LMFDB - Embedded newform 370.2.o.a.231.3

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			231.3
Root			$1.20734 - 2.09117i$ of defining polynomial
Character	$\chi$	$=$	370.231
Dual form			370.2.o.a.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(0.426173 - 2.41695i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.766044 + 0.642788i) q^{5} +2.45423 q^{6} +(-3.72980 - 3.12967i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.84094 - 1.03402i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(0.426173 - 2.41695i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.766044 + 0.642788i) q^{5} +2.45423 q^{6} +(-3.72980 - 3.12967i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.84094 - 1.03402i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.856002 - 1.48264i) q^{11} +(0.426173 + 2.41695i) q^{12} +(5.20412 - 1.89414i) q^{13} +(2.43445 - 4.21660i) q^{14} +(1.88005 - 1.57755i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-6.01497 - 2.18927i) q^{17} +(0.524984 - 2.97733i) q^{18} +(-0.404202 + 2.29235i) q^{19} +(-0.939693 - 0.342020i) q^{20} +(-9.15381 + 7.68095i) q^{21} +(1.31147 - 1.10045i) q^{22} +(2.13527 - 3.69840i) q^{23} +(-2.30623 + 0.839397i) q^{24} +(0.173648 + 0.984808i) q^{25} +(2.76905 + 4.79614i) q^{26} +(-0.0285488 + 0.0494479i) q^{27} +(4.57528 + 1.66527i) q^{28} +(0.304151 + 0.526805i) q^{29} +(1.88005 + 1.57755i) q^{30} -0.470242 q^{31} +(0.766044 + 0.642788i) q^{32} +(-3.94827 + 1.43705i) q^{33} +(1.11152 - 6.30375i) q^{34} +(-0.845477 - 4.79494i) q^{35} +3.02326 q^{36} +(-0.963008 + 6.00605i) q^{37} -2.32771 q^{38} +(-2.36019 - 13.3853i) q^{39} +(0.173648 - 0.984808i) q^{40} +(8.81777 - 3.20941i) q^{41} +(-9.15381 - 7.68095i) q^{42} +4.62507 q^{43} +(1.31147 + 1.10045i) q^{44} +(-1.51163 - 2.61822i) q^{45} +(4.01300 + 1.46061i) q^{46} +(4.44560 - 7.70000i) q^{47} +(-1.22712 - 2.12543i) q^{48} +(2.90102 + 16.4525i) q^{49} +(-0.939693 + 0.342020i) q^{50} +(-7.85477 + 13.6049i) q^{51} +(-4.24244 + 3.55983i) q^{52} +(-7.58694 + 6.36619i) q^{53} +(-0.0536541 - 0.0195285i) q^{54} +(0.297286 - 1.68599i) q^{55} +(-0.845477 + 4.79494i) q^{56} +(5.36822 + 1.95387i) q^{57} +(-0.465986 + 0.391009i) q^{58} +(-2.73315 + 2.29338i) q^{59} +(-1.22712 + 2.12543i) q^{60} +(11.4106 - 4.15313i) q^{61} +(-0.0816566 - 0.463098i) q^{62} +(7.36000 + 12.7479i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.20412 + 1.89414i) q^{65} +(-2.10083 - 3.63874i) q^{66} +(9.53915 + 8.00430i) q^{67} +6.40100 q^{68} +(-8.02884 - 6.73700i) q^{69} +(4.57528 - 1.66527i) q^{70} +(-1.62659 + 9.22487i) q^{71} +(0.524984 + 2.97733i) q^{72} +8.42854 q^{73} +(-6.08203 + 0.0945612i) q^{74} +2.45423 q^{75} +(-0.404202 - 2.29235i) q^{76} +(-1.44746 + 8.20895i) q^{77} +(12.7721 - 4.64867i) q^{78} +(-7.88571 - 6.61689i) q^{79} +1.00000 q^{80} +(-6.84052 - 5.73988i) q^{81} +(4.69184 + 8.12651i) q^{82} +(-0.117480 - 0.0427591i) q^{83} +(5.97472 - 10.3485i) q^{84} +(-3.20050 - 5.54343i) q^{85} +(0.803136 + 4.55481i) q^{86} +(1.40288 - 0.510607i) q^{87} +(-0.856002 + 1.48264i) q^{88} +(-2.48909 + 2.08860i) q^{89} +(2.31596 - 1.94332i) q^{90} +(-25.3384 - 9.22242i) q^{91} +(-0.741572 + 4.20566i) q^{92} +(-0.200404 + 1.13655i) q^{93} +(8.35499 + 3.04097i) q^{94} +(-1.78313 + 1.49622i) q^{95} +(1.88005 - 1.57755i) q^{96} +(2.43778 - 4.22236i) q^{97} +(-15.6988 + 5.71389i) q^{98} +(0.898775 + 5.09721i) 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	0.426173	−	2.41695i	0.246051	−	1.39543i	−0.571987	−	0.820263i	$-0.693827\pi$
$3$	0.426173	−	2.41695i	0.246051	−	1.39543i	0.818038	−	0.575163i	$-0.195062\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$6$	2.45423			1.00194
$7$	−3.72980	−	3.12967i	−1.40973	−	1.18291i	−0.956579	−	0.291473i	$-0.905855\pi$
$7$	−3.72980	−	3.12967i	−1.40973	−	1.18291i	−0.453153	−	0.891433i	$-0.649701\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.84094	−	1.03402i	−0.946980	−	0.344672i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−0.856002	−	1.48264i	−0.258094	−	0.447032i	0.707637	−	0.706576i	$-0.249761\pi$
$11$	−0.856002	−	1.48264i	−0.258094	−	0.447032i	−0.965731	+	0.259544i	$0.916428\pi$
$12$	0.426173	+	2.41695i	0.123026	+	0.697713i
$13$	5.20412	−	1.89414i	1.44336	−	0.525341i	0.502633	−	0.864500i	$-0.332365\pi$
$13$	5.20412	−	1.89414i	1.44336	−	0.525341i	0.940729	+	0.339159i	$0.110142\pi$
$14$	2.43445	−	4.21660i	0.650635	−	1.12693i
$15$	1.88005	−	1.57755i	0.485427	−	0.407322i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−6.01497	−	2.18927i	−1.45884	−	0.530976i	−0.513798	−	0.857911i	$-0.671762\pi$
$17$	−6.01497	−	2.18927i	−1.45884	−	0.530976i	−0.945047	+	0.326935i	$0.893984\pi$
$18$	0.524984	−	2.97733i	0.123740	−	0.701765i
$19$	−0.404202	+	2.29235i	−0.0927304	+	0.525900i	0.902689	+	0.430294i	$0.141590\pi$
$19$	−0.404202	+	2.29235i	−0.0927304	+	0.525900i	−0.995419	+	0.0956062i	$0.969521\pi$
$20$	−0.939693	−	0.342020i	−0.210122	−	0.0764780i
$21$	−9.15381	+	7.68095i	−1.99752	+	1.67612i
$22$	1.31147	−	1.10045i	0.279606	−	0.234618i
$23$	2.13527	−	3.69840i	0.445235	−	0.771169i	−0.552834	−	0.833292i	$-0.686454\pi$
$23$	2.13527	−	3.69840i	0.445235	−	0.771169i	0.998069	+	0.0621224i	$0.0197869\pi$
$24$	−2.30623	+	0.839397i	−0.470756	+	0.171341i
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	2.76905	+	4.79614i	0.543056	+	0.940601i
$27$	−0.0285488	+	0.0494479i	−0.00549421	+	0.00951625i
$28$	4.57528	+	1.66527i	0.864646	+	0.314706i
$29$	0.304151	+	0.526805i	0.0564794	+	0.0978252i	0.892883	−	0.450289i	$-0.148679\pi$
$29$	0.304151	+	0.526805i	0.0564794	+	0.0978252i	−0.836403	+	0.548114i	$0.815346\pi$
$30$	1.88005	+	1.57755i	0.343249	+	0.288020i
$31$	−0.470242			−0.0844579			−0.0422290	−	0.999108i	$-0.513446\pi$
$31$	−0.470242			−0.0844579			−0.0422290	+	0.999108i	$0.513446\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−3.94827	+	1.43705i	−0.687305	+	0.250159i
$34$	1.11152	−	6.30375i	0.190624	−	1.08108i
$35$	−0.845477	−	4.79494i	−0.142912	−	0.810493i
$36$	3.02326			0.503877
$37$	−0.963008	+	6.00605i	−0.158318	+	0.987388i
$37$	−0.963008	+	6.00605i	−0.158318	+	0.987388i
$38$	−2.32771			−0.377604
$39$	−2.36019	−	13.3853i	−0.377933	−	2.14337i
$40$	0.173648	−	0.984808i	0.0274562	−	0.155712i
$41$	8.81777	−	3.20941i	1.37711	−	0.501225i	0.455806	−	0.890079i	$-0.349351\pi$
$41$	8.81777	−	3.20941i	1.37711	−	0.501225i	0.921299	+	0.388854i	$0.127129\pi$
$42$	−9.15381	−	7.68095i	−1.41246	−	1.18520i
$43$	4.62507			0.705317			0.352659	−	0.935752i	$-0.385278\pi$
$43$	4.62507			0.705317			0.352659	+	0.935752i	$0.385278\pi$
$44$	1.31147	+	1.10045i	0.197712	+	0.165900i
$45$	−1.51163	−	2.61822i	−0.225341	−	0.390302i
$46$	4.01300	+	1.46061i	0.591684	+	0.215355i
$47$	4.44560	−	7.70000i	0.648457	−	1.12316i	−0.335034	−	0.942206i	$-0.608748\pi$
$47$	4.44560	−	7.70000i	0.648457	−	1.12316i	0.983491	−	0.180955i	$-0.0579188\pi$
$48$	−1.22712	−	2.12543i	−0.177119	−	0.306779i
$49$	2.90102	+	16.4525i	0.414431	+	2.35035i
$50$	−0.939693	+	0.342020i	−0.132893	+	0.0483690i
$51$	−7.85477	+	13.6049i	−1.09989	+	1.90506i
$52$	−4.24244	+	3.55983i	−0.588320	+	0.493659i
$53$	−7.58694	+	6.36619i	−1.04215	+	0.874464i	−0.992246	−	0.124290i	$-0.960335\pi$
$53$	−7.58694	+	6.36619i	−1.04215	+	0.874464i	−0.0498998	+	0.998754i	$0.515890\pi$
$54$	−0.0536541	−	0.0195285i	−0.00730140	−	0.00265749i
$55$	0.297286	−	1.68599i	0.0400861	−	0.227339i
$56$	−0.845477	+	4.79494i	−0.112982	+	0.640751i
$57$	5.36822	+	1.95387i	0.711038	+	0.258797i
$58$	−0.465986	+	0.391009i	−0.0611870	+	0.0513420i
$59$	−2.73315	+	2.29338i	−0.355825	+	0.298573i	−0.803124	−	0.595812i	$-0.796830\pi$
$59$	−2.73315	+	2.29338i	−0.355825	+	0.298573i	0.447299	+	0.894385i	$0.352386\pi$
$60$	−1.22712	+	2.12543i	−0.158420	+	0.274392i
$61$	11.4106	−	4.15313i	1.46098	−	0.531754i	0.515346	−	0.856982i	$-0.327664\pi$
$61$	11.4106	−	4.15313i	1.46098	−	0.531754i	0.945635	+	0.325229i	$0.105441\pi$
$62$	−0.0816566	−	0.463098i	−0.0103704	−	0.0588135i
$63$	7.36000	+	12.7479i	0.927273	+	1.60608i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	5.20412	+	1.89414i	0.645491	+	0.234940i
$66$	−2.10083	−	3.63874i	−0.258594	−	0.447898i
$67$	9.53915	+	8.00430i	1.16539	+	0.977881i	0.999965	−	0.00834145i	$-0.00265520\pi$
$67$	9.53915	+	8.00430i	1.16539	+	0.977881i	0.165427	+	0.986222i	$0.447100\pi$
$68$	6.40100			0.776235
$69$	−8.02884	−	6.73700i	−0.966559	−	0.811039i
$70$	4.57528	−	1.66527i	0.546850	−	0.199037i
$71$	−1.62659	+	9.22487i	−0.193041	+	1.09479i	0.722140	+	0.691747i	$0.243159\pi$
$71$	−1.62659	+	9.22487i	−0.193041	+	1.09479i	−0.915181	+	0.403043i	$0.867952\pi$
$72$	0.524984	+	2.97733i	0.0618700	+	0.350882i
$73$	8.42854			0.986486			0.493243	−	0.869892i	$-0.335811\pi$
$73$	8.42854			0.986486			0.493243	+	0.869892i	$0.335811\pi$
$74$	−6.08203	+	0.0945612i	−0.707021	+	0.0109925i
$75$	2.45423			0.283391
$76$	−0.404202	−	2.29235i	−0.0463652	−	0.262950i
$77$	−1.44746	+	8.20895i	−0.164953	+	0.935497i
$78$	12.7721	−	4.64867i	1.44616	−	0.526358i
$79$	−7.88571	−	6.61689i	−0.887211	−	0.744459i	0.0804374	−	0.996760i	$-0.474368\pi$
