LMFDB - Embedded newform 370.2.v.b.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(99,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.v (of order $18$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.5
Character	$\chi$	$=$	370.289
Dual form			370.2.v.b.169.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.362370 + 0.995603i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.12894 - 0.683822i) q^{5} +1.05950i q^{6} +(-1.06185 + 0.187234i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.43822 + 1.20681i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.362370 + 0.995603i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.12894 - 0.683822i) q^{5} +1.05950i q^{6} +(-1.06185 + 0.187234i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.43822 + 1.20681i) q^{9} +(1.76667 - 1.37072i) q^{10} +(0.436261 - 0.755627i) q^{11} +(0.362370 + 0.995603i) q^{12} +(1.18263 - 0.992348i) q^{13} +(-0.933779 + 0.539117i) q^{14} +(-0.0906487 + 2.36738i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.626355 - 0.525574i) q^{17} +(1.76424 + 0.642130i) q^{18} +(-0.570090 + 1.56631i) q^{19} +(1.19131 - 1.89229i) q^{20} +(0.198374 - 1.12503i) q^{21} +(0.151512 - 0.859267i) q^{22} +(2.32537 + 4.02766i) q^{23} +(0.681032 + 0.811623i) q^{24} +(4.06478 - 2.91163i) q^{25} +(0.771910 - 1.33699i) q^{26} +(-4.47533 + 2.58383i) q^{27} +(-0.693076 + 0.825976i) q^{28} +(-1.84171 - 1.06331i) q^{29} +(0.724508 + 2.25561i) q^{30} -2.18324i q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.594216 + 0.708159i) q^{33} +(-0.768338 - 0.279652i) q^{34} +(-2.13259 + 1.12473i) q^{35} +1.87746 q^{36} +(-4.86631 - 3.64952i) q^{37} +1.66683i q^{38} +(0.559434 + 1.53703i) q^{39} +(0.472263 - 2.18563i) q^{40} +(1.27193 - 1.06727i) q^{41} +(-0.198374 - 1.12503i) q^{42} -2.12972 q^{43} +(-0.151512 - 0.859267i) q^{44} +(3.88713 + 1.58574i) q^{45} +(3.56267 + 2.98944i) q^{46} +(-4.23630 + 2.44583i) q^{47} +(0.917552 + 0.529749i) q^{48} +(-5.48537 + 1.99651i) q^{49} +(2.82380 - 4.12627i) q^{50} +(0.750235 - 0.433149i) q^{51} +(0.268082 - 1.52037i) q^{52} +(4.91073 + 0.865893i) q^{53} +(-3.32171 + 3.95866i) q^{54} +(0.412060 - 1.90701i) q^{55} +(-0.368778 + 1.01321i) q^{56} +(-1.35284 - 1.13517i) q^{57} +(-2.09432 - 0.369284i) q^{58} +(-10.8290 - 1.90944i) q^{59} +(1.45228 + 1.87178i) q^{60} +(1.22233 + 1.45671i) q^{61} +(-0.746712 - 2.05157i) q^{62} +(-1.75314 - 1.01217i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.83917 - 2.92136i) q^{65} +(0.800585 + 0.462218i) q^{66} +(-5.75930 + 1.01552i) q^{67} -0.817648 q^{68} +(-4.85259 + 0.855643i) q^{69} +(-1.61930 + 1.78629i) q^{70} +(-10.2016 - 3.71309i) q^{71} +(1.76424 - 0.642130i) q^{72} -10.5379i q^{73} +(-5.82105 - 1.76505i) q^{74} +(1.42588 + 5.10199i) q^{75} +(0.570090 + 1.56631i) q^{76} +(-0.321767 + 0.884048i) q^{77} +(1.05139 + 1.25300i) q^{78} +(-4.86694 + 0.858174i) q^{79} +(-0.303747 - 2.21534i) q^{80} +(0.0273076 + 0.154869i) q^{81} +(0.830191 - 1.43793i) q^{82} +(2.61137 - 3.11211i) q^{83} +(-0.571194 - 0.989337i) q^{84} +(-1.69287 - 0.690601i) q^{85} +(-2.00128 + 0.728408i) q^{86} +(1.72602 - 1.44830i) q^{87} +(-0.436261 - 0.755627i) q^{88} +(-15.0870 - 2.66025i) q^{89} +(4.19506 + 0.160632i) q^{90} +(-1.06998 + 1.27516i) q^{91} +(4.37026 + 1.59065i) q^{92} +(2.17364 + 0.791140i) q^{93} +(-3.14430 + 3.74723i) q^{94} +(-0.142611 + 3.72442i) q^{95} +(1.04340 + 0.183980i) q^{96} +(5.51919 + 9.55952i) q^{97} +(-4.47172 + 3.75221i) q^{98} +(1.53934 - 0.560273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9	$ 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} - 6 q^{15} - 3 q^{17} - 12 q^{18} + 3 q^{19} + 3 q^{20} + 12 q^{21} + 3 q^{22} + 18 q^{23} - 18 q^{25} - 27 q^{26} + 18 q^{30} + 66 q^{33} + 21 q^{34} + 9 q^{35} - 72 q^{36} - 6 q^{37} + 12 q^{39} + 12 q^{40} - 57 q^{41} - 12 q^{42} - 60 q^{43} - 3 q^{44} + 9 q^{45} - 21 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{55} - 30 q^{57} - 15 q^{58} - 12 q^{59} - 9 q^{60} + 42 q^{61} + 12 q^{62} + 9 q^{63} - 30 q^{64} - 15 q^{65} + 18 q^{67} + 24 q^{68} + 36 q^{69} - 12 q^{70} + 18 q^{71} - 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} - 21 q^{77} - 6 q^{78} - 24 q^{79} - 36 q^{81} - 27 q^{82} - 30 q^{83} + 12 q^{84} - 30 q^{85} - 18 q^{86} + 30 q^{87} - 6 q^{88} + 3 q^{89} + 57 q^{91} - 15 q^{92} - 60 q^{93} + 3 q^{94} + 6 q^{95} - 84 q^{97} + 6 q^{98} - 45 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 - 6 * q^15 - 3 * q^17 - 12 * q^18 + 3 * q^19 + 3 * q^20 + 12 * q^21 + 3 * q^22 + 18 * q^23 - 18 * q^25 - 27 * q^26 + 18 * q^30 + 66 * q^33 + 21 * q^34 + 9 * q^35 - 72 * q^36 - 6 * q^37 + 12 * q^39 + 12 * q^40 - 57 * q^41 - 12 * q^42 - 60 * q^43 - 3 * q^44 + 9 * q^45 - 21 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^55 - 30 * q^57 - 15 * q^58 - 12 * q^59 - 9 * q^60 + 42 * q^61 + 12 * q^62 + 9 * q^63 - 30 * q^64 - 15 * q^65 + 18 * q^67 + 24 * q^68 + 36 * q^69 - 12 * q^70 + 18 * q^71 - 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 - 21 * q^77 - 6 * q^78 - 24 * q^79 - 36 * q^81 - 27 * q^82 - 30 * q^83 + 12 * q^84 - 30 * q^85 - 18 * q^86 + 30 * q^87 - 6 * q^88 + 3 * q^89 + 57 * q^91 - 15 * q^92 - 60 * q^93 + 3 * q^94 + 6 * q^95 - 84 * q^97 + 6 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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
$3$	−0.362370	+	0.995603i	−0.209214	+	0.574812i	−0.999269	−	0.0382246i	$-0.987830\pi$
$3$	−0.362370	+	0.995603i	−0.209214	+	0.574812i	0.790055	+	0.613036i	$0.210052\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	2.12894	−	0.683822i	0.952091	−	0.305814i
$5$	2.12894	−	0.683822i	0.952091	−	0.305814i
$6$			1.05950i			0.432538i
$7$	−1.06185	+	0.187234i	−0.401343	+	0.0707676i	−0.370676	−	0.928762i	$-0.620874\pi$
$7$	−1.06185	+	0.187234i	−0.401343	+	0.0707676i	−0.0306666	+	0.999530i	$0.509763\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.43822	+	1.20681i	0.479407	+	0.402270i
$10$	1.76667	−	1.37072i	0.558670	−	0.433461i
$11$	0.436261	−	0.755627i	0.131538	−	0.227830i	−0.792732	−	0.609571i	$-0.791342\pi$
$11$	0.436261	−	0.755627i	0.131538	−	0.227830i	0.924270	+	0.381741i	$0.124675\pi$
$12$	0.362370	+	0.995603i	0.104607	+	0.287406i
$13$	1.18263	−	0.992348i	0.328004	−	0.275228i	−0.463882	−	0.885897i	$-0.653544\pi$
$13$	1.18263	−	0.992348i	0.328004	−	0.275228i	0.791886	+	0.610669i	$0.209099\pi$
$14$	−0.933779	+	0.539117i	−0.249563	+	0.144085i
$15$	−0.0906487	+	2.36738i	−0.0234054	+	0.611254i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.626355	−	0.525574i	−0.151913	−	0.127470i	0.563663	−	0.826005i	$-0.309392\pi$
$17$	−0.626355	−	0.525574i	−0.151913	−	0.127470i	−0.715577	+	0.698534i	$0.753836\pi$
$18$	1.76424	+	0.642130i	0.415835	+	0.151352i
$19$	−0.570090	+	1.56631i	−0.130788	+	0.359336i	−0.987750	−	0.156042i	$-0.950126\pi$
$19$	−0.570090	+	1.56631i	−0.130788	+	0.359336i	0.856963	+	0.515378i	$0.172349\pi$
$20$	1.19131	−	1.89229i	0.266385	−	0.423130i
$21$	0.198374	−	1.12503i	0.0432887	−	0.245502i
$22$	0.151512	−	0.859267i	0.0323025	−	0.183196i
$23$	2.32537	+	4.02766i	0.484873	+	0.839825i	0.999849	−	0.0173800i	$-0.00553250\pi$
$23$	2.32537	+	4.02766i	0.484873	+	0.839825i	−0.514976	+	0.857205i	$0.672199\pi$
$24$	0.681032	+	0.811623i	0.139015	+	0.165672i
$25$	4.06478	−	2.91163i	0.812955	−	0.582326i
$26$	0.771910	−	1.33699i	0.151384	−	0.262205i
$27$	−4.47533	+	2.58383i	−0.861277	+	0.497259i
$28$	−0.693076	+	0.825976i	−0.130979	+	0.156095i
$29$	−1.84171	−	1.06331i	−0.341997	−	0.197452i	0.319158	−	0.947702i	$-0.396600\pi$
$29$	−1.84171	−	1.06331i	−0.341997	−	0.197452i	−0.661155	+	0.750249i	$0.729933\pi$
$30$	0.724508	+	2.25561i	0.132276	+	0.411816i
$31$		−	2.18324i		−	0.392122i	−0.980592	−	0.196061i	$-0.937185\pi$
$31$		−	2.18324i		−	0.392122i	0.980592	−	0.196061i	$-0.0628150\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.594216	+	0.708159i	0.103440	+	0.123275i
$34$	−0.768338	−	0.279652i	−0.131769	−	0.0479600i
$35$	−2.13259	+	1.12473i	−0.360473	+	0.190114i
$36$	1.87746			0.312911
$37$	−4.86631	−	3.64952i	−0.800017	−	0.599977i
$37$	−4.86631	−	3.64952i	−0.800017	−	0.599977i
$38$			1.66683i			0.270396i
$39$	0.559434	+	1.53703i	0.0895811	+	0.246122i
$40$	0.472263	−	2.18563i	0.0746713	−	0.345578i
$41$	1.27193	−	1.06727i	0.198642	−	0.166680i	−0.538041	−	0.842919i	$-0.680836\pi$
$41$	1.27193	−	1.06727i	0.198642	−	0.166680i	0.736683	+	0.676238i	$0.236391\pi$
$42$	−0.198374	−	1.12503i	−0.0306097	−	0.173596i
$43$	−2.12972			−0.324780			−0.162390	−	0.986727i	$-0.551920\pi$
$43$	−2.12972			−0.324780			−0.162390	+	0.986727i	$0.551920\pi$
$44$	−0.151512	−	0.859267i	−0.0228413	−	0.129539i
$45$	3.88713	+	1.58574i	0.579459	+	0.236388i
$46$	3.56267	+	2.98944i	0.525287	+	0.440768i
$47$	−4.23630	+	2.44583i	−0.617928	+	0.356761i	−0.776062	−	0.630657i	$-0.782786\pi$
$47$	−4.23630	+	2.44583i	−0.617928	+	0.356761i	0.158134	+	0.987418i	$0.449452\pi$
$48$	0.917552	+	0.529749i	0.132437	+	0.0764627i
$49$	−5.48537	+	1.99651i	−0.783624	+	0.285216i
$50$	2.82380	−	4.12627i	0.399346	−	0.583543i
$51$	0.750235	−	0.433149i	0.105054	−	0.0606529i
$52$	0.268082	−	1.52037i	0.0371762	−	0.210837i
$53$	4.91073	+	0.865893i	0.674540	+	0.118940i	0.500417	−	0.865784i	$-0.333180\pi$
$53$	4.91073	+	0.865893i	0.674540	+	0.118940i	0.174123	+	0.984724i	$0.444291\pi$
$54$	−3.32171	+	3.95866i	−0.452028	+	0.538705i
$55$	0.412060	−	1.90701i	0.0555622	−	0.257141i
$56$	−0.368778	+	1.01321i	−0.0492800	+	0.135396i
$57$	−1.35284	−	1.13517i	−0.179188	−	0.150357i
$58$	−2.09432	−	0.369284i	−0.274997	−	0.0484894i
$59$	−10.8290	−	1.90944i	−1.40981	−	0.248588i	−0.583642	−	0.812011i	$-0.698373\pi$
