LMFDB - Embedded newform 361.2.e.a.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			99.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	361.99
Dual form			361.2.e.a.62.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37939 - 0.866025i) q^{2} +(0.113341 + 0.642788i) q^{3} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(0.286989 - 1.62760i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(-3.05303 - 5.28801i) q^{8} +(2.41875 - 0.880352i) q^{9} +O(q^{10})$	\(q+(-2.37939 - 0.866025i) q^{2} +(0.113341 + 0.642788i) q^{3} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(0.286989 - 1.62760i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(-3.05303 - 5.28801i) q^{8} +(2.41875 - 0.880352i) q^{9} +(3.20574 - 1.16679i) q^{10} +(0.592396 + 1.02606i) q^{11} +(-1.43969 + 2.49362i) q^{12} +(-0.471782 + 2.67561i) q^{13} +(2.97178 - 2.49362i) q^{14} +(-0.673648 - 0.565258i) q^{15} +(1.15270 + 6.53731i) q^{16} +(-3.64543 - 1.32683i) q^{17} -6.51754 q^{18} -5.94356 q^{20} +(-0.939693 - 0.342020i) q^{21} +(-0.520945 - 2.95442i) q^{22} +(-3.87939 - 3.25519i) q^{23} +(3.05303 - 2.56180i) q^{24} +(-0.553033 + 3.13641i) q^{25} +(3.43969 - 5.95772i) q^{26} +(1.81908 + 3.15074i) q^{27} +(-6.35117 + 2.31164i) q^{28} +(-4.37211 + 1.59132i) q^{29} +(1.11334 + 1.92836i) q^{30} +(-1.91875 + 3.32337i) q^{31} +(0.798133 - 4.52644i) q^{32} +(-0.592396 + 0.497079i) q^{33} +(7.52481 + 6.31407i) q^{34} +(-0.358441 - 2.03282i) q^{35} +(10.6702 + 3.88365i) q^{36} +4.10607 q^{37} -1.77332 q^{39} +(7.73055 + 2.81369i) q^{40} +(1.73396 + 9.83375i) q^{41} +(1.93969 + 1.62760i) q^{42} +(-6.66637 + 5.59375i) q^{43} +(-0.907604 + 5.14728i) q^{44} +(-1.73396 + 3.00330i) q^{45} +(6.41147 + 11.1050i) q^{46} +(-0.539363 + 0.196312i) q^{47} +(-4.07145 + 1.48189i) q^{48} +(2.32635 + 4.02936i) q^{49} +(4.03209 - 6.98378i) q^{50} +(0.439693 - 2.49362i) q^{51} +(-9.18139 + 7.70410i) q^{52} +(-2.25490 - 1.89209i) q^{53} +(-1.59967 - 9.07218i) q^{54} +(-1.50000 - 0.545955i) q^{55} +9.35504 q^{56} +11.7811 q^{58} +(-3.69846 - 1.34613i) q^{59} +(-0.673648 - 3.82045i) q^{60} +(-3.46064 - 2.90382i) q^{61} +(7.44356 - 6.24589i) q^{62} +(-0.684793 + 3.88365i) q^{63} +(0.819078 - 1.41868i) q^{64} +(-1.83022 - 3.17004i) q^{65} +(1.84002 - 0.669713i) q^{66} +(-3.65270 + 1.32948i) q^{67} +(-8.55690 - 14.8210i) q^{68} +(1.65270 - 2.86257i) q^{69} +(-0.907604 + 5.14728i) q^{70} +(5.31315 - 4.45826i) q^{71} +(-12.0398 - 10.1026i) q^{72} +(1.06418 + 6.03525i) q^{73} +(-9.76991 - 3.55596i) q^{74} -2.07873 q^{75} -1.81521 q^{77} +(4.21941 + 1.53574i) q^{78} +(-1.70321 - 9.65939i) q^{79} +(-6.85117 - 5.74881i) q^{80} +(4.09627 - 3.43718i) q^{81} +(4.39053 - 24.8999i) q^{82} +(-6.15910 + 10.6679i) q^{83} +(-2.20574 - 3.82045i) q^{84} +(4.91147 - 1.78763i) q^{85} +(20.7062 - 7.53644i) q^{86} +(-1.51842 - 2.62998i) q^{87} +(3.61721 - 6.26519i) q^{88} +(0.421274 - 2.38917i) q^{89} +(6.72668 - 5.64436i) q^{90} +(-3.18866 - 2.67561i) q^{91} +(-3.87939 - 22.0011i) q^{92} +(-2.35369 - 0.856674i) q^{93} +1.45336 q^{94} +3.00000 q^{96} +(6.92514 + 2.52055i) q^{97} +(-2.04576 - 11.6021i) q^{98} +(2.33615 + 1.96026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9	$ 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9} + 9 q^{10} - 3 q^{12} + 12 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 12 q^{23} + 6 q^{24} + 9 q^{25} + 15 q^{26} - 6 q^{27} - 12 q^{28} + 3 q^{29} - 9 q^{31} - 9 q^{32} + 18 q^{34} + 6 q^{35} + 21 q^{36} - 24 q^{39} + 9 q^{40} + 15 q^{41} + 6 q^{42} - 21 q^{43} - 9 q^{44} - 15 q^{45} + 18 q^{46} - 12 q^{47} - 24 q^{48} + 15 q^{49} + 15 q^{50} - 3 q^{51} - 6 q^{52} - 15 q^{53} - 24 q^{54} - 9 q^{55} + 6 q^{56} + 36 q^{58} + 6 q^{59} - 3 q^{60} - 12 q^{61} + 15 q^{62} + 3 q^{63} - 12 q^{64} + 12 q^{65} - 9 q^{66} - 24 q^{67} - 15 q^{68} + 12 q^{69} - 9 q^{70} - 12 q^{71} - 15 q^{72} - 12 q^{73} - 30 q^{74} - 30 q^{75} - 18 q^{77} - 6 q^{78} - 15 q^{79} - 15 q^{80} - 3 q^{81} + 9 q^{82} - 3 q^{84} + 9 q^{85} + 48 q^{86} - 21 q^{87} - 9 q^{88} - 15 q^{89} + 27 q^{90} + 12 q^{91} - 12 q^{92} + 27 q^{93} - 18 q^{94} + 18 q^{96} + 18 q^{98} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9 + 9 * q^10 - 3 * q^12 + 12 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 12 * q^23 + 6 * q^24 + 9 * q^25 + 15 * q^26 - 6 * q^27 - 12 * q^28 + 3 * q^29 - 9 * q^31 - 9 * q^32 + 18 * q^34 + 6 * q^35 + 21 * q^36 - 24 * q^39 + 9 * q^40 + 15 * q^41 + 6 * q^42 - 21 * q^43 - 9 * q^44 - 15 * q^45 + 18 * q^46 - 12 * q^47 - 24 * q^48 + 15 * q^49 + 15 * q^50 - 3 * q^51 - 6 * q^52 - 15 * q^53 - 24 * q^54 - 9 * q^55 + 6 * q^56 + 36 * q^58 + 6 * q^59 - 3 * q^60 - 12 * q^61 + 15 * q^62 + 3 * q^63 - 12 * q^64 + 12 * q^65 - 9 * q^66 - 24 * q^67 - 15 * q^68 + 12 * q^69 - 9 * q^70 - 12 * q^71 - 15 * q^72 - 12 * q^73 - 30 * q^74 - 30 * q^75 - 18 * q^77 - 6 * q^78 - 15 * q^79 - 15 * q^80 - 3 * q^81 + 9 * q^82 - 3 * q^84 + 9 * q^85 + 48 * q^86 - 21 * q^87 - 9 * q^88 - 15 * q^89 + 27 * q^90 + 12 * q^91 - 12 * q^92 + 27 * q^93 - 18 * q^94 + 18 * q^96 + 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.37939	−	0.866025i	−1.68248	−	0.612372i	−0.688833	−	0.724920i	$-0.741877\pi$
$2$	−2.37939	−	0.866025i	−1.68248	−	0.612372i	−0.993646	+	0.112548i	$0.964099\pi$
$3$	0.113341	+	0.642788i	0.0654373	+	0.371114i	0.999887	+	0.0150189i	$0.00478084\pi$
$3$	0.113341	+	0.642788i	0.0654373	+	0.371114i	−0.934450	+	0.356095i	$0.884108\pi$
$4$	3.37939	+	2.83564i	1.68969	+	1.41782i
$5$	−1.03209	+	0.866025i	−0.461564	+	0.387298i	−0.843706	−	0.536805i	$-0.819631\pi$
$5$	−1.03209	+	0.866025i	−0.461564	+	0.387298i	0.382142	+	0.924104i	$0.375187\pi$
$6$	0.286989	−	1.62760i	0.117163	−	0.664463i
$7$	−0.766044	+	1.32683i	−0.289538	+	0.501494i	−0.973699	−	0.227836i	$-0.926835\pi$
$7$	−0.766044	+	1.32683i	−0.289538	+	0.501494i	0.684162	+	0.729330i	$0.260168\pi$
$8$	−3.05303	−	5.28801i	−1.07941	−	1.86959i
$9$	2.41875	−	0.880352i	0.806249	−	0.293451i
$10$	3.20574	−	1.16679i	1.01374	−	0.368972i
$11$	0.592396	+	1.02606i	0.178614	+	0.309369i	0.941406	−	0.337275i	$-0.109505\pi$
$11$	0.592396	+	1.02606i	0.178614	+	0.309369i	−0.762792	+	0.646644i	$0.776172\pi$
$12$	−1.43969	+	2.49362i	−0.415603	+	0.719846i
$13$	−0.471782	+	2.67561i	−0.130849	+	0.742080i	0.846812	+	0.531892i	$0.178519\pi$
$13$	−0.471782	+	2.67561i	−0.130849	+	0.742080i	−0.977661	+	0.210188i	$0.932592\pi$
$14$	2.97178	−	2.49362i	0.794242	−	0.666448i
$15$	−0.673648	−	0.565258i	−0.173935	−	0.145949i
$16$	1.15270	+	6.53731i	0.288176	+	1.63433i
$17$	−3.64543	−	1.32683i	−0.884147	−	0.321803i	−0.140265	−	0.990114i	$-0.544795\pi$
$17$	−3.64543	−	1.32683i	−0.884147	−	0.321803i	−0.743882	+	0.668311i	$0.767018\pi$
$18$	−6.51754			−1.53620
$19$		0			0
$19$		0			0
$20$	−5.94356			−1.32902
$21$	−0.939693	−	0.342020i	−0.205058	−	0.0746349i
$22$	−0.520945	−	2.95442i	−0.111066	−	0.629885i
$23$	−3.87939	−	3.25519i	−0.808908	−	0.678754i	0.141439	−	0.989947i	$-0.454827\pi$
$23$	−3.87939	−	3.25519i	−0.808908	−	0.678754i	−0.950347	+	0.311193i	$0.899272\pi$
$24$	3.05303	−	2.56180i	0.623198	−	0.522925i
$25$	−0.553033	+	3.13641i	−0.110607	+	0.627282i
$26$	3.43969	−	5.95772i	0.674579	−	1.16841i
$27$	1.81908	+	3.15074i	0.350082	+	0.606359i
$28$	−6.35117	+	2.31164i	−1.20026	+	0.436858i
$29$	−4.37211	+	1.59132i	−0.811881	+	0.295500i	−0.714400	−	0.699737i	$-0.753300\pi$
$29$	−4.37211	+	1.59132i	−0.811881	+	0.295500i	−0.0974802	+	0.995237i	$0.531078\pi$
$30$	1.11334	+	1.92836i	0.203267	+	0.352069i
$31$	−1.91875	+	3.32337i	−0.344617	+	0.596895i	−0.985284	−	0.170924i	$-0.945325\pi$
$31$	−1.91875	+	3.32337i	−0.344617	+	0.596895i	0.640667	+	0.767819i	$0.278658\pi$
$32$	0.798133	−	4.52644i	0.141091	−	0.800169i
$33$	−0.592396	+	0.497079i	−0.103123	+	0.0865304i
$34$	7.52481	+	6.31407i	1.29050	+	1.08285i
$35$	−0.358441	−	2.03282i	−0.0605875	−	0.343609i
$36$	10.6702	+	3.88365i	1.77837	+	0.647275i
$37$	4.10607			0.675033			0.337517	−	0.941320i	$-0.390413\pi$
$37$	4.10607			0.675033			0.337517	+	0.941320i	$0.390413\pi$
$38$		0			0
$39$	−1.77332			−0.283958
$40$	7.73055	+	2.81369i	1.22231	+	0.444884i
$41$	1.73396	+	9.83375i	0.270798	+	1.53577i	0.752000	+	0.659164i	$0.229090\pi$
$41$	1.73396	+	9.83375i	0.270798	+	1.53577i	−0.481201	+	0.876610i	$0.659799\pi$
$42$	1.93969	+	1.62760i	0.299301	+	0.251143i
$43$	−6.66637	+	5.59375i	−1.01661	+	0.853039i	−0.989198	−	0.146585i	$-0.953172\pi$
$43$	−6.66637	+	5.59375i	−1.01661	+	0.853039i	−0.0274145	+	0.999624i	$0.508727\pi$
$44$	−0.907604	+	5.14728i	−0.136826	+	0.775981i
$45$	−1.73396	+	3.00330i	−0.258483	+	0.447705i
$46$	6.41147	+	11.1050i	0.945320	+	1.63734i
$47$	−0.539363	+	0.196312i	−0.0786742	+	0.0286351i	−0.381057	−	0.924551i	$-0.624440\pi$
$47$	−0.539363	+	0.196312i	−0.0786742	+	0.0286351i	0.302383	+	0.953186i	$0.402218\pi$
$48$	−4.07145	+	1.48189i	−0.587663	+	0.213892i
$49$	2.32635	+	4.02936i	0.332336	+	0.575623i
$50$	4.03209	−	6.98378i	0.570223	−	0.987656i
$51$	0.439693	−	2.49362i	0.0615693	−	0.349177i
$52$	−9.18139	+	7.70410i	−1.27323	+	1.06837i
$53$	−2.25490	−	1.89209i	−0.309734	−	0.259898i	0.474648	−	0.880176i	$-0.342575\pi$
$53$	−2.25490	−	1.89209i	−0.309734	−	0.259898i	−0.784382	+	0.620278i	$0.787020\pi$
$54$	−1.59967	−	9.07218i	−0.217688	−	1.23457i
$55$	−1.50000	−	0.545955i	−0.202260	−	0.0736166i
$56$	9.35504			1.25012
$57$		0			0
$58$	11.7811			1.54693
$59$	−3.69846	−	1.34613i	−0.481499	−	0.175251i	0.0898553	−	0.995955i	$-0.471360\pi$
$59$	−3.69846	−	1.34613i	−0.481499	−	0.175251i	−0.571354	+	0.820704i	$0.693582\pi$
