LMFDB - Embedded newform 134.2.e.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [134,2,Mod(9,134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(134, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("134.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 134 = 2 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	134.e (of order $11$, degree $10$, 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:	$1.06999538709$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	134.81
Dual form			134.2.e.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(-0.736673 - 0.473431i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.156423 - 1.08794i) q^{5} +(-0.124623 + 0.866771i) q^{6} +(-1.31230 - 2.87354i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.927695 - 2.03137i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.736673 - 0.473431i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.156423 - 1.08794i) q^{5} +(-0.124623 + 0.866771i) q^{6} +(-1.31230 - 2.87354i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.927695 - 2.03137i) q^{9} +(-0.924649 + 0.594236i) q^{10} +(-0.110515 - 0.768648i) q^{11} +(0.840213 - 0.246709i) q^{12} +(-3.31666 + 0.973859i) q^{13} +(-2.06872 + 2.38743i) q^{14} +(-0.399834 + 0.875514i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(5.14354 + 5.93596i) q^{17} +(-1.46242 + 1.68772i) q^{18} +(2.84156 - 6.22215i) q^{19} +(0.924649 + 0.594236i) q^{20} +(-0.393686 + 2.73815i) q^{21} +(-0.653278 + 0.419836i) q^{22} +(-2.31562 - 1.48816i) q^{23} +(-0.573451 - 0.661798i) q^{24} +(3.63831 - 1.06830i) q^{25} +(2.26364 + 2.61238i) q^{26} +(-0.652174 + 4.53597i) q^{27} +(3.03106 + 0.889998i) q^{28} +7.69137 q^{29} +0.962493 q^{30} +(0.776234 + 0.227923i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-0.282488 + 0.618563i) q^{33} +(3.26283 - 7.14461i) q^{34} +(-2.92098 + 1.87720i) q^{35} +(2.14272 + 0.629159i) q^{36} -1.48643 q^{37} -6.84029 q^{38} +(2.90435 + 0.852793i) q^{39} +(0.156423 - 1.08794i) q^{40} +(1.50439 + 1.73616i) q^{41} +(2.65425 - 0.779358i) q^{42} +(-1.62154 - 1.87136i) q^{43} +(0.653278 + 0.419836i) q^{44} +(-2.06490 + 1.32703i) q^{45} +(-0.391733 + 2.72457i) q^{46} +(2.68975 + 1.72859i) q^{47} +(-0.363772 + 0.796551i) q^{48} +(-1.95109 + 2.25168i) q^{49} +(-2.48317 - 2.86573i) q^{50} +(-0.978838 - 6.80796i) q^{51} +(1.43596 - 3.14431i) q^{52} +(-6.26998 + 7.23595i) q^{53} +(4.39698 - 1.29107i) q^{54} +(-0.818960 + 0.240468i) q^{55} +(-0.449575 - 3.12686i) q^{56} +(-5.03906 + 3.23841i) q^{57} +(-3.19511 - 6.99632i) q^{58} +(-0.0676806 - 0.0198728i) q^{59} +(-0.399834 - 0.875514i) q^{60} +(0.510081 - 3.54769i) q^{61} +(-0.115133 - 0.800770i) q^{62} +(-4.61981 + 5.33155i) q^{63} +(0.841254 + 0.540641i) q^{64} +(1.57831 + 3.45601i) q^{65} +0.680015 q^{66} +(-8.11967 - 1.03489i) q^{67} -7.85440 q^{68} +(1.00131 + 2.19257i) q^{69} +(2.92098 + 1.87720i) q^{70} +(5.88060 - 6.78657i) q^{71} +(-0.317814 - 2.21045i) q^{72} +(1.63573 - 11.3767i) q^{73} +(0.617486 + 1.35210i) q^{74} +(-3.18601 - 0.935497i) q^{75} +(2.84156 + 6.22215i) q^{76} +(-2.06372 + 1.32627i) q^{77} +(-0.430781 - 2.99615i) q^{78} +(-5.72867 + 1.68209i) q^{79} +(-1.05461 + 0.309661i) q^{80} +(-1.75935 + 2.03040i) q^{81} +(0.954318 - 2.08967i) q^{82} +(-1.15986 - 8.06702i) q^{83} +(-1.81154 - 2.09063i) q^{84} +(5.65342 - 6.52440i) q^{85} +(-1.02864 + 2.25240i) q^{86} +(-5.66602 - 3.64133i) q^{87} +(0.110515 - 0.768648i) q^{88} +(-2.18462 + 1.40397i) q^{89} +(2.06490 + 1.32703i) q^{90} +(7.15089 + 8.25257i) q^{91} +(2.64108 - 0.775492i) q^{92} +(-0.463925 - 0.535398i) q^{93} +(0.455024 - 3.16476i) q^{94} +(-7.21384 - 2.11817i) q^{95} +0.875684 q^{96} +18.8975 q^{97} +(2.85871 + 0.839394i) q^{98} +(-1.45888 + 0.937568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9} + 3 q^{10} + q^{11} - q^{12} - 11 q^{13} - 22 q^{14} + 18 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 16 q^{19} - 3 q^{20} - 27 q^{21} - q^{22} + 12 q^{24} + 2 q^{25} - 11 q^{26} + 14 q^{27} - 11 q^{28} + 26 q^{30} + 18 q^{31} + 3 q^{32} + 9 q^{33} - 14 q^{34} - 90 q^{35} - 8 q^{36} - 48 q^{37} + 28 q^{38} - q^{39} + 3 q^{40} - 51 q^{41} - 17 q^{42} + 10 q^{43} + q^{44} - 4 q^{45} - 11 q^{46} + 10 q^{47} + 10 q^{48} - 19 q^{49} - 24 q^{50} + 4 q^{51} + 11 q^{52} - 8 q^{53} - 25 q^{54} + 25 q^{55} + 31 q^{57} + 22 q^{58} + 66 q^{59} + 18 q^{60} + 34 q^{61} - 29 q^{62} + 80 q^{63} - 3 q^{64} + 26 q^{65} + 90 q^{66} - 3 q^{67} - 8 q^{68} - 46 q^{69} + 90 q^{70} + 39 q^{71} - 3 q^{72} + 78 q^{73} - 18 q^{74} - 11 q^{75} + 16 q^{76} + 73 q^{77} - 10 q^{78} + 34 q^{79} + 8 q^{80} - 134 q^{81} + 7 q^{82} - 11 q^{83} + 6 q^{84} - 31 q^{85} + q^{86} - 110 q^{87} - q^{88} - 30 q^{89} + 4 q^{90} + 14 q^{91} + 11 q^{92} - 13 q^{93} + 23 q^{94} - 39 q^{95} - 10 q^{96} + 24 q^{97} + 19 q^{98} - 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9 + 3 * q^10 + q^11 - q^12 - 11 * q^13 - 22 * q^14 + 18 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 16 * q^19 - 3 * q^20 - 27 * q^21 - q^22 + 12 * q^24 + 2 * q^25 - 11 * q^26 + 14 * q^27 - 11 * q^28 + 26 * q^30 + 18 * q^31 + 3 * q^32 + 9 * q^33 - 14 * q^34 - 90 * q^35 - 8 * q^36 - 48 * q^37 + 28 * q^38 - q^39 + 3 * q^40 - 51 * q^41 - 17 * q^42 + 10 * q^43 + q^44 - 4 * q^45 - 11 * q^46 + 10 * q^47 + 10 * q^48 - 19 * q^49 - 24 * q^50 + 4 * q^51 + 11 * q^52 - 8 * q^53 - 25 * q^54 + 25 * q^55 + 31 * q^57 + 22 * q^58 + 66 * q^59 + 18 * q^60 + 34 * q^61 - 29 * q^62 + 80 * q^63 - 3 * q^64 + 26 * q^65 + 90 * q^66 - 3 * q^67 - 8 * q^68 - 46 * q^69 + 90 * q^70 + 39 * q^71 - 3 * q^72 + 78 * q^73 - 18 * q^74 - 11 * q^75 + 16 * q^76 + 73 * q^77 - 10 * q^78 + 34 * q^79 + 8 * q^80 - 134 * q^81 + 7 * q^82 - 11 * q^83 + 6 * q^84 - 31 * q^85 + q^86 - 110 * q^87 - q^88 - 30 * q^89 + 4 * q^90 + 14 * q^91 + 11 * q^92 - 13 * q^93 + 23 * q^94 - 39 * q^95 - 10 * q^96 + 24 * q^97 + 19 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/134\mathbb{Z}\right)^\times$.

$n$	$69$
$\chi(n)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$	−0.736673	−	0.473431i	−0.425318	−	0.273335i	0.310423	−	0.950599i	$-0.399529\pi$
$3$	−0.736673	−	0.473431i	−0.425318	−	0.273335i	−0.735741	+	0.677263i	$0.763166\pi$
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	−0.156423	−	1.08794i	−0.0699544	−	0.486543i	−0.994438	−	0.105322i	$-0.966413\pi$
$5$	−0.156423	−	1.08794i	−0.0699544	−	0.486543i	0.924484	−	0.381221i	$-0.124496\pi$
$6$	−0.124623	+	0.866771i	−0.0508771	+	0.353858i
$7$	−1.31230	−	2.87354i	−0.496004	−	1.08610i	−0.977747	−	0.209785i	$-0.932723\pi$
$7$	−1.31230	−	2.87354i	−0.496004	−	1.08610i	0.481743	−	0.876312i	$-0.340004\pi$
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	−0.927695	−	2.03137i	−0.309232	−	0.677123i
$10$	−0.924649	+	0.594236i	−0.292400	+	0.187914i
$11$	−0.110515	−	0.768648i	−0.0333215	−	0.231756i	0.966354	−	0.257214i	$-0.0828046\pi$
$11$	−0.110515	−	0.768648i	−0.0333215	−	0.231756i	−0.999676	+	0.0254581i	$0.991896\pi$
$12$	0.840213	−	0.246709i	0.242549	−	0.0712187i
$13$	−3.31666	+	0.973859i	−0.919876	+	0.270100i	−0.707192	−	0.707021i	$-0.750039\pi$
$13$	−3.31666	+	0.973859i	−0.919876	+	0.270100i	−0.212684	+	0.977121i	$0.568220\pi$
$14$	−2.06872	+	2.38743i	−0.552888	+	0.638067i
$15$	−0.399834	+	0.875514i	−0.103237	+	0.226057i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	5.14354	+	5.93596i	1.24749	+	1.43968i	0.853935	+	0.520380i	$0.174210\pi$
$17$	5.14354	+	5.93596i	1.24749	+	1.43968i	0.393556	+	0.919301i	$0.371245\pi$
$18$	−1.46242	+	1.68772i	−0.344696	+	0.397800i
$19$	2.84156	−	6.22215i	0.651899	−	1.42746i	−0.237984	−	0.971269i	$-0.576486\pi$
$19$	2.84156	−	6.22215i	0.651899	−	1.42746i	0.889882	−	0.456190i	$-0.150786\pi$
$20$	0.924649	+	0.594236i	0.206758	+	0.132875i
$21$	−0.393686	+	2.73815i	−0.0859093	+	0.597513i
$22$	−0.653278	+	0.419836i	−0.139279	+	0.0895093i
$23$	−2.31562	−	1.48816i	−0.482840	−	0.310303i	0.276480	−	0.961020i	$-0.410832\pi$
$23$	−2.31562	−	1.48816i	−0.482840	−	0.310303i	−0.759320	+	0.650717i	$0.774468\pi$
$24$	−0.573451	−	0.661798i	−0.117055	−	0.135089i
$25$	3.63831	−	1.06830i	0.727662	−	0.213661i
$26$	2.26364	+	2.61238i	0.443937	+	0.512331i
$27$	−0.652174	+	4.53597i	−0.125511	+	0.872947i
$28$	3.03106	+	0.889998i	0.572816	+	0.168194i
$29$	7.69137			1.42825			0.714126	−	0.700017i	$-0.246824\pi$
$29$	7.69137			1.42825			0.714126	+	0.700017i	$0.246824\pi$
$30$	0.962493			0.175726
$31$	0.776234	+	0.227923i	0.139416	+	0.0409362i	0.350696	−	0.936489i	$-0.385945\pi$
$31$	0.776234	+	0.227923i	0.139416	+	0.0409362i	−0.211280	+	0.977426i	$0.567763\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	−0.282488	+	0.618563i	−0.0491749	+	0.107678i
$34$	3.26283	−	7.14461i	0.559571	−	1.22529i
$35$	−2.92098	+	1.87720i	−0.493736	+	0.317305i
$36$	2.14272	+	0.629159i	0.357120	+	0.104860i
$37$	−1.48643			−0.244368			−0.122184	−	0.992507i	$-0.538990\pi$
$37$	−1.48643			−0.244368			−0.122184	+	0.992507i	$0.538990\pi$
$38$	−6.84029			−1.10964
$39$	2.90435	+	0.852793i	0.465068	+	0.136556i
$40$	0.156423	−	1.08794i	0.0247326	−	0.172019i
$41$	1.50439	+	1.73616i	0.234946	+	0.271142i	0.860963	−	0.508667i	$-0.169862\pi$
$41$	1.50439	+	1.73616i	0.234946	+	0.271142i	−0.626017	+	0.779809i	$0.715316\pi$
$42$	2.65425	−	0.779358i	0.409559	−	0.120258i
$43$	−1.62154	−	1.87136i	−0.247283	−	0.285380i	0.618515	−	0.785773i	$-0.287734\pi$
$43$	−1.62154	−	1.87136i	−0.247283	−	0.285380i	−0.865799	+	0.500393i	$0.833189\pi$
$44$	0.653278	+	0.419836i	0.0984853	+	0.0632927i
$45$	−2.06490	+	1.32703i	−0.307818	+	0.197822i
$46$	−0.391733	+	2.72457i	−0.0577579	+	0.401715i
$47$	2.68975	+	1.72859i	0.392340	+	0.252141i	0.721906	−	0.691991i	$-0.243266\pi$
$47$	2.68975	+	1.72859i	0.392340	+	0.252141i	−0.329566	+	0.944132i	$0.606903\pi$
$48$	−0.363772	+	0.796551i	−0.0525060	+	0.114972i
