LMFDB - Embedded newform 378.2.u.e.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	378.85
Dual form			378.2.u.e.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-1.62983 - 0.586228i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.184482 - 1.04625i) q^{5} +(-1.33103 - 1.10831i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.31267 + 1.91090i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-1.62983 - 0.586228i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.184482 - 1.04625i) q^{5} +(-1.33103 - 1.10831i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.31267 + 1.91090i) q^{9} +(0.531195 - 0.920056i) q^{10} +(-0.543294 - 3.08117i) q^{11} +(-0.871700 - 1.49671i) q^{12} +(2.26907 - 0.825875i) q^{13} +(0.939693 - 0.342020i) q^{14} +(-0.914015 + 1.59706i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.26347 - 5.65249i) q^{17} +(1.51963 + 2.58664i) q^{18} +(-0.751074 - 1.30090i) q^{19} +(0.813838 - 0.682891i) q^{20} +(-1.62534 + 0.598556i) q^{21} +(0.543294 - 3.08117i) q^{22} +(2.03055 + 1.70383i) q^{23} +(-0.307225 - 1.70459i) q^{24} +(3.63786 + 1.32407i) q^{25} +2.41470 q^{26} +(-2.64903 - 4.47019i) q^{27} +1.00000 q^{28} +(-0.635950 - 0.231467i) q^{29} +(-1.40512 + 1.18813i) q^{30} +(-1.62387 - 1.36259i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.920795 + 5.34027i) q^{33} +(4.99993 - 4.19544i) q^{34} +(-0.531195 - 0.920056i) q^{35} +(0.543307 + 2.95039i) q^{36} +(-2.73500 + 4.73716i) q^{37} +(-0.260845 - 1.47933i) q^{38} +(-4.18235 + 0.0158389i) q^{39} +(0.998320 - 0.363359i) q^{40} +(1.25302 - 0.456064i) q^{41} +(-1.73204 + 0.00655936i) q^{42} +(1.48811 + 8.43951i) q^{43} +(1.56435 - 2.70954i) q^{44} +(2.42593 - 2.06711i) q^{45} +(1.32535 + 2.29557i) q^{46} +(-6.38690 + 5.35924i) q^{47} +(0.294306 - 1.70686i) q^{48} +(0.173648 - 0.984808i) q^{49} +(2.96561 + 2.48844i) q^{50} +(-8.63254 + 7.29945i) q^{51} +(2.26907 + 0.825875i) q^{52} -2.45812 q^{53} +(-0.960380 - 5.10663i) q^{54} -3.32390 q^{55} +(0.939693 + 0.342020i) q^{56} +(0.461498 + 2.56054i) q^{57} +(-0.518432 - 0.435016i) q^{58} +(1.42126 - 8.06034i) q^{59} +(-1.72674 + 0.635899i) q^{60} +(-7.39042 + 6.20130i) q^{61} +(-1.05991 - 1.83581i) q^{62} +(2.99991 - 0.0227221i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.445468 - 2.52637i) q^{65} +(-2.69175 + 4.70328i) q^{66} +(-8.57615 + 3.12146i) q^{67} +(6.13332 - 2.23234i) q^{68} +(-2.31061 - 3.96732i) q^{69} +(-0.184482 - 1.04625i) q^{70} +(3.25701 - 5.64130i) q^{71} +(-0.498553 + 2.95828i) q^{72} +(2.37064 + 4.10606i) q^{73} +(-4.19026 + 3.51605i) q^{74} +(-5.15287 - 4.29062i) q^{75} +(0.260845 - 1.47933i) q^{76} +(-2.39673 - 2.01109i) q^{77} +(-3.93554 - 1.41556i) q^{78} +(5.08023 + 1.84905i) q^{79} +1.06239 q^{80} +(1.69691 + 8.83858i) q^{81} +1.33344 q^{82} +(-14.4780 - 5.26957i) q^{83} +(-1.62983 - 0.586228i) q^{84} +(-5.31187 - 4.45719i) q^{85} +(-1.48811 + 8.43951i) q^{86} +(0.900797 + 0.750063i) q^{87} +(2.39673 - 2.01109i) q^{88} +(7.63422 + 13.2229i) q^{89} +(2.98662 - 1.11273i) q^{90} +(1.20735 - 2.09119i) q^{91} +(0.460288 + 2.61042i) q^{92} +(1.84784 + 3.17274i) q^{93} +(-7.83469 + 2.85159i) q^{94} +(-1.49962 + 0.545819i) q^{95} +(0.860339 - 1.50327i) q^{96} +(2.85268 + 16.1784i) q^{97} +(0.500000 - 0.866025i) q^{98} +(4.63136 - 8.16392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−1.62983	−	0.586228i	−0.940981	−	0.338459i
$3$	−1.62983	−	0.586228i	−0.940981	−	0.338459i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.184482	−	1.04625i	0.0825029	−	0.467897i	−0.915365	−	0.402626i	$-0.868098\pi$
$5$	0.184482	−	1.04625i	0.0825029	−	0.467897i	0.997868	−	0.0652713i	$-0.0207913\pi$
$6$	−1.33103	−	1.10831i	−0.543393	−	0.452465i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.31267	+	1.91090i	0.770891	+	0.636967i
$10$	0.531195	−	0.920056i	0.167979	−	0.290947i
$11$	−0.543294	−	3.08117i	−0.163809	−	0.929008i	−0.950284	−	0.311386i	$-0.899207\pi$
$11$	−0.543294	−	3.08117i	−0.163809	−	0.929008i	0.786474	−	0.617623i	$-0.211904\pi$
$12$	−0.871700	−	1.49671i	−0.251638	−	0.432063i
$13$	2.26907	−	0.825875i	0.629327	−	0.229056i	−0.00761118	−	0.999971i	$-0.502423\pi$
$13$	2.26907	−	0.825875i	0.629327	−	0.229056i	0.636938	+	0.770915i	$0.280201\pi$
$14$	0.939693	−	0.342020i	0.251143	−	0.0914087i
$15$	−0.914015	+	1.59706i	−0.235998	+	0.412358i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	3.26347	−	5.65249i	0.791508	−	1.37093i	−0.133526	−	0.991045i	$-0.542630\pi$
$17$	3.26347	−	5.65249i	0.791508	−	1.37093i	0.925033	−	0.379886i	$-0.124037\pi$
$18$	1.51963	+	2.58664i	0.358181	+	0.609677i
$19$	−0.751074	−	1.30090i	−0.172308	−	0.298447i	0.766918	−	0.641745i	$-0.221789\pi$
$19$	−0.751074	−	1.30090i	−0.172308	−	0.298447i	−0.939226	+	0.343298i	$0.888456\pi$
$20$	0.813838	−	0.682891i	0.181980	−	0.152699i
$21$	−1.62534	+	0.598556i	−0.354678	+	0.130616i
$22$	0.543294	−	3.08117i	0.115831	−	0.656908i
$23$	2.03055	+	1.70383i	0.423399	+	0.355274i	0.829454	−	0.558575i	$-0.188652\pi$
$23$	2.03055	+	1.70383i	0.423399	+	0.355274i	−0.406056	+	0.913848i	$0.633096\pi$
$24$	−0.307225	−	1.70459i	−0.0627120	−	0.347947i
$25$	3.63786	+	1.32407i	0.727572	+	0.264814i
$26$	2.41470			0.473561
$27$	−2.64903	−	4.47019i	−0.509807	−	0.860289i
$28$	1.00000			0.188982
$29$	−0.635950	−	0.231467i	−0.118093	−	0.0429824i	0.282298	−	0.959327i	$-0.408903\pi$
$29$	−0.635950	−	0.231467i	−0.118093	−	0.0429824i	−0.400391	+	0.916344i	$0.631126\pi$
$30$	−1.40512	+	1.18813i	−0.256538	+	0.216922i
$31$	−1.62387	−	1.36259i	−0.291655	−	0.244728i	0.485206	−	0.874400i	$-0.338745\pi$
$31$	−1.62387	−	1.36259i	−0.291655	−	0.244728i	−0.776861	+	0.629672i	$0.783189\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−0.920795	+	5.34027i	−0.160290	+	0.929622i
$34$	4.99993	−	4.19544i	0.857480	−	0.719511i
$35$	−0.531195	−	0.920056i	−0.0897883	−	0.155518i
$36$	0.543307	+	2.95039i	0.0905511	+	0.491732i
$37$	−2.73500	+	4.73716i	−0.449631	+	0.778784i	−0.998362	−	0.0572151i	$-0.981778\pi$
$37$	−2.73500	+	4.73716i	−0.449631	+	0.778784i	0.548731	+	0.835999i	$0.315111\pi$
$38$	−0.260845	−	1.47933i	−0.0423147	−	0.239979i
$39$	−4.18235	+	0.0158389i	−0.669711	+	0.00253625i
$40$	0.998320	−	0.363359i	0.157848	−	0.0574520i
$41$	1.25302	−	0.456064i	0.195690	−	0.0712252i	−0.242316	−	0.970197i	$-0.577907\pi$
$41$	1.25302	−	0.456064i	0.195690	−	0.0712252i	0.438006	+	0.898972i	$0.355685\pi$
$42$	−1.73204	+	0.00655936i	−0.267259	+	0.00101213i
$43$	1.48811	+	8.43951i	0.226935	+	1.28701i	0.858951	+	0.512058i	$0.171117\pi$
$43$	1.48811	+	8.43951i	0.226935	+	1.28701i	−0.632016	+	0.774956i	$0.717772\pi$
$44$	1.56435	−	2.70954i	0.235835	−	0.408478i
$45$	2.42593	−	2.06711i	0.361636	−	0.308146i
$46$	1.32535	+	2.29557i	0.195412	+	0.338463i
$47$	−6.38690	+	5.35924i	−0.931625	+	0.781726i	−0.976108	−	0.217284i	$-0.930280\pi$
$47$	−6.38690	+	5.35924i	−0.931625	+	0.781726i	0.0444836	+	0.999010i	$0.485836\pi$
$48$	0.294306	−	1.70686i	0.0424794	−	0.246365i
$49$	0.173648	−	0.984808i	0.0248069	−	0.140687i
$50$	2.96561	+	2.48844i	0.419401	+	0.351919i
$51$	−8.63254	+	7.29945i	−1.20880	+	1.02213i
$52$	2.26907	+	0.825875i	0.314664	+	0.114528i
$53$	−2.45812			−0.337648			−0.168824	−	0.985646i	$-0.553997\pi$
$53$	−2.45812			−0.337648			−0.168824	+	0.985646i	$0.553997\pi$
$54$	−0.960380	−	5.10663i	−0.130691	−	0.694924i
$55$	−3.32390			−0.448195
$56$	0.939693	+	0.342020i	0.125572	+	0.0457044i
$57$	0.461498	+	2.56054i	0.0611268	+	0.339152i
$58$	−0.518432	−	0.435016i	−0.0680734	−	0.0571204i
$59$	1.42126	−	8.06034i	0.185032	−	1.04937i	−0.740883	−	0.671634i	$-0.765593\pi$
$59$	1.42126	−	8.06034i	0.185032	−	1.04937i	0.925915	−	0.377733i	$-0.123296\pi$
$60$	−1.72674	+	0.635899i	−0.222922	+	0.0820943i
$61$	−7.39042	+	6.20130i	−0.946246	+	0.793995i	−0.978661	−	0.205480i	$-0.934125\pi$
$61$	−7.39042	+	6.20130i	−0.946246	+	0.793995i	0.0324151	+	0.999474i	$0.489680\pi$
$62$	−1.05991	−	1.83581i	−0.134608	−	0.233148i
$63$	2.99991	−	0.0227221i	0.377954	−	0.00286272i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.445468	−	2.52637i	−0.0552535	−	0.313358i
$66$	−2.69175	+	4.70328i	−0.331331	+	0.578934i
$67$	−8.57615	+	3.12146i	−1.04774	+	0.381348i	−0.807811	−	0.589442i	$-0.799348\pi$
$67$	−8.57615	+	3.12146i	−1.04774	+	0.381348i	−0.239933	+	0.970789i	$0.577125\pi$
$68$	6.13332	−	2.23234i	0.743774	−	0.270712i
$69$	−2.31061	−	3.96732i	−0.278165	−	0.477609i
$70$	−0.184482	−	1.04625i	−0.0220498	−	0.125051i
$71$	3.25701	−	5.64130i	0.386536	−	0.669500i	−0.605445	−	0.795887i	$-0.707005\pi$
$71$	3.25701	−	5.64130i	0.386536	−	0.669500i	0.991981	+	0.126387i	$0.0403382\pi$
$72$	−0.498553	+	2.95828i	−0.0587550	+	0.348637i
$73$	2.37064	+	4.10606i	0.277462	+	0.480578i	0.970753	−	0.240079i	$-0.0771735\pi$
$73$	2.37064	+	4.10606i	0.277462	+	0.480578i	−0.693291	+	0.720657i	$0.743840\pi$
$74$	−4.19026	+	3.51605i	−0.487108	+	0.408732i
$75$	−5.15287	−	4.29062i	−0.595002	−	0.495439i
$76$	0.260845	−	1.47933i	0.0299210	−	0.169690i
$77$	−2.39673	−	2.01109i	−0.273132	−	0.229185i
$78$	−3.93554	−	1.41556i	−0.445612	−	0.160281i
$79$	5.08023	+	1.84905i	0.571571	+	0.208035i	0.611605	−	0.791164i	$-0.290524\pi$
