LMFDB - Embedded newform 387.2.y.c.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			253.1
Character	$\chi$	$=$	387.253
Dual form			387.2.y.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.377390 + 1.65345i) q^{2} +(-0.789549 - 0.380227i) q^{4} +(-0.140805 - 0.358765i) q^{5} +(1.74586 + 3.02391i) q^{7} +(-1.18819 + 1.48995i) q^{8} +O(q^{10})$	\(q+(-0.377390 + 1.65345i) q^{2} +(-0.789549 - 0.380227i) q^{4} +(-0.140805 - 0.358765i) q^{5} +(1.74586 + 3.02391i) q^{7} +(-1.18819 + 1.48995i) q^{8} +(0.646339 - 0.0974200i) q^{10} +(3.90633 - 1.88119i) q^{11} +(1.26408 + 0.190529i) q^{13} +(-5.65876 + 1.74550i) q^{14} +(-3.10791 - 3.89720i) q^{16} +(-0.205594 + 0.523844i) q^{17} +(-6.30490 + 4.29861i) q^{19} +(-0.0252397 + 0.336800i) q^{20} +(1.63625 + 7.16888i) q^{22} +(-0.553943 + 7.39185i) q^{23} +(3.55637 - 3.29983i) q^{25} +(-0.792080 + 2.01819i) q^{26} +(-0.228667 - 3.05134i) q^{28} +(-3.26143 + 1.00602i) q^{29} +(-0.717059 - 0.665333i) q^{31} +(4.18276 - 2.01431i) q^{32} +(-0.788563 - 0.537633i) q^{34} +(0.839048 - 1.05213i) q^{35} +(-2.19799 + 3.80703i) q^{37} +(-4.72814 - 12.0471i) q^{38} +(0.701843 + 0.216490i) q^{40} +(1.07956 - 4.72986i) q^{41} +(3.30784 - 5.66200i) q^{43} -3.79952 q^{44} +(-12.0130 - 3.70553i) q^{46} +(-3.93826 - 1.89657i) q^{47} +(-2.59602 + 4.49644i) q^{49} +(4.11398 + 7.12562i) q^{50} +(-0.925605 - 0.631067i) q^{52} +(9.56301 - 1.44139i) q^{53} +(-1.22493 - 1.13657i) q^{55} +(-6.57987 - 0.991756i) q^{56} +(-0.432573 - 5.77229i) q^{58} +(2.92222 + 3.66435i) q^{59} +(3.96588 - 3.67980i) q^{61} +(1.37071 - 0.934533i) q^{62} +(-0.466364 - 2.04327i) q^{64} +(-0.109633 - 0.480333i) q^{65} +(10.8402 - 7.39075i) q^{67} +(0.361505 - 0.335428i) q^{68} +(1.42300 + 1.78439i) q^{70} +(-0.570335 - 7.61059i) q^{71} +(-2.05301 - 0.309442i) q^{73} +(-5.46525 - 5.07101i) q^{74} +(6.61247 - 0.996670i) q^{76} +(12.5084 + 8.52811i) q^{77} +(4.14234 + 7.17474i) q^{79} +(-0.960569 + 1.66375i) q^{80} +(7.41318 + 3.57000i) q^{82} +(11.1319 + 3.43375i) q^{83} +0.216885 q^{85} +(8.11351 + 7.60614i) q^{86} +(-1.83860 + 8.05544i) q^{88} +(-2.60667 - 0.804052i) q^{89} +(1.63075 + 4.15509i) q^{91} +(3.24794 - 5.62560i) q^{92} +(4.62215 - 5.79599i) q^{94} +(2.42995 + 1.65671i) q^{95} +(0.441741 - 0.212731i) q^{97} +(-6.45494 - 5.98931i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{2}{21}\right)$	$1$

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 $

$2$	−0.377390	+	1.65345i	−0.266855	+	1.16917i	0.646794	+	0.762665i	$0.276109\pi$
$2$	−0.377390	+	1.65345i	−0.266855	+	1.16917i	−0.913649	+	0.406504i	$0.866748\pi$
$3$		0			0
$3$		0			0
$4$	−0.789549	−	0.380227i	−0.394774	−	0.190113i
$5$	−0.140805	−	0.358765i	−0.0629698	−	0.160444i	0.895926	−	0.444204i	$-0.146513\pi$
$5$	−0.140805	−	0.358765i	−0.0629698	−	0.160444i	−0.958895	+	0.283760i	$0.908418\pi$
$6$		0			0
$7$	1.74586	+	3.02391i	0.659871	+	1.14293i	0.980649	+	0.195776i	$0.0627225\pi$
$7$	1.74586	+	3.02391i	0.659871	+	1.14293i	−0.320777	+	0.947155i	$0.603944\pi$
$8$	−1.18819	+	1.48995i	−0.420089	+	0.526775i
$9$		0			0
$10$	0.646339	−	0.0974200i	0.204390	−	0.0308069i
$11$	3.90633	−	1.88119i	1.17780	−	0.567200i	0.260533	−	0.965465i	$-0.416102\pi$
$11$	3.90633	−	1.88119i	1.17780	−	0.567200i	0.917270	+	0.398265i	$0.130388\pi$
$12$		0			0
$13$	1.26408	+	0.190529i	0.350591	+	0.0528432i	0.321977	−	0.946747i	$-0.395653\pi$
$13$	1.26408	+	0.190529i	0.350591	+	0.0528432i	0.0286141	+	0.999591i	$0.490891\pi$
$14$	−5.65876	+	1.74550i	−1.51237	+	0.466504i
$15$		0			0
$16$	−3.10791	−	3.89720i	−0.776978	−	0.974300i
$17$	−0.205594	+	0.523844i	−0.0498638	+	0.127051i	−0.953636	−	0.300964i	$-0.902692\pi$
$17$	−0.205594	+	0.523844i	−0.0498638	+	0.127051i	0.903772	+	0.428015i	$0.140787\pi$
$18$		0			0
$19$	−6.30490	+	4.29861i	−1.44644	+	0.986169i	−0.450830	+	0.892610i	$0.648872\pi$
$19$	−6.30490	+	4.29861i	−1.44644	+	0.986169i	−0.995614	+	0.0935586i	$0.970176\pi$
$20$	−0.0252397	+	0.336800i	−0.00564376	+	0.0753107i
$21$		0			0
$22$	1.63625	+	7.16888i	0.348850	+	1.52841i
$23$	−0.553943	+	7.39185i	−0.115505	+	1.54131i	0.575105	+	0.818080i	$0.304961\pi$
$23$	−0.553943	+	7.39185i	−0.115505	+	1.54131i	−0.690610	+	0.723228i	$0.742658\pi$
$24$		0			0
$25$	3.55637	−	3.29983i	0.711275	−	0.659966i
$26$	−0.792080	+	2.01819i	−0.155340	+	0.395799i
$27$		0			0
$28$	−0.228667	−	3.05134i	−0.0432139	−	0.576650i
$29$	−3.26143	+	1.00602i	−0.605633	+	0.186813i	−0.582380	−	0.812917i	$-0.697878\pi$
$29$	−3.26143	+	1.00602i	−0.605633	+	0.186813i	−0.0232528	+	0.999730i	$0.507402\pi$
$30$		0			0
$31$	−0.717059	−	0.665333i	−0.128788	−	0.119497i	0.613150	−	0.789967i	$-0.289902\pi$
$31$	−0.717059	−	0.665333i	−0.128788	−	0.119497i	−0.741937	+	0.670469i	$0.766093\pi$
$32$	4.18276	−	2.01431i	0.739415	−	0.356083i
$33$		0			0
$34$	−0.788563	−	0.537633i	−0.135237	−	0.0922033i
$35$	0.839048	−	1.05213i	0.141825	−	0.177843i
$36$		0			0
$37$	−2.19799	+	3.80703i	−0.361348	+	0.625872i	−0.988183	−	0.153279i	$-0.951017\pi$
$37$	−2.19799	+	3.80703i	−0.361348	+	0.625872i	0.626835	+	0.779152i	$0.284350\pi$
$38$	−4.72814	−	12.0471i	−0.767006	−	1.95430i
$39$		0			0
$40$	0.701843	+	0.216490i	0.110971	+	0.0342301i
$41$	1.07956	−	4.72986i	0.168599	−	0.738679i	−0.817960	−	0.575275i	$-0.804895\pi$
$41$	1.07956	−	4.72986i	0.168599	−	0.738679i	0.986559	−	0.163405i	$-0.0522477\pi$
$42$		0			0
$43$	3.30784	−	5.66200i	0.504440	−	0.863447i
$43$	3.30784	−	5.66200i	0.504440	−	0.863447i
$44$	−3.79952			−0.572799
$45$		0			0
$46$	−12.0130	−	3.70553i	−1.77122	−	0.546351i
$47$	−3.93826	−	1.89657i	−0.574455	−	0.276643i	0.124017	−	0.992280i	$-0.460422\pi$
$47$	−3.93826	−	1.89657i	−0.574455	−	0.276643i	−0.698472	+	0.715637i	$0.746136\pi$
$48$		0			0
$49$	−2.59602	+	4.49644i	−0.370860	+	0.642348i
$50$	4.11398	+	7.12562i	0.581805	+	1.00772i
$51$		0			0
$52$	−0.925605	−	0.631067i	−0.128358	−	0.0875132i
$53$	9.56301	−	1.44139i	1.31358	−	0.197990i	0.545374	−	0.838193i	$-0.316387\pi$
$53$	9.56301	−	1.44139i	1.31358	−	0.197990i	0.768207	+	0.640202i	$0.221149\pi$
$54$		0			0
$55$	−1.22493	−	1.13657i	−0.165170	−	0.153256i
$56$	−6.57987	−	0.991756i	−0.879272	−	0.132529i
$57$		0			0
$58$	−0.432573	−	5.77229i	−0.0567997	−	0.757939i
$59$	2.92222	+	3.66435i	0.380441	+	0.477058i	0.934777	−	0.355235i	$-0.115599\pi$
$59$	2.92222	+	3.66435i	0.380441	+	0.477058i	−0.554336	+	0.832293i	$0.687028\pi$
$60$		0			0
$61$	3.96588	−	3.67980i	0.507779	−	0.471150i	−0.384185	−	0.923256i	$-0.625518\pi$
$61$	3.96588	−	3.67980i	0.507779	−	0.471150i	0.891964	+	0.452106i	$0.149327\pi$
$62$	1.37071	−	0.934533i	0.174080	−	0.118686i
$63$		0			0
$64$	−0.466364	−	2.04327i	−0.0582955	−	0.255409i
$65$	−0.109633	−	0.480333i	−0.0135983	−	0.0595780i
$66$		0			0
$67$	10.8402	−	7.39075i	1.32435	−	0.902924i	0.325259	−	0.945625i	$-0.394549\pi$
$67$	10.8402	−	7.39075i	1.32435	−	0.902924i	0.999088	+	0.0427010i	$0.0135963\pi$
$68$	0.361505	−	0.335428i	0.0438390	−	0.0406766i
$69$		0			0
$70$	1.42300	+	1.78439i	0.170082	+	0.213275i
$71$	−0.570335	−	7.61059i	−0.0676863	−	0.903211i	−0.922926	−	0.384978i	$-0.874209\pi$
$71$	−0.570335	−	7.61059i	−0.0676863	−	0.903211i	0.855239	−	0.518233i	$-0.173410\pi$
$72$		0			0
$73$	−2.05301	−	0.309442i	−0.240287	−	0.0362175i	0.0277945	−	0.999614i	$-0.491152\pi$
$73$	−2.05301	−	0.309442i	−0.240287	−	0.0362175i	−0.268082	+	0.963396i	$0.586390\pi$
$74$	−5.46525	−	5.07101i	−0.635323	−	0.589493i
$75$		0			0
$76$	6.61247	−	0.996670i	0.758502	−	0.114326i
$77$	12.5084	+	8.52811i	1.42547	+	0.971868i
$78$		0			0
$79$	4.14234	+	7.17474i	0.466049	+	0.807221i	0.999248	−	0.0387687i	$-0.0123436\pi$
$79$	4.14234	+	7.17474i	0.466049	+	0.807221i	−0.533199	+	0.845990i	$0.679010\pi$
