LMFDB - Embedded newform 370.2.o.d.71.3

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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	370.71
Dual form			370.2.o.d.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.479302 - 0.402182i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{5} +0.625684 q^{6} +(0.117038 + 0.0425983i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.452965 + 2.56889i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.479302 - 0.402182i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{5} +0.625684 q^{6} +(0.117038 + 0.0425983i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.452965 + 2.56889i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.69168 - 2.93008i) q^{11} +(0.479302 + 0.402182i) q^{12} +(1.17159 + 6.64441i) q^{13} +(0.0622746 + 0.107863i) q^{14} +(0.587950 - 0.213996i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.825204 - 4.67996i) q^{17} +(-1.99824 + 1.67672i) q^{18} +(3.58155 - 3.00528i) q^{19} +(-0.173648 + 0.984808i) q^{20} +(0.0732287 - 0.0266531i) q^{21} +(3.17932 - 1.15718i) q^{22} +(-1.45014 - 2.51172i) q^{23} +(0.108649 + 0.616178i) q^{24} +(0.766044 + 0.642788i) q^{25} +(-3.37345 + 5.84299i) q^{26} +(1.75458 + 3.03902i) q^{27} +(-0.0216277 + 0.122657i) q^{28} +(-1.53804 + 2.66396i) q^{29} +(0.587950 + 0.213996i) q^{30} -8.39259 q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.367598 - 2.08475i) q^{33} +(3.64036 - 3.05463i) q^{34} +(0.0954102 + 0.0800587i) q^{35} -2.60852 q^{36} +(-3.50487 - 4.97151i) q^{37} +4.67539 q^{38} +(3.23380 + 2.71348i) q^{39} +(-0.766044 + 0.642788i) q^{40} +(-0.863590 - 4.89766i) q^{41} +(0.0732287 + 0.0266531i) q^{42} +5.19420 q^{43} +(3.17932 + 1.15718i) q^{44} +(-1.30426 + 2.25904i) q^{45} +(0.503628 - 2.85622i) q^{46} +(3.13351 + 5.42740i) q^{47} +(-0.312842 + 0.541858i) q^{48} +(-5.35043 - 4.48954i) q^{49} +(0.173648 + 0.984808i) q^{50} +(-1.48667 - 2.57500i) q^{51} +(-6.34002 + 2.30758i) q^{52} +(-6.14339 + 2.23601i) q^{53} +(-0.609359 + 3.45585i) q^{54} +(2.59181 - 2.17478i) q^{55} +(-0.0954102 + 0.0800587i) q^{56} +(0.507975 - 2.88087i) q^{57} +(-2.89057 + 1.05208i) q^{58} +(2.46979 - 0.898929i) q^{59} +(0.312842 + 0.541858i) q^{60} +(-1.29796 - 7.36110i) q^{61} +(-6.42910 - 5.39466i) q^{62} +(-0.162445 + 0.281362i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.17159 + 6.64441i) q^{65} +(1.05846 - 1.83330i) q^{66} +(-7.74691 - 2.81964i) q^{67} +4.75216 q^{68} +(-1.70522 - 0.620650i) q^{69} +(0.0216277 + 0.122657i) q^{70} +(10.5092 - 8.81828i) q^{71} +(-1.99824 - 1.67672i) q^{72} -4.64166 q^{73} +(0.510737 - 6.06128i) q^{74} +0.625684 q^{75} +(3.58155 + 3.00528i) q^{76} +(0.322807 - 0.270867i) q^{77} +(0.733044 + 4.15730i) q^{78} +(-10.5483 - 3.83926i) q^{79} -1.00000 q^{80} +(-5.29041 - 1.92555i) q^{81} +(2.48661 - 4.30693i) q^{82} +(-1.17320 + 6.65357i) q^{83} +(0.0389642 + 0.0674880i) q^{84} +(2.37608 - 4.11549i) q^{85} +(3.97899 + 3.33876i) q^{86} +(0.334212 + 1.89541i) q^{87} +(1.69168 + 2.93008i) q^{88} +(5.00007 - 1.81988i) q^{89} +(-2.45121 + 0.892166i) q^{90} +(-0.145920 + 0.827555i) q^{91} +(2.22174 - 1.86426i) q^{92} +(-4.02258 + 3.37535i) q^{93} +(-1.08826 + 6.17181i) q^{94} +(4.39343 - 1.59908i) q^{95} +(-0.587950 + 0.213996i) q^{96} +(1.55496 + 2.69326i) q^{97} +(-1.21284 - 6.87838i) q^{98} +(6.76078 + 5.67297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9	$ 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9} + 12 q^{10} - 3 q^{11} - 3 q^{14} + 6 q^{17} - 6 q^{18} - 18 q^{19} + 18 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 12 q^{27} + 9 q^{28} - 18 q^{29} - 6 q^{31} - 45 q^{33} - 3 q^{34} + 30 q^{36} - 18 q^{37} - 24 q^{38} + 12 q^{39} + 3 q^{41} + 18 q^{42} + 3 q^{44} + 15 q^{45} + 9 q^{46} - 36 q^{47} - 3 q^{48} - 15 q^{49} + 54 q^{51} - 9 q^{52} - 6 q^{53} + 45 q^{54} - 3 q^{55} + 3 q^{57} - 15 q^{58} - 9 q^{59} + 3 q^{60} - 24 q^{61} + 81 q^{62} - 45 q^{63} - 12 q^{64} - 3 q^{66} + 12 q^{67} + 12 q^{68} + 60 q^{69} - 9 q^{70} + 42 q^{71} - 6 q^{72} - 42 q^{73} + 12 q^{74} + 6 q^{75} - 18 q^{76} + 9 q^{77} + 30 q^{78} - 6 q^{79} - 24 q^{80} - 66 q^{81} - 24 q^{82} - 3 q^{83} - 42 q^{84} + 6 q^{85} - 18 q^{86} - 84 q^{87} - 3 q^{88} + 27 q^{89} + 6 q^{90} + 153 q^{91} - 9 q^{92} - 54 q^{93} - 21 q^{94} - 9 q^{95} - 9 q^{97} - 24 q^{98} + 165 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9 + 12 * q^10 - 3 * q^11 - 3 * q^14 + 6 * q^17 - 6 * q^18 - 18 * q^19 + 18 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 12 * q^27 + 9 * q^28 - 18 * q^29 - 6 * q^31 - 45 * q^33 - 3 * q^34 + 30 * q^36 - 18 * q^37 - 24 * q^38 + 12 * q^39 + 3 * q^41 + 18 * q^42 + 3 * q^44 + 15 * q^45 + 9 * q^46 - 36 * q^47 - 3 * q^48 - 15 * q^49 + 54 * q^51 - 9 * q^52 - 6 * q^53 + 45 * q^54 - 3 * q^55 + 3 * q^57 - 15 * q^58 - 9 * q^59 + 3 * q^60 - 24 * q^61 + 81 * q^62 - 45 * q^63 - 12 * q^64 - 3 * q^66 + 12 * q^67 + 12 * q^68 + 60 * q^69 - 9 * q^70 + 42 * q^71 - 6 * q^72 - 42 * q^73 + 12 * q^74 + 6 * q^75 - 18 * q^76 + 9 * q^77 + 30 * q^78 - 6 * q^79 - 24 * q^80 - 66 * q^81 - 24 * q^82 - 3 * q^83 - 42 * q^84 + 6 * q^85 - 18 * q^86 - 84 * q^87 - 3 * q^88 + 27 * q^89 + 6 * q^90 + 153 * q^91 - 9 * q^92 - 54 * q^93 - 21 * q^94 - 9 * q^95 - 9 * q^97 - 24 * q^98 + 165 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.479302	−	0.402182i	0.276725	−	0.232200i	−0.493853	−	0.869545i	$-0.664412\pi$
$3$	0.479302	−	0.402182i	0.276725	−	0.232200i	0.770578	+	0.637345i	$0.219968\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$6$	0.625684			0.255434
$7$	0.117038	+	0.0425983i	0.0442362	+	0.0161007i	0.364043	−	0.931382i	$-0.381396\pi$
$7$	0.117038	+	0.0425983i	0.0442362	+	0.0161007i	−0.319807	+	0.947483i	$0.603618\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.452965	+	2.56889i	−0.150988	+	0.856297i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.69168	−	2.93008i	0.510061	−	0.883452i	−0.489871	−	0.871795i	$-0.662956\pi$
$11$	1.69168	−	2.93008i	0.510061	−	0.883452i	0.999932	−	0.0116567i	$-0.00371052\pi$
$12$	0.479302	+	0.402182i	0.138362	+	0.116100i
$13$	1.17159	+	6.64441i	0.324940	+	1.84283i	0.510096	+	0.860118i	$0.329610\pi$
$13$	1.17159	+	6.64441i	0.324940	+	1.84283i	−0.185156	+	0.982709i	$0.559279\pi$
$14$	0.0622746	+	0.107863i	0.0166436	+	0.0288275i
$15$	0.587950	−	0.213996i	0.151808	−	0.0552536i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.825204	−	4.67996i	0.200141	−	1.13506i	−0.704763	−	0.709443i	$-0.748947\pi$
$17$	0.825204	−	4.67996i	0.200141	−	1.13506i	0.904904	−	0.425615i	$-0.139942\pi$
$18$	−1.99824	+	1.67672i	−0.470990	+	0.395208i
$19$	3.58155	−	3.00528i	0.821665	−	0.689459i	−0.131696	−	0.991290i	$-0.542042\pi$
$19$	3.58155	−	3.00528i	0.821665	−	0.689459i	0.953361	+	0.301831i	$0.0975979\pi$
$20$	−0.173648	+	0.984808i	−0.0388289	+	0.220210i
$21$	0.0732287	−	0.0266531i	0.0159798	−	0.00581618i
$22$	3.17932	−	1.15718i	0.677833	−	0.246711i
$23$	−1.45014	−	2.51172i	−0.302375	−	0.523729i	0.674298	−	0.738459i	$-0.264446\pi$
$23$	−1.45014	−	2.51172i	−0.302375	−	0.523729i	−0.976673	+	0.214730i	$0.931113\pi$
$24$	0.108649	+	0.616178i	0.0221779	+	0.125777i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	−3.37345	+	5.84299i	−0.661589	+	1.14591i
$27$	1.75458	+	3.03902i	0.337669	+	0.584860i
$28$	−0.0216277	+	0.122657i	−0.00408726	+	0.0231800i
$29$	−1.53804	+	2.66396i	−0.285606	+	0.494685i	−0.972756	−	0.231831i	$-0.925528\pi$
$29$	−1.53804	+	2.66396i	−0.285606	+	0.494685i	0.687150	+	0.726516i	$0.258862\pi$
$30$	0.587950	+	0.213996i	0.107345	+	0.0390702i
$31$	−8.39259			−1.50735			−0.753677	−	0.657245i	$-0.771722\pi$
$31$	−8.39259			−1.50735			−0.753677	+	0.657245i	$0.771722\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−0.367598	−	2.08475i	−0.0639907	−	0.362909i
$34$	3.64036	−	3.05463i	0.624317	−	0.523865i
$35$	0.0954102	+	0.0800587i	0.0161273	+	0.0135324i
$36$	−2.60852			−0.434753
$37$	−3.50487	−	4.97151i	−0.576197	−	0.817311i
$37$	−3.50487	−	4.97151i	−0.576197	−	0.817311i
$38$	4.67539			0.758448
$39$	3.23380	+	2.71348i	0.517823	+	0.434505i
$40$	−0.766044	+	0.642788i	−0.121122	+	0.101634i
$41$	−0.863590	−	4.89766i	−0.134870	−	0.764887i	−0.974950	−	0.222424i	$-0.928603\pi$
$41$	−0.863590	−	4.89766i	−0.134870	−	0.764887i	0.840080	−	0.542463i	$-0.182508\pi$
$42$	0.0732287	+	0.0266531i	0.0112994	+	0.00411266i
$43$	5.19420			0.792107			0.396054	−	0.918227i	$-0.370379\pi$
$43$	5.19420			0.792107			0.396054	+	0.918227i	$0.370379\pi$
$44$	3.17932	+	1.15718i	0.479301	+	0.174451i
$45$	−1.30426	+	2.25904i	−0.194428	+	0.336758i
$46$	0.503628	−	2.85622i	0.0742560	−	0.421126i
$47$	3.13351	+	5.42740i	0.457069	+	0.791667i	0.998805	−	0.0488821i	$-0.0155658\pi$
$47$	3.13351	+	5.42740i	0.457069	+	0.791667i	−0.541735	+	0.840549i	$0.682233\pi$
$48$	−0.312842	+	0.541858i	−0.0451548	+	0.0782105i
$49$	−5.35043	−	4.48954i	−0.764347	−	0.641363i
$50$	0.173648	+	0.984808i	0.0245576	+	0.139273i
$51$	−1.48667	−	2.57500i	−0.208176	−	0.360571i
$52$	−6.34002	+	2.30758i	−0.879202	+	0.320004i
$53$	−6.14339	+	2.23601i	−0.843860	+	0.307140i	−0.727534	−	0.686071i	$-0.759334\pi$
$53$	−6.14339	+	2.23601i	−0.843860	+	0.307140i	−0.116325	+	0.993211i	$0.537112\pi$
$54$	−0.609359	+	3.45585i	−0.0829233	+	0.470281i
$55$	2.59181	−	2.17478i	0.349479	−	0.293248i
$56$	−0.0954102	+	0.0800587i	−0.0127497	+	0.0106983i
$57$	0.507975	−	2.88087i	0.0672830	−	0.381581i
$58$	−2.89057	+	1.05208i	−0.379550	+	0.138145i
$59$	2.46979	−	0.898929i	0.321539	−	0.117031i	−0.176208	−	0.984353i	$-0.556383\pi$
$59$	2.46979	−	0.898929i	0.321539	−	0.117031i	0.497747	+	0.867322i	$0.334161\pi$