$79$	5.08023	+	1.84905i	0.571571	+	0.208035i	−0.0400340	+	0.999198i	$0.512747\pi$
$80$	1.06239			0.118779
$81$	1.69691	+	8.83858i	0.188546	+	0.982064i
$82$	1.33344			0.147254
$83$	−14.4780	−	5.26957i	−1.58917	−	0.578410i	−0.611998	−	0.790860i	$-0.709634\pi$
$83$	−14.4780	−	5.26957i	−1.58917	−	0.578410i	−0.977172	+	0.212449i	$0.931856\pi$
$84$	−1.62983	−	0.586228i	−0.177829	−	0.0639627i
$85$	−5.31187	−	4.45719i	−0.576153	−	0.483450i
$86$	−1.48811	+	8.43951i	−0.160467	+	0.910056i
$87$	0.900797	+	0.750063i	0.0965756	+	0.0804152i
$88$	2.39673	−	2.01109i	0.255492	−	0.214383i
$89$	7.63422	+	13.2229i	0.809225	+	1.40162i	0.913401	+	0.407061i	$0.133446\pi$
$89$	7.63422	+	13.2229i	0.809225	+	1.40162i	−0.104176	+	0.994559i	$0.533220\pi$
$90$	2.98662	−	1.11273i	0.314817	−	0.117292i
$91$	1.20735	−	2.09119i	0.126564	−	0.219216i
$92$	0.460288	+	2.61042i	0.0479883	+	0.272155i
$93$	1.84784	+	3.17274i	0.191612	+	0.328998i
$94$	−7.83469	+	2.85159i	−0.808087	+	0.294119i
$95$	−1.49962	+	0.545819i	−0.153858	+	0.0559998i
$96$	0.860339	−	1.50327i	0.0878079	−	0.153427i
$97$	2.85268	+	16.1784i	0.289646	+	1.64267i	0.688201	+	0.725521i	$0.258401\pi$
$97$	2.85268	+	16.1784i	0.289646	+	1.64267i	−0.398554	+	0.917145i	$0.630488\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	4.63136	−	8.16392i	0.465469	−	0.820505i
$100$	1.93566	+	3.35267i	0.193566	+	0.335267i
$101$	−0.833414	+	0.699318i	−0.0829278	+	0.0695847i	−0.683309	−	0.730129i	$-0.739460\pi$
$101$	−0.833414	+	0.699318i	−0.0829278	+	0.0695847i	0.600381	+	0.799714i	$0.295015\pi$
$102$	−10.6085	+	3.90674i	−1.05040	+	0.386825i
$103$	−0.556135	+	3.15400i	−0.0547976	+	0.310773i	−0.999871	−	0.0160868i	$-0.994879\pi$
$103$	−0.556135	+	3.15400i	−0.0547976	+	0.310773i	0.945073	+	0.326859i	$0.105990\pi$
$104$	1.84976	+	1.55214i	0.181384	+	0.152200i
$105$	0.326393	+	1.81093i	0.0318527	+	0.176729i
$106$	−2.30988	−	0.840726i	−0.224355	−	0.0816585i
$107$	−2.53568			−0.245133			−0.122567	−	0.992460i	$-0.539113\pi$
$107$	−2.53568			−0.245133			−0.122567	+	0.992460i	$0.539113\pi$
$108$	0.844108	−	5.12713i	0.0812243	−	0.493359i
$109$	15.9825			1.53084			0.765421	−	0.643530i	$-0.222531\pi$
$109$	15.9825			1.53084			0.765421	+	0.643530i	$0.222531\pi$
$110$	−3.12345	−	1.13684i	−0.297809	−	0.108394i
$111$	7.23463	−	6.11742i	0.686681	−	0.580639i
$112$	0.766044	+	0.642788i	0.0723844	+	0.0607377i
$113$	2.80305	−	15.8969i	0.263689	−	1.49545i	−0.509055	−	0.860734i	$-0.670005\pi$
$113$	2.80305	−	15.8969i	0.263689	−	1.49545i	0.772744	−	0.634718i	$-0.218884\pi$
$114$	−0.442091	+	2.56396i	−0.0414056	+	0.240137i
$115$	2.15723	−	1.81013i	0.201163	−	0.168796i
$116$	−0.338382	−	0.586095i	−0.0314180	−	0.0544176i
$117$	6.82579	+	2.42599i	0.631044	+	0.224283i
$118$	4.09234	−	7.08815i	0.376731	−	0.652517i
$119$	−1.13339	−	6.42778i	−0.103898	−	0.589234i
$120$	−1.84010	+	0.00696860i	−0.167977	+	0.000636143i
$121$	1.13817	−	0.414258i	0.103470	−	0.0376598i
$122$	−9.06569	+	3.29964i	−0.820769	+	0.298736i
$123$	−2.30957	+	0.00874652i	−0.208247	+	0.000788647i
$124$	−0.368101	−	2.08761i	−0.0330565	−	0.187473i
$125$	4.71240	−	8.16212i	0.421490	−	0.730042i
$126$	2.82677	+	1.00468i	0.251829	+	0.0895039i
$127$	−6.51127	−	11.2778i	−0.577781	−	1.00075i	−0.995733	−	0.0922775i	$-0.970585\pi$
$127$	−6.51127	−	11.2778i	−0.577781	−	1.00075i	0.417952	−	0.908469i	$-0.362748\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	2.52211	−	14.6273i	0.222060	−	1.28786i
$130$	0.445468	−	2.52637i	0.0390701	−	0.221578i
$131$	7.38585	+	6.19746i	0.645305	+	0.541475i	0.905642	−	0.424043i	$-0.139389\pi$
$131$	7.38585	+	6.19746i	0.645305	+	0.541475i	−0.260338	+	0.965518i	$0.583834\pi$
$132$	−4.13803	+	3.49901i	−0.360169	+	0.304550i
$133$	−1.41156	−	0.513765i	−0.122398	−	0.0445491i
$134$	−9.12655			−0.788414
$135$	−5.16564	+	1.94688i	−0.444587	+	0.167561i
$136$	6.52694			0.559680
$137$	−15.8001	−	5.75075i	−1.34989	−	0.491320i	−0.436977	−	0.899473i	$-0.643951\pi$
$137$	−15.8001	−	5.75075i	−1.34989	−	0.491320i	−0.912913	+	0.408153i	$0.866173\pi$
$138$	−0.814359	−	4.51833i	−0.0693229	−	0.384626i
$139$	5.16098	+	4.33057i	0.437748	+	0.367314i	0.834866	−	0.550453i	$-0.185545\pi$
$139$	5.16098	+	4.33057i	0.437748	+	0.367314i	−0.397118	+	0.917768i	$0.629990\pi$
$140$	0.184482	−	1.04625i	0.0155916	−	0.0884242i
$141$	13.5513	−	4.99046i	1.14122	−	0.420273i
$142$	4.99003	−	4.18713i	0.418754	−	0.351376i
$143$	−3.77743	−	6.54271i	−0.315885	−	0.547129i
$144$	−1.48028	+	2.60936i	−0.123357	+	0.217447i
$145$	−0.359494	+	0.622661i	−0.0298543	+	0.0517092i
$146$	0.823313	+	4.66924i	0.0681379	+	0.386429i
$147$	−0.860339	+	1.50327i	−0.0709595	+	0.123988i
$148$	−5.14012	+	1.87085i	−0.422515	+	0.153783i
$149$	11.7104	−	4.26225i	0.959357	−	0.349177i	0.185575	−	0.982630i	$-0.440585\pi$
$149$	11.7104	−	4.26225i	0.959357	−	0.349177i	0.773781	+	0.633453i	$0.218363\pi$
$150$	−3.37464	−	5.79425i	−0.275538	−	0.473099i
$151$	3.63005	+	20.5870i	0.295409	+	1.67535i	0.665534	+	0.746368i	$0.268204\pi$
$151$	3.63005	+	20.5870i	0.295409	+	1.67535i	−0.370125	+	0.928982i	$0.620685\pi$
$152$	0.751074	−	1.30090i	0.0609202	−	0.105517i
$153$	18.3487	−	6.83620i	1.48340	−	0.552674i
$154$	−1.56435	−	2.70954i	−0.126059	−	0.218341i
$155$	−1.72518	+	1.44760i	−0.138570	+	0.116274i
$156$	−3.21404	−	2.67623i	−0.257329	−	0.214270i
$157$	1.14868	−	6.51449i	0.0916747	−	0.519913i	−0.904041	−	0.427446i	$-0.859414\pi$
$157$	1.14868	−	6.51449i	0.0916747	−	0.519913i	0.995716	−	0.0924673i	$-0.0294753\pi$
$158$	4.14144	+	3.47508i	0.329475	+	0.276463i
$159$	4.00631	+	1.44102i	0.317721	+	0.114280i
$160$	0.998320	+	0.363359i	0.0789241	+	0.0287260i
$161$	2.65069			0.208904
$162$	−1.42840	+	8.88593i	−0.112225	+	0.698144i
$163$	−0.942654			−0.0738344			−0.0369172	−	0.999318i	$-0.511754\pi$
$163$	−0.942654			−0.0738344			−0.0369172	+	0.999318i	$0.511754\pi$
$164$	1.25302	+	0.456064i	0.0978448	+	0.0356126i
$165$	5.41739	+	1.94857i	0.421743	+	0.151696i
$166$	−11.8026	−	9.90355i	−0.916059	−	0.768665i
$167$	−3.72664	+	21.1348i	−0.288376	+	1.63546i	0.404595	+	0.914496i	$0.367413\pi$
$167$	−3.72664	+	21.1348i	−0.288376	+	1.63546i	−0.692971	+	0.720966i	$0.743698\pi$
$168$	−1.33103	−	1.10831i	−0.102692	−	0.0855078i
$169$	−5.49196	+	4.60830i	−0.422458	+	0.354485i
$170$	−3.46708	−	6.00515i	−0.265913	−	0.460574i
$171$	0.748900	−	4.44378i	0.0572698	−	0.339824i
$172$	−4.28485	+	7.42158i	−0.326717	+	0.565890i
$173$	1.59488	+	9.04503i	0.121257	+	0.687681i	0.983461	+	0.181120i	$0.0579722\pi$
$173$	1.59488	+	9.04503i	0.121257	+	0.687681i	−0.862204	+	0.506561i	$0.830917\pi$
$174$	0.589935	+	1.01292i	0.0447229	+	0.0767892i
$175$	3.63786	−	1.32407i	0.274996	−	0.100090i
$176$	2.94002	−	1.07008i	0.221612	−	0.0806603i
$177$	−7.04160	+	12.3038i	−0.529279	+	0.924809i
$178$	2.65134	+	15.0365i	0.198726	+	1.12703i
$179$	−5.64190	+	9.77205i	−0.421695	+	0.730398i	−0.996105	−	0.0881700i	$-0.971898\pi$
$179$	−5.64190	+	9.77205i	−0.421695	+	0.730398i	0.574410	+	0.818568i	$0.305231\pi$
$180$	3.18708	−	0.0241398i	0.237551	−	0.00179927i
$181$	−2.28832	−	3.96348i	−0.170089	−	0.294603i	0.768362	−	0.640016i	$-0.221072\pi$
$181$	−2.28832	−	3.96348i	−0.170089	−	0.294603i	−0.938451	+	0.345413i	$0.887739\pi$
$182$	1.84976	−	1.55214i	0.137114	−	0.115052i
$183$	15.6805	−	5.77457i	1.15913	−	0.426869i
$184$	−0.460288	+	2.61042i	−0.0339329	+	0.192443i
$185$	4.45169	+	3.73541i	0.327295	+	0.274633i
$186$	0.651259	+	3.61340i	0.0477526	+	0.264947i
$187$	−19.1893	−	6.98435i	−1.40326	−	0.510746i
$188$	−8.33750			−0.608075
$189$	−4.90266	−	1.72160i	−0.356616	−	0.125228i
$190$	−1.59587			−0.115776
$191$	−3.47043	−	1.26313i	−0.251111	−	0.0913970i	0.213398	−	0.976965i	$-0.431547\pi$
$191$	−3.47043	−	1.26313i	−0.251111	−	0.0913970i	−0.464509	+	0.885568i	$0.653769\pi$
$192$	1.32260	−	1.11836i	0.0954506	−	0.0807105i
$193$	2.85186	+	2.39299i	0.205281	+	0.172251i	0.739632	−	0.673011i	$-0.234999\pi$
$193$	2.85186	+	2.39299i	0.205281	+	0.172251i	−0.534351	+	0.845263i	$0.679444\pi$
$194$	−2.85268	+	16.1784i	−0.204811	+	1.16154i
$195$	−0.754996	+	4.37870i	−0.0540664	+	0.313565i
$196$	0.766044	−	0.642788i	0.0547175	−	0.0459134i
$197$	−4.13815	−	7.16748i	−0.294831	−	0.510662i	0.680115	−	0.733106i	$-0.261930\pi$
$197$	−4.13815	−	7.16748i	−0.294831	−	0.510662i	−0.974946	+	0.222444i	$0.928597\pi$
$198$	7.14428	−	6.08756i	0.507722	−	0.432624i
$199$	14.0634	−	24.3586i	0.996931	−	1.72673i	0.430664	−	0.902512i	$-0.358279\pi$
$199$	14.0634	−	24.3586i	0.996931	−	1.72673i	0.566267	−	0.824222i	$-0.308387\pi$
$200$	0.672249	+	3.81251i	0.0475352	+	0.269585i
$201$	15.8075	−	0.0598644i	1.11498	−	0.00422251i
$202$	−1.02233	+	0.372099i	−0.0719312	+	0.0261808i
$203$	−0.635950	+	0.231467i	−0.0446350	+	0.0162458i
$204$	−11.3049	+	0.0428126i	−0.791502	+	0.00299748i
$205$	−0.245996	−	1.39511i	−0.0171811	−	0.0974388i
$206$	−1.60133	+	2.77358i	−0.111570	+	0.193244i
$207$	1.44014	+	7.82059i	0.100097	+	0.543568i
$208$	1.20735	+	2.09119i	0.0837145	+	0.144998i
$209$	−3.60024	+	3.02096i	−0.249034	+	0.208964i
$210$	−0.312667	+	1.81335i	−0.0215761	+	0.125133i
$211$	4.25918	−	24.1550i	0.293214	−	1.66290i	−0.381158	−	0.924510i	$-0.624475\pi$