$80$	−0.960569	+	1.66375i	−0.107395	+	0.186013i
$81$		0			0
$82$	7.41318	+	3.57000i	0.818649	+	0.394241i
$83$	11.1319	+	3.43375i	1.22189	+	0.376903i	0.837587	−	0.546305i	$-0.183966\pi$
$83$	11.1319	+	3.43375i	1.22189	+	0.376903i	0.384302	+	0.923207i	$0.374442\pi$
$84$		0			0
$85$	0.216885			0.0235245
$86$	8.11351	+	7.60614i	0.874902	+	0.820191i
$87$		0			0
$88$	−1.83860	+	8.05544i	−0.195995	+	0.858712i
$89$	−2.60667	−	0.804052i	−0.276307	−	0.0852293i	0.153505	−	0.988148i	$-0.450944\pi$
$89$	−2.60667	−	0.804052i	−0.276307	−	0.0852293i	−0.429812	+	0.902919i	$0.641420\pi$
$90$		0			0
$91$	1.63075	+	4.15509i	0.170949	+	0.435571i
$92$	3.24794	−	5.62560i	0.338621	−	0.586509i
$93$		0			0
$94$	4.62215	−	5.79599i	0.476738	−	0.597811i
$95$	2.42995	+	1.65671i	0.249308	+	0.169975i
$96$		0			0
$97$	0.441741	−	0.212731i	0.0448520	−	0.0215996i	−0.411323	−	0.911490i	$-0.634933\pi$
$97$	0.441741	−	0.212731i	0.0448520	−	0.0215996i	0.456175	+	0.889890i	$0.349219\pi$
$98$	−6.45494	−	5.98931i	−0.652048	−	0.605012i
$99$		0			0
$100$	−4.06261	+	1.25315i	−0.406261	+	0.125315i
$101$	−0.164575	−	2.19611i	−0.0163759	−	0.218521i	−0.999388	−	0.0349802i	$-0.988863\pi$
$101$	−0.164575	−	2.19611i	−0.0163759	−	0.218521i	0.983012	−	0.183541i	$-0.0587559\pi$
$102$		0			0
$103$	−1.86980	+	4.76417i	−0.184237	+	0.469427i	−0.992915	−	0.118823i	$-0.962088\pi$
$103$	−1.86980	+	4.76417i	−0.184237	+	0.469427i	0.808679	+	0.588250i	$0.200183\pi$
$104$	−1.78584	+	1.65702i	−0.175116	+	0.162484i
$105$		0			0
$106$	−1.22571	+	16.3560i	−0.119052	+	1.58863i
$107$	−2.28640	−	10.0174i	−0.221035	−	0.968418i	−0.956701	−	0.291073i	$-0.905988\pi$
$107$	−2.28640	−	10.0174i	−0.221035	−	0.968418i	0.735666	−	0.677345i	$-0.236869\pi$
$108$		0			0
$109$	−0.0839896	+	1.12076i	−0.00804474	+	0.107350i	−0.999781	−	0.0209470i	$-0.993332\pi$
$109$	−0.0839896	+	1.12076i	−0.00804474	+	0.107350i	0.991736	+	0.128297i	$0.0409509\pi$
$110$	2.34155	−	1.59644i	0.223258	−	0.152215i
$111$		0			0
$112$	6.35882	−	16.2020i	0.600852	−	1.53094i
$113$	−9.95806	−	12.4870i	−0.936776	−	1.17468i	−0.984423	−	0.175815i	$-0.943744\pi$
$113$	−9.95806	−	12.4870i	−0.936776	−	1.17468i	0.0476475	−	0.998864i	$-0.484828\pi$
$114$		0			0
$115$	2.72993	−	0.842073i	0.254568	−	0.0785237i
$116$	2.95757	+	0.445783i	0.274604	+	0.0413899i
$117$		0			0
$118$	−7.16165	+	3.44887i	−0.659283	+	0.317494i
$119$	−1.94299	+	0.292859i	−0.178114	+	0.0268463i
$120$		0			0
$121$	4.86216	−	6.09695i	0.442014	−	0.554268i
$122$	4.58770	+	7.94612i	0.415351	+	0.719408i
$123$		0			0
$124$	0.313175	+	0.797957i	0.0281240	+	0.0716587i
$125$	−3.42081	−	1.64738i	−0.305967	−	0.147346i
$126$		0			0
$127$	0.749226	−	3.28258i	0.0664831	−	0.291281i	−0.930747	−	0.365665i	$-0.880842\pi$
$127$	0.749226	−	3.28258i	0.0664831	−	0.291281i	0.997230	+	0.0743833i	$0.0236988\pi$
$128$	12.8395			1.13486
$129$		0			0
$130$	0.835583			0.0732855
$131$	−0.342281	+	1.49963i	−0.0299053	+	0.131024i	−0.987677	−	0.156506i	$-0.949977\pi$
$131$	−0.342281	+	1.49963i	−0.0299053	+	0.131024i	0.957772	+	0.287530i	$0.0928340\pi$
$132$		0			0
$133$	−24.0060	−	11.5607i	−2.08159	−	1.00244i
$134$	8.12927	+	20.7130i	0.702262	+	1.78933i
$135$		0			0
$136$	−0.536214	−	0.928750i	−0.0459800	−	0.0796397i
$137$	1.98722	−	2.49190i	0.169780	−	0.212897i	−0.689661	−	0.724132i	$-0.742240\pi$
$137$	1.98722	−	2.49190i	0.169780	−	0.212897i	0.859441	+	0.511235i	$0.170812\pi$
$138$		0			0
$139$	19.8520	−	2.99220i	1.68382	−	0.253795i	0.763741	−	0.645523i	$-0.223360\pi$
$139$	19.8520	−	2.99220i	1.68382	−	0.253795i	0.920081	+	0.391727i	$0.128122\pi$
$140$	−1.06252	+	0.511681i	−0.0897991	+	0.0432450i
$141$		0			0
$142$	12.7990	+	1.92914i	1.07407	+	0.161890i
$143$	5.29632	−	1.63370i	0.442900	−	0.136617i
$144$		0			0
$145$	0.820149	+	1.02843i	0.0681097	+	0.0854069i
$146$	1.28644	−	3.27778i	0.106466	−	0.271271i
$147$		0			0
$148$	3.18296	−	2.17010i	0.261637	−	0.178381i
$149$	0.944726	−	12.6065i	0.0773949	−	1.03276i	−0.814394	−	0.580312i	$-0.802931\pi$
$149$	0.944726	−	12.6065i	0.0773949	−	1.03276i	0.891789	−	0.452451i	$-0.149450\pi$
$150$		0			0
$151$	−0.223758	−	0.980350i	−0.0182092	−	0.0797798i	0.965007	−	0.262224i	$-0.0844561\pi$
$151$	−0.223758	−	0.980350i	−0.0182092	−	0.0797798i	−0.983216	+	0.182445i	$0.941599\pi$
$152$	1.08674	−	14.5015i	0.0881462	−	1.17623i
$153$		0			0
$154$	−18.8214	+	17.4637i	−1.51667	+	1.40726i
$155$	−0.137733	+	0.350937i	−0.0110630	+	0.0281880i
$156$		0			0
$157$	0.355966	+	4.75004i	0.0284092	+	0.379095i	0.993228	+	0.116180i	$0.0370648\pi$
$157$	0.355966	+	4.75004i	0.0284092	+	0.379095i	−0.964819	+	0.262915i	$0.915316\pi$
$158$	−13.4264	+	4.14149i	−1.06815	+	0.329479i
$159$		0			0
$160$	−1.31162	−	1.21700i	−0.103692	−	0.0962125i
$161$	−23.3194	+	11.2300i	−1.83783	+	0.885050i
$162$		0			0
$163$	−7.84688	−	5.34991i	−0.614615	−	0.419037i	0.215599	−	0.976482i	$-0.430829\pi$
$163$	−7.84688	−	5.34991i	−0.614615	−	0.419037i	−0.830214	+	0.557445i	$0.811782\pi$
$164$	−2.65078	+	3.32397i	−0.206991	+	0.259559i
$165$		0			0
$166$	−9.87862	+	17.1103i	−0.766730	+	1.32802i
$167$	8.26817	+	21.0670i	0.639810	+	1.63021i	0.769494	+	0.638654i	$0.220509\pi$
$167$	8.26817	+	21.0670i	0.639810	+	1.63021i	−0.129684	+	0.991555i	$0.541396\pi$
$168$		0			0
$169$	−10.8609	−	3.35013i	−0.835451	−	0.257702i
$170$	−0.0818503	+	0.358610i	−0.00627763	+	0.0275041i
$171$		0			0
$172$	−4.76454	+	3.21269i	−0.363293	+	0.244966i
$173$	−9.30235			−0.707245			−0.353622	−	0.935388i	$-0.615050\pi$
$173$	−9.30235			−0.707245			−0.353622	+	0.935388i	$0.615050\pi$
$174$		0			0
$175$	16.1873	+	4.99312i	1.22365	+	0.377445i
$176$	−19.4719	−	9.37718i	−1.46775	−	0.706831i
$177$		0			0
$178$	2.31319	−	4.00657i	0.173381	−	0.300305i
$179$	3.61481	+	6.26104i	0.270184	+	0.467972i	0.968909	−	0.247418i	$-0.0795822\pi$
$179$	3.61481	+	6.26104i	0.270184	+	0.467972i	−0.698725	+	0.715390i	$0.746249\pi$
$180$		0			0
$181$	−15.5329	−	10.5902i	−1.15455	−	0.787162i	−0.174259	−	0.984700i	$-0.555753\pi$
$181$	−15.5329	−	10.5902i	−1.15455	−	0.787162i	−0.980295	+	0.197538i	$0.936705\pi$
$182$	−7.48567	+	1.12828i	−0.554875	+	0.0836339i
$183$		0			0
$184$	−10.3553	−	9.60828i	−0.763400	−	0.708332i
$185$	1.67532	+	0.252513i	0.123172	+	0.0185652i
$186$		0			0
$187$	0.182333	+	2.43307i	0.0133335	+	0.177924i
$188$	2.38833	+	2.99487i	0.174187	+	0.218423i
$189$		0			0
$190$	−3.65634	+	3.39258i	−0.265258	+	0.246124i
$191$	5.81055	−	3.96157i	0.420437	−	0.286649i	−0.334564	−	0.942373i	$-0.608589\pi$
$191$	5.81055	−	3.96157i	0.420437	−	0.286649i	0.755001	+	0.655724i	$0.227637\pi$
$192$		0			0
$193$	0.916048	+	4.01347i	0.0659385	+	0.288896i	0.997137	−	0.0756172i	$-0.0240927\pi$
$193$	0.916048	+	4.01347i	0.0659385	+	0.288896i	−0.931198	+	0.364513i	$0.881236\pi$
$194$	0.185033	+	0.810682i	0.0132846	+	0.0582035i
$195$		0			0
$196$	3.75935	−	2.56308i	0.268525	−	0.183077i
$197$	1.32247	−	1.22707i	0.0942220	−	0.0874252i	−0.631656	−	0.775249i	$-0.717624\pi$
$197$	1.32247	−	1.22707i	0.0942220	−	0.0874252i	0.725878	+	0.687824i	$0.241434\pi$
$198$		0			0
$199$	−14.1954	−	17.8005i	−1.00629	−	1.26185i	−0.964877	−	0.262704i	$-0.915386\pi$
$199$	−14.1954	−	17.8005i	−1.00629	−	1.26185i	−0.0414119	−	0.999142i	$-0.513186\pi$
$200$	0.690916	+	9.21964i	0.0488552	+	0.651927i
$201$		0			0
$202$	3.69327	+	0.556671i	0.259858	+	0.0391672i
$203$	−8.73610	−	8.10592i	−0.613154	−	0.568924i
$204$		0			0
$205$	−1.84891	+	0.278679i	−0.129134	+	0.0194638i
$206$	−7.17169	−	4.88957i	−0.499675	−	0.340673i
$207$		0			0
$208$	−3.18611	−	5.51850i	−0.220917	−	0.382639i
$209$	−16.5425	+	28.6525i	−1.14427	+	1.98194i
$210$		0			0
