LMFDB - Embedded newform 300.2.w.a.103.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.17
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.275181 - 1.38718i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.84855 - 0.763453i) q^{4} +(-1.17964 + 1.89959i) q^{5} +(-0.0547899 + 1.41315i) q^{6} +(-1.39751 - 1.39751i) q^{7} +(-1.56773 + 2.35419i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(0.275181 - 1.38718i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.84855 - 0.763453i) q^{4} +(-1.17964 + 1.89959i) q^{5} +(-0.0547899 + 1.41315i) q^{6} +(-1.39751 - 1.39751i) q^{7} +(-1.56773 + 2.35419i) q^{8} +(0.951057 - 0.309017i) q^{9} +(2.31047 + 2.15910i) q^{10} +(1.17837 + 0.382876i) q^{11} +(1.94522 + 0.464876i) q^{12} +(-2.63087 + 5.16338i) q^{13} +(-2.32317 + 1.55403i) q^{14} +(0.867952 - 2.06074i) q^{15} +(2.83428 + 2.82256i) q^{16} +(-0.916613 + 5.78726i) q^{17} +(-0.166950 - 1.40432i) q^{18} +(-3.68988 + 2.68086i) q^{19} +(3.63087 - 2.61090i) q^{20} +(1.59892 + 1.16169i) q^{21} +(0.855385 - 1.52926i) q^{22} +(-0.0552946 - 0.108522i) q^{23} +(1.18016 - 2.57045i) q^{24} +(-2.21691 - 4.48166i) q^{25} +(6.43858 + 5.07037i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(1.51644 + 3.65030i) q^{28} +(3.15410 - 4.34124i) q^{29} +(-2.61978 - 1.77108i) q^{30} +(-6.30517 - 8.67832i) q^{31} +(4.69535 - 3.15495i) q^{32} +(-1.22376 - 0.193825i) q^{33} +(7.77576 + 2.86405i) q^{34} +(4.30325 - 1.00615i) q^{35} +(-1.99400 - 0.154853i) q^{36} +(-3.90325 - 1.98881i) q^{37} +(2.70345 + 5.85626i) q^{38} +(1.79075 - 5.51137i) q^{39} +(-2.62265 - 5.75515i) q^{40} +(1.88978 + 5.81615i) q^{41} +(2.05146 - 1.89832i) q^{42} +(-6.87625 + 6.87625i) q^{43} +(-1.88597 - 1.60740i) q^{44} +(-0.534894 + 2.17115i) q^{45} +(-0.165756 + 0.0468406i) q^{46} +(-0.721759 - 4.55701i) q^{47} +(-3.24093 - 2.34443i) q^{48} -3.09393i q^{49} +(-6.82694 + 1.84200i) q^{50} -5.85940i q^{51} +(8.80530 - 7.53622i) q^{52} +(0.00324925 + 0.0205149i) q^{53} +(0.384580 + 1.36092i) q^{54} +(-2.11736 + 1.78677i) q^{55} +(5.48093 - 1.09908i) q^{56} +(3.22508 - 3.22508i) q^{57} +(-5.15414 - 5.56993i) q^{58} +(2.84365 + 8.75185i) q^{59} +(-3.17773 + 3.14675i) q^{60} +(0.217081 - 0.668108i) q^{61} +(-13.7735 + 6.35831i) q^{62} +(-1.76096 - 0.897256i) q^{63} +(-3.08442 - 7.38149i) q^{64} +(-6.70485 - 11.0885i) q^{65} +(-0.605625 + 1.64424i) q^{66} +(7.05089 + 1.11675i) q^{67} +(6.11271 - 9.99826i) q^{68} +(0.0715904 + 0.0985357i) q^{69} +(-0.211536 - 6.24627i) q^{70} +(-4.63594 + 6.38083i) q^{71} +(-0.763519 + 2.72342i) q^{72} +(-4.73873 + 2.41450i) q^{73} +(-3.83294 + 4.86724i) q^{74} +(2.89071 + 4.07968i) q^{75} +(8.86765 - 2.13865i) q^{76} +(-1.11171 - 2.18186i) q^{77} +(-7.15249 - 4.00072i) q^{78} +(10.1840 + 7.39910i) q^{79} +(-8.70514 + 2.05438i) q^{80} +(0.809017 - 0.587785i) q^{81} +(8.58809 - 1.02098i) q^{82} +(-0.455567 + 2.87634i) q^{83} +(-2.06880 - 3.36814i) q^{84} +(-9.91218 - 8.56806i) q^{85} +(7.64640 + 11.4308i) q^{86} +(-2.43614 + 4.78120i) q^{87} +(-2.74874 + 2.17386i) q^{88} +(9.16320 + 2.97730i) q^{89} +(2.86459 + 1.33946i) q^{90} +(10.8925 - 3.53920i) q^{91} +(0.0193637 + 0.242823i) q^{92} +(7.58513 + 7.58513i) q^{93} +(-6.52001 - 0.252790i) q^{94} +(-0.739818 - 10.1717i) q^{95} +(-4.14400 + 3.85062i) q^{96} +(-7.28707 + 1.15416i) q^{97} +(-4.29185 - 0.851392i) q^{98} +1.23901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	0.275181	−	1.38718i	0.194582	−	0.980886i
$2$	0.275181	−	1.38718i	0.194582	−	0.980886i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$4$	−1.84855	−	0.763453i	−0.924275	−	0.381726i
$5$	−1.17964	+	1.89959i	−0.527550	+	0.849524i
$5$	−1.17964	+	1.89959i	−0.527550	+	0.849524i
$6$	−0.0547899	+	1.41315i	−0.0223679	+	0.576917i
$7$	−1.39751	−	1.39751i	−0.528209	−	0.528209i	0.391829	−	0.920038i	$-0.371842\pi$
$7$	−1.39751	−	1.39751i	−0.528209	−	0.528209i	−0.920038	+	0.391829i	$0.871842\pi$
$8$	−1.56773	+	2.35419i	−0.554278	+	0.832332i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	2.31047	+	2.15910i	0.730635	+	0.682769i
$11$	1.17837	+	0.382876i	0.355293	+	0.115442i	0.481225	−	0.876597i	$-0.340192\pi$
$11$	1.17837	+	0.382876i	0.355293	+	0.115442i	−0.125932	+	0.992039i	$0.540192\pi$
$12$	1.94522	+	0.464876i	0.561537	+	0.134198i
$13$	−2.63087	+	5.16338i	−0.729673	+	1.43206i	0.165438	+	0.986220i	$0.447096\pi$
$13$	−2.63087	+	5.16338i	−0.729673	+	1.43206i	−0.895111	+	0.445844i	$0.852904\pi$
$14$	−2.32317	+	1.55403i	−0.620893	+	0.415333i
$15$	0.867952	−	2.06074i	0.224104	−	0.532081i
$16$	2.83428	+	2.82256i	0.708570	+	0.705640i
$17$	−0.916613	+	5.78726i	−0.222311	+	1.40362i	0.583821	+	0.811882i	$0.301557\pi$
$17$	−0.916613	+	5.78726i	−0.222311	+	1.40362i	−0.806132	+	0.591735i	$0.798443\pi$
$18$	−0.166950	−	1.40432i	−0.0393506	−	0.331002i
$19$	−3.68988	+	2.68086i	−0.846518	+	0.615031i	−0.924184	−	0.381948i	$-0.875253\pi$
$19$	−3.68988	+	2.68086i	−0.846518	+	0.615031i	0.0776661	+	0.996979i	$0.475253\pi$
$20$	3.63087	−	2.61090i	0.811887	−	0.583815i
$21$	1.59892	+	1.16169i	0.348914	+	0.253501i
$22$	0.855385	−	1.52926i	0.182369	−	0.326039i
$23$	−0.0552946	−	0.108522i	−0.0115297	−	0.0226284i	0.885170	−	0.465268i	$-0.154042\pi$
$23$	−0.0552946	−	0.108522i	−0.0115297	−	0.0226284i	−0.896700	+	0.442640i	$0.854042\pi$
$24$	1.18016	−	2.57045i	0.240898	−	0.524692i
$25$	−2.21691	−	4.48166i	−0.443383	−	0.896332i
$26$	6.43858	+	5.07037i	1.26271	+	0.994380i
$27$	−0.891007	+	0.453990i	−0.171474	+	0.0873705i
$28$	1.51644	+	3.65030i	0.286579	+	0.689842i
$29$	3.15410	−	4.34124i	0.585701	−	0.806148i	−0.408605	−	0.912711i	$-0.633985\pi$
$29$	3.15410	−	4.34124i	0.585701	−	0.806148i	0.994306	+	0.106563i	$0.0339847\pi$
$30$	−2.61978	−	1.77108i	−0.478305	−	0.323354i
$31$	−6.30517	−	8.67832i	−1.13244	−	1.55867i	−0.783348	−	0.621583i	$-0.786490\pi$
$31$	−6.30517	−	8.67832i	−1.13244	−	1.55867i	−0.349093	−	0.937088i	$-0.613510\pi$
$32$	4.69535	−	3.15495i	0.830028	−	0.557721i
$33$	−1.22376	−	0.193825i	−0.213029	−	0.0337405i
$34$	7.77576	+	2.86405i	1.33353	+	0.491181i
$35$	4.30325	−	1.00615i	0.727383	−	0.170070i
$36$	−1.99400	−	0.154853i	−0.332333	−	0.0258088i
$37$	−3.90325	−	1.98881i	−0.641691	−	0.326958i	0.102690	−	0.994713i	$-0.467255\pi$
$37$	−3.90325	−	1.98881i	−0.641691	−	0.326958i	−0.744381	+	0.667756i	$0.767255\pi$
$38$	2.70345	+	5.85626i	0.438558	+	0.950012i
$39$	1.79075	−	5.51137i	0.286750	−	0.882525i
$40$	−2.62265	−	5.75515i	−0.414677	−	0.909969i
$41$	1.88978	+	5.81615i	0.295134	+	0.908330i	0.983176	+	0.182659i	$0.0584704\pi$
$41$	1.88978	+	5.81615i	0.295134	+	0.908330i	−0.688042	+	0.725671i	$0.741530\pi$
$42$	2.05146	−	1.89832i	0.316548	−	0.292918i
$43$	−6.87625	+	6.87625i	−1.04862	+	1.04862i	−0.0498626	+	0.998756i	$0.515878\pi$
$43$	−6.87625	+	6.87625i	−1.04862	+	1.04862i	−0.998756	+	0.0498626i	$0.984122\pi$
$44$	−1.88597	−	1.60740i	−0.284321	−	0.242324i
$45$	−0.534894	+	2.17115i	−0.0797374	+	0.323656i
$46$	−0.165756	+	0.0468406i	−0.0244393	+	0.00690627i
$47$	−0.721759	−	4.55701i	−0.105279	−	0.664708i	−0.982731	−	0.185042i	$-0.940758\pi$
$47$	−0.721759	−	4.55701i	−0.105279	−	0.664708i	0.877451	−	0.479666i	$-0.159242\pi$
$48$	−3.24093	−	2.34443i	−0.467788	−	0.338390i
$49$		−	3.09393i		−	0.441990i
$50$	−6.82694	+	1.84200i	−0.965474	+	0.260498i
$51$		−	5.85940i		−	0.820481i
$52$	8.80530	−	7.53622i	1.22108	−	1.04509i
$53$	0.00324925	+	0.0205149i	0.000446318	+	0.00281794i	0.987910	−	0.155025i	$-0.0495459\pi$
$53$	0.00324925	+	0.0205149i	0.000446318	+	0.00281794i	−0.987464	+	0.157843i	$0.949546\pi$
$54$	0.384580	+	1.36092i	0.0523347	+	0.185198i
$55$	−2.11736	+	1.78677i	−0.285505	+	0.240929i
$56$	5.48093	−	1.09908i	0.732420	−	0.146871i
$57$	3.22508	−	3.22508i	0.427172	−	0.427172i
$58$	−5.15414	−	5.56993i	−0.676772	−	0.731368i
$59$	2.84365	+	8.75185i	0.370212	+	1.13939i	0.946653	+	0.322255i	$0.104441\pi$
$59$	2.84365	+	8.75185i	0.370212	+	1.13939i	−0.576441	+	0.817139i	$0.695559\pi$
$60$	−3.17773	+	3.14675i	−0.410243	+	0.406243i
$61$	0.217081	−	0.668108i	0.0277944	−	0.0855424i	−0.936197	−	0.351476i	$-0.885680\pi$
$61$	0.217081	−	0.668108i	0.0277944	−	0.0855424i	0.963991	+	0.265933i	$0.0856800\pi$
$62$	−13.7735	+	6.35831i	−1.74923	+	0.807506i
$63$	−1.76096	−	0.897256i	−0.221861	−	0.113044i
$64$	−3.08442	−	7.38149i	−0.385552	−	0.922686i
$65$	−6.70485	−	11.0885i	−0.831634	−	1.37536i
$66$	−0.605625	+	1.64424i	−0.0745473	+	0.202392i
$67$	7.05089	+	1.11675i	0.861403	+	0.136433i	0.571479	−	0.820617i	$-0.306370\pi$
$67$	7.05089	+	1.11675i	0.861403	+	0.136433i	0.289924	+	0.957050i	$0.406370\pi$
$68$	6.11271	−	9.99826i	0.741275	−	1.21247i
$69$	0.0715904	+	0.0985357i	0.00861847	+	0.0118623i
$70$	−0.211536	−	6.24627i	−0.0252834	−	0.746572i
$71$	−4.63594	+	6.38083i	−0.550185	+	0.757265i	−0.990037	−	0.140805i	$-0.955031\pi$
$71$	−4.63594	+	6.38083i	−0.550185	+	0.757265i	0.439852	+	0.898070i	$0.355031\pi$
$72$	−0.763519	+	2.72342i	−0.0899816	+	0.320959i
$73$	−4.73873	+	2.41450i	−0.554626	+	0.282596i	−0.708755	−	0.705455i	$-0.750743\pi$
$73$	−4.73873	+	2.41450i	−0.554626	+	0.282596i	0.154129	+	0.988051i	$0.450743\pi$
$74$	−3.83294	+	4.86724i	−0.445570	+	0.565805i
$75$	2.89071	+	4.07968i	0.333790	+	0.471081i
$76$	8.86765	−	2.13865i	1.01719	−	0.245320i
$77$	−1.11171	−	2.18186i	−0.126692	−	0.248646i
$78$	−7.15249	−	4.00072i	−0.809860	−	0.452993i