$59$	−10.8290	−	1.90944i	−1.40981	−	0.248588i	−0.826168	+	0.563423i	$0.809484\pi$
$60$	1.45228	+	1.87178i	0.187488	+	0.241646i
$61$	1.22233	+	1.45671i	0.156503	+	0.186513i	0.838598	−	0.544750i	$-0.183376\pi$
$61$	1.22233	+	1.45671i	0.156503	+	0.186513i	−0.682095	+	0.731263i	$0.738931\pi$
$62$	−0.746712	−	2.05157i	−0.0948325	−	0.260550i
$63$	−1.75314	−	1.01217i	−0.220874	−	0.127522i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.83917	−	2.92136i	0.228121	−	0.362350i
$66$	0.800585	+	0.462218i	0.0985452	+	0.0568951i
$67$	−5.75930	+	1.01552i	−0.703610	+	0.124065i	−0.513995	−	0.857793i	$-0.671835\pi$
$67$	−5.75930	+	1.01552i	−0.703610	+	0.124065i	−0.189615	+	0.981859i	$0.560724\pi$
$68$	−0.817648			−0.0991544
$69$	−4.85259	+	0.855643i	−0.584183	+	0.103007i
$70$	−1.61930	+	1.78629i	−0.193543	+	0.213502i
$71$	−10.2016	−	3.71309i	−1.21071	−	0.440663i	−0.343761	−	0.939057i	$-0.611701\pi$
$71$	−10.2016	−	3.71309i	−1.21071	−	0.440663i	−0.866951	+	0.498394i	$0.833923\pi$
$72$	1.76424	−	0.642130i	0.207917	−	0.0756758i
$73$		−	10.5379i		−	1.23336i	−0.787212	−	0.616682i	$-0.788477\pi$
$73$		−	10.5379i		−	1.23336i	0.787212	−	0.616682i	$-0.211523\pi$
$74$	−5.82105	−	1.76505i	−0.676683	−	0.205183i
$75$	1.42588	+	5.10199i	0.164646	+	0.589127i
$76$	0.570090	+	1.56631i	0.0653938	+	0.179668i
$77$	−0.321767	+	0.884048i	−0.0366688	+	0.100747i
$78$	1.05139	+	1.25300i	0.119047	+	0.141874i
$79$	−4.86694	+	0.858174i	−0.547574	+	0.0965521i	−0.440590	−	0.897709i	$-0.645231\pi$
$79$	−4.86694	+	0.858174i	−0.547574	+	0.0965521i	−0.106984	+	0.994261i	$0.534119\pi$
$80$	−0.303747	−	2.21534i	−0.0339599	−	0.247683i
$81$	0.0273076	+	0.154869i	0.00303418	+	0.0172077i
$82$	0.830191	−	1.43793i	0.0916793	−	0.158793i
$83$	2.61137	−	3.11211i	0.286635	−	0.341598i	−0.603443	−	0.797406i	$-0.706205\pi$
$83$	2.61137	−	3.11211i	0.286635	−	0.341598i	0.890078	+	0.455808i	$0.150650\pi$
$84$	−0.571194	−	0.989337i	−0.0623224	−	0.107946i
$85$	−1.69287	−	0.690601i	−0.183618	−	0.0749062i
$86$	−2.00128	+	0.728408i	−0.215804	+	0.0785463i
$87$	1.72602	−	1.44830i	0.185048	−	0.155274i
$88$	−0.436261	−	0.755627i	−0.0465056	−	0.0805501i
$89$	−15.0870	−	2.66025i	−1.59922	−	0.281986i	−0.698247	−	0.715857i	$-0.746036\pi$
$89$	−15.0870	−	2.66025i	−1.59922	−	0.281986i	−0.900975	+	0.433871i	$0.857147\pi$
$90$	4.19506	+	0.160632i	0.442198	+	0.0169321i
$91$	−1.06998	+	1.27516i	−0.112165	+	0.133673i
$92$	4.37026	+	1.59065i	0.455632	+	0.165836i
$93$	2.17364	+	0.791140i	0.225396	+	0.0820374i
$94$	−3.14430	+	3.74723i	−0.324309	+	0.386497i
$95$	−0.142611	+	3.72442i	−0.0146316	+	0.382118i
$96$	1.04340	+	0.183980i	0.106492	+	0.0187774i
$97$	5.51919	+	9.55952i	0.560389	+	0.970622i	0.997462	+	0.0711965i	$0.0226817\pi$
$97$	5.51919	+	9.55952i	0.560389	+	0.970622i	−0.437073	+	0.899426i	$0.643985\pi$
$98$	−4.47172	+	3.75221i	−0.451711	+	0.379031i
$99$	1.53934	−	0.560273i	0.154709	−	0.0563096i
$100$	1.24224	−	4.84323i	0.124224	−	0.484323i
$101$	1.28806	+	2.23099i	0.128167	+	0.221992i	0.922966	−	0.384881i	$-0.125757\pi$
$101$	1.28806	+	2.23099i	0.128167	+	0.221992i	−0.794800	+	0.606872i	$0.792424\pi$
$102$	0.556845	−	0.663622i	0.0551359	−	0.0657084i
$103$	2.51846	−	4.36211i	0.248152	−	0.429811i	−0.714861	−	0.699266i	$-0.753510\pi$
$103$	2.51846	−	4.36211i	0.248152	−	0.429811i	0.963013	+	0.269455i	$0.0868435\pi$
$104$	−0.268082	−	1.52037i	−0.0262876	−	0.149084i
$105$	−0.346996	−	2.53078i	−0.0338634	−	0.246979i
$106$	4.91073	−	0.865893i	0.476972	−	0.0841030i
$107$	1.57623	+	1.87848i	0.152380	+	0.181599i	0.836834	−	0.547457i	$-0.184404\pi$
$107$	1.57623	+	1.87848i	0.152380	+	0.181599i	−0.684454	+	0.729056i	$0.739959\pi$
$108$	−1.76745	+	4.85602i	−0.170072	+	0.467270i
$109$	3.11601	+	8.56118i	0.298460	+	0.820012i	0.994758	+	0.102259i	$0.0326071\pi$
$109$	3.11601	+	8.56118i	0.298460	+	0.820012i	−0.696298	+	0.717753i	$0.745171\pi$
$110$	−0.265026	−	1.93294i	−0.0252692	−	0.184298i
$111$	5.39688	−	3.52244i	0.512249	−	0.334335i
$112$			1.07823i			0.101884i
$113$	9.25336	−	3.36795i	0.870483	−	0.316830i	0.132120	−	0.991234i	$-0.457822\pi$
$113$	9.25336	−	3.36795i	0.870483	−	0.316830i	0.738363	+	0.674404i	$0.235599\pi$
$114$	−1.65950	−	0.604010i	−0.155427	−	0.0565707i
$115$	7.70477	+	6.98450i	0.718474	+	0.651308i
$116$	−2.09432	+	0.369284i	−0.194452	+	0.0342872i
$117$	2.89847			0.267963
$118$	−10.8290	+	1.90944i	−0.996886	+	0.175778i
$119$	0.763503	+	0.440809i	0.0699902	+	0.0404088i
$120$	2.00488	+	1.26219i	0.183020	+	0.115222i
$121$	5.11935	+	8.86698i	0.465396	+	0.806089i
$122$	1.64684	+	0.950801i	0.149097	+	0.0860815i
$123$	0.601672	+	1.65308i	0.0542510	+	0.149053i
$124$	−1.40336	−	1.67246i	−0.126025	−	0.150191i
$125$	6.66263	−	8.97827i	0.595923	−	0.803041i
$126$	−1.99359	−	0.351524i	−0.177603	−	0.0313162i
$127$	17.5015	+	3.08598i	1.55300	+	0.273836i	0.883305	−	0.468798i	$-0.155313\pi$
$127$	17.5015	+	3.08598i	1.55300	+	0.273836i	0.669697	+	0.742634i	$0.266424\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	0.771747	−	2.12036i	0.0679485	−	0.186687i
$130$	0.729089	−	3.37422i	0.0639453	−	0.295938i
$131$	−4.45501	+	5.30927i	−0.389236	+	0.463873i	−0.924707	−	0.380680i	$-0.875690\pi$
$131$	−4.45501	+	5.30927i	−0.389236	+	0.463873i	0.535471	+	0.844554i	$0.320134\pi$
$132$	0.910392	+	0.160527i	0.0792394	+	0.0139721i
$133$	0.312087	−	1.76993i	0.0270614	−	0.153473i
$134$	−5.06464	+	2.92407i	−0.437518	+	0.252601i
$135$	−7.76083	+	8.56115i	−0.667946	+	0.736827i
$136$	−0.768338	+	0.279652i	−0.0658845	+	0.0239800i
$137$	−5.53751	−	3.19708i	−0.473101	−	0.273145i	0.244436	−	0.969665i	$-0.421397\pi$
$137$	−5.53751	−	3.19708i	−0.473101	−	0.273145i	−0.717537	+	0.696520i	$0.754731\pi$
$138$	−4.26730	+	2.46372i	−0.363256	+	0.209726i
$139$	6.69739	+	5.61978i	0.568065	+	0.476663i	0.881003	−	0.473110i	$-0.156869\pi$
$139$	6.69739	+	5.61978i	0.568065	+	0.476663i	−0.312938	+	0.949774i	$0.601313\pi$
$140$	−0.910697	+	2.23239i	−0.0769680	+	0.188672i
$141$	−0.899967	−	5.10396i	−0.0757909	−	0.429831i
$142$	−10.8564			−0.911045
$143$	−0.233907	−	1.32655i	−0.0195603	−	0.110932i
$144$	1.43822	−	1.20681i	0.119852	−	0.100568i
$145$	−4.64801	−	1.00433i	−0.385996	−	0.0834048i
$146$	−3.60416	−	9.90235i	−0.298283	−	0.819525i
$147$		−	6.18473i		−	0.510108i
$148$	−6.07368	+	0.332312i	−0.499253	+	0.0273159i
$149$	2.57942			0.211314			0.105657	−	0.994403i	$-0.466305\pi$
$149$	2.57942			0.211314			0.105657	+	0.994403i	$0.466305\pi$
$150$	3.08487	+	4.30662i	0.251879	+	0.351634i
$151$	20.9296	+	7.61777i	1.70323	+	0.619925i	0.996187	−	0.0872457i	$-0.0278065\pi$
$151$	20.9296	+	7.61777i	1.70323	+	0.619925i	0.707043	+	0.707171i	$0.250029\pi$
$152$	1.07142	+	1.27687i	0.0869036	+	0.103568i
$153$	−0.266568	−	1.51178i	−0.0215508	−	0.122220i
$154$			0.940784i			0.0758105i
$155$	−1.49295	−	4.64799i	−0.119916	−	0.373335i
$156$	1.41654	+	0.817837i	0.113414	+	0.0654794i
$157$	4.13022	−	4.92220i	0.329627	−	0.392834i	−0.575622	−	0.817716i	$-0.695240\pi$
$157$	4.13022	−	4.92220i	0.329627	−	0.392834i	0.905249	+	0.424882i	$0.139684\pi$
$158$	−4.27992	+	2.47101i	−0.340492	+	0.196583i
$159$	−2.64158	+	4.57536i	−0.209491	+	0.362850i
$160$	−1.04312	−	1.97785i	−0.0824659	−	0.156363i
$161$	−3.22331	−	3.84140i	−0.254033	−	0.302744i
$162$	0.0786291	+	0.136190i	0.00617769	+	0.0107001i
$163$	0.526085	−	2.98357i	0.0412061	−	0.233692i	−0.957248	−	0.289267i	$-0.906588\pi$
$163$	0.526085	−	2.98357i	0.0412061	−	0.233692i	0.998454	+	0.0555758i	$0.0176994\pi$
$164$	0.288322	−	1.63516i	0.0225142	−	0.127684i
$165$	1.74931	+	1.10129i	0.136183	+	0.0857354i
$166$	1.38948	−	3.81756i	0.107845	−	0.296300i
$167$	−0.265056	−	0.0964724i	−0.0205106	−	0.00746526i	0.331744	−	0.943369i	$-0.392363\pi$
$167$	−0.265056	−	0.0964724i	−0.0205106	−	0.00746526i	−0.352255	+	0.935904i	$0.614585\pi$
$168$	−0.875120	−	0.734313i	−0.0675170	−	0.0566535i
$169$	−1.84356	+	10.4553i	−0.141812	+	0.804256i
$170$	−1.82698	−	0.0699565i	−0.140123	−	0.00536542i
$171$	−2.71015	+	1.56471i	−0.207251	+	0.119656i
$172$	−1.63146	+	1.36896i	−0.124398	+	0.104382i
$173$	−5.80274	−	15.9429i	−0.441174	−	1.21212i	−0.938721	−	0.344679i	$-0.887988\pi$
$173$	−5.80274	−	15.9429i	−0.441174	−	1.21212i	0.497546	−	0.867438i	$-0.334235\pi$
$174$	1.12658	−	1.95129i	0.0854056	−	0.147927i
$175$	−3.77104	+	3.85279i	−0.285064	+	0.291244i
$176$	−0.668391	−	0.560847i	−0.0503819	−	0.0422754i
$177$	5.82513	−	10.0894i	0.437843	−	0.758367i
$178$	−15.0870	+	2.66025i	−1.13082	+	0.199394i
$179$		−	14.3771i		−	1.07459i	−0.843393	−	0.537297i	$-0.819446\pi$
$179$		−	14.3771i		−	1.07459i	0.843393	−	0.537297i	$-0.180554\pi$
$180$	3.99701	−	1.28385i	0.297919	−	0.0956926i
$181$	11.8298	−	9.92638i	0.879302	−	0.737822i	−0.0867336	−	0.996232i	$-0.527643\pi$
$181$	11.8298	−	9.92638i	0.879302	−	0.737822i	0.966035	+	0.258410i	$0.0831985\pi$
$182$	−0.569327	+	1.56421i	−0.0422013	+	0.115947i
$183$	−1.89324	+	0.689083i	−0.139952	+	0.0509385i
$184$	4.65074			0.342857
$185$	−12.8557	−	4.44192i	−0.945171	−	0.326576i
$186$	2.31314			0.169608
$187$	−0.670392	+	0.244003i	−0.0490239	+	0.0178433i
$188$	−1.67304	+	4.59665i	−0.122019	+	0.335245i
$189$	4.26837	−	3.58158i	0.310478	−	0.260522i
$190$	1.13982	+	3.54859i	0.0826910	+	0.257442i
$191$		−	3.30124i		−	0.238869i	−0.992842	−	0.119435i	$-0.961892\pi$
$191$		−	3.30124i		−	0.238869i	0.992842	−	0.119435i	$-0.0381082\pi$
$192$	1.04340	−	0.183980i	0.0753011	−	0.0132776i
$193$	5.47500	−	9.48298i	0.394099	−	0.682600i	−0.598886	−	0.800834i	$-0.704390\pi$
$193$	5.47500	−	9.48298i	0.394099	−	0.682600i	0.992986	+	0.118234i	$0.0377232\pi$
$194$	8.45589	+	7.09534i	0.607098	+	0.509416i
$195$	2.24206	+	2.88970i	0.160557	+	0.206935i
$196$	−2.91870	+	5.05535i	−0.208479	+	0.361096i
