LMFDB - Embedded newform 297.2.n.b.280.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			280.5
Character	$\chi$	$=$	297.280
Dual form			297.2.n.b.262.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.190802 + 0.211907i) q^{2} +(0.200558 + 1.90818i) q^{4} +(-1.81250 - 2.01298i) q^{5} +(-3.72118 - 1.65677i) q^{7} +(-0.904002 - 0.656796i) q^{8} +0.772391 q^{10} +(-1.48164 + 2.96728i) q^{11} +(-3.76680 - 0.800659i) q^{13} +(1.06109 - 0.472427i) q^{14} +(-3.44186 + 0.731590i) q^{16} +(1.33502 - 4.10876i) q^{17} +(1.31246 + 0.953561i) q^{19} +(3.47762 - 3.86229i) q^{20} +(-0.346086 - 0.880131i) q^{22} +(-0.932117 + 1.61447i) q^{23} +(-0.244308 + 2.32444i) q^{25} +(0.888377 - 0.645443i) q^{26} +(2.41511 - 7.43295i) q^{28} +(-3.24614 - 1.44528i) q^{29} +(4.75829 + 1.01141i) q^{31} +(1.61909 - 2.80435i) q^{32} +(0.615950 + 1.06686i) q^{34} +(3.40956 + 10.4936i) q^{35} +(-6.26542 + 4.55210i) q^{37} +(-0.452486 + 0.0961788i) q^{38} +(0.316383 + 3.01018i) q^{40} +(-6.27802 + 2.79515i) q^{41} +(-0.492496 - 0.853027i) q^{43} +(-5.95925 - 2.23213i) q^{44} +(-0.164268 - 0.505566i) q^{46} +(0.613200 - 5.83421i) q^{47} +(6.41834 + 7.12829i) q^{49} +(-0.445949 - 0.495276i) q^{50} +(0.772339 - 7.34832i) q^{52} +(0.485721 + 1.49489i) q^{53} +(8.65855 - 2.39567i) q^{55} +(2.27579 + 3.94178i) q^{56} +(0.925632 - 0.412118i) q^{58} +(1.18770 + 11.3002i) q^{59} +(8.41938 - 1.78960i) q^{61} +(-1.12221 + 0.815335i) q^{62} +(-1.88937 - 5.81490i) q^{64} +(5.21561 + 9.03370i) q^{65} +(0.870282 - 1.50737i) q^{67} +(8.10800 + 1.72341i) q^{68} +(-2.87420 - 1.27968i) q^{70} +(1.77418 - 5.46036i) q^{71} +(3.27379 - 2.37855i) q^{73} +(0.230833 - 2.19623i) q^{74} +(-1.55634 + 2.69566i) q^{76} +(10.4296 - 8.58702i) q^{77} +(-2.86398 + 3.18077i) q^{79} +(7.71104 + 5.60240i) q^{80} +(0.605544 - 1.86367i) q^{82} +(-6.35814 + 1.35146i) q^{83} +(-10.6906 + 4.75975i) q^{85} +(0.274731 + 0.0583959i) q^{86} +(3.28830 - 1.70929i) q^{88} -9.26243 q^{89} +(12.6904 + 9.22014i) q^{91} +(-3.26765 - 1.45485i) q^{92} +(1.11931 + 1.24312i) q^{94} +(-0.459336 - 4.37029i) q^{95} +(-4.96005 + 5.50870i) q^{97} -2.73516 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.190802	+	0.211907i	−0.134917	+	0.149841i	−0.806817	−	0.590801i	$-0.798812\pi$
$2$	−0.190802	+	0.211907i	−0.134917	+	0.149841i	0.671900	+	0.740642i	$0.265478\pi$
$3$		0			0
$3$		0			0
$4$	0.200558	+	1.90818i	0.100279	+	0.954090i
$5$	−1.81250	−	2.01298i	−0.810573	−	0.900233i	0.186034	−	0.982543i	$-0.440437\pi$
$5$	−1.81250	−	2.01298i	−0.810573	−	0.900233i	−0.996607	+	0.0823107i	$0.973770\pi$
$6$		0			0
$7$	−3.72118	−	1.65677i	−1.40647	−	0.626202i	−0.443616	−	0.896217i	$-0.646305\pi$
$7$	−3.72118	−	1.65677i	−1.40647	−	0.626202i	−0.962856	+	0.270015i	$0.912971\pi$
$8$	−0.904002	−	0.656796i	−0.319613	−	0.232212i
$9$		0			0
$10$	0.772391			0.244251
$11$	−1.48164	+	2.96728i	−0.446732	+	0.894668i
$11$	−1.48164	+	2.96728i	−0.446732	+	0.894668i
$12$		0			0
$13$	−3.76680	−	0.800659i	−1.04472	−	0.222063i	−0.346580	−	0.938021i	$-0.612657\pi$
$13$	−3.76680	−	0.800659i	−1.04472	−	0.222063i	−0.698144	+	0.715958i	$0.745990\pi$
$14$	1.06109	−	0.472427i	0.283588	−	0.126261i
$15$		0			0
$16$	−3.44186	+	0.731590i	−0.860465	+	0.182898i
$17$	1.33502	−	4.10876i	0.323789	−	0.996520i	−0.648195	−	0.761474i	$-0.724476\pi$
$17$	1.33502	−	4.10876i	0.323789	−	0.996520i	0.971984	−	0.235046i	$-0.0755241\pi$
$18$		0			0
$19$	1.31246	+	0.953561i	0.301100	+	0.218762i	0.728068	−	0.685505i	$-0.240418\pi$
$19$	1.31246	+	0.953561i	0.301100	+	0.218762i	−0.426968	+	0.904267i	$0.640418\pi$
$20$	3.47762	−	3.86229i	0.777619	−	0.863634i
$21$		0			0
$22$	−0.346086	−	0.880131i	−0.0737859	−	0.187644i
$23$	−0.932117	+	1.61447i	−0.194360	+	0.336641i	−0.946691	−	0.322145i	$-0.895596\pi$
$23$	−0.932117	+	1.61447i	−0.194360	+	0.336641i	0.752331	+	0.658786i	$0.228930\pi$
$24$		0			0
$25$	−0.244308	+	2.32444i	−0.0488616	+	0.464887i
$26$	0.888377	−	0.645443i	0.174225	−	0.126582i
$27$		0			0
$28$	2.41511	−	7.43295i	0.456413	−	1.40470i
$29$	−3.24614	−	1.44528i	−0.602793	−	0.268381i	0.0825663	−	0.996586i	$-0.473688\pi$
$29$	−3.24614	−	1.44528i	−0.602793	−	0.268381i	−0.685360	+	0.728205i	$0.740355\pi$
$30$		0			0
$31$	4.75829	+	1.01141i	0.854614	+	0.181654i	0.614330	−	0.789049i	$-0.289426\pi$
$31$	4.75829	+	1.01141i	0.854614	+	0.181654i	0.240283	+	0.970703i	$0.422760\pi$
$32$	1.61909	−	2.80435i	0.286218	−	0.495744i
$33$		0			0
$34$	0.615950	+	1.06686i	0.105634	+	0.182964i
$35$	3.40956	+	10.4936i	0.576321	+	1.77374i
$36$		0			0
$37$	−6.26542	+	4.55210i	−1.03003	+	0.748360i	−0.968314	−	0.249734i	$-0.919657\pi$
$37$	−6.26542	+	4.55210i	−1.03003	+	0.748360i	−0.0617145	+	0.998094i	$0.519657\pi$
$38$	−0.452486	+	0.0961788i	−0.0734029	+	0.0156023i
$39$		0			0
$40$	0.316383	+	3.01018i	0.0500245	+	0.475951i
$41$	−6.27802	+	2.79515i	−0.980462	+	0.436530i	−0.833444	−	0.552604i	$-0.813634\pi$
$41$	−6.27802	+	2.79515i	−0.980462	+	0.436530i	−0.147018	+	0.989134i	$0.546967\pi$
$42$		0			0
$43$	−0.492496	−	0.853027i	−0.0751049	−	0.130085i	0.826027	−	0.563631i	$-0.190596\pi$
$43$	−0.492496	−	0.853027i	−0.0751049	−	0.130085i	−0.901132	+	0.433545i	$0.857262\pi$
$44$	−5.95925	−	2.23213i	−0.898391	−	0.336506i
$45$		0			0
$46$	−0.164268	−	0.505566i	−0.0242200	−	0.0745416i
$47$	0.613200	−	5.83421i	0.0894445	−	0.851007i	−0.854177	−	0.519982i	$-0.825939\pi$
$47$	0.613200	−	5.83421i	0.0894445	−	0.851007i	0.943622	−	0.331026i	$-0.107395\pi$
$48$		0			0
$49$	6.41834	+	7.12829i	0.916906	+	1.01833i
$50$	−0.445949	−	0.495276i	−0.0630667	−	0.0700426i
$51$		0			0
$52$	0.772339	−	7.34832i	0.107104	−	1.01903i
$53$	0.485721	+	1.49489i	0.0667189	+	0.205340i	0.978858	−	0.204541i	$-0.0655703\pi$
$53$	0.485721	+	1.49489i	0.0667189	+	0.205340i	−0.912139	+	0.409881i	$0.865570\pi$
$54$		0			0
$55$	8.65855	−	2.39567i	1.16752	−	0.323032i
$56$	2.27579	+	3.94178i	0.304115	+	0.526743i
$57$		0			0
$58$	0.925632	−	0.412118i	0.121541	−	0.0541137i
$59$	1.18770	+	11.3002i	0.154626	+	1.47117i	0.746634	+	0.665235i	$0.231669\pi$
$59$	1.18770	+	11.3002i	0.154626	+	1.47117i	−0.592008	+	0.805932i	$0.701665\pi$
$60$		0			0
$61$	8.41938	−	1.78960i	1.07799	−	0.229134i	0.365498	−	0.930812i	$-0.380899\pi$
$61$	8.41938	−	1.78960i	1.07799	−	0.229134i	0.712494	+	0.701678i	$0.247566\pi$
$62$	−1.12221	+	0.815335i	−0.142521	+	0.103548i
$63$		0			0
$64$	−1.88937	−	5.81490i	−0.236172	−	0.726862i
$65$	5.21561	+	9.03370i	0.646916	+	1.12049i
$66$		0			0
$67$	0.870282	−	1.50737i	0.106322	−	0.184155i	−0.807956	−	0.589243i	$-0.799426\pi$
$67$	0.870282	−	1.50737i	0.106322	−	0.184155i	0.914277	+	0.405088i	$0.132759\pi$
$68$	8.10800	+	1.72341i	0.983239	+	0.208994i
$69$		0			0
$70$	−2.87420	−	1.27968i	−0.343533	−	0.152951i
$71$	1.77418	−	5.46036i	0.210556	−	0.648026i	−0.788883	−	0.614543i	$-0.789340\pi$
$71$	1.77418	−	5.46036i	0.210556	−	0.648026i	0.999439	−	0.0334822i	$-0.0106597\pi$
$72$		0			0
$73$	3.27379	−	2.37855i	0.383168	−	0.278388i	−0.379482	−	0.925199i	$-0.623898\pi$
$73$	3.27379	−	2.37855i	0.383168	−	0.278388i	0.762650	+	0.646811i	$0.223898\pi$
$74$	0.230833	−	2.19623i	0.0268338	−	0.255307i
$75$		0			0
$76$	−1.55634	+	2.69566i	−0.178524	+	0.309213i
$77$	10.4296	−	8.58702i	1.18856	−	0.978582i
$78$		0			0
$79$	−2.86398	+	3.18077i	−0.322223	+	0.357864i	−0.882393	−	0.470513i	$-0.844069\pi$
$79$	−2.86398	+	3.18077i	−0.322223	+	0.357864i	0.560171	+	0.828377i	$0.310736\pi$
$80$	7.71104	+	5.60240i	0.862120	+	0.626367i
$81$		0			0
$82$	0.605544	−	1.86367i	0.0668711	−	0.205808i
$83$	−6.35814	+	1.35146i	−0.697897	+	0.148343i	−0.543180	−	0.839616i	$-0.682780\pi$
$83$	−6.35814	+	1.35146i	−0.697897	+	0.148343i	−0.154717	+	0.987959i	$0.549446\pi$
