LMFDB - Embedded newform 252.2.bf.f.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(19,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("252.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bf (of order $6$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$0.856419 + 1.12541i$ of defining polynomial
Character	$\chi$	$=$	252.19
Dual form			252.2.bf.f.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40284 + 0.178976i) q^{2} +(1.93594 - 0.502151i) q^{4} +(3.33878 + 1.92764i) q^{5} +(-1.59285 + 2.11254i) q^{7} +(-2.62594 + 1.05092i) q^{8} +O(q^{10})$	\(q+(-1.40284 + 0.178976i) q^{2} +(1.93594 - 0.502151i) q^{4} +(3.33878 + 1.92764i) q^{5} +(-1.59285 + 2.11254i) q^{7} +(-2.62594 + 1.05092i) q^{8} +(-5.02878 - 2.10662i) q^{10} +(1.17975 - 0.681127i) q^{11} -0.369798i q^{13} +(1.85642 - 3.24865i) q^{14} +(3.49569 - 1.94426i) q^{16} +(-3.89853 + 2.25082i) q^{17} +(-0.0330925 + 0.0573178i) q^{19} +(7.43162 + 2.05523i) q^{20} +(-1.53309 + 1.16666i) q^{22} +(2.77902 + 1.60447i) q^{23} +(4.93162 + 8.54182i) q^{25} +(0.0661849 + 0.518768i) q^{26} +(-2.02283 + 4.88960i) q^{28} +3.11951 q^{29} +(3.01852 + 5.22824i) q^{31} +(-4.55593 + 3.35314i) q^{32} +(5.06618 - 3.85529i) q^{34} +(-9.39039 + 3.98287i) q^{35} +(2.74593 - 4.75609i) q^{37} +(0.0361650 - 0.0863307i) q^{38} +(-10.7932 - 1.55307i) q^{40} -8.45017i q^{41} -6.30324i q^{43} +(1.94188 - 1.91103i) q^{44} +(-4.18569 - 1.75344i) q^{46} +(-0.712838 + 1.23467i) q^{47} +(-1.92568 - 6.72992i) q^{49} +(-8.44708 - 11.1002i) q^{50} +(-0.185694 - 0.715904i) q^{52} +(-1.27259 - 2.20420i) q^{53} +5.25188 q^{55} +(1.96260 - 7.22137i) q^{56} +(-4.37618 + 0.558317i) q^{58} +(1.71879 + 2.97703i) q^{59} +(1.23998 + 0.715904i) q^{61} +(-5.17024 - 6.79415i) q^{62} +(5.79112 - 5.51933i) q^{64} +(0.712838 - 1.23467i) q^{65} +(-8.45877 + 4.88367i) q^{67} +(-6.41706 + 6.31509i) q^{68} +(12.4604 - 7.26800i) q^{70} -12.9518i q^{71} +(-1.56024 + 0.900803i) q^{73} +(-3.00088 + 7.16350i) q^{74} +(-0.0352827 + 0.127581i) q^{76} +(-0.440245 + 3.57719i) q^{77} +(-10.8156 - 6.24438i) q^{79} +(15.4192 + 0.246989i) q^{80} +(1.51238 + 11.8543i) q^{82} +12.2889 q^{83} -17.3551 q^{85} +(1.12813 + 8.84246i) q^{86} +(-2.38213 + 3.02842i) q^{88} +(-1.11951 - 0.646349i) q^{89} +(0.781213 + 0.589031i) q^{91} +(6.18569 + 1.71066i) q^{92} +(0.779023 - 1.85963i) q^{94} +(-0.220977 + 0.127581i) q^{95} -2.88422i q^{97} +(3.90592 + 9.09636i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8	$ 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8} - 13 q^{10} + 6 q^{11} + 10 q^{14} + 7 q^{16} + 6 q^{19} + 22 q^{20} - 6 q^{22} + 2 q^{25} - 12 q^{26} - 7 q^{28} + 16 q^{29} - 6 q^{31} - 21 q^{32} + 28 q^{34} - 12 q^{35} + 6 q^{37} - 8 q^{38} - 13 q^{40} - 19 q^{44} - 12 q^{46} + 4 q^{47} + 4 q^{49} - 2 q^{50} + 20 q^{52} + 4 q^{53} + 8 q^{55} + q^{56} - 23 q^{58} - 14 q^{59} + 12 q^{61} - 48 q^{62} + 2 q^{64} - 4 q^{65} - 42 q^{67} + 10 q^{68} + 35 q^{70} - 18 q^{73} + 28 q^{74} - 44 q^{76} - 8 q^{77} + 6 q^{79} + 33 q^{80} - 14 q^{82} + 4 q^{83} - 32 q^{85} + 42 q^{86} + 11 q^{88} + 34 q^{91} + 28 q^{92} - 16 q^{94} - 24 q^{95} + 19 q^{98}+O(q^{100}) $ 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8 - 13 * q^10 + 6 * q^11 + 10 * q^14 + 7 * q^16 + 6 * q^19 + 22 * q^20 - 6 * q^22 + 2 * q^25 - 12 * q^26 - 7 * q^28 + 16 * q^29 - 6 * q^31 - 21 * q^32 + 28 * q^34 - 12 * q^35 + 6 * q^37 - 8 * q^38 - 13 * q^40 - 19 * q^44 - 12 * q^46 + 4 * q^47 + 4 * q^49 - 2 * q^50 + 20 * q^52 + 4 * q^53 + 8 * q^55 + q^56 - 23 * q^58 - 14 * q^59 + 12 * q^61 - 48 * q^62 + 2 * q^64 - 4 * q^65 - 42 * q^67 + 10 * q^68 + 35 * q^70 - 18 * q^73 + 28 * q^74 - 44 * q^76 - 8 * q^77 + 6 * q^79 + 33 * q^80 - 14 * q^82 + 4 * q^83 - 32 * q^85 + 42 * q^86 + 11 * q^88 + 34 * q^91 + 28 * q^92 - 16 * q^94 - 24 * q^95 + 19 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.40284	+	0.178976i	−0.991960	+	0.126555i
$2$	−1.40284	+	0.178976i	−0.991960	+	0.126555i
$3$		0			0
$3$		0			0
$4$	1.93594	−	0.502151i	0.967968	−	0.251075i
$5$	3.33878	+	1.92764i	1.49315	+	0.862069i	0.999969	−	0.00785986i	$-0.00250190\pi$
$5$	3.33878	+	1.92764i	1.49315	+	0.862069i	0.493178	+	0.869929i	$0.335835\pi$
$6$		0			0
$7$	−1.59285	+	2.11254i	−0.602040	+	0.798466i
$7$	−1.59285	+	2.11254i	−0.602040	+	0.798466i
$8$	−2.62594	+	1.05092i	−0.928410	+	0.371558i
$9$		0			0
$10$	−5.02878	−	2.10662i	−1.59024	−	0.666172i
$11$	1.17975	−	0.681127i	0.355707	−	0.205367i	−0.311489	−	0.950250i	$-0.600828\pi$
$11$	1.17975	−	0.681127i	0.355707	−	0.205367i	0.667196	+	0.744882i	$0.267494\pi$
$12$		0			0
$13$		−	0.369798i		−	0.102563i	−0.998684	−	0.0512817i	$-0.983669\pi$
$13$		−	0.369798i		−	0.102563i	0.998684	−	0.0512817i	$-0.0163306\pi$
$14$	1.85642	−	3.24865i	0.496149	−	0.868237i
$15$		0			0
$16$	3.49569	−	1.94426i	0.873922	−	0.486065i
$17$	−3.89853	+	2.25082i	−0.945533	+	0.545904i	−0.891690	−	0.452646i	$-0.850480\pi$
$17$	−3.89853	+	2.25082i	−0.945533	+	0.545904i	−0.0538425	+	0.998549i	$0.517147\pi$
$18$		0			0
$19$	−0.0330925	+	0.0573178i	−0.00759193	+	0.0131496i	−0.869796	−	0.493411i	$-0.835750\pi$
$19$	−0.0330925	+	0.0573178i	−0.00759193	+	0.0131496i	0.862204	+	0.506560i	$0.169083\pi$
$20$	7.43162	+	2.05523i	1.66176	+	0.459562i
$21$		0			0
$22$	−1.53309	+	1.16666i	−0.326856	+	0.248733i
$23$	2.77902	+	1.60447i	0.579466	+	0.334555i	0.760921	−	0.648844i	$-0.224747\pi$
$23$	2.77902	+	1.60447i	0.579466	+	0.334555i	−0.181455	+	0.983399i	$0.558081\pi$
$24$		0			0
$25$	4.93162	+	8.54182i	0.986325	+	1.70836i
$26$	0.0661849	+	0.518768i	0.0129799	+	0.101739i
$27$		0			0
$28$	−2.02283	+	4.88960i	−0.382280	+	0.924047i
$29$	3.11951			0.579278			0.289639	−	0.957136i	$-0.406465\pi$
$29$	3.11951			0.579278			0.289639	+	0.957136i	$0.406465\pi$
$30$		0			0
$31$	3.01852	+	5.22824i	0.542143	+	0.939019i	0.998781	+	0.0493663i	$0.0157202\pi$
$31$	3.01852	+	5.22824i	0.542143	+	0.939019i	−0.456638	+	0.889653i	$0.650946\pi$
$32$	−4.55593	+	3.35314i	−0.805382	+	0.592757i
$33$		0			0
$34$	5.06618	−	3.85529i	0.868844	−	0.661177i
$35$	−9.39039	+	3.98287i	−1.58727	+	0.673228i
$36$		0			0
$37$	2.74593	−	4.75609i	0.451428	−	0.781897i	−0.547047	−	0.837102i	$-0.684248\pi$
$37$	2.74593	−	4.75609i	0.451428	−	0.781897i	0.998475	+	0.0552054i	$0.0175814\pi$
$38$	0.0361650	−	0.0863307i	0.00586674	−	0.0140047i
$39$		0			0
$40$	−10.7932	−	1.55307i	−1.70656	−	0.245563i
$41$		−	8.45017i		−	1.31970i	−0.751399	−	0.659848i	$-0.770621\pi$
$41$		−	8.45017i		−	1.31970i	0.751399	−	0.659848i	$-0.229379\pi$
$42$		0			0
$43$		−	6.30324i		−	0.961236i	−0.876930	−	0.480618i	$-0.840412\pi$
$43$		−	6.30324i		−	0.961236i	0.876930	−	0.480618i	$-0.159588\pi$
$44$	1.94188	−	1.91103i	0.292750	−	0.288098i
$45$		0			0
$46$	−4.18569	−	1.75344i	−0.617147	−	0.258531i
$47$	−0.712838	+	1.23467i	−0.103978	+	0.180095i	−0.913320	−	0.407242i	$-0.866491\pi$
$47$	−0.712838	+	1.23467i	−0.103978	+	0.180095i	0.809342	+	0.587338i	$0.199824\pi$
$48$		0			0
$49$	−1.92568	−	6.72992i	−0.275097	−	0.961417i
$50$	−8.44708	−	11.1002i	−1.19460	−	1.56980i
$51$		0			0
$52$	−0.185694	−	0.715904i	−0.0257511	−	0.0992781i
$53$	−1.27259	−	2.20420i	−0.174804	−	0.302770i	0.765289	−	0.643686i	$-0.222596\pi$
$53$	−1.27259	−	2.20420i	−0.174804	−	0.302770i	−0.940093	+	0.340917i	$0.889263\pi$
$54$		0			0
$55$	5.25188			0.708163
$56$	1.96260	−	7.22137i	0.262263	−	0.964996i
$57$		0			0
$58$	−4.37618	+	0.558317i	−0.574621	+	0.0733107i
$59$	1.71879	+	2.97703i	0.223767	+	0.387576i	0.955949	−	0.293533i	$-0.0948312\pi$
$59$	1.71879	+	2.97703i	0.223767	+	0.387576i	−0.732182	+	0.681109i	$0.761498\pi$
$60$		0			0
$61$	1.23998	+	0.715904i	0.158763	+	0.0916621i	0.577277	−	0.816549i	$-0.304115\pi$
$61$	1.23998	+	0.715904i	0.158763	+	0.0916621i	−0.418513	+	0.908211i	$0.637449\pi$
$62$	−5.17024	−	6.79415i	−0.656622	−	0.862858i
$63$		0			0