$211$	4.25918	−	24.1550i	0.293214	−	1.66290i	0.674372	−	0.738391i	$-0.264414\pi$
$212$	−1.88303	−	1.58005i	−0.129327	−	0.108518i
$213$	−8.61545	+	7.28500i	−0.590321	+	0.499160i
$214$	−2.38276	−	0.867253i	−0.162882	−	0.0592842i
$215$	9.10437			0.620913
$216$	2.54678	−	4.52923i	0.173287	−	0.308175i
$217$	−2.11981			−0.143902
$218$	15.0186	+	5.46632i	1.01719	+	0.370226i
$219$	−1.45664	−	8.08190i	−0.0984304	−	0.546124i
$220$	−2.54626	−	2.13656i	−0.171669	−	0.144047i
$221$	2.73679	−	15.5211i	0.184097	−	1.04406i
$222$	8.89061	−	3.27410i	0.596699	−	0.219743i
$223$	0.249324	−	0.209207i	0.0166959	−	0.0140096i	−0.634401	−	0.773004i	$-0.718753\pi$
$223$	0.249324	−	0.209207i	0.0166959	−	0.0140096i	0.651097	+	0.758994i	$0.274309\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	5.88301	+	10.0137i	0.392200	+	0.667582i
$226$	8.07105	−	13.9795i	0.536878	−	0.929901i
$227$	2.36825	+	13.4310i	0.157186	+	0.891447i	0.956760	+	0.290879i	$0.0939478\pi$
$227$	2.36825	+	13.4310i	0.157186	+	0.891447i	−0.799574	+	0.600568i	$0.794941\pi$
$228$	−1.29236	+	2.25813i	−0.0855884	+	0.149549i
$229$	−26.5031	+	9.64633i	−1.75137	+	0.637447i	−0.999755	−	0.0221521i	$-0.992948\pi$
$229$	−26.5031	+	9.64633i	−1.75137	+	0.637447i	−0.751617	+	0.659599i	$0.770726\pi$
$230$	2.64624	−	0.963152i	0.174488	−	0.0635084i
$231$	2.72729	+	4.68276i	0.179443	+	0.308103i
$232$	−0.117519	−	0.666483i	−0.00771549	−	0.0437567i
$233$	10.0302	−	17.3728i	0.657100	−	1.13813i	−0.324262	−	0.945967i	$-0.605116\pi$
$233$	10.0302	−	17.3728i	0.657100	−	1.13813i	0.981363	−	0.192164i	$-0.0615506\pi$
$234$	5.58440	+	4.61425i	0.365064	+	0.301643i
$235$	4.42884	+	7.67097i	0.288906	+	0.500399i
$236$	6.26983	−	5.26102i	0.408131	−	0.342463i
$237$	−7.19593	−	5.99181i	−0.467426	−	0.389210i
$238$	1.13339	−	6.42778i	0.0734668	−	0.416651i
$239$	19.7474	+	16.5701i	1.27736	+	1.07183i	0.993603	+	0.112932i	$0.0360242\pi$
$239$	19.7474	+	16.5701i	1.27736	+	1.07183i	0.283754	+	0.958897i	$0.408420\pi$
$240$	−1.73151	−	0.622803i	−0.111769	−	0.0402017i
$241$	−15.6975	−	5.71343i	−1.01117	−	0.368034i	−0.217285	−	0.976108i	$-0.569720\pi$
$241$	−15.6975	−	5.71343i	−1.01117	−	0.368034i	−0.793880	+	0.608074i	$0.791942\pi$
$242$	1.21121			0.0778595
$243$	2.41575	−	15.4001i	0.154971	−	0.987919i
$244$	−9.64751			−0.617618
$245$	−0.998320	−	0.363359i	−0.0637803	−	0.0232141i
$246$	−2.17328	−	0.781701i	−0.138563	−	0.0498394i
$247$	−2.77862	−	2.33154i	−0.176799	−	0.148352i
$248$	0.368101	−	2.08761i	0.0233744	−	0.132563i
$249$	20.5075	+	17.0759i	1.29961	+	1.08214i
$250$	7.21982	−	6.05815i	0.456622	−	0.383151i
$251$	2.76184	+	4.78364i	0.174326	+	0.301941i	0.939928	−	0.341374i	$-0.110892\pi$
$251$	2.76184	+	4.78364i	0.174326	+	0.301941i	−0.765602	+	0.643314i	$0.777559\pi$
$252$	2.31267	+	1.91090i	0.145685	+	0.120375i
$253$	4.14662	−	7.18215i	0.260696	−	0.451538i
$254$	−2.26134	−	12.8247i	−0.141889	−	0.804693i
$255$	6.04450	+	10.3784i	0.378521	+	0.649921i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−5.47869	+	1.99408i	−0.341751	+	0.124387i	−0.507194	−	0.861832i	$-0.669317\pi$
$257$	−5.47869	+	1.99408i	−0.341751	+	0.124387i	0.165442	+	0.986219i	$0.447095\pi$
$258$	7.37285	−	12.8826i	0.459013	−	0.802034i
$259$	0.949855	+	5.38690i	0.0590211	+	0.334726i
$260$	1.28267	−	2.22166i	0.0795481	−	0.137781i
$261$	−1.02843	−	1.75055i	−0.0636585	−	0.108356i
$262$	4.82077	+	8.34982i	0.297828	+	0.515854i
$263$	−8.66170	+	7.26803i	−0.534103	+	0.448166i	−0.869516	−	0.493906i	$-0.835569\pi$
$263$	−8.66170	+	7.26803i	−0.534103	+	0.448166i	0.335412	+	0.942071i	$0.391124\pi$
$264$	−5.08521	+	1.87270i	−0.312973	+	0.115257i
$265$	−0.453479	+	2.57181i	−0.0278570	+	0.157985i
$266$	−1.15071	−	0.965562i	−0.0705547	−	0.0592024i
$267$	−4.69085	−	26.0264i	−0.287075	−	1.59279i
$268$	−8.57615	−	3.12146i	−0.523872	−	0.190674i
$269$	0.618572			0.0377150			0.0188575	−	0.999822i	$-0.493997\pi$
$269$	0.618572			0.0377150			0.0188575	+	0.999822i	$0.493997\pi$
$270$	−5.51998	+	0.0627162i	−0.335935	+	0.00381679i
$271$	−13.0340			−0.791758			−0.395879	−	0.918303i	$-0.629560\pi$
$271$	−13.0340			−0.791758			−0.395879	+	0.918303i	$0.629560\pi$
$272$	6.13332	+	2.23234i	0.371887	+	0.135356i
$273$	−3.19368	+	2.70049i	−0.193290	+	0.163441i
$274$	−12.8803	−	10.8079i	−0.778129	−	0.652928i
$275$	2.10327	−	11.9282i	0.126832	−	0.719299i
$276$	0.780114	−	4.52437i	0.0469573	−	0.272335i
$277$	7.02077	−	5.89113i	0.421837	−	0.353964i	−0.407024	−	0.913417i	$-0.633433\pi$
$277$	7.02077	−	5.89113i	0.421837	−	0.353964i	0.828862	+	0.559454i	$0.188989\pi$
$278$	3.36859	+	5.83457i	0.202035	+	0.349934i
$279$	−1.15171	−	6.25427i	−0.0689509	−	0.374434i
$280$	0.531195	−	0.920056i	0.0317450	−	0.0549839i
$281$	3.56865	+	20.2388i	0.212888	+	1.20735i	0.884534	+	0.466475i	$0.154476\pi$
$281$	3.56865	+	20.2388i	0.212888	+	1.20735i	−0.671647	+	0.740872i	$0.734413\pi$
$282$	14.4409	−	0.0546887i	0.859942	−	0.00325667i
$283$	20.4258	−	7.43437i	1.21419	−	0.441928i	0.346032	−	0.938223i	$-0.387529\pi$
$283$	20.4258	−	7.43437i	1.21419	−	0.441928i	0.868154	+	0.496295i	$0.165307\pi$
$284$	6.12117	−	2.22792i	0.363225	−	0.132203i
$285$	2.76410	−	0.0104679i	0.163731	−	0.000620063i
$286$	−1.31189	−	7.44009i	−0.0775736	−	0.439942i
$287$	0.666720	−	1.15479i	0.0393553	−	0.0681653i
$288$	−2.28346	+	1.94571i	−0.134554	+	0.114652i
$289$	−12.8005	−	22.1711i	−0.752969	−	1.30418i
$290$	−0.550776	+	0.462156i	−0.0323427	+	0.0271387i
$291$	4.83484	−	28.0403i	0.283423	−	1.64375i
$292$	−0.823313	+	4.66924i	−0.0481807	+	0.273247i
$293$	−2.87963	−	2.41629i	−0.168230	−	0.141161i	0.554786	−	0.831993i	$-0.312800\pi$
$293$	−2.87963	−	2.41629i	−0.168230	−	0.141161i	−0.723016	+	0.690832i	$0.757245\pi$
$294$	−1.32260	+	1.11836i	−0.0771357	+	0.0652239i
$295$	−8.17094	−	2.97398i	−0.475730	−	0.173152i
$296$	−5.47000			−0.317937
$297$	−12.3342	+	10.5908i	−0.715705	+	0.614538i
$298$	12.4620			0.721904
$299$	6.01461	+	2.18914i	0.347834	+	0.126601i
$300$	−1.18937	−	6.59901i	−0.0686682	−	0.380994i
$301$	6.56477	+	5.50850i	0.378387	+	0.317505i
$302$	−3.63005	+	20.5870i	−0.208886	+	1.18465i
$303$	1.76828	−	0.651196i	0.101585	−	0.0374102i
$304$	1.15071	−	0.965562i	0.0659979	−	0.0553788i
$305$	5.12471	+	8.87625i	0.293440	+	0.508253i
$306$	19.5803	−	0.148306i	1.11933	−	0.00847809i
$307$	−2.24475	+	3.88802i	−0.128115	+	0.221901i	−0.922946	−	0.384929i	$-0.874226\pi$
$307$	−2.24475	+	3.88802i	−0.128115	+	0.221901i	0.794831	+	0.606830i	$0.207559\pi$
$308$	−0.543294	−	3.08117i	−0.0309570	−	0.175566i
$309$	2.75537	−	4.81445i	0.156747	−	0.273884i
$310$	−2.11625	+	0.770251i	−0.120195	+	0.0437473i
$311$	−13.4163	+	4.88314i	−0.760770	+	0.276898i	−0.693130	−	0.720812i	$-0.743769\pi$
$311$	−13.4163	+	4.88314i	−0.760770	+	0.276898i	−0.0676395	+	0.997710i	$0.521547\pi$
$312$	−2.10489	−	3.61410i	−0.119166	−	0.204608i
$313$	−1.26506	−	7.17451i	−0.0715054	−	0.405528i	−0.999461	−	0.0328360i	$-0.989546\pi$
$313$	−1.26506	−	7.17451i	−0.0715054	−	0.405528i	0.927955	−	0.372691i	$-0.121565\pi$
$314$	3.30749	−	5.72875i	0.186653	−	0.323292i
$315$	0.529657	−	3.14285i	0.0298428	−	0.177080i
$316$	2.70313	+	4.68197i	0.152063	+	0.263381i
$317$	−25.0340	+	21.0060i	−1.40605	+	1.17982i	−0.447714	+	0.894177i	$0.647762\pi$
$317$	−25.0340	+	21.0060i	−1.40605	+	1.17982i	−0.958337	+	0.285641i	$0.907794\pi$
$318$	3.27184	+	2.72435i	0.183476	+	0.152774i
$319$	−0.367682	+	2.08523i	−0.0205862	+	0.116750i
$320$	0.813838	+	0.682891i	0.0454949	+	0.0381748i
$321$	4.13272	+	1.48649i	0.230666	+	0.0829675i
$322$	2.49084	+	0.906590i	0.138809	+	0.0505223i
$323$	−9.80443			−0.545533
$324$	−4.38142	+	7.86150i	−0.243412	+	0.436750i
$325$	9.34808			0.518538
$326$	−0.885805	−	0.322407i	−0.0490602	−	0.0178565i
$327$	−26.0486	−	9.36937i	−1.44049	−	0.518127i
$328$	1.02147	+	0.857119i	0.0564015	+	0.0473265i
$329$	−1.44779	+	8.21084i	−0.0798194	+	0.452678i
$330$	4.42423	+	3.68391i	0.243546	+	0.202792i
$331$	22.4182	−	18.8111i	1.23221	−	1.03395i	0.234123	−	0.972207i	$-0.424778\pi$
$331$	22.4182	−	18.8111i	1.23221	−	1.03395i	0.998092	−	0.0617440i	$-0.0196662\pi$
$332$	−7.70360	−	13.3430i	−0.422790	−	0.732293i
$333$	−15.3774	+	5.72918i	−0.842676	+	0.313957i
$334$	−10.7304	+	18.5857i	−0.587143	+	1.01696i
$335$	1.68368	+	9.54865i	0.0919895	+	0.521698i
$336$	−0.871700	−	1.49671i	−0.0475551	−	0.0816522i
$337$	−21.0364	+	7.65662i	−1.14593	+	0.417083i	−0.844050	−	0.536265i	$-0.819835\pi$
$337$	−21.0364	+	7.65662i	−1.14593	+	0.417083i	−0.301875	+	0.953347i	$0.597613\pi$
$338$	−6.73689	+	2.45203i	−0.366438	+	0.133373i
$339$	−13.8877	+	24.2659i	−0.754275	+	1.31794i
$340$	−1.20410	−	6.82881i	−0.0653016	−	0.370344i
$341$	−3.31613	+	5.74370i	−0.179578	+	0.311039i
$342$	2.22360	−	3.91965i	0.120238	−	0.211950i
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	−6.56477	+	5.50850i	−0.353949	+	0.296998i
$345$	−4.57707	+	1.68557i	−0.246421	+	0.0907483i
$346$	−1.59488	+	9.04503i	−0.0857414	+	0.486264i
$347$	−10.5775	−	8.87555i	−0.567828	−	0.476464i	0.313096	−	0.949721i	$-0.398634\pi$
$347$	−10.5775	−	8.87555i	−0.567828	−	0.476464i	−0.880924	+	0.473257i	$0.843078\pi$
$348$	0.207919	+	1.15360i	0.0111456	+	0.0618396i
$349$	−20.1452	−	7.33227i	−1.07835	−	0.392487i	−0.259057	−	0.965862i	$-0.583412\pi$