$84$		0			0
$85$	−10.6906	+	4.75975i	−1.15956	+	0.516267i
$86$	0.274731	+	0.0583959i	0.0296250	+	0.00629699i
$87$		0			0
$88$	3.28830	−	1.70929i	0.350534	−	0.182211i
$89$	−9.26243			−0.981816			−0.490908	−	0.871211i	$-0.663335\pi$
$89$	−9.26243			−0.981816			−0.490908	+	0.871211i	$0.663335\pi$
$90$		0			0
$91$	12.6904	+	9.22014i	1.33032	+	0.966533i
$92$	−3.26765	−	1.45485i	−0.340676	−	0.151679i
$93$		0			0
$94$	1.11931	+	1.24312i	0.115448	+	0.128218i
$95$	−0.459336	−	4.37029i	−0.0471269	−	0.448382i
$96$		0			0
$97$	−4.96005	+	5.50870i	−0.503617	+	0.559323i	−0.940324	−	0.340280i	$-0.889478\pi$
$97$	−4.96005	+	5.50870i	−0.503617	+	0.559323i	0.436707	+	0.899604i	$0.356145\pi$
$98$	−2.73516			−0.276293
$99$		0			0
$100$	−4.48444			−0.448444
$101$	9.17887	−	10.1942i	0.913332	−	1.01436i	−0.0865045	−	0.996251i	$-0.527570\pi$
$101$	9.17887	−	10.1942i	0.913332	−	1.01436i	0.999836	−	0.0181060i	$-0.00576362\pi$
$102$		0			0
$103$	−0.530508	−	5.04744i	−0.0522725	−	0.497339i	−0.989068	−	0.147462i	$-0.952890\pi$
$103$	−0.530508	−	5.04744i	−0.0522725	−	0.497339i	0.936795	−	0.349878i	$-0.113777\pi$
$104$	2.87933	+	3.19782i	0.282341	+	0.313572i
$105$		0			0
$106$	−0.409454	−	0.182301i	−0.0397697	−	0.0177066i
$107$	−2.24824	−	1.63344i	−0.217346	−	0.157911i	0.473785	−	0.880640i	$-0.342887\pi$
$107$	−2.24824	−	1.63344i	−0.217346	−	0.157911i	−0.691131	+	0.722730i	$0.742887\pi$
$108$		0			0
$109$	−17.3573			−1.66253			−0.831263	−	0.555879i	$-0.812382\pi$
$109$	−17.3573			−1.66253			−0.831263	+	0.555879i	$0.812382\pi$
$110$	−1.14441	+	2.29190i	−0.109115	+	0.218524i
$111$		0			0
$112$	14.0199	+	2.98001i	1.32475	+	0.281585i
$113$	−0.862071	+	0.383819i	−0.0810968	+	0.0361066i	−0.446884	−	0.894592i	$-0.647466\pi$
$113$	−0.862071	+	0.383819i	−0.0810968	+	0.0361066i	0.365787	+	0.930698i	$0.380800\pi$
$114$		0			0
$115$	4.93937	−	1.04989i	0.460598	−	0.0979032i
$116$	2.10681	−	6.48408i	0.195612	−	0.602032i
$117$		0			0
$118$	−2.62121	−	1.90442i	−0.241302	−	0.175316i
$119$	−11.7751	+	13.0776i	−1.07942	+	1.19882i
$120$		0			0
$121$	−6.60948	−	8.79288i	−0.600862	−	0.799353i
$122$	−1.22720	+	2.12558i	−0.111106	+	0.192441i
$123$		0			0
$124$	−0.975631	+	9.28251i	−0.0876143	+	0.833594i
$125$	−5.83521	+	4.23953i	−0.521917	+	0.379195i
$126$		0			0
$127$	0.757216	−	2.33047i	0.0671920	−	0.206796i	−0.911823	−	0.410583i	$-0.865325\pi$
$127$	0.757216	−	2.33047i	0.0671920	−	0.206796i	0.979015	+	0.203787i	$0.0653251\pi$
$128$	7.50917	+	3.34330i	0.663723	+	0.295508i
$129$		0			0
$130$	−2.90945	−	0.618422i	−0.255175	−	0.0542392i
$131$	1.99869	−	3.46183i	0.174626	−	0.302461i	−0.765406	−	0.643548i	$-0.777462\pi$
$131$	1.99869	−	3.46183i	0.174626	−	0.302461i	0.940032	+	0.341087i	$0.110795\pi$
$132$		0			0
$133$	−3.30407	−	5.72282i	−0.286500	−	0.496232i
$134$	0.153371	+	0.472027i	0.0132492	+	0.0407769i
$135$		0			0
$136$	−3.90547	+	2.83749i	−0.334892	+	0.243313i
$137$	1.06545	−	0.226469i	0.0910278	−	0.0193486i	−0.162173	−	0.986762i	$-0.551850\pi$
$137$	1.06545	−	0.226469i	0.0910278	−	0.0193486i	0.253200	+	0.967414i	$0.418517\pi$
$138$		0			0
$139$	−0.301557	−	2.86912i	−0.0255777	−	0.243356i	−0.999839	−	0.0179347i	$-0.994291\pi$
$139$	−0.301557	−	2.86912i	−0.0255777	−	0.243356i	0.974261	−	0.225421i	$-0.0723758\pi$
$140$	−19.3398	+	8.61062i	−1.63451	+	0.727731i
$141$		0			0
$142$	0.818570	+	1.41780i	0.0686929	+	0.118980i
$143$	7.95683	−	9.99087i	0.665383	−	0.835478i
$144$		0			0
$145$	2.97431	+	9.15398i	0.247003	+	0.760197i
$146$	−0.120614	+	1.14757i	−0.00998210	+	0.0949733i
$147$		0			0
$148$	−9.94279	−	11.0426i	−0.817293	−	0.907695i
$149$	−13.4996	−	14.9928i	−1.10593	−	1.22826i	−0.971425	−	0.237346i	$-0.923723\pi$
$149$	−13.4996	−	14.9928i	−1.10593	−	1.22826i	−0.134504	−	0.990913i	$-0.542944\pi$
$150$		0			0
$151$	1.15800	−	11.0177i	0.0942370	−	0.896605i	−0.840631	−	0.541609i	$-0.817815\pi$
$151$	1.15800	−	11.0177i	0.0942370	−	0.896605i	0.934868	−	0.354996i	$-0.115518\pi$
$152$	−0.560175	−	1.72404i	−0.0454362	−	0.139838i
$153$		0			0
$154$	−0.170330	+	3.84851i	−0.0137255	+	0.310122i
$155$	−6.58844	−	11.4115i	−0.529196	−	0.916595i
$156$		0			0
$157$	0.304014	−	0.135356i	0.0242629	−	0.0108025i	−0.394569	−	0.918866i	$-0.629106\pi$
$157$	0.304014	−	0.135356i	0.0242629	−	0.0108025i	0.418832	+	0.908064i	$0.362440\pi$
$158$	−0.127575	−	1.21379i	−0.0101493	−	0.0965640i
$159$		0			0
$160$	−8.57970	+	1.82367i	−0.678285	+	0.144174i
$161$	6.14339	−	4.46344i	0.484167	−	0.351768i
$162$		0			0
$163$	4.12168	+	12.6852i	0.322835	+	0.993584i	0.972408	+	0.233285i	$0.0749475\pi$
$163$	4.12168	+	12.6852i	0.322835	+	0.993584i	−0.649574	+	0.760299i	$0.725053\pi$
$164$	−6.59276	−	11.4190i	−0.514808	−	0.891674i
$165$		0			0
$166$	0.926759	−	1.60519i	0.0719304	−	0.124587i
$167$	−18.5018	−	3.93268i	−1.43171	−	0.304320i	−0.574172	−	0.818735i	$-0.694676\pi$
$167$	−18.5018	−	3.93268i	−1.43171	−	0.304320i	−0.857541	+	0.514415i	$0.828009\pi$
$168$		0			0
$169$	1.67166	+	0.744272i	0.128589	+	0.0572517i
$170$	1.03115	−	3.17357i	0.0790860	−	0.243402i
$171$		0			0
$172$	1.52896	−	1.11085i	0.116582	−	0.0847016i
$173$	−0.158265	+	1.50579i	−0.0120327	+	0.114483i	−0.998890	−	0.0471135i	$-0.984998\pi$
$173$	−0.158265	+	1.50579i	−0.0120327	+	0.114483i	0.986857	+	0.161597i	$0.0516644\pi$
$174$		0			0
$175$	4.76018	−	8.24487i	0.359836	−	0.623254i
$176$	2.92877	−	11.2969i	0.220764	−	0.851537i
$177$		0			0
$178$	1.76729	−	1.96277i	0.132464	−	0.147116i
$179$	10.6703	+	7.75244i	0.797537	+	0.579445i	0.910191	−	0.414190i	$-0.135935\pi$
$179$	10.6703	+	7.75244i	0.797537	+	0.579445i	−0.112653	+	0.993634i	$0.535935\pi$
$180$		0			0
$181$	0.864886	−	2.66185i	0.0642865	−	0.197853i	−0.913754	−	0.406267i	$-0.866830\pi$
$181$	0.864886	−	2.66185i	0.0642865	−	0.197853i	0.978041	+	0.208414i	$0.0668301\pi$
$182$	−4.37516	+	0.929969i	−0.324308	+	0.0689339i
$183$		0			0
$184$	1.90302	−	0.847278i	0.140292	−	0.0624621i
$185$	20.5193	+	4.36152i	1.50861	+	0.320665i
$186$		0			0
$187$	10.2138	+	10.0491i	0.746908	+	0.734861i
$188$	11.2557			0.820907
$189$		0			0
$190$	1.01374	+	0.736522i	0.0735441	+	0.0534329i
$191$	15.2942	+	6.80940i	1.10665	+	0.492711i	0.876965	−	0.480555i	$-0.159565\pi$
$191$	15.2942	+	6.80940i	1.10665	+	0.492711i	0.229682	+	0.973266i	$0.426231\pi$
$192$		0			0
$193$	−14.7472	−	16.3784i	−1.06153	−	1.17895i	−0.983296	−	0.182011i	$-0.941739\pi$
$193$	−14.7472	−	16.3784i	−1.06153	−	1.17895i	−0.0782316	−	0.996935i	$-0.524927\pi$
$194$	−0.220943	−	2.10214i	−0.0158628	−	0.150925i
$195$		0			0
$196$	−12.3148	+	13.6770i	−0.879629	+	0.976927i
$197$	−18.2247			−1.29845			−0.649227	−	0.760595i	$-0.724907\pi$
$197$	−18.2247			−1.29845			−0.649227	+	0.760595i	$0.724907\pi$
$198$		0			0
$199$	−25.0958			−1.77899			−0.889497	−	0.456942i	$-0.848945\pi$
$199$	−25.0958			−1.77899			−0.889497	+	0.456942i	$0.848945\pi$
$200$	1.74753	−	1.94083i	0.123569	−	0.137238i
$201$		0			0
$202$	0.408869	+	3.89012i	0.0287679	+	0.273708i
$203$	9.68497	+	10.7563i	0.679752	+	0.754941i
$204$		0			0
$205$	17.0055	+	7.57133i	1.18771	+	0.528804i
$206$	1.17081	+	0.850642i	0.0815741	+	0.0592670i
$207$		0			0
$208$	13.5506			0.939563
$209$	−4.77408	+	2.48161i	−0.330230	+	0.171657i
$210$		0			0
$211$	−8.08930	−	1.71943i	−0.556891	−	0.118371i	−0.0791356	−	0.996864i	$-0.525216\pi$
$211$	−8.08930	−	1.71943i	−0.556891	−	0.118371i	−0.477755	+	0.878493i	$0.658549\pi$
$212$	−2.75511	+	1.22666i	−0.189222	+	0.0842470i
$213$		0			0
$214$	0.775105	−	0.164754i	0.0529851	−	0.0112623i
$215$	−0.824482	+	2.53749i	−0.0562292	+	0.173056i
$216$		0			0
$217$	−16.0308	−	11.6470i	−1.08824	−	0.790652i
$218$	3.31180	−	3.67812i	0.224303	−	0.249114i
$219$		0			0
