LMFDB - Embedded newform 370.2.o.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 20 x^{15} + 180 x^{14} - 126 x^{13} + 1002 x^{12} - 270 x^{11} + \cdots + 81 $ x^18 - 3x^17 + 21x^16 - 20x^15 + 180x^14 - 126x^13 + 1002x^12 - 270x^11 + 3294x^10 - 1172x^9 + 6585x^8 - 1464x^7 + 8092x^6 - 2088x^5 + 5598x^4 + 180x^3 + 972x^2 - 162*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			71.2
Root			$0.571872 + 0.990512i$ of defining polynomial
Character	$\chi$	$=$	370.71
Dual form			370.2.o.a.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-0.646156 + 0.542189i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} -0.843496 q^{6} +(0.282141 + 0.102691i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.397396 + 2.25375i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-0.646156 + 0.542189i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} -0.843496 q^{6} +(0.282141 + 0.102691i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.397396 + 2.25375i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-3.09102 + 5.35380i) q^{11} +(-0.646156 - 0.542189i) q^{12} +(-0.104672 - 0.593624i) q^{13} +(0.150124 + 0.260023i) q^{14} +(0.792627 - 0.288493i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.274214 + 1.55515i) q^{17} +(-1.75310 + 1.47103i) q^{18} +(3.68175 - 3.08936i) q^{19} +(0.173648 - 0.984808i) q^{20} +(-0.237985 + 0.0866195i) q^{21} +(-5.80922 + 2.11438i) q^{22} +(3.32542 + 5.75979i) q^{23} +(-0.146472 - 0.830682i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.301391 - 0.522024i) q^{26} +(-2.23042 - 3.86320i) q^{27} +(-0.0521376 + 0.295687i) q^{28} +(-0.0493223 + 0.0854287i) q^{29} +(0.792627 + 0.288493i) q^{30} -9.46289 q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.905493 - 5.13531i) q^{33} +(-1.20969 + 1.01505i) q^{34} +(-0.230004 - 0.192996i) q^{35} -2.28851 q^{36} +(5.42664 - 2.74801i) q^{37} +4.80619 q^{38} +(0.389491 + 0.326822i) q^{39} +(0.766044 - 0.642788i) q^{40} +(-1.46448 - 8.30548i) q^{41} +(-0.237985 - 0.0866195i) q^{42} +5.55271 q^{43} +(-5.80922 - 2.11438i) q^{44} +(1.14426 - 1.98191i) q^{45} +(-1.15490 + 6.54979i) q^{46} +(5.91104 + 10.2382i) q^{47} +(0.421748 - 0.730489i) q^{48} +(-5.29325 - 4.44157i) q^{49} +(0.173648 + 0.984808i) q^{50} +(-0.665998 - 1.15354i) q^{51} +(0.566429 - 0.206163i) q^{52} +(12.8417 - 4.67398i) q^{53} +(0.774617 - 4.39307i) q^{54} +(4.73572 - 3.97374i) q^{55} +(-0.230004 + 0.192996i) q^{56} +(-0.703970 + 3.99241i) q^{57} +(-0.0926955 + 0.0337384i) q^{58} +(10.9842 - 3.99792i) q^{59} +(0.421748 + 0.730489i) q^{60} +(1.63364 + 9.26486i) q^{61} +(-7.24900 - 6.08263i) q^{62} +(-0.343561 + 0.595066i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.104672 + 0.593624i) q^{65} +(2.60726 - 4.51591i) q^{66} +(3.75338 + 1.36612i) q^{67} -1.57914 q^{68} +(-5.27163 - 1.91872i) q^{69} +(-0.0521376 - 0.295687i) q^{70} +(-6.27737 + 5.26734i) q^{71} +(-1.75310 - 1.47103i) q^{72} -4.14584 q^{73} +(5.92343 + 1.38308i) q^{74} -0.843496 q^{75} +(3.68175 + 3.08936i) q^{76} +(-1.42189 + 1.19311i) q^{77} +(0.0882904 + 0.500720i) q^{78} +(6.38657 + 2.32452i) q^{79} +1.00000 q^{80} +(-2.91571 - 1.06123i) q^{81} +(4.21680 - 7.30372i) q^{82} +(1.46015 - 8.28093i) q^{83} +(-0.126629 - 0.219328i) q^{84} +(0.789568 - 1.36757i) q^{85} +(4.25363 + 3.56922i) q^{86} +(-0.0144486 - 0.0819422i) q^{87} +(-3.09102 - 5.35380i) q^{88} +(5.34859 - 1.94673i) q^{89} +(2.15050 - 0.782718i) q^{90} +(0.0314276 - 0.178235i) q^{91} +(-5.09483 + 4.27507i) q^{92} +(6.11450 - 5.13068i) q^{93} +(-2.05288 + 11.6425i) q^{94} +(-4.51634 + 1.64381i) q^{95} +(0.792627 - 0.288493i) q^{96} +(-5.32953 - 9.23102i) q^{97} +(-1.19988 - 6.80487i) q^{98} +(-10.8378 - 9.09396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9	$ 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9} - 9 q^{10} + 3 q^{11} + 9 q^{13} - 6 q^{17} + 6 q^{18} + 9 q^{19} - 6 q^{21} + 21 q^{23} + 6 q^{26} + 12 q^{27} - 3 q^{28} + 6 q^{29} - 30 q^{31} - 45 q^{33} - 15 q^{34} + 6 q^{35} + 24 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{39} + 15 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{45} + 24 q^{47} + 3 q^{48} + 33 q^{49} - 42 q^{51} - 12 q^{53} + 27 q^{54} + 6 q^{56} + 51 q^{57} - 15 q^{58} - 15 q^{59} + 3 q^{60} + 72 q^{61} - 57 q^{62} - 30 q^{63} - 9 q^{64} + 9 q^{65} - 3 q^{66} + 18 q^{67} + 24 q^{69} - 3 q^{70} + 6 q^{72} - 66 q^{73} - 24 q^{74} - 6 q^{75} + 9 q^{76} - 66 q^{77} + 6 q^{78} - 12 q^{79} + 18 q^{80} + 66 q^{81} + 45 q^{82} + 9 q^{83} + 42 q^{84} + 12 q^{86} + 48 q^{87} + 3 q^{88} + 6 q^{90} - 78 q^{91} + 18 q^{92} + 24 q^{94} - 3 q^{97} - 48 q^{98} - 96 q^{99}+O(q^{100}) $ 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9 - 9 * q^10 + 3 * q^11 + 9 * q^13 - 6 * q^17 + 6 * q^18 + 9 * q^19 - 6 * q^21 + 21 * q^23 + 6 * q^26 + 12 * q^27 - 3 * q^28 + 6 * q^29 - 30 * q^31 - 45 * q^33 - 15 * q^34 + 6 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^39 + 15 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 24 * q^47 + 3 * q^48 + 33 * q^49 - 42 * q^51 - 12 * q^53 + 27 * q^54 + 6 * q^56 + 51 * q^57 - 15 * q^58 - 15 * q^59 + 3 * q^60 + 72 * q^61 - 57 * q^62 - 30 * q^63 - 9 * q^64 + 9 * q^65 - 3 * q^66 + 18 * q^67 + 24 * q^69 - 3 * q^70 + 6 * q^72 - 66 * q^73 - 24 * q^74 - 6 * q^75 + 9 * q^76 - 66 * q^77 + 6 * q^78 - 12 * q^79 + 18 * q^80 + 66 * q^81 + 45 * q^82 + 9 * q^83 + 42 * q^84 + 12 * q^86 + 48 * q^87 + 3 * q^88 + 6 * q^90 - 78 * q^91 + 18 * q^92 + 24 * q^94 - 3 * q^97 - 48 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−0.646156	+	0.542189i	−0.373058	+	0.313033i	−0.809970	−	0.586471i	$-0.800517\pi$
$3$	−0.646156	+	0.542189i	−0.373058	+	0.313033i	0.436912	+	0.899504i	$0.356072\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$	−0.843496			−0.344356
$7$	0.282141	+	0.102691i	0.106639	+	0.0388136i	0.394789	−	0.918772i	$-0.370818\pi$
$7$	0.282141	+	0.102691i	0.106639	+	0.0388136i	−0.288149	+	0.957585i	$0.593040\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.397396	+	2.25375i	−0.132465	+	0.751249i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−3.09102	+	5.35380i	−0.931978	+	1.61423i	−0.152041	+	0.988374i	$0.548585\pi$
$11$	−3.09102	+	5.35380i	−0.931978	+	1.61423i	−0.779937	+	0.625858i	$0.784749\pi$
$12$	−0.646156	−	0.542189i	−0.186529	−	0.156516i
$13$	−0.104672	−	0.593624i	−0.0290308	−	0.164642i	0.966846	−	0.255361i	$-0.0821944\pi$
$13$	−0.104672	−	0.593624i	−0.0290308	−	0.164642i	−0.995876	+	0.0907196i	$0.971083\pi$
$14$	0.150124	+	0.260023i	0.0401224	+	0.0694940i
$15$	0.792627	−	0.288493i	0.204655	−	0.0744885i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.274214	+	1.55515i	−0.0665067	+	0.377178i	0.933328	+	0.359024i	$0.116890\pi$
$17$	−0.274214	+	1.55515i	−0.0665067	+	0.377178i	−0.999835	+	0.0181547i	$0.994221\pi$
$18$	−1.75310	+	1.47103i	−0.413210	+	0.346725i
$19$	3.68175	−	3.08936i	0.844652	−	0.708747i	−0.113953	−	0.993486i	$-0.536351\pi$
$19$	3.68175	−	3.08936i	0.844652	−	0.708747i	0.958605	+	0.284739i	$0.0919069\pi$
$20$	0.173648	−	0.984808i	0.0388289	−	0.220210i
$21$	−0.237985	+	0.0866195i	−0.0519326	+	0.0189019i
$22$	−5.80922	+	2.11438i	−1.23853	+	0.450788i
$23$	3.32542	+	5.75979i	0.693397	+	1.20100i	0.970718	+	0.240222i	$0.0772202\pi$
$23$	3.32542	+	5.75979i	0.693397	+	1.20100i	−0.277321	+	0.960777i	$0.589446\pi$
$24$	−0.146472	−	0.830682i	−0.0298984	−	0.169562i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	0.301391	−	0.522024i	0.0591076	−	0.102377i
$27$	−2.23042	−	3.86320i	−0.429245	−	0.743474i
$28$	−0.0521376	+	0.295687i	−0.00985308	+	0.0558796i
$29$	−0.0493223	+	0.0854287i	−0.00915892	+	0.0158637i	−0.870569	−	0.492047i	$-0.836249\pi$
$29$	−0.0493223	+	0.0854287i	−0.00915892	+	0.0158637i	0.861410	+	0.507911i	$0.169582\pi$
$30$	0.792627	+	0.288493i	0.144713	+	0.0526713i
$31$	−9.46289			−1.69959			−0.849793	−	0.527117i	$-0.823273\pi$
$31$	−9.46289			−1.69959			−0.849793	+	0.527117i	$0.823273\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−0.905493	−	5.13531i	−0.157626	−	0.893942i
$34$	−1.20969	+	1.01505i	−0.207460	+	0.174080i
$35$	−0.230004	−	0.192996i	−0.0388777	−	0.0326223i
$36$	−2.28851			−0.381419
$37$	5.42664	−	2.74801i	0.892135	−	0.451769i
$37$	5.42664	−	2.74801i	0.892135	−	0.451769i
$38$	4.80619			0.779667
$39$	0.389491	+	0.326822i	0.0623684	+	0.0523333i
$40$	0.766044	−	0.642788i	0.121122	−	0.101634i
$41$	−1.46448	−	8.30548i	−0.228713	−	1.29710i	−0.855458	−	0.517873i	$-0.826724\pi$
$41$	−1.46448	−	8.30548i	−0.228713	−	1.29710i	0.626744	−	0.779225i	$-0.284387\pi$
$42$	−0.237985	−	0.0866195i	−0.0367219	−	0.0133657i
$43$	5.55271			0.846781			0.423391	−	0.905947i	$-0.360840\pi$
$43$	5.55271			0.846781			0.423391	+	0.905947i	$0.360840\pi$
$44$	−5.80922	−	2.11438i	−0.875773	−	0.318755i
$45$	1.14426	−	1.98191i	0.170576	−	0.295446i
$46$	−1.15490	+	6.54979i	−0.170281	+	0.965714i
$47$	5.91104	+	10.2382i	0.862213	+	1.49340i	0.869788	+	0.493426i	$0.164256\pi$
$47$	5.91104	+	10.2382i	0.862213	+	1.49340i	−0.00757468	+	0.999971i	$0.502411\pi$
$48$	0.421748	−	0.730489i	0.0608741	−	0.105437i
$49$	−5.29325	−	4.44157i	−0.756179	−	0.634510i
$50$	0.173648	+	0.984808i	0.0245576	+	0.139273i
$51$	−0.665998	−	1.15354i	−0.0932584	−	0.161528i
$52$	0.566429	−	0.206163i	0.0785496	−	0.0285897i
$53$	12.8417	−	4.67398i	1.76394	−	0.642021i	0.763943	−	0.645284i	$-0.223261\pi$
$53$	12.8417	−	4.67398i	1.76394	−	0.642021i	0.999995	+	0.00326300i	$0.00103865\pi$
$54$	0.774617	−	4.39307i	0.105412	−	0.597821i
$55$	4.73572	−	3.97374i	0.638564	−	0.535819i
$56$	−0.230004	+	0.192996i	−0.0307355	+	0.0257902i
$57$	−0.703970	+	3.99241i	−0.0932431	+	0.528808i
