LMFDB - Embedded newform 671.2.f.a.538.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (of order $4$, degree $2$, 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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.2
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91322 - 1.91322i) q^{2} -0.958783i q^{3} +5.32085i q^{4} -2.33392i q^{5} +(-1.83437 + 1.83437i) q^{6} +(-0.592146 - 0.592146i) q^{7} +(6.35353 - 6.35353i) q^{8} +2.08073 q^{9} +O(q^{10})$	\(q+(-1.91322 - 1.91322i) q^{2} -0.958783i q^{3} +5.32085i q^{4} -2.33392i q^{5} +(-1.83437 + 1.83437i) q^{6} +(-0.592146 - 0.592146i) q^{7} +(6.35353 - 6.35353i) q^{8} +2.08073 q^{9} +(-4.46532 + 4.46532i) q^{10} +(-1.36370 + 3.02330i) q^{11} +5.10154 q^{12} -4.08412i q^{13} +2.26582i q^{14} -2.23773 q^{15} -13.6697 q^{16} +(5.38605 - 5.38605i) q^{17} +(-3.98091 - 3.98091i) q^{18} -5.62579 q^{19} +12.4185 q^{20} +(-0.567740 + 0.567740i) q^{21} +(8.39331 - 3.17517i) q^{22} +(0.966831 - 0.966831i) q^{23} +(-6.09166 - 6.09166i) q^{24} -0.447202 q^{25} +(-7.81383 + 7.81383i) q^{26} -4.87132i q^{27} +(3.15072 - 3.15072i) q^{28} +(-2.42384 + 2.42384i) q^{29} +(4.28127 + 4.28127i) q^{30} +(-4.15421 - 4.15421i) q^{31} +(13.4462 + 13.4462i) q^{32} +(2.89868 + 1.30750i) q^{33} -20.6094 q^{34} +(-1.38202 + 1.38202i) q^{35} +11.0713i q^{36} +(-3.09968 - 3.09968i) q^{37} +(10.7634 + 10.7634i) q^{38} -3.91578 q^{39} +(-14.8287 - 14.8287i) q^{40} +6.63329 q^{41} +2.17243 q^{42} +(-4.40478 + 4.40478i) q^{43} +(-16.0865 - 7.25606i) q^{44} -4.85628i q^{45} -3.69953 q^{46} -11.3005 q^{47} +13.1063i q^{48} -6.29873i q^{49} +(0.855598 + 0.855598i) q^{50} +(-5.16405 - 5.16405i) q^{51} +21.7310 q^{52} +(-2.37366 + 2.37366i) q^{53} +(-9.31993 + 9.31993i) q^{54} +(7.05614 + 3.18278i) q^{55} -7.52444 q^{56} +5.39392i q^{57} +9.27471 q^{58} +(3.54716 + 3.54716i) q^{59} -11.9066i q^{60} +(5.18327 + 5.84241i) q^{61} +15.8959i q^{62} +(-1.23210 - 1.23210i) q^{63} -24.1118i q^{64} -9.53202 q^{65} +(-3.04430 - 8.04736i) q^{66} +(-2.40262 - 2.40262i) q^{67} +(28.6584 + 28.6584i) q^{68} +(-0.926981 - 0.926981i) q^{69} +5.28825 q^{70} +(4.46228 + 4.46228i) q^{71} +(13.2200 - 13.2200i) q^{72} +16.0876i q^{73} +11.8608i q^{74} +0.428770i q^{75} -29.9340i q^{76} +(2.59775 - 0.982722i) q^{77} +(7.49177 + 7.49177i) q^{78} +(-0.984715 - 0.984715i) q^{79} +31.9042i q^{80} +1.57166 q^{81} +(-12.6910 - 12.6910i) q^{82} -13.7065i q^{83} +(-3.02086 - 3.02086i) q^{84} +(-12.5706 - 12.5706i) q^{85} +16.8546 q^{86} +(2.32394 + 2.32394i) q^{87} +(10.5443 + 27.8729i) q^{88} +(9.01441 + 9.01441i) q^{89} +(-9.29115 + 9.29115i) q^{90} +(-2.41840 + 2.41840i) q^{91} +(5.14436 + 5.14436i) q^{92} +(-3.98299 + 3.98299i) q^{93} +(21.6204 + 21.6204i) q^{94} +13.1302i q^{95} +(12.8920 - 12.8920i) q^{96} +2.06420i q^{97} +(-12.0509 + 12.0509i) q^{98} +(-2.83750 + 6.29068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.91322	−	1.91322i	−1.35285	−	1.35285i	−0.882453	−	0.470400i	$-0.844110\pi$
$2$	−1.91322	−	1.91322i	−1.35285	−	1.35285i	−0.470400	−	0.882453i	$-0.655890\pi$
$3$		−	0.958783i		−	0.553554i	−0.960934	−	0.276777i	$-0.910734\pi$
$3$		−	0.958783i		−	0.553554i	0.960934	−	0.276777i	$-0.0892663\pi$
$4$			5.32085i			2.66043i
$5$		−	2.33392i		−	1.04376i	−0.853018	−	0.521881i	$-0.825230\pi$
$5$		−	2.33392i		−	1.04376i	0.853018	−	0.521881i	$-0.174770\pi$
$6$	−1.83437	+	1.83437i	−0.748877	+	0.748877i
$7$	−0.592146	−	0.592146i	−0.223810	−	0.223810i	0.586291	−	0.810101i	$-0.300588\pi$
$7$	−0.592146	−	0.592146i	−0.223810	−	0.223810i	−0.810101	+	0.586291i	$0.800588\pi$
$8$	6.35353	−	6.35353i	2.24631	−	2.24631i
$9$	2.08073			0.693578
$10$	−4.46532	+	4.46532i	−1.41206	+	1.41206i
$11$	−1.36370	+	3.02330i	−0.411172	+	0.911558i
$11$	−1.36370	+	3.02330i	−0.411172	+	0.911558i
$12$	5.10154			1.47269
$13$		−	4.08412i		−	1.13273i	−0.824154	−	0.566365i	$-0.808349\pi$
$13$		−	4.08412i		−	1.13273i	0.824154	−	0.566365i	$-0.191651\pi$
$14$			2.26582i			0.605565i
$15$	−2.23773			−0.577779
$16$	−13.6697			−3.41744
$17$	5.38605	−	5.38605i	1.30631	−	1.30631i	0.382249	−	0.924059i	$-0.375150\pi$
$17$	5.38605	−	5.38605i	1.30631	−	1.30631i	0.924059	−	0.382249i	$-0.124850\pi$
$18$	−3.98091	−	3.98091i	−0.938310	−	0.938310i
$19$	−5.62579			−1.29065			−0.645323	−	0.763910i	$-0.723277\pi$
$19$	−5.62579			−1.29065			−0.645323	+	0.763910i	$0.723277\pi$
$20$	12.4185			2.77685
$21$	−0.567740	+	0.567740i	−0.123891	+	0.123891i
$22$	8.39331	−	3.17517i	1.78946	−	0.676949i
$23$	0.966831	−	0.966831i	0.201598	−	0.201598i	−0.599086	−	0.800684i	$-0.704469\pi$
$23$	0.966831	−	0.966831i	0.201598	−	0.201598i	0.800684	+	0.599086i	$0.204469\pi$
$24$	−6.09166	−	6.09166i	−1.24345	−	1.24345i
$25$	−0.447202			−0.0894405
$26$	−7.81383	+	7.81383i	−1.53242	+	1.53242i
$27$		−	4.87132i		−	0.937487i
$28$	3.15072	−	3.15072i	0.595431	−	0.595431i
$29$	−2.42384	+	2.42384i	−0.450097	+	0.450097i	−0.895386	−	0.445290i	$-0.853101\pi$
$29$	−2.42384	+	2.42384i	−0.450097	+	0.450097i	0.445290	+	0.895386i	$0.353101\pi$
$30$	4.28127	+	4.28127i	0.781650	+	0.781650i
$31$	−4.15421	−	4.15421i	−0.746118	−	0.746118i	0.227629	−	0.973748i	$-0.426903\pi$
$31$	−4.15421	−	4.15421i	−0.746118	−	0.746118i	−0.973748	+	0.227629i	$0.926903\pi$
$32$	13.4462	+	13.4462i	2.37698	+	2.37698i
$33$	2.89868	+	1.30750i	0.504596	+	0.227606i
$34$	−20.6094			−3.53449
$35$	−1.38202	+	1.38202i	−0.233605	+	0.233605i
$36$			11.0713i			1.84521i
$37$	−3.09968	−	3.09968i	−0.509584	−	0.509584i	0.404814	−	0.914399i	$-0.367336\pi$
$37$	−3.09968	−	3.09968i	−0.509584	−	0.509584i	−0.914399	+	0.404814i	$0.867336\pi$
$38$	10.7634	+	10.7634i	1.74605	+	1.74605i
$39$	−3.91578			−0.627027
$40$	−14.8287	−	14.8287i	−2.34462	−	2.34462i
$41$	6.63329			1.03595			0.517973	−	0.855397i	$-0.326687\pi$
$41$	6.63329			1.03595			0.517973	+	0.855397i	$0.326687\pi$
$42$	2.17243			0.335213
$43$	−4.40478	+	4.40478i	−0.671722	+	0.671722i	−0.958113	−	0.286391i	$-0.907544\pi$
$43$	−4.40478	+	4.40478i	−0.671722	+	0.671722i	0.286391	+	0.958113i	$0.407544\pi$
$44$	−16.0865	−	7.25606i	−2.42513	−	1.09389i
$45$		−	4.85628i		−	0.723931i
$46$	−3.69953			−0.545466
$47$	−11.3005			−1.64835			−0.824173	−	0.566339i	$-0.808359\pi$
$47$	−11.3005			−1.64835			−0.824173	+	0.566339i	$0.808359\pi$
$48$			13.1063i			1.89173i
$49$		−	6.29873i		−	0.899818i
$50$	0.855598	+	0.855598i	0.121000	+	0.121000i
$51$	−5.16405	−	5.16405i	−0.723112	−	0.723112i
$52$	21.7310			3.01355
$53$	−2.37366	+	2.37366i	−0.326047	+	0.326047i	−0.851081	−	0.525034i	$-0.824052\pi$
$53$	−2.37366	+	2.37366i	−0.326047	+	0.326047i	0.525034	+	0.851081i	$0.324052\pi$
$54$	−9.31993	+	9.31993i	−1.26828	+	1.26828i
$55$	7.05614	+	3.18278i	0.951450	+	0.429166i
$56$	−7.52444			−1.00550
$57$			5.39392i			0.714442i
$58$	9.27471			1.21783
$59$	3.54716	+	3.54716i	0.461801	+	0.461801i	0.899245	−	0.437444i	$-0.144116\pi$
$59$	3.54716	+	3.54716i	0.461801	+	0.461801i	−0.437444	+	0.899245i	$0.644116\pi$
$60$		−	11.9066i		−	1.53714i
$61$	5.18327	+	5.84241i	0.663649	+	0.748044i
$61$	5.18327	+	5.84241i	0.663649	+	0.748044i
$62$			15.8959i			2.01878i
$63$	−1.23210	−	1.23210i	−0.155230	−	0.155230i
$64$		−	24.1118i		−	3.01397i
$65$	−9.53202			−1.18230
$66$	−3.04430	−	8.04736i	−0.374728	−	0.990562i
$67$	−2.40262	−	2.40262i	−0.293527	−	0.293527i	0.544945	−	0.838472i	$-0.316551\pi$
$67$	−2.40262	−	2.40262i	−0.293527	−	0.293527i	−0.838472	+	0.544945i	$0.816551\pi$
$68$	28.6584	+	28.6584i	3.47534	+	3.47534i
$69$	−0.926981	−	0.926981i	−0.111595	−	0.111595i
$70$	5.28825			0.632066
$71$	4.46228	+	4.46228i	0.529575	+	0.529575i	0.920446	−	0.390870i	$-0.127826\pi$
$71$	4.46228	+	4.46228i	0.529575	+	0.529575i	−0.390870	+	0.920446i	$0.627826\pi$
$72$	13.2200	−	13.2200i	1.55799	−	1.55799i
$73$			16.0876i			1.88291i	0.337134	+	0.941457i	$0.390543\pi$
$73$			16.0876i			1.88291i	−0.337134	+	0.941457i	$0.609457\pi$
$74$			11.8608i			1.37879i
$75$			0.428770i			0.0495101i
$76$		−	29.9340i		−	3.43367i