$64$	5.79112	−	5.51933i	0.723890	−	0.689916i
$65$	0.712838	−	1.23467i	0.0884167	−	0.153142i
$66$		0			0
$67$	−8.45877	+	4.88367i	−1.03340	+	0.596636i	−0.917958	−	0.396678i	$-0.870163\pi$
$67$	−8.45877	+	4.88367i	−1.03340	+	0.596636i	−0.115445	+	0.993314i	$0.536830\pi$
$68$	−6.41706	+	6.31509i	−0.778182	+	0.765817i
$69$		0			0
$70$	12.4604	−	7.26800i	1.48930	−	0.868692i
$71$		−	12.9518i		−	1.53710i	−0.639792	−	0.768549i	$-0.720979\pi$
$71$		−	12.9518i		−	1.53710i	0.639792	−	0.768549i	$-0.279021\pi$
$72$		0			0
$73$	−1.56024	+	0.900803i	−0.182612	+	0.105431i	−0.588519	−	0.808483i	$-0.700289\pi$
$73$	−1.56024	+	0.900803i	−0.182612	+	0.105431i	0.405907	+	0.913914i	$0.366956\pi$
$74$	−3.00088	+	7.16350i	−0.348845	+	0.832740i
$75$		0			0
$76$	−0.0352827	+	0.127581i	−0.00404720	+	0.0146345i
$77$	−0.440245	+	3.57719i	−0.0501706	+	0.407659i
$78$		0			0
$79$	−10.8156	−	6.24438i	−1.21685	−	0.702548i	−0.252606	−	0.967569i	$-0.581288\pi$
$79$	−10.8156	−	6.24438i	−1.21685	−	0.702548i	−0.964243	+	0.265021i	$0.914621\pi$
$80$	15.4192	+	0.246989i	1.72392	+	0.0276142i
$81$		0			0
$82$	1.51238	+	11.8543i	0.167014	+	1.30908i
$83$	12.2889			1.34888			0.674442	−	0.738327i	$-0.264384\pi$
$83$	12.2889			1.34888			0.674442	+	0.738327i	$0.264384\pi$
$84$		0			0
$85$	−17.3551			−1.88243
$86$	1.12813	+	8.84246i	0.121649	+	0.953507i
$87$		0			0
$88$	−2.38213	+	3.02842i	−0.253936	+	0.322831i
$89$	−1.11951	−	0.646349i	−0.118668	−	0.0685128i	0.439491	−	0.898247i	$-0.355159\pi$
$89$	−1.11951	−	0.646349i	−0.118668	−	0.0685128i	−0.558159	+	0.829734i	$0.688492\pi$
$90$		0			0
$91$	0.781213	+	0.589031i	0.0818934	+	0.0617472i
$92$	6.18569	+	1.71066i	0.644903	+	0.178349i
$93$		0			0
$94$	0.779023	−	1.85963i	0.0803501	−	0.191806i
$95$	−0.220977	+	0.127581i	−0.0226717	+	0.0130895i
$96$		0			0
$97$		−	2.88422i		−	0.292848i	−0.989222	−	0.146424i	$-0.953224\pi$
$97$		−	2.88422i		−	0.292848i	0.989222	−	0.146424i	$-0.0467764\pi$
$98$	3.90592	+	9.09636i	0.394557	+	0.918871i
$99$		0			0
$100$	13.8366	+	14.0600i	1.38366	+	1.40600i
$101$	−5.35949	+	3.09430i	−0.533289	+	0.307895i	−0.742355	−	0.670007i	$-0.766291\pi$
$101$	−5.35949	+	3.09430i	−0.533289	+	0.307895i	0.209066	+	0.977902i	$0.432958\pi$
$102$		0			0
$103$	8.89634	−	15.4089i	0.876583	−	1.51829i	0.0215154	−	0.999769i	$-0.493151\pi$
$103$	8.89634	−	15.4089i	0.876583	−	1.51829i	0.855067	−	0.518517i	$-0.173516\pi$
$104$	0.388629	+	0.971066i	0.0381082	+	0.0952209i
$105$		0			0
$106$	2.17975	+	2.86438i	0.211716	+	0.278213i
$107$	−5.27683	−	3.04658i	−0.510131	−	0.294524i	0.222757	−	0.974874i	$-0.428494\pi$
$107$	−5.27683	−	3.04658i	−0.510131	−	0.294524i	−0.732887	+	0.680350i	$0.761828\pi$
$108$		0			0
$109$	−3.93162	−	6.80977i	−0.376581	−	0.652258i	0.613981	−	0.789321i	$-0.289567\pi$
$109$	−3.93162	−	6.80977i	−0.376581	−	0.652258i	−0.990562	+	0.137063i	$0.956234\pi$
$110$	−7.36756	+	0.939961i	−0.702469	+	0.0896217i
$111$		0			0
$112$	−1.46076	+	10.4817i	−0.138029	+	0.990428i
$113$	−4.70669			−0.442768			−0.221384	−	0.975187i	$-0.571057\pi$
$113$	−4.70669			−0.442768			−0.221384	+	0.975187i	$0.571057\pi$
$114$		0			0
$115$	6.18569	+	10.7139i	0.576819	+	0.999080i
$116$	6.03917	−	1.56646i	0.560723	−	0.145442i
$117$		0			0
$118$	−2.94400	−	3.86868i	−0.271017	−	0.356141i
$119$	1.45481	−	11.8210i	0.133363	−	1.08363i
$120$		0			0
$121$	−4.57213	+	7.91917i	−0.415648	+	0.719924i
$122$	−1.86763	−	0.782374i	−0.169087	−	0.0708328i
$123$		0			0
$124$	8.46903	+	8.60577i	0.760541	+	0.772821i
$125$			18.7492i			1.67698i
$126$		0			0
$127$			2.70312i			0.239863i	0.992782	+	0.119931i	$0.0382675\pi$
$127$			2.70312i			0.239863i	−0.992782	+	0.119931i	$0.961733\pi$
$128$	−7.13620	+	8.77922i	−0.630757	+	0.775981i
$129$		0			0
$130$	−0.779023	+	1.85963i	−0.0683249	+	0.163100i
$131$	−3.88644	+	6.73151i	−0.339560	+	0.588135i	−0.984350	−	0.176225i	$-0.943611\pi$
$131$	−3.88644	+	6.73151i	−0.339560	+	0.588135i	0.644790	+	0.764360i	$0.276945\pi$
$132$		0			0
$133$	−0.0683751	−	0.161208i	−0.00592888	−	0.0139785i
$134$	10.9923	−	8.36494i	0.949587	−	0.722621i
$135$		0			0
$136$	7.87187	−	10.0076i	0.675007	−	0.858143i
$137$	1.42568	+	2.46934i	0.121804	+	0.210970i	0.920479	−	0.390792i	$-0.127799\pi$
$137$	1.42568	+	2.46934i	0.121804	+	0.210970i	−0.798675	+	0.601762i	$0.794465\pi$
$138$		0			0
$139$	7.15656			0.607011			0.303506	−	0.952830i	$-0.401843\pi$
$139$	7.15656			0.607011			0.303506	+	0.952830i	$0.401843\pi$
$140$	−16.1792	+	12.4260i	−1.36739	+	1.05019i
$141$		0			0
$142$	2.31806	+	18.1694i	0.194528	+	1.52474i
$143$	−0.251879	−	0.436267i	−0.0210632	−	0.0364825i
$144$		0			0
$145$	10.4153	+	6.01330i	0.864948	+	0.499378i
$146$	2.02754	−	1.54293i	0.167801	−	0.127694i
$147$		0			0
$148$	2.92767	−	10.5864i	0.240653	−	0.870193i
$149$	10.6776	−	18.4941i	0.874739	−	1.51509i	0.0176994	−	0.999843i	$-0.494366\pi$
$149$	10.6776	−	18.4941i	0.874739	−	1.51509i	0.857040	−	0.515250i	$-0.172301\pi$
$150$		0			0
$151$	19.2373	−	11.1067i	1.56551	−	0.903848i	0.568828	−	0.822457i	$-0.307397\pi$
$151$	19.2373	−	11.1067i	1.56551	−	0.903848i	0.996682	−	0.0813911i	$-0.0259363\pi$
$152$	0.0266621	−	0.185291i	0.00216258	−	0.0150291i
$153$		0			0
$154$	−0.0226371	−	5.09703i	−0.00182415	−	0.410731i
$155$			23.2746i			1.86946i
$156$		0			0
$157$	−4.71898	+	2.72451i	−0.376616	+	0.217439i	−0.676345	−	0.736585i	$-0.736437\pi$
$157$	−4.71898	+	2.72451i	−0.376616	+	0.217439i	0.299729	+	0.954024i	$0.403104\pi$
$158$	16.2902	+	6.82416i	1.29598	+	0.542901i
$159$		0			0
$160$	−21.6749	+	2.41318i	−1.71355	+	0.190778i
$161$	−7.81607	+	3.31513i	−0.615993	+	0.261269i
$162$		0			0
$163$	−4.11951	−	2.37840i	−0.322665	−	0.186291i	0.329915	−	0.944011i	$-0.392980\pi$
$163$	−4.11951	−	2.37840i	−0.322665	−	0.186291i	−0.652580	+	0.757720i	$0.726313\pi$
$164$	−4.24326	−	16.3590i	−0.331343	−	1.27742i
$165$		0			0
$166$	−17.2394	+	2.19942i	−1.33804	+	0.170708i
$167$	14.0618			1.08814			0.544068	−	0.839041i	$-0.316884\pi$
$167$	14.0618			1.08814			0.544068	+	0.839041i	$0.316884\pi$
$168$		0			0
$169$	12.8632			0.989481
$170$	24.3465	−	3.10615i	1.86729	−	0.238231i
$171$		0			0
$172$	−3.16518	−	12.2027i	−0.241342	−	0.930445i
$173$	−1.53904	−	0.888566i	−0.117011	−	0.0675564i	0.440352	−	0.897825i	$-0.354854\pi$
$173$	−1.53904	−	0.888566i	−0.117011	−	0.0675564i	−0.557363	+	0.830269i	$0.688187\pi$
$174$		0			0
$175$	−25.9003	−	3.18755i	−1.95788	−	0.240956i
$176$	2.79974	−	4.67474i	0.211038	−	0.352372i
$177$		0			0
$178$	1.68618	+	0.706360i	0.126384	+	0.0529440i
$179$	−2.81607	+	1.62586i	−0.210483	+	0.121522i	−0.601536	−	0.798846i	$-0.705444\pi$
$179$	−2.81607	+	1.62586i	−0.210483	+	0.121522i	0.391053	+	0.920368i	$0.372111\pi$
$180$		0			0
$181$			23.5015i			1.74685i	0.486954	+	0.873427i	$0.338108\pi$
$181$			23.5015i			1.74685i	−0.486954	+	0.873427i	$0.661892\pi$
$182$	−1.20134	−	0.686499i	−0.0890494	−	0.0508867i
$183$		0			0
$184$	−8.98372	−	1.29270i	−0.662289	−	0.0952989i
$185$	18.3361	−	10.5864i	1.34810	−	0.778324i
$186$		0			0
$187$	−3.06618	+	5.31079i	−0.224222	+	0.388363i
$188$	−0.760017	+	2.74820i	−0.0554300	+	0.200433i
$189$		0			0
$190$	0.287162	−	0.218526i	0.0208329	−	0.0158535i
$191$	−20.6956	−	11.9486i	−1.49748	−	0.864571i	−0.497485	−	0.867473i	$-0.665743\pi$
$191$	−20.6956	−	11.9486i	−1.49748	−	0.864571i	−0.999996	+	0.00290157i	$0.999076\pi$
$192$		0			0
$193$	−9.93757	−	17.2124i	−0.715322	−	1.23897i	−0.962835	−	0.270090i	$-0.912947\pi$
$193$	−9.93757	−	17.2124i	−0.715322	−	1.23897i	0.247513	−	0.968885i	$-0.420387\pi$
$194$	0.516207	+	4.04611i	0.0370615	+	0.290494i
$195$		0			0
$196$	−7.10742	−	12.0617i	−0.507673	−	0.861550i
$197$	−19.0198			−1.35511			−0.677553	−	0.735474i	$-0.736959\pi$
$197$	−19.0198			−1.35511			−0.677553	+	0.735474i	$0.736959\pi$
$198$		0			0
$199$	−7.42568	−	12.8616i	−0.526392	−	0.911738i	−0.999527	−	0.0307481i	$-0.990211\pi$