$79$	10.1840	+	7.39910i	1.14579	+	0.832463i	0.987915	−	0.154996i	$-0.0495365\pi$
$79$	10.1840	+	7.39910i	1.14579	+	0.832463i	0.157872	+	0.987460i	$0.449537\pi$
$80$	−8.70514	+	2.05438i	−0.973265	+	0.229687i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	8.58809	−	1.02098i	0.948396	−	0.112748i
$83$	−0.455567	+	2.87634i	−0.0500050	+	0.315719i	0.949989	+	0.312283i	$0.101094\pi$
$83$	−0.455567	+	2.87634i	−0.0500050	+	0.315719i	−0.999994	+	0.00343616i	$0.998906\pi$
$84$	−2.06880	−	3.36814i	−0.225724	−	0.367494i
$85$	−9.91218	−	8.56806i	−1.07513	−	0.929337i
$86$	7.64640	+	11.4308i	0.824533	+	1.23262i
$87$	−2.43614	+	4.78120i	−0.261182	+	0.512599i
$88$	−2.74874	+	2.17386i	−0.293017	+	0.231735i
$89$	9.16320	+	2.97730i	0.971297	+	0.315594i	0.751340	−	0.659916i	$-0.229408\pi$
$89$	9.16320	+	2.97730i	0.971297	+	0.315594i	0.219958	+	0.975509i	$0.429408\pi$
$90$	2.86459	+	1.33946i	0.301954	+	0.141191i
$91$	10.8925	−	3.53920i	1.14185	−	0.371009i
$92$	0.0193637	+	0.242823i	0.00201880	+	0.0253160i
$93$	7.58513	+	7.58513i	0.786541	+	0.786541i
$94$	−6.52001	−	0.252790i	−0.672488	−	0.0260733i
$95$	−0.739818	−	10.1717i	−0.0759037	−	1.04360i
$96$	−4.14400	+	3.85062i	−0.422945	+	0.393002i
$97$	−7.28707	+	1.15416i	−0.739890	+	0.117187i	−0.514992	−	0.857195i	$-0.672205\pi$
$97$	−7.28707	+	1.15416i	−0.739890	+	0.117187i	−0.224898	+	0.974382i	$0.572205\pi$
$98$	−4.29185	−	0.851392i	−0.433542	−	0.0860035i
$99$	1.23901			0.124526
$100$	0.676542	+	9.97709i	0.0676542	+	0.997709i
$101$	−5.34748			−0.532094			−0.266047	−	0.963960i	$-0.585718\pi$
$101$	−5.34748			−0.532094			−0.266047	+	0.963960i	$0.585718\pi$
$102$	−8.12806	−	1.61240i	−0.804798	−	0.159651i
$103$	−1.35980	+	0.215371i	−0.133985	+	0.0212212i	−0.223067	−	0.974803i	$-0.571607\pi$
$103$	−1.35980	+	0.215371i	−0.133985	+	0.0212212i	0.0890816	+	0.996024i	$0.471607\pi$
$104$	−8.03107	−	14.2884i	−0.787511	−	1.40109i
$105$	−4.09288	+	1.66694i	−0.399424	+	0.162676i
$106$	0.0293521	+	0.00113802i	0.00285093	+	0.000110534i
$107$	−4.98173	−	4.98173i	−0.481602	−	0.481602i	0.424041	−	0.905643i	$-0.360611\pi$
$107$	−4.98173	−	4.98173i	−0.481602	−	0.481602i	−0.905643	+	0.424041i	$0.860611\pi$
$108$	1.99367	−	0.158983i	0.191841	−	0.0152982i
$109$	17.6116	−	5.72235i	1.68688	−	0.548102i	0.700657	−	0.713499i	$-0.252890\pi$
$109$	17.6116	−	5.72235i	1.68688	−	0.548102i	0.986227	+	0.165397i	$0.0528905\pi$
$110$	1.89592	+	3.42885i	0.180769	+	0.326928i
$111$	4.16632	+	1.35372i	0.395449	+	0.128489i
$112$	−0.0163767	−	7.90549i	−0.00154746	−	0.746999i
$113$	3.70475	−	7.27098i	0.348514	−	0.683997i	−0.648501	−	0.761214i	$-0.724604\pi$
$113$	3.70475	−	7.27098i	0.348514	−	0.683997i	0.997014	+	0.0772176i	$0.0246036\pi$
$114$	−3.58629	−	5.36125i	−0.335887	−	0.502127i
$115$	0.271375	+	0.0229790i	0.0253058	+	0.00214280i
$116$	−9.14484	+	5.61700i	−0.849077	+	0.521525i
$117$	−0.906537	+	5.72365i	−0.0838094	+	0.529152i
$118$	12.9229	−	1.53632i	1.18965	−	0.141429i
$119$	9.36873	−	6.80678i	0.858830	−	0.623977i
$120$	3.49066	+	5.27402i	0.318652	+	0.481450i
$121$	−7.65722	−	5.56330i	−0.696111	−	0.505754i
$122$	−0.867051	−	0.484982i	−0.0784991	−	0.0439082i
$123$	−2.77636	−	5.44892i	−0.250336	−	0.491312i
$124$	5.02994	+	20.8560i	0.451702	+	1.87292i
$125$	11.1285	+	1.07550i	0.995362	+	0.0961953i
$126$	−1.72924	+	2.19587i	−0.154053	+	0.195624i
$127$	−5.50456	+	2.80471i	−0.488450	+	0.248878i	−0.680828	−	0.732443i	$-0.738380\pi$
$127$	−5.50456	+	2.80471i	−0.488450	+	0.248878i	0.192378	+	0.981321i	$0.438380\pi$
$128$	−11.0882	+	2.24741i	−0.980072	+	0.198645i
$129$	5.71591	−	7.86728i	0.503258	−	0.692675i
$130$	−17.2268	+	6.24950i	−1.51089	+	0.548118i
$131$	1.66608	+	2.29316i	0.145566	+	0.200354i	0.875574	−	0.483085i	$-0.160484\pi$
$131$	1.66608	+	2.29316i	0.145566	+	0.200354i	−0.730008	+	0.683439i	$0.760484\pi$
$132$	2.11421	+	1.29258i	0.184018	+	0.112504i
$133$	8.90317	+	1.41012i	0.772003	+	0.122273i
$134$	3.48941	−	9.47356i	0.301439	−	0.818391i
$135$	0.188666	−	2.22809i	0.0162378	−	0.191764i
$136$	−12.1873	−	11.2308i	−1.04505	−	0.963031i
$137$	7.68229	+	3.91432i	0.656342	+	0.334423i	0.750246	−	0.661158i	$-0.229935\pi$
$137$	7.68229	+	3.91432i	0.656342	+	0.334423i	−0.0939045	+	0.995581i	$0.529935\pi$
$138$	0.156387	−	0.0721938i	0.0133126	−	0.00614554i
$139$	−3.17990	+	9.78673i	−0.269716	+	0.830100i	0.720854	+	0.693087i	$0.243750\pi$
$139$	−3.17990	+	9.78673i	−0.269716	+	0.830100i	−0.990569	+	0.137012i	$0.956250\pi$
$140$	−8.72293	−	1.42542i	−0.737222	−	0.120470i
$141$	1.42575	+	4.38799i	0.120069	+	0.369536i
$142$	7.57565	+	8.18678i	0.635734	+	0.687019i
$143$	−5.07708	+	5.07708i	−0.424567	+	0.424567i
$144$	3.56778	+	1.80858i	0.297315	+	0.150715i
$145$	4.52591	+	11.1126i	0.375856	+	0.922850i
$146$	2.04535	+	7.23790i	0.169274	+	0.599013i
$147$	0.483998	+	3.05584i	0.0399195	+	0.252042i
$148$	5.69700	+	6.65636i	0.468291	+	0.547149i
$149$			21.2963i			1.74466i	0.488914	+	0.872332i	$0.337393\pi$
$149$			21.2963i			1.74466i	−0.488914	+	0.872332i	$0.662607\pi$
$150$	6.45473	−	2.88729i	0.527027	−	0.235746i
$151$		−	3.72566i		−	0.303190i	−0.988443	−	0.151595i	$-0.951559\pi$
$151$		−	3.72566i		−	0.303190i	0.988443	−	0.151595i	$-0.0484409\pi$
$152$	−0.526490	−	12.8896i	−0.0427040	−	1.04548i
$153$	0.916613	+	5.78726i	0.0741037	+	0.467873i
$154$	−3.33256	+	0.941743i	−0.268545	+	0.0758878i
$155$	23.9231	−	1.73999i	1.92155	−	0.139760i
$156$	−7.51797	+	8.82089i	−0.601919	+	0.706236i
$157$	9.67619	−	9.67619i	0.772244	−	0.772244i	−0.206254	−	0.978498i	$-0.566127\pi$
$157$	9.67619	−	9.67619i	0.772244	−	0.772244i	0.978498	+	0.206254i	$0.0661274\pi$
$158$	13.0663	−	12.0910i	1.03950	−	0.961904i
$159$	−0.00641848	−	0.0197541i	−0.000509019	−	0.00156660i
$160$	0.454316	+	12.6409i	0.0359168	+	0.999355i
$161$	−0.0743855	+	0.228935i	−0.00586240	+	0.0180426i
$162$	−0.592739	−	1.28400i	−0.0465700	−	0.100881i
$163$	20.6862	+	10.5402i	1.62027	+	0.825569i	0.999123	+	0.0418764i	$0.0133336\pi$
$163$	20.6862	+	10.5402i	1.62027	+	0.825569i	0.621148	+	0.783693i	$0.286666\pi$
$164$	0.946997	−	12.1942i	0.0739480	−	0.952207i
$165$	1.81178	−	2.09600i	0.141047	−	0.163174i
$166$	3.86464	+	1.42347i	0.299955	+	0.110483i
$167$	−19.6135	−	3.10647i	−1.51773	−	0.240386i	−0.658740	−	0.752370i	$-0.728910\pi$
$167$	−19.6135	−	3.10647i	−1.51773	−	0.240386i	−0.858995	+	0.511985i	$0.828910\pi$
$168$	−5.24151	+	1.94295i	−0.404392	+	0.149902i
$169$	−12.0978	−	16.6512i	−0.930599	−	1.28086i
$170$	−14.6131	+	11.3922i	−1.12077	+	0.873745i
$171$	−2.68086	+	3.68988i	−0.205010	+	0.282173i
$172$	17.9608	−	7.46141i	1.36950	−	0.568927i
$173$	−0.813910	+	0.414708i	−0.0618804	+	0.0315297i	−0.484657	−	0.874704i	$-0.661056\pi$
$173$	−0.813910	+	0.414708i	−0.0618804	+	0.0315297i	0.422776	+	0.906234i	$0.361056\pi$
$174$	5.96202	+	4.69507i	0.451979	+	0.355932i
$175$	−3.16501	+	9.36132i	−0.239252	+	0.707650i
$176$	2.25915	+	4.41121i	0.170290	+	0.332507i
$177$	−4.17773	−	8.19926i	−0.314017	−	0.616294i
$178$	6.65160	−	11.8917i	0.498559	−	0.891323i
$179$	4.51834	+	3.28277i	0.337717	+	0.245366i	0.743698	−	0.668516i	$-0.233070\pi$
$179$	4.51834	+	3.28277i	0.337717	+	0.245366i	−0.405981	+	0.913882i	$0.633070\pi$
$180$	2.64635	−	3.60511i	0.197247	−	0.268709i
$181$	−4.12766	+	2.99892i	−0.306807	+	0.222908i	−0.730525	−	0.682886i	$-0.760725\pi$
$181$	−4.12766	+	2.99892i	−0.306807	+	0.222908i	0.423718	+	0.905794i	$0.360725\pi$
$182$	−1.91210	−	16.0839i	−0.141734	−	1.19222i
$183$	−0.109894	+	0.693841i	−0.00812357	+	0.0512902i
$184$	0.342168	+	0.0399593i	0.0252250	+	0.00294584i
$185$	8.38235	−	5.06853i	0.616282	−	0.372645i
$186$	12.6092	−	8.43467i	0.924554	−	0.618460i
$187$	−3.29592	+	6.46860i	−0.241021	+	0.473031i
$188$	−2.14485	+	8.97489i	−0.156429	+	0.654561i
$189$	1.87965	+	0.610734i	0.136724	+	0.0444244i
$190$	−14.3136	−	1.77280i	−1.03842	−	0.128613i
$191$	2.86970	−	0.932423i	0.207645	−	0.0674678i	−0.203348	−	0.979107i	$-0.565182\pi$
$191$	2.86970	−	0.932423i	0.207645	−	0.0674678i	0.410992	+	0.911639i	$0.365182\pi$
$192$	4.20116	+	6.80810i	0.303193	+	0.491332i
$193$	10.1768	+	10.1768i	0.732542	+	0.732542i	0.971123	−	0.238581i	$-0.0766822\pi$
$193$	10.1768	+	10.1768i	0.732542	+	0.732542i	−0.238581	+	0.971123i	$0.576682\pi$
$194$	−0.404235	+	10.4261i	−0.0290224	+	0.748550i
$195$	8.35693	+	9.90312i	0.598452	+	0.709177i
$196$	−2.36207	+	5.71929i	−0.168719	+	0.408521i
$197$	0.100082	−	0.0158515i	0.00713057	−	0.00112937i	−0.152868	−	0.988247i	$-0.548851\pi$
$197$	0.100082	−	0.0158515i	0.00713057	−	0.00112937i	0.159999	+	0.987117i	$0.448851\pi$
$198$	0.340953	−	1.71874i	0.0242305	−	0.122145i
$199$	−13.0628			−0.926000			−0.463000	−	0.886358i	$-0.653227\pi$
$199$	−13.0628			−0.926000			−0.463000	+	0.886358i	$0.653227\pi$
$200$	14.0262	+	1.80702i	0.991803	+	0.127775i
$201$	−7.13878			−0.503531
$202$	−1.47153	+	7.41793i	−0.103536	+	0.521924i
$203$	−10.4748	+	1.65905i	−0.735187	+	0.116442i
$204$	−4.47338	+	10.8314i	−0.313199	+	0.758350i
$205$	−13.2776	−	3.27113i	−0.927346	−	0.228465i
$206$	−0.0754320	+	1.94556i	−0.00525560	+	0.135553i
$207$	−0.0861234	−	0.0861234i	−0.00598599	−	0.00598599i
$208$	−22.0306	+	7.20866i	−1.52755	+	0.499831i
$209$	−5.37450	+	1.74628i	−0.371762	+	0.120793i
$210$	1.18606	+	6.13628i	0.0818462	+	0.423443i
$211$	−26.4223	−	8.58513i	−1.81899	−	0.591025i	−0.999848	−	0.0174306i	$-0.994451\pi$
$211$	−26.4223	−	8.58513i	−1.81899	−	0.591025i	−0.819140	−	0.573594i	$-0.805549\pi$
