LMFDB - Embedded newform 350.4.e.l.51.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(51,350)]

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, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.e (of order $3$, 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:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 33x^{6} - 74x^{5} + 1019x^{4} - 1221x^{3} + 3679x^{2} + 2590x + 4900 $ x^8 + 33x^6 - 74x^5 + 1019x^4 - 1221x^3 + 3679x^2 + 2590x + 4900
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.4
Root			$1.21436 - 2.10334i$ of defining polynomial
Character	$\chi$	$=$	350.51
Dual form			350.4.e.l.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(4.74942 + 8.22624i) q^{3} +(-2.00000 - 3.46410i) q^{4} -18.9977 q^{6} +(-11.3178 + 14.6597i) q^{7} +8.00000 q^{8} +(-31.6140 + 54.7570i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(4.74942 + 8.22624i) q^{3} +(-2.00000 - 3.46410i) q^{4} -18.9977 q^{6} +(-11.3178 + 14.6597i) q^{7} +8.00000 q^{8} +(-31.6140 + 54.7570i) q^{9} +(35.9318 + 62.2357i) q^{11} +(18.9977 - 32.9049i) q^{12} +70.4406 q^{13} +(-14.0735 - 34.2627i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-12.6599 - 21.9276i) q^{17} +(-63.2280 - 109.514i) q^{18} +(-35.4404 + 61.3846i) q^{19} +(-174.347 - 23.4780i) q^{21} -143.727 q^{22} +(60.0826 - 104.066i) q^{23} +(37.9954 + 65.8099i) q^{24} +(-70.4406 + 122.007i) q^{26} -344.124 q^{27} +(73.4183 + 9.88667i) q^{28} +13.7508 q^{29} +(-122.005 - 211.318i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-341.310 + 591.167i) q^{33} +50.6396 q^{34} +252.912 q^{36} +(37.2186 - 64.4645i) q^{37} +(-70.8808 - 122.769i) q^{38} +(334.552 + 579.461i) q^{39} -90.8195 q^{41} +(215.012 - 278.500i) q^{42} +9.31938 q^{43} +(143.727 - 248.943i) q^{44} +(120.165 + 208.132i) q^{46} +(139.189 - 241.082i) q^{47} -151.981 q^{48} +(-86.8139 - 331.832i) q^{49} +(120.254 - 208.287i) q^{51} +(-140.881 - 244.013i) q^{52} +(-45.9993 - 79.6731i) q^{53} +(344.124 - 596.040i) q^{54} +(-90.5426 + 117.278i) q^{56} -673.286 q^{57} +(-13.7508 + 23.8171i) q^{58} +(-18.9480 - 32.8189i) q^{59} +(-96.4258 + 167.014i) q^{61} +488.019 q^{62} +(-444.921 - 1083.18i) q^{63} +64.0000 q^{64} +(-682.621 - 1182.33i) q^{66} +(214.997 + 372.385i) q^{67} +(-50.6396 + 87.7104i) q^{68} +1141.43 q^{69} +76.0899 q^{71} +(-252.912 + 438.056i) q^{72} +(399.172 + 691.387i) q^{73} +(74.4372 + 128.929i) q^{74} +283.523 q^{76} +(-1319.03 - 177.623i) q^{77} -1338.21 q^{78} +(5.52061 - 9.56198i) q^{79} +(-780.810 - 1352.40i) q^{81} +(90.8195 - 157.304i) q^{82} +603.005 q^{83} +(267.365 + 650.913i) q^{84} +(-9.31938 + 16.1416i) q^{86} +(65.3084 + 113.117i) q^{87} +(287.454 + 497.886i) q^{88} +(-400.161 + 693.100i) q^{89} +(-797.234 + 1032.64i) q^{91} -480.660 q^{92} +(1158.90 - 2007.28i) q^{93} +(278.377 + 482.163i) q^{94} +(151.981 - 263.240i) q^{96} -44.6934 q^{97} +(661.563 + 181.466i) q^{98} -4543.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + q^{3} - 16 q^{4} - 4 q^{6} + 7 q^{7} + 64 q^{8} - 73 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + q^3 - 16 * q^4 - 4 * q^6 + 7 * q^7 + 64 * q^8 - 73 * q^9	$ 8 q - 8 q^{2} + q^{3} - 16 q^{4} - 4 q^{6} + 7 q^{7} + 64 q^{8} - 73 q^{9} + 10 q^{11} + 4 q^{12} + 188 q^{13} - 70 q^{14} - 64 q^{16} - 99 q^{17} - 146 q^{18} - 246 q^{19} - 535 q^{21} - 40 q^{22} + 2 q^{23} + 8 q^{24} - 188 q^{26} - 392 q^{27} + 112 q^{28} - 196 q^{29} - 304 q^{31} - 128 q^{32} - 526 q^{33} + 396 q^{34} + 584 q^{36} + 82 q^{37} - 492 q^{38} + 214 q^{39} + 704 q^{41} + 634 q^{42} + 262 q^{43} + 40 q^{44} + 4 q^{46} + 491 q^{47} - 32 q^{48} + 1283 q^{49} + 1437 q^{51} - 376 q^{52} + 140 q^{53} + 392 q^{54} + 56 q^{56} + 438 q^{57} + 196 q^{58} - 673 q^{59} - 1425 q^{61} + 1216 q^{62} - 1226 q^{63} + 512 q^{64} - 1052 q^{66} + 666 q^{67} - 396 q^{68} + 1876 q^{69} - 12 q^{71} - 584 q^{72} + 78 q^{73} + 164 q^{74} + 1968 q^{76} - 2575 q^{77} - 856 q^{78} - 1744 q^{79} - 1708 q^{81} - 704 q^{82} + 1852 q^{83} + 872 q^{84} - 262 q^{86} - 1931 q^{87} + 80 q^{88} + 871 q^{89} - 797 q^{91} - 16 q^{92} + 3106 q^{93} + 982 q^{94} + 32 q^{96} - 2924 q^{97} - 1244 q^{98} - 10562 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + q^3 - 16 * q^4 - 4 * q^6 + 7 * q^7 + 64 * q^8 - 73 * q^9 + 10 * q^11 + 4 * q^12 + 188 * q^13 - 70 * q^14 - 64 * q^16 - 99 * q^17 - 146 * q^18 - 246 * q^19 - 535 * q^21 - 40 * q^22 + 2 * q^23 + 8 * q^24 - 188 * q^26 - 392 * q^27 + 112 * q^28 - 196 * q^29 - 304 * q^31 - 128 * q^32 - 526 * q^33 + 396 * q^34 + 584 * q^36 + 82 * q^37 - 492 * q^38 + 214 * q^39 + 704 * q^41 + 634 * q^42 + 262 * q^43 + 40 * q^44 + 4 * q^46 + 491 * q^47 - 32 * q^48 + 1283 * q^49 + 1437 * q^51 - 376 * q^52 + 140 * q^53 + 392 * q^54 + 56 * q^56 + 438 * q^57 + 196 * q^58 - 673 * q^59 - 1425 * q^61 + 1216 * q^62 - 1226 * q^63 + 512 * q^64 - 1052 * q^66 + 666 * q^67 - 396 * q^68 + 1876 * q^69 - 12 * q^71 - 584 * q^72 + 78 * q^73 + 164 * q^74 + 1968 * q^76 - 2575 * q^77 - 856 * q^78 - 1744 * q^79 - 1708 * q^81 - 704 * q^82 + 1852 * q^83 + 872 * q^84 - 262 * q^86 - 1931 * q^87 + 80 * q^88 + 871 * q^89 - 797 * q^91 - 16 * q^92 + 3106 * q^93 + 982 * q^94 + 32 * q^96 - 2924 * q^97 - 1244 * q^98 - 10562 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	4.74942	+	8.22624i	0.914026	+	1.58314i	0.808321	+	0.588743i	$0.200377\pi$
$3$	4.74942	+	8.22624i	0.914026	+	1.58314i	0.105706	+	0.994397i	$0.466290\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−18.9977			−1.29263
$7$	−11.3178	+	14.6597i	−0.611105	+	0.791550i
$7$	−11.3178	+	14.6597i	−0.611105	+	0.791550i
$8$	8.00000			0.353553
$9$	−31.6140	+	54.7570i	−1.17089	+	2.02804i
$10$		0			0
$11$	35.9318	+	62.2357i	0.984895	+	1.70589i	0.642401	+	0.766368i	$0.277938\pi$
$11$	35.9318	+	62.2357i	0.984895	+	1.70589i	0.342494	+	0.939520i	$0.388728\pi$
$12$	18.9977	−	32.9049i	0.457013	−	0.791570i
$13$	70.4406			1.50282			0.751412	−	0.659833i	$-0.229373\pi$
$13$	70.4406			1.50282			0.751412	+	0.659833i	$0.229373\pi$
$14$	−14.0735	−	34.2627i	−0.268665	−	0.654079i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−12.6599	−	21.9276i	−0.180616	−	0.312837i	0.761474	−	0.648195i	$-0.224476\pi$
$17$	−12.6599	−	21.9276i	−0.180616	−	0.312837i	−0.942091	+	0.335358i	$0.891143\pi$
$18$	−63.2280	−	109.514i	−0.827943	−	1.43404i
$19$	−35.4404	+	61.3846i	−0.427926	+	0.741189i	−0.996689	−	0.0813124i	$-0.974089\pi$
$19$	−35.4404	+	61.3846i	−0.427926	+	0.741189i	0.568763	+	0.822502i	$0.307422\pi$
$20$		0			0
$21$	−174.347	−	23.4780i	−1.81170	−	0.243967i
$22$	−143.727			−1.39285
$23$	60.0826	−	104.066i	0.544699	−	0.943446i	−0.453927	−	0.891039i	$-0.649977\pi$
$23$	60.0826	−	104.066i	0.544699	−	0.943446i	0.998626	−	0.0524075i	$-0.0166895\pi$
$24$	37.9954	+	65.8099i	0.323157	+	0.559725i
$25$		0			0
$26$	−70.4406	+	122.007i	−0.531329	+	0.920288i
$27$	−344.124			−2.45284
$28$	73.4183	+	9.88667i	0.495527	+	0.0667287i
$29$	13.7508			0.0880504			0.0440252	−	0.999030i	$-0.485982\pi$
$29$	13.7508			0.0880504			0.0440252	+	0.999030i	$0.485982\pi$
$30$		0			0
$31$	−122.005	−	211.318i	−0.706861	−	1.22432i	−0.966016	−	0.258483i	$-0.916777\pi$
$31$	−122.005	−	211.318i	−0.706861	−	1.22432i	0.259155	−	0.965836i	$-0.416556\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−341.310	+	591.167i	−1.80044	+	3.11845i
$34$	50.6396			0.255430
$35$		0			0
$36$	252.912			1.17089
$37$	37.2186	−	64.4645i	0.165370	−	0.286430i	−0.771417	−	0.636331i	$-0.780451\pi$
$37$	37.2186	−	64.4645i	0.165370	−	0.286430i	0.936787	+	0.349901i	$0.113785\pi$
$38$	−70.8808	−	122.769i	−0.302589	−	0.524100i
$39$	334.552	+	579.461i	1.37362	+	2.37918i
$40$		0			0
$41$	−90.8195			−0.345942			−0.172971	−	0.984927i	$-0.555337\pi$
$41$	−90.8195			−0.345942			−0.172971	+	0.984927i	$0.555337\pi$
$42$	215.012	−	278.500i	0.789931	−	1.02318i
$43$	9.31938			0.0330510			0.0165255	−	0.999863i	$-0.494740\pi$
$43$	9.31938			0.0330510			0.0165255	+	0.999863i	$0.494740\pi$
$44$	143.727	−	248.943i	0.492448	−	0.852944i
$45$		0			0
$46$	120.165	+	208.132i	0.385160	+	0.667117i
$47$	139.189	−	241.082i	0.431973	−	0.748200i	−0.565070	−	0.825043i	$-0.691151\pi$
$47$	139.189	−	241.082i	0.431973	−	0.748200i	0.997043	+	0.0768434i	$0.0244841\pi$
