LMFDB - Embedded newform 400.3.r.g.51.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(51,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("400.51");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			51.9
Character	$\chi$	$=$	400.51
Dual form			400.3.r.g.251.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.755534 + 1.85180i) q^{2} +(1.37405 - 1.37405i) q^{3} +(-2.85834 - 2.79820i) q^{4} +(1.50632 + 3.58260i) q^{6} -5.00956 q^{7} +(7.34128 - 3.17893i) q^{8} +5.22398i q^{9} +O(q^{10})$	\(q+(-0.755534 + 1.85180i) q^{2} +(1.37405 - 1.37405i) q^{3} +(-2.85834 - 2.79820i) q^{4} +(1.50632 + 3.58260i) q^{6} -5.00956 q^{7} +(7.34128 - 3.17893i) q^{8} +5.22398i q^{9} +(-6.42909 - 6.42909i) q^{11} +(-7.77235 + 0.0826298i) q^{12} +(11.0519 + 11.0519i) q^{13} +(3.78490 - 9.27672i) q^{14} +(0.340161 + 15.9964i) q^{16} +14.8302 q^{17} +(-9.67378 - 3.94690i) q^{18} +(-17.5407 + 17.5407i) q^{19} +(-6.88338 + 6.88338i) q^{21} +(16.7628 - 7.04800i) q^{22} +4.37435 q^{23} +(5.71926 - 14.4553i) q^{24} +(-28.8160 + 12.1158i) q^{26} +(19.5444 + 19.5444i) q^{27} +(14.3190 + 14.0178i) q^{28} +(18.8676 + 18.8676i) q^{29} +32.9924i q^{31} +(-29.8791 - 11.4559i) q^{32} -17.6678 q^{33} +(-11.2048 + 27.4627i) q^{34} +(14.6177 - 14.9319i) q^{36} +(18.0984 - 18.0984i) q^{37} +(-19.2293 - 45.7346i) q^{38} +30.3717 q^{39} +76.1027i q^{41} +(-7.54602 - 17.9473i) q^{42} +(19.1807 + 19.1807i) q^{43} +(0.386620 + 36.3664i) q^{44} +(-3.30497 + 8.10042i) q^{46} +59.1180i q^{47} +(22.4472 + 21.5124i) q^{48} -23.9043 q^{49} +(20.3775 - 20.3775i) q^{51} +(-0.664617 - 62.5155i) q^{52} +(21.5406 - 21.5406i) q^{53} +(-50.9589 + 21.4259i) q^{54} +(-36.7766 + 15.9251i) q^{56} +48.2036i q^{57} +(-49.1941 + 20.6839i) q^{58} +(-53.6021 - 53.6021i) q^{59} +(-25.4876 - 25.4876i) q^{61} +(-61.0955 - 24.9269i) q^{62} -26.1699i q^{63} +(43.7888 - 46.6749i) q^{64} +(13.3486 - 32.7172i) q^{66} +(5.92820 - 5.92820i) q^{67} +(-42.3898 - 41.4980i) q^{68} +(6.01056 - 6.01056i) q^{69} -25.9177 q^{71} +(16.6067 + 38.3507i) q^{72} -31.2154i q^{73} +(19.8407 + 47.1886i) q^{74} +(99.2197 - 1.05483i) q^{76} +(32.2069 + 32.2069i) q^{77} +(-22.9469 + 56.2423i) q^{78} -122.054i q^{79} +6.69413 q^{81} +(-140.927 - 57.4982i) q^{82} +(-115.988 + 115.988i) q^{83} +(38.9361 - 0.413939i) q^{84} +(-50.0105 + 21.0271i) q^{86} +51.8499 q^{87} +(-67.6354 - 26.7601i) q^{88} +85.3925i q^{89} +(-55.3652 - 55.3652i) q^{91} +(-12.5033 - 12.2403i) q^{92} +(45.3332 + 45.3332i) q^{93} +(-109.475 - 44.6657i) q^{94} +(-56.7963 + 25.3144i) q^{96} +16.3915 q^{97} +(18.0605 - 44.2659i) q^{98} +(33.5855 - 33.5855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{4} - 4 q^{6}+O(q^{10}) $ 44 * q + 4 * q^4 - 4 * q^6	$ 44 q + 4 q^{4} - 4 q^{6} - 4 q^{11} - 4 q^{14} - 32 q^{16} + 36 q^{19} + 32 q^{21} - 16 q^{24} - 56 q^{26} + 4 q^{29} + 192 q^{34} + 212 q^{36} + 8 q^{39} - 224 q^{44} + 124 q^{46} + 148 q^{49} + 128 q^{51} - 24 q^{54} + 360 q^{56} + 68 q^{59} + 28 q^{61} + 16 q^{64} + 448 q^{66} - 128 q^{69} - 264 q^{71} - 480 q^{74} - 464 q^{76} - 116 q^{81} + 496 q^{84} - 852 q^{86} + 384 q^{91} + 340 q^{94} - 1128 q^{96} - 484 q^{99}+O(q^{100}) $ 44 * q + 4 * q^4 - 4 * q^6 - 4 * q^11 - 4 * q^14 - 32 * q^16 + 36 * q^19 + 32 * q^21 - 16 * q^24 - 56 * q^26 + 4 * q^29 + 192 * q^34 + 212 * q^36 + 8 * q^39 - 224 * q^44 + 124 * q^46 + 148 * q^49 + 128 * q^51 - 24 * q^54 + 360 * q^56 + 68 * q^59 + 28 * q^61 + 16 * q^64 + 448 * q^66 - 128 * q^69 - 264 * q^71 - 480 * q^74 - 464 * q^76 - 116 * q^81 + 496 * q^84 - 852 * q^86 + 384 * q^91 + 340 * q^94 - 1128 * q^96 - 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.755534	+	1.85180i	−0.377767	+	0.925901i
$2$	−0.755534	+	1.85180i	−0.377767	+	0.925901i
$3$	1.37405	−	1.37405i	0.458016	−	0.458016i	−0.439988	−	0.898004i	$-0.645017\pi$
$3$	1.37405	−	1.37405i	0.458016	−	0.458016i	0.898004	+	0.439988i	$0.145017\pi$
$4$	−2.85834	−	2.79820i	−0.714584	−	0.699550i
$5$		0			0
$5$		0			0
$6$	1.50632	+	3.58260i	0.251054	+	0.597101i
$7$	−5.00956			−0.715652			−0.357826	−	0.933788i	$-0.616482\pi$
$7$	−5.00956			−0.715652			−0.357826	+	0.933788i	$0.616482\pi$
$8$	7.34128	−	3.17893i	0.917660	−	0.397367i
$9$			5.22398i			0.580443i
$10$		0			0
$11$	−6.42909	−	6.42909i	−0.584463	−	0.584463i	0.351664	−	0.936126i	$-0.385616\pi$
$11$	−6.42909	−	6.42909i	−0.584463	−	0.584463i	−0.936126	+	0.351664i	$0.885616\pi$
$12$	−7.77235	+	0.0826298i	−0.647696	+	0.00688581i
$13$	11.0519	+	11.0519i	0.850146	+	0.850146i	0.990151	−	0.140005i	$-0.0447117\pi$
$13$	11.0519	+	11.0519i	0.850146	+	0.850146i	−0.140005	+	0.990151i	$0.544712\pi$
$14$	3.78490	−	9.27672i	0.270350	−	0.662623i
$15$		0			0
$16$	0.340161	+	15.9964i	0.0212601	+	0.999774i
$17$	14.8302			0.872367			0.436184	−	0.899858i	$-0.356330\pi$
$17$	14.8302			0.872367			0.436184	+	0.899858i	$0.356330\pi$
$18$	−9.67378	−	3.94690i	−0.537432	−	0.219272i
$19$	−17.5407	+	17.5407i	−0.923196	+	0.923196i	−0.997254	−	0.0740578i	$-0.976405\pi$
$19$	−17.5407	+	17.5407i	−0.923196	+	0.923196i	0.0740578	+	0.997254i	$0.476405\pi$
$20$		0			0
$21$	−6.88338	+	6.88338i	−0.327780	+	0.327780i
$22$	16.7628	−	7.04800i	0.761945	−	0.320363i
$23$	4.37435			0.190189			0.0950945	−	0.995468i	$-0.469685\pi$
$23$	4.37435			0.190189			0.0950945	+	0.995468i	$0.469685\pi$
$24$	5.71926	−	14.4553i	0.238303	−	0.602303i
$25$		0			0
$26$	−28.8160	+	12.1158i	−1.10831	+	0.465994i
$27$	19.5444	+	19.5444i	0.723868	+	0.723868i
$28$	14.3190	+	14.0178i	0.511393	+	0.500634i
$29$	18.8676	+	18.8676i	0.650605	+	0.650605i	0.953139	−	0.302533i	$-0.0978324\pi$
$29$	18.8676	+	18.8676i	0.650605	+	0.650605i	−0.302533	+	0.953139i	$0.597832\pi$
$30$		0			0
$31$			32.9924i			1.06427i	0.846659	+	0.532136i	$0.178611\pi$
$31$			32.9924i			1.06427i	−0.846659	+	0.532136i	$0.821389\pi$
$32$	−29.8791	−	11.4559i	−0.933723	−	0.357997i
$33$	−17.6678			−0.535386
$34$	−11.2048	+	27.4627i	−0.329552	+	0.807726i
$35$		0			0
$36$	14.6177	−	14.9319i	0.406049	−	0.414775i
$37$	18.0984	−	18.0984i	0.489146	−	0.489146i	−0.418891	−	0.908037i	$-0.637581\pi$
$37$	18.0984	−	18.0984i	0.489146	−	0.489146i	0.908037	+	0.418891i	$0.137581\pi$
$38$	−19.2293	−	45.7346i	−0.506035	−	1.20354i
$39$	30.3717			0.778761
$40$		0			0
$41$			76.1027i			1.85616i	0.372376	+	0.928082i	$0.378543\pi$
$41$			76.1027i			1.85616i	−0.372376	+	0.928082i	$0.621457\pi$
$42$	−7.54602	−	17.9473i	−0.179667	−	0.427316i
$43$	19.1807	+	19.1807i	0.446062	+	0.446062i	0.894043	−	0.447981i	$-0.147857\pi$
$43$	19.1807	+	19.1807i	0.446062	+	0.446062i	−0.447981	+	0.894043i	$0.647857\pi$
$44$	0.386620	+	36.3664i	0.00878681	+	0.826508i
$45$		0			0
$46$	−3.30497	+	8.10042i	−0.0718471	+	0.176096i
$47$			59.1180i			1.25783i	0.777474	+	0.628915i	$0.216501\pi$
$47$			59.1180i			1.25783i	−0.777474	+	0.628915i	$0.783499\pi$
$48$	22.4472	+	21.5124i	0.467650	+	0.448175i
$49$	−23.9043			−0.487842
$50$		0			0
$51$	20.3775	−	20.3775i	0.399558	−	0.399558i
$52$	−0.664617	−	62.5155i	−0.0127811	−	1.20222i
$53$	21.5406	−	21.5406i	0.406427	−	0.406427i	−0.474064	−	0.880491i	$-0.657213\pi$
$53$	21.5406	−	21.5406i	0.406427	−	0.406427i	0.880491	+	0.474064i	$0.157213\pi$
$54$	−50.9589	+	21.4259i	−0.943683	+	0.396776i
$55$		0			0
$56$	−36.7766	+	15.9251i	−0.656725	+	0.284376i
$57$			48.2036i			0.845677i
$58$	−49.1941	+	20.6839i	−0.848173	+	0.356619i
$59$	−53.6021	−	53.6021i	−0.908511	−	0.908511i	0.0876411	−	0.996152i	$-0.472067\pi$
$59$	−53.6021	−	53.6021i	−0.908511	−	0.908511i	−0.996152	+	0.0876411i	$0.972067\pi$
$60$		0			0
$61$	−25.4876	−	25.4876i	−0.417830	−	0.417830i	0.466625	−	0.884455i	$-0.345470\pi$
$61$	−25.4876	−	25.4876i	−0.417830	−	0.417830i	−0.884455	+	0.466625i	$0.845470\pi$
$62$	−61.0955	−	24.9269i	−0.985411	−	0.402047i
$63$		−	26.1699i		−	0.415395i
$64$	43.7888	−	46.6749i	0.684200	−	0.729295i
$65$		0			0
$66$	13.3486	−	32.7172i	0.202251	−	0.495715i
$67$	5.92820	−	5.92820i	0.0884806	−	0.0884806i	−0.661481	−	0.749962i	$-0.730072\pi$
$67$	5.92820	−	5.92820i	0.0884806	−	0.0884806i	0.749962	+	0.661481i	$0.230072\pi$
