LMFDB - Embedded newform 95.2.k.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(6,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("95.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.k (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:	$0.758578819202$
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} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			81.2
Root			$0.597039 - 1.03410i$ of defining polynomial
Character	$\chi$	$=$	95.81
Dual form			95.2.k.b.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12207 - 0.408399i) q^{2} +(0.394733 - 2.23864i) q^{3} +(-0.439845 + 0.369074i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.471342 - 2.67312i) q^{6} +(1.09825 + 1.90222i) q^{7} +(-1.53688 + 2.66196i) q^{8} +(-2.03663 - 0.741274i) q^{9} +O(q^{10})$	\(q+(1.12207 - 0.408399i) q^{2} +(0.394733 - 2.23864i) q^{3} +(-0.439845 + 0.369074i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.471342 - 2.67312i) q^{6} +(1.09825 + 1.90222i) q^{7} +(-1.53688 + 2.66196i) q^{8} +(-2.03663 - 0.741274i) q^{9} +(-1.12207 - 0.408399i) q^{10} +(1.41324 - 2.44780i) q^{11} +(0.652604 + 1.13034i) q^{12} +(0.708694 + 4.01920i) q^{13} +(2.00917 + 1.68589i) q^{14} +(-1.74136 + 1.46117i) q^{15} +(-0.437935 + 2.48365i) q^{16} +(-0.359555 + 0.130867i) q^{17} -2.58797 q^{18} +(-2.75520 - 3.37770i) q^{19} +0.574177 q^{20} +(4.69190 - 1.70771i) q^{21} +(0.586069 - 3.32376i) q^{22} +(-2.27970 + 1.91290i) q^{23} +(5.35253 + 4.49130i) q^{24} +(0.173648 + 0.984808i) q^{25} +(2.43664 + 4.22038i) q^{26} +(0.946391 - 1.63920i) q^{27} +(-1.18512 - 0.431347i) q^{28} +(-8.05787 - 2.93282i) q^{29} +(-1.35718 + 2.35070i) q^{30} +(2.34622 + 4.06377i) q^{31} +(-0.544580 - 3.08847i) q^{32} +(-4.92191 - 4.12997i) q^{33} +(-0.349999 + 0.293684i) q^{34} +(0.381417 - 2.16312i) q^{35} +(1.16939 - 0.425623i) q^{36} -10.7694 q^{37} +(-4.47097 - 2.66478i) q^{38} +9.27731 q^{39} +(2.88840 - 1.05129i) q^{40} +(0.544445 - 3.08770i) q^{41} +(4.56720 - 3.83233i) q^{42} +(1.53900 + 1.29137i) q^{43} +(0.281814 + 1.59824i) q^{44} +(1.08367 + 1.87697i) q^{45} +(-1.77675 + 3.07743i) q^{46} +(10.2405 + 3.72722i) q^{47} +(5.38714 + 1.96076i) q^{48} +(1.08771 - 1.88398i) q^{49} +(0.597039 + 1.03410i) q^{50} +(0.151037 + 0.856574i) q^{51} +(-1.79510 - 1.50627i) q^{52} +(5.72676 - 4.80532i) q^{53} +(0.392467 - 2.22579i) q^{54} +(-2.65602 + 0.966713i) q^{55} -6.75150 q^{56} +(-8.64904 + 4.83463i) q^{57} -10.2392 q^{58} +(12.1961 - 4.43900i) q^{59} +(0.226647 - 1.28538i) q^{60} +(4.57784 - 3.84126i) q^{61} +(4.29225 + 3.60163i) q^{62} +(-0.826660 - 4.68822i) q^{63} +(-4.39435 - 7.61123i) q^{64} +(2.04060 - 3.53443i) q^{65} +(-7.20938 - 2.62400i) q^{66} +(-0.986138 - 0.358925i) q^{67} +(0.109849 - 0.190264i) q^{68} +(3.38242 + 5.85853i) q^{69} +(-0.455441 - 2.58294i) q^{70} +(-5.99626 - 5.03146i) q^{71} +(5.10332 - 4.28219i) q^{72} +(-2.44663 + 13.8755i) q^{73} +(-12.0840 + 4.39822i) q^{74} +2.27318 q^{75} +(2.45848 + 0.468792i) q^{76} +6.20833 q^{77} +(10.4098 - 3.78884i) q^{78} +(-2.33355 + 13.2342i) q^{79} +(1.93194 - 1.62109i) q^{80} +(-8.27685 - 6.94510i) q^{81} +(-0.650110 - 3.68695i) q^{82} +(2.77807 + 4.81175i) q^{83} +(-1.43344 + 2.48279i) q^{84} +(0.359555 + 0.130867i) q^{85} +(2.25425 + 0.820481i) q^{86} +(-9.74626 + 16.8810i) q^{87} +(4.34397 + 7.52398i) q^{88} +(-1.13984 - 6.46435i) q^{89} +(1.98250 + 1.66352i) q^{90} +(-6.86708 + 5.76216i) q^{91} +(0.296716 - 1.68276i) q^{92} +(10.0235 - 3.64824i) q^{93} +13.0127 q^{94} +(-0.0605361 + 4.35848i) q^{95} -7.12895 q^{96} +(-13.5750 + 4.94091i) q^{97} +(0.451074 - 2.55817i) q^{98} +(-4.69275 + 3.93768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{6} - 12 q^{8} - 21 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^6 - 12 * q^8 - 21 * q^9	\( 18 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{6} - 12 q^{8} - 21 q^{9} - 3 q^{10} + 6 q^{12} - 3 q^{13} + 24 q^{14} + 3 q^{15} + 21 q^{16} - 24 q^{17} - 12 q^{18} - 12 q^{19} - 12 q^{20} + 3 q^{21} + 15 q^{22} + 21 q^{23} + 21 q^{24} - 21 q^{26} + 6 q^{27} - 24 q^{28} - 9 q^{29} - 12 q^{30} + 30 q^{31} + 45 q^{32} - 3 q^{33} + 24 q^{34} - 6 q^{35} - 21 q^{36} - 60 q^{37} - 15 q^{38} + 12 q^{39} - 6 q^{40} - 6 q^{41} + 39 q^{42} - 6 q^{43} - 30 q^{44} + 6 q^{45} + 21 q^{46} + 33 q^{47} - 63 q^{48} - 3 q^{49} + 27 q^{51} + 9 q^{52} + 24 q^{53} + 30 q^{54} - 3 q^{55} - 72 q^{56} - 30 q^{57} + 36 q^{58} + 18 q^{59} + 15 q^{60} + 6 q^{61} + 12 q^{62} + 24 q^{63} - 24 q^{64} + 3 q^{65} - 33 q^{66} - 24 q^{67} - 3 q^{68} + 27 q^{69} + 39 q^{70} + 24 q^{71} + 18 q^{72} + 6 q^{73} - 39 q^{74} - 6 q^{75} + 27 q^{76} + 24 q^{77} + 72 q^{78} + 9 q^{79} + 33 q^{80} + 15 q^{81} - 57 q^{82} - 12 q^{84} + 24 q^{85} - 33 q^{86} - 45 q^{87} + 39 q^{88} - 6 q^{89} - 21 q^{90} - 6 q^{91} - 66 q^{92} - 72 q^{93} - 66 q^{94} - 15 q^{95} - 18 q^{96} - 87 q^{97} + 39 q^{98} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^6 - 12 * q^8 - 21 * q^9 - 3 * q^10 + 6 * q^12 - 3 * q^13 + 24 * q^14 + 3 * q^15 + 21 * q^16 - 24 * q^17 - 12 * q^18 - 12 * q^19 - 12 * q^20 + 3 * q^21 + 15 * q^22 + 21 * q^23 + 21 * q^24 - 21 * q^26 + 6 * q^27 - 24 * q^28 - 9 * q^29 - 12 * q^30 + 30 * q^31 + 45 * q^32 - 3 * q^33 + 24 * q^34 - 6 * q^35 - 21 * q^36 - 60 * q^37 - 15 * q^38 + 12 * q^39 - 6 * q^40 - 6 * q^41 + 39 * q^42 - 6 * q^43 - 30 * q^44 + 6 * q^45 + 21 * q^46 + 33 * q^47 - 63 * q^48 - 3 * q^49 + 27 * q^51 + 9 * q^52 + 24 * q^53 + 30 * q^54 - 3 * q^55 - 72 * q^56 - 30 * q^57 + 36 * q^58 + 18 * q^59 + 15 * q^60 + 6 * q^61 + 12 * q^62 + 24 * q^63 - 24 * q^64 + 3 * q^65 - 33 * q^66 - 24 * q^67 - 3 * q^68 + 27 * q^69 + 39 * q^70 + 24 * q^71 + 18 * q^72 + 6 * q^73 - 39 * q^74 - 6 * q^75 + 27 * q^76 + 24 * q^77 + 72 * q^78 + 9 * q^79 + 33 * q^80 + 15 * q^81 - 57 * q^82 - 12 * q^84 + 24 * q^85 - 33 * q^86 - 45 * q^87 + 39 * q^88 - 6 * q^89 - 21 * q^90 - 6 * q^91 - 66 * q^92 - 72 * q^93 - 66 * q^94 - 15 * q^95 - 18 * q^96 - 87 * q^97 + 39 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	1.12207	−	0.408399i	0.793421	−	0.288782i	0.0866635	−	0.996238i	$-0.472380\pi$
$2$	1.12207	−	0.408399i	0.793421	−	0.288782i	0.706757	+	0.707456i	$0.250157\pi$
$3$	0.394733	−	2.23864i	0.227899	−	1.29248i	−0.629165	−	0.777272i	$-0.716603\pi$
$3$	0.394733	−	2.23864i	0.227899	−	1.29248i	0.857064	−	0.515210i	$-0.172286\pi$
$4$	−0.439845	+	0.369074i	−0.219923	+	0.184537i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$6$	−0.471342	−	2.67312i	−0.192425	−	1.09129i
$7$	1.09825	+	1.90222i	0.415098	+	0.718970i	0.995439	−	0.0954033i	$-0.0304141\pi$
$7$	1.09825	+	1.90222i	0.415098	+	0.718970i	−0.580341	+	0.814374i	$0.697081\pi$
$8$	−1.53688	+	2.66196i	−0.543371	+	0.941146i
$9$	−2.03663	−	0.741274i	−0.678878	−	0.247091i
$10$	−1.12207	−	0.408399i	−0.354829	−	0.129147i
$11$	1.41324	−	2.44780i	0.426108	−	0.738040i	−0.570415	−	0.821356i	$-0.693218\pi$
$11$	1.41324	−	2.44780i	0.426108	−	0.738040i	0.996523	+	0.0833161i	$0.0265511\pi$
$12$	0.652604	+	1.13034i	0.188391	+	0.326302i
$13$	0.708694	+	4.01920i	0.196556	+	1.11473i	0.910185	+	0.414202i	$0.135939\pi$
$13$	0.708694	+	4.01920i	0.196556	+	1.11473i	−0.713628	+	0.700524i	$0.752949\pi$
$14$	2.00917	+	1.68589i	0.536972	+	0.450573i
$15$	−1.74136	+	1.46117i	−0.449616	+	0.377273i
$16$	−0.437935	+	2.48365i	−0.109484	+	0.620913i
$17$	−0.359555	+	0.130867i	−0.0872049	+	0.0317400i	−0.385254	−	0.922810i	$-0.625886\pi$
$17$	−0.359555	+	0.130867i	−0.0872049	+	0.0317400i	0.298049	+	0.954550i	$0.403664\pi$
$18$	−2.58797			−0.609992
$19$	−2.75520	−	3.37770i	−0.632087	−	0.774898i
$19$	−2.75520	−	3.37770i	−0.632087	−	0.774898i
$20$	0.574177			0.128390
$21$	4.69190	−	1.70771i	1.02386	−	0.372653i
$22$	0.586069	−	3.32376i	0.124950	−	0.708628i
$23$	−2.27970	+	1.91290i	−0.475351	+	0.398867i	−0.848742	−	0.528807i	$-0.822639\pi$
$23$	−2.27970	+	1.91290i	−0.475351	+	0.398867i	0.373391	+	0.927674i	$0.378195\pi$
$24$	5.35253	+	4.49130i	1.09258	+	0.916783i
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	2.43664	+	4.22038i	0.477864	+	0.827686i
$27$	0.946391	−	1.63920i	0.182133	−	0.315464i
$28$	−1.18512	−	0.431347i	−0.223966	−	0.0815170i
$29$	−8.05787	−	2.93282i	−1.49631	−	0.544612i	−0.541207	−	0.840889i	$-0.682032\pi$
$29$	−8.05787	−	2.93282i	−1.49631	−	0.544612i	−0.955102	+	0.296278i	$0.904255\pi$
$30$	−1.35718	+	2.35070i	−0.247785	+	0.429177i
$31$	2.34622	+	4.06377i	0.421393	+	0.729874i	0.996076	−	0.0885019i	$-0.0282079\pi$
$31$	2.34622	+	4.06377i	0.421393	+	0.729874i	−0.574683	+	0.818376i	$0.694875\pi$
$32$	−0.544580	−	3.08847i	−0.0962691	−	0.545969i
$33$	−4.92191	−	4.12997i	−0.856794	−	0.718935i
$34$	−0.349999	+	0.293684i	−0.0600243	+	0.0503663i
$35$	0.381417	−	2.16312i	0.0644712	−	0.365634i
$36$	1.16939	−	0.425623i	0.194898	−	0.0709372i
$37$	−10.7694			−1.77048			−0.885242	−	0.465131i	$-0.846007\pi$
$37$	−10.7694			−1.77048			−0.885242	+	0.465131i	$0.846007\pi$
$38$	−4.47097	−	2.66478i	−0.725287	−	0.432285i
$39$	9.27731			1.48556
$40$	2.88840	−	1.05129i	0.456696	−	0.166224i
$41$	0.544445	−	3.08770i	0.0850280	−	0.482218i	−0.912323	−	0.409472i	$-0.865713\pi$
$41$	0.544445	−	3.08770i	0.0850280	−	0.482218i	0.997351	−	0.0727454i	$-0.0231760\pi$
$42$	4.56720	−	3.83233i	0.704734	−	0.591342i
$43$	1.53900	+	1.29137i	0.234695	+	0.196933i	0.752549	−	0.658537i	$-0.228824\pi$
$43$	1.53900	+	1.29137i	0.234695	+	0.196933i	−0.517853	+	0.855469i	$0.673269\pi$
$44$	0.281814	+	1.59824i	0.0424850	+	0.240944i
$45$	1.08367	+	1.87697i	0.161544	+	0.279803i
$46$	−1.77675	+	3.07743i	−0.261968	+	0.453742i
$47$	10.2405	+	3.72722i	1.49372	+	0.543671i	0.954427	−	0.298444i	$-0.0964677\pi$
$47$	10.2405	+	3.72722i	1.49372	+	0.543671i	0.539297	+	0.842115i	$0.318690\pi$
$48$	5.38714	+	1.96076i	0.777567	+	0.283011i
$49$	1.08771	−	1.88398i	0.155388	−	0.269140i
