130643i
$668$	−1.42253e6	+	1.42253e6i	−0.123345	+	0.123345i
$669$	4.30617e6	+	1.79120e6i	0.371985	+	0.154731i
$670$		0			0
$671$			1.87322e7i			1.60614i
$672$	1.94968e6	−	804180.i	0.166548	−	0.0686958i
$673$	−1.16320e7	−	1.16320e7i	−0.989957	−	0.989957i	0.00999292	−	0.999950i	$-0.496819\pi$
$673$	−1.16320e7	−	1.16320e7i	−0.989957	−	0.989957i	−0.999950	+	0.00999292i	$0.996819\pi$
$674$	−5.04568e6			−0.427829
$675$		0			0
$676$	4.26631e6			0.359076
$677$	−4.03672e6	−	4.03672e6i	−0.338499	−	0.338499i	0.517303	−	0.855802i	$-0.326936\pi$
$677$	−4.03672e6	−	4.03672e6i	−0.338499	−	0.338499i	−0.855802	+	0.517303i	$0.826936\pi$
$678$	494908.	−	204134.i	0.0413476	−	0.0170546i
$679$			9.01435e6i			0.750344i
$680$		0			0
$681$	1.39126e7	+	5.78708e6i	1.14958	+	0.478180i
$682$	−1.23440e7	+	1.23440e7i	−1.01624	+	1.01624i
$683$	1.63594e6	−	1.63594e6i	0.134188	−	0.134188i	−0.636822	−	0.771011i	$-0.719752\pi$
$683$	1.63594e6	−	1.63594e6i	0.134188	−	0.134188i	0.771011	+	0.636822i	$0.219752\pi$
$684$	4.89534e6	−	4.86624e6i	0.400076	−	0.397698i
$685$		0			0
$686$			8.53916e6i			0.692795i
$687$	7.81407e6	+	1.89446e7i	0.631663	+	1.53142i
$688$	3.00197e6	+	3.00197e6i	0.241788	+	0.241788i
$689$	−2.80600e6			−0.225185
$690$		0			0
$691$	−1.24457e7			−0.991570			−0.495785	−	0.868445i	$-0.665120\pi$
$691$	−1.24457e7			−0.991570			−0.495785	+	0.868445i	$0.665120\pi$
$692$	−1.61331e6	−	1.61331e6i	−0.128072	−	0.128072i
$693$	−1.70927e7	−	50954.0i	−1.35200	−	0.00403037i
$694$		−	6.64234e6i		−	0.523507i
$695$		0			0
$696$	−559011.	+	1.34390e6i	−0.0437419	+	0.105159i
$697$	−8.13947e6	+	8.13947e6i	−0.634621	+	0.634621i
$698$	−8.30876e6	+	8.30876e6i	−0.645502	+	0.645502i
$699$	3.78124e6	−	9.09037e6i	0.292712	−	0.703702i
$700$		0			0
$701$			8.32784e6i			0.640085i	0.947403	+	0.320042i	$0.103697\pi$
$701$			8.32784e6i			0.640085i	−0.947403	+	0.320042i	$0.896303\pi$
$702$	4.52004e6	+	1.89598e6i	0.346178	+	0.145208i
$703$	6.99583e6	+	6.99583e6i	0.533889	+	0.533889i
$704$	2.18067e6			0.165828
$705$		0			0
$706$	1.20399e7			0.909097
$707$	1.56841e7	+	1.56841e7i	1.18008	+	1.18008i
$708$	3.89318e6	+	9.43872e6i	0.291891	+	0.707669i
$709$			1.38568e7i			1.03526i	0.855606	+	0.517628i	$0.173185\pi$
$709$			1.38568e7i			1.03526i	−0.855606	+	0.517628i	$0.826815\pi$
$710$		0			0
$711$	−9.48755e6	−	9.54429e6i	−0.703850	−	0.708059i
$712$	−729284.	+	729284.i	−0.0539134	+	0.0539134i
$713$	843426.	−	843426.i	0.0621331	−	0.0621331i
$714$	−1.34602e7	−	5.59894e6i	−0.988115	−	0.411017i
$715$		0			0
$716$		−	8.82935e6i		−	0.643645i
$717$	1.13019e7	−	4.66169e6i	0.821022	−	0.338646i
$718$	33376.0	+	33376.0i	0.00241615	+	0.00241615i
$719$	713507.			0.0514726			0.0257363	−	0.999669i	$-0.491807\pi$
$719$	713507.			0.0514726			0.0257363	+	0.999669i	$0.491807\pi$
$720$		0			0
