LMFDB - Embedded newform 156.2.c.d.131.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(131,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("156.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.c (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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.78003431400411136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{8} - 4x^{6} - 4x^{4} + 64 $ x^12 - x^8 - 4x^6 - 4x^4 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.10
Root			$0.960471 - 1.03802i$ of defining polynomial
Character	$\chi$	$=$	156.131
Dual form			156.2.c.d.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.960471 + 1.03802i) q^{2} +(1.58957 + 0.687941i) q^{3} +(-0.154992 + 1.99399i) q^{4} -0.716254i q^{5} +(0.812636 + 2.31076i) q^{6} -4.43857i q^{7} +(-2.21867 + 1.75428i) q^{8} +(2.05347 + 2.18706i) q^{9} +(0.743490 - 0.687941i) q^{10} -6.03554 q^{11} +(-1.61812 + 3.06296i) q^{12} -1.00000 q^{13} +(4.60734 - 4.26311i) q^{14} +(0.492741 - 1.13854i) q^{15} +(-3.95196 - 0.618103i) q^{16} +2.94162i q^{17} +(-0.297925 + 4.23217i) q^{18} -2.16149i q^{19} +(1.42820 + 0.111014i) q^{20} +(3.05347 - 7.05542i) q^{21} +(-5.79696 - 6.26505i) q^{22} +2.19366 q^{23} +(-4.73358 + 1.26224i) q^{24} +4.48698 q^{25} +(-0.960471 - 1.03802i) q^{26} +(1.75957 + 4.88916i) q^{27} +(8.85044 + 0.687941i) q^{28} +(1.65509 - 0.582054i) q^{30} +3.96388i q^{31} +(-3.15413 - 4.69590i) q^{32} +(-9.59393 - 4.15210i) q^{33} +(-3.05347 + 2.82534i) q^{34} -3.17914 q^{35} +(-4.67924 + 3.75562i) q^{36} +4.10695 q^{37} +(2.24368 - 2.07605i) q^{38} +(-1.58957 - 0.687941i) q^{39} +(1.25651 + 1.58913i) q^{40} +6.07884i q^{41} +(10.2565 - 3.60694i) q^{42} -7.50125i q^{43} +(0.935460 - 12.0348i) q^{44} +(1.56649 - 1.47081i) q^{45} +(2.10695 + 2.27707i) q^{46} +5.69554 q^{47} +(-5.85670 - 3.70123i) q^{48} -12.7009 q^{49} +(4.30961 + 4.65760i) q^{50} +(-2.02366 + 4.67591i) q^{51} +(0.154992 - 1.99399i) q^{52} -5.88324i q^{53} +(-3.38506 + 6.52238i) q^{54} +4.32298i q^{55} +(7.78649 + 9.84772i) q^{56} +(1.48698 - 3.43585i) q^{57} -1.64822 q^{59} +(2.19386 + 1.15898i) q^{60} -4.61997 q^{61} +(-4.11460 + 3.80719i) q^{62} +(9.70743 - 9.11448i) q^{63} +(1.84501 - 7.78434i) q^{64} +0.716254i q^{65} +(-4.90470 - 13.9467i) q^{66} +11.9880i q^{67} +(-5.86554 - 0.455927i) q^{68} +(3.48698 + 1.50911i) q^{69} +(-3.05347 - 3.30003i) q^{70} +0.662741 q^{71} +(-8.39270 - 1.25001i) q^{72} -4.97396 q^{73} +(3.94460 + 4.26311i) q^{74} +(7.13237 + 3.08678i) q^{75} +(4.30998 + 0.335014i) q^{76} +26.7892i q^{77} +(-0.812636 - 2.31076i) q^{78} +7.02656i q^{79} +(-0.442719 + 2.83060i) q^{80} +(-0.566494 + 8.98215i) q^{81} +(-6.30998 + 5.83854i) q^{82} -6.68103 q^{83} +(13.5951 + 7.18211i) q^{84} +2.10695 q^{85} +(7.78649 - 7.20473i) q^{86} +(13.3909 - 10.5880i) q^{88} -8.94385i q^{89} +(3.03131 + 0.213390i) q^{90} +4.43857i q^{91} +(-0.339999 + 4.37413i) q^{92} +(-2.72691 + 6.30086i) q^{93} +(5.47040 + 5.91212i) q^{94} -1.54818 q^{95} +(-1.78321 - 9.63432i) q^{96} +8.97396 q^{97} +(-12.1988 - 13.1838i) q^{98} +(-12.3938 - 13.2001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 5 q^{6} - 2 q^{9} - 14 q^{10} - 5 q^{12} - 12 q^{13} + 4 q^{16} + 9 q^{18} + 10 q^{21} - 20 q^{22} - 29 q^{24} + 8 q^{25} + 30 q^{28} + 19 q^{30} - 16 q^{33} - 10 q^{34} - 19 q^{36} - 4 q^{37} + 38 q^{40}+ \cdots + 16 q^{97}+O(q^{100}) $ 12 * q + 5 * q^6 - 2 * q^9 - 14 * q^10 - 5 * q^12 - 12 * q^13 + 4 * q^16 + 9 * q^18 + 10 * q^21 - 20 * q^22 - 29 * q^24 + 8 * q^25 + 30 * q^28 + 19 * q^30 - 16 * q^33 - 10 * q^34 - 19 * q^36 - 4 * q^37 + 38 * q^40 + 25 * q^42 + 38 * q^45 - 28 * q^46 - 33 * q^48 + 24 * q^54 - 28 * q^57 - 9 * q^60 - 48 * q^61 + 24 * q^64 + 48 * q^66 - 4 * q^69 - 10 * q^70 - 29 * q^72 + 32 * q^73 + 48 * q^76 - 5 * q^78 - 26 * q^81 - 72 * q^82 - 19 * q^84 - 28 * q^85 + 12 * q^88 + 5 * q^90 + 28 * q^93 - 18 * q^94 - q^96 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.960471	+	1.03802i	0.679155	+	0.733995i
$2$	0.960471	+	1.03802i	0.679155	+	0.733995i
$3$	1.58957	+	0.687941i	0.917739	+	0.397183i
$3$	1.58957	+	0.687941i	0.917739	+	0.397183i
$4$	−0.154992	+	1.99399i	−0.0774959	+	0.996993i
$5$		−	0.716254i		−	0.320319i	−0.987091	−	0.160159i	$-0.948799\pi$
$5$		−	0.716254i		−	0.320319i	0.987091	−	0.160159i	$-0.0512008\pi$
$6$	0.812636	+	2.31076i	0.331757	+	0.943365i
$7$		−	4.43857i		−	1.67762i	−0.544424	−	0.838810i	$-0.683252\pi$
$7$		−	4.43857i		−	1.67762i	0.544424	−	0.838810i	$-0.316748\pi$
$8$	−2.21867	+	1.75428i	−0.784419	+	0.620231i
$9$	2.05347	+	2.18706i	0.684491	+	0.729021i
$10$	0.743490	−	0.687941i	0.235112	−	0.217546i
$11$	−6.03554			−1.81978			−0.909892	−	0.414844i	$-0.863836\pi$
$11$	−6.03554			−1.81978			−0.909892	+	0.414844i	$0.863836\pi$
$12$	−1.61812	+	3.06296i	−0.467110	+	0.884199i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	4.60734	−	4.26311i	1.23136	−	1.13937i
$15$	0.492741	−	1.13854i	0.127225	−	0.293969i
$16$	−3.95196	−	0.618103i	−0.987989	−	0.154526i
$17$			2.94162i			0.713447i	0.934210	+	0.356724i	$0.116106\pi$
$17$			2.94162i			0.713447i	−0.934210	+	0.356724i	$0.883894\pi$
$18$	−0.297925	+	4.23217i	−0.0702217	+	0.997531i
$19$		−	2.16149i		−	0.495880i	−0.968775	−	0.247940i	$-0.920246\pi$
$19$		−	2.16149i		−	0.495880i	0.968775	−	0.247940i	$-0.0797536\pi$
$20$	1.42820	+	0.111014i	0.319355	+	0.0248234i
$21$	3.05347	−	7.05542i	0.666323	−	1.53962i
$22$	−5.79696	−	6.26505i	−1.23592	−	1.33571i
$23$	2.19366			0.457410			0.228705	−	0.973496i	$-0.426551\pi$
$23$	2.19366			0.457410			0.228705	+	0.973496i	$0.426551\pi$
$24$	−4.73358	+	1.26224i	−0.966238	+	0.257653i
$25$	4.48698			0.897396
$26$	−0.960471	−	1.03802i	−0.188364	−	0.203573i
$27$	1.75957	+	4.88916i	0.338630	+	0.940920i
$28$	8.85044	+	0.687941i	1.67258	+	0.130009i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	1.65509	−	0.582054i	0.302177	−	0.106268i
$31$			3.96388i			0.711933i	0.934499	+	0.355967i	$0.115848\pi$
$31$			3.96388i			0.711933i	−0.934499	+	0.355967i	$0.884152\pi$
$32$	−3.15413	−	4.69590i	−0.557577	−	0.830125i
$33$	−9.59393	−	4.15210i	−1.67009	−	0.722788i
$34$	−3.05347	+	2.82534i	−0.523666	+	0.484542i
$35$	−3.17914			−0.537373
$36$	−4.67924	+	3.75562i	−0.779874	+	0.625937i
$37$	4.10695			0.675178			0.337589	−	0.941294i	$-0.390389\pi$
$37$	4.10695			0.675178			0.337589	+	0.941294i	$0.390389\pi$
$38$	2.24368	−	2.07605i	0.363973	−	0.336780i
$39$	−1.58957	−	0.687941i	−0.254535	−	0.110159i
$40$	1.25651	+	1.58913i	0.198672	+	0.251264i
$41$			6.07884i			0.949355i	0.880160	+	0.474677i	$0.157435\pi$
$41$			6.07884i			0.949355i	−0.880160	+	0.474677i	$0.842565\pi$
$42$	10.2565	−	3.60694i	1.58261	−	0.556563i
$43$		−	7.50125i		−	1.14393i	−0.820278	−	0.571965i	$-0.806181\pi$
$43$		−	7.50125i		−	1.14393i	0.820278	−	0.571965i	$-0.193819\pi$
$44$	0.935460	−	12.0348i	0.141026	−	1.81431i
$45$	1.56649	−	1.47081i	0.233519	−	0.219255i
$46$	2.10695	+	2.27707i	0.310652	+	0.335736i
$47$	5.69554			0.830781			0.415390	−	0.909643i	$-0.363645\pi$
$47$	5.69554			0.830781			0.415390	+	0.909643i	$0.363645\pi$
$48$	−5.85670	−	3.70123i	−0.845341	−	0.534227i
$49$	−12.7009			−1.81441
$50$	4.30961	+	4.65760i	0.609471	+	0.658684i
$51$	−2.02366	+	4.67591i	−0.283369	+	0.654759i
$52$	0.154992	−	1.99399i	0.0214935	−	0.276516i
$53$		−	5.88324i		−	0.808125i	−0.914731	−	0.404062i	$-0.867598\pi$
$53$		−	5.88324i		−	0.808125i	0.914731	−	0.404062i	$-0.132402\pi$
$54$	−3.38506	+	6.52238i	−0.460648	+	0.887583i
$55$			4.32298i			0.582911i
$56$	7.78649	+	9.84772i	1.04051	+	1.31596i
$57$	1.48698	−	3.43585i	0.196955	−	0.455089i
$58$		0			0
$59$	−1.64822			−0.214580			−0.107290	−	0.994228i	$-0.534217\pi$
$59$	−1.64822			−0.214580			−0.107290	+	0.994228i	$0.534217\pi$
$60$	2.19386	+	1.15898i	0.283226	+	0.149624i
$61$	−4.61997			−0.591526			−0.295763	−	0.955261i	$-0.595574\pi$
$61$	−4.61997			−0.591526			−0.295763	+	0.955261i	$0.595574\pi$
$62$	−4.11460	+	3.80719i	−0.522555	+	0.483513i
$63$	9.70743	−	9.11448i	1.22302	−	1.14832i
$64$	1.84501	−	7.78434i	0.230626	−	0.973042i
$65$			0.716254i			0.0888404i
$66$	−4.90470	−	13.9467i	−0.603727	−	1.71672i
