LMFDB - Embedded newform 1050.2.j.c.407.5

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			407.5
Root			$1.85804i$ of defining polynomial
Character	$\chi$	$=$	1050.407
Dual form			1050.2.j.c.743.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.510256 + 1.65519i) q^{3} -1.00000i q^{4} +(0.809587 + 1.53120i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.47928 - 1.68914i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.510256 + 1.65519i) q^{3} -1.00000i q^{4} +(0.809587 + 1.53120i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.47928 - 1.68914i) q^{9} -0.598662i q^{11} +(1.65519 + 0.510256i) q^{12} +(-2.55914 + 2.55914i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.20435 + 4.20435i) q^{17} +(-2.94751 + 0.558713i) q^{18} +5.70208i q^{19} +(1.53120 - 0.809587i) q^{21} +(-0.423318 - 0.423318i) q^{22} +(2.23887 + 2.23887i) q^{23} +(1.53120 - 0.809587i) q^{24} +3.61917i q^{26} +(4.06090 - 3.24177i) q^{27} +(-0.707107 + 0.707107i) q^{28} -0.0410252 q^{29} -8.68243 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.990896 + 0.305471i) q^{33} +5.94585i q^{34} +(-1.68914 + 2.47928i) q^{36} +(-1.56975 - 1.56975i) q^{37} +(4.03198 + 4.03198i) q^{38} +(-2.93004 - 5.54167i) q^{39} +5.79231i q^{41} +(0.510256 - 1.65519i) q^{42} +(-0.325797 + 0.325797i) q^{43} -0.598662 q^{44} +3.16624 q^{46} +(1.56415 - 1.56415i) q^{47} +(0.510256 - 1.65519i) q^{48} +1.00000i q^{49} +(-4.81369 - 9.10428i) q^{51} +(2.55914 + 2.55914i) q^{52} +(2.01202 + 2.01202i) q^{53} +(0.579214 - 5.16377i) q^{54} +1.00000i q^{56} +(-9.43801 - 2.90952i) q^{57} +(-0.0290092 + 0.0290092i) q^{58} -9.35820 q^{59} -14.8424 q^{61} +(-6.13941 + 6.13941i) q^{62} +(0.558713 + 2.94751i) q^{63} +1.00000i q^{64} +(0.916670 - 0.484669i) q^{66} +(-5.89503 - 5.89503i) q^{67} +(4.20435 + 4.20435i) q^{68} +(-4.84814 + 2.56335i) q^{69} +14.4437i q^{71} +(0.558713 + 2.94751i) q^{72} +(9.67606 - 9.67606i) q^{73} -2.21997 q^{74} +5.70208 q^{76} +(-0.423318 + 0.423318i) q^{77} +(-5.99040 - 1.84671i) q^{78} -11.7772i q^{79} +(3.29363 + 8.37568i) q^{81} +(4.09578 + 4.09578i) q^{82} +(1.04802 + 1.04802i) q^{83} +(-0.809587 - 1.53120i) q^{84} +0.460746i q^{86} +(0.0209334 - 0.0679043i) q^{87} +(-0.423318 + 0.423318i) q^{88} +18.1407 q^{89} +3.61917 q^{91} +(2.23887 - 2.23887i) q^{92} +(4.43026 - 14.3710i) q^{93} -2.21204i q^{94} +(-0.809587 - 1.53120i) q^{96} +(4.69359 + 4.69359i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-1.01122 + 1.48425i) 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
$3$	−0.510256	+	1.65519i	−0.294597	+	0.955622i
$3$	−0.510256	+	1.65519i	−0.294597	+	0.955622i
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	0.809587	+	1.53120i	0.330513	+	0.625109i
$7$	−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
$9$	−2.47928	−	1.68914i	−0.826426	−	0.563046i
$10$		0			0
$11$		−	0.598662i		−	0.180503i	−0.995919	−	0.0902516i	$-0.971233\pi$
$11$		−	0.598662i		−	0.180503i	0.995919	−	0.0902516i	$-0.0287671\pi$
$12$	1.65519	+	0.510256i	0.477811	+	0.147298i
$13$	−2.55914	+	2.55914i	−0.709778	+	0.709778i	−0.966488	−	0.256710i	$-0.917361\pi$
$13$	−2.55914	+	2.55914i	−0.709778	+	0.709778i	0.256710	+	0.966488i	$0.417361\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.20435	+	4.20435i	−1.01971	+	1.01971i	−0.0199035	+	0.999802i	$0.506336\pi$
$17$	−4.20435	+	4.20435i	−1.01971	+	1.01971i	−0.999802	+	0.0199035i	$0.993664\pi$
$18$	−2.94751	+	0.558713i	−0.694736	+	0.131690i
$19$			5.70208i			1.30815i	0.756431	+	0.654074i	$0.226941\pi$
$19$			5.70208i			1.30815i	−0.756431	+	0.654074i	$0.773059\pi$
$20$		0			0
$21$	1.53120	−	0.809587i	0.334135	−	0.176666i
$22$	−0.423318	−	0.423318i	−0.0902516	−	0.0902516i
$23$	2.23887	+	2.23887i	0.466837	+	0.466837i	0.900888	−	0.434051i	$-0.142916\pi$
$23$	2.23887	+	2.23887i	0.466837	+	0.466837i	−0.434051	+	0.900888i	$0.642916\pi$
$24$	1.53120	−	0.809587i	0.312555	−	0.165256i
$25$		0			0
$26$			3.61917i			0.709778i
$27$	4.06090	−	3.24177i	0.781521	−	0.623879i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−0.0410252			−0.00761819			−0.00380909	−	0.999993i	$-0.501212\pi$
$29$	−0.0410252			−0.00761819			−0.00380909	+	0.999993i	$0.501212\pi$
$30$		0			0
$31$	−8.68243			−1.55941			−0.779705	−	0.626147i	$-0.784631\pi$
$31$	−8.68243			−1.55941			−0.779705	+	0.626147i	$0.784631\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.990896	+	0.305471i	0.172493	+	0.0531756i
$34$			5.94585i			1.01971i
$35$		0			0
$36$	−1.68914	+	2.47928i	−0.281523	+	0.413213i
$37$	−1.56975	−	1.56975i	−0.258066	−	0.258066i	0.566201	−	0.824267i	$-0.308413\pi$
$37$	−1.56975	−	1.56975i	−0.258066	−	0.258066i	−0.824267	+	0.566201i	$0.808413\pi$
$38$	4.03198	+	4.03198i	0.654074	+	0.654074i
$39$	−2.93004	−	5.54167i	−0.469181	−	0.887378i
$40$		0			0
$41$			5.79231i			0.904608i	0.891864	+	0.452304i	$0.149398\pi$
$41$			5.79231i			0.904608i	−0.891864	+	0.452304i	$0.850602\pi$
$42$	0.510256	−	1.65519i	0.0787343	−	0.255401i
$43$	−0.325797	+	0.325797i	−0.0496835	+	0.0496835i	−0.731512	−	0.681829i	$-0.761185\pi$
$43$	−0.325797	+	0.325797i	−0.0496835	+	0.0496835i	0.681829	+	0.731512i	$0.261185\pi$
$44$	−0.598662			−0.0902516
$45$		0			0
$46$	3.16624			0.466837
$47$	1.56415	−	1.56415i	0.228154	−	0.228154i	−0.583767	−	0.811921i	$-0.698422\pi$
$47$	1.56415	−	1.56415i	0.228154	−	0.228154i	0.811921	+	0.583767i	$0.198422\pi$
$48$	0.510256	−	1.65519i	0.0736492	−	0.238905i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−4.81369	−	9.10428i	−0.674051	−	1.27485i
$52$	2.55914	+	2.55914i	0.354889	+	0.354889i
$53$	2.01202	+	2.01202i	0.276372	+	0.276372i	0.831659	−	0.555287i	$-0.187392\pi$
$53$	2.01202	+	2.01202i	0.276372	+	0.276372i	−0.555287	+	0.831659i	$0.687392\pi$
$54$	0.579214	−	5.16377i	0.0788210	−	0.702700i
$55$		0			0
$56$			1.00000i			0.133631i
$57$	−9.43801	−	2.90952i	−1.25009	−	0.385376i
$58$	−0.0290092	+	0.0290092i	−0.00380909	+	0.00380909i
$59$	−9.35820			−1.21833			−0.609167	−	0.793042i	$-0.708496\pi$
$59$	−9.35820			−1.21833			−0.609167	+	0.793042i	$0.708496\pi$
$60$		0			0
$61$	−14.8424			−1.90038			−0.950190	−	0.311670i	$-0.899112\pi$
$61$	−14.8424			−1.90038			−0.950190	+	0.311670i	$0.899112\pi$
$62$	−6.13941	+	6.13941i	−0.779705	+	0.779705i
$63$	0.558713	+	2.94751i	0.0703912	+	0.371352i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.916670	−	0.484669i	0.112834	−	0.0596586i
$67$	−5.89503	−	5.89503i	−0.720192	−	0.720192i	0.248452	−	0.968644i	$-0.420078\pi$
$67$	−5.89503	−	5.89503i	−0.720192	−	0.720192i	−0.968644	+	0.248452i	$0.920078\pi$
$68$	4.20435	+	4.20435i	0.509853	+	0.509853i
$69$	−4.84814	+	2.56335i	−0.583648	+	0.308591i
$70$		0			0
$71$			14.4437i			1.71415i	0.515194	+	0.857074i	$0.327720\pi$
$71$			14.4437i			1.71415i	−0.515194	+	0.857074i	$0.672280\pi$
$72$	0.558713	+	2.94751i	0.0658450	+	0.347368i
$73$	9.67606	−	9.67606i	1.13250	−	1.13250i	0.142737	−	0.989761i	$-0.454410\pi$
$73$	9.67606	−	9.67606i	1.13250	−	1.13250i	0.989761	−	0.142737i	$-0.0455903\pi$
$74$	−2.21997			−0.258066
$75$		0			0
$76$	5.70208			0.654074
$77$	−0.423318	+	0.423318i	−0.0482415	+	0.0482415i
$78$	−5.99040	−	1.84671i	−0.678280	−	0.209098i
$79$		−	11.7772i		−	1.32504i	−0.749046	−	0.662518i	$-0.769488\pi$
$79$		−	11.7772i		−	1.32504i	0.749046	−	0.662518i	$-0.230512\pi$
$80$		0			0
$81$	3.29363	+	8.37568i	0.365959	+	0.930631i
$82$	4.09578	+	4.09578i	0.452304	+	0.452304i
$83$	1.04802	+	1.04802i	0.115035	+	0.115035i	0.762281	−	0.647246i	$-0.224079\pi$
$83$	1.04802	+	1.04802i	0.115035	+	0.115035i	−0.647246	+	0.762281i	$0.724079\pi$