$50$	0.597039	+	1.03410i	0.0844341	+	0.146244i
$51$	0.151037	+	0.856574i	0.0211494	+	0.119944i
$52$	−1.79510	−	1.50627i	−0.248936	−	0.208882i
$53$	5.72676	−	4.80532i	0.786631	−	0.660062i	−0.158278	−	0.987395i	$-0.550594\pi$
$53$	5.72676	−	4.80532i	0.786631	−	0.660062i	0.944909	+	0.327333i	$0.106150\pi$
$54$	0.392467	−	2.22579i	0.0534080	−	0.302892i
$55$	−2.65602	+	0.966713i	−0.358138	+	0.130352i
$56$	−6.75150			−0.902208
$57$	−8.64904	+	4.83463i	−1.14559	+	0.640362i
$58$	−10.2392			−1.34448
$59$	12.1961	−	4.43900i	1.58779	−	0.577909i	0.610912	−	0.791698i	$-0.290803\pi$
$59$	12.1961	−	4.43900i	1.58779	−	0.577909i	0.976880	+	0.213789i	$0.0685806\pi$
$60$	0.226647	−	1.28538i	0.0292600	−	0.165942i
$61$	4.57784	−	3.84126i	0.586132	−	0.491823i	−0.300822	−	0.953680i	$-0.597261\pi$
$61$	4.57784	−	3.84126i	0.586132	−	0.491823i	0.886954	+	0.461857i	$0.152817\pi$
$62$	4.29225	+	3.60163i	0.545116	+	0.457407i
$63$	−0.826660	−	4.68822i	−0.104149	−	0.590660i
$64$	−4.39435	−	7.61123i	−0.549294	−	0.951404i
$65$	2.04060	−	3.53443i	0.253106	−	0.438392i
$66$	−7.20938	−	2.62400i	−0.887413	−	0.322992i
$67$	−0.986138	−	0.358925i	−0.120476	−	0.0438496i	0.281079	−	0.959685i	$-0.409308\pi$
$67$	−0.986138	−	0.358925i	−0.120476	−	0.0438496i	−0.401555	+	0.915835i	$0.631530\pi$
$68$	0.109849	−	0.190264i	0.0133211	−	0.0230729i
$69$	3.38242	+	5.85853i	0.407196	+	0.705284i
$70$	−0.455441	−	2.58294i	−0.0544356	−	0.308720i
$71$	−5.99626	−	5.03146i	−0.711625	−	0.597124i	0.213430	−	0.976958i	$-0.431537\pi$
$71$	−5.99626	−	5.03146i	−0.711625	−	0.597124i	−0.925055	+	0.379834i	$0.875981\pi$
$72$	5.10332	−	4.28219i	0.601432	−	0.504661i
$73$	−2.44663	+	13.8755i	−0.286357	+	1.62401i	0.414042	+	0.910258i	$0.364117\pi$
$73$	−2.44663	+	13.8755i	−0.286357	+	1.62401i	−0.700399	+	0.713752i	$0.746995\pi$
$74$	−12.0840	+	4.39822i	−1.40474	+	0.511283i
$75$	2.27318			0.262484
$76$	2.45848	+	0.468792i	0.282008	+	0.0537741i
$77$	6.20833			0.707505
$78$	10.4098	−	3.78884i	1.17867	−	0.429002i
$79$	−2.33355	+	13.2342i	−0.262545	+	1.48897i	0.513390	+	0.858156i	$0.328390\pi$
$79$	−2.33355	+	13.2342i	−0.262545	+	1.48897i	−0.775935	+	0.630813i	$0.782722\pi$
$80$	1.93194	−	1.62109i	0.215997	−	0.181243i
$81$	−8.27685	−	6.94510i	−0.919650	−	0.771678i
$82$	−0.650110	−	3.68695i	−0.0717926	−	0.407156i
$83$	2.77807	+	4.81175i	0.304932	+	0.528158i	0.977246	−	0.212108i	$-0.0680328\pi$
$83$	2.77807	+	4.81175i	0.304932	+	0.528158i	−0.672314	+	0.740266i	$0.734699\pi$
$84$	−1.43344	+	2.48279i	−0.156401	+	0.270894i
$85$	0.359555	+	0.130867i	0.0389992	+	0.0141946i
$86$	2.25425	+	0.820481i	0.243082	+	0.0884748i
$87$	−9.74626	+	16.8810i	−1.04491	+	1.80984i
$88$	4.34397	+	7.52398i	0.463069	+	0.802059i
$89$	−1.13984	−	6.46435i	−0.120823	−	0.685220i	−0.983702	−	0.179809i	$-0.942452\pi$
$89$	−1.13984	−	6.46435i	−0.120823	−	0.685220i	0.862879	−	0.505411i	$-0.168659\pi$
$90$	1.98250	+	1.66352i	0.208974	+	0.175350i
$91$	−6.86708	+	5.76216i	−0.719865	+	0.604039i
$92$	0.296716	−	1.68276i	0.0309347	−	0.175440i
$93$	10.0235	−	3.64824i	1.03938	−	0.378305i
$94$	13.0127			1.34215
$95$	−0.0605361	+	4.35848i	−0.00621087	+	0.447170i
$96$	−7.12895			−0.727595
$97$	−13.5750	+	4.94091i	−1.37834	+	0.501673i	−0.921674	−	0.387966i	$-0.873178\pi$
$97$	−13.5750	+	4.94091i	−1.37834	+	0.501673i	−0.456663	+	0.889640i	$0.650955\pi$
$98$	0.451074	−	2.55817i	0.0455654	−	0.258414i
$99$	−4.69275	+	3.93768i	−0.471639	+	0.395752i
$100$	−0.439845	−	0.369074i	−0.0439845	−	0.0369074i
$101$	0.738074	+	4.18582i	0.0734411	+	0.416505i	0.999257	+	0.0385313i	$0.0122679\pi$
$101$	0.738074	+	4.18582i	0.0734411	+	0.416505i	−0.925816	+	0.377974i	$0.876621\pi$
$102$	0.519297	+	0.899449i	0.0514181	+	0.0890587i
$103$	7.33528	−	12.7051i	0.722767	−	1.25187i	−0.237119	−	0.971481i	$-0.576203\pi$
$103$	7.33528	−	12.7051i	0.722767	−	1.25187i	0.959887	−	0.280389i	$-0.0904634\pi$
$104$	−11.7882	−	4.29054i	−1.15592	−	0.420722i
$105$	−4.69190	−	1.70771i	−0.457883	−	0.166656i
$106$	4.46332	−	7.73070i	0.433516	−	0.750872i
$107$	3.09023	+	5.35244i	0.298744	+	0.517439i	0.975849	−	0.218447i	$-0.0700991\pi$
$107$	3.09023	+	5.35244i	0.298744	+	0.517439i	−0.677105	+	0.735886i	$0.736766\pi$
$108$	0.188720	+	1.07028i	0.0181595	+	0.102988i
$109$	0.577493	+	0.484574i	0.0553138	+	0.0464138i	0.670025	−	0.742338i	$-0.266283\pi$
$109$	0.577493	+	0.484574i	0.0553138	+	0.0464138i	−0.614712	+	0.788752i	$0.710728\pi$
$110$	−2.58543	+	2.16943i	−0.246511	+	0.206847i
$111$	−4.25105	+	24.1089i	−0.403492	+	2.28832i
$112$	−5.20540	+	1.89461i	−0.491864	+	0.179024i
$113$	0.870003			0.0818430			0.0409215	−	0.999162i	$-0.486971\pi$
$113$	0.870003			0.0818430			0.0409215	+	0.999162i	$0.486971\pi$
$114$	−7.73034	+	8.95703i	−0.724013	+	0.838903i
$115$	2.97594			0.277508
$116$	4.62665	−	1.68396i	0.429573	−	0.156352i
$117$	1.53598	−	8.71099i	0.142002	−	0.805331i
$118$	11.8719	−	9.96171i	1.09290	−	0.917050i
$119$	−0.643818	−	0.540227i	−0.0590187	−	0.0495225i
$120$	−1.21332	−	6.88107i	−0.110760	−	0.628153i
$121$	1.50551	+	2.60762i	0.136864	+	0.237056i
$122$	3.56787	−	6.17973i	0.323020	−	0.559487i
$123$	−6.69735	−	2.43764i	−0.603880	−	0.219794i
$124$	−2.53180	−	0.921502i	−0.227363	−	0.0827533i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	−2.84223	−	4.92289i	−0.253206	−	0.438566i
$127$	−0.598116	−	3.39209i	−0.0530743	−	0.300999i	0.946703	−	0.322108i	$-0.104391\pi$
$127$	−0.598116	−	3.39209i	−0.0530743	−	0.300999i	−0.999777	+	0.0211090i	$0.993280\pi$
$128$	−3.23436	−	2.71395i	−0.285880	−	0.239882i
$129$	3.49842	−	2.93552i	0.308019	−	0.258458i
$130$	0.846236	−	4.79924i	0.0742198	−	0.420922i
$131$	−9.67954	+	3.52307i	−0.845706	+	0.307812i	−0.728288	−	0.685271i	$-0.759684\pi$
$131$	−9.67954	+	3.52307i	−0.845706	+	0.307812i	−0.117418	+	0.993083i	$0.537462\pi$
$132$	3.68914			0.321099
$133$	3.39923	−	8.95054i	0.294751	−	0.776110i
$134$	−1.25310			−0.108251
$135$	−1.77863	+	0.647370i	−0.153080	+	0.0557167i
$136$	0.204231	−	1.15825i	0.0175126	−	0.0993191i
$137$	1.12449	−	0.943562i	0.0960720	−	0.0806140i	−0.593487	−	0.804844i	$-0.702249\pi$
$137$	1.12449	−	0.943562i	0.0960720	−	0.0806140i	0.689559	+	0.724230i	$0.257805\pi$
$138$	6.18792	+	5.19228i	0.526750	+	0.441996i
$139$	−1.27243	−	7.21629i	−0.107926	−	0.612078i	−0.990011	−	0.140988i	$-0.954972\pi$
$139$	−1.27243	−	7.21629i	−0.107926	−	0.612078i	0.882085	−	0.471090i	$-0.156139\pi$
$140$	0.630588	+	1.09221i	0.0532944	+	0.0923086i
$141$	12.3862	−	21.4535i	1.04310	−	1.80671i
$142$	−8.78304	−	3.19677i	−0.737057	−	0.268267i
$143$	10.8398	+	3.94535i	0.906467	+	0.329927i
$144$	2.73298	−	4.73366i	0.227748	−	0.394472i
$145$	4.28750	+	7.42617i	0.356058	+	0.616710i
$146$	2.92147	+	16.5685i	0.241783	+	1.37122i
$147$	−3.78820	−	3.17868i	−0.312445	−	0.262173i
$148$	4.73689	−	3.97472i	0.389370	−	0.326720i
$149$	1.73507	−	9.84006i	0.142142	−	0.806129i	−0.827475	−	0.561503i	$-0.810223\pi$
$149$	1.73507	−	9.84006i	0.142142	−	0.806129i	0.969617	−	0.244627i	$-0.0786654\pi$
$150$	2.55066	−	0.928363i	0.208260	−	0.0758006i
$151$	15.0689			1.22629			0.613144	−	0.789971i	$-0.289905\pi$
$151$	15.0689			1.22629			0.613144	+	0.789971i	$0.289905\pi$
$152$	13.2257	−	2.14311i	1.07275	−	0.173829i
$153$	0.829291			0.0670442
$154$	6.96616	−	2.53548i	0.561349	−	0.204314i
$155$	0.814833	−	4.62115i	0.0654490	−	0.371179i
$156$	−4.08058	+	3.42402i	−0.326708	+	0.274141i
$157$	7.92438	+	6.64935i	0.632435	+	0.530676i	0.901684	−	0.432395i	$-0.142331\pi$
$157$	7.92438	+	6.64935i	0.632435	+	0.530676i	−0.269250	+	0.963070i	$0.586776\pi$
$158$	2.78645	+	15.8027i	0.221678	+	1.25720i
$159$	−8.49687	−	14.7170i	−0.673845	−	1.16713i
$160$	−1.56806	+	2.71595i	−0.123966	+	0.214715i
$161$	−6.14242	−	2.23566i	−0.484090	−	0.176194i
$162$	−12.1235	−	4.41261i	−0.952515	−	0.346687i
$163$	3.45005	−	5.97565i	0.270228	−	0.468049i	−0.698692	−	0.715423i	$-0.746234\pi$
$163$	3.45005	−	5.97565i	0.270228	−	0.468049i	0.968920	+	0.247373i	$0.0795674\pi$
$164$	0.900118	+	1.55905i	0.0702874	+	0.121741i
$165$	1.11571	+	6.32748i	0.0868575	+	0.492594i
$166$	5.08229	+	4.26455i	0.394462	+	0.330993i
$167$	9.08683	−	7.62476i	0.703160	−	0.590022i	−0.219510	−	0.975610i	$-0.570446\pi$
$167$	9.08683	−	7.62476i	0.703160	−	0.590022i	0.922671	+	0.385589i	$0.126002\pi$
$168$	−2.66504	+	15.1142i	−0.205613	+	1.16609i
$169$	−3.43575	+	1.25051i	−0.264289	+	0.0961932i
$170$	0.456891			0.0350419
$171$	3.10754	+	8.92150i	0.237639	+	0.682244i
$172$	−1.15353			−0.0879561
$173$	−23.8744	+	8.68955i	−1.81513	+	0.660655i	−0.818901	+	0.573935i	$0.805416\pi$
$173$	−23.8744	+	8.68955i	−1.81513	+	0.660655i	−0.996233	+	0.0867194i	$0.972362\pi$
$174$	−4.04176	+	22.9220i	−0.306405	+	1.73771i
$175$	−1.68261	+	1.41188i	−0.127193	+	0.106728i
$176$	5.46058	+	4.58197i	0.411607	+	0.345379i
$177$	−5.12316	−	29.0549i	−0.385080	−	2.18390i
$178$	−3.91901	−	6.78792i	−0.293742	−	0.508776i
$179$	0.194400	−	0.336710i	0.0145301	−	0.0251669i	−0.858669	−	0.512531i	$-0.828708\pi$
$179$	0.194400	−	0.336710i	0.0145301	−	0.0251669i	0.873199	+	0.487364i	$0.162041\pi$
$180$	−1.16939	−	0.425623i	−0.0871612	−	0.0317241i
$181$	−4.49536	−	1.63618i	−0.334137	−	0.121616i	0.169502	−	0.985530i	$-0.445784\pi$
$181$	−4.49536	−	1.63618i	−0.334137	−	0.121616i	−0.503640	+	0.863914i	$0.668006\pi$
$182$	−5.35206	+	9.27003i	−0.396721	+	0.687141i
$183$	−6.79219	−	11.7644i	−0.502093	−	0.869651i
$184$	−1.58842	−	9.00838i	−0.117100	−	0.664107i
$185$	8.24986	+	6.92246i	0.606542	+	0.508949i
$186$	9.75705	−	8.18714i	0.715422	−	0.600310i
$187$	−0.187800	+	1.06507i	−0.0137333	+	0.0778854i
$188$	−5.87984	+	2.14009i	−0.428831	+	0.156082i
$189$	4.15748			0.302412
$190$	1.71207	+	4.91523i	0.124207	+	0.356588i
$191$	−23.8516			−1.72584			−0.862921	−	0.505338i	$-0.831368\pi$
$191$	−23.8516			−1.72584			−0.862921	+	0.505338i	$0.831368\pi$