$220$	6.30790	+	16.0416i	0.425279	+	1.08152i
$221$	−8.31846	+	14.4080i	−0.559560	+	0.969187i
$222$		0			0
$223$	0.768502	−	7.31181i	0.0514627	−	0.489635i	−0.938187	−	0.346129i	$-0.887496\pi$
$223$	0.768502	−	7.31181i	0.0514627	−	0.489635i	0.989650	−	0.143506i	$-0.0458375\pi$
$224$	−10.6711	+	7.75301i	−0.712993	+	0.518020i
$225$		0			0
$226$	0.0831507	−	0.255912i	0.00553110	−	0.0170230i
$227$	17.3036	+	7.70408i	1.14848	+	0.511338i	0.890577	−	0.454832i	$-0.150301\pi$
$227$	17.3036	+	7.70408i	1.14848	+	0.511338i	0.257906	+	0.966170i	$0.416968\pi$
$228$		0			0
$229$	7.68770	+	1.63407i	0.508017	+	0.107982i	0.454788	−	0.890600i	$-0.349715\pi$
$229$	7.68770	+	1.63407i	0.508017	+	0.107982i	0.0532297	+	0.998582i	$0.483048\pi$
$230$	−0.719959	+	1.24701i	−0.0474727	+	0.0822251i
$231$		0			0
$232$	1.98527	+	3.43859i	0.130339	+	0.225754i
$233$	2.03006	+	6.24789i	0.132994	+	0.409313i	0.995273	−	0.0971212i	$-0.0309634\pi$
$233$	2.03006	+	6.24789i	0.132994	+	0.409313i	−0.862279	+	0.506434i	$0.830963\pi$
$234$		0			0
$235$	−12.8556	+	9.34013i	−0.838606	+	0.609283i
$236$	−21.3247	+	4.53271i	−1.38812	+	0.295054i
$237$		0			0
$238$	−0.524517	−	4.99045i	−0.0339994	−	0.323483i
$239$	23.3377	−	10.3906i	1.50959	−	0.672113i	0.525664	−	0.850692i	$-0.323817\pi$
$239$	23.3377	−	10.3906i	1.50959	−	0.672113i	0.983925	+	0.178580i	$0.0571502\pi$
$240$		0			0
$241$	1.49099	+	2.58247i	0.0960432	+	0.166352i	0.910044	−	0.414513i	$-0.136048\pi$
$241$	1.49099	+	2.58247i	0.0960432	+	0.166352i	−0.814000	+	0.580864i	$0.802715\pi$
$242$	3.12437	+	0.277103i	0.200842	+	0.0178129i
$243$		0			0
$244$	5.10344	+	15.7068i	0.326714	+	1.00552i
$245$	2.71589	−	25.8400i	0.173512	−	1.65086i
$246$		0			0
$247$	−4.18032	−	4.64271i	−0.265987	−	0.295409i
$248$	−3.63722	−	4.03954i	−0.230963	−	0.256511i
$249$		0			0
$250$	0.214983	−	2.04543i	0.0135967	−	0.129364i
$251$	−3.60577	−	11.0974i	−0.227594	−	0.700463i	−0.998018	−	0.0629308i	$-0.979955\pi$
$251$	−3.60577	−	11.0974i	−0.227594	−	0.700463i	0.770424	−	0.637532i	$-0.220045\pi$
$252$		0			0
$253$	−3.40953	−	5.15792i	−0.214355	−	0.324276i
$254$	0.349364	+	0.605116i	0.0219211	+	0.0379684i
$255$		0			0
$256$	9.02987	−	4.02036i	0.564367	−	0.251272i
$257$	2.16630	+	20.6109i	0.135130	+	1.28567i	0.826402	+	0.563080i	$0.190384\pi$
$257$	2.16630	+	20.6109i	0.135130	+	1.28567i	−0.691273	+	0.722594i	$0.742950\pi$
$258$		0			0
$259$	30.8565	−	6.55876i	1.91733	−	0.407541i
$260$	−16.1919	+	11.7641i	−1.00418	+	0.729578i
$261$		0			0
$262$	0.352231	+	1.08406i	0.0217609	+	0.0669732i
$263$	4.54273	+	7.86823i	0.280117	+	0.485176i	0.971413	−	0.237395i	$-0.0762936\pi$
$263$	4.54273	+	7.86823i	0.280117	+	0.485176i	−0.691297	+	0.722571i	$0.742960\pi$
$264$		0			0
$265$	2.12883	−	3.68724i	0.130773	−	0.226505i
$266$	1.84313	+	0.391769i	0.113009	+	0.0240209i
$267$		0			0
$268$	3.05088	+	1.35834i	0.186362	+	0.0829737i
$269$	−2.45399	+	7.55261i	−0.149623	+	0.460491i	−0.997576	−	0.0695792i	$-0.977834\pi$
$269$	−2.45399	+	7.55261i	−0.149623	+	0.460491i	0.847954	+	0.530070i	$0.177834\pi$
$270$		0			0
$271$	−3.01249	+	2.18870i	−0.182995	+	0.132954i	−0.675512	−	0.737349i	$-0.736077\pi$
$271$	−3.01249	+	2.18870i	−0.182995	+	0.132954i	0.492516	+	0.870303i	$0.336077\pi$
$272$	−1.58901	+	15.1185i	−0.0963481	+	0.916691i
$273$		0			0
$274$	−0.155300	+	0.268987i	−0.00938201	+	0.0162501i
$275$	−6.53527	−	4.16891i	−0.394092	−	0.251395i
$276$		0			0
$277$	−2.61004	+	2.89874i	−0.156822	+	0.174168i	−0.816436	−	0.577436i	$-0.804053\pi$
$277$	−2.61004	+	2.89874i	−0.156822	+	0.174168i	0.659614	+	0.751605i	$0.270720\pi$
$278$	0.665523	+	0.483531i	0.0399154	+	0.0290003i
$279$		0			0
$280$	3.80987	−	11.7256i	0.227684	−	0.700738i
$281$	0.0387572	−	0.00823810i	0.00231206	−	0.000491444i	−0.206756	−	0.978393i	$-0.566290\pi$
$281$	0.0387572	−	0.00823810i	0.00231206	−	0.000491444i	0.209068	+	0.977901i	$0.432957\pi$
$282$		0			0
$283$	5.84109	−	2.60062i	0.347217	−	0.154591i	−0.225716	−	0.974193i	$-0.572472\pi$
$283$	5.84109	−	2.60062i	0.347217	−	0.154591i	0.572933	+	0.819602i	$0.305806\pi$
$284$	10.7752	+	2.29033i	0.639389	+	0.135906i
$285$		0			0
$286$	0.598955	+	3.59238i	0.0354169	+	0.212422i
$287$	27.9925			1.65235
$288$		0			0
$289$	−1.34634	−	0.978174i	−0.0791965	−	0.0575397i
$290$	−2.50729	−	1.11632i	−0.147233	−	0.0655524i
$291$		0			0
$292$	5.19528	+	5.76994i	0.304031	+	0.337660i
$293$	−2.44674	−	23.2792i	−0.142940	−	1.35998i	−0.797200	−	0.603715i	$-0.793686\pi$
$293$	−2.44674	−	23.2792i	−0.142940	−	1.35998i	0.654260	−	0.756270i	$-0.272980\pi$
$294$		0			0
$295$	20.5945	−	22.8725i	1.19906	−	1.33169i
$296$	8.65375			0.502989
$297$		0			0
$298$	5.75282			0.333252
$299$	4.80375	−	5.33510i	0.277808	−	0.308537i
$300$		0			0
$301$	0.419389	+	3.99022i	0.0241732	+	0.229992i
$302$	2.11377	+	2.34758i	0.121634	+	0.135088i
$303$		0			0
$304$	−5.21493	−	2.32184i	−0.299097	−	0.133166i
$305$	−18.8625	−	13.7044i	−1.08007	−	0.784713i
$306$		0			0
$307$	29.1494			1.66365			0.831823	−	0.555042i	$-0.187298\pi$
$307$	29.1494			1.66365			0.831823	+	0.555042i	$0.187298\pi$
$308$	18.4773	+	18.1793i	1.05284	+	1.03586i
$309$		0			0
$310$	3.67526	+	0.781200i	0.208741	+	0.0443692i
$311$	18.0021	−	8.01504i	1.02080	−	0.454491i	0.173068	−	0.984910i	$-0.444632\pi$
$311$	18.0021	−	8.01504i	1.02080	−	0.454491i	0.847736	+	0.530418i	$0.177965\pi$
$312$		0			0
$313$	−1.30913	+	0.278264i	−0.0739964	+	0.0157284i	−0.244761	−	0.969583i	$-0.578710\pi$
$313$	−1.30913	+	0.278264i	−0.0739964	+	0.0157284i	0.170765	+	0.985312i	$0.445376\pi$
$314$	−0.0293235	+	0.0902485i	−0.00165482	+	0.00509302i
$315$		0			0
$316$	−6.64387	−	4.82706i	−0.373747	−	0.271543i
$317$	−2.67712	+	2.97324i	−0.150362	+	0.166994i	−0.813620	−	0.581397i	$-0.802506\pi$
$317$	−2.67712	+	2.97324i	−0.150362	+	0.166994i	0.663258	+	0.748391i	$0.269173\pi$
$318$		0			0
$319$	9.09815	−	7.49083i	0.509399	−	0.419406i
$320$	−8.28080	+	14.3428i	−0.462911	+	0.801785i
$321$		0			0
$322$	−0.226337	+	2.15346i	−0.0126133	+	0.120007i
$323$	5.67011	−	4.11958i	0.315493	−	0.229219i
$324$		0			0
$325$	2.78134	−	8.56008i	0.154281	−	0.474828i
$326$	−3.47451	−	1.54695i	−0.192435	−	0.0856776i
$327$		0			0
$328$	7.51119	+	1.59655i	0.414736	+	0.0881548i
$329$	−11.9478	+	20.6942i	−0.658704	+	1.14091i
$330$		0			0
$331$	−1.59017	−	2.75425i	−0.0874034	−	0.151387i	0.819009	−	0.573780i	$-0.194524\pi$
$331$	−1.59017	−	2.75425i	−0.0874034	−	0.151387i	−0.906413	+	0.422393i	$0.861190\pi$
$332$	−3.85401	−	11.8614i	−0.211516	−	0.650980i
$333$		0			0
$334$	4.36353	−	3.17029i	0.238762	−	0.173471i
$335$	−4.61169	+	0.980246i	−0.251964	+	0.0535566i
$336$		0			0
$337$	1.90219	+	18.0981i	0.103619	+	0.985867i	0.915575	+	0.402148i	$0.131736\pi$
$337$	1.90219	+	18.0981i	0.103619	+	0.985867i	−0.811956	+	0.583719i	$0.801597\pi$
$338$	−0.476672	+	0.212228i	−0.0259275	+	0.0115437i
$339$		0			0
$340$	−11.2265	−	19.4449i	−0.608844	−	1.05455i
$341$	−10.0512	+	12.6206i	−0.544303	+	0.683445i
$342$		0			0
$343$	−3.26270	−	10.0416i	−0.176169	−	0.542193i
$344$	−0.115048	+	1.09461i	−0.00620297	+	0.0590173i
$345$		0			0
$346$	−0.288890	−	0.320845i	−0.0155308	−	0.0172487i
$347$	18.3436	+	20.3726i	0.984737	+	1.09366i	0.995599	+	0.0937200i	$0.0298758\pi$
$347$	18.3436	+	20.3726i	0.984737	+	1.09366i	−0.0108618	+	0.999941i	$0.503457\pi$
$348$		0			0
$349$	−2.39428	+	22.7800i	−0.128163	+	1.21939i	0.721633	+	0.692276i	$0.243392\pi$
$349$	−2.39428	+	22.7800i	−0.128163	+	1.21939i	−0.849796	+	0.527112i	$0.823275\pi$
$350$	0.838893	+	2.58185i	0.0448407	+	0.138006i
$351$		0			0
$352$	5.92237	+	8.95933i	0.315663	+	0.477534i
$353$	−14.8524	−	25.7250i	−0.790511	−	1.36921i	−0.925651	−	0.378379i	$-0.876482\pi$