$60$	−0.673648	−	3.82045i	−0.0869676	−	0.493218i
$61$	−3.46064	−	2.90382i	−0.443089	−	0.371796i	0.393775	−	0.919207i	$-0.371169\pi$
$61$	−3.46064	−	2.90382i	−0.443089	−	0.371796i	−0.836864	+	0.547411i	$0.815613\pi$
$62$	7.44356	−	6.24589i	0.945333	−	0.793229i
$63$	−0.684793	+	3.88365i	−0.0862757	+	0.489294i
$64$	0.819078	−	1.41868i	0.102385	−	0.177336i
$65$	−1.83022	−	3.17004i	−0.227011	−	0.393195i
$66$	1.84002	−	0.669713i	0.226491	−	0.0824360i
$67$	−3.65270	+	1.32948i	−0.446249	+	0.162421i	−0.555363	−	0.831608i	$-0.687421\pi$
$67$	−3.65270	+	1.32948i	−0.446249	+	0.162421i	0.109114	+	0.994029i	$0.465199\pi$
$68$	−8.55690	−	14.8210i	−1.03768	−	1.79731i
$69$	1.65270	−	2.86257i	0.198962	−	0.344613i
$70$	−0.907604	+	5.14728i	−0.108479	+	0.615217i
$71$	5.31315	−	4.45826i	0.630555	−	0.529098i	−0.270547	−	0.962707i	$-0.587204\pi$
$71$	5.31315	−	4.45826i	0.630555	−	0.529098i	0.901101	+	0.433609i	$0.142760\pi$
$72$	−12.0398	−	10.1026i	−1.41891	−	1.19060i
$73$	1.06418	+	6.03525i	0.124553	+	0.706373i	0.981573	+	0.191090i	$0.0612021\pi$
$73$	1.06418	+	6.03525i	0.124553	+	0.706373i	−0.857020	+	0.515283i	$0.827687\pi$
$74$	−9.76991	−	3.55596i	−1.13573	−	0.413372i
$75$	−2.07873			−0.240031
$76$		0			0
$77$	−1.81521			−0.206862
$78$	4.21941	+	1.53574i	0.477754	+	0.173888i
$79$	−1.70321	−	9.65939i	−0.191626	−	1.08677i	−0.917142	−	0.398561i	$-0.869510\pi$
$79$	−1.70321	−	9.65939i	−0.191626	−	1.08677i	0.725516	−	0.688206i	$-0.241601\pi$
$80$	−6.85117	−	5.74881i	−0.765984	−	0.642737i
$81$	4.09627	−	3.43718i	0.455141	−	0.381908i
$82$	4.39053	−	24.8999i	0.484853	−	2.74974i
$83$	−6.15910	+	10.6679i	−0.676049	+	1.17095i	0.300112	+	0.953904i	$0.402976\pi$
$83$	−6.15910	+	10.6679i	−0.676049	+	1.17095i	−0.976161	+	0.217047i	$0.930357\pi$
$84$	−2.20574	−	3.82045i	−0.240666	−	0.416845i
$85$	4.91147	−	1.78763i	0.532724	−	0.193896i
$86$	20.7062	−	7.53644i	2.23281	−	0.812675i
$87$	−1.51842	−	2.62998i	−0.162792	−	0.281963i
$88$	3.61721	−	6.26519i	0.385596	−	0.667872i
$89$	0.421274	−	2.38917i	0.0446550	−	0.253251i	−0.954306	−	0.298832i	$-0.903403\pi$
$89$	0.421274	−	2.38917i	0.0446550	−	0.253251i	0.998961	+	0.0455813i	$0.0145140\pi$
$90$	6.72668	−	5.64436i	0.709054	−	0.594967i
$91$	−3.18866	−	2.67561i	−0.334263	−	0.280480i
$92$	−3.87939	−	22.0011i	−0.404454	−	2.29377i
$93$	−2.35369	−	0.856674i	−0.244067	−	0.0888330i
$94$	1.45336			0.149903
$95$		0			0
$96$	3.00000			0.306186
$97$	6.92514	+	2.52055i	0.703142	+	0.255923i	0.668752	−	0.743486i	$-0.266829\pi$
$97$	6.92514	+	2.52055i	0.703142	+	0.255923i	0.0343901	+	0.999408i	$0.489051\pi$
$98$	−2.04576	−	11.6021i	−0.206653	−	1.17199i
$99$	2.33615	+	1.96026i	0.234792	+	0.197014i
$100$	−10.7626	+	9.03093i	−1.07626	+	0.903093i
$101$	0.376859	−	2.13727i	0.0374989	−	0.212667i	−0.960301	−	0.278966i	$-0.910008\pi$
$101$	0.376859	−	2.13727i	0.0374989	−	0.212667i	0.997800	+	0.0662996i	$0.0211193\pi$
$102$	−3.20574	+	5.55250i	−0.317415	+	0.549779i
$103$	−6.23783	−	10.8042i	−0.614631	−	1.06457i	−0.990449	−	0.137879i	$-0.955971\pi$
$103$	−6.23783	−	10.8042i	−0.614631	−	1.06457i	0.375818	−	0.926694i	$-0.377362\pi$
$104$	15.5890	−	5.67393i	1.52863	−	0.556375i
$105$	1.26604	−	0.460802i	0.123553	−	0.0449697i
$106$	3.72668	+	6.45480i	0.361967	+	0.626946i
$107$	−3.34002	+	5.78509i	−0.322892	+	0.559266i	−0.981083	−	0.193585i	$-0.937988\pi$
$107$	−3.34002	+	5.78509i	−0.322892	+	0.559266i	0.658191	+	0.752851i	$0.271322\pi$
$108$	−2.78699	+	15.8058i	−0.268178	+	1.52091i
$109$	−7.24170	+	6.07650i	−0.693629	+	0.582024i	−0.919953	−	0.392028i	$-0.871773\pi$
$109$	−7.24170	+	6.07650i	−0.693629	+	0.582024i	0.226324	+	0.974052i	$0.427329\pi$
$110$	3.09627	+	2.59808i	0.295217	+	0.247717i
$111$	0.465385	+	2.63933i	0.0441724	+	0.250514i
$112$	−9.55690	−	3.47843i	−0.903043	−	0.328681i
$113$	−1.31046			−0.123278			−0.0616388	−	0.998099i	$-0.519633\pi$
$113$	−1.31046			−0.123278			−0.0616388	+	0.998099i	$0.519633\pi$
$114$		0			0
$115$	6.82295			0.636243
$116$	−19.2875	−	7.02006i	−1.79080	−	0.651796i
$117$	1.21436	+	6.88695i	0.112267	+	0.636699i
$118$	7.63429	+	6.40593i	0.702793	+	0.589713i
$119$	4.55303	−	3.82045i	0.417376	−	0.350220i
$120$	−0.932419	+	5.28801i	−0.0851178	+	0.482727i
$121$	4.79813	−	8.31061i	0.436194	−	0.755510i
$122$	5.71941	+	9.90630i	0.517811	+	0.896875i
$123$	−6.12449	+	2.22913i	−0.552226	+	0.200994i
$124$	−15.9081	+	5.79006i	−1.42859	+	0.519963i
$125$	−5.51367	−	9.54996i	−0.493158	−	0.854174i
$126$	4.99273	−	8.64766i	0.444787	−	0.770394i
$127$	2.51842	−	14.2827i	0.223473	−	1.26738i	−0.642108	−	0.766614i	$-0.721940\pi$
$127$	2.51842	−	14.2827i	0.223473	−	1.26738i	0.865582	−	0.500767i	$-0.166949\pi$
$128$	−10.2194	+	8.57510i	−0.903277	+	0.757939i
$129$	−4.35117	−	3.65106i	−0.383099	−	0.321458i
$130$	1.60947	+	9.12776i	0.141160	+	0.800558i
$131$	18.6138	+	6.77487i	1.62630	+	0.591923i	0.984567	−	0.175008i	$-0.0559952\pi$
$131$	18.6138	+	6.77487i	1.62630	+	0.591923i	0.641729	+	0.766932i	$0.278217\pi$
$132$	−3.41147			−0.296931
$133$		0			0
$134$	9.84255			0.850267
$135$	−4.60607	−	1.67647i	−0.396427	−	0.144288i
$136$	4.11334	+	23.3279i	0.352716	+	2.00035i
$137$	7.81702	+	6.55926i	0.667853	+	0.560395i	0.912429	−	0.409235i	$-0.134204\pi$
$137$	7.81702	+	6.55926i	0.667853	+	0.560395i	−0.244576	+	0.969630i	$0.578649\pi$
$138$	−6.41147	+	5.37987i	−0.545781	+	0.457965i
$139$	−0.288333	+	1.63522i	−0.0244561	+	0.138697i	−0.994591	−	0.103868i	$-0.966878\pi$
$139$	−0.288333	+	1.63522i	−0.0244561	+	0.138697i	0.970135	+	0.242566i	$0.0779890\pi$
$140$	4.55303	−	7.88609i	0.384802	−	0.666496i
$141$	−0.187319	−	0.324446i	−0.0157751	−	0.0273232i
$142$	−16.5030	+	6.00660i	−1.38490	+	0.504063i
$143$	−3.02481	+	1.10094i	−0.252948	+	0.0920654i
$144$	8.54323	+	14.7973i	0.711936	+	1.23311i
$145$	3.13429	−	5.42874i	0.260288	−	0.450832i
$146$	2.69459	−	15.2818i	0.223006	−	1.26473i
$147$	−2.32635	+	1.95204i	−0.191874	+	0.161002i
$148$	13.8760	+	11.6433i	1.14060	+	0.957076i
$149$	1.94609	+	11.0368i	0.159430	+	0.904172i	0.954623	+	0.297816i	$0.0962581\pi$
$149$	1.94609	+	11.0368i	0.159430	+	0.904172i	−0.795194	+	0.606356i	$0.792631\pi$
$150$	4.94609	+	1.80023i	0.403846	+	0.146988i
$151$	11.0419			0.898576			0.449288	−	0.893387i	$-0.351678\pi$
$151$	11.0419			0.898576			0.449288	+	0.893387i	$0.351678\pi$
$152$		0			0
$153$	−9.98545			−0.807276
$154$	4.31908	+	1.57202i	0.348041	+	0.126677i
$155$	−0.897804	−	5.09170i	−0.0721133	−	0.408975i
$156$	−5.99273	−	5.02849i	−0.479802	−	0.402602i
$157$	8.42127	−	7.06629i	0.672091	−	0.563951i	−0.241593	−	0.970378i	$-0.577670\pi$
$157$	8.42127	−	7.06629i	0.672091	−	0.563951i	0.913683	+	0.406427i	$0.133225\pi$
$158$	−4.31268	+	24.4584i	−0.343098	+	1.94581i
$159$	0.960637	−	1.66387i	0.0761835	−	0.131954i
$160$	3.09627	+	5.36289i	0.244781	+	0.423974i
$161$	7.29086	−	2.65366i	0.574600	−	0.209137i
$162$	−12.7233	+	4.63089i	−0.999635	+	0.363837i
$163$	3.16637	+	5.48432i	0.248010	+	0.429565i	0.962973	−	0.269596i	$-0.0868902\pi$
$163$	3.16637	+	5.48432i	0.248010	+	0.429565i	−0.714964	+	0.699161i	$0.753557\pi$
$164$	−22.0253	+	38.1489i	−1.71989	+	2.97893i
$165$	0.180922	−	1.02606i	0.0140848	−	0.0798787i
$166$	23.8935	−	20.0490i	1.85450	−	1.55611i
$167$	10.5548	+	8.85657i	0.816758	+	0.685342i	0.952211	−	0.305442i	$-0.0988043\pi$
$167$	10.5548	+	8.85657i	0.816758	+	0.685342i	−0.135452	+	0.990784i	$0.543249\pi$
$168$	1.06031	+	6.01330i	0.0818045	+	0.463936i
$169$	5.27972	+	1.92166i	0.406132	+	0.147820i
$170$	−13.2344			−1.01503
$171$		0			0
$172$	−38.3901			−2.92722
$173$	23.7246	+	8.63506i	1.80375	+	0.656511i	0.997927	+	0.0643540i	$0.0204987\pi$
$173$	23.7246	+	8.63506i	1.80375	+	0.656511i	0.805822	+	0.592157i	$0.201724\pi$
$174$	1.33527	+	7.57272i	0.101227	+	0.574086i
$175$	−3.73783	−	3.13641i	−0.282553	−	0.237090i
$176$	−6.02481	+	5.05542i	−0.454138	+	0.381067i
$177$	0.446089	−	2.52990i	0.0335301	−	0.190159i
$178$	−3.07145	+	5.31991i	−0.230215	+	0.398744i
$179$	2.91534	+	5.04952i	0.217903	+	0.377419i	0.954167	−	0.299276i	$-0.0967450\pi$
$179$	2.91534	+	5.04952i	0.217903	+	0.377419i	−0.736264	+	0.676695i	$0.763412\pi$
$180$	−14.3760	+	5.23243i	−1.07152	+	0.390002i
$181$	12.7442	−	4.63852i	0.947271	−	0.344778i	0.178238	−	0.983987i	$-0.442960\pi$
$181$	12.7442	−	4.63852i	0.947271	−	0.344778i	0.769033	+	0.639209i	$0.220738\pi$
$182$	5.26991	+	9.12776i	0.390632	+	0.676595i
$183$	1.47431	−	2.55358i	0.108984	−	0.188766i
$184$	−5.36959	+	30.4524i	−0.395851	+	2.24498i
$185$	−4.23783	+	3.55596i	−0.311571	+	0.261439i
$186$	4.85844	+	4.07672i	0.356238	+	0.298919i
$187$	−0.798133	−	4.52644i	−0.0583653	−	0.331006i
$188$	−2.37939	−	0.866025i	−0.173535	−	0.0631614i
$189$	−5.57398			−0.405447
$190$		0			0
$191$	−10.2841			−0.744128			−0.372064	−	0.928207i	$-0.621350\pi$
$191$	−10.2841			−0.744128			−0.372064	+	0.928207i	$0.621350\pi$
$192$	1.00475	+	0.365698i	0.0725114	+	0.0263920i
$193$	−2.39646	−	13.5910i	−0.172501	−	0.978301i	−0.940989	−	0.338437i	$-0.890102\pi$
$193$	−2.39646	−	13.5910i	−0.172501	−	0.978301i	0.768488	−	0.639864i	$-0.221009\pi$
$194$	−14.2947	−	11.9947i	−1.02630	−	0.861169i
$195$	1.83022	−	1.53574i	0.131065	−	0.109977i
$196$	−3.56418	+	20.2135i	−0.254584	+	1.44382i
$197$	3.97044	−	6.87700i	0.282882	−	0.489966i	−0.689211	−	0.724560i	$-0.742043\pi$
$197$	3.97044	−	6.87700i	0.282882	−	0.489966i	0.972093	+	0.234594i	$0.0753762\pi$
$198$	−3.86097	−	6.68739i	−0.274387	−	0.475252i
$199$	−25.4047	+	9.24654i	−1.80089	+	0.655470i	−0.802631	+	0.596476i	$0.796567\pi$
$199$	−25.4047	+	9.24654i	−1.80089	+	0.655470i	−0.998258	+	0.0589938i	$0.981211\pi$
