LMFDB - Embedded newform 1050.2.j.c.407.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(407,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("1050.407");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			407.1
Root			$-0.297931i$ of defining polynomial
Character	$\chi$	$=$	1050.407
Dual form			1050.2.j.c.743.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.33413 - 1.10458i) q^{3} -1.00000i q^{4} +(1.72443 - 0.162311i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.559788 + 2.94731i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.33413 - 1.10458i) q^{3} -1.00000i q^{4} +(1.72443 - 0.162311i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.559788 + 2.94731i) q^{9} -0.780604i q^{11} +(-1.10458 + 1.33413i) q^{12} +(3.85292 - 3.85292i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-2.97331 + 2.97331i) q^{17} +(-2.47989 - 1.68823i) q^{18} +5.79249i q^{19} +(-0.162311 - 1.72443i) q^{21} +(0.551971 + 0.551971i) q^{22} +(-1.74679 - 1.74679i) q^{23} +(-0.162311 - 1.72443i) q^{24} +5.44886i q^{26} +(2.50872 - 4.55042i) q^{27} +(0.707107 - 0.707107i) q^{28} -3.33651 q^{29} +1.20515 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.862243 + 1.04143i) q^{33} -4.20489i q^{34} +(2.94731 - 0.559788i) q^{36} +(6.28770 + 6.28770i) q^{37} +(-4.09591 - 4.09591i) q^{38} +(-9.39617 + 0.884411i) q^{39} +0.410091i q^{41} +(1.33413 + 1.10458i) q^{42} +(0.397015 - 0.397015i) q^{43} -0.780604 q^{44} +2.47033 q^{46} +(4.50070 - 4.50070i) q^{47} +(1.33413 + 1.10458i) q^{48} +1.00000i q^{49} +(7.25104 - 0.682501i) q^{51} +(-3.85292 - 3.85292i) q^{52} +(7.69577 + 7.69577i) q^{53} +(1.44370 + 4.99157i) q^{54} +1.00000i q^{56} +(6.39829 - 7.72791i) q^{57} +(2.35927 - 2.35927i) q^{58} +12.6753 q^{59} +9.11230 q^{61} +(-0.852168 + 0.852168i) q^{62} +(-1.68823 + 2.47989i) q^{63} +1.00000i q^{64} +(-0.126701 - 1.34610i) q^{66} +(-4.95979 - 4.95979i) q^{67} +(2.97331 + 2.97331i) q^{68} +(0.400963 + 4.25991i) q^{69} -1.88593i q^{71} +(-1.68823 + 2.47989i) q^{72} +(8.48507 - 8.48507i) q^{73} -8.89215 q^{74} +5.79249 q^{76} +(0.551971 - 0.551971i) q^{77} +(6.01872 - 7.26947i) q^{78} -12.5532i q^{79} +(-8.37327 + 3.29974i) q^{81} +(-0.289978 - 0.289978i) q^{82} +(3.60601 + 3.60601i) q^{83} +(-1.72443 + 0.162311i) q^{84} +0.561464i q^{86} +(4.45132 + 3.68545i) q^{87} +(0.551971 - 0.551971i) q^{88} +18.5847 q^{89} +5.44886 q^{91} +(-1.74679 + 1.74679i) q^{92} +(-1.60782 - 1.33119i) q^{93} +6.36495i q^{94} +(-1.72443 + 0.162311i) q^{96} +(8.82001 + 8.82001i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(2.30068 - 0.436973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3}+O(q^{10}) $ 12 * q - 4 * q^3	$ 12 q - 4 q^{3} + 4 q^{12} - 12 q^{14} - 12 q^{16} - 28 q^{17} - 4 q^{21} - 4 q^{22} + 24 q^{23} - 4 q^{24} + 20 q^{27} + 8 q^{29} - 8 q^{31} - 4 q^{33} + 4 q^{36} + 20 q^{37} + 4 q^{38} - 40 q^{39} + 4 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{46} - 16 q^{47} + 4 q^{48} + 8 q^{51} + 24 q^{53} - 4 q^{54} + 12 q^{57} + 8 q^{58} + 32 q^{59} - 28 q^{62} - 8 q^{63} - 8 q^{66} + 28 q^{68} - 32 q^{69} - 8 q^{72} + 24 q^{73} + 8 q^{74} - 4 q^{77} - 36 q^{81} - 32 q^{82} + 24 q^{83} + 64 q^{87} - 4 q^{88} + 48 q^{89} + 24 q^{91} + 24 q^{92} - 76 q^{93} - 8 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 + 4 * q^12 - 12 * q^14 - 12 * q^16 - 28 * q^17 - 4 * q^21 - 4 * q^22 + 24 * q^23 - 4 * q^24 + 20 * q^27 + 8 * q^29 - 8 * q^31 - 4 * q^33 + 4 * q^36 + 20 * q^37 + 4 * q^38 - 40 * q^39 + 4 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 - 16 * q^47 + 4 * q^48 + 8 * q^51 + 24 * q^53 - 4 * q^54 + 12 * q^57 + 8 * q^58 + 32 * q^59 - 28 * q^62 - 8 * q^63 - 8 * q^66 + 28 * q^68 - 32 * q^69 - 8 * q^72 + 24 * q^73 + 8 * q^74 - 4 * q^77 - 36 * q^81 - 32 * q^82 + 24 * q^83 + 64 * q^87 - 4 * q^88 + 48 * q^89 + 24 * q^91 + 24 * q^92 - 76 * q^93 - 8 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.33413	−	1.10458i	−0.770258	−	0.637732i
$3$	−1.33413	−	1.10458i	−0.770258	−	0.637732i
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	1.72443	−	0.162311i	0.703995	−	0.0662633i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.559788	+	2.94731i	0.186596	+	0.982437i
$10$		0			0
$11$		−	0.780604i		−	0.235361i	−0.993052	−	0.117681i	$-0.962454\pi$
$11$		−	0.780604i		−	0.235361i	0.993052	−	0.117681i	$-0.0375459\pi$
$12$	−1.10458	+	1.33413i	−0.318866	+	0.385129i
$13$	3.85292	−	3.85292i	1.06861	−	1.06861i	0.0711428	−	0.997466i	$-0.477335\pi$
$13$	3.85292	−	3.85292i	1.06861	−	1.06861i	0.997466	−	0.0711428i	$-0.0226646\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.97331	+	2.97331i	−0.721133	+	0.721133i	−0.968836	−	0.247703i	$-0.920324\pi$
$17$	−2.97331	+	2.97331i	−0.721133	+	0.721133i	0.247703	+	0.968836i	$0.420324\pi$
$18$	−2.47989	−	1.68823i	−0.584516	−	0.397920i
$19$			5.79249i			1.32889i	0.747338	+	0.664444i	$0.231332\pi$
$19$			5.79249i			1.32889i	−0.747338	+	0.664444i	$0.768668\pi$
$20$		0			0
$21$	−0.162311	−	1.72443i	−0.0354192	−	0.376301i
$22$	0.551971	+	0.551971i	0.117681	+	0.117681i
$23$	−1.74679	−	1.74679i	−0.364231	−	0.364231i	0.501137	−	0.865368i	$-0.332915\pi$
$23$	−1.74679	−	1.74679i	−0.364231	−	0.364231i	−0.865368	+	0.501137i	$0.832915\pi$
$24$	−0.162311	−	1.72443i	−0.0331316	−	0.351998i
$25$		0			0
$26$			5.44886i			1.06861i
$27$	2.50872	−	4.55042i	0.482804	−	0.875728i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	−3.33651			−0.619574			−0.309787	−	0.950806i	$-0.600258\pi$
$29$	−3.33651			−0.619574			−0.309787	+	0.950806i	$0.600258\pi$
$30$		0			0
$31$	1.20515			0.216451			0.108225	−	0.994126i	$-0.465483\pi$
$31$	1.20515			0.216451			0.108225	+	0.994126i	$0.465483\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.862243	+	1.04143i	−0.150097	+	0.181289i
$34$		−	4.20489i		−	0.721133i
$35$		0			0
$36$	2.94731	−	0.559788i	0.491218	−	0.0932981i
$37$	6.28770	+	6.28770i	1.03369	+	1.03369i	0.999412	+	0.0342797i	$0.0109137\pi$
$37$	6.28770	+	6.28770i	1.03369	+	1.03369i	0.0342797	+	0.999412i	$0.489086\pi$
$38$	−4.09591	−	4.09591i	−0.664444	−	0.664444i
$39$	−9.39617	+	0.884411i	−1.50459	+	0.141619i
$40$		0			0
$41$			0.410091i			0.0640455i	0.999487	+	0.0320227i	$0.0101949\pi$
$41$			0.410091i			0.0640455i	−0.999487	+	0.0320227i	$0.989805\pi$
$42$	1.33413	+	1.10458i	0.205860	+	0.170441i
$43$	0.397015	−	0.397015i	0.0605442	−	0.0605442i	−0.676186	−	0.736731i	$-0.736369\pi$
$43$	0.397015	−	0.397015i	0.0605442	−	0.0605442i	0.736731	+	0.676186i	$0.236369\pi$
$44$	−0.780604			−0.117681
$45$		0			0
$46$	2.47033			0.364231
$47$	4.50070	−	4.50070i	0.656495	−	0.656495i	−0.298054	−	0.954549i	$-0.596338\pi$
$47$	4.50070	−	4.50070i	0.656495	−	0.656495i	0.954549	+	0.298054i	$0.0963376\pi$
$48$	1.33413	+	1.10458i	0.192565	+	0.159433i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	7.25104	−	0.682501i	1.01535	−	0.0955693i
$52$	−3.85292	−	3.85292i	−0.534304	−	0.534304i
$53$	7.69577	+	7.69577i	1.05710	+	1.05710i	0.998268	+	0.0588277i	$0.0187363\pi$
$53$	7.69577	+	7.69577i	1.05710	+	1.05710i	0.0588277	+	0.998268i	$0.481264\pi$
$54$	1.44370	+	4.99157i	0.196462	+	0.679266i
$55$		0			0
$56$			1.00000i			0.133631i
$57$	6.39829	−	7.72791i	0.847474	−	1.02359i
$58$	2.35927	−	2.35927i	0.309787	−	0.309787i
$59$	12.6753			1.65019			0.825093	−	0.564996i	$-0.191122\pi$
$59$	12.6753			1.65019			0.825093	+	0.564996i	$0.191122\pi$
$60$		0			0
$61$	9.11230			1.16671			0.583355	−	0.812217i	$-0.301740\pi$
$61$	9.11230			1.16671			0.583355	+	0.812217i	$0.301740\pi$
$62$	−0.852168	+	0.852168i	−0.108225	+	0.108225i
$63$	−1.68823	+	2.47989i	−0.212697	+	0.312437i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−0.126701	−	1.34610i	−0.0155958	−	0.165693i
$67$	−4.95979	−	4.95979i	−0.605934	−	0.605934i	0.335947	−	0.941881i	$-0.390944\pi$
$67$	−4.95979	−	4.95979i	−0.605934	−	0.605934i	−0.941881	+	0.335947i	$0.890944\pi$