$68$	−42.3898	−	41.4980i	−0.623380	−	0.610264i
$69$	6.01056	−	6.01056i	0.0871096	−	0.0871096i
$70$		0			0
$71$	−25.9177			−0.365038			−0.182519	−	0.983202i	$-0.558425\pi$
$71$	−25.9177			−0.365038			−0.182519	+	0.983202i	$0.558425\pi$
$72$	16.6067	+	38.3507i	0.230649	+	0.532649i
$73$		−	31.2154i		−	0.427608i	−0.976877	−	0.213804i	$-0.931415\pi$
$73$		−	31.2154i		−	0.427608i	0.976877	−	0.213804i	$-0.0685854\pi$
$74$	19.8407	+	47.1886i	0.268117	+	0.637684i
$75$		0			0
$76$	99.2197	−	1.05483i	1.30552	−	0.0138793i
$77$	32.2069	+	32.2069i	0.418272	+	0.418272i
$78$	−22.9469	+	56.2423i	−0.294190	+	0.721055i
$79$		−	122.054i		−	1.54499i	−0.635019	−	0.772497i	$-0.719008\pi$
$79$		−	122.054i		−	1.54499i	0.635019	−	0.772497i	$-0.280992\pi$
$80$		0			0
$81$	6.69413			0.0826436
$82$	−140.927	−	57.4982i	−1.71862	−	0.701198i
$83$	−115.988	+	115.988i	−1.39745	+	1.39745i	−0.590169	+	0.807280i	$0.700939\pi$
$83$	−115.988	+	115.988i	−1.39745	+	1.39745i	−0.807280	+	0.590169i	$0.799061\pi$
$84$	38.9361	−	0.413939i	0.463525	−	0.00492785i
$85$		0			0
$86$	−50.0105	+	21.0271i	−0.581517	+	0.244502i
$87$	51.8499			0.595975
$88$	−67.6354	−	26.7601i	−0.768584	−	0.304092i
$89$			85.3925i			0.959466i	0.877415	+	0.479733i	$0.159266\pi$
$89$			85.3925i			0.959466i	−0.877415	+	0.479733i	$0.840734\pi$
$90$		0			0
$91$	−55.3652	−	55.3652i	−0.608409	−	0.608409i
$92$	−12.5033	−	12.2403i	−0.135906	−	0.133047i
$93$	45.3332	+	45.3332i	0.487454	+	0.487454i
$94$	−109.475	−	44.6657i	−1.16463	−	0.475167i
$95$		0			0
$96$	−56.7963	+	25.3144i	−0.591628	+	0.263692i
$97$	16.3915			0.168984			0.0844921	−	0.996424i	$-0.473073\pi$
$97$	16.3915			0.168984			0.0844921	+	0.996424i	$0.473073\pi$
$98$	18.0605	−	44.2659i	0.184291	−	0.451693i
$99$	33.5855	−	33.5855i	0.339247	−	0.339247i
$100$		0			0
$101$	105.008	−	105.008i	1.03969	−	1.03969i	0.0405066	−	0.999179i	$-0.487103\pi$
$101$	105.008	−	105.008i	1.03969	−	1.03969i	0.999179	−	0.0405066i	$-0.0128972\pi$
$102$	22.3391	+	53.1309i	0.219011	+	0.520891i
$103$	47.2447			0.458687			0.229343	−	0.973346i	$-0.426342\pi$
$103$	47.2447			0.458687			0.229343	+	0.973346i	$0.426342\pi$
$104$	116.268	+	46.0018i	1.11796	+	0.442325i
$105$		0			0
$106$	23.6143	+	56.1637i	0.222776	+	0.529846i
$107$	55.7447	+	55.7447i	0.520979	+	0.520979i	0.917867	−	0.396888i	$-0.129910\pi$
$107$	55.7447	+	55.7447i	0.520979	+	0.520979i	−0.396888	+	0.917867i	$0.629910\pi$
$108$	−1.17532	−	110.554i	−0.0108826	−	1.02365i
$109$	129.985	+	129.985i	1.19253	+	1.19253i	0.976356	+	0.216169i	$0.0693563\pi$
$109$	129.985	+	129.985i	1.19253	+	1.19253i	0.216169	+	0.976356i	$0.430644\pi$
$110$		0			0
$111$		−	49.7362i		−	0.448074i
$112$	−1.70406	−	80.1349i	−0.0152148	−	0.715490i
$113$	−47.6474			−0.421658			−0.210829	−	0.977523i	$-0.567616\pi$
$113$	−47.6474			−0.421658			−0.210829	+	0.977523i	$0.567616\pi$
$114$	−89.2635	−	36.4195i	−0.783013	−	0.319469i
$115$		0			0
$116$	−1.13462	−	106.725i	−0.00978120	−	0.920043i
$117$	−57.7350	+	57.7350i	−0.493461	+	0.493461i
$118$	139.759	−	58.7623i	1.18440	−	0.497985i
$119$	−74.2931			−0.624312
$120$		0			0
$121$		−	38.3336i		−	0.316807i
$122$	66.4548	−	27.9412i	0.544711	−	0.229027i
$123$	104.569	+	104.569i	0.850153	+	0.850153i
$124$	92.3194	−	94.3035i	0.744512	−	0.760512i
$125$		0			0
$126$	48.4614	+	19.7723i	0.384614	+	0.156923i
$127$		−	178.817i		−	1.40801i	−0.710195	−	0.704005i	$-0.751393\pi$
$127$		−	178.817i		−	1.40801i	0.710195	−	0.704005i	$-0.248607\pi$
$128$	53.3486	+	116.353i	0.416786	+	0.909004i
$129$	52.7103			0.408607
$130$		0			0
$131$	50.1661	−	50.1661i	0.382948	−	0.382948i	−0.489215	−	0.872163i	$-0.662717\pi$
$131$	50.1661	−	50.1661i	0.382948	−	0.382948i	0.872163	+	0.489215i	$0.162717\pi$
$132$	50.5004	+	49.4379i	0.382579	+	0.374530i
$133$	87.8714	−	87.8714i	0.660687	−	0.660687i
$134$	6.49889	+	15.4568i	0.0484992	+	0.115349i
$135$		0			0
$136$	108.873	−	47.1444i	0.800537	−	0.346650i
$137$			4.72138i			0.0344626i	0.999852	+	0.0172313i	$0.00548517\pi$
$137$			4.72138i			0.0344626i	−0.999852	+	0.0172313i	$0.994515\pi$
$138$	6.58918	+	15.6715i	0.0477477	+	0.113562i
$139$	−72.2925	−	72.2925i	−0.520090	−	0.520090i	0.397509	−	0.917598i	$-0.369875\pi$
$139$	−72.2925	−	72.2925i	−0.520090	−	0.520090i	−0.917598	+	0.397509i	$0.869875\pi$
$140$		0			0
$141$	81.2310	+	81.2310i	0.576106	+	0.576106i
$142$	19.5817	−	47.9945i	0.137899	−	0.337989i
$143$		−	142.107i		−	0.993757i
$144$	−83.5649	+	1.77700i	−0.580311	+	0.0123403i
$145$		0			0
$146$	57.8047	+	23.5843i	0.395922	+	0.161536i
$147$	−32.8456	+	32.8456i	−0.223439	+	0.223439i
$148$	−102.374	+	1.08837i	−0.691718	+	0.00735383i
$149$	−82.5656	+	82.5656i	−0.554131	+	0.554131i	−0.927631	−	0.373499i	$-0.878158\pi$
$149$	−82.5656	+	82.5656i	−0.554131	+	0.554131i	0.373499	+	0.927631i	$0.378158\pi$
$150$		0			0
$151$	95.3210			0.631265			0.315632	−	0.948882i	$-0.397783\pi$
$151$	95.3210			0.631265			0.315632	+	0.948882i	$0.397783\pi$
$152$	−73.0106	+	184.532i	−0.480333	+	1.21403i
$153$			77.4730i			0.506359i
$154$	−83.9743	+	35.3074i	−0.545288	+	0.229269i
$155$		0			0
$156$	−86.8125	−	84.9860i	−0.556490	−	0.544782i
$157$	103.454	+	103.454i	0.658941	+	0.658941i	0.955130	−	0.296188i	$-0.0957156\pi$
$157$	103.454	+	103.454i	0.658941	+	0.658941i	−0.296188	+	0.955130i	$0.595716\pi$
$158$	226.021	+	92.2164i	1.43051	+	0.583648i
$159$		−	59.1957i		−	0.372300i
$160$		0			0
$161$	−21.9136			−0.136109
$162$	−5.05765	+	12.3962i	−0.0312200	+	0.0765198i
$163$	129.670	−	129.670i	0.795524	−	0.795524i	−0.186862	−	0.982386i	$-0.559832\pi$
$163$	129.670	−	129.670i	0.795524	−	0.795524i	0.982386	+	0.186862i	$0.0598318\pi$
$164$	212.951	−	217.527i	1.29848	−	1.32638i
$165$		0			0
$166$	−127.154	−	302.420i	−0.765988	−	1.82181i
$167$	50.8326			0.304387			0.152193	−	0.988351i	$-0.451366\pi$
$167$	50.8326			0.304387			0.152193	+	0.988351i	$0.451366\pi$
$168$	−28.6510	+	72.4146i	−0.170542	+	0.431040i
$169$			75.2890i			0.445497i
$170$		0			0
$171$	−91.6325	−	91.6325i	−0.535862	−	0.535862i
$172$	−1.15345	−	108.496i	−0.00670610	−	0.630792i
$173$	118.979	+	118.979i	0.687738	+	0.687738i	0.961732	−	0.273993i	$-0.0883446\pi$
$173$	118.979	+	118.979i	0.687738	+	0.687738i	−0.273993	+	0.961732i	$0.588345\pi$
$174$	−39.1744	+	96.0156i	−0.225140	+	0.551814i
$175$		0			0
$176$	100.655	−	105.029i	0.571905	−	0.596756i
$177$	−147.304			−0.832225
$178$	−158.130	−	64.5170i	−0.888370	−	0.362455i
$179$	171.651	−	171.651i	0.958946	−	0.958946i	−0.0402443	−	0.999190i	$-0.512814\pi$
$179$	171.651	−	171.651i	0.958946	−	0.958946i	0.999190	+	0.0402443i	$0.0128136\pi$
$180$		0			0
$181$	−144.176	+	144.176i	−0.796550	+	0.796550i	−0.982550	−	0.186000i	$-0.940448\pi$
$181$	−144.176	+	144.176i	−0.796550	+	0.796550i	0.186000	+	0.982550i	$0.440448\pi$
$182$	144.356	−	60.6950i	0.793163	−	0.333489i
$183$	−70.0424			−0.382746
$184$	32.1133	−	13.9058i	0.174529	−	0.0755747i
$185$		0			0
$186$	−118.199	+	49.6973i	−0.635478	+	0.267190i
$187$	−95.3450	−	95.3450i	−0.509866	−	0.509866i
$188$	165.424	−	168.979i	0.879915	−	0.898825i
$189$	−97.9091	−	97.9091i	−0.518038	−	0.518038i
$190$		0			0
$191$		−	49.0166i		−	0.256631i	−0.991733	−	0.128316i	$-0.959043\pi$
$191$		−	49.0166i		−	0.256631i	0.991733	−	0.128316i	$-0.0409571\pi$
$192$	−3.96563	−	124.301i	−0.0206543	−	0.647403i
$193$	−371.977			−1.92734			−0.963671	−	0.267094i	$-0.913937\pi$
$193$	−371.977			−1.92734			−0.963671	+	0.267094i	$0.913937\pi$
$194$	−12.3843	+	30.3537i	−0.0638367	+	0.156463i
$195$		0			0
$196$	68.3264	+	66.8889i	0.348604	+	0.341270i
$197$	164.712	−	164.712i	0.836102	−	0.836102i	−0.152241	−	0.988343i	$-0.548649\pi$
$197$	164.712	−	164.712i	0.836102	−	0.836102i	0.988343	+	0.152241i	$0.0486490\pi$
$198$	36.8186	+	87.5686i	0.185953	+	0.442265i
$199$	−141.117			−0.709130			−0.354565	−	0.935031i	$-0.615371\pi$
$199$	−141.117			−0.709130			−0.354565	+	0.935031i	$0.615371\pi$
$200$		0			0
$201$		−	16.2913i		−	0.0810511i
$202$	115.117	+	273.792i	0.569887	+	1.35541i
$203$	−94.5182	−	94.5182i	−0.465607	−	0.465607i