$200$	18.2738	−	6.65111i	1.29215	−	0.470305i
$201$	−1.26857	−	2.19723i	−0.0894781	−	0.154981i
$202$	−2.74763	+	4.75903i	−0.193322	+	0.334844i
$203$	1.23783	−	7.02006i	0.0868784	−	0.492712i
$204$	8.55690	−	7.18009i	0.599103	−	0.502707i
$205$	−10.3059	−	8.64766i	−0.719793	−	0.603978i
$206$	5.48545	+	31.1095i	0.382190	+	2.16750i
$207$	−12.2490	−	4.45826i	−0.851362	−	0.309871i
$208$	−18.0351			−1.25051
$209$		0			0
$210$	−3.41147			−0.235414
$211$	−7.58512	−	2.76076i	−0.522181	−	0.190058i	0.0674625	−	0.997722i	$-0.478510\pi$
$211$	−7.58512	−	2.76076i	−0.522181	−	0.190058i	−0.589644	+	0.807663i	$0.700732\pi$
$212$	−2.25490	−	12.7882i	−0.154867	−	0.878295i
$213$	3.46791	+	2.90992i	0.237617	+	0.199385i
$214$	12.9572	−	10.8724i	0.885738	−	0.743223i
$215$	2.03596	−	11.5465i	0.138851	−	0.787465i
$216$	11.1074	−	19.2386i	0.755764	−	1.30902i
$217$	−2.93969	−	5.09170i	−0.199559	−	0.345647i
$218$	22.4932	−	8.18685i	1.52343	−	0.554484i
$219$	−3.75877	+	1.36808i	−0.253994	+	0.0924463i
$220$	−3.52094	−	6.09845i	−0.237382	−	0.411158i
$221$	5.26991	−	9.12776i	0.354493	−	0.614000i
$222$	1.17840	−	6.68302i	0.0790888	−	0.448535i
$223$	11.8550	−	9.94756i	0.793872	−	0.666138i	−0.152829	−	0.988253i	$-0.548838\pi$
$223$	11.8550	−	9.94756i	0.793872	−	0.666138i	0.946701	+	0.322115i	$0.104394\pi$
$224$	5.39440	+	4.52644i	0.360429	+	0.302435i
$225$	1.42350	+	8.07305i	0.0948997	+	0.538203i
$226$	3.11809	+	1.13489i	0.207412	+	0.0754919i
$227$	−9.87258			−0.655266			−0.327633	−	0.944805i	$-0.606251\pi$
$227$	−9.87258			−0.655266			−0.327633	+	0.944805i	$0.606251\pi$
$228$		0			0
$229$	20.1189			1.32949			0.664746	−	0.747070i	$-0.268540\pi$
$229$	20.1189			1.32949			0.664746	+	0.747070i	$0.268540\pi$
$230$	−16.2344	−	5.90885i	−1.07047	−	0.389618i
$231$	−0.205737	−	1.16679i	−0.0135365	−	0.0767693i
$232$	21.7631	+	18.2614i	1.42882	+	1.19892i
$233$	2.70780	−	2.27211i	0.177394	−	0.148851i	−0.549768	−	0.835318i	$-0.685284\pi$
$233$	2.70780	−	2.27211i	0.177394	−	0.148851i	0.727161	+	0.686467i	$0.240839\pi$
$234$	3.07486	−	17.4384i	0.201010	−	1.13998i
$235$	0.386659	−	0.669713i	0.0252229	−	0.0436873i
$236$	−8.68139	−	15.0366i	−0.565110	−	0.978800i
$237$	6.01589	−	2.18961i	0.390774	−	0.142230i
$238$	−14.1420	+	5.14728i	−0.916691	+	0.333648i
$239$	−5.98680	−	10.3694i	−0.387254	−	0.670743i	0.604825	−	0.796358i	$-0.293243\pi$
$239$	−5.98680	−	10.3694i	−0.387254	−	0.670743i	−0.992079	+	0.125615i	$0.959910\pi$
$240$	2.91875	−	5.05542i	0.188404	−	0.326326i
$241$	−2.24035	+	12.7057i	−0.144314	+	0.818444i	0.823602	+	0.567168i	$0.191961\pi$
$241$	−2.24035	+	12.7057i	−0.144314	+	0.818444i	−0.967916	+	0.251276i	$0.919150\pi$
$242$	−18.6138	+	15.6188i	−1.19654	+	1.00402i
$243$	11.0346	+	9.25914i	0.707871	+	0.593974i
$244$	−3.46064	−	19.6262i	−0.221545	−	1.25644i
$245$	−5.89053	−	2.14398i	−0.376332	−	0.136974i
$246$	16.5030			1.05219
$247$		0			0
$248$	23.4320			1.48793
$249$	−7.55525	−	2.74989i	−0.478795	−	0.174267i
$250$	4.84864	+	27.4980i	0.306655	+	1.73913i
$251$	11.0025	+	9.23222i	0.694473	+	0.582732i	0.920195	−	0.391459i	$-0.128030\pi$
$251$	11.0025	+	9.23222i	0.694473	+	0.582732i	−0.225722	+	0.974192i	$0.572474\pi$
$252$	−13.3268	+	11.1825i	−0.839511	+	0.704433i
$253$	1.04189	−	5.90885i	0.0655030	−	0.371486i
$254$	−18.3614	+	31.8029i	−1.15210	+	1.99549i
$255$	1.70574	+	2.95442i	0.106817	+	0.185013i
$256$	28.6634	−	10.4326i	1.79146	−	0.652040i
$257$	4.67752	−	1.70248i	0.291776	−	0.106198i	−0.191985	−	0.981398i	$-0.561493\pi$
$257$	4.67752	−	1.70248i	0.291776	−	0.106198i	0.483761	+	0.875200i	$0.339270\pi$
$258$	7.19119	+	12.4555i	0.447704	+	0.775446i
$259$	−3.14543	+	5.44804i	−0.195447	+	0.338525i
$260$	2.80406	−	15.9026i	0.173901	−	0.986239i
$261$	−9.17412	+	7.69800i	−0.567863	+	0.476494i
$262$	−38.4222	−	32.2401i	−2.37373	−	1.99180i
$263$	−4.17499	−	23.6776i	−0.257441	−	1.46002i	−0.789728	−	0.613457i	$-0.789778\pi$
$263$	−4.17499	−	23.6776i	−0.257441	−	1.46002i	0.532287	−	0.846564i	$-0.321333\pi$
$264$	4.43717	+	1.61500i	0.273089	+	0.0993962i
$265$	3.96585			0.243620
$266$		0			0
$267$	1.58347			0.0969070
$268$	−16.1138	−	5.86495i	−0.984307	−	0.358259i
$269$	2.27672	+	12.9119i	0.138814	+	0.787254i	0.972127	+	0.234453i	$0.0753300\pi$
$269$	2.27672	+	12.9119i	0.138814	+	0.787254i	−0.833313	+	0.552801i	$0.813559\pi$
$270$	9.50774	+	7.97794i	0.578623	+	0.485522i
$271$	−20.3537	+	17.0788i	−1.23640	+	1.03746i	−0.238602	+	0.971117i	$0.576689\pi$
$271$	−20.3537	+	17.0788i	−1.23640	+	1.03746i	−0.997797	+	0.0663443i	$0.978866\pi$
$272$	4.47178	−	25.3607i	0.271142	−	1.53772i
$273$	1.35844	−	2.35289i	0.0822166	−	0.142403i
$274$	−12.9192	−	22.3767i	−0.780478	−	1.35183i
$275$	−3.54576	+	1.29055i	−0.213817	+	0.0778231i
$276$	13.7023	−	4.98724i	0.824784	−	0.300197i
$277$	8.25537	+	14.2987i	0.496017	+	0.859127i	0.999989	−	0.00459317i	$-0.00146206\pi$
$277$	8.25537	+	14.2987i	0.496017	+	0.859127i	−0.503973	+	0.863720i	$0.668129\pi$
$278$	2.10220	−	3.64111i	0.126081	−	0.218379i
$279$	−1.71523	+	9.72757i	−0.102688	+	0.582374i
$280$	−9.65523	+	8.10170i	−0.577010	+	0.484169i
$281$	14.8537	+	12.4637i	0.886097	+	0.743524i	0.967423	−	0.253164i	$-0.0814712\pi$
$281$	14.8537	+	12.4637i	0.886097	+	0.743524i	−0.0813264	+	0.996688i	$0.525916\pi$
$282$	0.164725	+	0.934204i	0.00980925	+	0.0556310i
$283$	10.6284	+	3.86841i	0.631790	+	0.229953i	0.638010	−	0.770028i	$-0.279758\pi$
$283$	10.6284	+	3.86841i	0.631790	+	0.229953i	−0.00622012	+	0.999981i	$0.501980\pi$
$284$	30.5972			1.81561
$285$		0			0
$286$	8.15064			0.481958
$287$	−14.3760	−	5.23243i	−0.848587	−	0.308861i
$288$	−2.05438	−	11.6510i	−0.121055	−	0.686539i
$289$	−1.49407	−	1.25367i	−0.0878865	−	0.0737455i
$290$	−12.1591	+	10.2027i	−0.714007	+	0.599123i
$291$	−0.835275	+	4.73708i	−0.0489647	+	0.277692i
$292$	−13.5175	+	23.4131i	−0.791054	+	1.37015i
$293$	1.94949	+	3.37662i	0.113891	+	0.197264i	0.917336	−	0.398115i	$-0.130335\pi$
$293$	1.94949	+	3.37662i	0.113891	+	0.197264i	−0.803445	+	0.595379i	$0.797002\pi$
$294$	7.22580	−	2.62998i	0.421417	−	0.153383i
$295$	4.98293	−	1.81364i	0.290117	−	0.105594i
$296$	−12.5360	−	21.7129i	−0.728638	−	1.26204i
$297$	−2.15523	+	3.73297i	−0.125059	+	0.216609i
$298$	4.92767	−	27.9462i	0.285452	−	1.61888i
$299$	10.5398	−	8.84397i	0.609534	−	0.511460i
$300$	−7.02481	−	5.89452i	−0.405578	−	0.340320i
$301$	−2.31521	−	13.1302i	−0.133446	−	0.756812i
$302$	−26.2729	−	9.56256i	−1.51184	−	0.550263i
$303$	1.41653			0.0813773
$304$		0			0
$305$	6.08647			0.348510
$306$	23.7592	+	8.64766i	1.35823	+	0.494354i
$307$	−4.02435	−	22.8232i	−0.229682	−	1.30259i	−0.853530	−	0.521044i	$-0.825543\pi$
$307$	−4.02435	−	22.8232i	−0.229682	−	1.30259i	0.623848	−	0.781546i	$-0.285568\pi$
$308$	−6.13429	−	5.14728i	−0.349533	−	0.293293i
$309$	6.23783	−	5.23416i	0.354858	−	0.297761i
$310$	−2.27332	+	12.8926i	−0.129116	+	0.732252i
$311$	1.73055	−	2.99740i	0.0981306	−	0.169967i	−0.812780	−	0.582570i	$-0.802047\pi$
$311$	1.73055	−	2.99740i	0.0981306	−	0.169967i	0.910911	+	0.412603i	$0.135380\pi$
$312$	5.41400	+	9.37732i	0.306507	+	0.530886i
$313$	21.5094	−	7.82878i	1.21578	−	0.442509i	0.347077	−	0.937837i	$-0.387174\pi$
$313$	21.5094	−	7.82878i	1.21578	−	0.442509i	0.868706	+	0.495328i	$0.164952\pi$
$314$	−26.1570	+	9.52038i	−1.47613	+	0.537266i
$315$	−2.65657	−	4.60132i	−0.149681	−	0.259255i
$316$	21.6348	−	37.4725i	1.21705	−	2.10799i
$317$	−4.53580	+	25.7238i	−0.254756	+	1.44479i	0.541943	+	0.840415i	$0.317689\pi$
$317$	−4.53580	+	25.7238i	−0.254756	+	1.44479i	−0.796699	+	0.604376i	$0.793422\pi$
$318$	−3.72668	+	3.12706i	−0.208982	+	0.175357i
$319$	−4.22281	−	3.54336i	−0.236432	−	0.198390i
$320$	0.383256	+	2.17355i	0.0214246	+	0.121505i
$321$	−4.09714	−	1.49124i	−0.228680	−	0.0832328i
$322$	−19.6459			−1.09482
$323$		0			0
$324$	23.5895			1.31053
$325$	−8.13088	−	2.95940i	−0.451020	−	0.164158i
$326$	−2.78446	−	15.7915i	−0.154217	−	0.874609i
$327$	−4.72668	−	3.96616i	−0.261386	−	0.219329i
$328$	46.7071	−	39.1919i	2.57897	−	2.16401i
$329$	0.152704	−	0.866025i	0.00841882	−	0.0477455i
$330$	−1.31908	+	2.28471i	−0.0726128	+	0.125769i
$331$	9.52229	+	16.4931i	0.523392	+	0.906542i	0.999629	+	0.0272251i	$0.00866710\pi$
$331$	9.52229	+	16.4931i	0.523392	+	0.906542i	−0.476237	+	0.879317i	$0.658000\pi$
$332$	−51.0642	+	18.5859i	−2.80251	+	1.02003i
$333$	9.93154	−	3.61479i	0.544245	−	0.198089i
$334$	−17.4440	−	30.2139i	−0.954495	−	1.65323i
$335$	2.61856	−	4.53547i	0.143067	−	0.247799i
$336$	1.15270	−	6.53731i	0.0628851	−	0.356639i
$337$	−1.30335	+	1.09364i	−0.0709979	+	0.0595743i	−0.677596	−	0.735434i	$-0.736978\pi$
$337$	−1.30335	+	1.09364i	−0.0709979	+	0.0595743i	0.606598	+	0.795009i	$0.292534\pi$
$338$	−10.8983	−	9.14473i	−0.592788	−	0.497408i
$339$	−0.148529	−	0.842347i	−0.00806696	−	0.0457500i
$340$	21.6668	+	7.88609i	1.17505	+	0.427683i
$341$	−4.54664			−0.246214
$342$		0			0
$343$	−17.8530			−0.963970
$344$	49.9325	+	18.1739i	2.69218	+	0.979873i
$345$	0.773318	+	4.38571i	0.0416341	+	0.236119i
$346$	−48.9718	−	41.0923i	−2.63274	−	2.20913i
$347$	−3.75490	+	3.15074i	−0.201574	+	0.169140i	−0.737987	−	0.674815i	$-0.764223\pi$
$347$	−3.75490	+	3.15074i	−0.201574	+	0.169140i	0.536413	+	0.843956i	$0.319779\pi$
$348$	2.32635	−	13.1934i	0.124706	−	0.707240i
$349$	14.0646	−	24.3607i	0.752863	−	1.30400i	−0.193566	−	0.981087i	$-0.562006\pi$
$349$	14.0646	−	24.3607i	0.752863	−	1.30400i	0.946430	−	0.322910i	$-0.104661\pi$
$350$	6.17752	+	10.6998i	0.330202	+	0.571927i
$351$	−9.28833	+	3.38068i	−0.495775	+	0.180447i
$352$	5.11721	−	1.86251i	0.272748	−	0.0992723i
