LMFDB - Embedded newform 418.2.v.a.29.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			29.5
Character	$\chi$	$=$	418.29
Dual form			418.2.v.a.173.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438371 + 0.898794i) q^{2} +(-0.559221 + 0.225940i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.807264 + 0.231479i) q^{5} +(0.0420729 - 0.601670i) q^{6} +(0.675252 - 3.17681i) q^{7} +(0.978148 - 0.207912i) q^{8} +(-1.89634 + 1.83127i) q^{9} +O(q^{10})$	\(q+(-0.438371 + 0.898794i) q^{2} +(-0.559221 + 0.225940i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.807264 + 0.231479i) q^{5} +(0.0420729 - 0.601670i) q^{6} +(0.675252 - 3.17681i) q^{7} +(0.978148 - 0.207912i) q^{8} +(-1.89634 + 1.83127i) q^{9} +(0.145829 - 0.827038i) q^{10} +(2.13791 + 2.53562i) q^{11} +(0.522334 + 0.301570i) q^{12} +(-1.16445 - 4.67037i) q^{13} +(2.55929 + 1.99954i) q^{14} +(0.399139 - 0.311841i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(5.29638 - 5.48456i) q^{17} +(-0.814638 - 2.50720i) q^{18} +(2.17404 - 3.77803i) q^{19} +(0.679410 + 0.493620i) q^{20} +(0.340154 + 1.92911i) q^{21} +(-3.21619 + 0.809997i) q^{22} +(1.96403 - 0.714847i) q^{23} +(-0.500025 + 0.337271i) q^{24} +(-3.64215 + 2.27587i) q^{25} +(4.70817 + 1.00075i) q^{26} +(1.38267 - 3.10553i) q^{27} +(-2.91909 + 1.42374i) q^{28} +(6.57063 - 0.923442i) q^{29} +(0.105310 + 0.495446i) q^{30} +(0.271767 + 0.610398i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.76846 - 0.934931i) q^{33} +(2.60771 + 7.16462i) q^{34} +(0.190259 + 2.72083i) q^{35} +(2.61057 + 0.366891i) q^{36} +(6.86264 - 2.22981i) q^{37} +(2.44264 + 3.61020i) q^{38} +(1.70641 + 2.34867i) q^{39} +(-0.741496 + 0.394261i) q^{40} +(0.734325 + 1.81752i) q^{41} +(-1.88298 - 0.539937i) q^{42} +(-2.99960 + 8.24132i) q^{43} +(0.681866 - 3.24578i) q^{44} +(1.10695 - 1.91729i) q^{45} +(-0.218472 + 2.07862i) q^{46} +(-5.54068 - 2.94603i) q^{47} +(-0.0839407 - 0.597269i) q^{48} +(-3.24135 - 1.44314i) q^{49} +(-0.448923 - 4.27121i) q^{50} +(-1.72266 + 4.26374i) q^{51} +(-2.96339 + 3.79297i) q^{52} +(2.51374 - 8.76644i) q^{53} +(2.18511 + 2.60411i) q^{54} +(-2.31280 - 1.55203i) q^{55} -3.24778i q^{56} +(-0.362162 + 2.60396i) q^{57} +(-2.05039 + 6.31045i) q^{58} +(-5.73747 - 10.7906i) q^{59} +(-0.491469 - 0.122537i) q^{60} +(-6.34205 - 4.27777i) q^{61} +(-0.667757 - 0.0233186i) q^{62} +(4.53711 + 7.26089i) q^{63} +(0.913545 - 0.406737i) q^{64} +(2.02112 + 3.50068i) q^{65} +(1.61555 - 1.17963i) q^{66} +(-7.37788 - 1.30092i) q^{67} +(-7.58267 - 0.796970i) q^{68} +(-0.936812 + 0.843509i) q^{69} +(-2.52887 - 1.02173i) q^{70} +(3.18975 + 11.1240i) q^{71} +(-1.47416 + 2.18553i) q^{72} +(1.91425 - 3.06344i) q^{73} +(-1.00425 + 7.14558i) q^{74} +(1.52256 - 2.09562i) q^{75} +(-4.31561 + 0.612819i) q^{76} +(9.49881 - 5.07955i) q^{77} +(-2.85902 + 0.504122i) q^{78} +(10.5838 - 0.740094i) q^{79} +(-0.0293085 - 0.839285i) q^{80} +(0.204453 - 5.85477i) q^{81} +(-1.95548 - 0.136740i) q^{82} +(-10.9847 + 1.15454i) q^{83} +(1.31074 - 1.45572i) q^{84} +(-3.00601 + 5.65349i) q^{85} +(-6.09231 - 6.30878i) q^{86} +(-3.46579 + 2.00098i) q^{87} +(2.61837 + 2.03571i) q^{88} +(-1.09642 + 1.30666i) q^{89} +(1.23799 + 1.83540i) q^{90} +(-15.6232 + 0.545574i) q^{91} +(-1.77248 - 1.10757i) q^{92} +(-0.289891 - 0.279945i) q^{93} +(5.07675 - 3.68847i) q^{94} +(-0.880492 + 3.55312i) q^{95} +(0.573619 + 0.186380i) q^{96} +(12.0957 + 5.89945i) q^{97} +(2.71801 - 2.28068i) q^{98} +(-8.69761 - 0.893297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.438371	+	0.898794i	−0.309975	+	0.635543i
$2$	−0.438371	+	0.898794i	−0.309975	+	0.635543i
$3$	−0.559221	+	0.225940i	−0.322866	+	0.130446i	−0.530318	−	0.847799i	$-0.677927\pi$
$3$	−0.559221	+	0.225940i	−0.322866	+	0.130446i	0.207452	+	0.978245i	$0.433483\pi$
$4$	−0.615661	−	0.788011i	−0.307831	−	0.394005i
$5$	−0.807264	+	0.231479i	−0.361020	+	0.103521i	−0.451244	−	0.892401i	$-0.649019\pi$
$5$	−0.807264	+	0.231479i	−0.361020	+	0.103521i	0.0902240	+	0.995921i	$0.471242\pi$
$6$	0.0420729	−	0.601670i	0.0171762	−	0.245631i
$7$	0.675252	−	3.17681i	0.255221	−	1.20072i	−0.644619	−	0.764504i	$-0.722984\pi$
$7$	0.675252	−	3.17681i	0.255221	−	1.20072i	0.899841	−	0.436219i	$-0.143683\pi$
$8$	0.978148	−	0.207912i	0.345827	−	0.0735079i
$9$	−1.89634	+	1.83127i	−0.632113	+	0.610425i
$10$	0.145829	−	0.827038i	0.0461152	−	0.261532i
$11$	2.13791	+	2.53562i	0.644603	+	0.764517i
$11$	2.13791	+	2.53562i	0.644603	+	0.764517i
$12$	0.522334	+	0.301570i	0.150785	+	0.0870556i
$13$	−1.16445	−	4.67037i	−0.322962	−	1.29533i	−0.883980	−	0.467525i	$-0.845146\pi$
$13$	−1.16445	−	4.67037i	−0.322962	−	1.29533i	0.561018	−	0.827804i	$-0.310410\pi$
$14$	2.55929	+	1.99954i	0.683999	+	0.534398i
$15$	0.399139	−	0.311841i	0.103057	−	0.0805171i
$16$	−0.241922	+	0.970296i	−0.0604805	+	0.242574i
$17$	5.29638	−	5.48456i	1.28456	−	1.33020i	0.368252	−	0.929726i	$-0.379956\pi$
$17$	5.29638	−	5.48456i	1.28456	−	1.33020i	0.916308	−	0.400475i	$-0.131155\pi$
$18$	−0.814638	−	2.50720i	−0.192012	−	0.590952i
$19$	2.17404	−	3.77803i	0.498760	−	0.866740i
$19$	2.17404	−	3.77803i	0.498760	−	0.866740i
$20$	0.679410	+	0.493620i	0.151921	+	0.110377i
$21$	0.340154	+	1.92911i	0.0742276	+	0.420966i
$22$	−3.21619	+	0.809997i	−0.685695	+	0.172692i
$23$	1.96403	−	0.714847i	0.409528	−	0.149056i	−0.129037	−	0.991640i	$-0.541189\pi$
$23$	1.96403	−	0.714847i	0.409528	−	0.149056i	0.538565	+	0.842584i	$0.318967\pi$
$24$	−0.500025	+	0.337271i	−0.102067	+	0.0688452i
$25$	−3.64215	+	2.27587i	−0.728429	+	0.455173i
$26$	4.70817	+	1.00075i	0.923348	+	0.196264i
$27$	1.38267	−	3.10553i	0.266095	−	0.597660i
$28$	−2.91909	+	1.42374i	−0.551656	+	0.269061i
$29$	6.57063	−	0.923442i	1.22014	−	0.171479i	0.500441	−	0.865770i	$-0.333171\pi$
$29$	6.57063	−	0.923442i	1.22014	−	0.171479i	0.719694	+	0.694292i	$0.244282\pi$
$30$	0.105310	+	0.495446i	0.0192269	+	0.0904556i
$31$	0.271767	+	0.610398i	0.0488108	+	0.109631i	0.936305	−	0.351188i	$-0.114222\pi$
$31$	0.271767	+	0.610398i	0.0488108	+	0.109631i	−0.887494	+	0.460819i	$0.847556\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−1.76846	−	0.934931i	−0.307849	−	0.162751i
$34$	2.60771	+	7.16462i	0.447219	+	1.22872i
$35$	0.190259	+	2.72083i	0.0321597	+	0.459905i
$36$	2.61057	+	0.366891i	0.435095	+	0.0611486i
$37$	6.86264	−	2.22981i	1.12821	−	0.366578i	0.315315	−	0.948987i	$-0.397890\pi$
$37$	6.86264	−	2.22981i	1.12821	−	0.366578i	0.812896	+	0.582409i	$0.197890\pi$
$38$	2.44264	+	3.61020i	0.396248	+	0.585652i
$39$	1.70641	+	2.34867i	0.273244	+	0.376089i
$40$	−0.741496	+	0.394261i	−0.117241	+	0.0623381i
$41$	0.734325	+	1.81752i	0.114682	+	0.283848i	0.973598	−	0.228268i	$-0.0733062\pi$
$41$	0.734325	+	1.81752i	0.114682	+	0.283848i	−0.858916	+	0.512116i	$0.828862\pi$
$42$	−1.88298	−	0.539937i	−0.290551	−	0.0833140i
$43$	−2.99960	+	8.24132i	−0.457434	+	1.25679i	0.469955	+	0.882691i	$0.344270\pi$
$43$	−2.99960	+	8.24132i	−0.457434	+	1.25679i	−0.927389	+	0.374099i	$0.877952\pi$
$44$	0.681866	−	3.24578i	0.102795	−	0.489319i
$45$	1.10695	−	1.91729i	0.165014	−	0.285812i
$46$	−0.218472	+	2.07862i	−0.0322120	+	0.306476i
$47$	−5.54068	−	2.94603i	−0.808191	−	0.429723i	0.0133231	−	0.999911i	$-0.495759\pi$
$47$	−5.54068	−	2.94603i	−0.808191	−	0.429723i	−0.821514	+	0.570189i	$0.806870\pi$
$48$	−0.0839407	−	0.597269i	−0.0121158	−	0.0862084i
$49$	−3.24135	−	1.44314i	−0.463051	−	0.206163i
$50$	−0.448923	−	4.27121i	−0.0634873	−	0.604041i
$51$	−1.72266	+	4.26374i	−0.241221	+	0.597043i
$52$	−2.96339	+	3.79297i	−0.410949	+	0.525991i
$53$	2.51374	−	8.76644i	0.345288	−	1.20416i	−0.576704	−	0.816953i	$-0.695661\pi$
$53$	2.51374	−	8.76644i	0.345288	−	1.20416i	0.921992	−	0.387209i	$-0.126561\pi$
$54$	2.18511	+	2.60411i	0.297356	+	0.354375i
$55$	−2.31280	−	1.55203i	−0.311858	−	0.209276i
$56$		−	3.24778i		−	0.434003i
$57$	−0.362162	+	2.60396i	−0.0479696	+	0.344903i
$58$	−2.05039	+	6.31045i	−0.269229	+	0.828603i
$59$	−5.73747	−	10.7906i	−0.746956	−	1.40482i	−0.908471	−	0.417949i	$-0.862749\pi$
$59$	−5.73747	−	10.7906i	−0.746956	−	1.40482i	0.161515	−	0.986870i	$-0.448362\pi$
$60$	−0.491469	−	0.122537i	−0.0634483	−	0.0158194i
$61$	−6.34205	−	4.27777i	−0.812016	−	0.547712i	0.0815363	−	0.996670i	$-0.474017\pi$
$61$	−6.34205	−	4.27777i	−0.812016	−	0.547712i	−0.893553	+	0.448958i	$0.851795\pi$
$62$	−0.667757	−	0.0233186i	−0.0848053	−	0.00296146i
$63$	4.53711	+	7.26089i	0.571622	+	0.914786i
$64$	0.913545	−	0.406737i	0.114193	−	0.0508421i
$65$	2.02112	+	3.50068i	0.250689	+	0.434206i
$66$	1.61555	−	1.17963i	0.198861	−	0.145203i
$67$	−7.37788	−	1.30092i	−0.901351	−	0.158932i	−0.296277	−	0.955102i	$-0.595745\pi$
$67$	−7.37788	−	1.30092i	−0.901351	−	0.158932i	−0.605074	+	0.796169i	$0.706856\pi$
$68$	−7.58267	−	0.796970i	−0.919533	−	0.0966469i
$69$	−0.936812	+	0.843509i	−0.112779	+	0.101547i
$70$	−2.52887	−	1.02173i	−0.302258	−	0.122120i
$71$	3.18975	+	11.1240i	0.378554	+	1.32017i	0.888068	+	0.459712i	$0.152047\pi$
$71$	3.18975	+	11.1240i	0.378554	+	1.32017i	−0.509514	+	0.860462i	$0.670175\pi$
$72$	−1.47416	+	2.18553i	−0.173731	+	0.257567i
$73$	1.91425	−	3.06344i	0.224046	−	0.358549i	−0.716859	−	0.697218i	$-0.754421\pi$
$73$	1.91425	−	3.06344i	0.224046	−	0.358549i	0.940906	+	0.338669i	$0.109977\pi$
$74$	−1.00425	+	7.14558i	−0.116741	+	0.830657i
$75$	1.52256	−	2.09562i	0.175810	−	0.241981i
$76$	−4.31561	+	0.612819i	−0.495034	+	0.0702952i
$77$	9.49881	−	5.07955i	1.08249	−	0.578868i