$79$	−7.88571	−	6.61689i	−0.887211	−	0.744459i	−0.967649	+	0.252301i	$0.918813\pi$
$80$	1.00000			0.111803
$81$	−6.84052	−	5.73988i	−0.760058	−	0.637764i
$82$	4.69184	+	8.12651i	0.518127	+	0.897422i
$83$	−0.117480	−	0.0427591i	−0.0128951	−	0.00469342i	0.335565	−	0.942017i	$-0.391073\pi$
$83$	−0.117480	−	0.0427591i	−0.0128951	−	0.00469342i	−0.348460	+	0.937324i	$0.613295\pi$
$84$	5.97472	−	10.3485i	0.651896	−	1.12912i
$85$	−3.20050	−	5.54343i	−0.347143	−	0.601269i
$86$	0.803136	+	4.55481i	0.0866043	+	0.491158i
$87$	1.40288	−	0.510607i	0.150405	−	0.0547428i
$88$	−0.856002	+	1.48264i	−0.0912501	+	0.158050i
$89$	−2.48909	+	2.08860i	−0.263843	+	0.221391i	−0.765106	−	0.643904i	$-0.777313\pi$
$89$	−2.48909	+	2.08860i	−0.263843	+	0.221391i	0.501263	+	0.865295i	$0.332869\pi$
$90$	2.31596	−	1.94332i	0.244123	−	0.204844i
$91$	−25.3384	−	9.22242i	−2.65618	−	0.966772i
$92$	−0.741572	+	4.20566i	−0.0773142	+	0.438471i
$93$	−0.200404	+	1.13655i	−0.0207810	+	0.117855i
$94$	8.35499	+	3.04097i	0.861752	+	0.313652i
$95$	−1.78313	+	1.49622i	−0.182945	+	0.153509i
$96$	1.88005	−	1.57755i	0.191882	−	0.161008i
$97$	2.43778	−	4.22236i	0.247519	−	0.428715i	−0.715318	−	0.698799i	$-0.753718\pi$
$97$	2.43778	−	4.22236i	0.247519	−	0.428715i	0.962837	+	0.270084i	$0.0870514\pi$
$98$	−15.6988	+	5.71389i	−1.58582	+	0.577190i
$99$	0.898775	+	5.09721i	0.0903303	+	0.512289i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.98345	+	13.8277i	−0.794383	+	1.37591i	0.128848	+	0.991664i	$0.458872\pi$
$101$	−7.98345	+	13.8277i	−0.794383	+	1.37591i	−0.923230	+	0.384247i	$0.874461\pi$
$102$	−14.7621	−	5.37298i	−1.46167	−	0.532005i
$103$	−3.88600	−	6.73075i	−0.382899	−	0.663201i	0.608576	−	0.793496i	$-0.291741\pi$
$103$	−3.88600	−	6.73075i	−0.382899	−	0.663201i	−0.991475	+	0.130295i	$0.958408\pi$
$104$	−4.24244	−	3.55983i	−0.416005	−	0.349070i
$105$	−11.9494			−1.16615
$106$	−7.58694	−	6.36619i	−0.736908	−	0.618339i
$107$	9.97392	−	3.63021i	0.964215	−	0.350946i	0.188531	−	0.982067i	$-0.439627\pi$
$107$	9.97392	−	3.63021i	0.964215	−	0.350946i	0.775684	+	0.631122i	$0.217405\pi$
$108$	0.00991488	−	0.0562301i	0.000954060	−	0.00541074i
$109$	0.130011	+	0.737328i	0.0124528	+	0.0706232i	0.990401	−	0.138225i	$-0.0441397\pi$
$109$	0.130011	+	0.737328i	0.0124528	+	0.0706232i	−0.977948	+	0.208848i	$0.933029\pi$
$110$	1.71200			0.163233
$111$	14.1059	+	4.88716i	1.33887	+	0.463869i
$112$	−4.86891			−0.460069
$113$	−0.465913	−	2.64232i	−0.0438294	−	0.248569i	0.955019	−	0.296544i	$-0.0958342\pi$
$113$	−0.465913	−	2.64232i	−0.0438294	−	0.248569i	−0.998849	+	0.0479753i	$0.984723\pi$
$114$	−0.992007	+	5.62595i	−0.0929100	+	0.526919i
$115$	4.01300	−	1.46061i	0.374214	−	0.136203i
$116$	−0.465986	−	0.391009i	−0.0432657	−	0.0363042i
$117$	−16.7432			−1.54791
$118$	−2.73315	−	2.29338i	−0.251606	−	0.211123i
$119$	15.5829	+	26.9904i	1.42849	+	2.47421i
$120$	−2.30623	−	0.839397i	−0.210529	−	0.0766262i
$121$	4.03452	−	6.98800i	0.366775	−	0.635273i
$122$	6.07147	+	10.5161i	0.549685	+	0.952082i
$123$	−3.99907	−	22.6799i	−0.360584	−	2.04498i
$124$	0.441883	−	0.160832i	0.0396822	−	0.0144432i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	−11.2762	+	9.46184i	−1.00456	+	0.842927i
$127$	−8.02245	+	6.73164i	−0.711877	+	0.597336i	−0.925125	−	0.379662i	$-0.876040\pi$
$127$	−8.02245	+	6.73164i	−0.711877	+	0.597336i	0.213248	+	0.976998i	$0.431596\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	1.97108	−	11.1786i	0.173544	−	0.984218i
$130$	−0.961682	+	5.45397i	−0.0843451	+	0.478345i
$131$	−11.8142	−	4.30001i	−1.03221	−	0.375694i	−0.230288	−	0.973122i	$-0.573967\pi$
$131$	−11.8142	−	4.30001i	−1.03221	−	0.375694i	−0.801922	+	0.597428i	$0.796189\pi$
$132$	3.21866	−	2.70077i	0.280148	−	0.235072i
$133$	8.68189	−	7.28497i	0.752815	−	0.631687i
$134$	−6.22624	+	10.7842i	−0.537865	+	0.931610i
$135$	−0.0536541	+	0.0195285i	−0.00461781	+	0.00168075i
$136$	1.11152	+	6.30375i	0.0953122	+	0.540542i
$137$	0.328057	+	0.568211i	0.0280278	+	0.0485455i	0.879699	−	0.475531i	$-0.157744\pi$
$137$	0.328057	+	0.568211i	0.0280278	+	0.0485455i	−0.851671	+	0.524076i	$0.824411\pi$
$138$	5.24045	−	9.07673i	0.446097	−	0.772663i
$139$	15.6294	+	5.68864i	1.32567	+	0.482504i	0.905271	−	0.424835i	$-0.139668\pi$
$139$	15.6294	+	5.68864i	1.32567	+	0.482504i	0.420399	+	0.907340i	$0.361890\pi$
$140$	2.43445	+	4.21660i	0.205749	+	0.356368i
$141$	−16.7159	−	14.0263i	−1.40773	−	1.18123i
$142$	−9.36718			−0.786076
$143$	−7.26306	−	6.09443i	−0.607368	−	0.509642i
$144$	−2.84094	+	1.03402i	−0.236745	+	0.0861681i
$145$	−0.105630	+	0.599060i	−0.00877213	+	0.0497492i
$146$	1.46360	+	8.30049i	0.121128	+	0.686954i
$147$	41.0011			3.38172
$148$	−1.14926	−	5.97321i	−0.0944684	−	0.490995i
$149$	−5.96317			−0.488522			−0.244261	−	0.969710i	$-0.578545\pi$
$149$	−5.96317			−0.488522			−0.244261	+	0.969710i	$0.578545\pi$
$150$	0.426173	+	2.41695i	0.0347969	+	0.197343i
$151$	2.95063	−	16.7338i	0.240119	−	1.36178i	−0.591442	−	0.806348i	$-0.701441\pi$
$151$	2.95063	−	16.7338i	0.240119	−	1.36178i	0.831561	−	0.555434i	$-0.187448\pi$
$152$	2.18733	−	0.796123i	0.177416	−	0.0645741i
$153$	14.8244	+	12.4392i	1.19848	+	1.00565i
$154$	−8.33559			−0.671701
$155$	−0.360226	−	0.302266i	−0.0289341	−	0.0242786i
$156$	6.79590	+	11.7709i	0.544108	+	0.942422i
$157$	5.05836	+	1.84109i	0.403701	+	0.146935i	0.535887	−	0.844290i	$-0.319977\pi$
$157$	5.05836	+	1.84109i	0.403701	+	0.146935i	−0.132186	+	0.991225i	$0.542200\pi$
$158$	5.14703	−	8.91492i	0.409476	−	0.709233i
$159$	12.1534	+	21.0503i	0.963829	+	1.66940i
$160$	0.173648	+	0.984808i	0.0137281	+	0.0778559i
$161$	−19.5389	+	7.11158i	−1.53988	+	0.560471i
$162$	4.46483	−	7.73332i	0.350790	−	0.607587i
$163$	8.43555	−	7.07826i	0.660723	−	0.554412i	−0.249580	−	0.968354i	$-0.580293\pi$
$163$	8.43555	−	7.07826i	0.660723	−	0.554412i	0.910303	+	0.413942i	$0.135848\pi$
$164$	−7.18832	+	6.03171i	−0.561313	+	0.470998i
$165$	−3.94827	−	1.43705i	−0.307372	−	0.111874i
$166$	0.0217094	−	0.123120i	0.00168497	−	0.00955596i
$167$	0.377107	−	2.13868i	0.0291814	−	0.165496i	−0.966734	−	0.255782i	$-0.917667\pi$
$167$	0.377107	−	2.13868i	0.0291814	−	0.165496i	0.995916	+	0.0902861i	$0.0287782\pi$
$168$	11.2288	+	4.08695i	0.866321	+	0.315315i
$169$	13.5365	−	11.3585i	1.04127	−	0.873727i
$170$	4.90345	−	4.11448i	0.376077	−	0.315566i
$171$	3.51864	−	6.09446i	0.269077	−	0.466055i
$172$	−4.34615	+	1.58187i	−0.331391	+	0.120616i
$173$	−0.275368	−	1.56169i	−0.0209358	−	0.118733i	0.972549	−	0.232699i	$-0.0747556\pi$
$173$	−0.275368	−	1.56169i	−0.0209358	−	0.118733i	−0.993485	+	0.113966i	$0.963645\pi$
$174$	0.746457	+	1.29290i	0.0565888	+	0.0980146i
$175$	2.43445	−	4.21660i	0.184027	−	0.318745i
$176$	−1.60876	−	0.585540i	−0.121265	−	0.0441367i
$177$	4.37819	+	7.58325i	0.329085	+	0.569992i
$178$	−2.48909	−	2.08860i	−0.186565	−	0.156547i
$179$	9.81806			0.733836			0.366918	−	0.930253i	$-0.380413\pi$
$179$	9.81806			0.733836			0.366918	+	0.930253i	$0.380413\pi$
$180$	2.31596	+	1.94332i	0.172621	+	0.144846i
$181$	13.4175	−	4.88359i	0.997318	−	0.362994i	0.208768	−	0.977965i	$-0.433055\pi$
$181$	13.4175	−	4.88359i	0.997318	−	0.362994i	0.788550	+	0.614971i	$0.210832\pi$
$182$	4.68234	−	26.5549i	0.347078	−	1.96838i
$183$	−5.17499	−	29.3489i	−0.382547	−	2.16953i
$184$	−4.27054			−0.314828
$185$	−4.59832	+	3.98189i	−0.338075	+	0.292754i
$186$	−1.15408			−0.0846215
$187$	1.90293	+	10.7920i	0.139156	+	0.789193i
$188$	−1.54394	+	8.75612i	−0.112603	+	0.638606i
$189$	0.261237	−	0.0950825i	0.0190022	−	0.00691623i
$190$	−1.78313	−	1.49622i	−0.129362	−	0.108547i
$191$	−3.92648			−0.284110			−0.142055	−	0.989859i	$-0.545371\pi$
$191$	−3.92648			−0.284110			−0.142055	+	0.989859i	$0.545371\pi$
$192$	1.88005	+	1.57755i	0.135681	+	0.113850i
$193$	−1.38873	−	2.40536i	−0.0999632	−	0.173141i	0.811706	−	0.584066i	$-0.198539\pi$
$193$	−1.38873	−	2.40536i	−0.0999632	−	0.173141i	−0.911669	+	0.410925i	$0.865206\pi$
$194$	4.58153	+	1.66754i	0.328934	+	0.119722i
$195$	6.79590	−	11.7709i	0.486665	−	0.842928i
$196$	−8.35314	−	14.4681i	−0.596653	−	1.03343i
$197$	−2.47328	−	14.0267i	−0.176214	−	0.999361i	−0.936733	−	0.350045i	$-0.886166\pi$
$197$	−2.47328	−	14.0267i	−0.176214	−	0.999361i	0.760519	−	0.649316i	$-0.224945\pi$
$198$	−4.86370	+	1.77024i	−0.345648	+	0.125806i
$199$	−7.32946	+	12.6950i	−0.519572	+	0.899925i	0.480169	+	0.877176i	$0.340575\pi$
$199$	−7.32946	+	12.6950i	−0.519572	+	0.899925i	−0.999741	+	0.0227492i	$0.992758\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	23.4113	−	19.6444i	1.65131	−	1.38561i
$202$	−15.0040	−	5.46100i	−1.05568	−	0.384235i
$203$	0.514305	−	2.91677i	0.0360971	−	0.204717i
$204$	2.72793	−	15.4709i	0.190994	−	1.08318i
$205$	8.81777	+	3.20941i	0.615860	+	0.224155i
$206$	5.95370	−	4.99575i	0.414814	−	0.348070i
$207$	−9.89038	+	8.29902i	−0.687429	+	0.576821i
$208$	2.76905	−	4.79614i	0.191999	−	0.332553i
$209$	3.74472	−	1.36297i	0.259027	−	0.0942783i
$210$	−2.07500	−	11.7679i	−0.143189	−	0.812063i
$211$	−1.02181	−	1.76982i	−0.0703442	−	0.121840i	0.828708	−	0.559681i	$-0.189076\pi$