$353$	4.15998	+	7.20529i	0.221413	+	0.383499i	0.955237	−	0.295841i	$-0.0955997\pi$
$353$	4.15998	+	7.20529i	0.221413	+	0.383499i	−0.733824	+	0.679340i	$0.762266\pi$
$354$	−3.25237	+	5.63328i	−0.172862	+	0.299405i
$355$	−1.62267	+	9.20264i	−0.0861226	+	0.488426i
$356$	8.19846	−	6.87933i	0.434518	−	0.364604i
$357$	2.97178	+	2.49362i	0.157283	+	0.131976i
$358$	−2.56371	−	14.5395i	−0.135496	−	0.768438i
$359$	−23.4256	−	8.52623i	−1.23636	−	0.449997i	−0.360587	−	0.932726i	$-0.617423\pi$
$359$	−23.4256	−	8.52623i	−1.23636	−	0.449997i	−0.875770	+	0.482729i	$0.839646\pi$
$360$	21.1753			1.11604
$361$		0			0
$362$	−34.3405			−1.80490
$363$	5.88578	+	2.14225i	0.308923	+	0.112439i
$364$	−3.18866	−	18.0838i	−0.167131	−	0.947849i
$365$	−6.32501	−	5.30731i	−0.331066	−	0.277797i
$366$	−5.71941	+	4.79915i	−0.298958	+	0.250856i
$367$	−0.449026	+	2.54655i	−0.0234390	+	0.132929i	−0.994282	−	0.106788i	$-0.965943\pi$
$367$	−0.449026	+	2.54655i	−0.0234390	+	0.132929i	0.970843	+	0.239717i	$0.0770546\pi$
$368$	16.8084	−	29.1130i	0.876198	−	1.51762i
$369$	12.8512	+	22.2589i	0.669005	+	1.15875i
$370$	13.1630	−	4.79093i	0.684310	−	0.249069i
$371$	4.23783	−	1.54244i	0.220017	−	0.0800796i
$372$	−5.52481	−	9.56926i	−0.286448	−	0.496143i
$373$	−11.6917	+	20.2505i	−0.605371	+	1.04853i	0.386622	+	0.922238i	$0.373642\pi$
$373$	−11.6917	+	20.2505i	−0.605371	+	1.04853i	−0.991993	+	0.126295i	$0.959691\pi$
$374$	−2.02094	+	11.4613i	−0.104501	+	0.592652i
$375$	5.51367	−	4.62652i	0.284725	−	0.238912i
$376$	2.68479	+	2.25281i	0.138458	+	0.116180i
$377$	−2.19506	−	12.4488i	−0.113051	−	0.641146i
$378$	13.2626	+	4.82721i	0.682157	+	0.248285i
$379$	−25.4388			−1.30670			−0.653352	−	0.757054i	$-0.726638\pi$
$379$	−25.4388			−1.30670			−0.653352	+	0.757054i	$0.726638\pi$
$380$		0			0
$381$	9.46616			0.484966
$382$	24.4697	+	8.90625i	1.25198	+	0.455683i
$383$	4.77197	+	27.0632i	0.243836	+	1.38287i	0.823179	+	0.567781i	$0.192198\pi$
$383$	4.77197	+	27.0632i	0.243836	+	1.38287i	−0.579343	+	0.815084i	$0.696691\pi$
$384$	−6.67024	−	5.59700i	−0.340389	−	0.285621i
$385$	1.87346	−	1.57202i	0.0954801	−	0.0801173i
$386$	−6.06805	+	34.4136i	−0.308856	+	1.75161i
$387$	−11.1998	+	19.3986i	−0.569318	+	0.986088i
$388$	16.2554	+	28.1551i	0.825241	+	1.42936i
$389$	3.14068	−	1.14311i	0.159239	−	0.0579582i	−0.261171	−	0.965293i	$-0.584109\pi$
$389$	3.14068	−	1.14311i	0.159239	−	0.0579582i	0.420410	+	0.907334i	$0.361886\pi$
$390$	−5.68479	+	2.06910i	−0.287861	+	0.104773i
$391$	9.82295	+	17.0138i	0.496768	+	0.860427i
$392$	14.2049	−	24.6035i	0.717454	−	1.24267i
$393$	−2.24510	+	12.7326i	−0.113250	+	0.642274i
$394$	−15.4029	+	12.9245i	−0.775985	+	0.651128i
$395$	10.1231	+	8.49432i	0.509351	+	0.427396i
$396$	2.33615	+	13.2490i	0.117396	+	0.665786i
$397$	12.3319	+	4.48843i	0.618919	+	0.225268i	0.632401	−	0.774641i	$-0.282069\pi$
$397$	12.3319	+	4.48843i	0.618919	+	0.225268i	−0.0134823	+	0.999909i	$0.504292\pi$
$398$	68.4552			3.43135
$399$		0			0
$400$	−21.1411			−1.05706
$401$	16.0817	+	5.85327i	0.803083	+	0.292298i	0.710763	−	0.703431i	$-0.248350\pi$
$401$	16.0817	+	5.85327i	0.803083	+	0.292298i	0.0923194	+	0.995729i	$0.470572\pi$
$402$	1.11556	+	6.32667i	0.0556392	+	0.315546i
$403$	−7.98680	−	6.70172i	−0.397851	−	0.333836i
$404$	7.33409	−	6.15403i	0.364885	−	0.306175i
$405$	−1.25103	+	7.09494i	−0.0621642	+	0.352551i
$406$	−9.02481	+	15.6314i	−0.447894	+	0.775775i
$407$	2.43242	+	4.21307i	0.120571	+	0.208834i
$408$	−14.5287	+	5.28801i	−0.719277	+	0.261795i
$409$	−8.26739	+	3.00908i	−0.408796	+	0.148790i	−0.538229	−	0.842799i	$-0.680906\pi$
$409$	−8.26739	+	3.00908i	−0.408796	+	0.148790i	0.129433	+	0.991588i	$0.458684\pi$
$410$	17.0326	+	29.5013i	0.841178	+	1.45696i
$411$	−3.33022	+	5.76811i	−0.164268	+	0.284520i
$412$	9.55690	−	54.1999i	0.470835	−	2.67024i
$413$	4.61927	−	3.87603i	0.227299	−	0.190727i
$414$	25.2841	+	21.2158i	1.24264	+	1.04270i
$415$	−2.88191	−	16.3441i	−0.141467	−	0.802302i
$416$	11.7344	+	4.27098i	0.575327	+	0.209402i
$417$	−1.08378			−0.0530728
$418$		0			0
$419$	6.84018			0.334165			0.167082	−	0.985943i	$-0.446565\pi$
$419$	6.84018			0.334165			0.167082	+	0.985943i	$0.446565\pi$
$420$	5.58512	+	2.03282i	0.272526	+	0.0991914i
$421$	0.837496	+	4.74968i	0.0408171	+	0.231485i	0.998391	−	0.0567022i	$-0.0180585\pi$
$421$	0.837496	+	4.74968i	0.0408171	+	0.231485i	−0.957574	+	0.288187i	$0.906947\pi$
$422$	15.6570	+	13.1378i	0.762173	+	0.639539i
$423$	−1.13176	+	0.949659i	−0.0550280	+	0.0461740i
$424$	−3.12108	+	17.7005i	−0.151573	+	0.859614i
$425$	6.17752	−	10.6998i	0.299654	−	0.519015i
$426$	−5.73143	−	9.92713i	−0.277689	−	0.480971i
$427$	6.50387	−	2.36722i	0.314744	−	0.114558i
$428$	−27.6917	+	10.0789i	−1.33853	+	0.487184i
$429$	−1.05051	−	1.81953i	−0.0507190	−	0.0878478i
$430$	−14.8439	+	25.7104i	−0.715836	+	1.23986i
$431$	−0.226377	+	1.28385i	−0.0109042	+	0.0618407i	−0.989774	−	0.142642i	$-0.954440\pi$
$431$	−0.226377	+	1.28385i	−0.0109042	+	0.0618407i	0.978870	+	0.204483i	$0.0655513\pi$
$432$	−18.5005	+	15.5237i	−0.890104	+	0.746886i
$433$	−15.1860	−	12.7425i	−0.729791	−	0.612368i	0.200283	−	0.979738i	$-0.435814\pi$
$433$	−15.1860	−	12.7425i	−0.729791	−	0.612368i	−0.930075	+	0.367370i	$0.880258\pi$
$434$	2.58512	+	14.6610i	0.124090	+	0.703748i
$435$	3.84477	+	1.39938i	0.184343	+	0.0670952i
$436$	−41.7033			−1.99722
$437$		0			0
$438$	10.1284			0.483952
$439$	−32.4825	−	11.8227i	−1.55031	−	0.564265i	−0.581817	−	0.813320i	$-0.697658\pi$
$439$	−32.4825	−	11.8227i	−1.55031	−	0.564265i	−0.968489	+	0.249055i	$0.919880\pi$
$440$	1.69253	+	9.59883i	0.0806884	+	0.457606i
$441$	9.17412	+	7.69800i	0.436863	+	0.366571i
$442$	−20.4440	+	17.1546i	−0.972423	+	0.815960i
$443$	2.95377	−	16.7517i	0.140338	−	0.795896i	−0.830655	−	0.556788i	$-0.812034\pi$
$443$	2.95377	−	16.7517i	0.140338	−	0.795896i	0.970993	−	0.239109i	$-0.0768552\pi$
$444$	−5.91147	+	10.2390i	−0.280546	+	0.485920i
$445$	1.63429	+	2.83067i	0.0774726	+	0.134186i
$446$	−36.8225	+	13.4023i	−1.74360	+	0.634618i
$447$	−6.87376	+	2.50184i	−0.325118	+	0.118333i
$448$	1.25490	+	2.17355i	0.0592885	+	0.102691i
$449$	18.7049	−	32.3978i	0.882737	−	1.52895i	0.0344512	−	0.999406i	$-0.489032\pi$
$449$	18.7049	−	32.3978i	0.882737	−	1.52895i	0.848286	−	0.529539i	$-0.177635\pi$
$450$	3.60442	−	20.4417i	0.169914	−	0.963630i
$451$	−9.06283	+	7.60462i	−0.426752	+	0.358088i
$452$	−4.42855	−	3.71599i	−0.208301	−	0.174786i
$453$	1.25150	+	7.09759i	0.0588004	+	0.333474i
$454$	23.4907	+	8.54990i	1.10247	+	0.401267i
$455$	5.60813			0.262913
$456$		0			0
$457$	9.11112			0.426200			0.213100	−	0.977030i	$-0.431644\pi$
$457$	9.11112			0.426200			0.213100	+	0.977030i	$0.431644\pi$
$458$	−47.8705	−	17.4234i	−2.23684	−	0.814144i
$459$	−2.45084	−	13.8994i	−0.114395	−	0.648768i
$460$	23.0574	+	19.3474i	1.07506	+	0.902079i
$461$	−18.7285	+	15.7151i	−0.872273	+	0.731924i	−0.964575	−	0.263807i	$-0.915022\pi$
$461$	−18.7285	+	15.7151i	−0.872273	+	0.731924i	0.0923026	+	0.995731i	$0.470577\pi$
$462$	−0.520945	+	2.95442i	−0.0242365	+	0.137452i
$463$	0.125362	−	0.217134i	0.00582609	−	0.0100911i	−0.863098	−	0.505037i	$-0.831479\pi$
$463$	0.125362	−	0.217134i	0.00582609	−	0.0100911i	0.868924	+	0.494946i	$0.164812\pi$
$464$	−15.4427	−	26.7475i	−0.716909	−	1.24172i
$465$	3.17112	−	1.15419i	0.147057	−	0.0535245i
$466$	−8.41060	+	3.06121i	−0.389613	+	0.141808i
$467$	−7.68092	−	13.3037i	−0.355431	−	0.615624i	0.631761	−	0.775163i	$-0.282332\pi$
$467$	−7.68092	−	13.3037i	−0.355431	−	0.615624i	−0.987192	+	0.159539i	$0.948999\pi$
$468$	−15.4251	+	26.7171i	−0.713028	+	1.23500i
$469$	1.03415	−	5.86495i	0.0477525	−	0.270818i
$470$	−1.50000	+	1.25865i	−0.0691898	+	0.0580572i
$471$	5.49660	+	4.61219i	0.253270	+	0.212519i
$472$	4.17318	+	23.6673i	0.192086	+	1.08938i
$473$	−9.68866	−	3.52638i	−0.445485	−	0.162143i
$474$	−16.2104			−0.744567
$475$		0			0
$476$	26.2199			1.20179
$477$	−7.11974	−	2.59137i	−0.325990	−	0.118651i
$478$	5.26470	+	29.8576i	0.240802	+	1.36565i
$479$	−0.550974	−	0.462322i	−0.0251746	−	0.0211240i	0.630114	−	0.776503i	$-0.283008\pi$
$479$	−0.550974	−	0.462322i	−0.0251746	−	0.0211240i	−0.655288	+	0.755379i	$0.727453\pi$
$480$	−3.09627	+	2.59808i	−0.141325	+	0.118585i
$481$	−1.93717	+	10.9862i	−0.0883272	+	0.500928i
$482$	16.3341	−	28.2915i	0.743998	−	1.28864i
$483$	2.53209	+	4.38571i	0.115214	+	0.199557i
$484$	39.7806	−	14.4790i	1.80821	−	0.658135i
$485$	−9.33022	+	3.39592i	−0.423664	+	0.154201i
$486$	−18.2369	−	31.5873i	−0.827245	−	1.43283i
$487$	5.87346	−	10.1731i	0.266152	−	0.460988i	−0.701713	−	0.712460i	$-0.747581\pi$
$487$	5.87346	−	10.1731i	0.266152	−	0.460988i	0.967865	+	0.251471i	$0.0809145\pi$
$488$	−4.78998	+	27.1653i	−0.216832	+	1.22972i
$489$	−3.16637	+	2.65690i	−0.143188	+	0.120149i
$490$	12.1591	+	10.2027i	0.549292	+	0.460911i
$491$	0.0154253	+	0.0874810i	0.000696133	+	0.00394796i	0.985154	−	0.171674i	$-0.0549175\pi$
$491$	0.0154253	+	0.0874810i	0.000696133	+	0.00394796i	−0.984458	+	0.175622i	$0.943806\pi$
$492$	−27.0180	−	9.83375i	−1.21807	−	0.443340i
$493$	18.0496			0.812914
$494$		0			0
$495$	−4.10876			−0.184675
$496$	−23.9376	−	8.71259i	−1.07483	−	0.391207i
$497$	1.84524	+	10.4649i	0.0827702	+	0.469413i
$498$	15.5954	+	13.0861i	0.698846	+	0.586402i
$499$	11.2536	−	9.44285i	0.503778	−	0.422720i	−0.355155	−	0.934807i	$-0.615572\pi$
$499$	11.2536	−	9.44285i	0.503778	−	0.422720i	0.858934	+	0.512087i	$0.171128\pi$
$500$	8.44743	−	47.9078i	0.377781	−	2.14250i
$501$	−4.49660	+	7.78833i	−0.200893	+	0.347957i
$502$	−18.1839	−	31.4955i	−0.811588	−	1.40571i