$197$	6.48938	+	17.8294i	0.462349	+	1.27029i	0.923714	+	0.383084i	$0.125138\pi$
$197$	6.48938	+	17.8294i	0.462349	+	1.27029i	−0.461364	+	0.887211i	$0.652640\pi$
$198$	1.25488	−	1.05297i	0.0891804	−	0.0748312i
$199$	7.88126	−	4.55025i	0.558688	−	0.322558i	−0.193931	−	0.981015i	$-0.562124\pi$
$199$	7.88126	−	4.55025i	0.558688	−	0.322558i	0.752619	+	0.658457i	$0.228790\pi$
$200$	−0.489160	−	4.97601i	−0.0345888	−	0.351857i
$201$	1.07594	−	6.10197i	0.0758910	−	0.430399i
$202$	1.97342	+	1.65590i	0.138850	+	0.116509i
$203$	2.15472	+	0.784252i	0.151231	+	0.0550437i
$204$	0.296291	−	0.814053i	0.0207445	−	0.0569951i
$205$	1.97803	−	3.14193i	0.138152	−	0.219442i
$206$	0.874653	−	4.96041i	0.0609400	−	0.345608i
$207$	−1.51622	+	8.59894i	−0.105385	+	0.597667i
$208$	−0.771910	−	1.33699i	−0.0535223	−	0.0927034i
$209$	0.934838	+	1.11410i	0.0646641	+	0.0770636i
$210$	−1.19165	−	2.25948i	−0.0822315	−	0.155919i
$211$	7.52679	−	13.0368i	0.518165	−	0.897489i	−0.481612	−	0.876385i	$-0.659949\pi$
$211$	7.52679	−	13.0368i	0.518165	−	0.897489i	0.999777	−	0.0211041i	$-0.00671815\pi$
$212$	4.31842	−	2.49324i	0.296590	−	0.171236i
$213$	7.39353	−	8.81127i	0.506596	−	0.603738i
$214$	2.12365	+	1.22609i	0.145170	+	0.0838137i
$215$	−4.53405	+	1.45635i	−0.309220	+	0.0993223i
$216$			5.16766i			0.351615i
$217$	0.408776	+	2.31828i	0.0277495	+	0.157375i
$218$	5.85619	+	6.97914i	0.396631	+	0.472687i
$219$	10.4915	+	3.81860i	0.708952	+	0.258037i
$220$	−0.910145	−	1.72572i	−0.0613620	−	0.116348i
$221$	−1.26230			−0.0849116
$222$	3.86666	−	5.15585i	0.259513	−	0.346038i
$223$			21.7384i			1.45571i	0.685730	+	0.727856i	$0.259483\pi$
$223$			21.7384i			1.45571i	−0.685730	+	0.727856i	$0.740517\pi$
$224$	0.368778	+	1.01321i	0.0246400	+	0.0676979i
$225$	9.35983	+	0.717843i	0.623989	+	0.0478562i
$226$	7.54341	−	6.32967i	0.501780	−	0.421043i
$227$	−2.20438	−	12.5017i	−0.146310	−	0.829764i	−0.966306	−	0.257395i	$-0.917136\pi$
$227$	−2.20438	−	12.5017i	−0.146310	−	0.829764i	0.819996	−	0.572369i	$-0.193975\pi$
$228$	−1.76601			−0.116957
$229$	−1.74813	−	9.91413i	−0.115520	−	0.655144i	−0.986492	−	0.163812i	$-0.947621\pi$
$229$	−1.74813	−	9.91413i	−0.115520	−	0.655144i	0.870972	−	0.491332i	$-0.163490\pi$
$230$	9.62896	+	3.92810i	0.634915	+	0.259011i
$231$	−0.763562	−	0.640704i	−0.0502387	−	0.0421553i
$232$	−1.84171	+	1.06331i	−0.120914	+	0.0698099i
$233$	6.64095	+	3.83415i	0.435063	+	0.251184i	0.701501	−	0.712668i	$-0.252513\pi$
$233$	6.64095	+	3.83415i	0.435063	+	0.251184i	−0.266438	+	0.963852i	$0.585847\pi$
$234$	2.72367	−	0.991333i	0.178052	−	0.0648055i
$235$	−7.34632	+	8.10390i	−0.479221	+	0.528640i
$236$	−9.52283	+	5.49801i	−0.619883	+	0.357890i
$237$	0.909234	−	5.15652i	0.0590611	−	0.334952i
$238$	0.868223	+	0.153091i	0.0562786	+	0.00992343i
$239$	−4.23812	+	5.05080i	−0.274141	+	0.326709i	−0.885495	−	0.464648i	$-0.846181\pi$
$239$	−4.23812	+	5.05080i	−0.274141	+	0.326709i	0.611354	+	0.791357i	$0.290625\pi$
$240$	2.31567	+	0.500362i	0.149476	+	0.0322982i
$241$	−9.22443	+	25.3439i	−0.594197	+	1.63254i	0.168435	+	0.985713i	$0.446129\pi$
$241$	−9.22443	+	25.3439i	−0.594197	+	1.63254i	−0.762633	+	0.646832i	$0.776094\pi$
$242$	7.84330	+	6.58131i	0.504187	+	0.423063i
$243$	−15.4316	−	2.72100i	−0.989934	−	0.174552i
$244$	1.87271	+	0.330210i	0.119888	+	0.0211395i
$245$	−10.3128	+	8.00147i	−0.658859	+	0.511195i
$246$	1.13077	+	1.34760i	0.0720955	+	0.0859201i
$247$	0.880117	+	2.41810i	0.0560005	+	0.153860i
$248$	−1.89074	−	1.09162i	−0.120062	−	0.0693179i
$249$	2.15214	+	3.72762i	0.136386	+	0.236228i
$250$	3.19007	−	10.7156i	0.201758	−	0.677712i
$251$	4.49165	+	2.59325i	0.283510	+	0.163685i	0.635011	−	0.772503i	$-0.280995\pi$
$251$	4.49165	+	2.59325i	0.283510	+	0.163685i	−0.351501	+	0.936187i	$0.614329\pi$
$252$	−1.99359	+	0.351524i	−0.125584	+	0.0221439i
$253$	4.05787			0.255116
$254$	17.5015	−	3.08598i	1.09814	−	0.193631i
$255$	1.30101	−	1.43517i	0.0814724	−	0.0898741i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−19.8471	+	7.22375i	−1.23803	+	0.450605i	−0.876340	−	0.481694i	$-0.840022\pi$
$257$	−19.8471	+	7.22375i	−1.23803	+	0.450605i	−0.361689	+	0.932299i	$0.617800\pi$
$258$		−	2.25644i		−	0.140480i
$259$	5.85063	+	2.96412i	0.363540	+	0.184181i
$260$	−0.468930	−	3.42009i	−0.0290818	−	0.212105i
$261$	−1.36557	−	3.75187i	−0.0845267	−	0.232235i
$262$	−2.37046	+	6.51279i	−0.146448	+	0.402361i
$263$	19.4723	+	23.2062i	1.20072	+	1.43096i	0.874062	+	0.485814i	$0.161477\pi$
$263$	19.4723	+	23.2062i	1.20072	+	1.43096i	0.326654	+	0.945144i	$0.394079\pi$
$264$	0.910392	−	0.160527i	0.0560307	−	0.00987973i
$265$	11.0468	−	1.51463i	0.678597	−	0.0930428i
$266$	−0.312087	−	1.76993i	−0.0191353	−	0.108522i
$267$	8.11564	−	14.0567i	0.496669	−	0.860256i
$268$	−3.75911	+	4.47994i	−0.229624	+	0.273656i
$269$	−4.54723	−	7.87603i	−0.277250	−	0.480210i	0.693451	−	0.720504i	$-0.256090\pi$
$269$	−4.54723	−	7.87603i	−0.277250	−	0.480210i	−0.970700	+	0.240294i	$0.922756\pi$
$270$	−4.36471	+	10.6992i	−0.265627	+	0.651133i
$271$	−12.8176	+	4.66521i	−0.778612	+	0.283391i	−0.700594	−	0.713561i	$-0.747081\pi$
$271$	−12.8176	+	4.66521i	−0.778612	+	0.283391i	−0.0780180	+	0.996952i	$0.524859\pi$
$272$	−0.626355	+	0.525574i	−0.0379784	+	0.0318676i
$273$	−0.881821	−	1.52736i	−0.0533702	−	0.0924399i
$274$	−6.29702	−	1.11033i	−0.380417	−	0.0670778i
$275$	−0.426803	−	4.34168i	−0.0257372	−	0.261813i
$276$	−3.16730	+	3.77465i	−0.190649	+	0.227207i
$277$	22.5852	+	8.22034i	1.35701	+	0.493913i	0.915130	−	0.403160i	$-0.132088\pi$
$277$	22.5852	+	8.22034i	1.35701	+	0.493913i	0.441884	+	0.897072i	$0.354310\pi$
$278$	8.21557	+	2.99022i	0.492737	+	0.179342i
$279$	2.63476	−	3.13998i	0.157739	−	0.187986i
$280$	−0.0922517	+	2.40924i	−0.00551310	+	0.143980i
$281$	−9.23169	−	1.62780i	−0.550716	−	0.0971061i	−0.108636	−	0.994082i	$-0.534648\pi$
$281$	−9.23169	−	1.62780i	−0.550716	−	0.0971061i	−0.442080	+	0.896975i	$0.645759\pi$
$282$	−2.59135	−	4.48835i	−0.154313	−	0.267277i
$283$	8.38991	−	7.03997i	0.498729	−	0.418483i	−0.358414	−	0.933563i	$-0.616682\pi$
$283$	8.38991	−	7.03997i	0.498729	−	0.418483i	0.857142	+	0.515080i	$0.172238\pi$
$284$	−10.2016	+	3.71309i	−0.605356	+	0.220332i
$285$	−3.65637	−	1.49160i	−0.216584	−	0.0883549i
$286$	−0.673509	−	1.16655i	−0.0398254	−	0.0689796i
$287$	−1.15077	+	1.37144i	−0.0679279	+	0.0809533i
$288$	0.938732	−	1.62593i	0.0553153	−	0.0958089i
$289$	−2.83593	−	16.0833i	−0.166819	−	0.946079i
$290$	−4.71120	+	0.645955i	−0.276651	+	0.0379318i
$291$	−11.5175	+	2.03084i	−0.675166	+	0.119050i
$292$	−6.77361	−	8.07247i	−0.396395	−	0.472406i
$293$	1.24458	−	3.41945i	0.0727090	−	0.199766i	−0.898015	−	0.439966i	$-0.854991\pi$
$293$	1.24458	−	3.41945i	0.0727090	−	0.199766i	0.970724	+	0.240199i	$0.0772128\pi$
$294$	−2.11530	−	5.81174i	−0.123367	−	0.338948i
$295$	−24.3599	+	3.34000i	−1.41829	+	0.194462i
$296$	−5.59373	+	2.38959i	−0.325129	+	0.138892i
$297$			4.50890i			0.261633i
$298$	2.42386	−	0.882214i	0.140411	−	0.0511053i
$299$	6.74690	+	2.45567i	0.390183	+	0.142015i
$300$	4.37178	+	2.99181i	0.252405	+	0.172732i
$301$	2.26145	−	0.398755i	0.130348	−	0.0229839i
$302$	22.2729			1.28166
$303$	−2.68793	+	0.473955i	−0.154418	+	0.0272280i
$304$	1.44352	+	0.833416i	0.0827915	+	0.0477997i
$305$	3.59839	+	2.26540i	0.206043	+	0.129716i
$306$	−0.767552	−	1.32944i	−0.0438781	−	0.0759990i
$307$	0.732784	+	0.423073i	0.0418222	+	0.0241461i	0.520765	−	0.853700i	$-0.325647\pi$
$307$	0.732784	+	0.423073i	0.0418222	+	0.0241461i	−0.478943	+	0.877846i	$0.658980\pi$
$308$	0.321767	+	0.884048i	0.0183344	+	0.0503733i
$309$	3.43031	+	4.08809i	0.195144	+	0.232563i
$310$	−2.99262	−	3.85706i	−0.169969	−	0.219066i
$311$	−12.8692	−	2.26918i	−0.729745	−	0.128674i	−0.203582	−	0.979058i	$-0.565258\pi$
$311$	−12.8692	−	2.26918i	−0.729745	−	0.128674i	−0.526162	+	0.850384i	$0.676370\pi$
$312$	1.61083	+	0.284032i	0.0911950	+	0.0160801i
$313$	4.47117	+	3.75176i	0.252726	+	0.212062i	0.760345	−	0.649520i	$-0.225030\pi$
$313$	4.47117	+	3.75176i	0.252726	+	0.212062i	−0.507619	+	0.861581i	$0.669474\pi$
$314$	2.19764	−	6.03797i	0.124020	−	0.340743i
$315$	−4.42447	−	0.956024i	−0.249290	−	0.0538658i
$316$	−3.17667	+	3.78581i	−0.178702	+	0.212968i
$317$	−18.3987	−	3.24419i	−1.03338	−	0.182212i	−0.368859	−	0.929485i	$-0.620252\pi$
$317$	−18.3987	−	3.24419i	−1.03338	−	0.182212i	−0.664517	+	0.747273i	$0.731363\pi$
$318$	−0.917413	+	5.20291i	−0.0514460	+	0.291764i
$319$	−1.60693	+	0.927764i	−0.0899710	+	0.0519448i
$320$	−1.65668	−	1.50181i	−0.0926111	−	0.0839535i
$321$	−2.44139	+	0.888595i	−0.136265	+	0.0495965i
$322$	−4.34276	−	2.50729i	−0.242013	−	0.139726i
$323$	1.18029	−	0.681442i	0.0656732	−	0.0379164i
$324$	0.120467	+	0.101084i	0.00669260	+	0.00561576i
$325$	1.91779	−	7.47707i	0.106380	−	0.414753i
$326$	−0.526085	−	2.98357i	−0.0291371	−	0.165245i
$327$	−9.65268			−0.533795
$328$	−0.288322	−	1.63516i	−0.0159199	−	0.0902865i
$329$	4.04039	−	3.39029i	0.222754	−	0.186913i
$330$	2.02047	+	0.436577i	0.111223	+	0.0240328i
$331$	2.62689	+	7.21733i	0.144387	+	0.396700i	0.990714	−	0.135964i	$-0.0434131\pi$
$331$	2.62689	+	7.21733i	0.144387	+	0.396700i	−0.846327	+	0.532664i	$0.821191\pi$
$332$		−	4.06257i		−	0.222962i
$333$	−2.59455	−	11.1215i	−0.142181	−	0.609456i
$334$	−0.282066			−0.0154340
$335$	−11.5668	+	6.10031i	−0.631960	+	0.333296i
$336$	−1.07349	−	0.390720i	−0.0585639	−	0.0213155i
$337$	10.3303	+	12.3112i	0.562728	+	0.670633i	0.970121	−	0.242620i	$-0.0780067\pi$
$337$	10.3303	+	12.3112i	0.562728	+	0.670633i	−0.407394	+	0.913253i	$0.633562\pi$
$338$	1.84356	+	10.4553i	0.100276	+	0.568695i
$339$			10.4331i			0.566649i
$340$	−1.74072	+	0.559126i	−0.0944041	+	0.0303229i