$49$	−1.95109	+	2.25168i	−0.278727	+	0.321668i
$50$	−2.48317	−	2.86573i	−0.351174	−	0.405276i
$51$	−0.978838	−	6.80796i	−0.137065	−	0.953306i
$52$	1.43596	−	3.14431i	0.199131	−	0.436037i
$53$	−6.26998	+	7.23595i	−0.861248	+	0.993934i	0.138745	+	0.990328i	$0.455693\pi$
$53$	−6.26998	+	7.23595i	−0.861248	+	0.993934i	−0.999994	+	0.00360549i	$0.998852\pi$
$54$	4.39698	−	1.29107i	0.598354	−	0.175692i
$55$	−0.818960	+	0.240468i	−0.110428	+	0.0324247i
$56$	−0.449575	−	3.12686i	−0.0600770	−	0.417845i
$57$	−5.03906	+	3.23841i	−0.667439	+	0.428937i
$58$	−3.19511	−	6.99632i	−0.419539	−	0.918661i
$59$	−0.0676806	−	0.0198728i	−0.00881127	−	0.00258722i	0.277324	−	0.960776i	$-0.410552\pi$
$59$	−0.0676806	−	0.0198728i	−0.00881127	−	0.00258722i	−0.286135	+	0.958189i	$0.592371\pi$
$60$	−0.399834	−	0.875514i	−0.0516183	−	0.113028i
$61$	0.510081	−	3.54769i	0.0653091	−	0.454235i	−0.930758	−	0.365635i	$-0.880852\pi$
$61$	0.510081	−	3.54769i	0.0653091	−	0.454235i	0.996067	−	0.0885996i	$-0.0282392\pi$
$62$	−0.115133	−	0.800770i	−0.0146219	−	0.101698i
$63$	−4.61981	+	5.33155i	−0.582042	+	0.671712i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	1.57831	+	3.45601i	0.195765	+	0.428665i
$66$	0.680015			0.0837041
$67$	−8.11967	−	1.03489i	−0.991975	−	0.126432i
$67$	−8.11967	−	1.03489i	−0.991975	−	0.126432i
$68$	−7.85440			−0.952485
$69$	1.00131	+	2.19257i	0.120544	+	0.263955i
$70$	2.92098	+	1.87720i	0.349124	+	0.224368i
$71$	5.88060	−	6.78657i	0.697898	−	0.805418i	−0.290569	−	0.956854i	$-0.593844\pi$
$71$	5.88060	−	6.78657i	0.697898	−	0.805418i	0.988467	+	0.151436i	$0.0483899\pi$
$72$	−0.317814	−	2.21045i	−0.0374548	−	0.260504i
$73$	1.63573	−	11.3767i	0.191448	−	1.33155i	−0.636732	−	0.771085i	$-0.719714\pi$
$73$	1.63573	−	11.3767i	0.191448	−	1.33155i	0.828180	−	0.560462i	$-0.189377\pi$
$74$	0.617486	+	1.35210i	0.0717812	+	0.157179i
$75$	−3.18601	−	0.935497i	−0.367889	−	0.108022i
$76$	2.84156	+	6.22215i	0.325949	+	0.713730i
$77$	−2.06372	+	1.32627i	−0.235182	+	0.151142i
$78$	−0.430781	−	2.99615i	−0.0487764	−	0.339247i
$79$	−5.72867	+	1.68209i	−0.644526	+	0.189250i	−0.587629	−	0.809130i	$-0.699939\pi$
$79$	−5.72867	+	1.68209i	−0.644526	+	0.189250i	−0.0568963	+	0.998380i	$0.518120\pi$
$80$	−1.05461	+	0.309661i	−0.117909	+	0.0346212i
$81$	−1.75935	+	2.03040i	−0.195484	+	0.225600i
$82$	0.954318	−	2.08967i	0.105387	−	0.230765i
$83$	−1.15986	−	8.06702i	−0.127311	−	0.885470i	−0.948942	−	0.315450i	$-0.897844\pi$
$83$	−1.15986	−	8.06702i	−0.127311	−	0.885470i	0.821631	−	0.570020i	$-0.193065\pi$
$84$	−1.81154	−	2.09063i	−0.197656	−	0.228107i
$85$	5.65342	−	6.52440i	0.613200	−	0.707670i
$86$	−1.02864	+	2.25240i	−0.110921	+	0.242883i
$87$	−5.66602	−	3.64133i	−0.607461	−	0.390392i
$88$	0.110515	−	0.768648i	0.0117809	−	0.0819382i
$89$	−2.18462	+	1.40397i	−0.231570	+	0.148821i	−0.651280	−	0.758837i	$-0.725768\pi$
$89$	−2.18462	+	1.40397i	−0.231570	+	0.148821i	0.419711	+	0.907658i	$0.362131\pi$
$90$	2.06490	+	1.32703i	0.217660	+	0.139882i
$91$	7.15089	+	8.25257i	0.749617	+	0.865104i
$92$	2.64108	−	0.775492i	0.275352	−	0.0808506i
$93$	−0.463925	−	0.535398i	−0.0481067	−	0.0555181i
$94$	0.455024	−	3.16476i	0.0469322	−	0.326420i
$95$	−7.21384	−	2.11817i	−0.740124	−	0.217320i
$96$	0.875684			0.0893742
$97$	18.8975			1.91875			0.959374	−	0.282136i	$-0.0910431\pi$
$97$	18.8975			1.91875			0.959374	+	0.282136i	$0.0910431\pi$
$98$	2.85871	+	0.839394i	0.288774	+	0.0847916i
$99$	−1.45888	+	0.937568i	−0.146623	+	0.0942291i
$100$	−1.57522	+	3.44924i	−0.157522	+	0.344924i
$101$	−0.356715	+	0.781097i	−0.0354945	+	0.0777220i	−0.926549	−	0.376175i	$-0.877239\pi$
$101$	−0.356715	+	0.781097i	−0.0354945	+	0.0777220i	0.891054	+	0.453897i	$0.149967\pi$
$102$	−5.78612	+	3.71851i	−0.572911	+	0.368188i
$103$	15.8317	+	4.64861i	1.55994	+	0.458041i	0.944054	−	0.329791i	$-0.106978\pi$
$103$	15.8317	+	4.64861i	1.55994	+	0.458041i	0.615890	+	0.787832i	$0.288796\pi$
$104$	−3.45668			−0.338955
$105$	3.04053			0.296726
$106$	9.18669	+	2.69746i	0.892291	+	0.262000i
$107$	−0.732613	+	5.09544i	−0.0708244	+	0.492595i	0.923277	+	0.384136i	$0.125501\pi$
$107$	−0.732613	+	5.09544i	−0.0708244	+	0.492595i	−0.994101	+	0.108459i	$0.965409\pi$
$108$	−3.00097	−	3.46331i	−0.288769	−	0.333257i
$109$	−19.8231	+	5.82060i	−1.89871	+	0.557513i	−0.908513	+	0.417856i	$0.862782\pi$
$109$	−19.8231	+	5.82060i	−1.89871	+	0.557513i	−0.990200	+	0.139657i	$0.955400\pi$
$110$	0.558946	+	0.645058i	0.0532934	+	0.0615038i
$111$	1.09501	+	0.703722i	0.103934	+	0.0667943i
$112$	−2.65754	+	1.70789i	−0.251114	+	0.161381i
$113$	−0.510633	+	3.55153i	−0.0480363	+	0.334100i	0.951605	+	0.307323i	$0.0994334\pi$
$113$	−0.510633	+	3.55153i	−0.0480363	+	0.334100i	−0.999641	+	0.0267766i	$0.991476\pi$
$114$	5.03906	+	3.23841i	0.471951	+	0.303304i
$115$	−1.25682	+	2.75205i	−0.117199	+	0.256630i
$116$	−5.03678	+	5.81275i	−0.467653	+	0.539700i
$117$	5.05512	+	5.83392i	0.467346	+	0.539346i
$118$	0.0100386	+	0.0698199i	0.000924127	+	0.00642745i
$119$	10.3074	−	22.5700i	0.944874	−	2.06898i
$120$	−0.630299	+	0.727403i	−0.0575381	+	0.0664025i
$121$	9.97582	−	2.92916i	0.906892	−	0.266288i
$122$	−3.43899	+	1.00978i	−0.311351	+	0.0914209i
$123$	−0.286292	−	1.99120i	−0.0258141	−	0.179541i
$124$	−0.680578	+	0.437381i	−0.0611177	+	0.0392779i
$125$	−4.01435	−	8.79020i	−0.359054	−	0.786219i
$126$	6.76888	+	1.98752i	0.603020	+	0.177063i
$127$	−0.955692	−	2.09267i	−0.0848040	−	0.185695i	0.862479	−	0.506093i	$-0.168911\pi$
$127$	−0.955692	−	2.09267i	−0.0848040	−	0.185695i	−0.947283	+	0.320398i	$0.896183\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	0.308587	+	2.14627i	0.0271696	+	0.188969i
$130$	2.48804	−	2.87135i	0.218216	−	0.251834i
$131$	16.2124	+	10.4191i	1.41649	+	0.910321i	0.999999	+	0.00118032i	$0.000375708\pi$
$131$	16.2124	+	10.4191i	1.41649	+	0.910321i	0.416488	+	0.909141i	$0.363261\pi$
$132$	−0.282488	−	0.618563i	−0.0245875	−	0.0538390i
$133$	−21.6086			−1.87370
$134$	2.43166	+	7.81582i	0.210063	+	0.675184i
$135$	5.03689			0.433507
$136$	3.26283	+	7.14461i	0.279786	+	0.612645i
$137$	12.3125	+	7.91274i	1.05192	+	0.676031i	0.947908	−	0.318544i	$-0.103194\pi$
$137$	12.3125	+	7.91274i	1.05192	+	0.676031i	0.104017	+	0.994576i	$0.466830\pi$
$138$	1.57847	−	1.82165i	0.134368	−	0.155070i
$139$	2.54328	+	17.6889i	0.215719	+	1.50036i	0.753599	+	0.657334i	$0.228316\pi$
$139$	2.54328	+	17.6889i	0.215719	+	1.50036i	−0.537881	+	0.843021i	$0.680775\pi$
$140$	0.494142	−	3.43684i	0.0417627	−	0.290466i
$141$	−1.16309	−	2.54682i	−0.0979500	−	0.214481i
$142$	−8.61617	−	2.52994i	−0.723053	−	0.212307i
$143$	1.11510	+	2.44172i	0.0932490	+	0.204187i
$144$	−1.87867	+	1.20735i	−0.156556	+	0.100612i
$145$	−1.20311	−	8.36778i	−0.0999125	−	0.694906i
$146$	−11.0282	+	3.23816i	−0.912697	+	0.267992i
$147$	2.50333	−	0.735044i	0.206471	−	0.0606254i
$148$	0.973405	−	1.12337i	0.0800134	−	0.0923404i
$149$	1.48444	−	3.25047i	0.121610	−	0.266289i	−0.839030	−	0.544085i	$-0.816877\pi$
$149$	1.48444	−	3.25047i	0.121610	−	0.266289i	0.960640	+	0.277796i	$0.0896040\pi$
$150$	0.472559	+	3.28672i	0.0385843	+	0.268359i
$151$	−0.993157	−	1.14616i	−0.0808219	−	0.0932735i	0.713898	−	0.700249i	$-0.246928\pi$
$151$	−0.993157	−	1.14616i	−0.0808219	−	0.0932735i	−0.794720	+	0.606976i	$0.792382\pi$
$152$	4.47944	−	5.16955i	0.363331	−	0.419306i
$153$	7.28649	−	15.9552i	0.589077	−	1.28990i
$154$	2.06372	+	1.32627i	0.166299	+	0.106874i
$155$	0.126547	−	0.880152i	0.0101645	−	0.0706955i
$156$	−2.54644	+	1.63650i	−0.203878	+	0.131025i
$157$	−4.24329	−	2.72700i	−0.338651	−	0.217638i	0.360251	−	0.932856i	$-0.382691\pi$
$157$	−4.24329	−	2.72700i	−0.338651	−	0.217638i	−0.698902	+	0.715218i	$0.746328\pi$
$158$	3.90986	+	4.51222i	0.311052	+	0.358973i
$159$	8.04464	−	2.36212i	0.637982	−	0.187328i
$160$	0.719778	+	0.830668i	0.0569035	+	0.0656701i
$161$	−1.23749	+	8.60695i	−0.0975281	+	0.678323i
$162$	2.57778	+	0.756905i	0.202530	+	0.0594681i
$163$	−18.6159			−1.45811			−0.729054	−	0.684456i	$-0.760040\pi$
$163$	−18.6159			−1.45811			−0.729054	+	0.684456i	$0.760040\pi$
$164$	−2.29726			−0.179386
$165$	0.717150	+	0.210574i	0.0558301	+	0.0163932i
$166$	−6.85619	+	4.40621i	−0.532144	+	0.341988i
$167$	−7.17623	+	15.7138i	−0.555314	+	1.21597i	0.398942	+	0.916976i	$0.369377\pi$
$167$	−7.17623	+	15.7138i	−0.555314	+	1.21597i	−0.954256	+	0.298991i	$0.903350\pi$
$168$	−1.14916	+	2.51632i	−0.0886599	+	0.194138i
$169$	−0.884465	+	0.568411i	−0.0680357	+	0.0437239i
$170$	−8.28332	−	2.43220i	−0.635302	−	0.186541i
$171$	−15.2756			−1.16815
$172$	2.47617			0.188806
$173$	−17.5985	−	5.16739i	−1.33799	−	0.392869i	−0.467037	−	0.884238i	$-0.654679\pi$
$173$	−17.5985	−	5.16739i	−1.33799	−	0.392869i	−0.870952	+	0.491369i	$0.836497\pi$
$174$	−0.958521	+	6.66666i	−0.0726653	+	0.505398i
$175$	−7.84439	−	9.05291i	−0.592980	−	0.684335i
$176$	−0.745097	+	0.218780i	−0.0561638	+	0.0164912i
$177$	0.0404501	+	0.0466819i	0.00304041	+	0.00350882i
$178$	2.18462	+	1.40397i	0.163744	+	0.105232i
$179$	8.03383	−	5.16303i	0.600476	−	0.385903i	−0.204799	−	0.978804i	$-0.565654\pi$
$179$	8.03383	−	5.16303i	0.600476	−	0.385903i	0.805275	+	0.592901i	$0.202018\pi$
$180$	0.349320	−	2.42957i	0.0260368	−	0.181090i
$181$	−4.41621	−	2.83812i	−0.328254	−	0.210956i	0.366125	−	0.930566i	$-0.380684\pi$
$181$	−4.41621	−	2.83812i	−0.328254	−	0.210956i	−0.694379	+	0.719610i	$0.744321\pi$
$182$	4.53621	−	9.93292i	0.336247	−	0.736277i
$183$	−2.05535	+	2.37200i	−0.151936	+	0.175343i
$184$	−1.80256	−	2.08026i	−0.132886	−	0.153359i
$185$	0.232512	+	1.61715i	0.0170946	+	0.118896i
$186$	−0.294293	+	0.644413i	−0.0215786	+	0.0472506i
$187$	3.99423	−	4.60958i	0.292087	−	0.337086i
$188$	−3.06779	+	0.900785i	−0.223742	+	0.0656965i
$189$	13.8902	−	4.07852i	1.01036	−	0.296668i
$190$	1.06998	+	7.44186i	0.0776243	+	0.539889i
