LMFDB - Embedded newform 187.2.e.b.89.4

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			89.4
Character	$\chi$	$=$	187.89
Dual form			187.2.e.b.166.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.23360i q^{2} +(1.72482 - 1.72482i) q^{3} +0.478229 q^{4} +(-1.98987 + 1.98987i) q^{5} +(-2.12774 - 2.12774i) q^{6} +(-2.20951 - 2.20951i) q^{7} -3.05715i q^{8} -2.94999i q^{9} +O(q^{10})$	\(q-1.23360i q^{2} +(1.72482 - 1.72482i) q^{3} +0.478229 q^{4} +(-1.98987 + 1.98987i) q^{5} +(-2.12774 - 2.12774i) q^{6} +(-2.20951 - 2.20951i) q^{7} -3.05715i q^{8} -2.94999i q^{9} +(2.45471 + 2.45471i) q^{10} +(0.707107 + 0.707107i) q^{11} +(0.824857 - 0.824857i) q^{12} +5.06832 q^{13} +(-2.72566 + 2.72566i) q^{14} +6.86434i q^{15} -2.81484 q^{16} +(-0.768616 + 4.05083i) q^{17} -3.63911 q^{18} -1.88317i q^{19} +(-0.951615 + 0.951615i) q^{20} -7.62201 q^{21} +(0.872288 - 0.872288i) q^{22} +(5.34893 + 5.34893i) q^{23} +(-5.27302 - 5.27302i) q^{24} -2.91920i q^{25} -6.25228i q^{26} +(0.0862570 + 0.0862570i) q^{27} +(-1.05665 - 1.05665i) q^{28} +(-3.70748 + 3.70748i) q^{29} +8.46786 q^{30} +(-0.506938 + 0.506938i) q^{31} -2.64190i q^{32} +2.43926 q^{33} +(4.99711 + 0.948165i) q^{34} +8.79330 q^{35} -1.41077i q^{36} +(-6.36542 + 6.36542i) q^{37} -2.32308 q^{38} +(8.74193 - 8.74193i) q^{39} +(6.08333 + 6.08333i) q^{40} +(-0.731537 - 0.731537i) q^{41} +9.40252i q^{42} -4.66481i q^{43} +(0.338159 + 0.338159i) q^{44} +(5.87011 + 5.87011i) q^{45} +(6.59845 - 6.59845i) q^{46} -7.38146 q^{47} +(-4.85508 + 4.85508i) q^{48} +2.76389i q^{49} -3.60112 q^{50} +(5.66122 + 8.31267i) q^{51} +2.42382 q^{52} +6.59761i q^{53} +(0.106407 - 0.106407i) q^{54} -2.81411 q^{55} +(-6.75480 + 6.75480i) q^{56} +(-3.24812 - 3.24812i) q^{57} +(4.57355 + 4.57355i) q^{58} -11.0605i q^{59} +3.28272i q^{60} +(-6.97846 - 6.97846i) q^{61} +(0.625360 + 0.625360i) q^{62} +(-6.51804 + 6.51804i) q^{63} -8.88873 q^{64} +(-10.0853 + 10.0853i) q^{65} -3.00907i q^{66} +6.09852 q^{67} +(-0.367574 + 1.93722i) q^{68} +18.4519 q^{69} -10.8474i q^{70} +(4.01208 - 4.01208i) q^{71} -9.01855 q^{72} +(10.0292 - 10.0292i) q^{73} +(7.85239 + 7.85239i) q^{74} +(-5.03508 - 5.03508i) q^{75} -0.900586i q^{76} -3.12472i q^{77} +(-10.7840 - 10.7840i) q^{78} +(0.766509 + 0.766509i) q^{79} +(5.60118 - 5.60118i) q^{80} +9.14753 q^{81} +(-0.902424 + 0.902424i) q^{82} +2.54437i q^{83} -3.64507 q^{84} +(-6.53119 - 9.59009i) q^{85} -5.75451 q^{86} +12.7895i q^{87} +(2.16173 - 2.16173i) q^{88} -13.8261 q^{89} +(7.24137 - 7.24137i) q^{90} +(-11.1985 - 11.1985i) q^{91} +(2.55801 + 2.55801i) q^{92} +1.74875i q^{93} +9.10578i q^{94} +(3.74727 + 3.74727i) q^{95} +(-4.55680 - 4.55680i) q^{96} +(-1.23810 + 1.23810i) q^{97} +3.40954 q^{98} +(2.08596 - 2.08596i) 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 $

$2$		−	1.23360i		−	0.872288i	−0.899877	−	0.436144i	$-0.856344\pi$
$2$		−	1.23360i		−	0.872288i	0.899877	−	0.436144i	$-0.143656\pi$
$3$	1.72482	−	1.72482i	0.995824	−	0.995824i	−0.00416748	−	0.999991i	$-0.501327\pi$
$3$	1.72482	−	1.72482i	0.995824	−	0.995824i	0.999991	+	0.00416748i	$0.00132655\pi$
$4$	0.478229			0.239114
$5$	−1.98987	+	1.98987i	−0.889899	+	0.889899i	−0.994513	−	0.104614i	$-0.966639\pi$
$5$	−1.98987	+	1.98987i	−0.889899	+	0.889899i	0.104614	+	0.994513i	$0.466639\pi$
$6$	−2.12774	−	2.12774i	−0.868645	−	0.868645i
$7$	−2.20951	−	2.20951i	−0.835117	−	0.835117i	0.153094	−	0.988212i	$-0.451076\pi$
$7$	−2.20951	−	2.20951i	−0.835117	−	0.835117i	−0.988212	+	0.153094i	$0.951076\pi$
$8$		−	3.05715i		−	1.08086i
$9$		−	2.94999i		−	0.983330i
$10$	2.45471	+	2.45471i	0.776248	+	0.776248i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	0.824857	−	0.824857i	0.238116	−	0.238116i
$13$	5.06832			1.40570			0.702850	−	0.711339i	$-0.251911\pi$
$13$	5.06832			1.40570			0.702850	+	0.711339i	$0.251911\pi$
$14$	−2.72566	+	2.72566i	−0.728463	+	0.728463i
$15$			6.86434i			1.77236i
$16$	−2.81484			−0.703710
$17$	−0.768616	+	4.05083i	−0.186417	+	0.982471i
$17$	−0.768616	+	4.05083i	−0.186417	+	0.982471i
$18$	−3.63911			−0.857747
$19$		−	1.88317i		−	0.432029i	−0.976390	−	0.216014i	$-0.930694\pi$
$19$		−	1.88317i		−	0.432029i	0.976390	−	0.216014i	$-0.0693058\pi$
$20$	−0.951615	+	0.951615i	−0.212788	+	0.212788i
$21$	−7.62201			−1.66326
$22$	0.872288	−	0.872288i	0.185972	−	0.185972i
$23$	5.34893	+	5.34893i	1.11533	+	1.11533i	0.992418	+	0.122911i	$0.0392231\pi$
$23$	5.34893	+	5.34893i	1.11533	+	1.11533i	0.122911	+	0.992418i	$0.460777\pi$
$24$	−5.27302	−	5.27302i	−1.07635	−	1.07635i
$25$		−	2.91920i		−	0.583839i
$26$		−	6.25228i		−	1.22617i
$27$	0.0862570	+	0.0862570i	0.0166002	+	0.0166002i
$28$	−1.05665	−	1.05665i	−0.199689	−	0.199689i
$29$	−3.70748	+	3.70748i	−0.688462	+	0.688462i	−0.961892	−	0.273430i	$-0.911842\pi$
$29$	−3.70748	+	3.70748i	−0.688462	+	0.688462i	0.273430	+	0.961892i	$0.411842\pi$
$30$	8.46786			1.54601
$31$	−0.506938	+	0.506938i	−0.0910488	+	0.0910488i	−0.751164	−	0.660115i	$-0.770507\pi$
$31$	−0.506938	+	0.506938i	−0.0910488	+	0.0910488i	0.660115	+	0.751164i	$0.270507\pi$
$32$		−	2.64190i		−	0.467027i
$33$	2.43926			0.424621
$34$	4.99711	+	0.948165i	0.856997	+	0.162609i
$35$	8.79330			1.48634
$36$		−	1.41077i		−	0.235128i
$37$	−6.36542	+	6.36542i	−1.04647	+	1.04647i	−0.0476019	+	0.998866i	$0.515158\pi$
$37$	−6.36542	+	6.36542i	−1.04647	+	1.04647i	−0.998866	+	0.0476019i	$0.984842\pi$
$38$	−2.32308			−0.376853
$39$	8.74193	−	8.74193i	1.39983	−	1.39983i
$40$	6.08333	+	6.08333i	0.961860	+	0.961860i
$41$	−0.731537	−	0.731537i	−0.114247	−	0.114247i	0.647672	−	0.761919i	$-0.275743\pi$
$41$	−0.731537	−	0.731537i	−0.114247	−	0.114247i	−0.761919	+	0.647672i	$0.775743\pi$
$42$			9.40252i			1.45084i
$43$		−	4.66481i		−	0.711376i	−0.934605	−	0.355688i	$-0.884247\pi$
$43$		−	4.66481i		−	0.711376i	0.934605	−	0.355688i	$-0.115753\pi$
$44$	0.338159	+	0.338159i	0.0509794	+	0.0509794i
$45$	5.87011	+	5.87011i	0.875064	+	0.875064i
$46$	6.59845	−	6.59845i	0.972888	−	0.972888i
$47$	−7.38146			−1.07670			−0.538348	−	0.842722i	$-0.680952\pi$
$47$	−7.38146			−1.07670			−0.538348	+	0.842722i	$0.680952\pi$
$48$	−4.85508	+	4.85508i	−0.700771	+	0.700771i
$49$			2.76389i			0.394842i
$50$	−3.60112			−0.509276
$51$	5.66122	+	8.31267i	0.792730	+	1.16401i
$52$	2.42382			0.336123
$53$			6.59761i			0.906251i	0.891447	+	0.453125i	$0.149691\pi$
$53$			6.59761i			0.906251i	−0.891447	+	0.453125i	$0.850309\pi$
$54$	0.106407	−	0.106407i	0.0144801	−	0.0144801i
$55$	−2.81411			−0.379454
$56$	−6.75480	+	6.75480i	−0.902648	+	0.902648i
$57$	−3.24812	−	3.24812i	−0.430224	−	0.430224i
$58$	4.57355	+	4.57355i	0.600537	+	0.600537i
$59$		−	11.0605i		−	1.43995i	−0.693999	−	0.719976i	$-0.744153\pi$
$59$		−	11.0605i		−	1.43995i	0.693999	−	0.719976i	$-0.255847\pi$
$60$			3.28272i			0.423798i
$61$	−6.97846	−	6.97846i	−0.893501	−	0.893501i	0.101350	−	0.994851i	$-0.467684\pi$
$61$	−6.97846	−	6.97846i	−0.893501	−	0.893501i	−0.994851	+	0.101350i	$0.967684\pi$
$62$	0.625360	+	0.625360i	0.0794207	+	0.0794207i
$63$	−6.51804	+	6.51804i	−0.821196	+	0.821196i
$64$	−8.88873			−1.11109
$65$	−10.0853	+	10.0853i	−1.25093	+	1.25093i
$66$		−	3.00907i		−	0.370391i
$67$	6.09852			0.745053			0.372527	−	0.928022i	$-0.378492\pi$
$67$	6.09852			0.745053			0.372527	+	0.928022i	$0.378492\pi$
$68$	−0.367574	+	1.93722i	−0.0445749	+	0.234923i
$69$	18.4519			2.22134
$70$		−	10.8474i		−	1.29652i
$71$	4.01208	−	4.01208i	0.476146	−	0.476146i	−0.427751	−	0.903897i	$-0.640694\pi$
$71$	4.01208	−	4.01208i	0.476146	−	0.476146i	0.903897	+	0.427751i	$0.140694\pi$
$72$	−9.01855			−1.06285
$73$	10.0292	−	10.0292i	1.17382	−	1.17382i	0.192535	−	0.981290i	$-0.438329\pi$
$73$	10.0292	−	10.0292i	1.17382	−	1.17382i	0.981290	−	0.192535i	$-0.0616707\pi$
$74$	7.85239	+	7.85239i	0.912821	+	0.912821i
$75$	−5.03508	−	5.03508i	−0.581401	−	0.581401i
$76$		−	0.900586i		−	0.103304i
$77$		−	3.12472i		−	0.356095i