$341$	−1.64971	−	0.952463i	−0.0893371	−	0.0515788i
$342$	−2.01155	+	2.39727i	−0.108772	+	0.129630i
$343$	11.9873	−	6.92087i	0.647253	−	0.373692i
$344$	−1.06486	+	1.84439i	−0.0574135	+	0.0994431i
$345$	−9.74577	+	5.13992i	−0.524695	+	0.276724i
$346$	−10.9056	−	12.9968i	−0.586288	−	0.698711i
$347$	−10.0777	−	17.4551i	−0.541001	−	0.937041i	−0.998847	−	0.0480094i	$-0.984712\pi$
$347$	−10.0777	−	17.4551i	−0.541001	−	0.937041i	0.457846	−	0.889031i	$-0.348621\pi$
$348$	0.391256	−	2.21892i	0.0209735	−	0.118947i
$349$	−0.0949475	+	0.538474i	−0.00508242	+	0.0288239i	−0.987244	−	0.159218i	$-0.949103\pi$
$349$	−0.0949475	+	0.538474i	−0.00508242	+	0.0288239i	0.982161	+	0.188042i	$0.0602140\pi$
$350$	−2.22589	+	4.91021i	−0.118979	+	0.262462i
$351$	−2.72862	+	7.49681i	−0.145643	+	0.400150i
$352$	−0.819903	−	0.298420i	−0.0437010	−	0.0159059i
$353$	−9.42472	−	7.90828i	−0.501627	−	0.420915i	0.356544	−	0.934278i	$-0.383955\pi$
$353$	−9.42472	−	7.90828i	−0.501627	−	0.420915i	−0.858171	+	0.513363i	$0.828399\pi$
$354$	2.02305	−	11.4733i	0.107524	−	0.609797i
$355$	−24.2578	−	0.928849i	−1.28747	−	0.0492982i
$356$	−13.2673	+	7.65989i	−0.703166	+	0.405973i
$357$	−0.715540	+	0.600410i	−0.0378704	+	0.0317771i
$358$	−4.91725	−	13.5100i	−0.259885	−	0.714028i
$359$	13.2940	−	23.0258i	0.701629	−	1.21526i	−0.266265	−	0.963900i	$-0.585790\pi$
$359$	13.2940	−	23.0258i	0.701629	−	1.21526i	0.967894	−	0.251358i	$-0.0808771\pi$
$360$	3.31686	−	2.57348i	0.174814	−	0.135634i
$361$	12.4265	+	10.4271i	0.654027	+	0.548794i
$362$	7.72135	−	13.3738i	0.405825	−	0.702910i
$363$	−10.6831	+	1.88372i	−0.560717	+	0.0988695i
$364$			1.66460i			0.0872488i
$365$	−7.20602	−	22.4345i	−0.377180	−	1.17427i
$366$	−1.54338	+	1.29505i	−0.0806739	+	0.0676935i
$367$	3.36052	−	9.23295i	0.175418	−	0.481956i	−0.820560	−	0.571561i	$-0.806338\pi$
$367$	3.36052	−	9.23295i	0.175418	−	0.481956i	0.995977	+	0.0896048i	$0.0285604\pi$
$368$	4.37026	−	1.59065i	0.227816	−	0.0829182i
$369$	3.11731			0.162280
$370$	−13.5996	+	0.222876i	−0.707012	+	0.0115867i
$371$	−5.37660			−0.279139
$372$	2.17364	−	0.791140i	0.112698	−	0.0410187i
$373$	−8.97241	+	24.6515i	−0.464574	+	1.27641i	0.457437	+	0.889242i	$0.348767\pi$
$373$	−8.97241	+	24.6515i	−0.464574	+	1.27641i	−0.922011	+	0.387164i	$0.873455\pi$
$374$	−0.546509	+	0.458575i	−0.0282593	+	0.0237124i
$375$	6.52446	+	9.88678i	0.336922	+	0.510551i
$376$			4.89166i			0.252268i
$377$	−3.23325	+	0.570109i	−0.166521	+	0.0293621i
$378$	2.78598	−	4.82545i	0.143295	−	0.248195i
$379$	−3.82454	−	3.20917i	−0.196453	−	0.164844i	0.539255	−	0.842143i	$-0.318706\pi$
$379$	−3.82454	−	3.20917i	−0.196453	−	0.164844i	−0.735708	+	0.677299i	$0.763150\pi$
$380$	2.28477	+	2.94474i	0.117206	+	0.151062i
$381$	−9.41440	+	16.3062i	−0.482315	+	0.835393i
$382$	−1.12909	−	3.10215i	−0.0577692	−	0.158720i
$383$	−24.8001	+	20.8097i	−1.26722	+	1.06333i	−0.272351	+	0.962198i	$0.587801\pi$
$383$	−24.8001	+	20.8097i	−1.26722	+	1.06333i	−0.994873	+	0.101130i	$0.967754\pi$
$384$	0.917552	−	0.529749i	0.0468237	−	0.0270336i
$385$	−0.0804917	+	2.10212i	−0.00410224	+	0.107134i
$386$	1.90145	−	10.7837i	0.0967812	−	0.548873i
$387$	−3.06301	−	2.57017i	−0.155702	−	0.130649i
$388$	10.3727	+	3.77535i	0.526594	+	0.191664i
$389$	−6.55864	+	18.0197i	−0.332536	+	0.913636i	0.654914	+	0.755704i	$0.272705\pi$
$389$	−6.55864	+	18.0197i	−0.332536	+	0.913636i	−0.987450	+	0.157932i	$0.949517\pi$
$390$	3.09518	+	1.94860i	0.156730	+	0.0986710i
$391$	0.660327	−	3.74490i	0.0333941	−	0.189388i
$392$	−1.01366	+	5.74873i	−0.0511973	+	0.290355i
$393$	−3.67157	−	6.35934i	−0.185206	−	0.320786i
$394$	12.1961	+	14.5347i	0.614428	+	0.732247i
$395$	−9.77460	+	5.15512i	−0.491813	+	0.259382i
$396$	0.819064	−	1.41866i	0.0411595	−	0.0712904i
$397$	−28.7635	+	16.6066i	−1.44360	+	0.833461i	−0.998088	−	0.0618156i	$-0.980311\pi$
$397$	−28.7635	+	16.6066i	−1.44360	+	0.833461i	−0.445510	+	0.895277i	$0.646978\pi$
$398$	5.84969	−	6.97138i	0.293218	−	0.349444i
$399$	1.64906	+	0.952085i	0.0825562	+	0.0476639i
$400$	−2.16156	−	4.50862i	−0.108078	−	0.225431i
$401$		−	6.78294i		−	0.338724i	−0.985554	−	0.169362i	$-0.945829\pi$
$401$		−	6.78294i		−	0.338724i	0.985554	−	0.169362i	$-0.0541707\pi$
$402$	−1.07594	−	6.10197i	−0.0536631	−	0.304338i
$403$	−2.16653	−	2.58198i	−0.107923	−	0.128617i
$404$	2.42076	+	0.881086i	0.120437	+	0.0438357i
$405$	0.164039	+	0.311034i	0.00815117	+	0.0154554i
$406$	2.29300			0.113800
$407$	−4.88066	+	2.08497i	−0.241925	+	0.103348i
$408$		−	0.866297i		−	0.0428881i
$409$	−3.95396	−	10.8634i	−0.195511	−	0.537161i	0.802737	−	0.596333i	$-0.203376\pi$
$409$	−3.95396	−	10.8634i	−0.195511	−	0.537161i	−0.998248	+	0.0591720i	$0.981154\pi$
$410$	0.784137	−	3.62898i	0.0387258	−	0.179222i
$411$	5.18965	−	4.35463i	0.255986	−	0.214798i
$412$	−0.874653	−	4.96041i	−0.0430911	−	0.244382i
$413$	11.8563			0.583410
$414$	1.51622	+	8.59894i	0.0745184	+	0.422615i
$415$	3.43132	−	8.41120i	0.168437	−	0.412889i
$416$	−1.18263	−	0.992348i	−0.0579834	−	0.0486539i
$417$	−8.02200	+	4.63150i	−0.392839	+	0.226806i
$418$	1.25950	+	0.727174i	0.0616043	+	0.0355673i
$419$	16.0572	−	5.84436i	0.784448	−	0.285516i	0.0814217	−	0.996680i	$-0.474054\pi$
$419$	16.0572	−	5.84436i	0.784448	−	0.285516i	0.703026	+	0.711164i	$0.251832\pi$
$420$	−1.89257	−	1.71564i	−0.0923479	−	0.0837149i
$421$	1.95703	−	1.12989i	0.0953798	−	0.0550675i	−0.451551	−	0.892245i	$-0.649129\pi$
$421$	1.95703	−	1.12989i	0.0953798	−	0.0550675i	0.546931	+	0.837178i	$0.315796\pi$
$422$	2.61403	−	14.8249i	0.127249	−	0.721664i
$423$	−9.04438	−	1.59477i	−0.439753	−	0.0775403i
$424$	3.20525	−	3.81987i	0.155661	−	0.185509i
$425$	−4.07627	−	0.312626i	−0.197728	−	0.0151646i
$426$	3.93402	−	10.8086i	0.190604	−	0.523679i
$427$	−1.57068	−	1.31795i	−0.0760104	−	0.0637803i
$428$	2.41492	+	0.425816i	0.116730	+	0.0205826i
$429$	1.40548	+	0.247824i	0.0678573	+	0.0119651i
$430$	−3.76251	+	2.91926i	−0.181445	+	0.140779i
$431$	−9.25962	−	11.0352i	−0.446020	−	0.531546i	0.495453	−	0.868635i	$-0.335002\pi$
$431$	−9.25962	−	11.0352i	−0.446020	−	0.531546i	−0.941473	+	0.337089i	$0.890558\pi$
$432$	1.76745	+	4.85602i	0.0850362	+	0.233635i
$433$	−8.73101	−	5.04085i	−0.419586	−	0.242248i	0.275314	−	0.961354i	$-0.411218\pi$
$433$	−8.73101	−	5.04085i	−0.419586	−	0.242248i	−0.694900	+	0.719106i	$0.744551\pi$
$434$	1.17702	+	2.03866i	0.0564989	+	0.0978590i
$435$	2.68421	−	4.26363i	0.128698	−	0.204426i
$436$	7.89003	+	4.55531i	0.377864	+	0.218160i
$437$	−7.63423	+	1.34612i	−0.365195	+	0.0643937i
$438$	11.1648			0.533477
$439$	−9.15624	+	1.61449i	−0.437003	+	0.0770555i	−0.387822	−	0.921734i	$-0.626772\pi$
$439$	−9.15624	+	1.61449i	−0.437003	+	0.0770555i	−0.0491815	+	0.998790i	$0.515661\pi$
$440$	−1.44549	−	1.31036i	−0.0689109	−	0.0624689i
$441$	−10.2986	−	3.74838i	−0.490409	−	0.178494i
$442$	−1.18618	+	0.431733i	−0.0564206	+	0.0205354i
$443$		−	35.7351i		−	1.69783i	−0.528531	−	0.848914i	$-0.677257\pi$
$443$		−	35.7351i		−	1.69783i	0.528531	−	0.848914i	$-0.322743\pi$
$444$	1.87007	−	6.16739i	0.0887494	−	0.292691i
$445$	−33.9385	+	4.65333i	−1.60884	+	0.220589i
$446$	7.43498	+	20.4274i	0.352056	+	0.967267i
$447$	−0.934704	+	2.56808i	−0.0442100	+	0.121466i
$448$	0.693076	+	0.825976i	0.0327448	+	0.0390237i
$449$	18.1541	−	3.20105i	0.856743	−	0.151067i	0.272012	−	0.962294i	$-0.412311\pi$
$449$	18.1541	−	3.20105i	0.856743	−	0.151067i	0.584731	+	0.811227i	$0.301200\pi$
$450$	9.04088	−	2.52670i	0.426191	−	0.119110i
$451$	−0.251568	−	1.42671i	−0.0118459	−	0.0671812i
$452$	4.92361	−	8.52794i	0.231587	−	0.401121i
$453$	−15.1685	+	18.0772i	−0.712680	+	0.849339i
$454$	−6.34726	−	10.9938i	−0.297891	−	0.515963i
$455$	−1.40595	+	3.44641i	−0.0659121	+	0.161570i
$456$	−1.65950	+	0.604010i	−0.0777134	+	0.0282853i
$457$	−25.8346	+	21.6778i	−1.20849	+	1.01404i	−0.209144	+	0.977885i	$0.567068\pi$
$457$	−25.8346	+	21.6778i	−1.20849	+	1.01404i	−0.999346	+	0.0361587i	$0.988488\pi$
$458$	−5.03353	−	8.71834i	−0.235202	−	0.407381i
$459$	4.16114	+	0.733721i	0.194225	+	0.0342472i
$460$	10.3918	+	0.397908i	0.484518	+	0.0185526i
$461$	19.5455	−	23.2934i	0.910323	−	1.08488i	−0.0857480	−	0.996317i	$-0.527328\pi$
$461$	19.5455	−	23.2934i	0.910323	−	1.08488i	0.996071	−	0.0885633i	$-0.0282276\pi$
$462$	−0.936647	−	0.340912i	−0.0435768	−	0.0158606i
$463$	31.3726	+	11.4187i	1.45801	+	0.530672i	0.944816	−	0.327600i	$-0.106240\pi$
$463$	31.3726	+	11.4187i	1.45801	+	0.530672i	0.513194	+	0.858273i	$0.328462\pi$
$464$	−1.36697	+	1.62909i	−0.0634599	+	0.0756286i
$465$	5.16855	+	0.197908i	0.239686	+	0.00917776i
$466$	7.55181	+	1.33159i	0.349831	+	0.0616846i
$467$	−9.94276	−	17.2214i	−0.460096	−	0.796910i	0.538869	−	0.842390i	$-0.318852\pi$
$467$	−9.94276	−	17.2214i	−0.460096	−	0.796910i	−0.998965	+	0.0454795i	$0.985518\pi$
$468$	2.22035	−	1.86310i	0.102636	−	0.0861217i
$469$	5.92539	−	2.15667i	0.273609	−	0.0995856i
$470$	−4.13158	+	10.1278i	−0.190576	+	0.467159i
$471$	3.40389	+	5.89571i	0.156843	+	0.271660i
$472$	−7.06810	+	8.42343i	−0.325336	+	0.387720i
$473$	−0.929115	+	1.60928i	−0.0427208	+	0.0739946i
$474$	−0.909234	−	5.15652i	−0.0417625	−	0.236847i
$475$	2.24323	+	8.02659i	0.102926	+	0.368285i
$476$	0.868223	−	0.153091i	0.0397949	−	0.00701692i
$477$	6.01774	+	7.17166i	0.275533	+	0.328368i
$478$	−2.25506	+	6.19572i	−0.103144	+	0.283386i
$479$	7.41314	+	20.3674i	0.338715	+	0.930612i	0.985760	+	0.168160i	$0.0537824\pi$
$479$	7.41314	+	20.3674i	0.338715	+	0.930612i	−0.647045	+	0.762452i	$0.723995\pi$
$480$	2.34715	−	0.321819i	0.107132	−	0.0146890i
$481$	−9.37667	+	0.513030i	−0.427539	+	0.0233921i
$482$			26.9704i			1.22847i
$483$	4.99254	−	1.81713i	0.227168	−	0.0826825i
$484$	9.62124	+	3.50184i	0.437329	+	0.159175i