$199$	−7.42568	−	12.8616i	−0.526392	−	0.911738i	0.473135	−	0.880990i	$-0.343122\pi$
$200$	−21.9270	−	17.2476i	−1.55047	−	1.21959i
$201$		0			0
$202$	6.96472	−	5.30004i	0.490036	−	0.372910i
$203$	−4.96890	+	6.59010i	−0.348748	+	0.462534i
$204$		0			0
$205$	16.2889	−	28.2132i	1.13767	−	1.97050i
$206$	−9.72234	+	23.2085i	−0.677388	+	1.61701i
$207$		0			0
$208$	−0.718983	−	1.29270i	−0.0498525	−	0.0896325i
$209$			0.0901606i			0.00623654i
$210$		0			0
$211$			19.6676i			1.35398i	0.735994	+	0.676988i	$0.236715\pi$
$211$			19.6676i			1.35398i	−0.735994	+	0.676988i	$0.763285\pi$
$212$	−3.57050	−	3.62815i	−0.245223	−	0.249182i
$213$		0			0
$214$	7.94783	+	3.32945i	0.543303	+	0.227596i
$215$	12.1504	−	21.0451i	0.828651	−	1.43527i
$216$		0			0
$217$	−15.8529	−	1.95102i	−1.07617	−	0.132444i
$218$	6.73424	+	8.84937i	0.456100	+	0.599355i
$219$		0			0
$220$	10.1673	−	2.63723i	0.685479	−	0.177802i
$221$	0.832347	+	1.44167i	0.0559897	+	0.0969771i
$222$		0			0
$223$	8.10323			0.542633			0.271316	−	0.962490i	$-0.412541\pi$
$223$	8.10323			0.542633			0.271316	+	0.962490i	$0.412541\pi$
$224$	0.173245	−	14.9656i	0.0115754	−	0.999933i
$225$		0			0
$226$	6.60275	−	0.842385i	0.439208	−	0.0560346i
$227$	6.04300	+	10.4668i	0.401088	+	0.694704i	0.993857	−	0.110668i	$-0.0352989\pi$
$227$	6.04300	+	10.4668i	0.401088	+	0.694704i	−0.592770	+	0.805372i	$0.701966\pi$
$228$		0			0
$229$	20.5963	+	11.8913i	1.36104	+	0.785799i	0.989763	−	0.142722i	$-0.0455856\pi$
$229$	20.5963	+	11.8913i	1.36104	+	0.785799i	0.371280	+	0.928521i	$0.378919\pi$
$230$	−10.5951	−	13.9229i	−0.698620	−	0.918047i
$231$		0			0
$232$	−8.19164	+	3.27837i	−0.537808	+	0.215235i
$233$	−9.96472	+	17.2594i	−0.652810	+	1.13070i	0.329628	+	0.944111i	$0.393077\pi$
$233$	−9.96472	+	17.2594i	−0.652810	+	1.13070i	−0.982438	+	0.186590i	$0.940257\pi$
$234$		0			0
$235$	−4.76002	+	2.74820i	−0.310509	+	0.179273i
$236$	4.82237	+	4.90024i	0.313910	+	0.318978i
$237$		0			0
$238$	0.0748055	+	16.8434i	0.00484892	+	1.09180i
$239$		−	9.60993i		−	0.621615i	−0.950473	−	0.310807i	$-0.899401\pi$
$239$		−	9.60993i		−	0.621615i	0.950473	−	0.310807i	$-0.100599\pi$
$240$		0			0
$241$	−9.01386	+	5.20415i	−0.580634	+	0.335229i	−0.761385	−	0.648300i	$-0.775480\pi$
$241$	−9.01386	+	5.20415i	−0.580634	+	0.335229i	0.180752	+	0.983529i	$0.442147\pi$
$242$	4.99664	−	11.9276i	0.321196	−	0.766738i
$243$		0			0
$244$	2.76002	+	0.763286i	0.176692	+	0.0488644i
$245$	6.54348	−	26.1817i	0.418047	−	1.67269i
$246$		0			0
$247$	0.0211960	+	0.0122375i	0.00134867	+	0.000778654i
$248$	−13.4209	−	10.5568i	−0.852231	−	0.670357i
$249$		0			0
$250$	−3.35566	−	26.3022i	−0.212231	−	1.66350i
$251$	−20.6860			−1.30569			−0.652846	−	0.757491i	$-0.726425\pi$
$251$	−20.6860			−1.30569			−0.652846	+	0.757491i	$0.726425\pi$
$252$		0			0
$253$	4.37139			0.274827
$254$	−0.483793	−	3.79205i	−0.0303559	−	0.237934i
$255$		0			0
$256$	8.43969	−	13.5931i	0.527481	−	0.849567i
$257$	15.3732	+	8.87569i	0.958951	+	0.553651i	0.895850	−	0.444357i	$-0.146568\pi$
$257$	15.3732	+	8.87569i	0.958951	+	0.553651i	0.0631009	+	0.998007i	$0.479901\pi$
$258$		0			0
$259$	5.67360	+	13.3766i	0.352540	+	0.831183i
$260$	0.760017	−	2.74820i	0.0471343	−	0.170436i
$261$		0			0
$262$	4.24728	−	10.1388i	0.262398	−	0.626379i
$263$	−1.80241	+	1.04062i	−0.111141	+	0.0641675i	−0.554540	−	0.832157i	$-0.687106\pi$
$263$	−1.80241	+	1.04062i	−0.111141	+	0.0641675i	0.443399	+	0.896324i	$0.353773\pi$
$264$		0			0
$265$		−	9.81243i		−	0.602773i
$266$	0.124772	+	0.213912i	0.00765026	+	0.0131158i
$267$		0			0
$268$	−13.9233	+	13.7020i	−0.850500	+	0.836986i
$269$	−3.08075	+	1.77867i	−0.187837	+	0.108448i	−0.590970	−	0.806694i	$-0.701255\pi$
$269$	−3.08075	+	1.77867i	−0.187837	+	0.108448i	0.403133	+	0.915142i	$0.367921\pi$
$270$		0			0
$271$	−6.18399	+	10.7110i	−0.375650	+	0.650646i	−0.990424	−	0.138058i	$-0.955914\pi$
$271$	−6.18399	+	10.7110i	−0.375650	+	0.650646i	0.614774	+	0.788704i	$0.289247\pi$
$272$	−9.25188	+	15.4479i	−0.560978	+	0.936668i
$273$		0			0
$274$	−2.44195	−	3.20894i	−0.147524	−	0.193859i
$275$	11.6361	+	6.71812i	0.701685	+	0.405118i
$276$		0			0
$277$	5.93162	+	10.2739i	0.356397	+	0.617297i	0.987356	−	0.158519i	$-0.0506718\pi$
$277$	5.93162	+	10.2739i	0.356397	+	0.617297i	−0.630959	+	0.775816i	$0.717338\pi$
$278$	−10.0395	+	1.28085i	−0.602131	+	0.0768204i
$279$		0			0
$280$	20.4729	−	20.3274i	1.22349	−	1.21479i
$281$	19.3428			1.15390			0.576948	−	0.816781i	$-0.304244\pi$
$281$	19.3428			1.15390			0.576948	+	0.816781i	$0.304244\pi$
$282$		0			0
$283$	12.4707	+	21.5998i	0.741304	+	1.28398i	0.951902	+	0.306404i	$0.0991257\pi$
$283$	12.4707	+	21.5998i	0.741304	+	1.28398i	−0.210598	+	0.977573i	$0.567541\pi$
$284$	−6.50376	−	25.0739i	−0.385927	−	1.48786i
$285$		0			0
$286$	0.431428	+	0.566934i	0.0255109	+	0.0335235i
$287$	17.8514	+	13.4598i	1.05373	+	0.794509i
$288$		0			0
$289$	1.63237	−	2.82735i	0.0960218	−	0.166315i
$290$	−15.6873	−	6.57162i	−0.921192	−	0.385899i
$291$		0			0
$292$	−2.56818	+	2.52737i	−0.150291	+	0.147903i
$293$		−	6.88234i		−	0.402071i	−0.979584	−	0.201035i	$-0.935569\pi$
$293$		−	6.88234i		−	0.402071i	0.979584	−	0.201035i	$-0.0644306\pi$
$294$		0			0
$295$			13.2528i			0.771610i
$296$	−2.21236	+	15.3750i	−0.128591	+	0.893652i
$297$		0			0
$298$	−11.6689	+	27.8553i	−0.675963	+	1.61361i
$299$	0.593329	−	1.02768i	0.0343131	−	0.0594321i
$300$		0			0
$301$	13.3159	+	10.0401i	0.767514	+	0.578702i
$302$	−24.9991	+	19.0239i	−1.43854	+	1.09470i
$303$		0			0
$304$	−0.00424013	+	0.264706i	−0.000243188	+	0.0151819i
$305$	2.76002	+	4.78049i	0.158038	+	0.273730i
$306$		0			0
$307$	−17.4213			−0.994286			−0.497143	−	0.867669i	$-0.665618\pi$
$307$	−17.4213			−0.994286			−0.497143	+	0.867669i	$0.665618\pi$
$308$	0.944003	+	7.14629i	0.0537896	+	0.407197i
$309$		0			0
$310$	−4.16559	−	32.6505i	−0.236590	−	1.85443i
$311$	12.5580	+	21.7512i	0.712101	+	1.23340i	0.964067	+	0.265660i	$0.0855898\pi$
$311$	12.5580	+	21.7512i	0.712101	+	1.23340i	−0.251965	+	0.967736i	$0.581077\pi$
$312$		0			0
$313$	−19.1361	−	11.0482i	−1.08164	−	0.624484i	−0.150300	−	0.988640i	$-0.548024\pi$
$313$	−19.1361	−	11.0482i	−1.08164	−	0.624484i	−0.931338	+	0.364156i	$0.881357\pi$
$314$	6.13237	−	4.66664i	0.346070	−	0.263354i
$315$		0			0
$316$	−24.0739	−	6.65767i	−1.35426	−	0.374523i
$317$	−0.811634	+	1.40579i	−0.0455859	+	0.0789571i	−0.887918	−	0.460002i	$-0.847849\pi$
$317$	−0.811634	+	1.40579i	−0.0455859	+	0.0789571i	0.842332	+	0.538959i	$0.181182\pi$
$318$		0			0
$319$	3.68023	−	2.12478i	0.206053	−	0.118965i
$320$	29.9746	−	7.26459i	1.67563	−	0.406103i
$321$		0			0
$322$	10.3714	−	6.04950i	0.577975	−	0.337125i
$323$		−	0.297941i		−	0.0165779i
$324$		0			0
$325$	3.15875	−	1.82370i	0.175216	−	0.101161i
$326$	6.20470	+	2.59923i	0.343647	+	0.143958i
$327$		0			0
$328$	8.88049	+	22.1896i	0.490343	+	1.22522i
$329$	−1.47286	−	3.47255i	−0.0812012	−	0.191448i
$330$		0			0
$331$	−23.0949	−	13.3338i	−1.26941	−	0.732894i	−0.294534	−	0.955641i	$-0.595164\pi$
$331$	−23.0949	−	13.3338i	−1.26941	−	0.732894i	−0.974876	+	0.222747i	$0.928498\pi$
$332$	23.7906	−	6.17089i	1.30568	−	0.338672i
$333$		0			0
$334$	−19.7265	+	2.51673i	−1.07939	+	0.137709i
$335$	−37.6559			−2.05736
$336$		0			0
$337$	29.8426			1.62563			0.812815	−	0.582522i	$-0.197934\pi$
$337$	29.8426			1.62563			0.812815	+	0.582522i	$0.197934\pi$
$338$	−18.0451	+	2.30221i	−0.981525	+	0.125224i
$339$		0			0
$340$	−33.5984	+	8.71488i	−1.82213	+	0.472631i
$341$	7.12218	+	4.11199i	0.385688	+	0.222677i
$342$		0			0
$343$	17.2845	+	6.65165i	0.933278	+	0.359155i
$344$	6.62423	+	16.5519i	0.357155	+	0.892421i
$345$		0			0
$346$	2.31806	+	0.971066i	0.124620	+	0.0522048i
$347$	0.820451	−	0.473688i	0.0440441	−	0.0254289i	−0.477816	−	0.878460i	$-0.658572\pi$
$347$	0.820451	−	0.473688i	0.0440441	−	0.0254289i	0.521860	+	0.853031i	$0.325238\pi$