$60$	0.312842	+	0.541858i	0.0403877	+	0.0699536i
$61$	−1.29796	−	7.36110i	−0.166187	−	0.942492i	−0.947832	−	0.318769i	$-0.896731\pi$
$61$	−1.29796	−	7.36110i	−0.166187	−	0.942492i	0.781646	−	0.623723i	$-0.214381\pi$
$62$	−6.42910	−	5.39466i	−0.816496	−	0.685122i
$63$	−0.162445	+	0.281362i	−0.0204661	+	0.0354483i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.17159	+	6.64441i	−0.145318	+	0.824137i
$66$	1.05846	−	1.83330i	0.130287	−	0.225664i
$67$	−7.74691	−	2.81964i	−0.946435	−	0.344474i	−0.177731	−	0.984079i	$-0.556876\pi$
$67$	−7.74691	−	2.81964i	−0.946435	−	0.344474i	−0.768704	+	0.639605i	$0.779098\pi$
$68$	4.75216			0.576284
$69$	−1.70522	−	0.620650i	−0.205284	−	0.0747174i
$70$	0.0216277	+	0.122657i	0.00258501	+	0.0146603i
$71$	10.5092	−	8.81828i	1.24722	−	1.04654i	0.250291	−	0.968171i	$-0.419474\pi$
$71$	10.5092	−	8.81828i	1.24722	−	1.04654i	0.996925	−	0.0783670i	$-0.0249706\pi$
$72$	−1.99824	−	1.67672i	−0.235495	−	0.197604i
$73$	−4.64166			−0.543266			−0.271633	−	0.962401i	$-0.587564\pi$
$73$	−4.64166			−0.543266			−0.271633	+	0.962401i	$0.587564\pi$
$74$	0.510737	−	6.06128i	0.0593719	−	0.704610i
$75$	0.625684			0.0722477
$76$	3.58155	+	3.00528i	0.410833	+	0.344729i
$77$	0.322807	−	0.270867i	0.0367873	−	0.0308682i
$78$	0.733044	+	4.15730i	0.0830009	+	0.470721i
$79$	−10.5483	−	3.83926i	−1.18678	−	0.431951i	−0.328185	−	0.944613i	$-0.606437\pi$
$79$	−10.5483	−	3.83926i	−1.18678	−	0.431951i	−0.858590	+	0.512662i	$0.828659\pi$
$80$	−1.00000			−0.111803
$81$	−5.29041	−	1.92555i	−0.587823	−	0.213950i
$82$	2.48661	−	4.30693i	0.274600	−	0.475621i
$83$	−1.17320	+	6.65357i	−0.128776	+	0.730325i	0.850217	+	0.526432i	$0.176470\pi$
$83$	−1.17320	+	6.65357i	−0.128776	+	0.730325i	−0.978993	+	0.203893i	$0.934641\pi$
$84$	0.0389642	+	0.0674880i	0.00425134	+	0.00736354i
$85$	2.37608	−	4.11549i	0.257722	−	0.446388i
$86$	3.97899	+	3.33876i	0.429065	+	0.360028i
$87$	0.334212	+	1.89541i	0.0358313	+	0.203209i
$88$	1.69168	+	2.93008i	0.180334	+	0.312347i
$89$	5.00007	−	1.81988i	0.530006	−	0.192907i	−0.0631347	−	0.998005i	$-0.520110\pi$
$89$	5.00007	−	1.81988i	0.530006	−	0.192907i	0.593141	+	0.805098i	$0.297888\pi$
$90$	−2.45121	+	0.892166i	−0.258380	+	0.0940426i
$91$	−0.145920	+	0.827555i	−0.0152966	+	0.0867514i
$92$	2.22174	−	1.86426i	0.231633	−	0.194363i
$93$	−4.02258	+	3.37535i	−0.417122	+	0.350007i
$94$	−1.08826	+	6.17181i	−0.112245	+	0.636573i
$95$	4.39343	−	1.59908i	0.450756	−	0.164062i
$96$	−0.587950	+	0.213996i	−0.0600074	+	0.0218409i
$97$	1.55496	+	2.69326i	0.157882	+	0.273459i	0.934105	−	0.356999i	$-0.116200\pi$
$97$	1.55496	+	2.69326i	0.157882	+	0.273459i	−0.776223	+	0.630459i	$0.782867\pi$
$98$	−1.21284	−	6.87838i	−0.122516	−	0.694821i
$99$	6.76078	+	5.67297i	0.679484	+	0.570154i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−6.99893	−	12.1225i	−0.696420	−	1.20623i	−0.969700	−	0.244300i	$-0.921442\pi$
$101$	−6.99893	−	12.1225i	−0.696420	−	1.20623i	0.273280	−	0.961935i	$-0.411892\pi$
$102$	0.516317	−	2.92818i	0.0511230	−	0.289933i
$103$	−2.25885	+	3.91245i	−0.222571	+	0.385505i	−0.955588	−	0.294706i	$-0.904778\pi$
$103$	−2.25885	+	3.91245i	−0.222571	+	0.385505i	0.733017	+	0.680211i	$0.238112\pi$
$104$	−6.34002	−	2.30758i	−0.621690	−	0.226277i
$105$	0.0779284			0.00760503
$106$	−6.14339	−	2.23601i	−0.596699	−	0.217181i
$107$	−0.143253	−	0.812427i	−0.0138488	−	0.0785403i	0.977100	−	0.212780i	$-0.0682518\pi$
$107$	−0.143253	−	0.812427i	−0.0138488	−	0.0785403i	−0.990949	+	0.134240i	$0.957141\pi$
$108$	−2.68817	+	2.25564i	−0.258669	+	0.217049i
$109$	11.4237	+	9.58566i	1.09420	+	0.918139i	0.997021	−	0.0771280i	$-0.0245750\pi$
$109$	11.4237	+	9.58566i	1.09420	+	0.918139i	0.0971747	+	0.995267i	$0.469019\pi$
$110$	3.38336			0.322591
$111$	−3.67934	−	0.973256i	−0.349227	−	0.0923774i
$112$	−0.124549			−0.0117688
$113$	12.3251	+	10.3420i	1.15944	+	0.972890i	0.999898	−	0.0143005i	$-0.00455215\pi$
$113$	12.3251	+	10.3420i	1.15944	+	0.972890i	0.159547	+	0.987190i	$0.448997\pi$
$114$	2.24092	−	1.88036i	0.209881	−	0.176111i
$115$	−0.503628	−	2.85622i	−0.0469636	−	0.266344i
$116$	−2.89057	−	1.05208i	−0.268382	−	0.0976831i
$117$	−17.5994			−1.62707
$118$	2.46979	+	0.898929i	0.227362	+	0.0827531i
$119$	0.295939	−	0.512581i	0.0271287	−	0.0469882i
$120$	−0.108649	+	0.616178i	−0.00991824	+	0.0562491i
$121$	−0.223569	−	0.387233i	−0.0203245	−	0.0352030i
$122$	3.73733	−	6.47324i	0.338362	−	0.586060i
$123$	−2.38367	−	2.00014i	−0.214928	−	0.180346i
$124$	−1.45736	−	8.26509i	−0.130875	−	0.742227i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−0.305296	+	0.111119i	−0.0271979	+	0.00989923i
$127$	19.4799	−	7.09011i	1.72856	−	0.629145i	0.730036	−	0.683408i	$-0.239503\pi$
$127$	19.4799	−	7.09011i	1.72856	−	0.629145i	0.998527	+	0.0542629i	$0.0172809\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	2.48959	−	2.08901i	0.219196	−	0.183927i
$130$	−5.16843	+	4.33683i	−0.453301	+	0.380365i
$131$	2.93454	−	16.6426i	0.256392	−	1.45407i	−0.536083	−	0.844165i	$-0.680097\pi$
$131$	2.93454	−	16.6426i	0.256392	−	1.45407i	0.792475	−	0.609904i	$-0.208792\pi$
$132$	1.98925	−	0.724027i	0.173142	−	0.0630185i
$133$	0.547198	−	0.199164i	0.0474481	−	0.0172697i
$134$	−4.12204	−	7.13959i	−0.356090	−	0.616767i
$135$	0.609359	+	3.45585i	0.0524453	+	0.297432i
$136$	3.64036	+	3.05463i	0.312159	+	0.261932i
$137$	−4.03565	+	6.98995i	−0.344789	+	0.597191i	−0.985315	−	0.170745i	$-0.945383\pi$
$137$	−4.03565	+	6.98995i	−0.344789	+	0.597191i	0.640527	+	0.767936i	$0.278716\pi$
$138$	−0.907329	−	1.57154i	−0.0772370	−	0.133778i
$139$	0.186281	−	1.05645i	0.0158002	−	0.0896073i	−0.975888	−	0.218272i	$-0.929958\pi$
$139$	0.186281	−	1.05645i	0.0158002	−	0.0896073i	0.991688	+	0.128665i	$0.0410691\pi$
$140$	−0.0622746	+	0.107863i	−0.00526316	+	0.00911607i
$141$	3.68470	+	1.34112i	0.310307	+	0.112943i
$142$	13.7188			1.15126
$143$	21.4506	+	7.80737i	1.79379	+	0.652885i
$144$	−0.452965	−	2.56889i	−0.0377471	−	0.214074i
$145$	−2.35641	+	1.97726i	−0.195689	+	0.164203i
$146$	−3.55572	−	2.98360i	−0.294273	−	0.246925i
$147$	−4.37008			−0.360438
$148$	4.28736	−	4.31492i	0.352419	−	0.354684i
$149$	−16.5210			−1.35345			−0.676726	−	0.736235i	$-0.736602\pi$
$149$	−16.5210			−1.35345			−0.676726	+	0.736235i	$0.736602\pi$
$150$	0.479302	+	0.402182i	0.0391348	+	0.0328380i
$151$	1.09221	−	0.916474i	0.0888829	−	0.0745816i	−0.597264	−	0.802045i	$-0.703745\pi$
$151$	1.09221	−	0.916474i	0.0888829	−	0.0745816i	0.686146	+	0.727463i	$0.259301\pi$
$152$	0.811873	+	4.60436i	0.0658516	+	0.373463i
$153$	11.6485	+	4.23972i	0.941727	+	0.342761i
$154$	0.421395			0.0339570
$155$	−7.88646	−	2.87044i	−0.633456	−	0.230559i
$156$	−2.11072	+	3.65587i	−0.168992	+	0.292704i
$157$	−3.37782	+	19.1566i	−0.269579	+	1.52886i	0.486092	+	0.873908i	$0.338422\pi$
$157$	−3.37782	+	19.1566i	−0.269579	+	1.52886i	−0.755671	+	0.654951i	$0.772689\pi$
$158$	−5.61263	−	9.72136i	−0.446517	−	0.773390i
$159$	−2.04525	+	3.54248i	−0.162199	+	0.280937i
$160$	−0.766044	−	0.642788i	−0.0605611	−	0.0508168i
$161$	−0.0627265	−	0.355740i	−0.00494354	−	0.0280362i
$162$	−2.81497	−	4.87567i	−0.221165	−	0.383069i
$163$	−12.5018	+	4.55027i	−0.979213	+	0.356405i	−0.781534	−	0.623862i	$-0.785563\pi$
$163$	−12.5018	+	4.55027i	−0.979213	+	0.356405i	−0.197679	+	0.980267i	$0.563340\pi$
$164$	4.67330	−	1.70094i	0.364923	−	0.132821i
$165$	0.367598	−	2.08475i	0.0286175	−	0.162298i
$166$	−5.17556	+	4.34281i	−0.401701	+	0.337068i
$167$	−17.9635	+	15.0732i	−1.39006	+	1.16640i	−0.424746	+	0.905313i	$0.639636\pi$
$167$	−17.9635	+	15.0732i	−1.39006	+	1.16640i	−0.965315	+	0.261087i	$0.915919\pi$
$168$	−0.0135321	+	0.0767445i	−0.00104403	+	0.00592097i
$169$	−30.5595	+	11.1228i	−2.35073	+	0.855597i
$170$	4.46557	−	1.62533i	0.342493	−	0.124657i
$171$	6.09792	+	10.5619i	0.466320	+	0.807689i
$172$	0.901963	+	5.11528i	0.0687740	+	0.390037i
$173$	13.2932	+	11.1543i	1.01066	+	0.848045i	0.988425	−	0.151707i	$-0.0484771\pi$
$173$	13.2932	+	11.1543i	1.01066	+	0.848045i	0.0222357	+	0.999753i	$0.492922\pi$
$174$	−0.962325	+	1.66680i	−0.0729537	+	0.126359i
$175$	0.0622746	+	0.107863i	0.00470752	+	0.00815366i
$176$	−0.587515	+	3.33196i	−0.0442856	+	0.251156i
$177$	0.822240	−	1.42416i	0.0618033	−	0.107047i
$178$	5.00007	+	1.81988i	0.374771	+	0.136406i
$179$	22.9365			1.71436			0.857179	−	0.515019i	$-0.172215\pi$
$179$	22.9365			1.71436			0.857179	+	0.515019i	$0.172215\pi$
$180$	−2.45121	−	0.892166i	−0.182702	−	0.0664982i
$181$	0.841836	+	4.77429i	0.0625732	+	0.354870i	0.999978	+	0.00662872i	$0.00211000\pi$
$181$	0.841836	+	4.77429i	0.0625732	+	0.354870i	−0.937405	+	0.348242i	$0.886779\pi$
$182$	−0.643724	+	0.540148i	−0.0477160	+	0.0400385i
$183$	−3.58261	−	3.00617i	−0.264834	−	0.222222i
$184$	2.90028			0.213812
$185$	−1.59315	−	5.87042i	−0.117130	−	0.431602i
$186$	−5.25111			−0.385030
$187$	−12.3167	−	10.3349i	−0.900684	−	0.755764i
$188$	−4.80081	+	4.02836i	−0.350135	+	0.293798i
$189$	0.0758952	+	0.430423i	0.00552056	+	0.0313087i
$190$	4.39343	+	1.59908i	0.318733	+	0.116009i
$191$	20.8866			1.51130			0.755651	−	0.654974i	$-0.227321\pi$
$191$	20.8866			1.51130			0.755651	+	0.654974i	$0.227321\pi$
$192$	−0.587950	−	0.213996i	−0.0424317	−	0.0154439i
$193$	1.18143	−	2.04630i	0.0850414	−	0.147296i	−0.820367	−	0.571837i	$-0.806231\pi$
$193$	1.18143	−	2.04630i	0.0850414	−	0.147296i	0.905409	+	0.424541i	$0.139564\pi$
$194$	−0.540030	+	3.06266i	−0.0387719	+	0.219886i
$195$	2.11072	+	3.65587i	0.151151	+	0.261802i
$196$	3.49224	−	6.04874i	0.249446	−	0.432053i
$197$	16.7425	+	14.0487i	1.19286	+	1.00093i	0.999805	+	0.0197367i	$0.00628281\pi$