$78$	−2.85902	+	0.504122i	−0.323720	+	0.0570805i
$79$	10.5838	−	0.740094i	1.19077	−	0.0832671i	0.539418	−	0.842038i	$-0.318644\pi$
$79$	10.5838	−	0.740094i	1.19077	−	0.0832671i	0.651357	+	0.758771i	$0.274200\pi$
$80$	−0.0293085	−	0.839285i	−0.00327679	−	0.0938349i
$81$	0.204453	−	5.85477i	0.0227170	−	0.650530i
$82$	−1.95548	−	0.136740i	−0.215947	−	0.0151005i
$83$	−10.9847	+	1.15454i	−1.20573	+	0.126727i	−0.685998	−	0.727603i	$-0.740634\pi$
$83$	−10.9847	+	1.15454i	−1.20573	+	0.126727i	−0.519730	+	0.854331i	$0.673967\pi$
$84$	1.31074	−	1.45572i	0.143013	−	0.158832i
$85$	−3.00601	+	5.65349i	−0.326048	+	0.613207i
$86$	−6.09231	−	6.30878i	−0.656951	−	0.680293i
$87$	−3.46579	+	2.00098i	−0.371572	+	0.214527i
$88$	2.61837	+	2.03571i	0.279120	+	0.217008i
$89$	−1.09642	+	1.30666i	−0.116220	+	0.138506i	−0.821018	−	0.570903i	$-0.806593\pi$
$89$	−1.09642	+	1.30666i	−0.116220	+	0.138506i	0.704798	+	0.709408i	$0.251038\pi$
$90$	1.23799	+	1.83540i	0.130496	+	0.193468i
$91$	−15.6232	+	0.545574i	−1.63776	+	0.0571917i
$92$	−1.77248	−	1.10757i	−0.184794	−	0.115472i
$93$	−0.289891	−	0.279945i	−0.0300603	−	0.0290289i
$94$	5.07675	−	3.68847i	0.523626	−	0.380437i
$95$	−0.880492	+	3.55312i	−0.0903366	+	0.364542i
$96$	0.573619	+	0.186380i	0.0585448	+	0.0190224i
$97$	12.0957	+	5.89945i	1.22813	+	0.598999i	0.934173	−	0.356820i	$-0.116139\pi$
$97$	12.0957	+	5.89945i	1.22813	+	0.598999i	0.293956	+	0.955819i	$0.405028\pi$
$98$	2.71801	−	2.28068i	0.274560	−	0.230383i
$99$	−8.69761	−	0.893297i	−0.874143	−	0.0897797i
$100$	4.03574	+	1.46889i	0.403574	+	0.146889i
$101$	−10.6302	+	2.65042i	−1.05775	+	0.263726i	−0.731700	−	0.681627i	$-0.761273\pi$
$101$	−10.6302	+	2.65042i	−1.05775	+	0.263726i	−0.326048	+	0.945353i	$0.605717\pi$
$102$	−3.07706	−	3.41742i	−0.304674	−	0.338375i
$103$	−5.06175	−	4.55762i	−0.498749	−	0.449076i	0.380958	−	0.924593i	$-0.375594\pi$
$103$	−5.06175	−	4.55762i	−0.498749	−	0.449076i	−0.879707	+	0.475517i	$0.842261\pi$
$104$	−2.11003	−	4.32621i	−0.206906	−	0.424220i
$105$	−0.721142	−	1.47856i	−0.0703763	−	0.144293i
$106$	6.77727	+	6.10228i	0.658267	+	0.592706i
$107$	0.481519	+	0.534781i	0.0465502	+	0.0516992i	0.765970	−	0.642876i	$-0.222259\pi$
$107$	0.481519	+	0.534781i	0.0465502	+	0.0516992i	−0.719420	+	0.694575i	$0.755592\pi$
$108$	−3.29845	+	0.822396i	−0.317393	+	0.0791351i
$109$	−6.64776	−	2.41959i	−0.636740	−	0.231754i	0.00342218	−	0.999994i	$-0.498911\pi$
$109$	−6.64776	−	2.41959i	−0.636740	−	0.231754i	−0.640162	+	0.768240i	$0.721133\pi$
$110$	2.40882	−	1.39836i	0.229672	−	0.133329i
$111$	−3.33393	+	2.79750i	−0.316442	+	0.265527i
$112$	2.91909	+	1.42374i	0.275828	+	0.134530i
$113$	15.2356	+	4.95036i	1.43325	+	0.465691i	0.919786	−	0.392421i	$-0.128362\pi$
$113$	15.2356	+	4.95036i	1.43325	+	0.465691i	0.513463	+	0.858112i	$0.328362\pi$
$114$	−2.18166	−	1.46701i	−0.204331	−	0.137398i
$115$	−1.42002	+	1.03170i	−0.132417	+	0.0962067i
$116$	−4.77297	−	4.60920i	−0.443159	−	0.427953i
$117$	10.7609	+	6.72418i	0.994849	+	0.621651i
$118$	12.2137	−	0.426511i	1.12436	−	0.0392636i
$119$	−13.8470	−	20.5291i	−1.26935	−	1.88190i
$120$	0.325581	−	0.388012i	0.0297214	−	0.0354205i
$121$	−1.85870	+	10.8418i	−0.168973	+	0.985621i
$122$	6.62500	−	3.82495i	0.599800	−	0.346294i
$123$	−0.821299	−	0.850480i	−0.0740541	−	0.0766852i
$124$	0.313684	−	0.589954i	0.0281697	−	0.0529794i
$125$	5.22303	−	5.80076i	0.467162	−	0.518836i
$126$	−8.51498	+	0.894961i	−0.758575	+	0.0797294i
$127$	−18.7852	−	1.31359i	−1.66692	−	0.116562i	−0.795128	−	0.606442i	$-0.792596\pi$
$127$	−18.7852	−	1.31359i	−1.66692	−	0.116562i	−0.871790	+	0.489880i	$0.837041\pi$
$128$	−0.0348995	+	0.999391i	−0.00308471	+	0.0883345i
$129$	−0.184607	−	5.28645i	−0.0162537	−	0.465446i
$130$	−4.03239	+	0.281972i	−0.353664	+	0.0247306i
$131$	−13.3679	+	2.35713i	−1.16796	+	0.205943i	−0.723804	−	0.690006i	$-0.757608\pi$
$131$	−13.3679	+	2.35713i	−1.16796	+	0.205943i	−0.444157	+	0.895949i	$0.646497\pi$
$132$	0.352036	+	1.96917i	0.0306408	+	0.171394i
$133$	−10.5341	−	9.45766i	−0.913420	−	0.820083i
$134$	4.40351	−	6.06091i	0.380405	−	0.523582i
$135$	−0.397315	+	2.82704i	−0.0341954	+	0.243313i
$136$	4.04033	−	6.46589i	0.346456	−	0.554445i
$137$	−7.69006	+	11.4010i	−0.657007	+	0.974052i	0.342398	+	0.939555i	$0.388761\pi$
$137$	−7.69006	+	11.4010i	−0.657007	+	0.974052i	−0.999405	+	0.0344974i	$0.989017\pi$
$138$	−0.347470	−	1.21177i	−0.0295786	−	0.103153i
$139$	2.72386	+	1.10051i	0.231035	+	0.0933440i	0.487205	−	0.873288i	$-0.338016\pi$
$139$	2.72386	+	1.10051i	0.231035	+	0.0933440i	−0.256171	+	0.966632i	$0.582461\pi$
$140$	2.02691	−	1.82504i	0.171305	−	0.154244i
$141$	3.76409	+	0.395622i	0.316993	+	0.0333173i
$142$	−11.3965	−	2.00950i	−0.956370	−	0.168634i
$143$	9.35278	−	12.9374i	0.782119	−	1.08188i
$144$	−1.31811	−	2.28304i	−0.109843	−	0.190253i
$145$	−5.09048	+	2.26643i	−0.422741	+	0.188216i
$146$	1.91425	+	3.06344i	0.158425	+	0.253532i
$147$	2.13870	+	0.0746850i	0.176397	+	0.00615991i
$148$	−5.98217	−	4.03503i	−0.491731	−	0.331677i
$149$	19.3449	+	4.82322i	1.58479	+	0.395133i	0.932016	−	0.362416i	$-0.118048\pi$
$149$	19.3449	+	4.82322i	1.58479	+	0.395133i	0.652777	+	0.757550i	$0.273604\pi$
$150$	1.21608	+	2.28712i	0.0992929	+	0.186743i
$151$	1.09714	−	3.37664i	0.0892838	−	0.274787i	−0.896438	−	0.443169i	$-0.853854\pi$
$151$	1.09714	−	3.37664i	0.0892838	−	0.274787i	0.985722	+	0.168382i	$0.0538542\pi$
$152$	1.34104	−	4.14748i	0.108773	−	0.336405i
$153$			20.0997i			1.62497i
$154$	0.401466	+	10.7642i	0.0323511	+	0.867404i
$155$	−0.360682	−	0.429845i	−0.0289707	−	0.0345259i
$156$	0.800208	−	2.79066i	0.0640679	−	0.223431i
$157$	7.57451	−	9.69493i	0.604512	−	0.773739i	−0.384252	−	0.923228i	$-0.625541\pi$
$157$	7.57451	−	9.69493i	0.604512	−	0.773739i	0.988763	+	0.149489i	$0.0477628\pi$
$158$	−3.97446	+	9.83713i	−0.316191	+	0.782600i
$159$	0.574955	+	5.47033i	0.0455969	+	0.433825i
$160$	0.767192	+	0.341576i	0.0606519	+	0.0270040i
$161$	−0.944722	−	6.72205i	−0.0744545	−	0.529771i
$162$	5.17261	+	2.75033i	0.406399	+	0.216086i
$163$	−1.64821	+	15.6817i	−0.129098	+	1.22828i	0.717694	+	0.696358i	$0.245197\pi$
$163$	−1.64821	+	15.6817i	−0.129098	+	1.22828i	−0.846792	+	0.531924i	$0.821469\pi$
$164$	0.980128	−	1.69763i	0.0765351	−	0.132563i
$165$	1.64403	+	0.345375i	0.127988	+	0.0268874i
$166$	3.77768	−	10.3791i	0.293205	−	0.805575i
$167$	23.0810	+	6.61838i	1.78606	+	0.512145i	0.995025	−	0.0996222i	$-0.0317634\pi$
$167$	23.0810	+	6.61838i	1.78606	+	0.512145i	0.791038	+	0.611768i	$0.209541\pi$
$168$	0.733804	+	1.81623i	0.0566142	+	0.140125i
$169$	−8.97812	+	4.77375i	−0.690624	+	0.367211i
$170$	−3.76357	−	5.18012i	−0.288653	−	0.397297i
$171$	2.79589	+	11.1457i	0.213807	+	0.852334i
$172$	8.34098	−	2.71015i	0.635994	−	0.206647i
$173$	16.7919	+	2.35994i	1.27666	+	0.179423i	0.744731	−	0.667365i	$-0.232578\pi$
$173$	16.7919	+	2.35994i	1.27666	+	0.179423i	0.531930	+	0.846788i	$0.321467\pi$
$174$	−0.279162	−	3.99220i	−0.0211632	−	0.302648i
$175$	4.77063	+	13.1072i	0.360626	+	0.990811i
$176$	−2.97750	+	1.46098i	−0.224438	+	0.110126i
$177$	5.64655	+	4.73802i	0.424420	+	0.356131i
$178$	−0.693781	−	1.55826i	−0.0520010	−	0.116796i
$179$	0.0911178	+	0.428676i	0.00681047	+	0.0320407i	0.981422	−	0.191863i	$-0.0614531\pi$
$179$	0.0911178	+	0.428676i	0.00681047	+	0.0320407i	−0.974611	+	0.223904i	$0.928120\pi$
$180$	−2.19235	+	0.308114i	−0.163408	+	0.0229655i
$181$	−7.79129	+	3.80007i	−0.579122	+	0.282457i	−0.704560	−	0.709645i	$-0.748855\pi$
$181$	−7.79129	+	3.80007i	−0.579122	+	0.282457i	0.125438	+	0.992102i	$0.459967\pi$
$182$	6.35840	−	14.2812i	0.471316	−	1.05859i
$183$	4.51313	+	0.959294i	0.333620	+	0.0709131i
$184$	1.77248	−	1.10757i	0.130669	−	0.0816512i
$185$	−5.02381	+	3.38860i	−0.369358	+	0.249135i
$186$	0.378692	−	0.137833i	0.0277671	−	0.0101064i
$187$	25.2299	+	1.70410i	1.84499	+	0.124616i
$188$	1.08968	+	6.17987i	0.0794729	+	0.450713i
$189$	−8.93204	−	6.48951i	−0.649710	−	0.472042i
$190$	−2.80754	−	2.34897i	−0.203680	−	0.170412i
$191$	2.69431	+	8.29224i	0.194954	+	0.600005i	0.999977	+	0.00676256i	$0.00215261\pi$
$191$	2.69431	+	8.29224i	0.194954	+	0.600005i	−0.805024	+	0.593243i	$0.797847\pi$
$192$	−0.418976	+	0.433862i	−0.0302370	+	0.0313113i
$193$	4.53189	−	18.1764i	0.326213	−	1.30837i	−0.553495	−	0.832853i	$-0.686706\pi$
$193$	4.53189	−	18.1764i	0.326213	−	1.30837i	0.879708	−	0.475515i	$-0.157738\pi$
$194$	−10.6048	+	8.28537i	−0.761379	+	0.594855i
$195$	−1.92119	−	1.50100i	−0.137580	−	0.107489i
$196$	0.858364	+	3.44271i	0.0613117	+	0.245908i
$197$	13.8141	+	7.97556i	0.984212	+	0.568235i	0.903539	−	0.428506i	$-0.140960\pi$
$197$	13.8141	+	7.97556i	0.984212	+	0.568235i	0.0806725	+	0.996741i	$0.474293\pi$
$198$	4.61567	−	7.42576i	0.328021	−	0.527726i
$199$	−1.72165	+	9.76399i	−0.122045	+	0.692151i	0.860974	+	0.508648i	$0.169855\pi$
$199$	−1.72165	+	9.76399i	−0.122045	+	0.692151i	−0.983019	+	0.183502i	$0.941256\pi$
$200$	−3.08938	+	2.98338i	−0.218452	+	0.210957i
$201$	4.41979	−	0.939456i	0.311748	−	0.0662641i
$202$	2.27781	−	10.7163i	0.160266	−	0.753993i
$203$	1.50323	−	21.4972i	0.105506	−	1.50881i
$204$	4.42045	−	1.26754i	0.309494	−	0.0887459i
$205$	−1.01351	−	1.29724i	−0.0707867	−	0.0906029i
$206$	6.31529	−	2.55154i	0.440007	−	0.177774i
$207$	−2.41538	+	4.95227i	−0.167881	+	0.344206i
$208$	4.81335			0.333746
$209$	14.2275	−	2.56454i	0.984140	−	0.177393i
$210$	1.64505			0.113519