$353$	−14.8524	−	25.7250i	−0.790511	−	1.36921i	0.135140	−	0.990827i	$-0.456852\pi$
$354$		0			0
$355$	−14.2073	+	6.32550i	−0.754045	+	0.335722i
$356$	−1.85765	−	17.6744i	−0.0984554	−	0.936741i
$357$		0			0
$358$	−3.67871	+	0.781933i	−0.194426	+	0.0413265i
$359$	−29.8183	+	21.6643i	−1.57375	+	1.14340i	−0.650299	+	0.759678i	$0.725356\pi$
$359$	−29.8183	+	21.6643i	−1.57375	+	1.14340i	−0.923450	+	0.383718i	$0.874644\pi$
$360$		0			0
$361$	−5.05804	−	15.5670i	−0.266213	−	0.819318i
$362$	0.399041	+	0.691159i	0.0209731	+	0.0363265i
$363$		0			0
$364$	−15.0485	+	26.0648i	−0.788756	+	1.36617i
$365$	−10.7217	−	2.27897i	−0.561199	−	0.119287i
$366$		0			0
$367$	−22.7113	−	10.1117i	−1.18552	−	0.527828i	−0.283270	−	0.959040i	$-0.591419\pi$
$367$	−22.7113	−	10.1117i	−1.18552	−	0.527828i	−0.902251	+	0.431212i	$0.858086\pi$
$368$	2.02708	−	6.23872i	0.105669	−	0.325216i
$369$		0			0
$370$	−4.83936	+	3.51600i	−0.251586	+	0.182788i
$371$	0.669251	−	6.36750i	0.0347458	−	0.330584i
$372$		0			0
$373$	−9.13952	+	15.8301i	−0.473227	+	0.819653i	−0.999530	−	0.0306440i	$-0.990244\pi$
$373$	−9.13952	+	15.8301i	−0.473227	+	0.819653i	0.526304	+	0.850297i	$0.323578\pi$
$374$	−4.07828	+	0.246996i	−0.210883	+	0.0127719i
$375$		0			0
$376$	−4.38622	+	4.87139i	−0.226202	+	0.251223i
$377$	11.0704	+	8.04312i	0.570155	+	0.414242i
$378$		0			0
$379$	−9.72145	+	29.9196i	−0.499357	+	1.53686i	0.310697	+	0.950509i	$0.399438\pi$
$379$	−9.72145	+	29.9196i	−0.499357	+	1.53686i	−0.810054	+	0.586355i	$0.800562\pi$
$380$	8.24717	−	1.75299i	0.423071	−	0.0899265i
$381$		0			0
$382$	−4.36111	+	1.94169i	−0.223134	+	0.0993455i
$383$	−12.1601	−	2.58471i	−0.621352	−	0.132073i	−0.113530	−	0.993535i	$-0.536216\pi$
$383$	−12.1601	−	2.58471i	−0.621352	−	0.132073i	−0.507822	+	0.861462i	$0.669549\pi$
$384$		0			0
$385$	−36.1891	−	5.43056i	−1.84437	−	0.276767i
$386$	6.28449			0.319872
$387$		0			0
$388$	−11.5064	−	8.35986i	−0.584147	−	0.424408i
$389$	−6.68686	−	2.97718i	−0.339037	−	0.150949i	0.230154	−	0.973154i	$-0.426077\pi$
$389$	−6.68686	−	2.97718i	−0.339037	−	0.150949i	−0.569191	+	0.822205i	$0.692744\pi$
$390$		0			0
$391$	5.38909	+	5.98520i	0.272538	+	0.302684i
$392$	−1.12036	−	10.6595i	−0.0565868	−	0.538388i
$393$		0			0
$394$	3.47729	−	3.86193i	0.175184	−	0.194561i
$395$	11.5938			0.583346
$396$		0			0
$397$	34.2087			1.71688			0.858442	−	0.512911i	$-0.171433\pi$
$397$	34.2087			1.71688			0.858442	+	0.512911i	$0.171433\pi$
$398$	4.78831	−	5.31796i	0.240016	−	0.266565i
$399$		0			0
$400$	−0.859660	−	8.17911i	−0.0429830	−	0.408956i
$401$	−5.00227	−	5.55558i	−0.249801	−	0.277433i	0.605183	−	0.796086i	$-0.293100\pi$
$401$	−5.00227	−	5.55558i	−0.249801	−	0.277433i	−0.854984	+	0.518654i	$0.826433\pi$
$402$		0			0
$403$	−17.1137	−	7.61953i	−0.852496	−	0.379556i
$404$	21.2932	+	15.4704i	1.05938	+	0.769682i
$405$		0			0
$406$	−4.12723			−0.204831
$407$	−4.22423	−	25.3358i	−0.209387	−	1.25585i
$408$		0			0
$409$	−2.35753	−	0.501108i	−0.116572	−	0.0247782i	0.149256	−	0.988799i	$-0.452312\pi$
$409$	−2.35753	−	0.501108i	−0.116572	−	0.0247782i	−0.265828	+	0.964020i	$0.585645\pi$
$410$	−4.84908	+	2.15895i	−0.239479	+	0.106623i
$411$		0			0
$412$	9.52503	−	2.02461i	0.469265	−	0.0997453i
$413$	14.3023	−	44.0180i	0.703771	−	2.16598i
$414$		0			0
$415$	14.2446	+	10.3493i	0.699239	+	0.508027i
$416$	−8.34413	+	9.26709i	−0.409104	+	0.454357i
$417$		0			0
$418$	0.385032	−	1.48515i	0.0188325	−	0.0726412i
$419$	−5.60088	+	9.70101i	−0.273621	+	0.473925i	−0.969786	−	0.243956i	$-0.921555\pi$
$419$	−5.60088	+	9.70101i	−0.273621	+	0.473925i	0.696165	+	0.717881i	$0.254888\pi$
$420$		0			0
$421$	0.721755	−	6.86704i	0.0351762	−	0.334679i	−0.962754	−	0.270378i	$-0.912851\pi$
$421$	0.721755	−	6.86704i	0.0351762	−	0.334679i	0.997931	−	0.0643013i	$-0.0204819\pi$
$422$	1.90781	−	1.38611i	0.0928708	−	0.0674746i
$423$		0			0
$424$	0.542748	−	1.67041i	0.0263582	−	0.0811222i
$425$	9.22439	+	4.10696i	0.447449	+	0.199217i
$426$		0			0
$427$	−34.2950	−	7.28962i	−1.65965	−	0.352770i
$428$	2.66600	−	4.61765i	0.128866	−	0.223202i
$429$		0			0
$430$	−0.380399	−	0.658871i	−0.0183445	−	0.0317736i
$431$	9.01729	+	27.7524i	0.434348	+	1.33678i	0.893754	+	0.448558i	$0.148062\pi$
$431$	9.01729	+	27.7524i	0.434348	+	1.33678i	−0.459406	+	0.888226i	$0.651938\pi$
$432$		0			0
$433$	29.5582	−	21.4753i	1.42048	−	1.03204i	0.428785	−	0.903407i	$-0.358942\pi$
$433$	29.5582	−	21.4753i	1.42048	−	1.03204i	0.991693	−	0.128630i	$-0.0410581\pi$
$434$	5.52677	−	1.17475i	0.265294	−	0.0563899i
$435$		0			0
$436$	−3.48114	−	33.1208i	−0.166716	−	1.58620i
$437$	−2.76287	+	1.23011i	−0.132166	+	0.0588441i
$438$		0			0
$439$	10.7487	+	18.6173i	0.513009	+	0.888557i	0.999886	+	0.0150869i	$0.00480250\pi$
$439$	10.7487	+	18.6173i	0.513009	+	0.888557i	−0.486877	+	0.873470i	$0.661864\pi$
$440$	−9.40081	−	3.52121i	−0.448166	−	0.167867i
$441$		0			0
$442$	−1.46597	−	4.51180i	−0.0697293	−	0.214605i
$443$	−3.49595	+	33.2618i	−0.166098	+	1.58031i	0.520876	+	0.853633i	$0.325605\pi$
$443$	−3.49595	+	33.2618i	−0.166098	+	1.58031i	−0.686974	+	0.726682i	$0.741061\pi$
$444$		0			0
$445$	16.7881	+	18.6451i	0.795834	+	0.883863i
$446$	1.40279	+	1.55795i	0.0664240	+	0.0737713i
$447$		0			0
$448$	−2.60328	+	24.7685i	−0.122993	+	1.17020i
$449$	−12.2165	−	37.5984i	−0.576530	−	1.77438i	−0.630908	−	0.775858i	$-0.717318\pi$
$449$	−12.2165	−	37.5984i	−0.576530	−	1.77438i	0.0543777	−	0.998520i	$-0.482682\pi$
$450$		0			0
$451$	1.00777	−	22.7700i	0.0474540	−	1.07220i
$452$	−0.905290	−	1.56801i	−0.0425813	−	0.0737529i
$453$		0			0
$454$	−4.93411	+	2.19681i	−0.231569	+	0.103101i
$455$	−4.44140	−	42.2571i	−0.208216	−	1.98104i
$456$		0			0
$457$	−36.6926	+	7.79925i	−1.71641	+	0.364834i	−0.957960	−	0.286901i	$-0.907375\pi$
$457$	−36.6926	+	7.79925i	−1.71641	+	0.364834i	−0.758447	+	0.651735i	$0.774041\pi$
$458$	−1.81309	+	1.31729i	−0.0847204	+	0.0615529i
$459$		0			0
$460$	2.99402	+	9.21464i	0.139597	+	0.429635i
$461$	9.68265	+	16.7708i	0.450966	+	0.781096i	0.998446	−	0.0557228i	$-0.0177463\pi$
$461$	9.68265	+	16.7708i	0.450966	+	0.781096i	−0.547480	+	0.836818i	$0.684413\pi$
$462$		0			0
$463$	7.17464	−	12.4268i	0.333434	−	0.577524i	−0.649749	−	0.760149i	$-0.725126\pi$
$463$	7.17464	−	12.4268i	0.333434	−	0.577524i	0.983183	+	0.182625i	$0.0584594\pi$
$464$	12.2301	+	2.59959i	0.567769	+	0.120683i
$465$		0			0
$466$	−1.71131	−	0.761923i	−0.0792748	−	0.0352954i
$467$	6.89755	−	21.2285i	0.319180	−	0.982336i	−0.654819	−	0.755786i	$-0.727255\pi$
$467$	6.89755	−	21.2285i	0.319180	−	0.982336i	0.973999	−	0.226551i	$-0.0727449\pi$
$468$		0			0
$469$	−5.73585	+	4.16734i	−0.264857	+	0.192430i
$470$	0.473631	−	4.50629i	0.0218469	−	0.207860i
$471$		0			0
$472$	6.34827	−	10.9955i	0.292203	−	0.506110i
$473$	3.26087	−	0.197491i	0.149935	−	0.00908065i
$474$		0			0
$475$	−2.53713	+	2.81777i	−0.116412	+	0.129288i
$476$	−27.3160	−	19.8462i	−1.25203	−	0.909651i
$477$		0			0
$478$	−2.25103	+	6.92795i	−0.102960	+	0.316877i
$479$	−22.7533	+	4.83637i	−1.03963	+	0.220979i	−0.695936	−	0.718104i	$-0.745010\pi$
$479$	−22.7533	+	4.83637i	−1.03963	+	0.220979i	−0.343690	+	0.939083i	$0.611677\pi$
$480$		0			0
$481$	27.2453	−	12.1304i	1.24228	−	0.553098i
$482$	−0.831726	−	0.176789i	−0.0378841	−	0.00805251i
$483$		0			0
$484$	15.4528	−	14.3756i	0.702401	−	0.653434i
$485$	20.0790			0.911740
$486$		0			0
$487$	−0.219083	−	0.159173i	−0.00992760	−	0.00721282i	0.582810	−	0.812608i	$-0.301953\pi$
$487$	−0.219083	−	0.159173i	−0.00992760	−	0.00721282i	−0.592738	+	0.805395i	$0.701953\pi$
$488$	−8.78654	−	3.91202i	−0.397748	−	0.177089i
$489$		0			0
$490$	4.95747	+	5.50583i	0.223956	+	0.248728i
$491$	−0.439705	−	4.18351i	−0.0198436	−	0.188799i	0.980110	−	0.198456i	$-0.0635927\pi$