$211$	7.10545	+	3.42180i	0.489159	+	0.235567i	0.662170	−	0.749353i	$-0.269635\pi$
$211$	7.10545	+	3.42180i	0.489159	+	0.235567i	−0.173011	+	0.984920i	$0.555350\pi$
$212$	−8.09852	−	2.49806i	−0.556209	−	0.171568i
$213$		0			0
$214$	17.4262			1.19123
$215$	−2.49708	−	0.389499i	−0.170300	−	0.0265636i
$216$		0			0
$217$	0.760027	−	3.32990i	0.0515940	−	0.226048i
$218$	−1.82143	−	0.561838i	−0.123363	−	0.0380524i
$219$		0			0
$220$	0.534990	+	1.36313i	0.0360690	+	0.0919024i
$221$	−0.359693	+	0.623007i	−0.0241956	+	0.0419080i
$222$		0			0
$223$	5.36853	−	6.73192i	0.359503	−	0.450803i	−0.568884	−	0.822418i	$-0.692625\pi$
$223$	5.36853	−	6.73192i	0.359503	−	0.450803i	0.928387	+	0.371615i	$0.121196\pi$
$224$	13.3936	+	9.13160i	0.894897	+	0.610131i
$225$		0			0
$226$	24.4048	−	11.7527i	1.62338	−	0.781779i
$227$	−5.97274	−	5.54190i	−0.396425	−	0.367829i	0.456624	−	0.889660i	$-0.349059\pi$
$227$	−5.97274	−	5.54190i	−0.396425	−	0.367829i	−0.853049	+	0.521831i	$0.825249\pi$
$228$		0			0
$229$	−23.6766	+	7.30327i	−1.56460	+	0.482614i	−0.951565	−	0.307446i	$-0.900526\pi$
$229$	−23.6766	+	7.30327i	−1.56460	+	0.482614i	−0.613030	+	0.790060i	$0.710049\pi$
$230$	0.362079	+	4.83161i	0.0238748	+	0.318587i
$231$		0			0
$232$	2.37630	−	6.05470i	0.156011	−	0.397511i
$233$	6.32022	−	5.86431i	0.414051	−	0.384183i	−0.445459	−	0.895303i	$-0.646959\pi$
$233$	6.32022	−	5.86431i	0.414051	−	0.384183i	0.859510	+	0.511119i	$0.170769\pi$
$234$		0			0
$235$	−0.125895	+	1.67996i	−0.00821251	+	0.109588i
$236$	−0.913952	−	4.00429i	−0.0594932	−	0.260657i
$237$		0			0
$238$	0.249037	−	3.32317i	0.0161427	−	0.215409i
$239$	−2.78125	+	1.89623i	−0.179904	+	0.122657i	−0.649924	−	0.759999i	$-0.725199\pi$
$239$	−2.78125	+	1.89623i	−0.179904	+	0.122657i	0.470020	+	0.882656i	$0.344247\pi$
$240$		0			0
$241$	−9.87013	+	25.1487i	−0.635791	+	1.61997i	0.140854	+	0.990030i	$0.455015\pi$
$241$	−9.87013	+	25.1487i	−0.635791	+	1.61997i	−0.776645	+	0.629939i	$0.783080\pi$
$242$	8.24610	+	10.3403i	0.530079	+	0.664698i
$243$		0			0
$244$	−4.53041	+	1.39745i	−0.290030	+	0.0894624i
$245$	1.97870	+	0.298240i	0.126414	+	0.0190539i
$246$		0			0
$247$	−8.78888	+	4.23250i	−0.559223	+	0.269308i
$248$	1.84331	−	0.277835i	0.117051	−	0.0176425i
$249$		0			0
$250$	4.01484	−	5.03445i	0.253921	−	0.318407i
$251$	−5.38285	−	9.32338i	−0.339763	−	0.588486i	0.644625	−	0.764499i	$-0.277013\pi$
$251$	−5.38285	−	9.32338i	−0.339763	−	0.588486i	−0.984388	+	0.176012i	$0.943680\pi$
$252$		0			0
$253$	11.7416	+	29.9171i	0.738188	+	1.88087i
$254$	5.14484	+	2.47762i	0.322816	+	0.155460i
$255$		0			0
$256$	−3.91277	+	17.1430i	−0.244548	+	1.07143i
$257$	−12.7546			−0.795610			−0.397805	−	0.917470i	$-0.630228\pi$
$257$	−12.7546			−0.795610			−0.397805	+	0.917470i	$0.630228\pi$
$258$		0			0
$259$	−15.3495			−0.953772
$260$	−0.0960749	+	0.420932i	−0.00595831	+	0.0261051i
$261$		0			0
$262$	−2.35040	−	1.13189i	−0.145208	−	0.0699286i
$263$	5.41921	+	13.8079i	0.334163	+	0.851433i	0.994905	+	0.100820i	$0.0321465\pi$
$263$	5.41921	+	13.8079i	0.334163	+	0.851433i	−0.660742	+	0.750613i	$0.729758\pi$
$264$		0			0
$265$	−1.86364	−	3.22792i	−0.114482	−	0.198289i
$266$	28.1747	−	35.3300i	1.72750	−	2.16622i
$267$		0			0
$268$	−11.3691	+	1.71361i	−0.694476	+	0.104675i
$269$	9.64831	−	4.64638i	0.588268	−	0.283295i	−0.115977	−	0.993252i	$-0.537000\pi$
$269$	9.64831	−	4.64638i	0.588268	−	0.283295i	0.704245	+	0.709957i	$0.251286\pi$
$270$		0			0
$271$	−14.3276	−	2.15955i	−0.870343	−	0.131183i	−0.301338	−	0.953517i	$-0.597433\pi$
$271$	−14.3276	−	2.15955i	−0.870343	−	0.131183i	−0.569005	+	0.822334i	$0.692671\pi$
$272$	2.68049	−	0.826822i	0.162529	−	0.0501335i
$273$		0			0
$274$	3.37028	+	4.22620i	0.203606	+	0.255314i
$275$	7.68476	−	19.5804i	0.463408	−	1.18075i
$276$		0			0
$277$	16.8697	−	11.5016i	1.01360	−	0.691061i	0.0618982	−	0.998082i	$-0.480285\pi$
$277$	16.8697	−	11.5016i	1.01360	−	0.691061i	0.951703	+	0.307021i	$0.0993322\pi$
$278$	−2.54447	+	33.9535i	−0.152607	+	2.03640i
$279$		0			0
$280$	0.570670	+	2.50027i	0.0341041	+	0.149420i
$281$	0.541902	−	7.23118i	0.0323272	−	0.431376i	−0.957435	−	0.288649i	$-0.906794\pi$
$281$	0.541902	−	7.23118i	0.0323272	−	0.431376i	0.989762	−	0.142727i	$-0.0455871\pi$
$282$		0			0
$283$	22.3431	−	20.7313i	1.32816	−	1.23235i	0.376044	−	0.926602i	$-0.377284\pi$
$283$	22.3431	−	20.7313i	1.32816	−	1.23235i	0.952113	−	0.305748i	$-0.0989065\pi$
$284$	−2.44344	+	6.22579i	−0.144992	+	0.369433i
$285$		0			0
$286$	0.702466	+	9.37376i	0.0415377	+	0.554282i
$287$	16.1874	−	4.99316i	0.955513	−	0.294737i
$288$		0			0
$289$	12.2297	+	11.3475i	0.719396	+	0.667502i
$290$	−2.00999	+	0.967958i	−0.118030	+	0.0568405i
$291$		0			0
$292$	1.50330	+	1.02493i	0.0879738	+	0.0599795i
$293$	−16.0151	+	20.0823i	−0.935611	+	1.17322i	0.0490592	+	0.998796i	$0.484378\pi$
$293$	−16.0151	+	20.0823i	−0.935611	+	1.17322i	−0.984671	+	0.174424i	$0.944194\pi$
$294$		0			0
$295$	0.903177	−	1.56435i	0.0525850	−	0.0910799i
$296$	−3.06064	−	7.79837i	−0.177896	−	0.453271i
$297$		0			0
$298$	20.4877	+	6.31962i	1.18682	+	0.366086i
$299$	−2.10859	+	9.23832i	−0.121943	+	0.534266i
$300$		0			0
$301$	22.8964	+	0.117571i	1.31973	+	0.00677671i
$302$	1.70541			0.0981352
$303$		0			0
$304$	36.3476	+	11.2118i	2.08468	+	0.643038i
$305$	−1.87860	−	0.904685i	−0.107568	−	0.0518021i
$306$		0			0
$307$	−7.92491	+	13.7263i	−0.452298	+	0.783404i	−0.998528	−	0.0542314i	$-0.982729\pi$
$307$	−7.92491	+	13.7263i	−0.452298	+	0.783404i	0.546230	+	0.837635i	$0.316062\pi$
$308$	−6.63340	−	11.4894i	−0.377973	−	0.654669i
$309$		0			0
$310$	−0.528280	−	0.360175i	−0.0300043	−	0.0204566i
$311$	26.7139	−	4.02647i	1.51481	−	0.228320i	0.661585	−	0.749870i	$-0.269884\pi$
$311$	26.7139	−	4.02647i	1.51481	−	0.228320i	0.853221	+	0.521550i	$0.174646\pi$
$312$		0			0
$313$	−14.1284	−	13.1093i	−0.798586	−	0.740979i	0.171121	−	0.985250i	$-0.445261\pi$
$313$	−14.1284	−	13.1093i	−0.798586	−	0.740979i	−0.969707	+	0.244271i	$0.921452\pi$
$314$	−7.98831	−	1.20404i	−0.450807	−	0.0679481i
$315$		0			0
$316$	−0.542550	−	7.23983i	−0.0305208	−	0.407272i
$317$	8.01912	+	10.0557i	0.450399	+	0.564782i	0.954251	−	0.299008i	$-0.0966557\pi$
$317$	8.01912	+	10.0557i	0.450399	+	0.564782i	−0.503852	+	0.863790i	$0.668084\pi$
$318$		0			0
$319$	−10.8477	+	10.0652i	−0.607356	+	0.563544i
$320$	−0.667388	+	0.455018i	−0.0373081	+	0.0254363i
$321$		0			0
$322$	−9.76783	−	42.7956i	−0.544340	−	2.38491i
$323$	−0.955553	−	4.18655i	−0.0531684	−	0.232946i
$324$		0			0
$325$	5.12424	−	3.49365i	0.284242	−	0.193793i
$326$	11.8072	−	10.9554i	0.653938	−	0.606766i
$327$		0			0
$328$	5.76451	+	7.22846i	0.318292	+	0.399125i
$329$	−1.14059	−	15.2201i	−0.0628827	−	0.839111i
$330$		0			0
$331$	2.51633	+	0.379275i	0.138310	+	0.0208469i	0.217832	−	0.975986i	$-0.430101\pi$
$331$	2.51633	+	0.379275i	0.138310	+	0.0208469i	−0.0795224	+	0.996833i	$0.525340\pi$
$332$	−7.48360	−	6.94377i	−0.410716	−	0.381089i
$333$		0			0
$334$	−37.9536	+	5.72058i	−2.07673	+	0.313016i
$335$	−4.17790	−	2.84844i	−0.228263	−	0.155627i
$336$		0			0
$337$	−0.368739	−	0.638675i	−0.0200865	−	0.0347908i	0.855807	−	0.517295i	$-0.173061\pi$
$337$	−0.368739	−	0.638675i	−0.0200865	−	0.0347908i	−0.875894	+	0.482504i	$0.839727\pi$
$338$	9.63807	−	16.6936i	0.524242	−	0.908014i
$339$		0			0
$340$	−0.171241	−	0.0824655i	−0.00928687	−	0.00447232i
$341$	−4.05269	−	1.25009i	−0.219465	−	0.0676961i
$342$		0			0
$343$	6.31287			0.340863
$344$	4.50572	+	11.6560i	0.242932	+	0.628451i
$345$		0			0
$346$	3.51062	−	15.3810i	0.188732	−	0.826888i
$347$	5.00949	+	1.54522i	0.268923	+	0.0829519i	0.426284	−	0.904589i	$-0.359822\pi$
$347$	5.00949	+	1.54522i	0.268923	+	0.0829519i	−0.157361	+	0.987541i	$0.550299\pi$