$212$	0.00965578	−	0.0404035i	0.000663162	−	0.00277493i
$213$	3.58068	−	7.02749i	0.245344	−	0.481516i
$214$	−8.28144	+	5.53969i	−0.566108	+	0.378685i
$215$	−4.95061	−	21.1736i	−0.337629	−	1.44403i
$216$	0.328082	−	2.80933i	0.0223231	−	0.191151i
$217$	−3.31650	+	20.9396i	−0.225139	+	1.42147i
$218$	−3.09157	−	26.0052i	−0.209388	−	1.76129i
$219$	4.30267	−	3.12607i	0.290748	−	0.211241i
$220$	5.27817	−	1.68644i	0.355854	−	0.113700i
$221$	−27.4703	−	19.9584i	−1.84786	−	1.34255i
$222$	3.02434	−	5.40692i	0.202981	−	0.362889i
$223$	5.31608	+	10.4334i	0.355991	+	0.698672i	0.997664	−	0.0683061i	$-0.0217595\pi$
$223$	5.31608	+	10.4334i	0.355991	+	0.698672i	−0.641673	+	0.766978i	$0.721759\pi$
$224$	−10.9709	−	2.15272i	−0.733022	−	0.143835i
$225$	−3.49332	−	3.57725i	−0.232888	−	0.238483i
$226$	−9.06670	−	7.14000i	−0.603108	−	0.474946i
$227$	7.65507	−	3.90045i	0.508085	−	0.258882i	−0.181104	−	0.983464i	$-0.557967\pi$
$227$	7.65507	−	3.90045i	0.508085	−	0.258882i	0.689189	+	0.724582i	$0.257967\pi$
$228$	−8.42391	+	3.49953i	−0.557887	+	0.231762i
$229$	−4.14701	+	5.70787i	−0.274042	+	0.377187i	−0.923749	−	0.382998i	$-0.874892\pi$
$229$	−4.14701	+	5.70787i	−0.274042	+	0.377187i	0.649707	+	0.760185i	$0.274892\pi$
$230$	0.106553	−	0.370123i	0.00702591	−	0.0244052i
$231$	1.43934	+	1.98109i	0.0947019	+	0.130346i
$232$	5.27532	+	14.2312i	0.346342	+	0.934327i
$233$	17.7542	+	2.81199i	1.16312	+	0.184220i	0.708000	−	0.706212i	$-0.249597\pi$
$233$	17.7542	+	2.81199i	1.16312	+	0.184220i	0.455117	+	0.890432i	$0.349597\pi$
$234$	7.69029	+	2.83257i	0.502730	+	0.185171i
$235$	9.50787	+	4.00456i	0.620225	+	0.261229i
$236$	1.42499	−	18.3492i	0.0927592	−	1.19443i
$237$	−11.2161	−	5.71488i	−0.728562	−	0.371221i
$238$	−6.86415	−	14.8692i	−0.444937	−	0.963830i
$239$	−3.97832	+	12.2440i	−0.257336	+	0.792000i	0.736024	+	0.676956i	$0.236701\pi$
$239$	−3.97832	+	12.2440i	−0.257336	+	0.792000i	−0.993360	+	0.115045i	$0.963299\pi$
$240$	8.27659	−	3.39088i	0.534252	−	0.218880i
$241$	3.86025	+	11.8806i	0.248661	+	0.765298i	0.995013	+	0.0997473i	$0.0318034\pi$
$241$	3.86025	+	11.8806i	0.248661	+	0.765298i	−0.746352	+	0.665551i	$0.768197\pi$
$242$	−9.82443	+	9.09105i	−0.631538	+	0.584395i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−0.911355	+	1.06930i	−0.0583435	+	0.0684549i
$245$	5.87722	+	3.64972i	0.375482	+	0.233172i
$246$	−8.32264	+	2.35188i	−0.530632	+	0.149950i
$247$	−4.13467	−	26.1053i	−0.263083	−	1.66104i
$248$	30.3152	−	1.23826i	1.92502	−	0.0786298i
$249$		−	2.91219i		−	0.184553i
$250$	4.55426	−	15.1413i	0.288037	−	0.957619i
$251$			7.61447i			0.480621i	0.970696	+	0.240310i	$0.0772492\pi$
$251$			7.61447i			0.480621i	−0.970696	+	0.240310i	$0.922751\pi$
$252$	2.57022	+	3.00304i	0.161909	+	0.189174i
$253$	−0.0236072	−	0.149050i	−0.00148417	−	0.00937070i
$254$	2.37590	+	8.40763i	0.149077	+	0.527541i
$255$	11.1305	+	6.91197i	0.697018	+	0.432844i
$256$	0.0662898	+	15.9999i	0.00414311	+	0.999991i
$257$	2.44416	−	2.44416i	0.152462	−	0.152462i	−0.626755	−	0.779217i	$-0.715617\pi$
$257$	2.44416	−	2.44416i	0.152462	−	0.152462i	0.779217	+	0.626755i	$0.215617\pi$
$258$	−9.34044	−	10.0939i	−0.581510	−	0.628421i
$259$	2.67546	+	8.23421i	0.166245	+	0.511649i
$260$	3.92871	+	25.6165i	0.243648	+	1.58867i
$261$	1.65821	−	5.10343i	0.102640	−	0.315895i
$262$	3.63950	−	1.68012i	0.224849	−	0.103798i
$263$	−15.1052	−	7.69647i	−0.931424	−	0.474584i	−0.0786724	−	0.996901i	$-0.525068\pi$
$263$	−15.1052	−	7.69647i	−0.931424	−	0.474584i	−0.852752	+	0.522316i	$0.825068\pi$
$264$	2.37483	−	2.57710i	0.146161	−	0.158609i
$265$	−0.0428030	−	0.0180279i	−0.00262937	−	0.00110745i
$266$	4.40608	−	11.9623i	0.270154	−	0.733455i
$267$	−9.51614	−	1.50721i	−0.582378	−	0.0922397i
$268$	−12.1813	−	7.44739i	−0.744094	−	0.454922i
$269$	−8.95792	−	12.3295i	−0.546174	−	0.751744i	0.443313	−	0.896367i	$-0.353803\pi$
$269$	−8.95792	−	12.3295i	−0.546174	−	0.751744i	−0.989487	+	0.144623i	$0.953803\pi$
$270$	−3.03886	−	0.874844i	−0.184939	−	0.0532413i
$271$	18.2940	−	25.1795i	1.11128	−	1.52954i	0.291759	−	0.956492i	$-0.405759\pi$
$271$	18.2940	−	25.1795i	1.11128	−	1.52954i	0.819519	−	0.573052i	$-0.194241\pi$
$272$	−18.9328	+	13.8155i	−1.14797	+	0.837690i
$273$	−10.2048	+	5.19960i	−0.617622	+	0.314694i
$274$	7.54389	−	9.57959i	0.455743	−	0.578724i
$275$	−0.896428	−	6.12987i	−0.0540566	−	0.369645i
$276$	−0.0571111	−	0.236804i	−0.00343768	−	0.0142539i
$277$	−3.66725	−	7.19739i	−0.220344	−	0.432449i	0.754200	−	0.656644i	$-0.228025\pi$
$277$	−3.66725	−	7.19739i	−0.220344	−	0.432449i	−0.974544	+	0.224195i	$0.928025\pi$
$278$	12.7009	+	7.10423i	0.761752	+	0.426083i
$279$	−8.67832	−	6.30517i	−0.519557	−	0.377480i
$280$	−4.37770	+	11.7080i	−0.261618	+	0.699690i
$281$	−7.55906	+	5.49198i	−0.450936	+	0.327624i	−0.789965	−	0.613152i	$-0.789901\pi$
$281$	−7.55906	+	5.49198i	−0.450936	+	0.327624i	0.339029	+	0.940776i	$0.389901\pi$
$282$	6.47929	−	0.770277i	0.385836	−	0.0458693i
$283$	2.54702	−	16.0813i	0.151405	−	0.955933i	−0.788633	−	0.614864i	$-0.789211\pi$
$283$	2.54702	−	16.0813i	0.151405	−	0.955933i	0.940038	−	0.341069i	$-0.110789\pi$
$284$	13.4412	−	8.25596i	0.797590	−	0.489901i
$285$	2.32192	+	9.93076i	0.137539	+	0.588247i
$286$	5.64573	+	8.43996i	0.333839	+	0.499065i
$287$	5.48714	−	10.7691i	0.323895	−	0.635681i
$288$	3.49061	−	4.45148i	0.205686	−	0.262306i
$289$	−16.4843	−	5.35607i	−0.969664	−	0.315063i
$290$	16.6606	−	3.22028i	0.978346	−	0.189102i
$291$	7.01680	−	2.27990i	0.411332	−	0.133650i
$292$	10.6031	−	0.845536i	0.620501	−	0.0494813i
$293$	−12.7759	−	12.7759i	−0.746377	−	0.746377i	0.227420	−	0.973797i	$-0.426971\pi$
$293$	−12.7759	−	12.7759i	−0.746377	−	0.746377i	−0.973797	+	0.227420i	$0.926971\pi$
$294$	4.37220	+	0.169516i	0.254992	+	0.00988639i
$295$	−19.9794	−	4.92223i	−1.16325	−	0.286583i
$296$	10.8013	−	6.07108i	0.627812	−	0.352874i
$297$	−1.22376	+	0.193825i	−0.0710097	+	0.0112468i
$298$	29.5419	+	5.86035i	1.71132	+	0.339481i
$299$	0.705812			0.0408182
$300$	−2.22897	−	9.74842i	−0.128690	−	0.562825i
$301$	19.2193			1.10778
$302$	−5.16817	−	1.02523i	−0.297395	−	0.0589954i
$303$	5.28164	−	0.836530i	0.303423	−	0.0480574i
$304$	−18.0251	−	2.81662i	−1.03381	−	0.161544i
$305$	1.01306	+	1.20049i	0.0580074	+	0.0687399i
$306$	8.28023	+	0.321036i	0.473349	+	0.0183524i
$307$	0.652214	+	0.652214i	0.0372238	+	0.0372238i	0.725474	−	0.688250i	$-0.241621\pi$
$307$	0.652214	+	0.652214i	0.0372238	+	0.0372238i	−0.688250	+	0.725474i	$0.741621\pi$
$308$	0.389312	+	4.88202i	0.0221831	+	0.278179i
$309$	1.30937	−	0.425439i	0.0744873	−	0.0242024i
$310$	4.16949	−	33.6645i	0.236811	−	1.91201i
$311$	12.8402	+	4.17202i	0.728098	+	0.236573i	0.649531	−	0.760335i	$-0.274965\pi$
$311$	12.8402	+	4.17202i	0.728098	+	0.236573i	0.0785675	+	0.996909i	$0.474965\pi$
$312$	10.1674	+	12.8561i	0.575615	+	0.727835i
$313$	6.05363	−	11.8809i	0.342171	−	0.671549i	−0.654231	−	0.756295i	$-0.727008\pi$
$313$	6.05363	−	11.8809i	0.342171	−	0.671549i	0.996403	+	0.0847455i	$0.0270077\pi$
$314$	−10.7599	−	16.0854i	−0.607219	−	0.907749i
$315$	3.78172	−	2.28668i	0.213076	−	0.128840i
$316$	−13.1767	−	21.4526i	−0.741250	−	1.20680i
$317$	−4.07058	+	25.7006i	−0.228627	+	1.44349i	0.559935	+	0.828536i	$0.310826\pi$
$317$	−4.07058	+	25.7006i	−0.228627	+	1.44349i	−0.788562	+	0.614956i	$0.789174\pi$
$318$	−0.0291687	+	0.00346767i	−0.00163570	+	0.000194457i
$319$	5.37886	−	3.90797i	0.301158	−	0.218804i
$320$	17.6603	+	2.84833i	0.987242	+	0.159227i
$321$	5.69971	+	4.14108i	0.318127	+	0.231133i
$322$	0.297105	+	0.166185i	0.0165570	+	0.00926112i
$323$	−12.1326	−	23.8116i	−0.675078	−	1.32492i
$324$	−1.94426	+	0.468905i	−0.108014	+	0.0260503i
$325$	28.9729	+	0.343915i	1.60713	+	0.0190770i
$326$	20.3136	−	25.7951i	1.12507	−	1.42866i
$327$	−16.4996	+	8.40696i	−0.912429	+	0.464906i
$328$	−16.6550	−	4.66927i	−0.919618	−	0.257817i
$329$	−5.35980	+	7.37713i	−0.295495	+	0.406714i
$330$	−2.40897	−	3.09005i	−0.132610	−	0.170102i
$331$	−2.57253	−	3.54078i	−0.141399	−	0.194619i	0.732444	−	0.680827i	$-0.238380\pi$
$331$	−2.57253	−	3.54078i	−0.141399	−	0.194619i	−0.873843	+	0.486208i	$0.838380\pi$
$332$	3.03809	−	4.96926i	0.166737	−	0.272723i
$333$	−4.32679	−	0.685296i	−0.237107	−	0.0375540i
$334$	−9.70649	+	26.3526i	−0.531115	+	1.44195i
$335$	−10.4389	+	12.0765i	−0.570336	+	0.659808i
$336$	1.25287	+	7.80560i	0.0683495	+	0.425830i
$337$	18.8970	+	9.62852i	1.02939	+	0.524499i	0.885278	−	0.465063i	$-0.153968\pi$
$337$	18.8970	+	9.62852i	1.02939	+	0.524499i	0.144109	+	0.989562i	$0.453968\pi$
$338$	−26.4273	+	12.1997i	−1.43746	+	0.663579i
$339$	−2.52171	+	7.76102i	−0.136960	+	0.421521i
$340$	11.7819	+	23.4060i	0.638961	+	1.26937i
$341$	−4.10711	−	12.6404i	−0.222413	−	0.684515i
$342$	4.38082	+	4.73423i	0.236888	+	0.255998i
$343$	−14.1064	+	14.1064i	−0.761672	+	0.761672i
$344$	−5.40787	−	26.9681i	−0.291573	−	1.45402i
$345$	−0.271628	+	0.0197563i	−0.0146240	+	0.00106364i
$346$	0.351303	+	1.24316i	0.0188862	+	0.0668328i
$347$	5.32267	+	33.6060i	0.285736	+	1.80407i	0.545193	+	0.838311i	$0.316456\pi$
$347$	5.32267	+	33.6060i	0.285736	+	1.80407i	−0.259457	+	0.965755i	$0.583544\pi$
$348$	8.15356	−	6.97841i	0.437076	−	0.374082i
$349$			30.3857i			1.62651i	0.581907	+	0.813255i	$0.302307\pi$
$349$			30.3857i			1.62651i	−0.581907	+	0.813255i	$0.697693\pi$
$350$	12.1149	+	6.96650i	0.647570	+	0.372375i