$78$	−10.7840	−	10.7840i	−1.22105	−	1.22105i
$79$	0.766509	+	0.766509i	0.0862390	+	0.0862390i	0.748910	−	0.662671i	$-0.230577\pi$
$79$	0.766509	+	0.766509i	0.0862390	+	0.0862390i	−0.662671	+	0.748910i	$0.730577\pi$
$80$	5.60118	−	5.60118i	0.626231	−	0.626231i
$81$	9.14753			1.01639
$82$	−0.902424	+	0.902424i	−0.0996561	+	0.0996561i
$83$			2.54437i			0.279281i	0.990202	+	0.139641i	$0.0445947\pi$
$83$			2.54437i			0.279281i	−0.990202	+	0.139641i	$0.955405\pi$
$84$	−3.64507			−0.397709
$85$	−6.53119	−	9.59009i	−0.708407	−	1.04019i
$86$	−5.75451			−0.620525
$87$			12.7895i			1.37117i
$88$	2.16173	−	2.16173i	0.230441	−	0.230441i
$89$	−13.8261			−1.46556			−0.732779	−	0.680466i	$-0.761777\pi$
$89$	−13.8261			−1.46556			−0.732779	+	0.680466i	$0.761777\pi$
$90$	7.24137	−	7.24137i	0.763308	−	0.763308i
$91$	−11.1985	−	11.1985i	−1.17392	−	1.17392i
$92$	2.55801	+	2.55801i	0.266691	+	0.266691i
$93$			1.74875i			0.181337i
$94$			9.10578i			0.939189i
$95$	3.74727	+	3.74727i	0.384462	+	0.384462i
$96$	−4.55680	−	4.55680i	−0.465076	−	0.465076i
$97$	−1.23810	+	1.23810i	−0.125710	+	0.125710i	−0.767163	−	0.641453i	$-0.778332\pi$
$97$	−1.23810	+	1.23810i	−0.125710	+	0.125710i	0.641453	+	0.767163i	$0.278332\pi$
$98$	3.40954			0.344416
$99$	2.08596	−	2.08596i	0.209647	−	0.209647i
$100$		−	1.39604i		−	0.139604i
$101$	−18.0905			−1.80007			−0.900035	−	0.435818i	$-0.856459\pi$
$101$	−18.0905			−1.80007			−0.900035	+	0.435818i	$0.856459\pi$
$102$	10.2545	−	6.98369i	1.01535	−	0.691488i
$103$	−2.45602			−0.241998			−0.120999	−	0.992653i	$-0.538610\pi$
$103$	−2.45602			−0.241998			−0.120999	+	0.992653i	$0.538610\pi$
$104$		−	15.4946i		−	1.51937i
$105$	15.1668	−	15.1668i	1.48013	−	1.48013i
$106$	8.13881			0.790511
$107$	0.958012	−	0.958012i	0.0926145	−	0.0926145i	−0.659282	−	0.751896i	$-0.729139\pi$
$107$	0.958012	−	0.958012i	0.0926145	−	0.0926145i	0.751896	+	0.659282i	$0.229139\pi$
$108$	0.0412506	+	0.0412506i	0.00396934	+	0.00396934i
$109$	−2.82409	−	2.82409i	−0.270499	−	0.270499i	0.558802	−	0.829301i	$-0.311261\pi$
$109$	−2.82409	−	2.82409i	−0.270499	−	0.270499i	−0.829301	+	0.558802i	$0.811261\pi$
$110$			3.47148i			0.330993i
$111$			21.9584i			2.08420i
$112$	6.21942	+	6.21942i	0.587680	+	0.587680i
$113$	−4.05935	−	4.05935i	−0.381872	−	0.381872i	0.489904	−	0.871776i	$-0.337032\pi$
$113$	−4.05935	−	4.05935i	−0.381872	−	0.381872i	−0.871776	+	0.489904i	$0.837032\pi$
$114$	−4.00689	+	4.00689i	−0.375279	+	0.375279i
$115$	−21.2874			−1.98506
$116$	−1.77302	+	1.77302i	−0.164621	+	0.164621i
$117$		−	14.9515i		−	1.38227i
$118$	−13.6442			−1.25605
$119$	10.6486	−	7.25210i	0.976158	−	0.664799i
$120$	20.9853			1.91569
$121$			1.00000i			0.0909091i
$122$	−8.60864	+	8.60864i	−0.779390	+	0.779390i
$123$	−2.52353			−0.227539
$124$	−0.242432	+	0.242432i	−0.0217711	+	0.0217711i
$125$	−4.14054	−	4.14054i	−0.370341	−	0.370341i
$126$	8.04066	+	8.04066i	0.716319	+	0.716319i
$127$			12.4262i			1.10265i	0.834291	+	0.551324i	$0.185877\pi$
$127$			12.4262i			1.10265i	−0.834291	+	0.551324i	$0.814123\pi$
$128$			5.68134i			0.502165i
$129$	−8.04594	−	8.04594i	−0.708406	−	0.708406i
$130$	12.4413	+	12.4413i	1.09117	+	1.09117i
$131$	−7.12044	+	7.12044i	−0.622116	+	0.622116i	−0.946072	−	0.323956i	$-0.894987\pi$
$131$	−7.12044	+	7.12044i	−0.622116	+	0.622116i	0.323956	+	0.946072i	$0.394987\pi$
$132$	1.16652			0.101533
$133$	−4.16089	+	4.16089i	−0.360795	+	0.360795i
$134$		−	7.52314i		−	0.649901i
$135$	−0.343281			−0.0295449
$136$	12.3840	+	2.34977i	1.06192	+	0.201491i
$137$	13.1798			1.12603			0.563013	−	0.826448i	$-0.309642\pi$
$137$	13.1798			1.12603			0.563013	+	0.826448i	$0.309642\pi$
$138$		−	22.7622i		−	1.93765i
$139$	−7.94745	+	7.94745i	−0.674094	+	0.674094i	−0.958657	−	0.284563i	$-0.908151\pi$
$139$	−7.94745	+	7.94745i	−0.674094	+	0.674094i	0.284563	+	0.958657i	$0.408151\pi$
$140$	4.20521			0.355405
$141$	−12.7317	+	12.7317i	−1.07220	+	1.07220i
$142$	−4.94930	−	4.94930i	−0.415336	−	0.415336i
$143$	3.58384	+	3.58384i	0.299696	+	0.299696i
$144$			8.30375i			0.691979i
$145$		−	14.7548i		−	1.22532i
$146$	−12.3720	−	12.3720i	−1.02391	−	1.02391i
$147$	4.76721	+	4.76721i	0.393193	+	0.393193i
$148$	−3.04413	+	3.04413i	−0.250226	+	0.250226i
$149$	21.9582			1.79889			0.899443	−	0.437039i	$-0.143973\pi$
$149$	21.9582			1.79889			0.899443	+	0.437039i	$0.143973\pi$
$150$	−6.21128	+	6.21128i	−0.507149	+	0.507149i
$151$			5.52687i			0.449770i	0.974385	+	0.224885i	$0.0722007\pi$
$151$			5.52687i			0.449770i	−0.974385	+	0.224885i	$0.927799\pi$
$152$	−5.75712			−0.466964
$153$	11.9499	+	2.26741i	0.966093	+	0.183309i
$154$	−3.85466			−0.310617
$155$		−	2.01749i		−	0.162048i
$156$	4.18064	−	4.18064i	0.334719	−	0.334719i
$157$	23.7868			1.89839			0.949195	−	0.314689i	$-0.101900\pi$
$157$	23.7868			1.89839			0.949195	+	0.314689i	$0.101900\pi$
$158$	0.945566	−	0.945566i	0.0752252	−	0.0752252i
$159$	11.3797	+	11.3797i	0.902466	+	0.902466i
$160$	5.25705	+	5.25705i	0.415606	+	0.415606i
$161$		−	23.6371i		−	1.86286i
$162$		−	11.2844i		−	0.886586i
$163$	8.36373	+	8.36373i	0.655098	+	0.655098i	0.954216	−	0.299118i	$-0.0966925\pi$
$163$	8.36373	+	8.36373i	0.655098	+	0.655098i	−0.299118	+	0.954216i	$0.596693\pi$
$164$	−0.349842	−	0.349842i	−0.0273181	−	0.0273181i
$165$	−4.85382	+	4.85382i	−0.377869	+	0.377869i
$166$	3.13874			0.243614
$167$	0.248472	−	0.248472i	0.0192274	−	0.0192274i	−0.697428	−	0.716655i	$-0.745672\pi$
$167$	0.248472	−	0.248472i	0.0192274	−	0.0192274i	0.716655	+	0.697428i	$0.245672\pi$
$168$			23.3016i			1.79776i
$169$	12.6879			0.975990
$170$	−11.8303	+	8.05689i	−0.907346	+	0.617935i
$171$	−5.55533			−0.424827
$172$		−	2.23084i		−	0.170100i
$173$	−13.4445	+	13.4445i	−1.02217	+	1.02217i	−0.0224184	+	0.999749i	$0.507137\pi$
$173$	−13.4445	+	13.4445i	−1.02217	+	1.02217i	−0.999749	+	0.0224184i	$0.992863\pi$
$174$	15.7771			1.19606
$175$	−6.45000	+	6.45000i	−0.487574	+	0.487574i
$176$	−1.99039	−	1.99039i	−0.150031	−	0.150031i
$177$	−19.0773	−	19.0773i	−1.43394	−	1.43394i
$178$			17.0558i			1.27839i
$179$		−	10.7639i		−	0.804532i	−0.915523	−	0.402266i	$-0.868223\pi$
$179$		−	10.7639i		−	0.804532i	0.915523	−	0.402266i	$-0.131777\pi$
$180$	2.80726	+	2.80726i	0.209240	+	0.209240i
$181$	10.4722	+	10.4722i	0.778389	+	0.778389i	0.979557	−	0.201168i	$-0.0644737\pi$
$181$	10.4722	+	10.4722i	0.778389	+	0.778389i	−0.201168	+	0.979557i	$0.564474\pi$
$182$	−13.8145	+	13.8145i	−1.02400	+	1.02400i
$183$	−24.0732			−1.77954
$184$	16.3525	−	16.3525i	1.20552	−	1.20552i
$185$		−	25.3328i		−	1.86250i
$186$	2.15726			0.158178
$187$	−3.40786	+	2.32088i	−0.249208	+	0.169719i
$188$	−3.53003			−0.257454
$189$		−	0.381172i		−	0.0277262i
$190$	4.62264	−	4.62264i	0.335361	−	0.335361i
$191$	0.665900			0.0481828			0.0240914	−	0.999710i	$-0.492331\pi$
$191$	0.665900			0.0481828			0.0240914	+	0.999710i	$0.492331\pi$
$192$	−15.3314	+	15.3314i	−1.10645	+	1.10645i
$193$	−2.83013	−	2.83013i	−0.203717	−	0.203717i	0.597873	−	0.801591i	$-0.296013\pi$
$193$	−2.83013	−	2.83013i	−0.203717	−	0.203717i	−0.801591	+	0.597873i	$0.796013\pi$
$194$	1.52732	+	1.52732i	0.109655	+	0.109655i
$195$			34.7907i			2.49141i
$196$			1.32177i			0.0944124i
$197$	−4.75276	−	4.75276i	−0.338620	−	0.338620i	0.517228	−	0.855848i	$-0.326964\pi$
$197$	−4.75276	−	4.75276i	−0.338620	−	0.338620i	−0.855848	+	0.517228i	$0.826964\pi$
$198$	−2.57324	−	2.57324i	−0.182872	−	0.182872i
$199$	1.10359	−	1.10359i	0.0782316	−	0.0782316i	−0.666908	−	0.745140i	$-0.732383\pi$
$199$	1.10359	−	1.10359i	0.0782316	−	0.0782316i	0.745140	+	0.666908i	$0.232383\pi$
$200$	−8.92441			−0.631051
$201$	10.5188	−	10.5188i	0.741942	−	0.741942i
$202$			22.3164i			1.57018i
$203$	16.3835			1.14989
$204$	2.70736	+	3.97536i	0.189553	+	0.278331i
$205$	2.91133			0.203336
$206$			3.02974i			0.211092i
$207$	15.7793	−	15.7793i	1.09674	−	1.09674i
$208$	−14.2665			−0.989204
$209$	1.33160	−	1.33160i	0.0921088	−	0.0921088i