$721$	−1.33081e7			−0.953409
$722$	1.91124e6	+	1.91124e6i	0.136450	+	0.136450i
$723$	1.11971e7	−	4.61845e6i	0.796635	−	0.328587i
$724$		−	7.00734e6i		−	0.496829i
$725$		0			0
$726$	−7.04604e6	−	2.93088e6i	−0.496139	−	0.206375i
$727$	9.95425e6	−	9.95425e6i	0.698510	−	0.698510i	−0.265579	−	0.964089i	$-0.585563\pi$
$727$	9.95425e6	−	9.95425e6i	0.698510	−	0.698510i	0.964089	+	0.265579i	$0.0855632\pi$
$728$	−1.93423e6	+	1.93423e6i	−0.135263	+	0.135263i
$729$	−1.00551e7	−	1.02365e7i	−0.700755	−	0.713402i
$730$		0			0
$731$		−	2.93459e7i		−	2.03121i
$732$	−3.34623e6	−	8.11270e6i	−0.230823	−	0.559613i
$733$	−8.41698e6	−	8.41698e6i	−0.578624	−	0.578624i	0.355900	−	0.934524i	$-0.384174\pi$
$733$	−8.41698e6	−	8.41698e6i	−0.578624	−	0.578624i	−0.934524	+	0.355900i	$0.884174\pi$
$734$	3.64576e6			0.249774
$735$		0			0
$736$	−148997.			−0.0101387
$737$	648105.	+	648105.i	0.0439518	+	0.0439518i
$738$	18848.5	−	6.32279e6i	0.00127390	−	0.427335i
$739$		−	1.97536e6i		−	0.133056i	−0.997785	−	0.0665281i	$-0.978808\pi$
$739$		−	1.97536e6i		−	0.133056i	0.997785	−	0.0665281i	$-0.0211922\pi$
$740$		0			0
$741$	−3.43835e6	+	8.26604e6i	−0.230041	+	0.553034i
$742$	−3.24147e6	+	3.24147e6i	−0.216139	+	0.216139i
$743$	−6.00318e6	+	6.00318e6i	−0.398941	+	0.398941i	−0.877860	−	0.478918i	$-0.841029\pi$
$743$	−6.00318e6	+	6.00318e6i	−0.398941	+	0.398941i	0.478918	+	0.877860i	$0.341029\pi$
$744$	3.14098e6	−	7.55115e6i	0.208034	−	0.500128i
$745$		0			0
$746$			534834.i			0.0351862i
$747$	41493.2	−	1.39190e7i	0.00272067	−	0.912657i
$748$	−1.06586e7	−	1.06586e7i	−0.696541	−	0.696541i
$749$	−3.02276e6			−0.196879
$750$		0			0
$751$	−4.79997e6			−0.310555			−0.155278	−	0.987871i	$-0.549627\pi$
$751$	−4.79997e6			−0.310555			−0.155278	+	0.987871i	$0.549627\pi$
$752$	2.74179e6	+	2.74179e6i	0.176803	+	0.176803i
$753$	−2.88129e6	−	6.98548e6i	−0.185182	−	0.448961i
$754$		−	1.88784e6i		−	0.120931i
$755$		0			0
$756$	7.41175e6	−	3.03129e6i	0.471646	−	0.192896i
$757$	−1.08011e7	+	1.08011e7i	−0.685058	+	0.685058i	−0.961135	−	0.276078i	$-0.910965\pi$
$757$	−1.08011e7	+	1.08011e7i	−0.685058	+	0.685058i	0.276078	+	0.961135i	$0.410965\pi$
$758$	7.33979e6	−	7.33979e6i	0.463992	−	0.463992i
$759$	1.11496e6	+	463778.i	0.0702511	+	0.0292217i
$760$		0			0
$761$		−	1.57703e7i		−	0.987137i	−0.869707	−	0.493569i	$-0.835692\pi$
$761$		−	1.57703e7i		−	0.987137i	0.869707	−	0.493569i	$-0.164308\pi$
$762$	4.86906e6	−	2.00833e6i	0.303779	−	0.125299i
$763$	−1.62855e7	−	1.62855e7i	−1.01272	−	1.01272i
$764$	−4.30979e6			−0.267130
$765$		0			0
$766$	4.76313e6			0.293306
$767$	−9.36395e6	−	9.36395e6i	−0.574739	−	0.574739i
$768$	−944422.	+	389544.i	−0.0577781	+	0.0238316i
$769$		−	9279.89i		−	0.000565883i	−1.00000		0.000282942i	$-0.999910\pi$
$769$		−	9279.89i		−	0.000565883i	1.00000		0.000282942i	$-9.00631e-5\pi$