$77$	2.59775	−	0.982722i	0.296041	−	0.111992i
$78$	7.49177	+	7.49177i	0.848276	+	0.848276i
$79$	−0.984715	−	0.984715i	−0.110789	−	0.110789i	0.649539	−	0.760328i	$-0.274962\pi$
$79$	−0.984715	−	0.984715i	−0.110789	−	0.110789i	−0.760328	+	0.649539i	$0.774962\pi$
$80$			31.9042i			3.56699i
$81$	1.57166			0.174629
$82$	−12.6910	−	12.6910i	−1.40148	−	1.40148i
$83$		−	13.7065i		−	1.50449i	−0.658884	−	0.752244i	$-0.728971\pi$
$83$		−	13.7065i		−	1.50449i	0.658884	−	0.752244i	$-0.271029\pi$
$84$	−3.02086	−	3.02086i	−0.329603	−	0.329603i
$85$	−12.5706	−	12.5706i	−1.36348	−	1.36348i
$86$	16.8546			1.81748
$87$	2.32394	+	2.32394i	0.249153	+	0.249153i
$88$	10.5443	+	27.8729i	1.12402	+	2.97126i
$89$	9.01441	+	9.01441i	0.955526	+	0.955526i	0.999052	−	0.0435265i	$-0.0138593\pi$
$89$	9.01441	+	9.01441i	0.955526	+	0.955526i	−0.0435265	+	0.999052i	$0.513859\pi$
$90$	−9.29115	+	9.29115i	−0.979373	+	0.979373i
$91$	−2.41840	+	2.41840i	−0.253517	+	0.253517i
$92$	5.14436	+	5.14436i	0.536337	+	0.536337i
$93$	−3.98299	+	3.98299i	−0.413017	+	0.413017i
$94$	21.6204	+	21.6204i	2.22997	+	2.22997i
$95$			13.1302i			1.34713i
$96$	12.8920	−	12.8920i	1.31579	−	1.31579i
$97$			2.06420i			0.209588i	0.994494	+	0.104794i	$0.0334184\pi$
$97$			2.06420i			0.209588i	−0.994494	+	0.104794i	$0.966582\pi$
$98$	−12.0509	+	12.0509i	−1.21732	+	1.21732i
$99$	−2.83750	+	6.29068i	−0.285180	+	0.632237i
$100$		−	2.37950i		−	0.237950i
$101$	−0.0419437	−	0.0419437i	−0.00417355	−	0.00417355i	0.705017	−	0.709190i	$-0.250939\pi$
$101$	−0.0419437	−	0.0419437i	−0.00417355	−	0.00417355i	−0.709190	+	0.705017i	$0.750939\pi$
$102$			19.7600i			1.95653i
$103$	−16.8142			−1.65675			−0.828376	−	0.560172i	$-0.810735\pi$
$103$	−16.8142			−1.65675			−0.828376	+	0.560172i	$0.810735\pi$
$104$	−25.9486	−	25.9486i	−2.54447	−	2.54447i
$105$	1.32506	+	1.32506i	0.129313	+	0.129313i
$106$	9.08267			0.882187
$107$	10.7530			1.03953			0.519765	−	0.854309i	$-0.326019\pi$
$107$	10.7530			1.03953			0.519765	+	0.854309i	$0.326019\pi$
$108$	25.9196			2.49411
$109$	−6.09471			−0.583767			−0.291884	−	0.956454i	$-0.594282\pi$
$109$	−6.09471			−0.583767			−0.291884	+	0.956454i	$0.594282\pi$
$110$	−7.41061	−	19.5893i	−0.706574	−	1.86777i
$111$	−2.97192	+	2.97192i	−0.282082	+	0.282082i
$112$	8.09449	+	8.09449i	0.764858	+	0.764858i
$113$		−	11.9692i		−	1.12596i	−0.826469	−	0.562982i	$-0.809654\pi$
$113$		−	11.9692i		−	1.12596i	0.826469	−	0.562982i	$-0.190346\pi$
$114$	10.3198	−	10.3198i	0.966535	−	0.966535i
$115$	−2.25651	−	2.25651i	−0.210421	−	0.210421i
$116$	−12.8969	−	12.8969i	−1.19745	−	1.19745i
$117$		−	8.49797i		−	0.785637i
$118$		−	13.5730i		−	1.24950i
$119$	−6.37866			−0.584731
$120$	−14.2175	+	14.2175i	−1.29787	+	1.29787i
$121$	−7.28063	−	8.24575i	−0.661875	−	0.749614i
$122$	1.26109	−	21.0946i	0.114174	−	1.90981i
$123$		−	6.35989i		−	0.573452i
$124$	22.1039	−	22.1039i	1.98499	−	1.98499i
$125$		−	10.6259i		−	0.950408i
$126$			4.71456i			0.420007i
$127$	−3.82377			−0.339305			−0.169652	−	0.985504i	$-0.554264\pi$
$127$	−3.82377			−0.339305			−0.169652	+	0.985504i	$0.554264\pi$
$128$	−19.2388	+	19.2388i	−1.70048	+	1.70048i
$129$	4.22323	+	4.22323i	0.371834	+	0.371834i
$130$	18.2369	+	18.2369i	1.59948	+	1.59948i
$131$		−	12.4911i		−	1.09136i	−0.837995	−	0.545678i	$-0.816272\pi$
$131$		−	12.4911i		−	1.09136i	0.837995	−	0.545678i	$-0.183728\pi$
$132$	−6.95699	+	15.4235i	−0.605528	+	1.34244i
$133$	3.33129	+	3.33129i	0.288860	+	0.288860i
$134$			9.19350i			0.794198i
$135$	−11.3693			−0.978513
$136$		−	68.4408i		−	5.86875i
$137$	−13.3749			−1.14270			−0.571349	−	0.820707i	$-0.693580\pi$
$137$	−13.3749			−1.14270			−0.571349	+	0.820707i	$0.693580\pi$
$138$			3.54705i			0.301945i
$139$	1.84990	−	1.84990i	0.156906	−	0.156906i	−0.624288	−	0.781194i	$-0.714611\pi$
$139$	1.84990	−	1.84990i	0.156906	−	0.156906i	0.781194	+	0.624288i	$0.214611\pi$
$140$	−7.35355	−	7.35355i	−0.621488	−	0.621488i
$141$			10.8347i			0.912448i
$142$		−	17.0747i		−	1.43288i
$143$	12.3475	+	5.56952i	1.03255	+	0.465747i
$144$	−28.4431			−2.37026
$145$	5.65707	+	5.65707i	0.469794	+	0.469794i
$146$	30.7792	−	30.7792i	2.54731	−	2.54731i
$147$	−6.03911			−0.498098
$148$	16.4929	−	16.4929i	1.35571	−	1.35571i
$149$	−15.4663			−1.26705			−0.633526	−	0.773721i	$-0.718393\pi$
$149$	−15.4663			−1.26705			−0.633526	+	0.773721i	$0.718393\pi$
$150$	0.820333	−	0.820333i	0.0669799	−	0.0669799i
$151$	4.76741	−	4.76741i	0.387966	−	0.387966i	−0.485995	−	0.873962i	$-0.661543\pi$
$151$	4.76741	−	4.76741i	0.387966	−	0.387966i	0.873962	+	0.485995i	$0.161543\pi$
$152$	−35.7436	+	35.7436i	−2.89919	+	2.89919i
$153$	11.2069	−	11.2069i	0.906027	−	0.906027i
$154$	−6.85023	−	3.08990i	−0.552008	−	0.248991i
$155$	−9.69561	+	9.69561i	−0.778771	+	0.778771i
$156$		−	20.8353i		−	1.66816i
$157$	−8.37319	−	8.37319i	−0.668253	−	0.668253i	0.289058	−	0.957312i	$-0.406658\pi$
$157$	−8.37319	−	8.37319i	−0.668253	−	0.668253i	−0.957312	+	0.289058i	$0.906658\pi$
$158$			3.76796i			0.299763i
$159$	2.27582	+	2.27582i	0.180484	+	0.180484i
$160$	31.3825	−	31.3825i	2.48100	−	2.48100i
$161$	−1.14501			−0.0902395
$162$	−3.00694	−	3.00694i	−0.236248	−	0.236248i
$163$			0.0580409i			0.00454612i	0.999997	+	0.00227306i	$0.000723538\pi$
$163$			0.0580409i			0.00454612i	−0.999997	+	0.00227306i	$0.999276\pi$
$164$			35.2947i			2.75606i
$165$	3.05159	−	6.76531i	0.237566	−	0.526679i
$166$	−26.2237	+	26.2237i	−2.03535	+	2.03535i
$167$	−1.02878			−0.0796094			−0.0398047	−	0.999207i	$-0.512674\pi$
$167$	−1.02878			−0.0796094			−0.0398047	+	0.999207i	$0.512674\pi$
$168$			7.21431i			0.556596i
$169$	−3.68003			−0.283079
$170$			48.1008i			3.68917i
$171$	−11.7058			−0.895164
$172$	−23.4372	−	23.4372i	−1.78707	−	1.78707i
$173$	6.75990	+	6.75990i	0.513946	+	0.513946i	0.915733	−	0.401787i	$-0.131611\pi$
$173$	6.75990	+	6.75990i	0.513946	+	0.513946i	−0.401787	+	0.915733i	$0.631611\pi$
$174$		−	8.89244i		−	0.674134i
$175$	0.264809	+	0.264809i	0.0200177	+	0.0200177i
$176$	18.6415	−	41.3277i	1.40515	−	3.11519i
$177$	3.40096	−	3.40096i	0.255632	−	0.255632i
$178$		−	34.4932i		−	2.58537i
$179$	12.2063			0.912341			0.456170	−	0.889892i	$-0.349221\pi$
$179$	12.2063			0.912341			0.456170	+	0.889892i	$0.349221\pi$
$180$	25.8395			1.92596
$181$	−2.26745	−	2.26745i	−0.168538	−	0.168538i	0.617799	−	0.786336i	$-0.288025\pi$
$181$	−2.26745	−	2.26745i	−0.168538	−	0.168538i	−0.786336	+	0.617799i	$0.788025\pi$
$182$	9.25387			0.685942
$183$	5.60160	−	4.96963i	0.414082	−	0.367366i
$184$		−	12.2856i		−	0.905705i
$185$	−7.23442	+	7.23442i	−0.531885	+	0.531885i
$186$	15.2407			1.11750
$187$	8.93865	+	23.6286i	0.653659	+	1.72789i
$188$		−	60.1282i		−	4.38530i
$189$	−2.88454	+	2.88454i	−0.209819	+	0.209819i
$190$	25.1210	−	25.1210i	1.82247	−	1.82247i
$191$	−2.30719	−	2.30719i	−0.166943	−	0.166943i	0.618691	−	0.785634i	$-0.287663\pi$
$191$	−2.30719	−	2.30719i	−0.166943	−	0.166943i	−0.785634	+	0.618691i	$0.787663\pi$
$192$	−23.1180			−1.66840
$193$	0.328861	−	0.328861i	0.0236719	−	0.0236719i	−0.695172	−	0.718844i	$-0.744672\pi$
$193$	0.328861	−	0.328861i	0.0236719	−	0.0236719i	0.718844	+	0.695172i	$0.244672\pi$
$194$	3.94928	−	3.94928i	0.283542	−	0.283542i
$195$			9.13914i			0.654468i
$196$	33.5146			2.39390
$197$	−8.89551			−0.633779			−0.316890	−	0.948462i	$-0.602638\pi$
$197$	−8.89551			−0.633779			−0.316890	+	0.948462i	$0.602638\pi$
$198$	17.4642	−	6.60669i	1.24113	−	0.469517i
$199$	19.1048			1.35430			0.677150	−	0.735845i	$-0.263215\pi$
$199$	19.1048			1.35430			0.677150	+	0.735845i	$0.263215\pi$
$200$	−2.84131	+	2.84131i	−0.200911	+	0.200911i
$201$	−2.30359	+	2.30359i	−0.162483	+	0.162483i
$202$			0.160495i			0.0112924i
$203$	2.87054			0.201473
$204$	27.4771	−	27.4771i	1.92379	−	1.92379i
$205$		−	15.4816i		−	1.08128i
$206$	32.1693	+	32.1693i	2.24134	+	2.24134i
$207$	2.01172	−	2.01172i	0.139824	−	0.139824i
$208$			55.8289i			3.87104i
$209$	7.67191	−	17.0084i	0.530677	−	1.17650i