$485$	18.2870	+	16.5775i	0.830372	+	0.752746i
$486$	−15.4316	+	2.72100i	−0.699989	+	0.123427i
$487$	36.5419			1.65587			0.827937	−	0.560822i	$-0.189515\pi$
$487$	36.5419			1.65587			0.827937	+	0.560822i	$0.189515\pi$
$488$	1.87271	−	0.330210i	0.0847737	−	0.0149479i
$489$	2.77982	+	1.60493i	0.125708	+	0.0725774i
$490$	−6.95417	+	11.0461i	−0.314157	+	0.499012i
$491$	11.9230	+	20.6513i	0.538078	+	0.931979i	0.999008	+	0.0445419i	$0.0141828\pi$
$491$	11.9230	+	20.6513i	0.538078	+	0.931979i	−0.460929	+	0.887437i	$0.652484\pi$
$492$	1.52349	+	0.879586i	0.0686841	+	0.0396548i
$493$	0.594715	+	1.63397i	0.0267846	+	0.0735902i
$494$	1.65408	+	1.97125i	0.0744205	+	0.0886909i
$495$	2.89403	−	2.24542i	0.130077	−	0.100924i
$496$	−2.15007	−	0.379116i	−0.0965411	−	0.0170228i
$497$	11.5279	+	2.03267i	0.517095	+	0.0911779i
$498$	3.29727	+	2.76674i	0.147754	+	0.123981i
$499$	12.9665	−	35.6251i	0.580458	−	1.59480i	−0.206941	−	0.978353i	$-0.566351\pi$
$499$	12.9665	−	35.6251i	0.580458	−	1.59480i	0.787399	−	0.616443i	$-0.211427\pi$
$500$	−0.667256	−	11.1604i	−0.0298406	−	0.499109i
$501$	0.192096	−	0.228932i	0.00858223	−	0.0102279i
$502$	5.10771	+	0.900627i	0.227968	+	0.0401970i
$503$	−6.98751	+	39.6282i	−0.311558	+	1.76693i	0.279346	+	0.960191i	$0.409882\pi$
$503$	−6.98751	+	39.6282i	−0.311558	+	1.76693i	−0.590904	+	0.806742i	$0.701229\pi$
$504$	−1.75314	+	1.01217i	−0.0780909	+	0.0450858i
$505$	4.26780	+	3.86883i	0.189915	+	0.172161i
$506$	3.81315	−	1.38787i	0.169515	−	0.0616985i
$507$	−9.74131	−	5.62415i	−0.432627	−	0.249777i
$508$	15.3905	−	8.88572i	0.682844	−	0.394240i
$509$	15.7389	+	13.2065i	0.697617	+	0.585370i	0.921094	−	0.389339i	$-0.127297\pi$
$509$	15.7389	+	13.2065i	0.697617	+	0.585370i	−0.223478	+	0.974709i	$0.571741\pi$
$510$	0.731691	−	1.79359i	0.0323998	−	0.0794217i
$511$	1.97304	+	11.1897i	0.0872822	+	0.495002i
$512$	−1.00000			−0.0441942
$513$	−1.49574	−	8.48277i	−0.0660386	−	0.374523i
$514$	−16.1795	+	13.5762i	−0.713647	+	0.598821i
$515$	2.37876	−	11.0088i	0.104820	−	0.485108i
$516$	−0.771747	−	2.12036i	−0.0339743	−	0.0933435i
$517$			4.26808i			0.187710i
$518$	6.51158	+	0.784329i	0.286102	+	0.0344615i
$519$	17.9755			0.789039
$520$	−1.61039	−	3.05345i	−0.0706202	−	0.133903i
$521$	−7.39970	−	2.69327i	−0.324187	−	0.117994i	0.174800	−	0.984604i	$-0.444072\pi$
$521$	−7.39970	−	2.69327i	−0.324187	−	0.117994i	−0.498987	+	0.866610i	$0.666294\pi$
$522$	−2.56643	−	3.05855i	−0.112330	−	0.133869i
$523$	−2.06053	−	11.6858i	−0.0901006	−	0.510986i	−0.996139	−	0.0877905i	$-0.972019\pi$
$523$	−2.06053	−	11.6858i	−0.0901006	−	0.510986i	0.906038	−	0.423196i	$-0.139092\pi$
$524$			6.93076i			0.302772i
$525$	−2.46934	−	5.15060i	−0.107771	−	0.224790i
$526$	26.2350	+	15.1468i	1.14390	+	0.660432i
$527$	−1.14745	+	1.36748i	−0.0499839	+	0.0595685i
$528$	0.800585	−	0.462218i	0.0348410	−	0.0201155i
$529$	0.685317	−	1.18700i	0.0297964	−	0.0516089i
$530$	9.86253	−	5.20150i	0.428401	−	0.225939i
$531$	−13.2701	−	15.8147i	−0.575873	−	0.686299i
$532$	−0.898618	−	1.55645i	−0.0389601	−	0.0674808i
$533$	0.445118	−	2.52439i	0.0192802	−	0.109343i
$534$	2.81853	−	15.9847i	0.121970	−	0.691725i
$535$	4.64024	+	2.92130i	0.200615	+	0.126299i
$536$	−2.00018	+	5.49546i	−0.0863947	+	0.237368i
$537$	14.3139	+	5.20982i	0.617689	+	0.224820i
$538$	−6.96676	−	5.84581i	−0.300358	−	0.252031i
$539$	−0.884437	+	5.01589i	−0.0380954	+	0.216050i
$540$	−0.442136	+	11.5468i	−0.0190265	+	0.496895i
$541$	36.1647	−	20.8797i	1.55484	−	0.897689i	0.557106	−	0.830441i	$-0.311912\pi$
$541$	36.1647	−	20.8797i	1.55484	−	0.897689i	0.997736	−	0.0672476i	$-0.0214217\pi$
$542$	−10.4490	+	8.76773i	−0.448822	+	0.376606i
$543$	5.59597	+	15.3748i	0.240146	+	0.659796i
$544$	−0.408824	+	0.708104i	−0.0175282	+	0.0303597i
$545$	12.4881	+	16.0954i	0.534933	+	0.689453i
$546$	−1.35103	−	1.13365i	−0.0578186	−	0.0485156i
$547$	21.5669	−	37.3550i	0.922135	−	1.59718i	0.126030	−	0.992026i	$-0.459777\pi$
$547$	21.5669	−	37.3550i	0.922135	−	1.59718i	0.796105	−	0.605158i	$-0.206890\pi$
$548$	−6.29702	+	1.11033i	−0.268995	+	0.0474311i
$549$			3.57019i			0.152372i
$550$	−1.88601	−	3.93387i	−0.0804196	−	0.167741i
$551$	2.71542	−	2.27851i	0.115681	−	0.0970677i
$552$	−1.68529	+	4.63029i	−0.0717306	+	0.197078i
$553$	5.00731	−	1.82251i	0.212932	−	0.0775010i
$554$	24.0347			1.02114
$555$	9.08091	−	11.1896i	0.385463	−	0.474971i
$556$	8.74282			0.370778
$557$	−25.8419	+	9.40569i	−1.09496	+	0.398532i	−0.825455	−	0.564468i	$-0.809081\pi$
$557$	−25.8419	+	9.40569i	−1.09496	+	0.398532i	−0.269502	+	0.963000i	$0.586859\pi$
$558$	1.40192	−	3.85176i	0.0593482	−	0.163058i
$559$	−2.51868	+	2.11343i	−0.106529	+	0.0893884i
$560$	0.737321	+	2.29550i	0.0311575	+	0.0970025i
$561$		−	0.755864i		−	0.0319126i
$562$	−9.23169	+	1.62780i	−0.389415	+	0.0686644i
$563$	14.0675	−	24.3656i	0.592873	−	1.02689i	−0.400970	−	0.916091i	$-0.631327\pi$
$563$	14.0675	−	24.3656i	0.592873	−	1.02689i	0.993843	−	0.110795i	$-0.0353398\pi$
$564$	−3.97018	−	3.33138i	−0.167175	−	0.140276i
$565$	17.3968	−	13.4978i	0.731888	−	0.567857i
$566$	5.47613	−	9.48493i	0.230179	−	0.398681i
$567$	−0.0579934	−	0.159336i	−0.00243549	−	0.00669146i
$568$	−8.31645	+	6.97833i	−0.348951	+	0.292804i
$569$	31.5420	−	18.2108i	1.32231	−	0.763437i	0.338214	−	0.941069i	$-0.390177\pi$
$569$	31.5420	−	18.2108i	1.32231	−	0.763437i	0.984097	+	0.177633i	$0.0568439\pi$
$570$	−3.94602	−	0.151096i	−0.165281	−	0.00632872i
$571$	−2.64393	+	14.9945i	−0.110645	+	0.627499i	0.878170	+	0.478349i	$0.158765\pi$
$571$	−2.64393	+	14.9945i	−0.110645	+	0.627499i	−0.988815	+	0.149150i	$0.952346\pi$
$572$	−1.03188	−	0.865846i	−0.0431449	−	0.0362028i
$573$	3.28672	+	1.19627i	0.137305	+	0.0499748i
$574$	−0.612312	+	1.68231i	−0.0255574	+	0.0702185i
$575$	21.1792	+	9.60090i	0.883232	+	0.400385i
$576$	0.326018	−	1.84894i	0.0135841	−	0.0770392i
$577$	−4.51304	+	25.5947i	−0.187880	+	1.06552i	0.734318	+	0.678805i	$0.237502\pi$
$577$	−4.51304	+	25.5947i	−0.187880	+	1.06552i	−0.922199	+	0.386716i	$0.873609\pi$
$578$	−8.16573	−	14.1435i	−0.339649	−	0.588290i
$579$	7.45731	+	8.88728i	0.309915	+	0.369343i
$580$	−4.20615	+	2.21832i	−0.174651	+	0.0921109i
$581$	−2.19020	+	3.79354i	−0.0908648	+	0.157382i
$582$	−10.1283	+	5.84758i	−0.419831	+	0.242390i
$583$	2.79665	−	3.33292i	0.115825	−	0.138035i
$584$	−9.12606	−	5.26893i	−0.377639	−	0.218030i
$585$	6.17066	−	1.98203i	0.255125	−	0.0819470i
$586$		−	3.63890i		−	0.150322i
$587$	−7.24062	−	41.0636i	−0.298852	−	1.69488i	−0.651119	−	0.758976i	$-0.725700\pi$
$587$	−7.24062	−	41.0636i	−0.298852	−	1.69488i	0.352267	−	0.935900i	$-0.385411\pi$
$588$	−3.97547	−	4.73777i	−0.163945	−	0.195383i
$589$	3.41963	+	1.24464i	0.140903	+	0.0512847i
$590$	−21.7485	+	11.4702i	−0.895371	+	0.472219i
$591$	−20.1026			−0.826910
$592$	−4.43910	+	4.15865i	−0.182446	+	0.170919i
$593$			28.6164i			1.17514i	0.809175	+	0.587568i	$0.199915\pi$
$593$			28.6164i			1.17514i	−0.809175	+	0.587568i	$0.800085\pi$
$594$	1.54214	+	4.23698i	0.0632746	+	0.173846i
$595$	1.92689	+	0.416355i	0.0789946	+	0.0170689i
$596$	1.97595	−	1.65802i	0.0809381	−	0.0679152i
$597$	1.67431	+	9.49548i	0.0685249	+	0.388624i
$598$	7.17990			0.293608
$599$	−4.18335	−	23.7249i	−0.170927	−	0.969375i	−0.942741	−	0.333526i	$-0.891761\pi$
$599$	−4.18335	−	23.7249i	−0.170927	−	0.969375i	0.771814	−	0.635849i	$-0.219350\pi$
$600$	5.13139	+	1.31615i	0.209488	+	0.0537315i
$601$	3.35161	+	2.81234i	0.136715	+	0.114718i	0.708581	−	0.705630i	$-0.249336\pi$
$601$	3.35161	+	2.81234i	0.136715	+	0.114718i	−0.571866	+	0.820347i	$0.693780\pi$
$602$	1.98869	−	1.14817i	0.0810529	−	0.0467959i
$603$	−9.50868	−	5.48984i	−0.387223	−	0.223563i
$604$	20.9296	−	7.61777i	0.851615	−	0.309962i
$605$	16.9622	+	15.3765i	0.689613	+	0.625145i
$606$	−2.36373	+	1.36470i	−0.0960199	+	0.0554371i
$607$	4.77849	−	27.1002i	0.193953	−	1.09996i	−0.719949	−	0.694027i	$-0.755835\pi$
$607$	4.77849	−	27.1002i	0.193953	−	1.09996i	0.913902	−	0.405935i	$-0.133054\pi$
$608$	1.64151	+	0.289442i	0.0665720	+	0.0117384i
$609$	−1.56161	+	1.86105i	−0.0632795	+	0.0754136i
$610$	4.15619	+	0.898056i	0.168279	+	0.0363612i
$611$	−2.58288	+	7.09640i	−0.104492	+	0.287090i
$612$	−1.17596	−	0.986746i	−0.0475353	−	0.0398869i
$613$	−17.8488	−	3.14722i	−0.720906	−	0.127115i	−0.198854	−	0.980029i	$-0.563722\pi$
$613$	−17.8488	−	3.14722i	−0.720906	−	0.127115i	−0.522052	+	0.852914i	$0.674833\pi$
$614$	0.833291	+	0.146932i	0.0336289	+	0.00592968i
$615$	2.41134	+	3.10787i	0.0972345	+	0.125322i
$616$	0.604724	+	0.720682i	0.0243650	+	0.0290371i
$617$	3.72701	+	10.2399i	0.150044	+	0.412242i	0.991830	−	0.127570i	$-0.0407176\pi$
$617$	3.72701	+	10.2399i	0.150044	+	0.412242i	−0.841786	+	0.539812i	$0.818495\pi$
$618$	4.62165	+	2.66831i	0.185910	+	0.107335i
$619$	−1.39499	−	2.41619i	−0.0560692	−	0.0971148i	0.836628	−	0.547771i	$-0.184523\pi$
$619$	−1.39499	−	2.41619i	−0.0560692	−	0.0971148i	−0.892698	+	0.450656i	$0.851190\pi$
$620$	−4.13133	−	2.60092i	−0.165918	−	0.104455i
$621$	−20.8136	−	12.0167i	−0.835220	−	0.482215i
$622$	−12.8692	+	2.26918i	−0.516007	+	0.0909860i
$623$	16.5183			0.661792
$624$	1.61083	−	0.284032i	0.0644846	−	0.0113704i
$625$	8.04479	−	23.6703i	0.321792	−	0.946810i
$626$	5.48470	+	1.99627i	0.219213	+	0.0797869i
$627$	−1.44795	+	0.527012i	−0.0578257	+	0.0210468i
$628$		−	6.42548i		−	0.256404i
$629$	1.12995	+	4.84350i	0.0450539	+	0.193123i
$630$	−4.48462	+	0.614888i	−0.178671	+	0.0244977i
$631$	5.08822	+	13.9798i	0.202559	+	0.556525i	0.998827	−	0.0484180i	$-0.0154180\pi$
$631$	5.08822	+	13.9798i	0.202559	+	0.556525i	−0.796268	+	0.604943i	$0.793196\pi$
$632$	−1.69027	+	4.64398i	−0.0672354	+	0.184728i
$633$	10.2520	+	12.2178i	0.407479	+	0.485615i