$58$	−0.0926955	+	0.0337384i	−0.0121715	+	0.00443007i
$59$	10.9842	−	3.99792i	1.43002	−	0.520484i	0.493082	−	0.869983i	$-0.335870\pi$
$59$	10.9842	−	3.99792i	1.43002	−	0.520484i	0.936937	+	0.349498i	$0.113648\pi$
$60$	0.421748	+	0.730489i	0.0544475	+	0.0943058i
$61$	1.63364	+	9.26486i	0.209167	+	1.18624i	0.890747	+	0.454500i	$0.150182\pi$
$61$	1.63364	+	9.26486i	0.209167	+	1.18624i	−0.681580	+	0.731743i	$0.738707\pi$
$62$	−7.24900	−	6.08263i	−0.920624	−	0.772495i
$63$	−0.343561	+	0.595066i	−0.0432847	+	0.0749712i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.104672	+	0.593624i	−0.0129830	+	0.0736300i
$66$	2.60726	−	4.51591i	0.320932	−	0.555871i
$67$	3.75338	+	1.36612i	0.458549	+	0.166898i	0.560958	−	0.827844i	$-0.310433\pi$
$67$	3.75338	+	1.36612i	0.458549	+	0.166898i	−0.102409	+	0.994742i	$0.532655\pi$
$68$	−1.57914			−0.191498
$69$	−5.27163	−	1.91872i	−0.634630	−	0.230986i
$70$	−0.0521376	−	0.295687i	−0.00623163	−	0.0353414i
$71$	−6.27737	+	5.26734i	−0.744987	+	0.625118i	−0.934172	−	0.356823i	$-0.883860\pi$
$71$	−6.27737	+	5.26734i	−0.744987	+	0.625118i	0.189185	+	0.981941i	$0.439415\pi$
$72$	−1.75310	−	1.47103i	−0.206605	−	0.173362i
$73$	−4.14584			−0.485234			−0.242617	−	0.970122i	$-0.578006\pi$
$73$	−4.14584			−0.485234			−0.242617	+	0.970122i	$0.578006\pi$
$74$	5.92343	+	1.38308i	0.688585	+	0.160780i
$75$	−0.843496			−0.0973986
$76$	3.68175	+	3.08936i	0.422326	+	0.354374i
$77$	−1.42189	+	1.19311i	−0.162040	+	0.135967i
$78$	0.0882904	+	0.500720i	0.00999692	+	0.0566953i
$79$	6.38657	+	2.32452i	0.718546	+	0.261529i	0.675308	−	0.737536i	$-0.264011\pi$
$79$	6.38657	+	2.32452i	0.718546	+	0.261529i	0.0432373	+	0.999065i	$0.486233\pi$
$80$	1.00000			0.111803
$81$	−2.91571	−	1.06123i	−0.323968	−	0.117915i
$82$	4.21680	−	7.30372i	0.465668	−	0.806561i
$83$	1.46015	−	8.28093i	0.160272	−	0.908950i	−0.793533	−	0.608527i	$-0.791761\pi$
$83$	1.46015	−	8.28093i	0.160272	−	0.908950i	0.953806	−	0.300424i	$-0.0971281\pi$
$84$	−0.126629	−	0.219328i	−0.0138164	−	0.0239307i
$85$	0.789568	−	1.36757i	0.0856407	−	0.148334i
$86$	4.25363	+	3.56922i	0.458680	+	0.384878i
$87$	−0.0144486	−	0.0819422i	−0.00154906	−	0.00878513i
$88$	−3.09102	−	5.35380i	−0.329504	−	0.570717i
$89$	5.34859	−	1.94673i	0.566950	−	0.206353i	−0.0426116	−	0.999092i	$-0.513568\pi$
$89$	5.34859	−	1.94673i	0.566950	−	0.206353i	0.609561	+	0.792739i	$0.291346\pi$
$90$	2.15050	−	0.782718i	0.226683	−	0.0825057i
$91$	0.0314276	−	0.178235i	0.00329451	−	0.0186841i
$92$	−5.09483	+	4.27507i	−0.531173	+	0.445707i
$93$	6.11450	−	5.13068i	0.634044	−	0.532026i
$94$	−2.05288	+	11.6425i	−0.211739	+	1.20083i
$95$	−4.51634	+	1.64381i	−0.463367	+	0.168652i
$96$	0.792627	−	0.288493i	0.0808972	−	0.0294442i
$97$	−5.32953	−	9.23102i	−0.541132	−	0.937268i	−0.998839	−	0.0481650i	$-0.984663\pi$
$97$	−5.32953	−	9.23102i	−0.541132	−	0.937268i	0.457708	−	0.889103i	$-0.348671\pi$
$98$	−1.19988	−	6.80487i	−0.121206	−	0.687396i
$99$	−10.8378	−	9.09396i	−1.08924	−	0.913977i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−1.13781	−	1.97074i	−0.113216	−	0.196096i	0.803849	−	0.594833i	$-0.202782\pi$
$101$	−1.13781	−	1.97074i	−0.113216	−	0.196096i	−0.917065	+	0.398737i	$0.869449\pi$
$102$	0.231299	−	1.31176i	0.0229020	−	0.129884i
$103$	−0.711816	+	1.23290i	−0.0701373	+	0.121481i	−0.898961	−	0.438028i	$-0.855677\pi$
$103$	−0.711816	+	1.23290i	−0.0701373	+	0.121481i	0.828824	+	0.559509i	$0.189010\pi$
$104$	0.566429	+	0.206163i	0.0555430	+	0.0202160i
$105$	0.253258			0.0247155
$106$	12.8417	+	4.67398i	1.24729	+	0.453977i
$107$	2.86071	+	16.2239i	0.276555	+	1.56842i	0.733978	+	0.679174i	$0.237662\pi$
$107$	2.86071	+	16.2239i	0.276555	+	1.56842i	−0.457422	+	0.889250i	$0.651227\pi$
$108$	3.41720	−	2.86737i	0.328821	−	0.275913i
$109$	5.76852	+	4.84037i	0.552524	+	0.463623i	0.875795	−	0.482684i	$-0.160338\pi$
$109$	5.76852	+	4.84037i	0.552524	+	0.463623i	−0.323270	+	0.946307i	$0.604782\pi$
$110$	6.18204			0.589434
$111$	−2.01652	+	4.71791i	−0.191399	+	0.447804i
$112$	−0.300248			−0.0283708
$113$	1.64719	+	1.38216i	0.154955	+	0.130023i	0.716969	−	0.697105i	$-0.245529\pi$
$113$	1.64719	+	1.38216i	0.154955	+	0.130023i	−0.562014	+	0.827128i	$0.689973\pi$
$114$	−3.10555	+	2.60586i	−0.290861	+	0.244061i
$115$	−1.15490	−	6.54979i	−0.107695	−	0.610771i
$116$	−0.0926955	−	0.0337384i	−0.00860657	−	0.00313253i
$117$	1.37947			0.127532
$118$	10.9842	+	3.99792i	1.01118	+	0.368038i
$119$	−0.237067	+	0.410612i	−0.0217319	+	0.0376407i
$120$	−0.146472	+	0.830682i	−0.0133710	+	0.0758305i
$121$	−13.6088	−	23.5712i	−1.23716	−	2.14283i
$122$	−4.70389	+	8.14738i	−0.425870	+	0.737629i
$123$	5.44942	+	4.57261i	0.491358	+	0.412298i
$124$	−1.64321	−	9.31913i	−0.147565	−	0.836883i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−0.645684	+	0.235010i	−0.0575221	+	0.0209363i
$127$	−8.50846	+	3.09682i	−0.755003	+	0.274799i	−0.690710	−	0.723132i	$-0.742702\pi$
$127$	−8.50846	+	3.09682i	−0.755003	+	0.274799i	−0.0642938	+	0.997931i	$0.520479\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−3.58792	+	3.01062i	−0.315899	+	0.265070i
$130$	−0.461757	+	0.387461i	−0.0404988	+	0.0339825i
$131$	−2.64389	+	14.9942i	−0.230997	+	1.31005i	0.619884	+	0.784694i	$0.287180\pi$
$131$	−2.64389	+	14.9942i	−0.230997	+	1.31005i	−0.850881	+	0.525358i	$0.823931\pi$
$132$	4.90005	−	1.78347i	0.426495	−	0.155231i
$133$	1.35602	−	0.493552i	0.117582	−	0.0427964i
$134$	1.99713	+	3.45914i	0.172526	+	0.298824i
$135$	0.774617	+	4.39307i	0.0666684	+	0.378095i
$136$	−1.20969	−	1.01505i	−0.103730	−	0.0870398i
$137$	−1.50643	+	2.60921i	−0.128703	+	0.222920i	−0.923174	−	0.384382i	$-0.874415\pi$
$137$	−1.50643	+	2.60921i	−0.128703	+	0.222920i	0.794471	+	0.607301i	$0.207748\pi$
$138$	−2.80498	−	4.85836i	−0.238775	−	0.413571i
$139$	−1.43014	+	8.11075i	−0.121303	+	0.687945i	0.862132	+	0.506684i	$0.169129\pi$
$139$	−1.43014	+	8.11075i	−0.121303	+	0.687945i	−0.983435	+	0.181261i	$0.941982\pi$
$140$	0.150124	−	0.260023i	0.0126878	−	0.0219759i
$141$	−9.37050	−	3.41058i	−0.789138	−	0.287223i
$142$	−8.19453			−0.687669
$143$	3.50169	+	1.27451i	0.292826	+	0.106580i
$144$	−0.397396	−	2.25375i	−0.0331164	−	0.187812i
$145$	0.0755661	−	0.0634075i	0.00627542	−	0.00526571i
$146$	−3.17590	−	2.66490i	−0.262839	−	0.220548i
$147$	5.82843			0.480721
$148$	3.64858	+	4.86701i	0.299912	+	0.400066i
$149$	−18.0139			−1.47576			−0.737878	−	0.674934i	$-0.764172\pi$
$149$	−18.0139			−1.47576			−0.737878	+	0.674934i	$0.764172\pi$
$150$	−0.646156	−	0.542189i	−0.0527584	−	0.0442695i
$151$	0.560450	−	0.470274i	0.0456088	−	0.0382703i	−0.619698	−	0.784840i	$-0.712745\pi$
$151$	0.560450	−	0.470274i	0.0456088	−	0.0382703i	0.665307	+	0.746570i	$0.268301\pi$
$152$	0.834586	+	4.73317i	0.0676938	+	0.383911i
$153$	−3.39593	−	1.23602i	−0.274545	−	0.0999262i
$154$	−1.85615			−0.149573
$155$	8.89221	+	3.23650i	0.714240	+	0.259962i
$156$	−0.254222	+	0.440325i	−0.0203541	+	0.0352543i
$157$	3.23177	−	18.3283i	0.257923	−	1.46275i	−0.530534	−	0.847664i	$-0.678008\pi$
$157$	3.23177	−	18.3283i	0.257923	−	1.46275i	0.788457	−	0.615090i	$-0.210880\pi$
$158$	3.39822	+	5.88590i	0.270348	+	0.468257i
$159$	−5.76353	+	9.98273i	−0.457078	+	0.791682i
$160$	0.766044	+	0.642788i	0.0605611	+	0.0508168i
$161$	0.346758	+	1.96656i	0.0273284	+	0.154987i
$162$	−1.55142	−	2.68714i	−0.121891	−	0.211121i
$163$	−5.49541	+	2.00017i	−0.430434	+	0.156665i	−0.548146	−	0.836383i	$-0.684666\pi$
$163$	−5.49541	+	2.00017i	−0.430434	+	0.156665i	0.117712	+	0.993048i	$0.462444\pi$
$164$	7.92500	−	2.88446i	0.618838	−	0.225239i
$165$	−0.905493	+	5.13531i	−0.0704926	+	0.399783i
$166$	6.44142	−	5.40500i	0.499951	−	0.419509i
$167$	9.40347	−	7.89045i	0.727662	−	0.610581i	−0.201831	−	0.979420i	$-0.564689\pi$
$167$	9.40347	−	7.89045i	0.727662	−	0.610581i	0.929493	+	0.368839i	$0.120245\pi$
$168$	0.0439779	−	0.249411i	0.00339297	−	0.0192425i
$169$	11.8746	−	4.32199i	0.913429	−	0.332461i
$170$	1.48390	−	0.540097i	0.113810	−	0.0414235i
$171$	5.49951	+	9.52544i	0.420558	+	0.728428i
$172$	0.964219	+	5.46836i	0.0735210	+	0.416958i
$173$	−2.58811	−	2.17169i	−0.196771	−	0.165110i	0.539079	−	0.842255i	$-0.318772\pi$
$173$	−2.58811	−	2.17169i	−0.196771	−	0.165110i	−0.735850	+	0.677145i	$0.763217\pi$
$174$	0.0416032	−	0.0720588i	0.00315393	−	0.00546276i
$175$	0.150124	+	0.260023i	0.0113483	+	0.0196559i
$176$	1.07350	−	6.08812i	0.0809181	−	0.458909i
$177$	−4.92987	+	8.53878i	−0.370552	+	0.641814i
$178$	5.34859	+	1.94673i	0.400894	+	0.145913i
$179$	−3.65051			−0.272852			−0.136426	−	0.990650i	$-0.543562\pi$
$179$	−3.65051			−0.272852			−0.136426	+	0.990650i	$0.543562\pi$
$180$	2.15050	+	0.782718i	0.160289	+	0.0583403i
$181$	2.56442	+	14.5436i	0.190612	+	1.08101i	0.918530	+	0.395350i	$0.129377\pi$
$181$	2.56442	+	14.5436i	0.190612	+	1.08101i	−0.727918	+	0.685664i	$0.759512\pi$
$182$	0.138642	−	0.116334i	0.0102768	−	0.00862328i
$183$	−6.07889	−	5.10080i	−0.449365	−	0.377062i
$184$	−6.65083			−0.490306
$185$	−6.03925	+	0.726259i	−0.444015	+	0.0533956i
$186$	7.98192			0.585262
$187$	−7.47835	−	6.27508i	−0.546871	−	0.458879i
$188$	−9.05623	+	7.59908i	−0.660494	+	0.554220i
$189$	−0.232578	−	1.31901i	−0.0169175	−	0.0959441i
$190$	−4.51634	−	1.64381i	−0.327650	−	0.119255i
$191$	−23.2400			−1.68159			−0.840793	−	0.541357i	$-0.817911\pi$
$191$	−23.2400			−1.68159			−0.840793	+	0.541357i	$0.817911\pi$
$192$	0.792627	+	0.288493i	0.0572030	+	0.0208202i
$193$	2.43735	−	4.22162i	0.175444	−	0.303879i	−0.764871	−	0.644184i	$-0.777197\pi$
$193$	2.43735	−	4.22162i	0.175444	−	0.303879i	0.940315	+	0.340305i	$0.110530\pi$
$194$	1.85093	−	10.4971i	0.132889	−	0.753650i
