LMFDB - Embedded newform 1050.3.q.a.649.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.a.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(1.88064 + 6.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(1.88064 + 6.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(-1.73205 + 3.00000i) q^{12} +17.8639 q^{13} +(-2.46447 + 9.58783i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(9.37769 + 16.2426i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(14.7426 + 8.51167i) q^{19} +(-8.48528 + 8.66025i) q^{21} -8.48528i q^{22} +(-11.6531 - 6.72792i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(21.8787 + 12.6317i) q^{26} -5.19615 q^{27} +(-9.79796 + 10.0000i) q^{28} -33.9411 q^{29} +(12.7721 - 7.37396i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(5.19615 - 9.00000i) q^{33} +26.5241i q^{34} -6.00000 q^{36} +(5.17066 + 2.98528i) q^{37} +(12.0373 + 20.8492i) q^{38} +(15.4706 + 26.7958i) q^{39} +35.2354i q^{41} +(-16.5160 + 4.60660i) q^{42} +15.4853i q^{43} +(6.00000 - 10.3923i) q^{44} +(-9.51472 - 16.4800i) q^{46} +(-16.6031 + 28.7574i) q^{47} -6.92820 q^{48} +(-41.9264 + 25.3609i) q^{49} +(-16.2426 + 28.1331i) q^{51} +(17.8639 + 30.9411i) q^{52} +(-29.9161 + 17.2721i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-19.0711 + 5.31925i) q^{56} +29.4853i q^{57} +(-41.5692 - 24.0000i) q^{58} +(-23.6985 + 13.6823i) q^{59} +(-34.9706 - 20.1903i) q^{61} +20.8567 q^{62} +(-20.3389 - 5.22792i) q^{63} -8.00000 q^{64} +(12.7279 - 7.34847i) q^{66} +(99.0707 - 57.1985i) q^{67} +(-18.7554 + 32.4853i) q^{68} -23.3062i q^{69} +18.6030 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-58.5161 - 101.353i) q^{73} +(4.22183 + 7.31242i) q^{74} +34.0467i q^{76} +(29.3939 - 30.0000i) q^{77} +43.7574i q^{78} +(-44.1690 + 76.5030i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-24.9152 + 43.1543i) q^{82} -75.7601 q^{83} +(-23.4853 - 6.03668i) q^{84} +(-10.9497 + 18.9655i) q^{86} +(-29.3939 - 50.9117i) q^{87} +(14.6969 - 8.48528i) q^{88} +(18.0000 + 10.3923i) q^{89} +(33.5955 + 120.450i) q^{91} -26.9117i q^{92} +(22.1219 + 12.7721i) q^{93} +(-40.6690 + 23.4803i) q^{94} +(-8.48528 - 4.89898i) q^{96} +30.5826 q^{97} +(-69.2820 + 1.41421i) q^{98} +18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 12 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 12 * q^9	$ 8 q + 8 q^{4} - 12 q^{9} - 24 q^{11} - 48 q^{14} - 16 q^{16} + 84 q^{19} + 192 q^{26} + 204 q^{31} - 48 q^{36} - 12 q^{39} + 48 q^{44} - 144 q^{46} + 4 q^{49} - 96 q^{51} - 96 q^{56} + 48 q^{59} - 144 q^{61} - 64 q^{64} + 624 q^{71} + 96 q^{74} + 20 q^{79} - 36 q^{81} - 120 q^{84} - 48 q^{86} + 144 q^{89} - 444 q^{91} + 48 q^{94} + 144 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 - 12 * q^9 - 24 * q^11 - 48 * q^14 - 16 * q^16 + 84 * q^19 + 192 * q^26 + 204 * q^31 - 48 * q^36 - 12 * q^39 + 48 * q^44 - 144 * q^46 + 4 * q^49 - 96 * q^51 - 96 * q^56 + 48 * q^59 - 144 * q^61 - 64 * q^64 + 624 * q^71 + 96 * q^74 + 20 * q^79 - 36 * q^81 - 120 * q^84 - 48 * q^86 + 144 * q^89 - 444 * q^91 + 48 * q^94 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	1.88064	+	6.74264i	0.268662	+	0.963234i
$7$	1.88064	+	6.74264i	0.268662	+	0.963234i
$8$			2.82843i			0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.272727	−	0.472377i	0.696832	−	0.717234i	$-0.254592\pi$
$11$	−3.00000	−	5.19615i	−0.272727	−	0.472377i	−0.969559	+	0.244857i	$0.921259\pi$
$12$	−1.73205	+	3.00000i	−0.144338	+	0.250000i
$13$	17.8639			1.37414			0.687072	−	0.726590i	$-0.258896\pi$
$13$	17.8639			1.37414			0.687072	+	0.726590i	$0.258896\pi$
$14$	−2.46447	+	9.58783i	−0.176033	+	0.684845i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	9.37769	+	16.2426i	0.551629	+	0.955449i	0.998157	+	0.0606799i	$0.0193269\pi$
$17$	9.37769	+	16.2426i	0.551629	+	0.955449i	−0.446528	+	0.894770i	$0.647340\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	14.7426	+	8.51167i	0.775928	+	0.447983i	0.834985	−	0.550272i	$-0.185476\pi$
$19$	14.7426	+	8.51167i	0.775928	+	0.447983i	−0.0590569	+	0.998255i	$0.518809\pi$
$20$		0			0
$21$	−8.48528	+	8.66025i	−0.404061	+	0.412393i
$22$		−	8.48528i		−	0.385695i
$23$	−11.6531	−	6.72792i	−0.506657	−	0.292518i	0.224802	−	0.974405i	$-0.427827\pi$
$23$	−11.6531	−	6.72792i	−0.506657	−	0.292518i	−0.731458	+	0.681886i	$0.761160\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$		0			0
$26$	21.8787	+	12.6317i	0.841488	+	0.485833i
$27$	−5.19615			−0.192450
$28$	−9.79796	+	10.0000i	−0.349927	+	0.357143i
$29$	−33.9411			−1.17038			−0.585192	−	0.810895i	$-0.698981\pi$
$29$	−33.9411			−1.17038			−0.585192	+	0.810895i	$0.698981\pi$
$30$		0			0
$31$	12.7721	−	7.37396i	0.412003	−	0.237870i	−0.279647	−	0.960103i	$-0.590218\pi$
$31$	12.7721	−	7.37396i	0.412003	−	0.237870i	0.691650	+	0.722233i	$0.256884\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	5.19615	−	9.00000i	0.157459	−	0.272727i
$34$			26.5241i			0.780121i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	5.17066	+	2.98528i	0.139748	+	0.0806833i	0.568244	−	0.822860i	$-0.307623\pi$
$37$	5.17066	+	2.98528i	0.139748	+	0.0806833i	−0.428496	+	0.903544i	$0.640956\pi$
$38$	12.0373	+	20.8492i	0.316771	+	0.548664i
$39$	15.4706	+	26.7958i	0.396681	+	0.687072i
$40$		0			0
$41$			35.2354i			0.859399i	0.902972	+	0.429700i	$0.141381\pi$
$41$			35.2354i			0.859399i	−0.902972	+	0.429700i	$0.858619\pi$
$42$	−16.5160	+	4.60660i	−0.393239	+	0.109681i
$43$			15.4853i			0.360123i	0.983655	+	0.180061i	$0.0576296\pi$
$43$			15.4853i			0.360123i	−0.983655	+	0.180061i	$0.942370\pi$
$44$	6.00000	−	10.3923i	0.136364	−	0.236189i
$45$		0			0
$46$	−9.51472	−	16.4800i	−0.206842	−	0.358260i
$47$	−16.6031	+	28.7574i	−0.353257	+	0.611859i	−0.986818	−	0.161834i	$-0.948259\pi$
$47$	−16.6031	+	28.7574i	−0.353257	+	0.611859i	0.633561	+	0.773693i	$0.281592\pi$
$48$	−6.92820			−0.144338
$49$	−41.9264	+	25.3609i	−0.855641	+	0.517570i
$50$		0			0
$51$	−16.2426	+	28.1331i	−0.318483	+	0.551629i
$52$	17.8639	+	30.9411i	0.343536	+	0.595022i
$53$	−29.9161	+	17.2721i	−0.564455	+	0.325888i	−0.754932	−	0.655803i	$-0.772330\pi$
$53$	−29.9161	+	17.2721i	−0.564455	+	0.325888i	0.190477	+	0.981692i	$0.438997\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−19.0711	+	5.31925i	−0.340555	+	0.0949865i
$57$			29.4853i			0.517286i
$58$	−41.5692	−	24.0000i	−0.716711	−	0.413793i
$59$	−23.6985	+	13.6823i	−0.401669	+	0.231904i	−0.687204	−	0.726465i	$-0.741162\pi$
$59$	−23.6985	+	13.6823i	−0.401669	+	0.231904i	0.285535	+	0.958368i	$0.407829\pi$
$60$		0			0
$61$	−34.9706	−	20.1903i	−0.573288	−	0.330988i	0.185174	−	0.982706i	$-0.440715\pi$
$61$	−34.9706	−	20.1903i	−0.573288	−	0.330988i	−0.758461	+	0.651718i	$0.774049\pi$
$62$	20.8567			0.336399
$63$	−20.3389	−	5.22792i	−0.322839	−	0.0829829i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	12.7279	−	7.34847i	0.192847	−	0.111340i
$67$	99.0707	−	57.1985i	1.47867	−	0.853709i	0.478958	−	0.877838i	$-0.341015\pi$
$67$	99.0707	−	57.1985i	1.47867	−	0.853709i	0.999709	+	0.0241291i	$0.00768127\pi$
$68$	−18.7554	+	32.4853i	−0.275814	+	0.477725i
$69$		−	23.3062i		−	0.337771i
$70$		0			0
$71$	18.6030			0.262015			0.131007	−	0.991381i	$-0.458179\pi$
$71$	18.6030			0.262015			0.131007	+	0.991381i	$0.458179\pi$
$72$	−7.34847	−	4.24264i	−0.102062	−	0.0589256i
$73$	−58.5161	−	101.353i	−0.801590	−	1.38839i	−0.918569	−	0.395260i	$-0.870654\pi$
$73$	−58.5161	−	101.353i	−0.801590	−	1.38839i	0.116979	−	0.993134i	$-0.462679\pi$
$74$	4.22183	+	7.31242i	0.0570517	+	0.0988164i
$75$		0			0
$76$			34.0467i			0.447983i
$77$	29.3939	−	30.0000i	0.381739	−	0.389610i
$78$			43.7574i			0.560992i
$79$	−44.1690	+	76.5030i	−0.559102	+	0.968393i	0.438470	+	0.898746i	$0.355521\pi$
$79$	−44.1690	+	76.5030i	−0.559102	+	0.968393i	−0.997572	+	0.0696469i	$0.977813\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−24.9152	+	43.1543i	−0.303843	+	0.526272i