$191$	17.2206	−	11.0670i	1.24604	−	0.800779i	0.259726	−	0.965682i	$-0.416368\pi$
$191$	17.2206	−	11.0670i	1.24604	−	0.800779i	0.986310	+	0.164904i	$0.0527313\pi$
$192$	−0.363772	−	0.796551i	−0.0262530	−	0.0574861i
$193$	3.53317	+	1.03743i	0.254323	+	0.0746759i	0.406409	−	0.913691i	$-0.366781\pi$
$193$	3.53317	+	1.03743i	0.254323	+	0.0746759i	−0.152086	+	0.988367i	$0.548599\pi$
$194$	−7.85030	−	17.1898i	−0.563619	−	1.23415i
$195$	0.473486	−	3.29316i	0.0339070	−	0.235828i
$196$	−0.424013	−	2.94907i	−0.0302866	−	0.210648i
$197$	12.2957	−	14.1900i	0.876034	−	1.01100i	−0.123791	−	0.992308i	$-0.539505\pi$
$197$	12.2957	−	14.1900i	0.876034	−	1.01100i	0.999825	−	0.0186891i	$-0.00594926\pi$
$198$	1.45888	+	0.937568i	0.103678	+	0.0666301i
$199$	3.92798	+	8.60108i	0.278447	+	0.609714i	0.996249	−	0.0865333i	$-0.0275789\pi$
$199$	3.92798	+	8.60108i	0.278447	+	0.609714i	−0.717802	+	0.696247i	$0.754852\pi$
$200$	3.79191			0.268128
$201$	5.49159	+	4.60648i	0.387347	+	0.324916i
$202$	0.858695			0.0604176
$203$	−10.0934	−	22.1015i	−0.708419	−	1.55122i
$204$	5.78612	+	3.71851i	0.405109	+	0.260348i
$205$	1.65352	−	1.90827i	0.115487	−	0.133279i
$206$	−2.34821	−	16.3321i	−0.163607	−	1.13791i
$207$	−0.874810	+	6.08444i	−0.0608035	+	0.422898i
$208$	1.43596	+	3.14431i	0.0995657	+	0.218018i
$209$	−5.09668	−	1.49652i	−0.352545	−	0.103516i
$210$	−1.26308	−	2.76577i	−0.0871610	−	0.190856i
$211$	−0.106905	+	0.0687035i	−0.00735962	+	0.00472974i	−0.544315	−	0.838881i	$-0.683211\pi$
$211$	−0.106905	+	0.0687035i	−0.00735962	+	0.00472974i	0.536956	+	0.843610i	$0.319574\pi$
$212$	−1.36260	−	9.47707i	−0.0935836	−	0.650888i
$213$	−7.54505	+	2.21543i	−0.516978	+	0.151798i
$214$	4.93931	−	1.45031i	0.337644	−	0.0991413i
$215$	−1.78229	+	2.05687i	−0.121551	+	0.140278i
$216$	−1.90369	+	4.16849i	−0.129529	+	0.283630i
$217$	−0.363708	−	2.52965i	−0.0246901	−	0.171724i
$218$	13.5294	+	15.6138i	0.916329	+	1.05750i
$219$	−6.59110	+	7.60653i	−0.445385	+	0.514002i
$220$	0.354571	−	0.776402i	0.0239052	−	0.0523450i
$221$	−22.8401	−	14.6785i	−1.53639	−	0.987381i
$222$	0.185243	−	1.28840i	0.0124327	−	0.0864714i
$223$	−15.0400	+	9.66560i	−1.00715	+	0.647256i	−0.936654	−	0.350256i	$-0.886095\pi$
$223$	−15.0400	+	9.66560i	−1.00715	+	0.647256i	−0.0704963	+	0.997512i	$0.522458\pi$
$224$	2.65754	+	1.70789i	0.177564	+	0.114113i
$225$	−5.54536	−	6.39969i	−0.369691	−	0.426646i
$226$	3.44271	−	1.01087i	0.229006	−	0.0672422i
$227$	13.5823	+	15.6748i	0.901487	+	1.04037i	0.998981	+	0.0451354i	$0.0143719\pi$
$227$	13.5823	+	15.6748i	0.901487	+	1.04037i	−0.0974938	+	0.995236i	$0.531083\pi$
$228$	0.852457	−	5.92897i	0.0564554	−	0.392656i
$229$	14.9832	+	4.39946i	0.990117	+	0.290725i	0.736394	−	0.676552i	$-0.236527\pi$
$229$	14.9832	+	4.39946i	0.990117	+	0.290725i	0.253723	+	0.967277i	$0.418345\pi$
$230$	3.02545			0.199492
$231$	2.14818			0.141340
$232$	7.37982	+	2.16691i	0.484509	+	0.142265i
$233$	−12.2581	+	7.87778i	−0.803053	+	0.516091i	−0.876611	−	0.481200i	$-0.840201\pi$
$233$	−12.2581	+	7.87778i	−0.803053	+	0.516091i	0.0735581	+	0.997291i	$0.476565\pi$
$234$	3.20675	−	7.02179i	0.209631	−	0.459029i
$235$	1.45988	−	3.19668i	0.0952319	−	0.208529i
$236$	0.0593403	−	0.0381357i	0.00386272	−	0.00248242i
$237$	5.01651	+	1.47298i	0.325857	+	0.0956803i
$238$	−24.8122			−1.60834
$239$	−29.3826			−1.90060			−0.950301	−	0.311332i	$-0.899225\pi$
$239$	−29.3826			−1.90060			−0.950301	+	0.311332i	$0.899225\pi$
$240$	0.923505	+	0.271166i	0.0596120	+	0.0175037i
$241$	−0.982628	+	6.83433i	−0.0632966	+	0.440238i	0.933388	+	0.358870i	$0.116838\pi$
$241$	−0.982628	+	6.83433i	−0.0632966	+	0.440238i	−0.996684	+	0.0813677i	$0.974071\pi$
$242$	−6.80856	−	7.85750i	−0.437671	−	0.505099i
$243$	15.4483	−	4.53602i	0.991007	−	0.290986i
$244$	2.34713	+	2.70873i	0.150260	+	0.173409i
$245$	2.75490	+	1.77046i	0.176004	+	0.113111i
$246$	−1.69233	+	1.08760i	−0.107899	+	0.0693426i
$247$	−3.36499	+	23.4040i	−0.214109	+	1.48916i
$248$	0.680578	+	0.437381i	0.0432167	+	0.0277737i
$249$	−2.96474	+	6.49187i	−0.187882	+	0.411405i
$250$	−6.32823	+	7.30316i	−0.400232	+	0.461892i
$251$	9.73069	+	11.2298i	0.614195	+	0.708819i	0.974594	−	0.223979i	$-0.0719047\pi$
$251$	9.73069	+	11.2298i	0.614195	+	0.708819i	−0.360398	+	0.932798i	$0.617359\pi$
$252$	−1.00398	−	6.98284i	−0.0632449	−	0.439878i
$253$	−0.887960	+	1.94436i	−0.0558256	+	0.122241i
$254$	−1.50655	+	1.73866i	−0.0945296	+	0.109093i
$255$	−7.25357	+	2.12984i	−0.454236	+	0.133376i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−0.959684	−	6.67475i	−0.0598634	−	0.416359i	−0.997613	−	0.0690481i	$-0.978004\pi$
$257$	−0.959684	−	6.67475i	−0.0598634	−	0.416359i	0.937750	−	0.347311i	$-0.112905\pi$
$258$	1.82412	−	1.17229i	0.113565	−	0.0729838i
$259$	1.95065	+	4.27132i	0.121207	+	0.265407i
$260$	−3.64545	−	1.07040i	−0.226081	−	0.0663834i
$261$	−7.13525	−	15.6240i	−0.441661	−	0.967102i
$262$	2.74266	−	19.0756i	0.169442	−	1.17850i
$263$	2.79951	+	19.4710i	0.172625	+	1.20064i	0.873310	+	0.487165i	$0.161969\pi$
$263$	2.79951	+	19.4710i	0.172625	+	1.20064i	−0.700685	+	0.713471i	$0.747122\pi$
$264$	−0.445315	+	0.513921i	−0.0274073	+	0.0316297i
$265$	8.85307	+	5.68953i	0.543840	+	0.349505i
$266$	8.97654	+	19.6559i	0.550387	+	1.20518i
$267$	2.27404			0.139169
$268$	6.09937	−	5.45872i	0.372578	−	0.333445i
$269$	13.9339			0.849567			0.424784	−	0.905295i	$-0.360350\pi$
$269$	13.9339			0.849567			0.424784	+	0.905295i	$0.360350\pi$
$270$	−2.09240	−	4.58172i	−0.127340	−	0.278835i
$271$	20.9577	+	13.4687i	1.27309	+	0.818165i	0.990019	−	0.140934i	$-0.0450107\pi$
$271$	20.9577	+	13.4687i	1.27309	+	0.818165i	0.283070	+	0.959099i	$0.408647\pi$
$272$	5.14354	−	5.93596i	0.311873	−	0.359920i
$273$	−1.36085	−	9.46490i	−0.0823622	−	0.572842i
$274$	2.08290	−	14.4869i	0.125833	−	0.875185i
$275$	−1.22324	−	2.67852i	−0.0737640	−	0.161521i
$276$	−2.31276	−	0.679086i	−0.139212	−	0.0408762i
$277$	−8.26953	−	18.1078i	−0.496868	−	1.08799i	−0.977475	−	0.211053i	$-0.932311\pi$
$277$	−8.26953	−	18.1078i	−0.496868	−	1.08799i	0.480606	−	0.876936i	$-0.340417\pi$
$278$	15.0339	−	9.66170i	0.901673	−	0.579470i
$279$	−0.257113	−	1.78826i	−0.0153930	−	0.107060i
$280$	−3.33153	+	0.978226i	−0.199097	+	0.0584602i
$281$	9.59479	−	2.81728i	0.572377	−	0.168065i	0.0172802	−	0.999851i	$-0.494499\pi$
$281$	9.59479	−	2.81728i	0.572377	−	0.168065i	0.555097	+	0.831786i	$0.312681\pi$
$282$	−1.83350	+	2.11597i	−0.109183	+	0.126004i
$283$	−9.29837	+	20.3606i	−0.552731	+	1.21031i	0.402764	+	0.915304i	$0.368050\pi$
$283$	−9.29837	+	20.3606i	−0.552731	+	1.21031i	−0.955495	+	0.295008i	$0.904678\pi$
$284$	1.27798	+	8.88852i	0.0758339	+	0.527436i
$285$	4.31143	+	4.97565i	0.255387	+	0.294732i
$286$	1.75784	−	2.02865i	0.103943	−	0.119957i
$287$	3.01471	−	6.60129i	0.177953	−	0.389662i
$288$	1.87867	+	1.20735i	0.110702	+	0.0711436i
$289$	−6.36027	+	44.2366i	−0.374133	+	2.60216i
$290$	−7.11181	+	4.57049i	−0.417620	+	0.268388i
$291$	−13.9213	−	8.94665i	−0.816079	−	0.524462i
$292$	7.52679	+	8.68638i	0.440472	+	0.508332i
$293$	0.155585	−	0.0456838i	0.00908936	−	0.00266888i	−0.277185	−	0.960817i	$-0.589401\pi$
$293$	0.155585	−	0.0456838i	0.00908936	−	0.00266888i	0.286274	+	0.958148i	$0.407583\pi$
$294$	−1.70854	−	1.97176i	−0.0996441	−	0.114995i
$295$	−0.0110337	+	0.0767413i	−0.000642409	+	0.00446805i
$296$	−1.42622	−	0.418776i	−0.0828973	−	0.0243409i
$297$	3.55864			0.206493
$298$	−3.57339			−0.207001
$299$	9.12938	+	2.68063i	0.527966	+	0.155025i
$300$	2.79340	−	1.79521i	0.161277	−	0.103646i
$301$	−3.24948	+	7.11538i	−0.187297	+	0.410124i
$302$	−0.630015	+	1.37954i	−0.0362533	+	0.0793836i
$303$	0.632577	−	0.406533i	0.0363406	−	0.0233547i
$304$	−6.56321	−	1.92713i	−0.376426	−	0.110529i
$305$	−3.93948			−0.225574
$306$	−17.5403			−1.00271
$307$	1.24992	+	0.367009i	0.0713366	+	0.0209463i	0.317206	−	0.948357i	$-0.397255\pi$
$307$	1.24992	+	0.367009i	0.0713366	+	0.0209463i	−0.245870	+	0.969303i	$0.579073\pi$
$308$	0.349119	−	2.42817i	0.0198929	−	0.138358i
$309$	−9.46199	−	10.9197i	−0.538274	−	0.621201i
$310$	−0.853183	+	0.250517i	−0.0484576	+	0.0142284i
$311$	−0.0175000	−	0.0201960i	−0.000992332	−	0.00114521i	0.755253	−	0.655433i	$-0.227514\pi$
$311$	−0.0175000	−	0.0201960i	−0.000992332	−	0.00114521i	−0.756246	+	0.654288i	$0.772968\pi$
$312$	2.54644	+	1.63650i	0.144164	+	0.0926485i
$313$	11.8159	−	7.59359i	0.667871	−	0.429215i	−0.162286	−	0.986744i	$-0.551887\pi$
$313$	11.8159	−	7.59359i	0.667871	−	0.429215i	0.830158	+	0.557529i	$0.188250\pi$
$314$	−0.717837	+	4.99266i	−0.0405099	+	0.281752i
$315$	6.52307	+	4.19212i	0.367533	+	0.236199i
$316$	2.48024	−	5.43097i	0.139525	−	0.305516i
$317$	−16.7400	+	19.3190i	−0.940214	+	1.08506i	0.0560259	+	0.998429i	$0.482157\pi$
$317$	−16.7400	+	19.3190i	−0.940214	+	1.08506i	−0.996240	+	0.0866356i	$0.972388\pi$
$318$	−5.49053	−	6.33641i	−0.307893	−	0.355328i
$319$	−0.850011	−	5.91196i	−0.0475915	−	0.331006i
$320$	0.456596	−	0.999806i	0.0255245	−	0.0558908i
$321$	2.95203	−	3.40683i	0.164766	−	0.190151i
$322$	8.34323	−	2.44979i	0.464950	−	0.136522i
$323$	51.5501	−	15.1365i	2.86832	−	0.842216i
$324$	−0.382344	−	2.65926i	−0.0212413	−	0.147737i
$325$	−11.0267	+	7.08640i	−0.611649	+	0.393083i
$326$	7.73331	+	16.9336i	0.428309	+	0.937865i
$327$	17.3588	+	5.09701i	0.959945	+	0.281865i
$328$	0.954318	+	2.08967i	0.0526934	+	0.115382i
$329$	1.43743	−	9.99754i	0.0792481	−	0.551182i
$330$	−0.106370	−	0.739818i	−0.00585547	−	0.0407257i
$331$	11.9528	−	13.7942i	0.656983	−	0.758199i	−0.325298	−	0.945612i	$-0.605465\pi$
$331$	11.9528	−	13.7942i	0.656983	−	0.758199i	0.982281	+	0.187412i	$0.0600100\pi$
$332$	6.85619	+	4.40621i	0.376283	+	0.241822i
$333$	1.37895	+	3.01949i	0.0755662	+	0.165467i
$334$	17.2749			0.945238
$335$	0.144195	+	8.99563i	0.00787821	+	0.491484i
$336$	2.76630			0.150914