$195$	−0.254222	−	0.440325i	−0.0182052	−	0.0315324i
$196$	3.45493	−	5.98411i	0.246780	−	0.427436i
$197$	−11.7170	−	9.83169i	−0.834798	−	0.700479i	0.121589	−	0.992581i	$-0.461201\pi$
$197$	−11.7170	−	9.83169i	−0.834798	−	0.700479i	−0.956387	+	0.292101i	$0.905646\pi$
$198$	−2.45672	−	13.9327i	−0.174591	−	0.990157i
$199$	−2.68829	−	4.65626i	−0.190568	−	0.330073i	0.754871	−	0.655874i	$-0.227700\pi$
$199$	−2.68829	−	4.65626i	−0.190568	−	0.330073i	−0.945439	+	0.325800i	$0.894366\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$	−3.16596	+	1.15232i	−0.223310	+	0.0812782i
$202$	0.395156	−	2.24104i	0.0278031	−	0.157679i
$203$	−0.0226886	+	0.0190380i	−0.00159243	+	0.00133621i
$204$	1.02037	−	0.856191i	0.0714401	−	0.0599453i
$205$	−1.46448	+	8.30548i	−0.102284	+	0.580080i
$206$	−1.33778	+	0.486911i	−0.0932073	+	0.0339247i
$207$	−14.3026	+	5.20573i	−0.994100	+	0.361823i
$208$	0.301391	+	0.522024i	0.0208977	+	0.0361959i
$209$	5.15944	+	29.2607i	0.356886	+	2.02400i
$210$	0.194007	+	0.162791i	0.0133878	+	0.0112337i
$211$	10.7745	−	18.6621i	0.741750	−	1.28475i	−0.209948	−	0.977713i	$-0.567329\pi$
$211$	10.7745	−	18.6621i	0.741750	−	1.28475i	0.951698	−	0.307036i	$-0.0993373\pi$
$212$	6.83290	+	11.8349i	0.469286	+	0.812827i
$213$	1.20027	−	6.80704i	0.0822408	−	0.466411i
$214$	−8.23709	+	14.2671i	−0.563076	+	0.975276i
$215$	−5.21784	−	1.89914i	−0.355854	−	0.129520i
$216$	4.46084			0.303522
$217$	−2.66987	−	0.971754i	−0.181243	−	0.0659670i
$218$	1.30762	+	7.41587i	0.0885631	+	0.502266i
$219$	2.67886	−	2.24783i	0.181021	−	0.151894i
$220$	4.73572	+	3.97374i	0.319282	+	0.267909i
$221$	0.951875			0.0640300
$222$	−4.57735	+	2.31793i	−0.307212	+	0.155569i
$223$	0.342888			0.0229615			0.0114807	−	0.999934i	$-0.496345\pi$
$223$	0.342888			0.0229615			0.0114807	+	0.999934i	$0.496345\pi$
$224$	−0.230004	−	0.192996i	−0.0153678	−	0.0128951i
$225$	−1.75310	+	1.47103i	−0.116874	+	0.0980686i
$226$	0.373389	+	2.11759i	0.0248375	+	0.140860i
$227$	20.8382	+	7.58448i	1.38308	+	0.503400i	0.923110	−	0.384535i	$-0.125638\pi$
$227$	20.8382	+	7.58448i	1.38308	+	0.503400i	0.459969	+	0.887935i	$0.347861\pi$
$228$	−4.05400			−0.268483
$229$	−2.15420	−	0.784063i	−0.142353	−	0.0518124i	0.269861	−	0.962899i	$-0.413022\pi$
$229$	−2.15420	−	0.784063i	−0.142353	−	0.0518124i	−0.412214	+	0.911087i	$0.635244\pi$
$230$	3.32542	−	5.75979i	0.219271	−	0.379789i
$231$	0.271873	−	1.54187i	0.0178879	−	0.101447i
$232$	−0.0493223	−	0.0854287i	−0.00323817	−	0.00560867i
$233$	1.11562	−	1.93231i	0.0730866	−	0.126590i	−0.827166	−	0.561958i	$-0.810048\pi$
$233$	1.11562	−	1.93231i	0.0730866	−	0.126590i	0.900253	+	0.435368i	$0.143382\pi$
$234$	1.05674	+	0.886709i	0.0690812	+	0.0579660i
$235$	−2.05288	−	11.6425i	−0.133915	−	0.759471i
$236$	5.84456	+	10.1231i	0.380449	+	0.658957i
$237$	−5.38705	+	1.96073i	−0.349927	+	0.127363i
$238$	−0.445540	+	0.162163i	−0.0288800	+	0.0105115i
$239$	−4.16932	+	23.6454i	−0.269691	+	1.52949i	0.485645	+	0.874156i	$0.338585\pi$
$239$	−4.16932	+	23.6454i	−0.269691	+	1.52949i	−0.755336	+	0.655337i	$0.772526\pi$
$240$	−0.646156	+	0.542189i	−0.0417092	+	0.0349982i
$241$	−0.148823	+	0.124877i	−0.00958651	+	0.00804404i	−0.647568	−	0.762007i	$-0.724214\pi$
$241$	−0.148823	+	0.124877i	−0.00958651	+	0.00804404i	0.637982	+	0.770051i	$0.279770\pi$
$242$	4.72629	−	26.8041i	0.303817	−	1.72303i
$243$	15.0349	−	5.47224i	0.964486	−	0.351044i
$244$	−8.84042	+	3.21765i	−0.565950	+	0.205989i
$245$	3.45493	+	5.98411i	0.220727	+	0.382311i
$246$	1.23528	+	7.00564i	0.0787588	+	0.446663i
$247$	−2.21929	−	1.86221i	−0.141210	−	0.118489i
$248$	4.73145	−	8.19511i	0.300447	−	0.520390i
$249$	3.54635	+	6.14245i	0.224741	+	0.389262i
$250$	0.173648	−	0.984808i	0.0109825	−	0.0622847i
$251$	7.06750	−	12.2413i	0.446096	−	0.772662i	−0.552031	−	0.833823i	$-0.686147\pi$
$251$	7.06750	−	12.2413i	0.446096	−	0.772662i	0.998128	+	0.0611616i	$0.0194805\pi$
$252$	−0.645684	−	0.235010i	−0.0406743	−	0.0148042i
$253$	−41.1157			−2.58492
$254$	−8.50846	−	3.09682i	−0.533868	−	0.194312i
$255$	0.231299	+	1.31176i	0.0144845	+	0.0821456i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	20.0513	+	16.8251i	1.25077	+	1.04952i	0.996603	+	0.0823569i	$0.0262447\pi$
$257$	20.0513	+	16.8251i	1.25077	+	1.04952i	0.254164	+	0.967161i	$0.418200\pi$
$258$	−4.68369			−0.291594
$259$	1.81328	−	0.218058i	0.112671	−	0.0135495i
$260$	−0.602782			−0.0373829
$261$	−0.172934	−	0.145109i	−0.0107044	−	0.00898202i
$262$	−11.6634	+	9.78679i	−0.720570	+	0.604630i
$263$	1.29448	+	7.34136i	0.0798210	+	0.452687i	0.998354	+	0.0573442i	$0.0182632\pi$
$263$	1.29448	+	7.34136i	0.0798210	+	0.452687i	−0.918533	+	0.395343i	$0.870626\pi$
$264$	4.90005	+	1.78347i	0.301577	+	0.109765i
$265$	−13.6658			−0.839484
$266$	1.35602	+	0.493552i	0.0831432	+	0.0302616i
$267$	−2.40053	+	4.15784i	−0.146910	+	0.254456i
$268$	−0.693597	+	3.93358i	−0.0423682	+	0.240282i
$269$	3.63530	+	6.29652i	0.221648	+	0.383906i	0.955309	−	0.295611i	$-0.0955231\pi$
$269$	3.63530	+	6.29652i	0.221648	+	0.383906i	−0.733661	+	0.679516i	$0.762190\pi$
$270$	−2.23042	+	3.86320i	−0.135739	+	0.235107i
$271$	12.9423	+	10.8599i	0.786192	+	0.659693i	0.944800	−	0.327649i	$-0.106256\pi$
$271$	12.9423	+	10.8599i	0.786192	+	0.659693i	−0.158608	+	0.987342i	$0.550701\pi$
$272$	−0.274214	−	1.55515i	−0.0166267	−	0.0942946i
$273$	0.0763298	+	0.132207i	0.00461969	+	0.00800153i
$274$	−2.83116	+	1.03046i	−0.171036	+	0.0622522i
$275$	−5.80922	+	2.11438i	−0.350309	+	0.127502i
$276$	0.974158	−	5.52473i	0.0586374	−	0.332549i
$277$	0.486288	−	0.408044i	0.0292182	−	0.0245170i	−0.628062	−	0.778164i	$-0.716151\pi$
$277$	0.486288	−	0.408044i	0.0292182	−	0.0245170i	0.657280	+	0.753647i	$0.271707\pi$
$278$	−6.30904	+	5.29392i	−0.378391	+	0.317508i
$279$	3.76052	−	21.3270i	0.225136	−	1.27681i
$280$	0.282141	−	0.102691i	0.0168612	−	0.00613696i
$281$	−11.4427	+	4.16481i	−0.682616	+	0.248452i	−0.659970	−	0.751292i	$-0.729431\pi$
$281$	−11.4427	+	4.16481i	−0.682616	+	0.248452i	−0.0226457	+	0.999744i	$0.507209\pi$
$282$	−4.98594	−	8.63590i	−0.296908	−	0.514260i
$283$	4.67745	+	26.5271i	0.278046	+	1.57687i	0.729119	+	0.684387i	$0.239930\pi$
$283$	4.67745	+	26.5271i	0.278046	+	1.57687i	−0.451073	+	0.892487i	$0.648959\pi$
$284$	−6.27737	−	5.26734i	−0.372493	−	0.312559i
$285$	2.02700	−	3.51087i	0.120069	−	0.207966i
$286$	1.86321	+	3.22717i	0.110174	+	0.190827i
$287$	0.439708	−	2.49371i	0.0259551	−	0.147199i
$288$	1.14426	−	1.98191i	0.0674260	−	0.116785i
$289$	13.6315	+	4.96146i	0.801852	+	0.291850i
$290$	0.0986445			0.00579261
$291$	8.44866	+	3.07506i	0.495269	+	0.180263i
$292$	−0.719918	−	4.08286i	−0.0421300	−	0.238931i
$293$	0.0156116	−	0.0130997i	0.000912040	−	0.000765292i	−0.642331	−	0.766427i	$-0.722033\pi$
$293$	0.0156116	−	0.0130997i	0.000912040	−	0.000765292i	0.643244	+	0.765662i	$0.277588\pi$
$294$	4.46484	+	3.74645i	0.260395	+	0.218497i
$295$	−11.6891			−0.680567
$296$	−0.333479	+	6.07361i	−0.0193831	+	0.353022i
$297$	27.5771			1.60019
$298$	−13.7994	−	11.5791i	−0.799380	−	0.670760i
$299$	3.07107	−	2.57694i	0.177605	−	0.149028i
$300$	−0.146472	−	0.830682i	−0.00845654	−	0.0479594i
$301$	1.56665	+	0.570214i	0.0903002	+	0.0328666i
$302$	0.731616			0.0420998
$303$	1.80371	+	0.656497i	0.103621	+	0.0377148i
$304$	−2.40309	+	4.16228i	−0.137827	+	0.238723i
$305$	1.63364	−	9.26486i	0.0935422	−	0.530504i
$306$	−1.80694	−	3.12971i	−0.103296	−	0.178914i
$307$	8.56114	−	14.8283i	0.488610	−	0.846297i	−0.511304	−	0.859400i	$-0.670837\pi$
$307$	8.56114	−	14.8283i	0.488610	−	0.846297i	0.999914	+	0.0131026i	$0.00417081\pi$
$308$	−1.42189	−	1.19311i	−0.0810198	−	0.0679837i
$309$	−0.208522	−	1.18259i	−0.0118624	−	0.0672749i
$310$	4.73145	+	8.19511i	0.268728	+	0.465451i
$311$	0.657803	−	0.239421i	0.0373006	−	0.0135763i	−0.323302	−	0.946296i	$-0.604793\pi$
$311$	0.657803	−	0.239421i	0.0373006	−	0.0135763i	0.360603	+	0.932719i	$0.382571\pi$
$312$	−0.477781	+	0.173898i	−0.0270490	+	0.00984504i
$313$	2.98080	−	16.9050i	0.168485	−	0.955524i	−0.776914	−	0.629607i	$-0.783216\pi$
$313$	2.98080	−	16.9050i	0.168485	−	0.955524i	0.945398	−	0.325917i	$-0.105673\pi$
$314$	14.2569	−	11.9629i	0.804561	−	0.675107i
$315$	0.526367	−	0.441674i	0.0296574	−	0.0248855i
$316$	−1.18019	+	6.69320i	−0.0663909	+	0.376522i
$317$	22.2682	−	8.10496i	1.25071	−	0.455220i	0.370066	−	0.929006i	$-0.379335\pi$
$317$	22.2682	−	8.10496i	1.25071	−	0.455220i	0.880640	+	0.473786i	$0.157113\pi$
$318$	−10.8319	+	3.94249i	−0.607422	+	0.221084i
$319$	−0.304912	−	0.528124i	−0.0170718	−	0.0295692i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$	−10.6449	−	8.93212i	−0.594139	−	0.498542i
$322$	−0.998451	+	1.72937i	−0.0556415	+	0.0963739i
$323$	3.79481	+	6.57281i	0.211149	+	0.365721i
$324$	0.538802	−	3.05570i	0.0299334	−	0.169761i
$325$	0.301391	−	0.522024i	0.0167182	−	0.0289567i
$326$	−5.49541	−	2.00017i	−0.304363	−	0.110779i
$327$	−6.35176			−0.351253
$328$	7.92500	+	2.88446i	0.437585	+	0.159268i
$329$	0.616374	+	3.49563i	0.0339818	+	0.192720i
$330$	−3.99456	+	3.35183i	−0.219893	+	0.184512i
$331$	−15.3491	−	12.8794i	−0.843662	−	0.707917i	0.114722	−	0.993398i	$-0.463402\pi$
$331$	−15.3491	−	12.8794i	−0.843662	−	0.707917i	−0.958384	+	0.285481i	$0.907847\pi$
$332$	8.40868			0.461486
$333$	4.03678	+	13.3223i	0.221214	+	0.730059i
$334$	12.2754			0.671678
$335$	−3.05978	−	2.56746i	−0.167174	−	0.140276i
$336$	0.194007	−	0.162791i	0.0105840	−	0.00888100i
$337$	−0.219116	−	1.24267i	−0.0119360	−	0.0676924i	0.978258	−	0.207392i	$-0.0664975\pi$
$337$	−0.219116	−	1.24267i	−0.0119360	−	0.0676924i	−0.990194	+	0.139699i	$0.955386\pi$
$338$	11.8746	+	4.32199i	0.645892	+	0.235085i