$348$		0			0
$349$			6.41788i			0.343541i	0.985137	+	0.171771i	$0.0549488\pi$
$349$			6.41788i			0.343541i	−0.985137	+	0.171771i	$0.945051\pi$
$350$	36.9045	−	0.163902i	1.97263	−	0.00876091i
$351$		0			0
$352$	−3.09092	+	7.05901i	−0.164747	+	0.376247i
$353$	−12.0146	+	6.93665i	−0.639474	+	0.369200i	−0.784412	−	0.620240i	$-0.787035\pi$
$353$	−12.0146	+	6.93665i	−0.639474	+	0.369200i	0.144938	+	0.989441i	$0.453702\pi$
$354$		0			0
$355$	24.9665	−	43.2432i	1.32508	−	2.29511i
$356$	−2.49186	−	0.689127i	−0.132068	−	0.0365237i
$357$		0			0
$358$	3.65951	−	2.78483i	0.193411	−	0.147183i
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	0.649906	−	0.760014i	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$		0			0
$361$	9.49781	+	16.4507i	0.499885	+	0.865826i
$362$	−4.20621	−	32.9689i	−0.221074	−	1.73281i
$363$		0			0
$364$	1.80816	+	0.748039i	0.0947734	+	0.0392079i
$365$	−6.94571			−0.363555
$366$		0			0
$367$	−9.65903	−	16.7299i	−0.504197	−	0.873295i	−0.999988	−	0.00485350i	$-0.998455\pi$
$367$	−9.65903	−	16.7299i	−0.504197	−	0.873295i	0.495791	−	0.868442i	$-0.334878\pi$
$368$	12.8341	+	0.205580i	0.669024	+	0.0107166i
$369$		0			0
$370$	−23.8280	+	18.1327i	−1.23876	+	0.942675i
$371$	6.68350	+	0.822539i	0.346990	+	0.0427041i
$372$		0			0
$373$	−5.63832	+	9.76585i	−0.291941	+	0.505657i	−0.974269	−	0.225390i	$-0.927634\pi$
$373$	−5.63832	+	9.76585i	−0.291941	+	0.505657i	0.682328	+	0.731047i	$0.260968\pi$
$374$	3.35087	−	7.99897i	0.173269	−	0.413617i
$375$		0			0
$376$	0.574323	−	3.99131i	0.0296185	−	0.205836i
$377$		−	1.15359i		−	0.0594128i
$378$		0			0
$379$		−	25.1457i		−	1.29165i	−0.763486	−	0.645824i	$-0.776514\pi$
$379$		−	25.1457i		−	1.29165i	0.763486	−	0.645824i	$-0.223486\pi$
$380$	−0.363732	+	0.357952i	−0.0186590	+	0.0183626i
$381$		0			0
$382$	31.1712	+	13.0580i	1.59486	+	0.668105i
$383$	8.88226	−	15.3845i	0.453862	−	0.786112i	−0.544760	−	0.838592i	$-0.683379\pi$
$383$	8.88226	−	15.3845i	0.453862	−	0.786112i	0.998622	+	0.0524799i	$0.0167126\pi$
$384$		0			0
$385$	−8.36544	+	11.0948i	−0.426342	+	0.565444i
$386$	17.0215	+	22.3677i	0.866369	+	1.13848i
$387$		0			0
$388$	−1.44831	−	5.58367i	−0.0735270	−	0.283468i
$389$	7.07233	+	12.2496i	0.358581	+	0.621081i	0.987724	−	0.156209i	$-0.0499272\pi$
$389$	7.07233	+	12.2496i	0.358581	+	0.621081i	−0.629143	+	0.777290i	$0.716594\pi$
$390$		0			0
$391$	−14.4455			−0.730539
$392$	12.1293	+	15.6486i	0.612624	+	0.790374i
$393$		0			0
$394$	26.6818	−	3.40409i	1.34421	−	0.171496i
$395$	−24.0739	−	41.6972i	−1.21129	−	2.09801i
$396$		0			0
$397$	−10.9558	−	6.32534i	−0.549856	−	0.317460i	0.199208	−	0.979957i	$-0.436163\pi$
$397$	−10.9558	−	6.32534i	−0.549856	−	0.317460i	−0.749064	+	0.662498i	$0.769497\pi$
$398$	12.7190	+	16.7139i	0.637545	+	0.837790i
$399$		0			0
$400$	33.8470	+	20.2712i	1.69235	+	1.01356i
$401$	−12.3904	+	21.4608i	−0.618747	+	1.07170i	0.370968	+	0.928646i	$0.379026\pi$
$401$	−12.3904	+	21.4608i	−0.618747	+	1.07170i	−0.989715	+	0.143055i	$0.954307\pi$
$402$		0			0
$403$	1.93339	−	1.11624i	0.0963090	−	0.0556040i
$404$	−8.82182	+	8.68164i	−0.438902	+	0.431928i
$405$		0			0
$406$	5.79112	−	10.1342i	0.287408	−	0.502951i
$407$		−	7.48131i		−	0.370835i
$408$		0			0
$409$	−5.02003	+	2.89832i	−0.248225	+	0.143313i	−0.618951	−	0.785430i	$-0.712442\pi$
$409$	−5.02003	+	2.89832i	−0.248225	+	0.143313i	0.370726	+	0.928742i	$0.379109\pi$
$410$	−17.8013	+	42.4941i	−0.879144	+	2.09863i
$411$		0			0
$412$	9.48515	−	34.2980i	0.467300	−	1.68974i
$413$	−9.02686	−	1.11094i	−0.444183	−	0.0546656i
$414$		0			0
$415$	41.0300	+	23.6887i	2.01408	+	1.16283i
$416$	1.23998	+	1.68477i	0.0607951	+	0.0826027i
$417$		0			0
$418$	−0.0161366	−	0.126481i	−0.000789267	−	0.00618640i
$419$	2.42966			0.118697			0.0593484	−	0.998237i	$-0.481098\pi$
$419$	2.42966			0.118697			0.0593484	+	0.998237i	$0.481098\pi$
$420$		0			0
$421$	−25.9373			−1.26411			−0.632054	−	0.774924i	$-0.717788\pi$
$421$	−25.9373			−1.26411			−0.632054	+	0.774924i	$0.717788\pi$
$422$	−3.52003	−	27.5906i	−0.171353	−	1.34309i
$423$		0			0
$424$	5.65819	+	4.45069i	0.274786	+	0.216144i
$425$	−38.4522	−	22.2004i	−1.86521	−	1.07688i
$426$		0			0
$427$	−3.48748	+	1.47919i	−0.168771	+	0.0715830i
$428$	−11.7454	−	3.24822i	−0.567738	−	0.157009i
$429$		0			0
$430$	−13.2785	+	31.6976i	−0.640348	+	1.52860i
$431$	−12.7781	+	7.37742i	−0.615497	+	0.355358i	−0.775114	−	0.631821i	$-0.782308\pi$
$431$	−12.7781	+	7.37742i	−0.615497	+	0.355358i	0.159616	+	0.987179i	$0.448974\pi$
$432$		0			0
$433$		−	35.7396i		−	1.71754i	−0.512364	−	0.858769i	$-0.671230\pi$
$433$		−	35.7396i		−	1.71754i	0.512364	−	0.858769i	$-0.328770\pi$
$434$	22.5883	−	0.100320i	1.08428	−	0.00481551i
$435$		0			0
$436$	−11.0309	−	11.2090i	−0.528284	−	0.536814i
$437$	−0.183929	+	0.106192i	−0.00879854	+	0.00507984i
$438$		0			0
$439$	−9.91925	+	17.1806i	−0.473420	+	0.819987i	−0.999537	−	0.0304249i	$-0.990314\pi$
$439$	−9.91925	+	17.1806i	−0.473420	+	0.819987i	0.526117	+	0.850412i	$0.323647\pi$
$440$	−13.7911	+	5.51933i	−0.657466	+	0.263124i
$441$		0			0
$442$	−1.42568	−	1.87346i	−0.0678125	−	0.0891116i
$443$	16.4378	+	9.49035i	0.780982	+	0.450900i	0.836778	−	0.547542i	$-0.184436\pi$
$443$	16.4378	+	9.49035i	0.780982	+	0.450900i	−0.0557962	+	0.998442i	$0.517770\pi$
$444$		0			0
$445$	−2.49186	−	4.31603i	−0.118126	−	0.204599i
$446$	−11.3676	+	1.45028i	−0.538270	+	0.0686730i
$447$		0			0
$448$	2.43545	+	21.0254i	0.115064	+	0.993358i
$449$	25.2845			1.19325			0.596626	−	0.802520i	$-0.296508\pi$
$449$	25.2845			1.19325			0.596626	+	0.802520i	$0.296508\pi$
$450$		0			0
$451$	−5.75564	−	9.96906i	−0.271022	−	0.469425i
$452$	−9.11185	+	2.36347i	−0.428586	+	0.111168i
$453$		0			0
$454$	−10.3507	−	13.6017i	−0.485781	−	0.638359i
$455$	1.47286	+	3.47255i	0.0690485	+	0.162795i
$456$		0			0
$457$	−11.4837	+	19.8904i	−0.537186	+	0.930433i	0.461868	+	0.886949i	$0.347179\pi$
$457$	−11.4837	+	19.8904i	−0.537186	+	0.930433i	−0.999054	+	0.0434847i	$0.986154\pi$
$458$	−31.0217	−	12.9954i	−1.44955	−	0.607233i
$459$		0			0
$460$	17.3551	+	17.6353i	0.809186	+	0.822252i
$461$			2.95838i			0.137786i	0.997624	+	0.0688928i	$0.0219466\pi$
$461$			2.95838i			0.137786i	−0.997624	+	0.0688928i	$0.978053\pi$
$462$		0			0
$463$			3.30669i			0.153675i	0.997044	+	0.0768374i	$0.0244822\pi$
$463$			3.30669i			0.153675i	−0.997044	+	0.0768374i	$0.975518\pi$
$464$	10.9048	−	6.06514i	0.506244	−	0.281567i
$465$		0			0
$466$	10.8899	−	25.9957i	0.504465	−	1.20423i
$467$	−5.95282	+	10.3106i	−0.275464	+	0.477117i	−0.970252	−	0.242097i	$-0.922165\pi$
$467$	−5.95282	+	10.3106i	−0.275464	+	0.477117i	0.694788	+	0.719214i	$0.255498\pi$
$468$		0			0
$469$	3.15656	−	25.6485i	0.145756	−	1.18434i
$470$	6.18569	−	4.70722i	0.285325	−	0.217128i
$471$		0			0
$472$	−7.64206	−	6.01117i	−0.351754	−	0.276687i
$473$	−4.29331	−	7.43623i	−0.197406	−	0.341918i
$474$		0			0
$475$	−0.652798			−0.0299524
$476$	−3.11951	−	23.6153i	−0.142982	−	1.08240i
$477$		0			0
$478$	1.71995	+	13.4812i	0.0786686	+	0.616617i
$479$	5.95186	+	10.3089i	0.271947	+	0.471026i	0.969360	−	0.245643i	$-0.0789990\pi$
$479$	5.95186	+	10.3089i	0.271947	+	0.471026i	−0.697413	+	0.716669i	$0.745666\pi$
$480$		0			0
$481$	−1.75879	−	1.01544i	−0.0801940	−	0.0463000i
$482$	11.7136	−	8.91387i	0.533540	−	0.406016i
$483$		0			0
$484$	−4.87474	+	17.6269i	−0.221579	+	0.801222i
$485$	5.55975	−	9.62978i	0.252455	−	0.437266i
$486$		0			0
$487$	6.50151	−	3.75365i	0.294612	−	0.170094i	−0.345408	−	0.938453i	$-0.612260\pi$
$487$	6.50151	−	3.75365i	0.294612	−	0.170094i	0.640020	+	0.768358i	$0.278926\pi$
$488$	−4.00848	−	0.576794i	−0.181455	−	0.0261102i
$489$		0			0
$490$	−4.49357	+	37.9000i	−0.202999	+	1.71215i
$491$			22.0031i			0.992988i	0.868040	+	0.496494i	$0.165380\pi$
$491$			22.0031i			0.992988i	−0.868040	+	0.496494i	$0.834620\pi$
