LMFDB - Embedded newform 600.2.b.h.251.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(251,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("600.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.b (of order $2$, degree $1$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.537291533250985984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 14x^{8} - 30x^{6} + 56x^{4} - 80x^{2} + 64 $ x^12 - 5x^10 + 14x^8 - 30x^6 + 56x^4 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.8
Root			$-0.847808 - 1.13191i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.h.251.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.847808 + 1.13191i) q^{2} +(0.242431 - 1.71500i) q^{3} +(-0.562443 + 1.91929i) q^{4} +(2.14676 - 1.17958i) q^{6} +3.08957i q^{7} +(-2.64930 + 0.990551i) q^{8} +(-2.88245 - 0.831539i) q^{9} +O(q^{10})$	\(q+(0.847808 + 1.13191i) q^{2} +(0.242431 - 1.71500i) q^{3} +(-0.562443 + 1.91929i) q^{4} +(2.14676 - 1.17958i) q^{6} +3.08957i q^{7} +(-2.64930 + 0.990551i) q^{8} +(-2.88245 - 0.831539i) q^{9} +2.54654i q^{11} +(3.15522 + 1.42988i) q^{12} +5.06696i q^{13} +(-3.49711 + 2.61936i) q^{14} +(-3.36732 - 2.15898i) q^{16} +0.214179i q^{17} +(-1.50254 - 3.96767i) q^{18} +2.60975 q^{19} +(5.29861 + 0.749006i) q^{21} +(-2.88245 + 2.15898i) q^{22} +4.47647 q^{23} +(1.05652 + 4.78370i) q^{24} +(-5.73534 + 4.29581i) q^{26} +(-2.12489 + 4.74182i) q^{27} +(-5.92976 - 1.73770i) q^{28} +7.86770 q^{29} -4.58758i q^{31} +(-0.411070 - 5.64190i) q^{32} +(4.36732 + 0.617360i) q^{33} +(-0.242431 + 0.181582i) q^{34} +(3.21718 - 5.06456i) q^{36} +7.67714i q^{37} +(2.21257 + 2.95400i) q^{38} +(8.68984 + 1.22839i) q^{39} -9.26946i q^{41} +(3.64439 + 6.63256i) q^{42} -11.4049 q^{43} +(-4.88754 - 1.43228i) q^{44} +(3.79518 + 5.06696i) q^{46} -10.5972 q^{47} +(-4.51899 + 5.25155i) q^{48} -2.54541 q^{49} +(0.367316 + 0.0519235i) q^{51} +(-9.72494 - 2.84987i) q^{52} +9.51198 q^{53} +(-7.16881 + 1.61497i) q^{54} +(-3.06037 - 8.18520i) q^{56} +(0.632684 - 4.47572i) q^{57} +(6.67030 + 8.90553i) q^{58} -0.428357i q^{59} -1.11217i q^{61} +(5.19273 - 3.88939i) q^{62} +(2.56909 - 8.90553i) q^{63} +(6.03762 - 5.24854i) q^{64} +(3.00385 + 5.46681i) q^{66} -2.35998 q^{67} +(-0.411070 - 0.120463i) q^{68} +(1.08523 - 7.67714i) q^{69} -6.12075 q^{71} +(8.46018 - 0.652221i) q^{72} +12.0147 q^{73} +(-8.68984 + 6.50874i) q^{74} +(-1.46783 + 5.00885i) q^{76} -7.86770 q^{77} +(5.97689 + 10.8776i) q^{78} +11.6319i q^{79} +(7.61709 + 4.79374i) q^{81} +(10.4922 - 7.85873i) q^{82} +2.29913i q^{83} +(-4.41772 + 9.74827i) q^{84} +(-9.66919 - 12.9094i) q^{86} +(1.90737 - 13.4931i) q^{87} +(-2.52248 - 6.74655i) q^{88} -12.4853i q^{89} -15.6547 q^{91} +(-2.51776 + 8.59162i) q^{92} +(-7.86770 - 1.11217i) q^{93} +(-8.98440 - 11.9951i) q^{94} +(-9.77552 - 0.662786i) q^{96} +8.04496 q^{97} +(-2.15802 - 2.88118i) q^{98} +(2.11755 - 7.34028i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9	$ 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9} - 3 q^{12} - 6 q^{16} - 5 q^{18} - 4 q^{19} - 2 q^{22} + 5 q^{24} + 8 q^{27} - 20 q^{28} + 18 q^{33} - 2 q^{34} + 19 q^{36} - 14 q^{42} - 40 q^{43} - 16 q^{46} - 27 q^{48} - 36 q^{49} - 30 q^{51} - 4 q^{52} - 30 q^{54} + 42 q^{57} + 52 q^{58} + 10 q^{64} + 7 q^{66} - 60 q^{67} - 39 q^{72} + 12 q^{73} - 38 q^{76} + 54 q^{78} - 10 q^{81} + 58 q^{82} - 34 q^{84} + 34 q^{88} - 24 q^{91} + 28 q^{94} - 31 q^{96} - 32 q^{97} + 58 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9 - 3 * q^12 - 6 * q^16 - 5 * q^18 - 4 * q^19 - 2 * q^22 + 5 * q^24 + 8 * q^27 - 20 * q^28 + 18 * q^33 - 2 * q^34 + 19 * q^36 - 14 * q^42 - 40 * q^43 - 16 * q^46 - 27 * q^48 - 36 * q^49 - 30 * q^51 - 4 * q^52 - 30 * q^54 + 42 * q^57 + 52 * q^58 + 10 * q^64 + 7 * q^66 - 60 * q^67 - 39 * q^72 + 12 * q^73 - 38 * q^76 + 54 * q^78 - 10 * q^81 + 58 * q^82 - 34 * q^84 + 34 * q^88 - 24 * q^91 + 28 * q^94 - 31 * q^96 - 32 * q^97 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	0.847808	+	1.13191i	0.599491	+	0.800382i
$2$	0.847808	+	1.13191i	0.599491	+	0.800382i
$3$	0.242431	−	1.71500i	0.139968	−	0.990156i
$3$	0.242431	−	1.71500i	0.139968	−	0.990156i
$4$	−0.562443	+	1.91929i	−0.281221	+	0.959643i
$5$		0			0
$5$		0			0
$6$	2.14676	−	1.17958i	0.876412	−	0.481562i
$7$			3.08957i			1.16775i	0.811845	+	0.583873i	$0.198463\pi$
$7$			3.08957i			1.16775i	−0.811845	+	0.583873i	$0.801537\pi$
$8$	−2.64930	+	0.990551i	−0.936670	+	0.350213i
$9$	−2.88245	−	0.831539i	−0.960818	−	0.277180i
$10$		0			0
$11$			2.54654i			0.767810i	0.923373	+	0.383905i	$0.125421\pi$
$11$			2.54654i			0.767810i	−0.923373	+	0.383905i	$0.874579\pi$
$12$	3.15522	+	1.42988i	0.910834	+	0.412772i
$13$			5.06696i			1.40532i	0.711525	+	0.702661i	$0.248005\pi$
$13$			5.06696i			1.40532i	−0.711525	+	0.702661i	$0.751995\pi$
$14$	−3.49711	+	2.61936i	−0.934642	+	0.700053i
$15$		0			0
$16$	−3.36732	−	2.15898i	−0.841829	−	0.539744i
$17$			0.214179i			0.0519459i	0.999663	+	0.0259730i	$0.00826838\pi$
$17$			0.214179i			0.0519459i	−0.999663	+	0.0259730i	$0.991732\pi$
$18$	−1.50254	−	3.96767i	−0.354152	−	0.935188i
$19$	2.60975			0.598717			0.299359	−	0.954141i	$-0.403227\pi$
$19$	2.60975			0.598717			0.299359	+	0.954141i	$0.403227\pi$
$20$		0			0
$21$	5.29861	+	0.749006i	1.15625	+	0.163447i
$22$	−2.88245	+	2.15898i	−0.614541	+	0.460295i
$23$	4.47647			0.933408			0.466704	−	0.884414i	$-0.345441\pi$
$23$	4.47647			0.933408			0.466704	+	0.884414i	$0.345441\pi$
$24$	1.05652	+	4.78370i	0.215662	+	0.976468i
$25$		0			0
$26$	−5.73534	+	4.29581i	−1.12479	+	0.842478i
$27$	−2.12489	+	4.74182i	−0.408934	+	0.912564i
$28$	−5.92976	−	1.73770i	−1.12062	−	0.328395i
$29$	7.86770			1.46100			0.730498	−	0.682915i	$-0.239288\pi$
$29$	7.86770			1.46100			0.730498	+	0.682915i	$0.239288\pi$
$30$		0			0
$31$		−	4.58758i		−	0.823953i	−0.911194	−	0.411977i	$-0.864839\pi$
$31$		−	4.58758i		−	0.823953i	0.911194	−	0.411977i	$-0.135161\pi$
$32$	−0.411070	−	5.64190i	−0.0726676	−	0.997356i
$33$	4.36732	+	0.617360i	0.760252	+	0.107469i
$34$	−0.242431	+	0.181582i	−0.0415766	+	0.0311411i
$35$		0			0
$36$	3.21718	−	5.06456i	0.536196	−	0.844094i
$37$			7.67714i			1.26211i	0.775736	+	0.631057i	$0.217379\pi$
$37$			7.67714i			1.26211i	−0.775736	+	0.631057i	$0.782621\pi$
$38$	2.21257	+	2.95400i	0.358925	+	0.479202i
$39$	8.68984	+	1.22839i	1.39149	+	0.196700i
$40$		0			0
$41$		−	9.26946i		−	1.44765i	−0.689985	−	0.723823i	$-0.742383\pi$
$41$		−	9.26946i		−	1.44765i	0.689985	−	0.723823i	$-0.257617\pi$
$42$	3.64439	+	6.63256i	0.562342	+	1.02343i
$43$	−11.4049			−1.73924			−0.869618	−	0.493725i	$-0.835635\pi$
$43$	−11.4049			−1.73924			−0.869618	+	0.493725i	$0.835635\pi$
$44$	−4.88754	−	1.43228i	−0.736824	−	0.215925i
$45$		0			0
$46$	3.79518	+	5.06696i	0.559569	+	0.747082i
$47$	−10.5972			−1.54576			−0.772881	−	0.634551i	$-0.781185\pi$
$47$	−10.5972			−1.54576			−0.772881	+	0.634551i	$0.781185\pi$
$48$	−4.51899	+	5.25155i	−0.652260	+	0.757996i
$49$	−2.54541			−0.363631
$50$		0			0
$51$	0.367316	+	0.0519235i	0.0514346	+	0.00727075i
$52$	−9.72494	−	2.84987i	−1.34861	−	0.395206i
$53$	9.51198			1.30657			0.653285	−	0.757112i	$-0.273390\pi$
$53$	9.51198			1.30657			0.653285	+	0.757112i	$0.273390\pi$
$54$	−7.16881	+	1.61497i	−0.975552	+	0.219770i
$55$		0			0
$56$	−3.06037	−	8.18520i	−0.408960	−	1.09379i
$57$	0.632684	−	4.47572i	0.0838010	−	0.592823i
$58$	6.67030	+	8.90553i	0.875853	+	1.16935i
$59$		−	0.428357i		−	0.0557674i	−0.999611	−	0.0278837i	$-0.991123\pi$
$59$		−	0.428357i		−	0.0557674i	0.999611	−	0.0278837i	$-0.00887680\pi$
$60$		0			0
$61$		−	1.11217i		−	0.142399i	−0.997462	−	0.0711995i	$-0.977317\pi$
$61$		−	1.11217i		−	0.142399i	0.997462	−	0.0711995i	$-0.0226827\pi$
$62$	5.19273	−	3.88939i	0.659477	−	0.493953i
$63$	2.56909	−	8.90553i	0.323675	−	1.12199i