$348$		0			0
$349$	3.64385	+	9.28439i	0.195051	+	0.496982i	0.994620	−	0.103593i	$-0.0330338\pi$
$349$	3.64385	+	9.28439i	0.195051	+	0.496982i	−0.799569	+	0.600575i	$0.794939\pi$
$350$	−14.3648	+	24.8806i	−0.767832	+	1.32992i
$351$		0			0
$352$	12.5499	−	15.7371i	0.668914	−	0.838792i
$353$	−20.6981	−	14.1117i	−1.10165	−	0.751090i	−0.130948	−	0.991389i	$-0.541802\pi$
$353$	−20.6981	−	14.1117i	−1.10165	−	0.751090i	−0.970699	+	0.240299i	$0.922755\pi$
$354$		0			0
$355$	−2.65011	+	1.27622i	−0.140653	+	0.0677349i
$356$	1.75237	+	1.62596i	0.0928756	+	0.0861759i
$357$		0			0
$358$	−11.7165	+	3.61407i	−0.619238	+	0.191010i
$359$	−1.02841	−	13.7231i	−0.0542772	−	0.724279i	−0.956262	−	0.292511i	$-0.905509\pi$
$359$	−1.02841	−	13.7231i	−0.0542772	−	0.724279i	0.901985	−	0.431768i	$-0.142110\pi$
$360$		0			0
$361$	14.3323	−	36.5180i	0.754330	−	1.92200i
$362$	23.3723	−	21.6864i	1.22842	−	1.13981i
$363$		0			0
$364$	0.292317	−	3.90070i	0.0153216	−	0.204452i
$365$	0.178057	+	0.780120i	0.00931995	+	0.0408334i
$366$		0			0
$367$	−2.05378	+	27.4058i	−0.107206	+	1.43057i	0.641222	+	0.767355i	$0.278428\pi$
$367$	−2.05378	+	27.4058i	−0.107206	+	1.43057i	−0.748429	+	0.663215i	$0.769191\pi$
$368$	30.5291	−	20.8144i	1.59144	−	1.08503i
$369$		0			0
$370$	−1.04977	+	2.67476i	−0.0545748	+	0.139054i
$371$	21.0543	+	26.4012i	1.09308	+	1.37068i
$372$		0			0
$373$	15.0169	−	4.63210i	0.777545	−	0.239841i	0.119515	−	0.992832i	$-0.461866\pi$
$373$	15.0169	−	4.63210i	0.777545	−	0.239841i	0.658030	+	0.752992i	$0.271390\pi$
$374$	−4.09178	−	0.616736i	−0.211581	−	0.0318907i
$375$		0			0
$376$	7.50520	−	3.61431i	0.387051	−	0.186394i
$377$	−4.31437	+	0.650287i	−0.222201	+	0.0334915i
$378$		0			0
$379$	−16.0442	+	20.1188i	−0.824136	+	1.03343i	0.174672	+	0.984627i	$0.444113\pi$
$379$	−16.0442	+	20.1188i	−0.824136	+	1.03343i	−0.998808	+	0.0488070i	$0.984458\pi$
$380$	−1.28864	−	2.23199i	−0.0661057	−	0.114498i
$381$		0			0
$382$	4.35743	+	11.1025i	0.222945	+	0.568055i
$383$	−16.2586	−	7.82975i	−0.830777	−	0.400081i	−0.0303708	−	0.999539i	$-0.509669\pi$
$383$	−16.2586	−	7.82975i	−0.830777	−	0.400081i	−0.800407	+	0.599457i	$0.795383\pi$
$384$		0			0
$385$	1.29834	−	5.68838i	0.0661694	−	0.289907i
$386$	−6.98179			−0.355364
$387$		0			0
$388$	−0.429662			−0.0218128
$389$	−5.62992	+	24.6663i	−0.285448	+	1.25063i	0.605249	+	0.796036i	$0.293073\pi$
$389$	−5.62992	+	24.6663i	−0.285448	+	1.25063i	−0.890698	+	0.454596i	$0.849784\pi$
$390$		0			0
$391$	−3.75829	−	1.80990i	−0.190065	−	0.0915304i
$392$	−3.61488	−	9.21056i	−0.182579	−	0.465204i
$393$		0			0
$394$	1.52982	+	2.64973i	0.0770712	+	0.133491i
$395$	1.99078	−	2.49636i	0.100167	−	0.125606i
$396$		0			0
$397$	−2.61362	+	0.393940i	−0.131174	+	0.0197713i	−0.214301	−	0.976768i	$-0.568747\pi$
$397$	−2.61362	+	0.393940i	−0.131174	+	0.0197713i	0.0831270	+	0.996539i	$0.473509\pi$
$398$	34.7896	−	16.7538i	1.74384	−	0.839791i
$399$		0			0
$400$	−23.9130	−	3.60431i	−1.19565	−	0.180215i
$401$	−28.1025	+	8.66848i	−1.40337	+	0.432883i	−0.901771	−	0.432215i	$-0.857732\pi$
$401$	−28.1025	+	8.66848i	−1.40337	+	0.432883i	−0.501603	+	0.865098i	$0.667256\pi$
$402$		0			0
$403$	−0.779651	−	0.977651i	−0.0388372	−	0.0487003i
$404$	−0.705078	+	1.79651i	−0.0350789	+	0.0893797i
$405$		0			0
$406$	16.6997	−	11.3856i	0.828791	−	0.565060i
$407$	−1.42433	+	19.0064i	−0.0706014	+	0.942111i
$408$		0			0
$409$	0.0843680	+	0.369640i	0.00417173	+	0.0182775i	0.976971	−	0.213372i	$-0.0684448\pi$
$409$	0.0843680	+	0.369640i	0.00417173	+	0.0182775i	−0.972799	+	0.231650i	$0.925588\pi$
$410$	0.236979	−	3.16226i	0.0117035	−	0.156173i
$411$		0			0
$412$	3.28776	−	3.05059i	0.161976	−	0.150292i
$413$	−5.97889	+	15.2340i	−0.294202	+	0.749614i
$414$		0			0
$415$	−0.335522	−	4.47723i	−0.0164701	−	0.219779i
$416$	5.67111	−	1.74931i	0.278049	−	0.0857668i
$417$		0			0
$418$	−41.1326	−	38.1655i	−2.01186	−	1.86673i
$419$	14.9002	−	7.17556i	0.727922	−	0.350549i	−0.0329444	−	0.999457i	$-0.510488\pi$
$419$	14.9002	−	7.17556i	0.727922	−	0.350549i	0.760867	+	0.648908i	$0.224774\pi$
$420$		0			0
$421$	−7.57559	−	5.16495i	−0.369212	−	0.251724i	0.364473	−	0.931214i	$-0.381249\pi$
$421$	−7.57559	−	5.16495i	−0.369212	−	0.251724i	−0.733685	+	0.679489i	$0.762201\pi$
$422$	−8.33932	+	10.4572i	−0.405952	+	0.509047i
$423$		0			0
$424$	−9.21510	+	15.9610i	−0.447525	+	0.775136i
$425$	0.997429	+	2.54141i	0.0483824	+	0.123276i
$426$		0			0
$427$	18.0512	+	5.56807i	0.873561	+	0.269458i
$428$	−2.00365	+	8.77857i	−0.0968501	+	0.424328i
$429$		0			0
$430$	1.58639	−	3.98182i	0.0765027	−	0.192020i
$431$	−9.52715			−0.458907			−0.229453	−	0.973320i	$-0.573694\pi$
$431$	−9.52715			−0.458907			−0.229453	+	0.973320i	$0.573694\pi$
$432$		0			0
$433$	−27.5381	−	8.49437i	−1.32339	−	0.408213i	−0.449045	−	0.893509i	$-0.648236\pi$
$433$	−27.5381	−	8.49437i	−1.32339	−	0.408213i	−0.874350	+	0.485296i	$0.838712\pi$
$434$	5.21900	+	2.51334i	0.250520	+	0.120644i
$435$		0			0
$436$	0.492458	−	0.852961i	0.0235844	−	0.0408494i
$437$	−28.2821	−	48.9861i	−1.35292	−	2.34332i
$438$		0			0
$439$	−5.56118	−	3.79155i	−0.265421	−	0.180961i	0.423296	−	0.905992i	$-0.360873\pi$
$439$	−5.56118	−	3.79155i	−0.265421	−	0.180961i	−0.688716	+	0.725031i	$0.741825\pi$
$440$	3.14889	−	0.474619i	0.150117	−	0.0226266i
$441$		0			0
$442$	−0.894368	−	0.829852i	−0.0425408	−	0.0394720i
$443$	3.28651	+	0.495362i	0.156147	+	0.0235354i	0.226650	−	0.973976i	$-0.427222\pi$
$443$	3.28651	+	0.495362i	0.156147	+	0.0235354i	−0.0705035	+	0.997512i	$0.522461\pi$
$444$		0			0
$445$	0.0785665	+	1.04840i	0.00372441	+	0.0496988i
$446$	9.10489	+	11.4172i	0.431129	+	0.540619i
$447$		0			0
$448$	5.36447	−	4.97750i	0.253447	−	0.235165i
$449$	3.54373	−	2.41607i	0.167239	−	0.114022i	−0.476808	−	0.879007i	$-0.658206\pi$
$449$	3.54373	−	2.41607i	0.167239	−	0.114022i	0.644047	+	0.764986i	$0.277254\pi$
$450$		0			0
$451$	−4.68064	−	20.5072i	−0.220403	−	0.965648i
$452$	3.11448	+	13.6454i	0.146493	+	0.641827i
$453$		0			0
$454$	11.4173	−	7.78420i	0.535841	−	0.365331i
$455$	1.26108	−	1.17011i	0.0591204	−	0.0548557i
$456$		0			0
$457$	−1.37989	−	1.73032i	−0.0645484	−	0.0809412i	0.748509	−	0.663125i	$-0.230770\pi$
$457$	−1.37989	−	1.73032i	−0.0645484	−	0.0809412i	−0.813058	+	0.582183i	$0.802199\pi$
$458$	−3.14030	−	41.9044i	−0.146737	−	1.95806i
$459$		0			0
$460$	−2.47559	−	0.373136i	−0.115425	−	0.0173975i
$461$	11.1729	+	10.3670i	0.520375	+	0.482837i	0.896074	−	0.443904i	$-0.146407\pi$
$461$	11.1729	+	10.3670i	0.520375	+	0.482837i	−0.375699	+	0.926742i	$0.622597\pi$
$462$		0			0
$463$	10.6302	−	1.60224i	0.494027	−	0.0744626i	0.102697	−	0.994713i	$-0.467253\pi$
$463$	10.6302	−	1.60224i	0.494027	−	0.0744626i	0.391331	+	0.920250i	$0.372015\pi$
$464$	14.0569	+	9.58384i	0.652576	+	0.444918i
$465$		0			0
$466$	7.31117	+	12.6633i	0.338683	+	0.586617i
$467$	−7.41391	+	12.8413i	−0.343075	+	0.594223i	−0.985002	−	0.172543i	$-0.944802\pi$
$467$	−7.41391	+	12.8413i	−0.343075	+	0.594223i	0.641927	+	0.766766i	$0.278135\pi$
$468$		0			0
$469$	41.2745	+	19.8767i	1.90588	+	0.917822i
$470$	−2.73022	−	0.842161i	−0.125936	−	0.0388460i
$471$		0			0
$472$	−8.93184			−0.411121
$473$	2.27021	−	28.3403i	0.104384	−	1.30309i
$474$		0			0
$475$	−8.23789	+	36.0926i	−0.377981	+	1.65604i
$476$	1.64544	+	0.507551i	0.0754186	+	0.0232636i
$477$		0			0
$478$	−2.08571	−	5.31429i	−0.0953980	−	0.243070i
$479$	−17.1592	+	29.7205i	−0.784022	+	1.35797i	0.145559	+	0.989350i	$0.453502\pi$
$479$	−17.1592	+	29.7205i	−0.784022	+	1.35797i	−0.929581	+	0.368617i	$0.879831\pi$
$480$		0			0
$481$	−3.50378	+	4.39360i	−0.159758	+	0.200331i
$482$	−37.8573	−	25.8107i	−1.72435	−	1.17564i