$503$	4.60829	−	1.67728i	0.205473	−	0.0747862i	−0.237233	−	0.971453i	$-0.576241\pi$
$503$	4.60829	−	1.67728i	0.205473	−	0.0747862i	0.442707	+	0.896667i	$0.354018\pi$
$504$	22.6275	−	8.23573i	1.00791	−	0.366849i
$505$	1.46198	+	2.53223i	0.0650573	+	0.112683i
$506$	−7.59627	+	13.1571i	−0.337695	+	0.584905i
$507$	−0.636812	+	3.61154i	−0.0282818	+	0.160394i
$508$	49.0112	−	41.1253i	2.17452	−	1.82464i
$509$	−4.91329	−	4.12274i	−0.217778	−	0.182737i	0.527372	−	0.849635i	$-0.323177\pi$
$509$	−4.91329	−	4.12274i	−0.217778	−	0.182737i	−0.745149	+	0.666897i	$0.767622\pi$
$510$	−1.50000	−	8.50692i	−0.0664211	−	0.376693i
$511$	−8.82295	−	3.21129i	−0.390304	−	0.142059i
$512$	−50.5553			−2.23425
$513$		0			0
$514$	−12.6040			−0.555939
$515$	15.7947	+	5.74881i	0.695999	+	0.253323i
$516$	−4.35117	−	24.6767i	−0.191549	−	1.08633i
$517$	−0.520945	−	0.437124i	−0.0229111	−	0.0192247i
$518$	12.2023	−	10.2390i	0.536140	−	0.449875i
$519$	−2.86154	+	16.2286i	−0.125608	+	0.712356i
$520$	−11.1755	+	19.3565i	−0.490076	+	0.848837i
$521$	−17.9067	−	31.0154i	−0.784508	−	1.35881i	−0.929293	−	0.369344i	$-0.879582\pi$
$521$	−17.9067	−	31.0154i	−0.784508	−	1.35881i	0.144785	−	0.989463i	$-0.453751\pi$
$522$	28.4954	−	10.3715i	1.24721	−	0.453947i
$523$	36.4342	−	13.2610i	1.59316	−	0.579862i	0.615146	−	0.788413i	$-0.289097\pi$
$523$	36.4342	−	13.2610i	1.59316	−	0.579862i	0.978011	+	0.208551i	$0.0668748\pi$
$524$	43.6921	+	75.6770i	1.90870	+	3.30596i
$525$	1.59240	−	2.75811i	0.0694979	−	0.120374i
$526$	−10.5715	+	59.9537i	−0.460937	+	2.61410i
$527$	11.4042	−	9.56926i	0.496775	−	0.416844i
$528$	−3.93242	−	3.29969i	−0.171137	−	0.143601i
$529$	0.459455	+	2.60570i	0.0199763	+	0.113291i
$530$	−9.43629	−	3.43453i	−0.409886	−	0.149186i
$531$	−10.1307			−0.439636
$532$		0			0
$533$	−27.1293			−1.17510
$534$	−3.76769	−	1.37133i	−0.163044	−	0.0593432i
$535$	−1.56283	−	8.86327i	−0.0675672	−	0.383193i
$536$	18.1821	+	15.2566i	0.785347	+	0.658985i
$537$	−2.91534	+	2.44626i	−0.125806	+	0.105564i
$538$	5.76486	−	32.6942i	0.248541	−	1.40955i
$539$	−2.75624	+	4.77396i	−0.118720	+	0.205629i
$540$	−10.8118	−	18.7266i	−0.465266	−	0.805864i
$541$	−8.91787	+	3.24584i	−0.383409	+	0.139550i	−0.526532	−	0.850155i	$-0.676508\pi$
$541$	−8.91787	+	3.24584i	−0.383409	+	0.139550i	0.143123	+	0.989705i	$0.454286\pi$
$542$	63.2199	−	23.0102i	2.71553	−	0.988372i
$543$	4.42602	+	7.66610i	0.189939	+	0.328984i
$544$	−8.91534	+	15.4418i	−0.382242	+	0.662063i
$545$	2.21167	−	12.5430i	0.0947374	−	0.537282i
$546$	−5.26991	+	4.42198i	−0.225532	+	0.189243i
$547$	−10.8871	−	9.13538i	−0.465500	−	0.390601i	0.379650	−	0.925130i	$-0.376044\pi$
$547$	−10.8871	−	9.13538i	−0.465500	−	0.390601i	−0.845150	+	0.534529i	$0.820489\pi$
$548$	7.81702	+	44.3325i	0.333926	+	1.89379i
$549$	−10.9268	−	3.97703i	−0.466344	−	0.169735i
$550$	9.55438			0.407400
$551$		0			0
$552$	−20.1830			−0.859047
$553$	14.1211	+	5.13965i	0.600489	+	0.218560i
$554$	−7.25965	−	41.1715i	−0.308433	−	1.74921i
$555$	−2.76604	−	2.32099i	−0.117412	−	0.0985204i
$556$	−5.61128	+	4.70842i	−0.237971	+	0.199682i
$557$	3.91400	−	22.1974i	0.165842	−	0.940534i	−0.782351	−	0.622838i	$-0.785980\pi$
$557$	3.91400	−	22.1974i	0.165842	−	0.940534i	0.948193	−	0.317696i	$-0.102909\pi$
$558$	12.5055	−	21.6602i	0.529401	−	0.916949i
$559$	−11.8216	−	20.4756i	−0.500001	−	0.866026i
$560$	12.8760	−	4.68647i	0.544110	−	0.198040i
$561$	2.81908	−	1.02606i	0.119022	−	0.0433203i
$562$	−24.5488	−	42.5197i	−1.03553	−	1.79358i
$563$	−21.4859	+	37.2147i	−0.905524	+	1.56841i	−0.0853106	+	0.996354i	$0.527188\pi$
$563$	−21.4859	+	37.2147i	−0.905524	+	1.56841i	−0.820213	+	0.572058i	$0.806145\pi$
$564$	0.286989	−	1.62760i	0.0120844	−	0.0685341i
$565$	1.35251	−	1.13489i	0.0569006	−	0.0477452i
$566$	−21.9388	−	18.4089i	−0.922157	−	0.773782i
$567$	1.42262	+	8.06807i	0.0597444	+	0.338827i
$568$	−39.7965	−	14.4848i	−1.66983	−	0.607767i
$569$	−7.42696			−0.311354			−0.155677	−	0.987808i	$-0.549756\pi$
$569$	−7.42696			−0.311354			−0.155677	+	0.987808i	$0.549756\pi$
$570$		0			0
$571$	4.04458			0.169260			0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458			0.169260			0.0846301	+	0.996412i	$0.473029\pi$
$572$	−13.3439	−	4.85678i	−0.557936	−	0.203072i
$573$	−1.16560	−	6.61046i	−0.0486938	−	0.276156i
$574$	29.6746	+	24.8999i	1.23859	+	1.03930i
$575$	12.3550	−	10.3671i	0.515241	−	0.432338i
$576$	0.732201	−	4.15252i	0.0305084	−	0.173022i
$577$	−1.61721	+	2.80109i	−0.0673254	+	0.116611i	−0.897723	−	0.440560i	$-0.854780\pi$
$577$	−1.61721	+	2.80109i	−0.0673254	+	0.116611i	0.830398	+	0.557171i	$0.188113\pi$
$578$	2.46926	+	4.27688i	0.102707	+	0.177895i
$579$	8.46451	−	3.08083i	0.351773	−	0.128035i
$580$	25.9859	−	9.45810i	1.07901	−	0.392726i
$581$	−9.43629	−	16.3441i	−0.391483	−	0.678069i
$582$	6.08987	−	10.5480i	0.252433	−	0.437227i
$583$	0.605600	−	3.43453i	0.0250814	−	0.142244i
$584$	28.6655	−	24.0532i	1.18619	−	0.995329i
$585$	−7.21760	−	6.05628i	−0.298411	−	0.250396i
$586$	−1.71436	−	9.72259i	−0.0708194	−	0.401637i
$587$	38.3474	+	13.9573i	1.58276	+	0.576079i	0.975803	−	0.218652i	$-0.0701659\pi$
$587$	38.3474	+	13.9573i	1.58276	+	0.576079i	0.606962	+	0.794731i	$0.292388\pi$
$588$	−13.3969			−0.552480
$589$		0			0
$590$	−13.4270			−0.552779
$591$	4.87046	+	1.77270i	0.200344	+	0.0729193i
$592$	4.73308	+	26.8426i	0.194528	+	1.10322i
$593$	−8.47565	−	7.11192i	−0.348053	−	0.292051i	0.451955	−	0.892041i	$-0.350727\pi$
$593$	−8.47565	−	7.11192i	−0.348053	−	0.292051i	−0.800008	+	0.599990i	$0.795171\pi$
$594$	8.36097	−	7.01568i	0.343055	−	0.287857i
$595$	−1.39053	+	7.88609i	−0.0570062	+	0.323298i
$596$	−24.7199	+	42.8161i	−1.01257	+	1.75381i
$597$	−8.82295	−	15.2818i	−0.361099	−	0.625442i
$598$	−32.7374	+	11.9154i	−1.33873	+	0.487259i
$599$	−41.8705	+	15.2396i	−1.71078	+	0.622674i	−0.996979	−	0.0776714i	$-0.975251\pi$
$599$	−41.8705	+	15.2396i	−1.71078	+	0.622674i	−0.713804	+	0.700346i	$0.753029\pi$
$600$	6.34642	+	10.9923i	0.259091	+	0.448760i
$601$	−2.49953	+	4.32932i	−0.101958	+	0.176597i	−0.912491	−	0.409096i	$-0.865844\pi$
$601$	−2.49953	+	4.32932i	−0.101958	+	0.176597i	0.810533	+	0.585693i	$0.199177\pi$
$602$	−5.86231	+	33.2468i	−0.238930	+	1.35504i
$603$	−7.66456	+	6.43133i	−0.312125	+	0.261904i
$604$	37.3148	+	31.3108i	1.51832	+	1.27402i
$605$	2.24510	+	12.7326i	0.0912763	+	0.517654i
$606$	−3.37046	−	1.22675i	−0.136916	−	0.0498332i
$607$	31.1881			1.26589			0.632943	−	0.774199i	$-0.281847\pi$
$607$	31.1881			1.26589			0.632943	+	0.774199i	$0.281847\pi$
$608$		0			0
$609$	4.65270			0.188537
$610$	−14.4820	−	5.27103i	−0.586361	−	0.213418i
$611$	−0.270792	−	1.53574i	−0.0109551	−	0.0621293i
$612$	−33.7447	−	28.3152i	−1.36405	−	1.14457i
$613$	12.5398	−	10.5222i	0.506479	−	0.424986i	−0.353409	−	0.935469i	$-0.614978\pi$
$613$	12.5398	−	10.5222i	0.506479	−	0.424986i	0.859888	+	0.510483i	$0.170533\pi$
$614$	−10.1900	+	57.7904i	−0.411235	+	2.33223i
$615$	4.39053	−	7.60462i	0.177043	−	0.306648i
$616$	5.54189	+	9.59883i	0.223289	+	0.386748i
$617$	−15.0899	+	5.49226i	−0.607495	+	0.221110i	−0.627407	−	0.778692i	$-0.715884\pi$
$617$	−15.0899	+	5.49226i	−0.607495	+	0.221110i	0.0199117	+	0.999802i	$0.493662\pi$
$618$	−19.3751	+	7.05196i	−0.779381	+	0.283671i
$619$	−11.9213	−	20.6483i	−0.479156	−	0.829923i	0.520558	−	0.853826i	$-0.325724\pi$
$619$	−11.9213	−	20.6483i	−0.479156	−	0.829923i	−0.999714	+	0.0239031i	$0.992391\pi$
$620$	11.4042	−	19.7527i	0.458004	−	0.793286i
$621$	3.19934	−	18.1444i	0.128385	−	0.728108i
$622$	−6.71348	+	5.63328i	−0.269186	+	0.225874i
$623$	2.84730	+	2.38917i	0.114075	+	0.0957199i
$624$	−2.04411	−	11.5927i	−0.0818299	−	0.464081i
$625$	−1.00253	−	0.364890i	−0.0401010	−	0.0145956i
$626$	−57.9590			−2.31651
$627$		0			0
$628$	48.4962			1.93521
$629$	−14.9684	−	5.44804i	−0.596828	−	0.217228i
$630$	2.33615	+	13.2490i	0.0930745	+	0.527852i
$631$	16.4492	+	13.8026i	0.654834	+	0.549471i	0.908533	−	0.417812i	$-0.137203\pi$
$631$	16.4492	+	13.8026i	0.654834	+	0.549471i	−0.253699	+	0.967283i	$0.581647\pi$
$632$	−45.8790	+	38.4970i	−1.82497	+	1.53133i
$633$	0.914878	−	5.18853i	0.0363631	−	0.206226i
$634$	33.0699	−	57.2787i	1.31337	−	2.27483i
$635$	9.76991	+	16.9220i	0.387707	+	0.671529i
$636$	7.96451	−	2.89884i	0.315813	−	0.114947i
$637$	−11.8785	+	4.32342i	−0.470644	+	0.171300i
$638$	6.97906	+	12.0881i	0.276303	+	0.478572i
$639$	8.92633	−	15.4609i	0.353120	−	0.611622i
$640$	3.12108	−	17.7005i	0.123372	−	0.699675i
$641$	−9.76991	+	8.19793i	−0.385888	+	0.323799i	−0.815009	−	0.579448i	$-0.803268\pi$
$641$	−9.76991	+	8.19793i	−0.385888	+	0.323799i	0.429120	+	0.903247i	$0.358824\pi$
$642$	8.45723	+	7.09646i	0.333780	+	0.280075i
$643$	4.96775	+	28.1735i	0.195909	+	1.11105i	0.911118	+	0.412145i	$0.135220\pi$
$643$	4.96775	+	28.1735i	0.195909	+	1.11105i	−0.715210	+	0.698910i	$0.753669\pi$
$644$	32.1634	+	11.7065i	1.26742	+	0.461302i
$645$	7.65270			0.301325
$646$		0			0
$647$	16.7128			0.657046			0.328523	−	0.944496i	$-0.393449\pi$
$647$	16.7128			0.657046			0.328523	+	0.944496i	$0.393449\pi$
$648$	−30.6819	−	11.1673i	−1.20530	−	0.438692i
$649$	−0.809745	−	4.59229i	−0.0317853	−	0.180263i
$650$	16.7836	+	14.0831i	0.658306	+	0.552385i
$651$	2.93969	−	2.46669i	0.115216	−	0.0966774i
$652$	−4.85117	+	27.5123i	−0.189986	+	1.07747i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	7.81180	+	13.5304i	0.305466	+	0.529082i
$655$	−25.0783	+	9.12776i	−0.979891	+	0.356651i
$656$	−62.2875	+	22.6708i	−2.43192	+	0.885146i
$657$	7.88713	+	13.6609i	0.307706	+	0.532963i
$658$	−1.11334	+	1.92836i	−0.0434025	+	0.0751754i