$337$	−0.922063	−	2.01904i	−0.0502280	−	0.109984i	0.882854	−	0.469647i	$-0.155619\pi$
$337$	−0.922063	−	2.01904i	−0.0502280	−	0.109984i	−0.933082	+	0.359663i	$0.882892\pi$
$338$	0.884465	+	0.568411i	0.0481085	+	0.0309175i
$339$	2.05757	−	2.37457i	0.111752	−	0.128969i
$340$	1.22861	+	8.54515i	0.0666305	+	0.463426i
$341$	0.0894071	−	0.621840i	0.00484166	−	0.0336745i
$342$	6.34571	+	13.8952i	0.343137	+	0.751364i
$343$	−12.1867	−	3.57833i	−0.658018	−	0.193212i
$344$	−1.02864	−	2.25240i	−0.0554604	−	0.121441i
$345$	2.22877	−	1.43234i	0.119993	−	0.0771147i
$346$	2.61026	+	18.1548i	0.140329	+	0.976006i
$347$	−7.70823	+	2.26334i	−0.413799	+	0.121502i	−0.482004	−	0.876169i	$-0.660091\pi$
$347$	−7.70823	+	2.26334i	−0.413799	+	0.121502i	0.0682049	+	0.997671i	$0.478273\pi$
$348$	6.46239	−	1.89753i	0.346420	−	0.101718i
$349$	1.86030	−	2.14690i	0.0995797	−	0.114921i	−0.703772	−	0.710426i	$-0.748502\pi$
$349$	1.86030	−	2.14690i	0.0995797	−	0.114921i	0.803352	+	0.595505i	$0.203048\pi$
$350$	−4.97614	+	10.8962i	−0.265986	+	0.582427i
$351$	−2.25436	−	15.6794i	−0.120329	−	0.836904i
$352$	0.508534	+	0.586879i	0.0271049	+	0.0312808i
$353$	21.8784	−	25.2490i	1.16447	−	1.34387i	0.236316	−	0.971676i	$-0.424060\pi$
$353$	21.8784	−	25.2490i	1.16447	−	1.34387i	0.928155	−	0.372195i	$-0.121395\pi$
$354$	0.0256598	−	0.0561870i	0.00136380	−	0.00298631i
$355$	−8.30327	−	5.33619i	−0.440692	−	0.283215i
$356$	0.369573	−	2.57044i	0.0195873	−	0.136233i
$357$	−18.2785	+	11.7469i	−0.967399	+	0.621709i
$358$	−8.03383	−	5.16303i	−0.424601	−	0.272874i
$359$	−17.6126	−	20.3261i	−0.929559	−	1.07277i	−0.997179	−	0.0750573i	$-0.976086\pi$
$359$	−17.6126	−	20.3261i	−0.929559	−	1.07277i	0.0676201	−	0.997711i	$-0.478459\pi$
$360$	−2.35513	+	0.691528i	−0.124126	+	0.0364467i
$361$	−18.1983	−	21.0020i	−0.957807	−	1.10537i
$362$	−0.747089	+	5.19612i	−0.0392661	+	0.273102i
$363$	−8.73567	−	2.56502i	−0.458504	−	0.134629i
$364$	−10.9197			−0.572349
$365$	−12.6331			−0.661248
$366$	3.01147	+	0.884246i	0.157412	+	0.0462203i
$367$	10.8854	−	6.99560i	0.568211	−	0.365167i	−0.224771	−	0.974412i	$-0.572163\pi$
$367$	10.8854	−	6.99560i	0.568211	−	0.365167i	0.792983	+	0.609244i	$0.208527\pi$
$368$	−1.14346	+	2.50384i	−0.0596072	+	0.130522i
$369$	2.13116	−	4.66659i	0.110944	−	0.242933i
$370$	1.37443	−	0.883290i	0.0714530	−	0.0459201i
$371$	29.0209	+	8.52132i	1.50669	+	0.442405i
$372$	0.708432			0.0367305
$373$	7.93899			0.411065			0.205533	−	0.978650i	$-0.434107\pi$
$373$	7.93899			0.411065			0.205533	+	0.978650i	$0.434107\pi$
$374$	−5.85229	−	1.71839i	−0.302614	−	0.0888556i
$375$	−1.20429	+	8.37602i	−0.0621892	+	0.432536i
$376$	2.09379	+	2.41636i	0.107979	+	0.124614i
$377$	−25.5097	+	7.49031i	−1.31381	+	0.385771i
$378$	−9.48013	−	10.9407i	−0.487605	−	0.562726i
$379$	−7.86884	−	5.05700i	−0.404195	−	0.259760i	0.322711	−	0.946498i	$-0.395406\pi$
$379$	−7.86884	−	5.05700i	−0.404195	−	0.259760i	−0.726906	+	0.686737i	$0.759042\pi$
$380$	6.32487	−	4.06475i	0.324459	−	0.208517i
$381$	−0.286704	+	1.99407i	−0.0146883	+	0.102159i
$382$	−17.2206	−	11.0670i	−0.881080	−	0.566236i
$383$	−5.63014	+	12.3283i	−0.287687	+	0.629946i	−0.997203	−	0.0747434i	$-0.976186\pi$
$383$	−5.63014	+	12.3283i	−0.287687	+	0.629946i	0.709516	+	0.704689i	$0.248914\pi$
$384$	−0.573451	+	0.661798i	−0.0292638	+	0.0337722i
$385$	1.76572	+	2.03775i	0.0899894	+	0.103853i
$386$	−0.524050	−	3.64485i	−0.0266734	−	0.185518i
$387$	−2.29713	+	5.03001i	−0.116770	+	0.255690i
$388$	−12.3752	+	14.2818i	−0.628257	+	0.725047i
$389$	−6.57461	+	1.93048i	−0.333346	+	0.0978792i	−0.444122	−	0.895966i	$-0.646484\pi$
$389$	−6.57461	+	1.93048i	−0.333346	+	0.0978792i	0.110776	+	0.993845i	$0.464666\pi$
$390$	−3.19226	+	0.937332i	−0.161646	+	0.0474637i
$391$	−3.07683	−	21.3998i	−0.155602	−	1.08224i
$392$	−2.50643	+	1.61078i	−0.126594	+	0.0813569i
$393$	−7.01054	−	15.3509i	−0.353635	−	0.774352i
$394$	−18.0155	−	5.28984i	−0.907609	−	0.266498i
$395$	2.72611	+	5.96936i	0.137166	+	0.300351i
$396$	0.246799	−	1.71653i	0.0124021	−	0.0862588i
$397$	0.105766	+	0.735619i	0.00530824	+	0.0369197i	0.992303	−	0.123830i	$-0.0395178\pi$
$397$	0.105766	+	0.735619i	0.00530824	+	0.0369197i	−0.986995	+	0.160750i	$0.948609\pi$
$398$	6.19207	−	7.14603i	0.310381	−	0.358198i
$399$	15.9185	+	10.2302i	0.796921	+	0.512150i
$400$	−1.57522	−	3.44924i	−0.0787608	−	0.172462i
$401$	−10.2032			−0.509522			−0.254761	−	0.967004i	$-0.581997\pi$
$401$	−10.2032			−0.509522			−0.254761	+	0.967004i	$0.581997\pi$
$402$	1.90891	−	6.90892i	0.0952079	−	0.344586i
$403$	−2.79647			−0.139302
$404$	−0.356715	−	0.781097i	−0.0177472	−	0.0388610i
$405$	2.48417	+	1.59648i	0.123439	+	0.0793296i
$406$	−15.9113	+	18.3626i	−0.789663	+	0.911320i
$407$	0.164273	+	1.14254i	0.00814270	+	0.0566337i
$408$	0.978838	−	6.80796i	0.0484597	−	0.337044i
$409$	−6.52947	−	14.2975i	−0.322861	−	0.706968i	0.676710	−	0.736250i	$-0.263405\pi$
$409$	−6.52947	−	14.2975i	−0.322861	−	0.706968i	−0.999571	+	0.0292820i	$0.990678\pi$
$410$	−2.42272	−	0.711374i	−0.119649	−	0.0351323i
$411$	−5.32412	−	11.6582i	−0.262620	−	0.575057i
$412$	−13.8807	+	8.92061i	−0.683855	+	0.439487i
$413$	0.0317121	+	0.220562i	0.00156045	+	0.0108532i
$414$	5.89801	−	1.73181i	0.289871	−	0.0851139i
$415$	−8.59504	+	2.52373i	−0.421914	+	0.123885i
$416$	2.26364	−	2.61238i	0.110984	−	0.128083i
$417$	6.50092	−	14.2350i	0.318351	−	0.697092i
$418$	0.755955	+	5.25778i	0.0369750	+	0.257166i
$419$	−15.0359	−	17.3523i	−0.734551	−	0.847717i	0.258425	−	0.966031i	$-0.416796\pi$
$419$	−15.0359	−	17.3523i	−0.734551	−	0.847717i	−0.992976	+	0.118314i	$0.962251\pi$
$420$	−1.99113	+	2.29788i	−0.0971570	+	0.112125i
$421$	10.8510	−	23.7603i	0.528843	−	1.15800i	−0.437138	−	0.899394i	$-0.644008\pi$
$421$	10.8510	−	23.7603i	0.528843	−	1.15800i	0.965982	−	0.258611i	$-0.0832647\pi$
$422$	0.106905	+	0.0687035i	0.00520404	+	0.00334443i
$423$	1.01615	−	7.06747i	0.0494069	−	0.343632i
$424$	−8.05461	+	5.17638i	−0.391166	+	0.251387i
$425$	25.0552	+	16.1020i	1.21536	+	0.781061i
$426$	5.14955	+	5.94289i	0.249496	+	0.287934i
$427$	−10.8638	+	3.18991i	−0.525737	+	0.154370i
$428$	−3.37111	−	3.89047i	−0.162949	−	0.188053i
$429$	0.334524	−	2.32667i	0.0161510	−	0.112333i
$430$	2.61139	+	0.766773i	0.125932	+	0.0369771i
$431$	−13.3811			−0.644546			−0.322273	−	0.946647i	$-0.604447\pi$
$431$	−13.3811			−0.644546			−0.322273	+	0.946647i	$0.604447\pi$
$432$	4.58261			0.220481
$433$	15.3126	+	4.49619i	0.735877	+	0.216073i	0.628133	−	0.778106i	$-0.283819\pi$
$433$	15.3126	+	4.49619i	0.735877	+	0.216073i	0.107744	+	0.994179i	$0.465637\pi$
$434$	−2.14996	+	1.38169i	−0.103201	+	0.0663234i
$435$	−3.07527	+	6.73390i	−0.147448	+	0.322866i
$436$	8.58248	−	18.7930i	0.411026	−	0.900022i
$437$	−15.8395	+	10.1794i	−0.757707	+	0.486949i
$438$	9.65719	+	2.83561i	0.461438	+	0.135490i
$439$	−15.5157			−0.740526			−0.370263	−	0.928927i	$-0.620732\pi$
$439$	−15.5157			−0.740526			−0.370263	+	0.928927i	$0.620732\pi$
$440$	−0.853534			−0.0406906
$441$	6.38401	+	1.87451i	0.304000	+	0.0892626i
$442$	−3.86387	+	26.8738i	−0.183785	+	1.27826i
$443$	−8.14634	−	9.40138i	−0.387044	−	0.446673i	0.528474	−	0.848950i	$-0.322764\pi$
$443$	−8.14634	−	9.40138i	−0.387044	−	0.446673i	−0.915518	+	0.402277i	$0.868219\pi$
$444$	−1.24892	+	0.366716i	−0.0592710	+	0.0174036i
$445$	1.86917	+	2.15714i	0.0886071	+	0.102258i
$446$	15.0400	+	9.66560i	0.712163	+	0.457679i
$447$	−2.63242	+	1.69175i	−0.124509	+	0.0800172i
$448$	0.449575	−	3.12686i	0.0212404	−	0.147730i
$449$	22.9889	+	14.7741i	1.08491	+	0.697231i	0.955687	−	0.294384i	$-0.0951144\pi$
$449$	22.9889	+	14.7741i	1.08491	+	0.697231i	0.129226	+	0.991615i	$0.458751\pi$
$450$	−3.51774	+	7.70277i	−0.165828	+	0.363112i
$451$	1.16824	−	1.34822i	0.0550101	−	0.0634851i
$452$	−2.34968	−	2.71167i	−0.110519	−	0.127546i
$453$	0.189002	+	1.31454i	0.00888009	+	0.0617624i
$454$	8.61600	−	18.8664i	0.404369	−	0.885444i
$455$	7.85977	−	9.07066i	0.368472	−	0.425239i
$456$	−5.74730	+	1.68756i	−0.269142	+	0.0790273i
$457$	19.8625	−	5.83215i	0.929127	−	0.272816i	0.218056	−	0.975936i	$-0.430029\pi$
$457$	19.8625	−	5.83215i	0.929127	−	0.272816i	0.711071	+	0.703120i	$0.248210\pi$
$458$	−2.22235	−	15.4568i	−0.103844	−	0.722248i
$459$	−30.2798	+	19.4596i	−1.41334	+	0.908298i
$460$	−1.25682	−	2.75205i	−0.0585994	−	0.128315i
$461$	8.44795	+	2.48054i	0.393460	+	0.115530i	0.472477	−	0.881343i	$-0.343360\pi$
$461$	8.44795	+	2.48054i	0.393460	+	0.115530i	−0.0790169	+	0.996873i	$0.525178\pi$
$462$	−0.892386	−	1.95405i	−0.0415176	−	0.0909108i
$463$	−1.43243	+	9.96275i	−0.0665706	+	0.463008i	0.929083	+	0.369872i	$0.120598\pi$
$463$	−1.43243	+	9.96275i	−0.0665706	+	0.463008i	−0.995653	+	0.0931365i	$0.970311\pi$
$464$	−1.09460	−	7.61308i	−0.0508153	−	0.353428i
$465$	−0.509914	+	0.588472i	−0.0236467	+	0.0272898i
$466$	12.2581	+	7.87778i	0.567844	+	0.364931i
$467$	−9.13248	−	19.9973i	−0.422601	−	0.925367i	−0.994470	−	0.105022i	$-0.966509\pi$
$467$	−9.13248	−	19.9973i	−0.422601	−	0.925367i	0.571869	−	0.820345i	$-0.306219\pi$
$468$	−7.71938			−0.356828
$469$	7.68166	+	24.6903i	0.354706	+	1.14009i
$470$	−3.51426			−0.162101
$471$	1.83487	+	4.01781i	0.0845464	+	0.185131i
$472$	−0.0593403	−	0.0381357i	−0.00273136	−	0.00175534i
$473$	−1.25921	+	1.45321i	−0.0578988	+	0.0668187i
$474$	−0.744063	−	5.17507i	−0.0341759	−	0.237699i
$475$	3.69133	−	25.6738i	0.169370	−	1.17799i
$476$	10.3074	+	22.5700i	0.472437	+	1.03449i
$477$	20.5155	+	6.02390i	0.939341	+	0.275815i
$478$	12.2060	+	26.7274i	0.558288	+	1.22248i
$479$	−26.3247	+	16.9179i	−1.20281	+	0.772997i	−0.979440	−	0.201737i	$-0.935341\pi$
$479$	−26.3247	+	16.9179i	−1.20281	+	0.772997i	−0.223368	+	0.974734i	$0.571705\pi$
$480$	−0.136977	−	0.952696i	−0.00625212	−	0.0434844i
$481$	4.92999	−	1.44757i	0.224788	−	0.0660037i
$482$	6.62492	−	1.94525i	0.301757	−	0.0886038i