$192$	−18.7734	+	6.83297i	−1.35486	+	0.493127i
$193$	−1.94937	+	11.0554i	−0.140319	+	0.795787i	0.830688	+	0.556737i	$0.187947\pi$
$193$	−1.94937	+	11.0554i	−0.140319	+	0.795787i	−0.971007	+	0.239050i	$0.923164\pi$
$194$	−13.2142	+	11.0881i	−0.948727	+	0.796076i
$195$	−7.10683	−	5.96334i	−0.508931	−	0.427044i
$196$	0.216901	+	1.23011i	0.0154929	+	0.0878647i
$197$	8.43639	+	14.6122i	0.601068	+	1.04108i	0.992660	+	0.120941i	$0.0385911\pi$
$197$	8.43639	+	14.6122i	0.601068	+	1.04108i	−0.391592	+	0.920139i	$0.628076\pi$
$198$	−3.65743	+	6.33485i	−0.259922	+	0.450198i
$199$	14.7743	+	5.37740i	1.04732	+	0.381194i	0.807651	−	0.589660i	$-0.200738\pi$
$199$	14.7743	+	5.37740i	1.04732	+	0.381194i	0.239670	+	0.970854i	$0.422961\pi$
$200$	−2.88840	−	1.05129i	−0.204241	−	0.0743375i
$201$	−1.19277	+	2.06593i	−0.0841312	+	0.145720i
$202$	2.53765	+	4.39534i	0.178549	+	0.309255i
$203$	−3.27065	−	18.5488i	−0.229555	−	1.30187i
$204$	−0.382572	−	0.321016i	−0.0267854	−	0.0224756i
$205$	−2.40180	+	2.01535i	−0.167749	+	0.140758i
$206$	3.04194	−	17.2517i	0.211942	−	1.20198i
$207$	6.06090	−	2.20599i	0.421262	−	0.153327i
$208$	−10.2927			−0.713668
$209$	−12.1617	+	1.97069i	−0.841243	+	0.136316i
$210$	−5.96205			−0.411421
$211$	8.72857	−	3.17694i	0.600899	−	0.218709i	−0.0236172	−	0.999721i	$-0.507518\pi$
$211$	8.72857	−	3.17694i	0.600899	−	0.218709i	0.624517	+	0.781012i	$0.285296\pi$
$212$	−0.745369	+	4.22720i	−0.0511922	+	0.290325i
$213$	−13.6306	+	11.4374i	−0.933951	+	0.783678i
$214$	5.65337	+	4.74374i	0.386457	+	0.324276i
$215$	−0.348863	−	1.97850i	−0.0237922	−	0.134932i
$216$	2.90899	+	5.03851i	0.197932	+	0.342827i
$217$	−5.15344	+	8.92603i	−0.349839	+	0.605938i
$218$	0.845885	+	0.307877i	0.0572906	+	0.0208521i
$219$	30.0966	+	10.9543i	2.03374	+	0.740221i
$220$	0.811450	−	1.40547i	0.0547080	−	0.0947570i
$221$	−0.780797	−	1.35238i	−0.0525221	−	0.0909710i
$222$	5.07609	+	28.7879i	0.340685	+	1.93212i
$223$	−2.13799	−	1.79399i	−0.143170	−	0.120134i	0.568390	−	0.822759i	$-0.307567\pi$
$223$	−2.13799	−	1.79399i	−0.143170	−	0.120134i	−0.711560	+	0.702625i	$0.752011\pi$
$224$	5.27685	−	4.42781i	0.352575	−	0.295845i
$225$	0.376355	−	2.13441i	0.0250903	−	0.142294i
$226$	0.976201	−	0.355308i	0.0649359	−	0.0236347i
$227$	−0.844086			−0.0560240			−0.0280120	−	0.999608i	$-0.508918\pi$
$227$	−0.844086			−0.0560240			−0.0280120	+	0.999608i	$0.508918\pi$
$228$	2.01990	−	5.31862i	0.133771	−	0.352235i
$229$	21.9559			1.45089			0.725444	−	0.688282i	$-0.241635\pi$
$229$	21.9559			1.45089			0.725444	+	0.688282i	$0.241635\pi$
$230$	3.33920	−	1.21537i	0.220180	−	0.0801391i
$231$	2.45064	−	13.8982i	0.161240	−	0.914438i
$232$	20.1911	−	16.9423i	1.32561	−	1.11232i
$233$	−3.38242	−	2.83819i	−0.221590	−	0.185936i	0.525234	−	0.850958i	$-0.323978\pi$
$233$	−3.38242	−	2.83819i	−0.221590	−	0.185936i	−0.746824	+	0.665022i	$0.768422\pi$
$234$	−1.83408	−	10.4016i	−0.119898	−	0.679974i
$235$	−5.44883	−	9.43766i	−0.355443	−	0.615645i
$236$	−3.72606	+	6.45373i	−0.242546	+	0.420102i
$237$	28.7056	+	10.4480i	1.86463	+	0.678670i
$238$	−0.943034	−	0.343236i	−0.0611278	−	0.0222487i
$239$	−9.91358	+	17.1708i	−0.641256	+	1.11069i	0.343896	+	0.939008i	$0.388253\pi$
$239$	−9.91358	+	17.1708i	−0.641256	+	1.11069i	−0.985153	+	0.171681i	$0.945080\pi$
$240$	−2.86644	−	4.96482i	−0.185028	−	0.320478i
$241$	−3.62651	−	20.5670i	−0.233604	−	1.32484i	−0.845533	−	0.533923i	$-0.820717\pi$
$241$	−3.62651	−	20.5670i	−0.233604	−	1.32484i	0.611929	−	0.790913i	$-0.290394\pi$
$242$	2.75423	+	2.31107i	0.177049	+	0.148561i
$243$	−14.4649	+	12.1375i	−0.927923	+	0.778620i
$244$	−0.595830	+	3.37912i	−0.0381441	+	0.216326i
$245$	−2.04424	+	0.744041i	−0.130601	+	0.0475350i
$246$	−8.51040			−0.542603
$247$	11.6231	−	13.4675i	0.739558	−	0.856915i
$248$	−14.4235			−0.915891
$249$	11.8684	−	4.31974i	0.752129	−	0.273753i
$250$	0.207349	−	1.17594i	0.0131139	−	0.0743728i
$251$	4.25499	−	3.57036i	0.268573	−	0.225359i	−0.498548	−	0.866862i	$-0.666133\pi$
$251$	4.25499	−	3.57036i	0.268573	−	0.225359i	0.767121	+	0.641503i	$0.221689\pi$
$252$	2.09390	+	1.75699i	0.131904	+	0.110680i
$253$	1.46063	+	8.28364i	0.0918290	+	0.520788i
$254$	−2.05645	−	3.56188i	−0.129033	−	0.223492i
$255$	0.434894	−	0.753258i	0.0272341	−	0.0471709i
$256$	11.7798	+	4.28750i	0.736237	+	0.267969i
$257$	−18.9036	−	6.88036i	−1.17918	−	0.429185i	−0.323266	−	0.946308i	$-0.604781\pi$
$257$	−18.9036	−	6.88036i	−1.17918	−	0.429185i	−0.855911	+	0.517123i	$0.827003\pi$
$258$	2.72659	−	4.72260i	0.169750	−	0.294016i
$259$	−11.8275	−	20.4858i	−0.734924	−	1.27293i
$260$	0.406916	+	2.30774i	0.0252359	+	0.143120i
$261$	14.2369	+	11.9462i	0.881242	+	0.739450i
$262$	−9.42228	+	7.90623i	−0.582110	+	0.488448i
$263$	2.03312	−	11.5304i	0.125368	−	0.710995i	−0.855721	−	0.517437i	$-0.826886\pi$
$263$	2.03312	−	11.5304i	0.125368	−	0.710995i	0.981089	−	0.193558i	$-0.0620028\pi$
$264$	18.5582	−	6.75464i	1.14218	−	0.415719i
$265$	−7.47576			−0.459232
$266$	0.158773	−	11.4313i	0.00973499	−	0.700900i
$267$	−14.9213			−0.913169
$268$	0.566218	−	0.206086i	0.0345873	−	0.0125887i
$269$	−2.23756	+	12.6898i	−0.136426	+	0.773712i	0.837429	+	0.546545i	$0.184057\pi$
$269$	−2.23756	+	12.6898i	−0.136426	+	0.773712i	−0.973856	+	0.227167i	$0.927054\pi$
$270$	−1.73136	+	1.45278i	−0.105367	+	0.0884136i
$271$	−11.8097	−	9.90953i	−0.717389	−	0.601961i	0.209273	−	0.977857i	$-0.432890\pi$
$271$	−11.8097	−	9.90953i	−0.717389	−	0.601961i	−0.926662	+	0.375896i	$0.877335\pi$
$272$	−0.167567	−	0.950321i	−0.0101603	−	0.0576217i
$273$	10.1888	+	17.6475i	0.616652	+	1.06807i
$274$	0.876407	−	1.51798i	0.0529457	−	0.0917046i
$275$	2.65602	+	0.966713i	0.160164	+	0.0582950i
$276$	−3.64997	−	1.32848i	−0.219703	−	0.0799652i
$277$	−2.64855	+	4.58742i	−0.159136	+	0.275632i	−0.934557	−	0.355813i	$-0.884204\pi$
$277$	−2.64855	+	4.58742i	−0.159136	+	0.275632i	0.775421	+	0.631444i	$0.217537\pi$
$278$	−4.37487	−	7.57750i	−0.262387	−	0.454468i
$279$	−1.76602	−	10.0156i	−0.105729	−	0.599618i
$280$	5.17195	+	4.33978i	0.309083	+	0.259352i
$281$	−4.12384	+	3.46031i	−0.246008	+	0.206425i	−0.757451	−	0.652892i	$-0.773555\pi$
$281$	−4.12384	+	3.46031i	−0.246008	+	0.206425i	0.511443	+	0.859317i	$0.329111\pi$
$282$	5.13653	−	29.1307i	0.305876	−	1.73471i
$283$	−16.6106	+	6.04576i	−0.987397	+	0.359383i	−0.784712	−	0.619861i	$-0.787189\pi$
$283$	−16.6106	+	6.04576i	−0.987397	+	0.359383i	−0.202685	+	0.979244i	$0.564967\pi$
$284$	4.49441			0.266694
$285$	9.73319	+	1.85596i	0.576544	+	0.109937i
$286$	13.7742			0.814487
$287$	6.47141	−	2.35540i	0.381995	−	0.139035i
$288$	−1.18029	+	6.69377i	−0.0695494	+	0.394434i
$289$	−12.9106	+	10.8333i	−0.759447	+	0.637252i
$290$	7.84370	+	6.58165i	0.460598	+	0.386488i
$291$	5.70242	+	32.3400i	0.334282	+	1.89581i
$292$	−4.04496	−	7.00608i	−0.236714	−	0.410000i
$293$	−2.35524	+	4.07939i	−0.137594	+	0.238320i	−0.926586	−	0.376084i	$-0.877270\pi$
$293$	−2.35524	+	4.07939i	−0.137594	+	0.238320i	0.788991	+	0.614405i	$0.210604\pi$
$294$	−5.54878	−	2.01959i	−0.323611	−	0.117785i
$295$	−12.1961	−	4.43900i	−0.710082	−	0.258449i
$296$	16.5514	−	28.6678i	0.962029	−	1.66628i
$297$	−2.67495	−	4.63316i	−0.155217	−	0.268843i
$298$	−2.07181	−	11.7498i	−0.120017	−	0.680648i
$299$	−9.30394	−	7.80693i	−0.538061	−	0.451486i
$300$	−0.999847	+	0.838971i	−0.0577262	+	0.0484380i
$301$	−0.766273	+	4.34575i	−0.0441673	+	0.250485i
$302$	16.9083	−	6.15411i	0.972962	−	0.354129i
$303$	9.66191			0.555062
$304$	9.59563	−	5.36375i	0.550347	−	0.307632i
$305$	−5.97594			−0.342181
$306$	0.930520	−	0.338681i	0.0531943	−	0.0193611i
$307$	2.05006	−	11.6265i	0.117003	−	0.663557i	−0.868736	−	0.495275i	$-0.835067\pi$
$307$	2.05006	−	11.6265i	0.117003	−	0.663557i	0.985739	−	0.168281i	$-0.0538217\pi$
$308$	−2.73071	+	2.29134i	−0.155596	+	0.130561i
$309$	−25.5467	−	21.4362i	−1.45330	−	1.21946i
$310$	−0.972974	−	5.51801i	−0.0552612	−	0.313402i
$311$	4.47006	+	7.74236i	0.253474	+	0.439029i	0.964480	−	0.264157i	$-0.0850936\pi$
$311$	4.47006	+	7.74236i	0.253474	+	0.439029i	−0.711006	+	0.703186i	$0.751760\pi$
$312$	−14.2582	+	24.6959i	−0.807209	+	1.39813i
$313$	12.6205	+	4.59349i	0.713353	+	0.259639i	0.673101	−	0.739550i	$-0.264962\pi$
$313$	12.6205	+	4.59349i	0.713353	+	0.259639i	0.0402519	+	0.999190i	$0.487184\pi$
$314$	11.6073	+	4.22470i	0.655036	+	0.238414i
$315$	−2.38027	+	4.12275i	−0.134113	+	0.232291i
$316$	−3.85801	−	6.68227i	−0.217030	−	0.375907i
$317$	−1.92013	−	10.8896i	−0.107845	−	0.611622i	−0.990046	−	0.140747i	$-0.955049\pi$
$317$	−1.92013	−	10.8896i	−0.107845	−	0.611622i	0.882200	−	0.470875i	$-0.156062\pi$
$318$	−15.5445	−	13.0433i	−0.871690	−	0.731435i
$319$	−18.5667	+	15.5793i	−1.03953	+	0.872273i
$320$	−1.52614	+	8.65518i	−0.0853139	+	0.483839i
$321$	13.2020	−	4.80514i	0.736865	−	0.268197i
$322$	−7.80524			−0.434969
$323$	1.43268	+	0.853903i	0.0797163	+	0.0475124i
$324$	6.20379			0.344655
$325$	−3.83508	+	1.39586i	−0.212732	+	0.0774281i
$326$	1.43073	−	8.11408i	0.0792408	−	0.449397i
$327$	1.31275	−	1.10152i	0.0725950	−	0.0609144i
$328$	7.38259	+	6.19473i	0.407635	+	0.342047i
$329$	4.15655	+	23.5730i	0.229158	+	1.29962i
$330$	3.83603	+	6.64420i	0.211167	+	0.365751i
$331$	1.42273	−	2.46424i	0.0782003	−	0.135447i	−0.824273	−	0.566192i	$-0.808416\pi$
$331$	1.42273	−	2.46424i	0.0782003	−	0.135447i	0.902473	+	0.430745i	$0.141749\pi$
$332$	−2.99781	−	1.09111i	−0.164526	−	0.0598827i
$333$	21.9334	+	7.98310i	1.20194	+	0.437471i
$334$	7.08209	−	12.2665i	0.387515	−	0.671195i
$335$	0.524713	+	0.908829i	0.0286681	+	0.0496547i
$336$	2.18661	+	12.4009i	0.119290	+	0.676525i
$337$	4.90717	+	4.11760i	0.267311	+	0.224300i	0.766584	−	0.642145i	$-0.221955\pi$
$337$	4.90717	+	4.11760i	0.267311	+	0.224300i	−0.499273	+	0.866445i	$0.666400\pi$
$338$	−3.34444	+	2.80632i	−0.181913	+	0.152643i