$659$	7.62330	−	43.2339i	0.296962	−	1.68415i	−0.362159	−	0.932116i	$-0.617960\pi$
$659$	7.62330	−	43.2339i	0.296962	−	1.68415i	0.659121	−	0.752037i	$-0.270929\pi$
$660$	3.52094	−	2.95442i	0.137053	−	0.115001i
$661$	8.23964	+	6.91388i	0.320485	+	0.268919i	0.788809	−	0.614638i	$-0.210698\pi$
$661$	8.23964	+	6.91388i	0.320485	+	0.268919i	−0.468325	+	0.883556i	$0.655142\pi$
$662$	−8.37376	−	47.4900i	−0.325455	−	1.84575i
$663$	6.46451	+	2.35289i	0.251061	+	0.0913786i
$664$	75.2158			2.91894
$665$		0			0
$666$	−26.7615			−1.03699
$667$	22.1411	+	8.05872i	0.857309	+	0.312035i
$668$	10.5548	+	59.8595i	0.408379	+	2.31603i
$669$	7.73783	+	6.49281i	0.299162	+	0.251026i
$670$	−10.1584	+	8.52390i	−0.392453	+	0.329307i
$671$	0.929426	−	5.27103i	0.0358801	−	0.203486i
$672$	−2.29813	+	3.98048i	−0.0886524	+	0.153550i
$673$	2.32888	+	4.03374i	0.0897717	+	0.155489i	0.907415	−	0.420237i	$-0.138053\pi$
$673$	2.32888	+	4.03374i	0.0897717	+	0.155489i	−0.817643	+	0.575726i	$0.804720\pi$
$674$	4.04829	−	1.47346i	0.155934	−	0.0567554i
$675$	−10.8880	+	3.96291i	−0.419079	+	0.152532i
$676$	12.3931	+	21.4654i	0.476656	+	0.825592i
$677$	1.63429	−	2.83067i	0.0628107	−	0.108791i	−0.832910	−	0.553408i	$-0.813327\pi$
$677$	1.63429	−	2.83067i	0.0628107	−	0.108791i	0.895721	+	0.444617i	$0.146660\pi$
$678$	−0.376087	+	2.13290i	−0.0144436	+	0.0819135i
$679$	−8.64930	+	7.25762i	−0.331930	+	0.278522i
$680$	−24.4479	−	20.5142i	−0.937534	−	0.786685i
$681$	−1.11897	−	6.34597i	−0.0428789	−	0.243178i
$682$	10.8182	+	3.93750i	0.414250	+	0.150775i
$683$	−6.21894			−0.237961			−0.118981	−	0.992897i	$-0.537963\pi$
$683$	−6.21894			−0.237961			−0.118981	+	0.992897i	$0.537963\pi$
$684$		0			0
$685$	−13.7483			−0.525297
$686$	42.4791	+	15.4611i	1.62186	+	0.590309i
$687$	2.28029	+	12.9322i	0.0869984	+	0.493392i
$688$	−44.2524	−	37.1322i	−1.68711	−	1.41565i
$689$	6.12630	−	5.14057i	0.233393	−	0.195840i
$690$	1.95811	−	11.1050i	0.0745440	−	0.422760i
$691$	−11.1088	+	19.2409i	−0.422597	+	0.731959i	−0.996193	−	0.0871792i	$-0.972215\pi$
$691$	−11.1088	+	19.2409i	−0.422597	+	0.731959i	0.573596	+	0.819139i	$0.305548\pi$
$692$	55.6887	+	96.4557i	2.11697	+	3.66670i
$693$	−4.39053	+	1.59802i	−0.166782	+	0.0607038i
$694$	11.6630	−	4.24497i	0.442720	−	0.161137i
$695$	−1.11856	−	1.93739i	−0.0424292	−	0.0734896i
$696$	−9.27156	+	16.0588i	−0.351438	+	0.608708i
$697$	6.72668	−	38.1489i	0.254791	−	1.44499i
$698$	−54.5622	+	45.7831i	−2.06521	+	1.73292i
$699$	1.76739	+	1.48302i	0.0668488	+	0.0560928i
$700$	−3.73783	−	21.1983i	−0.141277	−	0.801219i
$701$	26.0976	+	9.49875i	0.985693	+	0.358763i	0.784051	−	0.620696i	$-0.213150\pi$
$701$	26.0976	+	9.49875i	0.985693	+	0.358763i	0.201642	+	0.979459i	$0.435372\pi$
$702$	25.0283			0.944631
$703$		0			0
$704$	1.94087			0.0731495
$705$	0.474308	+	0.172634i	0.0178635	+	0.00650177i
$706$	−3.65822	−	20.7468i	−0.137679	−	0.780817i
$707$	2.54710	+	2.13727i	0.0957937	+	0.0803805i
$708$	8.68139	−	7.28455i	0.326267	−	0.273770i
$709$	−1.06061	+	6.01503i	−0.0398321	+	0.225899i	−0.998225	−	0.0595527i	$-0.981033\pi$
$709$	−1.06061	+	6.01503i	−0.0398321	+	0.225899i	0.958393	+	0.285452i	$0.0921437\pi$
$710$	11.8307	−	20.4914i	0.443998	−	0.769027i
$711$	−12.6233	−	21.8642i	−0.473411	−	0.819972i
$712$	−13.9201	+	5.06650i	−0.521678	+	0.189875i
$713$	18.2618	−	6.64674i	0.683908	−	0.248922i
$714$	−4.91147	−	8.50692i	−0.183807	−	0.318364i
$715$	2.16843	−	3.75584i	0.0810948	−	0.140460i
$716$	−4.46657	+	25.3312i	−0.166923	+	0.946670i
$717$	5.98680	−	5.02352i	0.223581	−	0.187607i
$718$	48.3546	+	40.5743i	1.80458	+	1.51422i
$719$	6.72432	+	38.1355i	0.250775	+	1.42221i	0.806690	+	0.590975i	$0.201257\pi$
$719$	6.72432	+	38.1355i	0.250775	+	1.42221i	−0.555915	+	0.831239i	$0.687632\pi$
$720$	−21.6322	−	7.87349i	−0.806185	−	0.293428i
$721$	19.1138			0.711835
$722$		0			0
$723$	−8.42097			−0.313179
$724$	56.2208	+	20.4627i	2.08943	+	0.760490i
$725$	−2.57310	−	14.5928i	−0.0955626	−	0.541962i
$726$	−12.1493	−	10.1945i	−0.450903	−	0.378352i
$727$	−8.48617	+	7.12074i	−0.314735	+	0.264094i	−0.786446	−	0.617660i	$-0.788081\pi$
$727$	−8.48617	+	7.12074i	−0.314735	+	0.264094i	0.471711	+	0.881753i	$0.343637\pi$
$728$	−4.41353	+	25.0304i	−0.163576	+	0.927688i
$729$	3.31996	−	5.75033i	0.122961	−	0.212975i
$730$	10.4534	+	18.1058i	0.386896	+	0.670124i
$731$	31.7237	−	11.5465i	1.17335	−	0.427063i
$732$	12.2233	−	4.44891i	0.451785	−	0.164436i
$733$	7.90373	+	13.6897i	0.291931	+	0.505639i	0.974266	−	0.225400i	$-0.0723689\pi$
$733$	7.90373	+	13.6897i	0.291931	+	0.505639i	−0.682335	+	0.731039i	$0.739036\pi$
$734$	3.27379	−	5.67036i	0.120838	−	0.209297i
$735$	0.710485	−	4.02936i	0.0262066	−	0.148625i
$736$	−17.8307	+	14.9617i	−0.657248	+	0.551496i
$737$	−3.52797	−	2.96032i	−0.129954	−	0.109045i
$738$	−11.3011	−	64.0919i	−0.416000	−	2.35925i
$739$	−1.45589	−	0.529900i	−0.0535558	−	0.0194927i	0.315103	−	0.949057i	$-0.397961\pi$
$739$	−1.45589	−	0.529900i	−0.0535558	−	0.0194927i	−0.368659	+	0.929565i	$0.620183\pi$
$740$	−24.4047			−0.897133
$741$		0			0
$742$	−11.4192			−0.419213
$743$	35.8619	+	13.0527i	1.31565	+	0.478856i	0.902060	−	0.431610i	$-0.142054\pi$
$743$	35.8619	+	13.0527i	1.31565	+	0.478856i	0.413585	+	0.910465i	$0.364276\pi$
$744$	2.65580	+	15.0618i	0.0973664	+	0.552193i
$745$	−11.5667	−	9.70562i	−0.423771	−	0.355586i
$746$	45.3564	−	38.0586i	1.66062	−	1.39342i
$747$	−5.50582	+	31.2251i	−0.201448	+	1.14247i
$748$	10.1382	−	17.5598i	0.370688	−	0.642050i
$749$	−5.11721	−	8.86327i	−0.186979	−	0.323857i
$750$	−17.1258	+	6.23329i	−0.625347	+	0.227608i
$751$	−23.8195	+	8.66961i	−0.869188	+	0.316358i	−0.737838	−	0.674978i	$-0.764153\pi$
$751$	−23.8195	+	8.66961i	−0.869188	+	0.316358i	−0.131349	+	0.991336i	$0.541931\pi$
$752$	−1.90508	−	3.29969i	−0.0694710	−	0.120327i
$753$	−4.68732	+	8.11867i	−0.170815	+	0.295861i
$754$	−5.55809	+	31.5215i	−0.202414	+	1.14794i
$755$	−11.3962	+	9.56256i	−0.414751	+	0.348017i
$756$	−18.8366	−	15.8058i	−0.685081	−	0.574851i
$757$	7.35756	+	41.7268i	0.267415	+	1.51659i	0.762068	+	0.647496i	$0.224184\pi$
$757$	7.35756	+	41.7268i	0.267415	+	1.51659i	−0.494653	+	0.869090i	$0.664705\pi$
$758$	60.5287	+	22.0307i	2.19850	+	0.800190i
$759$	3.91622			0.142150
$760$		0			0
$761$	−2.85710			−0.103570			−0.0517848	−	0.998658i	$-0.516491\pi$
$761$	−2.85710			−0.103570			−0.0517848	+	0.998658i	$0.516491\pi$
$762$	−22.5236	−	8.19793i	−0.815945	−	0.296980i
$763$	−2.51501	−	14.2634i	−0.0910496	−	0.516368i
$764$	−34.7538	−	29.1619i	−1.25735	−	1.05504i
$765$	10.3059	−	8.64766i	0.372610	−	0.312657i
$766$	12.0831	−	68.5265i	0.436579	−	2.47596i
$767$	5.34658	−	9.26055i	0.193054	−	0.334379i
$768$	9.95471	+	17.2421i	0.359210	+	0.622169i
$769$	−17.9675	+	6.53964i	−0.647925	+	0.235825i	−0.645014	−	0.764170i	$-0.723149\pi$
$769$	−17.9675	+	6.53964i	−0.647925	+	0.235825i	−0.00291032	+	0.999996i	$0.500926\pi$
$770$	−5.81908	+	2.11797i	−0.209705	+	0.0763264i
$771$	1.62449	+	2.81369i	0.0585044	+	0.101333i
$772$	30.4406	−	52.7247i	1.09558	−	1.89760i
$773$	−0.436700	+	2.47665i	−0.0157070	+	0.0890788i	−0.991654	−	0.128931i	$-0.958845\pi$
$773$	−0.436700	+	2.47665i	−0.0157070	+	0.0890788i	0.975947	+	0.218010i	$0.0699565\pi$
$774$	43.4484	−	36.4575i	1.56172	−	1.31044i
$775$	−9.36231	−	7.85591i	−0.336304	−	0.282193i
$776$	−7.81403	−	44.3155i	−0.280507	−	1.59084i
$777$	−3.85844	−	1.40436i	−0.138421	−	0.0503810i
$778$	−8.46286			−0.303408
$779$		0			0
$780$	10.5398			0.377386
$781$	7.72193	+	2.81055i	0.276313	+	0.100570i
$782$	−8.63816	−	48.9894i	−0.308900	−	1.75186i
$783$	−12.9670	−	10.8806i	−0.463404	−	0.388842i
$784$	−23.6596	+	19.8527i	−0.844985	+	0.709026i
$785$	−2.57192	+	14.5861i	−0.0917957	+	0.520599i
$786$	16.3687	−	28.3514i	0.583852	−	1.01126i
$787$	1.36303	+	2.36083i	0.0485866	+	0.0841545i	0.889296	−	0.457332i	$-0.151195\pi$
$787$	1.36303	+	2.36083i	0.0485866	+	0.0841545i	−0.840709	+	0.541487i	$0.817862\pi$
$788$	32.9183	−	11.9813i	1.17267	−	0.426816i
$789$	14.7464	−	5.36727i	0.524987	−	0.191080i
$790$	−16.7306	−	28.9782i	−0.595246	−	1.03100i
$791$	1.00387	−	1.73875i	0.0356935	−	0.0618230i
$792$	3.23355	−	18.3383i	0.114899	−	0.651625i
$793$	9.40214	−	7.88933i	0.333880	−	0.280158i
$794$	−25.4552	−	21.3594i	−0.903370	−	0.758018i
$795$	0.449493	+	2.54920i	0.0159419	+	0.0904108i
$796$	−112.072	−	40.7909i	−3.97229	−	1.44579i
$797$	−22.0327			−0.780439			−0.390219	−	0.920722i	$-0.627601\pi$
$797$	−22.0327			−0.780439			−0.390219	+	0.920722i	$0.627601\pi$
$798$		0			0
$799$	2.22668			0.0787743
$800$	13.7554	+	5.00654i	0.486326	+	0.177008i
$801$	−1.08435	−	6.14966i	−0.0383137	−	0.217288i
$802$	−33.1955	−	27.8544i	−1.17217	−	0.983571i
$803$	−5.56212	+	4.66717i	−0.196283	+	0.164701i
$804$	1.94356	−	11.0225i	0.0685442	−	0.388733i
$805$	−5.22668	+	9.05288i	−0.184216	+	0.319072i
$806$	13.1998	+	22.8627i	0.464943	+	0.805306i
$807$	−8.04158	+	2.92690i	−0.283077	+	0.103032i
$808$	−12.4525	+	4.53233i	−0.438077	+	0.159447i
$809$	−27.3603	−	47.3893i	−0.961935	−	1.66612i	−0.717633	−	0.696422i	$-0.754774\pi$
$809$	−27.3603	−	47.3893i	−0.961935	−	1.66612i	−0.244302	−	0.969699i	$-0.578559\pi$
$810$	9.12108	−	15.7982i	0.320482	−	0.555091i
$811$	0.401207	−	2.27536i	0.0140883	−	0.0798986i	−0.976953	−	0.213455i	$-0.931528\pi$
$811$	0.401207	−	2.27536i	0.0140883	−	0.0798986i	0.991041	+	0.133556i	$0.0426396\pi$
$812$	24.0895	−	20.2135i	0.845374	−	0.709353i
$813$	−13.2849	−	11.1474i	−0.465923	−	0.390956i
$814$	−2.13903	−	12.1311i	−0.0749731	−	0.425193i
$815$	−8.01754	−	2.91815i	−0.280842	−	0.102218i
$816$	16.8084			0.588412
$817$		0			0