$351$		−	5.79500i		−	0.309314i
$352$	6.74083	−	1.91997i	0.359287	−	0.102335i
$353$	−2.80838	−	17.7314i	−0.149475	−	0.943750i	−0.942414	−	0.334448i	$-0.891450\pi$
$353$	−2.80838	−	17.7314i	−0.149475	−	0.943750i	0.792939	−	0.609301i	$-0.208550\pi$
$354$	−12.5235	+	3.53899i	−0.665616	+	0.188095i
$355$	−6.65225	−	16.3335i	−0.353065	−	0.866890i
$356$	−14.6656	−	12.4994i	−0.777276	−	0.662465i
$357$	−8.18857	+	8.18857i	−0.433385	+	0.433385i
$358$	5.79716	−	5.36441i	0.306390	−	0.283518i
$359$	−8.29609	−	25.5327i	−0.437851	−	1.34757i	−0.890137	−	0.455694i	$-0.849391\pi$
$359$	−8.29609	−	25.5327i	−0.437851	−	1.34757i	0.452286	−	0.891873i	$-0.350609\pi$
$360$	−4.27272	−	4.66303i	−0.225192	−	0.245763i
$361$	0.556924	−	1.71404i	0.0293118	−	0.0902124i
$362$	3.02420	+	6.55107i	0.158948	+	0.344317i
$363$	8.43324	+	4.29695i	0.442630	+	0.225531i
$364$	−22.8374	−	1.77355i	−1.19701	−	0.0929591i
$365$	1.00340	−	11.8499i	0.0525205	−	0.620251i
$366$	0.932244	+	0.343375i	0.0487292	+	0.0179485i
$367$	13.8004	+	2.18576i	0.720373	+	0.114096i	0.505848	−	0.862623i	$-0.331180\pi$
$367$	13.8004	+	2.18576i	0.720373	+	0.114096i	0.214525	+	0.976719i	$0.431180\pi$
$368$	0.149589	−	0.463653i	0.00779786	−	0.0241696i
$369$	3.59458	+	4.94751i	0.187126	+	0.257557i
$370$	−4.72431	−	13.0226i	−0.245605	−	0.677013i
$371$	0.0241290	−	0.0332107i	0.00125271	−	0.00172421i
$372$	−8.23061	−	19.8124i	−0.426737	−	1.02722i
$373$	−15.0990	+	7.69335i	−0.781799	+	0.398346i	−0.798867	−	0.601508i	$-0.794567\pi$
$373$	−15.0990	+	7.69335i	−0.781799	+	0.398346i	0.0170680	+	0.999854i	$0.494567\pi$
$374$	8.06616	+	6.35208i	0.417091	+	0.328458i
$375$	−11.1597	+	0.678624i	−0.576286	+	0.0350440i
$376$	11.8596	+	5.44502i	0.611611	+	0.280805i
$377$	14.1174	+	27.7070i	0.727085	+	1.42699i
$378$	1.36444	−	2.43935i	0.0701794	−	0.125467i
$379$	−1.79232	−	1.30219i	−0.0920651	−	0.0668892i	0.540800	−	0.841151i	$-0.318121\pi$
$379$	−1.79232	−	1.30219i	−0.0920651	−	0.0668892i	−0.632866	+	0.774262i	$0.718121\pi$
$380$	−6.39803	+	19.3678i	−0.328212	+	0.993545i
$381$	4.99803	−	3.63128i	0.256057	−	0.186036i
$382$	−0.503753	−	4.23739i	−0.0257743	−	0.216804i
$383$	−3.80588	+	24.0294i	−0.194471	+	1.22784i	0.676475	+	0.736465i	$0.263507\pi$
$383$	−3.80588	+	24.0294i	−0.194471	+	1.22784i	−0.870946	+	0.491378i	$0.836493\pi$
$384$	10.6002	−	3.95432i	0.540937	−	0.201793i
$385$	5.45607	+	0.461999i	0.278067	+	0.0235456i
$386$	16.9175	−	11.3166i	0.861080	−	0.576000i
$387$	−4.41483	+	8.66458i	−0.224418	+	0.440446i
$388$	14.3517	+	3.42981i	0.728595	+	0.174122i
$389$	−25.8405	−	8.39608i	−1.31016	−	0.425698i	−0.431058	−	0.902324i	$-0.641860\pi$
$389$	−25.8405	−	8.39608i	−1.31016	−	0.425698i	−0.879106	+	0.476626i	$0.841860\pi$
$390$	16.0371	−	8.86743i	0.812070	−	0.449020i
$391$	0.678728	−	0.220532i	0.0343247	−	0.0111528i
$392$	7.28371	+	4.85046i	0.367883	+	0.244985i
$393$	−2.00429	−	2.00429i	−0.101103	−	0.101103i
$394$	0.00555186	−	0.143195i	0.000279698	−	0.00721404i
$395$	−26.0687	+	10.6172i	−1.31166	+	0.534209i
$396$	−2.29038	−	0.945929i	−0.115096	−	0.0475347i
$397$	−9.09792	+	1.44097i	−0.456611	+	0.0723201i	−0.380504	−	0.924779i	$-0.624249\pi$
$397$	−9.09792	+	1.44097i	−0.456611	+	0.0723201i	−0.0761078	+	0.997100i	$0.524249\pi$
$398$	−3.59464	+	18.1205i	−0.180183	+	0.908300i
$399$	−9.01415			−0.451272
$400$	6.36641	−	18.9597i	0.318321	−	0.947983i
$401$	−29.1170			−1.45404			−0.727018	−	0.686619i	$-0.759094\pi$
$401$	−29.1170			−1.45404			−0.727018	+	0.686619i	$0.759094\pi$
$402$	−1.96446	+	9.90279i	−0.0979782	+	0.493906i
$403$	61.3975	−	9.72441i	3.05843	−	0.484408i
$404$	9.88509	+	4.08255i	0.491802	+	0.203114i
$405$	0.162207	+	2.23018i	0.00806014	+	0.110818i
$406$	−0.581067	+	14.9870i	−0.0288379	+	0.743792i
$407$	−3.83802	−	3.83802i	−0.190244	−	0.190244i
$408$	13.7941	+	9.18599i	0.682912	+	0.454774i
$409$	15.5052	−	5.03794i	0.766682	−	0.249110i	0.100538	−	0.994933i	$-0.467944\pi$
$409$	15.5052	−	5.03794i	0.766682	−	0.249110i	0.666144	+	0.745823i	$0.267944\pi$
$410$	−8.19139	+	17.5183i	−0.404544	+	0.865166i
$411$	−8.20004	−	2.66435i	−0.404478	−	0.131423i
$412$	2.67809	+	0.640019i	0.131940	+	0.0315314i
$413$	8.25677	−	16.2048i	0.406289	−	0.797387i
$414$	−0.143168	+	0.0957693i	−0.00703634	+	0.00470680i
$415$	−4.92647	−	4.25843i	−0.241831	−	0.209038i
$416$	3.93733	+	32.5441i	0.193044	+	1.59561i
$417$	1.60977	−	10.1637i	0.0788308	−	0.497718i
$418$	0.943449	+	7.93595i	0.0461456	+	0.388160i
$419$	12.1001	−	8.79126i	0.591130	−	0.429481i	−0.251589	−	0.967834i	$-0.580953\pi$
$419$	12.1001	−	8.79126i	0.591130	−	0.429481i	0.842720	+	0.538353i	$0.180953\pi$
$420$	8.83852	+	0.0433006i	0.431276	+	0.00211285i
$421$	8.70096	+	6.32162i	0.424059	+	0.308097i	0.779269	−	0.626690i	$-0.215591\pi$
$421$	8.70096	+	6.32162i	0.424059	+	0.308097i	−0.355210	+	0.934787i	$0.615591\pi$
$422$	−19.1801	+	34.2901i	−0.933671	+	1.66922i
$423$	−2.09463	−	4.11093i	−0.101844	−	0.199880i
$424$	−0.0533900	−	0.0245126i	−0.00259285	−	0.00119044i
$425$	27.9686	−	8.72192i	1.35668	−	0.423075i
$426$	−8.76307	−	6.90089i	−0.424572	−	0.334349i
$427$	−1.23706	+	0.630314i	−0.0598656	+	0.0305030i
$428$	5.40566	+	13.0123i	0.261293	+	0.628973i
$429$	4.22035	−	5.80881i	0.203760	−	0.280452i
$430$	−30.7339	+	1.04083i	−1.48212	+	0.0501934i
$431$	3.12873	+	4.30632i	0.150705	+	0.207428i	0.877694	−	0.479221i	$-0.159081\pi$
$431$	3.12873	+	4.30632i	0.150705	+	0.207428i	−0.726989	+	0.686649i	$0.759081\pi$
$432$	−3.80678	−	1.22818i	−0.183154	−	0.0590911i
$433$	−10.9195	−	1.72947i	−0.524755	−	0.0831131i	−0.111564	−	0.993757i	$-0.535586\pi$
$433$	−10.9195	−	1.72947i	−0.524755	−	0.0831131i	−0.413191	+	0.910644i	$0.635586\pi$
$434$	28.1344	+	10.3628i	1.35049	+	0.497428i
$435$	−6.20858	−	10.2678i	−0.297678	−	0.492302i
$436$	−36.9247	−	2.86755i	−1.76837	−	0.137331i
$437$	0.494962	+	0.252196i	0.0236772	+	0.0120642i
$438$	−3.15242	−	6.82883i	−0.150629	−	0.326294i
$439$	3.08468	−	9.49368i	0.147224	−	0.453109i	−0.850066	−	0.526676i	$-0.823438\pi$
$439$	3.08468	−	9.49368i	0.147224	−	0.453109i	0.997290	+	0.0735669i	$0.0234383\pi$
$440$	−0.886946	−	7.78586i	−0.0422835	−	0.371176i
$441$	−0.956078	−	2.94251i	−0.0455275	−	0.140119i
$442$	−35.2452	+	32.6142i	−1.67644	+	1.55130i
$443$	−18.8815	+	18.8815i	−0.897089	+	0.897089i	−0.995178	−	0.0980884i	$-0.968727\pi$
$443$	−18.8815	+	18.8815i	−0.897089	+	0.897089i	0.0980884	+	0.995178i	$0.468727\pi$
$444$	−6.66815	−	5.68320i	−0.316456	−	0.269713i
$445$	−16.4649	+	13.8942i	−0.780512	+	0.658649i
$446$	15.9359	−	4.50330i	0.754587	−	0.213238i
$447$	−3.33148	−	21.0341i	−0.157574	−	0.994881i
$448$	−6.00519	+	14.6262i	−0.283719	+	0.691023i
$449$			37.5326i			1.77127i	0.464381	+	0.885635i	$0.346277\pi$
$449$			37.5326i			1.77127i	−0.464381	+	0.885635i	$0.653723\pi$
$450$	−5.92359	+	3.86148i	−0.279241	+	0.182032i
$451$			7.57714i			0.356794i
$452$	−12.3995	+	10.6124i	−0.583222	+	0.499164i
$453$	0.582821	+	3.67979i	0.0273833	+	0.172892i
$454$	−3.30411	−	11.6923i	−0.155070	−	0.548747i
$455$	−6.12620	+	24.8664i	−0.287201	+	1.16575i
$456$	2.53638	+	12.6485i	0.118777	+	0.592321i
$457$	−5.19425	+	5.19425i	−0.242977	+	0.242977i	−0.818081	−	0.575104i	$-0.804962\pi$
$457$	−5.19425	+	5.19425i	−0.242977	+	0.242977i	0.575104	+	0.818081i	$0.304962\pi$
$458$	6.77668	+	7.32336i	0.316654	+	0.342198i
$459$	−1.81066	−	5.57262i	−0.0845141	−	0.260108i
$460$	−0.484107	−	0.249660i	−0.0225716	−	0.0116404i
$461$	−0.978097	+	3.01027i	−0.0455545	+	0.140202i	−0.971247	−	0.238075i	$-0.923484\pi$
$461$	−0.978097	+	3.01027i	−0.0455545	+	0.140202i	0.925692	+	0.378278i	$0.123484\pi$
$462$	3.14421	−	1.45148i	0.146282	−	0.0675288i
$463$	−13.3799	−	6.81738i	−0.621815	−	0.316830i	0.114548	−	0.993418i	$-0.463458\pi$
$463$	−13.3799	−	6.81738i	−0.621815	−	0.316830i	−0.736362	+	0.676587i	$0.763458\pi$
$464$	21.1930	−	3.40166i	0.983861	−	0.157918i
$465$	−23.3564	+	5.46097i	−1.08312	+	0.253246i
$466$	8.78637	−	23.8545i	0.407021	−	1.10504i
$467$	28.7602	+	4.55517i	1.33086	+	0.210788i	0.781034	−	0.624488i	$-0.214692\pi$
$467$	28.7602	+	4.55517i	1.33086	+	0.210788i	0.549830	+	0.835276i	$0.314692\pi$
$468$	6.04552	−	9.88836i	0.279454	−	0.457090i
$469$	−8.29302	−	11.4144i	−0.382936	−	0.527066i
$470$	8.17145	−	12.0872i	0.376921	−	0.557540i
$471$	−8.04337	+	11.0708i	−0.370619	+	0.510113i
$472$	−25.0616	−	7.02609i	−1.15355	−	0.323402i
$473$	−10.7355	+	5.47003i	−0.493621	+	0.251512i
$474$	−11.0140	+	13.9861i	−0.505891	+	0.642404i
$475$	20.1949	+	10.5936i	0.926603	+	0.486067i
$476$	−22.5152	+	5.43010i	−1.03198	+	0.248888i
$477$	0.00942968	+	0.0185068i	0.000431755	+	0.000847368i
$478$	15.8899	+	8.88799i	0.726789	+	0.406527i
$479$	28.4711	+	20.6854i	1.30088	+	0.945142i	0.999964	−	0.00850960i	$-0.00270872\pi$
$479$	28.4711	+	20.6854i	1.30088	+	0.945142i	0.300913	+	0.953652i	$0.402709\pi$
$480$	−2.42620	−	12.4142i	−0.110740	−	0.566630i
$481$	20.5379	−	14.9217i	0.936449	−	0.680370i
$482$	17.5429	−	2.08555i	0.799056	−	0.0949941i
$483$	0.0376563	−	0.237753i	0.00171342	−	0.0108181i
$484$	9.90745	+	16.1300i	0.450339	+	0.733180i
$485$	6.40366	−	15.2040i	0.290775	−	0.690376i
$486$	0.786304	+	1.17547i	0.0356675	+	0.0533203i
$487$	1.88944	−	3.70823i	0.0856186	−	0.168036i	−0.844227	−	0.535986i	$-0.819940\pi$
$487$	1.88944	−	3.70823i	0.0856186	−	0.168036i	0.929846	+	0.367950i	$0.119940\pi$
$488$	1.23253	+	1.55847i	0.0557939	+	0.0705485i