$48$	−151.981			−0.457013
$49$	−86.8139	−	331.832i	−0.253102	−	0.967440i
$50$		0			0
$51$	120.254	−	208.287i	0.330176	−	0.571882i
$52$	−140.881	−	244.013i	−0.375706	−	0.650742i
$53$	−45.9993	−	79.6731i	−0.119217	−	0.206489i	0.800241	−	0.599679i	$-0.204705\pi$
$53$	−45.9993	−	79.6731i	−0.119217	−	0.206489i	−0.919457	+	0.393189i	$0.871372\pi$
$54$	344.124	−	596.040i	0.867209	−	1.50205i
$55$		0			0
$56$	−90.5426	+	117.278i	−0.216058	+	0.279855i
$57$	−673.286			−1.56454
$58$	−13.7508	+	23.8171i	−0.0311305	+	0.0539197i
$59$	−18.9480	−	32.8189i	−0.0418105	−	0.0724179i	0.844363	−	0.535772i	$-0.179979\pi$
$59$	−18.9480	−	32.8189i	−0.0418105	−	0.0724179i	−0.886173	+	0.463354i	$0.846646\pi$
$60$		0			0
$61$	−96.4258	+	167.014i	−0.202394	+	0.350557i	−0.949299	−	0.314373i	$-0.898206\pi$
$61$	−96.4258	+	167.014i	−0.202394	+	0.350557i	0.746905	+	0.664931i	$0.231539\pi$
$62$	488.019			0.999652
$63$	−444.921	−	1083.18i	−0.889757	−	2.16616i
$64$	64.0000			0.125000
$65$		0			0
$66$	−682.621	−	1182.33i	−1.27310	−	2.20508i
$67$	214.997	+	372.385i	0.392031	+	0.679017i	0.992717	−	0.120468i	$-0.0384394\pi$
$67$	214.997	+	372.385i	0.392031	+	0.679017i	−0.600687	+	0.799485i	$0.705106\pi$
$68$	−50.6396	+	87.7104i	−0.0903082	+	0.156418i
$69$	1141.43			1.99148
$70$		0			0
$71$	76.0899			0.127186			0.0635931	−	0.997976i	$-0.479744\pi$
$71$	76.0899			0.127186			0.0635931	+	0.997976i	$0.479744\pi$
$72$	−252.912	+	438.056i	−0.413972	+	0.717020i
$73$	399.172	+	691.387i	0.639995	+	1.10850i	0.985433	+	0.170062i	$0.0543968\pi$
$73$	399.172	+	691.387i	0.639995	+	1.10850i	−0.345439	+	0.938441i	$0.612270\pi$
$74$	74.4372	+	128.929i	0.116934	+	0.202536i
$75$		0			0
$76$	283.523			0.427926
$77$	−1319.03	−	177.623i	−1.95217	−	0.262883i
$78$	−1338.21			−1.94259
$79$	5.52061	−	9.56198i	0.00786225	−	0.0136178i	−0.862068	−	0.506793i	$-0.830831\pi$
$79$	5.52061	−	9.56198i	0.00786225	−	0.0136178i	0.869930	+	0.493176i	$0.164164\pi$
$80$		0			0
$81$	−780.810	−	1352.40i	−1.07107	−	1.85515i
$82$	90.8195	−	157.304i	0.122309	−	0.211845i
$83$	603.005			0.797451			0.398726	−	0.917070i	$-0.369453\pi$
$83$	603.005			0.797451			0.398726	+	0.917070i	$0.369453\pi$
$84$	267.365	+	650.913i	0.347284	+	0.845481i
$85$		0			0
$86$	−9.31938	+	16.1416i	−0.0116853	+	0.0202395i
$87$	65.3084	+	113.117i	0.0804804	+	0.139396i
$88$	287.454	+	497.886i	0.348213	+	0.603123i
$89$	−400.161	+	693.100i	−0.476596	+	0.825488i	−0.999640	−	0.0268171i	$-0.991463\pi$
$89$	−400.161	+	693.100i	−0.476596	+	0.825488i	0.523044	+	0.852305i	$0.324796\pi$
$90$		0			0
$91$	−797.234	+	1032.64i	−0.918383	+	1.18956i
$92$	−480.660			−0.544699
$93$	1158.90	−	2007.28i	1.29218	−	2.23812i
$94$	278.377	+	482.163i	0.305451	+	0.529057i
$95$		0			0
$96$	151.981	−	263.240i	0.161579	−	0.279862i
$97$	−44.6934			−0.0467827			−0.0233914	−	0.999726i	$-0.507446\pi$
$97$	−44.6934			−0.0467827			−0.0233914	+	0.999726i	$0.507446\pi$
$98$	661.563	+	181.466i	0.681918	+	0.187049i
$99$	−4543.79			−4.61281
$100$		0			0
$101$	402.689	+	697.478i	0.396723	+	0.687145i	0.993319	−	0.115397i	$-0.0368140\pi$
$101$	402.689	+	697.478i	0.396723	+	0.687145i	−0.596596	+	0.802541i	$0.703481\pi$
$102$	240.509	+	416.574i	0.233470	+	0.404382i
$103$	527.097	−	912.958i	0.504237	−	0.873363i	−0.495751	−	0.868464i	$-0.665107\pi$
$103$	527.097	−	912.958i	0.504237	−	0.873363i	0.999988	−	0.00489889i	$-0.00155937\pi$
$104$	563.525			0.531329
$105$		0			0
$106$	183.997			0.168598
$107$	839.704	−	1454.41i	0.758666	−	1.31405i	−0.184865	−	0.982764i	$-0.559185\pi$
$107$	839.704	−	1454.41i	0.758666	−	1.31405i	0.943531	−	0.331284i	$-0.107482\pi$
$108$	688.247	+	1192.08i	0.613210	+	1.06211i
$109$	−353.495	−	612.271i	−0.310630	−	0.538027i	0.667869	−	0.744279i	$-0.267207\pi$
$109$	−353.495	−	612.271i	−0.310630	−	0.538027i	−0.978499	+	0.206252i	$0.933873\pi$
$110$		0			0
$111$	707.067			0.604611
$112$	−112.588	−	274.102i	−0.0949874	−	0.231252i
$113$	−1328.92			−1.10632			−0.553161	−	0.833075i	$-0.686578\pi$
$113$	−1328.92			−1.10632			−0.553161	+	0.833075i	$0.686578\pi$
$114$	673.286	−	1166.17i	0.553149	−	0.958082i
$115$		0			0
$116$	−27.5016	−	47.6342i	−0.0220126	−	0.0381270i
$117$	−2226.91	+	3857.12i	−1.75964	+	3.04778i
$118$	75.7920			0.0591290
$119$	464.735	+	62.5821i	0.358001	+	0.0482092i
$120$		0			0
$121$	−1916.69	+	3319.80i	−1.44004	+	2.49422i
$122$	−192.852	−	334.029i	−0.143114	−	0.247881i
$123$	−431.340	−	747.102i	−0.316200	−	0.547674i
$124$	−488.019	+	845.273i	−0.353430	+	0.612159i
$125$		0			0
$126$	2321.05	+	312.557i	1.64107	+	0.220990i
$127$	2072.96			1.44839			0.724193	−	0.689597i	$-0.242212\pi$
$127$	2072.96			1.44839			0.724193	+	0.689597i	$0.242212\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	44.2617	+	76.6635i	0.0302095	+	0.0523244i
$130$		0			0
$131$	959.579	−	1662.04i	0.639991	−	1.10850i	−0.345443	−	0.938440i	$-0.612271\pi$
$131$	959.579	−	1662.04i	0.639991	−	1.10850i	0.985434	−	0.170057i	$-0.0543953\pi$
$132$	2730.48			1.80044
$133$	−498.772	−	1214.29i	−0.325181	−	0.791669i
$134$	−859.987			−0.554415
$135$		0			0
$136$	−101.279	−	175.421i	−0.0638575	−	0.110604i
$137$	543.339	+	941.091i	0.338836	+	0.586882i	0.984214	−	0.176982i	$-0.0566333\pi$
$137$	543.339	+	941.091i	0.338836	+	0.586882i	−0.645378	+	0.763864i	$0.723300\pi$
$138$	−1141.43	+	1977.01i	−0.704094	+	1.21953i
$139$	240.132			0.146531			0.0732653	−	0.997312i	$-0.476658\pi$
$139$	240.132			0.146531			0.0732653	+	0.997312i	$0.476658\pi$
$140$		0			0
$141$	2644.26			1.57934
$142$	−76.0899	+	131.792i	−0.0449671	+	0.0778853i
$143$	2531.06	+	4383.92i	1.48012	+	2.56365i
$144$	−505.824	−	876.112i	−0.292722	−	0.507010i
$145$		0			0
$146$	−1596.69			−0.905089
$147$	2317.41	−	2290.16i	1.30025	−	1.28496i
$148$	−297.749			−0.165370
$149$	−1393.36	+	2413.37i	−0.766097	+	1.32692i	0.173568	+	0.984822i	$0.444470\pi$
$149$	−1393.36	+	2413.37i	−0.766097	+	1.32692i	−0.939665	+	0.342097i	$0.888863\pi$
$150$		0			0
$151$	525.412	+	910.041i	0.283162	+	0.490451i	0.972162	−	0.234311i	$-0.0752833\pi$
$151$	525.412	+	910.041i	0.283162	+	0.490451i	−0.689000	+	0.724761i	$0.741950\pi$
$152$	−283.523	+	491.077i	−0.151295	+	0.262050i
$153$	1600.92			0.845926
$154$	1626.68	−	2107.00i	0.851179	−	1.10251i
$155$		0			0
$156$	1338.21	−	2317.85i	0.686810	−	1.18959i
$157$	−563.858	−	976.630i	−0.286629	−	0.496456i	0.686374	−	0.727249i	$-0.259201\pi$
$157$	−563.858	−	976.630i	−0.286629	−	0.496456i	−0.973003	+	0.230793i	$0.925868\pi$
$158$	11.0412	+	19.1240i	0.00555945	+	0.00962925i
$159$	436.940	−	756.802i	0.217934	−	0.377473i
$160$		0			0
$161$	845.574	+	2058.59i	0.413917	+	1.00770i
$162$	3123.24			1.51472
$163$	−130.360	+	225.791i	−0.0626418	+	0.108499i	−0.895645	−	0.444769i	$-0.853286\pi$
$163$	−130.360	+	225.791i	−0.0626418	+	0.108499i	0.833004	+	0.553267i	$0.186619\pi$
$164$	181.639	+	314.608i	0.0864855	+	0.149797i
$165$		0			0
$166$	−603.005	+	1044.44i	−0.281942	+	0.488337i
$167$	546.074			0.253033			0.126516	−	0.991965i	$-0.459620\pi$
$167$	546.074			0.253033			0.126516	+	0.991965i	$0.459620\pi$
$168$	−1394.78	−	187.824i	−0.640533	−	0.0862555i
$169$	2764.88			1.25848
$170$		0			0
$171$	−2240.83	−	3881.22i	−1.00211	−	1.73570i
$172$	−18.6388	−	32.2833i	−0.00826275	−	0.0143115i
$173$	−934.614	+	1618.80i	−0.410737	+	0.711417i	−0.994970	−	0.100169i	$-0.968062\pi$
$173$	−934.614	+	1618.80i	−0.410737	+	0.711417i	0.584234	+	0.811585i	$0.301395\pi$
$174$	−261.234			−0.113816
$175$		0			0
$176$	−1149.82			−0.492448
$177$	179.984	−	311.741i	0.0764318	−	0.132384i
$178$	−800.323	−	1386.20i	−0.337004	−	0.583708i
$179$	−1568.55	−	2716.81i	−0.654967	−	1.13444i	−0.981902	−	0.189390i	$-0.939349\pi$
$179$	−1568.55	−	2716.81i	−0.654967	−	1.13444i	0.326935	−	0.945047i	$-0.393984\pi$
$180$		0			0
$181$	3955.06			1.62418			0.812091	−	0.583530i	$-0.198329\pi$
$181$	3955.06			1.62418			0.812091	+	0.583530i	$0.198329\pi$
$182$	−991.349	−	2413.49i	−0.403756	−	0.982965i
$183$	−1831.87			−0.739975
$184$	480.660	−	832.528i	0.192580	−	0.333559i
$185$		0			0
$186$	2317.81	+	4014.56i	0.913708	+	1.58259i
$187$	909.787	−	1575.80i	0.355776	−	0.616223i
$188$	−1113.51			−0.431973
$189$	3894.73	−	5044.75i	1.49894	−	1.94154i
$190$		0			0