$492$		0			0
$493$	−12.1615	+	7.02145i	−0.547727	+	0.316230i
$494$	−0.0319249	−	0.0133737i	−0.00143637	−	0.000601713i
$495$		0			0
$496$	20.7169	+	12.4075i	0.930215	+	0.557113i
$497$	27.3613	+	20.6303i	1.22732	+	0.925393i
$498$		0			0
$499$	1.22277	+	0.705968i	0.0547389	+	0.0316035i	0.527120	−	0.849791i	$-0.323272\pi$
$499$	1.22277	+	0.705968i	0.0547389	+	0.0316035i	−0.472381	+	0.881395i	$0.656605\pi$
$500$	9.41494	+	36.2973i	0.421049	+	1.62326i
$501$		0			0
$502$	29.0193	−	3.70231i	1.29519	−	0.165242i
$503$	26.2303			1.16955			0.584775	−	0.811196i	$-0.301183\pi$
$503$	26.2303			1.16955			0.584775	+	0.811196i	$0.301183\pi$
$504$		0			0
$505$	−23.8589			−1.06171
$506$	−6.13237	+	0.782374i	−0.272617	+	0.0347808i
$507$		0			0
$508$	1.35737	+	5.23306i	0.0602236	+	0.232179i
$509$	4.38419	+	2.53121i	0.194326	+	0.112194i	0.594006	−	0.804461i	$-0.297545\pi$
$509$	4.38419	+	2.53121i	0.194326	+	0.112194i	−0.399680	+	0.916655i	$0.630879\pi$
$510$		0			0
$511$	0.582233	−	4.73091i	0.0257565	−	0.209283i
$512$	−9.40673	+	20.5794i	−0.415723	+	0.909491i
$513$		0			0
$514$	−23.1547	−	9.69978i	−1.02131	−	0.427839i
$515$	59.4058	−	34.2980i	2.61773	−	1.51135i
$516$		0			0
$517$			1.94213i			0.0854149i
$518$	−10.3533	−	17.7499i	−0.454896	−	0.779884i
$519$		0			0
$520$	−0.574323	+	3.99131i	−0.0251857	+	0.175031i
$521$	8.60044	−	4.96547i	0.376792	−	0.217541i	−0.299630	−	0.954056i	$-0.596863\pi$
$521$	8.60044	−	4.96547i	0.376792	−	0.217541i	0.676422	+	0.736515i	$0.263530\pi$
$522$		0			0
$523$	−15.6686	+	27.1389i	−0.685142	+	1.18670i	0.288250	+	0.957555i	$0.406927\pi$
$523$	−15.6686	+	27.1389i	−0.685142	+	1.18670i	−0.973392	+	0.229146i	$0.926407\pi$
$524$	−4.14366	+	14.9833i	−0.181017	+	0.654550i
$525$		0			0
$526$	2.34225	−	1.78242i	0.102127	−	0.0777171i
$527$	−23.5356	−	13.5883i	−1.02523	−	0.591916i
$528$		0			0
$529$	−6.35135	−	11.0009i	−0.276146	−	0.478299i
$530$	1.75619	+	13.7653i	0.0762840	+	0.597926i
$531$		0			0
$532$	−0.213320	−	0.277753i	−0.00924861	−	0.0120421i
$533$	−3.12485			−0.135352
$534$		0			0
$535$	−11.7454	−	20.3437i	−0.507800	−	0.879535i
$536$	17.0798	−	21.7138i	0.737737	−	0.937891i
$537$		0			0
$538$	4.00347	−	3.04658i	0.172602	−	0.131347i
$539$	−6.85573	−	6.62796i	−0.295297	−	0.285486i
$540$		0			0
$541$	2.09313	−	3.62541i	0.0899908	−	0.155869i	−0.817516	−	0.575906i	$-0.804650\pi$
$541$	2.09313	−	3.62541i	0.0899908	−	0.155869i	0.907507	+	0.420037i	$0.137983\pi$
$542$	6.75815	−	16.1326i	0.290287	−	0.692955i
$543$		0			0
$544$	10.2141	−	23.3269i	0.437927	−	1.00013i
$545$		−	30.3151i		−	1.29856i
$546$		0			0
$547$		−	12.4674i		−	0.533067i	−0.963826	−	0.266533i	$-0.914122\pi$
$547$		−	12.4674i		−	0.533067i	0.963826	−	0.266533i	$-0.0858782\pi$
$548$	4.00000	+	4.06459i	0.170872	+	0.173631i
$549$		0			0
$550$	−17.5260	−	7.34188i	−0.747313	−	0.313059i
$551$	−0.103232	+	0.178803i	−0.00439784	+	0.00761728i
$552$		0			0
$553$	30.4191	−	12.9020i	1.29355	−	0.548651i
$554$	−10.1599	−	13.3510i	−0.431653	−	0.567230i
$555$		0			0
$556$	13.8546	−	3.59367i	0.587567	−	0.152405i
$557$	−18.2744	−	31.6521i	−0.774309	−	1.34114i	−0.935182	−	0.354168i	$-0.884764\pi$
$557$	−18.2744	−	31.6521i	−0.774309	−	1.34114i	0.160872	−	0.986975i	$-0.448569\pi$
$558$		0			0
$559$	−2.33092			−0.0985876
$560$	−25.0822	+	32.1803i	−1.05991	+	1.35986i
$561$		0			0
$562$	−27.1349	+	3.46190i	−1.14462	+	0.146032i
$563$	−21.3672	−	37.0091i	−0.900520	−	1.55975i	−0.826820	−	0.562466i	$-0.809853\pi$
$563$	−21.3672	−	37.0091i	−0.900520	−	1.55975i	−0.0737002	−	0.997280i	$-0.523481\pi$
$564$		0			0
$565$	−15.7146	−	9.07283i	−0.661118	−	0.381697i
$566$	−21.3602	−	28.0692i	−0.897838	−	1.17984i
$567$		0			0
$568$	13.6114	+	34.0107i	0.571120	+	1.42706i
$569$	10.7265	−	18.5788i	0.449678	−	0.778866i	−0.548687	−	0.836028i	$-0.684872\pi$
$569$	10.7265	−	18.5788i	0.449678	−	0.778866i	0.998365	+	0.0571625i	$0.0182053\pi$
$570$		0			0
$571$	−18.3349	+	10.5856i	−0.767291	+	0.442996i	−0.831907	−	0.554915i	$-0.812751\pi$
$571$	−18.3349	+	10.5856i	−0.767291	+	0.442996i	0.0646165	+	0.997910i	$0.479418\pi$
$572$	−0.706693	−	0.718104i	−0.0295483	−	0.0300254i
$573$		0			0
$574$	−27.4516	−	15.6871i	−1.14581	−	0.654765i
$575$			31.6506i			1.31992i
$576$		0			0
$577$	4.10289	−	2.36880i	0.170806	−	0.0986146i	−0.412160	−	0.911111i	$-0.635226\pi$
$577$	4.10289	−	2.36880i	0.170806	−	0.0986146i	0.582966	+	0.812497i	$0.301892\pi$
$578$	−1.78393	+	4.25848i	−0.0742017	+	0.177129i
$579$		0			0
$580$	23.1830	+	6.41129i	0.962623	+	0.266214i
$581$	−19.5744	+	25.9609i	−0.812082	+	1.07704i
$582$		0			0
$583$	−3.00267	−	1.73359i	−0.124358	−	0.0717981i
$584$	3.15041	−	4.00514i	0.130365	−	0.165734i
$585$		0			0
$586$	1.23177	+	9.65484i	0.0508841	+	0.398838i
$587$	−29.8450			−1.23184			−0.615918	−	0.787810i	$-0.711215\pi$
$587$	−29.8450			−1.23184			−0.615918	+	0.787810i	$0.711215\pi$
$588$		0			0
$589$	−0.399562			−0.0164636
$590$	−2.37194	−	18.5916i	−0.0976512	−	0.765406i
$591$		0			0
$592$	0.351835	−	21.9646i	0.0144603	−	0.902741i
$593$	−22.9586	−	13.2551i	−0.942796	−	0.544323i	−0.0519600	−	0.998649i	$-0.516547\pi$
$593$	−22.9586	−	13.2551i	−0.942796	−	0.544323i	−0.890836	+	0.454326i	$0.849880\pi$
$594$		0			0
$595$	27.6440	−	36.6634i	1.13330	−	1.50305i
$596$	11.3842	−	41.1651i	0.466317	−	1.68619i
$597$		0			0
$598$	−0.648418	+	1.54786i	−0.0265158	+	0.0632967i
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	−0.820416	−	0.571767i	$-0.806258\pi$
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	0.0849563	+	0.996385i	$0.472925\pi$
$600$		0			0
$601$			10.8255i			0.441581i	0.975321	+	0.220790i	$0.0708637\pi$
$601$			10.8255i			0.441581i	−0.975321	+	0.220790i	$0.929136\pi$
$602$	−20.4770	−	11.7015i	−0.834581	−	0.476916i
$603$		0			0
$604$	31.6650	−	31.1618i	1.28843	−	1.26796i
$605$	−30.5307	+	17.6269i	−1.24125	+	0.716635i
$606$		0			0
$607$	6.95330	−	12.0435i	0.282226	−	0.488830i	−0.689707	−	0.724089i	$-0.742261\pi$
$607$	6.95330	−	12.0435i	0.282226	−	0.488830i	0.971933	+	0.235259i	$0.0755939\pi$
$608$	−0.0414278	−	0.372099i	−0.00168012	−	0.0150906i
$609$		0			0
$610$	−4.72746	−	6.21230i	−0.191409	−	0.251529i
$611$	0.456579	+	0.263606i	0.0184712	+	0.0106644i
$612$		0			0
$613$	−0.322444	−	0.558490i	−0.0130234	−	0.0225572i	0.859440	−	0.511236i	$-0.170812\pi$
$613$	−0.322444	−	0.558490i	−0.0130234	−	0.0225572i	−0.872464	+	0.488679i	$0.837479\pi$
$614$	24.4393	−	3.11800i	0.986291	−	0.125832i
$615$		0			0
$616$	−2.60330	−	9.85616i	−0.104890	−	0.397116i
$617$	−12.3626			−0.497701			−0.248850	−	0.968542i	$-0.580053\pi$
$617$	−12.3626			−0.497701			−0.248850	+	0.968542i	$0.580053\pi$
$618$		0			0
$619$	5.69875	+	9.87053i	0.229052	+	0.396730i	0.957527	−	0.288342i	$-0.0931040\pi$
$619$	5.69875	+	9.87053i	0.229052	+	0.396730i	−0.728475	+	0.685072i	$0.759771\pi$
$620$	11.6873	+	45.0580i	0.469375	+	1.80957i
$621$		0			0
$622$	−21.5099	−	28.2659i	−0.862469	−	1.13336i
$623$	3.14865	−	1.33548i	0.126148	−	0.0535047i
$624$		0			0
$625$	−11.4837	+	19.8904i	−0.459349	+	0.795616i
$626$	28.8223	+	12.0740i	1.15197	+	0.482576i
$627$		0			0
$628$	−7.76753	+	7.64411i	−0.309958	+	0.305033i
$629$			24.7224i			0.985745i
$630$		0			0
$631$			10.8050i			0.430140i	0.976599	+	0.215070i	$0.0689979\pi$
$631$			10.8050i			0.430140i	−0.976599	+	0.215070i	$0.931002\pi$
$632$	34.9635	+	5.03101i	1.39077	+	0.200123i
$633$		0			0
$634$	0.886991	−	2.11737i	0.0352269	−	0.0840913i
$635$	−5.21065	+	9.02511i	−0.206778	+	0.358150i
$636$		0			0
$637$	−2.48871	+	0.712111i	−0.0986062	+	0.0282149i
$638$	−4.78250	+	3.63941i	−0.189341	+	0.144085i
$639$		0			0
$640$	−40.7494	+	15.5558i	−1.61076	+	0.614897i
$641$	1.12662	+	1.95136i	0.0444988	+	0.0770741i	0.887417	−	0.460968i	$-0.152498\pi$
$641$	1.12662	+	1.95136i	0.0444988	+	0.0770741i	−0.842918	+	0.538042i	$0.819164\pi$
$642$		0			0