$64$	6.03762	−	5.24854i	0.754702	−	0.656068i
$65$		0			0
$66$	3.00385	+	5.46681i	0.369748	+	0.672918i
$67$	−2.35998			−0.288317			−0.144159	−	0.989555i	$-0.546048\pi$
$67$	−2.35998			−0.288317			−0.144159	+	0.989555i	$0.546048\pi$
$68$	−0.411070	−	0.120463i	−0.0498495	−	0.0146083i
$69$	1.08523	−	7.67714i	0.130647	−	0.924219i
$70$		0			0
$71$	−6.12075			−0.726399			−0.363199	−	0.931711i	$-0.618316\pi$
$71$	−6.12075			−0.726399			−0.363199	+	0.931711i	$0.618316\pi$
$72$	8.46018	−	0.652221i	0.997042	−	0.0768650i
$73$	12.0147			1.40621			0.703106	−	0.711085i	$-0.251796\pi$
$73$	12.0147			1.40621			0.703106	+	0.711085i	$0.251796\pi$
$74$	−8.68984	+	6.50874i	−1.01017	+	0.756626i
$75$		0			0
$76$	−1.46783	+	5.00885i	−0.168372	+	0.574555i
$77$	−7.86770			−0.896608
$78$	5.97689	+	10.8776i	0.676750	+	1.23164i
$79$			11.6319i			1.30869i	0.756194	+	0.654347i	$0.227057\pi$
$79$			11.6319i			1.30869i	−0.756194	+	0.654347i	$0.772943\pi$
$80$		0			0
$81$	7.61709	+	4.79374i	0.846343	+	0.532638i
$82$	10.4922	−	7.85873i	1.15867	−	0.867851i
$83$			2.29913i			0.252362i	0.992007	+	0.126181i	$0.0402720\pi$
$83$			2.29913i			0.252362i	−0.992007	+	0.126181i	$0.959728\pi$
$84$	−4.41772	+	9.74827i	−0.482013	+	1.06362i
$85$		0			0
$86$	−9.66919	−	12.9094i	−1.04266	−	1.39205i
$87$	1.90737	−	13.4931i	0.204492	−	1.44661i
$88$	−2.52248	−	6.74655i	−0.268897	−	0.719185i
$89$		−	12.4853i		−	1.32344i	−0.749752	−	0.661719i	$-0.769827\pi$
$89$		−	12.4853i		−	1.32344i	0.749752	−	0.661719i	$-0.230173\pi$
$90$		0			0
$91$	−15.6547			−1.64106
$92$	−2.51776	+	8.59162i	−0.262494	+	0.895738i
$93$	−7.86770	−	1.11217i	−0.815842	−	0.115327i
$94$	−8.98440	−	11.9951i	−0.926670	−	1.23720i
$95$		0			0
$96$	−9.77552	−	0.662786i	−0.997709	−	0.0676453i
$97$	8.04496			0.816842			0.408421	−	0.912794i	$-0.366080\pi$
$97$	8.04496			0.816842			0.408421	+	0.912794i	$0.366080\pi$
$98$	−2.15802	−	2.88118i	−0.217993	−	0.291043i
$99$	2.11755	−	7.34028i	0.212821	−	0.737726i
$100$		0			0
$101$	−1.08523			−0.107985			−0.0539924	−	0.998541i	$-0.517195\pi$
$101$	−1.08523			−0.107985			−0.0539924	+	0.998541i	$0.517195\pi$
$102$	0.252641	+	0.459790i	0.0250152	+	0.0455260i
$103$		−	11.6319i		−	1.14613i	−0.819511	−	0.573064i	$-0.805755\pi$
$103$		−	11.6319i		−	1.14613i	0.819511	−	0.573064i	$-0.194245\pi$
$104$	−5.01908	−	13.4239i	−0.492162	−	1.31632i
$105$		0			0
$106$	8.06433	+	10.7667i	0.783277	+	1.04576i
$107$		−	6.50874i		−	0.629224i	−0.949220	−	0.314612i	$-0.898126\pi$
$107$		−	6.50874i		−	0.629224i	0.949220	−	0.314612i	$-0.101874\pi$
$108$	−7.90578	−	6.74526i	−0.760734	−	0.649063i
$109$		−	5.06696i		−	0.485327i	−0.970111	−	0.242663i	$-0.921979\pi$
$109$		−	5.06696i		−	0.485327i	0.970111	−	0.242663i	$-0.0780210\pi$
$110$		0			0
$111$	13.1663	+	1.86118i	1.24969	+	0.176655i
$112$	6.67030	−	10.4035i	0.630284	−	0.983043i
$113$		−	6.05364i		−	0.569479i	−0.958605	−	0.284739i	$-0.908093\pi$
$113$		−	6.05364i		−	0.569479i	0.958605	−	0.284739i	$-0.0919070\pi$
$114$	5.60251	−	3.07841i	0.524723	−	0.288319i
$115$		0			0
$116$	−4.42513	+	15.1004i	−0.410863	+	1.40203i
$117$	4.21337	−	14.6053i	0.389526	−	1.35026i
$118$	0.484862	−	0.363165i	0.0446352	−	0.0334320i
$119$	−0.661719			−0.0606597
$120$		0			0
$121$	4.51514			0.410467
$122$	1.25888	−	0.942908i	0.113973	−	0.0853668i
$123$	−15.8971	−	2.24720i	−1.43340	−	0.202624i
$124$	8.80487	+	2.58025i	0.790701	+	0.231713i
$125$		0			0
$126$	12.2584	−	4.64220i	1.09206	−	0.413560i
$127$		−	0.958763i		−	0.0850765i	−0.999095	−	0.0425382i	$-0.986456\pi$
$127$		−	0.958763i		−	0.0850765i	0.999095	−	0.0425382i	$-0.0135444\pi$
$128$	11.0596	+	2.38428i	0.977542	+	0.210743i
$129$	−2.76491	+	19.5595i	−0.243437	+	1.72211i
$130$		0			0
$131$		−	3.78126i		−	0.330370i	−0.986263	−	0.165185i	$-0.947178\pi$
$131$		−	3.78126i		−	0.330370i	0.986263	−	0.165185i	$-0.0528221\pi$
$132$	−3.64126	+	8.03490i	−0.316931	+	0.699348i
$133$			8.06299i			0.699149i
$134$	−2.00081	−	2.67128i	−0.172843	−	0.230764i
$135$		0			0
$136$	−0.212155	−	0.567424i	−0.0181921	−	0.0486562i
$137$			13.1878i			1.12671i	0.826215	+	0.563355i	$0.190490\pi$
$137$			13.1878i			1.12671i	−0.826215	+	0.563355i	$0.809510\pi$
$138$	9.60991	−	5.28036i	0.818050	−	0.449494i
$139$	17.2947			1.46692			0.733460	−	0.679733i	$-0.237904\pi$
$139$	17.2947			1.46692			0.733460	+	0.679733i	$0.237904\pi$
$140$		0			0
$141$	−2.56909	+	18.1742i	−0.216357	+	1.53055i
$142$	−5.18922	−	6.92814i	−0.435470	−	0.581396i
$143$	−12.9032			−1.07902
$144$	7.91086	+	9.02321i	0.659239	+	0.751934i
$145$		0			0
$146$	10.1861	+	13.5995i	0.843011	+	1.12551i
$147$	−0.617087	+	4.36539i	−0.0508965	+	0.360051i
$148$	−14.7346	−	4.31795i	−1.21118	−	0.354934i
$149$	−3.81475			−0.312516			−0.156258	−	0.987716i	$-0.549943\pi$
$149$	−3.81475			−0.312516			−0.156258	+	0.987716i	$0.549943\pi$
$150$		0			0
$151$		−	13.2235i		−	1.07611i	−0.842909	−	0.538056i	$-0.819159\pi$
$151$		−	13.2235i		−	1.07611i	0.842909	−	0.538056i	$-0.180841\pi$
$152$	−6.91401	+	2.58509i	−0.560800	+	0.209678i
$153$	0.178098	−	0.617360i	0.0143983	−	0.0499106i
$154$	−6.67030	−	8.90553i	−0.537508	−	0.717628i
$155$		0			0
$156$	−7.24516	+	15.9874i	−0.580077	+	1.28002i
$157$			6.56497i			0.523942i	0.965076	+	0.261971i	$0.0843725\pi$
$157$			6.56497i			0.523942i	−0.965076	+	0.261971i	$0.915628\pi$
$158$	−13.1663	+	9.86165i	−1.04746	+	0.784550i
$159$	2.30600	−	16.3131i	0.182878	−	1.29371i
$160$		0			0
$161$			13.8303i			1.08998i
$162$	1.03174	+	12.6860i	0.0810611	+	0.996709i
$163$	8.13957			0.637540			0.318770	−	0.947832i	$-0.396730\pi$
$163$	8.13957			0.637540			0.318770	+	0.947832i	$0.396730\pi$
$164$	17.7907	+	5.21354i	1.38922	+	0.407109i
$165$		0			0
$166$	−2.60241	+	1.94922i	−0.201986	+	0.151289i
$167$	21.8561			1.69128			0.845640	−	0.533754i	$-0.179219\pi$
$167$	21.8561			1.69128			0.845640	+	0.533754i	$0.179219\pi$
$168$	−14.7795	+	3.26420i	−1.14027	+	0.251838i
$169$	−12.6741			−0.974929
$170$		0			0
$171$	−7.52248	−	2.17011i	−0.575258	−	0.165952i
$172$	6.41462	−	21.8893i	0.489110	−	1.66905i
$173$	9.51198			0.723182			0.361591	−	0.932337i	$-0.382234\pi$
$173$	9.51198			0.723182			0.361591	+	0.932337i	$0.382234\pi$
$174$	16.8901	−	9.28059i	1.28043	−	0.703560i
$175$		0			0
$176$	5.49792	−	8.57500i	0.414421	−	0.646365i
$177$	−0.734633	−	0.103847i	−0.0552184	−	0.00780562i
$178$	14.1322	−	10.5851i	1.05926	−	0.793389i
$179$			16.2398i			1.21382i	0.794771	+	0.606910i	$0.207591\pi$
$179$			16.2398i			1.21382i	−0.794771	+	0.606910i	$0.792409\pi$
$180$		0			0
$181$			9.74808i			0.724569i	0.932068	+	0.362284i	$0.118003\pi$
$181$			9.74808i			0.724569i	−0.932068	+	0.362284i	$0.881997\pi$
$182$	−13.2722	−	17.7197i	−0.983800	−	1.31347i
$183$	−1.90737	−	0.269625i	−0.140997	−	0.0199312i
$184$	−11.8595	+	4.43417i	−0.874295	+	0.326891i
$185$		0			0
$186$	−5.41142	−	9.84844i	−0.396785	−	0.722123i
$187$	−0.545414			−0.0398846
$188$	5.96033	−	20.3391i	0.434701	−	1.48338i
$189$	−14.6502	−	6.56497i	−1.06564	−	0.477531i
$190$		0			0
$191$	−2.30600			−0.166856			−0.0834281	−	0.996514i	$-0.526587\pi$
$191$	−2.30600			−0.166856			−0.0834281	+	0.996514i	$0.526587\pi$
$192$	−7.53755	−	11.6269i	−0.543976	−	0.839101i
$193$	11.2498			0.809776			0.404888	−	0.914366i	$-0.367310\pi$
$193$	11.2498			0.809776			0.404888	+	0.914366i	$0.367310\pi$
$194$	6.82058	+	9.10617i	0.489689	+	0.653785i
$195$		0			0
$196$	1.43165	−	4.88538i	0.102261	−	0.348956i
$197$	−6.78247			−0.483231			−0.241615	−	0.970372i	$-0.577677\pi$
$197$	−6.78247			−0.483231			−0.241615	+	0.970372i	$0.577677\pi$
$198$	10.1038	−	3.82628i	0.718047	−	0.271922i
$199$			0.632789i			0.0448573i	0.999748	+	0.0224286i	$0.00713985\pi$
$199$			0.632789i			0.0448573i	−0.999748	+	0.0224286i	$0.992860\pi$
$200$		0			0
$201$	−0.572131	+	4.04736i	−0.0403550	+	0.285479i