$349$	−20.1452	−	7.33227i	−1.07835	−	0.392487i	−0.819293	+	0.573375i	$0.805634\pi$
$350$	3.87133			0.206931
$351$	−9.70266	−	7.95542i	−0.517890	−	0.424629i
$352$	3.12870			0.166760
$353$	15.0775	+	5.48777i	0.802495	+	0.292084i	0.710520	−	0.703677i	$-0.248460\pi$
$353$	15.0775	+	5.48777i	0.802495	+	0.292084i	0.0919750	+	0.995761i	$0.470682\pi$
$354$	−10.8251	+	9.15341i	−0.575347	+	0.486498i
$355$	−5.30135	−	4.44836i	−0.281367	−	0.236095i
$356$	−2.65134	+	15.0365i	−0.140521	+	0.796932i
$357$	−1.92091	+	11.1406i	−0.101666	+	0.589623i
$358$	−8.64389	+	7.25308i	−0.456844	+	0.383337i
$359$	9.88474	+	17.1209i	0.521697	+	0.903605i	0.999681	+	0.0252372i	$0.00803412\pi$
$359$	9.88474	+	17.1209i	0.521697	+	0.903605i	−0.477985	+	0.878368i	$0.658633\pi$
$360$	3.00313	+	1.06736i	0.158279	+	0.0562549i
$361$	8.37178	−	14.5003i	0.440620	−	0.763176i
$362$	−0.794724	−	4.50710i	−0.0417697	−	0.236888i
$363$	−2.09786	+	0.00794477i	−0.110109	+	0.000416992i
$364$	2.26907	−	0.825875i	0.118932	−	0.0432876i
$365$	4.73330	−	1.72278i	0.247752	−	0.0901745i
$366$	16.7099	−	0.0632815i	0.873438	−	0.00330778i
$367$	4.38594	+	24.8739i	0.228944	+	1.29841i	0.855000	+	0.518629i	$0.173557\pi$
$367$	4.38594	+	24.8739i	0.228944	+	1.29841i	−0.626055	+	0.779779i	$0.715332\pi$
$368$	−1.32535	+	2.29557i	−0.0690885	+	0.119665i
$369$	3.76933	+	1.33968i	0.196223	+	0.0697410i
$370$	2.90564	+	5.03271i	0.151057	+	0.261638i
$371$	−1.88303	+	1.58005i	−0.0977619	+	0.0820320i
$372$	−0.623872	+	3.61823i	−0.0323463	+	0.187596i
$373$	−4.20773	+	23.8632i	−0.217868	+	1.23559i	0.657991	+	0.753025i	$0.271406\pi$
$373$	−4.20773	+	23.8632i	−0.217868	+	1.23559i	−0.875860	+	0.482566i	$0.839705\pi$
$374$	−15.6433	−	13.1263i	−0.808895	−	0.678744i
$375$	−12.4653	+	10.5403i	−0.643704	+	0.544299i
$376$	−7.83469	−	2.85159i	−0.404043	−	0.147060i
$377$	−1.63418			−0.0841646
$378$	−4.01817	−	3.29458i	−0.206672	−	0.169455i
$379$	7.75804			0.398504			0.199252	−	0.979948i	$-0.436149\pi$
$379$	7.75804			0.398504			0.199252	+	0.979948i	$0.436149\pi$
$380$	−1.49962	−	0.545819i	−0.0769291	−	0.0279999i
$381$	4.00085	+	22.1980i	0.204970	+	1.13724i
$382$	−2.82912	−	2.37391i	−0.144750	−	0.121460i
$383$	−5.70755	+	32.3691i	−0.291642	+	1.65398i	0.388903	+	0.921279i	$0.372854\pi$
$383$	−5.70755	+	32.3691i	−0.291642	+	1.65398i	−0.680545	+	0.732706i	$0.738257\pi$
$384$	1.62534	−	0.598556i	0.0829428	−	0.0305449i
$385$	−2.54626	+	2.13656i	−0.129769	+	0.108889i
$386$	1.86142	+	3.22407i	0.0947437	+	0.164101i
$387$	−12.6856	+	22.3615i	−0.644843	+	1.13670i
$388$	−8.21398	+	14.2270i	−0.417002	+	0.722268i
$389$	−2.84323	−	16.1247i	−0.144157	−	0.817557i	−0.968040	−	0.250796i	$-0.919308\pi$
$389$	−2.84323	−	16.1247i	−0.144157	−	0.817557i	0.823883	−	0.566761i	$-0.191804\pi$
$390$	−2.20707	+	3.85641i	−0.111759	+	0.195277i
$391$	16.2575	−	5.91726i	0.822179	−	0.299249i
$392$	0.939693	−	0.342020i	0.0474616	−	0.0172746i
$393$	−8.40453	−	14.4306i	−0.423952	−	0.727927i
$394$	−1.43716	−	8.15056i	−0.0724033	−	0.410619i
$395$	2.87178	−	4.97407i	0.144495	−	0.250273i
$396$	8.79549	−	3.27695i	0.441990	−	0.164673i
$397$	−8.78309	−	15.2128i	−0.440811	−	0.763506i	0.556939	−	0.830553i	$-0.311976\pi$
$397$	−8.78309	−	15.2128i	−0.440811	−	0.763506i	−0.997750	+	0.0670470i	$0.978642\pi$
$398$	21.5464	−	18.0796i	1.08003	−	0.906249i
$399$	1.99941	+	1.66484i	0.100096	+	0.0833464i
$400$	−0.672249	+	3.81251i	−0.0336125	+	0.190626i
$401$	0.662550	+	0.555945i	0.0330862	+	0.0277626i	0.659181	−	0.751985i	$-0.270903\pi$
$401$	0.662550	+	0.555945i	0.0330862	+	0.0277626i	−0.626095	+	0.779747i	$0.715348\pi$
$402$	14.8747	+	5.35024i	0.741883	+	0.266846i
$403$	−4.81000	−	1.75070i	−0.239603	−	0.0872084i
$404$	−1.08795			−0.0541273
$405$	9.56041	−	0.144834i	0.475061	−	0.00719688i
$406$	−0.676764			−0.0335873
$407$	16.0819	+	5.85334i	0.797151	+	0.290139i
$408$	−10.6378	−	3.82628i	−0.526649	−	0.189429i
$409$	−13.0344	−	10.9371i	−0.644508	−	0.540806i	0.260891	−	0.965368i	$-0.415984\pi$
$409$	−13.0344	−	10.9371i	−0.644508	−	0.540806i	−0.905399	+	0.424562i	$0.860428\pi$
$410$	0.245996	−	1.39511i	0.0121489	−	0.0688997i
$411$	22.3801	+	18.6352i	1.10393	+	0.919205i
$412$	−2.45337	+	2.05863i	−0.120869	+	0.101421i
$413$	−4.09234	−	7.08815i	−0.201371	−	0.348785i
$414$	−1.32151	+	7.84150i	−0.0649487	+	0.385389i
$415$	−8.18422	+	14.1755i	−0.401748	+	0.695847i
$416$	0.419308	+	2.37801i	0.0205582	+	0.116592i
$417$	−5.87280	−	10.0836i	−0.287592	−	0.493796i
$418$	−4.41635	+	1.60742i	−0.216011	+	0.0786214i
$419$	−21.5593	+	7.84695i	−1.05324	+	0.383349i	−0.809885	−	0.586588i	$-0.800471\pi$
$419$	−21.5593	+	7.84695i	−1.05324	+	0.383349i	−0.243356	+	0.969937i	$0.578248\pi$
$420$	−0.914015	+	1.59706i	−0.0445994	+	0.0779284i
$421$	5.48117	+	31.0853i	0.267136	+	1.51500i	0.762883	+	0.646536i	$0.223783\pi$
$421$	5.48117	+	31.0853i	0.267136	+	1.51500i	−0.495747	+	0.868467i	$0.665106\pi$
$422$	12.2638	−	21.2416i	0.596994	−	1.03402i
$423$	−25.0118	+	0.189446i	−1.21611	+	0.00921117i
$424$	−1.22906	−	2.12879i	−0.0596884	−	0.103383i
$425$	19.3564	−	16.2419i	0.938921	−	0.787848i
$426$	−10.5875	+	3.89900i	−0.512966	+	0.188907i
$427$	−1.67527	+	9.50094i	−0.0810721	+	0.459783i
$428$	−1.94244	−	1.62990i	−0.0938915	−	0.0787843i
$429$	2.32104	+	12.8779i	0.112061	+	0.621752i
$430$	8.55530	+	3.11388i	0.412573	+	0.150164i
$431$	−23.4733			−1.13067			−0.565334	−	0.824862i	$-0.691253\pi$
$431$	−23.4733			−1.13067			−0.565334	+	0.824862i	$0.691253\pi$
$432$	3.94228	−	3.38503i	0.189673	−	0.162862i
$433$	−30.0449			−1.44386			−0.721932	−	0.691964i	$-0.756746\pi$
$433$	−30.0449			−1.44386			−0.721932	+	0.691964i	$0.756746\pi$
$434$	−1.99197	−	0.725018i	−0.0956176	−	0.0348020i
$435$	0.950934	−	0.804085i	0.0455938	−	0.0385529i
$436$	12.2433	+	10.2733i	0.586346	+	0.492003i
$437$	0.691421	−	3.92124i	0.0330751	−	0.187578i
$438$	1.39538	−	8.09270i	0.0666740	−	0.386684i
$439$	22.2835	−	18.6980i	1.06353	−	0.892409i	0.0690808	−	0.997611i	$-0.477993\pi$
$439$	22.2835	−	18.6980i	1.06353	−	0.892409i	0.994451	+	0.105202i	$0.0335489\pi$
$440$	−1.66195	−	2.87858i	−0.0792304	−	0.137231i
$441$	2.28346	−	1.94571i	0.108736	−	0.0926530i
$442$	7.88029	−	13.6491i	0.374827	−	0.649219i
$443$	−5.53935	−	31.4152i	−0.263182	−	1.49258i	−0.774162	−	0.632988i	$-0.781828\pi$
$443$	−5.53935	−	31.4152i	−0.263182	−	1.49258i	0.510979	−	0.859593i	$-0.329283\pi$
$444$	9.47425	−	0.0358797i	0.449628	−	0.00170278i
$445$	15.2428	−	5.54792i	0.722577	−	0.262997i
$446$	0.305841	−	0.111317i	0.0144820	−	0.00527101i
$447$	−21.5847	+	0.0817427i	−1.02092	+	0.00386630i
$448$	0.173648	+	0.984808i	0.00820411	+	0.0465278i
$449$	−8.51294	+	14.7449i	−0.401751	+	0.695853i	−0.993937	−	0.109948i	$-0.964931\pi$
$449$	−8.51294	+	14.7449i	−0.401751	+	0.695853i	0.592187	+	0.805801i	$0.298265\pi$
$450$	2.10332	+	11.4219i	0.0991514	+	0.538435i
$451$	−2.08597	−	3.61301i	−0.0982245	−	0.170130i
$452$	12.3656	−	10.3759i	0.581628	−	0.488043i
$453$	6.15235	−	35.6814i	0.289063	−	1.67646i
$454$	−2.36825	+	13.4310i	−0.111147	+	0.630349i
$455$	−1.96517	−	1.64897i	−0.0921286	−	0.0773051i
$456$	−1.98674	+	1.67994i	−0.0930378	+	0.0786703i
$457$	−14.6816	−	5.34368i	−0.686778	−	0.249967i	−0.0250231	−	0.999687i	$-0.507966\pi$
$457$	−14.6816	−	5.34368i	−0.686778	−	0.249967i	−0.661755	+	0.749720i	$0.730188\pi$
$458$	−28.2040			−1.31789
$459$	−33.9128	+	0.385306i	−1.58291	+	0.0179845i
$460$	2.81607			0.131300
$461$	−16.0085	−	5.82663i	−0.745591	−	0.271373i	−0.0588418	−	0.998267i	$-0.518741\pi$
$461$	−16.0085	−	5.82663i	−0.745591	−	0.271373i	−0.686749	+	0.726894i	$0.740963\pi$
$462$	0.961216	+	5.33314i	0.0447198	+	0.248120i
$463$	18.8665	+	15.8308i	0.876799	+	0.735721i	0.965518	−	0.260335i	$-0.0838331\pi$
$463$	18.8665	+	15.8308i	0.876799	+	0.735721i	−0.0887197	+	0.996057i	$0.528278\pi$
$464$	0.117519	−	0.666483i	0.00545568	−	0.0309407i
$465$	3.66037	−	1.34799i	0.169746	−	0.0625114i
$466$	15.3672	−	12.8946i	0.711870	−	0.597330i
$467$	5.87972	+	10.1840i	0.272081	+	0.471258i	0.969394	−	0.245508i	$-0.0789549\pi$
$467$	5.87972	+	10.1840i	0.272081	+	0.471258i	−0.697314	+	0.716766i	$0.745622\pi$
$468$	3.66946	+	6.24595i	0.169621	+	0.288719i
$469$	−4.56328	+	7.90382i	−0.210712	+	0.364965i
$470$	1.53812	+	8.72311i	0.0709482	+	0.402367i
$471$	−5.69113	+	9.94410i	−0.262233	+	0.458200i
$472$	7.69109	−	2.79933i	0.354011	−	0.128850i
$473$	25.1951	−	9.17027i	1.15847	−	0.421649i
$474$	−4.71264	−	8.09161i	−0.216459	−	0.371660i
$475$	−1.00982	−	5.72696i	−0.0463336	−	0.262771i
$476$	3.26347	−	5.65249i	0.149581	−	0.259082i
$477$	−5.68482	−	4.69722i	−0.260290	−	0.215071i
$478$	12.8892	+	22.3248i	0.589540	+	1.02111i
$479$	15.8563	−	13.3051i	0.724495	−	0.607924i	−0.204130	−	0.978944i	$-0.565436\pi$
$479$	15.8563	−	13.3051i	0.724495	−	0.607924i	0.928625	+	0.371020i	$0.120992\pi$
$480$	−1.41408	−	1.17746i	−0.0645435	−	0.0537432i
$481$	−2.29361	+	13.0077i	−0.104580	+	0.593101i
$482$	−12.7967	−	10.7377i	−0.582875	−	0.489090i
$483$	−4.32017	−	1.55391i	−0.196575	−	0.0707054i
$484$	1.13817	+	0.414258i	0.0517348	+	0.0188299i
$485$	17.4529			0.792495
$486$	7.53722	−	13.6452i	0.341895	−	0.618957i
$487$	9.13931			0.414142			0.207071	−	0.978326i	$-0.433607\pi$