$489$	−22.0804	−	7.17436i	−0.998510	−	0.324436i
$490$	6.68012	−	7.14844i	0.301777	−	0.322934i
$491$	−38.8459	+	12.6218i	−1.75309	+	0.569614i	−0.996448	−	0.0842114i	$-0.973163\pi$
$491$	−38.8459	+	12.6218i	−1.75309	+	0.569614i	−0.756645	+	0.653826i	$0.773163\pi$
$492$	0.972256	+	12.1922i	0.0438327	+	0.549668i
$493$	22.2328	+	22.2328i	1.00132	+	1.00132i
$494$	−37.3506	−	1.44813i	−1.68048	−	0.0651546i
$495$	−1.46159	+	2.35362i	−0.0656934	+	0.105788i
$496$	6.62448	−	42.3935i	0.297448	−	1.90352i
$497$	15.3960	−	2.43849i	0.690607	−	0.109381i
$498$	−4.03974	−	0.801380i	−0.181025	−	0.0359107i
$499$	−26.9181			−1.20502			−0.602510	−	0.798111i	$-0.705833\pi$
$499$	−26.9181			−1.20502			−0.602510	+	0.798111i	$0.705833\pi$
$500$	−19.7505	−	10.4842i	−0.883269	−	0.468867i
$501$	19.8579			0.887187
$502$	10.5627	+	2.09536i	0.471434	+	0.0935203i
$503$	15.6815	−	2.48371i	0.699205	−	0.110743i	0.203296	−	0.979117i	$-0.434835\pi$
$503$	15.6815	−	2.48371i	0.699205	−	0.110743i	0.495909	+	0.868374i	$0.334835\pi$
$504$	4.87304	−	2.73899i	0.217062	−	0.122004i
$505$	6.30809	−	10.1580i	0.280706	−	0.452027i
$506$	−0.213256	−	0.00826823i	−0.00948038	−	0.000367568i
$507$	14.5537	+	14.5537i	0.646351	+	0.646351i
$508$	12.3167	−	0.982184i	0.546466	−	0.0435774i
$509$	−16.5749	+	5.38552i	−0.734670	+	0.238709i	−0.652372	−	0.757899i	$-0.726226\pi$
$509$	−16.5749	+	5.38552i	−0.734670	+	0.238709i	−0.0822982	+	0.996608i	$0.526226\pi$
$510$	12.6511	−	13.5380i	0.560198	−	0.599472i
$511$	9.99670	+	3.24813i	0.442228	+	0.143689i
$512$	22.2130	+	4.31090i	0.981684	+	0.190517i
$513$	2.07063	−	4.06383i	0.0914204	−	0.179423i
$514$	−2.71791	−	4.06308i	−0.119882	−	0.179215i
$515$	1.19495	−	2.83713i	0.0526559	−	0.125019i
$516$	−16.5724	+	10.1792i	−0.729561	+	0.448116i
$517$	0.894269	−	5.64620i	0.0393299	−	0.248319i
$518$	12.1586	−	1.44545i	0.534218	−	0.0635094i
$519$	0.739015	−	0.536926i	0.0324392	−	0.0235684i
$520$	36.6159	+	1.59934i	1.60571	+	0.0701356i
$521$	33.3910	+	24.2600i	1.46289	+	1.06285i	0.982600	+	0.185737i	$0.0594672\pi$
$521$	33.3910	+	24.2600i	1.46289	+	1.06285i	0.480286	+	0.877112i	$0.340533\pi$
$522$	−6.62309	−	3.70460i	−0.289885	−	0.162146i
$523$	−13.4688	−	26.4340i	−0.588950	−	1.15588i	−0.972618	−	0.232409i	$-0.925339\pi$
$523$	−13.4688	−	26.4340i	−0.588950	−	1.15588i	0.383668	−	0.923471i	$-0.374661\pi$
$524$	−1.32911	−	5.51099i	−0.0580624	−	0.240749i
$525$	1.66161	−	9.74119i	0.0725184	−	0.425140i
$526$	−14.8331	+	18.8357i	−0.646752	+	0.821275i
$527$	56.0031	−	28.5350i	2.43953	−	1.24300i
$528$	−2.92140	−	4.00349i	−0.127137	−	0.174230i
$529$	13.5103	−	18.5954i	0.587406	−	0.808495i
$530$	−0.0367866	+	0.0544146i	−0.00159791	+	0.00236362i
$531$	5.40894	+	7.44477i	0.234728	+	0.323075i
$532$	−15.3814	−	9.40384i	−0.666869	−	0.407708i
$533$	−35.0028	−	5.54389i	−1.51614	−	0.240133i
$534$	−4.70943	+	12.7859i	−0.203797	+	0.553299i
$535$	15.3399	−	3.58663i	0.663201	−	0.155064i
$536$	−13.6830	+	14.8484i	−0.591014	+	0.641352i
$537$	−4.97625	−	2.53553i	−0.214741	−	0.109416i
$538$	−19.5683	+	9.03342i	−0.843651	+	0.389458i
$539$	1.18459	−	3.64581i	0.0510241	−	0.157036i
$540$	−2.04980	+	3.97471i	−0.0882095	+	0.171044i
$541$	−1.34195	−	4.13009i	−0.0576948	−	0.177566i	0.918056	−	0.396451i	$-0.129758\pi$
$541$	−1.34195	−	4.13009i	−0.0576948	−	0.177566i	−0.975751	+	0.218884i	$0.929758\pi$
$542$	−29.8944	−	32.3060i	−1.28407	−	1.38766i
$543$	3.60771	−	3.60771i	0.154822	−	0.154822i
$544$	13.9547	+	30.0651i	0.598303	+	1.28903i
$545$	−9.90513	+	40.2052i	−0.424289	+	1.72220i
$546$	4.40463	+	15.5867i	0.188501	+	0.667050i
$547$	2.17145	+	13.7100i	0.0928447	+	0.586198i	0.989620	+	0.143711i	$0.0459037\pi$
$547$	2.17145	+	13.7100i	0.0928447	+	0.586198i	−0.896775	+	0.442487i	$0.854096\pi$
$548$	−11.2127	−	13.1009i	−0.478983	−	0.559642i
$549$		−	0.702490i		−	0.0299815i
$550$	−8.74993	−	0.443315i	−0.373098	−	0.0189030i
$551$			24.4744i			1.04264i
$552$	−0.344206	+	0.0140595i	−0.0146504	+	0.000598414i
$553$	−3.89191	−	24.5725i	−0.165501	−	1.04493i
$554$	−10.9933	+	3.10656i	−0.467058	+	0.131985i
$555$	−7.48625	+	6.31741i	−0.317774	+	0.268159i
$556$	13.3499	−	15.6636i	0.566163	−	0.664283i
$557$	16.1147	−	16.1147i	0.682801	−	0.682801i	−0.277830	−	0.960630i	$-0.589615\pi$
$557$	16.1147	−	16.1147i	0.682801	−	0.682801i	0.960630	+	0.277830i	$0.0896150\pi$
$558$	−11.1345	+	10.3033i	−0.471362	+	0.436175i
$559$	−17.4142	−	53.5952i	−0.736540	−	2.26684i
$560$	15.0365	+	9.29450i	0.635410	+	0.392764i
$561$	2.24343	−	6.90456i	0.0947176	−	0.291511i
$562$	5.53827	+	11.9971i	0.233618	+	0.506066i
$563$	19.6615	+	10.0181i	0.828635	+	0.422211i	0.816240	−	0.577712i	$-0.196054\pi$
$563$	19.6615	+	10.0181i	0.828635	+	0.422211i	0.0123950	+	0.999923i	$0.496054\pi$
$564$	0.714462	−	9.19992i	0.0300843	−	0.387386i
$565$	9.44166	+	15.6146i	0.397213	+	0.656913i
$566$	−21.6068	−	7.95845i	−0.908200	−	0.334519i
$567$	−1.95204	−	0.309174i	−0.0819782	−	0.0129841i
$568$	−7.75375	−	20.9173i	−0.325340	−	0.877672i
$569$	1.69582	+	2.33410i	0.0710926	+	0.0978505i	0.843083	−	0.537784i	$-0.180738\pi$
$569$	1.69582	+	2.33410i	0.0710926	+	0.0978505i	−0.771990	+	0.635635i	$0.780738\pi$
$570$	14.4147	−	0.488168i	0.603766	−	0.0204471i
$571$	−9.81495	+	13.5091i	−0.410743	+	0.565339i	−0.963399	−	0.268070i	$-0.913614\pi$
$571$	−9.81495	+	13.5091i	−0.410743	+	0.565339i	0.552657	+	0.833409i	$0.313614\pi$
$572$	13.2614	−	5.50914i	0.554485	−	0.230349i
$573$	−2.68851	+	1.36986i	−0.112314	+	0.0572269i
$574$	−13.4288	−	10.5751i	−0.560506	−	0.441397i
$575$	−0.363774	+	0.488395i	−0.0151704	+	0.0203675i
$576$	−5.21446	−	6.06707i	−0.217269	−	0.252795i
$577$	−18.6192	−	36.5421i	−0.775126	−	1.52127i	−0.851597	−	0.524198i	$-0.824365\pi$
$577$	−18.6192	−	36.5421i	−0.775126	−	1.52127i	0.0764710	−	0.997072i	$-0.475635\pi$
$578$	−11.9660	+	21.3928i	−0.497720	+	0.889824i
$579$	−11.6435	−	8.45950i	−0.483888	−	0.351565i
$580$	0.117566	−	23.9975i	0.00488165	−	0.996442i
$581$	4.65637	−	3.38305i	0.193179	−	0.140353i
$582$	−1.23174	−	10.3610i	−0.0510574	−	0.429476i
$583$	−0.00402586	+	0.0254183i	−0.000166734	+	0.00105272i
$584$	1.74487	−	14.9412i	0.0722031	−	0.618269i
$585$	−9.80323	−	8.47388i	−0.405314	−	0.350352i
$586$	−21.2382	+	14.2068i	−0.877343	+	0.586879i
$587$	−11.6401	+	22.8450i	−0.480439	+	0.942915i	0.515836	+	0.856687i	$0.327481\pi$
$587$	−11.6401	+	22.8450i	−0.480439	+	0.942915i	−0.996275	+	0.0862280i	$0.972519\pi$
$588$	1.43830	−	6.01839i	0.0593143	−	0.248194i
$589$	46.5307	+	15.1187i	1.91726	+	0.622956i
$590$	−12.3260	+	26.3606i	−0.507453	+	1.08525i
$591$	−0.0963705	+	0.0313127i	−0.00396415	+	0.00128803i
$592$	−5.44938	−	16.6540i	−0.223968	−	0.684476i
$593$	5.99382	+	5.99382i	0.246137	+	0.246137i	0.819383	−	0.573246i	$-0.194316\pi$
$593$	5.99382	+	5.99382i	0.246137	+	0.246137i	−0.573246	+	0.819383i	$0.694316\pi$
$594$	−0.0678855	+	1.75092i	−0.00278537	+	0.0718409i
$595$	1.87842	+	25.8263i	0.0770078	+	1.05878i
$596$	16.2587	−	39.3674i	0.665984	−	1.61255i
$597$	12.9020	−	2.04348i	0.528044	−	0.0836339i
$598$	0.194226	−	0.979090i	0.00794249	−	0.0400380i
$599$	0.175663			0.00717738			0.00358869	−	0.999994i	$-0.498858\pi$
$599$	0.175663			0.00717738			0.00358869	+	0.999994i	$0.498858\pi$
$600$	−14.1362	+	0.409413i	−0.577108	+	0.0167142i
$601$	11.4170			0.465710			0.232855	−	0.972511i	$-0.425193\pi$
$601$	11.4170			0.465710			0.232855	+	0.972511i	$0.425193\pi$
$602$	5.28878	−	26.6606i	0.215554	−	1.08661i
$603$	7.05089	−	1.11675i	0.287134	−	0.0454776i
$604$	−2.84436	+	6.88707i	−0.115735	+	0.280231i
$605$	19.6007	−	7.98294i	0.796883	−	0.324553i
$606$	0.292988	−	7.55680i	0.0119018	−	0.306974i
$607$	10.6407	+	10.6407i	0.431893	+	0.431893i	0.889272	−	0.457379i	$-0.151212\pi$
$607$	10.6407	+	10.6407i	0.431893	+	0.431893i	−0.457379	+	0.889272i	$0.651212\pi$
$608$	−8.86732	+	24.2290i	−0.359617	+	0.982614i
$609$	10.0863	−	3.27724i	0.408718	−	0.132800i
$610$	1.94407	−	1.07494i	0.0787133	−	0.0435231i
$611$	25.4284	+	8.26219i	1.02872	+	0.334252i
$612$	2.72390	−	11.3978i	0.110107	−	0.460730i
$613$	0.467306	−	0.917140i	0.0188743	−	0.0370429i	−0.881377	−	0.472414i	$-0.843383\pi$
$613$	0.467306	−	0.917140i	0.0188743	−	0.0370429i	0.900251	+	0.435371i	$0.143383\pi$
$614$	1.08422	−	0.725263i	0.0437554	−	0.0292692i
$615$	13.6258	+	1.15378i	0.549446	+	0.0465250i
$616$	6.87939	+	0.803393i	0.277178	+	0.0323696i
$617$	6.87162	−	43.3857i	0.276641	−	1.74664i	−0.323024	−	0.946391i	$-0.604700\pi$
$617$	6.87162	−	43.3857i	0.276641	−	1.74664i	0.599665	−	0.800251i	$-0.295300\pi$
$618$	−0.229849	−	1.93340i	−0.00924588	−	0.0777729i
$619$	−15.7867	+	11.4697i	−0.634520	+	0.461006i	−0.857963	−	0.513711i	$-0.828270\pi$
$619$	−15.7867	+	11.4697i	−0.634520	+	0.461006i	0.223443	+	0.974717i	$0.428270\pi$
$620$	−45.5514	−	15.0477i	−1.82939	−	0.604329i
$621$	0.0985357	+	0.0715904i	0.00395410	+	0.00287282i
$622$	9.32072	−	16.6636i	0.373727	−	0.668149i
$623$	−8.64485	−	16.9665i	−0.346349	−	0.679747i
$624$	20.6317	−	10.5663i	0.825928	−	0.422989i
$625$	−15.1706	+	19.8709i	−0.606823	+	0.794837i
$626$	−14.8152	−	11.6669i	−0.592133	−	0.466303i
$627$	5.03515	−	2.56554i	0.201084	−	0.102458i
$628$	−25.2743	+	10.4996i	−1.00855	+	0.418980i
$629$	15.0875	−	20.7662i	0.601579	−	0.828002i
$630$	−2.13139	−	5.87519i	−0.0849165	−	0.234073i
$631$	19.8296	+	27.2931i	0.789403	+	1.08652i	0.994182	+	0.107712i	$0.0343525\pi$