$204$	−115.266	+	1.22542i	−0.565029	+	0.00600696i
$205$		0			0
$206$	−35.6950	+	87.4879i	−0.173277	+	0.424698i
$207$			22.8515i			0.110394i
$208$	−173.031	+	180.550i	−0.831880	+	0.868028i
$209$	225.542			1.07915
$210$		0			0
$211$	−167.007	+	167.007i	−0.791502	+	0.791502i	−0.981738	−	0.190236i	$-0.939075\pi$
$211$	−167.007	+	167.007i	−0.791502	+	0.791502i	0.190236	+	0.981738i	$0.439075\pi$
$212$	−121.845	+	1.29537i	−0.574742	+	0.00611023i
$213$	−35.6122	+	35.6122i	−0.167193	+	0.167193i
$214$	−145.345	+	61.1111i	−0.679183	+	0.285566i
$215$		0			0
$216$	205.612	+	81.3507i	0.951906	+	0.376624i
$217$		−	165.278i		−	0.761649i
$218$	−338.915	+	142.498i	−1.55466	+	0.653663i
$219$	−42.8914	−	42.8914i	−0.195851	−	0.195851i
$220$		0			0
$221$	163.902	+	163.902i	0.741640	+	0.741640i
$222$	92.1015	+	37.5774i	0.414872	+	0.169268i
$223$		−	360.595i		−	1.61702i	−0.588485	−	0.808508i	$-0.700275\pi$
$223$		−	360.595i		−	1.61702i	0.588485	−	0.808508i	$-0.299725\pi$
$224$	149.681	+	57.3891i	0.668221	+	0.256201i
$225$		0			0
$226$	35.9992	−	88.2335i	0.159289	−	0.390414i
$227$	−162.621	+	162.621i	−0.716392	+	0.716392i	−0.967865	−	0.251472i	$-0.919085\pi$
$227$	−162.621	+	162.621i	−0.716392	+	0.716392i	0.251472	+	0.967865i	$0.419085\pi$
$228$	134.883	−	137.782i	0.591593	−	0.604307i
$229$	6.11249	−	6.11249i	0.0266921	−	0.0266921i	−0.693635	−	0.720327i	$-0.743992\pi$
$229$	6.11249	−	6.11249i	0.0266921	−	0.0266921i	0.720327	+	0.693635i	$0.243992\pi$
$230$		0			0
$231$	88.5078			0.383150
$232$	198.491	+	78.5333i	0.855563	+	0.338506i
$233$			121.619i			0.521968i	0.965343	+	0.260984i	$0.0840470\pi$
$233$			121.619i			0.521968i	−0.965343	+	0.260984i	$0.915953\pi$
$234$	−63.2929	−	150.534i	−0.270483	−	0.643309i
$235$		0			0
$236$	3.22342	+	303.202i	0.0136586	+	1.28476i
$237$	−167.709	−	167.709i	−0.707632	−	0.707632i
$238$	56.1310	−	137.576i	0.235844	−	0.578050i
$239$			224.468i			0.939196i	0.882880	+	0.469598i	$0.155601\pi$
$239$			224.468i			0.939196i	−0.882880	+	0.469598i	$0.844399\pi$
$240$		0			0
$241$	−128.007			−0.531150			−0.265575	−	0.964090i	$-0.585562\pi$
$241$	−128.007			−0.531150			−0.265575	+	0.964090i	$0.585562\pi$
$242$	70.9863	+	28.9624i	0.293332	+	0.119679i
$243$	−166.702	+	166.702i	−0.686016	+	0.686016i
$244$	1.53272	+	144.172i	0.00628166	+	0.590867i
$245$		0			0
$246$	−272.646	+	114.635i	−1.10832	+	0.465997i
$247$	−387.717			−1.56970
$248$	104.881	+	242.207i	0.422906	+	0.976640i
$249$			318.747i			1.28011i
$250$		0			0
$251$	145.552	+	145.552i	0.579888	+	0.579888i	0.934872	−	0.354984i	$-0.115514\pi$
$251$	145.552	+	145.552i	0.579888	+	0.579888i	−0.354984	+	0.934872i	$0.615514\pi$
$252$	−73.2286	+	74.8023i	−0.290590	+	0.296835i
$253$	−28.1231	−	28.1231i	−0.111158	−	0.111158i
$254$	331.134	+	135.103i	1.30368	+	0.531900i
$255$		0			0
$256$	−255.769	+	10.8827i	−0.999096	+	0.0425106i
$257$	−450.082			−1.75129			−0.875646	−	0.482953i	$-0.839564\pi$
$257$	−450.082			−1.75129			−0.875646	+	0.482953i	$0.839564\pi$
$258$	−39.8245	+	97.6091i	−0.154358	+	0.378330i
$259$	−90.6652	+	90.6652i	−0.350059	+	0.350059i
$260$		0			0
$261$	−98.5638	+	98.5638i	−0.377639	+	0.377639i
$262$	54.9955	+	130.800i	0.209906	+	0.499236i
$263$	−199.203			−0.757427			−0.378713	−	0.925514i	$-0.623633\pi$
$263$	−199.203			−0.757427			−0.378713	+	0.925514i	$0.623633\pi$
$264$	−129.704	+	56.1646i	−0.491303	+	0.212745i
$265$		0			0
$266$	96.3305	+	229.110i	0.362145	+	0.861317i
$267$	117.333	+	117.333i	0.439451	+	0.439451i
$268$	−33.5331	+	0.356498i	−0.125123	+	0.00133022i
$269$	48.1424	+	48.1424i	0.178968	+	0.178968i	0.790906	−	0.611938i	$-0.209610\pi$
$269$	48.1424	+	48.1424i	0.178968	+	0.178968i	−0.611938	+	0.790906i	$0.709610\pi$
$270$		0			0
$271$		−	317.904i		−	1.17308i	−0.809921	−	0.586538i	$-0.800490\pi$
$271$		−	317.904i		−	1.17308i	0.809921	−	0.586538i	$-0.199510\pi$
$272$	5.04468	+	237.230i	0.0185466	+	0.872170i
$273$	−152.149			−0.557322
$274$	−8.74305	−	3.56716i	−0.0319089	−	0.0130188i
$275$		0			0
$276$	−33.9989	+	0.361451i	−0.123185	+	0.00130961i
$277$	68.3059	−	68.3059i	0.246592	−	0.246592i	−0.572979	−	0.819570i	$-0.694212\pi$
$277$	68.3059	−	68.3059i	0.246592	−	0.246592i	0.819570	+	0.572979i	$0.194212\pi$
$278$	188.491	−	79.2518i	0.678024	−	0.285079i
$279$	−172.352			−0.617749
$280$		0			0
$281$			131.237i			0.467035i	0.972353	+	0.233517i	$0.0750236\pi$
$281$			131.237i			0.467035i	−0.972353	+	0.233517i	$0.924976\pi$
$282$	−211.796	+	89.0508i	−0.751051	+	0.315783i
$283$	386.539	+	386.539i	1.36586	+	1.36586i	0.866246	+	0.499618i	$0.166526\pi$
$283$	386.539	+	386.539i	1.36586	+	1.36586i	0.499618	+	0.866246i	$0.333474\pi$
$284$	74.0815	+	72.5229i	0.260850	+	0.255362i
$285$		0			0
$286$	263.154	+	107.367i	0.920121	+	0.375409i
$287$		−	381.241i		−	1.32837i
$288$	59.8455	−	156.088i	0.207797	−	0.541973i
$289$	−69.0638			−0.238975
$290$		0			0
$291$	22.5227	−	22.5227i	0.0773975	−	0.0773975i
$292$	−87.3468	+	89.2240i	−0.299133	+	0.305562i
$293$	221.104	−	221.104i	0.754620	−	0.754620i	−0.220718	−	0.975338i	$-0.570840\pi$
$293$	221.104	−	221.104i	0.754620	−	0.754620i	0.975338	+	0.220718i	$0.0708400\pi$
$294$	−36.0075	−	85.6395i	−0.122475	−	0.291291i
$295$		0			0
$296$	75.3319	−	190.399i	0.254500	−	0.643240i
$297$		−	251.306i		−	0.846148i
$298$	−90.5139	−	215.276i	−0.303738	−	0.722403i
$299$	48.3448	+	48.3448i	0.161688	+	0.161688i
$300$		0			0
$301$	−96.0868	−	96.0868i	−0.319225	−	0.319225i
$302$	−72.0183	+	176.515i	−0.238471	+	0.584488i
$303$		−	288.573i		−	0.952386i
$304$	−286.555	−	274.622i	−0.942615	−	0.903360i
$305$		0			0
$306$	−143.465	−	58.5335i	−0.468838	−	0.191286i
$307$	80.4368	−	80.4368i	0.262009	−	0.262009i	−0.563861	−	0.825870i	$-0.690685\pi$
$307$	80.4368	−	80.4368i	0.262009	−	0.262009i	0.825870	+	0.563861i	$0.190685\pi$
$308$	−1.93680	−	182.180i	−0.00628830	−	0.591492i
$309$	64.9165	−	64.9165i	0.210086	−	0.210086i
$310$		0			0
$311$	−433.169			−1.39283			−0.696413	−	0.717641i	$-0.745222\pi$
$311$	−433.169			−1.39283			−0.696413	+	0.717641i	$0.745222\pi$
$312$	222.967	−	96.5495i	0.714638	−	0.309454i
$313$		−	269.601i		−	0.861346i	−0.902508	−	0.430673i	$-0.858276\pi$
$313$		−	269.601i		−	0.861346i	0.902508	−	0.430673i	$-0.141724\pi$
$314$	−269.739	+	113.413i	−0.859040	+	0.361188i
$315$		0			0
$316$	−341.533	+	348.873i	−1.08080	+	1.10403i
$317$	20.0627	+	20.0627i	0.0632894	+	0.0632894i	0.738043	−	0.674754i	$-0.235750\pi$
$317$	20.0627	+	20.0627i	0.0632894	+	0.0632894i	−0.674754	+	0.738043i	$0.735750\pi$
$318$	109.619	+	44.7244i	0.344713	+	0.140643i
$319$		−	242.602i		−	0.760509i
$320$		0			0
$321$	153.192			0.477233
$322$	16.5565	−	40.5796i	0.0514176	−	0.126024i
$323$	−260.133	+	260.133i	−0.805366	+	0.805366i
$324$	−19.1341	−	18.7315i	−0.0590558	−	0.0578133i
$325$		0			0
$326$	142.153	+	338.094i	0.436053	+	1.03710i
$327$	357.212			1.09239
$328$	241.925	+	558.691i	0.737577	+	1.70333i
$329$		−	296.155i		−	0.900169i
$330$		0			0
$331$	162.499	+	162.499i	0.490933	+	0.490933i	0.908600	−	0.417667i	$-0.137152\pi$
$331$	162.499	+	162.499i	0.490933	+	0.490933i	−0.417667	+	0.908600i	$0.637152\pi$
$332$	656.091	−	6.97507i	1.97618	−	0.0210092i
$333$	94.5458	+	94.5458i	0.283921	+	0.283921i
$334$	−38.4058	+	94.1319i	−0.114987	+	0.281832i
$335$		0			0
$336$	−112.451	−	107.768i	−0.334675	−	0.320737i
$337$	331.372			0.983301			0.491650	−	0.870793i	$-0.336394\pi$
$337$	331.372			0.983301			0.491650	+	0.870793i	$0.336394\pi$
$338$	−139.420	−	56.8835i	−0.412486	−	0.168294i
$339$	−65.4698	+	65.4698i	−0.193126	+	0.193126i
$340$		0			0
$341$	212.111	−	212.111i	0.622028	−	0.622028i
$342$	238.917	−	100.454i	0.698587	−	0.293724i
$343$	365.219			1.06478
$344$	201.785	+	79.8366i	0.586584	+	0.232083i
$345$		0			0
$346$	−310.217	+	130.432i	−0.896582	+	0.376972i
$347$	−140.935	−	140.935i	−0.406154	−	0.406154i	0.474241	−	0.880395i	$-0.342722\pi$
$347$	−140.935	−	140.935i	−0.406154	−	0.406154i	−0.880395	+	0.474241i	$0.842722\pi$
$348$	−148.204	−	145.086i	−0.425874	−	0.416914i