$202$	−0.920070	−	1.22839i	−0.0647359	−	0.0864291i
$203$			24.3078i			1.70607i
$204$	−0.306251	+	0.675781i	−0.0214418	+	0.0473141i
$205$		0			0
$206$	13.1663	−	9.86165i	0.917340	−	0.687093i
$207$	−12.9032	−	3.72235i	−0.896835	−	0.258722i
$208$	10.9394	−	17.0621i	0.758514	−	1.18304i
$209$			6.64582i			0.459701i
$210$		0			0
$211$	11.6400			0.801332			0.400666	−	0.916224i	$-0.368779\pi$
$211$	11.6400			0.801332			0.400666	+	0.916224i	$0.368779\pi$
$212$	−5.34994	+	18.2562i	−0.367436	+	1.25384i
$213$	−1.48386	+	10.4971i	−0.101672	+	0.719248i
$214$	7.36732	−	5.51817i	0.503619	−	0.377214i
$215$		0			0
$216$	0.932449	−	14.6673i	0.0634451	−	0.997985i
$217$	14.1736			0.962168
$218$	5.73534	−	4.29581i	0.388447	−	0.290949i
$219$	2.91273	−	20.6052i	0.196824	−	1.39237i
$220$		0			0
$221$	−1.08523			−0.0730008
$222$	9.05582	+	16.4810i	0.607787	+	1.10613i
$223$			10.7667i			0.720992i	0.932761	+	0.360496i	$0.117393\pi$
$223$			10.7667i			0.720992i	−0.932761	+	0.360496i	$0.882607\pi$
$224$	17.4310	−	1.27003i	1.16466	−	0.0848573i
$225$		0			0
$226$	6.85218	−	5.13233i	0.455800	−	0.341397i
$227$		−	12.8365i		−	0.851991i	−0.904725	−	0.425996i	$-0.859924\pi$
$227$		−	12.8365i		−	0.851991i	0.904725	−	0.425996i	$-0.140076\pi$
$228$	8.23433	+	3.73164i	0.545332	+	0.247134i
$229$			14.9684i			0.989143i	0.869137	+	0.494571i	$0.164675\pi$
$229$			14.9684i			0.989143i	−0.869137	+	0.494571i	$0.835325\pi$
$230$		0			0
$231$	−1.90737	+	13.4931i	−0.125496	+	0.887781i
$232$	−20.8439	+	7.79336i	−1.36847	+	0.511659i
$233$		−	20.8980i		−	1.36908i	−0.728977	−	0.684538i	$-0.760004\pi$
$233$		−	20.8980i		−	1.36908i	0.728977	−	0.684538i	$-0.239996\pi$
$234$	20.1040	−	7.61332i	1.31424	−	0.497698i
$235$		0			0
$236$	0.822140	+	0.240926i	0.0535167	+	0.0156830i
$237$	19.9488	+	2.81994i	1.29581	+	0.183175i
$238$	−0.561011	−	0.749006i	−0.0363649	−	0.0485509i
$239$	−28.6386			−1.85248			−0.926239	−	0.376937i	$-0.876977\pi$
$239$	−28.6386			−1.85248			−0.926239	+	0.376937i	$0.876977\pi$
$240$		0			0
$241$	9.24977			0.595830			0.297915	−	0.954592i	$-0.403709\pi$
$241$	9.24977			0.595830			0.297915	+	0.954592i	$0.403709\pi$
$242$	3.82797	+	5.11073i	0.246071	+	0.328530i
$243$	10.0679	−	11.9012i	0.645856	−	0.763460i
$244$	2.13457	+	0.625532i	0.136652	+	0.0400456i
$245$		0			0
$246$	−10.9341	−	19.8993i	−0.697132	−	1.26874i
$247$			13.2235i			0.841390i
$248$	4.54423	+	12.1539i	0.288559	+	0.771773i
$249$	3.94301	+	0.557380i	0.249878	+	0.0353225i
$250$		0			0
$251$			1.23472i			0.0779348i	0.999240	+	0.0389674i	$0.0124069\pi$
$251$			1.23472i			0.0779348i	−0.999240	+	0.0389674i	$0.987593\pi$
$252$	15.6473	+	9.93967i	0.985687	+	0.626141i
$253$			11.3995i			0.716680i
$254$	1.08523	−	0.812847i	0.0680937	−	0.0510026i
$255$		0			0
$256$	6.67764	+	14.5399i	0.417352	+	0.908745i
$257$		−	18.6054i		−	1.16057i	−0.814413	−	0.580286i	$-0.802941\pi$
$257$		−	18.6054i		−	1.16057i	0.814413	−	0.580286i	$-0.197059\pi$
$258$	−24.4837	+	13.4530i	−1.52429	+	0.837550i
$259$	−23.7190			−1.47383
$260$		0			0
$261$	−22.6783	−	6.54230i	−1.40375	−	0.404958i
$262$	4.28005	−	3.20578i	0.264422	−	0.198054i
$263$	−11.2589			−0.694255			−0.347128	−	0.937818i	$-0.612843\pi$
$263$	−11.2589			−0.694255			−0.347128	+	0.937818i	$0.612843\pi$
$264$	−12.1819	+	2.69048i	−0.749742	+	0.165587i
$265$		0			0
$266$	−9.12658	+	6.83586i	−0.559586	+	0.419134i
$267$	−21.4123	−	3.02682i	−1.31041	−	0.185238i
$268$	1.32735	−	4.52947i	0.0810809	−	0.276681i
$269$	−11.6824			−0.712291			−0.356146	−	0.934430i	$-0.615909\pi$
$269$	−11.6824			−0.712291			−0.356146	+	0.934430i	$0.615909\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	0.462407	−	0.721207i	0.0280375	−	0.0437296i
$273$	−3.79518	+	26.8478i	−0.229695	+	1.62490i
$274$	−14.9274	+	11.1807i	−0.901798	+	0.675452i
$275$		0			0
$276$	14.1243	+	6.40083i	0.850180	+	0.385285i
$277$			17.4252i			1.04698i	0.852032	+	0.523490i	$0.175370\pi$
$277$			17.4252i			1.04698i	−0.852032	+	0.523490i	$0.824630\pi$
$278$	14.6626	+	19.5761i	0.879405	+	1.17410i
$279$	−3.81475	+	13.2235i	−0.228383	+	0.791669i
$280$		0			0
$281$		−	12.9736i		−	0.773941i	−0.922092	−	0.386971i	$-0.873521\pi$
$281$		−	12.9736i		−	0.773941i	0.922092	−	0.386971i	$-0.126479\pi$
$282$	−22.7497	+	12.5003i	−1.35472	+	0.744381i
$283$	−12.3893			−0.736470			−0.368235	−	0.929733i	$-0.620038\pi$
$283$	−12.3893			−0.736470			−0.368235	+	0.929733i	$0.620038\pi$
$284$	3.44257	−	11.7475i	0.204279	−	0.697084i
$285$		0			0
$286$	−10.9394	−	14.6053i	−0.646863	−	0.863628i
$287$	28.6386			1.69048
$288$	−3.50657	+	16.6043i	−0.206626	+	0.978420i
$289$	16.9541			0.997302
$290$		0			0
$291$	1.95035	−	13.7971i	0.114331	−	0.808801i
$292$	−6.75757	+	23.0596i	−0.395457	+	1.34946i
$293$	−31.7916			−1.85729			−0.928644	−	0.370973i	$-0.879024\pi$
$293$	−31.7916			−1.85729			−0.928644	+	0.370973i	$0.879024\pi$
$294$	−5.46440	+	3.00252i	−0.318690	+	0.175111i
$295$		0			0
$296$	−7.60460	−	20.3391i	−0.442009	−	1.18219i
$297$	−12.0752	−	5.41110i	−0.700676	−	0.313984i
$298$	−3.23417	−	4.31795i	−0.187351	−	0.250132i
$299$			22.6821i			1.31174i
$300$		0			0
$301$		−	35.2363i		−	2.03099i
$302$	14.9678	−	11.2110i	0.861300	−	0.645119i
$303$	−0.263094	+	1.86118i	−0.0151144	+	0.106922i
$304$	−8.78785	−	5.63438i	−0.504017	−	0.323154i
$305$		0			0
$306$	0.849789	−	0.321812i	0.0485792	−	0.0183968i
$307$	10.3288			0.589495			0.294747	−	0.955575i	$-0.404764\pi$
$307$	10.3288			0.589495			0.294747	+	0.955575i	$0.404764\pi$
$308$	4.42513	−	15.1004i	0.252145	−	0.860423i
$309$	−19.9488	−	2.81994i	−1.13485	−	0.160421i
$310$		0			0
$311$	−5.13819			−0.291360			−0.145680	−	0.989332i	$-0.546537\pi$
$311$	−5.13819			−0.291360			−0.145680	+	0.989332i	$0.546537\pi$
$312$	−24.2388	+	5.35336i	−1.37225	+	0.303074i
$313$	−15.6741			−0.885951			−0.442976	−	0.896534i	$-0.646077\pi$
$313$	−15.6741			−0.885951			−0.442976	+	0.896534i	$0.646077\pi$
$314$	−7.43096	+	5.56584i	−0.419353	+	0.314098i
$315$		0			0
$316$	−22.3250	−	6.54230i	−1.25588	−	0.368033i
$317$	8.95293			0.502847			0.251423	−	0.967877i	$-0.419101\pi$
$317$	8.95293			0.502847			0.251423	+	0.967877i	$0.419101\pi$
$318$	20.4200	−	11.2202i	1.14509	−	0.629195i
$319$			20.0354i			1.12177i
$320$		0			0
$321$	−11.1625	−	1.57792i	−0.623030	−	0.0880710i
$322$	−15.6547	+	11.7255i	−0.872403	+	0.653435i
$323$			0.558952i			0.0311009i
$324$	−13.4847	+	11.9232i	−0.749152	+	0.662398i
$325$		0			0
$326$	6.90079	+	9.21326i	0.382199	+	0.510275i
$327$	−8.68984	−	1.22839i	−0.480549	−	0.0679300i
$328$	9.18188	+	24.5576i	0.506984	+	1.35597i
$329$		−	32.7408i		−	1.80506i
$330$		0			0
$331$	−4.48486			−0.246510			−0.123255	−	0.992375i	$-0.539333\pi$
$331$	−4.48486			−0.246510			−0.123255	+	0.992375i	$0.539333\pi$
$332$	−4.41268	−	1.29313i	−0.242178	−	0.0709696i
$333$	6.38384	−	22.1290i	0.349832	−	1.21266i
$334$	18.5298	+	24.7392i	1.01391	+	1.35367i
$335$		0			0
$336$	−16.2250	−	13.9617i	−0.885146	−	0.761674i
$337$	−25.9991			−1.41626			−0.708130	−	0.706082i	$-0.750461\pi$
$337$	−25.9991			−1.41626			−0.708130	+	0.706082i	$0.750461\pi$
$338$	−10.7452	−	14.3459i	−0.584461	−	0.780315i
$339$	−10.3820	−	1.46759i	−0.563873	−	0.0797085i
$340$		0			0
$341$	11.6824			0.632640
$342$	−3.92125	−	10.3546i	−0.212037	−	0.559913i
$343$			13.7627i			0.743118i
$344$	30.2151	−	11.2972i	1.62909	−	0.609103i
$345$		0			0
$346$	8.06433	+	10.7667i	0.433541	+	0.578822i
$347$			10.7184i			0.575392i	0.957722	+	0.287696i	$0.0928892\pi$
$347$			10.7184i			0.575392i	−0.957722	+	0.287696i	$0.907111\pi$
$348$	24.8243	+	11.2499i	1.33072	+	0.603058i
$349$			11.6319i			0.622643i	0.950305	+	0.311322i	$0.100772\pi$
$349$			11.6319i			0.622643i	−0.950305	+	0.311322i	$0.899228\pi$
$350$		0			0
$351$	−24.0266	−	10.7667i	−1.28245	−	0.574684i
$352$	14.3673	−	1.04681i	0.765781	−	0.0557949i