$770$		0			0
$771$	−1.82699e7	−	7.59958e6i	−1.10688	−	0.460419i
$772$	6.14169e6	−	6.14169e6i	0.370890	−	0.370890i
$773$	−165465.	+	165465.i	−0.00995995	+	0.00995995i	−0.712069	−	0.702109i	$-0.752242\pi$
$773$	−165465.	+	165465.i	−0.00995995	+	0.00995995i	0.702109	+	0.712069i	$0.252242\pi$
$774$	1.13641e7	+	1.14320e7i	0.681839	+	0.685916i
$775$		0			0
$776$		−	4.36654e6i		−	0.260306i
$777$	4.37650e6	+	1.06105e7i	0.260060	+	0.630498i
$778$	−1.17081e6	−	1.17081e6i	−0.0693484	−	0.0693484i
$779$	1.15485e7			0.681839
$780$		0			0
$781$	−3.87209e6			−0.227153
$782$	728266.	+	728266.i	0.0425866	+	0.0425866i
$783$	−2.13770e6	+	5.09628e6i	−0.124607	+	0.297063i
$784$			166233.i			0.00965889i
$785$		0			0
$786$	−6.63505e6	+	1.59511e7i	−0.383078	+	0.920948i
$787$	2.78608e6	−	2.78608e6i	0.160346	−	0.160346i	−0.622374	−	0.782720i	$-0.713832\pi$
$787$	2.78608e6	−	2.78608e6i	0.160346	−	0.160346i	0.782720	+	0.622374i	$0.213832\pi$
$788$	−2.68945e6	+	2.68945e6i	−0.154293	+	0.154293i
$789$	−1.76614e6	+	4.24593e6i	−0.101003	+	0.242818i
$790$		0			0
$791$			1.13437e6i			0.0644635i
$792$	8.27968e6	+	24682.1i	0.469030	+	0.00139820i
$793$	8.04843e6	+	8.04843e6i	0.454494	+	0.454494i
$794$	1.24479e7			0.700719
$795$		0			0
$796$	−2.79788e6			−0.156511
$797$	1.07963e7	+	1.07963e7i	0.602045	+	0.602045i	0.940855	−	0.338810i	$-0.110024\pi$
$797$	1.07963e7	+	1.07963e7i	0.602045	+	0.602045i	−0.338810	+	0.940855i	$0.610024\pi$
$798$	5.57692e6	+	1.35208e7i	0.310018	+	0.751617i
$799$		−	2.68025e7i		−	1.48528i
$800$		0			0
$801$	−2.77724e6	+	2.76073e6i	−0.152944	+	0.152035i
$802$	−7.07679e6	+	7.07679e6i	−0.388509	+	0.388509i
$803$	2.54520e7	−	2.54520e7i	1.39294	−	1.39294i
$804$	−396461.	−	164912.i	−0.0216302	−	0.00899732i
$805$		0			0
$806$			1.06074e7i			0.575139i
$807$	−2.80357e7	+	1.15638e7i	−1.51540	+	0.625055i
$808$	−7.59735e6	−	7.59735e6i	−0.409387	−	0.409387i
$809$	−2.33120e7			−1.25230			−0.626150	−	0.779702i	$-0.715370\pi$
$809$	−2.33120e7			−1.25230			−0.626150	+	0.779702i	$0.715370\pi$
$810$		0			0
$811$	3.62536e7			1.93552			0.967762	−	0.251865i	$-0.0810438\pi$
$811$	3.62536e7			1.93552			0.967762	+	0.251865i	$0.0810438\pi$
$812$	−2.18082e6	−	2.18082e6i	−0.116073	−	0.116073i
$813$	5.19343e6	−	2.14212e6i	0.275567	−	0.113663i
$814$			1.18676e7i			0.627772i
$815$		0			0
$816$	6.52013e6	+	2.71212e6i	0.342792	+	0.142588i
$817$	−2.08184e7	+	2.08184e7i	−1.09117	+	1.09117i
$818$	−8.78453e6	+	8.78453e6i	−0.459024	+	0.459024i
$819$	−7.36589e6	+	7.32211e6i	−0.383721	+	0.381440i
$820$		0			0
$821$			1.36940e7i			0.709040i	0.935048	+	0.354520i	$0.115356\pi$
$821$			1.36940e7i			0.709040i	−0.935048	+	0.354520i	$0.884644\pi$
$822$	−5.95844e6	−	1.44458e7i	−0.307577	−	0.745697i
$823$	1.26333e6	+	1.26333e6i	0.0650154	+	0.0650154i	0.738867	−	0.673851i	$-0.235361\pi$