$483$		0			0
$484$	−6.15713	+	2.96512i	−0.279870	+	0.134778i
$485$	−0.138520	−	0.128528i	−0.00628986	−	0.00583614i
$486$		0			0
$487$	−6.21312	+	1.91649i	−0.281543	+	0.0868446i	−0.432311	−	0.901725i	$-0.642302\pi$
$487$	−6.21312	+	1.91649i	−0.281543	+	0.0868446i	0.150768	+	0.988569i	$0.451825\pi$
$488$	0.770474	+	10.2813i	0.0348777	+	0.465411i
$489$		0			0
$490$	−1.23987	+	3.15913i	−0.0560115	+	0.142715i
$491$	−5.97382	+	5.54289i	−0.269595	+	0.250147i	−0.803372	−	0.595478i	$-0.796963\pi$
$491$	−5.97382	+	5.54289i	−0.269595	+	0.250147i	0.533777	+	0.845625i	$0.320772\pi$
$492$		0			0
$493$	0.143533	−	1.91531i	0.00646439	−	0.0862613i
$494$	−3.68141	−	16.1293i	−0.165634	−	0.725692i
$495$		0			0
$496$	−0.364380	+	4.86232i	−0.0163612	+	0.218325i
$497$	22.0180	−	15.0116i	0.987643	−	0.673364i
$498$		0			0
$499$	2.88373	−	7.34763i	0.129094	−	0.328925i	−0.851684	−	0.524056i	$-0.824418\pi$
$499$	2.88373	−	7.34763i	0.129094	−	0.328925i	0.980777	+	0.195131i	$0.0625133\pi$
$500$	2.07452	+	2.60137i	0.0927754	+	0.116337i
$501$		0			0
$502$	17.4472	−	5.38175i	0.778707	−	0.240199i
$503$	24.2178	+	3.65024i	1.07982	+	0.162756i	0.664773	−	0.747045i	$-0.268528\pi$
$503$	24.2178	+	3.65024i	1.07982	+	0.162756i	0.415044	+	0.909801i	$0.363766\pi$
$504$		0			0
$505$	−0.764713	+	0.368266i	−0.0340293	+	0.0163876i
$506$	−53.8977	+	8.12377i	−2.39604	+	0.361146i
$507$		0			0
$508$	−1.83967	+	2.30688i	−0.0816223	+	0.102351i
$509$	15.1556	+	26.2503i	0.671760	+	1.16352i	0.977405	+	0.211376i	$0.0677946\pi$
$509$	15.1556	+	26.2503i	0.671760	+	1.16352i	−0.305645	+	0.952146i	$0.598872\pi$
$510$		0			0
$511$	−2.64854	−	6.74837i	−0.117165	−	0.298530i
$512$	−3.73249	−	1.79747i	−0.164954	−	0.0794377i
$513$		0			0
$514$	4.81346	−	21.0891i	0.212313	−	0.930202i
$515$	1.97249			0.0869184
$516$		0			0
$517$	−18.9520			−0.833507
$518$	5.79275	−	25.3797i	0.254519	−	1.11512i
$519$		0			0
$520$	0.845935	+	0.407381i	0.0370967	+	0.0178648i
$521$	−4.59482	−	11.7074i	−0.201303	−	0.512911i	0.794199	−	0.607658i	$-0.207891\pi$
$521$	−4.59482	−	11.7074i	−0.201303	−	0.512911i	−0.995501	+	0.0947472i	$0.969796\pi$
$522$		0			0
$523$	18.0801	+	31.3157i	0.790589	+	1.36934i	0.925603	+	0.378496i	$0.123559\pi$
$523$	18.0801	+	31.3157i	0.790589	+	1.36934i	−0.135014	+	0.990844i	$0.543108\pi$
$524$	0.840448	−	1.05389i	0.0367151	−	0.0460393i
$525$		0			0
$526$	−24.8759	+	3.74944i	−1.08464	+	0.163483i
$527$	0.495953	−	0.238838i	0.0216041	−	0.0104040i
$528$		0			0
$529$	−31.5895	−	4.76135i	−1.37346	−	0.207015i
$530$	6.04053	−	1.86326i	0.262384	−	0.0809347i
$531$		0			0
$532$	14.5583	+	18.2555i	0.631180	+	0.791475i
$533$	2.26582	−	5.77321i	0.0981434	−	0.250065i
$534$		0			0
$535$	−3.27195	+	2.23078i	−0.141459	+	0.0964450i
$536$	−1.86847	+	24.9330i	−0.0807056	+	1.07694i
$537$		0			0
$538$	4.04140	+	17.7065i	0.174237	+	0.763383i
$539$	−1.68226	+	22.4482i	−0.0724600	+	0.966912i
$540$		0			0
$541$	3.25662	−	3.02170i	0.140013	−	0.129913i	−0.607057	−	0.794658i	$-0.707650\pi$
$541$	3.25662	−	3.02170i	0.140013	−	0.129913i	0.747070	+	0.664745i	$0.231460\pi$
$542$	8.97782	−	22.8751i	0.385630	−	0.982570i
$543$		0			0
$544$	0.195236	+	2.60524i	0.00837067	+	0.111699i
$545$	0.413916	−	0.127676i	0.0177302	−	0.00546905i
$546$		0			0
$547$	−0.724131	−	0.671896i	−0.0309616	−	0.0287282i	0.664540	−	0.747252i	$-0.268627\pi$
$547$	−0.724131	−	0.671896i	−0.0309616	−	0.0287282i	−0.695502	+	0.718524i	$0.744818\pi$
$548$	−2.51650	+	1.21188i	−0.107499	+	0.0517690i
$549$		0			0
$550$	29.4752	+	20.0959i	1.25683	+	0.856890i
$551$	16.2385	−	20.3625i	0.691785	−	0.867470i
$552$		0			0
$553$	−14.4638	+	25.0521i	−0.615065	+	1.06532i
$554$	12.6508	+	32.2338i	0.537483	+	1.36948i
$555$		0			0
$556$	−16.8118	−	5.18576i	−0.712980	−	0.219925i
$557$	2.10042	−	9.20253i	0.0889976	−	0.389924i	−0.910736	−	0.412988i	$-0.864485\pi$
$557$	2.10042	−	9.20253i	0.0889976	−	0.389924i	0.999734	+	0.0230643i	$0.00734223\pi$
$558$		0			0
$559$	5.26013	−	6.52695i	0.222480	−	0.276061i
$560$	−6.70806			−0.283467
$561$		0			0
$562$	11.7519	+	3.62499i	0.495725	+	0.152911i
$563$	−24.8446	−	11.9645i	−1.04708	−	0.504245i	−0.170425	−	0.985371i	$-0.554514\pi$
$563$	−24.8446	−	11.9645i	−1.04708	−	0.504245i	−0.876652	+	0.481125i	$0.840228\pi$
$564$		0			0
$565$	−3.07776	+	5.33083i	−0.129482	+	0.224270i
$566$	25.8462	+	44.7670i	1.08640	+	1.88170i
$567$		0			0
$568$	12.0170	+	8.19308i	0.504224	+	0.343774i
$569$	−20.0473	+	3.02164i	−0.840425	+	0.126674i	−0.555127	−	0.831765i	$-0.687330\pi$
$569$	−20.0473	+	3.02164i	−0.840425	+	0.126674i	−0.285297	+	0.958439i	$0.592092\pi$
$570$		0			0
$571$	13.1590	+	12.2098i	0.550688	+	0.510964i	0.905712	−	0.423893i	$-0.139337\pi$
$571$	13.1590	+	12.2098i	0.550688	+	0.510964i	−0.355024	+	0.934857i	$0.615527\pi$
$572$	−4.80287	−	0.723917i	−0.200818	−	0.0302685i
$573$		0			0
$574$	2.14698	+	28.6495i	0.0896134	+	1.19581i
$575$	22.4218	+	28.1161i	0.935055	+	1.17252i
$576$		0			0
$577$	−0.766879	+	0.711560i	−0.0319256	+	0.0296226i	−0.695974	−	0.718067i	$-0.745027\pi$
$577$	−0.766879	+	0.711560i	−0.0319256	+	0.0296226i	0.664049	+	0.747689i	$0.268837\pi$
$578$	−23.3780	+	15.9389i	−0.972397	+	0.662969i
$579$		0			0
$580$	−0.256510	−	1.12384i	−0.0106510	−	0.0466650i
$581$	9.05140	+	39.6568i	0.375516	+	1.64524i
$582$		0			0
$583$	34.6448	−	23.6204i	1.43484	−	0.978257i
$584$	2.90043	−	2.69120i	0.120021	−	0.111363i
$585$		0			0
$586$	−27.1612	−	34.0591i	−1.12202	−	1.40697i
$587$	1.23653	+	16.5003i	0.0510370	+	0.681042i	0.962781	+	0.270283i	$0.0871172\pi$
$587$	1.23653	+	16.5003i	0.0510370	+	0.681042i	−0.911744	+	0.410759i	$0.865264\pi$
$588$		0			0
$589$	7.38099	+	1.11251i	0.304128	+	0.0458400i
$590$	2.24573	+	2.08373i	0.0924551	+	0.0857858i
$591$		0			0
$592$	21.6679	−	3.26592i	0.890547	−	0.134228i
$593$	8.32969	+	5.67909i	0.342059	+	0.233212i	0.722149	−	0.691737i	$-0.243154\pi$
$593$	8.32969	+	5.67909i	0.342059	+	0.233212i	−0.380090	+	0.924950i	$0.624107\pi$
$594$		0			0
$595$	0.378650	+	0.655841i	0.0155231	+	0.0268869i
$596$	−5.53923	+	9.59422i	−0.226896	+	0.392995i
$597$		0			0
$598$	−14.4794	−	6.97290i	−0.592105	−	0.285143i
$599$	−32.4927	−	10.0227i	−1.32761	−	0.409515i	−0.451782	−	0.892129i	$-0.649211\pi$
$599$	−32.4927	−	10.0227i	−1.32761	−	0.409515i	−0.875833	+	0.482614i	$0.839688\pi$
$600$		0			0
$601$	−27.2454			−1.11136			−0.555681	−	0.831396i	$-0.687542\pi$
$601$	−27.2454			−1.11136			−0.555681	+	0.831396i	$0.687542\pi$
$602$	−8.83526	+	37.8137i	−0.360098	+	1.54117i
$603$		0			0
$604$	−0.196087	+	0.859113i	−0.00797866	+	0.0349568i
$605$	−2.87199	−	0.885890i	−0.116763	−	0.0360166i
$606$		0			0
$607$	−8.72876	−	22.2405i	−0.354289	−	0.902715i	−0.991272	−	0.131836i	$-0.957913\pi$
$607$	−8.72876	−	22.2405i	−0.354289	−	0.902715i	0.636982	−	0.770879i	$-0.280183\pi$
$608$	−17.7132	+	30.6801i	−0.718364	+	1.24424i
$609$		0			0
$610$	2.20482	−	2.76476i	0.0892705	−	0.111942i
$611$	−4.61691	−	3.14776i	−0.186780	−	0.127345i
$612$		0			0
$613$	30.1578	−	14.5232i	1.21806	−	0.586588i	0.289291	−	0.957241i	$-0.406581\pi$
$613$	30.1578	−	14.5232i	1.21806	−	0.586588i	0.928771	+	0.370654i	$0.120866\pi$
$614$	−19.7051	−	18.2837i	−0.795233	−	0.737868i
$615$		0			0
$616$	−27.5688	+	8.50386i	−1.11078	+	0.342630i
$617$	1.17887	+	15.7309i	0.0474594	+	0.633302i	0.969323	+	0.245789i	$0.0790469\pi$
$617$	1.17887	+	15.7309i	0.0474594	+	0.633302i	−0.921864	+	0.387513i	$0.873334\pi$
$618$		0			0
$619$	7.08652	−	18.0562i	0.284831	−	0.725738i	−0.714819	−	0.699309i	$-0.753491\pi$
$619$	7.08652	−	18.0562i	0.284831	−	0.725738i	0.999651	−	0.0264292i	$-0.00841367\pi$
$620$	0.242182	−	0.224712i	0.00972628	−	0.00902467i
$621$		0			0