$643$	22.0574			0.869860			0.434930	−	0.900464i	$-0.356773\pi$
$643$	22.0574			0.869860			0.434930	+	0.900464i	$0.356773\pi$
$644$	−13.4667	+	10.3427i	−0.530663	+	0.407560i
$645$		0			0
$646$	0.0533242	+	0.417964i	0.00209801	+	0.0164446i
$647$	−2.26417	−	3.92166i	−0.0890137	−	0.154176i	0.818081	−	0.575103i	$-0.195038\pi$
$647$	−2.26417	−	3.92166i	−0.0890137	−	0.154176i	−0.907094	+	0.420927i	$0.861705\pi$
$648$		0			0
$649$	4.05546	+	2.34142i	0.159191	+	0.0919089i
$650$	−4.10483	+	3.12371i	−0.161004	+	0.122522i
$651$		0			0
$652$	−9.16942	−	2.53581i	−0.359102	−	0.0993101i
$653$	20.6749	−	35.8099i	0.809071	−	1.40135i	−0.104438	−	0.994531i	$-0.533304\pi$
$653$	20.6749	−	35.8099i	0.809071	−	1.40135i	0.913508	−	0.406820i	$-0.133362\pi$
$654$		0			0
$655$	−25.9519	+	14.9833i	−1.01403	+	0.585448i
$656$	−16.4293	−	29.5392i	−0.641458	−	1.15331i
$657$		0			0
$658$	2.68769	+	4.60783i	0.104777	+	0.179632i
$659$		−	10.6413i		−	0.414526i	−0.978285	−	0.207263i	$-0.933544\pi$
$659$		−	10.6413i		−	0.414526i	0.978285	−	0.207263i	$-0.0664556\pi$
$660$		0			0
$661$	41.7871	−	24.1258i	1.62533	−	0.938384i	0.639867	−	0.768485i	$-0.278989\pi$
$661$	41.7871	−	24.1258i	1.62533	−	0.938384i	0.985462	−	0.169899i	$-0.0543441\pi$
$662$	34.7849	+	14.5719i	1.35196	+	0.566351i
$663$		0			0
$664$	−32.2700	+	12.9147i	−1.25232	+	0.501189i
$665$	0.0824618	−	0.670040i	0.00319773	−	0.0259830i
$666$		0			0
$667$	8.66919	+	5.00516i	0.335672	+	0.193801i
$668$	27.2227	−	7.06114i	1.05328	−	0.273204i
$669$		0			0
$670$	52.8254	−	6.73951i	2.04082	−	0.260370i
$671$	1.95049			0.0752977
$672$		0			0
$673$	−0.148647			−0.00572991			−0.00286496	−	0.999996i	$-0.500912\pi$
$673$	−0.148647			−0.00572991			−0.00286496	+	0.999996i	$0.500912\pi$
$674$	−41.8645	+	5.34111i	−1.61256	+	0.205732i
$675$		0			0
$676$	24.9024	−	6.45929i	0.957785	−	0.248434i
$677$	34.3935	+	19.8571i	1.32185	+	0.763170i	0.984023	−	0.178039i	$-0.0569754\pi$
$677$	34.3935	+	19.8571i	1.32185	+	0.763170i	0.337825	+	0.941209i	$0.390309\pi$
$678$		0			0
$679$	6.09304	+	4.59412i	0.233830	+	0.176306i
$680$	45.5735	−	18.2389i	1.74766	−	0.699430i
$681$		0			0
$682$	−10.7272	−	4.49378i	−0.410768	−	0.172076i
$683$	−36.9070	+	21.3083i	−1.41221	+	0.815339i	−0.995596	−	0.0937450i	$-0.970116\pi$
$683$	−36.9070	+	21.3083i	−1.41221	+	0.815339i	−0.416613	+	0.909084i	$0.636783\pi$
$684$		0			0
$685$			10.9928i			0.420013i
$686$	−25.4380	−	6.23770i	−0.971227	−	0.238157i
$687$		0			0
$688$	−12.2552	−	22.0342i	−0.467223	−	0.840045i
$689$	−0.815106	+	0.470602i	−0.0310531	+	0.0179285i
$690$		0			0
$691$	2.22317	−	3.85064i	0.0845733	−	0.146485i	−0.820636	−	0.571451i	$-0.806381\pi$
$691$	2.22317	−	3.85064i	0.0845733	−	0.146485i	0.905209	+	0.424966i	$0.139714\pi$
$692$	−3.42568	−	0.947375i	−0.130225	−	0.0360138i
$693$		0			0
$694$	−1.06618	+	0.811350i	−0.0404718	+	0.0307984i
$695$	23.8942	+	13.7953i	0.906357	+	0.523285i
$696$		0			0
$697$	19.0198	+	32.9433i	0.720427	+	1.24782i
$698$	−1.14865	−	9.00327i	−0.0434769	−	0.340779i
$699$		0			0
$700$	−51.7419	+	6.83496i	−1.95566	+	0.258337i
$701$	24.9907			0.943885			0.471942	−	0.881629i	$-0.343553\pi$
$701$	24.9907			0.943885			0.471942	+	0.881629i	$0.343553\pi$
$702$		0			0
$703$	0.181739	+	0.314782i	0.00685442	+	0.0118722i
$704$	3.07269	−	10.4559i	0.115806	−	0.394071i
$705$		0			0
$706$	15.6131	−	11.8814i	0.587608	−	0.447161i
$707$	2.00000	−	16.2509i	0.0752177	−	0.611178i
$708$		0			0
$709$	−9.07409	+	15.7168i	−0.340785	+	0.590257i	−0.984579	−	0.174942i	$-0.944026\pi$
$709$	−9.07409	+	15.7168i	−0.340785	+	0.590257i	0.643794	+	0.765199i	$0.277359\pi$
$710$	−27.2845	+	65.1318i	−1.02397	+	2.44435i
$711$		0			0
$712$	3.61903	+	0.520754i	0.135629	+	0.0195161i
$713$			19.3725i			0.725507i
$714$		0			0
$715$		−	1.94213i		−	0.0726316i
$716$	−4.63530	+	4.56165i	−0.173229	+	0.170477i
$717$		0			0
$718$	−9.03705	−	3.78573i	−0.337260	−	0.141282i
$719$	−20.5818	+	35.6488i	−0.767573	+	1.32948i	0.171302	+	0.985219i	$0.445203\pi$
$719$	−20.5818	+	35.6488i	−0.767573	+	1.32948i	−0.938875	+	0.344257i	$0.888131\pi$
$720$		0			0
$721$	18.3815	+	43.3380i	0.684562	+	1.61399i
$722$	−16.2682	−	21.3778i	−0.605440	−	0.795601i
$723$		0			0
$724$	11.8013	+	45.4974i	0.438592	+	1.69090i
$725$	15.3842	+	26.6463i	0.571357	+	0.989619i
$726$		0			0
$727$	5.77231			0.214083			0.107042	−	0.994255i	$-0.465862\pi$
$727$	5.77231			0.214083			0.107042	+	0.994255i	$0.465862\pi$
$728$	−2.67045	−	0.725764i	−0.0989733	−	0.0268986i
$729$		0			0
$730$	9.74374	−	1.24312i	0.360632	−	0.0460098i
$731$	14.1875	+	24.5734i	0.524742	+	0.908880i
$732$		0			0
$733$	−6.63928	−	3.83319i	−0.245227	−	0.141582i	0.372350	−	0.928093i	$-0.378552\pi$
$733$	−6.63928	−	3.83319i	−0.245227	−	0.141582i	−0.617577	+	0.786510i	$0.711886\pi$
$734$	16.5444	+	21.7407i	0.610663	+	0.802465i
$735$		0			0
$736$	−18.0410	+	2.00860i	−0.665001	+	0.0740381i
$737$	−6.65280	+	11.5230i	−0.245059	+	0.424455i
$738$		0			0
$739$	−17.3753	+	10.0317i	−0.639162	+	0.369021i	−0.784292	−	0.620392i	$-0.786973\pi$
$739$	−17.3753	+	10.0317i	−0.639162	+	0.369021i	0.145129	+	0.989413i	$0.453640\pi$
$740$	30.1816	−	29.7020i	1.10950	−	1.09187i
$741$		0			0
$742$	−9.52312	+	0.0422944i	−0.349605	+	0.00155267i
$743$		−	8.26368i		−	0.303165i	−0.988445	−	0.151583i	$-0.951563\pi$
$743$		−	8.26368i		−	0.303165i	0.988445	−	0.151583i	$-0.0484369\pi$
$744$		0			0
$745$	71.3000	−	41.1651i	2.61223	−	1.50817i
$746$	6.16182	−	14.7091i	0.225600	−	0.538538i
$747$		0			0
$748$	−3.26912	+	11.8210i	−0.119531	+	0.432220i
$749$	14.8412	−	6.29480i	0.542286	−	0.230007i
$750$		0			0
$751$	−23.4113	−	13.5165i	−0.854289	−	0.493224i	0.00780684	−	0.999970i	$-0.497515\pi$
$751$	−23.4113	−	13.5165i	−0.854289	−	0.493224i	−0.862096	+	0.506746i	$0.830848\pi$
$752$	−0.0913358	+	5.70197i	−0.00333067	+	0.207930i
$753$		0			0
$754$	0.206464	+	1.61830i	0.00751899	+	0.0589351i
$755$	85.6388			3.11672
$756$		0			0
$757$	21.9417			0.797486			0.398743	−	0.917063i	$-0.369447\pi$
$757$	21.9417			0.797486			0.398743	+	0.917063i	$0.369447\pi$
$758$	4.50048	+	35.2755i	0.163465	+	1.28126i
$759$		0			0
$760$	0.446194	−	0.567250i	0.0161851	−	0.0205763i
$761$	−1.02680	−	0.592825i	−0.0372216	−	0.0214899i	0.481274	−	0.876570i	$-0.340174\pi$
$761$	−1.02680	−	0.592825i	−0.0372216	−	0.0214899i	−0.518495	+	0.855080i	$0.673508\pi$
$762$		0			0
$763$	20.6484	+	2.54120i	0.747523	+	0.0919977i
$764$	−46.0653	−	12.7394i	−1.66659	−	0.460896i
$765$		0			0
$766$	−9.70695	+	23.1718i	−0.350726	+	0.837230i
$767$	1.10090	−	0.635603i	0.0397511	−	0.0229503i
$768$		0			0
$769$			19.0892i			0.688373i	0.938901	+	0.344186i	$0.111845\pi$
$769$			19.0892i			0.688373i	−0.938901	+	0.344186i	$0.888155\pi$
$770$	9.74969	−	17.0615i	0.351354	−	0.614854i
$771$		0			0
$772$	−27.8817	−	28.3319i	−1.00348	−	1.01969i
$773$	30.7887	−	17.7759i	1.10739	−	0.639353i	0.169240	−	0.985575i	$-0.445869\pi$
$773$	30.7887	−	17.7759i	1.10739	−	0.639353i	0.938153	+	0.346222i	$0.112535\pi$
$774$		0			0
$775$	−29.7725	+	51.5674i	−1.06946	+	1.85236i
$776$	3.03110	+	7.57379i	0.108810	+	0.271883i
$777$		0			0
$778$	−12.1138	−	15.9185i	−0.434299	−	0.570707i
$779$	0.484346	+	0.279637i	0.0173535	+	0.0100190i
$780$		0			0
$781$	−8.82182	−	15.2798i	−0.315670	−	0.546756i
$782$	20.2647	−	2.58540i	0.724666	−	0.0924536i
$783$		0			0
$784$	−19.8163	−	19.7817i	−0.707724	−	0.706489i
$785$	−21.0075			−0.749790
$786$		0			0
$787$	21.3018	+	36.8958i	0.759327	+	1.31519i	0.943194	+	0.332241i	$0.107805\pi$
$787$	21.3018	+	36.8958i	0.759327	+	1.31519i	−0.183868	+	0.982951i	$0.558862\pi$
$788$	−36.8211	+	9.55081i	−1.31170	+	0.340233i
$789$		0			0
$790$	41.2347	+	54.1860i	1.46706	+	1.92785i
$791$	7.49704	−	9.94309i	0.266564	−	0.353536i
$792$		0			0
$793$	0.264740	−	0.458543i	0.00940118	−	0.0162833i
$794$	16.5014	+	6.91263i	0.585612	+	0.245320i
$795$		0			0