$211$	−1.02181	−	1.76982i	−0.0703442	−	0.121840i	−0.899052	+	0.437842i	$0.855743\pi$
$212$	4.95202	−	8.57715i	0.340106	−	0.589081i
$213$	21.6028	+	7.86279i	1.48020	+	0.538749i
$214$	5.30701	+	9.19201i	0.362780	+	0.628353i
$215$	3.54301	+	2.97294i	0.241631	+	0.202753i
$216$	0.0570975			0.00388499
$217$	1.75391	+	1.47170i	0.119063	+	0.0999058i
$218$	−0.703550	+	0.256071i	−0.0476505	+	0.0173433i
$219$	3.59202	−	20.3714i	0.242726	−	1.37657i
$220$	0.297286	+	1.68599i	0.0200430	+	0.113670i
$221$	−35.4494			−2.38459
$222$	−2.36345	+	14.7402i	−0.158624	+	0.989301i
$223$	−8.90249			−0.596155			−0.298077	−	0.954542i	$-0.596345\pi$
$223$	−8.90249			−0.596155			−0.298077	+	0.954542i	$0.596345\pi$
$224$	−0.845477	−	4.79494i	−0.0564908	−	0.320375i
$225$	0.524984	−	2.97733i	0.0349990	−	0.198489i
$226$	2.52128	−	0.917670i	0.167713	−	0.0610425i
$227$	1.35138	+	1.13395i	0.0896945	+	0.0752626i	0.686532	−	0.727099i	$-0.259132\pi$
$227$	1.35138	+	1.13395i	0.0896945	+	0.0752626i	−0.596838	+	0.802362i	$0.703576\pi$
$228$	−5.71274			−0.378336
$229$	−16.6606	−	13.9799i	−1.10096	−	0.923818i	−0.103474	−	0.994632i	$-0.532996\pi$
$229$	−16.6606	−	13.9799i	−1.10096	−	0.923818i	−0.997490	+	0.0708145i	$0.977440\pi$
$230$	2.13527	+	3.69840i	0.140796	+	0.243865i
$231$	19.2237	+	6.99687i	1.26483	+	0.460360i
$232$	0.304151	−	0.526805i	0.0199685	−	0.0345864i
$233$	6.10307	+	10.5708i	0.399825	+	0.692517i	0.993704	−	0.112037i	$-0.0357375\pi$
$233$	6.10307	+	10.5708i	0.399825	+	0.692517i	−0.593879	+	0.804554i	$0.702404\pi$
$234$	−2.90742	−	16.4888i	−0.190064	−	1.07791i
$235$	8.35499	−	3.04097i	0.545020	−	0.198371i
$236$	1.78393	−	3.08986i	0.116124	−	0.201133i
$237$	−19.3534	+	16.2394i	−1.25714	+	1.05486i
$238$	−23.8745	+	20.0330i	−1.54755	+	1.29855i
$239$	−7.53332	−	2.74190i	−0.487290	−	0.177359i	0.0866788	−	0.996236i	$-0.472375\pi$
$239$	−7.53332	−	2.74190i	−0.487290	−	0.177359i	−0.573969	+	0.818877i	$0.694597\pi$
$240$	0.426173	−	2.41695i	0.0275094	−	0.156013i
$241$	−2.42969	+	13.7795i	−0.156510	+	0.887614i	0.800882	+	0.598822i	$0.204365\pi$
$241$	−2.42969	+	13.7795i	−0.156510	+	0.887614i	−0.957392	+	0.288791i	$0.906747\pi$
$242$	7.58242	+	2.75978i	0.487417	+	0.177405i
$243$	−16.9195	+	14.1971i	−1.08538	+	0.910745i
$244$	−9.30203	+	7.80533i	−0.595501	+	0.499685i
$245$	−8.35314	+	14.4681i	−0.533663	+	0.924331i
$246$	21.6409	−	7.87664i	1.37977	−	0.502196i
$247$	2.23852	+	12.6953i	0.142433	+	0.807779i
$248$	0.235121	+	0.407241i	0.0149302	+	0.0258599i
$249$	−0.153413	+	0.265720i	−0.00972217	+	0.0168393i
$250$	−0.939693	−	0.342020i	−0.0594314	−	0.0216313i
$251$	7.42686	+	12.8637i	0.468780	+	0.811950i	0.999363	−	0.0356826i	$-0.0113605\pi$
$251$	7.42686	+	12.8637i	0.468780	+	0.811950i	−0.530584	+	0.847633i	$0.678027\pi$
$252$	−11.2762	−	9.46184i	−0.710332	−	0.596040i
$253$	−7.31118			−0.459650
$254$	−8.02245	−	6.73164i	−0.503373	−	0.422380i
$255$	−14.7621	+	5.37298i	−0.924442	+	0.336469i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.946093	−	5.36556i	−0.0590156	−	0.334694i	0.940977	−	0.338470i	$-0.109909\pi$
$257$	−0.946093	−	5.36556i	−0.0590156	−	0.334694i	−0.999993	+	0.00377553i	$0.998798\pi$
$258$	11.3510			0.706683
$259$	22.3888	−	19.3875i	1.39117	−	1.20468i
$260$	−5.53811			−0.343459
$261$	−0.319349	−	1.81112i	−0.0197672	−	0.112105i
$262$	2.18317	−	12.3814i	0.134877	−	0.764925i
$263$	−26.0585	+	9.48451i	−1.60683	+	0.584840i	−0.980810	−	0.194965i	$-0.937541\pi$
$263$	−26.0585	+	9.48451i	−1.60683	+	0.584840i	−0.626023	+	0.779804i	$0.715319\pi$
$264$	3.21866	+	2.70077i	0.198095	+	0.166221i
$265$	−9.90404			−0.608400
$266$	8.68189	+	7.28497i	0.532321	+	0.446670i
$267$	3.98724	+	6.90611i	0.244015	+	0.422647i
$268$	−11.7015	−	4.25900i	−0.714783	−	0.260160i
$269$	9.09346	−	15.7503i	0.554438	−	0.960315i	−0.443509	−	0.896270i	$-0.646267\pi$
$269$	9.09346	−	15.7503i	0.554438	−	0.960315i	0.997947	−	0.0640448i	$-0.0204001\pi$
$270$	−0.0285488	−	0.0494479i	−0.00173742	−	0.00300930i
$271$	4.09801	+	23.2410i	0.248936	+	1.41179i	0.811170	+	0.584810i	$0.198831\pi$
$271$	4.09801	+	23.2410i	0.248936	+	1.41179i	−0.562234	+	0.826978i	$0.690058\pi$
$272$	−6.01497	+	2.18927i	−0.364711	+	0.132744i
$273$	−33.0886	+	57.3112i	−2.00262	+	3.46863i
$274$	−0.502612	+	0.421742i	−0.0303639	+	0.0254783i
$275$	1.31147	−	1.10045i	0.0790846	−	0.0663599i
$276$	9.84883	+	3.58468i	0.592830	+	0.215772i
$277$	4.34369	−	24.6343i	0.260987	−	1.48013i	−0.519236	−	0.854631i	$-0.673783\pi$
$277$	4.34369	−	24.6343i	0.260987	−	1.48013i	0.780223	−	0.625501i	$-0.215105\pi$
$278$	−2.88820	+	16.3798i	−0.173223	+	0.982394i
$279$	1.33593	+	0.486238i	0.0799800	+	0.0291103i
$280$	−3.72980	+	3.12967i	−0.222898	+	0.187034i
$281$	14.4106	−	12.0919i	0.859662	−	0.721342i	−0.102233	−	0.994760i	$-0.532599\pi$
$281$	14.4106	−	12.0919i	0.859662	−	0.721342i	0.961895	+	0.273418i	$0.0881542\pi$
$282$	10.9105	−	18.8976i	0.649713	−	1.12534i
$283$	12.0670	−	4.39202i	0.717308	−	0.261079i	0.0425253	−	0.999095i	$-0.486460\pi$
$283$	12.0670	−	4.39202i	0.717308	−	0.261079i	0.674782	+	0.738017i	$0.264237\pi$
$284$	−1.62659	−	9.22487i	−0.0965206	−	0.547395i
$285$	2.85637	+	4.94738i	0.169197	+	0.293057i
$286$	4.74063	−	8.21101i	0.280319	−	0.485527i
$287$	−42.9330	−	15.6263i	−2.53425	−	0.922392i
$288$	−1.51163	−	2.61822i	−0.0890738	−	0.154280i
$289$	18.3642	+	15.4094i	1.08025	+	0.906436i
$290$	−0.608302			−0.0357207
$291$	−9.16631	−	7.69144i	−0.537338	−	0.450880i
$292$	−7.92024	+	2.88273i	−0.463497	+	0.168699i
$293$	4.06027	−	23.0269i	0.237204	−	1.34525i	−0.600719	−	0.799460i	$-0.705119\pi$
$293$	4.06027	−	23.0269i	0.237204	−	1.34525i	0.837923	−	0.545788i	$-0.183770\pi$
$294$	7.11977	+	40.3782i	0.415233	+	2.35491i
$295$	−3.56787			−0.207729
$296$	5.68289	−	2.16903i	0.330312	−	0.126073i
$297$	0.0977511			0.00567210
$298$	−1.03549	−	5.87257i	−0.0599845	−	0.340189i
$299$	4.10690	−	23.2914i	0.237508	−	1.34698i
$300$	−2.30623	+	0.839397i	−0.133150	+	0.0484626i
$301$	−17.2506	−	14.4750i	−0.994308	−	0.834324i
$302$	16.9920			0.977779
$303$	30.0186	+	25.1886i	1.72452	+	1.44705i
$304$	1.16385	+	2.01585i	0.0667516	+	0.115617i
$305$	11.4106	+	4.15313i	0.653371	+	0.237807i
$306$	−9.67596	+	16.7592i	−0.553138	+	0.958063i
$307$	4.28809	+	7.42720i	0.244734	+	0.423892i	0.962057	−	0.272849i	$-0.0879659\pi$
$307$	4.28809	+	7.42720i	0.244734	+	0.423892i	−0.717322	+	0.696741i	$0.754633\pi$
$308$	−1.44746	−	8.20895i	−0.0824767	−	0.467748i
$309$	−17.9240	+	6.52380i	−1.01966	+	0.371126i
$310$	0.235121	−	0.407241i	0.0133540	−	0.0231298i
$311$	2.24764	−	1.88600i	0.127452	−	0.106945i	−0.576834	−	0.816862i	$-0.695712\pi$
$311$	2.24764	−	1.88600i	0.127452	−	0.106945i	0.704286	+	0.709917i	$0.251267\pi$
$312$	−10.4119	+	8.73665i	−0.589459	+	0.494615i
$313$	−27.0980	−	9.86287i	−1.53167	−	0.557482i	−0.567641	−	0.823277i	$-0.692144\pi$
$313$	−27.0980	−	9.86287i	−1.53167	−	0.557482i	−0.964030	+	0.265794i	$0.914366\pi$
$314$	−0.934748	+	5.30122i	−0.0527509	+	0.299165i
$315$	−2.55610	+	14.4964i	−0.144020	+	0.816778i
$316$	9.67325	+	3.52078i	0.544163	+	0.198059i
$317$	−24.1310	+	20.2483i	−1.35533	+	1.13726i	−0.377941	+	0.925830i	$0.623368\pi$
$317$	−24.1310	+	20.2483i	−1.35533	+	1.13726i	−0.977393	+	0.211431i	$0.932188\pi$
$318$	−18.6201	+	15.6241i	−1.04416	+	0.876158i
$319$	0.520707	−	0.901891i	0.0291540	−	0.0504962i
$320$	−0.939693	+	0.342020i	−0.0525304	+	0.0191195i
$321$	−4.52341	−	25.6536i	−0.252472	−	1.43184i
$322$	−10.3964	−	18.0072i	−0.579371	−	1.00350i
$323$	7.44983	−	12.9035i	0.414520	−	0.717969i
$324$	8.39114	+	3.05412i	0.466174	+	0.169674i
$325$	2.76905	+	4.79614i	0.153599	+	0.266042i
$326$	8.43555	+	7.07826i	0.467202	+	0.392029i
$327$	1.83749			0.101614
$328$	−7.18832	−	6.03171i	−0.396908	−	0.333046i
$329$	−40.6797	+	14.8062i	−2.24274	+	0.816292i
$330$	0.729610	−	4.13782i	0.0401637	−	0.227780i
$331$	1.41918	+	8.04856i	0.0780051	+	0.442389i	0.998648	+	0.0519831i	$0.0165542\pi$
$331$	1.41918	+	8.04856i	0.0780051	+	0.442389i	−0.920643	+	0.390406i	$0.872335\pi$
$332$	0.125019			0.00686132
$333$	8.94621	−	16.0671i	0.490249	−	0.880469i
$334$	2.17167			0.118829
$335$	2.16235	+	12.2633i	0.118142	+	0.670015i
$336$	−2.07500	+	11.7679i	−0.113200	+	0.641992i
$337$	−18.8898	+	6.87532i	−1.02899	+	0.374523i	−0.800697	−	0.599069i	$-0.795537\pi$
$337$	−18.8898	+	6.87532i	−1.02899	+	0.374523i	−0.228296	+	0.973592i	$0.573315\pi$
$338$	13.5365	+	11.3585i	0.736287	+	0.617818i
$339$	−6.58492			−0.357644
$340$	4.90345	+	4.11448i	0.265927	+	0.223139i
$341$	0.402528	+	0.697199i	0.0217981	+	0.0377554i
$342$	6.61288	+	2.40689i	0.357584	+	0.130150i
$343$	23.6295	−	40.9275i	1.27587	−	2.20988i
$344$	−2.31254	−	4.00543i	−0.124684	−	0.215958i
$345$	−1.81999	−	10.3217i	−0.0979850	−	0.555701i
$346$	1.49014	−	0.542368i	0.0801107	−	0.0291579i
$347$	6.84271	−	11.8519i	0.367336	−	0.636245i	−0.621812	−	0.783166i	$-0.713603\pi$
$347$	6.84271	−	11.8519i	0.367336	−	0.636245i	0.989148	+	0.146922i	$0.0469366\pi$
$348$	−1.14364	+	0.959627i	−0.0613055	+	0.0514414i