$210$		−	5.07028i		−	0.349883i
$211$	6.93336	−	6.93336i	0.477312	−	0.477312i	−0.426959	−	0.904271i	$-0.640415\pi$
$211$	6.93336	−	6.93336i	0.477312	−	0.477312i	0.904271	+	0.426959i	$0.140415\pi$
$212$	−12.6299	−	12.6299i	−0.867423	−	0.867423i
$213$	4.27836	−	4.27836i	0.293148	−	0.293148i
$214$	−20.5729	−	20.5729i	−1.40633	−	1.40633i
$215$	10.2804	+	10.2804i	0.701118	+	0.701118i
$216$	−30.9501	−	30.9501i	−2.10589	−	2.10589i
$217$			4.91980i			0.333978i
$218$	11.6605	+	11.6605i	0.789752	+	0.789752i
$219$	15.4245			1.04229
$220$	−16.9351	+	37.5447i	−1.14176	+	2.53126i
$221$	−21.9973	−	21.9973i	−1.47970	−	1.47970i
$222$	11.3719			0.763232
$223$	5.48848	−	5.48848i	0.367536	−	0.367536i	−0.499042	−	0.866578i	$-0.666315\pi$
$223$	5.48848	−	5.48848i	0.367536	−	0.367536i	0.866578	+	0.499042i	$0.166315\pi$
$224$		−	15.9243i		−	1.06398i
$225$	−0.930510			−0.0620340
$226$	−22.8997	+	22.8997i	−1.52326	+	1.52326i
$227$	1.18426	+	1.18426i	0.0786018	+	0.0786018i	0.745315	−	0.666713i	$-0.232299\pi$
$227$	1.18426	+	1.18426i	0.0786018	+	0.0786018i	−0.666713	+	0.745315i	$0.732299\pi$
$228$	−28.7002			−1.90072
$229$			18.4092i			1.21651i	0.793741	+	0.608256i	$0.208131\pi$
$229$			18.4092i			1.21651i	−0.793741	+	0.608256i	$0.791869\pi$
$230$			8.63442i			0.569337i
$231$	−0.942217	−	2.49067i	−0.0619933	−	0.163874i
$232$			30.7999i			2.02211i
$233$	−9.56541	−	9.56541i	−0.626651	−	0.626651i	0.320573	−	0.947224i	$-0.396125\pi$
$233$	−9.56541	−	9.56541i	−0.626651	−	0.626651i	−0.947224	+	0.320573i	$0.896125\pi$
$234$	−16.2585	+	16.2585i	−1.06285	+	1.06285i
$235$			26.3745i			1.72048i
$236$	−18.8739	+	18.8739i	−1.22859	+	1.22859i
$237$	−0.944128	+	0.944128i	−0.0613277	+	0.0613277i
$238$	12.2038	+	12.2038i	0.791055	+	0.791055i
$239$		−	28.1710i		−	1.82223i	−0.412150	−	0.911116i	$-0.635222\pi$
$239$		−	28.1710i		−	1.82223i	0.412150	−	0.911116i	$-0.364778\pi$
$240$	30.5892			1.97452
$241$			2.71439i			0.174849i	0.996171	+	0.0874247i	$0.0278637\pi$
$241$			2.71439i			0.174849i	−0.996171	+	0.0874247i	$0.972136\pi$
$242$	−1.84649	+	29.7054i	−0.118697	+	1.90954i
$243$		−	16.1209i		−	1.03415i
$244$	−31.0866	+	27.5794i	−1.99011	+	1.76559i
$245$	−14.7007			−0.939196
$246$	−12.1679	+	12.1679i	−0.775796	+	0.775796i
$247$			22.9764i			1.46195i
$248$	−52.7878			−3.35203
$249$	−13.1416			−0.832815
$250$	−20.3297	+	20.3297i	−1.28576	+	1.28576i
$251$	1.09015	−	1.09015i	0.0688098	−	0.0688098i	−0.671864	−	0.740674i	$-0.734506\pi$
$251$	1.09015	−	1.09015i	0.0688098	−	0.0688098i	0.740674	+	0.671864i	$0.234506\pi$
$252$	6.55582	−	6.55582i	0.412978	−	0.412978i
$253$	1.60455	+	4.24149i	0.100877	+	0.266660i
$254$	7.31573	+	7.31573i	0.459029	+	0.459029i
$255$	−12.0525	+	12.0525i	−0.754757	+	0.754757i
$256$	25.3926			1.58704
$257$	26.8258			1.67335			0.836674	−	0.547701i	$-0.184497\pi$
$257$	26.8258			1.67335			0.836674	+	0.547701i	$0.184497\pi$
$258$		−	16.1600i		−	1.00607i
$259$			3.67093i			0.228101i
$260$		−	50.7185i		−	3.14543i
$261$	−5.04338	+	5.04338i	−0.312177	+	0.312177i
$262$	−23.8983	+	23.8983i	−1.47644	+	1.47644i
$263$	24.9701			1.53972			0.769861	−	0.638212i	$-0.220326\pi$
$263$	24.9701			1.53972			0.769861	+	0.638212i	$0.220326\pi$
$264$	26.7241	−	10.1097i	1.64475	−	0.622207i
$265$	5.53993	+	5.53993i	0.340315	+	0.340315i
$266$		−	12.7470i		−	0.781570i
$267$	8.64287	−	8.64287i	0.528935	−	0.528935i
$268$	12.7840	−	12.7840i	0.780906	−	0.780906i
$269$	−11.4729			−0.699518			−0.349759	−	0.936840i	$-0.613736\pi$
$269$	−11.4729			−0.699518			−0.349759	+	0.936840i	$0.613736\pi$
$270$	21.7520	+	21.7520i	1.32379	+	1.32379i
$271$	−2.64643			−0.160759			−0.0803797	−	0.996764i	$-0.525613\pi$
$271$	−2.64643			−0.160759			−0.0803797	+	0.996764i	$0.525613\pi$
$272$	−73.6259	+	73.6259i	−4.46423	+	4.46423i
$273$	2.31872	+	2.31872i	0.140335	+	0.140335i
$274$	25.5893	+	25.5893i	1.54590	+	1.54590i
$275$	0.609851	−	1.35203i	0.0367754	−	0.0815302i
$276$	4.93233	−	4.93233i	0.296891	−	0.296891i
$277$	9.41910	+	9.41910i	0.565939	+	0.565939i	0.930988	−	0.365049i	$-0.118948\pi$
$277$	9.41910	+	9.41910i	0.565939	+	0.565939i	−0.365049	+	0.930988i	$0.618948\pi$
$278$	−7.07855			−0.424543
$279$	−8.64381	−	8.64381i	−0.517492	−	0.517492i
$280$			17.5615i			1.04950i
$281$	22.1616	−	22.1616i	1.32205	−	1.32205i	0.409936	−	0.912114i	$-0.365551\pi$
$281$	22.1616	−	22.1616i	1.32205	−	1.32205i	0.912114	−	0.409936i	$-0.134449\pi$
$282$	20.7292	−	20.7292i	1.23441	−	1.23441i
$283$	−10.9858			−0.653040			−0.326520	−	0.945190i	$-0.605876\pi$
$283$	−10.9858			−0.653040			−0.326520	+	0.945190i	$0.605876\pi$
$284$	−23.7431	+	23.7431i	−1.40890	+	1.40890i
$285$	12.5890			0.745707
$286$	−12.9678	−	34.2793i	−0.766801	−	2.02698i
$287$	−3.92788	−	3.92788i	−0.231855	−	0.231855i
$288$	27.9780	+	27.9780i	1.64862	+	1.64862i
$289$		−	41.0190i		−	2.41288i
$290$		−	21.6465i		−	1.27112i
$291$	1.97912			0.116018
$292$	−85.5998			−5.00935
$293$	25.9884			1.51826			0.759130	−	0.650940i	$-0.225625\pi$
$293$	25.9884			1.51826			0.759130	+	0.650940i	$0.225625\pi$
$294$	11.5542	+	11.5542i	0.673853	+	0.673853i
$295$	8.27880	−	8.27880i	0.482011	−	0.482011i
$296$	−39.3878			−2.28937
$297$	14.7274	+	6.64304i	0.854573	+	0.385468i
$298$	29.5906	+	29.5906i	1.71414	+	1.71414i
$299$	−3.94865	−	3.94865i	−0.228356	−	0.228356i
$300$	−2.28142			−0.131718
$301$	5.21655			0.300677
$302$	−18.2422			−1.04972
$303$	−0.0402149	+	0.0402149i	−0.00231029	+	0.00231029i
$304$	76.9032			4.41070
$305$	13.6357	−	12.0974i	0.780780	−	0.692692i
$306$	−42.8828			−2.45144
$307$	6.62909	+	6.62909i	0.378342	+	0.378342i	0.870504	−	0.492162i	$-0.163793\pi$
$307$	6.62909	+	6.62909i	0.378342	+	0.378342i	−0.492162	+	0.870504i	$0.663793\pi$
$308$	5.22892	+	13.8222i	0.297945	+	0.787594i
$309$			16.1212i			0.917101i
$310$	37.0998			2.10712
$311$	21.2947	+	21.2947i	1.20751	+	1.20751i	0.971831	+	0.235678i	$0.0757309\pi$
$311$	21.2947	+	21.2947i	1.20751	+	1.20751i	0.235678	+	0.971831i	$0.424269\pi$
$312$	−24.8791	+	24.8791i	−1.40850	+	1.40850i
$313$	21.5391	+	21.5391i	1.21746	+	1.21746i	0.968517	+	0.248947i	$0.0800846\pi$
$313$	21.5391	+	21.5391i	1.21746	+	1.21746i	0.248947	+	0.968517i	$0.419915\pi$
$314$			32.0396i			1.80810i
$315$	−2.87563	+	2.87563i	−0.162023	+	0.162023i
$316$	5.23952	−	5.23952i	0.294746	−	0.294746i
$317$	1.38049			0.0775362			0.0387681	−	0.999248i	$-0.487657\pi$
$317$	1.38049			0.0775362			0.0387681	+	0.999248i	$0.487657\pi$
$318$		−	8.70831i		−	0.488338i
$319$	−4.02259	−	10.6334i	−0.225222	−	0.595356i
$320$	−56.2751			−3.14587
$321$		−	10.3098i		−	0.575436i
$322$	2.19066	+	2.19066i	0.122081	+	0.122081i
$323$	−30.3008	+	30.3008i	−1.68598	+	1.68598i
$324$			8.36258i			0.464588i
$325$			1.82643i			0.101312i
$326$	0.111045	−	0.111045i	0.00615023	−	0.00615023i
$327$			5.84351i			0.323147i
$328$	42.1448	−	42.1448i	2.32706	−	2.32706i
$329$	6.69154	+	6.69154i	0.368917	+	0.368917i
$330$	−18.7819	+	7.10517i	−1.03391	+	0.391127i
$331$	20.9665	−	20.9665i	1.15242	−	1.15242i	0.166358	−	0.986065i	$-0.446799\pi$
$331$	20.9665	−	20.9665i	1.15242	−	1.15242i	0.986065	−	0.166358i	$-0.0532008\pi$
$332$	72.9305			4.00258
$333$	−6.44962	−	6.44962i	−0.353437	−	0.353437i
$334$	1.96829	+	1.96829i	0.107700	+	0.107700i
$335$	−5.60754	+	5.60754i	−0.306372	+	0.306372i
$336$	7.76086	−	7.76086i	0.423390	−	0.423390i
$337$	5.07438	+	5.07438i	0.276419	+	0.276419i	0.831678	−	0.555259i	$-0.187381\pi$
$337$	5.07438	+	5.07438i	0.276419	+	0.276419i	−0.555259	+	0.831678i	$0.687381\pi$
$338$	7.04071	+	7.04071i	0.382964	+	0.382964i
$339$	−11.4758			−0.623282
$340$	66.8864	−	66.8864i	3.62743	−	3.62743i
$341$	18.2245	−	6.89430i	0.986913	−	0.373347i
$342$	22.3958	+	22.3958i	1.21103	+	1.21103i
$343$	−7.87479	+	7.87479i	−0.425199	+	0.425199i
$344$			55.9718i			3.01779i
$345$	−2.16350	+	2.16350i	−0.116479	+	0.116479i
$346$		−	25.8664i		−	1.39059i
$347$		−	27.3926i		−	1.47051i	−0.677791	−	0.735255i	$-0.737063\pi$