$67$			11.9880i			1.46457i	0.680999	+	0.732284i	$0.261546\pi$
$67$			11.9880i			1.46457i	−0.680999	+	0.732284i	$0.738454\pi$
$68$	−5.86554	−	0.455927i	−0.711302	−	0.0552892i
$69$	3.48698	+	1.50911i	0.419783	+	0.181675i
$70$	−3.05347	−	3.30003i	−0.364960	−	0.394429i
$71$	0.662741			0.0786528			0.0393264	−	0.999226i	$-0.487479\pi$
$71$	0.662741			0.0786528			0.0393264	+	0.999226i	$0.487479\pi$
$72$	−8.39270	−	1.25001i	−0.989090	−	0.147315i
$73$	−4.97396			−0.582158			−0.291079	−	0.956699i	$-0.594014\pi$
$73$	−4.97396			−0.582158			−0.291079	+	0.956699i	$0.594014\pi$
$74$	3.94460	+	4.26311i	0.458551	+	0.495577i
$75$	7.13237	+	3.08678i	0.823576	+	0.356431i
$76$	4.30998	+	0.335014i	0.494389	+	0.0384287i
$77$			26.7892i			3.05291i
$78$	−0.812636	−	2.31076i	−0.0920130	−	0.261642i
$79$			7.02656i			0.790550i	0.918563	+	0.395275i	$0.129351\pi$
$79$			7.02656i			0.790550i	−0.918563	+	0.395275i	$0.870649\pi$
$80$	−0.442719	+	2.83060i	−0.0494975	+	0.316471i
$81$	−0.566494	+	8.98215i	−0.0629437	+	0.998017i
$82$	−6.30998	+	5.83854i	−0.696821	+	0.644759i
$83$	−6.68103			−0.733338			−0.366669	−	0.930351i	$-0.619502\pi$
$83$	−6.68103			−0.733338			−0.366669	+	0.930351i	$0.619502\pi$
$84$	13.5951	+	7.18211i	1.48335	+	0.783633i
$85$	2.10695			0.228530
$86$	7.78649	−	7.20473i	0.839638	−	0.776906i
$87$		0			0
$88$	13.3909	−	10.5880i	1.42747	−	1.12869i
$89$		−	8.94385i		−	0.948047i	−0.880512	−	0.474023i	$-0.842801\pi$
$89$		−	8.94385i		−	0.948047i	0.880512	−	0.474023i	$-0.157199\pi$
$90$	3.03131	+	0.213390i	0.319528	+	0.0224933i
$91$			4.43857i			0.465288i
$92$	−0.339999	+	4.37413i	−0.0354474	+	0.456034i
$93$	−2.72691	+	6.30086i	−0.282768	+	0.653369i
$94$	5.47040	+	5.91212i	0.564229	+	0.609788i
$95$	−1.54818			−0.158840
$96$	−1.78321	−	9.63432i	−0.181999	−	0.983299i
$97$	8.97396			0.911168			0.455584	−	0.890193i	$-0.349431\pi$
$97$	8.97396			0.911168			0.455584	+	0.890193i	$0.349431\pi$
$98$	−12.1988	−	13.1838i	−1.23227	−	1.33177i
$99$	−12.3938	−	13.2001i	−1.24563	−	1.32666i
$100$	−0.695445	+	8.94697i	−0.0695445	+	0.894697i
$101$		−	4.45073i		−	0.442864i	−0.975176	−	0.221432i	$-0.928927\pi$
$101$		−	4.45073i		−	0.442864i	0.975176	−	0.221432i	$-0.0710731\pi$
$102$	−6.79738	+	2.39047i	−0.673041	+	0.236691i
$103$		−	0.901192i		−	0.0887971i	−0.999014	−	0.0443985i	$-0.985863\pi$
$103$		−	0.901192i		−	0.0887971i	0.999014	−	0.0443985i	$-0.0141371\pi$
$104$	2.21867	−	1.75428i	0.217559	−	0.172021i
$105$	−5.05347	−	2.18706i	−0.493169	−	0.213436i
$106$	6.10695	−	5.65068i	0.593159	−	0.548842i
$107$	−5.03280			−0.486539			−0.243270	−	0.969959i	$-0.578220\pi$
$107$	−5.03280			−0.486539			−0.243270	+	0.969959i	$0.578220\pi$
$108$	−10.0216	+	2.75078i	−0.964333	+	0.264694i
$109$	−2.86701			−0.274610			−0.137305	−	0.990529i	$-0.543844\pi$
$109$	−2.86701			−0.274610			−0.137305	+	0.990529i	$0.543844\pi$
$110$	−4.48737	+	4.15210i	−0.427854	+	0.395887i
$111$	6.52828	+	2.82534i	0.619637	+	0.268169i
$112$	−2.74349	+	17.5410i	−0.259235	+	1.65747i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	4.99469	−	1.75651i	0.467796	−	0.164512i
$115$		−	1.57122i		−	0.146517i
$116$		0			0
$117$	−2.05347	−	2.18706i	−0.189844	−	0.202194i
$118$	−1.58307	−	1.71090i	−0.145733	−	0.157501i
$119$	13.0566			1.19689
$120$	0.904082	+	3.39045i	0.0825310	+	0.309504i
$121$	25.4278			2.31162
$122$	−4.43734	−	4.79564i	−0.401738	−	0.434177i
$123$	−4.18188	+	9.66274i	−0.377068	+	0.871260i
$124$	−7.90391	−	0.614368i	−0.709792	−	0.0551719i
$125$		−	6.79509i		−	0.607771i
$126$	18.7848	+	1.32236i	1.67348	+	0.117805i
$127$		−	3.65296i		−	0.324148i	−0.986779	−	0.162074i	$-0.948182\pi$
$127$		−	3.65296i		−	0.324148i	0.986779	−	0.162074i	$-0.0518183\pi$
$128$	9.85242	−	5.56147i	0.870839	−	0.491569i
$129$	5.16042	−	11.9238i	0.454350	−	1.04983i
$130$	−0.743490	+	0.687941i	−0.0652084	+	0.0603364i
$131$	−0.985482			−0.0861020			−0.0430510	−	0.999073i	$-0.513708\pi$
$131$	−0.985482			−0.0861020			−0.0430510	+	0.999073i	$0.513708\pi$
$132$	9.76621	−	18.4866i	0.850039	−	1.60905i
$133$	−9.59393			−0.831899
$134$	−12.4439	+	11.5141i	−1.07498	+	0.994669i
$135$	3.50188	−	1.26030i	0.301394	−	0.108469i
$136$	−5.16042	−	6.52649i	−0.442502	−	0.559642i
$137$		−	5.09038i		−	0.434901i	−0.976071	−	0.217450i	$-0.930226\pi$
$137$		−	5.09038i		−	0.434901i	0.976071	−	0.217450i	$-0.0697740\pi$
$138$	1.78265	+	5.06903i	0.151749	+	0.431504i
$139$		−	1.37588i		−	0.116701i	−0.998296	−	0.0583504i	$-0.981416\pi$
$139$		−	1.37588i		−	0.116701i	0.998296	−	0.0583504i	$-0.0185841\pi$
$140$	0.492741	−	6.33916i	0.0416442	−	0.535757i
$141$	9.05347	+	3.91820i	0.762440	+	0.329972i
$142$	0.636543	+	0.687941i	0.0534175	+	0.0577308i
$143$	6.03554			0.504718
$144$	−6.76341	−	9.91243i	−0.563617	−	0.826036i
$145$		0			0
$146$	−4.77734	−	5.16309i	−0.395376	−	0.427301i
$147$	−20.1889	−	8.73746i	−1.66516	−	0.720653i
$148$	−0.636543	+	8.18919i	−0.0523235	+	0.673147i
$149$		−	18.6806i		−	1.53037i	−0.643810	−	0.765186i	$-0.722647\pi$
$149$		−	18.6806i		−	1.53037i	0.643810	−	0.765186i	$-0.277353\pi$
$150$	3.64628	+	10.3683i	0.297718	+	0.846572i
$151$		−	11.5133i		−	0.936940i	−0.883479	−	0.468470i	$-0.844805\pi$
$151$		−	11.5133i		−	0.936940i	0.883479	−	0.468470i	$-0.155195\pi$
$152$	3.79186	+	4.79564i	0.307561	+	0.388978i
$153$	−6.43351	+	6.04054i	−0.520118	+	0.488348i
$154$	−27.8078	+	25.7302i	−2.24082	+	2.07340i
$155$	2.83914			0.228045
$156$	1.61812	−	3.06296i	0.129553	−	0.245233i
$157$	−15.5939			−1.24453			−0.622265	−	0.782806i	$-0.713788\pi$
$157$	−15.5939			−1.24453			−0.622265	+	0.782806i	$0.713788\pi$
$158$	−7.29374	+	6.74881i	−0.580259	+	0.536906i
$159$	4.04732	−	9.35182i	0.320973	−	0.741648i
$160$	−3.36346	+	2.25916i	−0.265905	+	0.178602i
$161$		−	9.73671i		−	0.767360i
$162$	−9.86780	+	8.03906i	−0.775288	+	0.631608i
$163$			15.5928i			1.22132i	0.791893	+	0.610660i	$0.209096\pi$
$163$			15.5928i			1.22132i	−0.791893	+	0.610660i	$0.790904\pi$
$164$	−12.1211	−	0.942170i	−0.946500	−	0.0735711i
$165$	−2.97396	+	6.87169i	−0.231522	+	0.534960i
$166$	−6.41693	−	6.93507i	−0.498050	−	0.538266i
$167$	−13.7193			−1.06163			−0.530816	−	0.847487i	$-0.678114\pi$
$167$	−13.7193			−1.06163			−0.530816	+	0.847487i	$0.678114\pi$
$168$	5.60252	+	21.0103i	0.432244	+	1.62098i
$169$	1.00000			0.0769231
$170$	2.02366	+	2.18706i	0.155208	+	0.167740i
$171$	4.72732	−	4.43857i	0.361507	−	0.339426i
$172$	14.9574	+	1.16263i	1.14049	+	0.0886499i
$173$		−	12.1577i		−	0.924331i	−0.886794	−	0.462165i	$-0.847073\pi$
$173$		−	12.1577i		−	0.924331i	0.886794	−	0.462165i	$-0.152927\pi$
$174$		0			0
$175$		−	19.9158i		−	1.50549i
$176$	23.8522	+	3.73059i	1.79793	+	0.281203i
$177$	−2.61997	−	1.13388i	−0.196929	−	0.0852277i
$178$	9.28394	−	8.59031i	0.695861	−	0.643871i
$179$	2.31096			0.172729			0.0863647	−	0.996264i	$-0.472475\pi$
$179$	2.31096			0.172729			0.0863647	+	0.996264i	$0.472475\pi$
$180$	2.68998	+	3.35153i	0.200499	+	0.249808i
$181$	−12.8339			−0.953933			−0.476967	−	0.878921i	$-0.658264\pi$
$181$	−12.8339			−0.953933			−0.476967	+	0.878921i	$0.658264\pi$
$182$	−4.60734	+	4.26311i	−0.341519	+	0.316003i
$183$	−7.34377	−	3.17827i	−0.542867	−	0.234944i
$184$	−4.86701	+	3.84829i	−0.358801	+	0.283700i
$185$		−	2.94162i		−	0.216272i
$186$	−9.15957	+	3.22119i	−0.671613	+	0.236189i
$187$		−	17.7543i		−	1.29832i
$188$	−0.882763	+	11.3568i	−0.0643821	+	0.828282i
$189$	21.7009	−	7.80997i	1.57851	−	0.568092i
$190$	−1.48698	−	1.60705i	−0.107877	−	0.116587i
$191$	11.8484			0.857319			0.428660	−	0.903466i	$-0.358986\pi$
$191$	11.8484			0.857319			0.428660	+	0.903466i	$0.358986\pi$
$192$	8.28794	−	11.1045i	0.598131	−	0.801399i
$193$	14.2139			1.02314			0.511569	−	0.859242i	$-0.329064\pi$
$193$	14.2139			1.02314			0.511569	+	0.859242i	$0.329064\pi$
$194$	8.61923	+	9.31519i	0.618824	+	0.668792i
$195$	−0.492741	+	1.13854i	−0.0352859	+	0.0815323i
$196$	1.96853	−	25.3254i	0.140609	−	1.80895i
$197$			20.6337i			1.47009i	0.678017	+	0.735046i	$0.262839\pi$
$197$			20.6337i			1.47009i	−0.678017	+	0.735046i	$0.737161\pi$
$198$	1.79814	−	25.5434i	0.127788	−	1.81529i
$199$		−	12.2989i		−	0.871848i	−0.899984	−	0.435924i	$-0.856422\pi$
