LMFDB - Embedded newform 1050.3.q.a.199.4

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			199.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.a.649.4

$q$-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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

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	−0.969559	−	0.244857i	$-0.921259\pi$
$11$	−3.00000	+	5.19615i	−0.272727	+	0.472377i	0.696832	+	0.717234i	$0.254592\pi$
$12$	−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	−0.446528	−	0.894770i	$-0.647340\pi$
$17$	9.37769	−	16.2426i	0.551629	−	0.955449i	0.998157	−	0.0606799i	$-0.0193269\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	14.7426	−	8.51167i	0.775928	−	0.447983i	−0.0590569	−	0.998255i	$-0.518809\pi$
$19$	14.7426	−	8.51167i	0.775928	−	0.447983i	0.834985	+	0.550272i	$0.185476\pi$
$20$		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	−0.731458	−	0.681886i	$-0.761160\pi$
$23$	−11.6531	+	6.72792i	−0.506657	+	0.292518i	0.224802	+	0.974405i	$0.427827\pi$
$24$	−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	0.691650	−	0.722233i	$-0.256884\pi$
$31$	12.7721	+	7.37396i	0.412003	+	0.237870i	−0.279647	+	0.960103i	$0.590218\pi$
$32$	−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	−0.428496	−	0.903544i	$-0.640956\pi$
$37$	5.17066	−	2.98528i	0.139748	−	0.0806833i	0.568244	+	0.822860i	$0.307623\pi$
$38$	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	$-0.858619\pi$
$41$		−	35.2354i		−	0.859399i	0.902972	−	0.429700i	$-0.141381\pi$
$42$	−16.5160	−	4.60660i	−0.393239	−	0.109681i
$43$		−	15.4853i		−	0.360123i	−0.983655	−	0.180061i	$-0.942370\pi$
$43$		−	15.4853i		−	0.360123i	0.983655	−	0.180061i	$-0.0576296\pi$
$44$	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	0.633561	−	0.773693i	$-0.281592\pi$
$47$	−16.6031	−	28.7574i	−0.353257	−	0.611859i	−0.986818	+	0.161834i	$0.948259\pi$
$48$	−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	0.190477	−	0.981692i	$-0.438997\pi$
$53$	−29.9161	−	17.2721i	−0.564455	−	0.325888i	−0.754932	+	0.655803i	$0.772330\pi$
$54$	−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	0.285535	−	0.958368i	$-0.407829\pi$
$59$	−23.6985	−	13.6823i	−0.401669	−	0.231904i	−0.687204	+	0.726465i	$0.741162\pi$
$60$		0			0
$61$	−34.9706	+	20.1903i	−0.573288	+	0.330988i	−0.758461	−	0.651718i	$-0.774049\pi$
$61$	−34.9706	+	20.1903i	−0.573288	+	0.330988i	0.185174	+	0.982706i	$0.440715\pi$
$62$	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	0.999709	−	0.0241291i	$-0.00768127\pi$
$67$	99.0707	+	57.1985i	1.47867	+	0.853709i	0.478958	+	0.877838i	$0.341015\pi$
$68$	−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	0.116979	+	0.993134i	$0.462679\pi$
$73$	−58.5161	+	101.353i	−0.801590	+	1.38839i	−0.918569	+	0.395260i	$0.870654\pi$
$74$	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	−0.997572	−	0.0696469i	$-0.977813\pi$
$79$	−44.1690	−	76.5030i	−0.559102	−	0.968393i	0.438470	−	0.898746i	$-0.355521\pi$
$80$		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	−0.395456	−	0.918485i	$-0.629413\pi$
$89$	18.0000	−	10.3923i	0.202247	−	0.116767i	0.597703	+	0.801717i	$0.296080\pi$
$90$		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	0.935500	−	0.353326i	$-0.114949\pi$
$101$	110.823	+	63.9839i	1.09726	+	0.633504i	0.161761	+	0.986830i	$0.448283\pi$