$634$	−18.3987	+	3.24419i	−0.730707	+	0.128843i
$635$	39.3698	−	5.39801i	1.56234	−	0.214214i
$636$	0.917413	+	5.20291i	0.0363778	+	0.206309i
$637$	−4.50595	+	7.80454i	−0.178532	+	0.309227i
$638$	−1.19271	+	1.42142i	−0.0472199	+	0.0562744i
$639$	−10.1912	−	17.6517i	−0.403158	−	0.698290i
$640$	−2.07042	−	0.844619i	−0.0818404	−	0.0333865i
$641$	−21.3389	+	7.76672i	−0.842835	+	0.306767i	−0.727116	−	0.686515i	$-0.759140\pi$
$641$	−21.3389	+	7.76672i	−0.842835	+	0.306767i	−0.115720	+	0.993282i	$0.536917\pi$
$642$	−1.99024	+	1.67001i	−0.0785486	+	0.0659101i
$643$	−14.1824	−	24.5646i	−0.559298	−	0.968733i	−0.997555	−	0.0698834i	$-0.977737\pi$
$643$	−14.1824	−	24.5646i	−0.559298	−	0.968733i	0.438257	−	0.898850i	$-0.355596\pi$
$644$	−4.93840	−	0.870774i	−0.194600	−	0.0343133i
$645$	0.193057	−	5.04185i	0.00760159	−	0.198523i
$646$	0.876044	−	1.04403i	0.0344675	−	0.0410768i
$647$	7.84861	+	2.85666i	0.308561	+	0.112307i	0.491659	−	0.870788i	$-0.336391\pi$
$647$	7.84861	+	2.85666i	0.308561	+	0.112307i	−0.183099	+	0.983095i	$0.558613\pi$
$648$	0.147774	+	0.0537855i	0.00580513	+	0.00211289i
$649$	−6.16708	+	7.34964i	−0.242079	+	0.288498i
$650$	−0.755175	−	7.68207i	−0.0296204	−	0.301316i
$651$	−2.45622	−	0.433097i	−0.0962667	−	0.0169744i
$652$	−1.51480	−	2.62371i	−0.0593242	−	0.102752i
$653$	9.84771	−	8.26321i	0.385371	−	0.323364i	−0.429436	−	0.903097i	$-0.641288\pi$
$653$	9.84771	−	8.26321i	0.385371	−	0.323364i	0.814807	+	0.579733i	$0.196843\pi$
$654$	−9.07056	+	3.30141i	−0.354687	+	0.129095i
$655$	−5.85385	+	14.3496i	−0.228729	+	0.560684i
$656$	−0.830191	−	1.43793i	−0.0324135	−	0.0561419i
$657$	12.7172	−	15.1558i	0.496145	−	0.591283i
$658$	2.63718	−	4.56772i	0.102808	−	0.178068i
$659$	3.18898	+	18.0856i	0.124225	+	0.704515i	0.981765	+	0.190098i	$0.0608805\pi$
$659$	3.18898	+	18.0856i	0.124225	+	0.704515i	−0.857540	+	0.514417i	$0.828008\pi$
$660$	2.04794	−	0.280794i	0.0797160	−	0.0109299i
$661$	−0.545303	+	0.0961516i	−0.0212098	+	0.00373987i	−0.184243	−	0.982881i	$-0.558983\pi$
$661$	−0.545303	+	0.0961516i	−0.0212098	+	0.00373987i	0.163033	+	0.986621i	$0.447872\pi$
$662$	4.93694	+	5.88362i	0.191880	+	0.228673i
$663$	0.457420	−	1.25675i	0.0177647	−	0.0488082i
$664$	−1.38948	−	3.81756i	−0.0539223	−	0.148150i
$665$	−0.545904	−	3.98149i	−0.0211693	−	0.154396i
$666$	−6.24187	−	9.56343i	−0.241868	−	0.370575i
$667$		−	9.89037i		−	0.382957i
$668$	−0.265056	+	0.0964724i	−0.0102553	+	0.00373263i
$669$	−21.6428	−	7.87735i	−0.836760	−	0.304556i
$670$	−8.78277	+	9.68849i	−0.339308	+	0.374299i
$671$	1.63398	−	0.288115i	0.0630792	−	0.0111226i
$672$	−1.14239			−0.0440686
$673$	−34.0710	+	6.00764i	−1.31334	+	0.231577i	−0.786079	−	0.618126i	$-0.787892\pi$
$673$	−34.0710	+	6.00764i	−1.31334	+	0.231577i	−0.527261	+	0.849703i	$0.676781\pi$
$674$	13.9180	+	8.03556i	0.536101	+	0.309518i
$675$	−10.6680	+	23.5332i	−0.410613	+	0.905794i
$676$	5.30831	+	9.19426i	0.204166	+	0.353625i
$677$	25.8495	+	14.9242i	0.993477	+	0.573584i	0.906312	−	0.422610i	$-0.138886\pi$
$677$	25.8495	+	14.9242i	0.993477	+	0.573584i	0.0871652	+	0.996194i	$0.472219\pi$
$678$	3.56834	+	9.80392i	0.137041	+	0.376517i
$679$	−7.65044	−	9.11744i	−0.293597	−	0.349895i
$680$	−1.44451	+	1.12077i	−0.0553946	+	0.0429795i
$681$	13.2455	+	2.33554i	0.507568	+	0.0894979i
$682$	−1.87599	−	0.330787i	−0.0718352	−	0.0126665i
$683$	−23.6104	−	19.8115i	−0.903428	−	0.758066i	0.0674291	−	0.997724i	$-0.478520\pi$
$683$	−23.6104	−	19.8115i	−0.903428	−	0.758066i	−0.970857	+	0.239658i	$0.922965\pi$
$684$	−1.07032	+	2.94069i	−0.0409248	+	0.112440i
$685$	−13.9753	−	3.01973i	−0.533967	−	0.115378i
$686$	8.89730	−	10.6034i	0.339700	−	0.404839i
$687$	10.5040	+	1.85214i	0.400753	+	0.0706635i
$688$	−0.369822	+	2.09737i	−0.0140993	+	0.0799614i
$689$	6.66686	−	3.84912i	0.253987	−	0.146640i
$690$	−7.40007	+	8.16319i	−0.281716	+	0.310767i
$691$	16.7698	−	6.10370i	0.637952	−	0.232196i	−0.00273673	−	0.999996i	$-0.500871\pi$
$691$	16.7698	−	6.10370i	0.637952	−	0.232196i	0.640689	+	0.767801i	$0.278649\pi$
$692$	−14.6931	−	8.48304i	−0.558546	−	0.322477i
$693$	−1.52965	+	0.883144i	−0.0581066	+	0.0335479i
$694$	−15.4400	−	12.9557i	−0.586093	−	0.491791i
$695$	18.1013	+	7.38435i	0.686620	+	0.280104i
$696$	−0.391256	−	2.21892i	−0.0148305	−	0.0841081i
$697$	−1.35761			−0.0514231
$698$	0.0949475	+	0.538474i	0.00359382	+	0.0203815i
$699$	−6.22378	+	5.22237i	−0.235405	+	0.197528i
$700$	−0.412260	+	5.37539i	−0.0155820	+	0.203171i
$701$	−3.08447	−	8.47452i	−0.116499	−	0.320078i	0.867715	−	0.497063i	$-0.165588\pi$
$701$	−3.08447	−	8.47452i	−0.116499	−	0.320078i	−0.984214	+	0.176984i	$0.943366\pi$
$702$			7.97794i			0.301108i
$703$	8.49052	−	5.54160i	0.320226	−	0.209005i
$704$	−0.872522			−0.0328844
$705$	−5.40618	−	10.2506i	−0.203608	−	0.386061i
$706$	−11.5611	−	4.20791i	−0.435109	−	0.158367i
$707$	−1.78545	−	2.12781i	−0.0671487	−	0.0800247i
$708$	−2.02305	−	11.4733i	−0.0760307	−	0.431192i
$709$			34.7424i			1.30478i	0.757884	+	0.652389i	$0.226233\pi$
$709$			34.7424i			1.30478i	−0.757884	+	0.652389i	$0.773767\pi$
$710$	−23.1125	+	7.42381i	−0.867398	+	0.278611i
$711$	−8.03539	−	4.63924i	−0.301351	−	0.173985i
$712$	−9.84736	+	11.7356i	−0.369045	+	0.439811i
$713$	8.79334	−	5.07684i	0.329313	−	0.190129i
$714$	−0.467036	+	0.808930i	−0.0174784	+	0.0302734i
$715$	−1.40510	−	2.66420i	−0.0525478	−	0.0996355i
$716$	−9.24141	−	11.0135i	−0.345368	−	0.411593i
$717$	−3.49282	−	6.04974i	−0.130442	−	0.225932i
$718$	4.61695	−	26.1840i	0.172303	−	0.977179i
$719$	−7.62793	+	43.2601i	−0.284474	+	1.61333i	0.422686	+	0.906276i	$0.361087\pi$
$719$	−7.62793	+	43.2601i	−0.284474	+	1.61333i	−0.707160	+	0.707054i	$0.750024\pi$
$720$	2.23664	−	3.55271i	0.0833547	−	0.132402i
$721$	−1.85751	+	5.10346i	−0.0691772	+	0.190063i
$722$	15.2434	+	5.54814i	0.567300	+	0.206480i
$723$	−21.8898	−	18.3677i	−0.814091	−	0.683103i
$724$	2.68160	−	15.2081i	0.0996608	−	0.565204i
$725$	−10.5821	+	1.04026i	−0.393010	+	0.0386343i
$726$	−9.39455	+	5.42395i	−0.348664	+	0.201301i
$727$	16.3714	−	13.7372i	0.607180	−	0.509484i	−0.286565	−	0.958061i	$-0.592513\pi$
$727$	16.3714	−	13.7372i	0.607180	−	0.509484i	0.893744	+	0.448577i	$0.148069\pi$
$728$	0.569327	+	1.56421i	0.0211007	+	0.0579736i
$729$	8.06507	−	13.9691i	0.298706	−	0.517375i
$730$	−14.4445	−	18.6169i	−0.534615	−	0.689043i
$731$	1.33396	+	1.11933i	0.0493384	+	0.0413998i
$732$	−1.00737	+	1.74482i	−0.0372335	+	0.0644904i
$733$	−49.0798	+	8.65409i	−1.81280	+	0.319646i	−0.974301	−	0.225251i	$-0.927680\pi$
$733$	−49.0798	+	8.65409i	−1.81280	+	0.319646i	−0.838503	+	0.544897i	$0.816569\pi$
$734$		−	9.82550i		−	0.362666i
$735$	−4.22925	−	13.1669i	−0.155998	−	0.485669i
$736$	3.56267	−	2.98944i	0.131322	−	0.110192i
$737$	−1.74520	+	4.79491i	−0.0642854	+	0.176623i
$738$	2.92931	−	1.06618i	0.107829	−	0.0392467i
$739$	−28.3679			−1.04353			−0.521765	−	0.853089i	$-0.674726\pi$
$739$	−28.3679			−1.04353			−0.521765	+	0.853089i	$0.674726\pi$
$740$	−12.7033	+	4.86079i	−0.466981	+	0.178686i
$741$	−2.72640			−0.100157
$742$	−5.05235	+	1.83890i	−0.185478	+	0.0675083i
$743$	−14.5077	+	39.8595i	−0.532235	+	1.46230i	0.324170	+	0.945999i	$0.394915\pi$
$743$	−14.5077	+	39.8595i	−0.532235	+	1.46230i	−0.856405	+	0.516305i	$0.827307\pi$
$744$	1.77197	−	1.48686i	0.0649635	−	0.0545108i
$745$	5.49144	−	1.76387i	0.201191	−	0.0646230i
$746$			26.2336i			0.960479i
$747$	7.51144	−	1.32447i	0.274829	−	0.0484598i
$748$	−0.356708	+	0.617837i	−0.0130425	+	0.0225904i
$749$	−2.02544	−	1.69954i	−0.0740079	−	0.0621000i
$750$	9.51247	+	7.05904i	0.347346	+	0.257760i
$751$	13.4911	−	23.3673i	0.492297	−	0.852683i	−0.507664	−	0.861555i	$-0.669491\pi$
$751$	13.4911	−	23.3673i	0.492297	−	0.852683i	0.999961	+	0.00887216i	$0.00282413\pi$
$752$	1.67304	+	4.59665i	0.0610097	+	0.167623i
$753$	−4.20949	+	3.53218i	−0.153402	+	0.128720i
$754$	−2.84327	+	1.64156i	−0.103546	+	0.0597822i
$755$	49.7671	+	1.90562i	1.81121	+	0.0693527i
$756$	0.967560	−	5.48730i	0.0351898	−	0.199571i
$757$	26.1873	+	21.9738i	0.951795	+	0.798651i	0.979599	−	0.200963i	$-0.0644070\pi$
$757$	26.1873	+	21.9738i	0.951795	+	0.798651i	−0.0278040	+	0.999613i	$0.508851\pi$
$758$	−4.69149	−	1.70756i	−0.170403	−	0.0620215i
$759$	−1.47045	+	4.04003i	−0.0533740	+	0.146644i
$760$	3.15414	+	1.98572i	0.114413	+	0.0720295i
$761$	−2.73193	+	15.4935i	−0.0990322	+	0.561640i	0.894405	+	0.447259i	$0.147600\pi$
$761$	−2.73193	+	15.4935i	−0.0990322	+	0.561640i	−0.993437	+	0.114381i	$0.963511\pi$
$762$	−3.26959	+	18.5428i	−0.118445	+	0.671733i
$763$	−4.91169	−	8.50730i	−0.177815	−	0.307985i
$764$	−2.12199	−	2.52889i	−0.0767710	−	0.0914922i
$765$	−1.60130	−	3.03621i	−0.0578951	−	0.109774i
$766$	−16.1871	+	28.0369i	−0.584864	+	1.01301i
$767$	−14.7015	+	8.48793i	−0.530841	+	0.306481i
$768$	0.681032	−	0.811623i	0.0245746	−	0.0292869i
$769$	−20.7470	−	11.9783i	−0.748157	−	0.431949i	0.0768704	−	0.997041i	$-0.475507\pi$
$769$	−20.7470	−	11.9783i	−0.748157	−	0.431949i	−0.825028	+	0.565092i	$0.808841\pi$
$770$	0.643329	+	2.00287i	0.0231840	+	0.0721785i
$771$		−	22.3775i		−	0.805906i
$772$	−1.90145	−	10.7837i	−0.0684346	−	0.388112i
$773$	26.1595	+	31.1757i	0.940892	+	1.12131i	0.992451	+	0.122642i	$0.0391367\pi$
$773$	26.1595	+	31.1757i	0.940892	+	1.12131i	−0.0515586	+	0.998670i	$0.516419\pi$
$774$	−3.75734	−	1.36756i	−0.135055	−	0.0491559i
$775$	−6.35679	−	8.87438i	−0.228343	−	0.318777i
$776$	11.0384			0.396255
$777$	−5.07118	+	4.75079i	−0.181927	+	0.170434i
$778$			19.1762i			0.687500i
$779$	0.946568	+	2.60067i	0.0339143	+	0.0931788i
$780$	3.57498	+	0.772469i	0.128005	+	0.0276588i
$781$	−7.25629	+	6.08875i	−0.259650	+	0.217873i
$782$	−0.660327	−	3.74490i	−0.0236132	−	0.133917i