$483$	4.98642	−	5.75464i	0.226890	−	0.261845i
$484$	−4.31906	+	9.45741i	−0.196321	+	0.429882i
$485$	−2.95600	−	20.5594i	−0.134225	−	0.933555i
$486$	−10.5436	−	12.1679i	−0.478265	−	0.551948i
$487$	26.4577	−	30.5338i	1.19891	−	1.38362i	0.295223	−	0.955428i	$-0.404606\pi$
$487$	26.4577	−	30.5338i	1.19891	−	1.38362i	0.903689	−	0.428190i	$-0.140849\pi$
$488$	1.48892	−	3.26028i	0.0674001	−	0.147586i
$489$	13.7138	+	8.81333i	0.620160	+	0.398552i
$490$	0.466046	−	3.24142i	0.0210538	−	0.146432i
$491$	−22.6924	+	14.5835i	−1.02409	+	0.658146i	−0.941004	−	0.338396i	$-0.890116\pi$
$491$	−22.6924	+	14.5835i	−1.02409	+	0.658146i	−0.0830909	+	0.996542i	$0.526479\pi$
$492$	1.69233	+	1.08760i	0.0762962	+	0.0490326i
$493$	39.5608	+	45.6556i	1.78173	+	2.05623i
$494$	22.6869	−	6.66148i	1.02073	−	0.299714i
$495$	1.24822	+	1.44053i	0.0561035	+	0.0647469i
$496$	0.115133	−	0.800770i	0.00516964	−	0.0359556i
$497$	−27.2186	−	7.99211i	−1.22092	−	0.358495i
$498$	7.13680			0.319808
$499$	21.7266			0.972617			0.486309	−	0.873787i	$-0.338343\pi$
$499$	21.7266			0.972617			0.486309	+	0.873787i	$0.338343\pi$
$500$	9.27203	+	2.72251i	0.414658	+	0.121755i
$501$	12.7259	−	8.17845i	0.568552	−	0.365386i
$502$	6.17272	−	13.5164i	0.275502	−	0.603265i
$503$	8.07831	−	17.6890i	0.360194	−	0.788715i	−0.639606	−	0.768703i	$-0.720902\pi$
$503$	8.07831	−	17.6890i	0.360194	−	0.788715i	0.999800	−	0.0200116i	$-0.00637033\pi$
$504$	−5.93475	+	3.81403i	−0.264355	+	0.169890i
$505$	0.905588	+	0.265905i	0.0402981	+	0.0118326i
$506$	2.13753			0.0950246
$507$	0.920664			0.0408881
$508$	2.20738	+	0.648146i	0.0979368	+	0.0287568i
$509$	−2.45603	+	17.0821i	−0.108862	+	0.757150i	0.860133	+	0.510069i	$0.170380\pi$
$509$	−2.45603	+	17.0821i	−0.108862	+	0.757150i	−0.968995	+	0.247080i	$0.920529\pi$
$510$	4.95062	+	5.71331i	0.219217	+	0.252990i
$511$	−34.8382	+	10.2294i	−1.54115	+	0.452522i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	26.3703	+	16.9471i	1.16428	+	0.748235i
$514$	−5.67290	+	3.64575i	−0.250221	+	0.160807i
$515$	2.58099	−	17.9512i	0.113732	−	0.791023i
$516$	−1.82412	−	1.17229i	−0.0803026	−	0.0516074i
$517$	1.03142	−	2.25850i	0.0453620	−	0.0993289i
$518$	3.07500	−	3.54874i	0.135108	−	0.155923i
$519$	10.5179	+	12.1383i	0.461686	+	0.532814i
$520$	0.540703	+	3.76067i	0.0237114	+	0.164917i
$521$	−11.9266	+	26.1156i	−0.522514	+	1.14415i	0.445965	+	0.895050i	$0.352861\pi$
$521$	−11.9266	+	26.1156i	−0.522514	+	1.14415i	−0.968479	+	0.249096i	$0.919867\pi$
$522$	−11.2480	+	12.9809i	−0.492312	+	0.568158i
$523$	12.8371	−	3.76930i	0.561325	−	0.164820i	0.0112525	−	0.999937i	$-0.496418\pi$
$523$	12.8371	−	3.76930i	0.561325	−	0.164820i	0.550073	+	0.835117i	$0.314600\pi$
$524$	−18.4911	+	5.42948i	−0.807789	+	0.237188i
$525$	1.49282	+	10.3828i	0.0651521	+	0.453143i
$526$	16.5485	−	10.6351i	0.721550	−	0.463712i
$527$	2.63965	+	5.78002i	0.114985	+	0.251782i
$528$	0.652470	+	0.191582i	0.0283951	+	0.00833755i
$529$	−6.40707	−	14.0295i	−0.278568	−	0.609979i
$530$	1.49767	−	10.4166i	0.0650548	−	0.452466i
$531$	0.0224179	+	0.155920i	0.000972856	+	0.00676636i
$532$	14.1506	−	16.3307i	0.613508	−	0.708026i
$533$	−6.68032	−	4.29318i	−0.289357	−	0.185958i
$534$	−0.944669	−	2.06854i	−0.0408798	−	0.0895143i
$535$	5.65815			0.244623
$536$	−7.49920	−	3.28055i	−0.323916	−	0.141698i
$537$	−8.36264			−0.360874
$538$	−5.78837	−	12.6748i	−0.249554	−	0.546448i
$539$	1.94637	+	1.25086i	0.0838363	+	0.0538783i
$540$	−3.29846	+	3.80663i	−0.141943	+	0.163811i
$541$	−0.839485	−	5.83874i	−0.0360923	−	0.251027i	0.963785	−	0.266680i	$-0.0859266\pi$
$541$	−0.839485	−	5.83874i	−0.0360923	−	0.251027i	−0.999877	+	0.0156525i	$0.995017\pi$
$542$	3.54541	−	24.6589i	0.152289	−	1.05919i
$543$	1.90964	+	4.18154i	0.0819506	+	0.179447i
$544$	−7.53624	−	2.21284i	−0.323114	−	0.0948747i
$545$	9.43328	+	20.6560i	0.404077	+	0.884806i
$546$	−8.04426	+	5.16973i	−0.344262	+	0.221244i
$547$	4.48047	+	31.1624i	0.191571	+	1.33241i	0.827851	+	0.560948i	$0.189563\pi$
$547$	4.48047	+	31.1624i	0.191571	+	1.33241i	−0.636280	+	0.771458i	$0.719528\pi$
$548$	−14.0430	+	4.12340i	−0.599887	+	0.176143i
$549$	−7.67986	+	2.25501i	−0.327769	+	0.0962415i
$550$	−1.92831	+	2.22539i	−0.0822236	+	0.0948911i
$551$	21.8555	−	47.8569i	0.931075	−	2.03877i
$552$	0.343035	+	2.38586i	0.0146005	+	0.101549i
$553$	12.3513	+	14.2542i	0.525231	+	0.606149i
$554$	−13.0361	+	15.0445i	−0.553851	+	0.639178i
$555$	0.594325	−	1.30139i	0.0252277	−	0.0552410i
$556$	−15.0339	−	9.66170i	−0.637579	−	0.409747i
$557$	−0.768680	+	5.34629i	−0.0325700	+	0.226529i	−0.999605	−	0.0281153i	$-0.991049\pi$
$557$	−0.768680	+	5.34629i	−0.0325700	+	0.226529i	0.967035	+	0.254645i	$0.0819585\pi$
$558$	−1.51985	+	0.976748i	−0.0643404	+	0.0413491i
$559$	7.20056	+	4.62752i	0.304551	+	0.195723i
$560$	2.27379	+	2.62410i	0.0960853	+	0.110888i
$561$	−5.12475	+	1.50476i	−0.216367	+	0.0635312i
$562$	−6.54851	−	7.55739i	−0.276232	−	0.318789i
$563$	−1.48349	+	10.3179i	−0.0625216	+	0.434847i	0.934386	+	0.356263i	$0.115949\pi$
$563$	−1.48349	+	10.3179i	−0.0625216	+	0.434847i	−0.996907	+	0.0785847i	$0.974960\pi$
$564$	2.68642	+	0.788804i	0.113119	+	0.0332146i
$565$	3.94374			0.165915
$566$	22.3833			0.940842
$567$	8.14326	+	2.39108i	0.341985	+	0.100416i
$568$	7.55439	−	4.85491i	0.316975	−	0.203708i
$569$	−14.3076	+	31.3293i	−0.599806	+	1.31339i	0.329526	+	0.944147i	$0.393111\pi$
$569$	−14.3076	+	31.3293i	−0.599806	+	1.31339i	−0.929332	+	0.369246i	$0.879616\pi$
$570$	2.73498	−	5.98877i	0.114556	−	0.250842i
$571$	−19.7966	+	12.7225i	−0.828460	+	0.532419i	−0.884788	−	0.465993i	$-0.845697\pi$
$571$	−19.7966	+	12.7225i	−0.828460	+	0.532419i	0.0563279	+	0.998412i	$0.482061\pi$
$572$	−2.57556	−	0.756253i	−0.107690	−	0.0316205i
$573$	−17.9254			−0.748843
$574$	−7.25710			−0.302906
$575$	−10.0147	−	2.94060i	−0.417644	−	0.122631i
$576$	0.317814	−	2.21045i	0.0132423	−	0.0921019i
$577$	−15.7972	−	18.2310i	−0.657648	−	0.758966i	0.324743	−	0.945802i	$-0.394722\pi$
$577$	−15.7972	−	18.2310i	−0.657648	−	0.758966i	−0.982391	+	0.186836i	$0.940177\pi$
$578$	42.8812	−	12.5911i	1.78362	−	0.523719i
$579$	−2.11163	−	2.43696i	−0.0877565	−	0.101276i
$580$	7.11181	+	4.57049i	0.295302	+	0.189779i
$581$	−21.6588	+	13.9193i	−0.898560	+	0.577470i
$582$	−2.35506	+	16.3798i	−0.0976203	+	0.678964i
$583$	6.25483	+	4.01973i	0.259048	+	0.166480i
$584$	4.77467	−	10.4551i	0.197577	−	0.432634i
$585$	5.55624	−	6.41224i	0.229722	−	0.265114i
$586$	−0.106188	−	0.122547i	−0.00438657	−	0.00506238i
$587$	1.02722	+	7.14446i	0.0423978	+	0.294883i	0.999977	+	0.00671454i	$0.00213732\pi$
$587$	1.02722	+	7.14446i	0.0423978	+	0.294883i	−0.957580	+	0.288169i	$0.906954\pi$
$588$	−1.08382	+	2.37324i	−0.0446961	+	0.0978708i
$589$	3.62389	−	4.18219i	0.149320	−	0.172324i
$590$	0.0743899	−	0.0218429i	0.00306259	−	0.000899256i
$591$	−15.7759	+	4.63223i	−0.648935	+	0.190544i
$592$	0.211541	+	1.47130i	0.00869429	+	0.0604701i
$593$	−22.1824	+	14.2558i	−0.910924	+	0.585415i	−0.910011	−	0.414584i	$-0.863927\pi$
$593$	−22.1824	+	14.2558i	−0.910924	+	0.585415i	−0.000913040		1.00000i	$0.500291\pi$
$594$	−1.47831	−	3.23705i	−0.0606559	−	0.132818i
$595$	−26.1672	−	7.68337i	−1.07275	−	0.314988i
$596$	1.48444	+	3.25047i	0.0608051	+	0.133145i
$597$	1.17838	−	8.19580i	0.0482278	−	0.335432i
$598$	−1.35410	−	9.41795i	−0.0553731	−	0.385129i
$599$	7.40457	−	8.54533i	0.302543	−	0.349153i	−0.584039	−	0.811726i	$-0.698528\pi$
$599$	7.40457	−	8.54533i	0.302543	−	0.349153i	0.886581	+	0.462573i	$0.153074\pi$
$600$	−2.79340	−	1.79521i	−0.114040	−	0.0732890i
$601$	−13.5170	−	29.5982i	−0.551372	−	1.20734i	−0.956138	−	0.292916i	$-0.905375\pi$
$601$	−13.5170	−	29.5982i	−0.551372	−	1.20734i	0.404767	−	0.914420i	$-0.367353\pi$
$602$	7.82226			0.318812
$603$	5.43033	+	17.4541i	0.221140	+	0.710786i
$604$	1.51659			0.0617093
$605$	−4.74721	−	10.3949i	−0.193002	−	0.422615i
$606$	−0.632577	−	0.406533i	−0.0256967	−	0.0165143i
$607$	14.2407	−	16.4346i	0.578012	−	0.667062i	−0.389164	−	0.921169i	$-0.627236\pi$
$607$	14.2407	−	16.4346i	0.578012	−	0.667062i	0.967176	+	0.254107i	$0.0817814\pi$
$608$	0.973475	+	6.77067i	0.0394796	+	0.274587i
$609$	−3.02798	+	21.0601i	−0.122700	+	0.853398i
$610$	1.63652	+	3.58347i	0.0662606	+	0.145091i
$611$	−10.6044	−	3.11373i	−0.429007	−	0.125968i
$612$	7.28649	+	15.9552i	0.294539	+	0.644950i
$613$	29.9225	−	19.2301i	1.20856	−	0.776695i	0.228143	−	0.973628i	$-0.426735\pi$
$613$	29.9225	−	19.2301i	1.20856	−	0.776695i	0.980417	+	0.196933i	$0.0630982\pi$
$614$	−0.185392	−	1.28943i	−0.00748180	−	0.0520370i
$615$	−2.12154	+	0.622939i	−0.0855486	+	0.0251193i
$616$	−2.35377	+	0.691131i	−0.0948363	+	0.0278464i
$617$	−29.0091	+	33.4783i	−1.16786	+	1.34778i	−0.241838	+	0.970317i	$0.577750\pi$
$617$	−29.0091	+	33.4783i	−1.16786	+	1.34778i	−0.926023	+	0.377467i	$0.876795\pi$
$618$	−6.00227	+	13.1431i	−0.241447	+	0.528695i
$619$	1.77016	+	12.3118i	0.0711489	+	0.494851i	0.993973	+	0.109629i	$0.0349662\pi$
$619$	1.77016	+	12.3118i	0.0711489	+	0.494851i	−0.922824	+	0.385223i	$0.874125\pi$
$620$	0.582304	+	0.672014i	0.0233859	+	0.0269887i
$621$	8.26042	−	9.53304i	0.331479	−	0.382548i
$622$	−0.0111012	+	0.0243083i	−0.000445118	+	0.000974673i
$623$	6.90127	+	4.43518i	0.276493	+	0.177692i
$624$	0.430781	−	2.99615i	0.0172451	−	0.119942i
$625$	7.01447	−	4.50793i	0.280579	−	0.180317i
$626$	−11.8159	−	7.59359i	−0.472256	−	0.303501i
$627$	3.04609	+	3.51537i	0.121649	+	0.140390i
$628$	4.83969	−	1.42106i	0.193125	−	0.0567065i
$629$	−7.64551	−	8.82339i	−0.304846	−	0.351812i
$630$	1.10351	−	7.67506i	0.0439648	−	0.305782i
$631$	31.1931	+	9.15913i	1.24178	+	0.364619i	0.835684	−	0.549211i	$-0.185072\pi$
$631$	31.1931	+	9.15913i	1.24178	+	0.364619i	0.406096	+	0.913830i	$0.366890\pi$
$632$	−5.97052			−0.237494
$633$	0.111280			0.00442299