$191$	−1174.88	+	2034.95i	−0.445085	+	0.770909i	−0.998058	−	0.0622896i	$-0.980160\pi$
$191$	−1174.88	+	2034.95i	−0.445085	+	0.770909i	0.552973	+	0.833199i	$0.313493\pi$
$192$	303.963	+	526.479i	0.114253	+	0.197893i
$193$	1779.83	+	3082.76i	0.663809	+	1.14975i	0.979607	+	0.200925i	$0.0643946\pi$
$193$	1779.83	+	3082.76i	0.663809	+	1.14975i	−0.315797	+	0.948827i	$0.602272\pi$
$194$	44.6934	−	77.4112i	0.0165402	−	0.0286485i
$195$		0			0
$196$	−975.871	+	964.396i	−0.355638	+	0.351456i
$197$	−1620.75			−0.586160			−0.293080	−	0.956088i	$-0.594680\pi$
$197$	−1620.75			−0.586160			−0.293080	+	0.956088i	$0.594680\pi$
$198$	4543.79	−	7870.08i	1.63087	−	2.82476i
$199$	1449.09	+	2509.90i	0.516197	+	0.894079i	0.999823	+	0.0188047i	$0.00598608\pi$
$199$	1449.09	+	2509.90i	0.516197	+	0.894079i	−0.483626	+	0.875275i	$0.660681\pi$
$200$		0			0
$201$	−2042.22	+	3537.23i	−0.716652	+	1.24128i
$202$	−1610.76			−0.561051
$203$	−155.629	+	201.583i	−0.0538080	+	0.0696963i
$204$	−962.035			−0.330176
$205$		0			0
$206$	1054.19	+	1825.92i	0.356549	+	0.617561i
$207$	3798.90	+	6579.88i	1.27556	+	2.20934i
$208$	−563.525	+	976.054i	−0.187853	+	0.325371i
$209$	−5093.75			−1.68585
$210$		0			0
$211$	5725.91			1.86819			0.934094	−	0.357026i	$-0.116209\pi$
$211$	5725.91			1.86819			0.934094	+	0.357026i	$0.116209\pi$
$212$	−183.997	+	318.692i	−0.0596083	+	0.103245i
$213$	361.383	+	625.934i	0.116251	+	0.201353i
$214$	1679.41	+	2908.82i	0.536458	+	0.929173i
$215$		0			0
$216$	−2752.99			−0.867209
$217$	4478.69	+	603.110i	1.40108	+	0.188672i
$218$	1413.98			0.439297
$219$	−3791.68	+	6567.38i	−1.16994	+	2.02640i
$220$		0			0
$221$	−891.772	−	1544.59i	−0.271435	−	0.470139i
$222$	−707.067	+	1224.68i	−0.213762	+	0.370247i
$223$	−1268.36			−0.380878			−0.190439	−	0.981699i	$-0.560991\pi$
$223$	−1268.36			−0.380878			−0.190439	+	0.981699i	$0.560991\pi$
$224$	587.347	+	79.0933i	0.175195	+	0.0235922i
$225$		0			0
$226$	1328.92	−	2301.76i	0.391144	−	0.677481i
$227$	−386.032	−	668.628i	−0.112872	−	0.195499i	0.804055	−	0.594555i	$-0.202672\pi$
$227$	−386.032	−	668.628i	−0.112872	−	0.195499i	−0.916927	+	0.399055i	$0.869338\pi$
$228$	1346.57	+	2332.33i	0.391135	+	0.677466i
$229$	−177.822	+	307.996i	−0.0513135	+	0.0888776i	−0.890541	−	0.454902i	$-0.849674\pi$
$229$	−177.822	+	307.996i	−0.0513135	+	0.0888776i	0.839228	+	0.543780i	$0.183007\pi$
$230$		0			0
$231$	−4803.44	−	11694.2i	−1.36815	−	3.33084i
$232$	110.007			0.0311305
$233$	−1451.14	+	2513.46i	−0.408016	+	0.706704i	−0.994667	−	0.103135i	$-0.967112\pi$
$233$	−1451.14	+	2513.46i	−0.408016	+	0.706704i	0.586652	+	0.809839i	$0.300446\pi$
$234$	−4453.82	−	7714.24i	−1.24425	−	2.15511i
$235$		0			0
$236$	−75.7920	+	131.276i	−0.0209052	+	0.0362089i
$237$	104.879			0.0287452
$238$	−573.130	+	742.362i	−0.156095	+	0.202186i
$239$	−5635.49			−1.52523			−0.762614	−	0.646853i	$-0.776085\pi$
$239$	−5635.49			−1.52523			−0.762614	+	0.646853i	$0.776085\pi$
$240$		0			0
$241$	−2037.81	−	3529.59i	−0.544676	−	0.943406i	−0.998627	−	0.0523795i	$-0.983319\pi$
$241$	−2037.81	−	3529.59i	−0.544676	−	0.943406i	0.453952	−	0.891026i	$-0.350014\pi$
$242$	−3833.38	−	6639.61i	−1.01826	−	1.76368i
$243$	2771.12	−	4799.73i	0.731554	−	1.26709i
$244$	771.406			0.202394
$245$		0			0
$246$	1725.36			0.447174
$247$	−2496.45	+	4323.97i	−0.643097	+	1.11388i
$248$	−976.037	−	1690.55i	−0.249913	−	0.432862i
$249$	2863.93	+	4960.47i	0.728891	+	1.26248i
$250$		0			0
$251$	1107.80			0.278582			0.139291	−	0.990252i	$-0.455518\pi$
$251$	1107.80			0.278582			0.139291	+	0.990252i	$0.455518\pi$
$252$	−2862.41	+	3707.61i	−0.715535	+	0.926816i
$253$	8635.50			2.14589
$254$	−2072.96	+	3590.46i	−0.512082	+	0.886952i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−3292.73	+	5703.17i	−0.799201	+	1.38426i	0.120935	+	0.992660i	$0.461411\pi$
$257$	−3292.73	+	5703.17i	−0.799201	+	1.38426i	−0.920137	+	0.391597i	$0.871923\pi$
$258$	−177.047			−0.0427227
$259$	523.797	+	1275.21i	0.125665	+	0.305937i
$260$		0			0
$261$	−434.718	+	752.954i	−0.103097	+	0.178570i
$262$	1919.16	+	3324.08i	0.452542	+	0.783826i
$263$	−2790.43	−	4833.17i	−0.654242	−	1.13318i	−0.982083	−	0.188447i	$-0.939655\pi$
$263$	−2790.43	−	4833.17i	−0.654242	−	1.13318i	0.327842	−	0.944733i	$-0.393679\pi$
$264$	−2730.48	+	4729.34i	−0.636552	+	1.10254i
$265$		0			0
$266$	2601.98	+	350.388i	0.599765	+	0.0807656i
$267$	−7602.14			−1.74248
$268$	859.987	−	1489.54i	0.196015	−	0.339508i
$269$	−3190.41	−	5525.95i	−0.723133	−	1.25250i	−0.959738	−	0.280897i	$-0.909368\pi$
$269$	−3190.41	−	5525.95i	−0.723133	−	1.25250i	0.236605	−	0.971606i	$-0.423965\pi$
$270$		0			0
$271$	−3519.61	+	6096.15i	−0.788934	+	1.36647i	0.137686	+	0.990476i	$0.456034\pi$
$271$	−3519.61	+	6096.15i	−0.788934	+	1.36647i	−0.926620	+	0.375998i	$0.877300\pi$
$272$	405.117			0.0903082
$273$	−12281.1	−	1653.80i	−2.72267	−	0.366640i
$274$	−2173.36			−0.479187
$275$		0			0
$276$	−2282.86	−	3954.03i	−0.497869	−	0.862335i
$277$	−3513.31	−	6085.23i	−0.762073	−	1.31995i	−0.941780	−	0.336230i	$-0.890848\pi$
$277$	−3513.31	−	6085.23i	−0.762073	−	1.31995i	0.179707	−	0.983720i	$-0.442485\pi$
$278$	−240.132	+	415.921i	−0.0518064	+	0.0897312i
$279$	15428.2			3.31062
$280$		0			0
$281$	−3971.78			−0.843191			−0.421596	−	0.906784i	$-0.638530\pi$
$281$	−3971.78			−0.843191			−0.421596	+	0.906784i	$0.638530\pi$
$282$	−2644.26	+	4579.99i	−0.558381	+	0.967144i
$283$	−2465.45	−	4270.29i	−0.517866	−	0.896970i	−0.999785	−	0.0207540i	$-0.993393\pi$
$283$	−2465.45	−	4270.29i	−0.517866	−	0.896970i	0.481919	−	0.876216i	$-0.339940\pi$
$284$	−152.180	−	263.583i	−0.0317965	−	0.0550732i
$285$		0			0
$286$	−10124.2			−2.09321
$287$	1027.88	−	1331.39i	0.211407	−	0.273830i
$288$	2023.30			0.413972
$289$	2135.95	−	3699.58i	0.434755	−	0.753019i
$290$		0			0
$291$	−212.268	−	367.658i	−0.0427607	−	0.0740636i
$292$	1596.69	−	2765.55i	0.319997	−	0.554252i
$293$	−12.9391			−0.00257991			−0.00128995	−	0.999999i	$-0.500411\pi$
$293$	−12.9391			−0.00257991			−0.00128995	+	0.999999i	$0.500411\pi$
$294$	1649.26	+	6304.03i	0.327167	+	1.25054i
$295$		0			0
$296$	297.749	−	515.716i	0.0584672	−	0.101268i
$297$	−12365.0	−	21416.8i	−2.41579	−	4.18427i
$298$	−2786.72	−	4826.74i	−0.541712	−	0.938273i
$299$	4232.25	−	7330.48i	0.818587	−	1.41783i
$300$		0			0
$301$	−105.475	+	136.619i	−0.0201976	+	0.0261615i
$302$	−2101.65			−0.400451
$303$	−3825.08	+	6625.23i	−0.725231	+	1.25614i
$304$	−567.047	−	982.154i	−0.106981	−	0.185297i
$305$		0			0
$306$	−1600.92	+	2772.88i	−0.299080	+	0.518022i
$307$	5488.27			1.02030			0.510150	−	0.860085i	$-0.329590\pi$
$307$	5488.27			1.02030			0.510150	+	0.860085i	$0.329590\pi$
$308$	2022.75	+	4924.49i	0.374211	+	0.911035i
$309$	10013.6			1.84354
$310$		0			0
$311$	1739.50	+	3012.91i	0.317165	+	0.549345i	0.979895	−	0.199513i	$-0.0639358\pi$
$311$	1739.50	+	3012.91i	0.317165	+	0.549345i	−0.662731	+	0.748858i	$0.730603\pi$
$312$	2676.42	+	4635.69i	0.485648	+	0.841168i
$313$	460.190	−	797.073i	0.0831038	−	0.143940i	−0.821478	−	0.570240i	$-0.806850\pi$
$313$	460.190	−	797.073i	0.0831038	−	0.143940i	0.904582	+	0.426300i	$0.140183\pi$
$314$	2255.43			0.405355
$315$		0			0
$316$	−44.1649			−0.00786225
$317$	474.352	−	821.602i	0.0840450	−	0.145570i	−0.820939	−	0.571016i	$-0.806549\pi$
$317$	474.352	−	821.602i	0.0840450	−	0.145570i	0.904984	+	0.425446i	$0.139883\pi$
$318$	873.879	+	1513.60i	0.154103	+	0.266914i
$319$	494.092	+	855.792i	0.0867204	+	0.150204i
$320$		0			0
$321$	15952.4			2.77376
$322$	−4411.16	−	594.016i	−0.763430	−	0.102805i
$323$	1794.69			0.309162
$324$	−3123.24	+	5409.61i	−0.535535	+	0.927574i
$325$		0			0
$326$	−260.721	−	451.582i	−0.0442945	−	0.0767202i
$327$	3357.79	−	5815.86i	0.567848	−	0.983541i
$328$	−726.556			−0.122309
$329$	1958.88	+	4768.98i	0.328256	+	0.799157i
$330$		0			0
$331$	−3129.91	+	5421.17i	−0.519745	+	0.900225i	0.479991	+	0.877273i	$0.340640\pi$
$331$	−3129.91	+	5421.17i	−0.519745	+	0.900225i	−0.999737	+	0.0229518i	$0.992694\pi$
$332$	−1206.01	−	2088.87i	−0.199363	−	0.345306i
$333$	2353.26	+	4075.96i	0.387260	+	0.670754i
$334$	−546.074	+	945.827i	−0.0894605	+	0.154950i
$335$		0			0
$336$	1720.10	−	2228.00i	0.279283	−	0.361749i