$347$		−	27.3926i		−	1.47051i	0.677791	−	0.735255i	$-0.262937\pi$
$348$	−12.3653	+	12.3653i	−0.662852	+	0.662852i
$349$	7.15005	+	7.15005i	0.382733	+	0.382733i	0.872086	−	0.489353i	$-0.162767\pi$
$349$	7.15005	+	7.15005i	0.382733	+	0.382733i	−0.489353	+	0.872086i	$0.662767\pi$
$350$		−	1.01328i		−	0.0541620i
$351$	−19.8951			−1.06192
$352$	−58.9886	+	22.3153i	−3.14410	+	1.18941i
$353$		−	29.3101i		−	1.56002i	−0.625767	−	0.780010i	$-0.715214\pi$
$353$		−	29.3101i		−	1.56002i	0.625767	−	0.780010i	$-0.284786\pi$
$354$	−13.0136			−0.691664
$355$	10.4146	−	10.4146i	0.552751	−	0.552751i
$356$	−47.9643	+	47.9643i	−2.54210	+	2.54210i
$357$			6.11575i			0.323680i
$358$	−23.3534	−	23.3534i	−1.23426	−	1.23426i
$359$	−14.7227	+	14.7227i	−0.777036	+	0.777036i	−0.979326	−	0.202290i	$-0.935162\pi$
$359$	−14.7227	+	14.7227i	−0.777036	+	0.777036i	0.202290	+	0.979326i	$0.435162\pi$
$360$	−30.8545	−	30.8545i	−1.62617	−	1.62617i
$361$	12.6495			0.665766
$362$			8.67626i			0.456014i
$363$	−7.90589	+	6.98055i	−0.414952	+	0.366384i
$364$	−12.8679	−	12.8679i	−0.674463	−	0.674463i
$365$	37.5473			1.96531
$366$	−20.2251	−	1.20911i	−1.05718	−	0.0632012i
$367$	0.443563			0.0231538			0.0115769	−	0.999933i	$-0.496315\pi$
$367$	0.443563			0.0231538			0.0115769	+	0.999933i	$0.496315\pi$
$368$	−13.2163	+	13.2163i	−0.688949	+	0.688949i
$369$	13.8021			0.718509
$370$	27.6821			1.43913
$371$	2.81110			0.145945
$372$	−21.1929	−	21.1929i	−1.09880	−	1.09880i
$373$	−6.90355	−	6.90355i	−0.357452	−	0.357452i	0.505421	−	0.862873i	$-0.331337\pi$
$373$	−6.90355	−	6.90355i	−0.357452	−	0.357452i	−0.862873	+	0.505421i	$0.831337\pi$
$374$	28.1051	−	62.3084i	1.45328	−	3.22189i
$375$	−10.1879			−0.526102
$376$	−71.7980	+	71.7980i	−3.70270	+	3.70270i
$377$	9.89927	+	9.89927i	0.509838	+	0.509838i
$378$	11.0375			0.567709
$379$	−14.8062			−0.760541			−0.380270	−	0.924875i	$-0.624169\pi$
$379$	−14.8062			−0.760541			−0.380270	+	0.924875i	$0.624169\pi$
$380$	−69.8637			−3.58393
$381$			3.66617i			0.187823i
$382$			8.82836i			0.451698i
$383$	17.9562	+	17.9562i	0.917518	+	0.917518i	0.996848	−	0.0793301i	$-0.0252781\pi$
$383$	17.9562	+	17.9562i	0.917518	+	0.917518i	−0.0793301	+	0.996848i	$0.525278\pi$
$384$	18.4458	+	18.4458i	0.941309	+	0.941309i
$385$	−2.29360	−	6.06294i	−0.116893	−	0.308996i
$386$	−1.25837			−0.0640493
$387$	−9.16517	+	9.16517i	−0.465892	+	0.465892i
$388$	−10.9833			−0.557594
$389$	−21.3025	+	21.3025i	−1.08008	+	1.08008i	−0.0835759	+	0.996501i	$0.526634\pi$
$389$	−21.3025	+	21.3025i	−1.08008	+	1.08008i	−0.996501	+	0.0835759i	$0.973366\pi$
$390$	17.4852	−	17.4852i	0.885399	−	0.885399i
$391$		−	10.4148i		−	0.526699i
$392$	−40.0191	−	40.0191i	−2.02127	−	2.02127i
$393$	−11.9763			−0.604124
$394$	17.0191	+	17.0191i	0.857410	+	0.857410i
$395$	−2.29825	+	2.29825i	−0.115638	+	0.115638i
$396$	−33.4717	−	15.0979i	−1.68202	−	0.758700i
$397$	1.54691	+	1.54691i	0.0776374	+	0.0776374i	0.744859	−	0.667222i	$-0.232517\pi$
$397$	1.54691	+	1.54691i	0.0776374	+	0.0776374i	−0.667222	+	0.744859i	$0.732517\pi$
$398$	−36.5517	−	36.5517i	−1.83217	−	1.83217i
$399$	3.19399	−	3.19399i	0.159899	−	0.159899i
$400$	6.11314			0.305657
$401$	−5.22928	−	5.22928i	−0.261138	−	0.261138i	0.564378	−	0.825516i	$-0.309116\pi$
$401$	−5.22928	−	5.22928i	−0.261138	−	0.261138i	−0.825516	+	0.564378i	$0.809116\pi$
$402$	8.81458			0.439631
$403$	−16.9663	+	16.9663i	−0.845151	+	0.845151i
$404$	0.223176	−	0.223176i	0.0111034	−	0.0111034i
$405$		−	3.66814i		−	0.182271i
$406$	−5.49199	−	5.49199i	−0.272563	−	0.272563i
$407$	13.5983	−	5.14421i	0.674043	−	0.254989i
$408$	−65.6199			−3.24867
$409$	5.23319	−	5.23319i	0.258765	−	0.258765i	−0.565787	−	0.824552i	$-0.691428\pi$
$409$	5.23319	−	5.23319i	0.258765	−	0.258765i	0.824552	+	0.565787i	$0.191428\pi$
$410$	−29.6198	+	29.6198i	−1.46282	+	1.46282i
$411$			12.8237i			0.632545i
$412$		−	89.4658i		−	4.40767i
$413$		−	4.20088i		−	0.206712i
$414$	−7.69774			−0.378323
$415$	−31.9900			−1.57033
$416$	54.9160	−	54.9160i	2.69248	−	2.69248i
$417$	−1.77365	−	1.77365i	−0.0868562	−	0.0868562i
$418$	−47.2190	+	17.8629i	−2.30956	+	0.873701i
$419$	−13.2292	+	13.2292i	−0.646287	+	0.646287i	−0.952094	−	0.305807i	$-0.901074\pi$
$419$	−13.2292	+	13.2292i	−0.646287	+	0.646287i	0.305807	+	0.952094i	$0.401074\pi$
$420$	−7.05046	+	7.05046i	−0.344027	+	0.344027i
$421$	3.84964	−	3.84964i	0.187620	−	0.187620i	−0.607047	−	0.794666i	$-0.707646\pi$
$421$	3.84964	−	3.84964i	0.187620	−	0.187620i	0.794666	+	0.607047i	$0.207646\pi$
$422$	−26.5301			−1.29147
$423$	−23.5133			−1.14326
$424$			30.1622i			1.46481i
$425$	−2.40865	+	2.40865i	−0.116837	+	0.116837i
$426$	−16.3709			−0.793174
$427$	0.390309	−	6.52881i	0.0188884	−	0.315951i
$428$			57.2150i			2.76559i
$429$	5.33997	−	11.8386i	0.257816	−	0.571572i
$430$		−	39.3375i		−	1.89702i
$431$	24.8000			1.19457			0.597287	−	0.802028i	$-0.296245\pi$
$431$	24.8000			1.19457			0.597287	+	0.802028i	$0.296245\pi$
$432$			66.5898i			3.20380i
$433$	15.1930	+	15.1930i	0.730131	+	0.730131i	0.970646	−	0.240515i	$-0.0773162\pi$
$433$	15.1930	+	15.1930i	0.730131	+	0.730131i	−0.240515	+	0.970646i	$0.577316\pi$
$434$	9.41268	−	9.41268i	0.451823	−	0.451823i
$435$	5.42390	−	5.42390i	0.260056	−	0.260056i
$436$		−	32.4290i		−	1.55307i
$437$	−5.43919	+	5.43919i	−0.260192	+	0.260192i
$438$	−29.5106	−	29.5106i	−1.41007	−	1.41007i
$439$		−	9.49247i		−	0.453051i	−0.974005	−	0.226526i	$-0.927263\pi$
$439$		−	9.49247i		−	0.453051i	0.974005	−	0.226526i	$-0.0727367\pi$
$440$	65.0533	−	24.6095i	3.10129	−	1.17321i
$441$		−	13.1060i		−	0.624094i
$442$			84.1714i			4.00362i
$443$	25.3626			1.20501			0.602506	−	0.798114i	$-0.294169\pi$
$443$	25.3626			1.20501			0.602506	+	0.798114i	$0.294169\pi$
$444$	−15.8132	−	15.8132i	−0.750459	−	0.750459i
$445$	21.0390	−	21.0390i	0.997342	−	0.997342i
$446$	−21.0014			−0.994445
$447$			14.8289i			0.701382i
$448$	−14.2777	+	14.2777i	−0.674558	+	0.674558i
$449$	−15.4282			−0.728104			−0.364052	−	0.931379i	$-0.618607\pi$
$449$	−15.4282			−0.728104			−0.364052	+	0.931379i	$0.618607\pi$
$450$	1.78027	+	1.78027i	0.0839229	+	0.0839229i
$451$	−9.04583	+	20.0544i	−0.425952	+	0.944324i
$452$	63.6861			2.99554
$453$	−4.57091	−	4.57091i	−0.214760	−	0.214760i
$454$		−	4.53149i		−	0.212673i
$455$	5.64435	+	5.64435i	0.264611	+	0.264611i
$456$	34.2704	+	34.2704i	1.60486	+	1.60486i
$457$	2.72118	+	2.72118i	0.127291	+	0.127291i	0.767882	−	0.640591i	$-0.221311\pi$
$457$	2.72118	+	2.72118i	0.127291	+	0.127291i	−0.640591	+	0.767882i	$0.721311\pi$
$458$	35.2209	−	35.2209i	1.64576	−	1.64576i
$459$	−26.2372	−	26.2372i	−1.22465	−	1.22465i
$460$	12.0066	−	12.0066i	0.559808	−	0.559808i
$461$			9.81208i			0.456994i	0.973545	+	0.228497i	$0.0733811\pi$
$461$			9.81208i			0.456994i	−0.973545	+	0.228497i	$0.926619\pi$
$462$	−2.96255	+	6.56789i	−0.137830	+	0.305566i
$463$			11.0395i			0.513049i	0.966538	+	0.256525i	$0.0825774\pi$
$463$			11.0395i			0.513049i	−0.966538	+	0.256525i	$0.917423\pi$
$464$	33.1333	−	33.1333i	1.53818	−	1.53818i
$465$	9.29599	+	9.29599i	0.431091	+	0.431091i
$466$			36.6015i			1.69553i
$467$	15.3855	−	15.3855i	0.711958	−	0.711958i	−0.254987	−	0.966945i	$-0.582071\pi$
$467$	15.3855	−	15.3855i	0.711958	−	0.711958i	0.966945	+	0.254987i	$0.0820711\pi$
$468$	45.2164			2.09013
$469$			2.84541i			0.131389i
$470$	50.4603	−	50.4603i	2.32756	−	2.32756i
$471$	−8.02807	+	8.02807i	−0.369914	+	0.369914i
$472$	45.0740			2.07470
$473$	−7.31013	−	19.3237i	−0.336120	−	0.888507i
$474$	3.61266			0.165935
$475$	2.51587			0.115436
$476$		−	33.9399i		−	1.55563i
$477$	−4.93895	+	4.93895i	−0.226139	+	0.226139i
$478$	−53.8975	+	53.8975i	−2.46521	+	2.46521i
$479$	−3.86128			−0.176426			−0.0882132	−	0.996102i	$-0.528116\pi$
$479$	−3.86128			−0.176426			−0.0882132	+	0.996102i	$0.528116\pi$
$480$	−30.0890	−	30.0890i	−1.37337	−	1.37337i
$481$	−12.6595	+	12.6595i	−0.577222	+	0.577222i
$482$	5.19324	−	5.19324i	0.236546	−	0.236546i