$634$	24.5273	+	7.20186i	0.974102	+	0.286022i
$635$	−2.12722	+	1.36708i	−0.0844162	+	0.0542510i
$636$	−3.48295	+	7.62660i	−0.138108	+	0.302414i
$637$	4.27829	−	9.36814i	0.169512	−	0.371179i
$638$	−5.02460	+	3.22911i	−0.198926	+	0.127842i
$639$	−19.2414	−	5.64979i	−0.761179	−	0.223502i
$640$	−1.09913			−0.0434470
$641$	10.1143			0.399489			0.199745	−	0.979848i	$-0.435989\pi$
$641$	10.1143			0.399489			0.199745	+	0.979848i	$0.435989\pi$
$642$	−4.32528	−	1.27002i	−0.170705	−	0.0501235i
$643$	5.05937	−	35.1887i	0.199522	−	1.38771i	−0.606152	−	0.795349i	$-0.707288\pi$
$643$	5.05937	−	35.1887i	0.199522	−	1.38771i	0.805674	−	0.592359i	$-0.201803\pi$
$644$	−5.69432	−	6.57159i	−0.224387	−	0.258957i
$645$	2.28675	−	0.671451i	0.0900408	−	0.0264384i
$646$	−35.1833	−	40.6037i	−1.38427	−	1.59753i
$647$	−34.3233	−	22.0583i	−1.34939	−	0.867200i	−0.351765	−	0.936088i	$-0.614418\pi$
$647$	−34.3233	−	22.0583i	−1.34939	−	0.867200i	−0.997624	+	0.0688883i	$0.978055\pi$
$648$	−2.26012	+	1.45249i	−0.0887859	+	0.0570592i
$649$	−0.00779549	+	0.0542189i	−0.000306000	+	0.00212828i
$650$	11.0267	+	7.08640i	0.432501	+	0.277952i
$651$	−0.929679	+	2.03571i	−0.0364370	+	0.0797858i
$652$	12.1908	−	14.0689i	0.477429	−	0.550982i
$653$	8.77874	+	10.1312i	0.343538	+	0.396465i	0.901058	−	0.433700i	$-0.142792\pi$
$653$	8.77874	+	10.1312i	0.343538	+	0.396465i	−0.557519	+	0.830164i	$0.688247\pi$
$654$	−2.57471	−	17.9075i	−0.100679	−	0.700239i
$655$	8.79941	−	19.2680i	0.343821	−	0.752864i
$656$	1.50439	−	1.73616i	0.0587365	−	0.0677855i
$657$	−24.6278	+	7.23138i	−0.960823	+	0.282123i
$658$	−9.69122	+	2.84560i	−0.377803	+	0.110933i
$659$	−2.90238	−	20.1865i	−0.113061	−	0.786355i	−0.964912	−	0.262572i	$-0.915429\pi$
$659$	−2.90238	−	20.1865i	−0.113061	−	0.786355i	0.851852	−	0.523783i	$-0.175480\pi$
$660$	−0.628775	+	0.404089i	−0.0244750	+	0.0157291i
$661$	16.0103	+	35.0577i	0.622729	+	1.36359i	0.913518	+	0.406798i	$0.133355\pi$
$661$	16.0103	+	35.0577i	0.622729	+	1.36359i	−0.290789	+	0.956787i	$0.593918\pi$
$662$	−17.5130	−	5.14229i	−0.680663	−	0.199861i
$663$	9.87647	+	21.6265i	0.383570	+	0.839902i
$664$	1.15986	−	8.06702i	0.0450114	−	0.313061i
$665$	3.38008	+	23.5090i	0.131074	+	0.911639i
$666$	2.17379	−	2.50868i	0.0842325	−	0.0972095i
$667$	−17.8103	−	11.4460i	−0.689617	−	0.443190i
$668$	−7.17623	−	15.7138i	−0.277657	−	0.607984i
$669$	15.6555			0.605277
$670$	8.12281	−	3.86808i	0.313811	−	0.149437i
$671$	−2.78330			−0.107448
$672$	−1.14916	−	2.51632i	−0.0443300	−	0.0970691i
$673$	−41.7998	−	26.8631i	−1.61126	−	1.03550i	−0.961289	−	0.275541i	$-0.911143\pi$
$673$	−41.7998	−	26.8631i	−1.61126	−	1.03550i	−0.649975	−	0.759955i	$-0.725221\pi$
$674$	−1.45354	+	1.67748i	−0.0559883	+	0.0646139i
$675$	2.47298	+	17.2000i	0.0951852	+	0.662027i
$676$	0.149625	−	1.04066i	0.00575480	−	0.0400255i
$677$	12.9029	+	28.2535i	0.495900	+	1.08587i	0.977780	+	0.209633i	$0.0672268\pi$
$677$	12.9029	+	28.2535i	0.495900	+	1.08587i	−0.481880	+	0.876237i	$0.660046\pi$
$678$	−3.01473	−	0.885204i	−0.115780	−	0.0339961i
$679$	−24.7992	−	54.3028i	−0.951707	−	2.08395i
$680$	7.26256	−	4.66736i	0.278506	−	0.178985i
$681$	−2.58477	−	17.9774i	−0.0990485	−	0.688897i
$682$	−0.602786	+	0.176994i	−0.0230819	+	0.00677745i
$683$	−24.3645	+	7.15406i	−0.932281	+	0.273743i	−0.712392	−	0.701782i	$-0.752388\pi$
$683$	−24.3645	+	7.15406i	−0.932281	+	0.273743i	−0.219890	+	0.975525i	$0.570570\pi$
$684$	10.0034	−	11.5445i	0.382489	−	0.441416i
$685$	6.68267	−	14.6330i	0.255332	−	0.559099i
$686$	1.80756	+	12.5719i	0.0690131	+	0.479996i
$687$	−8.95486	−	10.3345i	−0.341649	−	0.394284i
$688$	−1.62154	+	1.87136i	−0.0618208	+	0.0713450i
$689$	13.7486	−	30.1053i	0.523780	−	1.14692i
$690$	−2.22877	−	1.43234i	−0.0848477	−	0.0545283i
$691$	−6.89004	+	47.9213i	−0.262110	+	1.82301i	0.254826	+	0.966987i	$0.417982\pi$
$691$	−6.89004	+	47.9213i	−0.262110	+	1.82301i	−0.516935	+	0.856025i	$0.672927\pi$
$692$	15.4298	−	9.91614i	0.586554	−	0.376955i
$693$	4.60864	+	2.96179i	0.175068	+	0.112509i
$694$	5.26092	+	6.07143i	0.199702	+	0.230468i
$695$	18.8467	−	5.53390i	0.714898	−	0.209913i
$696$	−4.41063	−	5.09013i	−0.167184	−	0.192941i
$697$	−2.56788	+	17.8600i	−0.0972652	+	0.676495i
$698$	−2.72569	−	0.800335i	−0.103169	−	0.0302931i
$699$	12.7598			0.482619
$700$	11.9787			0.452753
$701$	−22.4902	−	6.60371i	−0.849443	−	0.249419i	−0.172094	−	0.985081i	$-0.555053\pi$
$701$	−22.4902	−	6.60371i	−0.849443	−	0.249419i	−0.677349	+	0.735662i	$0.736871\pi$
$702$	−13.3260	+	8.56409i	−0.502957	+	0.323231i
$703$	−4.22378	+	9.24880i	−0.159303	+	0.348825i
$704$	0.322592	−	0.706377i	0.0121581	−	0.0266226i
$705$	−2.58886	+	1.66376i	−0.0975021	+	0.0626608i
$706$	−32.0560	−	9.41248i	−1.20644	−	0.354243i
$707$	2.71263			0.102019
$708$	−0.0617690			−0.00232142
$709$	22.5243	+	6.61374i	0.845919	+	0.248384i	0.675842	−	0.737047i	$-0.263780\pi$
$709$	22.5243	+	6.61374i	0.845919	+	0.248384i	0.170077	+	0.985431i	$0.445598\pi$
$710$	−1.40466	+	9.76965i	−0.0527161	+	0.366649i
$711$	8.73140	+	10.0766i	0.327453	+	0.377901i
$712$	−2.49168	+	0.731622i	−0.0933795	+	0.0274187i
$713$	−1.45828	−	1.68294i	−0.0546129	−	0.0630267i
$714$	18.2785	+	11.7469i	0.684054	+	0.439615i
$715$	2.48203	−	1.59510i	0.0928226	−	0.0596535i
$716$	−1.35908	+	9.45263i	−0.0507913	+	0.353261i
$717$	21.6454	+	13.9106i	0.808361	+	0.519502i
$718$	−11.1727	+	24.4648i	−0.416961	+	0.913017i
$719$	8.11880	−	9.36960i	0.302780	−	0.349427i	−0.583887	−	0.811835i	$-0.698469\pi$
$719$	8.11880	−	9.36960i	0.302780	−	0.349427i	0.886667	+	0.462408i	$0.153014\pi$
$720$	1.60739	+	1.85503i	0.0599040	+	0.0691329i
$721$	−7.41802	−	51.5935i	−0.276262	−	1.92144i
$722$	−11.5442	+	25.2783i	−0.429632	+	0.940762i
$723$	3.95946	−	4.56946i	0.147254	−	0.169940i
$724$	5.03691	−	1.47897i	0.187195	−	0.0549655i
$725$	27.9836	−	8.21672i	1.03928	−	0.305161i
$726$	1.29570	+	9.01179i	0.0480879	+	0.334459i
$727$	33.5556	−	21.5649i	1.24451	−	0.799796i	0.258421	−	0.966032i	$-0.416798\pi$
$727$	33.5556	−	21.5649i	1.24451	−	0.799796i	0.986086	+	0.166236i	$0.0531615\pi$
$728$	4.53621	+	9.93292i	0.168123	+	0.368139i
$729$	−5.79447	−	1.70141i	−0.214610	−	0.0630151i
$730$	5.24799	+	11.4915i	0.194237	+	0.425319i
$731$	2.76785	−	19.2508i	0.102373	−	0.712018i
$732$	−0.446670	−	3.10666i	−0.0165094	−	0.114825i
$733$	−27.1954	+	31.3852i	−1.00448	+	1.15924i	−0.0172685	+	0.999851i	$0.505497\pi$
$733$	−27.1954	+	31.3852i	−1.00448	+	1.15924i	−0.987216	+	0.159386i	$0.949048\pi$
$734$	−10.8854	−	6.99560i	−0.401786	−	0.258212i
$735$	−1.19126	−	2.60851i	−0.0439405	−	0.0962162i
$736$	2.75258			0.101462
$737$	0.101876	+	6.35554i	0.00375264	+	0.234109i
$738$	−5.13020			−0.188845
$739$	−17.8307	−	39.0438i	−0.655913	−	1.43625i	−0.886282	−	0.463146i	$-0.846721\pi$
$739$	−17.8307	−	39.0438i	−0.655913	−	1.43625i	0.230369	−	0.973103i	$-0.426007\pi$
$740$	−1.37443	−	0.883290i	−0.0505249	−	0.0324704i
$741$	13.5591	−	15.6480i	0.498106	−	0.574844i
$742$	−4.30447	−	29.9383i	−0.158022	−	1.09907i
$743$	0.979161	−	6.81021i	0.0359219	−	0.249843i	−0.963946	−	0.266098i	$-0.914265\pi$
$743$	0.979161	−	6.81021i	0.0359219	−	0.249843i	0.999868	+	0.0162556i	$0.00517456\pi$
$744$	−0.294293	−	0.644413i	−0.0107893	−	0.0236253i
$745$	−3.76853	−	1.10654i	−0.138068	−	0.0405405i
$746$	−3.29798	−	7.22156i	−0.120747	−	0.264400i
$747$	−15.3111	+	9.83984i	−0.560204	+	0.360021i
$748$	0.868028	+	6.03727i	0.0317383	+	0.220744i
$749$	15.6034	−	4.58156i	0.570135	−	0.167407i
$750$	8.11937	−	2.38406i	0.296478	−	0.0870537i
$751$	−25.9280	+	29.9225i	−0.946126	+	1.09189i	0.0495299	+	0.998773i	$0.484228\pi$
$751$	−25.9280	+	29.9225i	−0.946126	+	1.09189i	−0.995655	+	0.0931144i	$0.970318\pi$
$752$	1.32821	−	2.90837i	0.0484348	−	0.106057i
$753$	−1.85179	−	12.8795i	−0.0674831	−	0.469355i
$754$	17.4105	+	20.0928i	0.634054	+	0.731737i
$755$	−1.09161	+	1.25979i	−0.0397278	+	0.0458483i
$756$	−6.01378	+	13.1683i	−0.218719	+	0.478928i
$757$	−18.8304	−	12.1015i	−0.684401	−	0.439838i	0.151690	−	0.988428i	$-0.451528\pi$
$757$	−18.8304	−	12.1015i	−0.684401	−	0.439838i	−0.836091	+	0.548590i	$0.815165\pi$
$758$	−1.33117	+	9.25850i	−0.0483503	+	0.336284i
$759$	1.57466	−	1.01197i	0.0571564	−	0.0367322i
$760$	−6.32487	−	4.06475i	−0.229427	−	0.147444i
$761$	−11.2539	−	12.9877i	−0.407955	−	0.470805i	0.514175	−	0.857685i	$-0.328098\pi$
$761$	−11.2539	−	12.9877i	−0.407955	−	0.470805i	−0.922130	+	0.386880i	$0.873553\pi$
$762$	1.93297	−	0.567572i	0.0700242	−	0.0205609i
$763$	42.7397	+	49.3243i	1.54728	+	1.78566i
$764$	−2.91320	+	20.2618i	−0.105396	+	0.733045i
$765$	−18.4981	−	5.43154i	−0.668801	−	0.196378i
$766$	13.5530			0.489691
$767$	0.243827			0.00880408
$768$	0.840213	+	0.246709i	0.0303186	+	0.00890234i
$769$	7.92869	−	5.09546i	0.285916	−	0.183747i	−0.389819	−	0.920891i	$-0.627463\pi$
$769$	7.92869	−	5.09546i	0.285916	−	0.183747i	0.675735	+	0.737144i	$0.263826\pi$
$770$	1.12010	−	2.45267i	0.0403654	−	0.0883880i
$771$	−2.45306	+	5.37145i	−0.0883447	+	0.193448i
$772$	−3.09777	+	1.99082i	−0.111491	+	0.0716510i
$773$	45.0566	+	13.2298i	1.62057	+	0.475843i	0.961172	−	0.275948i	$-0.0889919\pi$
$773$	45.0566	+	13.2298i	1.62057	+	0.475843i	0.659401	+	0.751792i	$0.270810\pi$
$774$	5.52972			0.198762
$775$	3.06767			0.110194
$776$	18.1320	+	5.32404i	0.650901	+	0.191122i
$777$	0.585187	−	4.07006i	0.0209935	−	0.146013i
$778$	4.48722	+	5.17853i	0.160875	+	0.185659i
$779$	15.0774	−	4.42714i	0.540205	−	0.158619i
$780$	2.17874	+	2.51440i	0.0780114	+	0.0900300i
$781$	−5.86638	−	3.77009i	−0.209916	−	0.134905i
$782$	−18.1878	+	11.6886i	−0.650394	+	0.417983i
$783$	−5.01611	+	34.8878i	−0.179261	+	1.24679i
$784$	2.50643	+	1.61078i	0.0895153	+	0.0575280i
$785$	−2.30307	+	5.04302i	−0.0822002	+	0.179993i
$786$	−11.0514	+	12.7540i	−0.394191	+	0.454921i
$787$	12.3180	+	14.2157i	0.439088	+	0.506734i	0.931557	−	0.363596i	$-0.118451\pi$
