LMFDB - Embedded newform 350.4.j.j.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(149,350)]

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([3, 2]))

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

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 66 x^{14} + 3127 x^{12} - 69136 x^{10} + 1110267 x^{8} - 6713681 x^{6} + 29846021 x^{4} + \cdots + 24010000 $ x^16 - 66x^14 + 3127x^12 - 69136x^10 + 1110267x^8 - 6713681x^6 + 29846021x^4 - 29346100*x^2 + 24010000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.4
Root			$-2.10334 + 1.21436i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.4.j.j.249.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{2} +(8.22624 - 4.74942i) q^{3} +(2.00000 + 3.46410i) q^{4} -18.9977 q^{6} +(-14.6597 - 11.3178i) q^{7} -8.00000i q^{8} +(31.6140 - 54.7570i) q^{9} +O(q^{10})$	\(q+(-1.73205 - 1.00000i) q^{2} +(8.22624 - 4.74942i) q^{3} +(2.00000 + 3.46410i) q^{4} -18.9977 q^{6} +(-14.6597 - 11.3178i) q^{7} -8.00000i q^{8} +(31.6140 - 54.7570i) q^{9} +(35.9318 + 62.2357i) q^{11} +(32.9049 + 18.9977i) q^{12} -70.4406i q^{13} +(14.0735 + 34.2627i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(21.9276 - 12.6599i) q^{17} +(-109.514 + 63.2280i) q^{18} +(35.4404 - 61.3846i) q^{19} +(-174.347 - 23.4780i) q^{21} -143.727i q^{22} +(-104.066 - 60.0826i) q^{23} +(-37.9954 - 65.8099i) q^{24} +(-70.4406 + 122.007i) q^{26} -344.124i q^{27} +(9.88667 - 73.4183i) q^{28} -13.7508 q^{29} +(-122.005 - 211.318i) q^{31} +(27.7128 - 16.0000i) q^{32} +(591.167 + 341.310i) q^{33} -50.6396 q^{34} +252.912 q^{36} +(64.4645 + 37.2186i) q^{37} +(-122.769 + 70.8808i) q^{38} +(-334.552 - 579.461i) q^{39} -90.8195 q^{41} +(278.500 + 215.012i) q^{42} -9.31938i q^{43} +(-143.727 + 248.943i) q^{44} +(120.165 + 208.132i) q^{46} +(241.082 + 139.189i) q^{47} +151.981i q^{48} +(86.8139 + 331.832i) q^{49} +(120.254 - 208.287i) q^{51} +(244.013 - 140.881i) q^{52} +(-79.6731 + 45.9993i) q^{53} +(-344.124 + 596.040i) q^{54} +(-90.5426 + 117.278i) q^{56} -673.286i q^{57} +(23.8171 + 13.7508i) q^{58} +(18.9480 + 32.8189i) q^{59} +(-96.4258 + 167.014i) q^{61} +488.019i q^{62} +(-1083.18 + 444.921i) q^{63} -64.0000 q^{64} +(-682.621 - 1182.33i) q^{66} +(-372.385 + 214.997i) q^{67} +(87.7104 + 50.6396i) q^{68} -1141.43 q^{69} +76.0899 q^{71} +(-438.056 - 252.912i) q^{72} +(691.387 - 399.172i) q^{73} +(-74.4372 - 128.929i) q^{74} +283.523 q^{76} +(177.623 - 1319.03i) q^{77} +1338.21i q^{78} +(-5.52061 + 9.56198i) q^{79} +(-780.810 - 1352.40i) q^{81} +(157.304 + 90.8195i) q^{82} -603.005i q^{83} +(-267.365 - 650.913i) q^{84} +(-9.31938 + 16.1416i) q^{86} +(-113.117 + 65.3084i) q^{87} +(497.886 - 287.454i) q^{88} +(400.161 - 693.100i) q^{89} +(-797.234 + 1032.64i) q^{91} -480.660i q^{92} +(-2007.28 - 1158.90i) q^{93} +(-278.377 - 482.163i) q^{94} +(151.981 - 263.240i) q^{96} -44.6934i q^{97} +(181.466 - 661.563i) q^{98} +4543.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 146 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 146 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 146 q^{9} + 20 q^{11} + 140 q^{14} - 128 q^{16} + 492 q^{19} - 1070 q^{21} - 16 q^{24} - 376 q^{26} + 392 q^{29} - 608 q^{31} - 792 q^{34} + 1168 q^{36} - 428 q^{39} + 1408 q^{41} - 80 q^{44} + 8 q^{46} - 2566 q^{49} + 2874 q^{51} - 784 q^{54} + 112 q^{56} + 1346 q^{59} - 2850 q^{61} - 1024 q^{64} - 2104 q^{66} - 3752 q^{69} - 24 q^{71} - 328 q^{74} + 3936 q^{76} + 3488 q^{79} - 3416 q^{81} - 1744 q^{84} - 524 q^{86} - 1742 q^{89} - 1594 q^{91} - 1964 q^{94} + 64 q^{96} + 21124 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 146 * q^9 + 20 * q^11 + 140 * q^14 - 128 * q^16 + 492 * q^19 - 1070 * q^21 - 16 * q^24 - 376 * q^26 + 392 * q^29 - 608 * q^31 - 792 * q^34 + 1168 * q^36 - 428 * q^39 + 1408 * q^41 - 80 * q^44 + 8 * q^46 - 2566 * q^49 + 2874 * q^51 - 784 * q^54 + 112 * q^56 + 1346 * q^59 - 2850 * q^61 - 1024 * q^64 - 2104 * q^66 - 3752 * q^69 - 24 * q^71 - 328 * q^74 + 3936 * q^76 + 3488 * q^79 - 3416 * q^81 - 1744 * q^84 - 524 * q^86 - 1742 * q^89 - 1594 * q^91 - 1964 * q^94 + 64 * q^96 + 21124 * 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 $

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	8.22624	−	4.74942i	1.58314	−	0.914026i	0.588743	−	0.808321i	$-0.299623\pi$
$3$	8.22624	−	4.74942i	1.58314	−	0.914026i	0.994397	−	0.105706i	$-0.0337102\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−18.9977			−1.29263
$7$	−14.6597	−	11.3178i	−0.791550	−	0.611105i
$7$	−14.6597	−	11.3178i	−0.791550	−	0.611105i
$8$		−	8.00000i		−	0.353553i
$9$	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	$0.388728\pi$
$12$	32.9049	+	18.9977i	0.791570	+	0.457013i
$13$		−	70.4406i		−	1.50282i	−0.659833	−	0.751412i	$-0.729373\pi$
$13$		−	70.4406i		−	1.50282i	0.659833	−	0.751412i	$-0.270627\pi$
$14$	14.0735	+	34.2627i	0.268665	+	0.654079i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	21.9276	−	12.6599i	0.312837	−	0.180616i	−0.335358	−	0.942091i	$-0.608857\pi$
$17$	21.9276	−	12.6599i	0.312837	−	0.180616i	0.648195	+	0.761474i	$0.275524\pi$
$18$	−109.514	+	63.2280i	−1.43404	+	0.827943i
$19$	35.4404	−	61.3846i	0.427926	−	0.741189i	−0.568763	−	0.822502i	$-0.692578\pi$
$19$	35.4404	−	61.3846i	0.427926	−	0.741189i	0.996689	+	0.0813124i	$0.0259111\pi$
$20$		0			0
$21$	−174.347	−	23.4780i	−1.81170	−	0.243967i
$22$		−	143.727i		−	1.39285i
$23$	−104.066	−	60.0826i	−0.943446	−	0.544699i	−0.0524075	−	0.998626i	$-0.516689\pi$
$23$	−104.066	−	60.0826i	−0.943446	−	0.544699i	−0.891039	+	0.453927i	$0.850023\pi$
$24$	−37.9954	−	65.8099i	−0.323157	−	0.559725i
$25$		0			0
$26$	−70.4406	+	122.007i	−0.531329	+	0.920288i
$27$		−	344.124i		−	2.45284i
$28$	9.88667	−	73.4183i	0.0667287	−	0.495527i
$29$	−13.7508			−0.0880504			−0.0440252	−	0.999030i	$-0.514018\pi$
$29$	−13.7508			−0.0880504			−0.0440252	+	0.999030i	$0.514018\pi$
$30$		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	$-0.416556\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	591.167	+	341.310i	3.11845	+	1.80044i
$34$	−50.6396			−0.255430
$35$		0			0
$36$	252.912			1.17089
$37$	64.4645	+	37.2186i	0.286430	+	0.165370i	0.636331	−	0.771417i	$-0.280451\pi$
$37$	64.4645	+	37.2186i	0.286430	+	0.165370i	−0.349901	+	0.936787i	$0.613785\pi$
$38$	−122.769	+	70.8808i	−0.524100	+	0.302589i
$39$	−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	$0.555337\pi$
$42$	278.500	+	215.012i	1.02318	+	0.789931i
$43$		−	9.31938i		−	0.0330510i	−0.999863	−	0.0165255i	$-0.994740\pi$
$43$		−	9.31938i		−	0.0330510i	0.999863	−	0.0165255i	$-0.00526047\pi$
$44$	−143.727	+	248.943i	−0.492448	+	0.852944i
$45$		0			0
$46$	120.165	+	208.132i	0.385160	+	0.667117i
$47$	241.082	+	139.189i	0.748200	+	0.431973i	0.825043	−	0.565070i	$-0.191151\pi$
$47$	241.082	+	139.189i	0.748200	+	0.431973i	−0.0768434	+	0.997043i	$0.524484\pi$
$48$			151.981i			0.457013i
$49$	86.8139	+	331.832i	0.253102	+	0.967440i
$50$		0			0
$51$	120.254	−	208.287i	0.330176	−	0.571882i
$52$	244.013	−	140.881i	0.650742	−	0.375706i
$53$	−79.6731	+	45.9993i	−0.206489	+	0.119217i	−0.599679	−	0.800241i	$-0.704705\pi$
$53$	−79.6731	+	45.9993i	−0.206489	+	0.119217i	0.393189	+	0.919457i	$0.371372\pi$
$54$	−344.124	+	596.040i	−0.867209	+	1.50205i
$55$		0			0
$56$	−90.5426	+	117.278i	−0.216058	+	0.279855i
$57$		−	673.286i		−	1.56454i
$58$	23.8171	+	13.7508i	0.0539197	+	0.0311305i