$353$			21.7547i			1.15789i	0.815367	+	0.578944i	$0.196535\pi$
$353$			21.7547i			1.15789i	−0.815367	+	0.578944i	$0.803465\pi$
$354$	−0.505282	−	0.919581i	−0.0268554	−	0.0488752i
$355$		0			0
$356$	23.9628	+	7.02226i	1.27003	+	0.372179i
$357$	−0.160421	+	1.13485i	−0.00849039	+	0.0600625i
$358$	−18.3820	+	13.7682i	−0.971519	+	0.727674i
$359$	−12.9032			−0.681005			−0.340503	−	0.940244i	$-0.610597\pi$
$359$	−12.9032			−0.681005			−0.340503	+	0.940244i	$0.610597\pi$
$360$		0			0
$361$	−12.1892			−0.641538
$362$	−11.0340	+	8.26450i	−0.579932	+	0.434372i
$363$	1.09461	−	7.74346i	0.0574521	−	0.406426i
$364$	8.80487	−	30.0459i	0.461501	−	1.57483i
$365$		0			0
$366$	−1.31190	−	2.38757i	−0.0685739	−	0.124800i
$367$			11.7255i			0.612065i	0.952021	+	0.306032i	$0.0990016\pi$
$367$			11.7255i			0.612065i	−0.952021	+	0.306032i	$0.900998\pi$
$368$	−15.0737	−	9.66459i	−0.785770	−	0.503801i
$369$	−7.70792	+	26.7188i	−0.401258	+	1.39093i
$370$		0			0
$371$			29.3879i			1.52574i
$372$	6.55970	−	14.4748i	0.340105	−	0.750485i
$373$		−	31.0944i		−	1.61001i	−0.593270	−	0.805004i	$-0.702163\pi$
$373$		−	31.0944i		−	1.61001i	0.593270	−	0.805004i	$-0.297837\pi$
$374$	−0.462407	−	0.617360i	−0.0239105	−	0.0319229i
$375$		0			0
$376$	28.0752	−	10.4971i	1.44787	−	0.541346i
$377$			39.8653i			2.05317i
$378$	−4.98957	−	22.1485i	−0.256636	−	1.13920i
$379$	12.6097			0.647719			0.323860	−	0.946105i	$-0.395019\pi$
$379$	12.6097			0.647719			0.323860	+	0.946105i	$0.395019\pi$
$380$		0			0
$381$	−1.64428	−	0.232434i	−0.0842390	−	0.0119080i
$382$	−1.95504	−	2.61018i	−0.100029	−	0.133549i
$383$	1.64428			0.0840188			0.0420094	−	0.999117i	$-0.486624\pi$
$383$	1.64428			0.0840188			0.0420094	+	0.999117i	$0.486624\pi$
$384$	6.77024	−	18.3892i	0.345493	−	0.938421i
$385$		0			0
$386$	9.53765	+	12.7337i	0.485453	+	0.648130i
$387$	32.8742	+	9.48364i	1.67109	+	0.482081i
$388$	−4.52483	+	15.4406i	−0.229713	+	0.783876i
$389$	37.4889			1.90076			0.950381	−	0.311090i	$-0.100694\pi$
$389$	37.4889			1.90076			0.950381	+	0.311090i	$0.100694\pi$
$390$		0			0
$391$			0.958763i			0.0484867i
$392$	6.74357	−	2.52136i	0.340602	−	0.127348i
$393$	−6.48486	−	0.916694i	−0.327118	−	0.0462411i
$394$	−5.75023	−	7.67714i	−0.289692	−	0.386769i
$395$		0			0
$396$	12.8971	+	8.19266i	0.648104	+	0.411697i
$397$		−	19.8820i		−	0.997849i	−0.866646	−	0.498924i	$-0.833729\pi$
$397$		−	19.8820i		−	0.997849i	0.866646	−	0.498924i	$-0.166271\pi$
$398$	−0.716261	+	0.536484i	−0.0359029	+	0.0268915i
$399$	13.8280	+	1.95472i	0.692267	+	0.0978583i
$400$		0			0
$401$		−	11.2570i		−	0.562150i	−0.959686	−	0.281075i	$-0.909309\pi$
$401$		−	11.2570i		−	0.562150i	0.959686	−	0.281075i	$-0.0906910\pi$
$402$	−5.06631	+	2.78378i	−0.252684	+	0.138843i
$403$	23.2451			1.15792
$404$	0.610382	−	2.08287i	0.0303676	−	0.103627i
$405$		0			0
$406$	−27.5142	+	20.6083i	−1.36551	+	1.02277i
$407$	−19.5501			−0.969065
$408$	−1.02457	+	0.226285i	−0.0507235	+	0.0112028i
$409$	16.9007			0.835685			0.417843	−	0.908519i	$-0.362786\pi$
$409$	16.9007			0.835685			0.417843	+	0.908519i	$0.362786\pi$
$410$		0			0
$411$	22.6171	+	3.19713i	1.11562	+	0.157703i
$412$	22.3250	+	6.54230i	1.09987	+	0.322316i
$413$	1.32344			0.0651221
$414$	−6.72608	−	17.7611i	−0.330569	−	0.872912i
$415$		0			0
$416$	28.5873	−	2.08287i	1.40161	−	0.102121i
$417$	4.19278	−	29.6605i	0.205321	−	1.45248i
$418$	−7.52248	+	5.63438i	−0.367936	+	0.275587i
$419$			7.21126i			0.352293i	0.984364	+	0.176147i	$0.0563633\pi$
$419$			7.21126i			0.352293i	−0.984364	+	0.176147i	$0.943637\pi$
$420$		0			0
$421$			11.3995i			0.555578i	0.960642	+	0.277789i	$0.0896015\pi$
$421$			11.3995i			0.555578i	−0.960642	+	0.277789i	$0.910398\pi$
$422$	9.86851	+	13.1755i	0.480391	+	0.641372i
$423$	30.5460	+	8.81199i	1.48520	+	0.428454i
$424$	−25.2001	+	9.42210i	−1.22383	+	0.457578i
$425$		0			0
$426$	−13.1398	+	7.21992i	−0.636625	+	0.349806i
$427$	3.43613			0.166286
$428$	12.4921	+	3.66080i	0.603830	+	0.176951i
$429$	−3.12814	+	22.1290i	−0.151028	+	1.06840i
$430$		0			0
$431$	3.95028			0.190278			0.0951391	−	0.995464i	$-0.469670\pi$
$431$	3.95028			0.190278			0.0951391	+	0.995464i	$0.469670\pi$
$432$	17.3926	−	11.3796i	0.836804	−	0.547503i
$433$	−20.6509			−0.992420			−0.496210	−	0.868203i	$-0.665275\pi$
$433$	−20.6509			−0.992420			−0.496210	+	0.868203i	$0.665275\pi$
$434$	12.0165	+	16.0433i	0.576811	+	0.770102i
$435$		0			0
$436$	9.72494	+	2.84987i	0.465740	+	0.136484i
$437$	11.6824			0.558847
$438$	25.7927	−	14.1723i	1.23242	−	0.677178i
$439$		−	28.5778i		−	1.36394i	−0.731379	−	0.681971i	$-0.761123\pi$
$439$		−	28.5778i		−	1.36394i	0.731379	−	0.681971i	$-0.238877\pi$
$440$		0			0
$441$	7.33704	+	2.11661i	0.349383	+	0.100791i
$442$	−0.920070	−	1.22839i	−0.0437633	−	0.0584285i
$443$		−	21.9689i		−	1.04378i	−0.853014	−	0.521888i	$-0.825228\pi$
$443$		−	21.9689i		−	1.04378i	0.853014	−	0.521888i	$-0.174772\pi$
$444$	−10.9774	+	24.2231i	−0.520965	+	1.14958i
$445$		0			0
$446$	−12.1870	+	9.12810i	−0.577069	+	0.432228i
$447$	−0.924813	+	6.54230i	−0.0437422	+	0.309440i
$448$	16.2157	+	18.6536i	0.766120	+	0.881300i
$449$			9.00493i			0.424969i	0.977164	+	0.212485i	$0.0681555\pi$
$449$			9.00493i			0.424969i	−0.977164	+	0.212485i	$0.931844\pi$
$450$		0			0
$451$	23.6050			1.11152
$452$	11.6187	+	3.40483i	0.546496	+	0.160150i
$453$	−22.6783	−	3.20578i	−1.06552	−	0.150621i
$454$	14.5298	−	10.8829i	0.681918	−	0.510761i
$455$		0			0
$456$	2.75726	+	12.4842i	0.129120	+	0.584628i
$457$	−18.5748			−0.868891			−0.434446	−	0.900698i	$-0.643056\pi$
$457$	−18.5748			−0.868891			−0.434446	+	0.900698i	$0.643056\pi$
$458$	−16.9429	+	12.6904i	−0.791692	+	0.592982i
$459$	−1.01560	−	0.455105i	−0.0474040	−	0.0212425i
$460$		0			0
$461$	34.2003			1.59287			0.796434	−	0.604726i	$-0.206717\pi$
$461$	34.2003			1.59287			0.796434	+	0.604726i	$0.206717\pi$
$462$	−16.8901	+	9.28059i	−0.785798	+	0.431772i
$463$		−	7.44471i		−	0.345985i	−0.984923	−	0.172992i	$-0.944656\pi$
$463$		−	7.44471i		−	0.345985i	0.984923	−	0.172992i	$-0.0553436\pi$
$464$	−26.4930	−	16.9862i	−1.22991	−	0.788564i
$465$		0			0
$466$	23.6547	−	17.7175i	1.09578	−	0.820748i
$467$		−	7.26161i		−	0.336027i	−0.985785	−	0.168014i	$-0.946265\pi$
$467$		−	7.26161i		−	0.336027i	0.985785	−	0.168014i	$-0.0537353\pi$
$468$	25.6619	+	16.3013i	1.18622	+	0.753528i
$469$		−	7.29130i		−	0.336681i
$470$		0			0
$471$	11.2589	+	1.59155i	0.518784	+	0.0733349i
$472$	0.424310	+	1.13485i	0.0195304	+	0.0522356i
$473$		−	29.0431i		−	1.33540i
$474$	13.7208	+	24.9710i	0.630218	+	1.14696i
$475$		0			0
$476$	0.372179	−	1.27003i	0.0170588	−	0.0582116i
$477$	−27.4178	−	7.90958i	−1.25538	−	0.362155i
$478$	−24.2800	−	32.4163i	−1.11054	−	1.48269i
$479$	23.3649			1.06757			0.533785	−	0.845620i	$-0.320769\pi$
$479$	23.3649			1.06757			0.533785	+	0.845620i	$0.320769\pi$
$480$		0			0
$481$	−38.8998			−1.77368
$482$	7.84203	+	10.4699i	0.357195	+	0.476891i
$483$	23.7190	+	3.35290i	1.07925	+	0.152562i
$484$	−2.53951	+	8.66584i	−0.115432	+	0.393902i
$485$		0			0
$486$	22.0067	+	1.30605i	0.998244	+	0.0592438i
$487$		−	7.77068i		−	0.352123i	−0.984379	−	0.176062i	$-0.943664\pi$
$487$		−	7.77068i		−	0.352123i	0.984379	−	0.176062i	$-0.0563358\pi$
$488$	1.10166	+	2.94648i	0.0498699	+	0.133381i
$489$	1.97328	−	13.9594i	0.0892349	−	0.631264i
$490$		0			0
$491$			20.5265i			0.926349i	0.886267	+	0.463174i	$0.153290\pi$
$491$			20.5265i			0.926349i	−0.886267	+	0.463174i	$0.846710\pi$
$492$	13.2543	−	29.2472i	0.597548	−	1.31857i
$493$			1.68509i			0.0758928i
$494$	−14.9678	+	11.2110i	−0.673433	+	0.504406i
$495$		0			0
$496$	−9.90447	+	15.4478i	−0.444724	+	0.693628i
$497$		−	18.9104i		−	0.848249i
$498$	2.71201	+	4.93568i	0.121528	+	0.221173i
$499$	−26.4958			−1.18611			−0.593057	−	0.805161i	$-0.702079\pi$
$499$	−26.4958			−1.18611			−0.593057	+	0.805161i	$0.702079\pi$