$349$	17.6230	−	14.7874i	0.943336	−	0.791553i	−0.0348265	−	0.999393i	$-0.511088\pi$
$349$	17.6230	−	14.7874i	0.943336	−	0.791553i	0.978163	+	0.207840i	$0.0666434\pi$
$350$	4.57528	+	1.66527i	0.244559	+	0.0890122i
$351$	−0.0549097	+	0.311408i	−0.00293086	+	0.0166217i
$352$	0.297286	−	1.68599i	0.0158454	−	0.0898638i
$353$	30.2457	+	11.0085i	1.60982	+	0.585926i	0.981404	−	0.191953i	$-0.0614821\pi$
$353$	30.2457	+	11.0085i	1.60982	+	0.585926i	0.628414	+	0.777879i	$0.283704\pi$
$354$	−6.70778	+	5.62850i	−0.356514	+	0.299151i
$355$	−7.17568	+	6.02111i	−0.380845	+	0.319567i
$356$	1.62464	−	2.81396i	0.0861057	−	0.149139i
$357$	71.8756	−	26.1606i	3.80406	−	1.38456i
$358$	1.70489	+	9.66890i	0.0901061	+	0.511017i
$359$	5.28107	+	9.14708i	0.278724	+	0.482764i	0.971068	−	0.238803i	$-0.0767552\pi$
$359$	5.28107	+	9.14708i	0.278724	+	0.482764i	−0.692344	+	0.721568i	$0.743422\pi$
$360$	−1.51163	+	2.61822i	−0.0796700	+	0.137993i
$361$	12.7627	+	4.64524i	0.671721	+	0.244486i
$362$	7.13933	+	12.3657i	0.375235	+	0.649925i
$363$	−15.1702	−	12.7293i	−0.796230	−	0.668117i
$364$	26.9645			1.41333
$365$	6.45664	+	5.41776i	0.337956	+	0.283579i
$366$	28.0044	−	10.1928i	1.46381	−	0.532784i
$367$	−4.76920	+	27.0475i	−0.248950	+	1.41187i	0.562186	+	0.827011i	$0.309961\pi$
$367$	−4.76920	+	27.0475i	−0.248950	+	1.41187i	−0.811136	+	0.584857i	$0.801151\pi$
$368$	−0.741572	−	4.20566i	−0.0386571	−	0.219235i
$369$	−28.3694			−1.47685
$370$	−4.71989	−	3.83701i	−0.245375	−	0.199477i
$371$	48.2219			2.50356
$372$	−0.200404	−	1.13655i	−0.0103905	−	0.0589274i
$373$	−3.86091	+	21.8963i	−0.199910	+	1.13375i	0.705340	+	0.708869i	$0.250794\pi$
$373$	−3.86091	+	21.8963i	−0.199910	+	1.13375i	−0.905251	+	0.424878i	$0.860317\pi$
$374$	−10.2976	+	3.74804i	−0.532479	+	0.193806i
$375$	1.88005	+	1.57755i	0.0970855	+	0.0814644i
$376$	−8.89120			−0.458528
$377$	2.58068	+	2.16545i	0.132912	+	0.111526i
$378$	0.139001	+	0.240757i	0.00714946	+	0.0123832i
$379$	3.73414	+	1.35911i	0.191810	+	0.0698130i	0.436139	−	0.899879i	$-0.356346\pi$
$379$	3.73414	+	1.35911i	0.191810	+	0.0698130i	−0.244329	+	0.969692i	$0.578568\pi$
$380$	1.16385	−	2.01585i	0.0597045	−	0.103411i
$381$	12.8511	+	22.2587i	0.658380	+	1.14035i
$382$	−0.681826	−	3.86683i	−0.0348853	−	0.197844i
$383$	−30.1448	+	10.9718i	−1.54033	+	0.560634i	−0.966124	−	0.258077i	$-0.916911\pi$
$383$	−30.1448	+	10.9718i	−1.54033	+	0.560634i	−0.574205	+	0.818711i	$0.694689\pi$
$384$	−1.22712	+	2.12543i	−0.0626211	+	0.108463i
$385$	−6.38543	+	5.35801i	−0.325432	+	0.273070i
$386$	2.12766	−	1.78532i	0.108295	−	0.0908705i
$387$	−13.1396	−	4.78241i	−0.667921	−	0.243103i
$388$	−0.846632	+	4.80149i	−0.0429812	+	0.243759i
$389$	−3.15468	+	17.8911i	−0.159949	+	0.907114i	0.794172	+	0.607692i	$0.207905\pi$
$389$	−3.15468	+	17.8911i	−0.159949	+	0.907114i	−0.954121	+	0.299421i	$0.903206\pi$
$390$	12.7721	+	4.64867i	0.646742	+	0.235395i
$391$	−20.9404	+	17.5711i	−1.05900	+	0.888607i
$392$	12.7978	−	10.7386i	0.646384	−	0.542381i
$393$	−15.4278	+	26.7217i	−0.778230	+	1.34793i
$394$	13.3841	−	4.87142i	0.674282	−	0.245419i
$395$	−1.78754	−	10.1377i	−0.0899411	−	0.510082i
$396$	−2.58792	−	4.48241i	−0.130048	−	0.225249i
$397$	−11.7286	+	20.3144i	−0.588639	+	1.01955i	0.405772	+	0.913974i	$0.367003\pi$
$397$	−11.7286	+	20.3144i	−0.588639	+	1.01955i	−0.994411	+	0.105578i	$0.966331\pi$
$398$	−13.7749	−	5.01365i	−0.690473	−	0.251312i
$399$	−13.9074	−	24.0883i	−0.696241	−	1.20593i
$400$	0.766044	+	0.642788i	0.0383022	+	0.0321394i
$401$	2.75599			0.137628			0.0688138	−	0.997630i	$-0.478079\pi$
$401$	2.75599			0.137628			0.0688138	+	0.997630i	$0.478079\pi$
$402$	23.4113	+	19.6444i	1.16765	+	0.979775i
$403$	−2.44719	+	0.890706i	−0.121903	+	0.0443692i
$404$	2.77262	−	15.7243i	0.137943	−	0.782314i
$405$	−1.55062	−	8.79400i	−0.0770509	−	0.436977i
$406$	2.96177			0.146990
$407$	9.72913	−	3.71339i	0.482255	−	0.184066i
$408$	15.7095			0.777739
$409$	5.16857	+	29.3124i	0.255569	+	1.44941i	0.794607	+	0.607124i	$0.207677\pi$
$409$	5.16857	+	29.3124i	0.255569	+	1.44941i	−0.539038	+	0.842282i	$0.681212\pi$
$410$	−1.62946	+	9.24112i	−0.0804732	+	0.456386i
$411$	1.51315	−	0.550740i	0.0746380	−	0.0271660i
$412$	5.95370	+	4.99575i	0.293318	+	0.246123i
$413$	17.3716			0.854802
$414$	−9.89038	−	8.29902i	−0.486086	−	0.407874i
$415$	−0.0625096	−	0.108270i	−0.00306848	−	0.00531476i
$416$	5.20412	+	1.89414i	0.255153	+	0.0928680i
$417$	20.4100	−	35.3511i	0.999481	−	1.73115i
$418$	1.99252	+	3.45115i	0.0974574	+	0.168801i
$419$	3.74592	+	21.2441i	0.183000	+	1.03784i	0.928498	+	0.371337i	$0.121101\pi$
$419$	3.74592	+	21.2441i	0.183000	+	1.03784i	−0.745498	+	0.666508i	$0.767788\pi$
$420$	11.2288	−	4.08695i	0.547910	−	0.199423i
$421$	9.95781	−	17.2474i	0.485314	−	0.840589i	−0.514543	−	0.857464i	$-0.672039\pi$
$421$	9.95781	−	17.2474i	0.485314	−	0.840589i	0.999858	+	0.0168756i	$0.00537193\pi$
$422$	1.56550	−	1.31361i	0.0762074	−	0.0639456i
$423$	−20.5916	+	17.2784i	−1.00120	+	0.840105i
$424$	9.30675	+	3.38738i	0.451976	+	0.164506i
$425$	1.11152	−	6.30375i	0.0539167	−	0.305777i
$426$	−3.99204	+	22.6400i	−0.193415	+	1.09691i
$427$	−55.5573	−	20.2212i	−2.68861	−	0.978573i
$428$	−8.13081	+	6.82256i	−0.393018	+	0.329781i
$429$	−17.8253	+	14.9572i	−0.860611	+	0.722139i
$430$	−2.31254	+	4.00543i	−0.111520	+	0.193159i
$431$	6.14543	−	2.23675i	0.296015	−	0.107741i	−0.189744	−	0.981834i	$-0.560766\pi$
$431$	6.14543	−	2.23675i	0.296015	−	0.107741i	0.485759	+	0.874093i	$0.338543\pi$
$432$	0.00991488	+	0.0562301i	0.000477030	+	0.00270537i
$433$	11.9591	+	20.7138i	0.574719	+	0.995443i	0.996072	+	0.0885459i	$0.0282220\pi$
$433$	11.9591	+	20.7138i	0.574719	+	0.995443i	−0.421353	+	0.906897i	$0.638445\pi$
$434$	−1.14478	+	1.98282i	−0.0549513	+	0.0951785i
$435$	1.40288	+	0.510607i	0.0672630	+	0.0244817i
$436$	−0.374351	−	0.648396i	−0.0179282	−	0.0310525i
$437$	7.61492	+	6.38968i	0.364271	+	0.305660i
$438$	20.6856			0.988397
$439$	−4.13292	−	3.46793i	−0.197253	−	0.165515i	0.538811	−	0.842427i	$-0.318874\pi$
$439$	−4.13292	−	3.46793i	−0.197253	−	0.165515i	−0.736065	+	0.676911i	$0.763318\pi$
$440$	−1.60876	+	0.585540i	−0.0766945	+	0.0279145i
$441$	8.77054	−	49.7402i	0.417645	−	2.36858i
$442$	−6.15573	−	34.9109i	−0.292798	−	1.66054i
$443$	−34.5180			−1.64000			−0.820000	−	0.572364i	$-0.806027\pi$
$443$	−34.5180			−1.64000			−0.820000	+	0.572364i	$0.806027\pi$
$444$	−14.9267	+	0.232075i	−0.708391	+	0.0110138i
$445$	−3.24928			−0.154031
$446$	−1.54590	−	8.76724i	−0.0732005	−	0.415141i
$447$	−2.54134	+	14.4127i	−0.120201	+	0.681696i
$448$	4.57528	−	1.66527i	0.216162	−	0.0786764i
$449$	16.3262	+	13.6993i	0.770479	+	0.646509i	0.940832	−	0.338874i	$-0.110046\pi$
$449$	16.3262	+	13.6993i	0.770479	+	0.646509i	−0.170352	+	0.985383i	$0.554491\pi$
$450$	3.02326			0.142518
$451$	−12.3064	−	10.3263i	−0.579487	−	0.486247i
$452$	1.34154	+	2.32362i	0.0631009	+	0.109294i
$453$	−39.1874	−	14.2630i	−1.84118	−	0.670136i
$454$	−0.882053	+	1.52776i	−0.0413968	+	0.0717014i
$455$	−13.4823	−	23.3520i	−0.632059	−	1.09476i
$456$	−0.992007	−	5.62595i	−0.0464550	−	0.263459i
$457$	26.8685	−	9.77935i	1.25686	−	0.457459i	0.374144	−	0.927371i	$-0.377936\pi$
$457$	26.8685	−	9.77935i	1.25686	−	0.457459i	0.882713	+	0.469912i	$0.155714\pi$
$458$	10.8744	−	18.8351i	0.508129	−	0.880105i
$459$	0.279975	−	0.234927i	0.0130681	−	0.0109654i
$460$	−3.27142	+	2.74505i	−0.152531	+	0.127989i
$461$	24.8260	+	9.03594i	1.15626	+	0.420846i	0.847761	−	0.530378i	$-0.177950\pi$
$461$	24.8260	+	9.03594i	1.15626	+	0.420846i	0.308503	+	0.951223i	$0.400172\pi$
$462$	−3.55241	+	20.1467i	−0.165273	+	0.937309i
$463$	−3.94672	+	22.3830i	−0.183420	+	1.04022i	0.744549	+	0.667567i	$0.232664\pi$
$463$	−3.94672	+	22.3830i	−0.183420	+	1.04022i	−0.927969	+	0.372657i	$0.878447\pi$
$464$	0.571617	+	0.208051i	0.0265366	+	0.00965854i
$465$	−0.884079	+	0.741831i	−0.0409982	+	0.0344016i
$466$	−9.35044	+	7.84595i	−0.433151	+	0.363457i
$467$	−16.1053	+	27.8952i	−0.745265	+	1.29084i	0.204806	+	0.978803i	$0.434344\pi$
$467$	−16.1053	+	27.8952i	−0.745265	+	1.29084i	−0.950071	+	0.312034i	$0.898990\pi$
$468$	15.7334	−	5.72650i	0.727278	−	0.264707i
$469$	−10.5283	−	59.7089i	−0.486151	−	2.75710i
$470$	4.44560	+	7.70000i	0.205060	+	0.355175i
$471$	6.60557	−	11.4412i	0.304368	−	0.527182i
$472$	3.35270	+	1.22028i	0.154321	+	0.0561681i
$473$	−3.95907	−	6.85731i	−0.182038	−	0.315299i
$474$	−19.3534	−	16.2394i	−0.888930	−	0.745901i
$475$	−2.32771			−0.106803
$476$	−23.8745	−	20.0330i	−1.09428	−	0.918213i
$477$	28.1368	−	10.2410i	1.28829	−	0.468901i
$478$	1.39210	−	7.89500i	0.0636732	−	0.361109i
$479$	3.21904	+	18.2561i	0.147081	+	0.834140i	0.965672	+	0.259763i	$0.0836446\pi$
$479$	3.21904	+	18.2561i	0.147081	+	0.834140i	−0.818591	+	0.574377i	$0.805244\pi$
$480$	2.45423			0.112020
$481$	6.36471	+	33.0803i	0.290206	+	1.50833i
$482$	−13.9920			−0.637320
$483$	8.86137	+	50.2553i	0.403206	+	2.28670i
$484$	−1.40117	+	7.94646i	−0.0636898	+	0.361203i
$485$	4.58153	−	1.66754i	0.208036	−	0.0757191i
$486$	−16.9195	−	14.1971i	−0.767482	−	0.643994i