$68$	2.97331	+	2.97331i	0.360567	+	0.360567i
$69$	0.400963	+	4.25991i	0.0482702	+	0.512833i
$70$		0			0
$71$		−	1.88593i		−	0.223819i	−0.993718	−	0.111910i	$-0.964303\pi$
$71$		−	1.88593i		−	0.223819i	0.993718	−	0.111910i	$-0.0356967\pi$
$72$	−1.68823	+	2.47989i	−0.198960	+	0.292258i
$73$	8.48507	−	8.48507i	0.993102	−	0.993102i	−0.00687462	−	0.999976i	$-0.502188\pi$
$73$	8.48507	−	8.48507i	0.993102	−	0.993102i	0.999976	+	0.00687462i	$0.00218828\pi$
$74$	−8.89215			−1.03369
$75$		0			0
$76$	5.79249			0.664444
$77$	0.551971	−	0.551971i	0.0629029	−	0.0629029i
$78$	6.01872	−	7.26947i	0.681486	−	0.823105i
$79$		−	12.5532i		−	1.41234i	−0.708041	−	0.706172i	$-0.750421\pi$
$79$		−	12.5532i		−	1.41234i	0.708041	−	0.706172i	$-0.249579\pi$
$80$		0			0
$81$	−8.37327	+	3.29974i	−0.930364	+	0.366638i
$82$	−0.289978	−	0.289978i	−0.0320227	−	0.0320227i
$83$	3.60601	+	3.60601i	0.395811	+	0.395811i	0.876753	−	0.480942i	$-0.159705\pi$
$83$	3.60601	+	3.60601i	0.395811	+	0.395811i	−0.480942	+	0.876753i	$0.659705\pi$
$84$	−1.72443	+	0.162311i	−0.188151	+	0.0177096i
$85$		0			0
$86$			0.561464i			0.0605442i
$87$	4.45132	+	3.68545i	0.477232	+	0.395122i
$88$	0.551971	−	0.551971i	0.0588403	−	0.0588403i
$89$	18.5847			1.96998			0.984988	−	0.172621i	$-0.0552236\pi$
$89$	18.5847			1.96998			0.984988	+	0.172621i	$0.0552236\pi$
$90$		0			0
$91$	5.44886			0.571196
$92$	−1.74679	+	1.74679i	−0.182115	+	0.182115i
$93$	−1.60782	−	1.33119i	−0.166723	−	0.138038i
$94$			6.36495i			0.656495i
$95$		0			0
$96$	−1.72443	+	0.162311i	−0.175999	+	0.0165658i
$97$	8.82001	+	8.82001i	0.895536	+	0.895536i	0.995037	−	0.0995012i	$-0.0317247\pi$
$97$	8.82001	+	8.82001i	0.895536	+	0.895536i	−0.0995012	+	0.995037i	$0.531725\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	2.30068	−	0.436973i	0.231227	−	0.0439175i
$100$		0			0
$101$		−	8.52395i		−	0.848165i	−0.905624	−	0.424083i	$-0.860597\pi$
$101$		−	8.52395i		−	0.848165i	0.905624	−	0.424083i	$-0.139403\pi$
$102$	−4.64466	+	5.60986i	−0.459890	+	0.555459i
$103$	−7.68570	+	7.68570i	−0.757294	+	0.757294i	−0.975829	−	0.218535i	$-0.929872\pi$
$103$	−7.68570	+	7.68570i	−0.757294	+	0.757294i	0.218535	+	0.975829i	$0.429872\pi$
$104$	5.44886			0.534304
$105$		0			0
$106$	−10.8835			−1.05710
$107$	−8.53379	+	8.53379i	−0.824993	+	0.824993i	−0.986819	−	0.161827i	$-0.948261\pi$
$107$	−8.53379	+	8.53379i	−0.824993	+	0.824993i	0.161827	+	0.986819i	$0.448261\pi$
$108$	−4.55042	−	2.50872i	−0.437864	−	0.241402i
$109$			3.67769i			0.352259i	0.984367	+	0.176129i	$0.0563577\pi$
$109$			3.67769i			0.352259i	−0.984367	+	0.176129i	$0.943642\pi$
$110$		0			0
$111$	−1.44330	−	15.3339i	−0.136992	−	1.45543i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	11.8416	+	11.8416i	1.11396	+	1.11396i	0.992609	+	0.121355i	$0.0387238\pi$
$113$	11.8416	+	11.8416i	1.11396	+	1.11396i	0.121355	+	0.992609i	$0.461276\pi$
$114$	0.940186	+	9.98874i	0.0880565	+	0.935531i
$115$		0			0
$116$			3.33651i			0.309787i
$117$	13.5126	+	9.19894i	1.24924	+	0.850442i
$118$	−8.96281	+	8.96281i	−0.825093	+	0.825093i
$119$	−4.20489			−0.385462
$120$		0			0
$121$	10.3907			0.944605
$122$	−6.44337	+	6.44337i	−0.583355	+	0.583355i
$123$	0.452980	−	0.547114i	0.0408438	−	0.0493316i
$124$		−	1.20515i		−	0.108225i
$125$		0			0
$126$	−0.559788	−	2.94731i	−0.0498699	−	0.262567i
$127$	−12.5290	−	12.5290i	−1.11177	−	1.11177i	−0.992911	−	0.118863i	$-0.962075\pi$
$127$	−12.5290	−	12.5290i	−1.11177	−	1.11177i	−0.118863	−	0.992911i	$-0.537925\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−0.968204	+	0.0911319i	−0.0852456	+	0.00802372i
$130$		0			0
$131$			11.8873i			1.03860i	0.854591	+	0.519301i	$0.173808\pi$
$131$			11.8873i			1.03860i	−0.854591	+	0.519301i	$0.826192\pi$
$132$	1.04143	+	0.862243i	0.0906444	+	0.0750486i
$133$	−4.09591	+	4.09591i	−0.355160	+	0.355160i
$134$	7.01420			0.605934
$135$		0			0
$136$	−4.20489			−0.360567
$137$	−4.34731	+	4.34731i	−0.371416	+	0.371416i	−0.867993	−	0.496577i	$-0.834590\pi$
$137$	−4.34731	+	4.34731i	−0.371416	+	0.371416i	0.496577	+	0.867993i	$0.334590\pi$
$138$	−3.29574	−	2.72869i	−0.280552	−	0.232281i
$139$			11.6395i			0.987250i	0.869675	+	0.493625i	$0.164328\pi$
$139$			11.6395i			0.987250i	−0.869675	+	0.493625i	$0.835672\pi$
$140$		0			0
$141$	−10.9759	+	1.03310i	−0.924338	+	0.0870030i
$142$	1.33356	+	1.33356i	0.111910	+	0.111910i
$143$	−3.00761	−	3.00761i	−0.251509	−	0.251509i
$144$	−0.559788	−	2.94731i	−0.0466490	−	0.245609i
$145$		0			0
$146$			11.9997i			0.993102i
$147$	1.10458	−	1.33413i	0.0911046	−	0.110037i
$148$	6.28770	−	6.28770i	0.516846	−	0.516846i
$149$	−5.78924			−0.474273			−0.237137	−	0.971476i	$-0.576209\pi$
$149$	−5.78924			−0.474273			−0.237137	+	0.971476i	$0.576209\pi$
$150$		0			0
$151$	0.326935			0.0266056			0.0133028	−	0.999912i	$-0.495765\pi$
$151$	0.326935			0.0266056			0.0133028	+	0.999912i	$0.495765\pi$
$152$	−4.09591	+	4.09591i	−0.332222	+	0.332222i
$153$	−10.4277	−	7.09884i	−0.843028	−	0.573907i
$154$			0.780604i			0.0629029i
$155$		0			0
$156$	0.884411	+	9.39617i	0.0708095	+	0.752296i
$157$	−15.7404	−	15.7404i	−1.25622	−	1.25622i	−0.952883	−	0.303339i	$-0.901899\pi$
$157$	−15.7404	−	15.7404i	−1.25622	−	1.25622i	−0.303339	−	0.952883i	$-0.598101\pi$
$158$	8.87644	+	8.87644i	0.706172	+	0.706172i
$159$	−1.76651	−	18.7678i	−0.140093	−	1.48838i
$160$		0			0
$161$		−	2.47033i		−	0.194689i
$162$	3.58753	−	8.25407i	0.281863	−	0.648501i
$163$	−0.261547	+	0.261547i	−0.0204859	+	0.0204859i	−0.717276	−	0.696790i	$-0.754611\pi$
$163$	−0.261547	+	0.261547i	−0.0204859	+	0.0204859i	0.696790	+	0.717276i	$0.254611\pi$
$164$	0.410091			0.0320227
$165$		0			0
$166$	−5.09967			−0.395811
$167$	7.48816	−	7.48816i	0.579451	−	0.579451i	−0.355301	−	0.934752i	$-0.615622\pi$
$167$	7.48816	−	7.48816i	0.579451	−	0.579451i	0.934752	+	0.355301i	$0.115622\pi$
$168$	1.10458	−	1.33413i	0.0852205	−	0.102930i
$169$		−	16.6901i		−	1.28385i
$170$		0			0
$171$	−17.0723	+	3.24257i	−1.30555	+	0.247965i
$172$	−0.397015	−	0.397015i	−0.0302721	−	0.0302721i
$173$	8.48843	+	8.48843i	0.645363	+	0.645363i	0.951869	−	0.306505i	$-0.0991598\pi$
$173$	8.48843	+	8.48843i	0.645363	+	0.645363i	−0.306505	+	0.951869i	$0.599160\pi$
$174$	−5.75357	+	0.541553i	−0.436177	+	0.0410550i
$175$		0			0
$176$			0.780604i			0.0588403i
$177$	−16.9105	−	14.0010i	−1.27107	−	1.05238i
$178$	−13.1414	+	13.1414i	−0.984988	+	0.984988i
$179$	−2.37051			−0.177180			−0.0885902	−	0.996068i	$-0.528236\pi$
$179$	−2.37051			−0.177180			−0.0885902	+	0.996068i	$0.528236\pi$
$180$		0			0
$181$	−6.15369			−0.457400			−0.228700	−	0.973497i	$-0.573447\pi$
$181$	−6.15369			−0.457400			−0.228700	+	0.973497i	$0.573447\pi$
$182$	−3.85292	+	3.85292i	−0.285598	+	0.285598i
$183$	−12.1570	−	10.0653i	−0.898669	−	0.744048i
$184$		−	2.47033i		−	0.182115i
$185$		0			0
$186$	2.07819	−	0.195609i	0.152380	−	0.0143428i
$187$	2.32098	+	2.32098i	0.169727	+	0.169727i
$188$	−4.50070	−	4.50070i	−0.328247	−	0.328247i
$189$	4.99157	−	1.44370i	0.363083	−	0.105014i
$190$		0			0
$191$		−	9.64185i		−	0.697660i	−0.937186	−	0.348830i	$-0.886579\pi$
$191$		−	9.64185i		−	0.697660i	0.937186	−	0.348830i	$-0.113421\pi$
$192$	1.10458	−	1.33413i	0.0797165	−	0.0962823i
$193$	6.77716	−	6.77716i	0.487830	−	0.487830i	−0.419791	−	0.907621i	$-0.637896\pi$
$193$	6.77716	−	6.77716i	0.487830	−	0.487830i	0.907621	+	0.419791i	$0.137896\pi$
$194$	−12.4734			−0.895536
$195$		0			0
$196$	1.00000			0.0714286
$197$	−2.34224	+	2.34224i	−0.166878	+	0.166878i	−0.785606	−	0.618728i	$-0.787648\pi$
$197$	−2.34224	+	2.34224i	−0.166878	+	0.166878i	0.618728	+	0.785606i	$0.287648\pi$
$198$	−1.31784	+	1.93582i	−0.0936549	+	0.137572i
$199$		−	9.94617i		−	0.705066i	−0.935799	−	0.352533i	$-0.885320\pi$
$199$		−	9.94617i		−	0.705066i	0.935799	−	0.352533i	$-0.114680\pi$
$200$		0			0