$211$	1.21123	−	2.48340i	0.0833848	−	0.170964i	−0.853027	−	0.521866i	$-0.825236\pi$
$211$	1.21123	−	2.48340i	0.0833848	−	0.170964i	0.936412	+	0.350902i	$0.114125\pi$
$212$	−8.45566	+	3.41631i	−0.580737	+	0.234633i
$213$	−4.29713	−	5.50007i	−0.294434	−	0.376859i
$214$	−0.691742	+	0.198354i	−0.0472865	+	0.0135592i
$215$	0.513771	−	7.34727i	0.0350389	−	0.501080i
$216$	0.706781	−	3.32514i	0.0480903	−	0.226247i
$217$	2.12263	−	0.451180i	0.144094	−	0.0306281i
$218$	5.08890	−	4.91429i	0.344664	−	0.332838i
$219$	−0.378336	+	2.14565i	−0.0255656	+	0.144989i
$220$	0.200884	+	2.77804i	0.0135436	+	0.187295i
$221$	−31.7823	−	18.3495i	−2.13791	−	1.23432i
$222$	−1.05288	−	4.22286i	−0.0706644	−	0.283420i
$223$	13.6860	+	10.6927i	0.916480	+	0.716033i	0.959103	−	0.283058i	$-0.0913490\pi$
$223$	13.6860	+	10.6927i	0.916480	+	0.716033i	−0.0426223	+	0.999091i	$0.513571\pi$
$224$	−2.55929	+	1.99954i	−0.171000	+	0.133600i
$225$	2.73901	−	10.9856i	0.182601	−	0.732373i
$226$	−11.1282	+	11.5236i	−0.740238	+	0.766539i
$227$	−0.280044	−	0.861887i	−0.0185872	−	0.0572055i	0.941333	−	0.337480i	$-0.109575\pi$
$227$	−0.280044	−	0.861887i	−0.0185872	−	0.0572055i	−0.959920	+	0.280274i	$0.909575\pi$
$228$	2.27492	−	1.31777i	0.150660	−	0.0872714i
$229$	−7.11049	−	5.16608i	−0.469875	−	0.341384i	0.327518	−	0.944845i	$-0.393788\pi$
$229$	−7.11049	−	5.16608i	−0.469875	−	0.341384i	−0.797392	+	0.603461i	$0.793788\pi$
$230$	−0.304794	−	1.72857i	−0.0200975	−	0.113979i
$231$	−4.16426	+	4.98675i	−0.273988	+	0.328104i
$232$	6.23505	−	2.26937i	0.409351	−	0.148992i
$233$	0.792888	−	0.534810i	0.0519438	−	0.0350365i	−0.532947	−	0.846149i	$-0.678915\pi$
$233$	0.792888	−	0.534810i	0.0519438	−	0.0350365i	0.584890	+	0.811112i	$0.301138\pi$
$234$	−10.7609	+	6.72418i	−0.703465	+	0.439573i
$235$	5.15474	+	1.09567i	0.336258	+	0.0714738i
$236$	−4.97078	+	11.1646i	−0.323570	+	0.726751i
$237$	−5.75149	+	2.80519i	−0.373599	+	0.182216i
$238$	24.5215	−	3.44628i	1.58949	−	0.223389i
$239$	2.22898	+	10.4865i	0.144181	+	0.678318i	0.989557	+	0.144145i	$0.0460433\pi$
$239$	2.22898	+	10.4865i	0.144181	+	0.678318i	−0.845376	+	0.534172i	$0.820623\pi$
$240$	0.206018	+	0.462724i	0.0132984	+	0.0298687i
$241$	1.80031	+	1.51064i	0.115968	+	0.0973090i	0.698928	−	0.715192i	$-0.253661\pi$
$241$	1.80031	+	1.51064i	0.115968	+	0.0973090i	−0.582959	+	0.812501i	$0.698105\pi$
$242$	−8.92977	−	6.42334i	−0.574027	−	0.412908i
$243$	4.69651	+	12.9036i	0.301281	+	0.827763i
$244$	0.533630	+	7.63126i	0.0341621	+	0.488541i
$245$	2.95069	+	0.414692i	0.188513	+	0.0264937i
$246$	1.12444	−	0.365353i	0.0716917	−	0.0232940i
$247$	−20.1764	−	5.75425i	−1.28379	−	0.366134i
$248$	0.392737	+	0.540556i	0.0249388	+	0.0343254i
$249$	5.88202	−	3.12753i	0.372758	−	0.198199i
$250$	2.92406	+	7.23731i	0.184934	+	0.457728i
$251$	21.9350	+	6.28977i	1.38453	+	0.397007i	0.883503	−	0.468426i	$-0.155179\pi$
$251$	21.9350	+	6.28977i	1.38453	+	0.397007i	0.501025	+	0.865433i	$0.332957\pi$
$252$	2.92834	−	8.04554i	0.184468	−	0.506821i
$253$	6.01149	+	3.45174i	0.377939	+	0.217009i
$254$	9.41554	−	16.3082i	0.590784	−	1.02327i
$255$	0.403677	−	3.84073i	0.0252792	−	0.240516i
$256$	−0.882948	−	0.469472i	−0.0551842	−	0.0293420i
$257$	−1.75418	−	12.4816i	−0.109423	−	0.778583i	−0.965251	−	0.261323i	$-0.915841\pi$
$257$	−1.75418	−	12.4816i	−0.109423	−	0.778583i	0.855829	−	0.517260i	$-0.173048\pi$
$258$	4.83235	+	2.15150i	0.300849	+	0.133947i
$259$	−2.44966	−	23.3070i	−0.152215	−	1.44823i
$260$	1.51425	−	3.74790i	0.0939097	−	0.232435i
$261$	−10.7691	+	13.7838i	−0.666589	+	0.853195i
$262$	3.74154	−	13.0483i	0.231153	−	0.806127i
$263$	13.7684	+	16.4085i	0.848993	+	1.01179i	0.999730	+	0.0232165i	$0.00739071\pi$
$263$	13.7684	+	16.4085i	0.848993	+	1.01179i	−0.150738	+	0.988574i	$0.548165\pi$
$264$	−1.92420	−	0.546817i	−0.118426	−	0.0336543i
$265$			7.65871i			0.470471i
$266$	13.1183	−	5.32200i	0.804336	−	0.326313i
$267$	0.317913	−	0.978436i	0.0194560	−	0.0598793i
$268$	3.51714	+	6.61477i	0.214843	+	0.404061i
$269$	−8.81175	−	2.19702i	−0.537262	−	0.133955i	−0.0361655	−	0.999346i	$-0.511514\pi$
$269$	−8.81175	−	2.19702i	−0.537262	−	0.133955i	−0.501097	+	0.865391i	$0.667070\pi$
$270$	−2.36676	−	1.59640i	−0.144036	−	0.0971538i
$271$	−30.5317	−	1.06619i	−1.85467	−	0.0647665i	−0.914324	−	0.404983i	$-0.867277\pi$
$271$	−30.5317	−	1.06619i	−1.85467	−	0.0647665i	−0.940347	+	0.340217i	$0.889500\pi$
$272$	4.04033	+	6.46589i	0.244981	+	0.392052i
$273$	8.61355	−	3.83500i	0.521316	−	0.232105i
$274$	−6.87604	−	11.9096i	−0.415397	−	0.719488i
$275$	−13.5573	−	4.36950i	−0.817536	−	0.263491i
$276$	1.24145	+	0.218902i	0.0747267	+	0.0131763i
$277$	−7.77701	−	0.817397i	−0.467275	−	0.0491126i	−0.132035	−	0.991245i	$-0.542151\pi$
$277$	−7.77701	−	0.817397i	−0.467275	−	0.0491126i	−0.335241	+	0.942133i	$0.608818\pi$
$278$	−2.18319	+	1.96576i	−0.130939	+	0.117898i
$279$	−1.63317	−	0.659843i	−0.0977753	−	0.0395038i
$280$	0.751795	+	2.62182i	0.0449283	+	0.156684i
$281$	8.84405	−	13.1118i	0.527592	−	0.782187i	−0.467196	−	0.884154i	$-0.654736\pi$
$281$	8.84405	−	13.1118i	0.527592	−	0.782187i	0.994788	+	0.101967i	$0.0325136\pi$
$282$	−2.00565	+	3.20971i	−0.119435	+	0.191135i
$283$	−3.20519	+	22.8061i	−0.190529	+	1.35568i	0.626650	+	0.779301i	$0.284426\pi$
$283$	−3.20519	+	22.8061i	−0.190529	+	1.35568i	−0.817179	+	0.576384i	$0.804463\pi$
$284$	6.80201	−	9.36217i	0.403625	−	0.555542i
$285$	−0.310402	−	2.18592i	−0.0183866	−	0.129482i
$286$	7.52810	+	14.0776i	0.445146	+	0.832427i
$287$	6.26977	−	1.10553i	0.370093	−	0.0652573i
$288$	2.62980	−	0.183894i	0.154963	−	0.0108360i
$289$	−1.43549	−	41.1069i	−0.0844404	−	2.41806i
$290$	0.194468	−	5.56883i	0.0114195	−	0.327013i
$291$	−8.09708	−	0.566203i	−0.474659	−	0.0331914i
$292$	−3.59256	+	0.377593i	−0.210239	+	0.0220970i
$293$	−0.113087	+	0.125596i	−0.00660663	+	0.00733741i	−0.746439	−	0.665454i	$-0.768238\pi$
$293$	−0.113087	+	0.125596i	−0.00660663	+	0.00733741i	0.739832	+	0.672791i	$0.234905\pi$
$294$	−1.00467	+	1.88951i	−0.0585935	+	0.110198i
$295$	7.12946	+	7.38278i	0.415093	+	0.429842i
$296$	6.24907	−	3.60790i	0.363220	−	0.209705i
$297$	10.8305	−	3.13341i	0.628447	−	0.181819i
$298$	−12.8153	+	15.2727i	−0.742371	+	0.884723i
$299$	−5.62562	−	8.34033i	−0.325338	−	0.482334i
$300$	−2.58875	+	0.0904011i	−0.149461	+	0.00521931i
$301$	24.1556	+	15.0941i	1.39231	+	0.870011i
$302$	2.55395	+	2.46632i	0.146963	+	0.141921i
$303$	5.34582	−	3.88396i	0.307109	−	0.223128i
$304$	3.13986	+	3.02345i	0.180083	+	0.173407i
$305$	6.10993	+	1.98524i	0.349853	+	0.113674i
$306$	−18.0655	−	8.81113i	−1.03274	−	0.503699i
$307$	−12.0209	+	10.0867i	−0.686069	+	0.575681i	−0.917773	−	0.397106i	$-0.870015\pi$
$307$	−12.0209	+	10.0867i	−0.686069	+	0.575681i	0.231703	+	0.972786i	$0.425570\pi$
$308$	−9.85079	−	4.35788i	−0.561301	−	0.248313i
$309$	3.86038	+	1.40507i	0.219610	+	0.0799314i
$310$	0.544454	−	0.135748i	0.0309229	−	0.00770995i
$311$	9.33608	+	10.3688i	0.529401	+	0.587959i	0.947225	−	0.320569i	$-0.103874\pi$
$311$	9.33608	+	10.3688i	0.529401	+	0.587959i	−0.417825	+	0.908528i	$0.637207\pi$
$312$	2.15744	+	1.94257i	0.122141	+	0.109976i
$313$	7.41528	+	15.2036i	0.419137	+	0.859357i	0.999003	+	0.0446456i	$0.0142159\pi$
$313$	7.41528	+	15.2036i	0.419137	+	0.859357i	−0.579866	+	0.814712i	$0.696895\pi$
$314$	5.39330	+	11.0579i	0.304361	+	0.624033i
$315$	−5.34339	−	4.81121i	−0.301066	−	0.271081i
$316$	−7.09926	−	7.88453i	−0.399365	−	0.443539i
$317$	−26.9870	+	6.72861i	−1.51574	+	0.377916i	−0.908936	−	0.416935i	$-0.863104\pi$
$317$	−26.9870	+	6.72861i	−1.51574	+	0.377916i	−0.606804	+	0.794852i	$0.707549\pi$
$318$	−5.16874	−	1.88127i	−0.289849	−	0.105496i
$319$	16.3889	+	14.6864i	0.917602	+	0.822279i
$320$	−0.643322	+	0.539811i	−0.0359628	+	0.0301763i
$321$	−0.390104	−	0.190266i	−0.0217735	−	0.0106196i
$322$	6.45587	+	2.09764i	0.359772	+	0.116897i
$323$	−9.20629	−	31.9336i	−0.512251	−	1.77683i
$324$	−4.73950	+	3.44345i	−0.263305	+	0.191303i
$325$	14.8703	+	14.3600i	0.824854	+	0.796552i
$326$	−13.3721	−	8.35579i	−0.740609	−	0.462784i
$327$	4.26425	−	0.148911i	0.235813	−	0.00823479i
$328$	1.09616	+	1.62513i	0.0605254	+	0.0897325i
$329$	−13.1003	+	15.6124i	−0.722245	+	0.860738i
$330$	−1.03112	+	1.32624i	−0.0567611	+	0.0730073i
$331$	−8.43964	+	4.87263i	−0.463885	+	0.267824i	−0.713676	−	0.700476i	$-0.752971\pi$
$331$	−8.43964	+	4.87263i	−0.463885	+	0.267824i	0.249792	+	0.968300i	$0.419638\pi$
$332$	7.67265	+	7.94526i	0.421091	+	0.436053i
$333$	−8.93051	+	16.7958i	−0.489389	+	0.920406i
$334$	−16.0666	+	17.8438i	−0.879126	+	0.976368i
$335$	6.25703	−	0.657641i	0.341858	−	0.0359307i
$336$	−1.95409	−	0.136644i	−0.106605	−	0.00745452i
$337$	0.727234	−	20.8253i	0.0396150	−	1.13442i	−0.803024	−	0.595946i	$-0.796777\pi$
$337$	0.727234	−	20.8253i	0.0396150	−	1.13442i	0.842639	−	0.538478i	$-0.181001\pi$
$338$	−0.354870	−	10.1622i	−0.0193024	−	0.552748i
$339$	−9.63857	+	0.673995i	−0.523495	+	0.0366064i
$340$	6.30570	−	1.11186i	0.341975	−	0.0602993i
$341$	−0.966724	+	1.99407i	−0.0523510	+	0.107985i
$342$	−11.2433	−	2.37303i	−0.607970	−	0.128319i
$343$	6.58967	−	9.06990i	0.355809	−	0.489729i
$344$	−1.22058	+	8.68488i	−0.0658093	+	0.468257i
$345$	0.561000	−	0.897788i	0.0302032	−	0.0483353i
$346$	−9.48216	+	14.0579i	−0.509764	+	0.755757i
$347$	−6.39820	−	22.3132i	−0.343473	−	1.19783i	−0.923616	−	0.383319i	$-0.874781\pi$
$347$	−6.39820	−	22.3132i	−0.343473	−	1.19783i	0.580143	−	0.814515i	$-0.302997\pi$
$348$	3.71054	+	1.49916i	0.198906	+	0.0803632i