$818$	22.2772			0.778906
$819$	−10.0680	−	3.66447i	−0.351806	−	0.128047i
$820$	−10.3059	−	58.4475i	−0.359897	−	2.04108i
$821$	0.851167	+	0.714214i	0.0297059	+	0.0249262i	0.657520	−	0.753437i	$-0.271606\pi$
$821$	0.851167	+	0.714214i	0.0297059	+	0.0249262i	−0.627814	+	0.778364i	$0.716050\pi$
$822$	12.9192	−	10.8405i	0.450609	−	0.378106i
$823$	3.58543	−	20.3340i	0.124980	−	0.708798i	−0.856340	−	0.516413i	$-0.827267\pi$
$823$	3.58543	−	20.3340i	0.124980	−	0.708798i	0.981320	−	0.192384i	$-0.0616220\pi$
$824$	−38.0886	+	65.9714i	−1.32688	+	2.29822i
$825$	−1.23143	−	2.13290i	−0.0428729	−	0.0742580i
$826$	−14.3478	+	5.22216i	−0.499223	+	0.181702i
$827$	34.1159	−	12.4172i	1.18633	−	0.431788i	0.327894	−	0.944714i	$-0.393661\pi$
$827$	34.1159	−	12.4172i	1.18633	−	0.431788i	0.858432	+	0.512927i	$0.171439\pi$
$828$	−28.7520	−	49.7999i	−0.999200	−	1.73066i
$829$	−3.57486	+	6.19183i	−0.124160	+	0.215051i	−0.921404	−	0.388606i	$-0.872957\pi$
$829$	−3.57486	+	6.19183i	−0.124160	+	0.215051i	0.797244	+	0.603657i	$0.206290\pi$
$830$	−7.29726	+	41.3848i	−0.253291	+	1.43649i
$831$	−8.25537	+	6.92708i	−0.286376	+	0.240298i
$832$	3.40941	+	2.86084i	0.118200	+	0.0991817i
$833$	−3.13429	−	17.7754i	−0.108597	−	0.615882i
$834$	2.57873	+	0.938579i	0.0892940	+	0.0325003i
$835$	−18.5635			−0.642418
$836$		0			0
$837$	−13.9614			−0.482577
$838$	−16.2754	−	5.92377i	−0.562226	−	0.204633i
$839$	6.00939	+	34.0809i	0.207467	+	1.17660i	0.893510	+	0.449044i	$0.148235\pi$
$839$	6.00939	+	34.0809i	0.207467	+	1.17660i	−0.686043	+	0.727561i	$0.740654\pi$
$840$	−6.30200	−	5.28801i	−0.217440	−	0.182454i
$841$	−5.63223	+	4.72600i	−0.194215	+	0.162965i
$842$	2.12061	−	12.0266i	0.0730812	−	0.414464i
$843$	−6.32800	+	10.9604i	−0.217948	+	0.377497i
$844$	−17.8045	−	30.8384i	−0.612857	−	1.06150i
$845$	−7.11334	+	2.58904i	−0.244706	+	0.0890658i
$846$	3.51532	−	1.27947i	0.120859	−	0.0439891i
$847$	7.35117	+	12.7326i	0.252589	+	0.437497i
$848$	9.76991	−	16.9220i	0.335500	−	0.581103i
$849$	−1.28194	+	7.27022i	−0.0439959	+	0.249513i
$850$	−23.9650	+	20.1090i	−0.821992	+	0.689733i
$851$	−15.9290	−	13.3660i	−0.546040	−	0.458182i
$852$	3.46791	+	19.6675i	0.118809	+	0.673797i
$853$	−31.2456	−	11.3725i	−1.06983	−	0.389385i	−0.253716	−	0.967279i	$-0.581653\pi$
$853$	−31.2456	−	11.3725i	−1.06983	−	0.389385i	−0.816112	+	0.577893i	$0.803875\pi$
$854$	−17.5253			−0.599703
$855$		0			0
$856$	40.7888			1.39413
$857$	−3.65183	−	1.32916i	−0.124744	−	0.0454031i	0.278894	−	0.960322i	$-0.410032\pi$
$857$	−3.65183	−	1.32916i	−0.124744	−	0.0454031i	−0.403638	+	0.914919i	$0.632254\pi$
$858$	0.923801	+	5.23913i	0.0315380	+	0.178861i
$859$	1.26991	+	1.06559i	0.0433289	+	0.0363573i	0.664195	−	0.747559i	$-0.268774\pi$
$859$	1.26991	+	1.06559i	0.0433289	+	0.0363573i	−0.620866	+	0.783917i	$0.713219\pi$
$860$	39.6220	−	33.2468i	1.35110	−	1.13371i
$861$	1.73396	−	9.83375i	0.0590930	−	0.335133i
$862$	1.65048	−	2.85872i	0.0562156	−	0.0973684i
$863$	−26.3594	−	45.6558i	−0.897284	−	1.55414i	−0.830953	−	0.556343i	$-0.812204\pi$
$863$	−26.3594	−	45.6558i	−0.897284	−	1.55414i	−0.0663308	−	0.997798i	$-0.521129\pi$
$864$	15.7135	−	5.71924i	0.534583	−	0.194572i
$865$	−31.9641	+	11.6340i	−1.08681	+	0.395567i
$866$	25.0979	+	43.4709i	0.852862	+	1.47720i
$867$	0.636507	−	1.10246i	0.0216169	−	0.0374416i
$868$	4.50387	−	25.5427i	0.152871	−	0.866976i
$869$	8.90214	−	7.46978i	0.301984	−	0.253395i
$870$	−7.93629	−	6.65934i	−0.269065	−	0.225773i
$871$	−1.83387	−	10.4004i	−0.0621385	−	0.352405i
$872$	54.2418	+	19.7424i	1.83686	+	0.668561i
$873$	18.9691			0.642008
$874$		0			0
$875$	16.8949			0.571151
$876$	−16.5817	−	6.03525i	−0.560244	−	0.203912i
$877$	3.67958	+	20.8679i	0.124251	+	0.704660i	0.981750	+	0.190175i	$0.0609056\pi$
$877$	3.67958	+	20.8679i	0.124251	+	0.704660i	−0.857500	+	0.514485i	$0.827983\pi$
$878$	67.0497	+	56.2614i	2.26282	+	1.89873i
$879$	−1.94949	+	1.63582i	−0.0657548	+	0.0551748i
$880$	1.84002	−	10.4353i	0.0620271	−	0.351773i
$881$	−16.0505	+	27.8003i	−0.540755	+	0.936616i	0.458106	+	0.888898i	$0.348528\pi$
$881$	−16.0505	+	27.8003i	−0.540755	+	0.936616i	−0.998861	+	0.0477179i	$0.984805\pi$
$882$	−15.1621	−	26.2615i	−0.510534	−	0.884271i
$883$	44.4445	−	16.1765i	1.49568	−	0.544382i	0.540739	−	0.841190i	$-0.318145\pi$
$883$	44.4445	−	16.1765i	1.49568	−	0.544382i	0.954937	+	0.296808i	$0.0959223\pi$
$884$	43.6921	−	15.9026i	1.46953	−	0.534863i
$885$	1.73055	+	2.99740i	0.0581719	+	0.100757i
$886$	−21.5355	+	37.3007i	−0.723501	+	1.25314i
$887$	−1.83425	+	10.4026i	−0.0615882	+	0.349284i	0.938405	+	0.345538i	$0.112304\pi$
$887$	−1.83425	+	10.4026i	−0.0615882	+	0.349284i	−0.999993	+	0.00374624i	$0.998808\pi$
$888$	12.5360	−	10.5189i	0.420679	−	0.352992i
$889$	17.0214	+	14.2827i	0.570880	+	0.479025i
$890$	−1.43717	−	8.15058i	−0.0481739	−	0.273208i
$891$	5.95336	+	2.16685i	0.199445	+	0.0725921i
$892$	68.2704			2.28586
$893$		0			0
$894$	18.5220			0.619468
$895$	−7.38191	−	2.68680i	−0.246750	−	0.0898097i
$896$	−3.54916	−	20.1283i	−0.118569	−	0.672439i
$897$	6.87939	+	5.77249i	0.229696	+	0.192738i
$898$	−72.5634	+	60.8879i	−2.42147	+	2.03186i
$899$	3.10044	−	17.5835i	0.103406	−	0.586442i
$900$	−18.0817	+	31.3185i	−0.602724	+	1.04395i
$901$	5.70961	+	9.88933i	0.190215	+	0.329461i
$902$	28.1498	−	10.2457i	0.937285	−	0.341144i
$903$	8.17752	−	2.97637i	0.272131	−	0.0990475i
$904$	4.00088	+	6.92972i	0.133067	+	0.230479i
$905$	−9.13610	+	15.8242i	−0.303694	+	0.526014i
$906$	3.16890	−	17.9717i	0.105280	−	0.597071i
$907$	−32.8790	+	27.5887i	−1.09173	+	0.916069i	−0.996841	−	0.0794191i	$-0.974693\pi$
$907$	−32.8790	+	27.5887i	−1.09173	+	0.916069i	−0.0948871	+	0.995488i	$0.530249\pi$
$908$	−33.3632	−	27.9951i	−1.10720	−	0.929050i
$909$	−0.970027	−	5.50130i	−0.0321738	−	0.182466i
$910$	−13.3439	−	4.85678i	−0.442346	−	0.161001i
$911$	55.1411			1.82691			0.913454	−	0.406942i	$-0.133405\pi$
$911$	55.1411			1.82691			0.913454	+	0.406942i	$0.133405\pi$
$912$		0			0
$913$	−14.5945			−0.483008
$914$	−21.6789	−	7.89046i	−0.717073	−	0.260993i
$915$	0.689845	+	3.91231i	0.0228056	+	0.129337i
$916$	67.9894	+	57.0499i	2.24643	+	1.88498i
$917$	−23.2481	+	19.5075i	−0.767720	+	0.644193i
$918$	−6.20574	+	35.1945i	−0.204820	+	1.16159i
$919$	12.2788	−	21.2676i	0.405041	−	0.701552i	−0.589285	−	0.807925i	$-0.700590\pi$
$919$	12.2788	−	21.2676i	0.405041	−	0.701552i	0.994326	+	0.106373i	$0.0339237\pi$
$920$	−20.8307	−	36.0798i	−0.686767	−	1.18952i
$921$	14.2144	−	5.17360i	0.468379	−	0.170476i
$922$	58.1719	−	21.1729i	1.91579	−	0.697291i
$923$	9.42190	+	16.3192i	0.310126	+	0.537154i
$924$	2.61334	−	4.52644i	0.0859726	−	0.148909i
$925$	−2.27079	+	12.8783i	−0.0746632	+	0.423436i
$926$	−0.486329	+	0.408079i	−0.0159818	+	0.0134103i
$927$	−24.5993	−	20.6412i	−0.807946	−	0.677947i
$928$	3.71348	+	21.0602i	0.121901	+	0.691334i
$929$	20.9338	+	7.61927i	0.686814	+	0.249980i	0.661771	−	0.749706i	$-0.269805\pi$
$929$	20.9338	+	7.61927i	0.686814	+	0.249980i	0.0250438	+	0.999686i	$0.492027\pi$
$930$	−8.54488			−0.280198
$931$		0			0
$932$	15.5936			0.510785
$933$	2.12284	+	0.772649i	0.0694985	+	0.0252954i
$934$	6.75449	+	38.3066i	0.221014	+	1.25343i
$935$	4.74376	+	3.98048i	0.155137	+	0.130176i
$936$	32.7108	−	27.4476i	1.06919	−	0.897153i
$937$	−1.65863	+	9.40658i	−0.0541852	+	0.307299i	−0.999840	−	0.0178719i	$-0.994311\pi$
$937$	−1.65863	+	9.40658i	−0.0541852	+	0.307299i	0.945655	+	0.325171i	$0.105422\pi$
$938$	−7.53983	+	13.0594i	−0.246184	+	0.426403i
$939$	7.47013	+	12.9386i	0.243779	+	0.422237i
$940$	3.20574	−	1.16679i	0.104560	−	0.0380566i
$941$	−52.3649	+	19.0593i	−1.70705	+	0.621314i	−0.996597	−	0.0824333i	$-0.973731\pi$
$941$	−52.3649	+	19.0593i	−1.70705	+	0.621314i	−0.710450	+	0.703748i	$0.751509\pi$
$942$	−9.08424	−	15.7344i	−0.295981	−	0.512654i
$943$	25.2841	−	43.7933i	0.823362	−	1.42610i
$944$	4.53684	−	25.7297i	0.147661	−	0.837430i
$945$	5.75284	−	4.82721i	0.187140	−	0.157029i
$946$	19.9991	+	16.7813i	0.650228	+	0.545606i
$947$	−4.69594	−	26.6320i	−0.152597	−	0.865423i	−0.960950	−	0.276724i	$-0.910751\pi$
$947$	−4.69594	−	26.6320i	−0.152597	−	0.865423i	0.808352	−	0.588699i	$-0.200360\pi$
$948$	26.5390	+	9.65939i	0.861945	+	0.313722i
$949$	−16.6500			−0.540482
$950$		0			0
$951$	−17.0490			−0.552852
$952$	−34.1031	−	12.4125i	−1.10529	−	0.402292i
$953$	−4.01666	−	22.7796i	−0.130112	−	0.737905i	−0.978139	−	0.207951i	$-0.933320\pi$
$953$	−4.01666	−	22.7796i	−0.130112	−	0.737905i	0.848027	−	0.529953i	$-0.177791\pi$
$954$	14.6964	+	12.3317i	0.475814	+	0.399255i
$955$	10.6141	−	8.90625i	0.343463	−	0.288199i
$956$	9.17230	−	52.0187i	0.296654	−	1.68241i
$957$	1.79901	−	3.11598i	0.0581538	−	0.100725i
$958$	0.910597	+	1.57720i	0.0294200	+	0.0509570i
$959$	−14.6912	+	5.34716i	−0.474403	+	0.172669i
$960$	−1.35369	+	0.492704i	−0.0436903	+	0.0159020i
$961$	8.13681	+	14.0934i	0.262478	+	0.454625i
$962$	14.1236	−	24.4628i	0.455363	−	0.788713i
$963$	−2.98576	+	16.9331i	−0.0962147	+	0.545660i
$964$	−43.5997	+	36.5845i	−1.40425	+	1.17831i
$965$	14.2435	+	11.9517i	0.458515	+	0.384740i
$966$	−2.22668	−	12.6281i	−0.0716423	−	0.406304i
$967$	−36.6810	−	13.3508i	−1.17958	−	0.429332i	−0.323527	−	0.946219i	$-0.604869\pi$
$967$	−36.6810	−	13.3508i	−1.17958	−	0.429332i	−0.856054	+	0.516887i	$0.827091\pi$
$968$	−58.5954			−1.88333
$969$		0			0
$970$	25.1411			0.807234
$971$	−38.7178	−	14.0921i	−1.24251	−	0.452238i	−0.364648	−	0.931145i	$-0.618811\pi$
$971$	−38.7178	−	14.0921i	−1.24251	−	0.452238i	−0.877865	+	0.478907i	$0.841033\pi$
$972$	11.0346	+	62.5804i	0.353935	+	2.00727i