$339$	−1.81374			−0.0985087
$340$	1.48390	+	0.540097i	0.0804759	+	0.0292909i
$341$	29.2500	−	50.6625i	1.58398	−	2.74353i
$342$	−1.90996	+	10.8319i	−0.103279	+	0.585724i
$343$	−2.08821	−	3.61688i	−0.112753	−	0.195293i
$344$	−2.77636	+	4.80879i	−0.149691	+	0.259273i
$345$	4.29747	+	3.60601i	0.231368	+	0.194141i
$346$	−0.586678	−	3.32722i	−0.0315400	−	0.178872i
$347$	−14.2697	−	24.7159i	−0.766039	−	1.32682i	−0.939696	−	0.342012i	$-0.888892\pi$
$347$	−14.2697	−	24.7159i	−0.766039	−	1.32682i	0.173657	−	0.984806i	$-0.444442\pi$
$348$	0.0781884	−	0.0284582i	0.00419134	−	0.00152552i
$349$	9.19485	−	3.34665i	0.492189	−	0.179142i	−0.0839884	−	0.996467i	$-0.526766\pi$
$349$	9.19485	−	3.34665i	0.492189	−	0.179142i	0.576178	+	0.817325i	$0.304544\pi$
$350$	−0.0521376	+	0.295687i	−0.00278687	+	0.0158051i
$351$	−2.05983	+	1.72840i	−0.109945	+	0.0922552i
$352$	4.73572	−	3.97374i	0.252415	−	0.211801i
$353$	−2.69112	+	15.2621i	−0.143234	+	0.812320i	0.825534	+	0.564352i	$0.190874\pi$
$353$	−2.69112	+	15.2621i	−0.143234	+	0.812320i	−0.968768	+	0.247968i	$0.920237\pi$
$354$	−9.26512	+	3.37223i	−0.492436	+	0.179232i
$355$	7.70034	−	2.80269i	0.408691	−	0.148751i
$356$	2.84593	+	4.92929i	0.150834	+	0.261252i
$357$	−0.0694471	−	0.393854i	−0.00367553	−	0.0208450i
$358$	−2.79645	−	2.34650i	−0.147797	−	0.124017i
$359$	6.54642	−	11.3387i	0.345507	−	0.598435i	−0.639939	−	0.768426i	$-0.721040\pi$
$359$	6.54642	−	11.3387i	0.345507	−	0.598435i	0.985446	+	0.169991i	$0.0543738\pi$
$360$	1.14426	+	1.98191i	0.0603076	+	0.104456i
$361$	0.711861	−	4.03716i	0.0374664	−	0.212482i
$362$	−7.38396	+	12.7894i	−0.388092	+	0.672195i
$363$	21.5734	+	7.85209i	1.13231	+	0.412128i
$364$	0.180984			0.00948615
$365$	3.89582	+	1.41796i	0.203916	+	0.0742195i
$366$	−1.37797	−	7.81487i	−0.0720278	−	0.408490i
$367$	16.9882	−	14.2548i	0.886778	−	0.744095i	−0.0807835	−	0.996732i	$-0.525742\pi$
$367$	16.9882	−	14.2548i	0.886778	−	0.744095i	0.967561	+	0.252637i	$0.0812978\pi$
$368$	−5.09483	−	4.27507i	−0.265587	−	0.222854i
$369$	19.3004			1.00474
$370$	−5.09316	−	3.32561i	−0.264781	−	0.172890i
$371$	4.10314			0.213024
$372$	6.11450	+	5.13068i	0.317022	+	0.266013i
$373$	−16.9581	+	14.2296i	−0.878059	+	0.736779i	−0.965779	−	0.259366i	$-0.916486\pi$
$373$	−16.9581	+	14.2296i	−0.878059	+	0.736779i	0.0877199	+	0.996145i	$0.472042\pi$
$374$	−1.69520	−	9.61398i	−0.0876569	−	0.497127i
$375$	0.792627	+	0.288493i	0.0409311	+	0.0148977i
$376$	−11.8221			−0.609677
$377$	0.0558752	+	0.0203369i	0.00287772	+	0.00104740i
$378$	0.669680	−	1.15992i	0.0344446	−	0.0596599i
$379$	3.96993	−	22.5146i	0.203921	−	1.15650i	−0.695207	−	0.718810i	$-0.744687\pi$
$379$	3.96993	−	22.5146i	0.203921	−	1.15650i	0.899128	−	0.437686i	$-0.144202\pi$
$380$	−2.40309	−	4.16228i	−0.123276	−	0.213521i
$381$	3.81872	−	6.61422i	0.195639	−	0.338857i
$382$	−17.8029	−	14.9384i	−0.910873	−	0.764313i
$383$	−2.20489	−	12.5046i	−0.112665	−	0.638954i	−0.987880	−	0.155220i	$-0.950391\pi$
$383$	−2.20489	−	12.5046i	−0.112665	−	0.638954i	0.875215	−	0.483734i	$-0.160720\pi$
$384$	0.421748	+	0.730489i	0.0215222	+	0.0372776i
$385$	1.74421	−	0.634840i	0.0888931	−	0.0323544i
$386$	4.58072	−	1.66725i	0.233153	−	0.0848606i
$387$	−2.20663	+	12.5144i	−0.112169	+	0.636143i
$388$	8.16531	−	6.85151i	0.414531	−	0.347833i
$389$	19.2322	−	16.1377i	0.975111	−	0.818215i	−0.00823399	−	0.999966i	$-0.502621\pi$
$389$	19.2322	−	16.1377i	0.975111	−	0.818215i	0.983345	+	0.181751i	$0.0581765\pi$
$390$	0.0882904	−	0.500720i	0.00447076	−	0.0253549i
$391$	−9.86919	+	3.59209i	−0.499106	+	0.181660i
$392$	6.49314	−	2.36331i	0.327953	−	0.119365i
$393$	−6.42134	−	11.1221i	−0.323914	−	0.561035i
$394$	−2.65602	−	15.0630i	−0.133808	−	0.758864i
$395$	−5.20638	−	4.36867i	−0.261961	−	0.219812i
$396$	7.07384	−	12.2523i	0.355474	−	0.615699i
$397$	−6.32870	−	10.9616i	−0.317628	−	0.550148i	0.662364	−	0.749182i	$-0.269553\pi$
$397$	−6.32870	−	10.9616i	−0.317628	−	0.550148i	−0.979993	+	0.199033i	$0.936220\pi$
$398$	0.933633	−	5.29490i	0.0467988	−	0.265409i
$399$	−0.608604	+	1.05413i	−0.0304683	+	0.0527727i
$400$	−0.939693	−	0.342020i	−0.0469846	−	0.0171010i
$401$	11.5087			0.574719			0.287359	−	0.957823i	$-0.407223\pi$
$401$	11.5087			0.574719			0.287359	+	0.957823i	$0.407223\pi$
$402$	−3.16596	−	1.15232i	−0.157904	−	0.0574723i
$403$	0.990499	+	5.61740i	0.0493403	+	0.279823i
$404$	1.74322	−	1.46273i	0.0867284	−	0.0727738i
$405$	2.37691	+	1.99447i	0.118110	+	0.0991058i
$406$	−0.0296179			−0.00146991
$407$	−2.06158	+	37.5473i	−0.102189	+	1.86115i
$408$	1.33200			0.0659436
$409$	−6.98644	−	5.86232i	−0.345457	−	0.289873i	0.453506	−	0.891253i	$-0.350173\pi$
$409$	−6.98644	−	5.86232i	−0.345457	−	0.289873i	−0.798963	+	0.601380i	$0.794618\pi$
$410$	−6.46052	+	5.42102i	−0.319062	+	0.267725i
$411$	−0.441298	−	2.50272i	−0.0217676	−	0.123450i
$412$	−1.33778	−	0.486911i	−0.0659075	−	0.0239884i
$413$	3.50964			0.172698
$414$	−14.3026	−	5.20573i	−0.702935	−	0.255847i
$415$	−4.20434	+	7.28213i	−0.206383	+	0.357466i
$416$	−0.104672	+	0.593624i	−0.00513196	+	0.0291048i
$417$	−3.47346	−	6.01622i	−0.170096	−	0.294615i
$418$	−14.8560	+	25.7314i	−0.726632	+	1.25856i
$419$	−15.9482	−	13.3821i	−0.779121	−	0.653760i	0.163906	−	0.986476i	$-0.447591\pi$
$419$	−15.9482	−	13.3821i	−0.779121	−	0.653760i	−0.943027	+	0.332716i	$0.892035\pi$
$420$	0.0439779	+	0.249411i	0.00214590	+	0.0121700i
$421$	7.80106	+	13.5118i	0.380200	+	0.658526i	0.991091	−	0.133189i	$-0.0425217\pi$
$421$	7.80106	+	13.5118i	0.380200	+	0.658526i	−0.610890	+	0.791715i	$0.709188\pi$
$422$	20.2495	−	7.37022i	0.985731	−	0.358777i
$423$	−25.4234	+	9.25335i	−1.23613	+	0.449913i
$424$	−2.37304	+	13.4582i	−0.115245	+	0.653588i
$425$	−1.20969	+	1.01505i	−0.0586785	+	0.0492371i
$426$	5.29494	−	4.44298i	0.256541	−	0.215263i
$427$	−0.490499	+	2.78176i	−0.0237369	+	0.134619i
$428$	−15.4807	+	5.63450i	−0.748286	+	0.272354i
$429$	−2.95366	+	1.07505i	−0.142604	+	0.0519037i
$430$	−2.77636	−	4.80879i	−0.133888	−	0.231901i
$431$	−1.46137	−	8.28783i	−0.0703917	−	0.399211i	−0.999563	−	0.0295615i	$-0.990589\pi$
$431$	−1.46137	−	8.28783i	−0.0703917	−	0.399211i	0.929171	−	0.369649i	$-0.120522\pi$
$432$	3.41720	+	2.86737i	0.164410	+	0.137957i
$433$	3.70995	−	6.42583i	0.178289	−	0.308806i	−0.763006	−	0.646392i	$-0.776277\pi$
$433$	3.70995	−	6.42583i	0.178289	−	0.308806i	0.941295	+	0.337586i	$0.109610\pi$
$434$	−1.42061	−	2.46057i	−0.0681914	−	0.118111i
$435$	−0.0144486	+	0.0819422i	−0.000692759	+	0.00392883i
$436$	−3.76514	+	6.52141i	−0.180317	+	0.312319i
$437$	30.0374	+	10.9327i	1.43688	+	0.522983i
$438$	3.49700			0.167093
$439$	−5.95965	−	2.16913i	−0.284438	−	0.103527i	0.195861	−	0.980632i	$-0.437250\pi$
$439$	−5.95965	−	2.16913i	−0.284438	−	0.103527i	−0.480300	+	0.877105i	$0.659472\pi$
$440$	1.07350	+	6.08812i	0.0511771	+	0.290240i
$441$	12.1137	−	10.1646i	0.576842	−	0.484028i
$442$	0.729178	+	0.611853i	0.0346835	+	0.0291029i
$443$	−23.3690			−1.11029			−0.555147	−	0.831752i	$-0.687338\pi$
$443$	−23.3690			−1.11029			−0.555147	+	0.831752i	$0.687338\pi$
$444$	−4.99640	−	1.16663i	−0.237118	−	0.0553657i
$445$	−5.69185			−0.269820
$446$	0.262667	+	0.220404i	0.0124377	+	0.0104364i
$447$	11.6398	−	9.76694i	0.550543	−	0.461960i
$448$	−0.0521376	−	0.295687i	−0.00246327	−	0.0139699i
$449$	−0.739665	−	0.269216i	−0.0349069	−	0.0127051i	0.324508	−	0.945883i	$-0.394801\pi$
$449$	−0.739665	−	0.269216i	−0.0349069	−	0.0127051i	−0.359415	+	0.933178i	$0.617024\pi$
$450$	−2.28851			−0.107882
$451$	48.9927	+	17.8319i	2.30697	+	0.839670i
$452$	−1.07513	+	1.86218i	−0.0505699	+	0.0875896i
$453$	−0.107161	+	0.607740i	−0.00503486	+	0.0285541i
$454$	11.0878	+	19.2046i	0.520375	+	0.901315i
$455$	−0.0904921	+	0.156737i	−0.00424234	+	0.00734794i
$456$	−3.10555	−	2.60586i	−0.145431	−	0.122031i
$457$	−4.52280	−	25.6501i	−0.211568	−	1.19986i	−0.886764	−	0.462222i	$-0.847052\pi$
$457$	−4.52280	−	25.6501i	−0.211568	−	1.19986i	0.675196	−	0.737638i	$-0.264059\pi$
$458$	−1.14622	−	1.98532i	−0.0535595	−	0.0927678i
$459$	6.61946	−	2.40929i	0.308970	−	0.112456i
$460$	6.24974	−	2.27472i	0.291396	−	0.106059i
$461$	−2.30860	+	13.0927i	−0.107522	+	0.609788i	0.882661	+	0.470010i	$0.155750\pi$
$461$	−2.30860	+	13.0927i	−0.107522	+	0.609788i	−0.990183	+	0.139777i	$0.955361\pi$
$462$	1.19936	−	1.00638i	0.0557993	−	0.0468212i
$463$	12.9258	−	10.8460i	0.600711	−	0.504057i	−0.290963	−	0.956734i	$-0.593976\pi$
$463$	12.9258	−	10.8460i	0.600711	−	0.504057i	0.891674	+	0.452678i	$0.149531\pi$
$464$	0.0171294	−	0.0971459i	0.000795215	−	0.00450989i
$465$	−7.50055	+	2.72998i	−0.347830	+	0.126600i
$466$	2.09668	−	0.763128i	0.0971266	−	0.0353512i
$467$	4.48592	+	7.76984i	0.207584	+	0.359545i	0.950953	−	0.309336i	$-0.100107\pi$
$467$	4.48592	+	7.76984i	0.207584	+	0.359545i	−0.743369	+	0.668881i	$0.766773\pi$
$468$	0.239543	+	1.35852i	0.0110729	+	0.0627975i
$469$	0.918696	+	0.770877i	0.0424214	+	0.0355958i
$470$	5.91104	−	10.2382i	0.272656	−	0.472254i
$471$	7.84916	+	13.5951i	0.361670	+	0.626431i
$472$	−2.02980	+	11.5115i	−0.0934289	+	0.529862i
$473$	−17.1636	+	29.7281i	−0.789181	+	1.36690i
$474$	−5.38705	−	1.96073i	−0.247435	−	0.0900591i
$475$	4.80619			0.220523
$476$	−0.445540	−	0.162163i	−0.0204213	−	0.00743274i
$477$	5.43074	+	30.7993i	0.248657	+	1.41020i
$478$	−18.3929	+	15.4334i	−0.841269	+	0.705909i
$479$	−26.5791	−	22.3025i	−1.21443	−	1.01903i	−0.999097	−	0.0424878i	$-0.986472\pi$
$479$	−26.5791	−	22.3025i	−1.21443	−	1.01903i	−0.215334	−	0.976541i	$-0.569084\pi$
$480$	−0.843496			−0.0385002
$481$	−2.19930	−	2.93375i	−0.100279	−	0.133767i
$482$	−0.194274			−0.00884895