$210$	−18.7098	−	18.7098i	−1.29110	−	1.29110i
$211$	−5.37970	−	5.37970i	−0.370354	−	0.370354i	0.497252	−	0.867606i	$-0.334342\pi$
$211$	−5.37970	−	5.37970i	−0.370354	−	0.370354i	−0.867606	+	0.497252i	$0.834342\pi$
$212$			3.15517i			0.216698i
$213$		−	13.8402i		−	0.948315i
$214$	−1.18180	−	1.18180i	−0.0807865	−	0.0807865i
$215$	9.28238	+	9.28238i	0.633053	+	0.633053i
$216$	0.263700	−	0.263700i	0.0179425	−	0.0179425i
$217$	2.24017			0.152073
$218$	−3.48380	+	3.48380i	−0.235953	+	0.235953i
$219$		−	34.5970i		−	2.33785i
$220$	−1.34579			−0.0907329
$221$	−3.89559	+	20.5309i	−0.262046	+	1.38106i
$222$	27.0879			1.81802
$223$			5.40989i			0.362273i	0.983458	+	0.181136i	$0.0579776\pi$
$223$			5.40989i			0.362273i	−0.983458	+	0.181136i	$0.942022\pi$
$224$	−5.83732	+	5.83732i	−0.390022	+	0.390022i
$225$	−8.61160			−0.574107
$226$	−5.00762	+	5.00762i	−0.333102	+	0.333102i
$227$	6.27817	+	6.27817i	0.416697	+	0.416697i	0.884064	−	0.467367i	$-0.154797\pi$
$227$	6.27817	+	6.27817i	0.416697	+	0.416697i	−0.467367	+	0.884064i	$0.654797\pi$
$228$	−1.55335	−	1.55335i	−0.102873	−	0.102873i
$229$			12.9224i			0.853936i	0.904267	+	0.426968i	$0.140418\pi$
$229$			12.9224i			0.853936i	−0.904267	+	0.426968i	$0.859582\pi$
$230$			26.2602i			1.73154i
$231$	−5.38958	−	5.38958i	−0.354608	−	0.354608i
$232$	11.3343	+	11.3343i	0.744134	+	0.744134i
$233$	3.76646	−	3.76646i	0.246749	−	0.246749i	−0.572886	−	0.819635i	$-0.694176\pi$
$233$	3.76646	−	3.76646i	0.246749	−	0.246749i	0.819635	+	0.572886i	$0.194176\pi$
$234$	−18.4442			−1.20573
$235$	14.6882	−	14.6882i	0.958151	−	0.958151i
$236$		−	5.28944i		−	0.344313i
$237$	2.64418			0.171758
$238$	−8.94619	−	13.1362i	−0.579895	−	0.851491i
$239$	3.15135			0.203844			0.101922	−	0.994792i	$-0.467501\pi$
$239$	3.15135			0.203844			0.101922	+	0.994792i	$0.467501\pi$
$240$		−	19.3220i		−	1.24723i
$241$	−17.5181	+	17.5181i	−1.12844	+	1.12844i	−0.138007	+	0.990431i	$0.544070\pi$
$241$	−17.5181	+	17.5181i	−1.12844	+	1.12844i	−0.990431	+	0.138007i	$0.955930\pi$
$242$	1.23360			0.0792989
$243$	15.5190	−	15.5190i	0.995547	−	0.995547i
$244$	−3.33730	−	3.33730i	−0.213649	−	0.213649i
$245$	−5.49980	−	5.49980i	−0.351369	−	0.351369i
$246$			3.11303i			0.198480i
$247$		−	9.54450i		−	0.607302i
$248$	1.54978	+	1.54978i	0.0984114	+	0.0984114i
$249$	4.38858	+	4.38858i	0.278115	+	0.278115i
$250$	−5.10777	+	5.10777i	−0.323044	+	0.323044i
$251$	−1.09040			−0.0688257			−0.0344129	−	0.999408i	$-0.510956\pi$
$251$	−1.09040			−0.0688257			−0.0344129	+	0.999408i	$0.510956\pi$
$252$	−3.11712	+	3.11712i	−0.196360	+	0.196360i
$253$			7.56453i			0.475578i
$254$	15.3290			0.961826
$255$	−27.8063	−	5.27604i	−1.74130	−	0.330398i
$256$	−10.7690			−0.673059
$257$		−	20.4430i		−	1.27520i	−0.770368	−	0.637599i	$-0.779928\pi$
$257$		−	20.4430i		−	1.27520i	0.770368	−	0.637599i	$-0.220072\pi$
$258$	−9.92548	+	9.92548i	−0.617933	+	0.617933i
$259$	28.1289			1.74785
$260$	−4.82309	+	4.82309i	−0.299115	+	0.299115i
$261$	10.9370	+	10.9370i	0.676986	+	0.676986i
$262$	8.78378	+	8.78378i	0.542664	+	0.542664i
$263$		−	16.7043i		−	1.03003i	−0.857180	−	0.515017i	$-0.827786\pi$
$263$		−	16.7043i		−	1.03003i	0.857180	−	0.515017i	$-0.172214\pi$
$264$		−	7.45717i		−	0.458957i
$265$	−13.1284	−	13.1284i	−0.806472	−	0.806472i
$266$	5.13287	+	5.13287i	0.314717	+	0.314717i
$267$	−23.8474	+	23.8474i	−1.45944	+	1.45944i
$268$	2.91649			0.178153
$269$	19.0166	−	19.0166i	1.15947	−	1.15947i	0.174875	−	0.984591i	$-0.444048\pi$
$269$	19.0166	−	19.0166i	1.15947	−	1.15947i	0.984591	−	0.174875i	$-0.0559520\pi$
$270$			0.423472i			0.0257717i
$271$	−20.7077			−1.25790			−0.628952	−	0.777444i	$-0.716516\pi$
$271$	−20.7077			−1.25790			−0.628952	+	0.777444i	$0.716516\pi$
$272$	2.16353	−	11.4024i	0.131183	−	0.691374i
$273$	−38.6308			−2.33804
$274$		−	16.2586i		−	0.982218i
$275$	2.06418	−	2.06418i	0.124475	−	0.124475i
$276$	8.82421			0.531155
$277$	13.3319	−	13.3319i	0.801037	−	0.801037i	−0.182221	−	0.983258i	$-0.558329\pi$
$277$	13.3319	−	13.3319i	0.801037	−	0.801037i	0.983258	+	0.182221i	$0.0583287\pi$
$278$	9.80398	+	9.80398i	0.588004	+	0.588004i
$279$	1.49546	+	1.49546i	0.0895310	+	0.0895310i
$280$		−	26.8824i		−	1.60653i
$281$		−	1.87104i		−	0.111617i	−0.998441	−	0.0558085i	$-0.982226\pi$
$281$		−	1.87104i		−	0.111617i	0.998441	−	0.0558085i	$-0.0177736\pi$
$282$	15.7058	+	15.7058i	0.935267	+	0.935267i
$283$	1.45723	+	1.45723i	0.0866232	+	0.0866232i	0.749091	−	0.662467i	$-0.230491\pi$
$283$	1.45723	+	1.45723i	0.0866232	+	0.0866232i	−0.662467	+	0.749091i	$0.730491\pi$
$284$	1.91869	−	1.91869i	0.113853	−	0.113853i
$285$	12.9267			0.765712
$286$	4.42103	−	4.42103i	0.261421	−	0.261421i
$287$			3.23268i			0.190819i
$288$	−7.79358			−0.459241
$289$	−15.8185	−	6.22707i	−0.930498	−	0.366298i
$290$	−18.2016			−1.06883
$291$			4.27099i			0.250370i
$292$	4.79623	−	4.79623i	0.280678	−	0.280678i
$293$	−3.18966			−0.186342			−0.0931711	−	0.995650i	$-0.529700\pi$
$293$	−3.18966			−0.186342			−0.0931711	+	0.995650i	$0.529700\pi$
$294$	5.88084	−	5.88084i	0.342977	−	0.342977i
$295$	22.0090	+	22.0090i	1.28141	+	1.28141i
$296$	19.4600	+	19.4600i	1.13109	+	1.13109i
$297$			0.121986i			0.00707833i
$298$		−	27.0876i		−	1.56915i
$299$	27.1101	+	27.1101i	1.56782	+	1.56782i
$300$	−2.40792	−	2.40792i	−0.139021	−	0.139021i
$301$	−10.3070	+	10.3070i	−0.594083	+	0.594083i
$302$	6.81795			0.392329
$303$	−31.2028	+	31.2028i	−1.79255	+	1.79255i
$304$			5.30082i			0.304023i
$305$	27.7725			1.59025
$306$	2.79708	−	14.7414i	0.159898	−	0.842711i
$307$	11.1890			0.638590			0.319295	−	0.947655i	$-0.396554\pi$
$307$	11.1890			0.638590			0.319295	+	0.947655i	$0.396554\pi$
$308$		−	1.49433i		−	0.0851475i
$309$	−4.23618	+	4.23618i	−0.240988	+	0.240988i
$310$	−2.48877			−0.141353
$311$	21.7193	−	21.7193i	1.23159	−	1.23159i	0.268237	−	0.963353i	$-0.413559\pi$
$311$	21.7193	−	21.7193i	1.23159	−	1.23159i	0.963353	−	0.268237i	$-0.0864410\pi$
$312$	−26.7253	−	26.7253i	−1.51302	−	1.51302i
$313$	−19.9961	−	19.9961i	−1.13024	−	1.13024i	−0.990136	−	0.140108i	$-0.955255\pi$
$313$	−19.9961	−	19.9961i	−1.13024	−	1.13024i	−0.140108	−	0.990136i	$-0.544745\pi$
$314$		−	29.3434i		−	1.65594i
$315$		−	25.9402i		−	1.46156i
$316$	0.366567	+	0.366567i	0.0206210	+	0.0206210i
$317$	−14.7041	−	14.7041i	−0.825866	−	0.825866i	0.161076	−	0.986942i	$-0.448503\pi$
$317$	−14.7041	−	14.7041i	−0.825866	−	0.825866i	−0.986942	+	0.161076i	$0.948503\pi$
$318$	14.0380	−	14.0380i	0.787210	−	0.787210i
$319$	−5.24317			−0.293561
$320$	17.6875	−	17.6875i	0.988759	−	0.988759i
$321$		−	3.30479i		−	0.184455i
$322$	−29.1587			−1.62495
$323$	7.62840	+	1.44743i	0.424456	+	0.0805374i
$324$	4.37461			0.243034
$325$		−	14.7954i		−	0.820703i
$326$	10.3175	−	10.3175i	0.571434	−	0.571434i
$327$	−9.74208			−0.538738
$328$	−2.23641	+	2.23641i	−0.123485	+	0.123485i
$329$	16.3094	+	16.3094i	0.899168	+	0.899168i
$330$	5.98768	+	5.98768i	0.329611	+	0.329611i
$331$		−	14.1654i		−	0.778603i	−0.921110	−	0.389302i	$-0.872716\pi$
$331$		−	14.1654i		−	0.778603i	0.921110	−	0.389302i	$-0.127284\pi$
$332$			1.21679i			0.0667802i
$333$	18.7779	+	18.7779i	1.02902	+	1.02902i
$334$	−0.306516	−	0.306516i	−0.0167718	−	0.0167718i
$335$	−12.1353	+	12.1353i	−0.663022	+	0.663022i
$336$	21.4547			1.17045
$337$	−5.57809	+	5.57809i	−0.303858	+	0.303858i	−0.842521	−	0.538663i	$-0.818930\pi$
$337$	−5.57809	+	5.57809i	−0.303858	+	0.303858i	0.538663	+	0.842521i	$0.318930\pi$
$338$		−	15.6518i		−	0.851344i
$339$	−14.0033			−0.760554
$340$	−3.12340	−	4.58626i	−0.169390	−	0.248725i
$341$	−0.716919			−0.0388233
$342$			6.85306i			0.370571i
$343$	−9.35973	+	9.35973i	−0.505378	+	0.505378i
$344$	−14.2610			−0.768901
$345$	−36.7169	+	36.7169i	−1.97677	+	1.97677i
$346$	16.5852	+	16.5852i	0.891624	+	0.891624i
$347$	2.19000	+	2.19000i	0.117565	+	0.117565i	0.763442	−	0.645877i	$-0.223508\pi$