$339$	0.343419	−	1.94763i	0.0186520	−	0.105781i
$340$	−0.206448	+	0.0751411i	−0.0111962	+	0.00407510i
$341$	13.2631			0.718235
$342$	7.13040	+	8.74140i	0.385568	+	0.472681i
$343$	20.1537			1.08820
$344$	−5.80285	+	2.11206i	−0.312869	+	0.113875i
$345$	1.17470	−	6.66207i	0.0632439	−	0.358674i
$346$	−23.2398	+	19.5005i	−1.24938	+	1.04835i
$347$	12.1057	+	10.1579i	0.649869	+	0.545305i	0.907031	−	0.421063i	$-0.138343\pi$
$347$	12.1057	+	10.1579i	0.649869	+	0.545305i	−0.257162	+	0.966368i	$0.582787\pi$
$348$	−1.94350	−	11.0221i	−0.104182	−	0.590848i
$349$	13.7825	+	23.8721i	0.737763	+	1.27784i	0.953501	+	0.301391i	$0.0974510\pi$
$349$	13.7825	+	23.8721i	0.737763	+	1.27784i	−0.215738	+	0.976451i	$0.569216\pi$
$350$	−1.31139	+	2.27140i	−0.0700968	+	0.121411i
$351$	7.25897	+	2.64205i	0.387455	+	0.141022i
$352$	−8.32959	−	3.03172i	−0.443968	−	0.161591i
$353$	2.11442	−	3.66228i	0.112539	−	0.194924i	−0.804254	−	0.594285i	$-0.797435\pi$
$353$	2.11442	−	3.66228i	0.112539	−	0.194924i	0.916793	+	0.399362i	$0.130768\pi$
$354$	−17.6145	−	30.5092i	−0.936200	−	1.62155i
$355$	1.35924	+	7.70864i	0.0721410	+	0.409132i
$356$	2.88718	+	2.42263i	0.153020	+	0.128399i
$357$	−1.46351	+	1.22803i	−0.0774573	+	0.0649944i
$358$	0.0806174	−	0.457204i	0.00426076	−	0.0241640i
$359$	−5.38553	+	1.96017i	−0.284237	+	0.103454i	−0.480205	−	0.877157i	$-0.659438\pi$
$359$	−5.38553	+	1.96017i	−0.284237	+	0.103454i	0.195967	+	0.980610i	$0.437215\pi$
$360$	−6.66191			−0.351113
$361$	−3.81772	+	18.6125i	−0.200932	+	0.979605i
$362$	−5.71231			−0.300232
$363$	6.43180	−	2.34099i	0.337582	−	0.122870i
$364$	0.893788	−	5.06892i	0.0468472	−	0.265684i
$365$	10.7933	−	9.05662i	0.564945	−	0.474045i
$366$	−12.4259	−	10.4265i	−0.649510	−	0.545004i
$367$	−0.164205	−	0.931253i	−0.00857143	−	0.0486110i	0.980222	−	0.197901i	$-0.0634124\pi$
$367$	−0.164205	−	0.931253i	−0.00857143	−	0.0486110i	−0.988793	+	0.149290i	$0.952301\pi$
$368$	−3.75261	−	6.49971i	−0.195618	−	0.338821i
$369$	−3.39767	+	5.88493i	−0.176876	+	0.306357i
$370$	12.0840	+	4.39822i	0.628218	+	0.228653i
$371$	15.4302	+	5.61612i	0.801094	+	0.291574i
$372$	−3.06230	+	5.30406i	−0.158773	+	0.275003i
$373$	−0.336649	−	0.583094i	−0.0174310	−	0.0301915i	0.857178	−	0.515020i	$-0.172215\pi$
$373$	−0.336649	−	0.583094i	−0.0174310	−	0.0301915i	−0.874609	+	0.484828i	$0.838882\pi$
$374$	0.224248	+	1.27177i	0.0115956	+	0.0657618i
$375$	−1.74136	−	1.46117i	−0.0899232	−	0.0754546i
$376$	−25.6601	+	21.5314i	−1.32332	+	1.11040i
$377$	6.07706	−	34.4647i	0.312984	−	1.77502i
$378$	4.66497	−	1.69791i	0.239940	−	0.0873310i
$379$	−34.7701			−1.78602			−0.893010	−	0.450037i	$-0.851411\pi$
$379$	−34.7701			−1.78602			−0.893010	+	0.450037i	$0.851411\pi$
$380$	−1.58198	−	1.93940i	−0.0811536	−	0.0994891i
$381$	−7.82977			−0.401131
$382$	−26.7631	+	9.74097i	−1.36932	+	0.498392i
$383$	4.73308	−	26.8426i	0.241849	−	1.37159i	−0.585849	−	0.810420i	$-0.699239\pi$
$383$	4.73308	−	26.8426i	0.241849	−	1.37159i	0.827698	−	0.561174i	$-0.189650\pi$
$384$	−7.35229	+	6.16930i	−0.375195	+	0.314826i
$385$	−4.75586	−	3.99064i	−0.242381	−	0.203382i
$386$	2.32770	+	13.2010i	0.118477	+	0.671916i
$387$	−2.17712	−	3.77088i	−0.110669	−	0.191684i
$388$	4.14736	−	7.18343i	0.210550	−	0.364684i
$389$	−34.2998	−	12.4841i	−1.73907	−	0.632969i	−0.739860	−	0.672761i	$-0.765108\pi$
$389$	−34.2998	−	12.4841i	−1.73907	−	0.632969i	−0.999208	+	0.0397915i	$0.987331\pi$
$390$	−10.4098	−	3.78884i	−0.527119	−	0.191856i
$391$	0.569343	−	0.986131i	0.0287929	−	0.0498708i
$392$	3.34338	+	5.79091i	0.168866	+	0.292485i
$393$	4.06605	+	23.0597i	0.205105	+	1.16321i
$394$	15.4338	+	12.9505i	0.777544	+	0.652437i
$395$	10.2944	−	8.63804i	0.517968	−	0.434627i
$396$	0.610786	−	3.46394i	0.0306932	−	0.174070i
$397$	13.0013	−	4.73209i	0.652517	−	0.237497i	0.00551465	−	0.999985i	$-0.498245\pi$
$397$	13.0013	−	4.73209i	0.652517	−	0.237497i	0.647002	+	0.762488i	$0.276022\pi$
$398$	18.7739			0.941048
$399$	−18.6953	−	11.1427i	−0.935934	−	0.557835i
$400$	−2.52197			−0.126098
$401$	−22.8095	+	8.30199i	−1.13905	+	0.414582i	−0.841572	−	0.540145i	$-0.818369\pi$
$401$	−22.8095	+	8.30199i	−1.13905	+	0.414582i	−0.297482	+	0.954727i	$0.596147\pi$
$402$	−0.494639	+	2.80524i	−0.0246703	+	0.139912i
$403$	−14.6704	+	12.3099i	−0.730783	+	0.613200i
$404$	−1.86952	−	1.56871i	−0.0930120	−	0.0780463i
$405$	1.87621	+	10.6405i	0.0932296	+	0.528731i
$406$	−11.2452	−	19.4772i	−0.558089	−	0.966638i
$407$	−15.2198	+	26.3614i	−0.754417	+	1.30669i
$408$	−2.51229	−	0.914400i	−0.124377	−	0.0452695i
$409$	31.8875	+	11.6061i	1.57674	+	0.573885i	0.974491	−	0.224426i	$-0.0720509\pi$
$409$	31.8875	+	11.6061i	1.57674	+	0.573885i	0.602245	+	0.798311i	$0.294273\pi$
$410$	−1.87192	+	3.24225i	−0.0924473	+	0.160123i
$411$	−1.66842	−	2.88980i	−0.0822973	−	0.142543i
$412$	1.46273	+	8.29554i	0.0720634	+	0.408692i
$413$	21.8382	+	18.3244i	1.07459	+	0.901686i
$414$	5.89981	−	4.95053i	0.289960	−	0.243305i
$415$	0.964812	−	5.47172i	0.0473608	−	0.268596i
$416$	12.0272	−	4.37756i	0.589684	−	0.214628i
$417$	−16.6570			−0.815696
$418$	−12.8414	+	7.17807i	−0.628094	+	0.351091i
$419$	21.4325			1.04705			0.523523	−	0.852012i	$-0.324618\pi$
$419$	21.4325			1.04705			0.523523	+	0.852012i	$0.324618\pi$
$420$	2.69398	−	0.980530i	0.131453	−	0.0478449i
$421$	−1.27528	+	7.23247i	−0.0621533	+	0.352489i	0.937832	+	0.347089i	$0.112830\pi$
$421$	−1.27528	+	7.23247i	−0.0621533	+	0.352489i	−0.999985	+	0.00539967i	$0.998281\pi$
$422$	8.49657	−	7.12947i	0.413607	−	0.347057i
$423$	−18.0932	−	15.1820i	−0.879720	−	0.738173i
$424$	3.99022	+	22.6297i	0.193782	+	1.09899i
$425$	−0.191315	−	0.331368i	−0.00928015	−	0.0160737i
$426$	−10.6234	+	18.4002i	−0.514704	+	0.891494i
$427$	12.3345	+	4.48939i	0.596908	+	0.217257i
$428$	−3.33467	−	1.21372i	−0.161187	−	0.0586674i
$429$	13.1111	−	22.7090i	0.633008	−	1.09640i
$430$	−1.19946	−	2.07753i	−0.0578433	−	0.100187i
$431$	0.0219443	+	0.124452i	0.00105702	+	0.00599466i	0.985332	−	0.170650i	$-0.0545868\pi$
$431$	0.0219443	+	0.124452i	0.00105702	+	0.00599466i	−0.984275	+	0.176645i	$0.943476\pi$
$432$	3.65674	+	3.06837i	0.175935	+	0.147627i
$433$	4.45694	−	3.73982i	0.214187	−	0.179724i	−0.529382	−	0.848384i	$-0.677576\pi$
$433$	4.45694	−	3.73982i	0.214187	−	0.179724i	0.743569	+	0.668660i	$0.233132\pi$
$434$	−2.13713	+	12.1203i	−0.102585	+	0.581791i
$435$	18.3170	−	6.66683i	0.878232	−	0.319650i
$436$	−0.432852			−0.0207298
$437$	12.7422	+	2.42973i	0.609544	+	0.116230i
$438$	38.2441			1.82738
$439$	−17.3872	+	6.32841i	−0.829844	+	0.302039i	−0.721795	−	0.692107i	$-0.756683\pi$
$439$	−17.3872	+	6.32841i	−0.829844	+	0.302039i	−0.108049	+	0.994146i	$0.534460\pi$
$440$	1.50865	−	8.55595i	0.0719218	−	0.407889i
$441$	−3.61182	+	3.03068i	−0.171992	+	0.144318i
$442$	−1.42842	−	1.19858i	−0.0679429	−	0.0570108i
$443$	3.84201	+	21.7891i	0.182539	+	1.03523i	0.929076	+	0.369889i	$0.120604\pi$
$443$	3.84201	+	21.7891i	0.182539	+	1.03523i	−0.746537	+	0.665344i	$0.768285\pi$
$444$	−7.02817	−	12.1732i	−0.333542	−	0.577712i
$445$	−3.28204	+	5.68465i	−0.155583	+	0.269478i
$446$	−3.13163	−	1.13982i	−0.148287	−	0.0539720i
$447$	−21.3435	−	7.76840i	−1.00951	−	0.367433i
$448$	9.65214	−	16.7180i	0.456021	−	0.789851i
$449$	10.2840	+	17.8124i	0.485331	+	0.840617i	0.999858	−	0.0168567i	$-0.00536591\pi$
$449$	10.2840	+	17.8124i	0.485331	+	0.840617i	−0.514527	+	0.857474i	$0.672033\pi$
$450$	−0.449397	−	2.54866i	−0.0211848	−	0.120145i
$451$	−6.78865	−	5.69635i	−0.319665	−	0.268231i
$452$	−0.382667	+	0.321096i	−0.0179991	+	0.0151031i
$453$	5.94819	−	33.7339i	0.279470	−	1.58495i
$454$	−0.947121	+	0.344724i	−0.0444506	+	0.0161787i
$455$	8.96433			0.420254
$456$	0.422979	−	30.4537i	0.0198078	−	1.42612i
$457$	20.3583			0.952323			0.476161	−	0.879358i	$-0.342028\pi$
$457$	20.3583			0.952323			0.476161	+	0.879358i	$0.342028\pi$
$458$	24.6360	−	8.96676i	1.15116	−	0.418989i
$459$	−0.125762	+	0.713233i	−0.00587008	+	0.0332909i
$460$	−1.30895	+	1.09834i	−0.0610303	+	0.0512105i
$461$	−4.24592	−	3.56275i	−0.197752	−	0.165934i	0.538535	−	0.842603i	$-0.318978\pi$
$461$	−4.24592	−	3.56275i	−0.197752	−	0.165934i	−0.736287	+	0.676670i	$0.763423\pi$
$462$	−2.92625	−	16.5956i	−0.136142	−	0.772097i
$463$	−16.3250	−	28.2757i	−0.758686	−	1.31408i	−0.943521	−	0.331313i	$-0.892508\pi$
$463$	−16.3250	−	28.2757i	−0.758686	−	1.31408i	0.184835	−	0.982770i	$-0.440825\pi$
$464$	10.8129	−	18.7286i	0.501978	−	0.869451i
$465$	−10.0235	−	3.64824i	−0.464827	−	0.169183i
$466$	−4.95442	−	1.80326i	−0.229509	−	0.0835344i
$467$	−14.3306	+	24.8214i	−0.663142	+	1.14860i	0.316643	+	0.948545i	$0.397444\pi$
$467$	−14.3306	+	24.8214i	−0.663142	+	1.14860i	−0.979785	+	0.200051i	$0.935889\pi$
$468$	2.53941	+	4.39838i	0.117384	+	0.203315i
$469$	−0.400268	−	2.27003i	−0.0184827	−	0.104820i
$470$	−9.96828	−	8.36438i	−0.459803	−	0.385820i
$471$	18.0135	−	15.1152i	0.830020	−	0.696469i
$472$	−6.92748	+	39.2877i	−0.318863	+	1.80836i
$473$	5.33600	−	1.94214i	0.245350	−	0.0892999i
$474$	36.4766			1.67542
$475$	2.84795	−	3.29988i	0.130673	−	0.151409i
$476$	0.482564			0.0221183
$477$	−15.2254	+	5.54159i	−0.697123	+	0.253732i
$478$	−4.11115	+	23.3155i	−0.188040	+	1.06643i
$479$	7.86922	−	6.60306i	0.359554	−	0.301701i	−0.445059	−	0.895501i	$-0.646817\pi$
$479$	7.86922	−	6.60306i	0.359554	−	0.301701i	0.804613	+	0.593800i	$0.202373\pi$
$480$	5.46109	+	4.58240i	0.249264	+	0.209157i
$481$	−7.63223	−	43.2846i	−0.348000	−	1.97361i
$482$	−12.4687	−	21.5964i	−0.567934	−	0.983691i
$483$	−7.42946	+	12.8682i	−0.338052	+	0.585523i
$484$	−1.62460	−	0.591304i	−0.0738453	−	0.0268775i
$485$	13.5750	+	4.94091i	0.616411	+	0.224355i
$486$	−11.2736	+	19.5265i	−0.511382	+	0.885740i
$487$	−5.56223	−	9.63406i	−0.252049	−	0.436561i	0.712041	−	0.702138i	$-0.247771\pi$