$483$			1.09782i			0.0499524i
$484$	43.8744	−	38.7391i	1.99429	−	1.76087i
$485$	4.81770			0.218760
$486$	−30.8428	+	30.8428i	−1.39906	+	1.39906i
$487$		−	29.6378i		−	1.34302i	−0.740998	−	0.671508i	$-0.765647\pi$
$487$		−	29.6378i		−	1.34302i	0.740998	−	0.671508i	$-0.234353\pi$
$488$	70.0520	+	4.18788i	3.17110	+	0.189577i
$489$	0.0556487			0.00251652
$490$	28.1258	+	28.1258i	1.27059	+	1.27059i
$491$	−15.0897			−0.680988			−0.340494	−	0.940247i	$-0.610594\pi$
$491$	−15.0897			−0.680988			−0.340494	+	0.940247i	$0.610594\pi$
$492$	33.8400			1.52563
$493$			26.1099i			1.17593i
$494$	43.9590	−	43.9590i	1.97781	−	1.97781i
$495$	14.6820	+	6.62252i	0.659905	+	0.297660i
$496$	56.7870	+	56.7870i	2.54981	+	2.54981i
$497$		−	5.28465i		−	0.237049i
$498$	25.1428	+	25.1428i	1.12668	+	1.12668i
$499$	18.0040	+	18.0040i	0.805968	+	0.805968i	0.984021	−	0.178053i	$-0.0569797\pi$
$499$	18.0040	+	18.0040i	0.805968	+	0.805968i	−0.178053	+	0.984021i	$0.556980\pi$
$500$	56.5387			2.52849
$501$			0.986378i			0.0440681i
$502$	−4.17141			−0.186179
$503$		−	5.58606i		−	0.249070i	−0.992215	−	0.124535i	$-0.960256\pi$
$503$		−	5.58606i		−	0.249070i	0.992215	−	0.124535i	$-0.0397439\pi$
$504$	−15.6564			−0.697390
$505$	−0.0978934	+	0.0978934i	−0.00435620	+	0.00435620i
$506$	5.04506	−	11.1848i	0.224280	−	0.497223i
$507$			3.52835i			0.156699i
$508$		−	20.3457i		−	0.902694i
$509$	−9.10392	−	9.10392i	−0.403524	−	0.403524i	0.475949	−	0.879473i	$-0.342105\pi$
$509$	−9.10392	−	9.10392i	−0.403524	−	0.403524i	−0.879473	+	0.475949i	$0.842105\pi$
$510$	46.1183			2.04215
$511$	9.52623	−	9.52623i	0.421415	−	0.421415i
$512$	−10.1042	−	10.1042i	−0.446547	−	0.446547i
$513$			27.4051i			1.20996i
$514$	−51.3238	−	51.3238i	−2.26379	−	2.26379i
$515$			39.2431i			1.72926i
$516$	−22.4712	+	22.4712i	−0.989237	+	0.989237i
$517$	15.4105	−	34.1647i	0.677753	−	1.50256i
$518$	7.02331	−	7.02331i	0.308587	−	0.308587i
$519$	6.48128	−	6.48128i	0.284496	−	0.284496i
$520$	−60.5620	+	60.5620i	−2.65582	+	2.65582i
$521$	14.5974	−	14.5974i	0.639524	−	0.639524i	−0.310914	−	0.950438i	$-0.600635\pi$
$521$	14.5974	−	14.5974i	0.639524	−	0.639524i	0.950438	+	0.310914i	$0.100635\pi$
$522$	19.2982			0.844660
$523$	12.1555	−	12.1555i	0.531523	−	0.531523i	−0.389502	−	0.921025i	$-0.627353\pi$
$523$	12.1555	−	12.1555i	0.531523	−	0.531523i	0.921025	+	0.389502i	$0.127353\pi$
$524$	66.4635			2.90347
$525$	0.253895	−	0.253895i	0.0110809	−	0.0110809i
$526$	−47.7733	−	47.7733i	−2.08302	−	2.08302i
$527$	−44.7496			−1.94932
$528$	−39.6243	−	17.8731i	−1.72443	−	0.777828i
$529$			21.1305i			0.918716i
$530$		−	21.1983i		−	0.920794i
$531$	7.38070	+	7.38070i	0.320295	+	0.320295i
$532$	−17.7253	+	17.7253i	−0.768490	+	0.768490i
$533$		−	27.0911i		−	1.17345i
$534$	−33.0715			−1.43114
$535$		−	25.0966i		−	1.08502i
$536$	−30.5302			−1.31871
$537$		−	11.7032i		−	0.505030i
$538$	21.9503	+	21.9503i	0.946345	+	0.946345i
$539$	19.0429	+	8.58959i	0.820236	+	0.369980i
$540$		−	60.4943i		−	2.60326i
$541$	−17.3373	−	17.3373i	−0.745390	−	0.745390i	0.228220	−	0.973610i	$-0.426710\pi$
$541$	−17.3373	−	17.3373i	−0.745390	−	0.745390i	−0.973610	+	0.228220i	$0.926710\pi$
$542$	5.06322	+	5.06322i	0.217484	+	0.217484i
$543$	−2.17399	+	2.17399i	−0.0932948	+	0.0932948i
$544$	144.844			6.21014
$545$			14.2246i			0.609315i
$546$		−	8.87245i		−	0.379706i
$547$	−3.33751	+	3.33751i	−0.142702	+	0.142702i	−0.774849	−	0.632147i	$-0.782174\pi$
$547$	−3.33751	+	3.33751i	−0.142702	+	0.142702i	0.632147	+	0.774849i	$0.282174\pi$
$548$		−	71.1661i		−	3.04006i
$549$	10.7850	+	12.1565i	0.460293	+	0.518827i
$550$	−3.75351	+	1.41994i	−0.160050	+	0.0605467i
$551$	13.6360	−	13.6360i	0.580915	−	0.580915i
$552$	−11.7792			−0.501356
$553$			1.16619i			0.0495915i
$554$		−	36.0417i		−	1.53127i
$555$	6.93624	+	6.93624i	0.294427	+	0.294427i
$556$	9.84304	+	9.84304i	0.417438	+	0.417438i
$557$	−14.7231	+	14.7231i	−0.623839	+	0.623839i	−0.946511	−	0.322672i	$-0.895419\pi$
$557$	−14.7231	+	14.7231i	−0.623839	+	0.623839i	0.322672	+	0.946511i	$0.395419\pi$
$558$			33.0751i			1.40018i
$559$	17.9896	+	17.9896i	0.760880	+	0.760880i
$560$	18.8919	−	18.8919i	0.798330	−	0.798330i
$561$	22.6547	−	8.57022i	0.956482	−	0.361835i
$562$	−84.8002			−3.57708
$563$	24.5979			1.03668			0.518338	−	0.855176i	$-0.326551\pi$
$563$	24.5979			1.03668			0.518338	+	0.855176i	$0.326551\pi$
$564$	−57.6499			−2.42750
$565$	−27.9351			−1.17524
$566$	21.0184	+	21.0184i	0.883468	+	0.883468i
$567$	−0.930654	−	0.930654i	−0.0390838	−	0.0390838i
$568$	56.7025			2.37918
$569$			18.1443i			0.760648i	0.924853	+	0.380324i	$0.124188\pi$
$569$			18.1443i			0.760648i	−0.924853	+	0.380324i	$0.875812\pi$
$570$	−24.0856	−	24.0856i	−1.00883	−	1.00883i
$571$		−	13.6382i		−	0.570743i	−0.958417	−	0.285371i	$-0.907883\pi$
$571$		−	13.6382i		−	0.570743i	0.958417	−	0.285371i	$-0.0921169\pi$
$572$	−29.6346	+	65.6992i	−1.23908	+	2.74702i
$573$	−2.21210	+	2.21210i	−0.0924118	+	0.0924118i
$574$			15.0298i			0.627333i
$575$	−0.432369	+	0.432369i	−0.0180310	+	0.0180310i
$576$		−	50.1702i		−	2.09043i
$577$	−14.7476	−	14.7476i	−0.613953	−	0.613953i	0.330021	−	0.943974i	$-0.392944\pi$
$577$	−14.7476	−	14.7476i	−0.613953	−	0.613953i	−0.943974	+	0.330021i	$0.892944\pi$
$578$	−78.4786	+	78.4786i	−3.26428	+	3.26428i
$579$	−0.315306	−	0.315306i	−0.0131037	−	0.0131037i
$580$	−30.1004	+	30.1004i	−1.24985	+	1.24985i
$581$	−8.11628	+	8.11628i	−0.336720	+	0.336720i
$582$	−3.78651	−	3.78651i	−0.156956	−	0.156956i
$583$	−3.93930	−	10.4132i	−0.163149	−	0.431272i
$584$	102.213	+	102.213i	4.22961	+	4.22961i
$585$	−19.8336			−0.820019
$586$	−49.7216	−	49.7216i	−2.05398	−	2.05398i
$587$	28.1862	+	28.1862i	1.16337	+	1.16337i	0.983733	+	0.179638i	$0.0574926\pi$
$587$	28.1862	+	28.1862i	1.16337	+	1.16337i	0.179638	+	0.983733i	$0.442507\pi$
$588$		−	32.1332i		−	1.32515i
$589$	23.3707	+	23.3707i	0.962974	+	0.962974i
$590$	−31.6784			−1.30418
$591$			8.52887i			0.350831i
$592$	42.3719	+	42.3719i	1.74147	+	1.74147i
$593$	−9.49098	−	9.49098i	−0.389748	−	0.389748i	0.484850	−	0.874598i	$-0.338874\pi$
$593$	−9.49098	−	9.49098i	−0.389748	−	0.389748i	−0.874598	+	0.484850i	$0.838874\pi$
$594$	−15.4673	−	40.8865i	−0.634631	−	1.67759i
$595$			14.8873i			0.610320i
$596$		−	82.2941i		−	3.37090i
$597$		−	18.3173i		−	0.749678i
$598$			15.1093i			0.617866i
$599$	−8.50353	+	8.50353i	−0.347445	+	0.347445i	−0.859157	−	0.511712i	$-0.829011\pi$
$599$	−8.50353	+	8.50353i	−0.347445	+	0.347445i	0.511712	+	0.859157i	$0.329011\pi$
$600$	2.72420	+	2.72420i	0.111215	+	0.111215i
$601$	18.9763			0.774059			0.387030	−	0.922067i	$-0.373501\pi$
$601$	18.9763			0.774059			0.387030	+	0.922067i	$0.373501\pi$
$602$	−9.98042	−	9.98042i	−0.406771	−	0.406771i
$603$	−4.99922	−	4.99922i	−0.203584	−	0.203584i
$604$	25.3667	+	25.3667i	1.03216	+	1.03216i
$605$	−19.2450	+	16.9924i	−0.782419	+	0.690841i
$606$	0.153880			0.00625095
$607$		−	5.13092i		−	0.208258i	−0.994564	−	0.104129i	$-0.966795\pi$
$607$		−	5.13092i		−	0.208258i	0.994564	−	0.104129i	$-0.0332054\pi$
$608$	−75.6457	−	75.6457i	−3.06784	−	3.06784i
$609$		−	2.75223i		−	0.111526i
$610$	−49.2332	−	2.94328i	−1.99339	−	0.119170i
$611$			46.1525i			1.86713i
$612$	59.6304	+	59.6304i	2.41042	+	2.41042i
$613$	−47.4338			−1.91583			−0.957917	−	0.287045i	$-0.907327\pi$
$613$	−47.4338			−1.91583			−0.957917	+	0.287045i	$0.907327\pi$
$614$		−	25.3659i		−	1.02368i
$615$	−14.8435			−0.598547
$616$	10.2611	−	22.7486i	0.413431	−	0.916567i
$617$	21.2889	−	21.2889i	0.857058	−	0.857058i	−0.133932	−	0.990990i	$-0.542760\pi$
$617$	21.2889	−	21.2889i	0.857058	−	0.857058i	0.990990	+	0.133932i	$0.0427605\pi$
$618$	30.8434	−	30.8434i	1.24070	−	1.24070i
$619$	−2.05714			−0.0826834			−0.0413417	−	0.999145i	$-0.513163\pi$
$619$	−2.05714			−0.0826834			−0.0413417	+	0.999145i	$0.513163\pi$
$620$	−51.5889	−	51.5889i	−2.07186	−	2.07186i
$621$	−4.70975	−	4.70975i	−0.188996	−	0.188996i
$622$		−	81.4829i		−	3.26717i