$59$	18.9480	+	32.8189i	0.0418105	+	0.0724179i	0.886173	−	0.463354i	$-0.153354\pi$
$59$	18.9480	+	32.8189i	0.0418105	+	0.0724179i	−0.844363	+	0.535772i	$0.820021\pi$
$60$		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	$0.231539\pi$
$62$			488.019i			0.999652i
$63$	−1083.18	+	444.921i	−2.16616	+	0.889757i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−682.621	−	1182.33i	−1.27310	−	2.20508i
$67$	−372.385	+	214.997i	−0.679017	+	0.392031i	−0.799485	−	0.600687i	$-0.794894\pi$
$67$	−372.385	+	214.997i	−0.679017	+	0.392031i	0.120468	+	0.992717i	$0.461561\pi$
$68$	87.7104	+	50.6396i	0.156418	+	0.0903082i
$69$	−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	$0.479744\pi$
$72$	−438.056	−	252.912i	−0.717020	−	0.413972i
$73$	691.387	−	399.172i	1.10850	−	0.639995i	0.170062	−	0.985433i	$-0.445603\pi$
$73$	691.387	−	399.172i	1.10850	−	0.639995i	0.938441	+	0.345439i	$0.112270\pi$
$74$	−74.4372	−	128.929i	−0.116934	−	0.202536i
$75$		0			0
$76$	283.523			0.427926
$77$	177.623	−	1319.03i	0.262883	−	1.95217i
$78$			1338.21i			1.94259i
$79$	−5.52061	+	9.56198i	−0.00786225	+	0.0136178i	−0.869930	−	0.493176i	$-0.835836\pi$
$79$	−5.52061	+	9.56198i	−0.00786225	+	0.0136178i	0.862068	+	0.506793i	$0.169169\pi$
$80$		0			0
$81$	−780.810	−	1352.40i	−1.07107	−	1.85515i
$82$	157.304	+	90.8195i	0.211845	+	0.122309i
$83$		−	603.005i		−	0.797451i	−0.917070	−	0.398726i	$-0.869453\pi$
$83$		−	603.005i		−	0.797451i	0.917070	−	0.398726i	$-0.130547\pi$
$84$	−267.365	−	650.913i	−0.347284	−	0.845481i
$85$		0			0
$86$	−9.31938	+	16.1416i	−0.0116853	+	0.0202395i
$87$	−113.117	+	65.3084i	−0.139396	+	0.0804804i
$88$	497.886	−	287.454i	0.603123	−	0.348213i
$89$	400.161	−	693.100i	0.476596	−	0.825488i	−0.523044	−	0.852305i	$-0.675204\pi$
$89$	400.161	−	693.100i	0.476596	−	0.825488i	0.999640	+	0.0268171i	$0.00853718\pi$
$90$		0			0
$91$	−797.234	+	1032.64i	−0.918383	+	1.18956i
$92$		−	480.660i		−	0.544699i
$93$	−2007.28	−	1158.90i	−2.23812	−	1.29218i
$94$	−278.377	−	482.163i	−0.305451	−	0.529057i
$95$		0			0
$96$	151.981	−	263.240i	0.161579	−	0.279862i
$97$		−	44.6934i		−	0.0467827i	−0.999726	−	0.0233914i	$-0.992554\pi$
$97$		−	44.6934i		−	0.0467827i	0.999726	−	0.0233914i	$-0.00744638\pi$
$98$	181.466	−	661.563i	0.187049	−	0.681918i
$99$	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	$0.703481\pi$
$102$	−416.574	+	240.509i	−0.404382	+	0.233470i
$103$	−912.958	−	527.097i	−0.873363	−	0.504237i	−0.00489889	−	0.999988i	$-0.501559\pi$
$103$	−912.958	−	527.097i	−0.873363	−	0.504237i	−0.868464	+	0.495751i	$0.834893\pi$
$104$	−563.525			−0.531329
$105$		0			0
$106$	183.997			0.168598
$107$	1454.41	+	839.704i	1.31405	+	0.758666i	0.982764	−	0.184865i	$-0.0591847\pi$
$107$	1454.41	+	839.704i	1.31405	+	0.758666i	0.331284	+	0.943531i	$0.392518\pi$
$108$	1192.08	−	688.247i	1.06211	−	0.613210i
$109$	353.495	+	612.271i	0.310630	+	0.538027i	0.978499	−	0.206252i	$-0.0661267\pi$
$109$	353.495	+	612.271i	0.310630	+	0.538027i	−0.667869	+	0.744279i	$0.732793\pi$
$110$		0			0
$111$	707.067			0.604611
$112$	274.102	−	112.588i	0.231252	−	0.0949874i
$113$			1328.92i			1.10632i	0.833075	+	0.553161i	$0.186578\pi$
$113$			1328.92i			1.10632i	−0.833075	+	0.553161i	$0.813422\pi$
$114$	−673.286	+	1166.17i	−0.553149	+	0.958082i
$115$		0			0
$116$	−27.5016	−	47.6342i	−0.0220126	−	0.0381270i
$117$	−3857.12	−	2226.91i	−3.04778	−	1.75964i
$118$		−	75.7920i		−	0.0591290i
$119$	−464.735	−	62.5821i	−0.358001	−	0.0482092i
$120$		0			0
$121$	−1916.69	+	3319.80i	−1.44004	+	2.49422i
$122$	334.029	−	192.852i	0.247881	−	0.143114i
$123$	−747.102	+	431.340i	−0.547674	+	0.316200i
$124$	488.019	−	845.273i	0.353430	−	0.612159i
$125$		0			0
$126$	2321.05	+	312.557i	1.64107	+	0.220990i
$127$			2072.96i			1.44839i	0.689597	+	0.724193i	$0.257788\pi$
$127$			2072.96i			1.44839i	−0.689597	+	0.724193i	$0.742212\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	−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	$-0.0543953\pi$
$132$			2730.48i			1.80044i
$133$	−1214.29	+	498.772i	−0.791669	+	0.325181i
$134$	859.987			0.554415
$135$		0			0
$136$	−101.279	−	175.421i	−0.0638575	−	0.110604i
$137$	−941.091	+	543.339i	−0.586882	+	0.338836i	−0.763864	−	0.645378i	$-0.776700\pi$
$137$	−941.091	+	543.339i	−0.586882	+	0.338836i	0.176982	+	0.984214i	$0.443367\pi$
$138$	1977.01	+	1141.43i	1.21953	+	0.704094i
$139$	−240.132			−0.146531			−0.0732653	−	0.997312i	$-0.523342\pi$
$139$	−240.132			−0.146531			−0.0732653	+	0.997312i	$0.523342\pi$
$140$		0			0
$141$	2644.26			1.57934
$142$	−131.792	−	76.0899i	−0.0778853	−	0.0449671i
$143$	4383.92	−	2531.06i	2.56365	−	1.48012i
$144$	505.824	+	876.112i	0.292722	+	0.507010i
$145$		0			0
$146$	−1596.69			−0.905089
$147$	2290.16	+	2317.41i	1.28496	+	1.30025i
$148$			297.749i			0.165370i
$149$	1393.36	−	2413.37i	0.766097	−	1.32692i	−0.173568	−	0.984822i	$-0.555530\pi$
$149$	1393.36	−	2413.37i	0.766097	−	1.32692i	0.939665	−	0.342097i	$-0.111137\pi$
$150$		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	$0.741950\pi$
$152$	−491.077	−	283.523i	−0.262050	−	0.151295i
$153$		−	1600.92i		−	0.845926i
$154$	−1626.68	+	2107.00i	−0.851179	+	1.10251i
$155$		0			0
$156$	1338.21	−	2317.85i	0.686810	−	1.18959i
$157$	976.630	−	563.858i	0.496456	−	0.286629i	−0.230793	−	0.973003i	$-0.574132\pi$
$157$	976.630	−	563.858i	0.496456	−	0.286629i	0.727249	+	0.686374i	$0.240799\pi$
$158$	19.1240	−	11.0412i	0.00962925	−	0.00555945i
$159$	−436.940	+	756.802i	−0.217934	+	0.377473i
$160$		0			0
$161$	845.574	+	2058.59i	0.413917	+	1.00770i
$162$			3123.24i			1.51472i
$163$	225.791	+	130.360i	0.108499	+	0.0626418i	0.553267	−	0.833004i	$-0.313381\pi$
$163$	225.791	+	130.360i	0.108499	+	0.0626418i	−0.444769	+	0.895645i	$0.646714\pi$
$164$	−181.639	−	314.608i	−0.0864855	−	0.149797i
$165$		0			0
$166$	−603.005	+	1044.44i	−0.281942	+	0.488337i
$167$			546.074i			0.253033i	0.991965	+	0.126516i	$0.0403796\pi$
$167$			546.074i			0.253033i	−0.991965	+	0.126516i	$0.959620\pi$
$168$	−187.824	+	1394.78i	−0.0862555	+	0.640533i
$169$	−2764.88			−1.25848
$170$		0			0
$171$	−2240.83	−	3881.22i	−1.00211	−	1.73570i
$172$	32.2833	−	18.6388i	0.0143115	−	0.00826275i
$173$	1618.80	+	934.614i	0.711417	+	0.410737i	0.811585	−	0.584234i	$-0.198605\pi$
$173$	1618.80	+	934.614i	0.711417	+	0.410737i	−0.100169	+	0.994970i	$0.531938\pi$
$174$	261.234			0.113816
$175$		0			0
$176$	−1149.82			−0.492448
$177$	311.741	+	179.984i	0.132384	+	0.0764318i
$178$	−1386.20	+	800.323i	−0.583708	+	0.337004i
$179$	1568.55	+	2716.81i	0.654967	+	1.13444i	0.981902	+	0.189390i	$0.0606509\pi$
$179$	1568.55	+	2716.81i	0.654967	+	1.13444i	−0.326935	+	0.945047i	$0.606016\pi$
$180$		0			0
$181$	3955.06			1.62418			0.812091	−	0.583530i	$-0.198329\pi$
$181$	3955.06			1.62418			0.812091	+	0.583530i	$0.198329\pi$
$182$	2413.49	−	991.349i	0.982965	−	0.403756i
$183$			1831.87i			0.739975i
$184$	−480.660	+	832.528i	−0.192580	+	0.333559i
$185$		0			0
$186$	2317.81	+	4014.56i	0.913708	+	1.58259i
$187$	1575.80	+	909.787i	0.616223	+	0.355776i
$188$			1113.51i			0.431973i
$189$	−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	$0.313493\pi$
$192$	−526.479	+	303.963i	−0.197893	+	0.114253i
$193$	3082.76	−	1779.83i	1.14975	−	0.663809i	0.200925	−	0.979607i	$-0.435605\pi$
$193$	3082.76	−	1779.83i	1.14975	−	0.663809i	0.948827	+	0.315797i	$0.102272\pi$
$194$	−44.6934	+	77.4112i	−0.0165402	+	0.0286485i
$195$		0			0