$197$	16.7425	+	14.0487i	1.19286	+	1.00093i	0.193051	+	0.981189i	$0.438162\pi$
$198$	1.53254	+	8.69149i	0.108913	+	0.617677i
$199$	5.13447	+	8.89317i	0.363973	+	0.630420i	0.988611	−	0.150495i	$-0.0480866\pi$
$199$	5.13447	+	8.89317i	0.363973	+	0.630420i	−0.624638	+	0.780915i	$0.714753\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$	−4.84711	+	1.76421i	−0.341889	+	0.124437i
$202$	2.43070	−	13.7852i	0.171024	−	0.969924i
$203$	−0.293489	+	0.246267i	−0.0205989	+	0.0172845i
$204$	2.27772	−	1.91123i	0.159472	−	0.133813i
$205$	0.863590	−	4.89766i	0.0603158	−	0.342068i
$206$	−4.24525	+	1.54515i	−0.295781	+	0.107655i
$207$	7.10919	−	2.58753i	0.494123	−	0.179846i
$208$	−3.37345	−	5.84299i	−0.233907	−	0.405139i
$209$	−2.74686	−	15.5782i	−0.190004	−	1.07757i
$210$	0.0596966	+	0.0500914i	0.00411946	+	0.00345664i
$211$	−4.25624	+	7.37203i	−0.293012	+	0.507512i	−0.974520	−	0.224299i	$-0.927991\pi$
$211$	−4.25624	+	7.37203i	−0.293012	+	0.507512i	0.681509	+	0.731810i	$0.261324\pi$
$212$	−3.26883	−	5.66178i	−0.224504	−	0.388853i
$213$	1.49053	−	8.45323i	0.102130	−	0.579206i
$214$	0.412480	−	0.714436i	0.0281965	−	0.0488379i
$215$	4.88095	+	1.77652i	0.332878	+	0.121158i
$216$	−3.50916			−0.238768
$217$	−0.982252	−	0.357510i	−0.0666796	−	0.0242694i
$218$	2.58955	+	14.6861i	0.175387	+	0.994667i
$219$	−2.22476	+	1.86679i	−0.150335	+	0.126146i
$220$	2.59181	+	2.17478i	0.174739	+	0.146624i
$221$	32.0624			2.15675
$222$	−2.19294	−	3.11059i	−0.147181	−	0.208769i
$223$	−1.35772			−0.0909197			−0.0454598	−	0.998966i	$-0.514475\pi$
$223$	−1.35772			−0.0909197			−0.0454598	+	0.998966i	$0.514475\pi$
$224$	−0.0954102	−	0.0800587i	−0.00637486	−	0.00534915i
$225$	−1.99824	+	1.67672i	−0.133216	+	0.111782i
$226$	2.79387	+	15.8448i	0.185845	+	1.05398i
$227$	3.55889	+	1.29533i	0.236212	+	0.0859741i	0.457414	−	0.889254i	$-0.348776\pi$
$227$	3.55889	+	1.29533i	0.236212	+	0.0859741i	−0.221202	+	0.975228i	$0.570998\pi$
$228$	2.92531			0.193734
$229$	−15.3420	−	5.58402i	−1.01383	−	0.369003i	−0.218925	−	0.975742i	$-0.570255\pi$
$229$	−15.3420	−	5.58402i	−1.01383	−	0.369003i	−0.794901	+	0.606739i	$0.792477\pi$
$230$	1.45014	−	2.51172i	0.0956194	−	0.165618i
$231$	0.0457841	−	0.259654i	0.00301237	−	0.0170840i
$232$	−1.53804	−	2.66396i	−0.100977	−	0.174897i
$233$	1.53122	−	2.65215i	0.100314	−	0.173748i	−0.811500	−	0.584352i	$-0.801349\pi$
$233$	1.53122	−	2.65215i	0.100314	−	0.173748i	0.911814	+	0.410604i	$0.134682\pi$
$234$	−13.4820	−	11.3127i	−0.881343	−	0.739535i
$235$	1.08826	+	6.17181i	0.0709900	+	0.402604i
$236$	1.31415	+	2.27617i	0.0855436	+	0.148166i
$237$	−6.59990	+	2.40217i	−0.428709	+	0.156037i
$238$	0.556183	−	0.202434i	0.0360520	−	0.0131218i
$239$	−3.73018	+	21.1549i	−0.241285	+	1.36840i	0.587679	+	0.809094i	$0.300042\pi$
$239$	−3.73018	+	21.1549i	−0.241285	+	1.36840i	−0.828964	+	0.559302i	$0.811069\pi$
$240$	−0.479302	+	0.402182i	−0.0309388	+	0.0259607i
$241$	−10.1594	+	8.52472i	−0.654422	+	0.549125i	−0.908409	−	0.418082i	$-0.862702\pi$
$241$	−10.1594	+	8.52472i	−0.654422	+	0.549125i	0.253987	+	0.967208i	$0.418258\pi$
$242$	0.0776447	−	0.440345i	0.00499119	−	0.0283065i
$243$	−13.2027	+	4.80540i	−0.846955	+	0.308266i
$244$	7.02388	−	2.55648i	0.449658	−	0.163662i
$245$	−3.49224	−	6.04874i	−0.223111	−	0.386440i
$246$	−0.540334	−	3.06439i	−0.0344505	−	0.195378i
$247$	24.1644	+	20.2764i	1.53755	+	1.29015i
$248$	4.19630	−	7.26820i	0.266465	−	0.461531i
$249$	2.11363	+	3.66091i	0.133946	+	0.232001i
$250$	−0.173648	+	0.984808i	−0.0109825	+	0.0622847i
$251$	6.66176	−	11.5385i	0.420486	−	0.728304i	−0.575501	−	0.817801i	$-0.695193\pi$
$251$	6.66176	−	11.5385i	0.420486	−	0.728304i	0.995987	+	0.0894977i	$0.0285262\pi$
$252$	−0.305296	−	0.111119i	−0.0192318	−	0.00699981i
$253$	−9.81270			−0.616919
$254$	19.4799	+	7.09011i	1.22228	+	0.444873i
$255$	−0.516317	−	2.92818i	−0.0323330	−	0.183370i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−3.48939	−	2.92794i	−0.217662	−	0.182640i	0.527437	−	0.849594i	$-0.323153\pi$
$257$	−3.48939	−	2.92794i	−0.217662	−	0.182640i	−0.745099	+	0.666954i	$0.767598\pi$
$258$	3.24992			0.202331
$259$	−0.198425	−	0.731157i	−0.0123295	−	0.0454319i
$260$	−6.74691			−0.418425
$261$	−6.14674	−	5.15773i	−0.380474	−	0.319255i
$262$	12.9456	−	10.8627i	0.799784	−	0.671098i
$263$	2.20567	+	12.5090i	0.136008	+	0.771338i	0.974153	+	0.225890i	$0.0725291\pi$
$263$	2.20567	+	12.5090i	0.136008	+	0.771338i	−0.838145	+	0.545447i	$0.816360\pi$
$264$	1.98925	+	0.724027i	0.122430	+	0.0445608i
$265$	−6.53766			−0.401605
$266$	0.547198	+	0.199164i	0.0335509	+	0.0122115i
$267$	1.66462	−	2.88321i	0.101873	−	0.176449i
$268$	1.43157	−	8.11884i	0.0874471	−	0.495937i
$269$	−10.0730	−	17.4469i	−0.614161	−	1.06376i	−0.990531	−	0.137289i	$-0.956161\pi$
$269$	−10.0730	−	17.4469i	−0.614161	−	1.06376i	0.376370	−	0.926469i	$-0.377172\pi$
$270$	−1.75458	+	3.03902i	−0.106780	+	0.184949i
$271$	−2.83327	−	2.37740i	−0.172109	−	0.144417i	0.552664	−	0.833404i	$-0.313611\pi$
$271$	−2.83327	−	2.37740i	−0.172109	−	0.144417i	−0.724774	+	0.688987i	$0.758056\pi$
$272$	0.825204	+	4.67996i	0.0500353	+	0.283764i
$273$	0.262888	+	0.455335i	0.0159107	+	0.0275581i
$274$	−7.58453	+	2.76054i	−0.458199	+	0.166771i
$275$	3.17932	−	1.15718i	0.191720	−	0.0697805i
$276$	0.315112	−	1.78709i	0.0189675	−	0.107570i
$277$	1.57905	−	1.32498i	0.0948759	−	0.0796104i	−0.594116	−	0.804379i	$-0.702498\pi$
$277$	1.57905	−	1.32498i	0.0948759	−	0.0796104i	0.688992	+	0.724769i	$0.258054\pi$
$278$	0.821776	−	0.689552i	0.0492868	−	0.0413566i
$279$	3.80155	−	21.5597i	0.227593	−	1.29074i
$280$	−0.117038	+	0.0425983i	−0.00699436	+	0.00254574i
$281$	−7.98760	+	2.90725i	−0.476500	+	0.173432i	−0.569095	−	0.822272i	$-0.692706\pi$
$281$	−7.98760	+	2.90725i	−0.476500	+	0.173432i	0.0925946	+	0.995704i	$0.470484\pi$
$282$	1.96059	+	3.39583i	0.116751	+	0.202219i
$283$	−2.36097	−	13.3897i	−0.140345	−	0.795935i	−0.970988	−	0.239129i	$-0.923138\pi$
$283$	−2.36097	−	13.3897i	−0.140345	−	0.795935i	0.830643	−	0.556806i	$-0.187973\pi$
$284$	10.5092	+	8.81828i	0.623608	+	0.523269i
$285$	1.46266	−	2.53340i	0.0866403	−	0.150065i
$286$	11.4136	+	19.7690i	0.674901	+	1.16896i
$287$	0.107559	−	0.610000i	0.00634903	−	0.0360072i
$288$	1.30426	−	2.25904i	0.0768543	−	0.133115i
$289$	−5.24632	−	1.90950i	−0.308607	−	0.112324i
$290$	−3.07608			−0.180633
$291$	1.82847	+	0.665510i	0.107187	+	0.0390129i
$292$	−0.806016	−	4.57115i	−0.0471685	−	0.267506i
$293$	7.45075	−	6.25192i	0.435278	−	0.365241i	−0.398661	−	0.917098i	$-0.630525\pi$
$293$	7.45075	−	6.25192i	0.435278	−	0.365241i	0.833939	+	0.551857i	$0.186081\pi$
$294$	−3.34768	−	2.80903i	−0.195240	−	0.163826i
$295$	2.62829			0.153025
$296$	6.05789	−	0.549553i	0.352108	−	0.0319421i
$297$	11.8728			0.688927
$298$	−12.6558	−	10.6195i	−0.733132	−	0.615171i
$299$	14.9899	−	12.5780i	0.866888	−	0.727406i
$300$	0.108649	+	0.616178i	0.00627284	+	0.0355751i
$301$	0.607918	+	0.221264i	0.0350398	+	0.0127534i
$302$	1.42578			0.0820444
$303$	−8.23005	−	2.99549i	−0.472804	−	0.172087i
$304$	−2.33769	+	4.04900i	−0.134076	+	0.232226i
$305$	1.29796	−	7.36110i	0.0743210	−	0.421495i
$306$	6.19805	+	10.7353i	0.354319	+	0.613698i
$307$	5.69188	−	9.85863i	0.324853	−	0.562662i	−0.656630	−	0.754213i	$-0.728019\pi$
$307$	5.69188	−	9.85863i	0.324853	−	0.562662i	0.981483	+	0.191552i	$0.0613519\pi$
$308$	0.322807	+	0.270867i	0.0183937	+	0.0154341i
$309$	0.490843	+	2.78371i	0.0279231	+	0.158360i
$310$	−4.19630	−	7.26820i	−0.238334	−	0.412806i
$311$	−6.58105	+	2.39531i	−0.373177	+	0.135825i	−0.521798	−	0.853069i	$-0.674739\pi$
$311$	−6.58105	+	2.39531i	−0.373177	+	0.135825i	0.148621	+	0.988894i	$0.452516\pi$
$312$	−3.96685	+	1.44381i	−0.224578	+	0.0817399i
$313$	4.19354	−	23.7827i	0.237033	−	1.34428i	−0.601257	−	0.799056i	$-0.705333\pi$
$313$	4.19354	−	23.7827i	0.237033	−	1.34428i	0.838290	−	0.545225i	$-0.183556\pi$
$314$	−14.9012	+	12.5036i	−0.840921	+	0.705616i
$315$	−0.248879	+	0.208835i	−0.0140228	+	0.0117665i
$316$	1.94925	−	11.0547i	0.109654	−	0.621877i
$317$	7.50402	−	2.73124i	0.421468	−	0.153402i	−0.122575	−	0.992459i	$-0.539115\pi$
$317$	7.50402	−	2.73124i	0.421468	−	0.153402i	0.544043	+	0.839058i	$0.316893\pi$
$318$	−3.84382	+	1.39904i	−0.215551	+	0.0784541i
$319$	5.20374	+	9.01314i	0.291353	+	0.504639i
$320$	−0.173648	−	0.984808i	−0.00970723	−	0.0550524i
$321$	−0.395405	−	0.331784i	−0.0220693	−	0.0185184i
$322$	0.180614	−	0.312832i	0.0100652	−	0.0174335i
$323$	−11.1091	−	19.2415i	−0.618126	−	1.07063i
$324$	0.977628	−	5.54440i	0.0543127	−	0.308022i
$325$	−3.37345	+	5.84299i	−0.187126	+	0.324111i
$326$	−12.5018	−	4.55027i	−0.692408	−	0.252016i
$327$	9.33059			0.515983
$328$	4.67330	+	1.70094i	0.258040	+	0.0939187i
$329$	0.135541	+	0.768694i	0.00747264	+	0.0423794i
$330$	1.62165	−	1.36073i	0.0892689	−	0.0749055i
$331$	−3.01543	−	2.53025i	−0.165743	−	0.139075i	0.556144	−	0.831086i	$-0.312280\pi$
$331$	−3.01543	−	2.53025i	−0.165743	−	0.139075i	−0.721887	+	0.692011i	$0.756725\pi$
$332$	−6.75622			−0.370796
$333$	14.3588	−	6.75171i	0.786860	−	0.369992i
$334$	−23.4497			−1.28311
$335$	−6.31534	−	5.29920i	−0.345044	−	0.289526i
$336$	−0.0596966	+	0.0500914i	−0.00325672	+	0.00273271i
$337$	2.74572	+	15.5717i	0.149569	+	0.848247i	0.963585	+	0.267404i	$0.0861658\pi$
$337$	2.74572	+	15.5717i	0.149569	+	0.848247i	−0.814016	+	0.580843i	$0.802723\pi$
$338$	−30.5595	−	11.1228i	−1.66222	−	0.604998i
$339$	10.0668			0.546752
$340$	4.46557	+	1.62533i	0.242179	+	0.0881461i
$341$	−14.1976	+	24.5909i	−0.768843	+	1.33167i
$342$	−2.11779	+	12.0106i	−0.114517	+	0.649457i