$201$	1.13848	+	12.0955i	0.0803024	+	0.853150i
$202$	6.02735	+	6.02735i	0.424083	+	0.424083i
$203$	−2.35927	−	2.35927i	−0.165588	−	0.165588i
$204$	−0.682501	−	7.25104i	−0.0477847	−	0.507674i
$205$		0			0
$206$		−	10.8692i		−	0.757294i
$207$	4.17050	−	6.12616i	0.289869	−	0.425797i
$208$	−3.85292	+	3.85292i	−0.267152	+	0.267152i
$209$	4.52164			0.312768
$210$		0			0
$211$	−14.9895			−1.03192			−0.515960	−	0.856613i	$-0.672565\pi$
$211$	−14.9895			−1.03192			−0.515960	+	0.856613i	$0.672565\pi$
$212$	7.69577	−	7.69577i	0.528548	−	0.528548i
$213$	−2.08317	+	2.51607i	−0.142737	+	0.172399i
$214$		−	12.0686i		−	0.824993i
$215$		0			0
$216$	4.99157	−	1.44370i	0.339633	−	0.0982311i
$217$	0.852168	+	0.852168i	0.0578489	+	0.0578489i
$218$	−2.60052	−	2.60052i	−0.176129	−	0.176129i
$219$	−20.6926	+	1.94769i	−1.39828	+	0.131612i
$220$		0			0
$221$			22.9119i			1.54122i
$222$	11.8633	+	9.82213i	0.796210	+	0.659218i
$223$	−7.97398	+	7.97398i	−0.533977	+	0.533977i	−0.921754	−	0.387776i	$-0.873243\pi$
$223$	−7.97398	+	7.97398i	−0.533977	+	0.533977i	0.387776	+	0.921754i	$0.373243\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−16.7465			−1.11396
$227$	20.3950	−	20.3950i	1.35366	−	1.35366i	0.472135	−	0.881526i	$-0.343484\pi$
$227$	20.3950	−	20.3950i	1.35366	−	1.35366i	0.881526	−	0.472135i	$-0.156516\pi$
$228$	−7.72791	−	6.39829i	−0.511794	−	0.423737i
$229$			19.5317i			1.29069i	0.763891	+	0.645346i	$0.223287\pi$
$229$			19.5317i			1.29069i	−0.763891	+	0.645346i	$0.776713\pi$
$230$		0			0
$231$	−1.34610	+	0.126701i	−0.0885667	+	0.00833630i
$232$	−2.35927	−	2.35927i	−0.154893	−	0.154893i
$233$	2.92961	+	2.92961i	0.191925	+	0.191925i	0.796527	−	0.604602i	$-0.206668\pi$
$233$	2.92961	+	2.92961i	0.191925	+	0.191925i	−0.604602	+	0.796527i	$0.706668\pi$
$234$	−16.0595	+	3.05021i	−1.04984	+	0.199398i
$235$		0			0
$236$		−	12.6753i		−	0.825093i
$237$	−13.8660	+	16.7475i	−0.900696	+	1.08787i
$238$	2.97331	−	2.97331i	0.192731	−	0.192731i
$239$	12.0343			0.778432			0.389216	−	0.921147i	$-0.372746\pi$
$239$	12.0343			0.778432			0.389216	+	0.921147i	$0.372746\pi$
$240$		0			0
$241$	5.77972			0.372304			0.186152	−	0.982521i	$-0.440398\pi$
$241$	5.77972			0.372304			0.186152	+	0.982521i	$0.440398\pi$
$242$	−7.34730	+	7.34730i	−0.472303	+	0.472303i
$243$	14.8158	+	4.84671i	0.950437	+	0.310917i
$244$		−	9.11230i		−	0.583355i
$245$		0			0
$246$	0.0665624	+	0.707173i	0.00424386	+	0.0450877i
$247$	22.3180	+	22.3180i	1.42006	+	1.42006i
$248$	0.852168	+	0.852168i	0.0541127	+	0.0541127i
$249$	−0.827733	−	8.79401i	−0.0524555	−	0.557298i
$250$		0			0
$251$			1.50663i			0.0950977i	0.998869	+	0.0475489i	$0.0151410\pi$
$251$			1.50663i			0.0950977i	−0.998869	+	0.0475489i	$0.984859\pi$
$252$	2.47989	+	1.68823i	0.156219	+	0.106349i
$253$	−1.36355	+	1.36355i	−0.0857257	+	0.0857257i
$254$	17.7188			1.11177
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.44942	+	3.44942i	−0.215169	+	0.215169i	−0.806459	−	0.591290i	$-0.798619\pi$
$257$	−3.44942	+	3.44942i	−0.215169	+	0.215169i	0.591290	+	0.806459i	$0.298619\pi$
$258$	0.620184	−	0.749064i	0.0386110	−	0.0466347i
$259$			8.89215i			0.552532i
$260$		0			0
$261$	−1.86774	−	9.83372i	−0.115610	−	0.608692i
$262$	−8.40562	−	8.40562i	−0.519301	−	0.519301i
$263$	−9.85402	−	9.85402i	−0.607625	−	0.607625i	0.334700	−	0.942325i	$-0.391365\pi$
$263$	−9.85402	−	9.85402i	−0.607625	−	0.607625i	−0.942325	+	0.334700i	$0.891365\pi$
$264$	−1.34610	+	0.126701i	−0.0828465	+	0.00779790i
$265$		0			0
$266$		−	5.79249i		−	0.355160i
$267$	−24.7944	−	20.5284i	−1.51739	−	1.25632i
$268$	−4.95979	+	4.95979i	−0.302967	+	0.302967i
$269$	−9.17881			−0.559642			−0.279821	−	0.960052i	$-0.590275\pi$
$269$	−9.17881			−0.559642			−0.279821	+	0.960052i	$0.590275\pi$
$270$		0			0
$271$	−7.85752			−0.477310			−0.238655	−	0.971104i	$-0.576707\pi$
$271$	−7.85752			−0.477310			−0.238655	+	0.971104i	$0.576707\pi$
$272$	2.97331	−	2.97331i	0.180283	−	0.180283i
$273$	−7.26947	−	6.01872i	−0.439968	−	0.364270i
$274$		−	6.14802i		−	0.371416i
$275$		0			0
$276$	4.25991	−	0.400963i	0.256417	−	0.0241351i
$277$	−2.82887	−	2.82887i	−0.169970	−	0.169970i	0.616996	−	0.786966i	$-0.288350\pi$
$277$	−2.82887	−	2.82887i	−0.169970	−	0.169970i	−0.786966	+	0.616996i	$0.788350\pi$
$278$	−8.23037	−	8.23037i	−0.493625	−	0.493625i
$279$	0.674628	+	3.55194i	0.0403889	+	0.212649i
$280$		0			0
$281$		−	0.990734i		−	0.0591022i	−0.999563	−	0.0295511i	$-0.990592\pi$
$281$		−	0.990734i		−	0.0591022i	0.999563	−	0.0295511i	$-0.00940778\pi$
$282$	7.03062	−	8.49165i	0.418668	−	0.505671i
$283$	16.0249	−	16.0249i	0.952584	−	0.952584i	−0.0463416	−	0.998926i	$-0.514756\pi$
$283$	16.0249	−	16.0249i	0.952584	−	0.952584i	0.998926	+	0.0463416i	$0.0147563\pi$
$284$	−1.88593			−0.111910
$285$		0			0
$286$	4.25340			0.251509
$287$	−0.289978	+	0.289978i	−0.0171169	+	0.0171169i
$288$	2.47989	+	1.68823i	0.146129	+	0.0994801i
$289$		−	0.681122i		−	0.0400660i
$290$		0			0
$291$	−2.02457	−	21.5095i	−0.118682	−	1.26091i
$292$	−8.48507	−	8.48507i	−0.496551	−	0.496551i
$293$	−0.328091	−	0.328091i	−0.0191673	−	0.0191673i	0.697458	−	0.716625i	$-0.254314\pi$
$293$	−0.328091	−	0.328091i	−0.0191673	−	0.0191673i	−0.716625	+	0.697458i	$0.754314\pi$
$294$	0.162311	+	1.72443i	0.00946618	+	0.100571i
$295$		0			0
$296$			8.89215i			0.516846i
$297$	−3.55208	−	1.95832i	−0.206112	−	0.113633i
$298$	4.09361	−	4.09361i	0.237137	−	0.237137i
$299$	−13.4605			−0.778440
$300$		0			0
$301$	0.561464			0.0323622
$302$	−0.231178	+	0.231178i	−0.0133028	+	0.0133028i
$303$	−9.41542	+	11.3720i	−0.540902	+	0.653306i
$304$		−	5.79249i		−	0.332222i
$305$		0			0
$306$	12.3931	−	2.35385i	0.708468	−	0.134561i
$307$	5.29402	+	5.29402i	0.302146	+	0.302146i	0.841853	−	0.539707i	$-0.181465\pi$
$307$	5.29402	+	5.29402i	0.302146	+	0.302146i	−0.539707	+	0.841853i	$0.681465\pi$
$308$	−0.551971	−	0.551971i	−0.0314514	−	0.0314514i
$309$	18.7432	−	1.76420i	1.06626	−	0.100362i
$310$		0			0
$311$		−	12.1390i		−	0.688340i	−0.938907	−	0.344170i	$-0.888160\pi$
$311$		−	12.1390i		−	0.688340i	0.938907	−	0.344170i	$-0.111840\pi$
$312$	−7.26947	−	6.01872i	−0.411553	−	0.340743i
$313$	−12.2205	+	12.2205i	−0.690745	+	0.690745i	−0.962396	−	0.271651i	$-0.912430\pi$
$313$	−12.2205	+	12.2205i	−0.690745	+	0.690745i	0.271651	+	0.962396i	$0.412430\pi$
$314$	22.2603			1.25622
$315$		0			0
$316$	−12.5532			−0.706172
$317$	−2.40772	+	2.40772i	−0.135231	+	0.135231i	−0.771482	−	0.636251i	$-0.780484\pi$
$317$	−2.40772	+	2.40772i	−0.135231	+	0.135231i	0.636251	+	0.771482i	$0.280484\pi$
$318$	14.5199	+	12.0217i	0.814237	+	0.674144i
$319$			2.60449i			0.145824i
$320$		0			0
$321$	20.8114	−	1.95887i	1.16158	−	0.109333i
$322$	1.74679	+	1.74679i	0.0973447	+	0.0973447i
$323$	−17.2229	−	17.2229i	−0.958305	−	0.958305i
$324$	3.29974	+	8.37327i	0.183319	+	0.465182i
$325$		0			0
$326$		−	0.369883i		−	0.0204859i
$327$	4.06232	−	4.90650i	0.224647	−	0.271330i
$328$	−0.289978	+	0.289978i	−0.0160114	+	0.0160114i
$329$	6.36495			0.350911
$330$		0			0
$331$	−15.2790			−0.839810			−0.419905	−	0.907568i	$-0.637937\pi$
$331$	−15.2790			−0.839810			−0.419905	+	0.907568i	$0.637937\pi$
$332$	3.60601	−	3.60601i	0.197905	−	0.197905i
$333$	−15.0120	+	22.0516i	−0.822654	+	1.20842i
$334$			10.5899i			0.579451i
$335$		0			0
$336$	0.162311	+	1.72443i	0.00885481	+	0.0940753i
$337$	−11.4834	−	11.4834i	−0.625541	−	0.625541i	0.321402	−	0.946943i	$-0.395846\pi$
$337$	−11.4834	−	11.4834i	−0.625541	−	0.625541i	−0.946943	+	0.321402i	$0.895846\pi$
$338$	11.8016	+	11.8016i	0.641925	+	0.641925i
$339$	−2.71815	−	28.8782i	−0.147630	−	1.56845i
$340$		0			0
$341$		−	0.940744i		−	0.0509441i
$342$	9.77907	−	14.3648i	0.528792	−	0.776757i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	0.561464			0.0302721
$345$		0			0
$346$	−12.0045			−0.645363