$83$	−75.7601			−0.912772			−0.456386	−	0.889782i	$-0.650856\pi$
$83$	−75.7601			−0.912772			−0.456386	+	0.889782i	$0.650856\pi$
$84$	−23.4853	−	6.03668i	−0.279587	−	0.0718653i
$85$		0			0
$86$	−10.9497	+	18.9655i	−0.127323	+	0.220529i
$87$	−29.3939	−	50.9117i	−0.337861	−	0.585192i
$88$	14.6969	−	8.48528i	0.167011	−	0.0964237i
$89$	18.0000	+	10.3923i	0.202247	+	0.116767i	0.597703	−	0.801717i	$-0.296080\pi$
$89$	18.0000	+	10.3923i	0.202247	+	0.116767i	−0.395456	+	0.918485i	$0.629413\pi$
$90$		0			0
$91$	33.5955	+	120.450i	0.369181	+	1.32362i
$92$		−	26.9117i		−	0.292518i
$93$	22.1219	+	12.7721i	0.237870	+	0.137334i
$94$	−40.6690	+	23.4803i	−0.432649	+	0.249790i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$	30.5826			0.315284			0.157642	−	0.987496i	$-0.449611\pi$
$97$	30.5826			0.315284			0.157642	+	0.987496i	$0.449611\pi$
$98$	−69.2820	+	1.41421i	−0.706960	+	0.0144308i
$99$	18.0000			0.181818
$100$		0			0
$101$	110.823	−	63.9839i	1.09726	−	0.633504i	0.161761	−	0.986830i	$-0.448283\pi$
$101$	110.823	−	63.9839i	1.09726	−	0.633504i	0.935500	+	0.353326i	$0.114949\pi$
$102$	−39.7862	+	22.9706i	−0.390061	+	0.225202i
$103$	40.4781	−	70.1102i	0.392992	−	0.680681i	−0.599851	−	0.800112i	$-0.704774\pi$
$103$	40.4781	−	70.1102i	0.392992	−	0.680681i	0.992843	+	0.119430i	$0.0381068\pi$
$104$			50.5266i			0.485833i
$105$		0			0
$106$	−48.8528			−0.460876
$107$	146.753	+	84.7279i	1.37152	+	0.791850i	0.991120	−	0.132971i	$-0.0424516\pi$
$107$	146.753	+	84.7279i	1.37152	+	0.791850i	0.380404	+	0.924820i	$0.375785\pi$
$108$	−5.19615	−	9.00000i	−0.0481125	−	0.0833333i
$109$	89.4706	+	154.968i	0.820831	+	1.42172i	0.905064	+	0.425275i	$0.139823\pi$
$109$	89.4706	+	154.968i	0.820831	+	1.42172i	−0.0842335	+	0.996446i	$0.526844\pi$
$110$		0			0
$111$			10.3413i			0.0931650i
$112$	−27.1185	−	6.97056i	−0.242129	−	0.0622372i
$113$		−	17.3970i		−	0.153955i	−0.997033	−	0.0769777i	$-0.975473\pi$
$113$		−	17.3970i		−	0.153955i	0.997033	−	0.0769777i	$-0.0245270\pi$
$114$	−20.8492	+	36.1119i	−0.182888	+	0.316771i
$115$		0			0
$116$	−33.9411	−	58.7878i	−0.292596	−	0.506791i
$117$	−26.7958	+	46.4117i	−0.229024	+	0.396681i
$118$	−38.6995			−0.327962
$119$	−91.8823	+	93.7769i	−0.772120	+	0.788041i
$120$		0			0
$121$	42.5000	−	73.6122i	0.351240	−	0.608365i
$122$	−28.5533	−	49.4558i	−0.234044	−	0.405376i
$123$	−52.8530	+	30.5147i	−0.429700	+	0.248087i
$124$	25.5442	+	14.7479i	0.206001	+	0.118935i
$125$		0			0
$126$	−21.2132	−	20.7846i	−0.168359	−	0.164957i
$127$		−	167.426i		−	1.31832i	−0.752004	−	0.659159i	$-0.770912\pi$
$127$		−	167.426i		−	1.31832i	0.752004	−	0.659159i	$-0.229088\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	−23.2279	+	13.4106i	−0.180061	+	0.103959i
$130$		0			0
$131$	−1.54416	−	0.891519i	−0.0117874	−	0.00680549i	0.494095	−	0.869408i	$-0.335500\pi$
$131$	−1.54416	−	0.891519i	−0.0117874	−	0.00680549i	−0.505882	+	0.862603i	$0.668833\pi$
$132$	20.7846			0.157459
$133$	−29.6656	+	115.412i	−0.223049	+	0.867757i
$134$	161.782			1.20733
$135$		0			0
$136$	−45.9411	+	26.5241i	−0.337802	+	0.195030i
$137$	−87.4431	+	50.4853i	−0.638271	+	0.368506i	−0.783948	−	0.620826i	$-0.786797\pi$
$137$	−87.4431	+	50.4853i	−0.638271	+	0.368506i	0.145677	+	0.989332i	$0.453464\pi$
$138$	16.4800	−	28.5442i	0.119420	−	0.206842i
$139$			140.542i			1.01110i	0.862799	+	0.505548i	$0.168710\pi$
$139$			140.542i			1.01110i	−0.862799	+	0.505548i	$0.831290\pi$
$140$		0			0
$141$	−57.5147			−0.407906
$142$	22.7840	+	13.1543i	0.160450	+	0.0926361i
$143$	−53.5916	−	92.8234i	−0.374766	−	0.649115i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$		0			0
$146$		−	165.508i		−	1.13362i
$147$	−74.3507	−	40.9264i	−0.505787	−	0.278411i
$148$			11.9411i			0.0806833i
$149$	91.4558	−	158.406i	0.613798	−	1.06313i	−0.376797	−	0.926296i	$-0.622974\pi$
$149$	91.4558	−	158.406i	0.613798	−	1.06313i	0.990594	−	0.136833i	$-0.0436922\pi$
$150$		0			0
$151$	144.397	+	250.103i	0.956271	+	1.65631i	0.731432	+	0.681915i	$0.238852\pi$
$151$	144.397	+	250.103i	0.956271	+	1.65631i	0.224840	+	0.974396i	$0.427814\pi$
$152$	−24.0746	+	41.6985i	−0.158386	+	0.274332i
$153$	−56.2662			−0.367753
$154$	57.2132	−	15.9577i	0.371514	−	0.103622i
$155$		0			0
$156$	−30.9411	+	53.5916i	−0.198341	+	0.343536i
$157$	−93.5307	−	162.000i	−0.595737	−	1.03185i	−0.993442	−	0.114334i	$-0.963527\pi$
$157$	−93.5307	−	162.000i	−0.595737	−	1.03185i	0.397705	−	0.917513i	$-0.369807\pi$
$158$	−108.192	+	62.4645i	−0.684757	+	0.395345i
$159$	−51.8162	−	29.9161i	−0.325888	−	0.188152i
$160$		0			0
$161$	23.4487	−	91.2255i	0.145644	−	0.566618i
$162$		−	12.7279i		−	0.0785674i
$163$	−13.9074	−	8.02944i	−0.0853214	−	0.0492604i	0.456732	−	0.889604i	$-0.349020\pi$
$163$	−13.9074	−	8.02944i	−0.0853214	−	0.0492604i	−0.542054	+	0.840344i	$0.682353\pi$
$164$	−61.0294	+	35.2354i	−0.372131	+	0.214850i
$165$		0			0
$166$	−92.7868	−	53.5705i	−0.558957	−	0.322714i
$167$	−176.117			−1.05459			−0.527297	−	0.849681i	$-0.676794\pi$
$167$	−176.117			−1.05459			−0.527297	+	0.849681i	$0.676794\pi$
$168$	−24.4949	−	24.0000i	−0.145803	−	0.142857i
$169$	150.118			0.888271
$170$		0			0
$171$	−44.2279	+	25.5350i	−0.258643	+	0.149328i
$172$	−26.8213	+	15.4853i	−0.155938	+	0.0900307i
$173$	115.576	−	200.184i	0.668070	−	1.15713i	−0.310373	−	0.950615i	$-0.600454\pi$
$173$	115.576	−	200.184i	0.668070	−	1.15713i	0.978443	−	0.206517i	$-0.0662128\pi$
$174$		−	83.1384i		−	0.477807i
$175$		0			0
$176$	24.0000			0.136364
$177$	−41.0470	−	23.6985i	−0.231904	−	0.133890i
$178$	14.6969	+	25.4558i	0.0825671	+	0.143010i
$179$	−42.6396	−	73.8540i	−0.238210	−	0.412592i	0.721991	−	0.691903i	$-0.243227\pi$
$179$	−42.6396	−	73.8540i	−0.238210	−	0.412592i	−0.960201	+	0.279311i	$0.909894\pi$
$180$		0			0
$181$		−	5.58655i		−	0.0308649i	−0.999881	−	0.0154325i	$-0.995087\pi$
$181$		−	5.58655i		−	0.0308649i	0.999881	−	0.0154325i	$-0.00491250\pi$
$182$	−44.0249	+	171.276i	−0.241895	+	0.941075i
$183$		−	69.9411i		−	0.382192i
$184$	19.0294	−	32.9600i	0.103421	−	0.179130i
$185$		0			0
$186$	18.0624	+	31.2851i	0.0971099	+	0.168199i
$187$	56.2662	−	97.4558i	0.300889	−	0.521154i
$188$	−66.4123			−0.353257
$189$	−9.77208	−	35.0358i	−0.0517041	−	0.185375i
$190$		0			0
$191$	−92.6985	+	160.558i	−0.485332	+	0.840620i	−0.999858	−	0.0168547i	$-0.994635\pi$
$191$	−92.6985	+	160.558i	−0.485332	+	0.840620i	0.514526	+	0.857475i	$0.327968\pi$
$192$	−6.92820	−	12.0000i	−0.0360844	−	0.0625000i
$193$	197.275	−	113.897i	1.02215	−	0.590140i	0.107425	−	0.994213i	$-0.465739\pi$
$193$	197.275	−	113.897i	1.02215	−	0.590140i	0.914727	+	0.404073i	$0.132406\pi$
$194$	37.4558	+	21.6251i	0.193071	+	0.111470i
$195$		0			0
$196$	−85.8528	−	47.2577i	−0.438025	−	0.241111i
$197$		−	123.161i		−	0.625185i	−0.949887	−	0.312593i	$-0.898803\pi$
$197$		−	123.161i		−	0.625185i	0.949887	−	0.312593i	$-0.101197\pi$
$198$	22.0454	+	12.7279i	0.111340	+	0.0642824i
$199$	−5.39697	+	3.11594i	−0.0271205	+	0.0156580i	−0.513499	−	0.858090i	$-0.671651\pi$
$199$	−5.39697	+	3.11594i	−0.0271205	+	0.0156580i	0.486378	+	0.873748i	$0.338318\pi$
$200$		0			0
$201$	171.595	+	99.0707i	0.853709	+	0.492889i
$202$	180.974			0.895910
$203$	−63.8309	−	228.853i	−0.314438	−	1.12735i
$204$	−64.9706			−0.318483
$205$		0			0
$206$	99.1508	−	57.2447i	0.481314	−	0.277887i
$207$	34.9593	−	20.1838i	0.168886	−	0.0975061i
$208$	−35.7277	+	61.8823i	−0.171768	+	0.297511i
$209$		−	102.140i		−	0.488708i
$210$		0			0
$211$	−124.912			−0.591999			−0.295999	−	0.955188i	$-0.595653\pi$
$211$	−124.912			−0.591999			−0.295999	+	0.955188i	$0.595653\pi$
$212$	−59.8322	−	34.5442i	−0.282228	−	0.162944i
$213$	16.1107	+	27.9045i	0.0756371	+	0.131007i
$214$	119.823	+	207.540i	0.559922	+	0.969814i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	73.7396	+	72.2498i	0.339814	+	0.332948i
$218$			253.061i			1.16083i