$487$	−5.56223	−	9.63406i	−0.252049	−	0.436561i	−0.964090	+	0.265577i	$0.914438\pi$
$488$	3.18968	+	18.0896i	0.144390	+	0.818878i
$489$	−12.0155	−	10.0822i	−0.543360	−	0.455934i
$490$	−1.98990	+	1.66973i	−0.0898946	+	0.0754305i
$491$	2.41105	−	13.6738i	0.108809	−	0.617089i	−0.880821	−	0.473450i	$-0.843009\pi$
$491$	2.41105	−	13.6738i	0.108809	−	0.617089i	0.989630	−	0.143639i	$-0.0458804\pi$
$492$	3.84547	−	1.39964i	0.173367	−	0.0631004i
$493$	3.28106			0.147771
$494$	7.54176	−	19.8583i	0.339320	−	0.893465i
$495$	6.12594			0.275341
$496$	−11.1205	+	4.04752i	−0.499324	+	0.181739i
$497$	2.98556	−	16.9320i	0.133921	−	0.759502i
$498$	11.5530	−	9.69408i	0.517700	−	0.434402i
$499$	9.79608	+	8.21989i	0.438533	+	0.367973i	0.835160	−	0.550007i	$-0.185375\pi$
$499$	9.79608	+	8.21989i	0.438533	+	0.367973i	−0.396627	+	0.917980i	$0.629819\pi$
$500$	0.0997049	+	0.565454i	0.00445894	+	0.0252879i
$501$	−13.4822	−	23.3519i	−0.602342	−	1.04329i
$502$	3.31625	−	5.74392i	0.148012	−	0.256364i
$503$	−9.83338	−	3.57906i	−0.438449	−	0.159582i	0.113358	−	0.993554i	$-0.463839\pi$
$503$	−9.83338	−	3.57906i	−0.438449	−	0.159582i	−0.551807	+	0.833972i	$0.686061\pi$
$504$	13.7503	+	5.00472i	0.612489	+	0.222928i
$505$	2.12520	−	3.68095i	0.0945701	−	0.163800i
$506$	5.02195	+	8.69828i	0.223253	+	0.386686i
$507$	1.44324	+	8.18505i	0.0640968	+	0.363511i
$508$	1.51501	+	1.27124i	0.0672177	+	0.0564024i
$509$	21.4000	−	17.9567i	0.948539	−	0.795919i	−0.0305117	−	0.999534i	$-0.509714\pi$
$509$	21.4000	−	17.9567i	0.948539	−	0.795919i	0.979051	+	0.203616i	$0.0652692\pi$
$510$	0.180350	−	1.02282i	0.00798603	−	0.0452910i
$511$	−29.0813	+	10.5847i	−1.28648	+	0.468241i
$512$	23.4130			1.03472
$513$	−8.14422	+	1.31970i	−0.359576	+	0.0582660i
$514$	−24.0211			−1.05952
$515$	−13.7858	+	5.01763i	−0.607476	+	0.221103i
$516$	−0.455338	+	2.58235i	−0.0200451	+	0.113682i
$517$	23.5957	−	19.7992i	1.03774	−	0.870766i
$518$	−21.6376	−	18.1561i	−0.950701	−	0.797733i
$519$	10.0288	+	56.8762i	0.440216	+	2.49659i
$520$	6.27234	+	10.8640i	0.275060	+	0.476419i
$521$	4.03138	−	6.98256i	0.176618	−	0.305912i	−0.764102	−	0.645095i	$-0.776818\pi$
$521$	4.03138	−	6.98256i	0.176618	−	0.305912i	0.940720	+	0.339184i	$0.110151\pi$
$522$	20.8536	+	7.59008i	0.912736	+	0.332209i
$523$	10.8457	+	3.94751i	0.474249	+	0.172612i	0.568076	−	0.822976i	$-0.307688\pi$
$523$	10.8457	+	3.94751i	0.474249	+	0.172612i	−0.0938274	+	0.995588i	$0.529910\pi$
$524$	2.95723	−	5.12207i	0.129187	−	0.223759i
$525$	2.49651	+	4.32408i	0.108957	+	0.188718i
$526$	−2.42771	−	13.7682i	−0.105853	−	0.600322i
$527$	−1.37541	−	1.15411i	−0.0599138	−	0.0502736i
$528$	12.4129	−	10.4156i	0.540201	−	0.453283i
$529$	−2.45604	+	13.9289i	−0.106784	+	0.605605i
$530$	−8.38830	+	3.05309i	−0.364364	+	0.132618i
$531$	−28.1294			−1.22071
$532$	1.80828	+	5.19142i	0.0783987	+	0.225077i
$533$	12.7959			0.554254
$534$	−16.7427	+	6.09385i	−0.724528	+	0.263706i
$535$	1.07323	−	6.08657i	0.0463996	−	0.263145i
$536$	2.47102	−	2.07343i	0.106732	−	0.0895587i
$537$	−0.677038	−	0.568103i	−0.0292164	−	0.0245154i
$538$	2.67182	+	15.1526i	0.115190	+	0.653277i
$539$	−3.07440	−	5.32502i	−0.132424	−	0.229365i
$540$	0.543396	−	0.941190i	0.0233841	−	0.0405024i
$541$	−32.1819	−	11.7133i	−1.38361	−	0.503593i	−0.460339	−	0.887743i	$-0.652272\pi$
$541$	−32.1819	−	11.7133i	−1.38361	−	0.503593i	−0.923270	+	0.384151i	$0.874494\pi$
$542$	−17.2983	−	6.29608i	−0.743027	−	0.270440i
$543$	−5.43729	+	9.41766i	−0.233336	+	0.404150i
$544$	0.599987	+	1.03921i	0.0257242	+	0.0445556i
$545$	−0.130907	−	0.742411i	−0.00560744	−	0.0318014i
$546$	18.6397	+	15.6405i	0.797704	+	0.669353i
$547$	−21.2152	+	17.8017i	−0.907098	+	0.761146i	−0.971565	−	0.236774i	$-0.923910\pi$
$547$	−21.2152	+	17.8017i	−0.907098	+	0.761146i	0.0644666	+	0.997920i	$0.479465\pi$
$548$	−0.146359	+	0.830043i	−0.00625214	+	0.0354577i
$549$	−12.1708	+	4.42981i	−0.519437	+	0.189060i
$550$	3.37504			0.143912
$551$	12.2949	+	35.2976i	0.523779	+	1.50373i
$552$	−20.7936			−0.885033
$553$	−27.7372	+	10.0955i	−1.17951	+	0.429305i
$554$	−1.09835	+	6.22906i	−0.0466645	+	0.264647i
$555$	18.7534	−	15.7360i	0.796038	−	0.667955i
$556$	3.22302	+	2.70443i	0.136686	+	0.114694i
$557$	2.36781	+	13.4285i	0.100327	+	0.568985i	0.992984	+	0.118248i	$0.0377277\pi$
$557$	2.36781	+	13.4285i	0.100327	+	0.568985i	−0.892657	+	0.450737i	$0.851161\pi$
$558$	−6.07195	−	10.5169i	−0.257046	−	0.445217i
$559$	−4.09961	+	7.10074i	−0.173395	+	0.300329i
$560$	5.20540	+	1.89461i	0.219968	+	0.0800619i
$561$	2.31017	+	0.840835i	0.0975356	+	0.0355001i
$562$	−3.21403	+	5.56687i	−0.135576	+	0.234824i
$563$	−19.5093	−	33.7910i	−0.822217	−	1.42412i	−0.904028	−	0.427474i	$-0.859404\pi$
$563$	−19.5093	−	33.7910i	−0.822217	−	1.42412i	0.0818108	−	0.996648i	$-0.473930\pi$
$564$	2.46992	+	14.0076i	0.104003	+	0.589828i
$565$	−0.666461	−	0.559227i	−0.0280382	−	0.0235269i
$566$	−16.1691	+	13.5675i	−0.679638	+	0.570284i
$567$	4.12107	−	23.3718i	0.173069	−	0.981522i
$568$	22.6091	−	8.22904i	0.948657	−	0.345283i
$569$	8.86810			0.371770			0.185885	−	0.982572i	$-0.440485\pi$
$569$	8.86810			0.371770			0.185885	+	0.982572i	$0.440485\pi$
$570$	11.6793	−	1.89252i	0.489190	−	0.0792688i
$571$	35.4054			1.48167			0.740834	−	0.671688i	$-0.234431\pi$
$571$	35.4054			1.48167			0.740834	+	0.671688i	$0.234431\pi$
$572$	−6.22395	+	2.26533i	−0.260237	+	0.0947184i
$573$	−9.41503	+	53.3953i	−0.393319	+	2.23062i
$574$	6.29941	−	5.28583i	0.262932	−	0.220626i
$575$	−2.27970	−	1.91290i	−0.0950702	−	0.0797733i
$576$	3.30767	+	18.7587i	0.137820	+	0.781613i
$577$	13.0041	+	22.5238i	0.541368	+	0.937677i	0.998826	+	0.0484454i	$0.0154267\pi$
$577$	13.0041	+	22.5238i	0.541368	+	0.937677i	−0.457458	+	0.889231i	$0.651240\pi$
$578$	−10.0623	+	17.4283i	−0.418535	+	0.724923i
$579$	23.9797	+	8.72790i	0.996562	+	0.362719i
$580$	−4.62665	−	1.68396i	−0.192111	−	0.0699227i
$581$	−6.10200	+	10.5690i	−0.253153	+	0.438475i
$582$	19.6061	+	33.9588i	0.812700	+	1.40764i
$583$	−3.66920	−	20.8091i	−0.151963	−	0.861823i
$584$	−33.1760	−	27.8379i	−1.37283	−	1.15194i
$585$	−6.77595	+	5.68569i	−0.280151	+	0.235075i
$586$	−0.976714	+	5.53922i	−0.0403477	+	0.228823i
$587$	−9.90499	+	3.60512i	−0.408823	+	0.148799i	−0.538241	−	0.842791i	$-0.680911\pi$
$587$	−9.90499	+	3.60512i	−0.408823	+	0.148799i	0.129419	+	0.991590i	$0.458689\pi$
$588$	2.83939			0.117094
$589$	7.26189	−	19.1213i	0.299221	−	0.787880i
$590$	−15.4977			−0.638029
$591$	36.0417	−	13.1181i	1.48256	−	0.539607i
$592$	4.71631	−	26.7475i	0.193839	−	1.09932i
$593$	−10.1307	+	8.50064i	−0.416017	+	0.349080i	−0.826645	−	0.562723i	$-0.809754\pi$
$593$	−10.1307	+	8.50064i	−0.416017	+	0.349080i	0.410629	+	0.911803i	$0.365309\pi$
$594$	−4.89365	−	4.10626i	−0.200789	−	0.168482i
$595$	0.145942	+	0.827676i	0.00598302	+	0.0339314i
$596$	2.86855	+	4.96848i	0.117500	+	0.203517i
$597$	17.8700	−	30.9517i	0.731370	−	1.26677i
$598$	−13.6280	−	4.96018i	−0.557289	−	0.202837i
$599$	3.49529	+	1.27218i	0.142814	+	0.0519800i	0.412438	−	0.910986i	$-0.364677\pi$
$599$	3.49529	+	1.27218i	0.142814	+	0.0519800i	−0.269624	+	0.962966i	$0.586900\pi$
$600$	−3.49361	+	6.05112i	−0.142626	+	0.247036i
$601$	21.0672	+	36.4895i	0.859349	+	1.48844i	0.872550	+	0.488524i	$0.162465\pi$
$601$	21.0672	+	36.4895i	0.859349	+	1.48844i	−0.0132009	+	0.999913i	$0.504202\pi$
$602$	0.914990	+	5.18917i	0.0372922	+	0.211495i
$603$	1.74234	+	1.46200i	0.0709536	+	0.0595371i
$604$	−6.62798	+	5.56153i	−0.269689	+	0.226296i
$605$	0.522858	−	2.96527i	0.0212572	−	0.120556i
$606$	10.8413	−	3.94591i	0.440398	−	0.160292i
$607$	−27.1082			−1.10029			−0.550144	−	0.835070i	$-0.685427\pi$
$607$	−27.1082			−1.10029			−0.550144	+	0.835070i	$0.685427\pi$
$608$	−8.93149	+	10.3488i	−0.362220	+	0.419699i
$609$	−42.8151			−1.73496
$610$	−6.70540	+	2.44057i	−0.271494	+	0.0988157i
$611$	−7.72311	+	43.8000i	−0.312444	+	1.77196i
$612$	−0.364760	+	0.306070i	−0.0147445	+	0.0123721i
$613$	−8.61611	−	7.22977i	−0.348001	−	0.292008i	0.451986	−	0.892025i	$-0.350716\pi$
$613$	−8.61611	−	7.22977i	−0.348001	−	0.292008i	−0.799987	+	0.600017i	$0.795160\pi$
$614$	−2.44793	−	13.8829i	−0.0987904	−	0.560268i
$615$	3.56359	+	6.17231i	0.143698	+	0.248892i
$616$	−9.54149	+	16.5263i	−0.384438	+	0.665866i
$617$	−28.8071	−	10.4849i	−1.15973	−	0.422108i	−0.310730	−	0.950498i	$-0.600573\pi$
$617$	−28.8071	−	10.4849i	−1.15973	−	0.422108i	−0.849001	+	0.528391i	$0.822796\pi$
$618$	−37.4196	−	13.6196i	−1.50524	−	0.547861i
$619$	20.1384	−	34.8807i	0.809431	−	1.40198i	−0.103828	−	0.994595i	$-0.533109\pi$
$619$	20.1384	−	34.8807i	0.809431	−	1.40198i	0.913259	−	0.407380i	$-0.133558\pi$
$620$	1.34715	+	2.33332i	0.0541027	+	0.0937085i
$621$	0.978126	+	5.54723i	0.0392509	+	0.222603i
$622$	8.17767	+	6.86188i	0.327895	+	0.275136i
$623$	11.0448	−	9.26766i	0.442499	−	0.371301i
$624$	−4.06286	+	23.0416i	−0.162644	+	0.922403i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	16.0370			0.640968
$627$	−0.388950	+	28.0036i	−0.0155332	+	1.11836i
$628$	−5.93960			−0.237016
$629$	3.87220	−	1.40937i	0.154395	−	0.0561951i
$630$	−0.987096	+	5.59810i	−0.0393269	+	0.223034i
$631$	29.6279	−	24.8608i	1.17947	−	0.989692i	0.179487	−	0.983760i	$-0.442556\pi$
$631$	29.6279	−	24.8608i	1.17947	−	0.989692i	0.999982	−	0.00593154i	$-0.00188808\pi$
$632$	−31.6426	−	26.5513i	−1.25868	−	1.05616i
$633$	−3.66658	−	20.7942i	−0.145733	−	0.826495i
$634$	−6.60183	−	11.4347i	−0.262192	−	0.454130i
$635$	−1.72221	+	2.98295i	−0.0683437	+	0.118375i
$636$	9.16897	+	3.33723i	0.363573	+	0.132330i
$637$	8.34295	+	3.03658i	0.330560	+	0.120314i
$638$	−14.4705	+	25.0636i	−0.572892	+	0.992278i
$639$	8.48250	+	14.6921i	0.335562	+	0.581211i
$640$	0.733171	+	4.15802i	0.0289811	+	0.164360i
$641$	−33.0725	−	27.7511i	−1.30628	−	1.09610i	−0.989023	−	0.147764i	$-0.952792\pi$
