LMFDB - Embedded newform 187.2.e.b.89.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(89,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("187.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.8
Character	$\chi$	$=$	187.89
Dual form			187.2.e.b.166.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.357045i q^{2} +(-2.24825 + 2.24825i) q^{3} +1.87252 q^{4} +(-2.10601 + 2.10601i) q^{5} +(-0.802728 - 0.802728i) q^{6} +(-1.27454 - 1.27454i) q^{7} +1.38266i q^{8} -7.10929i q^{9} +O(q^{10})$	\(q+0.357045i q^{2} +(-2.24825 + 2.24825i) q^{3} +1.87252 q^{4} +(-2.10601 + 2.10601i) q^{5} +(-0.802728 - 0.802728i) q^{6} +(-1.27454 - 1.27454i) q^{7} +1.38266i q^{8} -7.10929i q^{9} +(-0.751939 - 0.751939i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-4.20990 + 4.20990i) q^{12} -2.60982 q^{13} +(0.455067 - 0.455067i) q^{14} -9.46967i q^{15} +3.25136 q^{16} +(-4.11644 + 0.234279i) q^{17} +2.53834 q^{18} +5.05502i q^{19} +(-3.94353 + 3.94353i) q^{20} +5.73097 q^{21} +(-0.252469 + 0.252469i) q^{22} +(2.99837 + 2.99837i) q^{23} +(-3.10858 - 3.10858i) q^{24} -3.87051i q^{25} -0.931823i q^{26} +(9.23872 + 9.23872i) q^{27} +(-2.38660 - 2.38660i) q^{28} +(-6.06214 + 6.06214i) q^{29} +3.38110 q^{30} +(3.84932 - 3.84932i) q^{31} +3.92621i q^{32} -3.17951 q^{33} +(-0.0836481 - 1.46976i) q^{34} +5.36836 q^{35} -13.3123i q^{36} +(3.72224 - 3.72224i) q^{37} -1.80487 q^{38} +(5.86753 - 5.86753i) q^{39} +(-2.91190 - 2.91190i) q^{40} +(4.45063 + 4.45063i) q^{41} +2.04621i q^{42} +10.7465i q^{43} +(1.32407 + 1.32407i) q^{44} +(14.9722 + 14.9722i) q^{45} +(-1.07055 + 1.07055i) q^{46} +5.74772 q^{47} +(-7.30989 + 7.30989i) q^{48} -3.75111i q^{49} +1.38195 q^{50} +(8.72809 - 9.78153i) q^{51} -4.88693 q^{52} -1.56064i q^{53} +(-3.29864 + 3.29864i) q^{54} -2.97834 q^{55} +(1.76226 - 1.76226i) q^{56} +(-11.3650 - 11.3650i) q^{57} +(-2.16446 - 2.16446i) q^{58} +3.86779i q^{59} -17.7321i q^{60} +(-4.92720 - 4.92720i) q^{61} +(1.37438 + 1.37438i) q^{62} +(-9.06105 + 9.06105i) q^{63} +5.10089 q^{64} +(5.49629 - 5.49629i) q^{65} -1.13523i q^{66} -6.00442 q^{67} +(-7.70812 + 0.438692i) q^{68} -13.4822 q^{69} +1.91675i q^{70} +(-1.40417 + 1.40417i) q^{71} +9.82975 q^{72} +(-2.85622 + 2.85622i) q^{73} +(1.32901 + 1.32901i) q^{74} +(8.70190 + 8.70190i) q^{75} +9.46562i q^{76} -1.80247i q^{77} +(2.09497 + 2.09497i) q^{78} +(6.86495 + 6.86495i) q^{79} +(-6.84739 + 6.84739i) q^{80} -20.2141 q^{81} +(-1.58908 + 1.58908i) q^{82} -6.73786i q^{83} +10.7313 q^{84} +(8.17586 - 9.16265i) q^{85} -3.83699 q^{86} -27.2584i q^{87} +(-0.977691 + 0.977691i) q^{88} -3.09252 q^{89} +(-5.34575 + 5.34575i) q^{90} +(3.32631 + 3.32631i) q^{91} +(5.61451 + 5.61451i) q^{92} +17.3085i q^{93} +2.05220i q^{94} +(-10.6459 - 10.6459i) q^{95} +(-8.82712 - 8.82712i) q^{96} +(-3.74500 + 3.74500i) q^{97} +1.33931 q^{98} +(5.02703 - 5.02703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			0.357045i			0.252469i	0.992000	+	0.126234i	$0.0402892\pi$
$2$			0.357045i			0.252469i	−0.992000	+	0.126234i	$0.959711\pi$
$3$	−2.24825	+	2.24825i	−1.29803	+	1.29803i	−0.368338	+	0.929692i	$0.620073\pi$
$3$	−2.24825	+	2.24825i	−1.29803	+	1.29803i	−0.929692	+	0.368338i	$0.879927\pi$
$4$	1.87252			0.936259
$5$	−2.10601	+	2.10601i	−0.941834	+	0.941834i	−0.998399	−	0.0565648i	$-0.981985\pi$
$5$	−2.10601	+	2.10601i	−0.941834	+	0.941834i	0.0565648	+	0.998399i	$0.481985\pi$
$6$	−0.802728	−	0.802728i	−0.327712	−	0.327712i
$7$	−1.27454	−	1.27454i	−0.481730	−	0.481730i	0.423954	−	0.905684i	$-0.360642\pi$
$7$	−1.27454	−	1.27454i	−0.481730	−	0.481730i	−0.905684	+	0.423954i	$0.860642\pi$
$8$			1.38266i			0.488845i
$9$		−	7.10929i		−	2.36976i
$10$	−0.751939	−	0.751939i	−0.237784	−	0.237784i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	−4.20990	+	4.20990i	−1.21529	+	1.21529i
$13$	−2.60982			−0.723833			−0.361917	−	0.932210i	$-0.617878\pi$
$13$	−2.60982			−0.723833			−0.361917	+	0.932210i	$0.617878\pi$
$14$	0.455067	−	0.455067i	0.121622	−	0.121622i
$15$		−	9.46967i		−	2.44506i
$16$	3.25136			0.812841
$17$	−4.11644	+	0.234279i	−0.998384	+	0.0568210i
$17$	−4.11644	+	0.234279i	−0.998384	+	0.0568210i
$18$	2.53834			0.598292
$19$			5.05502i			1.15970i	0.814723	+	0.579850i	$0.196889\pi$
$19$			5.05502i			1.15970i	−0.814723	+	0.579850i	$0.803111\pi$
$20$	−3.94353	+	3.94353i	−0.881801	+	0.881801i
$21$	5.73097			1.25060
$22$	−0.252469	+	0.252469i	−0.0538266	+	0.0538266i
$23$	2.99837	+	2.99837i	0.625204	+	0.625204i	0.946857	−	0.321654i	$-0.104239\pi$
$23$	2.99837	+	2.99837i	0.625204	+	0.625204i	−0.321654	+	0.946857i	$0.604239\pi$
$24$	−3.10858	−	3.10858i	−0.634536	−	0.634536i
$25$		−	3.87051i		−	0.774103i
$26$		−	0.931823i		−	0.182745i
$27$	9.23872	+	9.23872i	1.77799	+	1.77799i
$28$	−2.38660	−	2.38660i	−0.451024	−	0.451024i
$29$	−6.06214	+	6.06214i	−1.12571	+	1.12571i	−0.134844	+	0.990867i	$0.543053\pi$
$29$	−6.06214	+	6.06214i	−1.12571	+	1.12571i	−0.990867	+	0.134844i	$0.956947\pi$
$30$	3.38110			0.617301
$31$	3.84932	−	3.84932i	0.691358	−	0.691358i	−0.271173	−	0.962531i	$-0.587411\pi$
$31$	3.84932	−	3.84932i	0.691358	−	0.691358i	0.962531	+	0.271173i	$0.0874114\pi$
$32$			3.92621i			0.694063i
$33$	−3.17951			−0.553482
$34$	−0.0836481	−	1.46976i	−0.0143455	−	0.252061i
$35$	5.36836			0.907419
$36$		−	13.3123i		−	2.21871i
$37$	3.72224	−	3.72224i	0.611932	−	0.611932i	−0.331517	−	0.943449i	$-0.607560\pi$
$37$	3.72224	−	3.72224i	0.611932	−	0.611932i	0.943449	+	0.331517i	$0.107560\pi$
$38$	−1.80487			−0.292788
$39$	5.86753	−	5.86753i	0.939557	−	0.939557i
$40$	−2.91190	−	2.91190i	−0.460411	−	0.460411i
$41$	4.45063	+	4.45063i	0.695072	+	0.695072i	0.963343	−	0.268271i	$-0.0864524\pi$
$41$	4.45063	+	4.45063i	0.695072	+	0.695072i	−0.268271	+	0.963343i	$0.586452\pi$
$42$			2.04621i			0.315738i
$43$			10.7465i			1.63883i	0.573202	+	0.819414i	$0.305701\pi$
$43$			10.7465i			1.63883i	−0.573202	+	0.819414i	$0.694299\pi$
$44$	1.32407	+	1.32407i	0.199611	+	0.199611i
$45$	14.9722	+	14.9722i	2.23192	+	2.23192i
$46$	−1.07055	+	1.07055i	−0.157845	+	0.157845i
$47$	5.74772			0.838391			0.419196	−	0.907896i	$-0.362312\pi$
$47$	5.74772			0.838391			0.419196	+	0.907896i	$0.362312\pi$
$48$	−7.30989	+	7.30989i	−1.05509	+	1.05509i
$49$		−	3.75111i		−	0.535873i
$50$	1.38195			0.195437
$51$	8.72809	−	9.78153i	1.22218	−	1.36969i
$52$	−4.88693			−0.677696
$53$		−	1.56064i		−	0.214371i	−0.994239	−	0.107185i	$-0.965816\pi$
$53$		−	1.56064i		−	0.214371i	0.994239	−	0.107185i	$-0.0341838\pi$
$54$	−3.29864	+	3.29864i	−0.448888	+	0.448888i
$55$	−2.97834			−0.401599
$56$	1.76226	−	1.76226i	0.235491	−	0.235491i
$57$	−11.3650	−	11.3650i	−1.50533	−	1.50533i
$58$	−2.16446	−	2.16446i	−0.284207	−	0.284207i
$59$			3.86779i			0.503543i	0.967787	+	0.251771i	$0.0810131\pi$
$59$			3.86779i			0.503543i	−0.967787	+	0.251771i	$0.918987\pi$
$60$		−	17.7321i		−	2.28921i
$61$	−4.92720	−	4.92720i	−0.630863	−	0.630863i	0.317421	−	0.948285i	$-0.397183\pi$
$61$	−4.92720	−	4.92720i	−0.630863	−	0.630863i	−0.948285	+	0.317421i	$0.897183\pi$
$62$	1.37438	+	1.37438i	0.174546	+	0.174546i
$63$	−9.06105	+	9.06105i	−1.14159	+	1.14159i
$64$	5.10089			0.637612
$65$	5.49629	−	5.49629i	0.681731	−	0.681731i
$66$		−	1.13523i		−	0.139737i
$67$	−6.00442			−0.733556			−0.366778	−	0.930308i	$-0.619539\pi$
$67$	−6.00442			−0.733556			−0.366778	+	0.930308i	$0.619539\pi$
$68$	−7.70812	+	0.438692i	−0.934747	+	0.0531992i
$69$	−13.4822			−1.62307
$70$			1.91675i			0.229095i
$71$	−1.40417	+	1.40417i	−0.166644	+	0.166644i	−0.785503	−	0.618858i	$-0.787595\pi$
$71$	−1.40417	+	1.40417i	−0.166644	+	0.166644i	0.618858	+	0.785503i	$0.287595\pi$
$72$	9.82975			1.15845
$73$	−2.85622	+	2.85622i	−0.334296	+	0.334296i	−0.854215	−	0.519920i	$-0.825962\pi$
$73$	−2.85622	+	2.85622i	−0.334296	+	0.334296i	0.519920	+	0.854215i	$0.325962\pi$
$74$	1.32901	+	1.32901i	0.154494	+	0.154494i
$75$	8.70190	+	8.70190i	1.00481	+	1.00481i