$349$	−1.55750	+	1.40238i	−0.0833710	+	0.0750676i	−0.709763	−	0.704441i	$-0.751198\pi$
$349$	−1.55750	+	1.40238i	−0.0833710	+	0.0750676i	0.626392	+	0.779509i	$0.284531\pi$
$350$	−13.8720	−	1.45800i	−0.741489	−	0.0779336i
$351$	−16.1140	−	2.84134i	−0.860104	−	0.151660i
$352$	−0.00786894	−	3.31662i	−0.000419416	−	0.176776i
$353$	4.74408	+	8.21699i	0.252502	+	0.437347i	0.964214	−	0.265125i	$-0.0854132\pi$
$353$	4.74408	+	8.21699i	0.252502	+	0.437347i	−0.711712	+	0.702471i	$0.752080\pi$
$354$	−6.73378	+	2.99807i	−0.357897	+	0.159346i
$355$	−5.14994	−	8.24163i	−0.273331	−	0.437420i
$356$	1.70469	+	0.0595289i	0.0903481	+	0.00315503i
$357$	12.3819	+	8.35168i	0.655319	+	0.442018i
$358$	−0.425235	−	0.106023i	−0.0224743	−	0.00560348i
$359$	2.36284	+	4.44385i	0.124706	+	0.234537i	0.937478	−	0.348044i	$-0.113154\pi$
$359$	2.36284	+	4.44385i	0.124706	+	0.234537i	−0.812773	+	0.582581i	$0.802043\pi$
$360$	0.684130	−	2.10554i	0.0360568	−	0.110971i
$361$	−9.54706	−	16.4272i	−0.502477	−	0.864591i
$362$		−	8.66860i		−	0.455612i
$363$	−1.41017	−	6.48293i	−0.0740150	−	0.340266i
$364$	10.0485	+	11.9754i	0.526686	+	0.627680i
$365$	−0.836184	+	2.91612i	−0.0437679	+	0.152637i
$366$	−2.84063	+	3.63584i	−0.148482	+	0.190049i
$367$	1.21509	−	3.00744i	0.0634270	−	0.156987i	−0.892142	−	0.451755i	$-0.850798\pi$
$367$	1.21509	−	3.00744i	0.0634270	−	0.156987i	0.955569	+	0.294768i	$0.0952424\pi$
$368$	0.218472	+	2.07862i	0.0113886	+	0.108356i
$369$	−4.72090	−	2.10188i	−0.245760	−	0.109420i
$370$	−0.843362	−	6.00083i	−0.0438443	−	0.311968i
$371$	−26.1519	−	13.9052i	−1.35774	−	0.721923i
$372$	−0.0421246	+	0.400788i	−0.00218406	+	0.0207799i
$373$	4.54041	−	7.86422i	0.235094	−	0.407194i	−0.724206	−	0.689583i	$-0.757794\pi$
$373$	4.54041	−	7.86422i	0.235094	−	0.407194i	0.959300	+	0.282389i	$0.0911270\pi$
$374$	−12.5917	+	21.9295i	−0.651101	+	1.13395i
$375$	−1.61020	+	4.42400i	−0.0831505	+	0.228454i
$376$	−6.03211	−	1.72968i	−0.311083	−	0.0892015i
$377$	−11.9640	−	29.6120i	−0.616178	−	1.52509i
$378$	9.74828	−	5.18325i	0.501397	−	0.266598i
$379$	−5.48419	−	7.54834i	−0.281704	−	0.387732i	0.644593	−	0.764526i	$-0.277027\pi$
$379$	−5.48419	−	7.54834i	−0.281704	−	0.387732i	−0.926297	+	0.376793i	$0.877027\pi$
$380$	3.34198	−	1.49368i	0.171440	−	0.0766242i
$381$	10.8019	−	3.50974i	0.553397	−	0.179810i
$382$	−8.63412	−	1.21345i	−0.441760	−	0.0620854i
$383$	0.105544	+	1.50935i	0.00539305	+	0.0771242i	0.999515	−	0.0311423i	$-0.00991449\pi$
$383$	0.105544	+	1.50935i	0.00539305	+	0.0771242i	−0.994122	+	0.108266i	$0.965470\pi$
$384$	−0.206286	−	0.566765i	−0.0105270	−	0.0289226i
$385$	−6.49224	+	6.29932i	−0.330875	+	0.321043i
$386$	14.3502	+	12.0413i	0.730406	+	0.612884i
$387$	−9.40387	−	21.1214i	−0.478025	−	1.07366i
$388$	−2.79801	−	13.1636i	−0.142047	−	0.668280i
$389$	5.88606	−	0.827232i	0.298435	−	0.0419423i	0.0116336	−	0.999932i	$-0.496297\pi$
$389$	5.88606	−	0.827232i	0.298435	−	0.0419423i	0.286802	+	0.957990i	$0.407408\pi$
$390$	2.19129	−	1.06876i	0.110960	−	0.0541189i
$391$	6.48160	−	14.5579i	0.327789	−	0.736226i
$392$	−3.47057	−	0.737692i	−0.175290	−	0.0372591i
$393$	6.94306	−	4.33850i	0.350231	−	0.218849i
$394$	−13.2241	+	8.91975i	−0.666219	+	0.449370i
$395$	−8.37264	+	3.04739i	−0.421273	+	0.153331i
$396$	4.65086	+	7.40378i	0.233714	+	0.372054i
$397$	−4.81331	−	27.2976i	−0.241573	−	1.37003i	−0.828318	−	0.560258i	$-0.810702\pi$
$397$	−4.81331	−	27.2976i	−0.241573	−	1.37003i	0.586745	−	0.809772i	$-0.300409\pi$
$398$	−8.02109	−	5.82766i	−0.402061	−	0.292114i
$399$	8.02774	+	2.90885i	0.401889	+	0.145625i
$400$	−1.32715	−	4.08454i	−0.0663574	−	0.204227i
$401$	−20.8847	+	21.6267i	−1.04293	+	1.07999i	−0.0462207	+	0.998931i	$0.514718\pi$
$401$	−20.8847	+	21.6267i	−1.04293	+	1.07999i	−0.996710	+	0.0810548i	$0.974171\pi$
$402$	−1.09313	+	4.38431i	−0.0545205	+	0.218670i
$403$	2.53433	−	1.98003i	0.126244	−	0.0986325i
$404$	8.63318	+	6.74498i	0.429517	+	0.335575i
$405$	1.19021	+	4.77368i	0.0591421	+	0.237206i
$406$	18.6626	+	10.7749i	0.926209	+	0.534747i
$407$	20.3256	+	12.6339i	1.00750	+	0.626239i
$408$	−0.798538	+	4.52873i	−0.0395335	+	0.224206i
$409$	11.0616	−	10.6821i	0.546963	−	0.528196i	−0.369016	−	0.929423i	$-0.620305\pi$
$409$	11.0616	−	10.6821i	0.546963	−	0.528196i	0.915979	+	0.401227i	$0.131416\pi$
$410$	1.61024	−	0.342268i	0.0795242	−	0.0169034i
$411$	1.72451	−	8.11316i	0.0850636	−	0.400193i
$412$	−0.475129	+	6.79466i	−0.0234079	+	0.334749i
$413$	−38.1540	+	10.9405i	−1.87744	+	0.538346i
$414$	−3.39223	−	4.34186i	−0.166719	−	0.213391i
$415$	8.60031	−	3.47475i	0.422173	−	0.170569i
$416$	−2.11003	+	4.32621i	−0.103453	+	0.212110i
$417$	−1.77189			−0.0867697
$418$	−3.93195	+	13.9119i	−0.192318	+	0.680451i
$419$	21.3932			1.04513			0.522564	−	0.852600i	$-0.324976\pi$
$419$	21.3932			1.04513			0.522564	+	0.852600i	$0.324976\pi$
$420$	−0.721142	+	1.47856i	−0.0351881	+	0.0721464i
$421$	−11.4765	+	4.63682i	−0.559332	+	0.225985i	−0.636826	−	0.771008i	$-0.719753\pi$
$421$	−11.4765	+	4.63682i	−0.559332	+	0.225985i	0.0774932	+	0.996993i	$0.475308\pi$
$422$	1.70109	+	2.17730i	0.0828079	+	0.105989i
$423$	15.9020	−	4.55982i	0.773182	−	0.221706i
$424$	0.636159	−	9.09750i	0.0308946	−	0.441814i
$425$	−6.80806	+	32.0294i	−0.330240	+	1.55365i
$426$	6.82717	−	1.45116i	0.330777	−	0.0703089i
$427$	−17.8721	+	17.2589i	−0.864894	+	0.835218i
$428$	0.124961	−	0.708686i	0.00604019	−	0.0342556i
$429$	−2.30719	+	9.34805i	−0.111392	+	0.451328i
$430$	6.37846	+	3.68261i	0.307597	+	0.177591i
$431$	2.86467	+	11.4895i	0.137986	+	0.553432i	0.998994	+	0.0448407i	$0.0142780\pi$
$431$	2.86467	+	11.4895i	0.137986	+	0.553432i	−0.861008	+	0.508591i	$0.830166\pi$
$432$	2.67878	+	2.09290i	0.128883	+	0.100695i
$433$	−25.7787	+	20.1405i	−1.23885	+	0.967892i	−0.999995	−	0.00316376i	$-0.998993\pi$
$433$	−25.7787	+	20.1405i	−1.23885	+	0.967892i	−0.238851	+	0.971056i	$0.576771\pi$
$434$	−0.524984	+	2.10559i	−0.0252000	+	0.101072i
$435$	2.33462	−	2.41757i	0.111937	−	0.115914i
$436$	2.18611	+	6.72815i	0.104696	+	0.322220i
$437$	1.56916	−	8.97427i	0.0750633	−	0.429297i
$438$	−1.76264	−	1.28064i	−0.0842224	−	0.0611912i
$439$	−2.78776	−	15.8102i	−0.133052	−	0.754577i	−0.976196	−	0.216889i	$-0.930409\pi$
$439$	−2.78776	−	15.8102i	−0.133052	−	0.754577i	0.843144	−	0.537688i	$-0.180702\pi$
$440$	−2.58494	−	1.03726i	−0.123232	−	0.0494493i
$441$	8.78950	−	3.19912i	0.418548	−	0.152339i
$442$	30.4249	−	20.5219i	1.44717	−	0.976125i
$443$	−8.83261	+	5.51923i	−0.419650	+	0.262226i	−0.723268	−	0.690567i	$-0.757361\pi$
$443$	−8.83261	+	5.51923i	−0.419650	+	0.262226i	0.303618	+	0.952794i	$0.401805\pi$
$444$	4.25703	+	0.904859i	0.202030	+	0.0429427i
$445$	0.582635	−	1.30862i	0.0276195	−	0.0620345i
$446$	−15.6100	+	7.61352i	−0.739156	+	0.360511i
$447$	−11.9078	+	1.67353i	−0.563220	+	0.0791554i
$448$	−0.675252	−	3.17681i	−0.0319027	−	0.150090i
$449$	12.4562	+	27.9772i	0.587847	+	1.32032i	0.925390	+	0.379015i	$0.123737\pi$
$449$	12.4562	+	27.9772i	0.587847	+	1.32032i	−0.337544	+	0.941310i	$0.609596\pi$
$450$	8.67308	+	7.27758i	0.408853	+	0.343068i
$451$	−3.03861	+	5.74765i	−0.143083	+	0.270646i
$452$	−5.47906	−	15.0536i	−0.257713	−	0.708062i
$453$	0.149376	+	2.13618i	0.00701829	+	0.100366i
$454$	0.897422	+	0.126124i	0.0421181	+	0.00591932i
$455$	12.4858	−	4.05687i	0.585342	−	0.190189i
$456$	0.187145	+	2.62235i	0.00876387	+	0.122803i
$457$	17.7679	+	24.4554i	0.831148	+	1.14398i	0.987708	+	0.156308i	$0.0499593\pi$
$457$	17.7679	+	24.4554i	0.831148	+	1.14398i	−0.156561	+	0.987668i	$0.550041\pi$
$458$	7.76027	−	4.12621i	0.362614	−	0.192805i
$459$	−9.70932	−	24.0314i	−0.453192	−	1.12169i
$460$	1.68724	+	0.483809i	0.0786681	+	0.0225577i
$461$	−3.61588	+	9.93455i	−0.168408	+	0.462698i	−0.994973	−	0.100144i	$-0.968070\pi$
$461$	−3.61588	+	9.93455i	−0.168408	+	0.462698i	0.826565	+	0.562842i	$0.190292\pi$
$462$	−2.65657	−	5.92886i	−0.123595	−	0.275835i
$463$	−4.32671	+	7.49408i	−0.201079	+	0.348279i	−0.948876	−	0.315648i	$-0.897778\pi$
$463$	−4.32671	+	7.49408i	−0.201079	+	0.348279i	0.747797	+	0.663927i	$0.231112\pi$
$464$	−0.693567	+	6.59885i	−0.0321981	+	0.306344i
$465$	0.298820	+	0.158885i	0.0138575	+	0.00736814i
$466$	0.133105	+	0.947088i	0.00616595	+	0.0438730i
$467$	−16.0889	−	7.16326i	−0.744507	−	0.331476i	−0.000816461	−	1.00000i	$-0.500260\pi$
$467$	−16.0889	−	7.16326i	−0.744507	−	0.331476i	−0.743691	+	0.668524i	$0.766927\pi$
$468$	−1.32637	−	12.6196i	−0.0613114	−	0.583339i
$469$	−9.11470	+	22.5597i	−0.420878	+	1.04171i
$470$	−3.24447	+	4.15273i	−0.149656	+	0.191551i
$471$	−2.04535	+	7.13299i	−0.0942448	+	0.328671i
$472$	−7.85559	−	9.36193i	−0.361583	−	0.430918i
$473$	−27.3097	+	10.0134i	−1.25570	+	0.460415i
$474$		−	6.39911i		−	0.293921i
$475$	0.680108	+	18.7080i	0.0312055	+	0.858381i
$476$	−7.65204	+	23.5506i	−0.350731	+	1.07944i
$477$	11.2869	+	21.2275i	0.516790	+	0.971940i
$478$	−10.4024	−	2.59360i	−0.475793	−	0.118628i
$479$	11.8597	+	7.99945i	0.541882	+	0.365504i	0.799428	−	0.600762i	$-0.205136\pi$
$479$	11.8597	+	7.99945i	0.541882	+	0.365504i	−0.257546	+	0.966266i	$0.582914\pi$
$480$	−0.506206	−	0.0176771i	−0.0231050	−	0.000806845i
$481$	−18.4053	−	29.4546i	−0.839207	−	1.34301i
$482$	−2.14696	+	0.955889i	−0.0977914	+	0.0435395i
$483$	2.04709	+	3.54566i	0.0931457	+	0.161333i
$484$	9.68781	−	5.21022i	0.440355	−	0.236828i
$485$	−11.1300	−	1.96252i	−0.505388	−	0.0891135i
$486$	−13.6565	−	1.43535i	−0.619469	−	0.0651088i