$641$	−33.0725	−	27.7511i	−1.30628	−	1.09610i	−0.317261	−	0.948338i	$-0.602763\pi$
$642$	12.8511	−	10.7834i	0.507193	−	0.425586i
$643$	0.760389	−	4.31238i	0.0299868	−	0.170064i	−0.966137	−	0.258032i	$-0.916926\pi$
$643$	0.760389	−	4.31238i	0.0299868	−	0.170064i	0.996123	+	0.0879678i	$0.0280373\pi$
$644$	3.52684	−	1.28366i	0.138977	−	0.0505834i
$645$	−4.56686			−0.179820
$646$	1.95629	+	0.373032i	0.0769693	+	0.0146768i
$647$	−16.4916			−0.648351			−0.324176	−	0.945997i	$-0.605087\pi$
$647$	−16.4916			−0.648351			−0.324176	+	0.945997i	$0.605087\pi$
$648$	31.2081	−	11.3588i	1.22597	−	0.446217i
$649$	6.37015	−	36.1269i	0.250050	−	1.41811i
$650$	−3.73315	+	3.13248i	−0.146426	+	0.122866i
$651$	17.9480	+	15.0601i	0.703436	+	0.590253i
$652$	0.687973	+	3.90169i	0.0269431	+	0.152802i
$653$	−0.813059	−	1.40826i	−0.0318175	−	0.0551095i	0.849678	−	0.527302i	$-0.176796\pi$
$653$	−0.813059	−	1.40826i	−0.0318175	−	0.0551095i	−0.881496	+	0.472192i	$0.843463\pi$
$654$	1.02313	−	1.77211i	0.0400074	−	0.0692949i
$655$	9.67954	+	3.52307i	0.378211	+	0.137658i
$656$	7.43034	+	2.70442i	0.290106	+	0.105590i
$657$	15.2685	−	26.4458i	0.595680	−	1.03175i
$658$	14.2911	+	24.7529i	0.557125	+	0.964969i
$659$	−0.331134	−	1.87796i	−0.0128992	−	0.0731548i	0.977679	−	0.210106i	$-0.0673808\pi$
$659$	−0.331134	−	1.87796i	−0.0128992	−	0.0731548i	−0.990578	+	0.136951i	$0.956270\pi$
$660$	−2.82605	−	2.37133i	−0.110004	−	0.0923041i
$661$	5.07136	−	4.25538i	0.197253	−	0.165515i	−0.538811	−	0.842426i	$-0.681126\pi$
$661$	5.07136	−	4.25538i	0.197253	−	0.165515i	0.736064	+	0.676911i	$0.236682\pi$
$662$	0.590004	−	3.34608i	0.0229312	−	0.130049i
$663$	−3.33571	+	1.21410i	−0.129548	+	0.0471516i
$664$	−17.0783			−0.662765
$665$	−8.35725	+	4.67153i	−0.324080	+	0.181154i
$666$	27.8710			1.07998
$667$	23.9797	−	8.72791i	0.928499	−	0.337946i
$668$	−1.18270	+	6.70743i	−0.0457601	+	0.259518i
$669$	−4.86003	+	4.07805i	−0.187900	+	0.157667i
$670$	0.959927	+	0.805475i	0.0370852	+	0.0311182i
$671$	−2.93307	−	16.6343i	−0.113230	−	0.642158i
$672$	−7.82933	−	13.5608i	−0.302023	−	0.523119i
$673$	6.22298	−	10.7785i	0.239878	−	0.415482i	−0.720801	−	0.693142i	$-0.756226\pi$
$673$	6.22298	−	10.7785i	0.239878	−	0.415482i	0.960679	+	0.277661i	$0.0895591\pi$
$674$	7.18779	+	2.61614i	0.276864	+	0.100770i
$675$	1.77863	+	0.647370i	0.0684596	+	0.0249173i
$676$	1.04967	−	1.81808i	0.0403719	−	0.0699261i
$677$	−2.35303	−	4.07556i	−0.0904342	−	0.156637i	0.817260	−	0.576270i	$-0.195492\pi$
$677$	−2.35303	−	4.07556i	−0.0904342	−	0.156637i	−0.907694	+	0.419633i	$0.862159\pi$
$678$	−0.410069	−	2.32562i	−0.0157486	−	0.0893149i
$679$	−24.3074	−	20.3963i	−0.932833	−	0.782739i
$680$	−0.900959	+	0.755994i	−0.0345502	+	0.0289910i
$681$	−0.333189	+	1.88961i	−0.0127678	+	0.0724100i
$682$	14.8820	−	5.41662i	0.569863	−	0.207413i
$683$	17.6914			0.676942			0.338471	−	0.940977i	$-0.390090\pi$
$683$	17.6914			0.676942			0.338471	+	0.940977i	$0.390090\pi$
$684$	−4.65953	−	2.77717i	−0.178162	−	0.106188i
$685$	−1.46792			−0.0560864
$686$	22.6138	−	8.23076i	0.863400	−	0.314252i
$687$	8.66673	−	49.1515i	0.330656	−	1.87524i
$688$	−3.88130	+	3.25680i	−0.147973	+	0.124164i
$689$	23.3721	+	19.6115i	0.890406	+	0.747140i
$690$	−1.40269	−	7.95503i	−0.0533994	−	0.302843i
$691$	−13.0639	−	22.6273i	−0.496974	−	0.860784i	0.503020	−	0.864275i	$-0.332222\pi$
$691$	−13.0639	−	22.6273i	−0.496974	−	0.860784i	−0.999994	+	0.00349090i	$0.998889\pi$
$692$	7.29394	−	12.6335i	0.277274	−	0.480252i
$693$	−12.6441	−	4.60208i	−0.480310	−	0.174819i
$694$	17.7319	+	6.45388i	0.673093	+	0.244986i
$695$	−3.66381	+	6.34590i	−0.138976	+	0.240714i
$696$	−29.9578	−	51.8883i	−1.13555	−	1.96682i
$697$	0.208321	+	1.18145i	0.00789073	+	0.0447505i
$698$	25.2143	+	21.1573i	0.954374	+	0.800814i
$699$	−7.68885	+	6.45171i	−0.290819	+	0.244026i
$700$	0.219001	−	1.24202i	0.00827745	−	0.0469438i
$701$	19.9867	−	7.27458i	0.754889	−	0.274757i	0.0642272	−	0.997935i	$-0.479542\pi$
$701$	19.9867	−	7.27458i	0.754889	−	0.274757i	0.690661	+	0.723178i	$0.257320\pi$
$702$	9.22406			0.348140
$703$	29.6720	+	36.3759i	1.11910	+	1.37194i
$704$	−24.8411			−0.936233
$705$	−23.2784	+	8.47264i	−0.876715	+	0.319098i
$706$	0.876847	−	4.97285i	0.0330006	−	0.187156i
$707$	−7.15176	+	6.00104i	−0.268970	+	0.225692i
$708$	12.9768	+	10.8888i	0.487698	+	0.409227i
$709$	1.84788	+	10.4798i	0.0693985	+	0.393578i	0.999645	+	0.0266433i	$0.00848181\pi$
$709$	1.84788	+	10.4798i	0.0693985	+	0.393578i	−0.930247	+	0.366935i	$0.880407\pi$
$710$	4.67336	+	8.09450i	0.175388	+	0.303781i
$711$	14.5628	−	25.2235i	0.546148	−	0.945956i
$712$	18.9597	+	6.90075i	0.710543	+	0.258617i
$713$	−13.1222	−	4.77611i	−0.491432	−	0.178867i
$714$	−1.14063	+	1.97563i	−0.0426871	+	0.0739361i
$715$	−5.76772	−	9.98999i	−0.215701	−	0.373604i
$716$	0.0387652	+	0.219848i	0.00144872	+	0.00821612i
$717$	34.5261	+	28.9709i	1.28940	+	1.08194i
$718$	−5.24239	+	4.39889i	−0.195644	+	0.164165i
$719$	−6.65775	+	37.7580i	−0.248292	+	1.40813i	0.564429	+	0.825481i	$0.309096\pi$
$719$	−6.65775	+	37.7580i	−0.248292	+	1.40813i	−0.812721	+	0.582653i	$0.802015\pi$
$720$	−5.13632	+	1.86947i	−0.191419	+	0.0696710i
$721$	32.2238			1.20008
$722$	3.31759	+	22.4436i	0.123468	+	0.835265i
$723$	−47.4736			−1.76556
$724$	2.58113	−	0.939456i	0.0959271	−	0.0349146i
$725$	1.48903	−	8.44473i	0.0553013	−	0.313629i
$726$	6.26086	−	5.25348i	0.232362	−	0.194975i
$727$	5.90339	+	4.95353i	0.218945	+	0.183716i	0.745663	−	0.666324i	$-0.232133\pi$
$727$	5.90339	+	4.95353i	0.218945	+	0.183716i	−0.526718	+	0.850040i	$0.676578\pi$
$728$	−4.78475	−	27.1357i	−0.177335	−	1.00572i
$729$	5.25474	+	9.10148i	0.194620	+	0.337092i
$730$	8.41204	−	14.5701i	0.311343	−	0.539263i
$731$	−0.722353	−	0.262915i	−0.0267172	−	0.00972427i
$732$	7.32946	+	2.66770i	0.270905	+	0.0986012i
$733$	−2.04263	+	3.53795i	−0.0754464	+	0.130677i	−0.901280	−	0.433236i	$-0.857372\pi$
$733$	−2.04263	+	3.53795i	−0.0754464	+	0.130677i	0.825834	+	0.563913i	$0.190705\pi$
$734$	−0.564571	−	0.977866i	−0.0208387	−	0.0360937i
$735$	0.858715	+	4.87001i	0.0316742	+	0.179633i
$736$	7.14941	+	5.99906i	0.263531	+	0.221128i
$737$	−2.27223	+	1.90662i	−0.0836985	+	0.0702314i
$738$	−1.40901	+	7.99089i	−0.0518663	+	0.294149i
$739$	23.1521	−	8.42669i	0.851665	−	0.309981i	0.120946	−	0.992659i	$-0.461407\pi$
$739$	23.1521	−	8.42669i	0.851665	−	0.309981i	0.730719	+	0.682678i	$0.239185\pi$
$740$	−6.18356			−0.227312
$741$	−25.5609	−	31.3360i	−0.939002	−	1.15116i
$742$	19.6073			0.719806
$743$	24.2217	−	8.81599i	0.888610	−	0.323427i	0.142931	−	0.989733i	$-0.454347\pi$
$743$	24.2217	−	8.81599i	0.888610	−	0.323427i	0.745679	+	0.666305i	$0.232125\pi$
$744$	−5.69342	+	32.2890i	−0.208731	+	1.18377i
$745$	−7.65421	+	6.42264i	−0.280429	+	0.235307i
$746$	−0.615878	−	0.516783i	−0.0225489	−	0.0189208i
$747$	−2.09108	−	11.8591i	−0.0765085	−	0.433901i
$748$	−0.310486	−	0.537777i	−0.0113525	−	0.0196631i
$749$	−6.78766	+	11.7566i	−0.248016	+	0.429576i
$750$	−2.55066	−	0.928363i	−0.0931368	−	0.0338990i
$751$	14.5890	+	5.30998i	0.532362	+	0.193764i	0.594193	−	0.804323i	$-0.297472\pi$
$751$	14.5890	+	5.30998i	0.532362	+	0.193764i	−0.0618308	+	0.998087i	$0.519694\pi$
$752$	−13.7418	+	23.8014i	−0.501111	+	0.867950i
$753$	−6.31319	−	10.9348i	−0.230065	−	0.398485i
$754$	−7.25648	−	41.1535i	−0.264265	−	1.49872i
$755$	−11.5434	−	9.68609i	−0.420108	−	0.352513i
$756$	−1.82865	+	1.53442i	−0.0665073	+	0.0558062i
$757$	−3.76351	+	21.3440i	−0.136787	+	0.775759i	0.836811	+	0.547492i	$0.184417\pi$
$757$	−3.76351	+	21.3440i	−0.136787	+	0.775759i	−0.973598	+	0.228268i	$0.926694\pi$
$758$	−39.0143	+	14.2001i	−1.41706	+	0.515769i
$759$	19.1207			0.694037
$760$	−11.5091	−	6.85962i	−0.417478	−	0.248825i
$761$	1.91229			0.0693204			0.0346602	−	0.999399i	$-0.488965\pi$
$761$	1.91229			0.0693204			0.0346602	+	0.999399i	$0.488965\pi$
$762$	−8.78552	+	3.19767i	−0.318266	+	0.115839i
$763$	−0.287536	+	1.63070i	−0.0104095	+	0.0590353i
$764$	10.4910	−	8.80302i	0.379552	−	0.318482i
$765$	−0.635274	−	0.533058i	−0.0229684	−	0.0192728i
$766$	−5.65167	−	32.0522i	−0.204203	−	1.15809i
$767$	26.4845	+	45.8726i	0.956301	+	1.65636i
$768$	14.2481	−	24.6784i	0.514133	−	0.890504i
$769$	−23.4461	−	8.53369i	−0.845489	−	0.307733i	−0.117289	−	0.993098i	$-0.537420\pi$
$769$	−23.4461	−	8.53369i	−0.845489	−	0.307733i	−0.728200	+	0.685365i	$0.759643\pi$
$770$	−6.96616	−	2.53548i	−0.251043	−	0.0913722i
$771$	−22.8646	+	39.6026i	−0.823448	+	1.42625i
$772$	−3.22285	−	5.58214i	−0.115993	−	0.200906i
$773$	−3.03236	−	17.1974i	−0.109067	−	0.618547i	−0.989518	−	0.144410i	$-0.953871\pi$
$773$	−3.03236	−	17.1974i	−0.109067	−	0.618547i	0.880451	−	0.474136i	$-0.157240\pi$
$774$	−3.98289	−	3.34204i	−0.143162	−	0.120127i
$775$	−3.59461	+	3.01624i	−0.129122	+	0.108347i
$776$	7.71075	−	43.7298i	0.276800	−	1.56981i
$777$	−50.5291	+	18.3911i	−1.81272	+	0.659777i
$778$	−43.5851			−1.56260
$779$	−11.9294	+	6.66827i	−0.427414	+	0.238915i
$780$	5.32682			0.190731
$781$	−20.7902	+	7.56700i	−0.743931	+	0.270769i
$782$	0.236106	−	1.33902i	0.00844313	−	0.0478834i
$783$	−12.4334	+	10.4328i	−0.444333	+	0.372839i
$784$	4.20279	+	3.52656i	0.150100	+	0.125949i
$785$	−1.79631	−	10.1874i	−0.0641131	−	0.363604i
$786$	13.9799	+	24.2140i	0.498648	+	0.863684i
$787$	24.5804	−	42.5745i	0.876196	−	1.51762i	0.0207128	−	0.999785i	$-0.493406\pi$
$787$	24.5804	−	42.5745i	0.876196	−	1.51762i	0.855483	−	0.517831i	$-0.173260\pi$
$788$	−9.10371	−	3.31348i	−0.324306	−	0.118038i
$789$	−25.0099	−	9.10287i	−0.890377	−	0.324071i
$790$	8.02325	−	13.8967i	0.285454	−	0.494422i
$791$	0.955477	+	1.65493i	0.0339728	+	0.0588427i
$792$	−3.26975	−	18.5437i	−0.116185	−	0.658921i
$793$	18.6831	+	15.6770i	0.663456	+	0.556706i
$794$	12.6558	−	10.6194i	0.449136	−	0.376870i
$795$	−2.95093	+	16.7356i	−0.104659	+	0.593549i