$349$	−94.5429	−	94.5429i	−0.270897	−	0.270897i	0.558564	−	0.829461i	$-0.311352\pi$
$349$	−94.5429	−	94.5429i	−0.270897	−	0.270897i	−0.829461	+	0.558564i	$0.811352\pi$
$350$		0			0
$351$			432.006i			1.23079i
$352$	118.445	+	265.747i	0.336490	+	0.754962i
$353$	−232.200			−0.657791			−0.328896	−	0.944366i	$-0.606676\pi$
$353$	−232.200			−0.657791			−0.328896	+	0.944366i	$0.606676\pi$
$354$	111.293	−	272.777i	0.314387	−	0.770558i
$355$		0			0
$356$	238.945	−	244.080i	0.671194	−	0.685619i
$357$	−102.082	+	102.082i	−0.285945	+	0.285945i
$358$	188.176	+	447.552i	0.525630	+	1.25015i
$359$	701.851			1.95502			0.977508	−	0.210899i	$-0.0676392\pi$
$359$	701.851			1.95502			0.977508	+	0.210899i	$0.0676392\pi$
$360$		0			0
$361$		−	254.354i		−	0.704582i
$362$	−158.055	−	375.914i	−0.436616	−	1.03844i
$363$	−52.6722	−	52.6722i	−0.145103	−	0.145103i
$364$	3.32944	+	313.175i	0.00914682	+	0.860372i
$365$		0			0
$366$	52.9195	−	129.705i	0.144589	−	0.354384i
$367$		−	126.106i		−	0.343612i	−0.985131	−	0.171806i	$-0.945040\pi$
$367$		−	126.106i		−	0.343612i	0.985131	−	0.171806i	$-0.0549603\pi$
$368$	1.48798	+	69.9737i	0.00404343	+	0.190146i
$369$	−397.559			−1.07740
$370$		0			0
$371$	−107.909	+	107.909i	−0.290860	+	0.290860i
$372$	−2.72616	−	256.429i	−0.00732838	−	0.689325i
$373$	414.853	−	414.853i	1.11221	−	1.11221i	0.119356	−	0.992852i	$-0.461917\pi$
$373$	414.853	−	414.853i	1.11221	−	1.11221i	0.992852	−	0.119356i	$-0.0380829\pi$
$374$	248.596	−	104.524i	0.664696	−	0.279475i
$375$		0			0
$376$	187.932	+	434.002i	0.499820	+	1.15426i
$377$			417.045i			1.10622i
$378$	255.282	−	107.335i	0.675349	−	0.283954i
$379$	117.567	+	117.567i	0.310204	+	0.310204i	0.844989	−	0.534784i	$-0.179607\pi$
$379$	117.567	+	117.567i	0.310204	+	0.310204i	−0.534784	+	0.844989i	$0.679607\pi$
$380$		0			0
$381$	−245.703	−	245.703i	−0.644891	−	0.644891i
$382$	90.7690	+	37.0337i	0.237615	+	0.0969469i
$383$			254.533i			0.664577i	0.943178	+	0.332289i	$0.107821\pi$
$383$			254.533i			0.664577i	−0.943178	+	0.332289i	$0.892179\pi$
$384$	233.178	+	86.5704i	0.607233	+	0.225444i
$385$		0			0
$386$	281.041	−	688.827i	0.728086	−	1.78453i
$387$	−100.200	+	100.200i	−0.258914	+	0.258914i
$388$	−46.8523	−	45.8666i	−0.120753	−	0.118213i
$389$	−32.2185	+	32.2185i	−0.0828240	+	0.0828240i	−0.747305	−	0.664481i	$-0.768653\pi$
$389$	−32.2185	+	32.2185i	−0.0828240	+	0.0828240i	0.664481	+	0.747305i	$0.268653\pi$
$390$		0			0
$391$	64.8726			0.165915
$392$	−175.488	+	75.9900i	−0.447673	+	0.193852i
$393$		−	137.861i		−	0.350792i
$394$	180.568	+	429.460i	0.458296	+	1.09000i
$395$		0			0
$396$	−189.977	+	2.01970i	−0.479741	+	0.00510024i
$397$	105.079	+	105.079i	0.264682	+	0.264682i	0.826953	−	0.562271i	$-0.190072\pi$
$397$	105.079	+	105.079i	0.264682	+	0.264682i	−0.562271	+	0.826953i	$0.690072\pi$
$398$	106.619	−	261.320i	0.267886	−	0.656584i
$399$		−	241.479i		−	0.605211i
$400$		0			0
$401$	248.416			0.619492			0.309746	−	0.950819i	$-0.399756\pi$
$401$	248.416			0.619492			0.309746	+	0.950819i	$0.399756\pi$
$402$	30.1682	+	12.3086i	0.0750452	+	0.0306184i
$403$	−364.629	+	364.629i	−0.904787	+	0.904787i
$404$	−593.983	+	6.31478i	−1.47025	+	0.0156306i
$405$		0			0
$406$	246.441	−	103.617i	0.606997	−	0.255215i
$407$	−232.713			−0.571775
$408$	84.8181	−	214.375i	0.207888	−	0.525430i
$409$		−	455.293i		−	1.11318i	−0.830786	−	0.556592i	$-0.812109\pi$
$409$		−	455.293i		−	1.11318i	0.830786	−	0.556592i	$-0.187891\pi$
$410$		0			0
$411$	6.48740	+	6.48740i	0.0157844	+	0.0157844i
$412$	−135.041	−	132.200i	−0.327770	−	0.320874i
$413$	268.523	+	268.523i	0.650178	+	0.650178i
$414$	−42.3165	−	17.2651i	−0.102214	−	0.0417032i
$415$		0			0
$416$	−203.612	−	456.831i	−0.489451	−	1.09815i
$417$	−198.667			−0.476419
$418$	−170.405	+	417.659i	−0.407666	+	0.999183i
$419$	−296.148	+	296.148i	−0.706797	+	0.706797i	−0.965860	−	0.259063i	$-0.916586\pi$
$419$	−296.148	+	296.148i	−0.706797	+	0.706797i	0.259063	+	0.965860i	$0.416586\pi$
$420$		0			0
$421$	−354.858	+	354.858i	−0.842893	+	0.842893i	−0.989234	−	0.146341i	$-0.953250\pi$
$421$	−354.858	+	354.858i	−0.842893	+	0.842893i	0.146341	+	0.989234i	$0.453250\pi$
$422$	−183.084	−	435.443i	−0.433849	−	1.03186i
$423$	−308.832			−0.730098
$424$	89.6596	−	226.612i	0.211461	−	0.534462i
$425$		0			0
$426$	−39.0405	−	92.8529i	−0.0916443	−	0.217965i
$427$	127.682	+	127.682i	0.299021	+	0.299021i
$428$	−3.35227	−	315.322i	−0.00783240	−	0.736734i
$429$	−195.262	−	195.262i	−0.455157	−	0.455157i
$430$		0			0
$431$			79.8832i			0.185344i	0.995697	+	0.0926719i	$0.0295408\pi$
$431$			79.8832i			0.185344i	−0.995697	+	0.0926719i	$0.970459\pi$
$432$	−305.992	+	319.289i	−0.708315	+	0.739094i
$433$	−1.57519			−0.00363785			−0.00181892	−	0.999998i	$-0.500579\pi$
$433$	−1.57519			−0.00363785			−0.00181892	+	0.999998i	$0.500579\pi$
$434$	306.062	+	124.873i	0.705211	+	0.287726i
$435$		0			0
$436$	−7.81679	−	735.266i	−0.0179284	−	1.68639i
$437$	−76.7292	+	76.7292i	−0.175582	+	0.175582i
$438$	111.832	−	47.0204i	0.255325	−	0.107353i
$439$	−249.750			−0.568907			−0.284453	−	0.958690i	$-0.591812\pi$
$439$	−249.750			−0.568907			−0.284453	+	0.958690i	$0.591812\pi$
$440$		0			0
$441$		−	124.875i		−	0.283164i
$442$	−427.349	+	179.681i	−0.966852	+	0.406518i
$443$	121.031	+	121.031i	0.273208	+	0.273208i	0.830390	−	0.557182i	$-0.188118\pi$
$443$	121.031	+	121.031i	0.273208	+	0.273208i	−0.557182	+	0.830390i	$0.688118\pi$
$444$	−139.172	+	142.163i	−0.313450	+	0.320186i
$445$		0			0
$446$	667.750	+	272.442i	1.49720	+	0.610856i
$447$			226.898i			0.507602i
$448$	−219.363	+	233.821i	−0.489649	+	0.521921i
$449$	297.105			0.661703			0.330852	−	0.943683i	$-0.392664\pi$
$449$	297.105			0.661703			0.330852	+	0.943683i	$0.392664\pi$
$450$		0			0
$451$	489.271	−	489.271i	1.08486	−	1.08486i
$452$	136.192	+	133.327i	0.301310	+	0.294971i
$453$	130.976	−	130.976i	0.289129	−	0.289129i
$454$	−178.276	−	424.008i	−0.392679	−	0.933938i
$455$		0			0
$456$	153.236	+	353.876i	0.336044	+	0.776044i
$457$			361.107i			0.790169i	0.918645	+	0.395085i	$0.129285\pi$
$457$			361.107i			0.790169i	−0.918645	+	0.395085i	$0.870715\pi$
$458$	6.70092	+	15.9373i	0.0146308	+	0.0347976i
$459$	289.849	+	289.849i	0.631479	+	0.631479i
$460$		0			0
$461$	−166.498	−	166.498i	−0.361167	−	0.361167i	0.503075	−	0.864243i	$-0.332202\pi$
$461$	−166.498	−	166.498i	−0.361167	−	0.361167i	−0.864243	+	0.503075i	$0.832202\pi$
$462$	−66.8707	+	163.899i	−0.144742	+	0.354759i
$463$		−	712.425i		−	1.53871i	−0.638819	−	0.769357i	$-0.720577\pi$
$463$		−	712.425i		−	1.53871i	0.638819	−	0.769357i	$-0.279423\pi$
$464$	−295.395	+	308.231i	−0.636626	+	0.664290i
$465$		0			0
$466$	−225.213	−	91.8871i	−0.483291	−	0.197183i
$467$	205.618	−	205.618i	0.440295	−	0.440295i	−0.451816	−	0.892111i	$-0.649224\pi$
$467$	205.618	−	205.618i	0.440295	−	0.440295i	0.892111	+	0.451816i	$0.149224\pi$
$468$	326.580	−	3.47195i	0.697820	−	0.00741870i
$469$	−29.6977	+	29.6977i	−0.0633213	+	0.0633213i
$470$		0			0
$471$	284.301			0.603611
$472$	−563.906	−	223.111i	−1.19472	−	0.472692i
$473$		−	246.629i		−	0.521413i
$474$	437.273	−	183.853i	0.922517	−	0.387877i
$475$		0			0
$476$	212.355	+	207.887i	0.446123	+	0.436737i
$477$	112.528	+	112.528i	0.235908	+	0.235908i
$478$	−415.670	−	169.593i	−0.869602	−	0.354798i
$479$			775.000i			1.61795i	0.587841	+	0.808977i	$0.299978\pi$
$479$			775.000i			1.61795i	−0.587841	+	0.808977i	$0.700022\pi$
$480$		0			0
$481$	400.044			0.831692
$482$	96.7139	−	237.044i	0.200651	−	0.491793i
$483$	−30.1103	+	30.1103i	−0.0623401	+	0.0623401i
$484$	−107.265	+	109.570i	−0.221622	+	0.226385i
$485$		0			0
$486$	−182.750	−	434.648i	−0.376028	−	0.894337i
$487$	267.618			0.549523			0.274762	−	0.961512i	$-0.411401\pi$
$487$	267.618			0.549523			0.274762	+	0.961512i	$0.411401\pi$
$488$	−268.135	−	106.088i	−0.549457	−	0.217394i
$489$		−	356.347i		−	0.728725i
$490$		0			0
$491$	−41.1597	−	41.1597i	−0.0838283	−	0.0838283i	0.663949	−	0.747778i	$-0.268879\pi$
$491$	−41.1597	−	41.1597i	−0.0838283	−	0.0838283i	−0.747778	+	0.663949i	$0.768879\pi$