$84$	−0.809587	−	1.53120i	−0.0883332	−	0.167067i
$85$		0			0
$86$			0.460746i			0.0496835i
$87$	0.0209334	−	0.0679043i	0.00224429	−	0.00728010i
$88$	−0.423318	+	0.423318i	−0.0451258	+	0.0451258i
$89$	18.1407			1.92292			0.961458	−	0.274953i	$-0.0886624\pi$
$89$	18.1407			1.92292			0.961458	+	0.274953i	$0.0886624\pi$
$90$		0			0
$91$	3.61917			0.379393
$92$	2.23887	−	2.23887i	0.233418	−	0.233418i
$93$	4.43026	−	14.3710i	0.459397	−	1.49021i
$94$		−	2.21204i		−	0.228154i
$95$		0			0
$96$	−0.809587	−	1.53120i	−0.0826281	−	0.156277i
$97$	4.69359	+	4.69359i	0.476562	+	0.476562i	0.904030	−	0.427469i	$-0.140595\pi$
$97$	4.69359	+	4.69359i	0.476562	+	0.476562i	−0.427469	+	0.904030i	$0.640595\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	−1.01122	+	1.48425i	−0.101632	+	0.149173i
$100$		0			0
$101$			8.02663i			0.798680i	0.916803	+	0.399340i	$0.130761\pi$
$101$			8.02663i			0.798680i	−0.916803	+	0.399340i	$0.869239\pi$
$102$	−9.84149	−	3.03391i	−0.974453	−	0.300402i
$103$	−9.14232	+	9.14232i	−0.900819	+	0.900819i	−0.995507	−	0.0946877i	$-0.969815\pi$
$103$	−9.14232	+	9.14232i	−0.900819	+	0.900819i	0.0946877	+	0.995507i	$0.469815\pi$
$104$	3.61917			0.354889
$105$		0			0
$106$	2.84542			0.276372
$107$	0.372768	−	0.372768i	0.0360368	−	0.0360368i	−0.688859	−	0.724896i	$-0.741888\pi$
$107$	0.372768	−	0.372768i	0.0360368	−	0.0360368i	0.724896	+	0.688859i	$0.241888\pi$
$108$	−3.24177	−	4.06090i	−0.311939	−	0.390761i
$109$		−	8.37785i		−	0.802453i	−0.915979	−	0.401226i	$-0.868584\pi$
$109$		−	8.37785i		−	0.802453i	0.915979	−	0.401226i	$-0.131416\pi$
$110$		0			0
$111$	3.39921	−	1.79726i	0.322639	−	0.170588i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	4.65789	+	4.65789i	0.438178	+	0.438178i	0.891398	−	0.453221i	$-0.149725\pi$
$113$	4.65789	+	4.65789i	0.438178	+	0.438178i	−0.453221	+	0.891398i	$0.649725\pi$
$114$	−8.73102	+	4.61633i	−0.817735	+	0.432359i
$115$		0			0
$116$			0.0410252i			0.00380909i
$117$	10.6676	−	2.02208i	0.986217	−	0.186941i
$118$	−6.61725	+	6.61725i	−0.609167	+	0.609167i
$119$	5.94585			0.545055
$120$		0			0
$121$	10.6416			0.967419
$122$	−10.4952	+	10.4952i	−0.950190	+	0.950190i
$123$	−9.58735	−	2.95556i	−0.864463	−	0.266494i
$124$			8.68243i			0.779705i
$125$		0			0
$126$	2.47928	+	1.68914i	0.220872	+	0.150480i
$127$	−2.75150	−	2.75150i	−0.244157	−	0.244157i	0.574411	−	0.818567i	$-0.305231\pi$
$127$	−2.75150	−	2.75150i	−0.244157	−	0.244157i	−0.818567	+	0.574411i	$0.805231\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.373014	−	0.705494i	−0.0328421	−	0.0621153i
$130$		0			0
$131$		−	15.2622i		−	1.33346i	−0.745298	−	0.666731i	$-0.767693\pi$
$131$		−	15.2622i		−	1.33346i	0.745298	−	0.666731i	$-0.232307\pi$
$132$	0.305471	−	0.990896i	0.0265878	−	0.0862464i
$133$	4.03198	−	4.03198i	0.349617	−	0.349617i
$134$	−8.33683			−0.720192
$135$		0			0
$136$	5.94585			0.509853
$137$	−3.68517	+	3.68517i	−0.314845	+	0.314845i	−0.846783	−	0.531938i	$-0.821464\pi$
$137$	−3.68517	+	3.68517i	−0.314845	+	0.314845i	0.531938	+	0.846783i	$0.321464\pi$
$138$	−1.61559	+	5.24071i	−0.137528	+	0.446119i
$139$		−	10.4104i		−	0.883003i	−0.897261	−	0.441501i	$-0.854446\pi$
$139$		−	10.4104i		−	0.883003i	0.897261	−	0.441501i	$-0.145554\pi$
$140$		0			0
$141$	1.79084	+	3.38706i	0.150816	+	0.285242i
$142$	10.2132	+	10.2132i	0.857074	+	0.857074i
$143$	1.53206	+	1.53206i	0.128117	+	0.128117i
$144$	2.47928	+	1.68914i	0.206606	+	0.140761i
$145$		0			0
$146$		−	13.6840i		−	1.13250i
$147$	−1.65519	−	0.510256i	−0.136517	−	0.0420852i
$148$	−1.56975	+	1.56975i	−0.129033	+	0.129033i
$149$	12.7565			1.04506			0.522529	−	0.852622i	$-0.324989\pi$
$149$	12.7565			1.04506			0.522529	+	0.852622i	$0.324989\pi$
$150$		0			0
$151$	−18.5026			−1.50572			−0.752862	−	0.658178i	$-0.771327\pi$
$151$	−18.5026			−1.50572			−0.752862	+	0.658178i	$0.771327\pi$
$152$	4.03198	−	4.03198i	0.327037	−	0.327037i
$153$	17.5255	−	3.32203i	1.41685	−	0.268570i
$154$			0.598662i			0.0482415i
$155$		0			0
$156$	−5.54167	+	2.93004i	−0.443689	+	0.234591i
$157$	0.0325033	+	0.0325033i	0.00259405	+	0.00259405i	0.708403	−	0.705809i	$-0.249416\pi$
$157$	0.0325033	+	0.0325033i	0.00259405	+	0.00259405i	−0.705809	+	0.708403i	$0.749416\pi$
$158$	−8.32772	−	8.32772i	−0.662518	−	0.662518i
$159$	−4.35690	+	2.30362i	−0.345525	+	0.182689i
$160$		0			0
$161$		−	3.16624i		−	0.249535i
$162$	8.25145	+	3.59355i	0.648295	+	0.282336i
$163$	−9.48125	+	9.48125i	−0.742629	+	0.742629i	−0.973083	−	0.230454i	$-0.925979\pi$
$163$	−9.48125	+	9.48125i	−0.742629	+	0.742629i	0.230454	+	0.973083i	$0.425979\pi$
$164$	5.79231			0.452304
$165$		0			0
$166$	1.48212			0.115035
$167$	14.2927	−	14.2927i	1.10600	−	1.10600i	0.112330	−	0.993671i	$-0.464168\pi$
$167$	14.2927	−	14.2927i	1.10600	−	1.10600i	0.993671	−	0.112330i	$-0.0358315\pi$
$168$	−1.65519	−	0.510256i	−0.127700	−	0.0393671i
$169$		−	0.0984218i		−	0.00757091i
$170$		0			0
$171$	9.63160	−	14.1370i	0.736547	−	1.08109i
$172$	0.325797	+	0.325797i	0.0248418	+	0.0248418i
$173$	13.1681	+	13.1681i	1.00115	+	1.00115i	0.999999	+	0.00115154i	$0.000366547\pi$
$173$	13.1681	+	13.1681i	1.00115	+	1.00115i	0.00115154	+	0.999999i	$0.499633\pi$
$174$	−0.0332135	−	0.0628177i	−0.00251791	−	0.00476220i
$175$		0			0
$176$			0.598662i			0.0451258i
$177$	4.77508	−	15.4896i	0.358917	−	1.16427i
$178$	12.8274	−	12.8274i	0.961458	−	0.961458i
$179$	3.19365			0.238705			0.119352	−	0.992852i	$-0.461918\pi$
$179$	3.19365			0.238705			0.119352	+	0.992852i	$0.461918\pi$
$180$		0			0
$181$	14.7718			1.09798			0.548990	−	0.835829i	$-0.315012\pi$
$181$	14.7718			1.09798			0.548990	+	0.835829i	$0.315012\pi$
$182$	2.55914	−	2.55914i	0.189696	−	0.189696i
$183$	7.57345	−	24.5670i	0.559846	−	1.81605i
$184$		−	3.16624i		−	0.233418i
$185$		0			0
$186$	−7.02918	−	13.2945i	−0.515405	−	0.974802i
$187$	2.51698	+	2.51698i	0.184060	+	0.184060i
$188$	−1.56415	−	1.56415i	−0.114077	−	0.114077i
$189$	−5.16377	−	0.579214i	−0.375609	−	0.0421316i
$190$		0			0
$191$		−	10.6699i		−	0.772049i	−0.922489	−	0.386024i	$-0.873848\pi$
$191$		−	10.6699i		−	0.772049i	0.922489	−	0.386024i	$-0.126152\pi$
$192$	−1.65519	−	0.510256i	−0.119453	−	0.0368246i
$193$	−0.840964	+	0.840964i	−0.0605339	+	0.0605339i	−0.736726	−	0.676192i	$-0.763629\pi$
$193$	−0.840964	+	0.840964i	−0.0605339	+	0.0605339i	0.676192	+	0.736726i	$0.263629\pi$
$194$	6.63773			0.476562
$195$		0			0
$196$	1.00000			0.0714286
$197$	−18.2786	+	18.2786i	−1.30230	+	1.30230i	−0.375456	+	0.926840i	$0.622514\pi$
$197$	−18.2786	+	18.2786i	−1.30230	+	1.30230i	−0.926840	+	0.375456i	$0.877486\pi$
$198$	0.334480	+	1.76456i	0.0237705	+	0.125402i
$199$			11.0697i			0.784713i	0.919813	+	0.392356i	$0.128340\pi$
$199$			11.0697i			0.784713i	−0.919813	+	0.392356i	$0.871660\pi$
$200$		0			0
$201$	12.7653	−	6.74939i	0.900398	−	0.476065i
$202$	5.67569	+	5.67569i	0.399340	+	0.399340i
$203$	0.0290092	+	0.0290092i	0.00203605	+	0.00203605i
$204$	−9.10428	+	4.81369i	−0.637427	+	0.337025i
$205$		0			0
$206$			12.9292i			0.900819i
$207$	−1.76902	−	9.33254i	−0.122955	−	0.648656i
$208$	2.55914	−	2.55914i	0.177445	−	0.177445i
$209$	3.41362			0.236125
$210$		0			0
$211$	−6.97584			−0.480236			−0.240118	−	0.970744i	$-0.577186\pi$
$211$	−6.97584			−0.480236			−0.240118	+	0.970744i	$0.577186\pi$
$212$	2.01202	−	2.01202i	0.138186	−	0.138186i
$213$	−23.9069	−	7.36997i	−1.63808	−	0.504982i
$214$		−	0.527173i		−	0.0360368i
$215$		0			0
$216$	−5.16377	−	0.579214i	−0.351350	−	0.0394105i