$483$	−1.29031	−	1.08270i	−0.0587111	−	0.0492645i
$484$	20.8499	−	17.4952i	0.947723	−	0.795234i
$485$	1.85093	+	10.4971i	0.0840462	+	0.476650i
$486$	15.0349	+	5.47224i	0.681995	+	0.248226i
$487$	6.94631			0.314768			0.157384	−	0.987538i	$-0.449694\pi$
$487$	6.94631			0.314768			0.157384	+	0.987538i	$0.449694\pi$
$488$	−8.84042	−	3.21765i	−0.400187	−	0.145656i
$489$	2.46642	−	4.27197i	0.111536	−	0.193185i
$490$	−1.19988	+	6.80487i	−0.0542052	+	0.307413i
$491$	−4.76317	−	8.25005i	−0.214959	−	0.372320i	0.738301	−	0.674471i	$-0.235628\pi$
$491$	−4.76317	−	8.25005i	−0.214959	−	0.372320i	−0.953260	+	0.302152i	$0.902295\pi$
$492$	−3.55686	+	6.16066i	−0.160356	+	0.277744i
$493$	−0.119329	−	0.100129i	−0.00537432	−	0.00450959i
$494$	−0.503073	−	2.85307i	−0.0226343	−	0.128366i
$495$	7.07384	+	12.2523i	0.317946	+	0.550698i
$496$	8.89221	−	3.23650i	0.399272	−	0.145323i
$497$	−2.31201	+	0.841504i	−0.103708	+	0.0377466i
$498$	−1.23163	+	6.98494i	−0.0551908	+	0.313003i
$499$	6.72944	−	5.64667i	0.301251	−	0.252780i	−0.479614	−	0.877480i	$-0.659223\pi$
$499$	6.72944	−	5.64667i	0.301251	−	0.252780i	0.780865	+	0.624700i	$0.214779\pi$
$500$	0.766044	−	0.642788i	0.0342585	−	0.0287463i
$501$	−1.79799	+	10.1969i	−0.0803283	+	0.455565i
$502$	13.2825	−	4.83445i	0.592829	−	0.215772i
$503$	−32.2136	+	11.7248i	−1.43633	+	0.522783i	−0.938740	−	0.344628i	$-0.888005\pi$
$503$	−32.2136	+	11.7248i	−1.43633	+	0.522783i	−0.497594	+	0.867410i	$0.665783\pi$
$504$	−0.343561	−	0.595066i	−0.0153034	−	0.0265063i
$505$	0.395156	+	2.24104i	0.0175842	+	0.0997250i
$506$	−31.4965	−	26.4287i	−1.40019	−	1.17490i
$507$	−5.32949	+	9.23094i	−0.236691	+	0.409960i
$508$	−4.52725	−	7.84144i	−0.200864	−	0.347907i
$509$	−3.47453	+	19.7051i	−0.154006	+	0.873411i	0.805683	+	0.592347i	$0.201799\pi$
$509$	−3.47453	+	19.7051i	−0.154006	+	0.873411i	−0.959689	+	0.281064i	$0.909313\pi$
$510$	−0.665998	+	1.15354i	−0.0294909	+	0.0510797i
$511$	−1.16971	−	0.425741i	−0.0517451	−	0.0188337i
$512$	1.00000			0.0441942
$513$	−20.1467	−	7.33279i	−0.889498	−	0.323751i
$514$	4.54526	+	25.7775i	0.200483	+	1.13700i
$515$	1.09057	−	0.915093i	0.0480561	−	0.0403238i
$516$	−3.58792	−	3.01062i	−0.157949	−	0.132535i
$517$	−73.0845			−3.21425
$518$	1.52921	+	0.998509i	0.0671898	+	0.0438720i
$519$	2.84979			0.125092
$520$	−0.461757	−	0.387461i	−0.0202494	−	0.0169913i
$521$	−12.4510	+	10.4477i	−0.545490	+	0.457720i	−0.873410	−	0.486985i	$-0.838097\pi$
$521$	−12.4510	+	10.4477i	−0.545490	+	0.457720i	0.327921	+	0.944705i	$0.393652\pi$
$522$	−0.0392010	−	0.222320i	−0.00171578	−	0.00973067i
$523$	−19.5630	−	7.12034i	−0.855429	−	0.311351i	−0.123177	−	0.992385i	$-0.539308\pi$
$523$	−19.5630	−	7.12034i	−0.855429	−	0.311351i	−0.732252	+	0.681034i	$0.761531\pi$
$524$	−15.2255			−0.665131
$525$	−0.237985	−	0.0866195i	−0.0103865	−	0.00378039i
$526$	−3.72730	+	6.45588i	−0.162518	+	0.281490i
$527$	2.59486	−	14.7162i	0.113034	−	0.641047i
$528$	2.60726	+	4.51591i	0.113467	+	0.196530i
$529$	−10.6168	+	18.3888i	−0.461599	+	0.799514i
$530$	−10.4686	−	8.78421i	−0.454728	−	0.381562i
$531$	4.64522	+	26.3443i	0.201585	+	1.14325i
$532$	0.721525	+	1.24972i	0.0312821	+	0.0541822i
$533$	−4.77704	+	1.73870i	−0.206917	+	0.0753115i
$534$	−4.51152	+	1.64206i	−0.195233	+	0.0710588i
$535$	2.86071	−	16.2239i	0.123679	−	0.701420i
$536$	−3.05978	+	2.56746i	−0.132163	+	0.110898i
$537$	2.35880	−	1.97927i	0.101790	−	0.0854117i
$538$	−1.26253	+	7.16014i	−0.0544313	+	0.308695i
$539$	40.1408	−	14.6101i	1.72899	−	0.629300i
$540$	−4.19182	+	1.52570i	−0.180387	+	0.0656556i
$541$	22.8264	+	39.5365i	0.981383	+	1.69981i	0.657020	+	0.753873i	$0.271817\pi$
$541$	22.8264	+	39.5365i	0.981383	+	1.69981i	0.324364	+	0.945932i	$0.394850\pi$
$542$	2.93379	+	16.6384i	0.126017	+	0.714679i
$543$	−9.54237	−	8.00700i	−0.409502	−	0.343613i
$544$	0.789568	−	1.36757i	0.0338525	−	0.0586342i
$545$	−3.76514	−	6.52141i	−0.161281	−	0.279346i
$546$	−0.0265091	+	0.150340i	−0.00113448	+	0.00643397i
$547$	7.61000	−	13.1809i	0.325380	−	0.563575i	−0.656209	−	0.754579i	$-0.727841\pi$
$547$	7.61000	−	13.1809i	0.325380	−	0.563575i	0.981589	+	0.191004i	$0.0611745\pi$
$548$	−2.83116	−	1.03046i	−0.120941	−	0.0440189i
$549$	−21.5298			−0.918871
$550$	−5.80922	−	2.11438i	−0.247706	−	0.0901576i
$551$	0.0823273	+	0.466902i	0.00350726	+	0.0198907i
$552$	4.29747	−	3.60601i	0.182913	−	0.153482i
$553$	1.56321	+	1.31169i	0.0664744	+	0.0557786i
$554$	0.634804			0.0269702
$555$	3.50853	−	3.74369i	0.148929	−	0.158911i
$556$	−8.23587			−0.349279
$557$	32.5018	+	27.2723i	1.37715	+	1.15556i	0.970255	+	0.242086i	$0.0778315\pi$
$557$	32.5018	+	27.2723i	1.37715	+	1.15556i	0.406891	+	0.913477i	$0.366613\pi$
$558$	16.5894	−	13.9202i	0.702287	−	0.589288i
$559$	−0.581213	−	3.29622i	−0.0245827	−	0.139415i
$560$	0.282141	+	0.102691i	0.0119226	+	0.00433949i
$561$	8.23445			0.347659
$562$	−11.4427	−	4.16481i	−0.482682	−	0.175682i
$563$	−2.94428	+	5.09964i	−0.124087	+	0.214924i	−0.921376	−	0.388674i	$-0.872933\pi$
$563$	−2.94428	+	5.09964i	−0.124087	+	0.214924i	0.797289	+	0.603598i	$0.206267\pi$
$564$	1.73160	−	9.82038i	0.0729134	−	0.413513i
$565$	−1.07513	−	1.86218i	−0.0452311	−	0.0783425i
$566$	−13.4682	+	23.3276i	−0.566110	+	0.980531i
$567$	−0.713664	−	0.598835i	−0.0299711	−	0.0251487i
$568$	−1.42296	−	8.07003i	−0.0597063	−	0.338611i
$569$	−11.8876	−	20.5900i	−0.498355	−	0.863176i	0.501643	−	0.865074i	$-0.332729\pi$
$569$	−11.8876	−	20.5900i	−0.498355	−	0.863176i	−0.999998	+	0.00189879i	$0.999396\pi$
$570$	3.80952	−	1.38655i	0.159563	−	0.0580762i
$571$	20.3019	−	7.38928i	0.849607	−	0.309232i	0.119727	−	0.992807i	$-0.461798\pi$
$571$	20.3019	−	7.38928i	0.849607	−	0.309232i	0.729880	+	0.683575i	$0.239576\pi$
$572$	−0.647086	+	3.66981i	−0.0270560	+	0.153442i
$573$	15.0166	−	12.6005i	0.627329	−	0.526392i
$574$	1.93976	−	1.62765i	0.0809640	−	0.0679369i
$575$	−1.15490	+	6.54979i	−0.0481629	+	0.273145i
$576$	2.15050	−	0.782718i	0.0896041	−	0.0326132i
$577$	−7.75523	+	2.82267i	−0.322854	+	0.117509i	−0.498363	−	0.866969i	$-0.666065\pi$
$577$	−7.75523	+	2.82267i	−0.322854	+	0.117509i	0.175508	+	0.984478i	$0.443843\pi$
$578$	7.25316	+	12.5628i	0.301692	+	0.522546i
$579$	0.714006	+	4.04933i	0.0296731	+	0.168284i
$580$	0.0755661	+	0.0634075i	0.00313771	+	0.00263285i
$581$	1.26235	−	2.18645i	0.0523710	−	0.0907092i
$582$	4.49544	+	7.78633i	0.186342	+	0.322754i
$583$	−14.6702	+	83.1991i	−0.607580	+	3.44575i
$584$	2.07292	−	3.59040i	0.0857781	−	0.148572i
$585$	−1.29628	−	0.471808i	−0.0535946	−	0.0195069i
$586$	0.0203795			0.000841870
$587$	−40.3454	−	14.6845i	−1.66523	−	0.606095i	−0.674060	−	0.738676i	$-0.735451\pi$
$587$	−40.3454	−	14.6845i	−1.66523	−	0.606095i	−0.991172	+	0.132581i	$0.957673\pi$
$588$	1.01210	+	5.73989i	0.0417382	+	0.236709i
$589$	−34.8400	+	29.2343i	−1.43556	+	1.20458i
$590$	−8.95439	−	7.51363i	−0.368646	−	0.309331i
$591$	12.9016			0.530701
$592$	−4.15950	+	4.43830i	−0.170955	+	0.182413i
$593$	23.0900			0.948194			0.474097	−	0.880473i	$-0.342775\pi$
$593$	23.0900			0.948194			0.474097	+	0.880473i	$0.342775\pi$
$594$	21.1253	+	17.7262i	0.866781	+	0.727316i
$595$	0.363207	−	0.304767i	0.0148900	−	0.0124942i
$596$	−3.12808	−	17.7402i	−0.128131	−	0.726668i
$597$	4.26162	+	1.55110i	0.174417	+	0.0634825i
$598$	4.00900			0.163940
$599$	20.5272	+	7.47131i	0.838721	+	0.305269i	0.725433	−	0.688293i	$-0.241640\pi$
$599$	20.5272	+	7.47131i	0.838721	+	0.305269i	0.113288	+	0.993562i	$0.463862\pi$
$600$	0.421748	−	0.730489i	0.0172178	−	0.0298221i
$601$	0.655846	−	3.71949i	0.0267525	−	0.151721i	−0.968505	−	0.248993i	$-0.919900\pi$
$601$	0.655846	−	3.71949i	0.0267525	−	0.151721i	0.995258	+	0.0972717i	$0.0310116\pi$
$602$	0.833597	+	1.44383i	0.0339749	+	0.0588462i
$603$	−4.57047	+	7.91628i	−0.186124	+	0.322376i
$604$	0.560450	+	0.470274i	0.0228044	+	0.0191352i
$605$	4.72629	+	26.8041i	0.192151	+	1.08974i
$606$	0.959735	+	1.66231i	0.0389866	+	0.0675267i
$607$	−8.93674	+	3.25271i	−0.362731	+	0.132023i	−0.516955	−	0.856013i	$-0.672935\pi$
$607$	−8.93674	+	3.25271i	−0.362731	+	0.132023i	0.154224	+	0.988036i	$0.450712\pi$
$608$	−4.51634	+	1.64381i	−0.183162	+	0.0666654i
$609$	0.00433818	−	0.0246030i	0.000175792	−	0.000996965i
$610$	7.20678	−	6.04721i	0.291794	−	0.244844i
$611$	5.45893	−	4.58059i	0.220845	−	0.185311i
$612$	0.627543	−	3.55897i	0.0253669	−	0.143863i
$613$	37.4188	−	13.6193i	1.51133	−	0.550079i	0.552365	−	0.833602i	$-0.313725\pi$
$613$	37.4188	−	13.6193i	1.51133	−	0.550079i	0.958966	+	0.283523i	$0.0915031\pi$
$614$	16.0897	−	5.85616i	0.649326	−	0.236335i
$615$	−3.55686	−	6.16066i	−0.143426	−	0.248422i
$616$	−0.322317	−	1.82795i	−0.0129865	−	0.0736502i
$617$	−21.8260	−	18.3142i	−0.878681	−	0.737301i	0.0872262	−	0.996189i	$-0.472200\pi$
$617$	−21.8260	−	18.3142i	−0.878681	−	0.737301i	−0.965908	+	0.258887i	$0.916644\pi$
$618$	0.600414	−	1.03995i	0.0241522	−	0.0418328i
$619$	−7.61137	−	13.1833i	−0.305927	−	0.529881i	0.671540	−	0.740968i	$-0.265633\pi$
$619$	−7.61137	−	13.1833i	−0.305927	−	0.529881i	−0.977467	+	0.211087i	$0.932300\pi$
$620$	−1.64321	+	9.31913i	−0.0659931	+	0.374265i
$621$	14.8342	−	25.6935i	0.595274	−	1.03105i
$622$	0.657803	+	0.239421i	0.0263755	+	0.00959989i
$623$	1.70897			0.0684685
$624$	−0.477781	−	0.173898i	−0.0191266	−	0.00696150i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	13.1497	−	11.0339i	0.525568	−	0.441004i
$627$	−19.1986	−	16.1095i	−0.766719	−	0.643353i
$628$	18.6110			0.742660
$629$	2.78549	+	9.19277i	0.111065	+	0.366540i
$630$	0.687123			0.0273756
$631$	−15.3291	−	12.8626i	−0.610240	−	0.512053i	0.284478	−	0.958682i	$-0.408180\pi$