$102$	−39.7862	−	22.9706i	−0.390061	−	0.225202i
$103$	40.4781	+	70.1102i	0.392992	+	0.680681i	0.992843	−	0.119430i	$-0.0381068\pi$
$103$	40.4781	+	70.1102i	0.392992	+	0.680681i	−0.599851	+	0.800112i	$0.704774\pi$
$104$		−	50.5266i		−	0.485833i
$105$		0			0
$106$	−48.8528			−0.460876
$107$	146.753	−	84.7279i	1.37152	−	0.791850i	0.380404	−	0.924820i	$-0.375785\pi$
$107$	146.753	−	84.7279i	1.37152	−	0.791850i	0.991120	+	0.132971i	$0.0424516\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	89.4706	−	154.968i	0.820831	−	1.42172i	−0.0842335	−	0.996446i	$-0.526844\pi$
$109$	89.4706	−	154.968i	0.820831	−	1.42172i	0.905064	−	0.425275i	$-0.139823\pi$
$110$		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	$0.0245270\pi$
$113$			17.3970i			0.153955i	−0.997033	+	0.0769777i	$0.975473\pi$
$114$	−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	$0.229088\pi$
$127$			167.426i			1.31832i	−0.752004	+	0.659159i	$0.770912\pi$
$128$	−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	−0.505882	−	0.862603i	$-0.668833\pi$
$131$	−1.54416	+	0.891519i	−0.0117874	+	0.00680549i	0.494095	+	0.869408i	$0.335500\pi$
$132$	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	0.145677	−	0.989332i	$-0.453464\pi$
$137$	−87.4431	−	50.4853i	−0.638271	−	0.368506i	−0.783948	+	0.620826i	$0.786797\pi$
$138$	16.4800	+	28.5442i	0.119420	+	0.206842i
$139$		−	140.542i		−	1.01110i	−0.862799	−	0.505548i	$-0.831290\pi$
$139$		−	140.542i		−	1.01110i	0.862799	−	0.505548i	$-0.168710\pi$
$140$		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	0.990594	+	0.136833i	$0.0436922\pi$
$149$	91.4558	+	158.406i	0.613798	+	1.06313i	−0.376797	+	0.926296i	$0.622974\pi$
$150$		0			0
$151$	144.397	−	250.103i	0.956271	−	1.65631i	0.224840	−	0.974396i	$-0.427814\pi$
$151$	144.397	−	250.103i	0.956271	−	1.65631i	0.731432	−	0.681915i	$-0.238852\pi$
$152$	−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	0.397705	+	0.917513i	$0.369807\pi$
$157$	−93.5307	+	162.000i	−0.595737	+	1.03185i	−0.993442	+	0.114334i	$0.963527\pi$
$158$	−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	−0.542054	−	0.840344i	$-0.682353\pi$
$163$	−13.9074	+	8.02944i	−0.0853214	+	0.0492604i	0.456732	+	0.889604i	$0.349020\pi$
$164$	−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	0.978443	+	0.206517i	$0.0662128\pi$
$173$	115.576	+	200.184i	0.668070	+	1.15713i	−0.310373	+	0.950615i	$0.600454\pi$
$174$			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	−0.960201	−	0.279311i	$-0.909894\pi$
$179$	−42.6396	+	73.8540i	−0.238210	+	0.412592i	0.721991	+	0.691903i	$0.243227\pi$
$180$		0			0
$181$			5.58655i			0.0308649i	0.999881	+	0.0154325i	$0.00491250\pi$
$181$			5.58655i			0.0308649i	−0.999881	+	0.0154325i	$0.995087\pi$
$182$	−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	0.514526	−	0.857475i	$-0.327968\pi$
$191$	−92.6985	−	160.558i	−0.485332	−	0.840620i	−0.999858	+	0.0168547i	$0.994635\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	197.275	+	113.897i	1.02215	+	0.590140i	0.914727	−	0.404073i	$-0.132406\pi$
$193$	197.275	+	113.897i	1.02215	+	0.590140i	0.107425	+	0.994213i	$0.465739\pi$
$194$	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	$0.101197\pi$
$197$			123.161i			0.625185i	−0.949887	+	0.312593i	$0.898803\pi$
$198$	22.0454	−	12.7279i	0.111340	−	0.0642824i
