LMFDB - Embedded newform 931.2.f.p.704.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(324,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("931.324");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.f (of order $3$, degree $2$, 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 15 x^{12} - 18 x^{11} + 86 x^{10} - 96 x^{9} + 310 x^{8} - 68 x^{7} + 220 x^{6} + \cdots + 1 $ x^14 - 3x^13 + 15x^12 - 18x^11 + 86x^10 - 96x^9 + 310x^8 - 68x^7 + 220x^6 - 18x^5 + 130x^4 + 4x^3 + 13x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			704.4
Root			$0.136852 + 0.237035i$ of defining polynomial
Character	$\chi$	$=$	931.704
Dual form			931.2.f.p.324.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.134831 - 0.233534i) q^{2} +(0.699343 - 1.21130i) q^{3} +(0.963641 - 1.66908i) q^{4} +(1.68994 + 2.92706i) q^{5} -0.377172 q^{6} -1.05904 q^{8} +(0.521837 + 0.903849i) q^{9} +O(q^{10})$	\(q+(-0.134831 - 0.233534i) q^{2} +(0.699343 - 1.21130i) q^{3} +(0.963641 - 1.66908i) q^{4} +(1.68994 + 2.92706i) q^{5} -0.377172 q^{6} -1.05904 q^{8} +(0.521837 + 0.903849i) q^{9} +(0.455711 - 0.789315i) q^{10} +(0.789885 - 1.36812i) q^{11} +(-1.34783 - 2.33451i) q^{12} -2.85128 q^{13} +4.72739 q^{15} +(-1.78449 - 3.09083i) q^{16} +(3.18994 - 5.52513i) q^{17} +(0.140719 - 0.243733i) q^{18} +(0.500000 + 0.866025i) q^{19} +6.51397 q^{20} -0.426004 q^{22} +(-1.14337 - 1.98038i) q^{23} +(-0.740631 + 1.28281i) q^{24} +(-3.21177 + 5.56296i) q^{25} +(0.384440 + 0.665870i) q^{26} +5.65584 q^{27} +8.17998 q^{29} +(-0.637397 - 1.10400i) q^{30} +(2.49760 - 4.32597i) q^{31} +(-1.54025 + 2.66778i) q^{32} +(-1.10480 - 1.91357i) q^{33} -1.72041 q^{34} +2.01146 q^{36} +(5.31659 + 9.20861i) q^{37} +(0.134831 - 0.233534i) q^{38} +(-1.99402 + 3.45375i) q^{39} +(-1.78971 - 3.09986i) q^{40} +0.539323 q^{41} +2.79641 q^{43} +(-1.52233 - 2.63676i) q^{44} +(-1.76374 + 3.05490i) q^{45} +(-0.308324 + 0.534033i) q^{46} +(-4.52325 - 7.83450i) q^{47} -4.99189 q^{48} +1.73218 q^{50} +(-4.46172 - 7.72793i) q^{51} +(-2.74761 + 4.75900i) q^{52} +(-1.35587 + 2.34844i) q^{53} +(-0.762581 - 1.32083i) q^{54} +5.33943 q^{55} +1.39869 q^{57} +(-1.10291 - 1.91030i) q^{58} +(-4.51563 + 7.82130i) q^{59} +(4.55550 - 7.89036i) q^{60} +(3.20555 + 5.55217i) q^{61} -1.34701 q^{62} -6.30728 q^{64} +(-4.81848 - 8.34585i) q^{65} +(-0.297923 + 0.516017i) q^{66} +(-0.488491 + 0.846091i) q^{67} +(-6.14791 - 10.6485i) q^{68} -3.19845 q^{69} -10.9930 q^{71} +(-0.552645 - 0.957210i) q^{72} +(1.53316 - 2.65551i) q^{73} +(1.43368 - 2.48321i) q^{74} +(4.49227 + 7.78083i) q^{75} +1.92728 q^{76} +1.07542 q^{78} +(-0.346177 - 0.599597i) q^{79} +(6.03136 - 10.4466i) q^{80} +(2.38986 - 4.13936i) q^{81} +(-0.0727174 - 0.125950i) q^{82} -4.23017 q^{83} +21.5632 q^{85} +(-0.377042 - 0.653057i) q^{86} +(5.72061 - 9.90839i) q^{87} +(-0.836518 + 1.44889i) q^{88} +(-2.02022 - 3.49913i) q^{89} +0.951228 q^{90} -4.40721 q^{92} +(-3.49336 - 6.05068i) q^{93} +(-1.21975 + 2.11266i) q^{94} +(-1.68994 + 2.92706i) q^{95} +(2.15432 + 3.73140i) q^{96} -15.0254 q^{97} +1.64877 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 2 q^{3} - 10 q^{4} - 2 q^{5} + 8 q^{6} + 24 q^{8} - 15 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 - 2 * q^5 + 8 * q^6 + 24 * q^8 - 15 * q^9	$ 14 q - 2 q^{2} - 2 q^{3} - 10 q^{4} - 2 q^{5} + 8 q^{6} + 24 q^{8} - 15 q^{9} - 7 q^{11} - 22 q^{12} - 12 q^{13} + 4 q^{15} - 24 q^{16} + 19 q^{17} + 12 q^{18} + 7 q^{19} + 16 q^{20} - 12 q^{22} + q^{23} + 20 q^{24} + 3 q^{25} + 12 q^{26} + 28 q^{27} + 48 q^{29} + 20 q^{30} - 26 q^{32} - 14 q^{33} - 12 q^{34} + 92 q^{36} - 8 q^{37} + 2 q^{38} - 16 q^{39} - 10 q^{40} + 8 q^{41} + 8 q^{43} - 26 q^{44} + 14 q^{45} + 16 q^{46} + 5 q^{47} + 56 q^{48} + 32 q^{50} + 4 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{54} + 60 q^{55} - 4 q^{57} - 16 q^{59} + 44 q^{60} + 5 q^{61} - 48 q^{62} + 64 q^{64} - 26 q^{65} + 68 q^{66} + 4 q^{67} + 22 q^{68} + 72 q^{69} + 24 q^{71} + 3 q^{73} + 4 q^{74} + 18 q^{75} - 20 q^{76} - 28 q^{78} + 20 q^{79} - 4 q^{80} - 27 q^{81} - 48 q^{82} + 22 q^{83} + 52 q^{85} - 36 q^{86} - 16 q^{87} + 32 q^{88} - 10 q^{89} - 64 q^{90} - 60 q^{92} + 4 q^{93} + 16 q^{94} + 2 q^{95} - 12 q^{96} + 8 q^{97} + 30 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 - 2 * q^5 + 8 * q^6 + 24 * q^8 - 15 * q^9 - 7 * q^11 - 22 * q^12 - 12 * q^13 + 4 * q^15 - 24 * q^16 + 19 * q^17 + 12 * q^18 + 7 * q^19 + 16 * q^20 - 12 * q^22 + q^23 + 20 * q^24 + 3 * q^25 + 12 * q^26 + 28 * q^27 + 48 * q^29 + 20 * q^30 - 26 * q^32 - 14 * q^33 - 12 * q^34 + 92 * q^36 - 8 * q^37 + 2 * q^38 - 16 * q^39 - 10 * q^40 + 8 * q^41 + 8 * q^43 - 26 * q^44 + 14 * q^45 + 16 * q^46 + 5 * q^47 + 56 * q^48 + 32 * q^50 + 4 * q^51 + 42 * q^52 - 20 * q^53 - 24 * q^54 + 60 * q^55 - 4 * q^57 - 16 * q^59 + 44 * q^60 + 5 * q^61 - 48 * q^62 + 64 * q^64 - 26 * q^65 + 68 * q^66 + 4 * q^67 + 22 * q^68 + 72 * q^69 + 24 * q^71 + 3 * q^73 + 4 * q^74 + 18 * q^75 - 20 * q^76 - 28 * q^78 + 20 * q^79 - 4 * q^80 - 27 * q^81 - 48 * q^82 + 22 * q^83 + 52 * q^85 - 36 * q^86 - 16 * q^87 + 32 * q^88 - 10 * q^89 - 64 * q^90 - 60 * q^92 + 4 * q^93 + 16 * q^94 + 2 * q^95 - 12 * q^96 + 8 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.134831	−	0.233534i	−0.0953398	−	0.165133i	0.814411	−	0.580289i	$-0.197060\pi$
$2$	−0.134831	−	0.233534i	−0.0953398	−	0.165133i	−0.909750	+	0.415156i	$0.863727\pi$
$3$	0.699343	−	1.21130i	0.403766	−	0.699343i	−0.590411	−	0.807103i	$-0.701034\pi$
$3$	0.699343	−	1.21130i	0.403766	−	0.699343i	0.994177	+	0.107759i	$0.0343676\pi$
$4$	0.963641	−	1.66908i	0.481821	−	0.834538i
$5$	1.68994	+	2.92706i	0.755763	+	1.30902i	0.944994	+	0.327087i	$0.106067\pi$
$5$	1.68994	+	2.92706i	0.755763	+	1.30902i	−0.189231	+	0.981933i	$0.560600\pi$
$6$	−0.377172			−0.153980
$7$		0			0
$7$		0			0
$8$	−1.05904			−0.374426
$9$	0.521837	+	0.903849i	0.173946	+	0.301283i
$10$	0.455711	−	0.789315i	0.144109	−	0.249603i
$11$	0.789885	−	1.36812i	0.238159	−	0.412504i	−0.722027	−	0.691865i	$-0.756789\pi$
$11$	0.789885	−	1.36812i	0.238159	−	0.412504i	0.960186	+	0.279361i	$0.0901226\pi$
$12$	−1.34783	−	2.33451i	−0.389086	−	0.673916i
$13$	−2.85128			−0.790802			−0.395401	−	0.918509i	$-0.629394\pi$
$13$	−2.85128			−0.790802			−0.395401	+	0.918509i	$0.629394\pi$
$14$		0			0
$15$	4.72739			1.22061
$16$	−1.78449	−	3.09083i	−0.446123	−	0.772708i
$17$	3.18994	−	5.52513i	0.773673	−	1.34004i	−0.161864	−	0.986813i	$-0.551750\pi$
$17$	3.18994	−	5.52513i	0.773673	−	1.34004i	0.935537	−	0.353228i	$-0.114916\pi$
$18$	0.140719	−	0.243733i	0.0331679	−	0.0574485i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$20$	6.51397			1.45657
$21$		0			0
$22$	−0.426004			−0.0908243
$23$	−1.14337	−	1.98038i	−0.238410	−	0.412938i	0.721848	−	0.692051i	$-0.243293\pi$
$23$	−1.14337	−	1.98038i	−0.238410	−	0.412938i	−0.960258	+	0.279113i	$0.909960\pi$
$24$	−0.740631	+	1.28281i	−0.151181	+	0.261853i
$25$	−3.21177	+	5.56296i	−0.642355	+	1.11259i
$26$	0.384440	+	0.665870i	0.0753949	+	0.130588i
$27$	5.65584			1.08847
$28$		0			0
$29$	8.17998			1.51898			0.759492	−	0.650517i	$-0.225448\pi$
$29$	8.17998			1.51898			0.759492	+	0.650517i	$0.225448\pi$
$30$	−0.637397	−	1.10400i	−0.116372	−	0.201563i
$31$	2.49760	−	4.32597i	0.448582	−	0.776967i	−0.549712	−	0.835354i	$-0.685262\pi$
$31$	2.49760	−	4.32597i	0.448582	−	0.776967i	0.998294	+	0.0583871i	$0.0185958\pi$
$32$	−1.54025	+	2.66778i	−0.272280	+	0.471602i
$33$	−1.10480	−	1.91357i	−0.192321	−	0.333110i
$34$	−1.72041			−0.295047
$35$		0			0
$36$	2.01146			0.335243
$37$	5.31659	+	9.20861i	0.874043	+	1.51389i	0.857779	+	0.514018i	$0.171844\pi$
$37$	5.31659	+	9.20861i	0.874043	+	1.51389i	0.0162634	+	0.999868i	$0.494823\pi$
$38$	0.134831	−	0.233534i	0.0218724	−	0.0378842i
$39$	−1.99402	+	3.45375i	−0.319299	+	0.553042i
$40$	−1.78971	−	3.09986i	−0.282977	−	0.490131i
$41$	0.539323			0.0842281			0.0421141	−	0.999113i	$-0.486591\pi$
$41$	0.539323			0.0842281			0.0421141	+	0.999113i	$0.486591\pi$
$42$		0			0
$43$	2.79641			0.426449			0.213224	−	0.977003i	$-0.431603\pi$
$43$	2.79641			0.426449			0.213224	+	0.977003i	$0.431603\pi$
$44$	−1.52233	−	2.63676i	−0.229500	−	0.397506i
$45$	−1.76374	+	3.05490i	−0.262924	+	0.455397i
$46$	−0.308324	+	0.534033i	−0.0454599	+	0.0787389i
$47$	−4.52325	−	7.83450i	−0.659784	−	1.14278i	−0.980671	−	0.195661i	$-0.937315\pi$