$631$	−15.3291	−	12.8626i	−0.610240	−	0.512053i	−0.894719	+	0.446630i	$0.852624\pi$
$632$	−5.20638	+	4.36867i	−0.207099	+	0.173776i
$633$	3.15633	+	17.9004i	0.125453	+	0.711478i
$634$	22.2682	+	8.10496i	0.884383	+	0.321889i
$635$	9.05451			0.359317
$636$	−10.8319	−	3.94249i	−0.429513	−	0.156330i
$637$	−2.08257	+	3.60711i	−0.0825142	+	0.142919i
$638$	0.105895	−	0.600560i	0.00419242	−	0.0237764i
$639$	−9.37664	−	16.2408i	−0.370934	−	0.642477i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	4.60901	+	3.86742i	0.182045	+	0.152754i	0.729256	−	0.684241i	$-0.239866\pi$
$641$	4.60901	+	3.86742i	0.182045	+	0.152754i	−0.547211	+	0.836994i	$0.684311\pi$
$642$	−2.41300	−	13.6848i	−0.0952335	−	0.540096i
$643$	4.83407	+	8.37286i	0.190637	+	0.330193i	0.945462	−	0.325734i	$-0.105611\pi$
$643$	4.83407	+	8.37286i	0.190637	+	0.330193i	−0.754824	+	0.655927i	$0.772278\pi$
$644$	−1.87647	+	0.682981i	−0.0739434	+	0.0269132i
$645$	4.40123	−	1.60192i	0.173298	−	0.0630755i
$646$	−1.31793	+	7.47432i	−0.0518531	+	0.294073i
$647$	−13.2083	+	11.0831i	−0.519272	+	0.435721i	−0.864378	−	0.502843i	$-0.832288\pi$
$647$	−13.2083	+	11.0831i	−0.519272	+	0.435721i	0.345106	+	0.938564i	$0.387843\pi$
$648$	2.37691	−	1.99447i	0.0933739	−	0.0783500i
$649$	−12.5483	+	71.1648i	−0.492563	+	2.79346i
$650$	0.566429	−	0.206163i	0.0222172	−	0.00808640i
$651$	2.25203	−	0.819671i	0.0882639	−	0.0321254i
$652$	−2.92405	−	5.06460i	−0.114515	−	0.198345i
$653$	−6.90305	−	39.1491i	−0.270137	−	1.53202i	−0.753996	−	0.656879i	$-0.771876\pi$
$653$	−6.90305	−	39.1491i	−0.270137	−	1.53202i	0.483859	−	0.875146i	$-0.339235\pi$
$654$	−4.86573	−	4.08283i	−0.190265	−	0.159651i
$655$	7.61277	−	13.1857i	0.297455	−	0.515208i
$656$	4.21680	+	7.30372i	0.164638	+	0.285162i
$657$	1.64754	−	9.34368i	0.0642767	−	0.364531i
$658$	−1.77478	+	3.07401i	−0.0691881	+	0.119837i
$659$	−43.3078	−	15.7627i	−1.68703	−	0.614029i	−0.692784	−	0.721145i	$-0.743616\pi$
$659$	−43.3078	−	15.7627i	−1.68703	−	0.614029i	−0.994247	+	0.107116i	$0.965838\pi$
$660$	−5.21453			−0.202975
$661$	−12.9607	−	4.71732i	−0.504114	−	0.183483i	0.0774293	−	0.996998i	$-0.475329\pi$
$661$	−12.9607	−	4.71732i	−0.504114	−	0.183483i	−0.581544	+	0.813515i	$0.697551\pi$
$662$	−3.47936	−	19.7324i	−0.135229	−	0.766922i
$663$	−0.615059	+	0.516096i	−0.0238869	+	0.0200435i
$664$	6.44142	+	5.40500i	0.249976	+	0.209754i
$665$	−1.44305			−0.0559591
$666$	−5.47107	+	12.8003i	−0.212000	+	0.496001i
$667$	−0.656068			−0.0254031
$668$	9.40347	+	7.89045i	0.363831	+	0.305291i
$669$	−0.221559	+	0.185910i	−0.00856597	+	0.00718770i
$670$	−0.693597	−	3.93358i	−0.0267960	−	0.151968i
$671$	−54.6519	−	19.8916i	−2.10981	−	0.767909i
$672$	0.253258			0.00976966
$673$	39.0378	+	14.2086i	1.50480	+	0.547702i	0.957298	−	0.289104i	$-0.0933573\pi$
$673$	39.0378	+	14.2086i	1.50480	+	0.547702i	0.547500	+	0.836806i	$0.315580\pi$
$674$	0.630918	−	1.09278i	0.0243021	−	0.0420924i
$675$	0.774617	−	4.39307i	0.0298150	−	0.169089i
$676$	6.31833	+	10.9437i	0.243013	+	0.420910i
$677$	−7.15746	+	12.3971i	−0.275084	+	0.476459i	−0.970156	−	0.242481i	$-0.922039\pi$
$677$	−7.15746	+	12.3971i	−0.275084	+	0.476459i	0.695073	+	0.718940i	$0.255372\pi$
$678$	−1.38940	−	1.16585i	−0.0533597	−	0.0447741i
$679$	−0.555738	−	3.15175i	−0.0213273	−	0.120953i
$680$	0.789568	+	1.36757i	0.0302786	+	0.0524440i
$681$	−17.5769	+	6.39748i	−0.673550	+	0.245152i
$682$	54.9720	−	20.0082i	2.10499	−	0.766153i
$683$	2.45920	−	13.9468i	0.0940985	−	0.533659i	−0.900921	−	0.433982i	$-0.857108\pi$
$683$	2.45920	−	13.9468i	0.0940985	−	0.533659i	0.995020	−	0.0996768i	$-0.0317809\pi$
$684$	−8.42574	+	7.07004i	−0.322166	+	0.270330i
$685$	2.30798	−	1.93663i	0.0881834	−	0.0739947i
$686$	0.725226	−	4.11296i	0.0276893	−	0.157034i
$687$	1.81706	−	0.661355i	0.0693250	−	0.0252322i
$688$	−5.21784	+	1.89914i	−0.198928	+	0.0724040i
$689$	−4.11875	−	7.13388i	−0.156912	−	0.271779i
$690$	0.974158	+	5.52473i	0.0370856	+	0.210323i
$691$	−5.72719	−	4.80569i	−0.217873	−	0.182817i	0.527319	−	0.849668i	$-0.323197\pi$
$691$	−5.72719	−	4.80569i	−0.217873	−	0.182817i	−0.745191	+	0.666851i	$0.767642\pi$
$692$	1.68927	−	2.92590i	0.0642165	−	0.111226i
$693$	−2.12391	−	3.67872i	−0.0806807	−	0.139743i
$694$	4.95582	−	28.1059i	0.188120	−	1.06688i
$695$	4.11794	−	7.13248i	0.156202	−	0.270550i
$696$	0.0781884	+	0.0284582i	0.00296372	+	0.00107871i
$697$	13.3178			0.504448
$698$	9.19485	+	3.34665i	0.348030	+	0.126673i
$699$	0.326813	+	1.85345i	0.0123612	+	0.0701038i
$700$	−0.230004	+	0.192996i	−0.00869332	+	0.00729456i
$701$	1.27623	+	1.07088i	0.0482025	+	0.0404467i	0.666571	−	0.745442i	$-0.267761\pi$
$701$	1.27623	+	1.07088i	0.0482025	+	0.0404467i	−0.618368	+	0.785889i	$0.712206\pi$
$702$	−2.68891			−0.101487
$703$	11.4900	−	26.8823i	0.433353	−	1.01389i
$704$	6.18204			0.232994
$705$	7.63890	+	6.40980i	0.287698	+	0.241407i
$706$	−11.8718	+	9.96164i	−0.446802	+	0.374911i
$707$	−0.118645	−	0.672869i	−0.00446210	−	0.0253058i
$708$	−9.26512	−	3.37223i	−0.348205	−	0.126736i
$709$	38.5837			1.44904			0.724520	−	0.689254i	$-0.242061\pi$
$709$	38.5837			1.44904			0.724520	+	0.689254i	$0.242061\pi$
$710$	7.70034	+	2.80269i	0.288988	+	0.105183i
$711$	−7.77688	+	13.4700i	−0.291656	+	0.505163i
$712$	−0.988380	+	5.60538i	−0.0370411	+	0.210071i
$713$	−31.4681	−	54.5043i	−1.17849	−	2.04120i
$714$	0.199965	−	0.346349i	0.00748350	−	0.0129618i
$715$	−2.85460	−	2.39530i	−0.106756	−	0.0895790i
$716$	−0.633904	−	3.59505i	−0.0236901	−	0.134353i
$717$	−10.1262	−	17.5392i	−0.378171	−	0.655012i
$718$	12.3032	−	4.47801i	0.459153	−	0.167118i
$719$	4.84393	−	1.76305i	0.180648	−	0.0657505i	−0.250112	−	0.968217i	$-0.580468\pi$
$719$	4.84393	−	1.76305i	0.180648	−	0.0657505i	0.430761	+	0.902466i	$0.358245\pi$
$720$	−0.397396	+	2.25375i	−0.0148101	+	0.0839922i
$721$	−0.327441	+	0.274755i	−0.0121945	+	0.0102324i
$722$	3.14036	−	2.63507i	0.116872	−	0.0980672i
$723$	0.0284557	−	0.161380i	0.00105828	−	0.00600179i
$724$	−13.8773	+	5.05092i	−0.515746	+	0.187716i
$725$	−0.0926955	+	0.0337384i	−0.00344263	+	0.00125301i
$726$	11.4790	+	19.8822i	0.426025	+	0.737897i
$727$	4.04505	+	22.9406i	0.150022	+	0.850820i	0.963196	+	0.268799i	$0.0866267\pi$
$727$	4.04505	+	22.9406i	0.150022	+	0.850820i	−0.813174	+	0.582021i	$0.802262\pi$
$728$	0.138642	+	0.116334i	0.00513841	+	0.00431164i
$729$	−2.09361	+	3.62625i	−0.0775412	+	0.134305i
$730$	2.07292	+	3.59040i	0.0767222	+	0.132887i
$731$	−1.52263	+	8.63528i	−0.0563166	+	0.319387i
$732$	3.96771	−	6.87228i	0.146651	−	0.254007i
$733$	−0.558954	−	0.203443i	−0.0206454	−	0.00751432i	0.331677	−	0.943393i	$-0.392386\pi$
$733$	−0.558954	−	0.203443i	−0.0206454	−	0.00751432i	−0.352322	+	0.935879i	$0.614608\pi$
$734$	22.1765			0.818551
$735$	−5.47694	−	1.99344i	−0.202020	−	0.0735292i
$736$	−1.15490	−	6.54979i	−0.0425704	−	0.241429i
$737$	−18.9157	+	15.8722i	−0.696769	+	0.584659i
$738$	14.7850	+	12.4061i	0.544243	+	0.456674i
$739$	13.0438			0.479824			0.239912	−	0.970795i	$-0.422881\pi$
$739$	13.0438			0.479824			0.239912	+	0.970795i	$0.422881\pi$
$740$	−1.76393	−	5.82139i	−0.0648434	−	0.213998i
$741$	2.44368			0.0897707
$742$	3.14319	+	2.63745i	0.115390	+	0.0968237i
$743$	4.17806	−	3.50580i	0.153278	−	0.128616i	−0.562924	−	0.826509i	$-0.690324\pi$
$743$	4.17806	−	3.50580i	0.153278	−	0.128616i	0.716202	+	0.697893i	$0.245879\pi$
$744$	1.38605	+	7.86065i	0.0508149	+	0.288186i
$745$	16.9275	+	6.16112i	0.620177	+	0.225726i
$746$	−22.1373			−0.810503
$747$	18.0829	+	6.58162i	0.661617	+	0.240809i
$748$	4.88114	−	8.45439i	0.178472	−	0.309123i
$749$	−0.858924	+	4.87120i	−0.0313844	+	0.177990i
$750$	0.421748	+	0.730489i	0.0154001	+	0.0266737i
$751$	−14.6774	+	25.4220i	−0.535586	+	0.927662i	0.463549	+	0.886071i	$0.346576\pi$
$751$	−14.6774	+	25.4220i	−0.535586	+	0.927662i	−0.999135	+	0.0415905i	$0.986758\pi$
$752$	−9.05623	−	7.59908i	−0.330247	−	0.277110i
$753$	2.07038	+	11.7417i	0.0754487	+	0.427891i
$754$	0.0297306	+	0.0514948i	0.00108272	+	0.00187533i
$755$	−0.687494	+	0.250227i	−0.0250205	+	0.00910671i
$756$	1.25859	−	0.458088i	0.0457744	−	0.0166605i
$757$	2.19172	−	12.4299i	0.0796595	−	0.451772i	−0.918722	−	0.394904i	$-0.870778\pi$
$757$	2.19172	−	12.4299i	0.0796595	−	0.451772i	0.998382	−	0.0568672i	$-0.0181112\pi$
$758$	17.5132	−	14.6953i	0.636109	−	0.533759i
$759$	26.5672	−	22.2925i	0.964327	−	0.809166i
$760$	0.834586	−	4.73317i	0.0302736	−	0.171690i
$761$	37.1470	−	13.5204i	1.34658	−	0.490114i	0.434700	−	0.900575i	$-0.356855\pi$
$761$	37.1470	−	13.5204i	1.34658	−	0.490114i	0.911878	+	0.410461i	$0.134632\pi$
$762$	7.17685	−	2.61216i	0.259990	−	0.0946286i
$763$	1.13048	+	1.95804i	0.0409260	+	0.0708859i
$764$	−4.03558	−	22.8869i	−0.146002	−	0.828019i
$765$	2.76839	+	2.32295i	0.100091	+	0.0839866i
$766$	6.34874	−	10.9963i	0.229389	−	0.397314i
$767$	−3.52300	−	6.10201i	−0.127208	−	0.220331i
$768$	−0.146472	+	0.830682i	−0.00528534	+	0.0299746i
$769$	−21.8129	+	37.7810i	−0.786592	+	1.36242i	0.141452	+	0.989945i	$0.454823\pi$
$769$	−21.8129	+	37.7810i	−0.786592	+	1.36242i	−0.928043	+	0.372472i	$0.878510\pi$
$770$	1.74421	+	0.634840i	0.0628569	+	0.0228780i
$771$	−22.0786			−0.795143
$772$	4.58072	+	1.66725i	0.164864	+	0.0600055i
$773$	−6.74608	−	38.2589i	−0.242640	−	1.37608i	−0.825911	−	0.563800i	$-0.809339\pi$
$773$	−6.74608	−	38.2589i	−0.242640	−	1.37608i	0.583271	−	0.812277i	$-0.301772\pi$
$774$	−9.73448	+	8.16820i	−0.349899	+	0.293600i
$775$	−7.24900	−	6.08263i	−0.260392	−	0.218495i
$776$	10.6591			0.382638
$777$	−1.05343	+	1.12404i	−0.0377916	+	0.0403246i
$778$	25.1058			0.900088
$779$	−31.0505	−	26.0544i	−1.11250	−	0.933497i
$780$	0.389491	−	0.326822i	0.0139460	−	0.0117021i