$76$			9.46562i			1.08578i
$77$		−	1.80247i		−	0.205410i
$78$	2.09497	+	2.09497i	0.237209	+	0.237209i
$79$	6.86495	+	6.86495i	0.772368	+	0.772368i	0.978520	−	0.206152i	$-0.0660942\pi$
$79$	6.86495	+	6.86495i	0.772368	+	0.772368i	−0.206152	+	0.978520i	$0.566094\pi$
$80$	−6.84739	+	6.84739i	−0.765561	+	0.765561i
$81$	−20.2141			−2.24601
$82$	−1.58908	+	1.58908i	−0.175484	+	0.175484i
$83$		−	6.73786i		−	0.739576i	−0.929116	−	0.369788i	$-0.879430\pi$
$83$		−	6.73786i		−	0.739576i	0.929116	−	0.369788i	$-0.120570\pi$
$84$	10.7313			1.17089
$85$	8.17586	−	9.16265i	0.886797	−	0.993828i
$86$	−3.83699			−0.413753
$87$		−	27.2584i		−	2.92241i
$88$	−0.977691	+	0.977691i	−0.104222	+	0.104222i
$89$	−3.09252			−0.327807			−0.163903	−	0.986476i	$-0.552409\pi$
$89$	−3.09252			−0.327807			−0.163903	+	0.986476i	$0.552409\pi$
$90$	−5.34575	+	5.34575i	−0.563491	+	0.563491i
$91$	3.32631	+	3.32631i	0.348692	+	0.348692i
$92$	5.61451	+	5.61451i	0.585353	+	0.585353i
$93$			17.3085i			1.79481i
$94$			2.05220i			0.211668i
$95$	−10.6459	−	10.6459i	−1.09225	−	1.09225i
$96$	−8.82712	−	8.82712i	−0.900914	−	0.900914i
$97$	−3.74500	+	3.74500i	−0.380247	+	0.380247i	−0.871191	−	0.490944i	$-0.836652\pi$
$97$	−3.74500	+	3.74500i	−0.380247	+	0.380247i	0.490944	+	0.871191i	$0.336652\pi$
$98$	1.33931			0.135291
$99$	5.02703	−	5.02703i	0.505235	−	0.505235i
$100$		−	7.24761i		−	0.724761i
$101$	9.07551			0.903047			0.451524	−	0.892259i	$-0.350881\pi$
$101$	9.07551			0.903047			0.451524	+	0.892259i	$0.350881\pi$
$102$	3.49245	+	3.11632i	0.345804	+	0.308562i
$103$	13.5901			1.33907			0.669535	−	0.742780i	$-0.266493\pi$
$103$	13.5901			1.33907			0.669535	+	0.742780i	$0.266493\pi$
$104$		−	3.60850i		−	0.353843i
$105$	−12.0694	+	12.0694i	−1.17786	+	1.17786i
$106$	0.557219			0.0541219
$107$	11.3579	−	11.3579i	1.09801	−	1.09801i	0.103370	−	0.994643i	$-0.467037\pi$
$107$	11.3579	−	11.3579i	1.09801	−	1.09801i	0.994643	−	0.103370i	$-0.0329626\pi$
$108$	17.2997	+	17.2997i	1.66466	+	1.66466i
$109$	−3.53555	−	3.53555i	−0.338644	−	0.338644i	0.517213	−	0.855857i	$-0.326970\pi$
$109$	−3.53555	−	3.53555i	−0.338644	−	0.338644i	−0.855857	+	0.517213i	$0.826970\pi$
$110$		−	1.06340i		−	0.101391i
$111$			16.7371i			1.58861i
$112$	−4.14399	−	4.14399i	−0.391570	−	0.391570i
$113$	−6.81161	−	6.81161i	−0.640783	−	0.640783i	0.309965	−	0.950748i	$-0.399683\pi$
$113$	−6.81161	−	6.81161i	−0.640783	−	0.640783i	−0.950748	+	0.309965i	$0.899683\pi$
$114$	4.05780	−	4.05780i	0.380048	−	0.380048i
$115$	−12.6292			−1.17768
$116$	−11.3515	+	11.3515i	−1.05396	+	1.05396i
$117$			18.5540i			1.71531i
$118$	−1.38097			−0.127129
$119$	5.54516	+	4.94797i	0.508324	+	0.453579i
$120$	13.0934			1.19526
$121$			1.00000i			0.0909091i
$122$	1.75923	−	1.75923i	0.159273	−	0.159273i
$123$	−20.0123			−1.80445
$124$	7.20792	−	7.20792i	0.647291	−	0.647291i
$125$	−2.37870	−	2.37870i	−0.212758	−	0.212758i
$126$	−3.23520	−	3.23520i	−0.288215	−	0.288215i
$127$			8.50313i			0.754531i	0.926105	+	0.377265i	$0.123136\pi$
$127$			8.50313i			0.754531i	−0.926105	+	0.377265i	$0.876864\pi$
$128$			9.67367i			0.855040i
$129$	−24.1609	−	24.1609i	−2.12725	−	2.12725i
$130$	1.96242	+	1.96242i	0.172116	+	0.172116i
$131$	3.75728	−	3.75728i	0.328275	−	0.328275i	−0.523655	−	0.851930i	$-0.675432\pi$
$131$	3.75728	−	3.75728i	0.328275	−	0.328275i	0.851930	+	0.523655i	$0.175432\pi$
$132$	−5.95369			−0.518203
$133$	6.44281	−	6.44281i	0.558662	−	0.558662i
$134$		−	2.14385i		−	0.185200i
$135$	−38.9136			−3.34915
$136$	−0.323929	−	5.69166i	−0.0277767	−	0.488056i
$137$	15.6263			1.33504			0.667522	−	0.744590i	$-0.267355\pi$
$137$	15.6263			1.33504			0.667522	+	0.744590i	$0.267355\pi$
$138$		−	4.81375i		−	0.409774i
$139$	7.82916	−	7.82916i	0.664061	−	0.664061i	−0.292274	−	0.956335i	$-0.594412\pi$
$139$	7.82916	−	7.82916i	0.664061	−	0.664061i	0.956335	+	0.292274i	$0.0944119\pi$
$140$	10.0524			0.849580
$141$	−12.9223	+	12.9223i	−1.08826	+	1.08826i
$142$	−0.501351	−	0.501351i	−0.0420725	−	0.0420725i
$143$	−1.84542	−	1.84542i	−0.154322	−	0.154322i
$144$		−	23.1149i		−	1.92624i
$145$		−	25.5338i		−	2.12047i
$146$	−1.01980	−	1.01980i	−0.0843993	−	0.0843993i
$147$	8.43344	+	8.43344i	0.695579	+	0.695579i
$148$	6.96996	−	6.96996i	0.572927	−	0.572927i
$149$	−6.28269			−0.514698			−0.257349	−	0.966319i	$-0.582849\pi$
$149$	−6.28269			−0.514698			−0.257349	+	0.966319i	$0.582849\pi$
$150$	−3.10697	+	3.10697i	−0.253683	+	0.253683i
$151$			0.291776i			0.0237444i	0.999930	+	0.0118722i	$0.00377912\pi$
$151$			0.291776i			0.0237444i	−0.999930	+	0.0118722i	$0.996221\pi$
$152$	−6.98939			−0.566914
$153$	1.66556	+	29.2650i	0.134652	+	2.36593i
$154$	0.643562			0.0518597
$155$			16.2134i			1.30229i
$156$	10.9871	−	10.9871i	0.879669	−	0.879669i
$157$	17.3996			1.38864			0.694318	−	0.719668i	$-0.255706\pi$
$157$	17.3996			1.38864			0.694318	+	0.719668i	$0.255706\pi$
$158$	−2.45110	+	2.45110i	−0.194999	+	0.194999i
$159$	3.50872	+	3.50872i	0.278259	+	0.278259i
$160$	−8.26862	−	8.26862i	−0.653692	−	0.653692i
$161$		−	7.64307i		−	0.602359i
$162$		−	7.21735i		−	0.567048i
$163$	−7.54370	−	7.54370i	−0.590868	−	0.590868i	0.346998	−	0.937866i	$-0.387201\pi$
$163$	−7.54370	−	7.54370i	−0.590868	−	0.590868i	−0.937866	+	0.346998i	$0.887201\pi$
$164$	8.33389	+	8.33389i	0.650768	+	0.650768i
$165$	6.69607	−	6.69607i	0.521288	−	0.521288i
$166$	2.40572			0.186720
$167$	−2.47558	+	2.47558i	−0.191566	+	0.191566i	−0.796373	−	0.604806i	$-0.793251\pi$
$167$	−2.47558	+	2.47558i	−0.191566	+	0.191566i	0.604806	+	0.796373i	$0.293251\pi$
$168$			7.92400i			0.611350i
$169$	−6.18885			−0.476065
$170$	3.27148	+	2.91915i	0.250911	+	0.223889i
$171$	35.9376			2.74822
$172$			20.1231i			1.53437i
$173$	12.6159	−	12.6159i	0.959167	−	0.959167i	−0.0400313	−	0.999198i	$-0.512746\pi$
$173$	12.6159	−	12.6159i	0.959167	−	0.959167i	0.999198	+	0.0400313i	$0.0127458\pi$
$174$	9.73249			0.737818
$175$	−4.93312	+	4.93312i	−0.372909	+	0.372909i
$176$	2.29906	+	2.29906i	0.173298	+	0.173298i
$177$	−8.69576	−	8.69576i	−0.653614	−	0.653614i
$178$		−	1.10417i		−	0.0827610i
$179$			13.2006i			0.986660i	0.869842	+	0.493330i	$0.164221\pi$
$179$			13.2006i			0.986660i	−0.869842	+	0.493330i	$0.835779\pi$
$180$	28.0357	+	28.0357i	2.08966	+	2.08966i
$181$	7.47404	+	7.47404i	0.555541	+	0.555541i	0.928035	−	0.372494i	$-0.121497\pi$
$181$	7.47404	+	7.47404i	0.555541	+	0.555541i	−0.372494	+	0.928035i	$0.621497\pi$
$182$	−1.18764	+	1.18764i	−0.0880340	+	0.0880340i
$183$	22.1552			1.63776
$184$	−4.14574	+	4.14574i	−0.305628	+	0.305628i
$185$			15.6781i			1.15268i
$186$	−6.17991			−0.453133
$187$	−3.07643	−	2.74511i	−0.224971	−	0.200742i
$188$	10.7627			0.784952
$189$		−	23.5502i		−	1.71302i
$190$	3.80106	−	3.80106i	0.275758	−	0.275758i
$191$	−19.3845			−1.40261			−0.701305	−	0.712861i	$-0.747399\pi$
$191$	−19.3845			−1.40261			−0.701305	+	0.712861i	$0.747399\pi$
$192$	−11.4681	+	11.4681i	−0.827639	+	0.827639i
$193$	16.4666	+	16.4666i	1.18529	+	1.18529i	0.978355	+	0.206935i	$0.0663489\pi$
$193$	16.4666	+	16.4666i	1.18529	+	1.18529i	0.206935	+	0.978355i	$0.433651\pi$
$194$	−1.33713	−	1.33713i	−0.0960007	−	0.0960007i
$195$			24.7141i			1.76981i
$196$		−	7.02402i		−	0.501716i
$197$	−7.24012	−	7.24012i	−0.515837	−	0.515837i	0.400472	−	0.916309i	$-0.368846\pi$
$197$	−7.24012	−	7.24012i	−0.515837	−	0.515837i	−0.916309	+	0.400472i	$0.868846\pi$
$198$	1.79487	+	1.79487i	0.127556	+	0.127556i
$199$	11.6359	−	11.6359i	0.824846	−	0.824846i	−0.161953	−	0.986798i	$-0.551779\pi$
$199$	11.6359	−	11.6359i	0.824846	−	0.824846i	0.986798	+	0.161953i	$0.0517792\pi$
$200$	5.35162			0.378417
$201$	13.4994	−	13.4994i	0.952178	−	0.952178i
$202$			3.24037i			0.227991i
$203$	15.4528			1.08458
$204$	16.3435	−	18.3161i	1.14428	−	1.28238i
$205$	−18.7461			−1.30929
$206$			4.85227i			0.338074i
$207$	21.3163	−	21.3163i	1.48158	−	1.48158i
$208$	−8.48547			−0.588362