$343$	−0.870878	−	1.50841i	−0.0470230	−	0.0814462i
$344$	−2.59710	+	4.49831i	−0.140026	+	0.242532i
$345$	−1.39011	−	1.16644i	−0.0748409	−	0.0627990i
$346$	3.01332	+	17.0894i	0.161997	+	0.918730i
$347$	−15.6134	−	27.0432i	−0.838170	−	1.45175i	−0.891423	−	0.453172i	$-0.850292\pi$
$347$	−15.6134	−	27.0432i	−0.838170	−	1.45175i	0.0532527	−	0.998581i	$-0.483041\pi$
$348$	−1.80858	+	0.658269i	−0.0969500	+	0.0352869i
$349$	−21.2556	+	7.73641i	−1.13779	+	0.414121i	−0.841114	−	0.540858i	$-0.818100\pi$
$349$	−21.2556	+	7.73641i	−1.13779	+	0.414121i	−0.296674	+	0.954979i	$0.595877\pi$
$350$	−0.0216277	+	0.122657i	−0.00115605	+	0.00655629i
$351$	−18.1368	+	15.2186i	−0.968073	+	0.812310i
$352$	−2.59181	+	2.17478i	−0.138144	+	0.115916i
$353$	1.18021	−	6.69332i	0.0628164	−	0.356249i	−0.937157	−	0.348909i	$-0.886552\pi$
$353$	1.18021	−	6.69332i	0.0628164	−	0.356249i	0.999973	−	0.00734062i	$-0.00233661\pi$
$354$	1.54531	−	0.562445i	0.0821321	−	0.0298936i
$355$	12.8915	−	4.69211i	0.684208	−	0.249031i
$356$	2.66048	+	4.60809i	0.141005	+	0.244228i
$357$	−0.0643068	−	0.364702i	−0.00340348	−	0.0193021i
$358$	17.5704	+	14.7433i	0.928625	+	0.779209i
$359$	−8.17138	+	14.1532i	−0.431269	+	0.746980i	−0.996983	−	0.0776219i	$-0.975267\pi$
$359$	−8.17138	+	14.1532i	−0.431269	+	0.746980i	0.565714	+	0.824602i	$0.308601\pi$
$360$	−1.30426	−	2.25904i	−0.0687405	−	0.119062i
$361$	0.496504	−	2.81581i	0.0261318	−	0.148201i
$362$	−2.42397	+	4.19844i	−0.127401	+	0.220665i
$363$	−0.262895	−	0.0956860i	−0.0137984	−	0.00502221i
$364$	−0.840322			−0.0440448
$365$	−4.36174	−	1.58754i	−0.228304	−	0.0830958i
$366$	−0.812112	−	4.60572i	−0.0424498	−	0.240745i
$367$	−10.4890	+	8.80132i	−0.547521	+	0.459425i	−0.874101	−	0.485745i	$-0.838548\pi$
$367$	−10.4890	+	8.80132i	−0.547521	+	0.459425i	0.326579	+	0.945170i	$0.394104\pi$
$368$	2.22174	+	1.86426i	0.115816	+	0.0971815i
$369$	12.9727			0.675334
$370$	2.55302	−	5.52106i	0.132725	−	0.287026i
$371$	−0.814260			−0.0422743
$372$	−4.02258	−	3.37535i	−0.208561	−	0.175004i
$373$	−11.2852	+	9.46942i	−0.584326	+	0.490308i	−0.886365	−	0.462988i	$-0.846777\pi$
$373$	−11.2852	+	9.46942i	−0.584326	+	0.490308i	0.302039	+	0.953296i	$0.402333\pi$
$374$	−2.79196	−	15.8340i	−0.144369	−	0.818757i
$375$	0.587950	+	0.213996i	0.0303616	+	0.0110507i
$376$	−6.26702			−0.323197
$377$	−19.5024	−	7.09828i	−1.00442	−	0.365580i
$378$	−0.218531	+	0.378508i	−0.0112400	+	0.0194683i
$379$	2.99895	−	17.0079i	0.154046	−	0.873636i	−0.805608	−	0.592449i	$-0.798161\pi$
$379$	2.99895	−	17.0079i	0.154046	−	0.873636i	0.959653	−	0.281186i	$-0.0907279\pi$
$380$	2.33769	+	4.04900i	0.119921	+	0.207710i
$381$	6.48524	−	11.2328i	0.332249	−	0.575472i
$382$	16.0001	+	13.4257i	0.818635	+	0.686916i
$383$	−5.52545	−	31.3364i	−0.282337	−	1.60121i	−0.714645	−	0.699488i	$-0.753412\pi$
$383$	−5.52545	−	31.3364i	−0.282337	−	1.60121i	0.432307	−	0.901726i	$-0.357700\pi$
$384$	−0.312842	−	0.541858i	−0.0159646	−	0.0276516i
$385$	0.395982	−	0.144126i	0.0201811	−	0.00734532i
$386$	2.22037	−	0.808148i	0.113014	−	0.0411336i
$387$	−2.35279	+	13.3433i	−0.119599	+	0.678279i
$388$	−2.38233	+	1.99901i	−0.120944	+	0.101484i
$389$	6.26278	−	5.25509i	0.317535	−	0.266444i	−0.470063	−	0.882633i	$-0.655769\pi$
$389$	6.26278	−	5.25509i	0.317535	−	0.266444i	0.787598	+	0.616189i	$0.211324\pi$
$390$	−0.733044	+	4.15730i	−0.0371191	+	0.210513i
$391$	−12.9514	+	4.71392i	−0.654981	+	0.238393i
$392$	6.56327	−	2.38884i	0.331495	−	0.120654i
$393$	−5.28682	−	9.15704i	−0.266685	−	0.461911i
$394$	3.79523	+	21.5238i	0.191201	+	1.08435i
$395$	−8.59905	−	7.21546i	−0.432665	−	0.363049i
$396$	−4.41278	+	7.64317i	−0.221751	+	0.384083i
$397$	−13.3008	−	23.0376i	−0.667546	−	1.15622i	−0.978588	−	0.205828i	$-0.934011\pi$
$397$	−13.3008	−	23.0376i	−0.667546	−	1.15622i	0.311042	−	0.950396i	$-0.399322\pi$
$398$	−1.78318	+	10.1129i	−0.0893829	+	0.506916i
$399$	0.182173	−	0.315532i	0.00912004	−	0.0157964i
$400$	−0.939693	−	0.342020i	−0.0469846	−	0.0171010i
$401$	26.4475			1.32073			0.660363	−	0.750947i	$-0.270403\pi$
$401$	26.4475			1.32073			0.660363	+	0.750947i	$0.270403\pi$
$402$	−4.84711	−	1.76421i	−0.241752	−	0.0879906i
$403$	−9.83266	−	55.7638i	−0.489800	−	2.77779i
$404$	10.7230	−	8.99766i	0.533489	−	0.447650i
$405$	−4.31278	−	3.61885i	−0.214304	−	0.179822i
$406$	−0.383123			−0.0190141
$407$	−20.4960	+	1.85934i	−1.01595	+	0.0921640i
$408$	2.97335			0.147203
$409$	11.4723	+	9.62637i	0.567267	+	0.475993i	0.880738	−	0.473604i	$-0.157047\pi$
$409$	11.4723	+	9.62637i	0.567267	+	0.475993i	−0.313471	+	0.949598i	$0.601492\pi$
$410$	3.80971	−	3.19672i	0.188148	−	0.157875i
$411$	0.876937	+	4.97335i	0.0432561	+	0.245318i
$412$	−4.24525	−	1.54515i	−0.209149	−	0.0761239i
$413$	0.327352			0.0161079
$414$	7.10919	+	2.58753i	0.349397	+	0.127170i
$415$	−3.37811	+	5.85105i	−0.165825	+	0.287217i
$416$	1.17159	−	6.64441i	0.0574418	−	0.325769i
$417$	−0.335602	−	0.581279i	−0.0164345	−	0.0284654i
$418$	7.90926	−	13.6992i	0.386855	−	0.670052i
$419$	12.6460	+	10.6112i	0.617795	+	0.518392i	0.897110	−	0.441808i	$-0.145663\pi$
$419$	12.6460	+	10.6112i	0.617795	+	0.518392i	−0.279314	+	0.960200i	$0.590107\pi$
$420$	0.0135321	+	0.0767445i	0.000660300	+	0.00374475i
$421$	11.6009	+	20.0933i	0.565393	+	0.979289i	0.997013	+	0.0772336i	$0.0246087\pi$
$421$	11.6009	+	20.0933i	0.565393	+	0.979289i	−0.431620	+	0.902055i	$0.642058\pi$
$422$	−7.99912	+	2.91144i	−0.389391	+	0.141727i
$423$	−15.3618	+	5.59122i	−0.746914	+	0.271854i
$424$	1.13525	−	6.43834i	0.0551328	−	0.312673i
$425$	3.64036	−	3.05463i	0.176584	−	0.148171i
$426$	6.57545	−	5.51746i	0.318582	−	0.267322i
$427$	0.161660	−	0.916819i	0.00782327	−	0.0443680i
$428$	0.775209	−	0.282153i	0.0374711	−	0.0136384i
$429$	13.4213	−	4.88495i	0.647985	−	0.235847i
$430$	2.59710	+	4.49831i	0.125243	+	0.216928i
$431$	−2.84509	−	16.1353i	−0.137043	−	0.777210i	−0.973415	−	0.229048i	$-0.926439\pi$
$431$	−2.84509	−	16.1353i	−0.137043	−	0.777210i	0.836372	−	0.548162i	$-0.184672\pi$
$432$	−2.68817	−	2.25564i	−0.129335	−	0.108525i
$433$	−13.6986	+	23.7267i	−0.658314	+	1.14023i	0.322738	+	0.946488i	$0.395397\pi$
$433$	−13.6986	+	23.7267i	−0.658314	+	1.14023i	−0.981052	+	0.193745i	$0.937937\pi$
$434$	−0.522645	−	0.905248i	−0.0250878	−	0.0434533i
$435$	−0.334212	+	1.89541i	−0.0160242	+	0.0908780i
$436$	−7.45632	+	12.9147i	−0.357093	+	0.618503i
$437$	−12.7422	−	4.63777i	−0.609541	−	0.221855i
$438$	−2.90421			−0.138769
$439$	−7.81789	−	2.84548i	−0.373128	−	0.135807i	0.148648	−	0.988890i	$-0.452508\pi$
$439$	−7.81789	−	2.84548i	−0.373128	−	0.135807i	−0.521775	+	0.853083i	$0.674730\pi$
$440$	0.587515	+	3.33196i	0.0280087	+	0.158845i
$441$	13.9567	−	11.7111i	0.664605	−	0.557670i
$442$	24.5612	+	20.6093i	1.16826	+	0.980284i
$443$	−15.8191			−0.751587			−0.375793	−	0.926703i	$-0.622630\pi$
$443$	−15.8191			−0.751587			−0.375793	+	0.926703i	$0.622630\pi$
$444$	0.319560	−	3.79245i	0.0151656	−	0.179982i
$445$	5.32096			0.252238
$446$	−1.04007	−	0.872726i	−0.0492489	−	0.0413248i
$447$	−7.91854	+	6.64444i	−0.374534	+	0.314271i
$448$	−0.0216277	−	0.122657i	−0.00102181	−	0.00579500i
$449$	1.28697	+	0.468417i	0.0607357	+	0.0221060i	0.372209	−	0.928149i	$-0.378600\pi$
$449$	1.28697	+	0.468417i	0.0607357	+	0.0221060i	−0.311474	+	0.950255i	$0.600823\pi$
$450$	−2.60852			−0.122967
$451$	−15.8115	−	5.75490i	−0.744532	−	0.270988i
$452$	−8.04462	+	13.9337i	−0.378387	+	0.655385i
$453$	0.154909	−	0.878535i	0.00727828	−	0.0412772i
$454$	1.89365	+	3.27989i	0.0888732	+	0.153933i
$455$	−0.420161	+	0.727740i	−0.0196974	+	0.0341170i
$456$	2.24092	+	1.88036i	0.104941	+	0.0880557i
$457$	4.58617	+	26.0094i	0.214532	+	1.21667i	0.881717	+	0.471779i	$0.156388\pi$
$457$	4.58617	+	26.0094i	0.214532	+	1.21667i	−0.667185	+	0.744892i	$0.732501\pi$
$458$	−8.16330	−	14.1392i	−0.381446	−	0.660683i
$459$	15.6704	−	5.70356i	0.731431	−	0.266219i
$460$	2.72537	−	0.991954i	0.127071	−	0.0462501i
$461$	0.549269	−	3.11506i	0.0255820	−	0.145083i	−0.969341	−	0.245718i	$-0.920976\pi$
$461$	0.549269	−	3.11506i	0.0255820	−	0.145083i	0.994923	+	0.100635i	$0.0320874\pi$
$462$	0.201975	−	0.169477i	0.00939674	−	0.00788480i
$463$	−10.7056	+	8.98311i	−0.497534	+	0.417480i	−0.856717	−	0.515787i	$-0.827500\pi$
$463$	−10.7056	+	8.98311i	−0.497534	+	0.417480i	0.359183	+	0.933267i	$0.383055\pi$
$464$	0.534155	−	3.02934i	0.0247975	−	0.140634i
$465$	−4.93443	+	1.79599i	−0.228829	+	0.0832868i
$466$	2.87775	−	1.04742i	0.133309	−	0.0485206i
$467$	−8.64194	−	14.9683i	−0.399901	−	0.692649i	0.593812	−	0.804604i	$-0.297622\pi$
$467$	−8.64194	−	14.9683i	−0.399901	−	0.692649i	−0.993713	+	0.111955i	$0.964289\pi$
$468$	−3.05611	−	17.3321i	−0.141269	−	0.801175i
$469$	−0.786570	−	0.660011i	−0.0363204	−	0.0304765i
$470$	−3.13351	+	5.42740i	−0.144538	+	0.250347i
$471$	6.08542	+	10.5403i	0.280401	+	0.485670i
$472$	−0.456398	+	2.58836i	−0.0210074	+	0.119139i
$473$	8.78692	−	15.2194i	0.404023	−	0.699789i
$474$	−6.59990	−	2.40217i	−0.303143	−	0.110335i
$475$	4.67539			0.214522
$476$	0.556183	+	0.202434i	0.0254926	+	0.00927855i
$477$	−2.96133	−	16.7945i	−0.135590	−	0.768969i
$478$	−16.4556	+	13.8079i	−0.752661	+	0.631557i
$479$	9.35210	+	7.84734i	0.427308	+	0.358554i	0.830935	−	0.556369i	$-0.187806\pi$
$479$	9.35210	+	7.84734i	0.427308	+	0.358554i	−0.403627	+	0.914924i	$0.632251\pi$
$480$	−0.625684			−0.0285584
$481$	28.9265	−	29.1123i	1.31893	−	1.32741i
$482$	−13.2621			−0.604072
$483$	−0.173137	−	0.145279i	−0.00787800	−	0.00661043i
$484$	0.342528	−	0.287415i	0.0155694	−	0.0130643i
$485$	0.540030	+	3.06266i	0.0245215	+	0.139068i
$486$	−13.2027	−	4.80540i	−0.598887	−	0.217977i