$47$	−4.52325	−	7.83450i	−0.659784	−	1.14278i	0.320888	−	0.947117i	$-0.396019\pi$
$48$	−4.99189			−0.720517
$49$		0			0
$50$	1.73218			0.244968
$51$	−4.46172	−	7.72793i	−0.624766	−	1.08213i
$52$	−2.74761	+	4.75900i	−0.381025	+	0.659955i
$53$	−1.35587	+	2.34844i	−0.186244	+	0.322583i	−0.943995	−	0.329960i	$-0.892965\pi$
$53$	−1.35587	+	2.34844i	−0.186244	+	0.322583i	0.757751	+	0.652544i	$0.226298\pi$
$54$	−0.762581	−	1.32083i	−0.103774	−	0.179742i
$55$	5.33943			0.719968
$56$		0			0
$57$	1.39869			0.185261
$58$	−1.10291	−	1.91030i	−0.144820	−	0.250835i
$59$	−4.51563	+	7.82130i	−0.587885	+	1.01825i	0.406624	+	0.913595i	$0.366706\pi$
$59$	−4.51563	+	7.82130i	−0.587885	+	1.01825i	−0.994509	+	0.104651i	$0.966628\pi$
$60$	4.55550	−	7.89036i	0.588113	−	1.01864i
$61$	3.20555	+	5.55217i	0.410428	+	0.710883i	0.994937	−	0.100505i	$-0.0320458\pi$
$61$	3.20555	+	5.55217i	0.410428	+	0.710883i	−0.584508	+	0.811388i	$0.698712\pi$
$62$	−1.34701			−0.171071
$63$		0			0
$64$	−6.30728			−0.788410
$65$	−4.81848	−	8.34585i	−0.597659	−	1.03518i
$66$	−0.297923	+	0.516017i	−0.0366718	+	0.0635174i
$67$	−0.488491	+	0.846091i	−0.0596787	+	0.103367i	−0.894321	−	0.447426i	$-0.852341\pi$
$67$	−0.488491	+	0.846091i	−0.0596787	+	0.103367i	0.834642	+	0.550792i	$0.185674\pi$
$68$	−6.14791	−	10.6485i	−0.745544	−	1.29132i
$69$	−3.19845			−0.385048
$70$		0			0
$71$	−10.9930			−1.30463			−0.652314	−	0.757949i	$-0.726202\pi$
$71$	−10.9930			−1.30463			−0.652314	+	0.757949i	$0.726202\pi$
$72$	−0.552645	−	0.957210i	−0.0651299	−	0.112808i
$73$	1.53316	−	2.65551i	0.179442	−	0.310804i	−0.762247	−	0.647286i	$-0.775904\pi$
$73$	1.53316	−	2.65551i	0.179442	−	0.310804i	0.941690	+	0.336482i	$0.109237\pi$
$74$	1.43368	−	2.48321i	0.166662	−	0.288667i
$75$	4.49227	+	7.78083i	0.518722	+	0.898453i
$76$	1.92728			0.221074
$77$		0			0
$78$	1.07542			0.121768
$79$	−0.346177	−	0.599597i	−0.0389480	−	0.0674599i	0.845894	−	0.533351i	$-0.179067\pi$
$79$	−0.346177	−	0.599597i	−0.0389480	−	0.0674599i	−0.884842	+	0.465891i	$0.845734\pi$
$80$	6.03136	−	10.4466i	0.674326	−	1.16797i
$81$	2.38986	−	4.13936i	0.265540	−	0.459929i
$82$	−0.0727174	−	0.125950i	−0.00803029	−	0.0139089i
$83$	−4.23017			−0.464322			−0.232161	−	0.972677i	$-0.574580\pi$
$83$	−4.23017			−0.464322			−0.232161	+	0.972677i	$0.574580\pi$
$84$		0			0
$85$	21.5632			2.33885
$86$	−0.377042	−	0.653057i	−0.0406575	−	0.0704209i
$87$	5.72061	−	9.90839i	0.613314	−	1.06229i
$88$	−0.836518	+	1.44889i	−0.0891731	+	0.154452i
$89$	−2.02022	−	3.49913i	−0.214143	−	0.370907i	0.738864	−	0.673855i	$-0.235363\pi$
$89$	−2.02022	−	3.49913i	−0.214143	−	0.370907i	−0.953007	+	0.302948i	$0.902029\pi$
$90$	0.951228			0.100268
$91$		0			0
$92$	−4.40721			−0.459483
$93$	−3.49336	−	6.05068i	−0.362245	−	0.627426i
$94$	−1.21975	+	2.11266i	−0.125807	+	0.217905i
$95$	−1.68994	+	2.92706i	−0.173384	+	0.300310i
$96$	2.15432	+	3.73140i	0.219875	+	0.380834i
$97$	−15.0254			−1.52559			−0.762797	−	0.646638i	$-0.776174\pi$
$97$	−15.0254			−1.52559			−0.762797	+	0.646638i	$0.776174\pi$
$98$		0			0
$99$	1.64877			0.165707
$100$	6.19000	+	10.7214i	0.619000	+	1.07214i
$101$	−6.31042	+	10.9300i	−0.627910	+	1.08757i	0.360060	+	0.932929i	$0.382756\pi$
$101$	−6.31042	+	10.9300i	−0.627910	+	1.08757i	−0.987970	+	0.154643i	$0.950577\pi$
$102$	−1.20316	+	2.08393i	−0.119130	+	0.206339i
$103$	2.04174	+	3.53641i	0.201179	+	0.348452i	0.948909	−	0.315551i	$-0.102189\pi$
$103$	2.04174	+	3.53641i	0.201179	+	0.348452i	−0.747730	+	0.664003i	$0.768856\pi$
$104$	3.01961			0.296097
$105$		0			0
$106$	0.731254			0.0710257
$107$	−2.49272	−	4.31751i	−0.240980	−	0.417390i	0.720014	−	0.693960i	$-0.244136\pi$
$107$	−2.49272	−	4.31751i	−0.240980	−	0.417390i	−0.960994	+	0.276570i	$0.910802\pi$
$108$	5.45020	−	9.44002i	0.524445	−	0.908366i
$109$	−5.45772	+	9.45306i	−0.522755	+	0.905439i	0.476894	+	0.878961i	$0.341762\pi$
$109$	−5.45772	+	9.45306i	−0.522755	+	0.905439i	−0.999649	+	0.0264778i	$0.991571\pi$
$110$	−0.719919	−	1.24694i	−0.0686416	−	0.118891i
$111$	14.8725			1.41164
$112$		0			0
$113$	−18.5659			−1.74654			−0.873268	−	0.487240i	$-0.838004\pi$
$113$	−18.5659			−1.74654			−0.873268	+	0.487240i	$0.838004\pi$
$114$	−0.188586	−	0.326641i	−0.0176627	−	0.0305927i
$115$	3.86446	−	6.69344i	0.360363	−	0.624167i
$116$	7.88256	−	13.6530i	0.731878	−	1.26765i
$117$	−1.48790	−	2.57712i	−0.137557	−	0.238255i
$118$	2.43538			0.224195
$119$		0			0
$120$	−5.00648			−0.457027
$121$	4.25216	+	7.36496i	0.386560	+	0.669542i
$122$	0.864413	−	1.49721i	0.0782603	−	0.135551i
$123$	0.377172	−	0.653281i	0.0340085	−	0.0589044i
$124$	−4.81358	−	8.33737i	−0.432272	−	0.748718i
$125$	−4.81142			−0.430346
$126$		0			0
$127$	−16.9441			−1.50355			−0.751774	−	0.659421i	$-0.770801\pi$
$127$	−16.9441			−1.50355			−0.751774	+	0.659421i	$0.770801\pi$
$128$	3.93091	+	6.80853i	0.347446	+	0.601795i
$129$	1.95565	−	3.38729i	0.172186	−	0.298234i
$130$	−1.29936	+	2.25056i	−0.113961	+	0.197387i
$131$	1.70103	+	2.94627i	0.148620	+	0.257417i	0.930718	−	0.365739i	$-0.119184\pi$
$131$	1.70103	+	2.94627i	0.148620	+	0.257417i	−0.782098	+	0.623156i	$0.785850\pi$
$132$	−4.25853			−0.370658
$133$		0			0
$134$	0.263455			0.0227590
$135$	9.55801	+	16.5550i	0.822622	+	1.42482i
$136$	−3.37826	+	5.85132i	−0.289684	+	0.501747i
$137$	−0.876850	+	1.51875i	−0.0749143	+	0.129755i	−0.901049	−	0.433717i	$-0.857202\pi$
$137$	−0.876850	+	1.51875i	−0.0749143	+	0.129755i	0.826135	+	0.563473i	$0.190535\pi$
$138$	0.431249	+	0.746945i	0.0367103	+	0.0635842i
$139$	19.4952			1.65356			0.826780	−	0.562525i	$-0.190170\pi$
$139$	19.4952			1.65356			0.826780	+	0.562525i	$0.190170\pi$
$140$		0			0
$141$	−12.6532			−1.06559
$142$	1.48219	+	2.56723i	0.124383	+	0.215438i
$143$	−2.25218	+	3.90090i	−0.188337	+	0.326209i
$144$	1.86243	−	3.22582i	0.155202	−	0.268818i
$145$	13.8236	+	23.9433i	1.14799	+	1.98838i
$146$	−0.826867			−0.0684320
$147$		0			0
$148$	20.4932			1.68453
$149$	1.92058	+	3.32655i	0.157340	+	0.272522i	0.933909	−	0.357511i	$-0.116375\pi$
$149$	1.92058	+	3.32655i	0.157340	+	0.272522i	−0.776568	+	0.630033i	$0.783041\pi$
$150$	1.21139	−	2.09819i	0.0989097	−	0.171317i
$151$	7.31423	−	12.6686i	0.595223	−	1.03096i	−0.398292	−	0.917259i	$-0.630397\pi$
$151$	7.31423	−	12.6686i	0.595223	−	1.03096i	0.993515	−	0.113699i	$-0.0362698\pi$
$152$	−0.529519	−	0.917153i	−0.0429496	−	0.0743909i
$153$	6.65851			0.538309
$154$		0			0
$155$	16.8832			1.35609
$156$	3.84305	+	6.65635i	0.307690	+	0.532935i
$157$	−4.42096	+	7.65732i	−0.352831	+	0.611121i	−0.986744	−	0.162283i	$-0.948114\pi$
$157$	−4.42096	+	7.65732i	−0.352831	+	0.611121i	0.633914	+	0.773404i	$0.281447\pi$
$158$	−0.0933507	+	0.161688i	−0.00742658	+	0.0128632i
$159$	1.89644	+	3.28474i	0.150398	+	0.260497i
$160$	−10.4117			−0.823115
$161$		0			0
$162$	−1.28891			−0.101266
$163$	−6.24659	−	10.8194i	−0.489271	−	0.847442i	0.510653	−	0.859787i	$-0.329404\pi$
$163$	−6.24659	−	10.8194i	−0.489271	−	0.847442i	−0.999924	+	0.0123450i	$0.996070\pi$
$164$	0.519714	−	0.900171i	0.0405829	−	0.0702916i
$165$	3.73409	−	6.46764i	0.290699	−	0.503505i
$166$	0.570358	+	0.987889i	0.0442684	+	0.0766750i
$167$	−2.57371			−0.199160			−0.0995799	−	0.995030i	$-0.531750\pi$
$167$	−2.57371			−0.199160			−0.0995799	+	0.995030i	$0.531750\pi$
$168$		0			0
$169$	−4.87021			−0.374632
$170$	−2.90738	−	5.03573i	−0.222986	−	0.386223i
$171$	−0.521837	+	0.903849i	−0.0399059	+	0.0691190i
$172$	2.69474	−	4.66742i	0.205472	−	0.355888i
$173$	−1.37425	−	2.38027i	−0.104482	−	0.180969i	0.809044	−	0.587748i	$-0.199985\pi$
$173$	−1.37425	−	2.38027i	−0.104482	−	0.180969i	−0.913527	+	0.406779i	$0.866652\pi$
$174$	−3.08526			−0.233893
$175$		0			0
$176$	−5.63818			−0.424994
$177$	6.31595	+	10.9395i	0.474736	+	0.822267i
$178$	−0.544777	+	0.943581i	−0.0408327	+	0.0707244i
$179$	−2.60531	+	4.51253i	−0.194730	+	0.337283i	−0.946812	−	0.321787i	$-0.895716\pi$
$179$	−2.60531	+	4.51253i	−0.194730	+	0.337283i	0.752082	+	0.659070i	$0.229050\pi$
$180$	3.39923	+	5.88765i	0.253364	+	0.438839i
$181$	−2.25178			−0.167373			−0.0836866	−	0.996492i	$-0.526669\pi$
$181$	−2.25178			−0.167373			−0.0836866	+	0.996492i	$0.526669\pi$
$182$		0			0
$183$	8.96712			0.662868
$184$	1.21088	+	2.09730i	0.0892670	+	0.154615i
$185$	−17.9694	+	31.1239i	−1.32114	+	2.28828i
$186$	−0.942025	+	1.63164i	−0.0690727	+	0.119637i