$217$	6.13941	+	6.13941i	0.416770	+	0.416770i
$218$	−5.92404	−	5.92404i	−0.401226	−	0.401226i
$219$	11.0784	+	20.9530i	0.748609	+	1.41587i
$220$		0			0
$221$		−	21.5191i		−	1.44753i
$222$	1.13275	−	3.67445i	0.0760253	−	0.246613i
$223$	6.44180	−	6.44180i	0.431375	−	0.431375i	−0.457721	−	0.889096i	$-0.651334\pi$
$223$	6.44180	−	6.44180i	0.431375	−	0.431375i	0.889096	+	0.457721i	$0.151334\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	6.58726			0.438178
$227$	3.80409	−	3.80409i	0.252487	−	0.252487i	−0.569503	−	0.821989i	$-0.692864\pi$
$227$	3.80409	−	3.80409i	0.252487	−	0.252487i	0.821989	+	0.569503i	$0.192864\pi$
$228$	−2.90952	+	9.43801i	−0.192688	+	0.625047i
$229$			16.2301i			1.07252i	0.844054	+	0.536258i	$0.180163\pi$
$229$			16.2301i			1.07252i	−0.844054	+	0.536258i	$0.819837\pi$
$230$		0			0
$231$	−0.484669	−	0.916670i	−0.0318889	−	0.0603124i
$232$	0.0290092	+	0.0290092i	0.00190455	+	0.00190455i
$233$	1.42491	+	1.42491i	0.0933492	+	0.0933492i	0.752239	−	0.658890i	$-0.228974\pi$
$233$	1.42491	+	1.42491i	0.0933492	+	0.0933492i	−0.658890	+	0.752239i	$0.728974\pi$
$234$	6.11328	−	8.97294i	0.399638	−	0.586579i
$235$		0			0
$236$			9.35820i			0.609167i
$237$	19.4934	+	6.00938i	1.26623	+	0.390351i
$238$	4.20435	−	4.20435i	0.272528	−	0.272528i
$239$	10.0287			0.648706			0.324353	−	0.945936i	$-0.394854\pi$
$239$	10.0287			0.648706			0.324353	+	0.945936i	$0.394854\pi$
$240$		0			0
$241$	−2.87963			−0.185493			−0.0927465	−	0.995690i	$-0.529565\pi$
$241$	−2.87963			−0.185493			−0.0927465	+	0.995690i	$0.529565\pi$
$242$	7.52475	−	7.52475i	0.483709	−	0.483709i
$243$	−15.5439	+	1.17782i	−0.997141	+	0.0755574i
$244$			14.8424i			0.950190i
$245$		0			0
$246$	−8.86918	+	4.68938i	−0.565478	+	0.298984i
$247$	−14.5924	−	14.5924i	−0.928495	−	0.928495i
$248$	6.13941	+	6.13941i	0.389853	+	0.389853i
$249$	−2.26942	+	1.19990i	−0.143818	+	0.0760408i
$250$		0			0
$251$		−	3.73681i		−	0.235865i	−0.993022	−	0.117933i	$-0.962373\pi$
$251$		−	3.73681i		−	0.235865i	0.993022	−	0.117933i	$-0.0376267\pi$
$252$	2.94751	−	0.558713i	0.185676	−	0.0351956i
$253$	1.34033	−	1.34033i	0.0842655	−	0.0842655i
$254$	−3.89122			−0.244157
$255$		0			0
$256$	1.00000			0.0625000
$257$	9.77237	−	9.77237i	0.609584	−	0.609584i	−0.333254	−	0.942837i	$-0.608147\pi$
$257$	9.77237	−	9.77237i	0.609584	−	0.609584i	0.942837	+	0.333254i	$0.108147\pi$
$258$	−0.762620	−	0.235099i	−0.0474787	−	0.0146366i
$259$			2.21997i			0.137942i
$260$		0			0
$261$	0.101713	+	0.0692972i	0.00629586	+	0.00428939i
$262$	−10.7920	−	10.7920i	−0.666731	−	0.666731i
$263$	−3.45891	−	3.45891i	−0.213285	−	0.213285i	0.592376	−	0.805662i	$-0.298190\pi$
$263$	−3.45891	−	3.45891i	−0.213285	−	0.213285i	−0.805662	+	0.592376i	$0.798190\pi$
$264$	−0.484669	−	0.916670i	−0.0298293	−	0.0564171i
$265$		0			0
$266$		−	5.70208i		−	0.349617i
$267$	−9.25643	+	30.0263i	−0.566484	+	1.83758i
$268$	−5.89503	+	5.89503i	−0.360096	+	0.360096i
$269$	−15.6157			−0.952106			−0.476053	−	0.879417i	$-0.657933\pi$
$269$	−15.6157			−0.952106			−0.476053	+	0.879417i	$0.657933\pi$
$270$		0			0
$271$	4.76022			0.289163			0.144581	−	0.989493i	$-0.453816\pi$
$271$	4.76022			0.289163			0.144581	+	0.989493i	$0.453816\pi$
$272$	4.20435	−	4.20435i	0.254926	−	0.254926i
$273$	−1.84671	+	5.99040i	−0.111768	+	0.362556i
$274$			5.21161i			0.314845i
$275$		0			0
$276$	2.56335	+	4.84814i	0.154295	+	0.291824i
$277$	8.63721	+	8.63721i	0.518960	+	0.518960i	0.917257	−	0.398297i	$-0.130399\pi$
$277$	8.63721	+	8.63721i	0.518960	+	0.518960i	−0.398297	+	0.917257i	$0.630399\pi$
$278$	−7.36130	−	7.36130i	−0.441501	−	0.441501i
$279$	21.5261	+	14.6658i	1.28874	+	0.878020i
$280$		0			0
$281$		−	11.1403i		−	0.664577i	−0.943178	−	0.332289i	$-0.892179\pi$
$281$		−	11.1403i		−	0.664577i	0.943178	−	0.332289i	$-0.107821\pi$
$282$	3.66133	+	1.12870i	0.218029	+	0.0672134i
$283$	−12.7294	+	12.7294i	−0.756686	+	0.756686i	−0.975718	−	0.219032i	$-0.929710\pi$
$283$	−12.7294	+	12.7294i	−0.756686	+	0.756686i	0.219032	+	0.975718i	$0.429710\pi$
$284$	14.4437			0.857074
$285$		0			0
$286$	2.16666			0.128117
$287$	4.09578	−	4.09578i	0.241767	−	0.241767i
$288$	2.94751	−	0.558713i	0.173684	−	0.0329225i
$289$		−	18.3532i		−	1.07960i
$290$		0			0
$291$	−10.1637	+	5.37382i	−0.595806	+	0.315019i
$292$	−9.67606	−	9.67606i	−0.566249	−	0.566249i
$293$	12.1490	+	12.1490i	0.709750	+	0.709750i	0.966483	−	0.256732i	$-0.0826459\pi$
$293$	12.1490	+	12.1490i	0.709750	+	0.709750i	−0.256732	+	0.966483i	$0.582646\pi$
$294$	−1.53120	+	0.809587i	−0.0893013	+	0.0472161i
$295$		0			0
$296$			2.21997i			0.129033i
$297$	−1.94072	−	2.43111i	−0.112612	−	0.141067i
$298$	9.02024	−	9.02024i	0.522529	−	0.522529i
$299$	−11.4592			−0.662701
$300$		0			0
$301$	0.460746			0.0265570
$302$	−13.0833	+	13.0833i	−0.752862	+	0.752862i
$303$	−13.2856	−	4.09564i	−0.763236	−	0.235288i
$304$		−	5.70208i		−	0.327037i
$305$		0			0
$306$	10.0434	−	14.7414i	0.574141	−	0.842711i
$307$	−11.2499	−	11.2499i	−0.642067	−	0.642067i	0.308996	−	0.951063i	$-0.400007\pi$
$307$	−11.2499	−	11.2499i	−0.642067	−	0.642067i	−0.951063	+	0.308996i	$0.900007\pi$
$308$	0.423318	+	0.423318i	0.0241208	+	0.0241208i
$309$	−10.4673	−	19.7972i	−0.595464	−	1.12622i
$310$		0			0
$311$			20.1891i			1.14482i	0.819967	+	0.572411i	$0.193992\pi$
$311$			20.1891i			1.14482i	−0.819967	+	0.572411i	$0.806008\pi$
$312$	−1.84671	+	5.99040i	−0.104549	+	0.339140i
$313$	2.05777	−	2.05777i	0.116312	−	0.116312i	−0.646555	−	0.762867i	$-0.723791\pi$
$313$	2.05777	−	2.05777i	0.116312	−	0.116312i	0.762867	+	0.646555i	$0.223791\pi$
$314$	0.0459667			0.00259405
$315$		0			0
$316$	−11.7772			−0.662518
$317$	−2.75877	+	2.75877i	−0.154948	+	0.154948i	−0.780324	−	0.625376i	$-0.784946\pi$
$317$	−2.75877	+	2.75877i	−0.154948	+	0.154948i	0.625376	+	0.780324i	$0.284946\pi$
$318$	−1.45189	+	4.70970i	−0.0814182	+	0.264107i
$319$			0.0245602i			0.00137511i
$320$		0			0
$321$	0.426792	+	0.807207i	0.0238212	+	0.0450539i
$322$	−2.23887	−	2.23887i	−0.124767	−	0.124767i
$323$	−23.9736	−	23.9736i	−1.33393	−	1.33393i
$324$	8.37568	−	3.29363i	0.465316	−	0.182979i
$325$		0			0
$326$			13.4085i			0.742629i
$327$	13.8669	+	4.27485i	0.766841	+	0.236400i
$328$	4.09578	−	4.09578i	0.226152	−	0.226152i
$329$	−2.21204			−0.121953
$330$		0			0
$331$	28.8209			1.58414			0.792070	−	0.610430i	$-0.209004\pi$
$331$	28.8209			1.58414			0.792070	+	0.610430i	$0.209004\pi$
$332$	1.04802	−	1.04802i	0.0575173	−	0.0575173i
$333$	1.24032	+	6.54338i	0.0679693	+	0.358575i
$334$		−	20.2129i		−	1.10600i
$335$		0			0
$336$	−1.53120	+	0.809587i	−0.0835337	+	0.0441666i
$337$	−9.09298	−	9.09298i	−0.495326	−	0.495326i	0.414653	−	0.909980i	$-0.363903\pi$
$337$	−9.09298	−	9.09298i	−0.495326	−	0.495326i	−0.909980	+	0.414653i	$0.863903\pi$
$338$	−0.0695947	−	0.0695947i	−0.00378545	−	0.00378545i
$339$	−10.0864	+	5.33296i	−0.547818	+	0.289647i
$340$		0			0
$341$			5.19784i			0.281479i
$342$	−3.18583	−	16.8070i	−0.172270	−	0.908817i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	0.460746			0.0248418
$345$		0			0
$346$	18.6225			1.00115
$347$	−13.3263	+	13.3263i	−0.715396	+	0.715396i	−0.967659	−	0.252263i	$-0.918825\pi$
$347$	−13.3263	+	13.3263i	−0.715396	+	0.715396i	0.252263	+	0.967659i	$0.418825\pi$
$348$	−0.0679043	−	0.0209334i	−0.00364005	−	0.00112215i
$349$		−	3.86507i		−	0.206893i	−0.994635	−	0.103446i	$-0.967013\pi$
$349$		−	3.86507i		−	0.206893i	0.994635	−	0.103446i	$-0.0329870\pi$
$350$		0			0
$351$	−2.09628	+	18.6886i	−0.111891	+	0.997523i
$352$	0.423318	+	0.423318i	0.0225629	+	0.0225629i