$487$	23.4309			1.06175			0.530877	−	0.847449i	$-0.321863\pi$
$487$	23.4309			1.06175			0.530877	+	0.847449i	$0.321863\pi$
$488$	7.02388	+	2.55648i	0.317956	+	0.115727i
$489$	−4.16208	+	7.20893i	−0.188216	+	0.325999i
$490$	1.21284	−	6.87838i	0.0547907	−	0.310733i
$491$	19.2870	+	33.4060i	0.870409	+	1.50759i	0.861574	+	0.507632i	$0.169479\pi$
$491$	19.2870	+	33.4060i	0.870409	+	1.50759i	0.00883514	+	0.999961i	$0.497188\pi$
$492$	1.55583	−	2.69478i	0.0701423	−	0.121490i
$493$	11.1980	+	9.39627i	0.504334	+	0.423187i
$494$	5.47763	+	31.0652i	0.246450	+	1.39769i
$495$	4.41278	+	7.64317i	0.198340	+	0.343535i
$496$	7.88646	−	2.87044i	0.354112	−	0.128886i
$497$	1.60562	−	0.584399i	0.0720220	−	0.0262139i
$498$	−0.734055	+	4.16303i	−0.0328938	+	0.186550i
$499$	17.0456	−	14.3030i	0.763067	−	0.640290i	−0.175856	−	0.984416i	$-0.556269\pi$
$499$	17.0456	−	14.3030i	0.763067	−	0.640290i	0.938923	+	0.344126i	$0.111825\pi$
$500$	−0.766044	+	0.642788i	−0.0342585	+	0.0287463i
$501$	−2.54779	+	14.4492i	−0.113827	+	0.645544i
$502$	12.5200	−	4.55691i	0.558795	−	0.203385i
$503$	8.22692	−	2.99435i	0.366820	−	0.133512i	−0.152032	−	0.988376i	$-0.548582\pi$
$503$	8.22692	−	2.99435i	0.366820	−	0.133512i	0.518852	+	0.854864i	$0.326359\pi$
$504$	−0.162445	−	0.281362i	−0.00723585	−	0.0125329i
$505$	−2.43070	−	13.7852i	−0.108165	−	0.613434i
$506$	−7.51696	−	6.30748i	−0.334170	−	0.280402i
$507$	−10.1739	+	17.6216i	−0.451837	+	0.782604i
$508$	10.3650	+	17.9528i	0.459875	+	0.796526i
$509$	0.0140329	−	0.0795846i	0.000621998	−	0.00352753i	−0.984495	−	0.175412i	$-0.943874\pi$
$509$	0.0140329	−	0.0795846i	0.000621998	−	0.00352753i	0.985117	+	0.171884i	$0.0549855\pi$
$510$	1.48667	−	2.57500i	0.0658310	−	0.114023i
$511$	−0.543251	−	0.197727i	−0.0240320	−	0.00874693i
$512$	1.00000			0.0441942
$513$	15.4172	+	5.61142i	0.680688	+	0.247750i
$514$	−0.790980	−	4.48587i	−0.0348886	−	0.197863i
$515$	−3.46076	+	2.90392i	−0.152499	+	0.127962i
$516$	2.48959	+	2.08901i	0.109598	+	0.0919636i
$517$	21.2036			0.932533
$518$	0.317976	−	0.687644i	0.0139711	−	0.0302133i
$519$	10.8575			0.476591
$520$	−5.16843	−	4.33683i	−0.226651	−	0.190183i
$521$	−2.82966	+	2.37437i	−0.123970	+	0.104023i	−0.702665	−	0.711521i	$-0.748007\pi$
$521$	−2.82966	+	2.37437i	−0.123970	+	0.104023i	0.578695	+	0.815544i	$0.303562\pi$
$522$	−1.39335	−	7.90210i	−0.0609854	−	0.345866i
$523$	−21.9051	−	7.97281i	−0.957844	−	0.348627i	−0.184656	−	0.982803i	$-0.559117\pi$
$523$	−21.9051	−	7.97281i	−0.957844	−	0.348627i	−0.773188	+	0.634176i	$0.781339\pi$
$524$	16.8993			0.738251
$525$	0.0732287	+	0.0266531i	0.00319596	+	0.00116324i
$526$	−6.35098	+	11.0002i	−0.276916	+	0.479633i
$527$	−6.92560	+	39.2770i	−0.301684	+	1.71093i
$528$	1.05846	+	1.83330i	0.0460634	+	0.0797842i
$529$	7.29419	−	12.6339i	0.317139	−	0.549300i
$530$	−5.00814	−	4.20233i	−0.217540	−	0.182537i
$531$	1.19052	+	6.75180i	0.0516643	+	0.293003i
$532$	0.291158	+	0.504300i	0.0126233	+	0.0218642i
$533$	31.5303	−	11.4761i	1.36573	−	0.497085i
$534$	3.12846	−	1.13867i	0.135382	−	0.0492750i
$535$	0.143253	−	0.812427i	0.00619336	−	0.0351243i
$536$	6.31534	−	5.29920i	0.272781	−	0.228890i
$537$	10.9935	−	9.22466i	0.474405	−	0.398073i
$538$	3.49831	−	19.8399i	0.150823	−	0.855359i
$539$	−22.2059	+	8.08229i	−0.956477	+	0.348129i
$540$	−3.29753	+	1.20020i	−0.141903	+	0.0516485i
$541$	−10.6024	−	18.3639i	−0.455832	−	0.789525i	0.542903	−	0.839795i	$-0.317325\pi$
$541$	−10.6024	−	18.3639i	−0.455832	−	0.789525i	−0.998736	+	0.0502705i	$0.983992\pi$
$542$	−0.642251	−	3.64239i	−0.0275871	−	0.156454i
$543$	2.32363	+	1.94975i	0.0997164	+	0.0836720i
$544$	−2.37608	+	4.11549i	−0.101874	+	0.176450i
$545$	7.45632	+	12.9147i	0.319394	+	0.553206i
$546$	−0.0913000	+	0.517788i	−0.00390728	+	0.0221593i
$547$	11.3346	−	19.6320i	0.484631	−	0.839405i	−0.515213	−	0.857062i	$-0.672287\pi$
$547$	11.3346	−	19.6320i	0.484631	−	0.839405i	0.999844	+	0.0176568i	$0.00562062\pi$
$548$	−7.58453	−	2.76054i	−0.323995	−	0.117925i
$549$	19.4978			0.832145
$550$	3.17932	+	1.15718i	0.135567	+	0.0493422i
$551$	2.49738	+	14.1634i	0.106392	+	0.603379i
$552$	1.39011	−	1.16644i	0.0591670	−	0.0496470i
$553$	−1.07100	−	0.898679i	−0.0455437	−	0.0382157i
$554$	2.06130			0.0875764
$555$	−3.12457	−	2.17297i	−0.132631	−	0.0922374i
$556$	1.07275			0.0454948
$557$	27.6814	+	23.2274i	1.17290	+	0.984179i	1.00000		0.000760995i	$-0.000242232\pi$
$557$	27.6814	+	23.2274i	1.17290	+	0.984179i	0.172899	+	0.984940i	$0.444687\pi$
$558$	16.7704	−	14.0721i	0.709949	−	0.595718i
$559$	6.08546	+	34.5124i	0.257387	+	1.45972i
$560$	−0.117038	−	0.0425983i	−0.00494576	−	0.00180011i
$561$	−10.0599			−0.424730
$562$	−7.98760	−	2.90725i	−0.336936	−	0.122635i
$563$	−16.2939	+	28.2218i	−0.686706	+	1.18941i	0.286192	+	0.958172i	$0.407611\pi$
$563$	−16.2939	+	28.2218i	−0.686706	+	1.18941i	−0.972898	+	0.231237i	$0.925723\pi$
$564$	−0.680904	+	3.86160i	−0.0286712	+	0.162603i
$565$	8.04462	+	13.9337i	0.338440	+	0.586195i
$566$	6.79813	−	11.7747i	0.285747	−	0.494928i
$567$	−0.537153	−	0.450725i	−0.0225583	−	0.0189287i
$568$	2.38225	+	13.5104i	0.0999569	+	0.566884i
$569$	10.7410	+	18.6039i	0.450285	+	0.779916i	0.998403	−	0.0564847i	$-0.0179892\pi$
$569$	10.7410	+	18.6039i	0.450285	+	0.779916i	−0.548119	+	0.836400i	$0.684656\pi$
$570$	2.74890	−	1.00052i	0.115139	−	0.0419070i
$571$	−34.3058	+	12.4863i	−1.43565	+	0.522535i	−0.938546	−	0.345155i	$-0.887826\pi$
$571$	−34.3058	+	12.4863i	−1.43565	+	0.522535i	−0.497106	+	0.867690i	$0.665604\pi$
$572$	−3.96391	+	22.4804i	−0.165739	+	0.939954i
$573$	10.0110	−	8.40022i	0.418215	−	0.350924i
$574$	0.474496	−	0.398149i	0.0198051	−	0.0166184i
$575$	0.503628	−	2.85622i	0.0210028	−	0.119113i
$576$	2.45121	−	0.892166i	0.102134	−	0.0371736i
$577$	22.3178	−	8.12303i	0.929103	−	0.338166i	0.167249	−	0.985915i	$-0.446512\pi$
$577$	22.3178	−	8.12303i	0.929103	−	0.338166i	0.761854	+	0.647749i	$0.224289\pi$
$578$	−2.79151	−	4.83503i	−0.116111	−	0.201111i
$579$	−0.256723	−	1.45595i	−0.0106690	−	0.0605071i
$580$	−2.35641	−	1.97726i	−0.0978446	−	0.0821014i
$581$	−0.420741	+	0.728744i	−0.0174553	+	0.0302334i
$582$	0.972910	+	1.68513i	0.0403284	+	0.0698509i
$583$	−3.84097	+	21.7832i	−0.159077	+	0.902169i
$584$	2.32083	−	4.01980i	0.0960367	−	0.166340i
$585$	−16.5381	−	6.01936i	−0.683765	−	0.248870i
$586$	9.72626			0.401788
$587$	3.51097	+	1.27789i	0.144913	+	0.0527441i	0.413459	−	0.910523i	$-0.364321\pi$
$587$	3.51097	+	1.27789i	0.144913	+	0.0527441i	−0.268545	+	0.963267i	$0.586543\pi$
$588$	−0.758856	−	4.30369i	−0.0312947	−	0.177481i
$589$	−30.0585	+	25.2221i	−1.23854	+	1.03926i
$590$	2.01339	+	1.68943i	0.0828899	+	0.0695529i
$591$	13.6748			0.562508
$592$	4.99386	+	3.47295i	0.205246	+	0.142737i
$593$	−17.5115			−0.719113			−0.359556	−	0.933123i	$-0.617072\pi$
$593$	−17.5115			−0.719113			−0.359556	+	0.933123i	$0.617072\pi$
$594$	9.09506	+	7.63166i	0.373175	+	0.313131i
$595$	0.453404	−	0.380452i	0.0185878	−	0.0155970i
$596$	−2.86884	−	16.2700i	−0.117512	−	0.666445i
$597$	6.03763	+	2.19752i	0.247104	+	0.0899384i
$598$	19.5679			0.800192
$599$	−20.5488	−	7.47914i	−0.839600	−	0.305589i	−0.113807	−	0.993503i	$-0.536305\pi$
$599$	−20.5488	−	7.47914i	−0.839600	−	0.305589i	−0.725793	+	0.687914i	$0.758527\pi$
$600$	−0.312842	+	0.541858i	−0.0127717	+	0.0221213i
$601$	−7.83970	+	44.4612i	−0.319788	+	1.81361i	0.224231	+	0.974536i	$0.428013\pi$
$601$	−7.83970	+	44.4612i	−0.319788	+	1.81361i	−0.544019	+	0.839073i	$0.683098\pi$
$602$	0.323466	+	0.560260i	0.0131835	+	0.0228345i
$603$	10.7524	−	18.6238i	0.437873	−	0.758418i
$604$	1.09221	+	0.916474i	0.0444414	+	0.0372908i
$605$	−0.0776447	−	0.440345i	−0.00315671	−	0.0179026i
$606$	−4.37912	−	7.58486i	−0.177890	−	0.308114i
$607$	26.1387	−	9.51370i	1.06094	−	0.386149i	0.248156	−	0.968720i	$-0.420175\pi$
$607$	26.1387	−	9.51370i	1.06094	−	0.386149i	0.812780	+	0.582571i	$0.197953\pi$
$608$	−4.39343	+	1.59908i	−0.178177	+	0.0648511i
$609$	−0.0416258	+	0.236072i	−0.00168676	+	0.00956611i
$610$	5.72592	−	4.80461i	0.231836	−	0.194533i
$611$	−32.3906	+	27.1790i	−1.31039	+	1.09954i
$612$	−2.15256	+	12.2078i	−0.0870121	+	0.493470i
$613$	−26.1961	+	9.53458i	−1.05805	+	0.385098i	−0.811695	−	0.584082i	$-0.801455\pi$
$613$	−26.1961	+	9.53458i	−1.05805	+	0.385098i	−0.246354	+	0.969180i	$0.579233\pi$
$614$	10.6972	−	3.89348i	0.431705	−	0.157128i
$615$	−1.55583	−	2.69478i	−0.0627372	−	0.108664i
$616$	0.0731745	+	0.414993i	0.00294828	+	0.0167205i
$617$	9.05397	+	7.59718i	0.364499	+	0.305851i	0.806581	−	0.591124i	$-0.201315\pi$
$617$	9.05397	+	7.59718i	0.364499	+	0.305851i	−0.442082	+	0.896975i	$0.645760\pi$
$618$	−1.41333	+	2.44795i	−0.0568524	+	0.0984712i
$619$	−16.8046	−	29.1064i	−0.675435	−	1.16989i	−0.976342	−	0.216233i	$-0.930623\pi$
$619$	−16.8046	−	29.1064i	−0.675435	−	1.16989i	0.300907	−	0.953653i	$-0.402711\pi$
$620$	1.45736	−	8.26509i	0.0585289	−	0.331934i
$621$	5.08877	−	8.81401i	0.204205	−	0.353694i
$622$	−6.58105	−	2.39531i	−0.263876	−	0.0960430i
$623$	0.662722			0.0265514
$624$	−3.96685	−	1.44381i	−0.158801	−	0.0577988i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	18.4997	−	15.5231i	0.739396	−	0.620427i
$627$	−7.58185	−	6.36192i	−0.302790	−	0.254071i
$628$	−19.4521			−0.776222
$629$	−26.1587	+	12.3002i	−1.04302	+	0.490439i
$630$	−0.324889			−0.0129439
$631$	20.4749	+	17.1805i	0.815092	+	0.683944i	0.951817	−	0.306665i	$-0.0992132\pi$
$631$	20.4749	+	17.1805i	0.815092	+	0.683944i	−0.136725	+	0.990609i	$0.543658\pi$
$632$	8.59905	−	7.21546i	0.342052	−	0.287015i
$633$	0.924872	+	5.24521i	0.0367604	+	0.208478i