$187$	−5.03937	−	8.72844i	−0.368515	−	0.638287i
$188$	−17.4352			−1.27159
$189$		0			0
$190$	0.911422			0.0661215
$191$	−0.681256	−	1.17997i	−0.0492940	−	0.0853797i	0.840326	−	0.542082i	$-0.182364\pi$
$191$	−0.681256	−	1.17997i	−0.0492940	−	0.0853797i	−0.889620	+	0.456702i	$0.849030\pi$
$192$	−4.41095	+	7.63999i	−0.318333	+	0.551369i
$193$	−13.8080	+	23.9161i	−0.993920	+	1.72152i	−0.401606	+	0.915813i	$0.631548\pi$
$193$	−13.8080	+	23.9161i	−0.993920	+	1.72152i	−0.592314	+	0.805707i	$0.701785\pi$
$194$	2.02588	+	3.50893i	0.145450	+	0.251926i
$195$	−13.4791			−0.965258
$196$		0			0
$197$	10.4969			0.747874			0.373937	−	0.927454i	$-0.378008\pi$
$197$	10.4969			0.747874			0.373937	+	0.927454i	$0.378008\pi$
$198$	−0.222305	−	0.385043i	−0.0157985	−	0.0273638i
$199$	−3.11966	+	5.40341i	−0.221147	+	0.383038i	−0.955157	−	0.296101i	$-0.904313\pi$
$199$	−3.11966	+	5.40341i	−0.221147	+	0.383038i	0.734010	+	0.679139i	$0.237647\pi$
$200$	3.40139	−	5.89138i	0.240515	−	0.416583i
$201$	0.683246	+	1.18342i	0.0481925	+	0.0834718i
$202$	3.40335			0.239459
$203$		0			0
$204$	−17.1980			−1.20410
$205$	0.911422	+	1.57863i	0.0636565	+	0.110256i
$206$	0.550580	−	0.953633i	0.0383607	−	0.0664427i
$207$	1.19331	−	2.06687i	0.0829408	−	0.143658i
$208$	5.08808	+	8.81282i	0.352795	+	0.611059i
$209$	1.57977			0.109275
$210$		0			0
$211$	−24.5399			−1.68940			−0.844698	−	0.535243i	$-0.820220\pi$
$211$	−24.5399			−1.68940			−0.844698	+	0.535243i	$0.820220\pi$
$212$	2.61315	+	4.52611i	0.179472	+	0.310855i
$213$	−7.68787	+	13.3158i	−0.526765	+	0.912383i
$214$	−0.672190	+	1.16427i	−0.0459500	+	0.0795877i
$215$	4.72576	+	8.18525i	0.322294	+	0.558230i
$216$	−5.98974			−0.407550
$217$		0			0
$218$	2.94348			0.199357
$219$	−2.14441	−	3.71422i	−0.144906	−	0.250984i
$220$	5.14529	−	8.91191i	0.346896	−	0.600841i
$221$	−9.09540	+	15.7537i	−0.611823	+	1.05971i
$222$	−2.00527	−	3.47323i	−0.134585	−	0.233108i
$223$	15.5804			1.04334			0.521670	−	0.853147i	$-0.325309\pi$
$223$	15.5804			1.04334			0.521670	+	0.853147i	$0.325309\pi$
$224$		0			0
$225$	−6.70410			−0.446940
$226$	2.50326	+	4.33577i	0.166514	+	0.288411i
$227$	−5.12962	+	8.88476i	−0.340465	+	0.589702i	−0.984519	−	0.175277i	$-0.943918\pi$
$227$	−5.12962	+	8.88476i	−0.340465	+	0.589702i	0.644054	+	0.764980i	$0.277251\pi$
$228$	1.34783	−	2.33451i	0.0892624	−	0.154607i
$229$	−10.4528	−	18.1048i	−0.690741	−	1.19640i	−0.971595	−	0.236648i	$-0.923951\pi$
$229$	−10.4528	−	18.1048i	−0.690741	−	1.19640i	0.280854	−	0.959750i	$-0.409382\pi$
$230$	−2.08419			−0.137428
$231$		0			0
$232$	−8.66290			−0.568747
$233$	−3.99514	−	6.91979i	−0.261730	−	0.453330i	0.704971	−	0.709236i	$-0.250960\pi$
$233$	−3.99514	−	6.91979i	−0.261730	−	0.453330i	−0.966702	+	0.255905i	$0.917626\pi$
$234$	−0.401230	+	0.694952i	−0.0262293	+	0.0454304i
$235$	15.2880	−	26.4796i	0.997280	−	1.72734i
$236$	8.70289	+	15.0738i	0.566510	+	0.981224i
$237$	−0.968387			−0.0629035
$238$		0			0
$239$	18.8239			1.21762			0.608809	−	0.793317i	$-0.291648\pi$
$239$	18.8239			1.21762			0.608809	+	0.793317i	$0.291648\pi$
$240$	−8.43598	−	14.6115i	−0.544540	−	0.943171i
$241$	−6.05490	+	10.4874i	−0.390030	+	0.675552i	−0.992453	−	0.122625i	$-0.960869\pi$
$241$	−6.05490	+	10.4874i	−0.390030	+	0.675552i	0.602423	+	0.798177i	$0.294202\pi$
$242$	1.14664	−	1.98605i	0.0737091	−	0.127668i
$243$	5.14109	+	8.90462i	0.329801	+	0.571232i
$244$	12.3560			0.791012
$245$		0			0
$246$	−0.203418			−0.0129694
$247$	−1.42564	−	2.46928i	−0.0907113	−	0.157116i
$248$	−2.64505	+	4.58137i	−0.167961	+	0.290917i
$249$	−2.95835	+	5.12400i	−0.187478	+	0.324721i
$250$	0.648727	+	1.12363i	0.0410291	+	0.0710645i
$251$	−15.5940			−0.984286			−0.492143	−	0.870514i	$-0.663786\pi$
$251$	−15.5940			−0.984286			−0.492143	+	0.870514i	$0.663786\pi$
$252$		0			0
$253$	−3.61254			−0.227118
$254$	2.28459	+	3.95702i	0.143348	+	0.248286i
$255$	15.0801	−	26.1194i	0.944350	−	1.63566i
$256$	−5.24726	+	9.08852i	−0.327954	+	0.568033i
$257$	−15.0367	−	26.0443i	−0.937963	−	1.62460i	−0.769263	−	0.638933i	$-0.779376\pi$
$257$	−15.0367	−	26.0443i	−0.937963	−	1.62460i	−0.168701	−	0.985667i	$-0.553957\pi$
$258$	−1.05473			−0.0656645
$259$		0			0
$260$	−18.5731			−1.15186
$261$	4.26862	+	7.39346i	0.264221	+	0.457644i
$262$	0.458702	−	0.794495i	0.0283387	−	0.0490841i
$263$	2.52444	−	4.37245i	0.155663	−	0.269617i	−0.777637	−	0.628714i	$-0.783582\pi$
$263$	2.52444	−	4.37245i	0.155663	−	0.269617i	0.933300	+	0.359097i	$0.116915\pi$
$264$	1.17003	+	2.02655i	0.0720102	+	0.124725i
$265$	−9.16537			−0.563024
$266$		0			0
$267$	−5.65132			−0.345855
$268$	0.941460	+	1.63066i	0.0575089	+	0.0996083i
$269$	1.80640	−	3.12878i	0.110138	−	0.190765i	−0.805688	−	0.592341i	$-0.798204\pi$
$269$	1.80640	−	3.12878i	0.110138	−	0.190765i	0.915826	+	0.401576i	$0.131537\pi$
$270$	2.57743	−	4.46423i	0.156857	−	0.271685i
$271$	4.09545	+	7.09352i	0.248781	+	0.430901i	0.963188	−	0.268830i	$-0.0866368\pi$
$271$	4.09545	+	7.09352i	0.248781	+	0.430901i	−0.714407	+	0.699730i	$0.753303\pi$
$272$	−22.7697			−1.38061
$273$		0			0
$274$	0.472905			0.0285693
$275$	5.07387	+	8.78820i	0.305966	+	0.529948i
$276$	−3.08215	+	5.33845i	−0.185524	+	0.321337i
$277$	6.35087	−	11.0000i	0.381587	−	0.660927i	−0.609703	−	0.792630i	$-0.708711\pi$
$277$	6.35087	−	11.0000i	0.381587	−	0.660927i	0.991289	+	0.131703i	$0.0420445\pi$
$278$	−2.62855	−	4.55279i	−0.157650	−	0.273058i
$279$	5.21337			0.312116
$280$		0			0
$281$	11.6373			0.694226			0.347113	−	0.937823i	$-0.387162\pi$
$281$	11.6373			0.694226			0.347113	+	0.937823i	$0.387162\pi$
$282$	1.70604	+	2.95495i	0.101593	+	0.175965i
$283$	10.8867	−	18.8563i	0.647146	−	1.12089i	−0.336655	−	0.941628i	$-0.609296\pi$
$283$	10.8867	−	18.8563i	0.647146	−	1.12089i	0.983801	−	0.179262i	$-0.0573709\pi$
$284$	−10.5933	+	18.3481i	−0.628597	+	1.08876i
$285$	2.36369	+	4.09404i	0.140013	+	0.242510i
$286$	1.21465			0.0718240
$287$		0			0
$288$	−3.21503			−0.189448
$289$	−11.8514	−	20.5272i	−0.697141	−	1.20748i
$290$	3.72771	−	6.45658i	0.218898	−	0.379143i
$291$	−10.5079	+	18.2002i	−0.615983	+	1.06691i
$292$	−2.95483	−	5.11791i	−0.172918	−	0.299503i
$293$	0.850550			0.0496897			0.0248448	−	0.999691i	$-0.492091\pi$
$293$	0.850550			0.0496897			0.0248448	+	0.999691i	$0.492091\pi$
$294$		0			0
$295$	−30.5245			−1.77721
$296$	−5.63047	−	9.75226i	−0.327264	−	0.566839i
$297$	4.46746	−	7.73787i	0.259228	−	0.448997i
$298$	0.517908	−	0.897043i	0.0300016	−	0.0519643i
$299$	3.26008	+	5.64662i	0.188535	+	0.326553i
$300$	17.3157			0.999725
$301$		0			0
$302$	−3.94473			−0.226994
$303$	8.82630	+	15.2876i	0.507058	+	0.878250i
$304$	1.78449	−	3.09083i	0.102348	−	0.177271i
$305$	−10.8344	+	18.7656i	−0.620373	+	1.07452i
$306$	−0.897773	−	1.55499i	−0.0513222	−	0.0888927i
$307$	21.8941			1.24956			0.624781	−	0.780800i	$-0.285188\pi$
$307$	21.8941			1.24956			0.624781	+	0.780800i	$0.285188\pi$
$308$		0			0
$309$	5.71152			0.324917
$310$	−2.27637	−	3.94279i	−0.129289	−	0.223935i
$311$	−0.959907	+	1.66261i	−0.0544314	+	0.0942779i	−0.891957	−	0.452120i	$-0.850668\pi$
$311$	−0.959907	+	1.66261i	−0.0544314	+	0.0942779i	0.837526	+	0.546398i	$0.184001\pi$
$312$	2.11174	−	3.65765i	0.119554	−	0.207074i
$313$	5.16392	+	8.94417i	0.291882	+	0.505555i	0.974255	−	0.225450i	$-0.0723852\pi$
$313$	5.16392	+	8.94417i	0.291882	+	0.505555i	−0.682373	+	0.731004i	$0.739052\pi$
$314$	2.38432			0.134555
$315$		0			0
$316$	−1.33436			−0.0750638
$317$	−8.47890	−	14.6859i	−0.476223	−	0.824842i	0.523406	−	0.852083i	$-0.324661\pi$
$317$	−8.47890	−	14.6859i	−0.476223	−	0.824842i	−0.999629	+	0.0272415i	$0.991328\pi$
$318$	0.511398	−	0.885767i	0.0286778	−	0.0496714i
$319$	6.46124	−	11.1912i	0.361760	−	0.626587i
$320$	−10.6589	−	18.4618i	−0.595851	−	1.03204i
$321$	−6.97307			−0.389199
$322$		0			0
$323$	6.37987			0.354986
$324$	−4.60593	−	7.97771i	−0.255885	−	0.443206i
$325$	9.15766	−	15.8615i	0.507976	−	0.879840i
$326$	−1.68447	+	2.91758i	−0.0932939	+	0.161590i
$327$	7.63365	+	13.2219i	0.422142	+	0.731171i
$328$	−0.571163			−0.0315372
$329$		0			0
$330$	−2.01388			−0.110861
$331$	8.25433	+	14.2969i	0.453699	+	0.785829i	0.998612	−	0.0526629i	$-0.0167709\pi$
$331$	8.25433	+	14.2969i	0.453699	+	0.785829i	−0.544914	+	0.838492i	$0.683438\pi$
$332$	−4.07637	+	7.06048i	−0.223720	+	0.387494i
$333$	−5.54879	+	9.61079i	−0.304072	+	0.526668i