$337$	8999.55			1.45471			0.727354	−	0.686262i	$-0.240750\pi$
$337$	8999.55			1.45471			0.727354	+	0.686262i	$0.240750\pi$
$338$	−2764.88	+	4788.91i	−0.444940	+	0.770659i
$339$	−6311.60	−	10932.0i	−1.01121	−	1.75146i
$340$		0			0
$341$	8767.70	−	15186.1i	1.39237	−	2.41165i
$342$	8963.30			1.41719
$343$	5847.10	+	2482.95i	0.920448	+	0.390864i
$344$	74.5551			0.0116853
$345$		0			0
$346$	−1869.23	−	3237.60i	−0.290435	−	0.503047i
$347$	2619.81	+	4537.64i	0.405299	+	0.701998i	0.994356	−	0.106093i	$-0.0338342\pi$
$347$	2619.81	+	4537.64i	0.405299	+	0.701998i	−0.589058	+	0.808091i	$0.700501\pi$
$348$	261.234	−	452.470i	0.0402402	−	0.0696981i
$349$	7955.14			1.22014			0.610070	−	0.792347i	$-0.291141\pi$
$349$	7955.14			1.22014			0.610070	+	0.792347i	$0.291141\pi$
$350$		0			0
$351$	−24240.3			−3.68618
$352$	1149.82	−	1991.54i	0.174107	−	0.301561i
$353$	223.663	+	387.396i	0.0337235	+	0.0584107i	0.882395	−	0.470510i	$-0.155930\pi$
$353$	223.663	+	387.396i	0.0337235	+	0.0584107i	−0.848671	+	0.528921i	$0.822597\pi$
$354$	359.968	+	623.483i	0.0540454	+	0.0936094i
$355$		0			0
$356$	3201.29			0.476596
$357$	1692.40	+	4120.25i	0.250901	+	0.610831i
$358$	6274.21			0.926264
$359$	−317.566	+	550.040i	−0.0466866	+	0.0808635i	−0.888424	−	0.459023i	$-0.848200\pi$
$359$	−317.566	+	550.040i	−0.0466866	+	0.0808635i	0.841738	+	0.539887i	$0.181533\pi$
$360$		0			0
$361$	917.453	+	1589.08i	0.133759	+	0.231678i
$362$	−3955.06	+	6850.36i	−0.574235	+	0.994605i
$363$	−36412.6			−5.26493
$364$	5171.63	+	696.423i	0.744690	+	0.100282i
$365$		0			0
$366$	1831.87	−	3172.89i	0.261621	−	0.453140i
$367$	−2071.31	−	3587.61i	−0.294609	−	0.510278i	0.680285	−	0.732948i	$-0.261856\pi$
$367$	−2071.31	−	3587.61i	−0.294609	−	0.510278i	−0.974894	+	0.222670i	$0.928523\pi$
$368$	961.321	+	1665.06i	0.136175	+	0.235862i
$369$	2871.17	−	4973.00i	0.405059	−	0.701583i
$370$		0			0
$371$	1688.59	+	227.390i	0.236300	+	0.0318207i
$372$	−9271.22			−1.29218
$373$	1423.48	−	2465.54i	0.197601	−	0.342255i	−0.750149	−	0.661269i	$-0.770018\pi$
$373$	1423.48	−	2465.54i	0.197601	−	0.342255i	0.947750	+	0.319014i	$0.103352\pi$
$374$	1819.57	+	3151.59i	0.251572	+	0.435735i
$375$		0			0
$376$	1113.51	−	1928.65i	0.152726	−	0.264529i
$377$	968.616			0.132324
$378$	4843.04	+	11790.6i	0.658992	+	1.60435i
$379$	882.678			0.119631			0.0598155	−	0.998209i	$-0.480949\pi$
$379$	882.678			0.119631			0.0598155	+	0.998209i	$0.480949\pi$
$380$		0			0
$381$	9845.34	+	17052.6i	1.32386	+	2.29300i
$382$	−2349.76	−	4069.90i	−0.314722	−	0.545115i
$383$	4949.03	−	8571.96i	0.660270	−	1.14362i	−0.320275	−	0.947325i	$-0.603775\pi$
$383$	4949.03	−	8571.96i	0.660270	−	1.14362i	0.980545	−	0.196296i	$-0.0628915\pi$
$384$	−1215.85			−0.161579
$385$		0			0
$386$	−7119.33			−0.938768
$387$	−294.623	+	510.302i	−0.0386990	+	0.0670287i
$388$	89.3868	+	154.822i	0.0116957	+	0.0202575i
$389$	4284.29	+	7420.62i	0.558412	+	0.967198i	0.997629	+	0.0688173i	$0.0219226\pi$
$389$	4284.29	+	7420.62i	0.558412	+	0.967198i	−0.439217	+	0.898381i	$0.644744\pi$
$390$		0			0
$391$	−3042.56			−0.393526
$392$	−694.511	−	2654.65i	−0.0894850	−	0.342042i
$393$	18229.8			2.33987
$394$	1620.75	−	2807.22i	0.207239	−	0.358948i
$395$		0			0
$396$	9087.58	+	15740.2i	1.15320	+	1.99740i
$397$	2310.15	−	4001.29i	0.292048	−	0.505841i	−0.682246	−	0.731122i	$-0.738997\pi$
$397$	2310.15	−	4001.29i	0.292048	−	0.505841i	0.974294	+	0.225281i	$0.0723301\pi$
$398$	−5796.36			−0.730013
$399$	7620.13	−	9870.17i	0.956099	−	1.23841i
$400$		0			0
$401$	1332.94	−	2308.72i	0.165994	−	0.287511i	−0.771014	−	0.636819i	$-0.780250\pi$
$401$	1332.94	−	2308.72i	0.165994	−	0.287511i	0.937008	+	0.349308i	$0.113583\pi$
$402$	−4084.44	−	7074.46i	−0.506750	−	0.877716i
$403$	−8594.09	−	14885.4i	−1.06229	−	1.83994i
$404$	1610.76	−	2789.91i	0.198362	−	0.343572i
$405$		0			0
$406$	−193.523	−	471.141i	−0.0236561	−	0.0575919i
$407$	5349.32			0.651489
$408$	962.035	−	1666.29i	0.116735	−	0.202191i
$409$	−7969.29	−	13803.2i	−0.963463	−	1.66877i	−0.713690	−	0.700462i	$-0.752977\pi$
$409$	−7969.29	−	13803.2i	−0.963463	−	1.66877i	−0.249773	−	0.968304i	$-0.580356\pi$
$410$		0			0
$411$	−5161.09	+	8939.27i	−0.619411	+	1.07285i
$412$	−4216.77			−0.504237
$413$	695.565	+	93.6663i	0.0828730	+	0.0111598i
$414$	−15195.6			−1.80392
$415$		0			0
$416$	−1127.05	−	1952.11i	−0.132832	−	0.230072i
$417$	1140.49	+	1975.38i	0.133933	+	0.231978i
$418$	5093.75	−	8822.64i	0.596037	−	1.03237i
$419$	−11451.6			−1.33520			−0.667600	−	0.744520i	$-0.732678\pi$
$419$	−11451.6			−1.33520			−0.667600	+	0.744520i	$0.732678\pi$
$420$		0			0
$421$	−6560.18			−0.759438			−0.379719	−	0.925102i	$-0.623979\pi$
$421$	−6560.18			−0.759438			−0.379719	+	0.925102i	$0.623979\pi$
$422$	−5725.91	+	9917.57i	−0.660505	+	1.14403i
$423$	8800.61	+	15243.1i	1.01158	+	1.75212i
$424$	−367.994	−	637.384i	−0.0421495	−	0.0730050i
$425$		0			0
$426$	−1445.53			−0.164404
$427$	−1357.05	−	3303.81i	−0.153799	−	0.374433i
$428$	−6717.63			−0.758666
$429$	−24042.1	+	41642.2i	−2.70574	+	4.68649i
$430$		0			0
$431$	−6600.92	−	11433.1i	−0.737715	−	1.27776i	−0.953522	−	0.301324i	$-0.902572\pi$
$431$	−6600.92	−	11433.1i	−0.737715	−	1.27776i	0.215807	−	0.976436i	$-0.430762\pi$
$432$	2752.99	−	4768.32i	0.306605	−	0.531055i
$433$	13414.4			1.48881			0.744403	−	0.667731i	$-0.232734\pi$
$433$	13414.4			1.48881			0.744403	+	0.667731i	$0.232734\pi$
$434$	−5523.31	+	7154.21i	−0.610892	+	0.791274i
$435$		0			0
$436$	−1413.98	+	2449.08i	−0.155315	+	0.269013i
$437$	4258.70	+	7376.29i	0.466182	+	0.807450i
$438$	−7583.35	−	13134.8i	−0.827275	−	1.43288i
$439$	−353.811	+	612.819i	−0.0384658	+	0.0666247i	−0.884617	−	0.466318i	$-0.845580\pi$
$439$	−353.811	+	612.819i	−0.0384658	+	0.0666247i	0.846152	+	0.532942i	$0.178914\pi$
$440$		0			0
$441$	20914.7	+	5736.85i	2.25836	+	0.619464i
$442$	3567.09			0.383867
$443$	−6688.64	+	11585.1i	−0.717351	+	1.24249i	0.244694	+	0.969600i	$0.421312\pi$
$443$	−6688.64	+	11585.1i	−0.717351	+	1.24249i	−0.962046	+	0.272889i	$0.912021\pi$
$444$	−1414.13	−	2449.35i	−0.151153	−	0.261804i
$445$		0			0
$446$	1268.36	−	2196.87i	0.134661	−	0.233239i
$447$	−26470.6			−2.80093
$448$	−724.340	+	938.221i	−0.0763881	+	0.0989437i
$449$	4057.83			0.426505			0.213253	−	0.976997i	$-0.431594\pi$
$449$	4057.83			0.426505			0.213253	+	0.976997i	$0.431594\pi$
$450$		0			0
$451$	−3263.31	−	5652.21i	−0.340716	−	0.590138i
$452$	2657.84	+	4603.52i	0.276580	+	0.479051i
$453$	−4990.81	+	8644.33i	−0.517635	+	0.896570i
$454$	1544.13			0.159625
$455$		0			0
$456$	−5386.29			−0.553149
$457$	−2261.36	+	3916.79i	−0.231470	+	0.400918i	−0.958241	−	0.285962i	$-0.907687\pi$
$457$	−2261.36	+	3916.79i	−0.231470	+	0.400918i	0.726771	+	0.686880i	$0.241020\pi$
$458$	−355.644	−	615.993i	−0.0362841	−	0.0628460i
$459$	4356.57	+	7545.81i	0.443023	+	0.767338i
$460$		0			0
$461$	4355.56			0.440040			0.220020	−	0.975495i	$-0.429388\pi$
$461$	4355.56			0.440040			0.220020	+	0.975495i	$0.429388\pi$
$462$	25058.5	+	3374.42i	2.52343	+	0.339810i
$463$	17178.7			1.72432			0.862160	−	0.506636i	$-0.169111\pi$
$463$	17178.7			1.72432			0.862160	+	0.506636i	$0.169111\pi$
$464$	−110.007	+	190.537i	−0.0110063	+	0.0190635i
$465$		0			0
$466$	−2902.29	−	5026.91i	−0.288511	−	0.499715i
$467$	−4020.39	+	6963.52i	−0.398376	+	0.690007i	−0.993526	−	0.113607i	$-0.963759\pi$
$467$	−4020.39	+	6963.52i	−0.398376	+	0.690007i	0.595150	+	0.803615i	$0.297093\pi$
$468$	17815.3			1.75964
$469$	−7892.36	−	1062.80i	−0.777047	−	0.104639i
$470$		0			0
$471$	5356.00	−	9276.86i	0.523973	−	0.907548i
$472$	−151.584	−	262.551i	−0.0147822	−	0.0256036i
$473$	334.862	+	579.998i	0.0325518	+	0.0563813i
$474$	−104.879	+	181.656i	−0.0101630	+	0.0176028i
$475$		0			0
$476$	−712.679	−	1735.05i	−0.0686251	−	0.167071i
$477$	5816.88			0.558358
$478$	5635.49	−	9760.96i	0.539250	−	0.934008i
$479$	−4260.08	−	7378.68i	−0.406364	−	0.703842i	0.588115	−	0.808777i	$-0.299870\pi$
$479$	−4260.08	−	7378.68i	−0.406364	−	0.703842i	−0.994479	+	0.104934i	$0.966537\pi$
$480$		0			0
$481$	2621.70	−	4540.92i	0.248522	−	0.430453i
$482$	8151.24			0.770288
$483$	−12918.5	+	16733.0i	−1.21700	+	1.57635i
$484$	15333.5			1.44004
$485$		0			0