$196$	−975.871	+	964.396i	−0.355638	+	0.351456i
$197$		−	1620.75i		−	0.586160i	−0.956088	−	0.293080i	$-0.905320\pi$
$197$		−	1620.75i		−	0.586160i	0.956088	−	0.293080i	$-0.0946803\pi$
$198$	−7870.08	−	4543.79i	−2.82476	−	1.63087i
$199$	−1449.09	−	2509.90i	−0.516197	−	0.894079i	−0.999823	−	0.0188047i	$-0.994014\pi$
$199$	−1449.09	−	2509.90i	−0.516197	−	0.894079i	0.483626	−	0.875275i	$-0.339319\pi$
$200$		0			0
$201$	−2042.22	+	3537.23i	−0.716652	+	1.24128i
$202$		−	1610.76i		−	0.561051i
$203$	201.583	+	155.629i	0.0696963	+	0.0538080i
$204$	962.035			0.330176
$205$		0			0
$206$	1054.19	+	1825.92i	0.356549	+	0.617561i
$207$	−6579.88	+	3798.90i	−2.20934	+	1.27556i
$208$	976.054	+	563.525i	0.325371	+	0.187853i
$209$	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	$0.116209\pi$
$212$	−318.692	−	183.997i	−0.103245	−	0.0596083i
$213$	625.934	−	361.383i	0.201353	−	0.116251i
$214$	−1679.41	−	2908.82i	−0.536458	−	0.929173i
$215$		0			0
$216$	−2752.99			−0.867209
$217$	−603.110	+	4478.69i	−0.188672	+	1.40108i
$218$		−	1413.98i		−	0.439297i
$219$	3791.68	−	6567.38i	1.16994	−	2.02640i
$220$		0			0
$221$	−891.772	−	1544.59i	−0.271435	−	0.470139i
$222$	−1224.68	−	707.067i	−0.370247	−	0.213762i
$223$			1268.36i			0.380878i	0.981699	+	0.190439i	$0.0609912\pi$
$223$			1268.36i			0.380878i	−0.981699	+	0.190439i	$0.939009\pi$
$224$	−587.347	−	79.0933i	−0.175195	−	0.0235922i
$225$		0			0
$226$	1328.92	−	2301.76i	0.391144	−	0.677481i
$227$	668.628	−	386.032i	0.195499	−	0.112872i	−0.399055	−	0.916927i	$-0.630662\pi$
$227$	668.628	−	386.032i	0.195499	−	0.112872i	0.594555	+	0.804055i	$0.297328\pi$
$228$	2332.33	−	1346.57i	0.677466	−	0.391135i
$229$	177.822	−	307.996i	0.0513135	−	0.0888776i	−0.839228	−	0.543780i	$-0.816993\pi$
$229$	177.822	−	307.996i	0.0513135	−	0.0888776i	0.890541	+	0.454902i	$0.150326\pi$
$230$		0			0
$231$	−4803.44	−	11694.2i	−1.36815	−	3.33084i
$232$			110.007i			0.0311305i
$233$	2513.46	+	1451.14i	0.706704	+	0.408016i	0.809839	−	0.586652i	$-0.199554\pi$
$233$	2513.46	+	1451.14i	0.706704	+	0.408016i	−0.103135	+	0.994667i	$0.532888\pi$
$234$	4453.82	+	7714.24i	1.24425	+	2.15511i
$235$		0			0
$236$	−75.7920	+	131.276i	−0.0209052	+	0.0362089i
$237$			104.879i			0.0287452i
$238$	742.362	+	573.130i	0.202186	+	0.156095i
$239$	5635.49			1.52523			0.762614	−	0.646853i	$-0.223915\pi$
$239$	5635.49			1.52523			0.762614	+	0.646853i	$0.223915\pi$
$240$		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	$-0.350014\pi$
$242$	6639.61	−	3833.38i	1.76368	−	1.01826i
$243$	−4799.73	−	2771.12i	−1.26709	−	0.731554i
$244$	−771.406			−0.202394
$245$		0			0
$246$	1725.36			0.447174
$247$	−4323.97	−	2496.45i	−1.11388	−	0.643097i
$248$	−1690.55	+	976.037i	−0.432862	+	0.249913i
$249$	−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	$0.455518\pi$
$252$	−3707.61	−	2862.41i	−0.926816	−	0.715535i
$253$		−	8635.50i		−	2.14589i
$254$	2072.96	−	3590.46i	0.512082	−	0.886952i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−5703.17	−	3292.73i	−1.38426	−	0.799201i	−0.391597	−	0.920137i	$-0.628077\pi$
$257$	−5703.17	−	3292.73i	−1.38426	−	0.799201i	−0.992660	+	0.120935i	$0.961411\pi$
$258$			177.047i			0.0427227i
$259$	−523.797	−	1275.21i	−0.125665	−	0.305937i
$260$		0			0
$261$	−434.718	+	752.954i	−0.103097	+	0.178570i
$262$	−3324.08	+	1919.16i	−0.783826	+	0.452542i
$263$	−4833.17	+	2790.43i	−1.13318	+	0.654242i	−0.944733	−	0.327842i	$-0.893679\pi$
$263$	−4833.17	+	2790.43i	−1.13318	+	0.654242i	−0.188447	+	0.982083i	$0.560345\pi$
$264$	2730.48	−	4729.34i	0.636552	−	1.10254i
$265$		0			0
$266$	2601.98	+	350.388i	0.599765	+	0.0807656i
$267$		−	7602.14i		−	1.74248i
$268$	−1489.54	−	859.987i	−0.339508	−	0.196015i
$269$	3190.41	+	5525.95i	0.723133	+	1.25250i	0.959738	+	0.280897i	$0.0906320\pi$
$269$	3190.41	+	5525.95i	0.723133	+	1.25250i	−0.236605	+	0.971606i	$0.576035\pi$
$270$		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	$0.877300\pi$
$272$			405.117i			0.0903082i
$273$	−1653.80	+	12281.1i	−0.366640	+	2.72267i
$274$	2173.36			0.479187
$275$		0			0
$276$	−2282.86	−	3954.03i	−0.497869	−	0.862335i
$277$	6085.23	−	3513.31i	1.31995	−	0.762073i	0.336230	−	0.941780i	$-0.390848\pi$
$277$	6085.23	−	3513.31i	1.31995	−	0.762073i	0.983720	+	0.179707i	$0.0575148\pi$
$278$	415.921	+	240.132i	0.0897312	+	0.0518064i
$279$	−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	$0.638530\pi$
$282$	−4579.99	−	2644.26i	−0.967144	−	0.558381i
$283$	−4270.29	+	2465.45i	−0.896970	+	0.517866i	−0.876216	−	0.481919i	$-0.839940\pi$
$283$	−4270.29	+	2465.45i	−0.896970	+	0.517866i	−0.0207540	+	0.999785i	$0.506607\pi$
$284$	152.180	+	263.583i	0.0317965	+	0.0550732i
$285$		0			0
$286$	−10124.2			−2.09321
$287$	1331.39	+	1027.88i	0.273830	+	0.211407i
$288$		−	2023.30i		−	0.413972i
$289$	−2135.95	+	3699.58i	−0.434755	+	0.753019i
$290$		0			0
$291$	−212.268	−	367.658i	−0.0427607	−	0.0740636i
$292$	2765.55	+	1596.69i	0.554252	+	0.319997i
$293$			12.9391i			0.00257991i	0.999999	+	0.00128995i	$0.000410605\pi$
$293$			12.9391i			0.00257991i	−0.999999	+	0.00128995i	$0.999589\pi$
$294$	−1649.26	−	6304.03i	−0.327167	−	1.25054i
$295$		0			0
$296$	297.749	−	515.716i	0.0584672	−	0.101268i
$297$	21416.8	−	12365.0i	4.18427	−	2.41579i
$298$	−4826.74	+	2786.72i	−0.938273	+	0.541712i
$299$	−4232.25	+	7330.48i	−0.818587	+	1.41783i
$300$		0			0
$301$	−105.475	+	136.619i	−0.0201976	+	0.0261615i
$302$		−	2101.65i		−	0.400451i
$303$	6625.23	+	3825.08i	1.25614	+	0.725231i
$304$	567.047	+	982.154i	0.106981	+	0.185297i
$305$		0			0
$306$	−1600.92	+	2772.88i	−0.299080	+	0.518022i
$307$			5488.27i			1.02030i	0.860085	+	0.510150i	$0.170410\pi$
$307$			5488.27i			1.02030i	−0.860085	+	0.510150i	$0.829590\pi$
$308$	4924.49	−	2022.75i	0.911035	−	0.374211i
$309$	−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	$0.730603\pi$
$312$	−4635.69	+	2676.42i	−0.841168	+	0.485648i
$313$	−797.073	−	460.190i	−0.143940	−	0.0831038i	0.426300	−	0.904582i	$-0.359817\pi$
$313$	−797.073	−	460.190i	−0.143940	−	0.0831038i	−0.570240	+	0.821478i	$0.693150\pi$
$314$	−2255.43			−0.405355
$315$		0			0
$316$	−44.1649			−0.00786225
$317$	821.602	+	474.352i	0.145570	+	0.0840450i	0.571016	−	0.820939i	$-0.306549\pi$
$317$	821.602	+	474.352i	0.145570	+	0.0840450i	−0.425446	+	0.904984i	$0.639883\pi$
$318$	1513.60	−	873.879i	0.266914	−	0.154103i
$319$	−494.092	−	855.792i	−0.0867204	−	0.150204i
$320$		0			0
$321$	15952.4			2.77376
$322$	594.016	−	4411.16i	0.102805	−	0.763430i
$323$		−	1794.69i		−	0.309162i
$324$	3123.24	−	5409.61i	0.535535	−	0.927574i
$325$		0			0
$326$	−260.721	−	451.582i	−0.0442945	−	0.0767202i
$327$	5815.86	+	3357.79i	0.983541	+	0.567848i
$328$			726.556i			0.122309i
$329$	−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	$0.992694\pi$
$332$	2088.87	−	1206.01i	0.345306	−	0.199363i
$333$	4075.96	−	2353.26i	0.670754	−	0.387260i
$334$	546.074	−	945.827i	0.0894605	−	0.154950i
$335$		0			0
$336$	1720.10	−	2228.00i	0.279283	−	0.361749i
$337$			8999.55i			1.45471i	0.686262	+	0.727354i	$0.259250\pi$
$337$			8999.55i			1.45471i	−0.686262	+	0.727354i	$0.740750\pi$
$338$	4788.91	+	2764.88i	0.770659	+	0.444940i
$339$	6311.60	+	10932.0i	1.01121	+	1.75146i
$340$		0			0
$341$	8767.70	−	15186.1i	1.39237	−	2.41165i
$342$			8963.30i			1.41719i
$343$	2482.95	−	5847.10i	0.390864	−	0.920448i
$344$	−74.5551			−0.0116853
$345$		0			0
$346$	−1869.23	−	3237.60i	−0.290435	−	0.503047i