$487$	9.13931			0.414142			0.207071	+	0.978326i	$0.433607\pi$
$488$	−9.06569	−	3.29964i	−0.410385	−	0.149368i
$489$	1.53636	+	0.552611i	0.0694768	+	0.0249899i
$490$	−0.813838	−	0.682891i	−0.0367654	−	0.0308499i
$491$	2.95842	−	16.7780i	0.133512	−	0.757182i	−0.842373	−	0.538895i	$-0.818842\pi$
$491$	2.95842	−	16.7780i	0.133512	−	0.757182i	0.975885	−	0.218287i	$-0.0700470\pi$
$492$	−1.77486	−	1.47786i	−0.0800167	−	0.0666272i
$493$	−3.38377	+	2.83932i	−0.152397	+	0.127877i
$494$	−1.81362	−	3.14127i	−0.0815984	−	0.141333i
$495$	−7.68710	−	6.35165i	−0.345509	−	0.285485i
$496$	1.05991	−	1.83581i	0.0475911	−	0.0824303i
$497$	−1.13115	−	6.41505i	−0.0507389	−	0.287754i
$498$	13.4304	+	23.0601i	0.601833	+	1.03335i
$499$	38.8888	−	14.1544i	1.74090	−	0.633637i	0.741596	−	0.670846i	$-0.234069\pi$
$499$	38.8888	−	14.1544i	1.74090	−	0.633637i	0.999308	+	0.0372091i	$0.0118468\pi$
$500$	8.85642	−	3.22347i	0.396071	−	0.144158i
$501$	18.4636	−	32.2615i	0.824893	−	1.44134i
$502$	0.959175	+	5.43975i	0.0428101	+	0.242788i
$503$	5.26812	−	9.12465i	0.234894	−	0.406848i	−0.724348	−	0.689434i	$-0.757859\pi$
$503$	5.26812	−	9.12465i	0.234894	−	0.406848i	0.959242	+	0.282587i	$0.0911924\pi$
$504$	1.51963	+	2.58664i	0.0676899	+	0.115218i
$505$	0.577911	+	1.00097i	0.0257167	+	0.0445426i
$506$	6.35299	−	5.33079i	0.282425	−	0.236982i
$507$	11.6525	−	4.29119i	0.517504	−	0.190579i
$508$	2.26134	−	12.8247i	0.100331	−	0.569004i
$509$	7.15833	+	6.00655i	0.317288	+	0.266236i	0.787496	−	0.616319i	$-0.211377\pi$
$509$	7.15833	+	6.00655i	0.317288	+	0.266236i	−0.470209	+	0.882555i	$0.655821\pi$
$510$	2.13035	+	11.8199i	0.0943333	+	0.523392i
$511$	4.45534	+	1.62161i	0.197092	+	0.0717358i
$512$	−1.00000			−0.0441942
$513$	−3.82565	+	6.80357i	−0.168906	+	0.300385i
$514$	−5.83030			−0.257164
$515$	3.19727	+	1.16371i	0.140889	+	0.0512793i
$516$	11.3343	−	9.58399i	0.498965	−	0.421912i
$517$	19.9827	+	16.7675i	0.878839	+	0.737433i
$518$	−0.949855	+	5.38690i	−0.0417343	+	0.236687i
$519$	2.70307	−	15.6768i	0.118651	−	0.688135i
$520$	1.96517	−	1.64897i	0.0861784	−	0.0723123i
$521$	−2.79119	−	4.83447i	−0.122284	−	0.211802i	0.798384	−	0.602149i	$-0.205689\pi$
$521$	−2.79119	−	4.83447i	−0.122284	−	0.211802i	−0.920668	+	0.390346i	$0.872355\pi$
$522$	−0.367690	−	1.99672i	−0.0160934	−	0.0873941i
$523$	−5.25249	+	9.09758i	−0.229675	+	0.397809i	−0.957712	−	0.287729i	$-0.907100\pi$
$523$	−5.25249	+	9.09758i	−0.229675	+	0.397809i	0.728037	+	0.685538i	$0.240433\pi$
$524$	1.67424	+	9.49506i	0.0731393	+	0.414794i
$525$	−6.70529	+	0.0253934i	−0.292643	+	0.00110826i
$526$	−10.6251	+	3.86724i	−0.463278	+	0.168620i
$527$	−13.0015	+	4.73215i	−0.566353	+	0.206136i
$528$	−5.41904	+	0.0205223i	−0.235833	+	0.000893119i
$529$	−2.77383	−	15.7311i	−0.120601	−	0.683963i
$530$	−1.30574	+	2.26161i	−0.0567177	+	0.0982379i
$531$	18.6894	−	15.9251i	0.811052	−	0.691089i
$532$	−0.751074	−	1.30090i	−0.0325632	−	0.0564011i
$533$	2.46655	−	2.06968i	0.106838	−	0.0896479i
$534$	4.49359	−	26.0611i	0.194456	−	1.12778i
$535$	−0.467787	+	2.65295i	−0.0202242	+	0.114697i
$536$	−6.99134	−	5.86643i	−0.301980	−	0.253391i
$537$	14.9240	−	12.6193i	0.644017	−	0.544564i
$538$	0.581267	+	0.211564i	0.0250602	+	0.00912117i
$539$	−3.12870			−0.134763
$540$	−5.20854	−	1.82901i	−0.224140	−	0.0787081i
$541$	23.3130			1.00230			0.501152	−	0.865360i	$-0.332910\pi$
$541$	23.3130			1.00230			0.501152	+	0.865360i	$0.332910\pi$
$542$	−12.2479	−	4.45789i	−0.526094	−	0.191483i
$543$	1.40606	+	7.80126i	0.0603396	+	0.334784i
$544$	4.99993	+	4.19544i	0.214370	+	0.179878i
$545$	2.94848	−	16.7216i	0.126299	−	0.716276i
$546$	−3.92470	+	1.44533i	−0.167962	+	0.0618544i
$547$	−7.23273	+	6.06898i	−0.309249	+	0.259491i	−0.784182	−	0.620531i	$-0.786917\pi$
$547$	−7.23273	+	6.06898i	−0.309249	+	0.259491i	0.474933	+	0.880022i	$0.342472\pi$
$548$	−8.40704	−	14.5614i	−0.359131	−	0.622033i
$549$	−28.9417	+	0.219212i	−1.23520	+	0.00935574i
$550$	6.05612	−	10.4895i	0.258234	−	0.447274i
$551$	0.176531	+	1.00116i	0.00752047	+	0.0426507i
$552$	2.28049	−	3.98470i	0.0970642	−	0.169600i
$553$	5.08023	−	1.84905i	0.216033	−	0.0786297i
$554$	8.61226	−	3.13460i	0.365900	−	0.133177i
$555$	−5.06568	−	8.69778i	−0.215026	−	0.369200i
$556$	1.16990	+	6.63482i	0.0496147	+	0.281379i
$557$	9.79046	−	16.9576i	0.414835	−	0.718515i	−0.580576	−	0.814206i	$-0.697173\pi$
$557$	9.79046	−	16.9576i	0.414835	−	0.718515i	0.995411	+	0.0956908i	$0.0305060\pi$
$558$	1.05684	−	6.27100i	0.0447395	−	0.265473i
$559$	10.3466	+	17.9209i	0.437615	+	0.757972i
$560$	0.813838	−	0.682891i	0.0343909	−	0.0288574i
$561$	27.1809	+	22.6326i	1.14758	+	0.955549i
$562$	−3.56865	+	20.2388i	−0.150534	+	0.853723i
$563$	5.52236	+	4.63381i	0.232740	+	0.195292i	0.751697	−	0.659508i	$-0.229235\pi$
$563$	5.52236	+	4.63381i	0.232740	+	0.195292i	−0.518958	+	0.854800i	$0.673680\pi$
$564$	13.5887	+	4.88768i	0.572187	+	0.205808i
$565$	−16.1150	−	5.86537i	−0.677962	−	0.246758i
$566$	21.7367			0.913660
$567$	6.98124	+	5.67999i	0.293185	+	0.238537i
$568$	6.51402			0.273322
$569$	−8.47003	−	3.08284i	−0.355082	−	0.129239i	0.158319	−	0.987388i	$-0.449393\pi$
$569$	−8.47003	−	3.08284i	−0.355082	−	0.129239i	−0.513401	+	0.858149i	$0.671615\pi$
$570$	2.60099	+	0.935542i	0.108943	+	0.0391855i
$571$	−5.02205	−	4.21400i	−0.210166	−	0.176350i	0.531628	−	0.846978i	$-0.321580\pi$
$571$	−5.02205	−	4.21400i	−0.210166	−	0.176350i	−0.741794	+	0.670628i	$0.766025\pi$
$572$	1.31189	−	7.44009i	0.0548528	−	0.311086i
$573$	4.91571	+	4.09315i	0.205357	+	0.170994i
$574$	1.02147	−	0.857119i	0.0426355	−	0.0357755i
$575$	5.13085	+	8.88690i	0.213971	+	0.370609i
$576$	−2.81123	+	1.04738i	−0.117134	+	0.0436410i
$577$	11.9349	−	20.6719i	0.496858	−	0.860583i	−0.503136	−	0.864207i	$-0.667820\pi$
$577$	11.9349	−	20.6719i	0.496858	−	0.860583i	0.999993	+	0.00362468i	$0.00115377\pi$
$578$	−4.44556	−	25.2120i	−0.184911	−	1.04868i
$579$	−3.24520	−	5.57201i	−0.134866	−	0.231565i
$580$	−0.675627	+	0.245908i	−0.0280539	+	0.0102108i
$581$	−14.4780	+	5.26957i	−0.600650	+	0.218619i
$582$	14.1336	−	24.6956i	0.585857	−	1.02367i
$583$	1.33548	+	7.57389i	0.0553099	+	0.313678i
$584$	−2.37064	+	4.10606i	−0.0980976	+	0.169910i
$585$	3.79743	−	6.69392i	0.157004	−	0.276760i
$586$	−1.87954	−	3.25546i	−0.0776432	−	0.134482i
$587$	8.39732	−	7.04619i	0.346595	−	0.290827i	−0.452826	−	0.891599i	$-0.649584\pi$
$587$	8.39732	−	7.04619i	0.346595	−	0.290827i	0.799421	+	0.600771i	$0.205140\pi$
$588$	−1.62534	+	0.598556i	−0.0670279	+	0.0246840i
$589$	−0.552943	+	3.13589i	−0.0227836	+	0.129212i
$590$	−6.66101	−	5.58925i	−0.274229	−	0.230106i
$591$	2.54269	+	14.1077i	0.104592	+	0.580311i
$592$	−5.14012	−	1.87085i	−0.211258	−	0.0768915i
$593$	37.5467			1.54186			0.770930	−	0.636920i	$-0.219792\pi$
$593$	37.5467			1.54186			0.770930	+	0.636920i	$0.219792\pi$
$594$	−15.2126	+	5.73350i	−0.624182	+	0.235248i
$595$	−6.93415			−0.284273
$596$	11.7104	+	4.26225i	0.479678	+	0.174589i
$597$	−37.2007	+	31.4559i	−1.52252	+	1.28740i
$598$	4.90316	+	4.11424i	0.200505	+	0.168244i
$599$	5.29469	−	30.0277i	0.216335	−	1.22690i	−0.662240	−	0.749292i	$-0.730394\pi$
$599$	5.29469	−	30.0277i	0.216335	−	1.22690i	0.878575	−	0.477605i	$-0.158495\pi$
$600$	1.13935	−	6.60783i	0.0465139	−	0.269764i
$601$	1.08058	−	0.906717i	0.0440779	−	0.0369858i	−0.620483	−	0.784220i	$-0.713063\pi$
$601$	1.08058	−	0.906717i	0.0440779	−	0.0369858i	0.664561	+	0.747234i	$0.268619\pi$
$602$	4.28485	+	7.42158i	0.174638	+	0.302481i
$603$	−25.7986	−	9.16926i	−1.05060	−	0.373401i
$604$	−10.4523	+	18.1039i	−0.425299	+	0.736639i
$605$	−0.223447	−	1.26723i	−0.00908439	−	0.0515202i
$606$	1.88436	−	0.00713623i	0.0765470	−	0.000289889i
$607$	34.4918	−	12.5540i	1.39998	−	0.509550i	0.471806	−	0.881702i	$-0.343602\pi$
$607$	34.4918	−	12.5540i	1.39998	−	0.509550i	0.928172	+	0.372152i	$0.121380\pi$
$608$	1.41156	−	0.513765i	0.0572462	−	0.0208359i
$609$	1.17218	−	0.00443914i	0.0474992	−	0.000179883i
$610$	1.77979	+	10.0937i	0.0720617	+	0.408682i
$611$	−10.0663	+	17.4353i	−0.407238	+	0.705356i
$612$	18.4501	+	6.55748i	0.745803	+	0.265070i
$613$	19.7254	+	34.1653i	0.796700	+	1.37993i	0.921754	+	0.387775i	$0.126756\pi$
$613$	19.7254	+	34.1653i	0.796700	+	1.37993i	−0.125054	+	0.992150i	$0.539910\pi$
$614$	−3.43916	+	2.88580i	−0.138793	+	0.116461i
$615$	−0.416923	+	2.41800i	−0.0168120	+	0.0975032i
$616$	0.543294	−	3.08117i	0.0218899	−	0.124144i
$617$	−37.5299	−	31.4914i	−1.51090	−	1.26779i	−0.861987	−	0.506930i	$-0.830780\pi$
$617$	−37.5299	−	31.4914i	−1.51090	−	1.26779i	−0.648911	−	0.760864i	$-0.724775\pi$
$618$	4.23583	−	3.58171i	0.170390	−	0.144078i
$619$	11.8719	+	4.32103i	0.477174	+	0.173677i	0.569399	−	0.822061i	$-0.307176\pi$
$619$	11.8719	+	4.32103i	0.477174	+	0.173677i	−0.0922256	+	0.995738i	$0.529398\pi$
$620$	−2.25206			−0.0904451
$621$	2.23747	−	13.5905i	0.0897866	−	0.545366i
$622$	−14.2774			−0.572470
$623$	14.3476	+	5.22211i	0.574826	+	0.209220i
$624$	−0.741855	−	4.11606i	−0.0296980	−	0.164774i
$625$	7.15778	+	6.00609i	0.286311	+	0.240244i
$626$	1.26506	−	7.17451i	0.0505620	−	0.286751i
$627$	7.63874	−	2.81308i	0.305062	−	0.112344i