$347$	−12.0974	+	12.0974i	−0.649425	+	0.649425i	−0.952854	−	0.303429i	$-0.901868\pi$
$347$	−12.0974	+	12.0974i	−0.649425	+	0.649425i	0.303429	+	0.952854i	$0.401868\pi$
$348$	3.68545	−	4.45132i	0.197561	−	0.238616i
$349$		−	0.114169i		−	0.00611132i	−0.999995	−	0.00305566i	$-0.999027\pi$
$349$		−	0.114169i		−	0.00611132i	0.999995	−	0.00305566i	$-0.000972649\pi$
$350$		0			0
$351$	−7.86650	−	27.1983i	−0.419883	−	1.45174i
$352$	−0.551971	−	0.551971i	−0.0294201	−	0.0294201i
$353$	17.4937	+	17.4937i	0.931097	+	0.931097i	0.997775	−	0.0666780i	$-0.0212400\pi$
$353$	17.4937	+	17.4937i	0.931097	+	0.931097i	−0.0666780	+	0.997775i	$0.521240\pi$
$354$	21.8577	−	2.05735i	1.16172	−	0.109347i
$355$		0			0
$356$		−	18.5847i		−	0.984988i
$357$	5.60986	+	4.64466i	0.296905	+	0.245821i
$358$	1.67621	−	1.67621i	0.0885902	−	0.0885902i
$359$	−25.4743			−1.34448			−0.672240	−	0.740333i	$-0.734668\pi$
$359$	−25.4743			−1.34448			−0.672240	+	0.740333i	$0.734668\pi$
$360$		0			0
$361$	−14.5529			−0.765944
$362$	4.35131	−	4.35131i	0.228700	−	0.228700i
$363$	−13.8625	−	11.4774i	−0.727590	−	0.602405i
$364$		−	5.44886i		−	0.285598i
$365$		0			0
$366$	15.7135	−	1.47903i	0.821359	−	0.0773101i
$367$	23.9590	+	23.9590i	1.25065	+	1.25065i	0.955428	+	0.295224i	$0.0953943\pi$
$367$	23.9590	+	23.9590i	1.25065	+	1.25065i	0.295224	+	0.955428i	$0.404606\pi$
$368$	1.74679	+	1.74679i	0.0910576	+	0.0910576i
$369$	−1.20867	+	0.229564i	−0.0629206	+	0.0119506i
$370$		0			0
$371$			10.8835i			0.565041i
$372$	−1.33119	+	1.60782i	−0.0690188	+	0.0833616i
$373$	−4.14472	+	4.14472i	−0.214605	+	0.214605i	−0.806221	−	0.591615i	$-0.798491\pi$
$373$	−4.14472	+	4.14472i	−0.214605	+	0.214605i	0.591615	+	0.806221i	$0.298491\pi$
$374$	−3.28236			−0.169727
$375$		0			0
$376$	6.36495			0.328247
$377$	−12.8553	+	12.8553i	−0.662082	+	0.662082i
$378$	−2.50872	+	4.55042i	−0.129035	+	0.234048i
$379$			13.5788i			0.697495i	0.937217	+	0.348748i	$0.113393\pi$
$379$			13.5788i			0.697495i	−0.937217	+	0.348748i	$0.886607\pi$
$380$		0			0
$381$	2.87595	+	30.5547i	0.147340	+	1.56537i
$382$	6.81782	+	6.81782i	0.348830	+	0.348830i
$383$	−11.0679	−	11.0679i	−0.565541	−	0.565541i	0.365335	−	0.930876i	$-0.380954\pi$
$383$	−11.0679	−	11.0679i	−0.565541	−	0.565541i	−0.930876	+	0.365335i	$0.880954\pi$
$384$	0.162311	+	1.72443i	0.00828291	+	0.0879994i
$385$		0			0
$386$			9.58435i			0.487830i
$387$	1.39237	+	0.947882i	0.0707782	+	0.0481835i
$388$	8.82001	−	8.82001i	0.447768	−	0.447768i
$389$	29.1746			1.47921			0.739605	−	0.673041i	$-0.235012\pi$
$389$	29.1746			1.47921			0.739605	+	0.673041i	$0.235012\pi$
$390$		0			0
$391$	10.3875			0.525317
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	13.1306	−	15.8592i	0.662350	−	0.799992i
$394$		−	3.31243i		−	0.166878i
$395$		0			0
$396$	−0.436973	−	2.30068i	−0.0219587	−	0.115614i
$397$	10.4013	+	10.4013i	0.522028	+	0.522028i	0.918183	−	0.396155i	$-0.129656\pi$
$397$	10.4013	+	10.4013i	0.522028	+	0.522028i	−0.396155	+	0.918183i	$0.629656\pi$
$398$	7.03301	+	7.03301i	0.352533	+	0.352533i
$399$	9.98874	−	0.940186i	0.500062	−	0.0470682i
$400$		0			0
$401$		−	3.08489i		−	0.154052i	−0.997029	−	0.0770260i	$-0.975458\pi$
$401$		−	3.08489i		−	0.154052i	0.997029	−	0.0770260i	$-0.0245425\pi$
$402$	−9.35783	−	7.74777i	−0.466726	−	0.386424i
$403$	4.64334	−	4.64334i	0.231301	−	0.231301i
$404$	−8.52395			−0.424083
$405$		0			0
$406$	3.33651			0.165588
$407$	4.90821	−	4.90821i	0.243291	−	0.243291i
$408$	5.60986	+	4.64466i	0.277729	+	0.229945i
$409$			2.47368i			0.122316i	0.998128	+	0.0611579i	$0.0194793\pi$
$409$			2.47368i			0.122316i	−0.998128	+	0.0611579i	$0.980521\pi$
$410$		0			0
$411$	10.6018	−	0.997893i	0.522950	−	0.0492224i
$412$	7.68570	+	7.68570i	0.378647	+	0.378647i
$413$	8.96281	+	8.96281i	0.441031	+	0.441031i
$414$	1.38286	+	7.28083i	0.0679640	+	0.357833i
$415$		0			0
$416$		−	5.44886i		−	0.267152i
$417$	12.8568	−	15.5286i	0.629601	−	0.760437i
$418$	−3.19728	+	3.19728i	−0.156384	+	0.156384i
$419$	−23.6148			−1.15366			−0.576828	−	0.816865i	$-0.695710\pi$
$419$	−23.6148			−1.15366			−0.576828	+	0.816865i	$0.695710\pi$
$420$		0			0
$421$	−19.6409			−0.957240			−0.478620	−	0.878022i	$-0.658863\pi$
$421$	−19.6409			−0.957240			−0.478620	+	0.878022i	$0.658863\pi$
$422$	10.5992	−	10.5992i	0.515960	−	0.515960i
$423$	15.7844	+	10.7455i	0.767464	+	0.522465i
$424$			10.8835i			0.528548i
$425$		0			0
$426$	−0.306108	−	3.25216i	−0.0148310	−	0.157568i
$427$	6.44337	+	6.44337i	0.311816	+	0.311816i
$428$	8.53379	+	8.53379i	0.412496	+	0.412496i
$429$	0.690375	+	7.33469i	0.0333316	+	0.354122i
$430$		0			0
$431$			28.9367i			1.39383i	0.717153	+	0.696915i	$0.245445\pi$
$431$			28.9367i			1.39383i	−0.717153	+	0.696915i	$0.754555\pi$
$432$	−2.50872	+	4.55042i	−0.120701	+	0.218932i
$433$	−18.0810	+	18.0810i	−0.868918	+	0.868918i	−0.992353	−	0.123434i	$-0.960609\pi$
$433$	−18.0810	+	18.0810i	−0.868918	+	0.868918i	0.123434	+	0.992353i	$0.460609\pi$
$434$	−1.20515			−0.0578489
$435$		0			0
$436$	3.67769			0.176129
$437$	10.1183	−	10.1183i	0.484022	−	0.484022i
$438$	13.2547	−	16.0091i	0.633333	−	0.764945i
$439$			12.4892i			0.596076i	0.954554	+	0.298038i	$0.0963323\pi$
$439$			12.4892i			0.596076i	−0.954554	+	0.298038i	$0.903668\pi$
$440$		0			0
$441$	−2.94731	+	0.559788i	−0.140348	+	0.0266566i
$442$	−16.2011	−	16.2011i	−0.770609	−	0.770609i
$443$	−19.6631	−	19.6631i	−0.934224	−	0.934224i	0.0637426	−	0.997966i	$-0.479696\pi$
$443$	−19.6631	−	19.6631i	−0.934224	−	0.934224i	−0.997966	+	0.0637426i	$0.979696\pi$
$444$	−15.3339	+	1.44330i	−0.727714	+	0.0684958i
$445$		0			0
$446$		−	11.2769i		−	0.533977i
$447$	7.72358	+	6.39470i	0.365313	+	0.302459i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	−36.8034			−1.73686			−0.868431	−	0.495810i	$-0.834871\pi$
$449$	−36.8034			−1.73686			−0.868431	+	0.495810i	$0.834871\pi$
$450$		0			0
$451$	0.320119			0.0150738
$452$	11.8416	−	11.8416i	0.556982	−	0.556982i
$453$	−0.436173	−	0.361127i	−0.0204932	−	0.0169672i
$454$			28.8428i			1.35366i
$455$		0			0
$456$	9.98874	−	0.940186i	0.467765	−	0.0440283i
$457$	−0.564472	−	0.564472i	−0.0264049	−	0.0264049i	0.693781	−	0.720186i	$-0.255944\pi$
$457$	−0.564472	−	0.564472i	−0.0264049	−	0.0264049i	−0.720186	+	0.693781i	$0.755944\pi$
$458$	−13.8110	−	13.8110i	−0.645346	−	0.645346i
$459$	6.07059	+	20.9890i	0.283351	+	0.979683i
$460$		0			0
$461$			1.34252i			0.0625275i	0.999511	+	0.0312638i	$0.00995319\pi$
$461$			1.34252i			0.0625275i	−0.999511	+	0.0312638i	$0.990047\pi$
$462$	0.862243	−	1.04143i	0.0401152	−	0.0484515i
$463$	27.2878	−	27.2878i	1.26817	−	1.26817i	0.321142	−	0.947031i	$-0.395933\pi$
$463$	27.2878	−	27.2878i	1.26817	−	1.26817i	0.947031	−	0.321142i	$-0.104067\pi$
$464$	3.33651			0.154893
$465$		0			0
$466$	−4.14309			−0.191925
$467$	−18.9254	+	18.9254i	−0.875765	+	0.875765i	−0.993093	−	0.117328i	$-0.962567\pi$
$467$	−18.9254	+	18.9254i	−0.875765	+	0.875765i	0.117328	+	0.993093i	$0.462567\pi$
$468$	9.19894	−	13.5126i	0.425221	−	0.624619i
$469$		−	7.01420i		−	0.323886i
$470$		0			0
$471$	3.61310	+	38.3863i	0.166483	+	1.76875i
$472$	8.96281	+	8.96281i	0.412547	+	0.412547i
$473$	−0.309911	−	0.309911i	−0.0142497	−	0.0142497i
$474$	−2.03752	−	21.6471i	−0.0935865	−	0.994283i
$475$		0			0
$476$			4.20489i			0.192731i
$477$	−18.3738	+	26.9898i	−0.841280	+	1.23578i
$478$	−8.50951	+	8.50951i	−0.389216	+	0.389216i
$479$	15.7320			0.718815			0.359408	−	0.933181i	$-0.382979\pi$
$479$	15.7320			0.718815			0.359408	+	0.933181i	$0.382979\pi$
$480$		0			0
$481$	48.4521			2.20922
$482$	−4.08688	+	4.08688i	−0.186152	+	0.186152i
$483$	−2.72869	+	3.29574i	−0.124160	+	0.149961i
$484$		−	10.3907i		−	0.472303i
$485$		0			0
$486$	−13.9035	+	7.04924i	−0.630677	+	0.319760i
$487$	−1.69131	−	1.69131i	−0.0766404	−	0.0766404i	0.667747	−	0.744388i	$-0.267259\pi$
$487$	−1.69131	−	1.69131i	−0.0766404	−	0.0766404i	−0.744388	+	0.667747i	$0.767259\pi$