$199$	−5.39697	−	3.11594i	−0.0271205	−	0.0156580i	0.486378	−	0.873748i	$-0.338318\pi$
$199$	−5.39697	−	3.11594i	−0.0271205	−	0.0156580i	−0.513499	+	0.858090i	$0.671651\pi$
$200$		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	−0.616661	−	0.787229i	$-0.711515\pi$
$227$	84.7685	−	146.823i	0.373430	−	0.646799i	0.990091	+	0.140430i	$0.0448484\pi$
$228$	−51.0700	−	29.4853i	−0.223991	−	0.129321i
$229$	−30.0442	+	17.3460i	−0.131197	+	0.0757467i	−0.564162	−	0.825664i	$-0.690801\pi$
$229$	−30.0442	+	17.3460i	−0.131197	+	0.0757467i	0.432965	+	0.901411i	$0.357467\pi$
$230$		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	0.0540833	−	0.998536i	$-0.482776\pi$
$233$	220.391	−	127.243i	0.945883	−	0.546106i	0.891800	+	0.452431i	$0.149443\pi$
$234$	−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	0.650462	−	0.759538i	$-0.274575\pi$
$241$	76.6173	+	44.2350i	0.317914	+	0.183548i	−0.332548	+	0.943086i	$0.607908\pi$
$242$	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	$0.141517\pi$
$251$			215.903i			0.860172i	−0.902788	+	0.430086i	$0.858483\pi$
$252$	−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	0.861808	−	0.507235i	$-0.169332\pi$
$257$	−2.15232	−	3.72792i	−0.00837477	−	0.0145055i	−0.870182	+	0.492730i	$0.835999\pi$
$258$	−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	0.887070	−	0.461635i	$-0.152737\pi$
$263$	244.805	+	141.338i	0.930817	+	0.537407i	0.0437468	+	0.999043i	$0.486071\pi$
$264$	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	0.966948	−	0.254974i	$-0.0820669\pi$
$269$	330.765	+	190.967i	1.22961	+	0.709914i	0.262660	+	0.964888i	$0.415400\pi$
$270$		0			0
$271$	−73.0294	+	42.1636i	−0.269481	+	0.155585i	−0.628652	−	0.777687i	$-0.716393\pi$
$271$	−73.0294	+	42.1636i	−0.269481	+	0.155585i	0.359171	+	0.933272i	$0.383060\pi$
$272$	−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	0.698789	−	0.715328i	$-0.253723\pi$
$277$	118.747	+	68.5589i	0.428691	+	0.247505i	−0.270098	+	0.962833i	$0.587056\pi$
$278$	−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	−0.641357	−	0.767242i	$-0.721628\pi$
$283$	97.2876	−	168.507i	0.343773	−	0.595432i	0.985130	+	0.171811i	$0.0549617\pi$
$284$	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	0.942810	−	0.333330i	$-0.108172\pi$
$311$	350.044	+	202.098i	1.12554	+	0.649832i	0.182732	+	0.983163i	$0.441506\pi$
$312$	−75.7900	−	43.7574i	−0.242917	−	0.140248i
$313$	65.6482	+	113.706i	0.209739	+	0.363278i	0.951632	−	0.307240i	$-0.0994053\pi$
$313$	65.6482	+	113.706i	0.209739	+	0.363278i	−0.741893	+	0.670518i	$0.766072\pi$
$314$			264.545i			0.842500i
$315$		0			0
$316$	−176.676			−0.559102
$317$	−81.3554	+	46.9706i	−0.256642	+	0.148172i	−0.622802	−	0.782380i	$-0.714006\pi$
$317$	−81.3554	+	46.9706i	−0.256642	+	0.148172i	0.366160	+	0.930552i	$0.380672\pi$
$318$	−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	0.993078	−	0.117460i	$-0.0374754\pi$
$331$	130.684	+	226.351i	0.394815	+	0.683840i	−0.598263	+	0.801300i	$0.704142\pi$
$332$	−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	$0.0648005\pi$
$337$			136.265i			0.404347i	−0.979350	+	0.202173i	$0.935200\pi$
$338$	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	0.844906	−	0.534915i	$-0.179657\pi$
$347$	279.026	+	161.095i	0.804108	+	0.464252i	−0.0407975	+	0.999167i	$0.512990\pi$