$823$	1.26333e6	+	1.26333e6i	0.0650154	+	0.0650154i	−0.673851	+	0.738867i	$0.735361\pi$
$824$	6.44645e6			0.330752
$825$		0			0
$826$	−2.16344e7			−1.10330
$827$	−3.91776e6	−	3.91776e6i	−0.199193	−	0.199193i	0.600461	−	0.799654i	$-0.294984\pi$
$827$	−3.91776e6	−	3.91776e6i	−0.199193	−	0.199193i	−0.799654	+	0.600461i	$0.794984\pi$
$828$	−565722.	−	1686.44i	−0.0286766	−	8.54860e-5i
$829$			3.63764e7i			1.83837i	0.393823	+	0.919186i	$0.371152\pi$
$829$			3.63764e7i			1.83837i	−0.393823	+	0.919186i	$0.628848\pi$
$830$		0			0
$831$	1.06403e7	−	2.55800e7i	0.534503	−	1.28498i
$832$	936940.	−	936940.i	0.0469249	−	0.0469249i
$833$	812510.	−	812510.i	0.0405711	−	0.0405711i
$834$	991097.	−	2.38267e6i	0.0493402	−	0.118617i
$835$		0			0
$836$			1.51227e7i			0.748367i
$837$	1.20113e7	−	2.86351e7i	0.592622	−	1.41281i
$838$	1.29012e7	+	1.29012e7i	0.634627	+	0.634627i
$839$	3.13078e7			1.53549			0.767747	−	0.640753i	$-0.221378\pi$
$839$	3.13078e7			1.53549			0.767747	+	0.640753i	$0.221378\pi$
$840$		0			0
$841$	−1.83826e7			−0.896226
$842$	1.61274e7	+	1.61274e7i	0.783945	+	0.783945i
$843$	3.55225e6	+	8.61217e6i	0.172161	+	0.417391i
$844$			6.49757e6i			0.313975i
$845$		0			0
$846$	1.03791e7	+	1.04412e7i	0.498581	+	0.501562i
$847$	1.14340e7	−	1.14340e7i	0.547632	−	0.547632i
$848$	1.57017e6	−	1.57017e6i	0.0749819	−	0.0749819i
$849$	−3.48218e7	−	1.44845e7i	−1.65799	−	0.689659i
$850$		0			0
$851$		−	810872.i		−	0.0383821i
$852$	1.67696e6	−	691693.i	0.0791450	−	0.0326448i
$853$	2.22778e7	+	2.22778e7i	1.04833	+	1.04833i	0.998771	+	0.0495610i	$0.0157822\pi$
$853$	2.22778e7	+	2.22778e7i	1.04833	+	1.04833i	0.0495610	+	0.998771i	$0.484218\pi$
$854$	1.85950e7			0.872472
$855$		0			0
$856$	1.46422e6			0.0683002
$857$	−1.81070e7	−	1.81070e7i	−0.842159	−	0.842159i	0.146980	−	0.989139i	$-0.453045\pi$
$857$	−1.81070e7	−	1.81070e7i	−0.842159	−	0.842159i	−0.989139	+	0.146980i	$0.953045\pi$
$858$	−9.92754e6	+	4.09480e6i	−0.460388	+	0.189895i
$859$		−	2.45541e6i		−	0.113538i	−0.998387	−	0.0567690i	$-0.981920\pi$
$859$		−	2.45541e6i		−	0.113538i	0.998387	−	0.0567690i	$-0.0180798\pi$
$860$		0			0
$861$	1.23700e7	+	5.14545e6i	0.568674	+	0.236546i
$862$	201928.	−	201928.i	0.00925610	−	0.00925610i
$863$	1.39932e7	−	1.39932e7i	0.639571	−	0.639571i	−0.310879	−	0.950450i	$-0.600623\pi$
$863$	1.39932e7	−	1.39932e7i	0.639571	−	0.639571i	0.950450	+	0.310879i	$0.100623\pi$
$864$	−3.59024e6	+	1.46835e6i	−0.163621	+	0.0669185i
$865$		0			0
$866$		−	1.07138e7i		−	0.485454i
$867$	−1.01731e7	−	2.46640e7i	−0.459628	−	1.11434i
$868$	1.22536e7	+	1.22536e7i	0.552034	+	0.552034i
$869$	2.94843e7			1.32447
$870$		0			0
$871$	556926.			0.0248744
$872$	7.88868e6	+	7.88868e6i	0.351328	+	0.351328i
$873$	49423.1	−	1.65792e7i	0.00219480	−	0.736252i
$874$		−	1.03328e6i		−	0.0457553i