$491$	−0.439705	−	4.18351i	−0.0198436	−	0.188799i	−0.999953	+	0.00965687i	$0.996926\pi$
$492$		0			0
$493$	−10.2719	+	11.4081i	−0.462625	+	0.513797i
$494$	1.78143			0.0801504
$495$		0			0
$496$	−17.1173			−0.768589
$497$	−15.6486	+	17.3796i	−0.701936	+	0.779579i
$498$		0			0
$499$	1.60600	+	15.2801i	0.0718944	+	0.684030i	0.969810	+	0.243862i	$0.0784144\pi$
$499$	1.60600	+	15.2801i	0.0718944	+	0.684030i	−0.897916	+	0.440168i	$0.854919\pi$
$500$	−9.26007	−	10.2844i	−0.414123	−	0.459930i
$501$		0			0
$502$	3.03960	+	1.35332i	0.135664	+	0.0604016i
$503$	3.16786	+	2.30159i	0.141248	+	0.102623i	0.656165	−	0.754617i	$-0.272177\pi$
$503$	3.16786	+	2.30159i	0.141248	+	0.102623i	−0.514917	+	0.857240i	$0.672177\pi$
$504$		0			0
$505$	−37.1573			−1.65348
$506$	1.74354	+	0.261637i	0.0775099	+	0.0116312i
$507$		0			0
$508$	4.59882	+	0.977510i	0.204040	+	0.0433700i
$509$	−26.0812	+	11.6121i	−1.15603	+	0.514696i	−0.892984	−	0.450088i	$-0.851393\pi$
$509$	−26.0812	+	11.6121i	−1.15603	+	0.514696i	−0.263043	+	0.964784i	$0.584726\pi$
$510$		0			0
$511$	−16.1231	+	3.42706i	−0.713242	+	0.151604i
$512$	−5.95109	+	18.3156i	−0.263004	+	0.809442i
$513$		0			0
$514$	−4.78092	−	3.47354i	−0.210877	−	0.153211i
$515$	−9.19887	+	10.2164i	−0.405351	+	0.450187i
$516$		0			0
$517$	16.4032	+	10.4637i	0.721411	+	0.460195i
$518$	−4.49763	+	7.79012i	−0.197615	+	0.342278i
$519$		0			0
$520$	1.21838	−	11.5921i	0.0534293	−	0.508346i
$521$	−11.5485	+	8.39049i	−0.505950	+	0.367594i	−0.811285	−	0.584651i	$-0.801232\pi$
$521$	−11.5485	+	8.39049i	−0.505950	+	0.367594i	0.305335	+	0.952245i	$0.401232\pi$
$522$		0			0
$523$	−10.2462	+	31.5345i	−0.448034	+	1.37891i	0.431088	+	0.902310i	$0.358130\pi$
$523$	−10.2462	+	31.5345i	−0.448034	+	1.37891i	−0.879122	+	0.476597i	$0.841870\pi$
$524$	7.00664	+	3.11956i	0.306086	+	0.136278i
$525$		0			0
$526$	−2.53409	−	0.538637i	−0.110492	−	0.0234857i
$527$	10.5080	−	18.2004i	0.457736	−	0.792822i
$528$		0			0
$529$	9.76231	+	16.9088i	0.424448	+	0.735166i
$530$	0.375166	+	1.15464i	0.0162962	+	0.0501545i
$531$		0			0
$532$	10.2575	−	7.45252i	0.444720	−	0.323108i
$533$	25.8860	−	5.50224i	1.12125	−	0.238329i
$534$		0			0
$535$	0.786839	+	7.48627i	0.0340180	+	0.323660i
$536$	−1.77677	+	0.791070i	−0.0767449	+	0.0341690i
$537$		0			0
$538$	−1.13222	−	1.96107i	−0.0488136	−	0.0845476i
$539$	−30.6613	+	8.48344i	−1.32068	+	0.365407i
$540$		0			0
$541$	−8.79490	−	27.0679i	−0.378122	−	1.16374i	−0.941348	−	0.337437i	$-0.890440\pi$
$541$	−8.79490	−	27.0679i	−0.378122	−	1.16374i	0.563226	−	0.826303i	$-0.309560\pi$
$542$	0.110987	−	1.05597i	0.00476731	−	0.0453579i
$543$		0			0
$544$	−9.36088	−	10.3963i	−0.401344	−	0.445738i
$545$	31.4600	+	34.9399i	1.34760	+	1.49666i
$546$		0			0
$547$	3.21390	−	30.5782i	0.137416	−	1.30743i	−0.680779	−	0.732489i	$-0.738359\pi$
$547$	3.21390	−	30.5782i	0.137416	−	1.30743i	0.818195	−	0.574940i	$-0.194975\pi$
$548$	0.645829	+	1.98766i	0.0275884	+	0.0849085i
$549$		0			0
$550$	2.13036	−	0.589432i	0.0908388	−	0.0251335i
$551$	−2.88228	−	4.99226i	−0.122789	−	0.212678i
$552$		0			0
$553$	15.9272	−	7.09124i	0.677293	−	0.301550i
$554$	−0.116263	−	1.10617i	−0.00493954	−	0.0469965i
$555$		0			0
$556$	5.41432	−	1.15085i	0.229618	−	0.0488069i
$557$	−5.90145	+	4.28765i	−0.250052	+	0.181674i	−0.705750	−	0.708461i	$-0.749390\pi$
$557$	−5.90145	+	4.28765i	−0.250052	+	0.181674i	0.455698	+	0.890135i	$0.349390\pi$
$558$		0			0
$559$	1.17215	+	3.60751i	0.0495767	+	0.152581i
$560$	−19.4122	−	33.6230i	−0.820316	−	1.42083i
$561$		0			0
$562$	−0.00564923	+	0.00978475i	−0.000238298	+	0.000412745i
$563$	−35.7742	−	7.60405i	−1.50770	−	0.320472i	−0.621369	−	0.783518i	$-0.713423\pi$
$563$	−35.7742	−	7.60405i	−1.50770	−	0.320472i	−0.886335	+	0.463045i	$0.846757\pi$
$564$		0			0
$565$	2.33512	+	1.03966i	0.0982393	+	0.0437389i
$566$	−0.563400	+	1.73397i	−0.0236815	+	0.0728841i
$567$		0			0
$568$	−5.19020	+	3.77090i	−0.217776	+	0.158224i
$569$	0.0158344	−	0.150654i	0.000663811	−	0.00631574i	−0.994185	−	0.107686i	$-0.965656\pi$
$569$	0.0158344	−	0.150654i	0.000663811	−	0.00631574i	0.994849	+	0.101370i	$0.0323226\pi$
$570$		0			0
$571$	−21.6127	+	37.4343i	−0.904463	+	1.56658i	−0.0828262	+	0.996564i	$0.526395\pi$
$571$	−21.6127	+	37.4343i	−0.904463	+	1.56658i	−0.821637	+	0.570012i	$0.806939\pi$
$572$	20.6602	+	13.1793i	0.863845	+	0.551055i
$573$		0			0
$574$	−5.34102	+	5.93180i	−0.222930	+	0.247589i
$575$	−3.52502	−	2.56108i	−0.147003	−	0.106804i
$576$		0			0
$577$	9.00017	−	27.6997i	0.374682	−	1.15315i	−0.569011	−	0.822330i	$-0.692674\pi$
$577$	9.00017	−	27.6997i	0.374682	−	1.15315i	0.943693	−	0.330822i	$-0.107326\pi$
$578$	0.464165	−	0.0986614i	0.0193067	−	0.00410377i
$579$		0			0
$580$	−16.8709	+	7.51142i	−0.700527	+	0.311895i
$581$	25.8988	+	5.50497i	1.07446	+	0.228385i
$582$		0			0
$583$	−5.15543	−	0.773629i	−0.213516	−	0.0320404i
$584$	−4.52173			−0.187111
$585$		0			0
$586$	5.39985	+	3.92322i	0.223066	+	0.162067i
$587$	20.7328	+	9.23084i	0.855734	+	0.380997i	0.787235	−	0.616654i	$-0.211512\pi$
$587$	20.7328	+	9.23084i	0.855734	+	0.380997i	0.0684998	+	0.997651i	$0.478179\pi$
$588$		0			0
$589$	5.28064	+	5.86475i	0.217585	+	0.241653i
$590$	0.917372	+	8.72821i	0.0377676	+	0.359335i
$591$		0			0
$592$	18.2344	−	20.2514i	0.749431	−	0.832327i
$593$	22.9308			0.941656			0.470828	−	0.882225i	$-0.343955\pi$
$593$	22.9308			0.941656			0.470828	+	0.882225i	$0.343955\pi$
$594$		0			0
$595$	47.6673			1.95417
$596$	25.9015	−	28.7666i	1.06097	−	1.17832i
$597$		0			0
$598$	0.213981	+	2.03589i	0.00875032	+	0.0832538i
$599$	8.36460	+	9.28982i	0.341768	+	0.379572i	0.889386	−	0.457156i	$-0.151132\pi$
$599$	8.36460	+	9.28982i	0.341768	+	0.379572i	−0.547618	+	0.836728i	$0.684465\pi$
$600$		0			0
$601$	20.5354	+	9.14296i	0.837658	+	0.372949i	0.780301	−	0.625405i	$-0.215066\pi$
$601$	20.5354	+	9.14296i	0.837658	+	0.372949i	0.0573569	+	0.998354i	$0.481733\pi$
$602$	−0.925574	−	0.672469i	−0.0377236	−	0.0274078i
$603$		0			0
$604$	21.2559			0.864892
$605$	−5.72025	+	29.2418i	−0.232561	+	1.18885i
$606$		0			0
$607$	−26.1212	−	5.55223i	−1.06023	−	0.225358i	−0.355383	−	0.934721i	$-0.615649\pi$
$607$	−26.1212	−	5.55223i	−1.06023	−	0.225358i	−0.704843	+	0.709363i	$0.748983\pi$
$608$	4.79912	−	2.13670i	0.194630	−	0.0866548i
$609$		0			0
$610$	6.50306	−	1.38227i	0.263301	−	0.0559664i
$611$	−6.98102	+	21.4854i	−0.282422	+	0.869205i
$612$		0			0
$613$	35.1797	+	25.5595i	1.42089	+	1.03234i	0.991623	+	0.129163i	$0.0412289\pi$
$613$	35.1797	+	25.5595i	1.42089	+	1.03234i	0.429269	+	0.903176i	$0.358771\pi$
$614$	−5.56175	+	6.17695i	−0.224454	+	0.249282i
$615$		0			0
$616$	−15.0683	+	0.912593i	−0.607118	+	0.0367694i
$617$	20.7128	−	35.8756i	0.833864	−	1.44430i	−0.0610871	−	0.998132i	$-0.519457\pi$
$617$	20.7128	−	35.8756i	0.833864	−	1.44430i	0.894952	−	0.446163i	$-0.147210\pi$
$618$		0			0
$619$	−0.931532	+	8.86293i	−0.0374414	+	0.356231i	0.959721	+	0.280954i	$0.0906508\pi$
$619$	−0.931532	+	8.86293i	−0.0374414	+	0.356231i	−0.997163	+	0.0752773i	$0.976016\pi$
$620$	20.4539	−	14.8606i	0.821446	−	0.596816i
$621$		0			0
$622$	−1.73638	+	5.34404i	−0.0696227	+	0.214277i
$623$	34.4672	+	15.3458i	1.38090	+	0.614815i
$624$		0			0
$625$	30.5412	+	6.49173i	1.22165	+	0.259669i
$626$	0.190818	−	0.330506i	0.00762662	−	0.0132097i
$627$		0			0
$628$	0.319255	+	0.552966i	0.0127397	+	0.0220657i
$629$	10.3390	+	31.8202i	0.412244	+	1.26876i
$630$		0			0
$631$	4.58752	−	3.33303i	0.182626	−	0.132686i	−0.492716	−	0.870190i	$-0.663996\pi$
$631$	4.58752	−	3.33303i	0.182626	−	0.132686i	0.675342	+	0.737504i	$0.263996\pi$
$632$	4.67816	−	0.994373i	0.186087	−	0.0395540i
$633$		0			0