$783$	10.9897			0.392739
$784$	1.01366	+	5.74873i	0.0362020	+	0.205312i
$785$	5.42708	−	13.3034i	0.193701	−	0.474819i
$786$	−5.62517	−	4.72007i	−0.200643	−	0.168359i
$787$	28.3359	−	16.3598i	1.01007	−	0.583162i	0.0988555	−	0.995102i	$-0.468482\pi$
$787$	28.3359	−	16.3598i	1.01007	−	0.583162i	0.911211	+	0.411940i	$0.135149\pi$
$788$	16.4317	+	9.48684i	0.585355	+	0.337955i
$789$	−30.1604	+	10.9775i	−1.07374	+	0.390809i
$790$	−7.42196	+	8.18734i	−0.264062	+	0.291293i
$791$	−9.19512	+	5.30881i	−0.326941	+	0.188759i
$792$	0.284458	−	1.61324i	0.0101078	−	0.0573241i
$793$	2.89113	+	0.509784i	0.102667	+	0.0181030i
$794$	−21.3490	+	25.4428i	−0.757649	+	0.902931i
$795$	−2.49505	+	11.5470i	−0.0884902	+	0.409531i
$796$	3.11255	−	8.55167i	0.110322	−	0.303106i
$797$	−12.3686	−	10.3785i	−0.438118	−	0.367625i	0.396886	−	0.917868i	$-0.370091\pi$
$797$	−12.3686	−	10.3785i	−0.438118	−	0.367625i	−0.835005	+	0.550243i	$0.814535\pi$
$798$	1.87524	+	0.330656i	0.0663828	+	0.0117051i
$799$	3.93889	+	0.694533i	0.139348	+	0.0245708i
$800$	−3.57324	−	3.49742i	−0.126333	−	0.123653i
$801$	−18.4881	−	22.0332i	−0.653243	−	0.778505i
$802$	−2.31990	−	6.37388i	−0.0819186	−	0.225070i
$803$	−7.96269	−	4.59726i	−0.280997	−	0.162234i
$804$	−3.09805	−	5.36598i	−0.109260	−	0.189243i
$805$	−9.48908	−	5.97393i	−0.334446	−	0.210553i
$806$	−2.91896	−	1.68526i	−0.102816	−	0.0593609i
$807$	9.48918	−	1.67320i	0.334035	−	0.0588994i
$808$	2.57612			0.0906277
$809$	−3.01409	+	0.531466i	−0.105970	+	0.0186853i	−0.226382	−	0.974039i	$-0.572690\pi$
$809$	−3.01409	+	0.531466i	−0.105970	+	0.0186853i	0.120412	+	0.992724i	$0.461579\pi$
$810$	0.260526	+	0.236171i	0.00915396	+	0.00829822i
$811$	16.3747	+	5.95991i	0.574994	+	0.209281i	0.613117	−	0.789992i	$-0.289916\pi$
$811$	16.3747	+	5.95991i	0.574994	+	0.209281i	−0.0381226	+	0.999273i	$0.512138\pi$
$812$	2.15472	−	0.784252i	0.0756157	−	0.0275219i
$813$		−	14.4517i		−	0.506844i
$814$	−3.87322	+	3.62852i	−0.135756	+	0.127179i
$815$	−0.920231	−	6.71160i	−0.0322343	−	0.235097i
$816$	−0.296291	−	0.814053i	−0.0103723	−	0.0284976i
$817$	1.21413	−	3.33581i	0.0424772	−	0.116705i
$818$	−7.43101	−	8.85593i	−0.259819	−	0.309640i
$819$	−3.07775	+	0.542690i	−0.107545	+	0.0189631i
$820$	−0.504335	−	3.67831i	−0.0176122	−	0.128452i
$821$	−0.251379	−	1.42564i	−0.00877319	−	0.0497553i	0.980107	−	0.198470i	$-0.0635974\pi$
$821$	−0.251379	−	1.42564i	−0.00877319	−	0.0497553i	−0.988880	+	0.148715i	$0.952486\pi$
$822$	3.38730	−	5.86698i	0.118146	−	0.204634i
$823$	−11.0717	+	13.1948i	−0.385936	+	0.459941i	−0.923679	−	0.383168i	$-0.874833\pi$
$823$	−11.0717	+	13.1948i	−0.385936	+	0.459941i	0.537742	+	0.843109i	$0.319277\pi$
$824$	−2.51846	−	4.36211i	−0.0877348	−	0.151961i
$825$	4.47725	+	1.14837i	0.155878	+	0.0399811i
$826$	11.1413	−	4.05509i	0.387654	−	0.141095i
$827$	3.68473	−	3.09185i	0.128131	−	0.107514i	−0.576470	−	0.817118i	$-0.695570\pi$
$827$	3.68473	−	3.09185i	0.128131	−	0.107514i	0.704601	+	0.709604i	$0.251126\pi$
$828$	4.36580	+	7.56178i	0.151722	+	0.262790i
$829$	−15.9631	−	2.81473i	−0.554423	−	0.0977596i	−0.110585	−	0.993867i	$-0.535272\pi$
$829$	−15.9631	−	2.81473i	−0.554423	−	0.0977596i	−0.443838	+	0.896107i	$0.646383\pi$
$830$	0.347585	−	9.07752i	0.0120649	−	0.315085i
$831$	−16.3684	+	19.5071i	−0.567813	+	0.676693i
$832$	−1.45072	−	0.528018i	−0.0502945	−	0.0183057i
$833$	4.48511	+	1.63244i	0.155400	+	0.0565609i
$834$	−5.95415	+	7.09587i	−0.206175	+	0.245710i
$835$	−0.630258	−	0.0241331i	−0.0218110	−	0.000835159i
$836$	1.43225	+	0.252545i	0.0495355	+	0.00873445i
$837$	5.64113	+	9.77072i	0.194986	+	0.337725i
$838$	13.0900	−	10.9838i	0.452186	−	0.379429i
$839$	−30.5392	+	11.1153i	−1.05433	+	0.383744i	−0.810295	−	0.586022i	$-0.800693\pi$
$839$	−30.5392	+	11.1153i	−1.05433	+	0.383744i	−0.244034	+	0.969767i	$0.578471\pi$
$840$	−2.36522	−	0.964882i	−0.0816078	−	0.0332916i
$841$	−12.2387	−	21.1981i	−0.422025	−	0.730969i
$842$	1.45256	−	1.73109i	0.0500585	−	0.0596575i
$843$	4.96592	−	8.60123i	0.171035	−	0.296242i
$844$	−2.61403	−	14.8249i	−0.0899785	−	0.510293i
$845$	3.22476	+	23.5194i	0.110935	+	0.809093i
$846$	−9.04438	+	1.59477i	−0.310952	+	0.0548293i
$847$	−7.09620	−	8.45692i	−0.243828	−	0.290583i
$848$	1.70548	−	4.68576i	0.0585663	−	0.160910i
$849$	3.96877	+	10.9041i	0.136208	+	0.374228i
$850$	−3.93737	+	1.10039i	−0.135051	+	0.0377432i
$851$	3.38304	−	28.0863i	0.115969	−	0.962787i
$852$		−	11.5023i		−	0.394062i
$853$	24.4129	−	8.88557i	0.835881	−	0.304236i	0.111611	−	0.993752i	$-0.464399\pi$
$853$	24.4129	−	8.88557i	0.835881	−	0.304236i	0.724270	+	0.689516i	$0.242177\pi$
$854$	−1.92672	−	0.701269i	−0.0659310	−	0.0239969i
$855$	−4.69978	+	5.18443i	−0.160729	+	0.177304i
$856$	2.41492	−	0.425816i	0.0825403	−	0.0145541i
$857$	34.7901			1.18841			0.594204	−	0.804314i	$-0.297467\pi$
$857$	34.7901			1.18841			0.594204	+	0.804314i	$0.297467\pi$
$858$	1.40548	−	0.247824i	0.0479823	−	0.00846058i
$859$	−46.6988	−	26.9616i	−1.59334	−	0.919917i	−0.992728	−	0.120379i	$-0.961589\pi$
$859$	−46.6988	−	26.9616i	−1.59334	−	0.919917i	−0.600615	−	0.799538i	$-0.705078\pi$
$860$	−2.53716	+	4.03006i	−0.0865165	+	0.137424i
$861$	−0.948400	−	1.64268i	−0.0323214	−	0.0559823i
$862$	−12.4755	−	7.20271i	−0.424916	−	0.245325i
$863$	17.7620	+	48.8008i	0.604627	+	1.66120i	0.741776	+	0.670648i	$0.233984\pi$
$863$	17.7620	+	48.8008i	0.604627	+	1.66120i	−0.137149	+	0.990550i	$0.543794\pi$
$864$	3.32171	+	3.95866i	0.113007	+	0.134676i
$865$	−23.2558	−	29.9735i	−0.790721	−	1.01913i
$866$	−9.92854	−	1.75067i	−0.337385	−	0.0594902i
$867$	17.0403	+	3.00466i	0.578718	+	0.102044i
$868$	1.80330	+	1.51315i	0.0612081	+	0.0513597i
$869$	−1.47480	+	4.05198i	−0.0500292	+	0.137454i
$870$	1.06408	−	4.92456i	0.0360758	−	0.166958i
$871$	−5.80340	+	6.91622i	−0.196641	+	0.234347i
$872$	8.97221	+	1.58204i	0.303837	+	0.0535747i
$873$	−3.59871	+	20.4093i	−0.121798	+	0.690751i
$874$	−6.71343	+	3.87600i	−0.227085	+	0.131108i
$875$	−5.39370	+	10.7811i	−0.182340	+	0.364467i
$876$	10.4915	−	3.81860i	0.354476	−	0.129019i
$877$	−3.13287	−	1.80876i	−0.105790	−	0.0610776i	0.446172	−	0.894947i	$-0.352787\pi$
$877$	−3.13287	−	1.80876i	−0.105790	−	0.0610776i	−0.551961	+	0.833870i	$0.686120\pi$
$878$	−8.05186	+	4.64874i	−0.271737	+	0.156887i
$879$	2.95342	+	2.47821i	0.0996163	+	0.0835880i
$880$	−1.80648	−	0.736949i	−0.0608966	−	0.0248425i
$881$	8.69325	+	49.3019i	0.292883	+	1.66102i	0.675684	+	0.737191i	$0.263848\pi$
$881$	8.69325	+	49.3019i	0.292883	+	1.66102i	−0.382801	+	0.923831i	$0.625041\pi$
$882$	−10.9595			−0.369026
$883$	2.65222	+	15.0415i	0.0892542	+	0.506186i	0.996357	+	0.0852772i	$0.0271776\pi$
$883$	2.65222	+	15.0415i	0.0892542	+	0.506186i	−0.907103	+	0.420909i	$0.861711\pi$
$884$	−0.966979	+	0.811392i	−0.0325230	+	0.0272901i
$885$	5.50199	−	25.4631i	0.184947	−	0.855933i
$886$	−12.2221	−	33.5801i	−0.410611	−	1.12814i
$887$		−	23.5038i		−	0.789181i	−0.918857	−	0.394591i	$-0.870886\pi$
$887$		−	23.5038i		−	0.789181i	0.918857	−	0.394591i	$-0.129114\pi$
$888$	−0.352084	−	6.43505i	−0.0118152	−	0.215946i
$889$	−19.1618			−0.642666
$890$	−30.3002	+	15.9804i	−1.01567	+	0.535663i
$891$	0.128937	+	0.0469291i	0.00431954	+	0.00157218i
$892$	13.9732	+	16.6526i	0.467857	+	0.557570i
$893$	−1.41585	−	8.02970i	−0.0473797	−	0.268704i
$894$			2.73289i			0.0914016i
$895$	−9.83136	−	30.6080i	−0.328626	−	1.02311i
$896$	0.933779	+	0.539117i	0.0311954	+	0.0180106i
$897$	−4.88975	+	5.82737i	−0.163264	+	0.194570i
$898$	15.9644	−	9.21706i	0.532739	−	0.307577i
$899$	−2.32147	+	4.02090i	−0.0774252	+	0.134104i
$900$	7.63147	−	5.46648i	0.254382	−	0.182216i
$901$	−2.62077	−	3.12331i	−0.0873104	−	0.104052i
$902$	−0.724360	−	1.25463i	−0.0241186	−	0.0417746i
$903$	−0.422481	+	2.39601i	−0.0140593	+	0.0797341i
$904$	1.70995	−	9.69762i	0.0568722	−	0.322538i
$905$	18.3971	−	29.2221i	0.611539	−	0.971377i
$906$	−8.07101	+	22.1749i	−0.268141	+	0.736712i
$907$	7.86850	+	2.86390i	0.261269	+	0.0950942i	0.469334	−	0.883021i	$-0.344494\pi$
$907$	7.86850	+	2.86390i	0.261269	+	0.0950942i	−0.208064	+	0.978115i	$0.566716\pi$
$908$	−9.72456	−	8.15987i	−0.322721	−	0.270795i
$909$	−0.839862	+	4.76310i	−0.0278565	+	0.157982i
$910$	−0.142420	+	3.71943i	−0.00472118	+	0.123298i
$911$	45.8295	−	26.4597i	1.51840	−	0.876648i	0.518633	−	0.854997i	$-0.326441\pi$
$911$	45.8295	−	26.4597i	1.51840	−	0.876648i	0.999766	−	0.0216508i	$-0.00689220\pi$
$912$	−1.35284	+	1.13517i	−0.0447970	+	0.0375891i
$913$	−1.21235	−	3.33091i	−0.0401230	−	0.110237i
$914$	−16.8623	+	29.2064i	−0.557756	+	0.966061i
$915$	−3.55938	+	2.76166i	−0.117670	+	0.0912975i
$916$	−7.71182	−	6.47099i	−0.254806	−	0.213807i
$917$	3.73650	−	6.47180i	0.123390	−	0.213718i
$918$	4.16114	−	0.733721i	0.137338	−	0.0242164i
$919$			25.9125i			0.854773i	0.904069	+	0.427387i	$0.140566\pi$
$919$			25.9125i			0.854773i	−0.904069	+	0.427387i	$0.859434\pi$
$920$	9.90114	−	3.18028i	0.326431	−	0.104851i
$921$	−0.686752	+	0.576253i	−0.0226292	+	0.0189882i
$922$	10.3999	−	28.5735i	0.342503	−	0.941019i
$923$	−15.7495	+	5.73235i	−0.518401	+	0.188682i
$924$	−0.996759			−0.0327910
$925$	−30.4065	−	0.665560i	−0.999761	−	0.0218835i
$926$	33.3861			1.09713
$927$	8.88634	−	3.23436i	0.291866	−	0.106230i
$928$	−0.727348	+	1.99837i	−0.0238764	+	0.0655998i
$929$	−6.55154	+	5.49740i	−0.214949	+	0.180364i	−0.743905	−	0.668286i	$-0.767028\pi$
$929$	−6.55154	+	5.49740i	−0.214949	+	0.180364i	0.528955	+	0.848650i	$0.322584\pi$
$930$	4.92454	−	1.58178i	0.161482	−	0.0518685i
$931$		−	9.72999i		−	0.318887i
$932$	7.55181	−	1.33159i	0.247368	−	0.0436176i
$933$	6.92261	−	11.9903i	0.226636	−	0.392545i
$934$	−15.2332	−	12.7822i	−0.498445	−	0.418245i