$623$		−	10.6757i		−	0.427713i
$624$	53.5278			2.14283
$625$	−27.0360			−1.08144
$626$		−	82.4184i		−	3.29410i
$627$	−16.3074	−	7.35570i	−0.651255	−	0.293758i
$628$	44.5525	−	44.5525i	1.77784	−	1.77784i
$629$	−33.3901			−1.33135
$630$	11.0034			0.438387
$631$	−2.97097	−	2.97097i	−0.118273	−	0.118273i	0.645493	−	0.763766i	$-0.276652\pi$
$631$	−2.97097	−	2.97097i	−0.118273	−	0.118273i	−0.763766	+	0.645493i	$0.776652\pi$
$632$	−12.5128			−0.497734
$633$	−6.64759	−	6.64759i	−0.264218	−	0.264218i
$634$	−2.64119	−	2.64119i	−0.104895	−	0.104895i
$635$			8.92439i			0.354153i
$636$	−12.1093	+	12.1093i	−0.480165	+	0.480165i
$637$	−25.7247			−1.01925
$638$	−12.6479	+	28.0402i	−0.500737	+	1.11012i
$639$	9.28483	+	9.28483i	0.367302	+	0.367302i
$640$	44.9018	+	44.9018i	1.77490	+	1.77490i
$641$	30.8425	+	30.8425i	1.21820	+	1.21820i	0.968260	+	0.249944i	$0.0804121\pi$
$641$	30.8425	+	30.8425i	1.21820	+	1.21820i	0.249944	+	0.968260i	$0.419588\pi$
$642$	−19.7249	+	19.7249i	−0.778480	+	0.778480i
$643$	−10.7661	+	10.7661i	−0.424574	+	0.424574i	−0.886775	−	0.462201i	$-0.847060\pi$
$643$	−10.7661	+	10.7661i	−0.424574	+	0.424574i	0.462201	+	0.886775i	$0.347060\pi$
$644$		−	6.09243i		−	0.240075i
$645$	9.85669	−	9.85669i	0.388107	−	0.388107i
$646$	115.944			4.56177
$647$	13.2169	+	13.2169i	0.519609	+	0.519609i	0.917453	−	0.397844i	$-0.130241\pi$
$647$	13.2169	+	13.2169i	0.519609	+	0.519609i	−0.397844	+	0.917453i	$0.630241\pi$
$648$	9.98560	−	9.98560i	0.392271	−	0.392271i
$649$	−15.5614	+	5.88684i	−0.610838	+	0.231079i
$650$	3.49437	−	3.49437i	0.137060	−	0.137060i
$651$	4.71702			0.184875
$652$	−0.308827			−0.0120946
$653$	13.3952	+	13.3952i	0.524193	+	0.524193i	0.918835	−	0.394642i	$-0.129131\pi$
$653$	13.3952	+	13.3952i	0.524193	+	0.524193i	−0.394642	+	0.918835i	$0.629131\pi$
$654$	11.1799	−	11.1799i	0.437170	−	0.437170i
$655$	−29.1534			−1.13912
$656$	−90.6754			−3.54028
$657$			33.4741i			1.30595i
$658$		−	25.6048i		−	0.998180i
$659$	10.4358			0.406519			0.203260	−	0.979125i	$-0.434846\pi$
$659$	10.4358			0.406519			0.203260	+	0.979125i	$0.434846\pi$
$660$	35.9972	+	16.2371i	1.40119	+	0.632027i
$661$	19.0838	−	19.0838i	0.742274	−	0.742274i	−0.230742	−	0.973015i	$-0.574115\pi$
$661$	19.0838	−	19.0838i	0.742274	−	0.742274i	0.973015	+	0.230742i	$0.0741152\pi$
$662$	−80.2272			−3.11812
$663$	−21.0906	+	21.0906i	−0.819091	+	0.819091i
$664$	−87.0849	−	87.0849i	−3.37955	−	3.37955i
$665$	7.77499	−	7.77499i	0.301501	−	0.301501i
$666$			24.6791i			0.956296i
$667$			4.68690i			0.181477i
$668$		−	5.47399i		−	0.211795i
$669$	−5.26226	−	5.26226i	−0.203451	−	0.203451i
$670$	21.4569			0.828954
$671$	−24.7318	+	7.70324i	−0.954759	+	0.297380i
$672$	−15.2679			−0.588973
$673$	−7.30270	−	7.30270i	−0.281498	−	0.281498i	0.552208	−	0.833706i	$-0.313785\pi$
$673$	−7.30270	−	7.30270i	−0.281498	−	0.281498i	−0.833706	+	0.552208i	$0.813785\pi$
$674$		−	19.4169i		−	0.747909i
$675$			2.17847i			0.0838493i
$676$		−	19.5809i		−	0.753110i
$677$	13.3872	−	13.3872i	0.514513	−	0.514513i	−0.401393	−	0.915906i	$-0.631474\pi$
$677$	13.3872	−	13.3872i	0.514513	−	0.514513i	0.915906	+	0.401393i	$0.131474\pi$
$678$	21.9558	+	21.9558i	0.843209	+	0.843209i
$679$	1.22231	−	1.22231i	0.0469080	−	0.0469080i
$680$	−159.736			−6.12558
$681$	1.13544	−	1.13544i	0.0435103	−	0.0435103i
$682$	−48.0579	−	21.6772i	−1.84023	−	0.830065i
$683$	−23.9565			−0.916671			−0.458335	−	0.888779i	$-0.651554\pi$
$683$	−23.9565			−0.916671			−0.458335	+	0.888779i	$0.651554\pi$
$684$		−	62.2847i		−	2.38152i
$685$			31.2161i			1.19271i
$686$	30.1325			1.15046
$687$	17.6504			0.673405
$688$	60.2122	−	60.2122i	2.29557	−	2.29557i
$689$	9.69429	+	9.69429i	0.369323	+	0.369323i
$690$	8.27853			0.315158
$691$	−28.0644			−1.06762			−0.533810	−	0.845604i	$-0.679240\pi$
$691$	−28.0644			−1.06762			−0.533810	+	0.845604i	$0.679240\pi$
$692$	−35.9684	+	35.9684i	−1.36731	+	1.36731i
$693$	5.40522	−	2.04478i	0.205327	−	0.0776749i
$694$	−52.4081	+	52.4081i	−1.98938	+	1.98938i
$695$	−4.31753	−	4.31753i	−0.163773	−	0.163773i
$696$	29.5305			1.11935
$697$	35.7272	−	35.7272i	1.35326	−	1.35326i
$698$		−	27.3593i		−	1.03556i
$699$	−9.17115	+	9.17115i	−0.346885	+	0.346885i
$700$	−1.40901	+	1.40901i	−0.0532556	+	0.0532556i
$701$	18.1975	+	18.1975i	0.687309	+	0.687309i	0.961636	−	0.274328i	$-0.0884552\pi$
$701$	18.1975	+	18.1975i	0.687309	+	0.687309i	−0.274328	+	0.961636i	$0.588455\pi$
$702$	38.0637	+	38.0637i	1.43662	+	1.43662i
$703$	17.4382	+	17.4382i	0.657693	+	0.657693i
$704$	72.8970	+	32.8813i	2.74741	+	1.23926i
$705$	25.2874			0.952379
$706$	−56.0768	+	56.0768i	−2.11048	+	2.11048i
$707$			0.0496736i			0.00186817i
$708$	18.0960	+	18.0960i	0.680089	+	0.680089i
$709$	3.95145	+	3.95145i	0.148400	+	0.148400i	0.777403	−	0.629003i	$-0.216537\pi$
$709$	3.95145	+	3.95145i	0.148400	+	0.148400i	−0.629003	+	0.777403i	$0.716537\pi$
$710$	−39.8510			−1.49558
$711$	−2.04893	−	2.04893i	−0.0768409	−	0.0768409i
$712$	114.547			4.29282
$713$	−8.03284			−0.300832
$714$	11.7008	−	11.7008i	0.437891	−	0.437891i
$715$	12.9988	−	28.8181i	0.486129	−	1.07774i
$716$			64.9478i			2.42721i
$717$	−27.0099			−1.00870
$718$	56.3357			2.10243
$719$		−	18.5238i		−	0.690823i	−0.938451	−	0.345411i	$-0.887739\pi$
$719$		−	18.5238i		−	0.690823i	0.938451	−	0.345411i	$-0.112261\pi$
$720$			66.3841i			2.47399i
$721$	9.95647	+	9.95647i	0.370798	+	0.370798i
$722$	−24.2014	−	24.2014i	−0.900684	−	0.900684i
$723$	2.60251			0.0967886
$724$	12.0647	−	12.0647i	0.448382	−	0.448382i
$725$	1.08395	−	1.08395i	0.0402569	−	0.0402569i
$726$	28.4811	+	1.77039i	1.05703	+	0.0657053i
$727$	−1.64479			−0.0610017			−0.0305009	−	0.999535i	$-0.509710\pi$
$727$	−1.64479			−0.0610017			−0.0305009	+	0.999535i	$0.509710\pi$
$728$			30.7307i			1.13896i
$729$	−10.7414			−0.397830
$730$	−71.8364	−	71.8364i	−2.65878	−	2.65878i
$731$			47.4487i			1.75495i
$732$	26.4426	+	29.8053i	0.977348	+	1.10164i
$733$		−	35.8149i		−	1.32286i	−0.750009	−	0.661428i	$-0.769951\pi$
$733$		−	35.8149i		−	1.32286i	0.750009	−	0.661428i	$-0.230049\pi$
$734$	−0.848635	−	0.848635i	−0.0313237	−	0.0313237i
$735$			14.0948i			0.519896i
$736$	26.0005			0.958389
$737$	10.5403	−	3.98737i	0.388257	−	0.146877i
$738$	−26.4065	−	26.4065i	−0.972038	−	0.972038i
$739$	5.78667	+	5.78667i	0.212866	+	0.212866i	0.805484	−	0.592618i	$-0.201906\pi$
$739$	5.78667	+	5.78667i	0.212866	+	0.212866i	−0.592618	+	0.805484i	$0.701906\pi$
$740$	−38.4933	−	38.4933i	−1.41504	−	1.41504i
$741$	22.0294			0.809270
$742$	−5.37827	−	5.37827i	−0.197443	−	0.197443i
$743$	20.7895	−	20.7895i	0.762694	−	0.762694i	−0.214114	−	0.976809i	$-0.568687\pi$
$743$	20.7895	−	20.7895i	0.762694	−	0.762694i	0.976809	+	0.214114i	$0.0686865\pi$
$744$			50.6121i			1.85553i
$745$			36.0973i			1.32250i
$746$			26.4161i			0.967161i
$747$		−	28.5197i		−	1.04348i
$748$	−125.724	+	47.5612i	−4.59693	+	1.73901i
$749$	−6.36734	−	6.36734i	−0.232658	−	0.232658i
$750$	19.4918	+	19.4918i	0.711739	+	0.711739i
$751$		−	42.5863i		−	1.55399i	−0.629504	−	0.776997i	$-0.716742\pi$
$751$		−	42.5863i		−	1.55399i	0.629504	−	0.776997i	$-0.283258\pi$
$752$	154.475			5.63311
$753$	−1.04522	−	1.04522i	−0.0380899	−	0.0380899i
$754$		−	37.8790i		−	1.37947i
$755$	−11.1268	−	11.1268i	−0.404945	−	0.404945i
$756$	−15.3482	−	15.3482i	−0.558208	−	0.558208i
$757$	−3.84821			−0.139866			−0.0699328	−	0.997552i	$-0.522278\pi$
$757$	−3.84821			−0.139866			−0.0699328	+	0.997552i	$0.522278\pi$
$758$	28.3275	+	28.3275i	1.02890	+	1.02890i
$759$	4.06667	−	1.53841i	0.147611	−	0.0558408i
$760$	83.4230	+	83.4230i	3.02607	+	3.02607i
$761$	23.0934	−	23.0934i	0.837135	−	0.837135i	−0.151346	−	0.988481i	$-0.548361\pi$
$761$	23.0934	−	23.0934i	0.837135	−	0.837135i	0.988481	+	0.151346i	$0.0483606\pi$
$762$	7.01419	−	7.01419i	0.254097	−	0.254097i
$763$	3.60896	+	3.60896i	0.130653	+	0.130653i
$764$	12.2762	−	12.2762i	0.444139	−	0.444139i
$765$	−26.1561	−	26.1561i	−0.945677	−	0.945677i