$488$	6.44337	+	6.44337i	0.291678	+	0.291678i
$489$	0.637837	−	0.0600362i	0.0288440	−	0.00271493i
$490$		0			0
$491$			8.25442i			0.372517i	0.982501	+	0.186258i	$0.0596361\pi$
$491$			8.25442i			0.372517i	−0.982501	+	0.186258i	$0.940364\pi$
$492$	−0.547114	−	0.452980i	−0.0246658	−	0.0204219i
$493$	9.92046	−	9.92046i	0.446795	−	0.446795i
$494$	−31.5624			−1.42006
$495$		0			0
$496$	−1.20515			−0.0541127
$497$	1.33356	−	1.33356i	0.0598182	−	0.0598182i
$498$	6.80360	+	5.63301i	0.304877	+	0.252421i
$499$			18.4475i			0.825823i	0.910771	+	0.412912i	$0.135488\pi$
$499$			18.4475i			0.825823i	−0.910771	+	0.412912i	$0.864512\pi$
$500$		0			0
$501$	−18.2615	+	1.71885i	−0.815862	+	0.0767927i
$502$	−1.06535	−	1.06535i	−0.0475489	−	0.0475489i
$503$	6.61830	+	6.61830i	0.295095	+	0.295095i	0.839089	−	0.543994i	$-0.183089\pi$
$503$	6.61830	+	6.61830i	0.295095	+	0.295095i	−0.543994	+	0.839089i	$0.683089\pi$
$504$	−2.94731	+	0.559788i	−0.131284	+	0.0249350i
$505$		0			0
$506$		−	1.92835i		−	0.0857257i
$507$	−18.4356	+	22.2666i	−0.818752	+	0.988896i
$508$	−12.5290	+	12.5290i	−0.555887	+	0.555887i
$509$	−0.871429			−0.0386254			−0.0193127	−	0.999813i	$-0.506148\pi$
$509$	−0.871429			−0.0386254			−0.0193127	+	0.999813i	$0.506148\pi$
$510$		0			0
$511$	11.9997			0.530835
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	26.3582	+	14.5317i	1.16375	+	0.641592i
$514$		−	4.87821i		−	0.215169i
$515$		0			0
$516$	0.0911319	+	0.968204i	0.00401186	+	0.0426228i
$517$	−3.51327	−	3.51327i	−0.154513	−	0.154513i
$518$	−6.28770	−	6.28770i	−0.276266	−	0.276266i
$519$	−1.94846	−	20.7008i	−0.0855278	−	0.908666i
$520$		0			0
$521$			3.35506i			0.146988i	0.997296	+	0.0734939i	$0.0234150\pi$
$521$			3.35506i			0.146988i	−0.997296	+	0.0734939i	$0.976585\pi$
$522$	8.27418	+	5.63280i	0.362151	+	0.246541i
$523$	0.214504	−	0.214504i	0.00937959	−	0.00937959i	−0.702401	−	0.711781i	$-0.747889\pi$
$523$	0.214504	−	0.214504i	0.00937959	−	0.00937959i	0.711781	+	0.702401i	$0.247889\pi$
$524$	11.8873			0.519301
$525$		0			0
$526$	13.9357			0.607625
$527$	−3.58328	+	3.58328i	−0.156090	+	0.156090i
$528$	0.862243	−	1.04143i	0.0375243	−	0.0453222i
$529$		−	16.8975i		−	0.734672i
$530$		0			0
$531$	7.09550	+	37.3581i	0.307919	+	1.62120i
$532$	4.09591	+	4.09591i	0.177580	+	0.177580i
$533$	1.58005	+	1.58005i	0.0684396	+	0.0684396i
$534$	32.0480	−	3.01651i	1.38685	−	0.130537i
$535$		0			0
$536$		−	7.01420i		−	0.302967i
$537$	3.16256	+	2.61843i	0.136475	+	0.112994i
$538$	6.49040	−	6.49040i	0.279821	−	0.279821i
$539$	0.780604			0.0336230
$540$		0			0
$541$	37.7416			1.62264			0.811318	−	0.584605i	$-0.198750\pi$
$541$	37.7416			1.62264			0.811318	+	0.584605i	$0.198750\pi$
$542$	5.55610	−	5.55610i	0.238655	−	0.238655i
$543$	8.20980	+	6.79726i	0.352316	+	0.291698i
$544$			4.20489i			0.180283i
$545$		0			0
$546$	9.39617	−	0.884411i	0.402119	−	0.0378493i
$547$	−13.1372	−	13.1372i	−0.561704	−	0.561704i	0.368087	−	0.929791i	$-0.380013\pi$
$547$	−13.1372	−	13.1372i	−0.561704	−	0.561704i	−0.929791	+	0.368087i	$0.880013\pi$
$548$	4.34731	+	4.34731i	0.185708	+	0.185708i
$549$	5.10096	+	26.8568i	0.217704	+	1.14622i
$550$		0			0
$551$		−	19.3267i		−	0.823344i
$552$	−2.72869	+	3.29574i	−0.116141	+	0.140276i
$553$	8.87644	−	8.87644i	0.377465	−	0.377465i
$554$	4.00063			0.169970
$555$		0			0
$556$	11.6395			0.493625
$557$	−2.16691	+	2.16691i	−0.0918149	+	0.0918149i	−0.751522	−	0.659708i	$-0.770680\pi$
$557$	−2.16691	+	2.16691i	−0.0918149	+	0.0918149i	0.659708	+	0.751522i	$0.270680\pi$
$558$	−2.98864	−	2.03457i	−0.126519	−	0.0861302i
$559$		−	3.05934i		−	0.129396i
$560$		0			0
$561$	−0.532764	−	5.66019i	−0.0224933	−	0.238973i
$562$	0.700555	+	0.700555i	0.0295511	+	0.0295511i
$563$	−20.7396	−	20.7396i	−0.874069	−	0.874069i	0.118844	−	0.992913i	$-0.462081\pi$
$563$	−20.7396	−	20.7396i	−0.874069	−	0.874069i	−0.992913	+	0.118844i	$0.962081\pi$
$564$	1.03310	+	10.9759i	0.0435015	+	0.462169i
$565$		0			0
$566$			22.6627i			0.952584i
$567$	−8.25407	−	3.58753i	−0.346638	−	0.150662i
$568$	1.33356	−	1.33356i	0.0559548	−	0.0559548i
$569$	20.8701			0.874918			0.437459	−	0.899238i	$-0.355879\pi$
$569$	20.8701			0.874918			0.437459	+	0.899238i	$0.355879\pi$
$570$		0			0
$571$	34.8812			1.45973			0.729865	−	0.683591i	$-0.239583\pi$
$571$	34.8812			1.45973			0.729865	+	0.683591i	$0.239583\pi$
$572$	−3.00761	+	3.00761i	−0.125754	+	0.125754i
$573$	−10.6502	+	12.8634i	−0.444920	+	0.537378i
$574$		−	0.410091i		−	0.0171169i
$575$		0			0
$576$	−2.94731	+	0.559788i	−0.122805	+	0.0233245i
$577$	−33.1884	−	33.1884i	−1.38165	−	1.38165i	−0.841693	−	0.539957i	$-0.818441\pi$
$577$	−33.1884	−	33.1884i	−1.38165	−	1.38165i	−0.539957	−	0.841693i	$-0.681559\pi$
$578$	0.481626	+	0.481626i	0.0200330	+	0.0200330i
$579$	−16.5275	+	1.55565i	−0.686861	+	0.0646505i
$580$		0			0
$581$			5.09967i			0.211570i
$582$	16.6411	+	13.7779i	0.689794	+	0.571112i
$583$	6.00735	−	6.00735i	0.248799	−	0.248799i
$584$	11.9997			0.496551
$585$		0			0
$586$	0.463991			0.0191673
$587$	−12.2341	+	12.2341i	−0.504957	+	0.504957i	−0.912974	−	0.408017i	$-0.866220\pi$
$587$	−12.2341	+	12.2341i	−0.504957	+	0.504957i	0.408017	+	0.912974i	$0.366220\pi$
$588$	−1.33413	−	1.10458i	−0.0550185	−	0.0455523i
$589$			6.98081i			0.287639i
$590$		0			0
$591$	5.71205	−	0.537645i	0.234962	−	0.0221158i
$592$	−6.28770	−	6.28770i	−0.258423	−	0.258423i
$593$	−17.2595	−	17.2595i	−0.708762	−	0.708762i	0.257513	−	0.966275i	$-0.417097\pi$
$593$	−17.2595	−	17.2595i	−0.708762	−	0.708762i	−0.966275	+	0.257513i	$0.917097\pi$
$594$	3.89644	−	1.12696i	0.159873	−	0.0462396i
$595$		0			0
$596$			5.78924i			0.237137i
$597$	−10.9864	+	13.2695i	−0.449643	+	0.543083i
$598$	9.51800	−	9.51800i	0.389220	−	0.389220i
$599$	15.9441			0.651458			0.325729	−	0.945463i	$-0.394390\pi$
$599$	15.9441			0.651458			0.325729	+	0.945463i	$0.394390\pi$
$600$		0			0
$601$	4.32631			0.176474			0.0882369	−	0.996100i	$-0.471877\pi$
$601$	4.32631			0.176474			0.0882369	+	0.996100i	$0.471877\pi$
$602$	−0.397015	+	0.397015i	−0.0161811	+	0.0161811i
$603$	11.8416	−	17.3945i	0.482227	−	0.708357i
$604$		−	0.326935i		−	0.0133028i
$605$		0			0
$606$	−1.38353	−	14.6990i	−0.0562022	−	0.597104i
$607$	11.2179	+	11.2179i	0.455322	+	0.455322i	0.897116	−	0.441795i	$-0.145658\pi$
$607$	11.2179	+	11.2179i	0.455322	+	0.455322i	−0.441795	+	0.897116i	$0.645658\pi$
$608$	4.09591	+	4.09591i	0.166111	+	0.166111i
$609$	0.541553	+	5.75357i	0.0219448	+	0.233146i
$610$		0			0
$611$		−	34.6817i		−	1.40307i
$612$	−7.09884	+	10.4277i	−0.286953	+	0.421514i
$613$	23.2421	−	23.2421i	0.938741	−	0.938741i	−0.0594881	−	0.998229i	$-0.518947\pi$
$613$	23.2421	−	23.2421i	0.938741	−	0.938741i	0.998229	+	0.0594881i	$0.0189468\pi$
$614$	−7.48687			−0.302146
$615$		0			0
$616$	0.780604			0.0314514
$617$	−18.0762	+	18.0762i	−0.727720	+	0.727720i	−0.970165	−	0.242445i	$-0.922051\pi$
$617$	−18.0762	+	18.0762i	−0.727720	+	0.727720i	0.242445	+	0.970165i	$0.422051\pi$
$618$	−12.0060	+	14.5009i	−0.482951	+	0.583312i
$619$			10.0672i			0.404634i	0.979320	+	0.202317i	$0.0648471\pi$
$619$			10.0672i			0.404634i	−0.979320	+	0.202317i	$0.935153\pi$
$620$		0			0
$621$	−12.3308	+	3.56641i	−0.494819	+	0.143115i
$622$	8.58358	+	8.58358i	0.344170	+	0.344170i
$623$	13.1414	+	13.1414i	0.526498	+	0.526498i
$624$	9.39617	−	0.884411i	0.376148	−	0.0354048i
$625$		0			0
$626$		−	17.2824i		−	0.690745i
$627$	−6.03244	−	4.99453i	−0.240913	−	0.199462i
$628$	−15.7404	+	15.7404i	−0.628111	+	0.628111i
$629$	−37.3906			−1.49086
$630$		0			0
$631$	11.7095			0.466149			0.233075	−	0.972459i	$-0.425121\pi$
$631$	11.7095			0.466149			0.233075	+	0.972459i	$0.425121\pi$
$632$	8.87644	−	8.87644i	0.353086	−	0.353086i
$633$	19.9979	+	16.5572i	0.794845	+	0.658088i
$634$		−	3.40503i		−	0.135231i
$635$		0			0