$219$	101.353	−	175.548i	0.462798	−	0.801590i
$220$		0			0
$221$	167.522	+	290.156i	0.758017	+	1.31292i
$222$	−7.31242	+	12.6655i	−0.0329388	+	0.0570517i
$223$	228.631			1.02525			0.512625	−	0.858613i	$-0.328673\pi$
$223$	228.631			1.02525			0.512625	+	0.858613i	$0.328673\pi$
$224$	−28.2843	−	27.7128i	−0.126269	−	0.123718i
$225$		0			0
$226$	12.3015	−	21.3068i	0.0544315	−	0.0942781i
$227$	84.7685	+	146.823i	0.373430	+	0.646799i	0.990091	−	0.140430i	$-0.0448484\pi$
$227$	84.7685	+	146.823i	0.373430	+	0.646799i	−0.616661	+	0.787229i	$0.711515\pi$
$228$	−51.0700	+	29.4853i	−0.223991	+	0.129321i
$229$	−30.0442	−	17.3460i	−0.131197	−	0.0757467i	0.432965	−	0.901411i	$-0.357467\pi$
$229$	−30.0442	−	17.3460i	−0.131197	−	0.0757467i	−0.564162	+	0.825664i	$0.690801\pi$
$230$		0			0
$231$	70.4558	+	18.1101i	0.305004	+	0.0783985i
$232$		−	96.0000i		−	0.413793i
$233$	220.391	+	127.243i	0.945883	+	0.546106i	0.891800	−	0.452431i	$-0.149443\pi$
$233$	220.391	+	127.243i	0.945883	+	0.546106i	0.0540833	+	0.998536i	$0.482776\pi$
$234$	−65.6360	+	37.8950i	−0.280496	+	0.161944i
$235$		0			0
$236$	−47.3970	−	27.3647i	−0.200835	−	0.115952i
$237$	−153.006			−0.645595
$238$	−178.843	+	49.8823i	−0.751440	+	0.209589i
$239$	−197.147			−0.824884			−0.412442	−	0.910984i	$-0.635324\pi$
$239$	−197.147			−0.824884			−0.412442	+	0.910984i	$0.635324\pi$
$240$		0			0
$241$	76.6173	−	44.2350i	0.317914	−	0.183548i	−0.332548	−	0.943086i	$-0.607908\pi$
$241$	76.6173	−	44.2350i	0.317914	−	0.183548i	0.650462	+	0.759538i	$0.274575\pi$
$242$	104.103	−	60.1041i	0.430179	−	0.248364i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$		−	80.7611i		−	0.330988i
$245$		0			0
$246$	−86.3087			−0.350848
$247$	263.361	+	152.051i	1.06624	+	0.615592i
$248$	20.8567	+	36.1249i	0.0840997	+	0.145665i
$249$	−65.6102	−	113.640i	−0.263495	−	0.456386i
$250$		0			0
$251$		−	215.903i		−	0.860172i	−0.902788	−	0.430086i	$-0.858483\pi$
$251$		−	215.903i		−	0.860172i	0.902788	−	0.430086i	$-0.141517\pi$
$252$	−11.2838	−	40.4558i	−0.0447771	−	0.160539i
$253$			80.7351i			0.319111i
$254$	118.388	−	205.055i	0.466096	−	0.807302i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−2.15232	+	3.72792i	−0.00837477	+	0.0145055i	−0.870182	−	0.492730i	$-0.835999\pi$
$257$	−2.15232	+	3.72792i	−0.00837477	+	0.0145055i	0.861808	+	0.507235i	$0.169332\pi$
$258$	−37.9310			−0.147020
$259$	−10.4045	+	40.4781i	−0.0401720	+	0.156286i
$260$		0			0
$261$	50.9117	−	88.1816i	0.195064	−	0.337861i
$262$	−1.26080	−	2.18377i	−0.00481221	−	0.00833499i
$263$	244.805	−	141.338i	0.930817	−	0.537407i	0.0437468	−	0.999043i	$-0.486071\pi$
$263$	244.805	−	141.338i	0.930817	−	0.537407i	0.887070	+	0.461635i	$0.152737\pi$
$264$	25.4558	+	14.6969i	0.0964237	+	0.0556702i
$265$		0			0
$266$	−117.941	+	120.373i	−0.443388	+	0.452531i
$267$			36.0000i			0.134831i
$268$	198.141	+	114.397i	0.739333	+	0.426854i
$269$	330.765	−	190.967i	1.22961	−	0.709914i	0.262660	−	0.964888i	$-0.415400\pi$
$269$	330.765	−	190.967i	1.22961	−	0.709914i	0.966948	+	0.254974i	$0.0820669\pi$
$270$		0			0
$271$	−73.0294	−	42.1636i	−0.269481	−	0.155585i	0.359171	−	0.933272i	$-0.383060\pi$
$271$	−73.0294	−	42.1636i	−0.269481	−	0.155585i	−0.628652	+	0.777687i	$0.716393\pi$
$272$	−75.0215			−0.275814
$273$	−151.580	+	154.706i	−0.555238	+	0.566687i
$274$	−142.794			−0.521146
$275$		0			0
$276$	40.3675	−	23.3062i	0.146259	−	0.0844428i
$277$	118.747	−	68.5589i	0.428691	−	0.247505i	−0.270098	−	0.962833i	$-0.587056\pi$
$277$	118.747	−	68.5589i	0.428691	−	0.247505i	0.698789	+	0.715328i	$0.253723\pi$
$278$	−99.3784	+	172.128i	−0.357476	+	0.619167i
$279$			44.2438i			0.158580i
$280$		0			0
$281$	−325.103			−1.15695			−0.578474	−	0.815701i	$-0.696352\pi$
$281$	−325.103			−1.15695			−0.578474	+	0.815701i	$0.696352\pi$
$282$	−70.4409	−	40.6690i	−0.249790	−	0.144216i
$283$	97.2876	+	168.507i	0.343773	+	0.595432i	0.985130	−	0.171811i	$-0.0549617\pi$
$283$	97.2876	+	168.507i	0.343773	+	0.595432i	−0.641357	+	0.767242i	$0.721628\pi$
$284$	18.6030	+	32.2214i	0.0655036	+	0.113456i
$285$		0			0
$286$		−	151.580i		−	0.530000i
$287$	−237.579	+	66.2649i	−0.827803	+	0.230888i
$288$		−	16.9706i		−	0.0589256i
$289$	−31.3823	+	54.3557i	−0.108589	+	0.188082i
$290$		0			0
$291$	26.4853	+	45.8739i	0.0910147	+	0.157642i
$292$	117.032	−	202.706i	0.400795	−	0.694197i
$293$	239.702			0.818095			0.409048	−	0.912513i	$-0.365861\pi$
$293$	239.702			0.818095			0.409048	+	0.912513i	$0.365861\pi$
$294$	−62.1213	−	102.698i	−0.211297	−	0.349314i
$295$		0			0
$296$	−8.44365	+	14.6248i	−0.0285258	+	0.0494082i
$297$	15.5885	+	27.0000i	0.0524864	+	0.0909091i
$298$	224.020	−	129.338i	0.751745	−	0.434020i
$299$	−208.169	−	120.187i	−0.696219	−	0.401962i
$300$		0			0
$301$	−104.412	+	29.1222i	−0.346883	+	0.0967515i
$302$			408.416i			1.35237i
$303$	191.952	+	110.823i	0.633504	+	0.365754i
$304$	−58.9706	+	34.0467i	−0.193982	+	0.111996i
$305$		0			0
$306$	−68.9117	−	39.7862i	−0.225202	−	0.130020i
$307$	540.272			1.75984			0.879921	−	0.475120i	$-0.157595\pi$
$307$	540.272			1.75984			0.879921	+	0.475120i	$0.157595\pi$
$308$	81.3554	+	20.9117i	0.264141	+	0.0678951i
$309$	140.220			0.453788
$310$		0			0
$311$	350.044	−	202.098i	1.12554	−	0.649832i	0.182732	−	0.983163i	$-0.441506\pi$
$311$	350.044	−	202.098i	1.12554	−	0.649832i	0.942810	+	0.333330i	$0.108172\pi$
$312$	−75.7900	+	43.7574i	−0.242917	+	0.140248i
$313$	65.6482	−	113.706i	0.209739	−	0.363278i	−0.741893	−	0.670518i	$-0.766072\pi$
$313$	65.6482	−	113.706i	0.209739	−	0.363278i	0.951632	+	0.307240i	$0.0994053\pi$
$314$		−	264.545i		−	0.842500i
$315$		0			0
$316$	−176.676			−0.559102
$317$	−81.3554	−	46.9706i	−0.256642	−	0.148172i	0.366160	−	0.930552i	$-0.380672\pi$
$317$	−81.3554	−	46.9706i	−0.256642	−	0.148172i	−0.622802	+	0.782380i	$0.714006\pi$
$318$	−42.3078	−	73.2792i	−0.133043	−	0.230438i
$319$	101.823	+	176.363i	0.319196	+	0.552863i
$320$		0			0
$321$			293.506i			0.914349i
$322$	93.2248	−	95.1472i	0.289518	−	0.295488i
$323$			319.279i			0.988481i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−11.3553	−	19.6680i	−0.0348323	−	0.0603314i
$327$	−154.968	+	268.412i	−0.473907	+	0.820831i
$328$	−99.6607			−0.303843
$329$	−225.125	−	57.8664i	−0.684270	−	0.175886i
$330$		0			0
$331$	130.684	−	226.351i	0.394815	−	0.683840i	−0.598263	−	0.801300i	$-0.704142\pi$
$331$	130.684	−	226.351i	0.394815	−	0.683840i	0.993078	+	0.117460i	$0.0374754\pi$
$332$	−75.7601	−	131.220i	−0.228193	−	0.395242i
$333$	−15.5120	+	8.95584i	−0.0465825	+	0.0268944i
$334$	−215.698	−	124.534i	−0.645804	−	0.372855i
$335$		0			0
$336$	−13.0294	−	46.7144i	−0.0387781	−	0.139031i
$337$		−	136.265i		−	0.404347i	−0.979350	−	0.202173i	$-0.935200\pi$
$337$		−	136.265i		−	0.404347i	0.979350	−	0.202173i	$-0.0648005\pi$
$338$	183.856	+	106.149i	0.543952	+	0.314051i
$339$	26.0955	−	15.0662i	0.0769777	−	0.0444431i
$340$		0			0
$341$	−76.6325	−	44.2438i	−0.224729	−	0.129747i
$342$	−72.2239			−0.211181
$343$	−249.848	−	235.000i	−0.728420	−	0.685131i
$344$	−43.7990			−0.127323
$345$		0			0
$346$	283.103	−	163.449i	0.818216	−	0.472397i
$347$	279.026	−	161.095i	0.804108	−	0.464252i	−0.0407975	−	0.999167i	$-0.512990\pi$
$347$	279.026	−	161.095i	0.804108	−	0.464252i	0.844906	+	0.534915i	$0.179657\pi$
$348$	58.7878	−	101.823i	0.168930	−	0.292596i
$349$		−	346.495i		−	0.992821i	−0.868088	−	0.496411i	$-0.834651\pi$
$349$		−	346.495i		−	0.992821i	0.868088	−	0.496411i	$-0.165349\pi$
$350$		0			0
$351$	−92.8234			−0.264454
$352$	29.3939	+	16.9706i	0.0835053	+	0.0482118i
$353$	−310.296	−	537.448i	−0.879025	−	1.52252i	−0.852413	−	0.522869i	$-0.824862\pi$
$353$	−310.296	−	537.448i	−0.879025	−	1.52252i	−0.0266116	−	0.999646i	$-0.508472\pi$
$354$	−33.5147	−	58.0492i	−0.0946743	−	0.163981i
$355$		0			0
$356$			41.5692i			0.116767i
$357$	−220.238	−	56.6102i	−0.616912	−	0.158572i
$358$		−	120.603i		−	0.336880i