$334$	0.347016	+	0.601049i	0.0189879	+	0.0328879i
$335$	−3.30208			−0.180412
$336$		0			0
$337$	7.11897			0.387795			0.193898	−	0.981022i	$-0.437887\pi$
$337$	7.11897			0.387795			0.193898	+	0.981022i	$0.437887\pi$
$338$	0.656654	+	1.13736i	0.0357173	+	0.0618642i
$339$	−12.9840	+	22.4889i	−0.705192	+	1.22143i
$340$	20.7792	−	35.9906i	1.12691	−	1.95186i
$341$	−3.94564	−	6.83404i	−0.213668	−	0.370084i
$342$	0.281439			0.0152185
$343$		0			0
$344$	−2.96150			−0.159674
$345$	−5.40517	−	9.36203i	−0.291005	−	0.504035i
$346$	−0.370583	+	0.641869i	−0.0199227	+	0.0345071i
$347$	9.29395	−	16.0976i	0.498926	−	0.864164i	−0.501074	−	0.865405i	$-0.667061\pi$
$347$	9.29395	−	16.0976i	0.498926	−	0.864164i	0.999999	+	0.00124019i	$0.000394765\pi$
$348$	−11.0252	−	19.0963i	−0.591015	−	1.02367i
$349$	19.2917			1.03266			0.516330	−	0.856389i	$-0.327298\pi$
$349$	19.2917			1.03266			0.516330	+	0.856389i	$0.327298\pi$
$350$		0			0
$351$	−16.1264			−0.860761
$352$	2.43324	+	4.21449i	0.129692	+	0.224633i
$353$	8.67442	−	15.0245i	0.461693	−	0.799675i	−0.537353	−	0.843358i	$-0.680576\pi$
$353$	8.67442	−	15.0245i	0.461693	−	0.799675i	0.999045	+	0.0436824i	$0.0139090\pi$
$354$	1.70317	−	2.94998i	0.0905224	−	0.156789i
$355$	−18.5775	−	32.1771i	−0.985989	−	1.70778i
$356$	−7.78708			−0.412715
$357$		0			0
$358$	1.40511			0.0742621
$359$	15.5430	+	26.9212i	0.820326	+	1.42085i	0.905440	+	0.424475i	$0.139541\pi$
$359$	15.5430	+	26.9212i	0.820326	+	1.42085i	−0.0851135	+	0.996371i	$0.527125\pi$
$360$	1.86787	−	3.23525i	0.0984455	−	0.170513i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	0.303609	+	0.525866i	0.0159573	+	0.0276389i
$363$	11.8949			0.624320
$364$		0			0
$365$	10.3638			0.542464
$366$	−1.20904	−	2.09413i	−0.0631977	−	0.109462i
$367$	−4.60138	+	7.96983i	−0.240190	+	0.416022i	−0.960768	−	0.277352i	$-0.910543\pi$
$367$	−4.60138	+	7.96983i	−0.240190	+	0.416022i	0.720578	+	0.693374i	$0.243877\pi$
$368$	−4.08068	+	7.06795i	−0.212720	+	0.368442i
$369$	0.281439	+	0.487467i	0.0146511	+	0.0253765i
$370$	9.69132			0.503828
$371$		0			0
$372$	−13.4654			−0.698148
$373$	9.48498	+	16.4285i	0.491114	+	0.850634i	0.999948	−	0.0102308i	$-0.00325662\pi$
$373$	9.48498	+	16.4285i	0.491114	+	0.850634i	−0.508834	+	0.860865i	$0.669923\pi$
$374$	−1.35892	+	2.35373i	−0.0702683	+	0.121708i
$375$	−3.36483	+	5.82806i	−0.173759	+	0.300960i
$376$	4.79029	+	8.29702i	0.247040	+	0.427886i
$377$	−23.3234			−1.20122
$378$		0			0
$379$	31.0591			1.59540			0.797699	−	0.603056i	$-0.206051\pi$
$379$	31.0591			1.59540			0.797699	+	0.603056i	$0.206051\pi$
$380$	3.25699	+	5.64127i	0.167080	+	0.289391i
$381$	−11.8498	+	20.5244i	−0.607082	+	1.05150i
$382$	−0.183709	+	0.318193i	−0.00939935	+	0.0162802i
$383$	6.98348	+	12.0957i	0.356839	+	0.618064i	0.987431	−	0.158051i	$-0.0505210\pi$
$383$	6.98348	+	12.0957i	0.356839	+	0.618064i	−0.630592	+	0.776115i	$0.717188\pi$
$384$	10.9962			0.561148
$385$		0			0
$386$	7.44696			0.379040
$387$	1.45927	+	2.52753i	0.0741790	+	0.128482i
$388$	−14.4790	+	25.0784i	−0.735062	+	1.27317i
$389$	−0.183570	+	0.317953i	−0.00930739	+	0.0161209i	−0.870642	−	0.491918i	$-0.836296\pi$
$389$	−0.183570	+	0.317953i	−0.00930739	+	0.0161209i	0.861334	+	0.508039i	$0.169629\pi$
$390$	1.81740	+	3.14782i	0.0920275	+	0.159396i
$391$	−14.5892			−0.737806
$392$		0			0
$393$	4.75841			0.240030
$394$	−1.41531	−	2.45138i	−0.0713021	−	0.123499i
$395$	1.17004	−	2.02656i	0.0588709	−	0.101967i
$396$	1.58882	−	2.75192i	0.0798412	−	0.138289i
$397$	10.1266	+	17.5398i	0.508240	+	0.880297i	0.999954	+	0.00954072i	$0.00303695\pi$
$397$	10.1266	+	17.5398i	0.508240	+	0.880297i	−0.491715	+	0.870756i	$0.663630\pi$
$398$	1.68251			0.0843364
$399$		0			0
$400$	22.9255			1.14628
$401$	−13.1327	−	22.7465i	−0.655815	−	1.13590i	−0.981689	−	0.190491i	$-0.938992\pi$
$401$	−13.1327	−	22.7465i	−0.655815	−	1.13590i	0.325874	−	0.945413i	$-0.394341\pi$
$402$	0.184245	−	0.319122i	0.00918932	−	0.0159164i
$403$	−7.12136	+	12.3345i	−0.354740	+	0.614428i
$404$	12.1620	+	21.0651i	0.605080	+	1.04803i
$405$	16.1548			0.802741
$406$		0			0
$407$	16.7980			0.832646
$408$	4.72513	+	8.18417i	0.233929	+	0.405177i
$409$	0.0371520	−	0.0643491i	0.00183705	−	0.00318186i	−0.865105	−	0.501590i	$-0.832749\pi$
$409$	0.0371520	−	0.0643491i	0.00183705	−	0.00318186i	0.866942	+	0.498408i	$0.166082\pi$
$410$	0.245776	−	0.425696i	0.0121380	−	0.0210236i
$411$	1.22644	+	2.12425i	0.0604957	+	0.104782i
$412$	7.87004			0.387729
$413$		0			0
$414$	−0.643580			−0.0316302
$415$	−7.14873	−	12.3820i	−0.350917	−	0.607807i
$416$	4.39167	−	7.60660i	0.215319	−	0.372944i
$417$	13.6338	−	23.6145i	0.667652	−	1.15641i
$418$	−0.213002	−	0.368930i	−0.0104183	−	0.0180449i
$419$	−14.9914			−0.732379			−0.366189	−	0.930540i	$-0.619338\pi$
$419$	−14.9914			−0.732379			−0.366189	+	0.930540i	$0.619338\pi$
$420$		0			0
$421$	14.4311			0.703330			0.351665	−	0.936126i	$-0.385616\pi$
$421$	14.4311			0.703330			0.351665	+	0.936126i	$0.385616\pi$
$422$	3.30873	+	5.73089i	0.161067	+	0.278976i
$423$	4.72080	−	8.17667i	0.229533	−	0.397563i
$424$	1.43592	−	2.48709i	0.0697345	−	0.120784i
$425$	20.4907	+	35.4910i	0.993946	+	1.72156i
$426$	4.14625			0.200886
$427$		0			0
$428$	−9.60835			−0.464437
$429$	3.15010	+	5.45613i	0.152088	+	0.263425i
$430$	1.27436	−	2.20725i	0.0614549	−	0.106443i
$431$	−11.2326	+	19.4554i	−0.541053	+	0.937132i	0.457791	+	0.889060i	$0.348641\pi$
$431$	−11.2326	+	19.4554i	−0.541053	+	0.937132i	−0.998844	+	0.0480716i	$0.984692\pi$
$432$	−10.0928	−	17.4812i	−0.485590	−	0.841066i
$433$	11.9702			0.575250			0.287625	−	0.957743i	$-0.407134\pi$
$433$	11.9702			0.575250			0.287625	+	0.957743i	$0.407134\pi$
$434$		0			0
$435$	38.6699			1.85408
$436$	10.5186	+	18.2187i	0.503748	+	0.872518i
$437$	1.14337	−	1.98038i	0.0546950	−	0.0947345i
$438$	−0.578264	+	1.00158i	−0.0276305	+	0.0478575i
$439$	−3.96053	−	6.85984i	−0.189026	−	0.327402i	0.755900	−	0.654687i	$-0.227200\pi$
$439$	−3.96053	−	6.85984i	−0.189026	−	0.327402i	−0.944926	+	0.327285i	$0.893866\pi$
$440$	−5.65465			−0.269575
$441$		0			0
$442$	4.90536			0.233324
$443$	−15.5065	−	26.8580i	−0.736735	−	1.27606i	−0.953958	−	0.299941i	$-0.903033\pi$
$443$	−15.5065	−	26.8580i	−0.736735	−	1.27606i	0.217223	−	0.976122i	$-0.430300\pi$
$444$	14.3318	−	24.8233i	0.680155	−	1.17806i
$445$	6.82810	−	11.8266i	0.323683	−	0.560636i
$446$	−2.10072	−	3.63855i	−0.0994718	−	0.172290i
$447$	5.37259			0.254115
$448$		0			0
$449$	17.3687			0.819681			0.409840	−	0.912157i	$-0.365584\pi$
$449$	17.3687			0.819681			0.409840	+	0.912157i	$0.365584\pi$
$450$	0.903919	+	1.56563i	0.0426111	+	0.0738046i
$451$	0.426004	−	0.737860i	0.0200597	−	0.0347445i
$452$	−17.8909	+	30.9879i	−0.841517	+	1.45755i
$453$	−10.2303	−	17.7194i	−0.480662	−	0.832531i
$454$	2.76652			0.129839
$455$		0			0
$456$	−1.48126			−0.0693664
$457$	1.54124	+	2.66951i	0.0720963	+	0.124874i	0.899820	−	0.436262i	$-0.143698\pi$
$457$	1.54124	+	2.66951i	0.0720963	+	0.124874i	−0.827724	+	0.561136i	$0.810364\pi$
$458$	−2.81872	+	4.88217i	−0.131710	+	0.228129i
$459$	18.0418	−	31.2492i	0.842117	−	1.45859i
$460$	−7.44791	−	12.9002i	−0.347261	−	0.601473i
$461$	39.9179			1.85916			0.929580	−	0.368620i	$-0.120170\pi$
$461$	39.9179			1.85916			0.929580	+	0.368620i	$0.120170\pi$
$462$		0			0
$463$	25.7081			1.19476			0.597379	−	0.801959i	$-0.296209\pi$
$463$	25.7081			1.19476			0.597379	+	0.801959i	$0.296209\pi$
$464$	−14.5971	−	25.2829i	−0.677653	−	1.17373i
$465$	11.8071	−	20.4505i	0.547542	−	0.948371i
$466$	−1.07734	+	1.86600i	−0.0499066	+	0.0864408i
$467$	−9.62206	−	16.6659i	−0.445256	−	0.771206i	0.552814	−	0.833305i	$-0.313554\pi$
$467$	−9.62206	−	16.6659i	−0.445256	−	0.771206i	−0.998070	+	0.0620988i	$0.980221\pi$
$468$	−5.73522			−0.265111
$469$		0			0
$470$	−8.24518			−0.380322
$471$	6.18353	+	10.7102i	0.284922	+	0.493500i
$472$	4.78222	−	8.28305i	0.220119	−	0.381258i
$473$	2.20884	−	3.82583i	0.101563	−	0.175912i
$474$	0.130568	+	0.226151i	0.00599721	+	0.0103875i
$475$	−6.42355			−0.294733
$476$		0			0
$477$	−2.83018			−0.129585
$478$	−2.53804	−	4.39602i	−0.116087	−	0.201069i
$479$	11.0639	−	19.1633i	0.505525	−	0.875594i	−0.494455	−	0.869203i	$-0.664632\pi$
$479$	11.0639	−	19.1633i	0.505525	−	0.875594i	0.999980	−	0.00639099i	$-0.00203433\pi$
$480$	−7.28134	+	12.6116i	−0.332346	+	0.575640i