$634$	7.50402	+	2.73124i	0.298023	+	0.108471i
$635$	20.7301			0.822649
$636$	−3.84382	−	1.39904i	−0.152417	−	0.0554754i
$637$	23.5618	−	40.8103i	0.933554	−	1.61696i
$638$	−1.80724	+	10.2494i	−0.0715493	+	0.405776i
$639$	17.8929	+	30.9914i	0.707832	+	1.22600i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	10.3995	+	8.72622i	0.410756	+	0.344665i	0.824633	−	0.565668i	$-0.191381\pi$
$641$	10.3995	+	8.72622i	0.410756	+	0.344665i	−0.413878	+	0.910333i	$0.635826\pi$
$642$	−0.0896309	−	0.508322i	−0.00353745	−	0.0200619i
$643$	3.37224	+	5.84090i	0.132988	+	0.230343i	0.924827	−	0.380388i	$-0.124209\pi$
$643$	3.37224	+	5.84090i	0.132988	+	0.230343i	−0.791839	+	0.610730i	$0.790876\pi$
$644$	0.339443	−	0.123547i	0.0133759	−	0.00486844i
$645$	3.05393	−	1.11154i	0.120248	−	0.0437668i
$646$	3.85815	−	21.8806i	0.151797	−	0.860882i
$647$	−23.2362	+	19.4975i	−0.913511	+	0.766527i	−0.972784	−	0.231715i	$-0.925566\pi$
$647$	−23.2362	+	19.4975i	−0.913511	+	0.766527i	0.0592729	+	0.998242i	$0.481122\pi$
$648$	4.31278	−	3.61885i	0.169422	−	0.142162i
$649$	1.54416	−	8.75737i	0.0606136	−	0.343757i
$650$	−6.34002	+	2.30758i	−0.248676	+	0.0905107i
$651$	−0.614579	+	0.223688i	−0.0240873	+	0.00876704i
$652$	−6.65205	−	11.5217i	−0.260514	−	0.451224i
$653$	0.244928	+	1.38906i	0.00958478	+	0.0543580i	0.989225	−	0.146403i	$-0.0467696\pi$
$653$	0.244928	+	1.38906i	0.00958478	+	0.0543580i	−0.979640	+	0.200761i	$0.935659\pi$
$654$	7.14765	+	5.99759i	0.279495	+	0.234524i
$655$	8.44966	−	14.6352i	0.330156	−	0.571846i
$656$	2.48661	+	4.30693i	0.0970858	+	0.168157i
$657$	2.10251	−	11.9239i	0.0820267	−	0.465197i
$658$	−0.390276	+	0.675978i	−0.0152145	+	0.0263524i
$659$	−7.55279	−	2.74899i	−0.294215	−	0.107085i	0.190696	−	0.981649i	$-0.438926\pi$
$659$	−7.55279	−	2.74899i	−0.294215	−	0.107085i	−0.484911	+	0.874564i	$0.661148\pi$
$660$	2.11691			0.0824008
$661$	36.7041	+	13.3592i	1.42762	+	0.519612i	0.936249	−	0.351336i	$-0.114273\pi$
$661$	36.7041	+	13.3592i	1.42762	+	0.519612i	0.491374	+	0.870949i	$0.336495\pi$
$662$	−0.683543	−	3.87657i	−0.0265667	−	0.150667i
$663$	15.3675	−	12.8949i	0.596826	−	0.500797i
$664$	−5.17556	−	4.34281i	−0.200851	−	0.168534i
$665$	0.582316			0.0225812
$666$	15.3394	+	4.05757i	0.594391	+	0.157228i
$667$	8.92148			0.345441
$668$	−17.9635	−	15.0732i	−0.695030	−	0.583200i
$669$	−0.650757	+	0.546050i	−0.0251597	+	0.0211115i
$670$	−1.43157	−	8.11884i	−0.0553064	−	0.313658i
$671$	−23.7643	−	8.64950i	−0.917411	−	0.333910i
$672$	−0.0779284			−0.00300615
$673$	23.8732	+	8.68915i	0.920245	+	0.334942i	0.758336	−	0.651864i	$-0.226013\pi$
$673$	23.8732	+	8.68915i	0.920245	+	0.334942i	0.161909	+	0.986806i	$0.448235\pi$
$674$	−7.90598	+	13.6936i	−0.304527	+	0.527456i
$675$	−0.609359	+	3.45585i	−0.0234542	+	0.133016i
$676$	−16.2604	−	28.1638i	−0.625399	−	1.08322i
$677$	−7.21162	+	12.4909i	−0.277165	+	0.480064i	−0.970679	−	0.240379i	$-0.922728\pi$
$677$	−7.21162	+	12.4909i	−0.277165	+	0.480064i	0.693514	+	0.720443i	$0.256062\pi$
$678$	7.71159	+	6.47080i	0.296162	+	0.248509i
$679$	0.0672603	+	0.381452i	0.00258122	+	0.0146388i
$680$	2.37608	+	4.11549i	0.0911185	+	0.157822i
$681$	2.22674	−	0.810467i	0.0853288	−	0.0310572i
$682$	−26.6827	+	9.71172i	−1.02174	+	0.371881i
$683$	0.957666	−	5.43119i	0.0366441	−	0.207819i	−0.960989	−	0.276588i	$-0.910796\pi$
$683$	0.957666	−	5.43119i	0.0366441	−	0.207819i	0.997633	+	0.0687694i	$0.0219073\pi$
$684$	−9.34256	+	7.83934i	−0.357222	+	0.299745i
$685$	−6.18297	+	5.18813i	−0.236239	+	0.198228i
$686$	0.302453	−	1.71530i	0.0115477	−	0.0654903i
$687$	−9.59923	+	3.49383i	−0.366233	+	0.133298i
$688$	−4.88095	+	1.77652i	−0.186084	+	0.0677292i
$689$	−22.0545	−	38.1995i	−0.840209	−	1.45529i
$690$	−0.315112	−	1.78709i	−0.0119961	−	0.0680333i
$691$	−30.0107	−	25.1820i	−1.14166	−	0.957968i	−0.142170	−	0.989842i	$-0.545408\pi$
$691$	−30.0107	−	25.1820i	−1.14166	−	0.957968i	−0.999492	+	0.0318745i	$0.989852\pi$
$692$	−8.67650	+	15.0281i	−0.329831	+	0.571284i
$693$	0.549609	+	0.951950i	0.0208779	+	0.0361616i
$694$	5.42247	−	30.7524i	0.205834	−	1.16734i
$695$	0.536376	−	0.929030i	0.0203459	−	0.0352401i
$696$	−1.80858	−	0.658269i	−0.0685540	−	0.0249516i
$697$	−23.6335			−0.895183
$698$	−21.2556	−	7.73641i	−0.804537	−	0.292828i
$699$	−0.332731	−	1.88701i	−0.0125850	−	0.0713732i
$700$	−0.0954102	+	0.0800587i	−0.00360617	+	0.00302593i
$701$	−7.00093	−	5.87447i	−0.264421	−	0.221876i	0.500931	−	0.865487i	$-0.332991\pi$
$701$	−7.00093	−	5.87447i	−0.264421	−	0.221876i	−0.765353	+	0.643611i	$0.777435\pi$
$702$	−23.6760			−0.893592
$703$	−27.4937	−	7.27260i	−1.03694	−	0.274291i
$704$	−3.38336			−0.127515
$705$	3.00379	+	2.52048i	0.113129	+	0.0949268i
$706$	5.20648	−	4.36875i	0.195948	−	0.164420i
$707$	−0.302742	−	1.71694i	−0.0113858	−	0.0645720i
$708$	1.54531	+	0.562445i	0.0580761	+	0.0211380i
$709$	−16.4563			−0.618031			−0.309015	−	0.951057i	$-0.599999\pi$
$709$	−16.4563			−0.618031			−0.309015	+	0.951057i	$0.599999\pi$
$710$	12.8915	+	4.69211i	0.483808	+	0.176092i
$711$	14.6407	−	25.3584i	0.549068	−	0.951013i
$712$	−0.923976	+	5.24013i	−0.0346275	+	0.196382i
$713$	12.1704	+	21.0798i	0.455786	+	0.789445i
$714$	0.185164	−	0.320714i	0.00692959	−	0.0120024i
$715$	17.4867	+	14.6731i	0.653964	+	0.548741i
$716$	3.98289	+	22.5881i	0.148847	+	0.844156i
$717$	6.72023	+	11.6398i	0.250972	+	0.434695i
$718$	−15.3572	+	5.58955i	−0.573124	+	0.208600i
$719$	35.4707	−	12.9103i	1.32283	−	0.481472i	0.418469	−	0.908231i	$-0.362567\pi$
$719$	35.4707	−	12.9103i	1.32283	−	0.481472i	0.904365	+	0.426759i	$0.140345\pi$
$720$	0.452965	−	2.56889i	0.0168810	−	0.0957369i
$721$	−0.431035	+	0.361681i	−0.0160526	+	0.0134697i
$722$	2.19031	−	1.83789i	0.0815150	−	0.0683992i
$723$	−1.44091	+	8.17182i	−0.0535881	+	0.303913i
$724$	−4.55558	+	1.65809i	−0.169307	+	0.0616226i
$725$	−2.89057	+	1.05208i	−0.107353	+	0.0390733i
$726$	−0.139884	−	0.242285i	−0.00519156	−	0.00899205i
$727$	−8.18883	−	46.4412i	−0.303707	−	1.72241i	−0.629530	−	0.776977i	$-0.716752\pi$
$727$	−8.18883	−	46.4412i	−0.303707	−	1.72241i	0.325823	−	0.945431i	$-0.394359\pi$
$728$	−0.643724	−	0.540148i	−0.0238580	−	0.0200192i
$729$	4.04946	−	7.01388i	0.149980	−	0.259773i
$730$	−2.32083	−	4.01980i	−0.0858978	−	0.148779i
$731$	4.28627	−	24.3086i	0.158533	−	0.899088i
$732$	2.33838	−	4.05020i	0.0864292	−	0.149700i
$733$	38.0607	+	13.8530i	1.40580	+	0.511671i	0.929895	−	0.367824i	$-0.119897\pi$
$733$	38.0607	+	13.8530i	1.40580	+	0.511671i	0.475908	+	0.879495i	$0.342119\pi$
$734$	−13.6924			−0.505396
$735$	−4.10653	−	1.49466i	−0.151472	−	0.0551312i
$736$	0.503628	+	2.85622i	0.0185640	+	0.105282i
$737$	−21.3671	+	17.9291i	−0.787066	+	0.660427i
$738$	9.93769	+	8.33872i	0.365812	+	0.306952i
$739$	−43.3467			−1.59453			−0.797267	−	0.603627i	$-0.793722\pi$
$739$	−43.3467			−1.59453			−0.797267	+	0.603627i	$0.793722\pi$
$740$	5.50459	−	2.58833i	0.202353	−	0.0951489i
$741$	19.7368			0.725050
$742$	−0.623760	−	0.523397i	−0.0228989	−	0.0192145i
$743$	−16.8499	+	14.1388i	−0.618164	+	0.518701i	−0.897226	−	0.441572i	$-0.854421\pi$
$743$	−16.8499	+	14.1388i	−0.618164	+	0.518701i	0.279062	+	0.960273i	$0.409977\pi$
$744$	−0.911846	−	5.17133i	−0.0334299	−	0.189590i
$745$	−15.5247	−	5.65051i	−0.568780	−	0.207019i
$746$	−14.7318			−0.539369
$747$	−16.5609	−	6.02767i	−0.605931	−	0.220541i
$748$	8.03914	−	13.9242i	0.293940	−	0.509119i
$749$	0.0178420	−	0.101187i	0.000651933	−	0.00369730i
$750$	0.312842	+	0.541858i	0.0114234	+	0.0197859i
$751$	−9.32464	+	16.1508i	−0.340261	+	0.589349i	−0.984481	−	0.175491i	$-0.943849\pi$
$751$	−9.32464	+	16.1508i	−0.340261	+	0.589349i	0.644220	+	0.764840i	$0.277182\pi$
$752$	−4.80081	−	4.02836i	−0.175068	−	0.146899i
$753$	−1.44758	−	8.20966i	−0.0527529	−	0.299177i
$754$	−10.3770	−	17.9735i	−0.377908	−	0.654556i
$755$	1.33980	−	0.487646i	0.0487601	−	0.0177472i
$756$	−0.410705	+	0.149484i	−0.0149372	+	0.00543669i
$757$	−4.24824	+	24.0930i	−0.154405	+	0.875674i	0.804923	+	0.593379i	$0.202207\pi$
$757$	−4.24824	+	24.0930i	−0.154405	+	0.875674i	−0.959328	+	0.282294i	$0.908905\pi$
$758$	13.2298	−	11.1011i	0.480527	−	0.403210i
$759$	−4.70324	+	3.94649i	−0.170717	+	0.143248i
$760$	−0.811873	+	4.60436i	−0.0294497	+	0.167018i
$761$	−21.3991	+	7.78864i	−0.775718	+	0.282338i	−0.699386	−	0.714744i	$-0.746543\pi$
$761$	−21.3991	+	7.78864i	−0.775718	+	0.282338i	−0.0763318	+	0.997082i	$0.524321\pi$
$762$	12.1883	−	4.43617i	0.441534	−	0.160705i
$763$	0.928678	+	1.60852i	0.0336204	+	0.0582323i
$764$	3.62692	+	20.5693i	0.131217	+	0.744171i
$765$	9.49596	+	7.96806i	0.343327	+	0.288086i
$766$	15.9099	−	27.5567i	0.574848	−	0.995666i
$767$	8.86642	+	15.3571i	0.320148	+	0.554513i
$768$	0.108649	−	0.616178i	0.00392053	−	0.0222344i
$769$	10.8685	−	18.8248i	0.391928	−	0.678839i	−0.600776	−	0.799418i	$-0.705142\pi$
$769$	10.8685	−	18.8248i	0.391928	−	0.678839i	0.992704	+	0.120578i	$0.0384749\pi$
$770$	0.395982	+	0.144126i	0.0142702	+	0.00519393i
$771$	−2.85003			−0.102641
$772$	2.22037	+	0.808148i	0.0799128	+	0.0290859i
$773$	−4.38441	−	24.8652i	−0.157696	−	0.894340i	−0.956279	−	0.292455i	$-0.905528\pi$
$773$	−4.38441	−	24.8652i	−0.157696	−	0.894340i	0.798583	−	0.601885i	$-0.205583\pi$
$774$	−10.3793	+	8.70923i	−0.373075	+	0.313047i
$775$	−6.42910	−	5.39466i	−0.230940	−	0.193782i
$776$	−3.10991			−0.111639
$777$	−0.389163	−	0.270642i	−0.0139612	−	0.00970921i
$778$	8.17548			0.293105
$779$	−17.8119	−	14.9459i	−0.638176	−	0.535493i
$780$	−3.23380	+	2.71348i	−0.115789	+	0.0971583i
$781$	−8.06000	−	45.7106i	−0.288410	−	1.63565i
$782$	−12.9514	−	4.71392i	−0.463141	−	0.168570i
$783$	−10.7944			−0.385762