$492$	−6.28835	−	591.497i	−0.0127812	−	1.20223i
$493$	279.810	+	279.810i	0.567567	+	0.567567i
$494$	292.933	−	717.974i	0.592983	−	1.45339i
$495$		0			0
$496$	−527.760	+	11.2228i	−1.06403	+	0.0226265i
$497$	129.836			0.261240
$498$	−590.256	−	240.824i	−1.18525	−	0.483583i
$499$	165.335	−	165.335i	0.331332	−	0.331332i	−0.521760	−	0.853092i	$-0.674724\pi$
$499$	165.335	−	165.335i	0.331332	−	0.331332i	0.853092	+	0.521760i	$0.174724\pi$
$500$		0			0
$501$	69.8464	−	69.8464i	0.139414	−	0.139414i
$502$	−379.503	+	159.564i	−0.755982	+	0.317856i
$503$	427.936			0.850767			0.425384	−	0.905013i	$-0.360139\pi$
$503$	427.936			0.850767			0.425384	+	0.905013i	$0.360139\pi$
$504$	−83.1923	−	192.120i	−0.165064	−	0.381191i
$505$		0			0
$506$	73.3262	−	30.8304i	0.144914	−	0.0609296i
$507$	103.451	+	103.451i	0.204045	+	0.204045i
$508$	−500.366	+	511.120i	−0.984973	+	1.00614i
$509$	465.764	+	465.764i	0.915056	+	0.915056i	0.996664	−	0.0816082i	$-0.0260056\pi$
$509$	465.764	+	465.764i	0.915056	+	0.915056i	−0.0816082	+	0.996664i	$0.526006\pi$
$510$		0			0
$511$			156.375i			0.306018i
$512$	173.089	−	481.855i	0.338065	−	0.941123i
$513$	−685.647			−1.33654
$514$	340.053	−	833.462i	0.661581	−	1.62152i
$515$		0			0
$516$	−150.664	−	147.494i	−0.291984	−	0.285841i
$517$	380.075	−	380.075i	0.735155	−	0.735155i
$518$	−99.3932	−	236.395i	−0.191879	−	0.456360i
$519$	326.965			0.629990
$520$		0			0
$521$		−	262.979i		−	0.504758i	−0.967628	−	0.252379i	$-0.918787\pi$
$521$		−	262.979i		−	0.504758i	0.967628	−	0.252379i	$-0.0812129\pi$
$522$	−108.052	−	256.989i	−0.206997	−	0.492316i
$523$	142.934	+	142.934i	0.273296	+	0.273296i	0.830426	−	0.557129i	$-0.188097\pi$
$523$	142.934	+	142.934i	0.273296	+	0.273296i	−0.557129	+	0.830426i	$0.688097\pi$
$524$	−283.766	+	3.01679i	−0.541539	+	0.00575723i
$525$		0			0
$526$	150.505	−	368.885i	0.286131	−	0.701302i
$527$			489.286i			0.928437i
$528$	−6.00989	−	282.620i	−0.0113824	−	0.535265i
$529$	−509.865			−0.963828
$530$		0			0
$531$	280.017	−	280.017i	0.527339	−	0.527339i
$532$	−497.048	+	5.28424i	−0.934300	+	0.00993277i
$533$	−841.080	+	841.080i	−1.57801	+	1.57801i
$534$	−305.927	+	128.629i	−0.572898	+	0.240878i
$535$		0			0
$536$	24.6752	−	62.3659i	0.0460359	−	0.116354i
$537$		−	471.714i		−	0.878425i
$538$	−125.523	+	52.7769i	−0.233315	+	0.0980983i
$539$	153.683	+	153.683i	0.285125	+	0.285125i
$540$		0			0
$541$	−214.719	−	214.719i	−0.396892	−	0.396892i	0.480243	−	0.877135i	$-0.340548\pi$
$541$	−214.719	−	214.719i	−0.396892	−	0.396892i	−0.877135	+	0.480243i	$0.840548\pi$
$542$	588.695	+	240.187i	1.08615	+	0.443150i
$543$			396.208i			0.729665i
$544$	−443.115	−	169.894i	−0.814549	−	0.312305i
$545$		0			0
$546$	114.954	−	281.750i	0.210538	−	0.516025i
$547$	−247.657	+	247.657i	−0.452754	+	0.452754i	−0.896268	−	0.443513i	$-0.853732\pi$
$547$	−247.657	+	247.657i	−0.452754	+	0.452754i	0.443513	+	0.896268i	$0.353732\pi$
$548$	13.2114	−	13.4953i	0.0241083	−	0.0246264i
$549$	133.147	−	133.147i	0.242526	−	0.242526i
$550$		0			0
$551$	−661.901			−1.20127
$552$	25.0180	−	63.2324i	0.0453225	−	0.114551i
$553$			611.440i			1.10568i
$554$	74.8815	+	178.096i	0.135165	+	0.321474i
$555$		0			0
$556$	4.34738	+	408.925i	0.00781903	+	0.735476i
$557$	252.575	+	252.575i	0.453456	+	0.453456i	0.896500	−	0.443044i	$-0.146101\pi$
$557$	252.575	+	252.575i	0.453456	+	0.453456i	−0.443044	+	0.896500i	$0.646101\pi$
$558$	130.218	−	319.162i	0.233365	−	0.571974i
$559$			423.966i			0.758436i
$560$		0			0
$561$	−262.017			−0.467054
$562$	−243.024	−	99.1539i	−0.432428	−	0.176430i
$563$	274.938	−	274.938i	0.488345	−	0.488345i	−0.419439	−	0.907784i	$-0.637773\pi$
$563$	274.938	−	274.938i	0.488345	−	0.488345i	0.907784	+	0.419439i	$0.137773\pi$
$564$	−4.88491	−	459.486i	−0.00866118	−	0.814691i
$565$		0			0
$566$	−1007.84	+	423.750i	−1.78063	+	0.748676i
$567$	−33.5347			−0.0591441
$568$	−190.269	+	82.3907i	−0.334981	+	0.145054i
$569$		−	985.556i		−	1.73208i	−0.499971	−	0.866042i	$-0.666656\pi$
$569$		−	985.556i		−	1.73208i	0.499971	−	0.866042i	$-0.333344\pi$
$570$		0			0
$571$	246.409	+	246.409i	0.431539	+	0.431539i	0.889152	−	0.457613i	$-0.151295\pi$
$571$	246.409	+	246.409i	0.431539	+	0.431539i	−0.457613	+	0.889152i	$0.651295\pi$
$572$	−397.645	+	406.190i	−0.695183	+	0.710123i
$573$	−67.3511	−	67.3511i	−0.117541	−	0.117541i
$574$	705.983	+	288.041i	1.22994	+	0.501814i
$575$		0			0
$576$	243.829	+	228.752i	0.423314	+	0.397139i
$577$	374.750			0.649481			0.324740	−	0.945803i	$-0.394723\pi$
$577$	374.750			0.649481			0.324740	+	0.945803i	$0.394723\pi$
$578$	52.1801	−	127.892i	0.0902770	−	0.221267i
$579$	−511.114	+	511.114i	−0.882753	+	0.882753i
$580$		0			0
$581$	581.051	−	581.051i	1.00009	−	1.00009i
$582$	24.6909	+	58.7242i	0.0424241	+	0.100901i
$583$	−276.973			−0.475083
$584$	−99.2316	−	229.161i	−0.169917	−	0.392399i
$585$		0			0
$586$	242.388	+	576.491i	0.413632	+	0.983773i
$587$	558.540	+	558.540i	0.951517	+	0.951517i	0.998878	−	0.0473610i	$-0.0150811\pi$
$587$	558.540	+	558.540i	0.951517	+	0.951517i	−0.0473610	+	0.998878i	$0.515081\pi$
$588$	185.792	−	1.97520i	0.315973	−	0.00335919i
$589$	−578.712	−	578.712i	−0.982532	−	0.982532i
$590$		0			0
$591$		−	452.645i		−	0.765897i
$592$	295.666	+	283.353i	0.499435	+	0.478636i
$593$	217.889			0.367435			0.183717	−	0.982979i	$-0.441187\pi$
$593$	217.889			0.367435			0.183717	+	0.982979i	$0.441187\pi$
$594$	465.368	+	189.870i	0.783449	+	0.319647i
$595$		0			0
$596$	467.035	−	4.96516i	0.783616	−	0.00833081i
$597$	−193.901	+	193.901i	−0.324793	+	0.324793i
$598$	−126.051	+	52.9988i	−0.210788	+	0.0886268i
$599$	−238.766			−0.398607			−0.199304	−	0.979938i	$-0.563868\pi$
$599$	−238.766			−0.398607			−0.199304	+	0.979938i	$0.563868\pi$
$600$		0			0
$601$			307.946i			0.512390i	0.966625	+	0.256195i	$0.0824688\pi$
$601$			307.946i			0.512390i	−0.966625	+	0.256195i	$0.917531\pi$
$602$	250.531	−	105.337i	0.416164	−	0.174978i
$603$	30.9688	+	30.9688i	0.0513579	+	0.0513579i
$604$	−272.459	−	266.727i	−0.451091	−	0.441601i
$605$		0			0
$606$	534.379	+	218.027i	0.881814	+	0.359780i
$607$			257.142i			0.423627i	0.977310	+	0.211814i	$0.0679370\pi$
$607$			257.142i			0.423627i	−0.977310	+	0.211814i	$0.932063\pi$
$608$	725.047	−	323.157i	1.19251	−	0.531508i
$609$	−259.745			−0.426511
$610$		0			0
$611$	−653.366	+	653.366i	−1.06934	+	1.06934i
$612$	216.785	−	221.444i	0.354224	−	0.361836i
$613$	352.976	−	352.976i	0.575817	−	0.575817i	−0.357931	−	0.933748i	$-0.616518\pi$
$613$	352.976	−	352.976i	0.575817	−	0.575817i	0.933748	+	0.357931i	$0.116518\pi$
$614$	88.1801	+	209.726i	0.143616	+	0.341573i
$615$		0			0
$616$	338.824	+	134.056i	0.550039	+	0.217624i
$617$		−	188.628i		−	0.305719i	−0.988248	−	0.152859i	$-0.951152\pi$
$617$		−	188.628i		−	0.305719i	0.988248	−	0.152859i	$-0.0488481\pi$
$618$	71.1658	+	169.259i	0.115155	+	0.273882i
$619$	387.137	+	387.137i	0.625424	+	0.625424i	0.946913	−	0.321490i	$-0.104183\pi$
$619$	387.137	+	387.137i	0.625424	+	0.625424i	−0.321490	+	0.946913i	$0.604183\pi$
$620$		0			0
$621$	85.4941	+	85.4941i	0.137672	+	0.137672i
$622$	327.274	−	802.143i	0.526164	−	1.28962i
$623$		−	427.779i		−	0.686644i
$624$	10.3313	+	485.837i	0.0165565	+	0.778585i
$625$		0			0
$626$	499.248	+	203.693i	0.797521	+	0.325388i
$627$	309.905	−	309.905i	0.494267	−	0.494267i
$628$	−6.22130	−	585.190i	−0.00990652	−	0.931831i
$629$	268.404	−	268.404i	0.426715	−	0.426715i
$630$		0			0
$631$	561.749			0.890252			0.445126	−	0.895468i	$-0.353159\pi$
$631$	561.749			0.890252			0.445126	+	0.895468i	$0.353159\pi$
$632$	−388.003	−	896.036i	−0.613929	−	1.41778i
$633$			458.951i			0.725041i
$634$	−52.3103	+	21.9941i	−0.0825083	+	0.0346910i
$635$		0			0
$636$	−165.641	+	169.201i	−0.260443	+	0.266040i
$637$	−264.188	−	264.188i	−0.414737	−	0.414737i
$638$	449.251	+	183.294i	0.704156	+	0.287295i
$639$		−	135.394i		−	0.211884i
$640$		0			0
$641$	−1009.43			−1.57477			−0.787387	−	0.616459i	$-0.788567\pi$
$641$	−1009.43			−1.57477			−0.787387	+	0.616459i	$0.788567\pi$