$787$	12.3180	+	14.2157i	0.439088	+	0.506734i	−0.492469	+	0.870330i	$0.663906\pi$
$788$	2.67212	+	18.5850i	0.0951902	+	0.662062i
$789$	7.15586	−	15.6692i	0.254755	−	0.557837i
$790$	4.29745	−	4.95952i	0.152896	−	0.176452i
$791$	10.8756	−	3.19336i	0.386691	−	0.113543i
$792$	−1.66393	+	0.488575i	−0.0591253	+	0.0173607i
$793$	1.76319	+	12.2632i	0.0626125	+	0.435480i
$794$	0.625206	−	0.401795i	0.0221877	−	0.0142592i
$795$	−3.82822	−	8.38264i	−0.135773	−	0.297301i
$796$	−9.07254	−	2.66394i	−0.321568	−	0.0944208i
$797$	−7.70464	−	16.8708i	−0.272913	−	0.597595i	0.722701	−	0.691161i	$-0.242901\pi$
$797$	−7.70464	−	16.8708i	−0.272913	−	0.597595i	−0.995613	+	0.0935662i	$0.970173\pi$
$798$	2.69293	−	18.7297i	0.0953286	−	0.663025i
$799$	3.57394	+	24.8573i	0.126437	+	0.879388i
$800$	−2.48317	+	2.86573i	−0.0877934	+	0.101319i
$801$	4.87865	+	3.13532i	0.172379	+	0.110781i
$802$	4.23855	+	9.28113i	0.149668	+	0.327728i
$803$	−8.92549			−0.314974
$804$	−7.07757	+	1.13366i	−0.249607	+	0.0399812i
$805$	9.55746			0.336856
$806$	1.16170	+	2.54376i	0.0409190	+	0.0896000i
$807$	−10.2648	−	6.59675i	−0.361336	−	0.232217i
$808$	−0.562326	+	0.648959i	−0.0197826	+	0.0228303i
$809$	3.26533	+	22.7109i	0.114803	+	0.798472i	0.963137	+	0.269011i	$0.0866967\pi$
$809$	3.26533	+	22.7109i	0.114803	+	0.798472i	−0.848334	+	0.529461i	$0.822394\pi$
$810$	0.420247	−	2.92288i	0.0147660	−	0.102700i
$811$	−15.4963	−	33.9321i	−0.544147	−	1.19152i	−0.959462	−	0.281838i	$-0.909056\pi$
$811$	−15.4963	−	33.9321i	−0.544147	−	1.19152i	0.415315	−	0.909678i	$-0.363671\pi$
$812$	23.3130	+	6.84531i	0.818125	+	0.240223i
$813$	−9.06247	−	19.8440i	−0.317835	−	0.695961i
$814$	0.971052	−	0.624057i	0.0340354	−	0.0218732i
$815$	2.91195	+	20.2530i	0.102001	+	0.709433i
$816$	−6.59937	+	1.93775i	−0.231024	+	0.0678348i
$817$	−16.2516	+	4.77191i	−0.568572	+	0.166948i
$818$	−10.2931	+	11.8788i	−0.359888	+	0.415333i
$819$	10.1302	−	22.1820i	0.353977	−	0.775101i
$820$	0.359345	+	2.49930i	0.0125489	+	0.0872792i
$821$	5.73472	+	6.61822i	0.200143	+	0.230978i	0.846945	−	0.531681i	$-0.178439\pi$
$821$	5.73472	+	6.61822i	0.200143	+	0.230978i	−0.646802	+	0.762658i	$0.723894\pi$
$822$	−8.39295	+	9.68598i	−0.292738	+	0.337837i
$823$	−16.1934	+	35.4586i	−0.564466	+	1.23601i	0.385225	+	0.922823i	$0.374124\pi$
$823$	−16.1934	+	35.4586i	−0.564466	+	1.23601i	−0.949692	+	0.313186i	$0.898604\pi$
$824$	13.8807	+	8.92061i	0.483559	+	0.310764i
$825$	−0.366967	+	2.55231i	−0.0127761	+	0.0888600i
$826$	0.187457	−	0.120471i	0.00652246	−	0.00419173i
$827$	−22.9892	−	14.7742i	−0.799412	−	0.513751i	0.0760118	−	0.997107i	$-0.475781\pi$
$827$	−22.9892	−	14.7742i	−0.799412	−	0.513751i	−0.875424	+	0.483356i	$0.839418\pi$
$828$	−4.02543	−	4.64560i	−0.139893	−	0.161446i
$829$	29.4551	−	8.64881i	1.02302	−	0.300385i	0.273150	−	0.961972i	$-0.411935\pi$
$829$	29.4551	−	8.64881i	1.02302	−	0.300385i	0.749869	+	0.661586i	$0.230116\pi$
$830$	5.86617	+	6.76993i	0.203618	+	0.234988i
$831$	−2.48083	+	17.2545i	−0.0860590	+	0.598553i
$832$	−3.31666	−	0.973859i	−0.114984	−	0.0337625i
$833$	−23.4014			−0.810810
$834$	−15.6492			−0.541888
$835$	18.2182	+	5.34935i	0.630468	+	0.185122i
$836$	4.46861	−	2.87180i	0.154550	−	0.0993233i
$837$	−1.54009	+	3.37233i	−0.0532333	+	0.116565i
$838$	−9.53811	+	20.8855i	−0.329488	+	0.721479i
$839$	7.71145	−	4.95584i	0.266229	−	0.171095i	−0.400715	−	0.916203i	$-0.631238\pi$
$839$	7.71145	−	4.95584i	0.266229	−	0.171095i	0.666944	+	0.745108i	$0.267602\pi$
$840$	2.91737	+	0.856617i	0.100659	+	0.0295561i
$841$	30.1572			1.03990
$842$	−26.1208			−0.900181
$843$	−8.40201	−	2.46705i	−0.289381	−	0.0849698i
$844$	0.0180851	−	0.125784i	0.000622514	−	0.00432968i
$845$	0.756750	+	0.873336i	0.0260330	+	0.0300437i
$846$	−6.85092	+	2.01161i	−0.235540	+	0.0691607i
$847$	−21.5084	−	24.8220i	−0.739037	−	0.852894i
$848$	8.05461	+	5.17638i	0.276596	+	0.177758i
$849$	16.4892	−	10.5970i	0.565907	−	0.363687i
$850$	4.23859	−	29.4800i	0.145382	−	1.01116i
$851$	3.44201	+	2.21204i	0.117991	+	0.0758279i
$852$	3.26665	−	7.15296i	0.111913	−	0.245056i
$853$	3.46810	−	4.00240i	0.118745	−	0.137040i	−0.693264	−	0.720683i	$-0.743828\pi$
$853$	3.46810	−	4.00240i	0.118745	−	0.137040i	0.812010	+	0.583644i	$0.198374\pi$
$854$	7.41463	+	8.55694i	0.253724	+	0.292813i
$855$	2.38945	+	16.6190i	0.0817174	+	0.568357i
$856$	−2.13849	+	4.68264i	−0.0730920	+	0.160049i
$857$	15.3801	−	17.7496i	0.525375	−	0.606315i	−0.429593	−	0.903023i	$-0.641343\pi$
$857$	15.3801	−	17.7496i	0.525375	−	0.606315i	0.954969	+	0.296707i	$0.0958885\pi$
$858$	−2.25538	+	0.662239i	−0.0769974	+	0.0226085i
$859$	−4.34985	+	1.27723i	−0.148415	+	0.0435786i	−0.355096	−	0.934830i	$-0.615552\pi$
$859$	−4.34985	+	1.27723i	−0.148415	+	0.0435786i	0.206681	+	0.978408i	$0.433734\pi$
$860$	−0.387329	−	2.69393i	−0.0132078	−	0.0918623i
$861$	−5.34611	+	3.43574i	−0.182195	+	0.117090i
$862$	5.55872	+	12.1719i	0.189331	+	0.414576i
$863$	48.2748	+	14.1748i	1.64329	+	0.482515i	0.967140	−	0.254245i	$-0.0818268\pi$
$863$	48.2748	+	14.1748i	1.64329	+	0.482515i	0.676155	+	0.736759i	$0.263645\pi$
$864$	−1.90369	−	4.16849i	−0.0647647	−	0.141815i
$865$	−2.86902	+	19.9545i	−0.0975497	+	0.678473i
$866$	−2.27121	−	15.7966i	−0.0771789	−	0.536791i
$867$	25.6284	−	29.5768i	0.870387	−	1.00448i
$868$	2.14996	+	1.38169i	0.0729743	+	0.0468977i
$869$	1.92604	+	4.21744i	0.0653364	+	0.143067i
$870$	7.40289			0.250981
$871$	27.9380	−	4.47502i	0.946644	−	0.151630i
$872$	−20.6600			−0.699637
$873$	−17.5311	−	38.3878i	−0.593338	−	1.29923i
$874$	15.8395	+	10.1794i	0.535780	+	0.344325i
$875$	−19.9910	+	23.0708i	−0.675819	+	0.779936i
$876$	−1.43238	−	9.96244i	−0.0483957	−	0.336600i
$877$	−1.00611	+	6.99762i	−0.0339738	+	0.236293i	−0.999732	−	0.0231510i	$-0.992630\pi$
$877$	−1.00611	+	6.99762i	−0.0339738	+	0.236293i	0.965758	+	0.259444i	$0.0835393\pi$
$878$	6.44548	+	14.1136i	0.217524	+	0.476312i
$879$	−0.136243	−	0.0400046i	−0.00459537	−	0.00134932i
$880$	0.354571	+	0.776402i	0.0119526	+	0.0261725i
$881$	−29.9951	+	19.2767i	−1.01056	+	0.649447i	−0.937538	−	0.347883i	$-0.886901\pi$
$881$	−29.9951	+	19.2767i	−1.01056	+	0.649447i	−0.0730220	+	0.997330i	$0.523264\pi$
$882$	−0.946895	−	6.58580i	−0.0318836	−	0.221755i
$883$	55.8120	−	16.3879i	1.87822	−	0.551496i	0.881353	−	0.472459i	$-0.156633\pi$
$883$	55.8120	−	16.3879i	1.87822	−	0.551496i	0.996872	−	0.0790378i	$-0.0251848\pi$
$884$	26.0504	−	7.64908i	0.876168	−	0.257266i
$885$	0.0444600	−	0.0513095i	0.00149450	−	0.00172475i
$886$	−5.16768	+	11.3156i	−0.173612	+	0.380157i
$887$	5.23556	+	36.4141i	0.175793	+	1.22267i	0.866368	+	0.499405i	$0.166448\pi$
$887$	5.23556	+	36.4141i	0.175793	+	1.22267i	−0.690576	+	0.723260i	$0.742643\pi$
$888$	0.852396	+	0.983717i	0.0286045	+	0.0330114i
$889$	−4.75923	+	5.49245i	−0.159620	+	0.184211i
$890$	1.18572	−	2.59636i	0.0397454	−	0.0870303i
$891$	1.75510	+	1.12794i	0.0587981	+	0.0377872i
$892$	2.54431	−	17.6961i	0.0851898	−	0.592508i
$893$	18.3987	−	11.8241i	0.615687	−	0.395678i
$894$	2.63242	+	1.69175i	0.0880413	+	0.0565807i
$895$	−6.87376	−	7.93274i	−0.229764	−	0.265162i
$896$	−3.03106	+	0.889998i	−0.101260	+	0.0297328i
$897$	−5.45627	−	6.29688i	−0.182180	−	0.210247i
$898$	3.88903	−	27.0488i	0.129779	−	0.902630i
$899$	5.97030	+	1.75304i	0.199121	+	0.0584671i
$900$	8.46800			0.282267
$901$	−75.2021			−2.50535
$902$	−1.71168	−	0.502596i	−0.0569929	−	0.0167346i
$903$	5.76244	−	3.70330i	0.191762	−	0.123238i
$904$	−1.49053	+	3.26381i	−0.0495743	+	0.108553i
$905$	−2.39692	+	5.24853i	−0.0796765	+	0.174467i
$906$	1.11723	−	0.718001i	0.0371175	−	0.0238540i
$907$	7.44080	+	2.18482i	0.247068	+	0.0725457i	0.402922	−	0.915234i	$-0.367995\pi$
$907$	7.44080	+	2.18482i	0.247068	+	0.0725457i	−0.155854	+	0.987780i	$0.549813\pi$
$908$	−20.7407			−0.688304
$909$	1.91762			0.0636034
$910$	−11.5160	−	3.38141i	−0.381753	−	0.112093i
$911$	−1.61761	+	11.2507i	−0.0535939	+	0.372754i	0.945319	+	0.326146i	$0.105750\pi$
$911$	−1.61761	+	11.2507i	−0.0535939	+	0.372754i	−0.998913	+	0.0466076i	$0.985159\pi$
$912$	3.92258	+	4.52689i	0.129889	+	0.149900i
$913$	−6.07252	+	1.78305i	−0.200971	+	0.0590104i
$914$	−13.5563	−	15.6448i	−0.448402	−	0.517483i
$915$	2.90210	+	1.86507i	0.0959406	+	0.0616573i
$916$	−13.1368	+	8.44250i	−0.434052	+	0.278948i
$917$	8.66411	−	60.2602i	0.286114	−	1.98997i
$918$	30.2798	+	19.4596i	0.999382	+	0.642264i
$919$	−24.6015	+	53.8698i	−0.811529	+	1.77700i	−0.210833	+	0.977522i	$0.567618\pi$
$919$	−24.6015	+	53.8698i	−0.811529	+	1.77700i	−0.600695	+	0.799478i	$0.705109\pi$
$920$	−1.98125	+	2.28648i	−0.0653199	+	0.0753831i
$921$	−0.747027	−	0.862115i	−0.0246154	−	0.0284077i
$922$	−1.25302	−	8.71498i	−0.0412662	−	0.287013i
$923$	−12.8948	+	28.2356i	−0.424437	+	0.929387i
$924$	−1.40676	+	1.62349i	−0.0462790	+	0.0534088i
$925$	−5.40810	+	1.58796i	−0.177817	+	0.0522118i
$926$	9.65749	−	2.83569i	0.317365	−	0.0931867i
$927$	−5.24396	−	36.4725i	−0.172234	−	1.19792i
$928$	−6.47039	+	4.15827i	−0.212401	+	0.136502i
$929$	−4.81583	−	10.5452i	−0.158002	−	0.345977i	0.814030	−	0.580822i	$-0.197269\pi$
$929$	−4.81583	−	10.5452i	−0.158002	−	0.345977i	−0.972033	+	0.234845i	$0.924542\pi$
$930$	0.747119	+	0.219374i	0.0244990	+	0.00719356i
$931$	8.46614	+	18.5383i	0.277467	+	0.607567i
$932$	2.07370	−	14.4229i	0.0679262	−	0.472437i
$933$	0.00333032	+	0.0231629i	0.000109030	+	0.000758319i
$934$	−14.3965	+	16.6144i	−0.471066	+	0.543640i
$935$	−5.63976	−	3.62445i	−0.184440	−	0.118532i
$936$	3.20675	+	7.02179i	0.104816	+	0.229514i
$937$	−5.59781			−0.182873			−0.0914363	−	0.995811i	$-0.529146\pi$
$937$	−5.59781			−0.182873			−0.0914363	+	0.995811i	$0.529146\pi$
$938$	19.2680	−	17.2442i	0.629123	−	0.563043i
$939$	−12.2995			−0.401377
$940$	1.45988	+	3.19668i	0.0476159	+	0.104264i