$347$	−4537.64	+	2619.81i	−0.701998	+	0.405299i	−0.808091	−	0.589058i	$-0.799499\pi$
$347$	−4537.64	+	2619.81i	−0.701998	+	0.405299i	0.106093	+	0.994356i	$0.466166\pi$
$348$	−452.470	−	261.234i	−0.0696981	−	0.0402402i
$349$	−7955.14			−1.22014			−0.610070	−	0.792347i	$-0.708859\pi$
$349$	−7955.14			−1.22014			−0.610070	+	0.792347i	$0.708859\pi$
$350$		0			0
$351$	−24240.3			−3.68618
$352$	1991.54	+	1149.82i	0.301561	+	0.174107i
$353$	387.396	−	223.663i	0.0584107	−	0.0337235i	−0.470510	−	0.882395i	$-0.655930\pi$
$353$	387.396	−	223.663i	0.0584107	−	0.0337235i	0.528921	+	0.848671i	$0.322597\pi$
$354$	−359.968	−	623.483i	−0.0540454	−	0.0936094i
$355$		0			0
$356$	3201.29			0.476596
$357$	−4120.25	+	1692.40i	−0.610831	+	0.250901i
$358$		−	6274.21i		−	0.926264i
$359$	317.566	−	550.040i	0.0466866	−	0.0808635i	−0.841738	−	0.539887i	$-0.818467\pi$
$359$	317.566	−	550.040i	0.0466866	−	0.0808635i	0.888424	+	0.459023i	$0.151800\pi$
$360$		0			0
$361$	917.453	+	1589.08i	0.133759	+	0.231678i
$362$	−6850.36	−	3955.06i	−0.994605	−	0.574235i
$363$			36412.6i			5.26493i
$364$	−5171.63	−	696.423i	−0.744690	−	0.100282i
$365$		0			0
$366$	1831.87	−	3172.89i	0.261621	−	0.453140i
$367$	3587.61	−	2071.31i	0.510278	−	0.294609i	−0.222670	−	0.974894i	$-0.571477\pi$
$367$	3587.61	−	2071.31i	0.510278	−	0.294609i	0.732948	+	0.680285i	$0.238144\pi$
$368$	1665.06	−	961.321i	0.235862	−	0.136175i
$369$	−2871.17	+	4973.00i	−0.405059	+	0.701583i
$370$		0			0
$371$	1688.59	+	227.390i	0.236300	+	0.0318207i
$372$		−	9271.22i		−	1.29218i
$373$	−2465.54	−	1423.48i	−0.342255	−	0.197601i	0.319014	−	0.947750i	$-0.396648\pi$
$373$	−2465.54	−	1423.48i	−0.342255	−	0.197601i	−0.661269	+	0.750149i	$0.729982\pi$
$374$	−1819.57	−	3151.59i	−0.251572	−	0.435735i
$375$		0			0
$376$	1113.51	−	1928.65i	0.152726	−	0.264529i
$377$			968.616i			0.132324i
$378$	11790.6	−	4843.04i	1.60435	−	0.658992i
$379$	−882.678			−0.119631			−0.0598155	−	0.998209i	$-0.519051\pi$
$379$	−882.678			−0.119631			−0.0598155	+	0.998209i	$0.519051\pi$
$380$		0			0
$381$	9845.34	+	17052.6i	1.32386	+	2.29300i
$382$	4069.90	−	2349.76i	0.545115	−	0.314722i
$383$	−8571.96	−	4949.03i	−1.14362	−	0.660270i	−0.196296	−	0.980545i	$-0.562891\pi$
$383$	−8571.96	−	4949.03i	−1.14362	−	0.660270i	−0.947325	+	0.320275i	$0.896225\pi$
$384$	1215.85			0.161579
$385$		0			0
$386$	−7119.33			−0.938768
$387$	−510.302	−	294.623i	−0.0670287	−	0.0386990i
$388$	154.822	−	89.3868i	0.0202575	−	0.0116957i
$389$	−4284.29	−	7420.62i	−0.558412	−	0.967198i	−0.997629	−	0.0688173i	$-0.978077\pi$
$389$	−4284.29	−	7420.62i	−0.558412	−	0.967198i	0.439217	−	0.898381i	$-0.355256\pi$
$390$		0			0
$391$	−3042.56			−0.393526
$392$	2654.65	−	694.511i	0.342042	−	0.0894850i
$393$		−	18229.8i		−	2.33987i
$394$	−1620.75	+	2807.22i	−0.207239	+	0.358948i
$395$		0			0
$396$	9087.58	+	15740.2i	1.15320	+	1.99740i
$397$	4001.29	+	2310.15i	0.505841	+	0.292048i	0.731122	−	0.682246i	$-0.238997\pi$
$397$	4001.29	+	2310.15i	0.505841	+	0.292048i	−0.225281	+	0.974294i	$0.572330\pi$
$398$			5796.36i			0.730013i
$399$	−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	$0.113583\pi$
$402$	7074.46	−	4084.44i	0.877716	−	0.506750i
$403$	−14885.4	+	8594.09i	−1.83994	+	1.06229i
$404$	−1610.76	+	2789.91i	−0.198362	+	0.343572i
$405$		0			0
$406$	−193.523	−	471.141i	−0.0236561	−	0.0575919i
$407$			5349.32i			0.651489i
$408$	−1666.29	−	962.035i	−0.202191	−	0.116735i
$409$	7969.29	+	13803.2i	0.963463	+	1.66877i	0.713690	+	0.700462i	$0.247023\pi$
$409$	7969.29	+	13803.2i	0.963463	+	1.66877i	0.249773	+	0.968304i	$0.419644\pi$
$410$		0			0
$411$	−5161.09	+	8939.27i	−0.619411	+	1.07285i
$412$		−	4216.77i		−	0.504237i
$413$	93.6663	−	695.565i	0.0111598	−	0.0828730i
$414$	15195.6			1.80392
$415$		0			0
$416$	−1127.05	−	1952.11i	−0.132832	−	0.230072i
$417$	−1975.38	+	1140.49i	−0.231978	+	0.133933i
$418$	−8822.64	−	5093.75i	−1.03237	−	0.596037i
$419$	11451.6			1.33520			0.667600	−	0.744520i	$-0.267322\pi$
$419$	11451.6			1.33520			0.667600	+	0.744520i	$0.267322\pi$
$420$		0			0
$421$	−6560.18			−0.759438			−0.379719	−	0.925102i	$-0.623979\pi$
$421$	−6560.18			−0.759438			−0.379719	+	0.925102i	$0.623979\pi$
$422$	−9917.57	−	5725.91i	−1.14403	−	0.660505i
$423$	15243.1	−	8800.61i	1.75212	−	1.01158i
$424$	367.994	+	637.384i	0.0421495	+	0.0730050i
$425$		0			0
$426$	−1445.53			−0.164404
$427$	3303.81	−	1357.05i	0.374433	−	0.153799i
$428$			6717.63i			0.758666i
$429$	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	$-0.430762\pi$
$432$	4768.32	+	2752.99i	0.531055	+	0.306605i
$433$		−	13414.4i		−	1.48881i	−0.667731	−	0.744403i	$-0.732734\pi$
$433$		−	13414.4i		−	1.48881i	0.667731	−	0.744403i	$-0.267266\pi$
$434$	5523.31	−	7154.21i	0.610892	−	0.791274i
$435$		0			0
$436$	−1413.98	+	2449.08i	−0.155315	+	0.269013i
$437$	−7376.29	+	4258.70i	−0.807450	+	0.466182i
$438$	−13134.8	+	7583.35i	−1.43288	+	0.827275i
$439$	353.811	−	612.819i	0.0384658	−	0.0666247i	−0.846152	−	0.532942i	$-0.821086\pi$
$439$	353.811	−	612.819i	0.0384658	−	0.0666247i	0.884617	+	0.466318i	$0.154420\pi$
$440$		0			0
$441$	20914.7	+	5736.85i	2.25836	+	0.619464i
$442$			3567.09i			0.383867i
$443$	11585.1	+	6688.64i	1.24249	+	0.717351i	0.969600	−	0.244694i	$-0.0786875\pi$
$443$	11585.1	+	6688.64i	1.24249	+	0.717351i	0.272889	+	0.962046i	$0.412021\pi$
$444$	1414.13	+	2449.35i	0.151153	+	0.261804i
$445$		0			0
$446$	1268.36	−	2196.87i	0.134661	−	0.233239i
$447$		−	26470.6i		−	2.80093i
$448$	938.221	+	724.340i	0.0989437	+	0.0763881i
$449$	−4057.83			−0.426505			−0.213253	−	0.976997i	$-0.568406\pi$
$449$	−4057.83			−0.426505			−0.213253	+	0.976997i	$0.568406\pi$
$450$		0			0
$451$	−3263.31	−	5652.21i	−0.340716	−	0.590138i
$452$	−4603.52	+	2657.84i	−0.479051	+	0.276580i
$453$	8644.33	+	4990.81i	0.896570	+	0.517635i
$454$	−1544.13			−0.159625
$455$		0			0
$456$	−5386.29			−0.553149
$457$	−3916.79	−	2261.36i	−0.400918	−	0.231470i	0.285962	−	0.958241i	$-0.407687\pi$
$457$	−3916.79	−	2261.36i	−0.400918	−	0.231470i	−0.686880	+	0.726771i	$0.741020\pi$
$458$	−615.993	+	355.644i	−0.0628460	+	0.0362841i
$459$	−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	$0.429388\pi$
$462$	−3374.42	+	25058.5i	−0.339810	+	2.52343i
$463$		−	17178.7i		−	1.72432i	−0.506636	−	0.862160i	$-0.669111\pi$
$463$		−	17178.7i		−	1.72432i	0.506636	−	0.862160i	$-0.330889\pi$
$464$	110.007	−	190.537i	0.0110063	−	0.0190635i
$465$		0			0
$466$	−2902.29	−	5026.91i	−0.288511	−	0.499715i
$467$	−6963.52	−	4020.39i	−0.690007	−	0.398376i	0.113607	−	0.993526i	$-0.463759\pi$
$467$	−6963.52	−	4020.39i	−0.690007	−	0.398376i	−0.803615	+	0.595150i	$0.797093\pi$
$468$		−	17815.3i		−	1.75964i
$469$	7892.36	+	1062.80i	0.777047	+	0.104639i
$470$		0			0
$471$	5356.00	−	9276.86i	0.523973	−	0.907548i
$472$	262.551	−	151.584i	0.0256036	−	0.0147822i
$473$	579.998	−	334.862i	0.0563813	−	0.0325518i
$474$	104.879	−	181.656i	0.0101630	−	0.0176028i
$475$		0			0
$476$	−712.679	−	1735.05i	−0.0686251	−	0.167071i
$477$			5816.88i			0.558358i
$478$	−9760.96	−	5635.49i	−0.934008	−	0.539250i
$479$	4260.08	+	7378.68i	0.406364	+	0.703842i	0.994479	−	0.104934i	$-0.0334633\pi$
$479$	4260.08	+	7378.68i	0.406364	+	0.703842i	−0.588115	+	0.808777i	$0.700130\pi$
$480$		0			0
$481$	2621.70	−	4540.92i	0.248522	−	0.430453i
$482$			8151.24i			0.770288i
$483$	16733.0	+	12918.5i	1.57635	+	1.21700i
$484$	−15333.5			−1.44004
$485$		0			0
$486$	5542.25	+	9599.46i	0.517287	+	0.895967i