$634$	−0.119251	−	1.13460i	−0.00473606	−	0.0450606i
$635$	−6.06365	+	2.69971i	−0.240628	+	0.107135i
$636$		0			0
$637$	−18.4693	−	31.9898i	−0.731780	−	1.26748i
$638$	−0.148586	+	3.35722i	−0.00588257	+	0.132914i
$639$		0			0
$640$	−6.88034	−	21.1755i	−0.271970	−	0.837036i
$641$	2.80327	−	26.6713i	0.110722	−	1.05345i	−0.788222	−	0.615390i	$-0.788998\pi$
$641$	2.80327	−	26.6713i	0.110722	−	1.05345i	0.898945	−	0.438062i	$-0.144335\pi$
$642$		0			0
$643$	9.46047	+	10.5069i	0.373085	+	0.414352i	0.900224	−	0.435426i	$-0.143402\pi$
$643$	9.46047	+	10.5069i	0.373085	+	0.414352i	−0.527140	+	0.849779i	$0.676736\pi$
$644$	9.74915	+	10.8275i	0.384170	+	0.426664i
$645$		0			0
$646$	−0.208900	+	1.98756i	−0.00821908	+	0.0781993i
$647$	0.393698	+	1.21168i	0.0154779	+	0.0476360i	0.958497	−	0.285102i	$-0.0920275\pi$
$647$	0.393698	+	1.21168i	0.0154779	+	0.0476360i	−0.943019	+	0.332738i	$0.892027\pi$
$648$		0			0
$649$	−35.2907	−	13.2187i	−1.38528	−	0.518878i
$650$	1.28325	+	2.22266i	0.0503334	+	0.0871799i
$651$		0			0
$652$	−23.3791	+	10.4090i	−0.915595	+	0.407649i
$653$	−0.504698	−	4.80188i	−0.0197504	−	0.187912i	0.980199	−	0.198017i	$-0.0634501\pi$
$653$	−0.504698	−	4.80188i	−0.0197504	−	0.187912i	−0.999949	+	0.0101049i	$0.996783\pi$
$654$		0			0
$655$	−10.5912	+	2.25123i	−0.413833	+	0.0879629i
$656$	19.5632	−	14.2135i	0.763813	−	0.554942i
$657$		0			0
$658$	−2.10558	−	6.48030i	−0.0820840	−	0.252628i
$659$	−11.0889	−	19.2065i	−0.431961	−	0.748178i	0.565082	−	0.825035i	$-0.308845\pi$
$659$	−11.0889	−	19.2065i	−0.431961	−	0.748178i	−0.997042	+	0.0768574i	$0.975511\pi$
$660$		0			0
$661$	13.6987	−	23.7269i	0.532820	−	0.922871i	−0.466446	−	0.884550i	$-0.654466\pi$
$661$	13.6987	−	23.7269i	0.532820	−	0.922871i	0.999265	−	0.0383209i	$-0.0122009\pi$
$662$	0.887049	+	0.188548i	0.0344761	+	0.00732813i
$663$		0			0
$664$	6.63541	+	2.95427i	0.257504	+	0.114648i
$665$	−5.53132	+	17.0236i	−0.214495	+	0.660148i
$666$		0			0
$667$	5.35915	−	3.89365i	0.207507	−	0.150763i
$668$	3.79358	−	36.0935i	0.146778	−	1.39650i
$669$		0			0
$670$	0.672198	−	1.16428i	0.0259693	−	0.0449801i
$671$	−7.16428	+	27.6342i	−0.276574	+	1.06681i
$672$		0			0
$673$	23.5825	−	26.1911i	0.909040	−	1.00959i	−0.0908659	−	0.995863i	$-0.528963\pi$
$673$	23.5825	−	26.1911i	0.909040	−	1.00959i	0.999906	−	0.0137279i	$-0.00436986\pi$
$674$	−4.19805	−	3.05006i	−0.161703	−	0.117484i
$675$		0			0
$676$	−1.08494	+	3.33910i	−0.0417285	+	0.128427i
$677$	−43.0874	+	9.15850i	−1.65598	+	0.351990i	−0.938685	−	0.344777i	$-0.887955\pi$
$677$	−43.0874	+	9.15850i	−1.65598	+	0.351990i	−0.717298	+	0.696767i	$0.754621\pi$
$678$		0			0
$679$	27.5839	−	12.2811i	1.05857	−	0.471307i
$680$	12.7905	+	2.71870i	0.490493	+	0.104257i
$681$		0			0
$682$	−0.756610	−	4.53795i	−0.0289721	−	0.173767i
$683$	−42.2845			−1.61797			−0.808985	−	0.587829i	$-0.799983\pi$
$683$	−42.2845			−1.61797			−0.808985	+	0.587829i	$0.799983\pi$
$684$		0			0
$685$	−2.38701	−	1.73426i	−0.0912029	−	0.0662628i
$686$	2.75040	+	1.22456i	0.105011	+	0.0467538i
$687$		0			0
$688$	2.31917	+	2.57570i	0.0884174	+	0.0981975i
$689$	−0.632714	−	6.01987i	−0.0241045	−	0.229339i
$690$		0			0
$691$	−5.66545	+	6.29212i	−0.215524	+	0.239363i	−0.841206	−	0.540715i	$-0.818154\pi$
$691$	−5.66545	+	6.29212i	−0.215524	+	0.239363i	0.625682	+	0.780078i	$0.284821\pi$
$692$	−2.90507			−0.110434
$693$		0			0
$694$	−7.81709			−0.296733
$695$	−5.22892	+	5.80730i	−0.198344	+	0.220284i
$696$		0			0
$697$	3.10335	+	29.5264i	0.117548	+	1.11839i
$698$	−4.37041	−	4.85383i	−0.165422	−	0.183720i
$699$		0			0
$700$	16.6874	+	7.42970i	0.630724	+	0.280816i
$701$	35.2342	+	25.5991i	1.33078	+	0.966865i	0.999730	+	0.0232503i	$0.00740148\pi$
$701$	35.2342	+	25.5991i	1.33078	+	0.966865i	0.331046	+	0.943615i	$0.392599\pi$
$702$		0			0
$703$	−12.5638			−0.473854
$704$	20.0538	+	3.00929i	0.755806	+	0.113417i
$705$		0			0
$706$	8.28515	+	1.76106i	0.311816	+	0.0662785i
$707$	−51.0456	+	22.7270i	−1.91977	+	0.854736i
$708$		0			0
$709$	5.89558	−	1.25314i	0.221413	−	0.0470628i	−0.0958693	−	0.995394i	$-0.530563\pi$
$709$	5.89558	−	1.25314i	0.221413	−	0.0470628i	0.317282	+	0.948331i	$0.397230\pi$
$710$	1.37036	−	4.21753i	0.0514287	−	0.158281i
$711$		0			0
$712$	8.37326	+	6.08353i	0.313801	+	0.227990i
$713$	−6.06817	+	6.73939i	−0.227255	+	0.252392i
$714$		0			0
$715$	−34.5332	+	2.09146i	−1.29147	+	0.0782163i
$716$	−12.6530	+	21.9157i	−0.472866	+	0.819028i
$717$		0			0
$718$	1.09858	−	10.4523i	0.0409985	−	0.390075i
$719$	32.6897	−	23.7504i	1.21912	−	0.885741i	0.223092	−	0.974797i	$-0.428385\pi$
$719$	32.6897	−	23.7504i	1.21912	−	0.885741i	0.996027	+	0.0890560i	$0.0283850\pi$
$720$		0			0
$721$	−6.38836	+	19.6614i	−0.237915	+	0.732227i
$722$	4.26384	+	1.89838i	0.158684	+	0.0706505i
$723$		0			0
$724$	5.25274	+	1.11650i	0.195216	+	0.0414945i
$725$	4.15251	−	7.19235i	0.154220	−	0.267117i
$726$		0			0
$727$	−9.36031	−	16.2125i	−0.347155	−	0.601290i	0.638588	−	0.769549i	$-0.279519\pi$
$727$	−9.36031	−	16.2125i	−0.347155	−	0.601290i	−0.985743	+	0.168259i	$0.946185\pi$
$728$	−5.41643	−	16.6700i	−0.200746	−	0.617833i
$729$		0			0
$730$	2.52864	−	1.83717i	0.0935893	−	0.0679966i
$731$	−4.16237	+	0.884740i	−0.153951	+	0.0327233i
$732$		0			0
$733$	−0.0589741	−	0.561101i	−0.00217826	−	0.0207247i	0.993379	−	0.114885i	$-0.0366500\pi$
$733$	−0.0589741	−	0.561101i	−0.00217826	−	0.0207247i	−0.995557	+	0.0941604i	$0.969983\pi$
$734$	6.47609	−	2.88334i	0.239037	−	0.106426i
$735$		0			0
$736$	3.01837	+	5.22796i	0.111258	+	0.192705i
$737$	3.18335	+	4.81575i	0.117260	+	0.177391i
$738$		0			0
$739$	0.602004	+	1.85278i	0.0221451	+	0.0681555i	0.961518	−	0.274741i	$-0.0885921\pi$
$739$	0.602004	+	1.85278i	0.0221451	+	0.0681555i	−0.939373	+	0.342896i	$0.888592\pi$
$740$	−4.20725	+	40.0293i	−0.154662	+	1.47151i
$741$		0			0
$742$	1.22162	+	1.35675i	0.0448471	+	0.0498077i
$743$	18.2423	+	20.2601i	0.669245	+	0.743272i	0.978168	−	0.207815i	$-0.0666352\pi$
$743$	18.2423	+	20.2601i	0.669245	+	0.743272i	−0.308923	+	0.951087i	$0.599968\pi$
$744$		0			0
$745$	−5.71229	+	54.3488i	−0.209282	+	1.99119i
$746$	−1.61067	−	4.95714i	−0.0589709	−	0.181494i
$747$		0			0
$748$	−17.1270	+	21.5052i	−0.626224	+	0.786308i
$749$	5.65985	+	9.80315i	0.206807	+	0.358199i
$750$		0			0
$751$	27.6861	−	12.3267i	1.01028	−	0.449806i	0.166241	−	0.986085i	$-0.446837\pi$
$751$	27.6861	−	12.3267i	1.01028	−	0.449806i	0.844041	+	0.536279i	$0.180170\pi$
$752$	2.15770	+	20.5292i	0.0786833	+	0.748621i
$753$		0			0
$754$	−3.81664	+	0.811252i	−0.138994	+	0.0295441i
$755$	−24.2772	+	17.6384i	−0.883539	+	0.641929i
$756$		0			0
$757$	3.43224	+	10.5634i	0.124747	+	0.383931i	0.993855	−	0.110691i	$-0.0353064\pi$
$757$	3.43224	+	10.5634i	0.124747	+	0.383931i	−0.869108	+	0.494622i	$0.835306\pi$
$758$	−4.48528	−	7.76874i	−0.162913	−	0.282173i
$759$		0			0
$760$	−2.45515	+	4.25244i	−0.0890576	+	0.154252i
$761$	−32.6124	−	6.93197i	−1.18220	−	0.251284i	−0.425444	−	0.904985i	$-0.639882\pi$
$761$	−32.6124	−	6.93197i	−1.18220	−	0.251284i	−0.756753	+	0.653701i	$0.773216\pi$
$762$		0			0
$763$	64.5895	+	28.7571i	2.33830	+	1.04108i
$764$	−9.92620	+	30.5497i	−0.359117	+	1.10525i
$765$		0			0
$766$	2.86788	−	2.08364i	0.103621	−	0.0752849i
$767$	4.57380	−	43.5168i	0.165150	−	1.57130i
$768$		0			0
$769$	25.9701	−	44.9815i	0.936504	−	1.62207i	0.164575	−	0.986364i	$-0.447375\pi$
$769$	25.9701	−	44.9815i	0.936504	−	1.62207i	0.771929	−	0.635709i	$-0.219292\pi$
$770$	8.05570	−	6.63254i	0.290307	−	0.239020i
$771$		0			0
$772$	28.2953	−	31.4252i	1.01837	−	1.13102i
$773$	−6.24784	−	4.53932i	−0.224719	−	0.163268i	0.469729	−	0.882811i	$-0.344352\pi$
$773$	−6.24784	−	4.53932i	−0.224719	−	0.163268i	−0.694448	+	0.719542i	$0.744352\pi$