$642$	−115.742	+	283.681i	−0.180283	+	0.441870i
$643$	775.300	−	775.300i	1.20575	−	1.20575i	0.233364	−	0.972389i	$-0.425027\pi$
$643$	775.300	−	775.300i	1.20575	−	1.20575i	0.972389	−	0.233364i	$-0.0749735\pi$
$644$	62.6363	+	61.3185i	0.0972614	+	0.0952151i
$645$		0			0
$646$	−285.175	−	678.255i	−0.441448	−	1.04993i
$647$	−5.25109			−0.00811606			−0.00405803	−	0.999992i	$-0.501292\pi$
$647$	−5.25109			−0.00811606			−0.00405803	+	0.999992i	$0.501292\pi$
$648$	49.1435	−	21.2802i	0.0758387	−	0.0328398i
$649$			689.226i			1.06198i
$650$		0			0
$651$	−227.100	−	227.100i	−0.348847	−	0.348847i
$652$	−733.485	+	7.79786i	−1.12498	+	0.0119599i
$653$	15.2963	+	15.2963i	0.0234247	+	0.0234247i	0.718722	−	0.695297i	$-0.244727\pi$
$653$	15.2963	+	15.2963i	0.0234247	+	0.0234247i	−0.695297	+	0.718722i	$0.744727\pi$
$654$	−269.886	+	661.485i	−0.412670	+	1.01145i
$655$		0			0
$656$	−1217.37	+	25.8872i	−1.85574	+	0.0394622i
$657$	163.069			0.248202
$658$	548.421	+	223.756i	0.833467	+	0.340054i
$659$	378.187	−	378.187i	0.573880	−	0.573880i	−0.359330	−	0.933211i	$-0.616995\pi$
$659$	378.187	−	378.187i	0.573880	−	0.573880i	0.933211	+	0.359330i	$0.116995\pi$
$660$		0			0
$661$	−42.5546	+	42.5546i	−0.0643791	+	0.0643791i	−0.738563	−	0.674184i	$-0.764495\pi$
$661$	−42.5546	+	42.5546i	−0.0643791	+	0.0643791i	0.674184	+	0.738563i	$0.264495\pi$
$662$	−423.689	+	178.142i	−0.640013	+	0.269097i
$663$	450.420			0.679366
$664$	−482.783	+	1220.22i	−0.727083	+	1.83768i
$665$		0			0
$666$	−246.513	+	103.647i	−0.370139	+	0.155627i
$667$	82.5332	+	82.5332i	0.123738	+	0.123738i
$668$	−145.297	−	142.240i	−0.217510	−	0.212934i
$669$	−495.475	−	495.475i	−0.740620	−	0.740620i
$670$		0			0
$671$			327.724i			0.488412i
$672$	284.525	−	126.814i	0.423400	−	0.188711i
$673$	1181.74			1.75593			0.877964	−	0.478727i	$-0.158902\pi$
$673$	1181.74			1.75593			0.877964	+	0.478727i	$0.158902\pi$
$674$	−250.363	+	613.636i	−0.371459	+	0.910439i
$675$		0			0
$676$	210.674	−	215.201i	0.311648	−	0.318345i
$677$	71.0492	−	71.0492i	0.104947	−	0.104947i	−0.652684	−	0.757631i	$-0.726357\pi$
$677$	71.0492	−	71.0492i	0.104947	−	0.104947i	0.757631	+	0.652684i	$0.226357\pi$
$678$	−71.7724	−	170.702i	−0.105859	−	0.251772i
$679$	−82.1141			−0.120934
$680$		0			0
$681$			446.898i			0.656238i
$682$	232.531	+	553.046i	0.340954	+	0.810917i
$683$	−246.349	−	246.349i	−0.360687	−	0.360687i	0.503379	−	0.864066i	$-0.332090\pi$
$683$	−246.349	−	246.349i	−0.360687	−	0.360687i	−0.864066	+	0.503379i	$0.832090\pi$
$684$	5.51041	+	518.322i	0.00805616	+	0.757781i
$685$		0			0
$686$	−275.935	+	676.312i	−0.402238	+	0.985878i
$687$		−	16.7977i		−	0.0244508i
$688$	−300.297	+	313.346i	−0.436478	+	0.455445i
$689$	476.130			0.691045
$690$		0			0
$691$	−176.426	+	176.426i	−0.255320	+	0.255320i	−0.823148	−	0.567827i	$-0.807784\pi$
$691$	−176.426	+	176.426i	−0.255320	+	0.255320i	0.567827	+	0.823148i	$0.307784\pi$
$692$	−7.15491	−	673.007i	−0.0103395	−	0.972554i
$693$	−168.249	+	168.249i	−0.242783	+	0.242783i
$694$	367.466	−	154.503i	0.529489	−	0.222626i
$695$		0			0
$696$	380.644	−	164.827i	0.546903	−	0.236821i
$697$			1128.62i			1.61926i
$698$	246.505	−	103.644i	0.353159	−	0.148487i
$699$	167.110	+	167.110i	0.239070	+	0.239070i
$700$		0			0
$701$	715.573	+	715.573i	1.02079	+	1.02079i	0.999779	+	0.0210094i	$0.00668799\pi$
$701$	715.573	+	715.573i	1.02079	+	1.02079i	0.0210094	+	0.999779i	$0.493312\pi$
$702$	−799.990	−	326.396i	−1.13959	−	0.464951i
$703$			634.919i			0.903156i
$704$	−581.599	+	18.5550i	−0.826135	+	0.0263565i
$705$		0			0
$706$	175.435	−	429.989i	0.248492	−	0.609049i
$707$	−526.046	+	526.046i	−0.744053	+	0.744053i
$708$	421.044	+	412.186i	0.594695	+	0.582183i
$709$	306.482	−	306.482i	0.432273	−	0.432273i	−0.457128	−	0.889401i	$-0.651122\pi$
$709$	306.482	−	306.482i	0.432273	−	0.432273i	0.889401	+	0.457128i	$0.151122\pi$
$710$		0			0
$711$	637.611			0.896780
$712$	271.457	+	626.890i	0.381260	+	0.880464i
$713$			144.320i			0.202413i
$714$	−111.909	−	266.163i	−0.156736	−	0.372777i
$715$		0			0
$716$	−970.951	+	10.3224i	−1.35608	+	0.0144168i
$717$	308.430	+	308.430i	0.430167	+	0.430167i
$718$	−530.272	+	1299.69i	−0.738541	+	1.81015i
$719$			87.8746i			0.122218i	0.998131	+	0.0611089i	$0.0194637\pi$
$719$			87.8746i			0.122218i	−0.998131	+	0.0611089i	$0.980536\pi$
$720$		0			0
$721$	−236.676			−0.328260
$722$	471.013	+	192.173i	0.652373	+	0.266168i
$723$	−175.888	+	175.888i	−0.243275	+	0.243275i
$724$	815.534	−	8.67014i	1.12643	−	0.0119753i
$725$		0			0
$726$	137.334	−	57.7428i	0.189166	−	0.0795356i
$727$	370.209			0.509228			0.254614	−	0.967043i	$-0.418052\pi$
$727$	370.209			0.509228			0.254614	+	0.967043i	$0.418052\pi$
$728$	−582.454	−	230.449i	−0.800074	−	0.316551i
$729$			518.360i			0.711056i
$730$		0			0
$731$	284.454	+	284.454i	0.389130	+	0.389130i
$732$	200.205	+	195.993i	0.273504	+	0.267750i
$733$	−626.686	−	626.686i	−0.854960	−	0.854960i	0.135779	−	0.990739i	$-0.456646\pi$
$733$	−626.686	−	626.686i	−0.854960	−	0.854960i	−0.990739	+	0.135779i	$0.956646\pi$
$734$	233.523	+	95.2772i	0.318151	+	0.129805i
$735$		0			0
$736$	−130.702	−	50.1121i	−0.177584	−	0.0680871i
$737$	−76.2259			−0.103427
$738$	300.370	−	736.201i	0.407005	−	0.997562i
$739$	388.772	−	388.772i	0.526078	−	0.526078i	−0.393322	−	0.919401i	$-0.628674\pi$
$739$	388.772	−	388.772i	0.526078	−	0.526078i	0.919401	+	0.393322i	$0.128674\pi$
$740$		0			0
$741$	−532.741	+	532.741i	−0.718949	+	0.718949i
$742$	−118.297	−	281.356i	−0.159430	−	0.379185i
$743$	−121.878			−0.164035			−0.0820173	−	0.996631i	$-0.526136\pi$
$743$	−121.878			−0.164035			−0.0820173	+	0.996631i	$0.526136\pi$
$744$	476.915	+	188.693i	0.641015	+	0.253619i
$745$		0			0
$746$	454.790	+	1081.66i	0.609638	+	1.44995i
$747$	−605.921	−	605.921i	−0.811139	−	0.811139i
$748$	5.73367	+	539.322i	0.00766533	+	0.721019i
$749$	−279.257	−	279.257i	−0.372840	−	0.372840i
$750$		0			0
$751$			914.610i			1.21786i	0.793225	+	0.608928i	$0.208400\pi$
$751$			914.610i			1.21786i	−0.793225	+	0.608928i	$0.791600\pi$
$752$	−945.674	+	20.1097i	−1.25755	+	0.0267416i
$753$	399.991			0.531196
$754$	−772.284	−	315.092i	−1.02425	−	0.417893i
$755$		0			0
$756$	5.88786	+	553.826i	0.00778818	+	0.732574i
$757$	−129.143	+	129.143i	−0.170599	+	0.170599i	−0.787242	−	0.616644i	$-0.788492\pi$
$757$	−129.143	+	129.143i	−0.170599	+	0.170599i	0.616644	+	0.787242i	$0.288492\pi$
$758$	−306.538	+	128.885i	−0.404403	+	0.170033i
$759$	−77.2849			−0.101825
$760$		0			0
$761$		−	352.217i		−	0.462835i	−0.972855	−	0.231417i	$-0.925664\pi$
$761$		−	352.217i		−	0.462835i	0.972855	−	0.231417i	$-0.0743363\pi$
$762$	640.631	−	269.356i	0.840723	−	0.353486i
$763$	−651.169	−	651.169i	−0.853433	−	0.853433i
$764$	−137.158	+	140.106i	−0.179526	+	0.183385i
$765$		0			0
$766$	−471.345	−	192.308i	−0.615332	−	0.251055i
$767$		−	1184.81i		−	1.54473i
$768$	−336.485	+	366.392i	−0.438131	+	0.477072i
$769$	−105.447			−0.137122			−0.0685611	−	0.997647i	$-0.521841\pi$
$769$	−105.447			−0.137122			−0.0685611	+	0.997647i	$0.521841\pi$
$770$		0			0
$771$	−618.434	+	618.434i	−0.802120	+	0.802120i
$772$	1063.23	+	1040.87i	1.37725	+	1.34827i
$773$	−124.080	+	124.080i	−0.160518	+	0.160518i	−0.782796	−	0.622278i	$-0.786207\pi$
$773$	−124.080	+	124.080i	−0.160518	+	0.160518i	0.622278	+	0.782796i	$0.286207\pi$
$774$	−109.845	−	261.254i	−0.141919	−	0.337537i
$775$		0			0
$776$	120.334	−	52.1074i	0.155070	−	0.0671487i
$777$			249.157i			0.320665i
$778$	−35.3201	−	84.0045i	−0.0453986	−	0.107975i
$779$	−1334.90	−	1334.90i	−1.71360	−	1.71360i
$780$		0			0
$781$	166.627	+	166.627i	0.213351	+	0.213351i
$782$	−49.0135	+	120.131i	−0.0626771	+	0.153620i
$783$			737.512i			0.941905i
$784$	−8.13131	−	382.382i	−0.0103716	−	0.487732i
$785$		0			0
$786$	255.292	+	104.159i	0.324799	+	0.132518i
$787$	615.831	−	615.831i	0.782505	−	0.782505i	−0.197748	−	0.980253i	$-0.563363\pi$
$787$	615.831	−	615.831i	0.782505	−	0.782505i	0.980253	+	0.197748i	$0.0633628\pi$
$788$	−931.700	+	9.90513i	−1.18236	+	0.0125700i