$487$	−2.60642			−0.118108			−0.0590540	−	0.998255i	$-0.518808\pi$
$487$	−2.60642			−0.118108			−0.0590540	+	0.998255i	$0.518808\pi$
$488$	−9.30203	−	7.80533i	−0.421083	−	0.353331i
$489$	−13.5128	−	23.4049i	−0.611070	−	1.05840i
$490$	−15.6988	−	5.71389i	−0.709198	−	0.258127i
$491$	−1.41689	+	2.45413i	−0.0639434	+	0.110753i	−0.896225	−	0.443600i	$-0.853701\pi$
$491$	−1.41689	+	2.45413i	−0.0639434	+	0.110753i	0.832281	+	0.554353i	$0.187034\pi$
$492$	11.5149	+	19.9443i	0.519131	+	0.899161i
$493$	−0.676140	−	3.83458i	−0.0304518	−	0.172701i
$494$	−12.1137	+	4.40901i	−0.545020	+	0.198371i
$495$	−2.58792	+	4.48241i	−0.116318	+	0.201469i
$496$	−0.360226	+	0.302266i	−0.0161746	+	0.0135721i
$497$	34.9377	−	29.3162i	1.56717	−	1.31501i
$498$	−0.288323	−	0.104941i	−0.0129200	−	0.00470251i
$499$	−2.13993	+	12.1362i	−0.0957965	+	0.543289i	0.898704	+	0.438556i	$0.144510\pi$
$499$	−2.13993	+	12.1362i	−0.0957965	+	0.543289i	−0.994500	+	0.104733i	$0.966601\pi$
$500$	0.173648	−	0.984808i	0.00776578	−	0.0440419i
$501$	−5.00837	−	1.82290i	−0.223757	−	0.0814410i
$502$	−11.3786	+	9.54779i	−0.507853	+	0.426139i
$503$	−6.40303	+	5.37278i	−0.285497	+	0.239560i	−0.774277	−	0.632847i	$-0.781886\pi$
$503$	−6.40303	+	5.37278i	−0.285497	+	0.239560i	0.488780	+	0.872407i	$0.337442\pi$
$504$	7.36000	−	12.7479i	0.327841	−	0.567836i
$505$	−15.0040	+	5.46100i	−0.667668	+	0.243011i
$506$	−1.26957	−	7.20011i	−0.0564394	−	0.320084i
$507$	−21.6839	−	37.5576i	−0.963016	−	1.66799i
$508$	5.23628	−	9.06951i	0.232323	−	0.402394i
$509$	−7.12216	−	2.59226i	−0.315684	−	0.114900i	0.179318	−	0.983791i	$-0.442611\pi$
$509$	−7.12216	−	2.59226i	−0.315684	−	0.114900i	−0.495003	+	0.868891i	$0.664833\pi$
$510$	−7.85477	−	13.6049i	−0.347815	−	0.602434i
$511$	−31.4368	−	26.3786i	−1.39068	−	1.16692i
$512$	1.00000			0.0441942
$513$	−0.101812	−	0.0854306i	−0.00449512	−	0.00377185i
$514$	5.11976	−	1.86344i	0.225823	−	0.0821928i
$515$	1.34959	−	7.65393i	0.0594702	−	0.337273i
$516$	1.97108	+	11.1786i	0.0867721	+	0.492109i
$517$	−15.2218			−0.669452
$518$	22.9807	+	18.6821i	1.00971	+	0.820843i
$519$	−3.89187			−0.170834
$520$	−0.961682	−	5.45397i	−0.0421725	−	0.239172i
$521$	−6.79269	+	38.5233i	−0.297593	+	1.68773i	0.358879	+	0.933384i	$0.383159\pi$
$521$	−6.79269	+	38.5233i	−0.297593	+	1.68773i	−0.656472	+	0.754350i	$0.727952\pi$
$522$	1.72815	−	0.628995i	0.0756390	−	0.0275303i
$523$	4.35428	+	3.65367i	0.190399	+	0.159764i	0.733004	−	0.680224i	$-0.238117\pi$
$523$	4.35428	+	3.65367i	0.190399	+	0.159764i	−0.542605	+	0.839988i	$0.682562\pi$
$524$	12.5724			0.549228
$525$	−9.15381	−	7.68095i	−0.399505	−	0.335224i
$526$	−13.8654	−	24.0156i	−0.604561	−	1.04713i
$527$	2.82849	+	1.02949i	0.123211	+	0.0448451i
$528$	−2.10083	+	3.63874i	−0.0914268	+	0.158356i
$529$	2.38124	+	4.12443i	0.103532	+	0.179323i
$530$	−1.71982	−	9.75358i	−0.0747041	−	0.423668i
$531$	10.1361	−	3.68924i	0.439869	−	0.160099i
$532$	−5.66670	+	9.81501i	−0.245683	+	0.425535i
$533$	39.8097	−	33.4043i	1.72435	−	1.44690i
$534$	−6.10881	+	5.12590i	−0.264354	+	0.221819i
$535$	9.97392	+	3.63021i	0.431210	+	0.156948i
$536$	2.16235	−	12.2633i	0.0933993	−	0.529694i
$537$	4.18419	−	23.7297i	0.180561	−	1.02401i
$538$	17.0901	+	6.22029i	0.736807	+	0.268176i
$539$	21.9098	−	18.3845i	0.943722	−	0.791877i
$540$	0.0437392	−	0.0367016i	0.00188224	−	0.00157938i
$541$	−3.18621	+	5.51867i	−0.136986	+	0.237266i	−0.926354	−	0.376653i	$-0.877075\pi$
$541$	−3.18621	+	5.51867i	−0.136986	+	0.237266i	0.789369	+	0.613920i	$0.210408\pi$
$542$	−22.1763	+	8.07150i	−0.952552	+	0.346701i
$543$	−6.08518	−	34.5108i	−0.261140	−	1.48100i
$544$	−3.20050	−	5.54343i	−0.137220	−	0.237672i
$545$	−0.374351	+	0.648396i	−0.0160355	+	0.0277742i
$546$	−62.1863	−	22.6340i	−2.66133	−	0.968644i
$547$	−12.3782	−	21.4396i	−0.529252	−	0.916692i	−0.999418	−	0.0341135i	$-0.989139\pi$
$547$	−12.3782	−	21.4396i	−0.529252	−	0.916692i	0.470166	−	0.882578i	$-0.344194\pi$
$548$	−0.502612	−	0.421742i	−0.0214705	−	0.0180159i
$549$	−36.7113			−1.56680
$550$	1.31147	+	1.10045i	0.0559213	+	0.0469235i
$551$	−1.33056	+	0.484283i	−0.0566836	+	0.0206311i
$552$	−1.81999	+	10.3217i	−0.0774639	+	0.439320i
$553$	8.70339	+	49.3594i	0.370106	+	2.09898i
$554$	25.0143			1.06276
$555$	7.66434	+	12.8109i	0.325333	+	0.543792i
$556$	−16.6325			−0.705374
$557$	3.79975	+	21.5495i	0.161001	+	0.913080i	0.953093	+	0.302678i	$0.0978808\pi$
$557$	3.79975	+	21.5495i	0.161001	+	0.913080i	−0.792092	+	0.610401i	$0.791008\pi$
$558$	−0.246870	+	1.40007i	−0.0104508	+	0.0592696i
$559$	24.0694	−	8.76055i	1.01803	−	0.370532i
$560$	−3.72980	−	3.12967i	−0.157613	−	0.132253i
$561$	26.8948			1.13550
$562$	14.4106	+	12.0919i	0.607873	+	0.510066i
$563$	−8.97719	−	15.5490i	−0.378344	−	0.655310i	0.612478	−	0.790488i	$-0.290173\pi$
$563$	−8.97719	−	15.5490i	−0.378344	−	0.655310i	−0.990821	+	0.135177i	$0.956840\pi$
$564$	20.5051	+	7.46325i	0.863421	+	0.314259i
$565$	1.34154	−	2.32362i	0.0564392	−	0.0977555i
$566$	6.42071	+	11.1210i	0.269882	+	0.467450i
$567$	7.54983	+	42.8172i	0.317063	+	1.79815i
$568$	8.80227	−	3.20376i	0.369335	−	0.134427i
$569$	9.81245	−	16.9957i	0.411359	−	0.712495i	−0.583679	−	0.811984i	$-0.698387\pi$
$569$	9.81245	−	16.9957i	0.411359	−	0.712495i	0.995039	+	0.0994889i	$0.0317208\pi$
$570$	−4.37621	+	3.67208i	−0.183299	+	0.153806i
$571$	−20.5006	+	17.2020i	−0.857923	+	0.719883i	−0.961520	−	0.274736i	$-0.911409\pi$
$571$	−20.5006	+	17.2020i	−0.857923	+	0.719883i	0.103596	+	0.994619i	$0.466965\pi$
$572$	8.90947	+	3.24278i	0.372523	+	0.135587i
$573$	−1.67336	+	9.49010i	−0.0699057	+	0.396455i
$574$	7.93369	−	44.9942i	0.331146	−	1.87802i
$575$	4.01300	+	1.46061i	0.167353	+	0.0609117i
$576$	2.31596	−	1.94332i	0.0964981	−	0.0809716i
$577$	16.3428	−	13.7132i	0.680360	−	0.570890i	−0.235752	−	0.971813i	$-0.575755\pi$
$577$	16.3428	−	13.7132i	0.680360	−	0.570890i	0.916111	+	0.400924i	$0.131311\pi$
$578$	−11.9864	+	20.7610i	−0.498568	+	0.863545i
$579$	−6.40547	+	2.33140i	−0.266202	+	0.0968896i
$580$	−0.105630	−	0.599060i	−0.00438607	−	0.0248746i
$581$	0.304354	+	0.527156i	0.0126267	+	0.0218701i
$582$	5.98288	−	10.3627i	0.247998	−	0.429546i
$583$	15.9332	+	5.79921i	0.659885	+	0.240179i
$584$	−4.21427	−	7.29933i	−0.174388	−	0.302048i
$585$	−12.8260	−	10.7623i	−0.530290	−	0.444966i
$586$	23.3822			0.965909
$587$	−3.22288	−	2.70432i	−0.133023	−	0.111619i	0.573849	−	0.818961i	$-0.305450\pi$
$587$	−3.22288	−	2.70432i	−0.133023	−	0.111619i	−0.706872	+	0.707342i	$0.749894\pi$
$588$	−38.5285	+	14.0232i	−1.58889	+	0.578308i
$589$	0.190073	−	1.07796i	0.00783181	−	0.0444164i
$590$	−0.619554	−	3.51366i	−0.0255066	−	0.144655i
$591$	−34.9559			−1.43789
$592$	3.12291	+	5.21991i	0.128351	+	0.214537i
$593$	−15.4461			−0.634296			−0.317148	−	0.948376i	$-0.602725\pi$
$593$	−15.4461			−0.634296			−0.317148	+	0.948376i	$0.602725\pi$
$594$	0.0169743	+	0.0962661i	0.000696464	+	0.00394984i
$595$	−5.41190	+	30.6924i	−0.221866	+	1.25827i
$596$	5.60354	−	2.03952i	0.229530	−	0.0835421i
$597$	27.5596	+	23.1252i	1.12794	+	0.946452i
$598$	23.6507			0.967149
$599$	23.0311	+	19.3254i	0.941025	+	0.789614i	0.977763	−	0.209711i	$-0.0672524\pi$
$599$	23.0311	+	19.3254i	0.941025	+	0.789614i	−0.0367383	+	0.999325i	$0.511697\pi$
$600$	−1.22712	−	2.12543i	−0.0500968	−	0.0867703i
$601$	38.2009	+	13.9040i	1.55825	+	0.567156i	0.970334	−	0.241767i	$-0.0777270\pi$
$601$	38.2009	+	13.9040i	1.55825	+	0.567156i	0.587914	+	0.808923i	$0.299949\pi$
$602$	11.2595	−	19.5021i	0.458904	−	0.794846i
$603$	−18.8236	−	32.6034i	−0.766555	−	1.32771i
$604$	2.95063	+	16.7338i	0.120059	+	0.680891i
$605$	7.58242	−	2.75978i	0.308269	−	0.112201i
$606$	−19.5932	+	33.9365i	−0.795921	+	1.37858i
$607$	25.2342	−	21.1740i	1.02423	−	0.859427i	0.0340727	−	0.999419i	$-0.489152\pi$
$607$	25.2342	−	21.1740i	1.02423	−	0.859427i	0.990153	+	0.139992i	$0.0447078\pi$
$608$	−1.78313	+	1.49622i	−0.0723154	+	0.0606798i
$609$	−6.83050	−	2.48610i	−0.276786	−	0.100742i
$610$	−2.10860	+	11.9585i	−0.0853747	+	0.484184i
$611$	8.55050	−	48.4923i	0.345916	−	1.96179i
$612$	−18.1849	−	6.61874i	−0.735079	−	0.267547i
$613$	28.2025	−	23.6647i	1.13909	−	0.955810i	0.139681	−	0.990197i	$-0.455392\pi$
$613$	28.2025	−	23.6647i	1.13909	−	0.955810i	0.999409	+	0.0343868i	$0.0109478\pi$
$614$	−6.56974	+	5.51267i	−0.265133	+	0.222473i
$615$	11.5149	−	19.9443i	0.464325	−	0.804234i
$616$	7.83289	−	2.85094i	0.315596	−	0.114868i
$617$	−1.57811	−	8.94989i	−0.0635322	−	0.360309i	−0.999955	−	0.00943657i	$-0.996996\pi$
$617$	−1.57811	−	8.94989i	−0.0635322	−	0.360309i	0.936423	−	0.350872i	$-0.114115\pi$
$618$	−9.53716	−	16.5188i	−0.383641	−	0.664485i
$619$	13.4547	−	23.3042i	0.540788	−	0.936673i	−0.458071	−	0.888916i	$-0.651459\pi$
$619$	13.4547	−	23.3042i	0.540788	−	0.936673i	0.998859	−	0.0477571i	$-0.0152073\pi$
$620$	0.441883	+	0.160832i	0.0177464	+	0.00645918i
$621$	0.121919	+	0.211169i	0.00489243	+	0.00847393i
$622$	2.24764	+	1.88600i	0.0901222	+	0.0756215i
$623$	15.8204			0.633833
$624$	−10.4119	−	8.73665i	−0.416811	−	0.349746i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	5.00751	−	28.3990i	0.200140	−	1.13505i