$348$	58.7878	+	101.823i	0.168930	+	0.292596i
$349$			346.495i			0.992821i	0.868088	+	0.496411i	$0.165349\pi$
$349$			346.495i			0.992821i	−0.868088	+	0.496411i	$0.834651\pi$
$350$		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	−0.0266116	+	0.999646i	$0.508472\pi$
$353$	−310.296	+	537.448i	−0.879025	+	1.52252i	−0.852413	+	0.522869i	$0.824862\pi$
$354$	−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	0.879773	−	0.475394i	$-0.157695\pi$
$359$	10.1177	+	17.5245i	0.0281831	+	0.0488146i	−0.851590	+	0.524209i	$0.824361\pi$
$360$		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	−0.571885	−	0.820334i	$-0.693788\pi$
$367$	155.787	−	269.831i	0.424488	−	0.735234i	0.996372	+	0.0850998i	$0.0271209\pi$
$368$	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	0.587457	−	0.809255i	$-0.300129\pi$
$373$	590.094	−	340.691i	1.58202	−	0.913380i	0.994564	−	0.104125i	$-0.0332043\pi$
$374$	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	0.761519	−	0.648143i	$-0.224454\pi$
$383$	−69.1502	−	119.772i	−0.180549	−	0.312720i	−0.942068	+	0.335423i	$0.891121\pi$
$384$			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	0.234838	+	0.972035i	$0.424544\pi$
$389$	−281.787	+	488.069i	−0.724388	+	1.25468i	−0.959226	+	0.282642i	$0.908789\pi$
$390$		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	−0.996468	−	0.0839711i	$-0.973240\pi$
$397$	−226.669	−	392.603i	−0.570955	−	0.988923i	0.425513	−	0.904952i	$-0.360094\pi$
$398$	−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	0.985140	−	0.171752i	$-0.0549429\pi$
$401$	137.875	+	238.807i	0.343828	+	0.595528i	−0.641312	+	0.767280i	$0.721610\pi$
$402$	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	0.884540	−	0.466465i	$-0.154473\pi$
$409$	377.441	+	217.916i	0.922839	+	0.532801i	0.0382993	+	0.999266i	$0.487806\pi$
$410$		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	$-0.882949\pi$
$419$		−	301.257i		−	0.718991i	0.933147	−	0.359496i	$-0.117051\pi$
$420$		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	−0.539840	−	0.841767i	$-0.681515\pi$
$431$	197.860	−	342.703i	0.459072	−	0.795136i	0.998912	+	0.0466317i	$0.0148487\pi$
$432$	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	−0.838154	−	0.545434i	$-0.816365\pi$
$439$	−344.558	+	198.931i	−0.784871	+	0.453146i	0.0532827	+	0.998579i	$0.483032\pi$
$440$		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	−0.379633	−	0.925137i	$-0.623950\pi$
$443$	102.662	−	59.2721i	0.231743	−	0.133797i	0.611376	+	0.791340i	$0.290616\pi$
$444$	−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	−0.613895	−	0.789388i	$-0.710398\pi$
$457$	−108.406	+	62.5883i	−0.237213	+	0.136955i	0.376682	+	0.926342i	$0.377065\pi$
$458$	−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	$-0.748132\pi$
$461$		−	655.767i		−	1.42249i	0.702945	−	0.711244i	$-0.251868\pi$
$462$	73.4847	−	72.0000i	0.159058	−	0.155844i
$463$		−	869.396i		−	1.87775i	−0.344265	−	0.938873i	$-0.611872\pi$
$463$		−	869.396i		−	1.87775i	0.344265	−	0.938873i	$-0.388128\pi$
$464$	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	0.686649	−	0.726989i	$-0.259081\pi$
$467$	−133.686	−	231.551i	−0.286266	−	0.495827i	−0.972915	+	0.231162i	$0.925747\pi$
$468$	−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	0.233816	−	0.972281i	$-0.424879\pi$