$487$	9.25960	−	8.33738i	0.419592	−	0.377803i	−0.432117	−	0.901818i	$-0.642233\pi$
$487$	9.25960	−	8.33738i	0.419592	−	0.377803i	0.851709	+	0.524015i	$0.175566\pi$
$488$	−7.09286	−	2.86570i	−0.321079	−	0.129724i
$489$	−2.62140	−	9.14191i	−0.118544	−	0.413411i
$490$	−1.66622	+	2.47027i	−0.0752721	+	0.111596i
$491$	11.6666	−	18.6705i	0.526509	−	0.842590i	−0.472746	−	0.881199i	$-0.656737\pi$
$491$	11.6666	−	18.6705i	0.526509	−	0.842590i	0.999254	+	0.0386091i	$0.0122927\pi$
$492$	−0.164545	+	1.17080i	−0.00741827	+	0.0527838i
$493$	29.7359	−	40.9279i	1.33924	−	1.84330i
$494$	14.0166	−	15.6119i	0.630638	−	0.702414i
$495$	7.22805	−	1.29219i	0.324877	−	0.0580796i
$496$	−0.658013	+	0.116026i	−0.0295457	+	0.00520970i
$497$	37.4927	−	2.62174i	1.68178	−	0.117601i
$498$	0.232493	+	6.65774i	0.0104183	+	0.298341i
$499$	0.174614	−	5.00028i	0.00781678	−	0.223843i	−0.989196	−	0.146602i	$-0.953166\pi$
$499$	0.174614	−	5.00028i	0.00781678	−	0.223843i	0.997012	−	0.0772418i	$-0.0246113\pi$
$500$	−7.78668	−	0.544498i	−0.348231	−	0.0243507i
$501$	−14.4027	+	1.51379i	−0.643467	+	0.0676311i
$502$	−15.2689	+	16.9578i	−0.681484	+	0.756865i
$503$	−5.09164	+	9.57598i	−0.227025	+	0.426972i	−0.970262	−	0.242056i	$-0.922178\pi$
$503$	−5.09164	+	9.57598i	−0.227025	+	0.426972i	0.743237	+	0.669028i	$0.233289\pi$
$504$	5.94759	+	6.15890i	0.264926	+	0.274339i
$505$	7.96789	−	4.60027i	0.354567	−	0.204709i
$506$	−5.73767	+	3.88994i	−0.255070	+	0.172929i
$507$	3.94217	−	4.69809i	0.175078	−	0.208650i
$508$	10.5302	+	15.6117i	0.467202	+	0.692656i
$509$	17.8099	−	0.621936i	0.789411	−	0.0275668i	0.362643	−	0.931928i	$-0.381874\pi$
$509$	17.8099	−	0.621936i	0.789411	−	0.0275668i	0.426768	+	0.904361i	$0.359652\pi$
$510$	3.27506	+	2.04649i	0.145022	+	0.0906200i
$511$	−8.43939	−	8.14982i	−0.373336	−	0.360527i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−8.72681	−	11.9753i	−0.385298	−	0.528724i
$514$	11.9874	+	3.89494i	0.528742	+	0.171799i
$515$	5.14117	+	2.50751i	0.226547	+	0.110494i
$516$	−4.05212	+	3.40013i	−0.178385	+	0.149683i
$517$	−4.37545	−	20.3474i	−0.192432	−	0.894876i
$518$	22.0220	+	8.01537i	0.967593	+	0.352175i
$519$	−9.92356	+	2.47422i	−0.435596	+	0.108606i
$520$	2.70478	+	3.00397i	0.118613	+	0.131733i
$521$	−8.40911	−	7.57160i	−0.368410	−	0.331718i	0.464044	−	0.885812i	$-0.346398\pi$
$521$	−8.40911	−	7.57160i	−0.368410	−	0.331718i	−0.832454	+	0.554094i	$0.813065\pi$
$522$	−7.66793	−	15.7216i	−0.335616	−	0.688115i
$523$	−0.439448	−	0.901002i	−0.0192157	−	0.0393981i	0.888970	−	0.457965i	$-0.151421\pi$
$523$	−0.439448	−	0.901002i	−0.0192157	−	0.0393981i	−0.908186	+	0.418567i	$0.862533\pi$
$524$	10.0876	+	9.08288i	0.440677	+	0.396787i
$525$	−5.62928	−	6.25195i	−0.245682	−	0.272857i
$526$	−20.7835	+	5.18191i	−0.906203	+	0.225942i
$527$	4.78715	+	1.74238i	0.208531	+	0.0758992i
$528$	1.33499	−	1.48975i	0.0580979	−	0.0648330i
$529$	−14.2726	+	11.9762i	−0.620549	+	0.520702i
$530$	−6.88360	−	3.35736i	−0.299005	−	0.145834i
$531$	30.6408	+	9.95580i	1.32970	+	0.432045i
$532$	−0.967311	+	14.1237i	−0.0419383	+	0.612339i
$533$	7.63340	−	5.54599i	0.330639	−	0.240223i
$534$	0.740049	+	0.714657i	0.0320250	+	0.0309262i
$535$	−0.512504	−	0.320248i	−0.0221575	−	0.0138455i
$536$	−7.48713	+	0.261456i	−0.323395	+	0.0112932i
$537$	−0.147810	−	0.219137i	−0.00637847	−	0.00945647i
$538$	5.83749	−	6.95684i	0.251672	−	0.299931i
$539$	−3.27046	−	11.3041i	−0.140868	−	0.486904i
$540$	2.47235	−	1.42741i	0.106393	−	0.0614261i
$541$	17.4936	+	18.1151i	0.752108	+	0.778831i	0.980873	−	0.194651i	$-0.0623575\pi$
$541$	17.4936	+	18.1151i	0.752108	+	0.778831i	−0.228765	+	0.973482i	$0.573469\pi$
$542$	14.3425	−	26.9744i	0.616064	−	1.15865i
$543$	3.49847	−	3.88544i	0.150134	−	0.166740i
$544$	−7.58267	+	0.796970i	−0.325104	+	0.0341698i
$545$	5.92659	+	0.414427i	0.253867	+	0.0177521i
$546$	−0.329057	+	9.42297i	−0.0140823	+	0.403266i
$547$	−0.860771	−	24.6493i	−0.0368039	−	1.05393i	−0.867573	−	0.497310i	$-0.834321\pi$
$547$	−0.860771	−	24.6493i	−0.0368039	−	1.05393i	0.830769	−	0.556617i	$-0.187901\pi$
$548$	13.7186	−	0.959297i	0.586029	−	0.0409791i
$549$	19.8605	−	3.50193i	0.847623	−	0.149459i
$550$	9.87041	−	10.2698i	0.420876	−	0.437904i
$551$	10.7960	−	26.8317i	0.459927	−	1.14307i
$552$	−0.740965	+	1.01985i	−0.0315376	+	0.0434077i
$553$	4.79562	−	34.1226i	0.203931	−	1.45104i
$554$	4.14389	−	6.63161i	0.176057	−	0.281750i
$555$	2.04380	−	3.03006i	0.0867544	−	0.128619i
$556$	−0.809761	−	2.82397i	−0.0343415	−	0.119763i
$557$	21.2083	+	8.56869i	0.898623	+	0.363067i	0.776994	−	0.629508i	$-0.216744\pi$
$557$	21.2083	+	8.56869i	0.898623	+	0.363067i	0.121629	+	0.992576i	$0.461188\pi$
$558$	1.30900	−	1.17863i	0.0554143	−	0.0498953i
$559$	41.9829	+	4.41258i	1.77569	+	0.186632i
$560$	−2.68604	−	0.473622i	−0.113506	−	0.0200142i
$561$	−14.4941	+	4.74747i	−0.611942	+	0.200438i
$562$	7.90787	+	13.6968i	0.333573	+	0.577766i
$563$	−15.2025	+	6.76860i	−0.640710	+	0.285262i	−0.701263	−	0.712902i	$-0.747380\pi$
$563$	−15.2025	+	6.76860i	−0.640710	+	0.285262i	0.0605531	+	0.998165i	$0.480714\pi$
$564$	−2.00565	−	3.20971i	−0.0844531	−	0.135153i
$565$	−13.4451	−	0.469513i	−0.565640	−	0.0197526i
$566$	−19.0930	−	12.8784i	−0.802537	−	0.541318i
$567$	−18.4615	−	4.60296i	−0.775308	−	0.193306i
$568$	5.43285	+	10.2177i	0.227957	+	0.428726i
$569$	−2.61360	+	8.04384i	−0.109568	+	0.337215i	−0.990775	−	0.135514i	$-0.956731\pi$
$569$	−2.61360	+	8.04384i	−0.109568	+	0.337215i	0.881207	+	0.472730i	$0.156731\pi$
$570$	2.10076	+	0.679255i	0.0879911	+	0.0284509i
$571$			22.2753i			0.932193i	0.884734	+	0.466096i	$0.154340\pi$
$571$			22.2753i			0.932193i	−0.884734	+	0.466096i	$0.845660\pi$
$572$	−15.9530	+	0.594990i	−0.667028	+	0.0248778i
$573$	−3.38026	−	4.02844i	−0.141213	−	0.168291i
$574$	−1.75484	+	6.11986i	−0.0732457	+	0.255438i
$575$	−5.52638	+	7.07344i	−0.230466	+	0.294983i
$576$	−0.987547	+	2.44426i	−0.0411478	+	0.101844i
$577$	−1.12564	−	10.7098i	−0.0468611	−	0.445853i	−0.992645	−	0.121058i	$-0.961371\pi$
$577$	−1.12564	−	10.7098i	−0.0468611	−	0.445853i	0.945784	−	0.324795i	$-0.105295\pi$
$578$	37.5759	+	16.7299i	1.56295	+	0.695872i
$579$	1.57245	+	11.1886i	0.0653488	+	0.464981i
$580$	4.91998	+	2.61600i	0.204291	+	0.108623i
$581$	−3.74969	+	35.6760i	−0.155564	+	1.48009i
$582$	4.05842	−	7.02940i	0.168227	−	0.291378i
$583$	27.6025	−	12.3680i	1.14318	−	0.512229i
$584$	1.23550	−	3.39450i	0.0511252	−	0.140465i
$585$	−10.2434	−	2.93726i	−0.423514	−	0.121441i
$586$	−0.0633109	−	0.156700i	−0.00261535	−	0.00647322i
$587$	−27.9180	+	14.8442i	−1.15230	+	0.612687i	−0.931897	−	0.362722i	$-0.881847\pi$
$587$	−27.9180	+	14.8442i	−1.15230	+	0.612687i	−0.220400	+	0.975410i	$0.570736\pi$
$588$	−1.25786	−	1.73130i	−0.0518733	−	0.0713975i
$589$	2.89694	+	0.300289i	0.119366	+	0.0123732i
$590$	−9.76095	+	3.17152i	−0.401852	+	0.130570i
$591$	−9.52711	−	1.33895i	−0.391893	−	0.0550770i
$592$	0.503349	+	7.19822i	0.0206875	+	0.295845i
$593$	3.26524	+	8.97117i	0.134087	+	0.368402i	0.988506	−	0.151184i	$-0.0483085\pi$
$593$	3.26524	+	8.97117i	0.134087	+	0.368402i	−0.854418	+	0.519586i	$0.826086\pi$
$594$	−1.93147	+	11.1080i	−0.0792491	+	0.455765i
$595$	15.9303	+	13.3671i	0.653077	+	0.547997i
$596$	−8.10914	−	18.2134i	−0.332163	−	0.746051i
$597$	−1.24329	−	5.84922i	−0.0508844	−	0.239392i
$598$	9.96235	−	1.40012i	0.407391	−	0.0572550i
$599$	17.3338	−	8.45428i	0.708241	−	0.345432i	−0.0487918	−	0.998809i	$-0.515537\pi$
$599$	17.3338	−	8.45428i	0.708241	−	0.345432i	0.757033	+	0.653377i	$0.226648\pi$
$600$	1.05358	−	2.36638i	0.0430123	−	0.0966071i
$601$	29.0758	+	6.18026i	1.18603	+	0.252098i	0.758359	−	0.651837i	$-0.226002\pi$
$601$	29.0758	+	6.18026i	1.18603	+	0.252098i	0.427669	+	0.903935i	$0.359335\pi$
$602$	−24.1556	+	15.0941i	−0.984511	+	0.615191i
$603$	16.3733	−	11.0439i	0.666772	−	0.449744i
$604$	−3.33629	+	1.21431i	−0.135752	+	0.0494097i
$605$	−1.00919	−	9.18247i	−0.0410295	−	0.373321i
$606$	1.14743	+	6.50740i	0.0466112	+	0.264345i
$607$	13.6129	+	9.89032i	0.552529	+	0.401436i	0.828717	−	0.559668i	$-0.189071\pi$
$607$	13.6129	+	9.89032i	0.552529	+	0.401436i	−0.276188	+	0.961104i	$0.589071\pi$
$608$	−4.09389	+	1.49669i	−0.166029	+	0.0606989i
$609$	4.01644	+	12.3613i	0.162754	+	0.500906i
$610$	−4.46273	+	4.62130i	−0.180691	+	0.187111i
$611$	−7.30719	+	29.3075i	−0.295617	+	1.18566i
$612$	15.8388	−	12.3746i	0.640245	−	0.500214i
$613$	−36.3954	−	28.4352i	−1.47000	−	1.14849i	−0.956996	−	0.290100i	$-0.906311\pi$
$613$	−36.3954	−	28.4352i	−1.47000	−	1.14849i	−0.513001	−	0.858388i	$-0.671466\pi$
$614$	−3.79628	−	15.2261i	−0.153205	−	0.614474i
$615$	0.859874	+	0.496449i	0.0346735	+	0.0200187i
$616$	8.23514	−	6.94346i	0.331803	−	0.279760i
$617$	3.65824	−	20.7469i	0.147275	−	0.835239i	−0.818237	−	0.574881i	$-0.805048\pi$
$617$	3.65824	−	20.7469i	0.147275	−	0.835239i	0.965512	−	0.260358i	$-0.0838406\pi$
$618$	−2.95515	+	2.85375i	−0.118873	+	0.114795i
$619$	−16.5850	+	3.52524i	−0.666606	+	0.141691i	−0.528772	−	0.848764i	$-0.677347\pi$
$619$	−16.5850	+	3.52524i	−0.666606	+	0.141691i	−0.137834	+	0.990455i	$0.544014\pi$
$620$	−0.116664	+	0.548860i	−0.00468533	+	0.0220428i
$621$	0.495623	−	7.08774i	0.0198887	−	0.284421i
$622$	−13.4121	+	3.84584i	−0.537774	+	0.154204i
$623$	3.41066	+	4.36544i	0.136645	+	0.174898i
$624$	−2.69173	+	1.08753i	−0.107755	+	0.0435360i
$625$	6.53985	−	13.4087i	0.261594	−	0.536347i
$626$	−16.9155			−0.676081