$209$	−3.57444	+	3.57444i	−0.247249	+	0.247249i
$210$	−4.30934	−	4.30934i	−0.297372	−	0.297372i
$211$	8.97501	+	8.97501i	0.617865	+	0.617865i	0.944983	−	0.327118i	$-0.106078\pi$
$211$	8.97501	+	8.97501i	0.617865	+	0.617865i	−0.327118	+	0.944983i	$0.606078\pi$
$212$		−	2.92233i		−	0.200707i
$213$		−	6.31385i		−	0.432618i
$214$	4.05529	+	4.05529i	0.277214	+	0.277214i
$215$	−22.6322	−	22.6322i	−1.54350	−	1.54350i
$216$	−12.7740	+	12.7740i	−0.869164	+	0.869164i
$217$	−9.81220			−0.666096
$218$	1.26235	−	1.26235i	0.0854971	−	0.0854971i
$219$		−	12.8430i		−	0.867851i
$220$	−5.57700			−0.376001
$221$	10.7432	−	0.611426i	0.722664	−	0.0411289i
$222$	−5.97589			−0.401075
$223$			13.7228i			0.918949i	0.888191	+	0.459475i	$0.151962\pi$
$223$			13.7228i			0.918949i	−0.888191	+	0.459475i	$0.848038\pi$
$224$	5.00410	−	5.00410i	0.334351	−	0.334351i
$225$	−27.5166			−1.83444
$226$	2.43205	−	2.43205i	0.161778	−	0.161778i
$227$	−7.24782	−	7.24782i	−0.481055	−	0.481055i	0.424414	−	0.905468i	$-0.360480\pi$
$227$	−7.24782	−	7.24782i	−0.481055	−	0.481055i	−0.905468	+	0.424414i	$0.860480\pi$
$228$	−21.2811	−	21.2811i	−1.40938	−	1.40938i
$229$		−	4.19435i		−	0.277170i	−0.990351	−	0.138585i	$-0.955745\pi$
$229$		−	4.19435i		−	0.277170i	0.990351	−	0.138585i	$-0.0442554\pi$
$230$		−	4.50918i		−	0.297327i
$231$	4.05241	+	4.05241i	0.266629	+	0.266629i
$232$	−8.38190	−	8.38190i	−0.550299	−	0.550299i
$233$	−14.3359	+	14.3359i	−0.939176	+	0.939176i	−0.998253	−	0.0590772i	$-0.981184\pi$
$233$	−14.3359	+	14.3359i	−0.939176	+	0.939176i	0.0590772	+	0.998253i	$0.481184\pi$
$234$	−6.62460			−0.433063
$235$	−12.1047	+	12.1047i	−0.789626	+	0.789626i
$236$			7.24250i			0.471447i
$237$	−30.8683			−2.00511
$238$	−1.76665	+	1.97987i	−0.114515	+	0.128336i
$239$	−6.88000			−0.445030			−0.222515	−	0.974929i	$-0.571427\pi$
$239$	−6.88000			−0.445030			−0.222515	+	0.974929i	$0.571427\pi$
$240$		−	30.7893i		−	1.98744i
$241$	−12.4282	+	12.4282i	−0.800572	+	0.800572i	−0.983185	−	0.182613i	$-0.941545\pi$
$241$	−12.4282	+	12.4282i	−0.800572	+	0.800572i	0.182613	+	0.983185i	$0.441545\pi$
$242$	−0.357045			−0.0229517
$243$	17.7303	−	17.7303i	1.13740	−	1.13740i
$244$	−9.22628	−	9.22628i	−0.590652	−	0.590652i
$245$	7.89985	+	7.89985i	0.504703	+	0.504703i
$246$		−	7.14529i		−	0.455567i
$247$		−	13.1927i		−	0.839430i
$248$	5.32231	+	5.32231i	0.337967	+	0.337967i
$249$	15.1484	+	15.1484i	0.959992	+	0.959992i
$250$	0.849303	−	0.849303i	0.0537147	−	0.0537147i
$251$	−28.8282			−1.81962			−0.909809	−	0.415026i	$-0.863772\pi$
$251$	−28.8282			−1.81962			−0.909809	+	0.415026i	$0.863772\pi$
$252$	−16.9670	+	16.9670i	−1.06882	+	1.06882i
$253$			4.24034i			0.266588i
$254$	−3.03600			−0.190496
$255$	2.21854	+	38.9814i	0.138931	+	2.44111i
$256$	6.74785			0.421741
$257$			5.28071i			0.329402i	0.986344	+	0.164701i	$0.0526658\pi$
$257$			5.28071i			0.329402i	−0.986344	+	0.164701i	$0.947334\pi$
$258$	8.62653	−	8.62653i	0.537064	−	0.537064i
$259$	−9.48827			−0.589572
$260$	10.2919	−	10.2919i	0.638277	−	0.638277i
$261$	43.0975	+	43.0975i	2.66767	+	2.66767i
$262$	1.34152	+	1.34152i	0.0828792	+	0.0828792i
$263$		−	16.6976i		−	1.02962i	−0.857305	−	0.514808i	$-0.827863\pi$
$263$		−	16.6976i		−	1.02962i	0.857305	−	0.514808i	$-0.172137\pi$
$264$		−	4.39619i		−	0.270567i
$265$	3.28672	+	3.28672i	0.201902	+	0.201902i
$266$	2.30037	+	2.30037i	0.141045	+	0.141045i
$267$	6.95278	−	6.95278i	0.425503	−	0.425503i
$268$	−11.2434			−0.686799
$269$	−2.15191	+	2.15191i	−0.131205	+	0.131205i	−0.769659	−	0.638455i	$-0.779574\pi$
$269$	−2.15191	+	2.15191i	−0.131205	+	0.131205i	0.638455	+	0.769659i	$0.279574\pi$
$270$		−	13.8939i		−	0.845556i
$271$	−9.36150			−0.568671			−0.284335	−	0.958725i	$-0.591773\pi$
$271$	−9.36150			−0.568671			−0.284335	+	0.958725i	$0.591773\pi$
$272$	−13.3841	+	0.761726i	−0.811528	+	0.0461864i
$273$	−14.9568			−0.905226
$274$			5.57929i			0.337057i
$275$	2.73687	−	2.73687i	0.165039	−	0.165039i
$276$	−25.2457			−1.51961
$277$	6.47182	−	6.47182i	0.388854	−	0.388854i	−0.485424	−	0.874279i	$-0.661335\pi$
$277$	6.47182	−	6.47182i	0.388854	−	0.388854i	0.874279	+	0.485424i	$0.161335\pi$
$278$	2.79536	+	2.79536i	0.167655	+	0.167655i
$279$	−27.3659	−	27.3659i	−1.63835	−	1.63835i
$280$			7.42264i			0.443588i
$281$			17.4741i			1.04242i	0.853430	+	0.521208i	$0.174518\pi$
$281$			17.4741i			1.04242i	−0.853430	+	0.521208i	$0.825482\pi$
$282$	−4.61386	−	4.61386i	−0.274751	−	0.274751i
$283$	−2.36548	−	2.36548i	−0.140613	−	0.140613i	0.633296	−	0.773910i	$-0.281702\pi$
$283$	−2.36548	−	2.36548i	−0.140613	−	0.140613i	−0.773910	+	0.633296i	$0.781702\pi$
$284$	−2.62933	+	2.62933i	−0.156022	+	0.156022i
$285$	47.8693			2.83553
$286$	0.658898	−	0.658898i	0.0389615	−	0.0389615i
$287$		−	11.3450i		−	0.669674i
$288$	27.9126			1.64476
$289$	16.8902	−	1.92879i	0.993543	−	0.113458i
$290$	9.11671			0.535352
$291$		−	16.8394i		−	0.987145i
$292$	−5.34833	+	5.34833i	−0.312987	+	0.312987i
$293$	12.1233			0.708253			0.354127	−	0.935197i	$-0.384778\pi$
$293$	12.1233			0.708253			0.354127	+	0.935197i	$0.384778\pi$
$294$	−3.01112	+	3.01112i	−0.175612	+	0.175612i
$295$	−8.14558	−	8.14558i	−0.474254	−	0.474254i
$296$	5.14661	+	5.14661i	0.299140	+	0.299140i
$297$			13.0655i			0.758139i
$298$		−	2.24320i		−	0.129945i
$299$	−7.82521	−	7.82521i	−0.452543	−	0.452543i
$300$	16.2945	+	16.2945i	0.940762	+	0.940762i
$301$	13.6968	−	13.6968i	0.789473	−	0.789473i
$302$	−0.104177			−0.00599472
$303$	−20.4041	+	20.4041i	−1.17218	+	1.17218i
$304$			16.4357i			0.942652i
$305$	20.7534			1.18834
$306$	−10.4489	+	0.594679i	−0.597325	+	0.0339955i
$307$	−8.91544			−0.508831			−0.254415	−	0.967095i	$-0.581883\pi$
$307$	−8.91544			−0.508831			−0.254415	+	0.967095i	$0.581883\pi$
$308$		−	3.37516i		−	0.192317i
$309$	−30.5540	+	30.5540i	−1.73815	+	1.73815i
$310$	−5.78890			−0.328788
$311$	3.41263	−	3.41263i	0.193513	−	0.193513i	−0.603699	−	0.797212i	$-0.706307\pi$
$311$	3.41263	−	3.41263i	0.193513	−	0.193513i	0.797212	+	0.603699i	$0.206307\pi$
$312$	8.11283	+	8.11283i	0.459298	+	0.459298i
$313$	11.0205	+	11.0205i	0.622918	+	0.622918i	0.946277	−	0.323359i	$-0.104812\pi$
$313$	11.0205	+	11.0205i	0.622918	+	0.622918i	−0.323359	+	0.946277i	$0.604812\pi$
$314$			6.21243i			0.350587i
$315$		−	38.1652i		−	2.15037i
$316$	12.8548	+	12.8548i	0.723137	+	0.723137i
$317$	−10.4814	−	10.4814i	−0.588694	−	0.588694i	0.348583	−	0.937278i	$-0.386663\pi$
$317$	−10.4814	−	10.4814i	−0.588694	−	0.588694i	−0.937278	+	0.348583i	$0.886663\pi$
$318$	−1.25277	+	1.25277i	−0.0702519	+	0.0702519i
$319$	−8.57316			−0.480005
$320$	−10.7425	+	10.7425i	−0.600525	+	0.600525i
$321$			51.0710i			2.85051i
$322$	2.72892			0.152077
$323$	−1.18428	−	20.8087i	−0.0658954	−	1.15783i
$324$	−37.8513			−2.10285
$325$			10.1013i			0.560322i
$326$	2.69344	−	2.69344i	0.149176	−	0.149176i
$327$	15.8976			0.879139
$328$	−6.15373	+	6.15373i	−0.339783	+	0.339783i
$329$	−7.32569	−	7.32569i	−0.403878	−	0.403878i
$330$	2.39080	+	2.39080i	0.131609	+	0.131609i
$331$			29.9896i			1.64838i	0.566315	+	0.824189i	$0.308369\pi$
$331$			29.9896i			1.64838i	−0.566315	+	0.824189i	$0.691631\pi$
$332$		−	12.6168i		−	0.692435i
$333$	−26.4625	−	26.4625i	−1.45013	−	1.45013i
$334$	−0.883894	−	0.883894i	−0.0483645	−	0.0483645i
$335$	12.6453	−	12.6453i	0.690888	−	0.690888i
$336$	18.6335			1.01654
$337$	−3.55864	+	3.55864i	−0.193852	+	0.193852i	−0.797358	−	0.603507i	$-0.793770\pi$
$337$	−3.55864	+	3.55864i	−0.193852	+	0.193852i	0.603507	+	0.797358i	$0.293770\pi$
$338$		−	2.20970i		−	0.120192i
$339$	30.6285			1.66351
$340$	15.3095	−	17.1572i	0.830272	−	0.930481i
$341$	5.44376			0.294796
$342$			12.8313i			0.693839i
$343$	−13.7027	+	13.7027i	−0.739876	+	0.739876i
$344$	−14.8588			−0.801134
$345$	28.3936	−	28.3936i	1.52866	−	1.52866i
$346$	4.50444	+	4.50444i	0.242160	+	0.242160i
$347$	7.09534	+	7.09534i	0.380898	+	0.380898i	0.871426	−	0.490528i	$-0.163196\pi$