$622$	−3.42397	+	45.6897i	−0.137289	+	1.83199i
$623$	−2.11949	−	9.28610i	−0.0849156	−	0.372040i
$624$		0			0
$625$	1.70340	−	22.7303i	0.0681359	−	0.909210i
$626$	27.0075	−	18.4134i	1.07944	−	0.735947i
$627$		0			0
$628$	1.52504	−	3.88574i	0.0608557	−	0.155058i
$629$	−1.54240	−	1.93411i	−0.0614994	−	0.0771178i
$630$		0			0
$631$	−1.52150	+	0.469320i	−0.0605699	+	0.0186833i	−0.324892	−	0.945751i	$-0.605328\pi$
$631$	−1.52150	+	0.469320i	−0.0605699	+	0.0186833i	0.264322	+	0.964434i	$0.414852\pi$
$632$	−15.6119	−	2.35311i	−0.621007	−	0.0936017i
$633$		0			0
$634$	−19.6529	+	9.46434i	−0.780516	+	0.375877i
$635$	−1.28317	+	0.193406i	−0.0509209	+	0.00767510i
$636$		0			0
$637$	−4.13827	+	5.18922i	−0.163964	+	0.205604i
$638$	−12.5485	−	21.7347i	−0.496802	−	0.860486i
$639$		0			0
$640$	−1.80786	−	4.60636i	−0.0714620	−	0.182082i
$641$	−6.14244	−	2.95804i	−0.242612	−	0.116836i	0.308627	−	0.951183i	$-0.400130\pi$
$641$	−6.14244	−	2.95804i	−0.242612	−	0.116836i	−0.551239	+	0.834347i	$0.685845\pi$
$642$		0			0
$643$	−3.83478	+	16.8013i	−0.151229	+	0.662578i	0.841300	+	0.540569i	$0.181791\pi$
$643$	−3.83478	+	16.8013i	−0.151229	+	0.662578i	−0.992529	+	0.122009i	$0.961066\pi$
$644$	22.6817			0.893786
$645$		0			0
$646$	7.28288			0.286541
$647$	3.00033	−	13.1453i	0.117955	−	0.516795i	−0.881084	−	0.472961i	$-0.843185\pi$
$647$	3.00033	−	13.1453i	0.117955	−	0.516795i	0.999039	−	0.0438349i	$-0.0139575\pi$
$648$		0			0
$649$	18.3085	+	8.81691i	0.718671	+	0.346094i
$650$	3.84275	+	9.79116i	0.150725	+	0.384041i
$651$		0			0
$652$	4.16131	+	7.20760i	0.162970	+	0.282272i
$653$	23.9528	−	30.0358i	0.937344	−	1.17539i	−0.0469569	−	0.998897i	$-0.514952\pi$
$653$	23.9528	−	30.0358i	0.937344	−	1.17539i	0.984301	−	0.176496i	$-0.0564762\pi$
$654$		0			0
$655$	0.586210	−	0.0883570i	0.0229051	−	0.00345239i
$656$	−21.7884	+	10.4927i	−0.850693	+	0.409672i
$657$		0			0
$658$	25.5962	+	3.85800i	0.997842	+	0.150401i
$659$	6.80245	−	2.09828i	0.264986	−	0.0817373i	−0.159415	−	0.987212i	$-0.550961\pi$
$659$	6.80245	−	2.09828i	0.264986	−	0.0817373i	0.424401	+	0.905474i	$0.360485\pi$
$660$		0			0
$661$	13.9581	+	17.5029i	0.542908	+	0.680785i	0.975296	−	0.220903i	$-0.0709003\pi$
$661$	13.9581	+	17.5029i	0.542908	+	0.680785i	−0.432388	+	0.901688i	$0.642329\pi$
$662$	−1.57675	+	4.01750i	−0.0612822	+	0.156144i
$663$		0			0
$664$	−18.3430	+	12.5060i	−0.711846	+	0.485328i
$665$	−0.767406	+	10.2403i	−0.0297587	+	0.397103i
$666$		0			0
$667$	−5.62969	−	24.6653i	−0.217983	−	0.955044i
$668$	1.48209	−	19.7772i	0.0573439	−	0.765201i
$669$		0			0
$670$	6.28647	−	5.83299i	0.242867	−	0.225348i
$671$	8.56964	−	21.8351i	0.330827	−	0.842935i
$672$		0			0
$673$	0.148095	+	1.97619i	0.00570864	+	0.0761765i	0.999330	−	0.0365873i	$-0.0116487\pi$
$673$	0.148095	+	1.97619i	0.00570864	+	0.0761765i	−0.993622	+	0.112764i	$0.964030\pi$
$674$	1.19518	−	0.368663i	0.0460365	−	0.0142004i
$675$		0			0
$676$	7.30137	+	6.77468i	0.280822	+	0.260565i
$677$	−6.11443	+	2.94456i	−0.234997	+	0.113168i	−0.547677	−	0.836690i	$-0.684488\pi$
$677$	−6.11443	+	2.94456i	−0.234997	+	0.113168i	0.312680	+	0.949859i	$0.398773\pi$
$678$		0			0
$679$	1.41450	+	0.964388i	0.0542834	+	0.0370098i
$680$	−0.257701	+	0.323147i	−0.00988240	+	0.0123921i
$681$		0			0
$682$	3.59641	−	6.22916i	0.137713	−	0.238527i
$683$	−3.77933	−	9.62958i	−0.144612	−	0.368466i	0.840154	−	0.542347i	$-0.182464\pi$
$683$	−3.77933	−	9.62958i	−0.144612	−	0.368466i	−0.984767	+	0.173881i	$0.944369\pi$
$684$		0			0
$685$	−1.17382	−	0.362074i	−0.0448492	−	0.0138342i
$686$	−2.38241	+	10.4380i	−0.0909610	+	0.398526i
$687$		0			0
$688$	−32.3464	+	4.70570i	−1.23320	+	0.179403i
$689$	12.3630			0.470993
$690$		0			0
$691$	−10.6685	−	3.29080i	−0.405850	−	0.125188i	0.0851075	−	0.996372i	$-0.472877\pi$
$691$	−10.6685	−	3.29080i	−0.405850	−	0.125188i	−0.490957	+	0.871184i	$0.663353\pi$
$692$	7.34466	+	3.53700i	0.279202	+	0.134457i
$693$		0			0
$694$	−4.44549	+	7.69981i	−0.168748	+	0.292281i
$695$	−3.86875	−	6.70087i	−0.146750	−	0.254179i
$696$		0			0
$697$	2.25576	+	1.53795i	0.0854428	+	0.0582539i
$698$	−16.7265	+	2.52111i	−0.633106	+	0.0954254i
$699$		0			0
$700$	−10.8821	−	10.0972i	−0.411306	−	0.381637i
$701$	−45.9912	−	6.93206i	−1.73706	−	0.261820i	−0.797285	−	0.603603i	$-0.793731\pi$
$701$	−45.9912	−	6.93206i	−1.73706	−	0.261820i	−0.939779	+	0.341783i	$0.888969\pi$
$702$		0			0
$703$	−2.50683	−	33.4513i	−0.0945467	−	1.26164i
$704$	−5.66556	−	7.10438i	−0.213529	−	0.267757i
$705$		0			0
$706$	31.1443	−	28.8977i	1.17213	−	1.08758i
$707$	6.35350	−	4.33175i	0.238948	−	0.162912i
$708$		0			0
$709$	−1.61013	−	7.05446i	−0.0604699	−	0.264936i	0.935652	−	0.352925i	$-0.114813\pi$
$709$	−1.61013	−	7.05446i	−0.0604699	−	0.264936i	−0.996121	+	0.0879894i	$0.971956\pi$
$710$	−1.11005	−	4.86346i	−0.0416596	−	0.182523i
$711$		0			0
$712$	4.29522	−	2.92843i	0.160970	−	0.109748i
$713$	5.31525	−	4.93183i	0.199058	−	0.184699i
$714$		0			0
$715$	−1.33186	−	1.67010i	−0.0498087	−	0.0624582i
$716$	−0.473457	−	6.31784i	−0.0176939	−	0.236109i
$717$		0			0
$718$	23.0787	+	3.47855i	0.861289	+	0.129818i
$719$	−26.6874	−	24.7623i	−0.995274	−	0.923479i	0.00179446	−	0.999998i	$-0.499429\pi$
$719$	−26.6874	−	24.7623i	−0.995274	−	0.923479i	−0.997068	+	0.0765194i	$0.975619\pi$
$720$		0			0
$721$	−17.6708	+	2.66345i	−0.658095	+	0.0991919i
$722$	54.9720	+	37.4793i	2.04585	+	1.39483i
$723$		0			0
$724$	8.23734	+	14.2675i	0.306138	+	0.530247i
$725$	−8.27918	+	14.3400i	−0.307481	+	0.532573i
$726$		0			0
$727$	−38.1354	−	18.3650i	−1.41436	−	0.681121i	−0.438343	−	0.898808i	$-0.644435\pi$
$727$	−38.1354	−	18.3650i	−1.41436	−	0.681121i	−0.976019	+	0.217687i	$0.930149\pi$
$728$	−8.12850	−	2.50731i	−0.301262	−	0.0929271i
$729$		0			0
$730$	−1.35709			−0.0502281
$731$	2.28593	+	2.89686i	0.0845483	+	0.107144i
$732$		0			0
$733$	4.08534	−	17.8990i	0.150895	−	0.661116i	−0.841731	−	0.539898i	$-0.818463\pi$
$733$	4.08534	−	17.8990i	0.150895	−	0.661116i	0.992626	−	0.121218i	$-0.0386800\pi$
$734$	−44.5391	−	13.7385i	−1.64397	−	0.507097i
$735$		0			0
$736$	12.5725	+	32.0342i	0.463428	+	1.18080i
$737$	28.4422	−	49.2633i	1.04768	−	1.81464i
$738$		0			0
$739$	19.5007	−	24.4531i	0.717345	−	0.899522i	−0.280839	−	0.959755i	$-0.590613\pi$
$739$	19.5007	−	24.4531i	0.717345	−	0.899522i	0.998184	+	0.0602326i	$0.0191843\pi$
$740$	−1.22673	−	0.836372i	−0.0450956	−	0.0307456i
$741$		0			0
$742$	−51.5989	+	24.8487i	−1.89425	+	0.912225i
$743$	17.5715	+	16.3039i	0.644635	+	0.598134i	0.933213	−	0.359323i	$-0.116992\pi$
$743$	17.5715	+	16.3039i	0.644635	+	0.598134i	−0.288579	+	0.957456i	$0.593183\pi$
$744$		0			0
$745$	−4.65579	+	1.43612i	−0.170575	+	0.0526153i
$746$	1.99173	+	26.5778i	0.0729225	+	0.973084i
$747$		0			0
$748$	0.781156	−	1.99035i	0.0285619	−	0.0727745i
$749$	26.3000	−	24.4028i	0.960980	−	0.891659i
$750$		0			0
$751$	−3.81330	+	50.8850i	−0.139149	+	1.85682i	0.294391	+	0.955685i	$0.404883\pi$
$751$	−3.81330	+	50.8850i	−0.139149	+	1.85682i	−0.433540	+	0.901134i	$0.642736\pi$
$752$	4.84848	+	21.2426i	0.176806	+	0.774637i
$753$		0			0
$754$	0.552982	−	7.37903i	0.0201384	−	0.268728i
$755$	−0.320209	+	0.218315i	−0.0116536	+	0.00794528i
$756$		0			0
$757$	8.24045	−	20.9963i	0.299504	−	0.763125i	−0.699327	−	0.714802i	$-0.746517\pi$
$757$	8.24045	−	20.9963i	0.299504	−	0.763125i	0.998832	−	0.0483232i	$-0.0153878\pi$
$758$	−27.2106	−	34.1210i	−0.988333	−	1.23933i
$759$		0			0
$760$	−5.35566	+	1.65200i	−0.194270	+	0.0599244i
$761$	35.6862	+	5.37882i	1.29362	+	0.194982i	0.759546	−	0.650454i	$-0.225421\pi$
$761$	35.6862	+	5.37882i	1.29362	+	0.194982i	0.534076	+	0.845436i	$0.320659\pi$
$762$		0			0
$763$	−3.53572	+	1.70271i	−0.128002	+	0.0616423i