$359$	10.1177	−	17.5245i	0.0281831	−	0.0488146i	−0.851590	−	0.524209i	$-0.824361\pi$
$359$	10.1177	−	17.5245i	0.0281831	−	0.0488146i	0.879773	+	0.475394i	$0.157695\pi$
$360$		0			0
$361$	−35.6030	−	61.6663i	−0.0986234	−	0.170821i
$362$	3.95029	−	6.84210i	0.0109124	−	0.0189008i
$363$	147.224			0.405577
$364$	−175.029	+	178.639i	−0.480850	+	0.490766i
$365$		0			0
$366$	49.4558	−	85.6600i	0.135125	−	0.234044i
$367$	155.787	+	269.831i	0.424488	+	0.735234i	0.996372	−	0.0850998i	$-0.0271209\pi$
$367$	155.787	+	269.831i	0.424488	+	0.735234i	−0.571885	+	0.820334i	$0.693788\pi$
$368$	46.6124	−	26.9117i	0.126664	−	0.0731296i
$369$	−91.5442	−	52.8530i	−0.248087	−	0.143233i
$370$		0			0
$371$	−172.721	−	169.231i	−0.465555	−	0.456149i
$372$			51.0883i			0.137334i
$373$	590.094	+	340.691i	1.58202	+	0.913380i	0.994564	+	0.104125i	$0.0332043\pi$
$373$	590.094	+	340.691i	1.58202	+	0.913380i	0.587457	+	0.809255i	$0.300129\pi$
$374$	137.823	−	79.5724i	0.368512	−	0.212760i
$375$		0			0
$376$	−81.3381	−	46.9606i	−0.216325	−	0.124895i
$377$	−606.320			−1.60828
$378$	12.8057	−	49.8198i	0.0338776	−	0.131798i
$379$	624.779			1.64849			0.824246	−	0.566231i	$-0.191599\pi$
$379$	624.779			1.64849			0.824246	+	0.566231i	$0.191599\pi$
$380$		0			0
$381$	251.140	−	144.996i	0.659159	−	0.380566i
$382$	−227.064	+	131.095i	−0.594408	+	0.343182i
$383$	−69.1502	+	119.772i	−0.180549	+	0.312720i	−0.942068	−	0.335423i	$-0.891121\pi$
$383$	−69.1502	+	119.772i	−0.180549	+	0.312720i	0.761519	+	0.648143i	$0.224454\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	322.149			0.834584
$387$	−40.2319	−	23.2279i	−0.103959	−	0.0600205i
$388$	30.5826	+	52.9706i	0.0788211	+	0.136522i
$389$	−281.787	−	488.069i	−0.724388	−	1.25468i	−0.959226	−	0.282642i	$-0.908789\pi$
$389$	−281.787	−	488.069i	−0.724388	−	1.25468i	0.234838	−	0.972035i	$-0.424544\pi$
$390$		0			0
$391$		−	252.370i		−	0.645446i
$392$	−71.7315	−	118.586i	−0.182989	−	0.302515i
$393$		−	3.08831i		−	0.00785830i
$394$	87.0883	−	150.841i	0.221036	−	0.382846i
$395$		0			0
$396$	18.0000	+	31.1769i	0.0454545	+	0.0787296i
$397$	−226.669	+	392.603i	−0.570955	+	0.988923i	0.425513	+	0.904952i	$0.360094\pi$
$397$	−226.669	+	392.603i	−0.570955	+	0.988923i	−0.996468	+	0.0839711i	$0.973240\pi$
$398$	−8.81321			−0.0221438
$399$	−198.809	+	55.4511i	−0.498267	+	0.138975i
$400$		0			0
$401$	137.875	−	238.807i	0.343828	−	0.595528i	−0.641312	−	0.767280i	$-0.721610\pi$
$401$	137.875	−	238.807i	0.343828	−	0.595528i	0.985140	+	0.171752i	$0.0549429\pi$
$402$	140.107	+	242.673i	0.348525	+	0.603663i
$403$	228.159	−	131.727i	0.566151	−	0.326867i
$404$	221.647	+	127.968i	0.548631	+	0.316752i
$405$		0			0
$406$	83.6468	−	325.422i	0.206026	−	0.801531i
$407$		−	35.8234i		−	0.0880181i
$408$	−79.5724	−	45.9411i	−0.195030	−	0.112601i
$409$	377.441	−	217.916i	0.922839	−	0.532801i	0.0382993	−	0.999266i	$-0.487806\pi$
$409$	377.441	−	217.916i	0.922839	−	0.532801i	0.884540	+	0.466465i	$0.154473\pi$
$410$		0			0
$411$	−151.456	−	87.4431i	−0.368506	−	0.212757i
$412$	161.913			0.392992
$413$	−136.823	−	134.059i	−0.331291	−	0.324598i
$414$	57.0883			0.137894
$415$		0			0
$416$	−87.5147	+	50.5266i	−0.210372	+	0.121458i
$417$	−210.813	+	121.713i	−0.505548	+	0.291878i
$418$	72.2239	−	125.095i	0.172784	−	0.299271i
$419$			301.257i			0.718991i	0.933147	+	0.359496i	$0.117051\pi$
$419$			301.257i			0.718991i	−0.933147	+	0.359496i	$0.882949\pi$
$420$		0			0
$421$	−203.794			−0.484071			−0.242036	−	0.970267i	$-0.577815\pi$
$421$	−203.794			−0.484071			−0.242036	+	0.970267i	$0.577815\pi$
$422$	−152.985	−	88.3259i	−0.362524	−	0.209303i
$423$	−49.8092	−	86.2721i	−0.117752	−	0.203953i
$424$	−48.8528	−	84.6156i	−0.115219	−	0.199565i
$425$		0			0
$426$			45.5679i			0.106967i
$427$	70.3688	−	273.765i	0.164798	−	0.641135i
$428$			338.912i			0.791850i
$429$	92.8234	−	160.775i	0.216372	−	0.374766i
$430$		0			0
$431$	197.860	+	342.703i	0.459072	+	0.795136i	0.998912	−	0.0466317i	$-0.0148487\pi$
$431$	197.860	+	342.703i	0.459072	+	0.795136i	−0.539840	+	0.841767i	$0.681515\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	44.2685			0.102237			0.0511184	−	0.998693i	$-0.483721\pi$
$433$	44.2685			0.102237			0.0511184	+	0.998693i	$0.483721\pi$
$434$	39.2239	+	140.629i	0.0903777	+	0.324031i
$435$		0			0
$436$	−178.941	+	309.935i	−0.410415	+	0.710860i
$437$	−114.532	−	198.375i	−0.262086	−	0.453947i
$438$	248.263	−	143.335i	0.566810	−	0.327248i
$439$	−344.558	−	198.931i	−0.784871	−	0.453146i	0.0532827	−	0.998579i	$-0.483032\pi$
$439$	−344.558	−	198.931i	−0.784871	−	0.453146i	−0.838154	+	0.545434i	$0.816365\pi$
$440$		0			0
$441$	−3.00000	−	146.969i	−0.00680272	−	0.333264i
$442$			473.823i			1.07200i
$443$	102.662	+	59.2721i	0.231743	+	0.133797i	0.611376	−	0.791340i	$-0.290616\pi$
$443$	102.662	+	59.2721i	0.231743	+	0.133797i	−0.379633	+	0.925137i	$0.623950\pi$
$444$	−17.9117	+	10.3413i	−0.0403416	+	0.0232913i
$445$		0			0
$446$	280.014	+	161.666i	0.627835	+	0.362481i
$447$	316.812			0.708752
$448$	−15.0451	−	53.9411i	−0.0335828	−	0.120404i
$449$	−713.897			−1.58997			−0.794985	−	0.606629i	$-0.792521\pi$
$449$	−713.897			−1.58997			−0.794985	+	0.606629i	$0.792521\pi$
$450$		0			0
$451$	183.088	−	105.706i	0.405961	−	0.234382i
$452$	30.1324	−	17.3970i	0.0666647	−	0.0384889i
$453$	−250.103	+	433.191i	−0.552104	+	0.956271i
$454$			239.762i			0.528109i
$455$		0			0
$456$	−83.3970			−0.182888
$457$	−108.406	−	62.5883i	−0.237213	−	0.136955i	0.376682	−	0.926342i	$-0.377065\pi$
$457$	−108.406	−	62.5883i	−0.237213	−	0.136955i	−0.613895	+	0.789388i	$0.710398\pi$
$458$	−24.5310	−	42.4889i	−0.0535610	−	0.0927704i
$459$	−48.7279	−	84.3992i	−0.106161	−	0.183876i
$460$		0			0
$461$			655.767i			1.42249i	0.702945	+	0.711244i	$0.251868\pi$
$461$			655.767i			1.42249i	−0.702945	+	0.711244i	$0.748132\pi$
$462$	73.4847	+	72.0000i	0.159058	+	0.155844i
$463$			869.396i			1.87775i	0.344265	+	0.938873i	$0.388128\pi$
$463$			869.396i			1.87775i	−0.344265	+	0.938873i	$0.611872\pi$
$464$	67.8823	−	117.576i	0.146298	−	0.253395i
$465$		0			0
$466$	179.948	+	311.680i	0.386155	+	0.668840i
$467$	−133.686	+	231.551i	−0.286266	+	0.495827i	−0.972915	−	0.231162i	$-0.925747\pi$
$467$	−133.686	+	231.551i	−0.286266	+	0.495827i	0.686649	+	0.726989i	$0.259081\pi$
$468$	−107.183			−0.229024
$469$	571.985	+	560.428i	1.21958	+	1.19494i
$470$		0			0
$471$	162.000	−	280.592i	0.343949	−	0.595737i
$472$	−38.6995	−	67.0294i	−0.0819904	−	0.142012i
$473$	80.4639	−	46.4558i	0.170114	−	0.0982153i
$474$	−187.393	−	108.192i	−0.395345	−	0.228252i
$475$		0			0
$476$	−254.309	−	65.3678i	−0.534262	−	0.137327i
$477$		−	103.632i		−	0.217259i
$478$	−241.455	−	139.404i	−0.505136	−	0.291640i
$479$	−235.331	+	135.868i	−0.491296	+	0.283650i	−0.725112	−	0.688631i	$-0.758212\pi$
$479$	−235.331	+	135.868i	−0.491296	+	0.283650i	0.233816	+	0.972281i	$0.424879\pi$
$480$		0			0
$481$	92.3680	+	53.3287i	0.192033	+	0.110870i
$482$	125.116			0.259576
$483$	157.145	−	43.8305i	0.325353	−	0.0907464i
$484$	170.000			0.351240
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	486.285	−	280.757i	0.998532	−	0.576503i	0.0907186	−	0.995877i	$-0.471084\pi$
$487$	486.285	−	280.757i	0.998532	−	0.576503i	0.907814	+	0.419374i	$0.137750\pi$
$488$	57.1067	−	98.9117i	0.117022	−	0.202688i
$489$		−	27.8148i		−	0.0568810i
$490$		0			0
$491$	−406.441			−0.827781			−0.413891	−	0.910327i	$-0.635830\pi$
$491$	−406.441			−0.827781			−0.413891	+	0.910327i	$0.635830\pi$
$492$	−105.706	−	61.0294i	−0.214850	−	0.124044i
$493$	−318.289	−	551.294i	−0.645618	−	1.11824i
$494$	215.033	+	372.448i	0.435289	+	0.753944i
$495$		0			0
$496$			58.9917i			0.118935i
$497$	34.9856	+	125.434i	0.0703935	+	0.252381i
$498$		−	185.574i		−	0.372638i
$499$	−185.713	+	321.665i	−0.372171	+	0.644619i	−0.989899	−	0.141773i	$-0.954720\pi$
$499$	−185.713	+	321.665i	−0.372171	+	0.644619i	0.617728	+	0.786391i	$0.288053\pi$