$796$	−20.8341	−	21.1705i	−0.738446	−	0.750369i
$797$			23.1179i			0.818879i	0.912337	+	0.409440i	$0.134276\pi$
$797$			23.1179i			0.818879i	−0.912337	+	0.409440i	$0.865724\pi$
$798$		0			0
$799$		−	6.41788i		−	0.227048i
$800$	−51.1100	−	22.3795i	−1.80701	−	0.791235i
$801$		0			0
$802$	13.5408	−	32.3237i	0.478142	−	1.14139i
$803$	−1.22712	+	2.12544i	−0.0433042	+	0.0750051i
$804$		0			0
$805$	−32.4865	−	3.99812i	−1.14500	−	0.140915i
$806$	−2.51246	+	1.91194i	−0.0884976	+	0.0673453i
$807$		0			0
$808$	10.8218	−	13.7579i	0.380710	−	0.484000i
$809$	−16.0852	−	27.8604i	−0.565525	−	0.979518i	−0.997001	−	0.0773937i	$-0.975340\pi$
$809$	−16.0852	−	27.8604i	−0.565525	−	0.979518i	0.431475	−	0.902125i	$-0.357993\pi$
$810$		0			0
$811$	−41.0797			−1.44250			−0.721251	−	0.692673i	$-0.756433\pi$
$811$	−41.0797			−1.44250			−0.721251	+	0.692673i	$0.756433\pi$
$812$	−6.31025	+	15.2531i	−0.221446	+	0.535280i
$813$		0			0
$814$	1.33897	+	10.4951i	0.0469310	+	0.367853i
$815$	−9.16942	−	15.8819i	−0.321191	−	0.556319i
$816$		0			0
$817$	0.361288	+	0.208590i	0.0126399	+	0.00729764i
$818$	6.52359	−	4.96435i	0.228092	−	0.173574i
$819$		0			0
$820$	17.3670	−	62.7985i	0.606482	−	2.19302i
$821$	−14.6233	+	25.3283i	−0.510358	+	0.883965i	0.489570	+	0.871964i	$0.337154\pi$
$821$	−14.6233	+	25.3283i	−0.510358	+	0.883965i	−0.999928	+	0.0120014i	$0.996180\pi$
$822$		0			0
$823$	17.0790	−	9.86059i	0.595338	−	0.343719i	−0.171867	−	0.985120i	$-0.554980\pi$
$823$	17.0790	−	9.86059i	0.595338	−	0.343719i	0.767205	+	0.641401i	$0.221647\pi$
$824$	−7.16765	+	49.8123i	−0.249697	+	1.73529i
$825$		0			0
$826$	12.8621	−	0.0571235i	0.447529	−	0.00198758i
$827$		−	16.1125i		−	0.560286i	−0.959958	−	0.280143i	$-0.909618\pi$
$827$		−	16.1125i		−	0.560286i	0.959958	−	0.280143i	$-0.0903819\pi$
$828$		0			0
$829$	−40.9056	+	23.6169i	−1.42071	+	0.820248i	−0.996360	−	0.0852497i	$-0.972831\pi$
$829$	−40.9056	+	23.6169i	−1.42071	+	0.820248i	−0.424351	+	0.905498i	$0.639498\pi$
$830$	−61.7983	−	25.8881i	−2.14505	−	0.898589i
$831$		0			0
$832$	−2.04103	−	2.14154i	−0.0707601	−	0.0742446i
$833$	22.6551	+	21.9024i	0.784954	+	0.758875i
$834$		0			0
$835$	46.9492	+	27.1062i	1.62475	+	0.938047i
$836$	0.0452742	+	0.174545i	0.00156584	+	0.00603677i
$837$		0			0
$838$	−3.40844	+	0.434852i	−0.117742	+	0.0150217i
$839$	−25.3551			−0.875356			−0.437678	−	0.899132i	$-0.644199\pi$
$839$	−25.3551			−0.875356			−0.437678	+	0.899132i	$0.644199\pi$
$840$		0			0
$841$	−19.2687			−0.664437
$842$	36.3860	−	4.64216i	1.25394	−	0.159980i
$843$		0			0
$844$	9.87611	+	38.0753i	0.339950	+	1.31060i
$845$	42.9475	+	24.7958i	1.47744	+	0.853000i
$846$		0			0
$847$	−9.44687	−	22.2728i	−0.324598	−	0.765304i
$848$	−8.73412	−	5.23093i	−0.299931	−	0.179631i
$849$		0			0
$850$	57.9157	+	24.2616i	1.98649	+	0.832167i
$851$	15.2620	−	8.81153i	0.523175	−	0.302055i
$852$		0			0
$853$		−	24.3802i		−	0.834763i	−0.908731	−	0.417382i	$-0.862948\pi$
$853$		−	24.3802i		−	0.834763i	0.908731	−	0.417382i	$-0.137052\pi$
$854$	4.62765	−	2.69925i	0.158355	−	0.0923663i
$855$		0			0
$856$	17.0584	+	2.45459i	0.583043	+	0.0838960i
$857$	22.4742	−	12.9755i	0.767705	−	0.443235i	−0.0643503	−	0.997927i	$-0.520498\pi$
$857$	22.4742	−	12.9755i	0.767705	−	0.443235i	0.832055	+	0.554693i	$0.187164\pi$
$858$		0			0
$859$	−28.4213	+	49.2271i	−0.969722	+	1.67961i	−0.273368	+	0.961909i	$0.588138\pi$
$859$	−28.4213	+	49.2271i	−0.969722	+	1.67961i	−0.696354	+	0.717698i	$0.745196\pi$
$860$	12.9546	−	46.8433i	0.441748	−	1.59734i
$861$		0			0
$862$	16.6052	−	12.6363i	0.565576	−	0.430395i
$863$	15.3044	+	8.83597i	0.520966	+	0.300780i	0.737330	−	0.675533i	$-0.236086\pi$
$863$	15.3044	+	8.83597i	0.520966	+	0.300780i	−0.216364	+	0.976313i	$0.569420\pi$
$864$		0			0
$865$	−3.42568	−	5.93345i	−0.116476	−	0.201743i
$866$	6.39654	+	50.1371i	0.217363	+	1.70373i
$867$		0			0
$868$	−31.6699	+	4.18351i	−1.07495	+	0.141997i
$869$	−17.0129			−0.577122
$870$		0			0
$871$	1.80597	+	3.12803i	0.0611930	+	0.105989i
$872$	17.4808	+	13.7502i	0.591973	+	0.465641i
$873$		0			0
$874$	0.239018	−	0.181889i	0.00808491	−	0.00615250i
$875$	−39.6086	−	29.8647i	−1.33901	−	1.00961i
$876$		0			0
$877$	6.17283	−	10.6917i	0.208442	−	0.361032i	−0.742782	−	0.669533i	$-0.766494\pi$
$877$	6.17283	−	10.6917i	0.208442	−	0.361032i	0.951224	+	0.308502i	$0.0998275\pi$
$878$	10.8402	−	25.8770i	0.365840	−	0.873308i
$879$		0			0
$880$	18.3589	−	10.2110i	0.618880	−	0.344214i
$881$		−	33.0442i		−	1.11329i	−0.830751	−	0.556644i	$-0.812089\pi$
$881$		−	33.0442i		−	1.11329i	0.830751	−	0.556644i	$-0.187911\pi$
$882$		0			0
$883$		−	39.2680i		−	1.32147i	−0.750618	−	0.660737i	$-0.770244\pi$
$883$		−	39.2680i		−	1.32147i	0.750618	−	0.660737i	$-0.229756\pi$
$884$	2.33531	+	2.37301i	0.0785448	+	0.0798130i
$885$		0			0
$886$	−24.7582	−	10.3715i	−0.831766	−	0.348437i
$887$	−19.7517	+	34.2109i	−0.663196	+	1.14869i	0.316576	+	0.948567i	$0.397467\pi$
$887$	−19.7517	+	34.2109i	−0.663196	+	1.14869i	−0.979771	+	0.200121i	$0.935866\pi$
$888$		0			0
$889$	−5.71045	−	4.30565i	−0.191522	−	0.144407i
$890$	4.26816	+	5.60873i	0.143069	+	0.188005i
$891$		0			0
$892$	15.6873	−	4.06904i	0.525251	−	0.136242i
$893$	−0.0471792	−	0.0817167i	−0.00157879	−	0.00273454i
$894$		0			0
$895$	−12.5363			−0.419043
$896$	−7.17961	−	29.0595i	−0.239854	−	0.970809i
$897$		0			0
$898$	−35.4702	+	4.52533i	−1.18366	+	0.151012i
$899$	9.41631	+	16.3095i	0.314052	+	0.543953i
$900$		0			0
$901$	9.92249	+	5.72875i	0.330566	+	0.190852i
$902$	9.85848	+	12.9549i	0.328251	+	0.431351i
$903$		0			0
$904$	12.3595	−	4.94638i	0.411071	−	0.164514i
$905$	−45.3026	+	78.4664i	−1.50591	+	2.60831i
$906$		0			0
$907$	4.46372	−	2.57713i	0.148215	−	0.0855722i	−0.424058	−	0.905635i	$-0.639395\pi$
$907$	4.46372	−	2.57713i	0.148215	−	0.0855722i	0.572274	+	0.820063i	$0.306062\pi$
$908$	16.9547	+	17.2285i	0.562663	+	0.571748i
$909$		0			0
$910$	−2.68769	−	4.60783i	−0.0890960	−	0.152748i
$911$		−	25.8365i		−	0.856002i	−0.903778	−	0.428001i	$-0.859218\pi$
$911$		−	25.8365i		−	0.856002i	0.903778	−	0.428001i	$-0.140782\pi$
$912$		0			0
$913$	14.4978	−	8.37031i	0.479807	−	0.277017i
$914$	12.5500	−	29.9584i	0.415116	−	0.990936i
$915$		0			0
$916$	45.8444	+	12.6783i	1.51474	+	0.418903i
$917$	−8.03010	−	18.9325i	−0.265177	−	0.625207i
$918$		0			0
$919$	30.6881	+	17.7178i	1.01231	+	0.584455i	0.911866	−	0.410488i	$-0.134642\pi$
$919$	30.6881	+	17.7178i	1.01231	+	0.584455i	0.100440	+	0.994943i	$0.467975\pi$
$920$	−27.5028	−	21.6335i	−0.906740	−	0.713234i
$921$		0			0
$922$	−0.529479	−	4.15014i	−0.0174375	−	0.136678i
$923$	−4.78955			−0.157650
$924$		0			0
$925$	54.1676			1.78102
$926$	−0.591818	−	4.63876i	−0.0194483	−	0.152439i
$927$		0			0
$928$	−14.2123	+	10.4601i	−0.466540	+	0.343371i
$929$	−47.6452	−	27.5080i	−1.56319	−	0.902508i	−0.996931	−	0.0782797i	$-0.975057\pi$
$929$	−47.6452	−	27.5080i	−1.56319	−	0.902508i	−0.566258	−	0.824228i	$-0.691609\pi$
$930$		0			0
$931$	0.449470	+	0.112334i	0.0147308	+	0.00368159i
$932$	−10.6242	+	38.4169i	−0.348008	+	1.25839i
$933$		0			0
$934$	6.50552	−	15.5295i	0.212867	−	0.508142i
$935$	−20.4746	+	11.8210i	−0.669592	+	0.386589i
$936$		0			0
$937$			6.90001i			0.225414i	0.993628	+	0.112707i	$0.0359521\pi$
$937$			6.90001i			0.225414i	−0.993628	+	0.112707i	$0.964048\pi$
$938$	0.162308	+	36.5457i	0.00529954	+	1.19326i
$939$		0			0
$940$	−7.83508	+	7.71058i	−0.255552	+	0.251491i
$941$	−16.2597	+	9.38756i	−0.530052	+	0.306026i	−0.741038	−	0.671463i	$-0.765666\pi$
$941$	−16.2597	+	9.38756i	−0.530052	+	0.306026i	0.210986	+	0.977489i	$0.432333\pi$
$942$		0			0
$943$	13.5580	−	23.4832i	0.441511	−	0.764719i
$944$	11.7965	+	7.06499i	0.383942	+	0.229946i
$945$		0			0
$946$	7.35374	+	9.66346i	0.239091	+	0.314186i
$947$	−25.7931	−	14.8916i	−0.838162	−	0.483913i	0.0184768	−	0.999829i	$-0.494118\pi$