$347$	7.09534	+	7.09534i	0.380898	+	0.380898i	−0.490528	+	0.871426i	$0.663196\pi$
$348$		−	51.0420i		−	2.73614i
$349$			8.74433i			0.468073i	0.972228	+	0.234037i	$0.0751936\pi$
$349$			8.74433i			0.468073i	−0.972228	+	0.234037i	$0.924806\pi$
$350$	−1.76134	−	1.76134i	−0.0941478	−	0.0941478i
$351$	−24.1114	−	24.1114i	−1.28697	−	1.28697i
$352$	−2.77625	+	2.77625i	−0.147975	+	0.147975i
$353$	−15.2680			−0.812634			−0.406317	−	0.913732i	$-0.633187\pi$
$353$	−15.2680			−0.812634			−0.406317	+	0.913732i	$0.633187\pi$
$354$	3.10478	−	3.10478i	0.165017	−	0.165017i
$355$		−	5.91437i		−	0.313902i
$356$	−5.79081			−0.306912
$357$	−23.5912	+	1.34264i	−1.24858	+	0.0710603i
$358$	−4.71321			−0.249101
$359$		−	24.0939i		−	1.27163i	−0.771843	−	0.635813i	$-0.780665\pi$
$359$		−	24.0939i		−	1.27163i	0.771843	−	0.635813i	$-0.219335\pi$
$360$	−20.7015	+	20.7015i	−1.09107	+	1.09107i
$361$	−6.55321			−0.344906
$362$	−2.66857	+	2.66857i	−0.140257	+	0.140257i
$363$	−2.24825	−	2.24825i	−0.118003	−	0.118003i
$364$	6.22858	+	6.22858i	0.326466	+	0.326466i
$365$		−	12.0304i		−	0.629702i
$366$			7.91040i			0.413483i
$367$	18.7009	+	18.7009i	0.976178	+	0.976178i	0.999723	−	0.0235448i	$-0.00749524\pi$
$367$	18.7009	+	18.7009i	0.976178	+	0.976178i	−0.0235448	+	0.999723i	$0.507495\pi$
$368$	9.74880	+	9.74880i	0.508191	+	0.508191i
$369$	31.6408	−	31.6408i	1.64716	−	1.64716i
$370$	−5.59779			−0.291015
$371$	−1.98910	+	1.98910i	−0.103269	+	0.103269i
$372$			32.4105i			1.68040i
$373$	23.0414			1.19304			0.596519	−	0.802599i	$-0.296550\pi$
$373$	23.0414			1.19304			0.596519	+	0.802599i	$0.296550\pi$
$374$	0.980126	−	1.09842i	0.0506811	−	0.0567981i
$375$	10.6958			0.552331
$376$			7.94717i			0.409844i
$377$	15.8211	−	15.8211i	0.814827	−	0.814827i
$378$	8.40848			0.432485
$379$	−24.0084	+	24.0084i	−1.23323	+	1.23323i	−0.270512	+	0.962717i	$0.587193\pi$
$379$	−24.0084	+	24.0084i	−1.23323	+	1.23323i	−0.962717	+	0.270512i	$0.912807\pi$
$380$	−19.9346	−	19.9346i	−1.02263	−	1.02263i
$381$	−19.1172	−	19.1172i	−0.979403	−	0.979403i
$382$		−	6.92112i		−	0.354116i
$383$		−	1.14709i		−	0.0586136i	−0.999570	−	0.0293068i	$-0.990670\pi$
$383$		−	1.14709i		−	0.0586136i	0.999570	−	0.0293068i	$-0.00932998\pi$
$384$	−21.7489	−	21.7489i	−1.10987	−	1.10987i
$385$	3.79601	+	3.79601i	0.193462	+	0.193462i
$386$	−5.87931	+	5.87931i	−0.299249	+	0.299249i
$387$	76.4001			3.88363
$388$	−7.01259	+	7.01259i	−0.356010	+	0.356010i
$389$		−	29.7967i		−	1.51075i	−0.655291	−	0.755376i	$-0.727454\pi$
$389$		−	29.7967i		−	1.51075i	0.655291	−	0.755376i	$-0.272546\pi$
$390$	−8.82405			−0.446823
$391$	−13.0451	−	11.6402i	−0.659718	−	0.588669i
$392$	5.18652			0.261959
$393$			16.8946i			0.852221i
$394$	2.58505	−	2.58505i	0.130233	−	0.130233i
$395$	−28.9153			−1.45488
$396$	9.41320	−	9.41320i	0.473031	−	0.473031i
$397$	−11.7167	−	11.7167i	−0.588044	−	0.588044i	0.349057	−	0.937101i	$-0.386502\pi$
$397$	−11.7167	−	11.7167i	−0.588044	−	0.588044i	−0.937101	+	0.349057i	$0.886502\pi$
$398$	4.15453	+	4.15453i	0.208248	+	0.208248i
$399$			28.9701i			1.45032i
$400$		−	12.5845i		−	0.629223i
$401$	−15.1238	−	15.1238i	−0.755246	−	0.755246i	0.220207	−	0.975453i	$-0.429327\pi$
$401$	−15.1238	−	15.1238i	−0.755246	−	0.755246i	−0.975453	+	0.220207i	$0.929327\pi$
$402$	4.81991	+	4.81991i	0.240395	+	0.240395i
$403$	−10.0460	+	10.0460i	−0.500428	+	0.500428i
$404$	16.9941			0.845486
$405$	42.5710	−	42.5710i	2.11537	−	2.11537i
$406$			5.51736i			0.273822i
$407$	5.26404			0.260929
$408$	13.5246	+	12.0680i	0.669566	+	0.597456i
$409$	26.1175			1.29143			0.645714	−	0.763579i	$-0.276560\pi$
$409$	26.1175			1.29143			0.645714	+	0.763579i	$0.276560\pi$
$410$		−	6.69321i		−	0.330554i
$411$	−35.1318	+	35.1318i	−1.73293	+	1.73293i
$412$	25.4477			1.25372
$413$	4.92964	−	4.92964i	0.242572	−	0.242572i
$414$	7.61087	+	7.61087i	0.374054	+	0.374054i
$415$	14.1900	+	14.1900i	0.696558	+	0.696558i
$416$		−	10.2467i		−	0.502386i
$417$			35.2039i			1.72394i
$418$	−1.27624	−	1.27624i	−0.0624227	−	0.0624227i
$419$	11.1137	+	11.1137i	0.542939	+	0.542939i	0.924389	−	0.381450i	$-0.124575\pi$
$419$	11.1137	+	11.1137i	0.542939	+	0.542939i	−0.381450	+	0.924389i	$0.624575\pi$
$420$	−22.6003	+	22.6003i	−1.10278	+	1.10278i
$421$	−16.1236			−0.785818			−0.392909	−	0.919577i	$-0.628531\pi$
$421$	−16.1236			−0.785818			−0.392909	+	0.919577i	$0.628531\pi$
$422$	−3.20448	+	3.20448i	−0.155992	+	0.155992i
$423$		−	40.8622i		−	1.98679i
$424$	2.15784			0.104794
$425$	0.906780	+	15.9328i	0.0439853	+	0.772852i
$426$	2.25433			0.109223
$427$			12.5598i			0.607811i
$428$	21.2679	−	21.2679i	1.02803	−	1.02803i
$429$	8.29795			0.400629
$430$	8.08072	−	8.08072i	0.389687	−	0.389687i
$431$	2.02714	+	2.02714i	0.0976439	+	0.0976439i	0.754241	−	0.656597i	$-0.228005\pi$
$431$	2.02714	+	2.02714i	0.0976439	+	0.0976439i	−0.656597	+	0.754241i	$0.728005\pi$
$432$	30.0384	+	30.0384i	1.44523	+	1.44523i
$433$		−	15.5292i		−	0.746286i	−0.927774	−	0.373143i	$-0.878280\pi$
$433$		−	15.5292i		−	0.746286i	0.927774	−	0.373143i	$-0.121720\pi$
$434$		−	3.50340i		−	0.168169i
$435$	57.4064	+	57.4064i	2.75243	+	2.75243i
$436$	−6.62037	−	6.62037i	−0.317058	−	0.317058i
$437$	−15.1568	+	15.1568i	−0.725049	+	0.725049i
$438$	4.58554			0.219105
$439$	5.00979	−	5.00979i	0.239104	−	0.239104i	−0.577375	−	0.816479i	$-0.695923\pi$
$439$	5.00979	−	5.00979i	0.239104	−	0.239104i	0.816479	+	0.577375i	$0.195923\pi$
$440$		−	4.11804i		−	0.196320i
$441$	−26.6677			−1.26989
$442$	0.218306	+	3.83580i	0.0103838	+	0.182450i
$443$	15.5943			0.740907			0.370454	−	0.928851i	$-0.379202\pi$
$443$	15.5943			0.740907			0.370454	+	0.928851i	$0.379202\pi$
$444$			31.3405i			1.48735i
$445$	6.51287	−	6.51287i	0.308740	−	0.308740i
$446$	−4.89967			−0.232006
$447$	14.1251	−	14.1251i	0.668093	−	0.668093i
$448$	−6.50128	−	6.50128i	−0.307157	−	0.307157i
$449$	3.94234	+	3.94234i	0.186050	+	0.186050i	0.793986	−	0.607936i	$-0.208002\pi$
$449$	3.94234	+	3.94234i	0.186050	+	0.186050i	−0.607936	+	0.793986i	$0.708002\pi$
$450$		−	9.82467i		−	0.463139i
$451$			6.29415i			0.296380i
$452$	−12.7549	−	12.7549i	−0.599939	−	0.599939i
$453$	−0.655986	−	0.655986i	−0.0308209	−	0.0308209i
$454$	2.58780	−	2.58780i	0.121451	−	0.121451i
$455$	−14.0105			−0.656820
$456$	15.7139	−	15.7139i	0.735872	−	0.735872i
$457$		−	41.6981i		−	1.95055i	−0.220985	−	0.975277i	$-0.570927\pi$
$457$		−	41.6981i		−	1.95055i	0.220985	−	0.975277i	$-0.429073\pi$
$458$	1.49757			0.0699769
$459$	−40.1951	−	35.8662i	−1.87615	−	1.67409i
$460$	−23.6484			−1.10261
$461$			2.69797i			0.125657i	0.998024	+	0.0628284i	$0.0200121\pi$
$461$			2.69797i			0.125657i	−0.998024	+	0.0628284i	$0.979988\pi$
$462$	−1.44689	+	1.44689i	−0.0673155	+	0.0673155i
$463$	14.2269			0.661181			0.330591	−	0.943774i	$-0.392752\pi$
$463$	14.2269			0.661181			0.330591	+	0.943774i	$0.392752\pi$
$464$	−19.7102	+	19.7102i	−0.915024	+	0.915024i
$465$	−36.4518	−	36.4518i	−1.69041	−	1.69041i
$466$	−5.11856	−	5.11856i	−0.237113	−	0.237113i
$467$		−	19.6313i		−	0.908427i	−0.890893	−	0.454213i	$-0.849920\pi$
$467$		−	19.6313i		−	0.908427i	0.890893	−	0.454213i	$-0.150080\pi$
$468$			34.7426i			1.60598i
$469$	7.65285	+	7.65285i	0.353376	+	0.353376i
$470$	−4.32193	−	4.32193i	−0.199356	−	0.199356i
$471$	−39.1186	+	39.1186i	−1.80249	+	1.80249i
$472$	−5.34785			−0.246155
$473$	−7.59893	+	7.59893i	−0.349399	+	0.349399i
$474$		−	11.0214i		−	0.506229i
$475$	19.5655			0.897728
$476$	10.3834	+	9.26516i	0.475923	+	0.424668i
$477$	−11.0950			−0.508007
$478$		−	2.45647i		−	0.112356i
$479$	16.8877	−	16.8877i	0.771619	−	0.771619i	−0.206770	−	0.978390i	$-0.566295\pi$
$479$	16.8877	−	16.8877i	0.771619	−	0.771619i	0.978390	+	0.206770i	$0.0662952\pi$
$480$	37.1799			1.69702
$481$	−9.71437	+	9.71437i	−0.442937	+	0.442937i
$482$	−4.43744	−	4.43744i	−0.202120	−	0.202120i
$483$	17.1836	+	17.1836i	0.781879	+	0.781879i