$875$		0			0
$876$	−6.47635e6	+	1.55696e7i	−0.285148	+	0.685516i
$877$	1.03040e7	−	1.03040e7i	0.452384	−	0.452384i	−0.443761	−	0.896145i	$-0.646356\pi$
$877$	1.03040e7	−	1.03040e7i	0.452384	−	0.452384i	0.896145	+	0.443761i	$0.146356\pi$
$878$	−5.56439e6	+	5.56439e6i	−0.243602	+	0.243602i
$879$	−6.73742e6	+	1.61972e7i	−0.294118	+	0.707081i
$880$		0			0
$881$		−	3.30764e7i		−	1.43575i	−0.696173	−	0.717874i	$-0.745115\pi$
$881$		−	3.30764e7i		−	1.43575i	0.696173	−	0.717874i	$-0.254885\pi$
$882$	−1881.52	+	631163.i	−8.14401e−5	+	0.0273193i
$883$	7.08357e6	+	7.08357e6i	0.305739	+	0.305739i	0.843254	−	0.537515i	$-0.180637\pi$
$883$	7.08357e6	+	7.08357e6i	0.305739	+	0.305739i	−0.537515	+	0.843254i	$0.680637\pi$
$884$	−9.15911e6			−0.394205
$885$		0			0
$886$	2.40204e7			1.02801
$887$	2.51472e7	+	2.51472e7i	1.07320	+	1.07320i	0.997100	+	0.0761016i	$0.0242473\pi$
$887$	2.51472e7	+	2.51472e7i	1.07320	+	1.07320i	0.0761016	+	0.997100i	$0.475753\pi$
$888$	−2.11997e6	−	5.13972e6i	−0.0902190	−	0.218729i
$889$			1.11603e7i			0.473611i
$890$		0			0
$891$	3.14365e7	+	187429.i	1.32660	+	0.00790936i
$892$	3.38491e6	−	3.38491e6i	0.142441	−	0.142441i
$893$	−1.90141e7	+	1.90141e7i	−0.797896	+	0.797896i
$894$	−2.89006e6	−	1.20215e6i	−0.120938	−	0.0503056i
$895$		0			0
$896$		−	2.16469e6i		−	0.0900796i
$897$	678315.	−	279783.i	0.0281482	−	0.0116102i
$898$	1.13714e7	+	1.13714e7i	0.470570	+	0.470570i
$899$	−1.19597e7			−0.493540
$900$		0			0
$901$	−1.53493e7			−0.629906
$902$	9.79532e6	+	9.79532e6i	0.400869	+	0.400869i
$903$	−3.15751e7	+	1.30237e7i	−1.28862	+	0.531515i
$904$		−	549488.i		−	0.0223634i
$905$		0			0
$906$	1.14162e7	+	4.74869e6i	0.462063	+	0.192200i
$907$	1.02818e7	−	1.02818e7i	0.415003	−	0.415003i	−0.468474	−	0.883477i	$-0.655196\pi$
$907$	1.02818e7	−	1.02818e7i	0.415003	−	0.415003i	0.883477	+	0.468474i	$0.155196\pi$
$908$	1.09361e7	−	1.09361e7i	0.440198	−	0.440198i
$909$	−2.87601e7	−	2.89321e7i	−1.15446	−	1.16137i
$910$		0			0
$911$		−	1.72313e7i		−	0.687894i	−0.938989	−	0.343947i	$-0.888236\pi$
$911$		−	1.72313e7i		−	0.687894i	0.938989	−	0.343947i	$-0.111764\pi$
$912$	−2.70145e6	−	6.54948e6i	−0.107550	−	0.260747i
$913$	2.15635e7	+	2.15635e7i	0.856134	+	0.856134i
$914$	−3.21731e6			−0.127388
$915$		0			0
$916$	2.10339e7			0.828289
$917$	−2.58847e7	−	2.58847e7i	−1.01653	−	1.01653i
$918$	2.47253e7	+	1.03713e7i	0.968356	+	0.406189i
$919$			4.49944e7i			1.75740i	0.477379	+	0.878698i	$0.341587\pi$
$919$			4.49944e7i			1.75740i	−0.477379	+	0.878698i	$0.658413\pi$
$920$		0			0
$921$	−7.80509e6	+	1.87640e7i	−0.303200	+	0.728914i
$922$	2.47642e6	−	2.47642e6i	0.0959395	−	0.0959395i
$923$	−1.66367e6	+	1.66367e6i	−0.0642782	+	0.0642782i
$924$	−6.73795e6	+	1.61985e7i	−0.259626	+	0.624160i
$925$		0			0
$926$			6.79789e6i			0.260523i