$353$	−21.9705	−	21.9705i	−1.16937	−	1.16937i	−0.982357	−	0.187018i	$-0.940118\pi$
$353$	−21.9705	−	21.9705i	−1.16937	−	1.16937i	−0.187018	−	0.982357i	$-0.559882\pi$
$354$	−7.57628	−	14.3293i	−0.402675	−	0.761592i
$355$		0			0
$356$		−	18.1407i		−	0.961458i
$357$	−3.03391	+	9.84149i	−0.160571	+	0.520867i
$358$	2.25825	−	2.25825i	0.119352	−	0.119352i
$359$	−14.8406			−0.783254			−0.391627	−	0.920124i	$-0.628088\pi$
$359$	−14.8406			−0.783254			−0.391627	+	0.920124i	$0.628088\pi$
$360$		0			0
$361$	−13.5138			−0.711250
$362$	10.4453	−	10.4453i	0.548990	−	0.548990i
$363$	−5.42995	+	17.6138i	−0.284998	+	0.924486i
$364$		−	3.61917i		−	0.189696i
$365$		0			0
$366$	−12.0163	−	22.7267i	−0.628100	−	1.18795i
$367$	−14.0652	−	14.0652i	−0.734196	−	0.734196i	0.237252	−	0.971448i	$-0.423753\pi$
$367$	−14.0652	−	14.0652i	−0.734196	−	0.734196i	−0.971448	+	0.237252i	$0.923753\pi$
$368$	−2.23887	−	2.23887i	−0.116709	−	0.116709i
$369$	9.78402	−	14.3608i	0.509335	−	0.747591i
$370$		0			0
$371$		−	2.84542i		−	0.147727i
$372$	−14.3710	−	4.43026i	−0.745103	−	0.229699i
$373$	−3.13757	+	3.13757i	−0.162457	+	0.162457i	−0.783654	−	0.621197i	$-0.786647\pi$
$373$	−3.13757	+	3.13757i	−0.162457	+	0.162457i	0.621197	+	0.783654i	$0.286647\pi$
$374$	3.55955			0.184060
$375$		0			0
$376$	−2.21204			−0.114077
$377$	0.104989	−	0.104989i	0.00540722	−	0.00540722i
$378$	−4.06090	+	3.24177i	−0.208870	+	0.166739i
$379$			2.17092i			0.111513i	0.998444	+	0.0557564i	$0.0177570\pi$
$379$			2.17092i			0.111513i	−0.998444	+	0.0557564i	$0.982243\pi$
$380$		0			0
$381$	5.95822	−	3.15028i	0.305249	−	0.161394i
$382$	−7.54478	−	7.54478i	−0.386024	−	0.386024i
$383$	−8.83769	−	8.83769i	−0.451585	−	0.451585i	0.444295	−	0.895880i	$-0.353454\pi$
$383$	−8.83769	−	8.83769i	−0.451585	−	0.451585i	−0.895880	+	0.444295i	$0.853454\pi$
$384$	−1.53120	+	0.809587i	−0.0781386	+	0.0413141i
$385$		0			0
$386$			1.18930i			0.0605339i
$387$	1.35806	−	0.257425i	0.0690338	−	0.0130856i
$388$	4.69359	−	4.69359i	0.238281	−	0.238281i
$389$	−2.07217			−0.105063			−0.0525315	−	0.998619i	$-0.516729\pi$
$389$	−2.07217			−0.105063			−0.0525315	+	0.998619i	$0.516729\pi$
$390$		0			0
$391$	−18.8260			−0.952072
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	25.2617	+	7.78762i	1.27429	+	0.392833i
$394$			25.8498i			1.30230i
$395$		0			0
$396$	1.48425	+	1.01122i	0.0745863	+	0.0508158i
$397$	1.16067	+	1.16067i	0.0582524	+	0.0582524i	0.735633	−	0.677380i	$-0.236885\pi$
$397$	1.16067	+	1.16067i	0.0582524	+	0.0582524i	−0.677380	+	0.735633i	$0.736885\pi$
$398$	7.82749	+	7.82749i	0.392356	+	0.392356i
$399$	4.61633	+	8.73102i	0.231106	+	0.437098i
$400$		0			0
$401$			34.3593i			1.71582i	0.513797	+	0.857912i	$0.328238\pi$
$401$			34.3593i			1.71582i	−0.513797	+	0.857912i	$0.671762\pi$
$402$	4.25392	−	13.7990i	0.212166	−	0.688231i
$403$	22.2196	−	22.2196i	1.10684	−	1.10684i
$404$	8.02663			0.399340
$405$		0			0
$406$	0.0410252			0.00203605
$407$	−0.939751	+	0.939751i	−0.0465817	+	0.0465817i
$408$	−3.03391	+	9.84149i	−0.150201	+	0.487226i
$409$			9.04629i			0.447310i	0.974668	+	0.223655i	$0.0717989\pi$
$409$			9.04629i			0.447310i	−0.974668	+	0.223655i	$0.928201\pi$
$410$		0			0
$411$	−4.21926	−	7.98002i	−0.208121	−	0.393625i
$412$	9.14232	+	9.14232i	0.450410	+	0.450410i
$413$	6.61725	+	6.61725i	0.325613	+	0.325613i
$414$	−7.84999	−	5.34821i	−0.385806	−	0.262850i
$415$		0			0
$416$		−	3.61917i		−	0.177445i
$417$	17.2312	+	5.31200i	0.843816	+	0.260130i
$418$	2.41379	−	2.41379i	0.118062	−	0.118062i
$419$	6.31612			0.308563			0.154281	−	0.988027i	$-0.450694\pi$
$419$	6.31612			0.308563			0.154281	+	0.988027i	$0.450694\pi$
$420$		0			0
$421$	−13.7613			−0.670683			−0.335341	−	0.942097i	$-0.608852\pi$
$421$	−13.7613			−0.670683			−0.335341	+	0.942097i	$0.608852\pi$
$422$	−4.93266	+	4.93266i	−0.240118	+	0.240118i
$423$	−6.52000	+	1.23589i	−0.317013	+	0.0600912i
$424$		−	2.84542i		−	0.138186i
$425$		0			0
$426$	−22.1161	+	11.6934i	−1.07153	+	0.566547i
$427$	10.4952	+	10.4952i	0.507898	+	0.507898i
$428$	−0.372768	−	0.372768i	−0.0180184	−	0.0180184i
$429$	−3.31759	+	1.75410i	−0.160175	+	0.0846888i
$430$		0			0
$431$		−	15.1437i		−	0.729448i	−0.931116	−	0.364724i	$-0.881163\pi$
$431$		−	15.1437i		−	0.729448i	0.931116	−	0.364724i	$-0.118837\pi$
$432$	−4.06090	+	3.24177i	−0.195380	+	0.155970i
$433$	−7.32819	+	7.32819i	−0.352170	+	0.352170i	−0.860916	−	0.508746i	$-0.830109\pi$
$433$	−7.32819	+	7.32819i	−0.352170	+	0.352170i	0.508746	+	0.860916i	$0.330109\pi$
$434$	8.68243			0.416770
$435$		0			0
$436$	−8.37785			−0.401226
$437$	−12.7662	+	12.7662i	−0.610691	+	0.610691i
$438$	22.6496	+	6.98236i	1.08224	+	0.333630i
$439$			4.14139i			0.197658i	0.995104	+	0.0988288i	$0.0315096\pi$
$439$			4.14139i			0.197658i	−0.995104	+	0.0988288i	$0.968490\pi$
$440$		0			0
$441$	1.68914	−	2.47928i	0.0804351	−	0.118061i
$442$	−15.2163	−	15.2163i	−0.723765	−	0.723765i
$443$	28.1456	+	28.1456i	1.33724	+	1.33724i	0.898723	+	0.438517i	$0.144496\pi$
$443$	28.1456	+	28.1456i	1.33724	+	1.33724i	0.438517	+	0.898723i	$0.355504\pi$
$444$	−1.79726	−	3.39921i	−0.0852940	−	0.161319i
$445$		0			0
$446$		−	9.11008i		−	0.431375i
$447$	−6.50911	+	21.1145i	−0.307870	+	0.998679i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−2.90662			−0.137172			−0.0685860	−	0.997645i	$-0.521849\pi$
$449$	−2.90662			−0.137172			−0.0685860	+	0.997645i	$0.521849\pi$
$450$		0			0
$451$	3.46764			0.163285
$452$	4.65789	−	4.65789i	0.219089	−	0.219089i
$453$	9.44109	−	30.6253i	0.443581	−	1.43890i
$454$		−	5.37980i		−	0.252487i
$455$		0			0
$456$	4.61633	+	8.73102i	0.216180	+	0.408868i
$457$	28.5766	+	28.5766i	1.33676	+	1.33676i	0.899181	+	0.437578i	$0.144163\pi$
$457$	28.5766	+	28.5766i	1.33676	+	1.33676i	0.437578	+	0.899181i	$0.355837\pi$
$458$	11.4764	+	11.4764i	0.536258	+	0.536258i
$459$	−3.44392	+	30.7030i	−0.160748	+	1.43309i
$460$		0			0
$461$		−	31.8861i		−	1.48508i	−0.669800	−	0.742542i	$-0.733620\pi$
$461$		−	31.8861i		−	1.48508i	0.669800	−	0.742542i	$-0.266380\pi$
$462$	−0.990896	−	0.305471i	−0.0461006	−	0.0142118i
$463$	1.03747	−	1.03747i	0.0482153	−	0.0482153i	−0.682588	−	0.730803i	$-0.739146\pi$
$463$	1.03747	−	1.03747i	0.0482153	−	0.0482153i	0.730803	+	0.682588i	$0.239146\pi$
$464$	0.0410252			0.00190455
$465$		0			0
$466$	2.01513			0.0933492
$467$	−17.9187	+	17.9187i	−0.829178	+	0.829178i	−0.987403	−	0.158226i	$-0.949423\pi$
$467$	−17.9187	+	17.9187i	−0.829178	+	0.829178i	0.158226	+	0.987403i	$0.449423\pi$
$468$	−2.02208	−	10.6676i	−0.0934707	−	0.493108i
$469$			8.33683i			0.384959i
$470$		0			0
$471$	−0.0703841	+	0.0372140i	−0.00324313	+	0.00171473i
$472$	6.61725	+	6.61725i	0.304583	+	0.304583i
$473$	0.195042	+	0.195042i	0.00896804	+	0.00896804i
$474$	18.0332	−	9.53465i	0.828292	−	0.437941i
$475$		0			0
$476$		−	5.94585i		−	0.272528i
$477$	−1.58977	−	8.38692i	−0.0727907	−	0.384011i
$478$	7.09139	−	7.09139i	0.324353	−	0.324353i
$479$	−17.9344			−0.819446			−0.409723	−	0.912210i	$-0.634375\pi$
$479$	−17.9344			−0.819446			−0.409723	+	0.912210i	$0.634375\pi$
$480$		0			0
$481$	8.03444			0.366339
$482$	−2.03620	+	2.03620i	−0.0927465	+	0.0927465i
$483$	5.24071	+	1.61559i	0.238461	+	0.0735121i
$484$		−	10.6416i		−	0.483709i
$485$		0			0
$486$	−10.1583	+	11.8240i	−0.460792	+	0.536349i
$487$	17.7003	+	17.7003i	0.802078	+	0.802078i	0.983420	−	0.181342i	$-0.0580441\pi$
$487$	17.7003	+	17.7003i	0.802078	+	0.802078i	−0.181342	+	0.983420i	$0.558044\pi$
$488$	10.4952	+	10.4952i	0.475095	+	0.475095i