$347$	2.19000	+	2.19000i	0.117565	+	0.117565i	−0.645877	+	0.763442i	$0.723508\pi$
$348$			6.11629i			0.327867i
$349$			6.05522i			0.324129i	0.986780	+	0.162064i	$0.0518152\pi$
$349$			6.05522i			0.324129i	−0.986780	+	0.162064i	$0.948185\pi$
$350$	7.95673	+	7.95673i	0.425305	+	0.425305i
$351$	0.437178	+	0.437178i	0.0233348	+	0.0233348i
$352$	1.86811	−	1.86811i	0.0995704	−	0.0995704i
$353$	5.32297			0.283313			0.141656	−	0.989916i	$-0.454757\pi$
$353$	5.32297			0.283313			0.141656	+	0.989916i	$0.454757\pi$
$354$	−23.5338	+	23.5338i	−1.25081	+	1.25081i
$355$			15.9671i			0.847444i
$356$	−6.61202			−0.350436
$357$	5.85840	−	30.8755i	0.310059	−	1.63410i
$358$	−13.2784			−0.701783
$359$			20.2098i			1.06663i	0.845916	+	0.533316i	$0.179054\pi$
$359$			20.2098i			1.06663i	−0.845916	+	0.533316i	$0.820946\pi$
$360$	17.9458	−	17.9458i	0.945826	−	0.945826i
$361$	15.4537			0.813351
$362$	12.9185	−	12.9185i	0.678979	−	0.678979i
$363$	1.72482	+	1.72482i	0.0905294	+	0.0905294i
$364$	−5.35545	−	5.35545i	−0.280702	−	0.280702i
$365$			39.9135i			2.08917i
$366$			29.6967i			1.55227i
$367$	−15.0463	−	15.0463i	−0.785411	−	0.785411i	0.195327	−	0.980738i	$-0.437423\pi$
$367$	−15.0463	−	15.0463i	−0.785411	−	0.785411i	−0.980738	+	0.195327i	$0.937423\pi$
$368$	−15.0564	−	15.0564i	−0.784868	−	0.784868i
$369$	−2.15803	+	2.15803i	−0.112342	+	0.112342i
$370$	−31.2505			−1.62464
$371$	14.5775	−	14.5775i	0.756826	−	0.756826i
$372$			0.836304i			0.0433603i
$373$	−5.90978			−0.305997			−0.152998	−	0.988226i	$-0.548893\pi$
$373$	−5.90978			−0.305997			−0.152998	+	0.988226i	$0.548893\pi$
$374$	2.86304	+	4.20394i	0.148044	+	0.217381i
$375$	−14.2833			−0.737588
$376$			22.5662i			1.16376i
$377$	−18.7907	+	18.7907i	−0.967771	+	0.967771i
$378$	−0.470214			−0.0241852
$379$	−7.08009	+	7.08009i	−0.363680	+	0.363680i	−0.865166	−	0.501486i	$-0.832787\pi$
$379$	−7.08009	+	7.08009i	−0.363680	+	0.363680i	0.501486	+	0.865166i	$0.332787\pi$
$380$	1.79205	+	1.79205i	0.0919303	+	0.0919303i
$381$	21.4329	+	21.4329i	1.09804	+	1.09804i
$382$		−	0.821455i		−	0.0420293i
$383$		−	33.5565i		−	1.71466i	−0.514770	−	0.857328i	$-0.672123\pi$
$383$		−	33.5565i		−	1.71466i	0.514770	−	0.857328i	$-0.327877\pi$
$384$	9.79928	+	9.79928i	0.500068	+	0.500068i
$385$	6.21781	+	6.21781i	0.316889	+	0.316889i
$386$	−3.49126	+	3.49126i	−0.177700	+	0.177700i
$387$	−13.7611			−0.699518
$388$	−0.592095	+	0.592095i	−0.0300591	+	0.0300591i
$389$			17.6198i			0.893358i	0.894694	+	0.446679i	$0.147393\pi$
$389$			17.6198i			0.893358i	−0.894694	+	0.446679i	$0.852607\pi$
$390$	42.9178			2.17323
$391$	−25.7789	+	17.5563i	−1.30369	+	0.887862i
$392$	8.44963			0.426771
$393$			24.5629i			1.23903i
$394$	−5.86301	+	5.86301i	−0.295374	+	0.295374i
$395$	−3.05051			−0.153488
$396$	0.997565	−	0.997565i	0.0501295	−	0.0501295i
$397$	17.3115	+	17.3115i	0.868839	+	0.868839i	0.992344	−	0.123505i	$-0.0394134\pi$
$397$	17.3115	+	17.3115i	0.868839	+	0.868839i	−0.123505	+	0.992344i	$0.539413\pi$
$398$	−1.36139	−	1.36139i	−0.0682404	−	0.0682404i
$399$			14.3535i			0.718576i
$400$			8.21707i			0.410854i
$401$	5.95114	+	5.95114i	0.297186	+	0.297186i	0.839911	−	0.542725i	$-0.182607\pi$
$401$	5.95114	+	5.95114i	0.297186	+	0.297186i	−0.542725	+	0.839911i	$0.682607\pi$
$402$	−12.9761	−	12.9761i	−0.647187	−	0.647187i
$403$	−2.56933	+	2.56933i	−0.127987	+	0.127987i
$404$	−8.65138			−0.430422
$405$	−18.2024	+	18.2024i	−0.904486	+	0.904486i
$406$		−	20.2107i		−	1.00304i
$407$	−9.00206			−0.446216
$408$	25.4130	−	17.3072i	1.25813	−	0.856833i
$409$	−10.1472			−0.501748			−0.250874	−	0.968020i	$-0.580718\pi$
$409$	−10.1472			−0.501748			−0.250874	+	0.968020i	$0.580718\pi$
$410$		−	3.59142i		−	0.177368i
$411$	22.7327	−	22.7327i	1.12132	−	1.12132i
$412$	−1.17454			−0.0578653
$413$	−24.4383	+	24.4383i	−1.20253	+	1.20253i
$414$	−19.4654	−	19.4654i	−0.956670	−	0.956670i
$415$	−5.06298	−	5.06298i	−0.248532	−	0.248532i
$416$		−	13.3900i		−	0.656499i
$417$			27.4158i			1.34256i
$418$	−1.64267	−	1.64267i	−0.0803454	−	0.0803454i
$419$	8.94468	+	8.94468i	0.436976	+	0.436976i	0.890993	−	0.454017i	$-0.150009\pi$
$419$	8.94468	+	8.94468i	0.436976	+	0.436976i	−0.454017	+	0.890993i	$0.650009\pi$
$420$	7.25322	−	7.25322i	0.353921	−	0.353921i
$421$	13.8275			0.673911			0.336956	−	0.941520i	$-0.390603\pi$
$421$	13.8275			0.673911			0.336956	+	0.941520i	$0.390603\pi$
$422$	−6.63641	+	6.63641i	−0.323055	+	0.323055i
$423$			21.7752i			1.05875i
$424$	20.1698			0.979534
$425$	11.8252	+	2.24374i	0.573605	+	0.108837i
$426$	−17.0733			−0.827204
$427$			30.8380i			1.49236i
$428$	0.458149	−	0.458149i	0.0221455	−	0.0221455i
$429$	12.3630			0.596889
$430$	11.4508	−	11.4508i	0.552204	−	0.552204i
$431$	−21.2863	−	21.2863i	−1.02533	−	1.02533i	−0.999671	−	0.0256552i	$-0.991833\pi$
$431$	−21.2863	−	21.2863i	−1.02533	−	1.02533i	−0.0256552	−	0.999671i	$-0.508167\pi$
$432$	−0.242800	−	0.242800i	−0.0116817	−	0.0116817i
$433$			1.46942i			0.0706158i	0.999376	+	0.0353079i	$0.0112412\pi$
$433$			1.46942i			0.0706158i	−0.999376	+	0.0353079i	$0.988759\pi$
$434$		−	2.76348i		−	0.132651i
$435$	−25.4494	−	25.4494i	−1.22021	−	1.22021i
$436$	−1.35056	−	1.35056i	−0.0646802	−	0.0646802i
$437$	10.0729	−	10.0729i	0.481854	−	0.481854i
$438$	−42.6788			−2.03927
$439$	21.6905	−	21.6905i	1.03523	−	1.03523i	0.0358753	−	0.999356i	$-0.488578\pi$
$439$	21.6905	−	21.6905i	1.03523	−	1.03523i	0.999356	−	0.0358753i	$-0.0114219\pi$
$440$			8.60313i			0.410138i
$441$	8.15346			0.388260
$442$	25.3269	+	4.80561i	1.20468	+	0.228579i
$443$	24.2615			1.15270			0.576349	−	0.817204i	$-0.304477\pi$
$443$	24.2615			1.15270			0.576349	+	0.817204i	$0.304477\pi$
$444$			10.5011i			0.498361i
$445$	27.5121	−	27.5121i	1.30420	−	1.30420i
$446$	6.67364			0.316006
$447$	37.8739	−	37.8739i	1.79137	−	1.79137i
$448$	19.6398	+	19.6398i	0.927892	+	0.927892i
$449$	12.2290	+	12.2290i	0.577121	+	0.577121i	0.934109	−	0.356988i	$-0.116196\pi$
$449$	12.2290	+	12.2290i	0.577121	+	0.577121i	−0.356988	+	0.934109i	$0.616196\pi$
$450$			10.6233i			0.500786i
$451$		−	1.03455i		−	0.0487150i
$452$	−1.94130	−	1.94130i	−0.0913110	−	0.0913110i
$453$	9.53284	+	9.53284i	0.447892	+	0.447892i
$454$	7.74476	−	7.74476i	0.363479	−	0.363479i
$455$	44.5673			2.08935
$456$	−9.92998	+	9.92998i	−0.465014	+	0.465014i
$457$		−	3.17739i		−	0.148632i	−0.997235	−	0.0743161i	$-0.976323\pi$
$457$		−	3.17739i		−	0.148632i	0.997235	−	0.0743161i	$-0.0236774\pi$
$458$	15.9411			0.744878
$459$	−0.415711	+	0.283114i	−0.0194037	+	0.0132146i
$460$	−10.1802			−0.474656
$461$		−	22.5912i		−	1.05218i	−0.850430	−	0.526088i	$-0.823658\pi$
$461$		−	22.5912i		−	1.05218i	0.850430	−	0.526088i	$-0.176342\pi$
$462$	−6.64859	+	6.64859i	−0.309320	+	0.309320i
$463$	16.3907			0.761741			0.380870	−	0.924628i	$-0.375624\pi$
$463$	16.3907			0.761741			0.380870	+	0.924628i	$0.375624\pi$
$464$	10.4360	−	10.4360i	0.484478	−	0.484478i
$465$	−3.47980	−	3.47980i	−0.161372	−	0.161372i
$466$	−4.64631	−	4.64631i	−0.215236	−	0.215236i
$467$			36.4595i			1.68714i	0.537016	+	0.843572i	$0.319551\pi$
$467$			36.4595i			1.68714i	−0.537016	+	0.843572i	$0.680449\pi$
$468$		−	7.15024i		−	0.330520i
$469$	−13.4748	−	13.4748i	−0.622207	−	0.622207i
$470$	−18.1193	−	18.1193i	−0.835783	−	0.835783i
$471$	41.0278	−	41.0278i	1.89046	−	1.89046i
$472$	−33.8135			−1.55639
$473$	3.29852	−	3.29852i	0.151666	−	0.151666i
$474$		−	3.26186i		−	0.149822i
$475$	−5.49734			−0.252235
$476$	5.09248	−	3.46816i	0.233413	−	0.158963i
$477$	19.4629			0.891144
$478$		−	3.88751i		−	0.177810i
$479$	−12.1666	+	12.1666i	−0.555906	+	0.555906i	−0.928139	−	0.372234i	$-0.878592\pi$
$479$	−12.1666	+	12.1666i	−0.555906	+	0.555906i	0.372234	+	0.928139i	$0.378592\pi$
$480$	18.1349			0.827742
$481$	−32.2620	+	32.2620i	−1.47102	+	1.47102i
$482$	21.6103	+	21.6103i	0.984323	+	0.984323i
$483$	−40.7696	−	40.7696i	−1.85508	−	1.85508i
$484$			0.478229i			0.0217377i
$485$		−	4.92733i		−	0.223738i