$481$	−15.1591	−	26.2563i	−0.691195	−	1.19718i
$482$	3.26555			0.148742
$483$		0			0
$484$	16.3902			0.745011
$485$	−25.3919	−	43.9801i	−1.15299	−	1.99703i
$486$	1.38635	−	2.40124i	0.0628863	−	0.108922i
$487$	2.63128	−	4.55751i	0.119235	−	0.206521i	−0.800230	−	0.599693i	$-0.795289\pi$
$487$	2.63128	−	4.55751i	0.119235	−	0.206521i	0.919465	+	0.393173i	$0.128623\pi$
$488$	−3.39480	−	5.87996i	−0.153675	−	0.266173i
$489$	−17.4741			−0.790204
$490$		0			0
$491$	−15.7852			−0.712375			−0.356188	−	0.934414i	$-0.615924\pi$
$491$	−15.7852			−0.712375			−0.356188	+	0.934414i	$0.615924\pi$
$492$	−0.726917	−	1.25906i	−0.0327720	−	0.0567627i
$493$	26.0936	−	45.1955i	1.17520	−	2.03550i
$494$	−0.384440	+	0.665870i	−0.0172968	+	0.0299589i
$495$	2.78631	+	4.82603i	0.125235	+	0.216914i
$496$	−17.8278			−0.800491
$497$		0			0
$498$	1.59550			0.0714963
$499$	−3.99935	−	6.92707i	−0.179035	−	0.310098i	0.762515	−	0.646971i	$-0.223964\pi$
$499$	−3.99935	−	6.92707i	−0.179035	−	0.310098i	−0.941550	+	0.336872i	$0.890631\pi$
$500$	−4.63648	+	8.03062i	−0.207350	+	0.359140i
$501$	−1.79991	+	3.11753i	−0.0804140	+	0.139281i
$502$	2.10255	+	3.64173i	0.0938416	+	0.162538i
$503$	−3.70541			−0.165216			−0.0826079	−	0.996582i	$-0.526325\pi$
$503$	−3.70541			−0.165216			−0.0826079	+	0.996582i	$0.526325\pi$
$504$		0			0
$505$	−42.6568			−1.89820
$506$	0.487081	+	0.843650i	0.0216534	+	0.0375048i
$507$	−3.40595	+	5.89928i	−0.151264	+	0.261996i
$508$	−16.3281	+	28.2810i	−0.724440	+	1.25477i
$509$	0.473068	+	0.819378i	0.0209684	+	0.0363183i	0.876319	−	0.481731i	$-0.159992\pi$
$509$	0.473068	+	0.819378i	0.0209684	+	0.0363183i	−0.855351	+	0.518049i	$0.826658\pi$
$510$	−8.13303			−0.360137
$511$		0			0
$512$	18.5536			0.819961
$513$	2.82792	+	4.89810i	0.124856	+	0.216256i
$514$	−4.05482	+	7.02315i	−0.178850	+	0.309778i
$515$	−6.90084	+	11.9526i	−0.304087	+	0.526695i
$516$	−3.76909	−	6.52826i	−0.165925	−	0.287391i
$517$	−14.2914			−0.628535
$518$		0			0
$519$	−3.84430			−0.168746
$520$	5.10295	+	8.83857i	0.223779	+	0.387597i
$521$	−3.03375	+	5.25461i	−0.132911	+	0.230209i	−0.924797	−	0.380460i	$-0.875766\pi$
$521$	−3.03375	+	5.25461i	−0.132911	+	0.230209i	0.791887	+	0.610668i	$0.209099\pi$
$522$	1.15108	−	1.99373i	0.0503815	−	0.0872633i
$523$	5.29615	+	9.17319i	0.231584	+	0.401116i	0.958275	−	0.285850i	$-0.0922758\pi$
$523$	5.29615	+	9.17319i	0.231584	+	0.401116i	−0.726690	+	0.686965i	$0.758942\pi$
$524$	6.55673			0.286432
$525$		0			0
$526$	−1.36149			−0.0593637
$527$	−15.9344	−	27.5992i	−0.694112	−	1.20224i
$528$	−3.94302	+	6.82951i	−0.171598	+	0.297216i
$529$	8.88539	−	15.3899i	0.386321	−	0.669128i
$530$	1.23577	+	2.14042i	0.0536786	+	0.0929741i
$531$	−9.42569			−0.409040
$532$		0			0
$533$	−1.53776			−0.0666078
$534$	0.761972	+	1.31977i	0.0329738	+	0.0571122i
$535$	8.42507	−	14.5927i	0.364248	−	0.630896i
$536$	0.517330	−	0.896042i	0.0223453	−	0.0387031i
$537$	3.64402	+	6.31162i	0.157251	+	0.272367i
$538$	−0.974235			−0.0420022
$539$		0			0
$540$	36.8420			1.58543
$541$	−8.09211	−	14.0159i	−0.347907	−	0.602592i	0.637971	−	0.770061i	$-0.279774\pi$
$541$	−8.09211	−	14.0159i	−0.347907	−	0.602592i	−0.985877	+	0.167468i	$0.946441\pi$
$542$	1.10438	−	1.91285i	0.0474374	−	0.0821640i
$543$	−1.57477	+	2.72757i	−0.0675797	+	0.117051i
$544$	9.82658	+	17.0201i	0.421311	+	0.729732i
$545$	−36.8928			−1.58032
$546$		0			0
$547$	−41.6886			−1.78247			−0.891237	−	0.453538i	$-0.850162\pi$
$547$	−41.6886			−1.78247			−0.891237	+	0.453538i	$0.850162\pi$
$548$	1.68994	+	2.92706i	0.0721905	+	0.125038i
$549$	−3.34555	+	5.79466i	−0.142785	+	0.247310i
$550$	1.36823	−	2.36984i	0.0583414	−	0.101050i
$551$	4.08999	+	7.08407i	0.174239	+	0.301791i
$552$	3.38727			0.144172
$553$		0			0
$554$	−3.42517			−0.145521
$555$	25.1336	+	43.5327i	1.06686	+	1.84786i
$556$	18.7864	−	32.5390i	0.796720	−	1.37996i
$557$	−9.18938	+	15.9165i	−0.389366	+	0.674402i	−0.992364	−	0.123340i	$-0.960639\pi$
$557$	−9.18938	+	15.9165i	−0.389366	+	0.674402i	0.602998	+	0.797743i	$0.293973\pi$
$558$	−0.702922	−	1.21750i	−0.0297571	−	0.0515408i
$559$	−7.97335			−0.337237
$560$		0			0
$561$	−14.0970			−0.595176
$562$	−1.56907	−	2.71771i	−0.0661873	−	0.114640i
$563$	3.37933	−	5.85317i	0.142422	−	0.246682i	−0.785986	−	0.618244i	$-0.787844\pi$
$563$	3.37933	−	5.85317i	0.142422	−	0.246682i	0.928408	+	0.371562i	$0.121178\pi$
$564$	−12.1932	+	21.1192i	−0.513425	+	0.889278i
$565$	−31.3753	−	54.3435i	−1.31997	−	2.28625i
$566$	−5.87144			−0.246795
$567$		0			0
$568$	11.6420			0.488487
$569$	−18.5111	−	32.0622i	−0.776027	−	1.34412i	−0.934215	−	0.356710i	$-0.883899\pi$
$569$	−18.5111	−	32.0622i	−0.776027	−	1.34412i	0.158188	−	0.987409i	$-0.449435\pi$
$570$	0.637397	−	1.10400i	0.0266976	−	0.0462417i
$571$	9.51679	−	16.4836i	0.398265	−	0.689815i	−0.595247	−	0.803543i	$-0.702946\pi$
$571$	9.51679	−	16.4836i	0.398265	−	0.689815i	0.993512	+	0.113727i	$0.0362791\pi$
$572$	4.34059	+	7.51813i	0.181489	+	0.314349i
$573$	−1.90573			−0.0796130
$574$		0			0
$575$	14.6890			0.612575
$576$	−3.29137	−	5.70082i	−0.137141	−	0.237534i
$577$	6.73863	−	11.6716i	0.280533	−	0.485897i	−0.690983	−	0.722871i	$-0.742822\pi$
$577$	6.73863	−	11.6716i	0.280533	−	0.485897i	0.971516	+	0.236974i	$0.0761555\pi$
$578$	−3.19587	+	5.53540i	−0.132931	+	0.230242i
$579$	19.3130	+	33.4512i	0.802622	+	1.39018i
$580$	53.2841			2.21250
$581$		0			0
$582$	5.66714			0.234911
$583$	2.14197	+	3.71000i	0.0887114	+	0.153653i
$584$	−1.62367	+	2.81228i	−0.0671880	+	0.116373i
$585$	5.02893	−	8.71036i	0.207921	−	0.360129i
$586$	−0.114680	−	0.198632i	−0.00473740	−	0.00820542i
$587$	−14.4778			−0.597562			−0.298781	−	0.954322i	$-0.596580\pi$
$587$	−14.4778			−0.597562			−0.298781	+	0.954322i	$0.596580\pi$
$588$		0			0
$589$	4.99520			0.205824
$590$	4.11564	+	7.12850i	0.169438	+	0.293476i
$591$	7.34095	−	12.7149i	0.301966	−	0.523021i
$592$	18.9748	−	32.8654i	0.779861	−	1.35076i
$593$	12.4152	+	21.5038i	0.509832	+	0.883055i	0.999935	+	0.0113904i	$0.00362576\pi$
$593$	12.4152	+	21.5038i	0.509832	+	0.883055i	−0.490103	+	0.871664i	$0.663041\pi$
$594$	−2.40941			−0.0988591
$595$		0			0
$596$	7.40302			0.303239
$597$	4.36343	+	7.55768i	0.178583	+	0.309315i
$598$	0.879118	−	1.52268i	0.0359498	−	0.0622669i
$599$	−19.0216	+	32.9464i	−0.777202	+	1.34615i	0.156346	+	0.987702i	$0.450029\pi$
$599$	−19.0216	+	32.9464i	−0.777202	+	1.34615i	−0.933548	+	0.358452i	$0.883305\pi$
$600$	−4.75748	−	8.24019i	−0.194223	−	0.336405i
$601$	16.1254			0.657768			0.328884	−	0.944370i	$-0.393328\pi$
$601$	16.1254			0.657768			0.328884	+	0.944370i	$0.393328\pi$
$602$		0			0
$603$	−1.01965			−0.0415234
$604$	−14.0966	−	24.4160i	−0.573582	−	0.993473i
$605$	−14.3718	+	24.8926i	−0.584296	+	1.01203i
$606$	2.38011	−	4.12248i	0.0966855	−	0.167464i
$607$	−1.02030	−	1.76721i	−0.0414127	−	0.0717289i	0.844576	−	0.535436i	$-0.179853\pi$
$607$	−1.02030	−	1.76721i	−0.0414127	−	0.0717289i	−0.885989	+	0.463707i	$0.846519\pi$
$608$	−3.08049			−0.124930
$609$		0			0
$610$	5.84322			0.236585
$611$	12.8970	+	22.3383i	0.521758	+	0.903712i
$612$	6.41642	−	11.1136i	0.259368	−	0.449239i
$613$	−3.15567	+	5.46579i	−0.127456	+	0.220761i	−0.922690	−	0.385542i	$-0.874015\pi$
$613$	−3.15567	+	5.46579i	−0.127456	+	0.220761i	0.795234	+	0.606303i	$0.207348\pi$
$614$	−2.95200	−	5.11301i	−0.119133	−	0.206344i
$615$	2.54959			0.102809
$616$		0			0
$617$	−36.7747			−1.48049			−0.740246	−	0.672336i	$-0.765291\pi$
$617$	−36.7747			−1.48049			−0.740246	+	0.672336i	$0.765291\pi$
$618$	−0.770089	−	1.33383i	−0.0309775	−	0.0536547i
$619$	−24.2384	+	41.9821i	−0.974224	+	1.68740i	−0.291750	+	0.956495i	$0.594237\pi$
$619$	−24.2384	+	41.9821i	−0.974224	+	1.68740i	−0.682474	+	0.730910i	$0.739096\pi$
$620$	16.2693	−	28.1793i	0.653391	−	1.13171i
$621$	−6.46674	−	11.2007i	−0.259501	−	0.449469i
$622$	0.517700			0.0207579
$623$		0			0
$624$	14.2333			0.569787
$625$	7.92788	+	13.7315i	0.317115	+	0.549260i
$626$	1.39251	−	2.41190i	0.0556559	−	0.0963989i
$627$	1.10480	−	1.91357i	0.0441216	−	0.0764208i
$628$	8.52043	+	14.7578i	0.340002	+	0.588901i
$629$	67.8384			2.70489
$630$		0			0
$631$	41.4306			1.64933			0.824663	−	0.565624i	$-0.191365\pi$
$631$	41.4306			1.64933			0.824663	+	0.565624i	$0.191365\pi$
$632$	0.366615	+	0.634995i	0.0145831	+	0.0252588i
$633$	−17.1618	+	29.7251i	−0.682121	+	1.18147i