$479$	−235.331	−	135.868i	−0.491296	−	0.283650i	−0.725112	+	0.688631i	$0.758212\pi$
$480$		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	0.907814	−	0.419374i	$-0.137750\pi$
$487$	486.285	+	280.757i	0.998532	+	0.576503i	0.0907186	+	0.995877i	$0.471084\pi$
$488$	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	0.617728	−	0.786391i	$-0.288053\pi$
$499$	−185.713	−	321.665i	−0.372171	−	0.644619i	−0.989899	+	0.141773i	$0.954720\pi$
$500$		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	−0.782410	+	0.622764i	$0.786010\pi$
$509$	−871.889	+	503.385i	−1.71294	+	0.988969i	−0.930534	+	0.366205i	$0.880657\pi$
$510$		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	0.157719	−	0.987484i	$-0.449586\pi$
$521$	−322.294	−	186.077i	−0.618607	−	0.357153i	−0.776327	+	0.630331i	$0.782919\pi$
$522$	124.708	+	72.0000i	0.238904	+	0.137931i
$523$	318.642	+	551.904i	0.609258	+	1.05527i	0.991363	+	0.131147i	$0.0418660\pi$
$523$	318.642	+	551.904i	0.609258	+	1.05527i	−0.382105	+	0.924119i	$0.624801\pi$
$524$			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	0.745754	−	0.666222i	$-0.232090\pi$
$541$	−110.412	−	191.239i	−0.204088	−	0.353491i	−0.949842	+	0.312731i	$0.898756\pi$
$542$	−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	$-0.953080\pi$
$547$		−	160.676i		−	0.293741i	0.989156	−	0.146870i	$-0.0469200\pi$
$548$	−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	0.821169	−	0.570685i	$-0.193322\pi$
$557$	410.802	+	237.177i	0.737526	+	0.425811i	−0.0836431	+	0.996496i	$0.526656\pi$
$558$	−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	−0.997784	−	0.0665378i	$-0.978805\pi$
$563$	−248.434	+	430.301i	−0.441269	+	0.764300i	0.556515	+	0.830837i	$0.312138\pi$
$564$	−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	0.971816	+	0.235740i	$0.0757512\pi$
$569$	392.647	+	680.084i	0.690065	+	1.19523i	−0.281752	+	0.959487i	$0.590915\pi$
$570$		0			0
$571$	357.521	−	619.245i	0.626132	−	1.08449i	−0.362189	−	0.932105i	$-0.617970\pi$
$571$	357.521	−	619.245i	0.626132	−	1.08449i	0.988321	−	0.152388i	$-0.0486963\pi$
$572$	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	0.308514	+	0.951220i	$0.400168\pi$
$577$	−386.315	+	669.117i	−0.669524	+	1.15965i	−0.978038	+	0.208429i	$0.933165\pi$
$578$	−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	−0.967290	−	0.253673i	$-0.918361\pi$
$593$	−417.076	−	722.397i	−0.703332	−	1.21821i	0.263958	−	0.964534i	$-0.414972\pi$
$594$		−	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	−0.228014	−	0.973658i	$-0.573223\pi$
$599$	436.794	−	756.549i	0.729205	−	1.26302i	0.957220	−	0.289363i	$-0.0934434\pi$
$600$		0			0
$601$		−	198.982i		−	0.331085i	−0.986203	−	0.165542i	$-0.947063\pi$
$601$		−	198.982i		−	0.331085i	0.986203	−	0.165542i	$-0.0529375\pi$
$602$	−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	0.924035	−	0.382307i	$-0.124870\pi$
$607$	79.4748	+	137.654i	0.130930	+	0.226778i	−0.793105	+	0.609085i	$0.791537\pi$
$608$	−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	−0.0986338	−	0.995124i	$-0.531447\pi$
$613$	−618.979	−	357.368i	−1.00975	−	0.582981i	−0.911119	+	0.412143i	$0.864781\pi$
$614$	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	$-0.826626\pi$
$617$		−	639.381i		−	1.03627i	0.855298	−	0.518137i	$-0.173374\pi$
$618$	171.734	−	99.1508i	0.277887	−	0.160438i