$486$	5542.25	+	9599.46i	0.517287	+	0.895967i
$487$	9885.09	+	17121.5i	0.919787	+	1.59312i	0.799738	+	0.600350i	$0.204972\pi$
$487$	9885.09	+	17121.5i	0.919787	+	1.59312i	0.120049	+	0.992768i	$0.461695\pi$
$488$	−771.406	+	1336.12i	−0.0715572	+	0.123941i
$489$	−2476.55			−0.229025
$490$		0			0
$491$	10047.0			0.923450			0.461725	−	0.887023i	$-0.347231\pi$
$491$	10047.0			0.923450			0.461725	+	0.887023i	$0.347231\pi$
$492$	−1725.36	+	2988.41i	−0.158100	+	0.273837i
$493$	−174.084	−	301.522i	−0.0159033	−	0.0275454i
$494$	−4992.89	−	8647.94i	−0.454738	−	0.787630i
$495$		0			0
$496$	3904.15			0.353430
$497$	−861.172	+	1115.46i	−0.0777241	+	0.100674i
$498$	−11455.7			−1.03081
$499$	6336.80	−	10975.7i	0.568486	−	0.984646i	−0.428230	−	0.903670i	$-0.640863\pi$
$499$	6336.80	−	10975.7i	0.568486	−	0.984646i	0.996716	−	0.0809764i	$-0.0258038\pi$
$500$		0			0
$501$	2593.53	+	4492.13i	0.231278	+	0.400586i
$502$	−1107.80	+	1918.77i	−0.0984935	+	0.170596i
$503$	5078.12			0.450144			0.225072	−	0.974342i	$-0.427738\pi$
$503$	5078.12			0.450144			0.225072	+	0.974342i	$0.427738\pi$
$504$	−3559.36	−	8665.45i	−0.314577	−	0.765853i
$505$		0			0
$506$	−8635.50	+	14957.1i	−0.758685	+	1.31408i
$507$	13131.6	+	22744.6i	1.15028	+	1.99235i
$508$	−4145.91	−	7180.93i	−0.362097	−	0.627170i
$509$	−5494.52	+	9516.78i	−0.478468	+	0.828731i	−0.999695	−	0.0246870i	$-0.992141\pi$
$509$	−5494.52	+	9516.78i	−0.478468	+	0.828731i	0.521227	+	0.853418i	$0.325474\pi$
$510$		0			0
$511$	−14653.3	−	1973.24i	−1.26854	−	0.170824i
$512$	512.000			0.0441942
$513$	12195.9	−	21123.9i	1.04963	−	1.81802i
$514$	−6585.46	−	11406.3i	−0.565121	−	0.978818i
$515$		0			0
$516$	177.047	−	306.654i	0.0151047	−	0.0261622i
$517$	20005.2			1.70179
$518$	−2732.53	−	367.968i	−0.231777	−	0.0312115i
$519$	−17755.5			−1.50170
$520$		0			0
$521$	−5716.39	−	9901.08i	−0.480691	−	0.832580i	0.519064	−	0.854735i	$-0.326281\pi$
$521$	−5716.39	−	9901.08i	−0.480691	−	0.832580i	−0.999755	+	0.0221549i	$0.992947\pi$
$522$	−869.436	−	1505.91i	−0.0729007	−	0.126268i
$523$	10677.0	−	18493.1i	0.892679	−	1.54617i	0.0560289	−	0.998429i	$-0.482156\pi$
$523$	10677.0	−	18493.1i	0.892679	−	1.54617i	0.836651	−	0.547737i	$-0.184511\pi$
$524$	−7676.63			−0.639991
$525$		0			0
$526$	11161.7			0.925237
$527$	−3089.14	+	5350.54i	−0.255341	+	0.442264i
$528$	−5460.97	−	9458.67i	−0.450110	−	0.779613i
$529$	−1136.33	−	1968.18i	−0.0933942	−	0.161763i
$530$		0			0
$531$	2396.09			0.195822
$532$	−3208.87	+	4156.37i	−0.261507	+	0.338725i
$533$	−6397.38			−0.519890
$534$	7602.14	−	13167.3i	0.616061	−	1.06705i
$535$		0			0
$536$	1719.97	+	2979.08i	0.138604	+	0.240069i
$537$	14899.4	−	25806.6i	1.19731	−	2.07381i
$538$	12761.6			1.02266
$539$	17532.4	−	17326.2i	1.40107	−	1.38459i
$540$		0			0
$541$	−3185.35	+	5517.20i	−0.253141	+	0.438452i	−0.964389	−	0.264488i	$-0.914797\pi$
$541$	−3185.35	+	5517.20i	−0.253141	+	0.438452i	0.711248	+	0.702941i	$0.248130\pi$
$542$	−7039.22	−	12192.3i	−0.557861	−	0.966243i
$543$	18784.2	+	32535.2i	1.48455	+	2.57131i
$544$	−405.117	+	701.683i	−0.0319288	+	0.0553022i
$545$		0			0
$546$	15145.6	−	19617.7i	1.18713	−	1.53766i
$547$	−19262.1			−1.50564			−0.752821	−	0.658225i	$-0.771308\pi$
$547$	−19262.1			−1.50564			−0.752821	+	0.658225i	$0.771308\pi$
$548$	2173.36	−	3764.36i	0.169418	−	0.293441i
$549$	−6096.81	−	10560.0i	−0.473962	−	0.820927i
$550$		0			0
$551$	−487.335	+	844.088i	−0.0376790	+	0.0652620i
$552$	9131.43			0.704094
$553$	77.6946	+	189.151i	0.00597452	+	0.0145453i
$554$	14053.2			1.07773
$555$		0			0
$556$	−480.264	−	831.842i	−0.0366326	−	0.0634496i
$557$	−2322.10	−	4022.00i	−0.176644	−	0.305956i	0.764085	−	0.645116i	$-0.223191\pi$
$557$	−2322.10	−	4022.00i	−0.176644	−	0.305956i	−0.940729	+	0.339159i	$0.889857\pi$
$558$	−15428.2	+	26722.5i	−1.17048	+	2.02733i
$559$	656.463			0.0496698
$560$		0			0
$561$	17283.8			1.30076
$562$	3971.78	−	6879.33i	0.298113	−	0.516347i
$563$	−11975.4	−	20742.0i	−0.896455	−	1.55271i	−0.831994	−	0.554785i	$-0.812801\pi$
$563$	−11975.4	−	20742.0i	−0.896455	−	1.55271i	−0.0644609	−	0.997920i	$-0.520533\pi$
$564$	−5288.52	−	9159.99i	−0.394835	−	0.683874i
$565$		0			0
$566$	9861.82			0.732373
$567$	28662.9	+	3859.81i	2.12298	+	0.285885i
$568$	608.720			0.0449671
$569$	7083.96	−	12269.8i	0.521924	−	0.903999i	−0.477750	−	0.878496i	$-0.658548\pi$
$569$	7083.96	−	12269.8i	0.521924	−	0.903999i	0.999675	−	0.0255038i	$-0.00811899\pi$
$570$		0			0
$571$	−205.604	−	356.117i	−0.0150688	−	0.0260998i	0.858393	−	0.512993i	$-0.171463\pi$
$571$	−205.604	−	356.117i	−0.0150688	−	0.0260998i	−0.873461	+	0.486893i	$0.838130\pi$
$572$	10124.2	−	17535.7i	0.740062	−	1.28183i
$573$	−22320.0			−1.62728
$574$	1278.15	+	3111.72i	0.0929425	+	0.226273i
$575$		0			0
$576$	−2023.30	+	3504.45i	−0.146361	+	0.253505i
$577$	4446.92	+	7702.29i	0.320845	+	0.555720i	0.980663	−	0.195706i	$-0.0626998\pi$
$577$	4446.92	+	7702.29i	0.320845	+	0.555720i	−0.659818	+	0.751426i	$0.729366\pi$
$578$	4271.91	+	7399.16i	0.307419	+	0.532465i
$579$	−16906.3	+	29282.7i	−1.21348	+	2.10181i
$580$		0			0
$581$	−6824.71	+	8839.88i	−0.487326	+	0.631222i
$582$	849.071			0.0604727
$583$	3305.67	−	5725.59i	0.234832	−	0.406741i
$584$	3193.38	+	5531.10i	0.226272	+	0.391915i
$585$		0			0
$586$	12.9391	−	22.4113i	0.000912135	−	0.00157986i
$587$	20146.2			1.41656			0.708281	−	0.705931i	$-0.249471\pi$
$587$	20146.2			1.41656			0.708281	+	0.705931i	$0.249471\pi$
$588$	−12568.2	−	3447.43i	−0.881467	−	0.241785i
$589$	17295.6			1.20994
$590$		0			0
$591$	−7697.62	−	13332.7i	−0.535766	−	0.927974i
$592$	595.497	+	1031.43i	0.0413425	+	0.0716074i
$593$	4513.48	−	7817.57i	0.312557	−	0.541365i	−0.666358	−	0.745632i	$-0.732148\pi$
$593$	4513.48	−	7817.57i	0.312557	−	0.541365i	0.978915	+	0.204267i	$0.0654811\pi$
$594$	49459.9			3.41644
$595$		0			0
$596$	11146.9			0.766097
$597$	−13764.7	+	23841.1i	−0.943635	+	1.63442i
$598$	8464.51	+	14661.0i	0.578828	+	1.00256i
$599$	4723.84	+	8181.92i	0.322222	+	0.558104i	0.980946	−	0.194280i	$-0.0622371\pi$
$599$	4723.84	+	8181.92i	0.322222	+	0.558104i	−0.658725	+	0.752384i	$0.728904\pi$
$600$		0			0
$601$	8237.41			0.559087			0.279543	−	0.960133i	$-0.409817\pi$
$601$	8237.41			0.559087			0.279543	+	0.960133i	$0.409817\pi$
$602$	−131.157	−	319.308i	−0.00887965	−	0.0216180i
$603$	−27187.6			−1.83610
$604$	2101.65	−	3640.16i	0.141581	−	0.245225i
$605$		0			0
$606$	−7650.15	−	13250.5i	−0.512816	−	0.888223i
$607$	1433.17	−	2482.33i	0.0958332	−	0.165988i	−0.814123	−	0.580693i	$-0.802782\pi$
$607$	1433.17	−	2482.33i	0.0958332	−	0.165988i	0.909956	+	0.414705i	$0.136115\pi$
$608$	2268.19			0.151295
$609$	−2397.42	−	322.841i	−0.159521	−	0.0214814i
$610$		0			0
$611$	9804.53	−	16981.9i	0.649180	−	1.12441i
$612$	−3201.84	−	5545.75i	−0.211482	−	0.366297i
$613$	7101.96	+	12301.0i	0.467937	+	0.810491i	0.999329	−	0.0366354i	$-0.0116640\pi$
$613$	7101.96	+	12301.0i	0.467937	+	0.810491i	−0.531392	+	0.847126i	$0.678331\pi$
$614$	−5488.27	+	9505.97i	−0.360731	+	0.624804i
$615$		0			0
$616$	−10552.2	−	1420.98i	−0.690196	−	0.0929432i
$617$	−22525.9			−1.46979			−0.734894	−	0.678182i	$-0.762768\pi$
$617$	−22525.9			−1.46979			−0.734894	+	0.678182i	$0.762768\pi$
$618$	−10013.6	+	17344.1i	−0.651791	+	1.12893i
$619$	6117.46	+	10595.8i	0.397224	+	0.688012i	0.993382	−	0.114855i	$-0.0366403\pi$
$619$	6117.46	+	10595.8i	0.397224	+	0.688012i	−0.596158	+	0.802867i	$0.703307\pi$
$620$		0			0
$621$	−20675.8	+	35811.6i	−1.33606	+	2.31412i
$622$	−6958.02			−0.448539
$623$	−5631.69	−	13710.6i	−0.362165	−	0.881709i
$624$	−10705.7			−0.686810
$625$		0			0
$626$	920.380	+	1594.15i	0.0587633	+	0.101781i
$627$	−24192.4	−	41902.4i	−1.54091	−	2.66893i
$628$	−2255.43	+	3906.52i	−0.143314	+	0.248228i
$629$	−1884.73			−0.119474
$630$		0			0
$631$	−6008.77			−0.379089			−0.189545	−	0.981872i	$-0.560701\pi$
$631$	−6008.77			−0.379089			−0.189545	+	0.981872i	$0.560701\pi$
$632$	44.1649	−	76.4959i	0.00277972	−	0.00481462i
$633$	27194.8	+	47102.7i	1.70757	+	2.95760i
$634$	948.704	+	1643.20i	0.0594288	+	0.102934i
$635$		0			0
$636$	−3495.52			−0.217934
$637$	−6115.23	−	23374.4i	−0.380367	−	1.45389i
$638$	−1976.37			−0.122641
$639$	−2405.51	+	4166.46i	−0.148921	+	0.257938i