$634$	−2.28643	+	3.96022i	−0.0908059	+	0.157280i
$635$	−28.6345	−	49.5964i	−1.13633	−	1.96817i
$636$	7.30997			0.289859
$637$		0			0
$638$	−3.48470			−0.137961
$639$	−5.73655	−	9.93600i	−0.226934	−	0.393062i
$640$	−13.2860	+	23.0120i	−0.525174	+	0.909628i
$641$	6.68332	−	11.5758i	0.263975	−	0.457218i	−0.703320	−	0.710874i	$-0.748300\pi$
$641$	6.68332	−	11.5758i	0.263975	−	0.457218i	0.967295	+	0.253656i	$0.0816330\pi$
$642$	0.940184	+	1.62845i	0.0371061	+	0.0642697i
$643$	−21.2566			−0.838278			−0.419139	−	0.907922i	$-0.637668\pi$
$643$	−21.2566			−0.838278			−0.419139	+	0.907922i	$0.637668\pi$
$644$		0			0
$645$	13.2197			0.520526
$646$	−0.860204	−	1.48992i	−0.0338443	−	0.0586200i
$647$	12.7951	−	22.1617i	0.503026	−	0.871267i	−0.496967	−	0.867769i	$-0.665553\pi$
$647$	12.7951	−	22.1617i	0.503026	−	0.871267i	0.999994	−	0.00349815i	$-0.00111350\pi$
$648$	−2.53095	+	4.38373i	−0.0994251	+	0.172209i
$649$	7.13366	+	12.3559i	0.280021	+	0.485010i
$650$	−4.93894			−0.193721
$651$		0			0
$652$	−24.0779			−0.942963
$653$	−20.9383	−	36.2662i	−0.819379	−	1.41921i	−0.906140	−	0.422977i	$-0.860985\pi$
$653$	−20.9383	−	36.2662i	−0.819379	−	1.41921i	0.0867612	−	0.996229i	$-0.472348\pi$
$654$	2.05850	−	3.56543i	0.0804938	−	0.139419i
$655$	−5.74926	+	9.95802i	−0.224642	+	0.389092i
$656$	−0.962418	−	1.66696i	−0.0375761	−	0.0650837i
$657$	3.20023			0.124853
$658$		0			0
$659$	−16.3252			−0.635940			−0.317970	−	0.948101i	$-0.603001\pi$
$659$	−16.3252			−0.635940			−0.317970	+	0.948101i	$0.603001\pi$
$660$	−7.19665	−	12.4650i	−0.280129	−	0.485198i
$661$	3.89785	−	6.75128i	0.151609	−	0.262594i	−0.780210	−	0.625517i	$-0.784888\pi$
$661$	3.89785	−	6.75128i	0.151609	−	0.262594i	0.931819	+	0.362923i	$0.118221\pi$
$662$	2.22587	−	3.85533i	0.0865111	−	0.149842i
$663$	12.7216	+	22.0345i	0.494067	+	0.855748i
$664$	4.47991			0.173854
$665$		0			0
$666$	2.99259			0.115961
$667$	−9.35277	−	16.1995i	−0.362141	−	0.627246i
$668$	−2.48014	+	4.29572i	−0.0959594	+	0.166206i
$669$	10.8960	−	18.8725i	0.421265	−	0.729653i
$670$	0.445222	+	0.771147i	0.0172004	+	0.0297920i
$671$	10.1281			0.390990
$672$		0			0
$673$	−12.5226			−0.482709			−0.241355	−	0.970437i	$-0.577592\pi$
$673$	−12.5226			−0.482709			−0.241355	+	0.970437i	$0.577592\pi$
$674$	−0.959857	−	1.66252i	−0.0369723	−	0.0640379i
$675$	−18.1653	+	31.4632i	−0.699181	+	1.21102i
$676$	−4.69314	+	8.12875i	−0.180505	+	0.312644i
$677$	−0.856017	−	1.48266i	−0.0328994	−	0.0569834i	0.849107	−	0.528221i	$-0.177141\pi$
$677$	−0.856017	−	1.48266i	−0.0328994	−	0.0569834i	−0.882006	+	0.471238i	$0.843807\pi$
$678$	7.00255			0.268931
$679$		0			0
$680$	−22.8362			−0.875728
$681$	7.17473	+	12.4270i	0.274936	+	0.476204i
$682$	−1.06399	+	1.84288i	−0.0407422	+	0.0705675i
$683$	14.3273	−	24.8156i	0.548218	−	0.949542i	−0.450179	−	0.892939i	$-0.648640\pi$
$683$	14.3273	−	24.8156i	0.548218	−	0.949542i	0.998397	−	0.0566031i	$-0.0180270\pi$
$684$	1.00573	+	1.74197i	0.0384550	+	0.0666060i
$685$	−5.92728			−0.226470
$686$		0			0
$687$	−29.2404			−1.11559
$688$	−4.99017	−	8.64323i	−0.190249	−	0.329520i
$689$	3.86598	−	6.69607i	0.147282	−	0.255100i
$690$	−1.45757	+	2.52458i	−0.0554886	+	0.0961091i
$691$	2.93490	+	5.08339i	0.111649	+	0.193381i	0.916435	−	0.400183i	$-0.131053\pi$
$691$	2.93490	+	5.08339i	0.111649	+	0.193381i	−0.804786	+	0.593565i	$0.797720\pi$
$692$	−5.29714			−0.201367
$693$		0			0
$694$	−5.01244			−0.190270
$695$	32.9456	+	57.0635i	1.24970	+	2.16454i
$696$	−6.05834	+	10.4934i	−0.229641	+	0.397750i
$697$	1.72041	−	2.97983i	0.0651651	−	0.112869i
$698$	−2.60111	−	4.50526i	−0.0984536	−	0.170527i
$699$	−11.1759			−0.422712
$700$		0			0
$701$	31.9494			1.20671			0.603355	−	0.797473i	$-0.293830\pi$
$701$	31.9494			1.20671			0.603355	+	0.797473i	$0.293830\pi$
$702$	2.17433	+	3.76605i	0.0820648	+	0.142140i
$703$	−5.31659	+	9.20861i	−0.200519	+	0.347309i
$704$	−4.98203	+	8.62912i	−0.187767	+	0.325222i
$705$	−21.3831	−	37.0367i	−0.805336	−	1.39488i
$706$	−4.67831			−0.176071
$707$		0			0
$708$	24.3452			0.914950
$709$	18.2140	+	31.5476i	0.684041	+	1.18479i	0.973737	+	0.227676i	$0.0731126\pi$
$709$	18.2140	+	31.5476i	0.684041	+	1.18479i	−0.289696	+	0.957119i	$0.593554\pi$
$710$	−5.00963	+	8.67693i	−0.188008	+	0.325639i
$711$	0.361296	−	0.625784i	0.0135497	−	0.0234687i
$712$	2.13949	+	3.70571i	0.0801809	+	0.138877i
$713$	−11.4228			−0.427786
$714$		0			0
$715$	−15.2242			−0.569352
$716$	5.02117	+	8.69693i	0.187650	+	0.325019i
$717$	13.1644	−	22.8014i	0.491633	−	0.851533i
$718$	4.19134	−	7.25961i	0.156419	−	0.270926i
$719$	−23.3837	−	40.5017i	−0.872065	−	1.51046i	−0.859857	−	0.510535i	$-0.829447\pi$
$719$	−23.3837	−	40.5017i	−0.872065	−	1.51046i	−0.0122077	−	0.999925i	$-0.503886\pi$
$720$	12.5896			0.469185
$721$		0			0
$722$	0.269662			0.0100358
$723$	8.46891	+	14.6686i	0.314962	+	0.545530i
$724$	−2.16991	+	3.75839i	−0.0806439	+	0.139679i
$725$	−26.2722	+	45.5049i	−0.975727	+	1.69001i
$726$	−1.60380	−	2.77786i	−0.0595225	−	0.103096i
$727$	−32.7260			−1.21374			−0.606870	−	0.794801i	$-0.707575\pi$
$727$	−32.7260			−1.21374			−0.606870	+	0.794801i	$0.707575\pi$
$728$		0			0
$729$	28.7207			1.06373
$730$	−1.39735	−	2.42029i	−0.0517184	−	0.0895789i
$731$	8.92038	−	15.4505i	0.329932	−	0.571459i
$732$	8.64109	−	14.9668i	0.319384	−	0.553189i
$733$	21.9360	+	37.9943i	0.810225	+	1.40335i	0.912707	+	0.408616i	$0.133988\pi$
$733$	21.9360	+	37.9943i	0.810225	+	1.40335i	−0.102482	+	0.994735i	$0.532678\pi$
$734$	2.48163			0.0915988
$735$		0			0
$736$	7.04431			0.259657
$737$	0.771704	+	1.33663i	0.0284261	+	0.0492354i
$738$	0.0758933	−	0.131451i	0.00279367	−	0.00483878i
$739$	−9.64628	+	16.7078i	−0.354844	+	0.614608i	−0.987091	−	0.160159i	$-0.948799\pi$
$739$	−9.64628	+	16.7078i	−0.354844	+	0.614608i	0.632247	+	0.774767i	$0.282133\pi$
$740$	34.6321	+	59.9846i	1.27310	+	2.20508i
$741$	−3.98805			−0.146505
$742$		0			0
$743$	−4.09248			−0.150138			−0.0750692	−	0.997178i	$-0.523918\pi$
$743$	−4.09248			−0.150138			−0.0750692	+	0.997178i	$0.523918\pi$
$744$	3.69960	+	6.40790i	0.135634	+	0.234925i
$745$	−6.49133	+	11.2433i	−0.237824	+	0.411923i
$746$	2.55774	−	4.43013i	0.0936453	−	0.162198i
$747$	−2.20746	−	3.82344i	−0.0807669	−	0.139892i
$748$	−19.4246			−0.710233
$749$		0			0
$750$	1.81473			0.0662646
$751$	18.1841	+	31.4957i	0.663546	+	1.14930i	0.979677	+	0.200580i	$0.0642826\pi$
$751$	18.1841	+	31.4957i	0.663546	+	1.14930i	−0.316132	+	0.948715i	$0.602384\pi$
$752$	−16.1434	+	27.9612i	−0.588689	+	1.01964i
$753$	−10.9056	+	18.8890i	−0.397421	+	0.688354i
$754$	3.14471	+	5.44680i	0.114524	+	0.198361i
$755$	49.4423			1.79939
$756$		0			0
$757$	−17.7179			−0.643968			−0.321984	−	0.946745i	$-0.604350\pi$
$757$	−17.7179			−0.643968			−0.321984	+	0.946745i	$0.604350\pi$
$758$	−4.18772	−	7.25334i	−0.152105	−	0.263453i
$759$	−2.52641	+	4.37586i	−0.0917027	+	0.158834i
$760$	1.78971	−	3.09986i	0.0649195	−	0.112444i
$761$	−16.7217	−	28.9629i	−0.606162	−	1.04990i	−0.991867	−	0.127281i	$-0.959375\pi$
$761$	−16.7217	−	28.9629i	−0.606162	−	1.04990i	0.385705	−	0.922622i	$-0.373958\pi$
$762$	6.39085			0.231516
$763$		0			0
$764$	−2.62595			−0.0950034
$765$	11.2525	+	19.4898i	0.406834	+	0.704657i
$766$	1.88318	−	3.26176i	0.0680420	−	0.117852i
$767$	12.8753	−	22.3007i	0.464901	−	0.805231i
$768$	7.33928	+	12.7120i	0.264833	+	0.458705i
$769$	−39.2814			−1.41652			−0.708262	−	0.705949i	$-0.750521\pi$
$769$	−39.2814			−1.41652			−0.708262	+	0.705949i	$0.750521\pi$
$770$		0			0
$771$	−42.0633			−1.51487
$772$	26.6119	+	46.0931i	0.957782	+	1.65893i
$773$	−22.7743	+	39.4463i	−0.819136	+	1.41879i	0.0871829	+	0.996192i	$0.472214\pi$
$773$	−22.7743	+	39.4463i	−0.819136	+	1.41879i	−0.906319	+	0.422594i	$0.861120\pi$
$774$	0.393510	−	0.681579i	0.0141444	−	0.0244988i
$775$	16.0435	+	27.7881i	0.576298	+	0.998178i
$776$	15.9124			0.571222
$777$		0			0
$778$	0.0990038			0.00354946
$779$	0.269662	+	0.467068i	0.00966163	+	0.0167344i
$780$	−12.9890	+	22.4976i	−0.465081	+	0.805544i
$781$	−8.68320	+	15.0397i	−0.310709	+	0.538164i
$782$	1.96707	+	3.40706i	0.0703422	+	0.121836i
$783$	46.2646			1.65336
$784$		0			0
$785$	−29.8845			−1.06663
$786$	−0.641581	−	1.11125i	−0.0228844	−	0.0396370i
$787$	−3.89354	+	6.74382i	−0.138790	+	0.240391i	−0.927039	−	0.374965i	$-0.877655\pi$
$787$	−3.89354	+	6.74382i	−0.138790	+	0.240391i	0.788249	+	0.615356i	$0.210988\pi$