$619$	−148.978	−	86.0126i	−0.240676	−	0.138954i	0.374812	−	0.927101i	$-0.377707\pi$
$619$	−148.978	−	86.0126i	−0.240676	−	0.138954i	−0.615487	+	0.788147i	$0.711041\pi$
$620$		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	−0.941438	−	0.337186i	$-0.890525\pi$
$641$	−114.551	+	198.409i	−0.178707	+	0.309530i	0.762731	+	0.646716i	$0.223858\pi$
$642$	−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	−0.0993530	+	0.995052i	$0.531677\pi$
$647$	−589.687	+	1021.37i	−0.911417	+	1.57862i	−0.812064	+	0.583568i	$0.801656\pi$
$648$	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	−0.393851	−	0.919174i	$-0.628857\pi$
$653$	134.029	−	77.3818i	0.205252	−	0.118502i	0.599103	+	0.800672i	$0.295524\pi$
$654$	−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	0.602458	−	0.798151i	$-0.294188\pi$
$661$	140.441	+	81.0837i	0.212468	+	0.122668i	−0.389990	+	0.920819i	$0.627522\pi$
$662$	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	$-0.989989\pi$
$673$		−	42.3238i		−	0.0628883i	0.999506	−	0.0314441i	$-0.0100106\pi$
$674$	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	0.989146	−	0.146937i	$-0.0469415\pi$
$677$	248.677	+	430.721i	0.367322	+	0.636220i	−0.621824	+	0.783157i	$0.713608\pi$
$678$	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	0.998709	+	0.0508015i	$0.0161776\pi$
$683$	1053.23	+	608.080i	1.54206	+	0.890308i	0.543350	+	0.839506i	$0.317156\pi$
$684$	−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	−0.988113	−	0.153731i	$-0.950871\pi$
$691$	−932.182	+	538.196i	−1.34903	+	0.778865i	−0.360921	+	0.932596i	$0.617538\pi$
$692$	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	0.941780	−	0.336229i	$-0.109152\pi$
$709$	127.412	+	220.684i	0.179707	+	0.311261i	−0.762073	+	0.647491i	$0.775818\pi$
$710$		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	0.354931	−	0.934892i	$-0.384504\pi$
$719$	964.925	−	557.100i	1.34204	−	0.774826i	0.987106	+	0.160066i	$0.0511709\pi$
$720$		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	−0.984369	−	0.176116i	$-0.943646\pi$
$733$	−472.569	−	818.514i	−0.644706	−	1.11666i	0.339663	−	0.940547i	$-0.389687\pi$
$734$		−	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	−0.793472	−	0.608607i	$-0.791729\pi$
$739$	96.3162	−	166.825i	0.130333	−	0.225744i	0.923805	+	0.382863i	$0.125062\pi$
$740$		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	$0.210227\pi$
$743$			911.616i			1.22694i	−0.789718	+	0.613470i	$0.789773\pi$
$744$	−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	0.966444	−	0.256877i	$-0.0826935\pi$
$751$	195.831	+	339.189i	0.260760	+	0.451650i	−0.705684	+	0.708527i	$0.749360\pi$
$752$	−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	$-0.967815\pi$
$757$		−	152.823i		−	0.201879i	0.994893	−	0.100940i	$-0.0321849\pi$
$758$	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	−0.570111	−	0.821568i	$-0.693100\pi$
$761$	−109.331	+	63.1223i	−0.143667	+	0.0829465i	0.426443	+	0.904514i	$0.359766\pi$
$762$	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	$-0.922847\pi$
$769$		−	369.148i		−	0.480037i	0.970768	−	0.240018i	$-0.0771535\pi$
$770$		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	−0.0910674	+	0.995845i	$0.529028\pi$
$773$	−701.853	+	1215.65i	−0.907961	+	1.57263i	−0.816893	+	0.576789i	$0.804305\pi$