$774$		0			0
$775$	−3.51343	+	10.8132i	−0.126206	+	0.388423i
$776$	8.10199	−	1.72213i	0.290844	−	0.0618209i
$777$		0			0
$778$	1.90675	−	0.848939i	0.0683602	−	0.0304359i
$779$	−10.9050	−	2.31793i	−0.390713	−	0.0830486i
$780$		0			0
$781$	13.5737	+	13.3548i	0.485706	+	0.477871i
$782$	−2.29655			−0.0821244
$783$		0			0
$784$	−27.3060	−	19.8390i	−0.975215	−	0.708535i
$785$	−0.823492	−	0.366642i	−0.0293917	−	0.0130860i
$786$		0			0
$787$	−13.1861	−	14.6446i	−0.470034	−	0.522025i	0.460782	−	0.887513i	$-0.347569\pi$
$787$	−13.1861	−	14.6446i	−0.470034	−	0.522025i	−0.930816	+	0.365488i	$0.880902\pi$
$788$	−3.65510	−	34.7759i	−0.130207	−	1.23884i
$789$		0			0
$790$	−2.21211	+	2.45680i	−0.0787034	+	0.0874089i
$791$	3.84382			0.136670
$792$		0			0
$793$	−33.1470			−1.17709
$794$	−6.52707	+	7.24904i	−0.231637	+	0.257259i
$795$		0			0
$796$	−5.03316	−	47.8873i	−0.178395	−	1.69732i
$797$	−9.38507	−	10.4232i	−0.332436	−	0.369208i	0.553633	−	0.832761i	$-0.313241\pi$
$797$	−9.38507	−	10.4232i	−0.332436	−	0.369208i	−0.886069	+	0.463553i	$0.846574\pi$
$798$		0			0
$799$	−23.1527	−	10.3083i	−0.819085	−	0.364680i
$800$	6.12297	+	4.44860i	0.216480	+	0.157282i
$801$		0			0
$802$	2.13170			0.0752731
$803$	2.20723	+	13.2384i	0.0778914	+	0.467173i
$804$		0			0
$805$	−20.1197	−	4.27657i	−0.709126	−	0.150729i
$806$	4.87996	−	2.17270i	0.171889	−	0.0765300i
$807$		0			0
$808$	−14.9932	+	3.18690i	−0.527459	+	0.112115i
$809$	6.46767	−	19.9055i	0.227391	−	0.699839i	−0.770649	−	0.637260i	$-0.780068\pi$
$809$	6.46767	−	19.9055i	0.227391	−	0.699839i	0.998040	−	0.0625783i	$-0.0199323\pi$
$810$		0			0
$811$	−1.57186	−	1.14203i	−0.0551956	−	0.0401019i	0.559845	−	0.828597i	$-0.310861\pi$
$811$	−1.57186	−	1.14203i	−0.0551956	−	0.0401019i	−0.615041	+	0.788495i	$0.710861\pi$
$812$	−18.5825	+	20.6379i	−0.652117	+	0.724249i
$813$		0			0
$814$	6.17482	+	3.93897i	0.216427	+	0.138061i
$815$	18.0646	−	31.2888i	0.632775	−	1.09600i
$816$		0			0
$817$	0.167031	−	1.58919i	0.00584367	−	0.0555988i
$818$	0.556008	−	0.403964i	0.0194404	−	0.0141243i
$819$		0			0
$820$	−11.0369	+	33.9680i	−0.385424	+	1.18621i
$821$	−9.90445	−	4.40974i	−0.345668	−	0.153901i	0.226557	−	0.973998i	$-0.427253\pi$
$821$	−9.90445	−	4.40974i	−0.345668	−	0.153901i	−0.572225	+	0.820097i	$0.693920\pi$
$822$		0			0
$823$	−46.6261	−	9.91069i	−1.62529	−	0.345465i	−0.696924	−	0.717145i	$-0.745449\pi$
$823$	−46.6261	−	9.91069i	−1.62529	−	0.345465i	−0.928361	+	0.371680i	$0.878782\pi$
$824$	−2.83556	+	4.91134i	−0.0987815	+	0.171094i
$825$		0			0
$826$	6.59880	+	11.4295i	0.229601	+	0.397681i
$827$	−11.5619	−	35.5838i	−0.402046	−	1.23737i	−0.923337	−	0.383991i	$-0.874549\pi$
$827$	−11.5619	−	35.5838i	−0.402046	−	1.23737i	0.521291	−	0.853379i	$-0.325451\pi$
$828$		0			0
$829$	−8.66207	+	6.29336i	−0.300846	+	0.218578i	−0.727959	−	0.685621i	$-0.759531\pi$
$829$	−8.66207	+	6.29336i	−0.300846	+	0.218578i	0.427113	+	0.904198i	$0.359531\pi$
$830$	−4.91097	+	1.04386i	−0.170462	+	0.0362329i
$831$		0			0
$832$	2.46115	+	23.4163i	0.0853252	+	0.811815i
$833$	37.8570	−	16.8550i	1.31167	−	0.583992i
$834$		0			0
$835$	25.6181	+	44.3718i	0.886549	+	1.53555i
$836$	−5.69284	−	8.61209i	−0.196891	−	0.297856i
$837$		0			0
$838$	−0.987051	−	3.03783i	−0.0340971	−	0.104940i
$839$	1.60571	−	15.2774i	0.0554354	−	0.527433i	−0.931202	−	0.364503i	$-0.881239\pi$
$839$	1.60571	−	15.2774i	0.0554354	−	0.527433i	0.986638	−	0.162930i	$-0.0520944\pi$
$840$		0			0
$841$	−10.9562	−	12.1681i	−0.377799	−	0.419588i
$842$	1.31746	+	1.46319i	0.0454026	+	0.0504247i
$843$		0			0
$844$	1.65862	−	15.7807i	0.0570920	−	0.543194i
$845$	−1.53168	−	4.71402i	−0.0526913	−	0.162167i
$846$		0			0
$847$	10.0272	+	43.6703i	0.344539	+	1.50053i
$848$	−2.76543	−	4.78987i	−0.0949654	−	0.164485i
$849$		0			0
$850$	−2.63032	+	1.17109i	−0.0902192	+	0.0401682i
$851$	−1.50913	−	14.3585i	−0.0517325	−	0.492201i
$852$		0			0
$853$	−40.5581	+	8.62090i	−1.38868	+	0.295174i	−0.840785	−	0.541370i	$-0.817906\pi$
$853$	−40.5581	+	8.62090i	−1.38868	+	0.295174i	−0.547900	+	0.836544i	$0.684573\pi$
$854$	8.08825	−	5.87646i	0.276774	−	0.201088i
$855$		0			0
$856$	0.959576	+	2.95327i	0.0327976	+	0.100941i
$857$	9.20273	+	15.9396i	0.314359	+	0.544486i	0.979301	−	0.202409i	$-0.0648770\pi$
$857$	9.20273	+	15.9396i	0.314359	+	0.544486i	−0.664942	+	0.746895i	$0.731544\pi$
$858$		0			0
$859$	7.52426	−	13.0324i	0.256725	−	0.444660i	−0.708638	−	0.705572i	$-0.750690\pi$
$859$	7.52426	−	13.0324i	0.256725	−	0.444660i	0.965363	+	0.260912i	$0.0840233\pi$
$860$	−5.00735	−	1.06435i	−0.170749	−	0.0362939i
$861$		0			0
$862$	−7.60142	−	3.38437i	−0.258905	−	0.115272i
$863$	4.45906	−	13.7236i	0.151788	−	0.467155i	−0.846033	−	0.533130i	$-0.821016\pi$
$863$	4.45906	−	13.7236i	0.151788	−	0.467155i	0.997821	+	0.0659746i	$0.0210156\pi$
$864$		0			0
$865$	3.31799	−	2.41066i	0.112815	−	0.0819649i
$866$	−1.08900	+	10.3611i	−0.0370056	+	0.352084i
$867$		0			0
$868$	19.0095	−	32.9255i	0.645225	−	1.11756i
$869$	−5.19484	−	13.2110i	−0.176223	−	0.448152i
$870$		0			0
$871$	−4.48507	+	4.98118i	−0.151971	+	0.168781i
$872$	15.6910	+	11.4002i	0.531365	+	0.386059i
$873$		0			0
$874$	0.266492	−	0.820177i	0.00901421	−	0.0277429i
$875$	28.7378	−	6.10840i	0.971514	−	0.206502i
$876$		0			0
$877$	−21.9939	+	9.79233i	−0.742683	+	0.330664i	−0.742960	−	0.669336i	$-0.766579\pi$
$877$	−21.9939	+	9.79233i	−0.742683	+	0.330664i	0.000276873		1.00000i	$0.499912\pi$
$878$	−5.99601	−	1.27449i	−0.202356	−	0.0430120i
$879$		0			0
$880$	−28.0489	+	14.5801i	−0.945527	+	0.491494i
$881$	10.0956			0.340129			0.170064	−	0.985433i	$-0.445602\pi$
$881$	10.0956			0.340129			0.170064	+	0.985433i	$0.445602\pi$
$882$		0			0
$883$	−41.0332	−	29.8124i	−1.38088	−	1.00327i	−0.996798	−	0.0799659i	$-0.974519\pi$
$883$	−41.0332	−	29.8124i	−1.38088	−	1.00327i	−0.384079	−	0.923300i	$-0.625481\pi$
$884$	−29.1614	−	12.9835i	−0.980803	−	0.436682i
$885$		0			0
$886$	−6.38136	−	7.08721i	−0.214386	−	0.238100i
$887$	−0.268921	−	2.55861i	−0.00902949	−	0.0859099i	0.989079	−	0.147386i	$-0.0470859\pi$
$887$	−0.268921	−	2.55861i	−0.00902949	−	0.0859099i	−0.998109	+	0.0614760i	$0.980419\pi$
$888$		0			0
$889$	−6.67880	+	7.41756i	−0.224000	+	0.248777i
$890$	−7.15422			−0.239810
$891$		0			0
$892$	14.1064			0.472316
$893$	6.36808	−	7.07247i	0.213100	−	0.236671i
$894$		0			0
$895$	−3.73440	−	35.5304i	−0.124827	−	1.18765i
$896$	−22.4038	−	24.8820i	−0.748460	−	0.831249i
$897$		0			0
$898$	10.2983	+	4.58508i	0.343658	+	0.153006i
$899$	−13.9843	−	10.1602i	−0.466403	−	0.338862i
$900$		0			0
$901$	6.79061			0.226228
$902$	4.63284	+	4.55811i	0.154257	+	0.151768i
$903$		0			0
$904$	1.03140	+	0.219232i	0.0343040	+	0.00729154i
$905$	−6.92585	+	3.08359i	−0.230223	+	0.102502i
$906$		0			0
$907$	−10.0699	+	2.14042i	−0.334366	+	0.0710716i	−0.372035	−	0.928219i	$-0.621340\pi$
$907$	−10.0699	+	2.14042i	−0.334366	+	0.0710716i	0.0376696	+	0.999290i	$0.488007\pi$
$908$	−11.2304	+	34.5636i	−0.372693	+	1.14703i
$909$		0			0
$910$	9.80197	+	7.12155i	0.324932	+	0.236077i
$911$	10.4401	−	11.5950i	0.345897	−	0.384158i	−0.544944	−	0.838472i	$-0.683449\pi$
$911$	10.4401	−	11.5950i	0.345897	−	0.384158i	0.890841	+	0.454315i	$0.150116\pi$
$912$		0			0
$913$	5.41031	−	20.8688i	0.179055	−	0.690655i
$914$	5.34829	−	9.26351i	0.176906	−	0.306410i
$915$		0			0
$916$	−1.57627	+	14.9972i	−0.0520815	+	0.495523i
$917$	−13.1729	+	9.57070i	−0.435009	+	0.316052i
$918$		0			0
$919$	3.46483	−	10.6637i	0.114294	−	0.351761i	−0.877505	−	0.479568i	$-0.840794\pi$
$919$	3.46483	−	10.6637i	0.114294	−	0.351761i	0.991799	+	0.127806i	$0.0407935\pi$
$920$	−5.15477	−	2.29505i	−0.169948	−	0.0756655i