$631$	19.8296	+	27.2931i	0.789403	+	1.08652i	−0.204779	+	0.978808i	$0.565647\pi$
$632$	−33.3847	+	12.3752i	−1.32797	+	0.492259i
$633$	27.4400	+	4.34607i	1.09064	+	0.172741i
$634$	34.5313	+	12.7190i	1.37141	+	0.505135i
$635$	1.16556	−	13.7650i	0.0462540	−	0.546246i
$636$	−0.00321640	+	0.0414166i	−0.000127538	+	0.00164228i
$637$	15.9752	+	8.13975i	0.632958	+	0.322508i
$638$	−3.94091	−	8.53686i	−0.156022	−	0.337977i
$639$	−2.43726	+	7.50111i	−0.0964165	+	0.296739i
$640$	8.81094	−	23.7143i	0.348283	−	0.937389i
$641$	−6.34839	−	19.5383i	−0.250746	−	0.771718i	−0.994638	−	0.103418i	$-0.967022\pi$
$641$	−6.34839	−	19.5383i	−0.250746	−	0.771718i	0.743892	−	0.668300i	$-0.232978\pi$
$642$	7.31288	−	6.76699i	0.288617	−	0.267072i
$643$	−7.64052	+	7.64052i	−0.301313	+	0.301313i	−0.841527	−	0.540215i	$-0.818343\pi$
$643$	−7.64052	+	7.64052i	−0.301313	+	0.301313i	0.540215	+	0.841527i	$0.318343\pi$
$644$	0.312286	−	0.366408i	0.0123058	−	0.0144385i
$645$	8.20193	+	20.1384i	0.322951	+	0.792950i
$646$	−36.3698	+	10.2777i	−1.43095	+	0.404370i
$647$	0.562777	+	3.55324i	0.0221251	+	0.139692i	0.996278	−	0.0861968i	$-0.0274714\pi$
$647$	0.562777	+	3.55324i	0.0221251	+	0.139692i	−0.974153	+	0.225889i	$0.927471\pi$
$648$	0.115434	+	2.82607i	0.00453469	+	0.111019i
$649$			11.4017i			0.447556i
$650$	8.44988	−	40.0961i	0.331431	−	1.57270i
$651$		−	21.2006i		−	0.830916i
$652$	−30.1926	−	35.2770i	−1.18244	−	1.38155i
$653$	−5.01226	−	31.6462i	−0.196145	−	1.23841i	−0.867562	−	0.497330i	$-0.834314\pi$
$653$	−5.01226	−	31.6462i	−0.196145	−	1.23841i	0.671417	−	0.741080i	$-0.265686\pi$
$654$	7.12161	+	25.2014i	0.278477	+	0.985451i
$655$	−6.32143	+	0.459776i	−0.246999	+	0.0179649i
$656$	−11.0603	+	21.8186i	−0.431831	+	0.851874i
$657$	−3.76067	+	3.76067i	−0.146718	+	0.146718i
$658$	8.75851	+	9.46506i	0.341442	+	0.368986i
$659$	8.42444	+	25.9278i	0.328170	+	1.01000i	0.969989	+	0.243147i	$0.0781797\pi$
$659$	8.42444	+	25.9278i	0.328170	+	1.01000i	−0.641820	+	0.766856i	$0.721820\pi$
$660$	−4.94937	+	2.49136i	−0.192654	+	0.0969761i
$661$	4.18817	−	12.8899i	0.162901	−	0.501358i	−0.835974	−	0.548768i	$-0.815097\pi$
$661$	4.18817	−	12.8899i	0.162901	−	0.501358i	0.998875	+	0.0474105i	$0.0150969\pi$
$662$	−5.61962	+	2.59421i	−0.218413	+	0.100827i
$663$	30.2543	+	15.4153i	1.17498	+	0.598682i
$664$	−6.05724	−	5.58183i	−0.235067	−	0.216617i
$665$	−13.1812	+	15.2490i	−0.511144	+	0.591330i
$666$	−2.14128	+	5.81347i	−0.0829730	+	0.225267i
$667$	−0.645523	−	0.102241i	−0.0249948	−	0.00395878i
$668$	33.8848	+	20.7164i	1.31104	+	0.801542i
$669$	−6.88277	−	9.47333i	−0.266103	−	0.366260i
$670$	13.8797	+	17.8038i	0.536219	+	0.687822i
$671$	0.511605	−	0.704165i	0.0197503	−	0.0271840i
$672$	11.1726	+	0.409998i	0.430991	+	0.0158160i
$673$	−10.6723	+	5.43780i	−0.411387	+	0.209612i	−0.647421	−	0.762133i	$-0.724152\pi$
$673$	−10.6723	+	5.43780i	−0.411387	+	0.209612i	0.236034	+	0.971745i	$0.424152\pi$
$674$	18.5566	−	23.5641i	0.714774	−	0.907653i
$675$	4.00992	+	2.98673i	0.154342	+	0.114959i
$676$	9.65099	+	40.0166i	0.371192	+	1.53910i
$677$	−10.4290	−	20.4681i	−0.400819	−	0.786652i	0.599082	−	0.800688i	$-0.295532\pi$
$677$	−10.4290	−	20.4681i	−0.400819	−	0.786652i	−0.999902	+	0.0140353i	$0.995532\pi$
$678$	10.0720	+	5.63375i	0.386814	+	0.216363i
$679$	11.7967	+	8.57080i	0.452716	+	0.328917i
$680$	35.7105	−	9.90271i	1.36944	−	0.379752i
$681$	−6.95065	+	5.04995i	−0.266350	+	0.193514i
$682$	−18.6647	+	2.21892i	−0.714709	+	0.0849668i
$683$	7.59793	−	47.9715i	0.290727	−	1.83558i	−0.219592	−	0.975592i	$-0.570473\pi$
$683$	7.59793	−	47.9715i	0.290727	−	1.83558i	0.510319	−	0.859985i	$-0.329527\pi$
$684$	7.77275	−	4.77423i	0.297199	−	0.182547i
$685$	−16.4979	+	9.97575i	−0.630353	+	0.381154i
$686$	15.6863	+	23.4499i	0.598906	+	0.895322i
$687$	3.20305	−	6.28633i	0.122204	−	0.239839i
$688$	−38.8979	+	0.0805794i	−1.48297	+	0.00307206i
$689$	−0.114475	−	0.0371951i	−0.00436114	−	0.00141702i
$690$	−0.0473414	+	0.382235i	−0.00180226	+	0.0145514i
$691$	15.8467	−	5.14891i	0.602838	−	0.195874i	0.00833210	−	0.999965i	$-0.497348\pi$
$691$	15.8467	−	5.14891i	0.602838	−	0.195874i	0.594506	+	0.804091i	$0.297348\pi$
$692$	1.82116	−	0.145227i	0.0692303	−	0.00552070i
$693$	−1.73153	−	1.73153i	−0.0657756	−	0.0657756i
$694$	48.0824	+	1.86422i	1.82518	+	0.0707649i
$695$	−14.8397	−	17.5853i	−0.562902	−	0.667049i
$696$	−7.43663	−	13.2308i	−0.281885	−	0.501512i
$697$	−35.3918	+	5.60551i	−1.34056	+	0.212324i
$698$	42.1505	+	8.36157i	1.59542	+	0.316490i
$699$	−17.9755			−0.679897
$700$	12.9976	−	14.8886i	0.491263	−	0.562734i
$701$	−11.4107			−0.430977			−0.215488	−	0.976506i	$-0.569134\pi$
$701$	−11.4107			−0.430977			−0.215488	+	0.976506i	$0.569134\pi$
$702$	−8.03872	−	1.59467i	−0.303402	−	0.0601870i
$703$	19.7343	−	3.12560i	0.744292	−	0.117884i
$704$	−0.808397	−	9.87909i	−0.0304676	−	0.372332i
$705$	−10.0173	−	2.46790i	−0.377272	−	0.0929465i
$706$	−25.3696	−	0.983614i	−0.954796	−	0.0370188i
$707$	7.47316	+	7.47316i	0.281057	+	0.281057i
$708$	1.46300	+	18.3462i	0.0549830	+	0.689494i
$709$	−22.2796	+	7.23907i	−0.836727	+	0.271869i	−0.695876	−	0.718162i	$-0.744984\pi$
$709$	−22.2796	+	7.23907i	−0.836727	+	0.271869i	−0.140851	+	0.990031i	$0.544984\pi$
$710$	−24.4881	+	4.73323i	−0.919021	+	0.177635i
$711$	11.9720	+	3.88994i	0.448985	+	0.145884i
$712$	−21.3746	+	16.9043i	−0.801047	+	0.633515i
$713$	−0.593144	+	1.16411i	−0.0222134	+	0.0435963i
$714$	9.10571	+	13.6124i	0.340772	+	0.509431i
$715$	−3.65528	−	15.6335i	−0.136700	−	0.584660i
$716$	−5.84615	−	9.51791i	−0.218481	−	0.355701i
$717$	2.01396	−	12.7156i	0.0752126	−	0.474874i
$718$	−37.7015	+	4.48207i	−1.40701	+	0.167269i
$719$	37.2385	−	27.0554i	1.38876	−	1.00900i	0.392764	−	0.919639i	$-0.371519\pi$
$719$	37.2385	−	27.0554i	1.38876	−	1.00900i	0.996000	−	0.0893562i	$-0.0284809\pi$
$720$	−7.64424	+	4.64387i	−0.284884	+	0.173067i
$721$	2.20132	+	1.59935i	0.0819814	+	0.0595629i
$722$	−2.22443	−	1.24423i	−0.0827846	−	0.0463053i
$723$	−5.67126	−	11.1305i	−0.210917	−	0.413947i
$724$	9.91973	−	2.39239i	0.368664	−	0.0889123i
$725$	−26.4483	−	4.51143i	−0.982266	−	0.167550i
$726$	8.28132	−	10.5160i	0.307349	−	0.390285i
$727$	−38.1000	+	19.4129i	−1.41305	+	0.719985i	−0.983135	−	0.182884i	$-0.941457\pi$
$727$	−38.1000	+	19.4129i	−1.41305	+	0.719985i	−0.429916	+	0.902869i	$0.641457\pi$
$728$	−8.74466	+	31.1916i	−0.324099	+	1.15604i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	−16.1618	−	4.65277i	−0.598177	−	0.172207i
$731$	−33.4918	−	46.0975i	−1.23874	−	1.70498i
$732$	0.732859	−	1.19870i	0.0270872	−	0.0443053i
$733$	−18.1115	−	2.86857i	−0.668962	−	0.105953i	−0.187290	−	0.982305i	$-0.559970\pi$
$733$	−18.1115	−	2.86857i	−0.668962	−	0.105953i	−0.481672	+	0.876352i	$0.659970\pi$
$734$	6.82965	−	18.5421i	0.252087	−	0.684403i
$735$	−6.37580	−	2.68538i	−0.235175	−	0.0990519i
$736$	−0.602008	−	0.335096i	−0.0221903	−	0.0123518i
$737$	7.88100	+	4.01557i	0.290300	+	0.147915i
$738$	7.85226	−	3.62487i	0.289046	−	0.133433i
$739$	−1.37964	+	4.24609i	−0.0507508	+	0.156195i	−0.973220	−	0.229876i	$-0.926168\pi$
$739$	−1.37964	+	4.24609i	−0.0507508	+	0.156195i	0.922469	+	0.386071i	$0.126168\pi$
$740$	−19.3648	+	2.96990i	−0.711863	+	0.109176i
$741$	8.16753	+	25.1371i	0.300042	+	0.923433i
$742$	−0.0394294	−	0.0426102i	−0.00144750	−	0.00156427i
$743$	−9.34530	+	9.34530i	−0.342846	+	0.342846i	−0.857436	−	0.514590i	$-0.827944\pi$
$743$	−9.34530	+	9.34530i	−0.342846	+	0.342846i	0.514590	+	0.857436i	$0.327944\pi$
$744$	−29.7483	+	5.96536i	−1.09063	+	0.218701i
$745$	−40.4544	−	25.1219i	−1.48213	−	0.920397i
$746$	6.51711	+	23.0622i	0.238608	+	0.844367i
$747$	0.455567	+	2.87634i	0.0166683	+	0.105240i
$748$	11.0311	−	9.44126i	0.403339	−	0.345207i
$749$			13.9240i			0.508773i
$750$	−2.12957	+	15.6673i	−0.0777608	+	0.572090i
$751$			34.9526i			1.27544i	0.770269	+	0.637719i	$0.220122\pi$
$751$			34.9526i			1.27544i	−0.770269	+	0.637719i	$0.779878\pi$
$752$	10.8168	−	14.9530i	0.394447	−	0.545281i
$753$	−1.19117	−	7.52072i	−0.0434085	−	0.274070i
$754$	42.3196	−	11.9590i	1.54119	−	0.435522i
$755$	7.07724	+	4.39492i	0.257567	+	0.159948i
$756$	−3.00836	−	2.56399i	−0.109413	−	0.0932516i
$757$	21.7005	−	21.7005i	0.788717	−	0.788717i	−0.192567	−	0.981284i	$-0.561681\pi$
$757$	21.7005	−	21.7005i	0.788717	−	0.788717i	0.981284	+	0.192567i	$0.0616812\pi$
$758$	−2.29959	+	2.12793i	−0.0835249	+	0.0772899i
$759$	0.0466331	+	0.143522i	0.00169268	+	0.00520952i
$760$	25.1060	+	14.2049i	0.910690	+	0.515265i
$761$	0.680896	−	2.09558i	0.0246825	−	0.0759648i	−0.937957	−	0.346753i	$-0.887284\pi$
$761$	0.680896	−	2.09558i	0.0246825	−	0.0759648i	0.962639	+	0.270788i	$0.0872843\pi$
$762$	−3.66189	−	7.93244i	−0.132656	−	0.287362i
$763$	−32.6094	−	16.6153i	−1.18054	−	0.601515i
$764$	−6.01666	−	0.467251i	−0.217675	−	0.0169045i
$765$	−12.0747	−	5.08568i	−0.436562	−	0.183873i
$766$	32.2858	+	11.8919i	1.16653	+	0.429671i
$767$	−52.6704	−	8.34217i	−1.90182	−	0.301218i
$768$	−2.56840	−	15.7925i	−0.0926793	−	0.569863i
$769$	−14.1415	−	19.4641i	−0.509955	−	0.701893i	0.473956	−	0.880548i	$-0.342825\pi$
$769$	−14.1415	−	19.4641i	−0.509955	−	0.701893i	−0.983912	+	0.178655i	$0.942825\pi$
$770$	2.14228	−	7.44143i	0.0772025	−	0.268170i
$771$	−2.03171	+	2.79641i	−0.0731704	+	0.100710i
$772$	−11.0428	−	26.5818i	−0.397440	−	0.956701i