$199$		−	12.2989i		−	0.871848i	0.899984	−	0.435924i	$-0.143578\pi$
$200$	−9.95514	+	7.87142i	−0.703934	+	0.556593i
$201$	−8.24705	+	19.0558i	−0.581702	+	1.34409i
$202$	4.61997	−	4.27479i	0.325060	−	0.300773i
$203$		0			0
$204$	−9.01005	−	4.75988i	−0.630830	−	0.333258i
$205$	4.35399			0.304096
$206$	0.935460	−	0.865568i	0.0651766	−	0.0603070i
$207$	4.50462	+	4.79768i	0.313093	+	0.333461i
$208$	3.95196	+	0.618103i	0.274019	+	0.0428577i
$209$			13.0458i			0.902395i
$210$	−2.58349	−	7.34624i	−0.178278	−	0.506939i
$211$			24.6337i			1.69585i	0.530114	+	0.847926i	$0.322149\pi$
$211$			24.6337i			1.69585i	−0.530114	+	0.847926i	$0.677851\pi$
$212$	11.7311	+	0.911853i	0.805694	+	0.0626263i
$213$	1.05347	+	0.455927i	0.0721828	+	0.0312396i
$214$	−4.83386	−	5.22418i	−0.330436	−	0.357117i
$215$	−5.37280			−0.366422
$216$	−12.4809	−	7.76067i	−0.849215	−	0.528047i
$217$	17.5939			1.19435
$218$	−2.75368	−	2.97603i	−0.186503	−	0.201562i
$219$	−7.90646	−	3.42179i	−0.534269	−	0.231223i
$220$	−8.61997	−	0.670027i	−0.581158	−	0.0451732i
$221$		−	2.94162i		−	0.197875i
$222$	3.33745	+	9.49018i	0.223995	+	0.636939i
$223$			14.8869i			0.996902i	0.866918	+	0.498451i	$0.166098\pi$
$223$			14.8869i			0.996902i	−0.866918	+	0.498451i	$0.833902\pi$
$224$	−20.8431	+	13.9998i	−1.39264	+	0.935402i
$225$	9.21389	+	9.81331i	0.614260	+	0.654221i
$226$		0			0
$227$	8.00651			0.531411			0.265705	−	0.964054i	$-0.414395\pi$
$227$	8.00651			0.531411			0.265705	+	0.964054i	$0.414395\pi$
$228$	6.62056	+	3.49754i	0.438457	+	0.231630i
$229$	27.5087			1.81783			0.908913	−	0.416986i	$-0.136914\pi$
$229$	27.5087			1.81783			0.908913	+	0.416986i	$0.136914\pi$
$230$	1.63096	−	1.50911i	0.107543	−	0.0995078i
$231$	−18.4294	+	42.5833i	−1.21256	+	2.80177i
$232$		0			0
$233$		−	20.4381i		−	1.33895i	−0.742836	−	0.669473i	$-0.766520\pi$
$233$		−	20.4381i		−	1.33895i	0.742836	−	0.669473i	$-0.233480\pi$
$234$	0.297925	−	4.23217i	0.0194760	−	0.276665i
$235$		−	4.07946i		−	0.266115i
$236$	0.255461	−	3.28653i	0.0166291	−	0.213935i
$237$	−4.83386	+	11.1692i	−0.313993	+	0.725519i
$238$	12.5405	+	13.5530i	0.812877	+	0.878513i
$239$	−6.37554			−0.412400			−0.206200	−	0.978510i	$-0.566110\pi$
$239$	−6.37554			−0.412400			−0.206200	+	0.978510i	$0.566110\pi$
$240$	−2.65102	+	4.19488i	−0.171123	+	0.270779i
$241$	−14.4278			−0.929375			−0.464688	−	0.885475i	$-0.653833\pi$
$241$	−14.4278			−0.929375			−0.464688	+	0.885475i	$0.653833\pi$
$242$	24.4226	+	26.3947i	1.56995	+	1.69671i
$243$	−7.07968	+	13.8881i	−0.454161	+	0.890919i
$244$	0.716057	−	9.21215i	0.0458408	−	0.589747i
$245$			9.09706i			0.581190i
$246$	−14.0467	+	4.93988i	−0.895588	+	0.314955i
$247$			2.16149i			0.137532i
$248$	−6.95375	−	8.79454i	−0.441563	−	0.558454i
$249$	−10.6200	−	4.59615i	−0.673013	−	0.291269i
$250$	7.05347	−	6.52649i	0.446101	−	0.412771i
$251$	23.9195			1.50978			0.754892	−	0.655849i	$-0.227689\pi$
$251$	23.9195			1.50978			0.754892	+	0.655849i	$0.227689\pi$
$252$	16.6696	+	20.7691i	1.05008	+	1.30833i
$253$	−13.2399			−0.832388
$254$	3.79186	−	3.50856i	0.237923	−	0.220147i
$255$	3.34914	+	1.44946i	0.209731	+	0.0907684i
$256$	15.2359	+	4.88543i	0.952244	+	0.305339i
$257$			16.5318i			1.03123i	0.856822	+	0.515613i	$0.172436\pi$
$257$			16.5318i			1.03123i	−0.856822	+	0.515613i	$0.827564\pi$
$258$	17.3336	−	6.09579i	1.07914	−	0.379507i
$259$		−	18.2290i		−	1.13269i
$260$	−1.42820	−	0.111014i	−0.0885732	−	0.00688477i
$261$		0			0
$262$	−0.946527	−	1.02295i	−0.0584766	−	0.0631984i
$263$	25.4677			1.57040			0.785201	−	0.619240i	$-0.212559\pi$
$263$	25.4677			1.57040			0.785201	+	0.619240i	$0.212559\pi$
$264$	28.5697	−	7.61828i	1.75834	−	0.468873i
$265$	−4.21389			−0.258857
$266$	−9.21469	−	9.95874i	−0.564989	−	0.610609i
$267$	6.15285	−	14.2169i	0.376548	−	0.870060i
$268$	−23.9039	−	1.85804i	−1.46016	−	0.113498i
$269$		−	22.4916i		−	1.37134i	−0.727913	−	0.685670i	$-0.759509\pi$
$269$		−	22.4916i		−	1.37134i	0.727913	−	0.685670i	$-0.240491\pi$
$270$	4.67168	+	2.42456i	0.284309	+	0.147554i
$271$		−	20.6216i		−	1.25267i	−0.779552	−	0.626337i	$-0.784553\pi$
$271$		−	20.6216i		−	1.25267i	0.779552	−	0.626337i	$-0.215447\pi$
$272$	1.81822	−	11.6251i	0.110246	−	0.704878i
$273$	−3.05347	+	7.05542i	−0.184805	+	0.427013i
$274$	5.28394	−	4.88916i	0.319215	−	0.295365i
$275$	−27.0814			−1.63307
$276$	−3.54960	+	6.71909i	−0.213661	+	0.404442i
$277$	−13.1879			−0.792381			−0.396191	−	0.918168i	$-0.629668\pi$
$277$	−13.1879			−0.792381			−0.396191	+	0.918168i	$0.629668\pi$
$278$	1.42820	−	1.32150i	0.0856578	−	0.0792580i
$279$	−8.66925	+	8.13971i	−0.519014	+	0.487312i
$280$	7.05347	−	5.57710i	0.421526	−	0.333296i
$281$			12.4061i			0.740087i	0.929014	+	0.370044i	$0.120657\pi$
$281$			12.4061i			0.740087i	−0.929014	+	0.370044i	$0.879343\pi$
$282$	4.62841	+	13.1610i	0.275618	+	0.783729i
$283$			10.4002i			0.618225i	0.951025	+	0.309113i	$0.100032\pi$
$283$			10.4002i			0.618225i	−0.951025	+	0.309113i	$0.899968\pi$
$284$	−0.102719	+	1.32150i	−0.00609527	+	0.0784163i
$285$	−2.46094	−	1.06506i	−0.145773	−	0.0630885i
$286$	5.79696	+	6.26505i	0.342782	+	0.370460i
$287$	26.9813			1.59266
$288$	3.79330	−	16.5412i	0.223522	−	0.974699i
$289$	8.34688			0.490993
$290$		0			0
$291$	14.2647	+	6.17356i	0.836214	+	0.361900i
$292$	0.770923	−	9.91800i	0.0451148	−	0.580407i
$293$			29.9264i			1.74832i	0.485640	+	0.874159i	$0.338587\pi$
$293$			29.9264i			1.74832i	−0.485640	+	0.874159i	$0.661413\pi$
$294$	−10.3212	−	29.3487i	−0.601944	−	1.71165i
$295$			1.18055i			0.0687341i
$296$	−9.11197	+	7.20473i	−0.529622	+	0.418767i
$297$	−10.6200	−	29.5088i	−0.616233	−	1.71227i
$298$	19.3909	−	17.9421i	1.12328	−	1.03936i
$299$	−2.19366			−0.126863
$300$	−7.26045	+	13.7434i	−0.419182	+	0.793477i
$301$	−33.2948			−1.91908
$302$	11.9511	−	11.0582i	0.687709	−	0.636328i
$303$	3.06184	−	7.07475i	0.175898	−	0.406434i
$304$	−1.33602	+	8.54212i	−0.0766262	+	0.489924i
$305$			3.30907i			0.189477i
$306$	−12.4494	−	0.876383i	−0.711686	−	0.0500995i
$307$			28.1711i			1.60781i	0.594760	+	0.803904i	$0.297247\pi$
$307$			28.1711i			1.60781i	−0.594760	+	0.803904i	$0.702753\pi$
$308$	−53.4172	−	4.15210i	−3.04373	−	0.236588i
$309$	0.619967	−	1.43251i	0.0352687	−	0.0814926i
$310$	2.72691	+	2.94710i	0.154878	+	0.167384i
$311$	−21.5031			−1.21933			−0.609665	−	0.792659i	$-0.708696\pi$
$311$	−21.5031			−1.21933			−0.609665	+	0.792659i	$0.708696\pi$
$312$	4.73358	−	1.26224i	0.267986	−	0.0714600i
$313$	−20.5347			−1.16069			−0.580346	−	0.814370i	$-0.697083\pi$
$313$	−20.5347			−1.16069			−0.580346	+	0.814370i	$0.697083\pi$
$314$	−14.9775	−	16.1869i	−0.845230	−	0.913479i
$315$	−6.52828	−	6.95299i	−0.367827	−	0.391756i
$316$	−14.0109	−	1.08906i	−0.788172	−	0.0612644i
$317$			1.78131i			0.100048i	0.998748	+	0.0500242i	$0.0159298\pi$
$317$			1.78131i			0.100048i	−0.998748	+	0.0500242i	$0.984070\pi$
$318$	13.5948	−	4.78093i	0.762356	−	0.268101i
$319$		0			0
$320$	−5.57557	−	1.32150i	−0.311684	−	0.0738738i
$321$	−8.00000	−	3.46227i	−0.446516	−	0.193245i
$322$	10.1069	−	9.35182i	0.563238	−	0.521157i
$323$	6.35828			0.353784
$324$	−17.8225	−	2.52174i	−0.990138	−	0.140097i
$325$	−4.48698			−0.248893
$326$	−16.1857	+	14.9764i	−0.896442	+	0.829466i
$327$	−4.55732	−	1.97234i	−0.252020	−	0.109070i
$328$	−10.6640	−	13.4869i	−0.588820	−	0.744692i
$329$		−	25.2801i		−	1.39373i
$330$	−9.98939	+	3.51301i	−0.549898	+	0.193385i
$331$		−	26.3687i		−	1.44935i	−0.689089	−	0.724677i	$-0.741989\pi$
$331$		−	26.3687i		−	1.44935i	0.689089	−	0.724677i	$-0.258011\pi$
$332$	1.03550	−	13.3219i	0.0568307	−	0.731133i
$333$	8.43351	+	8.98215i	0.462153	+	0.492219i
$334$	−13.1770	−	14.2410i	−0.721013	−	0.779232i
$335$	8.58646			0.469129
$336$	−16.4282	+	25.9953i	−0.896230	+	1.41816i
$337$	1.13299			0.0617178			0.0308589	−	0.999524i	$-0.490176\pi$
$337$	1.13299			0.0617178			0.0308589	+	0.999524i	$0.490176\pi$
$338$	0.960471	+	1.03802i	0.0522427	+	0.0564611i
$339$		0			0
$340$	−0.326559	+	4.20122i	−0.0177102	+	0.227843i
$341$		−	23.9241i		−	1.29557i
$342$	9.14780	+	0.643963i	0.494656	+	0.0348215i
$343$			25.3037i			1.36627i
$344$	13.1593	+	16.6428i	0.709501	+	0.897320i