$781$	−8.79682	−	49.8893i	−0.314775	−	1.78518i
$782$	−9.86919	−	3.59209i	−0.352922	−	0.128453i
$783$	0.440038			0.0157257
$784$	6.49314	+	2.36331i	0.231898	+	0.0844039i
$785$	−9.30550	+	16.1176i	−0.332128	+	0.575262i
$786$	2.23011	−	12.6476i	0.0795453	−	0.451124i
$787$	−12.3286	−	21.3537i	−0.439466	−	0.761178i	0.558182	−	0.829719i	$-0.311499\pi$
$787$	−12.3286	−	21.3537i	−0.439466	−	0.761178i	−0.997648	+	0.0685404i	$0.978166\pi$
$788$	7.64770	−	13.2462i	0.272438	−	0.471876i
$789$	−4.81684	−	4.04181i	−0.171484	−	0.143892i
$790$	−1.18019	−	6.69320i	−0.0419893	−	0.238133i
$791$	0.322806	+	0.559117i	0.0114777	+	0.0198799i
$792$	13.2945	−	4.83879i	0.472399	−	0.171939i
$793$	5.32884	−	1.93954i	0.189233	−	0.0688751i
$794$	2.19793	−	12.4651i	0.0780018	−	0.442370i
$795$	8.83024	−	7.40945i	0.313176	−	0.262786i
$796$	4.11870	−	3.45600i	0.145983	−	0.122495i
$797$	−0.536691	+	3.04372i	−0.0190106	+	0.107814i	−0.992837	−	0.119481i	$-0.961877\pi$
$797$	−0.536691	+	3.04372i	−0.0190106	+	0.107814i	0.973826	+	0.227295i	$0.0729881\pi$
$798$	−1.14380	+	0.416310i	−0.0404901	+	0.0147372i
$799$	−17.5428	+	6.38506i	−0.620620	+	0.225887i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	2.26192	+	12.8280i	0.0799211	+	0.453255i
$802$	8.81620	+	7.39767i	0.311311	+	0.261221i
$803$	12.8149	−	22.1960i	0.452227	−	0.783281i
$804$	−1.68457	−	2.91777i	−0.0594104	−	0.102902i
$805$	0.346758	−	1.96656i	0.0122216	−	0.0693123i
$806$	−2.85203	+	4.93986i	−0.100458	+	0.173999i
$807$	−5.76287	−	2.09751i	−0.202863	−	0.0738360i
$808$	2.27561			0.0800557
$809$	7.14500	+	2.60057i	0.251205	+	0.0914311i	0.464554	−	0.885545i	$-0.346215\pi$
$809$	7.14500	+	2.60057i	0.251205	+	0.0914311i	−0.213349	+	0.976976i	$0.568437\pi$
$810$	0.538802	+	3.05570i	0.0189316	+	0.107366i
$811$	42.2483	−	35.4505i	1.48354	−	1.24484i	0.581232	−	0.813738i	$-0.302571\pi$
$811$	42.2483	−	35.4505i	1.48354	−	1.24484i	0.902305	−	0.431098i	$-0.141874\pi$
$812$	−0.0226886	−	0.0190380i	−0.000796214	−	0.000668103i
$813$	−14.2509			−0.499801
$814$	−25.7142	+	27.4378i	−0.901283	+	0.961693i
$815$	5.84810			0.204850
$816$	1.02037	+	0.856191i	0.0357200	+	0.0299727i
$817$	20.4437	−	17.1543i	0.715235	−	0.600154i
$818$	−1.58370	−	8.98160i	−0.0553727	−	0.314034i
$819$	0.389207	+	0.141660i	0.0136000	+	0.00494999i
$820$	−8.43361			−0.294514
$821$	−31.4959	−	11.4636i	−1.09922	−	0.400082i	−0.272189	−	0.962244i	$-0.587748\pi$
$821$	−31.4959	−	11.4636i	−1.09922	−	0.400082i	−0.827027	+	0.562162i	$0.809970\pi$
$822$	1.27067	−	2.20086i	0.0443196	−	0.0767638i
$823$	−4.09670	+	23.2336i	−0.142802	+	0.809871i	0.826304	+	0.563225i	$0.190440\pi$
$823$	−4.09670	+	23.2336i	−0.142802	+	0.809871i	−0.969106	+	0.246646i	$0.920672\pi$
$824$	−0.711816	−	1.23290i	−0.0247973	−	0.0429502i
$825$	2.60726	−	4.51591i	0.0907733	−	0.157224i
$826$	2.68854	+	2.25595i	0.0935463	+	0.0784947i
$827$	4.73126	+	26.8323i	0.164522	+	0.933050i	0.949556	+	0.313598i	$0.101534\pi$
$827$	4.73126	+	26.8323i	0.164522	+	0.933050i	−0.785034	+	0.619453i	$0.787355\pi$
$828$	−7.61026	−	13.1814i	−0.264475	−	0.458084i
$829$	13.7850	−	5.01734i	0.478774	−	0.174260i	−0.0913488	−	0.995819i	$-0.529118\pi$
$829$	13.7850	−	5.01734i	0.478774	−	0.174260i	0.570123	+	0.821559i	$0.306896\pi$
$830$	−7.90157	+	2.87594i	−0.274268	+	0.0998253i
$831$	−0.0929808	+	0.527320i	−0.00322547	+	0.0182925i
$832$	−0.461757	+	0.387461i	−0.0160086	+	0.0134328i
$833$	8.35877	−	7.01384i	0.289614	−	0.243015i
$834$	1.20632	−	6.84139i	0.0417715	−	0.236898i
$835$	−11.5351	+	4.19842i	−0.399187	+	0.145292i
$836$	−27.9202	+	10.1621i	−0.965640	+	0.351464i
$837$	21.1062	+	36.5571i	0.729538	+	1.26360i
$838$	−3.61517	−	20.5026i	−0.124884	−	0.708252i
$839$	6.28794	+	5.27621i	0.217084	+	0.182155i	0.744844	−	0.667238i	$-0.232524\pi$
$839$	6.28794	+	5.27621i	0.217084	+	0.182155i	−0.527760	+	0.849393i	$0.676968\pi$
$840$	−0.126629	+	0.219328i	−0.00436912	+	0.00756754i
$841$	14.4951	+	25.1063i	0.499832	+	0.865735i
$842$	−2.70928	+	15.3651i	−0.0933679	+	0.529516i
$843$	5.13567	−	8.89524i	0.176882	−	0.306368i
$844$	20.2495	+	7.37022i	0.697017	+	0.253694i
$845$	−12.6367			−0.434714
$846$	−25.4234	−	9.25335i	−0.874073	−	0.318137i
$847$	−1.41906	−	8.04790i	−0.0487595	−	0.276529i
$848$	−10.4686	+	8.78421i	−0.359494	+	0.301651i
$849$	−17.4051	−	14.6046i	−0.597341	−	0.501228i
$850$	−1.57914			−0.0541639
$851$	33.8738	+	22.1181i	1.16118	+	0.758198i
$852$	6.91205			0.236803
$853$	−30.4136	−	25.5201i	−1.04134	−	0.873791i	−0.0491863	−	0.998790i	$-0.515663\pi$
$853$	−30.4136	−	25.5201i	−1.04134	−	0.873791i	−0.992157	+	0.124999i	$0.960107\pi$
$854$	−2.16382	+	1.81566i	−0.0740445	+	0.0621307i
$855$	−1.90996	−	10.8319i	−0.0653193	−	0.370444i
$856$	−15.4807	−	5.63450i	−0.529118	−	0.192583i
$857$	2.30636			0.0787839			0.0393919	−	0.999224i	$-0.487458\pi$
$857$	2.30636			0.0787839			0.0393919	+	0.999224i	$0.487458\pi$
$858$	−2.95366	−	1.07505i	−0.100836	−	0.0367014i
$859$	20.4831	−	35.4778i	0.698876	−	1.21049i	−0.269981	−	0.962866i	$-0.587017\pi$
$859$	20.4831	−	35.4778i	0.698876	−	1.21049i	0.968857	−	0.247622i	$-0.0796493\pi$
$860$	0.964219	−	5.46836i	0.0328796	−	0.186469i
$861$	1.06794	+	1.84973i	0.0363953	+	0.0630386i
$862$	4.20784	−	7.28820i	0.143320	−	0.248237i
$863$	−26.2387	−	22.0169i	−0.893176	−	0.749464i	0.0756683	−	0.997133i	$-0.475891\pi$
$863$	−26.2387	−	22.0169i	−0.893176	−	0.749464i	−0.968845	+	0.247669i	$0.920335\pi$
$864$	0.774617	+	4.39307i	0.0263530	+	0.149455i
$865$	1.68927	+	2.92590i	0.0574370	+	0.0994837i
$866$	6.97243	−	2.53776i	0.236933	−	0.0862365i
$867$	−11.4981	+	4.18497i	−0.390496	+	0.142129i
$868$	0.493373	−	2.79805i	0.0167462	−	0.0949722i
$869$	−32.1861	+	27.0073i	−1.09184	+	0.916160i
$870$	−0.0637397	+	0.0534840i	−0.00216098	+	0.00181328i
$871$	0.418087	−	2.37109i	0.0141664	−	0.0803414i
$872$	−7.07614	+	2.57551i	−0.239628	+	0.0872176i
$873$	22.9223	−	8.34304i	0.775802	−	0.282369i
$874$	15.9826	+	27.6826i	0.540619	+	0.936379i
$875$	−0.0521376	−	0.295687i	−0.00176257	−	0.00999605i
$876$	2.67886	+	2.24783i	0.0905103	+	0.0759471i
$877$	0.230083	−	0.398515i	0.00776935	−	0.0134569i	−0.862115	−	0.506713i	$-0.830860\pi$
$877$	0.230083	−	0.398515i	0.00776935	−	0.0134569i	0.869884	+	0.493256i	$0.164194\pi$
$878$	−3.17106	−	5.49244i	−0.107018	−	0.185361i
$879$	−0.00298502	+	0.0169289i	−0.000100682	+	0.000570997i
$880$	−3.09102	+	5.35380i	−0.104198	+	0.180477i
$881$	38.4712	+	14.0024i	1.29613	+	0.471752i	0.895734	−	0.444591i	$-0.146651\pi$
$881$	38.4712	+	14.0024i	1.29613	+	0.471752i	0.400394	+	0.916343i	$0.368873\pi$
$882$	15.8133			0.532461
$883$	26.4269	+	9.61860i	0.889335	+	0.323692i	0.745971	−	0.665978i	$-0.231986\pi$
$883$	26.4269	+	9.61860i	0.889335	+	0.323692i	0.143364	+	0.989670i	$0.454208\pi$
$884$	0.165291	+	0.937413i	0.00555935	+	0.0315286i
$885$	7.55300	−	6.33772i	0.253891	−	0.213040i
$886$	−17.9017	−	15.0213i	−0.601418	−	0.504650i
$887$	−28.4200			−0.954249			−0.477125	−	0.878836i	$-0.658321\pi$
$887$	−28.4200			−0.954249			−0.477125	+	0.878836i	$0.658321\pi$
$888$	−3.07757	−	4.10531i	−0.103276	−	0.137765i
$889$	−2.71860			−0.0911790
$890$	−4.36021	−	3.65865i	−0.146155	−	0.122638i
$891$	14.6942	−	12.3299i	0.492273	−	0.413066i
$892$	0.0595419	+	0.337679i	0.00199361	+	0.0113063i
$893$	53.3925	+	19.4333i	1.78671	+	0.650310i
$894$	15.1947			0.508185
$895$	3.43036	+	1.24855i	0.114664	+	0.0417344i
$896$	0.150124	−	0.260023i	0.00501530	−	0.00868675i
$897$	−0.587205	+	3.33020i	−0.0196062	+	0.111192i
$898$	−0.393568	−	0.681679i	−0.0131335	−	0.0227479i
$899$	0.466731	−	0.808402i	0.0155664	−	0.0269617i
$900$	−1.75310	−	1.47103i	−0.0584368	−	0.0490343i
$901$	3.74736	+	21.2523i	0.124843	+	0.708018i
$902$	26.0684	+	45.1519i	0.867984	+	1.50339i
$903$	−1.32146	+	0.480973i	−0.0439756	+	0.0160058i
$904$	−2.02058	+	0.735432i	−0.0672036	+	0.0244601i
$905$	2.56442	−	14.5436i	0.0852443	−	0.483444i
$906$	−0.472738	+	0.396674i	−0.0157057	+	0.0131786i
$907$	23.1329	−	19.4108i	0.768117	−	0.644527i	−0.172109	−	0.985078i	$-0.555058\pi$
$907$	23.1329	−	19.4108i	0.768117	−	0.644527i	0.940226	+	0.340551i	$0.110614\pi$
$908$	−3.85074	+	21.8386i	−0.127791	+	0.724741i
$909$	4.89370	−	1.78116i	0.162314	−	0.0590774i
$910$	−0.170070	+	0.0619003i	−0.00563775	+	0.00205197i
$911$	6.16596	+	10.6798i	0.204287	+	0.353836i	0.949905	−	0.312537i	$-0.101179\pi$
$911$	6.16596	+	10.6798i	0.204287	+	0.353836i	−0.745618	+	0.666374i	$0.767846\pi$
$912$	−0.703970	−	3.99241i	−0.0233108	−	0.132202i
$913$	39.8211	+	33.4139i	1.31789	+	1.10584i
$914$	13.0229	−	22.5563i	0.430759	−	0.746096i
$915$	3.96771	+	6.87228i	0.131169	+	0.227191i
$916$	0.398079	−	2.25762i	0.0131529	−	0.0745939i
$917$	−2.28572	+	3.95899i	−0.0754812	+	0.130737i
$918$	6.61946	+	2.40929i	0.218475	+	0.0795183i
$919$	−2.04361			−0.0674124			−0.0337062	−	0.999432i	$-0.510731\pi$
$919$	−2.04361			−0.0674124			−0.0337062	+	0.999432i	$0.510731\pi$
$920$	6.24974	+	2.27472i	0.206048	+	0.0749953i
$921$	2.50793	+	14.2232i	0.0826390	+	0.468669i
$922$	−10.1843	+	8.54565i	−0.335402	+	0.281436i
$923$	3.78388	+	3.17506i	0.124548	+	0.104508i
$924$	1.56565			0.0515062
$925$	5.92343	+	1.38308i	0.194761	+	0.0454756i
$926$	16.8734			0.554494
$927$	−2.49577	−	2.09420i	−0.0819720	−	0.0687826i
$928$	0.0755661	−	0.0634075i	0.00248058	−	0.00208145i
$929$	4.24842	+	24.0940i	0.139386	+	0.790498i	0.971704	+	0.236200i	$0.0759020\pi$
$929$	4.24842	+	24.0940i	0.139386	+	0.790498i	−0.832318	+	0.554298i	$0.812987\pi$
$930$	−7.50055	−	2.72998i	−0.245953	−	0.0895194i
$931$	−33.2100			−1.08842
$932$	2.09668	+	0.763128i	0.0686789	+	0.0249971i
$933$	−0.295232	+	0.511356i	−0.00966545	+	0.0167411i