$484$			1.87252i			0.0851145i
$485$		−	15.7740i		−	0.716260i
$486$	6.33051	+	6.33051i	0.287158	+	0.287158i
$487$	−6.86981	−	6.86981i	−0.311301	−	0.311301i	0.534113	−	0.845413i	$-0.320646\pi$
$487$	−6.86981	−	6.86981i	−0.311301	−	0.311301i	−0.845413	+	0.534113i	$0.820646\pi$
$488$	6.81266	−	6.81266i	0.308395	−	0.308395i
$489$	33.9203			1.53393
$490$	−2.82060	+	2.82060i	−0.127422	+	0.127422i
$491$			12.0897i			0.545599i	0.962071	+	0.272800i	$0.0879496\pi$
$491$			12.0897i			0.545599i	−0.962071	+	0.272800i	$0.912050\pi$
$492$	−37.4734			−1.68943
$493$	23.5342	−	26.3747i	1.05993	−	1.18786i
$494$	4.71038			0.211930
$495$			21.1739i			0.951695i
$496$	12.5155	−	12.5155i	0.561964	−	0.561964i
$497$	3.57933			0.160555
$498$	−5.40867	+	5.40867i	−0.242368	+	0.242368i
$499$	19.5757	+	19.5757i	0.876331	+	0.876331i	0.993153	−	0.116822i	$-0.0372707\pi$
$499$	19.5757	+	19.5757i	0.876331	+	0.876331i	−0.116822	+	0.993153i	$0.537271\pi$
$500$	−4.45416	−	4.45416i	−0.199196	−	0.199196i
$501$		−	11.1315i		−	0.497318i
$502$		−	10.2930i		−	0.459397i
$503$	30.9743	+	30.9743i	1.38108	+	1.38108i	0.842713	+	0.538364i	$0.180957\pi$
$503$	30.9743	+	30.9743i	1.38108	+	1.38108i	0.538364	+	0.842713i	$0.319043\pi$
$504$	−12.5284	−	12.5284i	−0.558059	−	0.558059i
$505$	−19.1131	+	19.1131i	−0.850521	+	0.850521i
$506$	−1.51399			−0.0673051
$507$	13.9141	−	13.9141i	0.617947	−	0.617947i
$508$			15.9223i			0.706436i
$509$	24.7764			1.09819			0.549097	−	0.835759i	$-0.314972\pi$
$509$	24.7764			1.09819			0.549097	+	0.835759i	$0.314972\pi$
$510$	−13.9181	+	0.792120i	−0.616304	+	0.0350757i
$511$	7.28073			0.322080
$512$			21.7566i			0.961516i
$513$	−46.7019	+	46.7019i	−2.06194	+	2.06194i
$514$	−1.88545			−0.0831637
$515$	−28.6208	+	28.6208i	−1.26118	+	1.26118i
$516$	−45.2417	−	45.2417i	−1.99166	−	1.99166i
$517$	4.06425	+	4.06425i	0.178746	+	0.178746i
$518$		−	3.38774i		−	0.148849i
$519$			56.7274i			2.49005i
$520$	7.59952	+	7.59952i	0.333261	+	0.333261i
$521$	11.3504	+	11.3504i	0.497268	+	0.497268i	0.910587	−	0.413318i	$-0.135630\pi$
$521$	11.3504	+	11.3504i	0.497268	+	0.497268i	−0.413318	+	0.910587i	$0.635630\pi$
$522$	−15.3877	+	15.3877i	−0.673503	+	0.673503i
$523$	−33.1059			−1.44762			−0.723810	−	0.689999i	$-0.757611\pi$
$523$	−33.1059			−1.44762			−0.723810	+	0.689999i	$0.757611\pi$
$524$	7.03557	−	7.03557i	0.307350	−	0.307350i
$525$		−	22.1818i		−	0.968093i
$526$	5.96179			0.259946
$527$	−14.9437	+	16.7473i	−0.650957	+	0.729525i
$528$	−10.3377			−0.449893
$529$		−	5.01954i		−	0.218241i
$530$	−1.17351	+	1.17351i	−0.0509739	+	0.0509739i
$531$	27.4972			1.19328
$532$	12.0643	−	12.0643i	0.523053	−	0.523053i
$533$	−11.6153	−	11.6153i	−0.503116	−	0.503116i
$534$	2.48245	+	2.48245i	0.107426	+	0.107426i
$535$			47.8397i			2.06829i
$536$		−	8.30209i		−	0.358596i
$537$	−29.6783	−	29.6783i	−1.28071	−	1.28071i
$538$	−0.768330	−	0.768330i	−0.0331251	−	0.0331251i
$539$	2.65243	−	2.65243i	0.114248	−	0.114248i
$540$	−72.8664			−3.13567
$541$	27.4996	−	27.4996i	1.18230	−	1.18230i	0.203152	−	0.979147i	$-0.434882\pi$
$541$	27.4996	−	27.4996i	1.18230	−	1.18230i	0.979147	−	0.203152i	$-0.0651185\pi$
$542$		−	3.34248i		−	0.143572i
$543$	−33.6071			−1.44222
$544$	−0.919829	−	16.1620i	−0.0394373	−	0.692941i
$545$	14.8918			0.637893
$546$		−	5.34025i		−	0.228541i
$547$	23.2663	−	23.2663i	0.994794	−	0.994794i	−0.00519216	−	0.999987i	$-0.501653\pi$
$547$	23.2663	−	23.2663i	0.994794	−	0.994794i	0.999987	+	0.00519216i	$0.00165272\pi$
$548$	29.2605			1.24995
$549$	−35.0289	+	35.0289i	−1.49500	+	1.49500i
$550$	0.977185	+	0.977185i	0.0416673	+	0.0416673i
$551$	−30.6442	−	30.6442i	−1.30549	−	1.30549i
$552$		−	18.6413i		−	0.793428i
$553$		−	17.4993i		−	0.744145i
$554$	2.31073	+	2.31073i	0.0981736	+	0.0981736i
$555$	−35.2484	−	35.2484i	−1.49621	−	1.49621i
$556$	14.6602	−	14.6602i	0.621733	−	0.621733i
$557$	−9.63597			−0.408289			−0.204145	−	0.978941i	$-0.565441\pi$
$557$	−9.63597			−0.408289			−0.204145	+	0.978941i	$0.565441\pi$
$558$	9.77086	−	9.77086i	0.413634	−	0.413634i
$559$		−	28.0465i		−	1.18624i
$560$	17.4545			0.737588
$561$	13.0883	−	0.744892i	0.552588	−	0.0314494i
$562$	−6.23903			−0.263178
$563$		−	23.8278i		−	1.00422i	−0.864804	−	0.502110i	$-0.832557\pi$
$563$		−	23.8278i		−	1.00422i	0.864804	−	0.502110i	$-0.167443\pi$
$564$	−24.1973	+	24.1973i	−1.01889	+	1.01889i
$565$	28.6906			1.20702
$566$	0.844585	−	0.844585i	0.0355005	−	0.0355005i
$567$	25.7636	+	25.7636i	1.08197	+	1.08197i
$568$	−1.94149	−	1.94149i	−0.0814632	−	0.0814632i
$569$		−	3.29524i		−	0.138144i	−0.997612	−	0.0690719i	$-0.977996\pi$
$569$		−	3.29524i		−	0.138144i	0.997612	−	0.0690719i	$-0.0220038\pi$
$570$			17.0915i			0.715885i
$571$	−16.9687	−	16.9687i	−0.710118	−	0.710118i	0.256442	−	0.966560i	$-0.417450\pi$
$571$	−16.9687	−	16.9687i	−0.710118	−	0.710118i	−0.966560	+	0.256442i	$0.917450\pi$
$572$	−3.45558	−	3.45558i	−0.144485	−	0.144485i
$573$	43.5812	−	43.5812i	1.82063	−	1.82063i
$574$	4.05067			0.169072
$575$	11.6052	−	11.6052i	0.483972	−	0.483972i
$576$		−	36.2637i		−	1.51099i
$577$	−34.9635			−1.45555			−0.727775	−	0.685816i	$-0.759445\pi$
$577$	−34.9635			−1.45555			−0.727775	+	0.685816i	$0.759445\pi$
$578$	0.688666	+	6.03057i	0.0286447	+	0.250839i
$579$	−74.0421			−3.07708
$580$		−	47.8125i		−	1.98531i
$581$	−8.58765	+	8.58765i	−0.356276	+	0.356276i
$582$	6.01244			0.249223
$583$	1.10354	−	1.10354i	0.0457040	−	0.0457040i
$584$	−3.94920	−	3.94920i	−0.163419	−	0.163419i
$585$	−39.0747	−	39.0747i	−1.61554	−	1.61554i
$586$			4.32858i			0.178812i
$587$			20.2451i			0.835606i	0.908538	+	0.417803i	$0.137200\pi$
$587$			20.2451i			0.835606i	−0.908538	+	0.417803i	$0.862800\pi$
$588$	15.7918	+	15.7918i	0.651242	+	0.651242i
$589$	19.4584	+	19.4584i	0.801768	+	0.801768i
$590$	2.90834	−	2.90834i	0.119734	−	0.119734i
$591$	32.5552			1.33914
$592$	12.1024	−	12.1024i	0.497404	−	0.497404i
$593$		−	7.66705i		−	0.314848i	−0.987531	−	0.157424i	$-0.949681\pi$
$593$		−	7.66705i		−	0.314848i	0.987531	−	0.157424i	$-0.0503189\pi$
$594$	−4.66498			−0.191406
$595$	−22.0986	+	1.25769i	−0.905953	+	0.0515605i
$596$	−11.7645			−0.481891
$597$			52.3208i			2.14135i
$598$	2.79395	−	2.79395i	0.114253	−	0.114253i
$599$	33.2945			1.36038			0.680188	−	0.733038i	$-0.261898\pi$
$599$	33.2945			1.36038			0.680188	+	0.733038i	$0.261898\pi$
$600$	−12.0318	+	12.0318i	−0.491196	+	0.491196i
$601$	−8.05906	−	8.05906i	−0.328736	−	0.328736i	0.523370	−	0.852106i	$-0.324675\pi$
$601$	−8.05906	−	8.05906i	−0.328736	−	0.328736i	−0.852106	+	0.523370i	$0.824675\pi$
$602$	4.89039	+	4.89039i	0.199317	+	0.199317i
$603$			42.6871i			1.73835i
$604$			0.546356i			0.0222309i
$605$	−2.10601	−	2.10601i	−0.0856213	−	0.0856213i
$606$	−7.28517	−	7.28517i	−0.295940	−	0.295940i
$607$	1.02989	−	1.02989i	0.0418021	−	0.0418021i	−0.685897	−	0.727699i	$-0.740590\pi$
$607$	1.02989	−	1.02989i	0.0418021	−	0.0418021i	0.727699	+	0.685897i	$0.240590\pi$
$608$	−19.8471			−0.804905
$609$	−34.7419	+	34.7419i	−1.40781	+	1.40781i
$610$			7.40990i			0.300018i
$611$	−15.0005			−0.606856
$612$	3.11879	+	54.7992i	0.126069	+	2.21513i
$613$	−27.6446			−1.11656			−0.558278	−	0.829654i	$-0.688538\pi$
$613$	−27.6446			−1.11656			−0.558278	+	0.829654i	$0.688538\pi$
$614$		−	3.18321i		−	0.128464i
$615$	42.1460	−	42.1460i	1.69949	−	1.69949i
$616$	2.49221			0.100414
$617$	6.07169	−	6.07169i	0.244437	−	0.244437i	−0.574246	−	0.818683i	$-0.694705\pi$
$617$	6.07169	−	6.07169i	0.244437	−	0.244437i	0.818683	+	0.574246i	$0.194705\pi$
$618$	−10.9091	−	10.9091i	−0.438830	−	0.438830i
$619$	19.3585	+	19.3585i	0.778085	+	0.778085i	0.979505	−	0.201420i	$-0.0645555\pi$
$619$	19.3585	+	19.3585i	0.778085	+	0.778085i	−0.201420	+	0.979505i	$0.564556\pi$
$620$			30.3598i			1.21928i
$621$			55.4022i			2.22321i
$622$	1.21846	+	1.21846i	0.0488559	+	0.0488559i
$623$	3.94154	+	3.94154i	0.157914	+	0.157914i