$345$	1.08091	−	2.49756i	0.0581940	−	0.134464i
$346$	12.6200	−	11.6771i	0.678454	−	0.627764i
$347$	20.2830			1.08885			0.544425	−	0.838809i	$-0.316748\pi$
$347$	20.2830			1.08885			0.544425	+	0.838809i	$0.316748\pi$
$348$		0			0
$349$	1.34688			0.0720969			0.0360484	−	0.999350i	$-0.488523\pi$
$349$	1.34688			0.0720969			0.0360484	+	0.999350i	$0.488523\pi$
$350$	20.6731	−	19.1285i	1.10502	−	1.02246i
$351$	−1.75957	−	4.88916i	−0.0939189	−	0.260964i
$352$	19.0369	+	28.3423i	1.01467	+	1.51065i
$353$		−	34.8978i		−	1.85742i	−0.370806	−	0.928710i	$-0.620919\pi$
$353$		−	34.8978i		−	1.85742i	0.370806	−	0.928710i	$-0.379081\pi$
$354$	−1.33941	−	3.80865i	−0.0711886	−	0.202427i
$355$		−	0.474691i		−	0.0251940i
$356$	17.8339	+	1.38622i	0.945195	+	0.0734697i
$357$	20.7543	+	8.98215i	1.09844	+	0.475386i
$358$	2.21961	+	2.39884i	0.117310	+	0.126783i
$359$	−26.8813			−1.41874			−0.709370	−	0.704837i	$-0.751020\pi$
$359$	−26.8813			−1.41874			−0.709370	+	0.704837i	$0.751020\pi$
$360$	−0.895325	+	6.01131i	−0.0471878	+	0.316824i
$361$	14.3280			0.754103
$362$	−12.3265	−	13.3219i	−0.647869	−	0.700182i
$363$	40.4193	+	17.4928i	2.12146	+	0.918135i
$364$	−8.85044	−	0.687941i	−0.463889	−	0.0360579i
$365$			3.56262i			0.186476i
$366$	−3.75435	−	10.6756i	−0.196243	−	0.558025i
$367$			12.9208i			0.674458i	0.941423	+	0.337229i	$0.109490\pi$
$367$			12.9208i			0.674458i	−0.941423	+	0.337229i	$0.890510\pi$
$368$	−8.66925	−	1.35591i	−0.451916	−	0.0706816i
$369$	−13.2948	+	12.4827i	−0.692100	+	0.649825i
$370$	3.05347	−	2.82534i	0.158743	−	0.146882i
$371$	−26.1131			−1.35573
$372$	−12.1412	−	6.41401i	−0.629491	−	0.332551i
$373$	−12.9740			−0.671766			−0.335883	−	0.941904i	$-0.609035\pi$
$373$	−12.9740			−0.671766			−0.335883	+	0.941904i	$0.609035\pi$
$374$	18.4294	−	17.0525i	0.952960	−	0.881761i
$375$	4.67462	−	10.8013i	0.241397	−	0.557776i
$376$	−12.6365	+	9.99158i	−0.651680	+	0.515276i
$377$		0			0
$378$	28.9500	+	15.0248i	1.48903	+	0.772792i
$379$			10.0892i			0.518250i	0.965844	+	0.259125i	$0.0834341\pi$
$379$			10.0892i			0.518250i	−0.965844	+	0.259125i	$0.916566\pi$
$380$	0.239955	−	3.08704i	0.0123094	−	0.158362i
$381$	2.51302	−	5.80664i	0.128746	−	0.297483i
$382$	11.3800	+	12.2989i	0.582253	+	0.629268i
$383$	−29.1577			−1.48989			−0.744945	−	0.667126i	$-0.767524\pi$
$383$	−29.1577			−1.48989			−0.744945	+	0.667126i	$0.767524\pi$
$384$	19.4871	−	2.06246i	0.994446	−	0.105250i
$385$	19.1879			0.977904
$386$	13.6520	+	14.7544i	0.694870	+	0.750978i
$387$	16.4057	−	15.4036i	0.833949	−	0.783010i
$388$	−1.39089	+	17.8939i	−0.0706117	+	0.908427i
$389$			7.31575i			0.370923i	0.982652	+	0.185462i	$0.0593780\pi$
$389$			7.31575i			0.370923i	−0.982652	+	0.185462i	$0.940622\pi$
$390$	−1.65509	+	0.582054i	−0.0838089	+	0.0294735i
$391$			6.45291i			0.326338i
$392$	28.1791	−	22.2809i	1.42326	−	1.12535i
$393$	−1.56649	−	0.677954i	−0.0790192	−	0.0341982i
$394$	−21.4183	+	19.8181i	−1.07904	+	0.998421i
$395$	5.03280			0.253228
$396$	28.2418	−	22.6672i	1.41920	−	1.13907i
$397$	10.4278			0.523356			0.261678	−	0.965155i	$-0.415724\pi$
$397$	10.4278			0.523356			0.261678	+	0.965155i	$0.415724\pi$
$398$	12.7666	−	11.8128i	0.639931	−	0.592120i
$399$	−15.2502	−	6.60006i	−0.763466	−	0.330416i
$400$	−17.7323	−	2.77341i	−0.886617	−	0.138671i
$401$			29.0145i			1.44892i	0.689319	+	0.724458i	$0.257910\pi$
$401$			29.0145i			1.44892i	−0.689319	+	0.724458i	$0.742090\pi$
$402$	−27.7014	+	9.74189i	−1.38162	+	0.485881i
$403$		−	3.96388i		−	0.197455i
$404$	8.87469	+	0.689826i	0.441532	+	0.0343201i
$405$	6.43351	+	0.405754i	0.319683	+	0.0201621i
$406$		0			0
$407$	−24.7877			−1.22868
$408$	−3.71302	−	13.9244i	−0.183822	−	0.689360i
$409$	6.81215			0.336839			0.168419	−	0.985715i	$-0.446134\pi$
$409$	6.81215			0.336839			0.168419	+	0.985715i	$0.446134\pi$
$410$	4.18188	+	4.51955i	0.206528	+	0.223205i
$411$	3.50188	−	8.09152i	0.172735	−	0.399125i
$412$	1.79696	+	0.139677i	0.0885300	+	0.00688141i
$413$			7.31575i			0.359984i
$414$	−0.653547	+	9.28394i	−0.0321201	+	0.456281i
$415$			4.78531i			0.234902i
$416$	3.15413	+	4.69590i	0.154644	+	0.230235i
$417$	0.946527	−	2.18706i	0.0463516	−	0.107101i
$418$	−13.5418	+	12.5301i	−0.662353	+	0.612867i
$419$	−12.4111			−0.606321			−0.303161	−	0.952939i	$-0.598042\pi$
$419$	−12.4111			−0.606321			−0.303161	+	0.952939i	$0.598042\pi$
$420$	5.14422	−	9.73758i	0.251012	−	0.475145i
$421$	30.2688			1.47521			0.737605	−	0.675233i	$-0.235957\pi$
$421$	30.2688			1.47521			0.737605	+	0.675233i	$0.235957\pi$
$422$	−25.5704	+	23.6599i	−1.24475	+	1.15175i
$423$	11.6956	+	12.4565i	0.568662	+	0.605657i
$424$	10.3208	+	13.0530i	0.501224	+	0.633908i
$425$			13.1990i			0.640245i
$426$	0.538567	+	1.53144i	0.0260937	+	0.0741983i
$427$			20.5060i			0.992356i
$428$	0.780043	−	10.0353i	0.0377048	−	0.485076i
$429$	9.59393	+	4.15210i	0.463199	+	0.200465i
$430$	−5.16042	−	5.57710i	−0.248858	−	0.268952i
$431$	30.4832			1.46832			0.734162	−	0.678974i	$-0.237575\pi$
$431$	30.4832			1.46832			0.734162	+	0.678974i	$0.237575\pi$
$432$	−3.93174	−	20.4093i	−0.189166	−	0.981945i
$433$	−18.7269			−0.899958			−0.449979	−	0.893039i	$-0.648569\pi$
$433$	−18.7269			−0.899958			−0.449979	+	0.893039i	$0.648569\pi$
$434$	16.8985	+	18.2629i	0.811152	+	0.876649i
$435$		0			0
$436$	0.444363	−	5.71678i	0.0212811	−	0.273784i
$437$		−	4.74158i		−	0.226821i
$438$	−4.04202	−	11.4936i	−0.193135	−	0.549187i
$439$		−	16.2944i		−	0.777688i	−0.921304	−	0.388844i	$-0.872875\pi$
$439$		−	16.2944i		−	0.777688i	0.921304	−	0.388844i	$-0.127125\pi$
$440$	−7.58372	−	9.59128i	−0.361540	−	0.457246i
$441$	−26.0809	−	27.7776i	−1.24195	−	1.32274i
$442$	3.05347	−	2.82534i	0.145239	−	0.134388i
$443$	2.95645			0.140465			0.0702325	−	0.997531i	$-0.477626\pi$
$443$	2.95645			0.140465			0.0702325	+	0.997531i	$0.477626\pi$
$444$	−6.64551	+	12.5794i	−0.315382	+	0.596992i
$445$	−6.40607			−0.303677
$446$	−15.4530	+	14.2985i	−0.731720	+	0.677051i
$447$	12.8511	−	29.6941i	0.607838	−	1.40448i
$448$	−34.5513	−	8.18919i	−1.63240	−	0.386903i
$449$			32.0327i			1.51172i	0.654734	+	0.755859i	$0.272781\pi$
$449$			32.0327i			1.51172i	−0.654734	+	0.755859i	$0.727219\pi$
$450$	−1.33679	+	18.9896i	−0.0630167	+	0.895181i
$451$		−	36.6891i		−	1.72762i
$452$		0			0
$453$	7.92049	−	18.3012i	0.372137	−	0.859867i
$454$	7.69002	+	8.31095i	0.360910	+	0.390052i
$455$	3.17914			0.149040
$456$	2.72831	+	10.2316i	0.127765	+	0.479138i
$457$	28.9077			1.35224			0.676122	−	0.736790i	$-0.263659\pi$
$457$	28.9077			1.35224			0.676122	+	0.736790i	$0.263659\pi$
$458$	26.4213	+	28.5547i	1.23459	+	1.33427i
$459$	−14.3821	+	5.17599i	−0.671297	+	0.241594i
$460$	3.13299	+	0.243526i	0.146076	+	0.0113545i
$461$		−	15.3477i		−	0.714816i	−0.933948	−	0.357408i	$-0.883661\pi$
$461$		−	15.3477i		−	0.714816i	0.933948	−	0.357408i	$-0.116339\pi$
$462$	−61.9034	+	21.7698i	−2.88001	+	1.01283i
$463$		−	17.3952i		−	0.808422i	−0.914666	−	0.404211i	$-0.867546\pi$
$463$		−	17.3952i		−	0.808422i	0.914666	−	0.404211i	$-0.132454\pi$
$464$		0			0
$465$	4.51302	+	1.95316i	0.209286	+	0.0905758i
$466$	21.2153	−	19.6302i	0.982779	−	0.909353i
$467$	−19.5322			−0.903840			−0.451920	−	0.892058i	$-0.649261\pi$
$467$	−19.5322			−0.903840			−0.451920	+	0.892058i	$0.649261\pi$
$468$	4.67924	−	3.75562i	0.216298	−	0.173604i
$469$	53.2096			2.45699
$470$	4.23458	−	3.91820i	0.195327	−	0.180733i
$471$	−24.7877	−	10.7277i	−1.14215	−	0.494307i
$472$	3.65686	−	2.89144i	0.168321	−	0.133089i
$473$			45.2741i			2.08171i
$474$	−16.2367	+	5.71004i	−0.745777	+	0.262271i
$475$		−	9.69857i		−	0.445001i
$476$	−2.02366	+	26.0346i	−0.0927543	+	1.19329i
$477$	12.8670	−	12.0811i	0.589140	−	0.553154i
$478$	−6.12352	−	6.61797i	−0.280083	−	0.302699i
$479$	−3.31370			−0.151407			−0.0757035	−	0.997130i	$-0.524120\pi$
$479$	−3.31370			−0.151407			−0.0757035	+	0.997130i	$0.524120\pi$
$480$	−6.90062	+	1.27723i	−0.314969	+	0.0582975i
$481$	−4.10695			−0.187261
$482$	−13.8575	−	14.9764i	−0.631190	−	0.682157i
$483$	6.69828	−	15.4772i	0.304782	−	0.704237i
$484$	−3.94110	+	50.7026i	−0.179141	+	2.30467i
$485$		−	6.42764i		−	0.291864i
$486$	−21.2160	+	5.99019i	−0.962376	+	0.271721i