$487$	−17121.5	+	9885.09i	−1.59312	+	0.919787i	−0.600350	+	0.799738i	$0.704972\pi$
$487$	−17121.5	+	9885.09i	−1.59312	+	0.919787i	−0.992768	+	0.120049i	$0.961695\pi$
$488$	1336.12	+	771.406i	0.123941	+	0.0715572i
$489$	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	$0.347231\pi$
$492$	−2988.41	−	1725.36i	−0.273837	−	0.158100i
$493$	−301.522	+	174.084i	−0.0275454	+	0.0159033i
$494$	4992.89	+	8647.94i	0.454738	+	0.787630i
$495$		0			0
$496$	3904.15			0.353430
$497$	−1115.46	−	861.172i	−0.100674	−	0.0777241i
$498$			11455.7i			1.03081i
$499$	−6336.80	+	10975.7i	−0.568486	+	0.984646i	0.428230	+	0.903670i	$0.359137\pi$
$499$	−6336.80	+	10975.7i	−0.568486	+	0.984646i	−0.996716	+	0.0809764i	$0.974196\pi$
$500$		0			0
$501$	2593.53	+	4492.13i	0.231278	+	0.400586i
$502$	−1918.77	−	1107.80i	−0.170596	−	0.0984935i
$503$		−	5078.12i		−	0.450144i	−0.974342	−	0.225072i	$-0.927738\pi$
$503$		−	5078.12i		−	0.450144i	0.974342	−	0.225072i	$-0.0722617\pi$
$504$	3559.36	+	8665.45i	0.314577	+	0.765853i
$505$		0			0
$506$	−8635.50	+	14957.1i	−0.758685	+	1.31408i
$507$	−22744.6	+	13131.6i	−1.99235	+	1.15028i
$508$	−7180.93	+	4145.91i	−0.627170	+	0.362097i
$509$	5494.52	−	9516.78i	0.478468	−	0.828731i	−0.521227	−	0.853418i	$-0.674526\pi$
$509$	5494.52	−	9516.78i	0.478468	−	0.828731i	0.999695	+	0.0246870i	$0.00785891\pi$
$510$		0			0
$511$	−14653.3	−	1973.24i	−1.26854	−	0.170824i
$512$			512.000i			0.0441942i
$513$	−21123.9	−	12195.9i	−1.81802	−	1.04963i
$514$	6585.46	+	11406.3i	0.565121	+	0.978818i
$515$		0			0
$516$	177.047	−	306.654i	0.0151047	−	0.0261622i
$517$			20005.2i			1.70179i
$518$	−367.968	+	2732.53i	−0.0312115	+	0.231777i
$519$	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	$0.992947\pi$
$522$	1505.91	−	869.436i	0.126268	−	0.0729007i
$523$	−18493.1	−	10677.0i	−1.54617	−	0.892679i	−0.998429	−	0.0560289i	$-0.982156\pi$
$523$	−18493.1	−	10677.0i	−1.54617	−	0.892679i	−0.547737	−	0.836651i	$-0.684511\pi$
$524$	7676.63			0.639991
$525$		0			0
$526$	11161.7			0.925237
$527$	−5350.54	−	3089.14i	−0.442264	−	0.255341i
$528$	−9458.67	+	5460.97i	−0.779613	+	0.450110i
$529$	1136.33	+	1968.18i	0.0933942	+	0.161763i
$530$		0			0
$531$	2396.09			0.195822
$532$	−4156.37	−	3208.87i	−0.338725	−	0.261507i
$533$			6397.38i			0.519890i
$534$	−7602.14	+	13167.3i	−0.616061	+	1.06705i
$535$		0			0
$536$	1719.97	+	2979.08i	0.138604	+	0.240069i
$537$	25806.6	+	14899.4i	2.07381	+	1.19731i
$538$		−	12761.6i		−	1.02266i
$539$	−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	$0.248130\pi$
$542$	12192.3	−	7039.22i	0.966243	−	0.557861i
$543$	32535.2	−	18784.2i	2.57131	−	1.48455i
$544$	405.117	−	701.683i	0.0319288	−	0.0553022i
$545$		0			0
$546$	15145.6	−	19617.7i	1.18713	−	1.53766i
$547$		−	19262.1i		−	1.50564i	−0.658225	−	0.752821i	$-0.728692\pi$
$547$		−	19262.1i		−	1.50564i	0.658225	−	0.752821i	$-0.271308\pi$
$548$	−3764.36	−	2173.36i	−0.293441	−	0.169418i
$549$	6096.81	+	10560.0i	0.473962	+	0.820927i
$550$		0			0
$551$	−487.335	+	844.088i	−0.0376790	+	0.0652620i
$552$			9131.43i			0.704094i
$553$	189.151	−	77.6946i	0.0145453	−	0.00597452i
$554$	−14053.2			−1.07773
$555$		0			0
$556$	−480.264	−	831.842i	−0.0366326	−	0.0634496i
$557$	4022.00	−	2322.10i	0.305956	−	0.176644i	−0.339159	−	0.940729i	$-0.610143\pi$
$557$	4022.00	−	2322.10i	0.305956	−	0.176644i	0.645116	+	0.764085i	$0.276809\pi$
$558$	26722.5	+	15428.2i	2.02733	+	1.17048i
$559$	−656.463			−0.0496698
$560$		0			0
$561$	17283.8			1.30076
$562$	6879.33	+	3971.78i	0.516347	+	0.298113i
$563$	−20742.0	+	11975.4i	−1.55271	+	0.896455i	−0.554785	+	0.831994i	$0.687199\pi$
$563$	−20742.0	+	11975.4i	−1.55271	+	0.896455i	−0.997920	+	0.0644609i	$0.979467\pi$
$564$	5288.52	+	9159.99i	0.394835	+	0.683874i
$565$		0			0
$566$	9861.82			0.732373
$567$	−3859.81	+	28662.9i	−0.285885	+	2.12298i
$568$		−	608.720i		−	0.0449671i
$569$	−7083.96	+	12269.8i	−0.521924	+	0.903999i	0.477750	+	0.878496i	$0.341452\pi$
$569$	−7083.96	+	12269.8i	−0.521924	+	0.903999i	−0.999675	+	0.0255038i	$0.991881\pi$
$570$		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	$0.838130\pi$
$572$	17535.7	+	10124.2i	1.28183	+	0.740062i
$573$			22320.0i			1.62728i
$574$	−1278.15	−	3111.72i	−0.0929425	−	0.226273i
$575$		0			0
$576$	−2023.30	+	3504.45i	−0.146361	+	0.253505i
$577$	−7702.29	+	4446.92i	−0.555720	+	0.320845i	−0.751426	−	0.659818i	$-0.770634\pi$
$577$	−7702.29	+	4446.92i	−0.555720	+	0.320845i	0.195706	+	0.980663i	$0.437300\pi$
$578$	7399.16	−	4271.91i	0.532465	−	0.307419i
$579$	16906.3	−	29282.7i	1.21348	−	2.10181i
$580$		0			0
$581$	−6824.71	+	8839.88i	−0.487326	+	0.631222i
$582$			849.071i			0.0604727i
$583$	−5725.59	−	3305.67i	−0.406741	−	0.234832i
$584$	−3193.38	−	5531.10i	−0.226272	−	0.391915i
$585$		0			0
$586$	12.9391	−	22.4113i	0.000912135	−	0.00157986i
$587$			20146.2i			1.41656i	0.705931	+	0.708281i	$0.250529\pi$
$587$			20146.2i			1.41656i	−0.705931	+	0.708281i	$0.749471\pi$
$588$	−3447.43	+	12568.2i	−0.241785	+	0.881467i
$589$	−17295.6			−1.20994
$590$		0			0
$591$	−7697.62	−	13332.7i	−0.535766	−	0.927974i
$592$	−1031.43	+	595.497i	−0.0716074	+	0.0413425i
$593$	−7817.57	−	4513.48i	−0.541365	−	0.312557i	0.204267	−	0.978915i	$-0.434519\pi$
$593$	−7817.57	−	4513.48i	−0.541365	−	0.312557i	−0.745632	+	0.666358i	$0.767852\pi$
$594$	−49459.9			−3.41644
$595$		0			0
$596$	11146.9			0.766097
$597$	−23841.1	−	13764.7i	−1.63442	−	0.943635i
$598$	14661.0	−	8464.51i	1.00256	−	0.578828i
$599$	−4723.84	−	8181.92i	−0.322222	−	0.558104i	0.658725	−	0.752384i	$-0.271096\pi$
$599$	−4723.84	−	8181.92i	−0.322222	−	0.558104i	−0.980946	+	0.194280i	$0.937763\pi$
$600$		0			0
$601$	8237.41			0.559087			0.279543	−	0.960133i	$-0.409817\pi$
$601$	8237.41			0.559087			0.279543	+	0.960133i	$0.409817\pi$
$602$	319.308	−	131.157i	0.0216180	−	0.00887965i
$603$			27187.6i			1.83610i
$604$	−2101.65	+	3640.16i	−0.141581	+	0.245225i
$605$		0			0
$606$	−7650.15	−	13250.5i	−0.512816	−	0.888223i
$607$	2482.33	+	1433.17i	0.165988	+	0.0958332i	0.580693	−	0.814123i	$-0.302782\pi$
$607$	2482.33	+	1433.17i	0.165988	+	0.0958332i	−0.414705	+	0.909956i	$0.636115\pi$
$608$		−	2268.19i		−	0.151295i
$609$	2397.42	+	322.841i	0.159521	+	0.0214814i
$610$		0			0
$611$	9804.53	−	16981.9i	0.649180	−	1.12441i
$612$	5545.75	−	3201.84i	0.366297	−	0.211482i
$613$	12301.0	−	7101.96i	0.810491	−	0.467937i	−0.0366354	−	0.999329i	$-0.511664\pi$
$613$	12301.0	−	7101.96i	0.810491	−	0.467937i	0.847126	+	0.531392i	$0.178331\pi$
$614$	5488.27	−	9505.97i	0.360731	−	0.624804i
$615$		0			0
$616$	−10552.2	−	1420.98i	−0.690196	−	0.0929432i
$617$		−	22525.9i		−	1.46979i	−0.678182	−	0.734894i	$-0.737232\pi$
$617$		−	22525.9i		−	1.46979i	0.678182	−	0.734894i	$-0.262768\pi$
$618$	17344.1	+	10013.6i	1.12893	+	0.651791i
$619$	−6117.46	−	10595.8i	−0.397224	−	0.688012i	0.596158	−	0.802867i	$-0.296693\pi$
$619$	−6117.46	−	10595.8i	−0.397224	−	0.688012i	−0.993382	+	0.114855i	$0.963360\pi$
$620$		0			0
$621$	−20675.8	+	35811.6i	−1.33606	+	2.31412i
$622$		−	6958.02i		−	0.448539i
$623$	−13710.6	+	5631.69i	−0.881709	+	0.362165i
$624$	10705.7			0.686810
$625$		0			0
$626$	920.380	+	1594.15i	0.0587633	+	0.101781i
$627$	41902.4	−	24192.4i	2.66893	−	1.54091i
$628$	3906.52	+	2255.43i	0.248228	+	0.143314i
$629$	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	$0.560701\pi$
$632$	76.4959	+	44.1649i	0.00481462	+	0.00277972i
$633$	47102.7	−	27194.8i	2.95760	−	1.70757i