$784$	6.56327	+	2.38884i	0.234403	+	0.0853156i
$785$	−9.72604	+	16.8460i	−0.347137	+	0.601259i
$786$	1.83609	−	10.4130i	0.0654912	−	0.371419i
$787$	4.70315	+	8.14609i	0.167649	+	0.290377i	0.937593	−	0.347735i	$-0.113049\pi$
$787$	4.70315	+	8.14609i	0.167649	+	0.290377i	−0.769944	+	0.638112i	$0.779716\pi$
$788$	−10.9279	+	18.9277i	−0.389291	+	0.674272i
$789$	6.08807	+	5.10850i	0.216741	+	0.181867i
$790$	−1.94925	−	11.0547i	−0.0693511	−	0.393309i
$791$	1.00195	+	1.73543i	0.0356253	+	0.0617048i
$792$	−8.29332	+	3.01852i	−0.294690	+	0.107258i
$793$	47.3894	−	17.2483i	1.68285	−	0.612507i
$794$	4.61931	−	26.1974i	0.163933	−	0.929710i
$795$	−3.13351	+	2.62933i	−0.111134	+	0.0932527i
$796$	−7.86647	+	6.60075i	−0.278820	+	0.233957i
$797$	8.01330	−	45.4457i	0.283846	−	1.60977i	−0.425535	−	0.904942i	$-0.639914\pi$
$797$	8.01330	−	45.4457i	0.283846	−	1.60977i	0.709380	−	0.704826i	$-0.248975\pi$
$798$	0.342373	−	0.124613i	0.0121199	−	0.00441127i
$799$	27.9858	−	10.1860i	0.990066	−	0.360355i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	2.41021	+	13.6690i	0.0851606	+	0.482970i
$802$	20.2600	+	17.0001i	0.715404	+	0.600295i
$803$	−7.85221	+	13.6004i	−0.277099	+	0.479949i
$804$	−2.57910	−	4.46713i	−0.0909577	−	0.157543i
$805$	0.0627265	−	0.355740i	0.00221082	−	0.0125382i
$806$	28.3120	−	49.0379i	0.997249	−	1.72729i
$807$	−11.8448	−	4.31117i	−0.416958	−	0.151760i
$808$	13.9979			0.492443
$809$	−27.1928	−	9.89736i	−0.956047	−	0.347973i	−0.183564	−	0.983008i	$-0.558763\pi$
$809$	−27.1928	−	9.89736i	−0.956047	−	0.347973i	−0.772483	+	0.635035i	$0.780986\pi$
$810$	−0.977628	−	5.54440i	−0.0343503	−	0.194811i
$811$	−28.0934	+	23.5731i	−0.986492	+	0.827765i	−0.985056	−	0.172234i	$-0.944901\pi$
$811$	−28.0934	+	23.5731i	−0.986492	+	0.827765i	−0.00143564	+	0.999999i	$0.500457\pi$
$812$	−0.293489	−	0.246267i	−0.0102994	−	0.00864226i
$813$	−2.31414			−0.0811604
$814$	−16.8960	−	11.7503i	−0.592205	−	0.411846i
$815$	−13.3041			−0.466022
$816$	2.27772	+	1.91123i	0.0797360	+	0.0669065i
$817$	18.6033	−	15.6100i	0.650847	−	0.546125i
$818$	2.60055	+	14.7485i	0.0909261	+	0.515668i
$819$	−2.05980	−	0.749707i	−0.0719753	−	0.0261969i
$820$	4.97322			0.173672
$821$	−24.4646	−	8.90439i	−0.853821	−	0.310765i	−0.122224	−	0.992503i	$-0.539003\pi$
$821$	−24.4646	−	8.90439i	−0.853821	−	0.310765i	−0.731597	+	0.681737i	$0.761225\pi$
$822$	−2.52504	+	4.37349i	−0.0880708	+	0.152543i
$823$	−7.32354	+	41.5339i	−0.255283	+	1.44778i	0.540064	+	0.841624i	$0.318400\pi$
$823$	−7.32354	+	41.5339i	−0.255283	+	1.44778i	−0.795346	+	0.606155i	$0.792711\pi$
$824$	−2.25885	−	3.91245i	−0.0786909	−	0.136297i
$825$	1.05846	−	1.83330i	0.0368508	−	0.0638274i
$826$	0.250766	+	0.210418i	0.00872526	+	0.00732137i
$827$	−7.50171	−	42.5443i	−0.260860	−	1.47941i	−0.780570	−	0.625068i	$-0.785071\pi$
$827$	−7.50171	−	42.5443i	−0.260860	−	1.47941i	0.519710	−	0.854343i	$-0.326040\pi$
$828$	3.78272	+	6.55186i	0.131459	+	0.227693i
$829$	−2.65815	+	0.967486i	−0.0923212	+	0.0336022i	−0.387768	−	0.921757i	$-0.626754\pi$
$829$	−2.65815	+	0.967486i	−0.0923212	+	0.0336022i	0.295447	+	0.955359i	$0.404532\pi$
$830$	−6.34877	+	2.31076i	−0.220369	+	0.0802077i
$831$	0.223958	−	1.27013i	0.00776903	−	0.0440603i
$832$	5.16843	−	4.33683i	0.179183	−	0.150352i
$833$	−25.4261	+	21.3350i	−0.880962	+	0.739215i
$834$	0.116553	−	0.661006i	0.00403591	−	0.0228888i
$835$	−22.0356	+	8.02029i	−0.762572	+	0.277553i
$836$	14.8646	−	5.41026i	0.514101	−	0.187118i
$837$	−14.7255	−	25.5053i	−0.508987	−	0.881591i
$838$	2.86661	+	16.2573i	0.0990252	+	0.561600i
$839$	28.9866	+	24.3227i	1.00073	+	0.839712i	0.987085	−	0.160195i	$-0.0512123\pi$
$839$	28.9866	+	24.3227i	1.00073	+	0.839712i	0.0136444	+	0.999907i	$0.495657\pi$
$840$	−0.0389642	+	0.0674880i	−0.00134439	+	0.00232856i
$841$	9.76888	+	16.9202i	0.336858	+	0.583455i
$842$	−4.02895	+	22.8493i	−0.138847	+	0.787439i
$843$	−2.65923	+	4.60591i	−0.0915886	+	0.158636i
$844$	−7.99912	−	2.91144i	−0.275341	−	0.100216i
$845$	−32.5208			−1.11875
$846$	−15.3618	−	5.59122i	−0.528148	−	0.192230i
$847$	−0.00967059	−	0.0548446i	−0.000332285	−	0.00188448i
$848$	5.00814	−	4.20233i	0.171980	−	0.144309i
$849$	−6.51671	−	5.46817i	−0.223653	−	0.187667i
$850$	4.75216			0.162998
$851$	−7.40446	+	16.0126i	−0.253822	+	0.548906i
$852$	8.58364			0.294071
$853$	−15.3953	−	12.9182i	−0.527126	−	0.442311i	0.339982	−	0.940432i	$-0.389579\pi$
$853$	−15.3953	−	12.9182i	−0.527126	−	0.442311i	−0.867108	+	0.498121i	$0.834024\pi$
$854$	0.713158	−	0.598411i	0.0244038	−	0.0204772i
$855$	2.11779	+	12.0106i	0.0724267	+	0.410752i
$856$	0.775209	+	0.282153i	0.0264961	+	0.00964379i
$857$	35.5333			1.21379			0.606897	−	0.794781i	$-0.292414\pi$
$857$	35.5333			1.21379			0.606897	+	0.794781i	$0.292414\pi$
$858$	13.4213	+	4.88495i	0.458195	+	0.166769i
$859$	−9.12418	+	15.8035i	−0.311313	+	0.539210i	−0.978647	−	0.205549i	$-0.934102\pi$
$859$	−9.12418	+	15.8035i	−0.311313	+	0.539210i	0.667334	+	0.744759i	$0.267435\pi$
$860$	−0.901963	+	5.11528i	−0.0307567	+	0.174430i
$861$	−0.193777	−	0.335632i	−0.00660392	−	0.0114383i
$862$	8.19210	−	14.1891i	0.279024	−	0.483284i
$863$	12.9220	+	10.8428i	0.439870	+	0.369095i	0.835661	−	0.549246i	$-0.185085\pi$
$863$	12.9220	+	10.8428i	0.439870	+	0.369095i	−0.395791	+	0.918341i	$0.629529\pi$
$864$	−0.609359	−	3.45585i	−0.0207308	−	0.117570i
$865$	8.67650	+	15.0281i	0.295010	+	0.510972i
$866$	−25.7450	+	9.37041i	−0.874850	+	0.318419i
$867$	−3.28253	+	1.19474i	−0.111481	+	0.0405757i
$868$	0.181513	−	1.02941i	0.00616095	−	0.0349405i
$869$	−29.0937	+	24.4125i	−0.986936	+	0.828138i
$870$	−1.47437	+	1.23714i	−0.0499857	+	0.0419430i
$871$	9.65868	−	54.7771i	0.327272	−	1.85605i
$872$	−14.0133	+	5.10042i	−0.474550	+	0.172722i
$873$	−7.62304	+	2.77456i	−0.258001	+	0.0939046i
$874$	−6.77997	−	11.7432i	−0.229336	−	0.397221i
$875$	0.0216277	+	0.122657i	0.000731151	+	0.00414656i
$876$	−2.22476	−	1.86679i	−0.0751675	−	0.0630731i
$877$	20.1289	−	34.8643i	0.679705	−	1.17728i	−0.295365	−	0.955385i	$-0.595441\pi$
$877$	20.1289	−	34.8643i	0.679705	−	1.17728i	0.975070	−	0.221899i	$-0.0712255\pi$
$878$	−4.15981	−	7.20501i	−0.140387	−	0.243157i
$879$	1.05675	−	5.99311i	0.0356432	−	0.202143i
$880$	−1.69168	+	2.93008i	−0.0570266	+	0.0987729i
$881$	−12.3907	−	4.50986i	−0.417454	−	0.151941i	0.124749	−	0.992188i	$-0.460187\pi$
$881$	−12.3907	−	4.50986i	−0.417454	−	0.151941i	−0.542203	+	0.840247i	$0.682410\pi$
$882$	18.2192			0.613472
$883$	−11.9714	−	4.35723i	−0.402870	−	0.146633i	0.132635	−	0.991165i	$-0.457656\pi$
$883$	−11.9714	−	4.35723i	−0.402870	−	0.146633i	−0.535504	+	0.844532i	$0.679878\pi$
$884$	5.56757	+	31.5753i	0.187258	+	1.06199i
$885$	1.25974	−	1.05705i	0.0423459	−	0.0355324i
$886$	−12.1181	−	10.1683i	−0.407116	−	0.341611i
$887$	−9.55721			−0.320900			−0.160450	−	0.987044i	$-0.551294\pi$
$887$	−9.55721			−0.320900			−0.160450	+	0.987044i	$0.551294\pi$
$888$	2.68253	−	2.69977i	0.0900200	−	0.0905985i
$889$	2.58192			0.0865947
$890$	4.07610	+	3.42025i	0.136631	+	0.114647i
$891$	−14.5917	+	12.2439i	−0.488840	+	0.410186i
$892$	−0.235766	−	1.33709i	−0.00789402	−	0.0447692i
$893$	27.5337	+	10.0214i	0.921380	+	0.335355i
$894$	−10.3369			−0.345718
$895$	21.5533	+	7.84476i	0.720447	+	0.262221i
$896$	0.0622746	−	0.107863i	0.00208045	−	0.00360344i
$897$	2.12603	−	12.0573i	0.0709862	−	0.402582i
$898$	0.684780	+	1.18607i	0.0228514	+	0.0395798i
$899$	12.9081	−	22.3575i	0.430510	−	0.745665i
$900$	−1.99824	−	1.67672i	−0.0666081	−	0.0558908i
$901$	5.39490	+	30.5960i	0.179730	+	1.01930i
$902$	−8.41310	−	14.5719i	−0.280126	−	0.485192i
$903$	0.380364	−	0.138441i	0.0126577	−	0.00460704i
$904$	−15.1189	+	5.50284i	−0.502848	+	0.183022i
$905$	−0.841836	+	4.77429i	−0.0279836	+	0.158703i
$906$	0.683379	−	0.573423i	0.0227037	−	0.0190507i
$907$	24.9757	−	20.9571i	0.829304	−	0.695869i	−0.125827	−	0.992052i	$-0.540158\pi$
$907$	24.9757	−	20.9571i	0.829304	−	0.695869i	0.955131	+	0.296183i	$0.0957139\pi$
$908$	−0.657656	+	3.72975i	−0.0218251	+	0.123776i
$909$	34.3117	−	12.4884i	1.13805	−	0.414215i
$910$	−0.789644	+	0.287407i	−0.0261765	+	0.00952745i
$911$	19.0077	+	32.9223i	0.629752	+	1.09076i	0.987601	+	0.156984i	$0.0501770\pi$
$911$	19.0077	+	32.9223i	0.629752	+	1.09076i	−0.357849	+	0.933780i	$0.616490\pi$
$912$	0.507975	+	2.88087i	0.0168207	+	0.0953952i
$913$	17.5108	+	14.6933i	0.579523	+	0.486277i
$914$	−13.2053	+	22.8723i	−0.436794	+	0.756549i
$915$	−2.33838	−	4.05020i	−0.0773046	−	0.133896i
$916$	2.83508	−	16.0786i	0.0936738	−	0.531250i
$917$	1.05240	−	1.82281i	0.0347533	−	0.0601944i
$918$	15.6704	+	5.70356i	0.517200	+	0.188245i
$919$	56.4046			1.86062			0.930308	−	0.366778i	$-0.119539\pi$
$919$	56.4046			1.86062			0.930308	+	0.366778i	$0.119539\pi$
$920$	2.72537	+	0.991954i	0.0898529	+	0.0327038i
$921$	−1.23683	−	7.01443i	−0.0407550	−	0.231133i
$922$	2.42309	−	2.03321i	0.0798001	−	0.0669602i
$923$	70.9047	+	59.4961i	2.33386	+	1.95834i
$924$	0.263660			0.00867378
$925$	0.510737	−	6.06128i	0.0167929	−	0.199294i
$926$	−13.9752			−0.459255
$927$	−9.02747	−	7.57495i	−0.296501	−	0.248794i
$928$	2.35641	−	1.97726i	0.0773530	−	0.0649068i
$929$	−4.50312	−	25.5385i	−0.147743	−	0.837891i	−0.965124	−	0.261793i	$-0.915686\pi$
$929$	−4.50312	−	25.5385i	−0.147743	−	0.837891i	0.817381	−	0.576097i	$-0.195425\pi$
$930$	−4.93443	−	1.79599i	−0.161806	−	0.0588927i
$931$	−32.6552			−1.07023
$932$	2.87775	+	1.04742i	0.0942639	+	0.0343093i
$933$	−2.19096	+	3.79485i	−0.0717287	+	0.124238i
$934$	3.00131	−	17.0213i	0.0982060	−	0.556954i
$935$	−8.03914	−	13.9242i	−0.262908	−	0.455370i
$936$	8.79972	−	15.2416i	0.287628	−	0.498186i