$487$			26.5998i			1.20535i	0.797985	+	0.602677i	$0.205899\pi$
$487$			26.5998i			1.20535i	−0.797985	+	0.602677i	$0.794101\pi$
$488$	10.2502	−	8.10471i	0.464004	−	0.366883i
$489$	−10.7269	+	24.7858i	−0.485088	+	1.12085i
$490$	−9.44297	+	8.73746i	−0.426590	+	0.394718i
$491$	7.53195			0.339912			0.169956	−	0.985452i	$-0.445637\pi$
$491$	7.53195			0.339912			0.169956	+	0.985452i	$0.445637\pi$
$492$	−18.6192	−	9.83626i	−0.839419	−	0.443453i
$493$		0			0
$494$	−2.24368	+	2.07605i	−0.100948	+	0.0934059i
$495$	−9.45464	+	8.87713i	−0.424955	+	0.398997i
$496$	2.45008	−	15.6651i	0.110012	−	0.703382i
$497$		−	2.94162i		−	0.131950i
$498$	−5.42925	−	15.4383i	−0.243290	−	0.691805i
$499$		−	11.8916i		−	0.532342i	−0.963926	−	0.266171i	$-0.914241\pi$
$499$		−	11.8916i		−	0.532342i	0.963926	−	0.266171i	$-0.0857586\pi$
$500$	13.5493	+	1.05318i	0.605944	+	0.0470998i
$501$	−21.8078	−	9.43808i	−0.974302	−	0.421662i
$502$	22.9740	+	24.8290i	1.02538	+	1.10817i
$503$	−24.1077			−1.07491			−0.537454	−	0.843293i	$-0.680614\pi$
$503$	−24.1077			−1.07491			−0.537454	+	0.843293i	$0.680614\pi$
$504$	−5.54825	+	37.2516i	−0.247139	+	1.65932i
$505$	−3.18785			−0.141858
$506$	−12.7166	−	13.7434i	−0.565320	−	0.610968i
$507$	1.58957	+	0.687941i	0.0705953	+	0.0305525i
$508$	7.28394	+	0.566178i	0.323173	+	0.0251201i
$509$		−	20.5571i		−	0.911179i	−0.890190	−	0.455589i	$-0.849429\pi$
$509$		−	20.5571i		−	0.911179i	0.890190	−	0.455589i	$-0.150571\pi$
$510$	1.71218	+	4.86865i	0.0758167	+	0.215588i
$511$			22.0773i			0.976640i
$512$	9.56244	+	20.5076i	0.422604	+	0.906314i
$513$	10.5679	−	3.80330i	0.466584	−	0.167920i
$514$	−17.1604	+	15.8783i	−0.756914	+	0.700362i
$515$	−0.645483			−0.0284434
$516$	22.9760	+	12.1379i	1.01146	+	0.534341i
$517$	−34.3757			−1.51184
$518$	18.9221	−	17.5084i	0.831390	−	0.769274i
$519$	8.36376	−	19.3255i	0.367129	−	0.848295i
$520$	−1.25651	−	1.58913i	−0.0551016	−	0.0696881i
$521$			32.5958i			1.42805i	0.700121	+	0.714024i	$0.253129\pi$
$521$			32.5958i			1.42805i	−0.700121	+	0.714024i	$0.746871\pi$
$522$		0			0
$523$		−	18.4243i		−	0.805638i	−0.915280	−	0.402819i	$-0.868030\pi$
$523$		−	18.4243i		−	0.805638i	0.915280	−	0.402819i	$-0.131970\pi$
$524$	0.152742	−	1.96504i	0.00667255	−	0.0858430i
$525$	13.7009	−	31.6575i	0.597955	−	1.38165i
$526$	24.4609	+	26.4361i	1.06655	+	1.15267i
$527$	−11.6602			−0.507927
$528$	35.3483	+	22.3389i	1.53834	+	0.972178i
$529$	−18.1879			−0.790776
$530$	−4.04732	−	4.37413i	−0.175804	−	0.190000i
$531$	−3.38458	−	3.60477i	−0.146878	−	0.156434i
$532$	1.48698	−	19.1301i	0.0644687	−	0.829397i
$533$		−	6.07884i		−	0.263304i
$534$	20.6671	−	7.26810i	0.894354	−	0.314521i
$535$			3.60477i			0.155848i
$536$	−21.0303	−	26.5975i	−0.908371	−	1.14883i
$537$	3.67344	+	1.58981i	0.158521	+	0.0686052i
$538$	23.3469	−	21.6026i	1.00656	−	0.931352i
$539$	76.6567			3.30184
$540$	1.97026	+	7.17804i	0.0847864	+	0.308894i
$541$	−41.2427			−1.77316			−0.886581	−	0.462572i	$-0.846927\pi$
$541$	−41.2427			−1.77316			−0.886581	+	0.462572i	$0.846927\pi$
$542$	21.4058	−	19.8065i	0.919456	−	0.850760i
$543$	−20.4003	−	8.82894i	−0.875462	−	0.378886i
$544$	13.8135	−	9.27825i	0.592251	−	0.397802i
$545$			2.05351i			0.0879627i
$546$	−10.2565	+	3.60694i	−0.438936	+	0.154363i
$547$		−	2.32526i		−	0.0994211i	−0.998764	−	0.0497106i	$-0.984170\pi$
$547$		−	2.32526i		−	0.0994211i	0.998764	−	0.0497106i	$-0.0158299\pi$
$548$	10.1501	+	0.788967i	0.433593	+	0.0337030i
$549$	−9.48698	−	10.1042i	−0.404894	−	0.431235i
$550$	−26.0109	−	28.1111i	−1.10911	−	1.19866i
$551$		0			0
$552$	−10.3839	+	2.76892i	−0.441967	+	0.117853i
$553$	31.1879			1.32624
$554$	−12.6665	−	13.6893i	−0.538150	−	0.581604i
$555$	2.02366	−	4.67591i	0.0858996	−	0.198481i
$556$	2.74349	+	0.213251i	0.116350	+	0.00904384i
$557$			17.1715i			0.727578i	0.931481	+	0.363789i	$0.118517\pi$
$557$			17.1715i			0.727578i	−0.931481	+	0.363789i	$0.881483\pi$
$558$	−16.7758	−	1.18094i	−0.710176	−	0.0499931i
$559$			7.50125i			0.317269i
$560$	12.5638	+	1.96504i	0.530919	+	0.0830379i
$561$	12.2139	−	28.2217i	0.515671	−	1.19152i
$562$	−12.8779	+	11.9157i	−0.543220	+	0.502634i
$563$	24.4822			1.03180			0.515900	−	0.856649i	$-0.327457\pi$
$563$	24.4822			1.03180			0.515900	+	0.856649i	$0.327457\pi$
$564$	−9.21605	+	17.4452i	−0.388066	+	0.734576i
$565$		0			0
$566$	−10.7956	+	9.98905i	−0.453774	+	0.419871i
$567$	39.8679	+	2.51442i	1.67429	+	0.105596i
$568$	−1.47040	+	1.16263i	−0.0616968	+	0.0487830i
$569$		−	30.1220i		−	1.26278i	−0.775466	−	0.631390i	$-0.782485\pi$
$569$		−	30.1220i		−	1.26278i	0.775466	−	0.631390i	$-0.217515\pi$
$570$	−1.25811	−	3.57747i	−0.0526963	−	0.149844i
$571$		−	22.2095i		−	0.929437i	−0.885458	−	0.464718i	$-0.846156\pi$
$571$		−	22.2095i		−	0.929437i	0.885458	−	0.464718i	$-0.153844\pi$
$572$	−0.935460	+	12.0348i	−0.0391135	+	0.503200i
$573$	18.8339	+	8.15100i	0.786796	+	0.340513i
$574$	25.9148	+	28.0073i	1.08166	+	1.16900i
$575$	9.84291			0.410478
$576$	20.8135	−	11.9498i	0.867230	−	0.497908i
$577$	−26.2139			−1.09130			−0.545649	−	0.838014i	$-0.683717\pi$
$577$	−26.2139			−1.09130			−0.545649	+	0.838014i	$0.683717\pi$
$578$	8.01694	+	8.66427i	0.333461	+	0.360386i
$579$	22.5940	+	9.77833i	0.938974	+	0.406373i
$580$		0			0
$581$			29.6542i			1.23026i
$582$	7.29257	+	20.7367i	0.302287	+	0.859563i
$583$			35.5085i			1.47061i
$584$	11.0356	−	8.72571i	0.456656	−	0.361073i
$585$	−1.56649	+	1.47081i	−0.0647665	+	0.0608105i
$586$	−31.0643	+	28.7434i	−1.28326	+	1.18738i
$587$	−24.4649			−1.00978			−0.504888	−	0.863185i	$-0.668466\pi$
$587$	−24.4649			−1.00978			−0.504888	+	0.863185i	$0.668466\pi$
$588$	20.5515	−	38.9022i	0.847529	−	1.60430i
$589$	8.56789			0.353034
$590$	−1.22544	+	1.13388i	−0.0504504	+	0.0466811i
$591$	−14.1948	+	32.7988i	−0.583896	+	1.34916i
$592$	−16.2305	−	2.53851i	−0.667068	−	0.104332i
$593$		−	23.7285i		−	0.974415i	−0.873286	−	0.487207i	$-0.838016\pi$
$593$		−	23.7285i		−	0.974415i	0.873286	−	0.487207i	$-0.161984\pi$
$594$	20.4307	−	39.3661i	0.838280	−	1.61521i
$595$		−	9.35182i		−	0.383387i
$596$	37.2488	+	2.89533i	1.52577	+	0.118597i
$597$	8.46094	−	19.5500i	0.346283	−	0.800129i
$598$	−2.10695	−	2.27707i	−0.0861595	−	0.0931165i
$599$	−47.5698			−1.94365			−0.971825	−	0.235702i	$-0.924261\pi$
$599$	−47.5698			−1.94365			−0.971825	+	0.235702i	$0.924261\pi$
$600$	−21.2395	+	5.66363i	−0.867098	+	0.231217i
$601$	−3.08091			−0.125673			−0.0628364	−	0.998024i	$-0.520015\pi$
$601$	−3.08091			−0.125673			−0.0628364	+	0.998024i	$0.520015\pi$
$602$	−31.9787	−	34.5608i	−1.30335	−	1.40859i
$603$	−26.2185	+	24.6171i	−1.06770	+	1.00248i
$604$	22.9574	+	1.78447i	0.934123	+	0.0726090i
$605$		−	18.2128i		−	0.740454i
$606$	10.2846	−	3.61682i	0.417782	−	0.146923i
$607$			26.5832i			1.07898i	0.841992	+	0.539490i	$0.181383\pi$
$607$			26.5832i			1.07898i	−0.841992	+	0.539490i	$0.818617\pi$
$608$	−10.1501	+	6.81763i	−0.411643	+	0.276491i
$609$		0			0
$610$	−3.43490	+	3.17827i	−0.139075	+	0.128684i
$611$	−5.69554			−0.230417
$612$	−11.0476	−	13.7646i	−0.446573	−	0.556399i
$613$	−6.42779			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$613$	−6.42779			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$614$	−29.2423	+	27.0575i	−1.18012	+	1.09195i
$615$	6.92098	+	2.99529i	0.279081	+	0.120782i
$616$	−46.9957	−	59.4364i	−1.89351	−	2.39476i
$617$		−	16.4128i		−	0.660754i	−0.943849	−	0.330377i	$-0.892824\pi$
$617$		−	16.4128i		−	0.660754i	0.943849	−	0.330377i	$-0.107176\pi$
$618$	2.08244	−	0.732341i	0.0837680	−	0.0294591i
$619$			6.48448i			0.260633i	0.991472	+	0.130317i	$0.0415994\pi$
$619$			6.48448i			0.260633i	−0.991472	+	0.130317i	$0.958401\pi$
$620$	−0.440044	+	5.66121i	−0.0176726	+	0.227360i
$621$	3.85990	+	10.7252i	0.154893	+	0.430386i
$622$	−20.6531	−	22.3208i	−0.828115	−	0.894982i
$623$	−39.6979			−1.59046
$624$	5.85670	+	3.70123i	0.234455	+	0.148168i
$625$	17.5679			0.702715
$626$	−19.7230	−	21.3156i	−0.788290	−	0.851941i
$627$	−8.97473	+	20.7372i	−0.358416	+	0.828164i
$628$	2.41693	−	31.0941i	0.0964460	−	1.24079i
$629$			12.0811i			0.481704i
$630$	0.947147	−	13.4547i	0.0377352	−	0.536047i
$631$		−	21.2435i		−	0.845688i	−0.906202	−	0.422844i	$-0.861032\pi$