$486$	−19.1443	−	19.1443i	−0.868403	−	0.868403i
$487$	−25.4773	−	25.4773i	−1.15449	−	1.15449i	−0.985643	−	0.168844i	$-0.945997\pi$
$487$	−25.4773	−	25.4773i	−1.15449	−	1.15449i	−0.168844	−	0.985643i	$-0.554003\pi$
$488$	−21.3342	+	21.3342i	−0.965753	+	0.965753i
$489$	28.8518			1.30472
$490$	−6.78456	+	6.78456i	−0.306495	+	0.306495i
$491$		−	9.01684i		−	0.406924i	−0.979083	−	0.203462i	$-0.934781\pi$
$491$		−	9.01684i		−	0.406924i	0.979083	−	0.203462i	$-0.0652194\pi$
$492$	−1.20683			−0.0544079
$493$	−12.1688	−	17.8680i	−0.548053	−	0.804735i
$494$	−11.7741			−0.529742
$495$			8.30159i			0.373129i
$496$	1.42695	−	1.42695i	0.0640720	−	0.0640720i
$497$	−17.7295			−0.795276
$498$	5.41376	−	5.41376i	0.242596	−	0.242596i
$499$	−0.803961	−	0.803961i	−0.0359902	−	0.0359902i	0.688883	−	0.724873i	$-0.258102\pi$
$499$	−0.803961	−	0.803961i	−0.0359902	−	0.0359902i	−0.724873	+	0.688883i	$0.758102\pi$
$500$	−1.98012	−	1.98012i	−0.0885538	−	0.0885538i
$501$		−	0.857139i		−	0.0382941i
$502$			1.34512i			0.0600358i
$503$	−11.7991	−	11.7991i	−0.526096	−	0.526096i	0.393310	−	0.919406i	$-0.371330\pi$
$503$	−11.7991	−	11.7991i	−0.526096	−	0.526096i	−0.919406	+	0.393310i	$0.871330\pi$
$504$	19.9266	+	19.9266i	0.887601	+	0.887601i
$505$	35.9978	−	35.9978i	1.60188	−	1.60188i
$506$	9.33161			0.414841
$507$	21.8843	−	21.8843i	0.971914	−	0.971914i
$508$			5.94257i			0.263659i
$509$	−11.9980			−0.531804			−0.265902	−	0.964000i	$-0.585670\pi$
$509$	−11.9980			−0.531804			−0.265902	+	0.964000i	$0.585670\pi$
$510$	−6.50853	+	34.3018i	−0.288202	+	1.51891i
$511$	−44.3191			−1.96056
$512$			24.6473i			1.08927i
$513$	0.162437	−	0.162437i	0.00717175	−	0.00717175i
$514$	−25.2185			−1.11234
$515$	4.88716	−	4.88716i	0.215354	−	0.215354i
$516$	−3.84780	−	3.84780i	−0.169390	−	0.169390i
$517$	−5.21948	−	5.21948i	−0.229553	−	0.229553i
$518$		−	34.6999i		−	1.52463i
$519$			46.3786i			2.03580i
$520$	30.8323	+	30.8323i	1.35209	+	1.35209i
$521$	−30.3114	−	30.3114i	−1.32797	−	1.32797i	−0.907142	−	0.420825i	$-0.861741\pi$
$521$	−30.3114	−	30.3114i	−1.32797	−	1.32797i	−0.420825	−	0.907142i	$-0.638259\pi$
$522$	13.4919	−	13.4919i	0.590526	−	0.590526i
$523$	39.8753			1.74363			0.871813	−	0.489839i	$-0.162944\pi$
$523$	39.8753			1.74363			0.871813	+	0.489839i	$0.162944\pi$
$524$	−3.40520	+	3.40520i	−0.148757	+	0.148757i
$525$			22.2502i			0.971077i
$526$	−20.6065			−0.898485
$527$	−1.66388	−	2.44316i	−0.0724798	−	0.106426i
$528$	−6.86613			−0.298810
$529$			34.2221i			1.48792i
$530$	−16.1952	+	16.1952i	−0.703475	+	0.703475i
$531$	−32.6283			−1.41595
$532$	−1.98986	+	1.98986i	−0.0862712	+	0.0862712i
$533$	−3.70766	−	3.70766i	−0.160597	−	0.160597i
$534$	29.4182	+	29.4182i	1.27305	+	1.27305i
$535$			3.81264i			0.164835i
$536$		−	18.6441i		−	0.805301i
$537$	−18.5658	−	18.5658i	−0.801172	−	0.801172i
$538$	−23.4590	−	23.4590i	−1.01139	−	1.01139i
$539$	−1.95437	+	1.95437i	−0.0841806	+	0.0841806i
$540$	−0.164167			−0.00706462
$541$	−5.74244	+	5.74244i	−0.246887	+	0.246887i	−0.819692	−	0.572805i	$-0.805855\pi$
$541$	−5.74244	+	5.74244i	−0.246887	+	0.246887i	0.572805	+	0.819692i	$0.305855\pi$
$542$			25.5450i			1.09725i
$543$	36.1251			1.55028
$544$	10.7019	+	2.03061i	0.458840	+	0.0870616i
$545$	11.2392			0.481433
$546$			47.6550i			2.03945i
$547$	23.8934	−	23.8934i	1.02161	−	1.02161i	0.0218470	−	0.999761i	$-0.493045\pi$
$547$	23.8934	−	23.8934i	1.02161	−	1.02161i	0.999761	−	0.0218470i	$-0.00695466\pi$
$548$	6.30295			0.269249
$549$	−20.5864	+	20.5864i	−0.878606	+	0.878606i
$550$	−2.54638	−	2.54638i	−0.108578	−	0.108578i
$551$	6.98182	+	6.98182i	0.297435	+	0.297435i
$552$		−	56.4100i		−	2.40097i
$553$		−	3.38722i		−	0.144039i
$554$	−16.4463	−	16.4463i	−0.698734	−	0.698734i
$555$	−43.6944	−	43.6944i	−1.85472	−	1.85472i
$556$	−3.80070	+	3.80070i	−0.161186	+	0.161186i
$557$	−7.27431			−0.308223			−0.154111	−	0.988053i	$-0.549251\pi$
$557$	−7.27431			−0.308223			−0.154111	+	0.988053i	$0.549251\pi$
$558$	1.84480	−	1.84480i	0.0780968	−	0.0780968i
$559$		−	23.6427i		−	0.999981i
$560$	−24.7517			−1.04595
$561$	−1.87485	+	9.88103i	−0.0791564	+	0.417177i
$562$	−2.30812			−0.0973622
$563$			32.8007i			1.38239i	0.722670	+	0.691193i	$0.242914\pi$
$563$			32.8007i			1.38239i	−0.722670	+	0.691193i	$0.757086\pi$
$564$	−6.08865	+	6.08865i	−0.256378	+	0.256378i
$565$	16.1552			0.679654
$566$	1.79764	−	1.79764i	0.0755604	−	0.0755604i
$567$	−20.2116	−	20.2116i	−0.848807	−	0.848807i
$568$	−12.2655	−	12.2655i	−0.514649	−	0.514649i
$569$		−	0.0905883i		−	0.00379766i	−0.999998	−	0.00189883i	$-0.999396\pi$
$569$		−	0.0905883i		−	0.00379766i	0.999998	−	0.00189883i	$-0.000604417\pi$
$570$		−	15.9464i		−	0.667921i
$571$	21.2721	+	21.2721i	0.890210	+	0.890210i	0.994542	−	0.104332i	$-0.0332706\pi$
$571$	21.2721	+	21.2721i	0.890210	+	0.890210i	−0.104332	+	0.994542i	$0.533271\pi$
$572$	1.71390	+	1.71390i	0.0716616	+	0.0716616i
$573$	1.14856	−	1.14856i	0.0479816	−	0.0479816i
$574$	3.98784			0.166449
$575$	15.6146	−	15.6146i	0.651173	−	0.651173i
$576$			26.2217i			1.09257i
$577$	−32.4542			−1.35109			−0.675543	−	0.737321i	$-0.736091\pi$
$577$	−32.4542			−1.35109			−0.675543	+	0.737321i	$0.736091\pi$
$578$	−7.68171	+	19.5137i	−0.319517	+	0.811661i
$579$	−9.76293			−0.405733
$580$		−	7.05619i		−	0.292992i
$581$	5.62183	−	5.62183i	0.233233	−	0.233233i
$582$	5.26870			0.218395
$583$	−4.66521	+	4.66521i	−0.193213	+	0.193213i
$584$	−30.6606	−	30.6606i	−1.26875	−	1.26875i
$585$	29.7516	+	29.7516i	1.23008	+	1.23008i
$586$			3.93477i			0.162544i
$587$			12.9524i			0.534602i	0.963613	+	0.267301i	$0.0861319\pi$
$587$			12.9524i			0.534602i	−0.963613	+	0.267301i	$0.913868\pi$
$588$	2.27982	+	2.27982i	0.0940181	+	0.0940181i
$589$	0.954651	+	0.954651i	0.0393357	+	0.0393357i
$590$	27.1503	−	27.1503i	1.11776	−	1.11776i
$591$	−16.3953			−0.674412
$592$	17.9176	−	17.9176i	0.736410	−	0.736410i
$593$			5.11853i			0.210193i	0.994462	+	0.105096i	$0.0335151\pi$
$593$			5.11853i			0.210193i	−0.994462	+	0.105096i	$0.966485\pi$
$594$	0.150482			0.00617434
$595$	−6.75867	+	35.6202i	−0.277079	+	1.46029i
$596$	10.5010			0.430139
$597$		−	3.80699i		−	0.155810i
$598$	33.4430	−	33.4430i	1.36759	−	1.36759i
$599$	−24.5697			−1.00389			−0.501946	−	0.864899i	$-0.667382\pi$
$599$	−24.5697			−1.00389			−0.501946	+	0.864899i	$0.667382\pi$
$600$	−15.3930	+	15.3930i	−0.628416	+	0.628416i
$601$	2.29902	+	2.29902i	0.0937790	+	0.0937790i	0.752440	−	0.658661i	$-0.228877\pi$
$601$	2.29902	+	2.29902i	0.0937790	+	0.0937790i	−0.658661	+	0.752440i	$0.728877\pi$
$602$	12.7147	+	12.7147i	0.518211	+	0.518211i
$603$		−	17.9906i		−	0.732633i
$604$			2.64311i			0.107547i
$605$	−1.98987	−	1.98987i	−0.0808999	−	0.0808999i
$606$	38.4918	+	38.4918i	1.56362	+	1.56362i
$607$	10.3381	−	10.3381i	0.419610	−	0.419610i	−0.465459	−	0.885069i	$-0.654111\pi$
$607$	10.3381	−	10.3381i	0.419610	−	0.419610i	0.885069	+	0.465459i	$0.154111\pi$
$608$	−4.97515			−0.201769
$609$	28.2585	−	28.2585i	1.14509	−	1.14509i
$610$		−	34.2602i		−	1.38716i
$611$	−37.4116			−1.51351
$612$	5.71479	+	1.08434i	0.231007	+	0.0438319i
$613$	14.5239			0.586616			0.293308	−	0.956018i	$-0.405244\pi$
$613$	14.5239			0.586616			0.293308	+	0.956018i	$0.405244\pi$
$614$		−	13.8028i		−	0.557034i
$615$	5.02151	−	5.02151i	0.202487	−	0.202487i
$616$	−9.55273			−0.384891
$617$	−7.83345	+	7.83345i	−0.315363	+	0.315363i	−0.846983	−	0.531620i	$-0.821583\pi$
$617$	−7.83345	+	7.83345i	−0.315363	+	0.315363i	0.531620	+	0.846983i	$0.321583\pi$
$618$	5.22575	+	5.22575i	0.210211	+	0.210211i
$619$	−18.7668	−	18.7668i	−0.754302	−	0.754302i	0.220977	−	0.975279i	$-0.429075\pi$
$619$	−18.7668	−	18.7668i	−0.754302	−	0.754302i	−0.975279	+	0.220977i	$0.929075\pi$
$620$		−	0.964820i		−	0.0387481i
$621$			0.922765i			0.0370293i
$622$	−26.7930	−	26.7930i	−1.07430	−	1.07430i
$623$	30.5488	+	30.5488i	1.22391	+	1.22391i