$941$	−6.13984	−	3.94584i	−0.200153	−	0.128631i	0.436725	−	0.899595i	$-0.356138\pi$
$941$	−6.13984	−	3.94584i	−0.200153	−	0.128631i	−0.636878	+	0.770964i	$0.719775\pi$
$942$	2.89249	−	3.33811i	0.0942425	−	0.108762i
$943$	−0.899915	−	6.25905i	−0.0293053	−	0.203823i
$944$	−0.0100386	+	0.0698199i	−0.000326728	+	0.00227245i
$945$	−6.60994	−	14.4737i	−0.215021	−	0.470831i
$946$	1.84498	+	0.541736i	0.0599856	+	0.0176134i
$947$	7.00255	+	15.3335i	0.227552	+	0.498270i	0.988626	−	0.150395i	$-0.0480546\pi$
$947$	7.00255	+	15.3335i	0.227552	+	0.498270i	−0.761074	+	0.648666i	$0.775327\pi$
$948$	−4.39832	+	2.82663i	−0.142851	+	0.0918046i
$949$	5.65419	+	39.3258i	0.183543	+	1.27657i
$950$	−24.8871	+	7.30752i	−0.807445	+	0.237087i
$951$	21.4782	−	6.30655i	0.696477	−	0.204504i
$952$	16.2485	−	18.7518i	0.526618	−	0.607749i
$953$	−8.49101	+	18.5927i	−0.275051	+	0.602277i	−0.995864	−	0.0908518i	$-0.971041\pi$
$953$	−8.49101	+	18.5927i	−0.275051	+	0.602277i	0.720814	+	0.693129i	$0.243768\pi$
$954$	−3.04292	−	21.1640i	−0.0985182	−	0.685209i
$955$	−14.7339	−	17.0039i	−0.476779	−	0.550233i
$956$	19.2415	−	22.2059i	0.622315	−	0.718190i
$957$	−2.17272	+	4.75760i	−0.0702342	+	0.153791i
$958$	26.3247	+	16.9179i	0.850513	+	0.546592i
$959$	6.57992	−	45.7643i	0.212477	−	1.47781i
$960$	−0.809700	+	0.520363i	−0.0261330	+	0.0167946i
$961$	−25.5283	−	16.4060i	−0.823493	−	0.529227i
$962$	−3.36475	−	3.88313i	−0.108484	−	0.125197i
$963$	11.0304	−	3.23880i	0.355448	−	0.104369i
$964$	−4.52156	−	5.21815i	−0.145630	−	0.168065i
$965$	0.576000	−	4.00617i	0.0185421	−	0.128963i
$966$	−7.30604	−	2.14525i	−0.235068	−	0.0690222i
$967$	−14.3613			−0.461829			−0.230915	−	0.972974i	$-0.574172\pi$
$967$	−14.3613			−0.461829			−0.230915	+	0.972974i	$0.574172\pi$
$968$	10.3970			0.334171
$969$	−45.1416	−	13.2548i	−1.45016	−	0.425805i
$970$	−17.4735	+	11.2296i	−0.561041	+	0.360559i
$971$	5.08450	−	11.1335i	0.163169	−	0.357291i	−0.810332	−	0.585970i	$-0.800713\pi$
$971$	5.08450	−	11.1335i	0.163169	−	0.357291i	0.973502	+	0.228679i	$0.0734407\pi$
$972$	−6.68837	+	14.6455i	−0.214530	+	0.469754i
$973$	47.4924	−	30.5215i	1.52254	−	0.978474i
$974$	−38.7654	−	11.3826i	−1.24212	−	0.364721i
$975$	11.4780			0.367589
$976$	−3.58417			−0.114726
$977$	39.1318	+	11.4901i	1.25194	+	0.367602i	0.839487	−	0.543379i	$-0.182855\pi$
$977$	39.1318	+	11.4901i	1.25194	+	0.367602i	0.412449	+	0.910981i	$0.364674\pi$
$978$	2.31996	−	16.1357i	0.0741843	−	0.515963i
$979$	1.32059	+	1.52405i	0.0422064	+	0.0487088i
$980$	−3.14210	+	0.922604i	−0.100371	+	0.0294715i
$981$	30.2136	+	34.8684i	0.964647	+	1.11326i
$982$	22.6924	+	14.5835i	0.724144	+	0.465379i
$983$	−5.71026	+	3.66976i	−0.182129	+	0.117047i	−0.628528	−	0.777787i	$-0.716342\pi$
$983$	−5.71026	+	3.66976i	−0.182129	+	0.117047i	0.446399	+	0.894834i	$0.352706\pi$
$984$	0.286292	−	1.99120i	0.00912665	−	0.0634772i
$985$	−17.3613	−	11.1574i	−0.553177	−	0.355505i
$986$	25.0957	−	54.9518i	0.799209	−	1.75002i
$987$	−5.79206	+	6.68439i	−0.184363	+	0.212767i
$988$	−15.4840	−	17.8695i	−0.492611	−	0.568504i
$989$	0.969998	+	6.74648i	0.0308441	+	0.214526i
$990$	0.791819	−	1.73384i	0.0251657	−	0.0551051i
$991$	−12.6826	+	14.6365i	−0.402877	+	0.464945i	−0.920545	−	0.390637i	$-0.872255\pi$
$991$	−12.6826	+	14.6365i	−0.402877	+	0.464945i	0.517668	+	0.855582i	$0.326800\pi$
$992$	−0.776234	+	0.227923i	−0.0246455	+	0.00723656i
$993$	−15.3359	+	4.50302i	−0.486670	+	0.142899i
$994$	4.03715	+	28.0790i	0.128051	+	0.890611i
$995$	8.74307	−	5.61883i	0.277174	−	0.178129i
$996$	−2.96474	−	6.49187i	−0.0939412	−	0.205703i
$997$	−25.2938	−	7.42692i	−0.801062	−	0.235213i	−0.144519	−	0.989502i	$-0.546164\pi$
$997$	−25.2938	−	7.42692i	−0.801062	−	0.235213i	−0.656542	+	0.754289i	$0.727982\pi$
$998$	−9.02556	−	19.7632i	−0.285699	−	0.625594i
$999$	0.969411	−	6.74240i	0.0306708	−	0.213320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	134.2.e.a.81.1	✓	30
67.15	even	11		8978.2.a.k.1.6		15
67.24	even	11	inner	134.2.e.a.91.1	yes	30
67.52	odd	22		8978.2.a.l.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
134.2.e.a.81.1	✓	30	1.1	even	1	trivial
134.2.e.a.91.1	yes	30	67.24	even	11	inner
8978.2.a.k.1.6		15	67.15	even	11
8978.2.a.l.1.10		15	67.52	odd	22

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:	\( N \)	\(=\)	\( 134 = 2 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	134.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.736673 - 0.473431i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.156423 - 1.08794i) q^{5} +(-0.124623 + 0.866771i) q^{6} +(-1.31230 - 2.87354i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.927695 - 2.03137i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.736673 - 0.473431i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.156423 - 1.08794i) q^{5} +(-0.124623 + 0.866771i) q^{6} +(-1.31230 - 2.87354i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.927695 - 2.03137i) q^{9} +(-0.924649 + 0.594236i) q^{10} +(-0.110515 - 0.768648i) q^{11} +(0.840213 - 0.246709i) q^{12} +(-3.31666 + 0.973859i) q^{13} +(-2.06872 + 2.38743i) q^{14} +(-0.399834 + 0.875514i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(5.14354 + 5.93596i) q^{17} +(-1.46242 + 1.68772i) q^{18} +(2.84156 - 6.22215i) q^{19} +(0.924649 + 0.594236i) q^{20} +(-0.393686 + 2.73815i) q^{21} +(-0.653278 + 0.419836i) q^{22} +(-2.31562 - 1.48816i) q^{23} +(-0.573451 - 0.661798i) q^{24} +(3.63831 - 1.06830i) q^{25} +(2.26364 + 2.61238i) q^{26} +(-0.652174 + 4.53597i) q^{27} +(3.03106 + 0.889998i) q^{28} +7.69137 q^{29} +0.962493 q^{30} +(0.776234 + 0.227923i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-0.282488 + 0.618563i) q^{33} +(3.26283 - 7.14461i) q^{34} +(-2.92098 + 1.87720i) q^{35} +(2.14272 + 0.629159i) q^{36} -1.48643 q^{37} -6.84029 q^{38} +(2.90435 + 0.852793i) q^{39} +(0.156423 - 1.08794i) q^{40} +(1.50439 + 1.73616i) q^{41} +(2.65425 - 0.779358i) q^{42} +(-1.62154 - 1.87136i) q^{43} +(0.653278 + 0.419836i) q^{44} +(-2.06490 + 1.32703i) q^{45} +(-0.391733 + 2.72457i) q^{46} +(2.68975 + 1.72859i) q^{47} +(-0.363772 + 0.796551i) q^{48} +(-1.95109 + 2.25168i) q^{49} +(-2.48317 - 2.86573i) q^{50} +(-0.978838 - 6.80796i) q^{51} +(1.43596 - 3.14431i) q^{52} +(-6.26998 + 7.23595i) q^{53} +(4.39698 - 1.29107i) q^{54} +(-0.818960 + 0.240468i) q^{55} +(-0.449575 - 3.12686i) q^{56} +(-5.03906 + 3.23841i) q^{57} +(-3.19511 - 6.99632i) q^{58} +(-0.0676806 - 0.0198728i) q^{59} +(-0.399834 - 0.875514i) q^{60} +(0.510081 - 3.54769i) q^{61} +(-0.115133 - 0.800770i) q^{62} +(-4.61981 + 5.33155i) q^{63} +(0.841254 + 0.540641i) q^{64} +(1.57831 + 3.45601i) q^{65} +0.680015 q^{66} +(-8.11967 - 1.03489i) q^{67} -7.85440 q^{68} +(1.00131 + 2.19257i) q^{69} +(2.92098 + 1.87720i) q^{70} +(5.88060 - 6.78657i) q^{71} +(-0.317814 - 2.21045i) q^{72} +(1.63573 - 11.3767i) q^{73} +(0.617486 + 1.35210i) q^{74} +(-3.18601 - 0.935497i) q^{75} +(2.84156 + 6.22215i) q^{76} +(-2.06372 + 1.32627i) q^{77} +(-0.430781 - 2.99615i) q^{78} +(-5.72867 + 1.68209i) q^{79} +(-1.05461 + 0.309661i) q^{80} +(-1.75935 + 2.03040i) q^{81} +(0.954318 - 2.08967i) q^{82} +(-1.15986 - 8.06702i) q^{83} +(-1.81154 - 2.09063i) q^{84} +(5.65342 - 6.52440i) q^{85} +(-1.02864 + 2.25240i) q^{86} +(-5.66602 - 3.64133i) q^{87} +(0.110515 - 0.768648i) q^{88} +(-2.18462 + 1.40397i) q^{89} +(2.06490 + 1.32703i) q^{90} +(7.15089 + 8.25257i) q^{91} +(2.64108 - 0.775492i) q^{92} +(-0.463925 - 0.535398i) q^{93} +(0.455024 - 3.16476i) q^{94} +(-7.21384 - 2.11817i) q^{95} +0.875684 q^{96} +18.8975 q^{97} +(2.85871 + 0.839394i) q^{98} +(-1.45888 + 0.937568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9} + 3 q^{10} + q^{11} - q^{12} - 11 q^{13} - 22 q^{14} + 18 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 16 q^{19} - 3 q^{20} - 27 q^{21} - q^{22} + 12 q^{24} + 2 q^{25} - 11 q^{26} + 14 q^{27} - 11 q^{28} + 26 q^{30} + 18 q^{31} + 3 q^{32} + 9 q^{33} - 14 q^{34} - 90 q^{35} - 8 q^{36} - 48 q^{37} + 28 q^{38} - q^{39} + 3 q^{40} - 51 q^{41} - 17 q^{42} + 10 q^{43} + q^{44} - 4 q^{45} - 11 q^{46} + 10 q^{47} + 10 q^{48} - 19 q^{49} - 24 q^{50} + 4 q^{51} + 11 q^{52} - 8 q^{53} - 25 q^{54} + 25 q^{55} + 31 q^{57} + 22 q^{58} + 66 q^{59} + 18 q^{60} + 34 q^{61} - 29 q^{62} + 80 q^{63} - 3 q^{64} + 26 q^{65} + 90 q^{66} - 3 q^{67} - 8 q^{68} - 46 q^{69} + 90 q^{70} + 39 q^{71} - 3 q^{72} + 78 q^{73} - 18 q^{74} - 11 q^{75} + 16 q^{76} + 73 q^{77} - 10 q^{78} + 34 q^{79} + 8 q^{80} - 134 q^{81} + 7 q^{82} - 11 q^{83} + 6 q^{84} - 31 q^{85} + q^{86} - 110 q^{87} - q^{88} - 30 q^{89} + 4 q^{90} + 14 q^{91} + 11 q^{92} - 13 q^{93} + 23 q^{94} - 39 q^{95} - 10 q^{96} + 24 q^{97} + 19 q^{98} - 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9 + 3 * q^10 + q^11 - q^12 - 11 * q^13 - 22 * q^14 + 18 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 16 * q^19 - 3 * q^20 - 27 * q^21 - q^22 + 12 * q^24 + 2 * q^25 - 11 * q^26 + 14 * q^27 - 11 * q^28 + 26 * q^30 + 18 * q^31 + 3 * q^32 + 9 * q^33 - 14 * q^34 - 90 * q^35 - 8 * q^36 - 48 * q^37 + 28 * q^38 - q^39 + 3 * q^40 - 51 * q^41 - 17 * q^42 + 10 * q^43 + q^44 - 4 * q^45 - 11 * q^46 + 10 * q^47 + 10 * q^48 - 19 * q^49 - 24 * q^50 + 4 * q^51 + 11 * q^52 - 8 * q^53 - 25 * q^54 + 25 * q^55 + 31 * q^57 + 22 * q^58 + 66 * q^59 + 18 * q^60 + 34 * q^61 - 29 * q^62 + 80 * q^63 - 3 * q^64 + 26 * q^65 + 90 * q^66 - 3 * q^67 - 8 * q^68 - 46 * q^69 + 90 * q^70 + 39 * q^71 - 3 * q^72 + 78 * q^73 - 18 * q^74 - 11 * q^75 + 16 * q^76 + 73 * q^77 - 10 * q^78 + 34 * q^79 + 8 * q^80 - 134 * q^81 + 7 * q^82 - 11 * q^83 + 6 * q^84 - 31 * q^85 + q^86 - 110 * q^87 - q^88 - 30 * q^89 + 4 * q^90 + 14 * q^91 + 11 * q^92 - 13 * q^93 + 23 * q^94 - 39 * q^95 - 10 * q^96 + 24 * q^97 + 19 * q^98 - 4 * q^99

Introduction

L-functions

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