$636$	−18.7678	+	1.76651i	−0.744190	+	0.0700467i
$637$	3.85292	+	3.85292i	0.152658	+	0.152658i
$638$	−1.84165	−	1.84165i	−0.0729118	−	0.0729118i
$639$	5.55843	−	1.05572i	0.219888	−	0.0417638i
$640$		0			0
$641$		−	17.2227i		−	0.680255i	−0.940379	−	0.340128i	$-0.889530\pi$
$641$		−	17.2227i		−	0.680255i	0.940379	−	0.340128i	$-0.110470\pi$
$642$	−13.3308	+	16.1010i	−0.526124	+	0.635458i
$643$	19.6141	−	19.6141i	0.773505	−	0.773505i	−0.205213	−	0.978717i	$-0.565789\pi$
$643$	19.6141	−	19.6141i	0.773505	−	0.773505i	0.978717	+	0.205213i	$0.0657886\pi$
$644$	−2.47033			−0.0973447
$645$		0			0
$646$	24.3568			0.958305
$647$	7.71110	−	7.71110i	0.303155	−	0.303155i	−0.539092	−	0.842247i	$-0.681233\pi$
$647$	7.71110	−	7.71110i	0.303155	−	0.303155i	0.842247	+	0.539092i	$0.181233\pi$
$648$	−8.25407	−	3.58753i	−0.324250	−	0.140931i
$649$		−	9.89441i		−	0.388390i
$650$		0			0
$651$	−0.195609	−	2.07819i	−0.00766652	−	0.0814508i
$652$	0.261547	+	0.261547i	0.0102430	+	0.0102430i
$653$	−28.8829	−	28.8829i	−1.13028	−	1.13028i	−0.990131	−	0.140145i	$-0.955243\pi$
$653$	−28.8829	−	28.8829i	−1.13028	−	1.13028i	−0.140145	−	0.990131i	$-0.544757\pi$
$654$	0.596931	+	6.34192i	0.0233418	+	0.247989i
$655$		0			0
$656$		−	0.410091i		−	0.0160114i
$657$	29.7580	+	20.2583i	1.16097	+	0.790351i
$658$	−4.50070	+	4.50070i	−0.175456	+	0.175456i
$659$	−46.5136			−1.81191			−0.905956	−	0.423371i	$-0.860847\pi$
$659$	−46.5136			−1.81191			−0.905956	+	0.423371i	$0.860847\pi$
$660$		0			0
$661$	−8.72550			−0.339383			−0.169691	−	0.985497i	$-0.554277\pi$
$661$	−8.72550			−0.339383			−0.169691	+	0.985497i	$0.554277\pi$
$662$	10.8039	−	10.8039i	0.419905	−	0.419905i
$663$	25.3081	−	30.5673i	0.982884	−	1.18714i
$664$			5.09967i			0.197905i
$665$		0			0
$666$	−4.97773	−	26.2079i	−0.192883	−	1.01554i
$667$	5.82817	+	5.82817i	0.225668	+	0.225668i
$668$	−7.48816	−	7.48816i	−0.289726	−	0.289726i
$669$	19.4462	−	1.83037i	0.751835	−	0.0707662i
$670$		0			0
$671$		−	7.11310i		−	0.274598i
$672$	−1.33413	−	1.10458i	−0.0514651	−	0.0426103i
$673$	−25.1132	+	25.1132i	−0.968043	+	0.968043i	−0.999505	−	0.0314620i	$-0.989984\pi$
$673$	−25.1132	+	25.1132i	−0.968043	+	0.968043i	0.0314620	+	0.999505i	$0.489984\pi$
$674$	16.2400			0.625541
$675$		0			0
$676$	−16.6901			−0.641925
$677$	9.97427	−	9.97427i	0.383342	−	0.383342i	−0.488962	−	0.872305i	$-0.662624\pi$
$677$	9.97427	−	9.97427i	0.383342	−	0.383342i	0.872305	+	0.488962i	$0.162624\pi$
$678$	22.3420	+	18.4980i	0.858040	+	0.710410i
$679$			12.4734i			0.478684i
$680$		0			0
$681$	−49.7374	+	4.68152i	−1.90594	+	0.179396i
$682$	0.665206	+	0.665206i	0.0254721	+	0.0254721i
$683$	−1.82278	−	1.82278i	−0.0697468	−	0.0697468i	0.671373	−	0.741120i	$-0.265705\pi$
$683$	−1.82278	−	1.82278i	−0.0697468	−	0.0697468i	−0.741120	+	0.671373i	$0.765705\pi$
$684$	3.24257	+	17.0723i	0.123983	+	0.652774i
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$	21.5744	−	26.0578i	0.823115	−	0.994166i
$688$	−0.397015	+	0.397015i	−0.0151360	+	0.0151360i
$689$	59.3025			2.25924
$690$		0			0
$691$	−26.8515			−1.02148			−0.510740	−	0.859735i	$-0.670629\pi$
$691$	−26.8515			−1.02148			−0.510740	+	0.859735i	$0.670629\pi$
$692$	8.48843	−	8.48843i	0.322682	−	0.322682i
$693$	1.93582	+	1.31784i	0.0735355	+	0.0500607i
$694$		−	17.1084i		−	0.649425i
$695$		0			0
$696$	0.541553	+	5.75357i	0.0205275	+	0.218088i
$697$	−1.21933	−	1.21933i	−0.0461853	−	0.0461853i
$698$	0.0807296	+	0.0807296i	0.00305566	+	0.00305566i
$699$	−0.672470	−	7.14447i	−0.0254352	−	0.270229i
$700$		0			0
$701$			40.3766i			1.52500i	0.646987	+	0.762501i	$0.276029\pi$
$701$			40.3766i			1.52500i	−0.646987	+	0.762501i	$0.723971\pi$
$702$	24.7946	+	13.6697i	0.935811	+	0.515929i
$703$	−36.4214	+	36.4214i	−1.37366	+	1.37366i
$704$	0.780604			0.0294201
$705$		0			0
$706$	−24.7399			−0.931097
$707$	6.02735	−	6.02735i	0.226682	−	0.226682i
$708$	−14.0010	+	16.9105i	−0.526188	+	0.635535i
$709$			14.0214i			0.526584i	0.964716	+	0.263292i	$0.0848082\pi$
$709$			14.0214i			0.526584i	−0.964716	+	0.263292i	$0.915192\pi$
$710$		0			0
$711$	36.9981	−	7.02713i	1.38754	−	0.263538i
$712$	13.1414	+	13.1414i	0.492494	+	0.492494i
$713$	−2.10514	−	2.10514i	−0.0788380	−	0.0788380i
$714$	−7.25104	+	0.682501i	−0.271363	+	0.0255420i
$715$		0			0
$716$			2.37051i			0.0885902i
$717$	−16.0552	−	13.2929i	−0.599594	−	0.496431i
$718$	18.0130	−	18.0130i	0.672240	−	0.672240i
$719$	15.3457			0.572299			0.286149	−	0.958185i	$-0.407625\pi$
$719$	15.3457			0.572299			0.286149	+	0.958185i	$0.407625\pi$
$720$		0			0
$721$	−10.8692			−0.404791
$722$	10.2905	−	10.2905i	0.382972	−	0.382972i
$723$	−7.71088	−	6.38419i	−0.286771	−	0.237430i
$724$			6.15369i			0.228700i
$725$		0			0
$726$	17.9179	−	1.68652i	0.664997	−	0.0625927i
$727$	−37.3012	−	37.3012i	−1.38342	−	1.38342i	−0.838459	−	0.544965i	$-0.816543\pi$
$727$	−37.3012	−	37.3012i	−1.38342	−	1.38342i	−0.544965	−	0.838459i	$-0.683457\pi$
$728$	3.85292	+	3.85292i	0.142799	+	0.142799i
$729$	−14.4126	−	22.8315i	−0.533801	−	0.845610i
$730$		0			0
$731$			2.36089i			0.0873209i
$732$	−10.0653	+	12.1570i	−0.372024	+	0.449334i
$733$	−0.763659	+	0.763659i	−0.0282064	+	0.0282064i	−0.721069	−	0.692863i	$-0.756349\pi$
$733$	−0.763659	+	0.763659i	−0.0282064	+	0.0282064i	0.692863	+	0.721069i	$0.256349\pi$
$734$	−33.8832			−1.25065
$735$		0			0
$736$	−2.47033			−0.0910576
$737$	−3.87163	+	3.87163i	−0.142613	+	0.142613i
$738$	0.692329	−	1.01698i	0.0254850	−	0.0374356i
$739$		−	5.91073i		−	0.217430i	−0.994073	−	0.108715i	$-0.965326\pi$
$739$		−	5.91073i		−	0.217430i	0.994073	−	0.108715i	$-0.0346736\pi$
$740$		0			0
$741$	−5.12294	−	54.4272i	−0.188196	−	1.99943i
$742$	−7.69577	−	7.69577i	−0.282521	−	0.282521i
$743$	29.0001	+	29.0001i	1.06391	+	1.06391i	0.997813	+	0.0660966i	$0.0210546\pi$
$743$	29.0001	+	29.0001i	1.06391	+	1.06391i	0.0660966	+	0.997813i	$0.478945\pi$
$744$	−0.195609	−	2.07819i	−0.00717138	−	0.0761902i
$745$		0			0
$746$		−	5.86152i		−	0.214605i
$747$	−8.60942	+	12.6466i	−0.315002	+	0.462716i
$748$	2.32098	−	2.32098i	0.0848633	−	0.0848633i
$749$	−12.0686			−0.440977
$750$		0			0
$751$	27.1470			0.990609			0.495304	−	0.868720i	$-0.335057\pi$
$751$	27.1470			0.990609			0.495304	+	0.868720i	$0.335057\pi$
$752$	−4.50070	+	4.50070i	−0.164124	+	0.164124i
$753$	1.66420	−	2.01004i	0.0606468	−	0.0732498i
$754$		−	18.1802i		−	0.662082i
$755$		0			0
$756$	−1.44370	−	4.99157i	−0.0525068	−	0.181542i
$757$	21.7239	+	21.7239i	0.789567	+	0.789567i	0.981423	−	0.191856i	$-0.0614507\pi$
$757$	21.7239	+	21.7239i	0.789567	+	0.789567i	−0.191856	+	0.981423i	$0.561451\pi$
$758$	−9.60165	−	9.60165i	−0.348748	−	0.348748i
$759$	3.32531	−	0.312993i	0.120701	−	0.0113609i
$760$		0			0
$761$		−	27.8482i		−	1.00950i	−0.863267	−	0.504748i	$-0.831585\pi$
$761$		−	27.8482i		−	1.00950i	0.863267	−	0.504748i	$-0.168415\pi$
$762$	−23.6391	−	19.5718i	−0.856353	−	0.709013i
$763$	−2.60052	+	2.60052i	−0.0941451	+	0.0941451i
$764$	−9.64185			−0.348830
$765$		0			0
$766$	15.6523			0.565541
$767$	48.8371	−	48.8371i	1.76340	−	1.76340i
$768$	−1.33413	−	1.10458i	−0.0481412	−	0.0398582i
$769$		−	28.9571i		−	1.04422i	−0.852878	−	0.522110i	$-0.825145\pi$
$769$		−	28.9571i		−	1.04422i	0.852878	−	0.522110i	$-0.174855\pi$
$770$		0			0
$771$	8.41213	−	0.791789i	0.302955	−	0.0285156i
$772$	−6.77716	−	6.77716i	−0.243915	−	0.243915i
$773$	−26.3889	−	26.3889i	−0.949144	−	0.949144i	0.0496237	−	0.998768i	$-0.484198\pi$
$773$	−26.3889	−	26.3889i	−0.949144	−	0.949144i	−0.998768	+	0.0496237i	$0.984198\pi$
$774$	−1.65481	+	0.314301i	−0.0594808	+	0.0112973i
$775$		0			0
$776$			12.4734i			0.447768i
$777$	9.82213	−	11.8633i	0.352367	−	0.425592i
$778$	−20.6295	+	20.6295i	−0.739605	+	0.739605i
$779$	−2.37545			−0.0851093
$780$		0			0
$781$	−1.47217			−0.0526783
$782$	−7.34506	+	7.34506i	−0.262659	+	0.262659i
$783$	−8.37037	+	15.1825i	−0.299133	+	0.542578i