$624$	19.0775	−	19.0775i	0.763711	−	0.763711i
$625$	29.3717			1.17487
$626$	−3.93483	+	3.93483i	−0.157267	+	0.157267i
$627$		−	16.0725i		−	0.641873i
$628$	32.5810			1.30012
$629$	−14.4503	+	16.1944i	−0.576173	+	0.645714i
$630$	13.6267			0.542901
$631$			9.79787i			0.390047i	0.980799	+	0.195024i	$0.0624783\pi$
$631$			9.79787i			0.390047i	−0.980799	+	0.195024i	$0.937522\pi$
$632$	−9.49192	+	9.49192i	−0.377568	+	0.377568i
$633$	−40.3562			−1.60401
$634$	3.74233	−	3.74233i	0.148627	−	0.148627i
$635$	−17.9076	−	17.9076i	−0.710643	−	0.710643i
$636$	6.57014	+	6.57014i	0.260523	+	0.260523i
$637$			9.78971i			0.387883i
$638$		−	3.06100i		−	0.121186i
$639$	9.98264	+	9.98264i	0.394907	+	0.394907i
$640$	−20.3728	−	20.3728i	−0.805306	−	0.805306i
$641$	12.3196	−	12.3196i	0.486596	−	0.486596i	−0.420634	−	0.907230i	$-0.638192\pi$
$641$	12.3196	−	12.3196i	0.486596	−	0.486596i	0.907230	+	0.420634i	$0.138192\pi$
$642$	−18.2347			−0.719665
$643$	−29.1065	+	29.1065i	−1.14785	+	1.14785i	−0.160875	+	0.986975i	$0.551431\pi$
$643$	−29.1065	+	29.1065i	−1.14785	+	1.14785i	−0.986975	+	0.160875i	$0.948569\pi$
$644$		−	14.3118i		−	0.563964i
$645$	101.766			4.00703
$646$	7.42964	−	0.422843i	0.292315	−	0.0166365i
$647$	4.49653			0.176777			0.0883884	−	0.996086i	$-0.471828\pi$
$647$	4.49653			0.176777			0.0883884	+	0.996086i	$0.471828\pi$
$648$		−	27.9493i		−	1.09795i
$649$	−2.73494	+	2.73494i	−0.107356	+	0.107356i
$650$	−3.60663			−0.141464
$651$	22.0603	−	22.0603i	0.864612	−	0.864612i
$652$	−14.1257	−	14.1257i	−0.553206	−	0.553206i
$653$	28.2416	+	28.2416i	1.10518	+	1.10518i	0.993775	+	0.111405i	$0.0355351\pi$
$653$	28.2416	+	28.2416i	1.10518	+	1.10518i	0.111405	+	0.993775i	$0.464465\pi$
$654$			5.67616i			0.221955i
$655$			15.8257i			0.618361i
$656$	14.4706	+	14.4706i	0.564983	+	0.564983i
$657$	20.3057	+	20.3057i	0.792201	+	0.792201i
$658$	2.61560	−	2.61560i	0.101967	−	0.101967i
$659$	12.8809			0.501770			0.250885	−	0.968017i	$-0.419278\pi$
$659$	12.8809			0.501770			0.250885	+	0.968017i	$0.419278\pi$
$660$	12.5385	−	12.5385i	0.488061	−	0.488061i
$661$			9.90637i			0.385313i	0.981266	+	0.192657i	$0.0617103\pi$
$661$			9.90637i			0.385313i	−0.981266	+	0.192657i	$0.938290\pi$
$662$	−10.7076			−0.416164
$663$	−22.7787	+	25.5280i	−0.884653	+	0.991426i
$664$	9.31619			0.361538
$665$			27.1372i			1.05233i
$666$	9.44829	−	9.44829i	0.366114	−	0.366114i
$667$	−36.3531			−1.40760
$668$	−4.63557	+	4.63557i	−0.179356	+	0.179356i
$669$	−30.8524	−	30.8524i	−1.19282	−	1.19282i
$670$	4.51495	+	4.51495i	0.174428	+	0.174428i
$671$		−	6.96811i		−	0.269001i
$672$			22.5010i			0.867994i
$673$	−26.3467	−	26.3467i	−1.01559	−	1.01559i	−0.999877	−	0.0157133i	$-0.994998\pi$
$673$	−26.3467	−	26.3467i	−1.01559	−	1.01559i	−0.0157133	−	0.999877i	$-0.505002\pi$
$674$	−1.27060	−	1.27060i	−0.0489415	−	0.0489415i
$675$	35.7586	−	35.7586i	1.37635	−	1.37635i
$676$	−11.5887			−0.445720
$677$	16.8239	−	16.8239i	0.646594	−	0.646594i	−0.305574	−	0.952168i	$-0.598848\pi$
$677$	16.8239	−	16.8239i	0.646594	−	0.646594i	0.952168	+	0.305574i	$0.0988483\pi$
$678$			10.9357i			0.419985i
$679$	9.54629			0.366353
$680$	12.6689	+	11.3045i	0.485828	+	0.433506i
$681$	32.5899			1.24885
$682$			1.94367i			0.0744269i
$683$	−19.8159	+	19.8159i	−0.758234	+	0.758234i	−0.976001	−	0.217767i	$-0.930123\pi$
$683$	−19.8159	+	19.8159i	−0.758234	+	0.758234i	0.217767	+	0.976001i	$0.430123\pi$
$684$	67.2938			2.57304
$685$	−32.9090	+	32.9090i	−1.25739	+	1.25739i
$686$	−4.89248	−	4.89248i	−0.186796	−	0.186796i
$687$	9.42995	+	9.42995i	0.359775	+	0.359775i
$688$			34.9408i			1.33211i
$689$			4.07299i			0.155169i
$690$	10.1378	+	10.1378i	0.385939	+	0.385939i
$691$	−8.71162	−	8.71162i	−0.331406	−	0.331406i	0.521714	−	0.853120i	$-0.325293\pi$
$691$	−8.71162	−	8.71162i	−0.331406	−	0.331406i	−0.853120	+	0.521714i	$0.825293\pi$
$692$	23.6235	−	23.6235i	0.898029	−	0.898029i
$693$	−12.8143			−0.486774
$694$	−2.53336	+	2.53336i	−0.0961649	+	0.0961649i
$695$			32.9765i			1.25087i
$696$	37.6893			1.42861
$697$	−19.3635	−	17.2781i	−0.733444	−	0.654454i
$698$	−3.12212			−0.118174
$699$		−	64.4615i		−	2.43816i
$700$	−9.23735	+	9.23735i	−0.349139	+	0.349139i
$701$	−50.5640			−1.90978			−0.954889	−	0.296963i	$-0.904026\pi$
$701$	−50.5640			−1.90978			−0.954889	+	0.296963i	$0.904026\pi$
$702$	8.60885	−	8.60885i	0.324920	−	0.324920i
$703$	18.8160	+	18.8160i	0.709658	+	0.709658i
$704$	3.60688	+	3.60688i	0.135939	+	0.135939i
$705$		−	54.4290i		−	2.04992i
$706$		−	5.45137i		−	0.205165i
$707$	−11.5671	−	11.5671i	−0.435025	−	0.435025i
$708$	−16.2830	−	16.2830i	−0.611952	−	0.611952i
$709$	−33.4141	+	33.4141i	−1.25489	+	1.25489i	−0.301391	+	0.953501i	$0.597451\pi$
$709$	−33.4141	+	33.4141i	−1.25489	+	1.25489i	−0.953501	+	0.301391i	$0.902549\pi$
$710$	2.11170			0.0792506
$711$	48.8049	−	48.8049i	1.83033	−	1.83033i
$712$		−	4.27592i		−	0.160247i
$713$	23.0834			0.864479
$714$	−0.479385	−	8.42312i	−0.0179405	−	0.315227i
$715$	7.77293			0.290691
$716$			24.7184i			0.923770i
$717$	15.4680	−	15.4680i	0.577662	−	0.577662i
$718$	8.60260			0.321046
$719$	6.03603	−	6.03603i	0.225106	−	0.225106i	−0.585539	−	0.810645i	$-0.699117\pi$
$719$	6.03603	−	6.03603i	0.225106	−	0.225106i	0.810645	+	0.585539i	$0.199117\pi$
$720$	48.6801	+	48.6801i	1.81420	+	1.81420i
$721$	−17.3211	−	17.3211i	−0.645070	−	0.645070i
$722$		−	2.33979i		−	0.0870780i
$723$		−	55.8836i		−	2.07833i
$724$	13.9953	+	13.9953i	0.520131	+	0.520131i
$725$	23.4636	+	23.4636i	0.871416	+	0.871416i
$726$	0.802728	−	0.802728i	0.0297920	−	0.0297920i
$727$	−22.1110			−0.820050			−0.410025	−	0.912074i	$-0.634480\pi$
$727$	−22.1110			−0.820050			−0.410025	+	0.912074i	$0.634480\pi$
$728$	−4.59917	+	4.59917i	−0.170457	+	0.170457i
$729$			19.0820i			0.706740i
$730$	4.29541			0.158980
$731$	−2.51768	−	44.2374i	−0.0931199	−	1.63618i
$732$	41.4860			1.53337
$733$			27.2869i			1.00786i	0.863743	+	0.503932i	$0.168114\pi$
$733$			27.2869i			1.00786i	−0.863743	+	0.503932i	$0.831886\pi$
$734$	−6.67706	+	6.67706i	−0.246455	+	0.246455i
$735$	−35.5217			−1.31024
$736$	−11.7722	+	11.7722i	−0.433930	+	0.433930i
$737$	−4.24576	−	4.24576i	−0.156395	−	0.156395i
$738$	11.2972	+	11.2972i	0.415856	+	0.415856i
$739$		−	15.6846i		−	0.576967i	−0.957485	−	0.288484i	$-0.906849\pi$
$739$		−	15.6846i		−	0.576967i	0.957485	−	0.288484i	$-0.0931511\pi$
$740$			29.3576i			1.07921i
$741$	29.6605	+	29.6605i	1.08961	+	1.08961i
$742$	−0.710197	−	0.710197i	−0.0260722	−	0.0260722i
$743$	−20.8151	+	20.8151i	−0.763632	+	0.763632i	−0.976977	−	0.213345i	$-0.931564\pi$
$743$	−20.8151	+	20.8151i	−0.763632	+	0.763632i	0.213345	+	0.976977i	$0.431564\pi$
$744$	−23.9318			−0.877383
$745$	13.2314	−	13.2314i	0.484760	−	0.484760i
$746$			8.22682i			0.301205i
$747$	−47.9014			−1.75262
$748$	−5.76067	−	5.14026i	−0.210631	−	0.187947i
$749$	−28.9522			−1.05789
$750$			3.81890i			0.139446i
$751$	17.4886	−	17.4886i	0.638169	−	0.638169i	−0.311934	−	0.950104i	$-0.600977\pi$
$751$	17.4886	−	17.4886i	0.638169	−	0.638169i	0.950104	+	0.311934i	$0.100977\pi$
$752$	18.6879			0.681479
$753$	64.8131	−	64.8131i	2.36192	−	2.36192i
$754$	5.64884	+	5.64884i	0.205719	+	0.205719i
$755$	−0.614481	−	0.614481i	−0.0223633	−	0.0223633i
$756$		−	44.0982i		−	1.60384i
$757$		−	36.0891i		−	1.31168i	−0.754900	−	0.655840i	$-0.772315\pi$
$757$		−	36.0891i		−	1.31168i	0.754900	−	0.655840i	$-0.227685\pi$
$758$	−8.57208	−	8.57208i	−0.311352	−	0.311352i
$759$	−9.53335	−	9.53335i	−0.346039	−	0.346039i
$760$	14.7197	−	14.7197i	0.533939	−	0.533939i
$761$	34.4723			1.24962			0.624810	−	0.780777i	$-0.285176\pi$
$761$	34.4723			1.24962			0.624810	+	0.780777i	$0.285176\pi$
$762$	6.82570	−	6.82570i	0.247269	−	0.247269i
$763$			9.01237i			0.326270i
$764$	−36.2978			−1.31321
$765$	−65.1399	−	58.1245i	−2.35514	−	2.10150i
$766$	0.409563			0.0147981
$767$		−	10.0942i		−	0.364481i
$768$	−15.1709	+	15.1709i	−0.547432	+	0.547432i