$764$	−6.09401	+	0.918524i	−0.220473	+	0.0332310i
$765$		0			0
$766$	19.0820	−	23.9280i	0.689460	−	0.864555i
$767$	2.99574	+	5.18878i	0.108170	+	0.187356i
$768$		0			0
$769$	−9.37295	−	23.8819i	−0.337997	−	0.861203i	−0.994292	−	0.106698i	$-0.965972\pi$
$769$	−9.37295	−	23.8819i	−0.337997	−	0.861203i	0.656294	−	0.754505i	$-0.272123\pi$
$770$	8.91550	+	4.29348i	0.321292	+	0.154726i
$771$		0			0
$772$	0.802762	−	3.51713i	0.0288921	−	0.126584i
$773$	30.1582			1.08472			0.542358	−	0.840148i	$-0.317532\pi$
$773$	30.1582			1.08472			0.542358	+	0.840148i	$0.317532\pi$
$774$		0			0
$775$	−4.74562			−0.170468
$776$	−0.207915	+	0.910936i	−0.00746372	+	0.0327007i
$777$		0			0
$778$	−38.6599	−	18.6176i	−1.38603	−	0.667475i
$779$	13.5253	+	34.4619i	0.484594	+	1.23472i
$780$		0			0
$781$	−16.5449	−	28.6566i	−0.592023	−	1.02541i
$782$	4.41092	−	5.53112i	0.157734	−	0.197792i
$783$		0			0
$784$	25.5917	−	3.85733i	0.913990	−	0.137762i
$785$	1.65403	−	0.796537i	0.0590347	−	0.0284296i
$786$		0			0
$787$	−20.5239	−	3.09348i	−0.731598	−	0.110271i	−0.227330	−	0.973818i	$-0.573000\pi$
$787$	−20.5239	−	3.09348i	−0.731598	−	0.110271i	−0.504268	+	0.863547i	$0.668238\pi$
$788$	−1.51072	+	0.465995i	−0.0538171	+	0.0166004i
$789$		0			0
$790$	3.37632	+	4.23377i	0.120124	+	0.150631i
$791$	20.3743	−	51.9128i	0.724426	−	1.84581i
$792$		0			0
$793$	5.71428	−	3.89593i	0.202920	−	0.138349i
$794$	0.334993	−	4.47018i	0.0118885	−	0.158641i
$795$		0			0
$796$	4.43976	+	19.4519i	0.157363	+	0.689453i
$797$	−1.25760	+	16.7815i	−0.0445463	+	0.594430i	0.929609	+	0.368549i	$0.120145\pi$
$797$	−1.25760	+	16.7815i	−0.0445463	+	0.594430i	−0.974155	+	0.225881i	$0.927474\pi$
$798$		0			0
$799$	1.80319	−	1.67311i	0.0637922	−	0.0591905i
$800$	8.22857	−	20.9661i	0.290924	−	0.741262i
$801$		0			0
$802$	−3.72732	−	49.7376i	−0.131616	−	1.75630i
$803$	−8.60187	+	2.65333i	−0.303554	+	0.0936339i
$804$		0			0
$805$	7.31242	+	6.78494i	0.257729	+	0.239138i
$806$	1.91073	−	0.920161i	0.0673027	−	0.0324113i
$807$		0			0
$808$	3.46763	+	2.36419i	0.121991	+	0.0831719i
$809$	−21.2357	+	26.6287i	−0.746608	+	0.936217i	−0.999511	−	0.0312750i	$-0.990043\pi$
$809$	−21.2357	+	26.6287i	−0.746608	+	0.936217i	0.252903	+	0.967492i	$0.418615\pi$
$810$		0			0
$811$	−6.69823	+	11.6017i	−0.235207	+	0.407390i	−0.959333	−	0.282278i	$-0.908910\pi$
$811$	−6.69823	+	11.6017i	−0.235207	+	0.407390i	0.724126	+	0.689668i	$0.242243\pi$
$812$	3.81549	+	9.72171i	0.133897	+	0.341165i
$813$		0			0
$814$	−30.8886	−	9.52788i	−1.08265	−	0.333952i
$815$	−0.814481	+	3.56848i	−0.0285300	+	0.124998i
$816$		0			0
$817$	3.48313	+	49.9174i	0.121859	+	1.74639i
$818$	−0.643023			−0.0224828
$819$		0			0
$820$	1.56577	+	0.482975i	0.0546790	+	0.0168662i
$821$	11.8336	+	5.69878i	0.412997	+	0.198889i	0.628832	−	0.777541i	$-0.283533\pi$
$821$	11.8336	+	5.69878i	0.412997	+	0.198889i	−0.215836	+	0.976430i	$0.569248\pi$
$822$		0			0
$823$	−9.61010	+	16.6452i	−0.334987	+	0.580215i	−0.983482	−	0.181004i	$-0.942065\pi$
$823$	−9.61010	+	16.6452i	−0.334987	+	0.580215i	0.648495	+	0.761219i	$0.275399\pi$
$824$	−4.87667	−	8.44664i	−0.169887	−	0.294253i
$825$		0			0
$826$	−22.9323	−	15.6350i	−0.797916	−	0.544010i
$827$	−32.5196	+	4.90154i	−1.13082	+	0.170443i	−0.687682	−	0.726012i	$-0.741372\pi$
$827$	−32.5196	+	4.90154i	−1.13082	+	0.170443i	−0.443135	+	0.896455i	$0.646134\pi$
$828$		0			0
$829$	8.73426	+	8.10421i	0.303353	+	0.281471i	0.817130	−	0.576453i	$-0.195564\pi$
$829$	8.73426	+	8.10421i	0.303353	+	0.281471i	−0.513777	+	0.857924i	$0.671754\pi$
$830$	7.52952	+	1.13489i	0.261354	+	0.0393927i
$831$		0			0
$832$	−0.200217	−	2.67171i	−0.00694127	−	0.0926248i
$833$	−1.82171	−	2.28435i	−0.0631184	−	0.0791480i
$834$		0			0
$835$	6.39388	−	5.93266i	0.221269	−	0.205308i
$836$	23.9556	−	16.3326i	0.828521	−	0.564876i
$837$		0			0
$838$	6.24126	+	27.3448i	0.215601	+	0.944609i
$839$	−11.8997	−	52.1359i	−0.410822	−	1.79993i	−0.580308	−	0.814397i	$-0.697068\pi$
$839$	−11.8997	−	52.1359i	−0.410822	−	1.79993i	0.169486	−	0.985533i	$-0.445789\pi$
$840$		0			0
$841$	−14.3361	+	9.77416i	−0.494347	+	0.337040i
$842$	11.3990	−	10.5767i	0.392834	−	0.364497i
$843$		0			0
$844$	−4.30903	−	5.40336i	−0.148323	−	0.185991i
$845$	0.327352	+	4.36821i	0.0112613	+	0.150271i
$846$		0			0
$847$	26.9253	+	4.05833i	0.925163	+	0.139446i
$848$	−35.3384	−	32.7893i	−1.21353	−	1.12599i
$849$		0			0
$850$	−4.57852	+	0.690101i	−0.157042	+	0.0236703i
$851$	−26.9235	−	18.3561i	−0.922924	−	0.629239i
$852$		0			0
$853$	−14.4537	−	25.0346i	−0.494886	−	0.857168i	0.505096	−	0.863063i	$-0.331457\pi$
$853$	−14.4537	−	25.0346i	−0.494886	−	0.857168i	−0.999983	+	0.00589491i	$0.998124\pi$
$854$	−16.0189	+	27.7456i	−0.548156	+	0.949434i
$855$		0			0
$856$	17.6421	+	8.49597i	0.602993	+	0.290386i
$857$	−36.3470	−	11.2116i	−1.24159	−	0.382980i	−0.396714	−	0.917942i	$-0.629849\pi$
$857$	−36.3470	−	11.2116i	−1.24159	−	0.382980i	−0.844876	+	0.534963i	$0.820326\pi$
$858$		0			0
$859$	38.9400			1.32861			0.664307	−	0.747460i	$-0.268727\pi$
$859$	38.9400			1.32861			0.664307	+	0.747460i	$0.268727\pi$
$860$	1.82347	+	1.25699i	0.0621799	+	0.0428629i
$861$		0			0
$862$	3.59545	−	15.7527i	0.122462	−	0.536539i
$863$	45.6356	+	14.0767i	1.55345	+	0.479177i	0.948418	−	0.317022i	$-0.102683\pi$
$863$	45.6356	+	14.0767i	1.55345	+	0.479177i	0.605035	+	0.796199i	$0.293159\pi$
$864$		0			0
$865$	1.30982	+	3.33736i	0.0445351	+	0.113474i
$866$	24.4376	−	42.3272i	0.830425	−	1.43834i
$867$		0			0
$868$	−1.86619	+	2.34013i	−0.0633427	+	0.0794292i
$869$	29.6784	+	20.2344i	1.00677	+	0.686404i
$870$		0			0
$871$	15.1110	−	7.27709i	0.512018	−	0.246575i
$872$	−1.57008	−	1.45682i	−0.0531696	−	0.0493342i
$873$		0			0
$874$	91.6696	−	28.2763i	3.10077	−	0.956461i
$875$	−0.990726	−	13.2203i	−0.0334926	−	0.446928i
$876$		0			0
$877$	−12.6609	+	32.2594i	−0.427527	+	1.08932i	0.541134	+	0.840936i	$0.317995\pi$
$877$	−12.6609	+	32.2594i	−0.427527	+	1.08932i	−0.968661	+	0.248385i	$0.920100\pi$
$878$	8.36788	−	7.76426i	0.282402	−	0.262031i
$879$		0			0
$880$	−0.622463	+	8.30619i	−0.0209832	+	0.280002i
$881$	−11.6579	−	51.0764i	−0.392763	−	1.72081i	−0.654845	−	0.755763i	$-0.727266\pi$
$881$	−11.6579	−	51.0764i	−0.392763	−	1.72081i	0.262081	−	0.965046i	$-0.415591\pi$
$882$		0			0
$883$	−2.16026	+	28.8267i	−0.0726985	+	0.970094i	0.834940	+	0.550341i	$0.185502\pi$
$883$	−2.16026	+	28.8267i	−0.0726985	+	0.970094i	−0.907638	+	0.419753i	$0.862117\pi$
$884$	0.520879	−	0.355129i	0.0175190	−	0.0119443i
$885$		0			0
$886$	−2.05936	+	5.24715i	−0.0691854	+	0.176282i
$887$	28.3829	+	35.5910i	0.953004	+	1.19503i	0.980721	+	0.195414i	$0.0626049\pi$
$887$	28.3829	+	35.5910i	0.953004	+	1.19503i	−0.0277167	+	0.999616i	$0.508824\pi$
$888$		0			0
$889$	11.2343	−	3.46531i	0.376785	−	0.116223i
$890$	−1.76313	−	0.265748i	−0.0591001	−	0.00890791i
$891$		0			0
$892$	−6.79837	+	3.27392i	−0.227626	+	0.109619i
$893$	32.9830	−	4.97138i	1.10373	−	0.166361i
$894$		0			0
$895$	1.73726	−	2.17845i	0.0580701	−	0.0728176i
$896$	22.4159	+	38.8255i	0.748862	+	1.29707i
$897$		0			0
$898$	2.65750	+	6.77120i	0.0886819	+	0.225958i
$899$	3.00798	+	1.44856i	0.100322	+	0.0483123i
$900$		0			0
$901$	−1.21103	+	5.30587i	−0.0403452	+	0.176764i
$902$	35.6742			1.18782
$903$		0			0
$904$	30.4371			1.01232
$905$	−1.61227	+	7.06382i	−0.0535937	+	0.234809i
$906$		0			0
$907$	−19.7496	−	9.51092i	−0.655775	−	0.315805i	0.0762434	−	0.997089i	$-0.475707\pi$
$907$	−19.7496	−	9.51092i	−0.655775	−	0.315805i	−0.732019	+	0.681284i	$0.761422\pi$
$908$	2.60859	+	6.64659i	0.0865693	+	0.220575i
$909$		0			0
$910$	1.45881	+	2.52673i	0.0483590	+	0.0837602i