$640$		0			0
$641$	−4272.30	−	7399.84i	−0.263254	−	0.455969i	0.703851	−	0.710348i	$-0.251462\pi$
$641$	−4272.30	−	7399.84i	−0.263254	−	0.455969i	−0.967105	+	0.254379i	$0.918129\pi$
$642$	−15952.4	+	27630.4i	−0.980674	+	1.69858i
$643$	2803.77			0.171959			0.0859796	−	0.996297i	$-0.472598\pi$
$643$	2803.77			0.171959			0.0859796	+	0.996297i	$0.472598\pi$
$644$	5440.03	−	7046.34i	0.332868	−	0.431156i
$645$		0			0
$646$	−1794.69	+	3108.49i	−0.109305	+	0.189322i
$647$	12892.5	+	22330.4i	0.783394	+	1.35688i	0.929954	+	0.367676i	$0.119847\pi$
$647$	12892.5	+	22330.4i	0.783394	+	1.35688i	−0.146560	+	0.989202i	$0.546820\pi$
$648$	−6246.48	−	10819.2i	−0.378681	−	0.655894i
$649$	1361.67	−	2358.48i	0.0823579	−	0.142648i
$650$		0			0
$651$	16309.9	+	39707.2i	0.981926	+	2.39055i
$652$	1042.88			0.0626418
$653$	−1519.02	+	2631.02i	−0.0910319	+	0.157672i	−0.907946	−	0.419088i	$-0.862350\pi$
$653$	−1519.02	+	2631.02i	−0.0910319	+	0.157672i	0.816914	+	0.576760i	$0.195683\pi$
$654$	6715.58	+	11631.7i	0.401529	+	0.695469i
$655$		0			0
$656$	726.556	−	1258.43i	0.0432427	−	0.0748986i
$657$	−50477.7			−2.99745
$658$	−10219.0	−	1376.11i	−0.605438	−	0.0815295i
$659$	−32561.4			−1.92475			−0.962377	−	0.271719i	$-0.912408\pi$
$659$	−32561.4			−1.92475			−0.962377	+	0.271719i	$0.912408\pi$
$660$		0			0
$661$	−4043.79	−	7004.04i	−0.237950	−	0.412142i	0.722176	−	0.691710i	$-0.243142\pi$
$661$	−4043.79	−	7004.04i	−0.237950	−	0.412142i	−0.960126	+	0.279568i	$0.909809\pi$
$662$	−6259.83	−	10842.3i	−0.367515	−	0.636555i
$663$	8470.80	−	14671.9i	0.496197	−	0.859438i
$664$	4824.04			0.281942
$665$		0			0
$666$	−9413.02			−0.547668
$667$	826.184	−	1430.99i	0.0479610	−	0.0830709i
$668$	−1092.15	−	1891.65i	−0.0632581	−	0.109566i
$669$	−6023.99	−	10433.9i	−0.348133	−	0.602984i
$670$		0			0
$671$	−13859.0			−0.797349
$672$	2138.92	+	5207.30i	0.122783	+	0.298923i
$673$	−25265.4			−1.44712			−0.723559	−	0.690262i	$-0.757495\pi$
$673$	−25265.4			−1.44712			−0.723559	+	0.690262i	$0.757495\pi$
$674$	−8999.55	+	15587.7i	−0.514317	+	0.890823i
$675$		0			0
$676$	−5529.76	−	9577.83i	−0.314620	−	0.544938i
$677$	3937.00	−	6819.08i	0.223502	−	0.387117i	−0.732367	−	0.680910i	$-0.761584\pi$
$677$	3937.00	−	6819.08i	0.223502	−	0.387117i	0.955869	+	0.293793i	$0.0949176\pi$
$678$	25246.4			1.43006
$679$	505.832	−	655.192i	0.0285892	−	0.0370309i
$680$		0			0
$681$	3666.86	−	6351.19i	0.206335	−	0.357383i
$682$	17535.4	+	30372.2i	0.984553	+	1.70530i
$683$	−7196.50	−	12464.7i	−0.403172	−	0.698314i	0.590935	−	0.806719i	$-0.298759\pi$
$683$	−7196.50	−	12464.7i	−0.403172	−	0.698314i	−0.994107	+	0.108405i	$0.965426\pi$
$684$	−8963.30	+	15524.9i	−0.501053	+	0.867850i
$685$		0			0
$686$	−10147.7	+	7644.53i	−0.564782	+	0.425466i
$687$	−3378.20			−0.187608
$688$	−74.5551	+	129.133i	−0.00413137	+	0.00715575i
$689$	−3240.22	−	5612.22i	−0.179162	−	0.310317i
$690$		0			0
$691$	−8172.35	+	14154.9i	−0.449915	+	0.779275i	−0.998380	−	0.0568983i	$-0.981879\pi$
$691$	−8172.35	+	14154.9i	−0.449915	+	0.779275i	0.548465	+	0.836173i	$0.315212\pi$
$692$	7476.92			0.410737
$693$	51425.8	−	66610.6i	2.81891	−	3.65127i
$694$	−10479.2			−0.573179
$695$		0			0
$696$	522.467	+	904.940i	0.0284541	+	0.0492840i
$697$	1149.77	+	1991.45i	0.0624828	+	0.108223i
$698$	−7955.14	+	13778.7i	−0.431385	+	0.747180i
$699$	−27568.4			−1.49175
$700$		0			0
$701$	21729.2			1.17075			0.585377	−	0.810761i	$-0.300946\pi$
$701$	21729.2			1.17075			0.585377	+	0.810761i	$0.300946\pi$
$702$	24240.3	−	41985.4i	1.30326	−	2.25732i
$703$	2638.08	+	4569.30i	0.141532	+	0.245141i
$704$	2299.64	+	3983.09i	0.123112	+	0.213236i
$705$		0			0
$706$	−894.652			−0.0476922
$707$	−14782.4	−	1990.63i	−0.786349	−	0.105891i
$708$	−1439.87			−0.0764318
$709$	4854.57	−	8408.37i	0.257147	−	0.445392i	−0.708329	−	0.705882i	$-0.750551\pi$
$709$	4854.57	−	8408.37i	0.257147	−	0.445392i	0.965477	+	0.260490i	$0.0838841\pi$
$710$		0			0
$711$	349.057	+	604.585i	0.0184116	+	0.0318899i
$712$	−3201.29	+	5544.80i	−0.168502	+	0.291854i
$713$	−29321.4			−1.54011
$714$	−8828.88	−	1188.92i	−0.462763	−	0.0623166i
$715$		0			0
$716$	−6274.21	+	10867.3i	−0.327484	+	0.567218i
$717$	−26765.3	−	46358.9i	−1.39410	−	2.41465i
$718$	−635.131	−	1100.08i	−0.0330124	−	0.0571791i
$719$	−7873.74	+	13637.7i	−0.408402	+	0.707373i	−0.994711	−	0.102715i	$-0.967247\pi$
$719$	−7873.74	+	13637.7i	−0.408402	+	0.707373i	0.586309	+	0.810087i	$0.300580\pi$
$720$		0			0
$721$	7418.11	+	18059.8i	0.383169	+	0.932845i
$722$	−3669.81			−0.189164
$723$	19356.8	−	33527.0i	0.995696	−	1.72460i
$724$	−7910.11	−	13700.7i	−0.406046	−	0.703292i
$725$		0			0
$726$	36412.6	−	63068.6i	1.86143	−	3.22410i
$727$	26775.1			1.36593			0.682967	−	0.730449i	$-0.260689\pi$
$727$	26775.1			1.36593			0.682967	+	0.730449i	$0.260689\pi$
$728$	−6377.87	+	8261.11i	−0.324697	+	0.420573i
$729$	10481.2			0.532498
$730$		0			0
$731$	−117.983	−	204.352i	−0.00596955	−	0.0103396i
$732$	3663.73	+	6345.77i	0.184994	+	0.320419i
$733$	437.525	−	757.815i	0.0220469	−	0.0381863i	−0.854791	−	0.518972i	$-0.826315\pi$
$733$	437.525	−	757.815i	0.0220469	−	0.0381863i	0.876838	+	0.480785i	$0.159648\pi$
$734$	8285.24			0.416640
$735$		0			0
$736$	−3845.28			−0.192580
$737$	−15450.4	+	26761.0i	−0.772218	+	1.33752i
$738$	5742.33	+	9946.01i	0.286420	+	0.496094i
$739$	3591.12	+	6220.00i	0.178757	+	0.309616i	0.941455	−	0.337138i	$-0.109459\pi$
$739$	3591.12	+	6220.00i	0.178757	+	0.309616i	−0.762698	+	0.646755i	$0.776126\pi$
$740$		0			0
$741$	−47426.7			−2.35123
$742$	−2082.45	+	2697.34i	−0.103031	+	0.133454i
$743$	9759.98			0.481910			0.240955	−	0.970536i	$-0.422539\pi$
$743$	9759.98			0.481910			0.240955	+	0.970536i	$0.422539\pi$
$744$	9271.22	−	16058.2i	0.456854	−	0.791295i
$745$		0			0
$746$	2846.96	+	4931.09i	0.139725	+	0.242011i
$747$	−19063.4	+	33018.8i	−0.933726	+	1.61726i
$748$	−7278.29			−0.355776
$749$	11817.6	+	28770.6i	0.576510	+	1.40354i
$750$		0			0
$751$	−17159.1	+	29720.5i	−0.833749	+	1.44410i	0.0612951	+	0.998120i	$0.480477\pi$
$751$	−17159.1	+	29720.5i	−0.833749	+	1.44410i	−0.895045	+	0.445977i	$0.852856\pi$
$752$	2227.02	+	3857.31i	0.107993	+	0.187050i
$753$	5261.43	+	9113.06i	0.254631	+	0.441034i
$754$	−968.616	+	1677.69i	−0.0467837	+	0.0810318i
$755$		0			0
$756$	−25265.0	−	3402.24i	−1.21545	−	0.163675i
$757$	−19677.7			−0.944780			−0.472390	−	0.881390i	$-0.656609\pi$
$757$	−19677.7			−0.944780			−0.472390	+	0.881390i	$0.656609\pi$
$758$	−882.678	+	1528.84i	−0.0422959	+	0.0732587i
$759$	41013.6	+	71037.7i	1.96140	+	3.39724i
$760$		0			0
$761$	13152.0	−	22779.9i	0.626489	−	1.08511i	−0.361762	−	0.932271i	$-0.617825\pi$
$761$	13152.0	−	22779.9i	0.626489	−	1.08511i	0.988251	−	0.152841i	$-0.0488421\pi$
$762$	−39381.3			−1.87223
$763$	12976.5	+	1747.44i	0.615702	+	0.0829118i
$764$	9399.02			0.445085
$765$		0			0
$766$	9898.05	+	17143.9i	0.466881	+	0.808662i
$767$	−1334.71	−	2311.78i	−0.0628338	−	0.108831i
$768$	1215.85	−	2105.92i	0.0571266	−	0.0989463i
$769$	−14236.3			−0.667588			−0.333794	−	0.942646i	$-0.608329\pi$
$769$	−14236.3			−0.667588			−0.333794	+	0.942646i	$0.608329\pi$
$770$		0			0
$771$	−62554.2			−2.92196
$772$	7119.33	−	12331.0i	0.331905	−	0.574876i
$773$	−487.222	−	843.894i	−0.0226703	−	0.0392662i	0.854468	−	0.519505i	$-0.173883\pi$
$773$	−487.222	−	843.894i	−0.0226703	−	0.0392662i	−0.877138	+	0.480238i	$0.840550\pi$
$774$	−589.246	−	1020.60i	−0.0273643	−	0.0473964i
$775$		0			0
$776$	−357.547			−0.0165402
$777$	−8002.45	+	10365.4i	−0.369481	+	0.478579i
$778$	−17137.2			−0.789714
$779$	3218.68	−	5574.92i	0.148037	−	0.256408i
$780$		0			0
$781$	2734.05	+	4735.51i	0.125265	+	0.216965i
$782$	3042.56	−	5269.87i	0.139133	−	0.240985i
$783$	−4731.98			−0.215973
$784$	5292.51	+	1451.73i	0.241095	+	0.0661318i
$785$		0			0
$786$	−18229.8	+	31574.9i	−0.827271	+	1.43287i
$787$	−9531.19	−	16508.5i	−0.431703	−	0.747732i	0.565317	−	0.824874i	$-0.308754\pi$
$787$	−9531.19	−	16508.5i	−0.431703	−	0.747732i	−0.997020	+	0.0771421i	$0.975421\pi$
$788$	3241.50	+	5614.44i	0.146540	+	0.253815i
$789$	26505.9	−	45909.5i	1.19599	−	2.07151i
$790$		0			0
$791$	15040.5	−	19481.6i	0.676078	−	0.875708i
$792$	−36350.3			−1.63087