$500$		0			0
$501$	−152.522	−	264.176i	−0.304435	−	0.527297i
$502$	152.667	−	264.426i	0.304117	−	0.526746i
$503$	−64.6292			−0.128488			−0.0642438	−	0.997934i	$-0.520464\pi$
$503$	−64.6292			−0.128488			−0.0642438	+	0.997934i	$0.520464\pi$
$504$	14.7868	−	57.5270i	0.0293389	−	0.114141i
$505$		0			0
$506$	−57.0883	+	98.8799i	−0.112823	+	0.195415i
$507$	130.006	+	225.177i	0.256422	+	0.444135i
$508$	289.991	−	167.426i	0.570849	−	0.329580i
$509$	−871.889	−	503.385i	−1.71294	−	0.988969i	−0.930534	−	0.366205i	$-0.880657\pi$
$509$	−871.889	−	503.385i	−1.71294	−	0.988969i	−0.782410	−	0.622764i	$-0.786010\pi$
$510$		0			0
$511$	573.338	−	585.161i	1.12199	−	1.14513i
$512$		−	22.6274i		−	0.0441942i
$513$	−76.6050	−	44.2279i	−0.149328	−	0.0862143i
$514$	−5.27208	+	3.04384i	−0.0102570	+	0.00592186i
$515$		0			0
$516$	−46.4558	−	26.8213i	−0.0900307	−	0.0519793i
$517$	199.237			0.385371
$518$	−41.3653	+	42.2183i	−0.0798557	+	0.0815024i
$519$	400.368			0.771421
$520$		0			0
$521$	−322.294	+	186.077i	−0.618607	+	0.357153i	−0.776327	−	0.630331i	$-0.782919\pi$
$521$	−322.294	+	186.077i	−0.618607	+	0.357153i	0.157719	+	0.987484i	$0.449586\pi$
$522$	124.708	−	72.0000i	0.238904	−	0.137931i
$523$	318.642	−	551.904i	0.609258	−	1.05527i	−0.382105	−	0.924119i	$-0.624801\pi$
$523$	318.642	−	551.904i	0.609258	−	1.05527i	0.991363	−	0.131147i	$-0.0418660\pi$
$524$		−	3.56608i		−	0.00680549i
$525$		0			0
$526$	399.765			0.760009
$527$	239.545	+	138.302i	0.454545	+	0.262432i
$528$	20.7846	+	36.0000i	0.0393648	+	0.0681818i
$529$	−173.970	−	301.325i	−0.328866	−	0.569613i
$530$		0			0
$531$		−	82.0940i		−	0.154603i
$532$	−229.564	+	64.0294i	−0.431512	+	0.120356i
$533$			629.440i			1.18094i
$534$	−25.4558	+	44.0908i	−0.0476701	+	0.0825671i
$535$		0			0
$536$	161.782	+	280.214i	0.301832	+	0.522788i
$537$	73.8540	−	127.919i	0.137531	−	0.238210i
$538$	540.136			1.00397
$539$	257.558	+	141.773i	0.477845	+	0.263030i
$540$		0			0
$541$	−110.412	+	191.239i	−0.204088	+	0.353491i	−0.949842	−	0.312731i	$-0.898756\pi$
$541$	−110.412	+	191.239i	−0.204088	+	0.353491i	0.745754	+	0.666222i	$0.232090\pi$
$542$	−59.6283	−	103.279i	−0.110015	−	0.190552i
$543$	8.37983	−	4.83810i	0.0154325	−	0.00890994i
$544$	−91.8823	−	53.0482i	−0.168901	−	0.0975152i
$545$		0			0
$546$	−295.040	+	82.2917i	−0.540367	+	0.150717i
$547$			160.676i			0.293741i	0.989156	+	0.146870i	$0.0469200\pi$
$547$			160.676i			0.293741i	−0.989156	+	0.146870i	$0.953080\pi$
$548$	−174.886	−	100.971i	−0.319135	−	0.184253i
$549$	104.912	−	60.5708i	0.191096	−	0.110329i
$550$		0			0
$551$	−500.382	−	288.896i	−0.908134	−	0.524311i
$552$	65.9199			0.119420
$553$	−598.898	−	153.942i	−1.08300	−	0.278375i
$554$	193.914			0.350025
$555$		0			0
$556$	−243.426	+	140.542i	−0.437817	+	0.252774i
$557$	410.802	−	237.177i	0.737526	−	0.425811i	−0.0836431	−	0.996496i	$-0.526656\pi$
$557$	410.802	−	237.177i	0.737526	−	0.425811i	0.821169	+	0.570685i	$0.193322\pi$
$558$	−31.2851	+	54.1873i	−0.0560664	+	0.0971099i
$559$			276.627i			0.494860i
$560$		0			0
$561$	194.912			0.347436
$562$	−398.168	−	229.882i	−0.708484	−	0.409043i
$563$	−248.434	−	430.301i	−0.441269	−	0.764300i	0.556515	−	0.830837i	$-0.312138\pi$
$563$	−248.434	−	430.301i	−0.441269	−	0.764300i	−0.997784	+	0.0665378i	$0.978805\pi$
$564$	−57.5147	−	99.6184i	−0.101976	−	0.176628i
$565$		0			0
$566$			275.171i			0.486168i
$567$	44.0908	−	45.0000i	0.0777616	−	0.0793651i
$568$			52.6173i			0.0926361i
$569$	392.647	−	680.084i	0.690065	−	1.19523i	−0.281752	−	0.959487i	$-0.590915\pi$
$569$	392.647	−	680.084i	0.690065	−	1.19523i	0.971816	−	0.235740i	$-0.0757512\pi$
$570$		0			0
$571$	357.521	+	619.245i	0.626132	+	1.08449i	0.988321	+	0.152388i	$0.0486963\pi$
$571$	357.521	+	619.245i	0.626132	+	1.08449i	−0.362189	+	0.932105i	$0.617970\pi$
$572$	107.183	−	185.647i	0.187383	−	0.324557i
$573$	−321.117			−0.560414
$574$	−337.831	−	86.8364i	−0.588555	−	0.151283i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−386.315	−	669.117i	−0.669524	−	1.15965i	−0.978038	−	0.208429i	$-0.933165\pi$
$577$	−386.315	−	669.117i	−0.669524	−	1.15965i	0.308514	−	0.951220i	$-0.400168\pi$
$578$	−76.8705	+	44.3812i	−0.132994	+	0.0767841i
$579$	341.691	+	197.275i	0.590140	+	0.340717i
$580$		0			0
$581$	−142.477	−	510.823i	−0.245228	−	0.879214i
$582$			74.9117i			0.128714i
$583$	179.497	+	103.632i	0.307885	+	0.177757i
$584$	286.669	−	165.508i	0.490872	−	0.283405i
$585$		0			0
$586$	293.574	+	169.495i	0.500979	+	0.289240i
$587$	−436.477			−0.743572			−0.371786	−	0.928318i	$-0.621254\pi$
$587$	−436.477			−0.743572			−0.371786	+	0.928318i	$0.621254\pi$
$588$	−3.46410	−	169.706i	−0.00589133	−	0.288615i
$589$	251.059			0.426246
$590$		0			0
$591$	184.742	−	106.661i	0.312593	−	0.180475i
$592$	−20.6826	+	11.9411i	−0.0349369	+	0.0201708i
$593$	−417.076	+	722.397i	−0.703332	+	1.21821i	0.263958	+	0.964534i	$0.414972\pi$
$593$	−417.076	+	722.397i	−0.703332	+	1.21821i	−0.967290	+	0.253673i	$0.918361\pi$
$594$			44.0908i			0.0742270i
$595$		0			0
$596$	365.823			0.613798
$597$	−9.34783	−	5.39697i	−0.0156580	−	0.00904015i
$598$	−169.970	−	294.396i	−0.284230	−	0.492301i
$599$	436.794	+	756.549i	0.729205	+	1.26302i	0.957220	+	0.289363i	$0.0934434\pi$
$599$	436.794	+	756.549i	0.729205	+	1.26302i	−0.228014	+	0.973658i	$0.573223\pi$
$600$		0			0
$601$			198.982i			0.331085i	0.986203	+	0.165542i	$0.0529375\pi$
$601$			198.982i			0.331085i	−0.986203	+	0.165542i	$0.947063\pi$
$602$	−148.470	−	38.1630i	−0.246628	−	0.0633936i
$603$			343.191i			0.569139i
$604$	−288.794	+	500.206i	−0.478136	+	0.828155i
$605$		0			0
$606$	156.728	+	271.461i	0.258627	+	0.447955i
$607$	79.4748	−	137.654i	0.130930	−	0.226778i	−0.793105	−	0.609085i	$-0.791537\pi$
$607$	79.4748	−	137.654i	0.130930	−	0.226778i	0.924035	+	0.382307i	$0.124870\pi$
$608$	−96.2985			−0.158386
$609$	288.000	−	293.939i	0.472906	−	0.482658i
$610$		0			0
$611$	−296.595	+	513.718i	−0.485426	+	0.840782i
$612$	−56.2662	−	97.4558i	−0.0919382	−	0.159242i
$613$	−618.979	+	357.368i	−1.00975	+	0.582981i	−0.911119	−	0.412143i	$-0.864781\pi$
$613$	−618.979	+	357.368i	−1.00975	+	0.582981i	−0.0986338	+	0.995124i	$0.531447\pi$
$614$	661.695	+	382.030i	1.07768	+	0.622198i
$615$		0			0
$616$	84.8528	+	83.1384i	0.137748	+	0.134965i
$617$			639.381i			1.03627i	0.855298	+	0.518137i	$0.173374\pi$
$617$			639.381i			1.03627i	−0.855298	+	0.518137i	$0.826626\pi$
$618$	171.734	+	99.1508i	0.277887	+	0.160438i
$619$	−148.978	+	86.0126i	−0.240676	+	0.138954i	−0.615487	−	0.788147i	$-0.711041\pi$
$619$	−148.978	+	86.0126i	−0.240676	+	0.138954i	0.374812	+	0.927101i	$0.377707\pi$
$620$		0			0
$621$	60.5513	+	34.9593i	0.0975061	+	0.0562952i
$622$	571.619			0.919002
$623$	−36.2201	+	140.912i	−0.0581382	+	0.226182i
$624$	−123.765			−0.198341
$625$		0			0
$626$	160.805	−	92.8406i	0.256876	−	0.148308i
$627$	153.210	−	88.4558i	0.244354	−	0.141078i
$628$	187.061	−	324.000i	0.297869	−	0.515924i
$629$			111.980i			0.178029i
$630$		0			0
$631$	−1141.06			−1.80833			−0.904166	−	0.427180i	$-0.859507\pi$
$631$	−1141.06			−1.80833			−0.904166	+	0.427180i	$0.859507\pi$
$632$	−216.383	−	124.929i	−0.342379	−	0.197672i
$633$	−108.177	−	187.368i	−0.170895	−	0.295999i
$634$	−66.4264	−	115.054i	−0.104774	−	0.181473i
$635$		0			0
$636$		−	119.664i		−	0.188152i
$637$	−748.968	+	453.044i	−1.17577	+	0.711215i
$638$			288.000i			0.451411i
$639$	−27.9045	+	48.3321i	−0.0436691	+	0.0756371i
$640$		0			0
$641$	−114.551	−	198.409i	−0.178707	−	0.309530i	0.762731	−	0.646716i	$-0.223858\pi$
$641$	−114.551	−	198.409i	−0.178707	−	0.309530i	−0.941438	+	0.337186i	$0.890525\pi$
$642$	−207.540	+	359.470i	−0.323271	+	0.559922i
$643$	−707.670			−1.10058			−0.550288	−	0.834975i	$-0.685482\pi$
$643$	−707.670			−1.10058			−0.550288	+	0.834975i	$0.685482\pi$
$644$	181.456	−	50.6111i	0.281764	−	0.0785887i