$911$	28.0122	−	35.1262i	0.928087	−	1.16378i	−0.0581272	−	0.998309i	$-0.518513\pi$
$911$	28.0122	−	35.1262i	0.928087	−	1.16378i	0.986214	−	0.165475i	$-0.0529157\pi$
$912$		0			0
$913$	49.9446	−	7.52793i	1.65292	−	0.249138i
$914$	3.38177	−	1.62857i	0.111859	−	0.0538684i
$915$		0			0
$916$	21.4707	+	3.23619i	0.709413	+	0.106927i
$917$	−5.13233	+	1.58311i	−0.169484	+	0.0522790i
$918$		0			0
$919$	−21.8856	−	27.4436i	−0.721938	−	0.905282i	0.276508	−	0.961012i	$-0.410823\pi$
$919$	−21.8856	−	27.4436i	−0.721938	−	0.905282i	−0.998446	+	0.0557299i	$0.982251\pi$
$920$	−1.98904	+	5.06800i	−0.0655768	+	0.167087i
$921$		0			0
$922$	−21.3578	+	14.5615i	−0.703383	+	0.479558i
$923$	0.729090	−	9.72903i	0.0239983	−	0.320235i
$924$		0			0
$925$	4.74569	+	20.7922i	0.156037	+	0.683644i
$926$	−1.36249	+	18.1812i	−0.0447743	+	0.597472i
$927$		0			0
$928$	−11.6154	+	10.7775i	−0.381293	+	0.353788i
$929$	−3.19040	+	8.12900i	−0.104674	+	0.266704i	−0.973609	−	0.228221i	$-0.926709\pi$
$929$	−3.19040	+	8.12900i	−0.104674	+	0.266704i	0.868936	+	0.494925i	$0.164804\pi$
$930$		0			0
$931$	−2.96078	−	39.5089i	−0.0970357	−	1.29485i
$932$	−7.21988	+	2.22704i	−0.236495	+	0.0729491i
$933$		0			0
$934$	−18.4345	−	17.1047i	−0.603196	−	0.559684i
$935$	0.847226	−	0.408002i	0.0277072	−	0.0133431i
$936$		0			0
$937$	−23.8766	−	16.2788i	−0.780015	−	0.531806i	0.106606	−	0.994301i	$-0.466002\pi$
$937$	−23.8766	−	16.2788i	−0.780015	−	0.531806i	−0.886621	+	0.462496i	$0.846954\pi$
$938$	−48.4418	+	60.7441i	−1.58168	+	1.98337i
$939$		0			0
$940$	0.738165	−	1.27854i	0.0240763	−	0.0417013i
$941$	1.16024	+	2.95624i	0.0378226	+	0.0963705i	0.948537	−	0.316666i	$-0.102563\pi$
$941$	1.16024	+	2.95624i	0.0378226	+	0.0963705i	−0.910714	+	0.413037i	$0.864468\pi$
$942$		0			0
$943$	34.3644	+	10.6000i	1.11906	+	0.345184i
$944$	5.19869	−	22.7770i	0.169203	−	0.741327i
$945$		0			0
$946$	46.0026	+	14.4490i	1.49567	+	0.469779i
$947$	−47.5288			−1.54448			−0.772239	−	0.635332i	$-0.780863\pi$
$947$	−47.5288			−1.54448			−0.772239	+	0.635332i	$0.780863\pi$
$948$		0			0
$949$	−2.53621	−	0.782316i	−0.0823288	−	0.0253951i
$950$	−56.5685	−	27.2420i	−1.83532	−	0.883846i
$951$		0			0
$952$	1.87230	−	3.24293i	0.0606817	−	0.105104i
$953$	20.3266	+	35.2067i	0.658443	+	1.14046i	0.981019	+	0.193913i	$0.0621178\pi$
$953$	20.3266	+	35.2067i	0.658443	+	1.14046i	−0.322576	+	0.946544i	$0.604549\pi$
$954$		0			0
$955$	−2.23943	−	1.52681i	−0.0724661	−	0.0494065i
$956$	2.91693	−	0.439657i	0.0943403	−	0.0142195i
$957$		0			0
$958$	−42.6659	−	39.5881i	−1.37847	−	1.27903i
$959$	11.0047	+	1.65869i	0.355360	+	0.0535619i
$960$		0			0
$961$	−2.24513	−	29.9592i	−0.0724235	−	0.966424i
$962$	−5.94232	−	7.45143i	−0.191588	−	0.240244i
$963$		0			0
$964$	17.3551	−	16.1032i	0.558972	−	0.518650i
$965$	1.31091	−	0.893761i	0.0421996	−	0.0287712i
$966$		0			0
$967$	1.68074	+	7.36380i	0.0540490	+	0.236804i	0.994736	−	0.102472i	$-0.0326751\pi$
$967$	1.68074	+	7.36380i	0.0540490	+	0.236804i	−0.940687	+	0.339276i	$0.889818\pi$
$968$	3.30695	+	14.4887i	0.106289	+	0.465684i
$969$		0			0
$970$	0.264791	−	0.180531i	0.00850191	−	0.00579650i
$971$	−15.3469	+	14.2398i	−0.492505	+	0.456978i	−0.886899	−	0.461964i	$-0.847145\pi$
$971$	−15.3469	+	14.2398i	−0.492505	+	0.456978i	0.394394	+	0.918942i	$0.370955\pi$
$972$		0			0
$973$	43.7068	+	54.8066i	1.40118	+	1.75702i
$974$	−0.824064	−	10.9964i	−0.0264047	−	0.352346i
$975$		0			0
$976$	−26.6665	−	4.01933i	−0.853575	−	0.128656i
$977$	17.9851	+	16.6877i	0.575395	+	0.533888i	0.913298	−	0.407293i	$-0.133527\pi$
$977$	17.9851	+	16.6877i	0.575395	+	0.533888i	−0.337903	+	0.941181i	$0.609718\pi$
$978$		0			0
$979$	−11.6951	+	1.76275i	−0.373777	+	0.0563378i
$980$	−1.44888	−	0.987828i	−0.0462827	−	0.0315550i
$981$		0			0
$982$	−6.91046	−	11.9693i	−0.220521	−	0.381954i
$983$	0.981609	−	1.70020i	0.0313085	−	0.0542279i	−0.849947	−	0.526869i	$-0.823366\pi$
$983$	0.981609	−	1.70020i	0.0313085	−	0.0542279i	0.881255	+	0.472641i	$0.156699\pi$
$984$		0			0
$985$	−0.626440	−	0.301678i	−0.0199600	−	0.00961225i
$986$	3.11271	+	0.960145i	0.0991290	+	0.0305772i
$987$		0			0
$988$	8.54856			0.271966
$989$	40.0203	+	27.5875i	1.27257	+	0.877230i
$990$		0			0
$991$	−3.67174	+	16.0869i	−0.116637	+	0.511019i	0.882532	+	0.470252i	$0.155837\pi$
$991$	−3.67174	+	16.0869i	−0.116637	+	0.511019i	−0.999169	+	0.0407664i	$0.987020\pi$
$992$	−4.33947	−	1.33855i	−0.137778	−	0.0424990i
$993$		0			0
$994$	16.5117	+	42.0710i	0.523718	+	1.33441i
$995$	−4.38741	+	7.59922i	−0.139090	+	0.240912i
$996$		0			0
$997$	−20.7198	+	25.9819i	−0.656204	+	0.822854i	−0.992924	−	0.118751i	$-0.962111\pi$
$997$	−20.7198	+	25.9819i	−0.656204	+	0.822854i	0.336720	+	0.941605i	$0.390682\pi$
$998$	11.0607	+	7.54104i	0.350120	+	0.238708i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.253.1		36
3.2	odd	2		43.2.g.a.38.3	yes	36
12.11	even	2		688.2.bg.c.81.3		36
43.17	even	21	inner	387.2.y.c.361.1		36
129.17	odd	42		43.2.g.a.17.3	✓	36
129.62	even	42		1849.2.a.o.1.13		18
129.110	odd	42		1849.2.a.n.1.6		18
516.275	even	42		688.2.bg.c.17.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.17.3	✓	36	129.17	odd	42
43.2.g.a.38.3	yes	36	3.2	odd	2
387.2.y.c.253.1		36	1.1	even	1	trivial
387.2.y.c.361.1		36	43.17	even	21	inner
688.2.bg.c.17.3		36	516.275	even	42
688.2.bg.c.81.3		36	12.11	even	2
1849.2.a.n.1.6		18	129.110	odd	42
1849.2.a.o.1.13		18	129.62	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.377390 + 1.65345i) q^{2} +(-0.789549 - 0.380227i) q^{4} +(-0.140805 - 0.358765i) q^{5} +(1.74586 + 3.02391i) q^{7} +(-1.18819 + 1.48995i) q^{8} +O(q^{10})\)	\(q+(-0.377390 + 1.65345i) q^{2} +(-0.789549 - 0.380227i) q^{4} +(-0.140805 - 0.358765i) q^{5} +(1.74586 + 3.02391i) q^{7} +(-1.18819 + 1.48995i) q^{8} +(0.646339 - 0.0974200i) q^{10} +(3.90633 - 1.88119i) q^{11} +(1.26408 + 0.190529i) q^{13} +(-5.65876 + 1.74550i) q^{14} +(-3.10791 - 3.89720i) q^{16} +(-0.205594 + 0.523844i) q^{17} +(-6.30490 + 4.29861i) q^{19} +(-0.0252397 + 0.336800i) q^{20} +(1.63625 + 7.16888i) q^{22} +(-0.553943 + 7.39185i) q^{23} +(3.55637 - 3.29983i) q^{25} +(-0.792080 + 2.01819i) q^{26} +(-0.228667 - 3.05134i) q^{28} +(-3.26143 + 1.00602i) q^{29} +(-0.717059 - 0.665333i) q^{31} +(4.18276 - 2.01431i) q^{32} +(-0.788563 - 0.537633i) q^{34} +(0.839048 - 1.05213i) q^{35} +(-2.19799 + 3.80703i) q^{37} +(-4.72814 - 12.0471i) q^{38} +(0.701843 + 0.216490i) q^{40} +(1.07956 - 4.72986i) q^{41} +(3.30784 - 5.66200i) q^{43} -3.79952 q^{44} +(-12.0130 - 3.70553i) q^{46} +(-3.93826 - 1.89657i) q^{47} +(-2.59602 + 4.49644i) q^{49} +(4.11398 + 7.12562i) q^{50} +(-0.925605 - 0.631067i) q^{52} +(9.56301 - 1.44139i) q^{53} +(-1.22493 - 1.13657i) q^{55} +(-6.57987 - 0.991756i) q^{56} +(-0.432573 - 5.77229i) q^{58} +(2.92222 + 3.66435i) q^{59} +(3.96588 - 3.67980i) q^{61} +(1.37071 - 0.934533i) q^{62} +(-0.466364 - 2.04327i) q^{64} +(-0.109633 - 0.480333i) q^{65} +(10.8402 - 7.39075i) q^{67} +(0.361505 - 0.335428i) q^{68} +(1.42300 + 1.78439i) q^{70} +(-0.570335 - 7.61059i) q^{71} +(-2.05301 - 0.309442i) q^{73} +(-5.46525 - 5.07101i) q^{74} +(6.61247 - 0.996670i) q^{76} +(12.5084 + 8.52811i) q^{77} +(4.14234 + 7.17474i) q^{79} +(-0.960569 + 1.66375i) q^{80} +(7.41318 + 3.57000i) q^{82} +(11.1319 + 3.43375i) q^{83} +0.216885 q^{85} +(8.11351 + 7.60614i) q^{86} +(-1.83860 + 8.05544i) q^{88} +(-2.60667 - 0.804052i) q^{89} +(1.63075 + 4.15509i) q^{91} +(3.24794 - 5.62560i) q^{92} +(4.62215 - 5.79599i) q^{94} +(2.42995 + 1.65671i) q^{95} +(0.441741 - 0.212731i) q^{97} +(-6.45494 - 5.98931i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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