$769$	2.61232			0.0942025			0.0471013	−	0.998890i	$-0.485002\pi$
$769$	2.61232			0.0942025			0.0471013	+	0.998890i	$0.485002\pi$
$770$	−1.35535	+	1.35535i	−0.0488433	+	0.0488433i
$771$	−11.8724	−	11.8724i	−0.427573	−	0.427573i
$772$	30.8340	+	30.8340i	1.10974	+	1.10974i
$773$		−	0.893065i		−	0.0321213i	−0.999871	−	0.0160607i	$-0.994888\pi$
$773$		−	0.893065i		−	0.0321213i	0.999871	−	0.0160607i	$-0.00511248\pi$
$774$			27.2783i			0.980497i
$775$	−14.8988	−	14.8988i	−0.535182	−	0.535182i
$776$	−5.17808	−	5.17808i	−0.185882	−	0.185882i
$777$	21.3320	−	21.3320i	0.765282	−	0.765282i
$778$	10.6388			0.381418
$779$	−22.4980	+	22.4980i	−0.806076	+	0.806076i
$780$			46.2776i			1.65701i
$781$	−1.98579			−0.0710573
$782$	4.15607	−	4.65768i	0.148621	−	0.166558i
$783$	−112.013			−4.00301
$784$		−	12.1962i		−	0.435579i
$785$	−36.6436	+	36.6436i	−1.30786	+	1.30786i
$786$	−6.03214			−0.215159
$787$	−13.5113	+	13.5113i	−0.481626	+	0.481626i	−0.905651	−	0.424025i	$-0.860617\pi$
$787$	−13.5113	+	13.5113i	−0.481626	+	0.481626i	0.424025	+	0.905651i	$0.360617\pi$
$788$	−13.5573	−	13.5573i	−0.482957	−	0.482957i
$789$	37.5404	+	37.5404i	1.33647	+	1.33647i
$790$		−	10.3241i		−	0.367313i
$791$			17.3633i			0.617368i
$792$	6.95069	+	6.95069i	0.246982	+	0.246982i
$793$	12.8591	+	12.8591i	0.456640	+	0.456640i
$794$	4.18339	−	4.18339i	0.148463	−	0.148463i
$795$	−14.7788			−0.524148
$796$	21.7884	−	21.7884i	0.772270	−	0.772270i
$797$			8.14629i			0.288556i	0.989537	+	0.144278i	$0.0460860\pi$
$797$			8.14629i			0.288556i	−0.989537	+	0.144278i	$0.953914\pi$
$798$	−10.3436			−0.366161
$799$	−23.6602	+	1.34657i	−0.837037	+	0.0476382i
$800$	15.1965			0.537276
$801$			21.9856i			0.776824i
$802$	5.39987	−	5.39987i	0.190676	−	0.190676i
$803$	−4.03931			−0.142544
$804$	25.2780	−	25.2780i	0.891485	−	0.891485i
$805$	16.0964	+	16.0964i	0.567322	+	0.567322i
$806$	−3.58688	−	3.58688i	−0.126343	−	0.126343i
$807$		−	9.67610i		−	0.340615i
$808$			12.5484i			0.441451i
$809$	12.9619	+	12.9619i	0.455717	+	0.455717i	0.897247	−	0.441529i	$-0.145564\pi$
$809$	12.9619	+	12.9619i	0.455717	+	0.455717i	−0.441529	+	0.897247i	$0.645564\pi$
$810$	15.1998	+	15.1998i	0.534065	+	0.534065i
$811$	3.73607	−	3.73607i	0.131191	−	0.131191i	−0.638462	−	0.769653i	$-0.720429\pi$
$811$	3.73607	−	3.73607i	0.131191	−	0.131191i	0.769653	+	0.638462i	$0.220429\pi$
$812$	28.9357			1.01545
$813$	21.0470	−	21.0470i	0.738151	−	0.738151i
$814$			1.87950i			0.0658764i
$815$	31.7741			1.11300
$816$	28.3782	−	31.8033i	0.993436	−	1.11334i
$817$	−54.3238			−1.90055
$818$			9.32513i			0.326046i
$819$	23.6477	−	23.6477i	0.826318	−	0.826318i
$820$	−35.1024			−1.22583
$821$	5.66625	−	5.66625i	0.197754	−	0.197754i	−0.601283	−	0.799036i	$-0.705343\pi$
$821$	5.66625	−	5.66625i	0.197754	−	0.197754i	0.799036	+	0.601283i	$0.205343\pi$
$822$	−12.5437	−	12.5437i	−0.437510	−	0.437510i
$823$	8.56736	+	8.56736i	0.298639	+	0.298639i	0.840481	−	0.541841i	$-0.182273\pi$
$823$	8.56736	+	8.56736i	0.298639	+	0.298639i	−0.541841	+	0.840481i	$0.682273\pi$
$824$			18.7905i			0.654599i
$825$			12.3063i			0.428452i
$826$	1.76010	+	1.76010i	0.0612418	+	0.0612418i
$827$	3.41855	+	3.41855i	0.118875	+	0.118875i	0.764042	−	0.645167i	$-0.223212\pi$
$827$	3.41855	+	3.41855i	0.118875	+	0.118875i	−0.645167	+	0.764042i	$0.723212\pi$
$828$	39.9151	−	39.9151i	1.38715	−	1.38715i
$829$	−22.4516			−0.779777			−0.389889	−	0.920862i	$-0.627487\pi$
$829$	−22.4516			−0.779777			−0.389889	+	0.920862i	$0.627487\pi$
$830$	−5.06646	+	5.06646i	−0.175859	+	0.175859i
$831$			29.1006i			1.00949i
$832$	−13.3124			−0.461525
$833$	0.878806	+	15.4412i	0.0304488	+	0.535007i
$834$	−12.5694			−0.435242
$835$		−	10.4272i		−	0.360847i
$836$	−6.69320	+	6.69320i	−0.231489	+	0.231489i
$837$	71.1256			2.45846
$838$	−3.96809	+	3.96809i	−0.137075	+	0.137075i
$839$	25.1626	+	25.1626i	0.868709	+	0.868709i	0.992330	−	0.123621i	$-0.0394506\pi$
$839$	25.1626	+	25.1626i	0.868709	+	0.868709i	−0.123621	+	0.992330i	$0.539451\pi$
$840$	−16.6880	−	16.6880i	−0.575790	−	0.575790i
$841$		−	44.4990i		−	1.53445i
$842$		−	5.75686i		−	0.198395i
$843$	−39.2861	−	39.2861i	−1.35309	−	1.35309i
$844$	16.8059	+	16.8059i	0.578482	+	0.578482i
$845$	13.0337	−	13.0337i	0.448374	−	0.448374i
$846$	14.5896			0.501602
$847$	1.27454	−	1.27454i	0.0437936	−	0.0437936i
$848$		−	5.07421i		−	0.174249i
$849$	10.6364			0.365041
$850$	−5.68871	+	0.323761i	−0.195121	+	0.0111049i
$851$	22.3213			0.765165
$852$		−	11.8228i		−	0.405043i
$853$	23.7669	−	23.7669i	0.813762	−	0.813762i	−0.171433	−	0.985196i	$-0.554840\pi$
$853$	23.7669	−	23.7669i	0.813762	−	0.813762i	0.985196	+	0.171433i	$0.0548399\pi$
$854$	−4.48442			−0.153454
$855$	−75.6847	+	75.6847i	−2.58836	+	2.58836i
$856$	15.7042	+	15.7042i	0.536759	+	0.536759i
$857$	−27.3074	−	27.3074i	−0.932804	−	0.932804i	0.0650762	−	0.997880i	$-0.479271\pi$
$857$	−27.3074	−	27.3074i	−0.932804	−	0.932804i	−0.997880	+	0.0650762i	$0.979271\pi$
$858$			2.96274i			0.101146i
$859$		−	9.54447i		−	0.325653i	−0.986655	−	0.162827i	$-0.947939\pi$
$859$		−	9.54447i		−	0.325653i	0.986655	−	0.162827i	$-0.0520611\pi$
$860$	−42.3792	−	42.3792i	−1.44512	−	1.44512i
$861$	25.5064	+	25.5064i	0.869257	+	0.869257i
$862$	−0.723780	+	0.723780i	−0.0246520	+	0.0246520i
$863$	54.1335			1.84272			0.921362	−	0.388705i	$-0.127077\pi$
$863$	54.1335			1.84272			0.921362	+	0.388705i	$0.127077\pi$
$864$	−36.2732	+	36.2732i	−1.23404	+	1.23404i
$865$			53.1382i			1.80675i
$866$	5.54463			0.188414
$867$	−33.6371	+	42.3099i	−1.14238	+	1.43692i
$868$	−18.3735			−0.623638
$869$			9.70851i			0.329339i
$870$	−20.4967	+	20.4967i	−0.694903	+	0.694903i
$871$	15.6704			0.530973
$872$	4.88847	−	4.88847i	0.165544	−	0.165544i
$873$	26.6243	+	26.6243i	0.901096	+	0.901096i
$874$	−5.41167	−	5.41167i	−0.183052	−	0.183052i
$875$			6.06349i			0.204983i
$876$		−	24.0488i		−	0.812534i
$877$	18.9119	+	18.9119i	0.638610	+	0.638610i	0.950213	−	0.311602i	$-0.100866\pi$
$877$	18.9119	+	18.9119i	0.638610	+	0.638610i	−0.311602	+	0.950213i	$0.600866\pi$
$878$	1.78872	+	1.78872i	0.0603664	+	0.0603664i
$879$	−27.2564	+	27.2564i	−0.919334	+	0.919334i
$880$	−9.68367			−0.326437
$881$	−13.1147	+	13.1147i	−0.441847	+	0.441847i	−0.892632	−	0.450786i	$-0.851144\pi$
$881$	−13.1147	+	13.1147i	−0.441847	+	0.441847i	0.450786	+	0.892632i	$0.351144\pi$
$882$		−	9.52157i		−	0.320608i
$883$	−7.19970			−0.242289			−0.121145	−	0.992635i	$-0.538656\pi$
$883$	−7.19970			−0.242289			−0.121145	+	0.992635i	$0.538656\pi$
$884$	20.1168	−	1.14491i	0.676601	−	0.0385074i
$885$	36.6266			1.23119
$886$			5.56786i			0.187056i
$887$	30.1978	−	30.1978i	1.01394	−	1.01394i	0.0140419	−	0.999901i	$-0.495530\pi$
$887$	30.1978	−	30.1978i	1.01394	−	1.01394i	0.999901	−	0.0140419i	$-0.00446983\pi$
$888$	−23.1417			−0.776586
$889$	10.8376	−	10.8376i	0.363480	−	0.363480i
$890$	2.32539	+	2.32539i	0.0779472	+	0.0779472i
$891$	−14.2935	−	14.2935i	−0.478851	−	0.478851i
$892$			25.6963i			0.860375i
$893$			29.0548i			0.972283i
$894$	5.04329	+	5.04329i	0.168673	+	0.168673i
$895$	−27.8006	−	27.8006i	−0.929270	−	0.929270i
$896$	12.3295	−	12.3295i	0.411898	−	0.411898i
$897$	35.1861			1.17483
$898$	−1.40759	+	1.40759i	−0.0469720	+	0.0469720i
$899$			46.6702i			1.55654i
$900$	−51.5254			−1.71751
$901$	0.365626	+	6.42429i	0.0121808	+	0.214024i
$902$	−2.24729			−0.0748267
$903$			61.5879i			2.04952i
$904$	9.41817	−	9.41817i	0.313244	−	0.313244i
$905$	−31.4807			−1.04646
$906$	0.234217	−	0.234217i	0.00778132	−	0.00778132i
$907$	7.58584	+	7.58584i	0.251884	+	0.251884i	0.821743	−	0.569859i	$-0.193002\pi$
$907$	7.58584	+	7.58584i	0.251884	+	0.251884i	−0.569859	+	0.821743i	$0.693002\pi$
$908$	−13.5717	−	13.5717i	−0.450392	−	0.450392i
$909$		−	64.5204i		−	2.14001i
$910$		−	5.00237i		−	0.165827i
$911$	1.77364	+	1.77364i	0.0587634	+	0.0587634i	0.735878	−	0.677114i	$-0.236770\pi$