$628$	5.06737	−	4.25203i	0.202210	−	0.169675i
$629$	17.8512	+	30.9191i	0.711773	+	1.23283i
$630$	1.57263	−	2.77216i	0.0626552	−	0.110445i
$631$	−2.19999	+	3.81049i	−0.0875800	+	0.151693i	−0.906488	−	0.422232i	$-0.861247\pi$
$631$	−2.19999	+	3.81049i	−0.0875800	+	0.151693i	0.818908	+	0.573925i	$0.194580\pi$
$632$	0.938789	+	5.32413i	0.0373430	+	0.211783i
$633$	−21.1021	+	36.8717i	−0.838733	+	1.46552i
$634$	−30.7088	+	11.1771i	−1.21960	+	0.443899i
$635$	−13.0006	+	4.73185i	−0.515915	+	0.187778i
$636$	2.14274	+	3.67909i	0.0849652	+	0.145885i
$637$	−0.419308	−	2.37801i	−0.0166136	−	0.0942202i
$638$	−1.05870	+	1.83372i	−0.0419142	+	0.0725976i
$639$	18.3124	−	6.82267i	0.724426	−	0.269901i
$640$	0.531195	+	0.920056i	0.0209973	+	0.0363684i
$641$	11.5794	−	9.71624i	0.457357	−	0.383768i	−0.384800	−	0.923000i	$-0.625730\pi$
$641$	11.5794	−	9.71624i	0.457357	−	0.383768i	0.842158	+	0.539232i	$0.181285\pi$
$642$	3.37507	+	2.81031i	0.133204	+	0.110914i
$643$	1.34999	−	7.65620i	0.0532386	−	0.301931i	−0.946549	−	0.322561i	$-0.895456\pi$
$643$	1.34999	−	7.65620i	0.0532386	−	0.301931i	0.999787	+	0.0206302i	$0.00656726\pi$
$644$	2.03055	+	1.70383i	0.0800148	+	0.0671404i
$645$	−14.8385	−	5.33724i	−0.584267	−	0.210153i
$646$	−9.21315	−	3.35331i	−0.362487	−	0.131934i
$647$	−0.538159			−0.0211572			−0.0105786	−	0.999944i	$-0.503367\pi$
$647$	−0.538159			−0.0211572			−0.0105786	+	0.999944i	$0.503367\pi$
$648$	−6.80598	+	5.88886i	−0.267364	+	0.231336i
$649$	−25.6075			−1.00518
$650$	8.78432	+	3.19723i	0.344549	+	0.125406i
$651$	3.45492	+	1.24269i	0.135409	+	0.0487050i
$652$	−0.722115	−	0.605926i	−0.0282802	−	0.0237299i
$653$	4.03416	−	22.8789i	0.157869	−	0.895319i	−0.798247	−	0.602330i	$-0.794239\pi$
$653$	4.03416	−	22.8789i	0.157869	−	0.895319i	0.956116	−	0.292989i	$-0.0946498\pi$
$654$	−21.2732	−	17.7135i	−0.831848	−	0.692652i
$655$	7.84665	−	6.58412i	0.306594	−	0.257263i
$656$	0.666720	+	1.15479i	0.0260311	+	0.0450871i
$657$	−2.36377	+	14.0260i	−0.0922196	+	0.547207i
$658$	−4.16875	+	7.22049i	−0.162515	+	0.281484i
$659$	5.65644	+	32.0793i	0.220344	+	1.24963i	0.871389	+	0.490592i	$0.163219\pi$
$659$	5.65644	+	32.0793i	0.220344	+	1.24963i	−0.651046	+	0.759038i	$0.725669\pi$
$660$	2.89745	+	4.97492i	0.112783	+	0.193648i
$661$	27.3911	−	9.96953i	1.06539	−	0.387770i	0.250939	−	0.968003i	$-0.419261\pi$
$661$	27.3911	−	9.96953i	1.06539	−	0.387770i	0.814451	+	0.580233i	$0.197039\pi$
$662$	27.5000	−	10.0092i	1.06882	−	0.389018i
$663$	−13.5594	+	23.6924i	−0.526605	+	0.920136i
$664$	−2.67543	−	15.1731i	−0.103827	−	0.588831i
$665$	−0.797933	+	1.38206i	−0.0309425	+	0.0535940i
$666$	−16.4095	+	0.124290i	−0.635856	+	0.00481614i
$667$	−0.896947	−	1.55356i	−0.0347299	−	0.0601540i
$668$	−16.4400	+	13.7948i	−0.636082	+	0.533736i
$669$	−0.528998	+	0.194811i	−0.0204522	+	0.00753184i
$670$	−1.68368	+	9.54865i	−0.0650464	+	0.368897i
$671$	23.1224	+	19.4020i	0.892632	+	0.749007i
$672$	−0.307225	−	1.70459i	−0.0118515	−	0.0657558i
$673$	−17.7008	−	6.44257i	−0.682316	−	0.248343i	−0.0224747	−	0.999747i	$-0.507155\pi$
$673$	−17.7008	−	6.44257i	−0.682316	−	0.248343i	−0.659842	+	0.751405i	$0.729377\pi$
$674$	−22.3865			−0.862294
$675$	−3.71795	−	19.7694i	−0.143104	−	0.760926i
$676$	−7.16924			−0.275740
$677$	−27.0896	−	9.85980i	−1.04114	−	0.378943i	−0.235826	−	0.971795i	$-0.575779\pi$
$677$	−27.0896	−	9.85980i	−1.04114	−	0.378943i	−0.805311	+	0.592853i	$0.798002\pi$
$678$	−21.3496	+	18.0526i	−0.819926	+	0.693308i
$679$	12.5845	+	10.5597i	0.482950	+	0.405244i
$680$	1.20410	−	6.82881i	0.0461752	−	0.261873i
$681$	4.01380	−	23.2786i	0.153809	−	0.892036i
$682$	−5.08060	+	4.26313i	−0.194546	+	0.163244i
$683$	−13.7305	−	23.7819i	−0.525383	−	0.909991i	−0.999563	−	0.0295626i	$-0.990589\pi$
$683$	−13.7305	−	23.7819i	−0.525383	−	0.909991i	0.474180	−	0.880428i	$-0.342745\pi$
$684$	3.43010	−	2.92275i	0.131153	−	0.111754i
$685$	−8.93155	+	15.4699i	−0.341257	+	0.591074i
$686$	−0.173648	−	0.984808i	−0.00662992	−	0.0376001i
$687$	48.8504	−	0.185000i	1.86376	−	0.00705819i
$688$	−8.05289	+	2.93101i	−0.307013	+	0.111744i
$689$	−5.57765	+	2.03010i	−0.212491	+	0.0773406i
$690$	−4.87754	+	0.0184716i	−0.185685	+	0.000703202i
$691$	−3.83707	−	21.7611i	−0.145969	−	0.827831i	−0.966584	−	0.256350i	$-0.917480\pi$
$691$	−3.83707	−	21.7611i	−0.145969	−	0.827831i	0.820615	−	0.571481i	$-0.193631\pi$
$692$	−4.59228	+	7.95406i	−0.174572	+	0.302368i
$693$	−1.69985	−	9.23091i	−0.0645718	−	0.350653i
$694$	−6.90395	−	11.9580i	−0.262070	−	0.453919i
$695$	5.48297	−	4.60076i	0.207981	−	0.174517i
$696$	−0.199176	+	1.15514i	−0.00754973	+	0.0437856i
$697$	1.51131	−	8.57106i	0.0572449	−	0.324652i
$698$	−16.4226	−	13.7802i	−0.621603	−	0.521587i
$699$	−26.5319	+	22.4347i	−1.00353	+	0.848558i
$700$	3.63786	+	1.32407i	0.137498	+	0.0500452i
$701$	−46.5889			−1.75964			−0.879819	−	0.475309i	$-0.842336\pi$
$701$	−46.5889			−1.75964			−0.879819	+	0.475309i	$0.842336\pi$
$702$	−6.39661	−	10.7942i	−0.241424	−	0.407399i
$703$	8.21675			0.309901
$704$	2.94002	+	1.07008i	0.110806	+	0.0403302i
$705$	−2.72130	−	15.0987i	−0.102490	−	0.568649i
$706$	12.2913	+	10.3136i	0.462589	+	0.388158i
$707$	−0.188920	+	1.07142i	−0.00710506	+	0.0402948i
$708$	−13.3029	+	4.89899i	−0.499954	+	0.184115i
$709$	40.3185	−	33.8313i	1.51419	−	1.27056i	0.659142	−	0.752019i	$-0.270920\pi$
$709$	40.3185	−	33.8313i	1.51419	−	1.27056i	0.855053	−	0.518541i	$-0.173525\pi$
$710$	−3.46021	−	5.99326i	−0.129859	−	0.224923i
$711$	8.21555	+	13.9841i	0.308107	+	0.524444i
$712$	−7.63422	+	13.2229i	−0.286104	+	0.495547i
$713$	−0.975723	−	5.53360i	−0.0365411	−	0.207235i
$714$	−5.61538	+	9.81174i	−0.210150	+	0.367195i
$715$	−7.54217	+	2.74513i	−0.282061	+	0.102662i
$716$	−10.6033	+	3.85929i	−0.396264	+	0.144228i
$717$	−22.4711	−	38.5829i	−0.839198	−	1.44090i
$718$	3.43294	+	19.4691i	0.128116	+	0.726582i
$719$	−13.9987	+	24.2465i	−0.522065	+	0.904243i	0.477605	+	0.878575i	$0.341505\pi$
$719$	−13.9987	+	24.2465i	−0.522065	+	0.904243i	−0.999670	+	0.0256689i	$0.991828\pi$
$720$	2.45696	+	2.03012i	0.0915655	+	0.0756582i
$721$	1.60133	+	2.77358i	0.0596365	+	0.103293i
$722$	12.8263	−	10.7625i	0.477346	−	0.400541i
$723$	22.2349	+	18.5142i	0.826923	+	0.688552i
$724$	0.794724	−	4.50710i	0.0295357	−	0.167505i
$725$	−2.00702	−	1.68409i	−0.0745388	−	0.0625455i
$726$	−1.97406	−	0.710046i	−0.0732644	−	0.0263523i
$727$	15.6872	+	5.70966i	0.581805	+	0.211760i	0.616121	−	0.787651i	$-0.288703\pi$
$727$	15.6872	+	5.70966i	0.581805	+	0.211760i	−0.0343163	+	0.999411i	$0.510925\pi$
$728$	2.41470			0.0894946
$729$	−12.9653	+	23.6834i	−0.480194	+	0.877162i
$730$	5.03708			0.186431
$731$	52.5607	+	19.1305i	1.94403	+	0.707568i
$732$	15.7238	+	5.65564i	0.581167	+	0.209039i
$733$	26.1447	+	21.9380i	0.965677	+	0.810299i	0.981867	−	0.189569i	$-0.0607092\pi$
$733$	26.1447	+	21.9380i	0.965677	+	0.810299i	−0.0161900	+	0.999869i	$0.505154\pi$
$734$	−4.38594	+	24.8739i	−0.161888	+	0.918113i
$735$	1.41408	+	1.17746i	0.0521590	+	0.0434311i
$736$	−2.03055	+	1.70383i	−0.0748470	+	0.0628041i
$737$	14.2771	+	24.7287i	0.525905	+	0.910894i
$738$	3.08381	+	2.54807i	0.113517	+	0.0937959i
$739$	−1.61775	+	2.80203i	−0.0595100	+	0.103074i	−0.894246	−	0.447577i	$-0.852287\pi$
$739$	−1.61775	+	2.80203i	−0.0595100	+	0.103074i	0.834736	+	0.550651i	$0.185620\pi$
$740$	1.00912	+	5.72298i	0.0370959	+	0.210381i
$741$	3.16186	+	5.42891i	0.116154	+	0.199436i
$742$	−2.30988	+	0.840726i	−0.0847982	+	0.0308640i
$743$	34.2336	−	12.4600i	1.25591	−	0.457113i	0.373514	−	0.927625i	$-0.378153\pi$
$743$	34.2336	−	12.4600i	1.25591	−	0.457113i	0.882394	+	0.470512i	$0.155931\pi$
$744$	−1.82375	+	3.18664i	−0.0668621	+	0.116828i
$745$	−2.29901	−	13.0384i	−0.0842294	−	0.477688i
$746$	−12.1157	+	20.9850i	−0.443587	+	0.768315i
$747$	−23.4133	−	39.8529i	−0.856648	−	1.45814i
$748$	−10.2104	−	17.6850i	−0.373330	−	0.646627i
$749$	−1.94244	+	1.62990i	−0.0709753	+	0.0595553i
$750$	−15.3185	+	5.64127i	−0.559353	+	0.205990i
$751$	2.61699	−	14.8417i	0.0954954	−	0.541581i	−0.899099	−	0.437745i	$-0.855777\pi$
$751$	2.61699	−	14.8417i	0.0954954	−	0.541581i	0.994594	−	0.103836i	$-0.0331117\pi$
$752$	−6.38690	−	5.35924i	−0.232906	−	0.195432i
$753$	−1.69701	−	9.41557i	−0.0618425	−	0.343122i
$754$	−1.53563	−	0.558922i	−0.0559242	−	0.0203548i
$755$	22.2089			0.808263
$756$	−2.64903	−	4.47019i	−0.0963444	−	0.162579i
$757$	20.7868			0.755508			0.377754	−	0.925906i	$-0.376696\pi$
$757$	20.7868			0.755508			0.377754	+	0.925906i	$0.376696\pi$
$758$	7.29017	+	2.65341i	0.264791	+	0.0963761i
$759$	−10.9686	+	9.27480i	−0.398137	+	0.336654i
$760$	−1.22250	−	1.02580i	−0.0443449	−	0.0372098i
$761$	8.46900	−	48.0301i	0.307001	−	1.74109i	−0.306933	−	0.951731i	$-0.599303\pi$
$761$	8.46900	−	48.0301i	0.307001	−	1.74109i	0.613934	−	0.789357i	$-0.289586\pi$
$762$	−3.83260	+	22.2277i	−0.138841	+	0.805224i
$763$	12.2433	−	10.2733i	0.443236	−	0.371919i
$764$	−1.84657	−	3.19836i	−0.0668067	−	0.115713i
$765$	−3.76737	−	20.4585i	−0.136210	−	0.739678i
$766$	−16.4342	+	28.4649i	−0.593793	+	1.02848i
$767$	−3.43190	−	19.4633i	−0.123919	−	0.702778i
$768$	1.73204	−	0.00655936i	0.0624996	−	0.000236691i