$774$	−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	−0.928964	−	0.370170i	$-0.879299\pi$
$787$	−113.253	+	196.161i	−0.143905	+	0.249251i	0.785059	+	0.619421i	$0.212633\pi$
$788$	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	−0.858108	−	0.513470i	$-0.828360\pi$
$809$	12.6396	−	21.8924i	0.0156237	−	0.0270611i	0.873732	+	0.486408i	$0.161693\pi$
$810$		0			0
$811$		−	1527.62i		−	1.88362i	−0.336145	−	0.941810i	$-0.609123\pi$
$811$		−	1527.62i		−	1.88362i	0.336145	−	0.941810i	$-0.390877\pi$
$812$	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	0.899361	−	0.437206i	$-0.144032\pi$
$821$	58.3310	+	101.032i	0.0710487	+	0.123060i	−0.828312	+	0.560266i	$0.810699\pi$
$822$	−123.663	+	214.191i	−0.150442	+	0.260573i
$823$	109.042	+	62.9554i	0.132493	+	0.0764950i	0.564782	−	0.825240i	$-0.308960\pi$
$823$	109.042	+	62.9554i	0.132493	+	0.0764950i	−0.432288	+	0.901735i	$0.642294\pi$
$824$	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	$-0.665899\pi$
$827$		−	1434.40i		−	1.73446i	0.497910	−	0.867229i	$-0.334101\pi$
$828$	69.9186	−	40.3675i	0.0844428	−	0.0487531i
$829$	32.3225	+	18.6614i	0.0389898	+	0.0225107i	0.519368	−	0.854551i	$-0.326167\pi$
$829$	32.3225	+	18.6614i	0.0389898	+	0.0225107i	−0.480378	+	0.877061i	$0.659501\pi$
$830$		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	$0.000583069\pi$
$839$			3.07370i			0.00366353i	−0.999998	+	0.00183177i	$0.999417\pi$
$840$		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	0.162436	−	0.986719i	$-0.448065\pi$
$857$	801.931	−	1388.98i	0.935742	−	1.62075i	0.773306	−	0.634033i	$-0.218602\pi$
$858$	227.370	+	131.272i	0.265000	+	0.152998i
$859$	−545.367	+	314.868i	−0.634886	+	0.366551i	−0.782642	−	0.622472i	$-0.786128\pi$
$859$	−545.367	+	314.868i	−0.634886	+	0.366551i	0.147756	+	0.989024i	$0.452795\pi$
$860$		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	−0.917848	−	0.396931i	$-0.870075\pi$
$863$	−891.496	+	514.706i	−1.03302	+	0.596414i	−0.115172	+	0.993346i	$0.536742\pi$
$864$	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	−0.144414	−	0.989517i	$-0.546130\pi$
$877$	561.566	−	324.220i	0.640326	−	0.369693i	0.784740	+	0.619825i	$0.212796\pi$
$878$	−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	$0.0662082\pi$
$881$			363.857i			0.413005i	−0.978446	+	0.206502i	$0.933792\pi$
$882$	100.249	+	182.121i	0.113661	+	0.206487i
$883$		−	1536.16i		−	1.73971i	−0.493312	−	0.869853i	$-0.664214\pi$
$883$		−	1536.16i		−	1.73971i	0.493312	−	0.869853i	$-0.335786\pi$
$884$	−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	0.986632	+	0.162964i	$0.0521056\pi$
$887$	562.755	+	974.720i	0.634447	+	1.09890i	−0.352185	+	0.935931i	$0.614561\pi$
$888$	−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	0.383648	−	0.923479i	$-0.374668\pi$
$907$	−203.426	−	117.448i	−0.224285	−	0.129491i	−0.607933	+	0.793989i	$0.708001\pi$
$908$	−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	−0.999966	−	0.00828836i	$-0.997362\pi$
$919$	−466.081	−	807.276i	−0.507161	−	0.878428i	0.492805	−	0.870140i	$-0.335972\pi$
$920$		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	−0.128776	−	0.991674i	$-0.541105\pi$
$929$	618.390	−	357.028i	0.665651	−	0.384314i	0.794427	+	0.607360i	$0.207771\pi$
$930$		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	0.873253	−	0.487267i	$-0.162006\pi$