$500$		0			0
$501$	5.29861	−	37.4833i	0.236724	−	1.67463i
$502$	−1.39759	+	1.04681i	−0.0623776	+	0.0467212i
$503$	−26.9943			−1.20362			−0.601809	−	0.798640i	$-0.705553\pi$
$503$	−26.9943			−1.20362			−0.601809	+	0.798640i	$0.705553\pi$
$504$	2.01508	+	26.1383i	0.0897588	+	1.16429i
$505$		0			0
$506$	−12.9032	+	9.66459i	−0.573618	+	0.429643i
$507$	−3.07259	+	21.7361i	−0.136459	+	0.965332i
$508$	1.84014	+	0.539249i	0.0816430	+	0.0239253i
$509$	25.8064			1.14385			0.571925	−	0.820306i	$-0.306197\pi$
$509$	25.8064			1.14385			0.571925	+	0.820306i	$0.306197\pi$
$510$		0			0
$511$			37.1201i			1.64210i
$512$	−10.7965	+	19.8855i	−0.477144	+	0.878825i
$513$	−5.54541	+	12.3750i	−0.244836	+	0.546368i
$514$	21.0596	−	15.7738i	0.928901	−	0.695753i
$515$		0			0
$516$	−35.9851	−	16.3077i	−1.58416	−	0.717908i
$517$		−	26.9862i		−	1.18685i
$518$	−20.1092	−	26.8478i	−0.883547	−	1.17963i
$519$	2.30600	−	16.3131i	0.101222	−	0.716063i
$520$		0			0
$521$			1.70694i			0.0747826i	0.999301	+	0.0373913i	$0.0119048\pi$
$521$			1.70694i			0.0747826i	−0.999301	+	0.0373913i	$0.988095\pi$
$522$	−11.8215	−	31.2164i	−0.517415	−	1.36630i
$523$	24.0790			1.05290			0.526451	−	0.850206i	$-0.323522\pi$
$523$	24.0790			1.05290			0.526451	+	0.850206i	$0.323522\pi$
$524$	7.25732	+	2.12674i	0.317037	+	0.0929071i
$525$		0			0
$526$	−9.54541	−	12.7441i	−0.416200	−	0.555669i
$527$	0.982561			0.0428010
$528$	−13.3733	−	11.5078i	−0.581997	−	0.500812i
$529$	−2.96125			−0.128750
$530$		0			0
$531$	−0.356195	+	1.23472i	−0.0154576	+	0.0535823i
$532$	−15.4752	−	4.53497i	−0.670934	−	0.196616i
$533$	46.9680			2.03441
$534$	−14.7274	−	26.8029i	−0.637317	−	1.15988i
$535$		0			0
$536$	6.25229	−	2.33768i	0.270058	−	0.100972i
$537$	27.8513	+	3.93703i	1.20187	+	0.169895i
$538$	−9.90447	−	13.2235i	−0.427012	−	0.570105i
$539$		−	6.48200i		−	0.279199i
$540$		0			0
$541$			16.6989i			0.717941i	0.933349	+	0.358971i	$0.116872\pi$
$541$			16.6989i			0.717941i	−0.933349	+	0.358971i	$0.883128\pi$
$542$		0			0
$543$	16.7180	+	2.36324i	0.717436	+	0.101416i
$544$	1.20837	−	0.0880424i	0.0518086	−	0.00377479i
$545$		0			0
$546$	−33.6069	+	18.4660i	−1.43824	+	0.790272i
$547$	−15.5833			−0.666292			−0.333146	−	0.942875i	$-0.608110\pi$
$547$	−15.5833			−0.666292			−0.333146	+	0.942875i	$0.608110\pi$
$548$	−25.3112	−	7.41738i	−1.08124	−	0.316855i
$549$	−0.924813	+	3.20578i	−0.0394701	+	0.136819i
$550$		0			0
$551$	20.5327			0.874723
$552$	4.72949	+	21.4141i	0.201300	+	0.911443i
$553$	−35.9376			−1.52822
$554$	−19.7238	+	14.7732i	−0.837984	+	0.627655i
$555$		0			0
$556$	−9.72729	+	33.1935i	−0.412529	+	1.40772i
$557$	−2.96772			−0.125746			−0.0628731	−	0.998022i	$-0.520026\pi$
$557$	−2.96772			−0.125746			−0.0628731	+	0.998022i	$0.520026\pi$
$558$	−18.2020	+	6.89302i	−0.770551	+	0.291805i
$559$		−	57.7883i		−	2.44419i
$560$		0			0
$561$	−0.132225	+	0.935386i	−0.00558256	+	0.0394920i
$562$	14.6850	−	10.9991i	0.619448	−	0.463971i
$563$		−	11.7057i		−	0.493335i	−0.969100	−	0.246668i	$-0.920664\pi$
$563$		−	11.7057i		−	0.493335i	0.969100	−	0.246668i	$-0.0793356\pi$
$564$	−33.4366	−	15.1528i	−1.40793	−	0.638047i
$565$		0			0
$566$	−10.5038	−	14.0236i	−0.441507	−	0.589457i
$567$	−14.8106	+	23.5335i	−0.621986	+	0.988314i
$568$	16.2157	−	6.06291i	0.680396	−	0.254394i
$569$		−	43.3618i		−	1.81782i	−0.416992	−	0.908910i	$-0.636916\pi$
$569$		−	43.3618i		−	1.81782i	0.416992	−	0.908910i	$-0.363084\pi$
$570$		0			0
$571$	−8.18544			−0.342550			−0.171275	−	0.985223i	$-0.554789\pi$
$571$	−8.18544			−0.342550			−0.171275	+	0.985223i	$0.554789\pi$
$572$	7.25732	−	24.7650i	0.303444	−	1.03547i
$573$	−0.559045	+	3.95479i	−0.0233545	+	0.165214i
$574$	24.2800	+	32.4163i	1.01343	+	1.35303i
$575$		0			0
$576$	−21.7675	+	10.1082i	−0.906980	+	0.421174i
$577$	18.9612			0.789367			0.394683	−	0.918817i	$-0.370854\pi$
$577$	18.9612			0.789367			0.394683	+	0.918817i	$0.370854\pi$
$578$	14.3738	+	19.1906i	0.597873	+	0.798222i
$579$	2.72729	−	19.2934i	0.113342	−	0.801805i
$580$		0			0
$581$	−7.10331			−0.294695
$582$	17.2706	−	9.48968i	0.715890	−	0.393360i
$583$			24.2226i			1.00320i
$584$	−31.8305	+	11.9012i	−1.31716	+	0.492473i
$585$		0			0
$586$	−26.9532	−	35.9853i	−1.11343	−	1.48654i
$587$		−	19.9546i		−	0.823614i	−0.911271	−	0.411807i	$-0.864898\pi$
$587$		−	19.9546i		−	0.823614i	0.911271	−	0.411807i	$-0.135102\pi$
$588$	−8.03135	−	3.63965i	−0.331207	−	0.150097i
$589$		−	11.9724i		−	0.493315i
$590$		0			0
$591$	−1.64428	+	11.6319i	−0.0676366	+	0.478474i
$592$	16.5748	−	25.8514i	0.681219	−	1.06248i
$593$			27.4465i			1.12709i	0.826085	+	0.563546i	$0.190563\pi$
$593$			27.4465i			1.12709i	−0.826085	+	0.563546i	$0.809437\pi$
$594$	−4.11259	−	18.2557i	−0.168742	−	0.749039i
$595$		0			0
$596$	2.14558	−	7.32159i	0.0878863	−	0.299904i
$597$	1.08523	+	0.153408i	0.0444157	+	0.00627856i
$598$	−25.6741	+	19.2300i	−1.04989	+	0.786375i
$599$	−13.8858			−0.567357			−0.283679	−	0.958919i	$-0.591555\pi$
$599$	−13.8858			−0.567357			−0.283679	+	0.958919i	$0.591555\pi$
$600$		0			0
$601$	−10.7502			−0.438511			−0.219255	−	0.975667i	$-0.570363\pi$
$601$	−10.7502			−0.438511			−0.219255	+	0.975667i	$0.570363\pi$
$602$	39.8843	−	29.8736i	1.62556	−	1.21756i
$603$	6.80252	+	1.96241i	0.277020	+	0.0799156i
$604$	25.3796	+	7.43745i	1.03268	+	0.302626i
$605$		0			0
$606$	−2.32974	+	1.28012i	−0.0946392	+	0.0520014i
$607$		−	30.7086i		−	1.24642i	−0.782054	−	0.623211i	$-0.785828\pi$
$607$		−	30.7086i		−	1.24642i	0.782054	−	0.623211i	$-0.214172\pi$
$608$	−1.07279	−	14.7239i	−0.0435073	−	0.597134i
$609$	41.6878	+	5.89296i	1.68928	+	0.238795i
$610$		0			0
$611$		−	53.6957i		−	2.17229i
$612$	1.08472	+	0.689050i	0.0438472	+	0.0278532i
$613$		−	13.3170i		−	0.537870i	−0.963158	−	0.268935i	$-0.913328\pi$
$613$		−	13.3170i		−	0.537870i	0.963158	−	0.268935i	$-0.0866716\pi$
$614$	8.75683	+	11.6913i	0.353397	+	0.471821i
$615$		0			0
$616$	20.8439	−	7.79336i	0.839826	−	0.314003i
$617$			38.3725i			1.54482i	0.635124	+	0.772410i	$0.280949\pi$
$617$			38.3725i			1.54482i	−0.635124	+	0.772410i	$0.719051\pi$
$618$	−13.7208	−	24.9710i	−0.551932	−	1.00448i
$619$	4.59507			0.184691			0.0923457	−	0.995727i	$-0.470564\pi$
$619$	4.59507			0.184691			0.0923457	+	0.995727i	$0.470564\pi$
$620$		0			0
$621$	−9.51198	+	21.2266i	−0.381703	+	0.851794i
$622$	−4.35620	−	5.81597i	−0.174668	−	0.233199i
$623$	38.5741			1.54544
$624$	−26.6094	−	22.8975i	−1.06523	−	0.916635i
$625$		0			0
$626$	−13.2886	−	17.7417i	−0.531120	−	0.709099i
$627$	11.3976	+	1.61115i	0.455176	+	0.0643433i
$628$	−12.6001	−	3.69242i	−0.502797	−	0.147344i
$629$	−1.64428			−0.0655617
$630$		0			0
$631$			40.2097i			1.60072i	0.599518	+	0.800362i	$0.295359\pi$
$631$			40.2097i			1.60072i	−0.599518	+	0.800362i	$0.704641\pi$
$632$	−11.5220	−	30.8165i	−0.458322	−	1.22582i
$633$	2.82190	−	19.9626i	0.112161	−	0.793444i
$634$	7.59037	+	10.1339i	0.301452	+	0.402469i
$635$		0			0
$636$	30.0124	+	13.6010i	1.19007	+	0.539316i
$637$		−	12.8975i		−	0.511018i
$638$	−22.6783	+	16.9862i	−0.897842	+	0.672489i
$639$	17.6428	+	5.08964i	0.697937	+	0.201343i
$640$		0			0
$641$			7.56252i			0.298702i	0.988784	+	0.149351i	$0.0477184\pi$
$641$			7.56252i			0.298702i	−0.988784	+	0.149351i	$0.952282\pi$
$642$	−7.67759	−	13.9727i	−0.303010	−	0.551460i
$643$	2.47018			0.0974145			0.0487072	−	0.998813i	$-0.484490\pi$
$643$	2.47018			0.0974145			0.0487072	+	0.998813i	$0.484490\pi$
$644$	−26.5444	−	7.77877i	−1.04599	−	0.306527i
$645$		0			0
$646$	−0.632684	+	0.473884i	−0.0248926	+	0.0186447i
$647$	−30.1474			−1.18522			−0.592608	−	0.805491i	$-0.701901\pi$
$647$	−30.1474			−1.18522			−0.592608	+	0.805491i	$0.701901\pi$
$648$	−24.9284	−	5.15497i	−0.979281	−	0.202506i
$649$	1.09083			0.0428188
$650$		0			0
$651$	3.43613	−	24.3078i	0.134672	−	0.952697i