$773$	−16.2534	+	8.28151i	−0.584594	+	0.297865i	−0.721163	−	0.692765i	$-0.756392\pi$
$773$	−16.2534	+	8.28151i	−0.584594	+	0.297865i	0.136570	+	0.990630i	$0.456392\pi$
$774$	10.8045	+	8.50850i	0.388359	+	0.305832i
$775$	−24.9153	+	47.4967i	−0.894983	+	1.70613i
$776$	8.70708	−	18.9646i	0.312566	−	0.680788i
$777$	−3.93063	−	7.71430i	−0.141011	−	0.276749i
$778$	−18.7577	+	33.5350i	−0.672496	+	1.20229i
$779$	−22.5653	−	16.3947i	−0.808487	−	0.587400i
$780$	−7.88764	−	24.6865i	−0.282423	−	0.883920i
$781$	−7.90593	+	5.74400i	−0.282897	+	0.205536i
$782$	−0.119145	−	1.00221i	−0.00426062	−	0.0358388i
$783$	−0.839438	+	5.30000i	−0.0299991	+	0.189407i
$784$	8.73282	−	8.76907i	0.311886	−	0.313181i
$785$	6.96644	+	29.7952i	0.248643	+	1.06344i
$786$	−3.33186	+	2.22878i	−0.118844	+	0.0794979i
$787$	12.5600	−	24.6504i	0.447716	−	0.878692i	−0.551299	−	0.834308i	$-0.685868\pi$
$787$	12.5600	−	24.6504i	0.447716	−	0.878692i	0.999015	−	0.0443837i	$-0.0141324\pi$
$788$	−0.197109	−	0.0471058i	−0.00702172	−	0.00167808i
$789$	16.1232	+	5.23874i	0.574001	+	0.186504i
$790$	7.55437	+	39.0837i	0.268772	+	1.39053i
$791$	−15.3387	+	4.98384i	−0.545381	+	0.177205i
$792$	−1.94244	+	2.91687i	−0.0690218	+	0.103647i
$793$	2.87858	+	2.87858i	0.102221	+	0.102221i
$794$	−0.504688	+	13.0170i	−0.0179107	+	0.461956i
$795$	0.0450962	+	0.0111101i	0.00159940	+	0.000394035i
$796$	24.1473	+	9.97285i	0.855879	+	0.353478i
$797$	−28.7658	+	4.55606i	−1.01894	+	0.161384i	−0.643486	−	0.765458i	$-0.722513\pi$
$797$	−28.7658	+	4.55606i	−1.01894	+	0.161384i	−0.375452	+	0.926842i	$0.622513\pi$
$798$	−2.48052	+	12.5043i	−0.0878096	+	0.442647i
$799$	27.0342			0.956400
$800$	−24.5486	−	14.0487i	−0.867924	−	0.496697i
$801$	9.63476			0.340428
$802$	−8.01246	+	40.3906i	−0.282930	+	1.42624i
$803$	−6.50844	+	1.03084i	−0.229678	+	0.0363774i
$804$	13.1964	+	5.45012i	0.465401	+	0.192211i
$805$	−0.347136	−	0.411362i	−0.0122349	−	0.0144986i
$806$	3.40590	−	87.8455i	0.119968	−	3.09423i
$807$	10.7764	+	10.7764i	0.379347	+	0.379347i
$808$	8.38343	−	12.5890i	0.294928	−	0.442879i
$809$	14.4231	−	4.68634i	0.507088	−	0.164763i	−0.0442896	−	0.999019i	$-0.514102\pi$
$809$	14.4231	−	4.68634i	0.507088	−	0.164763i	0.551377	+	0.834256i	$0.314102\pi$
$810$	3.13830	+	0.388691i	0.110269	+	0.0136572i
$811$	−20.0242	−	6.50627i	−0.703146	−	0.228466i	−0.0644451	−	0.997921i	$-0.520528\pi$
$811$	−20.0242	−	6.50627i	−0.703146	−	0.228466i	−0.638701	+	0.769455i	$0.720528\pi$
$812$	20.6298	+	4.93019i	0.723964	+	0.173016i
$813$	−14.1298	+	27.7313i	−0.495553	+	0.972578i
$814$	−6.38018	+	4.26788i	−0.223625	+	0.149589i
$815$	−44.4243	+	26.8619i	−1.55611	+	0.940931i
$816$	16.5385	−	16.6072i	0.578964	−	0.581368i
$817$	6.93832	−	43.8068i	0.242741	−	1.53261i
$818$	−2.72181	−	22.8949i	−0.0951658	−	0.800500i
$819$	9.26575	−	6.73196i	0.323772	−	0.235234i
$820$	22.0469	+	16.1836i	0.769912	+	0.565157i
$821$	36.0784	+	26.2125i	1.25915	+	0.914823i	0.998715	−	0.0506698i	$-0.0161356\pi$
$821$	36.0784	+	26.2125i	1.25915	+	0.914823i	0.260430	+	0.965493i	$0.416136\pi$
$822$	−5.95244	+	10.6418i	−0.207615	+	0.371174i
$823$	−4.13086	−	8.10727i	−0.143993	−	0.282602i	0.807735	−	0.589546i	$-0.200693\pi$
$823$	−4.13086	−	8.10727i	−0.143993	−	0.282602i	−0.951727	+	0.306945i	$0.900693\pi$
$824$	1.62478	−	3.53887i	0.0566019	−	0.123282i
$825$	1.84431	+	5.91417i	0.0642108	+	0.205905i
$826$	−20.2069	−	15.9129i	−0.703089	−	0.553681i
$827$	39.4863	−	20.1193i	1.37307	−	0.699615i	0.397154	−	0.917752i	$-0.369998\pi$
$827$	39.4863	−	20.1193i	1.37307	−	0.699615i	0.975918	+	0.218137i	$0.0699979\pi$
$828$	0.0934523	+	0.224954i	0.00324769	+	0.00781771i
$829$	−24.4195	+	33.6105i	−0.848123	+	1.16734i	0.136150	+	0.990688i	$0.456527\pi$
$829$	−24.4195	+	33.6105i	−0.848123	+	1.16734i	−0.984273	+	0.176653i	$0.943473\pi$
$830$	−7.26289	+	5.66208i	−0.252099	+	0.196534i
$831$	4.74802	+	6.53509i	0.164707	+	0.226700i
$832$	46.2281	+	3.49373i	1.60267	+	0.121123i
$833$	17.9054	+	2.83594i	0.620386	+	0.0982594i
$834$	−13.6559	−	5.02990i	−0.472866	−	0.174171i
$835$	29.0378	−	33.5931i	1.00489	−	1.16254i
$836$	11.2682	+	0.875086i	0.389720	+	0.0302655i
$837$	9.55782	+	4.86995i	0.330366	+	0.168330i
$838$	−8.86536	−	19.2043i	−0.306249	−	0.663401i
$839$	−7.90159	+	24.3186i	−0.272793	+	0.839571i	0.717002	+	0.697071i	$0.245514\pi$
$839$	−7.90159	+	24.3186i	−0.272793	+	0.839571i	−0.989795	+	0.142500i	$0.954486\pi$
$840$	2.49226	−	12.2487i	0.0859911	−	0.422621i
$841$	0.0634479	+	0.195272i	0.00218786	+	0.00673353i
$842$	11.1636	−	10.3302i	0.384722	−	0.356003i
$843$	6.60686	−	6.60686i	0.227552	−	0.227552i
$844$	42.2887	+	36.0422i	1.45564	+	1.24063i
$845$	45.9015	−	3.33854i	1.57906	−	0.114849i
$846$	−6.27902	+	1.77438i	−0.215877	+	0.0610043i
$847$	2.92628	+	18.4758i	0.100548	+	0.634836i
$848$	−0.0486954	+	0.0673163i	−0.00167221	+	0.00231165i
$849$			16.2817i			0.558788i
$850$	−4.40247	−	41.1977i	−0.151003	−	1.41307i
$851$			0.533558i			0.0182901i
$852$	−11.9842	+	10.2570i	−0.410573	+	0.351399i
$853$	5.86386	+	37.0230i	0.200775	+	1.26764i	0.857883	+	0.513846i	$0.171780\pi$
$853$	5.86386	+	37.0230i	0.200775	+	1.26764i	−0.657108	+	0.753797i	$0.728220\pi$
$854$	0.533945	+	1.88948i	0.0182712	+	0.0646566i
$855$	−3.84684	−	9.44526i	−0.131559	−	0.323021i
$856$	19.5380	−	3.91791i	0.667793	−	0.133911i
$857$	−1.38959	+	1.38959i	−0.0474676	+	0.0474676i	−0.730442	−	0.682975i	$-0.760686\pi$
$857$	−1.38959	+	1.38959i	−0.0474676	+	0.0474676i	0.682975	+	0.730442i	$0.260686\pi$
$858$	−6.89652	−	7.45286i	−0.235443	−	0.254437i
$859$	−6.44537	−	19.8368i	−0.219913	−	0.676824i	−0.998768	−	0.0496195i	$-0.984199\pi$
$859$	−6.44537	−	19.8368i	−0.219913	−	0.676824i	0.778855	−	0.627204i	$-0.215801\pi$
$860$	−7.01357	+	42.9200i	−0.239161	+	1.46356i
$861$	−3.73492	+	11.4949i	−0.127286	+	0.391745i
$862$	6.83462	−	3.15510i	0.232788	−	0.107463i
$863$	21.9733	+	11.1960i	0.747980	+	0.381115i	0.786052	−	0.618160i	$-0.212122\pi$
$863$	21.9733	+	11.1960i	0.747980	+	0.381115i	−0.0380720	+	0.999275i	$0.512122\pi$
$864$	−2.75127	+	4.94272i	−0.0936001	+	0.168155i
$865$	0.172342	−	2.03530i	0.00585979	−	0.0692024i
$866$	−5.40392	+	14.6714i	−0.183633	+	0.498553i
$867$	17.1192	+	2.71142i	0.581399	+	0.0920845i
$868$	22.1171	−	36.1759i	0.750703	−	1.22789i
$869$	9.16758	+	12.6181i	0.310989	+	0.428040i
$870$	−15.9517	+	5.78693i	−0.540815	+	0.196195i
$871$	−24.3162	+	33.4684i	−0.823923	+	1.13403i
$872$	−14.1388	+	50.4321i	−0.478800	+	1.70785i
$873$	−6.57376	+	3.34950i	−0.222488	+	0.113363i
$874$	0.486046	−	0.617203i	0.0164407	−	0.0208772i
$875$	−14.0492	−	17.0552i	−0.474948	−	0.576571i
$876$	−10.3403	+	2.49382i	−0.349367	+	0.0842584i
$877$	−8.82783	−	17.3256i	−0.298095	−	0.585044i	0.692572	−	0.721349i	$-0.256477\pi$
$877$	−8.82783	−	17.3256i	−0.298095	−	0.585044i	−0.990667	+	0.136305i	$0.956477\pi$
$878$	−12.3206	−	6.89150i	−0.415801	−	0.232577i
$879$	14.6172	+	10.6200i	0.493027	+	0.358205i
$880$	−11.0445	−	0.912164i	−0.372309	−	0.0307491i
$881$	2.94832	−	2.14208i	0.0993315	−	0.0721686i	−0.537011	−	0.843575i	$-0.680447\pi$
$881$	2.94832	−	2.14208i	0.0993315	−	0.0721686i	0.636342	+	0.771407i	$0.280447\pi$
$882$	−4.34489	+	0.516533i	−0.146300	+	0.0173926i
$883$	1.16799	−	7.37438i	0.0393059	−	0.248168i	−0.960210	−	0.279279i	$-0.909905\pi$
$883$	1.16799	−	7.37438i	0.0393059	−	0.248168i	0.999516	+	0.0311112i	$0.00990460\pi$
$884$	35.5431	+	57.8664i	1.19544	+	1.94626i
$885$	20.5035	+	1.73615i	0.689216	+	0.0583602i
$886$	20.9963	+	31.3880i	0.705385	+	1.05450i
$887$	12.7429	−	25.0093i	0.427864	−	0.839729i	−0.571948	−	0.820290i	$-0.693812\pi$
$887$	12.7429	−	25.0093i	0.427864	−	0.839729i	0.999811	−	0.0194392i	$-0.00618809\pi$
$888$	−9.71858	+	7.68603i	−0.326134	+	0.257926i
$889$	11.6123	+	3.77306i	0.389463	+	0.126544i
$890$	14.7430	+	26.6633i	0.494186	+	0.893755i
$891$	1.17837	−	0.382876i	0.0394770	−	0.0128268i
$892$	−1.86164	−	23.3452i	−0.0623324	−	0.781657i
$893$	14.8799	+	14.8799i	0.497937	+	0.497937i
$894$	−30.0950	−	1.16682i	−1.00653	−	0.0390244i
$895$	−11.5659	+	4.71054i	−0.386607	+	0.157456i
$896$	18.6367	+	12.3552i	0.622609	+	0.412757i
$897$	−0.697122	+	0.110413i	−0.0232762	+	0.00368659i
$898$	52.0645	+	10.3282i	1.73741	+	0.344658i
$899$	−57.5617			−1.91979
$900$	3.72652	+	9.27971i	0.124217	+	0.309324i
$901$	−0.121704			−0.00405454
$902$	10.5109	+	2.08509i	0.349974	+	0.0694258i
$903$	−18.9826	+	3.00655i	−0.631703	+	0.100052i
$904$	11.3092	+	20.1207i	0.376139	+	0.669203i
$905$	−0.827593	−	11.3785i	−0.0275101	−	0.378235i
$906$	5.26492	+	0.204128i	0.174915	+	0.00678171i
$907$	4.22368	+	4.22368i	0.140245	+	0.140245i	0.773744	−	0.633499i	$-0.218382\pi$
$907$	4.22368	+	4.22368i	0.140245	+	0.140245i	−0.633499	+	0.773744i	$0.718382\pi$
$908$	−17.1286	+	1.36590i	−0.568432	+	0.0453290i
$909$	−5.08576	+	1.65246i	−0.168684	+	0.0548087i
$910$	32.8084	+	15.3409i	1.08759	+	0.508546i
$911$	17.2161	+	5.59384i	0.570394	+	0.185332i	0.579993	−	0.814622i	$-0.303055\pi$
$911$	17.2161	+	5.59384i	0.570394	+	0.185332i	−0.00959850	+	0.999954i	$0.503055\pi$
$912$	18.2438	−	0.0377931i	0.604111	−	0.00125145i
$913$	−1.63811	+	3.21497i	−0.0542136	+	0.106400i
$914$	5.77602	+	8.63474i	0.191054	+	0.285612i
$915$	−1.18838	−	1.02723i	−0.0392867	−	0.0339593i
$916$	12.0237	−	7.38524i	0.397273	−	0.244015i
$917$	0.876352	−	5.53307i	0.0289397	−	0.182718i
$918$	−8.22850	+	0.978229i	−0.271581	+	0.0322864i