$624$	−24.6071	+	24.6071i	−0.985073	+	0.985073i
$625$	31.0743			1.24297
$626$	−24.6672	+	24.6672i	−0.985898	+	0.985898i
$627$		−	4.59354i		−	0.183448i
$628$	11.3755			0.453932
$629$	−20.8927	−	30.6778i	−0.833045	−	1.22320i
$630$	−31.9998			−1.27490
$631$		−	9.04426i		−	0.360046i	−0.983662	−	0.180023i	$-0.942383\pi$
$631$		−	9.04426i		−	0.360046i	0.983662	−	0.180023i	$-0.0576172\pi$
$632$	2.34333	−	2.34333i	0.0932126	−	0.0932126i
$633$	−18.5580			−0.737615
$634$	−18.1390	+	18.1390i	−0.720392	+	0.720392i
$635$	−24.7266	−	24.7266i	−0.981245	−	0.981245i
$636$	5.44208	+	5.44208i	0.215793	+	0.215793i
$637$			14.0083i			0.555029i
$638$			6.46798i			0.256070i
$639$	−11.8356	−	11.8356i	−0.468209	−	0.468209i
$640$	−11.3052	−	11.3052i	−0.446876	−	0.446876i
$641$	26.2346	−	26.2346i	1.03620	−	1.03620i	0.0368850	−	0.999320i	$-0.488256\pi$
$641$	26.2346	−	26.2346i	1.03620	−	1.03620i	0.999320	−	0.0368850i	$-0.0117435\pi$
$642$	−4.07679			−0.160898
$643$	6.15731	−	6.15731i	0.242821	−	0.242821i	−0.575195	−	0.818016i	$-0.695074\pi$
$643$	6.15731	−	6.15731i	0.242821	−	0.242821i	0.818016	+	0.575195i	$0.195074\pi$
$644$		−	11.3039i		−	0.445437i
$645$	32.0208			1.26082
$646$	1.78556	−	9.41040i	0.0702518	−	0.370247i
$647$	23.7909			0.935318			0.467659	−	0.883909i	$-0.345098\pi$
$647$	23.7909			0.935318			0.467659	+	0.883909i	$0.345098\pi$
$648$		−	27.9653i		−	1.09858i
$649$	7.82094	−	7.82094i	0.306999	−	0.306999i
$650$	−18.2517			−0.715889
$651$	3.86389	−	3.86389i	0.151438	−	0.151438i
$652$	3.99978	+	3.99978i	0.156643	+	0.156643i
$653$	6.60614	+	6.60614i	0.258518	+	0.258518i	0.824451	−	0.565933i	$-0.191484\pi$
$653$	6.60614	+	6.60614i	0.258518	+	0.258518i	−0.565933	+	0.824451i	$0.691484\pi$
$654$			12.0178i			0.469935i
$655$		−	28.3375i		−	1.10724i
$656$	2.05916	+	2.05916i	0.0803966	+	0.0803966i
$657$	−29.5859	−	29.5859i	−1.15426	−	1.15426i
$658$	20.1193	−	20.1193i	0.784333	−	0.784333i
$659$	26.1764			1.01969			0.509844	−	0.860267i	$-0.329703\pi$
$659$	26.1764			1.01969			0.509844	+	0.860267i	$0.329703\pi$
$660$	−2.32124	+	2.32124i	−0.0903540	+	0.0903540i
$661$			32.0595i			1.24697i	0.781836	+	0.623484i	$0.214283\pi$
$661$			32.0595i			1.24697i	−0.781836	+	0.623484i	$0.785717\pi$
$662$	−17.4745			−0.679166
$663$	28.6929	+	42.1313i	1.11434	+	1.63624i
$664$	7.77852			0.301865
$665$		−	16.5593i		−	0.642141i
$666$	23.1645	−	23.1645i	0.897605	−	0.897605i
$667$	−39.6621			−1.53572
$668$	0.118827	−	0.118827i	0.00459754	−	0.00459754i
$669$	9.33107	+	9.33107i	0.360760	+	0.360760i
$670$	14.9701	+	14.9701i	0.578346	+	0.578346i
$671$		−	9.86904i		−	0.380990i
$672$			20.1366i			0.776787i
$673$	13.6890	+	13.6890i	0.527672	+	0.527672i	0.919878	−	0.392205i	$-0.128288\pi$
$673$	13.6890	+	13.6890i	0.527672	+	0.527672i	−0.392205	+	0.919878i	$0.628288\pi$
$674$	6.88114	+	6.88114i	0.265051	+	0.265051i
$675$	0.251801	−	0.251801i	0.00969183	−	0.00969183i
$676$	6.06770			0.233373
$677$	11.5204	−	11.5204i	0.442764	−	0.442764i	−0.450176	−	0.892940i	$-0.648639\pi$
$677$	11.5204	−	11.5204i	0.442764	−	0.442764i	0.892940	+	0.450176i	$0.148639\pi$
$678$			17.2745i			0.663422i
$679$	5.47120			0.209965
$680$	−29.3183	+	19.9668i	−1.12431	+	0.765692i
$681$	21.6574			0.829913
$682$			0.884392i			0.0338651i
$683$	−4.31375	+	4.31375i	−0.165061	+	0.165061i	−0.784804	−	0.619743i	$-0.787237\pi$
$683$	−4.31375	+	4.31375i	−0.165061	+	0.165061i	0.619743	+	0.784804i	$0.287237\pi$
$684$	−2.65672			−0.101582
$685$	−26.2261	+	26.2261i	−1.00205	+	1.00205i
$686$	11.5462	+	11.5462i	0.440835	+	0.440835i
$687$	22.2888	+	22.2888i	0.850370	+	0.850370i
$688$			13.1307i			0.500603i
$689$			33.4388i			1.27392i
$690$	45.2940	+	45.2940i	1.72431	+	1.72431i
$691$	9.10587	+	9.10587i	0.346404	+	0.346404i	0.858768	−	0.512364i	$-0.171230\pi$
$691$	9.10587	+	9.10587i	0.346404	+	0.346404i	−0.512364	+	0.858768i	$0.671230\pi$
$692$	−6.42955	+	6.42955i	−0.244415	+	0.244415i
$693$	−9.21790			−0.350159
$694$	2.70158	−	2.70158i	0.102551	−	0.102551i
$695$		−	31.6288i		−	1.19975i
$696$	39.0992			1.48205
$697$	3.52560	−	2.40106i	0.133542	−	0.0909466i
$698$	7.46973			0.282733
$699$		−	12.9929i		−	0.491438i
$700$	−3.08458	+	3.08458i	−0.116586	+	0.116586i
$701$	−10.2877			−0.388560			−0.194280	−	0.980946i	$-0.562237\pi$
$701$	−10.2877			−0.388560			−0.194280	+	0.980946i	$0.562237\pi$
$702$	0.539303	−	0.539303i	0.0203547	−	0.0203547i
$703$	11.9872	+	11.9872i	0.452104	+	0.452104i
$704$	−6.28528	−	6.28528i	−0.236885	−	0.236885i
$705$		−	50.6689i		−	1.90830i
$706$		−	6.56642i		−	0.247130i
$707$	39.9711	+	39.9711i	1.50327	+	1.50327i
$708$	−9.12332	−	9.12332i	−0.342875	−	0.342875i
$709$	−26.7522	+	26.7522i	−1.00470	+	1.00470i	−0.00470982	+	0.999989i	$0.501499\pi$
$709$	−26.7522	+	26.7522i	−1.00470	+	1.00470i	−0.999989	+	0.00470982i	$0.998501\pi$
$710$	19.6970			0.739214
$711$	2.26119	−	2.26119i	0.0848014	−	0.0848014i
$712$			42.2682i			1.58407i
$713$	−5.42316			−0.203099
$714$	−38.0880	−	7.22693i	−1.42541	−	0.270461i
$715$	−14.2628			−0.533398
$716$		−	5.14761i		−	0.192375i
$717$	5.43550	−	5.43550i	0.202993	−	0.202993i
$718$	24.9308			0.930411
$719$	34.1402	−	34.1402i	1.27322	−	1.27322i	0.328824	−	0.944391i	$-0.393348\pi$
$719$	34.1402	−	34.1402i	1.27322	−	1.27322i	0.944391	−	0.328824i	$-0.106652\pi$
$720$	−16.5234	−	16.5234i	−0.615791	−	0.615791i
$721$	5.42660	+	5.42660i	0.202097	+	0.202097i
$722$		−	19.0637i		−	0.709476i
$723$			60.4310i			2.24745i
$724$	5.00808	+	5.00808i	0.186124	+	0.186124i
$725$	10.8229	+	10.8229i	0.401951	+	0.401951i
$726$	2.12774	−	2.12774i	0.0789677	−	0.0789677i
$727$	−32.1484			−1.19232			−0.596159	−	0.802866i	$-0.703307\pi$
$727$	−32.1484			−1.19232			−0.596159	+	0.802866i	$0.703307\pi$
$728$	−34.2355	+	34.2355i	−1.26885	+	1.26885i
$729$		−	26.0925i		−	0.966387i
$730$	49.2374			1.82236
$731$	18.8963	+	3.58545i	0.698906	+	0.132612i
$732$	−11.5125			−0.425513
$733$		−	3.44497i		−	0.127243i	−0.997974	−	0.0636214i	$-0.979735\pi$
$733$		−	3.44497i		−	0.127243i	0.997974	−	0.0636214i	$-0.0202650\pi$
$734$	−18.5611	+	18.5611i	−0.685104	+	0.685104i
$735$	−18.9723			−0.699804
$736$	14.1313	−	14.1313i	0.520888	−	0.520888i
$737$	4.31231	+	4.31231i	0.158846	+	0.158846i
$738$	2.66214	+	2.66214i	0.0979948	+	0.0979948i
$739$			16.5324i			0.608155i	0.952647	+	0.304078i	$0.0983482\pi$
$739$			16.5324i			0.608155i	−0.952647	+	0.304078i	$0.901652\pi$
$740$		−	12.1149i		−	0.445351i
$741$	−16.4625	−	16.4625i	−0.604766	−	0.604766i
$742$	−17.9828	−	17.9828i	−0.660170	−	0.660170i
$743$	9.31259	−	9.31259i	0.341646	−	0.341646i	−0.515340	−	0.856986i	$-0.672334\pi$
$743$	9.31259	−	9.31259i	0.341646	−	0.341646i	0.856986	+	0.515340i	$0.172334\pi$
$744$	5.34619			0.196001
$745$	−43.6940	+	43.6940i	−1.60083	+	1.60083i
$746$			7.29031i			0.266917i
$747$	7.50588			0.274626
$748$	−1.62974	+	1.10991i	−0.0595891	+	0.0405823i
$749$	−4.23348			−0.154688
$750$			17.6199i			0.643389i
$751$	−3.84055	+	3.84055i	−0.140144	+	0.140144i	−0.773698	−	0.633554i	$-0.781595\pi$
$751$	−3.84055	+	3.84055i	−0.140144	+	0.140144i	0.633554	+	0.773698i	$0.281595\pi$
$752$	20.7776			0.757682
$753$	−1.88075	+	1.88075i	−0.0685383	+	0.0685383i
$754$	23.1802	+	23.1802i	0.844174	+	0.844174i
$755$	−10.9978	−	10.9978i	−0.400250	−	0.400250i
$756$		−	0.182287i		−	0.00662973i
$757$			20.8191i			0.756685i	0.925666	+	0.378342i	$0.123506\pi$
$757$			20.8191i			0.756685i	−0.925666	+	0.378342i	$0.876494\pi$
$758$	8.73401	+	8.73401i	0.317234	+	0.317234i
$759$	13.0474	+	13.0474i	0.473592	+	0.473592i
$760$	11.4559	−	11.4559i	0.415551	−	0.415551i
$761$	−35.5898			−1.29013			−0.645065	−	0.764128i	$-0.723170\pi$
$761$	−35.5898			−1.29013			−0.645065	+	0.764128i	$0.723170\pi$
$762$	26.4397	−	26.4397i	0.957809	−	0.957809i
$763$			12.4797i			0.451797i
$764$	0.318453			0.0115212
$765$	−28.2907	+	19.2670i	−1.02285	+	0.696598i
$766$	−41.3953			−1.49567
$767$		−	56.0581i		−	2.02414i
$768$	−18.5745	+	18.5745i	−0.670249	+	0.670249i