$934$	−1.55794	+	8.83554i	−0.0509775	+	0.289108i
$935$	4.88114	+	8.45439i	0.159630	+	0.276488i
$936$	−0.689737	+	1.19466i	−0.0225448	+	0.0390487i
$937$	−25.4320	−	21.3400i	−0.830828	−	0.697148i	0.124653	−	0.992200i	$-0.460218\pi$
$937$	−25.4320	−	21.3400i	−0.830828	−	0.697148i	−0.955481	+	0.295053i	$0.904663\pi$
$938$	0.208251	+	1.18105i	0.00679965	+	0.0385627i
$939$	7.23962	+	12.5394i	0.236256	+	0.409207i
$940$	11.1091	−	4.04339i	0.362339	−	0.131881i
$941$	−52.2563	+	19.0197i	−1.70351	+	0.620026i	−0.996217	−	0.0868972i	$-0.972305\pi$
$941$	−52.2563	+	19.0197i	−1.70351	+	0.620026i	−0.707290	+	0.706923i	$0.750083\pi$
$942$	−2.72598	+	15.4598i	−0.0888173	+	0.503708i
$943$	42.9678	−	36.0543i	1.39922	−	1.17409i
$944$	−8.95439	+	7.51363i	−0.291441	+	0.244548i
$945$	−0.232578	+	1.31901i	−0.00756575	+	0.0429075i
$946$	−32.2569	+	11.7406i	−1.04876	+	0.381719i
$947$	−31.5789	+	11.4938i	−1.02618	+	0.373498i	−0.799624	−	0.600501i	$-0.794968\pi$
$947$	−31.5789	+	11.4938i	−1.02618	+	0.373498i	−0.226553	+	0.973999i	$0.572746\pi$
$948$	−2.86639	−	4.96473i	−0.0930960	−	0.161247i
$949$	0.433953	+	2.46107i	0.0140867	+	0.0798898i
$950$	3.68175	+	3.08936i	0.119452	+	0.100232i
$951$	−9.99430	+	17.3106i	−0.324087	+	0.561336i
$952$	−0.237067	−	0.410612i	−0.00768338	−	0.0133080i
$953$	6.33772	−	35.9430i	0.205299	−	1.16431i	−0.691670	−	0.722214i	$-0.743125\pi$
$953$	6.33772	−	35.9430i	0.205299	−	1.16431i	0.896969	−	0.442094i	$-0.145764\pi$
$954$	−15.6372	+	27.0844i	−0.506273	+	0.876890i
$955$	21.8384	+	7.94854i	0.706675	+	0.257209i
$956$	−24.0102			−0.776544
$957$	0.483364	+	0.175930i	0.0156249	+	0.00568701i
$958$	−6.02500	−	34.1695i	−0.194659	−	1.10396i
$959$	−0.692968	+	0.581469i	−0.0223771	+	0.0187766i
$960$	−0.646156	−	0.542189i	−0.0208546	−	0.0174991i
$961$	58.5463			1.88859
$962$	0.201015	−	3.66106i	0.00648099	−	0.118037i
$963$	−37.7014			−1.21491
$964$	−0.148823	−	0.124877i	−0.00479326	−	0.00402202i
$965$	−3.73424	+	3.13340i	−0.120209	+	0.100868i
$966$	−0.292489	−	1.65879i	−0.00941069	−	0.0533707i
$967$	23.9367	+	8.71225i	0.769752	+	0.280167i	0.696893	−	0.717175i	$-0.254565\pi$
$967$	23.9367	+	8.71225i	0.769752	+	0.280167i	0.0728595	+	0.997342i	$0.476788\pi$
$968$	27.2176			0.874808
$969$	−6.01575	−	2.18955i	−0.193254	−	0.0703386i
$970$	−5.32953	+	9.23102i	−0.171121	+	0.296390i
$971$	4.03926	−	22.9078i	0.129626	−	0.735145i	−0.848826	−	0.528672i	$-0.822690\pi$
$971$	4.03926	−	22.9078i	0.129626	−	0.735145i	0.978452	−	0.206473i	$-0.0661986\pi$
$972$	7.99988	+	13.8562i	0.256596	+	0.444438i
$973$	−1.23640	+	2.14151i	−0.0396373	+	0.0686538i
$974$	5.32119	+	4.46501i	0.170502	+	0.143068i
$975$	0.0882904	+	0.500720i	0.00282756	+	0.0160359i
$976$	−4.70389	−	8.14738i	−0.150568	−	0.260791i
$977$	−55.1327	+	20.0667i	−1.76385	+	0.641989i	−0.999994	−	0.00339593i	$-0.998919\pi$
$977$	−55.1327	+	20.0667i	−1.76385	+	0.641989i	−0.763857	+	0.645385i	$0.776697\pi$
$978$	4.63536	−	1.68713i	0.148223	−	0.0539486i
$979$	−6.11021	+	34.6527i	−0.195283	+	1.10751i
$980$	−5.29325	+	4.44157i	−0.169087	+	0.141881i
$981$	−13.2013	+	11.0772i	−0.421487	+	0.353669i
$982$	1.65423	−	9.38162i	0.0527887	−	0.299379i
$983$	18.9596	−	6.90074i	0.604718	−	0.220099i	−0.0214723	−	0.999769i	$-0.506835\pi$
$983$	18.9596	−	6.90074i	0.604718	−	0.220099i	0.626191	+	0.779670i	$0.284613\pi$
$984$	−6.68471	+	2.43303i	−0.213101	+	0.0775623i
$985$	7.64770	+	13.2462i	0.243676	+	0.422059i
$986$	−0.0270497	−	0.153407i	−0.000861439	−	0.00488546i
$987$	−2.29357	−	1.92453i	−0.0730051	−	0.0612585i
$988$	1.44854	−	2.50895i	0.0460842	−	0.0798202i
$989$	18.4651	+	31.9825i	0.587156	+	1.01698i
$990$	−2.45672	+	13.9327i	−0.0780797	+	0.442812i
$991$	−17.9823	+	31.1462i	−0.571225	+	0.989391i	0.425215	+	0.905092i	$0.360198\pi$
$991$	−17.9823	+	31.1462i	−0.571225	+	0.989391i	−0.996441	+	0.0842989i	$0.973135\pi$
$992$	8.89221	+	3.23650i	0.282328	+	0.102759i
$993$	16.9010			0.536336
$994$	−2.31201	−	0.841504i	−0.0733326	−	0.0266909i
$995$	0.933633	+	5.29490i	0.0295982	+	0.167860i
$996$	−5.43332	+	4.55909i	−0.172161	+	0.144460i
$997$	−5.16588	−	4.33469i	−0.163605	−	0.137281i	0.557310	−	0.830305i	$-0.311834\pi$
$997$	−5.16588	−	4.33469i	−0.163605	−	0.137281i	−0.720915	+	0.693024i	$0.756278\pi$
$998$	8.78466			0.278074
$999$	−22.7198	−	14.8350i	−0.718823	−	0.469359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.a.71.2	✓	18
37.12	even	9	inner	370.2.o.a.271.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.a.71.2	✓	18	1.1	even	1	trivial
370.2.o.a.271.2	yes	18	37.12	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.646156 + 0.542189i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} -0.843496 q^{6} +(0.282141 + 0.102691i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.397396 + 2.25375i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.646156 + 0.542189i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} -0.843496 q^{6} +(0.282141 + 0.102691i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.397396 + 2.25375i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-3.09102 + 5.35380i) q^{11} +(-0.646156 - 0.542189i) q^{12} +(-0.104672 - 0.593624i) q^{13} +(0.150124 + 0.260023i) q^{14} +(0.792627 - 0.288493i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.274214 + 1.55515i) q^{17} +(-1.75310 + 1.47103i) q^{18} +(3.68175 - 3.08936i) q^{19} +(0.173648 - 0.984808i) q^{20} +(-0.237985 + 0.0866195i) q^{21} +(-5.80922 + 2.11438i) q^{22} +(3.32542 + 5.75979i) q^{23} +(-0.146472 - 0.830682i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.301391 - 0.522024i) q^{26} +(-2.23042 - 3.86320i) q^{27} +(-0.0521376 + 0.295687i) q^{28} +(-0.0493223 + 0.0854287i) q^{29} +(0.792627 + 0.288493i) q^{30} -9.46289 q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.905493 - 5.13531i) q^{33} +(-1.20969 + 1.01505i) q^{34} +(-0.230004 - 0.192996i) q^{35} -2.28851 q^{36} +(5.42664 - 2.74801i) q^{37} +4.80619 q^{38} +(0.389491 + 0.326822i) q^{39} +(0.766044 - 0.642788i) q^{40} +(-1.46448 - 8.30548i) q^{41} +(-0.237985 - 0.0866195i) q^{42} +5.55271 q^{43} +(-5.80922 - 2.11438i) q^{44} +(1.14426 - 1.98191i) q^{45} +(-1.15490 + 6.54979i) q^{46} +(5.91104 + 10.2382i) q^{47} +(0.421748 - 0.730489i) q^{48} +(-5.29325 - 4.44157i) q^{49} +(0.173648 + 0.984808i) q^{50} +(-0.665998 - 1.15354i) q^{51} +(0.566429 - 0.206163i) q^{52} +(12.8417 - 4.67398i) q^{53} +(0.774617 - 4.39307i) q^{54} +(4.73572 - 3.97374i) q^{55} +(-0.230004 + 0.192996i) q^{56} +(-0.703970 + 3.99241i) q^{57} +(-0.0926955 + 0.0337384i) q^{58} +(10.9842 - 3.99792i) q^{59} +(0.421748 + 0.730489i) q^{60} +(1.63364 + 9.26486i) q^{61} +(-7.24900 - 6.08263i) q^{62} +(-0.343561 + 0.595066i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.104672 + 0.593624i) q^{65} +(2.60726 - 4.51591i) q^{66} +(3.75338 + 1.36612i) q^{67} -1.57914 q^{68} +(-5.27163 - 1.91872i) q^{69} +(-0.0521376 - 0.295687i) q^{70} +(-6.27737 + 5.26734i) q^{71} +(-1.75310 - 1.47103i) q^{72} -4.14584 q^{73} +(5.92343 + 1.38308i) q^{74} -0.843496 q^{75} +(3.68175 + 3.08936i) q^{76} +(-1.42189 + 1.19311i) q^{77} +(0.0882904 + 0.500720i) q^{78} +(6.38657 + 2.32452i) q^{79} +1.00000 q^{80} +(-2.91571 - 1.06123i) q^{81} +(4.21680 - 7.30372i) q^{82} +(1.46015 - 8.28093i) q^{83} +(-0.126629 - 0.219328i) q^{84} +(0.789568 - 1.36757i) q^{85} +(4.25363 + 3.56922i) q^{86} +(-0.0144486 - 0.0819422i) q^{87} +(-3.09102 - 5.35380i) q^{88} +(5.34859 - 1.94673i) q^{89} +(2.15050 - 0.782718i) q^{90} +(0.0314276 - 0.178235i) q^{91} +(-5.09483 + 4.27507i) q^{92} +(6.11450 - 5.13068i) q^{93} +(-2.05288 + 11.6425i) q^{94} +(-4.51634 + 1.64381i) q^{95} +(0.792627 - 0.288493i) q^{96} +(-5.32953 - 9.23102i) q^{97} +(-1.19988 - 6.80487i) q^{98} +(-10.8378 - 9.09396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9	\( 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9} - 9 q^{10} + 3 q^{11} + 9 q^{13} - 6 q^{17} + 6 q^{18} + 9 q^{19} - 6 q^{21} + 21 q^{23} + 6 q^{26} + 12 q^{27} - 3 q^{28} + 6 q^{29} - 30 q^{31} - 45 q^{33} - 15 q^{34} + 6 q^{35} + 24 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{39} + 15 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{45} + 24 q^{47} + 3 q^{48} + 33 q^{49} - 42 q^{51} - 12 q^{53} + 27 q^{54} + 6 q^{56} + 51 q^{57} - 15 q^{58} - 15 q^{59} + 3 q^{60} + 72 q^{61} - 57 q^{62} - 30 q^{63} - 9 q^{64} + 9 q^{65} - 3 q^{66} + 18 q^{67} + 24 q^{69} - 3 q^{70} + 6 q^{72} - 66 q^{73} - 24 q^{74} - 6 q^{75} + 9 q^{76} - 66 q^{77} + 6 q^{78} - 12 q^{79} + 18 q^{80} + 66 q^{81} + 45 q^{82} + 9 q^{83} + 42 q^{84} + 12 q^{86} + 48 q^{87} + 3 q^{88} + 6 q^{90} - 78 q^{91} + 18 q^{92} + 24 q^{94} - 3 q^{97} - 48 q^{98} - 96 q^{99}+O(q^{100}) \) 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9 - 9 * q^10 + 3 * q^11 + 9 * q^13 - 6 * q^17 + 6 * q^18 + 9 * q^19 - 6 * q^21 + 21 * q^23 + 6 * q^26 + 12 * q^27 - 3 * q^28 + 6 * q^29 - 30 * q^31 - 45 * q^33 - 15 * q^34 + 6 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^39 + 15 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 24 * q^47 + 3 * q^48 + 33 * q^49 - 42 * q^51 - 12 * q^53 + 27 * q^54 + 6 * q^56 + 51 * q^57 - 15 * q^58 - 15 * q^59 + 3 * q^60 + 72 * q^61 - 57 * q^62 - 30 * q^63 - 9 * q^64 + 9 * q^65 - 3 * q^66 + 18 * q^67 + 24 * q^69 - 3 * q^70 + 6 * q^72 - 66 * q^73 - 24 * q^74 - 6 * q^75 + 9 * q^76 - 66 * q^77 + 6 * q^78 - 12 * q^79 + 18 * q^80 + 66 * q^81 + 45 * q^82 + 9 * q^83 + 42 * q^84 + 12 * q^86 + 48 * q^87 + 3 * q^88 + 6 * q^90 - 78 * q^91 + 18 * q^92 + 24 * q^94 - 3 * q^97 - 48 * q^98 - 96 * q^99

Introduction

L-functions

Modular forms

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