$489$	−10.8554	−	20.5311i	−0.490896	−	0.928448i
$490$		0			0
$491$			32.5352i			1.46829i	0.678990	+	0.734147i	$0.262418\pi$
$491$			32.5352i			1.46829i	−0.678990	+	0.734147i	$0.737582\pi$
$492$	−2.95556	+	9.58735i	−0.133247	+	0.432231i
$493$	0.172484	−	0.172484i	0.00776830	−	0.00776830i
$494$	−20.6368			−0.928495
$495$		0			0
$496$	8.68243			0.389853
$497$	10.2132	−	10.2132i	0.458125	−	0.458125i
$498$	−0.756260	+	2.45318i	−0.0338888	+	0.109930i
$499$		−	17.2851i		−	0.773788i	−0.922124	−	0.386894i	$-0.873548\pi$
$499$		−	17.2851i		−	0.773788i	0.922124	−	0.386894i	$-0.126452\pi$
$500$		0			0
$501$	16.3641	+	30.9500i	0.731095	+	1.38274i
$502$	−2.64232	−	2.64232i	−0.117933	−	0.117933i
$503$	−9.37011	−	9.37011i	−0.417793	−	0.417793i	0.466650	−	0.884442i	$-0.345461\pi$
$503$	−9.37011	−	9.37011i	−0.417793	−	0.417793i	−0.884442	+	0.466650i	$0.845461\pi$
$504$	1.68914	−	2.47928i	0.0752402	−	0.110436i
$505$		0			0
$506$		−	1.89551i		−	0.0842655i
$507$	0.162906	+	0.0502203i	0.00723492	+	0.00223036i
$508$	−2.75150	+	2.75150i	−0.122078	+	0.122078i
$509$	−37.6289			−1.66787			−0.833937	−	0.551860i	$-0.813918\pi$
$509$	−37.6289			−1.66787			−0.833937	+	0.551860i	$0.813918\pi$
$510$		0			0
$511$	−13.6840			−0.605345
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	18.4848	+	23.1556i	0.816126	+	1.02234i
$514$		−	13.8202i		−	0.609584i
$515$		0			0
$516$	−0.705494	+	0.373014i	−0.0310576	+	0.0164210i
$517$	−0.936394	−	0.936394i	−0.0411825	−	0.0411825i
$518$	1.56975	+	1.56975i	0.0689710	+	0.0689710i
$519$	−28.5147	+	15.0765i	−1.25166	+	0.661786i
$520$		0			0
$521$			38.1318i			1.67059i	0.549805	+	0.835293i	$0.314702\pi$
$521$			38.1318i			1.67059i	−0.549805	+	0.835293i	$0.685298\pi$
$522$	0.120922	−	0.0229213i	0.00529263	−	0.00100324i
$523$	−24.0284	+	24.0284i	−1.05069	+	1.05069i	−0.0520439	+	0.998645i	$0.516574\pi$
$523$	−24.0284	+	24.0284i	−1.05069	+	1.05069i	−0.998645	+	0.0520439i	$0.983426\pi$
$524$	−15.2622			−0.666731
$525$		0			0
$526$	−4.89164			−0.213285
$527$	36.5040	−	36.5040i	1.59014	−	1.59014i
$528$	−0.990896	−	0.305471i	−0.0431232	−	0.0132939i
$529$		−	12.9749i		−	0.564127i
$530$		0			0
$531$	23.2016	+	15.8073i	1.00686	+	0.685978i
$532$	−4.03198	−	4.03198i	−0.174809	−	0.174809i
$533$	−14.8234	−	14.8234i	−0.642071	−	0.642071i
$534$	14.6865	+	27.7771i	0.635548	+	1.20203i
$535$		0			0
$536$			8.33683i			0.360096i
$537$	−1.62958	+	5.28609i	−0.0703216	+	0.228111i
$538$	−11.0420	+	11.0420i	−0.476053	+	0.476053i
$539$	0.598662			0.0257862
$540$		0			0
$541$	−5.81137			−0.249850			−0.124925	−	0.992166i	$-0.539869\pi$
$541$	−5.81137			−0.249850			−0.124925	+	0.992166i	$0.539869\pi$
$542$	3.36598	−	3.36598i	0.144581	−	0.144581i
$543$	−7.53741	+	24.4501i	−0.323461	+	1.04925i
$544$		−	5.94585i		−	0.254926i
$545$		0			0
$546$	2.93004	+	5.54167i	0.125394	+	0.237162i
$547$	−12.9045	−	12.9045i	−0.551755	−	0.551755i	0.375192	−	0.926947i	$-0.377577\pi$
$547$	−12.9045	−	12.9045i	−0.551755	−	0.551755i	−0.926947	+	0.375192i	$0.877577\pi$
$548$	3.68517	+	3.68517i	0.157423	+	0.157423i
$549$	36.7985	+	25.0709i	1.57052	+	1.07000i
$550$		0			0
$551$		−	0.233929i		−	0.00996571i
$552$	5.24071	+	1.61559i	0.223060	+	0.0687642i
$553$	−8.32772	+	8.32772i	−0.354131	+	0.354131i
$554$	12.2149			0.518960
$555$		0			0
$556$	−10.4104			−0.441501
$557$	−20.2842	+	20.2842i	−0.859467	+	0.859467i	−0.991275	−	0.131808i	$-0.957922\pi$
$557$	−20.2842	+	20.2842i	−0.859467	+	0.859467i	0.131808	+	0.991275i	$0.457922\pi$
$558$	25.5916	−	4.85099i	1.08338	−	0.205359i
$559$		−	1.66752i		−	0.0705286i
$560$		0			0
$561$	−5.45038	+	2.88177i	−0.230115	+	0.121668i
$562$	−7.87742	−	7.87742i	−0.332289	−	0.332289i
$563$	21.4141	+	21.4141i	0.902497	+	0.902497i	0.995652	−	0.0931543i	$-0.0296950\pi$
$563$	21.4141	+	21.4141i	0.902497	+	0.902497i	−0.0931543	+	0.995652i	$0.529695\pi$
$564$	3.38706	−	1.79084i	0.142621	−	0.0754078i
$565$		0			0
$566$			18.0021i			0.756686i
$567$	3.59355	−	8.25145i	0.150915	−	0.346528i
$568$	10.2132	−	10.2132i	0.428537	−	0.428537i
$569$	36.8247			1.54377			0.771885	−	0.635762i	$-0.219314\pi$
$569$	36.8247			1.54377			0.771885	+	0.635762i	$0.219314\pi$
$570$		0			0
$571$	29.8712			1.25007			0.625036	−	0.780596i	$-0.285084\pi$
$571$	29.8712			1.25007			0.625036	+	0.780596i	$0.285084\pi$
$572$	1.53206	−	1.53206i	0.0640587	−	0.0640587i
$573$	17.6607	+	5.44440i	0.737787	+	0.227443i
$574$		−	5.79231i		−	0.241767i
$575$		0			0
$576$	1.68914	−	2.47928i	0.0703807	−	0.103303i
$577$	19.6893	+	19.6893i	0.819678	+	0.819678i	0.986061	−	0.166383i	$-0.0532088\pi$
$577$	19.6893	+	19.6893i	0.819678	+	0.819678i	−0.166383	+	0.986061i	$0.553209\pi$
$578$	−12.9777	−	12.9777i	−0.539799	−	0.539799i
$579$	−0.962845	−	1.82106i	−0.0400145	−	0.0756806i
$580$		0			0
$581$		−	1.48212i		−	0.0614886i
$582$	−3.38695	+	10.9867i	−0.140393	+	0.455413i
$583$	1.20452	−	1.20452i	0.0498860	−	0.0498860i
$584$	−13.6840			−0.566249
$585$		0			0
$586$	17.1812			0.709750
$587$	−1.33177	+	1.33177i	−0.0549679	+	0.0549679i	−0.734056	−	0.679088i	$-0.762375\pi$
$587$	−1.33177	+	1.33177i	−0.0549679	+	0.0549679i	0.679088	+	0.734056i	$0.262375\pi$
$588$	−0.510256	+	1.65519i	−0.0210426	+	0.0682587i
$589$		−	49.5079i		−	2.03994i
$590$		0			0
$591$	−20.9277	−	39.5812i	−0.860850	−	1.62815i
$592$	1.56975	+	1.56975i	0.0645164	+	0.0645164i
$593$	15.2499	+	15.2499i	0.626239	+	0.626239i	0.947120	−	0.320881i	$-0.103979\pi$
$593$	15.2499	+	15.2499i	0.626239	+	0.626239i	−0.320881	+	0.947120i	$0.603979\pi$
$594$	−3.09135	−	0.346753i	−0.126840	−	0.0142275i
$595$		0			0
$596$		−	12.7565i		−	0.522529i
$597$	−18.3225	−	5.64840i	−0.749889	−	0.231174i
$598$	−8.10286	+	8.10286i	−0.331351	+	0.331351i
$599$	5.47995			0.223905			0.111952	−	0.993714i	$-0.464290\pi$
$599$	5.47995			0.223905			0.111952	+	0.993714i	$0.464290\pi$
$600$		0			0
$601$	18.7009			0.762825			0.381412	−	0.924405i	$-0.375438\pi$
$601$	18.7009			0.762825			0.381412	+	0.924405i	$0.375438\pi$
$602$	0.325797	−	0.325797i	0.0132785	−	0.0132785i
$603$	4.65789	+	24.5729i	0.189684	+	1.00069i
$604$			18.5026i			0.752862i
$605$		0			0
$606$	−12.2904	+	6.49826i	−0.499262	+	0.263974i
$607$	1.74605	+	1.74605i	0.0708699	+	0.0708699i	0.741653	−	0.670783i	$-0.234042\pi$
$607$	1.74605	+	1.74605i	0.0708699	+	0.0708699i	−0.670783	+	0.741653i	$0.734042\pi$
$608$	−4.03198	−	4.03198i	−0.163518	−	0.163518i
$609$	−0.0628177	+	0.0332135i	−0.00254550	+	0.00134588i
$610$		0			0
$611$			8.00574i			0.323878i
$612$	−3.32203	−	17.5255i	−0.134285	−	0.708426i
$613$	−11.8503	+	11.8503i	−0.478628	+	0.478628i	−0.904693	−	0.426064i	$-0.859900\pi$
$613$	−11.8503	+	11.8503i	−0.478628	+	0.478628i	0.426064	+	0.904693i	$0.359900\pi$
$614$	−15.9098			−0.642067
$615$		0			0
$616$	0.598662			0.0241208
$617$	8.20715	−	8.20715i	0.330407	−	0.330407i	−0.522334	−	0.852741i	$-0.674938\pi$
$617$	8.20715	−	8.20715i	0.330407	−	0.330407i	0.852741	+	0.522334i	$0.174938\pi$
$618$	−21.4002	−	6.59720i	−0.860842	−	0.265378i
$619$		−	17.6445i		−	0.709194i	−0.935019	−	0.354597i	$-0.884618\pi$
$619$		−	17.6445i		−	0.709194i	0.935019	−	0.354597i	$-0.115382\pi$
$620$		0			0
$621$	16.3497	+	1.83393i	0.656092	+	0.0735931i
$622$	14.2759	+	14.2759i	0.572411	+	0.572411i
$623$	−12.8274	−	12.8274i	−0.513921	−	0.513921i
$624$	2.93004	+	5.54167i	0.117295	+	0.221845i
$625$		0			0
$626$		−	2.91013i		−	0.116312i
$627$	−1.74182	+	5.65017i	−0.0695616	+	0.225646i
$628$	0.0325033	−	0.0325033i	0.00129702	−	0.00129702i
$629$	13.1996			0.526302
$630$		0			0