$769$	6.25393			0.225523			0.112761	−	0.993622i	$-0.464030\pi$
$769$	6.25393			0.225523			0.112761	+	0.993622i	$0.464030\pi$
$770$	7.67029	−	7.67029i	0.276418	−	0.276418i
$771$	−35.2604	−	35.2604i	−1.26987	−	1.26987i
$772$	−1.35345	−	1.35345i	−0.0487118	−	0.0487118i
$773$		−	1.30489i		−	0.0469336i	−0.999725	−	0.0234668i	$-0.992530\pi$
$773$		−	1.30489i		−	0.0469336i	0.999725	−	0.0234668i	$-0.00747040\pi$
$774$			16.9758i			0.610181i
$775$	1.47985	+	1.47985i	0.0531579	+	0.0531579i
$776$	3.78505	+	3.78505i	0.135875	+	0.135875i
$777$	48.5173	−	48.5173i	1.74055	−	1.74055i
$778$	21.7358			0.779265
$779$	−1.37761	+	1.37761i	−0.0493579	+	0.0493579i
$780$			16.6379i			0.595732i
$781$	5.67394			0.203029
$782$	21.6575	+	31.8009i	0.774471	+	1.13720i
$783$	−0.639593			−0.0228572
$784$		−	7.77992i		−	0.277854i
$785$	−47.3327	+	47.3327i	−1.68937	+	1.68937i
$786$	30.3008			1.08079
$787$	−11.6447	+	11.6447i	−0.415090	+	0.415090i	−0.883507	−	0.468418i	$-0.844824\pi$
$787$	−11.6447	+	11.6447i	−0.415090	+	0.415090i	0.468418	+	0.883507i	$0.344824\pi$
$788$	−2.27291	−	2.27291i	−0.0809690	−	0.0809690i
$789$	−28.8119	−	28.8119i	−1.02573	−	1.02573i
$790$			3.76311i			0.133886i
$791$			17.9384i			0.637815i
$792$	−6.37708	−	6.37708i	−0.226600	−	0.226600i
$793$	−35.3691	−	35.3691i	−1.25599	−	1.25599i
$794$	21.3555	−	21.3555i	0.757878	−	0.757878i
$795$	−45.2882			−1.60621
$796$	0.527769	−	0.527769i	0.0187063	−	0.0187063i
$797$			24.5938i			0.871157i	0.900151	+	0.435578i	$0.143456\pi$
$797$			24.5938i			0.871157i	−0.900151	+	0.435578i	$0.856544\pi$
$798$	17.7065			0.626805
$799$	5.67351	−	29.9010i	0.200714	−	1.05782i
$800$	−7.71223			−0.272669
$801$			40.7867i			1.44113i
$802$	7.34133	−	7.34133i	0.259231	−	0.259231i
$803$	14.1834			0.500521
$804$	5.03041	−	5.03041i	0.177409	−	0.177409i
$805$	47.0348	+	47.0348i	1.65776	+	1.65776i
$806$	3.16952	+	3.16952i	0.111642	+	0.111642i
$807$		−	65.6005i		−	2.30925i
$808$			55.3052i			1.94563i
$809$	13.4649	+	13.4649i	0.473401	+	0.473401i	0.903013	−	0.429613i	$-0.141350\pi$
$809$	13.4649	+	13.4649i	0.473401	+	0.473401i	−0.429613	+	0.903013i	$0.641350\pi$
$810$	22.4545	+	22.4545i	0.788972	+	0.788972i
$811$	26.9007	−	26.9007i	0.944611	−	0.944611i	−0.0539333	−	0.998545i	$-0.517176\pi$
$811$	26.9007	−	26.9007i	0.944611	−	0.944611i	0.998545	+	0.0539333i	$0.0171758\pi$
$812$	7.83504			0.274956
$813$	−35.7170	+	35.7170i	−1.25265	+	1.25265i
$814$			11.1050i			0.389228i
$815$	−33.2855			−1.16594
$816$	−15.9354	−	23.3988i	−0.557852	−	0.819123i
$817$	−8.78462			−0.307335
$818$			12.5176i			0.437668i
$819$	−33.0355	+	33.0355i	−1.15435	+	1.15435i
$820$	1.39228			0.0486206
$821$	15.9131	−	15.9131i	0.555370	−	0.555370i	−0.372615	−	0.927986i	$-0.621539\pi$
$821$	15.9131	−	15.9131i	0.555370	−	0.555370i	0.927986	+	0.372615i	$0.121539\pi$
$822$	−28.0431	−	28.0431i	−0.978116	−	0.978116i
$823$	38.1383	+	38.1383i	1.32942	+	1.32942i	0.905877	+	0.423541i	$0.139213\pi$
$823$	38.1383	+	38.1383i	1.32942	+	1.32942i	0.423541	+	0.905877i	$0.360787\pi$
$824$			7.50840i			0.261567i
$825$		−	7.12068i		−	0.247910i
$826$	30.1471	+	30.1471i	1.04895	+	1.04895i
$827$	−9.67200	−	9.67200i	−0.336328	−	0.336328i	0.518655	−	0.854983i	$-0.326433\pi$
$827$	−9.67200	−	9.67200i	−0.336328	−	0.336328i	−0.854983	+	0.518655i	$0.826433\pi$
$828$	7.54611	−	7.54611i	0.262246	−	0.262246i
$829$	−55.0780			−1.91294			−0.956469	−	0.291833i	$-0.905735\pi$
$829$	−55.0780			−1.91294			−0.956469	+	0.291833i	$0.905735\pi$
$830$	−6.24570	+	6.24570i	−0.216791	+	0.216791i
$831$		−	45.9902i		−	1.59538i
$832$	−45.0509			−1.56186
$833$	−11.1961	−	2.12437i	−0.387921	−	0.0736052i
$834$	33.8202			1.17110
$835$			0.988857i			0.0342208i
$836$	0.636810	−	0.636810i	0.0220245	−	0.0220245i
$837$	−0.0874540			−0.00302285
$838$	11.0342	−	11.0342i	0.381169	−	0.381169i
$839$	−27.6962	−	27.6962i	−0.956180	−	0.956180i	0.0428993	−	0.999079i	$-0.486341\pi$
$839$	−27.6962	−	27.6962i	−0.956180	−	0.956180i	−0.999079	+	0.0428993i	$0.986341\pi$
$840$	−46.3672	−	46.3672i	−1.59982	−	1.59982i
$841$			1.50914i			0.0520395i
$842$		−	17.0576i		−	0.587845i
$843$	−3.22721	−	3.22721i	−0.111151	−	0.111151i
$844$	−2.57273	−	2.57273i	−0.0885570	−	0.0885570i
$845$	−25.2473	+	25.2473i	−0.868532	+	0.868532i
$846$	26.8620			0.923533
$847$	2.20951	−	2.20951i	0.0759198	−	0.0759198i
$848$		−	18.5712i		−	0.637738i
$849$	5.02691			0.172523
$850$	2.76788	−	14.5875i	0.0949376	−	0.500349i
$851$	−68.0964			−2.33431
$852$		−	6.61878i		−	0.226756i
$853$	10.5626	−	10.5626i	0.361656	−	0.361656i	−0.502767	−	0.864422i	$-0.667684\pi$
$853$	10.5626	−	10.5626i	0.361656	−	0.361656i	0.864422	+	0.502767i	$0.167684\pi$
$854$	38.0418			1.30176
$855$	11.0544	−	11.0544i	0.378053	−	0.378053i
$856$	−2.92878	−	2.92878i	−0.100104	−	0.100104i
$857$	−18.2681	−	18.2681i	−0.624026	−	0.624026i	0.322533	−	0.946558i	$-0.395466\pi$
$857$	−18.2681	−	18.2681i	−0.624026	−	0.624026i	−0.946558	+	0.322533i	$0.895466\pi$
$858$		−	15.2509i		−	0.520659i
$859$			4.63679i			0.158205i	0.996866	+	0.0791025i	$0.0252055\pi$
$859$			4.63679i			0.158205i	−0.996866	+	0.0791025i	$0.974795\pi$
$860$	4.43910	+	4.43910i	0.151372	+	0.151372i
$861$	5.57578	+	5.57578i	0.190022	+	0.190022i
$862$	−26.2588	+	26.2588i	−0.894379	+	0.894379i
$863$	46.4251			1.58033			0.790164	−	0.612895i	$-0.209995\pi$
$863$	46.4251			1.58033			0.790164	+	0.612895i	$0.209995\pi$
$864$	0.227882	−	0.227882i	0.00775272	−	0.00775272i
$865$		−	53.5058i		−	1.81925i
$866$	1.81268			0.0615973
$867$	−38.0245	+	16.5434i	−1.29138	+	0.561843i
$868$	1.07132			0.0363628
$869$			1.08401i			0.0367724i
$870$	−31.3944	+	31.3944i	−1.06437	+	1.06437i
$871$	30.9093			1.04732
$872$	−8.63366	+	8.63366i	−0.292372	+	0.292372i
$873$	3.65238	+	3.65238i	0.123614	+	0.123614i
$874$	−12.4260	−	12.4260i	−0.420315	−	0.420315i
$875$			18.2971i			0.618556i
$876$		−	16.5453i		−	0.559012i
$877$	21.6794	+	21.6794i	0.732062	+	0.732062i	0.971028	−	0.238966i	$-0.0768085\pi$
$877$	21.6794	+	21.6794i	0.732062	+	0.732062i	−0.238966	+	0.971028i	$0.576809\pi$
$878$	−26.7574	−	26.7574i	−0.903020	−	0.903020i
$879$	−5.50159	+	5.50159i	−0.185564	+	0.185564i
$880$	7.92126			0.267026
$881$	11.1998	−	11.1998i	0.377332	−	0.377332i	−0.492807	−	0.870139i	$-0.664029\pi$
$881$	11.1998	−	11.1998i	0.377332	−	0.377332i	0.870139	+	0.492807i	$0.164029\pi$
$882$		−	10.0581i		−	0.338674i
$883$	41.1311			1.38417			0.692085	−	0.721816i	$-0.256692\pi$
$883$	41.1311			1.38417			0.692085	+	0.721816i	$0.256692\pi$
$884$	−1.86298	+	9.81847i	−0.0626589	+	0.330231i
$885$	75.9229			2.55212
$886$		−	29.9290i		−	1.00548i
$887$	−33.8335	+	33.8335i	−1.13602	+	1.13602i	−0.146862	+	0.989157i	$0.546917\pi$
$887$	−33.8335	+	33.8335i	−1.13602	+	1.13602i	−0.989157	+	0.146862i	$0.953083\pi$
$888$	67.1299			2.25273
$889$	27.4559	−	27.4559i	0.920840	−	0.920840i
$890$	−33.9390	−	33.9390i	−1.13764	−	1.13764i
$891$	6.46828	+	6.46828i	0.216695	+	0.216695i
$892$			2.58716i			0.0866247i
$893$			13.9005i			0.465164i
$894$	−46.7212	−	46.7212i	−1.56259	−	1.56259i
$895$	21.4188	+	21.4188i	0.715952	+	0.715952i
$896$	12.5530	−	12.5530i	0.419366	−	0.419366i
$897$	93.5199			3.12254
$898$	15.0857	−	15.0857i	0.503415	−	0.503415i
$899$		−	3.75893i		−	0.125367i
$900$	−4.11832			−0.137277
$901$	−26.7258	−	5.07103i	−0.890365	−	0.168940i
$902$	−1.27622			−0.0424935
$903$			35.5552i			1.18320i
$904$	−12.4100	+	12.4100i	−0.412751	+	0.412751i
$905$	−41.6765			−1.38537
$906$	11.7597	−	11.7597i	0.390691	−	0.390691i
$907$	−10.8850	−	10.8850i	−0.361431	−	0.361431i	0.502908	−	0.864340i	$-0.332263\pi$
$907$	−10.8850	−	10.8850i	−0.361431	−	0.361431i	−0.864340	+	0.502908i	$0.832263\pi$
$908$	3.00240	+	3.00240i	0.0996382	+	0.0996382i
$909$			53.3667i			1.77006i
$910$		−	54.9782i		−	1.82251i
$911$	−20.6994	−	20.6994i	−0.685803	−	0.685803i	0.275499	−	0.961301i	$-0.411157\pi$