$627$	−1.69832	−	9.63165i	−0.0678243	−	0.384651i
$628$	−5.38300			−0.214805
$629$	18.9413	−	34.0179i	0.755240	−	1.35638i
$630$	−14.7200			−0.586459
$631$	−6.99360	−	39.6627i	−0.278411	−	1.57895i	−0.727914	−	0.685668i	$-0.759510\pi$
$631$	−6.99360	−	39.6627i	−0.278411	−	1.57895i	0.449503	−	0.893279i	$-0.351601\pi$
$632$	−1.78754	+	10.1377i	−0.0711047	+	0.403255i
$633$	−4.71304	+	1.71541i	−0.187327	+	0.0681813i
$634$	−24.1310	−	20.2483i	−0.958366	−	0.804165i
$635$	−10.4726			−0.415591
$636$	−18.6201	−	15.6241i	−0.738336	−	0.619537i
$637$	46.2606	+	80.1257i	1.83291	+	3.17469i
$638$	0.978609	+	0.356185i	0.0387435	+	0.0141015i
$639$	14.1597	−	24.5254i	0.560150	−	0.970209i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−4.90047	−	27.7920i	−0.193557	−	1.09772i	−0.914459	−	0.404679i	$-0.867383\pi$
$641$	−4.90047	−	27.7920i	−0.193557	−	1.09772i	0.720902	−	0.693037i	$-0.243728\pi$
$642$	24.4783	−	8.90938i	0.966083	−	0.351625i
$643$	−5.88466	+	10.1925i	−0.232068	+	0.401954i	−0.958417	−	0.285373i	$-0.907883\pi$
$643$	−5.88466	+	10.1925i	−0.232068	+	0.401954i	0.726348	+	0.687327i	$0.241216\pi$
$644$	15.9283	−	13.3654i	0.627662	−	0.526671i
$645$	8.69538	−	7.29629i	0.342380	−	0.287291i
$646$	14.0011	+	5.09598i	0.550866	+	0.200499i
$647$	5.83163	−	33.0728i	0.229265	−	1.30023i	−0.625096	−	0.780548i	$-0.714940\pi$
$647$	5.83163	−	33.0728i	0.229265	−	1.30023i	0.854361	−	0.519680i	$-0.173949\pi$
$648$	−1.55062	+	8.79400i	−0.0609141	+	0.345461i
$649$	5.73983	+	2.08913i	0.225308	+	0.0820055i
$650$	−4.24244	+	3.55983i	−0.166402	+	0.139628i
$651$	4.30450	−	3.61191i	0.168707	−	0.141562i
$652$	−5.50591	+	9.53652i	−0.215628	+	0.373479i
$653$	−19.7186	+	7.17698i	−0.771649	+	0.280857i	−0.697686	−	0.716404i	$-0.745787\pi$
$653$	−19.7186	+	7.17698i	−0.771649	+	0.280857i	−0.0739628	+	0.997261i	$0.523565\pi$
$654$	0.319077	+	1.80958i	0.0124769	+	0.0707600i
$655$	−6.28620	−	10.8880i	−0.245622	−	0.425430i
$656$	4.69184	−	8.12651i	0.183186	−	0.317287i
$657$	−23.9450	−	8.71526i	−0.934183	−	0.340015i
$658$	−21.6452	−	37.4906i	−0.843818	−	1.46154i
$659$	4.59653	+	3.85694i	0.179055	+	0.150245i	0.727910	−	0.685672i	$-0.240492\pi$
$659$	4.59653	+	3.85694i	0.179055	+	0.150245i	−0.548855	+	0.835918i	$0.684936\pi$
$660$	4.20166			0.163549
$661$	9.50817	+	7.97830i	0.369825	+	0.310320i	0.808692	−	0.588232i	$-0.200176\pi$
$661$	9.50817	+	7.97830i	0.369825	+	0.310320i	−0.438867	+	0.898552i	$0.644620\pi$
$662$	−7.67985	+	2.79524i	−0.298486	+	0.108640i
$663$	−15.1076	+	85.6794i	−0.586730	+	3.32751i
$664$	0.0217094	+	0.123120i	0.000842487	+	0.00477798i
$665$	11.3334			0.439490
$666$	17.3765	+	6.02028i	0.673324	+	0.233281i
$667$	2.59778			0.100586
$668$	0.377107	+	2.13868i	0.0145907	+	0.0827480i
$669$	−3.79400	+	21.5169i	−0.146685	+	0.831890i
$670$	−11.7015	+	4.25900i	−0.452068	+	0.164539i
$671$	−15.9251	−	13.3627i	−0.614782	−	0.515863i
$672$	−11.9494			−0.460960
$673$	−8.45723	−	7.09646i	−0.326002	−	0.273548i	0.465066	−	0.885276i	$-0.346030\pi$
$673$	−8.45723	−	7.09646i	−0.326002	−	0.273548i	−0.791069	+	0.611727i	$0.790475\pi$
$674$	−10.0511	−	17.4089i	−0.387152	−	0.670567i
$675$	−0.0536541	−	0.0195285i	−0.00206515	−	0.000751652i
$676$	−8.83531	+	15.3032i	−0.339820	+	0.588585i
$677$	−1.27088	−	2.20123i	−0.0488439	−	0.0846001i	0.840570	−	0.541703i	$-0.182220\pi$
$677$	−1.27088	−	2.20123i	−0.0488439	−	0.0846001i	−0.889414	+	0.457103i	$0.848887\pi$
$678$	−1.14346	−	6.48488i	−0.0439143	−	0.249050i
$679$	−22.3070	+	8.11910i	−0.856066	+	0.311582i
$680$	−3.20050	+	5.54343i	−0.122734	+	0.212581i
$681$	3.31661	−	2.78297i	0.127093	−	0.106644i
$682$	−0.616708	+	0.517480i	−0.0236150	+	0.0198153i
$683$	−23.6446	−	8.60592i	−0.904735	−	0.329296i	−0.152586	−	0.988290i	$-0.548760\pi$
$683$	−23.6446	−	8.60592i	−0.904735	−	0.329296i	−0.752148	+	0.658994i	$0.770982\pi$
$684$	−1.22201	+	6.93037i	−0.0467247	+	0.264989i
$685$	−0.113933	+	0.646146i	−0.00435315	+	0.0246880i
$686$	44.4089	+	16.1635i	1.69554	+	0.617127i
$687$	−40.8890	+	34.3099i	−1.56001	+	1.30901i
$688$	3.54301	−	2.97294i	0.135076	−	0.113342i
$689$	−27.4248	+	47.5012i	−1.04480	+	1.80965i
$690$	9.84883	−	3.58468i	0.374939	−	0.136466i
$691$	3.10384	+	17.6028i	0.118076	+	0.669641i	0.985181	+	0.171517i	$0.0548667\pi$
$691$	3.10384	+	17.6028i	0.118076	+	0.669641i	−0.867105	+	0.498125i	$0.834022\pi$
$692$	0.792889	+	1.37332i	0.0301411	+	0.0522060i
$693$	12.6003	−	21.8244i	0.478648	−	0.829042i
$694$	12.8601	+	4.68069i	0.488162	+	0.177677i
$695$	8.31624	+	14.4041i	0.315453	+	0.546380i
$696$	−1.14364	−	0.959627i	−0.0433495	−	0.0363746i
$697$	−60.0649			−2.27512
$698$	17.6230	+	14.7874i	0.667039	+	0.559713i
$699$	28.1501	−	10.2458i	1.06473	−	0.387532i
$700$	−0.845477	+	4.79494i	−0.0319560	+	0.181232i
$701$	1.00127	+	5.67851i	0.0378176	+	0.214474i	0.997861	−	0.0653784i	$-0.0208255\pi$
$701$	1.00127	+	5.67851i	0.0378176	+	0.214474i	−0.960043	+	0.279853i	$0.909714\pi$
$702$	−0.316212			−0.0119347
$703$	−13.3787	−	4.63521i	−0.504587	−	0.174820i
$704$	1.71200			0.0645235
$705$	−3.78919	−	21.4896i	−0.142709	−	0.809344i
$706$	−5.58919	+	31.6979i	−0.210352	+	1.19296i
$707$	73.0530	−	26.5891i	2.74744	−	0.999987i
$708$	−6.70778	−	5.62850i	−0.252094	−	0.211532i
$709$	12.4032			0.465812			0.232906	−	0.972499i	$-0.425177\pi$
$709$	12.4032			0.465812			0.232906	+	0.972499i	$0.425177\pi$
$710$	−7.17568	−	6.02111i	−0.269298	−	0.225968i
$711$	15.5608	+	26.9522i	0.583577	+	1.01078i
$712$	3.05332	+	1.11132i	0.114428	+	0.0416484i
$713$	−1.00409	+	1.73914i	−0.0376036	+	0.0651313i
$714$	38.2442	+	66.2409i	1.43125	+	2.47900i
$715$	−1.64640	−	9.33721i	−0.0615720	−	0.349192i
$716$	−9.22596	+	3.35797i	−0.344790	+	0.125493i
$717$	−9.83754	+	17.0391i	−0.367390	+	0.636337i
$718$	−8.09107	+	6.78921i	−0.301956	+	0.253371i
$719$	−5.01153	+	4.20518i	−0.186899	+	0.156827i	−0.731436	−	0.681910i	$-0.761150\pi$
$719$	−5.01153	+	4.20518i	−0.186899	+	0.156827i	0.544538	+	0.838736i	$0.316705\pi$
$720$	−2.84094	−	1.03402i	−0.105876	−	0.0385356i
$721$	−6.57105	+	37.2663i	−0.244719	+	1.38787i
$722$	−2.35845	+	13.3754i	−0.0877724	+	0.497782i
$723$	32.2688	+	11.7449i	1.20009	+	0.436797i
$724$	−10.9381	+	9.17814i	−0.406511	+	0.341103i
$725$	−0.465986	+	0.391009i	−0.0173063	+	0.0145217i
$726$	9.90166	−	17.1502i	0.367485	−	0.636503i
$727$	−18.1029	+	6.58892i	−0.671399	+	0.244369i	−0.655150	−	0.755499i	$-0.727395\pi$
$727$	−18.1029	+	6.58892i	−0.671399	+	0.244369i	−0.0162491	+	0.999868i	$0.505172\pi$
$728$	4.68234	+	26.5549i	0.173539	+	0.984190i
$729$	13.7086	+	23.7439i	0.507725	+	0.879405i
$730$	−4.21427	+	7.29933i	−0.155977	+	0.270160i
$731$	−27.8197	−	10.1255i	−1.02895	−	0.374506i
$732$	14.9008	+	25.8089i	0.550750	+	0.953926i
$733$	21.6995	+	18.2081i	0.801490	+	0.672530i	0.948560	−	0.316596i	$-0.102540\pi$
$733$	21.6995	+	18.2081i	0.801490	+	0.672530i	−0.147071	+	0.989126i	$0.546984\pi$
$734$	−27.4648			−1.01374
$735$	31.4087	+	26.3550i	1.15853	+	0.972119i
$736$	4.01300	−	1.46061i	0.147921	−	0.0538388i
$737$	3.70195	−	20.9948i	0.136363	−	0.773353i
$738$	−4.92629	−	27.9384i	−0.181339	−	1.02843i
$739$	18.4183			0.677528			0.338764	−	0.940871i	$-0.389991\pi$
$739$	18.4183			0.677528			0.338764	+	0.940871i	$0.389991\pi$
$740$	2.95912	−	5.31447i	0.108779	−	0.195364i
$741$	31.6378			1.16224
$742$	8.37364	+	47.4893i	0.307406	+	1.74339i
$743$	7.87600	−	44.6670i	0.288942	−	1.63867i	−0.401911	−	0.915679i	$-0.631654\pi$
$743$	7.87600	−	44.6670i	0.288942	−	1.63867i	0.690853	−	0.722995i	$-0.257235\pi$
$744$	1.08448	−	0.394720i	0.0397591	−	0.0144711i
$745$	−4.56805	−	3.83305i	−0.167360	−	0.140432i
$746$	−22.2341			−0.814047
$747$	0.289539	+	0.242952i	0.0105937	+	0.00888915i
$748$	−5.47927	−	9.49037i	−0.200342	−	0.347002i
$749$	−48.5621	−	17.6752i	−1.77442	−	0.645836i
$750$	−1.22712	+	2.12543i	−0.0448080	+	0.0776097i
$751$	17.6690	+	30.6035i	0.644750	+	1.11674i	0.984359	+	0.176173i	$0.0563718\pi$
$751$	17.6690	+	30.6035i	0.644750	+	1.11674i	−0.339610	+	0.940567i	$0.610295\pi$
$752$	−1.54394	−	8.75612i	−0.0563017	−	0.319303i
$753$	34.2561	−	12.4682i	1.24836	−	0.454366i
$754$	−1.68442	+	2.91750i	−0.0613429	+	0.106249i
$755$	13.0166	−	10.9222i	0.473723	−	0.397501i
$756$	−0.212962	+	0.178697i	−0.00774537	+	0.00649913i
$757$	−10.2103	−	3.71626i	−0.371101	−	0.135070i	0.149736	−	0.988726i	$-0.452158\pi$
$757$	−10.2103	−	3.71626i	−0.371101	−	0.135070i	−0.520837	+	0.853656i	$0.674380\pi$
$758$	−0.690040	+	3.91341i	−0.0250634	+	0.142142i
$759$	−3.11583	+	17.6707i	−0.113097	+	0.641407i
$760$	2.18733	+	0.796123i	0.0793428	+	0.0288784i
$761$	−19.9205	+	16.7152i	−0.722116	+	0.605927i	−0.927970	−	0.372655i	$-0.878447\pi$
$761$	−19.9205	+	16.7152i	−0.722116	+	0.605927i	0.205854	+	0.978583i	$0.434003\pi$
$762$	−19.6890	+	16.5210i	−0.713256	+	0.598493i
$763$	1.82268	−	3.15698i	0.0659856	−	0.114290i
$764$	3.68969	−	1.34294i	0.133488	−	0.0485857i
$765$	3.36042	+	19.0579i	0.121496	+	0.689040i
$766$	−16.0397	−	27.7816i	−0.579539	−	1.00379i
$767$	−9.87962	+	17.1120i	−0.356732	+	0.617878i