$627$	−7.37691	+	4.64872i	−0.294605	+	0.185652i
$628$	−12.3030			−0.490945
$629$	24.1176	−	49.4484i	0.961632	−	1.97164i
$630$	6.66668	−	2.69351i	0.265607	−	0.107312i
$631$	−9.29569	−	11.8979i	−0.370056	−	0.473650i	0.566554	−	0.824025i	$-0.308276\pi$
$631$	−9.29569	−	11.8979i	−0.370056	−	0.473650i	−0.936609	+	0.350375i	$0.886054\pi$
$632$	10.1987	−	2.92442i	0.405682	−	0.116327i
$633$	−0.116249	+	1.66243i	−0.00462047	+	0.0660758i
$634$	5.78268	−	27.2054i	0.229660	−	1.08046i
$635$	15.4687	−	3.28797i	0.613857	−	0.130479i
$636$	3.95670	−	3.82094i	0.156893	−	0.151510i
$637$	−2.96561	+	16.8188i	−0.117502	+	0.666386i
$638$	−20.3844	+	8.29216i	−0.807027	+	0.328290i
$639$	−26.4199	−	15.2535i	−1.04516	−	0.603421i
$640$	−0.203165	−	0.814851i	−0.00803081	−	0.0322098i
$641$	−13.4985	−	10.5462i	−0.533160	−	0.416550i	0.312782	−	0.949825i	$-0.398739\pi$
$641$	−13.4985	−	10.5462i	−0.533160	−	0.416550i	−0.845942	+	0.533275i	$0.820961\pi$
$642$	0.342021	−	0.267216i	0.0134985	−	0.0105462i
$643$	1.39274	−	5.58597i	0.0549243	−	0.220289i	−0.936562	−	0.350503i	$-0.886011\pi$
$643$	1.39274	−	5.58597i	0.0549243	−	0.220289i	0.991486	+	0.130214i	$0.0415663\pi$
$644$	−4.71542	+	4.88296i	−0.185813	+	0.192415i
$645$	1.37273	+	4.22483i	0.0540512	+	0.166352i
$646$	32.7375	+	5.72420i	1.28804	+	0.225215i
$647$	16.2154	+	11.7812i	0.637494	+	0.463167i	0.858988	−	0.511995i	$-0.171093\pi$
$647$	16.2154	+	11.7812i	0.637494	+	0.463167i	−0.221494	+	0.975162i	$0.571093\pi$
$648$	−1.01729	−	5.76934i	−0.0399629	−	0.226641i
$649$	15.0947	−	37.6174i	0.592518	−	1.47661i
$650$	−19.4254	+	7.07027i	−0.761928	+	0.277319i
$651$	−1.08508	+	0.731896i	−0.0425277	+	0.0286853i
$652$	13.3721	−	8.35579i	0.523690	−	0.327238i
$653$	−12.8687	−	2.73532i	−0.503591	−	0.107041i	−0.0508903	−	0.998704i	$-0.516206\pi$
$653$	−12.8687	−	2.73532i	−0.503591	−	0.107041i	−0.452700	+	0.891663i	$0.649539\pi$
$654$	−1.73548	+	3.89796i	−0.0678628	+	0.152422i
$655$	10.2458	−	4.99722i	0.400338	−	0.195258i
$656$	−1.94118	+	0.272815i	−0.0757903	+	0.0106516i
$657$	1.97993	+	9.31485i	0.0772446	+	0.363407i
$658$	−8.28950	−	18.6185i	−0.323158	−	0.725826i
$659$	−13.3540	−	11.2053i	−0.520197	−	0.436497i	0.344504	−	0.938785i	$-0.388047\pi$
$659$	−13.3540	−	11.2053i	−0.520197	−	0.436497i	−0.864700	+	0.502288i	$0.832492\pi$
$660$	−0.740008	−	1.50815i	−0.0288048	−	0.0587046i
$661$	7.38869	+	20.3003i	0.287387	+	0.789588i	0.996430	+	0.0844235i	$0.0269049\pi$
$661$	7.38869	+	20.3003i	0.287387	+	0.789588i	−0.709043	+	0.705165i	$0.750873\pi$
$662$	−0.679795	−	9.72152i	−0.0264210	−	0.377838i
$663$	21.9192	+	3.08055i	0.851273	+	0.119639i
$664$	−10.5046	+	3.41316i	−0.407658	+	0.132456i
$665$	10.6930	+	5.19641i	0.414658	+	0.201508i
$666$	−11.1811	−	15.3895i	−0.433260	−	0.596331i
$667$	12.2448	−	6.51066i	0.474119	−	0.252094i
$668$	−8.99474	−	22.2628i	−0.348017	−	0.861372i
$669$	−10.0694	−	2.88735i	−0.389305	−	0.111631i
$670$	−2.15182	+	5.91207i	−0.0831320	+	0.228403i
$671$	−2.71194	−	25.2265i	−0.104693	−	0.973857i
$672$	0.979433	−	1.69643i	0.0377824	−	0.0654411i
$673$	−3.17598	+	30.2174i	−0.122425	+	1.16480i	0.744943	+	0.667129i	$0.232477\pi$
$673$	−3.17598	+	30.2174i	−0.122425	+	1.16480i	−0.867368	+	0.497668i	$0.834190\pi$
$674$	18.3988	+	9.78283i	0.708696	+	0.376821i
$675$	2.03188	+	14.4576i	0.0782071	+	0.556472i
$676$	9.28925	+	4.13584i	0.357279	+	0.159071i
$677$	2.78130	+	26.4623i	0.106894	+	1.01703i	0.908132	+	0.418684i	$0.137509\pi$
$677$	2.78130	+	26.4623i	0.106894	+	1.01703i	−0.801238	+	0.598346i	$0.795825\pi$
$678$	3.61949	−	8.95855i	0.139006	−	0.344051i
$679$	26.9091	−	34.4421i	1.03268	−	1.32177i
$680$	−1.76490	+	6.15493i	−0.0676808	+	0.236031i
$681$	0.351341	+	0.418712i	0.0134634	+	0.0160451i
$682$	−1.36848	−	1.74303i	−0.0524017	−	0.0667441i
$683$		−	18.8485i		−	0.721218i	−0.932717	−	0.360609i	$-0.882569\pi$
$683$		−	18.8485i		−	0.721218i	0.932717	−	0.360609i	$-0.117431\pi$
$684$	7.06162	−	9.06517i	0.270008	−	0.346616i
$685$	3.56882	−	10.9837i	0.136358	−	0.419666i
$686$	5.26325	+	9.89874i	0.200952	+	0.377936i
$687$	5.14356	+	1.28243i	0.196239	+	0.0489279i
$688$	−7.27085	−	4.90425i	−0.277199	−	0.186973i
$689$	−43.8697	−	1.53196i	−1.67130	−	0.0583631i
$690$	0.561000	+	0.897788i	0.0213569	+	0.0341782i
$691$	14.1468	−	6.29854i	0.538168	−	0.239608i	−0.119608	−	0.992821i	$-0.538164\pi$
$691$	14.1468	−	6.29854i	0.538168	−	0.239608i	0.657776	+	0.753213i	$0.271497\pi$
$692$	−8.47844	−	14.6851i	−0.322302	−	0.558243i
$693$	−8.71092	+	27.0275i	−0.330900	+	1.02669i
$694$	22.8597	+	4.03079i	0.867744	+	0.153007i
$695$	−2.45362	−	0.257886i	−0.0930711	−	0.00978216i
$696$	−2.97403	+	2.67783i	−0.112730	+	0.101503i
$697$	13.8575	+	5.59881i	0.524892	+	0.212070i
$698$	−0.577687	−	2.01463i	−0.0218658	−	0.0762550i
$699$	−0.322565	+	0.478222i	−0.0122005	+	0.0180880i
$700$	7.39152	−	11.8289i	0.279373	−	0.447091i
$701$	−1.82858	+	13.0110i	−0.0690645	+	0.491419i	0.924768	+	0.380531i	$0.124259\pi$
$701$	−1.82858	+	13.0110i	−0.0690645	+	0.491419i	−0.993833	+	0.110889i	$0.964630\pi$
$702$	9.61771	−	13.2376i	0.362997	−	0.499623i
$703$	6.49539	−	30.7750i	0.244978	−	1.16070i
$704$	2.98440	+	1.44684i	0.112479	+	0.0545297i
$705$	−3.13019	+	0.551937i	−0.117890	+	0.0207872i
$706$	−9.46506	+	0.661861i	−0.356222	+	0.0249095i
$707$	1.24178	+	35.5600i	0.0467020	+	1.33737i
$708$	0.257246	−	7.36655i	0.00966789	−	0.276852i
$709$	40.9119	+	2.86084i	1.53648	+	0.107441i	0.812737	−	0.582631i	$-0.197977\pi$
$709$	40.9119	+	2.86084i	1.53648	+	0.107441i	0.723741	+	0.690072i	$0.242421\pi$
$710$	9.66512	−	1.01584i	0.362725	−	0.0381240i
$711$	−18.7152	+	20.7854i	−0.701876	+	0.779513i
$712$	−0.800789	+	1.50607i	−0.0300108	+	0.0564422i
$713$	0.970099	+	1.00457i	0.0363305	+	0.0376213i
$714$	−12.9343	+	7.46762i	−0.484054	+	0.279469i
$715$	−4.55542	+	12.6089i	−0.170363	+	0.471546i
$716$	0.281703	−	0.335721i	0.0105277	−	0.0125465i
$717$	−3.61582	−	5.36067i	−0.135035	−	0.200198i
$718$	−5.02990	+	0.175648i	−0.187714	+	0.00655513i
$719$	12.7252	+	7.95160i	0.474570	+	0.296545i	0.746038	−	0.665903i	$-0.231954\pi$
$719$	12.7252	+	7.95160i	0.474570	+	0.296545i	−0.271468	+	0.962447i	$0.587509\pi$
$720$	1.59254	+	1.53790i	0.0593505	+	0.0573141i
$721$	−17.8967	+	13.0027i	−0.666507	+	0.484245i
$722$	18.9498	−	1.37963i	0.705240	−	0.0513443i
$723$	−1.34809	−	0.438020i	−0.0501359	−	0.0162901i
$724$	7.79129	+	3.80007i	0.289561	+	0.141228i
$725$	−21.8296	+	18.3172i	−0.810730	+	0.680283i
$726$	6.44500	+	1.57447i	0.239196	+	0.0584342i
$727$	−3.48640	−	1.26895i	−0.129303	−	0.0470626i	0.276558	−	0.960997i	$-0.410806\pi$
$727$	−3.48640	−	1.26895i	−0.129303	−	0.0470626i	−0.405861	+	0.913935i	$0.633028\pi$
$728$	−15.1684	+	3.78190i	−0.562177	+	0.140166i
$729$	6.21817	+	6.90598i	0.230303	+	0.255777i
$730$	−2.25443	−	2.02990i	−0.0834403	−	0.0751300i
$731$	29.3130	+	60.1006i	1.08418	+	2.22290i
$732$	−2.02262	−	4.14699i	−0.0747583	−	0.153277i
$733$	−23.2102	−	20.8986i	−0.857289	−	0.771907i	0.117959	−	0.993018i	$-0.462365\pi$
$733$	−23.2102	−	20.8986i	−0.857289	−	0.771907i	−0.975248	+	0.221112i	$0.929031\pi$
$734$	2.17041	+	2.41049i	0.0801114	+	0.0889728i
$735$	−1.74378	+	0.434774i	−0.0643204	+	0.0160369i
$736$	−1.96403	−	0.714847i	−0.0723950	−	0.0263496i
$737$	−12.4746	−	21.4887i	−0.459507	−	0.791547i
$738$	3.95867	−	3.32171i	0.145720	−	0.122274i
$739$	−32.5320	−	15.8669i	−1.19671	−	0.583673i	−0.271244	−	0.962511i	$-0.587435\pi$
$739$	−32.5320	−	15.8669i	−1.19671	−	0.583673i	−0.925463	+	0.378838i	$0.876324\pi$
$740$	5.76322	+	1.87258i	0.211860	+	0.0688375i
$741$	12.5832	−	1.34076i	0.462255	−	0.0492540i
$742$	23.9622	−	17.4095i	0.879679	−	0.639124i
$743$	14.3664	+	13.8735i	0.527052	+	0.508968i	0.909891	−	0.414847i	$-0.136165\pi$
$743$	14.3664	+	13.8735i	0.527052	+	0.508968i	−0.382839	+	0.923815i	$0.625054\pi$
$744$	−0.341760	−	0.213555i	−0.0125295	−	0.00782932i
$745$	−16.7329	+	0.584326i	−0.613046	+	0.0214080i
$746$	5.07793	+	7.52834i	0.185916	+	0.275632i
$747$	18.7165	−	22.3054i	0.684799	−	0.816112i
$748$	−14.1902	−	20.9306i	−0.518846	−	0.765298i
$749$	2.02405	−	1.16858i	0.0739570	−	0.0426991i
$750$	−3.27040	−	3.38659i	−0.119418	−	0.123661i
$751$	−1.28034	+	2.40796i	−0.0467202	+	0.0878678i	−0.905214	−	0.424956i	$-0.860290\pi$
$751$	−1.28034	+	2.40796i	−0.0467202	+	0.0878678i	0.858494	+	0.512824i	$0.171401\pi$
$752$	4.19893	−	4.66339i	0.153119	−	0.170056i
$753$	−13.6876	+	1.43863i	−0.498806	+	0.0524266i
$754$	31.8598	+	2.22785i	1.16026	+	0.0811336i
$755$	−0.104057	+	2.97981i	−0.00378703	+	0.108446i
$756$	0.385312	+	11.0339i	0.0140136	+	0.401298i
$757$	−15.8317	+	1.10706i	−0.575414	+	0.0402369i	−0.354500	−	0.935056i	$-0.615349\pi$
$757$	−15.8317	+	1.10706i	−0.575414	+	0.0402369i	−0.220915	+	0.975293i	$0.570904\pi$
$758$	9.18851	−	1.62018i	0.333742	−	0.0588477i
$759$	−4.14163	−	0.572052i	−0.150332	−	0.0207642i
$760$	−0.122516	+	3.65854i	−0.00444413	+	0.132709i
$761$	−21.7272	+	29.9050i	−0.787611	+	1.08405i	0.206790	+	0.978385i	$0.433698\pi$
$761$	−21.7272	+	29.9050i	−0.787611	+	1.08405i	−0.994401	+	0.105668i	$0.966302\pi$
$762$	−1.58070	+	11.2472i	−0.0572625	+	0.407444i
$763$	−12.1755	+	19.4849i	−0.440782	+	0.705399i
$764$	4.87559	−	7.22836i	0.176393	−	0.261513i
$765$	−4.65267	−	16.2258i	−0.168218	−	0.586644i
$766$	−1.40286	−	0.566793i	−0.0506875	−	0.0204791i
$767$	−43.7152	+	39.3613i	−1.57846	+	1.42126i
$768$	0.599835	+	0.0630452i	0.0216447	+	0.00227495i
$769$	−16.9411	−	2.98717i	−0.610912	−	0.107720i	−0.140372	−	0.990099i	$-0.544830\pi$