$769$	−23.6173	+	8.59599i	−0.851662	+	0.309979i	−0.730718	−	0.682680i	$-0.760814\pi$
$769$	−23.6173	+	8.59599i	−0.851662	+	0.309979i	−0.120944	+	0.992659i	$0.538592\pi$
$770$	−3.12345	+	1.13684i	−0.112561	+	0.0409689i
$771$	10.0983	−	0.0382431i	0.363682	−	0.00137729i
$772$	0.646464	+	3.66628i	0.0232667	+	0.131952i
$773$	−11.8424	+	20.5116i	−0.425941	+	0.737751i	−0.996508	−	0.0835002i	$-0.973390\pi$
$773$	−11.8424	+	20.5116i	−0.425941	+	0.737751i	0.570567	+	0.821251i	$0.306723\pi$
$774$	−19.5686	+	16.6742i	−0.703379	+	0.599341i
$775$	−4.10324	−	7.10702i	−0.147393	−	0.255292i
$776$	−12.5845	+	10.5597i	−0.451759	+	0.379071i
$777$	1.60985	−	9.33654i	0.0577531	−	0.334947i
$778$	2.84323	−	16.1247i	0.101935	−	0.578100i
$779$	−1.53441	−	1.28752i	−0.0549758	−	0.0461302i
$780$	−3.39293	+	2.86898i	−0.121487	+	0.102726i
$781$	−19.1513	−	6.97052i	−0.685289	−	0.249425i
$782$	17.3009			0.618679
$783$	0.649951	+	3.45599i	0.0232274	+	0.123507i
$784$	1.00000			0.0357143
$785$	−6.60387	−	2.40361i	−0.235702	−	0.0857886i
$786$	−2.96212	−	16.4348i	−0.105655	−	0.586211i
$787$	−31.8102	−	26.6919i	−1.13391	−	0.951464i	−0.134688	−	0.990888i	$-0.543003\pi$
$787$	−31.8102	−	26.6919i	−1.13391	−	0.951464i	−0.999223	+	0.0394240i	$0.987448\pi$
$788$	1.43716	−	8.15056i	0.0511968	−	0.290352i
$789$	18.3778	−	6.76790i	0.654267	−	0.240944i
$790$	4.39982	−	3.69189i	0.156539	−	0.131352i
$791$	−8.07105	−	13.9795i	−0.286974	−	0.497053i
$792$	9.38584	−	0.0710908i	0.333511	−	0.00252610i
$793$	−11.6479	+	20.1748i	−0.413629	+	0.716426i
$794$	−3.05033	−	17.2993i	−0.108252	−	0.613929i
$795$	2.24676	−	3.92576i	0.0796842	−	0.139232i
$796$	26.4306	−	9.61996i	0.936808	−	0.340970i
$797$	−29.9378	+	10.8965i	−1.06045	+	0.385972i	−0.812597	−	0.582826i	$-0.801947\pi$
$797$	−29.9378	+	10.8965i	−1.06045	+	0.385972i	−0.247853	+	0.968798i	$0.579725\pi$
$798$	1.30942	+	2.24828i	0.0463530	+	0.0795882i
$799$	9.44965	+	53.5916i	0.334305	+	1.89594i
$800$	−1.93566	+	3.35267i	−0.0684361	+	0.118535i
$801$	−7.61212	+	45.1684i	−0.268961	+	1.59595i
$802$	0.432449	+	0.749023i	0.0152703	+	0.0264489i
$803$	11.3635	−	9.53513i	0.401010	−	0.336488i
$804$	12.1478	+	10.1150i	0.428418	+	0.356730i
$805$	0.489005	−	2.77329i	0.0172352	−	0.0977455i
$806$	−3.92115	−	3.29023i	−0.138117	−	0.115894i
$807$	−1.00816	−	0.362624i	−0.0354891	−	0.0127650i
$808$	−1.02233	−	0.372099i	−0.0359656	−	0.0130904i
$809$	19.5911			0.688785			0.344392	−	0.938826i	$-0.388085\pi$
$809$	19.5911			0.688785			0.344392	+	0.938826i	$0.388085\pi$
$810$	9.03338	+	3.13375i	0.317401	+	0.110109i
$811$	−47.7582			−1.67702			−0.838509	−	0.544888i	$-0.816572\pi$
$811$	−47.7582			−1.67702			−0.838509	+	0.544888i	$0.816572\pi$
$812$	−0.635950	−	0.231467i	−0.0223175	−	0.00812290i
$813$	21.2431	+	7.64089i	0.745030	+	0.267978i
$814$	13.1101	+	11.0007i	0.459508	+	0.385573i
$815$	−0.173903	+	0.986252i	−0.00609155	+	0.0345469i
$816$	−8.68758	−	7.23386i	−0.304126	−	0.253236i
$817$	9.86126	−	8.27458i	0.345002	−	0.289491i
$818$	−8.50758	−	14.7356i	−0.297460	−	0.515217i
$819$	6.78825	−	2.52911i	0.237201	−	0.0883743i
$820$	0.708317	−	1.22684i	0.0247355	−	0.0428431i
$821$	0.414459	+	2.35051i	0.0144647	+	0.0820335i	0.991186	−	0.132481i	$-0.0422943\pi$
$821$	0.414459	+	2.35051i	0.0144647	+	0.0820335i	−0.976721	+	0.214514i	$0.931183\pi$
$822$	14.6568	+	25.1658i	0.511215	+	0.877757i
$823$	−27.8128	+	10.1230i	−0.969493	+	0.352867i	−0.777747	−	0.628578i	$-0.783637\pi$
$823$	−27.8128	+	10.1230i	−0.969493	+	0.352867i	−0.191746	+	0.981445i	$0.561415\pi$
$824$	−3.00951	+	1.09537i	−0.104841	+	0.0381591i
$825$	−10.4206	+	18.2080i	−0.362800	+	0.633920i
$826$	−1.42126	−	8.06034i	−0.0494518	−	0.280455i
$827$	−23.1349	+	40.0708i	−0.804479	+	1.39340i	0.112164	+	0.993690i	$0.464222\pi$
$827$	−23.1349	+	40.0708i	−0.804479	+	1.39340i	−0.916642	+	0.399708i	$0.869111\pi$
$828$	−3.92377	+	6.91662i	−0.136360	+	0.240369i
$829$	−9.84482	−	17.0517i	−0.341925	−	0.592231i	0.642865	−	0.765979i	$-0.277745\pi$
$829$	−9.84482	−	17.0517i	−0.341925	−	0.592231i	−0.984790	+	0.173748i	$0.944412\pi$
$830$	−12.5390	+	10.5214i	−0.435233	+	0.365204i
$831$	−14.8962	+	5.48575i	−0.516743	+	0.190298i
$832$	−0.419308	+	2.37801i	−0.0145369	+	0.0824427i
$833$	−4.99993	−	4.19544i	−0.173237	−	0.145363i
$834$	−2.06983	−	11.4841i	−0.0716723	−	0.397662i
$835$	21.4248	+	7.79799i	0.741436	+	0.269861i
$836$	−4.69978			−0.162545
$837$	−1.78935	+	10.8685i	−0.0618489	+	0.375672i
$838$	−22.9429			−0.792551
$839$	36.9916	+	13.4639i	1.27709	+	0.464824i	0.889470	−	0.456994i	$-0.151074\pi$
$839$	36.9916	+	13.4639i	1.27709	+	0.464824i	0.387624	+	0.921818i	$0.373296\pi$
$840$	−1.40512	+	1.18813i	−0.0484812	+	0.0409944i
$841$	−21.8644	−	18.3464i	−0.753946	−	0.632636i
$842$	−5.48117	+	31.0853i	−0.188894	+	1.07127i
$843$	6.04829	−	35.0778i	0.208314	−	1.20814i
$844$	18.7893	−	15.7661i	0.646754	−	0.542691i
$845$	3.80827	+	6.59611i	0.131008	+	0.226913i
$846$	−23.5682	−	8.37652i	−0.810291	−	0.287991i
$847$	0.605605	−	1.04894i	0.0208088	−	0.0360420i
$848$	−0.426848	−	2.42077i	−0.0146580	−	0.0831297i
$849$	−37.6487	+	0.142579i	−1.29210	+	0.00489329i
$850$	23.7441	−	8.64214i	0.814415	−	0.296423i
$851$	−13.6249	+	4.95905i	−0.467055	+	0.169994i
$852$	−11.2825	+	0.0427278i	−0.386533	+	0.00146383i
$853$	3.10167	+	17.5904i	0.106199	+	0.602285i	0.990735	+	0.135812i	$0.0433643\pi$
$853$	3.10167	+	17.5904i	0.106199	+	0.602285i	−0.884536	+	0.466473i	$0.845525\pi$
$854$	−4.82375	+	8.35499i	−0.165065	+	0.285902i
$855$	−4.51115	−	1.60333i	−0.154278	−	0.0548329i
$856$	−1.26784	−	2.19596i	−0.0433338	−	0.0750564i
$857$	−2.38086	+	1.99778i	−0.0813287	+	0.0682428i	−0.682546	−	0.730843i	$-0.739127\pi$
$857$	−2.38086	+	1.99778i	−0.0813287	+	0.0682428i	0.601217	+	0.799086i	$0.294683\pi$
$858$	−2.22344	+	12.8951i	−0.0759070	+	0.440233i
$859$	−0.000601735		0.00341261i	−2.05309e−5		0.000116437i	−0.984818	−	0.173590i	$-0.944463\pi$
$859$	−0.000601735		0.00341261i	−2.05309e−5		0.000116437i	0.984797	+	0.173706i	$0.0555744\pi$
$860$	6.97435	+	5.85217i	0.237823	+	0.199557i
$861$	−1.76361	+	1.49126i	−0.0601037	+	0.0508221i
$862$	−22.0577	−	8.02834i	−0.751288	−	0.273446i
$863$	−1.57071			−0.0534677			−0.0267338	−	0.999643i	$-0.508511\pi$
$863$	−1.57071			−0.0534677			−0.0267338	+	0.999643i	$0.508511\pi$
$864$	4.86228	−	1.83255i	0.165418	−	0.0623445i
$865$	9.75758			0.331768
$866$	−28.2330	−	10.2760i	−0.959395	−	0.349191i
$867$	7.86525	+	43.6390i	0.267118	+	1.48206i
$868$	−1.62387	−	1.36259i	−0.0551177	−	0.0462492i
$869$	2.93719	−	16.6576i	0.0996374	−	0.565072i
$870$	1.16860	−	0.430354i	0.0396192	−	0.0145904i
$871$	−16.8820	+	14.1657i	−0.572024	+	0.479985i
$872$	7.99123	+	13.8412i	0.270617	+	0.468723i
$873$	−24.3180	+	42.8665i	−0.823038	+	1.45081i
$874$	1.99087	−	3.44828i	0.0673421	−	0.116640i
$875$	−1.63660	−	9.28162i	−0.0553272	−	0.313776i
$876$	4.07910	−	7.12740i	0.137820	−	0.240813i
$877$	5.34817	−	1.94657i	0.180595	−	0.0657311i	−0.250140	−	0.968210i	$-0.580477\pi$
$877$	5.34817	−	1.94657i	0.180595	−	0.0657311i	0.430735	+	0.902479i	$0.358254\pi$
$878$	27.3347	−	9.94902i	0.922502	−	0.335763i
$879$	3.27680	+	5.62626i	0.110524	+	0.189769i
$880$	−0.577190	−	3.27341i	−0.0194571	−	0.110346i
$881$	0.351844	−	0.609411i	0.0118539	−	0.0205316i	−0.860038	−	0.510231i	$-0.829560\pi$
$881$	0.351844	−	0.609411i	0.0118539	−	0.0205316i	0.871892	+	0.489699i	$0.162893\pi$
$882$	2.81123	−	1.04738i	0.0946589	−	0.0352672i
$883$	10.2695	+	17.7873i	0.345597	+	0.598591i	0.985462	−	0.169896i	$-0.0543431\pi$
$883$	10.2695	+	17.7873i	0.345597	+	0.598591i	−0.639865	+	0.768487i	$0.721010\pi$
$884$	12.0733	−	10.1307i	0.406069	−	0.340732i
$885$	11.5738	+	9.63710i	0.389048	+	0.323948i
$886$	5.53935	−	31.4152i	0.186098	−	1.05541i
$887$	24.5981	+	20.6402i	0.825922	+	0.693031i	0.954351	−	0.298688i	$-0.0965490\pi$
$887$	24.5981	+	20.6402i	0.825922	+	0.693031i	−0.128429	+	0.991719i	$0.540993\pi$
$888$	8.91515	+	3.20667i	0.299173	+	0.107609i
$889$	−12.2372	−	4.45397i	−0.410422	−	0.149381i
$890$	16.2210			0.543730
$891$	26.3113	−	10.0304i	0.881460	−	0.336032i
$892$	0.325469			0.0108975
$893$	11.7689	+	4.28352i	0.393830	+	0.143342i
$894$	−20.3109	−	7.30557i	−0.679298	−	0.244335i
$895$	9.18318	+	7.70560i	0.306960	+	0.257570i
$896$	−0.173648	+	0.984808i	−0.00580118	+	0.0329001i
$897$	−8.51944	−	7.09386i	−0.284456	−	0.236857i
$898$	−13.0426	+	10.9440i	−0.435237	+	0.365207i
$899$	0.717306	+	1.24241i	0.0239235	+	0.0414367i
$900$	−1.93006	+	11.4525i	−0.0643354	+	0.381750i
$901$	−8.02199	+	13.8945i	−0.267251	+	0.462893i
$902$	−0.724450	−	4.10856i	−0.0241215	−	0.136800i
$903$	−7.47021	−	12.8264i	−0.248593	−	0.426834i
$904$	15.1686	−	5.52093i	0.504501	−	0.183623i
$905$	−4.56894	+	1.66296i	−0.151877	+	0.0552786i
$906$	17.9851	−	31.4253i	0.597514	−	1.04403i
$907$	−7.07716	−	40.1366i	−0.234993	−	1.33271i	−0.842628	−	0.538496i	$-0.818993\pi$
$907$	−7.07716	−	40.1366i	−0.234993	−	1.33271i	0.607635	−	0.794217i	$-0.292118\pi$
$908$	−6.81910	+	11.8110i	−0.226300	+	0.391963i
$909$	−3.26374	+	0.0247204i	−0.108251	+	0.000819925i
$910$	−1.28267	−	2.22166i	−0.0425202	−	0.0736472i
$911$	−18.5973	+	15.6050i	−0.616156	+	0.517017i	−0.896593	−	0.442856i	$-0.853965\pi$