$766$		−	68.7084i		−	2.48254i
$767$	14.4870	−	14.4870i	0.523096	−	0.523096i
$768$		−	24.3460i		−	0.878511i
$769$	−20.1746	+	20.1746i	−0.727515	+	0.727515i	−0.970124	−	0.242609i	$-0.921997\pi$
$769$	−20.1746	+	20.1746i	−0.727515	+	0.727515i	0.242609	+	0.970124i	$0.421997\pi$
$770$	−7.21160	+	15.9879i	−0.259888	+	0.576165i
$771$		−	25.7201i		−	0.926288i
$772$	1.74982	+	1.74982i	0.0629774	+	0.0629774i
$773$		−	49.6999i		−	1.78758i	−0.448485	−	0.893790i	$-0.648036\pi$
$773$		−	49.6999i		−	1.78758i	0.448485	−	0.893790i	$-0.351964\pi$
$774$	35.0700			1.26057
$775$	1.85777	+	1.85777i	0.0667332	+	0.0667332i
$776$	13.1150	+	13.1150i	0.470800	+	0.470800i
$777$	3.51963			0.126266
$778$	81.5127			2.92237
$779$	−37.3175			−1.33704
$780$	−48.6280			−1.74116
$781$	−19.5760	+	7.40557i	−0.700485	+	0.264992i
$782$	−19.9258	+	19.9258i	−0.712546	+	0.712546i
$783$	11.8073	+	11.8073i	0.421959	+	0.421959i
$784$			86.1020i			3.07507i
$785$	−19.5424	+	19.5424i	−0.697498	+	0.697498i
$786$	22.9133	+	22.9133i	0.817291	+	0.817291i
$787$	−21.7627	−	21.7627i	−0.775757	−	0.775757i	0.203349	−	0.979106i	$-0.434817\pi$
$787$	−21.7627	−	21.7627i	−0.775757	−	0.775757i	−0.979106	+	0.203349i	$0.934817\pi$
$788$		−	47.3317i		−	1.68612i
$789$		−	23.9409i		−	0.852318i
$790$	8.79414			0.312881
$791$	−7.08750	+	7.08750i	−0.252002	+	0.252002i
$792$	21.9398	+	57.9962i	0.779598	+	2.06080i
$793$	23.8611	−	21.1691i	0.847332	−	0.751736i
$794$		−	5.91918i		−	0.210064i
$795$	5.31160	−	5.31160i	0.188383	−	0.188383i
$796$			101.654i			3.60301i
$797$			17.4302i			0.617411i	0.951158	+	0.308705i	$0.0998958\pi$
$797$			17.4302i			0.617411i	−0.951158	+	0.308705i	$0.900104\pi$
$798$	−12.2216			−0.432641
$799$	−60.8649	+	60.8649i	−2.15325	+	2.15325i
$800$	−6.01318	−	6.01318i	−0.212598	−	0.212598i
$801$	18.7566	+	18.7566i	0.662732	+	0.662732i
$802$			20.0096i			0.706563i
$803$	−48.6376	−	21.9387i	−1.71638	−	0.774201i
$804$	−12.2571	−	12.2571i	−0.432274	−	0.432274i
$805$			2.67237i			0.0941886i
$806$	64.9206			2.28673
$807$			11.0001i			0.387221i
$808$	−0.532981			−0.0187502
$809$		−	16.3431i		−	0.574594i	−0.957842	−	0.287297i	$-0.907243\pi$
$809$		−	16.3431i		−	0.574594i	0.957842	−	0.287297i	$-0.0927566\pi$
$810$	−7.01797	+	7.01797i	−0.246586	+	0.246586i
$811$	9.20652	+	9.20652i	0.323285	+	0.323285i	0.850026	−	0.526741i	$-0.176586\pi$
$811$	9.20652	+	9.20652i	0.323285	+	0.323285i	−0.526741	+	0.850026i	$0.676586\pi$
$812$			15.2737i			0.536003i
$813$			2.53736i			0.0889890i
$814$	−35.8586	−	16.1746i	−1.25684	−	0.566918i
$815$	0.135463			0.00474507
$816$	70.5913	+	70.5913i	2.47119	+	2.47119i
$817$	24.7804	−	24.7804i	0.866955	−	0.866955i
$818$	−20.0245			−0.700141
$819$	−5.03204	+	5.03204i	−0.175834	+	0.175834i
$820$	82.3752			2.87667
$821$	−2.90222	+	2.90222i	−0.101288	+	0.101288i	−0.755935	−	0.654647i	$-0.772817\pi$
$821$	−2.90222	+	2.90222i	−0.101288	+	0.101288i	0.654647	+	0.755935i	$0.272817\pi$
$822$	24.5346	−	24.5346i	0.855741	−	0.855741i
$823$	−12.6648	+	12.6648i	−0.441466	+	0.441466i	−0.892504	−	0.451039i	$-0.851054\pi$
$823$	−12.6648	+	12.6648i	−0.441466	+	0.441466i	0.451039	+	0.892504i	$0.351054\pi$
$824$	−106.830	+	106.830i	−3.72158	+	3.72158i
$825$	−1.29630	−	0.584715i	−0.0451313	−	0.0203572i
$826$	−8.03722	+	8.03722i	−0.279651	+	0.279651i
$827$			47.2288i			1.64230i	0.570709	+	0.821152i	$0.306668\pi$
$827$			47.2288i			1.64230i	−0.570709	+	0.821152i	$0.693332\pi$
$828$	10.7041	+	10.7041i	0.371992	+	0.371992i
$829$		−	8.55925i		−	0.297275i	−0.988892	−	0.148637i	$-0.952511\pi$
$829$		−	8.55925i		−	0.297275i	0.988892	−	0.148637i	$-0.0474887\pi$
$830$	61.2041	+	61.2041i	2.12442	+	2.12442i
$831$	9.03088	−	9.03088i	0.313278	−	0.313278i
$832$	−98.4754			−3.41402
$833$	−33.9252	−	33.9252i	−1.17544	−	1.17544i
$834$			6.78679i			0.235007i
$835$			2.40110i			0.0830934i
$836$	90.4993	+	40.8211i	3.12998	+	1.41183i
$837$	−20.2365	+	20.2365i	−0.699476	+	0.699476i
$838$	50.6207			1.74866
$839$		−	41.1352i		−	1.42015i	−0.704128	−	0.710073i	$-0.748662\pi$
$839$		−	41.1352i		−	1.42015i	0.704128	−	0.710073i	$-0.251338\pi$
$840$	16.8376			0.580954
$841$			17.2500i			0.594826i
$842$	−14.7304			−0.507644
$843$	−21.2482	−	21.2482i	−0.731826	−	0.731826i
$844$	36.8913	+	36.8913i	1.26985	+	1.26985i
$845$			8.58890i			0.295467i
$846$	44.9862	+	44.9862i	1.54666	+	1.54666i
$847$	−0.571494	+	9.19389i	−0.0196368	+	0.315906i
$848$	32.4473	−	32.4473i	1.11424	−	1.11424i
$849$			10.5330i			0.361493i
$850$	9.21659			0.316126
$851$	−5.99374			−0.205463
$852$	22.7645	+	22.7645i	0.779899	+	0.779899i
$853$	4.99012			0.170858			0.0854292	−	0.996344i	$-0.472774\pi$
$853$	4.99012			0.170858			0.0854292	+	0.996344i	$0.472774\pi$
$854$	−13.2378	+	11.7443i	−0.452989	+	0.401883i
$855$			27.3204i			0.934338i
$856$	68.3194	−	68.3194i	2.33511	−	2.33511i
$857$	−48.7734			−1.66607			−0.833034	−	0.553222i	$-0.813398\pi$
$857$	−48.7734			−1.66607			−0.833034	+	0.553222i	$0.813398\pi$
$858$	−32.8664	+	12.4333i	−1.12204	+	0.424466i
$859$			10.9420i			0.373336i	0.982423	+	0.186668i	$0.0597689\pi$
$859$			10.9420i			0.373336i	−0.982423	+	0.186668i	$0.940231\pi$
$860$	−54.7005	+	54.7005i	−1.86527	+	1.86527i
$861$	−3.76598	+	3.76598i	−0.128344	+	0.128344i
$862$	−47.4479	−	47.4479i	−1.61608	−	1.61608i
$863$	43.1071			1.46738			0.733691	−	0.679483i	$-0.237796\pi$
$863$	43.1071			1.46738			0.733691	+	0.679483i	$0.237796\pi$
$864$	65.5009	−	65.5009i	2.22839	−	2.22839i
$865$	15.7771	−	15.7771i	0.536437	−	0.536437i
$866$		−	58.1354i		−	1.97552i
$867$	−39.3284			−1.33566
$868$	−26.1775			−0.888523
$869$	4.31994	−	1.63423i	0.146544	−	0.0554373i
$870$	−20.7543			−0.703636
$871$	−9.81259	+	9.81259i	−0.332487	+	0.332487i
$872$	−38.7229	+	38.7229i	−1.31132	+	1.31132i
$873$			4.29506i			0.145366i
$874$	20.8128			0.704003
$875$	−6.29208	+	6.29208i	−0.212711	+	0.212711i
$876$			82.0717i			2.77294i
$877$	−19.6706	−	19.6706i	−0.664230	−	0.664230i	0.292145	−	0.956374i	$-0.405631\pi$
$877$	−19.6706	−	19.6706i	−0.664230	−	0.664230i	−0.956374	+	0.292145i	$0.905631\pi$
$878$	−18.1612	+	18.1612i	−0.612912	+	0.612912i
$879$		−	24.9173i		−	0.840438i
$880$	−96.4557	−	43.5078i	−3.25152	−	1.46665i
$881$		−	12.6870i		−	0.427436i	−0.976895	−	0.213718i	$-0.931443\pi$
$881$		−	12.6870i		−	0.427436i	0.976895	−	0.213718i	$-0.0685574\pi$
$882$	−25.0747	+	25.0747i	−0.844308	+	0.844308i
$883$	2.12767	+	2.12767i	0.0716016	+	0.0716016i	0.742001	−	0.670399i	$-0.233877\pi$
$883$	2.12767	+	2.12767i	0.0716016	+	0.0716016i	−0.670399	+	0.742001i	$0.733877\pi$
$884$	117.044	−	117.044i	3.93662	−	3.93662i
$885$	−7.93758	−	7.93758i	−0.266819	−	0.266819i
$886$	−48.5243	−	48.5243i	−1.63020	−	1.63020i
$887$	−14.9074	−	14.9074i	−0.500541	−	0.500541i	0.411065	−	0.911606i	$-0.365157\pi$
$887$	−14.9074	−	14.9074i	−0.500541	−	0.500541i	−0.911606	+	0.411065i	$0.865157\pi$
$888$			37.7644i			1.26729i
$889$	2.26423	+	2.26423i	0.0759399	+	0.0759399i
$890$	−80.5045			−2.69852
$891$	−2.14328	+	4.75160i	−0.0718026	+	0.159185i
$892$	29.2034	+	29.2034i	0.977802	+	0.977802i
$893$	63.5742			2.12743
$894$	28.3710	−	28.3710i	0.948867	−	0.948867i
$895$		−	28.4886i		−	0.952267i
$896$	22.7843			0.761172
$897$	−3.78590	+	3.78590i	−0.126408	+	0.126408i
$898$	29.5177	+	29.5177i	0.985018	+	0.985018i
$899$	20.1383			0.671651
$900$		−	4.95110i		−	0.165037i
$901$			25.5693i			0.851835i
$902$	55.6752	−	21.0618i	1.85378	−	0.701282i
$903$		−	5.00154i		−	0.166441i
$904$	−76.0465	−	76.0465i	−2.52927	−	2.52927i
$905$	−5.29205	+	5.29205i	−0.175914	+	0.175914i
$906$			17.4904i			0.581078i
$907$	−23.4758	+	23.4758i	−0.779500	+	0.779500i	−0.979746	−	0.200246i	$-0.935826\pi$
$907$	−23.4758	+	23.4758i	−0.779500	+	0.779500i	0.200246	+	0.979746i	$0.435826\pi$
$908$	−6.30125	+	6.30125i	−0.209114	+	0.209114i
$909$	−0.0872737	−	0.0872737i	−0.00289468	−	0.00289468i
$910$		−	21.5978i		−	0.715961i
$911$	42.2868			1.40102			0.700512	−	0.713640i	$-0.252955\pi$