$652$	−4.57804	+	15.6222i	−0.179290	+	0.611811i
$653$	−8.42674			−0.329764			−0.164882	−	0.986313i	$-0.552724\pi$
$653$	−8.42674			−0.329764			−0.164882	+	0.986313i	$0.552724\pi$
$654$	−5.97689	−	10.8776i	−0.233715	−	0.425346i
$655$		0			0
$656$	−20.0126	+	31.2132i	−0.781359	+	1.21867i
$657$	−34.6318	−	9.99067i	−1.35111	−	0.389773i
$658$	37.0596	−	27.7579i	1.44474	−	1.08212i
$659$			13.5764i			0.528863i	0.964404	+	0.264432i	$0.0851843\pi$
$659$			13.5764i			0.528863i	−0.964404	+	0.264432i	$0.914816\pi$
$660$		0			0
$661$			1.68509i			0.0655425i	0.999463	+	0.0327713i	$0.0104333\pi$
$661$			1.68509i			0.0655425i	−0.999463	+	0.0327713i	$0.989567\pi$
$662$	−3.80230	−	5.07646i	−0.147781	−	0.197302i
$663$	−0.263094	+	1.86118i	−0.0102177	+	0.0722821i
$664$	−2.27740	−	6.09109i	−0.0883804	−	0.236380i
$665$		0			0
$666$	30.4603	−	11.5352i	1.18031	−	0.446981i
$667$	35.2195			1.36370
$668$	−12.2928	+	41.9482i	−0.475624	+	1.62302i
$669$	18.4649	+	2.61018i	0.713895	+	0.100916i
$670$		0			0
$671$	2.83219			0.109335
$672$	2.04772	−	30.2021i	0.0789925	−	1.16507i
$673$	7.03784			0.271289			0.135644	−	0.990758i	$-0.456690\pi$
$673$	7.03784			0.271289			0.135644	+	0.990758i	$0.456690\pi$
$674$	−22.0422	−	29.4286i	−0.849035	−	1.13355i
$675$		0			0
$676$	7.12844	−	24.3252i	0.274171	−	0.935584i
$677$	−41.8298			−1.60765			−0.803825	−	0.594866i	$-0.797205\pi$
$677$	−41.8298			−1.60765			−0.803825	+	0.594866i	$0.797205\pi$
$678$	−7.14076	−	12.9957i	−0.274239	−	0.499098i
$679$			24.8554i			0.953863i
$680$		0			0
$681$	−22.0147	−	3.11198i	−0.843604	−	0.119251i
$682$	9.90447	+	13.2235i	0.379262	+	0.506353i
$683$			28.2464i			1.08082i	0.841403	+	0.540409i	$0.181730\pi$
$683$			28.2464i			1.08082i	−0.841403	+	0.540409i	$0.818270\pi$
$684$	8.39602	−	13.2172i	0.321030	−	0.505373i
$685$		0			0
$686$	−15.5782	+	11.6682i	−0.594778	+	0.445492i
$687$	25.6709	+	3.62881i	0.979406	+	0.138448i
$688$	38.4040	+	24.6230i	1.46414	+	0.938742i
$689$			48.1968i			1.83615i
$690$		0			0
$691$	24.8633			0.945844			0.472922	−	0.881104i	$-0.343199\pi$
$691$	24.8633			0.945844			0.472922	+	0.881104i	$0.343199\pi$
$692$	−5.34994	+	18.2562i	−0.203374	+	0.693997i
$693$	22.6783	+	6.54230i	0.861477	+	0.248521i
$694$	−12.1322	+	9.08711i	−0.460533	+	0.344942i
$695$		0			0
$696$	8.31241	+	37.6367i	0.315081	+	1.42662i
$697$	1.98532			0.0751994
$698$	−13.1663	+	9.86165i	−0.498352	+	0.373269i
$699$	−35.8401	−	5.06633i	−1.35560	−	0.191626i
$700$		0			0
$701$	−42.6271			−1.61000			−0.805001	−	0.593274i	$-0.797835\pi$
$701$	−42.6271			−1.61000			−0.805001	+	0.593274i	$0.797835\pi$
$702$	−8.18301	−	36.3241i	−0.308848	−	1.37096i
$703$			20.0354i			0.755650i
$704$	13.3656	+	15.3750i	0.503736	+	0.579468i
$705$		0			0
$706$	−24.6244	+	18.4439i	−0.926753	+	0.694144i
$707$		−	3.35290i		−	0.126099i
$708$	0.612501	−	1.35156i	0.0230192	−	0.0507948i
$709$		−	17.0057i		−	0.638663i	−0.947643	−	0.319331i	$-0.896542\pi$
$709$		−	17.0057i		−	0.638663i	0.947643	−	0.319331i	$-0.103458\pi$
$710$		0			0
$711$	9.67240	−	33.5285i	0.362743	−	1.25742i
$712$	12.3673	+	33.0773i	0.463485	+	1.23962i
$713$		−	20.5361i		−	0.769085i
$714$	−1.42055	+	0.780551i	−0.0531628	+	0.0292114i
$715$		0			0
$716$	−31.1688	−	9.13396i	−1.16483	−	0.341352i
$717$	−6.94289	+	49.1152i	−0.259287	+	1.83424i
$718$	−10.9394	−	14.6053i	−0.408257	−	0.545064i
$719$	28.6386			1.06804			0.534020	−	0.845472i	$-0.320681\pi$
$719$	28.6386			1.06804			0.534020	+	0.845472i	$0.320681\pi$
$720$		0			0
$721$	35.9376			1.33839
$722$	−10.3341	−	13.7971i	−0.384596	−	0.513475i
$723$	2.24243	−	15.8634i	0.0833969	−	0.589965i
$724$	−18.7093	−	5.48274i	−0.695327	−	0.203764i
$725$		0			0
$726$	9.69293	−	5.32597i	0.359738	−	0.197665i
$727$		−	14.1822i		−	0.525990i	−0.964797	−	0.262995i	$-0.915290\pi$
$727$		−	14.1822i		−	0.525990i	0.964797	−	0.262995i	$-0.0847104\pi$
$728$	41.4741	−	15.5068i	1.53713	−	0.574720i
$729$	−17.9697	−	20.1517i	−0.665545	−	0.746357i
$730$		0			0
$731$		−	2.44269i		−	0.0903462i
$732$	1.59028	−	3.50915i	0.0587783	−	0.129702i
$733$		−	51.7027i		−	1.90968i	−0.297113	−	0.954842i	$-0.596024\pi$
$733$		−	51.7027i		−	1.90968i	0.297113	−	0.954842i	$-0.403976\pi$
$734$	−13.2722	+	9.94095i	−0.489885	+	0.366927i
$735$		0			0
$736$	−1.84014	−	25.2558i	−0.0678285	−	0.930940i
$737$		−	6.00977i		−	0.221373i
$738$	−36.7781	+	13.9277i	−1.35382	+	0.512688i
$739$	−16.7493			−0.616133			−0.308067	−	0.951365i	$-0.599682\pi$
$739$	−16.7493			−0.616133			−0.308067	+	0.951365i	$0.599682\pi$
$740$		0			0
$741$	22.6783	+	3.20578i	0.833108	+	0.117767i
$742$	−33.2645	+	24.9153i	−1.22118	+	0.914669i
$743$	13.5649			0.497649			0.248825	−	0.968549i	$-0.419956\pi$
$743$	13.5649			0.497649			0.248825	+	0.968549i	$0.419956\pi$
$744$	21.9456	−	4.84688i	0.804564	−	0.177695i
$745$		0			0
$746$	35.1961	−	26.3621i	1.28862	−	0.965185i
$747$	1.91181	−	6.62713i	0.0699496	−	0.242474i
$748$	0.306764	−	1.04681i	0.0112164	−	0.0382750i
$749$	20.1092			0.734774
$750$		0			0
$751$		−	37.3072i		−	1.36136i	−0.732581	−	0.680680i	$-0.761684\pi$
$751$		−	37.3072i		−	1.36136i	0.732581	−	0.680680i	$-0.238316\pi$
$752$	35.6842	+	22.8791i	1.30127	+	0.834316i
$753$	2.11755	+	0.299334i	0.0771676	+	0.0109084i
$754$	−45.1240	+	33.7981i	−1.64332	+	1.23086i
$755$		0			0
$756$	20.8399	−	24.4254i	0.757941	−	0.888344i
$757$		−	0.385842i		−	0.0140237i	−0.999975	−	0.00701183i	$-0.997768\pi$
$757$		−	0.385842i		−	0.0140237i	0.999975	−	0.00701183i	$-0.00223195\pi$
$758$	10.6906	+	14.2731i	0.388302	+	0.518423i
$759$	19.5501	+	2.76359i	0.709625	+	0.100312i
$760$		0			0
$761$		−	10.2235i		−	0.370603i	−0.982682	−	0.185302i	$-0.940674\pi$
$761$		−	10.2235i		−	0.370603i	0.982682	−	0.185302i	$-0.0593262\pi$
$762$	−1.13094	−	2.05824i	−0.0409696	−	0.0745621i
$763$	15.6547			0.566738
$764$	1.29699	−	4.42587i	0.0469235	−	0.160122i
$765$		0			0
$766$	1.39403	+	1.86118i	0.0503685	+	0.0672471i
$767$	2.17047			0.0783711
$768$	26.5548	−	7.92723i	0.958215	−	0.286049i
$769$	4.34816			0.156799			0.0783994	−	0.996922i	$-0.475019\pi$
$769$	4.34816			0.156799			0.0783994	+	0.996922i	$0.475019\pi$
$770$		0			0
$771$	−31.9083	−	4.51052i	−1.14915	−	0.162443i
$772$	−6.32735	+	21.5915i	−0.227726	+	0.777096i
$773$	21.4326			0.770878			0.385439	−	0.922733i	$-0.374050\pi$
$773$	21.4326			0.770878			0.385439	+	0.922733i	$0.374050\pi$
$774$	17.1364	+	45.2510i	0.615954	+	1.62651i
$775$		0			0
$776$	−21.3135	+	7.96894i	−0.765111	+	0.286068i
$777$	−5.75023	+	40.6782i	−0.206288	+	1.45932i
$778$	31.7834	+	42.4340i	1.13949	+	1.52133i
$779$		−	24.1910i		−	0.866731i
$780$		0			0
$781$		−	15.5867i		−	0.557737i
$782$	−1.08523	+	0.812847i	−0.0388079	+	0.0290674i
$783$	−16.7180	+	37.3072i	−0.597451	+	1.33325i
$784$	8.57121	+	5.49549i	0.306115	+	0.196267i
$785$		0			0
$786$	−4.46030	−	8.11746i	−0.159094	−	0.289540i
$787$	−32.2753			−1.15049			−0.575246	−	0.817980i	$-0.695094\pi$
$787$	−32.2753			−1.15049			−0.575246	+	0.817980i	$0.695094\pi$
$788$	3.81475	−	13.0175i	0.135895	−	0.463729i
$789$	−2.72951	+	19.3091i	−0.0971733	+	0.687421i
$790$		0			0
$791$	18.7031			0.665006
$792$	1.66091	+	21.5442i	0.0590178	+	0.765539i
$793$	5.63533			0.200116
$794$	22.5046	−	16.8561i	0.798660	−	0.598201i
$795$		0			0
$796$	−1.21450	−	0.355908i	−0.0430469	−	0.0126148i
$797$	−14.4120			−0.510498			−0.255249	−	0.966875i	$-0.582157\pi$
$797$	−14.4120			−0.510498			−0.255249	+	0.966875i	$0.582157\pi$
$798$	9.51095	+	17.3093i	0.336684	+	0.612743i
$799$		−	2.26970i		−	0.0802961i
$800$		0			0
$801$	−10.3820	+	35.9883i	−0.366830	+	1.27158i
$802$	12.7420	−	9.54382i	0.449935	−	0.337004i
$803$			30.5959i			1.07970i
$804$	−7.44625	−	3.37449i	−0.262609	−	0.119009i
$805$		0			0
$806$	19.7074	+	26.3113i	0.694162	+	0.926777i
$807$	−2.83219	+	20.0354i	−0.0996977	+	0.705280i