$645$		0			0
$646$	−225.765	+	391.036i	−0.349481	+	0.605318i
$647$	−589.687	−	1021.37i	−0.911417	−	1.57862i	−0.812064	−	0.583568i	$-0.801656\pi$
$647$	−589.687	−	1021.37i	−0.911417	−	1.57862i	−0.0993530	−	0.995052i	$-0.531677\pi$
$648$	22.0454	−	12.7279i	0.0340207	−	0.0196419i
$649$	142.191	+	82.0940i	0.219092	+	0.126493i
$650$		0			0
$651$	−44.5143	+	173.180i	−0.0683783	+	0.266021i
$652$		−	32.1177i		−	0.0492604i
$653$	134.029	+	77.3818i	0.205252	+	0.118502i	0.599103	−	0.800672i	$-0.295524\pi$
$653$	134.029	+	77.3818i	0.205252	+	0.118502i	−0.393851	+	0.919174i	$0.628857\pi$
$654$	−379.591	+	219.157i	−0.580415	+	0.335103i
$655$		0			0
$656$	−122.059	−	70.4707i	−0.186065	−	0.107425i
$657$	351.096			0.534393
$658$	−234.803	−	230.059i	−0.356843	−	0.349634i
$659$	−591.308			−0.897280			−0.448640	−	0.893712i	$-0.648092\pi$
$659$	−591.308			−0.897280			−0.448640	+	0.893712i	$0.648092\pi$
$660$		0			0
$661$	140.441	−	81.0837i	0.212468	−	0.122668i	−0.389990	−	0.920819i	$-0.627522\pi$
$661$	140.441	−	81.0837i	0.212468	−	0.122668i	0.602458	+	0.798151i	$0.294188\pi$
$662$	320.109	−	184.815i	0.483548	−	0.279176i
$663$	−290.156	+	502.566i	−0.437642	+	0.758017i
$664$		−	214.282i		−	0.322714i
$665$		0			0
$666$	−25.3310			−0.0380345
$667$	395.519	+	228.353i	0.592983	+	0.342359i
$668$	−176.117	−	305.044i	−0.263648	−	0.456652i
$669$	198.000	+	342.946i	0.295964	+	0.512625i
$670$		0			0
$671$			242.283i			0.361078i
$672$	17.0743	−	66.4264i	0.0254082	−	0.0988488i
$673$			42.3238i			0.0628883i	0.999506	+	0.0314441i	$0.0100106\pi$
$673$			42.3238i			0.0628883i	−0.999506	+	0.0314441i	$0.989989\pi$
$674$	96.3539	−	166.890i	0.142958	−	0.247611i
$675$		0			0
$676$	150.118	+	260.012i	0.222068	+	0.384632i
$677$	248.677	−	430.721i	0.367322	−	0.636220i	−0.621824	−	0.783157i	$-0.713608\pi$
$677$	248.677	−	430.721i	0.367322	−	0.636220i	0.989146	+	0.146937i	$0.0469415\pi$
$678$	42.6137			0.0628521
$679$	57.5147	+	206.207i	0.0847050	+	0.303693i
$680$		0			0
$681$	−146.823	+	254.306i	−0.215600	+	0.373430i
$682$	−62.5701	−	108.375i	−0.0917451	−	0.158907i
$683$	1053.23	−	608.080i	1.54206	−	0.890308i	0.543350	−	0.839506i	$-0.317156\pi$
$683$	1053.23	−	608.080i	1.54206	−	0.890308i	0.998709	−	0.0508015i	$-0.0161776\pi$
$684$	−88.4558	−	51.0700i	−0.129321	−	0.0746638i
$685$		0			0
$686$	−139.830	−	464.484i	−0.203834	−	0.677091i
$687$		−	60.0883i		−	0.0874648i
$688$	−53.6426	−	30.9706i	−0.0779689	−	0.0450154i
$689$	−534.418	+	308.546i	−0.775642	+	0.447817i
$690$		0			0
$691$	−932.182	−	538.196i	−1.34903	−	0.778865i	−0.360921	−	0.932596i	$-0.617538\pi$
$691$	−932.182	−	538.196i	−1.34903	−	0.778865i	−0.988113	+	0.153731i	$0.950871\pi$
$692$	462.305			0.668070
$693$	33.8515	+	121.368i	0.0488477	+	0.175134i
$694$	455.647			0.656552
$695$		0			0
$696$	144.000	−	83.1384i	0.206897	−	0.119452i
$697$	−572.315	+	330.426i	−0.821112	+	0.474069i
$698$	245.009	−	424.368i	0.351015	−	0.607976i
$699$			440.781i			0.630589i
$700$		0			0
$701$	−695.897			−0.992720			−0.496360	−	0.868117i	$-0.665330\pi$
$701$	−695.897			−0.992720			−0.496360	+	0.868117i	$0.665330\pi$
$702$	−113.685	−	65.6360i	−0.161944	−	0.0934986i
$703$	50.8194	+	88.0219i	0.0722894	+	0.125209i
$704$	24.0000	+	41.5692i	0.0340909	+	0.0590472i
$705$		0			0
$706$		−	877.649i		−	1.24313i
$707$	639.839	+	626.912i	0.905006	+	0.886721i
$708$		−	94.7939i		−	0.133890i
$709$	127.412	−	220.684i	0.179707	−	0.311261i	−0.762073	−	0.647491i	$-0.775818\pi$
$709$	127.412	−	220.684i	0.179707	−	0.311261i	0.941780	+	0.336229i	$0.109152\pi$
$710$		0			0
$711$	−132.507	−	229.509i	−0.186367	−	0.322798i
$712$	−29.3939	+	50.9117i	−0.0412835	+	0.0715052i
$713$	−198.446			−0.278325
$714$	−229.706	−	225.065i	−0.321717	−	0.315217i
$715$		0			0
$716$	85.2792	−	147.708i	0.119105	−	0.206296i
$717$	−170.734	−	295.721i	−0.238123	−	0.412442i
$718$	24.7833	−	14.3087i	0.0345172	−	0.0199285i
$719$	964.925	+	557.100i	1.34204	+	0.774826i	0.987106	−	0.160066i	$-0.0511709\pi$
$719$	964.925	+	557.100i	1.34204	+	0.774826i	0.354931	+	0.934892i	$0.384504\pi$
$720$		0			0
$721$	548.852	+	141.078i	0.761238	+	0.195669i
$722$		−	100.701i		−	0.139474i
$723$	132.705	+	76.6173i	0.183548	+	0.105971i
$724$	9.67619	−	5.58655i	0.0133649	−	0.00771623i
$725$		0			0
$726$	180.312	+	104.103i	0.248364	+	0.143393i
$727$	−398.345			−0.547930			−0.273965	−	0.961740i	$-0.588335\pi$
$727$	−398.345			−0.547930			−0.273965	+	0.961740i	$0.588335\pi$
$728$	−340.683	+	95.0223i	−0.467971	+	0.130525i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−251.522	+	145.216i	−0.344079	+	0.198654i
$732$	121.142	−	69.9411i	0.165494	−	0.0955480i
$733$	−472.569	+	818.514i	−0.644706	+	1.11666i	0.339663	+	0.940547i	$0.389687\pi$
$733$	−472.569	+	818.514i	−0.644706	+	1.11666i	−0.984369	+	0.176116i	$0.943646\pi$
$734$			440.632i			0.600316i
$735$		0			0
$736$	76.1177			0.103421
$737$	−594.424	−	343.191i	−0.806546	−	0.465659i
$738$	−74.7455	−	129.463i	−0.101281	−	0.175424i
$739$	96.3162	+	166.825i	0.130333	+	0.225744i	0.923805	−	0.382863i	$-0.125062\pi$
$739$	96.3162	+	166.825i	0.130333	+	0.225744i	−0.793472	+	0.608607i	$0.791729\pi$
$740$		0			0
$741$			526.721i			0.710825i
$742$	−91.8744	−	329.397i	−0.123820	−	0.443931i
$743$		−	911.616i		−	1.22694i	−0.789718	−	0.613470i	$-0.789773\pi$
$743$		−	911.616i		−	1.22694i	0.789718	−	0.613470i	$-0.210227\pi$
$744$	−36.1249	+	62.5701i	−0.0485550	+	0.0840997i
$745$		0			0
$746$	481.810	+	834.519i	0.645858	+	1.11866i
$747$	113.640	−	196.831i	0.152129	−	0.263495i
$748$	225.065			0.300889
$749$	−295.301	+	1148.85i	−0.394260	+	1.53384i
$750$		0			0
$751$	195.831	−	339.189i	0.260760	−	0.451650i	−0.705684	−	0.708527i	$-0.749360\pi$
$751$	195.831	−	339.189i	0.260760	−	0.451650i	0.966444	+	0.256877i	$0.0826935\pi$
$752$	−66.4123	−	115.029i	−0.0883142	−	0.152965i
$753$	323.855	−	186.978i	0.430086	−	0.248310i
$754$	−742.587	−	428.733i	−0.984863	−	0.568611i
$755$		0			0
$756$	50.9117	−	51.9615i	0.0673435	−	0.0687322i
$757$			152.823i			0.201879i	0.994893	+	0.100940i	$0.0321849\pi$
$757$			152.823i			0.201879i	−0.994893	+	0.100940i	$0.967815\pi$
$758$	765.195	+	441.785i	1.00949	+	0.582830i
$759$	−121.103	+	69.9186i	−0.159555	+	0.0921194i
$760$		0			0
$761$	−109.331	−	63.1223i	−0.143667	−	0.0829465i	0.426443	−	0.904514i	$-0.359766\pi$
$761$	−109.331	−	63.1223i	−0.143667	−	0.0829465i	−0.570111	+	0.821568i	$0.693100\pi$
$762$	410.109			0.538201
$763$	−876.629	+	894.706i	−1.14892	+	1.17262i
$764$	−370.794			−0.485332
$765$		0			0
$766$	−169.383	+	97.7931i	−0.221126	+	0.127667i
$767$	−423.347	+	244.419i	−0.551951	+	0.318669i
$768$	13.8564	−	24.0000i	0.0180422	−	0.0312500i
$769$			369.148i			0.480037i	0.970768	+	0.240018i	$0.0771535\pi$
$769$			369.148i			0.480037i	−0.970768	+	0.240018i	$0.922847\pi$
$770$		0			0
$771$	−7.45584			−0.00967036
$772$	394.551	+	227.794i	0.511076	+	0.295070i
$773$	−701.853	−	1215.65i	−0.907961	−	1.57263i	−0.816893	−	0.576789i	$-0.804305\pi$
$773$	−701.853	−	1215.65i	−0.907961	−	1.57263i	−0.0910674	−	0.995845i	$-0.529028\pi$
$774$	−32.8492	−	56.8966i	−0.0424409	−	0.0735098i
$775$		0			0
$776$			86.5006i			0.111470i
$777$	−69.7278	+	19.4483i	−0.0897398	+	0.0250299i
$778$		−	797.013i		−	1.02444i
$779$	−299.912	+	519.462i	−0.384996	+	0.666832i
$780$		0			0
$781$	−55.8091	−	96.6642i	−0.0714585	−	0.123770i
$782$	178.452	−	309.088i	0.228200	−	0.395254i
$783$	176.363			0.225240
$784$	−4.00000	−	195.959i	−0.00510204	−	0.249948i
$785$		0			0
$786$	2.18377	−	3.78239i	0.00277833	−	0.00481221i
$787$	−113.253	−	196.161i	−0.143905	−	0.249251i	0.785059	−	0.619421i	$-0.212633\pi$
$787$	−113.253	−	196.161i	−0.143905	−	0.249251i	−0.928964	+	0.370170i	$0.879299\pi$
$788$	213.322	−	123.161i	0.270713	−	0.156296i
$789$	424.014	+	244.805i	0.537407	+	0.310272i
$790$		0			0
$791$	117.302	−	32.7174i	0.148295	−	0.0413621i
$792$			50.9117i			0.0642824i