$911$	−20.6994	−	20.6994i	−0.685803	−	0.685803i	−0.961301	+	0.275499i	$0.911157\pi$
$912$	9.14295	+	9.14295i	0.302753	+	0.302753i
$913$	−1.79914	+	1.79914i	−0.0595430	+	0.0595430i
$914$	−3.91964			−0.129650
$915$	47.9025	−	47.9025i	1.58361	−	1.58361i
$916$			6.17987i			0.204188i
$917$	31.4654			1.03908
$918$	0.349250	+	0.512821i	0.0115270	+	0.0169256i
$919$	0.0561803			0.00185322			0.000926609	−	1.00000i	$-0.499705\pi$
$919$	0.0561803			0.00185322			0.000926609		1.00000i	$0.499705\pi$
$920$			65.0787i			2.14558i
$921$	19.2990	−	19.2990i	0.635923	−	0.635923i
$922$	−27.8685			−0.917800
$923$	20.3345	−	20.3345i	0.669318	−	0.669318i
$924$	−2.57745	−	2.57745i	−0.0847919	−	0.0847919i
$925$	18.5819	+	18.5819i	0.610969	+	0.610969i
$926$		−	20.2196i		−	0.664457i
$927$			7.24522i			0.237964i
$928$	9.79480	+	9.79480i	0.321530	+	0.321530i
$929$	−1.74001	−	1.74001i	−0.0570880	−	0.0570880i	0.677986	−	0.735074i	$-0.262853\pi$
$929$	−1.74001	−	1.74001i	−0.0570880	−	0.0570880i	−0.735074	+	0.677986i	$0.762853\pi$
$930$	−4.29268	+	4.29268i	−0.140763	+	0.140763i
$931$	5.20488			0.170583
$932$	1.80123	−	1.80123i	0.0590013	−	0.0590013i
$933$		−	74.9237i		−	2.45289i
$934$	44.9765			1.47167
$935$	2.16297	−	11.3995i	0.0707366	−	0.372803i
$936$	−45.7089			−1.49404
$937$		−	42.7519i		−	1.39664i	−0.715784	−	0.698322i	$-0.753931\pi$
$937$		−	42.7519i		−	1.39664i	0.715784	−	0.698322i	$-0.246069\pi$
$938$	−16.6225	+	16.6225i	−0.542743	+	0.542743i
$939$	−68.9791			−2.25105
$940$	7.02431	−	7.02431i	0.229108	−	0.229108i
$941$	−16.5185	−	16.5185i	−0.538486	−	0.538486i	0.384598	−	0.923084i	$-0.374340\pi$
$941$	−16.5185	−	16.5185i	−0.538486	−	0.538486i	−0.923084	+	0.384598i	$0.874340\pi$
$942$	−50.6120	−	50.6120i	−1.64903	−	1.64903i
$943$		−	7.82588i		−	0.254846i
$944$			31.1335i			1.01331i
$945$	0.758484	+	0.758484i	0.0246735	+	0.0246735i
$946$	−4.06905	−	4.06905i	−0.132296	−	0.132296i
$947$	−31.2579	+	31.2579i	−1.01575	+	1.01575i	−0.0158720	+	0.999874i	$0.505052\pi$
$947$	−31.2579	+	31.2579i	−1.01575	+	1.01575i	−0.999874	+	0.0158720i	$0.994948\pi$
$948$	1.26452			0.0410697
$949$	50.8310	−	50.8310i	1.65004	−	1.65004i
$950$			6.78153i			0.220022i
$951$	−50.7238			−1.64483
$952$	−22.1707	−	32.5544i	−0.718557	−	1.05509i
$953$	−21.4392			−0.694483			−0.347241	−	0.937776i	$-0.612882\pi$
$953$	−21.4392			−0.694483			−0.347241	+	0.937776i	$0.612882\pi$
$954$		−	24.0094i		−	0.777334i
$955$	−1.32506	+	1.32506i	−0.0428779	+	0.0428779i
$956$	1.50707			0.0487420
$957$	−9.04352	+	9.04352i	−0.292335	+	0.292335i
$958$	15.0087	+	15.0087i	0.484910	+	0.484910i
$959$	−29.1209	−	29.1209i	−0.940363	−	0.940363i
$960$		−	61.0153i		−	1.96926i
$961$			30.4860i			0.983420i
$962$	39.7984	+	39.7984i	1.28315	+	1.28315i
$963$	−2.82613	−	2.82613i	−0.0910706	−	0.0910706i
$964$	−8.37765	+	8.37765i	−0.269826	+	0.269826i
$965$	11.2632			0.362576
$966$	−50.2934	+	50.2934i	−1.61816	+	1.61816i
$967$			28.9580i			0.931227i	0.884988	+	0.465613i	$0.154166\pi$
$967$			28.9580i			0.931227i	−0.884988	+	0.465613i	$0.845834\pi$
$968$	3.05715			0.0982604
$969$	15.6542	−	10.6610i	0.502884	−	0.342482i
$970$	−6.07836			−0.195164
$971$			36.1492i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$971$			36.1492i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$972$	7.42165	−	7.42165i	0.238050	−	0.238050i
$973$	35.1200			1.12589
$974$	−31.4288	+	31.4288i	−1.00704	+	1.00704i
$975$	−25.5194	−	25.5194i	−0.817275	−	0.817275i
$976$	19.6433	+	19.6433i	0.628765	+	0.628765i
$977$			33.6680i			1.07714i	0.842582	+	0.538568i	$0.181035\pi$
$977$			33.6680i			1.07714i	−0.842582	+	0.538568i	$0.818965\pi$
$978$		−	35.5916i		−	1.13809i
$979$	−9.77649	−	9.77649i	−0.312458	−	0.312458i
$980$	−2.63016	−	2.63016i	−0.0840175	−	0.0840175i
$981$	−8.33104	+	8.33104i	−0.265990	+	0.265990i
$982$	−11.1232			−0.354955
$983$	2.75635	−	2.75635i	0.0879141	−	0.0879141i	−0.661782	−	0.749696i	$-0.730200\pi$
$983$	2.75635	−	2.75635i	0.0879141	−	0.0879141i	0.749696	+	0.661782i	$0.230200\pi$
$984$			7.71481i			0.245939i
$985$	18.9148			0.602675
$986$	−22.0420	+	15.0114i	−0.701960	+	0.478060i
$987$	56.2616			1.79083
$988$		−	4.56446i		−	0.145215i
$989$	24.9517	−	24.9517i	0.793419	−	0.793419i
$990$	10.2408			0.325476
$991$	22.7002	−	22.7002i	0.721096	−	0.721096i	−0.247733	−	0.968828i	$-0.579686\pi$
$991$	22.7002	−	22.7002i	0.721096	−	0.721096i	0.968828	+	0.247733i	$0.0796855\pi$
$992$	1.33928	+	1.33928i	0.0425222	+	0.0425222i
$993$	−24.4328	−	24.4328i	−0.775352	−	0.775352i
$994$			21.8711i			0.693709i
$995$			4.39202i			0.139236i
$996$	2.09875	+	2.09875i	0.0665013	+	0.0665013i
$997$	42.3652	+	42.3652i	1.34172	+	1.34172i	0.894349	+	0.447369i	$0.147639\pi$
$997$	42.3652	+	42.3652i	1.34172	+	1.34172i	0.447369	+	0.894349i	$0.352361\pi$
$998$	−0.991767	+	0.991767i	−0.0313938	+	0.0313938i
$999$	−1.09812			−0.0347431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.89.4	✓	28
17.8	even	8		3179.2.a.bd.1.4		14
17.9	even	8		3179.2.a.be.1.4		14
17.13	even	4	inner	187.2.e.b.166.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.4	✓	28	1.1	even	1	trivial
187.2.e.b.166.11	yes	28	17.13	even	4	inner
3179.2.a.bd.1.4		14	17.8	even	8
3179.2.a.be.1.4		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)

\(f(q)\)	\(=\)	\(q-1.23360i q^{2} +(1.72482 - 1.72482i) q^{3} +0.478229 q^{4} +(-1.98987 + 1.98987i) q^{5} +(-2.12774 - 2.12774i) q^{6} +(-2.20951 - 2.20951i) q^{7} -3.05715i q^{8} -2.94999i q^{9} +O(q^{10})\)	\(q-1.23360i q^{2} +(1.72482 - 1.72482i) q^{3} +0.478229 q^{4} +(-1.98987 + 1.98987i) q^{5} +(-2.12774 - 2.12774i) q^{6} +(-2.20951 - 2.20951i) q^{7} -3.05715i q^{8} -2.94999i q^{9} +(2.45471 + 2.45471i) q^{10} +(0.707107 + 0.707107i) q^{11} +(0.824857 - 0.824857i) q^{12} +5.06832 q^{13} +(-2.72566 + 2.72566i) q^{14} +6.86434i q^{15} -2.81484 q^{16} +(-0.768616 + 4.05083i) q^{17} -3.63911 q^{18} -1.88317i q^{19} +(-0.951615 + 0.951615i) q^{20} -7.62201 q^{21} +(0.872288 - 0.872288i) q^{22} +(5.34893 + 5.34893i) q^{23} +(-5.27302 - 5.27302i) q^{24} -2.91920i q^{25} -6.25228i q^{26} +(0.0862570 + 0.0862570i) q^{27} +(-1.05665 - 1.05665i) q^{28} +(-3.70748 + 3.70748i) q^{29} +8.46786 q^{30} +(-0.506938 + 0.506938i) q^{31} -2.64190i q^{32} +2.43926 q^{33} +(4.99711 + 0.948165i) q^{34} +8.79330 q^{35} -1.41077i q^{36} +(-6.36542 + 6.36542i) q^{37} -2.32308 q^{38} +(8.74193 - 8.74193i) q^{39} +(6.08333 + 6.08333i) q^{40} +(-0.731537 - 0.731537i) q^{41} +9.40252i q^{42} -4.66481i q^{43} +(0.338159 + 0.338159i) q^{44} +(5.87011 + 5.87011i) q^{45} +(6.59845 - 6.59845i) q^{46} -7.38146 q^{47} +(-4.85508 + 4.85508i) q^{48} +2.76389i q^{49} -3.60112 q^{50} +(5.66122 + 8.31267i) q^{51} +2.42382 q^{52} +6.59761i q^{53} +(0.106407 - 0.106407i) q^{54} -2.81411 q^{55} +(-6.75480 + 6.75480i) q^{56} +(-3.24812 - 3.24812i) q^{57} +(4.57355 + 4.57355i) q^{58} -11.0605i q^{59} +3.28272i q^{60} +(-6.97846 - 6.97846i) q^{61} +(0.625360 + 0.625360i) q^{62} +(-6.51804 + 6.51804i) q^{63} -8.88873 q^{64} +(-10.0853 + 10.0853i) q^{65} -3.00907i q^{66} +6.09852 q^{67} +(-0.367574 + 1.93722i) q^{68} +18.4519 q^{69} -10.8474i q^{70} +(4.01208 - 4.01208i) q^{71} -9.01855 q^{72} +(10.0292 - 10.0292i) q^{73} +(7.85239 + 7.85239i) q^{74} +(-5.03508 - 5.03508i) q^{75} -0.900586i q^{76} -3.12472i q^{77} +(-10.7840 - 10.7840i) q^{78} +(0.766509 + 0.766509i) q^{79} +(5.60118 - 5.60118i) q^{80} +9.14753 q^{81} +(-0.902424 + 0.902424i) q^{82} +2.54437i q^{83} -3.64507 q^{84} +(-6.53119 - 9.59009i) q^{85} -5.75451 q^{86} +12.7895i q^{87} +(2.16173 - 2.16173i) q^{88} -13.8261 q^{89} +(7.24137 - 7.24137i) q^{90} +(-11.1985 - 11.1985i) q^{91} +(2.55801 + 2.55801i) q^{92} +1.74875i q^{93} +9.10578i q^{94} +(3.74727 + 3.74727i) q^{95} +(-4.55680 - 4.55680i) q^{96} +(-1.23810 + 1.23810i) q^{97} +3.40954 q^{98} +(2.08596 - 2.08596i) 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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