$768$	−2.30623	−	0.839397i	−0.0832188	−	0.0302891i
$769$	−2.54703	−	4.41159i	−0.0918483	−	0.159086i	0.816441	−	0.577429i	$-0.195944\pi$
$769$	−2.54703	−	4.41159i	−0.0918483	−	0.159086i	−0.908289	+	0.418344i	$0.862611\pi$
$770$	−6.38543	−	5.35801i	−0.230115	−	0.193089i
$771$	−13.3715			−0.481562
$772$	2.12766	+	1.78532i	0.0765763	+	0.0642551i
$773$	−15.5676	+	5.66613i	−0.559927	+	0.203797i	−0.606452	−	0.795120i	$-0.707408\pi$
$773$	−15.5676	+	5.66613i	−0.559927	+	0.203797i	0.0465248	+	0.998917i	$0.485185\pi$
$774$	2.42809	−	13.7704i	0.0872759	−	0.494966i
$775$	−0.0816566	−	0.463098i	−0.00293319	−	0.0166350i
$776$	−4.87556			−0.175022
$777$	−37.3170	−	62.3750i	−1.33874	−	2.23769i
$778$	−18.1671			−0.651321
$779$	3.79291	+	21.5106i	0.135895	+	0.770698i
$780$	−2.36019	+	13.3853i	−0.0845085	+	0.479271i
$781$	15.0695	−	5.48485i	0.539230	−	0.196264i
$782$	−20.9404	−	17.5711i	−0.748827	−	0.628340i
$783$	−0.0347325			−0.00124124
$784$	12.7978	+	10.7386i	0.457063	+	0.383521i
$785$	2.69150	+	4.66181i	0.0960637	+	0.166387i
$786$	−28.9948	−	10.5532i	−1.03421	−	0.376422i
$787$	13.8263	−	23.9479i	0.492856	−	0.853651i	−0.507110	−	0.861881i	$-0.669286\pi$
$787$	13.8263	−	23.9479i	0.492856	−	0.853651i	0.999966	+	0.00822973i	$0.00261963\pi$
$788$	7.12154	+	12.3349i	0.253694	+	0.439412i
$789$	11.8181	+	67.0240i	0.420737	+	2.38612i
$790$	9.67325	−	3.52078i	0.344159	−	0.125264i
$791$	−6.53185	+	11.3135i	−0.232246	+	0.402262i
$792$	3.96492	−	3.32697i	0.140887	−	0.118219i
$793$	51.5156	−	43.2267i	1.82937	−	1.53503i
$794$	−22.0425	−	8.02280i	−0.782258	−	0.284719i
$795$	−4.22084	+	23.9376i	−0.149698	+	0.848978i
$796$	2.54550	−	14.4362i	0.0902227	−	0.511678i
$797$	−29.9554	−	10.9029i	−1.06108	−	0.386200i	−0.248244	−	0.968698i	$-0.579853\pi$
$797$	−29.9554	−	10.9029i	−1.06108	−	0.386200i	−0.812833	+	0.582497i	$0.802076\pi$
$798$	21.3074	−	17.8790i	0.754273	−	0.632911i
$799$	−43.5975	+	36.5827i	−1.54237	+	1.29420i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	9.23100	−	3.35981i	0.326161	−	0.118713i
$802$	0.478573	+	2.71412i	0.0168990	+	0.0958389i
$803$	−7.21485	−	12.4965i	−0.254606	−	0.440991i
$804$	−15.2806	+	26.4669i	−0.538907	+	0.933414i
$805$	−19.5389	−	7.11158i	−0.688656	−	0.250650i
$806$	−1.30212	−	2.25535i	−0.0458654	−	0.0794412i
$807$	−34.1924	−	28.6908i	−1.20363	−	1.00996i
$808$	15.9669			0.561713
$809$	−40.3266	−	33.8381i	−1.41781	−	1.18968i	−0.952501	−	0.304534i	$-0.901499\pi$
$809$	−40.3266	−	33.8381i	−1.41781	−	1.18968i	−0.465308	−	0.885149i	$-0.654056\pi$
$810$	8.39114	−	3.05412i	0.294835	−	0.107311i
$811$	−1.03825	+	5.88823i	−0.0364580	+	0.206764i	−0.997595	−	0.0693069i	$-0.977921\pi$
$811$	−1.03825	+	5.88823i	−0.0364580	+	0.206764i	0.961137	+	0.276070i	$0.0890323\pi$
$812$	0.514305	+	2.91677i	0.0180486	+	0.102359i
$813$	57.9187			2.03130
$814$	5.34643	+	8.93650i	0.187392	+	0.313224i
$815$	11.0118			0.385727
$816$	2.72793	+	15.4709i	0.0954968	+	0.541589i
$817$	−1.86947	+	10.6023i	−0.0654043	+	0.370926i
$818$	−27.9696	+	10.1801i	−0.977933	+	0.355939i
$819$	62.4487	+	52.4007i	2.18213	+	1.83103i
$820$	−9.38368			−0.327692
$821$	11.4912	+	9.64226i	0.401045	+	0.336517i	0.820898	−	0.571075i	$-0.193474\pi$
$821$	11.4912	+	9.64226i	0.401045	+	0.336517i	−0.419852	+	0.907593i	$0.637918\pi$
$822$	0.805128	+	1.39452i	0.0280821	+	0.0486396i
$823$	−5.89318	−	2.14494i	−0.205423	−	0.0747680i	0.237259	−	0.971446i	$-0.423751\pi$
$823$	−5.89318	−	2.14494i	−0.205423	−	0.0747680i	−0.442683	+	0.896678i	$0.645973\pi$
$824$	−3.88600	+	6.73075i	−0.135375	+	0.234477i
$825$	−2.10083	−	3.63874i	−0.0731415	−	0.126685i
$826$	3.01655	+	17.1077i	0.104959	+	0.595254i
$827$	12.3711	−	4.50270i	0.430184	−	0.156574i	−0.117848	−	0.993032i	$-0.537600\pi$
$827$	12.3711	−	4.50270i	0.430184	−	0.156574i	0.548032	+	0.836458i	$0.315377\pi$
$828$	6.45549	−	11.1812i	0.224344	−	0.388575i
$829$	−7.23878	+	6.07406i	−0.251413	+	0.210961i	−0.759781	−	0.650180i	$-0.774694\pi$
$829$	−7.23878	+	6.07406i	−0.251413	+	0.210961i	0.508367	+	0.861140i	$0.330249\pi$
$830$	0.0957703	−	0.0803608i	0.00332424	−	0.00278937i
$831$	−57.6887	−	20.9970i	−2.00120	−	0.728377i
$832$	−0.961682	+	5.45397i	−0.0333403	+	0.189082i
$833$	18.5694	−	105.312i	0.643391	−	3.64885i
$834$	38.3582	+	13.9613i	1.32824	+	0.483439i
$835$	1.66360	−	1.39592i	0.0575712	−	0.0483079i
$836$	−3.05272	+	2.56154i	−0.105581	+	0.0885926i
$837$	0.0134248	−	0.0232525i	0.000464030	−	0.000803723i
$838$	−20.2709	+	7.37802i	−0.700248	+	0.254869i
$839$	4.25764	+	24.1463i	0.146990	+	0.833622i	0.965748	+	0.259483i	$0.0835520\pi$
$839$	4.25764	+	24.1463i	0.146990	+	0.833622i	−0.818758	+	0.574139i	$0.805337\pi$
$840$	5.97472	+	10.3485i	0.206147	+	0.357058i
$841$	14.3150	−	24.7943i	0.493620	−	0.854975i
$842$	18.7146	+	6.81155i	0.644947	+	0.234741i
$843$	−23.0841	−	39.9828i	−0.795059	−	1.37708i
$844$	1.56550	+	1.31361i	0.0538868	+	0.0452164i
$845$	17.6706			0.607888
$846$	−20.5916	−	17.2784i	−0.707954	−	0.594044i
$847$	−36.9181	+	13.4371i	−1.26852	+	0.461704i
$848$	−1.71982	+	9.75358i	−0.0590588	+	0.334939i
$849$	−5.47267	−	31.0370i	−0.187821	−	1.06519i
$850$	6.40100			0.219552
$851$	20.1565	+	16.3861i	0.690955	+	0.561709i
$852$	−22.9892			−0.787599
$853$	3.79114	+	21.5006i	0.129806	+	0.736167i	0.978337	+	0.207020i	$0.0663767\pi$
$853$	3.79114	+	21.5006i	0.129806	+	0.736167i	−0.848531	+	0.529146i	$0.822512\pi$
$854$	10.2666	−	58.2247i	0.351315	−	1.99241i
$855$	6.61288	−	2.40689i	0.226156	−	0.0823139i
$856$	−8.13081	−	6.82256i	−0.277906	−	0.233190i
$857$	−35.2949			−1.20565			−0.602826	−	0.797873i	$-0.705959\pi$
$857$	−35.2949			−1.20565			−0.602826	+	0.797873i	$0.705959\pi$
$858$	−17.8253	−	14.9572i	−0.608544	−	0.510629i
$859$	−10.7355	−	18.5945i	−0.366291	−	0.634435i	0.622691	−	0.782468i	$-0.286039\pi$
$859$	−10.7355	−	18.5945i	−0.366291	−	0.634435i	−0.988983	+	0.148032i	$0.952706\pi$
$860$	−4.34615	−	1.58187i	−0.148202	−	0.0539413i
$861$	−56.0649	+	97.1072i	−1.91069	+	3.30941i
$862$	3.26992	+	5.66366i	0.111374	+	0.192905i
$863$	−2.32739	−	13.1993i	−0.0792251	−	0.449308i	−0.998454	−	0.0555844i	$-0.982298\pi$
$863$	−2.32739	−	13.1993i	−0.0792251	−	0.449308i	0.919229	−	0.393724i	$-0.128813\pi$
$864$	−0.0536541	+	0.0195285i	−0.00182535	+	0.000664373i
$865$	0.792889	−	1.37332i	0.0269590	−	0.0466944i
$866$	−18.3224	+	15.3744i	−0.622622	+	0.522442i
$867$	45.0701	−	37.8183i	1.53066	−	1.28438i
$868$	−2.15149	−	0.783077i	−0.0730262	−	0.0265794i
$869$	−3.06028	+	17.3557i	−0.103813	+	0.588753i
$870$	−0.259242	+	1.47023i	−0.00878912	+	0.0498456i
$871$	64.8041	+	23.5868i	2.19580	+	0.799208i
$872$	0.573540	−	0.481257i	0.0194225	−	0.0162974i
$873$	−11.2916	+	9.47476i	−0.382162	+	0.320672i
$874$	−4.97029	+	8.60879i	−0.168122	+	0.291197i
$875$	4.57528	−	1.66527i	0.154673	−	0.0562962i
$876$	3.59202	+	20.3714i	0.121363	+	0.688284i
$877$	−20.3474	−	35.2427i	−0.687083	−	1.19006i	−0.972777	−	0.231741i	$-0.925558\pi$
$877$	−20.3474	−	35.2427i	−0.687083	−	1.19006i	0.285695	−	0.958321i	$-0.407776\pi$
$878$	2.69757	−	4.67233i	0.0910386	−	0.157684i
$879$	−53.9246	−	19.6269i	−1.81883	−	0.662000i
$880$	−0.856002	−	1.48264i	−0.0288558	−	0.0499797i
$881$	−11.0491	−	9.27128i	−0.372253	−	0.312357i	0.437399	−	0.899268i	$-0.355900\pi$
$881$	−11.0491	−	9.27128i	−0.372253	−	0.312357i	−0.809652	+	0.586910i	$0.800344\pi$
$882$	50.5075			1.70068
$883$	33.2491	+	27.8993i	1.11892	+	0.938888i	0.998550	−	0.0538410i	$-0.0171464\pi$
$883$	33.2491	+	27.8993i	1.11892	+	0.938888i	0.120373	+	0.992729i	$0.461591\pi$
$884$	33.3115	−	12.1244i	1.12039	−	0.407788i
$885$	−1.52053	+	8.62336i	−0.0511121	+	0.289871i
$886$	−5.99399	−	33.9936i	−0.201372	−	1.14204i
$887$	20.2646			0.680419			0.340210	−	0.940350i	$-0.389502\pi$
$887$	20.2646			0.680419			0.340210	+	0.940350i	$0.389502\pi$
$888$	−2.82055	−	14.6596i	−0.0946514	−	0.491946i
$889$	50.9900			1.71015
$890$	−0.564231	−	3.19991i	−0.0189131	−	0.107261i
$891$	−2.65467	+	15.0554i	−0.0889347	+	0.504374i
$892$	8.36560	−	3.04483i	0.280101	−	0.101948i
$893$	15.8541	+	13.3032i	0.530539	+	0.445175i
$894$	−14.6350			−0.489468
$895$	7.52107	+	6.31093i	0.251402	+	0.210951i
$896$	2.43445	+	4.21660i	0.0813294	+	0.140867i
$897$	−54.5439	−	19.8523i	−1.82117	−	0.662851i
$898$	−10.6561	+	18.4570i	−0.355600	+	0.615918i
$899$	−0.143024	−	0.247726i	−0.00477013	−	0.00826211i
$900$	0.524984	+	2.97733i	0.0174995	+	0.0992445i
$901$	59.5725	−	21.6826i	1.98465	−	0.722353i
$902$	8.03245	−	13.9126i	0.267451	−	0.463239i
$903$	−42.3370	+	35.5250i	−1.40889	+	1.18220i
$904$	−2.05536	+	1.72466i	−0.0683604	+	0.0573612i
$905$	13.4175	+	4.88359i	0.446014	+	0.162336i
$906$	7.24153	−	41.0688i	0.240584	−	1.36442i
$907$	−7.17503	+	40.6916i	−0.238243	+	1.35114i	0.597432	+	0.801920i	$0.296188\pi$
$907$	−7.17503	+	40.6916i	−0.238243	+	1.35114i	−0.835675	+	0.549224i	$0.814923\pi$
$908$	−1.65772	−	0.603360i	−0.0550133	−	0.0200232i
$909$	36.9786	−	31.0287i	1.22650	−	1.02916i
$910$	20.6560	−	17.3325i	0.684741	−	0.574566i
$911$	−22.0893	+	38.2598i	−0.731850	+	1.26760i	0.224241	+	0.974534i	$0.428010\pi$