$788$	10.1153	−	17.5201i	0.360341	−	0.624129i
$789$	−3.53090	−	6.11569i	−0.125703	−	0.217724i
$790$	−0.631027			−0.0224509
$791$		0			0
$792$	−1.74611			−0.0620452
$793$	−9.13991	−	15.8308i	−0.324568	−	0.562168i
$794$	2.73076	−	4.72981i	0.0969109	−	0.167855i
$795$	−6.40974	+	11.1020i	−0.227330	+	0.393747i
$796$	6.01247	+	10.4139i	0.213106	+	0.369111i
$797$	−23.1468			−0.819903			−0.409951	−	0.912107i	$-0.634454\pi$
$797$	−23.1468			−0.819903			−0.409951	+	0.912107i	$0.634454\pi$
$798$		0			0
$799$	−57.7155			−2.04183
$800$	−9.89385	−	17.1366i	−0.349800	−	0.605872i
$801$	2.10846	−	3.65195i	0.0744986	−	0.129035i
$802$	−3.54138	+	6.13385i	−0.125050	+	0.216594i
$803$	−2.42204	−	4.19509i	−0.0854718	−	0.148042i
$804$	2.63362			0.0928805
$805$		0			0
$806$	3.84071			0.135283
$807$	−2.52659	−	4.37619i	−0.0889403	−	0.154049i
$808$	6.68297	−	11.5752i	0.235106	−	0.407216i
$809$	−4.09046	+	7.08488i	−0.143813	+	0.249091i	−0.928929	−	0.370257i	$-0.879270\pi$
$809$	−4.09046	+	7.08488i	−0.143813	+	0.249091i	0.785117	+	0.619348i	$0.212603\pi$
$810$	−2.17817	−	3.77270i	−0.0765331	−	0.132559i
$811$	11.5745			0.406437			0.203218	−	0.979133i	$-0.434860\pi$
$811$	11.5745			0.406437			0.203218	+	0.979133i	$0.434860\pi$
$812$		0			0
$813$	11.4565			0.401797
$814$	−2.26489	−	3.92290i	−0.0793843	−	0.137498i
$815$	21.1127	−	36.5683i	0.739545	−	1.28093i
$816$	−15.9238	+	27.5809i	−0.557445	+	0.965523i
$817$	1.39821	+	2.42176i	0.0489170	+	0.0847268i
$818$	−0.0200369			−0.000700574
$819$		0			0
$820$	3.51314			0.122684
$821$	−11.6832	−	20.2359i	−0.407746	−	0.706237i	0.586890	−	0.809666i	$-0.300352\pi$
$821$	−11.6832	−	20.2359i	−0.407746	−	0.706237i	−0.994637	+	0.103429i	$0.967019\pi$
$822$	0.330723	−	0.572830i	0.0115353	−	0.0199797i
$823$	5.48027	−	9.49210i	0.191030	−	0.330874i	−0.754562	−	0.656229i	$-0.772151\pi$
$823$	5.48027	−	9.49210i	0.191030	−	0.330874i	0.945592	+	0.325355i	$0.105484\pi$
$824$	−2.16228	−	3.74519i	−0.0753267	−	0.130470i
$825$	14.1935			0.494154
$826$		0			0
$827$	−26.1767			−0.910254			−0.455127	−	0.890427i	$-0.650406\pi$
$827$	−26.1767			−0.910254			−0.455127	+	0.890427i	$0.650406\pi$
$828$	−2.29985	−	3.98345i	−0.0799252	−	0.138435i
$829$	−15.7549	+	27.2883i	−0.547190	+	0.947760i	0.451276	+	0.892384i	$0.350969\pi$
$829$	−15.7549	+	27.2883i	−0.547190	+	0.947760i	−0.998466	+	0.0553758i	$0.982364\pi$
$830$	−1.92774	+	3.33894i	−0.0669128	+	0.115896i
$831$	−8.88287	−	15.3856i	−0.308143	−	0.533720i
$832$	17.9838			0.623476
$833$		0			0
$834$	−7.35304			−0.254615
$835$	−4.34941	−	7.53340i	−0.150518	−	0.260704i
$836$	1.52233	−	2.63676i	0.0526510	−	0.0911942i
$837$	14.1260	−	24.4670i	0.488267	−	0.845703i
$838$	2.02130	+	3.50100i	0.0698248	+	0.120940i
$839$	−12.9797			−0.448109			−0.224054	−	0.974577i	$-0.571929\pi$
$839$	−12.9797			−0.448109			−0.224054	+	0.974577i	$0.571929\pi$
$840$		0			0
$841$	37.9120			1.30731
$842$	−1.94576	−	3.37016i	−0.0670553	−	0.116143i
$843$	8.13850	−	14.0963i	0.280305	−	0.485502i
$844$	−23.6477	+	40.9589i	−0.813986	+	1.40986i
$845$	−8.23035	−	14.2554i	−0.283133	−	0.490400i
$846$	−2.54604			−0.0875346
$847$		0			0
$848$	9.67819			0.332350
$849$	−15.2271	−	26.3740i	−0.522591	−	0.905155i
$850$	5.52556	−	9.57055i	0.189525	−	0.328267i
$851$	12.1577	−	21.0578i	0.416761	−	0.721851i
$852$	14.8167	+	25.6633i	0.507612	+	0.879210i
$853$	−27.5739			−0.944114			−0.472057	−	0.881568i	$-0.656488\pi$
$853$	−27.5739			−0.944114			−0.472057	+	0.881568i	$0.656488\pi$
$854$		0			0
$855$	−3.52749			−0.120638
$856$	2.63988	+	4.57241i	0.0902293	+	0.156282i
$857$	8.90547	−	15.4247i	0.304205	−	0.526899i	−0.672879	−	0.739753i	$-0.734943\pi$
$857$	8.90547	−	15.4247i	0.304205	−	0.526899i	0.977084	+	0.212854i	$0.0682759\pi$
$858$	0.849461	−	1.47131i	0.0290001	−	0.0502297i
$859$	−4.43672	−	7.68462i	−0.151379	−	0.262196i	0.780356	−	0.625336i	$-0.215038\pi$
$859$	−4.43672	−	7.68462i	−0.151379	−	0.262196i	−0.931735	+	0.363140i	$0.881705\pi$
$860$	18.2157			0.621152
$861$		0			0
$862$	6.05798			0.206336
$863$	25.0784	+	43.4371i	0.853680	+	1.47862i	0.877865	+	0.478909i	$0.158968\pi$
$863$	25.0784	+	43.4371i	0.853680	+	1.47862i	−0.0241850	+	0.999707i	$0.507699\pi$
$864$	−8.71138	+	15.0886i	−0.296367	+	0.513323i
$865$	4.64480	−	8.04503i	0.157928	−	0.273539i
$866$	−1.61395	−	2.79544i	−0.0548442	−	0.0949930i
$867$	−33.1528			−1.12593
$868$		0			0
$869$	−1.09376			−0.0371033
$870$	−5.21389	−	9.03073i	−0.176768	−	0.306170i
$871$	1.39282	−	2.41244i	0.0471941	−	0.0817425i
$872$	5.77993	−	10.0111i	0.195733	−	0.339020i
$873$	−7.84079	−	13.5806i	−0.265371	−	0.459635i
$874$	−0.616648			−0.0208584
$875$		0			0
$876$	−8.26576			−0.279274
$877$	−5.52611	−	9.57150i	−0.186603	−	0.323207i	0.757512	−	0.652821i	$-0.226415\pi$
$877$	−5.52611	−	9.57150i	−0.186603	−	0.323207i	−0.944116	+	0.329614i	$0.893081\pi$
$878$	−1.06800	+	1.84984i	−0.0360434	+	0.0624289i
$879$	0.594826	−	1.03027i	0.0200630	−	0.0347501i
$880$	−9.52816	−	16.5033i	−0.321194	−	0.556325i
$881$	−24.5640			−0.827581			−0.413791	−	0.910372i	$-0.635795\pi$
$881$	−24.5640			−0.827581			−0.413791	+	0.910372i	$0.635795\pi$
$882$		0			0
$883$	−37.3221			−1.25599			−0.627994	−	0.778219i	$-0.716124\pi$
$883$	−37.3221			−1.25599			−0.627994	+	0.778219i	$0.716124\pi$
$884$	17.5294	+	30.3618i	0.589578	+	1.02118i
$885$	−21.3471	+	36.9743i	−0.717575	+	1.24288i
$886$	−4.18150	+	7.24257i	−0.140480	+	0.243319i
$887$	−7.86913	−	13.6297i	−0.264220	−	0.457642i	0.703139	−	0.711052i	$-0.251781\pi$
$887$	−7.86913	−	13.6297i	−0.264220	−	0.457642i	−0.967359	+	0.253410i	$0.918448\pi$
$888$	−15.7505			−0.528553
$889$		0			0
$890$	−3.68255			−0.123439
$891$	−3.77543	−	6.53924i	−0.126482	−	0.219073i
$892$	15.0139	−	26.0048i	0.502703	−	0.870707i
$893$	4.52325	−	7.83450i	0.151365	−	0.262171i
$894$	−0.724391	−	1.25468i	−0.0242273	−	0.0419628i
$895$	−17.6113			−0.588679
$896$		0			0
$897$	9.11966			0.304497
$898$	−2.34184	−	4.05618i	−0.0781482	−	0.135357i
$899$	20.4303	−	35.3863i	0.681389	−	1.18020i
$900$	−6.46034	+	11.1896i	−0.215345	+	0.372988i
$901$	8.65031	+	14.9828i	0.288184	+	0.499149i
$902$	−0.229754			−0.00764996
$903$		0			0
$904$	19.6620			0.653949
$905$	−3.80536	−	6.59108i	−0.126494	−	0.219095i
$906$	−2.75872	+	4.77825i	−0.0916524	+	0.158747i
$907$	9.16532	−	15.8748i	0.304329	−	0.527114i	−0.672782	−	0.739840i	$-0.734901\pi$
$907$	9.16532	−	15.8748i	0.304329	−	0.527114i	0.977112	+	0.212726i	$0.0682343\pi$
$908$	9.88623	+	17.1235i	0.328086	+	0.568262i
$909$	−13.1720			−0.436889
$910$		0			0
$911$	50.2669			1.66542			0.832708	−	0.553712i	$-0.186789\pi$
$911$	50.2669			1.66542			0.832708	+	0.553712i	$0.186789\pi$
$912$	−2.49595	−	4.32310i	−0.0826490	−	0.143152i
$913$	−3.34135	+	5.78739i	−0.110583	+	0.191535i
$914$	0.415614	−	0.719864i	0.0137473	−	0.0238110i
$915$	15.1539	+	26.2473i	0.500971	+	0.867708i
$916$	−40.2910			−1.33125
$917$		0			0
$918$	−9.73034			−0.321149
$919$	20.7134	+	35.8767i	0.683273	+	1.18346i	0.973976	+	0.226650i	$0.0727774\pi$
$919$	20.7134	+	35.8767i	0.683273	+	1.18346i	−0.290703	+	0.956813i	$0.593889\pi$
$920$	−4.09261	+	7.08861i	−0.134929	+	0.233704i
$921$	15.3115	−	26.5203i	0.504530	−	0.873872i
$922$	−5.38216	−	9.32217i	−0.177252	−	0.307009i
$923$	31.3441			1.03170
$924$		0			0
$925$	−68.3028			−2.24578
$926$	−3.46625	−	6.00371i	−0.113908	−	0.197294i
$927$	−2.13092	+	3.69086i	−0.0699885	+	0.121224i
$928$	−12.5992	+	21.8224i	−0.413588	+	0.716356i
$929$	23.7871	+	41.2005i	0.780429	+	1.35174i	0.931692	+	0.363250i	$0.118333\pi$
$929$	23.7871	+	41.2005i	0.780429	+	1.35174i	−0.151263	+	0.988494i	$0.548334\pi$
$930$	−6.36785			−0.208810
$931$		0			0
$932$	−15.3995			−0.504428
$933$	1.34261	+	2.32547i	0.0439551	+	0.0761324i
$934$	−2.59470	+	4.49415i	−0.0849012	+	0.147053i
$935$	17.0324	−	29.5010i	0.557020	−	0.964787i
$936$	1.57575	+	2.72927i	0.0515049	+	0.0892090i
$937$	−23.8222			−0.778239			−0.389119	−	0.921187i	$-0.627221\pi$
$937$	−23.8222			−0.778239			−0.389119	+	0.921187i	$0.627221\pi$
$938$		0			0
$939$	14.4454			0.471408
$940$	−29.4643	−	51.0337i	−0.961020	−	1.66454i
$941$	−11.0393	+	19.1206i	−0.359871	+	0.623315i	−0.987939	−	0.154843i	$-0.950513\pi$
$941$	−11.0393	+	19.1206i	−0.359871	+	0.623315i	0.628068	+	0.778159i	$0.283846\pi$
$942$	1.66746	−	2.88813i	0.0543288	−	0.0941003i
$943$	−0.616648	−	1.06807i	−0.0200808	−	0.0347810i