$793$	−624.709	−	360.676i	−0.787780	−	0.454825i
$794$	−555.224	+	320.559i	−0.699274	+	0.403726i
$795$		0			0
$796$	−10.7939	−	6.23188i	−0.0135602	−	0.00782900i
$797$	−688.414			−0.863756			−0.431878	−	0.901932i	$-0.642149\pi$
$797$	−688.414			−0.863756			−0.431878	+	0.901932i	$0.642149\pi$
$798$	−282.700	−	72.6655i	−0.354260	−	0.0910595i
$799$	−622.794			−0.779467
$800$		0			0
$801$	−54.0000	+	31.1769i	−0.0674157	+	0.0389225i
$802$	337.724	−	194.985i	0.421102	−	0.243123i
$803$	−351.096	+	608.117i	−0.437231	+	0.757306i
$804$			396.283i			0.492889i
$805$		0			0
$806$	372.582			0.462260
$807$	572.901	+	330.765i	0.709914	+	0.409869i
$808$	180.974	+	313.456i	0.223977	+	0.387940i
$809$	12.6396	+	21.8924i	0.0156237	+	0.0270611i	0.873732	−	0.486408i	$-0.161693\pi$
$809$	12.6396	+	21.8924i	0.0156237	+	0.0270611i	−0.858108	+	0.513470i	$0.828360\pi$
$810$		0			0
$811$			1527.62i			1.88362i	0.336145	+	0.941810i	$0.390877\pi$
$811$			1527.62i			1.88362i	−0.336145	+	0.941810i	$0.609123\pi$
$812$	332.554	−	339.411i	0.409549	−	0.417994i
$813$		−	146.059i		−	0.179654i
$814$	25.3310	−	43.8745i	0.0311191	−	0.0538999i
$815$		0			0
$816$	−64.9706	−	112.532i	−0.0796208	−	0.137907i
$817$	−131.806	+	228.294i	−0.161329	+	0.279430i
$818$	616.359			0.753495
$819$	−363.331	−	93.3909i	−0.443627	−	0.114030i
$820$		0			0
$821$	58.3310	−	101.032i	0.0710487	−	0.123060i	−0.828312	−	0.560266i	$-0.810699\pi$
$821$	58.3310	−	101.032i	0.0710487	−	0.123060i	0.899361	+	0.437206i	$0.144032\pi$
$822$	−123.663	−	214.191i	−0.150442	−	0.260573i
$823$	109.042	−	62.9554i	0.132493	−	0.0764950i	−0.432288	−	0.901735i	$-0.642294\pi$
$823$	109.042	−	62.9554i	0.132493	−	0.0764950i	0.564782	+	0.825240i	$0.308960\pi$
$824$	198.302	+	114.489i	0.240657	+	0.138943i
$825$		0			0
$826$	−72.7797	−	260.937i	−0.0881110	−	0.315904i
$827$			1434.40i			1.73446i	0.497910	+	0.867229i	$0.334101\pi$
$827$			1434.40i			1.73446i	−0.497910	+	0.867229i	$0.665899\pi$
$828$	69.9186	+	40.3675i	0.0844428	+	0.0487531i
$829$	32.3225	−	18.6614i	0.0389898	−	0.0225107i	−0.480378	−	0.877061i	$-0.659501\pi$
$829$	32.3225	−	18.6614i	0.0389898	−	0.0225107i	0.519368	+	0.854551i	$0.326167\pi$
$830$		0			0
$831$	205.677	+	118.747i	0.247505	+	0.142897i
$832$	−142.911			−0.171768
$833$	−805.101	−	443.169i	−0.966508	−	0.532015i
$834$	−344.257			−0.412778
$835$		0			0
$836$	176.912	−	102.140i	0.211617	−	0.122177i
$837$	−66.3657	+	38.3162i	−0.0792899	+	0.0457781i
$838$	−213.021	+	368.963i	−0.254202	+	0.440290i
$839$		−	3.07370i		−	0.00366353i	−0.999998	−	0.00183177i	$-0.999417\pi$
$839$		−	3.07370i		−	0.00366353i	0.999998	−	0.00183177i	$-0.000583069\pi$
$840$		0			0
$841$	311.000			0.369798
$842$	−249.596	−	144.104i	−0.296432	−	0.171145i
$843$	−281.547	−	487.654i	−0.333982	−	0.578474i
$844$	−124.912	−	216.353i	−0.148000	−	0.256343i
$845$		0			0
$846$		−	140.882i		−	0.166527i
$847$	576.267	+	148.124i	0.680363	+	0.174881i
$848$		−	138.177i		−	0.162944i
$849$	−168.507	+	291.863i	−0.198477	+	0.343773i
$850$		0			0
$851$	−40.1695	−	69.5756i	−0.0472027	−	0.0817574i
$852$	−32.2214	+	55.8091i	−0.0378185	+	0.0655036i
$853$	155.257			0.182013			0.0910063	−	0.995850i	$-0.470992\pi$
$853$	155.257			0.182013			0.0910063	+	0.995850i	$0.470992\pi$
$854$	279.765	−	285.533i	0.327593	−	0.334348i
$855$		0			0
$856$	−239.647	+	415.080i	−0.279961	+	0.484907i
$857$	801.931	+	1388.98i	0.935742	+	1.62075i	0.773306	+	0.634033i	$0.218602\pi$
$857$	801.931	+	1388.98i	0.935742	+	1.62075i	0.162436	+	0.986719i	$0.448065\pi$
$858$	227.370	−	131.272i	0.265000	−	0.152998i
$859$	−545.367	−	314.868i	−0.634886	−	0.366551i	0.147756	−	0.989024i	$-0.452795\pi$
$859$	−545.367	−	314.868i	−0.634886	−	0.366551i	−0.782642	+	0.622472i	$0.786128\pi$
$860$		0			0
$861$	−305.147	−	298.982i	−0.354410	−	0.347250i
$862$			559.632i			0.649226i
$863$	−891.496	−	514.706i	−1.03302	−	0.596414i	−0.115172	−	0.993346i	$-0.536742\pi$
$863$	−891.496	−	514.706i	−1.03302	−	0.596414i	−0.917848	+	0.396931i	$0.870075\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$		0			0
$866$	54.2176	+	31.3026i	0.0626070	+	0.0361462i
$867$	−108.711			−0.125388
$868$	−51.4007	+	199.971i	−0.0592174	+	0.230381i
$869$	530.029			0.609929
$870$		0			0
$871$	1769.79	−	1021.79i	2.03190	−	1.17312i
$872$	−438.314	+	253.061i	−0.502654	+	0.290208i
$873$	−45.8739	+	79.4558i	−0.0525474	+	0.0910147i
$874$		−	323.944i		−	0.370646i
$875$		0			0
$876$	405.411			0.462798
$877$	561.566	+	324.220i	0.640326	+	0.369693i	0.784740	−	0.619825i	$-0.212796\pi$
$877$	561.566	+	324.220i	0.640326	+	0.369693i	−0.144414	+	0.989517i	$0.546130\pi$
$878$	−281.331	−	487.279i	−0.320422	−	0.554988i
$879$	207.588	+	359.553i	0.236164	+	0.409048i
$880$		0			0
$881$		−	363.857i		−	0.413005i	−0.978446	−	0.206502i	$-0.933792\pi$
$881$		−	363.857i		−	0.413005i	0.978446	−	0.206502i	$-0.0662082\pi$
$882$	100.249	−	182.121i	0.113661	−	0.206487i
$883$			1536.16i			1.73971i	0.493312	+	0.869853i	$0.335786\pi$
$883$			1536.16i			1.73971i	−0.493312	+	0.869853i	$0.664214\pi$
$884$	−335.044	+	580.313i	−0.379009	+	0.656462i
$885$		0			0
$886$	83.8234	+	145.186i	0.0946088	+	0.163867i
$887$	562.755	−	974.720i	0.634447	−	1.09890i	−0.352185	−	0.935931i	$-0.614561\pi$
$887$	562.755	−	974.720i	0.634447	−	1.09890i	0.986632	−	0.162964i	$-0.0521056\pi$
$888$	−29.2497			−0.0329388
$889$	1128.90	−	314.868i	1.26985	−	0.354183i
$890$		0			0
$891$	−27.0000	+	46.7654i	−0.0303030	+	0.0524864i
$892$	228.631	+	396.000i	0.256312	+	0.443946i
$893$	−489.546	+	282.640i	−0.548204	+	0.316506i
$894$	388.014	+	224.020i	0.434020	+	0.250582i
$895$		0			0
$896$	19.7157	−	76.7026i	0.0220042	−	0.0856056i
$897$		−	416.339i		−	0.464146i
$898$	−874.341	−	504.801i	−0.973654	−	0.562139i
$899$	−433.499	+	250.281i	−0.482201	+	0.278399i
$900$		0			0
$901$	−561.088	−	323.944i	−0.622740	−	0.359539i
$902$	298.982			0.331466
$903$	−134.106	−	131.397i	−0.148512	−	0.145512i
$904$	49.2061			0.0544315
$905$		0			0
$906$	−612.624	+	353.699i	−0.676186	+	0.390396i
$907$	−203.426	+	117.448i	−0.224285	+	0.129491i	−0.607933	−	0.793989i	$-0.708001\pi$
$907$	−203.426	+	117.448i	−0.224285	+	0.129491i	0.383648	+	0.923479i	$0.374668\pi$
$908$	−169.537	+	293.647i	−0.186715	+	0.323400i
$909$			383.903i			0.422336i
$910$		0			0
$911$	224.278			0.246189			0.123095	−	0.992395i	$-0.460718\pi$
$911$	224.278			0.246189			0.123095	+	0.992395i	$0.460718\pi$
$912$	−102.140	−	58.9706i	−0.111996	−	0.0646607i
$913$	227.280	+	393.661i	0.248938	+	0.431173i
$914$	−88.5132	−	153.309i	−0.0968416	−	0.167735i
$915$		0			0
$916$		−	69.3840i		−	0.0757467i
$917$	3.10719	−	12.0883i	0.00338843	−	0.0131825i
$918$		−	137.823i		−	0.150134i
$919$	−466.081	+	807.276i	−0.507161	+	0.878428i	0.492805	+	0.870140i	$0.335972\pi$
$919$	−466.081	+	807.276i	−0.507161	+	0.878428i	−0.999966	+	0.00828836i	$0.997362\pi$
$920$		0			0
$921$	467.889	+	810.407i	0.508023	+	0.879921i
$922$	−463.697	+	803.147i	−0.502925	+	0.871092i
$923$	332.322			0.360046
$924$	39.0883	+	140.143i	0.0423034	+	0.151670i
$925$		0			0
$926$	−614.756	+	1064.79i	−0.663883	+	1.14988i
$927$	121.434	+	210.331i	0.130997	+	0.226894i
$928$	166.277	−	96.0000i	0.179178	−	0.103448i
$929$	618.390	+	357.028i	0.665651	+	0.384314i	0.794427	−	0.607360i	$-0.207771\pi$
$929$	618.390	+	357.028i	0.665651	+	0.384314i	−0.128776	+	0.991674i	$0.541105\pi$
$930$		0			0
$931$	−833.970	+	17.0233i	−0.895778	+	0.0182850i
$932$			508.971i			0.546106i
$933$	606.294	+	350.044i	0.649832	+	0.375181i
$934$	−327.463	+	189.061i	−0.350603	+	0.202421i
$935$		0			0
$936$	−131.272	−	75.7900i	−0.140248	−	0.0809722i
$937$	−1723.25			−1.83912			−0.919559	−	0.392952i	$-0.871454\pi$
$937$	−1723.25			−1.83912			−0.919559	+	0.392952i	$0.871454\pi$
$938$	304.253	+	1090.84i	0.324363	+	1.16294i
$939$	227.412			0.242185
$940$		0			0
$941$	835.508	−	482.381i	0.887893	−	0.512625i	0.0146405	−	0.999893i	$-0.495340\pi$