$911$	−22.0893	+	38.2598i	−0.731850	+	1.26760i	−0.956091	+	0.293068i	$0.905324\pi$
$912$	5.36822	−	1.95387i	0.177760	−	0.0646992i
$913$	0.0371665	+	0.210782i	0.00123003	+	0.00697586i
$914$	14.2965	+	24.7622i	0.472885	+	0.819060i
$915$	14.9008	−	25.8089i	0.492605	−	0.853218i
$916$	20.4372	+	7.43855i	0.675266	+	0.245777i
$917$	30.6069	+	53.0128i	1.01073	+	1.75064i
$918$	0.279975	+	0.234927i	0.00924054	+	0.00775374i
$919$	−20.9657			−0.691595			−0.345798	−	0.938309i	$-0.612392\pi$
$919$	−20.9657			−0.691595			−0.345798	+	0.938309i	$0.612392\pi$
$920$	−3.27142	−	2.74505i	−0.107856	−	0.0905016i
$921$	19.7786	−	7.19883i	0.651728	−	0.237210i
$922$	−4.58767	+	26.0180i	−0.151087	+	0.856856i
$923$	9.00825	+	51.0883i	0.296510	+	1.68159i
$924$	−20.4575			−0.673002
$925$	−6.08203	+	0.0945612i	−0.199976	+	0.00310915i
$926$	−22.7283			−0.746897
$927$	4.08018	+	23.1399i	0.134011	+	0.760013i
$928$	−0.105630	+	0.599060i	−0.00346749	+	0.0196651i
$929$	19.3995	−	7.06084i	0.636476	−	0.231658i	−0.00357128	−	0.999994i	$-0.501137\pi$
$929$	19.3995	−	7.06084i	0.636476	−	0.231658i	0.640048	+	0.768335i	$0.278915\pi$
$930$	−0.884079	−	0.741831i	−0.0289901	−	0.0243256i
$931$	−38.8874			−1.27448
$932$	−9.35044	−	7.84595i	−0.306284	−	0.257003i
$933$	−3.60047	−	6.23619i	−0.117874	−	0.204164i
$934$	−30.2681	−	11.0167i	−0.990402	−	0.360477i
$935$	−5.47927	+	9.49037i	−0.179191	+	0.310368i
$936$	8.37158	+	14.5000i	0.273634	+	0.473947i
$937$	6.41831	+	36.4000i	0.209677	+	1.18914i	0.889908	+	0.456140i	$0.150768\pi$
$937$	6.41831	+	36.4000i	0.209677	+	1.18914i	−0.680231	+	0.732998i	$0.738121\pi$
$938$	56.9735	−	20.7367i	1.86025	−	0.677076i
$939$	−35.3865	+	61.2912i	−1.15479	+	2.00016i
$940$	−6.81105	+	5.71515i	−0.222152	+	0.186408i
$941$	12.4649	−	10.4593i	0.406343	−	0.340963i	−0.416596	−	0.909092i	$-0.636777\pi$
$941$	12.4649	−	10.4593i	0.406343	−	0.340963i	0.822939	+	0.568129i	$0.192333\pi$
$942$	12.4144	+	4.51847i	0.404483	+	0.147220i
$943$	6.95867	−	39.4646i	0.226606	−	1.28514i
$944$	−0.619554	+	3.51366i	−0.0201648	+	0.114360i
$945$	0.261237	+	0.0950825i	0.00849804	+	0.00309303i
$946$	6.06565	−	5.08968i	0.197211	−	0.165480i
$947$	14.4222	−	12.1017i	0.468658	−	0.393251i	−0.377647	−	0.925950i	$-0.623267\pi$
$947$	14.4222	−	12.1017i	0.468658	−	0.393251i	0.846305	+	0.532699i	$0.178822\pi$
$948$	12.6320	−	21.8793i	0.410269	−	0.710607i
$949$	43.8631	−	15.9649i	1.42386	−	0.518242i
$950$	−0.404202	−	2.29235i	−0.0131141	−	0.0743735i
$951$	38.6552	+	66.9528i	1.25348	+	2.17109i
$952$	15.5829	−	26.9904i	0.505046	−	0.874765i
$953$	−8.99836	−	3.27513i	−0.291485	−	0.106092i	0.192139	−	0.981368i	$-0.438458\pi$
$953$	−8.99836	−	3.27513i	−0.291485	−	0.106092i	−0.483624	+	0.875276i	$0.660680\pi$
$954$	14.9713	+	25.9310i	0.484713	+	0.839547i
$955$	−3.00786	−	2.52389i	−0.0973320	−	0.0816713i
$956$	8.01679			0.259281
$957$	−1.95791	−	1.64288i	−0.0632904	−	0.0531069i
$958$	−17.4197	+	6.34026i	−0.562806	+	0.204845i
$959$	0.554729	−	3.14602i	0.0179131	−	0.101590i
$960$	0.426173	+	2.41695i	0.0137547	+	0.0780067i
$961$	−30.7789			−0.992867
$962$	−31.4725	+	12.0123i	−1.01471	+	0.387293i
$963$	−32.0890			−1.03405
$964$	−2.42969	−	13.7795i	−0.0782551	−	0.443807i
$965$	0.482302	−	2.73527i	0.0155259	−	0.0880515i
$966$	−47.9531	+	17.4535i	−1.54286	+	0.561557i
$967$	−17.2102	−	14.4410i	−0.553442	−	0.464393i	0.322663	−	0.946514i	$-0.395422\pi$
$967$	−17.2102	−	14.4410i	−0.553442	−	0.464393i	−0.876104	+	0.482121i	$0.839866\pi$
$968$	−8.06905			−0.259349
$969$	−28.0121	−	23.5050i	−0.899880	−	0.755089i
$970$	2.43778	+	4.22236i	0.0782724	+	0.135572i
$971$	−0.857329	−	0.312042i	−0.0275130	−	0.0100139i	0.328227	−	0.944599i	$-0.393549\pi$
$971$	−0.857329	−	0.312042i	−0.0275130	−	0.0100139i	−0.355740	+	0.934585i	$0.615771\pi$
$972$	11.0434	−	19.1277i	0.354217	−	0.613522i
$973$	−40.4910	−	70.1325i	−1.29808	−	2.24834i
$974$	−0.452600	−	2.56682i	−0.0145022	−	0.0822462i
$975$	12.7721	−	4.64867i	0.409035	−	0.148877i
$976$	6.07147	−	10.5161i	0.194343	−	0.336612i
$977$	30.1202	−	25.2739i	0.963631	−	0.808583i	−0.0179086	−	0.999840i	$-0.505701\pi$
$977$	30.1202	−	25.2739i	0.963631	−	0.808583i	0.981540	+	0.191257i	$0.0612563\pi$
$978$	20.7028	−	17.3717i	0.662003	−	0.555486i
$979$	5.22730	+	1.90258i	0.167065	+	0.0608067i
$980$	2.90102	−	16.4525i	0.0926695	−	0.525555i
$981$	0.393057	−	2.22914i	0.0125494	−	0.0711709i
$982$	−2.66288	−	0.969210i	−0.0849760	−	0.0309287i
$983$	3.45932	−	2.90271i	0.110335	−	0.0925822i	−0.585951	−	0.810346i	$-0.699279\pi$
$983$	3.45932	−	2.90271i	0.110335	−	0.0925822i	0.696286	+	0.717764i	$0.254834\pi$
$984$	−17.6418	+	14.8032i	−0.562400	+	0.471910i
$985$	7.12154	−	12.3349i	0.226911	−	0.393022i
$986$	3.65892	−	1.33174i	0.116524	−	0.0424111i
$987$	18.4492	+	104.631i	0.587245	+	3.33043i
$988$	−6.44555	−	11.1640i	−0.205060	−	0.355175i
$989$	9.87578	−	17.1054i	0.314032	−	0.543919i
$990$	−4.86370	−	1.77024i	−0.154578	−	0.0562620i
$991$	−2.73942	−	4.74481i	−0.0870204	−	0.150724i	0.819230	−	0.573465i	$-0.194401\pi$
$991$	−2.73942	−	4.74481i	−0.0870204	−	0.150724i	−0.906250	+	0.422741i	$0.861068\pi$
$992$	−0.360226	−	0.302266i	−0.0114372	−	0.00959694i
$993$	20.0578			0.636514
$994$	34.9377	+	29.3162i	1.10816	+	0.929854i
$995$	−13.7749	+	5.01365i	−0.436693	+	0.158943i
$996$	0.0532799	−	0.302165i	0.00168824	−	0.00957447i
$997$	3.25566	+	18.4638i	0.103108	+	0.584754i	0.991959	+	0.126558i	$0.0403930\pi$
$997$	3.25566	+	18.4638i	0.103108	+	0.584754i	−0.888851	+	0.458196i	$0.848496\pi$
$998$	−12.3234			−0.390090
$999$	−0.269494	−	0.219084i	−0.00852641	−	0.00693151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.a.231.3	yes	18
37.33	even	9	inner	370.2.o.a.181.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.a.181.3	✓	18	37.33	even	9	inner
370.2.o.a.231.3	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.426173 - 2.41695i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.766044 + 0.642788i) q^{5} +2.45423 q^{6} +(-3.72980 - 3.12967i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.84094 - 1.03402i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.426173 - 2.41695i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.766044 + 0.642788i) q^{5} +2.45423 q^{6} +(-3.72980 - 3.12967i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.84094 - 1.03402i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.856002 - 1.48264i) q^{11} +(0.426173 + 2.41695i) q^{12} +(5.20412 - 1.89414i) q^{13} +(2.43445 - 4.21660i) q^{14} +(1.88005 - 1.57755i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-6.01497 - 2.18927i) q^{17} +(0.524984 - 2.97733i) q^{18} +(-0.404202 + 2.29235i) q^{19} +(-0.939693 - 0.342020i) q^{20} +(-9.15381 + 7.68095i) q^{21} +(1.31147 - 1.10045i) q^{22} +(2.13527 - 3.69840i) q^{23} +(-2.30623 + 0.839397i) q^{24} +(0.173648 + 0.984808i) q^{25} +(2.76905 + 4.79614i) q^{26} +(-0.0285488 + 0.0494479i) q^{27} +(4.57528 + 1.66527i) q^{28} +(0.304151 + 0.526805i) q^{29} +(1.88005 + 1.57755i) q^{30} -0.470242 q^{31} +(0.766044 + 0.642788i) q^{32} +(-3.94827 + 1.43705i) q^{33} +(1.11152 - 6.30375i) q^{34} +(-0.845477 - 4.79494i) q^{35} +3.02326 q^{36} +(-0.963008 + 6.00605i) q^{37} -2.32771 q^{38} +(-2.36019 - 13.3853i) q^{39} +(0.173648 - 0.984808i) q^{40} +(8.81777 - 3.20941i) q^{41} +(-9.15381 - 7.68095i) q^{42} +4.62507 q^{43} +(1.31147 + 1.10045i) q^{44} +(-1.51163 - 2.61822i) q^{45} +(4.01300 + 1.46061i) q^{46} +(4.44560 - 7.70000i) q^{47} +(-1.22712 - 2.12543i) q^{48} +(2.90102 + 16.4525i) q^{49} +(-0.939693 + 0.342020i) q^{50} +(-7.85477 + 13.6049i) q^{51} +(-4.24244 + 3.55983i) q^{52} +(-7.58694 + 6.36619i) q^{53} +(-0.0536541 - 0.0195285i) q^{54} +(0.297286 - 1.68599i) q^{55} +(-0.845477 + 4.79494i) q^{56} +(5.36822 + 1.95387i) q^{57} +(-0.465986 + 0.391009i) q^{58} +(-2.73315 + 2.29338i) q^{59} +(-1.22712 + 2.12543i) q^{60} +(11.4106 - 4.15313i) q^{61} +(-0.0816566 - 0.463098i) q^{62} +(7.36000 + 12.7479i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.20412 + 1.89414i) q^{65} +(-2.10083 - 3.63874i) q^{66} +(9.53915 + 8.00430i) q^{67} +6.40100 q^{68} +(-8.02884 - 6.73700i) q^{69} +(4.57528 - 1.66527i) q^{70} +(-1.62659 + 9.22487i) q^{71} +(0.524984 + 2.97733i) q^{72} +8.42854 q^{73} +(-6.08203 + 0.0945612i) q^{74} +2.45423 q^{75} +(-0.404202 - 2.29235i) q^{76} +(-1.44746 + 8.20895i) q^{77} +(12.7721 - 4.64867i) q^{78} +(-7.88571 - 6.61689i) q^{79} +1.00000 q^{80} +(-6.84052 - 5.73988i) q^{81} +(4.69184 + 8.12651i) q^{82} +(-0.117480 - 0.0427591i) q^{83} +(5.97472 - 10.3485i) q^{84} +(-3.20050 - 5.54343i) q^{85} +(0.803136 + 4.55481i) q^{86} +(1.40288 - 0.510607i) q^{87} +(-0.856002 + 1.48264i) q^{88} +(-2.48909 + 2.08860i) q^{89} +(2.31596 - 1.94332i) q^{90} +(-25.3384 - 9.22242i) q^{91} +(-0.741572 + 4.20566i) q^{92} +(-0.200404 + 1.13655i) q^{93} +(8.35499 + 3.04097i) q^{94} +(-1.78313 + 1.49622i) q^{95} +(1.88005 - 1.57755i) q^{96} +(2.43778 - 4.22236i) q^{97} +(-15.6988 + 5.71389i) q^{98} +(0.898775 + 5.09721i) 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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