$973$	−1.94878	−	1.63522i	−0.0624749	−	0.0524227i
$974$	−22.7854	+	19.1192i	−0.730091	+	0.612619i
$975$	0.980704	−	5.56185i	0.0314077	−	0.178122i
$976$	14.9941	−	25.9705i	0.479948	−	0.831295i
$977$	11.2469	+	19.4802i	0.359821	+	0.623227i	0.987931	−	0.154897i	$-0.0495046\pi$
$977$	11.2469	+	19.4802i	0.359821	+	0.623227i	−0.628110	+	0.778125i	$0.716171\pi$
$978$	9.83497	−	3.57964i	0.314488	−	0.114464i
$979$	2.70099	−	0.983080i	0.0863240	−	0.0314194i
$980$	−13.8268	−	23.9488i	−0.441682	−	0.765015i
$981$	−12.1664	+	21.0728i	−0.388442	+	0.672802i
$982$	0.0390581	−	0.221510i	0.00124640	−	0.00706866i
$983$	34.1243	−	28.6337i	1.08840	−	0.913273i	0.0918061	−	0.995777i	$-0.470736\pi$
$983$	34.1243	−	28.6337i	1.08840	−	0.913273i	0.996591	+	0.0825035i	$0.0262916\pi$
$984$	30.4859	+	25.5807i	0.971856	+	0.815484i
$985$	1.85781	+	10.5362i	0.0591948	+	0.335710i
$986$	−42.9470	−	15.6314i	−1.36771	−	0.497806i
$987$	0.573978			0.0182699
$988$		0			0
$989$	44.0702			1.40135
$990$	9.77631	+	3.55829i	0.310712	+	0.113090i
$991$	7.87140	+	44.6409i	0.250043	+	1.41807i	0.808483	+	0.588520i	$0.200289\pi$
$991$	7.87140	+	44.6409i	0.250043	+	1.41807i	−0.558440	+	0.829545i	$0.688600\pi$
$992$	13.5116	+	11.3376i	0.428994	+	0.359969i
$993$	−9.52229	+	7.99015i	−0.302181	+	0.253560i
$994$	4.67230	−	26.4980i	0.148196	−	0.840464i
$995$	18.2121	−	31.5443i	0.577363	−	1.00002i
$996$	−17.7344	−	30.7169i	−0.561937	−	0.973303i
$997$	9.85844	−	3.58818i	0.312220	−	0.113639i	−0.181157	−	0.983454i	$-0.557984\pi$
$997$	9.85844	−	3.58818i	0.312220	−	0.113639i	0.493377	+	0.869815i	$0.335762\pi$
$998$	−34.9543	+	12.7223i	−1.10646	+	0.402718i
$999$	7.46926	+	12.9371i	0.236317	+	0.409313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.a.99.1		6
19.2	odd	18		19.2.e.a.16.1	yes	6
19.3	odd	18		361.2.e.f.245.1		6
19.4	even	9		361.2.c.h.292.1		6
19.5	even	9	inner	361.2.e.a.62.1		6
19.6	even	9		361.2.c.h.68.1		6
19.7	even	3		361.2.e.h.234.1		6
19.8	odd	6		361.2.e.f.28.1		6
19.9	even	9		361.2.a.h.1.3		3
19.10	odd	18		361.2.a.g.1.1		3
19.11	even	3		361.2.e.b.28.1		6
19.12	odd	6		19.2.e.a.6.1	✓	6
19.13	odd	18		361.2.c.i.68.3		6
19.14	odd	18		361.2.e.g.62.1		6
19.15	odd	18		361.2.c.i.292.3		6
19.16	even	9		361.2.e.b.245.1		6
19.17	even	9		361.2.e.h.54.1		6
19.18	odd	2		361.2.e.g.99.1		6
57.2	even	18		171.2.u.c.73.1		6
57.29	even	18		3249.2.a.z.1.3		3
57.47	odd	18		3249.2.a.s.1.1		3
57.50	even	6		171.2.u.c.82.1		6
76.31	even	6		304.2.u.b.177.1		6
76.47	odd	18		5776.2.a.bi.1.2		3
76.59	even	18		304.2.u.b.225.1		6
76.67	even	18		5776.2.a.br.1.2		3
95.2	even	36		475.2.u.a.149.2		12
95.9	even	18		9025.2.a.x.1.1		3
95.12	even	12		475.2.u.a.424.1		12
95.29	odd	18		9025.2.a.bd.1.3		3
95.59	odd	18		475.2.l.a.301.1		6
95.69	odd	6		475.2.l.a.101.1		6
95.78	even	36		475.2.u.a.149.1		12
95.88	even	12		475.2.u.a.424.2		12
133.2	odd	18		931.2.v.b.263.1		6
133.12	even	6		931.2.x.b.557.1		6
133.31	even	6		931.2.v.a.177.1		6
133.40	even	18		931.2.v.a.263.1		6
133.59	even	18		931.2.x.b.814.1		6
133.69	even	6		931.2.w.a.785.1		6
133.88	odd	6		931.2.v.b.177.1		6
133.97	even	18		931.2.w.a.491.1		6
133.107	odd	6		931.2.x.a.557.1		6
133.116	odd	18		931.2.x.a.814.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	19.12	odd	6
19.2.e.a.16.1	yes	6	19.2	odd	18
171.2.u.c.73.1		6	57.2	even	18
171.2.u.c.82.1		6	57.50	even	6
304.2.u.b.177.1		6	76.31	even	6
304.2.u.b.225.1		6	76.59	even	18
361.2.a.g.1.1		3	19.10	odd	18
361.2.a.h.1.3		3	19.9	even	9
361.2.c.h.68.1		6	19.6	even	9
361.2.c.h.292.1		6	19.4	even	9
361.2.c.i.68.3		6	19.13	odd	18
361.2.c.i.292.3		6	19.15	odd	18
361.2.e.a.62.1		6	19.5	even	9	inner
361.2.e.a.99.1		6	1.1	even	1	trivial
361.2.e.b.28.1		6	19.11	even	3
361.2.e.b.245.1		6	19.16	even	9
361.2.e.f.28.1		6	19.8	odd	6
361.2.e.f.245.1		6	19.3	odd	18
361.2.e.g.62.1		6	19.14	odd	18
361.2.e.g.99.1		6	19.18	odd	2
361.2.e.h.54.1		6	19.17	even	9
361.2.e.h.234.1		6	19.7	even	3
475.2.l.a.101.1		6	95.69	odd	6
475.2.l.a.301.1		6	95.59	odd	18
475.2.u.a.149.1		12	95.78	even	36
475.2.u.a.149.2		12	95.2	even	36
475.2.u.a.424.1		12	95.12	even	12
475.2.u.a.424.2		12	95.88	even	12
931.2.v.a.177.1		6	133.31	even	6
931.2.v.a.263.1		6	133.40	even	18
931.2.v.b.177.1		6	133.88	odd	6
931.2.v.b.263.1		6	133.2	odd	18
931.2.w.a.491.1		6	133.97	even	18
931.2.w.a.785.1		6	133.69	even	6
931.2.x.a.557.1		6	133.107	odd	6
931.2.x.a.814.1		6	133.116	odd	18
931.2.x.b.557.1		6	133.12	even	6
931.2.x.b.814.1		6	133.59	even	18
3249.2.a.s.1.1		3	57.47	odd	18
3249.2.a.z.1.3		3	57.29	even	18
5776.2.a.bi.1.2		3	76.47	odd	18
5776.2.a.br.1.2		3	76.67	even	18
9025.2.a.x.1.1		3	95.9	even	18
9025.2.a.bd.1.3		3	95.29	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.37939 - 0.866025i) q^{2} +(0.113341 + 0.642788i) q^{3} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(0.286989 - 1.62760i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(-3.05303 - 5.28801i) q^{8} +(2.41875 - 0.880352i) q^{9} +O(q^{10})\)	\(q+(-2.37939 - 0.866025i) q^{2} +(0.113341 + 0.642788i) q^{3} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(0.286989 - 1.62760i) q^{6} +(-0.766044 + 1.32683i) q^{7} +(-3.05303 - 5.28801i) q^{8} +(2.41875 - 0.880352i) q^{9} +(3.20574 - 1.16679i) q^{10} +(0.592396 + 1.02606i) q^{11} +(-1.43969 + 2.49362i) q^{12} +(-0.471782 + 2.67561i) q^{13} +(2.97178 - 2.49362i) q^{14} +(-0.673648 - 0.565258i) q^{15} +(1.15270 + 6.53731i) q^{16} +(-3.64543 - 1.32683i) q^{17} -6.51754 q^{18} -5.94356 q^{20} +(-0.939693 - 0.342020i) q^{21} +(-0.520945 - 2.95442i) q^{22} +(-3.87939 - 3.25519i) q^{23} +(3.05303 - 2.56180i) q^{24} +(-0.553033 + 3.13641i) q^{25} +(3.43969 - 5.95772i) q^{26} +(1.81908 + 3.15074i) q^{27} +(-6.35117 + 2.31164i) q^{28} +(-4.37211 + 1.59132i) q^{29} +(1.11334 + 1.92836i) q^{30} +(-1.91875 + 3.32337i) q^{31} +(0.798133 - 4.52644i) q^{32} +(-0.592396 + 0.497079i) q^{33} +(7.52481 + 6.31407i) q^{34} +(-0.358441 - 2.03282i) q^{35} +(10.6702 + 3.88365i) q^{36} +4.10607 q^{37} -1.77332 q^{39} +(7.73055 + 2.81369i) q^{40} +(1.73396 + 9.83375i) q^{41} +(1.93969 + 1.62760i) q^{42} +(-6.66637 + 5.59375i) q^{43} +(-0.907604 + 5.14728i) q^{44} +(-1.73396 + 3.00330i) q^{45} +(6.41147 + 11.1050i) q^{46} +(-0.539363 + 0.196312i) q^{47} +(-4.07145 + 1.48189i) q^{48} +(2.32635 + 4.02936i) q^{49} +(4.03209 - 6.98378i) q^{50} +(0.439693 - 2.49362i) q^{51} +(-9.18139 + 7.70410i) q^{52} +(-2.25490 - 1.89209i) q^{53} +(-1.59967 - 9.07218i) q^{54} +(-1.50000 - 0.545955i) q^{55} +9.35504 q^{56} +11.7811 q^{58} +(-3.69846 - 1.34613i) q^{59} +(-0.673648 - 3.82045i) q^{60} +(-3.46064 - 2.90382i) q^{61} +(7.44356 - 6.24589i) q^{62} +(-0.684793 + 3.88365i) q^{63} +(0.819078 - 1.41868i) q^{64} +(-1.83022 - 3.17004i) q^{65} +(1.84002 - 0.669713i) q^{66} +(-3.65270 + 1.32948i) q^{67} +(-8.55690 - 14.8210i) q^{68} +(1.65270 - 2.86257i) q^{69} +(-0.907604 + 5.14728i) q^{70} +(5.31315 - 4.45826i) q^{71} +(-12.0398 - 10.1026i) q^{72} +(1.06418 + 6.03525i) q^{73} +(-9.76991 - 3.55596i) q^{74} -2.07873 q^{75} -1.81521 q^{77} +(4.21941 + 1.53574i) q^{78} +(-1.70321 - 9.65939i) q^{79} +(-6.85117 - 5.74881i) q^{80} +(4.09627 - 3.43718i) q^{81} +(4.39053 - 24.8999i) q^{82} +(-6.15910 + 10.6679i) q^{83} +(-2.20574 - 3.82045i) q^{84} +(4.91147 - 1.78763i) q^{85} +(20.7062 - 7.53644i) q^{86} +(-1.51842 - 2.62998i) q^{87} +(3.61721 - 6.26519i) q^{88} +(0.421274 - 2.38917i) q^{89} +(6.72668 - 5.64436i) q^{90} +(-3.18866 - 2.67561i) q^{91} +(-3.87939 - 22.0011i) q^{92} +(-2.35369 - 0.856674i) q^{93} +1.45336 q^{94} +3.00000 q^{96} +(6.92514 + 2.52055i) q^{97} +(-2.04576 - 11.6021i) q^{98} +(2.33615 + 1.96026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9	\( 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9} + 9 q^{10} - 3 q^{12} + 12 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 12 q^{23} + 6 q^{24} + 9 q^{25} + 15 q^{26} - 6 q^{27} - 12 q^{28} + 3 q^{29} - 9 q^{31} - 9 q^{32} + 18 q^{34} + 6 q^{35} + 21 q^{36} - 24 q^{39} + 9 q^{40} + 15 q^{41} + 6 q^{42} - 21 q^{43} - 9 q^{44} - 15 q^{45} + 18 q^{46} - 12 q^{47} - 24 q^{48} + 15 q^{49} + 15 q^{50} - 3 q^{51} - 6 q^{52} - 15 q^{53} - 24 q^{54} - 9 q^{55} + 6 q^{56} + 36 q^{58} + 6 q^{59} - 3 q^{60} - 12 q^{61} + 15 q^{62} + 3 q^{63} - 12 q^{64} + 12 q^{65} - 9 q^{66} - 24 q^{67} - 15 q^{68} + 12 q^{69} - 9 q^{70} - 12 q^{71} - 15 q^{72} - 12 q^{73} - 30 q^{74} - 30 q^{75} - 18 q^{77} - 6 q^{78} - 15 q^{79} - 15 q^{80} - 3 q^{81} + 9 q^{82} - 3 q^{84} + 9 q^{85} + 48 q^{86} - 21 q^{87} - 9 q^{88} - 15 q^{89} + 27 q^{90} + 12 q^{91} - 12 q^{92} + 27 q^{93} - 18 q^{94} + 18 q^{96} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9 + 9 * q^10 - 3 * q^12 + 12 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 12 * q^23 + 6 * q^24 + 9 * q^25 + 15 * q^26 - 6 * q^27 - 12 * q^28 + 3 * q^29 - 9 * q^31 - 9 * q^32 + 18 * q^34 + 6 * q^35 + 21 * q^36 - 24 * q^39 + 9 * q^40 + 15 * q^41 + 6 * q^42 - 21 * q^43 - 9 * q^44 - 15 * q^45 + 18 * q^46 - 12 * q^47 - 24 * q^48 + 15 * q^49 + 15 * q^50 - 3 * q^51 - 6 * q^52 - 15 * q^53 - 24 * q^54 - 9 * q^55 + 6 * q^56 + 36 * q^58 + 6 * q^59 - 3 * q^60 - 12 * q^61 + 15 * q^62 + 3 * q^63 - 12 * q^64 + 12 * q^65 - 9 * q^66 - 24 * q^67 - 15 * q^68 + 12 * q^69 - 9 * q^70 - 12 * q^71 - 15 * q^72 - 12 * q^73 - 30 * q^74 - 30 * q^75 - 18 * q^77 - 6 * q^78 - 15 * q^79 - 15 * q^80 - 3 * q^81 + 9 * q^82 - 3 * q^84 + 9 * q^85 + 48 * q^86 - 21 * q^87 - 9 * q^88 - 15 * q^89 + 27 * q^90 + 12 * q^91 - 12 * q^92 + 27 * q^93 - 18 * q^94 + 18 * q^96 + 18 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more