$927$	2.44763e7	+	72964.8i	0.935504	+	0.00278878i
$928$	1.05639e6	+	1.05639e6i	0.0402674	+	0.0402674i
$929$	−1.31174e7			−0.498664			−0.249332	−	0.968418i	$-0.580211\pi$
$929$	−1.31174e7			−0.498664			−0.249332	+	0.968418i	$0.580211\pi$
$930$		0			0
$931$	−1.15281e6			−0.0435897
$932$	−7.14557e6	−	7.14557e6i	−0.269462	−	0.269462i
$933$	−1.88631e6	−	4.57323e6i	−0.0709430	−	0.171996i
$934$		−	1.79111e7i		−	0.671824i
$935$		0			0
$936$	3.56803e6	−	3.54682e6i	0.133119	−	0.132327i
$937$	2.18466e7	−	2.18466e7i	0.812898	−	0.812898i	−0.172170	−	0.985067i	$-0.555078\pi$
$937$	2.18466e7	−	2.18466e7i	0.812898	−	0.812898i	0.985067	+	0.172170i	$0.0550777\pi$
$938$	643358.	−	643358.i	0.0238751	−	0.0238751i
$939$	3.77473e7	+	1.57014e7i	1.39708	+	0.581131i
$940$		0			0
$941$			5.22143e7i			1.92227i	0.276074	+	0.961136i	$0.410966\pi$
$941$			5.22143e7i			1.92227i	−0.276074	+	0.961136i	$0.589034\pi$
$942$	−2.56220e7	+	1.05683e7i	−0.940775	+	0.388040i
$943$	−669281.	−	669281.i	−0.0245092	−	0.0245092i
$944$	1.04797e7			0.382752
$945$		0			0
$946$	−3.53159e7			−1.28305
$947$	1.74111e7	+	1.74111e7i	0.630887	+	0.630887i	0.948291	−	0.317403i	$-0.102811\pi$
$947$	1.74111e7	+	1.74111e7i	0.630887	+	0.630887i	−0.317403	+	0.948291i	$0.602811\pi$
$948$	−1.27693e7	+	5.26694e6i	−0.461473	+	0.190343i
$949$		−	2.18713e7i		−	0.788332i
$950$		0			0
$951$	−2.67002e7	−	1.11062e7i	−0.957333	−	0.398213i
$952$	−1.05805e7	+	1.05805e7i	−0.378369	+	0.378369i
$953$	1.96340e7	−	1.96340e7i	0.700289	−	0.700289i	−0.264183	−	0.964473i	$-0.585102\pi$
$953$	1.96340e7	−	1.96340e7i	0.700289	−	0.700289i	0.964473	+	0.264183i	$0.0851023\pi$
$954$	5.97947e6	−	5.94393e6i	0.212712	−	0.211448i
$955$		0			0
$956$		−	1.25483e7i		−	0.444060i
$957$	−4.61683e6	−	1.11932e7i	−0.162954	−	0.395070i
$958$	−9.40708e6	−	9.40708e6i	−0.331162	−	0.331162i
$959$	3.31110e7			1.16259
$960$		0			0
$961$	3.85705e7			1.34725
$962$	5.09900e6	+	5.09900e6i	0.177643	+	0.177643i
$963$	5.55944e6	+	16572.9i	0.193181	+	0.000575882i
$964$		−	1.24320e7i		−	0.430870i
$965$		0			0
$966$	460381.	−	1.10679e6i	0.0158736	−	0.0381612i
$967$	−2.13726e7	+	2.13726e7i	−0.735008	+	0.735008i	−0.971607	−	0.236600i	$-0.923967\pi$
$967$	−2.13726e7	+	2.13726e7i	−0.735008	+	0.735008i	0.236600	+	0.971607i	$0.423967\pi$
$968$	−5.53861e6	+	5.53861e6i	−0.189982	+	0.189982i
$969$	−1.88083e7	+	4.52165e7i	−0.643488	+	1.54699i
$970$		0			0
$971$		−	4.84810e7i		−	1.65015i	−0.565023	−	0.825075i	$-0.691133\pi$
$971$		−	4.84810e7i		−	1.65015i	0.565023	−	0.825075i	$-0.308867\pi$
$972$	−1.36483e7	+	5.53450e6i	−0.463353	+	0.187894i
$973$	3.86648e6	+	3.86648e6i	0.130928	+	0.130928i
$974$	5.93738e6			0.200538
$975$		0			0
$976$	−9.00740e6			−0.302674
$977$	−2.23164e7	−	2.23164e7i	−0.747976	−	0.747976i	0.226123	−	0.974099i	$-0.427395\pi$