$911$	−18.5973	+	15.6050i	−0.616156	+	0.517017i	0.280436	+	0.959873i	$0.409521\pi$
$912$	−2.44150	+	0.899120i	−0.0808462	+	0.0297728i
$913$	−8.37063	+	47.4722i	−0.277027	+	1.57110i
$914$	−11.9686	−	10.0428i	−0.395886	−	0.332187i
$915$	−3.14888	−	17.4710i	−0.104099	−	0.577574i
$916$	−26.5031	−	9.64633i	−0.875686	−	0.318724i
$917$	9.64154			0.318392
$918$	−31.9994	−	11.2368i	−1.05614	−	0.370869i
$919$	−39.6901			−1.30926			−0.654628	−	0.755951i	$-0.727175\pi$
$919$	−39.6901			−1.30926			−0.654628	+	0.755951i	$0.727175\pi$
$920$	2.64624	+	0.963152i	0.0872439	+	0.0317542i
$921$	5.93783	−	5.02087i	0.195658	−	0.165443i
$922$	−13.0503	−	10.9505i	−0.429788	−	0.360635i
$923$	2.73138	−	15.4904i	0.0899043	−	0.509873i
$924$	−0.920795	+	5.34027i	−0.0302919	+	0.175682i
$925$	−16.2219	+	13.6118i	−0.533372	+	0.447552i
$926$	12.3142	+	21.3288i	0.404670	+	0.700909i
$927$	−7.31313	+	6.23144i	−0.240195	+	0.204667i
$928$	0.338382	−	0.586095i	0.0111079	−	0.0192395i
$929$	−3.59199	−	20.3712i	−0.117849	−	0.668357i	−0.985300	−	0.170833i	$-0.945354\pi$
$929$	−3.59199	−	20.3712i	−0.117849	−	0.668357i	0.867451	−	0.497523i	$-0.165757\pi$
$930$	3.90066	−	0.0147721i	0.127908	−	0.000484396i
$931$	−1.41156	+	0.513765i	−0.0462619	+	0.0168380i
$932$	18.8506	−	6.86106i	0.617472	−	0.224742i
$933$	24.7289	−	0.0936503i	0.809589	−	0.00306597i
$934$	2.04200	+	11.5808i	0.0668164	+	0.378935i
$935$	−10.8475	+	18.7883i	−0.354750	+	0.614445i
$936$	1.31192	+	7.12430i	0.0428814	+	0.232865i
$937$	−17.8822	−	30.9729i	−0.584186	−	1.01184i	−0.994976	−	0.100110i	$-0.968081\pi$
$937$	−17.8822	−	30.9729i	−0.584186	−	1.01184i	0.410790	−	0.911730i	$-0.365253\pi$
$938$	−6.99134	+	5.86643i	−0.228275	+	0.191546i
$939$	−2.14407	+	12.4348i	−0.0699692	+	0.405795i
$940$	−1.53812	+	8.72311i	−0.0501679	+	0.284516i
$941$	6.46631	+	5.42588i	0.210796	+	0.176879i	0.742072	−	0.670320i	$-0.233843\pi$
$941$	6.46631	+	5.42588i	0.210796	+	0.176879i	−0.531277	+	0.847198i	$0.678287\pi$
$942$	−8.74900	+	7.39792i	−0.285058	+	0.241037i
$943$	3.32138	+	1.20888i	0.108159	+	0.0393667i
$944$	8.18469			0.266389
$945$	−2.70568	+	4.81180i	−0.0880157	+	0.156528i
$946$	26.8121			0.871736
$947$	−1.96694	−	0.715906i	−0.0639168	−	0.0232638i	0.309864	−	0.950781i	$-0.399717\pi$
$947$	−1.96694	−	0.715906i	−0.0639168	−	0.0232638i	−0.373781	+	0.927517i	$0.621939\pi$
$948$	−1.66094	−	9.21545i	−0.0539448	−	0.299304i
$949$	8.77023	+	7.35910i	0.284694	+	0.238886i
$950$	1.00982	−	5.72696i	0.0327628	−	0.185807i
$951$	53.1155	−	19.5606i	1.72239	−	0.634295i
$952$	4.99993	−	4.19544i	0.162049	−	0.135975i
$953$	−27.4754	−	47.5887i	−0.890014	−	1.54155i	−0.839856	−	0.542809i	$-0.817361\pi$
$953$	−27.4754	−	47.5887i	−0.890014	−	1.54155i	−0.0501582	−	0.998741i	$-0.515973\pi$
$954$	−3.73544	−	6.35827i	−0.120939	−	0.205857i
$955$	−1.96178	+	3.39791i	−0.0634818	+	0.109954i
$956$	4.47638	+	25.3868i	0.144777	+	0.821069i
$957$	1.82168	−	3.18301i	0.0588865	−	0.102892i
$958$	19.4507	−	7.07947i	0.628423	−	0.228727i
$959$	−15.8001	+	5.75075i	−0.510210	+	0.185701i
$960$	−0.926085	−	1.59009i	−0.0298893	−	0.0513199i
$961$	−4.60279	−	26.1037i	−0.148477	−	0.842055i
$962$	−6.60419	+	11.4388i	−0.212928	+	0.368802i
$963$	−5.86419	−	4.84543i	−0.188971	−	0.156142i
$964$	−8.35247	−	14.4669i	−0.269015	−	0.465948i
$965$	3.02979	−	2.54229i	0.0975322	−	0.0818393i
$966$	−3.52816	−	2.93778i	−0.113517	−	0.0945217i
$967$	7.39603	−	41.9450i	0.237840	−	1.34886i	−0.598709	−	0.800967i	$-0.704319\pi$
$967$	7.39603	−	41.9450i	0.237840	−	1.34886i	0.836549	−	0.547892i	$-0.184570\pi$
$968$	0.927841	+	0.778551i	0.0298219	+	0.0250236i
$969$	15.9795	+	5.74763i	0.513336	+	0.184641i
$970$	16.4004	+	5.96924i	0.526584	+	0.191661i
$971$	16.1495			0.518262			0.259131	−	0.965842i	$-0.416564\pi$
$971$	16.1495			0.518262			0.259131	+	0.965842i	$0.416564\pi$
$972$	11.7496	−	10.2444i	0.376868	−	0.328588i
$973$	6.73718			0.215984
$974$	8.58814	+	3.12583i	0.275182	+	0.100158i
$975$	−15.2358	−	5.48011i	−0.487935	−	0.175504i
$976$	−7.39042	−	6.20130i	−0.236562	−	0.198499i
$977$	−1.41408	+	8.01964i	−0.0452404	+	0.256571i	−0.999037	−	0.0438831i	$-0.986027\pi$
$977$	−1.41408	+	8.01964i	−0.0452404	+	0.256571i	0.953796	+	0.300454i	$0.0971382\pi$
$978$	1.25471	+	1.04475i	0.0401211	+	0.0334075i
$979$	36.5943	−	30.7062i	1.16956	−	0.981375i
$980$	−0.531195	−	0.920056i	−0.0169684	−	0.0293901i
$981$	36.9622	+	30.5409i	1.18011	+	0.975096i
$982$	8.51843	−	14.7544i	0.271834	−	0.470831i
$983$	1.26879	+	7.19565i	0.0404680	+	0.229506i	0.998333	−	0.0577125i	$-0.0183807\pi$
$983$	1.26879	+	7.19565i	0.0404680	+	0.229506i	−0.957865	+	0.287218i	$0.907270\pi$
$984$	−1.16236	−	1.99577i	−0.0370547	−	0.0636229i
$985$	−8.26239	+	3.00726i	−0.263262	+	0.0958194i
$986$	−4.15081	+	1.51077i	−0.132189	+	0.0481128i
$987$	7.17308	−	12.5335i	0.228322	−	0.398946i
$988$	−0.629862	−	3.57213i	−0.0200386	−	0.113644i
$989$	−11.3578	+	19.6723i	−0.361158	+	0.625544i
$990$	−5.05112	−	8.59774i	−0.160535	−	0.273254i
$991$	4.86555	+	8.42737i	0.154559	+	0.267704i	0.932898	−	0.360140i	$-0.117271\pi$
$991$	4.86555	+	8.42737i	0.154559	+	0.267704i	−0.778339	+	0.627844i	$0.783938\pi$
$992$	1.62387	−	1.36259i	0.0515579	−	0.0432622i
$993$	−47.5654	+	17.5167i	−1.50944	+	0.555874i
$994$	1.13115	−	6.41505i	0.0358778	−	0.203473i
$995$	−22.8907	−	19.2076i	−0.725684	−	0.608921i
$996$	4.73348	+	26.2629i	0.149986	+	0.832171i
$997$	−42.3323	−	15.4077i	−1.34068	−	0.487967i	−0.430652	−	0.902518i	$-0.641716\pi$
$997$	−42.3323	−	15.4077i	−1.34068	−	0.487967i	−0.910026	+	0.414551i	$0.863939\pi$
$998$	41.3846			1.31001
$999$	28.4211	−	0.322911i	0.899204	−	0.0102165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.85.1	✓	36
27.7	even	9	inner	378.2.u.e.169.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.85.1	✓	36	1.1	even	1	trivial
378.2.u.e.169.1	yes	36	27.7	even	9	inner

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-1.62983 - 0.586228i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.184482 - 1.04625i) q^{5} +(-1.33103 - 1.10831i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.31267 + 1.91090i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-1.62983 - 0.586228i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.184482 - 1.04625i) q^{5} +(-1.33103 - 1.10831i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.31267 + 1.91090i) q^{9} +(0.531195 - 0.920056i) q^{10} +(-0.543294 - 3.08117i) q^{11} +(-0.871700 - 1.49671i) q^{12} +(2.26907 - 0.825875i) q^{13} +(0.939693 - 0.342020i) q^{14} +(-0.914015 + 1.59706i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.26347 - 5.65249i) q^{17} +(1.51963 + 2.58664i) q^{18} +(-0.751074 - 1.30090i) q^{19} +(0.813838 - 0.682891i) q^{20} +(-1.62534 + 0.598556i) q^{21} +(0.543294 - 3.08117i) q^{22} +(2.03055 + 1.70383i) q^{23} +(-0.307225 - 1.70459i) q^{24} +(3.63786 + 1.32407i) q^{25} +2.41470 q^{26} +(-2.64903 - 4.47019i) q^{27} +1.00000 q^{28} +(-0.635950 - 0.231467i) q^{29} +(-1.40512 + 1.18813i) q^{30} +(-1.62387 - 1.36259i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.920795 + 5.34027i) q^{33} +(4.99993 - 4.19544i) q^{34} +(-0.531195 - 0.920056i) q^{35} +(0.543307 + 2.95039i) q^{36} +(-2.73500 + 4.73716i) q^{37} +(-0.260845 - 1.47933i) q^{38} +(-4.18235 + 0.0158389i) q^{39} +(0.998320 - 0.363359i) q^{40} +(1.25302 - 0.456064i) q^{41} +(-1.73204 + 0.00655936i) q^{42} +(1.48811 + 8.43951i) q^{43} +(1.56435 - 2.70954i) q^{44} +(2.42593 - 2.06711i) q^{45} +(1.32535 + 2.29557i) q^{46} +(-6.38690 + 5.35924i) q^{47} +(0.294306 - 1.70686i) q^{48} +(0.173648 - 0.984808i) q^{49} +(2.96561 + 2.48844i) q^{50} +(-8.63254 + 7.29945i) q^{51} +(2.26907 + 0.825875i) q^{52} -2.45812 q^{53} +(-0.960380 - 5.10663i) q^{54} -3.32390 q^{55} +(0.939693 + 0.342020i) q^{56} +(0.461498 + 2.56054i) q^{57} +(-0.518432 - 0.435016i) q^{58} +(1.42126 - 8.06034i) q^{59} +(-1.72674 + 0.635899i) q^{60} +(-7.39042 + 6.20130i) q^{61} +(-1.05991 - 1.83581i) q^{62} +(2.99991 - 0.0227221i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.445468 - 2.52637i) q^{65} +(-2.69175 + 4.70328i) q^{66} +(-8.57615 + 3.12146i) q^{67} +(6.13332 - 2.23234i) q^{68} +(-2.31061 - 3.96732i) q^{69} +(-0.184482 - 1.04625i) q^{70} +(3.25701 - 5.64130i) q^{71} +(-0.498553 + 2.95828i) q^{72} +(2.37064 + 4.10606i) q^{73} +(-4.19026 + 3.51605i) q^{74} +(-5.15287 - 4.29062i) q^{75} +(0.260845 - 1.47933i) q^{76} +(-2.39673 - 2.01109i) q^{77} +(-3.93554 - 1.41556i) q^{78} +(5.08023 + 1.84905i) q^{79} +1.06239 q^{80} +(1.69691 + 8.83858i) q^{81} +1.33344 q^{82} +(-14.4780 - 5.26957i) q^{83} +(-1.62983 - 0.586228i) q^{84} +(-5.31187 - 4.45719i) q^{85} +(-1.48811 + 8.43951i) q^{86} +(0.900797 + 0.750063i) q^{87} +(2.39673 - 2.01109i) q^{88} +(7.63422 + 13.2229i) q^{89} +(2.98662 - 1.11273i) q^{90} +(1.20735 - 2.09119i) q^{91} +(0.460288 + 2.61042i) q^{92} +(1.84784 + 3.17274i) q^{93} +(-7.83469 + 2.85159i) q^{94} +(-1.49962 + 0.545819i) q^{95} +(0.860339 - 1.50327i) q^{96} +(2.85268 + 16.1784i) q^{97} +(0.500000 - 0.866025i) q^{98} +(4.63136 - 8.16392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Introduction

L-functions

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