$941$	835.508	−	482.381i	0.887893	−	0.512625i	0.873253	+	0.487267i	$0.162006\pi$
$942$	396.817	−	229.103i	0.421250	−	0.243209i
$943$	237.061	−	410.601i	0.251390	−	0.435420i
$944$		−	109.459i		−	0.115952i
$945$		0			0
$946$	131.397			0.138897
$947$	1257.26	+	725.881i	1.32763	+	0.766506i	0.984932	−	0.172940i	$-0.0553268\pi$
$947$	1257.26	+	725.881i	1.32763	+	0.766506i	0.342695	+	0.939447i	$0.388660\pi$
$948$	−153.006	−	265.014i	−0.161399	−	0.279551i
$949$	−1045.32	−	1810.55i	−1.10150	−	1.90785i
$950$		0			0
$951$		−	162.711i		−	0.171094i
$952$	−265.241	−	259.882i	−0.278615	−	0.272986i
$953$			1147.43i			1.20401i	0.798491	+	0.602007i	$0.205632\pi$
$953$			1147.43i			1.20401i	−0.798491	+	0.602007i	$0.794368\pi$
$954$	73.2792	−	126.923i	0.0768126	−	0.133043i
$955$		0			0
$956$	−197.147	−	341.469i	−0.206221	−	0.357185i
$957$	−176.363	+	305.470i	−0.184288	+	0.319196i
$958$	−384.294			−0.401142
$959$	−504.853	−	494.653i	−0.526437	−	0.515801i
$960$		0			0
$961$	−371.749	+	643.889i	−0.386836	+	0.670020i
$962$	75.4181	+	130.628i	0.0783972	+	0.135788i
$963$	−440.259	+	254.184i	−0.457175	+	0.263950i
$964$	153.235	+	88.4701i	0.158957	+	0.0917739i
$965$		0			0
$966$	223.456	+	57.4374i	0.231321	+	0.0594590i
$967$		−	412.190i		−	0.426257i	−0.977024	−	0.213128i	$-0.931635\pi$
$967$		−	412.190i		−	0.426257i	0.977024	−	0.213128i	$-0.0683652\pi$
$968$	208.207	+	120.208i	0.215089	+	0.124182i
$969$	−478.919	+	276.504i	−0.494240	+	0.285350i
$970$		0			0
$971$	869.595	+	502.061i	0.895566	+	0.517056i	0.875759	−	0.482748i	$-0.160361\pi$
$971$	869.595	+	502.061i	0.895566	+	0.517056i	0.0198073	+	0.999804i	$0.493695\pi$
$972$	31.1769			0.0320750
$973$	−947.626	+	264.309i	−0.973922	+	0.271643i
$974$	794.101			0.815298
$975$		0			0
$976$	139.882	−	80.7611i	0.143322	−	0.0827470i
$977$	1375.45	−	794.117i	1.40783	−	0.812812i	0.412652	−	0.910889i	$-0.364603\pi$
$977$	1375.45	−	794.117i	1.40783	−	0.812812i	0.995179	+	0.0980772i	$0.0312692\pi$
$978$	19.6680	−	34.0660i	0.0201105	−	0.0348323i
$979$		−	124.708i		−	0.127383i
$980$		0			0
$981$	−536.823			−0.547221
$982$	−497.786	−	287.397i	−0.506911	−	0.292665i
$983$	416.767	+	721.861i	0.423974	+	0.734345i	0.996324	−	0.0856648i	$-0.0273014\pi$
$983$	416.767	+	721.861i	0.423974	+	0.734345i	−0.572350	+	0.820009i	$0.693968\pi$
$984$	−86.3087	−	149.491i	−0.0877121	−	0.151922i
$985$		0			0
$986$		−	900.259i		−	0.913041i
$987$	−108.164	−	387.801i	−0.109589	−	0.392909i
$988$			608.205i			0.615592i
$989$	104.184	−	180.452i	0.105343	−	0.182459i
$990$		0			0
$991$	−33.4483	−	57.9341i	−0.0337520	−	0.0584602i	0.848656	−	0.528945i	$-0.177412\pi$
$991$	−33.4483	−	57.9341i	−0.0337520	−	0.0584602i	−0.882408	+	0.470485i	$0.844079\pi$
$992$	−41.7134	+	72.2498i	−0.0420498	+	0.0728324i
$993$	452.702			0.455893
$994$	−45.8465	+	178.363i	−0.0461233	+	0.179439i
$995$		0			0
$996$	131.220	−	227.280i	0.131747	−	0.228193i
$997$	−732.453	−	1268.65i	−0.734657	−	1.27246i	−0.954874	−	0.297012i	$-0.904010\pi$
$997$	−732.453	−	1268.65i	−0.734657	−	1.27246i	0.220217	−	0.975451i	$-0.429323\pi$
$998$	−454.903	+	262.638i	−0.455814	+	0.263164i
$999$	−26.8675	−	15.5120i	−0.0268944	−	0.0155275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.a.649.4		8
5.2	odd	4		42.3.g.a.19.1	✓	4
5.3	odd	4		1050.3.p.a.901.2		4
5.4	even	2	inner	1050.3.q.a.649.1		8
7.3	odd	6	inner	1050.3.q.a.199.1		8
15.2	even	4		126.3.n.a.19.2		4
20.7	even	4		336.3.bh.e.145.2		4
35.2	odd	12		294.3.c.a.97.4		4
35.3	even	12		1050.3.p.a.451.2		4
35.12	even	12		294.3.c.a.97.3		4
35.17	even	12		42.3.g.a.31.1	yes	4
35.24	odd	6	inner	1050.3.q.a.199.4		8
35.27	even	4		294.3.g.a.19.1		4
35.32	odd	12		294.3.g.a.31.1		4
60.47	odd	4		1008.3.cg.h.145.1		4
105.2	even	12		882.3.c.b.685.2		4
105.17	odd	12		126.3.n.a.73.2		4
105.32	even	12		882.3.n.e.325.2		4
105.47	odd	12		882.3.c.b.685.1		4
105.62	odd	4		882.3.n.e.19.2		4
140.47	odd	12		2352.3.f.e.97.4		4
140.87	odd	12		336.3.bh.e.241.2		4
140.107	even	12		2352.3.f.e.97.1		4
420.227	even	12		1008.3.cg.h.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.1	✓	4	5.2	odd	4
42.3.g.a.31.1	yes	4	35.17	even	12
126.3.n.a.19.2		4	15.2	even	4
126.3.n.a.73.2		4	105.17	odd	12
294.3.c.a.97.3		4	35.12	even	12
294.3.c.a.97.4		4	35.2	odd	12
294.3.g.a.19.1		4	35.27	even	4
294.3.g.a.31.1		4	35.32	odd	12
336.3.bh.e.145.2		4	20.7	even	4
336.3.bh.e.241.2		4	140.87	odd	12
882.3.c.b.685.1		4	105.47	odd	12
882.3.c.b.685.2		4	105.2	even	12
882.3.n.e.19.2		4	105.62	odd	4
882.3.n.e.325.2		4	105.32	even	12
1008.3.cg.h.145.1		4	60.47	odd	4
1008.3.cg.h.577.1		4	420.227	even	12
1050.3.p.a.451.2		4	35.3	even	12
1050.3.p.a.901.2		4	5.3	odd	4
1050.3.q.a.199.1		8	7.3	odd	6	inner
1050.3.q.a.199.4		8	35.24	odd	6	inner
1050.3.q.a.649.1		8	5.4	even	2	inner
1050.3.q.a.649.4		8	1.1	even	1	trivial
2352.3.f.e.97.1		4	140.107	even	12
2352.3.f.e.97.4		4	140.47	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(1.88064 + 6.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(1.88064 + 6.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(-1.73205 + 3.00000i) q^{12} +17.8639 q^{13} +(-2.46447 + 9.58783i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(9.37769 + 16.2426i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(14.7426 + 8.51167i) q^{19} +(-8.48528 + 8.66025i) q^{21} -8.48528i q^{22} +(-11.6531 - 6.72792i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(21.8787 + 12.6317i) q^{26} -5.19615 q^{27} +(-9.79796 + 10.0000i) q^{28} -33.9411 q^{29} +(12.7721 - 7.37396i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(5.19615 - 9.00000i) q^{33} +26.5241i q^{34} -6.00000 q^{36} +(5.17066 + 2.98528i) q^{37} +(12.0373 + 20.8492i) q^{38} +(15.4706 + 26.7958i) q^{39} +35.2354i q^{41} +(-16.5160 + 4.60660i) q^{42} +15.4853i q^{43} +(6.00000 - 10.3923i) q^{44} +(-9.51472 - 16.4800i) q^{46} +(-16.6031 + 28.7574i) q^{47} -6.92820 q^{48} +(-41.9264 + 25.3609i) q^{49} +(-16.2426 + 28.1331i) q^{51} +(17.8639 + 30.9411i) q^{52} +(-29.9161 + 17.2721i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-19.0711 + 5.31925i) q^{56} +29.4853i q^{57} +(-41.5692 - 24.0000i) q^{58} +(-23.6985 + 13.6823i) q^{59} +(-34.9706 - 20.1903i) q^{61} +20.8567 q^{62} +(-20.3389 - 5.22792i) q^{63} -8.00000 q^{64} +(12.7279 - 7.34847i) q^{66} +(99.0707 - 57.1985i) q^{67} +(-18.7554 + 32.4853i) q^{68} -23.3062i q^{69} +18.6030 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-58.5161 - 101.353i) q^{73} +(4.22183 + 7.31242i) q^{74} +34.0467i q^{76} +(29.3939 - 30.0000i) q^{77} +43.7574i q^{78} +(-44.1690 + 76.5030i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-24.9152 + 43.1543i) q^{82} -75.7601 q^{83} +(-23.4853 - 6.03668i) q^{84} +(-10.9497 + 18.9655i) q^{86} +(-29.3939 - 50.9117i) q^{87} +(14.6969 - 8.48528i) q^{88} +(18.0000 + 10.3923i) q^{89} +(33.5955 + 120.450i) q^{91} -26.9117i q^{92} +(22.1219 + 12.7721i) q^{93} +(-40.6690 + 23.4803i) q^{94} +(-8.48528 - 4.89898i) q^{96} +30.5826 q^{97} +(-69.2820 + 1.41421i) q^{98} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 12 * q^9	\( 8 q + 8 q^{4} - 12 q^{9} - 24 q^{11} - 48 q^{14} - 16 q^{16} + 84 q^{19} + 192 q^{26} + 204 q^{31} - 48 q^{36} - 12 q^{39} + 48 q^{44} - 144 q^{46} + 4 q^{49} - 96 q^{51} - 96 q^{56} + 48 q^{59} - 144 q^{61} - 64 q^{64} + 624 q^{71} + 96 q^{74} + 20 q^{79} - 36 q^{81} - 120 q^{84} - 48 q^{86} + 144 q^{89} - 444 q^{91} + 48 q^{94} + 144 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 - 12 * q^9 - 24 * q^11 - 48 * q^14 - 16 * q^16 + 84 * q^19 + 192 * q^26 + 204 * q^31 - 48 * q^36 - 12 * q^39 + 48 * q^44 - 144 * q^46 + 4 * q^49 - 96 * q^51 - 96 * q^56 + 48 * q^59 - 144 * q^61 - 64 * q^64 + 624 * q^71 + 96 * q^74 + 20 * q^79 - 36 * q^81 - 120 * q^84 - 48 * q^86 + 144 * q^89 - 444 * q^91 + 48 * q^94 + 144 * q^99

Introduction

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