$769$	−16.9411	−	2.98717i	−0.610912	−	0.107720i	−0.470540	+	0.882379i	$0.655941\pi$
$770$	−2.81578	−	8.59662i	−0.101474	−	0.309801i
$771$	3.80107	+	6.58365i	0.136892	+	0.237104i
$772$	−17.1133	+	7.61934i	−0.615922	+	0.274226i
$773$	−4.27384	−	6.83958i	−0.153719	−	0.246002i	0.762221	−	0.647317i	$-0.224109\pi$
$773$	−4.27384	−	6.83958i	−0.153719	−	0.246002i	−0.915940	+	0.401315i	$0.868553\pi$
$774$	23.1062	+	0.806886i	0.830535	+	0.0290029i
$775$	−2.37900	−	1.60466i	−0.0854562	−	0.0576409i
$776$	13.0579	+	3.25571i	0.468752	+	0.116873i
$777$	6.63588	+	12.4803i	0.238061	+	0.447728i
$778$	−1.83677	+	5.65299i	−0.0658513	+	0.202670i
$779$	8.46309	+	1.17706i	0.303222	+	0.0421725i
$780$			2.43803i			0.0872955i
$781$	−21.3868	+	31.8700i	−0.765279	+	1.14040i
$782$	10.2432	+	12.2074i	0.366297	+	0.436536i
$783$	6.21724	−	21.6821i	0.222186	−	0.774855i
$784$	2.18443	−	2.79594i	0.0780154	−	0.0998552i
$785$	−3.87046	+	9.57971i	−0.138142	+	0.341915i
$786$	0.855785	+	8.14225i	0.0305248	+	0.290425i
$787$	41.1380	+	18.3158i	1.46641	+	0.652889i	0.975835	−	0.218508i	$-0.0701191\pi$
$787$	41.1380	+	18.3158i	1.46641	+	0.652889i	0.490578	+	0.871397i	$0.336786\pi$
$788$	−2.21997	−	15.7959i	−0.0790830	−	0.562705i
$789$	−11.4069	−	6.06515i	−0.406096	−	0.215925i
$790$	0.931346	−	8.86117i	0.0331358	−	0.315266i
$791$	26.0143	−	45.0580i	0.924961	−	1.60208i
$792$	−8.69327	+	0.934558i	−0.308902	+	0.0332081i
$793$	−12.5937	+	34.6010i	−0.447217	+	1.22872i
$794$	26.6450	+	7.64032i	0.945595	+	0.271145i
$795$	−1.73041	−	4.28291i	−0.0613712	−	0.151899i
$796$	8.75408	−	4.65463i	0.310280	−	0.164979i
$797$	14.3102	+	19.6962i	0.506892	+	0.697676i	0.983391	−	0.181498i	$-0.0580947\pi$
$797$	14.3102	+	19.6962i	0.506892	+	0.697676i	−0.476500	+	0.879175i	$0.658095\pi$
$798$	−6.13359	+	5.94013i	−0.217127	+	0.210278i
$799$	−45.5032	+	14.7849i	−1.60979	+	0.523052i
$800$	4.25295	+	0.597712i	0.150364	+	0.0211323i
$801$	−0.313672	−	4.48572i	−0.0110830	−	0.158495i
$802$	−10.2827	−	28.2515i	−0.363095	−	0.997596i
$803$	11.8602	−	1.69555i	0.418538	−	0.0598346i
$804$	−3.46140	−	2.90446i	−0.122074	−	0.102432i
$805$	2.31866	+	5.20779i	0.0817219	+	0.183550i
$806$	0.668667	+	3.14583i	0.0235528	+	0.110807i
$807$	5.42411	−	0.762309i	0.190938	−	0.0268346i
$808$	−9.84689	+	4.80265i	−0.346412	+	0.168957i
$809$	−5.77332	+	12.9671i	−0.202979	+	0.455899i	−0.986139	−	0.165922i	$-0.946940\pi$
$809$	−5.77332	+	12.9671i	−0.202979	+	0.455899i	0.783160	+	0.621821i	$0.213607\pi$
$810$	−4.81231	−	1.02289i	−0.169087	−	0.0359406i
$811$	18.6483	−	11.6527i	0.654829	−	0.409183i	−0.161418	−	0.986886i	$-0.551607\pi$
$811$	18.6483	−	11.6527i	0.654829	−	0.409183i	0.816247	+	0.577704i	$0.196051\pi$
$812$	−17.8655	+	12.0504i	−0.626957	+	0.422888i
$813$	17.3149	−	6.30210i	0.607259	−	0.221024i
$814$	−20.2654	+	12.7302i	−0.710303	+	0.446193i
$815$	−2.29944	−	13.0408i	−0.0805459	−	0.456798i
$816$	−3.72034	−	2.70299i	−0.130238	−	0.0946234i
$817$	24.6147	+	29.2496i	0.861160	+	1.02331i
$818$	4.75191	+	14.6249i	0.166146	+	0.511346i
$819$	28.6278	−	29.6450i	1.00034	−	1.03588i
$820$	−0.398256	+	1.59732i	−0.0139077	+	0.0557807i
$821$	29.6883	−	23.1950i	1.03613	−	0.809511i	0.0541542	−	0.998533i	$-0.482754\pi$
$821$	29.6883	−	23.1950i	1.03613	−	0.809511i	0.981973	+	0.189021i	$0.0605315\pi$
$822$	6.53609	+	5.10655i	0.227972	+	0.178111i
$823$	1.97466	+	7.91993i	0.0688324	+	0.276071i	0.994843	−	0.101426i	$-0.0323404\pi$
$823$	1.97466	+	7.91993i	0.0688324	+	0.276071i	−0.926011	+	0.377497i	$0.876785\pi$
$824$	−5.89872	−	3.40563i	−0.205492	−	0.118641i
$825$	8.56877	−	0.619620i	0.298326	−	0.0215724i
$826$	6.89238	−	39.0886i	0.239816	−	1.36007i
$827$	−28.5877	+	27.6068i	−0.994090	+	0.959982i	−0.999199	−	0.0400053i	$-0.987263\pi$
$827$	−28.5877	+	27.6068i	−0.994090	+	0.959982i	0.00510934	+	0.999987i	$0.498374\pi$
$828$	5.38950	−	1.14557i	0.187298	−	0.0398114i
$829$	8.60429	−	40.4800i	0.298839	−	1.40593i	−0.530737	−	0.847536i	$-0.678085\pi$
$829$	8.60429	−	40.4800i	0.298839	−	1.40593i	0.829577	−	0.558393i	$-0.188582\pi$
$830$	−0.647042	+	9.25314i	−0.0224592	+	0.321181i
$831$	4.53375	−	1.30003i	0.157274	−	0.0450976i
$832$	−2.96339	−	3.79297i	−0.102737	−	0.131498i
$833$	−25.0824	+	10.1340i	−0.869055	+	0.351121i
$834$	0.776744	−	1.59256i	0.0268965	−	0.0551459i
$835$	−20.1645			−0.697821
$836$	−10.7802	−	9.63257i	−0.372842	−	0.333149i
$837$	2.27138			0.0785102
$838$	−9.37817	+	19.2281i	−0.323964	+	0.664224i
$839$	−19.9463	+	8.05885i	−0.688624	+	0.278222i	−0.692131	−	0.721772i	$-0.743328\pi$
$839$	−19.9463	+	8.05885i	−0.688624	+	0.278222i	0.00350710	+	0.999994i	$0.498884\pi$
$840$	−1.01279	−	1.29632i	−0.0349447	−	0.0447272i
$841$	14.4438	−	4.14170i	0.498063	−	0.142817i
$842$	0.863435	−	12.3477i	0.0297559	−	0.425530i
$843$	−1.98329	+	9.33064i	−0.0683081	+	0.321364i
$844$	−2.70265	+	0.574467i	−0.0930292	+	0.0197740i
$845$	6.14269	−	5.93193i	0.211315	−	0.204064i
$846$	−2.87263	+	16.2915i	−0.0987632	+	0.560114i
$847$	33.1874	+	13.2257i	1.14033	+	0.454441i
$848$	7.89791	+	4.55986i	0.271215	+	0.156586i
$849$	−3.36041	−	13.4779i	−0.115329	−	0.462559i
$850$	−25.8034	−	20.1598i	−0.885049	−	0.691476i
$851$	11.8844	−	9.28513i	0.407393	−	0.318290i
$852$	−1.68854	+	6.77236i	−0.0578484	+	0.232017i
$853$	−9.09039	+	9.41337i	−0.311249	+	0.322308i	−0.856680	−	0.515848i	$-0.827477\pi$
$853$	−9.09039	+	9.41337i	−0.311249	+	0.322308i	0.545431	+	0.838156i	$0.316366\pi$
$854$	−7.67759	−	23.6292i	−0.262722	−	0.808575i
$855$	−4.83702	−	8.35034i	−0.165423	−	0.285576i
$856$	0.582184	+	0.422981i	0.0198986	+	0.0144572i
$857$	3.55013	+	20.1338i	0.121270	+	0.687757i	0.983453	+	0.181161i	$0.0579854\pi$
$857$	3.55013	+	20.1338i	0.121270	+	0.687757i	−0.862183	+	0.506596i	$0.830903\pi$
$858$	−7.39057	−	6.17160i	−0.252310	−	0.210695i
$859$	−39.0877	+	14.2268i	−1.33365	+	0.485411i	−0.907808	−	0.419385i	$-0.862246\pi$
$859$	−39.0877	+	14.2268i	−1.33365	+	0.485411i	−0.425846	+	0.904796i	$0.640023\pi$
$860$	−6.10604	+	4.11857i	−0.208214	+	0.140442i
$861$	−3.25640	+	2.03482i	−0.110978	+	0.0693467i
$862$	−11.5825	−	2.46194i	−0.394502	−	0.0838541i
$863$	3.79226	−	8.51755i	0.129090	−	0.289941i	−0.837425	−	0.546553i	$-0.815940\pi$
$863$	3.79226	−	8.51755i	0.129090	−	0.289941i	0.966514	+	0.256612i	$0.0826064\pi$
$864$	−3.05538	+	1.49021i	−0.103946	+	0.0506980i
$865$	−14.1017	+	1.98187i	−0.479474	+	0.0673856i
$866$	−6.80155	−	31.9988i	−0.231126	−	1.08736i
$867$	10.0905	+	22.6635i	0.342690	+	0.769694i
$868$	−1.66236	−	1.39488i	−0.0564241	−	0.0473454i
$869$	24.5039	+	25.2543i	0.831236	+	0.856694i
$870$	1.14947	+	3.15814i	0.0389707	+	0.107071i
$871$	2.51543	+	35.9723i	0.0852320	+	1.21887i
$872$	−7.00555	−	0.984566i	−0.237238	−	0.0333416i
$873$	−33.7410	+	10.9631i	−1.14196	+	0.371046i
$874$	7.37814	+	5.34441i	0.249569	+	0.180778i
$875$	−14.9011	−	20.5096i	−0.503748	−	0.693350i
$876$	1.92372	−	1.02286i	0.0649965	−	0.0345592i
$877$	13.0823	+	32.3799i	0.441759	+	1.09339i	0.969741	+	0.244136i	$0.0785044\pi$
$877$	13.0823	+	32.3799i	0.441759	+	1.09339i	−0.527982	+	0.849256i	$0.677051\pi$
$878$	15.4321	+	4.42510i	0.520810	+	0.149340i
$879$	0.0348636	−	0.0957870i	0.00117592	−	0.00323081i
$880$	2.06545	−	1.86863i	0.0696262	−	0.0629915i
$881$	1.29484	−	2.24273i	0.0436244	−	0.0755596i	−0.843389	−	0.537304i	$-0.819443\pi$
$881$	1.29484	−	2.24273i	0.0436244	−	0.0755596i	0.887013	+	0.461744i	$0.152776\pi$
$882$	−0.977717	+	9.30236i	−0.0329214	+	0.313227i
$883$	−19.4936	−	10.3649i	−0.656012	−	0.348808i	0.107869	−	0.994165i	$-0.465597\pi$
$883$	−19.4936	−	10.3649i	−0.656012	−	0.348808i	−0.763881	+	0.645357i	$0.776708\pi$
$884$	5.10752	+	36.3419i	0.171785	+	1.22231i
$885$	−5.65501	−	2.51777i	−0.190091	−	0.0846340i
$886$	−1.08869	−	10.3582i	−0.0365752	−	0.347989i
$887$	−3.47282	+	8.59554i	−0.116606	+	0.288610i	−0.974188	−	0.225737i	$-0.927521\pi$
$887$	−3.47282	+	8.59554i	−0.116606	+	0.288610i	0.857582	+	0.514347i	$0.171966\pi$
$888$	−2.67944	+	3.42953i	−0.0899161	+	0.115087i
$889$	−16.8578	+	58.7901i	−0.565392	+	1.97176i
$890$	0.920769	+	1.09733i	0.0308642	+	0.0367826i
$891$	15.2826	−	11.9985i	0.511985	−	0.401966i
$892$		−	17.3677i		−	0.581515i
$893$	−23.1759	+	14.5281i	−0.775551	+	0.486163i
$894$	3.71588	−	11.4363i	0.124278	−	0.382487i
$895$	−0.172786	−	0.324963i	−0.00577559	−	0.0108623i
$896$	3.15131	+	0.785710i	0.105278	+	0.0262487i
$897$	5.03038	+	3.39303i	0.167959	+	0.113290i
$898$	−30.6062	−	1.06879i	−1.02134	−	0.0356660i
$899$	2.34935	+	3.75974i	0.0783551	+	0.125394i
$900$	−10.3431	+	4.60503i	−0.344769	+	0.153501i
$901$	−34.7663	−	60.2171i	−1.15823	−	2.00612i
$902$	−3.83391	−	5.25069i	−0.127655	−	0.174829i
$903$	−16.9187	−	2.98322i	−0.563019	−	0.0992755i
$904$	15.9319	+	1.67451i	0.529889	+	0.0556935i
$905$	5.40999	−	4.87118i	0.179834	−	0.161924i
$906$	−1.98546	−	0.802180i	−0.0659626	−	0.0266506i
$907$	−3.93748	−	13.7316i	−0.130742	−	0.455951i	0.868466	−	0.495749i	$-0.165106\pi$
$907$	−3.93748	−	13.7316i	−0.130742	−	0.455951i	−0.999208	+	0.0397981i	$0.987329\pi$
$908$	−0.506764	+	0.751309i	−0.0168176	+	0.0249331i
$909$	15.3049	−	24.4930i	0.507632	−	0.812381i
$910$	−1.82711	+	13.0005i	−0.0605680	+	0.430964i
$911$	−10.2494	+	14.1070i	−0.339576	+	0.467387i	−0.944318	−	0.329035i	$-0.893277\pi$
$911$	−10.2494	+	14.1070i	−0.339576	+	0.467387i	0.604741	+	0.796422i	$0.293277\pi$
$912$	−2.43899	−	0.981359i	−0.0807632	−	0.0324961i
$913$	−26.4117	−	25.3847i	−0.874101	−	0.840111i