$977$	−2.23164e7	−	2.23164e7i	−0.747976	−	0.747976i	−0.974099	+	0.226123i	$0.927395\pi$
$978$	−1.15153e7	−	2.79180e7i	−0.384971	−	0.933334i
$979$		−	8.57948e6i		−	0.286091i
$980$		0			0
$981$	2.98629e7	+	3.00415e7i	0.990740	+	0.996665i
$982$	2.14155e7	−	2.14155e7i	0.708678	−	0.708678i
$983$	3.89242e7	−	3.89242e7i	1.28480	−	1.28480i	0.346898	−	0.937903i	$-0.387235\pi$
$983$	3.89242e7	−	3.89242e7i	1.28480	−	1.28480i	0.937903	−	0.346898i	$-0.112765\pi$
$984$	−5.99204e6	−	2.49245e6i	−0.197282	−	0.0820614i
$985$		0			0
$986$		−	1.03268e7i		−	0.338277i
$987$	−2.88384e7	+	1.18949e7i	−0.942277	+	0.388660i
$988$	6.49759e6	+	6.49759e6i	0.211768	+	0.211768i
$989$	2.41302e6			0.0784457
$990$		0			0
$991$	−3.26422e7			−1.05583			−0.527917	−	0.849296i	$-0.677027\pi$
$991$	−3.26422e7			−1.05583			−0.527917	+	0.849296i	$0.677027\pi$
$992$	−5.93565e6	−	5.93565e6i	−0.191509	−	0.191509i
$993$	355917.	−	146805.i	0.0114545	−	0.00472462i
$994$			3.84373e6i			0.123392i
$995$		0			0
$996$	−1.31909e7	−	5.48690e6i	−0.421334	−	0.175258i
$997$	−3.12724e7	+	3.12724e7i	−0.996375	+	0.996375i	−0.999993	−	0.00361863i	$-0.998848\pi$
$997$	−3.12724e7	+	3.12724e7i	−0.996375	+	0.996375i	0.00361863	+	0.999993i	$0.498848\pi$
$998$	1.00768e7	−	1.00768e7i	0.320256	−	0.320256i
$999$	−7.99106e6	−	1.95388e7i	−0.253332	−	0.619418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.e.b.143.1		20
3.2	odd	2	inner	150.6.e.b.143.8		20
5.2	odd	4	inner	150.6.e.b.107.8		20
5.3	odd	4		30.6.e.a.17.3	✓	20
5.4	even	2		30.6.e.a.23.10	yes	20
15.2	even	4	inner	150.6.e.b.107.1		20
15.8	even	4		30.6.e.a.17.10	yes	20
15.14	odd	2		30.6.e.a.23.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.6.e.a.17.3	✓	20	5.3	odd	4
30.6.e.a.17.10	yes	20	15.8	even	4
30.6.e.a.23.3	yes	20	15.14	odd	2
30.6.e.a.23.10	yes	20	5.4	even	2
150.6.e.b.107.1		20	15.2	even	4	inner
150.6.e.b.107.8		20	5.2	odd	4	inner
150.6.e.b.143.1		20	1.1	even	1	trivial
150.6.e.b.143.8		20	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82843 - 2.82843i) q^{2} +(-14.4107 + 5.94397i) q^{3} +16.0000i q^{4} +(57.5718 + 23.9476i) q^{6} +(-93.4247 + 93.4247i) q^{7} +(45.2548 - 45.2548i) q^{8} +(172.338 - 171.314i) q^{9} +O(q^{10})\)	\(q+(-2.82843 - 2.82843i) q^{2} +(-14.4107 + 5.94397i) q^{3} +16.0000i q^{4} +(57.5718 + 23.9476i) q^{6} +(-93.4247 + 93.4247i) q^{7} +(45.2548 - 45.2548i) q^{8} +(172.338 - 171.314i) q^{9} +532.389i q^{11} +(-95.1035 - 230.572i) q^{12} +(228.745 + 228.745i) q^{13} +528.490 q^{14} -256.000 q^{16} +(1251.27 + 1251.27i) q^{17} +(-971.996 - 2.89756i) q^{18} -1775.34i q^{19} +(791.005 - 1901.63i) q^{21} +(1505.82 - 1505.82i) q^{22} +(-102.888 + 102.888i) q^{23} +(-383.162 + 921.149i) q^{24} -1293.98i q^{26} +(-1465.24 + 3493.13i) q^{27} +(-1494.80 - 1494.80i) q^{28} +1458.94 q^{29} -8197.54 q^{31} +(724.077 + 