$935$	−1.26037	+	0.977897i	−0.0412185	+	0.0319806i
$936$	1.44923	−	2.51014i	0.0473696	−	0.0820466i
$937$	−11.6912	−	32.1214i	−0.381936	−	1.04936i	−0.970540	−	0.240940i	$-0.922544\pi$
$937$	−11.6912	−	32.1214i	−0.381936	−	1.04936i	0.588604	−	0.808422i	$-0.299678\pi$
$938$	4.83042	−	4.05321i	0.157719	−	0.132342i
$939$	−5.35548	+	3.09199i	−0.174769	+	0.100903i
$940$	−0.418521	+	10.9301i	−0.0136506	+	0.356499i
$941$	−5.69881	+	32.3196i	−0.185776	+	1.05359i	0.739178	+	0.673510i	$0.235214\pi$
$941$	−5.69881	+	32.3196i	−0.185776	+	1.05359i	−0.924954	+	0.380078i	$0.875897\pi$
$942$	5.21506	+	4.37596i	0.169916	+	0.142576i
$943$	7.25631	+	2.64108i	0.236298	+	0.0860054i
$944$	−3.76086	+	10.3329i	−0.122405	+	0.336306i
$945$	6.63793	−	10.5438i	0.215932	−	0.342989i
$946$	−0.322678	+	1.83000i	−0.0104912	+	0.0594984i
$947$	−5.11925	+	29.0327i	−0.166353	+	0.943436i	0.781305	+	0.624150i	$0.214554\pi$
$947$	−5.11925	+	29.0327i	−0.166353	+	0.943436i	−0.947658	+	0.319287i	$0.896557\pi$
$948$	−2.61803	−	4.53457i	−0.0850298	−	0.147276i
$949$	−10.4572	−	12.4624i	−0.339456	−	0.404548i
$950$	4.85320	+	6.77530i	0.157459	+	0.219820i
$951$	9.89708	−	17.1422i	0.320935	−	0.555875i
$952$	0.763503	−	0.440809i	0.0247453	−	0.0142867i
$953$	13.1824	−	15.7102i	0.427020	−	0.508902i	−0.509040	−	0.860743i	$-0.670000\pi$
$953$	13.1824	−	15.7102i	0.427020	−	0.508902i	0.936060	+	0.351841i	$0.114444\pi$
$954$	8.10767	+	4.68097i	0.262496	+	0.151552i
$955$	−2.25746	−	7.02814i	−0.0730496	−	0.227425i
$956$			6.59335i			0.213244i
$957$	−0.341380	−	1.93606i	−0.0110352	−	0.0625840i
$958$	13.9321	+	16.6037i	0.450127	+	0.536441i
$959$	6.47862	+	2.35803i	0.209206	+	0.0761446i
$960$	2.09553	−	1.10518i	0.0676330	−	0.0356696i
$961$	26.2335			0.846241
$962$	−8.63572	+	3.68910i	−0.278427	+	0.118941i
$963$			4.60387i			0.148358i
$964$	9.22443	+	25.3439i	0.297099	+	0.816272i
$965$	5.17128	−	23.9326i	0.166470	−	0.770419i
$966$	4.06995	−	3.41510i	0.130949	−	0.109879i
$967$	−2.60568	−	14.7775i	−0.0837930	−	0.475214i	−0.997611	−	0.0690888i	$-0.977991\pi$
$967$	−2.60568	−	14.7775i	−0.0837930	−	0.475214i	0.913817	−	0.406125i	$-0.133120\pi$
$968$	10.2387			0.329084
$969$	0.250743	+	1.42204i	0.00805503	+	0.0456824i
$970$	22.8540	+	9.32323i	0.733799	+	0.299351i
$971$	−7.81074	−	6.55399i	−0.250659	−	0.210327i	0.508797	−	0.860886i	$-0.330090\pi$
$971$	−7.81074	−	6.55399i	−0.250659	−	0.210327i	−0.759456	+	0.650559i	$0.774535\pi$
$972$	−13.5703	+	7.83480i	−0.435267	+	0.251301i
$973$	−8.16386	−	4.71341i	−0.261721	−	0.151105i
$974$	34.3382	−	12.4981i	1.10027	−	0.400464i
$975$	6.74924	+	4.61882i	0.216149	+	0.147921i
$976$	1.64684	−	0.950801i	0.0527139	−	0.0304344i
$977$	−3.07787	+	17.4554i	−0.0984697	+	0.558449i	0.895159	+	0.445747i	$0.147062\pi$
$977$	−3.07787	+	17.4554i	−0.0984697	+	0.558449i	−0.993629	+	0.112703i	$0.964049\pi$
$978$	3.16109	+	0.557386i	0.101081	+	0.0178232i
$979$	−8.59204	+	10.2396i	−0.274603	+	0.327259i
$980$	−2.75679	+	12.7584i	−0.0880625	+	0.407552i
$981$	−5.85020	+	16.0733i	−0.186783	+	0.513181i
$982$	18.2671	+	15.3279i	0.582927	+	0.489134i
$983$	−22.5758	−	3.98072i	−0.720056	−	0.126965i	−0.198400	−	0.980121i	$-0.563575\pi$
$983$	−22.5758	−	3.98072i	−0.720056	−	0.126965i	−0.521656	+	0.853156i	$0.674686\pi$
$984$	1.73245	+	0.305477i	0.0552284	+	0.00973825i
$985$	26.0077	+	33.5202i	0.828673	+	1.06804i
$986$	1.11770	+	1.33202i	0.0355948	+	0.0424202i
$987$	1.91127	+	5.25116i	0.0608363	+	0.167146i
$988$	2.22853	+	1.28664i	0.0708991	+	0.0409336i
$989$	−4.95239	−	8.57779i	−0.157477	−	0.272758i
$990$	1.95152	−	3.09982i	0.0620234	−	0.0985188i
$991$	37.5341	+	21.6703i	1.19231	+	0.688380i	0.958830	−	0.283982i	$-0.0916556\pi$
$991$	37.5341	+	21.6703i	1.19231	+	0.688380i	0.233479	+	0.972362i	$0.424989\pi$
$992$	−2.15007	+	0.379116i	−0.0682649	+	0.0120369i
$993$	−8.13750			−0.258236
$994$	11.5279	−	2.03267i	0.365642	−	0.0644725i
$995$	13.6672	−	15.0766i	0.433279	−	0.477960i
$996$	4.04470	+	1.47215i	0.128161	+	0.0466469i
$997$	−23.0591	+	8.39284i	−0.730290	+	0.265804i	−0.680288	−	0.732945i	$-0.738145\pi$
$997$	−23.0591	+	8.39284i	−0.730290	+	0.265804i	−0.0500023	+	0.998749i	$0.515923\pi$
$998$		−	37.9114i		−	1.20006i
$999$	31.2081	+	3.75906i	0.987381	+	0.118931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.v.b.289.5	yes	60
5.4	even	2		370.2.v.a.289.6	yes	60
37.21	even	18		370.2.v.a.169.6	✓	60
185.169	even	18	inner	370.2.v.b.169.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.v.a.169.6	✓	60	37.21	even	18
370.2.v.a.289.6	yes	60	5.4	even	2
370.2.v.b.169.5	yes	60	185.169	even	18	inner
370.2.v.b.289.5	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.362370 + 0.995603i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.12894 - 0.683822i) q^{5} +1.05950i q^{6} +(-1.06185 + 0.187234i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.43822 + 1.20681i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.362370 + 0.995603i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.12894 - 0.683822i) q^{5} +1.05950i q^{6} +(-1.06185 + 0.187234i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.43822 + 1.20681i) q^{9} +(1.76667 - 1.37072i) q^{10} +(0.436261 - 0.755627i) q^{11} +(0.362370 + 0.995603i) q^{12} +(1.18263 - 0.992348i) q^{13} +(-0.933779 + 0.539117i) q^{14} +(-0.0906487 + 2.36738i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.626355 - 0.525574i) q^{17} +(1.76424 + 0.642130i) q^{18} +(-0.570090 + 1.56631i) q^{19} +(1.19131 - 1.89229i) q^{20} +(0.198374 - 1.12503i) q^{21} +(0.151512 - 0.859267i) q^{22} +(2.32537 + 4.02766i) q^{23} +(0.681032 + 0.811623i) q^{24} +(4.06478 - 2.91163i) q^{25} +(0.771910 - 1.33699i) q^{26} +(-4.47533 + 2.58383i) q^{27} +(-0.693076 + 0.825976i) q^{28} +(-1.84171 - 1.06331i) q^{29} +(0.724508 + 2.25561i) q^{30} -2.18324i q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.594216 + 0.708159i) q^{33} +(-0.768338 - 0.279652i) q^{34} +(-2.13259 + 1.12473i) q^{35} +1.87746 q^{36} +(-4.86631 - 3.64952i) q^{37} +1.66683i q^{38} +(0.559434 + 1.53703i) q^{39} +(0.472263 - 2.18563i) q^{40} +(1.27193 - 1.06727i) q^{41} +(-0.198374 - 1.12503i) q^{42} -2.12972 q^{43} +(-0.151512 - 0.859267i) q^{44} +(3.88713 + 1.58574i) q^{45} +(3.56267 + 2.98944i) q^{46} +(-4.23630 + 2.44583i) q^{47} +(0.917552 + 0.529749i) q^{48} +(-5.48537 + 1.99651i) q^{49} +(2.82380 - 4.12627i) q^{50} +(0.750235 - 0.433149i) q^{51} +(0.268082 - 1.52037i) q^{52} +(4.91073 + 0.865893i) q^{53} +(-3.32171 + 3.95866i) q^{54} +(0.412060 - 1.90701i) q^{55} +(-0.368778 + 1.01321i) q^{56} +(-1.35284 - 1.13517i) q^{57} +(-2.09432 - 0.369284i) q^{58} +(-10.8290 - 1.90944i) q^{59} +(1.45228 + 1.87178i) q^{60} +(1.22233 + 1.45671i) q^{61} +(-0.746712 - 2.05157i) q^{62} +(-1.75314 - 1.01217i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.83917 - 2.92136i) q^{65} +(0.800585 + 0.462218i) q^{66} +(-5.75930 + 1.01552i) q^{67} -0.817648 q^{68} +(-4.85259 + 0.855643i) q^{69} +(-1.61930 + 1.78629i) q^{70} +(-10.2016 - 3.71309i) q^{71} +(1.76424 - 0.642130i) q^{72} -10.5379i q^{73} +(-5.82105 - 1.76505i) q^{74} +(1.42588 + 5.10199i) q^{75} +(0.570090 + 1.56631i) q^{76} +(-0.321767 + 0.884048i) q^{77} +(1.05139 + 1.25300i) q^{78} +(-4.86694 + 0.858174i) q^{79} +(-0.303747 - 2.21534i) q^{80} +(0.0273076 + 0.154869i) q^{81} +(0.830191 - 1.43793i) q^{82} +(2.61137 - 3.11211i) q^{83} +(-0.571194 - 0.989337i) q^{84} +(-1.69287 - 0.690601i) q^{85} +(-2.00128 + 0.728408i) q^{86} +(1.72602 - 1.44830i) q^{87} +(-0.436261 - 0.755627i) q^{88} +(-15.0870 - 2.66025i) q^{89} +(4.19506 + 0.160632i) q^{90} +(-1.06998 + 1.27516i) q^{91} +(4.37026 + 1.59065i) q^{92} +(2.17364 + 0.791140i) q^{93} +(-3.14430 + 3.74723i) q^{94} +(-0.142611 + 3.72442i) q^{95} +(1.04340 + 0.183980i) q^{96} +(5.51919 + 9.55952i) q^{97} +(-4.47172 + 3.75221i) q^{98} +(1.53934 - 0.560273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9	\( 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} - 6 q^{15} - 3 q^{17} - 12 q^{18} + 3 q^{19} + 3 q^{20} + 12 q^{21} + 3 q^{22} + 18 q^{23} - 18 q^{25} - 27 q^{26} + 18 q^{30} + 66 q^{33} + 21 q^{34} + 9 q^{35} - 72 q^{36} - 6 q^{37} + 12 q^{39} + 12 q^{40} - 57 q^{41} - 12 q^{42} - 60 q^{43} - 3 q^{44} + 9 q^{45} - 21 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{55} - 30 q^{57} - 15 q^{58} - 12 q^{59} - 9 q^{60} + 42 q^{61} + 12 q^{62} + 9 q^{63} - 30 q^{64} - 15 q^{65} + 18 q^{67} + 24 q^{68} + 36 q^{69} - 12 q^{70} + 18 q^{71} - 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} - 21 q^{77} - 6 q^{78} - 24 q^{79} - 36 q^{81} - 27 q^{82} - 30 q^{83} + 12 q^{84} - 30 q^{85} - 18 q^{86} + 30 q^{87} - 6 q^{88} + 3 q^{89} + 57 q^{91} - 15 q^{92} - 60 q^{93} + 3 q^{94} + 6 q^{95} - 84 q^{97} + 6 q^{98} - 45 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 - 6 * q^15 - 3 * q^17 - 12 * q^18 + 3 * q^19 + 3 * q^20 + 12 * q^21 + 3 * q^22 + 18 * q^23 - 18 * q^25 - 27 * q^26 + 18 * q^30 + 66 * q^33 + 21 * q^34 + 9 * q^35 - 72 * q^36 - 6 * q^37 + 12 * q^39 + 12 * q^40 - 57 * q^41 - 12 * q^42 - 60 * q^43 - 3 * q^44 + 9 * q^45 - 21 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^55 - 30 * q^57 - 15 * q^58 - 12 * q^59 - 9 * q^60 + 42 * q^61 + 12 * q^62 + 9 * q^63 - 30 * q^64 - 15 * q^65 + 18 * q^67 + 24 * q^68 + 36 * q^69 - 12 * q^70 + 18 * q^71 - 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 - 21 * q^77 - 6 * q^78 - 24 * q^79 - 36 * q^81 - 27 * q^82 - 30 * q^83 + 12 * q^84 - 30 * q^85 - 18 * q^86 + 30 * q^87 - 6 * q^88 + 3 * q^89 + 57 * q^91 - 15 * q^92 - 60 * q^93 + 3 * q^94 + 6 * q^95 - 84 * q^97 + 6 * q^98 - 45 * q^99

Introduction

L-functions

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