$793$	−6792.29	+	11764.6i	−0.304163	+	0.526826i
$794$	4620.29	+	8002.58i	0.206509	+	0.357684i
$795$		0			0
$796$	5796.36	−	10039.6i	0.258098	−	0.447040i
$797$	−7047.44			−0.313216			−0.156608	−	0.987661i	$-0.550056\pi$
$797$	−7047.44			−0.313216			−0.156608	+	0.987661i	$0.550056\pi$
$798$	9475.51	+	23068.6i	0.420338	+	1.02333i
$799$	−7048.46			−0.312086
$800$		0			0
$801$	−25301.4	−	43823.3i	−1.11608	−	1.93311i
$802$	2665.88	+	4617.43i	0.117376	+	0.203301i
$803$	−28686.0	+	49685.6i	−1.26066	+	2.18352i
$804$	16337.8			0.716652
$805$		0			0
$806$	34376.3			1.50230
$807$	30305.2	−	52490.1i	1.32193	−	2.28964i
$808$	3221.51	+	5579.82i	0.140263	+	0.242942i
$809$	20063.2	+	34750.4i	0.871920	+	1.51021i	0.860008	+	0.510281i	$0.170459\pi$
$809$	20063.2	+	34750.4i	0.871920	+	1.51021i	0.0119128	+	0.999929i	$0.496208\pi$
$810$		0			0
$811$	24210.0			1.04825			0.524124	−	0.851642i	$-0.324393\pi$
$811$	24210.0			1.04825			0.524124	+	0.851642i	$0.324393\pi$
$812$	1009.56	+	135.950i	0.0436314	+	0.00587549i
$813$	−66864.5			−2.88443
$814$	−5349.32	+	9265.30i	−0.230336	+	0.398954i
$815$		0			0
$816$	1924.07	+	3332.59i	0.0825441	+	0.142971i
$817$	−330.283	+	572.067i	−0.0141434	+	0.0244970i
$818$	31877.2			1.36254
$819$	−31340.5	−	76300.0i	−1.33715	−	3.25536i
$820$		0			0
$821$	−3461.35	+	5995.24i	−0.147140	+	0.254854i	−0.930169	−	0.367131i	$-0.880340\pi$
$821$	−3461.35	+	5995.24i	−0.147140	+	0.254854i	0.783029	+	0.621985i	$0.213674\pi$
$822$	−10322.2	−	17878.5i	−0.437990	−	0.758620i
$823$	437.505	+	757.782i	0.0185304	+	0.0320955i	0.875142	−	0.483866i	$-0.160768\pi$
$823$	437.505	+	757.782i	0.0185304	+	0.0320955i	−0.856612	+	0.515962i	$0.827435\pi$
$824$	4216.77	−	7303.66i	0.178275	−	0.308781i
$825$		0			0
$826$	−857.800	+	1111.09i	−0.0361340	+	0.0468035i
$827$	1029.69			0.0432960			0.0216480	−	0.999766i	$-0.493109\pi$
$827$	1029.69			0.0432960			0.0216480	+	0.999766i	$0.493109\pi$
$828$	15195.6	−	26319.5i	0.637782	−	1.10467i
$829$	9573.48	+	16581.8i	0.401087	+	0.694702i	0.993857	−	0.110669i	$-0.0352993\pi$
$829$	9573.48	+	16581.8i	0.401087	+	0.694702i	−0.592771	+	0.805371i	$0.701966\pi$
$830$		0			0
$831$	33372.4	−	57802.6i	1.39311	−	2.41294i
$832$	4508.20			0.187853
$833$	−6177.22	+	6104.58i	−0.256936	+	0.253915i
$834$	−4561.95			−0.189409
$835$		0			0
$836$	10187.5	+	17645.3i	0.421462	+	0.729994i
$837$	41984.7	+	72719.6i	1.73382	+	3.00306i
$838$	11451.6	−	19834.8i	0.472064	−	0.817640i
$839$	34619.2			1.42454			0.712270	−	0.701906i	$-0.247667\pi$
$839$	34619.2			1.42454			0.712270	+	0.701906i	$0.247667\pi$
$840$		0			0
$841$	−24199.9			−0.992247
$842$	6560.18	−	11362.6i	0.268502	−	0.465059i
$843$	−18863.7	−	32672.8i	−0.770699	−	1.33489i
$844$	−11451.8	−	19835.1i	−0.467047	−	0.808950i
$845$		0			0
$846$	−35202.4			−1.43060
$847$	−26974.6	−	65671.0i	−1.09428	−	2.66409i
$848$	1471.98			0.0596083
$849$	23419.0	−	40562.8i	0.946686	−	1.63971i
$850$		0			0
$851$	−4472.37	−	7746.38i	−0.180154	−	0.312036i
$852$	1445.53	−	2503.74i	0.0581257	−	0.100677i
$853$	18872.6			0.757543			0.378772	−	0.925490i	$-0.376347\pi$
$853$	18872.6			0.757543			0.378772	+	0.925490i	$0.376347\pi$
$854$	7079.42	+	953.330i	0.283668	+	0.0381994i
$855$		0			0
$856$	6717.63	−	11635.3i	0.268229	−	0.464586i
$857$	7036.26	+	12187.2i	0.280460	+	0.485771i	0.971498	−	0.237047i	$-0.0761797\pi$
$857$	7036.26	+	12187.2i	0.280460	+	0.485771i	−0.691038	+	0.722818i	$0.742846\pi$
$858$	−48084.2	−	83284.4i	−1.91325	−	3.31385i
$859$	14090.4	−	24405.3i	0.559673	−	0.969383i	−0.437850	−	0.899048i	$-0.644260\pi$
$859$	14090.4	−	24405.3i	0.559673	−	0.969383i	0.997523	−	0.0703346i	$-0.0224067\pi$
$860$		0			0
$861$	15834.1	+	2132.26i	0.626743	+	0.0843985i
$862$	26403.7			1.04329
$863$	−7956.76	+	13781.5i	−0.313849	+	0.543602i	−0.979192	−	0.202936i	$-0.934952\pi$
$863$	−7956.76	+	13781.5i	−0.313849	+	0.543602i	0.665344	+	0.746537i	$0.268285\pi$
$864$	5505.98	+	9536.64i	0.216802	+	0.375513i
$865$		0			0
$866$	−13414.4	+	23234.3i	−0.526372	+	0.911704i
$867$	40578.2			1.58951
$868$	−6868.15	−	16720.9i	−0.268572	−	0.653851i
$869$	793.463			0.0309740
$870$		0			0
$871$	15144.5	+	26231.1i	0.589153	+	1.02044i
$872$	−2827.96	−	4898.17i	−0.109824	−	0.190221i
$873$	1412.94	−	2447.28i	0.0547774	−	0.0948772i
$874$	−17034.8			−0.659280
$875$		0			0
$876$	30333.4			1.16994
$877$	−25090.0	+	43457.1i	−0.966053	+	1.67325i	−0.259296	+	0.965798i	$0.583490\pi$
$877$	−25090.0	+	43457.1i	−0.966053	+	1.67325i	−0.706758	+	0.707456i	$0.749843\pi$
$878$	−707.622	−	1225.64i	−0.0271994	−	0.0471108i
$879$	−61.4535	−	106.441i	−0.00235810	−	0.00408436i
$880$		0			0
$881$	−17892.6			−0.684240			−0.342120	−	0.939656i	$-0.611145\pi$
$881$	−17892.6			−0.684240			−0.342120	+	0.939656i	$0.611145\pi$
$882$	−30851.2	+	30488.4i	−1.17779	+	1.16394i
$883$	11685.8			0.445368			0.222684	−	0.974891i	$-0.428518\pi$
$883$	11685.8			0.445368			0.222684	+	0.974891i	$0.428518\pi$
$884$	−3567.09	+	6178.38i	−0.135717	+	0.235069i
$885$		0			0
$886$	−13377.3	−	23170.1i	−0.507244	−	0.878573i
$887$	18506.7	−	32054.5i	0.700557	−	1.21340i	−0.267715	−	0.963498i	$-0.586268\pi$
$887$	18506.7	−	32054.5i	0.700557	−	1.21340i	0.968271	−	0.249901i	$-0.0803982\pi$
$888$	5656.53			0.213762
$889$	−23461.3	+	30388.9i	−0.885116	+	1.14647i
$890$		0			0
$891$	56111.9	−	97188.6i	2.10978	−	3.65425i
$892$	2536.73	+	4393.74i	0.0952196	+	0.164925i
$893$	9865.80	+	17088.1i	0.369705	+	0.640348i
$894$	26470.6	−	45848.4i	0.990278	−	1.71521i
$895$		0			0
$896$	−900.706	−	2192.82i	−0.0335831	−	0.0817599i
$897$	80403.0			2.99284
$898$	−4057.83	+	7028.37i	−0.150792	+	0.261180i
$899$	−1677.66	−	2905.80i	−0.0622394	−	0.107802i
$900$		0			0
$901$	−1164.69	+	2017.31i	−0.0430650	+	0.0745907i
$902$	13053.2			0.481846
$903$	−1624.81	−	218.800i	−0.0598785	−	0.00806336i
$904$	−10631.4			−0.391144
$905$		0			0
$906$	−9981.61	−	17288.7i	−0.366023	−	0.633971i
$907$	−17412.5	−	30159.4i	−0.637457	−	1.10411i	−0.985989	−	0.166811i	$-0.946653\pi$
$907$	−17412.5	−	30159.4i	−0.637457	−	1.10411i	0.348531	−	0.937297i	$-0.386680\pi$
$908$	−1544.13	+	2674.51i	−0.0564358	+	0.0977497i
$909$	−50922.4			−1.85807
$910$		0			0
$911$	44600.4			1.62204			0.811020	−	0.585019i	$-0.198913\pi$
$911$	44600.4			1.62204			0.811020	+	0.585019i	$0.198913\pi$
$912$	5386.29	−	9329.32i	0.195568	−	0.338733i
$913$	21667.1	+	37528.5i	0.785406	+	1.36036i
$914$	−4522.71	−	7833.57i	−0.163674	−	0.283492i
$915$		0			0
$916$	1422.57			0.0513135
$917$	13504.7	+	32877.8i	0.486329	+	1.18399i
$918$	−17426.3			−0.626529
$919$	17632.0	−	30539.5i	0.632890	−	1.09620i	−0.354068	−	0.935220i	$-0.615202\pi$
$919$	17632.0	−	30539.5i	0.632890	−	1.09620i	0.986958	−	0.160978i	$-0.0514649\pi$
$920$		0			0
$921$	26066.1	+	45147.9i	0.932582	+	1.61528i
$922$	−4355.56	+	7544.05i	−0.155578	+	0.269468i
$923$	5359.82			0.191138
$924$	−30903.1	+	40028.1i	−1.10026	+	1.42514i
$925$		0			0
$926$	−17178.7	+	29754.3i	−0.609639	+	1.05593i
$927$	33327.2	+	57724.5i	1.18081	+	2.04522i
$928$	−220.013	−	381.074i	−0.00778263	−	0.0134799i
$929$	20379.1	−	35297.7i	0.719718	−	1.24659i	−0.241394	−	0.970427i	$-0.577604\pi$
$929$	20379.1	−	35297.7i	0.719718	−	1.24659i	0.961111	−	0.276161i	$-0.0890622\pi$
$930$		0			0
$931$	23446.1	+	6431.22i	0.825365	+	0.226396i
$932$	11609.2			0.408016
$933$	−16523.3	+	28619.1i	−0.579794	+	1.00423i
$934$	−8040.78	−	13927.0i	−0.281694	−	0.487909i
$935$		0			0
$936$	−17815.3	+	30857.0i	−0.622126	+	1.07755i
$937$	−21119.6			−0.736337			−0.368169	−	0.929759i	$-0.620015\pi$
$937$	−21119.6			−0.736337			−0.368169	+	0.929759i	$0.620015\pi$
$938$	9733.18	−	12607.2i	0.338806	−	0.438847i
$939$	8742.55			0.303836
$940$		0			0
$941$	−10860.2	−	18810.4i	−0.376229	−	0.651648i	0.614281	−	0.789087i	$-0.289446\pi$
$941$	−10860.2	−	18810.4i	−0.376229	−	0.651648i	−0.990510	+	0.137439i	$0.956113\pi$
$942$	10712.0	+	18553.7i	0.370505	+	0.641733i
$943$	−5456.67	+	9451.22i	−0.188434	+	0.326378i
$944$	606.336			0.0209052
$945$		0			0
$946$	−1339.45			−0.0460351
$947$	−1029.35	+	1782.88i	−0.0353214	+	0.0611784i	−0.883146	−	0.469099i	$-0.844579\pi$
$947$	−1029.35	+	1782.88i	−0.0353214	+	0.0611784i	0.847824	+	0.530277i	$0.177912\pi$
$948$	−209.758	−	363.311i	−0.00718630	−	0.0124470i