724.077i) q^{32} +(-3164.51 - 7672.12i) q^{33} -7078.26i q^{34} +(2741.02 + 2757.41i) q^{36} +(-3940.57 + 3940.57i) q^{37} +(-5021.41 + 5021.41i) q^{38} +(-4656.04 - 1936.73i) q^{39} +6504.96i q^{41} +(-7615.93 + 3141.33i) q^{42} +(-11726.4 - 11726.4i) q^{43} -8518.22 q^{44} +582.021 q^{46} +(-10710.1 - 10710.1i) q^{47} +(3689.15 - 1521.66i) q^{48} -649.348i q^{49} +(-25469.3 - 10594.2i) q^{51} +(-3659.92 + 3659.92i) q^{52} +(-6133.46 + 6133.46i) q^{53} +(14024.4 - 5735.76i) q^{54} +8455.84i q^{56} +(10552.6 + 25583.9i) q^{57} +(-4126.51 - 4126.51i) q^{58} -40936.2 q^{59} +35185.1 q^{61} +(23186.1 + 23186.1i) q^{62} +(-95.7082 + 32105.6i) q^{63} -4096.00i q^{64} +(-12749.4 + 30650.6i) q^{66} +(1217.35 - 1217.35i) q^{67} +(-20020.3 + 20020.3i) q^{68} +(871.126 - 2094.25i) q^{69} +7273.05i q^{71} +(46.3610 - 15551.9i) q^{72} +(-47807.2 - 47807.2i) q^{73} +22291.2 q^{74} +28405.4 q^{76} +(-49738.3 - 49738.3i) q^{77} +(7691.36 + 18647.2i) q^{78} -55381.1i q^{79} +(352.052 - 59048.0i) q^{81} +(18398.8 - 18398.8i) q^{82} +(40503.2 - 40503.2i) q^{83} +(30426.1 + 12656.1i) q^{84} +66334.8i q^{86} +(-21024.4 + 8671.91i) q^{87} +(24093.2 + 24093.2i) q^{88} -16115.1 q^{89} -42740.9 q^{91} +(-1646.20 - 1646.20i) q^{92} +(118133. - 48725.9i) q^{93} +60585.5i q^{94} +(-14738.4 - 6130.59i) q^{96} +(48244.0 - 48244.0i) q^{97} +(-1836.63 + 1836.63i) q^{98} +(91205.7 + 91751.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} + 80 q^{6} - 76 q^{7}+O(q^{10}) \) 20 * q + 4 * q^3 + 80 * q^6 - 76 * q^7	\( 20 q + 4 q^{3} + 80 q^{6} - 76 q^{7} - 64 q^{12} - 2640 q^{13} - 5120 q^{16} + 2272 q^{18} - 760 q^{21} + 464 q^{22} - 16556 q^{27} - 1216 q^{28} + 23960 q^{31} + 7684 q^{33} - 13120 q^{36} + 60696 q^{37} - 46864 q^{42} - 48024 q^{43} + 58880 q^{46} - 1024 q^{48} - 155240 q^{51} + 42240 q^{52} - 167744 q^{57} - 38000 q^{58} + 160680 q^{61} + 219364 q^{63} - 158560 q^{66} + 118736 q^{67} - 36352 q^{72} - 379100 q^{73} + 78080 q^{76} + 25440 q^{78} - 282260 q^{81} + 262976 q^{82} - 249380 q^{87} + 7424 q^{88} + 499200 q^{91} + 304072 q^{93} - 20480 q^{96} + 288228 q^{97}+O(q^{100}) \) 20 * q + 4 * q^3 + 80 * q^6 - 76 * q^7 - 64 * q^12 - 2640 * q^13 - 5120 * q^16 + 2272 * q^18 - 760 * q^21 + 464 * q^22 - 16556 * q^27 - 1216 * q^28 + 23960 * q^31 + 7684 * q^33 - 13120 * q^36 + 60696 * q^37 - 46864 * q^42 - 48024 * q^43 + 58880 * q^46 - 1024 * q^48 - 155240 * q^51 + 42240 * q^52 - 167744 * q^57 - 38000 * q^58 + 160680 * q^61 + 219364 * q^63 - 158560 * q^66 + 118736 * q^67 - 36352 * q^72 - 379100 * q^73 + 78080 * q^76 + 25440 * q^78 - 282260 * q^81 + 262976 * q^82 - 249380 * q^87 + 7424 * q^88 + 499200 * q^91 + 304072 * q^93 - 20480 * q^96 + 288228 * q^97

Introduction

L-functions

Modular forms

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