$921$		0			0
$922$	−5.40131	−	1.14808i	−0.177883	−	0.0378102i
$923$	−11.0549	+	19.1476i	−0.363875	+	0.630251i
$924$		0			0
$925$	−9.05036	−	15.6757i	−0.297574	−	0.515413i
$926$	1.26440	+	3.89141i	0.0415506	+	0.127880i
$927$		0			0
$928$	−9.30886	+	6.76328i	−0.305578	+	0.222016i
$929$	23.0134	−	4.89164i	0.755044	−	0.160490i	0.185720	−	0.982603i	$-0.440538\pi$
$929$	23.0134	−	4.89164i	0.755044	−	0.160490i	0.569324	+	0.822113i	$0.307205\pi$
$930$		0			0
$931$	1.62658	+	15.4759i	0.0533091	+	0.507202i
$932$	−11.5149	+	5.12678i	−0.377185	+	0.167933i
$933$		0			0
$934$	3.18239	+	5.51206i	0.104131	+	0.180360i
$935$	1.71609	−	38.7741i	0.0561221	−	1.26805i
$936$		0			0
$937$	5.76486	+	17.7424i	0.188330	+	0.579619i	0.999990	−	0.00451068i	$-0.00143580\pi$
$937$	5.76486	+	17.7424i	0.188330	+	0.579619i	−0.811660	+	0.584130i	$0.801436\pi$
$938$	0.211322	−	2.01060i	0.00689992	−	0.0656483i
$939$		0			0
$940$	−20.4009	−	22.6575i	−0.665405	−	0.739007i
$941$	21.7418	+	24.1467i	0.708763	+	0.787161i	0.984745	−	0.174002i	$-0.0556698\pi$
$941$	21.7418	+	24.1467i	0.708763	+	0.787161i	−0.275982	+	0.961163i	$0.589003\pi$
$942$		0			0
$943$	1.33914	−	12.7411i	0.0436085	−	0.414908i
$944$	−12.3551	−	38.0250i	−0.402123	−	1.23761i
$945$		0			0
$946$	−0.580329	+	0.728681i	−0.0188681	+	0.0236915i
$947$	−1.92137	−	3.32790i	−0.0624360	−	0.108142i	0.833118	−	0.553096i	$-0.186554\pi$
$947$	−1.92137	−	3.32790i	−0.0624360	−	0.108142i	−0.895554	+	0.444953i	$0.853220\pi$
$948$		0			0
$949$	−14.2361	+	6.33833i	−0.462124	+	0.205751i
$950$	−0.113016	−	1.07527i	−0.00366671	−	0.0348864i
$951$		0			0
$952$	19.2340	−	4.08832i	0.623379	−	0.132503i
$953$	15.4434	−	11.2203i	0.500262	−	0.363461i	−0.308855	−	0.951109i	$-0.599946\pi$
$953$	15.4434	−	11.2203i	0.500262	−	0.363461i	0.809117	+	0.587648i	$0.199946\pi$
$954$		0			0
$955$	−14.0134	−	43.1289i	−0.453464	−	1.39562i
$956$	24.5077	+	42.4486i	0.792636	+	1.37289i
$957$		0			0
$958$	3.31651	−	5.74436i	0.107152	−	0.185592i
$959$	−4.33995	−	0.922485i	−0.140144	−	0.0297886i
$960$		0			0
$961$	−6.70155	−	2.98372i	−0.216179	−	0.0962492i
$962$	−2.62793	+	8.08795i	−0.0847280	+	0.260766i
$963$		0			0
$964$	−4.62879	+	3.36302i	−0.149083	+	0.108315i
$965$	−6.24022	+	59.3718i	−0.200880	+	1.91124i
$966$		0			0
$967$	−13.2813	+	23.0039i	−0.427099	+	0.739757i	−0.996614	−	0.0822239i	$-0.973798\pi$
$967$	−13.2813	+	23.0039i	−0.427099	+	0.739757i	0.569515	+	0.821981i	$0.307131\pi$
$968$	0.199855	+	12.2899i	0.00642357	+	0.395011i
$969$		0			0
$970$	−3.83110	+	4.25487i	−0.123009	+	0.136616i
$971$	−41.3472	−	30.0405i	−1.32689	−	0.964045i	−0.999819	−	0.0190472i	$-0.993937\pi$
$971$	−41.3472	−	30.0405i	−1.32689	−	0.964045i	−0.327076	−	0.944998i	$-0.606063\pi$
$972$		0			0
$973$	−3.63134	+	11.1761i	−0.116415	+	0.358290i
$974$	0.0755312	−	0.0160547i	0.00242018	−	0.000514424i
$975$		0			0
$976$	−27.6691	+	12.3191i	−0.885666	+	0.394324i
$977$	−20.7119	−	4.40244i	−0.662631	−	0.140847i	−0.135694	−	0.990751i	$-0.543326\pi$
$977$	−20.7119	−	4.40244i	−0.662631	−	0.140847i	−0.526937	+	0.849904i	$0.676660\pi$
$978$		0			0
$979$	13.7236	−	27.4842i	0.438608	−	0.878399i
$980$	49.8521			1.59247
$981$		0			0
$982$	0.970410	+	0.705044i	0.0309670	+	0.0224989i
$983$	−46.4405	−	20.6766i	−1.48122	−	0.659482i	−0.502481	−	0.864588i	$-0.667579\pi$
$983$	−46.4405	−	20.6766i	−1.48122	−	0.659482i	−0.978740	+	0.205106i	$0.934246\pi$
$984$		0			0
$985$	33.0321	+	36.6859i	1.05249	+	1.16891i
$986$	−0.457559	−	4.35338i	−0.0145716	−	0.138640i
$987$		0			0
$988$	8.02073	−	8.90792i	0.255173	−	0.283399i
$989$	1.83625			0.0583895
$990$		0			0
$991$	−13.1480			−0.417662			−0.208831	−	0.977952i	$-0.566966\pi$
$991$	−13.1480			−0.417662			−0.208831	+	0.977952i	$0.566966\pi$
$992$	10.5404	−	11.7063i	0.334659	−	0.371677i
$993$		0			0
$994$	−0.697061	−	6.63209i	−0.0221094	−	0.210357i
$995$	45.4860	+	50.5174i	1.44200	+	1.60151i
$996$		0			0
$997$	−33.9918	−	15.1341i	−1.07653	−	0.479303i	−0.209629	−	0.977781i	$-0.567226\pi$
$997$	−33.9918	−	15.1341i	−1.07653	−	0.479303i	−0.866902	+	0.498478i	$0.833892\pi$
$998$	−3.54437	−	2.57514i	−0.112195	−	0.0815146i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.280.5		72
3.2	odd	2		99.2.m.b.49.5	yes	72
9.2	odd	6		99.2.m.b.16.5	✓	72
9.4	even	3		891.2.f.e.82.5		36
9.5	odd	6		891.2.f.f.82.5		36
9.7	even	3	inner	297.2.n.b.181.5		72
11.9	even	5	inner	297.2.n.b.64.5		72
33.8	even	10		1089.2.e.o.364.10		36
33.14	odd	10		1089.2.e.p.364.9		36
33.20	odd	10		99.2.m.b.31.5	yes	72
99.14	odd	30		9801.2.a.cm.1.10		18
99.20	odd	30		99.2.m.b.97.5	yes	72
99.31	even	15		891.2.f.e.163.5		36
99.41	even	30		9801.2.a.co.1.9		18
99.47	odd	30		1089.2.e.p.727.9		36
99.58	even	15		9801.2.a.cp.1.9		18
99.74	even	30		1089.2.e.o.727.10		36
99.85	odd	30		9801.2.a.cn.1.10		18
99.86	odd	30		891.2.f.f.163.5		36
99.97	even	15	inner	297.2.n.b.262.5		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.5	✓	72	9.2	odd	6
99.2.m.b.31.5	yes	72	33.20	odd	10
99.2.m.b.49.5	yes	72	3.2	odd	2
99.2.m.b.97.5	yes	72	99.20	odd	30
297.2.n.b.64.5		72	11.9	even	5	inner
297.2.n.b.181.5		72	9.7	even	3	inner
297.2.n.b.262.5		72	99.97	even	15	inner
297.2.n.b.280.5		72	1.1	even	1	trivial
891.2.f.e.82.5		36	9.4	even	3
891.2.f.e.163.5		36	99.31	even	15
891.2.f.f.82.5		36	9.5	odd	6
891.2.f.f.163.5		36	99.86	odd	30
1089.2.e.o.364.10		36	33.8	even	10
1089.2.e.o.727.10		36	99.74	even	30
1089.2.e.p.364.9		36	33.14	odd	10
1089.2.e.p.727.9		36	99.47	odd	30
9801.2.a.cm.1.10		18	99.14	odd	30
9801.2.a.cn.1.10		18	99.85	odd	30
9801.2.a.co.1.9		18	99.41	even	30
9801.2.a.cp.1.9		18	99.58	even	15

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.190802 + 0.211907i) q^{2} +(0.200558 + 1.90818i) q^{4} +(-1.81250 - 2.01298i) q^{5} +(-3.72118 - 1.65677i) q^{7} +(-0.904002 - 0.656796i) q^{8} +0.772391 q^{10} +(-1.48164 + 2.96728i) q^{11} +(-3.76680 - 0.800659i) q^{13} +(1.06109 - 0.472427i) q^{14} +(-3.44186 + 0.731590i) q^{16} +(1.33502 - 4.10876i) q^{17} +(1.31246 + 0.953561i) q^{19} +(3.47762 - 3.86229i) q^{20} +(-0.346086 - 0.880131i) q^{22} +(-0.932117 + 1.61447i) q^{23} +(-0.244308 + 2.32444i) q^{25} +(0.888377 - 0.645443i) q^{26} +(2.41511 - 7.43295i) q^{28} +(-3.24614 - 1.44528i) q^{29} +(4.75829 + 1.01141i) q^{31} +(1.61909 - 2.80435i) q^{32} +(0.615950 + 1.06686i) q^{34} +(3.40956 + 10.4936i) q^{35} +(-6.26542 + 4.55210i) q^{37} +(-0.452486 + 0.0961788i) q^{38} +(0.316383 + 3.01018i) q^{40} +(-6.27802 + 2.79515i) q^{41} +(-0.492496 - 0.853027i) q^{43} +(-5.95925 - 2.23213i) q^{44} +(-0.164268 - 0.505566i) q^{46} +(0.613200 - 5.83421i) q^{47} +(6.41834 + 7.12829i) q^{49} +(-0.445949 - 0.495276i) q^{50} +(0.772339 - 7.34832i) q^{52} +(0.485721 + 1.49489i) q^{53} +(8.65855 - 2.39567i) q^{55} +(2.27579 + 3.94178i) q^{56} +(0.925632 - 0.412118i) q^{58} +(1.18770 + 11.3002i) q^{59} +(8.41938 - 1.78960i) q^{61} +(-1.12221 + 0.815335i) q^{62} +(-1.88937 - 5.81490i) q^{64} +(5.21561 + 9.03370i) q^{65} +(0.870282 - 1.50737i) q^{67} +(8.10800 + 1.72341i) q^{68} +(-2.87420 - 1.27968i) q^{70} +(1.77418 - 5.46036i) q^{71} +(3.27379 - 2.37855i) q^{73} +(0.230833 - 2.19623i) q^{74} +(-1.55634 + 2.69566i) q^{76} +(10.4296 - 8.58702i) q^{77} +(-2.86398 + 3.18077i) q^{79} +(7.71104 + 5.60240i) q^{80} +(0.605544 - 1.86367i) q^{82} +(-6.35814 + 1.35146i) q^{83} +(-10.6906 + 4.75975i) q^{85} +(0.274731 + 0.0583959i) q^{86} +(3.28830 - 1.70929i) q^{88} -9.26243 q^{89} +(12.6904 + 9.22014i) q^{91} +(-3.26765 - 1.45485i) q^{92} +(1.11931 + 1.24312i) q^{94} +(-0.459336 - 4.37029i) q^{95} +(-4.96005 + 5.50870i) q^{97} -2.73516 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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