$634$	−948.704	−	1643.20i	−0.0594288	−	0.102934i
$635$		0			0
$636$	−3495.52			−0.217934
$637$	23374.4	−	6115.23i	1.45389	−	0.380367i
$638$			1976.37i			0.122641i
$639$	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	$0.918129\pi$
$642$	−27630.4	−	15952.4i	−1.69858	−	0.980674i
$643$		−	2803.77i		−	0.171959i	−0.996297	−	0.0859796i	$-0.972598\pi$
$643$		−	2803.77i		−	0.171959i	0.996297	−	0.0859796i	$-0.0274020\pi$
$644$	−5440.03	+	7046.34i	−0.332868	+	0.431156i
$645$		0			0
$646$	−1794.69	+	3108.49i	−0.109305	+	0.189322i
$647$	−22330.4	+	12892.5i	−1.35688	+	0.783394i	−0.989202	−	0.146560i	$-0.953180\pi$
$647$	−22330.4	+	12892.5i	−1.35688	+	0.783394i	−0.367676	+	0.929954i	$0.619847\pi$
$648$	−10819.2	+	6246.48i	−0.655894	+	0.378681i
$649$	−1361.67	+	2358.48i	−0.0823579	+	0.142648i
$650$		0			0
$651$	16309.9	+	39707.2i	0.981926	+	2.39055i
$652$			1042.88i			0.0626418i
$653$	2631.02	+	1519.02i	0.157672	+	0.0910319i	0.576760	−	0.816914i	$-0.304317\pi$
$653$	2631.02	+	1519.02i	0.157672	+	0.0910319i	−0.419088	+	0.907946i	$0.637650\pi$
$654$	−6715.58	−	11631.7i	−0.401529	−	0.695469i
$655$		0			0
$656$	726.556	−	1258.43i	0.0432427	−	0.0748986i
$657$		−	50477.7i		−	2.99745i
$658$	−1376.11	+	10219.0i	−0.0815295	+	0.605438i
$659$	32561.4			1.92475			0.962377	−	0.271719i	$-0.0875923\pi$
$659$	32561.4			1.92475			0.962377	+	0.271719i	$0.0875923\pi$
$660$		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	$0.909809\pi$
$662$	10842.3	−	6259.83i	0.636555	−	0.367515i
$663$	−14671.9	−	8470.80i	−0.859438	−	0.496197i
$664$	−4824.04			−0.281942
$665$		0			0
$666$	−9413.02			−0.547668
$667$	1430.99	+	826.184i	0.0830709	+	0.0479610i
$668$	−1891.65	+	1092.15i	−0.109566	+	0.0632581i
$669$	6023.99	+	10433.9i	0.348133	+	0.602984i
$670$		0			0
$671$	−13859.0			−0.797349
$672$	−5207.30	+	2138.92i	−0.298923	+	0.122783i
$673$			25265.4i			1.44712i	0.690262	+	0.723559i	$0.257495\pi$
$673$			25265.4i			1.44712i	−0.690262	+	0.723559i	$0.742505\pi$
$674$	8999.55	−	15587.7i	0.514317	−	0.890823i
$675$		0			0
$676$	−5529.76	−	9577.83i	−0.314620	−	0.544938i
$677$	6819.08	+	3937.00i	0.387117	+	0.223502i	0.680910	−	0.732367i	$-0.261584\pi$
$677$	6819.08	+	3937.00i	0.387117	+	0.223502i	−0.293793	+	0.955869i	$0.594918\pi$
$678$		−	25246.4i		−	1.43006i
$679$	−505.832	+	655.192i	−0.0285892	+	0.0370309i
$680$		0			0
$681$	3666.86	−	6351.19i	0.206335	−	0.357383i
$682$	−30372.2	+	17535.4i	−1.70530	+	0.984553i
$683$	−12464.7	+	7196.50i	−0.698314	+	0.403172i	−0.806719	−	0.590935i	$-0.798759\pi$
$683$	−12464.7	+	7196.50i	−0.698314	+	0.403172i	0.108405	+	0.994107i	$0.465426\pi$
$684$	8963.30	−	15524.9i	0.501053	−	0.867850i
$685$		0			0
$686$	−10147.7	+	7644.53i	−0.564782	+	0.425466i
$687$		−	3378.20i		−	0.187608i
$688$	129.133	+	74.5551i	0.00715575	+	0.00413137i
$689$	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	$0.315212\pi$
$692$			7476.92i			0.410737i
$693$	−66610.6	−	51425.8i	−3.65127	−	2.81891i
$694$	10479.2			0.573179
$695$		0			0
$696$	522.467	+	904.940i	0.0284541	+	0.0492840i
$697$	−1991.45	+	1149.77i	−0.108223	+	0.0624828i
$698$	13778.7	+	7955.14i	0.747180	+	0.431385i
$699$	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	$0.300946\pi$
$702$	41985.4	+	24240.3i	2.25732	+	1.30326i
$703$	4569.30	−	2638.08i	0.245141	−	0.141532i
$704$	−2299.64	−	3983.09i	−0.123112	−	0.213236i
$705$		0			0
$706$	−894.652			−0.0476922
$707$	1990.63	−	14782.4i	0.105891	−	0.786349i
$708$			1439.87i			0.0764318i
$709$	−4854.57	+	8408.37i	−0.257147	+	0.445392i	−0.965477	−	0.260490i	$-0.916116\pi$
$709$	−4854.57	+	8408.37i	−0.257147	+	0.445392i	0.708329	+	0.705882i	$0.249449\pi$
$710$		0			0
$711$	349.057	+	604.585i	0.0184116	+	0.0318899i
$712$	−5544.80	−	3201.29i	−0.291854	−	0.168502i
$713$			29321.4i			1.54011i
$714$	8828.88	+	1188.92i	0.462763	+	0.0623166i
$715$		0			0
$716$	−6274.21	+	10867.3i	−0.327484	+	0.567218i
$717$	46358.9	−	26765.3i	2.41465	−	1.39410i
$718$	−1100.08	+	635.131i	−0.0571791	+	0.0330124i
$719$	7873.74	−	13637.7i	0.408402	−	0.707373i	−0.586309	−	0.810087i	$-0.699420\pi$
$719$	7873.74	−	13637.7i	0.408402	−	0.707373i	0.994711	+	0.102715i	$0.0327529\pi$
$720$		0			0
$721$	7418.11	+	18059.8i	0.383169	+	0.932845i
$722$		−	3669.81i		−	0.189164i
$723$	−33527.0	−	19356.8i	−1.72460	−	0.995696i
$724$	7910.11	+	13700.7i	0.406046	+	0.703292i
$725$		0			0
$726$	36412.6	−	63068.6i	1.86143	−	3.22410i
$727$			26775.1i			1.36593i	0.730449	+	0.682967i	$0.239311\pi$
$727$			26775.1i			1.36593i	−0.730449	+	0.682967i	$0.760689\pi$
$728$	8261.11	+	6377.87i	0.420573	+	0.324697i
$729$	−10481.2			−0.532498
$730$		0			0
$731$	−117.983	−	204.352i	−0.00596955	−	0.0103396i
$732$	−6345.77	+	3663.73i	−0.320419	+	0.184994i
$733$	−757.815	−	437.525i	−0.0381863	−	0.0220469i	0.480785	−	0.876838i	$-0.340352\pi$
$733$	−757.815	−	437.525i	−0.0381863	−	0.0220469i	−0.518972	+	0.854791i	$0.673685\pi$
$734$	−8285.24			−0.416640
$735$		0			0
$736$	−3845.28			−0.192580
$737$	−26761.0	−	15450.4i	−1.33752	−	0.772218i
$738$	9946.01	−	5742.33i	0.496094	−	0.286420i
$739$	−3591.12	−	6220.00i	−0.178757	−	0.309616i	0.762698	−	0.646755i	$-0.223874\pi$
$739$	−3591.12	−	6220.00i	−0.178757	−	0.309616i	−0.941455	+	0.337138i	$0.890541\pi$
$740$		0			0
$741$	−47426.7			−2.35123
$742$	−2697.34	−	2082.45i	−0.133454	−	0.103031i
$743$		−	9759.98i		−	0.481910i	−0.970536	−	0.240955i	$-0.922539\pi$
$743$		−	9759.98i		−	0.481910i	0.970536	−	0.240955i	$-0.0774606\pi$
$744$	−9271.22	+	16058.2i	−0.456854	+	0.791295i
$745$		0			0
$746$	2846.96	+	4931.09i	0.139725	+	0.242011i
$747$	−33018.8	−	19063.4i	−1.61726	−	0.933726i
$748$			7278.29i			0.355776i
$749$	−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	$0.852856\pi$
$752$	−3857.31	+	2227.02i	−0.187050	+	0.107993i
$753$	9113.06	−	5261.43i	0.441034	−	0.254631i
$754$	968.616	−	1677.69i	0.0467837	−	0.0810318i
$755$		0			0
$756$	−25265.0	−	3402.24i	−1.21545	−	0.163675i
$757$		−	19677.7i		−	0.944780i	−0.881390	−	0.472390i	$-0.843391\pi$
$757$		−	19677.7i		−	0.944780i	0.881390	−	0.472390i	$-0.156609\pi$
$758$	1528.84	+	882.678i	0.0732587	+	0.0422959i
$759$	−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	$-0.0488421\pi$
$762$		−	39381.3i		−	1.87223i
$763$	1747.44	−	12976.5i	0.0829118	−	0.615702i
$764$	−9399.02			−0.445085
$765$		0			0
$766$	9898.05	+	17143.9i	0.466881	+	0.808662i
$767$	2311.78	−	1334.71i	0.108831	−	0.0628338i
$768$	−2105.92	−	1215.85i	−0.0989463	−	0.0571266i
$769$	14236.3			0.667588			0.333794	−	0.942646i	$-0.391671\pi$
$769$	14236.3			0.667588			0.333794	+	0.942646i	$0.391671\pi$
$770$		0			0
$771$	−62554.2			−2.92196
$772$	12331.0	+	7119.33i	0.574876	+	0.331905i
$773$	−843.894	+	487.222i	−0.0392662	+	0.0226703i	−0.519505	−	0.854468i	$-0.673883\pi$
$773$	−843.894	+	487.222i	−0.0392662	+	0.0226703i	0.480238	+	0.877138i	$0.340550\pi$
$774$	589.246	+	1020.60i	0.0273643	+	0.0473964i
$775$		0			0
$776$	−357.547			−0.0165402
$777$	−10365.4	−	8002.45i	−0.478579	−	0.369481i
$778$			17137.2i			0.789714i
$779$	−3218.68	+	5574.92i	−0.148037	+	0.256408i
$780$		0			0
$781$	2734.05	+	4735.51i	0.125265	+	0.216965i
$782$	5269.87	+	3042.56i	0.240985	+	0.139133i
$783$			4731.98i			0.215973i
$784$	−5292.51	−	1451.73i	−0.241095	−	0.0661318i
$785$		0			0
$786$	−18229.8	+	31574.9i	−0.827271	+	1.43287i
$787$	16508.5	−	9531.19i	0.747732	−	0.431703i	−0.0771421	−	0.997020i	$-0.524579\pi$