$949$	28118.0	+	48701.7i	0.961799	+	1.66589i
$950$		0			0
$951$	9011.59			0.307277
$952$	3717.88	+	500.657i	0.126573	+	0.0170445i
$953$	8010.67			0.272288			0.136144	−	0.990689i	$-0.456529\pi$
$953$	8010.67			0.272288			0.136144	+	0.990689i	$0.456529\pi$
$954$	−5816.88	+	10075.1i	−0.197409	+	0.341923i
$955$		0			0
$956$	11271.0	+	19521.9i	0.381307	+	0.660443i
$957$	−4693.30	+	8129.03i	−0.158530	+	0.274581i
$958$	17040.3			0.574685
$959$	−19945.5	−	2685.91i	−0.671611	−	0.0904405i
$960$		0			0
$961$	−14874.8	+	25763.9i	−0.499305	+	0.864821i
$962$	5243.40	+	9081.83i	0.175732	+	0.304376i
$963$	53092.8	+	91959.4i	1.77663	+	3.07721i
$964$	−8151.24	+	14118.4i	−0.272338	+	0.471703i
$965$		0			0
$966$	−16063.9	−	39108.5i	−0.535040	−	1.30258i
$967$	2477.77			0.0823988			0.0411994	−	0.999151i	$-0.486882\pi$
$967$	2477.77			0.0823988			0.0411994	+	0.999151i	$0.486882\pi$
$968$	−15333.5	+	26558.4i	−0.509130	+	0.881839i
$969$	8523.73	+	14763.5i	0.282582	+	0.489446i
$970$		0			0
$971$	−26974.7	+	46721.6i	−0.891514	+	1.54415i	−0.0534530	+	0.998570i	$0.517023\pi$
$971$	−26974.7	+	46721.6i	−0.891514	+	1.54415i	−0.838061	+	0.545577i	$0.816311\pi$
$972$	−22169.0			−0.731554
$973$	−2717.77	+	3520.27i	−0.0895455	+	0.115986i
$974$	−39540.4			−1.30077
$975$		0			0
$976$	−1542.81	−	2672.23i	−0.0505986	−	0.0876393i
$977$	−22200.5	−	38452.3i	−0.726976	−	1.25916i	−0.958155	−	0.286248i	$-0.907592\pi$
$977$	−22200.5	−	38452.3i	−0.726976	−	1.25916i	0.231179	−	0.972911i	$-0.425742\pi$
$978$	2476.55	−	4289.50i	0.0809726	−	0.140249i
$979$	−57514.1			−1.87759
$980$		0			0
$981$	44701.5			1.45485
$982$	−10047.0	+	17401.9i	−0.326489	+	0.565495i
$983$	−24326.6	−	42134.9i	−0.789317	−	1.36714i	−0.926386	−	0.376575i	$-0.877102\pi$
$983$	−24326.6	−	42134.9i	−0.789317	−	1.36714i	0.137070	−	0.990561i	$-0.456232\pi$
$984$	−3450.72	−	5976.82i	−0.111794	−	0.193632i
$985$		0			0
$986$	696.336			0.0224907
$987$	−29927.3	+	38764.1i	−0.965142	+	1.25013i
$988$	19971.6			0.643097
$989$	559.932	−	969.831i	0.0180028	−	0.0311818i
$990$		0			0
$991$	−17238.2	−	29857.5i	−0.552563	−	0.957068i	−0.998089	−	0.0617985i	$-0.980316\pi$
$991$	−17238.2	−	29857.5i	−0.552563	−	0.957068i	0.445525	−	0.895269i	$-0.353017\pi$
$992$	−3904.15	+	6762.19i	−0.124957	+	0.216431i
$993$	−59461.1			−1.90024
$994$	−1070.85	−	2607.05i	−0.0341705	−	0.0831897i
$995$		0			0
$996$	11455.7	−	19841.9i	0.364446	−	0.631238i
$997$	7127.61	+	12345.4i	0.226413	+	0.392159i	0.956742	−	0.290936i	$-0.0939668\pi$
$997$	7127.61	+	12345.4i	0.226413	+	0.392159i	−0.730329	+	0.683095i	$0.760633\pi$
$998$	12673.6	+	21951.3i	0.401980	+	0.696250i
$999$	−12807.8	+	22183.8i	−0.405626	+	0.702565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.e.l.51.4	✓	8
5.2	odd	4		350.4.j.j.149.4		16
5.3	odd	4		350.4.j.j.149.5		16
5.4	even	2		350.4.e.m.51.1	yes	8
7.2	even	3		2450.4.a.cq.1.1		4
7.4	even	3	inner	350.4.e.l.151.4	yes	8
7.5	odd	6		2450.4.a.cu.1.4		4
35.4	even	6		350.4.e.m.151.1	yes	8
35.9	even	6		2450.4.a.co.1.4		4
35.18	odd	12		350.4.j.j.249.4		16
35.19	odd	6		2450.4.a.ck.1.1		4
35.32	odd	12		350.4.j.j.249.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.l.51.4	✓	8	1.1	even	1	trivial
350.4.e.l.151.4	yes	8	7.4	even	3	inner
350.4.e.m.51.1	yes	8	5.4	even	2
350.4.e.m.151.1	yes	8	35.4	even	6
350.4.j.j.149.4		16	5.2	odd	4
350.4.j.j.149.5		16	5.3	odd	4
350.4.j.j.249.4		16	35.18	odd	12
350.4.j.j.249.5		16	35.32	odd	12
2450.4.a.ck.1.1		4	35.19	odd	6
2450.4.a.co.1.4		4	35.9	even	6
2450.4.a.cq.1.1		4	7.2	even	3
2450.4.a.cu.1.4		4	7.5	odd	6

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(4.74942 + 8.22624i) q^{3} +(-2.00000 - 3.46410i) q^{4} -18.9977 q^{6} +(-11.3178 + 14.6597i) q^{7} +8.00000 q^{8} +(-31.6140 + 54.7570i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(4.74942 + 8.22624i) q^{3} +(-2.00000 - 3.46410i) q^{4} -18.9977 q^{6} +(-11.3178 + 14.6597i) q^{7} +8.00000 q^{8} +(-31.6140 + 54.7570i) q^{9} +(35.9318 + 62.2357i) q^{11} +(18.9977 - 32.9049i) q^{12} +70.4406 q^{13} +(-14.0735 - 34.2627i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-12.6599 - 21.9276i) q^{17} +(-63.2280 - 109.514i) q^{18} +(-35.4404 + 61.3846i) q^{19} +(-174.347 - 23.4780i) q^{21} -143.727 q^{22} +(60.0826 - 104.066i) q^{23} +(37.9954 + 65.8099i) q^{24} +(-70.4406 + 122.007i) q^{26} -344.124 q^{27} +(73.4183 + 9.88667i) q^{28} +13.7508 q^{29} +(-122.005 - 211.318i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-341.310 + 591.167i) q^{33} +50.6396 q^{34} +252.912 q^{36} +(37.2186 - 64.4645i) q^{37} +(-70.8808 - 122.769i) q^{38} +(334.552 + 579.461i) q^{39} -90.8195 q^{41} +(215.012 - 278.500i) q^{42} +9.31938 q^{43} +(143.727 - 248.943i) q^{44} +(120.165 + 208.132i) q^{46} +(139.189 - 241.082i) q^{47} -151.981 q^{48} +(-86.8139 - 331.832i) q^{49} +(120.254 - 208.287i) q^{51} +(-140.881 - 244.013i) q^{52} +(-45.9993 - 79.6731i) q^{53} +(344.124 - 596.040i) q^{54} +(-90.5426 + 117.278i) q^{56} -673.286 q^{57} +(-13.7508 + 23.8171i) q^{58} +(-18.9480 - 32.8189i) q^{59} +(-96.4258 + 167.014i) q^{61} +488.019 q^{62} +(-444.921 - 1083.18i) q^{63} +64.0000 q^{64} +(-682.621 - 1182.33i) q^{66} +(214.997 + 372.385i) q^{67} +(-50.6396 + 87.7104i) q^{68} +1141.43 q^{69} +76.0899 q^{71} +(-252.912 + 438.056i) q^{72} +(399.172 + 691.387i) q^{73} +(74.4372 + 128.929i) q^{74} +283.523 q^{76} +(-1319.03 - 177.623i) q^{77} -1338.21 q^{78} +(5.52061 - 9.56198i) q^{79} +(-780.810 - 1352.40i) q^{81} +(90.8195 - 157.304i) q^{82} +603.005 q^{83} +(267.365 + 650.913i) q^{84} +(-9.31938 + 16.1416i) q^{86} +(65.3084 + 113.117i) q^{87} +(287.454 + 497.886i) q^{88} +(-400.161 + 693.100i) q^{89} +(-797.234 + 1032.64i) q^{91} -480.660 q^{92} +(1158.90 - 2007.28i) q^{93} +(278.377 + 482.163i) q^{94} +(151.981 - 263.240i) q^{96} -44.6934 q^{97} +(661.563 + 181.466i) q^{98} -4543.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + q^{3} - 16 q^{4} - 4 q^{6} + 7 q^{7} + 64 q^{8} - 73 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + q^3 - 16 * q^4 - 4 * q^6 + 7 * q^7 + 64 * q^8 - 73 * q^9	\( 8 q - 8 q^{2} + q^{3} - 16 q^{4} - 4 q^{6} + 7 q^{7} + 64 q^{8} - 73 q^{9} + 10 q^{11} + 4 q^{12} + 188 q^{13} - 70 q^{14} - 64 q^{16} - 99 q^{17} - 146 q^{18} - 246 q^{19} - 535 q^{21} - 40 q^{22} + 2 q^{23} + 8 q^{24} - 188 q^{26} - 392 q^{27} + 112 q^{28} - 196 q^{29} - 304 q^{31} - 128 q^{32} - 526 q^{33} + 396 q^{34} + 584 q^{36} + 82 q^{37} - 492 q^{38} + 214 q^{39} + 704 q^{41} + 634 q^{42} + 262 q^{43} + 40 q^{44} + 4 q^{46} + 491 q^{47} - 32 q^{48} + 1283 q^{49} + 1437 q^{51} - 376 q^{52} + 140 q^{53} + 392 q^{54} + 56 q^{56} + 438 q^{57} + 196 q^{58} - 673 q^{59} - 1425 q^{61} + 1216 q^{62} - 1226 q^{63} + 512 q^{64} - 1052 q^{66} + 666 q^{67} - 396 q^{68} + 1876 q^{69} - 12 q^{71} - 584 q^{72} + 78 q^{73} + 164 q^{74} + 1968 q^{76} - 2575 q^{77} - 856 q^{78} - 1744 q^{79} - 1708 q^{81} - 704 q^{82} + 1852 q^{83} + 872 q^{84} - 262 q^{86} - 1931 q^{87} + 80 q^{88} + 871 q^{89} - 797 q^{91} - 16 q^{92} + 3106 q^{93} + 982 q^{94} + 32 q^{96} - 2924 q^{97} - 1244 q^{98} - 10562 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + q^3 - 16 * q^4 - 4 * q^6 + 7 * q^7 + 64 * q^8 - 73 * q^9 + 10 * q^11 + 4 * q^12 + 188 * q^13 - 70 * q^14 - 64 * q^16 - 99 * q^17 - 146 * q^18 - 246 * q^19 - 535 * q^21 - 40 * q^22 + 2 * q^23 + 8 * q^24 - 188 * q^26 - 392 * q^27 + 112 * q^28 - 196 * q^29 - 304 * q^31 - 128 * q^32 - 526 * q^33 + 396 * q^34 + 584 * q^36 + 82 * q^37 - 492 * q^38 + 214 * q^39 + 704 * q^41 + 634 * q^42 + 262 * q^43 + 40 * q^44 + 4 * q^46 + 491 * q^47 - 32 * q^48 + 1283 * q^49 + 1437 * q^51 - 376 * q^52 + 140 * q^53 + 392 * q^54 + 56 * q^56 + 438 * q^57 + 196 * q^58 - 673 * q^59 - 1425 * q^61 + 1216 * q^62 - 1226 * q^63 + 512 * q^64 - 1052 * q^66 + 666 * q^67 - 396 * q^68 + 1876 * q^69 - 12 * q^71 - 584 * q^72 + 78 * q^73 + 164 * q^74 + 1968 * q^76 - 2575 * q^77 - 856 * q^78 - 1744 * q^79 - 1708 * q^81 - 704 * q^82 + 1852 * q^83 + 872 * q^84 - 262 * q^86 - 1931 * q^87 + 80 * q^88 + 871 * q^89 - 797 * q^91 - 16 * q^92 + 3106 * q^93 + 982 * q^94 + 32 * q^96 - 2924 * q^97 - 1244 * q^98 - 10562 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more