$911$	1.77364	+	1.77364i	0.0587634	+	0.0587634i	−0.677114	+	0.735878i	$0.736770\pi$
$912$	−36.9516	−	36.9516i	−1.22359	−	1.22359i
$913$	4.76439	−	4.76439i	0.157678	−	0.157678i
$914$	14.8881			0.492454
$915$	−46.6589	+	46.6589i	−1.54250	+	1.54250i
$916$		−	7.85399i		−	0.259503i
$917$	−9.57758			−0.316280
$918$	12.8059	−	14.3515i	0.422656	−	0.473669i
$919$	1.49629			0.0493580			0.0246790	−	0.999695i	$-0.492144\pi$
$919$	1.49629			0.0493580			0.0246790	+	0.999695i	$0.492144\pi$
$920$		−	17.4619i		−	0.575702i
$921$	20.0442	−	20.0442i	0.660477	−	0.660477i
$922$	−0.963296			−0.0317245
$923$	3.66462	−	3.66462i	0.120623	−	0.120623i
$924$	7.58821	+	7.58821i	0.249634	+	0.249634i
$925$	−14.4070	−	14.4070i	−0.473699	−	0.473699i
$926$			5.07965i			0.166928i
$927$		−	96.6158i		−	3.17328i
$928$	−23.8012	−	23.8012i	−0.781314	−	0.781314i
$929$	−15.8265	−	15.8265i	−0.519252	−	0.519252i	0.398093	−	0.917345i	$-0.369672\pi$
$929$	−15.8265	−	15.8265i	−0.519252	−	0.519252i	−0.917345	+	0.398093i	$0.869672\pi$
$930$	13.0149	−	13.0149i	0.426776	−	0.426776i
$931$	18.9619			0.621452
$932$	−26.8442	+	26.8442i	−0.879313	+	0.879313i
$933$			15.3449i			0.502370i
$934$	7.00925			0.229350
$935$	12.2602	−	0.697763i	0.400951	−	0.0228193i
$936$	−25.6539			−0.838523
$937$			34.8148i			1.13735i	0.822562	+	0.568675i	$0.192544\pi$
$937$			34.8148i			1.13735i	−0.822562	+	0.568675i	$0.807456\pi$
$938$	−2.73241	+	2.73241i	−0.0892165	+	0.0892165i
$939$	−49.5540			−1.61713
$940$	−22.6663	+	22.6663i	−0.739294	+	0.739294i
$941$	12.4775	+	12.4775i	0.406755	+	0.406755i	0.880605	−	0.473850i	$-0.157136\pi$
$941$	12.4775	+	12.4775i	0.406755	+	0.406755i	−0.473850	+	0.880605i	$0.657136\pi$
$942$	−13.9671	−	13.9671i	−0.455073	−	0.455073i
$943$			26.6893i			0.869123i
$944$			12.5756i			0.409300i
$945$	49.5968	+	49.5968i	1.61338	+	1.61338i
$946$	−2.71316	−	2.71316i	−0.0882125	−	0.0882125i
$947$	−8.02552	+	8.02552i	−0.260794	+	0.260794i	−0.825377	−	0.564582i	$-0.809037\pi$
$947$	−8.02552	+	8.02552i	−0.260794	+	0.260794i	0.564582	+	0.825377i	$0.309037\pi$
$948$	−57.8015			−1.87731
$949$	7.45422	−	7.45422i	0.241974	−	0.241974i
$950$			6.98577i			0.226648i
$951$	47.1297			1.52829
$952$	−6.84137	+	7.66709i	−0.221730	+	0.248492i
$953$	28.5991			0.926417			0.463208	−	0.886249i	$-0.346698\pi$
$953$	28.5991			0.926417			0.463208	+	0.886249i	$0.346698\pi$
$954$		−	3.96143i		−	0.128256i
$955$	40.8238	−	40.8238i	1.32103	−	1.32103i
$956$	−12.8829			−0.416664
$957$	19.2746	−	19.2746i	0.623060	−	0.623060i
$958$	6.02968	+	6.02968i	0.194810	+	0.194810i
$959$	−19.9163	−	19.9163i	−0.643130	−	0.643130i
$960$		−	48.3038i		−	1.55900i
$961$			1.36549i			0.0440480i
$962$	−3.46847	−	3.46847i	−0.111828	−	0.111828i
$963$	−80.7468	−	80.7468i	−2.60203	−	2.60203i
$964$	−23.2721	+	23.2721i	−0.749543	+	0.749543i
$965$	−69.3574			−2.23269
$966$	−6.13531	+	6.13531i	−0.197400	+	0.197400i
$967$		−	33.4633i		−	1.07611i	−0.842911	−	0.538053i	$-0.819160\pi$
$967$		−	33.4633i		−	1.07611i	0.842911	−	0.538053i	$-0.180840\pi$
$968$	−1.38266			−0.0444405
$969$	49.4458	+	44.1207i	1.58843	+	1.41736i
$970$	5.63203			0.180833
$971$		−	26.5831i		−	0.853092i	−0.904466	−	0.426546i	$-0.859730\pi$
$971$		−	26.5831i		−	0.853092i	0.904466	−	0.426546i	$-0.140270\pi$
$972$	33.2003	−	33.2003i	1.06490	−	1.06490i
$973$	−19.9571			−0.639796
$974$	2.45283	−	2.45283i	0.0785938	−	0.0785938i
$975$	−22.7104	−	22.7104i	−0.727314	−	0.727314i
$976$	−16.0201	−	16.0201i	−0.512792	−	0.512792i
$977$			12.9623i			0.414702i	0.978267	+	0.207351i	$0.0664842\pi$
$977$			12.9623i			0.414702i	−0.978267	+	0.207351i	$0.933516\pi$
$978$			12.1111i			0.387269i
$979$	−2.18674	−	2.18674i	−0.0698886	−	0.0698886i
$980$	14.7926	+	14.7926i	0.472533	+	0.472533i
$981$	−25.1352	+	25.1352i	−0.802505	+	0.802505i
$982$	−4.31656			−0.137747
$983$	5.20851	−	5.20851i	0.166126	−	0.166126i	−0.619148	−	0.785274i	$-0.712522\pi$
$983$	5.20851	−	5.20851i	0.166126	−	0.166126i	0.785274	+	0.619148i	$0.212522\pi$
$984$		−	27.6703i		−	0.882096i
$985$	30.4955			0.971666
$986$	9.41695	+	8.40278i	0.299897	+	0.267599i
$987$	32.9400			1.04849
$988$		−	24.7035i		−	0.785924i
$989$	−32.2220	+	32.2220i	−1.02460	+	1.02460i
$990$	−7.56003			−0.240274
$991$	23.6281	−	23.6281i	0.750570	−	0.750570i	−0.224016	−	0.974586i	$-0.571917\pi$
$991$	23.6281	−	23.6281i	0.750570	−	0.750570i	0.974586	+	0.224016i	$0.0719166\pi$
$992$	15.1132	+	15.1132i	0.479846	+	0.479846i
$993$	−67.4242	−	67.4242i	−2.13964	−	2.13964i
$994$			1.27798i			0.0405351i
$995$			49.0104i			1.55374i
$996$	28.3657	+	28.3657i	0.898801	+	0.898801i
$997$	−18.8599	−	18.8599i	−0.597301	−	0.597301i	0.342293	−	0.939593i	$-0.388797\pi$
$997$	−18.8599	−	18.8599i	−0.597301	−	0.597301i	−0.939593	+	0.342293i	$0.888797\pi$
$998$	−6.98942	+	6.98942i	−0.221246	+	0.221246i
$999$	68.7775			2.17602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.89.8	✓	28
17.8	even	8		3179.2.a.bd.1.8		14
17.9	even	8		3179.2.a.be.1.8		14
17.13	even	4	inner	187.2.e.b.166.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.8	✓	28	1.1	even	1	trivial
187.2.e.b.166.7	yes	28	17.13	even	4	inner
3179.2.a.bd.1.8		14	17.8	even	8
3179.2.a.be.1.8		14	17.9	even	8

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.357045i q^{2} +(-2.24825 + 2.24825i) q^{3} +1.87252 q^{4} +(-2.10601 + 2.10601i) q^{5} +(-0.802728 - 0.802728i) q^{6} +(-1.27454 - 1.27454i) q^{7} +1.38266i q^{8} -7.10929i q^{9} +O(q^{10})\)	\(q+0.357045i q^{2} +(-2.24825 + 2.24825i) q^{3} +1.87252 q^{4} +(-2.10601 + 2.10601i) q^{5} +(-0.802728 - 0.802728i) q^{6} +(-1.27454 - 1.27454i) q^{7} +1.38266i q^{8} -7.10929i q^{9} +(-0.751939 - 0.751939i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-4.20990 + 4.20990i) q^{12} -2.60982 q^{13} +(0.455067 - 0.455067i) q^{14} -9.46967i q^{15} +3.25136 q^{16} +(-4.11644 + 0.234279i) q^{17} +2.53834 q^{18} +5.05502i q^{19} +(-3.94353 + 3.94353i) q^{20} +5.73097 q^{21} +(-0.252469 + 0.252469i) q^{22} +(2.99837 + 2.99837i) q^{23} +(-3.10858 - 3.10858i) q^{24} -3.87051i q^{25} -0.931823i q^{26} +(9.23872 + 9.23872i) q^{27} +(-2.38660 - 2.38660i) q^{28} +(-6.06214 + 6.06214i) q^{29} +3.38110 q^{30} +(3.84932 - 3.84932i) q^{31} +3.92621i q^{32} -3.17951 q^{33} +(-0.0836481 - 1.46976i) q^{34} +5.36836 q^{35} -13.3123i q^{36} +(3.72224 - 3.72224i) q^{37} -1.80487 q^{38} +(5.86753 - 5.86753i) q^{39} +(-2.91190 - 2.91190i) q^{40} +(4.45063 + 4.45063i) q^{41} +2.04621i q^{42} +10.7465i q^{43} +(1.32407 + 1.32407i) q^{44} +(14.9722 + 14.9722i) q^{45} +(-1.07055 + 1.07055i) q^{46} +5.74772 q^{47} +(-7.30989 + 7.30989i) q^{48} -3.75111i q^{49} +1.38195 q^{50} +(8.72809 - 9.78153i) q^{51} -4.88693 q^{52} -1.56064i q^{53} +(-3.29864 + 3.29864i) q^{54} -2.97834 q^{55} +(1.76226 - 1.76226i) q^{56} +(-11.3650 - 11.3650i) q^{57} +(-2.16446 - 2.16446i) q^{58} +3.86779i q^{59} -17.7321i q^{60} +(-4.92720 - 4.92720i) q^{61} +(1.37438 + 1.37438i) q^{62} +(-9.06105 + 9.06105i) q^{63} +5.10089 q^{64} +(5.49629 - 5.49629i) q^{65} -1.13523i q^{66} -6.00442 q^{67} +(-7.70812 + 0.438692i) q^{68} -13.4822 q^{69} +1.91675i q^{70} +(-1.40417 + 1.40417i) q^{71} +9.82975 q^{72} +(-2.85622 + 2.85622i) q^{73} +(1.32901 + 1.32901i) q^{74} +(8.70190 + 8.70190i) q^{75} +9.46562i q^{76} -1.80247i q^{77} +(2.09497 + 2.09497i) q^{78} +(6.86495 + 6.86495i) q^{79} +(-6.84739 + 6.84739i) q^{80} -20.2141 q^{81} +(-1.58908 + 1.58908i) q^{82} -6.73786i q^{83} +10.7313 q^{84} +(8.17586 - 9.16265i) q^{85} -3.83699 q^{86} -27.2584i q^{87} +(-0.977691 + 0.977691i) q^{88} -3.09252 q^{89} +(-5.34575 + 5.34575i) q^{90} +(3.32631 + 3.32631i) q^{91} +(5.61451 + 5.61451i) q^{92} +17.3085i q^{93} +2.05220i q^{94} +(-10.6459 - 10.6459i) q^{95} +(-8.82712 - 8.82712i) q^{96} +(-3.74500 + 3.74500i) q^{97} +1.33931 q^{98} +(5.02703 - 5.02703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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