$796$	−8.48306	+	3.08758i	−0.300674	+	0.109436i
$797$	−35.4304			−1.25501			−0.627505	−	0.778613i	$-0.715924\pi$
$797$	−35.4304			−1.25501			−0.627505	+	0.778613i	$0.715924\pi$
$798$	−25.5280	−	4.86777i	−0.903682	−	0.172317i
$799$	−4.16978			−0.147516
$800$	2.94698	−	1.07261i	0.104192	−	0.0379226i
$801$	−2.47042	+	14.0105i	−0.0872880	+	0.495035i
$802$	−22.2033	+	18.6308i	−0.784026	+	0.657876i
$803$	30.5069	+	25.5983i	1.07657	+	0.903346i
$804$	−0.237849	−	1.34891i	−0.00838829	−	0.0475724i
$805$	3.26831	+	5.66088i	0.115193	+	0.199520i
$806$	−11.4338	+	19.8039i	−0.402738	+	0.697562i
$807$	27.5248	+	10.0182i	0.968917	+	0.352657i
$808$	−12.2768	−	4.46840i	−0.431898	−	0.157198i
$809$	18.1503	−	31.4373i	0.638131	−	1.10528i	−0.347711	−	0.937602i	$-0.613041\pi$
$809$	18.1503	−	31.4373i	0.638131	−	1.10528i	0.985842	−	0.167674i	$-0.0536257\pi$
$810$	6.45080	+	11.1731i	0.226658	+	0.392583i
$811$	−1.04633	−	5.93406i	−0.0367418	−	0.208373i	0.960910	−	0.276860i	$-0.0892939\pi$
$811$	−1.04633	−	5.93406i	−0.0367418	−	0.208373i	−0.997652	+	0.0684872i	$0.978183\pi$
$812$	8.28445	+	6.95148i	0.290727	+	0.243949i
$813$	−26.8456	+	22.5261i	−0.941516	+	0.790026i
$814$	−6.31163	+	35.7950i	−0.221223	+	1.25462i
$815$	−6.48397	+	2.35997i	−0.227123	+	0.0826662i
$816$	−2.19357			−0.0767905
$817$	0.121618	−	8.75627i	0.00425488	−	0.306343i
$818$	40.5198			1.41674
$819$	18.2571	−	6.64503i	0.637954	−	0.232196i
$820$	0.312608	−	1.77289i	0.0109167	−	0.0619119i
$821$	−28.0570	+	23.5426i	−0.979196	+	0.821643i	−0.983968	−	0.178345i	$-0.942926\pi$
$821$	−28.0570	+	23.5426i	−0.979196	+	0.821643i	0.00477169	+	0.999989i	$0.498481\pi$
$822$	−3.05227	−	2.56116i	−0.106460	−	0.0893307i
$823$	−2.65820	−	15.0754i	−0.0926590	−	0.525495i	−0.995440	−	0.0953939i	$-0.969589\pi$
$823$	−2.65820	−	15.0754i	−0.0926590	−	0.525495i	0.902781	−	0.430101i	$-0.141522\pi$
$824$	22.5470	+	39.0525i	0.785461	+	1.36046i
$825$	3.21255	−	5.56429i	0.111846	−	0.193724i
$826$	31.9876	+	11.6425i	1.11299	+	0.405096i
$827$	−19.8223	−	7.21472i	−0.689288	−	0.250880i	−0.0264579	−	0.999650i	$-0.508423\pi$
$827$	−19.8223	−	7.21472i	−0.689288	−	0.250880i	−0.662831	+	0.748769i	$0.730645\pi$
$828$	−1.85169	+	3.20722i	−0.0643506	+	0.111458i
$829$	−20.0967	−	34.8085i	−0.697987	−	1.20895i	−0.969163	−	0.246419i	$-0.920746\pi$
$829$	−20.0967	−	34.8085i	−0.697987	−	1.20895i	0.271177	−	0.962530i	$-0.412587\pi$
$830$	−1.15206	−	6.53366i	−0.0399886	−	0.226787i
$831$	9.22414	+	7.73997i	0.319982	+	0.268497i
$832$	27.4769	−	23.0558i	0.952589	−	0.799317i
$833$	−0.144542	+	0.819740i	−0.00500809	+	0.0284023i
$834$	−18.6902	+	6.80269i	−0.647190	+	0.235558i
$835$	−11.8620			−0.410502
$836$	4.62194	−	5.35537i	0.159853	−	0.185219i
$837$	8.88176			0.306998
$838$	24.0487	−	8.75300i	0.830747	−	0.302367i
$839$	4.84143	−	27.4571i	0.167145	−	0.947925i	−0.779681	−	0.626177i	$-0.784619\pi$
$839$	4.84143	−	27.4571i	0.167145	−	0.947925i	0.946825	−	0.321748i	$-0.104270\pi$
$840$	11.7568	−	9.86510i	0.405647	−	0.340378i
$841$	34.1125	+	28.6238i	1.17629	+	0.987027i
$842$	1.52278	+	8.63613i	0.0524786	+	0.297621i
$843$	6.11859	+	10.5977i	0.210735	+	0.365004i
$844$	−2.66669	+	4.61885i	−0.0917914	+	0.158987i
$845$	3.43575	+	1.25051i	0.118194	+	0.0430189i
$846$	−26.5021	−	9.64596i	−0.911159	−	0.331635i
$847$	−3.30684	+	5.72761i	−0.113624	+	0.196803i
$848$	9.42680	+	16.3277i	0.323718	+	0.560696i
$849$	6.97755	+	39.5717i	0.239469	+	1.35810i
$850$	−0.349999	−	0.293684i	−0.0120049	−	0.0100733i
$851$	24.5511	−	20.6008i	0.841601	−	0.706187i
$852$	1.77409	−	10.0614i	0.0607794	−	0.344697i
$853$	−18.9031	+	6.88015i	−0.647228	+	0.235572i	−0.644713	−	0.764425i	$-0.723023\pi$
$853$	−18.9031	+	6.88015i	−0.647228	+	0.235572i	−0.00251570	+	0.999997i	$0.500801\pi$
$854$	15.6736			0.536339
$855$	3.35412	−	8.83175i	0.114708	−	0.302040i
$856$	−18.9973			−0.649315
$857$	4.08976	−	1.48855i	0.139704	−	0.0508480i	−0.271222	−	0.962517i	$-0.587428\pi$
$857$	4.08976	−	1.48855i	0.139704	−	0.0508480i	0.410926	+	0.911669i	$0.365206\pi$
$858$	5.43715	−	30.8356i	0.185621	−	1.05271i
$859$	−4.22949	+	3.54896i	−0.144308	+	0.121089i	−0.712084	−	0.702094i	$-0.752249\pi$
$859$	−4.22949	+	3.54896i	−0.144308	+	0.121089i	0.567776	+	0.823183i	$0.307804\pi$
$860$	0.883658	+	0.741477i	0.0301325	+	0.0252842i
$861$	−2.71842	−	15.4169i	−0.0926435	−	0.525408i
$862$	0.0754492	+	0.130682i	0.00256981	+	0.00445104i
$863$	−17.9032	+	31.0093i	−0.609433	+	1.05557i	0.381901	+	0.924203i	$0.375270\pi$
$863$	−17.9032	+	31.0093i	−0.609433	+	1.05557i	−0.991334	+	0.131366i	$0.958064\pi$
$864$	−5.57800	−	2.03022i	−0.189767	−	0.0690697i
$865$	23.8744	+	8.68955i	0.811752	+	0.295454i
$866$	3.47365	−	6.01653i	0.118039	−	0.204450i
$867$	19.1556	+	33.1785i	0.650559	+	1.12680i
$868$	−1.02765	−	5.82808i	−0.0348806	−	0.197818i
$869$	29.0969	+	24.4152i	0.987046	+	0.828230i
$870$	17.8301	−	14.9613i	0.604498	−	0.507234i
$871$	0.743722	−	4.21786i	0.0252001	−	0.142917i
$872$	−2.17746	+	0.792530i	−0.0737381	+	0.0268385i
$873$	31.3100			1.05968
$874$	15.2899	−	2.47759i	0.517190	−	0.0838059i
$875$	2.19649			0.0742549
$876$	−17.2808	+	6.28970i	−0.583864	+	0.212509i
$877$	−4.25763	+	24.1462i	−0.143770	+	0.815360i	0.824577	+	0.565750i	$0.191413\pi$
$877$	−4.25763	+	24.1462i	−0.143770	+	0.815360i	−0.968347	+	0.249610i	$0.919698\pi$
$878$	−16.9250	+	14.2018i	−0.571193	+	0.479288i
$879$	8.20261	+	6.88280i	0.276667	+	0.232151i
$880$	−1.23781	−	7.01999i	−0.0417267	−	0.236644i
$881$	14.7421	+	25.5341i	0.496675	+	0.860266i	0.999993	−	0.00383530i	$-0.00122082\pi$
$881$	14.7421	+	25.5341i	0.496675	+	0.860266i	−0.503318	+	0.864101i	$0.667887\pi$
$882$	−2.81498	+	4.87569i	−0.0947853	+	0.164173i
$883$	7.54441	+	2.74594i	0.253890	+	0.0924083i	0.465830	−	0.884874i	$-0.345756\pi$
$883$	7.54441	+	2.74594i	0.253890	+	0.0924083i	−0.211940	+	0.977283i	$0.567978\pi$
$884$	0.842559	+	0.306666i	0.0283383	+	0.0103143i
$885$	−14.7515	+	25.5504i	−0.495868	+	0.858868i
$886$	13.2096	+	22.8798i	0.443787	+	0.768661i
$887$	3.63211	+	20.5987i	0.121954	+	0.691638i	0.983070	+	0.183229i	$0.0586550\pi$
$887$	3.63211	+	20.5987i	0.121954	+	0.691638i	−0.861116	+	0.508409i	$0.830234\pi$
$888$	−57.6437	−	48.3688i	−1.93439	−	1.62315i
$889$	5.79561	−	4.86309i	0.194378	−	0.163103i
$890$	−1.36106	+	7.71894i	−0.0456227	+	0.258739i
$891$	−28.6974	+	10.4450i	−0.961399	+	0.349921i
$892$	1.60250			0.0536556
$893$	−15.6251	−	44.8585i	−0.522874	−	1.50113i
$894$	−27.1214			−0.907077
$895$	−0.365352	+	0.132977i	−0.0122124	+	0.00444494i
$896$	1.61040	−	9.13305i	0.0537998	−	0.305114i
$897$	−21.1495	+	17.7465i	−0.706162	+	0.592540i
$898$	18.8138	+	15.7867i	0.627826	+	0.526809i
$899$	−6.98720	−	39.6264i	−0.233036	−	1.32161i
$900$	0.622219	+	1.07772i	0.0207406	+	0.0359238i
$901$	−1.43023	+	2.47723i	−0.0476478	+	0.0825283i
$902$	−9.94370	−	3.61921i	−0.331089	−	0.120506i
$903$	9.42612	+	3.43083i	0.313682	+	0.114171i
$904$	−1.33709	+	2.31591i	−0.0444711	+	0.0770262i
$905$	2.39193	+	4.14295i	0.0795105	+	0.137716i
$906$	−7.10260	−	40.2809i	−0.235968	−	1.33824i
$907$	−0.224543	−	0.188414i	−0.00745584	−	0.00625619i	0.639052	−	0.769163i	$-0.279327\pi$
$907$	−0.224543	−	0.188414i	−0.00745584	−	0.00625619i	−0.646508	+	0.762907i	$0.723771\pi$
$908$	0.371267	−	0.311530i	0.0123209	−	0.0103385i
$909$	1.59966	−	9.07211i	0.0530573	−	0.300903i
$910$	10.0586	−	3.66102i	0.333439	−	0.121362i
$911$	−22.0356			−0.730073			−0.365037	−	0.930993i	$-0.618944\pi$
$911$	−22.0356			−0.730073			−0.365037	+	0.930993i	$0.618944\pi$
$912$	−8.21981	−	23.5984i	−0.272185	−	0.781423i
$913$	15.7043			0.519736
$914$	22.8434	−	8.31432i	0.755592	−	0.275013i
$915$	−2.35890	+	13.3780i	−0.0779829	+	0.442263i
$916$	−9.65720	+	8.10336i	−0.319083	+	0.267742i
$917$	−17.3321	−	14.5434i	−0.572358	−	0.480265i
$918$	0.150170	+	0.851656i	0.00495635	+	0.0281089i
$919$	0.460757	+	0.798054i	0.0151990	+	0.0263254i	0.873525	−	0.486780i	$-0.161829\pi$
$919$	0.460757	+	0.798054i	0.0151990	+	0.0263254i	−0.858326	+	0.513105i	$0.828495\pi$
$920$	−4.57368	+	7.92184i	−0.150790	+	0.261175i
$921$	−25.2183	−	9.17870i	−0.830970	−	0.302448i
$922$	−6.21922	−	2.26361i	−0.204819	−	0.0745481i
$923$	15.9729	−	27.6660i	0.525756	−	0.910636i
$924$	4.05158	+	7.01755i	0.133287	+	0.230860i
$925$	−1.87009	−	10.6058i	−0.0614883	−	0.348717i
$926$	−29.8655	−	25.0601i	−0.981440	−	0.823526i
$927$	−24.3573	+	20.4382i	−0.799997	+	0.671277i
$928$	−4.66978	+	26.4836i	−0.153293	+	0.869368i
$929$	22.0825	−	8.03737i	0.724503	−	0.263697i	0.0466666	−	0.998911i	$-0.485140\pi$
$929$	22.0825	−	8.03737i	0.724503	−	0.263697i	0.677836	+	0.735213i	$0.262918\pi$
$930$	−12.7369			−0.417660
$931$	−9.36039	+	1.51677i	−0.306774	+	0.0497100i
$932$	2.53525			0.0830448
$933$	19.0969	−	6.95069i	0.625204	−	0.227556i
$934$	−5.94289	+	33.7038i	−0.194457	+	1.10282i
$935$	0.828475	−	0.695173i	0.0270940	−	0.0227346i
$936$	20.8277	+	17.4765i	0.680774	+	0.571238i
$937$	−9.25942	−	52.5128i	−0.302492	−	1.71552i	−0.635081	−	0.772445i	$-0.719033\pi$
$937$	−9.25942	−	52.5128i	−0.302492	−	1.71552i	0.332589	−	0.943072i	$-0.392078\pi$
$938$	−1.37621	−	2.38366i	−0.0449348	−	0.0778293i
$939$	15.2649	−	26.4396i	0.498152	−	0.862824i
$940$	5.87984	+	2.14009i	0.191779	+	0.0698019i
$941$	3.88045	+	1.41237i	0.126499	+	0.0460418i	0.404494	−	0.914541i	$-0.367448\pi$
$941$	3.88045	+	1.41237i	0.126499	+	0.0460418i	−0.277995	+	0.960583i	$0.589670\pi$
$942$	14.0394	−	24.3169i	0.457428	−	0.792288i
$943$	4.66528	+	8.08050i	0.151922	+	0.263137i
$944$	5.68386	+	32.2348i	0.184994	+	1.04915i
$945$	−3.18481	−	2.67238i	−0.103602	−	0.0869324i
$946$	5.19418	−	4.35843i	0.168877	−	0.141705i
$947$	1.46241	−	8.29375i	0.0475220	−	0.269511i	−0.951784	−	0.306770i	$-0.900752\pi$
$947$	1.46241	−	8.29375i	0.0475220	−	0.269511i	0.999306	+	0.0372596i	$0.0118628\pi$