$919$	2.80257	−	2.03619i	0.0924483	−	0.0671676i	−0.540601	−	0.841279i	$-0.681803\pi$
$919$	2.80257	−	2.03619i	0.0924483	−	0.0671676i	0.633049	+	0.774112i	$0.281803\pi$
$920$	−0.479540	+	0.602843i	−0.0158100	+	0.0198751i
$921$	−0.746213	−	0.542155i	−0.0245885	−	0.0178646i
$922$	3.90664	+	2.18517i	0.128658	+	0.0719647i
$923$	−20.7501	−	40.7243i	−0.682996	−	1.34046i
$924$	−1.14824	−	4.76101i	−0.0377742	−	0.156626i
$925$	−0.259982	+	21.9021i	−0.00854816	+	0.720136i
$926$	−13.1388	+	16.6843i	−0.431769	+	0.548280i
$927$	−1.22669	+	0.625032i	−0.0402899	+	0.0205287i
$928$	1.11319	−	30.3346i	0.0365422	−	0.995783i
$929$	−11.6360	+	16.0155i	−0.381764	+	0.525453i	−0.956051	−	0.293201i	$-0.905279\pi$
$929$	−11.6360	+	16.0155i	−0.381764	+	0.525453i	0.574287	+	0.818654i	$0.305279\pi$
$930$	1.14813	+	33.9023i	0.0376487	+	1.11170i
$931$	8.29439	+	11.4163i	0.271838	+	0.374153i
$932$	−30.6727	−	18.7526i	−1.00472	−	0.614262i
$933$	−13.3347	−	2.11201i	−0.436559	−	0.0691442i
$934$	14.2331	−	38.6422i	0.465722	−	1.26441i
$935$	−8.39973	−	13.8915i	−0.274701	−	0.454301i
$936$	−12.0533	−	11.1073i	−0.393976	−	0.363054i
$937$	0.205689	+	0.104804i	0.00671957	+	0.00342379i	0.457347	−	0.889288i	$-0.348800\pi$
$937$	0.205689	+	0.104804i	0.00671957	+	0.00342379i	−0.450627	+	0.892712i	$0.648800\pi$
$938$	−18.1159	+	8.36291i	−0.591504	+	0.273059i
$939$	−4.12051	+	12.6816i	−0.134468	+	0.413850i
$940$	−14.5185	−	14.6615i	−0.473541	−	0.478204i
$941$	8.65557	+	26.6391i	0.282163	+	0.868410i	0.987235	+	0.159273i	$0.0509150\pi$
$941$	8.65557	+	26.6391i	0.282163	+	0.868410i	−0.705071	+	0.709137i	$0.749085\pi$
$942$	13.1438	+	14.2041i	0.428247	+	0.462794i
$943$	0.526684	−	0.526684i	0.0171512	−	0.0171512i
$944$	−16.6429	+	32.8316i	−0.541682	+	1.06858i
$945$	−3.37745	+	2.85012i	−0.109868	+	0.0927144i
$946$	4.63372	+	16.3974i	0.150655	+	0.533126i
$947$	−4.02669	−	25.4235i	−0.130850	−	0.826152i	−0.962585	−	0.270980i	$-0.912652\pi$
$947$	−4.02669	−	25.4235i	−0.130850	−	0.826152i	0.831735	−	0.555172i	$-0.187348\pi$
$948$	16.3704	+	19.1272i	0.531687	+	0.621222i
$949$		−	30.8201i		−	1.00046i
$950$	20.2525	−	25.0988i	0.657077	−	0.814313i
$951$		−	26.0210i		−	0.843789i
$952$	1.33678	+	32.7270i	0.0433252	+	1.06069i
$953$	1.46424	+	9.24486i	0.0474314	+	0.299470i	0.999988	−	0.00489121i	$-0.00155693\pi$
$953$	1.46424	+	9.24486i	0.0474314	+	0.299470i	−0.952557	+	0.304361i	$0.901557\pi$
$954$	0.0282672	−	0.00798797i	0.000915183	−	0.000258620i
$955$	−1.61398	+	6.55119i	−0.0522273	+	0.211992i
$956$	16.7019	−	19.5964i	0.540177	−	0.633794i
$957$	−4.70129	+	4.70129i	−0.151971	+	0.151971i
$958$	36.5292	−	33.8023i	1.18020	−	1.09210i
$959$	−5.26577	−	16.2064i	−0.170041	−	0.523331i
$960$	−17.8885	−	0.0505794i	−0.577348	−	0.00163244i
$961$	−25.9785	+	79.9537i	−0.838017	+	2.57915i
$962$	−15.0474	−	32.5960i	−0.485149	−	1.05094i
$963$	−6.27734	−	3.19847i	−0.202285	−	0.103069i
$964$	1.93443	−	24.9091i	0.0623037	−	0.802267i
$965$	−31.3367	+	7.32686i	−1.00876	+	0.235860i
$966$	−0.319444	−	0.117661i	−0.0102780	−	0.00378569i
$967$	18.9790	+	3.00598i	0.610325	+	0.0966659i	0.453943	−	0.891031i	$-0.350017\pi$
$967$	18.9790	+	3.00598i	0.610325	+	0.0966659i	0.156382	+	0.987697i	$0.450017\pi$
$968$	25.1015	−	9.30478i	0.806794	−	0.299067i
$969$	15.7082	+	21.6205i	0.504621	+	0.694551i
$970$	−19.3285	−	13.0669i	−0.620601	−	0.419553i
$971$	6.41370	−	8.82770i	0.205825	−	0.283294i	−0.693608	−	0.720353i	$-0.743980\pi$
$971$	6.41370	−	8.82770i	0.205825	−	0.283294i	0.899433	+	0.437059i	$0.143980\pi$
$972$	1.84697	−	0.767280i	0.0592414	−	0.0246105i
$973$	18.1210	−	9.23311i	0.580933	−	0.296000i
$974$	−4.62406	−	3.64143i	−0.148164	−	0.116679i
$975$	−28.6700	+	4.19269i	−0.918176	+	0.134273i
$976$	2.50105	−	1.28088i	0.0800565	−	0.0409999i
$977$	21.8301	+	42.8440i	0.698408	+	1.37070i	0.918578	+	0.395241i	$0.129339\pi$
$977$	21.8301	+	42.8440i	0.698408	+	1.37070i	−0.220170	+	0.975461i	$0.570661\pi$
$978$	−16.0282	+	28.6553i	−0.512527	+	0.916295i
$979$	9.65772	+	7.01675i	0.308662	+	0.224256i
$980$	−8.07795	−	11.2337i	−0.258041	−	0.358846i
$981$	14.9813	−	10.8846i	0.478316	−	0.347517i
$982$	6.81909	+	57.3597i	0.217606	+	1.83042i
$983$	−6.21015	+	39.2093i	−0.198073	+	1.25058i	0.665515	+	0.746385i	$0.268212\pi$
$983$	−6.21015	+	39.2093i	−0.198073	+	1.25058i	−0.863588	+	0.504199i	$0.831788\pi$
$984$	17.1804	+	2.00637i	0.547690	+	0.0639607i
$985$	−0.0879494	+	0.208815i	−0.00280230	+	0.00665339i
$986$	36.9590	−	24.7229i	1.17702	−	0.787338i
$987$	4.13977	−	8.12476i	0.131770	−	0.258614i
$988$	−12.2870	+	51.4135i	−0.390901	+	1.63568i
$989$	1.12644	+	0.366003i	0.0358188	+	0.0116382i
$990$	2.86270	+	2.67516i	0.0909827	+	0.0850222i
$991$	14.6891	−	4.77277i	0.466614	−	0.151612i	−0.0662677	−	0.997802i	$-0.521109\pi$
$991$	14.6891	−	4.77277i	0.466614	−	0.151612i	0.532881	+	0.846190i	$0.321109\pi$
$992$	−56.9846	−	20.8552i	−1.80926	−	0.662155i
$993$	3.09476	+	3.09476i	0.0982092	+	0.0982092i
$994$	0.854063	−	22.0281i	0.0270892	−	0.698690i
$995$	15.4094	−	24.8141i	0.488511	−	0.786659i
$996$	−2.22332	+	5.38334i	−0.0704486	+	0.170578i
$997$	4.13055	−	0.654215i	0.130816	−	0.0207192i	−0.0906832	−	0.995880i	$-0.528905\pi$
$997$	4.13055	−	0.654215i	0.130816	−	0.0207192i	0.221499	+	0.975161i	$0.428905\pi$
$998$	−7.40736	+	37.3403i	−0.234476	+	1.18199i
$999$	4.38072			0.138600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.103.17	yes	240
3.2	odd	2		900.2.bj.f.703.14		240
4.3	odd	2	inner	300.2.w.a.103.6	yes	240
12.11	even	2		900.2.bj.f.703.25		240
25.17	odd	20	inner	300.2.w.a.67.6	✓	240
75.17	even	20		900.2.bj.f.667.25		240
100.67	even	20	inner	300.2.w.a.67.17	yes	240
300.167	odd	20		900.2.bj.f.667.14		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.6	✓	240	25.17	odd	20	inner
300.2.w.a.67.17	yes	240	100.67	even	20	inner
300.2.w.a.103.6	yes	240	4.3	odd	2	inner
300.2.w.a.103.17	yes	240	1.1	even	1	trivial
900.2.bj.f.667.14		240	300.167	odd	20
900.2.bj.f.667.25		240	75.17	even	20
900.2.bj.f.703.14		240	3.2	odd	2
900.2.bj.f.703.25		240	12.11	even	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.275181 - 1.38718i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.84855 - 0.763453i) q^{4} +(-1.17964 + 1.89959i) q^{5} +(-0.0547899 + 1.41315i) q^{6} +(-1.39751 - 1.39751i) q^{7} +(-1.56773 + 2.35419i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(0.275181 - 1.38718i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.84855 - 0.763453i) q^{4} +(-1.17964 + 1.89959i) q^{5} +(-0.0547899 + 1.41315i) q^{6} +(-1.39751 - 1.39751i) q^{7} +(-1.56773 + 2.35419i) q^{8} +(0.951057 - 0.309017i) q^{9} +(2.31047 + 2.15910i) q^{10} +(1.17837 + 0.382876i) q^{11} +(1.94522 + 0.464876i) q^{12} +(-2.63087 + 5.16338i) q^{13} +(-2.32317 + 1.55403i) q^{14} +(0.867952 - 2.06074i) q^{15} +(2.83428 + 2.82256i) q^{16} +(-0.916613 + 5.78726i) q^{17} +(-0.166950 - 1.40432i) q^{18} +(-3.68988 + 2.68086i) q^{19} +(3.63087 - 2.61090i) q^{20} +(1.59892 + 1.16169i) q^{21} +(0.855385 - 1.52926i) q^{22} +(-0.0552946 - 0.108522i) q^{23} +(1.18016 - 2.57045i) q^{24} +(-2.21691 - 4.48166i) q^{25} +(6.43858 + 5.07037i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(1.51644 + 3.65030i) q^{28} +(3.15410 - 4.34124i) q^{29} +(-2.61978 - 1.77108i) q^{30} +(-6.30517 - 8.67832i) q^{31} +(4.69535 - 3.15495i) q^{32} +(-1.22376 - 0.193825i) q^{33} +(7.77576 + 2.86405i) q^{34} +(4.30325 - 1.00615i) q^{35} +(-1.99400 - 0.154853i) q^{36} +(-3.90325 - 1.98881i) q^{37} +(2.70345 + 5.85626i) q^{38} +(1.79075 - 5.51137i) q^{39} +(-2.62265 - 5.75515i) q^{40} +(1.88978 + 5.81615i) q^{41} +(2.05146 - 1.89832i) q^{42} +(-6.87625 + 6.87625i) q^{43} +(-1.88597 - 1.60740i) q^{44} +(-0.534894 + 2.17115i) q^{45} +(-0.165756 + 0.0468406i) q^{46} +(-0.721759 - 4.55701i) q^{47} +(-3.24093 - 2.34443i) q^{48} -3.09393i q^{49} +(-6.82694 + 1.84200i) q^{50} -5.85940i q^{51} +(8.80530 - 7.53622i) q^{52} +(0.00324925 + 0.0205149i) q^{53} +(0.384580 + 1.36092i) q^{54} +(-2.11736 + 1.78677i) q^{55} +(5.48093 - 1.09908i) q^{56} +(3.22508 - 3.22508i) q^{57} +(-5.15414 - 5.56993i) q^{58} +(2.84365 + 8.75185i) q^{59} +(-3.17773 + 3.14675i) q^{60} +(0.217081 - 0.668108i) q^{61} +(-13.7735 + 6.35831i) q^{62} +(-1.76096 - 0.897256i) q^{63} +(-3.08442 - 7.38149i) q^{64} +(-6.70485 - 11.0885i) q^{65} +(-0.605625 + 1.64424i) q^{66} +(7.05089 + 1.11675i) q^{67} +(6.11271 - 9.99826i) q^{68} +(0.0715904 + 0.0985357i) q^{69} +(-0.211536 - 6.24627i) q^{70} +(-4.63594 + 6.38083i) q^{71} +(-0.763519 + 2.72342i) q^{72} +(-4.73873 + 2.41450i) q^{73} +(-3.83294 + 4.86724i) q^{74} +(2.89071 + 4.07968i) q^{75} +(8.86765 - 2.13865i) q^{76} +(-1.11171 - 2.18186i) q^{77} +(-7.15249 - 4.00072i) q^{78} +(10.1840 + 7.39910i) q^{79} +(-8.70514 + 2.05438i) q^{80} +(0.809017 - 0.587785i) q^{81} +(8.58809 - 1.02098i) q^{82} +(-0.455567 + 2.87634i) q^{83} +(-2.06880 - 3.36814i) q^{84} +(-9.91218 - 8.56806i) q^{85} +(7.64640 + 11.4308i) q^{86} +(-2.43614 + 4.78120i) q^{87} +(-2.74874 + 2.17386i) q^{88} +(9.16320 + 2.97730i) q^{89} +(2.86459 + 1.33946i) q^{90} +(10.8925 - 3.53920i) q^{91} +(0.0193637 + 0.242823i) q^{92} +(7.58513 + 7.58513i) q^{93} +(-6.52001 - 0.252790i) q^{94} +(-0.739818 - 10.1717i) q^{95} +(-4.14400 + 3.85062i) q^{96} +(-7.28707 + 1.15416i) q^{97} +(-4.29185 - 0.851392i) q^{98} +1.23901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more