$789$	−273.715	+	273.715i	−0.346914	+	0.346914i
$790$		0			0
$791$	238.693			0.301761
$792$	139.794	−	353.326i	0.176508	−	0.446119i
$793$		−	563.373i		−	0.710433i
$794$	−273.976	+	115.195i	−0.345058	+	0.145081i
$795$		0			0
$796$	403.359	+	394.873i	0.506733	+	0.496072i
$797$	−56.7101	−	56.7101i	−0.0711545	−	0.0711545i	0.670634	−	0.741788i	$-0.266022\pi$
$797$	−56.7101	−	56.7101i	−0.0711545	−	0.0711545i	−0.741788	+	0.670634i	$0.766022\pi$
$798$	447.171	+	182.446i	0.560365	+	0.228629i
$799$			876.735i			1.09729i
$800$		0			0
$801$	−446.089			−0.556915
$802$	−187.687	+	460.017i	−0.234024	+	0.573588i
$803$	−200.686	+	200.686i	−0.249921	+	0.249921i
$804$	−45.5862	+	46.5659i	−0.0566993	+	0.0579178i
$805$		0			0
$806$	−399.731	−	950.711i	−0.495944	−	1.17954i
$807$	132.300			0.163940
$808$	437.081	−	1104.71i	0.540942	−	1.36721i
$809$			556.339i			0.687688i	0.939027	+	0.343844i	$0.111729\pi$
$809$			556.339i			0.687688i	−0.939027	+	0.343844i	$0.888271\pi$
$810$		0			0
$811$	−993.474	−	993.474i	−1.22500	−	1.22500i	−0.965833	−	0.259166i	$-0.916552\pi$
$811$	−993.474	−	993.474i	−1.22500	−	1.22500i	−0.259166	−	0.965833i	$-0.583448\pi$
$812$	5.68395	+	534.646i	0.00699994	+	0.658431i
$813$	−436.815	−	436.815i	−0.537288	−	0.537288i
$814$	175.822	−	430.937i	0.215998	−	0.529407i
$815$		0			0
$816$	332.897	+	319.034i	0.407963	+	0.390973i
$817$	−672.886			−0.823606
$818$	843.111	+	343.989i	1.03070	+	0.420525i
$819$	289.227	−	289.227i	0.353147	−	0.353147i
$820$		0			0
$821$	620.009	−	620.009i	0.755188	−	0.755188i	−0.220255	−	0.975442i	$-0.570689\pi$
$821$	620.009	−	620.009i	0.755188	−	0.755188i	0.975442	+	0.220255i	$0.0706889\pi$
$822$	−16.9148	+	7.11192i	−0.0205776	+	0.00865197i
$823$	−646.223			−0.785204			−0.392602	−	0.919708i	$-0.628425\pi$
$823$	−646.223			−0.785204			−0.392602	+	0.919708i	$0.628425\pi$
$824$	346.837	−	150.188i	0.420918	−	0.182267i
$825$		0			0
$826$	−700.131	+	294.373i	−0.847616	+	0.356384i
$827$	−836.004	−	836.004i	−1.01089	−	1.01089i	−0.999940	−	0.0109471i	$-0.996515\pi$
$827$	−836.004	−	836.004i	−1.01089	−	1.01089i	−0.0109471	−	0.999940i	$-0.503485\pi$
$828$	63.9431	−	65.3173i	0.0772259	−	0.0788856i
$829$	234.984	+	234.984i	0.283454	+	0.283454i	0.834485	−	0.551031i	$-0.185765\pi$
$829$	234.984	+	234.984i	0.283454	+	0.283454i	−0.551031	+	0.834485i	$0.685765\pi$
$830$		0			0
$831$		−	187.711i		−	0.225886i
$832$	999.795	−	31.8968i	1.20168	−	0.0383375i
$833$	−354.506			−0.425578
$834$	150.100	−	367.891i	0.179975	−	0.441116i
$835$		0			0
$836$	−644.674	−	631.111i	−0.771141	−	0.754917i
$837$	−644.819	+	644.819i	−0.770393	+	0.770393i
$838$	−324.657	−	772.157i	−0.387419	−	0.921428i
$839$	219.575			0.261711			0.130855	−	0.991401i	$-0.458228\pi$
$839$	219.575			0.261711			0.130855	+	0.991401i	$0.458228\pi$
$840$		0			0
$841$		−	129.031i		−	0.153425i
$842$	−389.019	−	925.234i	−0.462018	−	1.09885i
$843$	180.326	+	180.326i	0.213909	+	0.213909i
$844$	944.681	−	10.0431i	1.11929	−	0.0118994i
$845$		0			0
$846$	233.333	−	571.895i	0.275807	−	0.675998i
$847$			192.035i			0.226723i
$848$	351.900	+	337.245i	0.414976	+	0.397695i
$849$	1062.25			1.25117
$850$		0			0
$851$	79.1687	−	79.1687i	0.0930302	−	0.0930302i
$852$	201.442	−	2.14158i	0.236434	−	0.00251359i
$853$	47.0723	−	47.0723i	0.0551844	−	0.0551844i	−0.678976	−	0.734160i	$-0.737576\pi$
$853$	47.0723	−	47.0723i	0.0551844	−	0.0551844i	0.734160	+	0.678976i	$0.237576\pi$
$854$	−332.910	+	139.973i	−0.389824	+	0.163903i
$855$		0			0
$856$	586.446	+	232.029i	0.685101	+	0.271062i
$857$		−	1620.86i		−	1.89132i	−0.325154	−	0.945661i	$-0.605416\pi$
$857$		−	1620.86i		−	1.89132i	0.325154	−	0.945661i	$-0.394584\pi$
$858$	509.114	−	214.060i	0.593373	−	0.249487i
$859$	317.610	+	317.610i	0.369744	+	0.369744i	0.867384	−	0.497640i	$-0.165800\pi$
$859$	317.610	+	317.610i	0.369744	+	0.369744i	−0.497640	+	0.867384i	$0.665800\pi$
$860$		0			0
$861$	−523.844	−	523.844i	−0.608414	−	0.608414i
$862$	−147.928	−	60.3545i	−0.171610	−	0.0700168i
$863$			1407.45i			1.63088i	0.578842	+	0.815439i	$0.303505\pi$
$863$			1407.45i			1.63088i	−0.578842	+	0.815439i	$0.696495\pi$
$864$	−360.071	−	807.870i	−0.416749	−	0.935035i
$865$		0			0
$866$	1.19011	−	2.91693i	0.00137426	−	0.00336828i
$867$	−94.8970	+	94.8970i	−0.109454	+	0.109454i
$868$	−462.480	+	472.419i	−0.532811	+	0.544262i
$869$	−784.699	+	784.699i	−0.902991	+	0.902991i
$870$		0			0
$871$	131.036			0.150443
$872$	1367.47	+	541.044i	1.56820	+	0.620463i
$873$			85.6288i			0.0980857i
$874$	−84.1157	−	200.059i	−0.0962422	−	0.228900i
$875$		0			0
$876$	2.57932	+	242.617i	0.00294443	+	0.276960i
$877$	−507.991	−	507.991i	−0.579237	−	0.579237i	0.355456	−	0.934693i	$-0.384326\pi$
$877$	−507.991	−	507.991i	−0.579237	−	0.579237i	−0.934693	+	0.355456i	$0.884326\pi$
$878$	188.695	−	462.487i	0.214914	−	0.526751i
$879$		−	607.614i		−	0.691256i
$880$		0			0
$881$	1167.86			1.32561			0.662803	−	0.748793i	$-0.269367\pi$
$881$	1167.86			1.32561			0.662803	+	0.748793i	$0.269367\pi$
$882$	231.245	+	94.3477i	0.262182	+	0.106970i
$883$	641.739	−	641.739i	0.726771	−	0.726771i	−0.243204	−	0.969975i	$-0.578198\pi$
$883$	641.739	−	641.739i	0.726771	−	0.726771i	0.969975	+	0.243204i	$0.0781984\pi$
$884$	−9.85644	−	927.120i	−0.0111498	−	1.04878i
$885$		0			0
$886$	−315.569	+	132.682i	−0.356172	+	0.149754i
$887$	−172.729			−0.194734			−0.0973670	−	0.995249i	$-0.531042\pi$
$887$	−172.729			−0.194734			−0.0973670	+	0.995249i	$0.531042\pi$
$888$	−158.108	−	365.127i	−0.178049	−	0.411179i
$889$			895.796i			1.00764i
$890$		0			0
$891$	−43.0372	−	43.0372i	−0.0483021	−	0.0483021i
$892$	−1009.02	+	1030.70i	−1.13118	+	1.15549i
$893$	−1036.97	−	1036.97i	−1.16122	−	1.16122i
$894$	−420.170	−	171.429i	−0.469989	−	0.191755i
$895$		0			0
$896$	−267.253	−	582.876i	−0.298274	−	0.650531i
$897$	132.856			0.148112
$898$	−224.473	+	550.179i	−0.249970	+	0.612671i
$899$	−622.487	+	622.487i	−0.692421	+	0.692421i
$900$		0			0
$901$	319.453	−	319.453i	0.354554	−	0.354554i
$902$	536.372	+	1275.69i	0.594647	+	1.41430i
$903$	−264.056			−0.292421
$904$	−349.793	+	151.468i	−0.386939	+	0.167553i
$905$		0			0
$906$	143.584	+	341.497i	0.158481	+	0.376929i
$907$	83.4405	+	83.4405i	0.0919962	+	0.0919962i	0.751607	−	0.659611i	$-0.229279\pi$
$907$	83.4405	+	83.4405i	0.0919962	+	0.0919962i	−0.659611	+	0.751607i	$0.729279\pi$
$908$	919.872	−	9.77938i	1.01307	−	0.0107702i
$909$	548.562	+	548.562i	0.603478	+	0.603478i
$910$		0			0
$911$		−	692.752i		−	0.760430i	−0.924898	−	0.380215i	$-0.875850\pi$
$911$		−	692.752i		−	0.760430i	0.924898	−	0.380215i	$-0.124150\pi$
$912$	−771.083	+	16.3970i	−0.845486	+	0.0179792i
$913$	1491.40			1.63351
$914$	−668.699	−	272.829i	−0.731618	−	0.298500i
$915$		0			0
$916$	−34.5755	+	0.367581i	−0.0377462	+	0.000401289i
$917$	−251.310	+	251.310i	−0.274057	+	0.274057i
$918$	−755.733	+	317.752i	−0.823239	+	0.346135i
$919$	23.1013			0.0251374			0.0125687	−	0.999921i	$-0.495999\pi$
$919$	23.1013			0.0251374			0.0125687	+	0.999921i	$0.495999\pi$
$920$		0			0
$921$		−	221.048i		−	0.240009i
$922$	434.116	−	182.526i	0.470842	−	0.197968i
$923$	−286.440	−	286.440i	−0.310336	−	0.310336i
$924$	−252.985	−	247.662i	−0.273793	−	0.268033i
$925$		0			0
$926$	1319.27	+	538.261i	1.42470	+	0.581276i
$927$			246.806i			0.266241i
$928$	−347.601	−	779.891i	−0.374570	−	0.840400i
$929$	−862.326			−0.928231			−0.464115	−	0.885775i	$-0.653628\pi$
$929$	−862.326			−0.928231			−0.464115	+	0.885775i	$0.653628\pi$
$930$		0			0
$931$	419.298	−	419.298i	0.450374	−	0.450374i
$932$	340.313	−	347.627i	0.365143	−	0.372990i
$933$	−595.195	+	595.195i	−0.637937	+	0.637937i
$934$	225.412	+	536.115i	0.241340	+	0.573998i
$935$		0			0
$936$	−240.313	+	607.384i	−0.256745	+	0.648915i
$937$		−	968.975i		−	1.03412i	−0.855948	−	0.517062i	$-0.827026\pi$
$937$		−	968.975i		−	1.03412i	0.855948	−	0.517062i	$-0.172974\pi$
$938$	−32.5566	−	77.4319i	−0.0347085	−	0.0825500i
$939$	−370.445	−	370.445i	−0.394510	−	0.394510i
$940$		0			0