$631$	25.6697			1.02190			0.510948	−	0.859612i	$-0.329295\pi$
$631$	25.6697			1.02190			0.510948	+	0.859612i	$0.329295\pi$
$632$	−8.32772	+	8.32772i	−0.331259	+	0.331259i
$633$	3.55946	−	11.5463i	0.141476	−	0.458924i
$634$			3.90148i			0.154948i
$635$		0			0
$636$	2.30362	+	4.35690i	0.0913443	+	0.172762i
$637$	−2.55914	−	2.55914i	−0.101397	−	0.101397i
$638$	0.0173667	+	0.0173667i	0.000687554	+	0.000687554i
$639$	24.3973	−	35.8098i	0.965143	−	1.41662i
$640$		0			0
$641$			12.3415i			0.487459i	0.969843	+	0.243729i	$0.0783709\pi$
$641$			12.3415i			0.487459i	−0.969843	+	0.243729i	$0.921629\pi$
$642$	0.872569	+	0.268993i	0.0344376	+	0.0106163i
$643$	−17.1538	+	17.1538i	−0.676482	+	0.676482i	−0.959202	−	0.282721i	$-0.908763\pi$
$643$	−17.1538	+	17.1538i	−0.676482	+	0.676482i	0.282721	+	0.959202i	$0.408763\pi$
$644$	−3.16624			−0.124767
$645$		0			0
$646$	−33.9038			−1.33393
$647$	−27.7839	+	27.7839i	−1.09230	+	1.09230i	−0.0970159	+	0.995283i	$0.530930\pi$
$647$	−27.7839	+	27.7839i	−1.09230	+	1.09230i	−0.995283	+	0.0970159i	$0.969070\pi$
$648$	3.59355	−	8.25145i	0.141168	−	0.324147i
$649$			5.60240i			0.219913i
$650$		0			0
$651$	−13.2945	+	7.02918i	−0.521053	+	0.275495i
$652$	9.48125	+	9.48125i	0.371315	+	0.371315i
$653$	−12.4080	−	12.4080i	−0.485561	−	0.485561i	0.421341	−	0.906902i	$-0.361559\pi$
$653$	−12.4080	−	12.4080i	−0.485561	−	0.485561i	−0.906902	+	0.421341i	$0.861559\pi$
$654$	12.8282	−	6.78260i	0.501621	−	0.265221i
$655$		0			0
$656$		−	5.79231i		−	0.226152i
$657$	−40.3338	+	7.64544i	−1.57357	+	0.298277i
$658$	−1.56415	+	1.56415i	−0.0609767	+	0.0609767i
$659$	−3.40992			−0.132832			−0.0664158	−	0.997792i	$-0.521156\pi$
$659$	−3.40992			−0.132832			−0.0664158	+	0.997792i	$0.521156\pi$
$660$		0			0
$661$	−48.9472			−1.90382			−0.951912	−	0.306372i	$-0.900885\pi$
$661$	−48.9472			−1.90382			−0.951912	+	0.306372i	$0.900885\pi$
$662$	20.3795	−	20.3795i	0.792070	−	0.792070i
$663$	35.6181	+	10.9802i	1.38329	+	0.426437i
$664$		−	1.48212i		−	0.0575173i
$665$		0			0
$666$	5.50391	+	3.74983i	0.213272	+	0.145303i
$667$	−0.0918500	−	0.0918500i	−0.00355645	−	0.00355645i
$668$	−14.2927	−	14.2927i	−0.553001	−	0.553001i
$669$	7.37540	+	13.9493i	0.285150	+	0.539313i
$670$		0			0
$671$			8.88560i			0.343025i
$672$	−0.510256	+	1.65519i	−0.0196836	+	0.0638502i
$673$	−13.0130	+	13.0130i	−0.501615	+	0.501615i	−0.911940	−	0.410325i	$-0.865415\pi$
$673$	−13.0130	+	13.0130i	−0.501615	+	0.501615i	0.410325	+	0.911940i	$0.365415\pi$
$674$	−12.8594			−0.495326
$675$		0			0
$676$	−0.0984218			−0.00378545
$677$	23.6302	−	23.6302i	0.908184	−	0.908184i	−0.0879415	−	0.996126i	$-0.528029\pi$
$677$	23.6302	−	23.6302i	0.908184	−	0.908184i	0.996126	+	0.0879415i	$0.0280289\pi$
$678$	−3.36119	+	10.9031i	−0.129086	+	0.418732i
$679$		−	6.63773i		−	0.254733i
$680$		0			0
$681$	4.35542	+	8.23755i	0.166900	+	0.315663i
$682$	3.67543	+	3.67543i	0.140739	+	0.140739i
$683$	−20.7794	−	20.7794i	−0.795100	−	0.795100i	0.187218	−	0.982318i	$-0.440053\pi$
$683$	−20.7794	−	20.7794i	−0.795100	−	0.795100i	−0.982318	+	0.187218i	$0.940053\pi$
$684$	−14.1370	−	9.63160i	−0.540543	−	0.368274i
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$	−26.8638	−	8.28152i	−1.02492	−	0.315960i
$688$	0.325797	−	0.325797i	0.0124209	−	0.0124209i
$689$	−10.2981			−0.392325
$690$		0			0
$691$	0.314417			0.0119610			0.00598048	−	0.999982i	$-0.498096\pi$
$691$	0.314417			0.0119610			0.00598048	+	0.999982i	$0.498096\pi$
$692$	13.1681	−	13.1681i	0.500575	−	0.500575i
$693$	1.76456	−	0.334480i	0.0670302	−	0.0127058i
$694$			18.8463i			0.715396i
$695$		0			0
$696$	−0.0628177	+	0.0332135i	−0.00238110	+	0.00125895i
$697$	−24.3529	−	24.3529i	−0.922433	−	0.922433i
$698$	−2.73302	−	2.73302i	−0.103446	−	0.103446i
$699$	−3.08557	+	1.63143i	−0.116707	+	0.0617062i
$700$		0			0
$701$		−	20.0199i		−	0.756143i	−0.925776	−	0.378071i	$-0.876587\pi$
$701$		−	20.0199i		−	0.756143i	0.925776	−	0.378071i	$-0.123413\pi$
$702$	11.7325	+	14.6971i	0.442816	+	0.554707i
$703$	8.95086	−	8.95086i	0.337588	−	0.337588i
$704$	0.598662			0.0225629
$705$		0			0
$706$	−31.0710			−1.16937
$707$	5.67569	−	5.67569i	0.213456	−	0.213456i
$708$	−15.4896	−	4.77508i	−0.582133	−	0.179459i
$709$			30.4538i			1.14372i	0.820352	+	0.571858i	$0.193777\pi$
$709$			30.4538i			1.14372i	−0.820352	+	0.571858i	$0.806223\pi$
$710$		0			0
$711$	−19.8933	+	29.1989i	−0.746056	+	1.09504i
$712$	−12.8274	−	12.8274i	−0.480729	−	0.480729i
$713$	−19.4388	−	19.4388i	−0.727990	−	0.727990i
$714$	4.81369	+	9.10428i	0.180148	+	0.340719i
$715$		0			0
$716$		−	3.19365i		−	0.119352i
$717$	−5.11723	+	16.5994i	−0.191106	+	0.619917i
$718$	−10.4939	+	10.4939i	−0.391627	+	0.391627i
$719$	−23.5199			−0.877145			−0.438573	−	0.898696i	$-0.644516\pi$
$719$	−23.5199			−0.877145			−0.438573	+	0.898696i	$0.644516\pi$
$720$		0			0
$721$	12.9292			0.481508
$722$	−9.55567	+	9.55567i	−0.355625	+	0.355625i
$723$	1.46935	−	4.76631i	0.0546456	−	0.177261i
$724$		−	14.7718i		−	0.548990i
$725$		0			0
$726$	8.61531	+	16.2944i	0.319744	+	0.604742i
$727$	−25.7430	−	25.7430i	−0.954754	−	0.954754i	0.0442655	−	0.999020i	$-0.485905\pi$
$727$	−25.7430	−	25.7430i	−0.954754	−	0.954754i	−0.999020	+	0.0442655i	$0.985905\pi$
$728$	−2.55914	−	2.55914i	−0.0948481	−	0.0948481i
$729$	5.98186	−	26.3290i	0.221550	−	0.975149i
$730$		0			0
$731$		−	2.73953i		−	0.101325i
$732$	−24.5670	−	7.57345i	−0.908023	−	0.279923i
$733$	−7.70481	+	7.70481i	−0.284584	+	0.284584i	−0.834934	−	0.550350i	$-0.814494\pi$
$733$	−7.70481	+	7.70481i	−0.284584	+	0.284584i	0.550350	+	0.834934i	$0.314494\pi$
$734$	−19.8912			−0.734196
$735$		0			0
$736$	−3.16624			−0.116709
$737$	−3.52913	+	3.52913i	−0.129997	+	0.129997i
$738$	−3.23624	−	17.0729i	−0.119128	−	0.628463i
$739$			37.0585i			1.36322i	0.731716	+	0.681610i	$0.238720\pi$
$739$			37.0585i			1.36322i	−0.731716	+	0.681610i	$0.761280\pi$
$740$		0			0
$741$	31.5991	−	16.7073i	1.16082	−	0.613759i
$742$	−2.01202	−	2.01202i	−0.0738634	−	0.0738634i
$743$	−7.81755	−	7.81755i	−0.286798	−	0.286798i	0.549015	−	0.835813i	$-0.315003\pi$
$743$	−7.81755	−	7.81755i	−0.286798	−	0.286798i	−0.835813	+	0.549015i	$0.815003\pi$
$744$	−13.2945	+	7.02918i	−0.487401	+	0.257702i
$745$		0			0
$746$			4.43719i			0.162457i
$747$	−0.828079	−	4.36856i	−0.0302978	−	0.159837i
$748$	2.51698	−	2.51698i	0.0920301	−	0.0920301i
$749$	−0.527173			−0.0192625
$750$		0			0
$751$	−31.7592			−1.15891			−0.579455	−	0.815004i	$-0.696735\pi$
$751$	−31.7592			−1.15891			−0.579455	+	0.815004i	$0.696735\pi$
$752$	−1.56415	+	1.56415i	−0.0570385	+	0.0570385i
$753$	6.18511	+	1.90673i	0.225398	+	0.0694851i
$754$		−	0.148477i		−	0.00540722i
$755$		0			0
$756$	−0.579214	+	5.16377i	−0.0210658	+	0.187804i
$757$	1.94012	+	1.94012i	0.0705150	+	0.0705150i	0.741485	−	0.670970i	$-0.234122\pi$
$757$	1.94012	+	1.94012i	0.0705150	+	0.0705150i	−0.670970	+	0.741485i	$0.734122\pi$
$758$	1.53507	+	1.53507i	0.0557564	+	0.0557564i
$759$	1.53458	+	2.90240i	0.0557016	+	0.105350i
$760$		0			0
$761$		−	41.3779i		−	1.49995i	−0.661467	−	0.749974i	$-0.730066\pi$
$761$		−	41.3779i		−	1.49995i	0.661467	−	0.749974i	$-0.269934\pi$
$762$	1.98552	−	6.44068i	0.0719277	−	0.233321i
$763$	−5.92404	+	5.92404i	−0.214465	+	0.214465i
$764$	−10.6699			−0.386024
$765$		0			0
$766$	−12.4984			−0.451585
$767$	23.9490	−	23.9490i	0.864747	−	0.864747i
$768$	−0.510256	+	1.65519i	−0.0184123	+	0.0597264i
$769$			9.04505i			0.326173i	0.986612	+	0.163086i	$0.0521449\pi$
$769$			9.04505i			0.326173i	−0.986612	+	0.163086i	$0.947855\pi$
$770$		0			0