$631$		−	21.2435i		−	0.845688i	0.906202	−	0.422844i	$-0.138968\pi$
$632$	−12.3265	−	15.5896i	−0.490324	−	0.620122i
$633$	−16.9465	+	39.1570i	−0.673564	+	1.55635i
$634$	−1.84904	+	1.71090i	−0.0734349	+	0.0679484i
$635$	−2.61645			−0.103831
$636$	18.0201	+	9.51976i	0.714543	+	0.377483i
$637$	12.7009			0.503227
$638$		0			0
$639$	1.36092	+	1.44946i	0.0538372	+	0.0573396i
$640$	−3.98342	−	7.05684i	−0.157459	−	0.278946i
$641$		−	19.0822i		−	0.753702i	−0.926274	−	0.376851i	$-0.877007\pi$
$641$		−	19.0822i		−	0.753702i	0.926274	−	0.376851i	$-0.122993\pi$
$642$	−4.08984	−	11.6296i	−0.161413	−	0.458984i
$643$			1.60278i			0.0632076i	0.999500	+	0.0316038i	$0.0100615\pi$
$643$			1.60278i			0.0632076i	−0.999500	+	0.0316038i	$0.989939\pi$
$644$	19.4149	+	1.50911i	0.765052	+	0.0594673i
$645$	−8.54045	−	3.69617i	−0.336280	−	0.145537i
$646$	6.10695	+	6.60006i	0.240275	+	0.259676i
$647$	−36.8587			−1.44907			−0.724533	−	0.689240i	$-0.757945\pi$
$647$	−36.8587			−1.44907			−0.724533	+	0.689240i	$0.757945\pi$
$648$	−14.5003	−	20.9222i	−0.569627	−	0.821903i
$649$	9.94792			0.390490
$650$	−4.30961	−	4.65760i	−0.169037	−	0.182686i
$651$	27.9668	+	12.1036i	1.09611	+	0.474377i
$652$	−31.0918	−	2.41675i	−1.21765	−	0.0946473i
$653$			34.9930i			1.36938i	0.728833	+	0.684691i	$0.240063\pi$
$653$			34.9930i			1.36938i	−0.728833	+	0.684691i	$0.759937\pi$
$654$	−2.32984	−	6.62498i	−0.0911039	−	0.259057i
$655$			0.705856i			0.0275801i
$656$	3.75734	−	24.0233i	0.146700	−	0.937952i
$657$	−10.2139	−	10.8784i	−0.398482	−	0.424405i
$658$	26.2413	−	24.2808i	1.02299	−	0.946562i
$659$	23.2740			0.906626			0.453313	−	0.891351i	$-0.350242\pi$
$659$	23.2740			0.906626			0.453313	+	0.891351i	$0.350242\pi$
$660$	−13.2411	−	6.99509i	−0.515410	−	0.272283i
$661$	−35.6677			−1.38731			−0.693657	−	0.720306i	$-0.744002\pi$
$661$	−35.6677			−1.38731			−0.693657	+	0.720306i	$0.744002\pi$
$662$	27.3713	−	25.3263i	1.06382	−	0.984336i
$663$	2.02366	−	4.67591i	0.0785925	−	0.181597i
$664$	14.8230	−	11.7204i	0.575244	−	0.454839i
$665$			6.87169i			0.266473i
$666$	−1.22356	+	17.3813i	−0.0474121	+	0.673511i
$667$		0			0
$668$	2.12638	−	27.3561i	0.0822721	−	1.05844i
$669$	−10.2413	+	23.6638i	−0.395953	+	0.914896i
$670$	8.24705	+	8.91296i	0.318611	+	0.344338i
$671$	27.8840			1.07645
$672$	−42.7626	+	7.91492i	−1.64960	+	0.305324i
$673$	11.1547			0.429982			0.214991	−	0.976616i	$-0.431028\pi$
$673$	11.1547			0.429982			0.214991	+	0.976616i	$0.431028\pi$
$674$	1.08820	+	1.17607i	0.0419159	+	0.0453005i
$675$	7.89516	+	21.9376i	0.303885	+	0.844378i
$676$	−0.154992	+	1.99399i	−0.00596122	+	0.0766917i
$677$		−	41.8119i		−	1.60696i	−0.595332	−	0.803480i	$-0.702979\pi$
$677$		−	41.8119i		−	1.60696i	0.595332	−	0.803480i	$-0.297021\pi$
$678$		0			0
$679$		−	39.8315i		−	1.52859i
$680$	−4.67462	+	3.69617i	−0.179264	+	0.141742i
$681$	12.7269	+	5.50801i	0.487696	+	0.211067i
$682$	24.8339	−	22.9784i	0.950938	−	0.879890i
$683$	22.4940			0.860707			0.430354	−	0.902660i	$-0.358389\pi$
$683$	22.4940			0.860707			0.430354	+	0.902660i	$0.358389\pi$
$684$	8.11774	+	10.1141i	0.310390	+	0.386724i
$685$	−3.64601			−0.139307
$686$	−26.2659	+	24.3035i	−1.00284	+	0.927911i
$687$	43.7270	+	18.9244i	1.66829	+	0.722010i
$688$	−4.63654	+	29.6446i	−0.176767	+	1.13019i
$689$			5.88324i			0.224133i
$690$	3.63071	−	1.27683i	0.138219	−	0.0486081i
$691$			7.27435i			0.276729i	0.990381	+	0.138365i	$0.0441846\pi$
$691$			7.27435i			0.276729i	−0.990381	+	0.138365i	$0.955815\pi$
$692$	24.2422	+	1.88434i	0.921551	+	0.0716318i
$693$	−58.5896	+	55.0108i	−2.22563	+	2.08969i
$694$	19.4813	+	21.0543i	0.739499	+	0.799210i
$695$	−0.985482			−0.0373815
$696$		0			0
$697$	−17.8816			−0.677314
$698$	1.29364	+	1.39810i	0.0489650	+	0.0529187i
$699$	14.0602	−	32.4879i	0.531807	−	1.22880i
$700$	39.7117	+	3.08678i	1.50096	+	0.116669i
$701$			13.1990i			0.498519i	0.968437	+	0.249259i	$0.0801872\pi$
$701$			13.1990i			0.498519i	−0.968437	+	0.249259i	$0.919813\pi$
$702$	3.38506	−	6.52238i	0.127761	−	0.246171i
$703$		−	8.87713i		−	0.334807i
$704$	−11.1356	+	46.9827i	−0.419690	+	1.77073i
$705$	2.80643	−	6.48459i	0.105696	−	0.244224i
$706$	36.2248	−	33.5183i	1.36334	−	1.26148i
$707$	−19.7549			−0.742958
$708$	2.66701	−	5.04843i	0.100233	−	0.189732i
$709$	−33.6156			−1.26246			−0.631231	−	0.775595i	$-0.717450\pi$
$709$	−33.6156			−1.26246			−0.631231	+	0.775595i	$0.717450\pi$
$710$	0.492741	−	0.455927i	0.0184922	−	0.0171106i
$711$	−15.3675	+	14.4289i	−0.576327	+	0.541124i
$712$	15.6900	+	19.8435i	0.588008	+	0.743666i
$713$			8.69540i			0.325645i
$714$	10.6102	+	30.1706i	0.397078	+	1.12911i
$715$		−	4.32298i		−	0.161670i
$716$	−0.358180	+	4.60803i	−0.0133858	+	0.172210i
$717$	−10.1344	−	4.38600i	−0.378475	−	0.163798i
$718$	−25.8187	−	27.9034i	−0.963544	−	1.04135i
$719$	31.6378			1.17989			0.589945	−	0.807444i	$-0.299150\pi$
$719$	31.6378			1.17989			0.589945	+	0.807444i	$0.299150\pi$
$720$	−7.09982	+	4.84432i	−0.264595	+	0.180537i
$721$	−4.00000			−0.148968
$722$	13.7616	+	14.8728i	0.512153	+	0.553507i
$723$	−22.9340	−	9.92547i	−0.852924	−	0.369132i
$724$	1.98914	−	25.5905i	0.0739259	−	0.951065i
$725$		0			0
$726$	20.6635	+	58.7576i	0.766896	+	2.18070i
$727$			46.9545i			1.74144i	0.491775	+	0.870722i	$0.336348\pi$
$727$			46.9545i			1.74144i	−0.491775	+	0.870722i	$0.663652\pi$
$728$	−7.78649	−	9.84772i	−0.288586	−	0.364981i
$729$	−20.8078	+	17.2057i	−0.770660	+	0.637247i
$730$	−3.69809	+	3.42179i	−0.136872	+	0.126646i
$731$	22.0658			0.816134
$732$	7.47564	−	14.1508i	0.276308	−	0.523027i
$733$	18.0549			0.666872			0.333436	−	0.942773i	$-0.391792\pi$
$733$	18.0549			0.666872			0.333436	+	0.942773i	$0.391792\pi$
$734$	−13.4121	+	12.4100i	−0.495049	+	0.458062i
$735$	−6.25824	+	14.4604i	−0.230839	+	0.533381i
$736$	−6.91909	−	10.3012i	−0.255041	−	0.379707i
$737$		−	72.3541i		−	2.66520i
$738$	−25.7267	−	1.81104i	−0.947011	−	0.0666653i
$739$		−	5.14442i		−	0.189241i	−0.995513	−	0.0946203i	$-0.969836\pi$
$739$		−	5.14442i		−	0.189241i	0.995513	−	0.0946203i	$-0.0301637\pi$
$740$	5.86554	+	0.455927i	0.215622	+	0.0167602i
$741$	−1.48698	+	3.43585i	−0.0546256	+	0.126219i
$742$	−25.0809	−	27.1061i	−0.920749	−	0.995096i
$743$	−6.37554			−0.233896			−0.116948	−	0.993138i	$-0.537311\pi$
$743$	−6.37554			−0.233896			−0.116948	+	0.993138i	$0.537311\pi$
$744$	−5.00335	−	18.7633i	−0.183432	−	0.687897i
$745$	−13.3800			−0.490206
$746$	−12.4611	−	13.4673i	−0.456234	−	0.493073i
$747$	−13.7193	−	14.6118i	−0.501963	−	0.534619i
$748$	35.4017	+	2.75177i	1.29442	+	0.100615i
$749$			22.3384i			0.816229i
$750$	15.7018	−	5.52194i	0.573350	−	0.201633i
$751$		−	35.4603i		−	1.29397i	−0.762504	−	0.646983i	$-0.776030\pi$
$751$		−	35.4603i		−	1.29397i	0.762504	−	0.646983i	$-0.223970\pi$
$752$	−22.5085	−	3.52043i	−0.820802	−	0.128377i
$753$	38.0217	+	16.4552i	1.38559	+	0.599661i
$754$		0			0
$755$	−8.24646			−0.300119
$756$	12.2095	+	44.4817i	0.444056	+	1.61778i
$757$	19.3800			0.704379			0.352190	−	0.935929i	$-0.385437\pi$
$757$	19.3800			0.704379			0.352190	+	0.935929i	$0.385437\pi$
$758$	−10.4729	+	9.69042i	−0.380392	+	0.351972i
$759$	−21.0458	−	9.10830i	−0.763915	−	0.330610i
$760$	3.43490	−	2.71594i	0.124597	−	0.0985174i
$761$			7.51134i			0.272286i	0.990689	+	0.136143i	$0.0434707\pi$
$761$			7.51134i			0.272286i	−0.990689	+	0.136143i	$0.956529\pi$
$762$	8.44112	−	2.96853i	0.305789	−	0.107538i
$763$			12.7254i			0.460691i
$764$	−1.83640	+	23.6255i	−0.0664387	+	0.854741i
$765$	4.32656	+	4.60803i	0.156427	+	0.166604i
$766$	−28.0051	−	30.2664i	−1.01187	−	1.09357i
$767$	1.64822			0.0595139
$768$	20.8577	+	18.2471i	0.752636	+	0.658437i
$769$	20.1618			0.727054			0.363527	−	0.931584i	$-0.381573\pi$
$769$	20.1618			0.727054			0.363527	+	0.931584i	$0.381573\pi$
$770$	18.4294	+	19.9175i	0.664148	+	0.717776i
$771$	−11.3729	+	26.2785i	−0.409585	+	0.946396i
$772$	−2.20304	+	28.3423i	−0.0792890	+	1.02006i
$773$			29.3820i			1.05680i	0.848997	+	0.528398i	$0.177207\pi$
$773$			29.3820i			1.05680i	−0.848997	+	0.528398i	$0.822793\pi$
$774$	31.7465	+	2.23481i	1.14111	+	0.0803287i
$775$			17.7858i			0.638886i