$947$	−25.7931	−	14.8916i	−0.838162	−	0.483913i	−0.856639	+	0.515916i	$0.827452\pi$
$948$		0			0
$949$	0.333115	+	0.576972i	0.0108134	+	0.0187293i
$950$	0.915774	−	0.116835i	0.0297116	−	0.00379064i
$951$		0			0
$952$	8.60275	+	32.5702i	0.278817	+	1.05561i
$953$	23.2676			0.753711			0.376856	−	0.926272i	$-0.377005\pi$
$953$	23.2676			0.753711			0.376856	+	0.926272i	$0.377005\pi$
$954$		0			0
$955$	−46.0653	−	79.7875i	−1.49064	−	2.58186i
$956$	−4.82563	−	18.6042i	−0.156072	−	0.601703i
$957$		0			0
$958$	−10.1946	−	13.3966i	−0.329372	−	0.432823i
$959$	−7.48748	−	0.921485i	−0.241783	−	0.0297563i
$960$		0			0
$961$	−2.72297	+	4.71632i	−0.0878377	+	0.152139i
$962$	2.64905	+	1.10972i	0.0854087	+	0.0357788i
$963$		0			0
$964$	−14.8370	+	14.6012i	−0.477867	+	0.470274i
$965$		−	76.6244i		−	2.46663i
$966$		0			0
$967$		−	16.9691i		−	0.545690i	−0.962058	−	0.272845i	$-0.912035\pi$
$967$		−	16.9691i		−	0.545690i	0.962058	−	0.272845i	$-0.0879646\pi$
$968$	3.68370	−	25.6002i	0.118399	−	0.822822i
$969$		0			0
$970$	−6.07596	+	14.5041i	−0.195087	+	0.465699i
$971$	22.8349	−	39.5512i	0.732806	−	1.26926i	−0.222873	−	0.974847i	$-0.571544\pi$
$971$	22.8349	−	39.5512i	0.732806	−	1.26926i	0.955679	−	0.294410i	$-0.0951231\pi$
$972$		0			0
$973$	−11.3993	+	15.1185i	−0.365445	+	0.484678i
$974$	−8.44878	+	6.42939i	−0.270717	+	0.206011i
$975$		0			0
$976$	5.72650	+	0.0917286i	0.183301	+	0.00293616i
$977$	−23.7102	−	41.0673i	−0.758557	−	1.31386i	−0.943586	−	0.331127i	$-0.892571\pi$
$977$	−23.7102	−	41.0673i	−0.758557	−	1.31386i	0.185029	−	0.982733i	$-0.440762\pi$
$978$		0			0
$979$	−1.76098			−0.0562812
$980$	−0.479413	−	53.9719i	−0.0153143	−	1.72407i
$981$		0			0
$982$	−3.93804	−	30.8670i	−0.125668	−	0.985004i
$983$	17.6956	+	30.6497i	0.564402	+	0.977573i	0.997105	+	0.0760363i	$0.0242265\pi$
$983$	17.6956	+	30.6497i	0.564402	+	0.977573i	−0.432703	+	0.901536i	$0.642440\pi$
$984$		0			0
$985$	−63.5029	−	36.6634i	−2.02337	−	1.16819i
$986$	15.8040	−	12.0266i	0.503302	−	0.383005i
$987$		0			0
$988$	0.0471792	+	0.0130475i	0.00150097	+	0.000415095i
$989$	10.1134	−	17.5169i	0.321586	−	0.557004i
$990$		0			0
$991$	10.0136	−	5.78134i	0.318092	−	0.183650i	−0.332450	−	0.943121i	$-0.607875\pi$
$991$	10.0136	−	5.78134i	0.318092	−	0.183650i	0.650542	+	0.759471i	$0.274542\pi$
$992$	−31.2832	−	13.6979i	−0.993242	−	0.434910i
$993$		0			0
$994$	−42.0759	−	24.0440i	−1.33457	−	0.762629i
$995$		−	57.2563i		−	1.81515i
$996$		0			0
$997$	−10.6832	+	6.16793i	−0.338339	+	0.195340i	−0.659537	−	0.751672i	$-0.729248\pi$
$997$	−10.6832	+	6.16793i	−0.338339	+	0.195340i	0.321198	+	0.947012i	$0.395914\pi$
$998$	−1.84171	−	0.771516i	−0.0582983	−	0.0244219i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bf.f.19.1		8
3.2	odd	2		84.2.o.b.19.4	yes	8
4.3	odd	2		252.2.bf.g.19.3		8
7.2	even	3		1764.2.b.j.1567.6		8
7.3	odd	6		252.2.bf.g.199.3		8
7.5	odd	6		1764.2.b.i.1567.6		8
12.11	even	2		84.2.o.a.19.2	✓	8
21.2	odd	6		588.2.b.a.391.3		8
21.5	even	6		588.2.b.b.391.3		8
21.11	odd	6		588.2.o.d.31.2		8
21.17	even	6		84.2.o.a.31.2	yes	8
21.20	even	2		588.2.o.b.19.4		8
24.5	odd	2		1344.2.bl.i.1279.4		8
24.11	even	2		1344.2.bl.j.1279.4		8
28.3	even	6	inner	252.2.bf.f.199.1		8
28.19	even	6		1764.2.b.j.1567.5		8
28.23	odd	6		1764.2.b.i.1567.5		8
84.11	even	6		588.2.o.b.31.4		8
84.23	even	6		588.2.b.b.391.4		8
84.47	odd	6		588.2.b.a.391.4		8
84.59	odd	6		84.2.o.b.31.4	yes	8
84.83	odd	2		588.2.o.d.19.2		8
168.59	odd	6		1344.2.bl.i.703.4		8
168.101	even	6		1344.2.bl.j.703.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.2	✓	8	12.11	even	2
84.2.o.a.31.2	yes	8	21.17	even	6
84.2.o.b.19.4	yes	8	3.2	odd	2
84.2.o.b.31.4	yes	8	84.59	odd	6
252.2.bf.f.19.1		8	1.1	even	1	trivial
252.2.bf.f.199.1		8	28.3	even	6	inner
252.2.bf.g.19.3		8	4.3	odd	2
252.2.bf.g.199.3		8	7.3	odd	6
588.2.b.a.391.3		8	21.2	odd	6
588.2.b.a.391.4		8	84.47	odd	6
588.2.b.b.391.3		8	21.5	even	6
588.2.b.b.391.4		8	84.23	even	6
588.2.o.b.19.4		8	21.20	even	2
588.2.o.b.31.4		8	84.11	even	6
588.2.o.d.19.2		8	84.83	odd	2
588.2.o.d.31.2		8	21.11	odd	6
1344.2.bl.i.703.4		8	168.59	odd	6
1344.2.bl.i.1279.4		8	24.5	odd	2
1344.2.bl.j.703.4		8	168.101	even	6
1344.2.bl.j.1279.4		8	24.11	even	2
1764.2.b.i.1567.5		8	28.23	odd	6
1764.2.b.i.1567.6		8	7.5	odd	6
1764.2.b.j.1567.5		8	28.19	even	6
1764.2.b.j.1567.6		8	7.2	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40284 + 0.178976i) q^{2} +(1.93594 - 0.502151i) q^{4} +(3.33878 + 1.92764i) q^{5} +(-1.59285 + 2.11254i) q^{7} +(-2.62594 + 1.05092i) q^{8} +O(q^{10})\)	\(q+(-1.40284 + 0.178976i) q^{2} +(1.93594 - 0.502151i) q^{4} +(3.33878 + 1.92764i) q^{5} +(-1.59285 + 2.11254i) q^{7} +(-2.62594 + 1.05092i) q^{8} +(-5.02878 - 2.10662i) q^{10} +(1.17975 - 0.681127i) q^{11} -0.369798i q^{13} +(1.85642 - 3.24865i) q^{14} +(3.49569 - 1.94426i) q^{16} +(-3.89853 + 2.25082i) q^{17} +(-0.0330925 + 0.0573178i) q^{19} +(7.43162 + 2.05523i) q^{20} +(-1.53309 + 1.16666i) q^{22} +(2.77902 + 1.60447i) q^{23} +(4.93162 + 8.54182i) q^{25} +(0.0661849 + 0.518768i) q^{26} +(-2.02283 + 4.88960i) q^{28} +3.11951 q^{29} +(3.01852 + 5.22824i) q^{31} +(-4.55593 + 3.35314i) q^{32} +(5.06618 - 3.85529i) q^{34} +(-9.39039 + 3.98287i) q^{35} +(2.74593 - 4.75609i) q^{37} +(0.0361650 - 0.0863307i) q^{38} +(-10.7932 - 1.55307i) q^{40} -8.45017i q^{41} -6.30324i q^{43} +(1.94188 - 1.91103i) q^{44} +(-4.18569 - 1.75344i) q^{46} +(-0.712838 + 1.23467i) q^{47} +(-1.92568 - 6.72992i) q^{49} +(-8.44708 - 11.1002i) q^{50} +(-0.185694 - 0.715904i) q^{52} +(-1.27259 - 2.20420i) q^{53} +5.25188 q^{55} +(1.96260 - 7.22137i) q^{56} +(-4.37618 + 0.558317i) q^{58} +(1.71879 + 2.97703i) q^{59} +(1.23998 + 0.715904i) q^{61} +(-5.17024 - 6.79415i) q^{62} +(5.79112 - 5.51933i) q^{64} +(0.712838 - 1.23467i) q^{65} +(-8.45877 + 4.88367i) q^{67} +(-6.41706 + 6.31509i) q^{68} +(12.4604 - 7.26800i) q^{70} -12.9518i q^{71} +(-1.56024 + 0.900803i) q^{73} +(-3.00088 + 7.16350i) q^{74} +(-0.0352827 + 0.127581i) q^{76} +(-0.440245 + 3.57719i) q^{77} +(-10.8156 - 6.24438i) q^{79} +(15.4192 + 0.246989i) q^{80} +(1.51238 + 11.8543i) q^{82} +12.2889 q^{83} -17.3551 q^{85} +(1.12813 + 8.84246i) q^{86} +(-2.38213 + 3.02842i) q^{88} +(-1.11951 - 0.646349i) q^{89} +(0.781213 + 0.589031i) q^{91} +(6.18569 + 1.71066i) q^{92} +(0.779023 - 1.85963i) q^{94} +(-0.220977 + 0.127581i) q^{95} -2.88422i q^{97} +(3.90592 + 9.09636i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8	\( 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8} - 13 q^{10} + 6 q^{11} + 10 q^{14} + 7 q^{16} + 6 q^{19} + 22 q^{20} - 6 q^{22} + 2 q^{25} - 12 q^{26} - 7 q^{28} + 16 q^{29} - 6 q^{31} - 21 q^{32} + 28 q^{34} - 12 q^{35} + 6 q^{37} - 8 q^{38} - 13 q^{40} - 19 q^{44} - 12 q^{46} + 4 q^{47} + 4 q^{49} - 2 q^{50} + 20 q^{52} + 4 q^{53} + 8 q^{55} + q^{56} - 23 q^{58} - 14 q^{59} + 12 q^{61} - 48 q^{62} + 2 q^{64} - 4 q^{65} - 42 q^{67} + 10 q^{68} + 35 q^{70} - 18 q^{73} + 28 q^{74} - 44 q^{76} - 8 q^{77} + 6 q^{79} + 33 q^{80} - 14 q^{82} + 4 q^{83} - 32 q^{85} + 42 q^{86} + 11 q^{88} + 34 q^{91} + 28 q^{92} - 16 q^{94} - 24 q^{95} + 19 q^{98}+O(q^{100}) \) 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8 - 13 * q^10 + 6 * q^11 + 10 * q^14 + 7 * q^16 + 6 * q^19 + 22 * q^20 - 6 * q^22 + 2 * q^25 - 12 * q^26 - 7 * q^28 + 16 * q^29 - 6 * q^31 - 21 * q^32 + 28 * q^34 - 12 * q^35 + 6 * q^37 - 8 * q^38 - 13 * q^40 - 19 * q^44 - 12 * q^46 + 4 * q^47 + 4 * q^49 - 2 * q^50 + 20 * q^52 + 4 * q^53 + 8 * q^55 + q^56 - 23 * q^58 - 14 * q^59 + 12 * q^61 - 48 * q^62 + 2 * q^64 - 4 * q^65 - 42 * q^67 + 10 * q^68 + 35 * q^70 - 18 * q^73 + 28 * q^74 - 44 * q^76 - 8 * q^77 + 6 * q^79 + 33 * q^80 - 14 * q^82 + 4 * q^83 - 32 * q^85 + 42 * q^86 + 11 * q^88 + 34 * q^91 + 28 * q^92 - 16 * q^94 - 24 * q^95 + 19 * q^98

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