$771$	11.1887	+	21.1615i	0.402950	+	0.762113i
$772$	0.840964	+	0.840964i	0.0302670	+	0.0302670i
$773$	−1.06409	−	1.06409i	−0.0382726	−	0.0382726i	0.687711	−	0.725984i	$-0.258615\pi$
$773$	−1.06409	−	1.06409i	−0.0382726	−	0.0382726i	−0.725984	+	0.687711i	$0.758615\pi$
$774$	0.778264	−	1.14232i	0.0279741	−	0.0410597i
$775$		0			0
$776$		−	6.63773i		−	0.238281i
$777$	−3.67445	−	1.13275i	−0.131820	−	0.0406372i
$778$	−1.46524	+	1.46524i	−0.0525315	+	0.0525315i
$779$	−33.0283			−1.18336
$780$		0			0
$781$	8.64687			0.309409
$782$	−13.3120	+	13.3120i	−0.476036	+	0.476036i
$783$	−0.166599	+	0.132994i	−0.00595377	+	0.00475283i
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$	23.3694	−	12.3561i	0.833559	−	0.440726i
$787$	29.2527	+	29.2527i	1.04275	+	1.04275i	0.999045	+	0.0437024i	$0.0139153\pi$
$787$	29.2527	+	29.2527i	1.04275	+	1.04275i	0.0437024	+	0.999045i	$0.486085\pi$
$788$	18.2786	+	18.2786i	0.651148	+	0.651148i
$789$	7.49007	−	3.96021i	0.266653	−	0.140987i
$790$		0			0
$791$		−	6.58726i		−	0.234216i
$792$	1.76456	−	0.334480i	0.0627010	−	0.0118852i
$793$	37.9839	−	37.9839i	1.34885	−	1.34885i
$794$	1.64144			0.0582524
$795$		0			0
$796$	11.0697			0.392356
$797$	27.0449	−	27.0449i	0.957979	−	0.957979i	−0.0411732	−	0.999152i	$-0.513110\pi$
$797$	27.0449	−	27.0449i	0.957979	−	0.957979i	0.999152	+	0.0411732i	$0.0131095\pi$
$798$	9.43801	+	2.90952i	0.334102	+	0.102996i
$799$			13.1524i			0.465300i
$800$		0			0
$801$	−44.9759	−	30.6422i	−1.58915	−	1.08269i
$802$	24.2957	+	24.2957i	0.857912	+	0.857912i
$803$	−5.79269	−	5.79269i	−0.204420	−	0.204420i
$804$	−6.74939	−	12.7653i	−0.238033	−	0.450199i
$805$		0			0
$806$		−	31.4232i		−	1.10684i
$807$	7.96801	−	25.8469i	0.280487	−	0.909853i
$808$	5.67569	−	5.67569i	0.199670	−	0.199670i
$809$	0.344140			0.0120993			0.00604965	−	0.999982i	$-0.498074\pi$
$809$	0.344140			0.0120993			0.00604965	+	0.999982i	$0.498074\pi$
$810$		0			0
$811$	−18.2804			−0.641911			−0.320955	−	0.947094i	$-0.604004\pi$
$811$	−18.2804			−0.641911			−0.320955	+	0.947094i	$0.604004\pi$
$812$	0.0290092	−	0.0290092i	0.00101802	−	0.00101802i
$813$	−2.42893	+	7.87905i	−0.0851864	+	0.276330i
$814$			1.32901i			0.0465817i
$815$		0			0
$816$	4.81369	+	9.10428i	0.168513	+	0.318714i
$817$	−1.85772	−	1.85772i	−0.0649934	−	0.0649934i
$818$	6.39669	+	6.39669i	0.223655	+	0.223655i
$819$	−8.97294	−	6.11328i	−0.313540	−	0.213615i
$820$		0			0
$821$		−	13.8883i		−	0.484704i	−0.970188	−	0.242352i	$-0.922081\pi$
$821$		−	13.8883i		−	0.484704i	0.970188	−	0.242352i	$-0.0779189\pi$
$822$	−8.62619	−	2.65926i	−0.300873	−	0.0927523i
$823$	6.37913	−	6.37913i	0.222362	−	0.222362i	−0.587130	−	0.809493i	$-0.699742\pi$
$823$	6.37913	−	6.37913i	0.222362	−	0.222362i	0.809493	+	0.587130i	$0.199742\pi$
$824$	12.9292			0.450410
$825$		0			0
$826$	9.35820			0.325613
$827$	2.61168	−	2.61168i	0.0908170	−	0.0908170i	−0.660239	−	0.751056i	$-0.729545\pi$
$827$	2.61168	−	2.61168i	0.0908170	−	0.0908170i	0.751056	+	0.660239i	$0.229545\pi$
$828$	−9.33254	+	1.76902i	−0.324328	+	0.0614777i
$829$			9.12880i			0.317056i	0.987354	+	0.158528i	$0.0506749\pi$
$829$			9.12880i			0.317056i	−0.987354	+	0.158528i	$0.949325\pi$
$830$		0			0
$831$	−18.7034	+	9.88900i	−0.648813	+	0.343045i
$832$	−2.55914	−	2.55914i	−0.0887223	−	0.0887223i
$833$	−4.20435	−	4.20435i	−0.145672	−	0.145672i
$834$	15.9405	−	8.42816i	0.551973	−	0.291843i
$835$		0			0
$836$		−	3.41362i		−	0.118062i
$837$	−35.2585	+	28.1464i	−1.21871	+	0.972883i
$838$	4.46617	−	4.46617i	0.154281	−	0.154281i
$839$	11.1650			0.385458			0.192729	−	0.981252i	$-0.438266\pi$
$839$	11.1650			0.385458			0.192729	+	0.981252i	$0.438266\pi$
$840$		0			0
$841$	−28.9983			−0.999942
$842$	−9.73068	+	9.73068i	−0.335341	+	0.335341i
$843$	18.4393	+	5.68443i	0.635085	+	0.195782i
$844$			6.97584i			0.240118i
$845$		0			0
$846$	−3.73643	+	5.48425i	−0.128461	+	0.188552i
$847$	−7.52475	−	7.52475i	−0.258553	−	0.258553i
$848$	−2.01202	−	2.01202i	−0.0690929	−	0.0690929i
$849$	−14.5743	−	27.5648i	−0.500188	−	0.946023i
$850$		0			0
$851$		−	7.02894i		−	0.240949i
$852$	−7.36997	+	23.9069i	−0.252491	+	0.819038i
$853$	25.4088	−	25.4088i	0.869980	−	0.869980i	−0.122490	−	0.992470i	$-0.539088\pi$
$853$	25.4088	−	25.4088i	0.869980	−	0.869980i	0.992470	+	0.122490i	$0.0390878\pi$
$854$	14.8424			0.507898
$855$		0			0
$856$	−0.527173			−0.0180184
$857$	5.49909	−	5.49909i	0.187845	−	0.187845i	−0.606919	−	0.794764i	$-0.707595\pi$
$857$	5.49909	−	5.49909i	0.187845	−	0.187845i	0.794764	+	0.606919i	$0.207595\pi$
$858$	−1.10555	+	3.58622i	−0.0377429	+	0.122432i
$859$			17.8783i			0.610000i	0.952352	+	0.305000i	$0.0986565\pi$
$859$			17.8783i			0.610000i	−0.952352	+	0.305000i	$0.901343\pi$
$860$		0			0
$861$	4.68938	+	8.86918i	0.159814	+	0.302261i
$862$	−10.7082	−	10.7082i	−0.364724	−	0.364724i
$863$	3.20549	+	3.20549i	0.109116	+	0.109116i	0.759557	−	0.650441i	$-0.225416\pi$
$863$	3.20549	+	3.20549i	0.109116	+	0.109116i	−0.650441	+	0.759557i	$0.725416\pi$
$864$	−0.579214	+	5.16377i	−0.0197053	+	0.175675i
$865$		0			0
$866$			10.3636i			0.352170i
$867$	30.3779	+	9.36482i	1.03169	+	0.318046i
$868$	6.13941	−	6.13941i	0.208385	−	0.208385i
$869$	−7.05055			−0.239173
$870$		0			0
$871$	30.1724			1.02235
$872$	−5.92404	+	5.92404i	−0.200613	+	0.200613i
$873$	−3.70859	−	19.5648i	−0.125517	−	0.662169i
$874$			18.0542i			0.610691i
$875$		0			0
$876$	20.9530	−	11.0784i	0.707935	−	0.374305i
$877$	11.2393	+	11.2393i	0.379526	+	0.379526i	0.870931	−	0.491405i	$-0.163517\pi$
$877$	11.2393	+	11.2393i	0.379526	+	0.379526i	−0.491405	+	0.870931i	$0.663517\pi$
$878$	2.92840	+	2.92840i	0.0988288	+	0.0988288i
$879$	−26.3079	+	13.9097i	−0.887343	+	0.469163i
$880$		0			0
$881$			7.11008i			0.239545i	0.992801	+	0.119772i	$0.0382165\pi$
$881$			7.11008i			0.239545i	−0.992801	+	0.119772i	$0.961784\pi$
$882$	−0.558713	−	2.94751i	−0.0188128	−	0.0992480i
$883$	9.93919	−	9.93919i	0.334480	−	0.334480i	−0.519805	−	0.854285i	$-0.673995\pi$
$883$	9.93919	−	9.93919i	0.334480	−	0.334480i	0.854285	+	0.519805i	$0.173995\pi$
$884$	−21.5191			−0.723765
$885$		0			0
$886$	39.8040			1.33724
$887$	−14.3454	+	14.3454i	−0.481672	+	0.481672i	−0.905665	−	0.423993i	$-0.860628\pi$
$887$	−14.3454	+	14.3454i	−0.481672	+	0.481672i	0.423993	+	0.905665i	$0.360628\pi$
$888$	−3.67445	−	1.13275i	−0.123307	−	0.0380127i
$889$			3.89122i			0.130507i
$890$		0			0
$891$	5.01420	−	1.97177i	0.167982	−	0.0660568i
$892$	−6.44180	−	6.44180i	−0.215687	−	0.215687i
$893$	8.91889	+	8.91889i	0.298459	+	0.298459i
$894$	10.3275	+	19.5328i	0.345405	+	0.653275i
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$	5.84712	−	18.9671i	0.195229	−	0.633292i
$898$	−2.05529	+	2.05529i	−0.0685860	+	0.0685860i
$899$	0.356198			0.0118799
$900$		0			0
$901$	−16.9185			−0.563635
$902$	2.45199	−	2.45199i	0.0816423	−	0.0816423i
$903$	−0.235099	+	0.762620i	−0.00782359	+	0.0253784i
$904$		−	6.58726i		−	0.219089i
$905$		0			0
$906$	−14.9795	−	28.3312i	−0.497661	−	0.941242i
$907$	−7.56005	−	7.56005i	−0.251027	−	0.251027i	0.570364	−	0.821392i	$-0.306802\pi$
$907$	−7.56005	−	7.56005i	−0.251027	−	0.251027i	−0.821392	+	0.570364i	$0.806802\pi$
$908$	−3.80409	−	3.80409i	−0.126243	−	0.126243i
$909$	13.5581	−	19.9002i	0.449693	−	0.660049i
$910$		0			0
$911$		−	31.3383i		−	1.03829i	−0.854688	−	0.519143i	$-0.826251\pi$
$911$		−	31.3383i		−	1.03829i	0.854688	−	0.519143i	$-0.173749\pi$
$912$	9.43801	+	2.90952i	0.312524	+	0.0963440i
$913$	0.627407	−	0.627407i	0.0207641	−	0.0207641i
$914$	40.4135			1.33676