$944$	32.2324			1.04908
$945$		0			0
$946$	−1.19128			−0.0387319
$947$	−7.83264	−	13.5665i	−0.254527	−	0.440853i	0.710240	−	0.703959i	$-0.248586\pi$
$947$	−7.83264	−	13.5665i	−0.254527	−	0.440853i	−0.964767	+	0.263106i	$0.915253\pi$
$948$	−0.933178	+	1.61631i	−0.0303082	+	0.0524954i
$949$	−4.37146	+	7.57159i	−0.141904	+	0.245784i
$950$	0.866092	+	1.50012i	0.0280997	+	0.0486702i
$951$	−23.7187			−0.769130
$952$		0			0
$953$	−9.89901			−0.320660			−0.160330	−	0.987063i	$-0.551256\pi$
$953$	−9.89901			−0.320660			−0.160330	+	0.987063i	$0.551256\pi$
$954$	0.381596	+	0.660944i	0.0123546	+	0.0213988i
$955$	2.30256	−	3.98815i	0.0745091	−	0.129054i
$956$	18.1395	−	31.4185i	0.586673	−	1.01615i
$957$	−9.03726	−	15.6530i	−0.292133	−	0.505989i
$958$	−5.96704			−0.192786
$959$		0			0
$960$	−29.8169			−0.962337
$961$	3.02398	+	5.23769i	0.0975478	+	0.168958i
$962$	−4.08782	+	7.08032i	−0.131797	+	0.228279i
$963$	2.60159	−	4.50608i	0.0838350	−	0.145206i
$964$	11.6695	+	20.2122i	0.375849	+	0.650990i
$965$	−93.3384			−3.00467
$966$		0			0
$967$	16.7558			0.538830			0.269415	−	0.963024i	$-0.413170\pi$
$967$	16.7558			0.538830			0.269415	+	0.963024i	$0.413170\pi$
$968$	−4.50320	−	7.79977i	−0.144738	−	0.250694i
$969$	4.46172	−	7.72793i	0.143331	−	0.248257i
$970$	−6.84722	+	11.8597i	−0.219851	+	0.380793i
$971$	21.8092	+	37.7747i	0.699891	+	1.21225i	0.968504	+	0.248999i	$0.0801015\pi$
$971$	21.8092	+	37.7747i	0.699891	+	1.21225i	−0.268613	+	0.963248i	$0.586565\pi$
$972$	19.8167			0.635620
$973$		0			0
$974$	−1.41911			−0.0454712
$975$	−12.8087	−	22.1853i	−0.410207	−	0.710499i
$976$	11.4405	−	19.8156i	0.366203	−	0.634282i
$977$	28.2938	−	49.0062i	0.905198	−	1.56785i	0.0845456	−	0.996420i	$-0.473056\pi$
$977$	28.2938	−	49.0062i	0.905198	−	1.56785i	0.820652	−	0.571428i	$-0.193611\pi$
$978$	2.35604	+	4.08078i	0.0753379	+	0.130489i
$979$	−6.38298			−0.204001
$980$		0			0
$981$	−11.3922			−0.363724
$982$	2.12833	+	3.68637i	0.0679177	+	0.117637i
$983$	2.77708	−	4.81004i	0.0885750	−	0.153416i	−0.818334	−	0.574743i	$-0.805102\pi$
$983$	2.77708	−	4.81004i	0.0885750	−	0.153416i	0.906909	+	0.421327i	$0.138435\pi$
$984$	−0.399439	+	0.691849i	−0.0127337	+	0.0220554i
$985$	17.7391	+	30.7251i	0.565215	+	0.978982i
$986$	−14.0729			−0.448172
$987$		0			0
$988$	−5.49522			−0.174826
$989$	−3.19734	−	5.53796i	−0.101670	−	0.176097i
$990$	0.751361	−	1.30140i	0.0238798	−	0.0413611i
$991$	6.46424	−	11.1964i	0.205343	−	0.355665i	−0.744899	−	0.667178i	$-0.767502\pi$
$991$	6.46424	−	11.1964i	0.205343	−	0.355665i	0.950242	+	0.311512i	$0.100836\pi$
$992$	7.69384	+	13.3261i	0.244280	+	0.423105i
$993$	23.0904			0.732753
$994$		0			0
$995$	−21.0881			−0.668539
$996$	5.70157	+	9.87540i	0.180661	+	0.312914i
$997$	6.11264	−	10.5874i	0.193589	−	0.335306i	−0.752848	−	0.658195i	$-0.771320\pi$
$997$	6.11264	−	10.5874i	0.193589	−	0.335306i	0.946437	+	0.322888i	$0.104654\pi$
$998$	−1.07847	+	1.86797i	−0.0341384	+	0.0591294i
$999$	30.0698	+	52.0824i	0.951366	+	1.64781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.f.p.704.4		14
7.2	even	3	inner	931.2.f.p.324.4		14
7.3	odd	6		931.2.a.n.1.4		7
7.4	even	3		931.2.a.o.1.4		7
7.5	odd	6		133.2.f.d.58.4	yes	14
7.6	odd	2		133.2.f.d.39.4	✓	14
21.5	even	6		1197.2.j.l.856.4		14
21.11	odd	6		8379.2.a.ck.1.4		7
21.17	even	6		8379.2.a.cl.1.4		7
21.20	even	2		1197.2.j.l.172.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.d.39.4	✓	14	7.6	odd	2
133.2.f.d.58.4	yes	14	7.5	odd	6
931.2.a.n.1.4		7	7.3	odd	6
931.2.a.o.1.4		7	7.4	even	3
931.2.f.p.324.4		14	7.2	even	3	inner
931.2.f.p.704.4		14	1.1	even	1	trivial
1197.2.j.l.172.4		14	21.20	even	2
1197.2.j.l.856.4		14	21.5	even	6
8379.2.a.ck.1.4		7	21.11	odd	6
8379.2.a.cl.1.4		7	21.17	even	6

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.134831 - 0.233534i) q^{2} +(0.699343 - 1.21130i) q^{3} +(0.963641 - 1.66908i) q^{4} +(1.68994 + 2.92706i) q^{5} -0.377172 q^{6} -1.05904 q^{8} +(0.521837 + 0.903849i) q^{9} +O(q^{10})\)	\(q+(-0.134831 - 0.233534i) q^{2} +(0.699343 - 1.21130i) q^{3} +(0.963641 - 1.66908i) q^{4} +(1.68994 + 2.92706i) q^{5} -0.377172 q^{6} -1.05904 q^{8} +(0.521837 + 0.903849i) q^{9} +(0.455711 - 0.789315i) q^{10} +(0.789885 - 1.36812i) q^{11} +(-1.34783 - 2.33451i) q^{12} -2.85128 q^{13} +4.72739 q^{15} +(-1.78449 - 3.09083i) q^{16} +(3.18994 - 5.52513i) q^{17} +(0.140719 - 0.243733i) q^{18} +(0.500000 + 0.866025i) q^{19} +6.51397 q^{20} -0.426004 q^{22} +(-1.14337 - 1.98038i) q^{23} +(-0.740631 + 1.28281i) q^{24} +(-3.21177 + 5.56296i) q^{25} +(0.384440 + 0.665870i) q^{26} +5.65584 q^{27} +8.17998 q^{29} +(-0.637397 - 1.10400i) q^{30} +(2.49760 - 4.32597i) q^{31} +(-1.54025 + 2.66778i) q^{32} +(-1.10480 - 1.91357i) q^{33} -1.72041 q^{34} +2.01146 q^{36} +(5.31659 + 9.20861i) q^{37} +(0.134831 - 0.233534i) q^{38} +(-1.99402 + 3.45375i) q^{39} +(-1.78971 - 3.09986i) q^{40} +0.539323 q^{41} +2.79641 q^{43} +(-1.52233 - 2.63676i) q^{44} +(-1.76374 + 3.05490i) q^{45} +(-0.308324 + 0.534033i) q^{46} +(-4.52325 - 7.83450i) q^{47} -4.99189 q^{48} +1.73218 q^{50} +(-4.46172 - 7.72793i) q^{51} +(-2.74761 + 4.75900i) q^{52} +(-1.35587 + 2.34844i) q^{53} +(-0.762581 - 1.32083i) q^{54} +5.33943 q^{55} +1.39869 q^{57} +(-1.10291 - 1.91030i) q^{58} +(-4.51563 + 7.82130i) q^{59} +(4.55550 - 7.89036i) q^{60} +(3.20555 + 5.55217i) q^{61} -1.34701 q^{62} -6.30728 q^{64} +(-4.81848 - 8.34585i) q^{65} +(-0.297923 + 0.516017i) q^{66} +(-0.488491 + 0.846091i) q^{67} +(-6.14791 - 10.6485i) q^{68} -3.19845 q^{69} -10.9930 q^{71} +(-0.552645 - 0.957210i) q^{72} +(1.53316 - 2.65551i) q^{73} +(1.43368 - 2.48321i) q^{74} +(4.49227 + 7.78083i) q^{75} +1.92728 q^{76} +1.07542 q^{78} +(-0.346177 - 0.599597i) q^{79} +(6.03136 - 10.4466i) q^{80} +(2.38986 - 4.13936i) q^{81} +(-0.0727174 - 0.125950i) q^{82} -4.23017 q^{83} +21.5632 q^{85} +(-0.377042 - 0.653057i) q^{86} +(5.72061 - 9.90839i) q^{87} +(-0.836518 + 1.44889i) q^{88} +(-2.02022 - 3.49913i) q^{89} +0.951228 q^{90} -4.40721 q^{92} +(-3.49336 - 6.05068i) q^{93} +(-1.21975 + 2.11266i) q^{94} +(-1.68994 + 2.92706i) q^{95} +(2.15432 + 3.73140i) q^{96} -15.0254 q^{97} +1.64877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 2 q^{3} - 10 q^{4} - 2 q^{5} + 8 q^{6} + 24 q^{8} - 15 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 - 2 * q^5 + 8 * q^6 + 24 * q^8 - 15 * q^9	\( 14 q - 2 q^{2} - 2 q^{3} - 10 q^{4} - 2 q^{5} + 8 q^{6} + 24 q^{8} - 15 q^{9} - 7 q^{11} - 22 q^{12} - 12 q^{13} + 4 q^{15} - 24 q^{16} + 19 q^{17} + 12 q^{18} + 7 q^{19} + 16 q^{20} - 12 q^{22} + q^{23} + 20 q^{24} + 3 q^{25} + 12 q^{26} + 28 q^{27} + 48 q^{29} + 20 q^{30} - 26 q^{32} - 14 q^{33} - 12 q^{34} + 92 q^{36} - 8 q^{37} + 2 q^{38} - 16 q^{39} - 10 q^{40} + 8 q^{41} + 8 q^{43} - 26 q^{44} + 14 q^{45} + 16 q^{46} + 5 q^{47} + 56 q^{48} + 32 q^{50} + 4 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{54} + 60 q^{55} - 4 q^{57} - 16 q^{59} + 44 q^{60} + 5 q^{61} - 48 q^{62} + 64 q^{64} - 26 q^{65} + 68 q^{66} + 4 q^{67} + 22 q^{68} + 72 q^{69} + 24 q^{71} + 3 q^{73} + 4 q^{74} + 18 q^{75} - 20 q^{76} - 28 q^{78} + 20 q^{79} - 4 q^{80} - 27 q^{81} - 48 q^{82} + 22 q^{83} + 52 q^{85} - 36 q^{86} - 16 q^{87} + 32 q^{88} - 10 q^{89} - 64 q^{90} - 60 q^{92} + 4 q^{93} + 16 q^{94} + 2 q^{95} - 12 q^{96} + 8 q^{97} + 30 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 - 2 * q^5 + 8 * q^6 + 24 * q^8 - 15 * q^9 - 7 * q^11 - 22 * q^12 - 12 * q^13 + 4 * q^15 - 24 * q^16 + 19 * q^17 + 12 * q^18 + 7 * q^19 + 16 * q^20 - 12 * q^22 + q^23 + 20 * q^24 + 3 * q^25 + 12 * q^26 + 28 * q^27 + 48 * q^29 + 20 * q^30 - 26 * q^32 - 14 * q^33 - 12 * q^34 + 92 * q^36 - 8 * q^37 + 2 * q^38 - 16 * q^39 - 10 * q^40 + 8 * q^41 + 8 * q^43 - 26 * q^44 + 14 * q^45 + 16 * q^46 + 5 * q^47 + 56 * q^48 + 32 * q^50 + 4 * q^51 + 42 * q^52 - 20 * q^53 - 24 * q^54 + 60 * q^55 - 4 * q^57 - 16 * q^59 + 44 * q^60 + 5 * q^61 - 48 * q^62 + 64 * q^64 - 26 * q^65 + 68 * q^66 + 4 * q^67 + 22 * q^68 + 72 * q^69 + 24 * q^71 + 3 * q^73 + 4 * q^74 + 18 * q^75 - 20 * q^76 - 28 * q^78 + 20 * q^79 - 4 * q^80 - 27 * q^81 - 48 * q^82 + 22 * q^83 + 52 * q^85 - 36 * q^86 - 16 * q^87 + 32 * q^88 - 10 * q^89 - 64 * q^90 - 60 * q^92 + 4 * q^93 + 16 * q^94 + 2 * q^95 - 12 * q^96 + 8 * q^97 + 30 * q^99

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