$808$	2.87511	−	1.07498i	0.101146	−	0.0378177i
$809$		−	27.3297i		−	0.960860i	−0.877033	−	0.480430i	$-0.840481\pi$
$809$		−	27.3297i		−	0.960860i	0.877033	−	0.480430i	$-0.159519\pi$
$810$		0			0
$811$	1.18452			0.0415942			0.0207971	−	0.999784i	$-0.493380\pi$
$811$	1.18452			0.0415942			0.0207971	+	0.999784i	$0.493380\pi$
$812$	−46.6536	−	13.6717i	−1.63722	−	0.479784i
$813$		0			0
$814$	−16.5748	−	22.1290i	−0.580946	−	0.775622i
$815$		0			0
$816$	−1.12477	−	0.967870i	−0.0393748	−	0.0338822i
$817$	−29.7640			−1.04131
$818$	14.3285	+	19.1301i	0.500986	+	0.668867i
$819$	45.1240	+	13.0175i	1.57676	+	0.454868i
$820$		0			0
$821$	16.8535			0.588191			0.294095	−	0.955776i	$-0.404982\pi$
$821$	16.8535			0.588191			0.294095	+	0.955776i	$0.404982\pi$
$822$	15.5561	+	28.3111i	0.542581	+	0.987462i
$823$		−	47.6544i		−	1.66113i	−0.556923	−	0.830564i	$-0.688018\pi$
$823$		−	47.6544i		−	1.66113i	0.556923	−	0.830564i	$-0.311982\pi$
$824$	11.5220	+	30.8165i	0.401389	+	1.07354i
$825$		0			0
$826$	1.12202	+	1.49801i	0.0390401	+	0.0521225i
$827$		−	11.4476i		−	0.398073i	−0.979992	−	0.199036i	$-0.936219\pi$
$827$		−	11.4476i		−	0.398073i	0.979992	−	0.199036i	$-0.0637812\pi$
$828$	14.4016	−	22.6713i	0.500490	−	0.787884i
$829$		−	13.6692i		−	0.474751i	−0.971418	−	0.237375i	$-0.923713\pi$
$829$		−	13.6692i		−	0.474751i	0.971418	−	0.237375i	$-0.0762871\pi$
$830$		0			0
$831$	29.8843	+	4.22441i	1.03667	+	0.146543i
$832$	26.5942	+	30.5924i	0.921986	+	1.06060i
$833$		−	0.545173i		−	0.0188891i
$834$	37.1277	−	20.4005i	1.28563	−	0.706413i
$835$		0			0
$836$	−12.7552	−	3.73790i	−0.441149	−	0.129278i
$837$	21.7535	+	9.74808i	0.751910	+	0.336943i
$838$	−8.16250	+	6.11377i	−0.281969	+	0.211197i
$839$	16.7180			0.577168			0.288584	−	0.957455i	$-0.406816\pi$
$839$	16.7180			0.577168			0.288584	+	0.957455i	$0.406816\pi$
$840$		0			0
$841$	32.9007			1.13451
$842$	−12.9032	+	9.66459i	−0.444674	+	0.333064i
$843$	−22.2498	−	3.14521i	−0.766323	−	0.108327i
$844$	−6.54685	+	22.3405i	−0.225352	+	0.768993i
$845$		0			0
$846$	15.9227	+	42.0462i	0.547435	+	1.44558i
$847$			13.9498i			0.479321i
$848$	−32.0298	−	20.5361i	−1.09991	−	0.705214i
$849$	−3.00356	+	21.2477i	−0.103082	+	0.729220i
$850$		0			0
$851$			34.3665i			1.17807i
$852$	−19.3123	−	8.75196i	−0.661629	−	0.299837i
$853$			7.83055i			0.268113i	0.990974	+	0.134056i	$0.0428004\pi$
$853$			7.83055i			0.268113i	−0.990974	+	0.134056i	$0.957200\pi$
$854$	2.91317	+	3.88939i	0.0996868	+	0.133092i
$855$		0			0
$856$	6.44725	+	17.2436i	0.220362	+	0.589375i
$857$		−	25.7234i		−	0.878696i	−0.898317	−	0.439348i	$-0.855210\pi$
$857$		−	25.7234i		−	0.878696i	0.898317	−	0.439348i	$-0.144790\pi$
$858$	−27.7001	+	15.2204i	−0.945667	+	0.519615i
$859$	−12.5142			−0.426980			−0.213490	−	0.976945i	$-0.568483\pi$
$859$	−12.5142			−0.426980			−0.213490	+	0.976945i	$0.568483\pi$
$860$		0			0
$861$	6.94289	−	49.1152i	0.236613	−	1.67384i
$862$	3.34908	+	4.47136i	0.114070	+	0.152295i
$863$	−24.1621			−0.822489			−0.411244	−	0.911525i	$-0.634906\pi$
$863$	−24.1621			−0.822489			−0.411244	+	0.911525i	$0.634906\pi$
$864$	27.6263	+	10.0392i	0.939867	+	0.341539i
$865$		0			0
$866$	−17.5080	−	23.3750i	−0.594947	−	0.794315i
$867$	4.11021	−	29.0763i	0.139590	−	0.987484i
$868$	−7.97185	+	27.2032i	−0.270582	+	0.923338i
$869$	−29.6212			−1.00483
$870$		0			0
$871$		−	11.9579i		−	0.405178i
$872$	5.01908	+	13.4239i	0.169968	+	0.454591i
$873$	−23.1892	−	6.68969i	−0.784836	−	0.226412i
$874$	9.90447	+	13.2235i	0.335024	+	0.447291i
$875$		0			0
$876$	37.9090	+	17.1796i	1.28083	+	0.580445i
$877$		−	18.7362i		−	0.632675i	−0.948647	−	0.316337i	$-0.897547\pi$
$877$		−	18.7362i		−	0.632675i	0.948647	−	0.316337i	$-0.102453\pi$
$878$	32.3475	−	24.2285i	1.09167	−	0.817671i
$879$	−7.70728	+	54.5227i	−0.259960	+	1.83900i
$880$		0			0
$881$			45.2764i			1.52540i	0.646752	+	0.762701i	$0.276127\pi$
$881$			45.2764i			1.52540i	−0.646752	+	0.762701i	$0.723873\pi$
$882$	3.82459	+	10.0994i	0.128781	+	0.340063i
$883$	−32.6703			−1.09944			−0.549722	−	0.835348i	$-0.685266\pi$
$883$	−32.6703			−1.09944			−0.549722	+	0.835348i	$0.685266\pi$
$884$	0.610382	−	2.08287i	0.0205294	−	0.0700547i
$885$		0			0
$886$	24.8669	−	18.6254i	0.835418	−	0.625734i
$887$	24.6883			0.828953			0.414477	−	0.910060i	$-0.363965\pi$
$887$	24.6883			0.828953			0.414477	+	0.910060i	$0.363965\pi$
$888$	−36.7251	+	8.11108i	−1.23241	+	0.272190i
$889$	2.96216			0.0993477
$890$		0			0
$891$	−12.2075	+	19.3972i	−0.408965	+	0.649831i
$892$	−20.6644	−	6.05566i	−0.691895	−	0.202758i
$893$	−27.6560			−0.925474
$894$	−8.18936	+	4.49981i	−0.273893	+	0.150496i
$895$		0			0
$896$	−7.36640	+	34.1694i	−0.246094	+	1.14152i
$897$	38.8998	+	5.49884i	1.29883	+	0.183601i
$898$	−10.1928	+	7.63446i	−0.340137	+	0.254765i
$899$		−	36.0937i		−	1.20379i
$900$		0			0
$901$			2.03726i			0.0678710i
$902$	20.0126	+	26.7188i	0.666345	+	0.889639i
$903$	−60.4302	−	8.54237i	−2.01099	−	0.284272i
$904$	5.99644	+	16.0379i	0.199439	+	0.533414i
$905$		0			0
$906$	−15.5982	−	28.3877i	−0.518215	−	0.943117i
$907$	15.7502			0.522978			0.261489	−	0.965206i	$-0.415787\pi$
$907$	15.7502			0.522978			0.261489	+	0.965206i	$0.415787\pi$
$908$	24.6370	+	7.21982i	0.817607	+	0.239598i
$909$	3.12814	+	0.902414i	0.103754	+	0.0299312i
$910$		0			0
$911$	−50.4948			−1.67297			−0.836483	−	0.547993i	$-0.815392\pi$
$911$	−50.4948			−1.67297			−0.836483	+	0.547993i	$0.815392\pi$
$912$	−11.7934	+	13.7052i	−0.390519	+	0.453825i
$913$	−5.85482			−0.193766
$914$	−15.7478	−	21.0250i	−0.520892	−	0.695445i
$915$		0			0
$916$	−28.7287	−	8.41889i	−0.949224	−	0.278168i
$917$	11.6824			0.385788
$918$	−0.345893	−	1.53541i	−0.0114162	−	0.0506759i
$919$			22.6311i			0.746530i	0.927725	+	0.373265i	$0.121762\pi$
$919$			22.6311i			0.746530i	−0.927725	+	0.373265i	$0.878238\pi$
$920$		0			0
$921$	2.50402	−	17.7139i	0.0825102	−	0.583692i
$922$	28.9953	+	38.7117i	0.954909	+	1.27490i
$923$		−	31.0136i		−	1.02082i
$924$	−24.8243	−	11.2499i	−0.816661	−	0.370094i
$925$		0			0
$926$	8.42674	−	6.31169i	0.276920	−	0.207415i
$927$	−9.67240	+	33.5285i	−0.317683	+	1.10122i
$928$	−3.23417	−	44.3888i	−0.106167	−	1.45713i
$929$			45.8021i			1.50272i	0.659893	+	0.751360i	$0.270602\pi$
$929$			45.8021i			1.50272i	−0.659893	+	0.751360i	$0.729398\pi$
$930$		0			0
$931$	−6.64289			−0.217712
$932$	40.1093	+	11.7539i	1.31382	+	0.385013i
$933$	−1.24566	+	8.81199i	−0.0407809	+	0.288492i
$934$	8.21949	−	6.15645i	0.268950	−	0.201445i
$935$		0			0
$936$	3.30478	+	42.8674i	0.108020	+	1.40116i
$937$	−4.77203			−0.155895			−0.0779477	−	0.996957i	$-0.524837\pi$
$937$	−4.77203			−0.155895			−0.0779477	+	0.996957i	$0.524837\pi$
$938$	8.25310	−	6.18162i	0.269473	−	0.201837i
$939$	−3.79988	+	26.8811i	−0.124004	+	0.877230i
$940$		0			0
$941$	−28.5031			−0.929174			−0.464587	−	0.885528i	$-0.653797\pi$
$941$	−28.5031			−0.929174			−0.464587	+	0.885528i	$0.653797\pi$
$942$	7.74392	+	14.0934i	0.252311	+	0.459189i
$943$		−	41.4944i		−	1.35124i
$944$	−0.924813	+	1.44241i	−0.0301001	+	0.0469466i
$945$		0			0
$946$	32.8742	−	24.6230i	1.06883	−	0.800562i
$947$			59.7387i			1.94125i	0.240606	+	0.970623i	$0.422654\pi$
$947$			59.7387i			1.94125i	−0.240606	+	0.970623i	$0.577346\pi$
$948$	−16.6323	+	36.7013i	−0.540192	+	1.19200i
$949$			60.8779i			1.97618i
$950$		0			0
$951$	2.17047	−	15.3543i	0.0703823	−	0.497897i
$952$	1.75309	−	0.655466i	0.0568181	−	0.0212438i
$953$		−	32.0009i		−	1.03661i	−0.855196	−	0.518305i	$-0.826563\pi$
$953$		−	32.0009i		−	1.03661i	0.855196	−	0.518305i	$-0.173437\pi$
$954$	−14.2921	−	37.7404i	−0.462725	−	1.22189i
$955$		0			0
$956$	16.1076	−	54.9657i	0.520956	−	1.77772i
$957$	34.3607	+	4.85720i	1.11072	+	0.157011i
$958$	19.8089	+	26.4470i	0.639998	+	0.854463i
$959$	−40.7446			−1.31571
$960$		0			0
$961$	9.95413			0.321101