$941$	835.508	+	482.381i	0.887893	+	0.512625i	0.0146405	+	0.999893i	$0.495340\pi$
$942$	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	0.342695	−	0.939447i	$-0.388660\pi$
$947$	1257.26	−	725.881i	1.32763	−	0.766506i	0.984932	+	0.172940i	$0.0553268\pi$
$948$	−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	$-0.794368\pi$
$953$		−	1147.43i		−	1.20401i	0.798491	−	0.602007i	$-0.205632\pi$
$954$	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	$0.0683652\pi$
$967$			412.190i			0.426257i	−0.977024	+	0.213128i	$0.931635\pi$
$968$	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	0.0198073	−	0.999804i	$-0.493695\pi$
$971$	869.595	−	502.061i	0.895566	−	0.517056i	0.875759	+	0.482748i	$0.160361\pi$
$972$	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	0.995179	−	0.0980772i	$-0.0312692\pi$
$977$	1375.45	+	794.117i	1.40783	+	0.812812i	0.412652	+	0.910889i	$0.364603\pi$
$978$	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	−0.572350	−	0.820009i	$-0.693968\pi$
$983$	416.767	−	721.861i	0.423974	−	0.734345i	0.996324	+	0.0856648i	$0.0273014\pi$
$984$	−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	−0.882408	−	0.470485i	$-0.844079\pi$
$991$	−33.4483	+	57.9341i	−0.0337520	+	0.0584602i	0.848656	+	0.528945i	$0.177412\pi$
$992$	−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	0.220217	+	0.975451i	$0.429323\pi$
$997$	−732.453	+	1268.65i	−0.734657	+	1.27246i	−0.954874	+	0.297012i	$0.904010\pi$
$998$	−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.199.4		8
5.2	odd	4		1050.3.p.a.451.2		4
5.3	odd	4		42.3.g.a.31.1	yes	4
5.4	even	2	inner	1050.3.q.a.199.1		8
7.5	odd	6	inner	1050.3.q.a.649.1		8
15.8	even	4		126.3.n.a.73.2		4
20.3	even	4		336.3.bh.e.241.2		4
35.3	even	12		294.3.c.a.97.4		4
35.12	even	12		1050.3.p.a.901.2		4
35.13	even	4		294.3.g.a.31.1		4
35.18	odd	12		294.3.c.a.97.3		4
35.19	odd	6	inner	1050.3.q.a.649.4		8
35.23	odd	12		294.3.g.a.19.1		4
35.33	even	12		42.3.g.a.19.1	✓	4
60.23	odd	4		1008.3.cg.h.577.1		4
105.23	even	12		882.3.n.e.19.2		4
105.38	odd	12		882.3.c.b.685.2		4
105.53	even	12		882.3.c.b.685.1		4
105.68	odd	12		126.3.n.a.19.2		4
105.83	odd	4		882.3.n.e.325.2		4
140.3	odd	12		2352.3.f.e.97.1		4
140.103	odd	12		336.3.bh.e.145.2		4
140.123	even	12		2352.3.f.e.97.4		4
420.383	even	12		1008.3.cg.h.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.1	✓	4	35.33	even	12
42.3.g.a.31.1	yes	4	5.3	odd	4
126.3.n.a.19.2		4	105.68	odd	12
126.3.n.a.73.2		4	15.8	even	4
294.3.c.a.97.3		4	35.18	odd	12
294.3.c.a.97.4		4	35.3	even	12
294.3.g.a.19.1		4	35.23	odd	12
294.3.g.a.31.1		4	35.13	even	4
336.3.bh.e.145.2		4	140.103	odd	12
336.3.bh.e.241.2		4	20.3	even	4
882.3.c.b.685.1		4	105.53	even	12
882.3.c.b.685.2		4	105.38	odd	12
882.3.n.e.19.2		4	105.23	even	12
882.3.n.e.325.2		4	105.83	odd	4
1008.3.cg.h.145.1		4	420.383	even	12
1008.3.cg.h.577.1		4	60.23	odd	4
1050.3.p.a.451.2		4	5.2	odd	4
1050.3.p.a.901.2		4	35.12	even	12
1050.3.q.a.199.1		8	5.4	even	2	inner
1050.3.q.a.199.4		8	1.1	even	1	trivial
1050.3.q.a.649.1		8	7.5	odd	6	inner
1050.3.q.a.649.4		8	35.19	odd	6	inner
2352.3.f.e.97.1		4	140.3	odd	12
2352.3.f.e.97.4		4	140.123	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
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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