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$	1.92945	+	20.4989i	0.0688212	+	0.731171i
$787$	15.9989	+	15.9989i	0.570300	+	0.570300i	0.932212	−	0.361912i	$-0.117876\pi$
$787$	15.9989	+	15.9989i	0.570300	+	0.570300i	−0.361912	+	0.932212i	$0.617876\pi$
$788$	2.34224	+	2.34224i	0.0834390	+	0.0834390i
$789$	2.26192	+	24.0311i	0.0805264	+	0.855530i
$790$		0			0
$791$			16.7465i			0.595439i
$792$	1.93582	+	1.31784i	0.0687862	+	0.0468275i
$793$	35.1090	−	35.1090i	1.24676	−	1.24676i
$794$	−14.7097			−0.522028
$795$		0			0
$796$	−9.94617			−0.352533
$797$	20.6511	−	20.6511i	0.731499	−	0.731499i	−0.239418	−	0.970917i	$-0.576957\pi$
$797$	20.6511	−	20.6511i	0.731499	−	0.731499i	0.970917	+	0.239418i	$0.0769565\pi$
$798$	−6.39829	+	7.72791i	−0.226497	+	0.273565i
$799$			26.7639i			0.946840i
$800$		0			0
$801$	10.4035	+	54.7749i	0.367590	+	1.93538i
$802$	2.18135	+	2.18135i	0.0770260	+	0.0770260i
$803$	−6.62348	−	6.62348i	−0.233737	−	0.233737i
$804$	12.0955	−	1.13848i	0.426575	−	0.0401512i
$805$		0			0
$806$			6.56668i			0.231301i
$807$	12.2457	+	10.1388i	0.431069	+	0.356902i
$808$	6.02735	−	6.02735i	0.212041	−	0.212041i
$809$	−15.4725			−0.543983			−0.271992	−	0.962300i	$-0.587682\pi$
$809$	−15.4725			−0.543983			−0.271992	+	0.962300i	$0.587682\pi$
$810$		0			0
$811$	23.4390			0.823054			0.411527	−	0.911398i	$-0.364996\pi$
$811$	23.4390			0.823054			0.411527	+	0.911398i	$0.364996\pi$
$812$	−2.35927	+	2.35927i	−0.0827940	+	0.0827940i
$813$	10.4829	+	8.67929i	0.367652	+	0.304396i
$814$			6.94125i			0.243291i
$815$		0			0
$816$	−7.25104	+	0.682501i	−0.253837	+	0.0238923i
$817$	2.29970	+	2.29970i	0.0804565	+	0.0804565i
$818$	−1.74916	−	1.74916i	−0.0611579	−	0.0611579i
$819$	3.05021	+	16.0595i	0.106583	+	0.561163i
$820$		0			0
$821$		−	26.9077i		−	0.939087i	−0.882909	−	0.469543i	$-0.844419\pi$
$821$		−	26.9077i		−	0.939087i	0.882909	−	0.469543i	$-0.155581\pi$
$822$	−6.79101	+	8.20224i	−0.236864	+	0.286086i
$823$	−29.5001	+	29.5001i	−1.02831	+	1.02831i	−0.0287224	+	0.999587i	$0.509144\pi$
$823$	−29.5001	+	29.5001i	−1.02831	+	1.02831i	−0.999587	+	0.0287224i	$0.990856\pi$
$824$	−10.8692			−0.378647
$825$		0			0
$826$	−12.6753			−0.441031
$827$	14.8938	−	14.8938i	0.517909	−	0.517909i	−0.399030	−	0.916938i	$-0.630653\pi$
$827$	14.8938	−	14.8938i	0.517909	−	0.517909i	0.916938	+	0.399030i	$0.130653\pi$
$828$	−6.12616	−	4.17050i	−0.212899	−	0.144935i
$829$		−	34.3997i		−	1.19475i	−0.801962	−	0.597375i	$-0.796210\pi$
$829$		−	34.3997i		−	1.19475i	0.801962	−	0.597375i	$-0.203790\pi$
$830$		0			0
$831$	0.649347	+	6.89880i	0.0225256	+	0.239317i
$832$	3.85292	+	3.85292i	0.133576	+	0.133576i
$833$	−2.97331	−	2.97331i	−0.103019	−	0.103019i
$834$	1.88922	+	20.0715i	0.0654184	+	0.695019i
$835$		0			0
$836$		−	4.52164i		−	0.156384i
$837$	3.02338	−	5.48393i	0.104503	−	0.189552i
$838$	16.6982	−	16.6982i	0.576828	−	0.576828i
$839$	−19.6850			−0.679602			−0.339801	−	0.940497i	$-0.610360\pi$
$839$	−19.6850			−0.679602			−0.339801	+	0.940497i	$0.610360\pi$
$840$		0			0
$841$	−17.8677			−0.616128
$842$	13.8882	−	13.8882i	0.478620	−	0.478620i
$843$	−1.09435	+	1.32176i	−0.0376914	+	0.0455240i
$844$			14.9895i			0.515960i
$845$		0			0
$846$	−18.7595	+	3.56303i	−0.644964	+	0.122499i
$847$	7.34730	+	7.34730i	0.252456	+	0.252456i
$848$	−7.69577	−	7.69577i	−0.264274	−	0.264274i
$849$	−39.0802	+	3.67841i	−1.34123	+	0.126243i
$850$		0			0
$851$		−	21.9666i		−	0.753004i
$852$	2.51607	+	2.08317i	0.0861993	+	0.0713683i
$853$	−0.519079	+	0.519079i	−0.0177729	+	0.0177729i	−0.715937	−	0.698164i	$-0.754000\pi$
$853$	−0.519079	+	0.519079i	−0.0177729	+	0.0177729i	0.698164	+	0.715937i	$0.254000\pi$
$854$	−9.11230			−0.311816
$855$		0			0
$856$	−12.0686			−0.412496
$857$	−3.46899	+	3.46899i	−0.118498	+	0.118498i	−0.763869	−	0.645371i	$-0.776703\pi$
$857$	−3.46899	+	3.46899i	−0.118498	+	0.118498i	0.645371	+	0.763869i	$0.276703\pi$
$858$	−5.67458	−	4.69824i	−0.193727	−	0.160395i
$859$		−	30.0887i		−	1.02661i	−0.858205	−	0.513307i	$-0.828420\pi$
$859$		−	30.0887i		−	1.02661i	0.858205	−	0.513307i	$-0.171580\pi$
$860$		0			0
$861$	0.707173	−	0.0665624i	0.0241004	−	0.00226844i
$862$	−20.4613	−	20.4613i	−0.696915	−	0.696915i
$863$	10.2849	+	10.2849i	0.350102	+	0.350102i	0.860147	−	0.510046i	$-0.170372\pi$
$863$	10.2849	+	10.2849i	0.350102	+	0.350102i	−0.510046	+	0.860147i	$0.670372\pi$
$864$	−1.44370	−	4.99157i	−0.0491156	−	0.169817i
$865$		0			0
$866$		−	25.5704i		−	0.868918i
$867$	−0.752356	+	0.908703i	−0.0255514	+	0.0308612i
$868$	0.852168	−	0.852168i	0.0289245	−	0.0289245i
$869$	−9.79907			−0.332411
$870$		0			0
$871$	−38.2194			−1.29501
$872$	−2.60052	+	2.60052i	−0.0880647	+	0.0880647i
$873$	−21.0580	+	30.9326i	−0.712704	+	1.04691i
$874$			14.3094i			0.484022i
$875$		0			0
$876$	1.94769	+	20.6926i	0.0658062	+	0.699139i
$877$	−25.3250	−	25.3250i	−0.855164	−	0.855164i	0.135600	−	0.990764i	$-0.456704\pi$
$877$	−25.3250	−	25.3250i	−0.855164	−	0.855164i	−0.990764	+	0.135600i	$0.956704\pi$
$878$	−8.83119	−	8.83119i	−0.298038	−	0.298038i
$879$	0.0753109	+	0.800119i	0.00254017	+	0.0269873i
$880$		0			0
$881$			9.27692i			0.312547i	0.987714	+	0.156274i	$0.0499482\pi$
$881$			9.27692i			0.312547i	−0.987714	+	0.156274i	$0.950052\pi$
$882$	1.68823	−	2.47989i	0.0568458	−	0.0835023i
$883$	−13.4381	+	13.4381i	−0.452228	+	0.452228i	−0.896093	−	0.443866i	$-0.853607\pi$
$883$	−13.4381	+	13.4381i	−0.452228	+	0.452228i	0.443866	+	0.896093i	$0.353607\pi$
$884$	22.9119			0.770609
$885$		0			0
$886$	27.8079			0.934224
$887$	39.1904	−	39.1904i	1.31589	−	1.31589i	0.398885	−	0.917001i	$-0.369397\pi$
$887$	39.1904	−	39.1904i	1.31589	−	1.31589i	0.917001	−	0.398885i	$-0.130603\pi$
$888$	9.82213	−	11.8633i	0.329609	−	0.398105i
$889$		−	17.7188i		−	0.594268i
$890$		0			0
$891$	2.57579	+	6.53621i	0.0862923	+	0.218971i
$892$	7.97398	+	7.97398i	0.266989	+	0.266989i
$893$	26.0703	+	26.0703i	0.872408	+	0.872408i
$894$	−9.98313	+	0.939659i	−0.333886	+	0.0314269i
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$	17.9580	+	14.8682i	0.599600	+	0.496436i
$898$	26.0240	−	26.0240i	0.868431	−	0.868431i
$899$	−4.02098			−0.134107
$900$		0			0
$901$	−45.7638			−1.52461
$902$	−0.226358	+	0.226358i	−0.00753691	+	0.00753691i
$903$	−0.749064	−	0.620184i	−0.0249273	−	0.0206384i
$904$			16.7465i			0.556982i
$905$		0			0
$906$	0.563776	−	0.0530653i	0.0187302	−	0.00176297i
$907$	23.8197	+	23.8197i	0.790921	+	0.790921i	0.981644	−	0.190723i	$-0.0610831\pi$
$907$	23.8197	+	23.8197i	0.790921	+	0.790921i	−0.190723	+	0.981644i	$0.561083\pi$
$908$	−20.3950	−	20.3950i	−0.676831	−	0.676831i
$909$	25.1227	−	4.77161i	0.833269	−	0.158264i
$910$		0			0
$911$		−	43.6041i		−	1.44467i	−0.691544	−	0.722335i	$-0.743069\pi$
$911$		−	43.6041i		−	1.44467i	0.691544	−	0.722335i	$-0.256931\pi$
$912$	−6.39829	+	7.72791i	−0.211869	+	0.255897i
$913$	2.81487	−	2.81487i	0.0931585	−	0.0931585i
$914$	0.798284			0.0264049
$915$		0			0
$916$	19.5317			0.645346
$917$	−8.40562	+	8.40562i	−0.277578	+	0.277578i
$918$	−19.1340	−	10.5489i	−0.631517	−	0.348166i
$919$		−	1.67169i		−	0.0551439i	−0.999620	−	0.0275720i	$-0.991222\pi$
$919$		−	1.67169i		−	0.0551439i	0.999620	−	0.0275720i	$-0.00877754\pi$
$920$		0			0
$921$	−1.21520	−	12.9106i	−0.0400423	−	0.425418i
$922$	−0.949307	−	0.949307i	−0.0312638	−	0.0312638i
$923$	−7.26636	−	7.26636i	−0.239175	−	0.239175i
$924$	0.126701	+	1.34610i	0.00416815	+	0.0442833i
$925$		0			0
$926$			38.5908i			1.26817i
$927$	−26.9545	−	18.3498i	−0.885302	−	0.602686i
$928$	−2.35927	+	2.35927i	−0.0774467	+	0.0774467i
$929$	35.1462			1.15311			0.576554	−	0.817059i	$-0.304397\pi$
$929$	35.1462			1.15311			0.576554	+	0.817059i	$0.304397\pi$
$930$		0			0
$931$	−5.79249			−0.189841
$932$	2.92961	−	2.92961i	0.0959625	−	0.0959625i
$933$	−13.4086	+	16.1950i	−0.438976	+	0.530200i