$962$	−32.9795	−	44.0311i	−1.06330	−	1.41962i
$963$	−5.41227	+	18.7612i	−0.174408	+	0.604570i
$964$	−5.20247	+	17.7530i	−0.167560	+	0.571784i
$965$		0			0
$966$	16.3140	+	29.6904i	0.524895	+	0.955274i
$967$		−	30.7086i		−	0.987521i	−0.869598	−	0.493761i	$-0.835622\pi$
$967$		−	30.7086i		−	0.987521i	0.869598	−	0.493761i	$-0.164378\pi$
$968$	−11.9620	+	4.47248i	−0.384472	+	0.143751i
$969$	0.958603	+	0.135507i	0.0307948	+	0.00435312i
$970$		0			0
$971$		−	54.2279i		−	1.74025i	−0.492827	−	0.870127i	$-0.664036\pi$
$971$		−	54.2279i		−	1.74025i	0.492827	−	0.870127i	$-0.335964\pi$
$972$	17.1791	+	26.0169i	0.551020	+	0.834492i
$973$			53.4332i			1.71299i
$974$	8.79572	−	6.58805i	0.281833	−	0.211095i
$975$		0			0
$976$	−2.40115	+	3.74503i	−0.0768590	+	0.119876i
$977$		−	11.5621i		−	0.369905i	−0.982748	−	0.184952i	$-0.940787\pi$
$977$		−	11.5621i		−	0.369905i	0.982748	−	0.184952i	$-0.0592131\pi$
$978$	17.4737	−	9.60128i	0.558748	−	0.307015i
$979$	31.7943			1.01615
$980$		0			0
$981$	−4.21337	+	14.6053i	−0.134523	+	0.466311i
$982$	−23.2342	+	17.4025i	−0.741432	+	0.555338i
$983$	48.8505			1.55809			0.779044	−	0.626969i	$-0.215705\pi$
$983$	48.8505			1.55809			0.779044	+	0.626969i	$0.215705\pi$
$984$	44.3423	−	9.79340i	1.41358	−	0.312202i
$985$		0			0
$986$	−1.90737	+	1.42864i	−0.0607432	+	0.0454970i
$987$	−56.1505	−	7.93738i	−1.78729	−	0.252650i
$988$	−25.3796	−	7.43745i	−0.807434	−	0.236617i
$989$	−51.0538			−1.62342
$990$		0			0
$991$		−	8.77480i		−	0.278741i	−0.990240	−	0.139370i	$-0.955492\pi$
$991$		−	8.77480i		−	0.278741i	0.990240	−	0.139370i	$-0.0445079\pi$
$992$	−25.8827	+	1.88582i	−0.821775	+	0.0598747i
$993$	−1.08727	+	7.69154i	−0.0345035	+	0.244084i
$994$	21.4049	−	16.0324i	0.678923	−	0.508518i
$995$		0			0
$996$	−3.28749	+	7.25426i	−0.104168	+	0.229860i
$997$			5.99205i			0.189770i	0.995488	+	0.0948851i	$0.0302484\pi$
$997$			5.99205i			0.189770i	−0.995488	+	0.0948851i	$0.969752\pi$
$998$	−22.4633	−	29.9908i	−0.711064	−	0.949343i
$999$	−36.4036	−	16.3131i	−1.15176	−	0.516122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.b.h.251.8	yes	12
3.2	odd	2	inner	600.2.b.h.251.5	yes	12
4.3	odd	2		2400.2.b.g.2351.7		12
5.2	odd	4		600.2.m.e.299.3		24
5.3	odd	4		600.2.m.e.299.22		24
5.4	even	2		600.2.b.g.251.5	✓	12
8.3	odd	2	inner	600.2.b.h.251.6	yes	12
8.5	even	2		2400.2.b.g.2351.8		12
12.11	even	2		2400.2.b.g.2351.5		12
15.2	even	4		600.2.m.e.299.21		24
15.8	even	4		600.2.m.e.299.4		24
15.14	odd	2		600.2.b.g.251.8	yes	12
20.3	even	4		2400.2.m.e.1199.1		24
20.7	even	4		2400.2.m.e.1199.24		24
20.19	odd	2		2400.2.b.h.2351.6		12
24.5	odd	2		2400.2.b.g.2351.6		12
24.11	even	2	inner	600.2.b.h.251.7	yes	12
40.3	even	4		600.2.m.e.299.24		24
40.13	odd	4		2400.2.m.e.1199.2		24
40.19	odd	2		600.2.b.g.251.7	yes	12
40.27	even	4		600.2.m.e.299.1		24
40.29	even	2		2400.2.b.h.2351.5		12
40.37	odd	4		2400.2.m.e.1199.23		24
60.23	odd	4		2400.2.m.e.1199.21		24
60.47	odd	4		2400.2.m.e.1199.4		24
60.59	even	2		2400.2.b.h.2351.8		12
120.29	odd	2		2400.2.b.h.2351.7		12
120.53	even	4		2400.2.m.e.1199.22		24
120.59	even	2		600.2.b.g.251.6	yes	12
120.77	even	4		2400.2.m.e.1199.3		24
120.83	odd	4		600.2.m.e.299.2		24
120.107	odd	4		600.2.m.e.299.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.b.g.251.5	✓	12	5.4	even	2
600.2.b.g.251.6	yes	12	120.59	even	2
600.2.b.g.251.7	yes	12	40.19	odd	2
600.2.b.g.251.8	yes	12	15.14	odd	2
600.2.b.h.251.5	yes	12	3.2	odd	2	inner
600.2.b.h.251.6	yes	12	8.3	odd	2	inner
600.2.b.h.251.7	yes	12	24.11	even	2	inner
600.2.b.h.251.8	yes	12	1.1	even	1	trivial
600.2.m.e.299.1		24	40.27	even	4
600.2.m.e.299.2		24	120.83	odd	4
600.2.m.e.299.3		24	5.2	odd	4
600.2.m.e.299.4		24	15.8	even	4
600.2.m.e.299.21		24	15.2	even	4
600.2.m.e.299.22		24	5.3	odd	4
600.2.m.e.299.23		24	120.107	odd	4
600.2.m.e.299.24		24	40.3	even	4
2400.2.b.g.2351.5		12	12.11	even	2
2400.2.b.g.2351.6		12	24.5	odd	2
2400.2.b.g.2351.7		12	4.3	odd	2
2400.2.b.g.2351.8		12	8.5	even	2
2400.2.b.h.2351.5		12	40.29	even	2
2400.2.b.h.2351.6		12	20.19	odd	2
2400.2.b.h.2351.7		12	120.29	odd	2
2400.2.b.h.2351.8		12	60.59	even	2
2400.2.m.e.1199.1		24	20.3	even	4
2400.2.m.e.1199.2		24	40.13	odd	4
2400.2.m.e.1199.3		24	120.77	even	4
2400.2.m.e.1199.4		24	60.47	odd	4
2400.2.m.e.1199.21		24	60.23	odd	4
2400.2.m.e.1199.22		24	120.53	even	4
2400.2.m.e.1199.23		24	40.37	odd	4
2400.2.m.e.1199.24		24	20.7	even	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.847808 + 1.13191i) q^{2} +(0.242431 - 1.71500i) q^{3} +(-0.562443 + 1.91929i) q^{4} +(2.14676 - 1.17958i) q^{6} +3.08957i q^{7} +(-2.64930 + 0.990551i) q^{8} +(-2.88245 - 0.831539i) q^{9} +O(q^{10})\)	\(q+(0.847808 + 1.13191i) q^{2} +(0.242431 - 1.71500i) q^{3} +(-0.562443 + 1.91929i) q^{4} +(2.14676 - 1.17958i) q^{6} +3.08957i q^{7} +(-2.64930 + 0.990551i) q^{8} +(-2.88245 - 0.831539i) q^{9} +2.54654i q^{11} +(3.15522 + 1.42988i) q^{12} +5.06696i q^{13} +(-3.49711 + 2.61936i) q^{14} +(-3.36732 - 2.15898i) q^{16} +0.214179i q^{17} +(-1.50254 - 3.96767i) q^{18} +2.60975 q^{19} +(5.29861 + 0.749006i) q^{21} +(-2.88245 + 2.15898i) q^{22} +4.47647 q^{23} +(1.05652 + 4.78370i) q^{24} +(-5.73534 + 4.29581i) q^{26} +(-2.12489 + 4.74182i) q^{27} +(-5.92976 - 1.73770i) q^{28} +7.86770 q^{29} -4.58758i q^{31} +(-0.411070 - 5.64190i) q^{32} +(4.36732 + 0.617360i) q^{33} +(-0.242431 + 0.181582i) q^{34} +(3.21718 - 5.06456i) q^{36} +7.67714i q^{37} +(2.21257 + 2.95400i) q^{38} +(8.68984 + 1.22839i) q^{39} -9.26946i q^{41} +(3.64439 + 6.63256i) q^{42} -11.4049 q^{43} +(-4.88754 - 1.43228i) q^{44} +(3.79518 + 5.06696i) q^{46} -10.5972 q^{47} +(-4.51899 + 5.25155i) q^{48} -2.54541 q^{49} +(0.367316 + 0.0519235i) q^{51} +(-9.72494 - 2.84987i) q^{52} +9.51198 q^{53} +(-7.16881 + 1.61497i) q^{54} +(-3.06037 - 8.18520i) q^{56} +(0.632684 - 4.47572i) q^{57} +(6.67030 + 8.90553i) q^{58} -0.428357i q^{59} -1.11217i q^{61} +(5.19273 - 3.88939i) q^{62} +(2.56909 - 8.90553i) q^{63} +(6.03762 - 5.24854i) q^{64} +(3.00385 + 5.46681i) q^{66} -2.35998 q^{67} +(-0.411070 - 0.120463i) q^{68} +(1.08523 - 7.67714i) q^{69} -6.12075 q^{71} +(8.46018 - 0.652221i) q^{72} +12.0147 q^{73} +(-8.68984 + 6.50874i) q^{74} +(-1.46783 + 5.00885i) q^{76} -7.86770 q^{77} +(5.97689 + 10.8776i) q^{78} +11.6319i q^{79} +(7.61709 + 4.79374i) q^{81} +(10.4922 - 7.85873i) q^{82} +2.29913i q^{83} +(-4.41772 + 9.74827i) q^{84} +(-9.66919 - 12.9094i) q^{86} +(1.90737 - 13.4931i) q^{87} +(-2.52248 - 6.74655i) q^{88} -12.4853i q^{89} -15.6547 q^{91} +(-2.51776 + 8.59162i) q^{92} +(-7.86770 - 1.11217i) q^{93} +(-8.98440 - 11.9951i) q^{94} +(-9.77552 - 0.662786i) q^{96} +8.04496 q^{97} +(-2.15802 - 2.88118i) q^{98} +(2.11755 - 7.34028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9	\( 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9} - 3 q^{12} - 6 q^{16} - 5 q^{18} - 4 q^{19} - 2 q^{22} + 5 q^{24} + 8 q^{27} - 20 q^{28} + 18 q^{33} - 2 q^{34} + 19 q^{36} - 14 q^{42} - 40 q^{43} - 16 q^{46} - 27 q^{48} - 36 q^{49} - 30 q^{51} - 4 q^{52} - 30 q^{54} + 42 q^{57} + 52 q^{58} + 10 q^{64} + 7 q^{66} - 60 q^{67} - 39 q^{72} + 12 q^{73} - 38 q^{76} + 54 q^{78} - 10 q^{81} + 58 q^{82} - 34 q^{84} + 34 q^{88} - 24 q^{91} + 28 q^{94} - 31 q^{96} - 32 q^{97} + 58 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9 - 3 * q^12 - 6 * q^16 - 5 * q^18 - 4 * q^19 - 2 * q^22 + 5 * q^24 + 8 * q^27 - 20 * q^28 + 18 * q^33 - 2 * q^34 + 19 * q^36 - 14 * q^42 - 40 * q^43 - 16 * q^46 - 27 * q^48 - 36 * q^49 - 30 * q^51 - 4 * q^52 - 30 * q^54 + 42 * q^57 + 52 * q^58 + 10 * q^64 + 7 * q^66 - 60 * q^67 - 39 * q^72 + 12 * q^73 - 38 * q^76 + 54 * q^78 - 10 * q^81 + 58 * q^82 - 34 * q^84 + 34 * q^88 - 24 * q^91 + 28 * q^94 - 31 * q^96 - 32 * q^97 + 58 * q^99

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