$937$	−22.3717	−	18.7721i	−0.730852	−	0.613257i	0.199512	−	0.979895i	$-0.436064\pi$
$937$	−22.3717	−	18.7721i	−0.730852	−	0.613257i	−0.930364	+	0.366638i	$0.880509\pi$
$938$	−0.178301	−	1.01120i	−0.00582173	−	0.0330167i
$939$	−7.55502	−	13.0857i	−0.246549	−	0.427035i
$940$	−5.88907	+	2.14345i	−0.192080	+	0.0699115i
$941$	−10.1298	+	3.68695i	−0.330222	+	0.120191i	−0.501810	−	0.864978i	$-0.667332\pi$
$941$	−10.1298	+	3.68695i	−0.330222	+	0.120191i	0.171588	+	0.985169i	$0.445110\pi$
$942$	−2.11345	+	11.9859i	−0.0688598	+	0.390523i
$943$	−11.0492	+	9.27139i	−0.359812	+	0.301918i
$944$	−2.01339	+	1.68943i	−0.0655302	+	0.0549864i
$945$	−0.0758952	+	0.430423i	−0.00246887	+	0.0140017i
$946$	16.5140	−	6.01061i	0.536917	−	0.195422i
$947$	−22.5946	+	8.22377i	−0.734227	+	0.267237i	−0.681953	−	0.731396i	$-0.738869\pi$
$947$	−22.5946	+	8.22377i	−0.734227	+	0.267237i	−0.0522738	+	0.998633i	$0.516647\pi$
$948$	−3.51173	−	6.08250i	−0.114056	−	0.197550i
$949$	−5.43812	−	30.8411i	−0.176529	−	1.00114i
$950$	3.58155	+	3.00528i	0.116201	+	0.0975042i
$951$	2.49823	−	4.32707i	0.0810108	−	0.140315i
$952$	0.295939	+	0.512581i	0.00959143	+	0.0166128i
$953$	1.26766	−	7.18923i	0.0410634	−	0.232882i	−0.957368	−	0.288871i	$-0.906720\pi$
$953$	1.26766	−	7.18923i	0.0410634	−	0.232882i	0.998431	+	0.0559891i	$0.0178312\pi$
$954$	8.52681	−	14.7689i	0.276066	−	0.478160i
$955$	19.6270	+	7.14364i	0.635115	+	0.231163i
$956$	−21.4812			−0.694753
$957$	6.11908	+	2.22716i	0.197802	+	0.0719940i
$958$	2.11995	+	12.0228i	0.0684924	+	0.388440i
$959$	−0.770084	+	0.646177i	−0.0248673	+	0.0208661i
$960$	−0.479302	−	0.402182i	−0.0154694	−	0.0129804i
$961$	39.4356			1.27212
$962$	40.8720	−	3.70779i	1.31777	−	0.119544i
$963$	2.15192			0.0693448
$964$	−10.1594	−	8.52472i	−0.327211	−	0.274563i
$965$	1.81006	−	1.51882i	0.0582679	−	0.0488926i
$966$	−0.0392470	−	0.222581i	−0.00126275	−	0.00716141i
$967$	12.8894	+	4.69135i	0.414494	+	0.150864i	0.540845	−	0.841122i	$-0.318104\pi$
$967$	12.8894	+	4.69135i	0.414494	+	0.150864i	−0.126351	+	0.991986i	$0.540327\pi$
$968$	0.447138			0.0143716
$969$	−13.0632	−	4.75461i	−0.419650	−	0.152740i
$970$	−1.55496	+	2.69326i	−0.0499266	+	0.0864754i
$971$	2.07903	−	11.7908i	0.0667193	−	0.378384i	−0.933104	−	0.359606i	$-0.882911\pi$
$971$	2.07903	−	11.7908i	0.0667193	−	0.378384i	0.999824	−	0.0187784i	$-0.00597769\pi$
$972$	−7.02502	−	12.1677i	−0.225328	−	0.390279i
$973$	0.0668052	−	0.115710i	0.00214168	−	0.00370949i
$974$	17.9491	+	15.0611i	0.575126	+	0.482588i
$975$	0.733044	+	4.15730i	0.0234762	+	0.133140i
$976$	3.73733	+	6.47324i	0.119629	+	0.207203i
$977$	−38.0285	+	13.8413i	−1.21664	+	0.442821i	−0.869002	−	0.494808i	$-0.835238\pi$
$977$	−38.0285	+	13.8413i	−1.21664	+	0.442821i	−0.347638	+	0.937629i	$0.613016\pi$
$978$	−7.82215	+	2.84703i	−0.250125	+	0.0910380i
$979$	3.12614	−	17.7292i	0.0999120	−	0.566629i
$980$	5.35043	−	4.48954i	0.170913	−	0.143413i
$981$	−29.7991	+	25.0044i	−0.951411	+	0.798328i
$982$	−6.69830	+	37.9879i	−0.213751	+	1.21224i
$983$	22.4172	−	8.15919i	0.714998	−	0.260238i	0.0411970	−	0.999151i	$-0.486883\pi$
$983$	22.4172	−	8.15919i	0.714998	−	0.260238i	0.673801	+	0.738913i	$0.264661\pi$
$984$	2.92401	−	1.06425i	0.0932139	−	0.0339271i
$985$	10.9279	+	18.9277i	0.348192	+	0.603087i
$986$	2.53839	+	14.3959i	0.0808388	+	0.458459i
$987$	0.374120	+	0.313924i	0.0119084	+	0.00999230i
$988$	−15.7722	+	27.3183i	−0.501781	+	0.869110i
$989$	−7.53231	−	13.0463i	−0.239514	−	0.414850i
$990$	−1.53254	+	8.69149i	−0.0487074	+	0.276234i
$991$	29.6351	−	51.3295i	0.941390	−	1.63054i	0.178569	−	0.983927i	$-0.442853\pi$
$991$	29.6351	−	51.3295i	0.941390	−	1.63054i	0.762822	−	0.646609i	$-0.223813\pi$
$992$	7.88646	+	2.87044i	0.250395	+	0.0911364i
$993$	−2.46292			−0.0781585
$994$	1.60562	+	0.584399i	0.0509272	+	0.0185360i
$995$	1.78318	+	10.1129i	0.0565307	+	0.320602i
$996$	−3.23826	+	2.71723i	−0.102608	+	0.0860986i
$997$	32.0897	+	26.9264i	1.01629	+	0.852768i	0.989157	−	0.146863i	$-0.0469178\pi$
$997$	32.0897	+	26.9264i	1.01629	+	0.852768i	0.0271330	+	0.999632i	$0.491362\pi$
$998$	22.2515			0.704359
$999$	8.95894	−	19.3743i	0.283448	−	0.612975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.d.71.3	✓	24
37.12	even	9	inner	370.2.o.d.271.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.d.71.3	✓	24	1.1	even	1	trivial
370.2.o.d.271.3	yes	24	37.12	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.479302 - 0.402182i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{5} +0.625684 q^{6} +(0.117038 + 0.0425983i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.452965 + 2.56889i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.479302 - 0.402182i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{5} +0.625684 q^{6} +(0.117038 + 0.0425983i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.452965 + 2.56889i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.69168 - 2.93008i) q^{11} +(0.479302 + 0.402182i) q^{12} +(1.17159 + 6.64441i) q^{13} +(0.0622746 + 0.107863i) q^{14} +(0.587950 - 0.213996i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.825204 - 4.67996i) q^{17} +(-1.99824 + 1.67672i) q^{18} +(3.58155 - 3.00528i) q^{19} +(-0.173648 + 0.984808i) q^{20} +(0.0732287 - 0.0266531i) q^{21} +(3.17932 - 1.15718i) q^{22} +(-1.45014 - 2.51172i) q^{23} +(0.108649 + 0.616178i) q^{24} +(0.766044 + 0.642788i) q^{25} +(-3.37345 + 5.84299i) q^{26} +(1.75458 + 3.03902i) q^{27} +(-0.0216277 + 0.122657i) q^{28} +(-1.53804 + 2.66396i) q^{29} +(0.587950 + 0.213996i) q^{30} -8.39259 q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.367598 - 2.08475i) q^{33} +(3.64036 - 3.05463i) q^{34} +(0.0954102 + 0.0800587i) q^{35} -2.60852 q^{36} +(-3.50487 - 4.97151i) q^{37} +4.67539 q^{38} +(3.23380 + 2.71348i) q^{39} +(-0.766044 + 0.642788i) q^{40} +(-0.863590 - 4.89766i) q^{41} +(0.0732287 + 0.0266531i) q^{42} +5.19420 q^{43} +(3.17932 + 1.15718i) q^{44} +(-1.30426 + 2.25904i) q^{45} +(0.503628 - 2.85622i) q^{46} +(3.13351 + 5.42740i) q^{47} +(-0.312842 + 0.541858i) q^{48} +(-5.35043 - 4.48954i) q^{49} +(0.173648 + 0.984808i) q^{50} +(-1.48667 - 2.57500i) q^{51} +(-6.34002 + 2.30758i) q^{52} +(-6.14339 + 2.23601i) q^{53} +(-0.609359 + 3.45585i) q^{54} +(2.59181 - 2.17478i) q^{55} +(-0.0954102 + 0.0800587i) q^{56} +(0.507975 - 2.88087i) q^{57} +(-2.89057 + 1.05208i) q^{58} +(2.46979 - 0.898929i) q^{59} +(0.312842 + 0.541858i) q^{60} +(-1.29796 - 7.36110i) q^{61} +(-6.42910 - 5.39466i) q^{62} +(-0.162445 + 0.281362i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.17159 + 6.64441i) q^{65} +(1.05846 - 1.83330i) q^{66} +(-7.74691 - 2.81964i) q^{67} +4.75216 q^{68} +(-1.70522 - 0.620650i) q^{69} +(0.0216277 + 0.122657i) q^{70} +(10.5092 - 8.81828i) q^{71} +(-1.99824 - 1.67672i) q^{72} -4.64166 q^{73} +(0.510737 - 6.06128i) q^{74} +0.625684 q^{75} +(3.58155 + 3.00528i) q^{76} +(0.322807 - 0.270867i) q^{77} +(0.733044 + 4.15730i) q^{78} +(-10.5483 - 3.83926i) q^{79} -1.00000 q^{80} +(-5.29041 - 1.92555i) q^{81} +(2.48661 - 4.30693i) q^{82} +(-1.17320 + 6.65357i) q^{83} +(0.0389642 + 0.0674880i) q^{84} +(2.37608 - 4.11549i) q^{85} +(3.97899 + 3.33876i) q^{86} +(0.334212 + 1.89541i) q^{87} +(1.69168 + 2.93008i) q^{88} +(5.00007 - 1.81988i) q^{89} +(-2.45121 + 0.892166i) q^{90} +(-0.145920 + 0.827555i) q^{91} +(2.22174 - 1.86426i) q^{92} +(-4.02258 + 3.37535i) q^{93} +(-1.08826 + 6.17181i) q^{94} +(4.39343 - 1.59908i) q^{95} +(-0.587950 + 0.213996i) q^{96} +(1.55496 + 2.69326i) q^{97} +(-1.21284 - 6.87838i) q^{98} +(6.76078 + 5.67297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9	\( 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9} + 12 q^{10} - 3 q^{11} - 3 q^{14} + 6 q^{17} - 6 q^{18} - 18 q^{19} + 18 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 12 q^{27} + 9 q^{28} - 18 q^{29} - 6 q^{31} - 45 q^{33} - 3 q^{34} + 30 q^{36} - 18 q^{37} - 24 q^{38} + 12 q^{39} + 3 q^{41} + 18 q^{42} + 3 q^{44} + 15 q^{45} + 9 q^{46} - 36 q^{47} - 3 q^{48} - 15 q^{49} + 54 q^{51} - 9 q^{52} - 6 q^{53} + 45 q^{54} - 3 q^{55} + 3 q^{57} - 15 q^{58} - 9 q^{59} + 3 q^{60} - 24 q^{61} + 81 q^{62} - 45 q^{63} - 12 q^{64} - 3 q^{66} + 12 q^{67} + 12 q^{68} + 60 q^{69} - 9 q^{70} + 42 q^{71} - 6 q^{72} - 42 q^{73} + 12 q^{74} + 6 q^{75} - 18 q^{76} + 9 q^{77} + 30 q^{78} - 6 q^{79} - 24 q^{80} - 66 q^{81} - 24 q^{82} - 3 q^{83} - 42 q^{84} + 6 q^{85} - 18 q^{86} - 84 q^{87} - 3 q^{88} + 27 q^{89} + 6 q^{90} + 153 q^{91} - 9 q^{92} - 54 q^{93} - 21 q^{94} - 9 q^{95} - 9 q^{97} - 24 q^{98} + 165 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9 + 12 * q^10 - 3 * q^11 - 3 * q^14 + 6 * q^17 - 6 * q^18 - 18 * q^19 + 18 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 12 * q^27 + 9 * q^28 - 18 * q^29 - 6 * q^31 - 45 * q^33 - 3 * q^34 + 30 * q^36 - 18 * q^37 - 24 * q^38 + 12 * q^39 + 3 * q^41 + 18 * q^42 + 3 * q^44 + 15 * q^45 + 9 * q^46 - 36 * q^47 - 3 * q^48 - 15 * q^49 + 54 * q^51 - 9 * q^52 - 6 * q^53 + 45 * q^54 - 3 * q^55 + 3 * q^57 - 15 * q^58 - 9 * q^59 + 3 * q^60 - 24 * q^61 + 81 * q^62 - 45 * q^63 - 12 * q^64 - 3 * q^66 + 12 * q^67 + 12 * q^68 + 60 * q^69 - 9 * q^70 + 42 * q^71 - 6 * q^72 - 42 * q^73 + 12 * q^74 + 6 * q^75 - 18 * q^76 + 9 * q^77 + 30 * q^78 - 6 * q^79 - 24 * q^80 - 66 * q^81 - 24 * q^82 - 3 * q^83 - 42 * q^84 + 6 * q^85 - 18 * q^86 - 84 * q^87 - 3 * q^88 + 27 * q^89 + 6 * q^90 + 153 * q^91 - 9 * q^92 - 54 * q^93 - 21 * q^94 - 9 * q^95 - 9 * q^97 - 24 * q^98 + 165 * q^99

Introduction

L-functions

Modular forms

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