$915$		0			0
$916$	16.2301			0.536258
$917$	−10.7920	+	10.7920i	−0.356383	+	0.356383i
$918$	19.2751	+	24.1455i	0.636173	+	0.796921i
$919$		−	6.42200i		−	0.211842i	−0.994375	−	0.105921i	$-0.966221\pi$
$919$		−	6.42200i		−	0.211842i	0.994375	−	0.105921i	$-0.0337791\pi$
$920$		0			0
$921$	24.3610	−	12.8804i	0.802724	−	0.424422i
$922$	−22.5469	−	22.5469i	−0.742542	−	0.742542i
$923$	−36.9634	−	36.9634i	−1.21666	−	1.21666i
$924$	−0.916670	+	0.484669i	−0.0301562	+	0.0159444i
$925$		0			0
$926$		−	1.46720i		−	0.0482153i
$927$	38.1090	−	7.22371i	1.25166	−	0.237258i
$928$	0.0290092	−	0.0290092i	0.000952273	−	0.000952273i
$929$	34.6015			1.13524			0.567619	−	0.823291i	$-0.307865\pi$
$929$	34.6015			1.13524			0.567619	+	0.823291i	$0.307865\pi$
$930$		0			0
$931$	−5.70208			−0.186878
$932$	1.42491	−	1.42491i	0.0466746	−	0.0466746i
$933$	−33.4168	−	10.3016i	−1.09402	−	0.337260i
$934$			25.3408i			0.829178i
$935$		0			0
$936$	−8.97294	−	6.11328i	−0.293290	−	0.199819i
$937$	−27.1028	−	27.1028i	−0.885410	−	0.885410i	0.108669	−	0.994078i	$-0.465341\pi$
$937$	−27.1028	−	27.1028i	−0.885410	−	0.885410i	−0.994078	+	0.108669i	$0.965341\pi$
$938$	5.89503	+	5.89503i	0.192479	+	0.192479i
$939$	2.35600	+	4.45598i	0.0768852	+	0.145416i
$940$		0			0
$941$			11.0796i			0.361184i	0.983558	+	0.180592i	$0.0578014\pi$
$941$			11.0796i			0.361184i	−0.983558	+	0.180592i	$0.942199\pi$
$942$	−0.0234548	+	0.0760833i	−0.000764198	+	0.00247893i
$943$	−12.9682	+	12.9682i	−0.422304	+	0.422304i
$944$	9.35820			0.304583
$945$		0			0
$946$	0.275831			0.00896804
$947$	−8.57908	+	8.57908i	−0.278783	+	0.278783i	−0.832623	−	0.553840i	$-0.813162\pi$
$947$	−8.57908	+	8.57908i	−0.278783	+	0.278783i	0.553840	+	0.832623i	$0.313162\pi$
$948$	6.00938	−	19.4934i	0.195176	−	0.633117i
$949$			49.5249i			1.60764i
$950$		0			0
$951$	−3.15859	−	5.97395i	−0.102424	−	0.193719i
$952$	−4.20435	−	4.20435i	−0.136264	−	0.136264i
$953$	−32.2510	−	32.2510i	−1.04471	−	1.04471i	−0.998952	−	0.0457608i	$-0.985429\pi$
$953$	−32.2510	−	32.2510i	−1.04471	−	1.04471i	−0.0457608	−	0.998952i	$-0.514571\pi$
$954$	−7.05459	−	4.80631i	−0.228401	−	0.155610i
$955$		0			0
$956$		−	10.0287i		−	0.324353i
$957$	−0.0406517	−	0.0125320i	−0.00131408	−	0.000405102i
$958$	−12.6816	+	12.6816i	−0.409723	+	0.409723i
$959$	5.21161			0.168292
$960$		0			0
$961$	44.3846			1.43176
$962$	5.68121	−	5.68121i	0.183170	−	0.183170i
$963$	−1.55385	+	0.294538i	−0.0500721	+	0.00949137i
$964$			2.87963i			0.0927465i
$965$		0			0
$966$	4.84814	−	2.56335i	0.155986	−	0.0824743i
$967$	11.6969	+	11.6969i	0.376148	+	0.376148i	0.869710	−	0.493563i	$-0.164306\pi$
$967$	11.6969	+	11.6969i	0.376148	+	0.376148i	−0.493563	+	0.869710i	$0.664306\pi$
$968$	−7.52475	−	7.52475i	−0.241855	−	0.241855i
$969$	51.9134	−	27.4480i	1.66770	−	0.881758i
$970$		0			0
$971$			36.2562i			1.16352i	0.813361	+	0.581759i	$0.197635\pi$
$971$			36.2562i			1.16352i	−0.813361	+	0.581759i	$0.802365\pi$
$972$	1.17782	+	15.5439i	0.0377787	+	0.498571i
$973$	−7.36130	+	7.36130i	−0.235992	+	0.235992i
$974$	25.0320			0.802078
$975$		0			0
$976$	14.8424			0.475095
$977$	29.9247	−	29.9247i	0.957377	−	0.957377i	−0.0417515	−	0.999128i	$-0.513294\pi$
$977$	29.9247	−	29.9247i	0.957377	−	0.957377i	0.999128	+	0.0417515i	$0.0132938\pi$
$978$	−22.1936	−	6.84178i	−0.709672	−	0.218776i
$979$		−	10.8602i		−	0.347092i
$980$		0			0
$981$	−14.1513	+	20.7710i	−0.451818	+	0.663168i
$982$	23.0059	+	23.0059i	0.734147	+	0.734147i
$983$	35.8103	+	35.8103i	1.14217	+	1.14217i	0.988052	+	0.154121i	$0.0492545\pi$
$983$	35.8103	+	35.8103i	1.14217	+	1.14217i	0.154121	+	0.988052i	$0.450746\pi$
$984$	4.68938	+	8.86918i	0.149492	+	0.282739i
$985$		0			0
$986$		−	0.243930i		−	0.00776830i
$987$	1.12870	−	3.66133i	0.0359271	−	0.116541i
$988$	−14.5924	+	14.5924i	−0.464248	+	0.464248i
$989$	−1.45883			−0.0463882
$990$		0			0
$991$	24.9238			0.791731			0.395866	−	0.918308i	$-0.370445\pi$
$991$	24.9238			0.791731			0.395866	+	0.918308i	$0.370445\pi$
$992$	6.13941	−	6.13941i	0.194926	−	0.194926i
$993$	−14.7060	+	47.7039i	−0.466682	+	1.51384i
$994$		−	14.4437i		−	0.458125i
$995$		0			0
$996$	1.19990	+	2.26942i	0.0380204	+	0.0719092i
$997$	−8.94298	−	8.94298i	−0.283227	−	0.283227i	0.551168	−	0.834395i	$-0.314182\pi$
$997$	−8.94298	−	8.94298i	−0.283227	−	0.283227i	−0.834395	+	0.551168i	$0.814182\pi$
$998$	−12.2224	−	12.2224i	−0.386894	−	0.386894i
$999$	−11.4634	−	1.28584i	−0.362686	−	0.0406820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.j.c.407.5		12
3.2	odd	2		1050.2.j.d.407.1		12
5.2	odd	4		210.2.j.b.113.6	yes	12
5.3	odd	4		1050.2.j.d.743.1		12
5.4	even	2		210.2.j.a.197.2	yes	12
15.2	even	4		210.2.j.a.113.2	✓	12
15.8	even	4	inner	1050.2.j.c.743.5		12
15.14	odd	2		210.2.j.b.197.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.2	✓	12	15.2	even	4
210.2.j.a.197.2	yes	12	5.4	even	2
210.2.j.b.113.6	yes	12	5.2	odd	4
210.2.j.b.197.6	yes	12	15.14	odd	2
1050.2.j.c.407.5		12	1.1	even	1	trivial
1050.2.j.c.743.5		12	15.8	even	4	inner
1050.2.j.d.407.1		12	3.2	odd	2
1050.2.j.d.743.1		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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.510256 + 1.65519i) q^{3} -1.00000i q^{4} +(0.809587 + 1.53120i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.47928 - 1.68914i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.510256 + 1.65519i) q^{3} -1.00000i q^{4} +(0.809587 + 1.53120i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.47928 - 1.68914i) q^{9} -0.598662i q^{11} +(1.65519 + 0.510256i) q^{12} +(-2.55914 + 2.55914i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.20435 + 4.20435i) q^{17} +(-2.94751 + 0.558713i) q^{18} +5.70208i q^{19} +(1.53120 - 0.809587i) q^{21} +(-0.423318 - 0.423318i) q^{22} +(2.23887 + 2.23887i) q^{23} +(1.53120 - 0.809587i) q^{24} +3.61917i q^{26} +(4.06090 - 3.24177i) q^{27} +(-0.707107 + 0.707107i) q^{28} -0.0410252 q^{29} -8.68243 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.990896 + 0.305471i) q^{33} +5.94585i q^{34} +(-1.68914 + 2.47928i) q^{36} +(-1.56975 - 1.56975i) q^{37} +(4.03198 + 4.03198i) q^{38} +(-2.93004 - 5.54167i) q^{39} +5.79231i q^{41} +(0.510256 - 1.65519i) q^{42} +(-0.325797 + 0.325797i) q^{43} -0.598662 q^{44} +3.16624 q^{46} +(1.56415 - 1.56415i) q^{47} +(0.510256 - 1.65519i) q^{48} +1.00000i q^{49} +(-4.81369 - 9.10428i) q^{51} +(2.55914 + 2.55914i) q^{52} +(2.01202 + 2.01202i) q^{53} +(0.579214 - 5.16377i) q^{54} +1.00000i q^{56} +(-9.43801 - 2.90952i) q^{57} +(-0.0290092 + 0.0290092i) q^{58} -9.35820 q^{59} -14.8424 q^{61} +(-6.13941 + 6.13941i) q^{62} +(0.558713 + 2.94751i) q^{63} +1.00000i q^{64} +(0.916670 - 0.484669i) q^{66} +(-5.89503 - 5.89503i) q^{67} +(4.20435 + 4.20435i) q^{68} +(-4.84814 + 2.56335i) q^{69} +14.4437i q^{71} +(0.558713 + 2.94751i) q^{72} +(9.67606 - 9.67606i) q^{73} -2.21997 q^{74} +5.70208 q^{76} +(-0.423318 + 0.423318i) q^{77} +(-5.99040 - 1.84671i) q^{78} -11.7772i q^{79} +(3.29363 + 8.37568i) q^{81} +(4.09578 + 4.09578i) q^{82} +(1.04802 + 1.04802i) q^{83} +(-0.809587 - 1.53120i) q^{84} +0.460746i q^{86} +(0.0209334 - 0.0679043i) q^{87} +(-0.423318 + 0.423318i) q^{88} +18.1407 q^{89} +3.61917 q^{91} +(2.23887 - 2.23887i) q^{92} +(4.43026 - 14.3710i) q^{93} -2.21204i q^{94} +(-0.809587 - 1.53120i) q^{96} +(4.69359 + 4.69359i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-1.01122 + 1.48425i) 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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