$776$	−19.9103	+	15.7428i	−0.714737	+	0.565135i
$777$	12.5405	−	28.9762i	0.449886	−	1.03952i
$778$	−7.59393	+	7.02656i	−0.272255	+	0.251914i
$779$	13.1394			0.470766
$780$	−2.19386	−	1.15898i	−0.0785526	−	0.0414982i
$781$	−4.00000			−0.143131
$782$	−6.69828	+	6.19783i	−0.239530	+	0.221634i
$783$		0			0
$784$	50.1933	+	7.85044i	1.79262	+	0.280373i
$785$			11.1692i			0.398646i
$786$	−0.800838	−	2.27721i	−0.0285650	−	0.0812255i
$787$		−	11.4293i		−	0.407410i	−0.979032	−	0.203705i	$-0.934702\pi$
$787$		−	11.4293i		−	0.407410i	0.979032	−	0.203705i	$-0.0652984\pi$
$788$	−41.1433	−	3.19806i	−1.46567	−	0.113926i
$789$	40.4827	+	17.5203i	1.44122	+	0.623738i
$790$	4.83386	+	5.22418i	0.171981	+	0.185868i
$791$		0			0
$792$	50.6545	+	7.54449i	1.79993	+	0.268082i
$793$	4.61997			0.164060
$794$	10.0156	+	10.8243i	0.355440	+	0.384140i
$795$	−6.69828	−	2.89891i	−0.237564	−	0.102814i
$796$	24.5239	+	1.90623i	0.869226	+	0.0675646i
$797$			17.7345i			0.628188i	0.949392	+	0.314094i	$0.101701\pi$
$797$			17.7345i			0.628188i	−0.949392	+	0.314094i	$0.898299\pi$
$798$	−7.79637	−	22.1693i	−0.275989	−	0.784784i
$799$			16.7541i			0.592718i
$800$	−14.1525	−	21.0704i	−0.500367	−	0.744951i
$801$	19.5608	−	18.3660i	0.691146	−	0.648929i
$802$	−30.1178	+	27.8676i	−1.06350	+	0.984039i
$803$	30.0205			1.05940
$804$	−36.7187	−	19.3980i	−1.29497	−	0.684114i
$805$	−6.97396			−0.245800
$806$	4.11460	−	3.80719i	0.144931	−	0.134102i
$807$	15.4729	−	35.7521i	0.544673	−	1.25853i
$808$	7.80782	+	9.87470i	0.274678	+	0.347391i
$809$		−	34.5727i		−	1.21551i	−0.794124	−	0.607756i	$-0.792070\pi$
$809$		−	34.5727i		−	1.21551i	0.794124	−	0.607756i	$-0.207930\pi$
$810$	5.75801	+	7.06785i	0.202316	+	0.248339i
$811$			38.5230i			1.35273i	0.736568	+	0.676363i	$0.236445\pi$
$811$			38.5230i			1.35273i	−0.736568	+	0.676363i	$0.763555\pi$
$812$		0			0
$813$	14.1865	−	32.7795i	0.497541	−	1.14963i
$814$	−23.8078	−	25.7302i	−0.834464	−	0.901843i
$815$	11.1684			0.391212
$816$	10.8876	−	17.2282i	0.381143	−	0.603106i
$817$	−16.2139			−0.567252
$818$	6.54287	+	7.07118i	0.228766	+	0.247238i
$819$	−9.70743	+	9.11448i	−0.339205	+	0.318486i
$820$	−0.674833	+	8.68180i	−0.0235662	+	0.303182i
$821$			27.5583i			0.961790i	0.876778	+	0.480895i	$0.159688\pi$
$821$			27.5583i			0.961790i	−0.876778	+	0.480895i	$0.840312\pi$
$822$	11.7627	−	4.13663i	0.410270	−	0.144282i
$823$			13.2483i			0.461807i	0.972977	+	0.230903i	$0.0741682\pi$
$823$			13.2483i			0.461807i	−0.972977	+	0.230903i	$0.925832\pi$
$824$	1.58094	+	1.99945i	0.0550747	+	0.0696541i
$825$	−43.0478	−	18.6304i	−1.49873	−	0.648627i
$826$	−7.59393	+	7.02656i	−0.264227	+	0.244485i
$827$	3.41910			0.118894			0.0594468	−	0.998231i	$-0.481066\pi$
$827$	3.41910			0.118894			0.0594468	+	0.998231i	$0.481066\pi$
$828$	−10.2647	+	8.23855i	−0.356722	+	0.286310i
$829$	33.0478			1.14780			0.573898	−	0.818927i	$-0.305431\pi$
$829$	33.0478			1.14780			0.573898	+	0.818927i	$0.305431\pi$
$830$	−4.96728	+	4.59615i	−0.172417	+	0.159535i
$831$	−20.9630	−	9.07247i	−0.727200	−	0.314720i
$832$	−1.84501	+	7.78434i	−0.0639642	+	0.269873i
$833$		−	37.3611i		−	1.29449i
$834$	3.17934	−	1.11809i	0.110091	−	0.0387164i
$835$			9.82651i			0.340061i
$836$	−26.0131	−	2.02199i	−0.899682	−	0.0699319i
$837$	−19.3800	+	6.97472i	−0.669872	+	0.241082i
$838$	−11.9205	−	12.8830i	−0.411786	−	0.445036i
$839$	−6.68103			−0.230655			−0.115327	−	0.993328i	$-0.536792\pi$
$839$	−6.68103			−0.230655			−0.115327	+	0.993328i	$0.536792\pi$
$840$	15.0487	−	4.01283i	0.519230	−	0.138456i
$841$	29.0000			1.00000
$842$	29.0723	+	31.4197i	1.00190	+	1.08280i
$843$	−8.53469	+	19.7204i	−0.293950	+	0.679207i
$844$	−49.1192	−	3.81802i	−1.69075	−	0.131422i
$845$		−	0.716254i		−	0.0246399i
$846$	−1.69685	+	24.1045i	−0.0583388	+	0.828730i
$847$		−	112.863i		−	3.87802i
$848$	−3.63644	+	23.2503i	−0.124876	+	0.798418i
$849$	−7.15470	+	16.5318i	−0.245549	+	0.567370i
$850$	−13.7009	+	12.6772i	−0.469936	+	0.434826i
$851$	9.00925			0.308833
$852$	−1.07239	+	2.02995i	−0.0367395	+	0.0695448i
$853$	−19.2948			−0.660641			−0.330321	−	0.943869i	$-0.607157\pi$
$853$	−19.2948			−0.660641			−0.330321	+	0.943869i	$0.607157\pi$
$854$	−21.2858	+	19.6954i	−0.728384	+	0.673964i
$855$	−3.17914	−	3.38596i	−0.108724	−	0.115798i
$856$	11.1661	−	8.82894i	0.381651	−	0.301767i
$857$			58.0291i			1.98223i	0.132990	+	0.991117i	$0.457542\pi$
$857$			58.0291i			1.98223i	−0.132990	+	0.991117i	$0.542458\pi$
$858$	4.90470	+	13.9467i	0.167444	+	0.476133i
$859$		−	30.7714i		−	1.04991i	−0.851131	−	0.524953i	$-0.824083\pi$
$859$		−	30.7714i		−	1.04991i	0.851131	−	0.524953i	$-0.175917\pi$
$860$	0.832740	−	10.7133i	0.0283962	−	0.365320i
$861$	42.8887	+	18.5616i	1.46164	+	0.632576i
$862$	29.2782	+	31.6423i	0.997220	+	1.07774i
$863$	14.0593			0.478584			0.239292	−	0.970948i	$-0.423085\pi$
$863$	14.0593			0.478584			0.239292	+	0.970948i	$0.423085\pi$
$864$	17.4091	−	23.6838i	0.592269	−	0.805740i
$865$	−8.70798			−0.296080
$866$	−17.9867	−	19.4390i	−0.611211	−	0.660564i
$867$	13.2680	+	5.74216i	0.450604	+	0.195014i
$868$	−2.72691	+	35.0820i	−0.0925575	+	1.19076i
$869$		−	42.4091i		−	1.43863i
$870$		0			0
$871$		−	11.9880i		−	0.406198i
$872$	6.36096	−	5.02954i	0.215409	−	0.170322i
$873$	18.4278	+	19.6266i	0.623686	+	0.664260i
$874$	4.92188	−	4.55415i	0.166485	−	0.154046i
$875$	−30.1605			−1.01961
$876$	8.04844	−	15.2350i	0.271932	−	0.514744i
$877$	−9.41318			−0.317861			−0.158930	−	0.987290i	$-0.550805\pi$
$877$	−9.41318			−0.317861			−0.158930	+	0.987290i	$0.550805\pi$
$878$	16.9140	−	15.6503i	0.570818	−	0.528171i
$879$	−20.5876	+	47.5701i	−0.694402	+	1.60450i
$880$	2.67205	−	17.0842i	0.0900747	−	0.575910i
$881$		−	31.0101i		−	1.04476i	−0.852714	−	0.522378i	$-0.825045\pi$
$881$		−	31.0101i		−	1.04476i	0.852714	−	0.522378i	$-0.174955\pi$
$882$	3.78391	−	53.7522i	0.127411	−	1.80993i
$883$		−	22.5038i		−	0.757312i	−0.925538	−	0.378656i	$-0.876386\pi$
$883$		−	22.5038i		−	0.757312i	0.925538	−	0.378656i	$-0.123614\pi$
$884$	5.86554	+	0.455927i	0.197280	+	0.0153345i
$885$	−0.812147	+	1.87656i	−0.0273000	+	0.0630800i
$886$	2.83958	+	3.06886i	0.0953975	+	0.103101i
$887$	52.4145			1.75991			0.879953	−	0.475061i	$-0.157574\pi$
$887$	52.4145			1.75991			0.879953	+	0.475061i	$0.157574\pi$
$888$	−19.4406	+	5.18394i	−0.652382	+	0.173962i
$889$	−16.2139			−0.543797
$890$	−6.15285	−	6.64966i	−0.206244	−	0.222897i
$891$	3.41910	−	54.2122i	0.114544	−	1.81618i
$892$	−29.6843	−	2.30735i	−0.993904	−	0.0772558i
$893$		−	12.3109i		−	0.411968i
$894$	43.1663	−	15.1805i	1.44370	−	0.507712i
$895$		−	1.65524i		−	0.0553285i
$896$	−24.6849	−	43.7306i	−0.824666	−	1.46094i
$897$	−3.48698	−	1.50911i	−0.116427	−	0.0503877i
$898$	−33.2508	+	30.7665i	−1.10959	+	1.02669i
$899$		0			0
$900$	−20.9957	+	16.8514i	−0.699856	+	0.561713i
$901$	17.3062			0.576554
$902$	38.0842	−	35.2388i	1.26806	−	1.17332i
$903$	−52.9245	−	22.9049i	−1.76122	−	0.762226i
$904$		0			0
$905$			9.19231i			0.305563i
$906$	26.6045	−	9.35614i	0.883877	−	0.310837i
$907$			19.7520i			0.655854i	0.944703	+	0.327927i	$0.106350\pi$
$907$			19.7520i			0.655854i	−0.944703	+	0.327927i	$0.893650\pi$
$908$	−1.24094	+	15.9649i	−0.0411821	+	0.529812i
$909$	9.73403	−	9.13945i	0.322857	−	0.303136i
$910$	3.05347	+	3.30003i	0.101222	+	0.109395i
$911$	9.19743			0.304724			0.152362	−	0.988325i	$-0.451312\pi$
$911$	9.19743			0.304724			0.152362	+	0.988325i	$0.451312\pi$
$912$	−8.00018	+	12.6592i	−0.264913	+	0.419188i
$913$	40.3236			1.33452
$914$	27.7650	+	30.0069i	0.918383	+	0.992539i
$915$	−2.27645	+	5.26000i	−0.0752570	+	0.173890i
$916$	−4.26362	+	54.8519i	−0.140874	+	1.81236i
$917$			4.37413i			0.144446i
$918$	−19.1863	−	9.95754i	−0.633244	−	0.328648i
$919$			26.6796i			0.880078i	0.897979	+	0.440039i	$0.145035\pi$
$919$			26.6796i			0.880078i	−0.897979	+	0.440039i	$0.854965\pi$
$920$	2.75636	+	3.48602i	0.0908744	+	0.114931i
$921$	−19.3800	+	44.7799i	−0.638594	+	1.47555i
$922$	15.9313	−	14.7411i	0.524671	−	0.485471i
$923$	−0.662741			−0.0218144
$924$	−82.0540	−	43.3480i	−2.69938	−	1.42604i
$925$	18.4278			0.605902
$926$	18.0566	−	16.7075i	0.593377	−	0.549044i