$948$	−16.4821	+	5.99900i	−0.535314	+	0.194838i
$949$	−57.5025			−1.86661
$950$	1.84792	−	4.86578i	0.0599545	−	0.157867i
$951$	−25.1359			−0.815088
$952$	2.42754	−	0.883552i	0.0786770	−	0.0286361i
$953$	−3.29483	+	18.6859i	−0.106730	+	0.605296i	0.883785	+	0.467893i	$0.154987\pi$
$953$	−3.29483	+	18.6859i	−0.106730	+	0.605296i	−0.990515	+	0.137403i	$0.956125\pi$
$954$	−14.8207	+	12.4361i	−0.479838	+	0.402632i
$955$	18.2714	+	15.3315i	0.591249	+	0.496117i
$956$	−1.97686	−	11.2114i	−0.0639364	−	0.362601i
$957$	27.5476	+	47.7138i	0.890487	+	1.54237i
$958$	6.13311	−	10.6229i	0.198152	−	0.343209i
$959$	3.02983	+	1.10277i	0.0978383	+	0.0356102i
$960$	18.7734	+	6.83297i	0.605910	+	0.220533i
$961$	4.49052	−	7.77782i	0.144856	−	0.250897i
$962$	−26.2412	−	45.4511i	−0.846051	−	1.46540i
$963$	−2.32605	−	13.1917i	−0.0749558	−	0.425095i
$964$	9.18584	+	7.70784i	0.295856	+	0.248253i
$965$	8.59960	−	7.21592i	0.276831	−	0.232289i
$966$	−3.08099	+	17.4732i	−0.0991292	+	0.562189i
$967$	3.53205	−	1.28556i	0.113583	−	0.0413408i	−0.284603	−	0.958645i	$-0.591862\pi$
$967$	3.53205	−	1.28556i	0.113583	−	0.0413408i	0.398186	+	0.917305i	$0.369640\pi$
$968$	−9.25517			−0.297473
$969$	2.47711	−	2.87019i	0.0795763	−	0.0922038i
$970$	17.2500			0.553863
$971$	−12.0598	+	4.38940i	−0.387016	+	0.140862i	−0.528198	−	0.849121i	$-0.677132\pi$
$971$	−12.0598	+	4.38940i	−0.387016	+	0.140862i	0.141182	+	0.989984i	$0.454910\pi$
$972$	1.88268	−	10.6772i	0.0603871	−	0.342472i
$973$	12.3295	−	10.3457i	0.395266	−	0.331668i
$974$	−10.1757	−	8.53845i	−0.326051	−	0.273590i
$975$	1.61099	+	9.13637i	0.0515929	+	0.292598i
$976$	7.53556	+	13.0520i	0.241207	+	0.417783i
$977$	13.7672	−	23.8455i	0.440453	−	0.762887i	−0.557270	−	0.830331i	$-0.688151\pi$
$977$	13.7672	−	23.8455i	0.440453	−	0.762887i	0.997723	+	0.0674446i	$0.0214846\pi$
$978$	−17.5998	−	6.40579i	−0.562779	−	0.204835i
$979$	−17.4343	−	6.34557i	−0.557203	−	0.202805i
$980$	0.624541	−	1.08174i	0.0199502	−	0.0345548i
$981$	−0.816940	−	1.41498i	−0.0260829	−	0.0451769i
$982$	−2.87899	−	16.3276i	−0.0918722	−	0.521033i
$983$	36.9720	+	31.0232i	1.17922	+	0.989486i	0.999984	+	0.00568028i	$0.00180810\pi$
$983$	36.9720	+	31.0232i	1.17922	+	0.989486i	0.179239	+	0.983805i	$0.442636\pi$
$984$	16.7819	−	14.0817i	0.534989	−	0.448909i
$985$	2.92993	−	16.6164i	0.0933552	−	0.529444i
$986$	3.68157	−	1.33998i	0.117245	−	0.0426737i
$987$	54.4122			1.73196
$988$	−0.141856	+	10.2134i	−0.00451305	+	0.324931i
$989$	−5.97872			−0.190112
$990$	6.87372	−	2.50183i	0.218461	−	0.0795133i
$991$	−7.57591	+	42.9651i	−0.240657	+	1.36483i	0.589710	+	0.807615i	$0.299242\pi$
$991$	−7.57591	+	42.9651i	−0.240657	+	1.36483i	−0.830367	+	0.557217i	$0.811869\pi$
$992$	11.2731	−	9.45927i	0.357922	−	0.300332i
$993$	−4.95495	−	4.15770i	−0.157241	−	0.131941i
$994$	−3.56499	−	20.2181i	−0.113075	−	0.641279i
$995$	−7.86124	−	13.6161i	−0.249218	−	0.431658i
$996$	−3.62595	+	6.28034i	−0.114893	+	0.199000i
$997$	−28.3767	−	10.3283i	−0.898698	−	0.327099i	−0.148967	−	0.988842i	$-0.547595\pi$
$997$	−28.3767	−	10.3283i	−0.898698	−	0.327099i	−0.749731	+	0.661743i	$0.769817\pi$
$998$	14.3488	+	5.22255i	0.454205	+	0.165317i
$999$	−10.1921	+	17.6532i	−0.322464	+	0.558523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.k.b.81.2	yes	18
3.2	odd	2		855.2.bs.b.271.2		18
5.2	odd	4		475.2.u.c.24.4		36
5.3	odd	4		475.2.u.c.24.3		36
5.4	even	2		475.2.l.b.176.2		18
19.2	odd	18		1805.2.a.u.1.6		9
19.4	even	9	inner	95.2.k.b.61.2	✓	18
19.17	even	9		1805.2.a.t.1.4		9
57.23	odd	18		855.2.bs.b.631.2		18
95.4	even	18		475.2.l.b.251.2		18
95.23	odd	36		475.2.u.c.99.4		36
95.42	odd	36		475.2.u.c.99.3		36
95.59	odd	18		9025.2.a.cd.1.4		9
95.74	even	18		9025.2.a.ce.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.2	✓	18	19.4	even	9	inner
95.2.k.b.81.2	yes	18	1.1	even	1	trivial
475.2.l.b.176.2		18	5.4	even	2
475.2.l.b.251.2		18	95.4	even	18
475.2.u.c.24.3		36	5.3	odd	4
475.2.u.c.24.4		36	5.2	odd	4
475.2.u.c.99.3		36	95.42	odd	36
475.2.u.c.99.4		36	95.23	odd	36
855.2.bs.b.271.2		18	3.2	odd	2
855.2.bs.b.631.2		18	57.23	odd	18
1805.2.a.t.1.4		9	19.17	even	9
1805.2.a.u.1.6		9	19.2	odd	18
9025.2.a.cd.1.4		9	95.59	odd	18
9025.2.a.ce.1.6		9	95.74	even	18

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12207 - 0.408399i) q^{2} +(0.394733 - 2.23864i) q^{3} +(-0.439845 + 0.369074i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.471342 - 2.67312i) q^{6} +(1.09825 + 1.90222i) q^{7} +(-1.53688 + 2.66196i) q^{8} +(-2.03663 - 0.741274i) q^{9} +O(q^{10})\)	\(q+(1.12207 - 0.408399i) q^{2} +(0.394733 - 2.23864i) q^{3} +(-0.439845 + 0.369074i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.471342 - 2.67312i) q^{6} +(1.09825 + 1.90222i) q^{7} +(-1.53688 + 2.66196i) q^{8} +(-2.03663 - 0.741274i) q^{9} +(-1.12207 - 0.408399i) q^{10} +(1.41324 - 2.44780i) q^{11} +(0.652604 + 1.13034i) q^{12} +(0.708694 + 4.01920i) q^{13} +(2.00917 + 1.68589i) q^{14} +(-1.74136 + 1.46117i) q^{15} +(-0.437935 + 2.48365i) q^{16} +(-0.359555 + 0.130867i) q^{17} -2.58797 q^{18} +(-2.75520 - 3.37770i) q^{19} +0.574177 q^{20} +(4.69190 - 1.70771i) q^{21} +(0.586069 - 3.32376i) q^{22} +(-2.27970 + 1.91290i) q^{23} +(5.35253 + 4.49130i) q^{24} +(0.173648 + 0.984808i) q^{25} +(2.43664 + 4.22038i) q^{26} +(0.946391 - 1.63920i) q^{27} +(-1.18512 - 0.431347i) q^{28} +(-8.05787 - 2.93282i) q^{29} +(-1.35718 + 2.35070i) q^{30} +(2.34622 + 4.06377i) q^{31} +(-0.544580 - 3.08847i) q^{32} +(-4.92191 - 4.12997i) q^{33} +(-0.349999 + 0.293684i) q^{34} +(0.381417 - 2.16312i) q^{35} +(1.16939 - 0.425623i) q^{36} -10.7694 q^{37} +(-4.47097 - 2.66478i) q^{38} +9.27731 q^{39} +(2.88840 - 1.05129i) q^{40} +(0.544445 - 3.08770i) q^{41} +(4.56720 - 3.83233i) q^{42} +(1.53900 + 1.29137i) q^{43} +(0.281814 + 1.59824i) q^{44} +(1.08367 + 1.87697i) q^{45} +(-1.77675 + 3.07743i) q^{46} +(10.2405 + 3.72722i) q^{47} +(5.38714 + 1.96076i) q^{48} +(1.08771 - 1.88398i) q^{49} +(0.597039 + 1.03410i) q^{50} +(0.151037 + 0.856574i) q^{51} +(-1.79510 - 1.50627i) q^{52} +(5.72676 - 4.80532i) q^{53} +(0.392467 - 2.22579i) q^{54} +(-2.65602 + 0.966713i) q^{55} -6.75150 q^{56} +(-8.64904 + 4.83463i) q^{57} -10.2392 q^{58} +(12.1961 - 4.43900i) q^{59} +(0.226647 - 1.28538i) q^{60} +(4.57784 - 3.84126i) q^{61} +(4.29225 + 3.60163i) q^{62} +(-0.826660 - 4.68822i) q^{63} +(-4.39435 - 7.61123i) q^{64} +(2.04060 - 3.53443i) q^{65} +(-7.20938 - 2.62400i) q^{66} +(-0.986138 - 0.358925i) q^{67} +(0.109849 - 0.190264i) q^{68} +(3.38242 + 5.85853i) q^{69} +(-0.455441 - 2.58294i) q^{70} +(-5.99626 - 5.03146i) q^{71} +(5.10332 - 4.28219i) q^{72} +(-2.44663 + 13.8755i) q^{73} +(-12.0840 + 4.39822i) q^{74} +2.27318 q^{75} +(2.45848 + 0.468792i) q^{76} +6.20833 q^{77} +(10.4098 - 3.78884i) q^{78} +(-2.33355 + 13.2342i) q^{79} +(1.93194 - 1.62109i) q^{80} +(-8.27685 - 6.94510i) q^{81} +(-0.650110 - 3.68695i) q^{82} +(2.77807 + 4.81175i) q^{83} +(-1.43344 + 2.48279i) q^{84} +(0.359555 + 0.130867i) q^{85} +(2.25425 + 0.820481i) q^{86} +(-9.74626 + 16.8810i) q^{87} +(4.34397 + 7.52398i) q^{88} +(-1.13984 - 6.46435i) q^{89} +(1.98250 + 1.66352i) q^{90} +(-6.86708 + 5.76216i) q^{91} +(0.296716 - 1.68276i) q^{92} +(10.0235 - 3.64824i) q^{93} +13.0127 q^{94} +(-0.0605361 + 4.35848i) q^{95} -7.12895 q^{96} +(-13.5750 + 4.94091i) q^{97} +(0.451074 - 2.55817i) q^{98} +(-4.69275 + 3.93768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{6} - 12 q^{8} - 21 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^6 - 12 * q^8 - 21 * q^9	\( 18 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{6} - 12 q^{8} - 21 q^{9} - 3 q^{10} + 6 q^{12} - 3 q^{13} + 24 q^{14} + 3 q^{15} + 21 q^{16} - 24 q^{17} - 12 q^{18} - 12 q^{19} - 12 q^{20} + 3 q^{21} + 15 q^{22} + 21 q^{23} + 21 q^{24} - 21 q^{26} + 6 q^{27} - 24 q^{28} - 9 q^{29} - 12 q^{30} + 30 q^{31} + 45 q^{32} - 3 q^{33} + 24 q^{34} - 6 q^{35} - 21 q^{36} - 60 q^{37} - 15 q^{38} + 12 q^{39} - 6 q^{40} - 6 q^{41} + 39 q^{42} - 6 q^{43} - 30 q^{44} + 6 q^{45} + 21 q^{46} + 33 q^{47} - 63 q^{48} - 3 q^{49} + 27 q^{51} + 9 q^{52} + 24 q^{53} + 30 q^{54} - 3 q^{55} - 72 q^{56} - 30 q^{57} + 36 q^{58} + 18 q^{59} + 15 q^{60} + 6 q^{61} + 12 q^{62} + 24 q^{63} - 24 q^{64} + 3 q^{65} - 33 q^{66} - 24 q^{67} - 3 q^{68} + 27 q^{69} + 39 q^{70} + 24 q^{71} + 18 q^{72} + 6 q^{73} - 39 q^{74} - 6 q^{75} + 27 q^{76} + 24 q^{77} + 72 q^{78} + 9 q^{79} + 33 q^{80} + 15 q^{81} - 57 q^{82} - 12 q^{84} + 24 q^{85} - 33 q^{86} - 45 q^{87} + 39 q^{88} - 6 q^{89} - 21 q^{90} - 6 q^{91} - 66 q^{92} - 72 q^{93} - 66 q^{94} - 15 q^{95} - 18 q^{96} - 87 q^{97} + 39 q^{98} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^6 - 12 * q^8 - 21 * q^9 - 3 * q^10 + 6 * q^12 - 3 * q^13 + 24 * q^14 + 3 * q^15 + 21 * q^16 - 24 * q^17 - 12 * q^18 - 12 * q^19 - 12 * q^20 + 3 * q^21 + 15 * q^22 + 21 * q^23 + 21 * q^24 - 21 * q^26 + 6 * q^27 - 24 * q^28 - 9 * q^29 - 12 * q^30 + 30 * q^31 + 45 * q^32 - 3 * q^33 + 24 * q^34 - 6 * q^35 - 21 * q^36 - 60 * q^37 - 15 * q^38 + 12 * q^39 - 6 * q^40 - 6 * q^41 + 39 * q^42 - 6 * q^43 - 30 * q^44 + 6 * q^45 + 21 * q^46 + 33 * q^47 - 63 * q^48 - 3 * q^49 + 27 * q^51 + 9 * q^52 + 24 * q^53 + 30 * q^54 - 3 * q^55 - 72 * q^56 - 30 * q^57 + 36 * q^58 + 18 * q^59 + 15 * q^60 + 6 * q^61 + 12 * q^62 + 24 * q^63 - 24 * q^64 + 3 * q^65 - 33 * q^66 - 24 * q^67 - 3 * q^68 + 27 * q^69 + 39 * q^70 + 24 * q^71 + 18 * q^72 + 6 * q^73 - 39 * q^74 - 6 * q^75 + 27 * q^76 + 24 * q^77 + 72 * q^78 + 9 * q^79 + 33 * q^80 + 15 * q^81 - 57 * q^82 - 12 * q^84 + 24 * q^85 - 33 * q^86 - 45 * q^87 + 39 * q^88 - 6 * q^89 - 21 * q^90 - 6 * q^91 - 66 * q^92 - 72 * q^93 - 66 * q^94 - 15 * q^95 - 18 * q^96 - 87 * q^97 + 39 * q^98 + 3 * q^99

Introduction

L-functions

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