$787$	16508.5	−	9531.19i	0.747732	−	0.431703i	0.824874	+	0.565317i	$0.191246\pi$
$788$	5614.44	−	3241.50i	0.253815	−	0.146540i
$789$	−26505.9	+	45909.5i	−1.19599	+	2.07151i
$790$		0			0
$791$	15040.5	−	19481.6i	0.676078	−	0.875708i
$792$		−	36350.3i		−	1.63087i
$793$	11764.6	+	6792.29i	0.526826	+	0.304163i
$794$	−4620.29	−	8002.58i	−0.206509	−	0.357684i
$795$		0			0
$796$	5796.36	−	10039.6i	0.258098	−	0.447040i
$797$		−	7047.44i		−	0.313216i	−0.987661	−	0.156608i	$-0.949944\pi$
$797$		−	7047.44i		−	0.313216i	0.987661	−	0.156608i	$-0.0500559\pi$
$798$	23068.6	−	9475.51i	1.02333	−	0.420338i
$799$	7048.46			0.312086
$800$		0			0
$801$	−25301.4	−	43823.3i	−1.11608	−	1.93311i
$802$	−4617.43	+	2665.88i	−0.203301	+	0.117376i
$803$	49685.6	+	28686.0i	2.18352	+	1.26066i
$804$	−16337.8			−0.716652
$805$		0			0
$806$	34376.3			1.50230
$807$	52490.1	+	30305.2i	2.28964	+	1.32193i
$808$	5579.82	−	3221.51i	0.242942	−	0.140263i
$809$	−20063.2	−	34750.4i	−0.871920	−	1.51021i	−0.860008	−	0.510281i	$-0.829541\pi$
$809$	−20063.2	−	34750.4i	−0.871920	−	1.51021i	−0.0119128	−	0.999929i	$-0.503792\pi$
$810$		0			0
$811$	24210.0			1.04825			0.524124	−	0.851642i	$-0.324393\pi$
$811$	24210.0			1.04825			0.524124	+	0.851642i	$0.324393\pi$
$812$	−135.950	+	1009.56i	−0.00587549	+	0.0436314i
$813$			66864.5i			2.88443i
$814$	5349.32	−	9265.30i	0.230336	−	0.398954i
$815$		0			0
$816$	1924.07	+	3332.59i	0.0825441	+	0.142971i
$817$	−572.067	−	330.283i	−0.0244970	−	0.0141434i
$818$		−	31877.2i		−	1.36254i
$819$	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	$0.213674\pi$
$822$	17878.5	−	10322.2i	0.758620	−	0.437990i
$823$	757.782	−	437.505i	0.0320955	−	0.0185304i	−0.483866	−	0.875142i	$-0.660768\pi$
$823$	757.782	−	437.505i	0.0320955	−	0.0185304i	0.515962	+	0.856612i	$0.327435\pi$
$824$	−4216.77	+	7303.66i	−0.178275	+	0.308781i
$825$		0			0
$826$	−857.800	+	1111.09i	−0.0361340	+	0.0468035i
$827$			1029.69i			0.0432960i	0.999766	+	0.0216480i	$0.00689131\pi$
$827$			1029.69i			0.0432960i	−0.999766	+	0.0216480i	$0.993109\pi$
$828$	−26319.5	−	15195.6i	−1.10467	−	0.637782i
$829$	−9573.48	−	16581.8i	−0.401087	−	0.694702i	0.592771	−	0.805371i	$-0.298034\pi$
$829$	−9573.48	−	16581.8i	−0.401087	−	0.694702i	−0.993857	+	0.110669i	$0.964701\pi$
$830$		0			0
$831$	33372.4	−	57802.6i	1.39311	−	2.41294i
$832$			4508.20i			0.187853i
$833$	6104.58	+	6177.22i	0.253915	+	0.256936i
$834$	4561.95			0.189409
$835$		0			0
$836$	10187.5	+	17645.3i	0.421462	+	0.729994i
$837$	−72719.6	+	41984.7i	−3.00306	+	1.73382i
$838$	−19834.8	−	11451.6i	−0.817640	−	0.472064i
$839$	−34619.2			−1.42454			−0.712270	−	0.701906i	$-0.752333\pi$
$839$	−34619.2			−1.42454			−0.712270	+	0.701906i	$0.752333\pi$
$840$		0			0
$841$	−24199.9			−0.992247
$842$	11362.6	+	6560.18i	0.465059	+	0.268502i
$843$	−32672.8	+	18863.7i	−1.33489	+	0.770699i
$844$	11451.8	+	19835.1i	0.467047	+	0.808950i
$845$		0			0
$846$	−35202.4			−1.43060
$847$	65671.0	−	26974.6i	2.66409	−	1.09428i
$848$		−	1471.98i		−	0.0596083i
$849$	−23419.0	+	40562.8i	−0.946686	+	1.63971i
$850$		0			0
$851$	−4472.37	−	7746.38i	−0.180154	−	0.312036i
$852$	2503.74	+	1445.53i	0.100677	+	0.0581257i
$853$		−	18872.6i		−	0.757543i	−0.925490	−	0.378772i	$-0.876347\pi$
$853$		−	18872.6i		−	0.757543i	0.925490	−	0.378772i	$-0.123653\pi$
$854$	−7079.42	−	953.330i	−0.283668	−	0.0381994i
$855$		0			0
$856$	6717.63	−	11635.3i	0.268229	−	0.464586i
$857$	−12187.2	+	7036.26i	−0.485771	+	0.280460i	−0.722818	−	0.691038i	$-0.757154\pi$
$857$	−12187.2	+	7036.26i	−0.485771	+	0.280460i	0.237047	+	0.971498i	$0.423820\pi$
$858$	−83284.4	+	48084.2i	−3.31385	+	1.91325i
$859$	−14090.4	+	24405.3i	−0.559673	+	0.969383i	0.437850	+	0.899048i	$0.355740\pi$
$859$	−14090.4	+	24405.3i	−0.559673	+	0.969383i	−0.997523	+	0.0703346i	$0.977593\pi$
$860$		0			0
$861$	15834.1	+	2132.26i	0.626743	+	0.0843985i
$862$			26403.7i			1.04329i
$863$	13781.5	+	7956.76i	0.543602	+	0.313849i	0.746537	−	0.665344i	$-0.231715\pi$
$863$	13781.5	+	7956.76i	0.543602	+	0.313849i	−0.202936	+	0.979192i	$0.565048\pi$
$864$	−5505.98	−	9536.64i	−0.216802	−	0.375513i
$865$		0			0
$866$	−13414.4	+	23234.3i	−0.526372	+	0.911704i
$867$			40578.2i			1.58951i
$868$	−16720.9	+	6868.15i	−0.653851	+	0.268572i
$869$	−793.463			−0.0309740
$870$		0			0
$871$	15144.5	+	26231.1i	0.589153	+	1.02044i
$872$	4898.17	−	2827.96i	0.190221	−	0.109824i
$873$	−2447.28	−	1412.94i	−0.0948772	−	0.0547774i
$874$	17034.8			0.659280
$875$		0			0
$876$	30333.4			1.16994
$877$	−43457.1	−	25090.0i	−1.67325	−	0.966053i	−0.965798	−	0.259296i	$-0.916510\pi$
$877$	−43457.1	−	25090.0i	−1.67325	−	0.966053i	−0.707456	−	0.706758i	$-0.750157\pi$
$878$	−1225.64	+	707.622i	−0.0471108	+	0.0271994i
$879$	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	$0.611145\pi$
$882$	−30488.4	−	30851.2i	−1.16394	−	1.17779i
$883$		−	11685.8i		−	0.445368i	−0.974891	−	0.222684i	$-0.928518\pi$
$883$		−	11685.8i		−	0.445368i	0.974891	−	0.222684i	$-0.0714818\pi$
$884$	3567.09	−	6178.38i	0.135717	−	0.235069i
$885$		0			0
$886$	−13377.3	−	23170.1i	−0.507244	−	0.878573i
$887$	32054.5	+	18506.7i	1.21340	+	0.700557i	0.963498	−	0.267715i	$-0.0862685\pi$
$887$	32054.5	+	18506.7i	1.21340	+	0.700557i	0.249901	+	0.968271i	$0.419602\pi$
$888$		−	5656.53i		−	0.213762i
$889$	23461.3	−	30388.9i	0.885116	−	1.14647i
$890$		0			0
$891$	56111.9	−	97188.6i	2.10978	−	3.65425i
$892$	−4393.74	+	2536.73i	−0.164925	+	0.0952196i
$893$	17088.1	−	9865.80i	0.640348	−	0.369705i
$894$	−26470.6	+	45848.4i	−0.990278	+	1.71521i
$895$		0			0
$896$	−900.706	−	2192.82i	−0.0335831	−	0.0817599i
$897$			80403.0i			2.99284i
$898$	7028.37	+	4057.83i	0.261180	+	0.150792i
$899$	1677.66	+	2905.80i	0.0622394	+	0.107802i
$900$		0			0
$901$	−1164.69	+	2017.31i	−0.0430650	+	0.0745907i
$902$			13053.2i			0.481846i
$903$	−218.800	+	1624.81i	−0.00806336	+	0.0598785i
$904$	10631.4			0.391144
$905$		0			0
$906$	−9981.61	−	17288.7i	−0.366023	−	0.633971i
$907$	30159.4	−	17412.5i	1.10411	−	0.637457i	0.166811	−	0.985989i	$-0.446653\pi$
$907$	30159.4	−	17412.5i	1.10411	−	0.637457i	0.937297	+	0.348531i	$0.113320\pi$
$908$	2674.51	+	1544.13i	0.0977497	+	0.0564358i
$909$	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	$0.198913\pi$
$912$	9329.32	+	5386.29i	0.338733	+	0.195568i
$913$	37528.5	−	21667.1i	1.36036	−	0.785406i
$914$	4522.71	+	7833.57i	0.163674	+	0.283492i
$915$		0			0
$916$	1422.57			0.0513135
$917$	−32877.8	+	13504.7i	−1.18399	+	0.486329i
$918$			17426.3i			0.626529i
$919$	−17632.0	+	30539.5i	−0.632890	+	1.09620i	0.354068	+	0.935220i	$0.384798\pi$
$919$	−17632.0	+	30539.5i	−0.632890	+	1.09620i	−0.986958	+	0.160978i	$0.948535\pi$
$920$		0			0
$921$	26066.1	+	45147.9i	0.932582	+	1.61528i
$922$	−7544.05	−	4355.56i	−0.269468	−	0.155578i
$923$		−	5359.82i		−	0.191138i
$924$	30903.1	−	40028.1i	1.10026	−	1.42514i
$925$		0			0
$926$	−17178.7	+	29754.3i	−0.609639	+	1.05593i
$927$	−57724.5	+	33327.2i	−2.04522	+	1.18081i
$928$	−381.074	+	220.013i	−0.0134799	+	0.00778263i
$929$	−20379.1	+	35297.7i	−0.719718	+	1.24659i	0.241394	+	0.970427i	$0.422396\pi$
$929$	−20379.1	+	35297.7i	−0.719718	+	1.24659i	−0.961111	+	0.276161i	$0.910938\pi$
$930$		0			0
$931$	23446.1	+	6431.22i	0.825365	+	0.226396i
$932$			11609.2i			0.408016i
$933$	28619.1	+	16523.3i	1.00423	+	0.579794i
$934$	8040.78	+	13927.0i	0.281694	+	0.487909i
$935$		0			0
$936$	−17815.3	+	30857.0i	−0.622126	+	1.07755i