$914$	−29.7693	+	5.24914i	−0.984682	+	0.173626i
$915$	−3.86534	+	0.270291i	−0.127784	+	0.00893555i
$916$	0.306734	+	8.78370i	0.0101348	+	0.290222i
$917$	−1.53858	+	44.0591i	−0.0508083	+	1.45496i
$918$	25.8556	+	1.80800i	0.853361	+	0.0596728i
$919$	−3.81473	+	0.400944i	−0.125836	+	0.0132259i	−0.167237	−	0.985917i	$-0.553485\pi$
$919$	−3.81473	+	0.400944i	−0.125836	+	0.0132259i	0.0414009	+	0.999143i	$0.486818\pi$
$920$	−1.17448	+	1.30440i	−0.0387215	+	0.0430046i
$921$	4.44335	−	8.35672i	0.146413	−	0.275363i
$922$	−7.34402	−	7.60495i	−0.241862	−	0.250456i
$923$	48.2388	−	27.8507i	1.58780	−	0.916717i
$924$	6.49339	+	0.211330i	0.213617	+	0.00695226i
$925$	−19.9200	+	23.7397i	−0.654965	+	0.780557i
$926$	−4.83893	−	7.17401i	−0.159017	−	0.235752i
$927$	17.9451	−	0.626655i	0.589393	−	0.0205821i
$928$	−5.62697	−	3.51612i	−0.184714	−	0.115422i
$929$	−5.79320	−	5.59443i	−0.190069	−	0.183547i	0.593535	−	0.804808i	$-0.297732\pi$
$929$	−5.79320	−	5.59443i	−0.190069	−	0.183547i	−0.783604	+	0.621261i	$0.786621\pi$
$930$	−0.273799	+	0.198927i	−0.00897824	+	0.00652307i
$931$	−12.4991	+	9.10849i	−0.409641	+	0.298519i
$932$	−0.909586	−	0.295542i	−0.0297945	−	0.00968081i
$933$	−7.56365	−	3.68904i	−0.247623	−	0.120774i
$934$	13.4912	−	11.3205i	0.441446	−	0.370417i
$935$	−20.7617	+	4.46454i	−0.678979	+	0.146006i
$936$	11.9238	+	4.33992i	0.389742	+	0.141855i
$937$	48.6152	−	12.1211i	1.58819	−	0.395980i	0.655075	−	0.755564i	$-0.272637\pi$
$937$	48.6152	−	12.1211i	1.58819	−	0.395980i	0.933113	+	0.359584i	$0.117081\pi$
$938$	−16.2809	−	18.0818i	−0.531590	−	0.590390i
$939$	−7.58188	−	6.82675i	−0.247425	−	0.222783i
$940$	−2.31017	−	4.73655i	−0.0753494	−	0.154489i
$941$	19.3000	+	39.5709i	0.629162	+	1.28997i	0.940539	+	0.339687i	$0.110321\pi$
$941$	19.3000	+	39.5709i	0.629162	+	1.28997i	−0.311377	+	0.950287i	$0.600790\pi$
$942$	−5.51447	−	4.96525i	−0.179671	−	0.161776i
$943$	2.74148	+	3.04472i	0.0892749	+	0.0991498i
$944$	11.8581	−	2.95656i	0.385949	−	0.0962278i
$945$	8.71270	+	3.17116i	0.283424	+	0.103158i
$946$	2.97184	−	28.9354i	0.0966227	−	0.940769i
$947$	13.0846	−	10.9793i	0.425192	−	0.356778i	−0.404942	−	0.914342i	$-0.632708\pi$
$947$	13.0846	−	10.9793i	0.425192	−	0.356778i	0.830134	+	0.557564i	$0.188264\pi$
$948$	5.75149	+	2.80519i	0.186800	+	0.0911082i
$949$	−16.5365	−	5.37303i	−0.536797	−	0.174416i
$950$	−17.1128	−	7.58976i	−0.555211	−	0.246244i
$951$	13.5714	−	9.86022i	0.440084	−	0.319739i
$952$	−17.8127	−	17.2015i	−0.577312	−	0.557504i
$953$	9.05273	+	5.65677i	0.293247	+	0.183241i	0.668562	−	0.743656i	$-0.266910\pi$
$953$	9.05273	+	5.65677i	0.293247	+	0.183241i	−0.375316	+	0.926897i	$0.622466\pi$
$954$	−24.0270	+	0.839040i	−0.777902	+	0.0271649i
$955$	−4.09450	−	6.07035i	−0.132495	−	0.196432i
$956$	6.89120	−	8.21262i	0.222877	−	0.265615i
$957$	−12.4832	−	4.51002i	−0.403526	−	0.145788i
$958$	−12.3888	+	7.15267i	−0.400264	+	0.231092i
$959$	31.0261	+	32.1284i	1.00188	+	1.03748i
$960$	0.237794	−	0.447226i	0.00767477	−	0.0144341i
$961$	20.4443	−	22.7057i	0.659494	−	0.732442i
$962$	34.5419	−	3.63050i	1.11368	−	0.117052i
$963$	−1.89245	−	0.132333i	−0.0609835	−	0.00426438i
$964$	0.0820188	−	2.34871i	0.00264165	−	0.0756469i
$965$	0.549032	+	15.7222i	0.0176740	+	0.506116i
$966$	−4.08420	+	0.285595i	−0.131407	+	0.00918887i
$967$	20.2977	−	3.57903i	0.652729	−	0.115094i	0.162529	−	0.986704i	$-0.448035\pi$
$967$	20.2977	−	3.57903i	0.652729	−	0.115094i	0.490200	+	0.871610i	$0.336924\pi$
$968$	0.436055	+	10.9914i	0.0140153	+	0.353275i
$969$	12.3634	+	15.7778i	0.397170	+	0.506857i
$970$	6.64298	−	9.14327i	0.213293	−	0.293573i
$971$	1.30002	−	9.25010i	0.0417195	−	0.296850i	−0.958222	−	0.286026i	$-0.907666\pi$
$971$	1.30002	−	9.25010i	0.0417195	−	0.296850i	0.999941	−	0.0108239i	$-0.00344543\pi$
$972$	7.27668	−	11.6451i	0.233400	−	0.373517i
$973$	5.33540	−	7.91006i	0.171045	−	0.253585i
$974$	3.43445	+	11.9773i	0.110047	+	0.383779i
$975$	−11.5603	−	4.67065i	−0.370225	−	0.149581i
$976$	5.68498	−	5.11878i	0.181972	−	0.163848i
$977$	−56.8907	−	5.97945i	−1.82010	−	0.191300i	−0.867889	−	0.496757i	$-0.834524\pi$
$977$	−56.8907	−	5.97945i	−1.82010	−	0.191300i	−0.952206	+	0.305458i	$0.901191\pi$
$978$	9.36584	+	1.65145i	0.299486	+	0.0528075i
$979$	−5.65723	+	0.0134222i	−0.180806	+	0.000428977i
$980$	−1.48984	−	2.58048i	−0.0475913	−	0.0824305i
$981$	17.0373	−	7.58552i	0.543961	−	0.242187i
$982$	11.6666	+	18.6705i	0.372298	+	0.595801i
$983$	−15.6494	−	0.546489i	−0.499138	−	0.0174303i	−0.215775	−	0.976443i	$-0.569228\pi$
$983$	−15.6494	−	0.546489i	−0.499138	−	0.0174303i	−0.283363	+	0.959013i	$0.591450\pi$
$984$	−0.980177	−	0.661137i	−0.0312469	−	0.0210763i
$985$	−12.9978	−	3.24071i	−0.414144	−	0.103258i
$986$	23.7504	+	44.6680i	0.756367	+	1.42252i
$987$	3.79852	−	11.6907i	0.120908	−	0.372118i
$988$	7.88742	+	19.4419i	0.250932	+	0.618529i
$989$			18.3304i			0.582874i
$990$	−2.00716	+	7.06299i	−0.0637916	+	0.224476i
$991$	8.17905	+	9.74741i	0.259816	+	0.309637i	0.880145	−	0.474705i	$-0.157445\pi$
$991$	8.17905	+	9.74741i	0.259816	+	0.309637i	−0.620329	+	0.784342i	$0.713001\pi$
$992$	0.184171	−	0.642281i	0.00584744	−	0.0203924i
$993$	3.61870	−	4.63173i	0.114836	−	0.146983i
$994$	−14.0793	+	34.8475i	−0.446569	+	1.10530i
$995$	−0.870331	−	8.28065i	−0.0275913	−	0.262514i
$996$	−6.08586	−	2.70960i	−0.192838	−	0.0858569i
$997$	−7.12089	−	50.6678i	−0.225521	−	1.60466i	−0.693186	−	0.720759i	$-0.743794\pi$
$997$	−7.12089	−	50.6678i	−0.225521	−	1.60466i	0.467665	−	0.883906i	$-0.345095\pi$
$998$	4.41768	+	2.34892i	0.139839	+	0.0743538i
$999$	2.56404	−	24.3952i	0.0811227	−	0.771830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.29.5	✓	240
11.8	odd	10		418.2.v.b.371.6	yes	240
19.2	odd	18		418.2.v.b.249.6	yes	240
209.173	even	90	inner	418.2.v.a.173.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.29.5	✓	240	1.1	even	1	trivial
418.2.v.a.173.5	yes	240	209.173	even	90	inner
418.2.v.b.249.6	yes	240	19.2	odd	18
418.2.v.b.371.6	yes	240	11.8	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.438371 + 0.898794i) q^{2} +(-0.559221 + 0.225940i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.807264 + 0.231479i) q^{5} +(0.0420729 - 0.601670i) q^{6} +(0.675252 - 3.17681i) q^{7} +(0.978148 - 0.207912i) q^{8} +(-1.89634 + 1.83127i) q^{9} +O(q^{10})\)	\(q+(-0.438371 + 0.898794i) q^{2} +(-0.559221 + 0.225940i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.807264 + 0.231479i) q^{5} +(0.0420729 - 0.601670i) q^{6} +(0.675252 - 3.17681i) q^{7} +(0.978148 - 0.207912i) q^{8} +(-1.89634 + 1.83127i) q^{9} +(0.145829 - 0.827038i) q^{10} +(2.13791 + 2.53562i) q^{11} +(0.522334 + 0.301570i) q^{12} +(-1.16445 - 4.67037i) q^{13} +(2.55929 + 1.99954i) q^{14} +(0.399139 - 0.311841i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(5.29638 - 5.48456i) q^{17} +(-0.814638 - 2.50720i) q^{18} +(2.17404 - 3.77803i) q^{19} +(0.679410 + 0.493620i) q^{20} +(0.340154 + 1.92911i) q^{21} +(-3.21619 + 0.809997i) q^{22} +(1.96403 - 0.714847i) q^{23} +(-0.500025 + 0.337271i) q^{24} +(-3.64215 + 2.27587i) q^{25} +(4.70817 + 1.00075i) q^{26} +(1.38267 - 3.10553i) q^{27} +(-2.91909 + 1.42374i) q^{28} +(6.57063 - 0.923442i) q^{29} +(0.105310 + 0.495446i) q^{30} +(0.271767 + 0.610398i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.76846 - 0.934931i) q^{33} +(2.60771 + 7.16462i) q^{34} +(0.190259 + 2.72083i) q^{35} +(2.61057 + 0.366891i) q^{36} +(6.86264 - 2.22981i) q^{37} +(2.44264 + 3.61020i) q^{38} +(1.70641 + 2.34867i) q^{39} +(-0.741496 + 0.394261i) q^{40} +(0.734325 + 1.81752i) q^{41} +(-1.88298 - 0.539937i) q^{42} +(-2.99960 + 8.24132i) q^{43} +(0.681866 - 3.24578i) q^{44} +(1.10695 - 1.91729i) q^{45} +(-0.218472 + 2.07862i) q^{46} +(-5.54068 - 2.94603i) q^{47} +(-0.0839407 - 0.597269i) q^{48} +(-3.24135 - 1.44314i) q^{49} +(-0.448923 - 4.27121i) q^{50} +(-1.72266 + 4.26374i) q^{51} +(-2.96339 + 3.79297i) q^{52} +(2.51374 - 8.76644i) q^{53} +(2.18511 + 2.60411i) q^{54} +(-2.31280 - 1.55203i) q^{55} -3.24778i q^{56} +(-0.362162 + 2.60396i) q^{57} +(-2.05039 + 6.31045i) q^{58} +(-5.73747 - 10.7906i) q^{59} +(-0.491469 - 0.122537i) q^{60} +(-6.34205 - 4.27777i) q^{61} +(-0.667757 - 0.0233186i) q^{62} +(4.53711 + 7.26089i) q^{63} +(0.913545 - 0.406737i) q^{64} +(2.02112 + 3.50068i) q^{65} +(1.61555 - 1.17963i) q^{66} +(-7.37788 - 1.30092i) q^{67} +(-7.58267 - 0.796970i) q^{68} +(-0.936812 + 0.843509i) q^{69} +(-2.52887 - 1.02173i) q^{70} +(3.18975 + 11.1240i) q^{71} +(-1.47416 + 2.18553i) q^{72} +(1.91425 - 3.06344i) q^{73} +(-1.00425 + 7.14558i) q^{74} +(1.52256 - 2.09562i) q^{75} +(-4.31561 + 0.612819i) q^{76} +(9.49881 - 5.07955i) q^{77} +(-2.85902 + 0.504122i) q^{78} +(10.5838 - 0.740094i) q^{79} +(-0.0293085 - 0.839285i) q^{80} +(0.204453 - 5.85477i) q^{81} +(-1.95548 - 0.136740i) q^{82} +(-10.9847 + 1.15454i) q^{83} +(1.31074 - 1.45572i) q^{84} +(-3.00601 + 5.65349i) q^{85} +(-6.09231 - 6.30878i) q^{86} +(-3.46579 + 2.00098i) q^{87} +(2.61837 + 2.03571i) q^{88} +(-1.09642 + 1.30666i) q^{89} +(1.23799 + 1.83540i) q^{90} +(-15.6232 + 0.545574i) q^{91} +(-1.77248 - 1.10757i) q^{92} +(-0.289891 - 0.279945i) q^{93} +(5.07675 - 3.68847i) q^{94} +(-0.880492 + 3.55312i) q^{95} +(0.573619 + 0.186380i) q^{96} +(12.0957 + 5.89945i) q^{97} +(2.71801 - 2.28068i) q^{98} +(-8.69761 - 0.893297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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