$927$	1.97096	−	1.85057i	0.0647349	−	0.0607808i
$928$		0			0
$929$			1.08371i			0.0355553i	0.999842	+	0.0177776i	$0.00565910\pi$
$929$			1.08371i			0.0355553i	−0.999842	+	0.0177776i	$0.994341\pi$
$930$	2.30719	+	6.56058i	0.0756558	+	0.215130i
$931$			27.4528i			0.899730i
$932$	40.7533	+	3.16774i	1.33492	+	0.103763i
$933$	−34.1807	−	14.7929i	−1.11903	−	0.484297i
$934$	−18.7601	−	20.2749i	−0.613848	−	0.663414i
$935$	−12.7166			−0.415876
$936$	8.39270	+	1.25001i	0.274324	+	0.0408579i
$937$	−28.0880			−0.917596			−0.458798	−	0.888541i	$-0.651720\pi$
$937$	−28.0880			−0.917596			−0.458798	+	0.888541i	$0.651720\pi$
$938$	51.1062	+	55.2329i	1.66868	+	1.80342i
$939$	−32.6414	−	14.1267i	−1.06521	−	0.461007i
$940$	8.13438	+	0.632282i	0.265314	+	0.0206228i
$941$		−	45.5463i		−	1.48477i	−0.669975	−	0.742384i	$-0.733695\pi$
$941$		−	45.5463i		−	1.48477i	0.669975	−	0.742384i	$-0.266305\pi$
$942$	−12.6722	−	36.0339i	−0.412882	−	1.17405i
$943$			13.3349i			0.434244i
$944$	6.51370	+	1.01877i	0.212003	+	0.0331582i
$945$	−5.59393	−	15.5433i	−0.181970	−	0.505625i
$946$	−46.9957	+	43.4845i	−1.52796	+	1.41380i
$947$	−31.0233			−1.00812			−0.504061	−	0.863668i	$-0.668161\pi$
$947$	−31.0233			−1.00812			−0.504061	+	0.863668i	$0.668161\pi$
$948$	−21.5220	−	11.3698i	−0.699004	−	0.369273i
$949$	4.97396			0.161462
$950$	10.0674	−	9.31519i	0.326628	−	0.302225i
$951$	−1.22544	+	2.83152i	−0.0397375	+	0.0918183i
$952$	−28.9682	+	22.9049i	−0.938866	+	0.742351i
$953$		−	17.4199i		−	0.564286i	−0.959372	−	0.282143i	$-0.908955\pi$
$953$		−	17.4199i		−	0.564286i	0.959372	−	0.282143i	$-0.0910453\pi$
$954$	24.8988	+	1.75277i	0.806130	+	0.0567479i
$955$		−	8.48646i		−	0.274615i
$956$	0.988157	−	12.7127i	0.0319593	−	0.411159i
$957$		0			0
$958$	−3.18272	−	3.43971i	−0.102829	−	0.111132i
$959$	−22.5940			−0.729598
$960$	−7.95365	−	5.93627i	−0.256703	−	0.191592i
$961$	15.2877			0.493151
$962$	−3.94460	−	4.26311i	−0.127179	−	0.137448i
$963$	−10.3347	−	11.0071i	−0.333032	−	0.354698i
$964$	2.23619	−	28.7688i	0.0720228	−	0.926581i
$965$		−	10.1808i		−	0.327730i
$966$	22.4992	−	7.91240i	0.723900	−	0.254577i
$967$		−	28.0239i		−	0.901188i	−0.892729	−	0.450594i	$-0.851212\pi$
$967$		−	28.0239i		−	0.901188i	0.892729	−	0.450594i	$-0.148788\pi$
$968$	−56.4159	+	44.6074i	−1.81328	+	1.43374i
$969$	10.1069	+	4.37413i	0.324682	+	0.140517i
$970$	6.67205	−	6.17356i	0.214227	−	0.198221i
$971$	−37.8323			−1.21410			−0.607048	−	0.794665i	$-0.707647\pi$
$971$	−37.8323			−1.21410			−0.607048	+	0.794665i	$0.707647\pi$
$972$	−26.5953	−	16.2693i	−0.853044	−	0.521838i
$973$	−6.10695			−0.195780
$974$	−27.6113	+	25.5484i	−0.884723	+	0.818622i
$975$	−7.13237	−	3.08678i	−0.228419	−	0.0988560i
$976$	18.2579	+	2.85561i	0.584421	+	0.0914060i
$977$			7.27335i			0.232695i	0.993209	+	0.116348i	$0.0371186\pi$
$977$			7.27335i			0.232695i	−0.993209	+	0.116348i	$0.962881\pi$
$978$	−36.0312	+	12.6713i	−1.15215	+	0.405182i
$979$			53.9810i			1.72524i
$980$	−18.1394	−	1.40997i	−0.579442	−	0.0450398i
$981$	−5.88733	−	6.27034i	−0.187968	−	0.200197i
$982$	7.23422	+	7.81835i	0.230853	+	0.249494i
$983$	48.2326			1.53838			0.769190	−	0.639020i	$-0.220660\pi$
$983$	48.2326			1.53838			0.769190	+	0.639020i	$0.220660\pi$
$984$	−7.67293	−	28.7746i	−0.244604	−	0.917302i
$985$	14.7790			0.470898
$986$		0			0
$987$	17.3912	−	40.1844i	0.553568	−	1.27908i
$988$	−4.30998	−	0.335014i	−0.137119	−	0.0106582i
$989$		−	16.4552i		−	0.523245i
$990$	−18.2956	−	1.28793i	−0.581472	−	0.0409330i
$991$		−	6.26994i		−	0.199171i	−0.995029	−	0.0995856i	$-0.968248\pi$
$991$		−	6.26994i		−	0.199171i	0.995029	−	0.0995856i	$-0.0317517\pi$
$992$	18.6140	−	12.5026i	0.590994	−	0.396957i
$993$	18.1401	−	41.9149i	0.575659	−	1.33013i
$994$	3.05347	−	2.82534i	0.0968503	−	0.0896143i
$995$	−8.80916			−0.279269
$996$	10.8107	−	20.4637i	0.342549	−	0.648417i
$997$	31.8816			1.00970			0.504850	−	0.863207i	$-0.331548\pi$
$997$	31.8816			1.00970			0.504850	+	0.863207i	$0.331548\pi$
$998$	12.3438	−	11.4216i	0.390736	−	0.361543i
$999$	7.22646	+	20.0795i	0.228635	+	0.635288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.c.d.131.10	yes	12
3.2	odd	2	inner	156.2.c.d.131.3	✓	12
4.3	odd	2	inner	156.2.c.d.131.4	yes	12
8.3	odd	2		2496.2.d.o.1535.12		12
8.5	even	2		2496.2.d.o.1535.1		12
12.11	even	2	inner	156.2.c.d.131.9	yes	12
24.5	odd	2		2496.2.d.o.1535.11		12
24.11	even	2		2496.2.d.o.1535.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.c.d.131.3	✓	12	3.2	odd	2	inner
156.2.c.d.131.4	yes	12	4.3	odd	2	inner
156.2.c.d.131.9	yes	12	12.11	even	2	inner
156.2.c.d.131.10	yes	12	1.1	even	1	trivial
2496.2.d.o.1535.1		12	8.5	even	2
2496.2.d.o.1535.2		12	24.11	even	2
2496.2.d.o.1535.11		12	24.5	odd	2
2496.2.d.o.1535.12		12	8.3	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.960471 + 1.03802i) q^{2} +(1.58957 + 0.687941i) q^{3} +(-0.154992 + 1.99399i) q^{4} -0.716254i q^{5} +(0.812636 + 2.31076i) q^{6} -4.43857i q^{7} +(-2.21867 + 1.75428i) q^{8} +(2.05347 + 2.18706i) q^{9} +(0.743490 - 0.687941i) q^{10} -6.03554 q^{11} +(-1.61812 + 3.06296i) q^{12} -1.00000 q^{13} +(4.60734 - 4.26311i) q^{14} +(0.492741 - 1.13854i) q^{15} +(-3.95196 - 0.618103i) q^{16} +2.94162i q^{17} +(-0.297925 + 4.23217i) q^{18} -2.16149i q^{19} +(1.42820 + 0.111014i) q^{20} +(3.05347 - 7.05542i) q^{21} +(-5.79696 - 6.26505i) q^{22} +2.19366 q^{23} +(-4.73358 + 1.26224i) q^{24} +4.48698 q^{25} +(-0.960471 - 1.03802i) q^{26} +(1.75957 + 4.88916i) q^{27} +(8.85044 + 0.687941i) q^{28} +(1.65509 - 0.582054i) q^{30} +3.96388i q^{31} +(-3.15413 - 4.69590i) q^{32} +(-9.59393 - 4.15210i) q^{33} +(-3.05347 + 2.82534i) q^{34} -3.17914 q^{35} +(-4.67924 + 3.75562i) q^{36} +4.10695 q^{37} +(2.24368 - 2.07605i) q^{38} +(-1.58957 - 0.687941i) q^{39} +(1.25651 + 1.58913i) q^{40} +6.07884i q^{41} +(10.2565 - 3.60694i) q^{42} -7.50125i q^{43} +(0.935460 - 12.0348i) q^{44} +(1.56649 - 1.47081i) q^{45} +(2.10695 + 2.27707i) q^{46} +5.69554 q^{47} +(-5.85670 - 3.70123i) q^{48} -12.7009 q^{49} +(4.30961 + 4.65760i) q^{50} +(-2.02366 + 4.67591i) q^{51} +(0.154992 - 1.99399i) q^{52} -5.88324i q^{53} +(-3.38506 + 6.52238i) q^{54} +4.32298i q^{55} +(7.78649 + 9.84772i) q^{56} +(1.48698 - 3.43585i) q^{57} -1.64822 q^{59} +(2.19386 + 1.15898i) q^{60} -4.61997 q^{61} +(-4.11460 + 3.80719i) q^{62} +(9.70743 - 9.11448i) q^{63} +(1.84501 - 7.78434i) q^{64} +0.716254i q^{65} +(-4.90470 - 13.9467i) q^{66} +11.9880i q^{67} +(-5.86554 - 0.455927i) q^{68} +(3.48698 + 1.50911i) q^{69} +(-3.05347 - 3.30003i) q^{70} +0.662741 q^{71} +(-8.39270 - 1.25001i) q^{72} -4.97396 q^{73} +(3.94460 + 4.26311i) q^{74} +(7.13237 + 3.08678i) q^{75} +(4.30998 + 0.335014i) q^{76} +26.7892i q^{77} +(-0.812636 - 2.31076i) q^{78} +7.02656i q^{79} +(-0.442719 + 2.83060i) q^{80} +(-0.566494 + 8.98215i) q^{81} +(-6.30998 + 5.83854i) q^{82} -6.68103 q^{83} +(13.5951 + 7.18211i) q^{84} +2.10695 q^{85} +(7.78649 - 7.20473i) q^{86} +(13.3909 - 10.5880i) q^{88} -8.94385i q^{89} +(3.03131 + 0.213390i) q^{90} +4.43857i q^{91} +(-0.339999 + 4.37413i) q^{92} +(-2.72691 + 6.30086i) q^{93} +(5.47040 + 5.91212i) q^{94} -1.54818 q^{95} +(-1.78321 - 9.63432i) q^{96} +8.97396 q^{97} +(-12.1988 - 13.1838i) q^{98} +(-12.3938 - 13.2001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 5 q^{6} - 2 q^{9} - 14 q^{10} - 5 q^{12} - 12 q^{13} + 4 q^{16} + 9 q^{18} + 10 q^{21} - 20 q^{22} - 29 q^{24} + 8 q^{25} + 30 q^{28} + 19 q^{30} - 16 q^{33} - 10 q^{34} - 19 q^{36} - 4 q^{37} + 38 q^{40}+ \cdots + 16 q^{97}+O(q^{100}) \) 12 * q + 5 * q^6 - 2 * q^9 - 14 * q^10 - 5 * q^12 - 12 * q^13 + 4 * q^16 + 9 * q^18 + 10 * q^21 - 20 * q^22 - 29 * q^24 + 8 * q^25 + 30 * q^28 + 19 * q^30 - 16 * q^33 - 10 * q^34 - 19 * q^36 - 4 * q^37 + 38 * q^40 + 25 * q^42 + 38 * q^45 - 28 * q^46 - 33 * q^48 + 24 * q^54 - 28 * q^57 - 9 * q^60 - 48 * q^61 + 24 * q^64 + 48 * q^66 - 4 * q^69 - 10 * q^70 - 29 * q^72 + 32 * q^73 + 48 * q^76 - 5 * q^78 - 26 * q^81 - 72 * q^82 - 19 * q^84 - 28 * q^85 + 12 * q^88 + 5 * q^90 + 28 * q^93 - 18 * q^94 - q^96 + 16 * q^97

Introduction

L-functions

Modular forms

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