$911$	42.2868			1.40102			0.700512	+	0.713640i	$0.252955\pi$
$912$		−	73.7335i		−	2.44156i
$913$	41.4389	+	18.6916i	1.37143	+	0.618603i
$914$		−	10.4124i		−	0.344413i
$915$	−11.5987	−	13.0737i	−0.383442	−	0.432204i
$916$	−97.9524			−3.23644
$917$	−7.39658	+	7.39658i	−0.244257	+	0.244257i
$918$			100.395i			3.31354i
$919$	−0.340712			−0.0112390			−0.00561952	−	0.999984i	$-0.501789\pi$
$919$	−0.340712			−0.0112390			−0.00561952	+	0.999984i	$0.501789\pi$
$920$	−28.6736			−0.945341
$921$	6.35586	−	6.35586i	0.209433	−	0.209433i
$922$	18.7727	−	18.7727i	0.618246	−	0.618246i
$923$	18.2245	−	18.2245i	0.599866	−	0.599866i
$924$	13.2525	−	5.01340i	0.435975	−	0.164929i
$925$	1.38619	+	1.38619i	0.0455775	+	0.0455775i
$926$	21.1210	−	21.1210i	0.694080	−	0.694080i
$927$	−34.9859			−1.14909
$928$	−65.1831			−2.13974
$929$		−	16.1048i		−	0.528382i	−0.964470	−	0.264191i	$-0.914895\pi$
$929$		−	16.1048i		−	0.528382i	0.964470	−	0.264191i	$-0.0851050\pi$
$930$		−	35.5706i		−	1.16641i
$931$			35.4353i			1.16135i
$932$	50.8961	−	50.8961i	1.66716	−	1.66716i
$933$	20.4170	−	20.4170i	0.668421	−	0.668421i
$934$	−58.8720			−1.92635
$935$	55.1473	−	20.8621i	1.80351	−	0.682264i
$936$	−53.9921	−	53.9921i	−1.76479	−	1.76479i
$937$			57.6198i			1.88236i	0.337908	+	0.941179i	$0.390281\pi$
$937$			57.6198i			1.88236i	−0.337908	+	0.941179i	$0.609719\pi$
$938$	5.44390	−	5.44390i	0.177750	−	0.177750i
$939$	20.6514	−	20.6514i	0.673932	−	0.673932i
$940$	−140.335			−4.57721
$941$	27.8117	+	27.8117i	0.906637	+	0.906637i	0.995999	−	0.0893622i	$-0.0284829\pi$
$941$	27.8117	+	27.8117i	0.906637	+	0.906637i	−0.0893622	+	0.995999i	$0.528483\pi$
$942$	30.7190			1.00088
$943$	6.41327	−	6.41327i	0.208845	−	0.208845i
$944$	−48.4888	−	48.4888i	−1.57818	−	1.57818i
$945$	6.73229	+	6.73229i	0.219001	+	0.219001i
$946$	−22.9847	+	50.9566i	−0.747298	+	1.65674i
$947$	−35.4909	+	35.4909i	−1.15330	+	1.15330i	−0.167411	+	0.985887i	$0.553541\pi$
$947$	−35.4909	+	35.4909i	−1.15330	+	1.15330i	−0.985887	+	0.167411i	$0.946459\pi$
$948$	−5.02357	−	5.02357i	−0.163158	−	0.163158i
$949$	65.7037			2.13283
$950$	−4.81342	−	4.81342i	−0.156168	−	0.156168i
$951$		−	1.32359i		−	0.0429205i
$952$	−40.5270	+	40.5270i	−1.31349	+	1.31349i
$953$	16.8693	−	16.8693i	0.546450	−	0.546450i	−0.378962	−	0.925412i	$-0.623719\pi$
$953$	16.8693	−	16.8693i	0.546450	−	0.546450i	0.925412	+	0.378962i	$0.123719\pi$
$954$	18.8986			0.611866
$955$	−5.38482	+	5.38482i	−0.174249	+	0.174249i
$956$	149.894			4.84791
$957$	−10.1951	+	3.85680i	−0.329562	+	0.124672i
$958$	7.38750	+	7.38750i	0.238679	+	0.238679i
$959$	7.91993	+	7.91993i	0.255748	+	0.255748i
$960$			53.9556i			1.74141i
$961$			3.51495i			0.113385i
$962$	48.4408			1.56179
$963$	22.3741			0.720996
$964$	−14.4429			−0.465174
$965$	−0.767536	−	0.767536i	−0.0247079	−	0.0247079i
$966$	2.10037	−	2.10037i	0.0675783	−	0.0675783i
$967$	54.3041			1.74630			0.873150	−	0.487451i	$-0.162073\pi$
$967$	54.3041			1.74630			0.873150	+	0.487451i	$0.162073\pi$
$968$	−98.6473	−	6.13193i	−3.17065	−	0.197088i
$969$	29.0519	+	29.0519i	0.933281	+	0.933281i
$970$	−9.21733	−	9.21733i	−0.295951	−	0.295951i
$971$	−13.5719			−0.435543			−0.217771	−	0.976000i	$-0.569879\pi$
$971$	−13.5719			−0.435543			−0.217771	+	0.976000i	$0.569879\pi$
$972$	85.7766			2.75129
$973$	−2.19082			−0.0702346
$974$	−56.7037	+	56.7037i	−1.81690	+	1.81690i
$975$	1.75115			0.0560816
$976$	−70.8539	−	79.8643i	−2.26798	−	2.55639i
$977$	−39.7371			−1.27130			−0.635651	−	0.771977i	$-0.719268\pi$
$977$	−39.7371			−1.27130			−0.635651	+	0.771977i	$0.719268\pi$
$978$	−0.106468	−	0.106468i	−0.00340448	−	0.00340448i
$979$	−39.5462	+	14.9603i	−1.26390	+	0.478132i
$980$		−	78.2205i		−	2.49866i
$981$	−12.6815			−0.404888
$982$	28.8700	+	28.8700i	0.921278	+	0.921278i
$983$	−28.6714	+	28.6714i	−0.914474	+	0.914474i	−0.996620	−	0.0821462i	$-0.973823\pi$
$983$	−28.6714	+	28.6714i	−0.914474	+	0.914474i	0.0821462	+	0.996620i	$0.473823\pi$
$984$	−40.4077	−	40.4077i	−1.28815	−	1.28815i
$985$			20.7615i			0.661515i
$986$	49.9540	−	49.9540i	1.59086	−	1.59086i
$987$	6.41574	−	6.41574i	0.204215	−	0.204215i
$988$	−122.254			−3.88942
$989$			8.51735i			0.270836i
$990$	−15.4195	−	40.7602i	−0.490064	−	1.29545i
$991$	18.7178			0.594591			0.297295	−	0.954786i	$-0.403915\pi$
$991$	18.7178			0.594591			0.297295	+	0.954786i	$0.403915\pi$
$992$		−	111.717i		−	3.54702i
$993$	−20.1023	−	20.1023i	−0.637928	−	0.637928i
$994$	−10.1107	+	10.1107i	−0.320692	+	0.320692i
$995$		−	44.5891i		−	1.41357i
$996$		−	69.9245i		−	2.21564i
$997$	20.9887	−	20.9887i	0.664719	−	0.664719i	−0.291770	−	0.956489i	$-0.594244\pi$
$997$	20.9887	−	20.9887i	0.664719	−	0.664719i	0.956489	+	0.291770i	$0.0942441\pi$
$998$		−	68.8913i		−	2.18071i
$999$	−15.0996	+	15.0996i	−0.477729	+	0.477729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.2	✓	120
11.10	odd	2	inner	671.2.f.a.538.59	yes	120
61.11	odd	4	inner	671.2.f.a.560.59	yes	120
671.560	even	4	inner	671.2.f.a.560.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.2	✓	120	1.1	even	1	trivial
671.2.f.a.538.59	yes	120	11.10	odd	2	inner
671.2.f.a.560.2	yes	120	671.560	even	4	inner
671.2.f.a.560.59	yes	120	61.11	odd	4	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91322 - 1.91322i) q^{2} -0.958783i q^{3} +5.32085i q^{4} -2.33392i q^{5} +(-1.83437 + 1.83437i) q^{6} +(-0.592146 - 0.592146i) q^{7} +(6.35353 - 6.35353i) q^{8} +2.08073 q^{9} +O(q^{10})\)	\(q+(-1.91322 - 1.91322i) q^{2} -0.958783i q^{3} +5.32085i q^{4} -2.33392i q^{5} +(-1.83437 + 1.83437i) q^{6} +(-0.592146 - 0.592146i) q^{7} +(6.35353 - 6.35353i) q^{8} +2.08073 q^{9} +(-4.46532 + 4.46532i) q^{10} +(-1.36370 + 3.02330i) q^{11} +5.10154 q^{12} -4.08412i q^{13} +2.26582i q^{14} -2.23773 q^{15} -13.6697 q^{16} +(5.38605 - 5.38605i) q^{17} +(-3.98091 - 3.98091i) q^{18} -5.62579 q^{19} +12.4185 q^{20} +(-0.567740 + 0.567740i) q^{21} +(8.39331 - 3.17517i) q^{22} +(0.966831 - 0.966831i) q^{23} +(-6.09166 - 6.09166i) q^{24} -0.447202 q^{25} +(-7.81383 + 7.81383i) q^{26} -4.87132i q^{27} +(3.15072 - 3.15072i) q^{28} +(-2.42384 + 2.42384i) q^{29} +(4.28127 + 4.28127i) q^{30} +(-4.15421 - 4.15421i) q^{31} +(13.4462 + 13.4462i) q^{32} +(2.89868 + 1.30750i) q^{33} -20.6094 q^{34} +(-1.38202 + 1.38202i) q^{35} +11.0713i q^{36} +(-3.09968 - 3.09968i) q^{37} +(10.7634 + 10.7634i) q^{38} -3.91578 q^{39} +(-14.8287 - 14.8287i) q^{40} +6.63329 q^{41} +2.17243 q^{42} +(-4.40478 + 4.40478i) q^{43} +(-16.0865 - 7.25606i) q^{44} -4.85628i q^{45} -3.69953 q^{46} -11.3005 q^{47} +13.1063i q^{48} -6.29873i q^{49} +(0.855598 + 0.855598i) q^{50} +(-5.16405 - 5.16405i) q^{51} +21.7310 q^{52} +(-2.37366 + 2.37366i) q^{53} +(-9.31993 + 9.31993i) q^{54} +(7.05614 + 3.18278i) q^{55} -7.52444 q^{56} +5.39392i q^{57} +9.27471 q^{58} +(3.54716 + 3.54716i) q^{59} -11.9066i q^{60} +(5.18327 + 5.84241i) q^{61} +15.8959i q^{62} +(-1.23210 - 1.23210i) q^{63} -24.1118i q^{64} -9.53202 q^{65} +(-3.04430 - 8.04736i) q^{66} +(-2.40262 - 2.40262i) q^{67} +(28.6584 + 28.6584i) q^{68} +(-0.926981 - 0.926981i) q^{69} +5.28825 q^{70} +(4.46228 + 4.46228i) q^{71} +(13.2200 - 13.2200i) q^{72} +16.0876i q^{73} +11.8608i q^{74} +0.428770i q^{75} -29.9340i q^{76} +(2.59775 - 0.982722i) q^{77} +(7.49177 + 7.49177i) q^{78} +(-0.984715 - 0.984715i) q^{79} +31.9042i q^{80} +1.57166 q^{81} +(-12.6910 - 12.6910i) q^{82} -13.7065i q^{83} +(-3.02086 - 3.02086i) q^{84} +(-12.5706 - 12.5706i) q^{85} +16.8546 q^{86} +(2.32394 + 2.32394i) q^{87} +(10.5443 + 27.8729i) q^{88} +(9.01441 + 9.01441i) q^{89} +(-9.29115 + 9.29115i) q^{90} +(-2.41840 + 2.41840i) q^{91} +(5.14436 + 5.14436i) q^{92} +(-3.98299 + 3.98299i) q^{93} +(21.6204 + 21.6204i) q^{94} +13.1302i q^{95} +(12.8920 - 12.8920i) q^{96} +2.06420i q^{97} +(-12.0509 + 12.0509i) q^{98} +(-2.83750 + 6.29068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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