$941$	165.112	+	165.112i	0.175465	+	0.175465i	0.789375	−	0.613911i	$-0.210405\pi$
$941$	165.112	+	165.112i	0.175465	+	0.175465i	−0.613911	+	0.789375i	$0.710405\pi$
$942$	−214.799	+	526.469i	−0.228025	+	0.558884i
$943$			332.900i			0.353022i
$944$	839.207	−	875.674i	0.888991	−	0.927621i
$945$		0			0
$946$	456.707	+	186.336i	0.482777	+	0.196973i
$947$	−347.438	+	347.438i	−0.366883	+	0.366883i	−0.866339	−	0.499456i	$-0.833533\pi$
$947$	−347.438	+	347.438i	−0.366883	+	0.366883i	0.499456	+	0.866339i	$0.333533\pi$
$948$	10.0853	+	948.650i	0.0106385	+	1.00069i
$949$	344.989	−	344.989i	0.363529	−	0.363529i
$950$		0			0
$951$	55.1343			0.0579751
$952$	−545.406	+	236.173i	−0.572906	+	0.248081i
$953$		−	1222.59i		−	1.28288i	−0.767171	−	0.641442i	$-0.778336\pi$
$953$		−	1222.59i		−	1.28288i	0.767171	−	0.641442i	$-0.221664\pi$
$954$	−293.398	+	123.361i	−0.307545	+	0.129309i
$955$		0			0
$956$	628.106	−	641.604i	0.657014	−	0.671134i
$957$	−333.347	−	333.347i	−0.348325	−	0.348325i
$958$	−1435.15	−	585.539i	−1.49806	−	0.611210i
$959$		−	23.6520i		−	0.0246632i
$960$		0			0
$961$	−127.502			−0.132676
$962$	−302.247	+	740.801i	−0.314186	+	0.770064i
$963$	−291.210	+	291.210i	−0.302398	+	0.302398i
$964$	365.888	+	358.190i	0.379552	+	0.371566i
$965$		0			0
$966$	−33.0089	−	78.5076i	−0.0341707	−	0.0812708i
$967$	−967.881			−1.00091			−0.500455	−	0.865762i	$-0.666834\pi$
$967$	−967.881			−1.00091			−0.500455	+	0.865762i	$0.666834\pi$
$968$	−121.860	−	281.418i	−0.125888	−	0.290721i
$969$			714.871i			0.737741i
$970$		0			0
$971$	−84.0735	−	84.0735i	−0.0865844	−	0.0865844i	0.662488	−	0.749072i	$-0.269501\pi$
$971$	−84.0735	−	84.0735i	−0.0865844	−	0.0865844i	−0.749072	+	0.662488i	$0.769501\pi$
$972$	942.955	−	10.0248i	0.970118	−	0.0103136i
$973$	362.154	+	362.154i	0.372203	+	0.372203i
$974$	−202.195	+	495.575i	−0.207592	+	0.508804i
$975$		0			0
$976$	399.040	−	416.380i	0.408852	−	0.426619i
$977$	759.084			0.776954			0.388477	−	0.921458i	$-0.373001\pi$
$977$	759.084			0.776954			0.388477	+	0.921458i	$0.373001\pi$
$978$	659.883	+	269.232i	0.674727	+	0.275289i
$979$	548.996	−	548.996i	0.560772	−	0.560772i
$980$		0			0
$981$	−679.041	+	679.041i	−0.692192	+	0.692192i
$982$	107.317	−	45.1220i	0.109284	−	0.0459491i
$983$	−278.089			−0.282899			−0.141449	−	0.989945i	$-0.545176\pi$
$983$	−278.089			−0.282899			−0.141449	+	0.989945i	$0.545176\pi$
$984$	1100.09	+	435.252i	1.11797	+	0.442329i
$985$		0			0
$986$	−729.560	+	306.747i	−0.739919	+	0.311102i
$987$	−406.932	−	406.932i	−0.412292	−	0.412292i
$988$	1108.22	+	1084.91i	1.12168	+	1.09809i
$989$	83.9029	+	83.9029i	0.0848361	+	0.0848361i
$990$		0			0
$991$		−	722.074i		−	0.728632i	−0.931275	−	0.364316i	$-0.881303\pi$
$991$		−	722.074i		−	0.728632i	0.931275	−	0.364316i	$-0.118697\pi$
$992$	377.958	−	985.786i	0.381006	−	0.993735i
$993$	446.562			0.449710
$994$	−98.0959	+	240.431i	−0.0986881	+	0.241883i
$995$		0			0
$996$	891.917	−	911.085i	0.895499	−	0.914744i
$997$	388.829	−	388.829i	0.389999	−	0.389999i	−0.484688	−	0.874687i	$-0.661067\pi$
$997$	388.829	−	388.829i	0.389999	−	0.389999i	0.874687	+	0.484688i	$0.161067\pi$
$998$	181.251	+	431.083i	0.181614	+	0.431946i
$999$	707.447			0.708155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.r.g.51.9		44
5.2	odd	4		80.3.k.a.19.3	✓	44
5.3	odd	4		80.3.k.a.19.20	yes	44
5.4	even	2	inner	400.3.r.g.51.14		44
16.11	odd	4	inner	400.3.r.g.251.9		44
20.3	even	4		320.3.k.a.239.7		44
20.7	even	4		320.3.k.a.239.16		44
40.3	even	4		640.3.k.a.479.16		44
40.13	odd	4		640.3.k.b.479.7		44
40.27	even	4		640.3.k.a.479.7		44
40.37	odd	4		640.3.k.b.479.16		44
80.3	even	4		640.3.k.b.159.16		44
80.13	odd	4		640.3.k.a.159.7		44
80.27	even	4		80.3.k.a.59.20	yes	44
80.37	odd	4		320.3.k.a.79.7		44
80.43	even	4		80.3.k.a.59.3	yes	44
80.53	odd	4		320.3.k.a.79.16		44
80.59	odd	4	inner	400.3.r.g.251.14		44
80.67	even	4		640.3.k.b.159.7		44
80.77	odd	4		640.3.k.a.159.16		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.3	✓	44	5.2	odd	4
80.3.k.a.19.20	yes	44	5.3	odd	4
80.3.k.a.59.3	yes	44	80.43	even	4
80.3.k.a.59.20	yes	44	80.27	even	4
320.3.k.a.79.7		44	80.37	odd	4
320.3.k.a.79.16		44	80.53	odd	4
320.3.k.a.239.7		44	20.3	even	4
320.3.k.a.239.16		44	20.7	even	4
400.3.r.g.51.9		44	1.1	even	1	trivial
400.3.r.g.51.14		44	5.4	even	2	inner
400.3.r.g.251.9		44	16.11	odd	4	inner
400.3.r.g.251.14		44	80.59	odd	4	inner
640.3.k.a.159.7		44	80.13	odd	4
640.3.k.a.159.16		44	80.77	odd	4
640.3.k.a.479.7		44	40.27	even	4
640.3.k.a.479.16		44	40.3	even	4
640.3.k.b.159.7		44	80.67	even	4
640.3.k.b.159.16		44	80.3	even	4
640.3.k.b.479.7		44	40.13	odd	4
640.3.k.b.479.16		44	40.37	odd	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.755534 + 1.85180i) q^{2} +(1.37405 - 1.37405i) q^{3} +(-2.85834 - 2.79820i) q^{4} +(1.50632 + 3.58260i) q^{6} -5.00956 q^{7} +(7.34128 - 3.17893i) q^{8} +5.22398i q^{9} +O(q^{10})\)	\(q+(-0.755534 + 1.85180i) q^{2} +(1.37405 - 1.37405i) q^{3} +(-2.85834 - 2.79820i) q^{4} +(1.50632 + 3.58260i) q^{6} -5.00956 q^{7} +(7.34128 - 3.17893i) q^{8} +5.22398i q^{9} +(-6.42909 - 6.42909i) q^{11} +(-7.77235 + 0.0826298i) q^{12} +(11.0519 + 11.0519i) q^{13} +(3.78490 - 9.27672i) q^{14} +(0.340161 + 15.9964i) q^{16} +14.8302 q^{17} +(-9.67378 - 3.94690i) q^{18} +(-17.5407 + 17.5407i) q^{19} +(-6.88338 + 6.88338i) q^{21} +(16.7628 - 7.04800i) q^{22} +4.37435 q^{23} +(5.71926 - 14.4553i) q^{24} +(-28.8160 + 12.1158i) q^{26} +(19.5444 + 19.5444i) q^{27} +(14.3190 + 14.0178i) q^{28} +(18.8676 + 18.8676i) q^{29} +32.9924i q^{31} +(-29.8791 - 11.4559i) q^{32} -17.6678 q^{33} +(-11.2048 + 27.4627i) q^{34} +(14.6177 - 14.9319i) q^{36} +(18.0984 - 18.0984i) q^{37} +(-19.2293 - 45.7346i) q^{38} +30.3717 q^{39} +76.1027i q^{41} +(-7.54602 - 17.9473i) q^{42} +(19.1807 + 19.1807i) q^{43} +(0.386620 + 36.3664i) q^{44} +(-3.30497 + 8.10042i) q^{46} +59.1180i q^{47} +(22.4472 + 21.5124i) q^{48} -23.9043 q^{49} +(20.3775 - 20.3775i) q^{51} +(-0.664617 - 62.5155i) q^{52} +(21.5406 - 21.5406i) q^{53} +(-50.9589 + 21.4259i) q^{54} +(-36.7766 + 15.9251i) q^{56} +48.2036i q^{57} +(-49.1941 + 20.6839i) q^{58} +(-53.6021 - 53.6021i) q^{59} +(-25.4876 - 25.4876i) q^{61} +(-61.0955 - 24.9269i) q^{62} -26.1699i q^{63} +(43.7888 - 46.6749i) q^{64} +(13.3486 - 32.7172i) q^{66} +(5.92820 - 5.92820i) q^{67} +(-42.3898 - 41.4980i) q^{68} +(6.01056 - 6.01056i) q^{69} -25.9177 q^{71} +(16.6067 + 38.3507i) q^{72} -31.2154i q^{73} +(19.8407 + 47.1886i) q^{74} +(99.2197 - 1.05483i) q^{76} +(32.2069 + 32.2069i) q^{77} +(-22.9469 + 56.2423i) q^{78} -122.054i q^{79} +6.69413 q^{81} +(-140.927 - 57.4982i) q^{82} +(-115.988 + 115.988i) q^{83} +(38.9361 - 0.413939i) q^{84} +(-50.0105 + 21.0271i) q^{86} +51.8499 q^{87} +(-67.6354 - 26.7601i) q^{88} +85.3925i q^{89} +(-55.3652 - 55.3652i) q^{91} +(-12.5033 - 12.2403i) q^{92} +(45.3332 + 45.3332i) q^{93} +(-109.475 - 44.6657i) q^{94} +(-56.7963 + 25.3144i) q^{96} +16.3915 q^{97} +(18.0605 - 44.2659i) q^{98} +(33.5855 - 33.5855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{4} - 4 q^{6}+O(q^{10}) \) 44 * q + 4 * q^4 - 4 * q^6	\( 44 q + 4 q^{4} - 4 q^{6} - 4 q^{11} - 4 q^{14} - 32 q^{16} + 36 q^{19} + 32 q^{21} - 16 q^{24} - 56 q^{26} + 4 q^{29} + 192 q^{34} + 212 q^{36} + 8 q^{39} - 224 q^{44} + 124 q^{46} + 148 q^{49} + 128 q^{51} - 24 q^{54} + 360 q^{56} + 68 q^{59} + 28 q^{61} + 16 q^{64} + 448 q^{66} - 128 q^{69} - 264 q^{71} - 480 q^{74} - 464 q^{76} - 116 q^{81} + 496 q^{84} - 852 q^{86} + 384 q^{91} + 340 q^{94} - 1128 q^{96} - 484 q^{99}+O(q^{100}) \) 44 * q + 4 * q^4 - 4 * q^6 - 4 * q^11 - 4 * q^14 - 32 * q^16 + 36 * q^19 + 32 * q^21 - 16 * q^24 - 56 * q^26 + 4 * q^29 + 192 * q^34 + 212 * q^36 + 8 * q^39 - 224 * q^44 + 124 * q^46 + 148 * q^49 + 128 * q^51 - 24 * q^54 + 360 * q^56 + 68 * q^59 + 28 * q^61 + 16 * q^64 + 448 * q^66 - 128 * q^69 - 264 * q^71 - 480 * q^74 - 464 * q^76 - 116 * q^81 + 496 * q^84 - 852 * q^86 + 384 * q^91 + 340 * q^94 - 1128 * q^96 - 484 * q^99

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