$937$		−	21119.6i		−	0.736337i	−0.929759	−	0.368169i	$-0.879985\pi$
$937$		−	21119.6i		−	0.736337i	0.929759	−	0.368169i	$-0.120015\pi$
$938$	−12607.2	−	9733.18i	−0.438847	−	0.338806i
$939$	−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	$0.956113\pi$
$942$	−18553.7	+	10712.0i	−0.641733	+	0.370505i
$943$	9451.22	+	5456.67i	0.326378	+	0.188434i
$944$	−606.336			−0.0209052
$945$		0			0
$946$	−1339.45			−0.0460351
$947$	−1782.88	−	1029.35i	−0.0611784	−	0.0353214i	0.469099	−	0.883146i	$-0.344579\pi$
$947$	−1782.88	−	1029.35i	−0.0611784	−	0.0353214i	−0.530277	+	0.847824i	$0.677912\pi$
$948$	−363.311	+	209.758i	−0.0124470	+	0.00718630i
$949$	−28118.0	−	48701.7i	−0.961799	−	1.66589i
$950$		0			0
$951$	9011.59			0.307277
$952$	−500.657	+	3717.88i	−0.0170445	+	0.126573i
$953$		−	8010.67i		−	0.272288i	−0.990689	−	0.136144i	$-0.956529\pi$
$953$		−	8010.67i		−	0.272288i	0.990689	−	0.136144i	$-0.0434711\pi$
$954$	5816.88	−	10075.1i	0.197409	−	0.341923i
$955$		0			0
$956$	11271.0	+	19521.9i	0.381307	+	0.660443i
$957$	−8129.03	−	4693.30i	−0.274581	−	0.158530i
$958$		−	17040.3i		−	0.574685i
$959$	19945.5	+	2685.91i	0.671611	+	0.0904405i
$960$		0			0
$961$	−14874.8	+	25763.9i	−0.499305	+	0.864821i
$962$	−9081.83	+	5243.40i	−0.304376	+	0.175732i
$963$	91959.4	−	53092.8i	3.07721	−	1.77663i
$964$	8151.24	−	14118.4i	0.272338	−	0.471703i
$965$		0			0
$966$	−16063.9	−	39108.5i	−0.535040	−	1.30258i
$967$			2477.77i			0.0823988i	0.999151	+	0.0411994i	$0.0131179\pi$
$967$			2477.77i			0.0823988i	−0.999151	+	0.0411994i	$0.986882\pi$
$968$	26558.4	+	15333.5i	0.881839	+	0.509130i
$969$	−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	$0.816311\pi$
$972$		−	22169.0i		−	0.731554i
$973$	3520.27	+	2717.77i	0.115986	+	0.0895455i
$974$	39540.4			1.30077
$975$		0			0
$976$	−1542.81	−	2672.23i	−0.0505986	−	0.0876393i
$977$	38452.3	−	22200.5i	1.25916	−	0.726976i	0.286248	−	0.958155i	$-0.407592\pi$
$977$	38452.3	−	22200.5i	1.25916	−	0.726976i	0.972911	+	0.231179i	$0.0742584\pi$
$978$	−4289.50	−	2476.55i	−0.140249	−	0.0809726i
$979$	57514.1			1.87759
$980$		0			0
$981$	44701.5			1.45485
$982$	−17401.9	−	10047.0i	−0.565495	−	0.326489i
$983$	−42134.9	+	24326.6i	−1.36714	+	0.789317i	−0.990561	−	0.137070i	$-0.956232\pi$
$983$	−42134.9	+	24326.6i	−1.36714	+	0.789317i	−0.376575	+	0.926386i	$0.622898\pi$
$984$	3450.72	+	5976.82i	0.111794	+	0.193632i
$985$		0			0
$986$	696.336			0.0224907
$987$	−38764.1	−	29927.3i	−1.25013	−	0.965142i
$988$		−	19971.6i		−	0.643097i
$989$	−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	$-0.353017\pi$
$992$	−6762.19	−	3904.15i	−0.216431	−	0.124957i
$993$			59461.1i			1.90024i
$994$	1070.85	+	2607.05i	0.0341705	+	0.0831897i
$995$		0			0
$996$	11455.7	−	19841.9i	0.364446	−	0.631238i
$997$	−12345.4	+	7127.61i	−0.392159	+	0.226413i	−0.683095	−	0.730329i	$-0.739367\pi$
$997$	−12345.4	+	7127.61i	−0.392159	+	0.226413i	0.290936	+	0.956742i	$0.406033\pi$
$998$	21951.3	−	12673.6i	0.696250	−	0.401980i
$999$	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.j.j.149.4		16
5.2	odd	4		350.4.e.m.51.1	yes	8
5.3	odd	4		350.4.e.l.51.4	✓	8
5.4	even	2	inner	350.4.j.j.149.5		16
7.4	even	3	inner	350.4.j.j.249.5		16
35.2	odd	12		2450.4.a.co.1.4		4
35.4	even	6	inner	350.4.j.j.249.4		16
35.12	even	12		2450.4.a.ck.1.1		4
35.18	odd	12		350.4.e.l.151.4	yes	8
35.23	odd	12		2450.4.a.cq.1.1		4
35.32	odd	12		350.4.e.m.151.1	yes	8
35.33	even	12		2450.4.a.cu.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.l.51.4	✓	8	5.3	odd	4
350.4.e.l.151.4	yes	8	35.18	odd	12
350.4.e.m.51.1	yes	8	5.2	odd	4
350.4.e.m.151.1	yes	8	35.32	odd	12
350.4.j.j.149.4		16	1.1	even	1	trivial
350.4.j.j.149.5		16	5.4	even	2	inner
350.4.j.j.249.4		16	35.4	even	6	inner
350.4.j.j.249.5		16	7.4	even	3	inner
2450.4.a.ck.1.1		4	35.12	even	12
2450.4.a.co.1.4		4	35.2	odd	12
2450.4.a.cq.1.1		4	35.23	odd	12
2450.4.a.cu.1.4		4	35.33	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(8.22624 - 4.74942i) q^{3} +(2.00000 + 3.46410i) q^{4} -18.9977 q^{6} +(-14.6597 - 11.3178i) q^{7} -8.00000i q^{8} +(31.6140 - 54.7570i) q^{9} +O(q^{10})\)	\(q+(-1.73205 - 1.00000i) q^{2} +(8.22624 - 4.74942i) q^{3} +(2.00000 + 3.46410i) q^{4} -18.9977 q^{6} +(-14.6597 - 11.3178i) q^{7} -8.00000i q^{8} +(31.6140 - 54.7570i) q^{9} +(35.9318 + 62.2357i) q^{11} +(32.9049 + 18.9977i) q^{12} -70.4406i q^{13} +(14.0735 + 34.2627i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(21.9276 - 12.6599i) q^{17} +(-109.514 + 63.2280i) q^{18} +(35.4404 - 61.3846i) q^{19} +(-174.347 - 23.4780i) q^{21} -143.727i q^{22} +(-104.066 - 60.0826i) q^{23} +(-37.9954 - 65.8099i) q^{24} +(-70.4406 + 122.007i) q^{26} -344.124i q^{27} +(9.88667 - 73.4183i) q^{28} -13.7508 q^{29} +(-122.005 - 211.318i) q^{31} +(27.7128 - 16.0000i) q^{32} +(591.167 + 341.310i) q^{33} -50.6396 q^{34} +252.912 q^{36} +(64.4645 + 37.2186i) q^{37} +(-122.769 + 70.8808i) q^{38} +(-334.552 - 579.461i) q^{39} -90.8195 q^{41} +(278.500 + 215.012i) q^{42} -9.31938i q^{43} +(-143.727 + 248.943i) q^{44} +(120.165 + 208.132i) q^{46} +(241.082 + 139.189i) q^{47} +151.981i q^{48} +(86.8139 + 331.832i) q^{49} +(120.254 - 208.287i) q^{51} +(244.013 - 140.881i) q^{52} +(-79.6731 + 45.9993i) q^{53} +(-344.124 + 596.040i) q^{54} +(-90.5426 + 117.278i) q^{56} -673.286i q^{57} +(23.8171 + 13.7508i) q^{58} +(18.9480 + 32.8189i) q^{59} +(-96.4258 + 167.014i) q^{61} +488.019i q^{62} +(-1083.18 + 444.921i) q^{63} -64.0000 q^{64} +(-682.621 - 1182.33i) q^{66} +(-372.385 + 214.997i) q^{67} +(87.7104 + 50.6396i) q^{68} -1141.43 q^{69} +76.0899 q^{71} +(-438.056 - 252.912i) q^{72} +(691.387 - 399.172i) q^{73} +(-74.4372 - 128.929i) q^{74} +283.523 q^{76} +(177.623 - 1319.03i) q^{77} +1338.21i q^{78} +(-5.52061 + 9.56198i) q^{79} +(-780.810 - 1352.40i) q^{81} +(157.304 + 90.8195i) q^{82} -603.005i q^{83} +(-267.365 - 650.913i) q^{84} +(-9.31938 + 16.1416i) q^{86} +(-113.117 + 65.3084i) q^{87} +(497.886 - 287.454i) q^{88} +(400.161 - 693.100i) q^{89} +(-797.234 + 1032.64i) q^{91} -480.660i q^{92} +(-2007.28 - 1158.90i) q^{93} +(-278.377 - 482.163i) q^{94} +(151.981 - 263.240i) q^{96} -44.6934i q^{97} +(181.466 - 661.563i) q^{98} +4543.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 146 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 146 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 146 q^{9} + 20 q^{11} + 140 q^{14} - 128 q^{16} + 492 q^{19} - 1070 q^{21} - 16 q^{24} - 376 q^{26} + 392 q^{29} - 608 q^{31} - 792 q^{34} + 1168 q^{36} - 428 q^{39} + 1408 q^{41} - 80 q^{44} + 8 q^{46} - 2566 q^{49} + 2874 q^{51} - 784 q^{54} + 112 q^{56} + 1346 q^{59} - 2850 q^{61} - 1024 q^{64} - 2104 q^{66} - 3752 q^{69} - 24 q^{71} - 328 q^{74} + 3936 q^{76} + 3488 q^{79} - 3416 q^{81} - 1744 q^{84} - 524 q^{86} - 1742 q^{89} - 1594 q^{91} - 1964 q^{94} + 64 q^{96} + 21124 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 146 * q^9 + 20 * q^11 + 140 * q^14 - 128 * q^16 + 492 * q^19 - 1070 * q^21 - 16 * q^24 - 376 * q^26 + 392 * q^29 - 608 * q^31 - 792 * q^34 + 1168 * q^36 - 428 * q^39 + 1408 * q^41 - 80 * q^44 + 8 * q^46 - 2566 * q^49 + 2874 * q^51 - 784 * q^54 + 112 * q^56 + 1346 * q^59 - 2850 * q^61 - 1024 * q^64 - 2104 * q^66 - 3752 * q^69 - 24 * q^71 - 328 * q^74 + 3936 * q^76 + 3488 * q^79 - 3416 * q^81 - 1744 * q^84 - 524 * q^86 - 1742 * q^89 - 1594 * q^91 - 1964 * q^94 + 64 * q^96 + 21124 * q^99

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