$934$		−	26.7646i		−	0.875765i
$935$		0			0
$936$	3.05021	+	16.0595i	0.0996992	+	0.524920i
$937$	−15.8397	−	15.8397i	−0.517459	−	0.517459i	0.399342	−	0.916802i	$-0.369238\pi$
$937$	−15.8397	−	15.8397i	−0.517459	−	0.517459i	−0.916802	+	0.399342i	$0.869238\pi$
$938$	4.95979	+	4.95979i	0.161943	+	0.161943i
$939$	29.8023	−	2.80513i	0.972562	−	0.0915421i
$940$		0			0
$941$		−	14.3284i		−	0.467093i	−0.972346	−	0.233546i	$-0.924967\pi$
$941$		−	14.3284i		−	0.467093i	0.972346	−	0.233546i	$-0.0750331\pi$
$942$	−29.6981	−	24.5884i	−0.967615	−	0.801133i
$943$	0.716343	−	0.716343i	0.0233273	−	0.0233273i
$944$	−12.6753			−0.412547
$945$		0			0
$946$	0.438281			0.0142497
$947$	−19.8875	+	19.8875i	−0.646255	+	0.646255i	−0.952086	−	0.305831i	$-0.901066\pi$
$947$	−19.8875	+	19.8875i	−0.646255	+	0.646255i	0.305831	+	0.952086i	$0.401066\pi$
$948$	16.7475	+	13.8660i	0.543935	+	0.450348i
$949$		−	65.3846i		−	2.12247i
$950$		0			0
$951$	5.87173	−	0.552675i	0.190404	−	0.0179217i
$952$	−2.97331	−	2.97331i	−0.0963655	−	0.0963655i
$953$	−0.913118	−	0.913118i	−0.0295788	−	0.0295788i	0.692163	−	0.721742i	$-0.256658\pi$
$953$	−0.913118	−	0.913118i	−0.0295788	−	0.0295788i	−0.721742	+	0.692163i	$0.756658\pi$
$954$	−6.09244	−	32.0770i	−0.197250	−	1.03853i
$955$		0			0
$956$		−	12.0343i		−	0.389216i
$957$	2.87688	−	3.47472i	0.0929963	−	0.112322i
$958$	−11.1242	+	11.1242i	−0.359408	+	0.359408i
$959$	−6.14802			−0.198530
$960$		0			0
$961$	−29.5476			−0.953149
$962$	−34.2608	+	34.2608i	−1.10461	+	1.10461i
$963$	−29.9288	−	20.3746i	−0.964444	−	0.656563i
$964$		−	5.77972i		−	0.186152i
$965$		0			0
$966$	−0.400963	−	4.25991i	−0.0129008	−	0.137060i
$967$	8.20069	+	8.20069i	0.263716	+	0.263716i	0.826562	−	0.562846i	$-0.190293\pi$
$967$	8.20069	+	8.20069i	0.263716	+	0.263716i	−0.562846	+	0.826562i	$0.690293\pi$
$968$	7.34730	+	7.34730i	0.236151	+	0.236151i
$969$	3.95338	+	42.0016i	0.127001	+	1.34928i
$970$		0			0
$971$			24.9665i			0.801214i	0.916250	+	0.400607i	$0.131201\pi$
$971$			24.9665i			0.801214i	−0.916250	+	0.400607i	$0.868799\pi$
$972$	4.84671	−	14.8158i	0.155458	−	0.475219i
$973$	−8.23037	+	8.23037i	−0.263854	+	0.263854i
$974$	2.39187			0.0766404
$975$		0			0
$976$	−9.11230			−0.291678
$977$	−5.79833	+	5.79833i	−0.185505	+	0.185505i	−0.793750	−	0.608245i	$-0.791874\pi$
$977$	−5.79833	+	5.79833i	−0.185505	+	0.185505i	0.608245	+	0.793750i	$0.291874\pi$
$978$	−0.408567	+	0.493471i	−0.0130645	+	0.0157795i
$979$		−	14.5073i		−	0.463656i
$980$		0			0
$981$	−10.8393	+	2.05873i	−0.346072	+	0.0657301i
$982$	−5.83675	−	5.83675i	−0.186258	−	0.186258i
$983$	−6.34808	−	6.34808i	−0.202472	−	0.202472i	0.598586	−	0.801058i	$-0.295729\pi$
$983$	−6.34808	−	6.34808i	−0.202472	−	0.202472i	−0.801058	+	0.598586i	$0.795729\pi$
$984$	0.707173	−	0.0665624i	0.0225439	−	0.00212193i
$985$		0			0
$986$			14.0297i			0.446795i
$987$	−8.49165	−	7.03062i	−0.270292	−	0.223787i
$988$	22.3180	−	22.3180i	0.710031	−	0.710031i
$989$	−1.38700			−0.0441041
$990$		0			0
$991$	−61.4308			−1.95141			−0.975707	−	0.219080i	$-0.929694\pi$
$991$	−61.4308			−1.95141			−0.975707	+	0.219080i	$0.929694\pi$
$992$	0.852168	−	0.852168i	0.0270564	−	0.0270564i
$993$	20.3841	+	16.8769i	0.646871	+	0.535574i
$994$			1.88593i			0.0598182i
$995$		0			0
$996$	−8.79401	+	0.827733i	−0.278649	+	0.0262277i
$997$	16.8640	+	16.8640i	0.534088	+	0.534088i	0.921786	−	0.387698i	$-0.126730\pi$
$997$	16.8640	+	16.8640i	0.534088	+	0.534088i	−0.387698	+	0.921786i	$0.626730\pi$
$998$	−13.0443	−	13.0443i	−0.412912	−	0.412912i
$999$	44.3858	−	12.8376i	1.40430	−	0.406163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.j.c.407.1		12
3.2	odd	2		1050.2.j.d.407.6		12
5.2	odd	4		210.2.j.b.113.1	yes	12
5.3	odd	4		1050.2.j.d.743.6		12
5.4	even	2		210.2.j.a.197.6	yes	12
15.2	even	4		210.2.j.a.113.6	✓	12
15.8	even	4	inner	1050.2.j.c.743.1		12
15.14	odd	2		210.2.j.b.197.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.6	✓	12	15.2	even	4
210.2.j.a.197.6	yes	12	5.4	even	2
210.2.j.b.113.1	yes	12	5.2	odd	4
210.2.j.b.197.1	yes	12	15.14	odd	2
1050.2.j.c.407.1		12	1.1	even	1	trivial
1050.2.j.c.743.1		12	15.8	even	4	inner
1050.2.j.d.407.6		12	3.2	odd	2
1050.2.j.d.743.6		12	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.33413 - 1.10458i) q^{3} -1.00000i q^{4} +(1.72443 - 0.162311i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.559788 + 2.94731i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.33413 - 1.10458i) q^{3} -1.00000i q^{4} +(1.72443 - 0.162311i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.559788 + 2.94731i) q^{9} -0.780604i q^{11} +(-1.10458 + 1.33413i) q^{12} +(3.85292 - 3.85292i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-2.97331 + 2.97331i) q^{17} +(-2.47989 - 1.68823i) q^{18} +5.79249i q^{19} +(-0.162311 - 1.72443i) q^{21} +(0.551971 + 0.551971i) q^{22} +(-1.74679 - 1.74679i) q^{23} +(-0.162311 - 1.72443i) q^{24} +5.44886i q^{26} +(2.50872 - 4.55042i) q^{27} +(0.707107 - 0.707107i) q^{28} -3.33651 q^{29} +1.20515 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.862243 + 1.04143i) q^{33} -4.20489i q^{34} +(2.94731 - 0.559788i) q^{36} +(6.28770 + 6.28770i) q^{37} +(-4.09591 - 4.09591i) q^{38} +(-9.39617 + 0.884411i) q^{39} +0.410091i q^{41} +(1.33413 + 1.10458i) q^{42} +(0.397015 - 0.397015i) q^{43} -0.780604 q^{44} +2.47033 q^{46} +(4.50070 - 4.50070i) q^{47} +(1.33413 + 1.10458i) q^{48} +1.00000i q^{49} +(7.25104 - 0.682501i) q^{51} +(-3.85292 - 3.85292i) q^{52} +(7.69577 + 7.69577i) q^{53} +(1.44370 + 4.99157i) q^{54} +1.00000i q^{56} +(6.39829 - 7.72791i) q^{57} +(2.35927 - 2.35927i) q^{58} +12.6753 q^{59} +9.11230 q^{61} +(-0.852168 + 0.852168i) q^{62} +(-1.68823 + 2.47989i) q^{63} +1.00000i q^{64} +(-0.126701 - 1.34610i) q^{66} +(-4.95979 - 4.95979i) q^{67} +(2.97331 + 2.97331i) q^{68} +(0.400963 + 4.25991i) q^{69} -1.88593i q^{71} +(-1.68823 + 2.47989i) q^{72} +(8.48507 - 8.48507i) q^{73} -8.89215 q^{74} +5.79249 q^{76} +(0.551971 - 0.551971i) q^{77} +(6.01872 - 7.26947i) q^{78} -12.5532i q^{79} +(-8.37327 + 3.29974i) q^{81} +(-0.289978 - 0.289978i) q^{82} +(3.60601 + 3.60601i) q^{83} +(-1.72443 + 0.162311i) q^{84} +0.561464i q^{86} +(4.45132 + 3.68545i) q^{87} +(0.551971 - 0.551971i) q^{88} +18.5847 q^{89} +5.44886 q^{91} +(-1.74679 + 1.74679i) q^{92} +(-1.60782 - 1.33119i) q^{93} +6.36495i q^{94} +(-1.72443 + 0.162311i) q^{96} +(8.82001 + 8.82001i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(2.30068 - 0.436973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3}+O(q^{10}) \) 12 * q - 4 * q^3	\( 12 q - 4 q^{3} + 4 q^{12} - 12 q^{14} - 12 q^{16} - 28 q^{17} - 4 q^{21} - 4 q^{22} + 24 q^{23} - 4 q^{24} + 20 q^{27} + 8 q^{29} - 8 q^{31} - 4 q^{33} + 4 q^{36} + 20 q^{37} + 4 q^{38} - 40 q^{39} + 4 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{46} - 16 q^{47} + 4 q^{48} + 8 q^{51} + 24 q^{53} - 4 q^{54} + 12 q^{57} + 8 q^{58} + 32 q^{59} - 28 q^{62} - 8 q^{63} - 8 q^{66} + 28 q^{68} - 32 q^{69} - 8 q^{72} + 24 q^{73} + 8 q^{74} - 4 q^{77} - 36 q^{81} - 32 q^{82} + 24 q^{83} + 64 q^{87} - 4 q^{88} + 48 q^{89} + 24 q^{91} + 24 q^{92} - 76 q^{93} - 8 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 + 4 * q^12 - 12 * q^14 - 12 * q^16 - 28 * q^17 - 4 * q^21 - 4 * q^22 + 24 * q^23 - 4 * q^24 + 20 * q^27 + 8 * q^29 - 8 * q^31 - 4 * q^33 + 4 * q^36 + 20 * q^37 + 4 * q^38 - 40 * q^39 + 4 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 - 16 * q^47 + 4 * q^48 + 8 * q^51 + 24 * q^53 - 4 * q^54 + 12 * q^57 + 8 * q^58 + 32 * q^59 - 28 * q^62 - 8 * q^63 - 8 * q^66 + 28 * q^68 - 32 * q^69 - 8 * q^72 + 24 * q^73 + 8 * q^74 - 4 * q^77 - 36 * q^81 - 32 * q^82 + 24 * q^83 + 64 * q^87 - 4 * q^88 + 48 * q^89 + 24 * q^91 + 24 * q^92 - 76 * q^93 - 8 * q^97 - 40 * q^99

Introduction

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